LMFDB - Embedded newform 729.2.e.q.325.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			325.2
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.q.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	0.0721247	−	0.997396i	$-0.477022\pi$
$2$	1.50881	−	1.26604i	1.06689	−	0.895229i	0.994767	+	0.102167i	$0.0325776\pi$
$3$		0			0
$3$		0			0
$4$	0.326352	−	1.85083i	0.163176	−	0.925417i
$5$	3.47843	−	1.26604i	1.55560	−	0.566192i	0.585877	−	0.810400i	$-0.300750\pi$
$5$	3.47843	−	1.26604i	1.55560	−	0.566192i	0.969723	+	0.244207i	$0.0785278\pi$
$6$		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	0.0144295	−	0.999896i	$-0.495407\pi$
$11$	−2.04715	−	0.745100i	−0.617237	−	0.224656i	−0.631667	+	0.775240i	$0.717629\pi$
$12$		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	−0.987278	−	0.159006i	$-0.949171\pi$
$17$	−1.46756	+	2.54189i	−0.355936	+	0.616499i	0.631342	+	0.775505i	$0.282504\pi$
$18$		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	−0.992761	−	0.120103i	$-0.961677\pi$
$23$	−0.0901285	+	0.511144i	−0.0187931	+	0.106581i	0.973968	+	0.226684i	$0.0727885\pi$
$24$		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	−0.359625	−	0.933097i	$-0.617095\pi$
$29$	2.67561	−	2.24510i	0.496848	−	0.416905i	0.856473	+	0.516192i	$0.172651\pi$
$30$		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	0.480973	−	0.876735i	$-0.340283\pi$
$41$	−1.91404	−	1.60607i	−0.298922	−	0.250826i	−0.779896	+	0.625910i	$0.784728\pi$
$42$		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	0.987669	−	0.156559i	$-0.0500402\pi$
$47$	0.0412527	+	0.233956i	0.00601732	+	0.0341259i	−0.981651	+	0.190685i	$0.938929\pi$
$48$		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	$-0.603865\pi$
$53$	−4.66717			−0.641085			−0.320543	+	0.947234i	$0.603865\pi$
$54$		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	−0.984989	−	0.172616i	$-0.944778\pi$
$59$	−12.5094	+	4.55303i	−1.62858	+	0.592754i	−0.643590	+	0.765370i	$0.722556\pi$
$60$		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	−0.828121	−	0.560549i	$-0.810590\pi$
$71$	0.601535	−	1.04189i	0.0713891	−	0.123649i	0.899510	+	0.436900i	$0.143923\pi$
$72$		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	−0.0288938	−	0.999582i	$-0.509198\pi$
$83$	8.65933	−	7.26604i	0.950485	−	0.797552i	0.979379	+	0.202030i	$0.0647540\pi$
$84$		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	0.883961	−	0.467560i	$-0.154867\pi$
$89$	0.349643	+	0.605600i	0.0370621	+	0.0641935i	−0.846899	+	0.531753i	$0.821533\pi$
$90$		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	$-0.980801\pi$
$101$	−0.812174	−	4.60607i	−0.0808143	−	0.458321i	0.917367	−	0.398042i	$-0.130310\pi$
$102$		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	$-0.690102\pi$
$107$	−11.6340			−1.12470			−0.562350	+	0.826900i	$0.690102\pi$
$108$		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	−0.126020	−	0.992028i	$-0.540220\pi$
$113$	4.41263	−	1.60607i	0.415106	−	0.151086i	0.541126	+	0.840942i	$0.317998\pi$
$114$		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	$0.204871\pi$
$131$	−1.79698	+	10.1912i	−0.157003	+	0.890408i	−0.956932	+	0.290313i	$0.906241\pi$
$132$		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	$0.581182\pi$
$137$	−14.6197	+	12.2674i	−1.24905	+	1.04807i	−0.996761	+	0.0804207i	$0.974374\pi$
$138$		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	0.00993072	−	0.999951i	$-0.496839\pi$
$149$	−11.8782	−	9.96703i	−0.973104	−	0.816531i	−0.983035	+	0.183419i	$0.941283\pi$
$150$		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	−0.477428	−	0.878671i	$-0.658431\pi$
$167$	−3.59721	+	1.30928i	−0.278361	+	0.101315i	0.199068	+	0.979986i	$0.436209\pi$
$168$		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	0.0784801	−	0.996916i	$-0.474993\pi$
$173$	−6.60549	−	2.40420i	−0.502206	−	0.182788i	−0.580686	+	0.814128i	$0.697216\pi$
$174$		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	$0.347338\pi$
$179$	−7.19269	+	12.4581i	−0.537607	+	0.931163i	−0.999032	+	0.0439838i	$0.985995\pi$
$180$		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	−0.933920	−	0.357482i	$-0.883635\pi$
$191$	−10.2829	+	8.62836i	−0.744043	+	0.624326i	0.189877	+	0.981808i	$0.439191\pi$
$192$		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	$-0.874054\pi$
$197$	−11.1606	−	19.3307i	−0.795158	−	1.37725i	0.127580	−	0.991828i	$-0.459279\pi$
$198$		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	−0.0128273	−	0.999918i	$-0.504083\pi$
$227$	−10.0251	−	3.64883i	−0.665388	−	0.242182i	−0.652561	+	0.757736i	$0.726305\pi$
$228$		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	−0.578376	−	0.815770i	$-0.696313\pi$
$233$	6.36965	−	11.0326i	0.417290	−	0.722767i	0.995666	+	0.0930034i	$0.0296467\pi$
$234$		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	$0.216968\pi$
$239$	−2.60743	+	14.7875i	−0.168660	+	0.956521i	−0.945210	+	0.326464i	$0.894143\pi$
$240$		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	0.966884	−	0.255216i	$-0.0821465\pi$
$251$	4.15749	+	7.20099i	0.262419	+	0.454522i	−0.704465	+	0.709738i	$0.748813\pi$
$252$		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	$0.0168985\pi$
$257$	19.6262	+	16.4684i	1.22425	+	1.02727i	0.225661	+	0.974206i	$0.427546\pi$
$258$		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	$-0.722696\pi$
$263$	−4.87343	−	27.6386i	−0.300509	−	1.70427i	0.343417	−	0.939183i	$-0.388415\pi$
$264$		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	$-0.128369\pi$
$269$	30.1710			1.83956			0.919778	+	0.392439i	$0.128369\pi$
$270$		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	0.292581	−	0.956241i	$-0.405486\pi$
$281$	−1.64192	−	0.597611i	−0.0979489	−	0.0356505i	−0.390530	+	0.920590i	$0.627708\pi$
$282$		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	$-0.796437\pi$
$293$	2.66565	−	15.1177i	0.155729	−	0.883184i	0.958116	−	0.286380i	$-0.0924520\pi$
$294$		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	0.224619	−	0.974447i	$-0.427886\pi$
$311$	−12.2744	−	10.2995i	−0.696020	−	0.584030i	−0.920638	+	0.390417i	$0.872331\pi$
$312$		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	$-0.904100\pi$
$317$	−2.83239	−	16.0633i	−0.159083	−	0.902205i	0.795874	−	0.605462i	$-0.207012\pi$
$318$		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	$-0.732320\pi$
$347$	3.99919	−	22.6805i	0.214688	−	1.21755i	0.881448	−	0.472281i	$-0.156569\pi$
$348$		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	−0.685267	−	0.728292i	$-0.740314\pi$
$353$	−1.63522	+	1.37211i	−0.0870339	+	0.0730301i	0.598233	+	0.801322i	$0.295870\pi$
$354$		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	$-0.945918\pi$
$359$	−12.1118	−	20.9782i	−0.639234	−	1.10719i	0.346367	−	0.938099i	$-0.387415\pi$
$360$		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	−0.358109	−	0.933680i	$-0.616578\pi$
$383$	−0.631708	+	0.229923i	−0.0322788	+	0.0117485i	0.325830	+	0.945428i	$0.394356\pi$
$384$		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	0.441486	−	0.897268i	$-0.354451\pi$
$389$	4.00243	+	1.45677i	0.202931	+	0.0738610i	−0.238555	+	0.971129i	$0.576674\pi$
$390$		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	$-0.567718\pi$
$401$	6.43956	−	36.5205i	0.321576	−	1.82375i	0.532718	−	0.846293i	$-0.321171\pi$
$402$		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	0.168447	−	0.985711i	$-0.446125\pi$
$419$	−15.8237	−	13.2777i	−0.773038	−	0.648656i	−0.941485	+	0.337055i	$0.890569\pi$
$420$		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	$-0.519800\pi$
$431$	−2.58110			−0.124327			−0.0621636	+	0.998066i	$0.519800\pi$
$432$		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	0.295153	−	0.955450i	$-0.404629\pi$
$443$	−1.95529	−	0.711667i	−0.0928986	−	0.0338123i	−0.388051	+	0.921638i	$0.626852\pi$
$444$		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	−0.963238	−	0.268649i	$-0.913423\pi$
$449$	−5.27541	+	9.13728i	−0.248962	+	0.431215i	0.714276	+	0.699864i	$0.246756\pi$
$450$		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	$0.641978\pi$
$461$	−29.9468	+	25.1284i	−1.39476	+	1.17034i	−0.963369	+	0.268180i	$0.913578\pi$
$462$		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	$0.130212\pi$
$467$	17.3576	+	30.0642i	0.803214	+	1.39121i	−0.114277	+	0.993449i	$0.536455\pi$
$468$		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	0.948237	−	0.317563i	$-0.102864\pi$
$479$	−1.12554	−	6.38326i	−0.0514272	−	0.291658i	−0.999664	+	0.0259046i	$0.991753\pi$
$480$		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	0.280420	−	0.959877i	$-0.409526\pi$
$491$	24.6454	−	8.97019i	1.11223	−	0.404819i	0.831811	+	0.555059i	$0.187304\pi$
$492$		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	−0.513292	−	0.858214i	$-0.671574\pi$
$503$	10.9131	−	18.9020i	0.486589	−	0.842798i	0.999881	+	0.0154166i	$0.00490745\pi$
$504$		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	$-0.721400\pi$
$509$	5.05196	−	28.6511i	0.223924	−	1.26994i	0.864731	−	0.502236i	$-0.167489\pi$
$510$		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	0.976134	−	0.217171i	$-0.0696829\pi$
$521$	6.84743	+	11.8601i	0.299991	+	0.519600i	−0.676142	+	0.736771i	$0.736350\pi$
$522$		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	$-0.461286\pi$
$557$	21.7196	−	37.6195i	0.920290	−	1.59399i	0.798966	−	0.601376i	$-0.205381\pi$
$558$		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	$0.291279\pi$
$563$	−5.55980	+	31.5312i	−0.234318	+	1.32888i	−0.844046	+	0.536271i	$0.819832\pi$
$564$		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	−0.745017	−	0.667046i	$-0.767559\pi$
$569$	−5.18761	+	4.35292i	−0.217476	+	0.182484i	0.527541	+	0.849530i	$0.323114\pi$
$570$		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	0.984339	−	0.176287i	$-0.0564086\pi$
$587$	−0.0225502	−	0.127889i	−0.000930748	−	0.00527853i	−0.985270	+	0.171008i	$0.945298\pi$
$588$		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	$-0.318715\pi$
$593$	26.2622			1.07846			0.539230	+	0.842158i	$0.318715\pi$
$594$		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	−0.812244	−	0.583317i	$-0.801754\pi$
$599$	−25.9310	+	9.43810i	−1.05951	+	0.385630i	−0.247266	+	0.968948i	$0.579532\pi$
$600$		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	$-0.783613\pi$
$617$	4.17567	−	23.6814i	0.168106	−	0.953377i	0.945804	−	0.324738i	$-0.105276\pi$
$618$		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	$-0.931941\pi$
$641$	−3.32947	−	18.8824i	−0.131506	−	0.745809i	0.845723	−	0.533622i	$-0.179170\pi$
$642$		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	$-0.444841\pi$
$647$	8.77141			0.344840			0.172420	+	0.985024i	$0.444841\pi$
$648$		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	−0.865488	−	0.500929i	$-0.832992\pi$
$653$	−30.8307	+	11.2215i	−1.20650	+	0.439130i	−0.341011	+	0.940059i	$0.610769\pi$
$654$		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	−0.0227199	−	0.999742i	$-0.507233\pi$
$659$	−17.5268	−	6.37922i	−0.682746	−	0.248499i	−0.660026	+	0.751243i	$0.729455\pi$
$660$		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	−0.0437064	−	0.999044i	$-0.513917\pi$
$677$	24.2648	−	20.3606i	0.932571	−	0.782520i	0.976277	+	0.216525i	$0.0694722\pi$
$678$		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	$0.0210297\pi$
$683$	14.5328	+	25.1716i	0.556083	+	0.963164i	−0.441735	+	0.897145i	$0.645637\pi$
$684$		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	$-0.660984\pi$
$701$	−25.6536			−0.968922			−0.484461	+	0.874813i	$0.660984\pi$
$702$		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	$0.426438\pi$
$719$	−19.5335	+	33.8330i	−0.728476	+	1.26176i	−0.957527	+	0.288343i	$0.906896\pi$
$720$		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	0.951422	−	0.307889i	$-0.0996226\pi$
$743$	22.1723	+	18.6048i	0.813423	+	0.682543i	−0.137999	+	0.990432i	$0.544067\pi$
$744$		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	−0.511907	−	0.859041i	$-0.671061\pi$
$761$	−9.70674	+	3.53297i	−0.351869	+	0.128070i	0.160038	+	0.987111i	$0.448838\pi$
$762$		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	$0.447481\pi$
$773$	−21.4677	+	37.1832i	−0.772141	+	1.33739i	−0.936388	+	0.350968i	$0.885853\pi$
$774$		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

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

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

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