LMFDB - Embedded newform 980.2.g.a.391.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (of order $2$, degree $1$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.13
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.431404 - 1.34681i) q^{2} -2.73718 q^{3} +(-1.62778 + 1.16204i) q^{4} -1.00000i q^{5} +(1.18083 + 3.68646i) q^{6} +(2.26727 + 1.69100i) q^{8} +4.49217 q^{9} +O(q^{10})$	\(q+(-0.431404 - 1.34681i) q^{2} -2.73718 q^{3} +(-1.62778 + 1.16204i) q^{4} -1.00000i q^{5} +(1.18083 + 3.68646i) q^{6} +(2.26727 + 1.69100i) q^{8} +4.49217 q^{9} +(-1.34681 + 0.431404i) q^{10} -0.100243i q^{11} +(4.45553 - 3.18071i) q^{12} -4.11735i q^{13} +2.73718i q^{15} +(1.29934 - 3.78308i) q^{16} -5.39735i q^{17} +(-1.93794 - 6.05009i) q^{18} -7.45934 q^{19} +(1.16204 + 1.62778i) q^{20} +(-0.135008 + 0.0432453i) q^{22} +1.50830i q^{23} +(-6.20593 - 4.62858i) q^{24} -1.00000 q^{25} +(-5.54528 + 1.77624i) q^{26} -4.08434 q^{27} -2.37688 q^{29} +(3.68646 - 1.18083i) q^{30} +5.44258 q^{31} +(-5.65562 - 0.117927i) q^{32} +0.274384i q^{33} +(-7.26919 + 2.32844i) q^{34} +(-7.31227 + 5.22007i) q^{36} +1.03852 q^{37} +(3.21799 + 10.0463i) q^{38} +11.2700i q^{39} +(1.69100 - 2.26727i) q^{40} +7.99125i q^{41} -7.04778i q^{43} +(0.116486 + 0.163174i) q^{44} -4.49217i q^{45} +(2.03139 - 0.650688i) q^{46} -4.44376 q^{47} +(-3.55654 + 10.3550i) q^{48} +(0.431404 + 1.34681i) q^{50} +14.7735i q^{51} +(4.78452 + 6.70215i) q^{52} +6.14261 q^{53} +(1.76200 + 5.50082i) q^{54} -0.100243 q^{55} +20.4176 q^{57} +(1.02540 + 3.20120i) q^{58} -8.52297 q^{59} +(-3.18071 - 4.45553i) q^{60} +7.90286i q^{61} +(-2.34795 - 7.33010i) q^{62} +(2.28103 + 7.66791i) q^{64} -4.11735 q^{65} +(0.369542 - 0.118370i) q^{66} +0.109800i q^{67} +(6.27192 + 8.78570i) q^{68} -4.12850i q^{69} +6.73221i q^{71} +(10.1850 + 7.59626i) q^{72} +6.14698i q^{73} +(-0.448022 - 1.39869i) q^{74} +2.73718 q^{75} +(12.1422 - 8.66802i) q^{76} +(15.1785 - 4.86190i) q^{78} +4.27445i q^{79} +(-3.78308 - 1.29934i) q^{80} -2.29692 q^{81} +(10.7627 - 3.44746i) q^{82} -6.50159 q^{83} -5.39735 q^{85} +(-9.49200 + 3.04044i) q^{86} +6.50596 q^{87} +(0.169511 - 0.227278i) q^{88} -3.19179i q^{89} +(-6.05009 + 1.93794i) q^{90} +(-1.75270 - 2.45519i) q^{92} -14.8973 q^{93} +(1.91706 + 5.98489i) q^{94} +7.45934i q^{95} +(15.4805 + 0.322788i) q^{96} +11.0691i q^{97} -0.450309i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.431404	−	1.34681i	−0.305049	−	0.952337i
$2$	−0.431404	−	1.34681i	−0.305049	−	0.952337i
$3$	−2.73718			−1.58031			−0.790157	−	0.612905i	$-0.790001\pi$
$3$	−2.73718			−1.58031			−0.790157	+	0.612905i	$0.790001\pi$
$4$	−1.62778	+	1.16204i	−0.813891	+	0.581018i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.18083	+	3.68646i	0.482073	+	1.50499i
$7$		0			0
$7$		0			0
$8$	2.26727	+	1.69100i	0.801601	+	0.597859i
$9$	4.49217			1.49739
$10$	−1.34681	+	0.431404i	−0.425898	+	0.136422i
$11$		−	0.100243i		−	0.0302244i	−0.999886	−	0.0151122i	$-0.995189\pi$
$11$		−	0.100243i		−	0.0302244i	0.999886	−	0.0151122i	$-0.00481055\pi$
$12$	4.45553	−	3.18071i	1.28620	−	0.918191i
$13$		−	4.11735i		−	1.14195i	−0.820968	−	0.570974i	$-0.806566\pi$
$13$		−	4.11735i		−	1.14195i	0.820968	−	0.570974i	$-0.193434\pi$
$14$		0			0
$15$			2.73718i			0.706738i
$16$	1.29934	−	3.78308i	0.324836	−	0.945770i
$17$		−	5.39735i		−	1.30905i	−0.756041	−	0.654525i	$-0.772869\pi$
$17$		−	5.39735i		−	1.30905i	0.756041	−	0.654525i	$-0.227131\pi$
$18$	−1.93794	−	6.05009i	−0.456777	−	1.42602i
$19$	−7.45934			−1.71129			−0.855645	−	0.517564i	$-0.826839\pi$
$19$	−7.45934			−1.71129			−0.855645	+	0.517564i	$0.826839\pi$
$20$	1.16204	+	1.62778i	0.259839	+	0.363983i
$21$		0			0
$22$	−0.135008	+	0.0432453i	−0.0287838	+	0.00921993i
$23$			1.50830i			0.314503i	0.987559	+	0.157251i	$0.0502633\pi$
$23$			1.50830i			0.314503i	−0.987559	+	0.157251i	$0.949737\pi$
$24$	−6.20593	−	4.62858i	−1.26678	−	0.944804i
$25$	−1.00000			−0.200000
$26$	−5.54528	+	1.77624i	−1.08752	+	0.348350i
$27$	−4.08434			−0.786032
$28$		0			0
$29$	−2.37688			−0.441376			−0.220688	−	0.975344i	$-0.570830\pi$
$29$	−2.37688			−0.441376			−0.220688	+	0.975344i	$0.570830\pi$
$30$	3.68646	−	1.18083i	0.673052	−	0.215589i
$31$	5.44258			0.977516			0.488758	−	0.872419i	$-0.337450\pi$
$31$	5.44258			0.977516			0.488758	+	0.872419i	$0.337450\pi$
$32$	−5.65562	−	0.117927i	−0.999783	−	0.0208468i
$33$			0.274384i			0.0477641i
$34$	−7.26919	+	2.32844i	−1.24666	+	0.399324i
$35$		0			0
$36$	−7.31227	+	5.22007i	−1.21871	+	0.870011i
$37$	1.03852			0.170732			0.0853659	−	0.996350i	$-0.472794\pi$
$37$	1.03852			0.170732			0.0853659	+	0.996350i	$0.472794\pi$
$38$	3.21799	+	10.0463i	0.522027	+	1.62972i
$39$			11.2700i			1.80464i
$40$	1.69100	−	2.26727i	0.267371	−	0.358487i
$41$			7.99125i			1.24802i	0.781415	+	0.624012i	$0.214498\pi$
$41$			7.99125i			1.24802i	−0.781415	+	0.624012i	$0.785502\pi$
$42$		0			0
$43$		−	7.04778i		−	1.07478i	−0.843335	−	0.537388i	$-0.819411\pi$
$43$		−	7.04778i		−	1.07478i	0.843335	−	0.537388i	$-0.180589\pi$
$44$	0.116486	+	0.163174i	0.0175609	+	0.0245994i
$45$		−	4.49217i		−	0.669653i
$46$	2.03139	−	0.650688i	0.299513	−	0.0959387i
$47$	−4.44376			−0.648189			−0.324095	−	0.946025i	$-0.605060\pi$
$47$	−4.44376			−0.648189			−0.324095	+	0.946025i	$0.605060\pi$
$48$	−3.55654	+	10.3550i	−0.513342	+	1.49461i
$49$		0			0
$50$	0.431404	+	1.34681i	0.0610097	+	0.190467i
$51$			14.7735i			2.06871i
$52$	4.78452	+	6.70215i	0.663493	+	0.929421i
$53$	6.14261			0.843753			0.421876	−	0.906653i	$-0.361372\pi$
$53$	6.14261			0.843753			0.421876	+	0.906653i	$0.361372\pi$
$54$	1.76200	+	5.50082i	0.239778	+	0.748567i
$55$	−0.100243			−0.0135168
$56$		0			0
$57$	20.4176			2.70437
$58$	1.02540	+	3.20120i	0.134641	+	0.420339i
$59$	−8.52297			−1.10960			−0.554798	−	0.831985i	$-0.687204\pi$
$59$	−8.52297			−1.10960			−0.554798	+	0.831985i	$0.687204\pi$
$60$	−3.18071	−	4.45553i	−0.410627	−	0.575207i
$61$			7.90286i			1.01186i	0.862575	+	0.505929i	$0.168850\pi$
$61$			7.90286i			1.01186i	−0.862575	+	0.505929i	$0.831150\pi$
$62$	−2.34795	−	7.33010i	−0.298190	−	0.930924i
$63$		0			0
$64$	2.28103	+	7.66791i	0.285129	+	0.958489i
$65$	−4.11735			−0.510695
$66$	0.369542	−	0.118370i	0.0454875	−	0.0145704i
$67$			0.109800i			0.0134142i	0.999978	+	0.00670710i	$0.00213495\pi$
$67$			0.109800i			0.0134142i	−0.999978	+	0.00670710i	$0.997865\pi$
$68$	6.27192	+	8.78570i	0.760582	+	1.06542i
$69$		−	4.12850i		−	0.497013i
$70$		0			0
$71$			6.73221i			0.798967i	0.916740	+	0.399483i	$0.130810\pi$
$71$			6.73221i			0.798967i	−0.916740	+	0.399483i	$0.869190\pi$
$72$	10.1850	+	7.59626i	1.20031	+	0.895228i
$73$			6.14698i			0.719450i	0.933058	+	0.359725i	$0.117129\pi$
$73$			6.14698i			0.719450i	−0.933058	+	0.359725i	$0.882871\pi$
$74$	−0.448022	−	1.39869i	−0.0520815	−	0.162594i
$75$	2.73718			0.316063
$76$	12.1422	−	8.66802i	1.39280	−	0.994290i
$77$		0			0
$78$	15.1785	−	4.86190i	1.71862	−	0.550502i
$79$			4.27445i			0.480914i	0.970660	+	0.240457i	$0.0772972\pi$
$79$			4.27445i			0.480914i	−0.970660	+	0.240457i	$0.922703\pi$
$80$	−3.78308	−	1.29934i	−0.422961	−	0.145271i
$81$	−2.29692			−0.255213
$82$	10.7627	−	3.44746i	1.18854	−	0.380708i
$83$	−6.50159			−0.713642			−0.356821	−	0.934173i	$-0.616139\pi$
$83$	−6.50159			−0.713642			−0.356821	+	0.934173i	$0.616139\pi$
$84$		0			0
$85$	−5.39735			−0.585425
$86$	−9.49200	+	3.04044i	−1.02355	+	0.327859i
$87$	6.50596			0.697512
$88$	0.169511	−	0.227278i	0.0180700	−	0.0242279i
$89$		−	3.19179i		−	0.338329i	−0.985588	−	0.169164i	$-0.945893\pi$
$89$		−	3.19179i		−	0.338329i	0.985588	−	0.169164i	$-0.0541068\pi$
$90$	−6.05009	+	1.93794i	−0.637735	+	0.204277i
$91$		0			0
$92$	−1.75270	−	2.45519i	−0.182732	−	0.255971i
$93$	−14.8973			−1.54478
$94$	1.91706	+	5.98489i	0.197729	+	0.617294i
$95$			7.45934i			0.765312i
$96$	15.4805	+	0.322788i	1.57997	+	0.0329444i
$97$			11.0691i			1.12390i	0.827173	+	0.561948i	$0.189948\pi$
$97$			11.0691i			1.12390i	−0.827173	+	0.561948i	$0.810052\pi$
$98$		0			0
$99$		−	0.450309i		−	0.0452578i
$100$	1.62778	−	1.16204i	0.162778	−	0.116204i
$101$			7.16390i			0.712835i	0.934327	+	0.356418i	$0.116002\pi$
$101$			7.16390i			0.712835i	−0.934327	+	0.356418i	$0.883998\pi$
$102$	19.8971	−	6.37336i	1.97011	−	0.631057i
$103$	−4.88608			−0.481440			−0.240720	−	0.970595i	$-0.577383\pi$
$103$	−4.88608			−0.481440			−0.240720	+	0.970595i	$0.577383\pi$
$104$	6.96245	−	9.33516i	0.682724	−	0.915388i
$105$		0			0
$106$	−2.64995	−	8.27292i	−0.257386	−	0.803537i
$107$			7.56872i			0.731695i	0.930675	+	0.365848i	$0.119221\pi$
$107$			7.56872i			0.731695i	−0.930675	+	0.365848i	$0.880779\pi$
$108$	6.64842	−	4.74615i	0.639744	−	0.456699i
$109$	−18.0532			−1.72919			−0.864593	−	0.502472i	$-0.832424\pi$
$109$	−18.0532			−1.72919			−0.864593	+	0.502472i	$0.832424\pi$
$110$	0.0432453	+	0.135008i	0.00412328	+	0.0128725i
$111$	−2.84262			−0.269810
$112$		0			0
$113$	−18.1432			−1.70677			−0.853384	−	0.521283i	$-0.825453\pi$
$113$	−18.1432			−1.70677			−0.853384	+	0.521283i	$0.825453\pi$
$114$	−8.80822	−	27.4985i	−0.824966	−	2.57547i
$115$	1.50830			0.140650
$116$	3.86904	−	2.76202i	0.359232	−	0.256447i
$117$		−	18.4959i		−	1.70994i
$118$	3.67684	+	11.4788i	0.338481	+	1.05671i
$119$		0			0
$120$	−4.62858	+	6.20593i	−0.422529	+	0.566522i
$121$	10.9900			0.999086
$122$	10.6436	−	3.40933i	0.963629	−	0.308666i
$123$		−	21.8735i		−	1.97227i
$124$	−8.85932	+	6.32447i	−0.795591	+	0.567954i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	4.37573i		−	0.388283i	−0.980974	−	0.194141i	$-0.937808\pi$
$127$		−	4.37573i		−	0.388283i	0.980974	−	0.194141i	$-0.0621921\pi$
$128$	9.34315	−	6.38008i	0.825826	−	0.563925i
$129$			19.2911i			1.69848i
$130$	1.77624	+	5.54528i	0.155787	+	0.486354i
$131$	2.98145			0.260491			0.130245	−	0.991482i	$-0.458423\pi$
$131$	2.98145			0.260491			0.130245	+	0.991482i	$0.458423\pi$
$132$	−0.318844	−	0.446637i	−0.0277518	−	0.0388747i
$133$		0			0
$134$	0.147879	−	0.0473681i	0.0127748	−	0.00409198i
$135$			4.08434i			0.351524i
$136$	9.12692	−	12.2373i	0.782627	−	1.04934i
$137$	−1.52475			−0.130268			−0.0651342	−	0.997877i	$-0.520748\pi$
$137$	−1.52475			−0.130268			−0.0651342	+	0.997877i	$0.520748\pi$
$138$	−5.56029	+	1.78105i	−0.473324	+	0.151613i
$139$	7.16082			0.607373			0.303686	−	0.952772i	$-0.401783\pi$
$139$	7.16082			0.607373			0.303686	+	0.952772i	$0.401783\pi$
$140$		0			0
$141$	12.1634			1.02434
$142$	9.06700	−	2.90430i	0.760885	−	0.243724i
$143$	−0.412736			−0.0345148
$144$	5.83687	−	16.9942i	0.486406	−	1.41619i
$145$			2.37688i			0.197389i
$146$	8.27880	−	2.65183i	0.685158	−	0.219467i
$147$		0			0
$148$	−1.69048	+	1.20680i	−0.138957	+	0.0991983i
$149$	−21.0473			−1.72426			−0.862129	−	0.506688i	$-0.830870\pi$
$149$	−21.0473			−1.72426			−0.862129	+	0.506688i	$0.830870\pi$
$150$	−1.18083	−	3.68646i	−0.0964145	−	0.300998i
$151$			3.82299i			0.311111i	0.987827	+	0.155555i	$0.0497167\pi$
$151$			3.82299i			0.311111i	−0.987827	+	0.155555i	$0.950283\pi$
$152$	−16.9123	−	12.6137i	−1.37177	−	1.02311i
$153$		−	24.2458i		−	1.96016i
$154$		0			0
$155$		−	5.44258i		−	0.437158i
$156$	−13.0961	−	18.3450i	−1.04853	−	1.46878i
$157$			1.28413i			0.102485i	0.998686	+	0.0512423i	$0.0163181\pi$
$157$			1.28413i			0.102485i	−0.998686	+	0.0512423i	$0.983682\pi$
$158$	5.75687	−	1.84402i	0.457992	−	0.146702i
$159$	−16.8135			−1.33339
$160$	−0.117927	+	5.65562i	−0.00932296	+	0.447116i
$161$		0			0
$162$	0.990900	+	3.09351i	0.0778525	+	0.243049i
$163$		−	8.60108i		−	0.673689i	−0.941560	−	0.336844i	$-0.890640\pi$
$163$		−	8.60108i		−	0.673689i	0.941560	−	0.336844i	$-0.109360\pi$
$164$	−9.28612	−	13.0080i	−0.725124	−	1.01575i
$165$	0.274384			0.0213607
$166$	2.80481	+	8.75639i	0.217696	+	0.679627i
$167$	−8.10448			−0.627144			−0.313572	−	0.949565i	$-0.601526\pi$
$167$	−8.10448			−0.627144			−0.313572	+	0.949565i	$0.601526\pi$
$168$		0			0
$169$	−3.95261			−0.304047
$170$	2.32844	+	7.26919i	0.178583	+	0.557522i
$171$	−33.5086			−2.56247
$172$	8.18977	+	11.4722i	0.624464	+	0.874750i
$173$		−	8.03376i		−	0.610795i	−0.952225	−	0.305398i	$-0.901211\pi$
$173$		−	8.03376i		−	0.610795i	0.952225	−	0.305398i	$-0.0987894\pi$
$174$	−2.80670	−	8.76228i	−0.212775	−	0.664267i
$175$		0			0
$176$	−0.379228	−	0.130250i	−0.0285854	−	0.00981797i
$177$	23.3289			1.75351
$178$	−4.29872	+	1.37695i	−0.322203	+	0.103207i
$179$			8.84857i			0.661373i	0.943741	+	0.330687i	$0.107280\pi$
$179$			8.84857i			0.661373i	−0.943741	+	0.330687i	$0.892720\pi$
$180$	5.22007	+	7.31227i	0.389081	+	0.545024i
$181$			21.3610i			1.58775i	0.608082	+	0.793874i	$0.291939\pi$
$181$			21.3610i			1.58775i	−0.608082	+	0.793874i	$0.708061\pi$
$182$		0			0
$183$		−	21.6316i		−	1.59905i
$184$	−2.55054	+	3.41973i	−0.188028	+	0.252106i
$185$		−	1.03852i		−	0.0763536i
$186$	6.42677	+	20.0638i	0.471234	+	1.47115i
$187$	−0.541047			−0.0395653
$188$	7.23347	−	5.16381i	0.527555	−	0.376610i
$189$		0			0
$190$	10.0463	−	3.21799i	0.728835	−	0.233457i
$191$		−	25.0235i		−	1.81063i	−0.424736	−	0.905317i	$-0.639633\pi$
$191$		−	25.0235i		−	1.81063i	0.424736	−	0.905317i	$-0.360367\pi$
$192$	−6.24361	−	20.9885i	−0.450594	−	1.51471i
$193$	8.16157			0.587483			0.293741	−	0.955885i	$-0.405100\pi$
$193$	8.16157			0.587483			0.293741	+	0.955885i	$0.405100\pi$
$194$	14.9079	−	4.77525i	1.07033	−	0.342843i
$195$	11.2700			0.807058
$196$		0			0
$197$	−12.4517			−0.887149			−0.443574	−	0.896238i	$-0.646290\pi$
$197$	−12.4517			−0.887149			−0.443574	+	0.896238i	$0.646290\pi$
$198$	−0.606480	+	0.194265i	−0.0431006	+	0.0138058i
$199$	23.1734			1.64272			0.821358	−	0.570413i	$-0.193217\pi$
$199$	23.1734			1.64272			0.821358	+	0.570413i	$0.193217\pi$
$200$	−2.26727	−	1.69100i	−0.160320	−	0.119572i
$201$		−	0.300542i		−	0.0211986i
$202$	9.64840	−	3.09054i	0.678859	−	0.217449i
$203$		0			0
$204$	−17.1674	−	24.0481i	−1.20196	−	1.68370i
$205$	7.99125			0.558133
$206$	2.10787	+	6.58061i	0.146863	+	0.458493i
$207$			6.77555i			0.470933i
$208$	−15.5763	−	5.34985i	−1.08002	−	0.370946i
$209$			0.747747i			0.0517228i
$210$		0			0
$211$		−	10.9759i		−	0.755613i	−0.925885	−	0.377807i	$-0.876678\pi$
$211$		−	10.9759i		−	0.755613i	0.925885	−	0.377807i	$-0.123322\pi$
$212$	−9.99883	+	7.13794i	−0.686722	+	0.490236i
$213$		−	18.4273i		−	1.26262i
$214$	10.1936	−	3.26518i	0.696820	−	0.223203i
$215$	−7.04778			−0.480654
$216$	−9.26031	−	6.90663i	−0.630084	−	0.469936i
$217$		0			0
$218$	7.78824	+	24.3142i	0.527486	+	1.64677i
$219$		−	16.8254i		−	1.13696i
$220$	0.163174	−	0.116486i	0.0110012	−	0.00785350i
$221$	−22.2228			−1.49487
$222$	1.22632	+	3.82846i	0.0823051	+	0.256950i
$223$	14.9798			1.00312			0.501559	−	0.865123i	$-0.332760\pi$
$223$	14.9798			1.00312			0.501559	+	0.865123i	$0.332760\pi$
$224$		0			0
$225$	−4.49217			−0.299478
$226$	7.82704	+	24.4354i	0.520647	+	1.62542i
$227$	1.50742			0.100051			0.0500254	−	0.998748i	$-0.484070\pi$
$227$	1.50742			0.100051			0.0500254	+	0.998748i	$0.484070\pi$
$228$	−33.2353	+	23.7260i	−2.20106	+	1.57129i
$229$			8.52548i			0.563380i	0.959505	+	0.281690i	$0.0908949\pi$
$229$			8.52548i			0.563380i	−0.959505	+	0.281690i	$0.909105\pi$
$230$	−0.650688	−	2.03139i	−0.0429051	−	0.133946i
$231$		0			0
$232$	−5.38904	−	4.01931i	−0.353808	−	0.263881i
$233$	−21.2233			−1.39039			−0.695193	−	0.718823i	$-0.744681\pi$
$233$	−21.2233			−1.39039			−0.695193	+	0.718823i	$0.744681\pi$
$234$	−24.9104	+	7.97919i	−1.62844	+	0.521616i
$235$			4.44376i			0.289879i
$236$	13.8735	−	9.90400i	0.903090	−	0.644696i
$237$		−	11.7000i		−	0.759994i
$238$		0			0
$239$			10.1532i			0.656754i	0.944547	+	0.328377i	$0.106502\pi$
$239$			10.1532i			0.656754i	−0.944547	+	0.328377i	$0.893498\pi$
$240$	10.3550	+	3.55654i	0.668412	+	0.229574i
$241$		−	19.0508i		−	1.22717i	−0.789629	−	0.613584i	$-0.789727\pi$
$241$		−	19.0508i		−	1.22717i	0.789629	−	0.613584i	$-0.210273\pi$
$242$	−4.74111	−	14.8013i	−0.304770	−	0.951467i
$243$	18.5401			1.18935
$244$	−9.18342	−	12.8641i	−0.587908	−	0.823542i
$245$		0			0
$246$	−29.4594	+	9.43632i	−1.87826	+	0.601638i
$247$			30.7127i			1.95420i
$248$	12.3398	+	9.20340i	0.783578	+	0.584417i
$249$	17.7960			1.12778
$250$	1.34681	−	0.431404i	0.0851796	−	0.0272844i
$251$	−9.46184			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$251$	−9.46184			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$252$		0			0
$253$	0.151197			0.00950567
$254$	−5.89326	+	1.88771i	−0.369776	+	0.118445i
$255$	14.7735			0.925155
$256$	−12.6234	−	9.83104i	−0.788964	−	0.614440i
$257$			2.74541i			0.171254i	0.996327	+	0.0856270i	$0.0272893\pi$
$257$			2.74541i			0.171254i	−0.996327	+	0.0856270i	$0.972711\pi$
$258$	25.9813	−	8.32224i	1.61753	−	0.518120i
$259$		0			0
$260$	6.70215	−	4.78452i	0.415650	−	0.296723i
$261$	−10.6774			−0.660912
$262$	−1.28621	−	4.01544i	−0.0794624	−	0.248075i
$263$			25.6767i			1.58330i	0.610978	+	0.791648i	$0.290777\pi$
$263$			25.6767i			1.58330i	−0.610978	+	0.791648i	$0.709223\pi$
$264$	−0.463983	+	0.622102i	−0.0285562	+	0.0382877i
$265$		−	6.14261i		−	0.377338i
$266$		0			0
$267$			8.73650i			0.534665i
$268$	−0.127592	−	0.178730i	−0.00779389	−	0.0109177i
$269$		−	8.19999i		−	0.499962i	−0.968251	−	0.249981i	$-0.919576\pi$
$269$		−	8.19999i		−	0.499962i	0.968251	−	0.249981i	$-0.0804244\pi$
$270$	5.50082	−	1.76200i	0.334769	−	0.107232i
$271$	−6.40727			−0.389214			−0.194607	−	0.980881i	$-0.562343\pi$
$271$	−6.40727			−0.389214			−0.194607	+	0.980881i	$0.562343\pi$
$272$	−20.4186	−	7.01301i	−1.23806	−	0.425226i
$273$		0			0
$274$	0.657785	+	2.05355i	0.0397382	+	0.124059i
$275$			0.100243i			0.00604489i
$276$	4.79747	+	6.72029i	0.288774	+	0.404514i
$277$	15.9691			0.959492			0.479746	−	0.877407i	$-0.340729\pi$
$277$	15.9691			0.959492			0.479746	+	0.877407i	$0.340729\pi$
$278$	−3.08921	−	9.64424i	−0.185278	−	0.578423i
$279$	24.4490			1.46372
$280$		0			0
$281$	−9.68409			−0.577704			−0.288852	−	0.957374i	$-0.593274\pi$
$281$	−9.68409			−0.577704			−0.288852	+	0.957374i	$0.593274\pi$
$282$	−5.24733	−	16.3817i	−0.312474	−	0.975518i
$283$	−26.1267			−1.55307			−0.776535	−	0.630074i	$-0.783025\pi$
$283$	−26.1267			−1.55307			−0.776535	+	0.630074i	$0.783025\pi$
$284$	−7.82308	−	10.9586i	−0.464214	−	0.650271i
$285$		−	20.4176i		−	1.20943i
$286$	0.178056	+	0.555877i	0.0105287	+	0.0328697i
$287$		0			0
$288$	−25.4060	−	0.529749i	−1.49706	−	0.0312158i
$289$	−12.1314			−0.713611
$290$	3.20120	−	1.02540i	0.187981	−	0.0602134i
$291$		−	30.2981i		−	1.77611i
$292$	−7.14302	−	10.0059i	−0.418013	−	0.585553i
$293$		−	16.2389i		−	0.948684i	−0.880341	−	0.474342i	$-0.842686\pi$
$293$		−	16.2389i		−	0.948684i	0.880341	−	0.474342i	$-0.157314\pi$
$294$		0			0
$295$			8.52297i			0.496226i
$296$	2.35461	+	1.75614i	0.136859	+	0.102074i
$297$			0.409427i			0.0237574i
$298$	9.07987	+	28.3466i	0.525983	+	1.64207i
$299$	6.21022			0.359146
$300$	−4.45553	+	3.18071i	−0.257240	+	0.183638i
$301$		0			0
$302$	5.14883	−	1.64925i	0.296282	−	0.0949039i
$303$		−	19.6089i		−	1.12650i
$304$	−9.69223	+	28.2193i	−0.555888	+	1.61849i
$305$	7.90286			0.452517
$306$	−32.6544	+	10.4597i	−1.86673	+	0.597944i
$307$	−23.5437			−1.34371			−0.671854	−	0.740684i	$-0.734502\pi$
$307$	−23.5437			−1.34371			−0.671854	+	0.740684i	$0.734502\pi$
$308$		0			0
$309$	13.3741			0.760825
$310$	−7.33010	+	2.34795i	−0.416322	+	0.133355i
$311$	5.39546			0.305949			0.152974	−	0.988230i	$-0.451115\pi$
$311$	5.39546			0.305949			0.152974	+	0.988230i	$0.451115\pi$
$312$	−19.0575	+	25.5520i	−1.07892	+	1.44660i
$313$			32.5614i			1.84048i	0.391355	+	0.920240i	$0.372007\pi$
$313$			32.5614i			1.84048i	−0.391355	+	0.920240i	$0.627993\pi$
$314$	1.72948	−	0.553979i	0.0975999	−	0.0312628i
$315$		0			0
$316$	−4.96707	−	6.95787i	−0.279420	−	0.391411i
$317$	13.7117			0.770128			0.385064	−	0.922890i	$-0.374179\pi$
$317$	13.7117			0.770128			0.385064	+	0.922890i	$0.374179\pi$
$318$	7.25339	+	22.6445i	0.406750	+	1.26984i
$319$			0.238266i			0.0133403i
$320$	7.66791	−	2.28103i	0.428649	−	0.127514i
$321$		−	20.7170i		−	1.15631i
$322$		0			0
$323$			40.2606i			2.24016i
$324$	3.73888	−	2.66910i	0.207716	−	0.148284i
$325$			4.11735i			0.228390i
$326$	−11.5840	+	3.71054i	−0.641578	+	0.205508i
$327$	49.4150			2.73266
$328$	−13.5132	+	18.1183i	−0.746142	+	1.00042i
$329$		0			0
$330$	−0.118370	−	0.369542i	−0.00651607	−	0.0203426i
$331$		−	5.68684i		−	0.312577i	−0.987711	−	0.156289i	$-0.950047\pi$
$331$		−	5.68684i		−	0.312577i	0.987711	−	0.156289i	$-0.0499530\pi$
$332$	10.5832	−	7.55508i	0.580826	−	0.414639i
$333$	4.66521			0.255652
$334$	3.49631	+	10.9152i	0.191309	+	0.597252i
$335$	0.109800			0.00599901
$336$		0			0
$337$	−14.7219			−0.801955			−0.400978	−	0.916088i	$-0.631330\pi$
$337$	−14.7219			−0.801955			−0.400978	+	0.916088i	$0.631330\pi$
$338$	1.70517	+	5.32341i	0.0927492	+	0.289555i
$339$	49.6612			2.69723
$340$	8.78570	−	6.27192i	0.476472	−	0.340142i
$341$		−	0.545581i		−	0.0295449i
$342$	14.4557	+	45.1296i	0.781677	+	2.44033i
$343$		0			0
$344$	11.9178	−	15.9792i	0.642564	−	0.861542i
$345$	−4.12850			−0.222271
$346$	−10.8199	+	3.46580i	−0.581683	+	0.186322i
$347$		−	15.4691i		−	0.830424i	−0.909725	−	0.415212i	$-0.863707\pi$
$347$		−	15.4691i		−	0.830424i	0.909725	−	0.415212i	$-0.136293\pi$
$348$	−10.5903	+	7.56016i	−0.567699	+	0.405267i
$349$			11.5290i			0.617132i	0.951203	+	0.308566i	$0.0998491\pi$
$349$			11.5290i			0.617132i	−0.951203	+	0.308566i	$0.900151\pi$
$350$		0			0
$351$			16.8167i			0.897608i
$352$	−0.0118214	+	0.566937i	−0.000630082	+	0.0302179i
$353$		−	20.4362i		−	1.08771i	−0.839179	−	0.543855i	$-0.816964\pi$
$353$		−	20.4362i		−	1.08771i	0.839179	−	0.543855i	$-0.183036\pi$
$354$	−10.0642	−	31.4196i	−0.534906	−	1.66993i
$355$	6.73221			0.357309
$356$	3.70897	+	5.19553i	0.196575	+	0.275362i
$357$		0			0
$358$	11.9173	−	3.81731i	0.629850	−	0.201751i
$359$			21.2189i			1.11989i	0.828529	+	0.559946i	$0.189178\pi$
$359$			21.2189i			1.11989i	−0.828529	+	0.559946i	$0.810822\pi$
$360$	7.59626	−	10.1850i	0.400358	−	0.536795i
$361$	36.6417			1.92851
$362$	28.7691	−	9.21521i	1.51207	−	0.484341i
$363$	−30.0815			−1.57887
$364$		0			0
$365$	6.14698			0.321748
$366$	−29.1336	+	9.33195i	−1.52284	+	0.487789i
$367$	−7.65147			−0.399404			−0.199702	−	0.979857i	$-0.563997\pi$
$367$	−7.65147			−0.399404			−0.199702	+	0.979857i	$0.563997\pi$
$368$	5.70603	+	1.95980i	0.297447	+	0.102162i
$369$			35.8980i			1.86878i
$370$	−1.39869	+	0.448022i	−0.0727143	+	0.0232916i
$371$		0			0
$372$	24.2496	−	17.3112i	1.25728	−	0.897546i
$373$	25.6343			1.32729			0.663647	−	0.748046i	$-0.269008\pi$
$373$	25.6343			1.32729			0.663647	+	0.748046i	$0.269008\pi$
$374$	0.233410	+	0.728686i	0.0120693	+	0.0376795i
$375$		−	2.73718i		−	0.141348i
$376$	−10.0752	−	7.51440i	−0.519589	−	0.387526i
$377$			9.78647i			0.504029i
$378$		0			0
$379$		−	29.1039i		−	1.49497i	−0.664279	−	0.747485i	$-0.731261\pi$
$379$		−	29.1039i		−	1.49497i	0.664279	−	0.747485i	$-0.268739\pi$
$380$	−8.66802	−	12.1422i	−0.444660	−	0.622880i
$381$			11.9772i			0.613609i
$382$	−33.7018	+	10.7952i	−1.72433	+	0.552332i
$383$	−8.64322			−0.441648			−0.220824	−	0.975314i	$-0.570875\pi$
$383$	−8.64322			−0.441648			−0.220824	+	0.975314i	$0.570875\pi$
$384$	−25.5739	+	17.4635i	−1.30506	+	0.891178i
$385$		0			0
$386$	−3.52093	−	10.9921i	−0.179211	−	0.559481i
$387$		−	31.6598i		−	1.60936i
$388$	−12.8627	−	18.0180i	−0.653004	−	0.914728i
$389$	−14.1769			−0.718799			−0.359399	−	0.933184i	$-0.617018\pi$
$389$	−14.1769			−0.718799			−0.359399	+	0.933184i	$0.617018\pi$
$390$	−4.86190	−	15.1785i	−0.246192	−	0.768591i
$391$	8.14084			0.411700
$392$		0			0
$393$	−8.16078			−0.411657
$394$	5.37173	+	16.7701i	0.270624	+	0.844864i
$395$	4.27445			0.215071
$396$	0.523276	+	0.733005i	0.0262956	+	0.0368349i
$397$			0.175006i			0.00878329i	0.999990	+	0.00439164i	$0.00139791\pi$
$397$			0.175006i			0.00878329i	−0.999990	+	0.00439164i	$0.998602\pi$
$398$	−9.99708	−	31.2101i	−0.501108	−	1.56442i
$399$		0			0
$400$	−1.29934	+	3.78308i	−0.0649671	+	0.189154i
$401$	24.0570			1.20135			0.600674	−	0.799494i	$-0.294899\pi$
$401$	24.0570			1.20135			0.600674	+	0.799494i	$0.294899\pi$
$402$	−0.404773	+	0.129655i	−0.0201882	+	0.00646662i
$403$		−	22.4090i		−	1.11627i
$404$	−8.32472	−	11.6613i	−0.414170	−	0.580170i
$405$			2.29692i			0.114135i
$406$		0			0
$407$		−	0.104105i		−	0.00516027i
$408$	−24.9821	+	33.4956i	−1.23680	+	1.65828i
$409$			11.9364i			0.590215i	0.955464	+	0.295108i	$0.0953555\pi$
$409$			11.9364i			0.590215i	−0.955464	+	0.295108i	$0.904644\pi$
$410$	−3.44746	−	10.7627i	−0.170258	−	0.531531i
$411$	4.17353			0.205865
$412$	7.95347	−	5.67780i	0.391839	−	0.279725i
$413$		0			0
$414$	9.12536	−	2.92300i	0.448487	−	0.143658i
$415$			6.50159i			0.319150i
$416$	−0.485548	+	23.2862i	−0.0238060	+	1.14170i
$417$	−19.6005			−0.959839
$418$	1.00707	−	0.322581i	0.0492575	−	0.0157780i
$419$	30.1003			1.47050			0.735249	−	0.677798i	$-0.237065\pi$
$419$	30.1003			1.47050			0.735249	+	0.677798i	$0.237065\pi$
$420$		0			0
$421$	6.78256			0.330562			0.165281	−	0.986247i	$-0.447147\pi$
$421$	6.78256			0.330562			0.165281	+	0.986247i	$0.447147\pi$
$422$	−14.7824	+	4.73505i	−0.719598	+	0.230499i
$423$	−19.9621			−0.970592
$424$	13.9270	+	10.3872i	0.676353	+	0.504445i
$425$			5.39735i			0.261810i
$426$	−24.8180	+	7.94961i	−1.20244	+	0.385160i
$427$		0			0
$428$	−8.79513	−	12.3202i	−0.425128	−	0.595520i
$429$	1.12974			0.0545441
$430$	3.04044	+	9.49200i	0.146623	+	0.457745i
$431$		−	15.9360i		−	0.767612i	−0.923414	−	0.383806i	$-0.874613\pi$
$431$		−	15.9360i		−	0.767612i	0.923414	−	0.383806i	$-0.125387\pi$
$432$	−5.30696	+	15.4514i	−0.255331	+	0.743406i
$433$			15.1291i			0.727057i	0.931583	+	0.363529i	$0.118428\pi$
$433$			15.1291i			0.727057i	−0.931583	+	0.363529i	$0.881572\pi$
$434$		0			0
$435$		−	6.50596i		−	0.311937i
$436$	29.3867	−	20.9785i	1.40737	−	1.00469i
$437$		−	11.2509i		−	0.538205i
$438$	−22.6606	+	7.25855i	−1.08276	+	0.346827i
$439$	4.36674			0.208413			0.104207	−	0.994556i	$-0.466770\pi$
$439$	4.36674			0.208413			0.104207	+	0.994556i	$0.466770\pi$
$440$	−0.227278	−	0.169511i	−0.0108351	−	0.00808113i
$441$		0			0
$442$	9.58701	+	29.9298i	0.456007	+	1.42362i
$443$		−	14.0982i		−	0.669825i	−0.942249	−	0.334913i	$-0.891293\pi$
$443$		−	14.0982i		−	0.669825i	0.942249	−	0.334913i	$-0.108707\pi$
$444$	4.62717	−	3.30323i	0.219596	−	0.156764i
$445$	−3.19179			−0.151305
$446$	−6.46233	−	20.1748i	−0.306000	−	0.955307i
$447$	57.6102			2.72487
$448$		0			0
$449$	17.0120			0.802848			0.401424	−	0.915892i	$-0.368515\pi$
$449$	17.0120			0.802848			0.401424	+	0.915892i	$0.368515\pi$
$450$	1.93794	+	6.05009i	0.0913554	+	0.285204i
$451$	0.801068			0.0377208
$452$	29.5331	−	21.0830i	1.38912	−	0.991663i
$453$		−	10.4642i		−	0.491652i
$454$	−0.650306	−	2.03020i	−0.0305204	−	0.0952820i
$455$		0			0
$456$	46.2922	+	34.5261i	2.16783	+	1.61683i
$457$	11.6647			0.545651			0.272825	−	0.962064i	$-0.412042\pi$
$457$	11.6647			0.545651			0.272825	+	0.962064i	$0.412042\pi$
$458$	11.4822	−	3.67793i	0.536527	−	0.171858i
$459$			22.0446i			1.02895i
$460$	−2.45519	+	1.75270i	−0.114474	+	0.0817202i
$461$		−	26.4488i		−	1.23184i	−0.787808	−	0.615921i	$-0.788784\pi$
$461$		−	26.4488i		−	1.23184i	0.787808	−	0.615921i	$-0.211216\pi$
$462$		0			0
$463$		−	3.13685i		−	0.145782i	−0.997340	−	0.0728909i	$-0.976778\pi$
$463$		−	3.13685i		−	0.145782i	0.997340	−	0.0728909i	$-0.0232225\pi$
$464$	−3.08838	+	8.99194i	−0.143375	+	0.417440i
$465$			14.8973i			0.690847i
$466$	9.15583	+	28.5837i	0.424136	+	1.32412i
$467$	8.14113			0.376727			0.188363	−	0.982099i	$-0.439682\pi$
$467$	8.14113			0.376727			0.188363	+	0.982099i	$0.439682\pi$
$468$	21.4929	+	30.1072i	0.993508	+	1.39171i
$469$		0			0
$470$	5.98489	−	1.91706i	0.276062	−	0.0884272i
$471$		−	3.51490i		−	0.161958i
$472$	−19.3239	−	14.4123i	−0.889454	−	0.663382i
$473$	−0.706491			−0.0324845
$474$	−15.7576	+	5.04741i	−0.723770	+	0.231835i
$475$	7.45934			0.342258
$476$		0			0
$477$	27.5937			1.26343
$478$	13.6744	−	4.38012i	0.625451	−	0.200342i
$479$	−24.7807			−1.13226			−0.566131	−	0.824316i	$-0.691560\pi$
$479$	−24.7807			−1.13226			−0.566131	+	0.824316i	$0.691560\pi$
$480$	0.322788	−	15.4805i	0.0147332	−	0.706584i
$481$		−	4.27596i		−	0.194967i
$482$	−25.6577	+	8.21858i	−1.16868	+	0.374346i
$483$		0			0
$484$	−17.8892	+	12.7707i	−0.813147	+	0.580487i
$485$	11.0691			0.502621
$486$	−7.99828	−	24.9700i	−0.362809	−	1.13266i
$487$		−	12.6945i		−	0.575244i	−0.957744	−	0.287622i	$-0.907135\pi$
$487$		−	12.6945i		−	0.575244i	0.957744	−	0.287622i	$-0.0928646\pi$
$488$	−13.3637	+	17.9179i	−0.604948	+	0.811107i
$489$			23.5427i			1.06464i
$490$		0			0
$491$		−	9.51192i		−	0.429267i	−0.976695	−	0.214633i	$-0.931144\pi$
$491$		−	9.51192i		−	0.429267i	0.976695	−	0.214633i	$-0.0688557\pi$
$492$	25.4178	+	35.6053i	1.14592	+	1.60521i
$493$			12.8289i			0.577783i
$494$	41.3641	−	13.2496i	1.86106	−	0.596128i
$495$	−0.450309			−0.0202399
$496$	7.07177	−	20.5897i	0.317532	−	0.924506i
$497$		0			0
$498$	−7.67728	−	23.9678i	−0.344027	−	1.07402i
$499$		−	8.49279i		−	0.380189i	−0.981766	−	0.190095i	$-0.939121\pi$
$499$		−	8.49279i		−	0.380189i	0.981766	−	0.190095i	$-0.0608795\pi$
$500$	−1.16204	−	1.62778i	−0.0519679	−	0.0727966i
$501$	22.1834			0.991083
$502$	4.08188	+	12.7433i	0.182183	+	0.568760i
$503$	−10.4796			−0.467261			−0.233630	−	0.972325i	$-0.575061\pi$
$503$	−10.4796			−0.467261			−0.233630	+	0.972325i	$0.575061\pi$
$504$		0			0
$505$	7.16390			0.318790
$506$	−0.0652270	−	0.203633i	−0.00289969	−	0.00905260i
$507$	10.8190			0.480490
$508$	5.08475	+	7.12272i	0.225599	+	0.316020i
$509$		−	22.8034i		−	1.01074i	−0.862902	−	0.505371i	$-0.831356\pi$
$509$		−	22.8034i		−	1.01074i	0.862902	−	0.505371i	$-0.168644\pi$
$510$	−6.37336	−	19.8971i	−0.282217	−	0.881059i
$511$		0			0
$512$	−7.79472	+	21.2425i	−0.344481	+	0.938793i
$513$	30.4665			1.34513
$514$	3.69754	−	1.18438i	0.163091	−	0.0522408i
$515$			4.88608i			0.215306i
$516$	−22.4169	−	31.4016i	−0.986849	−	1.38238i
$517$			0.445456i			0.0195912i
$518$		0			0
$519$			21.9899i			0.965248i
$520$	−9.33516	−	6.96245i	−0.409374	−	0.305324i
$521$			9.09960i			0.398661i	0.979932	+	0.199330i	$0.0638767\pi$
$521$			9.09960i			0.398661i	−0.979932	+	0.199330i	$0.936123\pi$
$522$	4.60626	+	14.3803i	0.201610	+	0.629411i
$523$	−4.76095			−0.208182			−0.104091	−	0.994568i	$-0.533193\pi$
$523$	−4.76095			−0.208182			−0.104091	+	0.994568i	$0.533193\pi$
$524$	−4.85315	+	3.46456i	−0.212011	+	0.151350i
$525$		0			0
$526$	34.5816	−	11.0771i	1.50783	−	0.482982i
$527$		−	29.3755i		−	1.27962i
$528$	1.03802	+	0.356518i	0.0451739	+	0.0155155i
$529$	20.7250			0.901088
$530$	−8.27292	+	2.64995i	−0.359353	+	0.115106i
$531$	−38.2866			−1.66150
$532$		0			0
$533$	32.9028			1.42518
$534$	11.7664	−	3.76896i	0.509181	−	0.163099i
$535$	7.56872			0.327224
$536$	−0.185672	+	0.248946i	−0.00801980	+	0.0107528i
$537$		−	24.2202i		−	1.04518i
$538$	−11.0438	+	3.53751i	−0.476133	+	0.152513i
$539$		0			0
$540$	−4.74615	−	6.64842i	−0.204242	−	0.286102i
$541$	−22.4624			−0.965734			−0.482867	−	0.875694i	$-0.660405\pi$
$541$	−22.4624			−0.965734			−0.482867	+	0.875694i	$0.660405\pi$
$542$	2.76412	+	8.62936i	0.118729	+	0.370663i
$543$		−	58.4689i		−	2.50914i
$544$	−0.636494	+	30.5254i	−0.0272895	+	1.30877i
$545$			18.0532i			0.773316i
$546$		0			0
$547$			24.4644i			1.04602i	0.852326	+	0.523012i	$0.175192\pi$
$547$			24.4644i			1.04602i	−0.852326	+	0.523012i	$0.824808\pi$
$548$	2.48196	−	1.77182i	0.106024	−	0.0756884i
$549$			35.5010i			1.51515i
$550$	0.135008	−	0.0432453i	0.00575677	−	0.00184399i
$551$	17.7300			0.755322
$552$	6.98130	−	9.36043i	0.297144	−	0.398406i
$553$		0			0
$554$	−6.88915	−	21.5073i	−0.292692	−	0.913759i
$555$			2.84262i			0.120663i
$556$	−11.6562	+	8.32113i	−0.494335	+	0.352895i
$557$	−8.43255			−0.357299			−0.178649	−	0.983913i	$-0.557173\pi$
$557$	−8.43255			−0.357299			−0.178649	+	0.983913i	$0.557173\pi$
$558$	−10.5474	−	32.9281i	−0.446507	−	1.39396i
$559$	−29.0182			−1.22734
$560$		0			0
$561$	1.48095			0.0625255
$562$	4.17775	+	13.0426i	0.176228	+	0.550169i
$563$	−27.1665			−1.14493			−0.572467	−	0.819928i	$-0.694013\pi$
$563$	−27.1665			−1.14493			−0.572467	+	0.819928i	$0.694013\pi$
$564$	−19.7993	+	14.1343i	−0.833702	+	0.595161i
$565$			18.1432i			0.763289i
$566$	11.2712	+	35.1876i	0.473762	+	1.47905i
$567$		0			0
$568$	−11.3842	+	15.2638i	−0.477669	+	0.640453i
$569$	14.2329			0.596672			0.298336	−	0.954461i	$-0.403568\pi$
$569$	14.2329			0.596672			0.298336	+	0.954461i	$0.403568\pi$
$570$	−27.4985	+	8.80822i	−1.15179	+	0.368936i
$571$			16.8436i			0.704884i	0.935834	+	0.352442i	$0.114649\pi$
$571$			16.8436i			0.704884i	−0.935834	+	0.352442i	$0.885351\pi$
$572$	0.671845	−	0.479615i	0.0280912	−	0.0200537i
$573$			68.4938i			2.86137i
$574$		0			0
$575$		−	1.50830i		−	0.0629006i
$576$	10.2468	+	34.4456i	0.426950	+	1.43523i
$577$		−	2.15337i		−	0.0896459i	−0.998995	−	0.0448230i	$-0.985728\pi$
$577$		−	2.15337i		−	0.0896459i	0.998995	−	0.0448230i	$-0.0142724\pi$
$578$	5.23353	+	16.3386i	0.217686	+	0.679598i
$579$	−22.3397			−0.928407
$580$	−2.76202	−	3.86904i	−0.114687	−	0.160653i
$581$		0			0
$582$	−40.8057	+	13.0707i	−1.69145	+	0.541799i
$583$		−	0.615755i		−	0.0255020i
$584$	−10.3945	+	13.9369i	−0.430129	+	0.576712i
$585$	−18.4959			−0.764710
$586$	−21.8706	+	7.00551i	−0.903467	+	0.289395i
$587$	−11.3061			−0.466652			−0.233326	−	0.972399i	$-0.574961\pi$
$587$	−11.3061			−0.466652			−0.233326	+	0.972399i	$0.574961\pi$
$588$		0			0
$589$	−40.5980			−1.67281
$590$	11.4788	−	3.67684i	0.472575	−	0.151373i
$591$	34.0827			1.40197
$592$	1.34939	−	3.92881i	0.0554598	−	0.161473i
$593$			17.0399i			0.699744i	0.936798	+	0.349872i	$0.113775\pi$
$593$			17.0399i			0.699744i	−0.936798	+	0.349872i	$0.886225\pi$
$594$	0.551420	−	0.176629i	0.0226250	−	0.00724716i
$595$		0			0
$596$	34.2603	−	24.4577i	1.40336	−	1.00183i
$597$	−63.4297			−2.59601
$598$	−2.67911	−	8.36397i	−0.109557	−	0.342028i
$599$		−	3.92441i		−	0.160347i	−0.996781	−	0.0801736i	$-0.974453\pi$
$599$		−	3.92441i		−	0.160347i	0.996781	−	0.0801736i	$-0.0255475\pi$
$600$	6.20593	+	4.62858i	0.253356	+	0.188961i
$601$			8.98026i			0.366312i	0.983084	+	0.183156i	$0.0586314\pi$
$601$			8.98026i			0.366312i	−0.983084	+	0.183156i	$0.941369\pi$
$602$		0			0
$603$			0.493240i			0.0200863i
$604$	−4.44245	−	6.22299i	−0.180761	−	0.253210i
$605$		−	10.9900i		−	0.446805i
$606$	−26.4094	+	8.45937i	−1.07281	+	0.343638i
$607$	−37.5791			−1.52529			−0.762644	−	0.646819i	$-0.776099\pi$
$607$	−37.5791			−1.52529			−0.762644	+	0.646819i	$0.776099\pi$
$608$	42.1872	+	0.879659i	1.71092	+	0.0356749i
$609$		0			0
$610$	−3.40933	−	10.6436i	−0.138040	−	0.430948i
$611$			18.2965i			0.740199i
$612$	28.1745	+	39.4669i	1.13889	+	1.59535i
$613$	−46.2598			−1.86841			−0.934207	−	0.356731i	$-0.883891\pi$
$613$	−46.2598			−1.86841			−0.934207	+	0.356731i	$0.883891\pi$
$614$	10.1568	+	31.7088i	0.409896	+	1.27966i
$615$	−21.8735			−0.882025
$616$		0			0
$617$	−42.8844			−1.72646			−0.863231	−	0.504809i	$-0.831563\pi$
$617$	−42.8844			−1.72646			−0.863231	+	0.504809i	$0.831563\pi$
$618$	−5.76964	−	18.0123i	−0.232089	−	0.724562i
$619$	29.5006			1.18573			0.592865	−	0.805302i	$-0.297997\pi$
$619$	29.5006			1.18573			0.592865	+	0.805302i	$0.297997\pi$
$620$	6.32447	+	8.85932i	0.253997	+	0.355799i
$621$		−	6.16042i		−	0.247209i
$622$	−2.32762	−	7.26665i	−0.0933293	−	0.291366i
$623$		0			0
$624$	42.6352	+	14.6435i	1.70677	+	0.586210i
$625$	1.00000			0.0400000
$626$	43.8540	−	14.0471i	1.75276	−	0.561436i
$627$		−	2.04672i		−	0.0817381i
$628$	−1.49221	−	2.09028i	−0.0595455	−	0.0834113i
$629$		−	5.60526i		−	0.223496i
$630$		0			0
$631$		−	20.5872i		−	0.819563i	−0.912184	−	0.409781i	$-0.865605\pi$
$631$		−	20.5872i		−	0.819563i	0.912184	−	0.409781i	$-0.134395\pi$
$632$	−7.22810	+	9.69134i	−0.287518	+	0.385501i
$633$			30.0431i			1.19411i
$634$	−5.91530	−	18.4671i	−0.234927	−	0.733422i
$635$	−4.37573			−0.173645
$636$	27.3686	−	19.5378i	1.08524	−	0.774726i
$637$		0			0
$638$	0.320899	−	0.102789i	0.0127045	−	0.00406945i
$639$			30.2422i			1.19636i
$640$	−6.38008	−	9.34315i	−0.252195	−	0.369321i
$641$	−36.8526			−1.45559			−0.727795	−	0.685794i	$-0.759455\pi$
$641$	−36.8526			−1.45559			−0.727795	+	0.685794i	$0.759455\pi$
$642$	−27.9018	+	8.93738i	−1.10119	+	0.352730i
$643$	−48.4719			−1.91154			−0.955772	−	0.294108i	$-0.904977\pi$
$643$	−48.4719			−1.91154			−0.955772	+	0.294108i	$0.904977\pi$
$644$		0			0
$645$	19.2911			0.759585
$646$	54.2233	−	17.3686i	2.13339	−	0.683359i
$647$	−39.1866			−1.54058			−0.770292	−	0.637692i	$-0.779889\pi$
$647$	−39.1866			−1.54058			−0.770292	+	0.637692i	$0.779889\pi$
$648$	−5.20774	−	3.88409i	−0.204579	−	0.152581i
$649$			0.854369i			0.0335369i
$650$	5.54528	−	1.77624i	0.217504	−	0.0696700i
$651$		0			0
$652$	9.99477	+	14.0007i	0.391425	+	0.548309i
$653$	6.88323			0.269362			0.134681	−	0.990889i	$-0.456999\pi$
$653$	6.88323			0.269362			0.134681	+	0.990889i	$0.456999\pi$
$654$	−21.3178	−	66.5525i	−0.833593	−	2.60241i
$655$		−	2.98145i		−	0.116495i
$656$	30.2315	+	10.3834i	1.18034	+	0.405402i
$657$			27.6133i			1.07730i
$658$		0			0
$659$			40.9792i			1.59632i	0.602444	+	0.798161i	$0.294194\pi$
$659$			40.9792i			1.59632i	−0.602444	+	0.798161i	$0.705806\pi$
$660$	−0.446637	+	0.318844i	−0.0173853	+	0.0124110i
$661$		−	12.0892i		−	0.470216i	−0.971969	−	0.235108i	$-0.924456\pi$
$661$		−	12.0892i		−	0.470216i	0.971969	−	0.235108i	$-0.0755443\pi$
$662$	−7.65908	+	2.45333i	−0.297679	+	0.0953512i
$663$	60.8279			2.36236
$664$	−14.7409	−	10.9942i	−0.572056	−	0.426657i
$665$		0			0
$666$	−2.01259	−	6.28314i	−0.0779863	−	0.243467i
$667$		−	3.58506i		−	0.138814i
$668$	13.1923	−	9.41770i	0.510426	−	0.364382i
$669$	−41.0023			−1.58524
$670$	−0.0473681	−	0.147879i	−0.00182999	−	0.00571308i
$671$	0.792208			0.0305828
$672$		0			0
$673$	29.0006			1.11789			0.558945	−	0.829205i	$-0.311206\pi$
$673$	29.0006			1.11789			0.558945	+	0.829205i	$0.311206\pi$
$674$	6.35111	+	19.8276i	0.244635	+	0.763732i
$675$	4.08434			0.157206
$676$	6.43399	−	4.59308i	0.247461	−	0.176657i
$677$			48.3082i			1.85663i	0.371791	+	0.928317i	$0.378744\pi$
$677$			48.3082i			1.85663i	−0.371791	+	0.928317i	$0.621256\pi$
$678$	−21.4240	−	66.8841i	−0.822786	−	2.56867i
$679$		0			0
$680$	−12.2373	−	9.12692i	−0.469277	−	0.350001i
$681$	−4.12607			−0.158112
$682$	−0.734792	+	0.235366i	−0.0281367	+	0.00901262i
$683$		−	13.2246i		−	0.506026i	−0.967463	−	0.253013i	$-0.918579\pi$
$683$		−	13.2246i		−	0.506026i	0.967463	−	0.253013i	$-0.0814215\pi$
$684$	54.5447	−	38.9382i	2.08557	−	1.48884i
$685$			1.52475i			0.0582578i
$686$		0			0
$687$		−	23.3358i		−	0.890317i
$688$	−26.6623	−	9.15748i	−1.01649	−	0.349125i
$689$		−	25.2913i		−	0.963522i
$690$	1.78105	+	5.56029i	0.0678035	+	0.211677i
$691$	39.8895			1.51747			0.758733	−	0.651401i	$-0.225819\pi$
$691$	39.8895			1.51747			0.758733	+	0.651401i	$0.225819\pi$
$692$	9.33552	+	13.0772i	0.354883	+	0.497121i
$693$		0			0
$694$	−20.8339	+	6.67342i	−0.790843	+	0.253320i
$695$		−	7.16082i		−	0.271625i
$696$	14.7508	+	11.0016i	0.559127	+	0.417014i
$697$	43.1316			1.63372
$698$	15.5273	−	4.97365i	0.587718	−	0.188255i
$699$	58.0921			2.19725
$700$		0			0
$701$	−5.82647			−0.220063			−0.110031	−	0.993928i	$-0.535095\pi$
$701$	−5.82647			−0.220063			−0.110031	+	0.993928i	$0.535095\pi$
$702$	22.6488	−	7.25479i	0.854825	−	0.273814i
$703$	−7.74668			−0.292171
$704$	0.768655	−	0.228658i	0.0289698	−	0.00861787i
$705$		−	12.1634i		−	0.458100i
$706$	−27.5237	+	8.81627i	−1.03587	+	0.331805i
$707$		0			0
$708$	−37.9744	+	27.1091i	−1.42716	+	1.01882i
$709$	−16.5923			−0.623137			−0.311569	−	0.950224i	$-0.600854\pi$
$709$	−16.5923			−0.623137			−0.311569	+	0.950224i	$0.600854\pi$
$710$	−2.90430	−	9.06700i	−0.108997	−	0.340278i
$711$			19.2016i			0.720115i
$712$	5.39731	−	7.23664i	0.202273	−	0.271205i
$713$			8.20905i			0.307431i
$714$		0			0
$715$			0.412736i			0.0154355i
$716$	−10.2824	−	14.4035i	−0.384270	−	0.538285i
$717$		−	27.7911i		−	1.03788i
$718$	28.5778	−	9.15394i	1.06652	−	0.341622i
$719$	−3.39845			−0.126741			−0.0633704	−	0.997990i	$-0.520185\pi$
$719$	−3.39845			−0.126741			−0.0633704	+	0.997990i	$0.520185\pi$
$720$	−16.9942	−	5.83687i	−0.633338	−	0.217527i
$721$		0			0
$722$	−15.8074	−	49.3493i	−0.588290	−	1.83659i
$723$			52.1455i			1.93931i
$724$	−24.8222	−	34.7710i	−0.922511	−	1.29225i
$725$	2.37688			0.0882752
$726$	12.9773	+	40.5140i	0.481632	+	1.50362i
$727$	−14.3045			−0.530526			−0.265263	−	0.964176i	$-0.585459\pi$
$727$	−14.3045			−0.530526			−0.265263	+	0.964176i	$0.585459\pi$
$728$		0			0
$729$	−43.8569			−1.62433
$730$	−2.65183	−	8.27880i	−0.0981487	−	0.306412i
$731$	−38.0393			−1.40694
$732$	25.1367	+	35.2115i	0.929079	+	1.30145i
$733$		−	49.4913i		−	1.82800i	−0.405711	−	0.914001i	$-0.632976\pi$
$733$		−	49.4913i		−	1.82800i	0.405711	−	0.914001i	$-0.367024\pi$
$734$	3.30088	+	10.3051i	0.121838	+	0.380367i
$735$		0			0
$736$	0.177870	−	8.53039i	0.00655637	−	0.314434i
$737$	0.0110067			0.000405437
$738$	48.3478	−	15.4866i	1.77971	−	0.570068i
$739$			26.8103i			0.986234i	0.869963	+	0.493117i	$0.164143\pi$
$739$			26.8103i			0.986234i	−0.869963	+	0.493117i	$0.835857\pi$
$740$	1.20680	+	1.69048i	0.0443628	+	0.0621435i
$741$		−	84.0664i		−	3.08826i
$742$		0			0
$743$		−	22.2896i		−	0.817727i	−0.912596	−	0.408863i	$-0.865925\pi$
$743$		−	22.2896i		−	0.817727i	0.912596	−	0.408863i	$-0.134075\pi$
$744$	−33.7763	−	25.1914i	−1.23830	−	0.923561i
$745$			21.0473i			0.771112i
$746$	−11.0587	−	34.5245i	−0.404890	−	1.26403i
$747$	−29.2062			−1.06860
$748$	0.880706	−	0.628717i	0.0322018	−	0.0229882i
$749$		0			0
$750$	−3.68646	+	1.18083i	−0.134610	+	0.0431179i
$751$		−	12.8665i		−	0.469505i	−0.972055	−	0.234752i	$-0.924572\pi$
$751$		−	12.8665i		−	0.469505i	0.972055	−	0.234752i	$-0.0754279\pi$
$752$	−5.77397	+	16.8111i	−0.210555	+	0.613038i
$753$	25.8988			0.943804
$754$	13.1805	−	4.22192i	0.480005	−	0.153753i
$755$	3.82299			0.139133
$756$		0			0
$757$	−3.66830			−0.133327			−0.0666633	−	0.997776i	$-0.521235\pi$
$757$	−3.66830			−0.133327			−0.0666633	+	0.997776i	$0.521235\pi$
$758$	−39.1974	+	12.5556i	−1.42371	+	0.456039i
$759$	−0.413854			−0.0150219
$760$	−12.6137	+	16.9123i	−0.457549	+	0.613475i
$761$		−	2.95761i		−	0.107213i	−0.998562	−	0.0536066i	$-0.982928\pi$
$761$		−	2.95761i		−	0.107213i	0.998562	−	0.0536066i	$-0.0170717\pi$
$762$	16.1309	−	5.16700i	0.584362	−	0.187181i
$763$		0			0
$764$	29.0782	+	40.7327i	1.05201	+	1.47366i
$765$	−24.2458			−0.876609
$766$	3.72872	+	11.6408i	0.134724	+	0.420598i
$767$			35.0921i			1.26710i
$768$	34.5526	+	26.9093i	1.24681	+	0.971007i
$769$		−	32.6324i		−	1.17676i	−0.808586	−	0.588378i	$-0.799767\pi$
$769$		−	32.6324i		−	1.17676i	0.808586	−	0.588378i	$-0.200233\pi$
$770$		0			0
$771$		−	7.51469i		−	0.270635i
$772$	−13.2852	+	9.48404i	−0.478147	+	0.341338i
$773$			5.49687i			0.197709i	0.995102	+	0.0988544i	$0.0315178\pi$
$773$			5.49687i			0.197709i	−0.995102	+	0.0988544i	$0.968482\pi$
$774$	−42.6397	+	13.6582i	−1.53265	+	0.490933i
$775$	−5.44258			−0.195503
$776$	−18.7178	+	25.0966i	−0.671931	+	0.900916i
$777$		0			0
$778$	6.11598	+	19.0936i	0.219269	+	0.684538i
$779$		−	59.6094i		−	2.13573i
$780$	−18.3450	+	13.0961i	−0.656857	+	0.468915i
$781$	0.674858			0.0241483
$782$	−3.51199	−	10.9641i	−0.125589	−

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.431404 - 1.34681i) q^{2} -2.73718 q^{3} +(-1.62778 + 1.16204i) q^{4} -1.00000i q^{5} +(1.18083 + 3.68646i) q^{6} +(2.26727 + 1.69100i) q^{8} +4.49217 q^{9} +O(q^{10})\)	\(q+(-0.431404 - 1.34681i) q^{2} -2.73718 q^{3} +(-1.62778 + 1.16204i) q^{4} -1.00000i q^{5} +(1.18083 + 3.68646i) q^{6} +(2.26727 + 1.69100i) q^{8} +4.49217 q^{9} +(-1.34681 + 0.431404i) q^{10} -0.100243i q^{11} +(4.45553 - 3.18071i) q^{12} -4.11735i q^{13} +2.73718i q^{15} +(1.29934 - 3.78308i) q^{16} -5.39735i q^{17} +(-1.93794 - 6.05009i) q^{18} -7.45934 q^{19} +(1.16204 + 1.62778i) q^{20} +(-0.135008 + 0.0432453i) q^{22} +1.50830i q^{23} +(-6.20593 - 4.62858i) q^{24} -1.00000 q^{25} +(-5.54528 + 1.77624i) q^{26} -4.08434 q^{27} -2.37688 q^{29} +(3.68646 - 1.18083i) q^{30} +5.44258 q^{31} +(-5.65562 - 0.117927i) q^{32} +0.274384i q^{33} +(-7.26919 + 2.32844i) q^{34} +(-7.31227 + 5.22007i) q^{36} +1.03852 q^{37} +(3.21799 + 10.0463i) q^{38} +11.2700i q^{39} +(1.69100 - 2.26727i) q^{40} +7.99125i q^{41} -7.04778i q^{43} +(0.116486 + 0.163174i) q^{44} -4.49217i q^{45} +(2.03139 - 0.650688i) q^{46} -4.44376 q^{47} +(-3.55654 + 10.3550i) q^{48} +(0.431404 + 1.34681i) q^{50} +14.7735i q^{51} +(4.78452 + 6.70215i) q^{52} +6.14261 q^{53} +(1.76200 + 5.50082i) q^{54} -0.100243 q^{55} +20.4176 q^{57} +(1.02540 + 3.20120i) q^{58} -8.52297 q^{59} +(-3.18071 - 4.45553i) q^{60} +7.90286i q^{61} +(-2.34795 - 7.33010i) q^{62} +(2.28103 + 7.66791i) q^{64} -4.11735 q^{65} +(0.369542 - 0.118370i) q^{66} +0.109800i q^{67} +(6.27192 + 8.78570i) q^{68} -4.12850i q^{69} +6.73221i q^{71} +(10.1850 + 7.59626i) q^{72} +6.14698i q^{73} +(-0.448022 - 1.39869i) q^{74} +2.73718 q^{75} +(12.1422 - 8.66802i) q^{76} +(15.1785 - 4.86190i) q^{78} +4.27445i q^{79} +(-3.78308 - 1.29934i) q^{80} -2.29692 q^{81} +(10.7627 - 3.44746i) q^{82} -6.50159 q^{83} -5.39735 q^{85} +(-9.49200 + 3.04044i) q^{86} +6.50596 q^{87} +(0.169511 - 0.227278i) q^{88} -3.19179i q^{89} +(-6.05009 + 1.93794i) q^{90} +(-1.75270 - 2.45519i) q^{92} -14.8973 q^{93} +(1.91706 + 5.98489i) q^{94} +7.45934i q^{95} +(15.4805 + 0.322788i) q^{96} +11.0691i q^{97} -0.450309i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

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