LMFDB - Embedded newform 351.2.bf.a.305.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(206,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.206"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bf (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.5
Character	$\chi$	$=$	351.305
Dual form			351.2.bf.a.206.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.242585 + 0.905339i) q^{2} +(0.971260 + 0.560757i) q^{4} +(-0.0271738 + 0.101414i) q^{5} +(0.258484 + 0.258484i) q^{7} +(-2.06880 + 2.06880i) q^{8} +(-0.0852221 - 0.0492030i) q^{10} +(3.07551 + 0.824082i) q^{11} +(-1.04439 + 3.45098i) q^{13} +(-0.296719 + 0.171311i) q^{14} +(-0.249589 - 0.432300i) q^{16} +(-0.713952 - 1.23660i) q^{17} +(2.92701 + 0.784289i) q^{19} +(-0.0832615 + 0.0832615i) q^{20} +(-1.49215 + 2.58447i) q^{22} -3.67374 q^{23} +(4.32058 + 2.49449i) q^{25} +(-2.87095 - 1.78269i) q^{26} +(0.106108 + 0.396001i) q^{28} +(4.47859 - 2.58571i) q^{29} +(-5.46656 - 1.46476i) q^{31} +(-5.20013 + 1.39337i) q^{32} +(1.29274 - 0.346388i) q^{34} +(-0.0332378 + 0.0191899i) q^{35} +(-4.32627 + 1.15922i) q^{37} +(-1.42009 + 2.45967i) q^{38} +(-0.153588 - 0.266022i) q^{40} +(4.81135 + 4.81135i) q^{41} -2.24631i q^{43} +(2.52501 + 2.52501i) q^{44} +(0.891194 - 3.32598i) q^{46} +(1.18436 + 4.42009i) q^{47} -6.86637i q^{49} +(-3.30646 + 3.30646i) q^{50} +(-2.94954 + 2.76614i) q^{52} -13.0901i q^{53} +(-0.167147 + 0.289507i) q^{55} -1.06950 q^{56} +(1.25451 + 4.68189i) q^{58} +(0.895419 + 3.34175i) q^{59} -6.24756 q^{61} +(2.65221 - 4.59376i) q^{62} -6.04425i q^{64} +(-0.321597 - 0.199692i) q^{65} +(10.8384 - 10.8384i) q^{67} -1.60142i q^{68} +(-0.00931034 - 0.0347467i) q^{70} +(1.56835 - 5.85317i) q^{71} +(-4.13084 - 4.13084i) q^{73} -4.19795i q^{74} +(2.40309 + 2.40309i) q^{76} +(0.581958 + 1.00798i) q^{77} +(8.15587 - 14.1264i) q^{79} +(0.0506235 - 0.0135645i) q^{80} +(-5.52307 + 3.18874i) q^{82} +(16.0296 - 4.29512i) q^{83} +(0.144809 - 0.0388016i) q^{85} +(2.03367 + 0.544920i) q^{86} +(-8.06747 + 4.65776i) q^{88} +(0.630472 + 2.35295i) q^{89} +(-1.16198 + 0.622062i) q^{91} +(-3.56816 - 2.06008i) q^{92} -4.28898 q^{94} +(-0.159076 + 0.275527i) q^{95} +(-8.74938 + 8.74938i) q^{97} +(6.21639 + 1.66568i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.242585	+	0.905339i	−0.171533	+	0.640171i	0.825583	+	0.564281i	$0.190847\pi$
$2$	−0.242585	+	0.905339i	−0.171533	+	0.640171i	−0.997116	+	0.0758902i	$0.975820\pi$
$3$		0			0
$3$		0			0
$4$	0.971260	+	0.560757i	0.485630	+	0.280379i
$5$	−0.0271738	+	0.101414i	−0.0121525	+	0.0453537i	−0.971736	−	0.236071i	$-0.924140\pi$
$5$	−0.0271738	+	0.101414i	−0.0121525	+	0.0453537i	0.959583	+	0.281425i	$0.0908069\pi$
$6$		0			0
$7$	0.258484	+	0.258484i	0.0976976	+	0.0976976i	0.754266	−	0.656569i	$-0.227993\pi$
$7$	0.258484	+	0.258484i	0.0976976	+	0.0976976i	−0.656569	+	0.754266i	$0.727993\pi$
$8$	−2.06880	+	2.06880i	−0.731430	+	0.731430i
$9$		0			0
$10$	−0.0852221	−	0.0492030i	−0.0269496	−	0.0155594i
$11$	3.07551	+	0.824082i	0.927303	+	0.248470i	0.690704	−	0.723138i	$-0.257301\pi$
$11$	3.07551	+	0.824082i	0.927303	+	0.248470i	0.236598	+	0.971608i	$0.423967\pi$
$12$		0			0
$13$	−1.04439	+	3.45098i	−0.289663	+	0.957129i
$13$	−1.04439	+	3.45098i	−0.289663	+	0.957129i
$14$	−0.296719	+	0.171311i	−0.0793016	+	0.0457848i
$15$		0			0
$16$	−0.249589	−	0.432300i	−0.0623971	−	0.108075i
$17$	−0.713952	−	1.23660i	−0.173159	−	0.299920i	0.766364	−	0.642407i	$-0.222064\pi$
$17$	−0.713952	−	1.23660i	−0.173159	−	0.299920i	−0.939523	+	0.342487i	$0.888731\pi$
$18$		0			0
$19$	2.92701	+	0.784289i	0.671501	+	0.179928i	0.578431	−	0.815731i	$-0.303665\pi$
$19$	2.92701	+	0.784289i	0.671501	+	0.179928i	0.0930701	+	0.995660i	$0.470332\pi$
$20$	−0.0832615	+	0.0832615i	−0.0186178	+	0.0186178i
$21$		0			0
$22$	−1.49215	+	2.58447i	−0.318127	+	0.551011i
$23$	−3.67374			−0.766028			−0.383014	−	0.923742i	$-0.625114\pi$
$23$	−3.67374			−0.766028			−0.383014	+	0.923742i	$0.625114\pi$
$24$		0			0
$25$	4.32058	+	2.49449i	0.864116	+	0.498898i
$26$	−2.87095	−	1.78269i	−0.563039	−	0.349613i
$27$		0			0
$28$	0.106108	+	0.396001i	0.0200526	+	0.0748372i
$29$	4.47859	−	2.58571i	0.831652	−	0.480155i	−0.0227657	−	0.999741i	$-0.507247\pi$
$29$	4.47859	−	2.58571i	0.831652	−	0.480155i	0.854418	+	0.519586i	$0.173914\pi$
$30$		0			0
$31$	−5.46656	−	1.46476i	−0.981823	−	0.263079i	−0.268011	−	0.963416i	$-0.586366\pi$
$31$	−5.46656	−	1.46476i	−0.981823	−	0.263079i	−0.713812	+	0.700337i	$0.753033\pi$
$32$	−5.20013	+	1.39337i	−0.919262	+	0.246316i
$33$		0			0
$34$	1.29274	−	0.346388i	0.221703	−	0.0594050i
$35$	−0.0332378	+	0.0191899i	−0.00561822	+	0.00324368i
$36$		0			0
$37$	−4.32627	+	1.15922i	−0.711234	+	0.190575i	−0.596257	−	0.802793i	$-0.703346\pi$
$37$	−4.32627	+	1.15922i	−0.711234	+	0.190575i	−0.114977	+	0.993368i	$0.536679\pi$
$38$	−1.42009	+	2.45967i	−0.230370	+	0.399012i
$39$		0			0
$40$	−0.153588	−	0.266022i	−0.0242844	−	0.0420618i
$41$	4.81135	+	4.81135i	0.751407	+	0.751407i	0.974742	−	0.223335i	$-0.0716942\pi$
$41$	4.81135	+	4.81135i	0.751407	+	0.751407i	−0.223335	+	0.974742i	$0.571694\pi$
$42$		0			0
$43$		−	2.24631i		−	0.342559i	−0.985222	−	0.171279i	$-0.945210\pi$
$43$		−	2.24631i		−	0.342559i	0.985222	−	0.171279i	$-0.0547901\pi$
$44$	2.52501	+	2.52501i	0.380660	+	0.380660i
$45$		0			0
$46$	0.891194	−	3.32598i	0.131399	−	0.490389i
$47$	1.18436	+	4.42009i	0.172756	+	0.644736i	0.996923	+	0.0783882i	$0.0249773\pi$
$47$	1.18436	+	4.42009i	0.172756	+	0.644736i	−0.824166	+	0.566348i	$0.808356\pi$
$48$		0			0
$49$		−	6.86637i		−	0.980910i
$50$	−3.30646	+	3.30646i	−0.467605	+	0.467605i
$51$		0			0
$52$	−2.94954	+	2.76614i	−0.409027	+	0.383595i
$53$		−	13.0901i		−	1.79807i	−0.437881	−	0.899033i	$-0.644271\pi$
$53$		−	13.0901i		−	1.79807i	0.437881	−	0.899033i	$-0.355729\pi$
$54$		0			0
$55$	−0.167147	+	0.289507i	−0.0225381	+	0.0390371i
$56$	−1.06950			−0.142918
$57$		0			0
$58$	1.25451	+	4.68189i	0.164725	+	0.614762i
$59$	0.895419	+	3.34175i	0.116574	+	0.435059i	0.999400	−	0.0346412i	$-0.0110288\pi$
$59$	0.895419	+	3.34175i	0.116574	+	0.435059i	−0.882826	+	0.469700i	$0.844362\pi$
$60$		0			0
$61$	−6.24756			−0.799919			−0.399959	−	0.916533i	$-0.630976\pi$
$61$	−6.24756			−0.799919			−0.399959	+	0.916533i	$0.630976\pi$
$62$	2.65221	−	4.59376i	0.336831	−	0.583408i
$63$		0			0
$64$		−	6.04425i		−	0.755531i
$65$	−0.321597	−	0.199692i	−0.0398892	−	0.0247688i
$66$		0			0
$67$	10.8384	−	10.8384i	1.32412	−	1.32412i	0.413712	−	0.910408i	$-0.364232\pi$
$67$	10.8384	−	10.8384i	1.32412	−	1.32412i	0.910408	−	0.413712i	$-0.135768\pi$
$68$		−	1.60142i		−	0.194200i
$69$		0			0
$70$	−0.00931034	−	0.0347467i	−0.00111280	−	0.00415302i
$71$	1.56835	−	5.85317i	0.186129	−	0.694643i	−0.808257	−	0.588830i	$-0.799589\pi$
$71$	1.56835	−	5.85317i	0.186129	−	0.694643i	0.994386	−	0.105813i	$-0.0337445\pi$
$72$		0			0
$73$	−4.13084	−	4.13084i	−0.483478	−	0.483478i	0.422763	−	0.906241i	$-0.361060\pi$
$73$	−4.13084	−	4.13084i	−0.483478	−	0.483478i	−0.906241	+	0.422763i	$0.861060\pi$
$74$		−	4.19795i		−	0.488002i
$75$		0			0
$76$	2.40309	+	2.40309i	0.275653	+	0.275653i
$77$	0.581958	+	1.00798i	0.0663203	+	0.114870i
$78$		0			0
$79$	8.15587	−	14.1264i	0.917607	−	1.58934i	0.114569	−	0.993415i	$-0.463451\pi$
$79$	8.15587	−	14.1264i	0.917607	−	1.58934i	0.803039	−	0.595927i	$-0.203215\pi$
$80$	0.0506235	−	0.0135645i	0.00565988	−	0.00151656i
$81$		0			0
$82$	−5.52307	+	3.18874i	−0.609921	+	0.352138i
$83$	16.0296	−	4.29512i	1.75948	−	0.471450i	0.772870	−	0.634565i	$-0.218821\pi$
$83$	16.0296	−	4.29512i	1.75948	−	0.471450i	0.986607	+	0.163114i	$0.0521539\pi$
$84$		0			0
$85$	0.144809	−	0.0388016i	0.0157068	−	0.00420862i
$86$	2.03367	+	0.544920i	0.219296	+	0.0587603i
$87$		0			0
$88$	−8.06747	+	4.65776i	−0.859995	+	0.496518i
$89$	0.630472	+	2.35295i	0.0668298	+	0.249412i	0.991257	−	0.131947i	$-0.0421228\pi$
$89$	0.630472	+	2.35295i	0.0668298	+	0.249412i	−0.924427	+	0.381359i	$0.875456\pi$
$90$		0			0
$91$	−1.16198	+	0.622062i	−0.121809	+	0.0652098i
$92$	−3.56816	−	2.06008i	−0.372006	−	0.214778i
$93$		0			0
$94$	−4.28898			−0.442375
$95$	−0.159076	+	0.275527i	−0.0163208	+	0.0282685i
$96$		0			0
$97$	−8.74938	+	8.74938i	−0.888365	+	0.888365i	−0.994366	−	0.106001i	$-0.966195\pi$
$97$	−8.74938	+	8.74938i	−0.888365	+	0.888365i	0.106001	+	0.994366i	$0.466195\pi$
$98$	6.21639	+	1.66568i	0.627951	+	0.168259i
$99$		0			0
$100$	2.79760	+	4.84559i	0.279760	+	0.484559i
$101$	−1.90137	−	3.29328i	−0.189194	−	0.327693i	0.755788	−	0.654817i	$-0.227254\pi$
$101$	−1.90137	−	3.29328i	−0.189194	−	0.327693i	−0.944982	+	0.327123i	$0.893921\pi$
$102$		0			0
$103$	5.80875	−	3.35368i	0.572353	−	0.330448i	−0.185736	−	0.982600i	$-0.559467\pi$
$103$	5.80875	−	3.35368i	0.572353	−	0.330448i	0.758089	+	0.652152i	$0.226133\pi$
$104$	−4.97873	−	9.30001i	−0.488204	−	0.911941i
$105$		0			0
$106$	11.8510	+	3.17546i	1.15107	+	0.308428i
$107$	−10.4912	−	6.05707i	−1.01422	−	0.585559i	−0.101795	−	0.994805i	$-0.532458\pi$
$107$	−10.4912	−	6.05707i	−1.01422	−	0.585559i	−0.912424	+	0.409246i	$0.865792\pi$
$108$		0			0
$109$	−0.643264	+	0.643264i	−0.0616135	+	0.0616135i	−0.737242	−	0.675629i	$-0.763872\pi$
$109$	−0.643264	+	0.643264i	−0.0616135	+	0.0616135i	0.675629	+	0.737242i	$0.263872\pi$
$110$	−0.221554	−	0.221554i	−0.0211244	−	0.0211244i
$111$		0			0
$112$	0.0472279	−	0.176257i	0.00446262	−	0.0166547i
$113$	2.66379	+	1.53794i	0.250588	+	0.144677i	0.620033	−	0.784575i	$-0.287119\pi$
$113$	2.66379	+	1.53794i	0.250588	+	0.144677i	−0.369446	+	0.929252i	$0.620452\pi$
$114$		0			0
$115$	0.0998296	−	0.372569i	0.00930915	−	0.0347422i
$116$	5.79983			0.538500
$117$		0			0
$118$	−3.24263			−0.298508
$119$	0.135096	−	0.504186i	0.0123843	−	0.0462187i
$120$		0			0
$121$	−0.746600	−	0.431050i	−0.0678728	−	0.0391864i
$122$	1.51556	−	5.65616i	0.137213	−	0.512085i
$123$		0			0
$124$	−4.48807	−	4.48807i	−0.403041	−	0.403041i
$125$	−0.741584	+	0.741584i	−0.0663293	+	0.0663293i
$126$		0			0
$127$	11.1811	+	6.45543i	0.992165	+	0.572827i	0.905921	−	0.423448i	$-0.139180\pi$
$127$	11.1811	+	6.45543i	0.992165	+	0.572827i	0.0862440	+	0.996274i	$0.472514\pi$
$128$	−4.92817	−	1.32050i	−0.435593	−	0.116717i
$129$		0			0
$130$	0.258804	−	0.242712i	0.0226986	−	0.0212873i
$131$	13.4537	−	7.76749i	1.17545	−	0.678649i	0.220495	−	0.975388i	$-0.429233\pi$
$131$	13.4537	−	7.76749i	1.17545	−	0.678649i	0.954958	+	0.296739i	$0.0958993\pi$
$132$		0			0
$133$	0.553857	+	0.959308i	0.0480255	+	0.0831826i
$134$	7.18319	+	12.4416i	0.620533	+	1.07479i
$135$		0			0
$136$	4.03530	+	1.08125i	0.346024	+	0.0927168i
$137$	−13.0356	+	13.0356i	−1.11371	+	1.11371i	−0.121062	+	0.992645i	$0.538630\pi$
$137$	−13.0356	+	13.0356i	−1.11371	+	1.11371i	−0.992645	+	0.121062i	$0.961370\pi$
$138$		0			0
$139$	−4.54133	+	7.86581i	−0.385190	+	0.667169i	−0.991796	−	0.127834i	$-0.959198\pi$
$139$	−4.54133	+	7.86581i	−0.385190	+	0.667169i	0.606605	+	0.795003i	$0.292531\pi$
$140$	−0.0430434			−0.00363783
$141$		0			0
$142$	4.91864	+	2.83978i	0.412763	+	0.238309i
$143$	−6.05594	+	9.75286i	−0.506423	+	0.815575i
$144$		0			0
$145$	0.140527	+	0.524455i	0.0116702	+	0.0435536i
$146$	4.74189	−	2.73773i	0.392441	−	0.226576i
$147$		0			0
$148$	−4.85197	−	1.30008i	−0.398830	−	0.106866i
$149$	−11.6315	+	3.11666i	−0.952892	+	0.255327i	−0.701589	−	0.712582i	$-0.747526\pi$
$149$	−11.6315	+	3.11666i	−0.952892	+	0.255327i	−0.251303	+	0.967908i	$0.580859\pi$
$150$		0			0
$151$	0.0407571	−	0.0109208i	0.00331676	−	0.000888724i	−0.257160	−	0.966369i	$-0.582787\pi$
$151$	0.0407571	−	0.0109208i	0.00331676	−	0.000888724i	0.260477	+	0.965480i	$0.416120\pi$
$152$	−7.67791	+	4.43284i	−0.622761	+	0.359551i
$153$		0			0
$154$	−1.05374	+	0.282348i	−0.0849127	+	0.0227523i
$155$	0.297094	−	0.514583i	0.0238632	−	0.0413323i
$156$		0			0
$157$	−6.95508	−	12.0466i	−0.555076	−	0.961420i	−0.997898	−	0.0648102i	$-0.979356\pi$
$157$	−6.95508	−	12.0466i	−0.555076	−	0.961420i	0.442822	−	0.896610i	$-0.353978\pi$
$158$	10.8107	+	10.8107i	0.860051	+	0.860051i
$159$		0			0
$160$		−	0.565229i		−	0.0446853i
$161$	−0.949602	−	0.949602i	−0.0748391	−	0.0748391i
$162$		0			0
$163$	0.208136	−	0.776776i	0.0163025	−	0.0608418i	−0.957295	−	0.289112i	$-0.906640\pi$
$163$	0.208136	−	0.776776i	0.0163025	−	0.0608418i	0.973598	+	0.228270i	$0.0733068\pi$
$164$	1.97507	+	7.37108i	0.154227	+	0.575584i
$165$		0			0
$166$			15.5541i			1.20724i
$167$	−10.9713	+	10.9713i	−0.848985	+	0.848985i	−0.990007	−	0.141021i	$-0.954961\pi$
$167$	−10.9713	+	10.9713i	−0.848985	+	0.848985i	0.141021	+	0.990007i	$0.454961\pi$
$168$		0			0
$169$	−10.8185	−	7.20836i	−0.832191	−	0.554489i
$170$			0.140514i			0.0107770i
$171$		0			0
$172$	1.25963	−	2.18175i	0.0960462	−	0.166357i
$173$	−15.3374			−1.16608			−0.583039	−	0.812444i	$-0.698137\pi$
$173$	−15.3374			−1.16608			−0.583039	+	0.812444i	$0.698137\pi$
$174$		0			0
$175$	0.472015	+	1.76158i	0.0356810	+	0.133163i
$176$	−0.411363	−	1.53523i	−0.0310076	−	0.115722i
$177$		0			0
$178$	−2.28316			−0.171130
$179$	−9.33636	+	16.1710i	−0.697832	+	1.20868i	0.271385	+	0.962471i	$0.412518\pi$
$179$	−9.33636	+	16.1710i	−0.697832	+	1.20868i	−0.969217	+	0.246209i	$0.920815\pi$
$180$		0			0
$181$			14.2199i			1.05695i	0.848947	+	0.528477i	$0.177237\pi$
$181$			14.2199i			1.05695i	−0.848947	+	0.528477i	$0.822763\pi$
$182$	−0.281298	−	1.20289i	−0.0208512	−	0.0891640i
$183$		0			0
$184$	7.60022	−	7.60022i	0.560296	−	0.560296i
$185$		−	0.470245i		−	0.0345731i
$186$		0			0
$187$	−1.17671	−	4.39154i	−0.0860495	−	0.321141i
$188$	−1.32827	+	4.95719i	−0.0968744	+	0.361540i
$189$		0			0
$190$	−0.210856	−	0.210856i	−0.0152971	−	0.0152971i
$191$		−	7.33571i		−	0.530793i	−0.964139	−	0.265397i	$-0.914497\pi$
$191$		−	7.33571i		−	0.530793i	0.964139	−	0.265397i	$-0.0855029\pi$
$192$		0			0
$193$	15.1355	+	15.1355i	1.08948	+	1.08948i	0.995582	+	0.0938977i	$0.0299327\pi$
$193$	15.1355	+	15.1355i	1.08948	+	1.08948i	0.0938977	+	0.995582i	$0.470067\pi$
$194$	−5.79868	−	10.0436i	−0.416321	−	0.721090i
$195$		0			0
$196$	3.85037	−	6.66903i	0.275026	−	0.476359i
$197$	3.74628	−	1.00381i	0.266911	−	0.0715186i	−0.122881	−	0.992421i	$-0.539213\pi$
$197$	3.74628	−	1.00381i	0.266911	−	0.0715186i	0.389792	+	0.920903i	$0.372547\pi$
$198$		0			0
$199$	8.87017	−	5.12119i	0.628790	−	0.363032i	−0.151494	−	0.988458i	$-0.548408\pi$
$199$	8.87017	−	5.12119i	0.628790	−	0.363032i	0.780283	+	0.625426i	$0.215075\pi$
$200$	−14.0990	+	3.77781i	−0.996949	+	0.267132i
$201$		0			0
$202$	3.44278	−	0.922489i	0.242233	−	0.0649061i
$203$	1.82600	+	0.489276i	0.128160	+	0.0343405i
$204$		0			0
$205$	−0.618682	+	0.357196i	−0.0432106	+	0.0249476i
$206$	1.62710	+	6.07244i	0.113366	+	0.423087i
$207$		0			0
$208$	1.75253	−	0.409832i	0.121516	−	0.0284168i
$209$	8.35573	+	4.82418i	0.577978	+	0.333696i
$210$		0			0
$211$	−18.0710			−1.24406			−0.622030	−	0.782994i	$-0.713692\pi$
$211$	−18.0710			−1.24406			−0.622030	+	0.782994i	$0.713692\pi$
$212$	7.34038	−	12.7139i	0.504139	−	0.873195i
$213$		0			0
$214$	8.02870	−	8.02870i	0.548831	−	0.548831i
$215$	0.227807	+	0.0610407i	0.0155363	+	0.00416294i
$216$		0			0
$217$	−1.03440	−	1.79163i	−0.0702196	−	0.121624i
$218$	−0.426326	−	0.738418i	−0.0288744	−	0.0500119i
$219$		0			0
$220$	−0.324686	+	0.187458i	−0.0218903	+	0.0126384i
$221$	5.01313	−	1.17233i	0.337220	−	0.0788596i
$222$		0			0
$223$	−3.09913	−	0.830410i	−0.207533	−	0.0556083i	0.153555	−	0.988140i	$-0.450928\pi$
$223$	−3.09913	−	0.830410i	−0.207533	−	0.0556083i	−0.361088	+	0.932532i	$0.617595\pi$
$224$	−1.70431	−	0.983985i	−0.113874	−	0.0657453i
$225$		0			0
$226$	−2.03855	+	2.03855i	−0.135602	+	0.135602i
$227$	2.68532	+	2.68532i	0.178231	+	0.178231i	0.790584	−	0.612353i	$-0.209777\pi$
$227$	2.68532	+	2.68532i	0.178231	+	0.178231i	−0.612353	+	0.790584i	$0.709777\pi$
$228$		0			0
$229$	−4.54078	+	16.9464i	−0.300063	+	1.11985i	0.637050	+	0.770823i	$0.280155\pi$
$229$	−4.54078	+	16.9464i	−0.300063	+	1.11985i	−0.937113	+	0.349027i	$0.886512\pi$
$230$	0.313084	+	0.180759i	0.0206441	+	0.0119189i
$231$		0			0
$232$	−3.91597	+	14.6146i	−0.257096	+	0.959495i
$233$	14.4728			0.948143			0.474072	−	0.880486i	$-0.342784\pi$
$233$	14.4728			0.948143			0.474072	+	0.880486i	$0.342784\pi$
$234$		0			0
$235$	−0.480442			−0.0313406
$236$	−1.00423	+	3.74782i	−0.0653695	+	0.243962i
$237$		0			0
$238$	0.423687	+	0.244616i	0.0274635	+	0.0158561i
$239$	5.30038	−	19.7813i	0.342853	−	1.27955i	−0.552247	−	0.833681i	$-0.686229\pi$
$239$	5.30038	−	19.7813i	0.342853	−	1.27955i	0.895100	−	0.445865i	$-0.147104\pi$
$240$		0			0
$241$	17.0780	+	17.0780i	1.10009	+	1.10009i	0.994399	+	0.105692i	$0.0337058\pi$
$241$	17.0780	+	17.0780i	1.10009	+	1.10009i	0.105692	+	0.994399i	$0.466294\pi$
$242$	0.571360	−	0.571360i	0.0367284	−	0.0367284i
$243$		0			0
$244$	−6.06801	−	3.50337i	−0.388464	−	0.224280i
$245$	0.696346	+	0.186585i	0.0444879	+	0.0119205i
$246$		0			0
$247$	−5.76351	+	9.28192i	−0.366723	+	0.590594i
$248$	14.3395	−	8.27891i	0.910558	−	0.525711i
$249$		0			0
$250$	−0.491488	−	0.851281i	−0.0310844	−	0.0538398i
$251$	3.92544	+	6.79906i	0.247772	+	0.429153i	0.962907	−	0.269833i	$-0.0869684\pi$
$251$	3.92544	+	6.79906i	0.247772	+	0.429153i	−0.715136	+	0.698986i	$0.753635\pi$
$252$		0			0
$253$	−11.2986	−	3.02746i	−0.710340	−	0.190335i
$254$	−8.55672	+	8.55672i	−0.536896	+	0.536896i
$255$		0			0
$256$	8.43525	−	14.6103i	0.527203	−	0.913142i
$257$	−26.3536			−1.64389			−0.821947	−	0.569564i	$-0.807112\pi$
$257$	−26.3536			−1.64389			−0.821947	+	0.569564i	$0.807112\pi$
$258$		0			0
$259$	−1.41791	−	0.818630i	−0.0881046	−	0.0508672i
$260$	−0.200376	−	0.374291i	−0.0124268	−	0.0232126i
$261$		0			0
$262$	3.76855	+	14.0644i	0.232822	+	0.868903i
$263$	18.2900	−	10.5598i	1.12781	−	0.651143i	0.184429	−	0.982846i	$-0.440957\pi$
$263$	18.2900	−	10.5598i	1.12781	−	0.651143i	0.943384	+	0.331703i	$0.107623\pi$
$264$		0			0
$265$	1.32752	+	0.355708i	0.0815490	+	0.0218510i
$266$	−1.00286	+	0.268715i	−0.0614891	+	0.0164759i
$267$		0			0
$268$	16.6046	−	4.44919i	1.01429	−	0.271777i
$269$	−3.78449	+	2.18498i	−0.230744	+	0.133220i	−0.610915	−	0.791696i	$-0.709198\pi$
$269$	−3.78449	+	2.18498i	−0.230744	+	0.133220i	0.380171	+	0.924916i	$0.375865\pi$
$270$		0			0
$271$	13.6523	−	3.65813i	0.829320	−	0.222216i	0.180903	−	0.983501i	$-0.442098\pi$
$271$	13.6523	−	3.65813i	0.829320	−	0.222216i	0.648417	+	0.761285i	$0.275431\pi$
$272$	−0.356389	+	0.617283i	−0.0216092	+	0.0374283i
$273$		0			0
$274$	−8.63940	−	14.9639i	−0.521925	−	0.904001i
$275$	11.2323	+	11.2323i	0.677336	+	0.677336i
$276$		0			0
$277$			24.5946i			1.47775i	0.673844	+	0.738874i	$0.264642\pi$
$277$			24.5946i			1.47775i	−0.673844	+	0.738874i	$0.735358\pi$
$278$	−6.01957	−	6.01957i	−0.361030	−	0.361030i
$279$		0			0
$280$	0.0290624	−	0.108462i	0.00173681	−	0.00648186i
$281$	−5.45626	−	20.3630i	−0.325493	−	1.21476i	−0.913815	−	0.406131i	$-0.866878\pi$
$281$	−5.45626	−	20.3630i	−0.325493	−	1.21476i	0.588322	−	0.808627i	$-0.299789\pi$
$282$		0			0
$283$			4.03021i			0.239571i	0.992800	+	0.119786i	$0.0382207\pi$
$283$			4.03021i			0.239571i	−0.992800	+	0.119786i	$0.961779\pi$
$284$	4.80548	−	4.80548i	0.285153	−	0.285153i
$285$		0			0
$286$	−7.36057	−	7.84857i	−0.435239	−	0.464096i
$287$			2.48731i			0.146821i
$288$		0			0
$289$	7.48054	−	12.9567i	0.440032	−	0.762158i
$290$	−0.508899			−0.0298836
$291$		0			0
$292$	−1.69572	−	6.32851i	−0.0992345	−	0.370348i
$293$	−2.98875	−	11.1541i	−0.174604	−	0.651632i	−0.996619	−	0.0821655i	$-0.973816\pi$
$293$	−2.98875	−	11.1541i	−0.174604	−	0.651632i	0.822014	−	0.569467i	$-0.192850\pi$
$294$		0			0
$295$	−0.363232			−0.0211482
$296$	6.55198	−	11.3484i	0.380826	−	0.659610i
$297$		0			0
$298$		−	11.2865i		−	0.653811i
$299$	3.83684	−	12.6780i	0.221890	−	0.733188i
$300$		0			0
$301$	0.580634	−	0.580634i	0.0334672	−	0.0334672i
$302$			0.0395482i			0.00227574i
$303$		0			0
$304$	−0.391499	−	1.46109i	−0.0224540	−	0.0837995i
$305$	0.169770	−	0.633591i	0.00972101	−	0.0362793i
$306$		0			0
$307$	−17.9190	−	17.9190i	−1.02269	−	1.02269i	−0.999737	−	0.0229527i	$-0.992693\pi$
$307$	−17.9190	−	17.9190i	−1.02269	−	1.02269i	−0.0229527	−	0.999737i	$-0.507307\pi$
$308$			1.30535i			0.0743792i
$309$		0			0
$310$	0.393801	+	0.393801i	0.0223664	+	0.0223664i
$311$	11.1301	+	19.2779i	0.631129	+	1.09315i	0.987321	+	0.158735i	$0.0507415\pi$
$311$	11.1301	+	19.2779i	0.631129	+	1.09315i	−0.356192	+	0.934413i	$0.615925\pi$
$312$		0			0
$313$	4.30058	−	7.44883i	0.243083	−	0.421033i	−0.718508	−	0.695519i	$-0.755175\pi$
$313$	4.30058	−	7.44883i	0.243083	−	0.421033i	0.961591	+	0.274486i	$0.0885078\pi$
$314$	12.5934	−	3.37439i	0.710687	−	0.190428i
$315$		0			0
$316$	15.8429	−	9.14693i	0.891235	−	0.514555i
$317$	−30.4177	+	8.15039i	−1.70843	+	0.457771i	−0.975038	−	0.222039i	$-0.928729\pi$
$317$	−30.4177	+	8.15039i	−1.70843	+	0.457771i	−0.733388	+	0.679810i	$0.762062\pi$
$318$		0			0
$319$	15.9048	−	4.26168i	0.890497	−	0.238608i
$320$	0.612971	+	0.164245i	0.0342661	+	0.00918158i
$321$		0			0
$322$	1.09007	−	0.629352i	0.0607472	−	0.0350724i
$323$	−1.11989	−	4.17948i	−0.0623123	−	0.232553i
$324$		0			0
$325$	−13.1208	+	12.3050i	−0.727812	+	0.682558i
$326$	0.652755	+	0.376868i	0.0361527	+	0.0208728i
$327$		0			0
$328$	−19.9074			−1.09920
$329$	−0.836382	+	1.44866i	−0.0461112	+	0.0798670i
$330$		0			0
$331$	−11.0641	+	11.0641i	−0.608138	+	0.608138i	−0.942459	−	0.334321i	$-0.891493\pi$
$331$	−11.0641	+	11.0641i	−0.608138	+	0.608138i	0.334321	+	0.942459i	$0.391493\pi$
$332$	17.9774	+	4.81704i	0.986639	+	0.264369i
$333$		0			0
$334$	−7.27128	−	12.5942i	−0.397867	−	0.689125i
$335$	0.804644	+	1.39368i	0.0439624	+	0.0761451i
$336$		0			0
$337$	−5.42515	+	3.13221i	−0.295527	+	0.170622i	−0.640432	−	0.768015i	$-0.721244\pi$
$337$	−5.42515	+	3.13221i	−0.295527	+	0.170622i	0.344905	+	0.938638i	$0.387911\pi$
$338$	9.15041	−	8.04575i	0.497717	−	0.437631i
$339$		0			0
$340$	0.162406	+	0.0435165i	0.00880770	+	0.00236002i
$341$	−15.6054	−	9.00978i	−0.845080	−	0.487907i
$342$		0			0
$343$	3.58423	−	3.58423i	0.193530	−	0.193530i
$344$	4.64715	+	4.64715i	0.250558	+	0.250558i
$345$		0			0
$346$	3.72061	−	13.8855i	0.200021	−	0.746490i
$347$	15.7963	+	9.12001i	0.847991	+	0.489588i	0.859972	−	0.510340i	$-0.170481\pi$
$347$	15.7963	+	9.12001i	0.847991	+	0.489588i	−0.0119815	+	0.999928i	$0.503814\pi$
$348$		0			0
$349$	2.07490	−	7.74363i	0.111067	−	0.414507i	−0.887896	−	0.460045i	$-0.847833\pi$
$349$	2.07490	−	7.74363i	0.111067	−	0.414507i	0.998963	+	0.0455376i	$0.0145001\pi$
$350$	−1.70933			−0.0913677
$351$		0			0
$352$	−17.1413			−0.913636
$353$	4.47040	−	16.6838i	0.237935	−	0.887987i	−0.738868	−	0.673850i	$-0.764639\pi$
$353$	4.47040	−	16.6838i	0.237935	−	0.887987i	0.976804	−	0.214137i	$-0.0686939\pi$
$354$		0			0
$355$	0.550975	+	0.318106i	0.0292427	+	0.0168833i
$356$	−0.707083	+	2.63887i	−0.0374753	+	0.139860i
$357$		0			0
$358$	−12.3754	−	12.3754i	−0.654061	−	0.654061i
$359$	21.8853	−	21.8853i	1.15506	−	1.15506i	0.169540	−	0.985523i	$-0.445772\pi$
$359$	21.8853	−	21.8853i	1.15506	−	1.15506i	0.985523	−	0.169540i	$-0.0542283\pi$
$360$		0			0
$361$	−8.50223	−	4.90877i	−0.447486	−	0.258356i
$362$	−12.8738	−	3.44952i	−0.676632	−	0.181303i
$363$		0			0
$364$	−1.47741	−	0.0474045i	−0.0774373	−	0.00248467i
$365$	0.531175	−	0.306674i	0.0278030	−	0.0160521i
$366$		0			0
$367$	0.655382	+	1.13515i	0.0342106	+	0.0592546i	0.882624	−	0.470080i	$-0.155775\pi$
$367$	0.655382	+	1.13515i	0.0342106	+	0.0592546i	−0.848413	+	0.529335i	$0.822442\pi$
$368$	0.916924	+	1.58816i	0.0477980	+	0.0827885i
$369$		0			0
$370$	0.425731	+	0.114074i	0.0221327	+	0.00593044i
$371$	3.38358	−	3.38358i	0.175667	−	0.175667i
$372$		0			0
$373$	14.4107	−	24.9601i	0.746157	−	1.29238i	−0.203495	−	0.979076i	$-0.565230\pi$
$373$	14.4107	−	24.9601i	0.746157	−	1.29238i	0.949652	−	0.313306i	$-0.101437\pi$
$374$	4.26128			0.220346
$375$		0			0
$376$	−11.5945	−	6.69406i	−0.597938	−	0.345220i
$377$	4.24582	+	18.1560i	0.218671	+	0.935081i
$378$		0			0
$379$	−4.45400	−	16.6226i	−0.228787	−	0.853843i	−0.980852	−	0.194755i	$-0.937609\pi$
$379$	−4.45400	−	16.6226i	−0.228787	−	0.853843i	0.752065	−	0.659088i	$-0.229058\pi$
$380$	−0.309008	+	0.178406i	−0.0158518	+	0.00915202i
$381$		0			0
$382$	6.64130	+	1.77953i	0.339798	+	0.0910487i
$383$	−30.9702	+	8.29843i	−1.58250	+	0.424030i	−0.939699	−	0.342003i	$-0.888895\pi$
$383$	−30.9702	+	8.29843i	−1.58250	+	0.424030i	−0.642802	+	0.766033i	$0.722228\pi$
$384$		0			0
$385$	−0.118037	+	0.0316280i	−0.00601575	+	0.00161191i
$386$	−17.3744	+	10.0311i	−0.884336	+	0.510571i
$387$		0			0
$388$	−13.4042	+	3.59164i	−0.680495	+	0.182338i
$389$	−8.01814	+	13.8878i	−0.406536	+	0.704141i	−0.994499	−	0.104747i	$-0.966597\pi$
$389$	−8.01814	+	13.8878i	−0.406536	+	0.704141i	0.587963	+	0.808888i	$0.299930\pi$
$390$		0			0
$391$	2.62288	+	4.54295i	0.132645	+	0.229747i
$392$	14.2051	+	14.2051i	0.717467	+	0.717467i
$393$		0			0
$394$			3.63516i			0.183137i
$395$	1.21099	+	1.21099i	0.0609314	+	0.0609314i
$396$		0			0
$397$	−7.81599	+	29.1697i	−0.392273	+	1.46398i	0.434102	+	0.900864i	$0.357066\pi$
$397$	−7.81599	+	29.1697i	−0.392273	+	1.46398i	−0.826375	+	0.563120i	$0.809601\pi$
$398$	2.48465	+	9.27283i	0.124544	+	0.464805i
$399$		0			0
$400$		−	2.49038i		−	0.124519i
$401$	−8.02571	+	8.02571i	−0.400785	+	0.400785i	−0.878510	−	0.477725i	$-0.841462\pi$
$401$	−8.02571	+	8.02571i	−0.400785	+	0.400785i	0.477725	+	0.878510i	$0.341462\pi$
$402$		0			0
$403$	10.7641	−	17.3352i	0.536198	−	0.863527i
$404$		−	4.26484i		−	0.212184i
$405$		0			0
$406$	−0.885922	+	1.53446i	−0.0439676	+	0.0761541i
$407$	−14.2608			−0.706881
$408$		0			0
$409$	3.04978	+	11.3819i	0.150802	+	0.562800i	0.999428	+	0.0338077i	$0.0107634\pi$
$409$	3.04978	+	11.3819i	0.150802	+	0.562800i	−0.848626	+	0.528993i	$0.822570\pi$
$410$	−0.173301	−	0.646767i	−0.00855871	−	0.0319415i
$411$		0			0
$412$	7.52240			0.370602
$413$	−0.632336	+	1.09524i	−0.0311152	+	0.0538931i
$414$		0			0
$415$			1.74234i			0.0855281i
$416$	0.622498	−	19.4008i	0.0305205	−	0.951201i
$417$		0			0
$418$	−6.39449	+	6.39449i	−0.312765	+	0.312765i
$419$		−	2.88440i		−	0.140912i	−0.997515	−	0.0704561i	$-0.977555\pi$
$419$		−	2.88440i		−	0.140912i	0.997515	−	0.0704561i	$-0.0224455\pi$
$420$		0			0
$421$	−0.648970	−	2.42199i	−0.0316288	−	0.118040i	0.948307	−	0.317356i	$-0.102795\pi$
$421$	−0.648970	−	2.42199i	−0.0316288	−	0.118040i	−0.979935	+	0.199315i	$0.936128\pi$
$422$	4.38375	−	16.3604i	0.213398	−	0.796411i
$423$		0			0
$424$	27.0808	+	27.0808i	1.31516	+	1.31516i
$425$		−	7.12378i		−	0.345554i
$426$		0			0
$427$	−1.61489	−	1.61489i	−0.0781501	−	0.0781501i
$428$	−6.79309	−	11.7660i	−0.328357	−	0.568730i
$429$		0			0
$430$	−0.110525	+	0.191435i	−0.00532999	+	0.00923182i
$431$	−14.9429	+	4.00393i	−0.719773	+	0.192863i	−0.600071	−	0.799947i	$-0.704861\pi$
$431$	−14.9429	+	4.00393i	−0.719773	+	0.192863i	−0.119703	+	0.992810i	$0.538194\pi$
$432$		0			0
$433$	4.53654	−	2.61917i	0.218012	−	0.125869i	−0.387017	−	0.922072i	$-0.626495\pi$
$433$	4.53654	−	2.61917i	0.218012	−	0.125869i	0.605029	+	0.796203i	$0.293161\pi$
$434$	1.87296	−	0.501859i	0.0899051	−	0.0240900i
$435$		0			0
$436$	−0.985491	+	0.264062i	−0.0471965	+	0.0126463i
$437$	−10.7531	−	2.88127i	−0.514389	−	0.137830i
$438$		0			0
$439$	−13.6623	+	7.88793i	−0.652066	+	0.376470i	−0.789247	−	0.614076i	$-0.789529\pi$
$439$	−13.6623	+	7.88793i	−0.652066	+	0.376470i	0.137182	+	0.990546i	$0.456196\pi$
$440$	−0.253138	−	0.944723i	−0.0120679	−	0.0450379i
$441$		0			0
$442$	−0.154751	+	4.82297i	−0.00736076	+	0.229405i
$443$	22.7538	+	13.1369i	1.08107	+	0.624155i	0.931184	−	0.364549i	$-0.118777\pi$
$443$	22.7538	+	13.1369i	1.08107	+	0.624155i	0.149884	+	0.988704i	$0.452110\pi$
$444$		0			0
$445$	−0.255755			−0.0121239
$446$	1.50360	−	2.60432i	0.0711977	−	0.123318i
$447$		0			0
$448$	1.56234	−	1.56234i	0.0738135	−	0.0738135i
$449$	12.2297	+	3.27694i	0.577156	+	0.154648i	0.535576	−	0.844487i	$-0.320094\pi$
$449$	12.2297	+	3.27694i	0.577156	+	0.154648i	0.0415795	+	0.999135i	$0.486761\pi$
$450$		0			0
$451$	10.8324	+	18.7623i	0.510080	+	0.883484i
$452$	1.72482	+	2.98747i	0.0811286	+	0.140519i
$453$		0			0
$454$	−3.08254	+	1.77971i	−0.144671	+	0.0835258i
$455$	−0.0315104	−	0.134745i	−0.00147723	−	0.00631693i
$456$		0			0
$457$	12.6635	+	3.39318i	0.592374	+	0.158726i	0.542538	−	0.840031i	$-0.317463\pi$
$457$	12.6635	+	3.39318i	0.592374	+	0.158726i	0.0498361	+	0.998757i	$0.484130\pi$
$458$	−14.2407	−	8.22188i	−0.665425	−	0.384183i
$459$		0			0
$460$	0.305881	−	0.305881i	0.0142618	−	0.0142618i
$461$	23.6909	+	23.6909i	1.10340	+	1.10340i	0.993998	+	0.109399i	$0.0348926\pi$
$461$	23.6909	+	23.6909i	1.10340	+	1.10340i	0.109399	+	0.993998i	$0.465107\pi$
$462$		0			0
$463$	−3.99555	+	14.9116i	−0.185689	+	0.693000i	0.808793	+	0.588093i	$0.200121\pi$
$463$	−3.99555	+	14.9116i	−0.185689	+	0.693000i	−0.994482	+	0.104907i	$0.966545\pi$
$464$	−2.23561	−	1.29073i	−0.103785	−	0.0599206i
$465$		0			0
$466$	−3.51088	+	13.1028i	−0.162638	+	0.606974i
$467$	−20.9252			−0.968302			−0.484151	−	0.874985i	$-0.660871\pi$
$467$	−20.9252			−0.968302			−0.484151	+	0.874985i	$0.660871\pi$
$468$		0			0
$469$	5.60309			0.258727
$470$	0.116548	−	0.434963i	0.00537596	−	0.0200633i
$471$		0			0
$472$	−8.76583	−	5.06096i	−0.403480	−	0.232949i
$473$	1.85114	−	6.90855i	0.0851156	−	0.317656i
$474$		0			0
$475$	10.6900	+	10.6900i	0.490489	+	0.490489i
$476$	0.413939	−	0.413939i	0.0189729	−	0.0189729i
$477$		0			0
$478$	16.6230	+	9.59729i	0.760318	+	0.438970i
$479$	21.9119	+	5.87127i	1.00118	+	0.268265i	0.721939	−	0.691957i	$-0.243251\pi$
$479$	21.9119	+	5.87127i	1.00118	+	0.268265i	0.279239	+	0.960222i	$0.409918\pi$
$480$		0			0
$481$	0.517889	−	16.1405i	0.0236137	−	0.735945i
$482$	−19.6042	+	11.3185i	−0.892949	+	0.515544i
$483$		0			0
$484$	−0.483429	−	0.837323i	−0.0219740	−	0.0380601i
$485$	−0.649556	−	1.12506i	−0.0294948	−	0.0510865i
$486$		0			0
$487$	6.17114	+	1.65355i	0.279641	+	0.0749295i	0.395914	−	0.918288i	$-0.370428\pi$
$487$	6.17114	+	1.65355i	0.279641	+	0.0749295i	−0.116273	+	0.993217i	$0.537095\pi$
$488$	12.9249	−	12.9249i	0.585084	−	0.585084i
$489$		0			0
$490$	−0.337846	+	0.585167i	−0.0152623	+	0.0264351i
$491$	13.8081			0.623152			0.311576	−	0.950221i	$-0.399143\pi$
$491$	13.8081			0.623152			0.311576	+	0.950221i	$0.399143\pi$
$492$		0			0
$493$	−6.39499	−	3.69215i	−0.288016	−	0.166286i
$494$	−7.00514	−	7.46958i	−0.315176	−	0.336072i
$495$		0			0
$496$	0.731175	+	2.72878i	0.0328307	+	0.122526i
$497$	1.91834	−	1.10755i	0.0860493	−	0.0496806i
$498$		0			0
$499$	3.79783	+	1.01763i	0.170014	+	0.0455552i	0.342822	−	0.939400i	$-0.388617\pi$
$499$	3.79783	+	1.01763i	0.170014	+	0.0455552i	−0.172808	+	0.984956i	$0.555284\pi$
$500$	−1.13612	+	0.304422i	−0.0508088	+	0.0136142i
$501$		0			0
$502$	−7.10771	+	1.90450i	−0.317232	+	0.0850022i
$503$	−9.04338	+	5.22120i	−0.403224	+	0.232802i	−0.687874	−	0.725830i	$-0.741456\pi$
$503$	−9.04338	+	5.22120i	−0.403224	+	0.232802i	0.284650	+	0.958632i	$0.408123\pi$
$504$		0			0
$505$	0.385652	−	0.103335i	0.0171613	−	0.00459835i
$506$	5.48176	−	9.49469i	0.243694	−	0.422090i
$507$		0			0
$508$	7.23985	+	12.5398i	0.321217	+	0.556363i
$509$	−22.1867	−	22.1867i	−0.983406	−	0.983406i	0.0164583	−	0.999865i	$-0.494761\pi$
$509$	−22.1867	−	22.1867i	−0.983406	−	0.983406i	−0.999865	+	0.0164583i	$0.994761\pi$
$510$		0			0
$511$		−	2.13551i		−	0.0944693i
$512$	3.96564	+	3.96564i	0.175258	+	0.175258i
$513$		0			0
$514$	6.39299	−	23.8590i	0.281983	−	1.05237i
$515$	0.182265	+	0.680221i	0.00803154	+	0.0299741i
$516$		0			0
$517$			14.5700i			0.640790i
$518$	1.08510	−	1.08510i	0.0476766	−	0.0476766i
$519$		0			0
$520$	1.07844	−	0.252196i	0.0472928	−	0.0110595i
$521$			22.8205i			0.999785i	0.866087	+	0.499893i	$0.166627\pi$
$521$			22.8205i			0.999785i	−0.866087	+	0.499893i	$0.833373\pi$
$522$		0			0
$523$	−1.54860	+	2.68225i	−0.0677156	+	0.117287i	−0.897895	−	0.440209i	$-0.854904\pi$
$523$	−1.54860	+	2.68225i	−0.0677156	+	0.117287i	0.830180	+	0.557496i	$0.188238\pi$
$524$	17.4227			0.761114
$525$		0			0
$526$	5.12328	+	19.1203i	0.223385	+	0.833686i
$527$	2.09154	+	7.80572i	0.0911088	+	0.340023i
$528$		0			0
$529$	−9.50362			−0.413201
$530$	−0.644073	+	1.11557i	−0.0279767	+	0.0484571i
$531$		0			0
$532$			1.24232i			0.0538613i
$533$	−21.6288	+	11.5789i	−0.936848	+	0.501539i
$534$		0			0
$535$	0.899357	−	0.899357i	0.0388826	−	0.0388826i
$536$			44.8448i			1.93700i
$537$		0			0
$538$	−1.06008	−	3.95629i	−0.0457035	−	0.170568i
$539$	5.65845	−	21.1176i	0.243727	−	0.909601i
$540$		0			0
$541$	−5.55366	−	5.55366i	−0.238771	−	0.238771i	0.577570	−	0.816341i	$-0.304001\pi$
$541$	−5.55366	−	5.55366i	−0.238771	−	0.238771i	−0.816341	+	0.577570i	$0.804001\pi$
$542$			13.2474i			0.569024i
$543$		0			0
$544$	5.43569	+	5.43569i	0.233053	+	0.233053i
$545$	−0.0477560	−	0.0827159i	−0.00204564	−	0.00354316i
$546$		0			0
$547$	−8.77561	+	15.1998i	−0.375218	+	0.649897i	−0.990360	−	0.138520i	$-0.955766\pi$
$547$	−8.77561	+	15.1998i	−0.375218	+	0.649897i	0.615142	+	0.788417i	$0.289099\pi$
$548$	−19.9708	+	5.35115i	−0.853109	+	0.228590i
$549$		0			0
$550$	−12.8939	+	7.44428i	−0.549797	+	0.317425i
$551$	15.1368	−	4.05589i	0.644849	−	0.172787i
$552$		0			0
$553$	5.75960	−	1.54328i	0.244923	−	0.0656269i
$554$	−22.2665	−	5.96628i	−0.946011	−	0.253483i
$555$		0			0
$556$	−8.82162	+	5.09316i	−0.374120	+	0.215998i
$557$	−4.44615	−	16.5933i	−0.188390	−	0.703079i	−0.993879	−	0.110470i	$-0.964764\pi$
$557$	−4.44615	−	16.5933i	−0.188390	−	0.703079i	0.805490	−	0.592609i	$-0.201902\pi$
$558$		0			0
$559$	7.75196	+	2.34603i	0.327873	+	0.0992266i
$560$	0.0165916	+	0.00957914i	0.000701121	+	0.000404793i
$561$		0			0
$562$	19.7591			0.833486
$563$	−4.66104	+	8.07315i	−0.196439	+	0.340243i	−0.947371	−	0.320137i	$-0.896271\pi$
$563$	−4.66104	+	8.07315i	−0.196439	+	0.340243i	0.750932	+	0.660379i	$0.229605\pi$
$564$		0			0
$565$	−0.228354	+	0.228354i	−0.00960690	+	0.00960690i
$566$	−3.64871	−	0.977668i	−0.153367	−	0.0410945i
$567$		0			0
$568$	8.86441	+	15.3536i	0.371942	+	0.644223i
$569$	13.0069	+	22.5286i	0.545278	+	0.944449i	0.998589	+	0.0530970i	$0.0169092\pi$
$569$	13.0069	+	22.5286i	0.545278	+	0.944449i	−0.453311	+	0.891352i	$0.649757\pi$
$570$		0			0
$571$	2.90676	−	1.67822i	0.121644	−	0.0702313i	−0.437943	−	0.899003i	$-0.644293\pi$
$571$	2.90676	−	1.67822i	0.121644	−	0.0702313i	0.559587	+	0.828771i	$0.310960\pi$
$572$	−11.3509	+	6.07665i	−0.474604	+	0.254078i
$573$		0			0
$574$	−2.25186	−	0.603384i	−0.0939908	−	0.0251848i
$575$	−15.8727	−	9.16411i	−0.661937	−	0.382170i
$576$		0			0
$577$	19.0194	−	19.0194i	0.791788	−	0.791788i	−0.189997	−	0.981785i	$-0.560848\pi$
$577$	19.0194	−	19.0194i	0.791788	−	0.791788i	0.981785	+	0.189997i	$0.0608478\pi$
$578$	9.91552	+	9.91552i	0.412431	+	0.412431i
$579$		0			0
$580$	−0.157603	+	0.588184i	−0.00654412	+	0.0244230i
$581$	5.25360	+	3.03317i	0.217956	+	0.125837i
$582$		0			0
$583$	10.7873	−	40.2588i	0.446765	−	1.66735i
$584$	17.0917			0.707260
$585$		0			0
$586$	10.8233			0.447107
$587$	−2.76844	+	10.3320i	−0.114266	+	0.426446i	−0.999231	−	0.0392112i	$-0.987515\pi$
$587$	−2.76844	+	10.3320i	−0.114266	+	0.426446i	0.884965	+	0.465658i	$0.154182\pi$
$588$		0			0
$589$	−14.8519	−	8.57472i	−0.611960	−	0.353315i
$590$	0.0881146	−	0.328848i	0.00362762	−	0.0135385i
$591$		0			0
$592$	1.58092	+	1.58092i	0.0649753	+	0.0649753i
$593$	11.0116	−	11.0116i	0.452191	−	0.452191i	−0.443890	−	0.896081i	$-0.646402\pi$
$593$	11.0116	−	11.0116i	0.452191	−	0.452191i	0.896081	+	0.443890i	$0.146402\pi$
$594$		0			0
$595$	0.0474604	+	0.0274013i	0.00194569	+	0.00112334i
$596$	−13.0449	−	3.49538i	−0.534341	−	0.143176i
$597$		0			0
$598$	10.5471	+	6.54913i	0.431304	+	0.267814i
$599$	18.9127	−	10.9193i	0.772752	−	0.446149i	−0.0611031	−	0.998131i	$-0.519462\pi$
$599$	18.9127	−	10.9193i	0.772752	−	0.446149i	0.833856	+	0.551983i	$0.186129\pi$
$600$		0			0
$601$	−6.14623	−	10.6456i	−0.250710	−	0.434242i	0.713012	−	0.701152i	$-0.247331\pi$
$601$	−6.14623	−	10.6456i	−0.250710	−	0.434242i	−0.963721	+	0.266910i	$0.913997\pi$
$602$	0.384817	+	0.666523i	0.0156840	+	0.0271655i
$603$		0			0
$604$	0.0457096	+	0.0122479i	0.00185990	+	0.000498358i
$605$	0.0640025	−	0.0640025i	0.00260207	−	0.00260207i
$606$		0			0
$607$	−12.5802	+	21.7895i	−0.510613	+	0.884408i	0.489311	+	0.872109i	$0.337248\pi$
$607$	−12.5802	+	21.7895i	−0.510613	+	0.884408i	−0.999924	+	0.0122987i	$0.996085\pi$
$608$	−16.3136			−0.661605
$609$		0			0
$610$	0.532430	+	0.307399i	0.0215575	+	0.0124462i
$611$	−16.4905	−	0.529120i	−0.667136	−	0.0214059i
$612$		0			0
$613$	−0.567750	−	2.11887i	−0.0229312	−	0.0855804i	0.953512	−	0.301355i	$-0.0974390\pi$
$613$	−0.567750	−	2.11887i	−0.0229312	−	0.0855804i	−0.976443	+	0.215775i	$0.930772\pi$
$614$	20.5696	−	11.8759i	0.830121	−	0.479271i
$615$		0			0
$616$	−3.28926	−	0.881355i	−0.132528	−	0.0355108i
$617$	−10.8043	+	2.89501i	−0.434966	+	0.116549i	−0.469656	−	0.882849i	$-0.655622\pi$
$617$	−10.8043	+	2.89501i	−0.434966	+	0.116549i	0.0346902	+	0.999398i	$0.488956\pi$
$618$		0			0
$619$	10.6571	−	2.85556i	0.428345	−	0.114775i	−0.0382041	−	0.999270i	$-0.512164\pi$
$619$	10.6571	−	2.85556i	0.428345	−	0.114775i	0.466549	+	0.884495i	$0.345497\pi$
$620$	0.577112	−	0.333196i	0.0231774	−	0.0133815i
$621$		0			0
$622$	−20.1530	+	5.39998i	−0.808061	+	0.216519i
$623$	−0.445233	+	0.771166i	−0.0178379	+	0.0308961i
$624$		0			0
$625$	12.4174	+	21.5075i	0.496695	+	0.860302i
$626$	5.70046	+	5.70046i	0.227836	+	0.227836i
$627$		0			0
$628$		−	15.6005i		−	0.622526i
$629$	4.52224	+	4.52224i	0.180314	+	0.180314i
$630$		0			0
$631$	−0.654527	+	2.44273i	−0.0260563	+	0.0972435i	−0.977729	−	0.209869i	$-0.932696\pi$
$631$	−0.654527	+	2.44273i	−0.0260563	+	0.0972435i	0.951673	+	0.307113i	$0.0993629\pi$
$632$	12.3518	+	46.0974i	0.491327	+	1.83366i
$633$		0			0
$634$		−	29.5154i		−	1.17221i
$635$	−0.958504	+	0.958504i	−0.0380371	+	0.0380371i
$636$		0			0
$637$	23.6957	+	7.17120i	0.938857	+	0.284133i
$638$			15.4330i			0.611000i
$639$		0			0
$640$	0.267834	−	0.463903i	0.0105871	−	0.0183374i
$641$	−17.9952			−0.710766			−0.355383	−	0.934721i	$-0.615650\pi$
$641$	−17.9952			−0.710766			−0.355383	+	0.934721i	$0.615650\pi$
$642$		0			0
$643$	−9.25856	−	34.5534i	−0.365122	−	1.36265i	−0.867255	−	0.497864i	$-0.834118\pi$
$643$	−9.25856	−	34.5534i	−0.365122	−	1.36265i	0.502133	−	0.864790i	$-0.332549\pi$
$644$	−0.389814	−	1.45481i	−0.0153608	−	0.0573274i
$645$		0			0
$646$	4.05552			0.159562
$647$	10.1566	−	17.5918i	0.399298	−	0.691605i	−0.594341	−	0.804213i	$-0.702587\pi$
$647$	10.1566	−	17.5918i	0.399298	−	0.691605i	0.993639	+	0.112608i	$0.0359205\pi$
$648$		0			0
$649$			11.0155i			0.432396i
$650$	−7.95728	−	14.8638i	−0.312110	−	0.583006i
$651$		0			0
$652$	0.637737	−	0.637737i	0.0249757	−	0.0249757i
$653$			29.2478i			1.14455i	0.820060	+	0.572277i	$0.193940\pi$
$653$			29.2478i			1.14455i	−0.820060	+	0.572277i	$0.806060\pi$
$654$		0			0
$655$	0.422144	+	1.57546i	0.0164945	+	0.0615585i
$656$	0.879090	−	3.28081i	0.0343227	−	0.128094i
$657$		0			0
$658$	−1.10863	−	1.10863i	−0.0432189	−	0.0432189i
$659$		−	42.0776i		−	1.63911i	−0.573001	−	0.819554i	$-0.694221\pi$
$659$		−	42.0776i		−	1.63911i	0.573001	−	0.819554i	$-0.305779\pi$
$660$		0			0
$661$	−13.2150	−	13.2150i	−0.514003	−	0.514003i	0.401748	−	0.915750i	$-0.368403\pi$
$661$	−13.2150	−	13.2150i	−0.514003	−	0.514003i	−0.915750	+	0.401748i	$0.868403\pi$
$662$	−7.33278	−	12.7007i	−0.284997	−	0.493628i
$663$		0			0
$664$	−24.2762	+	42.0477i	−0.942101	+	1.63177i
$665$	−0.112338	+	0.0301008i	−0.00435627	+	0.00116726i
$666$		0			0
$667$	−16.4532	+	9.49924i	−0.637069	+	0.367812i
$668$	−16.8082	+	4.50375i	−0.650330	+	0.174255i
$669$		0			0
$670$	−1.45695	+	0.390389i	−0.0562869	+	0.0150820i
$671$	−19.2145	−	5.14850i	−0.741767	−	0.198756i
$672$		0			0
$673$	5.20812	−	3.00691i	0.200758	−	0.115908i	−0.396251	−	0.918142i	$-0.629689\pi$
$673$	5.20812	−	3.00691i	0.200758	−	0.115908i	0.597009	+	0.802234i	$0.296356\pi$
$674$	−1.51965	−	5.67142i	−0.0585349	−	0.218455i
$675$		0			0
$676$	−6.46542	−	13.0677i	−0.248670	−	0.502605i
$677$	−23.1275	−	13.3527i	−0.888863	−	0.513185i	−0.0152925	−	0.999883i	$-0.504868\pi$
$677$	−23.1275	−	13.3527i	−0.888863	−	0.513185i	−0.873570	+	0.486698i	$0.838201\pi$
$678$		0			0
$679$	−4.52314			−0.173582
$680$	−0.219309	+	0.379854i	−0.00841011	+	0.0145667i
$681$		0			0
$682$	11.9425	−	11.9425i	0.457303	−	0.457303i
$683$	29.2534	+	7.83841i	1.11935	+	0.299929i	0.770620	−	0.637295i	$-0.219947\pi$
$683$	29.2534	+	7.83841i	1.11935	+	0.299929i	0.348729	+	0.937224i	$0.386613\pi$
$684$		0			0
$685$	−0.967766	−	1.67622i	−0.0369764	−	0.0640451i
$686$	2.37546	+	4.11442i	0.0906956	+	0.157089i
$687$		0			0
$688$	−0.971079	+	0.560653i	−0.0370220	+	0.0213747i
$689$	45.1737	+	13.6712i	1.72098	+	0.520833i
$690$		0			0
$691$	−41.2583	−	11.0551i	−1.56954	−	0.420557i	−0.633872	−	0.773438i	$-0.718536\pi$
$691$	−41.2583	−	11.0551i	−1.56954	−	0.420557i	−0.935668	+	0.352880i	$0.885202\pi$
$692$	−14.8966	−	8.60054i	−0.566283	−	0.326944i
$693$		0			0
$694$	−12.0886	+	12.0886i	−0.458879	+	0.458879i
$695$	−0.674298	−	0.674298i	−0.0255776	−	0.0255776i
$696$		0			0
$697$	2.51465	−	9.38480i	0.0952492	−	0.355475i
$698$	6.50727	+	3.75697i	0.246304	+	0.142204i
$699$		0			0
$700$	−0.529371	+	1.97564i	−0.0200084	+	0.0746722i
$701$	−23.1973			−0.876151			−0.438075	−	0.898938i	$-0.644340\pi$
$701$	−23.1973			−0.876151			−0.438075	+	0.898938i	$0.644340\pi$
$702$		0			0
$703$	−13.5722			−0.511884
$704$	4.98095	−	18.5892i	0.187727	−	0.700606i
$705$		0			0
$706$	14.0200	+	8.09445i	0.527650	+	0.304639i
$707$	0.359784	−	1.34273i	0.0135311	−	0.0504986i
$708$		0			0
$709$	−6.45646	−	6.45646i	−0.242477	−	0.242477i	0.575397	−	0.817874i	$-0.304848\pi$
$709$	−6.45646	−	6.45646i	−0.242477	−	0.242477i	−0.817874	+	0.575397i	$0.804848\pi$
$710$	−0.421651	+	0.421651i	−0.0158243	+	0.0158243i
$711$		0			0
$712$	−6.17209	−	3.56346i	−0.231309	−	0.133546i
$713$	20.0827	+	5.38115i	0.752104	+	0.201526i
$714$		0			0
$715$	−0.824514	−	0.879179i	−0.0308351	−	0.0328794i
$716$	−18.1361	+	10.4709i	−0.677776	+	0.391314i
$717$		0			0
$718$	14.5046	+	25.1227i	0.541307	+	0.937570i
$719$	−7.26683	−	12.5865i	−0.271007	−	0.469398i	0.698113	−	0.715988i	$-0.254023\pi$
$719$	−7.26683	−	12.5865i	−0.271007	−	0.469398i	−0.969120	+	0.246590i	$0.920690\pi$
$720$		0			0
$721$	2.36834	+	0.634594i	0.0882015	+	0.0236335i
$722$	6.50661	−	6.50661i	0.242151	−	0.242151i
$723$		0			0
$724$	−7.97389	+	13.8112i	−0.296347	+	0.513289i
$725$	25.8001			0.958192
$726$		0			0
$727$	23.7883	+	13.7342i	0.882259	+	0.509372i	0.871403	−	0.490569i	$-0.163211\pi$
$727$	23.7883	+	13.7342i	0.882259	+	0.509372i	0.0108564	+	0.999941i	$0.496544\pi$
$728$	1.11698	−	3.69082i	0.0413980	−	0.136791i
$729$		0			0
$730$	0.148789	+	0.555288i	0.00550693	+	0.0205521i
$731$	−2.77779	+	1.60376i	−0.102740	+	0.0593171i
$732$		0			0
$733$	−35.6888	−	9.56277i	−1.31819	−	0.353209i	−0.469893	−	0.882723i	$-0.655708\pi$
$733$	−35.6888	−	9.56277i	−1.31819	−	0.353209i	−0.848301	+	0.529514i	$0.822374\pi$
$734$	−1.18668	+	0.317971i	−0.0438013	+	0.0117365i
$735$		0			0
$736$	19.1039	−	5.11889i	0.704181	−	0.188685i
$737$	42.2653	−	24.4019i	1.55686	−	0.898856i
$738$		0			0
$739$	−6.91898	+	1.85394i	−0.254519	+	0.0681981i	−0.383822	−	0.923407i	$-0.625393\pi$
$739$	−6.91898	+	1.85394i	−0.254519	+	0.0681981i	0.129304	+	0.991605i	$0.458726\pi$
$740$	0.263693	−	0.456730i	0.00969355	−	0.0167897i
$741$		0			0
$742$	2.24248	+	3.88409i	0.0823241	+	0.142589i
$743$	−11.1879	−	11.1879i	−0.410445	−	0.410445i	0.471449	−	0.881894i	$-0.343731\pi$
$743$	−11.1879	−	11.1879i	−0.410445	−	0.410445i	−0.881894	+	0.471449i	$0.843731\pi$
$744$		0			0
$745$		−	1.26429i		−	0.0463201i
$746$	19.1015	+	19.1015i	0.699355	+	0.699355i
$747$		0			0
$748$	1.31970	−	4.92518i	0.0482529	−	0.180082i
$749$	−1.14614	−	4.27745i	−0.0418790	−	0.156294i
$750$		0			0
$751$		−	37.8476i		−	1.38108i	−0.723295	−	0.690539i	$-0.757373\pi$
$751$		−	37.8476i		−	1.38108i	0.723295	−	0.690539i	$-0.242627\pi$
$752$	1.61520	−	1.61520i	0.0589003	−	0.0589003i
$753$		0			0
$754$	−17.4673	−	0.560460i	−0.636122	−	0.0204108i
$755$			0.00443010i			0.000161228i
$756$		0			0
$757$	8.84072	−	15.3126i	0.321322	−	0.556545i	−0.659439	−	0.751758i	$-0.729206\pi$
$757$	8.84072	−	15.3126i	0.321322	−	0.556545i	0.980761	+	0.195212i	$0.0625396\pi$
$758$	16.1295			0.585850
$759$		0			0
$760$	−0.240914	−	0.899105i	−0.00873888	−	0.0326140i
$761$	−12.1299	−	45.2692i	−0.439707	−	1.64101i	−0.729545	−	0.683932i	$-0.760268\pi$
$761$	−12.1299	−	45.2692i	−0.439707	−	1.64101i	0.289839	−	0.957076i	$-0.406398\pi$
$762$		0			0
$763$	−0.332546			−0.0120390
$764$	4.11355	−	7.12488i	0.148823	−	0.257769i
$765$		0			0
$766$		−	30.0516i		−	1.08581i
$767$	−12.4675	−	0.400034i	−0.450174	−	0.0144444i
$768$		0			0
$769$	−13.5222	+	13.5222i	−0.487624	+	0.487624i	−0.907556	−	0.419932i	$-0.862054\pi$
$769$	−13.5222	+	13.5222i	−0.487624	+	0.487624i	0.419932	+	0.907556i	$0.362054\pi$
$770$		−	0.114536i		−	0.00412760i
$771$		0			0
$772$	6.21318	+	23.1879i	0.223617	+	0.834551i
$773$	5.12420	−	19.1238i	0.184305	−	0.687834i	−0.810474	−	0.585775i	$-0.800790\pi$
$773$	5.12420	−	19.1238i	0.184305	−	0.687834i	0.994778	−	0.102059i	$-0.0325431\pi$
$774$		0			0
$775$	−19.9649	−	19.9649i	−0.717160	−	0.717160i
$776$		−	36.2014i		−	1.29955i
$777$		0			0
$778$	−10.6281	−	10.6281i	−0.381036	−	0.381036i
$779$	10.3094	+	17.8563i	0.369371	+	0.639770i
$780$		0			0
$781$	9.64697	−	16.7090i	0.345196	−	0.597897i
$782$	−4.74918	+	1.27254i	−0.169830	+	0.0455059i
$783$		0			0
$784$	−2.96833	+	1.71377i	−0.106012	+	0.0612060i
$785$	1.41069	−	0.377992i	0.0503495	−	0.0134911i
$786$		0			0
$787$	−6.23713	+	1.67123i	−0.222330	+	0.0595730i	−0.368264	−	0.929721i	$-0.620048\pi$
$787$	−6.23713	+	1.67123i	−0.222330	+	0.0595730i	0.145935	+	0.989294i	$0.453381\pi$
$788$	4.20150	+	1.12579i	0.149672	+	0.0401046i
$789$		0			0
$790$	−1.39012	+	0.802587i	−0.0494583	+	0.0285547i
$791$	0.291013	+	1.08608i	0.0103472	+	0.0386164i
$792$		0			0
$793$	6.52492	−	21.5602i	0.231707	−	0.765625i
$794$	−24.5124	−	14.1522i	−0.869913	−	0.502244i
$795$		0			0
$796$	11.4870			0.407145
$797$	24.7313	−	42.8358i	0.876026	−	1.51732i	0.0203612	−	0.999793i	$-0.493518\pi$
$797$	24.7313	−	42.8358i	0.876026	−	1.51732i	0.855665	−	0.517530i	$-0.173148\pi$
$798$		0			0
$799$	4.62031	−	4.62031i	0.163455	−	0.163455i
$800$	−25.9433	−	6.95150i	−0.917235	−	0.245772i
$801$		0			0
$802$	−5.31907	−	9.21290i	−0.187823	−	0.325319i
$803$	−9.30030	−	16.1086i	−0.328201	−	0.568460i
$804$		0			0
$805$	0.122107	−	0.0704986i	0.00430371	−	0.00248475i
$806$	13.0830	+	13.9504i	0.460829	+	0.491382i
$807$		0			0
$808$	10.7467	+	2.87956i	0.378067	+	0.101303i
$809$	42.4000	+	24.4797i	1.49071	+	0.860659i	0.999943	−	0.0106348i	$-0.00338524\pi$
$809$	42.4000	+	24.4797i	1.49071	+	0.860659i	0.490762	+	0.871294i	$0.336719\pi$
$810$		0			0
$811$	2.24360	−	2.24360i	0.0787834	−	0.0787834i	−0.666617	−	0.745400i	$-0.732258\pi$
$811$	2.24360	−	2.24360i	0.0787834	−	0.0787834i	0.745400	+	0.666617i	$0.232258\pi$
$812$	1.49916	+	1.49916i	0.0526102	+	0.0526102i
$813$		0			0
$814$	3.45945	−	12.9109i	0.121254	−	0.452525i
$815$	0.0731201	+	0.0422159i	0.00256129	+	0.00147876i
$816$		0			0
$817$	1.76175	−	6.57496i	0.0616360	−	0.230029i
$818$	−11.0443			−0.386156
$819$		0			0
$820$	−0.801201			−0.0279791
$821$	3.22800	−	12.0471i	0.112658	−	0.420446i	−0.886443	−	0.462838i	$-0.846831\pi$
$821$	3.22800	−	12.0471i	0.112658	−	0.420446i	0.999101	+	0.0423922i	$0.0134979\pi$
$822$		0			0
$823$	10.8078	+	6.23987i	0.376735	+	0.217508i	0.676397	−	0.736537i	$-0.263540\pi$
$823$	10.8078	+	6.23987i	0.376735	+	0.217508i	−0.299662	+	0.954046i	$0.596874\pi$
$824$	−5.07903	+	18.9552i	−0.176936	+	0.660336i
$825$		0			0
$826$	−0.838166	−	0.838166i	−0.0291635	−	0.0291635i
$827$	−9.01542	+	9.01542i	−0.313497	+	0.313497i	−0.846263	−	0.532766i	$-0.821153\pi$
$827$	−9.01542	+	9.01542i	−0.313497	+	0.313497i	0.532766	+	0.846263i	$0.321153\pi$
$828$		0			0
$829$	−12.1868	−	7.03605i	−0.423265	−	0.244372i	0.273208	−	0.961955i	$-0.411915\pi$
$829$	−12.1868	−	7.03605i	−0.423265	−	0.244372i	−0.696473	+	0.717583i	$0.745249\pi$
$830$	−1.57741	−	0.422665i	−0.0547526	−	0.0146709i
$831$		0			0
$832$	20.8586	+	6.31258i	0.723140	+	0.218849i
$833$	−8.49097	+	4.90226i	−0.294195	+	0.169853i
$834$		0			0
$835$	−0.814512	−	1.41078i	−0.0281874	−	0.0488219i
$836$	5.41039	+	9.37107i	0.187122	+	0.324105i
$837$		0			0
$838$	2.61136	+	0.699711i	0.0902079	+	0.0241711i
$839$	−37.0235	+	37.0235i	−1.27819	+	1.27819i	−0.336514	+	0.941678i	$0.609248\pi$
$839$	−37.0235	+	37.0235i	−1.27819	+	1.27819i	−0.941678	+	0.336514i	$0.890752\pi$
$840$		0			0
$841$	−1.12818	+	1.95407i	−0.0389029	+	0.0673817i
$842$	2.35015			0.0809915
$843$		0			0
$844$	−17.5516	−	10.1334i	−0.604152	−	0.348808i
$845$	1.02501	−	0.901267i	0.0352614	−	0.0310045i
$846$		0			0
$847$	−0.0815646	−	0.304403i	−0.00280259	−	0.0104594i
$848$	−5.65886	+	3.26714i	−0.194326	+	0.112194i
$849$		0			0
$850$	6.44944	+	1.72812i	0.221214	+	0.0592741i
$851$	15.8936	−	4.25868i	0.544826	−	0.145986i
$852$		0			0
$853$	−14.0861	+	3.77435i	−0.482297	+	0.129231i	−0.491772	−	0.870724i	$-0.663651\pi$
$853$	−14.0861	+	3.77435i	−0.482297	+	0.129231i	0.00947475	+	0.999955i	$0.496984\pi$
$854$	1.85377	−	1.07028i	0.0634348	−	0.0366241i
$855$		0			0
$856$	34.2349	−	9.17322i	1.17013	−	0.313534i
$857$	−6.89566	+	11.9436i	−0.235551	+	0.407986i	−0.959433	−	0.281938i	$-0.909023\pi$
$857$	−6.89566	+	11.9436i	−0.235551	+	0.407986i	0.723882	+	0.689924i	$0.242356\pi$
$858$		0			0
$859$	14.9164	+	25.8359i	0.508940	+	0.881510i	0.999946	+	0.0103542i	$0.00329591\pi$
$859$	14.9164	+	25.8359i	0.508940	+	0.881510i	−0.491006	+	0.871156i	$0.663371\pi$
$860$	0.187031	+	0.187031i	0.00637770	+	0.00637770i
$861$		0			0
$862$		−	14.4997i		−	0.493861i
$863$	33.0412	+	33.0412i	1.12473	+	1.12473i	0.991020	+	0.133714i	$0.0426904\pi$
$863$	33.0412	+	33.0412i	1.12473	+	1.12473i	0.133714	+	0.991020i	$0.457310\pi$
$864$		0			0
$865$	0.416775	−	1.55542i	0.0141708	−	0.0528860i
$866$	1.27074	+	4.74247i	0.0431816	+	0.161156i
$867$		0			0
$868$		−	2.32019i		−	0.0787523i
$869$	36.7248	−	36.7248i	1.24580	−	1.24580i
$870$		0			0
$871$	26.0835	+	48.7226i	0.883805	+	1.65090i
$872$		−	2.66156i		−	0.0901319i
$873$		0			0
$874$	5.21706	−	9.03621i	0.176470	−	0.305654i
$875$	−0.383374			−0.0129604
$876$		0			0
$877$	−2.62939	−	9.81303i	−0.0887883	−	0.331362i	0.907216	−	0.420664i	$-0.138203\pi$
$877$	−2.62939	−	9.81303i	−0.0887883	−	0.331362i	−0.996005	+	0.0893021i	$0.971536\pi$
$878$	−3.82698	−	14.2825i	−0.129154	−	0.482011i
$879$		0			0
$880$	0.166872			0.00562524
$881$	−2.67563	+	4.63432i	−0.0901441	+	0.156134i	−0.907572	−	0.419897i	$-0.862066\pi$
$881$	−2.67563	+	4.63432i	−0.0901441	+	0.156134i	0.817428	+	0.576031i	$0.195399\pi$
$882$		0			0
$883$		−	11.6579i		−	0.392321i	−0.980572	−	0.196161i	$-0.937153\pi$
$883$		−	11.6579i		−	0.392321i	0.980572	−	0.196161i	$-0.0628474\pi$
$884$	5.52645	+	1.67251i	0.185874	+	0.0562526i
$885$		0			0
$886$	−17.4131	+	17.4131i	−0.585005	+	0.585005i
$887$			9.64645i			0.323896i	0.986799	+	0.161948i	$0.0517777\pi$
$887$			9.64645i			0.323896i	−0.986799	+	0.161948i	$0.948222\pi$
$888$		0			0
$889$	1.22152	+	4.55876i	0.0409683	+	0.152896i
$890$	0.0620422	−	0.231545i	0.00207966	−	0.00776139i
$891$		0			0
$892$	−2.54440	−	2.54440i	−0.0851929	−	0.0851929i
$893$			13.8665i			0.464024i
$894$		0			0
$895$	−1.38627	−	1.38627i	−0.0463378	−	0.0463378i
$896$	−0.932524	−	1.61518i	−0.0311534	−	0.0539593i
$897$		0			0
$898$	−5.93349	+	10.2771i	−0.198003	+	0.342951i
$899$	−28.2699	+	7.57490i	−0.942854	+	0.252637i
$900$		0			0
$901$	−16.1873	+	9.34572i	−0.539276	+	0.311351i
$902$	−19.6141	+	5.25557i	−0.653077	+	0.174991i
$903$		0			0
$904$	−8.69251	+	2.32915i	−0.289108	+	0.0774664i
$905$	−1.44209	−	0.386408i	−0.0479368	−	0.0128446i
$906$		0			0
$907$	37.7680	−	21.8053i	1.25406	−	0.724035i	0.282151	−	0.959370i	$-0.408952\pi$
$907$	37.7680	−	21.8053i	1.25406	−	0.724035i	0.971914	+	0.235336i	$0.0756189\pi$
$908$	1.10233	+	4.11396i	0.0365821	+	0.136526i
$909$		0			0
$910$	0.129634	+	0.00415946i	0.00429731	+	0.000137885i
$911$	−15.2019	−	8.77681i	−0.503661	−	0.290789i	0.226563	−	0.973996i	$-0.427251\pi$
$911$	−15.2019	−	8.77681i	−0.503661	−	0.290789i	−0.730224	+	0.683208i	$0.760584\pi$
$912$		0			0
$913$	52.8388			1.74871
$914$	−6.14395	+	10.6416i	−0.203224	+	0.351994i
$915$		0			0
$916$	−13.9131	+	13.9131i	−0.459702	+	0.459702i
$917$	5.48532	+	1.46979i	0.181141	+	0.0485367i
$918$		0			0
$919$	−2.44511	−	4.23505i	−0.0806566	−	0.139701i	0.822876	−	0.568222i	$-0.192368\pi$
$919$	−2.44511	−	4.23505i	−0.0806566	−	0.139701i	−0.903532	+	0.428520i	$0.859035\pi$
$920$	0.564242	+	0.977296i	0.0186025	+	0.0322205i
$921$		0			0
$922$	−27.1954	+	15.7013i	−0.895632	+	0.517094i
$923$	18.5612	+	11.5254i	0.610948	+	0.379362i
$924$		0			0
$925$	−21.5837	−	5.78332i	−0.709666	−	0.190154i
$926$	−12.5308	−	7.23465i	−0.411787	−	0.237745i
$927$		0			0
$928$	−19.6864	+	19.6864i	−0.646237	+	0.646237i
$929$	23.0818	+	23.0818i	0.757289	+	0.757289i	0.975828	−	0.218539i	$-0.0701292\pi$
$929$	23.0818	+	23.0818i	0.757289	+	0.757289i	−0.218539	+	0.975828i	$0.570129\pi$
$930$		0			0
$931$	5.38522	−	20.0979i	0.176493	−	0.658682i
$932$	14.0568	+	8.11571i	0.460447	+	0.265839i
$933$		0			0
$934$	5.07613	−	18.9444i	0.166096	−	0.619879i
$935$	0.477339			0.0156107
$936$		0			0
$937$	35.2389			1.15121			0.575603	−	0.817729i	$-0.304767\pi$
$937$	35.2389			1.15121			0.575603	+	0.817729i	$0.304767\pi$
$938$	−1.35922	+	5.07269i	−0.0443802	+	0.165629i
$939$		0			0
$940$	−0.466634	−	0.269411i	−0.0152199	−	0.00878723i
$941$	6.33017	−	23.6245i	0.206358	−	0.770137i	−0.782674	−	0.622432i	$-0.786145\pi$
$941$	6.33017	−	23.6245i	0.206358	−	0.770137i	0.989031	−	0.147705i	$-0.0471886\pi$
$942$		0			0
$943$	−17.6757	−	17.6757i	−0.575599	−	0.575599i
$944$	1.22115	−	1.22115i	0.0397451	−	0.0397451i
$945$		0			0
$946$	5.80552	+	3.35182i	0.188754	+	0.108977i
$947$	−3.70163	−	0.991850i	−0.120287	−	0.0322308i	0.198173	−	0.980167i	$-0.436499\pi$
$947$	−3.70163	−	0.991850i	−0.120287	−	0.0322308i	−0.318460	+	0.947936i	$0.603166\pi$
$948$		0			0
$949$	18.5696	−	9.94120i	0.602796	−	0.322705i
$950$	−12.2713	+	7.08482i	−0.398132	+	0.229862i
$951$		0			0
$952$	0.763571	+	1.32254i	0.0247475	+	0.0428639i
$953$	12.0041	+	20.7918i	0.388852	+	0.673512i	0.992295	−	0.123894i	$-0.0395384\pi$
$953$	12.0041	+	20.7918i	0.388852	+	0.673512i	−0.603443	+	0.797406i	$0.706205\pi$
$954$		0			0
$955$	0.743943	+	0.199339i	0.0240734	+	0.00645046i
$956$	16.2406	−	16.2406i	0.525257	−	0.525257i
$957$		0			0
$958$	−10.6310	+	18.4134i	−0.343471	+	0.594909i
$959$	−6.73898			−0.217613
$960$		0			0
$961$	0.890953	+	0.514392i	0.0287404	+	0.0165933i
$962$	14.4870	+	4.38431i	0.467080	+	0.141356i
$963$		0			0
$964$	7.01057	+	26.1638i	0.225795	+	0.842679i
$965$	−1.94625	+	1.12367i	−0.0626519	+	0.0361721i
$966$		0			0
$967$	10.3554	+	2.77473i	0.333009	+	0.0892294i	0.421449	−	0.906852i	$-0.361522\pi$
$967$	10.3554	+	2.77473i	0.333009	+	0.0892294i	−0.0884405	+	0.996081i	$0.528188\pi$
$968$	2.43632	−	0.652809i	0.0783062	−	0.0209821i
$969$		0			0
$970$	1.17614	−	0.315145i	0.0377634	−	0.0101187i
$971$	−46.2535	+	26.7045i	−1.48435	+	0.856988i	−0.999842	−	0.0178003i	$-0.994334\pi$
$971$	−46.2535	+	26.7045i	−1.48435	+	0.856988i	−0.484505	+	0.874788i	$0.661000\pi$
$972$		0			0
$973$	−3.20704	+	0.859324i	−0.102813	+	0.0275487i
$974$	−2.99405	+	5.18584i	−0.0959355	+	0.166165i
$975$		0			0
$976$	1.55932	+	2.70082i	0.0499126	+	0.0864512i
$977$	−26.3627	−	26.3627i	−0.843419	−	0.843419i	0.145883	−	0.989302i	$-0.453398\pi$
$977$	−26.3627	−	26.3627i	−0.843419	−	0.843419i	−0.989302	+	0.145883i	$0.953398\pi$
$978$		0			0
$979$			7.75610i			0.247886i
$980$	0.571704	+	0.571704i	0.0182624	+	0.0182624i
$981$		0			0
$982$	−3.34964	+	12.5010i	−0.106891	+	0.398924i
$983$	−4.23860	−	15.8187i	−0.135190	−	0.504537i	−0.999997	−	0.00243220i	$-0.999226\pi$
$983$	−4.23860	−	15.8187i	−0.135190	−	0.504537i	0.864807	−	0.502105i	$-0.167441\pi$
$984$		0			0
$985$			0.407202i			0.0129745i
$986$	4.89397	−	4.89397i	0.155856	−	0.155856i
$987$		0			0
$988$	−10.8028	+	5.78323i	−0.343682	+	0.183989i
$989$			8.25236i			0.262410i
$990$		0			0
$991$	−25.9576	+	44.9599i	−0.824571	+	1.42820i	0.0776754	+	0.996979i	$0.475250\pi$
$991$	−25.9576	+	44.9599i	−0.824571	+	1.42820i	−0.902247	+	0.431220i	$0.858083\pi$
$992$	30.4678			0.967353
$993$		0			0
$994$	0.537351	+	2.00542i	0.0170438	+	0.0636082i
$995$	0.278325	+	1.03872i	0.00882348	+	0.0329297i
$996$		0			0
$997$	1.46367			0.0463549			0.0231774	−	0.999731i	$-0.492622\pi$
$997$	1.46367			0.0463549			0.0231774	+	0.999731i	$0.492622\pi$
$998$	−1.84259	+	3.19146i	−0.0583262	+	0.101024i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bf.a.305.5		48
3.2	odd	2		117.2.bc.a.110.8	yes	48
9.4	even	3		117.2.x.a.32.5	yes	48
9.5	odd	6		351.2.ba.a.71.8		48
13.11	odd	12		351.2.ba.a.89.8		48
39.11	even	12		117.2.x.a.11.5	✓	48
117.50	even	12	inner	351.2.bf.a.206.5		48
117.76	odd	12		117.2.bc.a.50.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.5	✓	48	39.11	even	12
117.2.x.a.32.5	yes	48	9.4	even	3
117.2.bc.a.50.8	yes	48	117.76	odd	12
117.2.bc.a.110.8	yes	48	3.2	odd	2
351.2.ba.a.71.8		48	9.5	odd	6
351.2.ba.a.89.8		48	13.11	odd	12
351.2.bf.a.206.5		48	117.50	even	12	inner
351.2.bf.a.305.5		48	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bf (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.242585 + 0.905339i) q^{2} +(0.971260 + 0.560757i) q^{4} +(-0.0271738 + 0.101414i) q^{5} +(0.258484 + 0.258484i) q^{7} +(-2.06880 + 2.06880i) q^{8} +(-0.0852221 - 0.0492030i) q^{10} +(3.07551 + 0.824082i) q^{11} +(-1.04439 + 3.45098i) q^{13} +(-0.296719 + 0.171311i) q^{14} +(-0.249589 - 0.432300i) q^{16} +(-0.713952 - 1.23660i) q^{17} +(2.92701 + 0.784289i) q^{19} +(-0.0832615 + 0.0832615i) q^{20} +(-1.49215 + 2.58447i) q^{22} -3.67374 q^{23} +(4.32058 + 2.49449i) q^{25} +(-2.87095 - 1.78269i) q^{26} +(0.106108 + 0.396001i) q^{28} +(4.47859 - 2.58571i) q^{29} +(-5.46656 - 1.46476i) q^{31} +(-5.20013 + 1.39337i) q^{32} +(1.29274 - 0.346388i) q^{34} +(-0.0332378 + 0.0191899i) q^{35} +(-4.32627 + 1.15922i) q^{37} +(-1.42009 + 2.45967i) q^{38} +(-0.153588 - 0.266022i) q^{40} +(4.81135 + 4.81135i) q^{41} -2.24631i q^{43} +(2.52501 + 2.52501i) q^{44} +(0.891194 - 3.32598i) q^{46} +(1.18436 + 4.42009i) q^{47} -6.86637i q^{49} +(-3.30646 + 3.30646i) q^{50} +(-2.94954 + 2.76614i) q^{52} -13.0901i q^{53} +(-0.167147 + 0.289507i) q^{55} -1.06950 q^{56} +(1.25451 + 4.68189i) q^{58} +(0.895419 + 3.34175i) q^{59} -6.24756 q^{61} +(2.65221 - 4.59376i) q^{62} -6.04425i q^{64} +(-0.321597 - 0.199692i) q^{65} +(10.8384 - 10.8384i) q^{67} -1.60142i q^{68} +(-0.00931034 - 0.0347467i) q^{70} +(1.56835 - 5.85317i) q^{71} +(-4.13084 - 4.13084i) q^{73} -4.19795i q^{74} +(2.40309 + 2.40309i) q^{76} +(0.581958 + 1.00798i) q^{77} +(8.15587 - 14.1264i) q^{79} +(0.0506235 - 0.0135645i) q^{80} +(-5.52307 + 3.18874i) q^{82} +(16.0296 - 4.29512i) q^{83} +(0.144809 - 0.0388016i) q^{85} +(2.03367 + 0.544920i) q^{86} +(-8.06747 + 4.65776i) q^{88} +(0.630472 + 2.35295i) q^{89} +(-1.16198 + 0.622062i) q^{91} +(-3.56816 - 2.06008i) q^{92} -4.28898 q^{94} +(-0.159076 + 0.275527i) q^{95} +(-8.74938 + 8.74938i) q^{97} +(6.21639 + 1.66568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

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