LMFDB - Embedded newform 567.2.ba.a.143.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.14
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.575801 - 0.686212i) q^{2} +(0.207955 + 1.17937i) q^{4} +(-0.100696 + 0.0844942i) q^{5} +(-1.70219 + 2.02548i) q^{7} +(2.48059 + 1.43217i) q^{8} +0.117751i q^{10} +(-2.57587 + 3.06980i) q^{11} +(1.02604 - 2.81901i) q^{13} +(0.409789 + 2.33433i) q^{14} +(0.160408 - 0.0583836i) q^{16} +0.344621 q^{17} +4.89841i q^{19} +(-0.120590 - 0.101187i) q^{20} +(0.623349 + 3.53519i) q^{22} +(-2.18009 + 5.98976i) q^{23} +(-0.865240 + 4.90702i) q^{25} +(-1.34365 - 2.32726i) q^{26} +(-2.74277 - 1.58630i) q^{28} +(-2.29851 - 6.31510i) q^{29} +(8.59607 - 1.51572i) q^{31} +(-1.90702 + 5.23950i) q^{32} +(0.198433 - 0.236483i) q^{34} +(0.000262488 - 0.347783i) q^{35} +(3.64300 - 6.30985i) q^{37} +(3.36135 + 2.82051i) q^{38} +(-0.370796 + 0.0653813i) q^{40} +(9.04416 + 3.29180i) q^{41} +(0.350643 - 1.98860i) q^{43} +(-4.15611 - 2.39953i) q^{44} +(2.85495 + 4.94491i) q^{46} +(-0.771769 + 4.37692i) q^{47} +(-1.20513 - 6.89548i) q^{49} +(2.86905 + 3.41920i) q^{50} +(3.53803 + 0.623850i) q^{52} +(-5.49931 - 3.17503i) q^{53} -0.526764i q^{55} +(-7.12325 + 2.58656i) q^{56} +(-5.65698 - 2.05897i) q^{58} +(-0.167214 - 0.0608610i) q^{59} +(-4.60007 - 0.811116i) q^{61} +(3.90952 - 6.77148i) q^{62} +(2.66805 + 4.62120i) q^{64} +(0.134872 + 0.370558i) q^{65} +(8.83064 - 7.40979i) q^{67} +(0.0716657 + 0.406437i) q^{68} +(-0.238502 - 0.200434i) q^{70} +(-0.373587 + 0.215690i) q^{71} +(1.31951 - 0.761822i) q^{73} +(-2.23226 - 6.13309i) q^{74} +(-5.77706 + 1.01865i) q^{76} +(-1.83321 - 10.4427i) q^{77} +(1.81204 + 1.52049i) q^{79} +(-0.0112194 + 0.0194325i) q^{80} +(7.46651 - 4.31079i) q^{82} +(6.81615 - 2.48087i) q^{83} +(-0.0347021 + 0.0291185i) q^{85} +(-1.16270 - 1.38565i) q^{86} +(-10.7861 + 3.92584i) q^{88} +15.4181 q^{89} +(3.96334 + 6.87669i) q^{91} +(-7.51752 - 1.32554i) q^{92} +(2.55911 + 3.04983i) q^{94} +(-0.413888 - 0.493252i) q^{95} +(-12.2061 - 2.15226i) q^{97} +(-5.42568 - 3.14345i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

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

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

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.575801	−	0.686212i	0.407152	−	0.485225i	−0.523034	−	0.852312i	$-0.675200\pi$
$2$	0.575801	−	0.686212i	0.407152	−	0.485225i	0.930187	+	0.367086i	$0.119645\pi$
$3$		0			0
$3$		0			0
$4$	0.207955	+	1.17937i	0.103978	+	0.589686i
$5$	−0.100696	+	0.0844942i	−0.0450327	+	0.0377870i	−0.665026	−	0.746820i	$-0.731580\pi$
$5$	−0.100696	+	0.0844942i	−0.0450327	+	0.0377870i	0.619994	+	0.784607i	$0.287135\pi$
$6$		0			0
$7$	−1.70219	+	2.02548i	−0.643366	+	0.765559i
$7$	−1.70219	+	2.02548i	−0.643366	+	0.765559i
$8$	2.48059	+	1.43217i	0.877021	+	0.506348i
$9$		0			0
$10$			0.117751i			0.0372361i
$11$	−2.57587	+	3.06980i	−0.776654	+	0.925580i	−0.998777	−	0.0494386i	$-0.984257\pi$
$11$	−2.57587	+	3.06980i	−0.776654	+	0.925580i	0.222123	+	0.975019i	$0.428701\pi$
$12$		0			0
$13$	1.02604	−	2.81901i	0.284571	−	0.781852i	−0.712231	−	0.701945i	$-0.752315\pi$
$13$	1.02604	−	2.81901i	0.284571	−	0.781852i	0.996802	−	0.0799075i	$-0.0254625\pi$
$14$	0.409789	+	2.33433i	0.109521	+	0.623877i
$15$		0			0
$16$	0.160408	−	0.0583836i	0.0401019	−	0.0145959i
$17$	0.344621			0.0835829			0.0417914	−	0.999126i	$-0.486693\pi$
$17$	0.344621			0.0835829			0.0417914	+	0.999126i	$0.486693\pi$
$18$		0			0
$19$			4.89841i			1.12377i	0.827214	+	0.561887i	$0.189924\pi$
$19$			4.89841i			1.12377i	−0.827214	+	0.561887i	$0.810076\pi$
$20$	−0.120590	−	0.101187i	−0.0269649	−	0.0226262i
$21$		0			0
$22$	0.623349	+	3.53519i	0.132898	+	0.753704i
$23$	−2.18009	+	5.98976i	−0.454581	+	1.24895i	0.474887	+	0.880047i	$0.342489\pi$
$23$	−2.18009	+	5.98976i	−0.454581	+	1.24895i	−0.929468	+	0.368904i	$0.879733\pi$
$24$		0			0
$25$	−0.865240	+	4.90702i	−0.173048	+	0.981404i
$26$	−1.34365	−	2.32726i	−0.263511	−	0.456414i
$27$		0			0
$28$	−2.74277	−	1.58630i	−0.518335	−	0.299783i
$29$	−2.29851	−	6.31510i	−0.426822	−	1.17268i	−0.947731	−	0.319072i	$-0.896629\pi$
$29$	−2.29851	−	6.31510i	−0.426822	−	1.17268i	0.520908	−	0.853613i	$-0.325593\pi$
$30$		0			0
$31$	8.59607	−	1.51572i	1.54390	−	0.272231i	0.664125	−	0.747622i	$-0.268804\pi$
$31$	8.59607	−	1.51572i	1.54390	−	0.272231i	0.879775	+	0.475391i	$0.157693\pi$
$32$	−1.90702	+	5.23950i	−0.337117	+	0.926222i
$33$		0			0
$34$	0.198433	−	0.236483i	0.0340310	−	0.0405565i
$35$	0.000262488	−	0.347783i	4.43686e−5	−	0.0587861i
$36$		0			0
$37$	3.64300	−	6.30985i	0.598905	−	1.03733i	−0.394078	−	0.919077i	$-0.628936\pi$
$37$	3.64300	−	6.30985i	0.598905	−	1.03733i	0.992983	−	0.118257i	$-0.0377305\pi$
$38$	3.36135	+	2.82051i	0.545283	+	0.457547i
$39$		0			0
$40$	−0.370796	+	0.0653813i	−0.0586280	+	0.0103377i
$41$	9.04416	+	3.29180i	1.41246	+	0.514094i	0.931851	−	0.362841i	$-0.118193\pi$
$41$	9.04416	+	3.29180i	1.41246	+	0.514094i	0.480609	+	0.876935i	$0.340415\pi$
$42$		0			0
$43$	0.350643	−	1.98860i	0.0534726	−	0.303258i	−0.946328	−	0.323207i	$-0.895239\pi$
$43$	0.350643	−	1.98860i	0.0534726	−	0.303258i	0.999801	+	0.0199486i	$0.00635026\pi$
$44$	−4.15611	−	2.39953i	−0.626556	−	0.361743i
$45$		0			0
$46$	2.85495	+	4.94491i	0.420939	+	0.729088i
$47$	−0.771769	+	4.37692i	−0.112574	+	0.638439i	0.875349	+	0.483492i	$0.160632\pi$
$47$	−0.771769	+	4.37692i	−0.112574	+	0.638439i	−0.987923	+	0.154947i	$0.950479\pi$
$48$		0			0
$49$	−1.20513	−	6.89548i	−0.172161	−	0.985069i
$50$	2.86905	+	3.41920i	0.405745	+	0.483549i
$51$		0			0
$52$	3.53803	+	0.623850i	0.490637	+	0.0865125i
$53$	−5.49931	−	3.17503i	−0.755388	−	0.436123i	0.0722494	−	0.997387i	$-0.476982\pi$
$53$	−5.49931	−	3.17503i	−0.755388	−	0.436123i	−0.827637	+	0.561263i	$0.810316\pi$
$54$		0			0
$55$		−	0.526764i		−	0.0710288i
$56$	−7.12325	+	2.58656i	−0.951884	+	0.345644i
$57$		0			0
$58$	−5.65698	−	2.05897i	−0.742798	−	0.270356i
$59$	−0.167214	−	0.0608610i	−0.0217694	−	0.00792343i	0.331112	−	0.943591i	$-0.392576\pi$
$59$	−0.167214	−	0.0608610i	−0.0217694	−	0.00792343i	−0.352882	+	0.935668i	$0.614798\pi$
$60$		0			0
$61$	−4.60007	−	0.811116i	−0.588978	−	0.103853i	−0.128787	−	0.991672i	$-0.541108\pi$
$61$	−4.60007	−	0.811116i	−0.588978	−	0.103853i	−0.460192	+	0.887820i	$0.652219\pi$
$62$	3.90952	−	6.77148i	0.496509	−	0.859979i
$63$		0			0
$64$	2.66805	+	4.62120i	0.333506	+	0.577649i
$65$	0.134872	+	0.370558i	0.0167288	+	0.0459620i
$66$		0			0
$67$	8.83064	−	7.40979i	1.07883	−	0.905249i	0.0830108	−	0.996549i	$-0.473546\pi$
$67$	8.83064	−	7.40979i	1.07883	−	0.905249i	0.995824	+	0.0912992i	$0.0291020\pi$
$68$	0.0716657	+	0.406437i	0.00869075	+	0.0492877i
$69$		0			0
$70$	−0.238502	−	0.200434i	−0.0285064	−	0.0239564i
$71$	−0.373587	+	0.215690i	−0.0443366	+	0.0255977i	−0.522004	−	0.852943i	$-0.674816\pi$
$71$	−0.373587	+	0.215690i	−0.0443366	+	0.0255977i	0.477668	+	0.878540i	$0.341482\pi$
$72$		0			0
$73$	1.31951	−	0.761822i	0.154437	−	0.0891645i	−0.420790	−	0.907158i	$-0.638247\pi$
$73$	1.31951	−	0.761822i	0.154437	−	0.0891645i	0.575227	+	0.817994i	$0.304914\pi$
$74$	−2.23226	−	6.13309i	−0.259495	−	0.712957i
$75$		0			0
$76$	−5.77706	+	1.01865i	−0.662674	+	0.116847i
$77$	−1.83321	−	10.4427i	−0.208914	−	1.19006i
$78$		0			0
$79$	1.81204	+	1.52049i	0.203871	+	0.171068i	0.739007	−	0.673698i	$-0.235295\pi$
$79$	1.81204	+	1.52049i	0.203871	+	0.171068i	−0.535136	+	0.844766i	$0.679740\pi$
$80$	−0.0112194	+	0.0194325i	−0.00125436	+	0.00217262i
$81$		0			0
$82$	7.46651	−	4.31079i	0.824538	−	0.476047i
$83$	6.81615	−	2.48087i	0.748169	−	0.272311i	0.0603341	−	0.998178i	$-0.480783\pi$
$83$	6.81615	−	2.48087i	0.748169	−	0.272311i	0.687835	+	0.725867i	$0.258561\pi$
$84$		0			0
$85$	−0.0347021	+	0.0291185i	−0.00376397	+	0.00315834i
$86$	−1.16270	−	1.38565i	−0.125377	−	0.149418i
$87$		0			0
$88$	−10.7861	+	3.92584i	−1.14981	+	0.418496i
$89$	15.4181			1.63431			0.817156	−	0.576417i	$-0.195550\pi$
$89$	15.4181			1.63431			0.817156	+	0.576417i	$0.195550\pi$
$90$		0			0
$91$	3.96334	+	6.87669i	0.415471	+	0.720873i
$92$	−7.51752	−	1.32554i	−0.783756	−	0.138197i
$93$		0			0
$94$	2.55911	+	3.04983i	0.263952	+	0.314566i
$95$	−0.413888	−	0.493252i	−0.0424640	−	0.0506066i
$96$		0			0
$97$	−12.2061	−	2.15226i	−1.23934	−	0.218529i	−0.484708	−	0.874676i	$-0.661074\pi$
$97$	−12.2061	−	2.15226i	−1.23934	−	0.218529i	−0.754634	+	0.656147i	$0.772185\pi$
$98$	−5.42568	−	3.14345i	−0.548076	−	0.317536i
$99$		0			0
$100$	−5.96714			−0.596714
$101$	3.54678	−	1.29092i	0.352917	−	0.128451i	−0.159477	−	0.987202i	$-0.550981\pi$
$101$	3.54678	−	1.29092i	0.352917	−	0.128451i	0.512394	+	0.858750i	$0.328759\pi$
$102$		0			0
$103$	−6.43432	−	7.66812i	−0.633992	−	0.755563i	0.349416	−	0.936968i	$-0.386380\pi$
$103$	−6.43432	−	7.66812i	−0.633992	−	0.755563i	−0.983408	+	0.181405i	$0.941935\pi$
$104$	6.58247	−	5.52335i	0.645464	−	0.541609i
$105$		0			0
$106$	−5.34525	+	1.94551i	−0.519176	+	0.188965i
$107$	4.00378	−	2.31158i	0.387060	−	0.223469i	−0.293826	−	0.955859i	$-0.594928\pi$
$107$	4.00378	−	2.31158i	0.387060	−	0.223469i	0.680885	+	0.732390i	$0.261595\pi$
$108$		0			0
$109$	−5.95833	+	10.3201i	−0.570704	+	0.988489i	0.425789	+	0.904822i	$0.359996\pi$
$109$	−5.95833	+	10.3201i	−0.570704	+	0.988489i	−0.996494	+	0.0836667i	$0.973337\pi$
$110$	−0.361472	−	0.303311i	−0.0344650	−	0.0289196i
$111$		0			0
$112$	−0.154789	+	0.424282i	−0.0146262	+	0.0400909i
$113$	3.00669	−	0.530160i	0.282846	−	0.0498733i	−0.0304256	−	0.999537i	$-0.509686\pi$
$113$	3.00669	−	0.530160i	0.282846	−	0.0498733i	0.313271	+	0.949664i	$0.398575\pi$
$114$		0			0
$115$	−0.286573	−	0.787352i	−0.0267230	−	0.0734209i
$116$	6.96987	−	4.02405i	0.647136	−	0.373624i
$117$		0			0
$118$	−0.138046	+	0.0797007i	−0.0127081	+	0.00733704i
$119$	−0.586609	+	0.698023i	−0.0537744	+	0.0639876i
$120$		0			0
$121$	−0.878449	−	4.98193i	−0.0798590	−	0.452903i
$122$	−3.20532	+	2.68958i	−0.290196	+	0.243503i
$123$		0			0
$124$	3.57519	+	9.82277i	0.321062	+	0.882110i
$125$	−0.656113	−	1.13642i	−0.0586845	−	0.101645i
$126$		0			0
$127$	4.57273	−	7.92020i	0.405764	−	0.702804i	−0.588646	−	0.808391i	$-0.700339\pi$
$127$	4.57273	−	7.92020i	0.405764	−	0.702804i	0.994410	+	0.105587i	$0.0336720\pi$
$128$	−6.27472	−	1.10640i	−0.554612	−	0.0977931i
$129$		0			0
$130$	0.331941	+	0.120817i	0.0291131	+	0.0105963i
$131$	5.23893	+	1.90681i	0.457727	+	0.166599i	0.560585	−	0.828097i	$-0.310576\pi$
$131$	5.23893	+	1.90681i	0.457727	+	0.166599i	−0.102858	+	0.994696i	$0.532799\pi$
$132$		0			0
$133$	−9.92164	−	8.33801i	−0.860315	−	0.722997i
$134$		−	10.3263i		−	0.892052i
$135$		0			0
$136$	0.854863	+	0.493555i	0.0733039	+	0.0423220i
$137$	−14.2458	−	2.51192i	−1.21710	−	0.214608i	−0.472023	−	0.881586i	$-0.656476\pi$
$137$	−14.2458	−	2.51192i	−1.21710	−	0.214608i	−0.745077	+	0.666979i	$0.767587\pi$
$138$		0			0
$139$	−8.80185	−	10.4896i	−0.746563	−	0.889720i	0.250356	−	0.968154i	$-0.419452\pi$
$139$	−8.80185	−	10.4896i	−0.746563	−	0.889720i	−0.996919	+	0.0784343i	$0.975008\pi$
$140$	0.410220	−	0.0720137i	0.0346699	−	0.00608627i
$141$		0			0
$142$	−0.0671020	+	0.380554i	−0.00563107	+	0.0319354i
$143$	6.01086	+	10.4111i	0.502654	+	0.870622i
$144$		0			0
$145$	0.765040	+	0.441696i	0.0635331	+	0.0366809i
$146$	0.237005	−	1.34412i	0.0196147	−	0.111241i
$147$		0			0
$148$	8.19925	+	2.98428i	0.673974	+	0.245306i
$149$	−16.0341	+	2.82725i	−1.31357	+	0.231617i	−0.786175	−	0.618004i	$-0.787941\pi$
$149$	−16.0341	+	2.82725i	−1.31357	+	0.231617i	−0.527393	+	0.849622i	$0.676830\pi$
$150$		0			0
$151$	−3.24977	−	2.72688i	−0.264462	−	0.221910i	0.500908	−	0.865501i	$-0.333000\pi$
$151$	−3.24977	−	2.72688i	−0.264462	−	0.221910i	−0.765370	+	0.643590i	$0.777444\pi$
$152$	−7.01536	+	12.1510i	−0.569020	+	0.985572i
$153$		0			0
$154$	−8.22150	−	4.75496i	−0.662508	−	0.383166i
$155$	−0.737523	+	0.878945i	−0.0592393	+	0.0705986i
$156$		0			0
$157$	−1.56492	+	4.29960i	−0.124895	+	0.343145i	−0.986344	−	0.164698i	$-0.947335\pi$
$157$	−1.56492	+	4.29960i	−0.124895	+	0.343145i	0.861449	+	0.507843i	$0.169557\pi$
$158$	2.08675	−	0.367951i	0.166013	−	0.0292726i
$159$		0			0
$160$	−0.250677	−	0.688731i	−0.0198178	−	0.0544489i
$161$	−8.42121	−	14.6114i	−0.663684	−	1.15154i
$162$		0			0
$163$	−4.14531	−	7.17988i	−0.324686	−	0.562372i	0.656763	−	0.754097i	$-0.271925\pi$
$163$	−4.14531	−	7.17988i	−0.324686	−	0.562372i	−0.981449	+	0.191725i	$0.938592\pi$
$164$	−2.00148	+	11.3510i	−0.156290	+	0.886363i
$165$		0			0
$166$	2.22233	−	6.10581i	0.172487	−	0.473903i
$167$	−0.761050	−	4.31613i	−0.0588919	−	0.333992i	0.941100	−	0.338130i	$-0.109794\pi$
$167$	−0.761050	−	4.31613i	−0.0588919	−	0.333992i	−0.999991	+	0.00413722i	$0.998683\pi$
$168$		0			0
$169$	3.06452	+	2.57143i	0.235732	+	0.197803i
$170$			0.0405794i			0.00311230i
$171$		0			0
$172$	2.41821			0.184387
$173$	15.5919	−	5.67499i	1.18543	−	0.431462i	0.327314	−	0.944916i	$-0.393856\pi$
$173$	15.5919	−	5.67499i	1.18543	−	0.431462i	0.858117	+	0.513454i	$0.171634\pi$
$174$		0			0
$175$	−8.46627	−	10.1052i	−0.639990	−	0.763880i
$176$	−0.233963	+	0.642808i	−0.0176356	+	0.0484535i
$177$		0			0
$178$	8.87773	−	10.5801i	0.665414	−	0.793010i
$179$			10.4083i			0.777951i	0.921248	+	0.388976i	$0.127171\pi$
$179$			10.4083i			0.777951i	−0.921248	+	0.388976i	$0.872829\pi$
$180$		0			0
$181$	14.3465	+	8.28296i	1.06637	+	0.615668i	0.927187	−	0.374599i	$-0.122220\pi$
$181$	14.3465	+	8.28296i	1.06637	+	0.615668i	0.139181	+	0.990267i	$0.455553\pi$
$182$	7.00096	+	1.23991i	0.518946	+	0.0919081i
$183$		0			0
$184$	−13.9863	+	11.7359i	−1.03108	+	0.865179i
$185$	0.166310	+	0.943191i	0.0122274	+	0.0693448i
$186$		0			0
$187$	−0.887699	+	1.05792i	−0.0649150	+	0.0773626i
$188$	−5.32251			−0.388184
$189$		0			0
$190$	−0.576792			−0.0418449
$191$	6.66865	−	7.94739i	0.482527	−	0.575053i	−0.468774	−	0.883318i	$-0.655304\pi$
$191$	6.66865	−	7.94739i	0.482527	−	0.575053i	0.951300	+	0.308265i	$0.0997485\pi$
$192$		0			0
$193$	3.16593	+	17.9549i	0.227888	+	1.29242i	0.857086	+	0.515174i	$0.172273\pi$
$193$	3.16593	+	17.9549i	0.227888	+	1.29242i	−0.629197	+	0.777246i	$0.716616\pi$
$194$	−8.50519	+	7.13670i	−0.610637	+	0.512385i
$195$		0			0
$196$	7.88173	−	2.85525i	0.562981	−	0.203946i
$197$	18.9850	+	10.9610i	1.35263	+	0.780941i	0.988617	−	0.150454i	$-0.0480735\pi$
$197$	18.9850	+	10.9610i	1.35263	+	0.780941i	0.364012	+	0.931394i	$0.381407\pi$
$198$		0			0
$199$			7.25537i			0.514320i	0.966369	+	0.257160i	$0.0827867\pi$
$199$			7.25537i			0.514320i	−0.966369	+	0.257160i	$0.917213\pi$
$200$	−9.17399	+	10.9331i	−0.648699	+	0.773089i
$201$		0			0
$202$	1.15639	−	3.17715i	0.0813633	−	0.223544i
$203$	16.7036	+	6.09389i	1.17236	+	0.427707i
$204$		0			0
$205$	−1.18885	+	0.432707i	−0.0830330	+	0.0302215i
$206$	−8.96685			−0.624750
$207$		0			0
$208$		−	0.512094i		−	0.0355074i
$209$	−15.0372	−	12.6177i	−1.04014	−	0.872783i
$210$		0			0
$211$	0.796078	+	4.51478i	0.0548043	+	0.310810i	0.999871	−	0.0160673i	$-0.00511459\pi$
$211$	0.796078	+	4.51478i	0.0548043	+	0.310810i	−0.945067	+	0.326878i	$0.894003\pi$
$212$	2.60093	−	7.14600i	0.178633	−	0.490789i
$213$		0			0
$214$	0.719141	−	4.07845i	0.0491595	−	0.278797i
$215$	0.132716	+	0.229871i	0.00905118	+	0.0156771i
$216$		0			0
$217$	−11.5620	+	19.9912i	−0.784883	+	1.35709i
$218$	3.65099	+	10.0310i	0.247276	+	0.679386i
$219$		0			0
$220$	0.621251	−	0.109543i	0.0418847	−	0.00738540i
$221$	0.353593	−	0.971490i	0.0237853	−	0.0653495i
$222$		0			0
$223$	15.1586	−	18.0653i	1.01510	−	1.20974i	0.0374904	−	0.999297i	$-0.488064\pi$
$223$	15.1586	−	18.0653i	1.01510	−	1.20974i	0.977605	−	0.210447i	$-0.0674919\pi$
$224$	−7.36639	−	12.7812i	−0.492188	−	0.853982i
$225$		0			0
$226$	1.36745	−	2.36849i	0.0909615	−	0.157550i
$227$	1.87601	+	1.57416i	0.124515	+	0.104480i	0.702919	−	0.711270i	$-0.251880\pi$
$227$	1.87601	+	1.57416i	0.124515	+	0.104480i	−0.578404	+	0.815751i	$0.696324\pi$
$228$		0			0
$229$	0.258016	−	0.0454952i	0.0170502	−	0.00300640i	−0.165117	−	0.986274i	$-0.552800\pi$
$229$	0.258016	−	0.0454952i	0.0170502	−	0.00300640i	0.182167	+	0.983268i	$0.441689\pi$
$230$	−0.705299	−	0.256708i	−0.0465060	−	0.0169268i
$231$		0			0
$232$	3.34263	−	18.9570i	0.219455	−	1.24459i
$233$	25.1425	+	14.5160i	1.64714	+	0.950977i	0.978201	+	0.207662i	$0.0665853\pi$
$233$	25.1425	+	14.5160i	1.64714	+	0.950977i	0.668941	+	0.743316i	$0.266748\pi$
$234$		0			0
$235$	−0.292110	−	0.505950i	−0.0190552	−	0.0330045i
$236$	0.0370047	−	0.209864i	0.00240880	−	0.0136610i
$237$		0			0
$238$	0.141222	+	0.804460i	0.00915407	+	0.0521454i
$239$	−1.21344	−	1.44612i	−0.0784911	−	0.0935420i	0.725370	−	0.688359i	$-0.241669\pi$
$239$	−1.21344	−	1.44612i	−0.0784911	−	0.0935420i	−0.803861	+	0.594817i	$0.797224\pi$
$240$		0			0
$241$	18.0533	+	3.18328i	1.16291	+	0.205053i	0.721607	−	0.692303i	$-0.243404\pi$
$241$	18.0533	+	3.18328i	1.16291	+	0.205053i	0.441307	+	0.897356i	$0.354515\pi$
$242$	−3.92447	−	2.26580i	−0.252275	−	0.145651i
$243$		0			0
$244$		−	5.59387i		−	0.358111i
$245$	0.703980	+	0.592523i	0.0449757	+	0.0378549i
$246$		0			0
$247$	13.8087	+	5.02595i	0.878625	+	0.319793i
$248$	23.4941	+	8.55114i	1.49188	+	0.542998i
$249$		0			0
$250$	−1.15762	−	0.204119i	−0.0732141	−	0.0129096i
$251$	−3.29266	+	5.70305i	−0.207831	+	0.359973i	−0.951031	−	0.309096i	$-0.899974\pi$
$251$	−3.29266	+	5.70305i	−0.207831	+	0.359973i	0.743200	+	0.669069i	$0.233307\pi$
$252$		0			0
$253$	−12.7717	−	22.1213i	−0.802952	−	1.39075i
$254$	−2.80196	−	7.69832i	−0.175811	−	0.483036i
$255$		0			0
$256$	−12.5476	+	10.5287i	−0.784224	+	0.658042i
$257$	−5.02735	−	28.5115i	−0.313598	−	1.77850i	−0.579978	−	0.814632i	$-0.696939\pi$
$257$	−5.02735	−	28.5115i	−0.313598	−	1.77850i	0.266381	−	0.963868i	$-0.414172\pi$
$258$		0			0
$259$	6.57942	+	18.1193i	0.408825	+	1.12588i
$260$	−0.408978	+	0.236124i	−0.0253638	+	0.0146438i
$261$		0			0
$262$	4.32506	−	2.49707i	0.267203	−	0.154270i
$263$	7.94138	+	21.8188i	0.489686	+	1.34540i	0.900965	+	0.433892i	$0.142860\pi$
$263$	7.94138	+	21.8188i	0.489686	+	1.34540i	−0.411278	+	0.911510i	$0.634918\pi$
$264$		0			0
$265$	0.822031	−	0.144946i	0.0504970	−	0.00890398i
$266$	−11.4345	+	2.00732i	−0.701096	+	0.123077i
$267$		0			0
$268$	10.5753	+	8.87371i	0.645988	+	0.542048i
$269$	4.60903	−	7.98308i	0.281018	−	0.486737i	−0.690618	−	0.723220i	$-0.742661\pi$
$269$	4.60903	−	7.98308i	0.281018	−	0.486737i	0.971636	+	0.236483i	$0.0759947\pi$
$270$		0			0
$271$	25.5138	−	14.7304i	1.54985	−	0.894807i	0.551700	−	0.834043i	$-0.313980\pi$
$271$	25.5138	−	14.7304i	1.54985	−	0.894807i	0.998152	−	0.0607643i	$-0.0193538\pi$
$272$	0.0552799	−	0.0201202i	0.00335183	−	0.00121997i
$273$		0			0
$274$	−9.92644	+	8.32927i	−0.599678	+	0.503190i
$275$	−12.8348	−	15.2960i	−0.773970	−	0.922381i
$276$		0			0
$277$	−2.86248	+	1.04186i	−0.171990	+	0.0625991i	−0.426580	−	0.904450i	$-0.640282\pi$
$277$	−2.86248	+	1.04186i	−0.171990	+	0.0625991i	0.254590	+	0.967049i	$0.418059\pi$
$278$	−12.2662			−0.735680
$279$		0			0
$280$	0.498735	−	0.862331i	0.0298051	−	0.0515341i
$281$	−24.6845	−	4.35255i	−1.47256	−	0.259651i	−0.620956	−	0.783845i	$-0.713256\pi$
$281$	−24.6845	−	4.35255i	−1.47256	−	0.259651i	−0.851599	+	0.524194i	$0.824367\pi$
$282$		0			0
$283$	7.17877	+	8.55533i	0.426734	+	0.508562i	0.935977	−	0.352061i	$-0.114519\pi$
$283$	7.17877	+	8.55533i	0.426734	+	0.508562i	−0.509243	+	0.860623i	$0.670075\pi$
$284$	−0.332068	−	0.395744i	−0.0197046	−	0.0234831i
$285$		0			0
$286$	10.6053	+	1.87000i	0.627105	+	0.110575i
$287$	−22.0623	+	12.7155i	−1.30230	+	0.750572i
$288$		0			0
$289$	−16.8812			−0.993014
$290$	0.743608	−	0.270651i	0.0436662	−	0.0158932i
$291$		0			0
$292$	1.17287	+	1.39777i	0.0686371	+	0.0817986i
$293$	−3.69754	+	3.10260i	−0.216012	+	0.181256i	−0.744373	−	0.667764i	$-0.767251\pi$
$293$	−3.69754	+	3.10260i	−0.216012	+	0.181256i	0.528360	+	0.849020i	$0.322807\pi$
$294$		0			0
$295$	0.0219803	−	0.00800016i	0.00127974	−	0.000465787i
$296$	18.0735	−	10.4348i	1.05050	−	0.606508i
$297$		0			0
$298$	−7.29237	+	12.6308i	−0.422436	+	0.731680i
$299$	14.6483	+	12.2914i	0.847135	+	0.710830i
$300$		0			0
$301$	3.43100	+	4.09518i	0.197759	+	0.236042i
$302$	−3.74243	+	0.659892i	−0.215353	+	0.0379725i
$303$		0			0
$304$	0.285987	+	0.785743i	0.0164025	+	0.0450655i
$305$	0.531744	−	0.307003i	0.0304476	−	0.0175789i
$306$		0			0
$307$	−17.7257	+	10.2339i	−1.01166	+	0.584082i	−0.911677	−	0.410907i	$-0.865212\pi$
$307$	−17.7257	+	10.2339i	−1.01166	+	0.584082i	−0.0999825	+	0.994989i	$0.531879\pi$
$308$	11.9347	−	4.33366i	0.680040	−	0.246933i
$309$		0			0
$310$	0.178477	+	1.01219i	0.0101368	+	0.0574888i
$311$	−11.3004	+	9.48217i	−0.640787	+	0.537684i	−0.904260	−	0.426982i	$-0.859577\pi$
$311$	−11.3004	+	9.48217i	−0.640787	+	0.537684i	0.263473	+	0.964667i	$0.415132\pi$
$312$		0			0
$313$	4.05965	+	11.1538i	0.229465	+	0.630450i	0.999976	−	0.00697724i	$-0.00222094\pi$
$313$	4.05965	+	11.1538i	0.229465	+	0.630450i	−0.770511	+	0.637427i	$0.779999\pi$
$314$	2.04935	+	3.54958i	0.115652	+	0.200314i
$315$		0			0
$316$	−1.41639	+	2.45327i	−0.0796784	+	0.138007i
$317$	20.1601	+	3.55477i	1.13230	+	0.199656i	0.708237	−	0.705975i	$-0.249491\pi$
$317$	20.1601	+	3.55477i	1.13230	+	0.199656i	0.424067	+	0.905631i	$0.360602\pi$
$318$		0			0
$319$	25.3068	+	9.21090i	1.41691	+	0.515712i
$320$	−0.659127	−	0.239903i	−0.0368463	−	0.0134110i
$321$		0			0
$322$	−14.8755	−	2.63452i	−0.828977	−	0.146816i
$323$			1.68810i			0.0939282i
$324$		0			0
$325$	12.9452	+	7.47390i	0.718069	+	0.414577i
$326$	−7.31379	−	1.28962i	−0.405074	−	0.0714254i
$327$		0			0
$328$	17.7204	+	21.1184i	0.978447	+	1.16607i
$329$	−7.55166	−	9.01353i	−0.416337	−	0.496932i
$330$		0			0
$331$	−2.39022	+	13.5556i	−0.131378	+	0.745083i	0.845935	+	0.533285i	$0.179043\pi$
$331$	−2.39022	+	13.5556i	−0.131378	+	0.745083i	−0.977314	+	0.211798i	$0.932068\pi$
$332$	4.34333	+	7.52287i	0.238371	+	0.412871i
$333$		0			0
$334$	−3.40000	−	1.96299i	−0.186040	−	0.107410i
$335$	−0.263129	+	1.49228i	−0.0143762	+	0.0815317i
$336$		0			0
$337$	−11.8712	−	4.32077i	−0.646667	−	0.235367i	−0.00219742	−	0.999998i	$-0.500699\pi$
$337$	−11.8712	−	4.32077i	−0.646667	−	0.235367i	−0.644469	+	0.764630i	$0.722922\pi$
$338$	3.52910	−	0.622276i	0.191958	−	0.0338473i
$339$		0			0
$340$	−0.0415580	−	0.0348713i	−0.00225380	−	0.00189116i
$341$	−17.4894	+	30.2925i	−0.947104	+	1.64043i
$342$		0			0
$343$	16.0180	+	9.29642i	0.864891	+	0.501960i
$344$	3.71780	−	4.43071i	0.200451	−	0.238888i
$345$		0			0
$346$	5.08358	−	13.9670i	0.273295	−	0.750872i
$347$	−17.8481	+	3.14709i	−0.958134	+	0.168945i	−0.630784	−	0.775958i	$-0.717267\pi$
$347$	−17.8481	+	3.14709i	−0.958134	+	0.168945i	−0.327350	+	0.944903i	$0.606155\pi$
$348$		0			0
$349$	−6.17471	−	16.9649i	−0.330525	−	0.908109i	−0.987975	−	0.154612i	$-0.950587\pi$
$349$	−6.17471	−	16.9649i	−0.330525	−	0.908109i	0.657450	−	0.753498i	$-0.271635\pi$
$350$	−11.8092	−	0.00891295i	−0.631228	−	0.000476417i
$351$		0			0
$352$	−11.1720	−	19.3505i	−0.595469	−	1.03138i
$353$	2.71457	−	15.3951i	0.144482	−	0.819398i	−0.823300	−	0.567607i	$-0.807869\pi$
$353$	2.71457	−	15.3951i	0.144482	−	0.819398i	0.967782	−	0.251791i	$-0.0810195\pi$
$354$		0			0
$355$	0.0193942	−	0.0532851i	0.00102934	−	0.00282808i
$356$	3.20627	+	18.1836i	0.169932	+	0.963731i
$357$		0			0
$358$	7.14229	+	5.99309i	0.377482	+	0.316745i
$359$			10.1138i			0.533785i	0.963726	+	0.266892i	$0.0859968\pi$
$359$			10.1138i			0.533785i	−0.963726	+	0.266892i	$0.914003\pi$
$360$		0			0
$361$	−4.99446			−0.262866
$362$	13.9446	−	5.07542i	0.732912	−	0.266758i
$363$		0			0
$364$	−7.28598	+	6.10430i	−0.381889	+	0.319952i
$365$	−0.0685006	+	0.188204i	−0.00358549	+	0.00985105i
$366$		0			0
$367$	−17.9093	+	21.3435i	−0.934859	+	1.11412i	0.0584104	+	0.998293i	$0.481397\pi$
$367$	−17.9093	+	21.3435i	−0.934859	+	1.11412i	−0.993269	+	0.115829i	$0.963048\pi$
$368$			1.08809i			0.0567204i
$369$		0			0
$370$	0.742991	+	0.428966i	0.0386262	+	0.0223009i
$371$	15.7918	−	5.73425i	0.819869	−	0.297707i
$372$		0			0
$373$	15.1151	−	12.6831i	0.782632	−	0.656706i	−0.161278	−	0.986909i	$-0.551562\pi$
$373$	15.1151	−	12.6831i	0.782632	−	0.656706i	0.943910	+	0.330203i	$0.107117\pi$
$374$	0.214819	+	1.21830i	0.0111080	+	0.0629968i
$375$		0			0
$376$	−8.18293	+	9.75203i	−0.422002	+	0.502923i
$377$	−20.1607			−1.03833
$378$		0			0
$379$	3.29633			0.169321			0.0846605	−	0.996410i	$-0.473019\pi$
$379$	3.29633			0.169321			0.0846605	+	0.996410i	$0.473019\pi$
$380$	0.495658	−	0.590702i	0.0254267	−	0.0303024i
$381$		0			0
$382$	−1.61378	−	9.15222i	−0.0825684	−	0.468269i
$383$	23.6377	−	19.8344i	1.20783	−	1.01349i	0.208459	−	0.978031i	$-0.433155\pi$
$383$	23.6377	−	19.8344i	1.20783	−	1.01349i	0.999371	−	0.0354584i	$-0.0112891\pi$
$384$		0			0
$385$	1.06695	+	0.896649i	0.0543767	+	0.0456975i
$386$	14.1438	+	8.16592i	0.719900	+	0.415635i
$387$		0			0
$388$		−	14.8431i		−	0.753545i
$389$	8.64017	−	10.2969i	0.438074	−	0.522076i	−0.501160	−	0.865355i	$-0.667093\pi$
$389$	8.64017	−	10.2969i	0.438074	−	0.522076i	0.939234	+	0.343279i	$0.111538\pi$
$390$		0			0
$391$	−0.751306	+	2.06420i	−0.0379952	+	0.104391i
$392$	6.88606	−	18.8308i	0.347799	−	0.951099i
$393$		0			0
$394$	18.4532	−	6.71641i	0.929658	−	0.338368i
$395$	−0.310938			−0.0156450
$396$		0			0
$397$		−	32.3533i		−	1.62376i	−0.583821	−	0.811882i	$-0.698443\pi$
$397$		−	32.3533i		−	1.62376i	0.583821	−	0.811882i	$-0.301557\pi$
$398$	4.97873	+	4.17765i	0.249561	+	0.209407i
$399$		0			0
$400$	0.147699	+	0.837640i	0.00738493	+	0.0418820i
$401$	−13.0462	+	35.8442i	−0.651498	+	1.78998i	−0.0393585	+	0.999225i	$0.512531\pi$
$401$	−13.0462	+	35.8442i	−0.651498	+	1.78998i	−0.612139	+	0.790750i	$0.709691\pi$
$402$		0			0
$403$	4.54704	−	25.7876i	0.226504	−	1.28457i
$404$	2.26005	+	3.91452i	0.112442	+	0.194754i
$405$		0			0
$406$	13.7996	−	7.95334i	0.684864	−	0.394718i
$407$	9.98612	+	27.4366i	0.494993	+	1.35998i
$408$		0			0
$409$	−22.3158	+	3.93488i	−1.10345	+	0.194567i	−0.695562	−	0.718466i	$-0.744845\pi$
$409$	−22.3158	+	3.93488i	−1.10345	+	0.194567i	−0.407885	+	0.913033i	$0.633734\pi$
$410$	−0.387613	+	1.06496i	−0.0191428	+	0.0525945i
$411$		0			0
$412$	7.70552	−	9.18309i	0.379624	−	0.452418i
$413$	0.407902	−	0.235092i	0.0200716	−	0.0115681i
$414$		0			0
$415$	−0.476741	+	0.825740i	−0.0234023	+	0.0405340i
$416$	12.8135	+	10.7518i	0.628235	+	0.527152i
$417$		0			0
$418$	−17.3168	+	3.05342i	−0.846993	+	0.149348i
$419$	−1.24840	−	0.454379i	−0.0609881	−	0.0221979i	0.311346	−	0.950297i	$-0.399220\pi$
$419$	−1.24840	−	0.454379i	−0.0609881	−	0.0221979i	−0.372334	+	0.928099i	$0.621442\pi$
$420$		0			0
$421$	−0.798906	+	4.53082i	−0.0389363	+	0.220819i	−0.998067	−	0.0621441i	$-0.980206\pi$
$421$	−0.798906	+	4.53082i	−0.0389363	+	0.220819i	0.959131	+	0.282963i	$0.0913173\pi$
$422$	3.55648	+	2.05334i	0.173127	+	0.0999548i
$423$		0			0
$424$	−9.09435	−	15.7519i	−0.441661	−	0.764979i
$425$	−0.298180	+	1.69106i	−0.0144639	+	0.0820286i
$426$		0			0
$427$	9.47306	−	7.93667i	0.458434	−	0.384082i
$428$	3.55882	+	4.24124i	0.172022	+	0.205008i
$429$		0			0
$430$	0.234159	+	0.0412885i	0.0112921	+	0.00199111i
$431$	−15.3689	−	8.87327i	−0.740296	−	0.427410i	0.0818808	−	0.996642i	$-0.473907\pi$
$431$	−15.3689	−	8.87327i	−0.740296	−	0.427410i	−0.822177	+	0.569232i	$0.807241\pi$
$432$		0			0
$433$		−	1.22234i		−	0.0587418i	−0.999569	−	0.0293709i	$-0.990650\pi$
$433$		−	1.22234i		−	0.0587418i	0.999569	−	0.0293709i	$-0.00935038\pi$
$434$	7.06077	+	19.4450i	0.338928	+	0.933388i
$435$		0			0
$436$	−13.4103	−	4.88096i	−0.642239	−	0.233756i
$437$	−29.3403	−	10.6790i	−1.40354	−	0.510846i
$438$		0			0
$439$	4.79703	+	0.845847i	0.228950	+	0.0403701i	0.286946	−	0.957947i	$-0.407360\pi$
$439$	4.79703	+	0.845847i	0.228950	+	0.0403701i	−0.0579961	+	0.998317i	$0.518471\pi$
$440$	0.754414	−	1.30668i	0.0359653	−	0.0622937i
$441$		0			0
$442$	−0.463049	−	0.802024i	−0.0220250	−	0.0381484i
$443$	−7.95536	−	21.8572i	−0.377971	−	1.03847i	−0.972196	−	0.234168i	$-0.924764\pi$
$443$	−7.95536	−	21.8572i	−0.377971	−	1.03847i	0.594226	−	0.804298i	$-0.297459\pi$
$444$		0			0
$445$	−1.55254	+	1.30274i	−0.0735975	+	0.0617557i
$446$	−3.66832	−	20.8041i	−0.173700	−	0.985100i
$447$		0			0
$448$	−13.9016	−	2.46206i	−0.656791	−	0.116321i
$449$	−19.9333	+	11.5085i	−0.940710	+	0.543119i	−0.890183	−	0.455603i	$-0.849424\pi$
$449$	−19.9333	+	11.5085i	−0.940710	+	0.543119i	−0.0505273	+	0.998723i	$0.516090\pi$
$450$		0			0
$451$	−33.4018	+	19.2845i	−1.57283	+	0.908072i
$452$	1.25051	+	3.43576i	0.0588192	+	0.161604i
$453$		0			0
$454$	2.16041	−	0.380939i	0.101393	−	0.0178783i
$455$	−0.980134	−	0.357578i	−0.0459494	−	0.0167635i
$456$		0			0
$457$	20.3778	+	17.0990i	0.953231	+	0.799856i	0.979839	−	0.199790i	$-0.0640260\pi$
$457$	20.3778	+	17.0990i	0.953231	+	0.799856i	−0.0266074	+	0.999646i	$0.508470\pi$
$458$	0.117346	−	0.203250i	0.00548323	−	0.00949724i
$459$		0			0
$460$	0.868987	−	0.501710i	0.0405167	−	0.0233923i
$461$	25.7975	−	9.38952i	1.20151	−	0.437314i	0.337758	−	0.941233i	$-0.390331\pi$
$461$	25.7975	−	9.38952i	1.20151	−	0.437314i	0.863751	+	0.503919i	$0.168109\pi$
$462$		0			0
$463$	2.44473	−	2.05137i	0.113616	−	0.0953355i	−0.584210	−	0.811603i	$-0.698595\pi$
$463$	2.44473	−	2.05137i	0.113616	−	0.0953355i	0.697826	+	0.716267i	$0.254151\pi$
$464$	−0.737397	−	0.878795i	−0.0342328	−	0.0407970i
$465$		0			0
$466$	24.4382	−	8.89476i	1.13208	−	0.412042i
$467$	−16.9027			−0.782162			−0.391081	−	0.920356i	$-0.627899\pi$
$467$	−16.9027			−0.782162			−0.391081	+	0.920356i	$0.627899\pi$
$468$		0			0
$469$	−0.0230191	+	30.4991i	−0.00106292	+	1.40832i
$470$	−0.515386	−	0.0908765i	−0.0237730	−	0.00419182i
$471$		0			0
$472$	−0.327627	−	0.390450i	−0.0150802	−	0.0179719i
$473$	5.20138	+	6.19877i	0.239160	+	0.285020i
$474$		0			0
$475$	−24.0366	−	4.23831i	−1.10288	−	0.194467i
$476$	−0.945217	−	0.546673i	−0.0433240	−	0.0250567i
$477$		0			0
$478$	−1.69105			−0.0773468
$479$	−35.4520	+	12.9035i	−1.61984	+	0.589574i	−0.983352	−	0.181710i	$-0.941837\pi$
$479$	−35.4520	+	12.9035i	−1.61984	+	0.589574i	−0.636490	+	0.771285i	$0.719614\pi$
$480$		0			0
$481$	−14.0497	−	16.7438i	−0.640611	−	0.763450i
$482$	12.5795	−	10.5554i	0.572980	−	0.480787i
$483$		0			0
$484$	5.69287	−	2.07204i	0.258767	−	0.0941835i
$485$	1.41096	−	0.814620i	0.0640685	−	0.0369900i
$486$		0			0
$487$	−9.18231	+	15.9042i	−0.416090	+	0.720689i	−0.995542	−	0.0943172i	$-0.969933\pi$
$487$	−9.18231	+	15.9042i	−0.416090	+	0.720689i	0.579452	+	0.815006i	$0.303267\pi$
$488$	−10.2492	−	8.60012i	−0.463960	−	0.389309i
$489$		0			0
$490$	0.811949	−	0.141905i	0.0366801	−	0.00641062i
$491$	17.9717	−	3.16890i	0.811053	−	0.143011i	0.247284	−	0.968943i	$-0.420462\pi$
$491$	17.9717	−	3.16890i	0.811053	−	0.143011i	0.563769	+	0.825933i	$0.309351\pi$
$492$		0			0
$493$	−0.792114	−	2.17632i	−0.0356750	−	0.0980163i
$494$	11.3999	−	6.58174i	0.512906	−	0.296126i
$495$		0			0
$496$	1.29038	−	0.745003i	0.0579399	−	0.0334516i
$497$	0.199037	−	1.12384i	0.00892805	−	0.0504110i
$498$		0			0
$499$	6.49963	+	36.8612i	0.290963	+	1.65013i	0.683172	+	0.730258i	$0.260600\pi$
$499$	6.49963	+	36.8612i	0.290963	+	1.65013i	−0.392208	+	0.919876i	$0.628289\pi$
$500$	1.20382	−	1.01013i	0.0538365	−	0.0451742i
$501$		0			0
$502$	2.01759	+	5.54328i	0.0900494	+	0.247409i
$503$	−8.72136	−	15.1058i	−0.388866	−	0.673536i	0.603431	−	0.797415i	$-0.293800\pi$
$503$	−8.72136	−	15.1058i	−0.388866	−	0.673536i	−0.992297	+	0.123879i	$0.960466\pi$
$504$		0			0
$505$	−0.248072	+	0.429673i	−0.0110391	+	0.0191202i
$506$	−22.5339	−	3.97333i	−1.00175	−	0.176636i
$507$		0			0
$508$	10.2918	+	3.74591i	0.456625	+	0.166198i
$509$	−26.2302	−	9.54701i	−1.16263	−	0.423164i	−0.312595	−	0.949886i	$-0.601198\pi$
$509$	−26.2302	−	9.54701i	−1.16263	−	0.423164i	−0.850037	+	0.526723i	$0.823421\pi$
$510$		0			0
$511$	−0.703004	+	3.96941i	−0.0310991	+	0.175596i
$512$			1.92969i			0.0852812i
$513$		0			0
$514$	−22.4597	−	12.9671i	−0.990655	−	0.571955i
$515$	1.29582	+	0.228489i	0.0571008	+	0.0100684i
$516$		0			0
$517$	−11.4483	−	13.6436i	−0.503496	−	0.600043i
$518$	16.2222	+	5.91825i	0.712761	+	0.260033i
$519$		0			0
$520$	−0.196139	+	1.11236i	−0.00860127	+	0.0487802i
$521$	−3.13445	−	5.42902i	−0.137323	−	0.237850i	0.789160	−	0.614188i	$-0.210516\pi$
$521$	−3.13445	−	5.42902i	−0.137323	−	0.237850i	−0.926482	+	0.376338i	$0.877183\pi$
$522$		0			0
$523$	5.33996	+	3.08303i	0.233500	+	0.134811i	0.612186	−	0.790714i	$-0.290290\pi$
$523$	5.33996	+	3.08303i	0.233500	+	0.134811i	−0.378686	+	0.925525i	$0.623624\pi$
$524$	−1.15938	+	6.57518i	−0.0506478	+	0.287238i
$525$		0			0
$526$	19.5450	+	7.11378i	0.852200	+	0.310176i
$527$	2.96239	−	0.522349i	0.129044	−	0.0227539i
$528$		0			0
$529$	−13.5054	−	11.3324i	−0.587190	−	0.492711i
$530$	0.373862	−	0.647548i	0.0162395	−	0.0281277i
$531$		0			0
$532$	7.77036	−	13.4352i	0.336888	−	0.582491i
$533$	18.5593	−	22.1181i	0.803890	−	0.958039i
$534$		0			0
$535$	−0.207850	+	0.571064i	−0.00898615	+	0.0246892i
$536$	32.5172	−	5.73367i	1.40453	−	0.247657i
$537$		0			0
$538$	−2.82420	−	7.75944i	−0.121760	−	0.334533i
$539$	24.2720	+	14.0623i	1.04547	+	0.605708i
$540$		0			0
$541$	−10.3506	−	17.9278i	−0.445008	−	0.770777i	0.553045	−	0.833152i	$-0.313466\pi$
$541$	−10.3506	−	17.9278i	−0.445008	−	0.770777i	−0.998053	+	0.0623747i	$0.980133\pi$
$542$	4.58267	−	25.9896i	0.196843	−	1.11635i
$543$		0			0
$544$	−0.657200	+	1.80564i	−0.0281772	+	0.0774163i
$545$	−0.272010	−	1.54264i	−0.0116516	−	0.0660796i
$546$		0			0
$547$	−12.9704	−	10.8834i	−0.554573	−	0.465342i	0.321913	−	0.946769i	$-0.395674\pi$
$547$	−12.9704	−	10.8834i	−0.554573	−	0.465342i	−0.876486	+	0.481427i	$0.840118\pi$
$548$		−	17.3235i		−	0.740022i
$549$		0			0
$550$	−17.8866			−0.762687
$551$	30.9340	−	11.2590i	1.31783	−	0.479651i
$552$		0			0
$553$	−6.16415	+	1.08211i	−0.262126	+	0.0460160i
$554$	−0.933281	+	2.56417i	−0.0396513	+	0.108941i
$555$		0			0
$556$	10.5408	−	12.5620i	0.447030	−	0.532749i
$557$		−	42.9293i		−	1.81897i	−0.415735	−	0.909486i	$-0.636476\pi$
$557$		−	42.9293i		−	1.81897i	0.415735	−	0.909486i	$-0.363524\pi$
$558$		0			0
$559$	−5.24610	−	3.02883i	−0.221886	−	0.128106i
$560$	−0.0202627	−	0.0558024i	−0.000856257	−	0.00235808i
$561$		0			0
$562$	−17.2001	+	14.4326i	−0.725544	+	0.608804i
$563$	−0.471251	−	2.67260i	−0.0198609	−	0.112637i	0.973266	−	0.229682i	$-0.0737687\pi$
$563$	−0.471251	−	2.67260i	−0.0198609	−	0.112637i	−0.993127	+	0.117046i	$0.962658\pi$
$564$		0			0
$565$	−0.257967	+	0.307433i	−0.0108527	+	0.0129338i
$566$	10.0043			0.420513
$567$		0			0
$568$	−1.23562			−0.0518454
$569$	21.3534	−	25.4480i	0.895182	−	1.06684i	−0.102217	−	0.994762i	$-0.532594\pi$
$569$	21.3534	−	25.4480i	0.895182	−	1.06684i	0.997399	−	0.0720743i	$-0.0229619\pi$
$570$		0			0
$571$	0.378167	+	2.14469i	0.0158258	+	0.0897526i	0.991698	−	0.128591i	$-0.0410456\pi$
$571$	0.378167	+	2.14469i	0.0158258	+	0.0897526i	−0.975872	+	0.218344i	$0.929934\pi$
$572$	−11.0286	+	9.25410i	−0.461129	+	0.386933i
$573$		0			0
$574$	−3.97797	+	22.4610i	−0.166037	+	0.937505i
$575$	−27.5056	−	15.8803i	−1.14706	−	0.662256i
$576$		0			0
$577$		−	34.2253i		−	1.42482i	−0.701764	−	0.712410i	$-0.747604\pi$
$577$		−	34.2253i		−	1.42482i	0.701764	−	0.712410i	$-0.252396\pi$
$578$	−9.72023	+	11.5841i	−0.404308	+	0.481836i
$579$		0			0
$580$	−0.361830	+	0.994121i	−0.0150242	+	0.0412786i
$581$	−6.57739	+	18.0289i	−0.272876	+	0.747964i
$582$		0			0
$583$	23.9122	−	8.70333i	0.990342	−	0.360455i
$584$	4.36423			0.180593
$585$		0			0
$586$			4.32377i			0.178613i
$587$	−10.2925	−	8.63644i	−0.424817	−	0.356464i	0.405175	−	0.914239i	$-0.367211\pi$
$587$	−10.2925	−	8.63644i	−0.424817	−	0.356464i	−0.829992	+	0.557775i	$0.811655\pi$
$588$		0			0
$589$	7.42462	+	42.1071i	0.305926	+	1.73499i
$590$	0.00716644	−	0.0196896i	0.000295038	−	0.000810609i
$591$		0			0
$592$	0.215972	−	1.22484i	0.00887641	−	0.0503406i
$593$	−1.95066	−	3.37864i	−0.0801039	−	0.138744i	0.823190	−	0.567765i	$-0.192192\pi$
$593$	−1.95066	−	3.37864i	−0.0801039	−	0.138744i	−0.903294	+	0.429021i	$0.858859\pi$
$594$		0			0
$595$	9.04589e−5	−	0.119853i	3.70846e−6	−	0.00491351i
$596$	−6.66876	−	18.3223i	−0.273163	−	0.750510i
$597$		0			0
$598$	16.8690	−	2.97447i	0.689826	−	0.121635i
$599$	3.18327	−	8.74596i	0.130065	−	0.357350i	−0.857517	−	0.514456i	$-0.827994\pi$
$599$	3.18327	−	8.74596i	0.130065	−	0.357350i	0.987582	+	0.157105i	$0.0502163\pi$
$600$		0			0
$601$	−20.1709	+	24.0388i	−0.822789	+	0.980561i	−0.999993	−	0.00361252i	$-0.998850\pi$
$601$	−20.1709	+	24.0388i	−0.822789	+	0.980561i	0.177205	+	0.984174i	$0.443295\pi$
$602$	4.78573	+	0.00361202i	0.195052	+	0.000147215i
$603$		0			0
$604$	2.54020	−	4.39975i	0.103359	−	0.179023i
$605$	0.509401	+	0.427438i	0.0207101	+	0.0173778i
$606$		0			0
$607$	−7.05213	+	1.24348i	−0.286237	+	0.0504714i	−0.314923	−	0.949117i	$-0.601979\pi$
$607$	−7.05213	+	1.24348i	−0.286237	+	0.0504714i	0.0286860	+	0.999588i	$0.490868\pi$
$608$	−25.6653	−	9.34139i	−1.04086	−	0.378843i
$609$		0			0
$610$	0.0955096	−	0.541662i	0.00386707	−	0.0219312i
$611$	11.5467	+	6.66650i	0.467130	+	0.269698i
$612$		0			0
$613$	−17.4253	−	30.1815i	−0.703801	−	1.21902i	−0.967122	−	0.254311i	$-0.918151\pi$
$613$	−17.4253	−	30.1815i	−0.703801	−	1.21902i	0.263321	−	0.964708i	$-0.415182\pi$
$614$	−3.18381	+	18.0563i	−0.128488	+	0.728693i
$615$		0			0
$616$	10.4083	−	28.5296i	0.419363	−	1.14949i
$617$	−4.32090	−	5.14944i	−0.173953	−	0.207309i	0.672023	−	0.740530i	$-0.265426\pi$
$617$	−4.32090	−	5.14944i	−0.173953	−	0.207309i	−0.845976	+	0.533222i	$0.820981\pi$
$618$		0			0
$619$	−33.9380	−	5.98419i	−1.36408	−	0.240525i	−0.556780	−	0.830660i	$-0.687963\pi$
$619$	−33.9380	−	5.98419i	−1.36408	−	0.240525i	−0.807304	+	0.590135i	$0.799074\pi$
$620$	−1.18998	−	0.687033i	−0.0477906	−	0.0275919i
$621$		0			0
$622$			13.2143i			0.529846i
$623$	−26.2444	+	31.2290i	−1.05146	+	1.25116i
$624$		0			0
$625$	−23.2490	−	8.46196i	−0.929962	−	0.338478i
$626$	9.99142	+	3.63658i	0.399338	+	0.145347i
$627$		0			0
$628$	−5.39626	−	0.951506i	−0.215334	−	0.0379692i
$629$	1.25545	−	2.17451i	0.0500582	−	0.0867033i
$630$		0			0
$631$	13.2483	+	22.9468i	0.527407	+	0.913496i	0.999490	+	0.0319417i	$0.0101691\pi$
$631$	13.2483	+	22.9468i	0.527407	+	0.913496i	−0.472083	+	0.881554i	$0.656498\pi$
$632$	2.31734	+	6.36685i	0.0921790	+	0.253260i
$633$		0			0
$634$	14.0475	−	11.7873i	0.557899	−	0.468132i
$635$	0.208754	+	1.18390i	0.00828416	+	0.0469818i
$636$		0			0
$637$	−20.6749	−	3.67773i	−0.819170	−	0.145717i
$638$	20.8923	−	12.0622i	0.827133	−	0.477546i
$639$		0			0
$640$	0.725326	−	0.418767i	0.0286710	−	0.0165532i
$641$	−0.814710	−	2.23840i	−0.0321791	−	0.0884114i	0.922563	−	0.385847i	$-0.126091\pi$
$641$	−0.814710	−	2.23840i	−0.0321791	−	0.0884114i	−0.954742	+	0.297436i	$0.903869\pi$
$642$		0			0
$643$	9.49012	−	1.67336i	0.374254	−	0.0659911i	0.0166424	−	0.999862i	$-0.494702\pi$
$643$	9.49012	−	1.67336i	0.374254	−	0.0659911i	0.357612	+	0.933870i	$0.383591\pi$
$644$	15.4811	−	12.9703i	0.610039	−	0.511100i
$645$		0			0
$646$	1.15839	+	0.972007i	0.0455764	+	0.0382431i
$647$	1.16581	−	2.01925i	0.0458328	−	0.0793847i	−0.842199	−	0.539167i	$-0.818739\pi$
$647$	1.16581	−	2.01925i	0.0458328	−	0.0793847i	0.888032	+	0.459782i	$0.152073\pi$
$648$		0			0
$649$	0.617553	−	0.356545i	0.0242411	−	0.0139956i
$650$	12.5825	−	4.57966i	0.493527	−	0.179629i
$651$		0			0
$652$	7.60572	−	6.38196i	0.297863	−	0.249937i
$653$	−12.3603	−	14.7305i	−0.483698	−	0.576448i	0.467905	−	0.883779i	$-0.345009\pi$
$653$	−12.3603	−	14.7305i	−0.483698	−	0.576448i	−0.951603	+	0.307330i	$0.900564\pi$
$654$		0			0
$655$	−0.688655	+	0.250650i	−0.0269080	+	0.00979370i
$656$	1.64294			0.0641460
$657$		0			0
$658$	−10.5334	−	0.00795009i	−0.410637	−	0.000309927i
$659$	−38.6246	−	6.81055i	−1.50460	−	0.265301i	−0.640239	−	0.768176i	$-0.721165\pi$
$659$	−38.6246	−	6.81055i	−1.50460	−	0.265301i	−0.864360	+	0.502874i	$0.832276\pi$
$660$		0			0
$661$	−22.2105	−	26.4694i	−0.863888	−	1.02954i	−0.999249	−	0.0387452i	$-0.987664\pi$
$661$	−22.2105	−	26.4694i	−0.863888	−	1.02954i	0.135361	−	0.990796i	$-0.456781\pi$
$662$	7.92573	+	9.44552i	0.308042	+	0.367110i
$663$		0			0
$664$	20.4611	+	3.60784i	0.794044	+	0.140011i
$665$	1.70359	+	0.00128578i	0.0660622	+	4.98602e-5i
$666$		0			0
$667$	42.8369			1.65865
$668$	4.93206	−	1.79512i	0.190827	−	0.0694554i
$669$		0			0
$670$	0.872509	+	1.03982i	0.0337079	+	0.0401716i
$671$	14.3391	−	12.0320i	0.553556	−	0.464489i
$672$		0			0
$673$	13.9024	−	5.06006i	0.535898	−	0.195051i	−0.0598720	−	0.998206i	$-0.519069\pi$
$673$	13.9024	−	5.06006i	0.535898	−	0.195051i	0.595770	+	0.803155i	$0.296847\pi$
$674$	−9.80042	+	5.65828i	−0.377498	+	0.217949i
$675$		0			0
$676$	−2.39540	+	4.14895i	−0.0921307	+	0.159575i
$677$	−14.3500	−	12.0411i	−0.551516	−	0.462777i	0.323938	−	0.946078i	$-0.394993\pi$
$677$	−14.3500	−	12.0411i	−0.551516	−	0.462777i	−0.875454	+	0.483302i	$0.839437\pi$
$678$		0			0
$679$	25.1364	−	21.0596i	0.964647	−	0.808195i
$680$	−0.127784	+	0.0225318i	−0.00490030	+	0.000864055i
$681$		0			0
$682$	10.7167	+	29.4439i	0.410364	+	1.12746i
$683$	19.2619	−	11.1209i	0.737037	−	0.425529i	−0.0839538	−	0.996470i	$-0.526755\pi$
$683$	19.2619	−	11.1209i	0.737037	−	0.425529i	0.820991	+	0.570941i	$0.193421\pi$
$684$		0			0
$685$	1.64674	−	0.950746i	0.0629187	−	0.0363261i
$686$	15.6025	−	5.63887i	0.595706	−	0.215293i
$687$		0			0
$688$	−0.0598556	−	0.339458i	−0.00228197	−	0.0129417i
$689$	−14.5929	+	12.2449i	−0.555946	+	0.466494i
$690$		0			0
$691$	0.935144	+	2.56929i	0.0355745	+	0.0977403i	0.956208	−	0.292687i	$-0.0945495\pi$
$691$	0.935144	+	2.56929i	0.0355745	+	0.0977403i	−0.920634	+	0.390427i	$0.872327\pi$
$692$	9.93535	+	17.2085i	0.377685	+	0.654170i
$693$		0			0
$694$	−8.11734	+	14.0597i	−0.308130	+	0.533697i
$695$	1.77263	+	0.312562i	0.0672396	+	0.0118562i
$696$		0			0
$697$	3.11681	+	1.13443i	0.118058	+	0.0429694i
$698$	−15.1969	−	5.53123i	−0.575212	−	0.209360i
$699$		0			0
$700$	10.1572	−	12.0863i	0.383905	−	0.456820i
$701$			7.89910i			0.298345i	0.988811	+	0.149173i	$0.0476610\pi$
$701$			7.89910i			0.298345i	−0.988811	+	0.149173i	$0.952339\pi$
$702$		0			0
$703$	30.9083	+	17.8449i	1.16573	+	0.673033i
$704$	−21.0587	−	3.71322i	−0.793680	−	0.139947i
$705$		0			0
$706$	−9.00125	−	10.7273i	−0.338766	−	0.403726i
$707$	−3.42254	+	9.38131i	−0.128718	+	0.352820i
$708$		0			0
$709$	6.03163	−	34.2071i	0.226523	−	1.28467i	−0.633230	−	0.773964i	$-0.718271\pi$
$709$	6.03163	−	34.2071i	0.226523	−	1.28467i	0.859753	−	0.510711i	$-0.170618\pi$
$710$	−0.0253977	−	0.0439901i	−0.000953159	−	0.00165092i
$711$		0			0
$712$	38.2459	+	22.0813i	1.43332	+	0.827531i
$713$	−9.66145	+	54.7928i	−0.361824	+	2.05201i
$714$		0			0
$715$	−1.48495	−	0.540478i	−0.0555340	−	0.0202127i
$716$	−12.2752	+	2.16446i	−0.458747	+	0.0808895i
$717$		0			0
$718$	6.94020	+	5.82352i	0.259006	+	0.217332i
$719$	1.44565	−	2.50394i	0.0539137	−	0.0933812i	−0.837809	−	0.545963i	$-0.816164\pi$
$719$	1.44565	−	2.50394i	0.0539137	−	0.0933812i	0.891723	+	0.452582i	$0.149497\pi$
$720$		0			0
$721$	26.4840	+	0.0199887i	0.986317	+	0.000744419i
$722$	−2.87581	+	3.42726i	−0.107027	+	0.127549i
$723$		0			0
$724$	−6.78527	+	18.6424i	−0.252172	+	0.692838i
$725$	32.9771	−	5.81475i	1.22474	−	0.215954i
$726$		0			0
$727$	8.56203	+	23.5240i	0.317548	+	0.872456i	0.991076	+	0.133295i	$0.0425557\pi$
$727$	8.56203	+	23.5240i	0.317548	+	0.872456i	−0.673528	+	0.739161i	$0.735222\pi$
$728$	−0.0171587	+	22.7344i	−0.000635945	+	0.842593i
$729$		0			0
$730$	0.0897052	+	0.155374i	0.00332014	+	0.00575065i
$731$	0.120839	−	0.685312i	0.00446939	−	0.0253472i
$732$		0			0
$733$	6.23827	−	17.1395i	0.230416	−	0.633062i	−0.769569	−	0.638563i	$-0.779529\pi$
$733$	6.23827	−	17.1395i	0.230416	−	0.633062i	0.999985	+	0.00550162i	$0.00175123\pi$
$734$	4.33397	+	24.5792i	0.159970	+	0.907234i
$735$		0			0
$736$	−27.2259	−	22.8452i	−1.00356	−	0.842086i
$737$			46.1950i			1.70161i
$738$		0			0
$739$	23.7495			0.873641			0.436821	−	0.899549i	$-0.356104\pi$
$739$	23.7495			0.873641			0.436821	+	0.899549i	$0.356104\pi$
$740$	−1.07779	+	0.392283i	−0.0396203	+	0.0144206i
$741$		0			0
$742$	5.15801	−	14.1383i	0.189357	−	0.519034i
$743$	−3.47920	+	9.55903i	−0.127640	+	0.350687i	−0.987008	−	0.160670i	$-0.948635\pi$
$743$	−3.47920	+	9.55903i	−0.127640	+	0.350687i	0.859369	+	0.511357i	$0.170857\pi$
$744$		0			0
$745$	1.37569	−	1.63949i	0.0504014	−	0.0600661i
$746$		−	17.6751i		−	0.647132i
$747$		0			0
$748$	−1.43228	−	0.826928i	−0.0523694	−	0.0302355i
$749$	−2.13311	+	12.0443i	−0.0779422	+	0.440090i
$750$		0			0
$751$	−10.6919	+	8.97158i	−0.390153	+	0.327378i	−0.816673	−	0.577101i	$-0.804184\pi$
$751$	−10.6919	+	8.97158i	−0.390153	+	0.327378i	0.426520	+	0.904478i	$0.359740\pi$
$752$	0.131743	+	0.747150i	0.00480416	+	0.0272458i
$753$		0			0
$754$	−11.6085	+	13.8345i	−0.422757	+	0.503823i
$755$	0.557645			0.0202948
$756$		0			0
$757$	−23.1271			−0.840570			−0.420285	−	0.907392i	$-0.638070\pi$
$757$	−23.1271			−0.840570			−0.420285	+	0.907392i	$0.638070\pi$
$758$	1.89803	−	2.26198i	0.0689395	−	0.0821589i
$759$		0			0
$760$	−0.320265	−	1.81631i	−0.0116172	−	0.0658846i
$761$	−12.8791	+	10.8068i	−0.466866	+	0.391747i	−0.845650	−	0.533738i	$-0.820787\pi$
$761$	−12.8791	+	10.8068i	−0.466866	+	0.391747i	0.378784	+	0.925485i	$0.376342\pi$
$762$		0			0
$763$	−10.7610	−	29.6352i	−0.389575	−	1.07287i
$764$	10.7597	+	6.21212i	0.389273	+	0.224747i
$765$		0			0
$766$		−	27.6411i		−	0.998715i
$767$	−0.343135	+	0.408933i	−0.0123899	+	0.0147657i
$768$		0			0
$769$	−5.01510	+	13.7789i	−0.180849	+	0.496879i	−0.996681	−	0.0814109i	$-0.974057\pi$
$769$	−5.01510	+	13.7789i	−0.180849	+	0.496879i	0.815832	+	0.578290i	$0.196280\pi$
$770$	1.22964	−	0.215862i	0.0443132	−	0.00777913i
$771$		0			0
$772$	−20.5171	+	7.46762i	−0.738427	+	0.268765i
$773$	48.1829			1.73302			0.866508	−	0.499163i	$-0.166359\pi$
$773$	48.1829			1.73302			0.866508	+	0.499163i	$0.166359\pi$
$774$		0			0
$775$			43.4926i			1.56230i
$776$	−27.1959	−	22.8201i	−0.976276	−	0.819193i
$777$		0			0
$778$	−2.09088	−	11.8580i	−0.0749617	−	0.425129i
$779$	−16.1246	+	44.3020i	−0.577725	+	1.58729i
$780$		0			0
$781$	0.300184	−	1.70243i	0.0107414	−	0.0609176i
$782$	0.983875	+	1.70412i	0.0351833	+	0.0609393i
$783$		0			0
$784$	−0.595895	−	1.03573i	−0.0212820	−	0.0369903i
$785$	−0.205709	−	0.565180i	−0.00734206	−	0.0201722i
$786$		0			0
$787$	−24.8204	+	4.37651i	−0.884753	+	0.156006i	−0.597519	−	0.801855i	$-0.703847\pi$
$787$	−24.8204	+	4.37651i	−0.884753	+	0.156006i	−0.287234	+	0.957860i	$0.592736\pi$
$788$	−8.97909	+	24.6698i	−0.319867	+	0.878827i
$789$		0			0
$790$	−0.179038	+	0.213370i	−0.00636990	+	0.00759135i
$791$	−4.04411	+	6.99242i	−0.143792	+	0.248622i
$792$		0			0
$793$	−7.00637	+	12.1354i	−0.248804	+	0.430940i
$794$	−22.2012	−	18.6290i	−0.787892	−	0.661120i
$795$		0			0
$796$	−8.55679	+	1.50879i	−0.303287	+	0.0534777i
$797$	48.1785	+	17.5355i	1.70657	+	0.621140i	0.996546	−	0.0830393i	$-0.0264627\pi$
$797$	48.1785	+	17.5355i	1.70657	+	0.621140i	0.710022	+	0.704179i	$0.248685\pi$
$798$		0			0
$799$	−0.265968	+	1.50838i	−0.00940927	+	0.0533626i
$800$	−24.0603	−	13.8912i	−0.850661	−	0.491129i
$801$		0			0
$802$	17.0847	+	29.5916i	0.603283	+	1.04492i
$803$	−1.06025	+	6.01300i	−0.0374156	+	0.212194i
$804$		0			0
$805$	2.08256	+	0.759772i	0.0734007	+	0.0267784i
$806$	−15.0776	−	17.9687i	−0.531084	−	0.632922i
$807$		0			0
$808$	10.6469	+	1.87734i	0.374557	+	0.0660445i
$809$	17.0109	+	9.82125i	0.598072	+	0.345297i	0.768283	−	0.640111i	$-0.221112\pi$
$809$	17.0109	+	9.82125i	0.598072	+	0.345297i	−0.170211	+	0.985408i	$0.554445\pi$
$810$		0			0
$811$			18.4996i			0.649608i	0.945781	+	0.324804i	$0.105298\pi$
$811$			18.4996i			0.649608i	−0.945781	+	0.324804i	$0.894702\pi$
$812$	−3.71337	+	20.9670i	−0.130314	+	0.735798i
$813$		0			0
$814$	24.5774	+	8.94543i	0.861436	+	0.313537i
$815$	1.02408	+	0.372733i	0.0358718	+	0.0130563i
$816$		0			0
$817$	9.74096	+	1.71759i	0.340793	+	0.0600910i
$818$	−10.1493	+	17.5791i	−0.354862	+	0.614639i
$819$		0			0
$820$	−0.757550	−	1.31212i	−0.0264548	−	0.0458211i
$821$	10.8254	+	29.7424i	0.377808	+	1.03802i	0.972263	+	0.233889i	$0.0751453\pi$
$821$	10.8254	+	29.7424i	0.377808	+	1.03802i	−0.594456	+	0.804128i	$0.702632\pi$
$822$		0			0
$823$	21.5880	−	18.1145i	0.752509	−	0.631430i	−0.183656	−	0.982991i	$-0.558793\pi$
$823$	21.5880	−	18.1145i	0.752509	−	0.631430i	0.936165	+	0.351560i	$0.114349\pi$
$824$	−4.97885	−	28.2365i	−0.173447	−	0.983665i
$825$		0			0
$826$	0.0735472	−	0.415274i	0.00255903	−	0.0144492i
$827$	26.8439	−	15.4983i	0.933454	−	0.538930i	0.0455515	−	0.998962i	$-0.485495\pi$
$827$	26.8439	−	15.4983i	0.933454	−	0.538930i	0.887902	+	0.460032i	$0.152162\pi$
$828$		0			0
$829$	−8.33259	+	4.81082i	−0.289403	+	0.167087i	−0.637672	−	0.770308i	$-0.720103\pi$
$829$	−8.33259	+	4.81082i	−0.289403	+	0.167087i	0.348270	+	0.937394i	$0.386769\pi$
$830$	0.292125	+	0.802607i	0.0101398	+	0.0278589i
$831$		0			0
$832$	15.7647	−	2.77974i	0.546543	−	0.0963702i
$833$	−0.415313	−	2.37633i	−0.0143897	−	0.0823349i
$834$		0			0
$835$	0.441323	+	0.370314i	0.0152726	+	0.0128152i
$836$	11.7539	−	20.3583i	0.406517	−	0.704107i
$837$		0			0
$838$	−1.03063	+	0.595033i	−0.0356024	+	0.0205551i
$839$	−46.3318	+	16.8634i	−1.59955	+	0.582189i	−0.979335	−	0.202242i	$-0.935177\pi$
$839$	−46.3318	+	16.8634i	−1.59955	+	0.582189i	−0.620216	+	0.784431i	$0.712955\pi$
$840$		0			0
$841$	−12.3820	+	10.3898i	−0.426967	+	0.358268i
$842$	2.64909	+	3.15707i	0.0912938	+	0.108800i
$843$		0			0
$844$	−5.15906	+	1.87774i	−0.177582	+	0.0646346i
$845$	−0.525857			−0.0180900
$846$		0			0
$847$	11.5861	+	6.70089i	0.398102	+	0.230245i
$848$	−1.06750	−	0.188229i	−0.0366581	−	0.00646382i
$849$		0			0
$850$	0.988736	+	1.17833i	0.0339134	+	0.0404164i
$851$	29.8524	+	35.5767i	1.02333	+	1.21955i
$852$		0			0
$853$	15.1514	+	2.67160i	0.518774	+	0.0914738i	0.426903	−	0.904297i	$-0.359604\pi$
$853$	15.1514	+	2.67160i	0.518774	+	0.0914738i	0.0918701	+	0.995771i	$0.470716\pi$
$854$	0.00835540	−	11.0705i	0.000285916	−	0.378824i
$855$		0			0
$856$	13.2423			0.452613
$857$	2.89686	−	1.05437i	0.0989548	−	0.0360166i	−0.292068	−	0.956397i	$-0.594343\pi$
$857$	2.89686	−	1.05437i	0.0989548	−	0.0360166i	0.391023	+	0.920381i	$0.372121\pi$
$858$		0			0
$859$	−20.1100	−	23.9661i	−0.686143	−	0.817713i	0.304741	−	0.952435i	$-0.401430\pi$
$859$	−20.1100	−	23.9661i	−0.686143	−	0.817713i	−0.990883	+	0.134722i	$0.956986\pi$
$860$	−0.243505	+	0.204325i	−0.00830345	+	0.00696742i
$861$		0			0
$862$	−14.9384	+	5.43713i	−0.508804	+	0.185189i
$863$	5.09715	−	2.94284i	0.173509	−	0.100176i	−0.410730	−	0.911757i	$-0.634726\pi$
$863$	5.09715	−	2.94284i	0.173509	−	0.100176i	0.584239	+	0.811581i	$0.301393\pi$
$864$		0			0
$865$	−1.09054	+	1.88888i	−0.0370796	+	0.0642238i
$866$	−0.838783	−	0.703822i	−0.0285030	−	0.0239168i
$867$		0			0
$868$	−25.9815	−	9.47869i	−0.881868	−	0.321728i
$869$	−9.33518	+	1.64604i	−0.316674	+	0.0558382i
$870$		0			0
$871$	−11.8277	−	32.4963i	−0.400766	−	1.10110i
$872$	−29.5603	+	17.0667i	−1.00104	+	0.577950i
$873$		0			0
$874$	−24.2222	+	13.9847i	−0.819329	+	0.473040i
$875$	3.41862	+	0.605456i	0.115570	+	0.0204681i
$876$		0			0
$877$	2.60088	+	14.7504i	0.0878256	+	0.498084i	0.996711	+	0.0810379i	$0.0258235\pi$
$877$	2.60088	+	14.7504i	0.0878256	+	0.498084i	−0.908885	+	0.417046i	$0.863065\pi$
$878$	3.34257	−	2.80475i	0.112806	−	0.0946556i
$879$		0			0
$880$	−0.0307544	−	0.0844970i	−0.00103673	−	0.00284839i
$881$	−11.8885	−	20.5915i	−0.400533	−	0.693744i	0.593257	−	0.805013i	$-0.297842\pi$
$881$	−11.8885	−	20.5915i	−0.400533	−	0.693744i	−0.993790	+	0.111269i	$0.964508\pi$
$882$		0			0
$883$	−11.3387	+	19.6392i	−0.381578	+	0.660913i	−0.991288	−	0.131712i	$-0.957953\pi$
$883$	−11.3387	+	19.6392i	−0.381578	+	0.660913i	0.609710	+	0.792625i	$0.291286\pi$
$884$	1.21928	+	0.214992i	0.0410088	+	0.00723096i
$885$		0			0
$886$	−19.5794	−	7.12631i	−0.657782	−	0.239413i
$887$	10.8540	+	3.95053i	0.364442	+	0.132646i	0.517749	−	0.855533i	$-0.326770\pi$
$887$	10.8540	+	3.95053i	0.364442	+	0.132646i	−0.153307	+	0.988179i	$0.548992\pi$
$888$		0			0
$889$	8.25857	+	22.7436i	0.276984	+	0.762797i
$890$			1.81549i			0.0608554i
$891$		0			0
$892$	24.4581	+	14.1209i	0.818917	+	0.472802i
$893$	−21.4400	−	3.78044i	−0.717461	−	0.126508i
$894$		0			0
$895$	−0.879440	−	1.04808i	−0.0293964	−	0.0350333i
$896$	12.9217	−	10.8260i	0.431685	−	0.361672i
$897$		0			0
$898$	−3.58033	+	20.3051i	−0.119477	+	0.677589i
$899$	−29.3300	−	50.8011i	−0.978212	−	1.69431i
$900$		0			0
$901$	−1.89518	−	1.09418i	−0.0631375	−	0.0364525i
$902$	−5.99948	+	34.0247i	−0.199761	+	1.13290i
$903$		0			0
$904$	8.21764	+	2.99098i	0.273315	+	0.0994784i
$905$	−2.14450	+	0.378134i	−0.0712857	+	0.0125696i
$906$		0			0
$907$	−17.1444	−	14.3858i	−0.569269	−	0.477673i	0.312134	−	0.950038i	$-0.398956\pi$
$907$	−17.1444	−	14.3858i	−0.569269	−	0.477673i	−0.881403	+	0.472365i	$0.843401\pi$
$908$	−1.46639	+	2.53986i	−0.0486639	+	0.0842883i
$909$		0			0
$910$	−0.809736	+	0.466687i	−0.0268425	+	0.0154705i
$911$	29.6477	−	35.3327i	0.982271	−	1.17063i	−0.00306421	−	0.999995i	$-0.500975\pi$
$911$	29.6477	−	35.3327i	0.982271	−	1.17063i	0.985335	−	0.170630i	$-0.0545802\pi$
$912$		0			0
$913$	−9.94171	+	27.3146i	−0.329023	+	0.903982i
$914$	23.4670	−	4.13787i	0.776221	−	0.136869i
$915$		0			0
$916$	0.107311	+	0.294836i	0.00354567	+	0.00974165i
$917$	−12.7798	+	7.36558i	−0.422027	+	0.243233i
$918$		0			0
$919$	−8.95419	−	15.5091i	−0.295371	−	0.511598i	0.679700	−	0.733490i	$-0.262110\pi$
$919$	−8.95419	−	15.5091i	−0.295371	−	0.511598i	−0.975071	+	0.221892i	$0.928777\pi$
$920$	0.416752	−	2.36352i	0.0137399	−	0.0779228i
$921$		0			0
$922$	8.41101	−	23.1091i	0.277002	−	0.761056i
$923$	0.224720	+	1.27445i	0.00739674	+	0.0419490i
$924$		0			0
$925$	27.8105	+	23.3358i	0.914404	+	0.767276i
$926$		−	2.85879i		−	0.0939456i
$927$		0			0
$928$	37.4713			1.23005
$929$	27.6851	−	10.0766i	0.908320	−	0.330602i	0.154738	−	0.987955i	$-0.450547\pi$
$929$	27.6851	−	10.0766i	0.908320	−	0.330602i	0.753582	+	0.657354i	$0.228324\pi$
$930$		0			0
$931$	33.7769	−	5.90323i	1.10699	−	0.193470i
$932$	−11.8913	+	32.6711i	−0.389513	+	1.07018i
$933$		0			0
$934$	−9.73256	+	11.5988i	−0.318459	+	0.379525i
$935$		−	0.181534i		−	0.00593679i
$936$		0			0
$937$	42.6087	+	24.6001i	1.39196	+	0.803651i	0.993533	−	0.113547i	$-0.0362211\pi$
$937$	42.6087	+	24.6001i	1.39196	+	0.803651i	0.398432	+	0.917198i	$0.369554\pi$
$938$	20.9156	+	17.5772i	0.682919	+	0.573916i
$939$		0			0
$940$	0.535957	−	0.449721i	0.0174810	−	0.0146683i
$941$	−2.46173	−	13.9611i	−0.0802500	−	0.455120i	−0.998281	−	0.0586114i	$-0.981333\pi$
$941$	−2.46173	−	13.9611i	−0.0802500	−	0.455120i	0.918031	−	0.396509i	$-0.129778\pi$
$942$		0			0
$943$	−39.4342	+	46.9959i	−1.28416	+	1.53040i
$944$	−0.0303757			−0.000988646
$945$		0			0
$946$	7.24863			0.235673
$947$	−10.2975	+	12.2720i	−0.334622	+	0.398787i	−0.906950	−	0.421237i	$-0.861596\pi$
$947$	−10.2975	+	12.2720i	−0.334622	+	0.398787i	0.572328	+	0.820025i	$0.306040\pi$
$948$		0			0
$949$	−0.793715	−	4.50138i	−0.0257651	−	0.146121i
$950$	−16.7487	+	14.0538i	−0.543399	+	0.455966i
$951$		0			0
$952$	−2.45482	+	0.891384i	−0.0795612	+	0.0288899i
$953$	−38.0570	−	21.9722i	−1.23279	−	0.711750i	−0.265177	−	0.964200i	$-0.585430\pi$
$953$	−38.0570	−	21.9722i	−1.23279	−	0.711750i	−0.967610	+	0.252450i	$0.918764\pi$
$954$		0			0
$955$			1.36374i			0.0441294i
$956$	1.45318	−	1.73183i	0.0469991	−	0.0560114i
$957$		0			0
$958$	−11.5588	+	31.7574i	−0.373446	+	1.02604i
$959$	29.3368	−	24.5788i	0.947335	−	0.793691i
$960$		0			0
$961$	42.4645	−	15.4558i	1.36982	−	0.498575i
$962$	−19.5796			−0.631272
$963$		0			0
$964$			21.9535i			0.707075i
$965$	−1.83588	−	1.54049i	−0.0590990	−	0.0495900i
$966$		0			0
$967$	−5.36073	−	30.4022i	−0.172389	−	0.977669i	−0.941114	−	0.338089i	$-0.890219\pi$
$967$	−5.36073	−	30.4022i	−0.172389	−	0.977669i	0.768725	−	0.639580i	$-0.220892\pi$
$968$	4.95589	−	13.6162i	0.159288	−	0.437642i
$969$		0			0
$970$	0.253431	−	1.43728i	0.00813718	−	0.0461482i
$971$	26.8436	+	46.4945i	0.861453	+	1.49208i	0.870527	+	0.492121i	$0.163778\pi$
$971$	26.8436	+	46.4945i	0.861453	+	1.49208i	−0.00907360	+	0.999959i	$0.502888\pi$
$972$		0			0
$973$	36.2289	+	0.0273437i	1.16145	+	0.000876598i
$974$	5.62650	+	15.4587i	0.180285	+	0.495328i
$975$		0			0
$976$	−0.785242	+	0.138459i	−0.0251350	+	0.00443198i
$977$	8.60683	−	23.6471i	0.275357	−	0.756537i	−0.722517	−	0.691354i	$-0.757015\pi$
$977$	8.60683	−	23.6471i	0.275357	−	0.756537i	0.997873	−	0.0651829i	$-0.0207631\pi$
$978$		0			0
$979$	−39.7149	+	47.3304i	−1.26929	+	1.51269i
$980$	−0.552409	+	0.953473i	−0.0176461	+	0.0304576i
$981$		0			0
$982$	8.17359	−	14.1571i	0.260830	−	0.451771i
$983$	−20.1305	−	16.8915i	−0.642064	−	0.538756i	0.262587	−	0.964908i	$-0.415424\pi$
$983$	−20.1305	−	16.8915i	−0.642064	−	0.538756i	−0.904651	+	0.426152i	$0.859869\pi$
$984$		0			0
$985$	−2.83787	+	0.500392i	−0.0904220	+	0.0159438i
$986$	−1.94951	−	0.709565i	−0.0620852	−	0.0225972i
$987$		0			0
$988$	−3.05588	+	17.3307i	−0.0972204	+	0.551364i
$989$	11.1468	+	6.43559i	0.354447	+	0.204640i
$990$		0			0
$991$	−18.0463	−	31.2570i	−0.573258	−	0.992912i	−0.996228	−	0.0867687i	$-0.972346\pi$
$991$	−18.0463	−	31.2570i	−0.573258	−	0.992912i	0.422970	−	0.906144i	$-0.360987\pi$
$992$	−8.45129	+	47.9296i	−0.268329	+	1.52177i
$993$		0			0
$994$	−0.656585	−	0.783688i	−0.0208256	−	0.0248571i
$995$	−0.613037	−	0.730589i	−0.0194346	−	0.0231612i
$996$		0			0
$997$	−12.4645	−	2.19782i	−0.394754	−	0.0696058i	−0.0272522	−	0.999629i	$-0.508676\pi$
$997$	−12.4645	−	2.19782i	−0.394754	−	0.0696058i	−0.367502	+	0.930023i	$0.619787\pi$
$998$	29.0371	+	16.7646i	0.919153	+	0.530673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.14		132
3.2	odd	2		189.2.ba.a.101.9	✓	132
7.5	odd	6		567.2.bd.a.467.9		132
21.5	even	6		189.2.bd.a.47.14	yes	132
27.4	even	9		189.2.bd.a.185.14	yes	132
27.23	odd	18		567.2.bd.a.17.9		132
189.131	even	18	inner	567.2.ba.a.341.14		132
189.166	odd	18		189.2.ba.a.131.9	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.9	✓	132	3.2	odd	2
189.2.ba.a.131.9	yes	132	189.166	odd	18
189.2.bd.a.47.14	yes	132	21.5	even	6
189.2.bd.a.185.14	yes	132	27.4	even	9
567.2.ba.a.143.14		132	1.1	even	1	trivial
567.2.ba.a.341.14		132	189.131	even	18	inner
567.2.bd.a.17.9		132	27.23	odd	18
567.2.bd.a.467.9		132	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.575801 - 0.686212i) q^{2} +(0.207955 + 1.17937i) q^{4} +(-0.100696 + 0.0844942i) q^{5} +(-1.70219 + 2.02548i) q^{7} +(2.48059 + 1.43217i) q^{8} +0.117751i q^{10} +(-2.57587 + 3.06980i) q^{11} +(1.02604 - 2.81901i) q^{13} +(0.409789 + 2.33433i) q^{14} +(0.160408 - 0.0583836i) q^{16} +0.344621 q^{17} +4.89841i q^{19} +(-0.120590 - 0.101187i) q^{20} +(0.623349 + 3.53519i) q^{22} +(-2.18009 + 5.98976i) q^{23} +(-0.865240 + 4.90702i) q^{25} +(-1.34365 - 2.32726i) q^{26} +(-2.74277 - 1.58630i) q^{28} +(-2.29851 - 6.31510i) q^{29} +(8.59607 - 1.51572i) q^{31} +(-1.90702 + 5.23950i) q^{32} +(0.198433 - 0.236483i) q^{34} +(0.000262488 - 0.347783i) q^{35} +(3.64300 - 6.30985i) q^{37} +(3.36135 + 2.82051i) q^{38} +(-0.370796 + 0.0653813i) q^{40} +(9.04416 + 3.29180i) q^{41} +(0.350643 - 1.98860i) q^{43} +(-4.15611 - 2.39953i) q^{44} +(2.85495 + 4.94491i) q^{46} +(-0.771769 + 4.37692i) q^{47} +(-1.20513 - 6.89548i) q^{49} +(2.86905 + 3.41920i) q^{50} +(3.53803 + 0.623850i) q^{52} +(-5.49931 - 3.17503i) q^{53} -0.526764i q^{55} +(-7.12325 + 2.58656i) q^{56} +(-5.65698 - 2.05897i) q^{58} +(-0.167214 - 0.0608610i) q^{59} +(-4.60007 - 0.811116i) q^{61} +(3.90952 - 6.77148i) q^{62} +(2.66805 + 4.62120i) q^{64} +(0.134872 + 0.370558i) q^{65} +(8.83064 - 7.40979i) q^{67} +(0.0716657 + 0.406437i) q^{68} +(-0.238502 - 0.200434i) q^{70} +(-0.373587 + 0.215690i) q^{71} +(1.31951 - 0.761822i) q^{73} +(-2.23226 - 6.13309i) q^{74} +(-5.77706 + 1.01865i) q^{76} +(-1.83321 - 10.4427i) q^{77} +(1.81204 + 1.52049i) q^{79} +(-0.0112194 + 0.0194325i) q^{80} +(7.46651 - 4.31079i) q^{82} +(6.81615 - 2.48087i) q^{83} +(-0.0347021 + 0.0291185i) q^{85} +(-1.16270 - 1.38565i) q^{86} +(-10.7861 + 3.92584i) q^{88} +15.4181 q^{89} +(3.96334 + 6.87669i) q^{91} +(-7.51752 - 1.32554i) q^{92} +(2.55911 + 3.04983i) q^{94} +(-0.413888 - 0.493252i) q^{95} +(-12.2061 - 2.15226i) q^{97} +(-5.42568 - 3.14345i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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