LMFDB - Embedded newform 729.2.g.d.109.4

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			109.4
Character	$\chi$	$=$	729.109
Dual form			729.2.g.d.622.4

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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	0.645805	−	0.763503i	$-0.276522\pi$
$2$	−0.217727	−	0.230777i	−0.153956	−	0.163184i	−0.799761	+	0.600319i	$0.795040\pi$
$3$		0			0
$3$		0			0
$4$	0.110437	−	1.89612i	0.0552183	−	0.948062i
$5$	−2.10697	+	0.246269i	−0.942265	+	0.110135i	−0.573334	−	0.819322i	$-0.694350\pi$
$5$	−2.10697	+	0.246269i	−0.942265	+	0.110135i	−0.368931	+	0.929457i	$0.620276\pi$
$6$		0			0
$7$	−2.27300	−	1.14154i	−0.859112	−	0.431462i	−0.0360069	−	0.999352i	$-0.511464\pi$
$7$	−2.27300	−	1.14154i	−0.859112	−	0.431462i	−0.823105	+	0.567889i	$0.807760\pi$
$8$	−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	−0.997392	−	0.0721747i	$-0.977006\pi$
$11$	−1.21202	−	2.80978i	−0.365438	−	0.847181i	0.631954	−	0.775006i	$-0.282253\pi$
$12$		0			0
$13$	5.37024	+	1.27277i	1.48944	+	0.353003i	0.893147	−	0.449766i	$-0.148492\pi$
$13$	5.37024	+	1.27277i	1.48944	+	0.353003i	0.596291	+	0.802769i	$0.296641\pi$
$14$	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	0.750670	+	0.660678i	$0.229731\pi$
$17$	−0.745021	+	4.22522i	−0.180694	+	1.02477i	−0.931364	+	0.364090i	$0.881380\pi$
$18$		0			0
$19$	−0.0105922	−	0.0600713i	−0.00243002	−	0.0137813i	0.983569	−	0.180535i	$-0.0577828\pi$
$19$	−0.0105922	−	0.0600713i	−0.00243002	−	0.0137813i	−0.985999	+	0.166753i	$0.946672\pi$
$20$	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	−0.800457	−	0.599390i	$-0.795410\pi$
$23$	−3.82550	+	1.92124i	−0.797671	+	0.400606i	0.00278538	+	0.999996i	$0.499113\pi$
$24$		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	−0.159755	+	0.987157i	$0.551070\pi$
$29$	−3.06272	+	10.2302i	−0.568733	+	1.89970i	−0.408979	+	0.912544i	$0.634115\pi$
$30$		0			0
$31$	−3.85453	−	2.53516i	−0.692294	−	0.455329i	0.153982	−	0.988074i	$-0.450790\pi$
$31$	−3.85453	−	2.53516i	−0.692294	−	0.455329i	−0.846276	+	0.532745i	$0.821161\pi$
$32$	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	−0.599252	−	0.800560i	$-0.704535\pi$
$37$	−3.30730	+	1.20376i	−0.543716	+	0.197896i	0.0555362	+	0.998457i	$0.482313\pi$
$38$	−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	−0.848191	−	0.529690i	$-0.822308\pi$
$41$	−1.72935	+	1.83301i	−0.270080	+	0.286268i	0.578112	+	0.815958i	$0.303790\pi$
$42$		0			0
$43$	−0.463275	+	0.622287i	−0.0706488	+	0.0948978i	−0.836043	−	0.548664i	$-0.815137\pi$
$43$	−0.463275	+	0.622287i	−0.0706488	+	0.0948978i	0.765394	+	0.643562i	$0.222544\pi$
$44$	−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	−0.241379	−	0.970431i	$-0.577600\pi$
$47$	3.79858	−	2.49837i	0.554080	−	0.364424i	0.795460	+	0.606007i	$0.207229\pi$
$48$		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	−0.790297	−	0.612724i	$-0.790074\pi$
$53$	0.986349	−	1.70841i	0.135485	−	0.234668i	0.925783	+	0.378056i	$0.123407\pi$
$54$		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	−0.624717	−	0.780851i	$-0.714786\pi$
$59$	2.85708	−	6.62346i	0.371960	−	0.862301i	0.996677	−	0.0814496i	$-0.0259550\pi$
$60$		0			0
$61$	0.679073	+	11.6592i	0.0869464	+	1.49281i	0.706419	+	0.707794i	$0.250309\pi$
$61$	0.679073	+	11.6592i	0.0869464	+	1.49281i	−0.619473	+	0.785018i	$0.712654\pi$
$62$	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	0.976607	−	0.215034i	$-0.0689861\pi$
$67$	0.347884	+	1.16201i	0.0425008	+	0.141963i	−0.934106	+	0.356996i	$0.883801\pi$
$68$	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	−0.990629	−	0.136579i	$-0.956389\pi$
$71$	−10.9300	−	9.17137i	−1.29715	−	1.08844i	−0.306525	−	0.951863i	$-0.599166\pi$
$72$		0			0
$73$	7.44218	−	6.24473i	0.871042	−	0.730891i	−0.0932755	−	0.995640i	$-0.529734\pi$
$73$	7.44218	−	6.24473i	0.871042	−	0.730891i	0.964317	+	0.264750i	$0.0852893\pi$
$74$	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	0.662183	−	0.749342i	$-0.269630\pi$
$79$	−1.10564	−	1.17191i	−0.124395	−	0.131851i	−0.786577	+	0.617492i	$0.788149\pi$
$80$	7.22552			0.807838
$81$		0			0
$82$	0.799542			0.0882947
$83$	−2.26614	−	2.40196i	−0.248741	−	0.263650i	0.590958	−	0.806702i	$-0.298750\pi$
$83$	−2.26614	−	2.40196i	−0.248741	−	0.263650i	−0.839699	+	0.543053i	$0.817268\pi$
$84$		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	−0.999459	−	0.0328946i	$-0.989527\pi$
$89$	−10.7606	+	9.02919i	−1.14062	+	0.957092i	−0.141159	+	0.989987i	$0.545083\pi$
$90$		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	−0.245673	−	0.969353i	$-0.579009\pi$
$97$	−6.97567	−	0.815339i	−0.708272	−	0.0827851i	−0.462599	+	0.886568i	$0.653083\pi$
$98$	−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	−0.871642	−	0.490143i	$-0.836944\pi$
$101$	−0.631091	−	10.8354i	−0.0627959	−	1.07816i	0.808846	−	0.588021i	$-0.200093\pi$
$102$		0			0
$103$	−4.92595	+	11.4196i	−0.485368	+	1.12521i	0.482986	+	0.875628i	$0.339552\pi$
$103$	−4.92595	+	11.4196i	−0.485368	+	1.12521i	−0.968354	+	0.249582i	$0.919707\pi$
$104$	−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	0.720260	−	0.693704i	$-0.244023\pi$
$107$	−2.48915	−	4.31134i	−0.240636	−	0.416793i	−0.960896	+	0.276911i	$0.910689\pi$
$108$		0			0
$109$	−0.180626	+	0.312853i	−0.0173008	+	0.0299659i	−0.874546	−	0.484942i	$-0.838841\pi$
$109$	−0.180626	+	0.312853i	−0.0173008	+	0.0299659i	0.857245	+	0.514908i	$0.172174\pi$
$110$	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	−0.852200	−	0.523216i	$-0.824732\pi$
$113$	−11.7891	−	15.8355i	−1.10902	−	1.48968i	−0.256822	−	0.966459i	$-0.582675\pi$
$114$		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	0.864222	−	0.503111i	$-0.167811\pi$
$127$	13.5556	+	4.93382i	1.20286	+	0.437806i	0.338639	+	0.940916i	$0.390033\pi$
$128$	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	0.433099	−	0.901346i	$-0.357420\pi$
$131$	−2.55224	−	1.67864i	−0.222990	−	0.146663i	−0.656089	+	0.754683i	$0.727791\pi$
$132$		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	−0.120904	−	0.992664i	$-0.538579\pi$
$137$	2.53477	−	0.600750i	0.216560	−	0.0513256i	0.337463	+	0.941339i	$0.390431\pi$
$138$		0			0
$139$	−16.9648	+	8.52003i	−1.43893	+	0.722660i	−0.985665	−	0.168714i	$-0.946038\pi$
$139$	−16.9648	+	8.52003i	−1.43893	+	0.722660i	−0.453269	+	0.891374i	$0.649742\pi$
$140$	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	0.390665	−	0.920533i	$-0.372245\pi$
$149$	3.98717	+	0.944978i	0.326642	+	0.0774156i	−0.0640232	+	0.997948i	$0.520393\pi$
$150$		0			0
$151$	3.93753	+	9.12821i	0.320431	+	0.742843i	0.999958	+	0.00919237i	$0.00292606\pi$
$151$	3.93753	+	9.12821i	0.320431	+	0.742843i	−0.679526	+	0.733651i	$0.737815\pi$
$152$	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	−0.560790	−	0.827958i	$-0.689502\pi$
$157$	−11.4715	+	1.34082i	−0.915523	+	0.107009i	−0.354733	+	0.934968i	$0.615428\pi$
$158$	−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	0.145493	−	0.989359i	$-0.453523\pi$
$167$	6.65820	−	0.778232i	0.515227	−	0.0602214i	0.369733	+	0.929138i	$0.379449\pi$
$168$		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	−0.982045	−	0.188645i	$-0.939590\pi$
$173$	−5.85754	−	13.5793i	−0.445340	−	1.03242i	0.536705	−	0.843770i	$-0.319669\pi$
$174$		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	−0.988644	−	0.150275i	$-0.951984\pi$
$179$	−0.110050	+	0.624125i	−0.00822552	+	0.0466493i	0.980419	+	0.196924i	$0.0630953\pi$
$180$		0			0
$181$	−2.42311	−	13.7421i	−0.180108	−	1.02145i	−0.932081	−	0.362251i	$-0.882008\pi$
$181$	−2.42311	−	13.7421i	−0.180108	−	1.02145i	0.751972	−	0.659195i	$-0.229103\pi$
$182$	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	0.823515	+	0.567294i	$0.192010\pi$
$191$	−2.43589	+	8.13645i	−0.176255	+	0.588733i	−0.999770	+	0.0214386i	$0.993175\pi$
$192$		0			0
$193$	−11.0711	−	7.28156i	−0.796914	−	0.524138i	0.0845336	−	0.996421i	$-0.473060\pi$
$193$	−11.0711	−	7.28156i	−0.796914	−	0.524138i	−0.881447	+	0.472282i	$0.843430\pi$
$194$	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	0.582103	−	0.813115i	$-0.302230\pi$
$197$	7.09307	+	2.58167i	0.505360	+	0.183936i	−0.0767431	+	0.997051i	$0.524452\pi$
$198$		0			0
$199$	1.98595	−	0.722827i	0.140780	−	0.0512399i	−0.270669	−	0.962672i	$-0.587245\pi$
$199$	1.98595	−	0.722827i	0.140780	−	0.0512399i	0.411449	+	0.911433i	$0.365023\pi$
$200$	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	0.815412	−	0.578881i	$-0.196510\pi$
$211$	0.392021	+	0.526575i	0.0269878	+	0.0362509i	−0.788424	+	0.615132i	$0.789103\pi$
$212$	−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	−0.699904	−	0.714237i	$-0.746774\pi$
$223$	−1.30890	−	22.4729i	−0.0876503	−	1.50490i	0.612254	−	0.790661i	$-0.290263\pi$
$224$	−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	0.545937	−	0.837826i	$-0.316174\pi$
$227$	13.3179	+	1.55664i	0.883942	+	0.103318i	0.338005	+	0.941144i	$0.390248\pi$
$228$		0			0
$229$	−1.78489	−	5.96194i	−0.117949	−	0.393976i	0.878543	−	0.477663i	$-0.158516\pi$
$229$	−1.78489	−	5.96194i	−0.117949	−	0.393976i	−0.996492	+	0.0836862i	$0.973331\pi$
$230$	−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	0.276582	−	0.960990i	$-0.410798\pi$
$233$	−9.49107	−	7.96396i	−0.621781	−	0.521736i	−0.898363	+	0.439254i	$0.855243\pi$
$234$		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	−0.928000	−	0.372580i	$-0.878473\pi$
$239$	0.571683	−	9.81542i	0.0369791	−	0.634907i	0.964979	−	0.262327i	$-0.0844897\pi$
$240$		0			0
$241$	11.8975	+	12.6106i	0.766384	+	0.812320i	0.986605	−	0.163130i	$-0.0521591\pi$
$241$	11.8975	+	12.6106i	0.766384	+	0.812320i	−0.220220	+	0.975450i	$0.570678\pi$
$242$	−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	−0.211132	+	0.977458i	$0.567715\pi$
$251$	−19.1764	+	16.0909i	−1.21040	+	1.01565i	−0.999270	+	0.0381908i	$0.987841\pi$
$252$		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	0.933716	−	0.358013i	$-0.116546\pi$
$257$	−0.691327	−	2.30919i	−0.0431238	−	0.144044i	−0.976840	+	0.213970i	$0.931361\pi$
$258$		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	0.998012	+	0.0630218i	$0.0200737\pi$
$263$	0.228089	+	3.91614i	0.0140646	+	0.241480i	−0.983948	+	0.178458i	$0.942889\pi$
$264$		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	0.645981	−	0.763353i	$-0.276448\pi$
$269$	−5.54513	−	9.60445i	−0.338093	−	0.585594i	−0.984074	+	0.177760i	$0.943115\pi$
$270$		0			0
$271$	−0.397309	+	0.688159i	−0.0241348	+	0.0418027i	−0.877841	−	0.478953i	$-0.841016\pi$
$271$	−0.397309	+	0.688159i	−0.0241348	+	0.0418027i	0.853706	+	0.520756i	$0.174350\pi$
$272$	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	−0.468436	+	0.883497i	$0.655182\pi$
$277$	−24.3861	+	16.0390i	−1.46522	+	0.963688i	−0.996780	+	0.0801905i	$0.974447\pi$
$278$	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	−0.0356623	+	0.999364i	$0.511354\pi$
$281$	−16.4750	+	22.1297i	−0.982814	+	1.32015i	−0.947152	+	0.320785i	$0.896053\pi$
$282$		0			0
$283$	3.50574	−	3.71587i	0.208395	−	0.220886i	−0.614743	−	0.788728i	$-0.710740\pi$
$283$	3.50574	−	3.71587i	0.208395	−	0.220886i	0.823137	+	0.567842i	$0.192222\pi$
$284$	−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	0.605412	−	0.795913i	$-0.293009\pi$
$293$	1.95792	+	1.28775i	0.114383	+	0.0752310i	−0.491028	+	0.871144i	$0.663379\pi$
$294$		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	0.793620	+	0.608413i	$0.208194\pi$
$307$	−2.80743	+	15.9217i	−0.160228	+	0.908700i	−0.953849	+	0.300287i	$0.902918\pi$
$308$	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	−0.400527	−	0.916285i	$-0.631173\pi$
$311$	−20.6275	−	4.88881i	−1.16968	−	0.277219i	−0.769152	+	0.639066i	$0.779321\pi$
$312$		0			0
$313$	−2.14335	−	4.96885i	−0.121149	−	0.280856i	0.846840	−	0.531848i	$-0.178502\pi$
$313$	−2.14335	−	4.96885i	−0.121149	−	0.280856i	−0.967989	+	0.250992i	$0.919243\pi$
$314$	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	0.654130	−	0.756382i	$-0.273035\pi$
$317$	7.79902	+	3.91682i	0.438037	+	0.219990i	−0.216093	+	0.976373i	$0.569331\pi$
$318$		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	−0.104878	−	0.994485i	$-0.533445\pi$
$331$	−17.5604	−	8.81917i	−0.965207	−	0.484745i	−0.860329	+	0.509740i	$0.829742\pi$
$332$	−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	0.0312784	−	0.999511i	$-0.490042\pi$
$337$	−7.14751	−	1.69399i	−0.389350	−	0.0922776i	−0.420628	+	0.907233i	$0.638190\pi$
$338$	−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	0.0455174	−	0.998964i	$-0.485506\pi$
$347$	16.2806	−	8.17644i	0.873990	−	0.438934i	0.828473	+	0.560029i	$0.189210\pi$
$348$		0			0
$349$	−15.6760	+	3.71527i	−0.839116	+	0.198874i	−0.627635	−	0.778508i	$-0.715977\pi$
$349$	−15.6760	+	3.71527i	−0.839116	+	0.198874i	−0.211481	+	0.977382i	$0.567829\pi$
$350$	−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	−0.720795	−	0.693149i	$-0.756223\pi$
$353$	4.92839	−	16.4620i	0.262312	−	0.876183i	0.983107	−	0.183034i	$-0.0585919\pi$
$354$		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	0.931187	−	0.364543i	$-0.118775\pi$
$359$	26.7193	+	9.72505i	1.41019	+	0.513268i	0.479007	+	0.877811i	$0.340997\pi$
$360$		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	−0.610409	−	0.792086i	$-0.708995\pi$
$367$	6.19676	−	8.32370i	0.323468	−	0.434494i	0.933878	+	0.357593i	$0.116402\pi$
$368$	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	0.970344	−	0.241730i	$-0.0777147\pi$
$373$	8.89318	+	11.9456i	0.460472	+	0.618521i	−0.509872	+	0.860250i	$0.670307\pi$
$374$	−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	0.677253	−	0.735750i	$-0.263170\pi$
$379$	−5.81217	−	10.0670i	−0.298551	−	0.517106i	−0.975805	+	0.218644i	$0.929837\pi$
$380$	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	0.340408	+	0.940278i	$0.389435\pi$
$383$	−11.2946	+	26.1838i	−0.577127	+	1.33793i	−0.917535	+	0.397654i	$0.869824\pi$
$384$		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	0.0384301	−	0.999261i	$-0.487764\pi$
$389$	−3.04961	−	0.356448i	−0.154621	−	0.0180726i	−0.193051	+	0.981189i	$0.561838\pi$
$390$		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	−0.822063	−	0.569397i	$-0.807177\pi$
$397$	−8.05095	+	6.75555i	−0.404065	+	0.339051i	0.417997	+	0.908448i	$0.362732\pi$
$398$	−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	0.710092	+	0.704109i	$0.248653\pi$
$401$	−1.54074	+	26.4534i	−0.0769407	+	1.32102i	−0.787033	+	0.616912i	$0.788384\pi$
$402$		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	0.719463	+	0.694531i	$0.244388\pi$
$409$	−1.53226	+	26.3079i	−0.0757654	+	1.30084i	−0.795228	+	0.606311i	$0.792649\pi$
$410$	−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	0.885432	−	0.464768i	$-0.153862\pi$
$419$	−2.24612	−	7.50255i	−0.109730	−	0.366523i	−0.995162	+	0.0982448i	$0.968677\pi$
$420$		0			0
$421$	31.6365	+	3.69777i	1.54187	+	0.180218i	0.844131	−	0.536136i	$-0.180117\pi$
$421$	31.6365	+	3.69777i	1.54187	+	0.180218i	0.697736	+	0.716355i	$0.254191\pi$
$422$	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	0.918083	+	0.396389i	$0.129737\pi$
$431$	16.6567	+	28.8502i	0.802324	+	1.38967i	−0.115759	+	0.993277i	$0.536930\pi$
$432$		0			0
$433$	2.75793	−	4.77688i	0.132538	−	0.229562i	−0.792116	−	0.610370i	$-0.791021\pi$
$433$	2.75793	−	4.77688i	0.132538	−	0.229562i	0.924654	+	0.380808i	$0.124354\pi$
$434$	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	−0.481797	−	0.876283i	$-0.660016\pi$
$439$	2.76551	−	1.81890i	0.131990	−	0.0868114i	0.613787	+	0.789472i	$0.289645\pi$
$440$	−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	−0.488432	−	0.872602i	$-0.662431\pi$
$443$	10.2627	−	13.7852i	0.487595	−	0.654954i	0.976027	+	0.217648i	$0.0698385\pi$
$444$		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	0.0791375	−	0.996864i	$-0.474783\pi$
$449$	16.5392	−	6.01977i	0.780532	−	0.284090i	0.701394	+	0.712773i	$0.252561\pi$
$450$		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	0.750350	+	0.661041i	$0.229885\pi$
$457$	−5.12647	+	17.1236i	−0.239806	+	0.801009i	−0.990156	+	0.139968i	$0.955300\pi$
$458$	−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	−0.342944	−	0.939356i	$-0.611424\pi$
$461$	−4.89168	+	1.15935i	−0.227828	+	0.0539963i	0.115116	+	0.993352i	$0.463276\pi$
$462$		0			0
$463$	15.3751	−	7.72167i	0.714542	−	0.358857i	−0.0541001	−	0.998536i	$-0.517229\pi$
$463$	15.3751	−	7.72167i	0.714542	−	0.358857i	0.768642	+	0.639679i	$0.220933\pi$
$464$	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	−0.641812	−	0.766862i	$-0.721817\pi$
$467$	−6.50441	−	36.8883i	−0.300988	−	1.70699i	0.340824	−	0.940127i	$-0.389294\pi$
$468$		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	0.377548	−	0.925990i	$-0.376767\pi$
$479$	−3.05867	−	1.53612i	−0.139754	−	0.0701872i	−0.517302	+	0.855803i	$0.673064\pi$
$480$		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	−0.204688	−	0.978827i	$-0.565618\pi$
$491$	−3.94699	+	0.461337i	−0.178125	+	0.0208199i	0.0265626	+	0.999647i	$0.491544\pi$
$492$		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	−0.265037	−	0.964238i	$-0.585384\pi$
$499$	−20.8781	−	4.94820i	−0.934632	−	0.221512i	−0.669595	+	0.742727i	$0.733532\pi$
$500$	−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	−0.727031	−	0.686605i	$-0.759100\pi$
$503$	4.28340	−	24.2924i	0.190987	−	1.08314i	0.918018	−	0.396538i	$-0.129789\pi$
$504$		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	−0.588314	−	0.808633i	$-0.700208\pi$
$509$	−6.56544	+	3.29729i	−0.291008	+	0.146150i	0.297306	+	0.954782i	$0.403912\pi$
$510$		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	−0.286082	−	0.958205i	$-0.592353\pi$
$521$	−25.5909	−	9.31432i	−1.12116	−	0.408068i	−0.835074	+	0.550137i	$0.814575\pi$
$522$		0			0
$523$	−14.3006	+	5.20499i	−0.625321	+	0.227598i	−0.635193	−	0.772353i	$-0.719080\pi$
$523$	−14.3006	+	5.20499i	−0.625321	+	0.227598i	0.00987267	+	0.999951i	$0.496857\pi$
$524$	−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	0.630173	−	0.776455i	$-0.282984\pi$
$541$	−8.31159	−	14.3961i	−0.357343	−	0.618937i	−0.987516	+	0.157518i	$0.949651\pi$
$542$	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	−0.982856	−	0.184375i	$-0.940974\pi$
$547$	−0.656042	−	11.2638i	−0.0280503	−	0.481605i	0.954806	−	0.297231i	$-0.0960630\pi$
$548$	−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	0.978674	−	0.205421i	$-0.0658565\pi$
$557$	22.3339	+	18.7404i	0.946318	+	0.794055i	−0.0323557	+	0.999476i	$0.510301\pi$
$558$		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	−0.864034	−	0.503433i	$-0.832070\pi$
$563$	1.24814	−	21.4297i	0.0526028	−	0.903154i	0.916637	−	0.399721i	$-0.130893\pi$
$564$		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	0.764791	−	0.644279i	$-0.222842\pi$
$569$	1.83992	+	1.95021i	0.0771336	+	0.0817569i	−0.687657	+	0.726035i	$0.741361\pi$
$570$		0			0
$571$	0.165178	−	2.83600i	0.00691248	−	0.118683i	−0.993087	−	0.117383i	$-0.962549\pi$
$571$	0.165178	−	2.83600i	0.00691248	−	0.118683i	0.999999	−	0.00129937i	$-0.000413604\pi$
$572$	−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	0.732322	−	0.680959i	$-0.238437\pi$
$577$	4.53692	+	3.80692i	0.188874	+	0.158484i	−0.543447	+	0.839443i	$0.682881\pi$
$578$	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	0.984463	+	0.175592i	$0.0561838\pi$
$587$	0.655164	+	11.2487i	0.0270415	+	0.464285i	−0.957422	+	0.288694i	$0.906779\pi$
$588$		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	0.946870	−	0.321617i	$-0.104226\pi$
$593$	4.74627	+	8.22078i	0.194906	+	0.337587i	−0.751964	+	0.659205i	$0.770893\pi$
$594$		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	0.994484	−	0.104889i	$-0.0334488\pi$
$599$	14.8996	+	20.0136i	0.608780	+	0.817733i	−0.385704	+	0.922623i	$0.626041\pi$
$600$		0			0
$601$	9.59732	−	6.31226i	0.391483	−	0.257482i	−0.338474	−	0.940976i	$-0.609911\pi$
$601$	9.59732	−	6.31226i	0.391483	−	0.257482i	0.729957	+	0.683494i	$0.239540\pi$
$602$	−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	−0.127303	+	0.991864i	$0.540632\pi$
$607$	−27.3496	+	28.9889i	−1.11009	+	1.17662i	−0.982784	+	0.184759i	$0.940849\pi$
$608$	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	−0.0227782	−	0.999741i	$-0.507251\pi$
$613$	−16.9065	−	6.15347i	−0.682848	−	0.248536i	−0.660070	+	0.751204i	$0.729473\pi$
$614$	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	0.202098	−	0.979365i	$-0.435224\pi$
$617$	−15.3291	−	10.0821i	−0.617124	−	0.405889i	−0.819222	+	0.573476i	$0.805594\pi$
$618$		0			0
$619$	12.8881	−	43.0492i	0.518016	−	1.73029i	−0.152409	−	0.988317i	$-0.548703\pi$
$619$	12.8881	−	43.0492i	0.518016	−	1.73029i	0.670425	−	0.741977i	$-0.266112\pi$
$620$	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	−0.607203	−	0.794547i	$-0.707708\pi$
$631$	5.90645	−	33.4972i	0.235132	−	1.33350i	0.842335	−	0.538954i	$-0.181180\pi$
$632$	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	0.443238	−	0.896404i	$-0.353830\pi$
$641$	−0.281153	−	0.141200i	−0.0111049	−	0.00557707i	−0.454343	+	0.890827i	$0.650126\pi$
$642$		0			0
$643$	32.9098	−	3.84660i	1.29783	−	0.151695i	0.561027	−	0.827797i	$-0.310406\pi$
$643$	32.9098	−	3.84660i	1.29783	−	0.151695i	0.736808	+	0.676102i	$0.236332\pi$
$644$	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	0.817451	−	0.575999i	$-0.195387\pi$
$653$	44.6094	−	5.21409i	1.74570	−	0.204043i	0.928251	+	0.371955i	$0.121313\pi$
$654$		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	−0.954107	−	0.299465i	$-0.903192\pi$
$659$	−13.2766	−	30.7786i	−0.517182	−	1.19896i	0.436925	−	0.899498i	$-0.356067\pi$
$660$		0			0
$661$	15.7899	+	3.74227i	0.614156	+	0.145558i	0.525909	−	0.850541i	$-0.323725\pi$
$661$	15.7899	+	3.74227i	0.614156	+	0.145558i	0.0882470	+	0.996099i	$0.471874\pi$
$662$	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	−0.193559	−	0.981089i	$-0.562003\pi$
$673$	1.91409	−	0.453649i	0.0737829	−	0.0174869i	0.267342	+	0.963602i	$0.413855\pi$
$674$	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	0.767280	+	0.641312i	$0.221609\pi$
$677$	−5.88502	+	19.6573i	−0.226180	+	0.755493i	−0.993460	+	0.114181i	$0.963576\pi$
$678$		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	0.697271	−	0.716808i	$-0.254398\pi$
$683$	20.1405	+	7.33055i	0.770656	+	0.280496i	0.0733852	+	0.997304i	$0.476620\pi$
$684$		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	−0.365862	−	0.930669i	$-0.619226\pi$
$691$	16.5776	−	22.2675i	0.630640	−	0.847096i	0.996502	+	0.0835728i	$0.0266331\pi$
$692$	−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	−0.872649	−	0.488347i	$-0.837600\pi$
$701$	−0.354873	+	0.614659i	−0.0134034	+	0.0232153i	0.859246	+	0.511563i	$0.170933\pi$
$702$		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	0.945819	+	0.324694i	$0.105261\pi$
$709$	1.17399	+	20.1566i	0.0440900	+	0.756996i	−0.901729	+	0.432302i	$0.857702\pi$
$710$	−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	0.850148	−	0.526543i	$-0.176512\pi$
$719$	12.8502	+	10.7826i	0.479231	+	0.402123i	−0.370917	+	0.928666i	$0.620957\pi$
$720$		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	0.945402	−	0.325908i	$-0.105670\pi$
$727$	15.2361	+	16.1493i	0.565075	+	0.598945i	−0.380327	+	0.924852i	$0.624188\pi$
$728$	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	0.991540	+	0.129799i	$0.0414333\pi$
$733$	−0.226456	+	3.88810i	−0.00836434	+	0.143610i	−0.999905	+	0.0138108i	$0.995604\pi$
$734$	−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	0.318312	−	0.947986i	$-0.396884\pi$
$739$	−15.2233	−	12.7738i	−0.559997	−	0.469894i	−0.878310	+	0.478092i	$0.841328\pi$
$740$	−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	0.919022	−	0.394206i	$-0.128980\pi$
$743$	−1.78348	−	5.95723i	−0.0654294	−	0.218549i	−0.984452	+	0.175657i	$0.943795\pi$
$744$		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	−0.994085	−	0.108608i	$-0.965361\pi$
$751$	−6.38259	+	14.7965i	−0.232904	+	0.539933i	0.761181	+	0.648540i	$0.224620\pi$
$752$	−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	−0.338608	−	0.940928i	$-0.609956\pi$
$757$	17.7618	−	30.7643i	0.645563	−	1.11815i	0.984171	−	0.177221i	$-0.0567106\pi$
$758$	−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	0.525248	−	0.850949i	$-0.323973\pi$
$761$	−12.1544	−	16.3261i	−0.440595	−	0.591822i	−0.965843	+	0.259127i	$0.916565\pi$
$762$		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	−0.454755	−	0.890617i	$-0.650273\pi$
$769$	12.7783	−	13.5442i	0.460797	−	0.488416i	0.915552	+	0.402201i	$0.131755\pi$
$770$	−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	−0.274671	−	0.961538i	$-0.588569\pi$
$773$	3.69733	−	1.34572i	0.132984	−	0.0484021i	0.407655	+	0.913136i	$0.366347\pi$
$774$		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
$783$

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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more