LMFDB - Embedded newform 297.2.t.a.233.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			233.9
Character	$\chi$	$=$	297.233
Dual form			297.2.t.a.116.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.41844 - 0.514054i) q^{2} +(3.75749 - 1.67294i) q^{4} +(-0.425128 + 2.00007i) q^{5} +(1.07838 + 0.113342i) q^{7} +(4.22672 - 3.07089i) q^{8} +5.05558i q^{10} +(-3.29101 - 0.411437i) q^{11} +(-0.826275 + 0.743982i) q^{13} +(2.66625 - 0.280234i) q^{14} +(3.13907 - 3.48629i) q^{16} +(-2.03372 - 6.25916i) q^{17} +(-4.19112 - 5.76858i) q^{19} +(1.74859 + 8.22645i) q^{20} +(-8.17059 + 0.696721i) q^{22} +(4.70965 + 2.71912i) q^{23} +(0.748176 + 0.333109i) q^{25} +(-1.61585 + 2.22402i) q^{26} +(4.24160 - 1.37818i) q^{28} +(-0.774458 + 7.36848i) q^{29} +(-0.793766 - 0.881566i) q^{31} +(0.574983 - 0.995900i) q^{32} +(-8.13598 - 14.0919i) q^{34} +(-0.685140 + 2.10865i) q^{35} +(0.780793 + 0.567279i) q^{37} +(-13.1013 - 11.7965i) q^{38} +(4.34511 + 9.75927i) q^{40} +(0.115443 + 1.09836i) q^{41} +(-4.42893 + 2.55705i) q^{43} +(-13.0542 + 3.95969i) q^{44} +(12.7877 + 4.15499i) q^{46} +(1.74699 - 3.92381i) q^{47} +(-5.69698 - 1.21093i) q^{49} +(1.98065 + 0.421000i) q^{50} +(-1.86008 + 4.17781i) q^{52} +(10.3556 + 3.36474i) q^{53} +(2.22200 - 6.40733i) q^{55} +(4.90606 - 2.83251i) q^{56} +(1.91482 + 18.2183i) q^{58} +(0.897232 + 2.01522i) q^{59} +(4.31301 + 3.88345i) q^{61} +(-2.37284 - 1.72397i) q^{62} +(-2.02075 + 6.21923i) q^{64} +(-1.13674 - 1.96890i) q^{65} +(0.496739 - 0.860378i) q^{67} +(-18.1129 - 20.1164i) q^{68} +(-0.573009 + 5.45182i) q^{70} +(6.12170 - 1.98906i) q^{71} +(-0.486222 + 0.669227i) q^{73} +(2.17991 + 0.970558i) q^{74} +(-25.3986 - 14.6639i) q^{76} +(-3.50231 - 0.816693i) q^{77} +(-1.26766 - 5.96388i) q^{79} +(5.63833 + 7.76049i) q^{80} +(0.843809 + 2.59698i) q^{82} +(-1.46775 + 1.63010i) q^{83} +(13.3834 - 1.40665i) q^{85} +(-9.39663 + 8.46076i) q^{86} +(-15.1736 + 8.36730i) q^{88} -6.19738i q^{89} +(-0.975360 + 0.708641i) q^{91} +(22.2454 + 2.33808i) q^{92} +(2.20794 - 10.3875i) q^{94} +(13.3193 - 5.93015i) q^{95} +(9.31442 - 1.97984i) q^{97} -14.4003 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	2.41844	−	0.514054i	1.71009	−	0.363491i	0.754072	−	0.656792i	$-0.228087\pi$
$2$	2.41844	−	0.514054i	1.71009	−	0.363491i	0.956020	+	0.293301i	$0.0947538\pi$
$3$		0			0
$3$		0			0
$4$	3.75749	−	1.67294i	1.87874	−	0.836470i
$5$	−0.425128	+	2.00007i	−0.190123	+	0.894459i	0.774857	+	0.632136i	$0.217822\pi$
$5$	−0.425128	+	2.00007i	−0.190123	+	0.894459i	−0.964980	+	0.262323i	$0.915512\pi$
$6$		0			0
$7$	1.07838	+	0.113342i	0.407588	+	0.0428392i	0.306104	−	0.951998i	$-0.400974\pi$
$7$	1.07838	+	0.113342i	0.407588	+	0.0428392i	0.101484	+	0.994837i	$0.467641\pi$
$8$	4.22672	−	3.07089i	1.49437	−	1.08572i
$9$		0			0
$10$			5.05558i			1.59872i
$11$	−3.29101	−	0.411437i	−0.992276	−	0.124053i
$11$	−3.29101	−	0.411437i	−0.992276	−	0.124053i
$12$		0			0
$13$	−0.826275	+	0.743982i	−0.229168	+	0.206343i	−0.775713	−	0.631086i	$-0.782609\pi$
$13$	−0.826275	+	0.743982i	−0.229168	+	0.206343i	0.546545	+	0.837430i	$0.315943\pi$
$14$	2.66625	−	0.280234i	0.712585	−	0.0748957i
$15$		0			0
$16$	3.13907	−	3.48629i	0.784768	−	0.871573i
$17$	−2.03372	−	6.25916i	−0.493251	−	1.51807i	−0.819665	−	0.572843i	$-0.805841\pi$
$17$	−2.03372	−	6.25916i	−0.493251	−	1.51807i	0.326415	−	0.945227i	$-0.394159\pi$
$18$		0			0
$19$	−4.19112	−	5.76858i	−0.961508	−	1.32340i	−0.946221	−	0.323520i	$-0.895134\pi$
$19$	−4.19112	−	5.76858i	−0.961508	−	1.32340i	−0.0152869	−	0.999883i	$-0.504866\pi$
$20$	1.74859	+	8.22645i	0.390996	+	1.83949i
$21$		0			0
$22$	−8.17059	+	0.696721i	−1.74197	+	0.148541i
$23$	4.70965	+	2.71912i	0.982029	+	0.566975i	0.902882	−	0.429888i	$-0.141447\pi$
$23$	4.70965	+	2.71912i	0.982029	+	0.566975i	0.0791471	+	0.996863i	$0.474780\pi$
$24$		0			0
$25$	0.748176	+	0.333109i	0.149635	+	0.0666218i
$26$	−1.61585	+	2.22402i	−0.316894	+	0.436166i
$27$		0			0
$28$	4.24160	−	1.37818i	0.801587	−	0.260451i
$29$	−0.774458	+	7.36848i	−0.143813	+	1.36829i	0.649909	+	0.760012i	$0.274807\pi$
$29$	−0.774458	+	7.36848i	−0.143813	+	1.36829i	−0.793723	+	0.608280i	$0.791860\pi$
$30$		0			0
$31$	−0.793766	−	0.881566i	−0.142565	−	0.158334i	0.667634	−	0.744490i	$-0.267307\pi$
$31$	−0.793766	−	0.881566i	−0.142565	−	0.158334i	−0.810198	+	0.586156i	$0.800641\pi$
$32$	0.574983	−	0.995900i	0.101644	−	0.176052i
$33$		0			0
$34$	−8.13598	−	14.0919i	−1.39531	−	2.41675i
$35$	−0.685140	+	2.10865i	−0.115810	+	0.356426i
$36$		0			0
$37$	0.780793	+	0.567279i	0.128362	+	0.0932602i	0.650114	−	0.759837i	$-0.274721\pi$
$37$	0.780793	+	0.567279i	0.128362	+	0.0932602i	−0.521752	+	0.853097i	$0.674721\pi$
$38$	−13.1013	−	11.7965i	−2.12531	−	1.91364i
$39$		0			0
$40$	4.34511	+	9.75927i	0.687022	+	1.54308i
$41$	0.115443	+	1.09836i	0.0180291	+	0.171536i	0.999831	−	0.0183712i	$-0.00584807\pi$
$41$	0.115443	+	1.09836i	0.0180291	+	0.171536i	−0.981802	+	0.189907i	$0.939181\pi$
$42$		0			0
$43$	−4.42893	+	2.55705i	−0.675406	+	0.389946i	−0.798122	−	0.602496i	$-0.794173\pi$
$43$	−4.42893	+	2.55705i	−0.675406	+	0.389946i	0.122716	+	0.992442i	$0.460840\pi$
$44$	−13.0542	+	3.95969i	−1.96800	+	0.596945i
$45$		0			0
$46$	12.7877	+	4.15499i	1.88545	+	0.612620i
$47$	1.74699	−	3.92381i	0.254825	−	0.572347i	−0.740153	−	0.672439i	$-0.765247\pi$
$47$	1.74699	−	3.92381i	0.254825	−	0.572347i	0.994978	+	0.100091i	$0.0319135\pi$
$48$		0			0
$49$	−5.69698	−	1.21093i	−0.813855	−	0.172990i
$50$	1.98065	+	0.421000i	0.280106	+	0.0595384i
$51$		0			0
$52$	−1.86008	+	4.17781i	−0.257947	+	0.579358i
$53$	10.3556	+	3.36474i	1.42245	+	0.462183i	0.916380	−	0.400308i	$-0.131097\pi$
$53$	10.3556	+	3.36474i	1.42245	+	0.462183i	0.506072	+	0.862491i	$0.331097\pi$
$54$		0			0
$55$	2.22200	−	6.40733i	0.299615	−	0.863965i
$56$	4.90606	−	2.83251i	0.655600	−	0.378511i
$57$		0			0
$58$	1.91482	+	18.2183i	0.251428	+	2.39218i
$59$	0.897232	+	2.01522i	0.116810	+	0.262359i	0.962483	−	0.271342i	$-0.0874675\pi$
$59$	0.897232	+	2.01522i	0.116810	+	0.262359i	−0.845673	+	0.533701i	$0.820801\pi$
$60$		0			0
$61$	4.31301	+	3.88345i	0.552225	+	0.497225i	0.897343	−	0.441334i	$-0.145495\pi$
$61$	4.31301	+	3.88345i	0.552225	+	0.497225i	−0.345118	+	0.938559i	$0.612161\pi$
$62$	−2.37284	−	1.72397i	−0.301352	−	0.218945i
$63$		0			0
$64$	−2.02075	+	6.21923i	−0.252594	+	0.777404i
$65$	−1.13674	−	1.96890i	−0.140996	−	0.244212i
$66$		0			0
$67$	0.496739	−	0.860378i	0.0606864	−	0.105112i	−0.834086	−	0.551634i	$-0.814004\pi$
$67$	0.496739	−	0.860378i	0.0606864	−	0.105112i	0.894772	+	0.446523i	$0.147338\pi$
$68$	−18.1129	−	20.1164i	−2.19651	−	2.43947i
$69$		0			0
$70$	−0.573009	+	5.45182i	−0.0684877	+	0.651617i
$71$	6.12170	−	1.98906i	0.726512	−	0.236058i	0.0776676	−	0.996979i	$-0.475253\pi$
$71$	6.12170	−	1.98906i	0.726512	−	0.236058i	0.648844	+	0.760921i	$0.275253\pi$
$72$		0			0
$73$	−0.486222	+	0.669227i	−0.0569080	+	0.0783271i	−0.836523	−	0.547933i	$-0.815415\pi$
$73$	−0.486222	+	0.669227i	−0.0569080	+	0.0783271i	0.779615	+	0.626260i	$0.215415\pi$
$74$	2.17991	+	0.970558i	0.253409	+	0.112825i
$75$		0			0
$76$	−25.3986	−	14.6639i	−2.91341	−	1.68206i
$77$	−3.50231	−	0.816693i	−0.399125	−	0.0930708i
$78$		0			0
$79$	−1.26766	−	5.96388i	−0.142623	−	0.670989i	−0.990124	−	0.140195i	$-0.955227\pi$
$79$	−1.26766	−	5.96388i	−0.142623	−	0.670989i	0.847501	−	0.530794i	$-0.178106\pi$
$80$	5.63833	+	7.76049i	0.630384	+	0.867649i
$81$		0			0
$82$	0.843809	+	2.59698i	0.0931831	+	0.286788i
$83$	−1.46775	+	1.63010i	−0.161106	+	0.178927i	−0.818293	−	0.574801i	$-0.805080\pi$
$83$	−1.46775	+	1.63010i	−0.161106	+	0.178927i	0.657187	+	0.753728i	$0.271746\pi$
$84$		0			0
$85$	13.3834	−	1.40665i	1.45163	−	0.152572i
$86$	−9.39663	+	8.46076i	−1.01326	+	0.912347i
$87$		0			0
$88$	−15.1736	+	8.36730i	−1.61752	+	0.891957i
$89$		−	6.19738i		−	0.656921i	−0.944518	−	0.328460i	$-0.893470\pi$
$89$		−	6.19738i		−	0.656921i	0.944518	−	0.328460i	$-0.106530\pi$
$90$		0			0
$91$	−0.975360	+	0.708641i	−0.102246	+	0.0742857i
$92$	22.2454	+	2.33808i	2.31924	+	0.243762i
$93$		0			0
$94$	2.20794	−	10.3875i	0.227732	−	1.07139i
$95$	13.3193	−	5.93015i	1.36653	−	0.608420i
$96$		0			0
$97$	9.31442	−	1.97984i	0.945736	−	0.201022i	0.290866	−	0.956764i	$-0.406057\pi$
$97$	9.31442	−	1.97984i	0.945736	−	0.201022i	0.654870	+	0.755742i	$0.272723\pi$
$98$	−14.4003			−1.45465
$99$		0			0
$100$	3.36853			0.336853
$101$	−3.48402	+	0.740552i	−0.346673	+	0.0736876i	−0.377958	−	0.925823i	$-0.623374\pi$
$101$	−3.48402	+	0.740552i	−0.346673	+	0.0736876i	0.0312846	+	0.999511i	$0.490040\pi$
$102$		0			0
$103$	4.81204	−	2.14246i	0.474145	−	0.211103i	−0.155730	−	0.987800i	$-0.549773\pi$
$103$	4.81204	−	2.14246i	0.474145	−	0.211103i	0.629875	+	0.776697i	$0.283106\pi$
$104$	−1.20775	+	5.68201i	−0.118429	+	0.557167i
$105$		0			0
$106$	26.7740	+	2.81406i	2.60052	+	0.273326i
$107$	8.88743	−	6.45709i	0.859180	−	0.624231i	−0.0684817	−	0.997652i	$-0.521815\pi$
$107$	8.88743	−	6.45709i	0.859180	−	0.624231i	0.927662	+	0.373422i	$0.121815\pi$
$108$		0			0
$109$			2.65252i			0.254065i	0.991899	+	0.127033i	$0.0405453\pi$
$109$			2.65252i			0.254065i	−0.991899	+	0.127033i	$0.959455\pi$
$110$	2.08006	−	16.6380i	0.198326	−	1.58637i
$111$		0			0
$112$	3.78025	−	3.40375i	0.357200	−	0.321624i
$113$	−9.21722	+	0.968769i	−0.867083	+	0.0911341i	−0.527615	−	0.849484i	$-0.676914\pi$
$113$	−9.21722	+	0.968769i	−0.867083	+	0.0911341i	−0.339468	+	0.940618i	$0.610247\pi$
$114$		0			0
$115$	−7.44063	+	8.26366i	−0.693842	+	0.770590i
$116$	9.41701	+	28.9826i	0.874347	+	2.69096i
$117$		0			0
$118$	3.20583	+	4.41245i	0.295121	+	0.406199i
$119$	−1.48370	−	6.98024i	−0.136010	−	0.639877i
$120$		0			0
$121$	10.6614	+	2.70809i	0.969222	+	0.246190i
$122$	12.4270	+	7.17476i	1.12509	+	0.649572i
$123$		0			0
$124$	−4.45737	−	1.98455i	−0.400284	−	0.178218i
$125$	−6.99369	+	9.62600i	−0.625535	+	0.860975i
$126$		0			0
$127$	−11.0254	+	3.58238i	−0.978349	+	0.317885i	−0.754182	−	0.656666i	$-0.771966\pi$
$127$	−11.0254	+	3.58238i	−0.978349	+	0.317885i	−0.224167	+	0.974551i	$0.571966\pi$
$128$	−1.93044	+	18.3669i	−0.170629	+	1.62342i
$129$		0			0
$130$	−3.76126	−	4.17730i	−0.329884	−	0.366374i
$131$	5.18051	−	8.97291i	0.452624	−	0.783967i	−0.545924	−	0.837834i	$-0.683821\pi$
$131$	5.18051	−	8.97291i	0.452624	−	0.783967i	0.998548	+	0.0538672i	$0.0171548\pi$
$132$		0			0
$133$	−3.86578	−	6.69573i	−0.335206	−	0.580593i
$134$	0.759051	−	2.33612i	0.0655720	−	0.201810i
$135$		0			0
$136$	−27.8172	−	20.2104i	−2.38531	−	1.73303i
$137$	0.217988	+	0.196277i	0.0186240	+	0.0167691i	0.678390	−	0.734702i	$-0.262678\pi$
$137$	0.217988	+	0.196277i	0.0186240	+	0.0167691i	−0.659766	+	0.751471i	$0.729345\pi$
$138$		0			0
$139$	0.847460	+	1.90343i	0.0718806	+	0.161447i	0.945912	−	0.324422i	$-0.105170\pi$
$139$	0.847460	+	1.90343i	0.0718806	+	0.161447i	−0.874032	+	0.485869i	$0.838503\pi$
$140$	0.953233	+	9.06940i	0.0805629	+	0.766505i
$141$		0			0
$142$	13.7824	−	7.95730i	1.15660	−	0.667762i
$143$	3.02538	−	2.10849i	0.252995	−	0.176321i
$144$		0			0
$145$	−14.4082	−	4.68152i	−1.19654	−	0.388779i
$146$	−0.831878	+	1.86843i	−0.0688467	+	0.154632i
$147$		0			0
$148$	3.88284	+	0.825324i	0.319168	+	0.0678412i
$149$	−16.3836	−	3.48245i	−1.34220	−	0.285293i	−0.519841	−	0.854263i	$-0.674009\pi$
$149$	−16.3836	−	3.48245i	−1.34220	−	0.285293i	−0.822358	+	0.568970i	$0.807342\pi$
$150$		0			0
$151$	3.94131	−	8.85234i	0.320740	−	0.720393i	−0.679168	−	0.733983i	$-0.737659\pi$
$151$	3.94131	−	8.85234i	0.320740	−	0.720393i	0.999908	+	0.0135899i	$0.00432593\pi$
$152$	−35.4294	−	11.5117i	−2.87370	−	0.933723i
$153$		0			0
$154$	−8.88994	−	0.174742i	−0.716371	−	0.0140811i
$155$	2.10065	−	1.21281i	0.168728	−	0.0974152i
$156$		0			0
$157$	−0.308374	−	2.93399i	−0.0246110	−	0.234158i	−0.999912	−	0.0132772i	$-0.995774\pi$
$157$	−0.308374	−	2.93399i	−0.0246110	−	0.234158i	0.975301	−	0.220880i	$-0.0708931\pi$
$158$	−6.13152	−	13.7716i	−0.487797	−	1.09561i
$159$		0			0
$160$	1.74743	+	1.57339i	0.138146	+	0.124388i
$161$	4.77058	+	3.46603i	0.375975	+	0.273162i
$162$		0			0
$163$	6.82701	−	21.0114i	0.534733	−	1.64574i	−0.209493	−	0.977810i	$-0.567181\pi$
$163$	6.82701	−	21.0114i	0.534733	−	1.64574i	0.744226	−	0.667928i	$-0.232819\pi$
$164$	2.27127	+	3.93396i	0.177357	+	0.307190i
$165$		0			0
$166$	−2.71170	+	4.69680i	−0.210469	+	0.364542i
$167$	7.79845	+	8.66106i	0.603462	+	0.670213i	0.965032	−	0.262132i	$-0.0844257\pi$
$167$	7.79845	+	8.66106i	0.603462	+	0.670213i	−0.361570	+	0.932345i	$0.617759\pi$
$168$		0			0
$169$	−1.22965	+	11.6993i	−0.0945883	+	0.899948i
$170$	31.6437	−	10.2817i	2.42696	−	0.788567i
$171$		0			0
$172$	−12.3639	+	17.0174i	−0.942736	+	1.29756i
$173$	−10.9952	−	4.89540i	−0.835953	−	0.372190i	−0.0563092	−	0.998413i	$-0.517933\pi$
$173$	−10.9952	−	4.89540i	−0.835953	−	0.372190i	−0.779644	+	0.626223i	$0.784600\pi$
$174$		0			0
$175$	0.769060	+	0.444017i	0.0581354	+	0.0335645i
$176$	−11.7651	+	10.1819i	−0.886828	+	0.767488i
$177$		0			0
$178$	−3.18579	−	14.9880i	−0.238785	−	1.12340i
$179$	1.69252	+	2.32955i	0.126505	+	0.174119i	0.867571	−	0.497313i	$-0.165680\pi$
$179$	1.69252	+	2.32955i	0.126505	+	0.174119i	−0.741067	+	0.671431i	$0.765680\pi$
$180$		0			0
$181$	7.23838	+	22.2775i	0.538025	+	1.65587i	0.737021	+	0.675870i	$0.236232\pi$
$181$	7.23838	+	22.2775i	0.538025	+	1.65587i	−0.198996	+	0.980000i	$0.563768\pi$
$182$	−1.99457	+	2.21519i	−0.147847	+	0.164201i
$183$		0			0
$184$	28.2565	−	2.96988i	2.08310	−	0.218942i
$185$	−1.46654	+	1.32048i	−0.107822	+	0.0970833i
$186$		0			0
$187$	4.11775	+	21.4357i	0.301119	+	1.56753i
$188$		−	17.6663i		−	1.28845i
$189$		0			0
$190$	29.1635	−	21.1885i	2.11574	−	1.53718i
$191$	−0.815807	−	0.0857448i	−0.0590297	−	0.00620428i	0.0749675	−	0.997186i	$-0.476115\pi$
$191$	−0.815807	−	0.0857448i	−0.0590297	−	0.00620428i	−0.133997	+	0.990982i	$0.542781\pi$
$192$		0			0
$193$	−2.96036	+	13.9274i	−0.213091	+	1.00252i	0.733403	+	0.679794i	$0.237931\pi$
$193$	−2.96036	+	13.9274i	−0.213091	+	1.00252i	−0.946494	+	0.322721i	$0.895402\pi$
$194$	21.5086	−	9.57623i	1.54422	−	0.687533i
$195$		0			0
$196$	−23.4322	+	4.98066i	−1.67373	+	0.355761i
$197$	−13.4127			−0.955618			−0.477809	−	0.878464i	$-0.658569\pi$
$197$	−13.4127			−0.955618			−0.477809	+	0.878464i	$0.658569\pi$
$198$		0			0
$199$	21.2586			1.50698			0.753489	−	0.657460i	$-0.228369\pi$
$199$	21.2586			1.50698			0.753489	+	0.657460i	$0.228369\pi$
$200$	4.18527	−	0.889607i	0.295944	−	0.0629047i
$201$		0			0
$202$	−8.04520	+	3.58195i	−0.566058	+	0.252025i
$203$	−1.67031	+	7.85821i	−0.117233	+	0.551538i
$204$		0			0
$205$	−2.24588	−	0.236052i	−0.156859	−	0.0164866i
$206$	10.5363	−	7.65505i	0.734097	−	0.533353i
$207$		0			0
$208$			5.21605i			0.361668i
$209$	11.4196	+	20.7088i	0.789909	+	1.43246i
$210$		0			0
$211$	11.0990	−	9.99357i	0.764086	−	0.687986i	−0.191895	−	0.981415i	$-0.561463\pi$
$211$	11.0990	−	9.99357i	0.764086	−	0.687986i	0.955981	+	0.293429i	$0.0947966\pi$
$212$	44.5401	−	4.68135i	3.05902	−	0.321516i
$213$		0			0
$214$	18.1744	−	20.1847i	1.24237	−	1.37980i
$215$	−3.23141	−	9.94525i	−0.220380	−	0.678261i
$216$		0			0
$217$	−0.756060	−	1.04063i	−0.0513247	−	0.0706424i
$218$	1.36354	+	6.41494i	0.0923504	+	0.434475i
$219$		0			0
$220$	−2.36994	−	27.7927i	−0.159781	−	1.87379i
$221$	6.33712	+	3.65874i	0.426280	+	0.246113i
$222$		0			0
$223$	−22.9039	−	10.1975i	−1.53376	−	0.682872i	−0.545844	−	0.837887i	$-0.683791\pi$
$223$	−22.9039	−	10.1975i	−1.53376	−	0.682872i	−0.987912	+	0.155015i	$0.950457\pi$
$224$	0.732925	−	1.00879i	0.0489706	−	0.0674023i
$225$		0			0
$226$	−21.7932	+	7.08105i	−1.44966	+	0.471025i
$227$	−0.305215	+	2.90393i	−0.0202578	+	0.192740i	−0.999971	−	0.00766639i	$-0.997560\pi$
$227$	−0.305215	+	2.90393i	−0.0202578	+	0.192740i	0.979713	+	0.200407i	$0.0642264\pi$
$228$		0			0
$229$	−2.24082	−	2.48868i	−0.148077	−	0.164456i	0.664543	−	0.747250i	$-0.268626\pi$
$229$	−2.24082	−	2.48868i	−0.148077	−	0.164456i	−0.812620	+	0.582794i	$0.801960\pi$
$230$	−13.7467	+	23.8100i	−0.906432	+	1.56999i
$231$		0			0
$232$	19.3544	+	33.5228i	1.27068	+	2.20088i
$233$	3.74639	−	11.5302i	0.245434	−	0.755369i	−0.750131	−	0.661290i	$-0.770009\pi$
$233$	3.74639	−	11.5302i	0.245434	−	0.755369i	0.995565	−	0.0940790i	$-0.0299906\pi$
$234$		0			0
$235$	7.10521	+	5.16224i	0.463493	+	0.336747i
$236$	6.74268	+	6.07113i	0.438911	+	0.395197i
$237$		0			0
$238$	−7.17644	−	16.1186i	−0.465180	−	1.04481i
$239$	−0.710369	−	6.75871i	−0.0459499	−	0.437184i	−0.993177	−	0.116620i	$-0.962794\pi$
$239$	−0.710369	−	6.75871i	−0.0459499	−	0.437184i	0.947227	−	0.320565i	$-0.103873\pi$
$240$		0			0
$241$	−2.82339	+	1.63009i	−0.181871	+	0.105003i	−0.588171	−	0.808736i	$-0.700152\pi$
$241$	−2.82339	+	1.63009i	−0.181871	+	0.105003i	0.406301	+	0.913739i	$0.366819\pi$
$242$	27.1761	+	1.06877i	1.74695	+	0.0687032i
$243$		0			0
$244$	22.7029	+	7.37661i	1.45340	+	0.472239i
$245$	4.84390	−	10.8796i	0.309465	−	0.695070i
$246$		0			0
$247$	7.75473	+	1.64832i	0.493422	+	0.104880i
$248$	−6.06222	−	1.28857i	−0.384952	−	0.0818240i
$249$		0			0
$250$	−11.9655	+	26.8750i	−0.756766	+	1.69972i
$251$	−11.6389	−	3.78172i	−0.734643	−	0.238700i	−0.0822830	−	0.996609i	$-0.526221\pi$
$251$	−11.6389	−	3.78172i	−0.734643	−	0.238700i	−0.652360	+	0.757909i	$0.726221\pi$
$252$		0			0
$253$	−14.3807	−	10.8864i	−0.904109	−	0.684419i
$254$	−24.8227	+	14.3314i	−1.55752	+	0.899233i
$255$		0			0
$256$	3.40586	+	32.4046i	0.212867	+	2.02529i
$257$	6.47139	+	14.5350i	0.403674	+	0.906667i	0.994966	+	0.100209i	$0.0319513\pi$
$257$	6.47139	+	14.5350i	0.403674	+	0.906667i	−0.591292	+	0.806457i	$0.701382\pi$
$258$		0			0
$259$	0.777692	+	0.700237i	0.0483235	+	0.0435106i
$260$	−7.56514	−	5.49640i	−0.469170	−	0.340872i
$261$		0			0
$262$	7.91617	−	24.3635i	0.489063	−	1.50518i
$263$	−5.95707	−	10.3180i	−0.367329	−	0.636232i	0.621818	−	0.783162i	$-0.286394\pi$
$263$	−5.95707	−	10.3180i	−0.367329	−	0.636232i	−0.989147	+	0.146929i	$0.953061\pi$
$264$		0			0
$265$	−11.1322	+	19.2815i	−0.683845	+	1.18445i
$266$	−12.7911	−	14.2060i	−0.784273	−	0.871024i
$267$		0			0
$268$	0.427130	−	4.06387i	0.0260911	−	0.248241i
$269$	−24.0428	+	7.81198i	−1.46592	+	0.476305i	−0.929872	−	0.367884i	$-0.880082\pi$
$269$	−24.0428	+	7.81198i	−1.46592	+	0.476305i	−0.536045	+	0.844190i	$0.680082\pi$
$270$		0			0
$271$	4.66877	−	6.42601i	0.283608	−	0.390352i	−0.643317	−	0.765600i	$-0.722442\pi$
$271$	4.66877	−	6.42601i	0.283608	−	0.390352i	0.926925	+	0.375248i	$0.122442\pi$
$272$	−28.2053	−	12.5578i	−1.71020	−	0.761428i
$273$		0			0
$274$	0.628087	+	0.362626i	0.0379441	+	0.0219070i
$275$	−2.32520	−	1.40409i	−0.140215	−	0.0846699i
$276$		0			0
$277$	1.99496	+	9.38557i	0.119866	+	0.563924i	0.996560	+	0.0828758i	$0.0264105\pi$
$277$	1.99496	+	9.38557i	0.119866	+	0.563924i	−0.876694	+	0.481048i	$0.840256\pi$
$278$	3.02799	+	4.16767i	0.181607	+	0.249960i
$279$		0			0
$280$	3.57953	+	11.0167i	0.213918	+	0.658371i
$281$	12.1424	−	13.4855i	0.724355	−	0.804478i	−0.262697	−	0.964878i	$-0.584612\pi$
$281$	12.1424	−	13.4855i	0.724355	−	0.804478i	0.987052	+	0.160400i	$0.0512785\pi$
$282$		0			0
$283$	−19.2952	+	2.02800i	−1.14698	+	0.120552i	−0.658888	−	0.752241i	$-0.728973\pi$
$283$	−19.2952	+	2.02800i	−1.14698	+	0.120552i	−0.488090	+	0.872793i	$0.662306\pi$
$284$	19.6746	−	17.7151i	1.16747	−	1.05120i
$285$		0			0
$286$	6.23280	−	6.65445i	0.368553	−	0.393486i
$287$			1.19753i			0.0706882i
$288$		0			0
$289$	−21.2878	+	15.4665i	−1.25222	+	0.909792i
$290$	−37.2519	−	3.91534i	−2.18751	−	0.229916i
$291$		0			0
$292$	−0.707395	+	3.32803i	−0.0413972	+	0.194758i
$293$	−14.0529	+	6.25674i	−0.820978	+	0.365523i	−0.773852	−	0.633366i	$-0.781673\pi$
$293$	−14.0529	+	6.25674i	−0.820978	+	0.365523i	−0.0471254	+	0.998889i	$0.515006\pi$
$294$		0			0
$295$	−4.41202	+	0.937803i	−0.256878	+	0.0546010i
$296$	5.04225			0.293075
$297$		0			0
$298$	−41.4129			−2.39899
$299$	−5.91444	+	1.25715i	−0.342041	+	0.0727030i
$300$		0			0
$301$	−5.06588	+	2.25547i	−0.291992	+	0.130003i
$302$	4.98123	−	23.4348i	0.286638	−	1.34852i
$303$		0			0
$304$	−33.2672	−	3.49652i	−1.90800	−	0.200539i
$305$	−9.60077	+	6.97537i	−0.549738	+	0.399408i
$306$		0			0
$307$			5.86988i			0.335012i	0.985871	+	0.167506i	$0.0535713\pi$
$307$			5.86988i			0.335012i	−0.985871	+	0.167506i	$0.946429\pi$
$308$	−14.5262	+	2.79044i	−0.827705	+	0.159000i
$309$		0			0
$310$	4.45683	−	4.01295i	0.253131	−	0.227920i
$311$	−26.3050	+	2.76477i	−1.49162	+	0.156776i	−0.814958	−	0.579519i	$-0.803240\pi$
$311$	−26.3050	+	2.76477i	−1.49162	+	0.156776i	−0.676661	+	0.736295i	$0.736574\pi$
$312$		0			0
$313$	5.19128	−	5.76550i	0.293428	−	0.325885i	−0.578347	−	0.815791i	$-0.696302\pi$
$313$	5.19128	−	5.76550i	0.293428	−	0.325885i	0.871776	+	0.489906i	$0.162969\pi$
$314$	−2.25401	−	6.93714i	−0.127201	−	0.391485i
$315$		0			0
$316$	−14.7404	−	20.2885i	−0.829214	−	1.14132i
$317$	1.28282	+	6.03520i	0.0720505	+	0.338971i	0.999377	−	0.0352814i	$-0.0112328\pi$
$317$	1.28282	+	6.03520i	0.0720505	+	0.338971i	−0.927327	+	0.374252i	$0.877899\pi$
$318$		0			0
$319$	5.58041	−	23.9311i	0.312443	−	1.33988i
$320$	−11.5798	−	6.68562i	−0.647332	−	0.373738i
$321$		0			0
$322$	13.3191	+	5.93003i	0.742243	+	0.330468i
$323$	−27.5829	+	37.9646i	−1.53475	+	2.11241i
$324$		0			0
$325$	−0.866026	+	0.281389i	−0.0480385	+	0.0156086i
$326$	5.70969	−	54.3241i	0.316231	−	3.00873i
$327$		0			0
$328$	3.86090	+	4.28797i	0.213183	+	0.236763i
$329$	2.32865	−	4.03334i	0.128383	−	0.222365i
$330$		0			0
$331$	8.44643	+	14.6297i	0.464258	+	0.804118i	0.999168	−	0.0407908i	$-0.0129877\pi$
$331$	8.44643	+	14.6297i	0.464258	+	0.804118i	−0.534910	+	0.844909i	$0.679654\pi$
$332$	−2.78799	+	8.58054i	−0.153011	+	0.470918i
$333$		0			0
$334$	23.3123	+	16.9374i	1.27559	+	0.926772i
$335$	1.50964	+	1.35929i	0.0824804	+	0.0742657i
$336$		0			0
$337$	−12.2712	−	27.5616i	−0.668456	−	1.50138i	−0.854835	−	0.518899i	$-0.826342\pi$
$337$	−12.2712	−	27.5616i	−0.668456	−	1.50138i	0.186379	−	0.982478i	$-0.440325\pi$
$338$	3.04026	+	28.9261i	0.165368	+	1.57337i
$339$		0			0
$340$	47.9345	−	27.6750i	2.59962	−	1.50089i
$341$	2.24958	+	3.22782i	0.121822	+	0.174797i
$342$		0			0
$343$	−13.2250	−	4.29705i	−0.714081	−	0.232019i
$344$	−10.8675	+	24.4087i	−0.585934	+	1.31603i
$345$		0			0
$346$	−29.1078	−	6.18705i	−1.56484	−	0.332618i
$347$	17.3643	+	3.69089i	0.932163	+	0.198137i	0.648873	−	0.760897i	$-0.275241\pi$
$347$	17.3643	+	3.69089i	0.932163	+	0.198137i	0.283290	+	0.959034i	$0.408574\pi$
$348$		0			0
$349$	3.79504	−	8.52381i	0.203144	−	0.456269i	−0.783030	−	0.621984i	$-0.786327\pi$
$349$	3.79504	−	8.52381i	0.203144	−	0.456269i	0.986174	+	0.165716i	$0.0529934\pi$
$350$	2.08817	+	0.678487i	0.111617	+	0.0362667i
$351$		0			0
$352$	−2.30202	+	3.04094i	−0.122698	+	0.162083i
$353$	−12.6509	+	7.30399i	−0.673339	+	0.388752i	−0.797341	−	0.603530i	$-0.793761\pi$
$353$	−12.6509	+	7.30399i	−0.673339	+	0.388752i	0.124002	+	0.992282i	$0.460427\pi$
$354$		0			0
$355$	1.37576	+	13.0894i	0.0730175	+	0.694715i
$356$	−10.3678	−	23.2866i	−0.549495	−	1.23419i
$357$		0			0
$358$	5.29076	+	4.76382i	0.279625	+	0.251776i
$359$	13.4671	+	9.78443i	0.710767	+	0.516402i	0.883421	−	0.468580i	$-0.155234\pi$
$359$	13.4671	+	9.78443i	0.710767	+	0.516402i	−0.172654	+	0.984983i	$0.555234\pi$
$360$		0			0
$361$	−9.83971	+	30.2835i	−0.517880	+	1.59387i
$362$	28.9574	+	50.1557i	1.52197	+	2.63612i
$363$		0			0
$364$	−2.47939	+	4.29443i	−0.129955	+	0.225089i
$365$	−1.13180	−	1.25699i	−0.0592409	−	0.0657937i
$366$		0			0
$367$	−3.08671	+	29.3681i	−0.161125	+	1.53300i	0.553117	+	0.833104i	$0.313438\pi$
$367$	−3.08671	+	29.3681i	−0.161125	+	1.53300i	−0.714242	+	0.699899i	$0.753228\pi$
$368$	24.2636	−	7.88371i	1.26483	−	0.410967i
$369$		0			0
$370$	−2.86793	+	3.94736i	−0.149096	+	0.205214i
$371$	10.7859	+	4.80218i	0.559975	+	0.249317i
$372$		0			0
$373$	6.04790	+	3.49176i	0.313148	+	0.180796i	0.648334	−	0.761356i	$-0.275466\pi$
$373$	6.04790	+	3.49176i	0.313148	+	0.180796i	−0.335186	+	0.942152i	$0.608799\pi$
$374$	20.9776	+	49.7241i	1.08473	+	2.57117i
$375$		0			0
$376$	−4.66555	−	21.9497i	−0.240608	−	1.13197i
$377$	−4.84209	−	6.66457i	−0.249381	−	0.343243i
$378$		0			0
$379$	−10.0677	−	30.9850i	−0.517140	−	1.59159i	−0.779353	−	0.626585i	$-0.784452\pi$
$379$	−10.0677	−	30.9850i	−0.517140	−	1.59159i	0.262213	−	0.965010i	$-0.415548\pi$
$380$	40.1264	−	44.5649i	2.05844	−	2.28613i
$381$		0			0
$382$	−2.01705	+	0.212001i	−0.103201	+	0.0108469i
$383$	18.2292	−	16.4136i	0.931469	−	0.838698i	−0.0556889	−	0.998448i	$-0.517736\pi$
$383$	18.2292	−	16.4136i	0.931469	−	0.838698i	0.987157	+	0.159750i	$0.0510688\pi$
$384$		0			0
$385$	3.12238	−	6.65767i	0.159131	−	0.339306i
$386$			35.2043i			1.79185i
$387$		0			0
$388$	31.6866	−	23.0217i	1.60864	−	1.16875i
$389$	27.2434	+	2.86340i	1.38129	+	0.145180i	0.765860	−	0.643008i	$-0.222314\pi$
$389$	27.2434	+	2.86340i	1.38129	+	0.145180i	0.615435	+	0.788188i	$0.288980\pi$
$390$		0			0
$391$	7.44126	−	35.0084i	0.376321	−	1.77045i
$392$	−27.7982	+	12.3766i	−1.40402	+	0.625111i
$393$		0			0
$394$	−32.4379	+	6.89488i	−1.63420	+	0.347359i
$395$	12.4671			0.627288
$396$		0			0
$397$	20.5147			1.02960			0.514801	−	0.857310i	$-0.327866\pi$
$397$	20.5147			1.02960			0.514801	+	0.857310i	$0.327866\pi$
$398$	51.4124	−	10.9280i	2.57707	−	0.547774i
$399$		0			0
$400$	3.50989	−	1.56271i	0.175495	−	0.0781353i
$401$	−2.07986	+	9.78498i	−0.103863	+	0.488638i	0.895212	+	0.445641i	$0.147024\pi$
$401$	−2.07986	+	9.78498i	−0.103863	+	0.488638i	−0.999075	+	0.0429976i	$0.986309\pi$
$402$		0			0
$403$	1.31174	+	0.137869i	0.0653423	+	0.00686776i
$404$	−11.8523	+	8.61117i	−0.589672	+	0.428422i
$405$		0			0
$406$			19.8632i			0.985795i
$407$	−2.33619	−	2.18817i	−0.115801	−	0.108463i
$408$		0			0
$409$	−6.04473	+	5.44270i	−0.298893	+	0.269124i	−0.804907	−	0.593401i	$-0.797785\pi$
$409$	−6.04473	+	5.44270i	−0.298893	+	0.269124i	0.506015	+	0.862525i	$0.331118\pi$
$410$	−5.55287	+	0.583630i	−0.274237	+	0.0288234i
$411$		0			0
$412$	14.4970	−	16.1005i	0.714215	−	0.793216i
$413$	0.739146	+	2.27486i	0.0363710	+	0.111938i
$414$		0			0
$415$	−2.63634	−	3.62861i	−0.129413	−	0.178121i
$416$	0.265837	+	1.25066i	0.0130337	+	0.0613188i
$417$		0			0
$418$	38.2630	+	44.2126i	1.87150	+	2.16251i
$419$	−22.7014	−	13.1067i	−1.10904	−	0.640302i	−0.170456	−	0.985365i	$-0.554524\pi$
$419$	−22.7014	−	13.1067i	−1.10904	−	0.640302i	−0.938579	+	0.345064i	$0.887857\pi$
$420$		0			0
$421$	−34.2193	−	15.2354i	−1.66774	−	0.742528i	−0.667746	−	0.744389i	$-0.732741\pi$
$421$	−34.2193	−	15.2354i	−1.66774	−	0.742528i	−0.999998	+	0.00186147i	$0.999407\pi$
$422$	21.7049	−	29.8743i	1.05658	−	1.45426i
$423$		0			0
$424$	54.1031	−	17.5791i	2.62748	−	0.853719i
$425$	0.563401	−	5.36040i	0.0273290	−	0.260018i
$426$		0			0
$427$	4.21089	+	4.67667i	0.203779	+	0.226320i
$428$	22.5920	−	39.1306i	1.09203	−	1.89145i
$429$		0			0
$430$	−12.9274	−	22.3908i	−0.623412	−	1.07978i
$431$	7.37759	−	22.7059i	0.355366	−	1.09370i	−0.600431	−	0.799677i	$-0.705004\pi$
$431$	7.37759	−	22.7059i	0.355366	−	1.09370i	0.955797	−	0.294027i	$-0.0949957\pi$
$432$		0			0
$433$	17.3812	+	12.6282i	0.835286	+	0.606871i	0.921050	−	0.389445i	$-0.127333\pi$
$433$	17.3812	+	12.6282i	0.835286	+	0.606871i	−0.0857640	+	0.996315i	$0.527333\pi$
$434$	−2.36342	−	2.12803i	−0.113448	−	0.102149i
$435$		0			0
$436$	4.43750	+	9.96679i	0.212518	+	0.477323i
$437$	−4.05325	−	38.5641i	−0.193893	−	1.84477i
$438$		0			0
$439$	−8.94708	+	5.16560i	−0.427021	+	0.246541i	−0.698077	−	0.716023i	$-0.745961\pi$
$439$	−8.94708	+	5.16560i	−0.427021	+	0.246541i	0.271056	+	0.962564i	$0.412627\pi$
$440$	−10.2844	−	33.9056i	−0.490292	−	1.61638i
$441$		0			0
$442$	17.2067	+	5.59079i	0.818439	+	0.265927i
$443$	−12.9074	+	28.9906i	−0.613251	+	1.37738i	0.293598	+	0.955929i	$0.405147\pi$
$443$	−12.9074	+	28.9906i	−0.613251	+	1.37738i	−0.906849	+	0.421456i	$0.861519\pi$
$444$		0			0
$445$	12.3952	+	2.63468i	0.587589	+	0.124896i
$446$	−60.6335	−	12.8881i	−2.87108	−	0.610267i
$447$		0			0
$448$	−2.88403	+	6.47764i	−0.136258	+	0.306040i
$449$	8.43287	+	2.74001i	0.397972	+	0.129309i	0.501163	−	0.865353i	$-0.332906\pi$
$449$	8.43287	+	2.74001i	0.397972	+	0.129309i	−0.103192	+	0.994661i	$0.532906\pi$
$450$		0			0
$451$	0.0719854	−	3.66222i	0.00338966	−	0.172447i
$452$	−33.0129	+	19.0600i	−1.55279	+	0.896507i
$453$		0			0
$454$	0.754633	+	7.17985i	0.0354167	+	0.336967i
$455$	−1.00268	−	2.25205i	−0.0470063	−	0.105578i
$456$		0			0
$457$	−12.4905	−	11.2465i	−0.584280	−	0.526088i	0.323119	−	0.946358i	$-0.395269\pi$
$457$	−12.4905	−	11.2465i	−0.584280	−	0.526088i	−0.907399	+	0.420270i	$0.861935\pi$
$458$	−6.69858	−	4.86681i	−0.313004	−	0.227411i
$459$		0			0
$460$	−14.1335	+	43.4983i	−0.658976	+	2.02812i
$461$	4.98284	+	8.63053i	0.232074	+	0.401964i	0.958418	−	0.285367i	$-0.0921155\pi$
$461$	4.98284	+	8.63053i	0.232074	+	0.401964i	−0.726344	+	0.687331i	$0.758782\pi$
$462$		0			0
$463$	−17.6360	+	30.5465i	−0.819616	+	1.41962i	0.0863496	+	0.996265i	$0.472480\pi$
$463$	−17.6360	+	30.5465i	−0.819616	+	1.41962i	−0.905966	+	0.423352i	$0.860854\pi$
$464$	23.2576	+	25.8302i	1.07971	+	1.19914i
$465$		0			0
$466$	3.13325	−	29.8109i	0.145145	−	1.38096i
$467$	−3.77750	+	1.22739i	−0.174802	+	0.0567966i	−0.395110	−	0.918634i	$-0.629294\pi$
$467$	−3.77750	+	1.22739i	−0.174802	+	0.0567966i	0.220308	+	0.975430i	$0.429294\pi$
$468$		0			0
$469$	0.633189	−	0.871510i	0.0292379	−	0.0402426i
$470$	19.8372	+	8.83208i	0.915020	+	0.407393i
$471$		0			0
$472$	9.98087	+	5.76246i	0.459407	+	0.265239i
$473$	15.6277	−	6.59302i	0.718563	−	0.303148i
$474$		0			0
$475$	−1.21413	−	5.71201i	−0.0557079	−	0.262085i
$476$	−17.2525	−	23.7460i	−0.790766	−	1.08840i
$477$		0			0
$478$	−5.19232	−	15.9803i	−0.237491	−	0.730923i
$479$	22.6130	−	25.1143i	1.03322	−	1.14750i	0.0443004	−	0.999018i	$-0.485894\pi$
$479$	22.6130	−	25.1143i	1.03322	−	1.14750i	0.988915	−	0.148484i	$-0.0474392\pi$
$480$		0			0
$481$	−1.06720	+	0.112167i	−0.0486599	+	0.00511436i
$482$	−5.99024	+	5.39363i	−0.272848	+	0.245673i
$483$		0			0
$484$	44.5907	−	7.66036i	2.02685	−	0.348198i
$485$			19.4712i			0.884141i
$486$		0			0
$487$	12.5920	−	9.14862i	0.570598	−	0.414563i	−0.264725	−	0.964324i	$-0.585281\pi$
$487$	12.5920	−	9.14862i	0.570598	−	0.414563i	0.835322	+	0.549761i	$0.185281\pi$
$488$	30.1556	+	3.16948i	1.36508	+	0.143476i
$489$		0			0
$490$	6.12196	−	28.8016i	0.276562	−	1.30112i
$491$	−7.62322	+	3.39408i	−0.344031	+	0.153173i	−0.571477	−	0.820618i	$-0.693629\pi$
$491$	−7.62322	+	3.39408i	−0.344031	+	0.153173i	0.227446	+	0.973791i	$0.426963\pi$
$492$		0			0
$493$	47.6955	−	10.1380i	2.14810	−	0.456592i
$494$	19.6016			0.881920
$495$		0			0
$496$	−5.56509			−0.249880
$497$	6.82694	−	1.45111i	0.306230	−	0.0650912i
$498$		0			0
$499$	−0.166561	+	0.0741579i	−0.00745631	+	0.00331976i	−0.410461	−	0.911878i	$-0.634632\pi$
$499$	−0.166561	+	0.0741579i	−0.00745631	+	0.00331976i	0.403005	+	0.915198i	$0.367966\pi$
$500$	−10.1750	+	47.8696i	−0.455040	+	2.14079i
$501$		0			0
$502$	−30.0920	−	3.16280i	−1.34307	−	0.141163i
$503$	−11.2333	+	8.16148i	−0.500869	+	0.363902i	−0.809349	−	0.587328i	$-0.800180\pi$
$503$	−11.2333	+	8.16148i	−0.500869	+	0.363902i	0.308480	+	0.951231i	$0.400180\pi$
$504$		0			0
$505$		−	7.28312i		−	0.324095i
$506$	−40.3750	−	18.9355i	−1.79489	−	0.841784i
$507$		0			0
$508$	−35.4348	+	31.9056i	−1.57216	+	1.41558i
$509$	25.5376	−	2.68411i	1.13193	−	0.118971i	0.480015	−	0.877260i	$-0.340631\pi$
$509$	25.5376	−	2.68411i	1.13193	−	0.118971i	0.651919	+	0.758289i	$0.273964\pi$
$510$		0			0
$511$	−0.600182	+	0.666570i	−0.0265505	+	0.0294873i
$512$	13.4807	+	41.4893i	0.595768	+	1.83359i
$513$		0			0
$514$	23.1224	+	31.8252i	1.01988	+	1.40375i
$515$	2.23934	+	10.5353i	0.0986770	+	0.464239i
$516$		0			0
$517$	−7.36377	+	12.1945i	−0.323858	+	0.536314i
$518$	2.24076	+	1.29370i	0.0984533	+	0.0568420i
$519$		0			0
$520$	−10.8510	−	4.83116i	−0.475847	−	0.211861i
$521$	23.3218	−	32.0997i	1.02175	−	1.40631i	0.110774	−	0.993846i	$-0.464667\pi$
$521$	23.3218	−	32.0997i	1.02175	−	1.40631i	0.910972	−	0.412468i	$-0.135333\pi$
$522$		0			0
$523$	3.90330	−	1.26826i	0.170679	−	0.0554571i	−0.222431	−	0.974949i	$-0.571399\pi$
$523$	3.90330	−	1.26826i	0.170679	−	0.0554571i	0.393110	+	0.919491i	$0.371399\pi$
$524$	4.45456	−	42.3823i	0.194598	−	1.85148i
$525$		0			0
$526$	−19.7108	−	21.8910i	−0.859431	−	0.954495i
$527$	−3.90356	+	6.76117i	−0.170042	+	0.294521i
$528$		0			0
$529$	3.28719	+	5.69357i	0.142921	+	0.247547i
$530$	−17.0107	+	52.3536i	−0.738899	+	2.27410i
$531$		0			0
$532$	−25.7272	−	18.6919i	−1.11541	−	0.810396i
$533$	−0.912550	−	0.821663i	−0.0395269	−	0.0355902i
$534$		0			0
$535$	9.13635	+	20.5206i	0.394999	+	0.887182i
$536$	−0.542549	−	5.16201i	−0.0234346	−	0.222965i
$537$		0			0
$538$	−54.1302	+	31.2521i	−2.33372	+	1.34737i
$539$	18.2506	+	6.32913i	0.786108	+	0.272615i
$540$		0			0
$541$	23.5956	+	7.66668i	1.01445	+	0.329616i	0.768627	−	0.639697i	$-0.220940\pi$
$541$	23.5956	+	7.66668i	1.01445	+	0.329616i	0.245828	+	0.969314i	$0.420940\pi$
$542$	7.98780	−	17.9409i	0.343105	−	0.770627i
$543$		0			0
$544$	−7.40285	−	1.57352i	−0.317395	−	0.0674643i
$545$	−5.30522	−	1.12766i	−0.227251	−	0.0483036i
$546$		0			0
$547$	15.9137	−	35.7428i	0.680422	−	1.52825i	−0.160464	−	0.987042i	$-0.551299\pi$
$547$	15.9137	−	35.7428i	0.680422	−	1.52825i	0.840886	−	0.541212i	$-0.182034\pi$
$548$	1.14745	+	0.372828i	0.0490165	+	0.0159264i
$549$		0			0
$550$	−6.34512	−	2.20043i	−0.270557	−	0.0938265i
$551$	45.7515	−	26.4146i	1.94908	−	1.12530i
$552$		0			0
$553$	−0.691059	−	6.57499i	−0.0293868	−	0.279597i
$554$	9.64938	+	21.6729i	0.409963	+	0.920792i
$555$		0			0
$556$	6.36864	+	5.73435i	0.270090	+	0.243191i
$557$	4.19799	+	3.05002i	0.177874	+	0.129233i	0.673160	−	0.739497i	$-0.264937\pi$
$557$	4.19799	+	3.05002i	0.177874	+	0.129233i	−0.495285	+	0.868730i	$0.664937\pi$
$558$		0			0
$559$	1.75712	−	5.40787i	0.0743184	−	0.228728i
$560$	5.20065	+	9.00779i	0.219768	+	0.380649i
$561$		0			0
$562$	22.4333	−	38.8557i	0.946294	−	1.63903i
$563$	−5.38926	−	5.98538i	−0.227130	−	0.252254i	0.618798	−	0.785550i	$-0.287620\pi$
$563$	−5.38926	−	5.98538i	−0.227130	−	0.252254i	−0.845929	+	0.533296i	$0.820953\pi$
$564$		0			0
$565$	1.98089	−	18.8469i	0.0833368	−	0.792897i
$566$	−45.6216	+	14.8234i	−1.91762	+	0.623072i
$567$		0			0
$568$	19.7665	−	27.2063i	0.829385	−	1.14155i
$569$	−27.7469	−	12.3537i	−1.16321	−	0.517896i	−0.267949	−	0.963433i	$-0.586346\pi$
$569$	−27.7469	−	12.3537i	−1.16321	−	0.517896i	−0.895263	+	0.445537i	$0.853013\pi$
$570$		0			0
$571$	33.4911	+	19.3361i	1.40156	+	0.809190i	0.994553	−	0.104236i	$-0.0332397\pi$
$571$	33.4911	+	19.3361i	1.40156	+	0.809190i	0.407005	+	0.913426i	$0.366573\pi$
$572$	7.84044	−	12.9839i	0.327825	−	0.542884i
$573$		0			0
$574$	0.615598	+	2.89616i	0.0256945	+	0.120883i
$575$	2.61788	+	3.60320i	0.109173	+	0.150264i
$576$		0			0
$577$	5.09511	+	15.6811i	0.212112	+	0.652815i	0.999346	+	0.0361598i	$0.0115125\pi$
$577$	5.09511	+	15.6811i	0.212112	+	0.652815i	−0.787234	+	0.616655i	$0.788487\pi$
$578$	−43.5325	+	48.3477i	−1.81071	+	2.01100i
$579$		0			0
$580$	−61.9706	+	6.51338i	−2.57319	+	0.270453i
$581$	−1.76755	+	1.59151i	−0.0733302	+	0.0660268i
$582$		0			0
$583$	−32.6960	−	15.3341i	−1.35413	−	0.635072i
$584$			4.32178i			0.178836i
$585$		0			0
$586$	−30.7697	+	22.3555i	−1.27108	+	0.923496i
$587$	−45.0057	−	4.73029i	−1.85758	−	0.195240i	−0.891421	−	0.453175i	$-0.850291\pi$
$587$	−45.0057	−	4.73029i	−1.85758	−	0.195240i	−0.966162	+	0.257936i	$0.916958\pi$
$588$		0			0
$589$	−1.75862	+	8.27365i	−0.0724626	+	0.340910i
$590$	−10.1881	+	4.53603i	−0.419437	+	0.186745i
$591$		0			0
$592$	4.42867	−	0.941343i	0.182017	−	0.0386889i
$593$	−4.03343			−0.165633			−0.0828166	−	0.996565i	$-0.526392\pi$
$593$	−4.03343			−0.165633			−0.0828166	+	0.996565i	$0.526392\pi$
$594$		0			0
$595$	14.5917			0.598203
$596$	−67.3872	+	14.3236i	−2.76029	+	0.586717i
$597$		0			0
$598$	−13.6574	+	6.08068i	−0.558494	+	0.248658i
$599$	−1.28874	+	6.06305i	−0.0526566	+	0.247730i	−0.996602	−	0.0823731i	$-0.973750\pi$
$599$	−1.28874	+	6.06305i	−0.0526566	+	0.247730i	0.943945	+	0.330103i	$0.107083\pi$
$600$		0			0
$601$	47.3654	+	4.97830i	1.93207	+	0.203069i	0.990875	−	0.134786i	$-0.0430347\pi$
$601$	47.3654	+	4.97830i	1.93207	+	0.203069i	0.941198	+	0.337855i	$0.109701\pi$
$602$	−11.0921	+	8.05885i	−0.452079	+	0.328454i
$603$		0			0
$604$		−	39.8561i		−	1.62172i
$605$	−9.94884	+	20.1724i	−0.404478	+	0.820123i
$606$		0			0
$607$	6.16934	−	5.55490i	0.250406	−	0.225467i	−0.534363	−	0.845255i	$-0.679448\pi$
$607$	6.16934	−	5.55490i	0.250406	−	0.225467i	0.784769	+	0.619789i	$0.212782\pi$
$608$	−8.15475	+	0.857098i	−0.330719	+	0.0347599i
$609$		0			0
$610$	−19.6331	+	21.8048i	−0.794922	+	0.882850i
$611$	1.47575	+	4.54188i	0.0597023	+	0.183745i
$612$		0			0
$613$	−13.0470	−	17.9576i	−0.526962	−	0.725301i	0.459702	−	0.888073i	$-0.347956\pi$
$613$	−13.0470	−	17.9576i	−0.526962	−	0.725301i	−0.986664	+	0.162773i	$0.947956\pi$
$614$	3.01744	+	14.1959i	0.121774	+	0.572901i
$615$		0			0
$616$	−17.3113	+	7.30329i	−0.697491	+	0.294258i
$617$	2.63944	+	1.52388i	0.106260	+	0.0613492i	0.552188	−	0.833720i	$-0.313793\pi$
$617$	2.63944	+	1.52388i	0.106260	+	0.0613492i	−0.445928	+	0.895069i	$0.647126\pi$
$618$		0			0
$619$	22.5944	+	10.0597i	0.908144	+	0.404332i	0.807008	−	0.590541i	$-0.201085\pi$
$619$	22.5944	+	10.0597i	0.908144	+	0.404332i	0.101136	+	0.994873i	$0.467752\pi$
$620$	5.86420	−	8.07137i	0.235512	−	0.324154i
$621$		0			0
$622$	−62.1957	+	20.2086i	−2.49382	+	0.810291i
$623$	0.702423	−	6.68311i	0.0281420	−	0.267753i
$624$		0			0
$625$	−13.5394	−	15.0371i	−0.541577	−	0.601483i
$626$	9.59099	−	16.6121i	0.383333	−	0.663952i
$627$		0			0
$628$	−6.06710	−	10.5085i	−0.242104	−	0.419336i
$629$	1.96277	−	6.04080i	0.0782609	−	0.240862i
$630$		0			0
$631$	−15.6052	−	11.3378i	−0.621233	−	0.451352i	0.232119	−	0.972687i	$-0.425434\pi$
$631$	−15.6052	−	11.3378i	−0.621233	−	0.451352i	−0.853352	+	0.521335i	$0.825434\pi$
$632$	−23.6725	−	21.3148i	−0.941641	−	0.847858i
$633$		0			0
$634$	6.20484	+	13.9363i	0.246426	+	0.553482i
$635$	−2.47779	−	23.5746i	−0.0983282	−	0.935530i
$636$		0			0
$637$	5.60819	−	3.23789i	0.222204	−	0.128290i
$638$	1.19400	−	60.7443i	0.0472711	−	2.40489i
$639$		0			0
$640$	−35.9145	−	11.6693i	−1.41964	−	0.461270i
$641$	0.114473	−	0.257111i	0.00452142	−	0.0101553i	−0.911271	−	0.411808i	$-0.864897\pi$
$641$	0.114473	−	0.257111i	0.00452142	−	0.0101553i	0.915792	+	0.401653i	$0.131564\pi$
$642$		0			0
$643$	−11.9865	−	2.54781i	−0.472702	−	0.100476i	−0.0346001	−	0.999401i	$-0.511016\pi$
$643$	−11.9865	−	2.54781i	−0.472702	−	0.100476i	−0.438102	+	0.898925i	$0.644349\pi$
$644$	23.7239	+	5.04266i	0.934851	+	0.198709i
$645$		0			0
$646$	−47.1915	+	105.994i	−1.85673	+	4.17028i
$647$	−12.4773	−	4.05411i	−0.490532	−	0.159383i	0.0532987	−	0.998579i	$-0.483026\pi$
$647$	−12.4773	−	4.05411i	−0.490532	−	0.159383i	−0.543830	+	0.839195i	$0.683026\pi$
$648$		0			0
$649$	−2.12366	−	7.00125i	−0.0833610	−	0.274823i
$650$	−1.94978	+	1.12571i	−0.0764766	+	0.0441538i
$651$		0			0
$652$	−9.49839	−	90.3711i	−0.371986	−	3.53921i
$653$	2.84441	+	6.38866i	0.111310	+	0.250007i	0.960608	−	0.277907i	$-0.0896408\pi$
$653$	2.84441	+	6.38866i	0.111310	+	0.250007i	−0.849297	+	0.527915i	$0.822974\pi$
$654$		0			0
$655$	15.7441	+	14.1760i	0.615172	+	0.553904i
$656$	4.19160	+	3.04538i	0.163655	+	0.118902i
$657$		0			0
$658$	3.55833	−	10.9514i	0.138718	−	0.426931i
$659$	4.59171	+	7.95307i	0.178868	+	0.309808i	0.941493	−	0.337033i	$-0.109423\pi$
$659$	4.59171	+	7.95307i	0.178868	+	0.309808i	−0.762625	+	0.646840i	$0.776090\pi$
$660$		0			0
$661$	6.85052	−	11.8654i	0.266454	−	0.461512i	−0.701489	−	0.712680i	$-0.747481\pi$
$661$	6.85052	−	11.8654i	0.266454	−	0.461512i	0.967944	+	0.251168i	$0.0808145\pi$
$662$	27.9476	+	31.0389i	1.08621	+	1.20636i
$663$		0			0
$664$	−1.19790	+	11.3973i	−0.0464877	+	0.442301i
$665$	15.0354	−	4.88529i	0.583047	−	0.189444i
$666$		0			0
$667$	−23.6832	+	32.5971i	−0.917016	+	1.26216i
$668$	43.7920	+	19.4975i	1.69436	+	0.754379i
$669$		0			0
$670$	4.34971	+	2.51131i	0.168044	+	0.0970202i
$671$	−12.5963	−	14.5550i	−0.486277	−	0.561890i
$672$		0			0
$673$	3.75375	+	17.6600i	0.144696	+	0.680743i	0.989365	+	0.145454i	$0.0464642\pi$
$673$	3.75375	+	17.6600i	0.144696	+	0.680743i	−0.844669	+	0.535290i	$0.820202\pi$
$674$	−43.8453	−	60.3479i	−1.68886	−	2.32451i
$675$		0			0
$676$	14.9519	+	46.0171i	0.575072	+	1.76989i
$677$	−17.6773	+	19.6326i	−0.679393	+	0.754542i	−0.979955	−	0.199220i	$-0.936159\pi$
$677$	−17.6773	+	19.6326i	−0.679393	+	0.754542i	0.300562	+	0.953762i	$0.402826\pi$
$678$		0			0
$679$	10.2688	−	1.07930i	0.394082	−	0.0414197i
$680$	52.2481	−	47.0444i	2.00362	−	1.80407i
$681$		0			0
$682$	7.09974	+	6.64988i	0.271863	+	0.254637i
$683$		−	19.4399i		−	0.743848i	−0.928263	−	0.371924i	$-0.878698\pi$
$683$		−	19.4399i		−	0.743848i	0.928263	−	0.371924i	$-0.121302\pi$
$684$		0			0
$685$	−0.485241	+	0.352548i	−0.0185401	+	0.0134702i
$686$	−34.1926	−	3.59379i	−1.30548	−	0.137212i
$687$		0			0
$688$	−4.98813	+	23.4673i	−0.190171	+	0.894683i
$689$	−11.0599	+	4.92418i	−0.421348	+	0.187596i
$690$		0			0
$691$	26.5419	−	5.64165i	1.00970	−	0.214618i	0.326772	−	0.945103i	$-0.394039\pi$
$691$	26.5419	−	5.64165i	1.00970	−	0.214618i	0.682929	+	0.730485i	$0.260706\pi$
$692$	−49.5042			−1.88187
$693$		0			0
$694$	43.8917			1.66611
$695$	−4.16727	+	0.885780i	−0.158073	+	0.0335996i
$696$		0			0
$697$	6.64005	−	2.95634i	0.251510	−	0.111979i
$698$	4.79637	−	22.5651i	0.181545	−	0.854103i
$699$		0			0
$700$	3.63254	+	0.381796i	0.137297	+	0.0144305i
$701$	39.8170	−	28.9287i	1.50387	−	1.09262i	0.535058	−	0.844815i	$-0.320290\pi$
$701$	39.8170	−	28.9287i	1.50387	−	1.09262i	0.968809	−	0.247808i	$-0.0797103\pi$
$702$		0			0
$703$		−	6.88160i		−	0.259545i
$704$	9.20913	−	19.6361i	0.347082	−	0.740064i
$705$		0			0
$706$	−26.8407	+	24.1675i	−1.01016	+	0.909555i
$707$	−3.84102	+	0.403708i	−0.144457	+	0.0151830i
$708$		0			0
$709$	−16.7358	+	18.5870i	−0.628528	+	0.698051i	−0.970347	−	0.241715i	$-0.922290\pi$
$709$	−16.7358	+	18.5870i	−0.628528	+	0.698051i	0.341819	+	0.939766i	$0.388957\pi$
$710$	10.0559	+	30.9487i	0.377390	+	1.16149i
$711$		0			0
$712$	−19.0315	−	26.1946i	−0.713235	−	0.981684i
$713$	−1.34128	−	6.31021i	−0.0502312	−	0.236319i
$714$		0			0
$715$	2.93095	+	6.94735i	0.109611	+	0.259816i
$716$	10.2568	+	5.92177i	0.383315	+	0.221307i
$717$		0			0
$718$	37.5991	+	16.7402i	1.40318	+	0.624738i
$719$	−2.83956	+	3.90832i	−0.105898	+	0.145756i	−0.858677	−	0.512518i	$-0.828713\pi$
$719$	−2.83956	+	3.90832i	−0.105898	+	0.145756i	0.752779	+	0.658273i	$0.228713\pi$
$720$		0			0
$721$	5.43203	−	1.76497i	0.202299	−	0.0657310i
$722$	−8.22933	+	78.2969i	−0.306264	+	2.91391i
$723$		0			0
$724$	64.4670	+	71.5978i	2.39590	+	2.66091i
$725$	−3.03394	+	5.25493i	−0.112678	+	0.195163i
$726$		0			0
$727$	−26.6643	−	46.1840i	−0.988926	−	1.71287i	−0.622991	−	0.782229i	$-0.714083\pi$
$727$	−26.6643	−	46.1840i	−0.988926	−	1.71287i	−0.365934	−	0.930641i	$-0.619250\pi$
$728$	−1.94642	+	5.99045i	−0.0721390	+	0.222021i
$729$		0			0
$730$	−3.38333	−	2.45814i	−0.125223	−	0.0909797i
$731$	25.0122	+	22.5211i	0.925109	+	0.832972i
$732$		0			0
$733$	−16.2870	−	36.5813i	−0.601576	−	1.35116i	−0.915732	−	0.401790i	$-0.868388\pi$
$733$	−16.2870	−	36.5813i	−0.601576	−	1.35116i	0.314156	−	0.949371i	$-0.398278\pi$
$734$	7.63179	+	72.6116i	0.281694	+	2.68014i
$735$		0			0
$736$	5.41593	−	3.12689i	0.199634	−	0.115259i
$737$	−1.98876	+	2.62713i	−0.0732570	+	0.0967716i
$738$		0			0
$739$	−6.09069	−	1.97899i	−0.224050	−	0.0727982i	0.194841	−	0.980835i	$-0.437581\pi$
$739$	−6.09069	−	1.97899i	−0.224050	−	0.0727982i	−0.418891	+	0.908037i	$0.637581\pi$
$740$	−3.30141	+	7.41510i	−0.121362	+	0.272584i
$741$		0			0
$742$	28.5535	+	6.06924i	1.04823	+	0.222809i
$743$	18.4429	+	3.92017i	0.676606	+	0.143817i	0.533383	−	0.845874i	$-0.320920\pi$
$743$	18.4429	+	3.92017i	0.676606	+	0.143817i	0.143222	+	0.989691i	$0.454254\pi$
$744$		0			0
$745$	13.9303	−	31.2879i	0.510366	−	1.14630i
$746$	16.4214	+	5.33564i	0.601230	+	0.195352i
$747$		0			0
$748$	51.3330	+	73.6555i	1.87692	+	2.69311i
$749$	10.3159	−	5.95586i	0.376933	−	0.217622i
$750$		0			0
$751$	−2.02187	−	19.2368i	−0.0737789	−	0.701960i	−0.967420	−	0.253177i	$-0.918524\pi$
$751$	−2.02187	−	19.2368i	−0.0737789	−	0.701960i	0.893641	−	0.448782i	$-0.148142\pi$
$752$	−8.19562	−	18.4077i	−0.298864	−	0.671259i
$753$		0			0
$754$	−15.1362	−	13.6287i	−0.551229	−	0.496329i
$755$	16.0297	+	11.6463i	0.583382	+	0.423852i
$756$		0			0
$757$	−4.32387	+	13.3075i	−0.157154	+	0.483670i	−0.998373	−	0.0570248i	$-0.981839\pi$
$757$	−4.32387	+	13.3075i	−0.157154	+	0.483670i	0.841219	+	0.540695i	$0.181839\pi$
$758$	−40.2760	−	69.7600i	−1.46289	−	2.53380i
$759$		0			0
$760$	38.0863	−	65.9674i	1.38153	−	2.39289i
$761$	14.1298	+	15.6927i	0.512203	+	0.568860i	0.942661	−	0.333751i	$-0.108315\pi$
$761$	14.1298	+	15.6927i	0.512203	+	0.568860i	−0.430458	+	0.902611i	$0.641648\pi$
$762$		0			0
$763$	−0.300641	+	2.86041i	−0.0108839	+	0.103554i
$764$	−3.20883	+	1.04261i	−0.116091	+	0.0377204i
$765$		0			0
$766$	35.6486	−	49.0661i	1.28804	−	1.77283i
$767$	−2.24065	−	0.997600i	−0.0809050	−	0.0360212i
$768$		0			0
$769$	−36.6834	−	21.1791i	−1.32284	−	0.763740i	−0.338656	−	0.940910i	$-0.609972\pi$
$769$	−36.6834	−	21.1791i	−1.32284	−	0.763740i	−0.984180	+	0.177171i	$0.943305\pi$
$770$	4.12886	−	17.7062i	0.148794	−	0.638088i
$771$		0			0
$772$	12.1762	+	57.2845i	0.438231	+	2.06171i
$773$	−9.77676	−	13.4566i	−0.351646	−	0.483999i	0.596152	−	0.802872i	$-0.296696\pi$
$773$	−9.77676	−	13.4566i	−0.351646	−	0.483999i	−0.947797	+	0.318873i	$0.896696\pi$
$774$		0			0
$775$	−0.300218	−	0.923977i	−0.0107842	−	0.0331902i
$776$	33.2896	−	36.9718i	1.19503	−	1.32721i
$777$		0			0
$778$	67.3583	−	7.07965i	2.41491	−	0.253818i
$779$	5.85216	−	5.26931i	0.209676	−	0.188793i
$780$		0			0
$781$	−20.9649	+	4.02731i	−0.750184	+	0.144109i
$782$		−	88.4907i		−	3.16442i
$783$		0			0
$784$	−22.1049	+	16.0602i	−0.789461	+	0.573577i
$785$	5.99928	+	0.630550i	0.214124	+	0.0225053i
$786$		0			0
$787$	−7.87356	+	37.0422i	−0.280662	+	1.32041i	0.581403	+	0.813615i	$0.302504\pi$
$787$	−7.87356	+	37.0422i	−0.280662	+	1.32041i	−0.862066	+	0.506797i	$0.830829\pi$
$788$	−50.3982	+	22.4387i	−1.79536	+	0.799346i
$789$		0			0
$790$	30.1509	−	6.40877i	1.07272	−	0.228014i
$791$	−10.0494			−0.357317
$792$		0			0
$793$	−6.45295			−0.229151
$794$	49.6134	−	10.5457i	1.76071	−	0.374251i
$795$		0			0
$796$	79.8787	−	35.5643i	2.83123	−	1.26054i
$797$	6.25741	−	29.4388i	0.221649	−	1.04278i	−0.716779	−	0.697300i	$-0.754384\pi$
$797$	6.25741	−	29.4388i	0.221649	−	1.04278i	0.938428	−	0.345475i	$-0.112282\pi$
$798$		0			0
$799$	−28.1127	−	2.95476i	−0.994555	−	0.104532i
$800$	0.761931	−	0.553576i	0.0269383	−	0.0195719i
$801$		0			0
$802$			24.7335i			0.873370i
$803$	1.87551	−	2.00238i	0.0661851	−	0.0706625i
$804$		0			0
$805$	−8.96042	+	8.06800i	−0.315813	+	0.284360i
$806$	3.24323	−	0.340877i	0.114238	−	0.0120069i
$807$		0			0
$808$	−12.4518	+	13.8292i	−0.438054	+	0.486508i
$809$	13.7550	+	42.3334i	0.483599	+	1.48836i	0.834000	+	0.551765i	$0.186045\pi$
$809$	13.7550	+	42.3334i	0.483599	+	1.48836i	−0.350401	+	0.936600i	$0.613955\pi$
$810$		0			0
$811$	16.8211	+	23.1522i	0.590667	+	0.812984i	0.994814	−	0.101710i	$-0.0324314\pi$
$811$	16.8211	+	23.1522i	0.590667	+	0.812984i	−0.404147	+	0.914694i	$0.632431\pi$
$812$	6.87014	+	32.3215i	0.241095	+	1.13426i
$813$		0			0
$814$	−6.77477	−	4.09101i	−0.237456	−	0.143390i
$815$	39.1219	+	22.5870i	1.37038	+	0.791190i
$816$		0			0
$817$	33.3127	+	14.8318i	1.16546	+	0.518898i
$818$	−11.8209	+	16.2701i	−0.413309	+	0.568872i
$819$		0			0
$820$	−8.83378	+	2.87027i	−0.308489	+	0.100234i
$821$	0.649932	−	6.18369i	0.0226828	−	0.215812i	−0.977309	−	0.211818i	$-0.932062\pi$
$821$	0.649932	−	6.18369i	0.0226828	−	0.215812i	0.999992	−	0.00399476i	$-0.00127158\pi$
$822$		0			0
$823$	−21.3309	−	23.6903i	−0.743547	−	0.825793i	0.246110	−	0.969242i	$-0.420847\pi$
$823$	−21.3309	−	23.6903i	−0.743547	−	0.825793i	−0.989658	+	0.143449i	$0.954181\pi$
$824$	13.7599	−	23.8329i	0.479349	−	0.830257i
$825$		0			0
$826$	2.95698	+	5.12163i	0.102886	+	0.178204i
$827$	−3.59606	+	11.0675i	−0.125047	+	0.384856i	−0.993910	−	0.110198i	$-0.964852\pi$
$827$	−3.59606	+	11.0675i	−0.125047	+	0.384856i	0.868862	+	0.495054i	$0.164852\pi$
$828$		0			0
$829$	32.8784	+	23.8875i	1.14191	+	0.829649i	0.987385	−	0.158340i	$-0.0506141\pi$
$829$	32.8784	+	23.8875i	1.14191	+	0.829649i	0.154529	+	0.987988i	$0.450614\pi$
$830$	−8.24111	−	7.42033i	−0.286053	−	0.257563i
$831$		0			0
$832$	−2.95730	−	6.64220i	−0.102526	−	0.230277i
$833$	4.00668	+	38.1210i	0.138823	+	1.32082i
$834$		0			0
$835$	−20.6381	+	11.9154i	−0.714210	+	0.412349i
$836$	77.5535	+	58.7088i	2.68225	+	2.03049i
$837$		0			0
$838$	−61.6394	−	20.0278i	−2.12930	−	0.691850i
$839$	−0.816775	+	1.83451i	−0.0281982	+	0.0633342i	−0.927096	−	0.374825i	$-0.877703\pi$
$839$	−0.816775	+	1.83451i	−0.0281982	+	0.0633342i	0.898897	+	0.438159i	$0.144369\pi$
$840$		0			0
$841$	−25.3284	−	5.38371i	−0.873392	−	0.185645i
$842$	−90.5889	−	19.2553i	−3.12190	−	0.663580i
$843$		0			0
$844$	24.9856	−	56.1187i	0.860041	−	1.93168i
$845$	−22.8767	−	7.43309i	−0.786983	−	0.255706i
$846$		0			0
$847$	11.1901	+	4.12872i	0.384497	+	0.141865i
$848$	44.2375	−	25.5405i	1.51912	−	0.877065i
$849$		0			0
$850$	−1.39299	−	13.2534i	−0.0477791	−	0.454588i
$851$	2.13476	+	4.79475i	0.0731787	+	0.164362i
$852$		0			0
$853$	−7.37963	−	6.64465i	−0.252674	−	0.227508i	0.533054	−	0.846081i	$-0.321044\pi$
$853$	−7.37963	−	6.64465i	−0.252674	−	0.227508i	−0.785727	+	0.618573i	$0.787711\pi$
$854$	12.5878	+	9.14560i	0.430747	+	0.312956i
$855$		0			0
$856$	17.7356	−	54.5847i	0.606192	−	1.86567i
$857$	−18.3785	−	31.8325i	−0.627797	−	1.08738i	−0.987993	−	0.154500i	$-0.950623\pi$
$857$	−18.3785	−	31.8325i	−0.627797	−	1.08738i	0.360196	−	0.932877i	$-0.382710\pi$
$858$		0			0
$859$	−16.6007	+	28.7532i	−0.566407	+	0.981045i	0.430510	+	0.902586i	$0.358334\pi$
$859$	−16.6007	+	28.7532i	−0.566407	+	0.981045i	−0.996917	+	0.0784599i	$0.975000\pi$
$860$	−28.7798	−	31.9632i	−0.981383	−	1.08994i
$861$		0			0
$862$	6.17016	−	58.7052i	0.210157	−	1.99951i
$863$	0.486372	−	0.158032i	0.0165563	−	0.00537947i	−0.300727	−	0.953710i	$-0.597229\pi$
$863$	0.486372	−	0.158032i	0.0165563	−	0.00537947i	0.317283	+	0.948331i	$0.397229\pi$
$864$		0			0
$865$	14.4655	−	19.9101i	0.491843	−	0.676964i
$866$	48.5268	+	21.6055i	1.64901	+	0.734186i
$867$		0			0
$868$	−4.58179	−	2.64530i	−0.155516	−	0.0897873i
$869$	1.71812	+	20.1487i	0.0582832	+	0.683499i
$870$		0			0
$871$	0.229662	+	1.08047i	0.00778179	+	0.0366105i
$872$	8.14560	+	11.2115i	0.275845	+	0.379668i
$873$		0			0
$874$	−29.6266	−	91.1812i	−1.00213	−	3.08425i
$875$	−8.63287	+	9.58777i	−0.291844	+	0.324126i
$876$		0			0
$877$	−35.7079	+	3.75306i	−1.20577	+	0.126732i	−0.686018	−	0.727585i	$-0.740643\pi$
$877$	−35.7079	+	3.75306i	−1.20577	+	0.126732i	−0.519753	+	0.854316i	$0.673976\pi$
$878$	−18.9825	+	17.0920i	−0.640630	+	0.576825i
$879$		0			0
$880$	−15.3628	−	27.8596i	−0.517880	−	0.939148i
$881$			6.31663i			0.212813i	0.994323	+	0.106406i	$0.0339345\pi$
$881$			6.31663i			0.212813i	−0.994323	+	0.106406i	$0.966066\pi$
$882$		0			0
$883$	−20.5419	+	14.9246i	−0.691290	+	0.502252i	−0.877084	−	0.480337i	$-0.840514\pi$
$883$	−20.5419	+	14.9246i	−0.691290	+	0.502252i	0.185794	+	0.982589i	$0.440514\pi$
$884$	29.9325	+	3.14603i	1.00674	+	0.105812i
$885$		0			0
$886$	−16.3131	+	76.7470i	−0.548049	+	2.57837i
$887$	−35.1095	+	15.6318i	−1.17886	+	0.524863i	−0.900179	−	0.435520i	$-0.856564\pi$
$887$	−35.1095	+	15.6318i	−1.17886	+	0.524863i	−0.278683	+	0.960383i	$0.589898\pi$
$888$		0			0
$889$	−12.2956	+	2.61351i	−0.412381	+	0.0876543i
$890$	31.3314			1.05023
$891$		0			0
$892$	−103.121			−3.45274
$893$	−29.9567	+	6.36749i	−1.00246	+	0.213080i
$894$		0			0
$895$	−5.37880	+	2.39480i	−0.179794	+	0.0800492i
$896$	−4.16349	+	19.5877i	−0.139092	+	0.654378i
$897$		0			0
$898$	21.8029	+	2.29157i	0.727571	+	0.0764708i
$899$	7.11054	−	5.16611i	0.237150	−	0.172299i
$900$		0			0
$901$		−	71.6604i		−	2.38735i
$902$	−1.70849	−	8.89384i	−0.0568864	−	0.296133i
$903$		0			0
$904$	−35.9836	+	32.3998i	−1.19680	+	1.07760i
$905$	−47.6337	+	5.00651i	−1.58340	+	0.166422i
$906$		0			0
$907$	−17.4943	+	19.4294i	−0.580889	+	0.645142i	−0.959931	−	0.280237i	$-0.909587\pi$
$907$	−17.4943	+	19.4294i	−0.580889	+	0.645142i	0.379042	+	0.925379i	$0.376254\pi$
$908$	3.71125	+	11.4221i	0.123162	+	0.379055i
$909$		0			0
$910$	−3.58259	−	4.93101i	−0.118762	−	0.163461i
$911$	6.94164	+	32.6578i	0.229987	+	1.08200i	0.929911	+	0.367785i	$0.119884\pi$
$911$	6.94164	+	32.6578i	0.229987	+	1.08200i	−0.699924	+	0.714217i	$0.746783\pi$
$912$		0			0
$913$	5.50106	−	4.76079i	0.182058	−	0.157559i
$914$	−35.9887	−	20.7781i	−1.19040	−	0.687279i
$915$		0			0
$916$	−12.5832	−	5.60242i	−0.415762	−	0.185109i
$917$	6.60355	−	9.08901i	0.218069	−	0.300146i
$918$		0			0
$919$	−17.6258	+	5.72696i	−0.581420	+	0.188915i	−0.584937	−	0.811079i	$-0.698881\pi$
$919$	−17.6258	+	5.72696i	−0.581420	+	0.188915i	0.00351649	+	0.999994i	$0.498881\pi$
$920$	−6.07267	+	57.7776i	−0.200210	+	1.90487i
$921$		0			0
$922$	16.4872	+	18.3109i	0.542978	+	0.603038i
$923$	−3.57838	+	6.19794i	−0.117784	+	0.204008i
$924$		0			0
$925$	0.395204	+	0.684514i	0.0129942	+	0.0225067i
$926$	−26.9490	+	82.9406i	−0.885600	+	2.72560i
$927$		0			0
$928$	6.89296	+	5.00803i	0.226273	+	0.164397i
$929$	−25.0660	−	22.5696i	−0.822390	−	0.740483i	0.146171	−	0.989259i	$-0.453305\pi$
$929$	−25.0660	−	22.5696i	−0.822390	−	0.740483i	−0.968561	+	0.248776i	$0.919972\pi$
$930$		0			0
$931$	16.8914	+	37.9387i	0.553593	+	1.24339i
$932$	−5.21234	−	49.5921i	−0.170736	−	1.62444i
$933$		0			0
$934$	−8.50470	+	4.91019i	−0.278282	+	0.160666i
$935$	−44.6235	−	0.877128i	−1.45934	−	0.0286852i
$936$		0			0
$937$	−5.72211	−	1.85923i	−0.186933	−	0.0607383i	0.214054	−	0.976822i	$-0.431333\pi$
$937$	−5.72211	−	1.85923i	−0.186933	−	0.0607383i	−0.400988	+	0.916083i	$0.631333\pi$
$938$	1.08332	−	2.43318i	0.0353717	−	0.0794462i
$939$		0			0
$940$	35.3339	+	7.51044i	1.15246	+	0.244964i
$941$	42.5319	+	9.04044i	1.38650	+	0.294710i	0.839927	−	0.542700i	$-0.182598\pi$
$941$	42.5319	+	9.04044i	1.38650	+	0.294710i	0.546575	+	0.837410i	$0.315931\pi$
$942$		0			0
$943$	−2.44288	+	5.48681i	−0.0795513	+	0.178675i
$944$	9.84211	+	3.19790i	0.320334	+	0.104083i
$945$		0			0
$946$	34.4054	−	23.9783i	1.11862	−	0.779601i
$947$	5.19891	−	3.00159i	0.168942	−	0.0975387i	−0.413145	−	0.910665i	$-0.635570\pi$
$947$	5.19891	−	3.00159i	0.168942	−	0.0975387i	0.582087	+	0.813127i	$0.302236\pi$
$948$		0			0
$949$	−0.0961395	−	0.914706i	−0.00312082	−	0.0296926i
$950$	−5.87257	−	13.1900i	−0.190531	−	0.427940i
$951$		0			0
$952$	−27.7067	−	24.9473i	−0.897980	−	0.808545i
$953$	−4.38241	−	3.18400i	−0.141960	−	0.103140i	0.514539	−	0.857467i	$-0.327963\pi$
$953$	−4.38241	−	3.18400i	−0.141960	−	0.103140i	−0.656499	+	0.754327i	$0.727963\pi$
$954$		0			0
$955$	0.518319	−	1.59522i	0.0167724	−	0.0516201i
$956$	−13.9761	−	24.2073i	−0.452020	−	0.782921i
$957$		0			0
$958$	41.7780	−	72.3616i	1.34979	−	2.33790i
$959$	0.212827	+	0.236368i	0.00687253	+	0.00763271i
$960$		0			0
$961$	3.09329	−	29.4307i	0.0997835	−	0.949376i
$962$	−2.52328	+	0.819864i	−0.0813539	+	0.0264335i
$963$		0			0
$964$	−7.88182	+	10.8484i	−0.253856	+	0.349403i
$965$	−26.5973	−	11.8419i	−0.856196	−	0.381203i
$966$		0			0
$967$	30.2152	+	17.4447i	0.971654	+	0.560985i	0.899740	−	0.436426i	$-0.143756\pi$
$967$	30.2152	+	17.4447i	0.971654	+	0.560985i	0.0719138	+	0.997411i	$0.477089\pi$
$968$	53.3792	−	21.2938i	1.71567	−	0.684409i
$969$		0			0
$970$	10.0092	+	47.0898i	0.321377	+	1.51196i
$971$	25.4555	+	35.0365i	0.816907	+	1.12438i	0.990221	+	0.139509i	$0.0445526\pi$
$971$	25.4555	+	35.0365i	0.816907	+	1.12438i	−0.173314	+	0.984867i	$0.555447\pi$
$972$		0			0
$973$	0.698143	+	2.14866i	0.0223814	+	0.0688830i
$974$	25.7500	−	28.5983i	0.825084	−	0.916349i
$975$		0			0
$976$	27.0777	−	2.84598i	0.866736	−	0.0910977i
$977$	24.1135	−	21.7119i	0.771460	−	0.694625i	−0.186205	−	0.982511i	$-0.559619\pi$
$977$	24.1135	−	21.7119i	0.771460	−	0.694625i	0.957665	+	0.287885i	$0.0929522\pi$
$978$		0			0
$979$	−2.54983	+	20.3956i	−0.0814930	+	0.651847i
$980$		−	48.9834i		−	1.56472i
$981$		0			0
$982$	−16.6915	+	12.1271i	−0.532648	+	0.386991i
$983$	17.7699	+	1.86769i	0.566772	+	0.0595702i	0.383581	−	0.923507i	$-0.374691\pi$
$983$	17.7699	+	1.86769i	0.566772	+	0.0595702i	0.183191	+	0.983077i	$0.441357\pi$
$984$		0			0
$985$	5.70214	−	26.8264i	0.181685	−	0.854762i
$986$	110.137	−	49.0361i	3.50748	−	1.56163i
$987$		0			0
$988$	31.8958	−	6.77967i	1.01474	−	0.215690i
$989$	−27.8116			−0.884358
$990$		0			0
$991$	21.5914			0.685875			0.342937	−	0.939358i	$-0.388578\pi$
$991$	21.5914			0.685875			0.342937	+	0.939358i	$0.388578\pi$
$992$	−1.33435	+	0.283626i	−0.0423658	+	0.00900512i
$993$		0			0
$994$	15.7646	−	7.01883i	0.500021	−	0.222624i
$995$	−9.03761	+	42.5186i	−0.286512	+	1.34793i
$996$		0			0
$997$	−23.7892	−	2.50034i	−0.753411	−	0.0791867i	−0.279966	−	0.960010i	$-0.590323\pi$
$997$	−23.7892	−	2.50034i	−0.753411	−	0.0791867i	−0.473445	+	0.880823i	$0.656990\pi$
$998$	−0.364697	+	0.264968i	−0.0115443	+	0.00838740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.233.9		80
3.2	odd	2		99.2.p.a.68.2	yes	80
9.2	odd	6	inner	297.2.t.a.35.9		80
9.4	even	3		891.2.k.a.728.2		80
9.5	odd	6		891.2.k.a.728.19		80
9.7	even	3		99.2.p.a.2.2	✓	80
11.6	odd	10	inner	297.2.t.a.17.9		80
33.17	even	10		99.2.p.a.50.2	yes	80
99.50	even	30		891.2.k.a.809.2		80
99.61	odd	30		99.2.p.a.83.2	yes	80
99.83	even	30	inner	297.2.t.a.116.9		80
99.94	odd	30		891.2.k.a.809.19		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.2	✓	80	9.7	even	3
99.2.p.a.50.2	yes	80	33.17	even	10
99.2.p.a.68.2	yes	80	3.2	odd	2
99.2.p.a.83.2	yes	80	99.61	odd	30
297.2.t.a.17.9		80	11.6	odd	10	inner
297.2.t.a.35.9		80	9.2	odd	6	inner
297.2.t.a.116.9		80	99.83	even	30	inner
297.2.t.a.233.9		80	1.1	even	1	trivial
891.2.k.a.728.2		80	9.4	even	3
891.2.k.a.728.19		80	9.5	odd	6
891.2.k.a.809.2		80	99.50	even	30
891.2.k.a.809.19		80	99.94	odd	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.41844 - 0.514054i) q^{2} +(3.75749 - 1.67294i) q^{4} +(-0.425128 + 2.00007i) q^{5} +(1.07838 + 0.113342i) q^{7} +(4.22672 - 3.07089i) q^{8} +5.05558i q^{10} +(-3.29101 - 0.411437i) q^{11} +(-0.826275 + 0.743982i) q^{13} +(2.66625 - 0.280234i) q^{14} +(3.13907 - 3.48629i) q^{16} +(-2.03372 - 6.25916i) q^{17} +(-4.19112 - 5.76858i) q^{19} +(1.74859 + 8.22645i) q^{20} +(-8.17059 + 0.696721i) q^{22} +(4.70965 + 2.71912i) q^{23} +(0.748176 + 0.333109i) q^{25} +(-1.61585 + 2.22402i) q^{26} +(4.24160 - 1.37818i) q^{28} +(-0.774458 + 7.36848i) q^{29} +(-0.793766 - 0.881566i) q^{31} +(0.574983 - 0.995900i) q^{32} +(-8.13598 - 14.0919i) q^{34} +(-0.685140 + 2.10865i) q^{35} +(0.780793 + 0.567279i) q^{37} +(-13.1013 - 11.7965i) q^{38} +(4.34511 + 9.75927i) q^{40} +(0.115443 + 1.09836i) q^{41} +(-4.42893 + 2.55705i) q^{43} +(-13.0542 + 3.95969i) q^{44} +(12.7877 + 4.15499i) q^{46} +(1.74699 - 3.92381i) q^{47} +(-5.69698 - 1.21093i) q^{49} +(1.98065 + 0.421000i) q^{50} +(-1.86008 + 4.17781i) q^{52} +(10.3556 + 3.36474i) q^{53} +(2.22200 - 6.40733i) q^{55} +(4.90606 - 2.83251i) q^{56} +(1.91482 + 18.2183i) q^{58} +(0.897232 + 2.01522i) q^{59} +(4.31301 + 3.88345i) q^{61} +(-2.37284 - 1.72397i) q^{62} +(-2.02075 + 6.21923i) q^{64} +(-1.13674 - 1.96890i) q^{65} +(0.496739 - 0.860378i) q^{67} +(-18.1129 - 20.1164i) q^{68} +(-0.573009 + 5.45182i) q^{70} +(6.12170 - 1.98906i) q^{71} +(-0.486222 + 0.669227i) q^{73} +(2.17991 + 0.970558i) q^{74} +(-25.3986 - 14.6639i) q^{76} +(-3.50231 - 0.816693i) q^{77} +(-1.26766 - 5.96388i) q^{79} +(5.63833 + 7.76049i) q^{80} +(0.843809 + 2.59698i) q^{82} +(-1.46775 + 1.63010i) q^{83} +(13.3834 - 1.40665i) q^{85} +(-9.39663 + 8.46076i) q^{86} +(-15.1736 + 8.36730i) q^{88} -6.19738i q^{89} +(-0.975360 + 0.708641i) q^{91} +(22.2454 + 2.33808i) q^{92} +(2.20794 - 10.3875i) q^{94} +(13.3193 - 5.93015i) q^{95} +(9.31442 - 1.97984i) q^{97} -14.4003 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

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