LMFDB - Embedded newform 432.2.v.a.35.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(35,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			35.7
Character	$\chi$	$=$	432.35
Dual form			432.2.v.a.395.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.714386 - 1.22051i) q^{2} +(-0.979306 + 1.74383i) q^{4} +(0.247419 - 0.923380i) q^{5} +(-1.93471 + 3.35102i) q^{7} +(2.82798 - 0.0505136i) q^{8} +O(q^{10})$	\(q+(-0.714386 - 1.22051i) q^{2} +(-0.979306 + 1.74383i) q^{4} +(0.247419 - 0.923380i) q^{5} +(-1.93471 + 3.35102i) q^{7} +(2.82798 - 0.0505136i) q^{8} +(-1.30375 + 0.357671i) q^{10} +(-0.936987 - 3.49688i) q^{11} +(1.72498 - 6.43770i) q^{13} +(5.47210 - 0.0325780i) q^{14} +(-2.08192 - 3.41550i) q^{16} -3.74282i q^{17} +(3.09199 - 3.09199i) q^{19} +(1.36792 + 1.33573i) q^{20} +(-3.59862 + 3.64173i) q^{22} +(-0.327240 + 0.188932i) q^{23} +(3.53871 + 2.04308i) q^{25} +(-9.08960 + 2.49364i) q^{26} +(-3.94895 - 6.65550i) q^{28} +(-1.10982 - 4.14191i) q^{29} +(0.788179 - 0.455055i) q^{31} +(-2.68137 + 4.98099i) q^{32} +(-4.56816 + 2.67382i) q^{34} +(2.61558 + 2.61558i) q^{35} +(-2.13502 + 2.13502i) q^{37} +(-5.98269 - 1.56494i) q^{38} +(0.653052 - 2.62379i) q^{40} +(-3.66866 - 6.35430i) q^{41} +(2.47404 - 0.662918i) q^{43} +(7.01559 + 1.79057i) q^{44} +(0.464370 + 0.264431i) q^{46} +(0.0726386 - 0.125814i) q^{47} +(-3.98624 - 6.90437i) q^{49} +(-0.0344027 - 5.77859i) q^{50} +(9.53701 + 9.31256i) q^{52} +(5.67083 + 5.67083i) q^{53} -3.46078 q^{55} +(-5.30205 + 9.57435i) q^{56} +(-4.26241 + 4.31347i) q^{58} +(-3.99549 - 1.07059i) q^{59} +(-6.33446 + 1.69731i) q^{61} +(-1.11846 - 0.636898i) q^{62} +(7.99490 - 0.285702i) q^{64} +(-5.51765 - 3.18562i) q^{65} +(1.33594 + 0.357964i) q^{67} +(6.52686 + 3.66537i) q^{68} +(1.32382 - 5.06089i) q^{70} +9.88796i q^{71} -6.65482i q^{73} +(4.13105 + 1.08059i) q^{74} +(2.36391 + 8.41992i) q^{76} +(13.5309 + 3.62561i) q^{77} +(-2.18459 - 1.26127i) q^{79} +(-3.66891 + 1.07734i) q^{80} +(-5.13467 + 9.01707i) q^{82} +(0.261050 - 0.0699481i) q^{83} +(-3.45605 - 0.926045i) q^{85} +(-2.57652 - 2.54603i) q^{86} +(-2.82642 - 9.84177i) q^{88} -5.86860 q^{89} +(18.2356 + 18.2356i) q^{91} +(-0.00899811 - 0.755676i) q^{92} +(-0.205449 + 0.00122314i) q^{94} +(-2.09006 - 3.62010i) q^{95} +(5.07233 - 8.78553i) q^{97} +(-5.57917 + 9.79765i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.714386	−	1.22051i	−0.505147	−	0.863033i
$2$	−0.714386	−	1.22051i	−0.505147	−	0.863033i
$3$		0			0
$3$		0			0
$4$	−0.979306	+	1.74383i	−0.489653	+	0.871917i
$5$	0.247419	−	0.923380i	0.110649	−	0.412948i	−0.888276	−	0.459311i	$-0.848096\pi$
$5$	0.247419	−	0.923380i	0.110649	−	0.412948i	0.998925	+	0.0463628i	$0.0147630\pi$
$6$		0			0
$7$	−1.93471	+	3.35102i	−0.731253	+	1.26657i	0.225094	+	0.974337i	$0.427731\pi$
$7$	−1.93471	+	3.35102i	−0.731253	+	1.26657i	−0.956348	+	0.292231i	$0.905602\pi$
$8$	2.82798	−	0.0505136i	0.999841	−	0.0178592i
$9$		0			0
$10$	−1.30375	+	0.357671i	−0.412282	+	0.113106i
$11$	−0.936987	−	3.49688i	−0.282512	−	1.05435i	−0.950638	−	0.310302i	$-0.899570\pi$
$11$	−0.936987	−	3.49688i	−0.282512	−	1.05435i	0.668126	−	0.744048i	$-0.267097\pi$
$12$		0			0
$13$	1.72498	−	6.43770i	0.478423	−	1.78550i	−0.129587	−	0.991568i	$-0.541365\pi$
$13$	1.72498	−	6.43770i	0.478423	−	1.78550i	0.608010	−	0.793929i	$-0.291968\pi$
$14$	5.47210	−	0.0325780i	1.46248	−	0.00870684i
$15$		0			0
$16$	−2.08192	−	3.41550i	−0.520479	−	0.853874i
$17$		−	3.74282i		−	0.907767i	−0.891061	−	0.453884i	$-0.850038\pi$
$17$		−	3.74282i		−	0.907767i	0.891061	−	0.453884i	$-0.149962\pi$
$18$		0			0
$19$	3.09199	−	3.09199i	0.709351	−	0.709351i	−0.257048	−	0.966399i	$-0.582750\pi$
$19$	3.09199	−	3.09199i	0.709351	−	0.709351i	0.966399	+	0.257048i	$0.0827498\pi$
$20$	1.36792	+	1.33573i	0.305877	+	0.298678i
$21$		0			0
$22$	−3.59862	+	3.64173i	−0.767229	+	0.776419i
$23$	−0.327240	+	0.188932i	−0.0682344	+	0.0393951i	−0.533729	−	0.845656i	$-0.679210\pi$
$23$	−0.327240	+	0.188932i	−0.0682344	+	0.0393951i	0.465495	+	0.885051i	$0.345876\pi$
$24$		0			0
$25$	3.53871	+	2.04308i	0.707742	+	0.408615i
$26$	−9.08960	+	2.49364i	−1.78262	+	0.489044i
$27$		0			0
$28$	−3.94895	−	6.65550i	−0.746282	−	1.25777i
$29$	−1.10982	−	4.14191i	−0.206088	−	0.769133i	−0.989115	−	0.147144i	$-0.952992\pi$
$29$	−1.10982	−	4.14191i	−0.206088	−	0.769133i	0.783027	−	0.621988i	$-0.213675\pi$
$30$		0			0
$31$	0.788179	−	0.455055i	0.141561	−	0.0817303i	−0.427547	−	0.903993i	$-0.640622\pi$
$31$	0.788179	−	0.455055i	0.141561	−	0.0817303i	0.569108	+	0.822263i	$0.307289\pi$
$32$	−2.68137	+	4.98099i	−0.474003	+	0.880523i
$33$		0			0
$34$	−4.56816	+	2.67382i	−0.783433	+	0.458556i
$35$	2.61558	+	2.61558i	0.442114	+	0.442114i
$36$		0			0
$37$	−2.13502	+	2.13502i	−0.350996	+	0.350996i	−0.860480	−	0.509484i	$-0.829836\pi$
$37$	−2.13502	+	2.13502i	−0.350996	+	0.350996i	0.509484	+	0.860480i	$0.329836\pi$
$38$	−5.98269	−	1.56494i	−0.970520	−	0.253867i
$39$		0			0
$40$	0.653052	−	2.62379i	0.103257	−	0.414858i
$41$	−3.66866	−	6.35430i	−0.572948	−	0.992375i	−0.996261	−	0.0863918i	$-0.972466\pi$
$41$	−3.66866	−	6.35430i	−0.572948	−	0.992375i	0.423313	−	0.905983i	$-0.360867\pi$
$42$		0			0
$43$	2.47404	−	0.662918i	0.377288	−	0.101094i	−0.0651910	−	0.997873i	$-0.520766\pi$
$43$	2.47404	−	0.662918i	0.377288	−	0.101094i	0.442479	+	0.896779i	$0.354099\pi$
$44$	7.01559	+	1.79057i	1.05764	+	0.269939i
$45$		0			0
$46$	0.464370	+	0.264431i	0.0684677	+	0.0389882i
$47$	0.0726386	−	0.125814i	0.0105954	−	0.0183518i	−0.860679	−	0.509148i	$-0.829961\pi$
$47$	0.0726386	−	0.125814i	0.0105954	−	0.0183518i	0.871275	+	0.490796i	$0.163294\pi$
$48$		0			0
$49$	−3.98624	−	6.90437i	−0.569463	−	0.986339i
$50$	−0.0344027	−	5.77859i	−0.00486527	−	0.817216i
$51$		0			0
$52$	9.53701	+	9.31256i	1.32254	+	1.29142i
$53$	5.67083	+	5.67083i	0.778948	+	0.778948i	0.979652	−	0.200704i	$-0.0643229\pi$
$53$	5.67083	+	5.67083i	0.778948	+	0.778948i	−0.200704	+	0.979652i	$0.564323\pi$
$54$		0			0
$55$	−3.46078			−0.466652
$56$	−5.30205	+	9.57435i	−0.708517	+	1.27943i
$57$		0			0
$58$	−4.26241	+	4.31347i	−0.559682	+	0.566386i
$59$	−3.99549	−	1.07059i	−0.520169	−	0.139379i	−0.0108242	−	0.999941i	$-0.503446\pi$
$59$	−3.99549	−	1.07059i	−0.520169	−	0.139379i	−0.509345	+	0.860563i	$0.670112\pi$
$60$		0			0
$61$	−6.33446	+	1.69731i	−0.811044	+	0.217319i	−0.640427	−	0.768019i	$-0.721243\pi$
$61$	−6.33446	+	1.69731i	−0.811044	+	0.217319i	−0.170617	+	0.985337i	$0.554576\pi$
$62$	−1.11846	−	0.636898i	−0.142045	−	0.0808861i
$63$		0			0
$64$	7.99490	−	0.285702i	0.999362	−	0.0357128i
$65$	−5.51765	−	3.18562i	−0.684381	−	0.395127i
$66$		0			0
$67$	1.33594	+	0.357964i	0.163211	+	0.0437322i	0.339499	−	0.940606i	$-0.389742\pi$
$67$	1.33594	+	0.357964i	0.163211	+	0.0437322i	−0.176288	+	0.984339i	$0.556409\pi$
$68$	6.52686	+	3.66537i	0.791498	+	0.444491i
$69$		0			0
$70$	1.32382	−	5.06089i	0.158227	−	0.604892i
$71$			9.88796i			1.17348i	0.809774	+	0.586742i	$0.199590\pi$
$71$			9.88796i			1.17348i	−0.809774	+	0.586742i	$0.800410\pi$
$72$		0			0
$73$		−	6.65482i		−	0.778888i	−0.921050	−	0.389444i	$-0.872667\pi$
$73$		−	6.65482i		−	0.778888i	0.921050	−	0.389444i	$-0.127333\pi$
$74$	4.13105	+	1.08059i	0.480225	+	0.125617i
$75$		0			0
$76$	2.36391	+	8.41992i	0.271159	+	0.965831i
$77$	13.5309	+	3.62561i	1.54199	+	0.413176i
$78$		0			0
$79$	−2.18459	−	1.26127i	−0.245786	−	0.141904i	0.372047	−	0.928214i	$-0.378656\pi$
$79$	−2.18459	−	1.26127i	−0.245786	−	0.141904i	−0.617833	+	0.786309i	$0.711989\pi$
$80$	−3.66891	+	1.07734i	−0.410196	+	0.120451i
$81$		0			0
$82$	−5.13467	+	9.01707i	−0.567030	+	0.995769i
$83$	0.261050	−	0.0699481i	0.0286539	−	0.00767780i	−0.244464	−	0.969658i	$-0.578612\pi$
$83$	0.261050	−	0.0699481i	0.0286539	−	0.00767780i	0.273118	+	0.961981i	$0.411945\pi$
$84$		0			0
$85$	−3.45605	−	0.926045i	−0.374861	−	0.100444i
$86$	−2.57652	−	2.54603i	−0.277834	−	0.274545i
$87$		0			0
$88$	−2.82642	−	9.84177i	−0.301297	−	1.04914i
$89$	−5.86860			−0.622070			−0.311035	−	0.950398i	$-0.600676\pi$
$89$	−5.86860			−0.622070			−0.311035	+	0.950398i	$0.600676\pi$
$90$		0			0
$91$	18.2356	+	18.2356i	1.91161	+	1.91161i
$92$	−0.00899811	−	0.755676i	−0.000938117	−	0.0787847i
$93$		0			0
$94$	−0.205449	+	0.00122314i	−0.0211905	+	0.000126157i
$95$	−2.09006	−	3.62010i	−0.214436	−	0.371414i
$96$		0			0
$97$	5.07233	−	8.78553i	0.515017	−	0.892035i	−0.484831	−	0.874608i	$-0.661119\pi$
$97$	5.07233	−	8.78553i	0.515017	−	0.892035i	0.999848	−	0.0174277i	$-0.00554769\pi$
$98$	−5.57917	+	9.79765i	−0.563581	+	0.989712i
$99$		0			0
$100$	−7.02827	+	4.17013i	−0.702827	+	0.417013i
$101$	−0.725673	+	0.194443i	−0.0722072	+	0.0193479i	−0.294742	−	0.955577i	$-0.595234\pi$
$101$	−0.725673	+	0.194443i	−0.0722072	+	0.0193479i	0.222535	+	0.974925i	$0.428567\pi$
$102$		0			0
$103$	6.93904	+	12.0188i	0.683724	+	1.18424i	0.973836	+	0.227252i	$0.0729741\pi$
$103$	6.93904	+	12.0188i	0.683724	+	1.18424i	−0.290112	+	0.956993i	$0.593693\pi$
$104$	4.55300	−	18.2928i	0.446459	−	1.79376i
$105$		0			0
$106$	2.87016	−	10.9725i	0.278775	−	1.06574i
$107$	1.56287	−	1.56287i	0.151088	−	0.151088i	−0.627516	−	0.778604i	$-0.715928\pi$
$107$	1.56287	−	1.56287i	0.151088	−	0.151088i	0.778604	+	0.627516i	$0.215928\pi$
$108$		0			0
$109$	6.71432	+	6.71432i	0.643115	+	0.643115i	0.951320	−	0.308205i	$-0.0997283\pi$
$109$	6.71432	+	6.71432i	0.643115	+	0.643115i	−0.308205	+	0.951320i	$0.599728\pi$
$110$	2.47233	+	4.22393i	0.235728	+	0.402736i
$111$		0			0
$112$	15.4733	−	0.368545i	1.46209	−	0.0348243i
$113$	13.7148	−	7.91823i	1.29018	−	0.744885i	0.311492	−	0.950249i	$-0.399171\pi$
$113$	13.7148	−	7.91823i	1.29018	−	0.744885i	0.978686	+	0.205364i	$0.0658379\pi$
$114$		0			0
$115$	0.0934909	+	0.348913i	0.00871807	+	0.0325363i
$116$	8.30965	+	2.12085i	0.771532	+	0.196916i
$117$		0			0
$118$	1.54765	+	5.64137i	0.142473	+	0.519330i
$119$	12.5423	+	7.24129i	1.14975	+	0.663808i
$120$		0			0
$121$	−1.82398	+	1.05307i	−0.165816	+	0.0957339i
$122$	6.59684	+	6.51876i	0.597250	+	0.590180i
$123$		0			0
$124$	0.0216725	+	1.82009i	0.00194625	+	0.163449i
$125$	6.14189	−	6.14189i	0.549347	−	0.549347i
$126$		0			0
$127$		−	10.4492i		−	0.927219i	−0.886040	−	0.463609i	$-0.846554\pi$
$127$		−	10.4492i		−	0.927219i	0.886040	−	0.463609i	$-0.153446\pi$
$128$	−6.06014	−	9.55378i	−0.535646	−	0.844443i
$129$		0			0
$130$	0.0536416	+	9.01013i	0.00470468	+	0.790241i
$131$	−4.90101	+	18.2908i	−0.428203	+	1.59807i	0.328625	+	0.944461i	$0.393415\pi$
$131$	−4.90101	+	18.2908i	−0.428203	+	1.59807i	−0.756828	+	0.653614i	$0.773252\pi$
$132$		0			0
$133$	4.37921	+	16.3434i	0.379726	+	1.41716i
$134$	−0.517476	−	1.88626i	−0.0447031	−	0.162948i
$135$		0			0
$136$	−0.189063	−	10.5846i	−0.0162120	−	0.907623i
$137$	−7.93788	+	13.7488i	−0.678178	+	1.17464i	0.297350	+	0.954768i	$0.403897\pi$
$137$	−7.93788	+	13.7488i	−0.678178	+	1.17464i	−0.975529	+	0.219871i	$0.929436\pi$
$138$		0			0
$139$	4.40461	−	16.4382i	0.373594	−	1.39427i	−0.481794	−	0.876285i	$-0.660015\pi$
$139$	4.40461	−	16.4382i	0.373594	−	1.39427i	0.855388	−	0.517988i	$-0.173319\pi$
$140$	−7.12260	+	1.99969i	−0.601970	+	0.169004i
$141$		0			0
$142$	12.0684	−	7.06381i	1.01276	−	0.592782i
$143$	−24.1282			−2.01770
$144$		0			0
$145$	−4.09914			−0.340415
$146$	−8.12230	+	4.75411i	−0.672206	+	0.393453i
$147$		0			0
$148$	−1.63228	−	5.81397i	−0.134173	−	0.477905i
$149$	1.75301	−	6.54234i	0.143613	−	0.535969i	−0.856201	−	0.516643i	$-0.827181\pi$
$149$	1.75301	−	6.54234i	0.143613	−	0.535969i	0.999813	−	0.0193260i	$-0.00615204\pi$
$150$		0			0
$151$	−4.39506	+	7.61246i	−0.357665	+	0.619493i	−0.987570	−	0.157178i	$-0.949760\pi$
$151$	−4.39506	+	7.61246i	−0.357665	+	0.619493i	0.629906	+	0.776672i	$0.283094\pi$
$152$	8.58788	−	8.90026i	0.696569	−	0.721906i
$153$		0			0
$154$	−5.24121	−	19.1048i	−0.422349	−	1.53951i
$155$	−0.225179	−	0.840378i	−0.0180868	−	0.0675008i
$156$		0			0
$157$	1.95778	−	7.30654i	0.156248	−	0.583126i	−0.842747	−	0.538310i	$-0.819063\pi$
$157$	1.95778	−	7.30654i	0.156248	−	0.583126i	0.998995	−	0.0448162i	$-0.0142702\pi$
$158$	0.0212382	+	3.56736i	0.00168962	+	0.283804i
$159$		0			0
$160$	3.93593	+	3.70831i	0.311162	+	0.293168i
$161$		−	1.46212i		−	0.115231i
$162$		0			0
$163$	−3.88439	+	3.88439i	−0.304249	+	0.304249i	−0.842674	−	0.538425i	$-0.819020\pi$
$163$	−3.88439	+	3.88439i	−0.304249	+	0.304249i	0.538425	+	0.842674i	$0.319020\pi$
$164$	14.6736	−	0.174724i	1.14581	−	0.0136436i
$165$		0			0
$166$	−0.271863	−	0.268645i	−0.0211006	−	0.0208509i
$167$	−16.2578	+	9.38644i	−1.25807	+	0.726345i	−0.972698	−	0.232074i	$-0.925449\pi$
$167$	−16.2578	+	9.38644i	−1.25807	+	0.726345i	−0.285367	+	0.958418i	$0.592116\pi$
$168$		0			0
$169$	−27.2101	−	15.7098i	−2.09309	−	1.20844i
$170$	1.33870	+	4.87970i	0.102674	+	0.374256i
$171$		0			0
$172$	−1.26683	+	4.96352i	−0.0965947	+	0.378465i
$173$	1.19743	+	4.46886i	0.0910387	+	0.339761i	0.996389	−	0.0849043i	$-0.0270585\pi$
$173$	1.19743	+	4.46886i	0.0910387	+	0.339761i	−0.905350	+	0.424665i	$0.860392\pi$
$174$		0			0
$175$	−13.6928	+	7.90554i	−1.03508	+	0.597603i
$176$	−9.99287	+	10.4805i	−0.753241	+	0.789998i
$177$		0			0
$178$	4.19244	+	7.16270i	0.314237	+	0.536867i
$179$	−16.7079	−	16.7079i	−1.24881	−	1.24881i	−0.956248	−	0.292557i	$-0.905494\pi$
$179$	−16.7079	−	16.7079i	−1.24881	−	1.24881i	−0.292557	−	0.956248i	$-0.594506\pi$
$180$		0			0
$181$	−3.87025	+	3.87025i	−0.287673	+	0.287673i	−0.836160	−	0.548486i	$-0.815204\pi$
$181$	−3.87025	+	3.87025i	−0.287673	+	0.287673i	0.548486	+	0.836160i	$0.315204\pi$
$182$	9.22952	−	35.2840i	0.684138	−	2.61542i
$183$		0			0
$184$	−0.915885	+	0.550826i	−0.0675199	+	0.0406075i
$185$	1.44319	+	2.49968i	0.106106	+	0.183780i
$186$		0			0
$187$	−13.0882	+	3.50698i	−0.957105	+	0.256455i
$188$	0.148263	+	0.249880i	0.0108132	+	0.0182244i
$189$		0			0
$190$	−2.92527	+	5.13710i	−0.212221	+	0.372684i
$191$	−2.49854	+	4.32759i	−0.180788	+	0.313134i	−0.942149	−	0.335194i	$-0.891198\pi$
$191$	−2.49854	+	4.32759i	−0.180788	+	0.313134i	0.761361	+	0.648328i	$0.224531\pi$
$192$		0			0
$193$	8.77894	+	15.2056i	0.631922	+	1.09452i	0.987158	+	0.159744i	$0.0510670\pi$
$193$	8.77894	+	15.2056i	0.631922	+	1.09452i	−0.355237	+	0.934776i	$0.615600\pi$
$194$	−14.3465	+	0.0854112i	−1.03002	+	0.00613217i
$195$		0			0
$196$	15.9438	−	0.189849i	1.13885	−	0.0135606i
$197$	14.4859	+	14.4859i	1.03208	+	1.03208i	0.999468	+	0.0326073i	$0.0103811\pi$
$197$	14.4859	+	14.4859i	1.03208	+	1.03208i	0.0326073	+	0.999468i	$0.489619\pi$
$198$		0			0
$199$	−0.627801			−0.0445037			−0.0222518	−	0.999752i	$-0.507084\pi$
$199$	−0.627801			−0.0445037			−0.0222518	+	0.999752i	$0.507084\pi$
$200$	10.1106	+	5.59902i	0.714927	+	0.395910i
$201$		0			0
$202$	0.755731	+	0.746786i	0.0531731	+	0.0525437i
$203$	16.0268	+	4.29437i	1.12486	+	0.301406i
$204$		0			0
$205$	−6.77513	+	1.81539i	−0.473196	+	0.126792i
$206$	9.71192	−	17.0552i	0.676662	−	1.18829i
$207$		0			0
$208$	−25.5792	+	7.51111i	−1.77360	+	0.520802i
$209$	−13.7095	−	7.91517i	−0.948305	−	0.547504i
$210$		0			0
$211$	3.81624	+	1.02256i	0.262721	+	0.0703959i	0.387775	−	0.921754i	$-0.373244\pi$
$211$	3.81624	+	1.02256i	0.262721	+	0.0703959i	−0.125054	+	0.992150i	$0.539910\pi$
$212$	−15.4425	+	4.33551i	−1.06059	+	0.297764i
$213$		0			0
$214$	−3.02399	−	0.791010i	−0.206715	−	0.0540723i
$215$		−	2.44850i		−	0.166986i
$216$		0			0
$217$			3.52161i			0.239062i
$218$	3.39830	−	12.9915i	0.230162	−	0.879897i
$219$		0			0
$220$	3.38917	−	6.03503i	0.228498	−	0.406882i
$221$	−24.0952	−	6.45628i	−1.62082	−	0.434296i
$222$		0			0
$223$	−1.71289	−	0.988940i	−0.114704	−	0.0662243i	0.441550	−	0.897236i	$-0.354429\pi$
$223$	−1.71289	−	0.988940i	−0.114704	−	0.0662243i	−0.556254	+	0.831012i	$0.687762\pi$
$224$	−11.5037	−	18.6221i	−0.768626	−	1.24424i
$225$		0			0
$226$	−19.4619	−	11.0824i	−1.29459	−	0.737190i
$227$	28.7220	−	7.69603i	1.90634	−	0.510803i	0.911252	−	0.411848i	$-0.135117\pi$
$227$	28.7220	−	7.69603i	1.90634	−	0.510803i	0.995092	−	0.0989551i	$-0.0315500\pi$
$228$		0			0
$229$	−14.2508	−	3.81849i	−0.941720	−	0.252333i	−0.244875	−	0.969555i	$-0.578747\pi$
$229$	−14.2508	−	3.81849i	−0.941720	−	0.252333i	−0.696845	+	0.717222i	$0.745414\pi$
$230$	0.359064	−	0.363365i	0.0236760	−	0.0239596i
$231$		0			0
$232$	−3.34777	−	11.6571i	−0.219792	−	0.765329i
$233$	11.5384			0.755904			0.377952	−	0.925825i	$-0.376628\pi$
$233$	11.5384			0.755904			0.377952	+	0.925825i	$0.376628\pi$
$234$		0			0
$235$	−0.0982018	−	0.0982018i	−0.00640598	−	0.00640598i
$236$	5.77974	−	5.91904i	0.376229	−	0.385297i
$237$		0			0
$238$	−0.121934	−	20.4811i	−0.00790378	−	1.32759i
$239$	8.60624	+	14.9065i	0.556692	+	0.964218i	0.997770	+	0.0667495i	$0.0212628\pi$
$239$	8.60624	+	14.9065i	0.556692	+	0.964218i	−0.441078	+	0.897469i	$0.645404\pi$
$240$		0			0
$241$	4.64695	−	8.04875i	0.299336	−	0.518466i	−0.676648	−	0.736307i	$-0.736568\pi$
$241$	4.64695	−	8.04875i	0.299336	−	0.518466i	0.975984	+	0.217841i	$0.0699014\pi$
$242$	2.58831	+	1.47389i	0.166383	+	0.0947451i
$243$		0			0
$244$	3.24354	−	12.7084i	0.207647	−	0.813574i
$245$	−7.36163	+	1.97254i	−0.470317	+	0.126021i
$246$		0			0
$247$	−14.5717	−	25.2389i	−0.927175	−	1.60591i
$248$	2.20596	−	1.32670i	0.140079	−	0.0842455i
$249$		0			0
$250$	−11.8839	−	3.10858i	−0.751606	−	0.196604i
$251$	20.7722	−	20.7722i	1.31113	−	1.31113i	0.390545	−	0.920584i	$-0.372286\pi$
$251$	20.7722	−	20.7722i	1.31113	−	1.31113i	0.920584	−	0.390545i	$-0.127714\pi$
$252$		0			0
$253$	0.967295	+	0.967295i	0.0608133	+	0.0608133i
$254$	−12.7534	+	7.46478i	−0.800221	+	0.468382i
$255$		0			0
$256$	−7.33124	+	14.2216i	−0.458202	+	0.888848i
$257$	1.51801	−	0.876421i	0.0946906	−	0.0546697i	−0.451907	−	0.892065i	$-0.649256\pi$
$257$	1.51801	−	0.876421i	0.0946906	−	0.0546697i	0.546598	+	0.837395i	$0.315923\pi$
$258$		0			0
$259$	−3.02385	−	11.2852i	−0.187893	−	0.701227i
$260$	10.9587	−	6.50218i	0.679628	−	0.403248i
$261$		0			0
$262$	25.8254	−	7.08494i	1.59550	−	0.437709i
$263$	−0.172109	−	0.0993674i	−0.0106127	−	0.00612726i	0.494684	−	0.869073i	$-0.335284\pi$
$263$	−0.172109	−	0.0993674i	−0.0106127	−	0.00612726i	−0.505297	+	0.862946i	$0.668617\pi$
$264$		0			0
$265$	6.63940	−	3.83326i	0.407855	−	0.235475i
$266$	16.8189	−	17.0204i	1.03124	−	1.04359i
$267$		0			0
$268$	−1.93252	+	1.97910i	−0.118048	+	0.120893i
$269$	−16.7454	+	16.7454i	−1.02098	+	1.02098i	−0.0212085	+	0.999775i	$0.506751\pi$
$269$	−16.7454	+	16.7454i	−1.02098	+	1.02098i	−0.999775	+	0.0212085i	$0.993249\pi$
$270$		0			0
$271$		−	16.8714i		−	1.02487i	−0.858727	−	0.512433i	$-0.828744\pi$
$271$		−	16.8714i		−	1.02487i	0.858727	−	0.512433i	$-0.171256\pi$
$272$	−12.7836	+	7.79224i	−0.775119	+	0.472474i
$273$		0			0
$274$	22.4513	−	0.133663i	1.35633	−	0.00807489i
$275$	3.82867	−	14.2888i	0.230878	−	0.861647i
$276$		0			0
$277$	7.58262	+	28.2987i	0.455595	+	1.70031i	0.686331	+	0.727289i	$0.259220\pi$
$277$	7.58262	+	28.2987i	0.455595	+	1.70031i	−0.230736	+	0.973016i	$0.574113\pi$
$278$	−23.2097	+	6.36735i	−1.39202	+	0.381888i
$279$		0			0
$280$	7.52893	+	7.26469i	0.449940	+	0.434148i
$281$	−3.41297	+	5.91144i	−0.203601	+	0.352647i	−0.949686	−	0.313203i	$-0.898598\pi$
$281$	−3.41297	+	5.91144i	−0.203601	+	0.352647i	0.746085	+	0.665851i	$0.231931\pi$
$282$		0			0
$283$	−2.54482	+	9.49738i	−0.151274	+	0.564561i	0.848122	+	0.529801i	$0.177733\pi$
$283$	−2.54482	+	9.49738i	−0.151274	+	0.564561i	−0.999396	+	0.0347600i	$0.988933\pi$
$284$	−17.2430	−	9.68334i	−1.02318	−	0.574600i
$285$		0			0
$286$	17.2368	+	29.4488i	1.01923	+	1.74134i
$287$	28.3912			1.67588
$288$		0			0
$289$	2.99129			0.175959
$290$	2.92837	+	5.00306i	0.171960	+	0.293790i
$291$		0			0
$292$	11.6049	+	6.51711i	0.679126	+	0.381385i
$293$	−0.497626	+	1.85716i	−0.0290716	+	0.108497i	−0.978937	−	0.204162i	$-0.934553\pi$
$293$	−0.497626	+	1.85716i	−0.0290716	+	0.108497i	0.949865	+	0.312659i	$0.101220\pi$
$294$		0			0
$295$	−1.97712	+	3.42448i	−0.115112	+	0.199381i
$296$	−5.92995	+	6.14564i	−0.344671	+	0.357208i
$297$		0			0
$298$	−9.23734	+	2.53418i	−0.535105	+	0.146801i
$299$	0.651808	+	2.43258i	0.0376950	+	0.140680i
$300$		0			0
$301$	−2.56512	+	9.57314i	−0.147851	+	0.551787i
$302$	12.4309	−	0.0740068i	0.715316	−	0.00425861i
$303$		0			0
$304$	−16.9979	−	4.12341i	−0.974899	−	0.236494i
$305$			6.26906i			0.358965i
$306$		0			0
$307$	−9.86559	+	9.86559i	−0.563059	+	0.563059i	−0.930175	−	0.367116i	$-0.880345\pi$
$307$	−9.86559	+	9.86559i	−0.563059	+	0.563059i	0.367116	+	0.930175i	$0.380345\pi$
$308$	−19.5734	+	20.0452i	−1.11530	+	1.14218i
$309$		0			0
$310$	−0.864828	+	0.875187i	−0.0491189	+	0.0497073i
$311$	−3.17139	+	1.83100i	−0.179833	+	0.103827i	−0.587214	−	0.809432i	$-0.699775\pi$
$311$	−3.17139	+	1.83100i	−0.179833	+	0.103827i	0.407381	+	0.913258i	$0.366442\pi$
$312$		0			0
$313$	−1.08050	−	0.623827i	−0.0610735	−	0.0352608i	0.469152	−	0.883117i	$-0.344560\pi$
$313$	−1.08050	−	0.623827i	−0.0610735	−	0.0352608i	−0.530226	+	0.847856i	$0.677893\pi$
$314$	−10.3163	+	2.83019i	−0.582185	+	0.159717i
$315$		0			0
$316$	4.33884	−	2.57439i	0.244079	−	0.144821i
$317$	0.407988	+	1.52263i	0.0229149	+	0.0855195i	0.976436	−	0.215806i	$-0.0692377\pi$
$317$	0.407988	+	1.52263i	0.0229149	+	0.0855195i	−0.953521	+	0.301325i	$0.902571\pi$
$318$		0			0
$319$	−13.4439	+	7.76183i	−0.752713	+	0.434579i
$320$	1.71428	−	7.45302i	0.0958310	−	0.416636i
$321$		0			0
$322$	−1.78454	+	1.04452i	−0.0994484	+	0.0582087i
$323$	−11.5728	−	11.5728i	−0.643925	−	0.643925i
$324$		0			0
$325$	19.2569	−	19.2569i	1.06818	−	1.06818i
$326$	7.51590	+	1.96600i	0.416267	+	0.108886i
$327$		0			0
$328$	−10.6959	−	17.7845i	−0.590580	−	0.981984i
$329$	0.281070	+	0.486828i	0.0154959	+	0.0268397i
$330$		0			0
$331$	9.11372	−	2.44201i	0.500935	−	0.134225i	0.000501334	−	1.00000i	$-0.499840\pi$
$331$	9.11372	−	2.44201i	0.500935	−	0.134225i	0.500434	+	0.865775i	$0.333174\pi$
$332$	−0.133670	+	0.523728i	−0.00733609	+	0.0287433i
$333$		0			0
$334$	23.0706	+	13.1373i	1.26237	+	0.718842i
$335$	0.661073	−	1.14501i	0.0361183	−	0.0625587i
$336$		0			0
$337$	6.84951	+	11.8637i	0.373117	+	0.646257i	0.990043	−	0.140764i	$-0.0449558\pi$
$337$	6.84951	+	11.8637i	0.373117	+	0.646257i	−0.616927	+	0.787021i	$0.711622\pi$
$338$	0.264532	+	44.4332i	0.0143886	+	2.41685i
$339$		0			0
$340$	4.99940	−	5.11989i	0.271130	−	0.277665i
$341$	−2.32979	−	2.32979i	−0.126165	−	0.126165i
$342$		0			0
$343$	3.76296			0.203181
$344$	6.96305	−	1.99969i	0.375423	−	0.107816i
$345$		0			0
$346$	4.59888	−	4.65396i	0.247237	−	0.250199i
$347$	−4.97851	−	1.33399i	−0.267260	−	0.0716122i	0.122700	−	0.992444i	$-0.460845\pi$
$347$	−4.97851	−	1.33399i	−0.267260	−	0.0716122i	−0.389960	+	0.920832i	$0.627511\pi$
$348$		0			0
$349$	22.5875	−	6.05230i	1.20908	−	0.323972i	0.402679	−	0.915341i	$-0.368079\pi$
$349$	22.5875	−	6.05230i	1.20908	−	0.323972i	0.806401	+	0.591369i	$0.201412\pi$
$350$	19.4308	+	11.0646i	1.03862	+	0.591430i
$351$		0			0
$352$	19.9304	+	4.70931i	1.06229	+	0.251007i
$353$	25.4729	+	14.7068i	1.35578	+	0.782762i	0.989052	−	0.147564i	$-0.0471433\pi$
$353$	25.4729	+	14.7068i	1.35578	+	0.782762i	0.366732	+	0.930327i	$0.380477\pi$
$354$		0			0
$355$	9.13034	+	2.44647i	0.484588	+	0.129845i
$356$	5.74715	−	10.2339i	0.304599	−	0.542393i
$357$		0			0
$358$	−8.45632	+	32.3281i	−0.446931	+	1.70859i
$359$		−	21.1351i		−	1.11547i	−0.830020	−	0.557734i	$-0.811671\pi$
$359$		−	21.1351i		−	1.11547i	0.830020	−	0.557734i	$-0.188329\pi$
$360$		0			0
$361$		−	0.120784i		−	0.00635708i
$362$	7.48854	+	1.95884i	0.393589	+	0.102954i
$363$		0			0
$364$	−49.6580	+	13.9416i	−2.60279	+	0.730738i
$365$	−6.14493	−	1.64653i	−0.321640	−	0.0861833i
$366$		0			0
$367$	19.9277	+	11.5053i	1.04022	+	0.600569i	0.919895	−	0.392166i	$-0.128274\pi$
$367$	19.9277	+	11.5053i	1.04022	+	0.600569i	0.120322	+	0.992735i	$0.461607\pi$
$368$	1.32659	+	0.724347i	0.0691531	+	0.0377592i
$369$		0			0
$370$	2.01990	−	3.54717i	0.105010	−	0.184409i
$371$	−29.9745	+	8.03165i	−1.55620	+	0.416982i
$372$		0			0
$373$	9.82636	+	2.63297i	0.508790	+	0.136330i	0.504076	−	0.863659i	$-0.331833\pi$
$373$	9.82636	+	2.63297i	0.508790	+	0.136330i	0.00471336	+	0.999989i	$0.498500\pi$
$374$	13.6303	+	13.4690i	0.704808	+	0.696466i
$375$		0			0
$376$	0.199065	−	0.359468i	0.0102660	−	0.0185381i
$377$	−28.5788			−1.47188
$378$		0			0
$379$	−15.2258	−	15.2258i	−0.782098	−	0.782098i	0.198086	−	0.980185i	$-0.436527\pi$
$379$	−15.2258	−	15.2258i	−0.782098	−	0.782098i	−0.980185	+	0.198086i	$0.936527\pi$
$380$	8.35966	−	0.0995415i	0.428842	−	0.00510637i
$381$		0			0
$382$	7.06680	−	0.0420720i	0.361569	−	0.00215259i
$383$	−4.43034	−	7.67358i	−0.226380	−	0.392102i	0.730353	−	0.683070i	$-0.239356\pi$
$383$	−4.43034	−	7.67358i	−0.226380	−	0.392102i	−0.956733	+	0.290969i	$0.906022\pi$
$384$		0			0
$385$	6.69563	−	11.5972i	0.341241	−	0.591046i
$386$	12.2871	−	21.5775i	0.625395	−	1.09826i
$387$		0			0
$388$	10.3531	+	17.4490i	0.525601	+	0.885840i
$389$	29.6607	−	7.94756i	1.50386	−	0.402957i	0.589467	−	0.807792i	$-0.299338\pi$
$389$	29.6607	−	7.94756i	1.50386	−	0.402957i	0.914390	+	0.404835i	$0.132671\pi$
$390$		0			0
$391$	0.707140	+	1.22480i	0.0357616	+	0.0619409i
$392$	−11.6218	−	19.3240i	−0.586988	−	0.976012i
$393$		0			0
$394$	7.33170	−	28.0287i	0.369366	−	1.41207i
$395$	−1.70514	+	1.70514i	−0.0857951	+	0.0857951i
$396$		0			0
$397$	13.1585	+	13.1585i	0.660408	+	0.660408i	0.955476	−	0.295068i	$-0.0953425\pi$
$397$	13.1585	+	13.1585i	0.660408	+	0.660408i	−0.295068	+	0.955476i	$0.595342\pi$
$398$	0.448492	+	0.766240i	0.0224809	+	0.0384082i
$399$		0			0
$400$	−0.389187	−	16.3400i	−0.0194594	−	0.816999i
$401$	−30.5262	+	17.6243i	−1.52440	+	0.880115i	−0.524822	+	0.851212i	$0.675868\pi$
$401$	−30.5262	+	17.6243i	−1.52440	+	0.880115i	−0.999582	+	0.0289028i	$0.990799\pi$
$402$		0			0
$403$	−1.56992	−	5.85902i	−0.0782033	−	0.291859i
$404$	0.371579	−	1.45587i	0.0184867	−	0.0724324i
$405$		0			0
$406$	−6.20798	−	22.6288i	−0.308097	−	1.12305i
$407$	9.46642	+	5.46544i	0.469233	+	0.270912i
$408$		0			0
$409$	−1.13193	+	0.653522i	−0.0559705	+	0.0323146i	−0.527724	−	0.849416i	$-0.676955\pi$
$409$	−1.13193	+	0.653522i	−0.0559705	+	0.0323146i	0.471754	+	0.881730i	$0.343621\pi$
$410$	7.05577	+	6.97225i	0.348459	+	0.344335i
$411$		0			0
$412$	−27.7542	+	0.330479i	−1.36735	+	0.0162815i
$413$	11.3177	−	11.3177i	0.556908	−	0.556908i
$414$		0			0
$415$		−	0.258355i		−	0.0126821i
$416$	27.4408	+	25.8539i	1.34540	+	1.26759i
$417$		0			0
$418$	0.133281	+	22.3871i	0.00651898	+	1.09499i
$419$	1.26804	−	4.73240i	0.0619480	−	0.231193i	−0.928010	−	0.372555i	$-0.878482\pi$
$419$	1.26804	−	4.73240i	0.0619480	−	0.231193i	0.989958	+	0.141362i	$0.0451483\pi$
$420$		0			0
$421$	−3.68148	−	13.7395i	−0.179425	−	0.669621i	−0.995756	−	0.0920372i	$-0.970662\pi$
$421$	−3.68148	−	13.7395i	−0.179425	−	0.669621i	0.816331	−	0.577584i	$-0.196005\pi$
$422$	−1.47822	−	5.38828i	−0.0719587	−	0.262297i
$423$		0			0
$424$	16.3234	+	15.7505i	0.792735	+	0.764912i
$425$	7.64687	−	13.2448i	0.370928	−	0.642465i
$426$		0			0
$427$	6.56763	−	24.5107i	0.317830	−	1.18616i
$428$	1.19485	+	4.25590i	0.0577555	+	0.205717i
$429$		0			0
$430$	−2.98843	+	1.74917i	−0.144115	+	0.0843527i
$431$	−28.6229			−1.37871			−0.689357	−	0.724422i	$-0.742107\pi$
$431$	−28.6229			−1.37871			−0.689357	+	0.724422i	$0.742107\pi$
$432$		0			0
$433$	−15.4438			−0.742181			−0.371091	−	0.928597i	$-0.621016\pi$
$433$	−15.4438			−0.742181			−0.371091	+	0.928597i	$0.621016\pi$
$434$	4.29817	−	2.51579i	0.206319	−	0.120762i
$435$		0			0
$436$	−18.2840	+	5.13328i	−0.875646	+	0.245840i
$437$	−0.427647	+	1.59600i	−0.0204571	+	0.0763471i
$438$		0			0
$439$	7.33448	−	12.7037i	0.350056	−	0.606314i	−0.636203	−	0.771522i	$-0.719496\pi$
$439$	7.33448	−	12.7037i	0.350056	−	0.606314i	0.986259	+	0.165207i	$0.0528293\pi$
$440$	−9.78701	+	0.174817i	−0.466577	+	0.00833405i
$441$		0			0
$442$	9.33326	+	34.0207i	0.443938	+	1.61820i
$443$	−3.92938	−	14.6646i	−0.186690	−	0.696738i	−0.994262	−	0.106969i	$-0.965886\pi$
$443$	−3.92938	−	14.6646i	−0.186690	−	0.696738i	0.807572	−	0.589769i	$-0.200781\pi$
$444$		0			0
$445$	−1.45200	+	5.41894i	−0.0688315	+	0.256883i
$446$	0.0166524	+	2.79709i	0.000788515	+	0.132446i
$447$		0			0
$448$	−14.5104	+	27.3438i	−0.685554	+	1.29188i
$449$			24.2954i			1.14657i	0.819356	+	0.573285i	$0.194331\pi$
$449$			24.2954i			1.14657i	−0.819356	+	0.573285i	$0.805669\pi$
$450$		0			0
$451$	−18.7828	+	18.7828i	−0.884446	+	0.884446i
$452$	0.377114	+	31.6707i	0.0177380	+	1.48966i
$453$		0			0
$454$	−29.9117	−	29.5576i	−1.40382	−	1.38721i
$455$	21.3502	−	12.3265i	1.00091	−	0.577877i
$456$		0			0
$457$	28.9197	+	16.6968i	1.35281	+	0.781043i	0.988642	−	0.150292i	$-0.0480213\pi$
$457$	28.9197	+	16.6968i	1.35281	+	0.781043i	0.364164	+	0.931335i	$0.381355\pi$
$458$	5.52005	+	20.1212i	0.257935	+	0.940201i
$459$		0			0
$460$	−0.700002	−	0.178660i	−0.0326378	−	0.00833006i
$461$	−1.92845	−	7.19708i	−0.0898170	−	0.335201i	0.906366	−	0.422494i	$-0.138845\pi$
$461$	−1.92845	−	7.19708i	−0.0898170	−	0.335201i	−0.996183	+	0.0872924i	$0.972179\pi$
$462$		0			0
$463$	25.3264	−	14.6222i	1.17702	−	0.679550i	0.221693	−	0.975116i	$-0.428842\pi$
$463$	25.3264	−	14.6222i	1.17702	−	0.679550i	0.955322	+	0.295566i	$0.0955083\pi$
$464$	−11.8361	+	12.4137i	−0.549478	+	0.576291i
$465$		0			0
$466$	−8.24285	−	14.0827i	−0.381843	−	0.652371i
$467$	26.1748	+	26.1748i	1.21123	+	1.21123i	0.970623	+	0.240604i	$0.0773455\pi$
$467$	26.1748	+	26.1748i	1.21123	+	1.21123i	0.240604	+	0.970623i	$0.422654\pi$
$468$		0			0
$469$	−3.78421	+	3.78421i	−0.174738	+	0.174738i
$470$	−0.0497027	+	0.190011i	−0.00229261	+	0.00876453i
$471$		0			0
$472$	−11.3532	−	2.82577i	−0.522575	−	0.130067i
$473$	−4.63630	−	8.03030i	−0.213177	−	0.369234i
$474$		0			0
$475$	17.2588	−	4.62449i	0.791889	−	0.212186i
$476$	−24.9103	+	14.7802i	−1.14176	+	0.677450i
$477$		0			0
$478$	12.0453	−	21.1530i	0.550941	−	0.967515i
$479$	11.3632	−	19.6817i	0.519199	−	0.899279i	−0.480552	−	0.876966i	$-0.659564\pi$
$479$	11.3632	−	19.6817i	0.519199	−	0.899279i	0.999751	−	0.0223127i	$-0.00710295\pi$
$480$		0			0
$481$	10.0618	+	17.4275i	0.458777	+	0.794626i
$482$	−13.1433	+	0.0782484i	−0.598662	+	0.00356412i
$483$		0			0
$484$	−0.0501537	−	4.21199i	−0.00227972	−	0.191454i
$485$	−6.85739	−	6.85739i	−0.311378	−	0.311378i
$486$		0			0
$487$	−1.44462			−0.0654620			−0.0327310	−	0.999464i	$-0.510420\pi$
$487$	−1.44462			−0.0654620			−0.0327310	+	0.999464i	$0.510420\pi$
$488$	−17.8280	+	5.11994i	−0.807034	+	0.231769i
$489$		0			0
$490$	7.66656	+	7.57582i	0.346340	+	0.342240i
$491$	−5.81109	−	1.55708i	−0.262251	−	0.0702699i	0.125298	−	0.992119i	$-0.460011\pi$
$491$	−5.81109	−	1.55708i	−0.262251	−	0.0702699i	−0.387549	+	0.921849i	$0.626678\pi$
$492$		0			0
$493$	−15.5024	+	4.15386i	−0.698193	+	0.187080i
$494$	−20.3946	+	35.8153i	−0.917598	+	1.61140i
$495$		0			0
$496$	−3.19516	−	1.74463i	−0.143467	−	0.0783364i
$497$	−33.1348	−	19.1304i	−1.48630	−	0.858114i
$498$		0			0
$499$	5.08052	+	1.36132i	0.227435	+	0.0609411i	0.370737	−	0.928738i	$-0.379105\pi$
$499$	5.08052	+	1.36132i	0.227435	+	0.0609411i	−0.143302	+	0.989679i	$0.545772\pi$
$500$	4.69565	+	16.7252i	0.209996	+	0.747975i
$501$		0			0
$502$	−40.1921	−	10.5134i	−1.79386	−	0.469235i
$503$		−	10.8120i		−	0.482085i	−0.970515	−	0.241043i	$-0.922511\pi$
$503$		−	10.8120i		−	0.482085i	0.970515	−	0.241043i	$-0.0774893\pi$
$504$		0			0
$505$			0.718181i			0.0319586i
$506$	0.489575	−	1.87162i	0.0217643	−	0.0832036i
$507$		0			0
$508$	18.2217	+	10.2330i	0.808458	+	0.454016i
$509$	25.8141	+	6.91687i	1.14419	+	0.306585i	0.780635	−	0.624988i	$-0.214896\pi$
$509$	25.8141	+	6.91687i	1.14419	+	0.306585i	0.363556	+	0.931572i	$0.381563\pi$
$510$		0			0
$511$	22.3005	+	12.8752i	0.986515	+	0.569564i
$512$	22.5949	−	1.21181i	0.998565	−	0.0535550i
$513$		0			0
$514$	−2.15413	−	1.22664i	−0.0950144	−	0.0541050i
$515$	12.8147	−	3.43370i	0.564685	−	0.151307i
$516$		0			0
$517$	−0.508018	−	0.136123i	−0.0223426	−	0.00598668i
$518$	−11.6135	+	11.7526i	−0.510268	+	0.516380i
$519$		0			0
$520$	−15.7647	−	8.73014i	−0.691328	−	0.382842i
$521$	41.1590			1.80321			0.901605	−	0.432560i	$-0.142390\pi$
$521$	41.1590			1.80321			0.901605	+	0.432560i	$0.142390\pi$
$522$		0			0
$523$	5.58726	+	5.58726i	0.244314	+	0.244314i	0.818632	−	0.574318i	$-0.194733\pi$
$523$	5.58726	+	5.58726i	0.244314	+	0.244314i	−0.574318	+	0.818632i	$0.694733\pi$
$524$	−27.0965	−	26.4588i	−1.18372	−	1.15586i
$525$		0			0
$526$	0.00167321	+	0.281048i	7.29556e−5	+	0.0122543i
$527$	−1.70319	−	2.95001i	−0.0741921	−	0.128505i
$528$		0			0
$529$	−11.4286	+	19.7949i	−0.496896	+	0.860649i
$530$	−9.42164	−	5.36505i	−0.409250	−	0.233043i
$531$		0			0
$532$	−32.7889	−	8.36862i	−1.42158	−	0.362826i
$533$	−47.2355	+	12.6567i	−2.04599	+	0.548223i
$534$		0			0
$535$	−1.05644	−	1.82980i	−0.0456737	−	0.0791092i
$536$	3.79608	+	0.944830i	0.163966	+	0.0408104i
$537$		0			0
$538$	32.4006	+	8.47530i	1.39689	+	0.365396i
$539$	−20.4087	+	20.4087i	−0.879067	+	0.879067i
$540$		0			0
$541$	−17.0189	−	17.0189i	−0.731702	−	0.731702i	0.239255	−	0.970957i	$-0.423097\pi$
$541$	−17.0189	−	17.0189i	−0.731702	−	0.731702i	−0.970957	+	0.239255i	$0.923097\pi$
$542$	−20.5918	+	12.0527i	−0.884494	+	0.517708i
$543$		0			0
$544$	18.6430	+	10.0359i	0.799310	+	0.430285i
$545$	7.86112	−	4.53862i	0.336733	−	0.194413i
$546$		0			0
$547$	−6.95876	−	25.9705i	−0.297535	−	1.11042i	−0.939183	−	0.343417i	$-0.888416\pi$
$547$	−6.95876	−	25.9705i	−0.297535	−	1.11042i	0.641648	−	0.767000i	$-0.278251\pi$
$548$	−16.2020	−	27.3066i	−0.692116	−	1.16648i
$549$		0			0
$550$	−20.1748	+	5.53477i	−0.860258	+	0.236003i
$551$	−16.2383	−	9.37517i	−0.691774	−	0.399396i
$552$		0			0
$553$	8.45312	−	4.88041i	0.359463	−	0.207536i
$554$	29.1221	−	29.4709i	1.23728	−	1.25210i
$555$		0			0
$556$	24.3521	+	23.7790i	1.03276	+	1.00845i
$557$	−8.91025	+	8.91025i	−0.377539	+	0.377539i	−0.870214	−	0.492674i	$-0.836019\pi$
$557$	−8.91025	+	8.91025i	−0.377539	+	0.377539i	0.492674	+	0.870214i	$0.336019\pi$
$558$		0			0
$559$		−	17.0707i		−	0.722013i
$560$	3.48809	−	14.3790i	0.147399	−	0.607622i
$561$		0			0
$562$	9.65318	−	0.0574699i	0.407195	−	0.00242422i
$563$	−2.93610	+	10.9577i	−0.123742	+	0.461811i	−0.999792	−	0.0204094i	$-0.993503\pi$
$563$	−2.93610	+	10.9577i	−0.123742	+	0.461811i	0.876050	+	0.482221i	$0.160170\pi$
$564$		0			0
$565$	−3.91824	−	14.6231i	−0.164842	−	0.615197i
$566$	13.4097	−	3.67881i	0.563650	−	0.154632i
$567$		0			0
$568$	0.499476	+	27.9629i	0.0209575	+	1.17330i
$569$	11.0917	−	19.2114i	0.464989	−	0.805384i	−0.534212	−	0.845350i	$-0.679392\pi$
$569$	11.0917	−	19.2114i	0.464989	−	0.805384i	0.999201	+	0.0399662i	$0.0127250\pi$
$570$		0			0
$571$	1.44185	−	5.38105i	0.0603394	−	0.225190i	−0.929171	−	0.369650i	$-0.879478\pi$
$571$	1.44185	−	5.38105i	0.0603394	−	0.225190i	0.989511	+	0.144460i	$0.0461444\pi$
$572$	23.6289	−	42.0756i	0.987973	−	1.75927i
$573$		0			0
$574$	−20.2823	−	34.6519i	−0.846566	−	1.44634i
$575$	−1.54401			−0.0643898
$576$		0			0
$577$	−17.9547			−0.747466			−0.373733	−	0.927536i	$-0.621922\pi$
$577$	−17.9547			−0.747466			−0.373733	+	0.927536i	$0.621922\pi$
$578$	−2.13694	−	3.65092i	−0.0888849	−	0.151858i
$579$		0			0
$580$	4.01432	−	7.14823i	0.166685	−	0.296814i
$581$	−0.270659	+	1.01011i	−0.0112288	+	0.0419066i
$582$		0			0
$583$	14.5167	−	25.1437i	0.601222	−	1.04135i
$584$	−0.336159	−	18.8197i	−0.0139104	−	0.778764i
$585$		0			0
$586$	2.62219	−	0.719372i	0.108322	−	0.0297170i
$587$	7.51380	+	28.0419i	0.310128	+	1.15741i	0.928441	+	0.371480i	$0.121150\pi$
$587$	7.51380	+	28.0419i	0.310128	+	1.15741i	−0.618313	+	0.785932i	$0.712184\pi$
$588$		0			0
$589$	1.03001	−	3.84407i	0.0424410	−	0.158392i
$590$	5.59205	−	0.0332921i	0.230221	−	0.00137061i
$591$		0			0
$592$	11.7371	+	2.84722i	0.482392	+	0.117020i
$593$			0.243119i			0.00998372i	0.999988	+	0.00499186i	$0.00158896\pi$
$593$			0.243119i			0.00998372i	−0.999988	+	0.00499186i	$0.998411\pi$
$594$		0			0
$595$	9.78966	−	9.78966i	0.401337	−	0.401337i
$596$	9.69202	+	9.46392i	0.397001	+	0.387657i
$597$		0			0
$598$	2.50336	−	2.53334i	0.102370	−	0.103596i
$599$	0.307246	−	0.177389i	0.0125537	−	0.00724791i	−0.493710	−	0.869627i	$-0.664360\pi$
$599$	0.307246	−	0.177389i	0.0125537	−	0.00724791i	0.506264	+	0.862379i	$0.331026\pi$
$600$		0			0
$601$	12.9273	+	7.46358i	0.527316	+	0.304446i	0.739923	−	0.672692i	$-0.234862\pi$
$601$	12.9273	+	7.46358i	0.527316	+	0.304446i	−0.212607	+	0.977138i	$0.568195\pi$
$602$	13.5166	−	3.70816i	0.550897	−	0.151133i
$603$		0			0
$604$	−8.97076	−	15.1192i	−0.365015	−	0.615191i
$605$	0.521101	+	1.94477i	0.0211858	+	0.0790663i
$606$		0			0
$607$	−35.2640	+	20.3597i	−1.43132	+	0.826375i	−0.997222	−	0.0744894i	$-0.976267\pi$
$607$	−35.2640	+	20.3597i	−1.43132	+	0.826375i	−0.434101	+	0.900864i	$0.642934\pi$
$608$	7.11041	+	23.6919i	0.288365	+	0.960834i
$609$		0			0
$610$	7.65147	−	4.47853i	0.309799	−	0.181330i
$611$	−0.684652	−	0.684652i	−0.0276980	−	0.0276980i
$612$		0			0
$613$	30.0647	−	30.0647i	1.21430	−	1.21430i	0.244706	−	0.969597i	$-0.421309\pi$
$613$	30.0647	−	30.0647i	1.21430	−	1.21430i	0.969597	−	0.244706i	$-0.0786913\pi$
$614$	19.0889	+	4.99325i	0.770366	+	0.201511i
$615$		0			0
$616$	38.4483	+	9.56963i	1.54913	+	0.385571i
$617$	−10.8854	−	18.8541i	−0.438231	−	0.759038i	0.559323	−	0.828950i	$-0.311061\pi$
$617$	−10.8854	−	18.8541i	−0.438231	−	0.759038i	−0.997553	+	0.0699125i	$0.977728\pi$
$618$		0			0
$619$	−37.7889	+	10.1255i	−1.51886	+	0.406978i	−0.919368	−	0.393399i	$-0.871299\pi$
$619$	−37.7889	+	10.1255i	−1.51886	+	0.406978i	−0.599496	+	0.800378i	$0.704632\pi$
$620$	1.68600	+	0.430313i	0.0677113	+	0.0172818i
$621$		0			0
$622$	4.50036	+	2.56268i	0.180448	+	0.102754i
$623$	11.3541	−	19.6658i	0.454891	−	0.787894i
$624$		0			0
$625$	6.06371	+	10.5026i	0.242548	+	0.420106i
$626$	0.0105044	+	1.76442i	0.000419841	+	0.0705203i
$627$		0			0
$628$	10.8241	+	10.5694i	0.431930	+	0.421765i
$629$	7.99101	+	7.99101i	0.318622	+	0.318622i
$630$		0			0
$631$	−39.4346			−1.56987			−0.784934	−	0.619579i	$-0.787303\pi$
$631$	−39.4346			−1.56987			−0.784934	+	0.619579i	$0.787303\pi$
$632$	−6.24168	−	3.45650i	−0.248281	−	0.137492i
$633$		0			0
$634$	1.56693	−	1.58570i	0.0622308	−	0.0629762i
$635$	−9.64861	−	2.58534i	−0.382893	−	0.102596i
$636$		0			0
$637$	−51.3245	+	13.7524i	−2.03355	+	0.544888i
$638$	19.0775	+	10.8635i	0.755286	+	0.430090i
$639$		0			0
$640$	−10.3212	+	3.23203i	−0.407980	+	0.127757i
$641$	25.2321	+	14.5677i	0.996606	+	0.575391i	0.907242	−	0.420608i	$-0.138183\pi$
$641$	25.2321	+	14.5677i	0.996606	+	0.575391i	0.0893639	+	0.995999i	$0.471517\pi$
$642$		0			0
$643$	−0.887866	−	0.237903i	−0.0350140	−	0.00938197i	0.241270	−	0.970458i	$-0.422436\pi$
$643$	−0.887866	−	0.237903i	−0.0350140	−	0.00938197i	−0.276284	+	0.961076i	$0.589103\pi$
$644$	2.54970	+	1.43186i	0.100472	+	0.0564234i
$645$		0			0
$646$	−5.85730	+	22.3921i	−0.230452	+	0.881006i
$647$		−	36.0035i		−	1.41544i	−0.706491	−	0.707722i	$-0.749723\pi$
$647$		−	36.0035i		−	1.41544i	0.706491	−	0.707722i	$-0.250277\pi$
$648$		0			0
$649$			14.9749i			0.587817i
$650$	−37.2602	−	9.74646i	−1.46146	−	0.382288i
$651$		0			0
$652$	−2.96972	−	10.5777i	−0.116303	−	0.414256i
$653$	−0.824032	−	0.220799i	−0.0322468	−	0.00864052i	0.242660	−	0.970112i	$-0.421980\pi$
$653$	−0.824032	−	0.220799i	−0.0322468	−	0.00864052i	−0.274906	+	0.961471i	$0.588647\pi$
$654$		0			0
$655$	15.6768	+	9.05098i	0.612542	+	0.353651i
$656$	−14.0653	+	25.7594i	−0.549156	+	1.00574i
$657$		0			0
$658$	0.393387	−	0.690832i	0.0153358	−	0.0269315i
$659$	−7.69747	+	2.06253i	−0.299851	+	0.0803448i	−0.405608	−	0.914047i	$-0.632940\pi$
$659$	−7.69747	+	2.06253i	−0.299851	+	0.0803448i	0.105757	+	0.994392i	$0.466273\pi$
$660$		0			0
$661$	−21.2171	−	5.68510i	−0.825249	−	0.221125i	−0.178609	−	0.983920i	$-0.557160\pi$
$661$	−21.2171	−	5.68510i	−0.825249	−	0.221125i	−0.646640	+	0.762795i	$0.723826\pi$
$662$	−9.49122	−	9.37888i	−0.368887	−	0.364521i
$663$		0			0
$664$	0.734709	−	0.210998i	0.0285122	−	0.00818831i
$665$	16.1747			0.627228
$666$		0			0
$667$	1.14572	+	1.14572i	0.0443624	+	0.0443624i
$668$	−0.447039	−	37.5431i	−0.0172965	−	1.45259i
$669$		0			0
$670$	−1.86976	+	0.0111316i	−0.0722353	+	0.000430051i
$671$	11.8706	+	20.5605i	0.458260	+	0.793730i
$672$		0			0
$673$	22.9778	−	39.7988i	0.885731	−	1.53413i	0.0408565	−	0.999165i	$-0.486991\pi$
$673$	22.9778	−	39.7988i	0.885731	−	1.53413i	0.844874	−	0.534965i	$-0.179675\pi$
$674$	9.58662	−	16.8352i	0.369263	−	0.648467i
$675$		0			0
$676$	54.0423	−	32.0653i	2.07855	−	1.23328i
$677$	−7.36199	+	1.97264i	−0.282944	+	0.0758147i	−0.397500	−	0.917602i	$-0.630122\pi$
$677$	−7.36199	+	1.97264i	−0.282944	+	0.0758147i	0.114556	+	0.993417i	$0.463456\pi$
$678$		0			0
$679$	19.6270	+	33.9950i	0.753216	+	1.30461i
$680$	−9.82039	−	2.44426i	−0.376595	−	0.0937329i
$681$		0			0
$682$	−1.17917	+	4.50791i	−0.0451528	+	0.172617i
$683$	−17.1824	+	17.1824i	−0.657466	+	0.657466i	−0.954780	−	0.297314i	$-0.903909\pi$
$683$	−17.1824	+	17.1824i	−0.657466	+	0.657466i	0.297314	+	0.954780i	$0.403909\pi$
$684$		0			0
$685$	10.7314	+	10.7314i	0.410025	+	0.410025i
$686$	−2.68820	−	4.59274i	−0.102636	−	0.175352i
$687$		0			0
$688$	−7.41495	−	7.06995i	−0.282692	−	0.269539i
$689$	46.2891	−	26.7250i	1.76348	−	1.01814i
$690$		0			0
$691$	1.97900	+	7.38572i	0.0752846	+	0.280966i	0.993298	−	0.115584i	$-0.0368740\pi$
$691$	1.97900	+	7.38572i	0.0752846	+	0.280966i	−0.918013	+	0.396550i	$0.870207\pi$
$692$	−8.96559	−	2.28827i	−0.340821	−	0.0869868i
$693$		0			0
$694$	1.92843	+	7.02932i	0.0732020	+	0.266829i
$695$	−14.0890	−	8.13426i	−0.534424	−	0.308550i
$696$		0			0
$697$	−23.7830	+	13.7311i	−0.900846	+	0.520104i
$698$	−23.5231	−	23.2446i	−0.890362	−	0.879823i
$699$		0			0
$700$	−0.376510	−	31.6199i	−0.0142307	−	1.19512i
$701$	20.1418	−	20.1418i	0.760747	−	0.760747i	−0.215711	−	0.976457i	$-0.569207\pi$
$701$	20.1418	−	20.1418i	0.760747	−	0.760747i	0.976457	+	0.215711i	$0.0692068\pi$
$702$		0			0
$703$			13.2029i			0.497958i
$704$	−8.49019	−	27.6895i	−0.319986	−	1.04359i
$705$		0			0
$706$	−0.247642	−	41.5963i	−0.00932014	−	1.56550i
$707$	0.752385	−	2.80794i	0.0282964	−	0.105603i
$708$		0			0
$709$	−8.10188	−	30.2366i	−0.304272	−	1.13556i	−0.933570	−	0.358396i	$-0.883324\pi$
$709$	−8.10188	−	30.2366i	−0.304272	−	1.13556i	0.629297	−	0.777165i	$-0.283343\pi$
$710$	−3.53664	−	12.8914i	−0.132728	−	0.483807i
$711$		0			0
$712$	−16.5962	+	0.296444i	−0.621971	+	0.0111097i
$713$	−0.171949	+	0.297825i	−0.00643955	+	0.0111536i
$714$		0			0
$715$	−5.96977	+	22.2795i	−0.223257	+	0.833206i
$716$	45.4979	−	12.7736i	1.70034	−	0.477373i
$717$		0			0
$718$	−25.7957	+	15.0986i	−0.962686	+	0.563475i
$719$	45.7985			1.70800			0.853999	−	0.520275i	$-0.174171\pi$
$719$	45.7985			1.70800			0.853999	+	0.520275i	$0.174171\pi$
$720$		0			0
$721$	−53.7003			−1.99990
$722$	−0.147419	+	0.0862867i	−0.00548637	+	0.00321126i
$723$		0			0
$724$	−2.95891	−	10.5392i	−0.109967	−	0.391687i
$725$	4.53489	−	16.9245i	0.168422	−	0.628559i
$726$		0			0
$727$	4.35110	−	7.53632i	0.161373	−	0.279507i	−0.773988	−	0.633200i	$-0.781741\pi$
$727$	4.35110	−	7.53632i	0.161373	−	0.279507i	0.935361	+	0.353693i	$0.115074\pi$
$728$	52.4909	+	50.6486i	1.94544	+	1.87716i
$729$		0			0
$730$	2.38024	+	8.67623i	0.0880966	+	0.321122i
$731$	−2.48118	−	9.25990i	−0.0917699	−	0.342490i
$732$		0			0
$733$	6.74821	−	25.1847i	0.249251	−	0.930217i	−0.721948	−	0.691947i	$-0.756753\pi$
$733$	6.74821	−	25.1847i	0.249251	−	0.930217i	0.971199	−	0.238270i	$-0.0765802\pi$
$734$	−0.193733	−	32.5412i	−0.00715081	−	1.20112i
$735$		0			0
$736$	−0.0636183	−	2.13658i	−0.00234500	−	0.0787553i
$737$		−	5.00703i		−	0.184436i
$738$		0			0
$739$	4.46836	−	4.46836i	0.164371	−	0.164371i	−0.620129	−	0.784500i	$-0.712920\pi$
$739$	4.46836	−	4.46836i	0.164371	−	0.164371i	0.784500	+	0.620129i	$0.212920\pi$
$740$	−5.77236	+	0.0687336i	−0.212196	+	0.00252670i
$741$		0			0
$742$	31.2161	+	30.8466i	1.14598	+	1.13241i
$743$	6.20834	−	3.58439i	0.227762	−	0.131499i	−0.381777	−	0.924254i	$-0.624688\pi$
$743$	6.20834	−	3.58439i	0.227762	−	0.131499i	0.609539	+	0.792756i	$0.291354\pi$
$744$		0			0
$745$	−5.60734	−	3.23740i	−0.205437	−	0.118609i
$746$	−3.80624	−	13.8742i	−0.139356	−	0.507969i
$747$		0			0
$748$	6.70178	−	26.2581i	0.245041	−	0.960090i
$749$	2.21350	+	8.26090i	0.0808796	+	0.301847i
$750$		0			0
$751$	−11.9726	+	6.91239i	−0.436887	+	0.252237i	−0.702276	−	0.711905i	$-0.747833\pi$
$751$	−11.9726	+	6.91239i	−0.436887	+	0.252237i	0.265389	+	0.964141i	$0.414500\pi$
$752$	−0.580944	+	0.0138370i	−0.0211849	+	0.000504583i
$753$		0			0
$754$	20.4163	+	34.8808i	0.743516	+	1.27028i
$755$	5.94177	+	5.94177i	0.216243	+	0.216243i
$756$		0			0
$757$	−11.5484	+	11.5484i	−0.419735	+	0.419735i	−0.885112	−	0.465378i	$-0.845919\pi$
$757$	−11.5484	+	11.5484i	−0.419735	+	0.419735i	0.465378	+	0.885112i	$0.345919\pi$
$758$	−7.70621	+	29.4604i	−0.279902	+	1.07005i
$759$		0			0
$760$	−6.09352	−	10.1320i	−0.221035	−	0.367525i
$761$	24.0288	+	41.6190i	0.871042	+	1.50869i	0.860920	+	0.508741i	$0.169889\pi$
$761$	24.0288	+	41.6190i	0.871042	+	1.50869i	0.0101223	+	0.999949i	$0.496778\pi$
$762$		0			0
$763$	−35.4901	+	9.50955i	−1.28483	+	0.344269i
$764$	−5.09977	−	8.59507i	−0.184503	−	0.310959i
$765$		0			0
$766$	−6.20073	+	10.8892i	−0.224042	+	0.393442i
$767$	−13.7843	+	23.8751i	−0.497721	+	0.862078i
$768$		0			0
$769$	4.47454	+	7.75012i	0.161356	+	0.279477i	0.935355	−	0.353710i	$-0.115080\pi$
$769$	4.47454	+	7.75012i	0.161356	+	0.279477i	−0.773999	+	0.633186i	$0.781747\pi$
$770$	−18.9378	+	0.112745i	−0.682469	+	0.00406306i
$771$		0			0
$772$	−35.1133	+	0.418106i	−1.26375	+	0.0150480i
$773$	−26.5172	−	26.5172i	−0.953758	−	0.953758i	0.0452194	−	0.998977i	$-0.485601\pi$
$773$	−26.5172	−	26.5172i	−0.953758	−	0.953758i	−0.998977	+	0.0452194i	$0.985601\pi$
$774$		0			0
$775$	3.71885			0.133585
$776$	13.9006	−	25.1015i	0.499004	−	0.901091i
$777$		0			0
$778$	−30.8893	−	30.5237i	−1.10743	−	1.09433i
$779$	−30.9909	−	8.30398i	−1.11036	−	0.297521i
$780$		0			0
$781$	34.5770	−	9.26489i	1.23726	−	0.331524i
$782$	0.989717	−	1.73806i	0.0353922	−	0.0621527i
$783$		0			0
$784$	−15.2828	+	27.9893i	−0.545816	+	0.999619i
$785$	−6.26233	−	3.61556i	−0.223512	−	0.129045i
$786$		0			0
$787$	28.7151	+	7.69420i	1.02358	+	0.274268i	0.731295	−	0.682062i	$-0.238916\pi$
$787$	28.7151	+	7.69420i	1.02358	+	0.274268i	0.292289	+	0.956330i	$0.405583\pi$
$788$	−39.4471	+	11.0749i	−1.40524	+	0.394525i
$789$		0			0
$790$	3.29928	+	0.863021i	0.117383	+	0.0307049i
$791$			61.2781i			2.17880i
$792$		0			0
$793$			43.7072i			1.55209i
$794$	6.65990	−	25.4604i	0.236351	−	0.903557i
$795$		0			0
$796$	0.614810	−	1.09478i	0.0217914	−	0.0388035i
$797$	−20.6630	−	5.53663i	−0.731921	−	0.196118i	−0.126436	−	0.991975i	$-0.540354\pi$
$797$	−20.6630	−	5.53663i	−0.731921	−	0.196118i	−0.605485	+	0.795857i	$0.707021\pi$
$798$		0			0
$799$	−0.470898	−	0.271873i	−0.0166592	−	0.00961819i
$800$	−19.6651	+	12.1481i	−0.695267	+	0.429499i
$801$		0			0
$802$	43.3181	+	24.6671i	1.52962	+	0.871024i
$803$	−23.2711	+	6.23548i	−0.821221	+	0.220045i
$804$		0			0
$805$	−1.35009	−	0.361756i	−0.0475845	−	0.0127502i
$806$	−6.02949	+	6.10171i	−0.212380	+	0.214924i
$807$		0			0
$808$	−2.04236	+	0.586538i	−0.0718501	+	0.0206343i
$809$	−26.2708			−0.923632			−0.461816	−	0.886976i	$-0.652802\pi$
$809$	−26.2708			−0.923632			−0.461816	+	0.886976i	$0.652802\pi$
$810$		0			0
$811$	−0.268850	−	0.268850i	−0.00944059	−	0.00944059i	0.702371	−	0.711811i	$-0.252125\pi$
$811$	−0.268850	−	0.268850i	−0.00944059	−	0.00944059i	−0.711811	+	0.702371i	$0.752125\pi$
$812$	−23.1838	+	23.7426i	−0.813593	+	0.833202i
$813$		0			0
$814$	−0.0920306	−	15.4583i	−0.00322567	−	0.541814i
$815$	2.62570	+	4.54784i	0.0919741	+	0.159304i
$816$		0			0
$817$	5.59998	−	9.69945i	0.195919	−	0.339341i
$818$	1.60627	+	0.914674i	0.0561619	+	0.0319808i
$819$		0			0
$820$	3.46919	−	13.5925i	0.121149	−	0.474672i
$821$	−4.45834	+	1.19461i	−0.155597	+	0.0416921i	−0.335777	−	0.941942i	$-0.608999\pi$
$821$	−4.45834	+	1.19461i	−0.155597	+	0.0416921i	0.180180	+	0.983634i	$0.442332\pi$
$822$		0			0
$823$	26.4439	+	45.8021i	0.921776	+	1.59656i	0.796666	+	0.604420i	$0.206595\pi$
$823$	26.4439	+	45.8021i	0.921776	+	1.59656i	0.125110	+	0.992143i	$0.460072\pi$
$824$	20.2306	+	33.6383i	0.704765	+	1.17185i
$825$		0			0
$826$	−21.8986	−	5.72821i	−0.761951	−	0.199310i
$827$	−17.9135	+	17.9135i	−0.622914	+	0.622914i	−0.946275	−	0.323362i	$-0.895187\pi$
$827$	−17.9135	+	17.9135i	−0.622914	+	0.622914i	0.323362	+	0.946275i	$0.395187\pi$
$828$		0			0
$829$	−33.9865	−	33.9865i	−1.18040	−	1.18040i	−0.979641	−	0.200759i	$-0.935659\pi$
$829$	−33.9865	−	33.9865i	−1.18040	−	1.18040i	−0.200759	−	0.979641i	$-0.564341\pi$
$830$	−0.315325	+	0.184565i	−0.0109451	+	0.00640634i
$831$		0			0
$832$	11.9517	−	51.9616i	0.414352	−	1.80144i
$833$	−25.8418	+	14.9198i	−0.895366	+	0.516940i
$834$		0			0
$835$	4.64477	+	17.3345i	0.160739	+	0.599885i
$836$	27.2285	−	16.1557i	0.941719	−	0.558756i
$837$		0			0
$838$	−6.68183	+	1.83310i	−0.230820	+	0.0633233i
$839$	4.43002	+	2.55767i	0.152941	+	0.0883007i	0.574518	−	0.818492i	$-0.305190\pi$
$839$	4.43002	+	2.55767i	0.152941	+	0.0883007i	−0.421576	+	0.906793i	$0.638523\pi$
$840$		0			0
$841$	9.19106	−	5.30646i	0.316933	−	0.182981i
$842$	−14.1392	+	14.3086i	−0.487270	+	0.493107i
$843$		0			0
$844$	−5.52045	+	5.65350i	−0.190022	+	0.194601i
$845$	−21.2384	+	21.2384i	−0.730623	+	0.730623i
$846$		0			0
$847$		−	8.14959i		−	0.280023i
$848$	7.56249	−	31.1749i	0.259697	−	1.07055i
$849$		0			0
$850$	−21.6282	+	0.128763i	−0.741842	+	0.00441653i
$851$	0.295291	−	1.10204i	0.0101224	−	0.0377775i
$852$		0			0
$853$	3.18332	+	11.8803i	0.108995	+	0.406774i	0.998768	−	0.0496295i	$-0.0158041\pi$
$853$	3.18332	+	11.8803i	0.108995	+	0.406774i	−0.889773	+	0.456403i	$0.849137\pi$
$854$	−34.6075	+	9.49423i	−1.18424	+	0.324886i
$855$		0			0
$856$	4.34080	−	4.49869i	0.148365	−	0.153762i
$857$	−23.2496	+	40.2696i	−0.794193	+	1.37558i	0.129158	+	0.991624i	$0.458773\pi$
$857$	−23.2496	+	40.2696i	−0.794193	+	1.37558i	−0.923351	+	0.383958i	$0.874561\pi$
$858$		0			0
$859$	0.236185	−	0.881454i	0.00805852	−	0.0300748i	−0.961780	−	0.273825i	$-0.911711\pi$
$859$	0.236185	−	0.881454i	0.00805852	−	0.0300748i	0.969838	+	0.243750i	$0.0783777\pi$
$860$	4.26978	+	2.39783i	0.145598	+	0.0817655i
$861$		0			0
$862$	20.4478	+	34.9346i	0.696453	+	1.18988i
$863$	8.62192			0.293494			0.146747	−	0.989174i	$-0.453120\pi$
$863$	8.62192			0.293494			0.146747	+	0.989174i	$0.453120\pi$
$864$		0			0
$865$	4.42272			0.150377
$866$	11.0328	+	18.8494i	0.374911	+	0.640527i
$867$		0			0
$868$	−6.14110	−	3.44873i	−0.208443	−	0.117058i
$869$	−2.36359	+	8.82106i	−0.0801795	+	0.299234i
$870$		0			0
$871$	4.60893	−	7.98290i	0.156168	−	0.270490i
$872$	19.3271	+	18.6488i	0.654498	+	0.631527i
$873$		0			0
$874$	2.25345	−	0.618211i	0.0762239	−	0.0209113i
$875$	8.69881	+	32.4644i	0.294074	+	1.09750i
$876$		0			0
$877$	2.40037	−	8.95831i	0.0810548	−	0.302501i	−0.913483	−	0.406877i	$-0.866618\pi$
$877$	2.40037	−	8.95831i	0.0810548	−	0.302501i	0.994538	+	0.104376i	$0.0332845\pi$
$878$	−20.7447	+	0.123503i	−0.700099	+	0.00416802i
$879$		0			0
$880$	7.20506	+	11.8203i	0.242883	+	0.398462i
$881$			15.7006i			0.528967i	0.964390	+	0.264483i	$0.0852014\pi$
$881$			15.7006i			0.528967i	−0.964390	+	0.264483i	$0.914799\pi$
$882$		0			0
$883$	19.0929	−	19.0929i	0.642526	−	0.642526i	−0.308650	−	0.951176i	$-0.599877\pi$
$883$	19.0929	−	19.0929i	0.642526	−	0.642526i	0.951176	+	0.308650i	$0.0998771\pi$
$884$	34.8552	−	35.6953i	1.17231	−	1.20056i
$885$		0			0
$886$	−15.0913	+	15.2721i	−0.507002	+	0.513075i
$887$	13.7996	−	7.96720i	0.463345	−	0.267513i	−0.250105	−	0.968219i	$-0.580465\pi$
$887$	13.7996	−	7.96720i	0.463345	−	0.267513i	0.713450	+	0.700706i	$0.247132\pi$
$888$		0			0
$889$	35.0156	+	20.2163i	1.17439	+	0.678032i
$890$	7.65118	−	2.09903i	0.256468	−	0.0703596i
$891$		0			0
$892$	3.40200	−	2.01853i	0.113907	−	0.0675853i
$893$	−0.164417	−	0.613613i	−0.00550201	−	0.0205338i
$894$		0			0
$895$	−19.5616	+	11.2939i	−0.653871	+	0.377513i
$896$	43.7396	−	1.82385i	1.46124	−	0.0609306i
$897$		0			0
$898$	29.6528	−	17.3563i	0.989528	−	0.579186i
$899$	−2.75953	−	2.75953i	−0.0920356	−	0.0920356i
$900$		0			0
$901$	21.2249	−	21.2249i	0.707104	−	0.707104i
$902$	36.3428	+	9.50649i	1.21008	+	0.316531i
$903$		0			0
$904$	38.3851	−	23.0854i	1.27667	−	0.767807i
$905$	2.61614	+	4.53128i	0.0869634	+	0.150625i
$906$		0			0
$907$	−34.9013	+	9.35177i	−1.15888	+	0.310520i	−0.786517	−	0.617568i	$-0.788118\pi$
$907$	−34.9013	+	9.35177i	−1.15888	+	0.310520i	−0.372360	+	0.928088i	$0.621451\pi$
$908$	−14.7070	+	57.6231i	−0.488069	+	1.91229i
$909$		0			0
$910$	−30.2970	−	17.2523i	−1.00433	−	0.571908i
$911$	−22.5779	+	39.1061i	−0.748040	+	1.29564i	0.200721	+	0.979648i	$0.435671\pi$
$911$	−22.5779	+	39.1061i	−0.748040	+	1.29564i	−0.948761	+	0.315994i	$0.897662\pi$
$912$		0			0
$913$	−0.489201	−	0.847320i	−0.0161902	−	0.0280422i
$914$	−0.281152	−	47.2248i	−0.00929967	−	1.56206i
$915$		0			0
$916$	20.6147	−	21.1116i	0.681130	−	0.697546i
$917$	−51.8109	−	51.8109i	−1.71095	−	1.71095i
$918$		0			0
$919$	50.2366			1.65715			0.828575	−	0.559877i	$-0.189152\pi$
$919$	50.2366			1.65715			0.828575	+	0.559877i	$0.189152\pi$
$920$	0.282015	+	0.981995i	0.00929776	+	0.0323754i
$921$		0			0
$922$	−7.40648	+	7.49519i	−0.243919	+	0.246841i
$923$	63.6557	+	17.0565i	2.09525	+	0.561421i
$924$		0			0
$925$	−11.9172	+	3.19322i	−0.391837	+	0.104992i
$926$	−35.9394	−	20.4653i	−1.18104	−	0.672531i
$927$		0			0
$928$	23.6066	+	5.57797i	0.774926	+	0.183106i
$929$	34.6234	+	19.9898i	1.13596	+	0.655844i	0.945426	−	0.325837i	$-0.105646\pi$
$929$	34.6234	+	19.9898i	1.13596	+	0.655844i	0.190530	+	0.981681i	$0.438979\pi$
$930$		0			0
$931$	−33.6737	−	9.02283i	−1.10361	−	0.295711i
$932$	−11.2996	+	20.1210i	−0.370131	+	0.659086i
$933$		0			0
$934$	13.2478	−	50.6457i	0.433482	−	1.65718i
$935$			12.9531i			0.423611i
$936$		0			0
$937$		−	50.1813i		−	1.63935i	−0.572828	−	0.819675i	$-0.694154\pi$
$937$		−	50.1813i		−	1.63935i	0.572828	−	0.819675i	$-0.305846\pi$
$938$	7.32206	+	1.91529i	0.239074	+	0.0625365i
$939$		0			0
$940$	0.267417	−	0.0750780i	0.00872219	−	0.00244878i
$941$	38.2914	+	10.2601i	1.24826	+	0.334471i	0.821665	−	0.569970i	$-0.193045\pi$
$941$	38.2914	+	10.2601i	1.24826	+	0.334471i	0.426598	+	0.904442i	$0.359712\pi$
$942$		0			0
$943$	2.40107	+	1.38626i	0.0781895	+	0.0451427i
$944$	4.66170	+	15.8755i	0.151725	+	0.516703i
$945$		0			0
$946$	−6.48899	+	11.3954i	−0.210975	+	0.370496i
$947$	12.7131	−	3.40647i	0.413121	−	0.110695i	−0.0462714	−	0.998929i	$-0.514734\pi$
$947$	12.7131	−	3.40647i	0.413121	−	0.110695i	0.459392	+	0.888233i	$0.348067\pi$
$948$		0			0
$949$	−42.8418	−	11.4794i	−1.39070	−	0.372638i
$950$	−17.9737	−	17.7610i	−0.583144	−	0.576242i
$951$		0			0
$952$	35.8351	+	19.8446i	1.16142	+	0.643168i
$953$	−10.3207			−0.334320			−0.167160	−	0.985930i	$-0.553460\pi$
$953$	−10.3207			−0.334320			−0.167160	+	0.985930i	$0.553460\pi$
$954$		0			0
$955$	3.37783	+	3.37783i	0.109304	+	0.109304i
$956$	−34.4225	+	0.409882i	−1.11330	+	0.0132565i
$957$		0			0
$958$	−32.1395	+	0.191341i	−1.03838	+	0.00618196i
$959$	−30.7150	−	53.2000i	−0.991841	−	1.71792i
$960$		0			0
$961$	−15.0858	+	26.1295i	−0.486640	+	0.842886i
$962$	14.0825	−	24.7305i	0.454039	−	0.797343i
$963$		0			0
$964$	9.48490	+	15.9857i	0.305488	+	0.514865i
$965$	16.2126	−	4.34415i	0.521902	−	0.139843i
$966$		0			0
$967$	−25.6787	−	44.4768i	−0.825771	−	1.43028i	−0.901329	−	0.433136i	$-0.857407\pi$
$967$	−25.6787	−	44.4768i	−0.825771	−	1.43028i	0.0755575	−	0.997141i	$-0.475926\pi$
$968$	−5.10497	+	3.07020i	−0.164080	+	0.0986800i
$969$		0			0
$970$	−3.47072	+	13.2684i	−0.111438	+	0.426022i
$971$	−14.0572	+	14.0572i	−0.451117	+	0.451117i	−0.895725	−	0.444608i	$-0.853343\pi$
$971$	−14.0572	+	14.0572i	−0.451117	+	0.451117i	0.444608	+	0.895725i	$0.353343\pi$
$972$		0			0
$973$	46.5632	+	46.5632i	1.49275	+	1.49275i
$974$	1.03202	+	1.76318i	0.0330679	+	0.0564959i
$975$		0			0
$976$	18.9850	+	18.1017i	0.607695	+	0.579420i
$977$	−26.6234	+	15.3711i	−0.851759	+	0.491764i	−0.861244	−	0.508191i	$-0.830314\pi$
$977$	−26.6234	+	15.3711i	−0.851759	+	0.491764i	0.00948463	+	0.999955i	$0.496981\pi$
$978$		0			0
$979$	5.49880	+	20.5218i	0.175742	+	0.655880i
$980$	3.76950	−	14.7692i	0.120412	−	0.471785i
$981$		0			0
$982$	2.25093	+	8.20487i	0.0718300	+	0.261828i
$983$	−36.6682	−	21.1704i	−1.16953	−	0.675230i	−0.215963	−	0.976402i	$-0.569289\pi$
$983$	−36.6682	−	21.1704i	−1.16953	−	0.675230i	−0.953570	+	0.301172i	$0.902622\pi$
$984$		0			0
$985$	16.9600	−	9.79189i	0.540392	−	0.311995i
$986$	16.1445	+	15.9534i	0.514147	+	0.508061i
$987$		0			0
$988$	58.2826	−	0.693992i	1.85422	−	0.0220788i
$989$	−0.684361	+	0.684361i	−0.0217614	+	0.0217614i
$990$		0			0
$991$			37.3774i			1.18733i	0.804711	+	0.593666i	$0.202320\pi$
$991$			37.3774i			1.18733i	−0.804711	+	0.593666i	$0.797680\pi$
$992$	0.153229	+	5.14608i	0.00486501	+	0.163388i
$993$		0			0
$994$	0.322130	+	54.1079i	0.0102173	+	1.71620i
$995$	−0.155330	+	0.579699i	−0.00492429	+	0.0183777i
$996$		0			0
$997$	0.432008	+	1.61228i	0.0136818	+	0.0510613i	0.972429	−	0.233198i	$-0.0749190\pi$
$997$	0.432008	+	1.61228i	0.0136818	+	0.0510613i	−0.958747	+	0.284259i	$0.908252\pi$
$998$	−1.96794	−	7.17335i	−0.0622940	−	0.227068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.35.7		88
3.2	odd	2		144.2.u.a.83.16	yes	88
4.3	odd	2		1728.2.z.a.1007.14		88
9.4	even	3		144.2.u.a.131.22	yes	88
9.5	odd	6	inner	432.2.v.a.179.1		88
12.11	even	2		576.2.y.a.47.21		88
16.5	even	4		1728.2.z.a.143.14		88
16.11	odd	4	inner	432.2.v.a.251.1		88
36.23	even	6		1728.2.z.a.1583.14		88
36.31	odd	6		576.2.y.a.239.9		88
48.5	odd	4		576.2.y.a.335.9		88
48.11	even	4		144.2.u.a.11.22	✓	88
144.5	odd	12		1728.2.z.a.719.14		88
144.59	even	12	inner	432.2.v.a.395.7		88
144.85	even	12		576.2.y.a.527.21		88
144.139	odd	12		144.2.u.a.59.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.22	✓	88	48.11	even	4
144.2.u.a.59.16	yes	88	144.139	odd	12
144.2.u.a.83.16	yes	88	3.2	odd	2
144.2.u.a.131.22	yes	88	9.4	even	3
432.2.v.a.35.7		88	1.1	even	1	trivial
432.2.v.a.179.1		88	9.5	odd	6	inner
432.2.v.a.251.1		88	16.11	odd	4	inner
432.2.v.a.395.7		88	144.59	even	12	inner
576.2.y.a.47.21		88	12.11	even	2
576.2.y.a.239.9		88	36.31	odd	6
576.2.y.a.335.9		88	48.5	odd	4
576.2.y.a.527.21		88	144.85	even	12
1728.2.z.a.143.14		88	16.5	even	4
1728.2.z.a.719.14		88	144.5	odd	12
1728.2.z.a.1007.14		88	4.3	odd	2
1728.2.z.a.1583.14		88	36.23	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.714386 - 1.22051i) q^{2} +(-0.979306 + 1.74383i) q^{4} +(0.247419 - 0.923380i) q^{5} +(-1.93471 + 3.35102i) q^{7} +(2.82798 - 0.0505136i) q^{8} +O(q^{10})\)	\(q+(-0.714386 - 1.22051i) q^{2} +(-0.979306 + 1.74383i) q^{4} +(0.247419 - 0.923380i) q^{5} +(-1.93471 + 3.35102i) q^{7} +(2.82798 - 0.0505136i) q^{8} +(-1.30375 + 0.357671i) q^{10} +(-0.936987 - 3.49688i) q^{11} +(1.72498 - 6.43770i) q^{13} +(5.47210 - 0.0325780i) q^{14} +(-2.08192 - 3.41550i) q^{16} -3.74282i q^{17} +(3.09199 - 3.09199i) q^{19} +(1.36792 + 1.33573i) q^{20} +(-3.59862 + 3.64173i) q^{22} +(-0.327240 + 0.188932i) q^{23} +(3.53871 + 2.04308i) q^{25} +(-9.08960 + 2.49364i) q^{26} +(-3.94895 - 6.65550i) q^{28} +(-1.10982 - 4.14191i) q^{29} +(0.788179 - 0.455055i) q^{31} +(-2.68137 + 4.98099i) q^{32} +(-4.56816 + 2.67382i) q^{34} +(2.61558 + 2.61558i) q^{35} +(-2.13502 + 2.13502i) q^{37} +(-5.98269 - 1.56494i) q^{38} +(0.653052 - 2.62379i) q^{40} +(-3.66866 - 6.35430i) q^{41} +(2.47404 - 0.662918i) q^{43} +(7.01559 + 1.79057i) q^{44} +(0.464370 + 0.264431i) q^{46} +(0.0726386 - 0.125814i) q^{47} +(-3.98624 - 6.90437i) q^{49} +(-0.0344027 - 5.77859i) q^{50} +(9.53701 + 9.31256i) q^{52} +(5.67083 + 5.67083i) q^{53} -3.46078 q^{55} +(-5.30205 + 9.57435i) q^{56} +(-4.26241 + 4.31347i) q^{58} +(-3.99549 - 1.07059i) q^{59} +(-6.33446 + 1.69731i) q^{61} +(-1.11846 - 0.636898i) q^{62} +(7.99490 - 0.285702i) q^{64} +(-5.51765 - 3.18562i) q^{65} +(1.33594 + 0.357964i) q^{67} +(6.52686 + 3.66537i) q^{68} +(1.32382 - 5.06089i) q^{70} +9.88796i q^{71} -6.65482i q^{73} +(4.13105 + 1.08059i) q^{74} +(2.36391 + 8.41992i) q^{76} +(13.5309 + 3.62561i) q^{77} +(-2.18459 - 1.26127i) q^{79} +(-3.66891 + 1.07734i) q^{80} +(-5.13467 + 9.01707i) q^{82} +(0.261050 - 0.0699481i) q^{83} +(-3.45605 - 0.926045i) q^{85} +(-2.57652 - 2.54603i) q^{86} +(-2.82642 - 9.84177i) q^{88} -5.86860 q^{89} +(18.2356 + 18.2356i) q^{91} +(-0.00899811 - 0.755676i) q^{92} +(-0.205449 + 0.00122314i) q^{94} +(-2.09006 - 3.62010i) q^{95} +(5.07233 - 8.78553i) q^{97} +(-5.57917 + 9.79765i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) 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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