LMFDB - Embedded newform 864.2.bi.a.383.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(95,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.95"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			383.8
Character	$\chi$	$=$	864.383
Dual form			864.2.bi.a.767.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38351 - 1.04206i) q^{3} +(-1.14718 - 3.15185i) q^{5} +(3.41716 - 0.602538i) q^{7} +(0.828207 + 2.88341i) q^{9} +(5.46372 + 1.98863i) q^{11} +(2.22836 + 1.86981i) q^{13} +(-1.69729 + 5.55605i) q^{15} +(1.37724 + 0.795152i) q^{17} +(4.19994 - 2.42483i) q^{19} +(-5.35557 - 2.72728i) q^{21} +(-0.571328 + 3.24016i) q^{23} +(-4.78789 + 4.01752i) q^{25} +(1.85887 - 4.85228i) q^{27} +(-6.50285 - 7.74980i) q^{29} +(8.83663 + 1.55814i) q^{31} +(-5.48684 - 8.44484i) q^{33} +(-5.81920 - 10.0792i) q^{35} +(1.74012 - 3.01397i) q^{37} +(-1.13449 - 4.90900i) q^{39} +(-5.53501 + 6.59637i) q^{41} +(-1.13860 + 3.12829i) q^{43} +(8.13797 - 5.91817i) q^{45} +(-0.865755 - 4.90994i) q^{47} +(4.73611 - 1.72380i) q^{49} +(-1.07683 - 2.53528i) q^{51} -4.99058i q^{53} -19.5021i q^{55} +(-8.33749 - 1.02181i) q^{57} +(-2.57752 + 0.938141i) q^{59} +(1.47210 + 8.34868i) q^{61} +(4.56749 + 9.35407i) q^{63} +(3.33704 - 9.16845i) q^{65} +(-6.88635 + 8.20683i) q^{67} +(4.16689 - 3.88744i) q^{69} +(1.30322 - 2.25724i) q^{71} +(0.241869 + 0.418929i) q^{73} +(10.8106 - 0.568995i) q^{75} +(19.8687 + 3.50338i) q^{77} +(-0.268589 - 0.320092i) q^{79} +(-7.62815 + 4.77613i) q^{81} +(-1.52401 + 1.27879i) q^{83} +(0.926253 - 5.25304i) q^{85} +(0.920988 + 17.4983i) q^{87} +(12.3006 - 7.10173i) q^{89} +(8.74130 + 5.04679i) q^{91} +(-10.6019 - 11.3640i) q^{93} +(-12.4608 - 10.4558i) q^{95} +(-8.14933 - 2.96611i) q^{97} +(-1.20896 + 17.4012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$-1$

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
$3$	−1.38351	−	1.04206i	−0.798771	−	0.601636i
$3$	−1.38351	−	1.04206i	−0.798771	−	0.601636i
$4$		0			0
$5$	−1.14718	−	3.15185i	−0.513034	−	1.40955i	−0.878060	−	0.478551i	$-0.841162\pi$
$5$	−1.14718	−	3.15185i	−0.513034	−	1.40955i	0.365026	−	0.930997i	$-0.381060\pi$
$6$		0			0
$7$	3.41716	−	0.602538i	1.29157	−	0.227738i	0.514682	−	0.857381i	$-0.327910\pi$
$7$	3.41716	−	0.602538i	1.29157	−	0.227738i	0.776884	+	0.629643i	$0.216799\pi$
$8$		0			0
$9$	0.828207	+	2.88341i	0.276069	+	0.961138i
$10$		0			0
$11$	5.46372	+	1.98863i	1.64737	+	0.599595i	0.988305	−	0.152488i	$-0.0487284\pi$
$11$	5.46372	+	1.98863i	1.64737	+	0.599595i	0.659069	+	0.752083i	$0.270951\pi$
$12$		0			0
$13$	2.22836	+	1.86981i	0.618035	+	0.518593i	0.897185	−	0.441654i	$-0.145608\pi$
$13$	2.22836	+	1.86981i	0.618035	+	0.518593i	−0.279150	+	0.960247i	$0.590053\pi$
$14$		0			0
$15$	−1.69729	+	5.55605i	−0.438238	+	1.43457i
$16$		0			0
$17$	1.37724	+	0.795152i	0.334031	+	0.192853i	0.657629	−	0.753342i	$-0.271559\pi$
$17$	1.37724	+	0.795152i	0.334031	+	0.192853i	−0.323598	+	0.946195i	$0.604893\pi$
$18$		0			0
$19$	4.19994	−	2.42483i	0.963531	−	0.556295i	0.0662733	−	0.997802i	$-0.478889\pi$
$19$	4.19994	−	2.42483i	0.963531	−	0.556295i	0.897258	+	0.441506i	$0.145556\pi$
$20$		0			0
$21$	−5.35557	−	2.72728i	−1.16868	−	0.595142i
$22$		0			0
$23$	−0.571328	+	3.24016i	−0.119130	+	0.675620i	0.865492	+	0.500923i	$0.167006\pi$
$23$	−0.571328	+	3.24016i	−0.119130	+	0.675620i	−0.984622	+	0.174698i	$0.944105\pi$
$24$		0			0
$25$	−4.78789	+	4.01752i	−0.957579	+	0.803504i
$26$		0			0
$27$	1.85887	−	4.85228i	0.357739	−	0.933822i
$28$		0			0
$29$	−6.50285	−	7.74980i	−1.20755	−	1.43910i	−0.866588	−	0.499025i	$-0.833692\pi$
$29$	−6.50285	−	7.74980i	−1.20755	−	1.43910i	−0.340962	−	0.940077i	$-0.610753\pi$
$30$		0			0
$31$	8.83663	+	1.55814i	1.58711	+	0.279850i	0.896387	−	0.443273i	$-0.146183\pi$
$31$	8.83663	+	1.55814i	1.58711	+	0.279850i	0.690720	+	0.723123i	$0.257294\pi$
$32$		0			0
$33$	−5.48684	−	8.44484i	−0.955136	−	1.47006i
$34$		0			0
$35$	−5.81920	−	10.0792i	−0.983625	−	1.70369i
$36$		0			0
$37$	1.74012	−	3.01397i	0.286073	−	0.495494i	−0.686796	−	0.726851i	$-0.740983\pi$
$37$	1.74012	−	3.01397i	0.286073	−	0.495494i	0.972869	+	0.231357i	$0.0743166\pi$
$38$		0			0
$39$	−1.13449	−	4.90900i	−0.181664	−	0.786069i
$40$		0			0
$41$	−5.53501	+	6.59637i	−0.864423	+	1.03018i	0.134804	+	0.990872i	$0.456960\pi$
$41$	−5.53501	+	6.59637i	−0.864423	+	1.03018i	−0.999227	+	0.0393074i	$0.987485\pi$
$42$		0			0
$43$	−1.13860	+	3.12829i	−0.173635	+	0.477059i	−0.995732	−	0.0922884i	$-0.970582\pi$
$43$	−1.13860	+	3.12829i	−0.173635	+	0.477059i	0.822097	+	0.569347i	$0.192804\pi$
$44$		0			0
$45$	8.13797	−	5.91817i	1.21314	−	0.882229i
$46$		0			0
$47$	−0.865755	−	4.90994i	−0.126283	−	0.716189i	−0.980537	−	0.196333i	$-0.937097\pi$
$47$	−0.865755	−	4.90994i	−0.126283	−	0.716189i	0.854254	−	0.519856i	$-0.174014\pi$
$48$		0			0
$49$	4.73611	−	1.72380i	0.676587	−	0.246257i
$50$		0			0
$51$	−1.07683	−	2.53528i	−0.150787	−	0.355010i
$52$		0			0
$53$		−	4.99058i		−	0.685509i	−0.939425	−	0.342754i	$-0.888640\pi$
$53$		−	4.99058i		−	0.685509i	0.939425	−	0.342754i	$-0.111360\pi$
$54$		0			0
$55$		−	19.5021i		−	2.62967i
$56$		0			0
$57$	−8.33749	−	1.02181i	−1.10433	−	0.135343i
$58$		0			0
$59$	−2.57752	+	0.938141i	−0.335565	+	0.122135i	−0.504306	−	0.863525i	$-0.668252\pi$
$59$	−2.57752	+	0.938141i	−0.335565	+	0.122135i	0.168742	+	0.985660i	$0.446030\pi$
$60$		0			0
$61$	1.47210	+	8.34868i	0.188483	+	1.06894i	0.921398	+	0.388619i	$0.127048\pi$
$61$	1.47210	+	8.34868i	0.188483	+	1.06894i	−0.732916	+	0.680320i	$0.761841\pi$
$62$		0			0
$63$	4.56749	+	9.35407i	0.575449	+	1.17850i
$64$		0			0
$65$	3.33704	−	9.16845i	0.413909	−	1.13721i
$66$		0			0
$67$	−6.88635	+	8.20683i	−0.841301	+	1.00262i	0.158582	+	0.987346i	$0.449308\pi$
$67$	−6.88635	+	8.20683i	−0.841301	+	1.00262i	−0.999883	+	0.0152779i	$0.995137\pi$
$68$		0			0
$69$	4.16689	−	3.88744i	0.501635	−	0.467993i
$70$		0			0
$71$	1.30322	−	2.25724i	0.154664	−	0.267885i	−0.778273	−	0.627926i	$-0.783904\pi$
$71$	1.30322	−	2.25724i	0.154664	−	0.267885i	0.932936	+	0.360041i	$0.117237\pi$
$72$		0			0
$73$	0.241869	+	0.418929i	0.0283086	+	0.0490319i	0.879833	−	0.475284i	$-0.157655\pi$
$73$	0.241869	+	0.418929i	0.0283086	+	0.0490319i	−0.851524	+	0.524316i	$0.824321\pi$
$74$		0			0
$75$	10.8106	−	0.568995i	1.24830	−	0.0657018i
$76$		0			0
$77$	19.8687	+	3.50338i	2.26424	+	0.399247i
$78$		0			0
$79$	−0.268589	−	0.320092i	−0.0302186	−	0.0360131i	0.750723	−	0.660617i	$-0.229705\pi$
$79$	−0.268589	−	0.320092i	−0.0302186	−	0.0360131i	−0.780942	+	0.624603i	$0.785261\pi$
$80$		0			0
$81$	−7.62815	+	4.77613i	−0.847572	+	0.530681i
$82$		0			0
$83$	−1.52401	+	1.27879i	−0.167281	+	0.140366i	−0.722585	−	0.691282i	$-0.757046\pi$
$83$	−1.52401	+	1.27879i	−0.167281	+	0.140366i	0.555304	+	0.831647i	$0.312602\pi$
$84$		0			0
$85$	0.926253	−	5.25304i	0.100466	−	0.569773i
$86$		0			0
$87$	0.920988	+	17.4983i	0.0987403	+	1.87602i
$88$		0			0
$89$	12.3006	−	7.10173i	1.30386	−	0.752782i	0.322793	−	0.946469i	$-0.395378\pi$
$89$	12.3006	−	7.10173i	1.30386	−	0.752782i	0.981063	+	0.193687i	$0.0620448\pi$
$90$		0			0
$91$	8.74130	+	5.04679i	0.916337	+	0.529047i
$92$		0			0
$93$	−10.6019	−	11.3640i	−1.09937	−	1.17840i
$94$		0			0
$95$	−12.4608	−	10.4558i	−1.27845	−	1.07275i
$96$		0			0
$97$	−8.14933	−	2.96611i	−0.827439	−	0.301163i	−0.106632	−	0.994299i	$-0.534007\pi$
$97$	−8.14933	−	2.96611i	−0.827439	−	0.301163i	−0.720807	+	0.693135i	$0.756229\pi$
$98$		0			0
$99$	−1.20896	+	17.4012i	−0.121505	+	1.74888i
$100$		0			0
$101$	8.08222	−	1.42511i	0.804211	−	0.141804i	0.243592	−	0.969878i	$-0.421674\pi$
$101$	8.08222	−	1.42511i	0.804211	−	0.141804i	0.560619	+	0.828074i	$0.310563\pi$
$102$		0			0
$103$	−1.37956	−	3.79032i	−0.135932	−	0.373471i	0.852985	−	0.521935i	$-0.174790\pi$
$103$	−1.37956	−	3.79032i	−0.135932	−	0.373471i	−0.988918	+	0.148463i	$0.952567\pi$
$104$		0			0
$105$	−2.45219	+	20.0086i	−0.239309	+	1.95264i
$106$		0			0
$107$	−13.3604			−1.29160			−0.645799	−	0.763507i	$-0.723476\pi$
$107$	−13.3604			−1.29160			−0.645799	+	0.763507i	$0.723476\pi$
$108$		0			0
$109$	−16.2740			−1.55876			−0.779381	−	0.626550i	$-0.784466\pi$
$109$	−16.2740			−1.55876			−0.779381	+	0.626550i	$0.784466\pi$
$110$		0			0
$111$	−5.54822	+	2.35655i	−0.526614	+	0.223674i
$112$		0			0
$113$	2.68603	+	7.37980i	0.252680	+	0.694233i	0.999571	+	0.0292864i	$0.00932350\pi$
$113$	2.68603	+	7.37980i	0.252680	+	0.694233i	−0.746891	+	0.664947i	$0.768454\pi$
$114$		0			0
$115$	10.8679	−	1.91630i	1.01344	−	0.178696i
$116$		0			0
$117$	−3.54591	+	7.97387i	−0.327819	+	0.737184i
$118$		0			0
$119$	5.18538	+	1.88732i	0.475343	+	0.173011i
$120$		0			0
$121$	17.4711	+	14.6600i	1.58828	+	1.33273i
$122$		0			0
$123$	14.5316	−	3.35832i	1.31027	−	0.302809i
$124$		0			0
$125$	3.63139	+	2.09658i	0.324801	+	0.187524i
$126$		0			0
$127$	1.78382	−	1.02989i	0.158289	−	0.0913880i	−0.418763	−	0.908095i	$-0.637536\pi$
$127$	1.78382	−	1.02989i	0.158289	−	0.0913880i	0.577052	+	0.816707i	$0.304203\pi$
$128$		0			0
$129$	4.83514	−	3.14152i	0.425711	−	0.276596i
$130$		0			0
$131$	−0.674118	+	3.82311i	−0.0588979	+	0.334027i	−0.999992	−	0.00411945i	$-0.998689\pi$
$131$	−0.674118	+	3.82311i	−0.0588979	+	0.334027i	0.941094	+	0.338146i	$0.109800\pi$
$132$		0			0
$133$	12.8908	−	10.8167i	1.11778	−	0.937925i
$134$		0			0
$135$	−17.4261	−	0.292431i	−1.49980	−	0.0251685i
$136$		0			0
$137$	−11.5340	−	13.7457i	−0.985418	−	1.17438i	−0.984679	−	0.174376i	$-0.944209\pi$
$137$	−11.5340	−	13.7457i	−0.985418	−	1.17438i	−0.000738616	−	1.00000i	$-0.500235\pi$
$138$		0			0
$139$	−6.43005	−	1.13379i	−0.545389	−	0.0961669i	−0.105836	−	0.994384i	$-0.533752\pi$
$139$	−6.43005	−	1.13379i	−0.545389	−	0.0961669i	−0.439553	+	0.898217i	$0.644863\pi$
$140$		0			0
$141$	−3.91869	+	7.69513i	−0.330013	+	0.648047i
$142$		0			0
$143$	8.45675	+	14.6475i	0.707189	+	1.22489i
$144$		0			0
$145$	−16.9662	+	29.3864i	−1.40897	+	2.44041i
$146$		0			0
$147$	−8.34877	−	2.55043i	−0.688595	−	0.210356i
$148$		0			0
$149$	5.41231	−	6.45013i	0.443393	−	0.528416i	−0.497343	−	0.867554i	$-0.665691\pi$
$149$	5.41231	−	6.45013i	0.443393	−	0.528416i	0.940737	+	0.339138i	$0.110135\pi$
$150$		0			0
$151$	4.44170	−	12.2035i	0.361460	−	0.993104i	−0.617053	−	0.786921i	$-0.711674\pi$
$151$	4.44170	−	12.2035i	0.361460	−	0.993104i	0.978514	−	0.206183i	$-0.0661041\pi$
$152$		0			0
$153$	−1.15211	+	4.62972i	−0.0931425	+	0.374290i
$154$		0			0
$155$	−5.22619	−	29.6392i	−0.419777	−	2.38068i
$156$		0			0
$157$	−6.95618	+	2.53184i	−0.555163	+	0.202063i	−0.604339	−	0.796727i	$-0.706563\pi$
$157$	−6.95618	+	2.53184i	−0.555163	+	0.202063i	0.0491757	+	0.998790i	$0.484341\pi$
$158$		0			0
$159$	−5.20050	+	6.90452i	−0.412426	+	0.547564i
$160$		0			0
$161$			11.4164i			0.899739i
$162$		0			0
$163$			0.380973i			0.0298401i	0.999889	+	0.0149200i	$0.00474938\pi$
$163$			0.380973i			0.0298401i	−0.999889	+	0.0149200i	$0.995251\pi$
$164$		0			0
$165$	−20.3225	+	26.9814i	−1.58210	+	2.10050i
$166$		0			0
$167$	8.27607	−	3.01224i	0.640421	−	0.233094i	−0.00133952	−	0.999999i	$-0.500426\pi$
$167$	8.27607	−	3.01224i	0.640421	−	0.233094i	0.641761	+	0.766905i	$0.278204\pi$
$168$		0			0
$169$	−0.788053	−	4.46927i	−0.0606195	−	0.343790i
$170$		0			0
$171$	10.4702	+	10.1019i	0.800677	+	0.772511i
$172$		0			0
$173$	−2.82729	+	7.76792i	−0.214955	+	0.590584i	−0.999568	−	0.0294021i	$-0.990640\pi$
$173$	−2.82729	+	7.76792i	−0.214955	+	0.590584i	0.784613	+	0.619986i	$0.212862\pi$
$174$		0			0
$175$	−13.9403	+	16.6134i	−1.05379	+	1.25586i
$176$		0			0
$177$	4.54363	+	1.38801i	0.341520	+	0.104329i
$178$		0			0
$179$	−5.96207	+	10.3266i	−0.445626	+	0.771847i	−0.998096	−	0.0616861i	$-0.980352\pi$
$179$	−5.96207	+	10.3266i	−0.445626	+	0.771847i	0.552470	+	0.833533i	$0.313686\pi$
$180$		0			0
$181$	−3.09810	−	5.36606i	−0.230280	−	0.398856i	0.727611	−	0.685990i	$-0.240631\pi$
$181$	−3.09810	−	5.36606i	−0.230280	−	0.398856i	−0.957890	+	0.287134i	$0.907297\pi$
$182$		0			0
$183$	6.66319	−	13.0845i	0.492557	−	0.967235i
$184$		0			0
$185$	−11.4958	−	2.02702i	−0.845188	−	0.149029i
$186$		0			0
$187$	5.94361	+	7.08332i	0.434640	+	0.517984i
$188$		0			0
$189$	3.42837	−	17.7011i	0.249377	−	1.28756i
$190$		0			0
$191$	2.20191	−	1.84762i	0.159325	−	0.133689i	−0.559640	−	0.828736i	$-0.689061\pi$
$191$	2.20191	−	1.84762i	0.159325	−	0.133689i	0.718965	+	0.695046i	$0.244616\pi$
$192$		0			0
$193$	−0.920220	+	5.21883i	−0.0662389	+	0.375659i	0.933610	+	0.358290i	$0.116640\pi$
$193$	−0.920220	+	5.21883i	−0.0662389	+	0.375659i	−0.999849	+	0.0173692i	$0.994471\pi$
$194$		0			0
$195$	−14.1709	+	9.20724i	−1.01480	+	0.659344i
$196$		0			0
$197$	−6.17620	+	3.56583i	−0.440036	+	0.254055i	−0.703613	−	0.710583i	$-0.748431\pi$
$197$	−6.17620	+	3.56583i	−0.440036	+	0.254055i	0.263577	+	0.964638i	$0.415098\pi$
$198$		0			0
$199$	−6.84781	−	3.95359i	−0.485429	−	0.280262i	0.237247	−	0.971449i	$-0.423755\pi$
$199$	−6.84781	−	3.95359i	−0.485429	−	0.280262i	−0.722676	+	0.691187i	$0.757088\pi$
$200$		0			0
$201$	18.0794	−	4.17823i	1.27522	−	0.294710i
$202$		0			0
$203$	−26.8909	−	22.5641i	−1.88737	−	1.58369i
$204$		0			0
$205$	27.1404	+	9.87829i	1.89557	+	0.689930i
$206$		0			0
$207$	−9.81590	+	1.03615i	−0.682252	+	0.0720174i
$208$		0			0
$209$	27.7694	−	4.89649i	1.92085	−	0.338697i
$210$		0			0
$211$	9.08573	+	24.9628i	0.625487	+	1.71851i	0.693140	+	0.720803i	$0.256227\pi$
$211$	9.08573	+	24.9628i	0.625487	+	1.71851i	−0.0676530	+	0.997709i	$0.521551\pi$
$212$		0			0
$213$	−4.15520	+	1.76488i	−0.284710	+	0.120928i
$214$		0			0
$215$	11.1661			0.761519
$216$		0			0
$217$	31.1351			2.11359
$218$		0			0
$219$	0.101922	−	0.831636i	0.00688728	−	0.0561967i
$220$		0			0
$221$	1.58221	+	4.34707i	0.106431	+	0.292416i
$222$		0			0
$223$	3.47907	−	0.613455i	0.232976	−	0.0410800i	−0.0559411	−	0.998434i	$-0.517816\pi$
$223$	3.47907	−	0.613455i	0.232976	−	0.0410800i	0.288917	+	0.957354i	$0.406705\pi$
$224$		0			0
$225$	−15.5495	−	10.4781i	−1.03664	−	0.698543i
$226$		0			0
$227$	−1.41313	−	0.514339i	−0.0937930	−	0.0341378i	0.294697	−	0.955591i	$-0.404781\pi$
$227$	−1.41313	−	0.514339i	−0.0937930	−	0.0341378i	−0.388490	+	0.921453i	$0.627003\pi$
$228$		0			0
$229$	22.9309	+	19.2413i	1.51531	+	1.27150i	0.852517	+	0.522699i	$0.175075\pi$
$229$	22.9309	+	19.2413i	1.51531	+	1.27150i	0.662796	+	0.748800i	$0.269369\pi$
$230$		0			0
$231$	−23.8378	−	25.5514i	−1.56841	−	1.68116i
$232$		0			0
$233$	−4.13296	−	2.38617i	−0.270759	−	0.156323i	0.358473	−	0.933540i	$-0.383297\pi$
$233$	−4.13296	−	2.38617i	−0.270759	−	0.156323i	−0.629233	+	0.777217i	$0.716631\pi$
$234$		0			0
$235$	−14.4822	+	8.36131i	−0.944715	+	0.545431i
$236$		0			0
$237$	0.0380398	+	0.722737i	0.00247095	+	0.0469468i
$238$		0			0
$239$	−0.275320	+	1.56142i	−0.0178090	+	0.101000i	−0.992417	−	0.122920i	$-0.960774\pi$
$239$	−0.275320	+	1.56142i	−0.0178090	+	0.101000i	0.974608	+	0.223920i	$0.0718853\pi$
$240$		0			0
$241$	15.2130	−	12.7652i	0.979958	−	0.822282i	−0.00412544	−	0.999991i	$-0.501313\pi$
$241$	15.2130	−	12.7652i	0.979958	−	0.822282i	0.984083	+	0.177709i	$0.0568687\pi$
$242$		0			0
$243$	15.5307	+	1.34119i	0.996292	+	0.0860372i
$244$		0			0
$245$	−10.8663	−	12.9500i	−0.694224	−	0.827343i
$246$		0			0
$247$	13.8929	+	2.44970i	0.883987	+	0.155871i
$248$		0			0
$249$	3.44106	−	0.181113i	0.218068	−	0.0114776i
$250$		0			0
$251$	10.6471	+	18.4413i	0.672038	+	1.16400i	0.977325	+	0.211743i	$0.0679140\pi$
$251$	10.6471	+	18.4413i	0.672038	+	1.16400i	−0.305288	+	0.952260i	$0.598753\pi$
$252$		0			0
$253$	−9.56506	+	16.5672i	−0.601350	+	1.04157i
$254$		0			0
$255$	−6.75549	+	6.30243i	−0.423045	+	0.394673i
$256$		0			0
$257$	−14.0702	+	16.7682i	−0.877674	+	1.04597i	0.120905	+	0.992664i	$0.461420\pi$
$257$	−14.0702	+	16.7682i	−0.877674	+	1.04597i	−0.998578	+	0.0533065i	$0.983024\pi$
$258$		0			0
$259$	4.13023	−	11.3477i	0.256640	−	0.705113i
$260$		0			0
$261$	16.9602	−	25.1689i	1.04981	−	1.55791i
$262$		0			0
$263$	0.883706	+	5.01175i	0.0544917	+	0.309038i	0.999856	−	0.0169786i	$-0.00540472\pi$
$263$	0.883706	+	5.01175i	0.0544917	+	0.309038i	−0.945364	+	0.326016i	$0.894294\pi$
$264$		0			0
$265$	−15.7295	+	5.72508i	−0.966258	+	0.351689i
$266$		0			0
$267$	−24.4184	−	2.99264i	−1.49438	−	0.183147i
$268$		0			0
$269$		−	10.1810i		−	0.620745i	−0.950615	−	0.310372i	$-0.899546\pi$
$269$		−	10.1810i		−	0.620745i	0.950615	−	0.310372i	$-0.100454\pi$
$270$		0			0
$271$			4.13681i			0.251294i	0.992075	+	0.125647i	$0.0401006\pi$
$271$			4.13681i			0.251294i	−0.992075	+	0.125647i	$0.959899\pi$
$272$		0			0
$273$	−6.83461	−	16.0913i	−0.413649	−	0.973888i
$274$		0			0
$275$	−34.1491	+	12.4293i	−2.05927	+	0.749512i
$276$		0			0
$277$	−2.12569	−	12.0554i	−0.127721	−	0.724339i	−0.979655	−	0.200690i	$-0.935682\pi$
$277$	−2.12569	−	12.0554i	−0.127721	−	0.724339i	0.851934	−	0.523649i	$-0.175430\pi$
$278$		0			0
$279$	2.82581	+	26.7701i	0.169177	+	1.60269i
$280$		0			0
$281$	−5.79234	+	15.9143i	−0.345542	+	0.949369i	0.638214	+	0.769859i	$0.279673\pi$
$281$	−5.79234	+	15.9143i	−0.345542	+	0.949369i	−0.983756	+	0.179510i	$0.942549\pi$
$282$		0			0
$283$	16.0098	−	19.0798i	0.951685	−	1.13417i	−0.0391691	−	0.999233i	$-0.512471\pi$
$283$	16.0098	−	19.0798i	0.951685	−	1.13417i	0.990854	−	0.134941i	$-0.0430845\pi$
$284$		0			0
$285$	6.34398	+	27.4507i	0.375785	+	1.62604i
$286$		0			0
$287$	−14.9395	+	25.8759i	−0.881849	+	1.52741i
$288$		0			0
$289$	−7.23547	−	12.5322i	−0.425616	−	0.737188i
$290$		0			0
$291$	8.18381	+	12.5958i	0.479744	+	0.738377i
$292$		0			0
$293$	−25.4107	−	4.48059i	−1.48451	−	0.261759i	−0.628130	−	0.778108i	$-0.716179\pi$
$293$	−25.4107	−	4.48059i	−1.48451	−	0.261759i	−0.856378	+	0.516349i	$0.827291\pi$
$294$		0			0
$295$	5.91375	+	7.04773i	0.344312	+	0.410335i
$296$		0			0
$297$	19.8057	−	22.8149i	1.14924	−	1.32385i
$298$		0			0
$299$	−7.33162	+	6.15196i	−0.423999	+	0.355777i
$300$		0			0
$301$	−2.00588	+	11.3759i	−0.115617	+	0.655697i
$302$		0			0
$303$	−12.6669	−	6.45053i	−0.727695	−	0.370573i
$304$		0			0
$305$	24.6250	−	14.2172i	1.41002	−	0.814077i
$306$		0			0
$307$	−11.8296	−	6.82981i	−0.675149	−	0.389798i	0.122876	−	0.992422i	$-0.460788\pi$
$307$	−11.8296	−	6.82981i	−0.675149	−	0.389798i	−0.798025	+	0.602624i	$0.794122\pi$
$308$		0			0
$309$	−2.04111	+	6.68154i	−0.116115	+	0.380100i
$310$		0			0
$311$	11.4409	+	9.60004i	0.648753	+	0.544368i	0.906692	−	0.421793i	$-0.138599\pi$
$311$	11.4409	+	9.60004i	0.648753	+	0.544368i	−0.257939	+	0.966161i	$0.583044\pi$
$312$		0			0
$313$	−21.3115	−	7.75676i	−1.20460	−	0.438438i	−0.339772	−	0.940508i	$-0.610350\pi$
$313$	−21.3115	−	7.75676i	−1.20460	−	0.438438i	−0.864827	+	0.502070i	$0.832572\pi$
$314$		0			0
$315$	24.2429	−	25.1268i	1.36593	−	1.41573i
$316$		0			0
$317$	−18.0405	+	3.18103i	−1.01326	+	0.178665i	−0.655536	−	0.755164i	$-0.727557\pi$
$317$	−18.0405	+	3.18103i	−1.01326	+	0.178665i	−0.357721	+	0.933829i	$0.616446\pi$
$318$		0			0
$319$	−20.1183	−	55.2745i	−1.12641	−	3.09478i
$320$		0			0
$321$	18.4843	+	13.9224i	1.03169	+	0.777072i
$322$		0			0
$323$	7.71245			0.429132
$324$		0			0
$325$	−18.1812			−1.00851
$326$		0			0
$327$	22.5152	+	16.9585i	1.24509	+	0.937807i
$328$		0			0
$329$	−5.91686	−	16.2564i	−0.326207	−	0.896246i
$330$		0			0
$331$	13.4955	−	2.37962i	0.741778	−	0.130795i	0.210026	−	0.977696i	$-0.432645\pi$
$331$	13.4955	−	2.37962i	0.741778	−	0.130795i	0.531752	+	0.846900i	$0.321534\pi$
$332$		0			0
$333$	10.1317	+	2.52128i	0.555214	+	0.138165i
$334$		0			0
$335$	33.7665	+	12.2900i	1.84486	+	0.671475i
$336$		0			0
$337$	0.683923	+	0.573880i	0.0372557	+	0.0312612i	0.661225	−	0.750187i	$-0.270037\pi$
$337$	0.683923	+	0.573880i	0.0372557	+	0.0312612i	−0.623970	+	0.781449i	$0.714481\pi$
$338$		0			0
$339$	3.97407	−	13.0090i	0.215842	−	0.706554i
$340$		0			0
$341$	45.1823	+	26.0860i	2.44676	+	1.41264i
$342$		0			0
$343$	−5.88963	+	3.40038i	−0.318010	+	0.183603i
$344$		0			0
$345$	−17.0328	−	8.67382i	−0.917014	−	0.466983i
$346$		0			0
$347$	5.98689	−	33.9534i	0.321393	−	1.82271i	−0.212502	−	0.977161i	$-0.568161\pi$
$347$	5.98689	−	33.9534i	0.321393	−	1.82271i	0.533895	−	0.845551i	$-0.320728\pi$
$348$		0			0
$349$	−17.1946	+	14.4280i	−0.920407	+	0.772313i	−0.974070	−	0.226246i	$-0.927355\pi$
$349$	−17.1946	+	14.4280i	−0.920407	+	0.772313i	0.0536633	+	0.998559i	$0.482910\pi$
$350$		0			0
$351$	13.2151	−	7.33688i	0.705369	−	0.391614i
$352$		0			0
$353$	8.27872	+	9.86619i	0.440632	+	0.525124i	0.939958	−	0.341290i	$-0.110864\pi$
$353$	8.27872	+	9.86619i	0.440632	+	0.525124i	−0.499327	+	0.866414i	$0.666419\pi$
$354$		0			0
$355$	−8.60950	−	1.51809i	−0.456945	−	0.0805717i
$356$		0			0
$357$	−5.20732	−	8.01463i	−0.275601	−	0.424179i
$358$		0			0
$359$	4.46272	+	7.72966i	0.235533	+	0.407956i	0.959428	−	0.281955i	$-0.0909829\pi$
$359$	4.46272	+	7.72966i	0.235533	+	0.407956i	−0.723894	+	0.689911i	$0.757650\pi$
$360$		0			0
$361$	2.25964	−	3.91382i	0.118929	−	0.205990i
$362$		0			0
$363$	−8.89482	−	38.4883i	−0.466857	−	2.02011i
$364$		0			0
$365$	1.04293	−	1.24292i	0.0545896	−	0.0650574i
$366$		0			0
$367$	−3.48335	+	9.57042i	−0.181829	+	0.499572i	−0.996801	−	0.0799296i	$-0.974530\pi$
$367$	−3.48335	+	9.57042i	−0.181829	+	0.499572i	0.814971	+	0.579501i	$0.196753\pi$
$368$		0			0
$369$	−23.6042	−	10.4966i	−1.22879	−	0.546429i
$370$		0			0
$371$	−3.00701	−	17.0536i	−0.156116	−	0.885380i
$372$		0			0
$373$	16.0078	−	5.82637i	0.828854	−	0.301678i	0.107466	−	0.994209i	$-0.465726\pi$
$373$	16.0078	−	5.82637i	0.828854	−	0.301678i	0.721388	+	0.692531i	$0.243504\pi$
$374$		0			0
$375$	−2.83929	−	6.68478i	−0.146620	−	0.345200i
$376$		0			0
$377$		−	29.4285i		−	1.51564i
$378$		0			0
$379$		−	32.3208i		−	1.66021i	−0.557607	−	0.830105i	$-0.688281\pi$
$379$		−	32.3208i		−	1.66021i	0.557607	−	0.830105i	$-0.311719\pi$
$380$		0			0
$381$	−3.54115	−	0.433991i	−0.181419	−	0.0222340i
$382$		0			0
$383$	−7.49777	+	2.72897i	−0.383118	+	0.139444i	−0.526397	−	0.850239i	$-0.676458\pi$
$383$	−7.49777	+	2.72897i	−0.383118	+	0.139444i	0.143279	+	0.989682i	$0.454235\pi$
$384$		0			0
$385$	−11.7508	−	66.6420i	−0.598875	−	3.39639i
$386$		0			0
$387$	−9.96314	−	0.692194i	−0.506455	−	0.0351862i
$388$		0			0
$389$	−7.98283	+	21.9326i	−0.404746	+	1.11203i	0.555169	+	0.831737i	$0.312653\pi$
$389$	−7.98283	+	21.9326i	−0.404746	+	1.11203i	−0.959915	+	0.280292i	$0.909569\pi$
$390$		0			0
$391$	−3.36328	+	4.00820i	−0.170088	+	0.202703i
$392$		0			0
$393$	4.91657	−	4.58684i	0.248008	−	0.231376i
$394$		0			0
$395$	−0.700760	+	1.21375i	−0.0352591	+	0.0610705i
$396$		0			0
$397$	−0.972849	−	1.68502i	−0.0488259	−	0.0845689i	0.840580	−	0.541688i	$-0.182215\pi$
$397$	−0.972849	−	1.68502i	−0.0488259	−	0.0845689i	−0.889405	+	0.457119i	$0.848881\pi$
$398$		0			0
$399$	−29.1063	+	1.53195i	−1.45714	+	0.0766933i
$400$		0			0
$401$	−15.0987	−	2.66231i	−0.753993	−	0.132949i	−0.216576	−	0.976266i	$-0.569489\pi$
$401$	−15.0987	−	2.66231i	−0.753993	−	0.132949i	−0.537417	+	0.843316i	$0.680600\pi$
$402$		0			0
$403$	16.7778	+	19.9949i	0.835759	+	0.996019i
$404$		0			0
$405$	23.8045	+	18.5637i	1.18285	+	0.922436i
$406$		0			0
$407$	15.5012	−	13.0070i	0.768365	−	0.644735i
$408$		0			0
$409$	−3.10459	+	17.6070i	−0.153512	+	0.870612i	0.806621	+	0.591069i	$0.201294\pi$
$409$	−3.10459	+	17.6070i	−0.153512	+	0.870612i	−0.960133	+	0.279543i	$0.909817\pi$
$410$		0			0
$411$	1.63354	+	31.0365i	0.0805768	+	1.53092i
$412$		0			0
$413$	−8.24254	+	4.75883i	−0.405589	+	0.234167i
$414$		0			0
$415$	5.77886	+	3.33643i	0.283673	+	0.163779i
$416$		0			0
$417$	7.71456	+	8.26913i	0.377784	+	0.404941i
$418$		0			0
$419$	21.0982	+	17.7035i	1.03071	+	0.864871i	0.990936	−	0.134337i	$-0.0428905\pi$
$419$	21.0982	+	17.7035i	1.03071	+	0.864871i	0.0397778	+	0.999209i	$0.487335\pi$
$420$		0			0
$421$	−20.4069	−	7.42750i	−0.994570	−	0.361994i	−0.207082	−	0.978324i	$-0.566397\pi$
$421$	−20.4069	−	7.42750i	−0.994570	−	0.361994i	−0.787488	+	0.616330i	$0.788619\pi$
$422$		0			0
$423$	13.4404	−	6.56278i	0.653493	−	0.319093i
$424$		0			0
$425$	−9.78864	+	1.72600i	−0.474819	+	0.0837234i
$426$		0			0
$427$	10.0608	+	27.6418i	0.486876	+	1.33768i
$428$		0			0
$429$	3.56364	−	29.0775i	0.172054	−	1.40387i
$430$		0			0
$431$	−0.653581			−0.0314819			−0.0157409	−	0.999876i	$-0.505011\pi$
$431$	−0.653581			−0.0314819			−0.0157409	+	0.999876i	$0.505011\pi$
$432$		0			0
$433$	12.1518			0.583978			0.291989	−	0.956422i	$-0.405683\pi$
$433$	12.1518			0.583978			0.291989	+	0.956422i	$0.405683\pi$
$434$		0			0
$435$	54.0955	−	22.9765i	2.59368	−	1.10164i
$436$		0			0
$437$	5.45731	+	14.9938i	0.261059	+	0.717253i
$438$		0			0
$439$	19.0842	−	3.36507i	0.910841	−	0.160606i	0.301456	−	0.953480i	$-0.402527\pi$
$439$	19.0842	−	3.36507i	0.910841	−	0.160606i	0.609385	+	0.792874i	$0.291416\pi$
$440$		0			0
$441$	8.89291	+	12.2285i	0.423472	+	0.582309i
$442$		0			0
$443$	24.9273	+	9.07278i	1.18433	+	0.431061i	0.857729	−	0.514102i	$-0.171875\pi$
$443$	24.9273	+	9.07278i	1.18433	+	0.431061i	0.326600	+	0.945163i	$0.394097\pi$
$444$		0			0
$445$	−36.4945	−	30.6225i	−1.73001	−	1.45165i
$446$		0			0
$447$	−14.2094	+	3.28387i	−0.672083	+	0.155322i
$448$		0			0
$449$	−0.126259	−	0.0728959i	−0.00595855	−	0.00344017i	0.497018	−	0.867740i	$-0.334428\pi$
$449$	−0.126259	−	0.0728959i	−0.00595855	−	0.00344017i	−0.502976	+	0.864300i	$0.667762\pi$
$450$		0			0
$451$	−43.3595	+	25.0336i	−2.04172	+	1.17879i
$452$		0			0
$453$	−18.8619	+	12.2551i	−0.886211	+	0.575795i
$454$		0			0
$455$	5.87888	−	33.3408i	0.275606	−	1.56304i
$456$		0			0
$457$	13.4428	−	11.2799i	0.628828	−	0.527649i	−0.271737	−	0.962372i	$-0.587598\pi$
$457$	13.4428	−	11.2799i	0.628828	−	0.527649i	0.900565	+	0.434722i	$0.143153\pi$
$458$		0			0
$459$	6.41841	−	5.20469i	0.299586	−	0.242934i
$460$		0			0
$461$	−17.4050	−	20.7424i	−0.810629	−	0.966071i	0.189245	−	0.981930i	$-0.439396\pi$
$461$	−17.4050	−	20.7424i	−0.810629	−	0.966071i	−0.999874	+	0.0158593i	$0.994952\pi$
$462$		0			0
$463$	−15.7643	−	2.77967i	−0.732630	−	0.129182i	−0.205126	−	0.978735i	$-0.565761\pi$
$463$	−15.7643	−	2.77967i	−0.732630	−	0.129182i	−0.527503	+	0.849553i	$0.676872\pi$
$464$		0			0
$465$	−23.6554	+	46.4521i	−1.09699	+	2.15417i
$466$		0			0
$467$	8.83583	+	15.3041i	0.408873	+	0.708189i	0.994764	−	0.102201i	$-0.0325885\pi$
$467$	8.83583	+	15.3041i	0.408873	+	0.708189i	−0.585891	+	0.810390i	$0.699255\pi$
$468$		0			0
$469$	−18.5868	+	32.1934i	−0.858261	+	1.48655i
$470$		0			0
$471$	12.2623	+	3.74595i	0.565017	+	0.172604i
$472$		0			0
$473$	−12.4420	+	14.8278i	−0.572085	+	0.681784i
$474$		0			0
$475$	−10.3670	+	28.4832i	−0.475672	+	1.30690i
$476$		0			0
$477$	14.3899	−	4.13323i	0.658868	−	0.189248i
$478$		0			0
$479$	1.27385	+	7.22438i	0.0582038	+	0.330090i	0.999981	−	0.00614707i	$-0.00195669\pi$
$479$	1.27385	+	7.22438i	0.0582038	+	0.330090i	−0.941777	+	0.336237i	$0.890846\pi$
$480$		0			0
$481$	9.51316	−	3.46251i	0.433763	−	0.157877i
$482$		0			0
$483$	11.8966	−	15.7947i	0.541315	−	0.718685i
$484$		0			0
$485$			29.0881i			1.32082i
$486$		0			0
$487$		−	36.6472i		−	1.66064i	−0.557284	−	0.830322i	$-0.688157\pi$
$487$		−	36.6472i		−	1.66064i	0.557284	−	0.830322i	$-0.311843\pi$
$488$		0			0
$489$	0.396998	−	0.527080i	0.0179529	−	0.0238354i
$490$		0			0
$491$	19.5005	−	7.09761i	0.880046	−	0.320311i	0.137818	−	0.990458i	$-0.455991\pi$
$491$	19.5005	−	7.09761i	0.880046	−	0.320311i	0.742229	+	0.670147i	$0.233769\pi$
$492$		0			0
$493$	−2.79375	−	15.8441i	−0.125824	−	0.713584i
$494$		0			0
$495$	56.2327	−	16.1518i	2.52747	−	0.725969i
$496$		0			0
$497$	3.09324	−	8.49860i	0.138751	−	0.381214i
$498$		0			0
$499$	−27.6630	+	32.9675i	−1.23837	+	1.47583i	−0.413499	+	0.910505i	$0.635693\pi$
$499$	−27.6630	+	32.9675i	−1.23837	+	1.47583i	−0.824869	+	0.565324i	$0.808751\pi$
$500$		0			0
$501$	−14.5890	−	4.45672i	−0.651788	−	0.199111i
$502$		0			0
$503$	10.9000	−	18.8794i	0.486008	−	0.841791i	−0.513862	−	0.857873i	$-0.671786\pi$
$503$	10.9000	−	18.8794i	0.486008	−	0.841791i	0.999871	+	0.0160816i	$0.00511916\pi$
$504$		0			0
$505$	−13.7635	−	23.8391i	−0.612467	−	1.06082i
$506$		0			0
$507$	−3.56699	+	7.00449i	−0.158415	+	0.311080i
$508$		0			0
$509$	−14.2651	−	2.51531i	−0.632288	−	0.111489i	−0.151686	−	0.988429i	$-0.548470\pi$
$509$	−14.2651	−	2.51531i	−0.632288	−	0.111489i	−0.480601	+	0.876939i	$0.659581\pi$
$510$		0			0
$511$	1.07893	+	1.28581i	0.0477289	+	0.0568811i
$512$		0			0
$513$	−3.95885	−	24.8867i	−0.174788	−	1.09877i
$514$		0			0
$515$	−10.3639	+	8.69635i	−0.456688	+	0.383207i
$516$		0			0
$517$	5.03382	−	28.5482i	0.221387	−	1.25555i
$518$		0			0
$519$	12.0063	−	7.80079i	0.527016	−	0.342417i
$520$		0			0
$521$	28.7081	−	16.5746i	1.25773	−	0.726148i	0.285093	−	0.958500i	$-0.407975\pi$
$521$	28.7081	−	16.5746i	1.25773	−	0.726148i	0.972632	+	0.232352i	$0.0746421\pi$
$522$		0			0
$523$	10.5049	+	6.06501i	0.459347	+	0.265204i	0.711770	−	0.702413i	$-0.247894\pi$
$523$	10.5049	+	6.06501i	0.459347	+	0.265204i	−0.252422	+	0.967617i	$0.581227\pi$
$524$		0			0
$525$	36.5988	−	8.45816i	1.59730	−	0.369144i
$526$		0			0
$527$	10.9312	+	9.17241i	0.476173	+	0.399556i
$528$		0			0
$529$	11.4407	+	4.16408i	0.497422	+	0.181047i
$530$		0			0
$531$	−4.83977	−	6.65508i	−0.210028	−	0.288806i
$532$		0			0
$533$	−24.6680	+	4.34963i	−1.06849	+	0.188403i
$534$		0			0
$535$	15.3268	+	42.1099i	0.662633	+	1.82057i
$536$		0			0
$537$	19.0096	−	8.07412i	0.820324	−	0.348424i
$538$		0			0
$539$	29.3048			1.26225
$540$		0			0
$541$	11.1698			0.480227			0.240113	−	0.970745i	$-0.422815\pi$
$541$	11.1698			0.480227			0.240113	+	0.970745i	$0.422815\pi$
$542$		0			0
$543$	−1.30553	+	10.6524i	−0.0560254	+	0.457139i
$544$		0			0
$545$	18.6691	+	51.2930i	0.799698	+	2.19715i
$546$		0			0
$547$	−16.3793	+	2.88811i	−0.700327	+	0.123487i	−0.512464	−	0.858709i	$-0.671267\pi$
$547$	−16.3793	+	2.88811i	−0.700327	+	0.123487i	−0.187863	+	0.982195i	$0.560156\pi$
$548$		0			0
$549$	−22.8535	+	11.1591i	−0.975363	+	0.476259i
$550$		0			0
$551$	−46.1036	−	16.7803i	−1.96408	−	0.714866i
$552$		0			0
$553$	−1.11068	−	0.931970i	−0.0472309	−	0.0396314i
$554$		0			0
$555$	13.7923	+	14.7837i	0.585450	+	0.627535i
$556$		0			0
$557$	−10.4348	−	6.02454i	−0.442137	−	0.255268i	0.262367	−	0.964968i	$-0.415497\pi$
$557$	−10.4348	−	6.02454i	−0.442137	−	0.255268i	−0.704504	+	0.709700i	$0.748830\pi$
$558$		0			0
$559$	−8.38653	+	4.84196i	−0.354712	+	0.204793i
$560$		0			0
$561$	−0.841784	−	15.9935i	−0.0355401	−	0.675245i
$562$		0			0
$563$	0.365491	−	2.07280i	0.0154036	−	0.0873582i	−0.976137	−	0.217156i	$-0.930322\pi$
$563$	0.365491	−	2.07280i	0.0154036	−	0.0873582i	0.991540	+	0.129798i	$0.0414329\pi$
$564$		0			0
$565$	20.1786	−	16.9319i	0.848922	−	0.712330i
$566$		0			0
$567$	−23.1888	+	20.9171i	−0.973839	+	0.878434i
$568$		0			0
$569$	1.20299	+	1.43367i	0.0504319	+	0.0601024i	0.790671	−	0.612242i	$-0.209732\pi$
$569$	1.20299	+	1.43367i	0.0504319	+	0.0601024i	−0.740239	+	0.672344i	$0.765288\pi$
$570$		0			0
$571$	−41.8780	−	7.38422i	−1.75254	−	0.309020i	−0.797022	−	0.603951i	$-0.793592\pi$
$571$	−41.8780	−	7.38422i	−1.75254	−	0.309020i	−0.955519	+	0.294931i	$0.904703\pi$
$572$		0			0
$573$	−4.97171	+	0.261676i	−0.207696	+	0.0109317i
$574$		0			0
$575$	−10.2820	−	17.8089i	−0.428787	−	0.742681i
$576$		0			0
$577$	18.9664	−	32.8508i	0.789582	−	1.36760i	−0.136642	−	0.990621i	$-0.543631\pi$
$577$	18.9664	−	32.8508i	0.789582	−	1.36760i	0.926223	−	0.376975i	$-0.123036\pi$
$578$		0			0
$579$	6.71149	−	6.26138i	0.278920	−	0.260214i
$580$		0			0
$581$	−4.43726	+	5.28812i	−0.184088	+	0.219388i
$582$		0			0
$583$	9.92442	−	27.2671i	0.411028	−	1.12929i
$584$		0			0
$585$	29.2002	+	2.02870i	1.20728	+	0.0838764i
$586$		0			0
$587$	2.91662	+	16.5410i	0.120382	+	0.682719i	0.983944	+	0.178477i	$0.0571170\pi$
$587$	2.91662	+	16.5410i	0.120382	+	0.682719i	−0.863562	+	0.504242i	$0.831772\pi$
$588$		0			0
$589$	40.8915	−	14.8833i	1.68491	−	0.613256i
$590$		0			0
$591$	12.2607	+	1.50263i	0.504336	+	0.0618098i
$592$		0			0
$593$		−	7.62540i		−	0.313138i	−0.987667	−	0.156569i	$-0.949957\pi$
$593$		−	7.62540i		−	0.313138i	0.987667	−	0.156569i	$-0.0500433\pi$
$594$		0			0
$595$		−	18.5086i		−	0.758779i
$596$		0			0
$597$	5.35414	+	12.6057i	0.219130	+	0.515916i
$598$		0			0
$599$	−29.5427	+	10.7527i	−1.20708	+	0.439342i	−0.865691	−	0.500578i	$-0.833121\pi$
$599$	−29.5427	+	10.7527i	−1.20708	+	0.439342i	−0.341392	+	0.939921i	$0.610898\pi$
$600$		0			0
$601$	3.90591	+	22.1515i	0.159325	+	0.903579i	0.954724	+	0.297493i	$0.0961503\pi$
$601$	3.90591	+	22.1515i	0.159325	+	0.903579i	−0.795399	+	0.606086i	$0.792739\pi$
$602$		0			0
$603$	−29.3670	−	13.0592i	−1.19592	−	0.531813i
$604$		0			0
$605$	26.1636	−	71.8839i	1.06370	−	2.92249i
$606$		0			0
$607$	−25.9055	+	30.8729i	−1.05147	+	1.25309i	−0.0849830	+	0.996382i	$0.527084\pi$
$607$	−25.9055	+	30.8729i	−1.05147	+	1.25309i	−0.966488	+	0.256712i	$0.917361\pi$
$608$		0			0
$609$	13.6906	+	59.2397i	0.554770	+	2.40051i
$610$		0			0
$611$	7.25147	−	12.5599i	0.293363	−	0.508120i
$612$		0			0
$613$	−19.2398	−	33.3243i	−0.777089	−	1.34596i	−0.933613	−	0.358283i	$-0.883362\pi$
$613$	−19.2398	−	33.3243i	−0.777089	−	1.34596i	0.156524	−	0.987674i	$-0.449971\pi$
$614$		0			0
$615$	−27.2552	−	41.9487i	−1.09904	−	1.69154i
$616$		0			0
$617$	−18.4142	−	3.24692i	−0.741327	−	0.130716i	−0.209785	−	0.977748i	$-0.567276\pi$
$617$	−18.4142	−	3.24692i	−0.741327	−	0.130716i	−0.531542	+	0.847032i	$0.678387\pi$
$618$		0			0
$619$	1.54231	+	1.83806i	0.0619908	+	0.0738778i	0.796149	−	0.605101i	$-0.206867\pi$
$619$	1.54231	+	1.83806i	0.0619908	+	0.0738778i	−0.734158	+	0.678979i	$0.762423\pi$
$620$		0			0
$621$	14.6601	+	8.79527i	0.588291	+	0.352942i
$622$		0			0
$623$	37.7540	−	31.6793i	1.51258	−	1.26921i
$624$		0			0
$625$	−2.98438	+	16.9253i	−0.119375	+	0.677011i
$626$		0			0
$627$	−43.5217	−	22.1631i	−1.73809	−	0.885109i
$628$		0			0
$629$	4.79313	−	2.76732i	0.191115	−	0.110340i
$630$		0			0
$631$	1.88608	+	1.08893i	0.0750837	+	0.0433496i	0.537072	−	0.843537i	$-0.319530\pi$
$631$	1.88608	+	1.08893i	0.0750837	+	0.0433496i	−0.461988	+	0.886886i	$0.652864\pi$
$632$		0			0
$633$	13.4426	−	44.0043i	0.534297	−	1.74901i
$634$		0			0
$635$	−5.29242	−	4.44086i	−0.210023	−	0.176230i
$636$		0			0
$637$	13.7769	+	5.01439i	0.545862	+	0.198677i
$638$		0			0
$639$	7.58789	+	1.88825i	0.300172	+	0.0746982i
$640$		0			0
$641$	−13.0761	+	2.30566i	−0.516474	+	0.0910683i	−0.425809	−	0.904813i	$-0.640010\pi$
$641$	−13.0761	+	2.30566i	−0.516474	+	0.0910683i	−0.0906650	+	0.995881i	$0.528899\pi$
$642$		0			0
$643$	−3.47410	−	9.54501i	−0.137005	−	0.376418i	0.852149	−	0.523299i	$-0.175299\pi$
$643$	−3.47410	−	9.54501i	−0.137005	−	0.376418i	−0.989154	+	0.146881i	$0.953077\pi$
$644$		0			0
$645$	−15.4484	−	11.6357i	−0.608279	−	0.458157i
$646$		0			0
$647$	−2.76977			−0.108891			−0.0544454	−	0.998517i	$-0.517339\pi$
$647$	−2.76977			−0.108891			−0.0544454	+	0.998517i	$0.517339\pi$
$648$		0			0
$649$	−15.9485			−0.626032
$650$		0			0
$651$	−43.0757	−	32.4447i	−1.68827	−	1.27161i
$652$		0			0
$653$	5.04244	+	13.8540i	0.197326	+	0.542148i	0.998408	−	0.0564063i	$-0.0179642\pi$
$653$	5.04244	+	13.8540i	0.197326	+	0.542148i	−0.801082	+	0.598554i	$0.795742\pi$
$654$		0			0
$655$	12.8232	−	2.26107i	0.501044	−	0.0883475i
$656$		0			0
$657$	−1.00763	+	1.04437i	−0.0393113	+	0.0407447i
$658$		0			0
$659$	20.4458	+	7.44165i	0.796454	+	0.289885i	0.708016	−	0.706196i	$-0.249590\pi$
$659$	20.4458	+	7.44165i	0.796454	+	0.289885i	0.0884376	+	0.996082i	$0.471813\pi$
$660$		0			0
$661$	−15.8814	−	13.3261i	−0.617715	−	0.518325i	0.279369	−	0.960184i	$-0.409875\pi$
$661$	−15.8814	−	13.3261i	−0.617715	−	0.518325i	−0.897084	+	0.441859i	$0.854319\pi$
$662$		0			0
$663$	2.34093	−	7.66298i	0.0909141	−	0.297606i
$664$		0			0
$665$	−48.8806	−	28.2212i	−1.89551	−	1.09437i
$666$		0			0
$667$	28.8259	−	16.6426i	1.11614	−	0.644405i
$668$		0			0
$669$	−5.45260	−	2.77669i	−0.210810	−	0.107353i
$670$		0			0
$671$	−8.55932	+	48.5423i	−0.330429	+	1.87396i
$672$		0			0
$673$	−28.0079	+	23.5014i	−1.07963	+	0.905914i	−0.995890	−	0.0905741i	$-0.971130\pi$
$673$	−28.0079	+	23.5014i	−1.07963	+	0.905914i	−0.0837364	+	0.996488i	$0.526685\pi$
$674$		0			0
$675$	10.5941	+	30.7002i	0.407766	+	1.18165i
$676$		0			0
$677$	−4.14058	−	4.93456i	−0.159136	−	0.189650i	0.680585	−	0.732669i	$-0.261726\pi$
$677$	−4.14058	−	4.93456i	−0.159136	−	0.189650i	−0.839721	+	0.543019i	$0.817281\pi$
$678$		0			0
$679$	−29.6348	−	5.22541i	−1.13728	−	0.200533i
$680$		0			0
$681$	1.41911	+	2.18417i	0.0543805	+	0.0836975i
$682$		0			0
$683$	16.7347	+	28.9854i	0.640337	+	1.10910i	0.985358	+	0.170501i	$0.0545385\pi$
$683$	16.7347	+	28.9854i	0.640337	+	1.10910i	−0.345021	+	0.938595i	$0.612128\pi$
$684$		0			0
$685$	−30.0928	+	52.1222i	−1.14979	+	1.99149i
$686$		0			0
$687$	−11.6745	−	50.5159i	−0.445409	−	1.92730i
$688$		0			0
$689$	9.33145	−	11.1208i	0.355500	−	0.423668i
$690$		0			0
$691$	2.44673	−	6.72234i	0.0930780	−	0.255730i	−0.884414	−	0.466704i	$-0.845441\pi$
$691$	2.44673	−	6.72234i	0.0930780	−	0.255730i	0.977492	+	0.210974i	$0.0676636\pi$
$692$		0			0
$693$	6.35367	+	60.1911i	0.241356	+	2.28647i
$694$		0			0
$695$	3.80287	+	21.5672i	0.144251	+	0.818089i
$696$		0			0
$697$	−12.8682	+	4.68363i	−0.487417	+	0.177405i
$698$		0			0
$699$	3.23146	+	7.60810i	0.122225	+	0.287765i
$700$		0			0
$701$			46.9364i			1.77276i	0.462955	+	0.886382i	$0.346789\pi$
$701$			46.9364i			1.77276i	−0.462955	+	0.886382i	$0.653211\pi$
$702$		0			0
$703$		−	16.8780i		−	0.636565i
$704$		0			0
$705$	28.7493	+	3.52342i	1.08276	+	0.132700i
$706$		0			0
$707$	26.7596	−	9.73969i	1.00640	−	0.366299i
$708$		0			0
$709$	6.76220	+	38.3503i	0.253960	+	1.44028i	0.798729	+	0.601691i	$0.205506\pi$
$709$	6.76220	+	38.3503i	0.253960	+	1.44028i	−0.544769	+	0.838586i	$0.683383\pi$
$710$		0			0
$711$	0.700509	−	1.03955i	0.0262712	−	0.0389863i
$712$		0			0
$713$	−10.0972	+	27.7419i	−0.378144	+	1.03894i
$714$		0			0
$715$	36.4653	−	43.4577i	1.36373	−	1.62523i
$716$		0			0
$717$	2.00800	−	1.87334i	0.0749902	−	0.0699610i
$718$		0			0
$719$	−16.1643	+	27.9974i	−0.602826	+	1.04413i	0.389565	+	0.920999i	$0.372625\pi$
$719$	−16.1643	+	27.9974i	−0.602826	+	1.04413i	−0.992391	+	0.123126i	$0.960708\pi$
$720$		0			0
$721$	−6.99801	−	12.1209i	−0.260619	−	0.451406i
$722$		0			0
$723$	−34.3496	+	1.80792i	−1.27748	+	0.0672373i
$724$		0			0
$725$	62.2700	+	10.9799i	2.31265	+	0.407782i
$726$		0			0
$727$	−3.60694	−	4.29858i	−0.133774	−	0.159425i	0.694999	−	0.719011i	$-0.255405\pi$
$727$	−3.60694	−	4.29858i	−0.133774	−	0.159425i	−0.828773	+	0.559585i	$0.810960\pi$
$728$		0			0
$729$	−20.0892	−	18.0395i	−0.744046	−	0.668129i
$730$		0			0
$731$	−4.05560	+	3.40305i	−0.150002	+	0.125866i
$732$		0			0
$733$	7.24616	−	41.0950i	0.267643	−	1.51788i	−0.493759	−	0.869599i	$-0.664377\pi$
$733$	7.24616	−	41.0950i	0.267643	−	1.51788i	0.761402	−	0.648280i	$-0.224512\pi$
$734$		0			0
$735$	1.53898	+	29.2398i	0.0567661	+	1.07853i
$736$		0			0
$737$	−53.9454	+	31.1454i	−1.98711	+	1.14726i
$738$		0			0
$739$	18.7633	+	10.8330i	0.690218	+	0.398498i	0.803694	−	0.595043i	$-0.202865\pi$
$739$	18.7633	+	10.8330i	0.690218	+	0.398498i	−0.113476	+	0.993541i	$0.536198\pi$
$740$		0			0
$741$	−16.6683	−	17.8665i	−0.612326	−	0.656343i
$742$		0			0
$743$	3.58520	+	3.00834i	0.131528	+	0.110365i	0.706179	−	0.708034i	$-0.250418\pi$
$743$	3.58520	+	3.00834i	0.131528	+	0.110365i	−0.574651	+	0.818399i	$0.694862\pi$
$744$		0			0
$745$	−26.5387	−	9.65930i	−0.972303	−	0.353889i
$746$		0			0
$747$	−4.94948	−	3.33523i	−0.181092	−	0.122030i
$748$		0			0
$749$	−45.6547	+	8.05015i	−1.66819	+	0.294146i
$750$		0			0
$751$	7.04027	+	19.3430i	0.256903	+	0.705836i	0.999354	+	0.0359352i	$0.0114410\pi$
$751$	7.04027	+	19.3430i	0.256903	+	0.705836i	−0.742451	+	0.669900i	$0.766337\pi$
$752$		0			0
$753$	4.48663	−	36.6087i	0.163502	−	1.33409i
$754$		0			0
$755$	−43.5589			−1.58527
$756$		0			0
$757$	24.1617			0.878172			0.439086	−	0.898445i	$-0.355302\pi$
$757$	24.1617			0.878172			0.439086	+	0.898445i	$0.355302\pi$
$758$		0			0
$759$	30.4974	−	12.9535i	1.10699	−	0.470181i
$760$		0			0
$761$	8.13784	+	22.3585i	0.294996	+	0.810496i	0.995317	+	0.0966674i	$0.0308183\pi$
$761$	8.13784	+	22.3585i	0.294996	+	0.810496i	−0.700320	+	0.713829i	$0.746959\pi$
$762$		0			0
$763$	−55.6108	+	9.80568i	−2.01325	+	0.354990i
$764$		0			0
$765$	15.9138	−	1.67984i	0.575366	−	0.0607346i
$766$		0			0
$767$	−7.49778	−	2.72897i	−0.270729	−	0.0985374i
$768$		0			0
$769$	−6.27859	−	5.26836i	−0.226412	−	0.189982i	0.522524	−	0.852624i	$-0.324990\pi$
$769$	−6.27859	−	5.26836i	−0.226412	−	0.189982i	−0.748936	+	0.662643i	$0.769435\pi$
$770$		0			0
$771$	36.9398	−	8.53695i	1.33035	−	0.307451i
$772$		0			0
$773$	36.7083	+	21.1936i	1.32031	+	0.762280i	0.983777	−	0.179393i	$-0.0574135\pi$
$773$	36.7083	+	21.1936i	1.32031	+	0.762280i	0.336530	+	0.941673i	$0.390747\pi$
$774$		0			0
$775$	−48.5687	+	28.0412i	−1.74464	+	1.00727i
$776$		0			0
$777$	−17.5393	+	11.3957i	−0.629218	+	0.408820i
$778$		0			0
$779$	−7.25159	+	41.1258i	−0.259815	+	1.47349i
$780$		0			0
$781$	11.6092	−	9.74131i	0.415411	−	0.348571i
$782$		0			0
$783$	−49.6921	+	17.1478i	−1.77585	+	0.612813i
$784$		0			0
$785$	15.9599	+	19.0203i	0.569635	+	0.678865i
$786$		0			0
$787$	−8.56883	−	1.51092i	−0.305446	−	0.0538584i	0.0188244	−	0.999823i	$-0.494008\pi$
$787$	−8.56883	−	1.51092i	−0.305446	−	0.0538584i	−0.324270	+	0.945964i	$0.605119\pi$
$788$		0			0
$789$	3.99994	−	7.85469i	0.142402	−	0.279634i
$790$		0			0
$791$	13.6252	+	23.5995i	0.484456	+	0.839103i
$792$		0			0
$793$	−12.3301	+	21.3564i	−0.437855	+	0.758388i
$794$		0			0
$795$	27.7279	+	8.47046i	0.983407	+	0.300416i
$796$		0			0
$797$	−13.9119	+	16.5796i	−0.492785	+	0.587278i	−0.953923	−	0.300050i	$-0.902997\pi$
$797$	−13.9119	+	16.5796i	−0.492785	+	0.587278i	0.461139	+	0.887328i	$0.347441\pi$
$798$		0			0
$799$	2.71180	−	7.45060i	0.0959364	−	0.263583i
$800$		0			0
$801$	30.6646	+	29.5859i	1.08348	+	1.04537i
$802$		0			0
$803$	0.488408	+	2.76990i	0.0172355	+	0.0977476i
$804$		0			0
$805$	35.9828	−	13.0967i	1.26823	−	0.461596i
$806$		0			0
$807$	−10.6092	+	14.0855i	−0.373462	+	0.495833i
$808$		0			0
$809$			9.86094i			0.346692i	0.984861	+	0.173346i	$0.0554579\pi$
$809$			9.86094i			0.346692i	−0.984861	+	0.173346i	$0.944542\pi$
$810$		0			0
$811$		−	29.9307i		−	1.05101i	−0.850791	−	0.525504i	$-0.823877\pi$
$811$		−	29.9307i		−	1.05101i	0.850791	−	0.525504i	$-0.176123\pi$
$812$		0			0
$813$	4.31082	−	5.72333i	0.151187	−	0.200726i
$814$		0			0
$815$	1.20077	−	0.437044i	0.0420611	−	0.0153090i
$816$		0			0
$817$	2.80351	+	15.8995i	0.0980826	+	0.556254i
$818$		0			0
$819$	−7.31238	+	29.3846i	−0.255515	+	1.02678i
$820$		0			0
$821$	9.47855	−	26.0421i	0.330804	−	0.908875i	−0.657100	−	0.753804i	$-0.728217\pi$
$821$	9.47855	−	26.0421i	0.330804	−	0.908875i	0.987903	−	0.155072i	$-0.0495609\pi$
$822$		0			0
$823$	−8.40732	+	10.0195i	−0.293061	+	0.349256i	−0.892405	−	0.451235i	$-0.850984\pi$
$823$	−8.40732	+	10.0195i	−0.293061	+	0.349256i	0.599344	+	0.800491i	$0.295428\pi$
$824$		0			0
$825$	60.1977	+	18.3895i	2.09582	+	0.640241i
$826$		0			0
$827$	−22.6995	+	39.3167i	−0.789338	+	1.36717i	0.137034	+	0.990566i	$0.456243\pi$
$827$	−22.6995	+	39.3167i	−0.789338	+	1.36717i	−0.926373	+	0.376608i	$0.877090\pi$
$828$		0			0
$829$	−1.61195	−	2.79199i	−0.0559855	−	0.0969696i	0.836674	−	0.547701i	$-0.184497\pi$
$829$	−1.61195	−	2.79199i	−0.0559855	−	0.0969696i	−0.892660	+	0.450731i	$0.851163\pi$
$830$		0			0
$831$	−9.62158	+	18.8939i	−0.333769	+	0.655422i
$832$		0			0
$833$	7.89346	+	1.39183i	0.273492	+	0.0482241i
$834$		0			0
$835$	−18.9882	−	22.6293i	−0.657115	−	0.783120i
$836$		0			0
$837$	23.9866	−	39.9815i	0.829100	−	1.38196i
$838$		0			0
$839$	−4.73298	+	3.97144i	−0.163401	+	0.137109i	−0.720822	−	0.693120i	$-0.756235\pi$
$839$	−4.73298	+	3.97144i	−0.163401	+	0.137109i	0.557421	+	0.830230i	$0.311791\pi$
$840$		0			0
$841$	−12.7365	+	72.2322i	−0.439189	+	2.49077i
$842$		0			0
$843$	24.5975	−	15.9817i	0.847183	−	0.550438i
$844$		0			0
$845$	−13.1824	+	7.61088i	−0.453489	+	0.261822i
$846$		0			0
$847$	68.5348	+	39.5686i	2.35489	+	1.35959i
$848$		0			0
$849$	−42.0321	+	9.71381i	−1.44254	+	0.333377i
$850$		0			0
$851$	8.77157	+	7.36022i	0.300686	+	0.252305i
$852$		0			0
$853$	−35.3639	−	12.8714i	−1.21084	−	0.440708i	−0.343843	−	0.939027i	$-0.611729\pi$
$853$	−35.3639	−	12.8714i	−1.21084	−	0.440708i	−0.866994	+	0.498319i	$0.833951\pi$
$854$		0			0
$855$	19.8284	−	44.5892i	0.678117	−	1.52492i
$856$		0			0
$857$	46.0639	−	8.12231i	1.57351	−	0.277453i	0.682312	−	0.731061i	$-0.260974\pi$
$857$	46.0639	−	8.12231i	1.57351	−	0.277453i	0.891201	+	0.453608i	$0.149863\pi$
$858$		0			0
$859$	9.09399	+	24.9855i	0.310283	+	0.852496i	0.992599	+	0.121438i	$0.0387506\pi$
$859$	9.09399	+	24.9855i	0.310283	+	0.852496i	−0.682316	+	0.731057i	$0.739027\pi$
$860$		0			0
$861$	47.6333	−	20.2318i	1.62334	−	0.689496i
$862$		0			0
$863$	−3.97809			−0.135416			−0.0677079	−	0.997705i	$-0.521569\pi$
$863$	−3.97809			−0.135416			−0.0677079	+	0.997705i	$0.521569\pi$
$864$		0			0
$865$	27.7267			0.942736
$866$		0			0
$867$	−3.04899	+	24.8782i	−0.103549	+	0.844910i
$868$		0			0
$869$	−0.830950	−	2.28302i	−0.0281880	−	0.0774460i
$870$		0			0
$871$	−30.6905	+	5.41156i	−1.03991	+	0.183364i
$872$		0			0
$873$	1.80320	−	25.9544i	0.0610290	−	0.878425i
$874$		0			0
$875$	13.6723	+	4.97631i	0.462208	+	0.168230i
$876$		0			0
$877$	43.2551	+	36.2954i	1.46062	+	1.22561i	0.924341	+	0.381567i	$0.124615\pi$
$877$	43.2551	+	36.2954i	1.46062	+	1.22561i	0.536280	+	0.844040i	$0.319829\pi$
$878$		0			0
$879$	30.4869	+	32.6785i	1.02830	+	1.10222i
$880$		0			0
$881$	1.59619	+	0.921563i	0.0537772	+	0.0310483i	0.526648	−	0.850084i	$-0.323449\pi$
$881$	1.59619	+	0.921563i	0.0537772	+	0.0310483i	−0.472870	+	0.881132i	$0.656782\pi$
$882$		0			0
$883$	4.53672	−	2.61928i	0.152673	−	0.0881456i	−0.421717	−	0.906727i	$-0.638573\pi$
$883$	4.53672	−	2.61928i	0.152673	−	0.0881456i	0.574390	+	0.818582i	$0.305239\pi$
$884$		0			0
$885$	−0.837554	−	15.9131i	−0.0281541	−	0.534914i
$886$		0			0
$887$	0.735322	−	4.17022i	0.0246897	−	0.140022i	−0.969971	−	0.243220i	$-0.921796\pi$
$887$	0.735322	−	4.17022i	0.0246897	−	0.140022i	0.994661	+	0.103198i	$0.0329075\pi$
$888$		0			0
$889$	5.47506	−	4.59412i	0.183628	−	0.154082i
$890$		0			0
$891$	−51.1760	+	10.9259i	−1.71446	+	0.366030i
$892$		0			0
$893$	−15.5419	−	18.5221i	−0.520090	−	0.619820i
$894$		0			0
$895$	39.3874	+	6.94507i	1.31658	+	0.232148i
$896$		0			0
$897$	16.5541	−	0.871292i	0.552726	−	0.0290916i
$898$		0			0
$899$	−45.3881	−	78.6145i	−1.51378	−	2.62194i
$900$		0			0
$901$	3.96827	−	6.87324i	0.132202	−	0.228981i
$902$		0			0
$903$	14.6296	−	13.6485i	0.486842	−	0.454192i
$904$		0			0
$905$	−13.3589	+	15.9206i	−0.444066	+	0.529217i
$906$		0			0
$907$	0.432381	−	1.18796i	0.0143570	−	0.0394455i	−0.932307	−	0.361668i	$-0.882208\pi$
$907$	0.432381	−	1.18796i	0.0143570	−	0.0394455i	0.946664	+	0.322222i	$0.104430\pi$
$908$		0			0
$909$	10.8029	+	22.1241i	0.358311	+	0.733810i
$910$		0			0
$911$	7.56798	+	42.9202i	0.250738	+	1.42201i	0.806779	+	0.590853i	$0.201209\pi$
$911$	7.56798	+	42.9202i	0.250738	+	1.42201i	−0.556041	+	0.831155i	$0.687680\pi$
$912$		0			0
$913$	−10.8698	+	3.95628i	−0.359738	+	0.130934i
$914$		0			0
$915$	−48.8842	−	5.99109i	−1.61606	−	0.198059i
$916$		0			0
$917$			13.4704i			0.444831i
$918$		0			0
$919$		−	3.43998i		−	0.113475i	−0.998389	−	0.0567373i	$-0.981930\pi$
$919$		−	3.43998i		−	0.113475i	0.998389	−	0.0567373i	$-0.0180697\pi$
$920$		0			0
$921$	9.24925	+	21.7763i	0.304773	+	0.717553i
$922$		0			0
$923$	7.12465	−	2.59316i	0.234511	−	0.0853550i
$924$		0			0
$925$	3.77719	+	21.4215i	0.124193	+	0.704335i
$926$		0			0
$927$	9.78650	−	7.11702i	0.321431	−	0.233754i
$928$		0			0
$929$	−6.44699	+	17.7130i	−0.211519	+	0.581144i	−0.999398	−	0.0346860i	$-0.988957\pi$
$929$	−6.44699	+	17.7130i	−0.211519	+	0.581144i	0.787879	+	0.615830i	$0.211179\pi$
$930$		0			0
$931$	15.7114	−	18.7241i	0.514921	−	0.613659i
$932$		0			0
$933$	−5.82474	−	25.2039i	−0.190693	−	0.825138i
$934$		0			0
$935$	15.5072	−	26.8592i	0.507138	−	0.878389i
$936$		0			0
$937$	19.1876	+	33.2338i	0.626830	+	1.08570i	0.988184	+	0.153273i	$0.0489813\pi$
$937$	19.1876	+	33.2338i	0.626830	+	1.08570i	−0.361354	+	0.932429i	$0.617685\pi$
$938$		0			0
$939$	21.4017	+	32.9395i	0.698418	+	1.07494i
$940$		0			0
$941$	−22.0021	−	3.87956i	−0.717247	−	0.126470i	−0.196898	−	0.980424i	$-0.563087\pi$
$941$	−22.0021	−	3.87956i	−0.717247	−	0.126470i	−0.520349	+	0.853954i	$0.674198\pi$
$942$		0			0
$943$	−18.2110	−	21.7030i	−0.593031	−	0.706747i
$944$		0			0
$945$	−59.7240	+	9.50060i	−1.94282	+	0.309054i
$946$		0			0
$947$	−0.652233	+	0.547288i	−0.0211947	+	0.0177845i	−0.653323	−	0.757079i	$-0.726626\pi$
$947$	−0.652233	+	0.547288i	−0.0211947	+	0.0177845i	0.632129	+	0.774863i	$0.282181\pi$
$948$		0			0
$949$	−0.244349	+	1.38577i	−0.00793191	+	0.0449841i
$950$		0			0
$951$	28.2741	+	14.3984i	0.916851	+	0.466900i
$952$		0			0
$953$	−12.4899	+	7.21102i	−0.404586	+	0.233588i	−0.688461	−	0.725273i	$-0.741713\pi$
$953$	−12.4899	+	7.21102i	−0.404586	+	0.233588i	0.283875	+	0.958861i	$0.408380\pi$
$954$		0			0
$955$	−8.34941	−	4.82053i	−0.270181	−	0.155989i
$956$		0			0
$957$	−29.7657	+	97.4375i	−0.962189	+	3.14971i
$958$		0			0
$959$	−47.6959	−	40.0217i	−1.54018	−	1.29237i
$960$		0			0
$961$	46.5278	+	16.9348i	1.50090	+	0.546282i
$962$		0			0
$963$	−11.0652	−	38.5236i	−0.356570	−	1.24140i
$964$		0			0
$965$	17.5046	−	3.08653i	0.563493	−	0.0993590i
$966$		0			0
$967$	9.53902	+	26.2082i	0.306754	+	0.842800i	0.993284	+	0.115699i	$0.0369108\pi$
$967$	9.53902	+	26.2082i	0.306754	+	0.842800i	−0.686530	+	0.727101i	$0.740867\pi$
$968$		0			0
$969$	−10.6703	−	8.03686i	−0.342778	−	0.258181i
$970$		0			0
$971$	11.8273			0.379555			0.189777	−	0.981827i	$-0.439223\pi$
$971$	11.8273			0.379555			0.189777	+	0.981827i	$0.439223\pi$
$972$		0			0
$973$	−22.6557			−0.726307
$974$		0			0
$975$	25.1538	+	18.9459i	0.805567	+	0.606755i
$976$		0			0
$977$	−12.5347	−	34.4388i	−0.401021	−	1.10180i	−0.961781	−	0.273818i	$-0.911713\pi$
$977$	−12.5347	−	34.4388i	−0.401021	−	1.10180i	0.560760	−	0.827978i	$-0.310509\pi$
$978$		0			0
$979$	81.3296	−	14.3406i	2.59930	−	0.458327i
$980$		0			0
$981$	−13.4782	−	46.9246i	−0.430326	−	1.49819i
$982$		0			0
$983$	−37.7590	−	13.7431i	−1.20432	−	0.438338i	−0.339593	−	0.940573i	$-0.610289\pi$
$983$	−37.7590	−	13.7431i	−1.20432	−	0.438338i	−0.864731	+	0.502235i	$0.832511\pi$
$984$		0			0
$985$	18.3241	+	15.3758i	0.583856	+	0.489913i
$986$		0			0
$987$	−8.75419	+	28.6567i	−0.278649	+	0.912152i
$988$		0			0
$989$	−9.48563	−	5.47653i	−0.301626	−	0.174144i
$990$		0			0
$991$	−20.6696	+	11.9336i	−0.656592	+	0.379083i	−0.790977	−	0.611846i	$-0.790427\pi$
$991$	−20.6696	+	11.9336i	−0.656592	+	0.379083i	0.134385	+	0.990929i	$0.457094\pi$
$992$		0			0
$993$	−21.1508	−	10.7709i	−0.671202	−	0.341805i
$994$		0			0
$995$	−4.60543	+	26.1187i	−0.146002	+	0.828019i
$996$		0			0
$997$	−26.1895	+	21.9756i	−0.829430	+	0.695974i	−0.955160	−	0.296090i	$-0.904317\pi$
$997$	−26.1895	+	21.9756i	−0.829430	+	0.695974i	0.125730	+	0.992064i	$0.459873\pi$
$998$		0			0
$999$	−11.3900	−	14.0461i	−0.360363	−	0.444399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.383.8	✓	216
4.3	odd	2	inner	864.2.bi.a.383.29	yes	216
27.11	odd	18	inner	864.2.bi.a.767.29	yes	216
108.11	even	18	inner	864.2.bi.a.767.8	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.8	✓	216	1.1	even	1	trivial
864.2.bi.a.383.29	yes	216	4.3	odd	2	inner
864.2.bi.a.767.8	yes	216	108.11	even	18	inner
864.2.bi.a.767.29	yes	216	27.11	odd	18	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38351 - 1.04206i) q^{3} +(-1.14718 - 3.15185i) q^{5} +(3.41716 - 0.602538i) q^{7} +(0.828207 + 2.88341i) q^{9} +(5.46372 + 1.98863i) q^{11} +(2.22836 + 1.86981i) q^{13} +(-1.69729 + 5.55605i) q^{15} +(1.37724 + 0.795152i) q^{17} +(4.19994 - 2.42483i) q^{19} +(-5.35557 - 2.72728i) q^{21} +(-0.571328 + 3.24016i) q^{23} +(-4.78789 + 4.01752i) q^{25} +(1.85887 - 4.85228i) q^{27} +(-6.50285 - 7.74980i) q^{29} +(8.83663 + 1.55814i) q^{31} +(-5.48684 - 8.44484i) q^{33} +(-5.81920 - 10.0792i) q^{35} +(1.74012 - 3.01397i) q^{37} +(-1.13449 - 4.90900i) q^{39} +(-5.53501 + 6.59637i) q^{41} +(-1.13860 + 3.12829i) q^{43} +(8.13797 - 5.91817i) q^{45} +(-0.865755 - 4.90994i) q^{47} +(4.73611 - 1.72380i) q^{49} +(-1.07683 - 2.53528i) q^{51} -4.99058i q^{53} -19.5021i q^{55} +(-8.33749 - 1.02181i) q^{57} +(-2.57752 + 0.938141i) q^{59} +(1.47210 + 8.34868i) q^{61} +(4.56749 + 9.35407i) q^{63} +(3.33704 - 9.16845i) q^{65} +(-6.88635 + 8.20683i) q^{67} +(4.16689 - 3.88744i) q^{69} +(1.30322 - 2.25724i) q^{71} +(0.241869 + 0.418929i) q^{73} +(10.8106 - 0.568995i) q^{75} +(19.8687 + 3.50338i) q^{77} +(-0.268589 - 0.320092i) q^{79} +(-7.62815 + 4.77613i) q^{81} +(-1.52401 + 1.27879i) q^{83} +(0.926253 - 5.25304i) q^{85} +(0.920988 + 17.4983i) q^{87} +(12.3006 - 7.10173i) q^{89} +(8.74130 + 5.04679i) q^{91} +(-10.6019 - 11.3640i) q^{93} +(-12.4608 - 10.4558i) q^{95} +(-8.14933 - 2.96611i) q^{97} +(-1.20896 + 17.4012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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