LMFDB - Embedded newform 432.2.v.a.395.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] 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("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			395.9
Character	$\chi$	$=$	432.395
Dual form			432.2.v.a.35.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.378412 - 1.36265i) q^{2} +(-1.71361 + 1.03128i) q^{4} +(-1.00059 - 3.73424i) q^{5} +(-1.68236 - 2.91393i) q^{7} +(2.05372 + 1.94479i) q^{8} +(-4.70981 + 2.77653i) q^{10} +(-0.0566521 + 0.211428i) q^{11} +(0.727551 + 2.71526i) q^{13} +(-3.33403 + 3.39513i) q^{14} +(1.87291 - 3.53443i) q^{16} +4.23937i q^{17} +(-1.12365 - 1.12365i) q^{19} +(5.56567 + 5.36714i) q^{20} +(0.309540 - 0.00281033i) q^{22} +(-3.33369 - 1.92471i) q^{23} +(-8.61325 + 4.97286i) q^{25} +(3.42462 - 2.01888i) q^{26} +(5.88800 + 3.25835i) q^{28} +(-0.545635 + 2.03634i) q^{29} +(-7.21206 - 4.16388i) q^{31} +(-5.52491 - 1.21464i) q^{32} +(5.77677 - 1.60423i) q^{34} +(-9.19798 + 9.19798i) q^{35} +(-2.66564 - 2.66564i) q^{37} +(-1.10593 + 1.95634i) q^{38} +(5.20739 - 9.61503i) q^{40} +(1.70386 - 2.95117i) q^{41} +(4.68985 + 1.25664i) q^{43} +(-0.120963 - 0.420730i) q^{44} +(-1.36119 + 5.27098i) q^{46} +(-2.34998 - 4.07028i) q^{47} +(-2.16067 + 3.74239i) q^{49} +(10.0356 + 9.85502i) q^{50} +(-4.04693 - 3.90257i) q^{52} +(7.58271 - 7.58271i) q^{53} +0.846209 q^{55} +(2.21189 - 9.25626i) q^{56} +(2.98128 - 0.0270672i) q^{58} +(5.34305 - 1.43167i) q^{59} +(8.69958 + 2.33105i) q^{61} +(-2.94477 + 11.4031i) q^{62} +(0.435568 + 7.98813i) q^{64} +(9.41144 - 5.43370i) q^{65} +(-5.17504 + 1.38665i) q^{67} +(-4.37200 - 7.26463i) q^{68} +(16.0142 + 9.05296i) q^{70} -7.53614i q^{71} +3.22646i q^{73} +(-2.62362 + 4.64104i) q^{74} +(3.08429 + 0.766693i) q^{76} +(0.711397 - 0.190618i) q^{77} +(-4.98587 + 2.87859i) q^{79} +(-15.0724 - 3.45739i) q^{80} +(-4.66616 - 1.20500i) q^{82} +(-4.50604 - 1.20739i) q^{83} +(15.8308 - 4.24186i) q^{85} +(-0.0623381 - 6.86613i) q^{86} +(-0.527532 + 0.324039i) q^{88} +2.96157 q^{89} +(6.68807 - 6.68807i) q^{91} +(7.69756 - 0.139785i) q^{92} +(-4.65709 + 4.74243i) q^{94} +(-3.07166 + 5.32027i) q^{95} +(-7.63883 - 13.2308i) q^{97} +(5.91718 + 1.52806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.378412	−	1.36265i	−0.267578	−	0.963536i
$2$	−0.378412	−	1.36265i	−0.267578	−	0.963536i
$3$		0			0
$3$		0			0
$4$	−1.71361	+	1.03128i	−0.856804	+	0.515642i
$5$	−1.00059	−	3.73424i	−0.447476	−	1.67000i	−0.709315	−	0.704891i	$-0.750996\pi$
$5$	−1.00059	−	3.73424i	−0.447476	−	1.67000i	0.261839	−	0.965111i	$-0.415671\pi$
$6$		0			0
$7$	−1.68236	−	2.91393i	−0.635872	−	1.10136i	−0.986330	−	0.164785i	$-0.947307\pi$
$7$	−1.68236	−	2.91393i	−0.635872	−	1.10136i	0.350457	−	0.936579i	$-0.386026\pi$
$8$	2.05372	+	1.94479i	0.726101	+	0.687588i
$9$		0			0
$10$	−4.70981	+	2.77653i	−1.48937	+	0.878015i
$11$	−0.0566521	+	0.211428i	−0.0170812	+	0.0637480i	−0.973940	−	0.226804i	$-0.927172\pi$
$11$	−0.0566521	+	0.211428i	−0.0170812	+	0.0637480i	0.956859	+	0.290552i	$0.0938390\pi$
$12$		0			0
$13$	0.727551	+	2.71526i	0.201786	+	0.753076i	0.990405	+	0.138194i	$0.0441298\pi$
$13$	0.727551	+	2.71526i	0.201786	+	0.753076i	−0.788619	+	0.614882i	$0.789204\pi$
$14$	−3.33403	+	3.39513i	−0.891058	+	0.907386i
$15$		0			0
$16$	1.87291	−	3.53443i	0.468227	−	0.883608i
$17$			4.23937i			1.02820i	0.857731	+	0.514100i	$0.171874\pi$
$17$			4.23937i			1.02820i	−0.857731	+	0.514100i	$0.828126\pi$
$18$		0			0
$19$	−1.12365	−	1.12365i	−0.257782	−	0.257782i	0.566369	−	0.824152i	$-0.308348\pi$
$19$	−1.12365	−	1.12365i	−0.257782	−	0.257782i	−0.824152	+	0.566369i	$0.808348\pi$
$20$	5.56567	+	5.36714i	1.24452	+	1.20013i
$21$		0			0
$22$	0.309540	−	0.00281033i	0.0659941	−	0.000599165i
$23$	−3.33369	−	1.92471i	−0.695123	−	0.401329i	0.110405	−	0.993887i	$-0.464785\pi$
$23$	−3.33369	−	1.92471i	−0.695123	−	0.401329i	−0.805528	+	0.592557i	$0.798118\pi$
$24$		0			0
$25$	−8.61325	+	4.97286i	−1.72265	+	0.994572i
$26$	3.42462	−	2.01888i	0.671623	−	0.395935i
$27$		0			0
$28$	5.88800	+	3.25835i	1.11273	+	0.615771i
$29$	−0.545635	+	2.03634i	−0.101322	+	0.378138i	−0.997902	−	0.0647434i	$-0.979377\pi$
$29$	−0.545635	+	2.03634i	−0.101322	+	0.378138i	0.896580	+	0.442882i	$0.146044\pi$
$30$		0			0
$31$	−7.21206	−	4.16388i	−1.29532	−	0.747856i	−0.315731	−	0.948849i	$-0.602250\pi$
$31$	−7.21206	−	4.16388i	−1.29532	−	0.747856i	−0.979593	+	0.200993i	$0.935583\pi$
$32$	−5.52491	−	1.21464i	−0.976676	−	0.214720i
$33$		0			0
$34$	5.77677	−	1.60423i	0.990707	−	0.275123i
$35$	−9.19798	+	9.19798i	−1.55474	+	1.55474i
$36$		0			0
$37$	−2.66564	−	2.66564i	−0.438229	−	0.438229i	0.453187	−	0.891416i	$-0.350287\pi$
$37$	−2.66564	−	2.66564i	−0.438229	−	0.438229i	−0.891416	+	0.453187i	$0.850287\pi$
$38$	−1.10593	+	1.95634i	−0.179406	+	0.317359i
$39$		0			0
$40$	5.20739	−	9.61503i	0.823361	−	1.52027i
$41$	1.70386	−	2.95117i	0.266098	−	0.460895i	−0.701753	−	0.712420i	$-0.747599\pi$
$41$	1.70386	−	2.95117i	0.266098	−	0.460895i	0.967851	+	0.251526i	$0.0809323\pi$
$42$		0			0
$43$	4.68985	+	1.25664i	0.715195	+	0.191636i	0.598027	−	0.801476i	$-0.295952\pi$
$43$	4.68985	+	1.25664i	0.715195	+	0.191636i	0.117168	+	0.993112i	$0.462618\pi$
$44$	−0.120963	−	0.420730i	−0.0182359	−	0.0634274i
$45$		0			0
$46$	−1.36119	+	5.27098i	−0.200696	+	0.777163i
$47$	−2.34998	−	4.07028i	−0.342779	−	0.593711i	0.642168	−	0.766564i	$-0.278035\pi$
$47$	−2.34998	−	4.07028i	−0.342779	−	0.593711i	−0.984948	+	0.172852i	$0.944702\pi$
$48$		0			0
$49$	−2.16067	+	3.74239i	−0.308667	+	0.534628i
$50$	10.0356	+	9.85502i	1.41925	+	1.39371i
$51$		0			0
$52$	−4.04693	−	3.90257i	−0.561209	−	0.541190i
$53$	7.58271	−	7.58271i	1.04157	−	1.04157i	0.0424680	−	0.999098i	$-0.486478\pi$
$53$	7.58271	−	7.58271i	1.04157	−	1.04157i	0.999098	−	0.0424680i	$-0.0135220\pi$
$54$		0			0
$55$	0.846209			0.114103
$56$	2.21189	−	9.25626i	0.295576	−	1.23692i
$57$		0			0
$58$	2.98128	−	0.0270672i	0.391461	−	0.00355410i
$59$	5.34305	−	1.43167i	0.695605	−	0.186387i	0.106344	−	0.994329i	$-0.466085\pi$
$59$	5.34305	−	1.43167i	0.695605	−	0.186387i	0.589261	+	0.807942i	$0.299419\pi$
$60$		0			0
$61$	8.69958	+	2.33105i	1.11387	+	0.298460i	0.768399	−	0.639971i	$-0.221054\pi$
$61$	8.69958	+	2.33105i	1.11387	+	0.298460i	0.345468	+	0.938431i	$0.387720\pi$
$62$	−2.94477	+	11.4031i	−0.373986	+	1.44820i
$63$		0			0
$64$	0.435568	+	7.98813i	0.0544460	+	0.998517i
$65$	9.41144	−	5.43370i	1.16735	−	0.673967i
$66$		0			0
$67$	−5.17504	+	1.38665i	−0.632231	+	0.169406i	−0.560682	−	0.828031i	$-0.689461\pi$
$67$	−5.17504	+	1.38665i	−0.632231	+	0.169406i	−0.0715493	+	0.997437i	$0.522794\pi$
$68$	−4.37200	−	7.26463i	−0.530182	−	0.880965i
$69$		0			0
$70$	16.0142	+	9.05296i	1.91406	+	1.08204i
$71$		−	7.53614i		−	0.894375i	−0.894440	−	0.447187i	$-0.852426\pi$
$71$		−	7.53614i		−	0.894375i	0.894440	−	0.447187i	$-0.147574\pi$
$72$		0			0
$73$			3.22646i			0.377629i	0.982013	+	0.188814i	$0.0604644\pi$
$73$			3.22646i			0.377629i	−0.982013	+	0.188814i	$0.939536\pi$
$74$	−2.62362	+	4.64104i	−0.304989	+	0.539510i
$75$		0			0
$76$	3.08429	+	0.766693i	0.353792	+	0.0879457i
$77$	0.711397	−	0.190618i	0.0810712	−	0.0217230i
$78$		0			0
$79$	−4.98587	+	2.87859i	−0.560954	+	0.323867i	−0.753528	−	0.657415i	$-0.771650\pi$
$79$	−4.98587	+	2.87859i	−0.560954	+	0.323867i	0.192574	+	0.981282i	$0.438316\pi$
$80$	−15.0724	−	3.45739i	−1.68515	−	0.386548i
$81$		0			0
$82$	−4.66616	−	1.20500i	−0.515291	−	0.133070i
$83$	−4.50604	−	1.20739i	−0.494602	−	0.132528i	0.00289160	−	0.999996i	$-0.499080\pi$
$83$	−4.50604	−	1.20739i	−0.494602	−	0.132528i	−0.497494	+	0.867468i	$0.665746\pi$
$84$		0			0
$85$	15.8308	−	4.24186i	1.71710	−	0.460094i
$86$	−0.0623381	−	6.86613i	−0.00672209	−	0.740394i
$87$		0			0
$88$	−0.527532	+	0.324039i	−0.0562351	+	0.0345427i
$89$	2.96157			0.313926			0.156963	−	0.987605i	$-0.449830\pi$
$89$	2.96157			0.313926			0.156963	+	0.987605i	$0.449830\pi$
$90$		0			0
$91$	6.68807	−	6.68807i	0.701100	−	0.701100i
$92$	7.69756	−	0.139785i	0.802527	−	0.0145736i
$93$		0			0
$94$	−4.65709	+	4.74243i	−0.480342	+	0.489144i
$95$	−3.07166	+	5.32027i	−0.315146	+	0.545849i
$96$		0			0
$97$	−7.63883	−	13.2308i	−0.775606	−	1.34339i	−0.934453	−	0.356085i	$-0.884111\pi$
$97$	−7.63883	−	13.2308i	−0.775606	−	1.34339i	0.158848	−	0.987303i	$-0.449222\pi$
$98$	5.91718	+	1.52806i	0.597726	+	0.154358i
$99$		0			0
$100$	9.63131	−	17.4042i	0.963131	−	1.74042i
$101$	−0.129684	−	0.0347486i	−0.0129040	−	0.00345762i	0.252361	−	0.967633i	$-0.418793\pi$
$101$	−0.129684	−	0.0347486i	−0.0129040	−	0.00345762i	−0.265265	+	0.964175i	$0.585460\pi$
$102$		0			0
$103$	−4.09117	+	7.08611i	−0.403115	+	0.698215i	−0.994100	−	0.108467i	$-0.965406\pi$
$103$	−4.09117	+	7.08611i	−0.403115	+	0.698215i	0.590985	+	0.806682i	$0.298739\pi$
$104$	−3.78642	+	6.99132i	−0.371289	+	0.685555i
$105$		0			0
$106$	−13.2019	−	7.46316i	−1.28229	−	0.724887i
$107$	−8.28837	−	8.28837i	−0.801267	−	0.801267i	0.182027	−	0.983294i	$-0.441734\pi$
$107$	−8.28837	−	8.28837i	−0.801267	−	0.801267i	−0.983294	+	0.182027i	$0.941734\pi$
$108$		0			0
$109$	6.31291	−	6.31291i	0.604667	−	0.604667i	−0.336881	−	0.941547i	$-0.609372\pi$
$109$	6.31291	−	6.31291i	0.604667	−	0.604667i	0.941547	+	0.336881i	$0.109372\pi$
$110$	−0.320216	−	1.15308i	−0.0305314	−	0.109942i
$111$		0			0
$112$	−13.4500	+	0.488655i	−1.27091	+	0.0461736i
$113$	−14.6562	−	8.46178i	−1.37874	−	0.796017i	−0.386735	−	0.922191i	$-0.626397\pi$
$113$	−14.6562	−	8.46178i	−1.37874	−	0.796017i	−0.992008	+	0.126174i	$0.959730\pi$
$114$		0			0
$115$	−3.85167	+	14.3746i	−0.359171	+	1.34044i
$116$	−1.16504	−	4.05219i	−0.108171	−	0.376236i
$117$		0			0
$118$	−3.97273	−	6.73892i	−0.365719	−	0.620368i
$119$	12.3533	−	7.13215i	1.13242	−	0.653803i
$120$		0			0
$121$	9.48479	+	5.47604i	0.862253	+	0.497822i
$122$	−0.115636	−	12.7365i	−0.0104692	−	1.15311i
$123$		0			0
$124$	16.6528	−	0.302408i	1.49546	−	0.0271571i
$125$	13.5199	+	13.5199i	1.20926	+	1.20926i
$126$		0			0
$127$		−	13.4028i		−	1.18931i	−0.803981	−	0.594654i	$-0.797289\pi$
$127$		−	13.4028i		−	1.18931i	0.803981	−	0.594654i	$-0.202711\pi$
$128$	10.7202	−	3.61633i	0.947539	−	0.319641i
$129$		0			0
$130$	−10.9656	−	10.7683i	−0.961747	−	0.944441i
$131$	−0.169534	−	0.632708i	−0.0148122	−	0.0552800i	0.958124	−	0.286353i	$-0.0924430\pi$
$131$	−0.169534	−	0.632708i	−0.0148122	−	0.0552800i	−0.972936	+	0.231073i	$0.925776\pi$
$132$		0			0
$133$	−1.38385	+	5.16461i	−0.119995	+	0.447829i
$134$	3.84781	+	6.52702i	0.332400	+	0.563849i
$135$		0			0
$136$	−8.24470	+	8.70650i	−0.706977	+	0.746577i
$137$	−10.5230	−	18.2263i	−0.899037	−	1.55718i	−0.828727	−	0.559652i	$-0.810935\pi$
$137$	−10.5230	−	18.2263i	−0.899037	−	1.55718i	−0.0703095	−	0.997525i	$-0.522399\pi$
$138$		0			0
$139$	−1.72666	−	6.44400i	−0.146454	−	0.546573i	−0.999686	−	0.0250423i	$-0.992028\pi$
$139$	−1.72666	−	6.44400i	−0.146454	−	0.546573i	0.853233	−	0.521530i	$-0.174639\pi$
$140$	6.27601	−	25.2475i	0.530420	−	2.13380i
$141$		0			0
$142$	−10.2691	+	2.85176i	−0.861763	+	0.239315i
$143$	−0.615299			−0.0514539
$144$		0			0
$145$	8.15012			0.676831
$146$	4.39652	−	1.22093i	0.363859	−	0.101045i
$147$		0			0
$148$	7.31691	+	1.81884i	0.601446	+	0.149507i
$149$	5.78161	+	21.5773i	0.473648	+	1.76768i	0.626492	+	0.779428i	$0.284490\pi$
$149$	5.78161	+	21.5773i	0.473648	+	1.76768i	−0.152844	+	0.988250i	$0.548843\pi$
$150$		0			0
$151$	−9.97506	−	17.2773i	−0.811759	−	1.40601i	−0.911632	−	0.411007i	$-0.865177\pi$
$151$	−9.97506	−	17.2773i	−0.811759	−	1.40601i	0.0998734	−	0.995000i	$-0.468156\pi$
$152$	−0.122401	−	4.49292i	−0.00992807	−	0.364424i
$153$		0			0
$154$	−0.528947	−	0.897250i	−0.0426237	−	0.0723025i
$155$	−8.33265	+	31.0979i	−0.669295	+	2.49784i
$156$		0			0
$157$	3.85693	+	14.3943i	0.307817	+	1.14879i	0.930494	+	0.366308i	$0.119378\pi$
$157$	3.85693	+	14.3943i	0.307817	+	1.14879i	−0.622677	+	0.782479i	$0.713955\pi$
$158$	5.80922	+	5.70468i	0.462157	+	0.453840i
$159$		0			0
$160$	0.992392	+	21.8467i	0.0784555	+	1.72713i
$161$			12.9522i			1.02078i
$162$		0			0
$163$	−4.35766	−	4.35766i	−0.341318	−	0.341318i	0.515545	−	0.856863i	$-0.327590\pi$
$163$	−4.35766	−	4.35766i	−0.341318	−	0.341318i	−0.856863	+	0.515545i	$0.827590\pi$
$164$	0.123745	+	6.81430i	0.00966288	+	0.532108i
$165$		0			0
$166$	0.0598948	+	6.59703i	0.00464874	+	0.512029i
$167$	11.8952	+	6.86770i	0.920479	+	0.531439i	0.883788	−	0.467888i	$-0.154985\pi$
$167$	11.8952	+	6.86770i	0.920479	+	0.531439i	0.0366910	+	0.999327i	$0.488318\pi$
$168$		0			0
$169$	4.41505	−	2.54903i	0.339619	−	0.196079i
$170$	−11.7707	−	19.9667i	−0.902774	−	1.53137i
$171$		0			0
$172$	−9.33252	+	2.68317i	−0.711598	+	0.204590i
$173$	−1.40497	+	5.24342i	−0.106818	+	0.398650i	−0.998545	−	0.0539235i	$-0.982827\pi$
$173$	−1.40497	+	5.24342i	−0.106818	+	0.398650i	0.891727	+	0.452573i	$0.149494\pi$
$174$		0			0
$175$	28.9812	+	16.7323i	2.19077	+	1.26484i
$176$	0.641175	+	0.596219i	0.0483304	+	0.0449417i
$177$		0			0
$178$	−1.12069	−	4.03557i	−0.0839995	−	0.302479i
$179$	−0.380130	+	0.380130i	−0.0284123	+	0.0284123i	−0.721170	−	0.692758i	$-0.756395\pi$
$179$	−0.380130	+	0.380130i	−0.0284123	+	0.0284123i	0.692758	+	0.721170i	$0.256395\pi$
$180$		0			0
$181$	−4.98992	−	4.98992i	−0.370898	−	0.370898i	0.496906	−	0.867804i	$-0.334469\pi$
$181$	−4.98992	−	4.98992i	−0.370898	−	0.370898i	−0.867804	+	0.496906i	$0.834469\pi$
$182$	−11.6443	−	6.58263i	−0.863134	−	0.487937i
$183$		0			0
$184$	−3.10333	−	10.4362i	−0.228780	−	0.769364i
$185$	−7.28695	+	12.6214i	−0.535747	+	0.927941i
$186$		0			0
$187$	−0.896324	−	0.240169i	−0.0655457	−	0.0175629i
$188$	8.22455	+	4.55137i	0.599837	+	0.331943i
$189$		0			0
$190$	8.41200	+	2.17233i	0.610271	+	0.157598i
$191$	5.40555	+	9.36269i	0.391132	+	0.677461i	0.992599	−	0.121437i	$-0.0387502\pi$
$191$	5.40555	+	9.36269i	0.391132	+	0.677461i	−0.601467	+	0.798898i	$0.705417\pi$
$192$		0			0
$193$	2.60044	−	4.50410i	0.187184	−	0.324212i	−0.757126	−	0.653268i	$-0.773397\pi$
$193$	2.60044	−	4.50410i	0.187184	−	0.324212i	0.944310	+	0.329056i	$0.106731\pi$
$194$	−15.1383	+	15.4157i	−1.08687	+	1.10679i
$195$		0			0
$196$	−0.156922	−	8.64126i	−0.0112087	−	0.617233i
$197$	2.94550	−	2.94550i	0.209858	−	0.209858i	−0.594349	−	0.804207i	$-0.702590\pi$
$197$	2.94550	−	2.94550i	0.209858	−	0.209858i	0.804207	+	0.594349i	$0.202590\pi$
$198$		0			0
$199$	2.57285			0.182384			0.0911921	−	0.995833i	$-0.470932\pi$
$199$	2.57285			0.182384			0.0911921	+	0.995833i	$0.470932\pi$
$200$	−27.3604	−	6.53809i	−1.93467	−	0.462313i
$201$		0			0
$202$	0.00172377	+	0.189862i	0.000121284	+	0.0133587i
$203$	6.85170	−	1.83591i	0.480895	−	0.128856i
$204$		0			0
$205$	−12.7252	−	3.40971i	−0.888768	−	0.238145i
$206$	11.2040	+	2.89334i	0.780620	+	0.201589i
$207$		0			0
$208$	10.9595	+	2.51395i	0.759906	+	0.174311i
$209$	0.301228	−	0.173914i	0.0208364	−	0.0120299i
$210$		0			0
$211$	17.5700	−	4.70786i	1.20957	−	0.324103i	0.402975	−	0.915211i	$-0.367976\pi$
$211$	17.5700	−	4.70786i	1.20957	−	0.324103i	0.806592	+	0.591108i	$0.201309\pi$
$212$	−5.17388	+	20.8137i	−0.355343	+	1.42949i
$213$		0			0
$214$	−8.15769	+	14.4305i	−0.557648	+	0.986451i
$215$		−	18.7704i		−	1.28013i
$216$		0			0
$217$			28.0206i			1.90216i
$218$	−10.9911	−	6.21338i	−0.744414	−	0.420823i
$219$		0			0
$220$	−1.45007	+	0.872682i	−0.0977638	+	0.0588362i
$221$	−11.5110	+	3.08436i	−0.774312	+	0.207476i
$222$		0			0
$223$	2.82059	−	1.62847i	0.188881	−	0.109050i	−0.402578	−	0.915386i	$-0.631886\pi$
$223$	2.82059	−	1.62847i	0.188881	−	0.109050i	0.591458	+	0.806336i	$0.298552\pi$
$224$	5.75551	+	18.1427i	0.384556	+	1.21221i
$225$		0			0
$226$	−5.98432	+	23.1733i	−0.398071	+	1.54147i
$227$	8.83238	+	2.36663i	0.586226	+	0.157079i	0.539728	−	0.841840i	$-0.318527\pi$
$227$	8.83238	+	2.36663i	0.586226	+	0.157079i	0.0464979	+	0.998918i	$0.485194\pi$
$228$		0			0
$229$	−5.07755	+	1.36053i	−0.335534	+	0.0899061i	−0.422652	−	0.906292i	$-0.638901\pi$
$229$	−5.07755	+	1.36053i	−0.335534	+	0.0899061i	0.0871183	+	0.996198i	$0.472234\pi$
$230$	21.0451	−	0.191070i	1.38767	−	0.0125988i
$231$		0			0
$232$	−5.08083	+	3.12093i	−0.333573	+	0.204899i
$233$	−14.1506			−0.927034			−0.463517	−	0.886088i	$-0.653413\pi$
$233$	−14.1506			−0.927034			−0.463517	+	0.886088i	$0.653413\pi$
$234$		0			0
$235$	−12.8480	+	12.8480i	−0.838114	+	0.838114i
$236$	−7.67944	+	7.96351i	−0.499889	+	0.518380i
$237$		0			0
$238$	−14.3932	−	14.1342i	−0.932974	−	0.916185i
$239$	7.51536	−	13.0170i	0.486128	−	0.841999i	−0.513745	−	0.857943i	$-0.671742\pi$
$239$	7.51536	−	13.0170i	0.486128	−	0.841999i	0.999873	+	0.0159444i	$0.00507546\pi$
$240$		0			0
$241$	7.18920	+	12.4521i	0.463097	+	0.802108i	0.999113	−	0.0420996i	$-0.0134047\pi$
$241$	7.18920	+	12.4521i	0.463097	+	0.802108i	−0.536016	+	0.844208i	$0.680071\pi$
$242$	3.87275	−	14.9966i	0.248950	−	0.964019i
$243$		0			0
$244$	−17.3116	+	4.97723i	−1.10826	+	0.318635i
$245$	16.1369	+	4.32388i	1.03095	+	0.276242i
$246$		0			0
$247$	2.23348	−	3.86850i	0.142113	−	0.246147i
$248$	−6.71369	−	22.5774i	−0.426320	−	1.43367i
$249$		0			0
$250$	13.3067	−	23.5389i	0.841592	−	1.48873i
$251$	3.59758	+	3.59758i	0.227077	+	0.227077i	0.811471	−	0.584393i	$-0.198667\pi$
$251$	3.59758	+	3.59758i	0.227077	+	0.227077i	−0.584393	+	0.811471i	$0.698667\pi$
$252$		0			0
$253$	0.595798	−	0.595798i	0.0374575	−	0.0374575i
$254$	−18.2633	+	5.07179i	−1.14594	+	0.318233i
$255$		0			0
$256$	−8.98442	−	13.2393i	−0.561526	−	0.827459i
$257$	4.92640	+	2.84426i	0.307300	+	0.177420i	0.645718	−	0.763576i	$-0.276558\pi$
$257$	4.92640	+	2.84426i	0.307300	+	0.177420i	−0.338418	+	0.940996i	$0.609892\pi$
$258$		0			0
$259$	−3.28294	+	12.2521i	−0.203992	+	0.761307i
$260$	−10.5238	+	19.0171i	−0.652661	+	1.17939i
$261$		0			0
$262$	−0.798004	+	0.470439i	−0.0493008	+	0.0290638i
$263$	−18.8392	+	10.8768i	−1.16167	+	0.670693i	−0.951705	−	0.307015i	$-0.900670\pi$
$263$	−18.8392	+	10.8768i	−1.16167	+	0.670693i	−0.209970	+	0.977708i	$0.567337\pi$
$264$		0			0
$265$	−35.9028	−	20.7285i	−2.20549	−	1.27334i
$266$	7.56121	−	0.0686487i	0.463607	−	0.00420912i
$267$		0			0
$268$	7.43796	−	7.71310i	0.454346	−	0.471153i
$269$	7.43467	+	7.43467i	0.453300	+	0.453300i	0.896448	−	0.443148i	$-0.146139\pi$
$269$	7.43467	+	7.43467i	0.453300	+	0.453300i	−0.443148	+	0.896448i	$0.646139\pi$
$270$		0			0
$271$		−	11.8875i		−	0.722111i	−0.932544	−	0.361056i	$-0.882416\pi$
$271$		−	11.8875i		−	0.722111i	0.932544	−	0.361056i	$-0.117584\pi$
$272$	14.9838	+	7.93996i	0.908525	+	0.481431i
$273$		0			0
$274$	−20.8540	+	21.2361i	−1.25983	+	1.28292i
$275$	−0.563445	−	2.10281i	−0.0339770	−	0.126804i
$276$		0			0
$277$	2.68166	−	10.0081i	0.161126	−	0.601329i	−0.837377	−	0.546626i	$-0.815912\pi$
$277$	2.68166	−	10.0081i	0.161126	−	0.601329i	0.998503	−	0.0547032i	$-0.0174213\pi$
$278$	−8.12750	+	4.79132i	−0.487455	+	0.287364i
$279$		0			0
$280$	−36.7783	+	1.00196i	−2.19792	+	0.0598784i
$281$	7.05630	+	12.2219i	0.420944	+	0.729096i	0.996032	−	0.0889955i	$-0.0283657\pi$
$281$	7.05630	+	12.2219i	0.420944	+	0.729096i	−0.575088	+	0.818091i	$0.695032\pi$
$282$		0			0
$283$	3.42843	+	12.7951i	0.203799	+	0.760588i	0.989812	+	0.142378i	$0.0454749\pi$
$283$	3.42843	+	12.7951i	0.203799	+	0.760588i	−0.786013	+	0.618209i	$0.787858\pi$
$284$	7.77189	+	12.9140i	0.461177	+	0.766304i
$285$		0			0
$286$	0.232837	+	0.838435i	0.0137679	+	0.0495777i
$287$	−11.4660			−0.676817
$288$		0			0
$289$	−0.972286			−0.0571933
$290$	−3.08411	−	11.1057i	−0.181105	−	0.652151i
$291$		0			0
$292$	−3.32739	−	5.52889i	−0.194721	−	0.323554i
$293$	−7.96005	−	29.7073i	−0.465031	−	1.73552i	−0.656787	−	0.754077i	$-0.728085\pi$
$293$	−7.96005	−	29.7073i	−0.465031	−	1.73552i	0.191756	−	0.981443i	$-0.438582\pi$
$294$		0			0
$295$	−10.6924	−	18.5197i	−0.622533	−	1.07826i
$296$	−0.290375	−	10.6586i	−0.0168777	−	0.619520i
$297$		0			0
$298$	27.2143	−	16.0434i	1.57648	−	0.929368i
$299$	2.80065	−	10.4522i	0.161965	−	0.604463i
$300$		0			0
$301$	−4.22825	−	15.7800i	−0.243712	−	0.909546i
$302$	−19.7682	+	20.1304i	−1.13753	+	1.15838i
$303$		0			0
$304$	−6.07594	+	1.86697i	−0.348479	+	0.107078i
$305$		−	34.8187i		−	1.99371i
$306$		0			0
$307$	23.8109	+	23.8109i	1.35896	+	1.35896i	0.875202	+	0.483758i	$0.160728\pi$
$307$	23.8109	+	23.8109i	1.35896	+	1.35896i	0.483758	+	0.875202i	$0.339272\pi$
$308$	−1.02247	+	1.06030i	−0.0582609	+	0.0604160i
$309$		0			0
$310$	45.5286	−	0.413357i	2.58585	−	0.0234771i
$311$	9.20941	+	5.31706i	0.522218	+	0.301503i	0.737842	−	0.674974i	$-0.235845\pi$
$311$	9.20941	+	5.31706i	0.522218	+	0.301503i	−0.215624	+	0.976477i	$0.569178\pi$
$312$		0			0
$313$	16.4634	−	9.50514i	0.930565	−	0.537262i	0.0435750	−	0.999050i	$-0.486125\pi$
$313$	16.4634	−	9.50514i	0.930565	−	0.537262i	0.886990	+	0.461788i	$0.152792\pi$
$314$	18.1548	−	10.7026i	1.02453	−	0.603982i
$315$		0			0
$316$	5.57519	−	10.0746i	0.313629	−	0.566742i
$317$	3.18193	−	11.8751i	0.178715	−	0.666972i	−0.817174	−	0.576391i	$-0.804461\pi$
$317$	3.18193	−	11.8751i	0.178715	−	0.666972i	0.995889	−	0.0905818i	$-0.0288727\pi$
$318$		0			0
$319$	−0.399628	−	0.230725i	−0.0223749	−	0.0129181i
$320$	29.3938	−	9.61933i	1.64316	−	0.537737i
$321$		0			0
$322$	17.6493	−	4.90127i	0.983556	−	0.273137i
$323$	4.76356	−	4.76356i	0.265052	−	0.265052i
$324$		0			0
$325$	−19.7692	−	19.7692i	−1.09660	−	1.09660i
$326$	−4.28896	+	7.58694i	−0.237543	+	0.420202i
$327$		0			0
$328$	9.23866	−	2.74724i	0.510119	−	0.151691i
$329$	−7.90701	+	13.6953i	−0.435928	+	0.755049i
$330$		0			0
$331$	33.3960	+	8.94844i	1.83561	+	0.491851i	0.998478	−	0.0551468i	$-0.0175627\pi$
$331$	33.3960	+	8.94844i	1.83561	+	0.491851i	0.837134	+	0.546998i	$0.184229\pi$
$332$	8.96675	−	2.57801i	0.492114	−	0.141487i
$333$		0			0
$334$	4.85696	−	18.8078i	0.265761	−	1.02912i
$335$	10.3561	+	17.9374i	0.565817	+	0.980023i
$336$		0			0
$337$	−14.3693	+	24.8884i	−0.782746	+	1.35576i	0.147591	+	0.989049i	$0.452848\pi$
$337$	−14.3693	+	24.8884i	−0.782746	+	1.35576i	−0.930336	+	0.366707i	$0.880485\pi$
$338$	−5.14413	−	5.05156i	−0.279804	−	0.274769i
$339$		0			0
$340$	−22.7533	+	23.5950i	−1.23397	+	1.27962i
$341$	1.28894	−	1.28894i	0.0698001	−	0.0698001i
$342$		0			0
$343$	−9.01293			−0.486653
$344$	7.18775	+	11.7016i	0.387538	+	0.630907i
$345$		0			0
$346$	7.67659	−	0.0696962i	0.412696	−	0.00374689i
$347$	10.9346	−	2.92992i	0.587002	−	0.157287i	0.0469191	−	0.998899i	$-0.485060\pi$
$347$	10.9346	−	2.92992i	0.587002	−	0.157287i	0.540082	+	0.841612i	$0.318393\pi$
$348$		0			0
$349$	10.8496	+	2.90715i	0.580767	+	0.155616i	0.537230	−	0.843436i	$-0.319471\pi$
$349$	10.8496	+	2.90715i	0.580767	+	0.155616i	0.0435372	+	0.999052i	$0.486137\pi$
$350$	11.8334	−	45.8228i	0.632520	−	2.44933i
$351$		0			0
$352$	0.569807	−	1.09931i	0.0303708	−	0.0585935i
$353$	−1.85946	+	1.07356i	−0.0989689	+	0.0571397i	−0.548668	−	0.836041i	$-0.684865\pi$
$353$	−1.85946	+	1.07356i	−0.0989689	+	0.0571397i	0.449699	+	0.893180i	$0.351531\pi$
$354$		0			0
$355$	−28.1417	+	7.54056i	−1.49361	+	0.400211i
$356$	−5.07497	+	3.05422i	−0.268973	+	0.161873i
$357$		0			0
$358$	0.661829	+	0.374137i	0.0349787	+	0.0197738i
$359$			11.0166i			0.581435i	0.956809	+	0.290718i	$0.0938941\pi$
$359$			11.0166i			0.581435i	−0.956809	+	0.290718i	$0.906106\pi$
$360$		0			0
$361$		−	16.4748i		−	0.867097i
$362$	−4.91125	+	8.68775i	−0.258130	+	0.456618i
$363$		0			0
$364$	−4.56344	+	18.3580i	−0.239189	+	0.962222i
$365$	12.0484	−	3.22835i	0.630641	−	0.168980i
$366$		0			0
$367$	−20.1365	+	11.6258i	−1.05112	+	0.606863i	−0.922962	−	0.384891i	$-0.874239\pi$
$367$	−20.1365	+	11.6258i	−1.05112	+	0.606863i	−0.128156	+	0.991754i	$0.540906\pi$
$368$	−13.0465	+	8.17791i	−0.680094	+	0.426303i
$369$		0			0
$370$	19.9559	+	5.15345i	1.03746	+	0.267915i
$371$	−34.8524	−	9.33867i	−1.80945	−	0.484839i
$372$		0			0
$373$	9.93021	−	2.66079i	0.514167	−	0.137771i	0.00759967	−	0.999971i	$-0.497581\pi$
$373$	9.93021	−	2.66079i	0.514167	−	0.137771i	0.506567	+	0.862201i	$0.330914\pi$
$374$	0.0119140	+	1.31225i	0.000616061	+	0.0678551i
$375$		0			0
$376$	3.08964	−	12.9294i	0.159336	−	0.666785i
$377$	−5.92615			−0.305212
$378$		0			0
$379$	−6.14819	+	6.14819i	−0.315811	+	0.315811i	−0.847156	−	0.531345i	$-0.821687\pi$
$379$	−6.14819	+	6.14819i	−0.315811	+	0.315811i	0.531345	+	0.847156i	$0.321687\pi$
$380$	−0.223084	−	12.2846i	−0.0114440	−	0.630188i
$381$		0			0
$382$	10.7125	−	10.9088i	0.548100	−	0.558143i
$383$	1.40170	−	2.42782i	0.0716238	−	0.124056i	−0.827989	−	0.560744i	$-0.810515\pi$
$383$	1.40170	−	2.42782i	0.0716238	−	0.124056i	0.899613	+	0.436688i	$0.143849\pi$
$384$		0			0
$385$	−1.42363	−	2.46580i	−0.0725548	−	0.125669i
$386$	−7.12153	−	1.83908i	−0.362476	−	0.0936066i
$387$		0			0
$388$	26.7347	+	14.7947i	1.35725	+	0.751086i
$389$	−29.1977	−	7.82350i	−1.48038	−	0.396667i	−0.573905	−	0.818922i	$-0.694572\pi$
$389$	−29.1977	−	7.82350i	−1.48038	−	0.396667i	−0.906477	+	0.422255i	$0.861239\pi$
$390$		0			0
$391$	8.15956	−	14.1328i	0.412647	−	0.714725i
$392$	−11.7156	+	3.48379i	−0.591727	+	0.175958i
$393$		0			0
$394$	−5.12828	−	2.89906i	−0.258359	−	0.146052i
$395$	15.7382	+	15.7382i	0.791873	+	0.791873i
$396$		0			0
$397$	1.95789	−	1.95789i	0.0982636	−	0.0982636i	−0.656266	−	0.754530i	$-0.727865\pi$
$397$	1.95789	−	1.95789i	0.0982636	−	0.0982636i	0.754530	+	0.656266i	$0.227865\pi$
$398$	−0.973596	−	3.50588i	−0.0488020	−	0.175734i
$399$		0			0
$400$	1.44441	+	39.7567i	0.0722204	+	1.98783i
$401$	28.7356	+	16.5905i	1.43499	+	0.828489i	0.997495	−	0.0707337i	$-0.0225340\pi$
$401$	28.7356	+	16.5905i	1.43499	+	0.828489i	0.437490	+	0.899223i	$0.355867\pi$
$402$		0			0
$403$	6.05887	−	22.6120i	0.301814	−	1.12638i
$404$	0.258063	−	0.0741950i	0.0128391	−	0.00369134i
$405$		0			0
$406$	−5.09446	−	8.64172i	−0.252834	−	0.428881i
$407$	0.714607	−	0.412578i	0.0354217	−	0.0204508i
$408$		0			0
$409$	−22.8959	−	13.2190i	−1.13213	−	0.653636i	−0.187660	−	0.982234i	$-0.560090\pi$
$409$	−22.8959	−	13.2190i	−1.13213	−	0.653636i	−0.944470	+	0.328598i	$0.893424\pi$
$410$	0.169145	+	18.6302i	0.00835349	+	0.920082i
$411$		0			0
$412$	−0.297127	−	16.3620i	−0.0146384	−	0.806097i
$413$	−13.1607	−	13.1607i	−0.647596	−	0.647596i
$414$		0			0
$415$			18.0347i			0.885290i
$416$	−0.721592	−	15.8853i	−0.0353790	−	0.778839i
$417$		0			0
$418$	−0.350971	−	0.344656i	−0.0171666	−	0.0168577i
$419$	0.133835	+	0.499479i	0.00653827	+	0.0244012i	0.969118	−	0.246598i	$-0.0793127\pi$
$419$	0.133835	+	0.499479i	0.00653827	+	0.0244012i	−0.962580	+	0.270999i	$0.912646\pi$
$420$		0			0
$421$	−3.44352	+	12.8514i	−0.167827	+	0.626339i	0.829836	+	0.558008i	$0.188434\pi$
$421$	−3.44352	+	12.8514i	−0.167827	+	0.626339i	−0.997663	+	0.0683313i	$0.978233\pi$
$422$	−13.0638	−	22.1601i	−0.635938	−	1.07874i
$423$		0			0
$424$	30.3196	−	0.826002i	1.47245	−	0.0401142i
$425$	−21.0818	−	36.5148i	−1.02262	−	1.77123i
$426$		0			0
$427$	−7.84332	−	29.2717i	−0.379565	−	1.41655i
$428$	22.7507	+	5.65536i	1.09970	+	0.273362i
$429$		0			0
$430$	−25.5774	+	7.10295i	−1.23345	+	0.342534i
$431$	−8.61129			−0.414791			−0.207396	−	0.978257i	$-0.566499\pi$
$431$	−8.61129			−0.414791			−0.207396	+	0.978257i	$0.566499\pi$
$432$		0			0
$433$	6.43973			0.309474			0.154737	−	0.987956i	$-0.450547\pi$
$433$	6.43973			0.309474			0.154737	+	0.987956i	$0.450547\pi$
$434$	38.1822	−	10.6033i	1.83280	−	0.508976i
$435$		0			0
$436$	−4.30746	+	17.3282i	−0.206290	+	0.829873i
$437$	1.58320	+	5.90859i	0.0757348	+	0.282646i
$438$		0			0
$439$	14.4510	+	25.0298i	0.689707	+	1.19461i	0.971933	+	0.235260i	$0.0755941\pi$
$439$	14.4510	+	25.0298i	0.689707	+	1.19461i	−0.282225	+	0.959348i	$0.591073\pi$
$440$	1.73788	+	1.64570i	0.0828502	+	0.0784557i
$441$		0			0
$442$	8.55878	+	14.5182i	0.407100	+	0.690562i
$443$	8.35627	−	31.1860i	0.397018	−	1.48169i	−0.421297	−	0.906923i	$-0.638425\pi$
$443$	8.35627	−	31.1860i	0.397018	−	1.48169i	0.818315	−	0.574770i	$-0.194908\pi$
$444$		0			0
$445$	−2.96330	−	11.0592i	−0.140474	−	0.524257i
$446$	−3.28637	−	3.22723i	−0.155614	−	0.152814i
$447$		0			0
$448$	22.5441	−	14.7081i	1.06511	−	0.694894i
$449$			10.7097i			0.505423i	0.967542	+	0.252711i	$0.0813223\pi$
$449$			10.7097i			0.505423i	−0.967542	+	0.252711i	$0.918678\pi$
$450$		0			0
$451$	0.527433	+	0.527433i	0.0248359	+	0.0248359i
$452$	33.8415	−	0.614550i	1.59177	−	0.0289060i
$453$		0			0
$454$	−0.117401	−	12.9310i	−0.00550991	−	0.606880i
$455$	−31.6669	−	18.2829i	−1.48457	−	0.857114i
$456$		0			0
$457$	−13.1358	+	7.58393i	−0.614465	+	0.354761i	−0.774711	−	0.632316i	$-0.782105\pi$
$457$	−13.1358	+	7.58393i	−0.614465	+	0.354761i	0.160246	+	0.987077i	$0.448771\pi$
$458$	3.77532	+	6.40406i	0.176409	+	0.299242i
$459$		0			0
$460$	−8.22407	−	28.6047i	−0.383449	−	1.33370i
$461$	3.10006	−	11.5696i	0.144384	−	0.538849i	−0.855398	−	0.517971i	$-0.826687\pi$
$461$	3.10006	−	11.5696i	0.144384	−	0.538849i	0.999782	−	0.0208774i	$-0.00664596\pi$
$462$		0			0
$463$	2.03363	+	1.17412i	0.0945107	+	0.0545658i	0.546510	−	0.837452i	$-0.315956\pi$
$463$	2.03363	+	1.17412i	0.0945107	+	0.0545658i	−0.452000	+	0.892018i	$0.649289\pi$
$464$	6.17537	+	5.74238i	0.286684	+	0.266583i
$465$		0			0
$466$	5.35474	+	19.2822i	0.248054	+	0.893231i
$467$	24.1509	−	24.1509i	1.11757	−	1.11757i	0.125473	−	0.992097i	$-0.459955\pi$
$467$	24.1509	−	24.1509i	1.11757	−	1.11757i	0.992097	−	0.125473i	$-0.0400449\pi$
$468$		0			0
$469$	12.7469	+	12.7469i	0.588596	+	0.588596i
$470$	22.3692	+	12.6455i	1.03181	+	0.583292i
$471$		0			0
$472$	13.7574	+	7.45087i	0.633237	+	0.342954i
$473$	−0.531379	+	0.920376i	−0.0244328	+	0.0423189i
$474$		0			0
$475$	15.2660	+	4.09051i	0.700452	+	0.187685i
$476$	−13.8134	+	24.9614i	−0.633135	+	1.14410i
$477$		0			0
$478$	−20.5814	−	5.31499i	−0.941373	−	0.243102i
$479$	−2.40917	−	4.17281i	−0.110078	−	0.190660i	0.805724	−	0.592292i	$-0.201777\pi$
$479$	−2.40917	−	4.17281i	−0.110078	−	0.190660i	−0.915801	+	0.401631i	$0.868443\pi$
$480$		0			0
$481$	5.29851	−	9.17730i	0.241591	−	0.418449i
$482$	14.2473	−	14.5084i	0.648946	−	0.660837i
$483$		0			0
$484$	−21.9006	+	0.397706i	−0.995480	+	0.0180775i
$485$	−41.7638	+	41.7638i	−1.89640	+	1.89640i
$486$		0			0
$487$	37.5042			1.69948			0.849739	−	0.527204i	$-0.176760\pi$
$487$	37.5042			1.69948			0.849739	+	0.527204i	$0.176760\pi$
$488$	13.3331	+	21.7062i	0.603563	+	0.982593i
$489$		0			0
$490$	−0.214494	−	23.6251i	−0.00968986	−	1.06727i
$491$	1.88310	−	0.504576i	0.0849832	−	0.0227712i	−0.216077	−	0.976376i	$-0.569326\pi$
$491$	1.88310	−	0.504576i	0.0849832	−	0.0227712i	0.301060	+	0.953605i	$0.402660\pi$
$492$		0			0
$493$	−8.63279	−	2.31315i	−0.388801	−	0.104179i
$494$	−6.11657	−	1.57955i	−0.275198	−	0.0710675i
$495$		0			0
$496$	−28.2245	+	17.6920i	−1.26732	+	0.794392i
$497$	−21.9598	+	12.6785i	−0.985032	+	0.568708i
$498$		0			0
$499$	10.8793	−	2.91509i	0.487023	−	0.130497i	−0.00694794	−	0.999976i	$-0.502212\pi$
$499$	10.8793	−	2.91509i	0.487023	−	0.130497i	0.493971	+	0.869478i	$0.335545\pi$
$500$	−37.1106	−	9.22496i	−1.65964	−	0.412553i
$501$		0			0
$502$	3.54086	−	6.26360i	0.158036	−	0.279558i
$503$		−	15.3339i		−	0.683706i	−0.939753	−	0.341853i	$-0.888945\pi$
$503$		−	15.3339i		−	0.683706i	0.939753	−	0.341853i	$-0.111055\pi$
$504$		0			0
$505$			0.519039i			0.0230969i
$506$	−1.03732	−	0.586405i	−0.0461145	−	0.0260689i
$507$		0			0
$508$	13.8221	+	22.9672i	0.613257	+	1.01900i
$509$	−32.0866	+	8.59758i	−1.42221	+	0.381081i	−0.886269	−	0.463172i	$-0.846711\pi$
$509$	−32.0866	+	8.59758i	−1.42221	+	0.381081i	−0.535945	+	0.844253i	$0.680045\pi$
$510$		0			0
$511$	9.40169	−	5.42807i	0.415906	−	0.240124i
$512$	−14.6407	+	17.2525i	−0.647035	+	0.762461i
$513$		0			0
$514$	2.01151	−	7.78924i	0.0887238	−	0.343568i
$515$	30.5548	+	8.18713i	1.34641	+	0.360768i
$516$		0			0
$517$	0.993703	−	0.266262i	0.0437030	−	0.0117102i
$518$	17.9376	−	0.162856i	0.788131	−	0.00715549i
$519$		0			0
$520$	29.8959	+	7.14398i	1.31102	+	0.313284i
$521$	20.5032			0.898262			0.449131	−	0.893466i	$-0.351734\pi$
$521$	20.5032			0.898262			0.449131	+	0.893466i	$0.351734\pi$
$522$		0			0
$523$	−29.2406	+	29.2406i	−1.27860	+	1.27860i	−0.337151	+	0.941451i	$0.609463\pi$
$523$	−29.2406	+	29.2406i	−1.27860	+	1.27860i	−0.941451	+	0.337151i	$0.890537\pi$
$524$	0.943016	+	0.909377i	0.0411958	+	0.0397263i
$525$		0			0
$526$	21.9502	+	21.5552i	0.957076	+	0.939853i
$527$	17.6523	−	30.5746i	0.768944	−	1.33185i
$528$		0			0
$529$	−4.09099	−	7.08581i	−0.177869	−	0.308079i
$530$	−14.6596	+	56.7668i	−0.636771	+	2.46579i
$531$		0			0
$532$	−2.95479	−	10.2773i	−0.128107	−	0.445576i
$533$	9.25281	+	2.47928i	0.400784	+	0.107390i
$534$		0			0
$535$	−22.6575	+	39.2440i	−0.979570	+	1.69667i
$536$	−13.3248	−	7.21658i	−0.575545	−	0.311709i
$537$		0			0
$538$	7.31746	−	12.9442i	0.315478	−	0.558064i
$539$	−0.668841	−	0.668841i	−0.0288090	−	0.0288090i
$540$		0			0
$541$	20.5836	−	20.5836i	0.884956	−	0.884956i	−0.109077	−	0.994033i	$-0.534790\pi$
$541$	20.5836	−	20.5836i	0.884956	−	0.884956i	0.994033	+	0.109077i	$0.0347895\pi$
$542$	−16.1984	+	4.49836i	−0.695780	+	0.193221i
$543$		0			0
$544$	5.14932	−	23.4222i	0.220775	−	1.00422i
$545$	−29.8905	−	17.2573i	−1.28037	−	0.739221i
$546$		0			0
$547$	10.2029	−	38.0779i	0.436246	−	1.62809i	−0.301821	−	0.953365i	$-0.597594\pi$
$547$	10.2029	−	38.0779i	0.436246	−	1.62809i	0.738067	−	0.674728i	$-0.235739\pi$
$548$	36.8287	+	20.3806i	1.57324	+	0.870616i
$549$		0			0
$550$	−2.65217	+	1.56350i	−0.113089	+	0.0666680i
$551$	2.90122	−	1.67502i	0.123596	−	0.0713584i
$552$		0			0
$553$	16.7761	+	9.68566i	0.713391	+	0.411876i
$554$	−14.6523	+	0.133029i	−0.622516	+	0.00565186i
$555$		0			0
$556$	9.60441	+	9.26181i	0.407318	+	0.392788i
$557$	1.52288	+	1.52288i	0.0645265	+	0.0645265i	0.738634	−	0.674107i	$-0.235471\pi$
$557$	1.52288	+	1.52288i	0.0645265	+	0.0645265i	−0.674107	+	0.738634i	$0.735471\pi$
$558$		0			0
$559$			13.6484i			0.577266i
$560$	15.2827	+	49.7366i	0.645810	+	2.10176i
$561$		0			0
$562$	13.9839	−	14.2401i	0.589875	−	0.600684i
$563$	1.30147	+	4.85715i	0.0548504	+	0.204705i	0.987913	−	0.155010i	$-0.0495409\pi$
$563$	1.30147	+	4.85715i	0.0548504	+	0.204705i	−0.933063	+	0.359714i	$0.882874\pi$
$564$		0			0
$565$	−16.9335	+	63.1966i	−0.712397	+	2.65870i
$566$	16.1378	−	9.51354i	0.678322	−	0.399884i
$567$		0			0
$568$	14.6562	−	15.4771i	0.614961	−	0.649407i
$569$	17.4710	+	30.2606i	0.732421	+	1.26859i	0.955846	+	0.293869i	$0.0949430\pi$
$569$	17.4710	+	30.2606i	0.732421	+	1.26859i	−0.223425	+	0.974721i	$0.571724\pi$
$570$		0			0
$571$	−9.16034	−	34.1869i	−0.383348	−	1.43068i	−0.840754	−	0.541417i	$-0.817888\pi$
$571$	−9.16034	−	34.1869i	−0.383348	−	1.43068i	0.457406	−	0.889258i	$-0.348779\pi$
$572$	1.05438	−	0.634548i	0.0440859	−	0.0265318i
$573$		0			0
$574$	4.33887	+	15.6241i	0.181101	+	0.652137i
$575$	38.2852			1.59660
$576$		0			0
$577$	−17.4865			−0.727972			−0.363986	−	0.931404i	$-0.618584\pi$
$577$	−17.4865			−0.727972			−0.363986	+	0.931404i	$0.618584\pi$
$578$	0.367925	+	1.32488i	0.0153037	+	0.0551078i
$579$		0			0
$580$	−13.9661	+	8.40509i	−0.579912	+	0.349002i
$581$	4.06253	+	15.1616i	0.168542	+	0.629008i
$582$		0			0
$583$	1.17362	+	2.03278i	0.0486065	+	0.0841890i
$584$	−6.27479	+	6.62626i	−0.259653	+	0.274197i
$585$		0			0
$586$	−37.4684	+	22.0883i	−1.54780	+	0.912461i
$587$	−3.31081	+	12.3561i	−0.136652	+	0.509991i	0.863334	+	0.504633i	$0.168372\pi$
$587$	−3.31081	+	12.3561i	−0.136652	+	0.509991i	−0.999986	+	0.00535825i	$0.998294\pi$
$588$		0			0
$589$	3.42507	+	12.7825i	0.141128	+	0.526696i
$590$	−21.1897	+	21.5780i	−0.872366	+	0.888352i
$591$		0			0
$592$	−14.4140	+	4.42903i	−0.592414	+	0.182032i
$593$			25.7816i			1.05872i	0.848397	+	0.529361i	$0.177568\pi$
$593$			25.7816i			1.05872i	−0.848397	+	0.529361i	$0.822432\pi$
$594$		0			0
$595$	−38.9937	−	38.9937i	−1.59858	−	1.59858i
$596$	−32.1597	−	31.0125i	−1.31731	−	1.27032i
$597$		0			0
$598$	−15.3024	+	0.138931i	−0.625761	+	0.00568132i
$599$	27.3647	+	15.7990i	1.11809	+	0.645531i	0.940913	−	0.338647i	$-0.109969\pi$
$599$	27.3647	+	15.7990i	1.11809	+	0.645531i	0.177180	+	0.984179i	$0.443303\pi$
$600$		0			0
$601$	23.3729	−	13.4944i	0.953401	−	0.550447i	0.0592656	−	0.998242i	$-0.481124\pi$
$601$	23.3729	−	13.4944i	0.953401	−	0.550447i	0.894136	+	0.447796i	$0.147791\pi$
$602$	−19.9026	+	11.7330i	−0.811169	+	0.478200i
$603$		0			0
$604$	34.9111	+	19.3194i	1.42051	+	0.786097i
$605$	10.9585	−	40.8977i	0.445527	−	1.66273i
$606$		0			0
$607$	−21.2314	−	12.2579i	−0.861755	−	0.497534i	0.00284471	−	0.999996i	$-0.499095\pi$
$607$	−21.2314	−	12.2579i	−0.861755	−	0.497534i	−0.864600	+	0.502462i	$0.832428\pi$
$608$	4.84322	+	7.57288i	0.196419	+	0.307121i
$609$		0			0
$610$	−47.4456	+	13.1758i	−1.92102	+	0.533474i
$611$	9.34212	−	9.34212i	0.377942	−	0.377942i
$612$		0			0
$613$	−30.3894	−	30.3894i	−1.22742	−	1.22742i	−0.964937	−	0.262481i	$-0.915459\pi$
$613$	−30.3894	−	30.3894i	−1.22742	−	1.22742i	−0.262481	−	0.964937i	$-0.584541\pi$
$614$	23.4355	−	41.4562i	0.945780	−	1.67303i
$615$		0			0
$616$	1.83173	+	0.992042i	0.0738024	+	0.0399705i
$617$	15.8393	−	27.4345i	0.637668	−	1.10447i	−0.348275	−	0.937392i	$-0.613233\pi$
$617$	15.8393	−	27.4345i	0.637668	−	1.10447i	0.985943	−	0.167081i	$-0.0534341\pi$
$618$		0			0
$619$	−20.1312	−	5.39413i	−0.809141	−	0.216809i	−0.169547	−	0.985522i	$-0.554231\pi$
$619$	−20.1312	−	5.39413i	−0.809141	−	0.216809i	−0.639593	+	0.768713i	$0.720897\pi$
$620$	−17.7918	−	61.8829i	−0.714537	−	2.48528i
$621$		0			0
$622$	3.76031	−	14.5612i	0.150775	−	0.583851i
$623$	−4.98242	−	8.62981i	−0.199617	−	0.345746i
$624$		0			0
$625$	12.0944	−	20.9481i	0.483775	−	0.837923i
$626$	−19.1821	−	18.8369i	−0.766670	−	0.752874i
$627$		0			0
$628$	−21.4538	−	20.6885i	−0.856101	−	0.825563i
$629$	11.3007	−	11.3007i	0.450587	−	0.450587i
$630$		0			0
$631$	−19.9953			−0.796002			−0.398001	−	0.917385i	$-0.630296\pi$
$631$	−19.9953			−0.796002			−0.398001	+	0.917385i	$0.630296\pi$
$632$	−15.8379	−	3.78464i	−0.629997	−	0.150545i
$633$		0			0
$634$	−17.3856	+	0.157845i	−0.690472	+	0.00626884i
$635$	−50.0494	+	13.4107i	−1.98615	+	0.532187i
$636$		0			0
$637$	−11.7335	−	3.14400i	−0.464900	−	0.124570i
$638$	−0.163173	+	0.631861i	−0.00646008	+	0.0250156i
$639$		0			0
$640$	−24.2307	−	36.4133i	−0.957803	−	1.43936i
$641$	−12.6976	+	7.33098i	−0.501526	+	0.289556i	−0.729344	−	0.684148i	$-0.760174\pi$
$641$	−12.6976	+	7.33098i	−0.501526	+	0.289556i	0.227818	+	0.973704i	$0.426841\pi$
$642$		0			0
$643$	12.8777	−	3.45056i	0.507846	−	0.136077i	0.00420705	−	0.999991i	$-0.498661\pi$
$643$	12.8777	−	3.45056i	0.507846	−	0.136077i	0.503639	+	0.863914i	$0.331994\pi$
$644$	−13.3574	−	22.1950i	−0.526355	−	0.874606i
$645$		0			0
$646$	−8.29363	−	4.68846i	−0.326309	−	0.184465i
$647$			30.5078i			1.19939i	0.800231	+	0.599693i	$0.204710\pi$
$647$			30.5078i			1.19939i	−0.800231	+	0.599693i	$0.795290\pi$
$648$		0			0
$649$			1.21078i			0.0475272i
$650$	−19.4575	+	34.4193i	−0.763185	+	1.35003i
$651$		0			0
$652$	11.9613	+	2.97334i	0.468441	+	0.116445i
$653$	−20.1465	+	5.39824i	−0.788394	+	0.211249i	−0.630482	−	0.776204i	$-0.717143\pi$
$653$	−20.1465	+	5.39824i	−0.788394	+	0.211249i	−0.157912	+	0.987453i	$0.550476\pi$
$654$		0			0
$655$	−2.19305	+	1.26616i	−0.0856896	+	0.0494729i
$656$	−7.23953	−	11.5494i	−0.282656	−	0.450930i
$657$		0			0
$658$	21.6540	+	5.59198i	0.844162	+	0.217998i
$659$	14.5728	+	3.90477i	0.567676	+	0.152108i	0.531230	−	0.847227i	$-0.321730\pi$
$659$	14.5728	+	3.90477i	0.567676	+	0.152108i	0.0364452	+	0.999336i	$0.488397\pi$
$660$		0			0
$661$	−9.11835	+	2.44325i	−0.354663	+	0.0950316i	−0.431751	−	0.901993i	$-0.642104\pi$
$661$	−9.11835	+	2.44325i	−0.354663	+	0.0950316i	0.0770887	+	0.997024i	$0.475438\pi$
$662$	−0.443904	−	48.8932i	−0.0172528	−	1.90029i
$663$		0			0
$664$	−6.90604	−	11.2430i	−0.268006	−	0.436311i
$665$	20.6706			0.801570
$666$		0			0
$667$	5.73833	−	5.73833i	0.222189	−	0.222189i
$668$	−27.4663	+	0.498777i	−1.06270	+	0.0192983i
$669$		0			0
$670$	20.5234	−	20.8995i	0.792888	−	0.807417i
$671$	−0.985698	+	1.70728i	−0.0380525	+	0.0659088i
$672$		0			0
$673$	−16.1140	−	27.9103i	−0.621149	−	1.07586i	−0.989272	−	0.146085i	$-0.953333\pi$
$673$	−16.1140	−	27.9103i	−0.621149	−	1.07586i	0.368123	−	0.929777i	$-0.380001\pi$
$674$	39.3516	+	10.1622i	1.51577	+	0.391434i
$675$		0			0
$676$	−4.93689	+	8.92120i	−0.189880	+	0.343123i
$677$	15.5364	+	4.16296i	0.597111	+	0.159996i	0.544701	−	0.838630i	$-0.316643\pi$
$677$	15.5364	+	4.16296i	0.597111	+	0.159996i	0.0524101	+	0.998626i	$0.483310\pi$
$678$		0			0
$679$	−25.7025	+	44.5181i	−0.986372	+	1.70845i
$680$	40.7617	+	22.0761i	1.56314	+	0.846579i
$681$		0			0
$682$	−2.24412	−	1.26862i	−0.0859318	−	0.0485779i
$683$	−28.6734	−	28.6734i	−1.09716	−	1.09716i	−0.994742	−	0.102416i	$-0.967343\pi$
$683$	−28.6734	−	28.6734i	−1.09716	−	1.09716i	−0.102416	−	0.994742i	$-0.532657\pi$
$684$		0			0
$685$	−57.5322	+	57.5322i	−2.19819	+	2.19819i
$686$	3.41060	+	12.2814i	0.130217	+	0.468907i
$687$		0			0
$688$	13.2252	−	14.2224i	0.504205	−	0.542223i
$689$	26.1058	+	15.0722i	0.994552	+	0.574205i
$690$		0			0
$691$	−11.8033	+	44.0504i	−0.449017	+	1.67575i	0.256089	+	0.966653i	$0.417566\pi$
$691$	−11.8033	+	44.0504i	−0.449017	+	1.67575i	−0.705106	+	0.709102i	$0.749101\pi$
$692$	−2.99988	−	10.4341i	−0.114038	−	0.396645i
$693$		0			0
$694$	−8.13025	−	13.7913i	−0.308620	−	0.523511i
$695$	−22.3358	+	12.8956i	−0.847243	+	0.489156i
$696$		0			0
$697$	12.5111	+	7.22328i	0.473892	+	0.273601i
$698$	−0.144215	−	15.8843i	−0.00545861	−	0.601230i
$699$		0			0
$700$	−66.9181	+	1.21521i	−2.52927	+	0.0459305i
$701$	−13.0178	−	13.0178i	−0.491676	−	0.491676i	0.417158	−	0.908834i	$-0.363026\pi$
$701$	−13.0178	−	13.0178i	−0.491676	−	0.491676i	−0.908834	+	0.417158i	$0.863026\pi$
$702$		0			0
$703$			5.99049i			0.225935i
$704$	−1.71359	−	0.360453i	−0.0645835	−	0.0135851i
$705$		0			0
$706$	2.16652	+	2.12753i	0.0815380	+	0.0800708i
$707$	0.116919	+	0.436349i	0.00439721	+	0.0164106i
$708$		0			0
$709$	4.39011	−	16.3841i	0.164874	−	0.615319i	−0.833182	−	0.552999i	$-0.813483\pi$
$709$	4.39011	−	16.3841i	0.164874	−	0.615319i	0.998056	−	0.0623199i	$-0.0198499\pi$
$710$	20.9243	+	35.4938i	0.785274	+	1.33206i
$711$		0			0
$712$	6.08224	+	5.75963i	0.227942	+	0.215851i
$713$	16.0285	+	27.7622i	0.600273	+	1.03970i
$714$		0			0
$715$	0.615660	+	2.29767i	0.0230244	+	0.0859282i
$716$	0.259372	−	1.04342i	0.00969320	−	0.0389943i
$717$		0			0
$718$	15.0118	−	4.16883i	0.560234	−	0.155579i
$719$	−43.0731			−1.60635			−0.803177	−	0.595740i	$-0.796859\pi$
$719$	−43.0731			−1.60635			−0.803177	+	0.595740i	$0.796859\pi$
$720$		0			0
$721$	27.5313			1.02532
$722$	−22.4494	+	6.23428i	−0.835479	+	0.232016i
$723$		0			0
$724$	13.6968	+	3.40475i	0.509038	+	0.126537i
$725$	−5.42673	−	20.2528i	−0.201544	−	0.752171i
$726$		0			0
$727$	15.3101	+	26.5179i	0.567821	+	0.983495i	0.996781	+	0.0801716i	$0.0255468\pi$
$727$	15.3101	+	26.5179i	0.567821	+	0.983495i	−0.428960	+	0.903324i	$0.641120\pi$
$728$	26.7424	−	0.728547i	0.991138	−	0.0270017i
$729$		0			0
$730$	−8.95835	−	15.1960i	−0.331563	−	0.562430i
$731$	−5.32737	+	19.8820i	−0.197040	+	0.735363i
$732$		0			0
$733$	0.679676	+	2.53658i	0.0251044	+	0.0936909i	0.977341	−	0.211669i	$-0.0678899\pi$
$733$	0.679676	+	2.53658i	0.0251044	+	0.0936909i	−0.952237	+	0.305360i	$0.901223\pi$
$734$	23.4618	+	23.0396i	0.865990	+	0.850407i
$735$		0			0
$736$	16.0805	+	14.6831i	0.592736	+	0.541226i
$737$		−	1.17271i		−	0.0431972i
$738$		0			0
$739$	13.1402	+	13.1402i	0.483370	+	0.483370i	0.906206	−	0.422836i	$-0.138965\pi$
$739$	13.1402	+	13.1402i	0.483370	+	0.483370i	−0.422836	+	0.906206i	$0.638965\pi$
$740$	−0.529226	−	29.1430i	−0.0194547	−	1.07132i
$741$		0			0
$742$	0.463262	+	51.0253i	0.0170069	+	1.87320i
$743$	1.79055	+	1.03378i	0.0656890	+	0.0379255i	0.532485	−	0.846440i	$-0.321258\pi$
$743$	1.79055	+	1.03378i	0.0656890	+	0.0379255i	−0.466796	+	0.884365i	$0.654592\pi$
$744$		0			0
$745$	74.7897	−	43.1798i	2.74008	−	1.58199i
$746$	−7.38343	−	12.5245i	−0.270327	−	0.458554i
$747$		0			0
$748$	1.78363	−	0.512808i	0.0652160	−	0.0187501i
$749$	−10.2077	+	38.0958i	−0.372982	+	1.39199i
$750$		0			0
$751$	−7.86676	−	4.54188i	−0.287062	−	0.165735i	0.349554	−	0.936916i	$-0.386333\pi$
$751$	−7.86676	−	4.54188i	−0.287062	−	0.165735i	−0.636616	+	0.771181i	$0.719666\pi$
$752$	−18.7874	+	0.682570i	−0.685107	+	0.0248908i
$753$		0			0
$754$	2.24253	+	8.07525i	0.0816680	+	0.294083i
$755$	−54.5367	+	54.5367i	−1.98479	+	1.98479i
$756$		0			0
$757$	18.3910	+	18.3910i	0.668433	+	0.668433i	0.957353	−	0.288920i	$-0.0932961\pi$
$757$	18.3910	+	18.3910i	0.668433	+	0.668433i	−0.288920	+	0.957353i	$0.593296\pi$
$758$	10.7043	+	6.05125i	0.388799	+	0.219791i
$759$		0			0
$760$	−16.6552	+	4.95263i	−0.604147	+	0.179651i
$761$	14.1080	−	24.4358i	0.511415	−	0.885797i	−0.488497	−	0.872565i	$-0.662455\pi$
$761$	14.1080	−	24.4358i	0.511415	−	0.885797i	0.999912	−	0.0132318i	$-0.00421194\pi$
$762$		0			0
$763$	−29.0160	−	7.77481i	−1.05045	−	0.281467i
$764$	−18.9186	−	10.4693i	−0.684451	−	0.378767i
$765$		0			0
$766$	−3.83869	−	0.991310i	−0.138697	−	0.0358175i
$767$	7.77467	+	13.4661i	0.280727	+	0.486234i
$768$		0			0
$769$	−14.6064	+	25.2991i	−0.526722	+	0.912309i	0.472794	+	0.881173i	$0.343246\pi$
$769$	−14.6064	+	25.2991i	−0.526722	+	0.912309i	−0.999515	+	0.0311354i	$0.990088\pi$
$770$	−2.82129	+	2.87299i	−0.101672	+	0.103535i
$771$		0			0
$772$	0.188861	+	10.4001i	0.00679726	+	0.374306i
$773$	10.5491	−	10.5491i	0.379425	−	0.379425i	−0.491470	−	0.870895i	$-0.663540\pi$
$773$	10.5491	−	10.5491i	0.379425	−	0.379425i	0.870895	+	0.491470i	$0.163540\pi$
$774$		0			0
$775$	82.8256			2.97518
$776$	10.0432	−	42.0284i	0.360529	−	1.50873i
$777$		0			0
$778$	0.388099	+	42.7466i	0.0139140	+	1.53254i
$779$	−5.23060	+	1.40154i	−0.187406	+	0.0502152i
$780$		0			0
$781$	1.59335	+	0.426938i	0.0570146	+	0.0152770i
$782$	−22.3456	−	5.77058i	−0.799078	−	0.206356i
$783$		0			0
$784$	9.18049	+	14.6459i	0.327875	+	0.523068i
$785$	49.8924	−	28.8054i	1.78074	−	1.02811i
$786$		0			0
$787$	33.8023	−	9.05729i	1.20492	−	0.322857i	0.400153	−	0.916448i	$-0.368957\pi$
$787$	33.8023	−	9.05729i	1.20492	−	0.322857i	0.804767	+	0.593591i	$0.202290\pi$
$788$	−2.00979	+	8.08507i	−0.0715957	+	0.288019i
$789$		0			0
$790$	15.4900	−	27.4010i	0.551110	−	0.974885i
$791$			56.9431i			2.02466i
$792$		0			0
$793$			25.3175i			0.899052i
$794$	−3.40880	−	1.92702i	−0.120974	−	0.0683874i
$795$		0			0
$796$	−4.40885	+	2.65333i	−0.156268	+	0.0940449i
$797$	27.6668	−	7.41329i	0.980007	−	0.262592i	0.266959	−	0.963708i	$-0.413981\pi$
$797$	27.6668	−	7.41329i	0.980007	−	0.262592i	0.713048	+	0.701116i	$0.247314\pi$
$798$		0			0
$799$	17.2554	−	9.96243i	0.610453	−	0.352445i
$800$	53.6277	−	17.0126i	1.89602	−	0.601487i
$801$		0			0
$802$	11.7331	−	45.4344i	0.414309	−	1.60435i
$803$	−0.682165	−	0.182786i	−0.0240731	−	0.00645036i
$804$		0			0
$805$	48.3667	−	12.9598i	1.70470	−	0.456773i
$806$	−33.1049	+	0.300562i	−1.16607	+	0.0105868i
$807$		0			0
$808$	−0.198756	−	0.323572i	−0.00699220	−	0.0113832i
$809$	39.9831			1.40573			0.702865	−	0.711323i	$-0.251904\pi$
$809$	39.9831			1.40573			0.702865	+	0.711323i	$0.251904\pi$
$810$		0			0
$811$	−33.5121	+	33.5121i	−1.17677	+	1.17677i	−0.196204	+	0.980563i	$0.562862\pi$
$811$	−33.5121	+	33.5121i	−1.17677	+	1.17677i	−0.980563	+	0.196204i	$0.937138\pi$
$812$	−9.84780	+	10.2121i	−0.345590	+	0.358374i
$813$		0			0
$814$	−0.832614	−	0.817632i	−0.0291831	−	0.0286580i
$815$	−11.9123	+	20.6328i	−0.417271	+	0.722734i
$816$		0			0
$817$	−3.85771	−	6.68176i	−0.134964	−	0.233765i
$818$	−9.34868	+	36.2012i	−0.326869	+	1.26575i
$819$		0			0
$820$	25.3224	−	7.28039i	0.884297	−	0.254242i
$821$	10.8942	+	2.91908i	0.380209	+	0.101877i	0.443861	−	0.896096i	$-0.353608\pi$
$821$	10.8942	+	2.91908i	0.380209	+	0.101877i	−0.0636527	+	0.997972i	$0.520275\pi$
$822$		0			0
$823$	27.4702	−	47.5798i	0.957551	−	1.65853i	0.229131	−	0.973396i	$-0.426412\pi$
$823$	27.4702	−	47.5798i	0.957551	−	1.65853i	0.728420	−	0.685131i	$-0.240255\pi$
$824$	−22.1831	+	6.59645i	−0.772786	+	0.229798i
$825$		0			0
$826$	−12.9532	+	22.9136i	−0.450700	+	0.797265i
$827$	−14.2104	−	14.2104i	−0.494144	−	0.494144i	0.415465	−	0.909609i	$-0.363619\pi$
$827$	−14.2104	−	14.2104i	−0.494144	−	0.494144i	−0.909609	+	0.415465i	$0.863619\pi$
$828$		0			0
$829$	6.15512	−	6.15512i	0.213776	−	0.213776i	−0.592093	−	0.805869i	$-0.701698\pi$
$829$	6.15512	−	6.15512i	0.213776	−	0.213776i	0.805869	+	0.592093i	$0.201698\pi$
$830$	24.5750	−	6.82456i	0.853009	−	0.236884i
$831$		0			0
$832$	−21.3729	+	6.99445i	−0.740973	+	0.242489i
$833$	−15.8654	−	9.15989i	−0.549704	−	0.317371i
$834$		0			0
$835$	13.7435	−	51.2913i	0.475612	−	1.77501i
$836$	−0.336832	+	0.608672i	−0.0116496	+	0.0210513i
$837$		0			0
$838$	0.629969	−	0.371379i	0.0217619	−	0.0128291i
$839$	21.5384	−	12.4352i	0.743590	−	0.429312i	−0.0797833	−	0.996812i	$-0.525423\pi$
$839$	21.5384	−	12.4352i	0.743590	−	0.429312i	0.823373	+	0.567500i	$0.192089\pi$
$840$		0			0
$841$	21.2658	+	12.2778i	0.733303	+	0.423373i
$842$	18.8150	−	0.170822i	0.648407	−	0.00588693i
$843$		0			0
$844$	−25.2529	+	26.1871i	−0.869242	+	0.901396i
$845$	−13.9363	−	13.9363i	−0.479424	−	0.479424i
$846$		0			0
$847$		−	36.8507i		−	1.26621i
$848$	−12.5989	−	41.0023i	−0.432646	−	1.40803i
$849$		0			0
$850$	−41.7791	+	42.5447i	−1.43301	+	1.45927i
$851$	3.75585	+	14.0170i	0.128749	+	0.480497i
$852$		0			0
$853$	−5.05023	+	18.8477i	−0.172917	+	0.645334i	0.823980	+	0.566618i	$0.191749\pi$
$853$	−5.05023	+	18.8477i	−0.172917	+	0.645334i	−0.996897	+	0.0787157i	$0.974918\pi$
$854$	−36.9189	+	21.7644i	−1.26334	+	0.744763i
$855$		0			0
$856$	−0.902871	−	33.1412i	−0.0308595	−	1.13274i
$857$	18.6982	+	32.3862i	0.638717	+	1.10629i	0.985715	+	0.168424i	$0.0538679\pi$
$857$	18.6982	+	32.3862i	0.638717	+	1.10629i	−0.346998	+	0.937866i	$0.612799\pi$
$858$		0			0
$859$	−7.10549	−	26.5180i	−0.242436	−	0.904784i	−0.974655	−	0.223714i	$-0.928182\pi$
$859$	−7.10549	−	26.5180i	−0.242436	−	0.904784i	0.732219	−	0.681070i	$-0.238485\pi$
$860$	19.3576	+	32.1651i	0.660089	+	1.09682i
$861$		0			0
$862$	3.25862	+	11.7341i	0.110989	+	0.399667i
$863$	10.1797			0.346520			0.173260	−	0.984876i	$-0.444570\pi$
$863$	10.1797			0.346520			0.173260	+	0.984876i	$0.444570\pi$
$864$		0			0
$865$	20.9860			0.713545
$866$	−2.43687	−	8.77507i	−0.0828082	−	0.298189i
$867$		0			0
$868$	−28.8972	−	48.0164i	−0.980834	−	1.62978i
$869$	−0.326156	−	1.21723i	−0.0110641	−	0.0412918i
$870$		0			0
$871$	−7.53020	−	13.0427i	−0.255151	−	0.441935i
$872$	25.2423	−	0.687680i	0.854811	−	0.0232878i
$873$		0			0
$874$	7.45221	−	4.39322i	0.252075	−	0.148603i
$875$	16.6507	−	62.1414i	0.562897	−	2.10076i
$876$		0			0
$877$	−6.90717	−	25.7779i	−0.233239	−	0.870458i	−0.978935	−	0.204172i	$-0.934550\pi$
$877$	−6.90717	−	25.7779i	−0.233239	−	0.870458i	0.745696	−	0.666286i	$-0.232117\pi$
$878$	28.6384	−	29.1631i	0.966498	−	0.984208i
$879$		0			0
$880$	1.58487	−	2.99087i	0.0534261	−	0.100822i
$881$		−	30.7798i		−	1.03700i	−0.855078	−	0.518499i	$-0.826491\pi$
$881$		−	30.7798i		−	1.03700i	0.855078	−	0.518499i	$-0.173509\pi$
$882$		0			0
$883$	−19.8089	−	19.8089i	−0.666622	−	0.666622i	0.290310	−	0.956933i	$-0.406241\pi$
$883$	−19.8089	−	19.8089i	−0.666622	−	0.666622i	−0.956933	+	0.290310i	$0.906241\pi$
$884$	16.5445	−	17.1565i	0.556451	−	0.577034i
$885$		0			0
$886$	−45.6576	+	0.414528i	−1.53390	+	0.0139264i
$887$	−21.0940	−	12.1786i	−0.708266	−	0.408918i	0.102153	−	0.994769i	$-0.467427\pi$
$887$	−21.0940	−	12.1786i	−0.708266	−	0.408918i	−0.810419	+	0.585851i	$0.800760\pi$
$888$		0			0
$889$	−39.0550	+	22.5484i	−1.30986	+	0.756249i
$890$	−13.9484	+	8.22287i	−0.467552	+	0.275631i
$891$		0			0
$892$	−3.15397	+	5.69938i	−0.105603	+	0.190829i
$893$	−1.93301	+	7.21410i	−0.0646858	+	0.241411i
$894$		0			0
$895$	1.79985	+	1.03914i	0.0601624	+	0.0347348i
$896$	−28.5729	−	25.1539i	−0.954555	−	0.840333i
$897$		0			0
$898$	14.5935	−	4.05268i	0.486993	−	0.135240i
$899$	12.4142	−	12.4142i	0.414037	−	0.414037i
$900$		0			0
$901$	32.1460	+	32.1460i	1.07094	+	1.07094i
$902$	0.519118	−	0.918292i	0.0172847	−	0.0305758i
$903$		0			0
$904$	−13.6435	−	45.8815i	−0.453775	−	1.52600i
$905$	−13.6407	+	23.6264i	−0.453433	+	0.785369i
$906$		0			0
$907$	56.0698	+	15.0239i	1.86177	+	0.498859i	0.999965	−	0.00838605i	$-0.00266939\pi$
$907$	56.0698	+	15.0239i	1.86177	+	0.498859i	0.861802	+	0.507245i	$0.169336\pi$
$908$	−17.5759	+	5.05321i	−0.583277	+	0.167697i
$909$		0			0
$910$	−12.9300	+	50.0692i	−0.428624	+	1.65978i
$911$	−11.9347	−	20.6715i	−0.395414	−	0.684877i	0.597740	−	0.801690i	$-0.296066\pi$
$911$	−11.9347	−	20.6715i	−0.395414	−	0.684877i	−0.993154	+	0.116813i	$0.962732\pi$
$912$		0			0
$913$	0.510553	−	0.884303i	0.0168968	−	0.0292662i
$914$	15.3049	+	15.0295i	0.506242	+	0.497133i
$915$		0			0
$916$	7.29785	−	7.56780i	0.241128	−	0.250047i
$917$	−1.55845	+	1.55845i	−0.0514646	+	0.0514646i
$918$		0			0
$919$	−15.7779			−0.520466			−0.260233	−	0.965546i	$-0.583799\pi$
$919$	−15.7779			−0.520466			−0.260233	+	0.965546i	$0.583799\pi$
$920$	−35.8660	+	22.0309i	−1.18247	+	0.726336i
$921$		0			0
$922$	−16.9383	+	0.153784i	−0.557834	+	0.00506461i
$923$	20.4625	−	5.48292i	0.673533	−	0.180473i
$924$		0			0
$925$	36.2157	+	9.70397i	1.19077	+	0.319065i
$926$	0.830355	−	3.21541i	0.0272872	−	0.105665i
$927$		0			0
$928$	5.48800	−	10.5878i	0.180152	−	0.347563i
$929$	−14.3132	+	8.26371i	−0.469600	+	0.271123i	−0.716072	−	0.698026i	$-0.754062\pi$
$929$	−14.3132	+	8.26371i	−0.469600	+	0.271123i	0.246472	+	0.969150i	$0.420729\pi$
$930$		0			0
$931$	6.63296	−	1.77730i	0.217387	−	0.0582485i
$932$	24.2485	−	14.5932i	0.794287	−	0.478017i
$933$		0			0
$934$	−42.0481	−	23.7701i	−1.37586	−	0.777783i
$935$			3.58740i			0.117320i
$936$		0			0
$937$		−	5.92940i		−	0.193705i	−0.995299	−	0.0968526i	$-0.969122\pi$
$937$		−	5.92940i		−	0.193705i	0.995299	−	0.0968526i	$-0.0308775\pi$
$938$	12.5459	−	22.1930i	0.409638	−	0.724629i
$939$		0			0
$940$	8.76654	−	35.2665i	0.285933	−	1.15027i
$941$	20.6096	−	5.52232i	0.671853	−	0.180022i	0.0932635	−	0.995641i	$-0.470270\pi$
$941$	20.6096	−	5.52232i	0.671853	−	0.180022i	0.578589	+	0.815619i	$0.303603\pi$
$942$		0			0
$943$	−11.3603	+	6.55886i	−0.369941	+	0.213586i
$944$	4.94692	−	21.5660i	0.161008	−	0.701914i
$945$		0			0
$946$	1.45523	+	0.375800i	0.0473135	+	0.0122183i
$947$	31.9863	+	8.57071i	1.03942	+	0.278511i	0.737871	−	0.674941i	$-0.235831\pi$
$947$	31.9863	+	8.57071i	1.03942	+	0.278511i	0.301545	+	0.953452i	$0.402498\pi$
$948$		0			0
$949$	−8.76066	+	2.34741i	−0.284383	+	0.0762002i
$950$	−0.202917	−	22.3500i	−0.00658351	−	0.725131i
$951$		0			0
$952$	39.2407	+	9.37703i	1.27180	+	0.303911i
$953$	0.546564			0.0177049			0.00885247	−	0.999961i	$-0.497182\pi$
$953$	0.546564			0.0177049			0.00885247	+	0.999961i	$0.497182\pi$
$954$		0			0
$955$	29.5538	−	29.5538i	0.956339	−	0.956339i
$956$	0.545814	+	30.0565i	0.0176529	+	0.972096i
$957$		0			0
$958$	−4.77440	+	4.86189i	−0.154254	+	0.157080i
$959$	−35.4068	+	61.3264i	−1.14335	+	1.98033i
$960$		0			0
$961$	19.1758	+	33.2135i	0.618576	+	1.07140i
$962$	−14.5104	−	3.74720i	−0.467835	−	0.120815i
$963$		0			0
$964$	−25.1611	−	13.9239i	−0.810384	−	0.448457i
$965$	−19.4213	−	5.20393i	−0.625195	−	0.167521i
$966$		0			0
$967$	−7.49046	+	12.9739i	−0.240877	+	0.417211i	−0.960964	−	0.276672i	$-0.910768\pi$
$967$	−7.49046	+	12.9739i	−0.240877	+	0.417211i	0.720087	+	0.693883i	$0.244102\pi$
$968$	8.82937	+	29.6922i	0.283787	+	0.954344i
$969$		0			0
$970$	72.7133	+	41.1054i	2.33468	+	1.31981i
$971$	29.4725	+	29.4725i	0.945816	+	0.945816i	0.998606	−	0.0527896i	$-0.0168113\pi$
$971$	29.4725	+	29.4725i	0.945816	+	0.945816i	−0.0527896	+	0.998606i	$0.516811\pi$
$972$		0			0
$973$	−15.8725	+	15.8725i	−0.508849	+	0.508849i
$974$	−14.1920	−	51.1049i	−0.454742	−	1.63751i
$975$		0			0
$976$	24.5324	−	26.3822i	0.785264	−	0.844475i
$977$	−2.02199	−	1.16740i	−0.0646892	−	0.0373483i	0.467307	−	0.884095i	$-0.345224\pi$
$977$	−2.02199	−	1.16740i	−0.0646892	−	0.0373483i	−0.531996	+	0.846747i	$0.678558\pi$
$978$		0			0
$979$	−0.167779	+	0.626159i	−0.00536224	+	0.0200121i
$980$	−32.1115	+	9.23231i	−1.02577	+	0.294915i
$981$		0			0
$982$	−1.40015	−	2.37506i	−0.0446805	−	0.0757913i
$983$	−21.5089	+	12.4182i	−0.686029	+	0.396079i	−0.802123	−	0.597159i	$-0.796296\pi$
$983$	−21.5089	+	12.4182i	−0.686029	+	0.396079i	0.116094	+	0.993238i	$0.462963\pi$
$984$		0			0
$985$	−13.9464	−	8.05197i	−0.444370	−	0.256557i
$986$	0.114748	+	12.6388i	0.00365433	+	0.402500i
$987$		0			0
$988$	0.162210	+	8.93244i	0.00516058	+	0.284179i
$989$	−13.2158	−	13.2158i	−0.420240	−	0.420240i
$990$		0			0
$991$		−	7.12527i		−	0.226342i	−0.993576	−	0.113171i	$-0.963899\pi$
$991$		−	7.12527i		−	0.226342i	0.993576	−	0.113171i	$-0.0361008\pi$
$992$	34.7884	+	31.7651i	1.10453	+	1.00854i
$993$		0			0
$994$	25.5862	+	25.1257i	0.811544	+	0.796940i
$995$	−2.57436	−	9.60763i	−0.0816126	−	0.304582i
$996$		0			0
$997$	12.7516	−	47.5897i	0.403848	−	1.50718i	−0.402322	−	0.915498i	$-0.631797\pi$
$997$	12.7516	−	47.5897i	0.403848	−	1.50718i	0.806170	−	0.591684i	$-0.201537\pi$
$998$	−8.08908	−	13.7215i	−0.256055	−	0.434346i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.395.9		88
3.2	odd	2		144.2.u.a.59.14	yes	88
4.3	odd	2		1728.2.z.a.719.1		88
9.2	odd	6	inner	432.2.v.a.251.16		88
9.7	even	3		144.2.u.a.11.7	✓	88
12.11	even	2		576.2.y.a.527.3		88
16.3	odd	4	inner	432.2.v.a.179.16		88
16.13	even	4		1728.2.z.a.1583.1		88
36.7	odd	6		576.2.y.a.335.15		88
36.11	even	6		1728.2.z.a.143.1		88
48.29	odd	4		576.2.y.a.239.15		88
48.35	even	4		144.2.u.a.131.7	yes	88
144.29	odd	12		1728.2.z.a.1007.1		88
144.61	even	12		576.2.y.a.47.3		88
144.83	even	12	inner	432.2.v.a.35.9		88
144.115	odd	12		144.2.u.a.83.14	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	9.7	even	3
144.2.u.a.59.14	yes	88	3.2	odd	2
144.2.u.a.83.14	yes	88	144.115	odd	12
144.2.u.a.131.7	yes	88	48.35	even	4
432.2.v.a.35.9		88	144.83	even	12	inner
432.2.v.a.179.16		88	16.3	odd	4	inner
432.2.v.a.251.16		88	9.2	odd	6	inner
432.2.v.a.395.9		88	1.1	even	1	trivial
576.2.y.a.47.3		88	144.61	even	12
576.2.y.a.239.15		88	48.29	odd	4
576.2.y.a.335.15		88	36.7	odd	6
576.2.y.a.527.3		88	12.11	even	2
1728.2.z.a.143.1		88	36.11	even	6
1728.2.z.a.719.1		88	4.3	odd	2
1728.2.z.a.1007.1		88	144.29	odd	12
1728.2.z.a.1583.1		88	16.13	even	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.378412 - 1.36265i) q^{2} +(-1.71361 + 1.03128i) q^{4} +(-1.00059 - 3.73424i) q^{5} +(-1.68236 - 2.91393i) q^{7} +(2.05372 + 1.94479i) q^{8} +(-4.70981 + 2.77653i) q^{10} +(-0.0566521 + 0.211428i) q^{11} +(0.727551 + 2.71526i) q^{13} +(-3.33403 + 3.39513i) q^{14} +(1.87291 - 3.53443i) q^{16} +4.23937i q^{17} +(-1.12365 - 1.12365i) q^{19} +(5.56567 + 5.36714i) q^{20} +(0.309540 - 0.00281033i) q^{22} +(-3.33369 - 1.92471i) q^{23} +(-8.61325 + 4.97286i) q^{25} +(3.42462 - 2.01888i) q^{26} +(5.88800 + 3.25835i) q^{28} +(-0.545635 + 2.03634i) q^{29} +(-7.21206 - 4.16388i) q^{31} +(-5.52491 - 1.21464i) q^{32} +(5.77677 - 1.60423i) q^{34} +(-9.19798 + 9.19798i) q^{35} +(-2.66564 - 2.66564i) q^{37} +(-1.10593 + 1.95634i) q^{38} +(5.20739 - 9.61503i) q^{40} +(1.70386 - 2.95117i) q^{41} +(4.68985 + 1.25664i) q^{43} +(-0.120963 - 0.420730i) q^{44} +(-1.36119 + 5.27098i) q^{46} +(-2.34998 - 4.07028i) q^{47} +(-2.16067 + 3.74239i) q^{49} +(10.0356 + 9.85502i) q^{50} +(-4.04693 - 3.90257i) q^{52} +(7.58271 - 7.58271i) q^{53} +0.846209 q^{55} +(2.21189 - 9.25626i) q^{56} +(2.98128 - 0.0270672i) q^{58} +(5.34305 - 1.43167i) q^{59} +(8.69958 + 2.33105i) q^{61} +(-2.94477 + 11.4031i) q^{62} +(0.435568 + 7.98813i) q^{64} +(9.41144 - 5.43370i) q^{65} +(-5.17504 + 1.38665i) q^{67} +(-4.37200 - 7.26463i) q^{68} +(16.0142 + 9.05296i) q^{70} -7.53614i q^{71} +3.22646i q^{73} +(-2.62362 + 4.64104i) q^{74} +(3.08429 + 0.766693i) q^{76} +(0.711397 - 0.190618i) q^{77} +(-4.98587 + 2.87859i) q^{79} +(-15.0724 - 3.45739i) q^{80} +(-4.66616 - 1.20500i) q^{82} +(-4.50604 - 1.20739i) q^{83} +(15.8308 - 4.24186i) q^{85} +(-0.0623381 - 6.86613i) q^{86} +(-0.527532 + 0.324039i) q^{88} +2.96157 q^{89} +(6.68807 - 6.68807i) q^{91} +(7.69756 - 0.139785i) q^{92} +(-4.65709 + 4.74243i) q^{94} +(-3.07166 + 5.32027i) q^{95} +(-7.63883 - 13.2308i) q^{97} +(5.91718 + 1.52806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

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