LMFDB - Embedded newform 552.2.n.b.91.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(91,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.19
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07870 + 0.914558i) q^{2} -1.00000 q^{3} +(0.327167 + 1.97306i) q^{4} -0.969269 q^{5} +(-1.07870 - 0.914558i) q^{6} -4.55308 q^{7} +(-1.45156 + 2.42754i) q^{8} +1.00000 q^{9} +(-1.04555 - 0.886452i) q^{10} +0.915699i q^{11} +(-0.327167 - 1.97306i) q^{12} -4.49735i q^{13} +(-4.91139 - 4.16406i) q^{14} +0.969269 q^{15} +(-3.78592 + 1.29104i) q^{16} -5.37023i q^{17} +(1.07870 + 0.914558i) q^{18} +0.688174i q^{19} +(-0.317112 - 1.91242i) q^{20} +4.55308 q^{21} +(-0.837460 + 0.987761i) q^{22} +(-4.70330 - 0.937530i) q^{23} +(1.45156 - 2.42754i) q^{24} -4.06052 q^{25} +(4.11309 - 4.85127i) q^{26} -1.00000 q^{27} +(-1.48962 - 8.98350i) q^{28} +6.35610i q^{29} +(1.04555 + 0.886452i) q^{30} +5.64064i q^{31} +(-5.26459 - 2.06981i) q^{32} -0.915699i q^{33} +(4.91139 - 5.79284i) q^{34} +4.41316 q^{35} +(0.327167 + 1.97306i) q^{36} -3.25973 q^{37} +(-0.629375 + 0.742330i) q^{38} +4.49735i q^{39} +(1.40696 - 2.35294i) q^{40} -8.87354 q^{41} +(4.91139 + 4.16406i) q^{42} +9.54349i q^{43} +(-1.80673 + 0.299586i) q^{44} -0.969269 q^{45} +(-4.21600 - 5.31275i) q^{46} +0.156006i q^{47} +(3.78592 - 1.29104i) q^{48} +13.7305 q^{49} +(-4.38006 - 3.71358i) q^{50} +5.37023i q^{51} +(8.87354 - 1.47138i) q^{52} +2.42613 q^{53} +(-1.07870 - 0.914558i) q^{54} -0.887559i q^{55} +(6.60909 - 11.0528i) q^{56} -0.688174i q^{57} +(-5.81302 + 6.85630i) q^{58} +3.81302 q^{59} +(0.317112 + 1.91242i) q^{60} +12.2676 q^{61} +(-5.15869 + 6.08453i) q^{62} -4.55308 q^{63} +(-3.78592 - 7.04747i) q^{64} +4.35914i q^{65} +(0.837460 - 0.987761i) q^{66} +10.6451i q^{67} +(10.5958 - 1.75696i) q^{68} +(4.70330 + 0.937530i) q^{69} +(4.76045 + 4.03609i) q^{70} -14.9045i q^{71} +(-1.45156 + 2.42754i) q^{72} -8.18221 q^{73} +(-3.51625 - 2.98121i) q^{74} +4.06052 q^{75} +(-1.35781 + 0.225148i) q^{76} -4.16925i q^{77} +(-4.11309 + 4.85127i) q^{78} -12.0667 q^{79} +(3.66958 - 1.25136i) q^{80} +1.00000 q^{81} +(-9.57185 - 8.11537i) q^{82} -11.1608i q^{83} +(1.48962 + 8.98350i) q^{84} +5.20519i q^{85} +(-8.72808 + 10.2945i) q^{86} -6.35610i q^{87} +(-2.22290 - 1.32920i) q^{88} +10.9680i q^{89} +(-1.04555 - 0.886452i) q^{90} +20.4768i q^{91} +(0.311039 - 9.58662i) q^{92} -5.64064i q^{93} +(-0.142676 + 0.168283i) q^{94} -0.667026i q^{95} +(5.26459 + 2.06981i) q^{96} +17.8948i q^{97} +(14.8111 + 12.5574i) q^{98} +0.915699i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81}+ \cdots - 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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 $

$2$	1.07870	+	0.914558i	0.762753	+	0.646690i
$2$	1.07870	+	0.914558i	0.762753	+	0.646690i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.327167	+	1.97306i	0.163583	+	0.986530i
$5$	−0.969269			−0.433470			−0.216735	−	0.976230i	$-0.569541\pi$
$5$	−0.969269			−0.433470			−0.216735	+	0.976230i	$0.569541\pi$
$6$	−1.07870	−	0.914558i	−0.440375	−	0.373367i
$7$	−4.55308			−1.72090			−0.860451	−	0.509533i	$-0.829818\pi$
$7$	−4.55308			−1.72090			−0.860451	+	0.509533i	$0.829818\pi$
$8$	−1.45156	+	2.42754i	−0.513205	+	0.858266i
$9$	1.00000			0.333333
$10$	−1.04555	−	0.886452i	−0.330630	−	0.280321i
$11$			0.915699i			0.276094i	0.990426	+	0.138047i	$0.0440825\pi$
$11$			0.915699i			0.276094i	−0.990426	+	0.138047i	$0.955918\pi$
$12$	−0.327167	−	1.97306i	−0.0944449	−	0.569573i
$13$		−	4.49735i		−	1.24734i	−0.781687	−	0.623671i	$-0.785641\pi$
$13$		−	4.49735i		−	1.24734i	0.781687	−	0.623671i	$-0.214359\pi$
$14$	−4.91139	−	4.16406i	−1.31262	−	1.11289i
$15$	0.969269			0.250264
$16$	−3.78592	+	1.29104i	−0.946481	+	0.322760i
$17$		−	5.37023i		−	1.30247i	−0.758875	−	0.651236i	$-0.774251\pi$
$17$		−	5.37023i		−	1.30247i	0.758875	−	0.651236i	$-0.225749\pi$
$18$	1.07870	+	0.914558i	0.254251	+	0.215563i
$19$			0.688174i			0.157878i	0.996879	+	0.0789390i	$0.0251532\pi$
$19$			0.688174i			0.157878i	−0.996879	+	0.0789390i	$0.974847\pi$
$20$	−0.317112	−	1.91242i	−0.0709085	−	0.427631i
$21$	4.55308			0.993564
$22$	−0.837460	+	0.987761i	−0.178547	+	0.210591i
$23$	−4.70330	−	0.937530i	−0.980706	−	0.195489i
$23$	−4.70330	−	0.937530i	−0.980706	−	0.195489i
$24$	1.45156	−	2.42754i	0.296299	−	0.495520i
$25$	−4.06052			−0.812104
$26$	4.11309	−	4.85127i	0.806643	−	0.951413i
$27$	−1.00000			−0.192450
$28$	−1.48962	−	8.98350i	−0.281511	−	1.69772i
$29$			6.35610i			1.18030i	0.807294	+	0.590149i	$0.200931\pi$
$29$			6.35610i			1.18030i	−0.807294	+	0.590149i	$0.799069\pi$
$30$	1.04555	+	0.886452i	0.190890	+	0.161843i
$31$			5.64064i			1.01309i	0.862214	+	0.506544i	$0.169077\pi$
$31$			5.64064i			1.01309i	−0.862214	+	0.506544i	$0.830923\pi$
$32$	−5.26459	−	2.06981i	−0.930656	−	0.365894i
$33$		−	0.915699i		−	0.159403i
$34$	4.91139	−	5.79284i	0.842296	−	0.993464i
$35$	4.41316			0.745960
$36$	0.327167	+	1.97306i	0.0545278	+	0.328843i
$37$	−3.25973			−0.535896			−0.267948	−	0.963433i	$-0.586346\pi$
$37$	−3.25973			−0.535896			−0.267948	+	0.963433i	$0.586346\pi$
$38$	−0.629375	+	0.742330i	−0.102098	+	0.120422i
$39$			4.49735i			0.720153i
$40$	1.40696	−	2.35294i	0.222459	−	0.372033i
$41$	−8.87354			−1.38581			−0.692907	−	0.721027i	$-0.743670\pi$
$41$	−8.87354			−1.38581			−0.692907	+	0.721027i	$0.743670\pi$
$42$	4.91139	+	4.16406i	0.757843	+	0.642528i
$43$			9.54349i			1.45537i	0.685912	+	0.727684i	$0.259403\pi$
$43$			9.54349i			1.45537i	−0.685912	+	0.727684i	$0.740597\pi$
$44$	−1.80673	+	0.299586i	−0.272375	+	0.0451643i
$45$	−0.969269			−0.144490
$46$	−4.21600	−	5.31275i	−0.621616	−	0.783322i
$47$			0.156006i			0.0227558i	0.999935	+	0.0113779i	$0.00362177\pi$
$47$			0.156006i			0.0227558i	−0.999935	+	0.0113779i	$0.996378\pi$
$48$	3.78592	−	1.29104i	0.546451	−	0.186345i
$49$	13.7305			1.96151
$50$	−4.38006	−	3.71358i	−0.619434	−	0.525180i
$51$			5.37023i			0.751982i
$52$	8.87354	−	1.47138i	1.23054	−	0.204044i
$53$	2.42613			0.333255			0.166628	−	0.986020i	$-0.446712\pi$
$53$	2.42613			0.333255			0.166628	+	0.986020i	$0.446712\pi$
$54$	−1.07870	−	0.914558i	−0.146792	−	0.124456i
$55$		−	0.887559i		−	0.119678i
$56$	6.60909	−	11.0528i	0.883176	−	1.47699i
$57$		−	0.688174i		−	0.0911509i
$58$	−5.81302	+	6.85630i	−0.763287	+	0.900276i
$59$	3.81302			0.496413			0.248207	−	0.968707i	$-0.420159\pi$
$59$	3.81302			0.496413			0.248207	+	0.968707i	$0.420159\pi$
$60$	0.317112	+	1.91242i	0.0409390	+	0.246893i
$61$	12.2676			1.57070			0.785352	−	0.619049i	$-0.212482\pi$
$61$	12.2676			1.57070			0.785352	+	0.619049i	$0.212482\pi$
$62$	−5.15869	+	6.08453i	−0.655154	+	0.772736i
$63$	−4.55308			−0.573634
$64$	−3.78592	−	7.04747i	−0.473240	−	0.880933i
$65$			4.35914i			0.540685i
$66$	0.837460	−	0.987761i	0.103084	−	0.121585i
$67$			10.6451i			1.30050i	0.759719	+	0.650251i	$0.225336\pi$
$67$			10.6451i			1.30050i	−0.759719	+	0.650251i	$0.774664\pi$
$68$	10.5958	−	1.75696i	1.28493	−	0.213063i
$69$	4.70330	+	0.937530i	0.566211	+	0.112865i
$70$	4.76045	+	4.03609i	0.568983	+	0.482405i
$71$		−	14.9045i		−	1.76884i	−0.466689	−	0.884422i	$-0.654553\pi$
$71$		−	14.9045i		−	1.76884i	0.466689	−	0.884422i	$-0.345447\pi$
$72$	−1.45156	+	2.42754i	−0.171068	+	0.286089i
$73$	−8.18221			−0.957655			−0.478828	−	0.877909i	$-0.658938\pi$
$73$	−8.18221			−0.957655			−0.478828	+	0.877909i	$0.658938\pi$
$74$	−3.51625	−	2.98121i	−0.408756	−	0.346559i
$75$	4.06052			0.468868
$76$	−1.35781	+	0.225148i	−0.155751	+	0.0258262i
$77$		−	4.16925i		−	0.475130i
$78$	−4.11309	+	4.85127i	−0.465716	+	0.549298i
$79$	−12.0667			−1.35761			−0.678805	−	0.734318i	$-0.737502\pi$
$79$	−12.0667			−1.35761			−0.678805	+	0.734318i	$0.737502\pi$
$80$	3.66958	−	1.25136i	0.410271	−	0.139907i
$81$	1.00000			0.111111
$82$	−9.57185	−	8.11537i	−1.05703	−	0.896193i
$83$		−	11.1608i		−	1.22506i	−0.790447	−	0.612531i	$-0.790152\pi$
$83$		−	11.1608i		−	1.22506i	0.790447	−	0.612531i	$-0.209848\pi$
$84$	1.48962	+	8.98350i	0.162530	+	0.980180i
$85$			5.20519i			0.564582i
$86$	−8.72808	+	10.2945i	−0.941173	+	1.11009i
$87$		−	6.35610i		−	0.681446i
$88$	−2.22290	−	1.32920i	−0.236962	−	0.141693i
$89$			10.9680i			1.16260i	0.813688	+	0.581302i	$0.197456\pi$
$89$			10.9680i			1.16260i	−0.813688	+	0.581302i	$0.802544\pi$
$90$	−1.04555	−	0.886452i	−0.110210	−	0.0934403i
$91$			20.4768i			2.14655i
$92$	0.311039	−	9.58662i	0.0324281	−	0.999474i
$93$		−	5.64064i		−	0.584907i
$94$	−0.142676	+	0.168283i	−0.0147159	+	0.0173570i
$95$		−	0.667026i		−	0.0684354i
$96$	5.26459	+	2.06981i	0.537315	+	0.211249i
$97$			17.8948i			1.81695i	0.417944	+	0.908473i	$0.362751\pi$
$97$			17.8948i			1.81695i	−0.417944	+	0.908473i	$0.637249\pi$
$98$	14.8111	+	12.5574i	1.49614	+	1.26849i
$99$			0.915699i			0.0920312i
$100$	−1.32847	−	8.01164i	−0.132847	−	0.801164i
$101$		−	2.18685i		−	0.217600i	−0.994064	−	0.108800i	$-0.965299\pi$
$101$		−	2.18685i		−	0.217600i	0.994064	−	0.108800i	$-0.0347007\pi$
$102$	−4.91139	+	5.79284i	−0.486300	+	0.573577i
$103$	−1.82776			−0.180095			−0.0900475	−	0.995937i	$-0.528702\pi$
$103$	−1.82776			−0.180095			−0.0900475	+	0.995937i	$0.528702\pi$
$104$	10.9175	+	6.52820i	1.07055	+	0.640142i
$105$	−4.41316			−0.430680
$106$	2.61706	+	2.21884i	0.254191	+	0.215513i
$107$			2.63011i			0.254262i	0.991886	+	0.127131i	$0.0405769\pi$
$107$			2.63011i			0.254262i	−0.991886	+	0.127131i	$0.959423\pi$
$108$	−0.327167	−	1.97306i	−0.0314816	−	0.189858i
$109$	6.14687			0.588764			0.294382	−	0.955688i	$-0.404886\pi$
$109$	6.14687			0.588764			0.294382	+	0.955688i	$0.404886\pi$
$110$	0.811724	−	0.957405i	0.0773948	−	0.0912850i
$111$	3.25973			0.309400
$112$	17.2376	−	5.87820i	1.62880	−	0.555438i
$113$		−	18.8052i		−	1.76905i	−0.466495	−	0.884524i	$-0.654483\pi$
$113$		−	18.8052i		−	1.76905i	0.466495	−	0.884524i	$-0.345517\pi$
$114$	0.629375	−	0.742330i	0.0589464	−	0.0695256i
$115$	4.55876	+	0.908719i	0.425107	+	0.0847385i
$116$	−12.5410	+	2.07950i	−1.16440	+	0.193077i
$117$		−	4.49735i		−	0.415780i
$118$	4.11309	+	3.48723i	0.378641	+	0.321026i
$119$			24.4511i			2.24143i
$120$	−1.40696	+	2.35294i	−0.128437	+	0.214793i
$121$	10.1615			0.923772
$122$	13.2330	+	11.2194i	1.19806	+	1.01576i
$123$	8.87354			0.800100
$124$	−11.1293	+	1.84543i	−0.999441	+	0.165724i
$125$	8.78208			0.785493
$126$	−4.91139	−	4.16406i	−0.437541	−	0.370964i
$127$		−	0.261572i		−	0.0232107i	−0.999933	−	0.0116054i	$-0.996306\pi$
$127$		−	0.261572i		−	0.0232107i	0.999933	−	0.0116054i	$-0.00369418\pi$
$128$	2.36146	−	11.0645i	0.208726	−	0.977974i
$129$		−	9.54349i		−	0.840258i
$130$	−3.98669	+	4.70219i	−0.349656	+	0.412409i
$131$	−8.22618			−0.718725			−0.359362	−	0.933198i	$-0.617006\pi$
$131$	−8.22618			−0.718725			−0.359362	+	0.933198i	$0.617006\pi$
$132$	1.80673	−	0.299586i	0.157256	−	0.0260756i
$133$		−	3.13331i		−	0.271693i
$134$	−9.73554	+	11.4828i	−0.841022	+	0.991962i
$135$	0.969269			0.0834214
$136$	13.0365	+	7.79523i	1.11787	+	0.668435i
$137$		−	6.70631i		−	0.572959i	−0.958086	−	0.286479i	$-0.907515\pi$
$137$		−	6.70631i		−	0.572959i	0.958086	−	0.286479i	$-0.0924850\pi$
$138$	4.21600	+	5.31275i	0.358890	+	0.452251i
$139$	−7.42604			−0.629868			−0.314934	−	0.949114i	$-0.601982\pi$
$139$	−7.42604			−0.629868			−0.314934	+	0.949114i	$0.601982\pi$
$140$	1.44384	+	8.70742i	0.122027	+	0.735911i
$141$		−	0.156006i		−	0.0131381i
$142$	13.6311	−	16.0775i	1.14389	−	1.34919i
$143$	4.11822			0.344383
$144$	−3.78592	+	1.29104i	−0.315494	+	0.107587i
$145$		−	6.16077i		−	0.511624i
$146$	−8.82611	−	7.48311i	−0.730454	−	0.619306i
$147$	−13.7305			−1.13248
$148$	−1.06647	−	6.43163i	−0.0876636	−	0.528677i
$149$	−16.0149			−1.31199			−0.655997	−	0.754764i	$-0.727751\pi$
$149$	−16.0149			−1.31199			−0.655997	+	0.754764i	$0.727751\pi$
$150$	4.38006	+	3.71358i	0.357631	+	0.303213i
$151$			8.36872i			0.681037i	0.940238	+	0.340518i	$0.110603\pi$
$151$			8.36872i			0.681037i	−0.940238	+	0.340518i	$0.889397\pi$
$152$	−1.67057	−	0.998929i	−0.135501	−	0.0810238i
$153$		−	5.37023i		−	0.434157i
$154$	3.81302	−	4.49735i	0.307262	−	0.362407i
$155$		−	5.46729i		−	0.439143i
$156$	−8.87354	+	1.47138i	−0.710452	+	0.117805i
$157$	0.188409			0.0150366			0.00751832	−	0.999972i	$-0.497607\pi$
$157$	0.188409			0.0150366			0.00751832	+	0.999972i	$0.497607\pi$
$158$	−13.0163	−	11.0357i	−1.03552	−	0.877953i
$159$	−2.42613			−0.192405
$160$	5.10280	+	2.00620i	0.403412	+	0.158604i
$161$	21.4145	+	4.26865i	1.68770	+	0.336417i
$162$	1.07870	+	0.914558i	0.0847503	+	0.0718545i
$163$	6.04337			0.473354			0.236677	−	0.971588i	$-0.423942\pi$
$163$	6.04337			0.473354			0.236677	+	0.971588i	$0.423942\pi$
$164$	−2.90313	−	17.5080i	−0.226696	−	1.36715i
$165$			0.887559i			0.0690963i
$166$	10.2072	−	12.0391i	0.792235	−	0.934419i
$167$			3.28126i			0.253912i	0.991908	+	0.126956i	$0.0405207\pi$
$167$			3.28126i			0.253912i	−0.991908	+	0.126956i	$0.959479\pi$
$168$	−6.60909	+	11.0528i	−0.509902	+	0.852742i
$169$	−7.22618			−0.555860
$170$	−4.76045	+	5.61482i	−0.365110	+	0.430637i
$171$			0.688174i			0.0526260i
$172$	−18.8299	+	3.12231i	−1.43576	+	0.238074i
$173$			4.28422i			0.325723i	0.986649	+	0.162862i	$0.0520724\pi$
$173$			4.28422i			0.325723i	−0.986649	+	0.162862i	$0.947928\pi$
$174$	5.81302	−	6.85630i	0.440684	−	0.519774i
$175$	18.4879			1.39755
$176$	−1.18220	−	3.46677i	−0.0891119	−	0.261317i
$177$	−3.81302			−0.286604
$178$	−10.0309	+	11.8311i	−0.751844	+	0.886779i
$179$	−21.7569			−1.62618			−0.813092	−	0.582135i	$-0.802217\pi$
$179$	−21.7569			−1.62618			−0.813092	+	0.582135i	$0.802217\pi$
$180$	−0.317112	−	1.91242i	−0.0236362	−	0.142544i
$181$	−2.42739			−0.180426			−0.0902131	−	0.995922i	$-0.528755\pi$
$181$	−2.42739			−0.180426			−0.0902131	+	0.995922i	$0.528755\pi$
$182$	−18.7272	+	22.0882i	−1.38815	+	1.63729i
$183$	−12.2676			−0.906847
$184$	9.10304	−	10.0566i	0.671085	−	0.741381i
$185$	3.15955			0.232295
$186$	5.15869	−	6.08453i	0.378254	−	0.446139i
$187$	4.91751			0.359604
$188$	−0.307809	+	0.0510399i	−0.0224492	+	0.00372247i
$189$	4.55308			0.331188
$190$	0.610034	−	0.719517i	0.0442565	−	0.0521993i
$191$	8.94391			0.647158			0.323579	−	0.946201i	$-0.395114\pi$
$191$	8.94391			0.647158			0.323579	+	0.946201i	$0.395114\pi$
$192$	3.78592	+	7.04747i	0.273226	+	0.508607i
$193$	−12.2220			−0.879760			−0.439880	−	0.898057i	$-0.644979\pi$
$193$	−12.2220			−0.879760			−0.439880	+	0.898057i	$0.644979\pi$
$194$	−16.3659	+	19.3031i	−1.17500	+	1.38588i
$195$		−	4.35914i		−	0.312165i
$196$	4.49218	+	27.0912i	0.320870	+	1.93508i
$197$		−	10.5254i		−	0.749900i	−0.927045	−	0.374950i	$-0.877660\pi$
$197$		−	10.5254i		−	0.749900i	0.927045	−	0.374950i	$-0.122340\pi$
$198$	−0.837460	+	0.987761i	−0.0595157	+	0.0701971i
$199$	−16.2033			−1.14862			−0.574312	−	0.818637i	$-0.694730\pi$
$199$	−16.2033			−1.14862			−0.574312	+	0.818637i	$0.694730\pi$
$200$	5.89410	−	9.85708i	0.416776	−	0.697001i
$201$		−	10.6451i		−	0.750845i
$202$	2.00000	−	2.35894i	0.140720	−	0.165975i
$203$		−	28.9398i		−	2.03118i
$204$	−10.5958	+	1.75696i	−0.741853	+	0.123012i
$205$	8.60085			0.600709
$206$	−1.97160	−	1.67160i	−0.137368	−	0.116466i
$207$	−4.70330	−	0.937530i	−0.326902	−	0.0651629i
$208$	5.80626	+	17.0266i	0.402591	+	1.18058i
$209$	−0.630161			−0.0435891
$210$	−4.76045	−	4.03609i	−0.328502	−	0.278517i
$211$	6.20898			0.427444			0.213722	−	0.976895i	$-0.431441\pi$
$211$	6.20898			0.427444			0.213722	+	0.976895i	$0.431441\pi$
$212$	0.793751	+	4.78691i	0.0545150	+	0.328766i
$213$			14.9045i			1.02124i
$214$	−2.40539	+	2.83709i	−0.164429	+	0.193939i
$215$		−	9.25021i		−	0.630859i
$216$	1.45156	−	2.42754i	0.0987664	−	0.165173i
$217$		−	25.6823i		−	1.74343i
$218$	6.63060	+	5.62167i	0.449081	+	0.380748i
$219$	8.18221			0.552902
$220$	1.75121	−	0.290380i	0.118066	−	0.0195774i
$221$	−24.1518			−1.62463
$222$	3.51625	+	2.98121i	0.235995	+	0.200086i
$223$		−	22.7592i		−	1.52407i	−0.647538	−	0.762033i	$-0.724201\pi$
$223$		−	22.7592i		−	1.52407i	0.647538	−	0.762033i	$-0.275799\pi$
$224$	23.9701	+	9.42401i	1.60157	+	0.629668i
$225$	−4.06052			−0.270701
$226$	17.1985	−	20.2851i	1.14403	−	1.34935i
$227$			5.19084i			0.344528i	0.985051	+	0.172264i	$0.0551083\pi$
$227$			5.19084i			0.344528i	−0.985051	+	0.172264i	$0.944892\pi$
$228$	1.35781	−	0.225148i	0.0899230	−	0.0149108i
$229$	16.5481			1.09353			0.546764	−	0.837287i	$-0.315860\pi$
$229$	16.5481			1.09353			0.546764	+	0.837287i	$0.315860\pi$
$230$	4.08644	+	5.14948i	0.269452	+	0.339547i
$231$			4.16925i			0.274317i
$232$	−15.4297	−	9.22629i	−1.01301	−	0.605735i
$233$	−15.1175			−0.990382			−0.495191	−	0.868784i	$-0.664902\pi$
$233$	−15.1175			−0.990382			−0.495191	+	0.868784i	$0.664902\pi$
$234$	4.11309	−	4.85127i	0.268881	−	0.317138i
$235$		−	0.151211i		−	0.00986395i
$236$	1.24749	+	7.52332i	0.0812050	+	0.489726i
$237$	12.0667			0.783817
$238$	−22.3619	+	26.3753i	−1.44951	+	1.70965i
$239$			4.20687i			0.272120i	0.990701	+	0.136060i	$0.0434439\pi$
$239$			4.20687i			0.272120i	−0.990701	+	0.136060i	$0.956556\pi$
$240$	−3.66958	+	1.25136i	−0.236870	+	0.0807751i
$241$			11.2163i			0.722503i	0.932469	+	0.361251i	$0.117650\pi$
$241$			11.2163i			0.722503i	−0.932469	+	0.361251i	$0.882350\pi$
$242$	10.9612	+	9.29328i	0.704610	+	0.597395i
$243$	−1.00000			−0.0641500
$244$	4.01355	+	24.2047i	0.256941	+	1.54955i
$245$	−13.3086			−0.850254
$246$	9.57185	+	8.11537i	0.610279	+	0.517417i
$247$	3.09496			0.196928
$248$	−13.6929	−	8.18775i	−0.869499	−	0.519922i
$249$			11.1608i			0.707289i
$250$	9.47318	+	8.03172i	0.599137	+	0.507971i
$251$		−	19.6483i		−	1.24019i	−0.784526	−	0.620096i	$-0.787094\pi$
$251$		−	19.6483i		−	1.24019i	0.784526	−	0.620096i	$-0.212906\pi$
$252$	−1.48962	−	8.98350i	−0.0938370	−	0.565907i
$253$	0.858496	−	4.30681i	0.0539732	−	0.270767i
$254$	0.239222	−	0.282156i	0.0150101	−	0.0177040i
$255$		−	5.20519i		−	0.325962i
$256$	12.6664	−	9.77555i	0.791652	−	0.610972i
$257$	12.3772			0.772071			0.386036	−	0.922484i	$-0.373844\pi$
$257$	12.3772			0.772071			0.386036	+	0.922484i	$0.373844\pi$
$258$	8.72808	−	10.2945i	0.543386	−	0.640909i
$259$	14.8418			0.922224
$260$	−8.60085	+	1.42617i	−0.533402	+	0.0884471i
$261$			6.35610i			0.393433i
$262$	−8.87354	−	7.52332i	−0.548209	−	0.464792i
$263$	−0.300441			−0.0185260			−0.00926300	−	0.999957i	$-0.502949\pi$
$263$	−0.300441			−0.0185260			−0.00926300	+	0.999957i	$0.502949\pi$
$264$	2.22290	+	1.32920i	0.136810	+	0.0818064i
$265$	−2.35158			−0.144456
$266$	2.86560	−	3.37989i	0.175701	−	0.207234i
$267$		−	10.9680i		−	0.671230i
$268$	−21.0034	+	3.48271i	−1.28298	+	0.212741i
$269$		−	1.53065i		−	0.0933252i	−0.998911	−	0.0466626i	$-0.985141\pi$
$269$		−	1.53065i		−	0.0933252i	0.998911	−	0.0466626i	$-0.0148586\pi$
$270$	1.04555	+	0.886452i	0.0636299	+	0.0539478i
$271$		−	6.52820i		−	0.396560i	−0.980145	−	0.198280i	$-0.936465\pi$
$271$		−	6.52820i		−	0.396560i	0.980145	−	0.198280i	$-0.0635355\pi$
$272$	6.93317	+	20.3313i	0.420385	+	1.23276i
$273$		−	20.4768i		−	1.23931i
$274$	6.13331	−	7.23407i	0.370527	−	0.437026i
$275$		−	3.71821i		−	0.224217i
$276$	−0.311039	+	9.58662i	−0.0187223	+	0.577047i
$277$			7.38599i			0.443781i	0.975072	+	0.221891i	$0.0712228\pi$
$277$			7.38599i			0.443781i	−0.975072	+	0.221891i	$0.928777\pi$
$278$	−8.01043	−	6.79154i	−0.480434	−	0.407330i
$279$			5.64064i			0.337696i
$280$	−6.40598	+	10.7131i	−0.382831	+	0.640232i
$281$			7.79441i			0.464976i	0.972599	+	0.232488i	$0.0746866\pi$
$281$			7.79441i			0.464976i	−0.972599	+	0.232488i	$0.925313\pi$
$282$	0.142676	−	0.168283i	0.00849625	−	0.0100211i
$283$		−	27.8464i		−	1.65530i	−0.561246	−	0.827649i	$-0.689678\pi$
$283$		−	27.8464i		−	1.65530i	0.561246	−	0.827649i	$-0.310322\pi$
$284$	29.4075	−	4.87627i	1.74502	−	0.289353i
$285$			0.667026i			0.0395112i
$286$	4.44231	+	3.76635i	0.262679	+	0.222709i
$287$	40.4019			2.38485
$288$	−5.26459	−	2.06981i	−0.310219	−	0.121965i
$289$	−11.8393			−0.696432
$290$	5.63438	−	6.64559i	0.330862	−	0.390243i
$291$		−	17.8948i		−	1.04901i
$292$	−2.67695	−	16.1440i	−0.156656	−	0.944755i
$293$	12.2770			0.717232			0.358616	−	0.933485i	$-0.383249\pi$
$293$	12.2770			0.717232			0.358616	+	0.933485i	$0.383249\pi$
$294$	−14.8111	−	12.5574i	−0.863799	−	0.732361i
$295$	−3.69584			−0.215180
$296$	4.73170	−	7.91313i	0.275025	−	0.459941i
$297$		−	0.915699i		−	0.0531343i
$298$	−17.2752	−	14.6466i	−1.00073	−	0.848453i
$299$	−4.21640	+	21.1524i	−0.243841	+	1.22327i
$300$	1.32847	+	8.01164i	0.0766991	+	0.462552i
$301$		−	43.4523i		−	2.50455i
$302$	−7.65368	+	9.02730i	−0.440420	+	0.519463i
$303$			2.18685i			0.125631i
$304$	−0.888459	−	2.60537i	−0.0509566	−	0.149428i
$305$	−11.8906			−0.680853
$306$	4.91139	−	5.79284i	0.280765	−	0.331155i
$307$	−0.0911995			−0.00520503			−0.00260251	−	0.999997i	$-0.500828\pi$
$307$	−0.0911995			−0.00520503			−0.00260251	+	0.999997i	$0.500828\pi$
$308$	8.22618	−	1.36404i	0.468730	−	0.0777234i
$309$	1.82776			0.103978
$310$	5.00016	−	5.89754i	0.283990	−	0.334958i
$311$		−	2.75985i		−	0.156497i	−0.996934	−	0.0782483i	$-0.975067\pi$
$311$		−	2.75985i		−	0.156497i	0.996934	−	0.0782483i	$-0.0249327\pi$
$312$	−10.9175	−	6.52820i	−0.618083	−	0.369586i
$313$			11.2930i			0.638317i	0.947701	+	0.319158i	$0.103400\pi$
$313$			11.2930i			0.638317i	−0.947701	+	0.319158i	$0.896600\pi$
$314$	0.203235	+	0.172311i	0.0114692	+	0.00972405i
$315$	4.41316			0.248653
$316$	−3.94783	−	23.8083i	−0.222083	−	1.33932i
$317$			23.3082i			1.30912i	0.756010	+	0.654560i	$0.227146\pi$
$317$			23.3082i			1.30912i	−0.756010	+	0.654560i	$0.772854\pi$
$318$	−2.61706	−	2.21884i	−0.146757	−	0.124426i
$319$	−5.82028			−0.325873
$320$	3.66958	+	6.83089i	0.205136	+	0.381858i
$321$		−	2.63011i		−	0.146798i
$322$	19.1958	+	24.1894i	1.06974	+	1.34802i
$323$	3.69565			0.205632
$324$	0.327167	+	1.97306i	0.0181759	+	0.109614i
$325$			18.2616i			1.01297i
$326$	6.51896	+	5.52702i	0.361052	+	0.306113i
$327$	−6.14687			−0.339923
$328$	12.8805	−	21.5409i	0.711207	−	1.18940i
$329$		−	0.710307i		−	0.0391605i
$330$	−0.811724	+	0.957405i	−0.0446839	+	0.0527034i
$331$	−14.7506			−0.810766			−0.405383	−	0.914147i	$-0.632862\pi$
$331$	−14.7506			−0.810766			−0.405383	+	0.914147i	$0.632862\pi$
$332$	22.0210	−	3.65146i	1.20856	−	0.200400i
$333$	−3.25973			−0.178632
$334$	−3.00091	+	3.53948i	−0.164202	+	0.193672i
$335$		−	10.3179i		−	0.563729i
$336$	−17.2376	+	5.87820i	−0.940389	+	0.320682i
$337$		−	22.4118i		−	1.22085i	−0.792075	−	0.610423i	$-0.790999\pi$
$337$		−	22.4118i		−	1.22085i	0.792075	−	0.610423i	$-0.209001\pi$
$338$	−7.79485	−	6.60876i	−0.423984	−	0.359469i
$339$			18.8052i			1.02136i
$340$	−10.2702	+	1.70297i	−0.556977	+	0.0923563i
$341$	−5.16513			−0.279707
$342$	−0.629375	+	0.742330i	−0.0340327	+	0.0401406i
$343$	−30.6447			−1.65466
$344$	−23.1672	−	13.8530i	−1.24909	−	0.746903i
$345$	−4.55876	−	0.908719i	−0.245435	−	0.0489238i
$346$	−3.91817	+	4.62137i	−0.210642	+	0.248446i
$347$	8.93888			0.479864			0.239932	−	0.970790i	$-0.422875\pi$
$347$	8.93888			0.479864			0.239932	+	0.970790i	$0.422875\pi$
$348$	12.5410	−	2.07950i	0.672266	−	0.111473i
$349$			33.9944i			1.81968i	0.414960	+	0.909840i	$0.363796\pi$
$349$			33.9944i			1.81968i	−0.414960	+	0.909840i	$0.636204\pi$
$350$	19.9428	+	16.9082i	1.06599	+	0.903783i
$351$			4.49735i			0.240051i
$352$	1.89532	−	4.82078i	0.101021	−	0.256948i
$353$	−14.3436			−0.763430			−0.381715	−	0.924280i	$-0.624666\pi$
$353$	−14.3436			−0.763430			−0.381715	+	0.924280i	$0.624666\pi$
$354$	−4.11309	−	3.48723i	−0.218608	−	0.185344i
$355$			14.4465i			0.766741i
$356$	−21.6405	+	3.58836i	−1.14694	+	0.190183i
$357$		−	24.4511i		−	1.29409i
$358$	−23.4690	−	19.8979i	−1.24038	−	1.05164i
$359$	17.4705			0.922059			0.461029	−	0.887385i	$-0.347480\pi$
$359$	17.4705			0.922059			0.461029	+	0.887385i	$0.347480\pi$
$360$	1.40696	−	2.35294i	0.0741531	−	0.124011i
$361$	18.5264			0.975075
$362$	−2.61841	−	2.21999i	−0.137621	−	0.116680i
$363$	−10.1615			−0.533340
$364$	−40.4019	+	6.69933i	−2.11764	+	0.351140i
$365$	7.93076			0.415115
$366$	−13.2330	−	11.2194i	−0.691700	−	0.586449i
$367$	4.20241			0.219364			0.109682	−	0.993967i	$-0.465017\pi$
$367$	4.20241			0.219364			0.109682	+	0.993967i	$0.465017\pi$
$368$	19.0167	−	2.52272i	0.991315	−	0.131506i
$369$	−8.87354			−0.461938
$370$	3.40819	+	2.88959i	0.177183	+	0.150223i
$371$	−11.0464			−0.573500
$372$	11.1293	−	1.84543i	0.577028	−	0.0956810i
$373$	−37.2998			−1.93131			−0.965655	−	0.259826i	$-0.916335\pi$
$373$	−37.2998			−1.93131			−0.965655	+	0.259826i	$0.916335\pi$
$374$	5.30450	+	4.49735i	0.274289	+	0.232553i
$375$	−8.78208			−0.453504
$376$	−0.378711	−	0.226452i	−0.0195305	−	0.0116784i
$377$	28.5856			1.47223
$378$	4.91139	+	4.16406i	0.252614	+	0.214176i
$379$		−	12.0640i		−	0.619684i	−0.950788	−	0.309842i	$-0.899724\pi$
$379$		−	12.0640i		−	0.619684i	0.950788	−	0.309842i	$-0.100276\pi$
$380$	1.31608	−	0.218229i	0.0675135	−	0.0111949i
$381$			0.261572i			0.0134007i
$382$	9.64775	+	8.17972i	0.493622	+	0.418511i
$383$	15.8402			0.809395			0.404698	−	0.914451i	$-0.367377\pi$
$383$	15.8402			0.809395			0.404698	+	0.914451i	$0.367377\pi$
$384$	−2.36146	+	11.0645i	−0.120508	+	0.564634i
$385$			4.04113i			0.205955i
$386$	−13.1838	−	11.1777i	−0.671039	−	0.568932i
$387$			9.54349i			0.485123i
$388$	−35.3076	+	5.85460i	−1.79247	+	0.297222i
$389$	−2.04276			−0.103572			−0.0517860	−	0.998658i	$-0.516491\pi$
$389$	−2.04276			−0.103572			−0.0517860	+	0.998658i	$0.516491\pi$
$390$	3.98669	−	4.70219i	0.201874	−	0.238104i
$391$	−5.03475	+	25.2578i	−0.254618	+	1.27734i
$392$	−19.9308	+	33.3315i	−1.00666	+	1.68349i
$393$	8.22618			0.414956
$394$	9.62605	−	11.3536i	0.484953	−	0.571989i
$395$	11.6959			0.588484
$396$	−1.80673	+	0.299586i	−0.0907915	+	0.0150548i
$397$			34.7911i			1.74612i	0.487617	+	0.873058i	$0.337866\pi$
$397$			34.7911i			1.74612i	−0.487617	+	0.873058i	$0.662134\pi$
$398$	−17.4784	−	14.8189i	−0.876116	−	0.742804i
$399$			3.13331i			0.156862i
$400$	15.3728	−	5.24229i	0.768641	−	0.262114i
$401$			27.9532i			1.39592i	0.716138	+	0.697958i	$0.245908\pi$
$401$			27.9532i			1.39592i	−0.716138	+	0.697958i	$0.754092\pi$
$402$	9.73554	−	11.4828i	0.485564	−	0.572709i
$403$	25.3679			1.26367
$404$	4.31478	−	0.715464i	0.214668	−	0.0355957i
$405$	−0.969269			−0.0481633
$406$	26.4672	−	31.2173i	1.31354	−	1.54929i
$407$		−	2.98493i		−	0.147957i
$408$	−13.0365	−	7.79523i	−0.645401	−	0.385921i
$409$	−10.4393			−0.516192			−0.258096	−	0.966119i	$-0.583095\pi$
$409$	−10.4393			−0.516192			−0.258096	+	0.966119i	$0.583095\pi$
$410$	9.27769	+	7.86597i	0.458192	+	0.388473i
$411$			6.70631i			0.330798i
$412$	−0.597984	−	3.60629i	−0.0294605	−	0.177669i
$413$	−17.3610			−0.854279
$414$	−4.21600	−	5.31275i	−0.207205	−	0.261107i
$415$			10.8179i			0.531027i
$416$	−9.30867	+	23.6767i	−0.456395	+	1.16085i
$417$	7.42604			0.363655
$418$	−0.679751	−	0.576319i	−0.0332477	−	0.0281887i
$419$		−	27.9406i		−	1.36499i	−0.730891	−	0.682494i	$-0.760895\pi$
$419$		−	27.9406i		−	1.36499i	0.730891	−	0.682494i	$-0.239105\pi$
$420$	−1.44384	−	8.70742i	−0.0704521	−	0.424879i
$421$	−32.6815			−1.59280			−0.796400	−	0.604770i	$-0.793265\pi$
$421$	−32.6815			−1.59280			−0.796400	+	0.604770i	$0.793265\pi$
$422$	6.69760	+	5.67847i	0.326034	+	0.276424i
$423$			0.156006i			0.00758526i
$424$	−3.52169	+	5.88954i	−0.171028	+	0.286022i
$425$			21.8059i			1.05774i
$426$	−13.6311	+	16.0775i	−0.660427	+	0.778955i
$427$	−55.8553			−2.70303
$428$	−5.18936	+	0.860485i	−0.250837	+	0.0415931i
$429$	−4.11822			−0.198830
$430$	8.45985	−	9.97815i	0.407970	−	0.481189i
$431$	−16.1528			−0.778055			−0.389028	−	0.921226i	$-0.627189\pi$
$431$	−16.1528			−0.778055			−0.389028	+	0.921226i	$0.627189\pi$
$432$	3.78592	−	1.29104i	0.182150	−	0.0621151i
$433$		−	19.9138i		−	0.956996i	−0.878089	−	0.478498i	$-0.841181\pi$
$433$		−	19.9138i		−	0.956996i	0.878089	−	0.478498i	$-0.158819\pi$
$434$	23.4879	−	27.7033i	1.12746	−	1.32980i
$435$			6.16077i			0.295386i
$436$	2.01105	+	12.1281i	0.0963120	+	0.580833i
$437$	0.645184	−	3.23669i	0.0308633	−	0.154832i
$438$	8.82611	+	7.48311i	0.421728	+	0.357557i
$439$		−	29.3002i		−	1.39842i	−0.714915	−	0.699211i	$-0.753535\pi$
$439$		−	29.3002i		−	1.39842i	0.714915	−	0.699211i	$-0.246465\pi$
$440$	2.15459	+	1.28835i	0.102716	+	0.0614196i
$441$	13.7305			0.653835
$442$	−26.0524	−	22.0882i	−1.23919	−	1.05063i
$443$	32.9596			1.56596			0.782978	−	0.622049i	$-0.213699\pi$
$443$	32.9596			1.56596			0.782978	+	0.622049i	$0.213699\pi$
$444$	1.06647	+	6.43163i	0.0506126	+	0.305232i
$445$		−	10.6309i		−	0.503954i
$446$	20.8146	−	24.5502i	0.985599	−	1.16249i
$447$	16.0149			0.757480
$448$	17.2376	+	32.0877i	0.814401	+	1.51600i
$449$	16.6963			0.787949			0.393975	−	0.919121i	$-0.371100\pi$
$449$	16.6963			0.787949			0.393975	+	0.919121i	$0.371100\pi$
$450$	−4.38006	−	3.71358i	−0.206478	−	0.175060i
$451$		−	8.12550i		−	0.382615i
$452$	37.1038	−	6.15245i	1.74522	−	0.289387i
$453$		−	8.36872i		−	0.393197i
$454$	−4.74733	+	5.59934i	−0.222803	+	0.262790i
$455$		−	19.8475i		−	0.930466i
$456$	1.67057	+	0.998929i	0.0782317	+	0.0467791i
$457$		−	7.54667i		−	0.353018i	−0.984299	−	0.176509i	$-0.943519\pi$
$457$		−	7.54667i		−	0.353018i	0.984299	−	0.176509i	$-0.0564805\pi$
$458$	17.8503	+	15.1342i	0.834091	+	0.707173i
$459$			5.37023i			0.250661i
$460$	−0.301480	+	9.29201i	−0.0140566	+	0.433242i
$461$		−	22.0330i		−	1.02618i	−0.858335	−	0.513090i	$-0.828501\pi$
$461$		−	22.0330i		−	1.02618i	0.858335	−	0.513090i	$-0.171499\pi$
$462$	−3.81302	+	4.49735i	−0.177398	+	0.209236i
$463$			10.5899i			0.492153i	0.969250	+	0.246077i	$0.0791415\pi$
$463$			10.5899i			0.492153i	−0.969250	+	0.246077i	$0.920858\pi$
$464$	−8.20597	−	24.0637i	−0.380953	−	1.11713i
$465$			5.46729i			0.253540i
$466$	−16.3072	−	13.8259i	−0.755416	−	0.640470i
$467$			23.8323i			1.10283i	0.834231	+	0.551414i	$0.185912\pi$
$467$			23.8323i			1.10283i	−0.834231	+	0.551414i	$0.814088\pi$
$468$	8.87354	−	1.47138i	0.410180	−	0.0680148i
$469$		−	48.4679i		−	2.23804i
$470$	0.138292	−	0.163111i	0.00637892	−	0.00752375i
$471$	−0.188409			−0.00868141
$472$	−5.53485	+	9.25628i	−0.254762	+	0.426055i
$473$	−8.73897			−0.401818
$474$	13.0163	+	11.0357i	0.597858	+	0.506887i
$475$		−	2.79434i		−	0.128213i
$476$	−48.2434	+	7.99958i	−2.21123	+	0.366660i
$477$	2.42613			0.111085
$478$	−3.84742	+	4.53793i	−0.175977	+	0.207560i
$479$	18.4098			0.841165			0.420583	−	0.907254i	$-0.361826\pi$
$479$	18.4098			0.841165			0.420583	+	0.907254i	$0.361826\pi$
$480$	−5.10280	−	2.00620i	−0.232910	−	0.0915702i
$481$			14.6601i			0.668445i
$482$	−10.2579	+	12.0989i	−0.467235	+	0.551091i
$483$	−21.4145	−	4.26865i	−0.974394	−	0.194230i
$484$	3.32450	+	20.0492i	0.151114	+	0.911329i
$485$		−	17.3449i		−	0.787591i
$486$	−1.07870	−	0.914558i	−0.0489306	−	0.0414852i
$487$			39.6459i			1.79653i	0.439458	+	0.898263i	$0.355171\pi$
$487$			39.6459i			1.79653i	−0.439458	+	0.898263i	$0.644829\pi$
$488$	−17.8072	+	29.7801i	−0.806094	+	1.34808i
$489$	−6.04337			−0.273291
$490$	−14.3559	−	12.1715i	−0.648533	−	0.549851i
$491$	−30.1004			−1.35841			−0.679206	−	0.733947i	$-0.737676\pi$
$491$	−30.1004			−1.35841			−0.679206	+	0.733947i	$0.737676\pi$
$492$	2.90313	+	17.5080i	0.130883	+	0.789323i
$493$	34.1337			1.53730
$494$	3.33852	+	2.83052i	0.150207	+	0.127351i
$495$		−	0.887559i		−	0.0398928i
$496$	−7.28228	−	21.3550i	−0.326984	−	0.958869i
$497$			67.8616i			3.04401i
$498$	−10.2072	+	12.0391i	−0.457397	+	0.539487i
$499$	−21.5335			−0.963974			−0.481987	−	0.876178i	$-0.660085\pi$
$499$	−21.5335			−0.963974			−0.481987	+	0.876178i	$0.660085\pi$
$500$	2.87320	+	17.3276i	0.128494	+	0.774912i
$501$		−	3.28126i		−	0.146596i
$502$	17.9695	−	21.1946i	0.802020	−	0.945959i
$503$	−22.2489			−0.992030			−0.496015	−	0.868314i	$-0.665204\pi$
$503$	−22.2489			−0.992030			−0.496015	+	0.868314i	$0.665204\pi$
$504$	6.60909	−	11.0528i	0.294392	−	0.492331i
$505$			2.11964i			0.0943229i
$506$	4.86488	−	3.86059i	0.216270	−	0.171624i
$507$	7.22618			0.320926
$508$	0.516096	−	0.0855775i	0.0228981	−	0.00379689i
$509$		−	30.3648i		−	1.34590i	−0.739689	−	0.672949i	$-0.765028\pi$
$509$		−	30.3648i		−	1.34590i	0.739689	−	0.672949i	$-0.234972\pi$
$510$	4.76045	−	5.61482i	0.210796	−	0.248628i
$511$	37.2543			1.64803
$512$	22.6035	+	1.03936i	0.998944	+	0.0459336i
$513$		−	0.688174i		−	0.0303836i
$514$	13.3513	+	11.3197i	0.588900	+	0.499291i
$515$	1.77159			0.0780658
$516$	18.8299	−	3.12231i	0.828939	−	0.137452i
$517$	−0.142854			−0.00628273
$518$	16.0098	+	13.5737i	0.703429	+	0.596394i
$519$		−	4.28422i		−	0.188056i
$520$	−10.5820	−	6.32757i	−0.464052	−	0.277482i
$521$			35.7402i			1.56580i	0.622145	+	0.782902i	$0.286262\pi$
$521$			35.7402i			1.56580i	−0.622145	+	0.782902i	$0.713738\pi$
$522$	−5.81302	+	6.85630i	−0.254429	+	0.300092i
$523$			9.30899i			0.407054i	0.979069	+	0.203527i	$0.0652404\pi$
$523$			9.30899i			0.407054i	−0.979069	+	0.203527i	$0.934760\pi$
$524$	−2.69133	−	16.2307i	−0.117571	−	0.709043i
$525$	−18.4879			−0.806877
$526$	−0.324084	−	0.274771i	−0.0141308	−	0.0119806i
$527$	30.2915			1.31952
$528$	1.18220	+	3.46677i	0.0514488	+	0.150872i
$529$	21.2421	+	8.81897i	0.923568	+	0.383434i
$530$	−2.53663	−	2.15065i	−0.110184	−	0.0934184i
$531$	3.81302			0.165471
$532$	6.18221	−	1.02512i	0.268033	−	0.0444444i
$533$			39.9074i			1.72858i
$534$	10.0309	−	11.8311i	0.434078	−	0.511982i
$535$		−	2.54928i		−	0.110215i
$536$	−25.8414	−	15.4520i	−1.11618	−	0.667425i
$537$	21.7569			0.938878
$538$	1.39987	−	1.65110i	0.0603525	−	0.0711841i
$539$			12.5730i			0.541559i
$540$	0.317112	+	1.91242i	0.0136463	+	0.0822976i
$541$			20.3348i			0.874263i	0.899398	+	0.437131i	$0.144006\pi$
$541$			20.3348i			0.874263i	−0.899398	+	0.437131i	$0.855994\pi$
$542$	5.97041	−	7.04193i	0.256451	−	0.302477i
$543$	2.42739			0.104169
$544$	−11.1154	+	28.2720i	−0.476567	+	1.21215i
$545$	−5.95797			−0.255211
$546$	18.7272	−	22.0882i	0.801451	−	0.945289i
$547$	39.4942			1.68865			0.844324	−	0.535832i	$-0.180002\pi$
$547$	39.4942			1.68865			0.844324	+	0.535832i	$0.180002\pi$
$548$	13.2319	−	2.19408i	0.565241	−	0.0937265i
$549$	12.2676			0.523568
$550$	3.40052	−	4.01082i	0.144999	−	0.171022i
$551$	−4.37410			−0.186343
$552$	−9.10304	+	10.0566i	−0.387451	+	0.428036i
$553$	54.9407			2.33632
$554$	−6.75492	+	7.96723i	−0.286989	+	0.338495i
$555$	−3.15955			−0.134115
$556$	−2.42955	−	14.6520i	−0.103036	−	0.621384i
$557$	−0.909976			−0.0385569			−0.0192785	−	0.999814i	$-0.506137\pi$
$557$	−0.909976			−0.0385569			−0.0192785	+	0.999814i	$0.506137\pi$
$558$	−5.15869	+	6.08453i	−0.218385	+	0.257579i
$559$	42.9205			1.81534
$560$	−16.7079	+	5.69756i	−0.706037	+	0.240766i
$561$	−4.91751			−0.207618
$562$	−7.12845	+	8.40780i	−0.300695	+	0.354662i
$563$		−	24.7038i		−	1.04114i	−0.853819	−	0.520571i	$-0.825719\pi$
$563$		−	24.7038i		−	1.04114i	0.853819	−	0.520571i	$-0.174281\pi$
$564$	0.307809	−	0.0510399i	0.0129611	−	0.00214917i
$565$			18.2273i			0.766829i
$566$	25.4672	−	30.0378i	1.07047	−	1.26258i
$567$	−4.55308			−0.191211
$568$	36.1814	+	21.6349i	1.51814	+	0.907780i
$569$		−	4.12434i		−	0.172901i	−0.996256	−	0.0864507i	$-0.972448\pi$
$569$		−	4.12434i		−	0.172901i	0.996256	−	0.0864507i	$-0.0275525\pi$
$570$	−0.610034	+	0.719517i	−0.0255515	+	0.0301373i
$571$			27.5717i			1.15384i	0.816801	+	0.576919i	$0.195745\pi$
$571$			27.5717i			1.15384i	−0.816801	+	0.576919i	$0.804255\pi$
$572$	1.34735	+	8.12550i	0.0563354	+	0.339744i
$573$	−8.94391			−0.373637
$574$	43.5814	+	36.9499i	1.81905	+	1.54226i
$575$	19.0978	+	3.80686i	0.796435	+	0.158757i
$576$	−3.78592	−	7.04747i	−0.157747	−	0.293644i
$577$	−30.3113			−1.26188			−0.630938	−	0.775833i	$-0.717330\pi$
$577$	−30.3113			−1.26188			−0.630938	+	0.775833i	$0.717330\pi$
$578$	−12.7710	−	10.8278i	−0.531206	−	0.450376i
$579$	12.2220			0.507930
$580$	12.1556	−	2.01560i	0.504732	−	0.0836932i
$581$			50.8162i			2.10821i
$582$	16.3659	−	19.3031i	0.678387	−	0.800138i
$583$			2.22161i			0.0920097i
$584$	11.8770	−	19.8627i	0.491474	−	0.821923i
$585$			4.35914i			0.180228i
$586$	13.2432	+	11.2281i	0.547071	+	0.463827i
$587$	14.3608			0.592732			0.296366	−	0.955074i	$-0.404225\pi$
$587$	14.3608			0.592732			0.296366	+	0.955074i	$0.404225\pi$
$588$	−4.49218	−	27.0912i	−0.185254	−	1.11722i
$589$	−3.88174			−0.159944
$590$	−3.98669	−	3.38006i	−0.164129	−	0.139155i
$591$			10.5254i			0.432955i
$592$	12.3411	−	4.20843i	0.507215	−	0.172966i
$593$	−25.1240			−1.03172			−0.515859	−	0.856674i	$-0.672527\pi$
$593$	−25.1240			−1.03172			−0.515859	+	0.856674i	$0.672527\pi$
$594$	0.837460	−	0.987761i	0.0343614	−	0.0405283i
$595$		−	23.6997i		−	0.971591i
$596$	−5.23955	−	31.5984i	−0.214620	−	1.29432i
$597$	16.2033			0.663158
$598$	−23.8933	+	18.9608i	−0.977070	+	0.775367i
$599$			3.10960i			0.127055i	0.997980	+	0.0635274i	$0.0202350\pi$
$599$			3.10960i			0.127055i	−0.997980	+	0.0635274i	$0.979765\pi$
$600$	−5.89410	+	9.85708i	−0.240626	+	0.402414i
$601$	−14.1864			−0.578674			−0.289337	−	0.957227i	$-0.593435\pi$
$601$	−14.1864			−0.578674			−0.289337	+	0.957227i	$0.593435\pi$
$602$	39.7396	−	46.8718i	1.61967	−	1.91035i
$603$			10.6451i			0.433501i
$604$	−16.5120	+	2.73797i	−0.671863	+	0.111406i
$605$	−9.84922			−0.400428
$606$	−2.00000	+	2.35894i	−0.0812444	+	0.0958255i
$607$			6.65785i			0.270234i	0.990830	+	0.135117i	$0.0431410\pi$
$607$			6.65785i			0.270234i	−0.990830	+	0.135117i	$0.956859\pi$
$608$	1.42439	−	3.62295i	0.0577666	−	0.146930i
$609$			28.9398i			1.17270i
$610$	−12.8263	−	10.8746i	−0.519323	−	0.440301i
$611$	0.701613			0.0283842
$612$	10.5958	−	1.75696i	0.428309	−	0.0710209i
$613$	8.35314			0.337380			0.168690	−	0.985669i	$-0.446046\pi$
$613$	8.35314			0.337380			0.168690	+	0.985669i	$0.446046\pi$
$614$	−0.0983765	−	0.0834072i	−0.00397015	−	0.00336604i
$615$	−8.60085			−0.346820
$616$	10.1210	+	6.05194i	0.407788	+	0.243839i
$617$		−	8.98374i		−	0.361672i	−0.983513	−	0.180836i	$-0.942120\pi$
$617$		−	8.98374i		−	0.361672i	0.983513	−	0.180836i	$-0.0578803\pi$
$618$	1.97160	+	1.67160i	0.0793094	+	0.0672415i
$619$			25.1148i			1.00945i	0.863280	+	0.504725i	$0.168406\pi$
$619$			25.1148i			1.00945i	−0.863280	+	0.504725i	$0.831594\pi$
$620$	10.7873	−	1.78872i	0.433228	−	0.0718366i
$621$	4.70330	+	0.937530i	0.188737	+	0.0376218i
$622$	2.52404	−	2.97704i	0.101205	−	0.119368i
$623$		−	49.9381i		−	2.00073i
$624$	−5.80626	−	17.0266i	−0.232436	−	0.681611i
$625$	11.7904			0.471616
$626$	−10.3281	+	12.1817i	−0.412793	+	0.486878i
$627$	0.630161			0.0251662
$628$	0.0616410	+	0.371741i	0.00245974	+	0.0148341i
$629$			17.5055i			0.697989i
$630$	4.76045	+	4.03609i	0.189661	+	0.160802i
$631$	−16.1347			−0.642312			−0.321156	−	0.947026i	$-0.604071\pi$
$631$	−16.1347			−0.642312			−0.321156	+	0.947026i	$0.604071\pi$
$632$	17.5156	−	29.2924i	0.696733	−	1.16519i
$633$	−6.20898			−0.246785
$634$	−21.3167	+	25.1425i	−0.846595	+	0.998535i
$635$			0.253533i			0.0100612i
$636$	−0.793751	−	4.78691i	−0.0314743	−	0.189813i
$637$		−	61.7511i		−	2.44667i
$638$	−6.27831	−	5.32298i	−0.248560	−	0.210739i
$639$		−	14.9045i		−	0.589614i
$640$	−2.28889	+	10.7245i	−0.0904763	+	0.423923i
$641$			17.9723i			0.709865i	0.934892	+	0.354932i	$0.115496\pi$
$641$			17.9723i			0.709865i	−0.934892	+	0.354932i	$0.884504\pi$
$642$	2.40539	−	2.83709i	0.0949331	−	0.111971i
$643$		−	37.3857i		−	1.47435i	−0.675704	−	0.737173i	$-0.736160\pi$
$643$		−	37.3857i		−	1.47435i	0.675704	−	0.737173i	$-0.263840\pi$
$644$	−1.41619	+	43.6486i	−0.0558055	+	1.72000i
$645$			9.25021i			0.364227i
$646$	3.98648	+	3.37989i	0.156846	+	0.132980i
$647$		−	0.412854i		−	0.0162310i	−0.999967	−	0.00811548i	$-0.997417\pi$
$647$		−	0.412854i		−	0.0162310i	0.999967	−	0.00811548i	$-0.00258327\pi$
$648$	−1.45156	+	2.42754i	−0.0570228	+	0.0953629i
$649$			3.49158i			0.137057i
$650$	−16.7013	+	19.6987i	−0.655078	+	0.772646i
$651$			25.6823i			1.00657i
$652$	1.97719	+	11.9239i	0.0774328	+	0.466977i
$653$			47.0964i			1.84302i	0.388350	+	0.921512i	$0.373045\pi$
$653$			47.0964i			1.84302i	−0.388350	+	0.921512i	$0.626955\pi$
$654$	−6.63060	−	5.62167i	−0.259277	−	0.219825i
$655$	7.97338			0.311546
$656$	33.5946	−	11.4561i	1.31165	−	0.447285i
$657$	−8.18221			−0.319218
$658$	0.649617	−	0.766204i	0.0253247	−	0.0298698i
$659$			35.5752i			1.38581i	0.721027	+	0.692907i	$0.243670\pi$
$659$			35.5752i			1.38581i	−0.721027	+	0.692907i	$0.756330\pi$
$660$	−1.75121	+	0.290380i	−0.0681656	+	0.0113030i
$661$	−24.5240			−0.953872			−0.476936	−	0.878938i	$-0.658253\pi$
$661$	−24.5240			−0.953872			−0.476936	+	0.878938i	$0.658253\pi$
$662$	−15.9114	−	13.4903i	−0.618414	−	0.524315i
$663$	24.1518			0.937979
$664$	27.0934	+	16.2007i	1.05143	+	0.628708i
$665$			3.03702i			0.117771i
$666$	−3.51625	−	2.98121i	−0.136252	−	0.115520i
$667$	5.95904	−	29.8947i	0.230735	−	1.15753i
$668$	−6.47413	+	1.07352i	−0.250491	+	0.0415357i
$669$			22.7592i			0.879920i
$670$	9.43635	−	11.1299i	0.364558	−	0.429986i
$671$			11.2334i			0.433662i
$672$	−23.9701	−	9.42401i	−0.924666	−	0.363539i
$673$	−49.3893			−1.90382			−0.951910	−	0.306379i	$-0.900882\pi$
$673$	−49.3893			−1.90382			−0.951910	+	0.306379i	$0.900882\pi$
$674$	20.4969	−	24.1755i	0.789510	−	0.931204i
$675$	4.06052			0.156289
$676$	−2.36417	−	14.2577i	−0.0909295	−	0.548372i
$677$	−38.7298			−1.48851			−0.744254	−	0.667896i	$-0.767195\pi$
$677$	−38.7298			−1.48851			−0.744254	+	0.667896i	$0.767195\pi$
$678$	−17.1985	+	20.2851i	−0.660504	+	0.779045i
$679$		−	81.4766i		−	3.12679i
$680$	−12.6358	−	7.55567i	−0.484562	−	0.289747i
$681$		−	5.19084i		−	0.198914i
$682$	−5.57160	−	4.72381i	−0.213348	−	0.180884i
$683$	−11.5331			−0.441303			−0.220651	−	0.975353i	$-0.570818\pi$
$683$	−11.5331			−0.441303			−0.220651	+	0.975353i	$0.570818\pi$
$684$	−1.35781	+	0.225148i	−0.0519171	+	0.00860874i
$685$			6.50022i			0.248361i
$686$	−33.0563	−	28.0263i	−1.26209	−	1.07005i
$687$	−16.5481			−0.631348
$688$	−12.3210	−	36.1309i	−0.469734	−	1.37748i
$689$		−	10.9112i		−	0.415683i
$690$	−4.08644	−	5.14948i	−0.155568	−	0.196037i
$691$	−19.3937			−0.737771			−0.368885	−	0.929475i	$-0.620261\pi$
$691$	−19.3937			−0.737771			−0.368885	+	0.929475i	$0.620261\pi$
$692$	−8.45302	+	1.40165i	−0.321336	+	0.0532829i
$693$		−	4.16925i		−	0.158377i
$694$	9.64233	+	8.17513i	0.366018	+	0.310324i
$695$	7.19783			0.273029
$696$	15.4297	+	9.22629i	0.584861	+	0.349722i
$697$			47.6529i			1.80498i
$698$	−31.0899	+	36.6696i	−1.17677	+	1.38797i
$699$	15.1175			0.571797
$700$	6.04861	+	36.4777i	0.228616	+	1.37873i
$701$	−42.0341			−1.58761			−0.793803	−	0.608174i	$-0.791902\pi$
$701$	−42.0341			−1.58761			−0.793803	+	0.608174i	$0.791902\pi$
$702$	−4.11309	+	4.85127i	−0.155239	+	0.183099i
$703$		−	2.24326i		−	0.0846061i
$704$	6.45336	−	3.46677i	0.243220	−	0.130659i
$705$			0.151211i			0.00569495i
$706$	−15.4723	−	13.1180i	−0.582309	−	0.493703i
$707$			9.95690i			0.374468i
$708$	−1.24749	−	7.52332i	−0.0468837	−	0.282744i
$709$	7.00113			0.262933			0.131467	−	0.991321i	$-0.458031\pi$
$709$	7.00113			0.262933			0.131467	+	0.991321i	$0.458031\pi$
$710$	−13.2122	+	15.5834i	−0.495844	+	0.584833i
$711$	−12.0667			−0.452537
$712$	−26.6252	−	15.9207i	−0.997823	−	0.596654i
$713$	5.28827	−	26.5296i	0.198047	−	0.993542i
$714$	22.3619	−	26.3753i	0.836874	−	0.987069i
$715$	−3.99166			−0.149280
$716$	−7.11812	−	42.9276i	−0.266017	−	1.60428i
$717$		−	4.20687i		−	0.157108i
$718$	18.8454	+	15.9778i	0.703303	+	0.596287i
$719$			32.5628i			1.21439i	0.794554	+	0.607193i	$0.207705\pi$
$719$			32.5628i			1.21439i	−0.794554	+	0.607193i	$0.792295\pi$
$720$	3.66958	−	1.25136i	0.136757	−	0.0466356i
$721$	8.32196			0.309926
$722$	19.9844	+	16.9435i	0.743741	+	0.630571i
$723$		−	11.2163i		−	0.417137i
$724$	−0.794160	−	4.78938i	−0.0295147	−	0.177996i
$725$		−	25.8091i		−	0.958525i
$726$	−10.9612	−	9.29328i	−0.406807	−	0.344906i
$727$	−8.30822			−0.308135			−0.154067	−	0.988060i	$-0.549237\pi$
$727$	−8.30822			−0.308135			−0.154067	+	0.988060i	$0.549237\pi$
$728$	−49.7083	−	29.7234i	−1.84231	−	1.10162i
$729$	1.00000			0.0370370
$730$	8.55487	+	7.25314i	0.316630	+	0.268451i
$731$	51.2507			1.89558
$732$	−4.01355	−	24.2047i	−0.148345	−	0.894631i
$733$	−5.54133			−0.204674			−0.102337	−	0.994750i	$-0.532632\pi$
$733$	−5.54133			−0.204674			−0.102337	+	0.994750i	$0.532632\pi$
$734$	4.53312	+	3.84335i	0.167321	+	0.141861i
$735$	13.3086			0.490894
$736$	22.8204	+	14.6707i	0.841172	+	0.540767i
$737$	−9.74768			−0.359061
$738$	−9.57185	−	8.11537i	−0.352345	−	0.298731i
$739$	16.1333			0.593472			0.296736	−	0.954960i	$-0.404102\pi$
$739$	16.1333			0.593472			0.296736	+	0.954960i	$0.404102\pi$
$740$	1.03370	+	6.23398i	0.0379996	+	0.229166i
$741$	−3.09496			−0.113696
$742$	−11.9157	−	10.1026i	−0.437438	−	0.370877i
$743$	−46.0973			−1.69115			−0.845574	−	0.533859i	$-0.820741\pi$
$743$	−46.0973			−1.69115			−0.845574	+	0.533859i	$0.820741\pi$
$744$	13.6929	+	8.18775i	0.502006	+	0.300177i
$745$	15.5228			0.568710
$746$	−40.2351	−	34.1128i	−1.47311	−	1.24896i
$747$		−	11.1608i		−	0.408354i
$748$	1.60885	+	9.70255i	0.0588253	+	0.354760i
$749$		−	11.9751i		−	0.437561i
$750$	−9.47318	−	8.03172i	−0.345912	−	0.293277i
$751$	2.29470			0.0837349			0.0418675	−	0.999123i	$-0.486669\pi$
$751$	2.29470			0.0837349			0.0418675	+	0.999123i	$0.486669\pi$
$752$	−0.201409	−	0.590626i	−0.00734465	−	0.0215379i
$753$			19.6483i			0.716025i
$754$	30.8352	+	26.1432i	1.12295	+	0.952080i
$755$		−	8.11154i		−	0.295209i
$756$	1.48962	+	8.98350i	0.0541768	+	0.326727i
$757$	25.5612			0.929037			0.464518	−	0.885563i	$-0.346227\pi$
$757$	25.5612			0.929037			0.464518	+	0.885563i	$0.346227\pi$
$758$	11.0332	−	13.0133i	0.400744	−	0.472666i
$759$	−0.858496	+	4.30681i	−0.0311614	+	0.156327i
$760$	1.61923	+	0.968230i	0.0587357	+	0.0351214i
$761$	16.0610			0.582210			0.291105	−	0.956691i	$-0.405977\pi$
$761$	16.0610			0.582210			0.291105	+	0.956691i	$0.405977\pi$
$762$	−0.239222	+	0.282156i	−0.00866611	+	0.0102214i
$763$	−27.9872			−1.01321
$764$	2.92615	+	17.6469i	0.105864	+	0.638441i
$765$			5.20519i			0.188194i
$766$	17.0867	+	14.4868i	0.617368	+	0.523428i
$767$		−	17.1485i		−	0.619197i
$768$	−12.6664	+	9.77555i	−0.457061	+	0.352745i
$769$		−	28.1563i		−	1.01534i	−0.861551	−	0.507671i	$-0.830507\pi$
$769$		−	28.1563i		−	1.01534i	0.861551	−	0.507671i	$-0.169493\pi$
$770$	−3.69584	+	4.35914i	−0.133189	+	0.157093i
$771$	−12.3772			−0.445756
$772$	−3.99864	−	24.1148i	−0.143914	−	0.867909i
$773$	24.8284			0.893015			0.446508	−	0.894780i	$-0.352668\pi$
$773$	24.8284			0.893015			0.446508	+	0.894780i	$0.352668\pi$
$774$	−8.72808	+	10.2945i	−0.313724	+	0.370029i
$775$		−	22.9039i		−	0.822733i
$776$	−43.4405	−	25.9755i	−1.55942	−	0.932466i
$777$	−14.8418			−0.532447
$778$	−2.20351	−	1.86822i	−0.0789998	−	0.0669789i
$779$		−	6.10654i		−	0.218790i
$780$	8.60085	−	1.42617i	0.307960	−	0.0510650i
$781$	13.6481			0.488367
$782$	−28.5307	+	22.6409i	−1.02026	+	0.809637i
$783$		−	6.35610i		−	0.227149i
$784$	−51.9828	+	17.7267i	−1.85653	+	0.633095i
$785$	−0.182618			−0.00651793
$786$	8.87354	+	7.52332i	0.316509	+	0.268348i
$787$		−	30.2006i		−	1.07653i	−0.842774	−	0.538267i	$-0.819079\pi$
$787$		−	30.2006i		−	1.07653i	0.842774	−	0.538267i	$-0.180921\pi$
$788$	20.7671	−	3.44355i	0.739799	−	0.122671i
$789$	0.300441			0.0106960
$790$	12.6163	+	10.6966i	0.448867	+	0.380567i
$791$			85.6217i			3.04436i
$792$	−2.22290	−	1.32920i	−0.0789873	−	0.0472309i
$793$		−	55.1717i		−	1.95920i
$794$	−31.8185	+	37.5290i	−1.12920	+	1.33185i
$795$	2.35158			0.0834018
$796$	−5.30119	−	31.9701i	−0.187896	−	1.13315i
$797$	0.413948			0.0146628			0.00733139	−	0.999973i	$-0.497666\pi$
$797$	0.413948			0.0146628			0.00733139	+	0.999973i	$0.497666\pi$
$798$	−2.86560	+	3.37989i	−0.101441	+	0.119647i
$799$	0.837786			0.0296387
$800$	21.3770	+	8.40450i	0.755790	+	0.297144i
$801$			10.9680i			0.387535i
$802$	−25.5648	+	30.1530i	−0.902726	+	1.06474i
$803$		−	7.49244i		−	0.264403i
$804$	21.0034	−	3.48271i	0.740731	−	0.122826i
$805$	−20.7564	−	4.13747i	−0.731567	−	0.145827i
$806$	27.3643	+	23.2004i	0.963865	+	0.817201i
$807$			1.53065i			0.0538814i
$808$	5.30867	+	3.17435i	0.186758	+	0.111673i
$809$	3.27386			0.115103			0.0575513	−	0.998343i	$-0.481671\pi$
$809$	3.27386			0.115103			0.0575513	+	0.998343i	$0.481671\pi$
$810$	−1.04555	−	0.886452i	−0.0367367	−	0.0311468i
$811$	5.52427			0.193983			0.0969916	−	0.995285i	$-0.469078\pi$
$811$	5.52427			0.193983			0.0969916	+	0.995285i	$0.469078\pi$
$812$	57.1000	−	9.46815i	2.00382	−	0.332267i
$813$			6.52820i			0.228954i
$814$	2.72989	−	3.21983i	0.0956827	−	0.112855i
$815$	−5.85765			−0.205185
$816$	−6.93317	−	20.3313i	−0.242710	−	0.711737i
$817$	−6.56758			−0.229771
$818$	−11.2609	−	9.54737i	−0.393727	−	0.333816i
$819$			20.4768i			0.715518i
$820$	2.81391	+	16.9700i	0.0982660	+	0.592617i
$821$		−	40.6786i		−	1.41969i	−0.704356	−	0.709847i	$-0.748764\pi$
$821$		−	40.6786i		−	1.41969i	0.704356	−	0.709847i	$-0.251236\pi$
$822$	−6.13331	+	7.23407i	−0.213924	+	0.252317i
$823$			31.2641i			1.08980i	0.838502	+	0.544898i	$0.183432\pi$
$823$			31.2641i			1.08980i	−0.838502	+	0.544898i	$0.816568\pi$
$824$	2.65312	−	4.43698i	0.0924257	−	0.154569i
$825$			3.71821i			0.129452i
$826$	−18.7272	−	15.8776i	−0.651604	−	0.552454i
$827$		−	20.8630i		−	0.725478i	−0.931891	−	0.362739i	$-0.881842\pi$
$827$		−	20.8630i		−	0.725478i	0.931891	−	0.362739i	$-0.118158\pi$
$828$	0.311039	−	9.58662i	0.0108094	−	0.333158i
$829$		−	11.6152i		−	0.403414i	−0.979446	−	0.201707i	$-0.935351\pi$
$829$		−	11.6152i		−	0.403414i	0.979446	−	0.201707i	$-0.0646489\pi$
$830$	−9.89355	+	11.6692i	−0.343410	+	0.405043i
$831$		−	7.38599i		−	0.256217i
$832$	−31.6949	+	17.0266i	−1.09882	+	0.590292i
$833$		−	73.7361i		−	2.55481i
$834$	8.01043	+	6.79154i	0.277379	+	0.235172i
$835$		−	3.18042i		−	0.110063i
$836$	−0.206168	−	1.24334i	−0.00713046	−	0.0430020i
$837$		−	5.64064i		−	0.194969i
$838$	25.5533	−	30.1394i	0.882725	−	1.04115i
$839$	−35.2227			−1.21602			−0.608011	−	0.793929i	$-0.708032\pi$
$839$	−35.2227			−1.21602			−0.608011	+	0.793929i	$0.708032\pi$
$840$	6.40598	−	10.7131i	0.221027	−	0.369638i
$841$	−11.4000			−0.393104
$842$	−35.2534	−	29.8891i	−1.21491	−	1.03005i
$843$		−	7.79441i		−	0.268454i
$844$	2.03137	+	12.2507i	0.0699227	+	0.421686i
$845$	7.00411			0.240949
$846$	−0.142676	+	0.168283i	−0.00490531	+	0.00578568i
$847$	−46.2661			−1.58972
$848$	−9.18516	+	3.13223i	−0.315420	+	0.107561i
$849$			27.8464i			0.955687i
$850$	−19.9428	+	23.5219i	−0.684031	+	0.806796i
$851$	15.3315	+	3.05609i	0.525556	+	0.104762i
$852$	−29.4075	+	4.87627i	−1.00749	+	0.167058i
$853$			11.0149i			0.377145i	0.982059	+	0.188572i	$0.0603860\pi$
$853$			11.0149i			0.377145i	−0.982059	+	0.188572i	$0.939614\pi$
$854$	−60.2509	−	51.0829i	−2.06174	−	1.74802i
$855$		−	0.667026i		−	0.0228118i
$856$	−6.38470	−	3.81777i	−0.218225	−	0.130489i
$857$	4.44133			0.151713			0.0758565	−	0.997119i	$-0.475831\pi$
$857$	4.44133			0.151713			0.0758565	+	0.997119i	$0.475831\pi$
$858$	−4.44231	−	3.76635i	−0.151658	−	0.128581i
$859$	55.9465			1.90887			0.954436	−	0.298417i	$-0.0964587\pi$
$859$	55.9465			1.90887			0.954436	+	0.298417i	$0.0964587\pi$
$860$	18.2512	−	3.02636i	0.622361	−	0.103198i
$861$	−40.4019			−1.37689
$862$	−17.4240	−	14.7727i	−0.593464	−	0.503161i
$863$		−	19.0075i		−	0.647022i	−0.946224	−	0.323511i	$-0.895137\pi$
$863$		−	19.0075i		−	0.647022i	0.946224	−	0.323511i	$-0.104863\pi$
$864$	5.26459	+	2.06981i	0.179105	+	0.0704164i
$865$		−	4.15256i		−	0.141191i
$866$	18.2123	−	21.4809i	0.618880	−	0.729951i
$867$	11.8393			0.402085
$868$	50.6726	−	8.40239i	1.71994	−	0.285196i
$869$		−	11.0495i		−	0.374828i
$870$	−5.63438	+	6.64559i	−0.191023	+	0.225307i
$871$	47.8746			1.62217
$872$	−8.92258	+	14.9218i	−0.302157	+	0.505316i
$873$			17.8948i			0.605648i
$874$	3.65610	−	2.90134i	0.123669	−	0.0981394i
$875$	−39.9855			−1.35176
$876$	2.67695	+	16.1440i	0.0904457	+	0.545455i
$877$			39.4573i			1.33238i	0.745782	+	0.666190i	$0.232076\pi$
$877$			39.4573i			1.33238i	−0.745782	+	0.666190i	$0.767924\pi$
$878$	26.7967	−	31.6060i	0.904346	−	1.06665i
$879$	−12.2770			−0.414094
$880$	1.14587	+	3.36023i	0.0386274	+	0.113273i
$881$		−	17.9584i		−	0.605035i	−0.953144	−	0.302517i	$-0.902173\pi$
$881$		−	17.9584i		−	0.605035i	0.953144	−	0.302517i	$-0.0978270\pi$
$882$	14.8111	+	12.5574i	0.498715	+	0.422829i
$883$	−39.4681			−1.32821			−0.664104	−	0.747640i	$-0.731187\pi$
$883$	−39.4681			−1.32821			−0.664104	+	0.747640i	$0.731187\pi$
$884$	−7.90167	−	47.6529i	−0.265762	−	1.60274i
$885$	3.69584			0.124234
$886$	35.5533	+	30.1435i	1.19444	+	1.01269i
$887$		−	15.0370i		−	0.504892i	−0.967611	−	0.252446i	$-0.918765\pi$
$887$		−	15.0370i		−	0.504892i	0.967611	−	0.252446i	$-0.0812350\pi$
$888$	−4.73170	+	7.91313i	−0.158786	+	0.265547i
$889$			1.19096i			0.0399434i
$890$	9.72259	−	11.4675i	0.325902	−	0.384392i
$891$			0.915699i			0.0306771i
$892$	44.9052	−	7.44604i	1.50354	−	0.249312i
$893$	−0.107359			−0.00359264
$894$	17.2752	+	14.6466i	0.577770	+	0.489855i
$895$	21.0882			0.704902
$896$	−10.7519	+	50.3776i	−0.359196	+	1.68300i
$897$	4.21640	−	21.1524i	0.140782	−	0.706258i
$898$	18.0103	+	15.2698i	0.601010	+	0.509559i
$899$	−35.8525			−1.19575
$900$	−1.32847	−	8.01164i	−0.0442822	−	0.267055i
$901$		−	13.0289i		−	0.434055i
$902$	7.43124	−	8.76493i	0.247433	−	0.291840i
$903$			43.4523i			1.44600i
$904$	45.6505	+	27.2970i	1.51831	+	0.907885i
$905$	2.35279			0.0782094
$906$	7.65368	−	9.02730i	0.254276	−	0.299912i
$907$		−	9.18521i		−	0.304990i	−0.988304	−	0.152495i	$-0.951269\pi$
$907$		−	9.18521i		−	0.304990i	0.988304	−	0.152495i	$-0.0487308\pi$
$908$	−10.2418	+	1.69827i	−0.339887	+	0.0563591i
$909$		−	2.18685i		−	0.0725332i
$910$	18.1517	−	21.4094i	0.601724	−	0.709716i
$911$	−20.7570			−0.687710			−0.343855	−	0.939023i	$-0.611733\pi$
$911$	−20.7570			−0.687710			−0.343855	+	0.939023i	$0.611733\pi$
$912$	0.888459	+	2.60537i	0.0294198	+	0.0862726i
$913$	10.2200			0.338232
$914$	6.90187	−	8.14056i	0.228294	−	0.269266i
$915$	11.8906			0.393091
$916$	5.41398	+	32.6503i	0.178883	+	1.07880i
$917$	37.4545			1.23686
$918$	−4.91139	+	5.79284i	−0.162100	+	0.191192i
$919$	−51.6210			−1.70282			−0.851409	−	0.524502i	$-0.824251\pi$
$919$	−51.6210			−1.70282			−0.851409	+	0.524502i	$0.824251\pi$
$920$	−8.82329	+	9.74752i	−0.290895	+	0.321366i
$921$	0.0911995			0.00300513
$922$	20.1505	−	23.7669i	0.663620	−	0.782721i
$923$	−67.0310			−2.20635
$924$	−8.22618	+	1.36404i	−0.270621	+	0.0448736i
$925$	13.2362			0.435203
$926$	−9.68506	+	11.4233i	−0.318271	+	0.375391i
$927$	−1.82776			−0.0600317
$928$	13.1559	−	33.4623i	0.431864	−	1.09845i
$929$	36.6120			1.20120			0.600600	−	0.799549i	$-0.294928\pi$
$929$	36.6120			1.20120			0.600600	+	0.799549i	$0.294928\pi$
$930$	−5.00016	+	5.89754i	−0.163962	+	0.193388i
$931$			9.44900i			0.309679i
$932$	−4.94595	−	29.8278i	−0.162010	−	0.977041i
$933$			2.75985i			0.0903534i
$934$	−21.7961	+	25.7078i	−0.713189	+	0.841186i
$935$	−4.76639			−0.155878
$936$	10.9175	+	6.52820i	0.356850	+	0.213381i
$937$			6.16375i			0.201361i	0.994919	+	0.100680i	$0.0321020\pi$
$937$			6.16375i			0.201361i	−0.994919	+	0.100680i	$0.967898\pi$
$938$	44.3267	−	52.2820i	1.44732	−	1.70707i
$939$		−	11.2930i		−	0.368532i
$940$	0.298349	−	0.0494714i	0.00973107	−	0.00161358i
$941$	−12.0779			−0.393729			−0.196865	−	0.980431i	$-0.563076\pi$
$941$	−12.0779			−0.393729			−0.196865	+	0.980431i	$0.563076\pi$
$942$	−0.203235	−	0.172311i	−0.00662177	−	0.00561418i
$943$	41.7349	+	8.31921i	1.35908	+	0.270911i
$944$	−14.4358	+	4.92276i	−0.469846	+	0.160222i
$945$	−4.41316			−0.143560
$946$	−9.42668	−	7.99230i	−0.306488	−	0.259852i
$947$	−51.7679			−1.68223			−0.841115	−	0.540856i	$-0.818100\pi$
$947$	−51.7679			−1.68223			−0.841115	+	0.540856i	$0.818100\pi$
$948$	3.94783	+	23.8083i	0.128219	+	0.773258i
$949$			36.7983i			1.19452i
$950$	2.55559	−	3.01425i	0.0829143	−	0.0977950i
$951$		−	23.3082i		−	0.755821i
$952$	−59.3560	−	35.4923i	−1.92374	−	1.15031i
$953$		−	18.0036i		−	0.583193i	−0.956541	−	0.291597i	$-0.905813\pi$
$953$		−	18.0036i		−	0.583193i	0.956541	−	0.291597i	$-0.0941865\pi$
$954$	2.61706	+	2.21884i	0.0847304	+	0.0718376i
$955$	−8.66905			−0.280524
$956$	−8.30039	+	1.37635i	−0.268454	+	0.0445142i
$957$	5.82028			0.188143
$958$	19.8586	+	16.8368i	0.641601	+	0.543973i
$959$			30.5344i			0.986006i
$960$	−3.66958	−	6.83089i	−0.118435	−	0.220466i
$961$	−0.816783			−0.0263478
$962$	−13.4076	+	15.8138i	−0.432277	+	0.509858i
$963$			2.63011i			0.0847541i
$964$	−22.1303	+	3.66959i	−0.712770	+	0.118189i
$965$	11.8464			0.381350
$966$	−19.1958	−	24.1894i	−0.617615	−	0.778281i
$967$			51.6314i			1.66035i	0.557500	+	0.830177i	$0.311760\pi$
$967$			51.6314i			1.66035i	−0.557500	+	0.830177i	$0.688240\pi$
$968$	−14.7501	+	24.6675i	−0.474085	+	0.792842i
$969$	−3.69565			−0.118721
$970$	15.8629	−	18.7099i	0.509328	−	0.600738i
$971$			6.84543i			0.219680i	0.993949	+	0.109840i	$0.0350339\pi$
$971$			6.84543i			0.219680i	−0.993949	+	0.109840i	$0.964966\pi$
$972$	−0.327167	−	1.97306i	−0.0104939	−	0.0632859i
$973$	33.8113			1.08394
$974$	−36.2585	+	42.7658i	−1.16180	+	1.37031i
$975$		−	18.2616i		−	0.584839i
$976$	−46.4442	+	15.8379i	−1.48664	+	0.506960i
$977$		−	18.2136i		−	0.582706i	−0.956616	−	0.291353i	$-0.905895\pi$
$977$		−	18.2136i		−	0.582706i	0.956616	−	0.291353i	$-0.0941054\pi$
$978$	−6.51896	−	5.52702i	−0.208453	−	0.176734i
$979$	−10.0434			−0.320988
$980$	−4.35412	−	26.2586i	−0.139087	−	0.838801i
$981$	6.14687			0.196255
$982$	−32.4692	−	27.5286i	−1.03613	−	0.878472i
$983$	9.93131			0.316760			0.158380	−	0.987378i	$-0.449373\pi$
$983$	9.93131			0.316760			0.158380	+	0.987378i	$0.449373\pi$
$984$	−12.8805	+	21.5409i	−0.410616	+	0.686699i
$985$			10.2019i			0.325059i
$986$	36.8199	+	31.2173i	1.17258	+	0.994160i
$987$			0.710307i			0.0226093i
$988$	1.01257	+	6.10654i	0.0322141	+	0.194275i
$989$	8.94731	−	44.8859i	0.284508	−	1.42729i
$990$	0.811724	−	0.957405i	0.0257983	−	0.0304283i
$991$		−	26.5845i		−	0.844485i	−0.906483	−	0.422242i	$-0.861243\pi$
$991$		−	26.5845i		−	0.844485i	0.906483	−	0.422242i	$-0.138757\pi$
$992$	11.6750	−	29.6956i	0.370683	−	0.942837i
$993$	14.7506			0.468096
$994$	−62.0633	+	73.2019i	−1.96853	+	2.32182i
$995$	15.7054			0.497894
$996$	−22.0210	+	3.65146i	−0.697762	+	0.115701i
$997$			9.89264i			0.313303i	0.987654	+	0.156652i	$0.0500700\pi$
$997$			9.89264i			0.313303i	−0.987654	+	0.156652i	$0.949930\pi$
$998$	−23.2281	−	19.6937i	−0.735274	−	0.623392i
$999$	3.25973			0.103133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.b.91.19	yes	24
4.3	odd	2		2208.2.n.b.367.9		24
8.3	odd	2	inner	552.2.n.b.91.18	yes	24
8.5	even	2		2208.2.n.b.367.15		24
23.22	odd	2	inner	552.2.n.b.91.20	yes	24
92.91	even	2		2208.2.n.b.367.16		24
184.45	odd	2		2208.2.n.b.367.10		24
184.91	even	2	inner	552.2.n.b.91.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.17	✓	24	184.91	even	2	inner
552.2.n.b.91.18	yes	24	8.3	odd	2	inner
552.2.n.b.91.19	yes	24	1.1	even	1	trivial
552.2.n.b.91.20	yes	24	23.22	odd	2	inner
2208.2.n.b.367.9		24	4.3	odd	2
2208.2.n.b.367.10		24	184.45	odd	2
2208.2.n.b.367.15		24	8.5	even	2
2208.2.n.b.367.16		24	92.91	even	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07870 + 0.914558i) q^{2} -1.00000 q^{3} +(0.327167 + 1.97306i) q^{4} -0.969269 q^{5} +(-1.07870 - 0.914558i) q^{6} -4.55308 q^{7} +(-1.45156 + 2.42754i) q^{8} +1.00000 q^{9} +(-1.04555 - 0.886452i) q^{10} +0.915699i q^{11} +(-0.327167 - 1.97306i) q^{12} -4.49735i q^{13} +(-4.91139 - 4.16406i) q^{14} +0.969269 q^{15} +(-3.78592 + 1.29104i) q^{16} -5.37023i q^{17} +(1.07870 + 0.914558i) q^{18} +0.688174i q^{19} +(-0.317112 - 1.91242i) q^{20} +4.55308 q^{21} +(-0.837460 + 0.987761i) q^{22} +(-4.70330 - 0.937530i) q^{23} +(1.45156 - 2.42754i) q^{24} -4.06052 q^{25} +(4.11309 - 4.85127i) q^{26} -1.00000 q^{27} +(-1.48962 - 8.98350i) q^{28} +6.35610i q^{29} +(1.04555 + 0.886452i) q^{30} +5.64064i q^{31} +(-5.26459 - 2.06981i) q^{32} -0.915699i q^{33} +(4.91139 - 5.79284i) q^{34} +4.41316 q^{35} +(0.327167 + 1.97306i) q^{36} -3.25973 q^{37} +(-0.629375 + 0.742330i) q^{38} +4.49735i q^{39} +(1.40696 - 2.35294i) q^{40} -8.87354 q^{41} +(4.91139 + 4.16406i) q^{42} +9.54349i q^{43} +(-1.80673 + 0.299586i) q^{44} -0.969269 q^{45} +(-4.21600 - 5.31275i) q^{46} +0.156006i q^{47} +(3.78592 - 1.29104i) q^{48} +13.7305 q^{49} +(-4.38006 - 3.71358i) q^{50} +5.37023i q^{51} +(8.87354 - 1.47138i) q^{52} +2.42613 q^{53} +(-1.07870 - 0.914558i) q^{54} -0.887559i q^{55} +(6.60909 - 11.0528i) q^{56} -0.688174i q^{57} +(-5.81302 + 6.85630i) q^{58} +3.81302 q^{59} +(0.317112 + 1.91242i) q^{60} +12.2676 q^{61} +(-5.15869 + 6.08453i) q^{62} -4.55308 q^{63} +(-3.78592 - 7.04747i) q^{64} +4.35914i q^{65} +(0.837460 - 0.987761i) q^{66} +10.6451i q^{67} +(10.5958 - 1.75696i) q^{68} +(4.70330 + 0.937530i) q^{69} +(4.76045 + 4.03609i) q^{70} -14.9045i q^{71} +(-1.45156 + 2.42754i) q^{72} -8.18221 q^{73} +(-3.51625 - 2.98121i) q^{74} +4.06052 q^{75} +(-1.35781 + 0.225148i) q^{76} -4.16925i q^{77} +(-4.11309 + 4.85127i) q^{78} -12.0667 q^{79} +(3.66958 - 1.25136i) q^{80} +1.00000 q^{81} +(-9.57185 - 8.11537i) q^{82} -11.1608i q^{83} +(1.48962 + 8.98350i) q^{84} +5.20519i q^{85} +(-8.72808 + 10.2945i) q^{86} -6.35610i q^{87} +(-2.22290 - 1.32920i) q^{88} +10.9680i q^{89} +(-1.04555 - 0.886452i) q^{90} +20.4768i q^{91} +(0.311039 - 9.58662i) q^{92} -5.64064i q^{93} +(-0.142676 + 0.168283i) q^{94} -0.667026i q^{95} +(5.26459 + 2.06981i) q^{96} +17.8948i q^{97} +(14.8111 + 12.5574i) q^{98} +0.915699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81}+ \cdots - 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Introduction

L-functions

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