LMFDB - Embedded newform 2268.2.l.j.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.j.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	$-0.437902\pi$
$5$	0.866926			0.387701			0.193850	+	0.981031i	$0.437902\pi$
$6$		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	$-0.322250\pi$
$11$	3.51459			1.05969			0.529844	+	0.848095i	$0.322250\pi$
$12$		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	$-0.876742\pi$
$17$	−3.25729	−	5.64180i	−0.790010	−	1.36834i	0.135950	−	0.990716i	$-0.456591\pi$
$18$		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	$-0.857593\pi$
$23$	−8.64766			−1.80316			−0.901581	+	0.432610i	$0.857593\pi$
$24$		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	−0.655457	−	0.755232i	$-0.727524\pi$
$29$	1.75729	−	3.04372i	0.326321	−	0.565205i	0.981779	+	0.190027i	$0.0608575\pi$
$30$		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	$0.134225\pi$
$41$	5.19076	+	8.99066i	0.810660	+	1.40410i	−0.101743	+	0.994811i	$0.532442\pi$
$42$		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	0.998349	−	0.0574417i	$-0.0182943\pi$
$47$	3.08113	+	5.33667i	0.449428	+	0.778433i	−0.548920	+	0.835875i	$0.684961\pi$
$48$		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	0.991722	−	0.128401i	$-0.0409844\pi$
$53$	2.80039	+	4.85041i	0.384663	+	0.666256i	−0.607059	+	0.794656i	$0.707651\pi$
$54$		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	−0.989195	−	0.146607i	$-0.953165\pi$
$59$	−2.82383	+	4.89102i	−0.367632	+	0.636757i	0.621563	+	0.783364i	$0.286498\pi$
$60$		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	$-0.539506\pi$
$71$	−2.08619			−0.247585			−0.123792	+	0.992308i	$0.539506\pi$
$72$		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	−0.613734	−	0.789513i	$-0.710333\pi$
$83$	3.43346	−	5.94693i	0.376871	−	0.652761i	0.990605	+	0.136752i	$0.0436665\pi$
$84$		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	−0.985851	−	0.167625i	$-0.946390\pi$
$89$	−3.28074	+	5.68240i	−0.347758	+	0.602334i	0.638093	+	0.769959i	$0.279723\pi$
$90$		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	$-0.530072\pi$
$101$	−1.89610			−0.188669			−0.0943347	+	0.995541i	$0.530072\pi$
$102$		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	$-0.447069\pi$
$107$	9.69076	−	16.7849i	0.936841	−	1.62266i	0.771318	−	0.636450i	$-0.219598\pi$
$108$		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	0.854816	−	0.518931i	$-0.173670\pi$
$113$	−0.233851	−	0.405042i	−0.0219989	−	0.0381031i	−0.876815	+	0.480827i	$0.840336\pi$
$114$		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	$-0.286139\pi$
$131$	14.2484			1.24489			0.622446	+	0.782663i	$0.286139\pi$
$132$		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	$-0.764617\pi$
$137$	−17.2953			−1.47764			−0.738820	+	0.673903i	$0.764617\pi$
$138$		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	$-0.435102\pi$
$149$	4.94299			0.404946			0.202473	+	0.979288i	$0.435102\pi$
$150$		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	0.598696	−	0.800977i	$-0.295686\pi$
$167$	−5.09572	−	8.82604i	−0.394318	−	0.682979i	−0.993014	+	0.117997i	$0.962353\pi$
$168$		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	$-0.876189\pi$
$173$	−10.4050	−	18.0219i	−0.791074	−	1.37018i	0.134228	−	0.990950i	$-0.457145\pi$
$174$		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	$0.171258\pi$
$179$	11.6819	+	20.2336i	0.873146	+	1.51233i	0.0144222	+	0.999896i	$0.495409\pi$
$180$		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	$0.192588\pi$
$191$	12.4911	+	21.6353i	0.903828	+	1.56548i	0.0813442	+	0.996686i	$0.474079\pi$
$192$		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	$-0.441465\pi$
$197$	5.13307			0.365716			0.182858	+	0.983139i	$0.441465\pi$
$198$		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	$-0.320019\pi$
$227$	16.1445			1.07155			0.535776	+	0.844360i	$0.320019\pi$
$228$		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	−0.798950	−	0.601398i	$-0.794611\pi$
$233$	1.85234	−	3.20834i	0.121351	−	0.210185i	0.920301	+	0.391212i	$0.127944\pi$
$234$		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	0.891011	−	0.453982i	$-0.149997\pi$
$239$	0.809243	+	1.40165i	0.0523456	+	0.0906652i	−0.838665	+	0.544647i	$0.816664\pi$
$240$		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	$-0.711570\pi$
$251$	−19.5438			−1.23359			−0.616796	+	0.787123i	$0.711570\pi$
$252$		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	$-0.565605\pi$
$257$	−6.56148			−0.409294			−0.204647	+	0.978836i	$0.565605\pi$
$258$		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	$-0.703862\pi$
$263$	−19.3815			−1.19512			−0.597558	+	0.801826i	$0.703862\pi$
$264$		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	0.556213	−	0.831040i	$-0.312254\pi$
$269$	−7.24271	−	12.5447i	−0.441596	−	0.764866i	−0.997808	+	0.0661742i	$0.978921\pi$
$270$		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	−0.969345	−	0.245702i	$-0.920982\pi$
$281$	−4.55768	+	7.89414i	−0.271889	+	0.470925i	0.697457	+	0.716627i	$0.254315\pi$
$282$		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	$0.140537\pi$
$293$	14.0723	+	24.3739i	0.822111	+	1.42394i	−0.0819965	+	0.996633i	$0.526130\pi$
$294$		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	−0.735313	−	0.677728i	$-0.762965\pi$
$311$	3.86693	−	6.69771i	0.219273	−	0.379792i	0.954586	+	0.297936i	$0.0962981\pi$
$312$		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	$0.00957280\pi$
$317$	9.36186	+	16.2152i	0.525815	+	0.910738i	−0.473733	+	0.880668i	$0.657094\pi$
$318$		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	$0.358184\pi$
$347$	−10.5438	+	18.2623i	−0.566019	+	0.980374i	−0.996954	+	0.0779908i	$0.975150\pi$
$348$		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	$-0.303787\pi$
$353$	21.7237			1.15624			0.578119	+	0.815953i	$0.303787\pi$
$354$		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	−0.763086	−	0.646297i	$-0.776317\pi$
$359$	3.37578	−	5.84702i	0.178167	−	0.308594i	0.941253	+	0.337703i	$0.109650\pi$
$360$		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	$-0.539538\pi$
$383$	−4.84922			−0.247783			−0.123892	+	0.992296i	$0.539538\pi$
$384$		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	$-0.266492\pi$
$389$	26.4107			1.33908			0.669538	+	0.742778i	$0.266492\pi$
$390$		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	$-0.821373\pi$
$401$	−33.9076			−1.69326			−0.846632	+	0.532179i	$0.821373\pi$
$402$		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	$0.0150560\pi$
$419$	11.0615	+	19.1590i	0.540388	+	0.935980i	−0.458493	+	0.888698i	$0.651611\pi$
$420$		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	0.814078	−	0.580756i	$-0.197243\pi$
$431$	−1.99115	−	3.44877i	−0.0959101	−	0.166121i	−0.909988	+	0.414634i	$0.863909\pi$
$432$		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	0.862709	−	0.505701i	$-0.168766\pi$
$443$	−0.138809	−	0.240425i	−0.00659502	−	0.0114229i	−0.869304	+	0.494278i	$0.835433\pi$
$444$		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	$-0.502085\pi$
$449$	−0.277618			−0.0131016			−0.00655081	+	0.999979i	$0.502085\pi$
$450$		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	−0.942829	−	0.333278i	$-0.891845\pi$
$461$	−3.92461	+	6.79762i	−0.182787	+	0.316597i	0.760041	+	0.649875i	$0.225179\pi$
$462$		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	−0.941146	−	0.338001i	$-0.890249\pi$
$467$	−3.84348	+	6.65711i	−0.177855	+	0.308054i	0.763291	+	0.646055i	$0.223583\pi$
$468$		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	$-0.669237\pi$
$479$	−22.1914			−1.01395			−0.506976	+	0.861960i	$0.669237\pi$
$480$		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	$0.162766\pi$
$491$	19.0526	+	33.0001i	0.859833	+	1.48927i	−0.0122552	+	0.999925i	$0.503901\pi$
$492$		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	$-0.487360\pi$
$503$	1.78074			0.0793992			0.0396996	+	0.999212i	$0.487360\pi$
$504$		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	$-0.444836\pi$
$509$	7.78074			0.344875			0.172438	+	0.985020i	$0.444836\pi$
$510$		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	0.816106	−	0.577902i	$-0.196128\pi$
$521$	−2.10963	−	3.65399i	−0.0924246	−	0.160084i	−0.908531	+	0.417818i	$0.862795\pi$
$522$		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	0.690247	−	0.723574i	$-0.257502\pi$
$557$	−6.64387	−	11.5075i	−0.281510	−	0.487589i	−0.971757	+	0.235985i	$0.924169\pi$
$558$		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	$-0.612079\pi$
$563$	15.1965	−	26.3211i	0.640456	−	1.10930i	0.985331	−	0.170653i	$-0.0545879\pi$
$564$		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	$-0.797966\pi$
$569$	−21.8530	−	37.8505i	−0.916126	−	1.58678i	−0.110881	−	0.993834i	$-0.535367\pi$
$570$		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	−0.824239	−	0.566242i	$-0.808397\pi$
$587$	1.89610	−	3.28415i	0.0782606	−	0.135551i	0.902500	+	0.430691i	$0.141730\pi$
$588$		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	−0.826278	−	0.563262i	$-0.809546\pi$
$593$	1.81810	−	3.14904i	0.0746603	−	0.129315i	0.900938	+	0.433947i	$0.142879\pi$
$594$		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	$-0.541488\pi$
$599$	19.4253	−	33.6456i	0.793696	−	1.37472i	0.923664	−	0.383203i	$-0.125179\pi$
$600$		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	$-0.956912\pi$
$617$	−15.2091	−	26.3430i	−0.612297	−	1.06053i	0.378555	−	0.925579i	$-0.376421\pi$
$618$		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	$-0.529369\pi$
$641$	−4.66537			−0.184271			−0.0921356	+	0.995746i	$0.529369\pi$
$642$		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	$0.118547\pi$
$647$	19.8619	+	34.4018i	0.780850	+	1.35247i	−0.150596	+	0.988595i	$0.548119\pi$
$648$		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	$-0.232169\pi$
$653$	38.1052			1.49117			0.745587	+	0.666409i	$0.232169\pi$
$654$		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	$-0.647263\pi$
$659$	14.1660	−	24.5363i	0.551831	−	0.955799i	0.998143	−	0.0609214i	$-0.0194039\pi$
$660$		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	$0.101636\pi$
$677$	19.4253	+	33.6456i	0.746574	+	1.29310i	−0.202881	+	0.979203i	$0.565031\pi$
$678$		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	0.859664	−	0.510859i	$-0.170673\pi$
$683$	−0.328893	−	0.569659i	−0.0125847	−	0.0217974i	−0.872249	+	0.489062i	$0.837339\pi$
$684$		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	$-0.136531\pi$
$701$	48.1560			1.81883			0.909414	+	0.415893i	$0.136531\pi$
$702$		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	$0.559428\pi$
$719$	−25.3068	+	43.8327i	−0.943784	+	1.63468i	−0.758167	+	0.652060i	$0.773905\pi$
$720$		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	0.974877	−	0.222743i	$-0.0715012\pi$
$743$	8.02850	+	13.9058i	0.294537	+	0.510154i	−0.680340	+	0.732897i	$0.738168\pi$
$744$		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	$-0.613679\pi$
$761$	−19.2877			−0.699180			−0.349590	+	0.936903i	$0.613679\pi$
$762$		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	0.989509	−	0.144474i	$-0.0461491\pi$
$773$	10.2769	+	17.8002i	0.369636	+	0.640228i	−0.619873	+	0.784702i	$0.712816\pi$
$774$		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	$-0.869213\pi$
$797$	−22.7060	−	39.3280i	−0.804288	−	1.39307i	0.112482	−	0.993654i	$-0.464120\pi$
$798$		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	0.967307	−	0.253610i	$-0.0816179\pi$
$809$	7.50953	+	13.0069i	0.264021	+	0.457298i	−0.703286	+	0.710907i	$0.748285\pi$
$810$		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	$-0.996774\pi$
$821$	−14.5773	−	25.2487i	−0.508752	−	0.881185i	0.491196	−	0.871049i	$-0.336560\pi$
$822$		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	$-0.705222\pi$
$827$	−34.5654			−1.20196			−0.600978	+	0.799266i	$0.705222\pi$
$828$		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	−0.997150	−	0.0754495i	$-0.975961\pi$
$839$	−12.5488	+	21.7352i	−0.433234	+	0.750383i	0.563916	+	0.825832i	$0.309294\pi$
$840$		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	$-0.444156\pi$
$857$	10.2193			0.349083			0.174542	+	0.984650i	$0.444156\pi$
$858$		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	−0.968876	−	0.247545i	$-0.920376\pi$
$863$	−7.93346	+	13.7412i	−0.270058	+	0.467755i	0.698818	+	0.715299i	$0.253710\pi$
$864$		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	$-0.311326\pi$
$881$	33.1623			1.11726			0.558632	+	0.829415i	$0.311326\pi$
$882$		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	$-0.665086\pi$
$887$	−29.5261			−0.991388			−0.495694	+	0.868497i	$0.665086\pi$
$888$		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	$-0.664224\pi$
$911$	15.2915	−	26.4857i	0.506631	−	0.877511i	0.999971	−	0.00767396i	$-0.00244272\pi$
$912$		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	$0.0841818\pi$
$929$	21.6096	+	37.4290i	0.708989	+	1.22800i	−0.256244	+	0.966612i	$0.582485\pi$
$930$		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	−0.549812	−	0.835288i	$-0.685301\pi$
$941$	13.7573	−	23.8283i	0.448475	−	0.776781i	0.998287	+	0.0585070i	$0.0186340\pi$
$942$		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	0.964818	−	0.262919i	$-0.0846852\pi$
$947$	7.83842	+	13.5765i	0.254714	+	0.441178i	−0.710103	+	0.704097i	$0.751352\pi$
$948$		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	$-0.558204\pi$
$953$	−11.2268			−0.363673			−0.181837	+	0.983329i	$0.558204\pi$
$954$		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	−0.729547	−	0.683931i	$-0.760269\pi$
$971$	7.08998	−	12.2802i	0.227528	−	0.394091i	0.957075	+	0.289840i	$0.0936022\pi$
$972$		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	$0.456655\pi$
$977$	−24.6972	+	42.7767i	−0.790132	+	1.36855i	−0.925885	+	0.377807i	$0.876678\pi$
$978$		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	$-0.568843\pi$
$983$	−13.4562			−0.429187			−0.214594	+	0.976703i	$0.568843\pi$
$984$		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.j.541.2		6
3.2	odd	2		2268.2.l.k.541.2		6
7.4	even	3		2268.2.i.k.865.2		6
9.2	odd	6		756.2.k.e.541.2	yes	6
9.4	even	3		2268.2.i.k.2053.2		6
9.5	odd	6		2268.2.i.j.2053.2		6
9.7	even	3		756.2.k.f.541.2	yes	6
21.11	odd	6		2268.2.i.j.865.2		6
63.2	odd	6		5292.2.a.x.1.2		3
63.4	even	3	inner	2268.2.l.j.109.2		6
63.11	odd	6		756.2.k.e.109.2	✓	6
63.16	even	3		5292.2.a.u.1.2		3
63.25	even	3		756.2.k.f.109.2	yes	6
63.32	odd	6		2268.2.l.k.109.2		6
63.47	even	6		5292.2.a.v.1.2		3
63.61	odd	6		5292.2.a.w.1.2		3

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

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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