LMFDB - Embedded newform 729.2.g.d.622.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			622.4
Character	$\chi$	$=$	729.622
Dual form			729.2.g.d.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.217727 + 0.230777i) q^{2} +(0.110437 + 1.89612i) q^{4} +(-2.10697 - 0.246269i) q^{5} +(-2.27300 + 1.14154i) q^{7} +(-0.947719 - 0.795231i) q^{8} +O(q^{10})$	\(q+(-0.217727 + 0.230777i) q^{2} +(0.110437 + 1.89612i) q^{4} +(-2.10697 - 0.246269i) q^{5} +(-2.27300 + 1.14154i) q^{7} +(-0.947719 - 0.795231i) q^{8} +(0.515577 - 0.432621i) q^{10} +(-1.21202 + 2.80978i) q^{11} +(5.37024 - 1.27277i) q^{13} +(0.231451 - 0.773099i) q^{14} +(-3.38312 + 0.395430i) q^{16} +(-0.745021 - 4.22522i) q^{17} +(-0.0105922 + 0.0600713i) q^{19} +(0.234271 - 4.02227i) q^{20} +(-0.384543 - 0.891471i) q^{22} +(-3.82550 - 1.92124i) q^{23} +(-0.486554 - 0.115315i) q^{25} +(-0.875520 + 1.51644i) q^{26} +(-2.41553 - 4.18381i) q^{28} +(-3.06272 - 10.2302i) q^{29} +(-3.85453 + 2.53516i) q^{31} +(2.12290 - 2.85155i) q^{32} +(1.13730 + 0.748011i) q^{34} +(5.07026 - 1.84542i) q^{35} +(-3.30730 - 1.20376i) q^{37} +(-0.0115569 - 0.0155236i) q^{38} +(1.80097 + 1.90892i) q^{40} +(-1.72935 - 1.83301i) q^{41} +(-0.463275 - 0.622287i) q^{43} +(-5.46154 - 1.98784i) q^{44} +(1.27629 - 0.464532i) q^{46} +(3.79858 + 2.49837i) q^{47} +(-0.316716 + 0.425424i) q^{49} +(0.132548 - 0.0871782i) q^{50} +(3.00640 + 10.0421i) q^{52} +(0.986349 + 1.70841i) q^{53} +(3.24565 - 5.62164i) q^{55} +(3.06195 + 0.725696i) q^{56} +(3.02773 + 1.52058i) q^{58} +(2.85708 + 6.62346i) q^{59} +(0.679073 - 11.6592i) q^{61} +(0.254177 - 1.44151i) q^{62} +(-0.987085 - 5.59804i) q^{64} +(-11.6284 + 1.35916i) q^{65} +(0.347884 - 1.16201i) q^{67} +(7.92927 - 1.87927i) q^{68} +(-0.678050 + 1.57190i) q^{70} +(-10.9300 + 9.17137i) q^{71} +(7.44218 + 6.24473i) q^{73} +(0.997887 - 0.501157i) q^{74} +(-0.115072 - 0.0134500i) q^{76} +(-0.452562 - 7.77019i) q^{77} +(-1.10564 + 1.17191i) q^{79} +7.22552 q^{80} +0.799542 q^{82} +(-2.26614 + 2.40196i) q^{83} +(0.529193 + 9.08589i) q^{85} +(0.244477 + 0.0285753i) q^{86} +(3.38308 - 1.69905i) q^{88} +(-10.7606 - 9.02919i) q^{89} +(-10.7536 + 9.02336i) q^{91} +(3.22043 - 7.46579i) q^{92} +(-1.40362 + 0.332664i) q^{94} +(0.0371112 - 0.123960i) q^{95} +(-6.97567 + 0.815339i) q^{97} +(-0.0292204 - 0.165717i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	−0.217727	+	0.230777i	−0.153956	+	0.163184i	−0.799761	−	0.600319i	$-0.795040\pi$
$2$	−0.217727	+	0.230777i	−0.153956	+	0.163184i	0.645805	+	0.763503i	$0.276522\pi$
$3$		0			0
$3$		0			0
$4$	0.110437	+	1.89612i	0.0552183	+	0.948062i
$5$	−2.10697	−	0.246269i	−0.942265	−	0.110135i	−0.368931	−	0.929457i	$-0.620276\pi$
$5$	−2.10697	−	0.246269i	−0.942265	−	0.110135i	−0.573334	+	0.819322i	$0.694350\pi$
$6$		0			0
$7$	−2.27300	+	1.14154i	−0.859112	+	0.431462i	−0.823105	−	0.567889i	$-0.807760\pi$
$7$	−2.27300	+	1.14154i	−0.859112	+	0.431462i	−0.0360069	+	0.999352i	$0.511464\pi$
$8$	−0.947719	−	0.795231i	−0.335069	−	0.281157i
$9$		0			0
$10$	0.515577	−	0.432621i	0.163040	−	0.136807i
$11$	−1.21202	+	2.80978i	−0.365438	+	0.847181i	0.631954	+	0.775006i	$0.282253\pi$
$11$	−1.21202	+	2.80978i	−0.365438	+	0.847181i	−0.997392	+	0.0721747i	$0.977006\pi$
$12$		0			0
$13$	5.37024	−	1.27277i	1.48944	−	0.353003i	0.596291	−	0.802769i	$-0.296641\pi$
$13$	5.37024	−	1.27277i	1.48944	−	0.353003i	0.893147	+	0.449766i	$0.148492\pi$
$14$	0.231451	−	0.773099i	0.0618578	−	0.206620i
$15$		0			0
$16$	−3.38312	+	0.395430i	−0.845781	+	0.0988576i
$17$	−0.745021	−	4.22522i	−0.180694	−	1.02477i	−0.931364	−	0.364090i	$-0.881380\pi$
$17$	−0.745021	−	4.22522i	−0.180694	−	1.02477i	0.750670	−	0.660678i	$-0.229731\pi$
$18$		0			0
$19$	−0.0105922	+	0.0600713i	−0.00243002	+	0.0137813i	−0.985999	−	0.166753i	$-0.946672\pi$
$19$	−0.0105922	+	0.0600713i	−0.00243002	+	0.0137813i	0.983569	+	0.180535i	$0.0577828\pi$
$20$	0.234271	−	4.02227i	0.0523845	−	0.899407i
$21$		0			0
$22$	−0.384543	−	0.891471i	−0.0819849	−	0.190062i
$23$	−3.82550	−	1.92124i	−0.797671	−	0.400606i	0.00278538	−	0.999996i	$-0.499113\pi$
$23$	−3.82550	−	1.92124i	−0.797671	−	0.400606i	−0.800457	+	0.599390i	$0.795410\pi$
$24$		0			0
$25$	−0.486554	−	0.115315i	−0.0973108	−	0.0230631i
$26$	−0.875520	+	1.51644i	−0.171704	+	0.297399i
$27$		0			0
$28$	−2.41553	−	4.18381i	−0.456491	−	0.790666i
$29$	−3.06272	−	10.2302i	−0.568733	−	1.89970i	−0.408979	−	0.912544i	$-0.634115\pi$
$29$	−3.06272	−	10.2302i	−0.568733	−	1.89970i	−0.159755	−	0.987157i	$-0.551070\pi$
$30$		0			0
$31$	−3.85453	+	2.53516i	−0.692294	+	0.455329i	−0.846276	−	0.532745i	$-0.821161\pi$
$31$	−3.85453	+	2.53516i	−0.692294	+	0.455329i	0.153982	+	0.988074i	$0.450790\pi$
$32$	2.12290	−	2.85155i	0.375280	−	0.504088i
$33$		0			0
$34$	1.13730	+	0.748011i	0.195045	+	0.128283i
$35$	5.07026	−	1.84542i	0.857030	−	0.311933i
$36$		0			0
$37$	−3.30730	−	1.20376i	−0.543716	−	0.197896i	0.0555362	−	0.998457i	$-0.482313\pi$
$37$	−3.30730	−	1.20376i	−0.543716	−	0.197896i	−0.599252	+	0.800560i	$0.704535\pi$
$38$	−0.0115569	−	0.0155236i	−0.00187477	−	0.00251826i
$39$		0			0
$40$	1.80097	+	1.90892i	0.284759	+	0.301827i
$41$	−1.72935	−	1.83301i	−0.270080	−	0.286268i	0.578112	−	0.815958i	$-0.303790\pi$
$41$	−1.72935	−	1.83301i	−0.270080	−	0.286268i	−0.848191	+	0.529690i	$0.822308\pi$
$42$		0			0
$43$	−0.463275	−	0.622287i	−0.0706488	−	0.0948978i	0.765394	−	0.643562i	$-0.222544\pi$
$43$	−0.463275	−	0.622287i	−0.0706488	−	0.0948978i	−0.836043	+	0.548664i	$0.815137\pi$
$44$	−5.46154	−	1.98784i	−0.823359	−	0.299678i
$45$		0			0
$46$	1.27629	−	0.464532i	0.188179	−	0.0684915i
$47$	3.79858	+	2.49837i	0.554080	+	0.364424i	0.795460	−	0.606007i	$-0.207229\pi$
$47$	3.79858	+	2.49837i	0.554080	+	0.364424i	−0.241379	+	0.970431i	$0.577600\pi$
$48$		0			0
$49$	−0.316716	+	0.425424i	−0.0452452	+	0.0607748i
$50$	0.132548	−	0.0871782i	0.0187451	−	0.0123289i
$51$		0			0
$52$	3.00640	+	10.0421i	0.416913	+	1.39259i
$53$	0.986349	+	1.70841i	0.135485	+	0.234668i	0.925783	−	0.378056i	$-0.123407\pi$
$53$	0.986349	+	1.70841i	0.135485	+	0.234668i	−0.790297	+	0.612724i	$0.790074\pi$
$54$		0			0
$55$	3.24565	−	5.62164i	0.437644	−	0.758021i
$56$	3.06195	+	0.725696i	0.409170	+	0.0969752i
$57$		0			0
$58$	3.02773	+	1.52058i	0.397561	+	0.199662i
$59$	2.85708	+	6.62346i	0.371960	+	0.862301i	0.996677	+	0.0814496i	$0.0259550\pi$
$59$	2.85708	+	6.62346i	0.371960	+	0.862301i	−0.624717	+	0.780851i	$0.714786\pi$
$60$		0			0
$61$	0.679073	−	11.6592i	0.0869464	−	1.49281i	−0.619473	−	0.785018i	$-0.712654\pi$
$61$	0.679073	−	11.6592i	0.0869464	−	1.49281i	0.706419	−	0.707794i	$-0.250309\pi$
$62$	0.254177	−	1.44151i	0.0322805	−	0.183072i
$63$		0			0
$64$	−0.987085	−	5.59804i	−0.123386	−	0.699755i
$65$	−11.6284	+	1.35916i	−1.44232	+	0.168583i
$66$		0			0
$67$	0.347884	−	1.16201i	0.0425008	−	0.141963i	−0.934106	−	0.356996i	$-0.883801\pi$
$67$	0.347884	−	1.16201i	0.0425008	−	0.141963i	0.976607	+	0.215034i	$0.0689861\pi$
$68$	7.92927	−	1.87927i	0.961565	−	0.227895i
$69$		0			0
$70$	−0.678050	+	1.57190i	−0.0810425	+	0.187878i
$71$	−10.9300	+	9.17137i	−1.29715	+	1.08844i	−0.306525	+	0.951863i	$0.599166\pi$
$71$	−10.9300	+	9.17137i	−1.29715	+	1.08844i	−0.990629	+	0.136579i	$0.956389\pi$
$72$		0			0
$73$	7.44218	+	6.24473i	0.871042	+	0.730891i	0.964317	−	0.264750i	$-0.0852893\pi$
$73$	7.44218	+	6.24473i	0.871042	+	0.730891i	−0.0932755	+	0.995640i	$0.529734\pi$
$74$	0.997887	−	0.501157i	0.116002	−	0.0582584i
$75$		0			0
$76$	−0.115072	−	0.0134500i	−0.0131997	−	0.00154282i
$77$	−0.452562	−	7.77019i	−0.0515742	−	0.885496i
$78$		0			0
$79$	−1.10564	+	1.17191i	−0.124395	+	0.131851i	−0.786577	−	0.617492i	$-0.788149\pi$
$79$	−1.10564	+	1.17191i	−0.124395	+	0.131851i	0.662183	+	0.749342i	$0.269630\pi$
$80$	7.22552			0.807838
$81$		0			0
$82$	0.799542			0.0882947
$83$	−2.26614	+	2.40196i	−0.248741	+	0.263650i	−0.839699	−	0.543053i	$-0.817268\pi$
$83$	−2.26614	+	2.40196i	−0.248741	+	0.263650i	0.590958	+	0.806702i	$0.298750\pi$
$84$		0			0
$85$	0.529193	+	9.08589i	0.0573990	+	0.985503i
$86$	0.244477	+	0.0285753i	0.0263626	+	0.00308135i
$87$		0			0
$88$	3.38308	−	1.69905i	0.360637	−	0.181119i
$89$	−10.7606	−	9.02919i	−1.14062	−	0.957092i	−0.141159	−	0.989987i	$-0.545083\pi$
$89$	−10.7606	−	9.02919i	−1.14062	−	0.957092i	−0.999459	+	0.0328946i	$0.989527\pi$
$90$		0			0
$91$	−10.7536	+	9.02336i	−1.12729	+	0.945905i
$92$	3.22043	−	7.46579i	0.335753	−	0.778363i
$93$		0			0
$94$	−1.40362	+	0.332664i	−0.144772	+	0.0343117i
$95$	0.0371112	−	0.123960i	0.00380752	−	0.0127180i
$96$		0			0
$97$	−6.97567	+	0.815339i	−0.708272	+	0.0827851i	−0.462599	−	0.886568i	$-0.653083\pi$
$97$	−6.97567	+	0.815339i	−0.708272	+	0.0827851i	−0.245673	+	0.969353i	$0.579009\pi$
$98$	−0.0292204	−	0.165717i	−0.00295170	−	0.0167399i
$99$		0			0
$100$	0.164919	−	0.935301i	0.0164919	−	0.0935301i
$101$	−0.631091	+	10.8354i	−0.0627959	+	1.07816i	0.808846	+	0.588021i	$0.200093\pi$
$101$	−0.631091	+	10.8354i	−0.0627959	+	1.07816i	−0.871642	+	0.490143i	$0.836944\pi$
$102$		0			0
$103$	−4.92595	−	11.4196i	−0.485368	−	1.12521i	−0.968354	−	0.249582i	$-0.919707\pi$
$103$	−4.92595	−	11.4196i	−0.485368	−	1.12521i	0.482986	−	0.875628i	$-0.339552\pi$
$104$	−6.10163	−	3.06435i	−0.598314	−	0.300485i
$105$		0			0
$106$	−0.609016	−	0.144339i	−0.0591528	−	0.0140195i
$107$	−2.48915	+	4.31134i	−0.240636	+	0.416793i	−0.960896	−	0.276911i	$-0.910689\pi$
$107$	−2.48915	+	4.31134i	−0.240636	+	0.416793i	0.720260	+	0.693704i	$0.244023\pi$
$108$		0			0
$109$	−0.180626	−	0.312853i	−0.0173008	−	0.0299659i	0.857245	−	0.514908i	$-0.172174\pi$
$109$	−0.180626	−	0.312853i	−0.0173008	−	0.0299659i	−0.874546	+	0.484942i	$0.838841\pi$
$110$	0.590678	+	1.97300i	0.0563190	+	0.188119i
$111$		0			0
$112$	7.23843	−	4.76079i	0.683967	−	0.449852i
$113$	−11.7891	+	15.8355i	−1.10902	+	1.48968i	−0.256822	+	0.966459i	$0.582675\pi$
$113$	−11.7891	+	15.8355i	−1.10902	+	1.48968i	−0.852200	+	0.523216i	$0.824732\pi$
$114$		0			0
$115$	7.58706	+	4.99009i	0.707497	+	0.465328i
$116$	19.0595	−	6.93709i	1.76963	−	0.644092i
$117$		0			0
$118$	−2.15060	−	0.782756i	−0.197979	−	0.0720585i
$119$	6.51670	+	8.75344i	0.597385	+	0.802427i
$120$		0			0
$121$	1.12279	+	1.19008i	0.102072	+	0.108189i
$122$	2.54283	+	2.69524i	0.230217	+	0.244016i
$123$		0			0
$124$	−5.23266	−	7.02869i	−0.469907	−	0.631195i
$125$	10.9637	+	3.99045i	0.980620	+	0.356916i
$126$		0			0
$127$	13.5556	−	4.93382i	1.20286	−	0.437806i	0.338639	−	0.940916i	$-0.390033\pi$
$127$	13.5556	−	4.93382i	1.20286	−	0.437806i	0.864222	+	0.503111i	$0.167811\pi$
$128$	7.44714	+	4.89806i	0.658240	+	0.432932i
$129$		0			0
$130$	2.21815	−	2.97949i	0.194544	−	0.261318i
$131$	−2.55224	+	1.67864i	−0.222990	+	0.146663i	−0.656089	−	0.754683i	$-0.727791\pi$
$131$	−2.55224	+	1.67864i	−0.222990	+	0.146663i	0.433099	+	0.901346i	$0.357420\pi$
$132$		0			0
$133$	−0.0444979	−	0.148633i	−0.00385846	−	0.0128881i
$134$	0.192422	+	0.333285i	0.0166228	+	0.0287915i
$135$		0			0
$136$	−2.65396	+	4.59679i	−0.227575	+	0.394171i
$137$	2.53477	+	0.600750i	0.216560	+	0.0513256i	0.337463	−	0.941339i	$-0.390431\pi$
$137$	2.53477	+	0.600750i	0.216560	+	0.0513256i	−0.120904	+	0.992664i	$0.538579\pi$
$138$		0			0
$139$	−16.9648	−	8.52003i	−1.43893	−	0.722660i	−0.453269	−	0.891374i	$-0.649742\pi$
$139$	−16.9648	−	8.52003i	−1.43893	−	0.722660i	−0.985665	+	0.168714i	$0.946038\pi$
$140$	4.05909	+	9.41004i	0.343056	+	0.795293i
$141$		0			0
$142$	0.263216	−	4.51925i	0.0220886	−	0.379247i
$143$	−2.93264	+	16.6318i	−0.245240	+	1.39082i
$144$		0			0
$145$	3.93367	+	22.3090i	0.326674	+	1.85266i
$146$	−3.06150	+	0.357838i	−0.253372	+	0.0296149i
$147$		0			0
$148$	1.91723	−	6.40398i	0.157595	−	0.526404i
$149$	3.98717	−	0.944978i	0.326642	−	0.0774156i	−0.0640232	−	0.997948i	$-0.520393\pi$
$149$	3.98717	−	0.944978i	0.326642	−	0.0774156i	0.390665	+	0.920533i	$0.372245\pi$
$150$		0			0
$151$	3.93753	−	9.12821i	0.320431	−	0.742843i	−0.679526	−	0.733651i	$-0.737815\pi$
$151$	3.93753	−	9.12821i	0.320431	−	0.742843i	0.999958	−	0.00919237i	$-0.00292606\pi$
$152$	0.0578090	−	0.0485075i	0.00468893	−	0.00393448i
$153$		0			0
$154$	1.89172	+	1.58734i	0.152439	+	0.127911i
$155$	8.74570	−	4.39226i	0.702472	−	0.352795i
$156$		0			0
$157$	−11.4715	−	1.34082i	−0.915523	−	0.107009i	−0.354733	−	0.934968i	$-0.615428\pi$
$157$	−11.4715	−	1.34082i	−0.915523	−	0.107009i	−0.560790	+	0.827958i	$0.689502\pi$
$158$	−0.0297224	−	0.510314i	−0.00236459	−	0.0405984i
$159$		0			0
$160$	−5.17514	+	5.48533i	−0.409131	+	0.433653i
$161$	10.8885			0.858135
$162$		0			0
$163$	−14.1333			−1.10700			−0.553502	−	0.832848i	$-0.686709\pi$
$163$	−14.1333			−1.10700			−0.553502	+	0.832848i	$0.686709\pi$
$164$	3.28462	−	3.48150i	0.256486	−	0.271859i
$165$		0			0
$166$	−0.0609193	−	1.04594i	−0.00472825	−	0.0811810i
$167$	6.65820	+	0.778232i	0.515227	+	0.0602214i	0.369733	−	0.929138i	$-0.379449\pi$
$167$	6.65820	+	0.778232i	0.515227	+	0.0602214i	0.145493	+	0.989359i	$0.453523\pi$
$168$		0			0
$169$	15.6023	−	7.83578i	1.20018	−	0.602753i
$170$	−2.21203	−	1.85612i	−0.169655	−	0.142358i
$171$		0			0
$172$	1.12877	−	0.947150i	0.0860679	−	0.0722195i
$173$	−5.85754	+	13.5793i	−0.445340	+	1.03242i	0.536705	+	0.843770i	$0.319669\pi$
$173$	−5.85754	+	13.5793i	−0.445340	+	1.03242i	−0.982045	+	0.188645i	$0.939590\pi$
$174$		0			0
$175$	1.23757	−	0.293310i	0.0935517	−	0.0221722i
$176$	2.98934	−	9.98511i	0.225330	−	0.752656i
$177$		0			0
$178$	4.42659	−	0.517395i	0.331787	−	0.0387804i
$179$	−0.110050	−	0.624125i	−0.00822552	−	0.0466493i	0.980419	−	0.196924i	$-0.0630953\pi$
$179$	−0.110050	−	0.624125i	−0.00822552	−	0.0466493i	−0.988644	+	0.150275i	$0.951984\pi$
$180$		0			0
$181$	−2.42311	+	13.7421i	−0.180108	+	1.02145i	0.751972	+	0.659195i	$0.229103\pi$
$181$	−2.42311	+	13.7421i	−0.180108	+	1.02145i	−0.932081	+	0.362251i	$0.882008\pi$
$182$	0.258968	−	4.44631i	0.0191960	−	0.329583i
$183$		0			0
$184$	2.09767	+	4.86295i	0.154642	+	0.358501i
$185$	6.67192	+	3.35077i	0.490529	+	0.246353i
$186$		0			0
$187$	12.7749	+	3.02771i	0.934195	+	0.221408i
$188$	−4.31771	+	7.47849i	−0.314901	+	0.545425i
$189$		0			0
$190$	0.0205270	+	0.0355538i	0.00148918	+	0.00257934i
$191$	−2.43589	−	8.13645i	−0.176255	−	0.588733i	−0.999770	−	0.0214386i	$-0.993175\pi$
$191$	−2.43589	−	8.13645i	−0.176255	−	0.588733i	0.823515	−	0.567294i	$-0.192010\pi$
$192$		0			0
$193$	−11.0711	+	7.28156i	−0.796914	+	0.524138i	−0.881447	−	0.472282i	$-0.843430\pi$
$193$	−11.0711	+	7.28156i	−0.796914	+	0.524138i	0.0845336	+	0.996421i	$0.473060\pi$
$194$	1.33063	−	1.78735i	0.0955336	−	0.128324i
$195$		0			0
$196$	−0.841633	−	0.553551i	−0.0601167	−	0.0395394i
$197$	7.09307	−	2.58167i	0.505360	−	0.183936i	−0.0767431	−	0.997051i	$-0.524452\pi$
$197$	7.09307	−	2.58167i	0.505360	−	0.183936i	0.582103	+	0.813115i	$0.302230\pi$
$198$		0			0
$199$	1.98595	+	0.722827i	0.140780	+	0.0512399i	0.411449	−	0.911433i	$-0.365023\pi$
$199$	1.98595	+	0.722827i	0.140780	+	0.0512399i	−0.270669	+	0.962672i	$0.587245\pi$
$200$	0.369414	+	0.496209i	0.0261215	+	0.0350873i
$201$		0			0
$202$	−2.36316	−	2.50480i	−0.166271	−	0.176237i
$203$	18.6398	+	19.7570i	1.30825	+	1.38667i
$204$		0			0
$205$	3.19228	+	4.28798i	0.222958	+	0.299485i
$206$	3.70790	+	1.34957i	0.258342	+	0.0940287i
$207$		0			0
$208$	−17.6649	+	6.42950i	−1.22484	+	0.445805i
$209$	−0.155949	−	0.102569i	−0.0107872	−	0.00709488i
$210$		0			0
$211$	0.392021	−	0.526575i	0.0269878	−	0.0362509i	−0.788424	−	0.615132i	$-0.789103\pi$
$211$	0.392021	−	0.526575i	0.0269878	−	0.0362509i	0.815412	+	0.578881i	$0.196510\pi$
$212$	−3.13042	+	2.05891i	−0.214998	+	0.141407i
$213$		0			0
$214$	−0.453003	−	1.51313i	−0.0309666	−	0.103436i
$215$	0.822857	+	1.42523i	0.0561184	+	0.0971998i
$216$		0			0
$217$	5.86733	−	10.1625i	0.398301	−	0.689877i
$218$	0.111526	+	0.0264323i	0.00755352	+	0.00179022i
$219$		0			0
$220$	11.0178	+	5.53333i	0.742817	+	0.373057i
$221$	−9.37868	−	21.7422i	−0.630878	−	1.46254i
$222$		0			0
$223$	−1.30890	+	22.4729i	−0.0876503	+	1.50490i	0.612254	+	0.790661i	$0.290263\pi$
$223$	−1.30890	+	22.4729i	−0.0876503	+	1.50490i	−0.699904	+	0.714237i	$0.746774\pi$
$224$	−1.57018	+	8.90495i	−0.104912	+	0.594987i
$225$		0			0
$226$	−1.08766	−	6.16845i	−0.0723503	−	0.410319i
$227$	13.3179	−	1.55664i	0.883942	−	0.103318i	0.338005	−	0.941144i	$-0.390248\pi$
$227$	13.3179	−	1.55664i	0.883942	−	0.103318i	0.545937	+	0.837826i	$0.316174\pi$
$228$		0			0
$229$	−1.78489	+	5.96194i	−0.117949	+	0.393976i	−0.996492	−	0.0836862i	$-0.973331\pi$
$229$	−1.78489	+	5.96194i	−0.117949	+	0.393976i	0.878543	+	0.477663i	$0.158516\pi$
$230$	−2.80351	+	0.664443i	−0.184858	+	0.0438121i
$231$		0			0
$232$	−5.23277	+	12.1309i	−0.343548	+	0.796434i
$233$	−9.49107	+	7.96396i	−0.621781	+	0.521736i	−0.898363	−	0.439254i	$-0.855243\pi$
$233$	−9.49107	+	7.96396i	−0.621781	+	0.521736i	0.276582	+	0.960990i	$0.410798\pi$
$234$		0			0
$235$	−7.38822	−	6.19946i	−0.481955	−	0.404408i
$236$	−12.2434	+	6.14885i	−0.796975	+	0.400256i
$237$		0			0
$238$	−3.43895	−	0.401956i	−0.222914	−	0.0260549i
$239$	0.571683	+	9.81542i	0.0369791	+	0.634907i	0.964979	+	0.262327i	$0.0844897\pi$
$239$	0.571683	+	9.81542i	0.0369791	+	0.634907i	−0.928000	+	0.372580i	$0.878473\pi$
$240$		0			0
$241$	11.8975	−	12.6106i	0.766384	−	0.812320i	−0.220220	−	0.975450i	$-0.570678\pi$
$241$	11.8975	−	12.6106i	0.766384	−	0.812320i	0.986605	+	0.163130i	$0.0521591\pi$
$242$	−0.519105			−0.0333693
$243$		0			0
$244$	22.1823			1.42008
$245$	0.772080	−	0.818357i	0.0493264	−	0.0522829i
$246$		0			0
$247$	0.0195744	+	0.336079i	0.00124549	+	0.0213842i
$248$	5.66905	+	0.662617i	0.359985	+	0.0420762i
$249$		0			0
$250$	−3.30799	+	1.66133i	−0.209216	+	0.105072i
$251$	−19.1764	−	16.0909i	−1.21040	−	1.01565i	−0.999270	−	0.0381908i	$-0.987841\pi$
$251$	−19.1764	−	16.0909i	−1.21040	−	1.01565i	−0.211132	−	0.977458i	$-0.567715\pi$
$252$		0			0
$253$	10.0348	−	8.42023i	0.630885	−	0.529375i
$254$	−1.81280	+	4.20253i	−0.113745	+	0.263690i
$255$		0			0
$256$	8.31055	−	1.96964i	0.519409	−	0.123102i
$257$	−0.691327	+	2.30919i	−0.0431238	+	0.144044i	−0.976840	−	0.213970i	$-0.931361\pi$
$257$	−0.691327	+	2.30919i	−0.0431238	+	0.144044i	0.933716	+	0.358013i	$0.116546\pi$
$258$		0			0
$259$	8.89161	−	1.03928i	0.552498	−	0.0645777i
$260$	−3.86134	−	21.8987i	−0.239470	−	1.35810i
$261$		0			0
$262$	0.168301	−	0.954483i	0.0103977	−	0.0589682i
$263$	0.228089	−	3.91614i	0.0140646	−	0.241480i	−0.983948	−	0.178458i	$-0.942889\pi$
$263$	0.228089	−	3.91614i	0.0140646	−	0.241480i	0.998012	−	0.0630218i	$-0.0200737\pi$
$264$		0			0
$265$	−1.65748	−	3.84247i	−0.101818	−	0.236041i
$266$	0.0439895	+	0.0220924i	0.00269717	+	0.00135457i
$267$		0			0
$268$	2.24174	+	0.531302i	0.136936	+	0.0324545i
$269$	−5.54513	+	9.60445i	−0.338093	+	0.585594i	−0.984074	−	0.177760i	$-0.943115\pi$
$269$	−5.54513	+	9.60445i	−0.338093	+	0.585594i	0.645981	+	0.763353i	$0.276448\pi$
$270$		0			0
$271$	−0.397309	−	0.688159i	−0.0241348	−	0.0418027i	0.853706	−	0.520756i	$-0.174350\pi$
$271$	−0.397309	−	0.688159i	−0.0241348	−	0.0418027i	−0.877841	+	0.478953i	$0.841016\pi$
$272$	4.19128	+	13.9998i	0.254134	+	0.848865i
$273$		0			0
$274$	−0.690526	+	0.454166i	−0.0417162	+	0.0274372i
$275$	0.913725	−	1.22735i	0.0550997	−	0.0740117i
$276$		0			0
$277$	−24.3861	−	16.0390i	−1.46522	−	0.963688i	−0.996780	−	0.0801905i	$-0.974447\pi$
$277$	−24.3861	−	16.0390i	−1.46522	−	0.963688i	−0.468436	−	0.883497i	$-0.655182\pi$
$278$	5.65991	−	2.06004i	0.339459	−	0.123553i
$279$		0			0
$280$	−6.27272	−	2.28308i	−0.374867	−	0.136440i
$281$	−16.4750	−	22.1297i	−0.982814	−	1.32015i	−0.947152	−	0.320785i	$-0.896053\pi$
$281$	−16.4750	−	22.1297i	−0.982814	−	1.32015i	−0.0356623	−	0.999364i	$-0.511354\pi$
$282$		0			0
$283$	3.50574	+	3.71587i	0.208395	+	0.220886i	0.823137	−	0.567842i	$-0.192222\pi$
$283$	3.50574	+	3.71587i	0.208395	+	0.220886i	−0.614743	+	0.788728i	$0.710740\pi$
$284$	−18.5971	−	19.7118i	−1.10354	−	1.16968i
$285$		0			0
$286$	−3.19973	−	4.29798i	−0.189204	−	0.254145i
$287$	6.02327	+	2.19229i	0.355542	+	0.129407i
$288$		0			0
$289$	−1.32268	+	0.481415i	−0.0778046	+	0.0283185i
$290$	−6.00486	−	3.94946i	−0.352618	−	0.231920i
$291$		0			0
$292$	−11.0189	+	14.8009i	−0.644832	+	0.866160i
$293$	1.95792	−	1.28775i	0.114383	−	0.0752310i	−0.491028	−	0.871144i	$-0.663379\pi$
$293$	1.95792	−	1.28775i	0.114383	−	0.0752310i	0.605412	+	0.795913i	$0.293009\pi$
$294$		0			0
$295$	−4.38863	−	14.6590i	−0.255516	−	0.853482i
$296$	2.17712	+	3.77089i	0.126543	+	0.219178i
$297$		0			0
$298$	−0.650036	+	1.12590i	−0.0376556	+	0.0652214i
$299$	−22.9891	−	5.44853i	−1.32950	−	0.315096i
$300$		0			0
$301$	1.76339	+	0.885607i	0.101640	+	0.0510456i
$302$	1.24928	+	2.89615i	0.0718878	+	0.166655i
$303$		0			0
$304$	0.0120807	−	0.207417i	0.000692874	−	0.0118962i
$305$	−4.30210	+	24.3984i	−0.246337	+	1.39705i
$306$		0			0
$307$	−2.80743	−	15.9217i	−0.160228	−	0.908700i	−0.953849	−	0.300287i	$-0.902918\pi$
$307$	−2.80743	−	15.9217i	−0.160228	−	0.908700i	0.793620	−	0.608413i	$-0.208194\pi$
$308$	14.6833	−	1.71623i	0.836657	−	0.0977911i
$309$		0			0
$310$	−0.890543	+	2.97462i	−0.0505794	+	0.168947i
$311$	−20.6275	+	4.88881i	−1.16968	+	0.277219i	−0.769152	−	0.639066i	$-0.779321\pi$
$311$	−20.6275	+	4.88881i	−1.16968	+	0.277219i	−0.400527	+	0.916285i	$0.631173\pi$
$312$		0			0
$313$	−2.14335	+	4.96885i	−0.121149	+	0.280856i	−0.967989	−	0.250992i	$-0.919243\pi$
$313$	−2.14335	+	4.96885i	−0.121149	+	0.280856i	0.846840	+	0.531848i	$0.178502\pi$
$314$	2.80708	−	2.35542i	0.158413	−	0.132924i
$315$		0			0
$316$	−2.34420	−	1.96701i	−0.131871	−	0.110653i
$317$	7.79902	−	3.91682i	0.438037	−	0.219990i	−0.216093	−	0.976373i	$-0.569331\pi$
$317$	7.79902	−	3.91682i	0.438037	−	0.219990i	0.654130	+	0.756382i	$0.273035\pi$
$318$		0			0
$319$	32.4567	+	3.79364i	1.81723	+	0.212403i
$320$	0.701133	+	12.0380i	0.0391945	+	0.672944i
$321$		0			0
$322$	−2.37072	+	2.51282i	−0.132115	+	0.140034i
$323$	0.261706			0.0145617
$324$		0			0
$325$	−2.75968			−0.153080
$326$	3.07719	−	3.26163i	0.170430	−	0.180645i
$327$		0			0
$328$	0.181277	+	3.11241i	0.0100094	+	0.171854i
$329$	−11.4862	−	1.34254i	−0.633252	−	0.0740166i
$330$		0			0
$331$	−17.5604	+	8.81917i	−0.965207	+	0.484745i	−0.860329	−	0.509740i	$-0.829742\pi$
$331$	−17.5604	+	8.81917i	−0.965207	+	0.484745i	−0.104878	+	0.994485i	$0.533445\pi$
$332$	−4.80468	−	4.03161i	−0.263691	−	0.221263i
$333$		0			0
$334$	−1.62927	+	1.36712i	−0.0891495	+	0.0748053i
$335$	−1.01915	+	2.36265i	−0.0556821	+	0.129086i
$336$		0			0
$337$	−7.14751	+	1.69399i	−0.389350	+	0.0922776i	−0.420628	−	0.907233i	$-0.638190\pi$
$337$	−7.14751	+	1.69399i	−0.389350	+	0.0922776i	0.0312784	+	0.999511i	$0.490042\pi$
$338$	−1.58873	+	5.30672i	−0.0864154	+	0.288647i
$339$		0			0
$340$	−17.1695	+	2.00683i	−0.931148	+	0.108836i
$341$	−2.45148	−	13.9030i	−0.132755	−	0.752892i
$342$		0			0
$343$	3.32603	−	18.8629i	0.179589	−	1.01850i
$344$	−0.0558067	+	0.958164i	−0.00300889	+	0.0516607i
$345$		0			0
$346$	−1.85845	−	4.30836i	−0.0999107	−	0.231619i
$347$	16.2806	+	8.17644i	0.873990	+	0.438934i	0.828473	−	0.560029i	$-0.189210\pi$
$347$	16.2806	+	8.17644i	0.873990	+	0.438934i	0.0455174	+	0.998964i	$0.485506\pi$
$348$		0			0
$349$	−15.6760	−	3.71527i	−0.839116	−	0.198874i	−0.211481	−	0.977382i	$-0.567829\pi$
$349$	−15.6760	−	3.71527i	−0.839116	−	0.198874i	−0.627635	+	0.778508i	$0.715977\pi$
$350$	−0.201764	+	0.349465i	−0.0107847	+	0.0186797i
$351$		0			0
$352$	5.43923	+	9.42103i	0.289912	+	0.502142i
$353$	4.92839	+	16.4620i	0.262312	+	0.876183i	0.983107	+	0.183034i	$0.0585919\pi$
$353$	4.92839	+	16.4620i	0.262312	+	0.876183i	−0.720795	+	0.693149i	$0.756223\pi$
$354$		0			0
$355$	25.2878	−	16.6321i	1.34214	−	0.882739i
$356$	15.9321	−	21.4005i	0.844400	−	1.13423i
$357$		0			0
$358$	0.167994	+	0.110492i	0.00887878	+	0.00583967i
$359$	26.7193	−	9.72505i	1.41019	−	0.513268i	0.479007	−	0.877811i	$-0.340997\pi$
$359$	26.7193	−	9.72505i	1.41019	−	0.513268i	0.931187	+	0.364543i	$0.118775\pi$
$360$		0			0
$361$	17.8507	+	6.49711i	0.939509	+	0.341953i
$362$	−2.64379	−	3.55123i	−0.138955	−	0.186649i
$363$		0			0
$364$	−18.2970	−	19.3937i	−0.959023	−	1.01651i
$365$	−14.1426	−	14.9902i	−0.740256	−	0.784625i
$366$		0			0
$367$	6.19676	+	8.32370i	0.323468	+	0.434494i	0.933878	−	0.357593i	$-0.116402\pi$
$367$	6.19676	+	8.32370i	0.323468	+	0.434494i	−0.610409	+	0.792086i	$0.708995\pi$
$368$	13.7018	+	4.98706i	0.714258	+	0.259969i
$369$		0			0
$370$	−2.22594	+	0.810174i	−0.115721	+	0.0421190i
$371$	−4.19218	−	2.75724i	−0.217647	−	0.143149i
$372$		0			0
$373$	8.89318	−	11.9456i	0.460472	−	0.618521i	−0.509872	−	0.860250i	$-0.670307\pi$
$373$	8.89318	−	11.9456i	0.460472	−	0.618521i	0.970344	+	0.241730i	$0.0777147\pi$
$374$	−3.48017	+	2.28895i	−0.179955	+	0.118359i
$375$		0			0
$376$	−1.61321	−	5.38850i	−0.0831950	−	0.277891i
$377$	−29.4683	−	51.0405i	−1.51769	−	2.62872i
$378$		0			0
$379$	−5.81217	+	10.0670i	−0.298551	+	0.517106i	−0.975805	−	0.218644i	$-0.929837\pi$
$379$	−5.81217	+	10.0670i	−0.298551	+	0.517106i	0.677253	+	0.735750i	$0.263170\pi$
$380$	0.239142	+	0.0566776i	0.0122677	+	0.00290750i
$381$		0			0
$382$	2.40807	+	1.20938i	0.123207	+	0.0618771i
$383$	−11.2946	−	26.1838i	−0.577127	−	1.33793i	−0.917535	−	0.397654i	$-0.869824\pi$
$383$	−11.2946	−	26.1838i	−0.577127	−	1.33793i	0.340408	−	0.940278i	$-0.389435\pi$
$384$		0			0
$385$	−0.960026	+	16.4830i	−0.0489274	+	0.840052i
$386$	0.730054	−	4.14034i	0.0371588	−	0.210738i
$387$		0			0
$388$	−2.31635	−	13.1367i	−0.117595	−	0.666915i
$389$	−3.04961	+	0.356448i	−0.154621	+	0.0180726i	−0.193051	−	0.981189i	$-0.561838\pi$
$389$	−3.04961	+	0.356448i	−0.154621	+	0.0180726i	0.0384301	+	0.999261i	$0.487764\pi$
$390$		0			0
$391$	−5.26758	+	17.5949i	−0.266393	+	0.889814i
$392$	0.638468	−	0.151320i	0.0322475	−	0.00764280i
$393$		0			0
$394$	−0.948562	+	2.19901i	−0.0477879	+	0.110785i
$395$	2.61816	−	2.19690i	0.131734	−	0.110538i
$396$		0			0
$397$	−8.05095	−	6.75555i	−0.404065	−	0.339051i	0.417997	−	0.908448i	$-0.362732\pi$
$397$	−8.05095	−	6.75555i	−0.404065	−	0.339051i	−0.822063	+	0.569397i	$0.807177\pi$
$398$	−0.599207	+	0.300933i	−0.0300355	+	0.0150844i
$399$		0			0
$400$	1.69167	+	0.197728i	0.0845836	+	0.00988640i
$401$	−1.54074	−	26.4534i	−0.0769407	−	1.32102i	−0.787033	−	0.616912i	$-0.788384\pi$
$401$	−1.54074	−	26.4534i	−0.0769407	−	1.32102i	0.710092	−	0.704109i	$-0.248653\pi$
$402$		0			0
$403$	−17.4731	+	18.5204i	−0.870395	+	0.922565i
$404$	−20.6150			−1.02563
$405$		0			0
$406$	−8.61783			−0.427696
$407$	7.39081	−	7.83380i	0.366349	−	0.388307i
$408$		0			0
$409$	−1.53226	−	26.3079i	−0.0757654	−	1.30084i	−0.795228	−	0.606311i	$-0.792649\pi$
$409$	−1.53226	−	26.3079i	−0.0757654	−	1.30084i	0.719463	−	0.694531i	$-0.244388\pi$
$410$	−1.68461	−	0.196903i	−0.0831970	−	0.00972434i
$411$		0			0
$412$	21.1090	−	10.6014i	1.03997	−	0.522291i
$413$	−14.0551	−	11.7936i	−0.691605	−	0.580326i
$414$		0			0
$415$	5.36621	−	4.50278i	0.263417	−	0.221033i
$416$	7.77112	−	18.0155i	0.381011	−	0.883282i
$417$		0			0
$418$	0.0576250	−	0.0136574i	0.00281853	−	0.000668004i
$419$	−2.24612	+	7.50255i	−0.109730	+	0.366523i	−0.995162	−	0.0982448i	$-0.968677\pi$
$419$	−2.24612	+	7.50255i	−0.109730	+	0.366523i	0.885432	+	0.464768i	$0.153862\pi$
$420$		0			0
$421$	31.6365	−	3.69777i	1.54187	−	0.180218i	0.697736	−	0.716355i	$-0.254191\pi$
$421$	31.6365	−	3.69777i	1.54187	−	0.180218i	0.844131	+	0.536136i	$0.180117\pi$
$422$	0.0361680	+	0.205119i	0.00176063	+	0.00998504i
$423$		0			0
$424$	0.423796	−	2.40347i	0.0205813	−	0.116723i
$425$	−0.124740	+	2.14171i	−0.00605080	+	0.103888i
$426$		0			0
$427$	11.7660	+	27.2766i	0.569395	+	1.32001i
$428$	−8.44973	−	4.24361i	−0.408433	−	0.205123i
$429$		0			0
$430$	−0.508068	−	0.120414i	−0.0245012	−	0.00580690i
$431$	16.6567	−	28.8502i	0.802324	−	1.38967i	−0.115759	−	0.993277i	$-0.536930\pi$
$431$	16.6567	−	28.8502i	0.802324	−	1.38967i	0.918083	−	0.396389i	$-0.129737\pi$
$432$		0			0
$433$	2.75793	+	4.77688i	0.132538	+	0.229562i	0.924654	−	0.380808i	$-0.124354\pi$
$433$	2.75793	+	4.77688i	0.132538	+	0.229562i	−0.792116	+	0.610370i	$0.791021\pi$
$434$	1.06780	+	3.56670i	0.0512560	+	0.171207i
$435$		0			0
$436$	0.573261	−	0.377040i	0.0274542	−	0.0180569i
$437$	0.155932	−	0.209453i	0.00745922	−	0.0100195i
$438$		0			0
$439$	2.76551	+	1.81890i	0.131990	+	0.0868114i	0.613787	−	0.789472i	$-0.289645\pi$
$439$	2.76551	+	1.81890i	0.131990	+	0.0868114i	−0.481797	+	0.876283i	$0.660016\pi$
$440$	−7.54647	+	2.74669i	−0.359764	+	0.130943i
$441$		0			0
$442$	7.05960	+	2.56948i	0.335791	+	0.122218i
$443$	10.2627	+	13.7852i	0.487595	+	0.654954i	0.976027	−	0.217648i	$-0.0698385\pi$
$443$	10.2627	+	13.7852i	0.487595	+	0.654954i	−0.488432	+	0.872602i	$0.662431\pi$
$444$		0			0
$445$	20.4486	+	21.6742i	0.969355	+	1.02746i
$446$	−4.90125	−	5.19502i	−0.232081	−	0.245991i
$447$		0			0
$448$	8.63404	+	11.5975i	0.407920	+	0.547931i
$449$	16.5392	+	6.01977i	0.780532	+	0.284090i	0.701394	−	0.712773i	$-0.252561\pi$
$449$	16.5392	+	6.01977i	0.780532	+	0.284090i	0.0791375	+	0.996864i	$0.474783\pi$
$450$		0			0
$451$	7.24636	−	2.63746i	0.341218	−	0.124193i
$452$	−31.3279	−	20.6047i	−1.47354	−	0.969164i
$453$		0			0
$454$	−2.54043	+	3.41239i	−0.119228	+	0.160152i
$455$	24.8797	−	16.3636i	1.16638	−	0.767140i
$456$		0			0
$457$	−5.12647	−	17.1236i	−0.239806	−	0.801009i	−0.990156	−	0.139968i	$-0.955300\pi$
$457$	−5.12647	−	17.1236i	−0.239806	−	0.801009i	0.750350	−	0.661041i	$-0.229885\pi$
$458$	−0.987261	−	1.70999i	−0.0461317	−	0.0799024i
$459$		0			0
$460$	−8.62394	+	14.9371i	−0.402093	+	0.696446i
$461$	−4.89168	−	1.15935i	−0.227828	−	0.0539963i	0.115116	−	0.993352i	$-0.463276\pi$
$461$	−4.89168	−	1.15935i	−0.227828	−	0.0539963i	−0.342944	+	0.939356i	$0.611424\pi$
$462$		0			0
$463$	15.3751	+	7.72167i	0.714542	+	0.358857i	0.768642	−	0.639679i	$-0.220933\pi$
$463$	15.3751	+	7.72167i	0.714542	+	0.358857i	−0.0541001	+	0.998536i	$0.517229\pi$
$464$	14.4069	+	33.3989i	0.668823	+	1.55051i
$465$		0			0
$466$	0.228564	−	3.92429i	0.0105880	−	0.181789i
$467$	−6.50441	+	36.8883i	−0.300988	+	1.70699i	0.340824	+	0.940127i	$0.389294\pi$
$467$	−6.50441	+	36.8883i	−0.300988	+	1.70699i	−0.641812	+	0.766862i	$0.721817\pi$
$468$		0			0
$469$	0.535748	+	3.03838i	0.0247385	+	0.140299i
$470$	3.03931	−	0.355244i	0.140193	−	0.0163862i
$471$		0			0
$472$	2.55947	−	8.54921i	0.117809	−	0.393510i
$473$	2.30999	−	0.547477i	0.106213	−	0.0251730i
$474$		0			0
$475$	0.0120808	−	0.0280065i	0.000554306	−	0.00128503i
$476$	−15.8779	+	13.3232i	−0.727764	+	0.610666i
$477$		0			0
$478$	−2.38964	−	2.00515i	−0.109300	−	0.0917134i
$479$	−3.05867	+	1.53612i	−0.139754	+	0.0701872i	−0.517302	−	0.855803i	$-0.673064\pi$
$479$	−3.05867	+	1.53612i	−0.139754	+	0.0701872i	0.377548	+	0.925990i	$0.376767\pi$
$480$		0			0
$481$	−19.2931	−	2.25504i	−0.879689	−	0.102821i
$482$	0.319834	+	5.49133i	0.0145680	+	0.250123i
$483$		0			0
$484$	−2.13255	+	2.26037i	−0.0969341	+	0.102744i
$485$	14.8983			0.676498
$486$		0			0
$487$	−5.43342			−0.246212			−0.123106	−	0.992394i	$-0.539285\pi$
$487$	−5.43342			−0.246212			−0.123106	+	0.992394i	$0.539285\pi$
$488$	−9.91535	+	10.5097i	−0.448847	+	0.475750i
$489$		0			0
$490$	0.0207554	+	0.356357i	0.000937634	+	0.0160986i
$491$	−3.94699	−	0.461337i	−0.178125	−	0.0208199i	0.0265626	−	0.999647i	$-0.491544\pi$
$491$	−3.94699	−	0.461337i	−0.178125	−	0.0208199i	−0.204688	+	0.978827i	$0.565618\pi$
$492$		0			0
$493$	−40.9431	+	20.5624i	−1.84398	+	0.926084i
$494$	−0.0818212	−	0.0686561i	−0.00368131	−	0.00308898i
$495$		0			0
$496$	12.0379	−	10.1010i	0.540516	−	0.453547i
$497$	14.3744	−	33.3236i	0.644779	−	1.49477i
$498$		0			0
$499$	−20.8781	+	4.94820i	−0.934632	+	0.221512i	−0.669595	−	0.742727i	$-0.733532\pi$
$499$	−20.8781	+	4.94820i	−0.934632	+	0.221512i	−0.265037	+	0.964238i	$0.585384\pi$
$500$	−6.35559	+	21.2292i	−0.284231	+	0.949397i
$501$		0			0
$502$	7.88862	−	0.922048i	0.352086	−	0.0411530i
$503$	4.28340	+	24.2924i	0.190987	+	1.08314i	0.918018	+	0.396538i	$0.129789\pi$
$503$	4.28340	+	24.2924i	0.190987	+	1.08314i	−0.727031	+	0.686605i	$0.759100\pi$
$504$		0			0
$505$	3.99812	−	22.6745i	0.177914	−	1.00900i
$506$	−0.241659	+	4.14912i	−0.0107430	+	0.184451i
$507$		0			0
$508$	10.8522	+	25.1581i	0.481487	+	1.11621i
$509$	−6.56544	−	3.29729i	−0.291008	−	0.146150i	0.297306	−	0.954782i	$-0.403912\pi$
$509$	−6.56544	−	3.29729i	−0.291008	−	0.146150i	−0.588314	+	0.808633i	$0.700208\pi$
$510$		0			0
$511$	−24.0447	−	5.69869i	−1.06367	−	0.252095i
$512$	−10.2684	+	17.7854i	−0.453804	+	0.786011i
$513$		0			0
$514$	−0.382388	−	0.662316i	−0.0168664	−	0.0292135i
$515$	7.56652	+	25.2739i	0.333421	+	1.11370i
$516$		0			0
$517$	−11.6238	+	7.64511i	−0.511215	+	0.336232i
$518$	−1.69610	+	2.27826i	−0.0745224	+	0.100101i
$519$		0			0
$520$	12.1013	+	7.95914i	0.530676	+	0.349031i
$521$	−25.5909	+	9.31432i	−1.12116	+	0.408068i	−0.835074	−	0.550137i	$-0.814575\pi$
$521$	−25.5909	+	9.31432i	−1.12116	+	0.408068i	−0.286082	+	0.958205i	$0.592353\pi$
$522$		0			0
$523$	−14.3006	−	5.20499i	−0.625321	−	0.227598i	0.00987267	−	0.999951i	$-0.496857\pi$
$523$	−14.3006	−	5.20499i	−0.625321	−	0.227598i	−0.635193	+	0.772353i	$0.719080\pi$
$524$	−3.46476	−	4.65399i	−0.151359	−	0.203310i
$525$		0			0
$526$	0.854094	+	0.905286i	0.0372403	+	0.0394724i
$527$	13.5833	+	14.3975i	0.591699	+	0.627165i
$528$		0			0
$529$	−2.79137	−	3.74946i	−0.121364	−	0.163020i
$530$	1.24763	+	0.454101i	0.0541936	+	0.0197249i
$531$		0			0
$532$	0.276913	−	0.100788i	0.0120057	−	0.00436972i
$533$	−11.6200	−	7.64262i	−0.503320	−	0.331039i
$534$		0			0
$535$	6.30632	−	8.47086i	0.272646	−	0.366227i
$536$	−1.25377	+	0.824615i	−0.0541544	+	0.0356179i
$537$		0			0
$538$	−1.00916	−	3.37084i	−0.0435081	−	0.145327i
$539$	−0.811481	−	1.40553i	−0.0349530	−	0.0605403i
$540$		0			0
$541$	−8.31159	+	14.3961i	−0.357343	+	0.618937i	−0.987516	−	0.157518i	$-0.949651\pi$
$541$	−8.31159	+	14.3961i	−0.357343	+	0.618937i	0.630173	+	0.776455i	$0.282984\pi$
$542$	0.245316	+	0.0581409i	0.0105372	+	0.00249737i
$543$		0			0
$544$	−13.6300	−	6.84527i	−0.584383	−	0.293488i
$545$	0.303527	+	0.703655i	0.0130017	+	0.0301413i
$546$		0			0
$547$	−0.656042	+	11.2638i	−0.0280503	+	0.481605i	0.954806	+	0.297231i	$0.0960630\pi$
$547$	−0.656042	+	11.2638i	−0.0280503	+	0.481605i	−0.982856	+	0.184375i	$0.940974\pi$
$548$	−0.859166	+	4.87257i	−0.0367018	+	0.208146i
$549$		0			0
$550$	0.0843006	+	0.478093i	0.00359459	+	0.0203859i
$551$	0.646983	−	0.0756214i	0.0275624	−	0.00322158i
$552$		0			0
$553$	1.17533	−	3.92589i	0.0499803	−	0.166946i
$554$	9.01092	−	2.13563i	0.382837	−	0.0907341i
$555$		0			0
$556$	14.2815	−	33.1082i	0.605671	−	1.40410i
$557$	22.3339	−	18.7404i	0.946318	−	0.794055i	−0.0323557	−	0.999476i	$-0.510301\pi$
$557$	22.3339	−	18.7404i	0.946318	−	0.794055i	0.978674	+	0.205421i	$0.0658565\pi$
$558$		0			0
$559$	−3.27993	−	2.75219i	−0.138726	−	0.116405i
$560$	−16.4236	+	8.24823i	−0.694023	+	0.348551i
$561$		0			0
$562$	8.69407	+	1.01619i	0.366737	+	0.0428655i
$563$	1.24814	+	21.4297i	0.0526028	+	0.903154i	0.916637	+	0.399721i	$0.130893\pi$
$563$	1.24814	+	21.4297i	0.0526028	+	0.903154i	−0.864034	+	0.503433i	$0.832070\pi$
$564$		0			0
$565$	28.7390	−	30.4615i	1.20906	−	1.28153i
$566$	−1.62083			−0.0681286
$567$		0			0
$568$	17.6519			0.740659
$569$	1.83992	−	1.95021i	0.0771336	−	0.0817569i	−0.687657	−	0.726035i	$-0.741361\pi$
$569$	1.83992	−	1.95021i	0.0771336	−	0.0817569i	0.764791	+	0.644279i	$0.222842\pi$
$570$		0			0
$571$	0.165178	+	2.83600i	0.00691248	+	0.118683i	0.999999	+	0.00129937i	$0.000413604\pi$
$571$	0.165178	+	2.83600i	0.00691248	+	0.118683i	−0.993087	+	0.117383i	$0.962549\pi$
$572$	−31.8599	−	3.72388i	−1.33213	−	0.155703i
$573$		0			0
$574$	−1.81736	+	0.912711i	−0.0758550	+	0.0380958i
$575$	1.63976	+	1.37592i	0.0683828	+	0.0573800i
$576$		0			0
$577$	4.53692	−	3.80692i	0.188874	−	0.158484i	−0.543447	−	0.839443i	$-0.682881\pi$
$577$	4.53692	−	3.80692i	0.188874	−	0.158484i	0.732322	+	0.680959i	$0.238437\pi$
$578$	0.176883	−	0.410061i	0.00735736	−	0.0170563i
$579$		0			0
$580$	−41.8662	+	9.92246i	−1.73840	+	0.412008i
$581$	2.40898	−	8.04654i	0.0999412	−	0.333827i
$582$		0			0
$583$	−5.99572	+	0.700800i	−0.248318	+	0.0290242i
$584$	−2.08710	−	11.8365i	−0.0863646	−	0.489798i
$585$		0			0
$586$	−0.129110	+	0.732221i	−0.00533350	+	0.0302478i
$587$	0.655164	−	11.2487i	0.0270415	−	0.464285i	−0.957422	−	0.288694i	$-0.906779\pi$
$587$	0.655164	−	11.2487i	0.0270415	−	0.464285i	0.984463	−	0.175592i	$-0.0561838\pi$
$588$		0			0
$589$	−0.111463	−	0.258400i	−0.00459274	−	0.0106472i
$590$	4.33849	+	2.17887i	0.178613	+	0.0897027i
$591$		0			0
$592$	11.6650	+	2.76465i	0.479428	+	0.113627i
$593$	4.74627	−	8.22078i	0.194906	−	0.337587i	−0.751964	−	0.659205i	$-0.770893\pi$
$593$	4.74627	−	8.22078i	0.194906	−	0.337587i	0.946870	+	0.321617i	$0.104226\pi$
$594$		0			0
$595$	−11.5748	−	20.0481i	−0.474519	−	0.821892i
$596$	2.23212	+	7.45582i	0.0914314	+	0.305402i
$597$		0			0
$598$	6.26275	−	4.11907i	0.256103	−	0.168441i
$599$	14.8996	−	20.0136i	0.608780	−	0.817733i	−0.385704	−	0.922623i	$-0.626041\pi$
$599$	14.8996	−	20.0136i	0.608780	−	0.817733i	0.994484	+	0.104889i	$0.0334488\pi$
$600$		0			0
$601$	9.59732	+	6.31226i	0.391483	+	0.257482i	0.729957	−	0.683494i	$-0.239540\pi$
$601$	9.59732	+	6.31226i	0.391483	+	0.257482i	−0.338474	+	0.940976i	$0.609911\pi$
$602$	−0.588315	+	0.214129i	−0.0239779	+	0.00872725i
$603$		0			0
$604$	17.7431	+	6.45795i	0.721955	+	0.262770i
$605$	−2.07260	−	2.78398i	−0.0842630	−	0.113185i
$606$		0			0
$607$	−27.3496	−	28.9889i	−1.11009	−	1.17662i	−0.982784	−	0.184759i	$-0.940849\pi$
$607$	−27.3496	−	28.9889i	−1.11009	−	1.17662i	−0.127303	−	0.991864i	$-0.540632\pi$
$608$	0.148810	+	0.157730i	0.00603505	+	0.00639678i
$609$		0			0
$610$	−4.69391	−	6.30501i	−0.190051	−	0.255283i
$611$	23.5792	+	8.58211i	0.953911	+	0.347195i
$612$		0			0
$613$	−16.9065	+	6.15347i	−0.682848	+	0.248536i	−0.660070	−	0.751204i	$-0.729473\pi$
$613$	−16.9065	+	6.15347i	−0.682848	+	0.248536i	−0.0227782	+	0.999741i	$0.507251\pi$
$614$	4.28562	+	2.81869i	0.172953	+	0.113753i
$615$		0			0
$616$	−5.75019	+	7.72385i	−0.231682	+	0.311203i
$617$	−15.3291	+	10.0821i	−0.617124	+	0.405889i	−0.819222	−	0.573476i	$-0.805594\pi$
$617$	−15.3291	+	10.0821i	−0.617124	+	0.405889i	0.202098	+	0.979365i	$0.435224\pi$
$618$		0			0
$619$	12.8881	+	43.0492i	0.518016	+	1.73029i	0.670425	+	0.741977i	$0.266112\pi$
$619$	12.8881	+	43.0492i	0.518016	+	1.73029i	−0.152409	+	0.988317i	$0.548703\pi$
$620$	9.29411	+	16.0979i	0.373260	+	0.646506i
$621$		0			0
$622$	3.36294	−	5.82478i	0.134842	−	0.233553i
$623$	34.7659	+	8.23968i	1.39287	+	0.330116i
$624$		0			0
$625$	−19.8832	−	9.98569i	−0.795326	−	0.399428i
$626$	−0.680030	−	1.57649i	−0.0271795	−	0.0630091i
$627$		0			0
$628$	1.27549	−	21.8994i	0.0508978	−	0.873881i
$629$	−2.62214	+	14.8709i	−0.104552	+	0.592941i
$630$		0			0
$631$	5.90645	+	33.4972i	0.235132	+	1.33350i	0.842335	+	0.538954i	$0.181180\pi$
$631$	5.90645	+	33.4972i	0.235132	+	1.33350i	−0.607203	+	0.794547i	$0.707708\pi$
$632$	1.97978	−	0.231403i	0.0787515	−	0.00920473i
$633$		0			0
$634$	−0.794146	+	2.65263i	−0.0315396	+	0.105349i
$635$	−29.7762	+	7.05709i	−1.18163	+	0.280052i
$636$		0			0
$637$	−1.15938	+	2.68774i	−0.0459362	+	0.106492i
$638$	−7.94218	+	6.66428i	−0.314434	+	0.263841i
$639$		0			0
$640$	−14.4847	−	12.1541i	−0.572556	−	0.480432i
$641$	−0.281153	+	0.141200i	−0.0111049	+	0.00557707i	−0.454343	−	0.890827i	$-0.650126\pi$
$641$	−0.281153	+	0.141200i	−0.0111049	+	0.00557707i	0.443238	+	0.896404i	$0.353830\pi$
$642$		0			0
$643$	32.9098	+	3.84660i	1.29783	+	0.151695i	0.736808	−	0.676102i	$-0.236332\pi$
$643$	32.9098	+	3.84660i	1.29783	+	0.151695i	0.561027	+	0.827797i	$0.310406\pi$
$644$	1.20249	+	20.6460i	0.0473848	+	0.813565i
$645$		0			0
$646$	−0.0569804	+	0.0603957i	−0.00224187	+	0.00237624i
$647$	14.0510			0.552403			0.276201	−	0.961100i	$-0.410924\pi$
$647$	14.0510			0.552403			0.276201	+	0.961100i	$0.410924\pi$
$648$		0			0
$649$	−22.0733			−0.866453
$650$	0.600857	−	0.636871i	0.0235675	−	0.0249801i
$651$		0			0
$652$	−1.56083	−	26.7984i	−0.0611268	−	1.04951i
$653$	44.6094	+	5.21409i	1.74570	+	0.204043i	0.928251	−	0.371955i	$-0.121313\pi$
$653$	44.6094	+	5.21409i	1.74570	+	0.204043i	0.817451	+	0.575999i	$0.195387\pi$
$654$		0			0
$655$	5.79089	−	2.90830i	0.226269	−	0.113637i
$656$	6.57544	+	5.51745i	0.256728	+	0.215420i
$657$		0			0
$658$	2.81067	−	2.35843i	0.109571	−	0.0919413i
$659$	−13.2766	+	30.7786i	−0.517182	+	1.19896i	0.436925	+	0.899498i	$0.356067\pi$
$659$	−13.2766	+	30.7786i	−0.517182	+	1.19896i	−0.954107	+	0.299465i	$0.903192\pi$
$660$		0			0
$661$	15.7899	−	3.74227i	0.614156	−	0.145558i	0.0882470	−	0.996099i	$-0.471874\pi$
$661$	15.7899	−	3.74227i	0.614156	−	0.145558i	0.525909	+	0.850541i	$0.323725\pi$
$662$	1.78811	−	5.97271i	0.0694969	−	0.232136i
$663$		0			0
$664$	4.05778	−	0.474286i	0.157472	−	0.0184059i
$665$	0.0571518	+	0.324124i	0.00221625	+	0.0125690i
$666$		0			0
$667$	−7.93821	+	45.0198i	−0.307369	+	1.74317i
$668$	−0.740315	+	12.7107i	−0.0286436	+	0.491792i
$669$		0			0
$670$	−0.323350	−	0.749610i	−0.0124921	−	0.0289599i
$671$	31.9368	+	16.0393i	1.23291	+	0.619190i
$672$		0			0
$673$	1.91409	+	0.453649i	0.0737829	+	0.0174869i	0.267342	−	0.963602i	$-0.413855\pi$
$673$	1.91409	+	0.453649i	0.0737829	+	0.0174869i	−0.193559	+	0.981089i	$0.562003\pi$
$674$	1.16527	−	2.01831i	0.0448846	−	0.0777424i
$675$		0			0
$676$	16.5807	+	28.7186i	0.637719	+	1.10456i
$677$	−5.88502	−	19.6573i	−0.226180	−	0.755493i	−0.993460	−	0.114181i	$-0.963576\pi$
$677$	−5.88502	−	19.6573i	−0.226180	−	0.755493i	0.767280	−	0.641312i	$-0.221609\pi$
$678$		0			0
$679$	14.9249	−	9.81628i	0.572766	−	0.376714i
$680$	6.72385	−	9.03170i	0.257848	−	0.346350i
$681$		0			0
$682$	3.74226	+	2.46132i	0.143298	+	0.0942489i
$683$	20.1405	−	7.33055i	0.770656	−	0.280496i	0.0733852	−	0.997304i	$-0.476620\pi$
$683$	20.1405	−	7.33055i	0.770656	−	0.280496i	0.697271	+	0.716808i	$0.254398\pi$
$684$		0			0
$685$	−5.19273	−	1.89000i	−0.198404	−	0.0722131i
$686$	3.62895	+	4.87452i	0.138554	+	0.186110i
$687$		0			0
$688$	1.81339	+	1.92208i	0.0691348	+	0.0732786i
$689$	7.47134	+	7.91916i	0.284636	+	0.301696i
$690$		0			0
$691$	16.5776	+	22.2675i	0.630640	+	0.847096i	0.996502	−	0.0835728i	$-0.0266331\pi$
$691$	16.5776	+	22.2675i	0.630640	+	0.847096i	−0.365862	+	0.930669i	$0.619226\pi$
$692$	−26.3949	−	9.60696i	−1.00338	−	0.365202i
$693$		0			0
$694$	−5.43167	+	1.97696i	−0.206183	+	0.0750446i
$695$	33.6460	+	22.1293i	1.27627	+	0.839414i
$696$		0			0
$697$	−6.45646	+	8.67253i	−0.244556	+	0.328495i
$698$	4.27048	−	2.80874i	0.161640	−	0.106312i
$699$		0			0
$700$	0.692825	+	2.31420i	0.0261863	+	0.0874685i
$701$	−0.354873	−	0.614659i	−0.0134034	−	0.0232153i	0.859246	−	0.511563i	$-0.170933\pi$
$701$	−0.354873	−	0.614659i	−0.0134034	−	0.0232153i	−0.872649	+	0.488347i	$0.837600\pi$
$702$		0			0
$703$	0.107343	−	0.185923i	0.00404851	−	0.00701223i
$704$	16.9256	+	4.01145i	0.637909	+	0.151187i
$705$		0			0
$706$	−4.87209	−	2.44686i	−0.183364	−	0.0920886i
$707$	−10.9346	−	25.3493i	−0.411238	−	0.953357i
$708$		0			0
$709$	1.17399	−	20.1566i	0.0440900	−	0.756996i	−0.901729	−	0.432302i	$-0.857702\pi$
$709$	1.17399	−	20.1566i	0.0440900	−	0.756996i	0.945819	−	0.324694i	$-0.105261\pi$
$710$	−1.66754	+	9.45710i	−0.0625817	+	0.354919i
$711$		0			0
$712$	3.01771	+	17.1143i	0.113093	+	0.641385i
$713$	19.6161	−	2.29280i	0.734630	−	0.0858659i
$714$		0			0
$715$	10.2749	−	34.3205i	0.384259	−	1.28351i
$716$	1.17126	−	0.277595i	0.0437722	−	0.0103742i
$717$		0			0
$718$	−3.57320	+	8.28361i	−0.133351	+	0.309142i
$719$	12.8502	−	10.7826i	0.479231	−	0.402123i	−0.370917	−	0.928666i	$-0.620957\pi$
$719$	12.8502	−	10.7826i	0.479231	−	0.402123i	0.850148	+	0.526543i	$0.176512\pi$
$720$		0			0
$721$	24.2326	+	20.3336i	0.902471	+	0.757263i
$722$	−5.38595	+	2.70493i	−0.200444	+	0.100667i
$723$		0			0
$724$	−26.3244	−	3.07688i	−0.978339	−	0.114351i
$725$	0.310479	+	5.33072i	0.0115309	+	0.197978i
$726$		0			0
$727$	15.2361	−	16.1493i	0.565075	−	0.598945i	−0.380327	−	0.924852i	$-0.624188\pi$
$727$	15.2361	−	16.1493i	0.565075	−	0.598945i	0.945402	+	0.325908i	$0.105670\pi$
$728$	17.3671			0.643666
$729$		0			0
$730$	6.53862			0.242005
$731$	−2.28415	+	2.42106i	−0.0844823	+	0.0895461i
$732$		0			0
$733$	−0.226456	−	3.88810i	−0.00836434	−	0.143610i	−0.999905	−	0.0138108i	$-0.995604\pi$
$733$	−0.226456	−	3.88810i	−0.00836434	−	0.143610i	0.991540	−	0.129799i	$-0.0414333\pi$
$734$	−3.27012	−	0.382222i	−0.120702	−	0.0141081i
$735$		0			0
$736$	−13.5997	+	6.83001i	−0.501290	+	0.251757i
$737$	2.84336	+	2.38586i	0.104737	+	0.0878844i
$738$		0			0
$739$	−15.2233	+	12.7738i	−0.559997	+	0.469894i	−0.878310	−	0.478092i	$-0.841328\pi$
$739$	−15.2233	+	12.7738i	−0.559997	+	0.469894i	0.318312	+	0.947986i	$0.396884\pi$
$740$	−5.61664	+	13.0208i	−0.206472	+	0.478655i
$741$		0			0
$742$	1.54906	−	0.367134i	0.0568678	−	0.0134779i
$743$	−1.78348	+	5.95723i	−0.0654294	+	0.218549i	−0.984452	−	0.175657i	$-0.943795\pi$
$743$	−1.78348	+	5.95723i	−0.0654294	+	0.218549i	0.919022	+	0.394206i	$0.128980\pi$
$744$		0			0
$745$	−8.63357	+	1.00912i	−0.316310	+	0.0369713i
$746$	0.820489	+	4.65322i	0.0300402	+	0.170367i
$747$		0			0
$748$	−4.33010	+	24.5572i	−0.158324	+	0.897901i
$749$	0.736262	−	12.6411i	0.0269024	−	0.461897i
$750$		0			0
$751$	−6.38259	−	14.7965i	−0.232904	−	0.539933i	0.761181	−	0.648540i	$-0.224620\pi$
$751$	−6.38259	−	14.7965i	−0.232904	−	0.539933i	−0.994085	+	0.108608i	$0.965361\pi$
$752$	−13.8390	−	6.95021i	−0.504657	−	0.253448i
$753$		0			0
$754$	18.1950	+	4.31230i	0.662623	+	0.157045i
$755$	−10.5442	+	18.2632i	−0.383744	+	0.664665i
$756$		0			0
$757$	17.7618	+	30.7643i	0.645563	+	1.11815i	0.984171	+	0.177221i	$0.0567106\pi$
$757$	17.7618	+	30.7643i	0.645563	+	1.11815i	−0.338608	+	0.940928i	$0.609956\pi$
$758$	−1.05776	−	3.53317i	−0.0384196	−	0.128330i
$759$		0			0
$760$	−0.133748	+	0.0879672i	−0.00485154	+	0.00319091i
$761$	−12.1544	+	16.3261i	−0.440595	+	0.591822i	−0.965843	−	0.259127i	$-0.916565\pi$
$761$	−12.1544	+	16.3261i	−0.440595	+	0.591822i	0.525248	+	0.850949i	$0.323973\pi$
$762$		0			0
$763$	0.767697	+	0.504922i	0.0277925	+	0.0182794i
$764$	15.1587	−	5.51732i	0.548423	−	0.199610i
$765$		0			0
$766$	8.50177	+	3.09439i	0.307181	+	0.111805i
$767$	23.7734	+	31.9332i	0.858406	+	1.15304i
$768$		0			0
$769$	12.7783	+	13.5442i	0.460797	+	0.488416i	0.915552	−	0.402201i	$-0.131755\pi$
$769$	12.7783	+	13.5442i	0.460797	+	0.488416i	−0.454755	+	0.890617i	$0.650273\pi$
$770$	−3.59488	−	3.81035i	−0.129550	−	0.137315i
$771$		0			0
$772$	−15.0294	−	20.1880i	−0.540920	−	0.726582i
$773$	3.69733	+	1.34572i	0.132984	+	0.0484021i	0.407655	−	0.913136i	$-0.366347\pi$
$773$	3.69733	+	1.34572i	0.132984	+	0.0484021i	−0.274671	+	0.961538i	$0.588569\pi$
$774$		0			0
$775$	2.16778	−	0.789007i	0.0778689	−	0.0283420i
$776$	7.25936	+	4.77456i	0.260596	+	0.171397i
$777$		0			0
$778$	0.581721	−	0.781387i	0.0208557	−	0.0280141i
$779$	0.128429	−	0.0844689i	0.00460144	−	0.00302641i
$780$		0			0
$781$	−12.5221	−	41.8268i	−0.448077	−	1.49668i
$782$	−2.91361	−	5.04653i	−0.104191	−	0.180463i
$783$		0			0
$784$	0.903265	−	1.56450i	0.0322595	−	0.0558750i
$785$	23.8398	+	5.65014i	0.850880	+	0.201662i
$786$		0			0
$787$	6.59214	+	3.31070i	0.234984	+	0.118014i	0.562395	−	0.826868i	$-0.309880\pi$
$787$	6.59214	+	3.31070i	0.234984	+	0.118014i	−0.327411	+	0.944882i	$0.606176\pi$
$788$	5.67849	+	13.1642i	0.202288	+	0.468956i
$789$		0			0
$790$	−0.0630505	+	1.08254i	−0.00224324	+	0.0385149i
$791$	8.71966	−	49.4517i	0.310035	−	1.75830i
$792$		0			0
$793$	−11.1927	−	63.4772i	−0.397466	−	2.25414i
$794$	3.31193	−	0.387109i	0.117536	−	0.0137380i
$795$		0			0
$796$	−1.15125	+	3.84544i	−0.0408049	+	0.136298i
$797$	14.5445	−	3.44711i	0.515192	−	0.122103i	0.0352081	−	0.999380i	$-0.488791\pi$
$797$	14.5445	−	3.44711i	0.515192	−	0.122103i	0.479984	+	0.877277i	$0.340642\pi$
$798$		0			0
$799$	7.72613	−	17.9112i	0.273331	−	0.633652i
$800$	−1.36173	+	1.14263i	−0.0481446	+	0.0403981i
$801$		0			0
$802$	6.44030	+	5.40405i	0.227415	+	0.190824i
$803$	−26.5664	+	13.3422i	−0.937508	+	0.470834i
$804$		0			0
$805$	−22.9418	−	2.68151i	−0.808591	−	0.0945107i
$806$	−0.469719	−	8.06476i	−0.0165451	−	0.284069i
$807$		0			0
$808$	9.21475	−	9.76707i	0.324174	−	0.343604i
$809$	−28.6228			−1.00633			−0.503163	−	0.864192i	$-0.667830\pi$
$809$	−28.6228			−1.00633			−0.503163	+	0.864192i	$0.667830\pi$
$810$		0			0
$811$	15.2720			0.536273			0.268136	−	0.963381i	$-0.413592\pi$
$811$	15.2720			0.536273			0.268136	+	0.963381i	$0.413592\pi$
$812$	−35.4032	+	37.5252i	−1.24241	+	1.31688i
$813$		0			0
$814$	0.198683	+	3.41126i	0.00696384	+	0.119564i
$815$	29.7784	+	3.48059i	1.04309	+	0.121920i
$816$		0			0
$817$	0.0422887	−	0.0212382i	0.00147949	−	0.000743030i
$818$	6.40487	+	5.37433i	0.223941	+	0.187909i
$819$		0			0
$820$	−7.77799	+	6.52651i	−0.271619	+	0.227915i
$821$	−1.23281	+	2.85798i	−0.0430254	+	0.0997441i	−0.938373	−	0.345623i	$-0.887668\pi$
$821$	−1.23281	+	2.85798i	−0.0430254	+	0.0997441i	0.895348	+	0.445367i	$0.146927\pi$
$822$		0			0
$823$	37.4863	−	8.88442i	1.30669	−	0.309691i	0.482446	−	0.875926i	$-0.339748\pi$
$823$	37.4863	−	8.88442i	1.30669	−	0.309691i	0.824244	+	0.566234i	$0.191600\pi$
$824$	−4.41283	+	14.7399i	−0.153728	+	0.513488i
$825$		0			0
$826$	5.78186	−	0.675803i	0.201177	−	0.0235142i
$827$	−1.37656	−	7.80687i	−0.0478677	−	0.271471i	0.951475	−	0.307727i	$-0.0995682\pi$
$827$	−1.37656	−	7.80687i	−0.0478677	−	0.271471i	−0.999343	+	0.0362552i	$0.988457\pi$
$828$		0			0
$829$	5.51283	−	31.2648i	0.191469	−	1.08587i	−0.725890	−	0.687811i	$-0.758572\pi$
$829$	5.51283	−	31.2648i	0.191469	−	1.08587i	0.917359	−	0.398061i	$-0.130317\pi$
$830$	−0.129229	+	2.21877i	−0.00448560	+	0.0770148i
$831$		0			0
$832$	−12.4259	−	28.8065i	−0.430791	−	0.998686i
$833$	2.03347	+	1.02125i	0.0704556	+	0.0353841i
$834$		0			0
$835$	−13.8370	−	3.27942i	−0.478848	−	0.113489i
$836$	0.177262	−	0.307026i	0.00613073	−	0.0106187i
$837$		0			0
$838$	−1.24238	−	2.15186i	−0.0429172	−	0.0743347i
$839$	−12.9827	−	43.3653i	−0.448214	−	1.49714i	−0.821927	−	0.569593i	$-0.807101\pi$
$839$	−12.9827	−	43.3653i	−0.448214	−	1.49714i	0.373713	−	0.927544i	$-0.378084\pi$
$840$		0			0
$841$	−71.0476	+	46.7288i	−2.44992	+	1.61134i
$842$	−6.03475	+	8.10608i	−0.207971	+	0.279354i
$843$		0			0
$844$	1.04175	+	0.685167i	0.0358584	+	0.0235844i
$845$	−34.8033	+	12.6674i	−1.19727	+	0.435771i
$846$		0			0
$847$	−3.91062	−	1.42335i	−0.134370	−	0.0489069i
$848$	−4.01250	−	5.38972i	−0.137790	−	0.185084i
$849$		0			0
$850$	−0.467098	−	0.495095i	−0.0160213	−	0.0169816i
$851$	10.3393	+	10.9591i	0.354428	+	0.375672i
$852$		0			0
$853$	27.8462	+	37.4040i	0.953437	+	1.28069i	0.959793	+	0.280709i	$0.0905695\pi$
$853$	27.8462	+	37.4040i	0.953437	+	1.28069i	−0.00635570	+	0.999980i	$0.502023\pi$
$854$	−8.85657	−	3.22353i	−0.303066	−	0.110307i
$855$		0			0
$856$	5.78753	−	2.10649i	0.197814	−	0.0719983i
$857$	5.70365	+	3.75135i	0.194833	+	0.128144i	0.643177	−	0.765717i	$-0.277616\pi$
$857$	5.70365	+	3.75135i	0.194833	+	0.128144i	−0.448344	+	0.893861i	$0.647986\pi$
$858$		0			0
$859$	6.56110	−	8.81309i	0.223862	−	0.300699i	−0.675976	−	0.736924i	$-0.736278\pi$
$859$	6.56110	−	8.81309i	0.223862	−	0.300699i	0.899837	+	0.436225i	$0.143685\pi$
$860$	−2.61154	+	1.71764i	−0.0890527	+	0.0585709i
$861$		0			0
$862$	3.03136	+	10.1254i	0.103249	+	0.344874i
$863$	27.8142	+	48.1756i	0.946807	+	1.63992i	0.752092	+	0.659058i	$0.229045\pi$
$863$	27.8142	+	48.1756i	0.946807	+	1.63992i	0.194715	+	0.980860i	$0.437622\pi$
$864$		0			0
$865$	15.6858	−	27.1686i	0.533334	−	0.923761i
$866$	−1.70287	−	0.403587i	−0.0578659	−	0.0137145i
$867$		0			0
$868$	19.9174	+	10.0029i	0.676039	+	0.339520i
$869$	−1.95276	−	4.52700i	−0.0662427	−	0.153568i
$870$		0			0
$871$	0.389245	−	6.68307i	0.0131891	−	0.226447i
$872$	−0.0776079	+	0.440136i	−0.00262814	+	0.0149049i
$873$		0			0
$874$	0.0143863	+	0.0815889i	0.000486625	+	0.00275979i
$875$	−29.4756	+	3.44521i	−0.996458	+	0.116469i
$876$		0			0
$877$	−7.07646	+	23.6370i	−0.238955	+	0.798166i	0.751428	+	0.659815i	$0.229365\pi$
$877$	−7.07646	+	23.6370i	−0.238955	+	0.798166i	−0.990383	+	0.138351i	$0.955820\pi$
$878$	−1.02189	+	0.242191i	−0.0344870	+	0.00817356i
$879$		0			0
$880$	−8.75748	+	20.3021i	−0.295215	+	0.684384i
$881$	−13.2241	+	11.0964i	−0.445532	+	0.373846i	−0.837775	−	0.546016i	$-0.816144\pi$
$881$	−13.2241	+	11.0964i	−0.445532	+	0.373846i	0.392243	+	0.919862i	$0.371699\pi$
$882$		0			0
$883$	−24.0818	−	20.2071i	−0.810419	−	0.680022i	0.140289	−	0.990111i	$-0.455197\pi$
$883$	−24.0818	−	20.2071i	−0.810419	−	0.680022i	−0.950708	+	0.310089i	$0.899641\pi$
$884$	40.1902	−	20.1843i	1.35174	−	0.678871i
$885$		0			0
$886$	−5.41577	−	0.633012i	−0.181946	−	0.0212665i
$887$	−2.57144	−	44.1499i	−0.0863405	−	1.48241i	−0.711927	−	0.702254i	$-0.752177\pi$
$887$	−2.57144	−	44.1499i	−0.0863405	−	1.48241i	0.625586	−	0.780155i	$-0.284860\pi$
$888$		0			0
$889$	−25.1796	+	26.6888i	−0.844495	+	0.895113i
$890$	−9.45412			−0.316903
$891$		0			0
$892$	−42.7560			−1.43158
$893$	−0.190316	+	0.201723i	−0.00636867	+	0.00675039i
$894$		0			0
$895$	0.0781692	+	1.34211i	0.00261291	+	0.0448619i
$896$	−22.5187	−	2.63205i	−0.752296	−	0.0879307i
$897$		0			0
$898$	−4.99025	+	2.50620i	−0.166527	+	0.0836328i
$899$	37.7406	+	31.6681i	1.25872	+	1.05619i
$900$		0			0
$901$	6.48355	−	5.44034i	0.215998	−	0.181244i
$902$	−0.969062	+	2.24654i	−0.0322662	+	0.0748016i
$903$		0			0
$904$	23.7656	−	5.63254i	0.790431	−	0.187336i
$905$	8.48969	−	28.3575i	0.282207	−	0.942636i
$906$		0			0
$907$	−14.6813	+	1.71600i	−0.487486	+	0.0569790i	−0.356286	−	0.934377i	$-0.615957\pi$
$907$	−14.6813	+	1.71600i	−0.487486	+	0.0569790i	−0.131200	+	0.991356i	$0.541883\pi$
$908$	4.42237	+	25.0805i	0.146762	+	0.832327i
$909$		0			0
$910$	−1.64063	+	9.30447i	−0.0543863	+	0.308440i
$911$	2.25338	−	38.6890i	0.0746577	−	1.28182i	−0.728081	−	0.685492i	$-0.759587\pi$
$911$	2.25338	−	38.6890i	0.0746577	−	1.28182i	0.802738	−	0.596332i	$-0.203376\pi$
$912$		0			0
$913$	−4.00239	−	9.27857i	−0.132460	−	0.307076i
$914$	5.06791	+	2.54520i	0.167631	+	0.0841877i
$915$		0			0
$916$	−11.5017	−	2.72595i	−0.380027	−	0.0900680i
$917$	3.88500	−	6.72903i	0.128294	−	0.222212i
$918$		0			0
$919$	−20.8939	−	36.1894i	−0.689228	−	1.19378i	−0.972088	−	0.234616i	$-0.924617\pi$
$919$	−20.8939	−	36.1894i	−0.689228	−	1.19378i	0.282860	−	0.959161i	$-0.408717\pi$
$920$	−3.22213	−	10.7627i	−0.106231	−	0.354835i
$921$		0			0
$922$	1.33260	−	0.876466i	0.0438869	−	0.0288649i
$923$	−47.0238	+	63.1639i	−1.54781	+	2.07906i
$924$		0			0
$925$	1.47037	+	0.967075i	0.0483453	+	0.0317972i
$926$	−5.12956	+	1.86701i	−0.168568	+	0.0613536i
$927$		0			0
$928$	−35.6738	−	12.9842i	−1.17105	−	0.426227i
$929$	−15.8991	−	21.3562i	−0.521633	−	0.700675i	0.460755	−	0.887527i	$-0.347579\pi$
$929$	−15.8991	−	21.3562i	−0.521633	−	0.700675i	−0.982388	+	0.186853i	$0.940171\pi$
$930$		0			0
$931$	−0.0222011	−	0.0235317i	−0.000727610	−	0.000771222i
$932$	−16.1488	−	17.1167i	−0.528972	−	0.560677i
$933$		0			0
$934$	−7.09680	−	9.53265i	−0.232214	−	0.311918i
$935$	−26.1707	−	9.52537i	−0.855875	−	0.311513i
$936$		0			0
$937$	10.5874	−	3.85350i	0.345875	−	0.125888i	−0.163241	−	0.986586i	$-0.552195\pi$
$937$	10.5874	−	3.85350i	0.345875	−	0.125888i	0.509116	+	0.860698i	$0.329972\pi$
$938$	−0.817834	−	0.537898i	−0.0267032	−	0.0175630i
$939$		0			0
$940$	10.9390	−	14.6936i	0.356791	−	0.479254i
$941$	−14.7963	+	9.73168i	−0.482346	+	0.317244i	−0.767290	−	0.641300i	$-0.778395\pi$
$941$	−14.7963	+	9.73168i	−0.482346	+	0.317244i	0.284944	+	0.958544i	$0.408025\pi$
$942$		0			0
$943$	3.09399	+	10.3347i	0.100754	+	0.336543i
$944$	−12.2850	−	21.2782i	−0.399842	−	0.692546i
$945$		0			0
$946$	−0.376601	+	0.652293i	−0.0122444	+	0.0212079i
$947$	−57.8204	−	13.7037i	−1.87891	−	0.445310i	−0.879384	−	0.476113i	$-0.842045\pi$
$947$	−57.8204	−	13.7037i	−1.87891	−	0.445310i	−0.999525	+	0.0308032i	$0.990193\pi$
$948$		0			0
$949$	47.9144	+	24.0635i	1.55537	+	0.781135i
$950$	0.00383293	+	0.00888574i	0.000124357	+	0.000288292i
$951$		0			0
$952$	0.785009	−	13.4781i	0.0254423	−	0.436827i
$953$	9.46496	−	53.6784i	0.306600	−	1.73881i	−0.309277	−	0.950972i	$-0.600087\pi$
$953$	9.46496	−	53.6784i	0.306600	−	1.73881i	0.615876	−	0.787843i	$-0.288802\pi$
$954$		0			0
$955$	3.12859	+	17.7431i	0.101239	+	0.574155i
$956$	−18.5481	+	2.16796i	−0.599889	+	0.0701169i
$957$		0			0
$958$	0.311453	−	1.04033i	0.0100626	−	0.0336114i
$959$	−6.44729	+	1.52804i	−0.208194	+	0.0493429i
$960$		0			0
$961$	−3.84814	+	8.92099i	−0.124133	+	0.287774i
$962$	4.72103	−	3.96142i	0.152212	−	0.127721i
$963$		0			0
$964$	25.2252	+	21.1664i	0.812448	+	0.681725i
$965$	25.1197	−	12.6156i	0.808630	−	0.406109i
$966$		0			0
$967$	−28.1479	−	3.29002i	−0.905175	−	0.105800i	−0.349247	−	0.937031i	$-0.613563\pi$
$967$	−28.1479	−	3.29002i	−0.905175	−	0.105800i	−0.555927	+	0.831231i	$0.687637\pi$
$968$	−0.117695	−	2.02074i	−0.00378285	−	0.0649491i
$969$		0			0
$970$	−3.24376	+	3.43819i	−0.104151	+	0.110394i
$971$	−34.6038			−1.11049			−0.555244	−	0.831687i	$-0.687375\pi$
$971$	−34.6038			−1.11049			−0.555244	+	0.831687i	$0.687375\pi$
$972$		0			0
$973$	48.2868			1.54801
$974$	1.18300	−	1.25391i	0.0379058	−	0.0401778i
$975$		0			0
$976$	2.31303	+	39.7132i	0.0740382	+	1.27119i
$977$	13.1806	+	1.54060i	0.421686	+	0.0492880i	0.324290	−	0.945958i	$-0.394875\pi$
$977$	13.1806	+	1.54060i	0.421686	+	0.0492880i	0.0973958	+	0.995246i	$0.468949\pi$
$978$		0			0
$979$	38.4121	−	19.2913i	1.22766	−	0.616552i
$980$	1.63697	+	1.37358i	0.0522912	+	0.0438775i
$981$		0			0
$982$	0.965832	−	0.810430i	0.0308209	−	0.0258618i
$983$	14.2596	−	33.0575i	0.454811	−	1.05437i	−0.524390	−	0.851478i	$-0.675707\pi$
$983$	14.2596	−	33.0575i	0.454811	−	1.05437i	0.979201	−	0.202892i	$-0.0650341\pi$
$984$		0			0
$985$	−15.5807	+	3.69268i	−0.496441	+	0.117659i
$986$	4.16908	−	13.9257i	0.132771	−	0.443485i
$987$		0			0
$988$	−0.635085	+	0.0742308i	−0.0202048	+	0.00236160i
$989$	0.576698	+	3.27062i	0.0183379	+	0.104000i
$990$		0			0
$991$	9.06181	−	51.3921i	0.287858	−	1.63252i	−0.407037	−	0.913412i	$-0.633438\pi$
$991$	9.06181	−	51.3921i	0.287858	−	1.63252i	0.694895	−	0.719111i	$-0.255451\pi$
$992$	−0.953635	+	16.3733i	−0.0302780	+	0.519852i
$993$		0			0
$994$	4.56062	+	10.5727i	0.144654	+	0.335346i
$995$	−4.00633	−	2.01205i	−0.127009	−	0.0637864i
$996$		0			0
$997$	17.5636	+	4.16265i	0.556245	+	0.131833i	0.499118	−	0.866534i	$-0.333658\pi$
$997$	17.5636	+	4.16265i	0.556245	+	0.131833i	0.0571279	+	0.998367i	$0.481806\pi$
$998$	3.40379	−	5.89554i	0.107745	−	0.186620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.622.4		144
3.2	odd	2		729.2.g.a.622.5		144
9.2	odd	6		243.2.g.a.208.4		144
9.4	even	3		729.2.g.c.379.4		144
9.5	odd	6		729.2.g.b.379.5		144
9.7	even	3		81.2.g.a.16.5	✓	144
81.5	odd	54		729.2.g.b.352.5		144
81.22	even	27	inner	729.2.g.d.109.4		144
81.32	odd	54		243.2.g.a.118.4		144
81.34	even	27		6561.2.a.c.1.42		72
81.47	odd	54		6561.2.a.d.1.31		72
81.49	even	27		81.2.g.a.76.5	yes	144
81.59	odd	54		729.2.g.a.109.5		144
81.76	even	27		729.2.g.c.352.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.5	✓	144	9.7	even	3
81.2.g.a.76.5	yes	144	81.49	even	27
243.2.g.a.118.4		144	81.32	odd	54
243.2.g.a.208.4		144	9.2	odd	6
729.2.g.a.109.5		144	81.59	odd	54
729.2.g.a.622.5		144	3.2	odd	2
729.2.g.b.352.5		144	81.5	odd	54
729.2.g.b.379.5		144	9.5	odd	6
729.2.g.c.352.4		144	81.76	even	27
729.2.g.c.379.4		144	9.4	even	3
729.2.g.d.109.4		144	81.22	even	27	inner
729.2.g.d.622.4		144	1.1	even	1	trivial
6561.2.a.c.1.42		72	81.34	even	27
6561.2.a.d.1.31		72	81.47	odd	54

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.217727 + 0.230777i) q^{2} +(0.110437 + 1.89612i) q^{4} +(-2.10697 - 0.246269i) q^{5} +(-2.27300 + 1.14154i) q^{7} +(-0.947719 - 0.795231i) q^{8} +O(q^{10})\)	\(q+(-0.217727 + 0.230777i) q^{2} +(0.110437 + 1.89612i) q^{4} +(-2.10697 - 0.246269i) q^{5} +(-2.27300 + 1.14154i) q^{7} +(-0.947719 - 0.795231i) q^{8} +(0.515577 - 0.432621i) q^{10} +(-1.21202 + 2.80978i) q^{11} +(5.37024 - 1.27277i) q^{13} +(0.231451 - 0.773099i) q^{14} +(-3.38312 + 0.395430i) q^{16} +(-0.745021 - 4.22522i) q^{17} +(-0.0105922 + 0.0600713i) q^{19} +(0.234271 - 4.02227i) q^{20} +(-0.384543 - 0.891471i) q^{22} +(-3.82550 - 1.92124i) q^{23} +(-0.486554 - 0.115315i) q^{25} +(-0.875520 + 1.51644i) q^{26} +(-2.41553 - 4.18381i) q^{28} +(-3.06272 - 10.2302i) q^{29} +(-3.85453 + 2.53516i) q^{31} +(2.12290 - 2.85155i) q^{32} +(1.13730 + 0.748011i) q^{34} +(5.07026 - 1.84542i) q^{35} +(-3.30730 - 1.20376i) q^{37} +(-0.0115569 - 0.0155236i) q^{38} +(1.80097 + 1.90892i) q^{40} +(-1.72935 - 1.83301i) q^{41} +(-0.463275 - 0.622287i) q^{43} +(-5.46154 - 1.98784i) q^{44} +(1.27629 - 0.464532i) q^{46} +(3.79858 + 2.49837i) q^{47} +(-0.316716 + 0.425424i) q^{49} +(0.132548 - 0.0871782i) q^{50} +(3.00640 + 10.0421i) q^{52} +(0.986349 + 1.70841i) q^{53} +(3.24565 - 5.62164i) q^{55} +(3.06195 + 0.725696i) q^{56} +(3.02773 + 1.52058i) q^{58} +(2.85708 + 6.62346i) q^{59} +(0.679073 - 11.6592i) q^{61} +(0.254177 - 1.44151i) q^{62} +(-0.987085 - 5.59804i) q^{64} +(-11.6284 + 1.35916i) q^{65} +(0.347884 - 1.16201i) q^{67} +(7.92927 - 1.87927i) q^{68} +(-0.678050 + 1.57190i) q^{70} +(-10.9300 + 9.17137i) q^{71} +(7.44218 + 6.24473i) q^{73} +(0.997887 - 0.501157i) q^{74} +(-0.115072 - 0.0134500i) q^{76} +(-0.452562 - 7.77019i) q^{77} +(-1.10564 + 1.17191i) q^{79} +7.22552 q^{80} +0.799542 q^{82} +(-2.26614 + 2.40196i) q^{83} +(0.529193 + 9.08589i) q^{85} +(0.244477 + 0.0285753i) q^{86} +(3.38308 - 1.69905i) q^{88} +(-10.7606 - 9.02919i) q^{89} +(-10.7536 + 9.02336i) q^{91} +(3.22043 - 7.46579i) q^{92} +(-1.40362 + 0.332664i) q^{94} +(0.0371112 - 0.123960i) q^{95} +(-6.97567 + 0.815339i) q^{97} +(-0.0292204 - 0.165717i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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