LMFDB - Embedded newform 729.2.e.q.325.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(82,729)] 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("729.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6,0,0,-12,0,0,12,0,0,-30,0,0,18,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.1
Root			$-0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.q.406.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50881 + 1.26604i) q^{2} +(0.326352 - 1.85083i) q^{4} +(-3.47843 + 1.26604i) q^{5} +(-0.407604 - 2.31164i) q^{7} +(-0.118782 - 0.205737i) q^{8} +(3.64543 - 6.31407i) q^{10} +(2.04715 + 0.745100i) q^{11} +(-3.61334 - 3.03195i) q^{13} +(3.54163 + 2.97178i) q^{14} +(3.97178 + 1.44561i) q^{16} +(1.46756 - 2.54189i) q^{17} +(3.11334 + 5.39246i) q^{19} +(1.20805 + 6.85117i) q^{20} +(-4.03209 + 1.46756i) q^{22} +(0.0901285 - 0.511144i) q^{23} +(6.66637 - 5.59375i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(-2.67561 + 2.24510i) q^{29} +(-0.747626 + 4.24000i) q^{31} +(-7.37641 + 2.68479i) q^{32} +(1.00387 + 5.69323i) q^{34} +(4.34445 + 7.52481i) q^{35} +(-1.20574 + 2.08840i) q^{37} +(-11.5245 - 4.19459i) q^{38} +(0.673648 + 0.565258i) q^{40} +(1.91404 + 1.60607i) q^{41} +(-1.00000 - 0.363970i) q^{43} +(2.04715 - 3.54576i) q^{44} +(0.511144 + 0.885328i) q^{46} +(-0.0412527 - 0.233956i) q^{47} +(1.40033 - 0.509678i) q^{49} +(-2.97637 + 16.8799i) q^{50} +(-6.79086 + 5.69821i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(-0.427173 + 0.358441i) q^{56} +(1.19459 - 6.77487i) q^{58} +(12.5094 - 4.55303i) q^{59} +(-0.638156 - 3.61916i) q^{61} +(-4.24000 - 7.34389i) q^{62} +(3.50387 - 6.06888i) q^{64} +(16.4073 + 5.97178i) q^{65} +(10.9534 + 9.19096i) q^{67} +(-4.22567 - 3.54576i) q^{68} +(-16.0817 - 5.85327i) q^{70} +(-0.601535 + 1.04189i) q^{71} +(2.34002 + 4.05304i) q^{73} +(-0.824773 - 4.67752i) q^{74} +(10.9966 - 4.00243i) q^{76} +(0.887975 - 5.03596i) q^{77} +(-9.80587 + 8.22811i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(-8.65933 + 7.26604i) q^{83} +(-1.88666 + 10.6998i) q^{85} +(1.96962 - 0.716881i) q^{86} +(-0.0898700 - 0.509678i) q^{88} +(-0.349643 - 0.605600i) q^{89} +(-5.53596 + 9.58856i) q^{91} +(-0.916629 - 0.333626i) q^{92} +(0.358441 + 0.300767i) q^{94} +(-17.6566 - 14.8157i) q^{95} +(6.65910 + 2.42371i) q^{97} +(-1.46756 + 2.54189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52}+ \cdots + 6 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.50881	+	1.26604i	−1.06689	+	0.895229i	−0.994767	−	0.102167i	$-0.967422\pi$
$2$	−1.50881	+	1.26604i	−1.06689	+	0.895229i	−0.0721247	+	0.997396i	$0.522978\pi$
$3$		0			0
$3$		0			0
$4$	0.326352	−	1.85083i	0.163176	−	0.925417i
$5$	−3.47843	+	1.26604i	−1.55560	+	0.566192i	−0.969723	−	0.244207i	$-0.921472\pi$
$5$	−3.47843	+	1.26604i	−1.55560	+	0.566192i	−0.585877	+	0.810400i	$0.699250\pi$
$6$		0			0
$7$	−0.407604	−	2.31164i	−0.154060	−	0.873716i	−0.959640	−	0.281230i	$-0.909258\pi$
$7$	−0.407604	−	2.31164i	−0.154060	−	0.873716i	0.805581	−	0.592486i	$-0.201854\pi$
$8$	−0.118782	−	0.205737i	−0.0419959	−	0.0727390i
$9$		0			0
$10$	3.64543	−	6.31407i	1.15279	−	1.99668i
$11$	2.04715	+	0.745100i	0.617237	+	0.224656i	0.631667	−	0.775240i	$-0.282371\pi$
$11$	2.04715	+	0.745100i	0.617237	+	0.224656i	−0.0144295	+	0.999896i	$0.504593\pi$
$12$		0			0
$13$	−3.61334	−	3.03195i	−1.00216	−	0.840912i	−0.0148781	−	0.999889i	$-0.504736\pi$
$13$	−3.61334	−	3.03195i	−1.00216	−	0.840912i	−0.987282	+	0.158977i	$0.949180\pi$
$14$	3.54163	+	2.97178i	0.946541	+	0.794242i
$15$		0			0
$16$	3.97178	+	1.44561i	0.992945	+	0.361403i
$17$	1.46756	−	2.54189i	0.355936	−	0.616499i	−0.631342	−	0.775505i	$-0.717496\pi$
$17$	1.46756	−	2.54189i	0.355936	−	0.616499i	0.987278	+	0.159006i	$0.0508289\pi$
$18$		0			0
$19$	3.11334	+	5.39246i	0.714249	+	1.23712i	0.963248	+	0.268612i	$0.0865651\pi$
$19$	3.11334	+	5.39246i	0.714249	+	1.23712i	−0.248999	+	0.968504i	$0.580102\pi$
$20$	1.20805	+	6.85117i	0.270127	+	1.53197i
$21$		0			0
$22$	−4.03209	+	1.46756i	−0.859644	+	0.312885i
$23$	0.0901285	−	0.511144i	0.0187931	−	0.106581i	−0.973968	−	0.226684i	$-0.927211\pi$
$23$	0.0901285	−	0.511144i	0.0187931	−	0.106581i	0.992761	+	0.120103i	$0.0383226\pi$
$24$		0			0
$25$	6.66637	−	5.59375i	1.33327	−	1.11875i
$26$	9.29044			1.82201
$27$		0			0
$28$	−4.41147			−0.833690
$29$	−2.67561	+	2.24510i	−0.496848	+	0.416905i	−0.856473	−	0.516192i	$-0.827349\pi$
$29$	−2.67561	+	2.24510i	−0.496848	+	0.416905i	0.359625	+	0.933097i	$0.382905\pi$
$30$		0			0
$31$	−0.747626	+	4.24000i	−0.134278	+	0.761526i	0.841082	+	0.540907i	$0.181919\pi$
$31$	−0.747626	+	4.24000i	−0.134278	+	0.761526i	−0.975360	+	0.220619i	$0.929192\pi$
$32$	−7.37641	+	2.68479i	−1.30398	+	0.474609i
$33$		0			0
$34$	1.00387	+	5.69323i	0.172162	+	0.976381i
$35$	4.34445	+	7.52481i	0.734347	+	1.27193i
$36$		0			0
$37$	−1.20574	+	2.08840i	−0.198222	+	0.343330i	−0.947952	−	0.318413i	$-0.896850\pi$
$37$	−1.20574	+	2.08840i	−0.198222	+	0.343330i	0.749730	+	0.661744i	$0.230183\pi$
$38$	−11.5245	−	4.19459i	−1.86953	−	0.680453i
$39$		0			0
$40$	0.673648	+	0.565258i	0.106513	+	0.0893751i
$41$	1.91404	+	1.60607i	0.298922	+	0.250826i	0.779896	−	0.625910i	$-0.215272\pi$
$41$	1.91404	+	1.60607i	0.298922	+	0.250826i	−0.480973	+	0.876735i	$0.659717\pi$
$42$		0			0
$43$	−1.00000	−	0.363970i	−0.152499	−	0.0555049i	0.264643	−	0.964346i	$-0.414746\pi$
$43$	−1.00000	−	0.363970i	−0.152499	−	0.0555049i	−0.417142	+	0.908842i	$0.636968\pi$
$44$	2.04715	−	3.54576i	0.308619	−	0.534543i
$45$		0			0
$46$	0.511144	+	0.885328i	0.0753641	+	0.130534i
$47$	−0.0412527	−	0.233956i	−0.00601732	−	0.0341259i	0.981651	−	0.190685i	$-0.0610709\pi$
$47$	−0.0412527	−	0.233956i	−0.00601732	−	0.0341259i	−0.987669	+	0.156559i	$0.949960\pi$
$48$		0			0
$49$	1.40033	−	0.509678i	0.200047	−	0.0728112i
$50$	−2.97637	+	16.8799i	−0.420923	+	2.38717i
$51$		0			0
$52$	−6.79086	+	5.69821i	−0.941723	+	0.790199i
$53$	4.66717			0.641085			0.320543	−	0.947234i	$-0.396135\pi$
$53$	4.66717			0.641085			0.320543	+	0.947234i	$0.396135\pi$
$54$		0			0
$55$	−8.06418			−1.08737
$56$	−0.427173	+	0.358441i	−0.0570834	+	0.0478987i
$57$		0			0
$58$	1.19459	−	6.77487i	0.156858	−	0.889584i
$59$	12.5094	−	4.55303i	1.62858	−	0.592754i	0.643590	−	0.765370i	$-0.277444\pi$
$59$	12.5094	−	4.55303i	1.62858	−	0.592754i	0.984989	+	0.172616i	$0.0552219\pi$
$60$		0			0
$61$	−0.638156	−	3.61916i	−0.0817075	−	0.463386i	−0.998019	−	0.0629190i	$-0.979959\pi$
$61$	−0.638156	−	3.61916i	−0.0817075	−	0.463386i	0.916311	−	0.400467i	$-0.131152\pi$
$62$	−4.24000	−	7.34389i	−0.538480	−	0.932675i
$63$		0			0
$64$	3.50387	−	6.06888i	0.437984	−	0.758610i
$65$	16.4073	+	5.97178i	2.03508	+	0.740708i
$66$		0			0
$67$	10.9534	+	9.19096i	1.33817	+	1.12285i	0.982093	+	0.188397i	$0.0603291\pi$
$67$	10.9534	+	9.19096i	1.33817	+	1.12285i	0.356073	+	0.934458i	$0.384115\pi$
$68$	−4.22567	−	3.54576i	−0.512438	−	0.429986i
$69$		0			0
$70$	−16.0817	−	5.85327i	−1.92213	−	0.699599i
$71$	−0.601535	+	1.04189i	−0.0713891	+	0.123649i	−0.899510	−	0.436900i	$-0.856077\pi$
$71$	−0.601535	+	1.04189i	−0.0713891	+	0.123649i	0.828121	+	0.560549i	$0.189410\pi$
$72$		0			0
$73$	2.34002	+	4.05304i	0.273879	+	0.474372i	0.969852	−	0.243696i	$-0.0783599\pi$
$73$	2.34002	+	4.05304i	0.273879	+	0.474372i	−0.695973	+	0.718068i	$0.745027\pi$
$74$	−0.824773	−	4.67752i	−0.0958779	−	0.543750i
$75$		0			0
$76$	10.9966	−	4.00243i	1.26140	−	0.459111i
$77$	0.887975	−	5.03596i	0.101194	−	0.573901i
$78$		0			0
$79$	−9.80587	+	8.22811i	−1.10325	+	0.925734i	−0.997639	−	0.0686737i	$-0.978123\pi$
$79$	−9.80587	+	8.22811i	−1.10325	+	0.925734i	−0.105608	+	0.994408i	$0.533679\pi$
$80$	−15.6458			−1.74925
$81$		0			0
$82$	−4.92127			−0.543464
$83$	−8.65933	+	7.26604i	−0.950485	+	0.797552i	−0.979379	−	0.202030i	$-0.935246\pi$
$83$	−8.65933	+	7.26604i	−0.950485	+	0.797552i	0.0288938	+	0.999582i	$0.490802\pi$
$84$		0			0
$85$	−1.88666	+	10.6998i	−0.204637	+	1.16055i
$86$	1.96962	−	0.716881i	0.212389	−	0.0773033i
$87$		0			0
$88$	−0.0898700	−	0.509678i	−0.00958018	−	0.0543319i
$89$	−0.349643	−	0.605600i	−0.0370621	−	0.0641935i	0.846899	−	0.531753i	$-0.178467\pi$
$89$	−0.349643	−	0.605600i	−0.0370621	−	0.0641935i	−0.883961	+	0.467560i	$0.845133\pi$
$90$		0			0
$91$	−5.53596	+	9.58856i	−0.580326	+	1.00515i
$92$	−0.916629	−	0.333626i	−0.0955652	−	0.0347829i
$93$		0			0
$94$	0.358441	+	0.300767i	0.0369703	+	0.0310218i
$95$	−17.6566	−	14.8157i	−1.81153	−	1.52006i
$96$		0			0
$97$	6.65910	+	2.42371i	0.676129	+	0.246091i	0.657185	−	0.753730i	$-0.271747\pi$
$97$	6.65910	+	2.42371i	0.676129	+	0.246091i	0.0189446	+	0.999821i	$0.493969\pi$
$98$	−1.46756	+	2.54189i	−0.148246	+	0.256770i
$99$		0			0
$100$	−8.17752	−	14.1639i	−0.817752	−	1.41639i
$101$	0.812174	+	4.60607i	0.0808143	+	0.458321i	0.998182	+	0.0602789i	$0.0191990\pi$
$101$	0.812174	+	4.60607i	0.0808143	+	0.458321i	−0.917367	+	0.398042i	$0.869690\pi$
$102$		0			0
$103$	12.8020	−	4.65955i	1.26142	−	0.459119i	0.377174	−	0.926142i	$-0.376896\pi$
$103$	12.8020	−	4.65955i	1.26142	−	0.459119i	0.884245	+	0.467023i	$0.154674\pi$
$104$	−0.194584	+	1.10354i	−0.0190805	+	0.108211i
$105$		0			0
$106$	−7.04189	+	5.90885i	−0.683969	+	0.573918i
$107$	11.6340			1.12470			0.562350	−	0.826900i	$-0.309898\pi$
$107$	11.6340			1.12470			0.562350	+	0.826900i	$0.309898\pi$
$108$		0			0
$109$	14.6040			1.39881			0.699405	−	0.714725i	$-0.253448\pi$
$109$	14.6040			1.39881			0.699405	+	0.714725i	$0.253448\pi$
$110$	12.1673	−	10.2096i	1.16011	−	0.973448i
$111$		0			0
$112$	1.72281	−	9.77055i	0.162790	−	0.923230i
$113$	−4.41263	+	1.60607i	−0.415106	+	0.151086i	−0.541126	−	0.840942i	$-0.682002\pi$
$113$	−4.41263	+	1.60607i	−0.415106	+	0.151086i	0.126020	+	0.992028i	$0.459780\pi$
$114$		0			0
$115$	0.333626	+	1.89209i	0.0311108	+	0.176438i
$116$	3.28212	+	5.68479i	0.304737	+	0.527820i
$117$		0			0
$118$	−13.1099	+	22.7071i	−1.20687	+	2.09036i
$119$	−6.47410	−	2.35638i	−0.593480	−	0.216009i
$120$		0			0
$121$	−4.79086	−	4.02001i	−0.435533	−	0.365455i
$122$	5.54488	+	4.65270i	0.502010	+	0.421236i
$123$		0			0
$124$	7.60354	+	2.76746i	0.682818	+	0.248525i
$125$	−6.85240	+	11.8687i	−0.612897	+	1.06157i
$126$		0			0
$127$	−3.04576	−	5.27541i	−0.270267	−	0.468117i	0.698663	−	0.715451i	$-0.253779\pi$
$127$	−3.04576	−	5.27541i	−0.270267	−	0.468117i	−0.968930	+	0.247334i	$0.920445\pi$
$128$	−0.329421	−	1.86824i	−0.0291170	−	0.165131i
$129$		0			0
$130$	−32.3161	+	11.7621i	−2.83431	+	1.03161i
$131$	1.79698	−	10.1912i	0.157003	−	0.890408i	−0.799929	−	0.600095i	$-0.795129\pi$
$131$	1.79698	−	10.1912i	0.157003	−	0.890408i	0.956932	−	0.290313i	$-0.0937595\pi$
$132$		0			0
$133$	11.1964	−	9.39490i	0.970851	−	0.814641i
$134$	−28.1627			−2.43289
$135$		0			0
$136$	−0.697281			−0.0597914
$137$	14.6197	−	12.2674i	1.24905	−	1.04807i	0.252285	−	0.967653i	$-0.418818\pi$
$137$	14.6197	−	12.2674i	1.24905	−	1.04807i	0.996761	−	0.0804207i	$-0.0256264\pi$
$138$		0			0
$139$	−4.04664	+	22.9496i	−0.343231	+	1.94656i	−0.0213784	+	0.999771i	$0.506805\pi$
$139$	−4.04664	+	22.9496i	−0.343231	+	1.94656i	−0.321853	+	0.946790i	$0.604306\pi$
$140$	15.3450	−	5.58512i	1.29689	−	0.472029i
$141$		0			0
$142$	−0.411474	−	2.33359i	−0.0345301	−	0.195830i
$143$	−5.13793	−	8.89915i	−0.429655	−	0.744184i
$144$		0			0
$145$	6.46451	−	11.1969i	0.536848	−	0.929848i
$146$	−8.66198	−	3.15270i	−0.716871	−	0.260920i
$147$		0			0
$148$	3.47178	+	2.91317i	0.285379	+	0.239461i
$149$	11.8782	+	9.96703i	0.973104	+	0.816531i	0.983035	−	0.183419i	$-0.0587167\pi$
$149$	11.8782	+	9.96703i	0.973104	+	0.816531i	−0.00993072	+	0.999951i	$0.503161\pi$
$150$		0			0
$151$	5.54576	+	2.01849i	0.451308	+	0.164262i	0.557666	−	0.830065i	$-0.311697\pi$
$151$	5.54576	+	2.01849i	0.451308	+	0.164262i	−0.106359	+	0.994328i	$0.533919\pi$
$152$	0.739620	−	1.28106i	0.0599911	−	0.103908i
$153$		0			0
$154$	5.03596	+	8.72254i	0.405809	+	0.702882i
$155$	−2.76746	−	15.6951i	−0.222288	−	1.26066i
$156$		0			0
$157$	1.13903	−	0.414574i	0.0909047	−	0.0330866i	−0.296167	−	0.955136i	$-0.595709\pi$
$157$	1.13903	−	0.414574i	0.0909047	−	0.0330866i	0.387072	+	0.922049i	$0.373486\pi$
$158$	4.37808	−	24.8293i	0.348302	−	1.97532i
$159$		0			0
$160$	22.2592	−	18.6777i	1.75975	−	1.47660i
$161$	−1.21832			−0.0960168
$162$		0			0
$163$	2.77332			0.217223			0.108612	−	0.994084i	$-0.465360\pi$
$163$	2.77332			0.217223			0.108612	+	0.994084i	$0.465360\pi$
$164$	3.59721	−	3.01842i	0.280895	−	0.235699i
$165$		0			0
$166$	3.86618	−	21.9262i	0.300074	−	1.70180i
$167$	3.59721	−	1.30928i	0.278361	−	0.101315i	−0.199068	−	0.979986i	$-0.563791\pi$
$167$	3.59721	−	1.30928i	0.278361	−	0.101315i	0.477428	+	0.878671i	$0.341569\pi$
$168$		0			0
$169$	1.60607	+	9.10846i	0.123544	+	0.700651i
$170$	−10.6998	−	18.5326i	−0.820635	−	1.42138i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	6.60549	+	2.40420i	0.502206	+	0.182788i	0.580686	−	0.814128i	$-0.302784\pi$
$173$	6.60549	+	2.40420i	0.502206	+	0.182788i	−0.0784801	+	0.996916i	$0.525007\pi$
$174$		0			0
$175$	−15.6480	−	13.1302i	−1.18287	−	0.992549i
$176$	7.05369	+	5.91875i	0.531692	+	0.446142i
$177$		0			0
$178$	1.29426	+	0.471073i	0.0970091	+	0.0353084i
$179$	7.19269	−	12.4581i	0.537607	−	0.931163i	−0.461425	−	0.887179i	$-0.652662\pi$
$179$	7.19269	−	12.4581i	0.537607	−	0.931163i	0.999032	−	0.0439838i	$-0.0140050\pi$
$180$		0			0
$181$	−6.60014	−	11.4318i	−0.490584	−	0.849717i	0.509357	−	0.860555i	$-0.329883\pi$
$181$	−6.60014	−	11.4318i	−0.490584	−	0.849717i	−0.999941	+	0.0108384i	$0.996550\pi$
$182$	−3.78682	−	21.4761i	−0.280698	−	1.59192i
$183$		0			0
$184$	−0.115867	+	0.0421721i	−0.00854183	+	0.00310897i
$185$	1.55007	−	8.79086i	0.113963	−	0.646317i
$186$		0			0
$187$	4.89827	−	4.11014i	0.358197	−	0.300563i
$188$	−0.446476			−0.0325626
$189$		0			0
$190$	45.3979			3.29351
$191$	10.2829	−	8.62836i	0.744043	−	0.624326i	−0.189877	−	0.981808i	$-0.560809\pi$
$191$	10.2829	−	8.62836i	0.744043	−	0.624326i	0.933920	+	0.357482i	$0.116365\pi$
$192$		0			0
$193$	2.60560	−	14.7771i	0.187555	−	1.06368i	−0.735073	−	0.677988i	$-0.762852\pi$
$193$	2.60560	−	14.7771i	0.187555	−	1.06368i	0.922628	−	0.385690i	$-0.126037\pi$
$194$	−13.1159	+	4.77379i	−0.941664	+	0.342738i
$195$		0			0
$196$	−0.486329	−	2.75811i	−0.0347378	−	0.197008i
$197$	11.1606	+	19.3307i	0.795158	+	1.37725i	0.922739	+	0.385426i	$0.125946\pi$
$197$	11.1606	+	19.3307i	0.795158	+	1.37725i	−0.127580	+	0.991828i	$0.540721\pi$
$198$		0			0
$199$	4.55051	−	7.88171i	0.322577	−	0.558720i	−0.658442	−	0.752631i	$-0.728784\pi$
$199$	4.55051	−	7.88171i	0.322577	−	0.558720i	0.981019	+	0.193912i	$0.0621176\pi$
$200$	−1.94269	−	0.707081i	−0.137369	−	0.0499982i
$201$		0			0
$202$	−7.05690	−	5.92145i	−0.496522	−	0.416631i
$203$	6.28044	+	5.26991i	0.440800	+	0.369876i
$204$		0			0
$205$	−8.69119	−	3.16333i	−0.607019	−	0.220937i
$206$	−13.4166	+	23.2383i	−0.934781	+	1.61909i
$207$		0			0
$208$	−9.96838	−	17.2657i	−0.691183	−	1.19716i
$209$	2.35554	+	13.3589i	0.162936	+	0.924055i
$210$		0			0
$211$	5.61721	−	2.04450i	0.386705	−	0.140749i	−0.141349	−	0.989960i	$-0.545144\pi$
$211$	5.61721	−	2.04450i	0.386705	−	0.140749i	0.528054	+	0.849211i	$0.322922\pi$
$212$	1.52314	−	8.63816i	0.104610	−	0.593271i
$213$		0			0
$214$	−17.5535	+	14.7291i	−1.19993	+	1.00686i
$215$	3.93923			0.268653
$216$		0			0
$217$	10.1061			0.686045
$218$	−22.0347	+	18.4893i	−1.49238	+	1.25225i
$219$		0			0
$220$	−2.63176	+	14.9254i	−0.177433	+	1.00627i
$221$	−13.0097	+	4.73514i	−0.875126	+	0.318520i
$222$		0			0
$223$	−1.54576	−	8.76644i	−0.103512	−	0.587044i	−0.991804	−	0.127766i	$-0.959219\pi$
$223$	−1.54576	−	8.76644i	−0.103512	−	0.587044i	0.888293	−	0.459278i	$-0.151892\pi$
$224$	9.21291	+	15.9572i	0.615564	+	1.06619i
$225$		0			0
$226$	4.62449	−	8.00984i	0.307616	−	0.532807i
$227$	10.0251	+	3.64883i	0.665388	+	0.242182i	0.652561	−	0.757736i	$-0.273695\pi$
$227$	10.0251	+	3.64883i	0.665388	+	0.242182i	0.0128273	+	0.999918i	$0.495917\pi$
$228$		0			0
$229$	−6.33615	−	5.31666i	−0.418705	−	0.351335i	0.408965	−	0.912550i	$-0.365890\pi$
$229$	−6.33615	−	5.31666i	−0.418705	−	0.351335i	−0.827670	+	0.561215i	$0.810334\pi$
$230$	−2.89884	−	2.43242i	−0.191144	−	0.160389i
$231$		0			0
$232$	0.779715	+	0.283793i	0.0511908	+	0.0186319i
$233$	−6.36965	+	11.0326i	−0.417290	+	0.722767i	−0.995666	−	0.0930034i	$-0.970353\pi$
$233$	−6.36965	+	11.0326i	−0.417290	+	0.722767i	0.578376	+	0.815770i	$0.303687\pi$
$234$		0			0
$235$	0.439693	+	0.761570i	0.0286824	+	0.0496793i
$236$	−4.34445	−	24.6386i	−0.282800	−	1.60384i
$237$		0			0
$238$	12.7515	−	4.64117i	0.826557	−	0.300842i
$239$	2.60743	−	14.7875i	0.168660	−	0.956521i	−0.776549	−	0.630057i	$-0.783032\pi$
$239$	2.60743	−	14.7875i	0.168660	−	0.956521i	0.945210	−	0.326464i	$-0.105857\pi$
$240$		0			0
$241$	0.609470	−	0.511406i	0.0392594	−	0.0329426i	−0.622947	−	0.782264i	$-0.714065\pi$
$241$	0.609470	−	0.511406i	0.0392594	−	0.0329426i	0.662206	+	0.749322i	$0.269620\pi$
$242$	12.3180			0.791832
$243$		0			0
$244$	−6.90673			−0.442158
$245$	−4.22567	+	3.54576i	−0.269968	+	0.226530i
$246$		0			0
$247$	5.10014	−	28.9243i	0.324514	−	1.84041i
$248$	0.961130	−	0.349823i	0.0610318	−	0.0222138i
$249$		0			0
$250$	−4.68732	−	26.5831i	−0.296452	−	1.68126i
$251$	−4.15749	−	7.20099i	−0.262419	−	0.454522i	0.704465	−	0.709738i	$-0.251187\pi$
$251$	−4.15749	−	7.20099i	−0.262419	−	0.454522i	−0.966884	+	0.255216i	$0.917853\pi$
$252$		0			0
$253$	0.565360	−	0.979232i	0.0355439	−	0.0615638i
$254$	11.2744	+	4.10354i	0.707418	+	0.257479i
$255$		0			0
$256$	13.5988	+	11.4107i	0.849925	+	0.713171i
$257$	−19.6262	−	16.4684i	−1.22425	−	1.02727i	−0.998591	−	0.0530632i	$-0.983102\pi$
$257$	−19.6262	−	16.4684i	−1.22425	−	1.02727i	−0.225661	−	0.974206i	$-0.572454\pi$
$258$		0			0
$259$	5.31908	+	1.93599i	0.330511	+	0.120296i
$260$	16.4073	−	28.4183i	1.01754	−	1.76243i
$261$		0			0
$262$	10.1912	+	17.6517i	0.629614	+	1.09052i
$263$	4.87343	+	27.6386i	0.300509	+	1.70427i	0.643926	+	0.765088i	$0.277304\pi$
$263$	4.87343	+	27.6386i	0.300509	+	1.70427i	−0.343417	+	0.939183i	$0.611585\pi$
$264$		0			0
$265$	−16.2344	+	5.90885i	−0.997273	+	0.362978i
$266$	−4.99892	+	28.3503i	−0.306504	+	1.73827i
$267$		0			0
$268$	20.5856	−	17.2734i	1.25746	−	1.05514i
$269$	−30.1710			−1.83956			−0.919778	−	0.392439i	$-0.871631\pi$
$269$	−30.1710			−1.83956			−0.919778	+	0.392439i	$0.871631\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	9.50341	−	7.97431i	0.576229	−	0.483513i
$273$		0			0
$274$	−6.52734	+	37.0184i	−0.394331	+	2.23636i
$275$	17.8149	−	6.48411i	1.07428	−	0.391006i
$276$		0			0
$277$	3.66772	+	20.8007i	0.220372	+	1.24979i	0.871338	+	0.490684i	$0.163253\pi$
$277$	3.66772	+	20.8007i	0.220372	+	1.24979i	−0.650966	+	0.759107i	$0.725636\pi$
$278$	−22.9496	−	39.7499i	−1.37643	−	2.38404i
$279$		0			0
$280$	1.03209	−	1.78763i	0.0616791	−	0.106831i
$281$	1.64192	+	0.597611i	0.0979489	+	0.0356505i	0.390530	−	0.920590i	$-0.372292\pi$
$281$	1.64192	+	0.597611i	0.0979489	+	0.0356505i	−0.292581	+	0.956241i	$0.594514\pi$
$282$		0			0
$283$	−5.58306	−	4.68475i	−0.331879	−	0.278479i	0.461586	−	0.887095i	$-0.347281\pi$
$283$	−5.58306	−	4.68475i	−0.331879	−	0.278479i	−0.793465	+	0.608616i	$0.791725\pi$
$284$	1.73205	+	1.45336i	0.102778	+	0.0862412i
$285$		0			0
$286$	19.0189	+	6.92231i	1.12461	+	0.409325i
$287$	2.93247	−	5.07919i	0.173098	−	0.299815i
$288$		0			0
$289$	4.19253	+	7.26168i	0.246620	+	0.427158i
$290$	4.42198	+	25.0783i	0.259668	+	1.47265i
$291$		0			0
$292$	8.26517	−	3.00827i	0.483682	−	0.176046i
$293$	−2.66565	+	15.1177i	−0.155729	+	0.883184i	0.802387	+	0.596804i	$0.203563\pi$
$293$	−2.66565	+	15.1177i	−0.155729	+	0.883184i	−0.958116	+	0.286380i	$0.907548\pi$
$294$		0			0
$295$	−37.7486	+	31.6748i	−2.19781	+	1.84418i
$296$	0.572881			0.0332980
$297$		0			0
$298$	−30.5408			−1.76918
$299$	−1.87543	+	1.57367i	−0.108459	+	0.0910079i
$300$		0			0
$301$	−0.433763	+	2.45999i	−0.0250017	+	0.141792i
$302$	−10.9230	+	3.97565i	−0.628549	+	0.228773i
$303$		0			0
$304$	4.57011	+	25.9184i	0.262114	+	1.48652i
$305$	6.80180	+	11.7811i	0.389470	+	0.674581i
$306$		0			0
$307$	−8.38191	+	14.5179i	−0.478381	+	0.828580i	−0.999693	−	0.0247861i	$-0.992110\pi$
$307$	−8.38191	+	14.5179i	−0.478381	+	0.828580i	0.521312	+	0.853366i	$0.325443\pi$
$308$	−9.03093	−	3.28699i	−0.514585	−	0.187294i
$309$		0			0
$310$	24.0462	+	20.1772i	1.36573	+	1.14599i
$311$	12.2744	+	10.2995i	0.696020	+	0.584030i	0.920638	−	0.390417i	$-0.127669\pi$
$311$	12.2744	+	10.2995i	0.696020	+	0.584030i	−0.224619	+	0.974447i	$0.572114\pi$
$312$		0			0
$313$	−32.3307	−	11.7674i	−1.82744	−	0.665133i	−0.993577	−	0.113160i	$-0.963903\pi$
$313$	−32.3307	−	11.7674i	−1.82744	−	0.665133i	−0.833862	−	0.551973i	$-0.813875\pi$
$314$	−1.19372	+	2.06758i	−0.0673654	+	0.116680i
$315$		0			0
$316$	12.0287	+	20.8343i	0.676666	+	1.17202i
$317$	2.83239	+	16.0633i	0.159083	+	0.902205i	0.954957	+	0.296743i	$0.0959005\pi$
$317$	2.83239	+	16.0633i	0.159083	+	0.902205i	−0.795874	+	0.605462i	$0.792988\pi$
$318$		0			0
$319$	−7.15018	+	2.60245i	−0.400333	+	0.145709i
$320$	−4.50449	+	25.5462i	−0.251809	+	1.42808i
$321$		0			0
$322$	1.83821	−	1.54244i	0.102440	−	0.0859570i
$323$	18.2761			1.01691
$324$		0			0
$325$	−41.0479			−2.27693
$326$	−4.18442	+	3.51114i	−0.231754	+	0.194464i
$327$		0			0
$328$	0.103074	−	0.584561i	0.00569130	−	0.0322770i
$329$	−0.524005	+	0.190722i	−0.0288893	+	0.0105149i
$330$		0			0
$331$	−5.48380	−	31.1002i	−0.301417	−	1.70942i	−0.639908	−	0.768452i	$-0.721028\pi$
$331$	−5.48380	−	31.1002i	−0.301417	−	1.70942i	0.338491	−	0.940970i	$-0.390084\pi$
$332$	10.6222	+	18.3983i	0.582972	+	1.00974i
$333$		0			0
$334$	−3.76991	+	6.52968i	−0.206281	+	0.357288i
$335$	−49.7367	−	18.1027i	−2.71740	−	0.989054i
$336$		0			0
$337$	4.60014	+	3.85997i	0.250585	+	0.210266i	0.759424	−	0.650596i	$-0.225481\pi$
$337$	4.60014	+	3.85997i	0.250585	+	0.210266i	−0.508839	+	0.860862i	$0.669925\pi$
$338$	−13.9550	−	11.7096i	−0.759050	−	0.636919i
$339$		0			0
$340$	19.1878	+	6.98378i	1.04060	+	0.378749i
$341$	−4.68972	+	8.12284i	−0.253963	+	0.439876i
$342$		0			0
$343$	−9.96451	−	17.2590i	−0.538033	−	0.931900i
$344$	0.0439002	+	0.248970i	0.00236694	+	0.0134236i
$345$		0			0
$346$	−13.0103	+	4.73535i	−0.699436	+	0.254574i
$347$	−3.99919	+	22.6805i	−0.214688	+	1.21755i	0.666760	+	0.745272i	$0.267680\pi$
$347$	−3.99919	+	22.6805i	−0.214688	+	1.21755i	−0.881448	+	0.472281i	$0.843431\pi$
$348$		0			0
$349$	−8.86025	+	7.43463i	−0.474278	+	0.397967i	−0.848352	−	0.529432i	$-0.822405\pi$
$349$	−8.86025	+	7.43463i	−0.474278	+	0.397967i	0.374074	+	0.927399i	$0.377961\pi$
$350$	40.2332			2.15056
$351$		0			0
$352$	−17.1010			−0.911487
$353$	1.63522	−	1.37211i	0.0870339	−	0.0730301i	−0.598233	−	0.801322i	$-0.704130\pi$
$353$	1.63522	−	1.37211i	0.0870339	−	0.0730301i	0.685267	+	0.728292i	$0.259686\pi$
$354$		0			0
$355$	0.773318	−	4.38571i	0.0410435	−	0.232769i
$356$	−1.23497	+	0.449493i	−0.0654533	+	0.0238231i
$357$		0			0
$358$	4.92009	+	27.9032i	0.260035	+	1.47473i
$359$	12.1118	+	20.9782i	0.639234	+	1.10719i	0.985601	+	0.169087i	$0.0540818\pi$
$359$	12.1118	+	20.9782i	0.639234	+	1.10719i	−0.346367	+	0.938099i	$0.612585\pi$
$360$		0			0
$361$	−9.88578	+	17.1227i	−0.520304	+	0.901193i
$362$	24.4315	+	8.89234i	1.28409	+	0.467371i
$363$		0			0
$364$	15.9402	+	13.3754i	0.835491	+	0.701061i
$365$	−13.2709	−	11.1356i	−0.694632	−	0.582865i
$366$		0			0
$367$	2.66385	+	0.969561i	0.139052	+	0.0506107i	0.410609	−	0.911812i	$-0.365316\pi$
$367$	2.66385	+	0.969561i	0.139052	+	0.0506107i	−0.271557	+	0.962422i	$0.587538\pi$
$368$	1.09689	−	1.89986i	0.0571792	−	0.0990372i
$369$		0			0
$370$	8.79086	+	15.2262i	0.457015	+	0.791573i
$371$	−1.90236	−	10.7888i	−0.0987654	−	0.560127i
$372$		0			0
$373$	27.0945	−	9.86160i	1.40290	−	0.510614i	0.473863	−	0.880599i	$-0.342859\pi$
$373$	27.0945	−	9.86160i	1.40290	−	0.510614i	0.929038	+	0.369985i	$0.120637\pi$
$374$	−2.18696	+	12.4029i	−0.113085	+	0.641336i
$375$		0			0
$376$	−0.0432332	+	0.0362770i	−0.00222958	+	0.00187084i
$377$	16.4749			0.848501
$378$		0			0
$379$	32.1985			1.65393			0.826963	−	0.562256i	$-0.190066\pi$
$379$	32.1985			1.65393			0.826963	+	0.562256i	$0.190066\pi$
$380$	−33.1836	+	27.8444i	−1.70228	+	1.42839i
$381$		0			0
$382$	−4.59105	+	26.0372i	−0.234899	+	1.33218i
$383$	0.631708	−	0.229923i	0.0322788	−	0.0117485i	−0.325830	−	0.945428i	$-0.605644\pi$
$383$	0.631708	−	0.229923i	0.0322788	−	0.0117485i	0.358109	+	0.933680i	$0.383422\pi$
$384$		0			0
$385$	3.28699	+	18.6414i	0.167520	+	0.950056i
$386$	14.7771	+	25.5947i	0.752134	+	1.30273i
$387$		0			0
$388$	6.65910	−	11.5339i	0.338065	−	0.585545i
$389$	−4.00243	−	1.45677i	−0.202931	−	0.0738610i	0.238555	−	0.971129i	$-0.423326\pi$
$389$	−4.00243	−	1.45677i	−0.202931	−	0.0738610i	−0.441486	+	0.897268i	$0.645549\pi$
$390$		0			0
$391$	−1.16700	−	0.979232i	−0.0590179	−	0.0495219i
$392$	−0.271194	−	0.227559i	−0.0136974	−	0.0114935i
$393$		0			0
$394$	−41.3127	−	15.0366i	−2.08131	−	0.757533i
$395$	23.6919	−	41.0355i	1.19207	−	2.06472i
$396$		0			0
$397$	4.43242	+	7.67717i	0.222457	+	0.385306i	0.955553	−	0.294818i	$-0.0952591\pi$
$397$	4.43242	+	7.67717i	0.222457	+	0.385306i	−0.733097	+	0.680124i	$0.761926\pi$
$398$	3.11273	+	17.6532i	0.156027	+	0.884873i
$399$		0			0
$400$	34.5638	−	12.5802i	1.72819	−	0.629009i
$401$	−6.43956	+	36.5205i	−0.321576	+	1.82375i	0.211142	+	0.977455i	$0.432282\pi$
$401$	−6.43956	+	36.5205i	−0.321576	+	1.82375i	−0.532718	+	0.846293i	$0.678829\pi$
$402$		0			0
$403$	15.5569	−	13.0538i	0.774945	−	0.650256i
$404$	8.79012			0.437325
$405$		0			0
$406$	−16.1480			−0.801410
$407$	−4.02438	+	3.37686i	−0.199481	+	0.167385i
$408$		0			0
$409$	−0.588526	+	3.33770i	−0.0291007	+	0.165038i	−0.995895	−	0.0905183i	$-0.971148\pi$
$409$	−0.588526	+	3.33770i	−0.0291007	+	0.165038i	0.966794	+	0.255557i	$0.0822588\pi$
$410$	17.1183	−	6.23055i	0.845413	−	0.307705i
$411$		0			0
$412$	−4.44609	−	25.2150i	−0.219043	−	1.24226i
$413$	−15.6238	−	27.0612i	−0.768798	−	1.33160i
$414$		0			0
$415$	20.9217	−	36.2375i	1.02701	−	1.77883i
$416$	34.7936	+	12.6638i	1.70590	+	0.620896i
$417$		0			0
$418$	−20.4670	−	17.1739i	−1.00108	−	0.840002i
$419$	15.8237	+	13.2777i	0.773038	+	0.648656i	0.941485	−	0.337055i	$-0.109431\pi$
$419$	15.8237	+	13.2777i	0.773038	+	0.648656i	−0.168447	+	0.985711i	$0.553875\pi$
$420$		0			0
$421$	−25.8726	−	9.41685i	−1.26095	−	0.458949i	−0.376864	−	0.926269i	$-0.622998\pi$
$421$	−25.8726	−	9.41685i	−1.26095	−	0.458949i	−0.884088	+	0.467320i	$0.845220\pi$
$422$	−5.88690	+	10.1964i	−0.286570	+	0.496353i
$423$		0			0
$424$	−0.554378	−	0.960210i	−0.0269230	−	0.0466319i
$425$	−4.43539	−	25.1544i	−0.215148	−	1.22017i
$426$		0			0
$427$	−8.10607	+	2.95037i	−0.392280	+	0.142778i
$428$	3.79677	−	21.5326i	0.183524	−	1.04082i
$429$		0			0
$430$	−5.94356	+	4.98724i	−0.286624	+	0.240506i
$431$	2.58110			0.124327			0.0621636	−	0.998066i	$-0.480200\pi$
$431$	2.58110			0.124327			0.0621636	+	0.998066i	$0.480200\pi$
$432$		0			0
$433$	−27.0137			−1.29820			−0.649098	−	0.760704i	$-0.724854\pi$
$433$	−27.0137			−1.29820			−0.649098	+	0.760704i	$0.724854\pi$
$434$	−15.2482	+	12.7947i	−0.731935	+	0.614167i
$435$		0			0
$436$	4.76604	−	27.0296i	0.228252	−	1.29448i
$437$	3.03693	−	1.10535i	0.145276	−	0.0528761i
$438$		0			0
$439$	2.03343	+	11.5322i	0.0970505	+	0.550401i	0.994100	+	0.108470i	$0.0345951\pi$
$439$	2.03343	+	11.5322i	0.0970505	+	0.550401i	−0.897049	+	0.441931i	$0.854294\pi$
$440$	0.957882	+	1.65910i	0.0456652	+	0.0790945i
$441$		0			0
$442$	13.6343	−	23.6153i	0.648517	−	1.12326i
$443$	1.95529	+	0.711667i	0.0928986	+	0.0338123i	0.388051	−	0.921638i	$-0.373148\pi$
$443$	1.95529	+	0.711667i	0.0928986	+	0.0338123i	−0.295153	+	0.955450i	$0.595371\pi$
$444$		0			0
$445$	1.98293	+	1.66387i	0.0939997	+	0.0788751i
$446$	13.4310	+	11.2699i	0.635974	+	0.533646i
$447$		0			0
$448$	−15.4572	−	5.62597i	−0.730286	−	0.265802i
$449$	5.27541	−	9.13728i	0.248962	−	0.431215i	−0.714276	−	0.699864i	$-0.753244\pi$
$449$	5.27541	−	9.13728i	0.248962	−	0.431215i	0.963238	+	0.268649i	$0.0865772\pi$
$450$		0			0
$451$	2.72163	+	4.71400i	0.128157	+	0.221974i
$452$	1.53249	+	8.69119i	0.0720823	+	0.408799i
$453$		0			0
$454$	−19.7456	+	7.18680i	−0.926705	+	0.337293i
$455$	7.11689	−	40.3619i	0.333645	−	1.89220i
$456$		0			0
$457$	−6.05896	+	5.08407i	−0.283426	+	0.237823i	−0.773406	−	0.633911i	$-0.781449\pi$
$457$	−6.05896	+	5.08407i	−0.283426	+	0.237823i	0.489980	+	0.871734i	$0.337004\pi$
$458$	16.2912			0.761238
$459$		0			0
$460$	3.61081			0.168355
$461$	29.9468	−	25.1284i	1.39476	−	1.17034i	0.431393	−	0.902164i	$-0.358022\pi$
$461$	29.9468	−	25.1284i	1.39476	−	1.17034i	0.963369	−	0.268180i	$-0.0864222\pi$
$462$		0			0
$463$	4.11422	−	23.3329i	0.191204	−	1.08437i	−0.726518	−	0.687148i	$-0.758863\pi$
$463$	4.11422	−	23.3329i	0.191204	−	1.08437i	0.917722	−	0.397224i	$-0.130026\pi$
$464$	−13.8725	+	5.04916i	−0.644013	+	0.234402i
$465$		0			0
$466$	−4.35710	−	24.7103i	−0.201839	−	1.14468i
$467$	−17.3576	−	30.0642i	−0.803214	−	1.39121i	−0.917490	−	0.397758i	$-0.869788\pi$
$467$	−17.3576	−	30.0642i	−0.803214	−	1.39121i	0.114277	−	0.993449i	$-0.463545\pi$
$468$		0			0
$469$	16.7815	−	29.0665i	0.774899	−	1.34216i
$470$	−1.62760	−	0.592396i	−0.0750754	−	0.0273252i
$471$		0			0
$472$	−2.42262	−	2.03282i	−0.111510	−	0.0935680i
$473$	−1.77595	−	1.49020i	−0.0816583	−	0.0685195i
$474$		0			0
$475$	50.9188	+	18.5329i	2.33631	+	0.850349i
$476$	−6.47410	+	11.2135i	−0.296740	+	0.513969i
$477$		0			0
$478$	14.7875	+	25.6126i	0.676362	+	1.17149i
$479$	1.12554	+	6.38326i	0.0514272	+	0.291658i	0.999664	−	0.0259046i	$-0.00824661\pi$
$479$	1.12554	+	6.38326i	0.0514272	+	0.291658i	−0.948237	+	0.317563i	$0.897136\pi$
$480$		0			0
$481$	10.6887	−	3.89036i	0.487361	−	0.177385i
$482$	−0.272114	+	1.54323i	−0.0123944	+	0.0702923i
$483$		0			0
$484$	−9.00387	+	7.55514i	−0.409267	+	0.343416i
$485$	−26.2317			−1.19112
$486$		0			0
$487$	19.9828			0.905505			0.452753	−	0.891636i	$-0.350442\pi$
$487$	19.9828			0.905505			0.452753	+	0.891636i	$0.350442\pi$
$488$	−0.668794	+	0.561185i	−0.0302749	+	0.0254036i
$489$		0			0
$490$	1.88666	−	10.6998i	0.0852306	−	0.483367i
$491$	−24.6454	+	8.97019i	−1.11223	+	0.404819i	−0.831811	−	0.555059i	$-0.812696\pi$
$491$	−24.6454	+	8.97019i	−1.11223	+	0.404819i	−0.280420	+	0.959877i	$0.590474\pi$
$492$		0			0
$493$	1.78018	+	10.0959i	0.0801754	+	0.454697i
$494$	28.9243	+	50.0984i	1.30137	+	2.25403i
$495$		0			0
$496$	−9.09879	+	15.7596i	−0.408548	+	0.707626i
$497$	2.65366	+	0.965852i	0.119033	+	0.0433244i
$498$		0			0
$499$	4.83931	+	4.06066i	0.216637	+	0.181780i	0.744648	−	0.667458i	$-0.232617\pi$
$499$	4.83931	+	4.06066i	0.216637	+	0.181780i	−0.528011	+	0.849238i	$0.677062\pi$
$500$	19.7307	+	16.5560i	0.882384	+	0.740408i
$501$		0			0
$502$	15.3897	+	5.60138i	0.686874	+	0.250002i
$503$	−10.9131	+	18.9020i	−0.486589	+	0.842798i	−0.999881	−	0.0154166i	$-0.995093\pi$
$503$	−10.9131	+	18.9020i	−0.486589	+	0.842798i	0.513292	+	0.858214i	$0.328426\pi$
$504$		0			0
$505$	−8.65657	−	14.9936i	−0.385212	−	0.667208i
$506$	0.386729	+	2.19325i	0.0171922	+	0.0975018i
$507$		0			0
$508$	−10.7579	+	3.91555i	−0.477304	+	0.173725i
$509$	−5.05196	+	28.6511i	−0.223924	+	1.26994i	0.640806	+	0.767703i	$0.278600\pi$
$509$	−5.05196	+	28.6511i	−0.223924	+	1.26994i	−0.864731	+	0.502236i	$0.832511\pi$
$510$		0			0
$511$	8.41534	−	7.06131i	0.372273	−	0.312374i
$512$	−31.1704			−1.37755
$513$		0			0
$514$	50.4620			2.22579
$515$	−38.6317	+	32.4158i	−1.70231	+	1.42841i
$516$		0			0
$517$	0.0898700	−	0.509678i	0.00395248	−	0.0224156i
$518$	−10.4765	+	3.81315i	−0.460313	+	0.167540i
$519$		0			0
$520$	−0.720285	−	4.08494i	−0.0315866	−	0.179136i
$521$	−6.84743	−	11.8601i	−0.299991	−	0.519600i	0.676142	−	0.736771i	$-0.263650\pi$
$521$	−6.84743	−	11.8601i	−0.299991	−	0.519600i	−0.976134	+	0.217171i	$0.930317\pi$
$522$		0			0
$523$	−6.57532	+	11.3888i	−0.287519	+	0.497997i	−0.973217	−	0.229889i	$-0.926164\pi$
$523$	−6.57532	+	11.3888i	−0.287519	+	0.497997i	0.685698	+	0.727886i	$0.259497\pi$
$524$	−18.2757	−	6.65183i	−0.798380	−	0.290586i
$525$		0			0
$526$	−42.3448	−	35.5315i	−1.84632	−	1.54925i
$527$	9.68042	+	8.12284i	0.421686	+	0.353836i
$528$		0			0
$529$	21.3598	+	7.77433i	0.928686	+	0.338014i
$530$	17.0138	−	29.4688i	0.739034	−	1.28004i
$531$		0			0
$532$	−13.7344	−	23.7887i	−0.595463	−	1.03137i
$533$	−2.04655	−	11.6065i	−0.0886457	−	0.502735i
$534$		0			0
$535$	−40.4680	+	14.7291i	−1.74958	+	0.636796i
$536$	0.589856	−	3.34524i	0.0254779	−	0.144492i
$537$		0			0
$538$	45.5223	−	38.1978i	1.96261	−	1.64682i
$539$	3.24644			0.139834
$540$		0			0
$541$	6.26083			0.269174			0.134587	−	0.990902i	$-0.457029\pi$
$541$	6.26083			0.269174			0.134587	+	0.990902i	$0.457029\pi$
$542$	28.6674	−	24.0548i	1.23137	−	1.03324i
$543$		0			0
$544$	−4.00088	+	22.6901i	−0.171536	+	0.972830i
$545$	−50.7990	+	18.4893i	−2.17599	+	0.791996i
$546$		0			0
$547$	−5.44878	−	30.9016i	−0.232973	−	1.32126i	−0.846841	−	0.531846i	$-0.821498\pi$
$547$	−5.44878	−	30.9016i	−0.232973	−	1.32126i	0.613868	−	0.789409i	$-0.289613\pi$
$548$	−17.9337	−	31.0621i	−0.766091	−	1.32691i
$549$		0			0
$550$	−18.6702	+	32.3378i	−0.796102	+	1.37889i
$551$	−20.4367	−	7.43835i	−0.870632	−	0.316884i
$552$		0			0
$553$	23.0173	+	19.3138i	0.978795	+	0.821306i
$554$	−31.8685	−	26.7408i	−1.35396	−	1.13611i
$555$		0			0
$556$	41.1553	+	14.9793i	1.74537	+	0.635264i
$557$	−21.7196	+	37.6195i	−0.920290	+	1.59399i	−0.121324	+	0.992613i	$0.538714\pi$
$557$	−21.7196	+	37.6195i	−0.920290	+	1.59399i	−0.798966	+	0.601376i	$0.794619\pi$
$558$		0			0
$559$	2.50980	+	4.34710i	0.106153	+	0.183863i
$560$	6.37727	+	36.1673i	0.269489	+	1.52835i
$561$		0			0
$562$	−3.23396	+	1.17706i	−0.136416	+	0.0496514i
$563$	5.55980	−	31.5312i	0.234318	−	1.32888i	−0.609728	−	0.792611i	$-0.708721\pi$
$563$	5.55980	−	31.5312i	0.234318	−	1.32888i	0.844046	−	0.536271i	$-0.180168\pi$
$564$		0			0
$565$	13.3157	−	11.1732i	0.560195	−	0.470059i
$566$	14.3549			0.603381
$567$		0			0
$568$	0.285807			0.0119922
$569$	5.18761	−	4.35292i	0.217476	−	0.182484i	−0.527541	−	0.849530i	$-0.676886\pi$
$569$	5.18761	−	4.35292i	0.217476	−	0.182484i	0.745017	+	0.667046i	$0.232441\pi$
$570$		0			0
$571$	−3.67318	+	20.8316i	−0.153718	+	0.871777i	0.806231	+	0.591601i	$0.201504\pi$
$571$	−3.67318	+	20.8316i	−0.153718	+	0.871777i	−0.959949	+	0.280176i	$0.909607\pi$
$572$	−18.1476	+	6.60519i	−0.758790	+	0.276177i
$573$		0			0
$574$	2.00593	+	11.3762i	0.0837259	+	0.474833i
$575$	−2.25838	−	3.91164i	−0.0941811	−	0.163127i
$576$		0			0
$577$	−5.95811	+	10.3198i	−0.248039	+	0.429617i	−0.962982	−	0.269567i	$-0.913120\pi$
$577$	−5.95811	+	10.3198i	−0.248039	+	0.429617i	0.714942	+	0.699183i	$0.246453\pi$
$578$	−15.5194	−	5.64858i	−0.645520	−	0.234950i
$579$		0			0
$580$	−18.6138	−	15.6188i	−0.772896	−	0.648537i
$581$	20.3260	+	17.0556i	0.843266	+	0.707584i
$582$		0			0
$583$	9.55438	+	3.47751i	0.395702	+	0.144024i
$584$	0.555907	−	0.962859i	0.0230036	−	0.0398434i
$585$		0			0
$586$	−15.1177	−	26.1846i	−0.624506	−	1.08168i
$587$	0.0225502	+	0.127889i	0.000930748	+	0.00527853i	0.985270	−	0.171008i	$-0.0547025\pi$
$587$	0.0225502	+	0.127889i	0.000930748	+	0.00527853i	−0.984339	+	0.176287i	$0.943591\pi$
$588$		0			0
$589$	−25.1917	+	9.16901i	−1.03800	+	0.377803i
$590$	16.8538	−	95.5827i	0.693860	−	3.93508i
$591$		0			0
$592$	−7.80793	+	6.55163i	−0.320904	+	0.269271i
$593$	−26.2622			−1.07846			−0.539230	−	0.842158i	$-0.681285\pi$
$593$	−26.2622			−1.07846			−0.539230	+	0.842158i	$0.681285\pi$
$594$		0			0
$595$	25.5030			1.04552
$596$	22.3238	−	18.7319i	0.914419	−	0.767288i
$597$		0			0
$598$	0.837334	−	4.74876i	0.0342411	−	0.194191i
$599$	25.9310	−	9.43810i	1.05951	−	0.385630i	0.247266	−	0.968948i	$-0.420468\pi$
$599$	25.9310	−	9.43810i	1.05951	−	0.385630i	0.812244	+	0.583317i	$0.198246\pi$
$600$		0			0
$601$	0.231429	+	1.31250i	0.00944020	+	0.0535380i	0.989164	−	0.146815i	$-0.0469022\pi$
$601$	0.231429	+	1.31250i	0.00944020	+	0.0535380i	−0.979724	+	0.200353i	$0.935791\pi$
$602$	−2.45999	−	4.26083i	−0.100262	−	0.173658i
$603$		0			0
$604$	5.54576	−	9.60554i	0.225654	−	0.390844i
$605$	21.7542	+	7.91787i	0.884433	+	0.321907i
$606$		0			0
$607$	−9.62495	−	8.07629i	−0.390665	−	0.327807i	0.426207	−	0.904626i	$-0.359849\pi$
$607$	−9.62495	−	8.07629i	−0.390665	−	0.327807i	−0.816872	+	0.576819i	$0.804294\pi$
$608$	−37.4429	−	31.4183i	−1.51851	−	1.27418i
$609$		0			0
$610$	−25.1780	−	9.16404i	−1.01943	−	0.371041i
$611$	−0.560282	+	0.970437i	−0.0226666	+	0.0392597i
$612$		0			0
$613$	6.99912	+	12.1228i	0.282692	+	0.489637i	0.972047	−	0.234787i	$-0.0754393\pi$
$613$	6.99912	+	12.1228i	0.282692	+	0.489637i	−0.689355	+	0.724424i	$0.742106\pi$
$614$	−5.73357	−	32.5167i	−0.231388	−	1.31227i
$615$		0			0
$616$	−1.14156	+	0.415494i	−0.0459947	+	0.0167407i
$617$	−4.17567	+	23.6814i	−0.168106	+	0.953377i	0.777698	+	0.628638i	$0.216387\pi$
$617$	−4.17567	+	23.6814i	−0.168106	+	0.953377i	−0.945804	+	0.324738i	$0.894724\pi$
$618$		0			0
$619$	5.26399	−	4.41701i	0.211577	−	0.177535i	−0.530840	−	0.847472i	$-0.678124\pi$
$619$	5.26399	−	4.41701i	0.211577	−	0.177535i	0.742418	+	0.669937i	$0.233679\pi$
$620$	−29.9521			−1.20291
$621$		0			0
$622$	−31.5594			−1.26542
$623$	−1.25741	+	1.05509i	−0.0503771	+	0.0422714i
$624$		0			0
$625$	1.25356	−	7.10927i	0.0501422	−	0.284371i
$626$	63.6790	−	23.1773i	2.54513	−	0.926350i
$627$		0			0
$628$	−0.395582	−	2.24346i	−0.0157854	−	0.0895237i
$629$	3.53898	+	6.12970i	0.141109	+	0.244407i
$630$		0			0
$631$	17.6887	−	30.6377i	0.704175	−	1.21967i	−0.262814	−	0.964847i	$-0.584651\pi$
$631$	17.6887	−	30.6377i	0.704175	−	1.21967i	0.966989	−	0.254820i	$-0.0820161\pi$
$632$	2.85759	+	1.04008i	0.113669	+	0.0413721i
$633$		0			0
$634$	−24.6104	−	20.6506i	−0.977404	−	0.820139i
$635$	17.2734	+	14.4941i	0.685472	+	0.575180i
$636$		0			0
$637$	−6.60519	−	2.40409i	−0.261707	−	0.0952536i
$638$	7.49346	−	12.9791i	0.296669	−	0.513846i
$639$		0			0
$640$	3.51114	+	6.08148i	0.138790	+	0.240392i
$641$	3.32947	+	18.8824i	0.131506	+	0.745809i	0.977229	+	0.212187i	$0.0680585\pi$
$641$	3.32947	+	18.8824i	0.131506	+	0.745809i	−0.845723	+	0.533622i	$0.820830\pi$
$642$		0			0
$643$	−18.2079	+	6.62712i	−0.718048	+	0.261348i	−0.675097	−	0.737729i	$-0.735898\pi$
$643$	−18.2079	+	6.62712i	−0.718048	+	0.261348i	−0.0429509	+	0.999077i	$0.513676\pi$
$644$	−0.397600	+	2.25490i	−0.0156676	+	0.0888555i
$645$		0			0
$646$	−27.5752	+	23.1383i	−1.08493	+	0.910364i
$647$	−8.77141			−0.344840			−0.172420	−	0.985024i	$-0.555159\pi$
$647$	−8.77141			−0.344840			−0.172420	+	0.985024i	$0.555159\pi$
$648$		0			0
$649$	29.0009			1.13839
$650$	61.9336	−	51.9684i	2.42923	−	2.03837i
$651$		0			0
$652$	0.905078	−	5.13295i	0.0354456	−	0.201022i
$653$	30.8307	−	11.2215i	1.20650	−	0.439130i	0.341011	−	0.940059i	$-0.389231\pi$
$653$	30.8307	−	11.2215i	1.20650	−	0.439130i	0.865488	+	0.500929i	$0.167008\pi$
$654$		0			0
$655$	6.65183	+	37.7244i	0.259908	+	1.47401i
$656$	5.28039	+	9.14590i	0.206164	+	0.357087i
$657$		0			0
$658$	0.549163	−	0.951178i	0.0214086	−	0.0370808i
$659$	17.5268	+	6.37922i	0.682746	+	0.248499i	0.660026	−	0.751243i	$-0.270545\pi$
$659$	17.5268	+	6.37922i	0.682746	+	0.248499i	0.0227199	+	0.999742i	$0.492767\pi$
$660$		0			0
$661$	27.8897	+	23.4022i	1.08478	+	0.910240i	0.996309	−	0.0858386i	$-0.0273570\pi$
$661$	27.8897	+	23.4022i	1.08478	+	0.910240i	0.0884727	+	0.996079i	$0.471801\pi$
$662$	47.6483	+	39.9816i	1.85190	+	1.55393i
$663$		0			0
$664$	2.52347	+	0.918468i	0.0979297	+	0.0356435i
$665$	−27.0515	+	46.8546i	−1.04901	+	1.81694i
$666$		0			0
$667$	0.906422	+	1.56997i	0.0350968	+	0.0607894i
$668$	−1.24930	−	7.08512i	−0.0483368	−	0.274132i
$669$		0			0
$670$	97.9621	−	35.6553i	3.78461	−	1.37748i
$671$	1.39024	−	7.88444i	0.0536696	−	0.304375i
$672$		0			0
$673$	30.1746	−	25.3195i	1.16314	−	0.975994i	0.163201	−	0.986593i	$-0.447818\pi$
$673$	30.1746	−	25.3195i	1.16314	−	0.975994i	0.999944	+	0.0105986i	$0.00337371\pi$
$674$	−11.8276			−0.455584
$675$		0			0
$676$	17.3824			0.668553
$677$	−24.2648	+	20.3606i	−0.932571	+	0.782520i	−0.976277	−	0.216525i	$-0.930528\pi$
$677$	−24.2648	+	20.3606i	−0.932571	+	0.782520i	0.0437064	+	0.999044i	$0.486083\pi$
$678$		0			0
$679$	2.88847	−	16.3813i	0.110849	−	0.628658i
$680$	2.42544	−	0.882789i	0.0930115	−	0.0338534i
$681$		0			0
$682$	−3.20796	−	18.1932i	−0.122839	−	0.696655i
$683$	−14.5328	−	25.1716i	−0.556083	−	0.963164i	−0.997818	−	0.0660187i	$-0.978970\pi$
$683$	−14.5328	−	25.1716i	−0.556083	−	0.963164i	0.441735	−	0.897145i	$-0.354363\pi$
$684$		0			0
$685$	−35.3225	+	61.1804i	−1.34960	+	2.33758i
$686$	36.8853	+	13.4251i	1.40829	+	0.512574i
$687$		0			0
$688$	−3.44562	−	2.89122i	−0.131363	−	0.110227i
$689$	−16.8641	−	14.1506i	−0.642470	−	0.539097i
$690$		0			0
$691$	−5.03431	−	1.83234i	−0.191514	−	0.0697055i	0.244483	−	0.969654i	$-0.421382\pi$
$691$	−5.03431	−	1.83234i	−0.191514	−	0.0697055i	−0.435997	+	0.899948i	$0.643604\pi$
$692$	6.60549	−	11.4410i	0.251103	−	0.434923i
$693$		0			0
$694$	−22.6805	−	39.2838i	−0.860940	−	1.49119i
$695$	−14.9793	−	84.9518i	−0.568197	−	3.22241i
$696$		0			0
$697$	6.89141	−	2.50827i	0.261031	−	0.0950074i
$698$	3.95589	−	22.4349i	0.149732	−	0.849175i
$699$		0			0
$700$	−29.4085	+	24.6767i	−1.11154	+	0.932691i
$701$	25.6536			0.968922			0.484461	−	0.874813i	$-0.339016\pi$
$701$	25.6536			0.968922			0.484461	+	0.874813i	$0.339016\pi$
$702$		0			0
$703$	−15.0155			−0.566320
$704$	11.6949	−	9.81315i	0.440766	−	0.369847i
$705$		0			0
$706$	−0.730085	+	4.14052i	−0.0274771	+	0.155830i
$707$	10.3165	−	3.75490i	0.387992	−	0.141218i
$708$		0			0
$709$	−0.814492	−	4.61922i	−0.0305889	−	0.173478i	0.965686	−	0.259712i	$-0.0836278\pi$
$709$	−0.814492	−	4.61922i	−0.0305889	−	0.173478i	−0.996275	+	0.0862342i	$0.972517\pi$
$710$	4.38571	+	7.59627i	0.164593	+	0.285083i
$711$		0			0
$712$	−0.0830629	+	0.143869i	−0.00311291	+	0.00539173i
$713$	2.09987	+	0.764290i	0.0786407	+	0.0286229i
$714$		0			0
$715$	29.1386	+	24.4502i	1.08972	+	0.914386i
$716$	−20.7105	−	17.3782i	−0.773989	−	0.649454i
$717$		0			0
$718$	−44.8337	−	16.3181i	−1.67318	−	0.608987i
$719$	19.5335	−	33.8330i	0.728476	−	1.26176i	−0.229052	−	0.973414i	$-0.573562\pi$
$719$	19.5335	−	33.8330i	0.728476	−	1.26176i	0.957527	−	0.288343i	$-0.0931042\pi$
$720$		0			0
$721$	−15.9893	−	27.6943i	−0.595473	−	1.03139i
$722$	−6.76227	−	38.3508i	−0.251666	−	1.42727i
$723$		0			0
$724$	−23.3123	+	8.48497i	−0.866394	+	0.315342i
$725$	−5.27806	+	29.9334i	−0.196022	+	1.11170i
$726$		0			0
$727$	−8.29267	+	6.95838i	−0.307558	+	0.258072i	−0.783482	−	0.621415i	$-0.786558\pi$
$727$	−8.29267	+	6.95838i	−0.307558	+	0.258072i	0.475924	+	0.879487i	$0.342114\pi$
$728$	2.63030			0.0974853
$729$		0			0
$730$	34.1215			1.26290
$731$	−2.39273	+	2.00774i	−0.0884984	+	0.0742590i
$732$		0			0
$733$	−0.592558	+	3.36057i	−0.0218866	+	0.124125i	−0.993794	−	0.111240i	$-0.964518\pi$
$733$	−0.592558	+	3.36057i	−0.0218866	+	0.124125i	0.971907	+	0.235366i	$0.0756288\pi$
$734$	−5.24676	+	1.90966i	−0.193661	+	0.0704870i
$735$		0			0
$736$	0.707492	+	4.01239i	0.0260785	+	0.147898i
$737$	15.5749	+	26.9766i	0.573710	+	0.993695i
$738$		0			0
$739$	−13.1505	+	22.7773i	−0.483748	+	0.837877i	−0.999826	−	0.0186653i	$-0.994058\pi$
$739$	−13.1505	+	22.7773i	−0.483748	+	0.837877i	0.516077	+	0.856542i	$0.327392\pi$
$740$	−15.7645	−	5.73783i	−0.579516	−	0.210927i
$741$		0			0
$742$	16.5294	+	13.8698i	0.606813	+	0.509177i
$743$	−22.1723	−	18.6048i	−0.813423	−	0.682543i	0.137999	−	0.990432i	$-0.455933\pi$
$743$	−22.1723	−	18.6048i	−0.813423	−	0.682543i	−0.951422	+	0.307889i	$0.900377\pi$
$744$		0			0
$745$	−53.9363	−	19.6312i	−1.97607	−	0.719232i
$746$	−28.3953	+	49.1822i	−1.03963	+	1.80069i
$747$		0			0
$748$	−6.00862	−	10.4072i	−0.219697	−	0.380526i
$749$	−4.74205	−	26.8935i	−0.173271	−	0.982668i
$750$		0			0
$751$	18.2754	−	6.65171i	0.666880	−	0.242724i	0.0136761	−	0.999906i	$-0.495647\pi$
$751$	18.2754	−	6.65171i	0.666880	−	0.242724i	0.653204	+	0.757182i	$0.273424\pi$
$752$	0.174362	−	0.988856i	0.00635833	−	0.0360599i
$753$		0			0
$754$	−24.8576	+	20.8580i	−0.905259	+	0.759603i
$755$	−21.8460			−0.795058
$756$		0			0
$757$	6.59627			0.239745			0.119873	−	0.992789i	$-0.461751\pi$
$757$	6.59627			0.239745			0.119873	+	0.992789i	$0.461751\pi$
$758$	−48.5815	+	40.7648i	−1.76456	+	1.48064i
$759$		0			0
$760$	−0.950837	+	5.39246i	−0.0344905	+	0.195605i
$761$	9.70674	−	3.53297i	0.351869	−	0.128070i	−0.160038	−	0.987111i	$-0.551162\pi$
$761$	9.70674	−	3.53297i	0.351869	−	0.128070i	0.511907	+	0.859041i	$0.328939\pi$
$762$		0			0
$763$	−5.95265	−	33.7591i	−0.215500	−	1.22216i
$764$	−12.6138	−	21.8478i	−0.456352	−	0.790424i
$765$		0			0
$766$	−0.662037	+	1.14668i	−0.0239204	+	0.0414313i
$767$	−59.0052	−	21.4761i	−2.13055	−	0.775458i
$768$		0			0
$769$	34.3640	+	28.8348i	1.23920	+	1.03981i	0.997586	+	0.0694355i	$0.0221198\pi$
$769$	34.3640	+	28.8348i	1.23920	+	1.03981i	0.241610	+	0.970374i	$0.422325\pi$
$770$	−28.5603	−	23.9650i	−1.02924	−	0.863638i
$771$		0			0
$772$	−26.4996	−	9.64506i	−0.953741	−	0.347133i
$773$	21.4677	−	37.1832i	0.772141	−	1.33739i	−0.164247	−	0.986419i	$-0.552519\pi$
$773$	21.4677	−	37.1832i	0.772141	−	1.33739i	0.936388	−	0.350968i	$-0.114147\pi$
$774$		0			0
$775$	18.7335	+	32.4475i	0.672929	+	1.16555i
$776$	−0.292336	−	1.65792i	−0.0104942	−	0.0595158i
$777$		0			0
$778$	7.88326	−	2.86927i	0.282628	−	0.102868i
$779$	−2.70161	+	15.3216i	−0.0967953	+	0.548953i
$780$		0			0
$781$	−2.00774	+	1.68469i	−0.0718426	+	0.0602831i
$782$	3.00054			0.107299
$783$		0			0
$784$	6.29860			0.224950
$785$	−3.43718	+	2.88413i	−0.122678	+	0.102939i
$786$		0			0
$787$	0.0829008	−	0.470154i	0.00295509	−	0.0167592i	−0.983295	−	0.182021i	$-0.941736\pi$
$787$	0.0829008	−	0.470154i	0.00295509	−	0.0167592i	0.986250	+	0.165262i	$0.0528471\pi$
$788$	39.4202	−	14.3478i	1.40428	−	0.511118i
$789$		0			0
$790$	16.2062	+	91.9099i	0.576591	+	3.27001i
$791$	5.51125	+	9.54576i	0.195957	+	0.339408i
$792$		0			0
$793$	−8.66725	+	15.0121i	−0.307783	+	0.533096i
$794$	−16.4073	−	5.97178i	−0.582275	−	0.211931i
$795$		0			0
$796$	−13.1027	−	10.9944i	−0.464412	−	0.389688i
$797$	−8.78574	−	7.37211i	−0.311207	−	0.261134i	0.473784	−	0.880641i	$-0.342888\pi$
$797$	−8.78574	−	7.37211i	−0.311207	−	0.261134i	−0.784991	+	0.619508i	$0.787332\pi$
$798$		0			0
$799$	−0.655230	−	0.238484i	−0.0231804	−	0.00843696i
$800$	−34.1558	+	59.1596i	−1.20759	+	2.09161i
$801$		0			0
$802$	−36.5205	−	63.2554i	−1.28958	−	2.23363i
$803$	1.77045	+	10.0407i	0.0624777	+	0.354329i
$804$		0			0
$805$	4.23783	−	1.54244i	0.149364	−	0.0543640i
$806$	−6.94578	+	39.3915i	−0.244655	+	1.38751i
$807$		0			0
$808$	0.851167	−	0.714214i	0.0299439	−	0.0251260i
$809$	−42.7873			−1.50432			−0.752161	−	0.658979i	$-0.770988\pi$
$809$	−42.7873			−1.50432			−0.752161	+	0.658979i	$0.770988\pi$
$810$		0			0
$811$	−31.2098			−1.09592			−0.547962	−	0.836503i	$-0.684596\pi$
$811$	−31.2098			−1.09592			−0.547962	+	0.836503i	$0.684596\pi$
$812$	11.8034	−	9.90420i	0.414217	−	0.347569i
$813$		0			0
$814$	1.79679	−	10.1901i	0.0629774	−	0.357163i
$815$	−9.64679	+	3.51114i	−0.337912	+	0.122990i
$816$		0			0
$817$	−1.15064	−	6.52563i	−0.0402559	−	0.228303i
$818$	−3.33770	−	5.78106i	−0.116700	−	0.202130i
$819$		0			0
$820$	−8.69119	+	15.0536i	−0.303509	+	0.525694i
$821$	25.6076	+	9.32042i	0.893713	+	0.325285i	0.747731	−	0.664002i	$-0.231143\pi$
$821$	25.6076	+	9.32042i	0.893713	+	0.325285i	0.145982	+	0.989287i	$0.453366\pi$
$822$		0			0
$823$	−11.0621	−	9.28222i	−0.385601	−	0.323558i	0.429295	−	0.903164i	$-0.358762\pi$
$823$	−11.0621	−	9.28222i	−0.385601	−	0.323558i	−0.814897	+	0.579606i	$0.803206\pi$
$824$	−2.47929	−	2.08037i	−0.0863703	−	0.0724733i
$825$		0			0
$826$	57.8341	+	21.0499i	2.01231	+	0.732420i
$827$	3.51379	−	6.08606i	0.122186	−	0.211633i	−0.798443	−	0.602070i	$-0.794343\pi$
$827$	3.51379	−	6.08606i	0.122186	−	0.211633i	0.920630	+	0.390437i	$0.127676\pi$
$828$		0			0
$829$	21.0403	+	36.4429i	0.730760	+	1.26571i	0.956559	+	0.291539i	$0.0941673\pi$
$829$	21.0403	+	36.4429i	0.730760	+	1.26571i	−0.225799	+	0.974174i	$0.572499\pi$
$830$	14.3113	+	81.1635i	0.496753	+	2.81723i
$831$		0			0
$832$	−31.0612	+	11.3054i	−1.07685	+	0.391943i
$833$	0.759523	−	4.30747i	0.0263159	−	0.149245i
$834$		0			0
$835$	−10.8550	+	9.10846i	−0.375654	+	0.315211i
$836$	25.4938			0.881723
$837$		0			0
$838$	−40.6851			−1.40544
$839$	30.5815	−	25.6609i	1.05579	−	0.885913i	0.0620995	−	0.998070i	$-0.480220\pi$
$839$	30.5815	−	25.6609i	1.05579	−	0.885913i	0.993691	+	0.112157i	$0.0357759\pi$
$840$		0			0
$841$	−2.91740	+	16.5454i	−0.100600	+	0.570532i
$842$	50.9590	−	18.5476i	1.75616	−	0.639191i
$843$		0			0
$844$	−1.95084	−	11.0637i	−0.0671506	−	0.380830i
$845$	−17.1183	−	29.6498i	−0.588887	−	1.01998i
$846$		0			0
$847$	−7.34002	+	12.7133i	−0.252206	+	0.436834i
$848$	18.5370	+	6.74691i	0.636563	+	0.231690i
$849$		0			0
$850$	38.5387	+	32.3378i	1.32187	+	1.10918i
$851$	0.958801	+	0.804530i	0.0328673	+	0.0275789i
$852$		0			0
$853$	22.0649	+	8.03098i	0.755489	+	0.274976i	0.690914	−	0.722937i	$-0.257208\pi$
$853$	22.0649	+	8.03098i	0.755489	+	0.274976i	0.0645757	+	0.997913i	$0.479431\pi$
$854$	8.49524	−	14.7142i	0.290701	−	0.503509i
$855$		0			0
$856$	−1.38191	−	2.39354i	−0.0472328	−	0.0818095i
$857$	1.39521	+	7.91266i	0.0476596	+	0.270291i	0.999320	−	0.0368597i	$-0.0117355\pi$
$857$	1.39521	+	7.91266i	0.0476596	+	0.270291i	−0.951661	+	0.307151i	$0.900624\pi$
$858$		0			0
$859$	22.8307	−	8.30969i	0.778973	−	0.283523i	0.0782287	−	0.996935i	$-0.475074\pi$
$859$	22.8307	−	8.30969i	0.778973	−	0.283523i	0.700744	+	0.713412i	$0.252851\pi$
$860$	1.28558	−	7.29086i	0.0438378	−	0.248616i
$861$		0			0
$862$	−3.89440	+	3.26779i	−0.132644	+	0.111301i
$863$	−10.2828			−0.350029			−0.175015	−	0.984566i	$-0.555997\pi$
$863$	−10.2828			−0.350029			−0.175015	+	0.984566i	$0.555997\pi$
$864$		0			0
$865$	−26.0205			−0.884725
$866$	40.7587	−	34.2006i	1.38504	−	1.16218i
$867$		0			0
$868$	3.29813	−	18.7046i	0.111946	−	0.634877i
$869$	−26.2048	+	9.53777i	−0.888937	+	0.323547i
$870$		0			0
$871$	−11.7117	−	66.4202i	−0.396835	−	2.25056i
$872$	−1.73470	−	3.00459i	−0.0587443	−	0.101748i
$873$		0			0
$874$	−3.18273	+	5.51266i	−0.107658	+	0.186468i
$875$	30.2292	+	11.0025i	1.02193	+	0.371953i
$876$		0			0
$877$	−20.0915	−	16.8588i	−0.678442	−	0.569281i	0.237108	−	0.971483i	$-0.423800\pi$
$877$	−20.0915	−	16.8588i	−0.678442	−	0.569281i	−0.915551	+	0.402202i	$0.868245\pi$
$878$	−17.6683	−	14.8255i	−0.596277	−	0.500336i
$879$		0			0
$880$	−32.0292	−	11.6577i	−1.07970	−	0.392980i
$881$	19.6163	−	33.9764i	0.660890	−	1.14469i	−0.319492	−	0.947589i	$-0.603512\pi$
$881$	19.6163	−	33.9764i	0.660890	−	1.14469i	0.980382	−	0.197106i	$-0.0631543\pi$
$882$		0			0
$883$	−3.89915	−	6.75352i	−0.131217	−	0.227274i	0.792929	−	0.609314i	$-0.208555\pi$
$883$	−3.89915	−	6.75352i	−0.131217	−	0.227274i	−0.924146	+	0.382040i	$0.875222\pi$
$884$	4.51822	+	25.6241i	0.151964	+	0.861831i
$885$		0			0
$886$	−3.85117	+	1.40171i	−0.129382	+	0.0470914i
$887$	−3.96909	+	22.5098i	−0.133269	+	0.755805i	0.842781	+	0.538257i	$0.180917\pi$
$887$	−3.96909	+	22.5098i	−0.133269	+	0.755805i	−0.976050	+	0.217548i	$0.930194\pi$
$888$		0			0
$889$	−10.9534	+	9.19096i	−0.367364	+	0.308255i
$890$	−5.09840			−0.170899
$891$		0			0
$892$	−16.7297			−0.560151
$893$	1.13316	−	0.950837i	0.0379199	−	0.0318185i
$894$		0			0
$895$	−9.24675	+	52.4409i	−0.309085	+	1.75291i
$896$	−4.18442	+	1.52300i	−0.139792	+	0.0508800i
$897$		0			0
$898$	3.60859	+	20.4653i	0.120420	+	0.682938i
$899$	−7.51887	−	13.0231i	−0.250768	−	0.434343i
$900$		0			0
$901$	6.84936	−	11.8634i	0.228185	−	0.395228i
$902$	−10.0746	−	3.66684i	−0.335446	−	0.122092i
$903$		0			0
$904$	0.854570	+	0.717070i	0.0284226	+	0.0238494i
$905$	37.4312	+	31.4085i	1.24426	+	1.04406i
$906$		0			0
$907$	35.5660	+	12.9450i	1.18095	+	0.429830i	0.856537	−	0.516085i	$-0.172611\pi$
$907$	35.5660	+	12.9450i	1.18095	+	0.429830i	0.324412	+	0.945916i	$0.394834\pi$
$908$	10.0251	−	17.3640i	0.332694	−	0.576243i
$909$		0			0
$910$	40.3619	+	69.9089i	1.33798	+	2.31746i
$911$	−9.15204	−	51.9038i	−0.303221	−	1.71965i	−0.631764	−	0.775161i	$-0.717669\pi$
$911$	−9.15204	−	51.9038i	−0.303221	−	1.71965i	0.328544	−	0.944489i	$-0.393442\pi$
$912$		0			0
$913$	−23.1408	+	8.42258i	−0.765850	+	0.278747i
$914$	2.70518	−	15.3418i	0.0894794	−	0.507463i
$915$		0			0
$916$	−11.9081	+	9.99206i	−0.393454	+	0.330147i
$917$	−24.2908			−0.802152
$918$		0			0
$919$	−49.1052			−1.61983			−0.809916	−	0.586545i	$-0.800488\pi$
$919$	−49.1052			−1.61983			−0.809916	+	0.586545i	$0.800488\pi$
$920$	0.349643	−	0.293386i	0.0115274	−	0.00967264i
$921$		0			0
$922$	−13.3705	+	75.8280i	−0.440335	+	2.49726i
$923$	5.33251	−	1.94087i	0.175522	−	0.0638847i
$924$		0			0
$925$	3.64409	+	20.6666i	0.119817	+	0.679515i
$926$	23.3329	+	40.4138i	0.766766	+	1.32808i
$927$		0			0
$928$	13.7087	−	23.7442i	0.450011	−	0.779442i
$929$	16.8681	+	6.13950i	0.553426	+	0.201430i	0.603568	−	0.797312i	$-0.293745\pi$
$929$	16.8681	+	6.13950i	0.553426	+	0.201430i	−0.0501422	+	0.998742i	$0.515967\pi$
$930$		0			0
$931$	7.10813	+	5.96443i	0.232959	+	0.195476i
$932$	18.3407	+	15.3897i	0.600769	+	0.504105i
$933$		0			0
$934$	64.2520	+	23.3858i	2.10239	+	0.765207i
$935$	−11.8347	+	20.4982i	−0.387035	+	0.670364i
$936$		0			0
$937$	14.8990	+	25.8058i	0.486729	+	0.843039i	0.999884	−	0.0152572i	$-0.00485672\pi$
$937$	14.8990	+	25.8058i	0.486729	+	0.843039i	−0.513155	+	0.858296i	$0.671523\pi$
$938$	11.4792	+	65.1020i	0.374810	+	2.12566i
$939$		0			0
$940$	1.55303	−	0.565258i	0.0506544	−	0.0184367i
$941$	5.21140	−	29.5553i	0.169887	−	0.963476i	−0.773995	−	0.633192i	$-0.781744\pi$
$941$	5.21140	−	29.5553i	0.169887	−	0.963476i	0.943882	−	0.330284i	$-0.107144\pi$
$942$		0			0
$943$	0.993441	−	0.833596i	0.0323509	−	0.0271456i
$944$	56.2663			1.83131
$945$		0			0
$946$	4.56624			0.148461
$947$	−34.9326	+	29.3120i	−1.13516	+	0.952511i	−0.999270	−	0.0382132i	$-0.987833\pi$
$947$	−34.9326	+	29.3120i	−1.13516	+	0.952511i	−0.135889	+	0.990724i	$0.543389\pi$
$948$		0			0
$949$	3.83332	−	21.7398i	0.124435	−	0.705705i
$950$	−100.290	+	36.5027i	−3.25385	+	1.18431i
$951$		0			0
$952$	0.284214	+	1.61186i	0.00921144	+	0.0522407i
$953$	−6.59786	−	11.4278i	−0.213726	−	0.370184i	0.739152	−	0.673539i	$-0.235227\pi$
$953$	−6.59786	−	11.4278i	−0.213726	−	0.370184i	−0.952878	+	0.303355i	$0.901893\pi$
$954$		0			0
$955$	−24.8444	+	43.0317i	−0.803945	+	1.39247i
$956$	−26.5182	−	9.65183i	−0.857659	−	0.312162i
$957$		0			0
$958$	−9.77972	−	8.20616i	−0.315968	−	0.265129i
$959$	−34.3168	−	28.7952i	−1.10815	−	0.929845i
$960$		0			0
$961$	11.7118	+	4.26276i	0.377801	+	0.137508i
$962$	−11.2018	+	19.4021i	−0.361162	+	0.625550i
$963$		0			0
$964$	−0.747626	−	1.29493i	−0.0240794	−	0.0417068i
$965$	9.64506	+	54.6999i	0.310486	+	1.76085i
$966$		0			0
$967$	18.9393	−	6.89333i	0.609046	−	0.221675i	−0.0190396	−	0.999819i	$-0.506061\pi$
$967$	18.9393	−	6.89333i	0.609046	−	0.221675i	0.628086	+	0.778144i	$0.283839\pi$
$968$	−0.257995	+	1.46316i	−0.00829228	+	0.0470279i
$969$		0			0
$970$	39.5788	−	33.2105i	1.27080	−	1.06633i
$971$	26.5839			0.853118			0.426559	−	0.904460i	$-0.359726\pi$
$971$	26.5839			0.853118			0.426559	+	0.904460i	$0.359726\pi$
$972$		0			0
$973$	54.7006			1.75362
$974$	−30.1503	+	25.2991i	−0.966076	+	0.810634i
$975$		0			0
$976$	2.69728	−	15.2970i	0.0863379	−	0.489646i
$977$	13.5354	−	4.92649i	0.433036	−	0.157612i	−0.116299	−	0.993214i	$-0.537103\pi$
$977$	13.5354	−	4.92649i	0.433036	−	0.157612i	0.549335	+	0.835602i	$0.314881\pi$
$978$		0			0
$979$	−0.264538	−	1.50027i	−0.00845468	−	0.0479488i
$980$	5.18355	+	8.97818i	0.165583	+	0.286797i
$981$		0			0
$982$	25.8286	−	44.7365i	0.824225	−	1.42760i
$983$	−40.3956	−	14.7028i	−1.28842	−	0.468947i	−0.395212	−	0.918590i	$-0.629329\pi$
$983$	−40.3956	−	14.7028i	−1.28842	−	0.468947i	−0.893208	+	0.449644i	$0.851551\pi$
$984$		0			0
$985$	−63.2948	−	53.1106i	−2.01674	−	1.69225i
$986$	−15.4678	−	12.9791i	−0.492596	−	0.413337i
$987$		0			0
$988$	−51.8696	−	18.8790i	−1.65019	−	0.600621i
$989$	−0.276170	+	0.478340i	−0.00878169	+	0.0152103i
$990$		0			0
$991$	7.78968	+	13.4921i	0.247447	+	0.428591i	0.962817	−	0.270155i	$-0.0870750\pi$
$991$	7.78968	+	13.4921i	0.247447	+	0.428591i	−0.715370	+	0.698746i	$0.753742\pi$
$992$	−5.86872	−	33.2832i	−0.186332	−	1.05674i
$993$		0			0
$994$	−5.22668	+	1.90236i	−0.165780	+	0.0603391i
$995$	−5.85002	+	33.1771i	−0.185458	+	1.05179i
$996$		0			0
$997$	31.1156	−	26.1091i	0.985442	−	0.826884i	0.000540128	−	1.00000i	$-0.499828\pi$
$997$	31.1156	−	26.1091i	0.985442	−	0.826884i	0.984901	+	0.173116i	$0.0553836\pi$
$998$	−12.4426			−0.393863
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.q.325.1		12
3.2	odd	2	inner	729.2.e.q.325.2		12
9.2	odd	6		729.2.e.r.568.1		12
9.4	even	3		729.2.e.m.82.1		12
9.5	odd	6		729.2.e.m.82.2		12
9.7	even	3		729.2.e.r.568.2		12
27.2	odd	18		729.2.e.r.163.1		12
27.4	even	9		729.2.a.c.1.1	✓	6
27.5	odd	18		729.2.c.c.244.1		12
27.7	even	9		729.2.e.m.649.1		12
27.11	odd	18	inner	729.2.e.q.406.2		12
27.13	even	9		729.2.c.c.487.6		12
27.14	odd	18		729.2.c.c.487.1		12
27.16	even	9	inner	729.2.e.q.406.1		12
27.20	odd	18		729.2.e.m.649.2		12
27.22	even	9		729.2.c.c.244.6		12
27.23	odd	18		729.2.a.c.1.6	yes	6
27.25	even	9		729.2.e.r.163.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.1	✓	6	27.4	even	9
729.2.a.c.1.6	yes	6	27.23	odd	18
729.2.c.c.244.1		12	27.5	odd	18
729.2.c.c.244.6		12	27.22	even	9
729.2.c.c.487.1		12	27.14	odd	18
729.2.c.c.487.6		12	27.13	even	9
729.2.e.m.82.1		12	9.4	even	3
729.2.e.m.82.2		12	9.5	odd	6
729.2.e.m.649.1		12	27.7	even	9
729.2.e.m.649.2		12	27.20	odd	18
729.2.e.q.325.1		12	1.1	even	1	trivial
729.2.e.q.325.2		12	3.2	odd	2	inner
729.2.e.q.406.1		12	27.16	even	9	inner
729.2.e.q.406.2		12	27.11	odd	18	inner
729.2.e.r.163.1		12	27.2	odd	18
729.2.e.r.163.2		12	27.25	even	9
729.2.e.r.568.1		12	9.2	odd	6
729.2.e.r.568.2		12	9.7	even	3

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50881 + 1.26604i) q^{2} +(0.326352 - 1.85083i) q^{4} +(-3.47843 + 1.26604i) q^{5} +(-0.407604 - 2.31164i) q^{7} +(-0.118782 - 0.205737i) q^{8} +(3.64543 - 6.31407i) q^{10} +(2.04715 + 0.745100i) q^{11} +(-3.61334 - 3.03195i) q^{13} +(3.54163 + 2.97178i) q^{14} +(3.97178 + 1.44561i) q^{16} +(1.46756 - 2.54189i) q^{17} +(3.11334 + 5.39246i) q^{19} +(1.20805 + 6.85117i) q^{20} +(-4.03209 + 1.46756i) q^{22} +(0.0901285 - 0.511144i) q^{23} +(6.66637 - 5.59375i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(-2.67561 + 2.24510i) q^{29} +(-0.747626 + 4.24000i) q^{31} +(-7.37641 + 2.68479i) q^{32} +(1.00387 + 5.69323i) q^{34} +(4.34445 + 7.52481i) q^{35} +(-1.20574 + 2.08840i) q^{37} +(-11.5245 - 4.19459i) q^{38} +(0.673648 + 0.565258i) q^{40} +(1.91404 + 1.60607i) q^{41} +(-1.00000 - 0.363970i) q^{43} +(2.04715 - 3.54576i) q^{44} +(0.511144 + 0.885328i) q^{46} +(-0.0412527 - 0.233956i) q^{47} +(1.40033 - 0.509678i) q^{49} +(-2.97637 + 16.8799i) q^{50} +(-6.79086 + 5.69821i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(-0.427173 + 0.358441i) q^{56} +(1.19459 - 6.77487i) q^{58} +(12.5094 - 4.55303i) q^{59} +(-0.638156 - 3.61916i) q^{61} +(-4.24000 - 7.34389i) q^{62} +(3.50387 - 6.06888i) q^{64} +(16.4073 + 5.97178i) q^{65} +(10.9534 + 9.19096i) q^{67} +(-4.22567 - 3.54576i) q^{68} +(-16.0817 - 5.85327i) q^{70} +(-0.601535 + 1.04189i) q^{71} +(2.34002 + 4.05304i) q^{73} +(-0.824773 - 4.67752i) q^{74} +(10.9966 - 4.00243i) q^{76} +(0.887975 - 5.03596i) q^{77} +(-9.80587 + 8.22811i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(-8.65933 + 7.26604i) q^{83} +(-1.88666 + 10.6998i) q^{85} +(1.96962 - 0.716881i) q^{86} +(-0.0898700 - 0.509678i) q^{88} +(-0.349643 - 0.605600i) q^{89} +(-5.53596 + 9.58856i) q^{91} +(-0.916629 - 0.333626i) q^{92} +(0.358441 + 0.300767i) q^{94} +(-17.6566 - 14.8157i) q^{95} +(6.65910 + 2.42371i) q^{97} +(-1.46756 + 2.54189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52}+ \cdots + 6 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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