LMFDB - Embedded newform 2268.2.l.k.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(109,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("2268.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	2268.541
Dual form			2268.2.l.k.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.866926 q^{5} +(-0.0665372 - 2.64491i) q^{7} +O(q^{10})$	$q-0.866926 q^{5} +(-0.0665372 - 2.64491i) q^{7} -3.51459 q^{11} +(0.933463 + 1.61680i) q^{13} +(3.25729 + 5.64180i) q^{17} +(2.69076 - 4.66053i) q^{19} +8.64766 q^{23} -4.24844 q^{25} +(-1.75729 + 3.04372i) q^{29} +(0.933463 - 1.61680i) q^{31} +(0.0576828 + 2.29294i) q^{35} +(1.39037 - 2.40819i) q^{37} +(-5.19076 - 8.99066i) q^{41} +(2.89037 - 5.00627i) q^{43} +(-3.08113 - 5.33667i) q^{47} +(-6.99115 + 0.351971i) q^{49} +(-2.80039 - 4.85041i) q^{53} +3.04689 q^{55} +(2.82383 - 4.89102i) q^{59} +(-5.14766 - 8.91601i) q^{61} +(-0.809243 - 1.40165i) q^{65} +(0.676168 - 1.17116i) q^{67} +2.08619 q^{71} +(-3.62422 - 6.27733i) q^{73} +(0.233851 + 9.29579i) q^{77} +(-5.83842 - 10.1124i) q^{79} +(-3.43346 + 5.94693i) q^{83} +(-2.82383 - 4.89102i) q^{85} +(3.28074 - 5.68240i) q^{89} +(4.21420 - 2.57651i) q^{91} +(-2.33269 + 4.04033i) q^{95} +(1.64766 - 2.85384i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q + 2 * q^5 - 4 * q^7	$ 6 q + 2 q^{5} - 4 q^{7} + 10 q^{11} + 2 q^{13} + 4 q^{17} - 3 q^{19} + 28 q^{23} + 20 q^{25} + 5 q^{29} + 2 q^{31} - 26 q^{35} - 12 q^{41} + 9 q^{43} + 9 q^{47} - 12 q^{49} - 6 q^{53} + 16 q^{55} + 5 q^{59} - 7 q^{61} - 24 q^{65} + 16 q^{67} + 22 q^{71} + q^{73} - 13 q^{77} + 8 q^{79} - 17 q^{83} - 5 q^{85} + 3 q^{89} + 5 q^{91} - 32 q^{95} - 14 q^{97}+O(q^{100}) $ 6 * q + 2 * q^5 - 4 * q^7 + 10 * q^11 + 2 * q^13 + 4 * q^17 - 3 * q^19 + 28 * q^23 + 20 * q^25 + 5 * q^29 + 2 * q^31 - 26 * q^35 - 12 * q^41 + 9 * q^43 + 9 * q^47 - 12 * q^49 - 6 * q^53 + 16 * q^55 + 5 * q^59 - 7 * q^61 - 24 * q^65 + 16 * q^67 + 22 * q^71 + q^73 - 13 * q^77 + 8 * q^79 - 17 * q^83 - 5 * q^85 + 3 * q^89 + 5 * q^91 - 32 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−0.866926			−0.387701			−0.193850	−	0.981031i	$-0.562098\pi$
$5$	−0.866926			−0.387701			−0.193850	+	0.981031i	$0.562098\pi$
$6$		0			0
$7$	−0.0665372	−	2.64491i	−0.0251487	−	0.999684i
$7$	−0.0665372	−	2.64491i	−0.0251487	−	0.999684i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.51459			−1.05969			−0.529844	−	0.848095i	$-0.677750\pi$
$11$	−3.51459			−1.05969			−0.529844	+	0.848095i	$0.677750\pi$
$12$		0			0
$13$	0.933463	+	1.61680i	0.258896	+	0.448421i	0.965946	−	0.258742i	$-0.0833080\pi$
$13$	0.933463	+	1.61680i	0.258896	+	0.448421i	−0.707050	+	0.707163i	$0.749975\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.25729	+	5.64180i	0.790010	+	1.36834i	0.925960	+	0.377622i	$0.123258\pi$
$17$	3.25729	+	5.64180i	0.790010	+	1.36834i	−0.135950	+	0.990716i	$0.543409\pi$
$18$		0			0
$19$	2.69076	−	4.66053i	0.617302	−	1.06920i	−0.372674	−	0.927962i	$-0.621559\pi$
$19$	2.69076	−	4.66053i	0.617302	−	1.06920i	0.989976	−	0.141236i	$-0.0451077\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	8.64766			1.80316			0.901581	−	0.432610i	$-0.142407\pi$
$23$	8.64766			1.80316			0.901581	+	0.432610i	$0.142407\pi$
$24$		0			0
$25$	−4.24844			−0.849688
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.75729	+	3.04372i	−0.326321	+	0.565205i	−0.981779	−	0.190027i	$-0.939143\pi$
$29$	−1.75729	+	3.04372i	−0.326321	+	0.565205i	0.655457	+	0.755232i	$0.272476\pi$
$30$		0			0
$31$	0.933463	−	1.61680i	0.167655	−	0.290387i	−0.769940	−	0.638116i	$-0.779714\pi$
$31$	0.933463	−	1.61680i	0.167655	−	0.290387i	0.937595	+	0.347730i	$0.113047\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.0576828	+	2.29294i	0.00975018	+	0.387578i
$36$		0			0
$37$	1.39037	−	2.40819i	0.228575	−	0.395904i	−0.728811	−	0.684715i	$-0.759927\pi$
$37$	1.39037	−	2.40819i	0.228575	−	0.395904i	0.957386	+	0.288811i	$0.0932600\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.19076	−	8.99066i	−0.810660	−	1.40410i	−0.912403	−	0.409294i	$-0.865775\pi$
$41$	−5.19076	−	8.99066i	−0.810660	−	1.40410i	0.101743	−	0.994811i	$-0.467558\pi$
$42$		0			0
$43$	2.89037	−	5.00627i	0.440777	−	0.763448i	−0.556970	−	0.830532i	$-0.688036\pi$
$43$	2.89037	−	5.00627i	0.440777	−	0.763448i	0.997747	+	0.0670841i	$0.0213696\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.08113	−	5.33667i	−0.449428	−	0.778433i	0.548920	−	0.835875i	$-0.315039\pi$
$47$	−3.08113	−	5.33667i	−0.449428	−	0.778433i	−0.998349	+	0.0574417i	$0.981706\pi$
$48$		0			0
$49$	−6.99115	+	0.351971i	−0.998735	+	0.0502815i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.80039	−	4.85041i	−0.384663	−	0.666256i	0.607059	−	0.794656i	$-0.292349\pi$
$53$	−2.80039	−	4.85041i	−0.384663	−	0.666256i	−0.991722	+	0.128401i	$0.959016\pi$
$54$		0			0
$55$	3.04689			0.410842
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.82383	−	4.89102i	0.367632	−	0.636757i	−0.621563	−	0.783364i	$-0.713502\pi$
$59$	2.82383	−	4.89102i	0.367632	−	0.636757i	0.989195	+	0.146607i	$0.0468354\pi$
$60$		0			0
$61$	−5.14766	−	8.91601i	−0.659091	−	1.14158i	−0.980851	−	0.194758i	$-0.937608\pi$
$61$	−5.14766	−	8.91601i	−0.659091	−	1.14158i	0.321761	−	0.946821i	$-0.395725\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.809243	−	1.40165i	−0.100374	−	0.173853i
$66$		0			0
$67$	0.676168	−	1.17116i	0.0826071	−	0.143080i	−0.821762	−	0.569831i	$-0.807009\pi$
$67$	0.676168	−	1.17116i	0.0826071	−	0.143080i	0.904369	+	0.426751i	$0.140342\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.08619			0.247585			0.123792	−	0.992308i	$-0.460494\pi$
$71$	2.08619			0.247585			0.123792	+	0.992308i	$0.460494\pi$
$72$		0			0
$73$	−3.62422	−	6.27733i	−0.424183	−	0.734706i	0.572161	−	0.820141i	$-0.306105\pi$
$73$	−3.62422	−	6.27733i	−0.424183	−	0.734706i	−0.996344	+	0.0854351i	$0.972772\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.233851	+	9.29579i	0.0266498	+	1.05935i
$78$		0			0
$79$	−5.83842	−	10.1124i	−0.656874	−	1.13774i	−0.981421	−	0.191869i	$-0.938545\pi$
$79$	−5.83842	−	10.1124i	−0.656874	−	1.13774i	0.324547	−	0.945870i	$-0.394788\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.43346	+	5.94693i	−0.376871	+	0.652761i	−0.990605	−	0.136752i	$-0.956334\pi$
$83$	−3.43346	+	5.94693i	−0.376871	+	0.652761i	0.613734	+	0.789513i	$0.289667\pi$
$84$		0			0
$85$	−2.82383	−	4.89102i	−0.306288	−	0.530506i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.28074	−	5.68240i	0.347758	−	0.602334i	−0.638093	−	0.769959i	$-0.720277\pi$
$89$	3.28074	−	5.68240i	0.347758	−	0.602334i	0.985851	+	0.167625i	$0.0536099\pi$
$90$		0			0
$91$	4.21420	−	2.57651i	0.441768	−	0.270091i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.33269	+	4.04033i	−0.239329	+	0.414529i
$96$		0			0
$97$	1.64766	−	2.85384i	0.167295	−	0.289763i	−0.770173	−	0.637835i	$-0.779830\pi$
$97$	1.64766	−	2.85384i	0.167295	−	0.289763i	0.937468	+	0.348072i	$0.113163\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.89610			0.188669			0.0943347	−	0.995541i	$-0.469928\pi$
$101$	1.89610			0.188669			0.0943347	+	0.995541i	$0.469928\pi$
$102$		0			0
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.69076	+	16.7849i	−0.936841	+	1.62266i	−0.165523	+	0.986206i	$0.552931\pi$
$107$	−9.69076	+	16.7849i	−0.936841	+	1.62266i	−0.771318	+	0.636450i	$0.780402\pi$
$108$		0			0
$109$	−4.51459	−	7.81950i	−0.432419	−	0.748972i	0.564662	−	0.825322i	$-0.309007\pi$
$109$	−4.51459	−	7.81950i	−0.432419	−	0.748972i	−0.997081	+	0.0763503i	$0.975673\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.233851	+	0.405042i	0.0219989	+	0.0381031i	0.876815	−	0.480827i	$-0.159664\pi$
$113$	0.233851	+	0.405042i	0.0219989	+	0.0381031i	−0.854816	+	0.518931i	$0.826330\pi$
$114$		0			0
$115$	−7.49688			−0.699088
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.7053	−	8.99066i	1.34804	−	0.824172i
$120$		0			0
$121$	1.35234			0.122940
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.01771			0.717126
$126$		0			0
$127$	14.6768			1.30236			0.651180	−	0.758924i	$-0.274274\pi$
$127$	14.6768			1.30236			0.651180	+	0.758924i	$0.274274\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−14.2484			−1.24489			−0.622446	−	0.782663i	$-0.713861\pi$
$131$	−14.2484			−1.24489			−0.622446	+	0.782663i	$0.713861\pi$
$132$		0			0
$133$	−12.5057	−	6.80672i	−1.08438	−	0.590218i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	17.2953			1.47764			0.738820	−	0.673903i	$-0.235383\pi$
$137$	17.2953			1.47764			0.738820	+	0.673903i	$0.235383\pi$
$138$		0			0
$139$	6.06654	+	10.5076i	0.514557	+	0.891239i	0.999857	+	0.0168913i	$0.00537693\pi$
$139$	6.06654	+	10.5076i	0.514557	+	0.891239i	−0.485300	+	0.874348i	$0.661290\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.28074	−	5.68240i	−0.274349	−	0.475187i
$144$		0			0
$145$	1.52344	−	2.63868i	0.126515	−	0.219131i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.94299			−0.404946			−0.202473	−	0.979288i	$-0.564898\pi$
$149$	−4.94299			−0.404946			−0.202473	+	0.979288i	$0.564898\pi$
$150$		0			0
$151$	16.2484			1.32228			0.661140	−	0.750263i	$-0.270073\pi$
$151$	16.2484			1.32228			0.661140	+	0.750263i	$0.270073\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.809243	+	1.40165i	−0.0649999	+	0.112583i
$156$		0			0
$157$	0.699612	−	1.21176i	0.0558351	−	0.0967092i	−0.836757	−	0.547575i	$-0.815551\pi$
$157$	0.699612	−	1.21176i	0.0558351	−	0.0967092i	0.892592	+	0.450865i	$0.148885\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.575392	−	22.8723i	−0.0453472	−	1.80259i
$162$		0			0
$163$	10.0723	−	17.4457i	0.788921	−	1.36645i	−0.137707	−	0.990473i	$-0.543973\pi$
$163$	10.0723	−	17.4457i	0.788921	−	1.36645i	0.926628	−	0.375979i	$-0.122693\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.09572	+	8.82604i	0.394318	+	0.682979i	0.993014	−	0.117997i	$-0.0376474\pi$
$167$	5.09572	+	8.82604i	0.394318	+	0.682979i	−0.598696	+	0.800977i	$0.704314\pi$
$168$		0			0
$169$	4.75729	−	8.23988i	0.365946	−	0.633837i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.4050	+	18.0219i	0.791074	+	1.37018i	0.925302	+	0.379230i	$0.123811\pi$
$173$	10.4050	+	18.0219i	0.791074	+	1.37018i	−0.134228	+	0.990950i	$0.542855\pi$
$174$		0			0
$175$	0.282679	+	11.2368i	0.0213686	+	0.849419i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.6819	−	20.2336i	−0.873146	−	1.51233i	−0.858724	−	0.512438i	$-0.828742\pi$
$179$	−11.6819	−	20.2336i	−0.873146	−	1.51233i	−0.0144222	−	0.999896i	$-0.504591\pi$
$180$		0			0
$181$	9.33463			0.693837			0.346919	−	0.937895i	$-0.387228\pi$
$181$	9.33463			0.693837			0.346919	+	0.937895i	$0.387228\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.20535	+	2.08772i	−0.0886188	+	0.153492i
$186$		0			0
$187$	−11.4481	−	19.8286i	−0.837164	−	1.45001i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.4911	−	21.6353i	−0.903828	−	1.56548i	−0.822483	−	0.568789i	$-0.807412\pi$
$191$	−12.4911	−	21.6353i	−0.903828	−	1.56548i	−0.0813442	−	0.996686i	$-0.525921\pi$
$192$		0			0
$193$	11.9715	−	20.7352i	0.861727	−	1.49256i	−0.00853356	−	0.999964i	$-0.502716\pi$
$193$	11.9715	−	20.7352i	0.861727	−	1.49256i	0.870261	−	0.492592i	$-0.163950\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.13307			−0.365716			−0.182858	−	0.983139i	$-0.558535\pi$
$197$	−5.13307			−0.365716			−0.182858	+	0.983139i	$0.558535\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.16731	+	4.44537i	0.573233	+	0.312004i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.45691	+	16.3798i	−0.654148	+	1.13302i
$210$		0			0
$211$	2.77188	+	4.80104i	0.190824	+	0.330517i	0.945524	−	0.325553i	$-0.105551\pi$
$211$	2.77188	+	4.80104i	0.190824	+	0.330517i	−0.754699	+	0.656071i	$0.772217\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.50573	+	4.34006i	−0.170890	+	0.295990i
$216$		0			0
$217$	−4.33842	−	2.36135i	−0.294511	−	0.160299i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.08113	+	10.5328i	−0.409061	+	0.708514i
$222$		0			0
$223$	−9.80039	+	16.9748i	−0.656283	+	1.13671i	0.325288	+	0.945615i	$0.394539\pi$
$223$	−9.80039	+	16.9748i	−0.656283	+	1.13671i	−0.981571	+	0.191100i	$0.938795\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.1445			−1.07155			−0.535776	−	0.844360i	$-0.679981\pi$
$227$	−16.1445			−1.07155			−0.535776	+	0.844360i	$0.679981\pi$
$228$		0			0
$229$	−22.6768			−1.49853			−0.749264	−	0.662272i	$-0.769593\pi$
$229$	−22.6768			−1.49853			−0.749264	+	0.662272i	$0.769593\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.85234	+	3.20834i	−0.121351	+	0.210185i	−0.920301	−	0.391212i	$-0.872056\pi$
$233$	−1.85234	+	3.20834i	−0.121351	+	0.210185i	0.798950	+	0.601398i	$0.205389\pi$
$234$		0			0
$235$	2.67111	+	4.62649i	0.174244	+	0.301799i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.809243	−	1.40165i	−0.0523456	−	0.0906652i	0.838665	−	0.544647i	$-0.183336\pi$
$239$	−0.809243	−	1.40165i	−0.0523456	−	0.0906652i	−0.891011	+	0.453982i	$0.850003\pi$
$240$		0			0
$241$	4.20155			0.270646			0.135323	−	0.990802i	$-0.456793\pi$
$241$	4.20155			0.270646			0.135323	+	0.990802i	$0.456793\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.06080	−	0.305132i	0.387210	−	0.0194942i
$246$		0			0
$247$	10.0469			0.639268
$248$		0			0
$249$		0			0
$250$		0			0
$251$	19.5438			1.23359			0.616796	−	0.787123i	$-0.288430\pi$
$251$	19.5438			1.23359			0.616796	+	0.787123i	$0.288430\pi$
$252$		0			0
$253$	−30.3930			−1.91079
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.56148			0.409294			0.204647	−	0.978836i	$-0.434395\pi$
$257$	6.56148			0.409294			0.204647	+	0.978836i	$0.434395\pi$
$258$		0			0
$259$	−6.46197	−	3.51717i	−0.401527	−	0.218546i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	19.3815			1.19512			0.597558	−	0.801826i	$-0.296138\pi$
$263$	19.3815			1.19512			0.597558	+	0.801826i	$0.296138\pi$
$264$		0			0
$265$	2.42773	+	4.20495i	0.149134	+	0.258308i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.24271	+	12.5447i	0.441596	+	0.764866i	0.997808	−	0.0661742i	$-0.0210793\pi$
$269$	7.24271	+	12.5447i	0.441596	+	0.764866i	−0.556213	+	0.831040i	$0.687746\pi$
$270$		0			0
$271$	−2.67617	+	4.63526i	−0.162566	+	0.281572i	−0.935788	−	0.352563i	$-0.885310\pi$
$271$	−2.67617	+	4.63526i	−0.162566	+	0.281572i	0.773222	+	0.634135i	$0.218644\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	14.9315			0.900405
$276$		0			0
$277$	12.2193			0.734184			0.367092	−	0.930185i	$-0.380353\pi$
$277$	12.2193			0.734184			0.367092	+	0.930185i	$0.380353\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.55768	−	7.89414i	0.271889	−	0.470925i	−0.697457	−	0.716627i	$-0.745685\pi$
$281$	4.55768	−	7.89414i	0.271889	−	0.470925i	0.969345	+	0.245702i	$0.0790185\pi$
$282$		0			0
$283$	−6.90496	+	11.9597i	−0.410457	+	0.710933i	−0.994940	−	0.100474i	$-0.967964\pi$
$283$	−6.90496	+	11.9597i	−0.410457	+	0.710933i	0.584483	+	0.811406i	$0.301298\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−23.4341	+	14.3273i	−1.38327	+	0.845715i
$288$		0			0
$289$	−12.7199	+	22.0316i	−0.748231	+	1.29597i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.0723	−	24.3739i	−0.822111	−	1.42394i	−0.904107	−	0.427305i	$-0.859463\pi$
$293$	−14.0723	−	24.3739i	−0.822111	−	1.42394i	0.0819965	−	0.996633i	$-0.473870\pi$
$294$		0			0
$295$	−2.44805	+	4.24015i	−0.142531	+	0.246871i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.07227	+	13.9816i	0.466832	+	0.808576i
$300$		0			0
$301$	−13.4335	−	7.31168i	−0.774292	−	0.421438i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.46264	+	7.72952i	0.255530	+	0.442591i
$306$		0			0
$307$	7.24844			0.413690			0.206845	−	0.978374i	$-0.433680\pi$
$307$	7.24844			0.413690			0.206845	+	0.978374i	$0.433680\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.86693	+	6.69771i	−0.219273	+	0.379792i	−0.954586	−	0.297936i	$-0.903702\pi$
$311$	−3.86693	+	6.69771i	−0.219273	+	0.379792i	0.735313	+	0.677728i	$0.237035\pi$
$312$		0			0
$313$	4.92840	+	8.53624i	0.278570	+	0.482497i	0.971030	−	0.238960i	$-0.0768063\pi$
$313$	4.92840	+	8.53624i	0.278570	+	0.482497i	−0.692460	+	0.721456i	$0.743473\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.36186	−	16.2152i	−0.525815	−	0.910738i	−0.999548	−	0.0300693i	$-0.990427\pi$
$317$	−9.36186	−	16.2152i	−0.525815	−	0.910738i	0.473733	−	0.880668i	$-0.342906\pi$
$318$		0			0
$319$	6.17617	−	10.6974i	0.345799	−	0.598941i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	35.0584			1.95070
$324$		0			0
$325$	−3.96576	−	6.86890i	−0.219981	−	0.381018i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.9100	+	8.50440i	−0.766884	+	0.468863i
$330$		0			0
$331$	9.46264	+	16.3898i	0.520114	+	0.900864i	0.999727	+	0.0233833i	$0.00744380\pi$
$331$	9.46264	+	16.3898i	0.520114	+	0.900864i	−0.479613	+	0.877480i	$0.659223\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.586187	+	1.01531i	−0.0320268	+	0.0554721i
$336$		0			0
$337$	−14.6388	−	25.3552i	−0.797427	−	1.38118i	−0.921287	−	0.388884i	$-0.872861\pi$
$337$	−14.6388	−	25.3552i	−0.797427	−	1.38118i	0.123860	−	0.992300i	$-0.460473\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.28074	+	5.68240i	−0.177662	+	0.307719i
$342$		0			0
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.5438	−	18.2623i	0.566019	−	0.980374i	−0.430935	−	0.902383i	$-0.641816\pi$
$347$	10.5438	−	18.2623i	0.566019	−	0.980374i	0.996954	−	0.0779908i	$-0.0248505\pi$
$348$		0			0
$349$	−16.5957	+	28.7446i	−0.888348	+	1.53866i	−0.0465210	+	0.998917i	$0.514813\pi$
$349$	−16.5957	+	28.7446i	−0.888348	+	1.53866i	−0.841827	+	0.539747i	$0.818520\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−21.7237			−1.15624			−0.578119	−	0.815953i	$-0.696213\pi$
$353$	−21.7237			−1.15624			−0.578119	+	0.815953i	$0.696213\pi$
$354$		0			0
$355$	−1.80857			−0.0959889
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.37578	+	5.84702i	−0.178167	+	0.308594i	−0.941253	−	0.337703i	$-0.890350\pi$
$359$	−3.37578	+	5.84702i	−0.178167	+	0.308594i	0.763086	+	0.646297i	$0.223683\pi$
$360$		0			0
$361$	−4.98035	−	8.62622i	−0.262124	−	0.454012i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.14193	+	5.44198i	0.164456	+	0.284846i
$366$		0			0
$367$	35.0875			1.83155			0.915777	−	0.401687i	$-0.131576\pi$
$367$	35.0875			1.83155			0.915777	+	0.401687i	$0.131576\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.6426	+	7.72952i	−0.656371	+	0.401297i
$372$		0			0
$373$	17.4677			0.904443			0.452222	−	0.891906i	$-0.350632\pi$
$373$	17.4677			0.904443			0.452222	+	0.891906i	$0.350632\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.56148			−0.337933
$378$		0			0
$379$	2.86693			0.147264			0.0736320	−	0.997285i	$-0.476541\pi$
$379$	2.86693			0.147264			0.0736320	+	0.997285i	$0.476541\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.84922			0.247783			0.123892	−	0.992296i	$-0.460462\pi$
$383$	4.84922			0.247783			0.123892	+	0.992296i	$0.460462\pi$
$384$		0			0
$385$	−0.202731	−	8.05876i	−0.0103322	−	0.410712i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−26.4107			−1.33908			−0.669538	−	0.742778i	$-0.733508\pi$
$389$	−26.4107			−1.33908			−0.669538	+	0.742778i	$0.733508\pi$
$390$		0			0
$391$	28.1680	+	48.7884i	1.42452	+	2.46733i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.06148	+	8.76673i	0.254670	+	0.441102i
$396$		0			0
$397$	−14.5095	+	25.1312i	−0.728212	+	1.26130i	0.229426	+	0.973326i	$0.426315\pi$
$397$	−14.5095	+	25.1312i	−0.728212	+	1.26130i	−0.957638	+	0.287975i	$0.907018\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	33.9076			1.69326			0.846632	−	0.532179i	$-0.178627\pi$
$401$	33.9076			1.69326			0.846632	+	0.532179i	$0.178627\pi$
$402$		0			0
$403$	3.48541			0.173621
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.88658	+	8.46380i	−0.242219	+	0.419535i
$408$		0			0
$409$	18.1337	−	31.4086i	0.896656	−	1.55305i	0.0649147	−	0.997891i	$-0.479322\pi$
$409$	18.1337	−	31.4086i	0.896656	−	1.55305i	0.831741	−	0.555163i	$-0.187344\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.1242	−	7.14336i	−0.645801	−	0.351502i
$414$		0			0
$415$	2.97656	−	5.15555i	0.146113	−	0.253076i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.0615	−	19.1590i	−0.540388	−	0.935980i	−0.998882	−	0.0472823i	$-0.984944\pi$
$419$	−11.0615	−	19.1590i	−0.540388	−	0.935980i	0.458493	−	0.888698i	$-0.348389\pi$
$420$		0			0
$421$	−3.23764	+	5.60776i	−0.157793	+	0.273306i	−0.934073	−	0.357083i	$-0.883771\pi$
$421$	−3.23764	+	5.60776i	−0.157793	+	0.273306i	0.776279	+	0.630389i	$0.217105\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−13.8384	−	23.9688i	−0.671262	−	1.16266i
$426$		0			0
$427$	−23.2396	+	14.2084i	−1.12464	+	0.687592i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.99115	+	3.44877i	0.0959101	+	0.166121i	0.909988	−	0.414634i	$-0.136091\pi$
$431$	1.99115	+	3.44877i	0.0959101	+	0.166121i	−0.814078	+	0.580756i	$0.802757\pi$
$432$		0			0
$433$	−26.4690			−1.27202			−0.636011	−	0.771680i	$-0.719417\pi$
$433$	−26.4690			−1.27202			−0.636011	+	0.771680i	$0.719417\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	23.2688	−	40.3027i	1.11310	−	1.92794i
$438$		0			0
$439$	5.39610	+	9.34633i	0.257542	+	0.446076i	0.965583	−	0.260096i	$-0.0837541\pi$
$439$	5.39610	+	9.34633i	0.257542	+	0.446076i	−0.708041	+	0.706171i	$0.750421\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.138809	+	0.240425i	0.00659502	+	0.0114229i	0.869304	−	0.494278i	$-0.164567\pi$
$443$	0.138809	+	0.240425i	0.00659502	+	0.0114229i	−0.862709	+	0.505701i	$0.831234\pi$
$444$		0			0
$445$	−2.84416	+	4.92622i	−0.134826	+	0.233525i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.277618			0.0131016			0.00655081	−	0.999979i	$-0.497915\pi$
$449$	0.277618			0.0131016			0.00655081	+	0.999979i	$0.497915\pi$
$450$		0			0
$451$	18.2434	+	31.5985i	0.859047	+	1.48791i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.65340	+	2.23364i	−0.171274	+	0.104715i
$456$		0			0
$457$	18.8384	+	32.6291i	0.881224	+	1.52633i	0.849981	+	0.526813i	$0.176613\pi$
$457$	18.8384	+	32.6291i	0.881224	+	1.52633i	0.0312431	+	0.999512i	$0.490053\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.92461	−	6.79762i	0.182787	−	0.316597i	−0.760041	−	0.649875i	$-0.774821\pi$
$461$	3.92461	−	6.79762i	0.182787	−	0.316597i	0.942829	+	0.333278i	$0.108155\pi$
$462$		0			0
$463$	0.266149	+	0.460984i	0.0123690	+	0.0214237i	0.872144	−	0.489250i	$-0.162729\pi$
$463$	0.266149	+	0.460984i	0.0123690	+	0.0214237i	−0.859775	+	0.510674i	$0.829396\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.84348	−	6.65711i	0.177855	−	0.308054i	−0.763291	−	0.646055i	$-0.776417\pi$
$467$	3.84348	−	6.65711i	0.177855	−	0.308054i	0.941146	+	0.338001i	$0.109751\pi$
$468$		0			0
$469$	−3.14260	−	1.71048i	−0.145112	−	0.0789827i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.1585	+	17.5950i	−0.467086	+	0.809017i
$474$		0			0
$475$	−11.4315	+	19.8000i	−0.524514	+	0.908485i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	22.1914			1.01395			0.506976	−	0.861960i	$-0.330763\pi$
$479$	22.1914			1.01395			0.506976	+	0.861960i	$0.330763\pi$
$480$		0			0
$481$	5.19143			0.236709
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.42840	+	2.47406i	−0.0648604	+	0.112341i
$486$		0			0
$487$	3.99115	+	6.91287i	0.180856	+	0.313252i	0.942172	−	0.335129i	$-0.108780\pi$
$487$	3.99115	+	6.91287i	0.180856	+	0.313252i	−0.761316	+	0.648381i	$0.775447\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.0526	−	33.0001i	−0.859833	−	1.48927i	−0.872088	−	0.489349i	$-0.837234\pi$
$491$	−19.0526	−	33.0001i	−0.859833	−	1.48927i	0.0122552	−	0.999925i	$-0.496099\pi$
$492$		0			0
$493$	−22.8961			−1.03119
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.138809	−	5.51779i	−0.00622644	−	0.247507i
$498$		0			0
$499$	15.4500			0.691637			0.345818	−	0.938301i	$-0.387601\pi$
$499$	15.4500			0.691637			0.345818	+	0.938301i	$0.387601\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.78074			−0.0793992			−0.0396996	−	0.999212i	$-0.512640\pi$
$503$	−1.78074			−0.0793992			−0.0396996	+	0.999212i	$0.512640\pi$
$504$		0			0
$505$	−1.64378			−0.0731473
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.78074			−0.344875			−0.172438	−	0.985020i	$-0.555164\pi$
$509$	−7.78074			−0.344875			−0.172438	+	0.985020i	$0.555164\pi$
$510$		0			0
$511$	−16.3619	+	10.0034i	−0.723806	+	0.442526i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.06848			0.267409
$516$		0			0
$517$	10.8289	+	18.7562i	0.476254	+	0.824896i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.10963	+	3.65399i	0.0924246	+	0.160084i	0.908531	−	0.417818i	$-0.137205\pi$
$521$	2.10963	+	3.65399i	0.0924246	+	0.160084i	−0.816106	+	0.577902i	$0.803872\pi$
$522$		0			0
$523$	1.02850	−	1.78142i	0.0449734	−	0.0778962i	−0.842662	−	0.538442i	$-0.819013\pi$
$523$	1.02850	−	1.78142i	0.0449734	−	0.0778962i	0.887636	+	0.460546i	$0.152346\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.1623			0.529796
$528$		0			0
$529$	51.7821			2.25140
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.69076	−	16.7849i	0.419753	−	0.727034i
$534$		0			0
$535$	8.40116	−	14.5512i	0.363214	−	0.629105i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	24.5710	−	1.23703i	1.05835	−	0.0532827i
$540$		0			0
$541$	−8.63881	+	14.9629i	−0.371411	+	0.643303i	−0.989783	−	0.142582i	$-0.954459\pi$
$541$	−8.63881	+	14.9629i	−0.371411	+	0.643303i	0.618372	+	0.785886i	$0.287793\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.91381	+	6.77892i	0.167649	+	0.290377i
$546$		0			0
$547$	10.4246	−	18.0560i	0.445724	−	0.772017i	−0.552378	−	0.833594i	$-0.686280\pi$
$547$	10.4246	−	18.0560i	0.445724	−	0.772017i	0.998102	+	0.0615768i	$0.0196129\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.45691	+	16.3798i	0.402878	+	0.697805i
$552$		0			0
$553$	−26.3581	+	16.1150i	−1.12086	+	0.685279i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.64387	+	11.5075i	0.281510	+	0.487589i	0.971757	−	0.235985i	$-0.0758315\pi$
$557$	6.64387	+	11.5075i	0.281510	+	0.487589i	−0.690247	+	0.723574i	$0.742498\pi$
$558$		0			0
$559$	10.7922			0.456462
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.1965	+	26.3211i	−0.640456	+	1.10930i	0.344875	+	0.938648i	$0.387921\pi$
$563$	−15.1965	+	26.3211i	−0.640456	+	1.10930i	−0.985331	+	0.170653i	$0.945412\pi$
$564$		0			0
$565$	−0.202731	−	0.351141i	−0.00852898	−	0.0147726i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.8530	+	37.8505i	0.916126	+	1.58678i	0.805245	+	0.592943i	$0.202034\pi$
$569$	21.8530	+	37.8505i	0.916126	+	1.58678i	0.110881	+	0.993834i	$0.464633\pi$
$570$		0			0
$571$	19.1065	−	33.0934i	0.799583	−	1.38492i	−0.120306	−	0.992737i	$-0.538387\pi$
$571$	19.1065	−	33.0934i	0.799583	−	1.38492i	0.919888	−	0.392181i	$-0.128279\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−36.7391			−1.53213
$576$		0			0
$577$	−16.5957	−	28.7446i	−0.690889	−	1.19665i	−0.971547	−	0.236847i	$-0.923886\pi$
$577$	−16.5957	−	28.7446i	−0.690889	−	1.19665i	0.280658	−	0.959808i	$-0.409447\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.9576	+	8.68552i	0.662032	+	0.360336i
$582$		0			0
$583$	9.84221	+	17.0472i	0.407623	+	0.706024i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.89610	+	3.28415i	−0.0782606	+	0.135551i	−0.902500	−	0.430691i	$-0.858270\pi$
$587$	−1.89610	+	3.28415i	−0.0782606	+	0.135551i	0.824239	+	0.566242i	$0.191603\pi$
$588$		0			0
$589$	−5.02344	−	8.70086i	−0.206987	−	0.358513i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.81810	+	3.14904i	−0.0746603	+	0.129315i	−0.900938	−	0.433947i	$-0.857121\pi$
$593$	−1.81810	+	3.14904i	−0.0746603	+	0.129315i	0.826278	+	0.563262i	$0.190454\pi$
$594$		0			0
$595$	−12.7484	+	7.79423i	−0.522635	+	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−19.4253	+	33.6456i	−0.793696	+	1.37472i	0.129969	+	0.991518i	$0.458512\pi$
$599$	−19.4253	+	33.6456i	−0.793696	+	1.37472i	−0.923664	+	0.383203i	$0.874821\pi$
$600$		0			0
$601$	−16.3619	+	28.3396i	−0.667414	+	1.15600i	0.311210	+	0.950341i	$0.399266\pi$
$601$	−16.3619	+	28.3396i	−0.667414	+	1.15600i	−0.978625	+	0.205655i	$0.934068\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.17237			−0.0476638
$606$		0			0
$607$	−27.8099			−1.12877			−0.564385	−	0.825512i	$-0.690887\pi$
$607$	−27.8099			−1.12877			−0.564385	+	0.825512i	$0.690887\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.75223	−	9.96316i	0.232710	−	0.403066i
$612$		0			0
$613$	14.9684	+	25.9260i	0.604567	+	1.04714i	0.992120	+	0.125293i	$0.0399872\pi$
$613$	14.9684	+	25.9260i	0.604567	+	1.04714i	−0.387553	+	0.921848i	$0.626680\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.2091	+	26.3430i	0.612297	+	1.06053i	0.990852	+	0.134951i	$0.0430876\pi$
$617$	15.2091	+	26.3430i	0.612297	+	1.06053i	−0.378555	+	0.925579i	$0.623579\pi$
$618$		0			0
$619$	23.3054			0.936725			0.468363	−	0.883536i	$-0.344844\pi$
$619$	23.3054			0.936725			0.468363	+	0.883536i	$0.344844\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−15.2478	−	8.29918i	−0.610889	−	0.332500i
$624$		0			0
$625$	14.2914			0.571658
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.1154			0.722307
$630$		0			0
$631$	4.60078			0.183154			0.0915770	−	0.995798i	$-0.470809\pi$
$631$	4.60078			0.183154			0.0915770	+	0.995798i	$0.470809\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.7237			−0.504926
$636$		0			0
$637$	−7.09504	−	10.9748i	−0.281116	−	0.434836i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.66537			0.184271			0.0921356	−	0.995746i	$-0.470631\pi$
$641$	4.66537			0.184271			0.0921356	+	0.995746i	$0.470631\pi$
$642$		0			0
$643$	11.1996	+	19.3983i	0.441670	+	0.764994i	0.997814	−	0.0660918i	$-0.0210530\pi$
$643$	11.1996	+	19.3983i	0.441670	+	0.764994i	−0.556144	+	0.831086i	$0.687720\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.8619	−	34.4018i	−0.780850	−	1.35247i	−0.931447	−	0.363877i	$-0.881453\pi$
$647$	−19.8619	−	34.4018i	−0.780850	−	1.35247i	0.150596	−	0.988595i	$-0.451881\pi$
$648$		0			0
$649$	−9.92461	+	17.1899i	−0.389575	+	0.674764i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−38.1052			−1.49117			−0.745587	−	0.666409i	$-0.767831\pi$
$653$	−38.1052			−1.49117			−0.745587	+	0.666409i	$0.767831\pi$
$654$		0			0
$655$	12.3523			0.482646
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.1660	+	24.5363i	−0.551831	+	0.955799i	0.446312	+	0.894878i	$0.352737\pi$
$659$	−14.1660	+	24.5363i	−0.551831	+	0.955799i	−0.998143	+	0.0609214i	$0.980596\pi$
$660$		0			0
$661$	−21.5387	+	37.3061i	−0.837759	+	1.45104i	0.0540059	+	0.998541i	$0.482801\pi$
$661$	−21.5387	+	37.3061i	−0.837759	+	1.45104i	−0.891765	+	0.452500i	$0.850532\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.8415	+	5.90092i	0.420417	+	0.228828i
$666$		0			0
$667$	−15.1965	+	26.3211i	−0.588411	+	1.01916i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	18.0919	+	31.3361i	0.698431	+	1.20972i
$672$		0			0
$673$	−11.3815	+	19.7134i	−0.438725	+	0.759894i	−0.997591	−	0.0693635i	$-0.977903\pi$
$673$	−11.3815	+	19.7134i	−0.438725	+	0.759894i	0.558866	+	0.829258i	$0.311236\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.4253	−	33.6456i	−0.746574	−	1.29310i	−0.949456	−	0.313901i	$-0.898364\pi$
$677$	−19.4253	−	33.6456i	−0.746574	−	1.29310i	0.202881	−	0.979203i	$-0.434969\pi$
$678$		0			0
$679$	−7.65779	−	4.16804i	−0.293879	−	0.159955i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.328893	+	0.569659i	0.0125847	+	0.0217974i	0.872249	−	0.489062i	$-0.162661\pi$
$683$	0.328893	+	0.569659i	0.0125847	+	0.0217974i	−0.859664	+	0.510859i	$0.829327\pi$
$684$		0			0
$685$	−14.9938			−0.572882
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.22812	−	9.05536i	0.199175	−	0.344982i
$690$		0			0
$691$	2.36186	+	4.09087i	0.0898496	+	0.155624i	0.907447	−	0.420166i	$-0.138028\pi$
$691$	2.36186	+	4.09087i	0.0898496	+	0.155624i	−0.817598	+	0.575790i	$0.804695\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.25924	−	9.10926i	−0.199494	−	0.345534i
$696$		0			0
$697$	33.8157	−	58.5704i	1.28086	−	2.21851i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−48.1560			−1.81883			−0.909414	−	0.415893i	$-0.863469\pi$
$701$	−48.1560			−1.81883			−0.909414	+	0.415893i	$0.863469\pi$
$702$		0			0
$703$	−7.48229	−	12.9597i	−0.282200	−	0.488785i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.126162	−	5.01503i	−0.00474479	−	0.188610i
$708$		0			0
$709$	−0.271884	−	0.470916i	−0.0102108	−	0.0176856i	0.860875	−	0.508817i	$-0.169917\pi$
$709$	−0.271884	−	0.470916i	−0.0102108	−	0.0176856i	−0.871086	+	0.491131i	$0.836584\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.07227	−	13.9816i	0.302309	−	0.523614i
$714$		0			0
$715$	2.84416	+	4.92622i	0.106365	+	0.184230i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25.3068	−	43.8327i	0.943784	−	1.63468i	0.185617	−	0.982622i	$-0.440572\pi$
$719$	25.3068	−	43.8327i	0.943784	−	1.63468i	0.758167	−	0.652060i	$-0.226095\pi$
$720$		0			0
$721$	0.465761	+	18.5144i	0.0173458	+	0.689512i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.46576	−	12.9311i	0.277271	−	0.480248i
$726$		0			0
$727$	−11.6527	+	20.1831i	−0.432176	+	0.748550i	−0.997060	−	0.0766196i	$-0.975587\pi$
$727$	−11.6527	+	20.1831i	−0.432176	+	0.748550i	0.564885	+	0.825170i	$0.308921\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	37.6591			1.39287
$732$		0			0
$733$	−44.6122			−1.64779			−0.823895	−	0.566742i	$-0.808204\pi$
$733$	−44.6122			−1.64779			−0.823895	+	0.566742i	$0.808204\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.37645	+	4.11614i	−0.0875378	+	0.151620i
$738$		0			0
$739$	−18.9392	−	32.8037i	−0.696690	−	1.20670i	−0.969608	−	0.244665i	$-0.921322\pi$
$739$	−18.9392	−	32.8037i	−0.696690	−	1.20670i	0.272918	−	0.962037i	$-0.412011\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.02850	−	13.9058i	−0.294537	−	0.510154i	0.680340	−	0.732897i	$-0.261832\pi$
$743$	−8.02850	−	13.9058i	−0.294537	−	0.510154i	−0.974877	+	0.222743i	$0.928499\pi$
$744$		0			0
$745$	4.28520			0.156998
$746$		0			0
$747$		0			0
$748$		0			0
$749$	45.0394	+	24.5144i	1.64570	+	0.895737i
$750$		0			0
$751$	9.73385			0.355193			0.177597	−	0.984103i	$-0.443168\pi$
$751$	9.73385			0.355193			0.177597	+	0.984103i	$0.443168\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−14.0862			−0.512649
$756$		0			0
$757$	−16.7922			−0.610323			−0.305162	−	0.952301i	$-0.598710\pi$
$757$	−16.7922			−0.610323			−0.305162	+	0.952301i	$0.598710\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.2877			0.699180			0.349590	−	0.936903i	$-0.386321\pi$
$761$	19.2877			0.699180			0.349590	+	0.936903i	$0.386321\pi$
$762$		0			0
$763$	−20.3815	+	12.4610i	−0.737860	+	0.451118i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.5438			0.380713
$768$		0			0
$769$	0.794654	+	1.37638i	0.0286559	+	0.0496335i	0.879998	−	0.474978i	$-0.157544\pi$
$769$	0.794654	+	1.37638i	0.0286559	+	0.0496335i	−0.851342	+	0.524611i	$0.824211\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.2769	−	17.8002i	−0.369636	−	0.640228i	0.619873	−	0.784702i	$-0.287184\pi$
$773$	−10.2769	−	17.8002i	−0.369636	−	0.640228i	−0.989509	+	0.144474i	$0.953851\pi$
$774$		0			0
$775$	−3.96576	+	6.86890i	−0.142454	+	0.246738i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−55.8683			−2.00169
$780$		0			0
$781$	−7.33209			−0.262363
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.606511	+	1.05051i	−0.0216473	+	0.0374942i
$786$		0			0
$787$	15.1946	−	26.3177i	0.541627	−	0.938126i	−0.457184	−	0.889372i	$-0.651142\pi$
$787$	15.1946	−	26.3177i	0.541627	−	0.938126i	0.998811	−	0.0487536i	$-0.0155249\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.05574	−	0.645466i	0.0375378	−	0.0229501i
$792$		0			0
$793$	9.61030	−	16.6455i	0.341272	−	0.591100i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.7060	+	39.3280i	0.804288	+	1.39307i	0.916770	+	0.399415i	$0.130787\pi$
$797$	22.7060	+	39.3280i	0.804288	+	1.39307i	−0.112482	+	0.993654i	$0.535880\pi$
$798$		0			0
$799$	20.0723	−	34.7662i	0.710106	−	1.22994i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.7376	+	22.0622i	0.449502	+	0.778560i
$804$		0			0
$805$	0.498822	+	19.8286i	0.0175812	+	0.698867i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−7.50953	−	13.0069i	−0.264021	−	0.457298i	0.703286	−	0.710907i	$-0.251715\pi$
$809$	−7.50953	−	13.0069i	−0.264021	−	0.457298i	−0.967307	+	0.253610i	$0.918382\pi$
$810$		0			0
$811$	23.3930			0.821439			0.410719	−	0.911762i	$-0.365278\pi$
$811$	23.3930			0.821439			0.410719	+	0.911762i	$0.365278\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.73191	+	15.1241i	−0.305865	+	0.529775i
$816$		0			0
$817$	−15.5546	−	26.9413i	−0.544185	−	0.942557i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.5773	+	25.2487i	0.508752	+	0.881185i	0.999949	+	0.0101361i	$0.00322648\pi$
$821$	14.5773	+	25.2487i	0.508752	+	0.881185i	−0.491196	+	0.871049i	$0.663440\pi$
$822$		0			0
$823$	−1.59572	+	2.76386i	−0.0556231	+	0.0963421i	−0.892496	−	0.451055i	$-0.851048\pi$
$823$	−1.59572	+	2.76386i	−0.0556231	+	0.0963421i	0.836873	+	0.547397i	$0.184381\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	34.5654			1.20196			0.600978	−	0.799266i	$-0.294778\pi$
$827$	34.5654			1.20196			0.600978	+	0.799266i	$0.294778\pi$
$828$		0			0
$829$	11.7111	+	20.2842i	0.406743	+	0.704499i	0.994523	−	0.104522i	$-0.0333312\pi$
$829$	11.7111	+	20.2842i	0.406743	+	0.704499i	−0.587780	+	0.809021i	$0.699998\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−24.7580	−	38.2962i	−0.857813	−	1.32688i
$834$		0			0
$835$	−4.41761	−	7.65152i	−0.152878	−	0.264792i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.5488	−	21.7352i	0.433234	−	0.750383i	−0.563916	−	0.825832i	$-0.690706\pi$
$839$	12.5488	−	21.7352i	0.433234	−	0.750383i	0.997150	+	0.0754495i	$0.0240392\pi$
$840$		0			0
$841$	8.32383	+	14.4173i	0.287029	+	0.497148i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.12422	+	7.14336i	−0.141877	+	0.245739i
$846$		0			0
$847$	−0.0899807	−	3.57681i	−0.00309177	−	0.122901i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.0234	−	20.8252i	0.412158	−	0.713879i
$852$		0			0
$853$	5.97150	−	10.3429i	0.204460	−	0.354135i	−0.745500	−	0.666505i	$-0.767789\pi$
$853$	5.97150	−	10.3429i	0.204460	−	0.354135i	0.949961	+	0.312370i	$0.101123\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.2193			−0.349083			−0.174542	−	0.984650i	$-0.555844\pi$
$857$	−10.2193			−0.349083			−0.174542	+	0.984650i	$0.555844\pi$
$858$		0			0
$859$	−11.9430			−0.407490			−0.203745	−	0.979024i	$-0.565311\pi$
$859$	−11.9430			−0.407490			−0.203745	+	0.979024i	$0.565311\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.93346	−	13.7412i	0.270058	−	0.467755i	−0.698818	−	0.715299i	$-0.746290\pi$
$863$	7.93346	−	13.7412i	0.270058	−	0.467755i	0.968876	+	0.247545i	$0.0796237\pi$
$864$		0			0
$865$	−9.02032	−	15.6237i	−0.306700	−	0.531220i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	20.5197	+	35.5411i	0.696081	+	1.20565i
$870$		0			0
$871$	2.52471			0.0855466
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.533476	−	21.2062i	−0.0180348	−	0.716899i
$876$		0			0
$877$	−31.1813			−1.05292			−0.526459	−	0.850201i	$-0.676481\pi$
$877$	−31.1813			−1.05292			−0.526459	+	0.850201i	$0.676481\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−33.1623			−1.11726			−0.558632	−	0.829415i	$-0.688674\pi$
$881$	−33.1623			−1.11726			−0.558632	+	0.829415i	$0.688674\pi$
$882$		0			0
$883$	19.5045			0.656378			0.328189	−	0.944612i	$-0.393562\pi$
$883$	19.5045			0.656378			0.328189	+	0.944612i	$0.393562\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.5261			0.991388			0.495694	−	0.868497i	$-0.334914\pi$
$887$	29.5261			0.991388			0.495694	+	0.868497i	$0.334914\pi$
$888$		0			0
$889$	−0.976557	−	38.8190i	−0.0327527	−	1.30195i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33.1623			−1.10973
$894$		0			0
$895$	10.1273	+	17.5411i	0.338520	+	0.586333i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.28074	+	5.68240i	0.109419	+	0.189519i
$900$		0			0
$901$	18.2434	−	31.5985i	0.607775	−	1.05270i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.09243			−0.269001
$906$		0			0
$907$	32.4183			1.07643			0.538216	−	0.842807i	$-0.319099\pi$
$907$	32.4183			1.07643			0.538216	+	0.842807i	$0.319099\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−15.2915	+	26.4857i	−0.506631	+	0.877511i	0.493339	+	0.869837i	$0.335776\pi$
$911$	−15.2915	+	26.4857i	−0.506631	+	0.877511i	−0.999971	+	0.00767396i	$0.997557\pi$
$912$		0			0
$913$	12.0672	−	20.9010i	0.399366	−	0.691723i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.948052	+	37.6859i	0.0313074	+	1.24450i
$918$		0			0
$919$	24.1477	−	41.8250i	0.796558	−	1.37968i	−0.125287	−	0.992121i	$-0.539985\pi$
$919$	24.1477	−	41.8250i	0.796558	−	1.37968i	0.921845	−	0.387558i	$-0.126681\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.94738	+	3.37296i	0.0640987	+	0.111022i
$924$		0			0
$925$	−5.90690	+	10.2311i	−0.194218	+	0.336395i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−21.6096	−	37.4290i	−0.708989	−	1.22800i	−0.965233	−	0.261393i	$-0.915818\pi$
$929$	−21.6096	−	37.4290i	−0.708989	−	1.22800i	0.256244	−	0.966612i	$-0.417515\pi$
$930$		0			0
$931$	−17.1711	+	33.5295i	−0.562760	+	1.09888i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.92461	+	17.1899i	0.324569	+	0.562171i
$936$		0			0
$937$	37.3638			1.22062			0.610311	−	0.792162i	$-0.291044\pi$
$937$	37.3638			1.22062			0.610311	+	0.792162i	$0.291044\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.7573	+	23.8283i	−0.448475	+	0.776781i	−0.998287	−	0.0585070i	$-0.981366\pi$
$941$	−13.7573	+	23.8283i	−0.448475	+	0.776781i	0.549812	+	0.835288i	$0.314699\pi$
$942$		0			0
$943$	−44.8879	−	77.7482i	−1.46175	−	2.53183i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.83842	−	13.5765i	−0.254714	−	0.441178i	0.710103	−	0.704097i	$-0.248648\pi$
$947$	−7.83842	−	13.5765i	−0.254714	−	0.441178i	−0.964818	+	0.262919i	$0.915315\pi$
$948$		0			0
$949$	6.76615	−	11.7193i	0.219638	−	0.380425i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.2268			0.363673			0.181837	−	0.983329i	$-0.441796\pi$
$953$	11.2268			0.363673			0.181837	+	0.983329i	$0.441796\pi$
$954$		0			0
$955$	10.8289	+	18.7562i	0.350415	+	0.606936i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.15078	−	45.7447i	−0.0371607	−	1.47717i
$960$		0			0
$961$	13.7573	+	23.8283i	0.443784	+	0.768656i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−10.3784	+	17.9759i	−0.334092	+	0.578665i
$966$		0			0
$967$	−19.2434	−	33.3305i	−0.618825	−	1.07184i	−0.989700	−	0.143154i	$-0.954276\pi$
$967$	−19.2434	−	33.3305i	−0.618825	−	1.07184i	0.370875	−	0.928683i	$-0.379058\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.08998	+	12.2802i	−0.227528	+	0.394091i	−0.957075	−	0.289840i	$-0.906398\pi$
$971$	−7.08998	+	12.2802i	−0.227528	+	0.394091i	0.729547	+	0.683931i	$0.239731\pi$
$972$		0			0
$973$	27.3879	−	16.7446i	0.878016	−	0.536808i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.6972	−	42.7767i	0.790132	−	1.36855i	−0.135752	−	0.990743i	$-0.543345\pi$
$977$	24.6972	−	42.7767i	0.790132	−	1.36855i	0.925885	−	0.377807i	$-0.123322\pi$
$978$		0			0
$979$	−11.5304	+	19.9713i	−0.368515	+	0.638286i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.4562			0.429187			0.214594	−	0.976703i	$-0.431157\pi$
$983$	13.4562			0.429187			0.214594	+	0.976703i	$0.431157\pi$
$984$		0			0
$985$	4.44999			0.141789
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.9949	−	43.2925i	0.794793	−	1.37662i
$990$		0			0
$991$	1.09884	+	1.90324i	0.0349056	+	0.0604584i	0.882950	−	0.469466i	$-0.155554\pi$
$991$	1.09884	+	1.90324i	0.0349056	+	0.0604584i	−0.848045	+	0.529924i	$0.822220\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.03424	−	5.25546i	−0.0961919	−	0.166609i
$996$		0			0
$997$	−49.8329			−1.57822			−0.789111	−	0.614250i	$-0.789458\pi$
$997$	−49.8329			−1.57822			−0.789111	+	0.614250i	$0.789458\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.l.k.541.2		6
3.2	odd	2		2268.2.l.j.541.2		6
7.4	even	3		2268.2.i.j.865.2		6
9.2	odd	6		756.2.k.f.541.2	yes	6
9.4	even	3		2268.2.i.j.2053.2		6
9.5	odd	6		2268.2.i.k.2053.2		6
9.7	even	3		756.2.k.e.541.2	yes	6
21.11	odd	6		2268.2.i.k.865.2		6
63.2	odd	6		5292.2.a.u.1.2		3
63.4	even	3	inner	2268.2.l.k.109.2		6
63.11	odd	6		756.2.k.f.109.2	yes	6
63.16	even	3		5292.2.a.x.1.2		3
63.25	even	3		756.2.k.e.109.2	✓	6
63.32	odd	6		2268.2.l.j.109.2		6
63.47	even	6		5292.2.a.w.1.2		3
63.61	odd	6		5292.2.a.v.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.2	✓	6	63.25	even	3
756.2.k.e.541.2	yes	6	9.7	even	3
756.2.k.f.109.2	yes	6	63.11	odd	6
756.2.k.f.541.2	yes	6	9.2	odd	6
2268.2.i.j.865.2		6	7.4	even	3
2268.2.i.j.2053.2		6	9.4	even	3
2268.2.i.k.865.2		6	21.11	odd	6
2268.2.i.k.2053.2		6	9.5	odd	6
2268.2.l.j.109.2		6	63.32	odd	6
2268.2.l.j.541.2		6	3.2	odd	2
2268.2.l.k.109.2		6	63.4	even	3	inner
2268.2.l.k.541.2		6	1.1	even	1	trivial
5292.2.a.u.1.2		3	63.2	odd	6
5292.2.a.v.1.2		3	63.61	odd	6
5292.2.a.w.1.2		3	63.47	even	6
5292.2.a.x.1.2		3	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.866926 q^{5} +(-0.0665372 - 2.64491i) q^{7} +O(q^{10})\)	\(q-0.866926 q^{5} +(-0.0665372 - 2.64491i) q^{7} -3.51459 q^{11} +(0.933463 + 1.61680i) q^{13} +(3.25729 + 5.64180i) q^{17} +(2.69076 - 4.66053i) q^{19} +8.64766 q^{23} -4.24844 q^{25} +(-1.75729 + 3.04372i) q^{29} +(0.933463 - 1.61680i) q^{31} +(0.0576828 + 2.29294i) q^{35} +(1.39037 - 2.40819i) q^{37} +(-5.19076 - 8.99066i) q^{41} +(2.89037 - 5.00627i) q^{43} +(-3.08113 - 5.33667i) q^{47} +(-6.99115 + 0.351971i) q^{49} +(-2.80039 - 4.85041i) q^{53} +3.04689 q^{55} +(2.82383 - 4.89102i) q^{59} +(-5.14766 - 8.91601i) q^{61} +(-0.809243 - 1.40165i) q^{65} +(0.676168 - 1.17116i) q^{67} +2.08619 q^{71} +(-3.62422 - 6.27733i) q^{73} +(0.233851 + 9.29579i) q^{77} +(-5.83842 - 10.1124i) q^{79} +(-3.43346 + 5.94693i) q^{83} +(-2.82383 - 4.89102i) q^{85} +(3.28074 - 5.68240i) q^{89} +(4.21420 - 2.57651i) q^{91} +(-2.33269 + 4.04033i) q^{95} +(1.64766 - 2.85384i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q + 2 * q^5 - 4 * q^7	\( 6 q + 2 q^{5} - 4 q^{7} + 10 q^{11} + 2 q^{13} + 4 q^{17} - 3 q^{19} + 28 q^{23} + 20 q^{25} + 5 q^{29} + 2 q^{31} - 26 q^{35} - 12 q^{41} + 9 q^{43} + 9 q^{47} - 12 q^{49} - 6 q^{53} + 16 q^{55} + 5 q^{59} - 7 q^{61} - 24 q^{65} + 16 q^{67} + 22 q^{71} + q^{73} - 13 q^{77} + 8 q^{79} - 17 q^{83} - 5 q^{85} + 3 q^{89} + 5 q^{91} - 32 q^{95} - 14 q^{97}+O(q^{100}) \) 6 * q + 2 * q^5 - 4 * q^7 + 10 * q^11 + 2 * q^13 + 4 * q^17 - 3 * q^19 + 28 * q^23 + 20 * q^25 + 5 * q^29 + 2 * q^31 - 26 * q^35 - 12 * q^41 + 9 * q^43 + 9 * q^47 - 12 * q^49 - 6 * q^53 + 16 * q^55 + 5 * q^59 - 7 * q^61 - 24 * q^65 + 16 * q^67 + 22 * q^71 + q^73 - 13 * q^77 + 8 * q^79 - 17 * q^83 - 5 * q^85 + 3 * q^89 + 5 * q^91 - 32 * q^95 - 14 * q^97

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