LMFDB - Embedded newform 567.2.ba.a.143.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] 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("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.18
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08992 - 1.29892i) q^{2} +(-0.151961 - 0.861812i) q^{4} +(-1.13756 + 0.954530i) q^{5} +(2.51978 - 0.806679i) q^{7} +(1.65184 + 0.953692i) q^{8} +2.51796i q^{10} +(0.0836396 - 0.0996778i) q^{11} +(-0.311287 + 0.855253i) q^{13} +(1.69855 - 4.15219i) q^{14} +(4.68381 - 1.70477i) q^{16} +5.63249 q^{17} +0.0959743i q^{19} +(0.995491 + 0.835316i) q^{20} +(-0.0383126 - 0.217282i) q^{22} +(2.22151 - 6.10356i) q^{23} +(-0.485315 + 2.75236i) q^{25} +(0.771624 + 1.33649i) q^{26} +(-1.07811 - 2.04899i) q^{28} +(-0.238914 - 0.656410i) q^{29} +(-8.96076 + 1.58002i) q^{31} +(1.58590 - 4.35722i) q^{32} +(6.13896 - 7.31613i) q^{34} +(-2.09641 + 3.32285i) q^{35} +(1.72508 - 2.98792i) q^{37} +(0.124663 + 0.104604i) q^{38} +(-2.78941 + 0.491848i) q^{40} +(2.04536 + 0.744450i) q^{41} +(1.37972 - 7.82480i) q^{43} +(-0.0986135 - 0.0569345i) q^{44} +(-5.50674 - 9.53795i) q^{46} +(-2.18137 + 12.3712i) q^{47} +(5.69854 - 4.06530i) q^{49} +(3.04613 + 3.63023i) q^{50} +(0.784371 + 0.138306i) q^{52} +(-1.26661 - 0.731275i) q^{53} +0.193227i q^{55} +(4.93160 + 1.07058i) q^{56} +(-1.11302 - 0.405105i) q^{58} +(-5.96770 - 2.17206i) q^{59} +(-7.69007 - 1.35597i) q^{61} +(-7.71419 + 13.3614i) q^{62} +(1.05325 + 1.82428i) q^{64} +(-0.462256 - 1.27004i) q^{65} +(-11.0280 + 9.25358i) q^{67} +(-0.855917 - 4.85415i) q^{68} +(2.03119 + 6.34470i) q^{70} +(-2.38823 + 1.37884i) q^{71} +(-6.94774 + 4.01128i) q^{73} +(-2.00086 - 5.49732i) q^{74} +(0.0827118 - 0.0145843i) q^{76} +(0.130345 - 0.318636i) q^{77} +(0.310233 + 0.260316i) q^{79} +(-3.70088 + 6.41012i) q^{80} +(3.19626 - 1.84536i) q^{82} +(4.54412 - 1.65393i) q^{83} +(-6.40732 + 5.37638i) q^{85} +(-8.65997 - 10.3205i) q^{86} +(0.233222 - 0.0848857i) q^{88} -15.9719 q^{89} +(-0.0944582 + 2.40615i) q^{91} +(-5.59770 - 0.987026i) q^{92} +(13.6916 + 16.3170i) q^{94} +(-0.0916104 - 0.109177i) q^{95} +(10.2887 + 1.81418i) q^{97} +(0.930470 - 11.8328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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 $

$2$	1.08992	−	1.29892i	0.770690	−	0.918472i	−0.227784	−	0.973712i	$-0.573148\pi$
$2$	1.08992	−	1.29892i	0.770690	−	0.918472i	0.998473	+	0.0552397i	$0.0175923\pi$
$3$		0			0
$3$		0			0
$4$	−0.151961	−	0.861812i	−0.0759803	−	0.430906i
$5$	−1.13756	+	0.954530i	−0.508734	+	0.426879i	−0.860684	−	0.509140i	$-0.829963\pi$
$5$	−1.13756	+	0.954530i	−0.508734	+	0.426879i	0.351949	+	0.936019i	$0.385519\pi$
$6$		0			0
$7$	2.51978	−	0.806679i	0.952386	−	0.304896i
$7$	2.51978	−	0.806679i	0.952386	−	0.304896i
$8$	1.65184	+	0.953692i	0.584015	+	0.337181i
$9$		0			0
$10$			2.51796i			0.796250i
$11$	0.0836396	−	0.0996778i	0.0252183	−	0.0300540i	−0.753288	−	0.657691i	$-0.771533\pi$
$11$	0.0836396	−	0.0996778i	0.0252183	−	0.0300540i	0.778506	+	0.627637i	$0.215978\pi$
$12$		0			0
$13$	−0.311287	+	0.855253i	−0.0863354	+	0.237205i	−0.975346	−	0.220683i	$-0.929171\pi$
$13$	−0.311287	+	0.855253i	−0.0863354	+	0.237205i	0.889010	+	0.457887i	$0.151394\pi$
$14$	1.69855	−	4.15219i	0.453955	−	1.10972i
$15$		0			0
$16$	4.68381	−	1.70477i	1.17095	−	0.426191i
$17$	5.63249			1.36608			0.683040	−	0.730381i	$-0.260658\pi$
$17$	5.63249			1.36608			0.683040	+	0.730381i	$0.260658\pi$
$18$		0			0
$19$			0.0959743i			0.0220180i	0.999939	+	0.0110090i	$0.00350435\pi$
$19$			0.0959743i			0.0220180i	−0.999939	+	0.0110090i	$0.996496\pi$
$20$	0.995491	+	0.835316i	0.222598	+	0.186782i
$21$		0			0
$22$	−0.0383126	−	0.217282i	−0.00816828	−	0.0463246i
$23$	2.22151	−	6.10356i	0.463218	−	1.27268i	−0.459835	−	0.888005i	$-0.652091\pi$
$23$	2.22151	−	6.10356i	0.463218	−	1.27268i	0.923052	−	0.384675i	$-0.125687\pi$
$24$		0			0
$25$	−0.485315	+	2.75236i	−0.0970630	+	0.550472i
$26$	0.771624	+	1.33649i	0.151328	+	0.262108i
$27$		0			0
$28$	−1.07811	−	2.04899i	−0.203744	−	0.387223i
$29$	−0.238914	−	0.656410i	−0.0443651	−	0.121892i	0.915532	−	0.402246i	$-0.131770\pi$
$29$	−0.238914	−	0.656410i	−0.0443651	−	0.121892i	−0.959897	+	0.280354i	$0.909548\pi$
$30$		0			0
$31$	−8.96076	+	1.58002i	−1.60940	+	0.283781i	−0.904804	−	0.425828i	$-0.859983\pi$
$31$	−8.96076	+	1.58002i	−1.60940	+	0.283781i	−0.704596	+	0.709609i	$0.748872\pi$
$32$	1.58590	−	4.35722i	0.280350	−	0.770254i
$33$		0			0
$34$	6.13896	−	7.31613i	1.05282	−	1.25471i
$35$	−2.09641	+	3.32285i	−0.354358	+	0.561664i
$36$		0			0
$37$	1.72508	−	2.98792i	0.283601	−	0.491211i	−0.688668	−	0.725077i	$-0.741804\pi$
$37$	1.72508	−	2.98792i	0.283601	−	0.491211i	0.972269	+	0.233866i	$0.0751376\pi$
$38$	0.124663	+	0.104604i	0.0202229	+	0.0169691i
$39$		0			0
$40$	−2.78941	+	0.491848i	−0.441044	+	0.0777680i
$41$	2.04536	+	0.744450i	0.319432	+	0.116264i	0.496760	−	0.867888i	$-0.334523\pi$
$41$	2.04536	+	0.744450i	0.319432	+	0.116264i	−0.177328	+	0.984152i	$0.556745\pi$
$42$		0			0
$43$	1.37972	−	7.82480i	0.210406	−	1.19327i	−0.678297	−	0.734788i	$-0.737282\pi$
$43$	1.37972	−	7.82480i	0.210406	−	1.19327i	0.888703	−	0.458483i	$-0.151607\pi$
$44$	−0.0986135	−	0.0569345i	−0.0148665	−	0.00858320i
$45$		0			0
$46$	−5.50674	−	9.53795i	−0.811924	−	1.40629i
$47$	−2.18137	+	12.3712i	−0.318186	+	1.80452i	0.235585	+	0.971854i	$0.424299\pi$
$47$	−2.18137	+	12.3712i	−0.318186	+	1.80452i	−0.553771	+	0.832669i	$0.686812\pi$
$48$		0			0
$49$	5.69854	−	4.06530i	0.814077	−	0.580757i
$50$	3.04613	+	3.63023i	0.430787	+	0.513392i
$51$		0			0
$52$	0.784371	+	0.138306i	0.108773	+	0.0191795i
$53$	−1.26661	−	0.731275i	−0.173982	−	0.100448i	0.410480	−	0.911869i	$-0.365361\pi$
$53$	−1.26661	−	0.731275i	−0.173982	−	0.100448i	−0.584462	+	0.811421i	$0.698694\pi$
$54$		0			0
$55$			0.193227i			0.0260547i
$56$	4.93160	+	1.07058i	0.659013	+	0.143063i
$57$		0			0
$58$	−1.11302	−	0.405105i	−0.146146	−	0.0531929i
$59$	−5.96770	−	2.17206i	−0.776928	−	0.282779i	−0.0770368	−	0.997028i	$-0.524546\pi$
$59$	−5.96770	−	2.17206i	−0.776928	−	0.282779i	−0.699891	+	0.714250i	$0.746768\pi$
$60$		0			0
$61$	−7.69007	−	1.35597i	−0.984613	−	0.173614i	−0.341913	−	0.939732i	$-0.611075\pi$
$61$	−7.69007	−	1.35597i	−0.984613	−	0.173614i	−0.642700	+	0.766118i	$0.722186\pi$
$62$	−7.71419	+	13.3614i	−0.979703	+	1.69690i
$63$		0			0
$64$	1.05325	+	1.82428i	0.131656	+	0.228035i
$65$	−0.462256	−	1.27004i	−0.0573358	−	0.157529i
$66$		0			0
$67$	−11.0280	+	9.25358i	−1.34728	+	1.13050i	−0.367592	+	0.929987i	$0.619818\pi$
$67$	−11.0280	+	9.25358i	−1.34728	+	1.13050i	−0.979690	+	0.200517i	$0.935738\pi$
$68$	−0.855917	−	4.85415i	−0.103795	−	0.588652i
$69$		0			0
$70$	2.03119	+	6.34470i	0.242773	+	0.758337i
$71$	−2.38823	+	1.37884i	−0.283431	+	0.163639i	−0.634975	−	0.772532i	$-0.718990\pi$
$71$	−2.38823	+	1.37884i	−0.283431	+	0.163639i	0.351545	+	0.936171i	$0.385656\pi$
$72$		0			0
$73$	−6.94774	+	4.01128i	−0.813171	+	0.469485i	−0.848056	−	0.529907i	$-0.822227\pi$
$73$	−6.94774	+	4.01128i	−0.813171	+	0.469485i	0.0348847	+	0.999391i	$0.488894\pi$
$74$	−2.00086	−	5.49732i	−0.232595	−	0.639051i
$75$		0			0
$76$	0.0827118	−	0.0145843i	0.00948770	−	0.00167294i
$77$	0.130345	−	0.318636i	0.0148542	−	0.0363119i
$78$		0			0
$79$	0.310233	+	0.260316i	0.0349039	+	0.0292879i	0.660073	−	0.751202i	$-0.270525\pi$
$79$	0.310233	+	0.260316i	0.0349039	+	0.0292879i	−0.625169	+	0.780490i	$0.714970\pi$
$80$	−3.70088	+	6.41012i	−0.413771	+	0.716673i
$81$		0			0
$82$	3.19626	−	1.84536i	0.352968	−	0.203786i
$83$	4.54412	−	1.65393i	0.498782	−	0.181542i	−0.0803638	−	0.996766i	$-0.525608\pi$
$83$	4.54412	−	1.65393i	0.498782	−	0.181542i	0.579146	+	0.815224i	$0.303386\pi$
$84$		0			0
$85$	−6.40732	+	5.37638i	−0.694972	+	0.583150i
$86$	−8.65997	−	10.3205i	−0.933828	−	1.11289i
$87$		0			0
$88$	0.233222	−	0.0848857i	0.0248615	−	0.00904884i
$89$	−15.9719			−1.69302			−0.846508	−	0.532376i	$-0.821299\pi$
$89$	−15.9719			−1.69302			−0.846508	+	0.532376i	$0.821299\pi$
$90$		0			0
$91$	−0.0944582	+	2.40615i	−0.00990191	+	0.252233i
$92$	−5.59770	−	0.987026i	−0.583601	−	0.102905i
$93$		0			0
$94$	13.6916	+	16.3170i	1.41218	+	1.68297i
$95$	−0.0916104	−	0.109177i	−0.00939903	−	0.0112013i
$96$		0			0
$97$	10.2887	+	1.81418i	1.04466	+	0.184202i	0.669541	−	0.742775i	$-0.266491\pi$
$97$	10.2887	+	1.81418i	1.04466	+	0.184202i	0.375118	+	0.926977i	$0.377602\pi$
$98$	0.930470	−	11.8328i	0.0939916	−	1.19529i
$99$		0			0
$100$	2.44576			0.244576
$101$	−4.01032	+	1.45964i	−0.399042	+	0.145239i	−0.533743	−	0.845647i	$-0.679215\pi$
$101$	−4.01032	+	1.45964i	−0.399042	+	0.145239i	0.134701	+	0.990886i	$0.456993\pi$
$102$		0			0
$103$	−2.60642	−	3.10621i	−0.256818	−	0.306064i	0.622194	−	0.782863i	$-0.286241\pi$
$103$	−2.60642	−	3.10621i	−0.256818	−	0.306064i	−0.879012	+	0.476799i	$0.841797\pi$
$104$	−1.32985	+	1.11587i	−0.130402	+	0.109420i
$105$		0			0
$106$	−2.33036	+	0.848183i	−0.226345	+	0.0823828i
$107$	8.99730	−	5.19460i	0.869802	−	0.502181i	0.00251969	−	0.999997i	$-0.499198\pi$
$107$	8.99730	−	5.19460i	0.869802	−	0.502181i	0.867283	+	0.497816i	$0.165865\pi$
$108$		0			0
$109$	2.59277	−	4.49081i	0.248342	−	0.430142i	−0.714724	−	0.699407i	$-0.753447\pi$
$109$	2.59277	−	4.49081i	0.248342	−	0.430142i	0.963066	+	0.269265i	$0.0867808\pi$
$110$	0.250985	+	0.210601i	0.0239305	+	0.0200801i
$111$		0			0
$112$	10.4269	−	8.07395i	0.985253	−	0.762917i
$113$	15.1938	−	2.67908i	1.42931	−	0.252026i	0.595181	−	0.803592i	$-0.297080\pi$
$113$	15.1938	−	2.67908i	1.42931	−	0.252026i	0.834132	+	0.551565i	$0.185969\pi$
$114$		0			0
$115$	3.29892	+	9.06369i	0.307625	+	0.845194i
$116$	−0.529396	+	0.305647i	−0.0491532	+	0.0283786i
$117$		0			0
$118$	−9.32564	+	5.38416i	−0.858494	+	0.495652i
$119$	14.1926	−	4.54361i	1.30103	−	0.416512i
$120$		0			0
$121$	1.90719	+	10.8162i	0.173381	+	0.983292i
$122$	−10.1428	+	8.51086i	−0.918290	+	0.770537i
$123$		0			0
$124$	2.72337	+	7.48239i	0.244565	+	0.671938i
$125$	−5.78760	−	10.0244i	−0.517658	−	0.896611i
$126$		0			0
$127$	−0.565054	+	0.978702i	−0.0501404	+	0.0868458i	−0.890006	−	0.455948i	$-0.849300\pi$
$127$	−0.565054	+	0.978702i	−0.0501404	+	0.0868458i	0.839866	+	0.542794i	$0.182634\pi$
$128$	12.6503	+	2.23060i	1.11814	+	0.197159i
$129$		0			0
$130$	−2.15349	−	0.783808i	−0.188874	−	0.0687445i
$131$	−6.15002	−	2.23842i	−0.537330	−	0.195572i	0.0590784	−	0.998253i	$-0.481184\pi$
$131$	−6.15002	−	2.23842i	−0.537330	−	0.195572i	−0.596408	+	0.802681i	$0.703406\pi$
$132$		0			0
$133$	0.0774204	+	0.241834i	0.00671320	+	0.0209696i
$134$			24.4101i			2.10871i
$135$		0			0
$136$	9.30399	+	5.37166i	0.797811	+	0.460616i
$137$	−4.57928	−	0.807451i	−0.391234	−	0.0689852i	−0.0254292	−	0.999677i	$-0.508095\pi$
$137$	−4.57928	−	0.807451i	−0.391234	−	0.0689852i	−0.365805	+	0.930691i	$0.619206\pi$
$138$		0			0
$139$	−8.26472	−	9.84951i	−0.701005	−	0.835425i	0.291635	−	0.956530i	$-0.405801\pi$
$139$	−8.26472	−	9.84951i	−0.701005	−	0.835425i	−0.992640	+	0.121105i	$0.961356\pi$
$140$	3.18224	+	1.30177i	0.268949	+	0.110019i
$141$		0			0
$142$	−0.811975	+	4.60494i	−0.0681394	+	0.386438i
$143$	0.0592139	+	0.102561i	0.00495171	+	0.00857662i
$144$		0			0
$145$	0.898343	+	0.518658i	0.0746033	+	0.0430722i
$146$	−2.36216	+	13.3965i	−0.195494	+	1.10870i
$147$		0			0
$148$	−2.83717	−	1.03265i	−0.233214	−	0.0848829i
$149$	−20.1468	+	3.55243i	−1.65049	+	0.291027i	−0.920007	−	0.391901i	$-0.871818\pi$
$149$	−20.1468	+	3.55243i	−1.65049	+	0.291027i	−0.730486	+	0.682927i	$0.760707\pi$
$150$		0			0
$151$	−10.4393	−	8.75958i	−0.849535	−	0.712845i	0.110152	−	0.993915i	$-0.464866\pi$
$151$	−10.4393	−	8.75958i	−0.849535	−	0.712845i	−0.959687	+	0.281070i	$0.909311\pi$
$152$	−0.0915300	+	0.158535i	−0.00742406	+	0.0128589i
$153$		0			0
$154$	−0.271816	−	0.516595i	−0.0219035	−	0.0416284i
$155$	8.68526	−	10.3507i	0.697617	−	0.831388i
$156$		0			0
$157$	1.36266	−	3.74388i	0.108752	−	0.298794i	−0.873365	−	0.487067i	$-0.838067\pi$
$157$	1.36266	−	3.74388i	0.108752	−	0.298794i	0.982117	+	0.188273i	$0.0602889\pi$
$158$	0.676258	−	0.119242i	0.0538002	−	0.00948642i
$159$		0			0
$160$	2.35503	+	6.47040i	0.186182	+	0.511530i
$161$	0.674106	−	17.1716i	0.0531270	−	1.35332i
$162$		0			0
$163$	−12.3022	−	21.3081i	−0.963584	−	1.66898i	−0.713372	−	0.700785i	$-0.752833\pi$
$163$	−12.3022	−	21.3081i	−0.963584	−	1.66898i	−0.250212	−	0.968191i	$-0.580500\pi$
$164$	0.330762	−	1.87584i	0.0258282	−	0.146479i
$165$		0			0
$166$	2.80442	−	7.70508i	0.217665	−	0.598030i
$167$	3.18840	+	18.0823i	0.246726	+	1.39925i	0.816450	+	0.577417i	$0.195939\pi$
$167$	3.18840	+	18.0823i	0.246726	+	1.39925i	−0.569724	+	0.821836i	$0.692950\pi$
$168$		0			0
$169$	9.32402	+	7.82378i	0.717232	+	0.601829i
$170$			14.1824i			1.08774i
$171$		0			0
$172$	−6.95317			−0.530174
$173$	3.04671	−	1.10891i	0.231637	−	0.0843090i	−0.223594	−	0.974682i	$-0.571779\pi$
$173$	3.04671	−	1.10891i	0.231637	−	0.0843090i	0.455231	+	0.890373i	$0.349557\pi$
$174$		0			0
$175$	0.997384	+	7.32682i	0.0753951	+	0.553855i
$176$	0.221824	−	0.609457i	0.0167206	−	0.0459396i
$177$		0			0
$178$	−17.4081	+	20.7461i	−1.30479	+	1.55499i
$179$		−	19.6751i		−	1.47058i	−0.677750	−	0.735292i	$-0.737045\pi$
$179$		−	19.6751i		−	1.47058i	0.677750	−	0.735292i	$-0.262955\pi$
$180$		0			0
$181$	14.9844	+	8.65126i	1.11378	+	0.643043i	0.939806	−	0.341707i	$-0.111005\pi$
$181$	14.9844	+	8.65126i	1.11378	+	0.643043i	0.173976	+	0.984750i	$0.444338\pi$
$182$	3.02244	+	2.74521i	0.224038	+	0.203488i
$183$		0			0
$184$	9.49051	−	7.96348i	0.699650	−	0.587076i
$185$	0.889674	+	5.04559i	0.0654101	+	0.370959i
$186$		0			0
$187$	0.471099	−	0.561434i	0.0344502	−	0.0410561i
$188$	10.9931			0.801755
$189$		0			0
$190$	−0.241660			−0.0175318
$191$	−3.40180	+	4.05411i	−0.246146	+	0.293345i	−0.874945	−	0.484223i	$-0.839102\pi$
$191$	−3.40180	+	4.05411i	−0.246146	+	0.293345i	0.628799	+	0.777568i	$0.283547\pi$
$192$		0			0
$193$	3.06808	+	17.3999i	0.220845	+	1.25248i	0.870470	+	0.492221i	$0.163815\pi$
$193$	3.06808	+	17.3999i	0.220845	+	1.25248i	−0.649625	+	0.760255i	$0.725074\pi$
$194$	13.5703	−	11.3868i	0.974292	−	0.817528i
$195$		0			0
$196$	−4.36948	−	4.29330i	−0.312105	−	0.306665i
$197$	−17.9168	−	10.3443i	−1.27652	−	0.736997i	−0.300311	−	0.953841i	$-0.597090\pi$
$197$	−17.9168	−	10.3443i	−1.27652	−	0.736997i	−0.976206	+	0.216844i	$0.930424\pi$
$198$		0			0
$199$		−	12.7755i		−	0.905634i	−0.891604	−	0.452817i	$-0.850419\pi$
$199$		−	12.7755i		−	0.905634i	0.891604	−	0.452817i	$-0.149581\pi$
$200$	−3.42657	+	4.08362i	−0.242295	+	0.288756i
$201$		0			0
$202$	−2.47498	+	6.79996i	−0.174139	+	0.478443i
$203$	−1.13152	−	1.46128i	−0.0794172	−	0.102562i
$204$		0			0
$205$	−3.03733	+	1.10550i	−0.212136	+	0.0772113i
$206$	−6.87550			−0.479039
$207$		0			0
$208$			4.53651i			0.314550i
$209$	0.00956651	+	0.00802726i	0.000661729	+	0.000555257i
$210$		0			0
$211$	3.56749	+	20.2322i	0.245596	+	1.39284i	0.819104	+	0.573645i	$0.194471\pi$
$211$	3.56749	+	20.2322i	0.245596	+	1.39284i	−0.573508	+	0.819200i	$0.694418\pi$
$212$	−0.437747	+	1.20270i	−0.0300646	+	0.0826018i
$213$		0			0
$214$	3.05900	−	17.3484i	0.209109	−	1.18591i
$215$	5.89948	+	10.2182i	0.402341	+	0.696876i
$216$		0			0
$217$	−21.3045	+	11.2098i	−1.44625	+	0.760968i
$218$	−3.00727	−	8.26242i	−0.203678	−	0.559601i
$219$		0			0
$220$	0.166525	−	0.0293628i	0.0112271	−	0.00197964i
$221$	−1.75332	+	4.81720i	−0.117941	+	0.324040i
$222$		0			0
$223$	12.6494	−	15.0750i	0.847070	−	1.00950i	−0.152705	−	0.988272i	$-0.548798\pi$
$223$	12.6494	−	15.0750i	0.847070	−	1.00950i	0.999775	−	0.0212263i	$-0.00675706\pi$
$224$	0.481231	−	12.2585i	0.0321536	−	0.819056i
$225$		0			0
$226$	13.0801	−	22.6554i	0.870077	−	1.50702i
$227$	0.244120	+	0.204841i	0.0162028	+	0.0135958i	0.650853	−	0.759204i	$-0.274411\pi$
$227$	0.244120	+	0.204841i	0.0162028	+	0.0135958i	−0.634650	+	0.772799i	$0.718856\pi$
$228$		0			0
$229$	8.52907	−	1.50391i	0.563617	−	0.0993809i	0.115422	−	0.993317i	$-0.463178\pi$
$229$	8.52907	−	1.50391i	0.563617	−	0.0993809i	0.448195	+	0.893936i	$0.352067\pi$
$230$	15.3685	+	5.59369i	1.01337	+	0.368837i
$231$		0			0
$232$	0.231365	−	1.31214i	0.0151899	−	0.0861460i
$233$	6.35900	+	3.67137i	0.416592	+	0.240520i	0.693618	−	0.720343i	$-0.256016\pi$
$233$	6.35900	+	3.67137i	0.416592	+	0.240520i	−0.277026	+	0.960862i	$0.589349\pi$
$234$		0			0
$235$	−9.32722	−	16.1552i	−0.608440	−	1.05385i
$236$	−0.965055	+	5.47310i	−0.0628197	+	0.356268i
$237$		0			0
$238$	9.56704	−	23.3872i	0.620139	−	1.51596i
$239$	3.02456	+	3.60453i	0.195642	+	0.233157i	0.854943	−	0.518722i	$-0.173592\pi$
$239$	3.02456	+	3.60453i	0.195642	+	0.233157i	−0.659301	+	0.751879i	$0.729148\pi$
$240$		0			0
$241$	−6.53071	−	1.15154i	−0.420680	−	0.0741773i	−0.0406989	−	0.999171i	$-0.512958\pi$
$241$	−6.53071	−	1.15154i	−0.420680	−	0.0741773i	−0.379981	+	0.924994i	$0.624070\pi$
$242$	16.1280	+	9.31152i	1.03675	+	0.598567i
$243$		0			0
$244$			6.83345i			0.437467i
$245$	−2.60201	+	10.0640i	−0.166236	+	0.642963i
$246$		0			0
$247$	−0.0820823	−	0.0298755i	−0.00522277	−	0.00190093i
$248$	−16.3086	−	5.93585i	−1.03560	−	0.376927i
$249$		0			0
$250$	−19.3289	−	3.40820i	−1.22247	−	0.215554i
$251$	7.34905	−	12.7289i	0.463868	−	0.803443i	−0.535282	−	0.844674i	$-0.679795\pi$
$251$	7.34905	−	12.7289i	0.463868	−	0.803443i	0.999150	+	0.0412308i	$0.0131279\pi$
$252$		0			0
$253$	−0.422583	−	0.731935i	−0.0265675	−	0.0460163i
$254$	0.655388	+	1.80066i	0.0411227	+	0.112984i
$255$		0			0
$256$	13.4579	−	11.2925i	0.841118	−	0.705782i
$257$	2.45224	+	13.9074i	0.152967	+	0.867517i	0.960621	+	0.277861i	$0.0896255\pi$
$257$	2.45224	+	13.9074i	0.152967	+	0.867517i	−0.807655	+	0.589656i	$0.799263\pi$
$258$		0			0
$259$	1.93651	−	8.92047i	0.120329	−	0.554291i
$260$	−1.02429	+	0.591374i	−0.0635237	+	0.0366754i
$261$		0			0
$262$	−9.61055	+	5.54865i	−0.593742	+	0.342797i
$263$	−5.34900	−	14.6963i	−0.329834	−	0.906211i	−0.988153	−	0.153472i	$-0.950955\pi$
$263$	−5.34900	−	14.6963i	−0.329834	−	0.906211i	0.658319	−	0.752739i	$-0.271268\pi$
$264$		0			0
$265$	2.13887	−	0.377141i	0.131390	−	0.0231676i
$266$	0.398504	+	0.163017i	0.0244338	+	0.00999520i
$267$		0			0
$268$	9.65066	+	8.09787i	0.589508	+	0.494656i
$269$	2.15558	−	3.73358i	0.131428	−	0.227640i	−0.792799	−	0.609483i	$-0.791377\pi$
$269$	2.15558	−	3.73358i	0.131428	−	0.227640i	0.924227	+	0.381843i	$0.124710\pi$
$270$		0			0
$271$	16.1867	−	9.34540i	0.983272	−	0.567692i	0.0800157	−	0.996794i	$-0.474503\pi$
$271$	16.1867	−	9.34540i	0.983272	−	0.567692i	0.903256	+	0.429101i	$0.141170\pi$
$272$	26.3815	−	9.60207i	1.59961	−	0.582211i
$273$		0			0
$274$	−6.03986	+	5.06804i	−0.364881	+	0.306172i
$275$	0.233757	+	0.278581i	0.0140961	+	0.0167991i
$276$		0			0
$277$	−8.83184	+	3.21453i	−0.530654	+	0.193142i	−0.593430	−	0.804885i	$-0.702227\pi$
$277$	−8.83184	+	3.21453i	−0.530654	+	0.193142i	0.0627763	+	0.998028i	$0.480005\pi$
$278$	−21.8016			−1.30757
$279$		0			0
$280$	−6.63192	+	3.48950i	−0.396333	+	0.208538i
$281$	−27.0442	−	4.76862i	−1.61332	−	0.284472i	−0.707048	−	0.707166i	$-0.749973\pi$
$281$	−27.0442	−	4.76862i	−1.61332	−	0.284472i	−0.906272	+	0.422694i	$0.861084\pi$
$282$		0			0
$283$	−13.9408	−	16.6140i	−0.828694	−	0.987599i	−0.999997	−	0.00238075i	$-0.999242\pi$
$283$	−13.9408	−	16.6140i	−0.828694	−	0.987599i	0.171303	−	0.985218i	$-0.445202\pi$
$284$	1.55122	+	1.84867i	0.0920481	+	0.109699i
$285$		0			0
$286$	0.197757	+	0.0348699i	0.0116936	+	0.00206190i
$287$	5.75438	+	0.225899i	0.339670	+	0.0133344i
$288$		0			0
$289$	14.7249			0.866172
$290$	1.65281	−	0.601575i	0.0970566	−	0.0353257i
$291$		0			0
$292$	4.51275	+	5.37809i	0.264089	+	0.314729i
$293$	−7.22978	+	6.06651i	−0.422368	+	0.354409i	−0.829063	−	0.559155i	$-0.811126\pi$
$293$	−7.22978	+	6.06651i	−0.422368	+	0.354409i	0.406695	+	0.913564i	$0.366681\pi$
$294$		0			0
$295$	8.86194	−	3.22548i	0.515962	−	0.187795i
$296$	5.69911	−	3.29038i	0.331254	−	0.191250i
$297$		0			0
$298$	−17.3441	+	30.0409i	−1.00472	+	1.74022i
$299$	4.52856	+	3.79991i	0.261893	+	0.219755i
$300$		0			0
$301$	−2.83551	−	20.8297i	−0.163436	−	1.20061i
$302$	−22.7559	+	4.01248i	−1.30946	+	0.230892i
$303$		0			0
$304$	0.163614	+	0.449525i	0.00938389	+	0.0257820i
$305$	10.0423	−	5.79790i	0.575018	−	0.331987i
$306$		0			0
$307$	−4.86656	+	2.80971i	−0.277749	+	0.160358i	−0.632404	−	0.774639i	$-0.717932\pi$
$307$	−4.86656	+	2.80971i	−0.277749	+	0.160358i	0.354655	+	0.934997i	$0.384598\pi$
$308$	−0.294412	−	0.0639128i	−0.0167757	−	0.00364177i
$309$		0			0
$310$	−3.97844	−	22.5628i	−0.225960	−	1.28148i
$311$	13.3712	−	11.2198i	0.758213	−	0.636216i	−0.179448	−	0.983767i	$-0.557431\pi$
$311$	13.3712	−	11.2198i	0.758213	−	0.636216i	0.937661	+	0.347551i	$0.112987\pi$
$312$		0			0
$313$	0.170801	+	0.469272i	0.00965424	+	0.0265248i	0.944426	−	0.328724i	$-0.106618\pi$
$313$	0.170801	+	0.469272i	0.00965424	+	0.0265248i	−0.934772	+	0.355248i	$0.884396\pi$
$314$	−3.37779	−	5.85051i	−0.190620	−	0.330163i
$315$		0			0
$316$	0.177200	−	0.306920i	0.00996830	−	0.0172656i
$317$	−7.69250	−	1.35640i	−0.432054	−	0.0761828i	−0.0466081	−	0.998913i	$-0.514841\pi$
$317$	−7.69250	−	1.35640i	−0.432054	−	0.0761828i	−0.385446	+	0.922730i	$0.625952\pi$
$318$		0			0
$319$	−0.0854121	−	0.0310875i	−0.00478216	−	0.00174056i
$320$	−2.93946	−	1.06988i	−0.164321	−	0.0598079i
$321$		0			0
$322$	−21.5698	−	19.5913i	−1.20204	−	1.09178i
$323$			0.540574i			0.0300784i
$324$		0			0
$325$	−2.20289	−	1.27184i	−0.122194	−	0.0705490i
$326$	−41.0858	−	7.24454i	−2.27553	−	0.401238i
$327$		0			0
$328$	2.66864	+	3.18036i	0.147351	+	0.175606i
$329$	4.48300	+	32.9323i	0.247156	+	1.81562i
$330$		0			0
$331$	−5.48925	+	31.1311i	−0.301716	+	1.71112i	0.336855	+	0.941556i	$0.390637\pi$
$331$	−5.48925	+	31.1311i	−0.301716	+	1.71112i	−0.638572	+	0.769562i	$0.720474\pi$
$332$	−2.11590	−	3.66485i	−0.116125	−	0.201135i
$333$		0			0
$334$	26.9625	+	15.5668i	1.47532	+	0.851779i
$335$	3.71223	−	21.0531i	0.202821	−	1.15025i
$336$		0			0
$337$	−6.59007	−	2.39859i	−0.358984	−	0.130659i	0.156231	−	0.987721i	$-0.450066\pi$
$337$	−6.59007	−	2.39859i	−0.358984	−	0.130659i	−0.515215	+	0.857061i	$0.672288\pi$
$338$	20.3249	−	3.58382i	1.10553	−	0.194934i
$339$		0			0
$340$	5.60709	+	4.70491i	0.304087	+	0.255159i
$341$	−0.591981	+	1.02534i	−0.0320576	+	0.0555253i
$342$		0			0
$343$	11.0797	−	14.8405i	0.598245	−	0.801313i
$344$	9.74154	−	11.6095i	0.525229	−	0.625943i
$345$		0			0
$346$	1.88029	−	5.16605i	0.101085	−	0.277728i
$347$	10.4676	−	1.84572i	0.561929	−	0.0990832i	0.114533	−	0.993419i	$-0.463463\pi$
$347$	10.4676	−	1.84572i	0.561929	−	0.0990832i	0.447396	+	0.894336i	$0.352352\pi$
$348$		0			0
$349$	−2.52401	−	6.93467i	−0.135107	−	0.371204i	0.853627	−	0.520885i	$-0.174398\pi$
$349$	−2.52401	−	6.93467i	−0.135107	−	0.371204i	−0.988734	+	0.149680i	$0.952176\pi$
$350$	10.6040	+	6.69013i	0.566807	+	0.357602i
$351$		0			0
$352$	−0.301674	−	0.522514i	−0.0160793	−	0.0278501i
$353$	−2.89186	+	16.4006i	−0.153918	+	0.872915i	0.805850	+	0.592120i	$0.201709\pi$
$353$	−2.89186	+	16.4006i	−0.153918	+	0.872915i	−0.959768	+	0.280794i	$0.909402\pi$
$354$		0			0
$355$	1.40062	−	3.84816i	0.0743370	−	0.204239i
$356$	2.42710	+	13.7648i	0.128636	+	0.729531i
$357$		0			0
$358$	−25.5563	−	21.4443i	−1.35069	−	1.13336i
$359$			17.3398i			0.915160i	0.889169	+	0.457580i	$0.151284\pi$
$359$			17.3398i			0.915160i	−0.889169	+	0.457580i	$0.848716\pi$
$360$		0			0
$361$	18.9908			0.999515
$362$	27.5691	−	10.0343i	1.44900	−	0.527392i
$363$		0			0
$364$	2.08801	−	0.284236i	0.109441	−	0.0148980i
$365$	4.07462	−	11.1949i	0.213275	−	0.585969i
$366$		0			0
$367$	17.1783	−	20.4723i	0.896698	−	1.06864i	−0.100581	−	0.994929i	$-0.532070\pi$
$367$	17.1783	−	20.4723i	0.896698	−	1.06864i	0.997279	−	0.0737143i	$-0.0234853\pi$
$368$		−	32.3750i		−	1.68767i
$369$		0			0
$370$	7.52347	+	4.34368i	0.391127	+	0.225817i
$371$	−3.78147	−	0.820906i	−0.196324	−	0.0426193i
$372$		0			0
$373$	−14.1817	+	11.8999i	−0.734300	+	0.616151i	−0.931300	−	0.364253i	$-0.881325\pi$
$373$	−14.1817	+	11.8999i	−0.734300	+	0.616151i	0.197000	+	0.980403i	$0.436880\pi$
$374$	−0.215795	−	1.22384i	−0.0111585	−	0.0632831i
$375$		0			0
$376$	−15.4016	+	18.3549i	−0.794276	+	0.946582i
$377$	0.635767			0.0327437
$378$		0			0
$379$	35.2309			1.80969			0.904846	−	0.425739i	$-0.139986\pi$
$379$	35.2309			1.80969			0.904846	+	0.425739i	$0.139986\pi$
$380$	−0.0801689	+	0.0955416i	−0.00411258	+	0.00490118i
$381$		0			0
$382$	1.55825	+	8.83730i	0.0797272	+	0.452156i
$383$	12.7995	−	10.7400i	0.654022	−	0.548790i	−0.254266	−	0.967134i	$-0.581834\pi$
$383$	12.7995	−	10.7400i	0.654022	−	0.548790i	0.908288	+	0.418345i	$0.137390\pi$
$384$		0			0
$385$	0.155872	+	0.486887i	0.00794396	+	0.0248141i
$386$	25.9450	+	14.9794i	1.32057	+	0.762429i
$387$		0			0
$388$		−	9.14261i		−	0.464146i
$389$	−6.09977	+	7.26943i	−0.309271	+	0.368575i	−0.898183	−	0.439623i	$-0.855112\pi$
$389$	−6.09977	+	7.26943i	−0.309271	+	0.368575i	0.588912	+	0.808197i	$0.299557\pi$
$390$		0			0
$391$	12.5126	−	34.3782i	0.632792	−	1.73858i
$392$	13.2901	−	1.28058i	0.671253	−	0.0646793i
$393$		0			0
$394$	−32.9642	+	11.9980i	−1.66071	+	0.604449i
$395$	−0.601390			−0.0302592
$396$		0			0
$397$			38.0530i			1.90983i	0.296886	+	0.954913i	$0.404052\pi$
$397$			38.0530i			1.90983i	−0.296886	+	0.954913i	$0.595948\pi$
$398$	−16.5943	−	13.9243i	−0.831799	−	0.697962i
$399$		0			0
$400$	2.41901	+	13.7189i	0.120950	+	0.685943i
$401$	1.92376	−	5.28549i	0.0960680	−	0.263945i	−0.882345	−	0.470603i	$-0.844037\pi$
$401$	1.92376	−	5.28549i	0.0960680	−	0.263945i	0.978413	+	0.206658i	$0.0662588\pi$
$402$		0			0
$403$	1.43804	−	8.15556i	0.0716341	−	0.406257i
$404$	1.86734	+	3.23434i	0.0929039	+	0.160914i
$405$		0			0
$406$	−3.13134	−	0.122927i	−0.155406	−	0.00610076i
$407$	−0.153545	−	0.421860i	−0.00761092	−	0.0209108i
$408$		0			0
$409$	−2.17218	+	0.383014i	−0.107407	+	0.0189388i	−0.227093	−	0.973873i	$-0.572922\pi$
$409$	−2.17218	+	0.383014i	−0.107407	+	0.0189388i	0.119686	+	0.992812i	$0.461811\pi$
$410$	−1.87450	+	5.15014i	−0.0925749	+	0.254347i
$411$		0			0
$412$	−2.28090	+	2.71827i	−0.112372	+	0.133919i
$413$	−16.7894	−	0.659100i	−0.826153	−	0.0324322i
$414$		0			0
$415$	−3.59051	+	6.21895i	−0.176251	+	0.305276i
$416$	3.23285	+	2.71269i	0.158504	+	0.133000i
$417$		0			0
$418$	0.0208535	−	0.00367703i	0.00101998	−	0.000179849i
$419$	11.5894	+	4.21819i	0.566178	+	0.206072i	0.609220	−	0.793001i	$-0.291483\pi$
$419$	11.5894	+	4.21819i	0.566178	+	0.206072i	−0.0430419	+	0.999073i	$0.513705\pi$
$420$		0			0
$421$	3.05146	−	17.3057i	0.148719	−	0.843427i	−0.815587	−	0.578635i	$-0.803586\pi$
$421$	3.05146	−	17.3057i	0.148719	−	0.843427i	0.964306	−	0.264792i	$-0.0853034\pi$
$422$	30.1683	+	17.4176i	1.46857	+	0.847878i
$423$		0			0
$424$	−1.39482	−	2.41590i	−0.0677386	−	0.117327i
$425$	−2.73353	+	15.5026i	−0.132596	+	0.751988i
$426$		0			0
$427$	−20.4711	+	2.78668i	−0.990665	+	0.134857i
$428$	−5.84400	−	6.96461i	−0.282480	−	0.336647i
$429$		0			0
$430$	19.7026	+	3.47409i	0.950141	+	0.167536i
$431$	30.8867	+	17.8324i	1.48776	+	0.858957i	0.999902	−	0.0139669i	$-0.00444595\pi$
$431$	30.8867	+	17.8324i	1.48776	+	0.858957i	0.487856	+	0.872924i	$0.337779\pi$
$432$		0			0
$433$			7.92231i			0.380722i	0.981714	+	0.190361i	$0.0609659\pi$
$433$			7.92231i			0.380722i	−0.981714	+	0.190361i	$0.939034\pi$
$434$	−8.65970	+	39.8905i	−0.415679	+	1.91481i
$435$		0			0
$436$	−4.26424	−	1.55205i	−0.204220	−	0.0743299i
$437$	0.585785	+	0.213208i	0.0280219	+	0.0101991i
$438$		0			0
$439$	16.5370	+	2.91592i	0.789269	+	0.139169i	0.553731	−	0.832696i	$-0.313204\pi$
$439$	16.5370	+	2.91592i	0.789269	+	0.139169i	0.235538	+	0.971865i	$0.424315\pi$
$440$	−0.184279	+	0.319180i	−0.00878514	+	0.0152163i
$441$		0			0
$442$	4.34616	+	7.52778i	0.206726	+	0.358060i
$443$	5.93568	+	16.3082i	0.282013	+	0.774824i	0.997122	+	0.0758113i	$0.0241547\pi$
$443$	5.93568	+	16.3082i	0.282013	+	0.774824i	−0.715109	+	0.699013i	$0.753623\pi$
$444$		0			0
$445$	18.1690	−	15.2456i	0.861295	−	0.722713i
$446$	−5.79430	−	32.8611i	−0.274368	−	1.55602i
$447$		0			0
$448$	4.12555	+	3.74714i	0.194914	+	0.177036i
$449$	6.63080	−	3.82829i	0.312927	−	0.180668i	−0.335309	−	0.942108i	$-0.608841\pi$
$449$	6.63080	−	3.82829i	0.312927	−	0.180668i	0.648235	+	0.761440i	$0.275507\pi$
$450$		0			0
$451$	0.245278	−	0.141612i	0.0115497	−	0.00666823i
$452$	−4.61772	−	12.6871i	−0.217199	−	0.596750i
$453$		0			0
$454$	0.532142	−	0.0938310i	0.0249747	−	0.00440371i
$455$	−2.18929	−	2.82732i	−0.102636	−	0.132547i
$456$		0			0
$457$	22.7892	+	19.1224i	1.06603	+	0.894507i	0.994687	−	0.102945i	$-0.0328265\pi$
$457$	22.7892	+	19.1224i	1.06603	+	0.894507i	0.0713449	+	0.997452i	$0.477271\pi$
$458$	7.34256	−	12.7177i	0.343095	−	0.594258i
$459$		0			0
$460$	7.30989	−	4.22037i	0.340826	−	0.196776i
$461$	−0.444066	+	0.161627i	−0.0206822	+	0.00752772i	−0.352341	−	0.935872i	$-0.614614\pi$
$461$	−0.444066	+	0.161627i	−0.0206822	+	0.00752772i	0.331658	+	0.943400i	$0.392392\pi$
$462$		0			0
$463$	1.97532	−	1.65749i	0.0918008	−	0.0770300i	−0.595732	−	0.803183i	$-0.703138\pi$
$463$	1.97532	−	1.65749i	0.0918008	−	0.0770300i	0.687533	+	0.726153i	$0.258694\pi$
$464$	−2.23805	−	2.66720i	−0.103899	−	0.123822i
$465$		0			0
$466$	11.6996	−	4.25831i	0.541974	−	0.197262i
$467$	5.31125			0.245775			0.122888	−	0.992421i	$-0.460784\pi$
$467$	5.31125			0.245775			0.122888	+	0.992421i	$0.460784\pi$
$468$		0			0
$469$	−20.3234	+	32.2130i	−0.938447	+	1.48746i
$470$	−31.1502	−	5.49262i	−1.43685	−	0.253355i
$471$		0			0
$472$	−7.78622	−	9.27925i	−0.358390	−	0.427112i
$473$	−0.664559	−	0.791991i	−0.0305565	−	0.0364158i
$474$		0			0
$475$	−0.264156	−	0.0465778i	−0.0121203	−	0.00213714i
$476$	−6.07245	−	11.5409i	−0.278330	−	0.528977i
$477$		0			0
$478$	7.97850			0.364928
$479$	−30.9511	+	11.2653i	−1.41419	+	0.514723i	−0.932357	−	0.361539i	$-0.882251\pi$
$479$	−30.9511	+	11.2653i	−1.41419	+	0.514723i	−0.481834	+	0.876262i	$0.660029\pi$
$480$		0			0
$481$	2.01843	+	2.40548i	0.0920327	+	0.109680i
$482$	−8.61371	+	7.22776i	−0.392344	+	0.329215i
$483$		0			0
$484$	9.03172	−	3.28728i	0.410533	−	0.149422i
$485$	−13.4357	+	7.75713i	−0.610086	+	0.352233i
$486$		0			0
$487$	−12.1204	+	20.9931i	−0.549226	+	0.951288i	0.449101	+	0.893481i	$0.351744\pi$
$487$	−12.1204	+	20.9931i	−0.549226	+	0.951288i	−0.998328	+	0.0578073i	$0.981589\pi$
$488$	−11.4096	−	9.57381i	−0.516489	−	0.433386i
$489$		0			0
$490$	10.2363	+	14.3487i	0.462427	+	0.648208i
$491$	11.3569	−	2.00253i	0.512529	−	0.0903727i	0.0885987	−	0.996067i	$-0.471761\pi$
$491$	11.3569	−	2.00253i	0.512529	−	0.0903727i	0.423931	+	0.905695i	$0.360650\pi$
$492$		0			0
$493$	−1.34568	−	3.69722i	−0.0606063	−	0.166514i
$494$	−0.128269	+	0.0740561i	−0.00577109	+	0.00333194i
$495$		0			0
$496$	−39.2769	+	22.6765i	−1.76358	+	1.01821i
$497$	−4.90552	+	5.40091i	−0.220043	+	0.242264i
$498$		0			0
$499$	0.886056	+	5.02507i	0.0396653	+	0.224953i	0.998196	−	0.0600353i	$-0.0191213\pi$
$499$	0.886056	+	5.02507i	0.0396653	+	0.224953i	−0.958531	+	0.284988i	$0.908010\pi$
$500$	−7.75967	+	6.51114i	−0.347023	+	0.291187i
$501$		0			0
$502$	−8.52393	−	23.4193i	−0.380442	−	1.04525i
$503$	−12.9688	−	22.4626i	−0.578251	−	1.00156i	−0.995680	−	0.0928501i	$-0.970402\pi$
$503$	−12.9688	−	22.4626i	−0.578251	−	1.00156i	0.417429	−	0.908709i	$-0.362931\pi$
$504$		0			0
$505$	3.16873	−	5.48841i	0.141007	−	0.244231i
$506$	−1.41130	−	0.248851i	−0.0627401	−	0.0110628i
$507$		0			0
$508$	0.929323	+	0.338246i	0.0412321	+	0.0150072i
$509$	25.9098	+	9.43040i	1.14843	+	0.417995i	0.844952	−	0.534843i	$-0.179629\pi$
$509$	25.9098	+	9.43040i	1.14843	+	0.417995i	0.303480	+	0.952838i	$0.401851\pi$
$510$		0			0
$511$	−14.2709	+	15.7121i	−0.631309	+	0.695063i
$512$		−	4.09759i		−	0.181090i
$513$		0			0
$514$	20.7372	+	11.9726i	0.914680	+	0.528091i
$515$	5.92995	+	1.04561i	0.261305	+	0.0460751i
$516$		0			0
$517$	1.05068	+	1.25216i	0.0462090	+	0.0550697i
$518$	−9.47629	−	12.2380i	−0.416364	−	0.537705i
$519$		0			0
$520$	0.447651	−	2.53875i	0.0196308	−	0.111332i
$521$	6.28697	+	10.8894i	0.275437	+	0.477071i	0.970245	−	0.242124i	$-0.0778441\pi$
$521$	6.28697	+	10.8894i	0.275437	+	0.477071i	−0.694808	+	0.719195i	$0.744511\pi$
$522$		0			0
$523$	2.96092	+	1.70949i	0.129472	+	0.0747507i	0.563337	−	0.826227i	$-0.309517\pi$
$523$	2.96092	+	1.70949i	0.129472	+	0.0747507i	−0.433865	+	0.900978i	$0.642851\pi$
$524$	−0.994539	+	5.64031i	−0.0434467	+	0.246398i
$525$		0			0
$526$	−24.9192	−	9.06984i	−1.08653	−	0.395464i
$527$	−50.4714	+	8.89946i	−2.19857	+	0.387667i
$528$		0			0
$529$	−14.6993	−	12.3342i	−0.639099	−	0.536268i
$530$	1.84132	−	3.18927i	0.0799820	−	0.138533i
$531$		0			0
$532$	0.196650	−	0.103471i	0.00852588	−	0.00448604i
$533$	−1.27339	+	1.51756i	−0.0551565	+	0.0657330i
$534$		0			0
$535$	−5.27662	+	14.4974i	−0.228128	+	0.626777i
$536$	−27.0416	+	4.76816i	−1.16802	+	0.205953i
$537$		0			0
$538$	−2.50019	−	6.86922i	−0.107791	−	0.296153i
$539$	0.0714035	−	0.908038i	0.00307557	−	0.0391120i
$540$		0			0
$541$	−1.35102	−	2.34004i	−0.0580850	−	0.100606i	0.835521	−	0.549459i	$-0.185166\pi$
$541$	−1.35102	−	2.34004i	−0.0580850	−	0.100606i	−0.893606	+	0.448853i	$0.851833\pi$
$542$	5.50332	−	31.2109i	0.236388	−	1.34062i
$543$		0			0
$544$	8.93255	−	24.5420i	0.382980	−	1.05223i
$545$	1.33717	+	7.58347i	0.0572781	+	0.324840i
$546$		0			0
$547$	23.8134	+	19.9818i	1.01819	+	0.854362i	0.989399	−	0.145224i	$-0.0463903\pi$
$547$	23.8134	+	19.9818i	1.01819	+	0.854362i	0.0287897	+	0.999585i	$0.490835\pi$
$548$			4.06918i			0.173827i
$549$		0			0
$550$	0.616631			0.0262932
$551$	0.0629985	−	0.0229296i	0.00268383	−	0.000976833i
$552$		0			0
$553$	0.991708	+	0.405680i	0.0421717	+	0.0172513i
$554$	−5.45060	+	14.9754i	−0.231574	+	0.636244i
$555$		0			0
$556$	−7.23252	+	8.61938i	−0.306727	+	0.365543i
$557$			31.1769i			1.32101i	0.750822	+	0.660504i	$0.229657\pi$
$557$			31.1769i			1.32101i	−0.750822	+	0.660504i	$0.770343\pi$
$558$		0			0
$559$	6.26269	+	3.61577i	0.264884	+	0.152931i
$560$	−4.15449	+	19.1375i	−0.175559	+	0.808706i
$561$		0			0
$562$	−35.6700	+	29.9307i	−1.50465	+	1.26255i
$563$	−4.71848	−	26.7598i	−0.198860	−	1.12779i	−0.906813	−	0.421533i	$-0.861492\pi$
$563$	−4.71848	−	26.7598i	−0.198860	−	1.12779i	0.707953	−	0.706260i	$-0.249619\pi$
$564$		0			0
$565$	−14.7267	+	17.5506i	−0.619556	+	0.738358i
$566$	−36.7745			−1.54575
$567$		0			0
$568$	−5.25997			−0.220704
$569$	10.4176	−	12.4152i	0.436729	−	0.520473i	−0.502122	−	0.864797i	$-0.667447\pi$
$569$	10.4176	−	12.4152i	0.436729	−	0.520473i	0.938851	+	0.344324i	$0.111892\pi$
$570$		0			0
$571$	6.42712	+	36.4500i	0.268967	+	1.52539i	0.757497	+	0.652839i	$0.226422\pi$
$571$	6.42712	+	36.4500i	0.268967	+	1.52539i	−0.488530	+	0.872547i	$0.662467\pi$
$572$	0.0793905	−	0.0666165i	0.00331948	−	0.00278538i
$573$		0			0
$574$	6.56524	−	7.22825i	0.274028	−	0.301701i
$575$	15.7210	+	9.07655i	0.655613	+	0.378518i
$576$		0			0
$577$		−	43.3528i		−	1.80480i	−0.430899	−	0.902400i	$-0.641804\pi$
$577$		−	43.3528i		−	1.80480i	0.430899	−	0.902400i	$-0.358196\pi$
$578$	16.0490	−	19.1264i	0.667550	−	0.795555i
$579$		0			0
$580$	0.310473	−	0.853018i	0.0128917	−	0.0354196i
$581$	10.1160	−	7.83317i	0.419682	−	0.324975i
$582$		0			0
$583$	−0.178830	+	0.0650889i	−0.00740639	+	0.00269571i
$584$	−15.3021			−0.633205
$585$		0			0
$586$			16.0029i			0.661073i
$587$	−26.0768	−	21.8811i	−1.07631	−	0.903128i	−0.0806972	−	0.996739i	$-0.525715\pi$
$587$	−26.0768	−	21.8811i	−1.07631	−	0.903128i	−0.995609	+	0.0936106i	$0.970159\pi$
$588$		0			0
$589$	−0.151642	−	0.860003i	−0.00624829	−	0.0354358i
$590$	5.46917	−	15.0264i	0.225162	−	0.618628i
$591$		0			0
$592$	2.98622	−	16.9357i	0.122733	−	0.696053i
$593$	−1.09399	−	1.89484i	−0.0449246	−	0.0778118i	0.842689	−	0.538401i	$-0.180971\pi$
$593$	−1.09399	−	1.89484i	−0.0449246	−	0.0778118i	−0.887613	+	0.460589i	$0.847638\pi$
$594$		0			0
$595$	−11.8080	+	18.7159i	−0.484081	+	0.767278i
$596$	6.12306	+	16.8230i	0.250810	+	0.689095i
$597$		0			0
$598$	9.87153	−	1.74062i	0.403677	−	0.0711791i
$599$	−0.819728	+	2.25218i	−0.0334932	+	0.0920217i	−0.955312	−	0.295599i	$-0.904481\pi$
$599$	−0.819728	+	2.25218i	−0.0334932	+	0.0920217i	0.921819	+	0.387621i	$0.126703\pi$
$600$		0			0
$601$	−9.51673	+	11.3416i	−0.388196	+	0.462634i	−0.924383	−	0.381465i	$-0.875420\pi$
$601$	−9.51673	+	11.3416i	−0.388196	+	0.462634i	0.536187	+	0.844099i	$0.319864\pi$
$602$	−30.1465	−	19.0197i	−1.22868	−	0.775183i
$603$		0			0
$604$	−5.96276	+	10.3278i	−0.242621	+	0.420232i
$605$	−12.4940	−	10.4837i	−0.507951	−	0.426222i
$606$		0			0
$607$	1.02359	−	0.180486i	0.0415461	−	0.00732570i	−0.152836	−	0.988251i	$-0.548841\pi$
$607$	1.02359	−	0.180486i	0.0415461	−	0.00732570i	0.194383	+	0.980926i	$0.437730\pi$
$608$	0.418181	+	0.152205i	0.0169595	+	0.00617274i
$609$		0			0
$610$	3.41427	−	19.3633i	0.138240	−	0.783997i
$611$	−9.90146	−	5.71661i	−0.400570	−	0.231269i
$612$		0			0
$613$	−12.0184	−	20.8164i	−0.485417	−	0.840768i	0.514442	−	0.857525i	$-0.327999\pi$
$613$	−12.0184	−	20.8164i	−0.485417	−	0.840768i	−0.999860	+	0.0167574i	$0.994666\pi$
$614$	−1.65458	+	9.38360i	−0.0667735	+	0.378691i
$615$		0			0
$616$	0.519190	−	0.402028i	0.0209188	−	0.0161982i
$617$	10.4252	+	12.4243i	0.419702	+	0.500182i	0.933922	−	0.357477i	$-0.116363\pi$
$617$	10.4252	+	12.4243i	0.419702	+	0.500182i	−0.514220	+	0.857659i	$0.671918\pi$
$618$		0			0
$619$	2.85812	+	0.503964i	0.114878	+	0.0202560i	0.230791	−	0.973003i	$-0.425869\pi$
$619$	2.85812	+	0.503964i	0.114878	+	0.0202560i	−0.115914	+	0.993259i	$0.536980\pi$
$620$	−10.2402	−	5.91216i	−0.411255	−	0.237438i
$621$		0			0
$622$		−	29.5968i		−	1.18672i
$623$	−40.2455	+	12.8842i	−1.61240	+	0.516193i
$624$		0			0
$625$	3.02102	+	1.09956i	0.120841	+	0.0439825i
$626$	0.795704	+	0.289612i	0.0318027	+	0.0115752i
$627$		0			0
$628$	−3.43359	−	0.605435i	−0.137015	−	0.0241595i
$629$	9.71647	−	16.8294i	0.387421	−	0.671033i
$630$		0			0
$631$	−23.7928	−	41.2104i	−0.947177	−	1.64056i	−0.751333	−	0.659923i	$-0.770589\pi$
$631$	−23.7928	−	41.2104i	−0.947177	−	1.64056i	−0.195844	−	0.980635i	$-0.562745\pi$
$632$	0.264194	+	0.725868i	0.0105091	+	0.0288735i
$633$		0			0
$634$	−10.1461	+	8.51355i	−0.402951	+	0.338116i
$635$	−0.291415	−	1.65270i	−0.0115645	−	0.0655854i
$636$		0			0
$637$	1.70298	+	6.13917i	0.0674745	+	0.243243i
$638$	−0.133472	+	0.0770603i	−0.00528422	+	0.00305085i
$639$		0			0
$640$	−16.5198	+	9.53769i	−0.653001	+	0.377010i
$641$	13.3093	+	36.5671i	0.525687	+	1.44431i	0.864103	+	0.503315i	$0.167887\pi$
$641$	13.3093	+	36.5671i	0.525687	+	1.44431i	−0.338416	+	0.940997i	$0.609891\pi$
$642$		0			0
$643$	−11.9667	+	2.11005i	−0.471919	+	0.0832121i	−0.404550	−	0.914516i	$-0.632572\pi$
$643$	−11.9667	+	2.11005i	−0.471919	+	0.0832121i	−0.0673696	+	0.997728i	$0.521461\pi$
$644$	−14.9012	+	2.02846i	−0.587188	+	0.0799326i
$645$		0			0
$646$	0.702160	+	0.589183i	0.0276261	+	0.0231811i
$647$	−1.58605	+	2.74713i	−0.0623542	+	0.108001i	−0.895517	−	0.445027i	$-0.853194\pi$
$647$	−1.58605	+	2.74713i	−0.0623542	+	0.108001i	0.833163	+	0.553027i	$0.186528\pi$
$648$		0			0
$649$	−0.715642	+	0.413176i	−0.0280914	+	0.0162186i
$650$	−4.05299	+	1.47517i	−0.158971	+	0.0578608i
$651$		0			0
$652$	−16.4941	+	13.8402i	−0.645958	+	0.542023i
$653$	0.976148	+	1.16333i	0.0381996	+	0.0455246i	0.784806	−	0.619742i	$-0.212763\pi$
$653$	0.976148	+	1.16333i	0.0381996	+	0.0455246i	−0.746606	+	0.665266i	$0.768318\pi$
$654$		0			0
$655$	9.13269	−	3.32403i	0.356844	−	0.129881i
$656$	10.8492			0.423590
$657$		0			0
$658$	47.6624	+	30.0705i	1.85807	+	1.17227i
$659$	37.4050	+	6.59551i	1.45709	+	0.256925i	0.845384	−	0.534159i	$-0.179372\pi$
$659$	37.4050	+	6.59551i	1.45709	+	0.256925i	0.611708	+	0.791083i	$0.290483\pi$
$660$		0			0
$661$	16.6985	+	19.9005i	0.649495	+	0.774038i	0.985838	−	0.167701i	$-0.0536344\pi$
$661$	16.6985	+	19.9005i	0.649495	+	0.774038i	−0.336342	+	0.941740i	$0.609190\pi$
$662$	34.4538	+	41.0604i	1.33909	+	1.59586i
$663$		0			0
$664$	9.08352	+	1.60167i	0.352509	+	0.0621568i
$665$	−0.318908	−	0.201201i	−0.0123667	−	0.00780226i
$666$		0			0
$667$	−4.53718			−0.175680
$668$	15.0991	−	5.49561i	0.584200	−	0.212631i
$669$		0			0
$670$	−23.3002	−	27.7680i	−0.900164	−	1.07277i
$671$	−0.778354	+	0.653117i	−0.0300480	+	0.0252133i
$672$		0			0
$673$	−27.9585	+	10.1760i	−1.07772	+	0.392258i	−0.819058	−	0.573710i	$-0.805503\pi$
$673$	−27.9585	+	10.1760i	−1.07772	+	0.392258i	−0.258661	+	0.965968i	$0.583281\pi$
$674$	−10.2982	+	5.94568i	−0.396672	+	0.229019i
$675$		0			0
$676$	5.32574	−	9.22446i	0.204836	−	0.354787i
$677$	13.8303	+	11.6050i	0.531543	+	0.446018i	0.868634	−	0.495455i	$-0.164998\pi$
$677$	13.8303	+	11.6050i	0.531543	+	0.446018i	−0.337091	+	0.941472i	$0.609443\pi$
$678$		0			0
$679$	27.3887	−	3.72836i	1.05108	−	0.143081i
$680$	−15.7113	+	2.77033i	−0.602501	+	0.106237i
$681$		0			0
$682$	0.686620	+	1.88647i	0.0262920	+	0.0722368i
$683$	−5.53793	+	3.19733i	−0.211903	+	0.122342i	−0.602195	−	0.798349i	$-0.705707\pi$
$683$	−5.53793	+	3.19733i	−0.211903	+	0.122342i	0.390292	+	0.920691i	$0.372374\pi$
$684$		0			0
$685$	5.97996	−	3.45253i	0.228483	−	0.131915i
$686$	−7.20067	−	30.5665i	−0.274923	−	1.16704i
$687$		0			0
$688$	−6.87710	−	39.0019i	−0.262187	−	1.48694i
$689$	1.01970	−	0.855632i	0.0388476	−	0.0325970i
$690$		0			0
$691$	8.16206	+	22.4251i	0.310500	+	0.853091i	0.992556	+	0.121791i	$0.0388637\pi$
$691$	8.16206	+	22.4251i	0.310500	+	0.853091i	−0.682056	+	0.731300i	$0.738914\pi$
$692$	−1.41865	−	2.45718i	−0.0539291	−	0.0934080i
$693$		0			0
$694$	9.01139	−	15.6082i	0.342068	−	0.592478i
$695$	18.8033	+	3.31553i	0.713251	+	0.125765i
$696$		0			0
$697$	11.5205	+	4.19311i	0.436369	+	0.158825i
$698$	−11.7585	−	4.27975i	−0.445066	−	0.161991i
$699$		0			0
$700$	6.16278	−	1.97295i	0.232931	−	0.0745703i
$701$			7.66638i			0.289555i	0.989464	+	0.144778i	$0.0462467\pi$
$701$			7.66638i			0.289555i	−0.989464	+	0.144778i	$0.953753\pi$
$702$		0			0
$703$	0.286764	+	0.165563i	0.0108155	+	0.00624433i
$704$	0.269933	+	0.0475965i	0.0101735	+	0.00179386i
$705$		0			0
$706$	18.1511	+	21.6316i	0.683124	+	0.814116i
$707$	−8.92765	+	6.91300i	−0.335759	+	0.259990i
$708$		0			0
$709$	−2.85710	+	16.2034i	−0.107301	+	0.608533i	0.882976	+	0.469419i	$0.155537\pi$
$709$	−2.85710	+	16.2034i	−0.107301	+	0.608533i	−0.990276	+	0.139114i	$0.955575\pi$
$710$	−3.47188	−	6.01347i	−0.130297	−	0.225682i
$711$		0			0
$712$	−26.3830	−	15.2323i	−0.988746	−	0.570853i
$713$	−10.2627	+	58.2025i	−0.384340	+	2.17970i
$714$		0			0
$715$	−0.165258	−	0.0601488i	−0.00618028	−	0.00224944i
$716$	−16.9562	+	2.98984i	−0.633684	+	0.111736i
$717$		0			0
$718$	22.5229	+	18.8990i	0.840549	+	0.705304i
$719$	−23.3674	+	40.4735i	−0.871457	+	1.50941i	−0.0109676	+	0.999940i	$0.503491\pi$
$719$	−23.3674	+	40.4735i	−0.871457	+	1.50941i	−0.860490	+	0.509468i	$0.829842\pi$
$720$		0			0
$721$	−9.07331	−	5.72441i	−0.337908	−	0.213188i
$722$	20.6984	−	24.6674i	0.770316	−	0.918027i
$723$		0			0
$724$	5.17871	−	14.2284i	0.192465	−	0.528794i
$725$	1.92262	−	0.339010i	0.0714044	−	0.0125905i
$726$		0			0
$727$	−2.15305	−	5.91545i	−0.0798522	−	0.219392i	0.893342	−	0.449378i	$-0.148354\pi$
$727$	−2.15305	−	5.91545i	−0.0798522	−	0.219392i	−0.973194	+	0.229986i	$0.926132\pi$
$728$	−2.45076	+	3.88451i	−0.0908312	+	0.143969i
$729$		0			0
$730$	−10.1002	−	17.4941i	−0.373827	−	0.647487i
$731$	7.77128	−	44.0731i	0.287431	−	1.63010i
$732$		0			0
$733$	4.65518	−	12.7900i	0.171943	−	0.472409i	−0.823550	−	0.567243i	$-0.808010\pi$
$733$	4.65518	−	12.7900i	0.171943	−	0.472409i	0.995493	+	0.0948343i	$0.0302321\pi$
$734$	−7.86881	−	44.6262i	−0.290443	−	1.64718i
$735$		0			0
$736$	−23.0714	−	19.3592i	−0.850424	−	0.713590i
$737$			1.87321i			0.0690006i
$738$		0			0
$739$	25.3280			0.931705			0.465852	−	0.884863i	$-0.345748\pi$
$739$	25.3280			0.931705			0.465852	+	0.884863i	$0.345748\pi$
$740$	4.21316	−	1.53346i	0.154879	−	0.0563712i
$741$		0			0
$742$	−5.18778	+	4.01708i	−0.190449	+	0.147472i
$743$	−7.84457	+	21.5528i	−0.287789	+	0.790695i	0.708586	+	0.705625i	$0.249334\pi$
$743$	−7.84457	+	21.5528i	−0.287789	+	0.790695i	−0.996375	+	0.0850699i	$0.972889\pi$
$744$		0			0
$745$	19.5274	−	23.2719i	0.715430	−	0.852616i
$746$			31.3907i			1.14930i
$747$		0			0
$748$	−0.555439	−	0.320683i	−0.0203089	−	0.0117253i
$749$	18.4808	−	20.3471i	0.675274	−	0.743469i
$750$		0			0
$751$	0.154318	−	0.129489i	0.00563116	−	0.00472510i	−0.639968	−	0.768402i	$-0.721052\pi$
$751$	0.154318	−	0.129489i	0.00563116	−	0.00472510i	0.645599	+	0.763677i	$0.276608\pi$
$752$	10.8728	+	61.6629i	0.396492	+	2.24862i
$753$		0			0
$754$	0.692935	−	0.825808i	0.0252352	−	0.0300741i
$755$	20.2366			0.736486
$756$		0			0
$757$	−32.2011			−1.17037			−0.585184	−	0.810901i	$-0.698978\pi$
$757$	−32.2011			−1.17037			−0.585184	+	0.810901i	$0.698978\pi$
$758$	38.3989	−	45.7620i	1.39471	−	1.66215i
$759$		0			0
$760$	−0.0472048	−	0.267712i	−0.00171230	−	0.00971092i
$761$	40.6980	−	34.1497i	1.47530	−	1.23792i	0.564269	−	0.825591i	$-0.309158\pi$
$761$	40.6980	−	34.1497i	1.47530	−	1.23792i	0.911033	−	0.412334i	$-0.135286\pi$
$762$		0			0
$763$	2.91056	−	13.4074i	0.105369	−	0.485380i
$764$	4.01082	+	2.31565i	0.145106	+	0.0837772i
$765$		0			0
$766$		−	28.3312i		−	1.02365i
$767$	3.71533	−	4.42776i	0.134153	−	0.159877i
$768$		0			0
$769$	2.05952	−	5.65850i	0.0742683	−	0.204051i	−0.897003	−	0.442024i	$-0.854261\pi$
$769$	2.05952	−	5.65850i	0.0742683	−	0.204051i	0.971272	+	0.237973i	$0.0764830\pi$
$770$	0.802313	+	0.328204i	0.0289134	+	0.0118277i
$771$		0			0
$772$	14.5292	−	5.28821i	0.522919	−	0.190327i
$773$	30.0117			1.07944			0.539722	−	0.841843i	$-0.318529\pi$
$773$	30.0117			1.07944			0.539722	+	0.841843i	$0.318529\pi$
$774$		0			0
$775$		−	25.4300i		−	0.913474i
$776$	15.2652	+	12.8090i	0.547987	+	0.459816i
$777$		0			0
$778$	2.79411	+	15.8462i	0.100174	+	0.568113i
$779$	−0.0714481	+	0.196302i	−0.00255989	+	0.00703325i
$780$		0			0
$781$	−0.0623103	+	0.353379i	−0.00222964	+	0.0126449i
$782$	−31.0166	−	53.7224i	−1.10915	−	1.92111i
$783$		0			0
$784$	19.7605	−	28.7557i	0.705731	−	1.02699i
$785$	2.02353	+	5.55961i	0.0722230	+	0.198431i
$786$		0			0
$787$	21.3412	−	3.76304i	0.760733	−	0.134138i	0.220193	−	0.975456i	$-0.429331\pi$
$787$	21.3412	−	3.76304i	0.760733	−	0.134138i	0.540540	+	0.841319i	$0.318220\pi$
$788$	−6.19215	+	17.0128i	−0.220586	+	0.606056i
$789$		0			0
$790$	−0.655466	+	0.781154i	−0.0233204	+	0.0277922i
$791$	36.1238	−	19.0072i	1.28442	−	0.675818i
$792$		0			0
$793$	3.55351	−	6.15486i	0.126189	−	0.218566i
$794$	49.4277	+	41.4747i	1.75412	+	1.47188i
$795$		0			0
$796$	−11.0101	+	1.94138i	−0.390243	+	0.0688103i
$797$	−24.4999	−	8.91724i	−0.867832	−	0.315865i	−0.130543	−	0.991443i	$-0.541672\pi$
$797$	−24.4999	−	8.91724i	−0.867832	−	0.315865i	−0.737289	+	0.675578i	$0.763894\pi$
$798$		0			0
$799$	−12.2866	+	69.6805i	−0.434667	+	2.46512i
$800$	11.2230	+	6.47958i	0.396792	+	0.229088i
$801$		0			0
$802$	−4.76866	−	8.25956i	−0.168387	−	0.291655i
$803$	−0.181271	+	1.02804i	−0.00639690	+	0.0362786i
$804$		0			0
$805$	15.6240	+	20.1773i	0.550674	+	0.711157i
$806$	−9.02603	−	10.7568i	−0.317928	−	0.378892i
$807$		0			0
$808$	−8.01647	−	1.41352i	−0.282018	−	0.0497275i
$809$	−27.9055	−	16.1113i	−0.981106	−	0.566442i	−0.0785018	−	0.996914i	$-0.525014\pi$
$809$	−27.9055	−	16.1113i	−0.981106	−	0.566442i	−0.902604	+	0.430472i	$0.858347\pi$
$810$		0			0
$811$		−	40.6903i		−	1.42883i	−0.699722	−	0.714415i	$-0.746693\pi$
$811$		−	40.6903i		−	1.42883i	0.699722	−	0.714415i	$-0.253307\pi$
$812$	−1.08740	+	1.19721i	−0.0381603	+	0.0420140i
$813$		0			0
$814$	−0.715312	−	0.260352i	−0.0250717	−	0.00912535i
$815$	34.3338	+	12.4965i	1.20266	+	0.437732i
$816$		0			0
$817$	0.750980	+	0.132418i	0.0262735	+	0.00463272i
$818$	−1.87000	+	3.23893i	−0.0653829	+	0.113247i
$819$		0			0
$820$	1.41429	+	2.44962i	0.0493890	+	0.0855443i
$821$	−5.34412	−	14.6829i	−0.186511	−	0.512435i	0.810832	−	0.585279i	$-0.199015\pi$
$821$	−5.34412	−	14.6829i	−0.186511	−	0.512435i	−0.997343	+	0.0728435i	$0.976793\pi$
$822$		0			0
$823$	−17.5657	+	14.7394i	−0.612301	+	0.513782i	−0.895373	−	0.445317i	$-0.853091\pi$
$823$	−17.5657	+	14.7394i	−0.612301	+	0.513782i	0.283072	+	0.959099i	$0.408647\pi$
$824$	−1.34303	−	7.61670i	−0.0467867	−	0.265340i
$825$		0			0
$826$	−19.1552	+	21.0897i	−0.666496	+	0.733803i
$827$	10.7093	−	6.18300i	0.372398	−	0.215004i	−0.302108	−	0.953274i	$-0.597690\pi$
$827$	10.7093	−	6.18300i	0.372398	−	0.215004i	0.674506	+	0.738270i	$0.264357\pi$
$828$		0			0
$829$	−44.8345	+	25.8852i	−1.55717	+	0.899030i	−0.559640	+	0.828736i	$0.689061\pi$
$829$	−44.8345	+	25.8852i	−1.55717	+	0.899030i	−0.997526	+	0.0702945i	$0.977606\pi$
$830$	4.16452	+	11.4419i	0.144553	+	0.397155i
$831$		0			0
$832$	−1.88808	+	0.332919i	−0.0654574	+	0.0115419i
$833$	32.0970	−	22.8977i	1.11209	−	0.793360i
$834$		0			0
$835$	−20.8871	−	17.5264i	−0.722830	−	0.606526i
$836$	0.00546425	−	0.00946436i	0.000188985	−	0.000327332i
$837$		0			0
$838$	18.1106	−	10.4561i	0.625619	−	0.361201i
$839$	21.8923	−	7.96815i	0.755806	−	0.275091i	0.0647595	−	0.997901i	$-0.479372\pi$
$839$	21.8923	−	7.96815i	0.755806	−	0.275091i	0.691047	+	0.722810i	$0.257150\pi$
$840$		0			0
$841$	21.8415	−	18.3272i	0.753155	−	0.631972i
$842$	−19.1528	−	22.8254i	−0.660048	−	0.786615i
$843$		0			0
$844$	16.8943	−	6.14901i	0.581525	−	0.211658i
$845$	−18.0747			−0.621789
$846$		0			0
$847$	13.5309	+	25.7159i	0.464927	+	0.883610i
$848$	−7.17919	−	1.26588i	−0.246534	−	0.0434706i
$849$		0			0
$850$	17.1573	+	20.4472i	0.588490	+	0.701335i
$851$	−14.4047	−	17.1668i	−0.493785	−	0.588471i
$852$		0			0
$853$	−33.4290	−	5.89444i	−1.14459	−	0.201822i	−0.430976	−	0.902363i	$-0.641831\pi$
$853$	−33.4290	−	5.89444i	−1.14459	−	0.201822i	−0.713612	+	0.700541i	$0.752942\pi$
$854$	−18.6922	+	29.6275i	−0.639633	+	1.01383i
$855$		0			0
$856$	19.8162			0.677303
$857$	28.5626	−	10.3959i	0.975680	−	0.355119i	0.195521	−	0.980699i	$-0.437360\pi$
$857$	28.5626	−	10.3959i	0.975680	−	0.355119i	0.780159	+	0.625581i	$0.215138\pi$
$858$		0			0
$859$	−22.8877	−	27.2765i	−0.780919	−	0.930663i	0.218056	−	0.975936i	$-0.430029\pi$
$859$	−22.8877	−	27.2765i	−0.780919	−	0.930663i	−0.998975	+	0.0452734i	$0.985584\pi$
$860$	7.90968	−	6.63701i	0.269718	−	0.226320i
$861$		0			0
$862$	56.8268	−	20.6833i	1.93553	−	0.704475i
$863$	−0.566188	+	0.326889i	−0.0192733	+	0.0111274i	−0.509606	−	0.860408i	$-0.670209\pi$
$863$	−0.566188	+	0.326889i	−0.0192733	+	0.0111274i	0.490332	+	0.871535i	$0.336875\pi$
$864$		0			0
$865$	−2.40734	+	4.16964i	−0.0818521	+	0.141772i
$866$	10.2904	+	8.63468i	0.349683	+	0.293419i
$867$		0			0
$868$	12.8982	+	16.6571i	0.437792	+	0.565377i
$869$	0.0518955	−	0.00915058i	0.00176043	−	0.000310412i
$870$		0			0
$871$	−4.48129	−	12.3122i	−0.151843	−	0.417184i
$872$	8.56571	−	4.94541i	0.290071	−	0.167473i
$873$		0			0
$874$	0.915398	−	0.528505i	0.0309638	−	0.0178770i
$875$	−22.6699	−	20.5905i	−0.766383	−	0.696087i
$876$		0			0
$877$	6.18570	+	35.0809i	0.208876	+	1.18460i	0.891222	+	0.453567i	$0.149849\pi$
$877$	6.18570	+	35.0809i	0.208876	+	1.18460i	−0.682346	+	0.731030i	$0.739040\pi$
$878$	21.8116	−	18.3021i	0.736104	−	0.617665i
$879$		0			0
$880$	0.329406	+	0.905035i	0.0111043	+	0.0305087i
$881$	23.1789	+	40.1470i	0.780916	+	1.35259i	0.931409	+	0.363975i	$0.118581\pi$
$881$	23.1789	+	40.1470i	0.780916	+	1.35259i	−0.150492	+	0.988611i	$0.548086\pi$
$882$		0			0
$883$	7.99748	−	13.8520i	0.269137	−	0.466158i	−0.699503	−	0.714630i	$-0.746595\pi$
$883$	7.99748	−	13.8520i	0.269137	−	0.466158i	0.968639	+	0.248472i	$0.0799284\pi$
$884$	4.41796	+	0.779005i	0.148592	+	0.0262008i
$885$		0			0
$886$	27.6523	+	10.0646i	0.928999	+	0.338128i
$887$	−20.8828	−	7.60073i	−0.701177	−	0.255207i	−0.0332635	−	0.999447i	$-0.510590\pi$
$887$	−20.8828	−	7.60073i	−0.701177	−	0.255207i	−0.667913	+	0.744239i	$0.732812\pi$
$888$		0			0
$889$	−0.634311	+	2.92193i	−0.0212741	+	0.0979983i
$890$		−	40.2166i		−	1.34806i
$891$		0			0
$892$	−14.9141	−	8.61063i	−0.499359	−	0.288305i
$893$	−1.18732	−	0.209356i	−0.0397320	−	0.00700583i
$894$		0			0
$895$	18.7805	+	22.3817i	0.627762	+	0.748137i
$896$	33.6754	−	4.58416i	1.12502	−	0.153146i
$897$		0			0
$898$	2.25441	−	12.7854i	0.0752305	−	0.426653i
$899$	3.17799	+	5.50444i	0.105992	+	0.183583i
$900$		0			0
$901$	−7.13414	−	4.11890i	−0.237673	−	0.137220i
$902$	0.0833923	−	0.472941i	0.00277666	−	0.0157472i
$903$		0			0
$904$	27.6528	+	10.0648i	0.919718	+	0.334750i
$905$	−25.3036	+	4.46171i	−0.841121	+	0.148312i
$906$		0			0
$907$	17.5317	+	14.7108i	0.582130	+	0.488465i	0.885646	−	0.464361i	$-0.153716\pi$
$907$	17.5317	+	14.7108i	0.582130	+	0.488465i	−0.303516	+	0.952826i	$0.598160\pi$
$908$	0.139438	−	0.241513i	0.00462740	−	0.00801490i
$909$		0			0
$910$	−6.05861	−	0.237842i	−0.200841	−	0.00788439i
$911$	18.2077	−	21.6991i	0.603248	−	0.718923i	−0.374846	−	0.927087i	$-0.622304\pi$
$911$	18.2077	−	21.6991i	0.603248	−	0.718923i	0.978094	+	0.208164i	$0.0667488\pi$
$912$		0			0
$913$	0.215209	−	0.591282i	0.00712238	−	0.0195686i
$914$	49.6767	−	8.75934i	1.64316	−	0.289733i
$915$		0			0
$916$	−2.59217	−	7.12192i	−0.0856476	−	0.235315i
$917$	−17.3024	−	0.679237i	−0.571374	−	0.0224304i
$918$		0			0
$919$	0.486170	+	0.842071i	0.0160373	+	0.0277774i	0.873933	−	0.486047i	$-0.161562\pi$
$919$	0.486170	+	0.842071i	0.0160373	+	0.0277774i	−0.857895	+	0.513824i	$0.828228\pi$
$920$	−3.19468	+	18.1180i	−0.105326	+	0.597331i
$921$		0			0
$922$	−0.274057	+	0.752965i	−0.00902558	+	0.0247976i
$923$	−0.435837	−	2.47176i	−0.0143458	−	0.0813588i
$924$		0			0
$925$	7.38662	+	6.19811i	0.242871	+	0.203793i
$926$		−	4.37230i		−	0.143683i
$927$		0			0
$928$	−3.23901			−0.106326
$929$	2.35873	−	0.858508i	0.0773875	−	0.0281667i	−0.303036	−	0.952979i	$-0.598000\pi$
$929$	2.35873	−	0.858508i	0.0773875	−	0.0281667i	0.380424	+	0.924812i	$0.375778\pi$
$930$		0			0
$931$	0.390164	+	0.546913i	0.0127871	+	0.0179244i
$932$	2.19771	−	6.03817i	0.0719885	−	0.197787i
$933$		0			0
$934$	5.78884	−	6.89887i	0.189417	−	0.225738i
$935$			1.08835i			0.0355927i
$936$		0			0
$937$	6.98943	+	4.03535i	0.228335	+	0.131829i	0.609804	−	0.792553i	$-0.291248\pi$
$937$	6.98943	+	4.03535i	0.228335	+	0.131829i	−0.381469	+	0.924382i	$0.624582\pi$
$938$	19.6911	+	61.5079i	0.642937	+	2.00830i
$939$		0			0
$940$	−12.5054	+	10.4933i	−0.407881	+	0.342252i
$941$	−8.17252	−	46.3487i	−0.266417	−	1.51092i	−0.764971	−	0.644065i	$-0.777247\pi$
$941$	−8.17252	−	46.3487i	−0.266417	−	1.51092i	0.498554	−	0.866858i	$-0.333864\pi$
$942$		0			0
$943$	9.08759	−	10.8302i	0.295933	−	0.352679i
$944$	−31.6544			−1.03026
$945$		0			0
$946$	−1.75305			−0.0569964
$947$	23.2570	−	27.7166i	0.755749	−	0.900667i	−0.241822	−	0.970321i	$-0.577745\pi$
$947$	23.2570	−	27.7166i	0.755749	−	0.900667i	0.997571	+	0.0696536i	$0.0221894\pi$
$948$		0			0
$949$	−1.26792	−	7.19073i	−0.0411584	−	0.233421i
$950$	−0.348409	+	0.292350i	−0.0113039	+	0.00948509i
$951$		0			0
$952$	27.7772	+	6.03005i	0.900263	+	0.195435i
$953$	−41.0448	−	23.6972i	−1.32957	−	0.767629i	−0.344339	−	0.938845i	$-0.611897\pi$
$953$	−41.0448	−	23.6972i	−1.32957	−	0.767629i	−0.985233	+	0.171216i	$0.945230\pi$
$954$		0			0
$955$		−	7.85893i		−	0.254309i
$956$	2.64681	−	3.15435i	0.0856039	−	0.102019i
$957$		0			0
$958$	−19.1016	+	52.4811i	−0.617143	+	1.69559i
$959$	−12.1901	+	1.65941i	−0.393639	+	0.0535852i
$960$		0			0
$961$	48.6682	−	17.7138i	1.56994	−	0.571413i
$962$	5.32444			0.171667
$963$		0			0
$964$			5.80324i			0.186910i
$965$	−20.0989	−	16.8650i	−0.647007	−	0.542903i
$966$		0			0
$967$	−9.82570	−	55.7243i	−0.315973	−	1.79197i	−0.566710	−	0.823918i	$-0.691784\pi$
$967$	−9.82570	−	55.7243i	−0.315973	−	1.79197i	0.250736	−	0.968055i	$-0.419327\pi$
$968$	−7.16496	+	19.6856i	−0.230290	+	0.632718i
$969$		0			0
$970$	−4.56802	+	25.9066i	−0.146670	+	0.831809i
$971$	−3.04373	−	5.27190i	−0.0976780	−	0.169183i	0.813045	−	0.582201i	$-0.197808\pi$
$971$	−3.04373	−	5.27190i	−0.0976780	−	0.169183i	−0.910723	+	0.413017i	$0.864475\pi$
$972$		0			0
$973$	−28.7706	−	18.1516i	−0.922344	−	0.581913i
$974$	14.0580	+	38.6241i	0.450448	+	1.23760i
$975$		0			0
$976$	−38.3304	+	6.75868i	−1.22693	+	0.216340i
$977$	−5.88779	+	16.1766i	−0.188367	+	0.517535i	−0.997545	−	0.0700293i	$-0.977691\pi$
$977$	−5.88779	+	16.1766i	−0.188367	+	0.517535i	0.809178	+	0.587564i	$0.199913\pi$
$978$		0			0
$979$	−1.33588	+	1.59204i	−0.0426950	+	0.0508819i
$980$	9.06865	+	0.713113i	0.289687	+	0.0227796i
$981$		0			0
$982$	9.77699	−	16.9342i	0.311996	−	0.540393i
$983$	8.63928	+	7.24922i	0.275550	+	0.231214i	0.770081	−	0.637946i	$-0.220216\pi$
$983$	8.63928	+	7.24922i	0.275550	+	0.231214i	−0.494531	+	0.869160i	$0.664660\pi$
$984$		0			0
$985$	30.2554	−	5.33484i	0.964017	−	0.169982i
$986$	−6.26906	−	2.28175i	−0.199647	−	0.0726657i
$987$		0			0
$988$	−0.0132738	+	0.0752794i	−0.000422296	+	0.00239496i
$989$	−44.6940	−	25.8041i	−1.42119	−	0.820523i
$990$		0			0
$991$	−17.6534	−	30.5766i	−0.560780	−	0.971299i	−0.997429	−	0.0716671i	$-0.977168\pi$
$991$	−17.6534	−	30.5766i	−0.560780	−	0.971299i	0.436649	−	0.899632i	$-0.356165\pi$
$992$	−7.32633	+	41.5497i	−0.232611	+	1.31920i
$993$		0			0
$994$	1.66871	+	12.2584i	0.0529283	+	0.388813i
$995$	12.1946	+	14.5330i	0.386596	+	0.460727i
$996$		0			0
$997$	1.60718	+	0.283390i	0.0509001	+	0.00897505i	0.199040	−	0.979991i	$-0.436218\pi$
$997$	1.60718	+	0.283390i	0.0509001	+	0.00897505i	−0.148140	+	0.988966i	$0.547329\pi$
$998$	7.49288	+	4.32601i	0.237183	+	0.136938i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.18		132
3.2	odd	2		189.2.ba.a.101.5	✓	132
7.5	odd	6		567.2.bd.a.467.5		132
21.5	even	6		189.2.bd.a.47.18	yes	132
27.4	even	9		189.2.bd.a.185.18	yes	132
27.23	odd	18		567.2.bd.a.17.5		132
189.131	even	18	inner	567.2.ba.a.341.18		132
189.166	odd	18		189.2.ba.a.131.5	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.5	✓	132	3.2	odd	2
189.2.ba.a.131.5	yes	132	189.166	odd	18
189.2.bd.a.47.18	yes	132	21.5	even	6
189.2.bd.a.185.18	yes	132	27.4	even	9
567.2.ba.a.143.18		132	1.1	even	1	trivial
567.2.ba.a.341.18		132	189.131	even	18	inner
567.2.bd.a.17.5		132	27.23	odd	18
567.2.bd.a.467.5		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.08992 - 1.29892i) q^{2} +(-0.151961 - 0.861812i) q^{4} +(-1.13756 + 0.954530i) q^{5} +(2.51978 - 0.806679i) q^{7} +(1.65184 + 0.953692i) q^{8} +2.51796i q^{10} +(0.0836396 - 0.0996778i) q^{11} +(-0.311287 + 0.855253i) q^{13} +(1.69855 - 4.15219i) q^{14} +(4.68381 - 1.70477i) q^{16} +5.63249 q^{17} +0.0959743i q^{19} +(0.995491 + 0.835316i) q^{20} +(-0.0383126 - 0.217282i) q^{22} +(2.22151 - 6.10356i) q^{23} +(-0.485315 + 2.75236i) q^{25} +(0.771624 + 1.33649i) q^{26} +(-1.07811 - 2.04899i) q^{28} +(-0.238914 - 0.656410i) q^{29} +(-8.96076 + 1.58002i) q^{31} +(1.58590 - 4.35722i) q^{32} +(6.13896 - 7.31613i) q^{34} +(-2.09641 + 3.32285i) q^{35} +(1.72508 - 2.98792i) q^{37} +(0.124663 + 0.104604i) q^{38} +(-2.78941 + 0.491848i) q^{40} +(2.04536 + 0.744450i) q^{41} +(1.37972 - 7.82480i) q^{43} +(-0.0986135 - 0.0569345i) q^{44} +(-5.50674 - 9.53795i) q^{46} +(-2.18137 + 12.3712i) q^{47} +(5.69854 - 4.06530i) q^{49} +(3.04613 + 3.63023i) q^{50} +(0.784371 + 0.138306i) q^{52} +(-1.26661 - 0.731275i) q^{53} +0.193227i q^{55} +(4.93160 + 1.07058i) q^{56} +(-1.11302 - 0.405105i) q^{58} +(-5.96770 - 2.17206i) q^{59} +(-7.69007 - 1.35597i) q^{61} +(-7.71419 + 13.3614i) q^{62} +(1.05325 + 1.82428i) q^{64} +(-0.462256 - 1.27004i) q^{65} +(-11.0280 + 9.25358i) q^{67} +(-0.855917 - 4.85415i) q^{68} +(2.03119 + 6.34470i) q^{70} +(-2.38823 + 1.37884i) q^{71} +(-6.94774 + 4.01128i) q^{73} +(-2.00086 - 5.49732i) q^{74} +(0.0827118 - 0.0145843i) q^{76} +(0.130345 - 0.318636i) q^{77} +(0.310233 + 0.260316i) q^{79} +(-3.70088 + 6.41012i) q^{80} +(3.19626 - 1.84536i) q^{82} +(4.54412 - 1.65393i) q^{83} +(-6.40732 + 5.37638i) q^{85} +(-8.65997 - 10.3205i) q^{86} +(0.233222 - 0.0848857i) q^{88} -15.9719 q^{89} +(-0.0944582 + 2.40615i) q^{91} +(-5.59770 - 0.987026i) q^{92} +(13.6916 + 16.3170i) q^{94} +(-0.0916104 - 0.109177i) q^{95} +(10.2887 + 1.81418i) q^{97} +(0.930470 - 11.8328i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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