LMFDB - Embedded newform 729.2.e.m.649.1

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			649.1
Root			$-0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.m.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 1.93969i) q^{2} +(-1.76604 - 0.642788i) q^{4} +(2.83564 - 2.37939i) q^{5} +(2.20574 - 0.802823i) q^{7} +(-0.118782 + 0.205737i) q^{8} +O(q^{10})$	\(q+(-0.342020 + 1.93969i) q^{2} +(-1.76604 - 0.642788i) q^{4} +(2.83564 - 2.37939i) q^{5} +(2.20574 - 0.802823i) q^{7} +(-0.118782 + 0.205737i) q^{8} +(3.64543 + 6.31407i) q^{10} +(-1.66885 - 1.40033i) q^{11} +(-0.819078 - 4.64522i) q^{13} +(0.802823 + 4.55303i) q^{14} +(-3.23783 - 2.71686i) q^{16} +(1.46756 + 2.54189i) q^{17} +(3.11334 - 5.39246i) q^{19} +(-6.53731 + 2.37939i) q^{20} +(3.28699 - 2.75811i) q^{22} +(-0.487728 - 0.177519i) q^{23} +(1.51114 - 8.57013i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(-0.606511 + 3.43969i) q^{29} +(4.04576 + 1.47254i) q^{31} +(6.01330 - 5.04576i) q^{32} +(-5.43242 + 1.97724i) q^{34} +(4.34445 - 7.52481i) q^{35} +(-1.20574 - 2.08840i) q^{37} +(9.39490 + 7.88326i) q^{38} +(0.152704 + 0.866025i) q^{40} +(0.433877 + 2.46064i) q^{41} +(0.815207 + 0.684040i) q^{43} +(2.04715 + 3.54576i) q^{44} +(0.511144 - 0.885328i) q^{46} +(0.223238 - 0.0812519i) q^{47} +(-1.14156 + 0.957882i) q^{49} +(16.1066 + 5.86231i) q^{50} +(-1.53936 + 8.73016i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(-0.0968323 + 0.549163i) q^{56} +(-6.46451 - 2.35289i) q^{58} +(-10.1977 + 8.55690i) q^{59} +(3.45336 - 1.25692i) q^{61} +(-4.24000 + 7.34389i) q^{62} +(3.50387 + 6.06888i) q^{64} +(-13.3754 - 11.2233i) q^{65} +(2.48293 + 14.0814i) q^{67} +(-0.957882 - 5.43242i) q^{68} +(13.1099 + 11.0005i) q^{70} +(-0.601535 - 1.04189i) q^{71} +(2.34002 - 4.05304i) q^{73} +(4.46324 - 1.62449i) q^{74} +(-8.96451 + 7.52211i) q^{76} +(-4.80526 - 1.74897i) q^{77} +(-2.22281 + 12.6062i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(-1.96291 + 11.1322i) q^{83} +(10.2096 + 3.71599i) q^{85} +(-1.60565 + 1.34730i) q^{86} +(0.486329 - 0.177009i) q^{88} +(-0.349643 + 0.605600i) q^{89} +(-5.53596 - 9.58856i) q^{91} +(0.747243 + 0.627011i) q^{92} +(0.0812519 + 0.460802i) q^{94} +(-4.00243 - 22.6989i) q^{95} +(-5.42855 - 4.55509i) q^{97} +(-1.46756 - 2.54189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q - 12 * q^4 + 6 * q^7	$ 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100}) $ 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.342020	+	1.93969i	−0.241845	+	1.37157i	0.585863	+	0.810410i	$0.300756\pi$
$2$	−0.342020	+	1.93969i	−0.241845	+	1.37157i	−0.827708	+	0.561160i	$0.810355\pi$
$3$		0			0
$3$		0			0
$4$	−1.76604	−	0.642788i	−0.883022	−	0.321394i
$5$	2.83564	−	2.37939i	1.26814	−	1.06409i	0.273372	−	0.961908i	$-0.411861\pi$
$5$	2.83564	−	2.37939i	1.26814	−	1.06409i	0.994765	−	0.102185i	$-0.0325834\pi$
$6$		0			0
$7$	2.20574	−	0.802823i	0.833690	−	0.303438i	0.110318	−	0.993896i	$-0.464813\pi$
$7$	2.20574	−	0.802823i	0.833690	−	0.303438i	0.723373	+	0.690458i	$0.242591\pi$
$8$	−0.118782	+	0.205737i	−0.0419959	+	0.0727390i
$9$		0			0
$10$	3.64543	+	6.31407i	1.15279	+	1.99668i
$11$	−1.66885	−	1.40033i	−0.503177	−	0.422215i	0.355544	−	0.934660i	$-0.384296\pi$
$11$	−1.66885	−	1.40033i	−0.503177	−	0.422215i	−0.858720	+	0.512444i	$0.828740\pi$
$12$		0			0
$13$	−0.819078	−	4.64522i	−0.227171	−	1.28835i	−0.858490	−	0.512829i	$-0.828597\pi$
$13$	−0.819078	−	4.64522i	−0.227171	−	1.28835i	0.631319	−	0.775523i	$-0.282514\pi$
$14$	0.802823	+	4.55303i	0.214563	+	1.21685i
$15$		0			0
$16$	−3.23783	−	2.71686i	−0.809456	−	0.679215i
$17$	1.46756	+	2.54189i	0.355936	+	0.616499i	0.987278	−	0.159006i	$-0.0508289\pi$
$17$	1.46756	+	2.54189i	0.355936	+	0.616499i	−0.631342	+	0.775505i	$0.717496\pi$
$18$		0			0
$19$	3.11334	−	5.39246i	0.714249	−	1.23712i	−0.248999	−	0.968504i	$-0.580102\pi$
$19$	3.11334	−	5.39246i	0.714249	−	1.23712i	0.963248	−	0.268612i	$-0.0865651\pi$
$20$	−6.53731	+	2.37939i	−1.46179	+	0.532047i
$21$		0			0
$22$	3.28699	−	2.75811i	0.700788	−	0.588031i
$23$	−0.487728	−	0.177519i	−0.101698	−	0.0370152i	0.290670	−	0.956823i	$-0.406122\pi$
$23$	−0.487728	−	0.177519i	−0.101698	−	0.0370152i	−0.392368	+	0.919808i	$0.628344\pi$
$24$		0			0
$25$	1.51114	−	8.57013i	0.302229	−	1.71403i
$26$	9.29044			1.82201
$27$		0			0
$28$	−4.41147			−0.833690
$29$	−0.606511	+	3.43969i	−0.112626	+	0.638735i	0.875272	+	0.483631i	$0.160682\pi$
$29$	−0.606511	+	3.43969i	−0.112626	+	0.638735i	−0.987898	+	0.155104i	$0.950429\pi$
$30$		0			0
$31$	4.04576	+	1.47254i	0.726640	+	0.264475i	0.678742	−	0.734377i	$-0.262526\pi$
$31$	4.04576	+	1.47254i	0.726640	+	0.264475i	0.0478980	+	0.998852i	$0.484748\pi$
$32$	6.01330	−	5.04576i	1.06301	−	0.891973i
$33$		0			0
$34$	−5.43242	+	1.97724i	−0.931652	+	0.339094i
$35$	4.34445	−	7.52481i	0.734347	−	1.27193i
$36$		0			0
$37$	−1.20574	−	2.08840i	−0.198222	−	0.343330i	0.749730	−	0.661744i	$-0.230183\pi$
$37$	−1.20574	−	2.08840i	−0.198222	−	0.343330i	−0.947952	+	0.318413i	$0.896850\pi$
$38$	9.39490	+	7.88326i	1.52405	+	1.27883i
$39$		0			0
$40$	0.152704	+	0.866025i	0.0241446	+	0.136931i
$41$	0.433877	+	2.46064i	0.0677602	+	0.384287i	0.999762	+	0.0218325i	$0.00695005\pi$
$41$	0.433877	+	2.46064i	0.0677602	+	0.384287i	−0.932001	+	0.362454i	$0.881939\pi$
$42$		0			0
$43$	0.815207	+	0.684040i	0.124318	+	0.104315i	0.702827	−	0.711361i	$-0.251921\pi$
$43$	0.815207	+	0.684040i	0.124318	+	0.104315i	−0.578509	+	0.815676i	$0.696365\pi$
$44$	2.04715	+	3.54576i	0.308619	+	0.534543i
$45$		0			0
$46$	0.511144	−	0.885328i	0.0753641	−	0.130534i
$47$	0.223238	−	0.0812519i	0.0325626	−	0.0118518i	−0.325688	−	0.945477i	$-0.605596\pi$
$47$	0.223238	−	0.0812519i	0.0325626	−	0.0118518i	0.358250	+	0.933626i	$0.383374\pi$
$48$		0			0
$49$	−1.14156	+	0.957882i	−0.163080	+	0.136840i
$50$	16.1066	+	5.86231i	2.27781	+	0.829056i
$51$		0			0
$52$	−1.53936	+	8.73016i	−0.213471	+	1.21066i
$53$	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
$56$	−0.0968323	+	0.549163i	−0.0129398	+	0.0733850i
$57$		0			0
$58$	−6.46451	−	2.35289i	−0.848831	−	0.308949i
$59$	−10.1977	+	8.55690i	−1.32763	+	1.11401i	−0.343005	+	0.939334i	$0.611445\pi$
$59$	−10.1977	+	8.55690i	−1.32763	+	1.11401i	−0.984625	+	0.174680i	$0.944111\pi$
$60$		0			0
$61$	3.45336	−	1.25692i	0.442158	−	0.160932i	−0.111341	−	0.993782i	$-0.535515\pi$
$61$	3.45336	−	1.25692i	0.442158	−	0.160932i	0.553499	+	0.832850i	$0.313292\pi$
$62$	−4.24000	+	7.34389i	−0.538480	+	0.932675i
$63$		0			0
$64$	3.50387	+	6.06888i	0.437984	+	0.758610i
$65$	−13.3754	−	11.2233i	−1.65901	−	1.39208i
$66$		0			0
$67$	2.48293	+	14.0814i	0.303338	+	1.72031i	0.631228	+	0.775598i	$0.282551\pi$
$67$	2.48293	+	14.0814i	0.303338	+	1.72031i	−0.327890	+	0.944716i	$0.606338\pi$
$68$	−0.957882	−	5.43242i	−0.116160	−	0.658778i
$69$		0			0
$70$	13.1099	+	11.0005i	1.56694	+	1.31482i
$71$	−0.601535	−	1.04189i	−0.0713891	−	0.123649i	0.828121	−	0.560549i	$-0.189410\pi$
$71$	−0.601535	−	1.04189i	−0.0713891	−	0.123649i	−0.899510	+	0.436900i	$0.856077\pi$
$72$		0			0
$73$	2.34002	−	4.05304i	0.273879	−	0.474372i	−0.695973	−	0.718068i	$-0.745027\pi$
$73$	2.34002	−	4.05304i	0.273879	−	0.474372i	0.969852	+	0.243696i	$0.0783599\pi$
$74$	4.46324	−	1.62449i	0.518841	−	0.188843i
$75$		0			0
$76$	−8.96451	+	7.52211i	−1.02830	+	0.862846i
$77$	−4.80526	−	1.74897i	−0.547610	−	0.199314i
$78$		0			0
$79$	−2.22281	+	12.6062i	−0.250086	+	1.41831i	0.558293	+	0.829644i	$0.311457\pi$
$79$	−2.22281	+	12.6062i	−0.250086	+	1.41831i	−0.808379	+	0.588663i	$0.799655\pi$
$80$	−15.6458			−1.74925
$81$		0			0
$82$	−4.92127			−0.543464
$83$	−1.96291	+	11.1322i	−0.215458	+	1.22192i	0.664653	+	0.747152i	$0.268579\pi$
$83$	−1.96291	+	11.1322i	−0.215458	+	1.22192i	−0.880111	+	0.474768i	$0.842532\pi$
$84$		0			0
$85$	10.2096	+	3.71599i	1.10739	+	0.403056i
$86$	−1.60565	+	1.34730i	−0.173141	+	0.145283i
$87$		0			0
$88$	0.486329	−	0.177009i	0.0518429	−	0.0188693i
$89$	−0.349643	+	0.605600i	−0.0370621	+	0.0641935i	−0.883961	−	0.467560i	$-0.845133\pi$
$89$	−0.349643	+	0.605600i	−0.0370621	+	0.0641935i	0.846899	+	0.531753i	$0.178467\pi$
$90$		0			0
$91$	−5.53596	−	9.58856i	−0.580326	−	1.00515i
$92$	0.747243	+	0.627011i	0.0779055	+	0.0653705i
$93$		0			0
$94$	0.0812519	+	0.460802i	0.00838049	+	0.0475281i
$95$	−4.00243	−	22.6989i	−0.410641	−	2.32886i
$96$		0			0
$97$	−5.42855	−	4.55509i	−0.551186	−	0.462500i	0.324157	−	0.946003i	$-0.394919\pi$
$97$	−5.42855	−	4.55509i	−0.551186	−	0.462500i	−0.875342	+	0.483504i	$0.839364\pi$
$98$	−1.46756	−	2.54189i	−0.148246	−	0.256770i
$99$		0			0
$100$	−8.17752	+	14.1639i	−0.817752	+	1.41639i
$101$	−4.39506	+	1.59967i	−0.437325	+	0.159173i	−0.551294	−	0.834311i	$-0.685866\pi$
$101$	−4.39506	+	1.59967i	−0.437325	+	0.159173i	0.113969	+	0.993484i	$0.463643\pi$
$102$		0			0
$103$	−10.4363	+	8.75709i	−1.02832	+	0.862861i	−0.990650	−	0.136429i	$-0.956437\pi$
$103$	−10.4363	+	8.75709i	−1.02832	+	0.862861i	−0.0376683	+	0.999290i	$0.511993\pi$
$104$	1.05299	+	0.383256i	0.103254	+	0.0375813i
$105$		0			0
$106$	−1.59627	+	9.05288i	−0.155043	+	0.879293i
$107$	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	$0.253448\pi$
$110$	2.75811	−	15.6420i	0.262976	−	1.49141i
$111$		0			0
$112$	−9.32295	−	3.39328i	−0.880936	−	0.320634i
$113$	3.59721	−	3.01842i	0.338397	−	0.283949i	−0.457714	−	0.889100i	$-0.651332\pi$
$113$	3.59721	−	3.01842i	0.338397	−	0.283949i	0.796111	+	0.605151i	$0.206887\pi$
$114$		0			0
$115$	−1.80541	+	0.657115i	−0.168355	+	0.0612762i
$116$	3.28212	−	5.68479i	0.304737	−	0.527820i
$117$		0			0
$118$	−13.1099	−	22.7071i	−1.20687	−	2.09036i
$119$	5.27774	+	4.42855i	0.483809	+	0.405964i
$120$		0			0
$121$	−1.08600	−	6.15901i	−0.0987272	−	0.559910i
$122$	1.25692	+	7.12836i	0.113796	+	0.645371i
$123$		0			0
$124$	−6.19846	−	5.20113i	−0.556638	−	0.467075i
$125$	−6.85240	−	11.8687i	−0.612897	−	1.06157i
$126$		0			0
$127$	−3.04576	+	5.27541i	−0.270267	+	0.468117i	−0.968930	−	0.247334i	$-0.920445\pi$
$127$	−3.04576	+	5.27541i	−0.270267	+	0.468117i	0.698663	+	0.715451i	$0.253779\pi$
$128$	1.78265	−	0.648833i	0.157566	−	0.0573493i
$129$		0			0
$130$	26.3444	−	22.1055i	2.31055	−	1.93878i
$131$	−9.72432	−	3.53936i	−0.849618	−	0.309236i	−0.119733	−	0.992806i	$-0.538204\pi$
$131$	−9.72432	−	3.53936i	−0.849618	−	0.309236i	−0.729884	+	0.683571i	$0.760426\pi$
$132$		0			0
$133$	2.53802	−	14.3938i	0.220074	−	1.24810i
$134$	−28.1627			−2.43289
$135$		0			0
$136$	−0.697281			−0.0597914
$137$	3.31402	−	18.7947i	0.283136	−	1.60574i	−0.428734	−	0.903431i	$-0.641040\pi$
$137$	3.31402	−	18.7947i	0.283136	−	1.60574i	0.711870	−	0.702311i	$-0.247849\pi$
$138$		0			0
$139$	21.8983	+	7.97032i	1.85739	+	0.676034i	0.980870	+	0.194662i	$0.0623610\pi$
$139$	21.8983	+	7.97032i	1.85739	+	0.676034i	0.876517	+	0.481371i	$0.159861\pi$
$140$	−12.5094	+	10.4966i	−1.05723	+	0.887124i
$141$		0			0
$142$	2.22668	−	0.810446i	0.186859	−	0.0680111i
$143$	−5.13793	+	8.89915i	−0.429655	+	0.744184i
$144$		0			0
$145$	6.46451	+	11.1969i	0.536848	+	0.929848i
$146$	7.06131	+	5.92514i	0.584398	+	0.490368i
$147$		0			0
$148$	0.786989	+	4.46324i	0.0646901	+	0.366876i
$149$	2.69258	+	15.2704i	0.220585	+	1.25100i	0.870948	+	0.491375i	$0.163506\pi$
$149$	2.69258	+	15.2704i	0.220585	+	1.25100i	−0.650363	+	0.759623i	$0.725383\pi$
$150$		0			0
$151$	−4.52094	−	3.79352i	−0.367909	−	0.308713i	0.440025	−	0.897986i	$-0.354970\pi$
$151$	−4.52094	−	3.79352i	−0.367909	−	0.308713i	−0.807934	+	0.589273i	$0.799414\pi$
$152$	0.739620	+	1.28106i	0.0599911	+	0.103908i
$153$		0			0
$154$	5.03596	−	8.72254i	0.405809	−	0.702882i
$155$	14.9761	−	5.45084i	1.20291	−	0.437822i
$156$		0			0
$157$	−0.928548	+	0.779145i	−0.0741062	+	0.0621825i	−0.679088	−	0.734057i	$-0.737625\pi$
$157$	−0.928548	+	0.779145i	−0.0741062	+	0.0621825i	0.604982	+	0.796239i	$0.293180\pi$
$158$	−23.6919	−	8.62314i	−1.88483	−	0.686020i
$159$		0			0
$160$	5.04576	−	28.6159i	0.398902	−	2.26229i
$161$	−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	$0.465360\pi$
$164$	0.815422	−	4.62449i	0.0636737	−	0.361112i
$165$		0			0
$166$	−20.9217	−	7.61489i	−1.62384	−	0.591030i
$167$	−2.93247	+	2.46064i	−0.226922	+	0.190410i	−0.749159	−	0.662390i	$-0.769542\pi$
$167$	−2.93247	+	2.46064i	−0.226922	+	0.190410i	0.522237	+	0.852800i	$0.325098\pi$
$168$		0			0
$169$	−8.69119	+	3.16333i	−0.668553	+	0.243333i
$170$	−10.6998	+	18.5326i	−0.820635	+	1.42138i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−5.38484	−	4.51842i	−0.409402	−	0.343529i	0.414712	−	0.909953i	$-0.363882\pi$
$173$	−5.38484	−	4.51842i	−0.409402	−	0.343529i	−0.824114	+	0.566424i	$0.808327\pi$
$174$		0			0
$175$	−3.54710	−	20.1166i	−0.268136	−	1.52067i
$176$	1.59894	+	9.06805i	0.120525	+	0.683530i
$177$		0			0
$178$	−1.05509	−	0.885328i	−0.0790825	−	0.0663581i
$179$	7.19269	+	12.4581i	0.537607	+	0.931163i	0.999032	+	0.0439838i	$0.0140050\pi$
$179$	7.19269	+	12.4581i	0.537607	+	0.931163i	−0.461425	+	0.887179i	$0.652662\pi$
$180$		0			0
$181$	−6.60014	+	11.4318i	−0.490584	+	0.849717i	−0.999941	−	0.0108384i	$-0.996550\pi$
$181$	−6.60014	+	11.4318i	−0.490584	+	0.849717i	0.509357	+	0.860555i	$0.329883\pi$
$182$	20.4923	−	7.45858i	1.51899	−	0.552867i
$183$		0			0
$184$	0.0944557	−	0.0792577i	0.00696336	−	0.00584296i
$185$	−8.38814	−	3.05303i	−0.616708	−	0.224463i
$186$		0			0
$187$	1.11035	−	6.29710i	0.0811967	−	0.460489i
$188$	−0.446476			−0.0325626
$189$		0			0
$190$	45.3979			3.29351
$191$	2.33094	−	13.2194i	0.168661	−	0.956523i	−0.776548	−	0.630058i	$-0.783031\pi$
$191$	2.33094	−	13.2194i	0.168661	−	0.956523i	0.945209	−	0.326465i	$-0.105858\pi$
$192$		0			0
$193$	−14.1001	−	5.13203i	−1.01495	−	0.369412i	−0.219618	−	0.975586i	$-0.570481\pi$
$193$	−14.1001	−	5.13203i	−1.01495	−	0.369412i	−0.795332	+	0.606174i	$0.792703\pi$
$194$	10.6922	−	8.97178i	0.767652	−	0.644136i
$195$		0			0
$196$	2.63176	−	0.957882i	0.187983	−	0.0684201i
$197$	11.1606	−	19.3307i	0.795158	−	1.37725i	−0.127580	−	0.991828i	$-0.540721\pi$
$197$	11.1606	−	19.3307i	0.795158	−	1.37725i	0.922739	−	0.385426i	$-0.125946\pi$
$198$		0			0
$199$	4.55051	+	7.88171i	0.322577	+	0.558720i	0.981019	−	0.193912i	$-0.0621176\pi$
$199$	4.55051	+	7.88171i	0.322577	+	0.558720i	−0.658442	+	0.752631i	$0.728784\pi$
$200$	1.58370	+	1.32888i	0.111984	+	0.0939659i
$201$		0			0
$202$	−1.59967	−	9.07218i	−0.112552	−	0.638316i
$203$	1.42366	+	8.07398i	0.0999214	+	0.566682i
$204$		0			0
$205$	7.08512	+	5.94512i	0.494846	+	0.415225i
$206$	−13.4166	−	23.2383i	−0.934781	−	1.61909i
$207$		0			0
$208$	−9.96838	+	17.2657i	−0.691183	+	1.19716i
$209$	−12.7469	+	4.63950i	−0.881723	+	0.320921i
$210$		0			0
$211$	−4.57919	+	3.84240i	−0.315245	+	0.264522i	−0.786656	−	0.617392i	$-0.788189\pi$
$211$	−4.57919	+	3.84240i	−0.315245	+	0.264522i	0.471411	+	0.881914i	$0.343745\pi$
$212$	−8.24243	−	3.00000i	−0.566093	−	0.206041i
$213$		0			0
$214$	−3.97906	+	22.5663i	−0.272003	+	1.54260i
$215$	3.93923			0.268653
$216$		0			0
$217$	10.1061			0.686045
$218$	−4.99486	+	28.3273i	−0.338295	+	1.91857i
$219$		0			0
$220$	14.2417	+	5.18355i	0.960175	+	0.349475i
$221$	10.6056	−	8.89915i	0.713409	−	0.598621i
$222$		0			0
$223$	8.36484	−	3.04455i	0.560151	−	0.203878i	−0.0463999	−	0.998923i	$-0.514775\pi$
$223$	8.36484	−	3.04455i	0.560151	−	0.203878i	0.606551	+	0.795045i	$0.292553\pi$
$224$	9.21291	−	15.9572i	0.615564	−	1.06619i
$225$		0			0
$226$	4.62449	+	8.00984i	0.307616	+	0.532807i
$227$	−8.17253	−	6.85756i	−0.542430	−	0.455152i	0.329938	−	0.944003i	$-0.392972\pi$
$227$	−8.17253	−	6.85756i	−0.542430	−	0.455152i	−0.872368	+	0.488850i	$0.837417\pi$
$228$		0			0
$229$	−1.43629	−	8.14560i	−0.0949127	−	0.538276i	−0.994774	−	0.102101i	$-0.967444\pi$
$229$	−1.43629	−	8.14560i	−0.0949127	−	0.538276i	0.899861	−	0.436176i	$-0.143667\pi$
$230$	−0.657115	−	3.72668i	−0.0433288	−	0.245730i
$231$		0			0
$232$	−0.635630	−	0.533356i	−0.0417311	−	0.0350166i
$233$	−6.36965	−	11.0326i	−0.417290	−	0.722767i	0.578376	−	0.815770i	$-0.303687\pi$
$233$	−6.36965	−	11.0326i	−0.417290	−	0.722767i	−0.995666	+	0.0930034i	$0.970353\pi$
$234$		0			0
$235$	0.439693	−	0.761570i	0.0286824	−	0.0496793i
$236$	23.5099	−	8.55690i	1.53036	−	0.557007i
$237$		0			0
$238$	−10.3951	+	8.72254i	−0.673815	+	0.565398i
$239$	−14.1100	−	5.13563i	−0.912702	−	0.332196i	−0.157371	−	0.987540i	$-0.550302\pi$
$239$	−14.1100	−	5.13563i	−0.912702	−	0.332196i	−0.755331	+	0.655343i	$0.772524\pi$
$240$		0			0
$241$	0.138156	−	0.783520i	0.00889939	−	0.0504710i	−0.980035	−	0.198827i	$-0.936287\pi$
$241$	0.138156	−	0.783520i	0.00889939	−	0.0504710i	0.988934	+	0.148356i	$0.0473980\pi$
$242$	12.3180			0.791832
$243$		0			0
$244$	−6.90673			−0.442158
$245$	−0.957882	+	5.43242i	−0.0611968	+	0.347064i
$246$		0			0
$247$	−27.5993	−	10.0453i	−1.75610	−	0.639168i
$248$	−0.783520	+	0.657451i	−0.0497536	+	0.0417482i
$249$		0			0
$250$	25.3653	−	9.23222i	1.60424	−	0.583897i
$251$	−4.15749	+	7.20099i	−0.262419	+	0.454522i	−0.966884	−	0.255216i	$-0.917853\pi$
$251$	−4.15749	+	7.20099i	−0.262419	+	0.454522i	0.704465	+	0.709738i	$0.251187\pi$
$252$		0			0
$253$	0.565360	+	0.979232i	0.0355439	+	0.0615638i
$254$	−9.19096	−	7.71213i	−0.576692	−	0.483902i
$255$		0			0
$256$	3.08260	+	17.4823i	0.192662	+	1.09264i
$257$	−4.44891	−	25.2310i	−0.277515	−	1.57387i	−0.730857	−	0.682531i	$-0.760879\pi$
$257$	−4.44891	−	25.2310i	−0.277515	−	1.57387i	0.453341	−	0.891337i	$-0.350232\pi$
$258$		0			0
$259$	−4.33615	−	3.63846i	−0.269435	−	0.226083i
$260$	16.4073	+	28.4183i	1.01754	+	1.76243i
$261$		0			0
$262$	10.1912	−	17.6517i	0.629614	−	1.09052i
$263$	−26.3725	+	9.59879i	−1.62620	+	0.591887i	−0.984548	−	0.175113i	$-0.943971\pi$
$263$	−26.3725	+	9.59879i	−1.62620	+	0.591887i	−0.641648	+	0.767000i	$0.721749\pi$
$264$		0			0
$265$	13.2344	−	11.1050i	0.812984	−	0.682175i
$266$	27.0515	+	9.84595i	1.65864	+	0.603694i
$267$		0			0
$268$	4.66637	−	26.4643i	0.285044	−	1.61657i
$269$	−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	$0.695809\pi$
$272$	2.15425	−	12.2173i	0.130620	−	0.740786i
$273$		0			0
$274$	35.3225	+	12.8564i	2.13391	+	0.776681i
$275$	−14.5229	+	12.1861i	−0.875762	+	0.734852i
$276$		0			0
$277$	−19.8478	+	7.22400i	−1.19254	+	0.434048i	−0.860613	−	0.509259i	$-0.829920\pi$
$277$	−19.8478	+	7.22400i	−1.19254	+	0.434048i	−0.331923	+	0.943306i	$0.607697\pi$
$278$	−22.9496	+	39.7499i	−1.37643	+	2.38404i
$279$		0			0
$280$	1.03209	+	1.78763i	0.0616791	+	0.106831i
$281$	−1.33851	−	1.12314i	−0.0798487	−	0.0670010i	0.601990	−	0.798504i	$-0.294375\pi$
$281$	−1.33851	−	1.12314i	−0.0798487	−	0.0670010i	−0.681838	+	0.731503i	$0.738819\pi$
$282$		0			0
$283$	−1.26558	−	7.17745i	−0.0752308	−	0.426655i	−0.999040	−	0.0438023i	$-0.986053\pi$
$283$	−1.26558	−	7.17745i	−0.0752308	−	0.426655i	0.923809	−	0.382853i	$-0.125058\pi$
$284$	0.392624	+	2.22668i	0.0232980	+	0.132129i
$285$		0			0
$286$	−15.5043	−	13.0097i	−0.916791	−	0.769279i
$287$	2.93247	+	5.07919i	0.173098	+	0.299815i
$288$		0			0
$289$	4.19253	−	7.26168i	0.246620	−	0.427158i
$290$	−23.9294	+	8.70961i	−1.40519	+	0.511446i
$291$		0			0
$292$	−6.73783	+	5.65371i	−0.394301	+	0.330858i
$293$	14.4251	+	5.25031i	0.842725	+	0.306727i	0.727070	−	0.686563i	$-0.240881\pi$
$293$	14.4251	+	5.25031i	0.842725	+	0.306727i	0.115654	+	0.993290i	$0.463104\pi$
$294$		0			0
$295$	−8.55690	+	48.5286i	−0.498202	+	2.82545i
$296$	0.572881			0.0332980
$297$		0			0
$298$	−30.5408			−1.76918
$299$	−0.425126	+	2.41101i	−0.0245857	+	0.139432i
$300$		0			0
$301$	2.34730	+	0.854346i	0.135296	+	0.0492437i
$302$	8.90452	−	7.47178i	0.512398	−	0.429953i
$303$		0			0
$304$	−24.7310	+	9.00135i	−1.41842	+	0.516263i
$305$	6.80180	−	11.7811i	0.389470	−	0.674581i
$306$		0			0
$307$	−8.38191	−	14.5179i	−0.478381	−	0.828580i	0.521312	−	0.853366i	$-0.325443\pi$
$307$	−8.38191	−	14.5179i	−0.478381	−	0.828580i	−0.999693	+	0.0247861i	$0.992110\pi$
$308$	7.36208	+	6.17752i	0.419493	+	0.351997i
$309$		0			0
$310$	5.45084	+	30.9132i	0.309587	+	1.75575i
$311$	2.78239	+	15.7797i	0.157775	+	0.894786i	0.956205	+	0.292698i	$0.0945531\pi$
$311$	2.78239	+	15.7797i	0.157775	+	0.894786i	−0.798430	+	0.602088i	$0.794336\pi$
$312$		0			0
$313$	26.3562	+	22.1155i	1.48974	+	1.25004i	0.894954	+	0.446159i	$0.147208\pi$
$313$	26.3562	+	22.1155i	1.48974	+	1.25004i	0.594788	+	0.803883i	$0.297236\pi$
$314$	−1.19372	−	2.06758i	−0.0673654	−	0.116680i
$315$		0			0
$316$	12.0287	−	20.8343i	0.676666	−	1.17202i
$317$	−15.3274	+	5.57873i	−0.860874	+	0.313332i	−0.734466	−	0.678646i	$-0.762567\pi$
$317$	−15.3274	+	5.57873i	−0.860874	+	0.313332i	−0.126408	+	0.991978i	$0.540345\pi$
$318$		0			0
$319$	5.82888	−	4.89101i	0.326355	−	0.273844i
$320$	24.3759	+	8.87211i	1.36266	+	0.495966i
$321$		0			0
$322$	0.416689	−	2.36316i	0.0232212	−	0.131694i
$323$	18.2761			1.01691
$324$		0			0
$325$	−41.0479			−2.27693
$326$	−0.948531	+	5.37939i	−0.0525343	+	0.297937i
$327$		0			0
$328$	−0.557781	−	0.203016i	−0.0307983	−	0.0112097i
$329$	0.427173	−	0.358441i	0.0235508	−	0.0197615i
$330$		0			0
$331$	29.6755	−	10.8010i	1.63111	−	0.593676i	0.645658	−	0.763627i	$-0.276583\pi$
$331$	29.6755	−	10.8010i	1.63111	−	0.593676i	0.985453	+	0.169951i	$0.0543609\pi$
$332$	10.6222	−	18.3983i	0.582972	−	1.00974i
$333$		0			0
$334$	−3.76991	−	6.52968i	−0.206281	−	0.357288i
$335$	40.5457	+	34.0219i	2.21525	+	1.85881i
$336$		0			0
$337$	1.04277	+	5.91382i	0.0568031	+	0.322146i	0.999948	−	0.0102366i	$-0.00325846\pi$
$337$	1.04277	+	5.91382i	0.0568031	+	0.322146i	−0.943144	+	0.332383i	$0.892147\pi$
$338$	−3.16333	−	17.9402i	−0.172063	−	0.975816i
$339$		0			0
$340$	−15.6420	−	13.1252i	−0.848308	−	0.711815i
$341$	−4.68972	−	8.12284i	−0.253963	−	0.439876i
$342$		0			0
$343$	−9.96451	+	17.2590i	−0.538033	+	0.931900i
$344$	−0.237565	+	0.0864665i	−0.0128086	+	0.00466196i
$345$		0			0
$346$	10.6061	−	8.89955i	0.570186	−	0.478443i
$347$	21.6415	+	7.87686i	1.16178	+	0.422852i	0.849732	−	0.527216i	$-0.176764\pi$
$347$	21.6415	+	7.87686i	1.16178	+	0.422852i	0.312045	+	0.950067i	$0.398986\pi$
$348$		0			0
$349$	−2.00846	+	11.3905i	−0.107510	+	0.609721i	0.882678	+	0.469979i	$0.155738\pi$
$349$	−2.00846	+	11.3905i	−0.107510	+	0.609721i	−0.990188	+	0.139742i	$0.955373\pi$
$350$	40.2332			2.15056
$351$		0			0
$352$	−17.1010			−0.911487
$353$	0.370674	−	2.10220i	0.0197290	−	0.111889i	−0.973353	−	0.229312i	$-0.926352\pi$
$353$	0.370674	−	2.10220i	0.0197290	−	0.111889i	0.993082	+	0.117423i	$0.0374635\pi$
$354$		0			0
$355$	−4.18479	−	1.52314i	−0.222106	−	0.0808399i
$356$	1.00676	−	0.844770i	0.0533581	−	0.0447727i
$357$		0			0
$358$	−26.6250	+	9.69069i	−1.40717	+	0.512169i
$359$	12.1118	−	20.9782i	0.639234	−	1.10719i	−0.346367	−	0.938099i	$-0.612585\pi$
$359$	12.1118	−	20.9782i	0.639234	−	1.10719i	0.985601	−	0.169087i	$-0.0540818\pi$
$360$		0			0
$361$	−9.88578	−	17.1227i	−0.520304	−	0.901193i
$362$	−19.9167	−	16.7121i	−1.04680	−	0.878370i
$363$		0			0
$364$	3.61334	+	20.4923i	0.189391	+	1.07409i
$365$	−3.00827	−	17.0608i	−0.157460	−	0.893002i
$366$		0			0
$367$	−2.17159	−	1.82218i	−0.113356	−	0.0951170i	0.584348	−	0.811503i	$-0.301350\pi$
$367$	−2.17159	−	1.82218i	−0.113356	−	0.0951170i	−0.697704	+	0.716386i	$0.745795\pi$
$368$	1.09689	+	1.89986i	0.0571792	+	0.0990372i
$369$		0			0
$370$	8.79086	−	15.2262i	0.457015	−	0.791573i
$371$	10.2946	−	3.74691i	0.534467	−	0.194530i
$372$		0			0
$373$	−22.0876	+	18.5337i	−1.14366	+	0.959641i	−0.999552	−	0.0299222i	$-0.990474\pi$
$373$	−22.0876	+	18.5337i	−1.14366	+	0.959641i	−0.144103	+	0.989563i	$0.546030\pi$
$374$	11.8347	+	4.30747i	0.611956	+	0.222734i
$375$		0			0
$376$	−0.00980018	+	0.0555796i	−0.000505406	+	0.00286630i
$377$	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	$0.190066\pi$
$380$	−7.52211	+	42.6600i	−0.385876	+	2.18841i
$381$		0			0
$382$	24.8444	+	9.04261i	1.27115	+	0.462660i
$383$	−0.514973	+	0.432114i	−0.0263139	+	0.0220800i	−0.655850	−	0.754891i	$-0.727690\pi$
$383$	−0.514973	+	0.432114i	−0.0263139	+	0.0220800i	0.629536	+	0.776971i	$0.283245\pi$
$384$		0			0
$385$	−17.7875	+	6.47410i	−0.906533	+	0.329951i
$386$	14.7771	−	25.5947i	0.752134	−	1.30273i
$387$		0			0
$388$	6.65910	+	11.5339i	0.338065	+	0.585545i
$389$	3.26281	+	2.73783i	0.165431	+	0.138813i	0.721745	−	0.692159i	$-0.243340\pi$
$389$	3.26281	+	2.73783i	0.165431	+	0.138813i	−0.556314	+	0.830972i	$0.687785\pi$
$390$		0			0
$391$	−0.264538	−	1.50027i	−0.0133783	−	0.0758719i
$392$	−0.0614747	−	0.348641i	−0.00310494	−	0.0176090i
$393$		0			0
$394$	33.6785	+	28.2596i	1.69670	+	1.42370i
$395$	23.6919	+	41.0355i	1.19207	+	2.06472i
$396$		0			0
$397$	4.43242	−	7.67717i	0.222457	−	0.385306i	−0.733097	−	0.680124i	$-0.761926\pi$
$397$	4.43242	−	7.67717i	0.222457	−	0.385306i	0.955553	+	0.294818i	$0.0952591\pi$
$398$	−16.8445	+	6.13088i	−0.844336	+	0.307313i
$399$		0			0
$400$	−28.1766	+	23.6430i	−1.40883	+	1.18215i
$401$	34.8475	+	12.6834i	1.74020	+	0.633381i	0.999270	−	0.0382006i	$-0.0121626\pi$
$401$	34.8475	+	12.6834i	1.74020	+	0.633381i	0.740930	+	0.671582i	$0.234385\pi$
$402$		0			0
$403$	3.52646	−	19.9996i	0.175666	−	0.996250i
$404$	8.79012			0.437325
$405$		0			0
$406$	−16.1480			−0.801410
$407$	−0.912254	+	5.17365i	−0.0452187	+	0.256448i
$408$		0			0
$409$	3.18479	+	1.15917i	0.157478	+	0.0573173i	0.419556	−	0.907729i	$-0.362186\pi$
$409$	3.18479	+	1.15917i	0.157478	+	0.0573173i	−0.262078	+	0.965047i	$0.584408\pi$
$410$	−13.9550	+	11.7096i	−0.689187	+	0.578296i
$411$		0			0
$412$	24.0599	−	8.75709i	1.18535	−	0.431431i
$413$	−15.6238	+	27.0612i	−0.768798	+	1.33160i
$414$		0			0
$415$	20.9217	+	36.2375i	1.02701	+	1.77883i
$416$	−28.3640	−	23.8002i	−1.39066	−	1.16690i
$417$		0			0
$418$	−4.63950	−	26.3119i	−0.226925	−	1.28696i
$419$	3.58694	+	20.3425i	0.175233	+	0.993799i	0.937874	+	0.346976i	$0.112791\pi$
$419$	3.58694	+	20.3425i	0.175233	+	0.993799i	−0.762641	+	0.646823i	$0.776097\pi$
$420$		0			0
$421$	21.0915	+	17.6979i	1.02794	+	0.862542i	0.990604	−	0.136761i	$-0.0436691\pi$
$421$	21.0915	+	17.6979i	1.02794	+	0.862542i	0.0373336	+	0.999303i	$0.488114\pi$
$422$	−5.88690	−	10.1964i	−0.286570	−	0.496353i
$423$		0			0
$424$	−0.554378	+	0.960210i	−0.0269230	+	0.0466319i
$425$	24.0020	−	8.73601i	1.16427	−	0.423759i
$426$		0			0
$427$	6.60813	−	5.54488i	0.319790	−	0.268335i
$428$	−20.5461	−	7.47818i	−0.993134	−	0.361471i
$429$		0			0
$430$	−1.34730	+	7.64090i	−0.0649724	+	0.368477i
$431$	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	$0.724854\pi$
$434$	−3.45648	+	19.6027i	−0.165916	+	0.940958i
$435$		0			0
$436$	−25.7913	−	9.38728i	−1.23518	−	0.449569i
$437$	−2.47573	+	2.07738i	−0.118430	+	0.0993746i
$438$		0			0
$439$	−11.0039	+	4.00508i	−0.525186	+	0.191152i	−0.590988	−	0.806681i	$-0.701262\pi$
$439$	−11.0039	+	4.00508i	−0.525186	+	0.191152i	0.0658015	+	0.997833i	$0.479040\pi$
$440$	0.957882	−	1.65910i	0.0456652	−	0.0790945i
$441$		0			0
$442$	13.6343	+	23.6153i	0.648517	+	1.12326i
$443$	−1.59397	−	1.33750i	−0.0757316	−	0.0635464i	0.604136	−	0.796881i	$-0.293518\pi$
$443$	−1.59397	−	1.33750i	−0.0757316	−	0.0635464i	−0.679868	+	0.733335i	$0.737963\pi$
$444$		0			0
$445$	0.449493	+	2.54920i	0.0213080	+	0.120844i
$446$	3.04455	+	17.2665i	0.144164	+	0.817593i
$447$		0			0
$448$	12.6009	+	10.5734i	0.595334	+	0.499545i
$449$	5.27541	+	9.13728i	0.248962	+	0.431215i	0.963238	−	0.268649i	$-0.0865772\pi$
$449$	5.27541	+	9.13728i	0.248962	+	0.431215i	−0.714276	+	0.699864i	$0.753244\pi$
$450$		0			0
$451$	2.72163	−	4.71400i	0.128157	−	0.221974i
$452$	−8.29304	+	3.01842i	−0.390072	+	0.141974i
$453$		0			0
$454$	16.0967	−	13.5068i	0.755457	−	0.633904i
$455$	−38.5129	−	14.0175i	−1.80551	−	0.657152i
$456$		0			0
$457$	−1.37346	+	7.78925i	−0.0642475	+	0.364366i	0.935686	+	0.352834i	$0.114782\pi$
$457$	−1.37346	+	7.78925i	−0.0642475	+	0.364366i	−0.999934	+	0.0115320i	$0.996329\pi$
$458$	16.2912			0.761238
$459$		0			0
$460$	3.61081			0.168355
$461$	6.78839	−	38.4989i	0.316167	−	1.79307i	−0.249434	−	0.968392i	$-0.580244\pi$
$461$	6.78839	−	38.4989i	0.316167	−	1.79307i	0.565600	−	0.824679i	$-0.308644\pi$
$462$		0			0
$463$	−22.2640	−	8.10343i	−1.03470	−	0.376598i	−0.231828	−	0.972757i	$-0.574471\pi$
$463$	−22.2640	−	8.10343i	−1.03470	−	0.376598i	−0.802867	+	0.596158i	$0.796693\pi$
$464$	11.3089	−	9.48932i	0.525004	−	0.440531i
$465$		0			0
$466$	23.5783	−	8.58180i	1.09224	−	0.397544i
$467$	−17.3576	+	30.0642i	−0.803214	+	1.39121i	0.114277	+	0.993449i	$0.463545\pi$
$467$	−17.3576	+	30.0642i	−0.803214	+	1.39121i	−0.917490	+	0.397758i	$0.869788\pi$
$468$		0			0
$469$	16.7815	+	29.0665i	0.774899	+	1.34216i
$470$	1.32683	+	1.11334i	0.0612020	+	0.0513546i
$471$		0			0
$472$	−0.549163	−	3.11446i	−0.0252773	−	0.143355i
$473$	−0.402575	−	2.28312i	−0.0185104	−	0.104978i
$474$		0			0
$475$	−41.5094	−	34.8305i	−1.90458	−	1.59813i
$476$	−6.47410	−	11.2135i	−0.296740	−	0.513969i
$477$		0			0
$478$	14.7875	−	25.6126i	0.676362	−	1.17149i
$479$	−6.09083	+	2.21688i	−0.278297	+	0.101292i	−0.477398	−	0.878687i	$-0.658420\pi$
$479$	−6.09083	+	2.21688i	−0.278297	+	0.101292i	0.199101	+	0.979979i	$0.436198\pi$
$480$		0			0
$481$	−8.71348	+	7.31148i	−0.397300	+	0.333375i
$482$	1.47254	+	0.535959i	0.0670722	+	0.0244123i
$483$		0			0
$484$	−2.04101	+	11.5752i	−0.0927733	+	0.526143i
$485$	−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	$0.350442\pi$
$488$	−0.151603	+	0.859785i	−0.00686276	+	0.0389206i
$489$		0			0
$490$	−10.2096	−	3.71599i	−0.461223	−	0.167871i
$491$	20.0911	−	16.8584i	0.906699	−	0.760811i	−0.0647892	−	0.997899i	$-0.520637\pi$
$491$	20.0911	−	16.8584i	0.906699	−	0.760811i	0.971488	+	0.237088i	$0.0761930\pi$
$492$		0			0
$493$	−9.63341	+	3.50627i	−0.433867	+	0.157915i
$494$	28.9243	−	50.0984i	1.30137	−	2.25403i
$495$		0			0
$496$	−9.09879	−	15.7596i	−0.408548	−	0.707626i
$497$	−2.16328	−	1.81521i	−0.0970364	−	0.0814232i
$498$		0			0
$499$	1.09698	+	6.22129i	0.0491077	+	0.278503i	0.999467	−	0.0326518i	$-0.0103952\pi$
$499$	1.09698	+	6.22129i	0.0491077	+	0.278503i	−0.950359	+	0.311155i	$0.899284\pi$
$500$	4.47259	+	25.3653i	0.200020	+	1.13437i
$501$		0			0
$502$	−12.5458	−	10.5271i	−0.559945	−	0.469849i
$503$	−10.9131	−	18.9020i	−0.486589	−	0.842798i	0.513292	−	0.858214i	$-0.328426\pi$
$503$	−10.9131	−	18.9020i	−0.486589	−	0.842798i	−0.999881	+	0.0154166i	$0.995093\pi$
$504$		0			0
$505$	−8.65657	+	14.9936i	−0.385212	+	0.667208i
$506$	−2.09277	+	0.761707i	−0.0930351	+	0.0338620i
$507$		0			0
$508$	8.76991	−	7.35883i	0.389102	−	0.326495i
$509$	27.3386	+	9.95043i	1.21176	+	0.441045i	0.867314	−	0.497761i	$-0.165844\pi$
$509$	27.3386	+	9.95043i	1.21176	+	0.441045i	0.344447	+	0.938806i	$0.388067\pi$
$510$		0			0
$511$	1.90760	−	10.8186i	0.0843874	−	0.478585i
$512$	−31.1704			−1.37755
$513$		0			0
$514$	50.4620			2.22579
$515$	−8.75709	+	49.6639i	−0.385883	+	2.18845i
$516$		0			0
$517$	−0.486329	−	0.177009i	−0.0213887	−	0.00778487i
$518$	8.54055	−	7.16637i	0.375250	−	0.314872i
$519$		0			0
$520$	3.89780	−	1.41868i	0.170930	−	0.0622134i
$521$	−6.84743	+	11.8601i	−0.299991	+	0.519600i	−0.976134	−	0.217171i	$-0.930317\pi$
$521$	−6.84743	+	11.8601i	−0.299991	+	0.519600i	0.676142	+	0.736771i	$0.263650\pi$
$522$		0			0
$523$	−6.57532	−	11.3888i	−0.287519	−	0.497997i	0.685698	−	0.727886i	$-0.259497\pi$
$523$	−6.57532	−	11.3888i	−0.287519	−	0.497997i	−0.973217	+	0.229889i	$0.926164\pi$
$524$	14.8985	+	12.5013i	0.650845	+	0.546124i
$525$		0			0
$526$	−9.59879	−	54.4375i	−0.418527	−	2.37359i
$527$	2.19437	+	12.4449i	0.0955884	+	0.542109i
$528$		0			0
$529$	−17.4127	−	14.6110i	−0.757072	−	0.635259i
$530$	17.0138	+	29.4688i	0.739034	+	1.28004i
$531$		0			0
$532$	−13.7344	+	23.7887i	−0.595463	+	1.03137i
$533$	11.0748	−	4.03091i	0.479704	−	0.174598i
$534$		0			0
$535$	32.9898	−	27.6817i	1.42627	−	1.19679i
$536$	−3.19199	−	1.16179i	−0.137873	−	0.0501816i
$537$		0			0
$538$	10.3191	−	58.5224i	0.444887	−	2.52308i
$539$	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	$0.457029\pi$
$542$	6.49838	−	36.8542i	0.279129	−	1.58302i
$543$		0			0
$544$	21.6506	+	7.88019i	0.928264	+	0.337860i
$545$	41.4117	−	34.7486i	1.77388	−	1.48846i
$546$		0			0
$547$	29.4859	−	10.7320i	1.26073	−	0.458867i	0.376714	−	0.926330i	$-0.377054\pi$
$547$	29.4859	−	10.7320i	1.26073	−	0.458867i	0.884013	+	0.467463i	$0.154832\pi$
$548$	−17.9337	+	31.0621i	−0.766091	+	1.32691i
$549$		0			0
$550$	−18.6702	−	32.3378i	−0.796102	−	1.37889i
$551$	16.6601	+	13.9795i	0.709746	+	0.595548i
$552$		0			0
$553$	5.21760	+	29.5905i	0.221875	+	1.25831i
$554$	−7.22400	−	40.9693i	−0.306918	−	1.74062i
$555$		0			0
$556$	−33.5501	−	28.1519i	−1.42284	−	1.19391i
$557$	−21.7196	−	37.6195i	−0.920290	−	1.59399i	−0.798966	−	0.601376i	$-0.794619\pi$
$557$	−21.7196	−	37.6195i	−0.920290	−	1.59399i	−0.121324	−	0.992613i	$-0.538714\pi$
$558$		0			0
$559$	2.50980	−	4.34710i	0.106153	−	0.183863i
$560$	−34.5104	+	12.5608i	−1.45833	+	0.530790i
$561$		0			0
$562$	2.63634	−	2.21216i	0.111207	−	0.0933142i
$563$	−30.0867	−	10.9507i	−1.26800	−	0.461516i	−0.381557	−	0.924345i	$-0.624612\pi$
$563$	−30.0867	−	10.9507i	−1.26800	−	0.461516i	−0.886447	+	0.462829i	$0.846834\pi$
$564$		0			0
$565$	3.01842	−	17.1183i	0.126986	−	0.720172i
$566$	14.3549			0.603381
$567$		0			0
$568$	0.285807			0.0119922
$569$	1.17594	−	6.66906i	0.0492978	−	0.279582i	−0.950187	−	0.311681i	$-0.899108\pi$
$569$	1.17594	−	6.66906i	0.0492978	−	0.279582i	0.999485	+	0.0320990i	$0.0102192\pi$
$570$		0			0
$571$	19.8773	+	7.23475i	0.831840	+	0.302765i	0.722614	−	0.691252i	$-0.242940\pi$
$571$	19.8773	+	7.23475i	0.831840	+	0.302765i	0.109226	+	0.994017i	$0.465163\pi$
$572$	14.7941	−	12.4137i	0.618571	−	0.519043i
$573$		0			0
$574$	−10.8550	+	3.95091i	−0.453080	+	0.164908i
$575$	−2.25838	+	3.91164i	−0.0941811	+	0.163127i
$576$		0			0
$577$	−5.95811	−	10.3198i	−0.248039	−	0.429617i	0.714942	−	0.699183i	$-0.246453\pi$
$577$	−5.95811	−	10.3198i	−0.248039	−	0.429617i	−0.962982	+	0.269567i	$0.913120\pi$
$578$	12.6515	+	10.6159i	0.526233	+	0.441562i
$579$		0			0
$580$	−4.21941	−	23.9294i	−0.175201	−	0.993616i
$581$	4.60754	+	26.1306i	0.191153	+	1.08408i
$582$		0			0
$583$	−7.78880	−	6.53558i	−0.322579	−	0.270676i
$584$	0.555907	+	0.962859i	0.0230036	+	0.0398434i
$585$		0			0
$586$	−15.1177	+	26.1846i	−0.624506	+	1.08168i
$587$	−0.122030	+	0.0444153i	−0.00503672	+	0.00183322i	−0.344537	−	0.938773i	$-0.611964\pi$
$587$	−0.122030	+	0.0444153i	−0.00503672	+	0.00183322i	0.339501	+	0.940606i	$0.389742\pi$
$588$		0			0
$589$	20.5364	−	17.2321i	0.846189	−	0.710037i
$590$	−91.2040	−	33.1955i	−3.75481	−	1.36664i
$591$		0			0
$592$	−1.76991	+	10.0377i	−0.0727431	+	0.412546i
$593$	−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
$596$	5.06040	−	28.6989i	0.207282	−	1.17555i
$597$		0			0
$598$	−4.53121	−	1.64923i	−0.185295	−	0.0674419i
$599$	−21.1391	+	17.7378i	−0.863721	+	0.724748i	−0.962766	−	0.270335i	$-0.912866\pi$
$599$	−21.1391	+	17.7378i	−0.863721	+	0.724748i	0.0990454	+	0.995083i	$0.468421\pi$
$600$		0			0
$601$	−1.25237	+	0.455827i	−0.0510854	+	0.0185936i	−0.367436	−	0.930049i	$-0.619764\pi$
$601$	−1.25237	+	0.455827i	−0.0510854	+	0.0185936i	0.316351	+	0.948642i	$0.397542\pi$
$602$	−2.45999	+	4.26083i	−0.100262	+	0.173658i
$603$		0			0
$604$	5.54576	+	9.60554i	0.225654	+	0.390844i
$605$	−17.7342	−	14.8807i	−0.720996	−	0.604988i
$606$		0			0
$607$	−2.18180	−	12.3736i	−0.0885565	−	0.502229i	−0.996532	−	0.0832064i	$-0.973484\pi$
$607$	−2.18180	−	12.3736i	−0.0885565	−	0.502229i	0.907976	−	0.419023i	$-0.137627\pi$
$608$	−8.48762	−	48.1357i	−0.344218	−	1.95216i
$609$		0			0
$610$	20.5253	+	17.2228i	0.831044	+	0.697329i
$611$	−0.560282	−	0.970437i	−0.0226666	−	0.0392597i
$612$		0			0
$613$	6.99912	−	12.1228i	0.282692	−	0.489637i	−0.689355	−	0.724424i	$-0.742106\pi$
$613$	6.99912	−	12.1228i	0.282692	−	0.489637i	0.972047	+	0.234787i	$0.0754393\pi$
$614$	31.0270	−	11.2929i	1.25215	−	0.455745i
$615$		0			0
$616$	0.930608	−	0.780873i	0.0374953	−	0.0314623i
$617$	22.5965	+	8.22446i	0.909702	+	0.331104i	0.754134	−	0.656721i	$-0.228057\pi$
$617$	22.5965	+	8.22446i	0.909702	+	0.331104i	0.155568	+	0.987825i	$0.450279\pi$
$618$		0			0
$619$	1.19325	−	6.76725i	0.0479607	−	0.271999i	−0.951392	−	0.307984i	$-0.900346\pi$
$619$	1.19325	−	6.76725i	0.0479607	−	0.271999i	0.999352	+	0.0359850i	$0.0114569\pi$
$620$	−29.9521			−1.20291
$621$		0			0
$622$	−31.5594			−1.26542
$623$	−0.285032	+	1.61650i	−0.0114196	+	0.0647635i
$624$		0			0
$625$	−6.78359	−	2.46902i	−0.271343	−	0.0987609i
$626$	−51.9116	+	43.5590i	−2.07481	+	1.74097i
$627$		0			0
$628$	2.14068	−	0.779145i	0.0854225	−	0.0310913i
$629$	3.53898	−	6.12970i	0.141109	−	0.244407i
$630$		0			0
$631$	17.6887	+	30.6377i	0.704175	+	1.21967i	0.966989	+	0.254820i	$0.0820161\pi$
$631$	17.6887	+	30.6377i	0.704175	+	1.21967i	−0.262814	+	0.964847i	$0.584651\pi$
$632$	−2.32953	−	1.95471i	−0.0926637	−	0.0777541i
$633$		0			0
$634$	−5.57873	−	31.6385i	−0.221560	−	1.25653i
$635$	3.91555	+	22.2062i	0.155384	+	0.881226i
$636$		0			0
$637$	5.38460	+	4.51822i	0.213346	+	0.179018i
$638$	7.49346	+	12.9791i	0.296669	+	0.513846i
$639$		0			0
$640$	3.51114	−	6.08148i	0.138790	−	0.240392i
$641$	−18.0174	+	6.55778i	−0.711643	+	0.259017i	−0.672374	−	0.740212i	$-0.734725\pi$
$641$	−18.0174	+	6.55778i	−0.711643	+	0.259017i	−0.0392691	+	0.999229i	$0.512503\pi$
$642$		0			0
$643$	14.8432	−	12.4549i	0.585358	−	0.491173i	−0.301344	−	0.953516i	$-0.597435\pi$
$643$	14.8432	−	12.4549i	0.585358	−	0.491173i	0.886702	+	0.462342i	$0.152991\pi$
$644$	2.15160	+	0.783119i	0.0847849	+	0.0308592i
$645$		0			0
$646$	−6.25078	+	35.4499i	−0.245934	+	1.39476i
$647$	−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
$650$	14.0392	−	79.6203i	0.550663	−	3.12296i
$651$		0			0
$652$	−4.89780	−	1.78265i	−0.191813	−	0.0698141i
$653$	−25.1334	+	21.0895i	−0.983547	+	0.825294i	−0.984621	−	0.174705i	$-0.944103\pi$
$653$	−25.1334	+	21.0895i	−0.983547	+	0.825294i	0.00107333	+	0.999999i	$0.499658\pi$
$654$		0			0
$655$	−35.9962	+	13.1015i	−1.40649	+	0.511920i
$656$	5.28039	−	9.14590i	0.206164	−	0.357087i
$657$		0			0
$658$	0.549163	+	0.951178i	0.0214086	+	0.0370808i
$659$	−14.2880	−	11.9890i	−0.556580	−	0.467026i	0.320582	−	0.947221i	$-0.396121\pi$
$659$	−14.2880	−	11.9890i	−0.556580	−	0.467026i	−0.877162	+	0.480195i	$0.840566\pi$
$660$		0			0
$661$	6.32207	+	35.8542i	0.245900	+	1.39457i	0.818393	+	0.574659i	$0.194865\pi$
$661$	6.32207	+	35.8542i	0.245900	+	1.39457i	−0.572493	+	0.819910i	$0.694024\pi$
$662$	10.8010	+	61.2554i	0.419792	+	2.38076i
$663$		0			0
$664$	−2.05715	−	1.72616i	−0.0798330	−	0.0669878i
$665$	−27.0515	−	46.8546i	−1.04901	−	1.81694i
$666$		0			0
$667$	0.906422	−	1.56997i	0.0350968	−	0.0607894i
$668$	6.76055	−	2.46064i	0.261573	−	0.0952049i
$669$		0			0
$670$	−79.8594	+	67.0100i	−3.08524	+	2.58882i
$671$	−7.52324	−	2.73824i	−0.290432	−	0.105708i
$672$		0			0
$673$	6.84002	−	38.7917i	0.263663	−	1.49531i	−0.509151	−	0.860677i	$-0.670040\pi$
$673$	6.84002	−	38.7917i	0.263663	−	1.49531i	0.772814	−	0.634632i	$-0.218849\pi$
$674$	−11.8276			−0.455584
$675$		0			0
$676$	17.3824			0.668553
$677$	−5.50038	+	31.1942i	−0.211397	+	1.19889i	0.675654	+	0.737218i	$0.263861\pi$
$677$	−5.50038	+	31.1942i	−0.211397	+	1.19889i	−0.887051	+	0.461671i	$0.847250\pi$
$678$		0			0
$679$	−15.6309	−	5.68918i	−0.599858	−	0.218331i
$680$	−1.97724	+	1.65910i	−0.0758236	+	0.0636236i
$681$		0			0
$682$	17.3598	−	6.31844i	0.664741	−	0.241946i
$683$	−14.5328	+	25.1716i	−0.556083	+	0.963164i	0.441735	+	0.897145i	$0.354363\pi$
$683$	−14.5328	+	25.1716i	−0.556083	+	0.963164i	−0.997818	+	0.0660187i	$0.978970\pi$
$684$		0			0
$685$	−35.3225	−	61.1804i	−1.34960	−	2.33758i
$686$	−30.0692	−	25.2310i	−1.14805	−	0.963325i
$687$		0			0
$688$	−0.781059	−	4.42961i	−0.0297776	−	0.168877i
$689$	−3.82278	−	21.6800i	−0.145636	−	0.825944i
$690$		0			0
$691$	4.10401	+	3.44367i	0.156124	+	0.131003i	0.717503	−	0.696555i	$-0.245285\pi$
$691$	4.10401	+	3.44367i	0.156124	+	0.131003i	−0.561380	+	0.827558i	$0.689729\pi$
$692$	6.60549	+	11.4410i	0.251103	+	0.434923i
$693$		0			0
$694$	−22.6805	+	39.2838i	−0.860940	+	1.49119i
$695$	81.0601	−	29.5035i	3.07478	−	1.11913i
$696$		0			0
$697$	−5.61793	+	4.71400i	−0.212794	+	0.178555i
$698$	−21.4072	−	7.79157i	−0.810274	−	0.294915i
$699$		0			0
$700$	−6.66637	+	37.8069i	−0.251965	+	1.42897i
$701$	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
$704$	2.65101	−	15.0346i	0.0999136	−	0.566638i
$705$		0			0
$706$	3.95084	+	1.43799i	0.148692	+	0.0541194i
$707$	−8.41009	+	7.05690i	−0.316294	+	0.265402i
$708$		0			0
$709$	4.40760	−	1.60424i	0.165531	−	0.0602484i	−0.257925	−	0.966165i	$-0.583039\pi$
$709$	4.40760	−	1.60424i	0.165531	−	0.0602484i	0.423456	+	0.905916i	$0.360817\pi$
$710$	4.38571	−	7.59627i	0.164593	−	0.285083i
$711$		0			0
$712$	−0.0830629	−	0.143869i	−0.00311291	−	0.00539173i
$713$	−1.71183	−	1.43639i	−0.0641085	−	0.0537934i
$714$		0			0
$715$	6.60519	+	37.4599i	0.247020	+	1.40092i
$716$	−4.69470	−	26.6250i	−0.175449	−	0.995021i
$717$		0			0
$718$	36.5488	+	30.6680i	1.36399	+	1.14452i
$719$	19.5335	+	33.8330i	0.728476	+	1.26176i	0.957527	+	0.288343i	$0.0931042\pi$
$719$	19.5335	+	33.8330i	0.728476	+	1.26176i	−0.229052	+	0.973414i	$0.573562\pi$
$720$		0			0
$721$	−15.9893	+	27.6943i	−0.595473	+	1.03139i
$722$	36.5939	−	13.3191i	1.36188	−	0.495685i
$723$		0			0
$724$	19.0043	−	15.9465i	0.706291	−	0.592648i
$725$	28.5621	+	10.3957i	1.06077	+	0.386088i
$726$		0			0
$727$	−1.87980	+	10.6609i	−0.0697178	+	0.395389i	0.929902	+	0.367808i	$0.119892\pi$
$727$	−1.87980	+	10.6609i	−0.0697178	+	0.395389i	−0.999620	+	0.0275812i	$0.991220\pi$
$728$	2.63030			0.0974853
$729$		0			0
$730$	34.1215			1.26290
$731$	−0.542388	+	3.07604i	−0.0200610	+	0.113771i
$732$		0			0
$733$	3.20661	+	1.16711i	0.118439	+	0.0431083i	0.400560	−	0.916271i	$-0.368816\pi$
$733$	3.20661	+	1.16711i	0.118439	+	0.0431083i	−0.282121	+	0.959379i	$0.591038\pi$
$734$	4.27719	−	3.58899i	0.157874	−	0.132472i
$735$		0			0
$736$	−3.82857	+	1.39349i	−0.141123	+	0.0513646i
$737$	15.5749	−	26.9766i	0.573710	−	0.993695i
$738$		0			0
$739$	−13.1505	−	22.7773i	−0.483748	−	0.837877i	0.516077	−	0.856542i	$-0.327392\pi$
$739$	−13.1505	−	22.7773i	−0.483748	−	0.837877i	−0.999826	+	0.0186653i	$0.994058\pi$
$740$	12.8514	+	10.7836i	0.472426	+	0.396412i
$741$		0			0
$742$	3.74691	+	21.2498i	0.137553	+	0.780104i
$743$	−5.02606	−	28.5042i	−0.184388	−	1.04572i	−0.926739	−	0.375706i	$-0.877400\pi$
$743$	−5.02606	−	28.5042i	−0.184388	−	1.04572i	0.742351	−	0.670011i	$-0.233711\pi$
$744$		0			0
$745$	43.9693	+	36.8946i	1.61091	+	1.35171i
$746$	−28.3953	−	49.1822i	−1.03963	−	1.80069i
$747$		0			0
$748$	−6.00862	+	10.4072i	−0.219697	+	0.380526i
$749$	25.6615	−	9.34002i	0.937651	−	0.341277i
$750$		0			0
$751$	−14.8983	+	12.5011i	−0.543646	+	0.456173i	−0.872782	−	0.488109i	$-0.837687\pi$
$751$	−14.8983	+	12.5011i	−0.543646	+	0.456173i	0.329137	+	0.944282i	$0.393242\pi$
$752$	−0.943555	−	0.343426i	−0.0344079	−	0.0125235i
$753$		0			0
$754$	−5.63475	+	31.9563i	−0.205206	+	1.16378i
$755$	−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	$0.461751\pi$
$758$	−11.0125	+	62.4552i	−0.399994	+	2.26848i
$759$		0			0
$760$	5.14543	+	1.87278i	0.186644	+	0.0679330i
$761$	−7.91301	+	6.63980i	−0.286846	+	0.240693i	−0.774844	−	0.632152i	$-0.782172\pi$
$761$	−7.91301	+	6.63980i	−0.286846	+	0.240693i	0.487998	+	0.872845i	$0.337727\pi$
$762$		0			0
$763$	32.2126	−	11.7244i	1.16617	−	0.424453i
$764$	−12.6138	+	21.8478i	−0.456352	+	0.790424i
$765$		0			0
$766$	−0.662037	−	1.14668i	−0.0239204	−	0.0414313i
$767$	48.1014	+	40.3619i	1.73684	+	1.45738i
$768$		0			0
$769$	7.78968	+	44.1775i	0.280903	+	1.59308i	0.719563	+	0.694427i	$0.244342\pi$
$769$	7.78968	+	44.1775i	0.280903	+	1.59308i	−0.438660	+	0.898653i	$0.644547\pi$
$770$	−6.47410	−	36.7165i	−0.233311	−	1.32317i
$771$		0			0
$772$	21.6027	+	18.1268i	0.777497	+	0.652397i
$773$	21.4677	+	37.1832i	0.772141	+	1.33739i	0.936388	+	0.350968i	$0.114147\pi$
$773$	21.4677	+	37.1832i	0.772141	+	1.33739i	−0.164247	+	0.986419i	$0.552519\pi$
$774$		0			0
$775$	18.7335	−	32.4475i	0.672929	−	1.16555i
$776$	1.58197	−	0.575789i	0.0567893	−	0.0206696i
$777$		0			0
$778$	−6.42649	+	5.39246i	−0.230401	+	0.193329i
$779$	14.6197	+	5.32114i	0.523805	+	0.190650i
$780$		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)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 1.93969i) q^{2} +(-1.76604 - 0.642788i) q^{4} +(2.83564 - 2.37939i) q^{5} +(2.20574 - 0.802823i) q^{7} +(-0.118782 + 0.205737i) q^{8} +O(q^{10})\)	\(q+(-0.342020 + 1.93969i) q^{2} +(-1.76604 - 0.642788i) q^{4} +(2.83564 - 2.37939i) q^{5} +(2.20574 - 0.802823i) q^{7} +(-0.118782 + 0.205737i) q^{8} +(3.64543 + 6.31407i) q^{10} +(-1.66885 - 1.40033i) q^{11} +(-0.819078 - 4.64522i) q^{13} +(0.802823 + 4.55303i) q^{14} +(-3.23783 - 2.71686i) q^{16} +(1.46756 + 2.54189i) q^{17} +(3.11334 - 5.39246i) q^{19} +(-6.53731 + 2.37939i) q^{20} +(3.28699 - 2.75811i) q^{22} +(-0.487728 - 0.177519i) q^{23} +(1.51114 - 8.57013i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(-0.606511 + 3.43969i) q^{29} +(4.04576 + 1.47254i) q^{31} +(6.01330 - 5.04576i) q^{32} +(-5.43242 + 1.97724i) q^{34} +(4.34445 - 7.52481i) q^{35} +(-1.20574 - 2.08840i) q^{37} +(9.39490 + 7.88326i) q^{38} +(0.152704 + 0.866025i) q^{40} +(0.433877 + 2.46064i) q^{41} +(0.815207 + 0.684040i) q^{43} +(2.04715 + 3.54576i) q^{44} +(0.511144 - 0.885328i) q^{46} +(0.223238 - 0.0812519i) q^{47} +(-1.14156 + 0.957882i) q^{49} +(16.1066 + 5.86231i) q^{50} +(-1.53936 + 8.73016i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(-0.0968323 + 0.549163i) q^{56} +(-6.46451 - 2.35289i) q^{58} +(-10.1977 + 8.55690i) q^{59} +(3.45336 - 1.25692i) q^{61} +(-4.24000 + 7.34389i) q^{62} +(3.50387 + 6.06888i) q^{64} +(-13.3754 - 11.2233i) q^{65} +(2.48293 + 14.0814i) q^{67} +(-0.957882 - 5.43242i) q^{68} +(13.1099 + 11.0005i) q^{70} +(-0.601535 - 1.04189i) q^{71} +(2.34002 - 4.05304i) q^{73} +(4.46324 - 1.62449i) q^{74} +(-8.96451 + 7.52211i) q^{76} +(-4.80526 - 1.74897i) q^{77} +(-2.22281 + 12.6062i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(-1.96291 + 11.1322i) q^{83} +(10.2096 + 3.71599i) q^{85} +(-1.60565 + 1.34730i) q^{86} +(0.486329 - 0.177009i) q^{88} +(-0.349643 + 0.605600i) q^{89} +(-5.53596 - 9.58856i) q^{91} +(0.747243 + 0.627011i) q^{92} +(0.0812519 + 0.460802i) q^{94} +(-4.00243 - 22.6989i) q^{95} +(-5.42855 - 4.55509i) q^{97} +(-1.46756 - 2.54189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q - 12 * q^4 + 6 * q^7	\( 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100}) \) 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

Introduction

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