LMFDB - Embedded newform 648.2.t.a.397.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			397.31
Character	$\chi$	$=$	648.397
Dual form			648.2.t.a.253.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34345 + 0.441744i) q^{2} +(1.60972 + 1.18692i) q^{4} +(0.721676 + 0.860059i) q^{5} +(1.31793 - 0.479686i) q^{7} +(1.63827 + 2.30566i) q^{8} +(0.589610 + 1.47424i) q^{10} +(-1.05816 + 1.26106i) q^{11} +(-0.671077 + 0.118329i) q^{13} +(1.98247 - 0.0622489i) q^{14} +(1.18243 + 3.82124i) q^{16} +(-0.907443 - 1.57174i) q^{17} +(2.96777 + 1.71344i) q^{19} +(0.140874 + 2.24103i) q^{20} +(-1.97865 + 1.22674i) q^{22} +(3.62278 + 1.31858i) q^{23} +(0.649354 - 3.68267i) q^{25} +(-0.953831 - 0.137475i) q^{26} +(2.69085 + 0.792115i) q^{28} +(-3.92395 - 0.691898i) q^{29} +(-6.21468 - 2.26196i) q^{31} +(-0.0994769 + 5.65598i) q^{32} +(-0.524800 - 2.51241i) q^{34} +(1.36367 + 0.787317i) q^{35} +(3.83532 - 2.21432i) q^{37} +(3.23015 + 3.61292i) q^{38} +(-0.800705 + 3.07295i) q^{40} +(-0.952217 - 5.40029i) q^{41} +(-7.26017 + 8.65234i) q^{43} +(-3.20013 + 0.774013i) q^{44} +(4.28455 + 3.37179i) q^{46} +(11.5469 - 4.20273i) q^{47} +(-3.85548 + 3.23513i) q^{49} +(2.49917 - 4.66064i) q^{50} +(-1.22070 - 0.606040i) q^{52} -6.89741i q^{53} -1.84824 q^{55} +(3.26511 + 2.25283i) q^{56} +(-4.96599 - 2.66291i) q^{58} +(6.78921 + 8.09106i) q^{59} +(1.24084 + 3.40917i) q^{61} +(-7.34992 - 5.78413i) q^{62} +(-2.63214 + 7.55459i) q^{64} +(-0.586070 - 0.491771i) q^{65} +(-11.9425 + 2.10578i) q^{67} +(0.404798 - 3.60713i) q^{68} +(1.48424 + 1.66012i) q^{70} +(-6.80355 - 11.7841i) q^{71} +(4.73823 - 8.20685i) q^{73} +(6.13073 - 1.28061i) q^{74} +(2.74357 + 6.28068i) q^{76} +(-0.789660 + 2.16957i) q^{77} +(1.59290 - 9.03380i) q^{79} +(-2.43316 + 3.77465i) q^{80} +(1.10629 - 7.67567i) q^{82} +(-1.29853 - 0.228966i) q^{83} +(0.696908 - 1.91474i) q^{85} +(-13.5758 + 8.41686i) q^{86} +(-4.64114 - 0.373789i) q^{88} +(3.52339 - 6.10270i) q^{89} +(-0.827669 + 0.477855i) q^{91} +(4.26662 + 6.42251i) q^{92} +(17.3692 - 0.545389i) q^{94} +(0.668104 + 3.78901i) q^{95} +(-6.33275 - 5.31381i) q^{97} +(-6.60875 + 2.64311i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.34345	+	0.441744i	0.949964	+	0.312360i
$2$	1.34345	+	0.441744i	0.949964	+	0.312360i
$3$		0			0
$3$		0			0
$4$	1.60972	+	1.18692i	0.804862	+	0.593462i
$5$	0.721676	+	0.860059i	0.322743	+	0.384630i	0.902883	−	0.429887i	$-0.141447\pi$
$5$	0.721676	+	0.860059i	0.322743	+	0.384630i	−0.580140	+	0.814517i	$0.697002\pi$
$6$		0			0
$7$	1.31793	−	0.479686i	0.498129	−	0.181304i	−0.0807232	−	0.996737i	$-0.525723\pi$
$7$	1.31793	−	0.479686i	0.498129	−	0.181304i	0.578852	+	0.815432i	$0.303501\pi$
$8$	1.63827	+	2.30566i	0.579216	+	0.815174i
$9$		0			0
$10$	0.589610	+	1.47424i	0.186451	+	0.466197i
$11$	−1.05816	+	1.26106i	−0.319047	+	0.380225i	−0.901602	−	0.432566i	$-0.857608\pi$
$11$	−1.05816	+	1.26106i	−0.319047	+	0.380225i	0.582556	+	0.812791i	$0.302053\pi$
$12$		0			0
$13$	−0.671077	+	0.118329i	−0.186123	+	0.0328186i	−0.265933	−	0.963992i	$-0.585680\pi$
$13$	−0.671077	+	0.118329i	−0.186123	+	0.0328186i	0.0798095	+	0.996810i	$0.474569\pi$
$14$	1.98247	−	0.0622489i	0.529837	−	0.0166367i
$15$		0			0
$16$	1.18243	+	3.82124i	0.295607	+	0.955310i
$17$	−0.907443	−	1.57174i	−0.220087	−	0.381202i	0.734747	−	0.678341i	$-0.237301\pi$
$17$	−0.907443	−	1.57174i	−0.220087	−	0.381202i	−0.954834	+	0.297139i	$0.903968\pi$
$18$		0			0
$19$	2.96777	+	1.71344i	0.680853	+	0.393091i	0.800176	−	0.599765i	$-0.204739\pi$
$19$	2.96777	+	1.71344i	0.680853	+	0.393091i	−0.119323	+	0.992855i	$0.538073\pi$
$20$	0.140874	+	2.24103i	0.0315004	+	0.501110i
$21$		0			0
$22$	−1.97865	+	1.22674i	−0.421850	+	0.261543i
$23$	3.62278	+	1.31858i	0.755401	+	0.274944i	0.690877	−	0.722973i	$-0.257225\pi$
$23$	3.62278	+	1.31858i	0.755401	+	0.274944i	0.0645244	+	0.997916i	$0.479447\pi$
$24$		0			0
$25$	0.649354	−	3.68267i	0.129871	−	0.736534i
$26$	−0.953831	−	0.137475i	−0.187062	−	0.0269611i
$27$		0			0
$28$	2.69085	+	0.792115i	0.508522	+	0.149696i
$29$	−3.92395	−	0.691898i	−0.728659	−	0.128482i	−0.203001	−	0.979179i	$-0.565070\pi$
$29$	−3.92395	−	0.691898i	−0.728659	−	0.128482i	−0.525657	+	0.850696i	$0.676181\pi$
$30$		0			0
$31$	−6.21468	−	2.26196i	−1.11619	−	0.406260i	−0.282930	−	0.959141i	$-0.591306\pi$
$31$	−6.21468	−	2.26196i	−1.11619	−	0.406260i	−0.833260	+	0.552881i	$0.813529\pi$
$32$	−0.0994769	+	5.65598i	−0.0175852	+	0.999845i
$33$		0			0
$34$	−0.524800	−	2.51241i	−0.0900025	−	0.430875i
$35$	1.36367	+	0.787317i	0.230503	+	0.133081i
$36$		0			0
$37$	3.83532	−	2.21432i	0.630522	−	0.364032i	−0.150432	−	0.988620i	$-0.548066\pi$
$37$	3.83532	−	2.21432i	0.630522	−	0.364032i	0.780954	+	0.624588i	$0.214733\pi$
$38$	3.23015	+	3.61292i	0.524000	+	0.586093i
$39$		0			0
$40$	−0.800705	+	3.07295i	−0.126603	+	0.485876i
$41$	−0.952217	−	5.40029i	−0.148711	−	0.843384i	−0.964312	−	0.264769i	$-0.914704\pi$
$41$	−0.952217	−	5.40029i	−0.148711	−	0.843384i	0.815601	−	0.578615i	$-0.196407\pi$
$42$		0			0
$43$	−7.26017	+	8.65234i	−1.10717	+	1.31947i	−0.164257	+	0.986418i	$0.552523\pi$
$43$	−7.26017	+	8.65234i	−1.10717	+	1.31947i	−0.942909	+	0.333051i	$0.891922\pi$
$44$	−3.20013	+	0.774013i	−0.482438	+	0.116687i
$45$		0			0
$46$	4.28455	+	3.37179i	0.631722	+	0.497144i
$47$	11.5469	−	4.20273i	1.68429	−	0.613031i	0.690402	−	0.723426i	$-0.257434\pi$
$47$	11.5469	−	4.20273i	1.68429	−	0.613031i	0.993888	+	0.110395i	$0.0352116\pi$
$48$		0			0
$49$	−3.85548	+	3.23513i	−0.550783	+	0.462162i
$50$	2.49917	−	4.66064i	0.353437	−	0.659114i
$51$		0			0
$52$	−1.22070	−	0.606040i	−0.169280	−	0.0840426i
$53$		−	6.89741i		−	0.947432i	−0.880678	−	0.473716i	$-0.842912\pi$
$53$		−	6.89741i		−	0.947432i	0.880678	−	0.473716i	$-0.157088\pi$
$54$		0			0
$55$	−1.84824			−0.249216
$56$	3.26511	+	2.25283i	0.436319	+	0.301048i
$57$		0			0
$58$	−4.96599	−	2.66291i	−0.652067	−	0.349657i
$59$	6.78921	+	8.09106i	0.883880	+	1.05337i	0.998203	+	0.0599230i	$0.0190855\pi$
$59$	6.78921	+	8.09106i	0.883880	+	1.05337i	−0.114323	+	0.993444i	$0.536470\pi$
$60$		0			0
$61$	1.24084	+	3.40917i	0.158873	+	0.436499i	0.993433	−	0.114418i	$-0.0365003\pi$
$61$	1.24084	+	3.40917i	0.158873	+	0.436499i	−0.834560	+	0.550917i	$0.814278\pi$
$62$	−7.34992	−	5.78413i	−0.933441	−	0.734586i
$63$		0			0
$64$	−2.63214	+	7.55459i	−0.329017	+	0.944324i
$65$	−0.586070	−	0.491771i	−0.0726930	−	0.0609967i
$66$		0			0
$67$	−11.9425	+	2.10578i	−1.45901	+	0.257263i	−0.846156	−	0.532935i	$-0.821089\pi$
$67$	−11.9425	+	2.10578i	−1.45901	+	0.257263i	−0.612852	+	0.790198i	$0.709978\pi$
$68$	0.404798	−	3.60713i	0.0490890	−	0.437429i
$69$		0			0
$70$	1.48424	+	1.66012i	0.177400	+	0.198422i
$71$	−6.80355	−	11.7841i	−0.807432	−	1.39851i	−0.914637	−	0.404277i	$-0.867523\pi$
$71$	−6.80355	−	11.7841i	−0.807432	−	1.39851i	0.107204	−	0.994237i	$-0.465810\pi$
$72$		0			0
$73$	4.73823	−	8.20685i	0.554567	−	0.960539i	−0.443370	−	0.896339i	$-0.646217\pi$
$73$	4.73823	−	8.20685i	0.554567	−	0.960539i	0.997937	−	0.0642000i	$-0.0204496\pi$
$74$	6.13073	−	1.28061i	0.712682	−	0.148867i
$75$		0			0
$76$	2.74357	+	6.28068i	0.314709	+	0.720444i
$77$	−0.789660	+	2.16957i	−0.0899901	+	0.247246i
$78$		0			0
$79$	1.59290	−	9.03380i	0.179215	−	1.01638i	−0.753949	−	0.656933i	$-0.771854\pi$
$79$	1.59290	−	9.03380i	0.179215	−	1.01638i	0.933165	−	0.359449i	$-0.117035\pi$
$80$	−2.43316	+	3.77465i	−0.272036	+	0.422019i
$81$		0			0
$82$	1.10629	−	7.67567i	0.122169	−	0.847635i
$83$	−1.29853	−	0.228966i	−0.142532	−	0.0251322i	0.101927	−	0.994792i	$-0.467499\pi$
$83$	−1.29853	−	0.228966i	−0.142532	−	0.0251322i	−0.244459	+	0.969660i	$0.578610\pi$
$84$		0			0
$85$	0.696908	−	1.91474i	0.0755903	−	0.207683i
$86$	−13.5758	+	8.41686i	−1.46392	+	0.907613i
$87$		0			0
$88$	−4.64114	−	0.373789i	−0.494747	−	0.0398461i
$89$	3.52339	−	6.10270i	0.373479	−	0.646884i	−0.616619	−	0.787262i	$-0.711498\pi$
$89$	3.52339	−	6.10270i	0.373479	−	0.646884i	0.990098	+	0.140377i	$0.0448315\pi$
$90$		0			0
$91$	−0.827669	+	0.477855i	−0.0867633	+	0.0500928i
$92$	4.26662	+	6.42251i	0.444825	+	0.669593i
$93$		0			0
$94$	17.3692	−	0.545389i	1.79150	−	0.0562525i
$95$	0.668104	+	3.78901i	0.0685460	+	0.388744i
$96$		0			0
$97$	−6.33275	−	5.31381i	−0.642993	−	0.539535i	0.261943	−	0.965083i	$-0.415637\pi$
$97$	−6.33275	−	5.31381i	−0.642993	−	0.539535i	−0.904936	+	0.425548i	$0.860081\pi$
$98$	−6.60875	+	2.64311i	−0.667585	+	0.266994i
$99$		0			0
$100$	5.41633	−	5.15735i	0.541633	−	0.515735i
$101$	−6.04137	−	16.5985i	−0.601139	−	1.65162i	−0.748971	−	0.662603i	$-0.769452\pi$
$101$	−6.04137	−	16.5985i	−0.601139	−	1.65162i	0.147832	−	0.989012i	$-0.452770\pi$
$102$		0			0
$103$	−2.98038	+	2.50084i	−0.293666	+	0.246415i	−0.777702	−	0.628633i	$-0.783615\pi$
$103$	−2.98038	+	2.50084i	−0.293666	+	0.246415i	0.484036	+	0.875048i	$0.339170\pi$
$104$	−1.37223	−	1.35342i	−0.134558	−	0.132714i
$105$		0			0
$106$	3.04689	−	9.26634i	0.295940	−	0.900026i
$107$			4.16409i			0.402558i	0.979534	+	0.201279i	$0.0645098\pi$
$107$			4.16409i			0.402558i	−0.979534	+	0.201279i	$0.935490\pi$
$108$		0			0
$109$		−	20.6082i		−	1.97391i	−0.161002	−	0.986954i	$-0.551473\pi$
$109$		−	20.6082i		−	1.97391i	0.161002	−	0.986954i	$-0.448527\pi$
$110$	−2.48302	−	0.816448i	−0.236746	−	0.0778452i
$111$		0			0
$112$	3.39134	+	4.46892i	0.320452	+	0.422273i
$113$	−2.03205	+	1.70510i	−0.191160	+	0.160402i	−0.733344	−	0.679857i	$-0.762042\pi$
$113$	−2.03205	+	1.70510i	−0.191160	+	0.160402i	0.542185	+	0.840259i	$0.317597\pi$
$114$		0			0
$115$	1.48041	+	4.06739i	0.138049	+	0.379286i
$116$	−5.49524	−	5.77119i	−0.510221	−	0.535841i
$117$		0			0
$118$	5.54679	+	13.8690i	0.510624	+	1.27675i
$119$	−1.94988	−	1.63615i	−0.178745	−	0.149985i
$120$		0			0
$121$	1.43955	+	8.16407i	0.130868	+	0.742188i
$122$	0.161023	+	5.12818i	0.0145784	+	0.464284i
$123$		0			0
$124$	−7.31916	−	11.0175i	−0.657280	−	0.989399i
$125$	8.49749	−	4.90603i	0.760039	−	0.438809i
$126$		0			0
$127$	−2.14785	+	3.72019i	−0.190591	+	0.330113i	−0.945446	−	0.325778i	$-0.894374\pi$
$127$	−2.14785	+	3.72019i	−0.190591	+	0.330113i	0.754855	+	0.655891i	$0.227707\pi$
$128$	−6.87334	+	8.98650i	−0.607524	+	0.794302i
$129$		0			0
$130$	−0.570120	−	0.919563i	−0.0500028	−	0.0806510i
$131$	−2.70846	+	7.44142i	−0.236639	+	0.650160i	0.763352	+	0.645982i	$0.223552\pi$
$131$	−2.70846	+	7.44142i	−0.236639	+	0.650160i	−0.999991	+	0.00417788i	$0.998670\pi$
$132$		0			0
$133$	4.73321	+	0.834593i	0.410422	+	0.0723684i
$134$	−16.9744	−	2.44651i	−1.46636	−	0.211346i
$135$		0			0
$136$	2.13726	−	4.66719i	0.183268	−	0.400208i
$137$	−2.73472	+	15.5094i	−0.233643	+	1.32506i	0.611809	+	0.791006i	$0.290442\pi$
$137$	−2.73472	+	15.5094i	−0.233643	+	1.32506i	−0.845452	+	0.534051i	$0.820669\pi$
$138$		0			0
$139$	0.133147	−	0.365819i	0.0112934	−	0.0310283i	−0.933918	−	0.357488i	$-0.883633\pi$
$139$	0.133147	−	0.365819i	0.0112934	−	0.0310283i	0.945211	+	0.326459i	$0.105856\pi$
$140$	1.26065	+	2.88594i	0.106545	+	0.243906i
$141$		0			0
$142$	−3.93469	−	18.8368i	−0.330191	−	1.58075i
$143$	0.560885	−	0.971482i	0.0469036	−	0.0812394i
$144$		0			0
$145$	−2.23674	−	3.87415i	−0.185751	−	0.321731i
$146$	9.99090	−	8.93242i	0.826853	−	0.739252i
$147$		0			0
$148$	8.80203	+	0.987780i	0.723523	+	0.0811950i
$149$	−11.6562	+	2.05530i	−0.954913	+	0.168377i	−0.629331	−	0.777137i	$-0.716671\pi$
$149$	−11.6562	+	2.05530i	−0.954913	+	0.168377i	−0.325581	+	0.945514i	$0.605560\pi$
$150$		0			0
$151$	7.05111	+	5.91658i	0.573811	+	0.481485i	0.882908	−	0.469546i	$-0.155582\pi$
$151$	7.05111	+	5.91658i	0.573811	+	0.481485i	−0.309097	+	0.951031i	$0.600027\pi$
$152$	0.911394	+	9.64975i	0.0739238	+	0.782698i
$153$		0			0
$154$	−2.01927	+	2.56589i	−0.162717	+	0.206765i
$155$	−2.53957	−	6.97740i	−0.203983	−	0.560438i
$156$		0			0
$157$	−8.84016	−	10.5353i	−0.705521	−	0.840807i	0.287618	−	0.957745i	$-0.407137\pi$
$157$	−8.84016	−	10.5353i	−0.705521	−	0.840807i	−0.993139	+	0.116938i	$0.962692\pi$
$158$	6.13061	−	11.4328i	0.487725	−	0.909546i
$159$		0			0
$160$	−4.93627	+	3.99623i	−0.390246	+	0.315929i
$161$	5.40706			0.426136
$162$		0			0
$163$		−	12.7196i		−	0.996272i	−0.867099	−	0.498136i	$-0.834018\pi$
$163$		−	12.7196i		−	0.996272i	0.867099	−	0.498136i	$-0.165982\pi$
$164$	4.87692	−	9.82319i	0.380824	−	0.767062i
$165$		0			0
$166$	−1.64337	−	0.881221i	−0.127550	−	0.0683960i
$167$	−15.1696	+	12.7288i	−1.17386	+	0.984986i	−0.173861	+	0.984770i	$0.555624\pi$
$167$	−15.1696	+	12.7288i	−1.17386	+	0.984986i	−1.00000		0.000215714i	$0.999931\pi$
$168$		0			0
$169$	−11.7797	+	4.28745i	−0.906128	+	0.329804i
$170$	1.78209	−	2.26450i	0.136680	−	0.173680i
$171$		0			0
$172$	−21.9565	+	5.31061i	−1.67417	+	0.404930i
$173$	3.14984	−	3.75384i	0.239478	−	0.285399i	−0.632897	−	0.774236i	$-0.718134\pi$
$173$	3.14984	−	3.75384i	0.239478	−	0.285399i	0.872375	+	0.488837i	$0.162579\pi$
$174$		0			0
$175$	−0.910724	−	5.16497i	−0.0688443	−	0.390435i
$176$	−6.07002	−	2.55236i	−0.457545	−	0.192392i
$177$		0			0
$178$	7.42934	−	6.64224i	0.556852	−	0.497857i
$179$	3.21176	−	1.85431i	0.240058	−	0.138598i	−0.375145	−	0.926966i	$-0.622407\pi$
$179$	3.21176	−	1.85431i	0.240058	−	0.138598i	0.615204	+	0.788368i	$0.289074\pi$
$180$		0			0
$181$	14.1322	+	8.15921i	1.05044	+	0.606470i	0.922771	−	0.385348i	$-0.125919\pi$
$181$	14.1322	+	8.15921i	1.05044	+	0.606470i	0.127665	+	0.991817i	$0.459252\pi$
$182$	−1.32302	+	0.276357i	−0.0980690	+	0.0204850i
$183$		0			0
$184$	2.89489	+	10.5131i	0.213414	+	0.775035i
$185$	4.67230	+	1.70058i	0.343515	+	0.125029i
$186$		0			0
$187$	2.94228	+	0.518804i	0.215161	+	0.0379387i
$188$	23.5757	+	6.94005i	1.71943	+	0.506155i
$189$		0			0
$190$	−0.776205	+	5.38548i	−0.0563118	+	0.390704i
$191$	−1.19811	+	6.79482i	−0.0866922	+	0.491656i	0.910286	+	0.413979i	$0.135861\pi$
$191$	−1.19811	+	6.79482i	−0.0866922	+	0.491656i	−0.996979	+	0.0776767i	$0.975250\pi$
$192$		0			0
$193$	8.95564	+	3.25959i	0.644641	+	0.234630i	0.643591	−	0.765369i	$-0.277444\pi$
$193$	8.95564	+	3.25959i	0.644641	+	0.234630i	0.00104978	+	0.999999i	$0.499666\pi$
$194$	−6.16040	−	9.93630i	−0.442291	−	0.713385i
$195$		0			0
$196$	−10.0461	+	0.631512i	−0.717580	+	0.0451080i
$197$	−1.74001	−	1.00460i	−0.123971	−	0.0715746i	0.436732	−	0.899592i	$-0.356136\pi$
$197$	−1.74001	−	1.00460i	−0.123971	−	0.0715746i	−0.560703	+	0.828017i	$0.689469\pi$
$198$		0			0
$199$	10.6564	+	18.4573i	0.755409	+	1.30841i	0.945171	+	0.326576i	$0.105895\pi$
$199$	10.6564	+	18.4573i	0.755409	+	1.30841i	−0.189762	+	0.981830i	$0.560772\pi$
$200$	9.55481	−	4.53602i	0.675627	−	0.320745i
$201$		0			0
$202$	−0.783989	−	24.9681i	−0.0551613	−	1.75675i
$203$	−5.50336	+	0.970392i	−0.386260	+	0.0681081i
$204$		0			0
$205$	3.95738	−	4.71622i	0.276395	−	0.329395i
$206$	−5.10873	+	2.04319i	−0.355942	+	0.142356i
$207$		0			0
$208$	−1.24566	−	2.42443i	−0.0863711	−	0.168104i
$209$	−5.30113	+	1.92945i	−0.366687	+	0.133463i
$210$		0			0
$211$	5.98817	+	7.13642i	0.412242	+	0.491291i	0.931712	−	0.363197i	$-0.118315\pi$
$211$	5.98817	+	7.13642i	0.412242	+	0.491291i	−0.519470	+	0.854489i	$0.673870\pi$
$212$	8.18670	−	11.1029i	0.562265	−	0.762552i
$213$		0			0
$214$	−1.83946	+	5.59426i	−0.125743	+	0.382416i
$215$	−12.6810			−0.864838
$216$		0			0
$217$	−9.27552			−0.629664
$218$	9.10355	−	27.6861i	0.616570	−	1.87514i
$219$		0			0
$220$	−2.97515	−	2.19372i	−0.200585	−	0.147900i
$221$	0.794946	+	0.947380i	0.0534739	+	0.0637277i
$222$		0			0
$223$	23.1313	−	8.41909i	1.54898	−	0.563784i	0.580805	−	0.814043i	$-0.302738\pi$
$223$	23.1313	−	8.41909i	1.54898	−	0.563784i	0.968179	+	0.250259i	$0.0805157\pi$
$224$	2.58199	+	7.50188i	0.172516	+	0.501240i
$225$		0			0
$226$	−3.48318	+	1.39307i	−0.231698	+	0.0926654i
$227$	−2.62591	+	3.12944i	−0.174288	+	0.207708i	−0.846116	−	0.532999i	$-0.821065\pi$
$227$	−2.62591	+	3.12944i	−0.174288	+	0.207708i	0.671828	+	0.740707i	$0.265509\pi$
$228$		0			0
$229$	12.4279	−	2.19138i	0.821261	−	0.144810i	0.252798	−	0.967519i	$-0.418649\pi$
$229$	12.4279	−	2.19138i	0.821261	−	0.144810i	0.568463	+	0.822709i	$0.307538\pi$
$230$	0.192113	+	6.11831i	0.0126675	+	0.403429i
$231$		0			0
$232$	−4.83321	−	10.1808i	−0.317316	−	0.668402i
$233$	12.2882	+	21.2839i	0.805030	+	1.39435i	0.916271	+	0.400559i	$0.131184\pi$
$233$	12.2882	+	21.2839i	0.805030	+	1.39435i	−0.111241	+	0.993793i	$0.535483\pi$
$234$		0			0
$235$	11.9477	+	6.89802i	0.779383	+	0.449977i
$236$	1.32528	+	21.0827i	0.0862686	+	1.37236i
$237$		0			0
$238$	−1.89682	−	3.05943i	−0.122952	−	0.198314i
$239$	10.1778	+	3.70441i	0.658346	+	0.239618i	0.649522	−	0.760343i	$-0.274969\pi$
$239$	10.1778	+	3.70441i	0.658346	+	0.239618i	0.00882395	+	0.999961i	$0.497191\pi$
$240$		0			0
$241$	−2.29103	+	12.9931i	−0.147579	+	0.836959i	0.817682	+	0.575670i	$0.195259\pi$
$241$	−2.29103	+	12.9931i	−0.147579	+	0.836959i	−0.965261	+	0.261289i	$0.915852\pi$
$242$	−1.67247	+	11.6039i	−0.107510	+	0.745930i
$243$		0			0
$244$	−2.04902	+	6.96060i	−0.131175	+	0.445607i
$245$	−5.56481	−	0.981227i	−0.355523	−	0.0626883i
$246$		0			0
$247$	−2.19435	−	0.798678i	−0.139623	−	0.0508187i
$248$	−4.96602	−	18.0347i	−0.315343	−	1.14520i
$249$		0			0
$250$	13.5832	−	2.83730i	0.859076	−	0.179446i
$251$	17.6367	+	10.1826i	1.11322	+	0.642717i	0.939661	−	0.342106i	$-0.111140\pi$
$251$	17.6367	+	10.1826i	1.11322	+	0.642717i	0.173558	+	0.984824i	$0.444474\pi$
$252$		0			0
$253$	−5.49629	+	3.17328i	−0.345549	+	0.199503i
$254$	−4.52890	+	4.04909i	−0.284169	+	0.254063i
$255$		0			0
$256$	−13.2037	+	9.03667i	−0.825234	+	0.564792i
$257$	−2.07937	−	11.7927i	−0.129707	−	0.735606i	−0.978400	−	0.206720i	$-0.933721\pi$
$257$	−2.07937	−	11.7927i	−0.129707	−	0.735606i	0.848693	−	0.528886i	$-0.177390\pi$
$258$		0			0
$259$	3.99249	−	4.75806i	0.248081	−	0.295651i
$260$	−0.359717	−	1.48724i	−0.0223087	−	0.0922344i
$261$		0			0
$262$	−6.92589	+	8.80075i	−0.427883	+	0.543712i
$263$	9.28725	−	3.38028i	0.572677	−	0.208437i	−0.0394166	−	0.999223i	$-0.512550\pi$
$263$	9.28725	−	3.38028i	0.572677	−	0.208437i	0.612093	+	0.790786i	$0.290328\pi$
$264$		0			0
$265$	5.93218	−	4.97769i	0.364411	−	0.305777i
$266$	5.99017	+	3.21210i	0.367281	+	0.196947i
$267$		0			0
$268$	−21.7235	−	10.7851i	−1.32698	−	0.658805i
$269$			5.38944i			0.328600i	0.986410	+	0.164300i	$0.0525365\pi$
$269$			5.38944i			0.328600i	−0.986410	+	0.164300i	$0.947463\pi$
$270$		0			0
$271$	−6.24978			−0.379647			−0.189823	−	0.981818i	$-0.560792\pi$
$271$	−6.24978			−0.379647			−0.189823	+	0.981818i	$0.560792\pi$
$272$	4.93300	−	5.32602i	0.299107	−	0.322937i
$273$		0			0
$274$	−10.5252	+	19.6281i	−0.635848	+	1.18578i
$275$	3.95697	+	4.71573i	0.238614	+	0.284369i
$276$		0			0
$277$	4.85450	+	13.3376i	0.291679	+	0.801381i	0.995821	+	0.0913223i	$0.0291093\pi$
$277$	4.85450	+	13.3376i	0.291679	+	0.801381i	−0.704143	+	0.710059i	$0.748668\pi$
$278$	0.340475	−	0.432643i	0.0204203	−	0.0259482i
$279$		0			0
$280$	0.418780	+	4.43401i	0.0250269	+	0.264983i
$281$	−21.3543	−	17.9184i	−1.27389	−	1.06892i	−0.994055	−	0.108875i	$-0.965275\pi$
$281$	−21.3543	−	17.9184i	−1.27389	−	1.06892i	−0.279837	−	0.960047i	$-0.590280\pi$
$282$		0			0
$283$	−22.0316	+	3.88476i	−1.30964	+	0.230925i	−0.784521	−	0.620102i	$-0.787091\pi$
$283$	−22.0316	+	3.88476i	−1.30964	+	0.230925i	−0.525121	+	0.851027i	$0.675980\pi$
$284$	3.03497	−	27.0444i	0.180093	−	1.60479i
$285$		0			0
$286$	1.18267	−	1.05737i	0.0699327	−	0.0625237i
$287$	−3.84539	−	6.66042i	−0.226986	−	0.393152i
$288$		0			0
$289$	6.85309	−	11.8699i	0.403123	−	0.698230i
$290$	−1.29357	−	6.19280i	−0.0759612	−	0.363654i
$291$		0			0
$292$	17.3681	−	7.58685i	1.01639	−	0.443987i
$293$	0.130208	−	0.357742i	0.00760680	−	0.0208995i	−0.935831	−	0.352449i	$-0.885349\pi$
$293$	0.130208	−	0.357742i	0.00760680	−	0.0208995i	0.943438	+	0.331549i	$0.107571\pi$
$294$		0			0
$295$	−2.05919	+	11.6782i	−0.119891	+	0.679934i
$296$	11.3888	+	5.21528i	0.661958	+	0.303132i
$297$		0			0
$298$	−16.5675	−	2.38786i	−0.959727	−	0.138325i
$299$	−2.58719	−	0.456191i	−0.149621	−	0.0263822i
$300$		0			0
$301$	−5.41797	+	14.8857i	−0.312286	+	0.858000i
$302$	6.85921	+	11.0634i	0.394703	+	0.636629i
$303$		0			0
$304$	−3.03830	+	13.3666i	−0.174259	+	0.766626i
$305$	−2.03661	+	3.52751i	−0.116616	+	0.201984i
$306$		0			0
$307$	−9.47107	+	5.46813i	−0.540543	+	0.312083i	−0.745299	−	0.666731i	$-0.767693\pi$
$307$	−9.47107	+	5.46813i	−0.540543	+	0.312083i	0.204756	+	0.978813i	$0.434360\pi$
$308$	−3.84625	+	2.55515i	−0.219161	+	0.145593i
$309$		0			0
$310$	−0.329560	−	10.4956i	−0.0187177	−	0.596112i
$311$	3.17033	+	17.9798i	0.179773	+	1.01954i	0.932490	+	0.361197i	$0.117632\pi$
$311$	3.17033	+	17.9798i	0.179773	+	1.01954i	−0.752717	+	0.658344i	$0.771257\pi$
$312$		0			0
$313$	2.49125	+	2.09041i	0.140814	+	0.118157i	0.710474	−	0.703724i	$-0.248481\pi$
$313$	2.49125	+	2.09041i	0.140814	+	0.118157i	−0.569660	+	0.821880i	$0.692925\pi$
$314$	−7.22242	−	18.0587i	−0.407585	−	1.01911i
$315$		0			0
$316$	13.2866	−	12.6513i	0.747427	−	0.711690i
$317$	5.82505	+	16.0042i	0.327167	+	0.898885i	0.988825	+	0.149079i	$0.0476309\pi$
$317$	5.82505	+	16.0042i	0.327167	+	0.898885i	−0.661658	+	0.749806i	$0.730147\pi$
$318$		0			0
$319$	5.02469	−	4.21621i	0.281328	−	0.236063i
$320$	−8.39695	+	3.18817i	−0.469404	+	0.178224i
$321$		0			0
$322$	7.26412	+	2.38853i	0.404814	+	0.133108i
$323$		−	6.21940i		−	0.346057i
$324$		0			0
$325$			2.54819i			0.141348i
$326$	5.61879	−	17.0881i	0.311196	−	0.946423i
$327$		0			0
$328$	10.8912	−	11.0426i	0.601368	−	0.609727i
$329$	13.2020	−	11.0778i	0.727849	−	0.610737i
$330$		0			0
$331$	1.92215	+	5.28106i	0.105651	+	0.290273i	0.981242	−	0.192780i	$-0.0617502\pi$
$331$	1.92215	+	5.28106i	0.105651	+	0.290273i	−0.875591	+	0.483053i	$0.839528\pi$
$332$	−1.81851	−	1.90983i	−0.0998036	−	0.104815i
$333$		0			0
$334$	−26.0025	+	10.3995i	−1.42280	+	0.569034i
$335$	−10.4297	−	8.75156i	−0.569836	−	0.478149i
$336$		0			0
$337$	3.30062	+	18.7188i	0.179796	+	1.01968i	0.932461	+	0.361271i	$0.117657\pi$
$337$	3.30062	+	18.7188i	0.179796	+	1.01968i	−0.752665	+	0.658404i	$0.771232\pi$
$338$	−17.7194	+	0.556382i	−0.963806	+	0.0302632i
$339$		0			0
$340$	3.39448	−	2.25503i	0.184091	−	0.122296i
$341$	9.42860	−	5.44360i	0.510587	−	0.294788i
$342$		0			0
$343$	−8.43817	+	14.6153i	−0.455618	+	0.789154i
$344$	−31.8435	−	2.56462i	−1.71689	−	0.138275i
$345$		0			0
$346$	5.88990	−	3.65167i	0.316643	−	0.196315i
$347$	−3.17358	+	8.71933i	−0.170366	+	0.468078i	−0.995265	−	0.0972035i	$-0.969010\pi$
$347$	−3.17358	+	8.71933i	−0.170366	+	0.468078i	0.824898	+	0.565282i	$0.191232\pi$
$348$		0			0
$349$	−7.31028	−	1.28900i	−0.391310	−	0.0689985i	−0.0254684	−	0.999676i	$-0.508108\pi$
$349$	−7.31028	−	1.28900i	−0.391310	−	0.0689985i	−0.365842	+	0.930677i	$0.619219\pi$
$350$	1.05808	−	7.34120i	0.0565569	−	0.392404i
$351$		0			0
$352$	−7.02729	−	6.11037i	−0.374556	−	0.325684i
$353$	−4.91102	+	27.8518i	−0.261387	+	1.48240i	0.517742	+	0.855537i	$0.326773\pi$
$353$	−4.91102	+	27.8518i	−0.261387	+	1.48240i	−0.779129	+	0.626864i	$0.784338\pi$
$354$		0			0
$355$	5.22506	−	14.3557i	0.277318	−	0.761924i
$356$	12.9151	−	5.64166i	0.684500	−	0.299007i
$357$		0			0
$358$	5.13398	−	1.07240i	0.271339	−	0.0566782i
$359$	−8.47821	+	14.6847i	−0.447463	+	0.775029i	−0.998220	−	0.0596369i	$-0.981006\pi$
$359$	−8.47821	+	14.6847i	−0.447463	+	0.775029i	0.550757	+	0.834666i	$0.314339\pi$
$360$		0			0
$361$	−3.62823	−	6.28428i	−0.190960	−	0.330752i
$362$	15.3816	+	17.2043i	0.808439	+	0.904239i
$363$		0			0
$364$	−1.89950	−	0.213165i	−0.0995607	−	0.0111729i
$365$	10.4778	−	1.84753i	0.548435	−	0.0967039i
$366$		0			0
$367$	6.19539	+	5.19855i	0.323397	+	0.271362i	0.790003	−	0.613103i	$-0.210079\pi$
$367$	6.19539	+	5.19855i	0.323397	+	0.271362i	−0.466606	+	0.884465i	$0.654523\pi$
$368$	−0.754954	+	15.4026i	−0.0393547	+	0.802917i
$369$		0			0
$370$	5.52579	+	4.34861i	0.287272	+	0.226073i
$371$	−3.30859	−	9.09028i	−0.171773	−	0.471944i
$372$		0			0
$373$	−14.1644	−	16.8805i	−0.733405	−	0.874038i	0.262454	−	0.964944i	$-0.415468\pi$
$373$	−14.1644	−	16.8805i	−0.733405	−	0.874038i	−0.995859	+	0.0909062i	$0.971024\pi$
$374$	3.72363	+	1.99672i	0.192545	+	0.103248i
$375$		0			0
$376$	28.6070	+	19.7380i	1.47529	+	1.01791i
$377$	2.71514			0.139837
$378$		0			0
$379$		−	9.42240i		−	0.483996i	−0.970277	−	0.241998i	$-0.922197\pi$
$379$		−	9.42240i		−	0.483996i	0.970277	−	0.241998i	$-0.0778027\pi$
$380$	−3.42180	+	6.89225i	−0.175534	+	0.353565i
$381$		0			0
$382$	−4.61117	+	8.59925i	−0.235928	+	0.439976i
$383$	13.2473	−	11.1158i	0.676904	−	0.567989i	−0.238196	−	0.971217i	$-0.576556\pi$
$383$	13.2473	−	11.1158i	0.676904	−	0.567989i	0.915100	+	0.403228i	$0.132112\pi$
$384$		0			0
$385$	−2.43584	+	0.886573i	−0.124142	+	0.0451840i
$386$	10.5916	+	8.33520i	0.539097	+	0.424250i
$387$		0			0
$388$	−3.88690	−	16.0703i	−0.197327	−	0.815844i
$389$	−15.9667	+	19.0284i	−0.809546	+	0.964780i	−0.999856	−	0.0169443i	$-0.994606\pi$
$389$	−15.9667	+	19.0284i	−0.809546	+	0.964780i	0.190310	+	0.981724i	$0.439051\pi$
$390$		0			0
$391$	−1.21500	−	6.89059i	−0.0614451	−	0.348472i
$392$	−13.7754	−	3.58940i	−0.695765	−	0.181292i
$393$		0			0
$394$	−1.89385	−	2.11827i	−0.0954108	−	0.106717i
$395$	8.91916	−	5.14948i	0.448772	−	0.259098i
$396$		0			0
$397$	−5.94466	−	3.43215i	−0.298354	−	0.172255i	0.343349	−	0.939208i	$-0.388439\pi$
$397$	−5.94466	−	3.43215i	−0.298354	−	0.172255i	−0.641703	+	0.766953i	$0.721772\pi$
$398$	6.16287	+	29.5039i	0.308917	+	1.47890i
$399$		0			0
$400$	14.8402	−	1.87315i	0.742009	−	0.0936574i
$401$	−11.8463	−	4.31169i	−0.591574	−	0.215315i	0.0288475	−	0.999584i	$-0.490816\pi$
$401$	−11.8463	−	4.31169i	−0.591574	−	0.215315i	−0.620422	+	0.784268i	$0.713039\pi$
$402$		0			0
$403$	4.43819	+	0.782572i	0.221082	+	0.0389827i
$404$	9.97624	−	33.8897i	0.496336	−	1.68608i
$405$		0			0
$406$	−7.82217	−	1.12740i	−0.388208	−	0.0559521i
$407$	−1.26597	+	7.17969i	−0.0627519	+	0.355884i
$408$		0			0
$409$	32.0334	+	11.6592i	1.58395	+	0.576510i	0.976058	−	0.217510i	$-0.0697935\pi$
$409$	32.0334	+	11.6592i	1.58395	+	0.576510i	0.607891	+	0.794020i	$0.292016\pi$
$410$	7.39991	−	4.58787i	0.365455	−	0.226579i
$411$		0			0
$412$	−7.76590	+	0.488175i	−0.382598	+	0.0240506i
$413$	12.8288	+	7.40673i	0.631266	+	0.364462i
$414$		0			0
$415$	−0.740192	−	1.28205i	−0.0363346	−	0.0629334i
$416$	−0.602510	−	3.80737i	−0.0295405	−	0.186672i
$417$		0			0
$418$	−7.97414	+	0.250385i	−0.390028	+	0.0122467i
$419$	10.9419	−	1.92935i	0.534545	−	0.0942547i	0.100142	−	0.994973i	$-0.468070\pi$
$419$	10.9419	−	1.92935i	0.534545	−	0.0942547i	0.434403	+	0.900718i	$0.356959\pi$
$420$		0			0
$421$	−12.6851	+	15.1175i	−0.618232	+	0.736780i	−0.980765	−	0.195190i	$-0.937468\pi$
$421$	−12.6851	+	15.1175i	−0.618232	+	0.736780i	0.362533	+	0.931971i	$0.381912\pi$
$422$	4.89234	+	12.2327i	0.238156	+	0.595477i
$423$		0			0
$424$	15.9031	−	11.2998i	0.772322	−	0.548768i
$425$	−6.37744	+	2.32120i	−0.309352	+	0.112595i
$426$		0			0
$427$	3.27066	+	3.89782i	0.158278	+	0.188629i
$428$	−4.94246	+	6.70304i	−0.238903	+	0.324004i
$429$		0			0
$430$	−17.0363	−	5.60176i	−0.821565	−	0.270141i
$431$	0.293057			0.0141161			0.00705803	−	0.999975i	$-0.497753\pi$
$431$	0.293057			0.0141161			0.00705803	+	0.999975i	$0.497753\pi$
$432$		0			0
$433$	18.2482			0.876954			0.438477	−	0.898742i	$-0.355518\pi$
$433$	18.2482			0.876954			0.438477	+	0.898742i	$0.355518\pi$
$434$	−12.4612	−	4.09741i	−0.598158	−	0.196682i
$435$		0			0
$436$	24.4604	−	33.1735i	1.17144	−	1.58872i
$437$	8.49225	+	10.1207i	0.406239	+	0.484137i
$438$		0			0
$439$	0.920498	−	0.335034i	0.0439330	−	0.0159903i	−0.319960	−	0.947431i	$-0.603670\pi$
$439$	0.920498	−	0.335034i	0.0439330	−	0.0159903i	0.363893	+	0.931441i	$0.381447\pi$
$440$	−3.02791	−	4.26141i	−0.144350	−	0.203155i
$441$		0			0
$442$	0.649472	+	1.62392i	0.0308923	+	0.0772421i
$443$	3.31318	−	3.94849i	0.157414	−	0.187599i	−0.681573	−	0.731750i	$-0.738704\pi$
$443$	3.31318	−	3.94849i	0.157414	−	0.187599i	0.838987	+	0.544151i	$0.183148\pi$
$444$		0			0
$445$	7.79143	−	1.37384i	0.369349	−	0.0651262i
$446$	34.7948	−	1.09255i	1.64758	−	0.0517336i
$447$		0			0
$448$	0.154869	+	11.2190i	0.00731685	+	0.530048i
$449$	6.21921	+	10.7720i	0.293503	+	0.508362i	0.974635	−	0.223798i	$-0.0718457\pi$
$449$	6.21921	+	10.7720i	0.293503	+	0.508362i	−0.681133	+	0.732160i	$0.738512\pi$
$450$		0			0
$451$	7.81771	+	4.51356i	0.368122	+	0.212535i
$452$	−5.29486	+	0.332842i	−0.249049	+	0.0156556i
$453$		0			0
$454$	−4.91019	+	3.04427i	−0.230447	+	0.142875i
$455$	−1.00829	−	0.366988i	−0.0472695	−	0.0172047i
$456$		0			0
$457$	−4.18789	+	23.7507i	−0.195901	+	1.11101i	0.715228	+	0.698891i	$0.246323\pi$
$457$	−4.18789	+	23.7507i	−0.195901	+	1.11101i	−0.911129	+	0.412121i	$0.864788\pi$
$458$	17.6644	+	2.54595i	0.825401	+	0.118964i
$459$		0			0
$460$	−2.44463	+	8.30451i	−0.113981	+	0.387200i
$461$	36.0117	+	6.34983i	1.67723	+	0.295741i	0.929654	−	0.368434i	$-0.120106\pi$
$461$	36.0117	+	6.34983i	1.67723	+	0.295741i	0.747577	+	0.664175i	$0.231217\pi$
$462$		0			0
$463$	−21.2745	−	7.74329i	−0.988711	−	0.359861i	−0.203490	−	0.979077i	$-0.565228\pi$
$463$	−21.2745	−	7.74329i	−0.988711	−	0.359861i	−0.785221	+	0.619216i	$0.787451\pi$
$464$	−1.99587	−	15.8125i	−0.0926560	−	0.734075i
$465$		0			0
$466$	7.10665	+	34.0221i	0.329209	+	1.57604i
$467$	−20.1982	−	11.6614i	−0.934662	−	0.539628i	−0.0463792	−	0.998924i	$-0.514768\pi$
$467$	−20.1982	−	11.6614i	−0.934662	−	0.539628i	−0.888283	+	0.459296i	$0.848102\pi$
$468$		0			0
$469$	−14.7292	+	8.50392i	−0.680132	+	0.392674i
$470$	13.0040	+	14.5450i	0.599831	+	0.670910i
$471$		0			0
$472$	−7.53268	+	28.9090i	−0.346720	+	1.33064i
$473$	−3.22874	−	18.3111i	−0.148458	−	0.841945i
$474$		0			0
$475$	8.23718	−	9.81669i	0.377948	−	0.450420i
$476$	−1.19679	−	4.94811i	−0.0548550	−	0.226796i
$477$		0			0
$478$	12.0370	+	9.47267i	0.550558	+	0.433270i
$479$	37.4812	−	13.6420i	1.71256	−	0.623320i	0.715405	−	0.698710i	$-0.246242\pi$
$479$	37.4812	−	13.6420i	1.71256	−	0.623320i	0.997154	+	0.0753898i	$0.0240201\pi$
$480$		0			0
$481$	−2.31177	+	1.93981i	−0.105408	+	0.0884477i
$482$	−8.81752	+	16.4436i	−0.401627	+	0.748983i
$483$		0			0
$484$	−7.37286	+	14.8505i	−0.335130	+	0.675025i
$485$		−	9.28139i		−	0.421446i
$486$		0			0
$487$	−32.0323			−1.45152			−0.725762	−	0.687946i	$-0.758512\pi$
$487$	−32.0323			−1.45152			−0.725762	+	0.687946i	$0.758512\pi$
$488$	−5.82756	+	8.44609i	−0.263801	+	0.382336i
$489$		0			0
$490$	−7.04260	−	3.77645i	−0.318152	−	0.170603i
$491$	−16.9415	−	20.1901i	−0.764559	−	0.911166i	0.233568	−	0.972341i	$-0.424960\pi$
$491$	−16.9415	−	20.1901i	−0.764559	−	0.911166i	−0.998127	+	0.0611743i	$0.980515\pi$
$492$		0			0
$493$	2.47328	+	6.79527i	0.111391	+	0.306044i
$494$	−2.59519	−	2.04233i	−0.116763	−	0.0918886i
$495$		0			0
$496$	1.29508	−	26.4224i	0.0581510	−	1.18640i
$497$	−14.6192	−	12.2670i	−0.655762	−	0.550250i
$498$		0			0
$499$	0.796549	−	0.140453i	0.0356584	−	0.00628755i	−0.155790	−	0.987790i	$-0.549792\pi$
$499$	0.796549	−	0.140453i	0.0356584	−	0.00628755i	0.191449	+	0.981503i	$0.438681\pi$
$500$	19.5017	+	2.18852i	0.872143	+	0.0978734i
$501$		0			0
$502$	19.1960	+	21.4707i	0.856759	+	0.958284i
$503$	0.838775	+	1.45280i	0.0373991	+	0.0647772i	0.884119	−	0.467262i	$-0.154759\pi$
$503$	0.838775	+	1.45280i	0.0373991	+	0.0647772i	−0.846720	+	0.532039i	$0.821426\pi$
$504$		0			0
$505$	9.91581	−	17.1747i	0.441248	−	0.764264i
$506$	−8.78578	+	1.83520i	−0.390576	+	0.0815847i
$507$		0			0
$508$	−7.87302	+	3.43914i	−0.349309	+	0.152587i
$509$	−2.89525	+	7.95462i	−0.128330	+	0.352583i	−0.987173	−	0.159656i	$-0.948961\pi$
$509$	−2.89525	+	7.95462i	−0.128330	+	0.352583i	0.858843	+	0.512239i	$0.171184\pi$
$510$		0			0
$511$	2.30792	−	13.0889i	0.102096	−	0.579018i
$512$	−21.7305	+	6.30765i	−0.960360	+	0.278762i
$513$		0			0
$514$	2.41581	−	16.7614i	0.106557	−	0.739315i
$515$	−4.30174	−	0.758513i	−0.189557	−	0.0334241i
$516$		0			0
$517$	−6.91855	+	19.0085i	−0.304277	+	0.835995i
$518$	7.46555	−	4.62857i	0.328018	−	0.203367i
$519$		0			0
$520$	0.173716	−	2.15693i	0.00761793	−	0.0945877i
$521$	−1.96303	+	3.40007i	−0.0860020	+	0.148960i	−0.905818	−	0.423668i	$-0.860742\pi$
$521$	−1.96303	+	3.40007i	−0.0860020	+	0.148960i	0.819816	+	0.572627i	$0.194076\pi$
$522$		0			0
$523$	14.9783	−	8.64774i	0.654956	−	0.378139i	−0.135396	−	0.990792i	$-0.543231\pi$
$523$	14.9783	−	8.64774i	0.654956	−	0.378139i	0.790353	+	0.612652i	$0.209897\pi$
$524$	−13.1923	+	8.76391i	−0.576307	+	0.382853i
$525$		0			0
$526$	13.9702	−	0.438660i	0.609129	−	0.0191265i
$527$	2.08426	+	11.8205i	0.0907920	+	0.514907i
$528$		0			0
$529$	−6.23317	−	5.23025i	−0.271008	−	0.227402i
$530$	10.1685	−	4.06678i	0.441690	−	0.176650i
$531$		0			0
$532$	6.62857	+	6.96143i	0.287385	+	0.301816i
$533$	1.27802	+	3.51134i	0.0553573	+	0.152093i
$534$		0			0
$535$	−3.58137	+	3.00512i	−0.154836	+	0.129923i
$536$	−24.4203	−	24.0855i	−1.05480	−	1.04033i
$537$		0			0
$538$	−2.38075	+	7.24046i	−0.102642	+	0.312158i
$539$		−	8.28529i		−	0.356873i
$540$		0			0
$541$			11.4118i			0.490630i	0.969443	+	0.245315i	$0.0788914\pi$
$541$			11.4118i			0.490630i	−0.969443	+	0.245315i	$0.921109\pi$
$542$	−8.39627	−	2.76080i	−0.360651	−	0.118587i
$543$		0			0
$544$	8.97999	−	4.97613i	0.385014	−	0.213350i
$545$	17.7243	−	14.8724i	0.759225	−	0.637065i
$546$		0			0
$547$	−4.84214	−	13.3037i	−0.207035	−	0.568824i	0.792101	−	0.610390i	$-0.208987\pi$
$547$	−4.84214	−	13.3037i	−0.207035	−	0.568824i	−0.999136	+	0.0415665i	$0.986765\pi$
$548$	−22.8106	+	21.7199i	−0.974421	+	0.927830i
$549$		0			0
$550$	3.23285	+	8.08332i	0.137849	+	0.344674i
$551$	−10.4598	−	8.77685i	−0.445604	−	0.373906i
$552$		0			0
$553$	−2.23406	−	12.6700i	−0.0950018	−	0.538782i
$554$	0.629969	+	20.0629i	0.0267648	+	0.852392i
$555$		0			0
$556$	0.648529	−	0.430832i	0.0275037	−	0.0182713i
$557$	−29.6837	+	17.1379i	−1.25774	+	0.726155i	−0.972634	−	0.232342i	$-0.925361\pi$
$557$	−29.6837	+	17.1379i	−1.25774	+	0.726155i	−0.285103	+	0.958497i	$0.592028\pi$
$558$		0			0
$559$	3.84831	−	6.66547i	0.162766	−	0.281919i
$560$	−1.39608	+	6.14187i	−0.0589953	+	0.259541i
$561$		0			0
$562$	−20.7732	−	33.5057i	−0.876263	−	1.41335i
$563$	11.1729	−	30.6973i	0.470882	−	1.29374i	−0.446162	−	0.894952i	$-0.647210\pi$
$563$	11.1729	−	30.6973i	0.470882	−	1.29374i	0.917044	−	0.398786i	$-0.130568\pi$
$564$		0			0
$565$	−2.93297	−	0.517161i	−0.123391	−	0.0217571i
$566$	−31.3144	−	4.51333i	−1.31624	−	0.189709i
$567$		0			0
$568$	16.0240	−	34.9922i	0.672354	−	1.46824i
$569$	−4.57663	+	25.9553i	−0.191862	+	1.08810i	0.724955	+	0.688797i	$0.241861\pi$
$569$	−4.57663	+	25.9553i	−0.191862	+	1.08810i	−0.916817	+	0.399308i	$0.869250\pi$
$570$		0			0
$571$	14.3103	−	39.3171i	0.598865	−	1.64537i	−0.154673	−	0.987966i	$-0.549432\pi$
$571$	14.3103	−	39.3171i	0.598865	−	1.64537i	0.753539	−	0.657404i	$-0.228345\pi$
$572$	2.05595	−	0.898091i	0.0859634	−	0.0375511i
$573$		0			0
$574$	−2.22390	−	10.6466i	−0.0928239	−	0.444382i
$575$	7.20837	−	12.4853i	0.300610	−	0.520672i
$576$		0			0
$577$	−6.39933	−	11.0840i	−0.266408	−	0.461431i	0.701524	−	0.712646i	$-0.252503\pi$
$577$	−6.39933	−	11.0840i	−0.266408	−	0.461431i	−0.967931	+	0.251215i	$0.919170\pi$
$578$	14.4503	−	12.9193i	0.601052	−	0.537373i
$579$		0			0
$580$	0.997782	−	8.89116i	0.0414306	−	0.369185i
$581$	−1.82120	+	0.321126i	−0.0755560	+	0.0133226i
$582$		0			0
$583$	8.69808	+	7.29856i	0.360238	+	0.302275i
$584$	26.6847	−	2.52030i	1.10422	−	0.104291i
$585$		0			0
$586$	0.332958	−	0.423091i	0.0137544	−	0.0174777i
$587$	−4.86117	−	13.3560i	−0.200642	−	0.551260i	0.798039	−	0.602606i	$-0.205871\pi$
$587$	−4.86117	−	13.3560i	−0.200642	−	0.551260i	−0.998681	+	0.0513464i	$0.983649\pi$
$588$		0			0
$589$	−14.5680	−	17.3615i	−0.600264	−	0.715367i
$590$	−7.92522	+	14.7795i	−0.326276	+	0.608463i
$591$		0			0
$592$	12.9964	+	12.0374i	0.534150	+	0.494734i
$593$	22.4225			0.920782			0.460391	−	0.887716i	$-0.347709\pi$
$593$	22.4225			0.920782			0.460391	+	0.887716i	$0.347709\pi$
$594$		0			0
$595$		−	2.85778i		−	0.117158i
$596$	−21.2027	−	10.5265i	−0.868498	−	0.431184i
$597$		0			0
$598$	−3.27424	−	1.75575i	−0.133894	−	0.0717978i
$599$	−3.21966	+	2.70162i	−0.131552	+	0.110385i	−0.706190	−	0.708023i	$-0.749587\pi$
$599$	−3.21966	+	2.70162i	−0.131552	+	0.110385i	0.574638	+	0.818408i	$0.305143\pi$
$600$		0			0
$601$	−12.5218	+	4.55756i	−0.510775	+	0.185907i	−0.584534	−	0.811369i	$-0.698723\pi$
$601$	−12.5218	+	4.55756i	−0.510775	+	0.185907i	0.0737590	+	0.997276i	$0.476500\pi$
$602$	−13.8545	+	17.6049i	−0.564666	+	0.717523i
$603$		0			0
$604$	4.32781	+	17.8932i	0.176096	+	0.728064i
$605$	−5.98270	+	7.12991i	−0.243231	+	0.289872i
$606$		0			0
$607$	−5.79180	−	32.8469i	−0.235082	−	1.33322i	−0.842441	−	0.538789i	$-0.818882\pi$
$607$	−5.79180	−	32.8469i	−0.235082	−	1.33322i	0.607359	−	0.794428i	$-0.292229\pi$
$608$	−9.98642	+	16.6152i	−0.405003	+	0.673835i
$609$		0			0
$610$	−4.29434	+	3.83938i	−0.173873	+	0.155452i
$611$	−7.25156	+	4.18669i	−0.293367	+	0.169375i
$612$		0			0
$613$	11.1640	+	6.44552i	0.450908	+	0.260332i	0.708214	−	0.705998i	$-0.249501\pi$
$613$	11.1640	+	6.44552i	0.450908	+	0.260332i	−0.257305	+	0.966330i	$0.582835\pi$
$614$	−15.1394	+	3.16237i	−0.610978	+	0.127623i
$615$		0			0
$616$	−6.29598	+	1.73366i	−0.253672	+	0.0698512i
$617$	−20.7471	−	7.55132i	−0.835246	−	0.304005i	−0.111236	−	0.993794i	$-0.535481\pi$
$617$	−20.7471	−	7.55132i	−0.835246	−	0.304005i	−0.724010	+	0.689789i	$0.757703\pi$
$618$		0			0
$619$	0.110454	+	0.0194760i	0.00443952	+	0.000782807i	0.175867	−	0.984414i	$-0.443727\pi$
$619$	0.110454	+	0.0194760i	0.00443952	+	0.000782807i	−0.171428	+	0.985197i	$0.554838\pi$
$620$	4.19364	−	14.2460i	0.168420	−	0.572131i
$621$		0			0
$622$	−3.68329	+	25.5555i	−0.147687	+	1.02468i
$623$	1.71619	−	9.73302i	0.0687579	−	0.389945i
$624$		0			0
$625$	−7.21791	−	2.62710i	−0.288716	−	0.105084i
$626$	2.42345	+	3.90885i	0.0968604	+	0.156229i
$627$		0			0
$628$	−1.72564	−	27.4515i	−0.0688604	−	1.09543i
$629$	−6.96066	−	4.01874i	−0.277540	−	0.160238i
$630$		0			0
$631$	−7.25883	−	12.5727i	−0.288970	−	0.500510i	0.684595	−	0.728924i	$-0.259979\pi$
$631$	−7.25883	−	12.5727i	−0.288970	−	0.500510i	−0.973564	+	0.228414i	$0.926646\pi$
$632$	23.4385	−	11.1271i	0.932332	−	0.442613i
$633$		0			0
$634$	0.755917	+	24.0740i	0.0300213	+	0.956102i
$635$	−4.74963	+	0.837488i	−0.188483	+	0.0332347i
$636$		0			0
$637$	2.20451	−	2.62724i	0.0873460	−	0.104095i
$638$	8.61291	−	3.44465i	0.340988	−	0.136375i
$639$		0			0
$640$	−12.6892	+	0.573851i	−0.501586	+	0.0226835i
$641$	26.9693	−	9.81603i	1.06522	−	0.387710i	0.250835	−	0.968030i	$-0.419295\pi$
$641$	26.9693	−	9.81603i	1.06522	−	0.387710i	0.814389	+	0.580320i	$0.197072\pi$
$642$		0			0
$643$	16.9076	+	20.1497i	0.666772	+	0.794628i	0.988341	−	0.152258i	$-0.0486546\pi$
$643$	16.9076	+	20.1497i	0.666772	+	0.794628i	−0.321569	+	0.946886i	$0.604210\pi$
$644$	8.70387	+	6.41776i	0.342981	+	0.252895i
$645$		0			0
$646$	2.74738	−	8.35547i	0.108094	−	0.328742i
$647$	−31.9679			−1.25679			−0.628394	−	0.777895i	$-0.716287\pi$
$647$	−31.9679			−1.25679			−0.628394	+	0.777895i	$0.716287\pi$
$648$		0			0
$649$	−17.3874			−0.682516
$650$	−1.12565	+	3.42337i	−0.0441516	+	0.134276i
$651$		0			0
$652$	15.0971	−	20.4750i	0.591249	−	0.801862i
$653$	−24.4383	−	29.1244i	−0.956344	−	1.13973i	−0.990109	−	0.140297i	$-0.955194\pi$
$653$	−24.4383	−	29.1244i	−0.956344	−	1.13973i	0.0337653	−	0.999430i	$-0.489250\pi$
$654$		0			0
$655$	−8.35469	+	3.04086i	−0.326445	+	0.118816i
$656$	19.5099	−	10.0241i	0.761733	−	0.391375i
$657$		0			0
$658$	22.6298	−	9.05056i	0.882200	−	0.352828i
$659$	−13.8230	+	16.4736i	−0.538469	+	0.641722i	−0.964844	−	0.262825i	$-0.915346\pi$
$659$	−13.8230	+	16.4736i	−0.538469	+	0.641722i	0.426375	+	0.904546i	$0.359790\pi$
$660$		0			0
$661$	40.0325	−	7.05881i	1.55708	−	0.274556i	0.672201	−	0.740369i	$-0.265349\pi$
$661$	40.0325	−	7.05881i	1.55708	−	0.274556i	0.884883	+	0.465813i	$0.154238\pi$
$662$	0.249437	+	7.94394i	0.00969465	+	0.308750i
$663$		0			0
$664$	−1.59942	−	3.36907i	−0.0620697	−	0.130745i
$665$	2.69804	+	4.67315i	0.104626	+	0.181217i
$666$		0			0
$667$	−13.3033	−	7.68064i	−0.515104	−	0.297396i
$668$	−39.5271	+	2.48472i	−1.52935	+	0.0961368i
$669$		0			0
$670$	−10.1459	−	16.3646i	−0.391969	−	0.632218i
$671$	−5.61218	−	2.04267i	−0.216656	−	0.0788563i
$672$		0			0
$673$	7.13129	−	40.4435i	0.274891	−	1.55898i	−0.464417	−	0.885616i	$-0.653736\pi$
$673$	7.13129	−	40.4435i	0.274891	−	1.55898i	0.739308	−	0.673367i	$-0.235153\pi$
$674$	−3.83467	+	26.6058i	−0.147706	+	1.02482i
$675$		0			0
$676$	−24.0509	−	7.07995i	−0.925034	−	0.272306i
$677$	−17.2637	−	3.04406i	−0.663499	−	0.116993i	−0.168251	−	0.985744i	$-0.553812\pi$
$677$	−17.2637	−	3.04406i	−0.663499	−	0.116993i	−0.495248	+	0.868752i	$0.664923\pi$
$678$		0			0
$679$	−10.8951	−	3.96547i	−0.418114	−	0.152181i
$680$	5.55646	−	1.53003i	0.213081	−	0.0586739i
$681$		0			0
$682$	15.0715	−	3.14819i	0.577119	−	0.120551i
$683$	−34.2463	−	19.7721i	−1.31040	−	0.756558i	−0.328235	−	0.944596i	$-0.606454\pi$
$683$	−34.2463	−	19.7721i	−1.31040	−	0.756558i	−0.982162	+	0.188038i	$0.939787\pi$
$684$		0			0
$685$	−15.3126	+	8.84073i	−0.585064	+	0.337787i
$686$	−17.7925	+	15.9075i	−0.679321	+	0.607351i
$687$		0			0
$688$	−41.6473	−	17.5121i	−1.58779	−	0.667643i
$689$	0.816164	+	4.62869i	0.0310934	+	0.176339i
$690$		0			0
$691$	13.9569	−	16.6332i	0.530946	−	0.632757i	−0.432186	−	0.901784i	$-0.642258\pi$
$691$	13.9569	−	16.6332i	0.530946	−	0.632757i	0.963133	+	0.269027i	$0.0867022\pi$
$692$	9.52589	−	2.30402i	0.362120	−	0.0875857i
$693$		0			0
$694$	−8.11526	+	10.3121i	−0.308051	+	0.391441i
$695$	0.410715	−	0.149488i	0.0155793	−	0.00567040i
$696$		0			0
$697$	−7.62376	+	6.39709i	−0.288770	+	0.242307i
$698$	−9.25159	−	4.96098i	−0.350178	−	0.187776i
$699$		0			0
$700$	4.66441	−	9.39515i	0.176298	−	0.355103i
$701$			24.5820i			0.928448i	0.885718	+	0.464224i	$0.153667\pi$
$701$			24.5820i			0.928448i	−0.885718	+	0.464224i	$0.846333\pi$
$702$		0			0
$703$	15.1764			0.572390
$704$	−6.74161	−	11.3133i	−0.254084	−	0.426384i
$705$		0			0
$706$	−18.9011	+	35.2481i	−0.711351	+	1.32658i
$707$	−15.9242	−	18.9777i	−0.598889	−	0.713729i
$708$		0			0
$709$	−14.8834	−	40.8919i	−0.558959	−	1.53573i	−0.821151	−	0.570711i	$-0.806668\pi$
$709$	−14.8834	−	40.8919i	−0.558959	−	1.53573i	0.262193	−	0.965016i	$-0.415554\pi$
$710$	13.3612	−	16.9781i	0.501436	−	0.637177i
$711$		0			0
$712$	19.8430	−	1.87412i	0.743648	−	0.0702357i
$713$	−19.5318	−	16.3891i	−0.731473	−	0.613778i
$714$		0			0
$715$	1.24031	−	0.218700i	0.0463850	−	0.00817892i
$716$	7.37098	+	0.827184i	0.275466	+	0.0309133i
$717$		0			0
$718$	−17.8769	+	15.9830i	−0.667162	+	0.596480i
$719$	−2.30085	−	3.98520i	−0.0858074	−	0.148623i	0.819928	−	0.572467i	$-0.194014\pi$
$719$	−2.30085	−	3.98520i	−0.0858074	−	0.148623i	−0.905735	+	0.423844i	$0.860680\pi$
$720$		0			0
$721$	−2.72831	+	4.72557i	−0.101607	+	0.175989i
$722$	−2.09831	−	10.0454i	−0.0780910	−	0.373850i
$723$		0			0
$724$	13.0645	+	29.9079i	0.485540	+	1.11152i
$725$	−5.09606	+	14.0013i	−0.189263	+	0.519996i
$726$		0			0
$727$	−0.922052	+	5.22921i	−0.0341970	+	0.193941i	−0.997120	−	0.0758339i	$-0.975838\pi$
$727$	−0.922052	+	5.22921i	−0.0341970	+	0.193941i	0.962923	+	0.269775i	$0.0869492\pi$
$728$	−2.45772	−	1.12547i	−0.0910891	−	0.0417126i
$729$		0			0
$730$	14.8926	+	2.14646i	0.551200	+	0.0794441i
$731$	20.1874	+	3.55958i	0.746658	+	0.131656i
$732$		0			0
$733$	−17.7690	+	48.8201i	−0.656315	+	1.80321i	−0.0633350	+	0.997992i	$0.520174\pi$
$733$	−17.7690	+	48.8201i	−0.656315	+	1.80321i	−0.592980	+	0.805217i	$0.702049\pi$
$734$	6.02677	+	9.72077i	0.222452	+	0.358800i
$735$		0			0
$736$	−7.81826	+	20.3592i	−0.288185	+	0.750449i
$737$	9.98153	−	17.2885i	0.367674	−	0.636831i
$738$		0			0
$739$	−8.21344	+	4.74203i	−0.302136	+	0.174439i	−0.643402	−	0.765528i	$-0.722478\pi$
$739$	−8.21344	+	4.74203i	−0.302136	+	0.174439i	0.341266	+	0.939967i	$0.389144\pi$
$740$	5.50266	+	8.28313i	0.202282	+	0.304494i
$741$		0			0
$742$	−0.429356	−	13.6739i	−0.0157622	−	0.501985i
$743$	−1.45201	−	8.23477i	−0.0532691	−	0.302104i	0.946520	−	0.322646i	$-0.104572\pi$
$743$	−1.45201	−	8.23477i	−0.0532691	−	0.302104i	−0.999789	+	0.0205412i	$0.993461\pi$
$744$		0			0
$745$	−10.1797	−	8.54176i	−0.372954	−	0.312946i
$746$	−11.5723	−	28.9352i	−0.423694	−	1.05939i
$747$		0			0
$748$	4.12048	+	4.32739i	0.150660	+	0.158225i
$749$	1.99746	+	5.48797i	0.0729855	+	0.200526i
$750$		0			0
$751$	36.5089	−	30.6346i	1.33223	−	1.11787i	0.348680	−	0.937242i	$-0.386630\pi$
$751$	36.5089	−	30.6346i	1.33223	−	1.11787i	0.983551	−	0.180632i	$-0.0578143\pi$
$752$	29.7130	+	39.1541i	1.08352	+	1.42780i
$753$		0			0
$754$	3.64766	+	1.19940i	0.132840	+	0.0436795i
$755$			10.3342i			0.376101i
$756$		0			0
$757$			22.8271i			0.829666i	0.909898	+	0.414833i	$0.136160\pi$
$757$			22.8271i			0.829666i	−0.909898	+	0.414833i	$0.863840\pi$
$758$	4.16229	−	12.6585i	0.151181	−	0.459779i
$759$		0			0
$760$	−7.64163	+	7.74784i	−0.277191	+	0.281044i
$761$	9.00453	−	7.55570i	0.326414	−	0.273894i	−0.464823	−	0.885404i	$-0.653882\pi$
$761$	9.00453	−	7.55570i	0.326414	−	0.273894i	0.791237	+	0.611510i	$0.209438\pi$
$762$		0			0
$763$	−9.88546	−	27.1601i	−0.357878	−	0.983261i
$764$	−9.99355	+	9.51572i	−0.361554	+	0.344267i
$765$		0			0
$766$	22.7074	−	9.08161i	0.820451	−	0.328132i
$767$	−5.51349	−	4.62637i	−0.199081	−	0.167048i
$768$		0			0
$769$	−3.03895	−	17.2347i	−0.109587	−	0.621501i	−0.989288	−	0.145974i	$-0.953369\pi$
$769$	−3.03895	−	17.2347i	−0.109587	−	0.621501i	0.879701	−	0.475527i	$-0.157743\pi$
$770$	−3.66407	+	0.115051i	−0.132044	+	0.00414614i
$771$		0			0
$772$	10.5472	+	15.8767i	0.379603	+	0.571415i
$773$	20.9933	−	12.1205i	0.755076	−	0.435943i	−0.0724491	−	0.997372i	$-0.523081\pi$
$773$	20.9933	−	12.1205i	0.755076	−	0.435943i	0.827525	+	0.561429i	$0.189748\pi$
$774$		0			0
$775$	−12.3656	+	21.4178i	−0.444185	+	0.769351i
$776$	1.87708	−	23.3066i	0.0673831	−	0.836659i
$777$		0			0
$778$	−29.8562	+	18.5106i	−1.07040	+	0.663636i
$779$	6.42713	−	17.6584i	0.230276	−	0.632677i
$780$		0			0
$781$	22.0597	+	3.88972i	0.789359	+	0.139185i
$782$	1.41159	−	9.79390i	0.0504783	−	0.350229i
$783$		0			0
$784$	−16.9210	−	10.9074i	−0.604323	−	0.389550i
$785$	2.68125	−	15.2061i	0.0956979	−	0.542730i
$786$		0			0
$787$	2.60184	−	7.14850i	0.0927457	−	0.254817i	−0.884642	−	0.466270i	$-0.845597\pi$
$787$	2.60184	−	7.14850i	0.0927457	−	0.254817i	0.977388	+	0.211454i	$0.0678197\pi$
$788$	−1.60856	−	3.68239i	−0.0573027	−	0.131180i
$789$		0			0
$790$	14.2572	−	2.97809i	0.507249	−	0.105956i
$791$	−1.86019	+	3.22194i	−0.0661406	+	0.114559i
$792$		0			0
$793$	−1.23610	−	2.14099i	−0.0438952	−	0.0760287i
$794$	−6.47023	−	7.23694i	−0.229620	−	0.256830i
$795$		0			0
$796$	−4.75366	+	42.3595i	−0.168489	+	1.50139i
$797$	13.7809	−	2.42995i	0.488146	−	0.0860733i	0.0758424	−	0.997120i	$-0.475835\pi$
$797$	13.7809	−	2.42995i	0.488146	−	0.0860733i	0.412304	+	0.911047i	$0.364724\pi$
$798$		0			0
$799$	−17.0837	−	14.3350i	−0.604380	−	0.507135i
$800$	20.7645	+	4.03908i	0.734137	+	0.142803i
$801$		0			0
$802$	−14.0102	−	11.0256i	−0.494718	−	0.389326i
$803$	5.33557	+	14.6594i	0.188288	+	0.517317i
$804$		0			0
$805$	3.90214	+	4.65039i	0.137532	+	0.163905i
$806$	5.61679	+	3.01189i	0.197843	+	0.106089i
$807$		0			0
$808$	28.3732	−	41.1222i	0.998164	−	1.44667i
$809$	20.7183			0.728415			0.364208	−	0.931318i	$-0.381340\pi$
$809$	20.7183			0.728415			0.364208	+	0.931318i	$0.381340\pi$
$810$		0			0
$811$			43.7615i			1.53668i	0.640045	+	0.768338i	$0.278916\pi$
$811$			43.7615i			1.53668i	−0.640045	+	0.768338i	$0.721084\pi$
$812$	−10.0107	−	4.97001i	−0.351306	−	0.174413i
$813$		0			0
$814$	−4.87236	+	9.08632i	−0.170776	+	0.318476i
$815$	10.9396	−	9.17939i	0.383197	−	0.321540i
$816$		0			0
$817$	−36.3718	+	13.2382i	−1.27249	+	0.463148i
$818$	37.8849	+	29.8141i	1.32462	+	1.04243i
$819$		0			0
$820$	11.9681	−	2.89471i	0.417944	−	0.101088i
$821$	12.4887	−	14.8834i	0.435858	−	0.519435i	−0.502745	−	0.864435i	$-0.667677\pi$
$821$	12.4887	−	14.8834i	0.435858	−	0.519435i	0.938603	+	0.345000i	$0.112121\pi$
$822$		0			0
$823$	6.24682	+	35.4275i	0.217750	+	1.23492i	0.876069	+	0.482185i	$0.160157\pi$
$823$	6.24682	+	35.4275i	0.217750	+	1.23492i	−0.658319	+	0.752739i	$0.728732\pi$
$824$	−10.6488	−	2.77470i	−0.370967	−	0.0966613i
$825$		0			0
$826$	13.9630	+	15.6177i	0.485837	+	0.543408i
$827$	−35.6157	+	20.5627i	−1.23848	+	0.715037i	−0.968783	−	0.247909i	$-0.920257\pi$
$827$	−35.6157	+	20.5627i	−1.23848	+	0.715037i	−0.269697	+	0.962945i	$0.586923\pi$
$828$		0			0
$829$	−43.3862	−	25.0490i	−1.50687	−	0.869989i	−0.999968	−	0.00798294i	$-0.997459\pi$
$829$	−43.3862	−	25.0490i	−1.50687	−	0.869989i	−0.506897	−	0.862006i	$-0.669208\pi$
$830$	−0.428074	−	2.04935i	−0.0148587	−	0.0711339i
$831$		0			0
$832$	0.872440	−	5.38117i	0.0302464	−	0.186559i
$833$	8.58341	+	3.12411i	0.297397	+	0.108244i
$834$		0			0
$835$	−21.8951	−	3.86070i	−0.757711	−	0.133605i
$836$	−10.8235	−	3.18615i	−0.374338	−	0.110195i
$837$		0			0
$838$	15.5521	+	2.24152i	0.537240	+	0.0774320i
$839$	−2.93816	+	16.6631i	−0.101436	+	0.575275i	0.891148	+	0.453714i	$0.149901\pi$
$839$	−2.93816	+	16.6631i	−0.101436	+	0.575275i	−0.992584	+	0.121561i	$0.961210\pi$
$840$		0			0
$841$	−12.3325	−	4.48865i	−0.425257	−	0.154781i
$842$	−23.7198	+	14.7060i	−0.817439	+	0.506804i
$843$		0			0
$844$	1.16892	+	18.5952i	0.0402358	+	0.640072i
$845$	−12.1886	−	7.03706i	−0.419299	−	0.242082i
$846$		0			0
$847$	5.81341	+	10.0691i	0.199751	+	0.345979i
$848$	26.3567	−	8.15568i	0.905091	−	0.280067i
$849$		0			0
$850$	−9.59316	+	0.301222i	−0.329043	+	0.0103318i
$851$	16.8143	−	2.96481i	0.576385	−	0.101632i
$852$		0			0
$853$	−16.8126	+	20.0365i	−0.575653	+	0.686037i	−0.972781	−	0.231726i	$-0.925563\pi$
$853$	−16.8126	+	20.0365i	−0.575653	+	0.686037i	0.397128	+	0.917763i	$0.370007\pi$
$854$	2.67213	+	6.68133i	0.0914386	+	0.228630i
$855$		0			0
$856$	−9.60099	+	6.82191i	−0.328155	+	0.233168i
$857$	39.5672	−	14.4013i	1.35159	−	0.491938i	0.438146	−	0.898904i	$-0.355635\pi$
$857$	39.5672	−	14.4013i	1.35159	−	0.491938i	0.913444	+	0.406965i	$0.133413\pi$
$858$		0			0
$859$	27.7503	+	33.0715i	0.946827	+	1.12838i	0.991594	+	0.129387i	$0.0413011\pi$
$859$	27.7503	+	33.0715i	0.946827	+	1.12838i	−0.0447668	+	0.998997i	$0.514254\pi$
$860$	−20.4129	−	15.0514i	−0.696075	−	0.513248i
$861$		0			0
$862$	0.393708	+	0.129456i	0.0134097	+	0.00440929i
$863$	31.5239			1.07308			0.536542	−	0.843873i	$-0.319730\pi$
$863$	31.5239			1.07308			0.536542	+	0.843873i	$0.319730\pi$
$864$		0			0
$865$	5.50169			0.187063
$866$	24.5156	+	8.06105i	0.833075	+	0.273926i
$867$		0			0
$868$	−14.9310	−	11.0093i	−0.506792	−	0.373681i
$869$	9.70666	+	11.5679i	0.329276	+	0.392416i
$870$		0			0
$871$	7.76516	−	2.82629i	0.263112	−	0.0957651i
$872$	47.5155	−	33.7618i	1.60908	−	1.14332i
$873$		0			0
$874$	6.93818	+	17.3480i	0.234687	+	0.586806i
$875$	8.84571	−	10.5419i	0.299040	−	0.356382i
$876$		0			0
$877$	22.1917	−	3.91299i	0.749360	−	0.132132i	0.214091	−	0.976814i	$-0.431321\pi$
$877$	22.1917	−	3.91299i	0.749360	−	0.132132i	0.535269	+	0.844681i	$0.320210\pi$
$878$	1.38464	−	0.0434774i	0.0467295	−	0.00146729i
$879$		0			0
$880$	−2.18540	−	7.06256i	−0.0736700	−	0.238079i
$881$	−15.0315	−	26.0353i	−0.506424	−	0.877153i	−0.999972	−	0.00743425i	$-0.997634\pi$
$881$	−15.0315	−	26.0353i	−0.506424	−	0.877153i	0.493548	−	0.869719i	$-0.335700\pi$
$882$		0			0
$883$	−11.7757	−	6.79869i	−0.396283	−	0.228794i	0.288596	−	0.957451i	$-0.406812\pi$
$883$	−11.7757	−	6.79869i	−0.396283	−	0.228794i	−0.684879	+	0.728657i	$0.740145\pi$
$884$	0.155177	+	2.46856i	0.00521917	+	0.0830267i
$885$		0			0
$886$	6.19532	−	3.84103i	0.208136	−	0.129042i
$887$	−34.6577	−	12.6144i	−1.16369	−	0.423549i	−0.313277	−	0.949662i	$-0.601427\pi$
$887$	−34.6577	−	12.6144i	−1.16369	−	0.423549i	−0.850415	+	0.526112i	$0.823649\pi$
$888$		0			0
$889$	−1.04619	+	5.93322i	−0.0350880	+	0.198994i
$890$	11.0743	+	1.59613i	0.371211	+	0.0535024i
$891$		0			0
$892$	47.2278	+	13.9026i	1.58130	+	0.465494i
$893$	41.4697	+	7.31222i	1.38773	+	0.244694i
$894$		0			0
$895$	3.91267	+	1.42409i	0.130786	+	0.0476022i
$896$	−4.74786	+	15.1406i	−0.158615	+	0.505811i
$897$		0			0
$898$	3.59675	+	17.2189i	0.120025	+	0.574604i
$899$	22.8210	+	13.1757i	0.761124	+	0.439435i
$900$		0			0
$901$	−10.8409	+	6.25901i	−0.361163	+	0.208518i
$902$	8.50888	+	9.51717i	0.283315	+	0.316887i
$903$		0			0
$904$	−7.26043	−	1.89182i	−0.241478	−	0.0629209i
$905$	3.18143	+	18.0428i	0.105754	+	0.599763i
$906$		0			0
$907$	2.75537	−	3.28372i	0.0914905	−	0.109034i	−0.718357	−	0.695675i	$-0.755105\pi$
$907$	2.75537	−	3.28372i	0.0914905	−	0.109034i	0.809847	+	0.586641i	$0.199550\pi$
$908$	−7.94140	+	1.92078i	−0.263544	+	0.0637433i
$909$		0			0
$910$	−1.19248	−	0.938438i	−0.0395302	−	0.0311089i
$911$	26.1940	−	9.53385i	0.867847	−	0.315871i	0.130552	−	0.991441i	$-0.458325\pi$
$911$	26.1940	−	9.53385i	0.867847	−	0.315871i	0.737295	+	0.675571i	$0.236103\pi$
$912$		0			0
$913$	1.66279	−	1.39525i	0.0550303	−	0.0461759i
$914$	−16.1180	+	30.0580i	−0.533135	+	0.994229i
$915$		0			0
$916$	22.6065	+	11.2235i	0.746941	+	0.370834i
$917$			11.1065i			0.366767i
$918$		0			0
$919$	54.1746			1.78705			0.893527	−	0.449009i	$-0.148223\pi$
$919$	54.1746			1.78705			0.893527	+	0.449009i	$0.148223\pi$
$920$	−6.95271	+	10.0768i	−0.229224	+	0.332223i
$921$		0			0
$922$	45.5750	+	24.4386i	1.50093	+	0.804844i
$923$	5.96010	+	7.10297i	0.196179	+	0.233797i
$924$		0			0
$925$	−5.66414	−	15.5621i	−0.186236	−	0.511678i
$926$	−25.1607	−	19.8006i	−0.826833	−	0.650689i
$927$		0			0
$928$	4.30370	−	22.1249i	0.141276	−	0.726287i
$929$	26.4712	+	22.2120i	0.868491	+	0.728751i	0.963780	−	0.266699i	$-0.0859330\pi$
$929$	26.4712	+	22.2120i	0.868491	+	0.728751i	−0.0952887	+	0.995450i	$0.530377\pi$
$930$		0			0
$931$	−16.9854	+	2.99498i	−0.556674	+	0.0981566i
$932$	−5.48163	+	48.8464i	−0.179557	+	1.60002i
$933$		0			0
$934$	−21.9840	−	24.5890i	−0.719337	−	0.804578i
$935$	1.67717	+	2.90494i	0.0548493	+	0.0950018i
$936$		0			0
$937$	−13.1443	+	22.7665i	−0.429404	+	0.743750i	−0.996820	−	0.0796811i	$-0.974610\pi$
$937$	−13.1443	+	22.7665i	−0.429404	+	0.743750i	0.567416	+	0.823431i	$0.307943\pi$
$938$	−23.5445	+	4.91806i	−0.768756	+	0.160580i
$939$		0			0
$940$	11.0451	+	25.2849i	0.360252	+	0.824704i
$941$	13.8588	−	38.0767i	0.451784	−	1.24127i	−0.479683	−	0.877442i	$-0.659248\pi$
$941$	13.8588	−	38.0767i	0.451784	−	1.24127i	0.931467	−	0.363825i	$-0.118529\pi$
$942$		0			0
$943$	3.67106	−	20.8196i	0.119546	−	0.677980i
$944$	−22.8901	+	35.5103i	−0.745011	+	1.15576i
$945$		0			0
$946$	3.75116	−	26.0263i	0.121961	−	0.846189i
$947$	38.4009	+	6.77112i	1.24786	+	0.220032i	0.758282	−	0.651926i	$-0.226039\pi$
$947$	38.4009	+	6.77112i	1.24786	+	0.220032i	0.489580	+	0.871958i	$0.337150\pi$
$948$		0			0
$949$	−2.20861	+	6.06810i	−0.0716944	+	0.196979i
$950$	15.4027	−	9.54952i	0.499730	−	0.309827i
$951$		0			0
$952$	0.577960	−	7.17622i	0.0187318	−	0.232583i
$953$	−12.7586	+	22.0985i	−0.413291	+	0.715842i	−0.995247	−	0.0973785i	$-0.968954\pi$
$953$	−12.7586	+	22.0985i	−0.413291	+	0.715842i	0.581956	+	0.813220i	$0.302288\pi$
$954$		0			0
$955$	−6.70859	+	3.87321i	−0.217085	+	0.125334i
$956$	11.9866	+	18.0433i	0.387674	+	0.583563i
$957$		0			0
$958$	56.3804	−	1.77033i	1.82157	−	0.0571967i
$959$	3.83547	+	21.7520i	0.123854	+	0.702410i
$960$		0			0
$961$	9.75845	+	8.18831i	0.314789	+	0.264139i
$962$	−3.96266	+	1.58483i	−0.127761	+	0.0510969i
$963$		0			0
$964$	−19.1098	+	18.1960i	−0.615484	+	0.586055i
$965$	3.65963	+	10.0547i	0.117808	+	0.323674i
$966$		0			0
$967$	−35.3489	+	29.6612i	−1.13674	+	0.953841i	−0.999327	−	0.0366729i	$-0.988324\pi$
$967$	−35.3489	+	29.6612i	−1.13674	+	0.953841i	−0.137416	+	0.990513i	$0.543880\pi$
$968$	−16.4652	+	16.6941i	−0.529212	+	0.536568i
$969$		0			0
$970$	4.10000	−	12.4691i	0.131643	−	0.400358i
$971$		−	1.40859i		−	0.0452039i	−0.999745	−	0.0226020i	$-0.992805\pi$
$971$		−	1.40859i		−	0.0452039i	0.999745	−	0.0226020i	$-0.00719504\pi$
$972$		0			0
$973$		−	0.545991i		−	0.0175037i
$974$	−43.0339	−	14.1501i	−1.37889	−	0.453398i
$975$		0			0
$976$	−11.5601	+	8.77262i	−0.370028	+	0.280805i
$977$	−36.5361	+	30.6574i	−1.16889	+	0.980817i	−0.999988	−	0.00481536i	$-0.998467\pi$
$977$	−36.5361	+	30.6574i	−1.16889	+	0.980817i	−0.168904	+	0.985633i	$0.554023\pi$
$978$		0			0
$979$	3.96758	+	10.9008i	0.126805	+	0.348393i
$980$	−7.79317	−	8.18451i	−0.248944	−	0.261445i
$981$		0			0
$982$	−13.8412	−	34.6082i	−0.441692	−	1.10439i
$983$	−13.2755	−	11.1394i	−0.423421	−	0.355293i	0.406041	−	0.913855i	$-0.366909\pi$
$983$	−13.2755	−	11.1394i	−0.423421	−	0.355293i	−0.829463	+	0.558562i	$0.811353\pi$
$984$		0			0
$985$	−0.391712	−	2.22151i	−0.0124810	−	0.0707832i
$986$	0.320957	+	10.2217i	0.0102214	+	0.325524i
$987$		0			0
$988$	−2.58433	−	3.89018i	−0.0822185	−	0.123763i
$989$	−37.7108	+	21.7723i	−1.19913	+	0.692320i
$990$		0			0
$991$	16.1511	−	27.9745i	0.513056	−	0.888638i	−0.486830	−	0.873497i	$-0.661847\pi$
$991$	16.1511	−	27.9745i	0.513056	−	0.888638i	0.999885	−	0.0151416i	$-0.00481989\pi$
$992$	13.4118	−	34.9251i	0.425826	−	1.10887i
$993$		0			0
$994$	−14.2214	−	22.9381i	−0.451074	−	0.727551i
$995$	−8.18398	+	22.4853i	−0.259450	+	0.712832i
$996$		0			0
$997$	−24.1513	−	4.25852i	−0.764879	−	0.134869i	−0.222420	−	0.974951i	$-0.571396\pi$
$997$	−24.1513	−	4.25852i	−0.764879	−	0.134869i	−0.542459	+	0.840082i	$0.682507\pi$
$998$	1.13217	+	0.163179i	0.0358382	+	0.00516534i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.397.31		204
3.2	odd	2		216.2.t.a.133.4	yes	204
8.5	even	2	inner	648.2.t.a.397.1		204
12.11	even	2		864.2.bf.a.241.1		204
24.5	odd	2		216.2.t.a.133.34	yes	204
24.11	even	2		864.2.bf.a.241.34		204
27.13	even	9	inner	648.2.t.a.253.1		204
27.14	odd	18		216.2.t.a.13.34	yes	204
108.95	even	18		864.2.bf.a.337.34		204
216.13	even	18	inner	648.2.t.a.253.31		204
216.149	odd	18		216.2.t.a.13.4	✓	204
216.203	even	18		864.2.bf.a.337.1		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.4	✓	204	216.149	odd	18
216.2.t.a.13.34	yes	204	27.14	odd	18
216.2.t.a.133.4	yes	204	3.2	odd	2
216.2.t.a.133.34	yes	204	24.5	odd	2
648.2.t.a.253.1		204	27.13	even	9	inner
648.2.t.a.253.31		204	216.13	even	18	inner
648.2.t.a.397.1		204	8.5	even	2	inner
648.2.t.a.397.31		204	1.1	even	1	trivial
864.2.bf.a.241.1		204	12.11	even	2
864.2.bf.a.241.34		204	24.11	even	2
864.2.bf.a.337.1		204	216.203	even	18
864.2.bf.a.337.34		204	108.95	even	18

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.34345 + 0.441744i) q^{2} +(1.60972 + 1.18692i) q^{4} +(0.721676 + 0.860059i) q^{5} +(1.31793 - 0.479686i) q^{7} +(1.63827 + 2.30566i) q^{8} +(0.589610 + 1.47424i) q^{10} +(-1.05816 + 1.26106i) q^{11} +(-0.671077 + 0.118329i) q^{13} +(1.98247 - 0.0622489i) q^{14} +(1.18243 + 3.82124i) q^{16} +(-0.907443 - 1.57174i) q^{17} +(2.96777 + 1.71344i) q^{19} +(0.140874 + 2.24103i) q^{20} +(-1.97865 + 1.22674i) q^{22} +(3.62278 + 1.31858i) q^{23} +(0.649354 - 3.68267i) q^{25} +(-0.953831 - 0.137475i) q^{26} +(2.69085 + 0.792115i) q^{28} +(-3.92395 - 0.691898i) q^{29} +(-6.21468 - 2.26196i) q^{31} +(-0.0994769 + 5.65598i) q^{32} +(-0.524800 - 2.51241i) q^{34} +(1.36367 + 0.787317i) q^{35} +(3.83532 - 2.21432i) q^{37} +(3.23015 + 3.61292i) q^{38} +(-0.800705 + 3.07295i) q^{40} +(-0.952217 - 5.40029i) q^{41} +(-7.26017 + 8.65234i) q^{43} +(-3.20013 + 0.774013i) q^{44} +(4.28455 + 3.37179i) q^{46} +(11.5469 - 4.20273i) q^{47} +(-3.85548 + 3.23513i) q^{49} +(2.49917 - 4.66064i) q^{50} +(-1.22070 - 0.606040i) q^{52} -6.89741i q^{53} -1.84824 q^{55} +(3.26511 + 2.25283i) q^{56} +(-4.96599 - 2.66291i) q^{58} +(6.78921 + 8.09106i) q^{59} +(1.24084 + 3.40917i) q^{61} +(-7.34992 - 5.78413i) q^{62} +(-2.63214 + 7.55459i) q^{64} +(-0.586070 - 0.491771i) q^{65} +(-11.9425 + 2.10578i) q^{67} +(0.404798 - 3.60713i) q^{68} +(1.48424 + 1.66012i) q^{70} +(-6.80355 - 11.7841i) q^{71} +(4.73823 - 8.20685i) q^{73} +(6.13073 - 1.28061i) q^{74} +(2.74357 + 6.28068i) q^{76} +(-0.789660 + 2.16957i) q^{77} +(1.59290 - 9.03380i) q^{79} +(-2.43316 + 3.77465i) q^{80} +(1.10629 - 7.67567i) q^{82} +(-1.29853 - 0.228966i) q^{83} +(0.696908 - 1.91474i) q^{85} +(-13.5758 + 8.41686i) q^{86} +(-4.64114 - 0.373789i) q^{88} +(3.52339 - 6.10270i) q^{89} +(-0.827669 + 0.477855i) q^{91} +(4.26662 + 6.42251i) q^{92} +(17.3692 - 0.545389i) q^{94} +(0.668104 + 3.78901i) q^{95} +(-6.33275 - 5.31381i) q^{97} +(-6.60875 + 2.64311i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

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