LMFDB - Embedded newform 2268.2.bm.i.593.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(593,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.593"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.1
Root			$1.07992 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	2268.593
Dual form			2268.2.bm.i.1025.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-3.12105 q^{5} +(-2.20291 + 1.46533i) q^{7} +3.74094i q^{11} +(2.53803 - 1.46533i) q^{13} +(2.71678 + 4.70560i) q^{17} +(-6.07338 - 3.50647i) q^{19} +1.66487i q^{23} +4.74094 q^{25} +(6.12340 + 3.53534i) q^{29} +(-6.60872 - 3.81555i) q^{31} +(6.87538 - 4.57338i) q^{35} +(-4.03534 + 6.98942i) q^{37} +(-4.80027 - 8.31431i) q^{41} +(2.87047 - 4.97180i) q^{43} +(1.56052 + 2.70291i) q^{47} +(2.70560 - 6.45599i) q^{49} +(-3.11266 + 1.79709i) q^{53} -11.6756i q^{55} +(-2.20220 + 3.81431i) q^{59} +(2.57069 - 1.48419i) q^{61} +(-7.92132 + 4.57338i) q^{65} +(4.90850 - 8.50177i) q^{67} -7.33513i q^{71} +(2.46466 - 1.42297i) q^{73} +(-5.48172 - 8.24094i) q^{77} +(-2.57338 - 4.45722i) q^{79} +(7.80262 - 13.5145i) q^{83} +(-8.47919 - 14.6864i) q^{85} +(2.59808 - 4.50000i) q^{89} +(-3.44385 + 6.94706i) q^{91} +(18.9553 + 10.9438i) q^{95} +(2.07606 + 1.19862i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} - 18 q^{61} + 54 q^{73} + 24 q^{79} + 6 q^{85} + 42 q^{91} - 36 q^{97}+O(q^{100}) $ 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 - 18 * q^61 + 54 * q^73 + 24 * q^79 + 6 * q^85 + 42 * q^91 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.12105			−1.39577			−0.697887	−	0.716207i	$-0.745876\pi$
$5$	−3.12105			−1.39577			−0.697887	+	0.716207i	$0.745876\pi$
$6$		0			0
$7$	−2.20291	+	1.46533i	−0.832620	+	0.553844i
$7$	−2.20291	+	1.46533i	−0.832620	+	0.553844i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			3.74094i			1.12794i	0.825797	+	0.563968i	$0.190726\pi$
$11$			3.74094i			1.12794i	−0.825797	+	0.563968i	$0.809274\pi$
$12$		0			0
$13$	2.53803	−	1.46533i	0.703923	−	0.406410i	−0.104884	−	0.994485i	$-0.533447\pi$
$13$	2.53803	−	1.46533i	0.703923	−	0.406410i	0.808807	+	0.588074i	$0.200114\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.71678	+	4.70560i	0.658915	+	1.14127i	0.980897	+	0.194529i	$0.0623177\pi$
$17$	2.71678	+	4.70560i	0.658915	+	1.14127i	−0.321982	+	0.946746i	$0.604349\pi$
$18$		0			0
$19$	−6.07338	−	3.50647i	−1.39333	−	0.804438i	−0.399646	−	0.916670i	$-0.630867\pi$
$19$	−6.07338	−	3.50647i	−1.39333	−	0.804438i	−0.993682	+	0.112231i	$0.964200\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			1.66487i			0.347150i	0.984821	+	0.173575i	$0.0555320\pi$
$23$			1.66487i			0.347150i	−0.984821	+	0.173575i	$0.944468\pi$
$24$		0			0
$25$	4.74094			0.948188
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.12340	+	3.53534i	1.13709	+	0.656497i	0.945707	−	0.325019i	$-0.105371\pi$
$29$	6.12340	+	3.53534i	1.13709	+	0.656497i	0.191379	+	0.981516i	$0.438704\pi$
$30$		0			0
$31$	−6.60872	−	3.81555i	−1.18696	−	0.685292i	−0.229347	−	0.973345i	$-0.573659\pi$
$31$	−6.60872	−	3.81555i	−1.18696	−	0.685292i	−0.957615	+	0.288053i	$0.906992\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.87538	−	4.57338i	1.16215	−	0.773042i
$36$		0			0
$37$	−4.03534	+	6.98942i	−0.663406	+	1.14905i	0.316308	+	0.948656i	$0.397557\pi$
$37$	−4.03534	+	6.98942i	−0.663406	+	1.14905i	−0.979715	+	0.200397i	$0.935777\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.80027	−	8.31431i	−0.749677	−	1.29848i	−0.947978	−	0.318337i	$-0.896876\pi$
$41$	−4.80027	−	8.31431i	−0.749677	−	1.29848i	0.198301	−	0.980141i	$-0.436458\pi$
$42$		0			0
$43$	2.87047	−	4.97180i	0.437742	−	0.758192i	−0.559773	−	0.828646i	$-0.689111\pi$
$43$	2.87047	−	4.97180i	0.437742	−	0.758192i	0.997515	+	0.0704541i	$0.0224448\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.56052	+	2.70291i	0.227626	+	0.394259i	0.957104	−	0.289745i	$-0.0935704\pi$
$47$	1.56052	+	2.70291i	0.227626	+	0.394259i	−0.729478	+	0.684004i	$0.760237\pi$
$48$		0			0
$49$	2.70560	−	6.45599i	0.386514	−	0.922284i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.11266	+	1.79709i	−0.427556	+	0.246850i	−0.698305	−	0.715800i	$-0.746062\pi$
$53$	−3.11266	+	1.79709i	−0.427556	+	0.246850i	0.270749	+	0.962650i	$0.412729\pi$
$54$		0			0
$55$		−	11.6756i		−	1.57434i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.20220	+	3.81431i	−0.286701	+	0.496581i	−0.973020	−	0.230719i	$-0.925892\pi$
$59$	−2.20220	+	3.81431i	−0.286701	+	0.496581i	0.686319	+	0.727301i	$0.259225\pi$
$60$		0			0
$61$	2.57069	−	1.48419i	0.329143	−	0.190031i	−0.326318	−	0.945260i	$-0.605808\pi$
$61$	2.57069	−	1.48419i	0.329143	−	0.190031i	0.655460	+	0.755229i	$0.272475\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.92132	+	4.57338i	−0.982519	+	0.567257i
$66$		0			0
$67$	4.90850	−	8.50177i	0.599669	−	1.03866i	−0.393201	−	0.919453i	$-0.628632\pi$
$67$	4.90850	−	8.50177i	0.599669	−	1.03866i	0.992870	−	0.119204i	$-0.0380344\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.33513i		−	0.870519i	−0.900305	−	0.435260i	$-0.856657\pi$
$71$		−	7.33513i		−	0.870519i	0.900305	−	0.435260i	$-0.143343\pi$
$72$		0			0
$73$	2.46466	−	1.42297i	0.288466	−	0.166546i	−0.348784	−	0.937203i	$-0.613405\pi$
$73$	2.46466	−	1.42297i	0.288466	−	0.166546i	0.637250	+	0.770657i	$0.280072\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.48172	−	8.24094i	−0.624700	−	0.939142i
$78$		0			0
$79$	−2.57338	−	4.45722i	−0.289527	−	0.501476i	0.684170	−	0.729323i	$-0.260165\pi$
$79$	−2.57338	−	4.45722i	−0.289527	−	0.501476i	−0.973697	+	0.227847i	$0.926831\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.80262	−	13.5145i	0.856449	−	1.48341i	−0.0188457	−	0.999822i	$-0.505999\pi$
$83$	7.80262	−	13.5145i	0.856449	−	1.48341i	0.875294	−	0.483590i	$-0.160668\pi$
$84$		0			0
$85$	−8.47919	−	14.6864i	−0.919697	−	1.59296i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	−0.694839	−	0.719165i	$-0.744525\pi$
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	0.970235	+	0.242166i	$0.0778579\pi$
$90$		0			0
$91$	−3.44385	+	6.94706i	−0.361013	+	0.728249i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	18.9553	+	10.9438i	1.94477	+	1.12281i
$96$		0			0
$97$	2.07606	+	1.19862i	0.210792	+	0.121701i	0.601680	−	0.798738i	$-0.294498\pi$
$97$	2.07606	+	1.19862i	0.210792	+	0.121701i	−0.390887	+	0.920439i	$0.627832\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−19.7554			−1.96574			−0.982870	−	0.184299i	$-0.940999\pi$
$101$	−19.7554			−1.96574			−0.982870	+	0.184299i	$0.940999\pi$
$102$		0			0
$103$		−	12.2938i		−	1.21135i	−0.795714	−	0.605673i	$-0.792904\pi$
$103$		−	12.2938i		−	1.21135i	0.795714	−	0.605673i	$-0.207096\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.7155	−	9.07338i	−1.51928	−	0.877156i	−0.999742	−	0.0227086i	$-0.992771\pi$
$107$	−15.7155	−	9.07338i	−1.51928	−	0.877156i	−0.519537	−	0.854448i	$-0.673896\pi$
$108$		0			0
$109$	−5.74094	−	9.94360i	−0.549882	−	0.952424i	−0.998282	−	0.0585909i	$-0.981339\pi$
$109$	−5.74094	−	9.94360i	−0.549882	−	0.952424i	0.448400	−	0.893833i	$-0.351994\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.56891	−	0.905813i	0.147591	−	0.0852117i	−0.424386	−	0.905481i	$-0.639510\pi$
$113$	1.56891	−	0.905813i	0.147591	−	0.0852117i	0.571977	+	0.820270i	$0.306177\pi$
$114$		0			0
$115$		−	5.19615i		−	0.484544i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.8801	−	6.38500i	−1.18071	−	0.585312i
$120$		0			0
$121$	−2.99462			−0.272238
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.808542			0.0723182
$126$		0			0
$127$	−7.47650			−0.663432			−0.331716	−	0.943379i	$-0.607628\pi$
$127$	−7.47650			−0.663432			−0.331716	+	0.943379i	$0.607628\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.05064			0.616017			0.308009	−	0.951384i	$-0.400337\pi$
$131$	7.05064			0.616017			0.308009	+	0.951384i	$0.400337\pi$
$132$		0			0
$133$	18.5172	−	1.17511i	1.60565	−	0.101895i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	14.6703i		−	1.25336i	−0.779275	−	0.626682i	$-0.784412\pi$
$137$		−	14.6703i		−	1.25336i	0.779275	−	0.626682i	$-0.215588\pi$
$138$		0			0
$139$	1.46734	−	0.847172i	0.124459	−	0.0718562i	−0.436478	−	0.899715i	$-0.643774\pi$
$139$	1.46734	−	0.847172i	0.124459	−	0.0718562i	0.560937	+	0.827859i	$0.310441\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.48172	+	9.49462i	0.458405	+	0.793980i
$144$		0			0
$145$	−19.1114	−	11.0340i	−1.58712	−	0.916322i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			14.8170i			1.21386i	0.794757	+	0.606928i	$0.207598\pi$
$149$			14.8170i			1.21386i	−0.794757	+	0.606928i	$0.792402\pi$
$150$		0			0
$151$	−6.07069			−0.494026			−0.247013	−	0.969012i	$-0.579449\pi$
$151$	−6.07069			−0.494026			−0.247013	+	0.969012i	$0.579449\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.6261	+	11.9085i	1.65673	+	0.956514i
$156$		0			0
$157$	12.1141	+	6.99408i	0.966810	+	0.558188i	0.898262	−	0.439460i	$-0.144830\pi$
$157$	12.1141	+	6.99408i	0.966810	+	0.558188i	0.0685479	+	0.997648i	$0.478163\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.43960	−	3.66756i	−0.192267	−	0.289044i
$162$		0			0
$163$	−0.926624	+	1.60496i	−0.0725788	+	0.125710i	−0.900031	−	0.435826i	$-0.856456\pi$
$163$	−0.926624	+	1.60496i	−0.0725788	+	0.125710i	0.827452	+	0.561536i	$0.189790\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.27495	+	2.20828i	0.0986588	+	0.170882i	0.911130	−	0.412120i	$-0.135211\pi$
$167$	1.27495	+	2.20828i	0.0986588	+	0.170882i	−0.812471	+	0.583002i	$0.801878\pi$
$168$		0			0
$169$	−2.20560	+	3.82020i	−0.169661	+	0.293862i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.95640	+	3.38859i	0.148743	+	0.257630i	0.930763	−	0.365623i	$-0.119144\pi$
$173$	1.95640	+	3.38859i	0.148743	+	0.257630i	−0.782020	+	0.623253i	$0.785811\pi$
$174$		0			0
$175$	−10.4438	+	6.94706i	−0.789481	+	0.525148i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.9284	+	9.77359i	−1.26529	+	0.730513i	−0.974092	−	0.226152i	$-0.927386\pi$
$179$	−16.9284	+	9.77359i	−1.26529	+	0.730513i	−0.291193	+	0.956664i	$0.594052\pi$
$180$		0			0
$181$			18.1929i			1.35226i	0.736780	+	0.676132i	$0.236345\pi$
$181$			18.1929i			1.35226i	−0.736780	+	0.676132i	$0.763655\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.5945	−	21.8143i	0.925966	−	1.60382i
$186$		0			0
$187$	−17.6033	+	10.1633i	−1.28728	+	0.743214i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.0609	−	7.54072i	0.945054	−	0.545627i	0.0535132	−	0.998567i	$-0.482958\pi$
$191$	13.0609	−	7.54072i	0.945054	−	0.545627i	0.891541	+	0.452940i	$0.149625\pi$
$192$		0			0
$193$	5.57338	−	9.65337i	0.401180	−	0.694865i	−0.592688	−	0.805432i	$-0.701933\pi$
$193$	5.57338	−	9.65337i	0.401180	−	0.694865i	0.993869	+	0.110567i	$0.0352667\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.3696i			1.45127i	0.688079	+	0.725636i	$0.258454\pi$
$197$			20.3696i			1.45127i	−0.688079	+	0.725636i	$0.741546\pi$
$198$		0			0
$199$	6.42931	−	3.71197i	0.455762	−	0.263134i	−0.254499	−	0.967073i	$-0.581910\pi$
$199$	6.42931	−	3.71197i	0.455762	−	0.263134i	0.710261	+	0.703939i	$0.248577\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.6697	+	1.18478i	−1.31036	+	0.0831556i
$204$		0			0
$205$	14.9819	+	25.9494i	1.04638	+	1.81238i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	13.1175	−	22.7201i	0.907355	−	1.57158i
$210$		0			0
$211$	6.77628	+	11.7369i	0.466499	+	0.807999i	0.999268	−	0.0382614i	$-0.0121820\pi$
$211$	6.77628	+	11.7369i	0.466499	+	0.807999i	−0.532769	+	0.846261i	$0.678849\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.95887	+	15.5172i	−0.610990	+	1.05827i
$216$		0			0
$217$	20.1494	−	1.27869i	1.36783	−	0.0868029i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	13.7905	+	7.96197i	0.927652	+	0.535580i
$222$		0			0
$223$	−7.61410	−	4.39600i	−0.509878	−	0.294378i	0.222906	−	0.974840i	$-0.428446\pi$
$223$	−7.61410	−	4.39600i	−0.509878	−	0.294378i	−0.732783	+	0.680462i	$0.761779\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.7048			−0.843248			−0.421624	−	0.906771i	$-0.638540\pi$
$227$	−12.7048			−0.843248			−0.421624	+	0.906771i	$0.638540\pi$
$228$		0			0
$229$		−	27.9670i		−	1.84811i	−0.382258	−	0.924056i	$-0.624854\pi$
$229$		−	27.9670i		−	1.84811i	0.382258	−	0.924056i	$-0.375146\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.2737	+	8.24094i	0.935103	+	0.539882i	0.888422	−	0.459028i	$-0.151802\pi$
$233$	14.2737	+	8.24094i	0.935103	+	0.539882i	0.0466810	+	0.998910i	$0.485136\pi$
$234$		0			0
$235$	−4.87047	−	8.43590i	−0.317714	−	0.550297i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.78349	+	2.76175i	−0.309418	+	0.178643i	−0.646666	−	0.762773i	$-0.723837\pi$
$239$	−4.78349	+	2.76175i	−0.309418	+	0.178643i	0.337248	+	0.941416i	$0.390504\pi$
$240$		0			0
$241$		−	21.5252i		−	1.38656i	−0.720668	−	0.693280i	$-0.756165\pi$
$241$		−	21.5252i		−	1.38656i	0.720668	−	0.693280i	$-0.243835\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.44429	+	20.1494i	−0.539486	+	1.28730i
$246$		0			0
$247$	−20.5526			−1.30773
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.808542			−0.0510347			−0.0255174	−	0.999674i	$-0.508123\pi$
$251$	−0.808542			−0.0510347			−0.0255174	+	0.999674i	$0.508123\pi$
$252$		0			0
$253$	−6.22819			−0.391563
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.9634			−0.683881			−0.341941	−	0.939722i	$-0.611084\pi$
$257$	−10.9634			−0.683881			−0.341941	+	0.939722i	$0.611084\pi$
$258$		0			0
$259$	−1.35235	−	21.3102i	−0.0840308	−	1.32415i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	7.33513i		−	0.452303i	−0.974092	−	0.226152i	$-0.927386\pi$
$263$		−	7.33513i		−	0.452303i	0.974092	−	0.226152i	$-0.0726145\pi$
$264$		0			0
$265$	9.71475	−	5.60881i	0.596772	−	0.344547i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.28569	−	7.42303i	−0.261303	−	0.452590i	0.705285	−	0.708924i	$-0.250819\pi$
$269$	−4.28569	−	7.42303i	−0.261303	−	0.452590i	−0.966588	+	0.256333i	$0.917486\pi$
$270$		0			0
$271$	6.79619	+	3.92378i	0.412839	+	0.238353i	0.692009	−	0.721889i	$-0.256726\pi$
$271$	6.79619	+	3.92378i	0.412839	+	0.238353i	−0.279170	+	0.960242i	$0.590059\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			17.7356i			1.06949i
$276$		0			0
$277$	−2.26981			−0.136380			−0.0681900	−	0.997672i	$-0.521722\pi$
$277$	−2.26981			−0.136380			−0.0681900	+	0.997672i	$0.521722\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	25.0787	+	14.4792i	1.49607	+	0.863756i	0.999990	−	0.00452108i	$-0.00143911\pi$
$281$	25.0787	+	14.4792i	1.49607	+	0.863756i	0.496080	+	0.868277i	$0.334772\pi$
$282$		0			0
$283$	−2.11679	−	1.22213i	−0.125830	−	0.0726479i	0.435764	−	0.900061i	$-0.356478\pi$
$283$	−2.11679	−	1.22213i	−0.125830	−	0.0726479i	−0.561594	+	0.827413i	$0.689812\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	22.7578	+	11.2817i	1.34335	+	0.665935i
$288$		0			0
$289$	−6.26175	+	10.8457i	−0.368338	+	0.637980i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.27730	+	7.40850i	0.249883	+	0.432809i	0.963493	−	0.267733i	$-0.0862747\pi$
$293$	4.27730	+	7.40850i	0.249883	+	0.432809i	−0.713610	+	0.700543i	$0.752941\pi$
$294$		0			0
$295$	6.87316	−	11.9047i	0.400171	−	0.693116i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.43960	+	4.22550i	0.141086	+	0.244367i
$300$		0			0
$301$	0.961968	+	15.1586i	0.0554469	+	0.873727i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.02324	+	4.63222i	−0.459409	+	0.265240i
$306$		0			0
$307$		−	23.8000i		−	1.35834i	−0.733982	−	0.679169i	$-0.762340\pi$
$307$		−	23.8000i		−	1.35834i	0.733982	−	0.679169i	$-0.237660\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.55460	−	14.8170i	0.485087	−	0.840195i	−0.514766	−	0.857331i	$-0.672121\pi$
$311$	8.55460	−	14.8170i	0.485087	−	0.840195i	0.999853	+	0.0171354i	$0.00545463\pi$
$312$		0			0
$313$	−1.35325	+	0.781298i	−0.0764901	+	0.0441616i	−0.537757	−	0.843100i	$-0.680728\pi$
$313$	−1.35325	+	0.781298i	−0.0764901	+	0.0441616i	0.461267	+	0.887261i	$0.347395\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.5511	+	13.0199i	−1.26660	+	0.731271i	−0.974343	−	0.225069i	$-0.927739\pi$
$317$	−22.5511	+	13.0199i	−1.26660	+	0.731271i	−0.292256	+	0.956340i	$0.594406\pi$
$318$		0			0
$319$	−13.2255	+	22.9072i	−0.740486	+	1.28256i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	38.1051i		−	2.12023i
$324$		0			0
$325$	12.0327	−	6.94706i	0.667452	−	0.385353i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.39835	−	3.66756i	−0.407884	−	0.202199i
$330$		0			0
$331$	15.1087	+	26.1691i	0.830450	+	1.43838i	0.897682	+	0.440645i	$0.145250\pi$
$331$	15.1087	+	26.1691i	0.830450	+	1.43838i	−0.0672312	+	0.997737i	$0.521417\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−15.3197	+	26.5344i	−0.837003	+	1.44973i
$336$		0			0
$337$	11.1114	+	19.2455i	0.605277	+	1.04837i	0.992008	+	0.126178i	$0.0402710\pi$
$337$	11.1114	+	19.2455i	0.605277	+	1.04837i	−0.386731	+	0.922193i	$0.626396\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.2737	−	24.7228i	0.772966	−	1.33882i
$342$		0			0
$343$	3.50000	+	18.1865i	0.188982	+	0.981981i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−31.6853	−	18.2935i	−1.70095	−	0.982047i	−0.944796	−	0.327658i	$-0.893741\pi$
$347$	−31.6853	−	18.2935i	−1.70095	−	0.982047i	−0.756159	−	0.654388i	$-0.772926\pi$
$348$		0			0
$349$	−7.96197	−	4.59684i	−0.426194	−	0.246063i	0.271530	−	0.962430i	$-0.412470\pi$
$349$	−7.96197	−	4.59684i	−0.426194	−	0.246063i	−0.697724	+	0.716367i	$0.745804\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.554360			−0.0295056			−0.0147528	−	0.999891i	$-0.504696\pi$
$353$	−0.554360			−0.0295056			−0.0147528	+	0.999891i	$0.504696\pi$
$354$		0			0
$355$			22.8933i			1.21505i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.3487	−	7.12953i	−0.651740	−	0.376282i	0.137383	−	0.990518i	$-0.456131\pi$
$359$	−12.3487	−	7.12953i	−0.651740	−	0.376282i	−0.789123	+	0.614236i	$0.789464\pi$
$360$		0			0
$361$	15.0906	+	26.1377i	0.794242	+	1.37567i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.69231	+	4.44116i	−0.402634	+	0.232461i
$366$		0			0
$367$		−	13.9504i		−	0.728207i	−0.931358	−	0.364104i	$-0.881375\pi$
$367$		−	13.9504i		−	0.728207i	0.931358	−	0.364104i	$-0.118625\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.22355	−	8.51991i	0.219276	−	0.442332i
$372$		0			0
$373$	16.4349			0.850966			0.425483	−	0.904966i	$-0.360104\pi$
$373$	16.4349			0.850966			0.425483	+	0.904966i	$0.360104\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.7218			1.06723
$378$		0			0
$379$	34.5217			1.77326			0.886630	−	0.462479i	$-0.153040\pi$
$379$	34.5217			1.77326			0.886630	+	0.462479i	$0.153040\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.92959			−0.200793			−0.100396	−	0.994948i	$-0.532011\pi$
$383$	−3.92959			−0.200793			−0.100396	+	0.994948i	$0.532011\pi$
$384$		0			0
$385$	17.1087	+	25.7204i	0.871941	+	1.31083i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	21.4765i		−	1.08890i	−0.838793	−	0.544451i	$-0.816738\pi$
$389$		−	21.4765i		−	1.08890i	0.838793	−	0.544451i	$-0.183262\pi$
$390$		0			0
$391$	−7.83422	+	4.52309i	−0.396194	+	0.228743i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.03163	+	13.9112i	0.404115	+	0.699948i
$396$		0			0
$397$	−15.8913	−	9.17483i	−0.797560	−	0.460472i	0.0450569	−	0.998984i	$-0.485653\pi$
$397$	−15.8913	−	9.17483i	−0.797560	−	0.460472i	−0.842617	+	0.538513i	$0.818986\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	5.52350i		−	0.275830i	−0.990444	−	0.137915i	$-0.955960\pi$
$401$		−	5.52350i		−	0.275830i	0.990444	−	0.137915i	$-0.0440401\pi$
$402$		0			0
$403$	−22.3642			−1.11404
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−26.1470	−	15.0960i	−1.29606	−	0.748280i
$408$		0			0
$409$	8.64406	+	4.99065i	0.427421	+	0.246772i	0.698248	−	0.715856i	$-0.253963\pi$
$409$	8.64406	+	4.99065i	0.427421	+	0.246772i	−0.270826	+	0.962628i	$0.587297\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.738012	−	11.6295i	−0.0363152	−	0.572252i
$414$		0			0
$415$	−24.3523	+	42.1795i	−1.19541	+	2.07051i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.14798	−	8.91657i	−0.251495	−	0.435603i	0.712442	−	0.701731i	$-0.247589\pi$
$419$	−5.14798	−	8.91657i	−0.251495	−	0.435603i	−0.963938	+	0.266128i	$0.914256\pi$
$420$		0			0
$421$	−5.24363	+	9.08223i	−0.255559	+	0.442641i	−0.965047	−	0.262076i	$-0.915593\pi$
$421$	−5.24363	+	9.08223i	−0.255559	+	0.442641i	0.709488	+	0.704717i	$0.248926\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.8801	+	22.3089i	0.624775	+	1.08214i
$426$		0			0
$427$	−3.48816	+	7.03644i	−0.168804	+	0.340517i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.26668	+	3.04072i	−0.253687	+	0.146466i	−0.621451	−	0.783453i	$-0.713457\pi$
$431$	−5.26668	+	3.04072i	−0.253687	+	0.146466i	0.367764	+	0.929919i	$0.380123\pi$
$432$		0			0
$433$		−	25.6452i		−	1.23243i	−0.787579	−	0.616214i	$-0.788666\pi$
$433$		−	25.6452i		−	1.23243i	0.787579	−	0.616214i	$-0.211334\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.83782	−	10.1114i	0.279261	−	0.483694i
$438$		0			0
$439$	−24.7228	+	14.2737i	−1.17996	+	0.681248i	−0.956004	−	0.293353i	$-0.905229\pi$
$439$	−24.7228	+	14.2737i	−1.17996	+	0.681248i	−0.223951	+	0.974600i	$0.571896\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.3702	−	10.6060i	0.872794	−	0.503908i	0.00451818	−	0.999990i	$-0.498562\pi$
$443$	18.3702	−	10.6060i	0.872794	−	0.503908i	0.868276	+	0.496082i	$0.165228\pi$
$444$		0			0
$445$	−8.10872	+	14.0447i	−0.384390	+	0.665783i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	22.5633i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$449$		−	22.5633i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$450$		0			0
$451$	31.1033	−	17.9575i	1.46460	−	0.845587i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.7484	−	21.6821i	0.503893	−	1.01647i
$456$		0			0
$457$	−6.72013	−	11.6396i	−0.314354	−	0.544478i	0.664946	−	0.746892i	$-0.268455\pi$
$457$	−6.72013	−	11.6396i	−0.314354	−	0.544478i	−0.979300	+	0.202414i	$0.935121\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.99642	+	17.3143i	−0.465580	+	0.806408i	−0.999227	−	0.0392989i	$-0.987488\pi$
$461$	−9.99642	+	17.3143i	−0.465580	+	0.806408i	0.533648	+	0.845707i	$0.320821\pi$
$462$		0			0
$463$	−5.00538	−	8.66957i	−0.232620	−	0.402909i	0.725959	−	0.687738i	$-0.241396\pi$
$463$	−5.00538	−	8.66957i	−0.232620	−	0.402909i	−0.958578	+	0.284829i	$0.908063\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.7699	−	29.0463i	0.776018	−	1.34410i	−0.158203	−	0.987407i	$-0.550570\pi$
$467$	16.7699	−	29.0463i	0.776018	−	1.34410i	0.934221	−	0.356695i	$-0.116097\pi$
$468$		0			0
$469$	1.64496	+	25.9212i	0.0759574	+	1.19693i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.5992	+	10.7383i	0.855192	+	0.493745i
$474$		0			0
$475$	−28.7935	−	16.6239i	−1.32114	−	0.762759i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.31720			0.380023			0.190011	−	0.981782i	$-0.439148\pi$
$479$	8.31720			0.380023			0.190011	+	0.981782i	$0.439148\pi$
$480$		0			0
$481$			23.6525i			1.07846i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.47950	−	3.74094i	−0.294219	−	0.169867i
$486$		0			0
$487$	−1.36509	−	2.36441i	−0.0618583	−	0.107142i	0.833438	−	0.552613i	$-0.186369\pi$
$487$	−1.36509	−	2.36441i	−0.0618583	−	0.107142i	−0.895296	+	0.445472i	$0.853036\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.00704	+	5.20022i	−0.406482	+	0.234683i	−0.689277	−	0.724498i	$-0.742072\pi$
$491$	−9.00704	+	5.20022i	−0.406482	+	0.234683i	0.282795	+	0.959180i	$0.408738\pi$
$492$		0			0
$493$			38.4190i			1.73030i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.7484	+	16.1586i	0.482132	+	0.724812i
$498$		0			0
$499$	−10.7517			−0.481312			−0.240656	−	0.970610i	$-0.577363\pi$
$499$	−10.7517			−0.481312			−0.240656	+	0.970610i	$0.577363\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17.3466			−0.773447			−0.386723	−	0.922196i	$-0.626393\pi$
$503$	−17.3466			−0.773447			−0.386723	+	0.922196i	$0.626393\pi$
$504$		0			0
$505$	61.6577			2.74373
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.37968			0.0611534			0.0305767	−	0.999532i	$-0.490266\pi$
$509$	1.37968			0.0611534			0.0305767	+	0.999532i	$0.490266\pi$
$510$		0			0
$511$	−3.34428	+	6.74621i	−0.147942	+	0.298435i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			38.3696i			1.69077i
$516$		0			0
$517$	−10.1114	+	5.83782i	−0.444699	+	0.256747i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.19381	+	3.79978i	0.0961123	+	0.166471i	0.910072	−	0.414450i	$-0.136026\pi$
$521$	2.19381	+	3.79978i	0.0961123	+	0.166471i	−0.813960	+	0.580921i	$0.802693\pi$
$522$		0			0
$523$	−30.6494	−	17.6955i	−1.34021	−	0.773769i	−0.353369	−	0.935484i	$-0.614964\pi$
$523$	−30.6494	−	17.6955i	−1.34021	−	0.773769i	−0.986837	+	0.161715i	$0.948297\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	41.4639i		−	1.80620i
$528$		0			0
$529$	20.2282			0.879487
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−24.3665	−	14.0680i	−1.05543	−	0.609353i
$534$		0			0
$535$	49.0490	+	28.3184i	2.12057	+	1.22431i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	24.1514	+	10.1215i	1.04028	+	0.435962i
$540$		0			0
$541$	−23.1114	+	40.0301i	−0.993637	+	1.72103i	−0.399278	+	0.916830i	$0.630739\pi$
$541$	−23.1114	+	40.0301i	−0.993637	+	1.72103i	−0.594359	+	0.804200i	$0.702594\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.9177	+	31.0344i	0.767512	+	1.32937i
$546$		0			0
$547$	−2.14406	+	3.71363i	−0.0916735	+	0.158783i	−0.908215	−	0.418503i	$-0.862555\pi$
$547$	−2.14406	+	3.71363i	−0.0916735	+	0.158783i	0.816542	+	0.577286i	$0.195888\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−24.7931	−	42.9429i	−1.05622	−	1.82943i
$552$		0			0
$553$	12.2002	+	6.04798i	0.518806	+	0.257186i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.49023	−	5.47919i	0.402114	−	0.232161i	−0.285282	−	0.958444i	$-0.592087\pi$
$557$	9.49023	−	5.47919i	0.402114	−	0.232161i	0.687396	+	0.726283i	$0.258754\pi$
$558$		0			0
$559$		−	16.8248i		−	0.711612i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.3572	+	28.3315i	−0.689375	+	1.19403i	0.282666	+	0.959218i	$0.408781\pi$
$563$	−16.3572	+	28.3315i	−0.689375	+	1.19403i	−0.972040	+	0.234813i	$0.924552\pi$
$564$		0			0
$565$	−4.89666	+	2.82709i	−0.206004	+	0.118936i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	31.8124	−	18.3669i	1.33364	−	0.769980i	0.347788	−	0.937573i	$-0.386933\pi$
$569$	31.8124	−	18.3669i	1.33364	−	0.769980i	0.985856	+	0.167594i	$0.0535997\pi$
$570$		0			0
$571$	−7.10603	+	12.3080i	−0.297378	+	0.515074i	−0.975535	−	0.219843i	$-0.929446\pi$
$571$	−7.10603	+	12.3080i	−0.297378	+	0.515074i	0.678157	+	0.734917i	$0.262779\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			7.89307i			0.329164i
$576$		0			0
$577$	22.1848	−	12.8084i	0.923565	−	0.533220i	0.0387941	−	0.999247i	$-0.487648\pi$
$577$	22.1848	−	12.8084i	0.923565	−	0.533220i	0.884771	+	0.466027i	$0.154315\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.61486	+	41.2047i	0.108483	+	1.70946i
$582$		0			0
$583$	−6.72282	−	11.6443i	−0.278431	−	0.482256i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.05064	+	12.2121i	−0.291011	+	0.504046i	−0.974049	−	0.226337i	$-0.927325\pi$
$587$	−7.05064	+	12.2121i	−0.291011	+	0.504046i	0.683038	+	0.730383i	$0.260658\pi$
$588$		0			0
$589$	26.7582	+	46.3465i	1.10255	+	1.90967i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.9721	+	32.8606i	−0.779090	+	1.34942i	0.153377	+	0.988168i	$0.450985\pi$
$593$	−18.9721	+	32.8606i	−0.779090	+	1.34942i	−0.932467	+	0.361255i	$0.882348\pi$
$594$		0			0
$595$	40.1993	+	19.9279i	1.64801	+	0.816964i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.9032	−	9.75906i	−0.690646	−	0.398744i	0.113208	−	0.993571i	$-0.463887\pi$
$599$	−16.9032	−	9.75906i	−0.690646	−	0.398744i	−0.803854	+	0.594827i	$0.797221\pi$
$600$		0			0
$601$	33.0436	+	19.0777i	1.34788	+	0.778197i	0.987948	−	0.154783i	$-0.0494679\pi$
$601$	33.0436	+	19.0777i	1.34788	+	0.778197i	0.359928	+	0.932980i	$0.382801\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.34636			0.379984
$606$		0			0
$607$			34.0355i			1.38146i	0.723114	+	0.690729i	$0.242710\pi$
$607$			34.0355i			1.38146i	−0.723114	+	0.690729i	$0.757290\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.92132	+	4.57338i	0.320462	+	0.185019i
$612$		0			0
$613$	−10.6676	−	18.4768i	−0.430859	−	0.746269i	0.566089	−	0.824344i	$-0.308456\pi$
$613$	−10.6676	−	18.4768i	−0.430859	−	0.746269i	−0.996947	+	0.0780750i	$0.975123\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.7263	+	10.8116i	−0.753892	+	0.435260i	−0.827098	−	0.562057i	$-0.810010\pi$
$617$	−18.7263	+	10.8116i	−0.753892	+	0.435260i	0.0732065	+	0.997317i	$0.476677\pi$
$618$		0			0
$619$		−	19.8495i		−	0.797818i	−0.916990	−	0.398909i	$-0.869389\pi$
$619$		−	19.8495i		−	0.797818i	0.916990	−	0.398909i	$-0.130611\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.870682	+	13.7201i	0.0348831	+	0.549685i
$624$		0			0
$625$	−26.2282			−1.04913
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−43.8525			−1.74851
$630$		0			0
$631$	−26.3803			−1.05018			−0.525092	−	0.851045i	$-0.675969\pi$
$631$	−26.3803			−1.05018			−0.525092	+	0.851045i	$0.675969\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	23.3345			0.926002
$636$		0			0
$637$	−2.59329	−	20.3501i	−0.102750	−	0.806300i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	35.5002i		−	1.40217i	−0.713076	−	0.701087i	$-0.752699\pi$
$641$		−	35.5002i		−	1.40217i	0.713076	−	0.701087i	$-0.247301\pi$
$642$		0			0
$643$	−5.61947	+	3.24440i	−0.221610	+	0.127947i	−0.606696	−	0.794934i	$-0.707505\pi$
$643$	−5.61947	+	3.24440i	−0.221610	+	0.127947i	0.385085	+	0.922881i	$0.374172\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.8076	+	37.7718i	0.857343	+	1.48496i	0.874454	+	0.485109i	$0.161220\pi$
$647$	21.8076	+	37.7718i	0.857343	+	1.48496i	−0.0171104	+	0.999854i	$0.505447\pi$
$648$		0			0
$649$	−14.2691	−	8.23828i	−0.560112	−	0.323381i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	25.0707i		−	0.981092i	−0.871415	−	0.490546i	$-0.836797\pi$
$653$		−	25.0707i		−	0.981092i	0.871415	−	0.490546i	$-0.163203\pi$
$654$		0			0
$655$	−22.0054			−0.859821
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11.6617	−	6.73287i	−0.454275	−	0.262276i	0.255359	−	0.966846i	$-0.417806\pi$
$659$	−11.6617	−	6.73287i	−0.454275	−	0.262276i	−0.709634	+	0.704571i	$0.751140\pi$
$660$		0			0
$661$	−40.4783	−	23.3702i	−1.57442	−	0.908994i	−0.995617	−	0.0935285i	$-0.970185\pi$
$661$	−40.4783	−	23.3702i	−1.57442	−	0.908994i	−0.578806	−	0.815465i	$-0.696481\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−57.7931	+	3.66756i	−2.24112	+	0.142222i
$666$		0			0
$667$	−5.88590	+	10.1947i	−0.227903	+	0.394740i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.55225	+	9.61679i	0.214342	+	0.371252i
$672$		0			0
$673$	18.9638	−	32.8462i	0.730999	−	1.26613i	−0.225458	−	0.974253i	$-0.572388\pi$
$673$	18.9638	−	32.8462i	0.730999	−	1.26613i	0.956457	−	0.291875i	$-0.0942790\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.56891	−	2.71744i	−0.0602983	−	0.104440i	0.834300	−	0.551310i	$-0.185872\pi$
$677$	−1.56891	−	2.71744i	−0.0602983	−	0.104440i	−0.894599	+	0.446870i	$0.852539\pi$
$678$		0			0
$679$	−6.32975	+	0.401687i	−0.242913	+	0.0154153i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.1449	+	7.01184i	−0.464711	+	0.268301i	−0.714023	−	0.700122i	$-0.753129\pi$
$683$	−12.1449	+	7.01184i	−0.464711	+	0.268301i	0.249312	+	0.968423i	$0.419795\pi$
$684$		0			0
$685$			45.7866i			1.74941i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.26668	+	9.12216i	−0.200645	+	0.347527i
$690$		0			0
$691$	−28.6141	+	16.5204i	−1.08853	+	0.628464i	−0.933185	−	0.359396i	$-0.882983\pi$
$691$	−28.6141	+	16.5204i	−1.08853	+	0.628464i	−0.155346	+	0.987860i	$0.549649\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.57965	+	2.64406i	−0.173716	+	0.100295i
$696$		0			0
$697$	26.0825	−	45.1763i	0.987946	−	1.71117i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			32.4058i			1.22395i	0.790877	+	0.611975i	$0.209625\pi$
$701$			32.4058i			1.22395i	−0.790877	+	0.611975i	$0.790375\pi$
$702$		0			0
$703$	49.0163	−	28.2996i	1.84869	−	1.06734i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	43.5194	−	28.9483i	1.63672	−	1.08871i
$708$		0			0
$709$	23.7528	+	41.1410i	0.892055	+	1.54508i	0.837408	+	0.546578i	$0.184070\pi$
$709$	23.7528	+	41.1410i	0.892055	+	1.54508i	0.0546463	+	0.998506i	$0.482597\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.35241	−	11.0027i	0.237899	−	0.412054i
$714$		0			0
$715$	−17.1087	−	29.6332i	−0.639830	−	1.10822i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−23.1139	+	40.0344i	−0.862003	+	1.49303i	0.00798976	+	0.999968i	$0.497457\pi$
$719$	−23.1139	+	40.0344i	−0.862003	+	1.49303i	−0.869993	+	0.493065i	$0.835877\pi$
$720$		0			0
$721$	18.0145	+	27.0821i	0.670896	+	1.00859i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	29.0306	+	16.7608i	1.07817	+	0.622482i
$726$		0			0
$727$	−12.3262	−	7.11651i	−0.457152	−	0.263937i	0.253694	−	0.967285i	$-0.418354\pi$
$727$	−12.3262	−	7.11651i	−0.457152	−	0.263937i	−0.710846	+	0.703348i	$0.751688\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	31.1937			1.15374
$732$		0			0
$733$		−	40.0914i		−	1.48081i	−0.672162	−	0.740404i	$-0.734634\pi$
$733$		−	40.0914i		−	1.48081i	0.672162	−	0.740404i	$-0.265366\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	31.8046	+	18.3624i	1.17154	+	0.676388i
$738$		0			0
$739$	2.99731	+	5.19150i	0.110258	+	0.190972i	0.915874	−	0.401465i	$-0.131499\pi$
$739$	2.99731	+	5.19150i	0.110258	+	0.190972i	−0.805616	+	0.592438i	$0.798166\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.20912	−	4.16219i	0.264477	−	0.152696i	−0.361898	−	0.932218i	$-0.617871\pi$
$743$	7.20912	−	4.16219i	0.264477	−	0.152696i	0.626375	+	0.779522i	$0.284538\pi$
$744$		0			0
$745$		−	46.2446i		−	1.69427i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	47.9154	−	3.04072i	1.75079	−	0.111106i
$750$		0			0
$751$	10.9530			0.399681			0.199840	−	0.979828i	$-0.435958\pi$
$751$	10.9530			0.399681			0.199840	+	0.979828i	$0.435958\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	18.9469			0.689548
$756$		0			0
$757$	−3.28275			−0.119314			−0.0596568	−	0.998219i	$-0.519001\pi$
$757$	−3.28275			−0.119314			−0.0596568	+	0.998219i	$0.519001\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−46.9232			−1.70097			−0.850483	−	0.526003i	$-0.823690\pi$
$761$	−46.9232			−1.70097			−0.850483	+	0.526003i	$0.823690\pi$
$762$		0			0
$763$	27.2174	+	13.4924i	0.985337	+	0.488459i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			12.9078i			0.466074i
$768$		0			0
$769$	−3.91587	+	2.26083i	−0.141210	+	0.0815276i	−0.568940	−	0.822379i	$-0.692647\pi$
$769$	−3.91587	+	2.26083i	−0.141210	+	0.0815276i	0.427731	+	0.903906i	$0.359313\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.8635	−	36.1367i	−0.750409	−	1.29975i	−0.947625	−	0.319386i	$-0.896523\pi$
$773$	−20.8635	−	36.1367i	−0.750409	−	1.29975i	0.197216	−	0.980360i	$-0.436810\pi$
$774$		0			0
$775$	−31.3315	−	18.0893i	−1.12546	−	0.649786i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			67.3279i			2.41227i
$780$		0			0
$781$	27.4403			0.981890
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−37.8087	−	21.8288i	−1.34945	−	0.779105i
$786$		0			0
$787$	−6.86957	−	3.96615i	−0.244874	−	0.141378i	0.372541	−	0.928016i	$-0.378487\pi$
$787$	−6.86957	−	3.96615i	−0.244874	−	0.141378i	−0.617415	+	0.786638i	$0.711820\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.12885	+	4.29440i	−0.0756933	+	0.152691i
$792$		0			0
$793$	4.34966	−	7.53383i	0.154461	−	0.267534i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.79200	−	15.2282i	−0.311429	−	0.539410i	0.667243	−	0.744840i	$-0.267474\pi$
$797$	−8.79200	−	15.2282i	−0.311429	−	0.539410i	−0.978672	+	0.205430i	$0.934141\pi$
$798$		0			0
$799$	−8.47919	+	14.6864i	−0.299972	+	0.519567i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.32324	+	9.22013i	0.187853	+	0.325371i
$804$		0			0
$805$	7.61410	+	11.4466i	0.268362	+	0.403441i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	45.9338	−	26.5199i	1.61495	−	0.932390i	0.626747	−	0.779223i	$-0.284386\pi$
$809$	45.9338	−	26.5199i	1.61495	−	0.932390i	0.988200	−	0.153168i	$-0.0489475\pi$
$810$		0			0
$811$			0.966384i			0.0339343i	0.999856	+	0.0169672i	$0.00540108\pi$
$811$			0.966384i			0.0339343i	−0.999856	+	0.0169672i	$0.994599\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.89204	−	5.00916i	0.101304	−	0.175463i
$816$		0			0
$817$	−34.8669	+	20.1304i	−1.21984	+	0.704274i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	38.5209	−	22.2400i	1.34439	−	0.776183i	0.356940	−	0.934127i	$-0.383820\pi$
$821$	38.5209	−	22.2400i	1.34439	−	0.776183i	0.987448	+	0.157945i	$0.0504868\pi$
$822$		0			0
$823$	−13.0327	+	22.5732i	−0.454290	+	0.786853i	−0.998647	−	0.0520005i	$-0.983440\pi$
$823$	−13.0327	+	22.5732i	−0.454290	+	0.786853i	0.544357	+	0.838853i	$0.316774\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.4166i			0.466540i	0.972412	+	0.233270i	$0.0749426\pi$
$827$			13.4166i			0.466540i	−0.972412	+	0.233270i	$0.925057\pi$
$828$		0			0
$829$	−0.407601	+	0.235328i	−0.0141566	+	0.00817329i	−0.507062	−	0.861910i	$-0.669268\pi$
$829$	−0.407601	+	0.235328i	−0.0141566	+	0.00817329i	0.492905	+	0.870083i	$0.335935\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	37.7298	−	4.80804i	1.30726	−	0.166589i
$834$		0			0
$835$	−3.97919	−	6.89216i	−0.137706	−	0.238513i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.7154	+	20.2917i	−0.404461	+	0.700548i	−0.994259	−	0.107004i	$-0.965874\pi$
$839$	−11.7154	+	20.2917i	−0.404461	+	0.700548i	0.589797	+	0.807551i	$0.299208\pi$
$840$		0			0
$841$	10.4973	+	18.1819i	0.361976	+	0.626961i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.88377	−	11.9230i	0.236809	−	0.410165i
$846$		0			0
$847$	6.59688	−	4.38812i	0.226671	−	0.150778i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−11.6365	−	6.71834i	−0.398894	−	0.230302i
$852$		0			0
$853$	−16.4266	−	9.48392i	−0.562437	−	0.324723i	0.191686	−	0.981456i	$-0.438604\pi$
$853$	−16.4266	−	9.48392i	−0.562437	−	0.324723i	−0.754123	+	0.656733i	$0.771938\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.1964			−0.450780			−0.225390	−	0.974269i	$-0.572366\pi$
$857$	−13.1964			−0.450780			−0.225390	+	0.974269i	$0.572366\pi$
$858$		0			0
$859$		−	8.98985i		−	0.306730i	−0.988170	−	0.153365i	$-0.950989\pi$
$859$		−	8.98985i		−	0.306730i	0.988170	−	0.153365i	$-0.0490110\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.0178	−	6.93847i	−0.409090	−	0.236188i	0.281309	−	0.959617i	$-0.409232\pi$
$863$	−12.0178	−	6.93847i	−0.409090	−	0.236188i	−0.690399	+	0.723429i	$0.742565\pi$
$864$		0			0
$865$	−6.10603	−	10.5760i	−0.207611	−	0.359593i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	16.6742	−	9.62684i	0.565633	−	0.326568i
$870$		0			0
$871$		−	28.7704i		−	0.974847i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.78114	+	1.18478i	−0.0602136	+	0.0400530i
$876$		0			0
$877$	−10.1306			−0.342087			−0.171043	−	0.985263i	$-0.554714\pi$
$877$	−10.1306			−0.342087			−0.171043	+	0.985263i	$0.554714\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−30.7189			−1.03495			−0.517473	−	0.855700i	$-0.673127\pi$
$881$	−30.7189			−1.03495			−0.517473	+	0.855700i	$0.673127\pi$
$882$		0			0
$883$	−35.4403			−1.19266			−0.596330	−	0.802740i	$-0.703375\pi$
$883$	−35.4403			−1.19266			−0.596330	+	0.802740i	$0.703375\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	36.2767			1.21805			0.609027	−	0.793150i	$-0.291560\pi$
$887$	36.2767			1.21805			0.609027	+	0.793150i	$0.291560\pi$
$888$		0			0
$889$	16.4700	−	10.9556i	0.552387	−	0.367438i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	21.8877i		−	0.732444i
$894$		0			0
$895$	52.8342	−	30.5039i	1.76605	−	1.01963i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−26.9785	−	46.7282i	−0.899785	−	1.55847i
$900$		0			0
$901$	−16.9128	−	9.76460i	−0.563447	−	0.325306i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	56.7808i		−	1.88746i
$906$		0			0
$907$	7.85862			0.260941			0.130471	−	0.991452i	$-0.458351\pi$
$907$	7.85862			0.260941			0.130471	+	0.991452i	$0.458351\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.0787	−	14.4792i	−0.830894	−	0.479717i	0.0232646	−	0.999729i	$-0.492594\pi$
$911$	−25.0787	−	14.4792i	−0.830894	−	0.479717i	−0.854159	+	0.520012i	$0.825927\pi$
$912$		0			0
$913$	50.5570	+	29.1891i	1.67319	+	0.966019i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.5319	+	10.3315i	−0.512908	+	0.341177i
$918$		0			0
$919$	17.1993	−	29.7901i	0.567353	−	0.982684i	−0.429473	−	0.903080i	$-0.641301\pi$
$919$	17.1993	−	29.7901i	0.567353	−	0.982684i	0.996826	−	0.0796049i	$-0.0253659\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−10.7484	−	18.6168i	−0.353788	−	0.612779i
$924$		0			0
$925$	−19.1313	+	33.1364i	−0.629034	+	1.08952i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.05052	−	5.28365i	−0.100084	−	0.173351i	0.811635	−	0.584165i	$-0.198578\pi$
$929$	−3.05052	−	5.28365i	−0.100084	−	0.173351i	−0.911719	+	0.410814i	$0.865245\pi$
$930$		0			0
$931$	−39.0698	+	29.7226i	−1.28046	+	0.974117i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	54.9409	−	31.7201i	1.79676	−	1.03736i
$936$		0			0
$937$		−	50.7128i		−	1.65671i	−0.560201	−	0.828357i	$-0.689276\pi$
$937$		−	50.7128i		−	1.65671i	0.560201	−	0.828357i	$-0.310724\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.5616	+	30.4177i	−0.572493	+	0.991587i	0.423816	+	0.905748i	$0.360690\pi$
$941$	−17.5616	+	30.4177i	−0.572493	+	0.991587i	−0.996309	+	0.0858389i	$0.972643\pi$
$942$		0			0
$943$	13.8423	−	7.99185i	0.450767	−	0.260250i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−34.2973	+	19.8016i	−1.11451	+	0.643465i	−0.939995	−	0.341189i	$-0.889170\pi$
$947$	−34.2973	+	19.8016i	−1.11451	+	0.643465i	−0.174519	+	0.984654i	$0.555837\pi$
$948$		0			0
$949$	4.17025	−	7.22309i	0.135372	−	0.234471i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			12.5942i			0.407966i	0.978974	+	0.203983i	$0.0653887\pi$
$953$			12.5942i			0.407966i	−0.978974	+	0.203983i	$0.934611\pi$
$954$		0			0
$955$	−40.7637	+	23.5349i	−1.31908	+	0.761573i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	21.4968	+	32.3172i	0.694168	+	1.04358i
$960$		0			0
$961$	13.6168	+	23.5850i	0.439251	+	0.760805i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.3948	+	30.1286i	−0.559958	+	0.969875i
$966$		0			0
$967$	−25.9203	−	44.8954i	−0.833542	−	1.44374i	−0.895212	−	0.445641i	$-0.852976\pi$
$967$	−25.9203	−	44.8954i	−0.833542	−	1.44374i	0.0616698	−	0.998097i	$-0.480357\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.918852	+	1.59150i	−0.0294874	+	0.0510736i	−0.880392	−	0.474246i	$-0.842721\pi$
$971$	−0.918852	+	1.59150i	−0.0294874	+	0.0510736i	0.850905	+	0.525319i	$0.176054\pi$
$972$		0			0
$973$	−1.99103	+	4.01639i	−0.0638296	+	0.128760i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.2808	−	13.4412i	−0.744818	−	0.430021i	0.0790007	−	0.996875i	$-0.474827\pi$
$977$	−23.2808	−	13.4412i	−0.744818	−	0.430021i	−0.823818	+	0.566854i	$0.808160\pi$
$978$		0			0
$979$	16.8342	+	9.71924i	0.538024	+	0.310628i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.3970			0.522983			0.261492	−	0.965206i	$-0.415786\pi$
$983$	16.3970			0.522983			0.261492	+	0.965206i	$0.415786\pi$
$984$		0			0
$985$		−	63.5744i		−	2.02565i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.27742	+	4.77897i	0.263207	+	0.151962i
$990$		0			0
$991$	1.17941	+	2.04279i	0.0374651	+	0.0648915i	0.884150	−	0.467203i	$-0.154738\pi$
$991$	1.17941	+	2.04279i	0.0374651	+	0.0648915i	−0.846685	+	0.532095i	$0.821405\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.0662	+	11.5852i	−0.636141	+	0.367276i
$996$		0			0
$997$		−	15.1398i		−	0.479481i	−0.970837	−	0.239740i	$-0.922938\pi$
$997$		−	15.1398i		−	0.479481i	0.970837	−	0.239740i	$-0.0770623\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.bm.i.593.1		12
3.2	odd	2	inner	2268.2.bm.i.593.6		12
7.3	odd	6		2268.2.w.i.269.1		12
9.2	odd	6		756.2.t.e.593.1	yes	12
9.4	even	3		2268.2.w.i.1349.6		12
9.5	odd	6		2268.2.w.i.1349.1		12
9.7	even	3		756.2.t.e.593.6	yes	12
21.17	even	6		2268.2.w.i.269.6		12
63.2	odd	6		5292.2.f.e.2645.11		12
63.16	even	3		5292.2.f.e.2645.2		12
63.31	odd	6	inner	2268.2.bm.i.1025.6		12
63.38	even	6		756.2.t.e.269.6	yes	12
63.47	even	6		5292.2.f.e.2645.1		12
63.52	odd	6		756.2.t.e.269.1	✓	12
63.59	even	6	inner	2268.2.bm.i.1025.1		12
63.61	odd	6		5292.2.f.e.2645.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.1	✓	12	63.52	odd	6
756.2.t.e.269.6	yes	12	63.38	even	6
756.2.t.e.593.1	yes	12	9.2	odd	6
756.2.t.e.593.6	yes	12	9.7	even	3
2268.2.w.i.269.1		12	7.3	odd	6
2268.2.w.i.269.6		12	21.17	even	6
2268.2.w.i.1349.1		12	9.5	odd	6
2268.2.w.i.1349.6		12	9.4	even	3
2268.2.bm.i.593.1		12	1.1	even	1	trivial
2268.2.bm.i.593.6		12	3.2	odd	2	inner
2268.2.bm.i.1025.1		12	63.59	even	6	inner
2268.2.bm.i.1025.6		12	63.31	odd	6	inner
5292.2.f.e.2645.1		12	63.47	even	6
5292.2.f.e.2645.2		12	63.16	even	3
5292.2.f.e.2645.11		12	63.2	odd	6
5292.2.f.e.2645.12		12	63.61	odd	6

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.12105 q^{5} +(-2.20291 + 1.46533i) q^{7} +3.74094i q^{11} +(2.53803 - 1.46533i) q^{13} +(2.71678 + 4.70560i) q^{17} +(-6.07338 - 3.50647i) q^{19} +1.66487i q^{23} +4.74094 q^{25} +(6.12340 + 3.53534i) q^{29} +(-6.60872 - 3.81555i) q^{31} +(6.87538 - 4.57338i) q^{35} +(-4.03534 + 6.98942i) q^{37} +(-4.80027 - 8.31431i) q^{41} +(2.87047 - 4.97180i) q^{43} +(1.56052 + 2.70291i) q^{47} +(2.70560 - 6.45599i) q^{49} +(-3.11266 + 1.79709i) q^{53} -11.6756i q^{55} +(-2.20220 + 3.81431i) q^{59} +(2.57069 - 1.48419i) q^{61} +(-7.92132 + 4.57338i) q^{65} +(4.90850 - 8.50177i) q^{67} -7.33513i q^{71} +(2.46466 - 1.42297i) q^{73} +(-5.48172 - 8.24094i) q^{77} +(-2.57338 - 4.45722i) q^{79} +(7.80262 - 13.5145i) q^{83} +(-8.47919 - 14.6864i) q^{85} +(2.59808 - 4.50000i) q^{89} +(-3.44385 + 6.94706i) q^{91} +(18.9553 + 10.9438i) q^{95} +(2.07606 + 1.19862i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} - 18 q^{61} + 54 q^{73} + 24 q^{79} + 6 q^{85} + 42 q^{91} - 36 q^{97}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 - 18 * q^61 + 54 * q^73 + 24 * q^79 + 6 * q^85 + 42 * q^91 - 36 * q^97

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