LMFDB - Embedded newform 2160.2.br.d.1439.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2160,2,Mod(719,2160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2160, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5, 3]))

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

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

chi := DirichletCharacter("2160.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2160.br (of order $6$, 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:	$17.2476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1439.3
Character	$\chi$	$=$	2160.1439
Dual form			2160.2.br.d.719.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74305 - 1.40063i) q^{5} +(-2.45766 + 4.25679i) q^{7} +O(q^{10})$	$q+(-1.74305 - 1.40063i) q^{5} +(-2.45766 + 4.25679i) q^{7} +(-1.62292 + 2.81098i) q^{11} +(3.94659 - 2.27856i) q^{13} +4.68147 q^{17} -2.29982i q^{19} +(2.41968 - 1.39700i) q^{23} +(1.07645 + 4.88275i) q^{25} +(-0.841610 - 0.485904i) q^{29} +(-8.33350 + 4.81135i) q^{31} +(10.2460 - 3.97752i) q^{35} -2.32167i q^{37} +(-8.23509 + 4.75453i) q^{41} +(0.256227 - 0.443798i) q^{43} +(-7.37017 - 4.25517i) q^{47} +(-8.58018 - 14.8613i) q^{49} -9.90660 q^{53} +(6.76598 - 2.62656i) q^{55} +(1.48077 + 2.56476i) q^{59} +(1.67840 - 2.90707i) q^{61} +(-10.0705 - 1.55607i) q^{65} +(-4.05210 - 7.01844i) q^{67} -8.66662 q^{71} -3.66953i q^{73} +(-7.97717 - 13.8169i) q^{77} +(0.00584899 + 0.00337691i) q^{79} +(-2.41968 - 1.39700i) q^{83} +(-8.16004 - 6.55703i) q^{85} -0.952424i q^{89} +22.3997i q^{91} +(-3.22120 + 4.00870i) q^{95} +(-3.07057 - 1.77279i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{5}+O(q^{10}) $ 24 * q - 3 * q^5	$ 24 q - 3 q^{5} + 6 q^{11} + 3 q^{25} - 12 q^{29} - 18 q^{31} + 30 q^{35} + 12 q^{41} - 12 q^{49} - 6 q^{59} - 3 q^{65} - 96 q^{71} - 18 q^{79} - 24 q^{95}+O(q^{100}) $ 24 * q - 3 * q^5 + 6 * q^11 + 3 * q^25 - 12 * q^29 - 18 * q^31 + 30 * q^35 + 12 * q^41 - 12 * q^49 - 6 * q^59 - 3 * q^65 - 96 * q^71 - 18 * q^79 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.74305	−	1.40063i	−0.779516	−	0.626382i
$5$	−1.74305	−	1.40063i	−0.779516	−	0.626382i
$6$		0			0
$7$	−2.45766	+	4.25679i	−0.928908	+	1.60892i	−0.143755	+	0.989613i	$0.545918\pi$
$7$	−2.45766	+	4.25679i	−0.928908	+	1.60892i	−0.785152	+	0.619302i	$0.787415\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.62292	+	2.81098i	−0.489329	+	0.847542i	−0.999925	−	0.0122787i	$-0.996091\pi$
$11$	−1.62292	+	2.81098i	−0.489329	+	0.847542i	0.510596	+	0.859821i	$0.329425\pi$
$12$		0			0
$13$	3.94659	−	2.27856i	1.09459	−	0.631960i	0.159793	−	0.987151i	$-0.448917\pi$
$13$	3.94659	−	2.27856i	1.09459	−	0.631960i	0.934794	+	0.355191i	$0.115584\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.68147			1.13542			0.567712	−	0.823227i	$-0.307829\pi$
$17$	4.68147			1.13542			0.567712	+	0.823227i	$0.307829\pi$
$18$		0			0
$19$		−	2.29982i		−	0.527615i	−0.964575	−	0.263807i	$-0.915022\pi$
$19$		−	2.29982i		−	0.527615i	0.964575	−	0.263807i	$-0.0849783\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.41968	−	1.39700i	0.504538	−	0.291295i	−0.226048	−	0.974116i	$-0.572581\pi$
$23$	2.41968	−	1.39700i	0.504538	−	0.291295i	0.730585	+	0.682821i	$0.239247\pi$
$24$		0			0
$25$	1.07645	+	4.88275i	0.215290	+	0.976550i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.841610	−	0.485904i	−0.156283	−	0.0902301i	0.419819	−	0.907608i	$-0.362094\pi$
$29$	−0.841610	−	0.485904i	−0.156283	−	0.0902301i	−0.576102	+	0.817378i	$0.695427\pi$
$30$		0			0
$31$	−8.33350	+	4.81135i	−1.49674	+	0.864144i	−0.999993	−	0.00375071i	$-0.998806\pi$
$31$	−8.33350	+	4.81135i	−1.49674	+	0.864144i	−0.496748	+	0.867895i	$0.665473\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	10.2460	−	3.97752i	1.73190	−	0.672324i
$36$		0			0
$37$		−	2.32167i		−	0.381679i	−0.981621	−	0.190840i	$-0.938879\pi$
$37$		−	2.32167i		−	0.381679i	0.981621	−	0.190840i	$-0.0611211\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.23509	+	4.75453i	−1.28611	+	0.742533i	−0.977957	−	0.208805i	$-0.933043\pi$
$41$	−8.23509	+	4.75453i	−1.28611	+	0.742533i	−0.308148	+	0.951338i	$0.599709\pi$
$42$		0			0
$43$	0.256227	−	0.443798i	0.0390743	−	0.0676786i	−0.845827	−	0.533457i	$-0.820892\pi$
$43$	0.256227	−	0.443798i	0.0390743	−	0.0676786i	0.884901	+	0.465779i	$0.154226\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.37017	−	4.25517i	−1.07505	−	0.620680i	−0.145493	−	0.989359i	$-0.546477\pi$
$47$	−7.37017	−	4.25517i	−1.07505	−	0.620680i	−0.929557	+	0.368679i	$0.879810\pi$
$48$		0			0
$49$	−8.58018	−	14.8613i	−1.22574	−	2.12304i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.90660			−1.36078			−0.680388	−	0.732852i	$-0.738189\pi$
$53$	−9.90660			−1.36078			−0.680388	+	0.732852i	$0.738189\pi$
$54$		0			0
$55$	6.76598	−	2.62656i	0.912325	−	0.354166i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.48077	+	2.56476i	0.192779	+	0.333904i	0.946170	−	0.323669i	$-0.104917\pi$
$59$	1.48077	+	2.56476i	0.192779	+	0.333904i	−0.753391	+	0.657573i	$0.771583\pi$
$60$		0			0
$61$	1.67840	−	2.90707i	0.214897	−	0.372212i	−0.738344	−	0.674424i	$-0.764392\pi$
$61$	1.67840	−	2.90707i	0.214897	−	0.372212i	0.953241	+	0.302212i	$0.0977252\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.0705	−	1.55607i	−1.24910	−	0.193007i
$66$		0			0
$67$	−4.05210	−	7.01844i	−0.495042	−	0.857439i	0.504941	−	0.863154i	$-0.331514\pi$
$67$	−4.05210	−	7.01844i	−0.495042	−	0.857439i	−0.999984	+	0.00571511i	$0.998181\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.66662			−1.02854			−0.514270	−	0.857629i	$-0.671937\pi$
$71$	−8.66662			−1.02854			−0.514270	+	0.857629i	$0.671937\pi$
$72$		0			0
$73$		−	3.66953i		−	0.429486i	−0.976671	−	0.214743i	$-0.931109\pi$
$73$		−	3.66953i		−	0.429486i	0.976671	−	0.214743i	$-0.0688914\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.97717	−	13.8169i	−0.909083	−	1.57458i
$78$		0			0
$79$	0.00584899	+	0.00337691i	0.000658062	+	0.000379932i	0.500329	−	0.865835i	$-0.333212\pi$
$79$	0.00584899	+	0.00337691i	0.000658062	+	0.000379932i	−0.499671	+	0.866215i	$0.666546\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.41968	−	1.39700i	−0.265594	−	0.153341i	0.361290	−	0.932454i	$-0.382337\pi$
$83$	−2.41968	−	1.39700i	−0.265594	−	0.153341i	−0.626884	+	0.779113i	$0.715670\pi$
$84$		0			0
$85$	−8.16004	−	6.55703i	−0.885081	−	0.711210i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	0.952424i		−	0.100957i	−0.998725	−	0.0504784i	$-0.983925\pi$
$89$		−	0.952424i		−	0.100957i	0.998725	−	0.0504784i	$-0.0160746\pi$
$90$		0			0
$91$			22.3997i			2.34813i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.22120	+	4.00870i	−0.330489	+	0.411284i
$96$		0			0
$97$	−3.07057	−	1.77279i	−0.311769	−	0.180000i	0.335949	−	0.941880i	$-0.390943\pi$
$97$	−3.07057	−	1.77279i	−0.311769	−	0.180000i	−0.647718	+	0.761880i	$0.724276\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.59275	−	3.22898i	−0.556499	−	0.321295i	0.195240	−	0.980756i	$-0.437451\pi$
$101$	−5.59275	−	3.22898i	−0.556499	−	0.321295i	−0.751739	+	0.659460i	$0.770785\pi$
$102$		0			0
$103$	−3.43413	−	5.94809i	−0.338375	−	0.586083i	0.645752	−	0.763547i	$-0.276544\pi$
$103$	−3.43413	−	5.94809i	−0.338375	−	0.586083i	−0.984127	+	0.177464i	$0.943211\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			8.35683i			0.807886i	0.914784	+	0.403943i	$0.132361\pi$
$107$			8.35683i			0.807886i	−0.914784	+	0.403943i	$0.867639\pi$
$108$		0			0
$109$	−8.40624			−0.805172			−0.402586	−	0.915382i	$-0.631889\pi$
$109$	−8.40624			−0.805172			−0.402586	+	0.915382i	$0.631889\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.70815	+	13.3509i	0.725121	+	1.25595i	0.958924	+	0.283663i	$0.0915497\pi$
$113$	7.70815	+	13.3509i	0.725121	+	1.25595i	−0.233803	+	0.972284i	$0.575117\pi$
$114$		0			0
$115$	−6.17431	−	0.954038i	−0.575757	−	0.0889645i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.5055	+	19.9281i	−1.05470	+	1.82680i
$120$		0			0
$121$	0.232264	+	0.402293i	0.0211149	+	0.0365721i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.96264	−	10.0186i	0.443872	−	0.896090i
$126$		0			0
$127$	3.57050			0.316830			0.158415	−	0.987373i	$-0.449362\pi$
$127$	3.57050			0.316830			0.158415	+	0.987373i	$0.449362\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.63122	+	4.55740i	0.229891	+	0.398182i	0.957775	−	0.287517i	$-0.0928298\pi$
$131$	2.63122	+	4.55740i	0.229891	+	0.398182i	−0.727885	+	0.685699i	$0.759497\pi$
$132$		0			0
$133$	9.78985	+	5.65217i	0.848888	+	0.490105i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.02560	−	10.4366i	0.514802	−	0.891663i	−0.485051	−	0.874486i	$-0.661199\pi$
$137$	6.02560	−	10.4366i	0.514802	−	0.891663i	0.999852	−	0.0171767i	$-0.00546779\pi$
$138$		0			0
$139$	15.8635	−	9.15882i	1.34553	−	0.776841i	0.357916	−	0.933754i	$-0.383487\pi$
$139$	15.8635	−	9.15882i	1.34553	−	0.776841i	0.987612	+	0.156913i	$0.0501542\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			14.7917i			1.23694i
$144$		0			0
$145$	0.786396	+	2.02574i	0.0653066	+	0.168229i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−20.2462	+	11.6891i	−1.65863	+	0.957612i	−0.685286	+	0.728274i	$0.740323\pi$
$149$	−20.2462	+	11.6891i	−1.65863	+	0.957612i	−0.973347	+	0.229338i	$0.926344\pi$
$150$		0			0
$151$	−15.4153	−	8.90005i	−1.25448	−	0.724276i	−0.282486	−	0.959272i	$-0.591159\pi$
$151$	−15.4153	−	8.90005i	−1.25448	−	0.724276i	−0.971996	+	0.234996i	$0.924492\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	21.2647	+	3.28576i	1.70802	+	0.263919i
$156$		0			0
$157$	−2.22723	+	1.28589i	−0.177753	+	0.102626i	−0.586236	−	0.810140i	$-0.699391\pi$
$157$	−2.22723	+	1.28589i	−0.177753	+	0.102626i	0.408484	+	0.912766i	$0.366058\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			13.7334i			1.08234i
$162$		0			0
$163$	4.61388			0.361387			0.180694	−	0.983539i	$-0.442166\pi$
$163$	4.61388			0.361387			0.180694	+	0.983539i	$0.442166\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.72157	+	2.72600i	−0.365366	+	0.210944i	−0.671432	−	0.741066i	$-0.734320\pi$
$167$	−4.72157	+	2.72600i	−0.365366	+	0.210944i	0.306066	+	0.952010i	$0.400987\pi$
$168$		0			0
$169$	3.88370	−	6.72677i	0.298746	−	0.517444i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.0583	−	19.1535i	0.840746	−	1.45621i	−0.0485189	−	0.998822i	$-0.515450\pi$
$173$	11.0583	−	19.1535i	0.840746	−	1.45621i	0.889265	−	0.457393i	$-0.151217\pi$
$174$		0			0
$175$	−23.4304	−	7.41792i	−1.77117	−	0.560742i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.02225			−0.674355			−0.337177	−	0.941441i	$-0.609472\pi$
$179$	−9.02225			−0.674355			−0.337177	+	0.941441i	$0.609472\pi$
$180$		0			0
$181$	−13.6415			−1.01396			−0.506982	−	0.861957i	$-0.669239\pi$
$181$	−13.6415			−1.01396			−0.506982	+	0.861957i	$0.669239\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.25180	+	4.04678i	−0.239077	+	0.297525i
$186$		0			0
$187$	−7.59766	+	13.1595i	−0.555596	+	0.962320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.28131	−	9.14750i	0.382142	−	0.661890i	−0.609226	−	0.792997i	$-0.708520\pi$
$191$	5.28131	−	9.14750i	0.382142	−	0.661890i	0.991368	+	0.131107i	$0.0418531\pi$
$192$		0			0
$193$	−13.6860	+	7.90162i	−0.985140	+	0.568771i	−0.903818	−	0.427917i	$-0.859248\pi$
$193$	−13.6860	+	7.90162i	−0.985140	+	0.568771i	−0.0813222	+	0.996688i	$0.525914\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	19.0230			1.35533			0.677666	−	0.735370i	$-0.262992\pi$
$197$	19.0230			1.35533			0.677666	+	0.735370i	$0.262992\pi$
$198$		0			0
$199$		−	1.43855i		−	0.101976i	−0.998699	−	0.0509881i	$-0.983763\pi$
$199$		−	1.43855i		−	0.101976i	0.998699	−	0.0509881i	$-0.0162371\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.13678	−	2.38837i	0.290345	−	0.167631i
$204$		0			0
$205$	21.0135	+	3.24696i	1.46765	+	0.226777i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.46474	+	3.73242i	0.447176	+	0.258177i
$210$		0			0
$211$	15.4153	−	8.90005i	1.06124	−	0.612704i	0.135462	−	0.990783i	$-0.456748\pi$
$211$	15.4153	−	8.90005i	1.06124	−	0.612704i	0.925774	+	0.378078i	$0.123415\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.06822	+	0.414683i	−0.0728517	+	0.0282811i
$216$		0			0
$217$		−	47.2986i		−	3.21084i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.4758	−	10.6670i	1.24282	−	0.717542i
$222$		0			0
$223$	−0.772004	+	1.33715i	−0.0516972	+	0.0895422i	−0.890716	−	0.454560i	$-0.849796\pi$
$223$	−0.772004	+	1.33715i	−0.0516972	+	0.0895422i	0.839019	+	0.544102i	$0.183130\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.32514	−	4.22917i	−0.486187	−	0.280700i	0.236804	−	0.971557i	$-0.423900\pi$
$227$	−7.32514	−	4.22917i	−0.486187	−	0.280700i	−0.722991	+	0.690857i	$0.757233\pi$
$228$		0			0
$229$	4.13038	+	7.15403i	0.272943	+	0.472752i	0.969614	−	0.244639i	$-0.0786696\pi$
$229$	4.13038	+	7.15403i	0.272943	+	0.472752i	−0.696671	+	0.717391i	$0.745336\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.6573			−0.960229			−0.480115	−	0.877206i	$-0.659405\pi$
$233$	−14.6573			−0.960229			−0.480115	+	0.877206i	$0.659405\pi$
$234$		0			0
$235$	6.88665	+	17.7399i	0.449235	+	1.15722i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.171965	+	0.297852i	0.0111235	+	0.0192664i	0.871534	−	0.490336i	$-0.163126\pi$
$239$	0.171965	+	0.297852i	0.0111235	+	0.0192664i	−0.860410	+	0.509602i	$0.829793\pi$
$240$		0			0
$241$	4.93539	−	8.54834i	0.317916	−	0.550647i	−0.662137	−	0.749383i	$-0.730350\pi$
$241$	4.93539	−	8.54834i	0.317916	−	0.550647i	0.980053	+	0.198736i	$0.0636836\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.85956	+	37.9217i	−0.374354	+	2.42273i
$246$		0			0
$247$	−5.24028	−	9.07644i	−0.333431	−	0.577520i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	16.5795			1.04649			0.523243	−	0.852183i	$-0.324722\pi$
$251$	16.5795			1.04649			0.523243	+	0.852183i	$0.324722\pi$
$252$		0			0
$253$			9.06888i			0.570156i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.09105	−	12.2821i	−0.442327	−	0.766133i	0.555534	−	0.831494i	$-0.312514\pi$
$257$	−7.09105	−	12.2821i	−0.442327	−	0.766133i	−0.997862	+	0.0653601i	$0.979180\pi$
$258$		0			0
$259$	9.88284	+	5.70586i	0.614090	+	0.354545i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.76712	−	2.75230i	−0.293953	−	0.169714i	0.345770	−	0.938319i	$-0.387618\pi$
$263$	−4.76712	−	2.75230i	−0.293953	−	0.169714i	−0.639723	+	0.768605i	$0.720951\pi$
$264$		0			0
$265$	17.2677	+	13.8755i	1.06075	+	0.852367i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			23.3589i			1.42422i	0.702069	+	0.712109i	$0.252260\pi$
$269$			23.3589i			1.42422i	−0.702069	+	0.712109i	$0.747740\pi$
$270$		0			0
$271$		−	19.4755i		−	1.18305i	−0.806287	−	0.591525i	$-0.798526\pi$
$271$		−	19.4755i		−	1.18305i	0.806287	−	0.591525i	$-0.201474\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−15.4723	−	4.89843i	−0.933015	−	0.295387i
$276$		0			0
$277$	−21.4830	−	12.4032i	−1.29079	−	0.745236i	−0.311994	−	0.950084i	$-0.600997\pi$
$277$	−21.4830	−	12.4032i	−1.29079	−	0.745236i	−0.978794	+	0.204848i	$0.934330\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−22.2519	−	12.8471i	−1.32743	−	0.766395i	−0.342532	−	0.939506i	$-0.611285\pi$
$281$	−22.2519	−	12.8471i	−1.32743	−	0.766395i	−0.984902	+	0.173112i	$0.944618\pi$
$282$		0			0
$283$	−7.17373	−	12.4253i	−0.426434	−	0.738605i	0.570119	−	0.821562i	$-0.306897\pi$
$283$	−7.17373	−	12.4253i	−0.426434	−	0.738605i	−0.996553	+	0.0829568i	$0.973564\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	46.7401i		−	2.75898i
$288$		0			0
$289$	4.91619			0.289188
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.76145	+	15.1753i	0.511849	+	0.886549i	0.999906	+	0.0137369i	$0.00437272\pi$
$293$	8.76145	+	15.1753i	0.511849	+	0.886549i	−0.488056	+	0.872812i	$0.662294\pi$
$294$		0			0
$295$	1.01124	−	6.54452i	0.0588768	−	0.381037i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.36631	−	11.0268i	0.368173	−	0.637695i
$300$		0			0
$301$	1.25944	+	2.18141i	0.0725928	+	0.125734i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.99727	+	2.71635i	−0.400663	+	0.155538i
$306$		0			0
$307$	−0.415391			−0.0237076			−0.0118538	−	0.999930i	$-0.503773\pi$
$307$	−0.415391			−0.0237076			−0.0118538	+	0.999930i	$0.503773\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.8799	+	18.8446i	0.616943	+	1.06858i	0.990040	+	0.140784i	$0.0449624\pi$
$311$	10.8799	+	18.8446i	0.616943	+	1.06858i	−0.373097	+	0.927792i	$0.621704\pi$
$312$		0			0
$313$	17.8846	+	10.3257i	1.01090	+	0.583641i	0.911454	−	0.411403i	$-0.134961\pi$
$313$	17.8846	+	10.3257i	1.01090	+	0.583641i	0.0994419	+	0.995043i	$0.468294\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.28802	−	9.15912i	0.297005	−	0.514428i	−0.678444	−	0.734652i	$-0.737346\pi$
$317$	5.28802	−	9.15912i	0.297005	−	0.514428i	0.975449	+	0.220224i	$0.0706789\pi$
$318$		0			0
$319$	2.73173	−	1.57717i	0.152948	−	0.0883044i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	10.7665i		−	0.599066i
$324$		0			0
$325$	15.3740	+	16.8174i	0.852794	+	0.932864i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	36.2267	−	20.9155i	1.99725	−	1.15311i
$330$		0			0
$331$	2.59592	+	1.49876i	0.142685	+	0.0823791i	0.569643	−	0.821892i	$-0.307082\pi$
$331$	2.59592	+	1.49876i	0.142685	+	0.0823791i	−0.426958	+	0.904271i	$0.640415\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.76725	+	17.9090i	−0.151191	+	0.978473i
$336$		0			0
$337$	−24.9848	+	14.4250i	−1.36101	+	0.785780i	−0.989758	−	0.142752i	$-0.954405\pi$
$337$	−24.9848	+	14.4250i	−1.36101	+	0.785780i	−0.371252	+	0.928532i	$0.621072\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	31.2337i		−	1.69140i
$342$		0			0
$343$	49.9414			2.69658
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.84132	+	4.52719i	−0.420944	+	0.243032i	−0.695481	−	0.718544i	$-0.744809\pi$
$347$	−7.84132	+	4.52719i	−0.420944	+	0.243032i	0.274537	+	0.961577i	$0.411475\pi$
$348$		0			0
$349$	−7.32154	+	12.6813i	−0.391913	+	0.678813i	−0.992702	−	0.120595i	$-0.961520\pi$
$349$	−7.32154	+	12.6813i	−0.391913	+	0.678813i	0.600789	+	0.799408i	$0.294853\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.20672	+	9.01831i	−0.277126	+	0.479996i	−0.970669	−	0.240419i	$-0.922715\pi$
$353$	−5.20672	+	9.01831i	−0.277126	+	0.479996i	0.693543	+	0.720415i	$0.256049\pi$
$354$		0			0
$355$	15.1064	+	12.1388i	0.801763	+	0.644259i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−22.0275			−1.16257			−0.581283	−	0.813701i	$-0.697449\pi$
$359$	−22.0275			−1.16257			−0.581283	+	0.813701i	$0.697449\pi$
$360$		0			0
$361$	13.7108			0.721623
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.13967	+	6.39618i	−0.269023	+	0.334791i
$366$		0			0
$367$	−17.7698	+	30.7782i	−0.927577	+	1.60661i	−0.140214	+	0.990121i	$0.544779\pi$
$367$	−17.7698	+	30.7782i	−0.927577	+	1.60661i	−0.787363	+	0.616490i	$0.788554\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	24.3471	−	42.1703i	1.26404	−	2.18937i
$372$		0			0
$373$	−5.66594	+	3.27123i	−0.293371	+	0.169378i	−0.639461	−	0.768823i	$-0.720843\pi$
$373$	−5.66594	+	3.27123i	−0.293371	+	0.169378i	0.346090	+	0.938201i	$0.387509\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.42865			−0.228087
$378$		0			0
$379$			14.2443i			0.731682i	0.930677	+	0.365841i	$0.119219\pi$
$379$			14.2443i			0.731682i	−0.930677	+	0.365841i	$0.880781\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.10979	−	4.68219i	0.414391	−	0.239249i	−0.278284	−	0.960499i	$-0.589766\pi$
$383$	8.10979	−	4.68219i	0.414391	−	0.239249i	0.692675	+	0.721250i	$0.256432\pi$
$384$		0			0
$385$	−5.44775	+	35.2566i	−0.277643	+	1.79684i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.64156	+	4.41186i	0.387442	+	0.223690i	0.681051	−	0.732236i	$-0.261523\pi$
$389$	7.64156	+	4.41186i	0.387442	+	0.223690i	−0.293609	+	0.955926i	$0.594856\pi$
$390$		0			0
$391$	11.3277	−	6.54002i	0.572864	−	0.330743i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.00546526	−	0.0140784i	−0.000274987	−	0.000708362i
$396$		0			0
$397$		−	1.68445i		−	0.0845401i	−0.999106	−	0.0422700i	$-0.986541\pi$
$397$		−	1.68445i		−	0.0845401i	0.999106	−	0.0422700i	$-0.0134590\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.7375	−	7.93137i	0.686020	−	0.396074i	−0.116099	−	0.993238i	$-0.537039\pi$
$401$	13.7375	−	7.93137i	0.686020	−	0.396074i	0.802119	+	0.597164i	$0.203706\pi$
$402$		0			0
$403$	−21.9259	+	37.9768i	−1.09221	+	1.89176i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.52615	+	3.76788i	0.323489	+	0.186767i
$408$		0			0
$409$	−0.0555181	−	0.0961601i	−0.00274519	−	0.00475481i	0.864650	−	0.502376i	$-0.167540\pi$
$409$	−0.0555181	−	0.0961601i	−0.00274519	−	0.00475481i	−0.867395	+	0.497621i	$0.834207\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−14.5569			−0.716297
$414$		0			0
$415$	2.26093	+	5.82412i	0.110985	+	0.285895i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.66122	−	16.7337i	−0.471981	−	0.817496i	0.527505	−	0.849552i	$-0.323128\pi$
$419$	−9.66122	−	16.7337i	−0.471981	−	0.817496i	−0.999486	+	0.0320563i	$0.989794\pi$
$420$		0			0
$421$	−18.4323	+	31.9258i	−0.898337	+	1.55597i	−0.0687183	+	0.997636i	$0.521891\pi$
$421$	−18.4323	+	31.9258i	−0.898337	+	1.55597i	−0.829619	+	0.558330i	$0.811442\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.03937	+	22.8585i	0.244445	+	1.10880i
$426$		0			0
$427$	8.24986	+	14.2892i	0.399239	+	0.691502i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.5407			−0.748571			−0.374286	−	0.927313i	$-0.622112\pi$
$431$	−15.5407			−0.748571			−0.374286	+	0.927313i	$0.622112\pi$
$432$		0			0
$433$			8.23429i			0.395715i	0.980231	+	0.197857i	$0.0633983\pi$
$433$			8.23429i			0.395715i	−0.980231	+	0.197857i	$0.936602\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.21285	−	5.56482i	−0.153691	−	0.266201i
$438$		0			0
$439$	−28.8199	−	16.6392i	−1.37550	−	0.794145i	−0.383886	−	0.923381i	$-0.625414\pi$
$439$	−28.8199	−	16.6392i	−1.37550	−	0.794145i	−0.991614	+	0.129235i	$0.958748\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.6345	+	6.71718i	0.552772	+	0.319143i	0.750239	−	0.661167i	$-0.229938\pi$
$443$	11.6345	+	6.71718i	0.552772	+	0.319143i	−0.197467	+	0.980309i	$0.563272\pi$
$444$		0			0
$445$	−1.33400	+	1.66012i	−0.0632376	+	0.0786974i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	30.4331i		−	1.43622i	−0.695927	−	0.718112i	$-0.745006\pi$
$449$		−	30.4331i		−	1.43622i	0.695927	−	0.718112i	$-0.254994\pi$
$450$		0			0
$451$		−	30.8649i		−	1.45337i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	31.3738	−	39.0439i	1.47083	−	1.83040i
$456$		0			0
$457$	6.90969	+	3.98931i	0.323222	+	0.186612i	0.652828	−	0.757507i	$-0.273583\pi$
$457$	6.90969	+	3.98931i	0.323222	+	0.186612i	−0.329606	+	0.944119i	$0.606916\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.8613	+	13.1990i	1.06476	+	0.614738i	0.926745	−	0.375692i	$-0.122595\pi$
$461$	22.8613	+	13.1990i	1.06476	+	0.614738i	0.138014	+	0.990430i	$0.455928\pi$
$462$		0			0
$463$	0.473161	+	0.819539i	0.0219896	+	0.0380872i	0.876811	−	0.480836i	$-0.159667\pi$
$463$	0.473161	+	0.819539i	0.0219896	+	0.0380872i	−0.854821	+	0.518923i	$0.826333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			34.4606i			1.59464i	0.603554	+	0.797322i	$0.293751\pi$
$467$			34.4606i			1.59464i	−0.603554	+	0.797322i	$0.706249\pi$
$468$		0			0
$469$	39.8347			1.83940
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.831672	+	1.44050i	0.0382403	+	0.0662342i
$474$		0			0
$475$	11.2294	−	2.47564i	0.515242	−	0.113590i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.07387	+	5.32411i	−0.140449	+	0.243265i	−0.927666	−	0.373412i	$-0.878188\pi$
$479$	−3.07387	+	5.32411i	−0.140449	+	0.243265i	0.787217	+	0.616676i	$0.211521\pi$
$480$		0			0
$481$	−5.29006	−	9.16265i	−0.241206	−	0.417781i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.86912	+	7.39081i	0.130280	+	0.335600i
$486$		0			0
$487$	−19.7766			−0.896164			−0.448082	−	0.893992i	$-0.647893\pi$
$487$	−19.7766			−0.896164			−0.448082	+	0.893992i	$0.647893\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.30861	+	5.73068i	0.149316	+	0.258622i	0.930975	−	0.365084i	$-0.118960\pi$
$491$	3.30861	+	5.73068i	0.149316	+	0.258622i	−0.781659	+	0.623706i	$0.785626\pi$
$492$		0			0
$493$	−3.93998	−	2.27475i	−0.177448	−	0.102449i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.2996	−	36.8920i	0.955418	−	1.65483i
$498$		0			0
$499$	−14.7185	+	8.49775i	−0.658892	+	0.380412i	−0.791855	−	0.610710i	$-0.790884\pi$
$499$	−14.7185	+	8.49775i	−0.658892	+	0.380412i	0.132963	+	0.991121i	$0.457551\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			15.4892i			0.690631i	0.938487	+	0.345316i	$0.112228\pi$
$503$			15.4892i			0.690631i	−0.938487	+	0.345316i	$0.887772\pi$
$504$		0			0
$505$	5.22583	+	13.4617i	0.232547	+	0.599036i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.57111	−	4.37118i	0.335584	−	0.193749i	−0.322734	−	0.946490i	$-0.604602\pi$
$509$	7.57111	−	4.37118i	0.335584	−	0.193749i	0.658317	+	0.752741i	$0.271269\pi$
$510$		0			0
$511$	15.6204	+	9.01846i	0.691007	+	0.398953i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.34523	+	15.1778i	−0.103343	+	0.668813i
$516$		0			0
$517$	23.9224	−	13.8116i	1.05211	−	0.607433i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			34.5835i			1.51513i	0.652758	+	0.757566i	$0.273612\pi$
$521$			34.5835i			1.51513i	−0.652758	+	0.757566i	$0.726388\pi$
$522$		0			0
$523$	−10.1425			−0.443501			−0.221751	−	0.975103i	$-0.571177\pi$
$523$	−10.1425			−0.443501			−0.221751	+	0.975103i	$0.571177\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−39.0131	+	22.5242i	−1.69944	+	0.981170i
$528$		0			0
$529$	−7.59678	+	13.1580i	−0.330295	+	0.572087i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−21.6670	+	37.5284i	−0.938503	+	1.62553i
$534$		0			0
$535$	11.7049	−	14.5664i	0.506045	−	0.629760i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	55.6998			2.39916
$540$		0			0
$541$	21.9906			0.945450			0.472725	−	0.881210i	$-0.343270\pi$
$541$	21.9906			0.945450			0.472725	+	0.881210i	$0.343270\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.6525	+	11.7741i	0.627645	+	0.504346i
$546$		0			0
$547$	−6.66047	+	11.5363i	−0.284781	+	0.493256i	−0.972556	−	0.232668i	$-0.925254\pi$
$547$	−6.66047	+	11.5363i	−0.284781	+	0.493256i	0.687775	+	0.725924i	$0.258588\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.11749	+	1.93555i	−0.0476067	+	0.0824573i
$552$		0			0
$553$	−0.0287496	+	0.0165986i	−0.00122256	+	0.000705845i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.2286			0.475771			0.237885	−	0.971293i	$-0.423546\pi$
$557$	11.2286			0.475771			0.237885	+	0.971293i	$0.423546\pi$
$558$		0			0
$559$		−	2.33532i		−	0.0987735i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	26.3748	−	15.2275i	1.11157	−	0.641764i	0.172332	−	0.985039i	$-0.444870\pi$
$563$	26.3748	−	15.2275i	1.11157	−	0.641764i	0.939235	+	0.343275i	$0.111536\pi$
$564$		0			0
$565$	5.26403	−	34.0676i	0.221460	−	1.43323i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.2927	+	12.2934i	0.892638	+	0.515365i	0.874804	−	0.484476i	$-0.160990\pi$
$569$	21.2927	+	12.2934i	0.892638	+	0.515365i	0.0178334	+	0.999841i	$0.494323\pi$
$570$		0			0
$571$	9.86354	−	5.69472i	0.412776	−	0.238317i	−0.279206	−	0.960231i	$-0.590071\pi$
$571$	9.86354	−	5.69472i	0.412776	−	0.238317i	0.691982	+	0.721915i	$0.256738\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.42587	+	10.3109i	0.393086	+	0.429993i
$576$		0			0
$577$			3.96503i			0.165066i	0.996588	+	0.0825331i	$0.0263010\pi$
$577$			3.96503i			0.165066i	−0.996588	+	0.0825331i	$0.973699\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.8935	−	6.86671i	0.493425	−	0.284879i
$582$		0			0
$583$	16.0776	−	27.8473i	0.665867	−	1.15332i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−28.6601	−	16.5469i	−1.18293	−	0.682965i	−0.226240	−	0.974072i	$-0.572643\pi$
$587$	−28.6601	−	16.5469i	−1.18293	−	0.682965i	−0.956691	+	0.291106i	$0.905977\pi$
$588$		0			0
$589$	11.0652	+	19.1655i	0.455935	+	0.789703i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.4391			0.839334			0.419667	−	0.907678i	$-0.362147\pi$
$593$	20.4391			0.839334			0.419667	+	0.907678i	$0.362147\pi$
$594$		0			0
$595$	47.9665	−	18.6207i	1.96644	−	0.763373i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−21.8710	−	37.8817i	−0.893625	−	1.54780i	−0.835497	−	0.549496i	$-0.814820\pi$
$599$	−21.8710	−	37.8817i	−0.893625	−	1.54780i	−0.0581288	−	0.998309i	$-0.518513\pi$
$600$		0			0
$601$	−11.1919	+	19.3850i	−0.456529	+	0.790732i	−0.998775	−	0.0494884i	$-0.984241\pi$
$601$	−11.1919	+	19.3850i	−0.456529	+	0.790732i	0.542246	+	0.840220i	$0.317574\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.158617	−	1.02653i	0.00644871	−	0.0417345i
$606$		0			0
$607$	−12.1622	−	21.0656i	−0.493649	−	0.855025i	0.506325	−	0.862343i	$-0.331004\pi$
$607$	−12.1622	−	21.0656i	−0.493649	−	0.855025i	−0.999973	+	0.00731837i	$0.997670\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−38.7827			−1.56898
$612$		0			0
$613$		−	15.7753i		−	0.637157i	−0.947896	−	0.318579i	$-0.896795\pi$
$613$		−	15.7753i		−	0.637157i	0.947896	−	0.318579i	$-0.103205\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.17947	+	5.50700i	0.128001	+	0.221703i	0.922902	−	0.385035i	$-0.125811\pi$
$617$	3.17947	+	5.50700i	0.128001	+	0.221703i	−0.794901	+	0.606739i	$0.792477\pi$
$618$		0			0
$619$	27.7015	+	15.9935i	1.11342	+	0.642832i	0.939712	−	0.341966i	$-0.111093\pi$
$619$	27.7015	+	15.9935i	1.11342	+	0.642832i	0.173705	+	0.984798i	$0.444426\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.05427	+	2.34073i	0.162431	+	0.0937795i
$624$		0			0
$625$	−22.6825	+	10.5121i	−0.907300	+	0.420483i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	10.8688i		−	0.433368i
$630$		0			0
$631$			20.8543i			0.830196i	0.909777	+	0.415098i	$0.136253\pi$
$631$			20.8543i			0.830196i	−0.909777	+	0.415098i	$0.863747\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.22356	−	5.00096i	−0.246974	−	0.198457i
$636$		0			0
$637$	−67.7249	−	39.1010i	−2.68336	−	1.54924i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	26.5324	+	15.3185i	1.04797	+	0.605043i	0.922079	−	0.387002i	$-0.126489\pi$
$641$	26.5324	+	15.3185i	1.04797	+	0.605043i	0.125886	+	0.992045i	$0.459823\pi$
$642$		0			0
$643$	−19.0142	−	32.9335i	−0.749846	−	1.29877i	−0.947896	−	0.318580i	$-0.896794\pi$
$643$	−19.0142	−	32.9335i	−0.749846	−	1.29877i	0.198050	−	0.980192i	$-0.436539\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	28.3431i		−	1.11428i	−0.830417	−	0.557142i	$-0.811898\pi$
$647$		−	28.3431i		−	1.11428i	0.830417	−	0.557142i	$-0.188102\pi$
$648$		0			0
$649$	−9.61266			−0.377330
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.2134	+	19.4221i	0.438813	+	0.760046i	0.997598	−	0.0692663i	$-0.0220658\pi$
$653$	11.2134	+	19.4221i	0.438813	+	0.760046i	−0.558785	+	0.829312i	$0.688732\pi$
$654$		0			0
$655$	1.79691	−	11.6292i	0.0702110	−	0.454389i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.01881	−	6.96078i	0.156551	−	0.271154i	−0.777072	−	0.629412i	$-0.783296\pi$
$659$	4.01881	−	6.96078i	0.156551	−	0.271154i	0.933623	+	0.358258i	$0.116629\pi$
$660$		0			0
$661$	10.1926	+	17.6542i	0.396448	+	0.686668i	0.993285	−	0.115695i	$-0.0369095\pi$
$661$	10.1926	+	17.6542i	0.396448	+	0.686668i	−0.596837	+	0.802362i	$0.703576\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.14758	−	23.5640i	−0.354728	−	0.913773i
$666$		0			0
$667$	−2.71523			−0.105134
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.44781	+	9.43588i	0.210310	+	0.364268i
$672$		0			0
$673$	23.6402	+	13.6487i	0.911264	+	0.526119i	0.880838	−	0.473418i	$-0.156980\pi$
$673$	23.6402	+	13.6487i	0.911264	+	0.526119i	0.0304264	+	0.999537i	$0.490313\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.7854	−	32.5373i	0.721981	−	1.25051i	−0.238223	−	0.971210i	$-0.576565\pi$
$677$	18.7854	−	32.5373i	0.721981	−	1.25051i	0.960205	−	0.279298i	$-0.0901017\pi$
$678$		0			0
$679$	15.0928	−	8.71385i	0.579210	−	0.334407i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			0.779851i			0.0298402i	0.999889	+	0.0149201i	$0.00474938\pi$
$683$			0.779851i			0.0298402i	−0.999889	+	0.0149201i	$0.995251\pi$
$684$		0			0
$685$	−25.1208	+	9.75194i	−0.959818	+	0.372602i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−39.0973	+	22.5728i	−1.48949	+	0.859956i
$690$		0			0
$691$	22.5980	+	13.0469i	0.859668	+	0.496329i	0.863901	−	0.503662i	$-0.168014\pi$
$691$	22.5980	+	13.0469i	0.859668	+	0.496329i	−0.00423336	+	0.999991i	$0.501348\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−40.4791	−	6.25473i	−1.53546	−	0.237255i
$696$		0			0
$697$	−38.5524	+	22.2582i	−1.46028	+	0.843090i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			16.3745i			0.618458i	0.950988	+	0.309229i	$0.100071\pi$
$701$			16.3745i			0.618458i	−0.950988	+	0.309229i	$0.899929\pi$
$702$		0			0
$703$	−5.33941			−0.201380
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.4901	−	15.8714i	1.03387	−	0.596907i
$708$		0			0
$709$	9.64926	−	16.7130i	0.362385	−	0.627670i	−0.625968	−	0.779849i	$-0.715296\pi$
$709$	9.64926	−	16.7130i	0.362385	−	0.627670i	0.988353	+	0.152179i	$0.0486291\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.4429	+	23.2838i	−0.503441	+	0.871986i
$714$		0			0
$715$	20.7178	−	25.7827i	0.774800	−	0.964218i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	46.2738			1.72572			0.862860	−	0.505442i	$-0.168671\pi$
$719$	46.2738			1.72572			0.862860	+	0.505442i	$0.168671\pi$
$720$		0			0
$721$	33.7597			1.25728
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.46660	−	4.63243i	0.0544680	−	0.172044i
$726$		0			0
$727$	9.16075	−	15.8669i	0.339753	−	0.588470i	−0.644633	−	0.764492i	$-0.722990\pi$
$727$	9.16075	−	15.8669i	0.339753	−	0.588470i	0.984386	+	0.176022i	$0.0563231\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.19952	−	2.07763i	0.0443659	−	0.0768439i
$732$		0			0
$733$	4.01463	−	2.31785i	0.148284	−	0.0856117i	−0.424022	−	0.905652i	$-0.639382\pi$
$733$	4.01463	−	2.31785i	0.148284	−	0.0856117i	0.572306	+	0.820040i	$0.306049\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	26.3049			0.968954
$738$		0			0
$739$		−	11.4405i		−	0.420844i	−0.977611	−	0.210422i	$-0.932516\pi$
$739$		−	11.4405i		−	0.420844i	0.977611	−	0.210422i	$-0.0674839\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.6156	+	13.6345i	−0.866373	+	0.500201i	−0.866141	−	0.499799i	$-0.833407\pi$
$743$	−23.6156	+	13.6345i	−0.866373	+	0.500201i	−0.000231838		1.00000i	$0.500074\pi$
$744$		0			0
$745$	51.6624	+	7.98273i	1.89276	+	0.292465i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−35.5733	−	20.5383i	−1.29982	−	0.750451i
$750$		0			0
$751$	−24.9256	+	14.3908i	−0.909549	+	0.525128i	−0.880286	−	0.474443i	$-0.842649\pi$
$751$	−24.9256	+	14.3908i	−0.909549	+	0.525128i	−0.0292631	+	0.999572i	$0.509316\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	14.4040	+	37.1045i	0.524215	+	1.35037i
$756$		0			0
$757$		−	38.6191i		−	1.40363i	−0.712357	−	0.701817i	$-0.752372\pi$
$757$		−	38.6191i		−	1.40363i	0.712357	−	0.701817i	$-0.247628\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−10.7901	+	6.22969i	−0.391142	+	0.225826i	−0.682655	−	0.730741i	$-0.739175\pi$
$761$	−10.7901	+	6.22969i	−0.391142	+	0.225826i	0.291513	+	0.956567i	$0.405841\pi$
$762$		0			0
$763$	20.6597	−	35.7836i	0.747931	−	1.29545i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.6879	+	6.74804i	0.422027	+	0.243658i
$768$		0			0
$769$	20.7262	+	35.8988i	0.747405	+	1.29454i	0.949062	+	0.315088i	$0.102034\pi$
$769$	20.7262	+	35.8988i	0.747405	+	1.29454i	−0.201657	+	0.979456i	$0.564633\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.8158			0.460954			0.230477	−	0.973078i	$-0.425971\pi$
$773$	12.8158			0.460954			0.230477	+	0.973078i	$0.425971\pi$
$774$		0			0
$775$	−32.4632	−	35.5112i	−1.16611	−	1.27560i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.9346	+	18.9392i	0.391772	+	0.678568i
$780$		0			0
$781$	14.0652	−	24.3617i	0.503294	−	0.871730i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.68325	+	0.878161i	0.202844	+	0.0313429i
$786$		0			0
$787$	1.29742	+	2.24720i	0.0462481	+	0.0801041i	0.888223	−	0.459413i	$-0.151940\pi$
$787$	1.29742	+	2.24720i	0.0462481	+	0.0801041i	−0.841975	+	0.539517i	$0.818607\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−75.7760			−2.69428
$792$		0			0
$793$		−	15.2973i		−	0.543225i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.96403	+	3.40180i	0.0695695	+	0.120498i	0.898712	−	0.438540i	$-0.144504\pi$
$797$	1.96403	+	3.40180i	0.0695695	+	0.120498i	−0.829142	+	0.559038i	$0.811171\pi$
$798$		0			0
$799$	−34.5033	−	19.9205i	−1.22064	−	0.704736i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.3150	+	5.95535i	0.364008	+	0.210160i
$804$		0			0
$805$	19.2355	−	23.9380i	0.677962	−	0.843705i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	23.6490i		−	0.831454i	−0.909489	−	0.415727i	$-0.863527\pi$
$809$		−	23.6490i		−	0.831454i	0.909489	−	0.415727i	$-0.136473\pi$
$810$		0			0
$811$			30.1396i			1.05834i	0.848515	+	0.529172i	$0.177497\pi$
$811$			30.1396i			1.05834i	−0.848515	+	0.529172i	$0.822503\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.04223	−	6.46236i	−0.281707	−	0.226367i
$816$		0			0
$817$	−1.02066	−	0.589276i	−0.0357082	−	0.0206162i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−28.5981	−	16.5111i	−0.998081	−	0.576242i	−0.0904010	−	0.995905i	$-0.528815\pi$
$821$	−28.5981	−	16.5111i	−0.998081	−	0.576242i	−0.907680	+	0.419663i	$0.862148\pi$
$822$		0			0
$823$	27.3286	+	47.3345i	0.952615	+	1.64998i	0.739734	+	0.672900i	$0.234951\pi$
$823$	27.3286	+	47.3345i	0.952615	+	1.64998i	0.212881	+	0.977078i	$0.431715\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	7.83653i		−	0.272503i	−0.990674	−	0.136251i	$-0.956494\pi$
$827$		−	7.83653i		−	0.272503i	0.990674	−	0.136251i	$-0.0435055\pi$
$828$		0			0
$829$	−45.3314			−1.57442			−0.787211	−	0.616683i	$-0.788476\pi$
$829$	−45.3314			−1.57442			−0.787211	+	0.616683i	$0.788476\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−40.1679	−	69.5728i	−1.39173	−	2.41056i
$834$		0			0
$835$	12.0481	+	1.86163i	0.416940	+	0.0644245i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.1201	−	20.9926i	0.418432	−	0.724745i	−0.577350	−	0.816497i	$-0.695913\pi$
$839$	12.1201	−	20.9926i	0.418432	−	0.724745i	0.995782	+	0.0917514i	$0.0292465\pi$
$840$		0			0
$841$	−14.0278	−	24.2969i	−0.483717	−	0.837823i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.1912	+	6.28546i	−0.556995	+	0.216226i
$846$		0			0
$847$	−2.28330			−0.0784552
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.24337	−	5.61768i	−0.111181	−	0.192572i
$852$		0			0
$853$	−13.9184	−	8.03581i	−0.476558	−	0.275141i	0.242423	−	0.970171i	$-0.422058\pi$
$853$	−13.9184	−	8.03581i	−0.476558	−	0.275141i	−0.718981	+	0.695030i	$0.755391\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.14515	+	1.98346i	−0.0391177	+	0.0677538i	−0.884921	−	0.465740i	$-0.845788\pi$
$857$	−1.14515	+	1.98346i	−0.0391177	+	0.0677538i	0.845804	+	0.533494i	$0.179121\pi$
$858$		0			0
$859$	−25.7347	+	14.8579i	−0.878056	+	0.506946i	−0.870017	−	0.493022i	$-0.835892\pi$
$859$	−25.7347	+	14.8579i	−0.878056	+	0.506946i	−0.00803922	+	0.999968i	$0.502559\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			34.7002i			1.18121i	0.806961	+	0.590605i	$0.201111\pi$
$863$			34.7002i			1.18121i	−0.806961	+	0.590605i	$0.798889\pi$
$864$		0			0
$865$	−46.1022	+	17.8969i	−1.56752	+	0.608514i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.0189849	+	0.0109609i	−0.000644018	+	0.000371824i
$870$		0			0
$871$	−31.9839	−	18.4659i	−1.08373	−	0.625694i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	30.4506	+	45.7472i	1.02942	+	1.54654i
$876$		0			0
$877$	4.08267	−	2.35713i	0.137862	−	0.0795947i	−0.429483	−	0.903075i	$-0.641304\pi$
$877$	4.08267	−	2.35713i	0.137862	−	0.0795947i	0.567345	+	0.823480i	$0.307971\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			41.1882i			1.38766i	0.720136	+	0.693832i	$0.244079\pi$
$881$			41.1882i			1.38766i	−0.720136	+	0.693832i	$0.755921\pi$
$882$		0			0
$883$	−26.9479			−0.906870			−0.453435	−	0.891289i	$-0.649802\pi$
$883$	−26.9479			−0.906870			−0.453435	+	0.891289i	$0.649802\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.0614320	−	0.0354678i	0.00206269	−	0.00119089i	−0.498968	−	0.866620i	$-0.666288\pi$
$887$	0.0614320	−	0.0354678i	0.00206269	−	0.00119089i	0.501031	+	0.865429i	$0.332954\pi$
$888$		0			0
$889$	−8.77507	+	15.1989i	−0.294306	+	0.509753i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.78612	+	16.9501i	−0.327480	+	0.567212i
$894$		0			0
$895$	15.7262	+	12.6369i	0.525670	+	0.422404i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.35142			0.311887
$900$		0			0
$901$	−46.3775			−1.54506
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.7778	+	19.1067i	0.790401	+	0.635129i
$906$		0			0
$907$	−18.5017	+	32.0459i	−0.614340	+	1.06407i	0.376160	+	0.926555i	$0.377244\pi$
$907$	−18.5017	+	32.0459i	−0.614340	+	1.06407i	−0.990500	+	0.137513i	$0.956089\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.7405	+	28.9954i	−0.554637	+	0.960660i	0.443294	+	0.896376i	$0.353810\pi$
$911$	−16.7405	+	28.9954i	−0.554637	+	0.960660i	−0.997932	+	0.0642840i	$0.979524\pi$
$912$		0			0
$913$	7.85388	−	4.53444i	0.259926	−	0.150068i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−25.8665			−0.854189
$918$		0			0
$919$			37.0547i			1.22232i	0.791506	+	0.611161i	$0.209297\pi$
$919$			37.0547i			1.22232i	−0.791506	+	0.611161i	$0.790703\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−34.2036	+	19.7475i	−1.12583	+	0.649995i
$924$		0			0
$925$	11.3361	−	2.49916i	0.372729	−	0.0821718i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.32859	−	1.92176i	−0.109208	−	0.0630510i	0.444401	−	0.895828i	$-0.353416\pi$
$929$	−3.32859	−	1.92176i	−0.109208	−	0.0630510i	−0.553609	+	0.832777i	$0.686750\pi$
$930$		0			0
$931$	−34.1783	+	19.7329i	−1.12015	+	0.646718i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	31.6748	−	12.2962i	1.03588	−	0.402128i
$936$		0			0
$937$		−	20.6287i		−	0.673912i	−0.941520	−	0.336956i	$-0.890603\pi$
$937$		−	20.6287i		−	0.673912i	0.941520	−	0.336956i	$-0.109397\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	21.3168	−	12.3072i	0.694907	−	0.401205i	−0.110541	−	0.993872i	$-0.535258\pi$
$941$	21.3168	−	12.3072i	0.694907	−	0.401205i	0.805448	+	0.592667i	$0.201925\pi$
$942$		0			0
$943$	−13.2842	+	23.0089i	−0.432592	+	0.749272i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−22.4985	−	12.9895i	−0.731104	−	0.422103i	0.0877216	−	0.996145i	$-0.472041\pi$
$947$	−22.4985	−	12.9895i	−0.731104	−	0.422103i	−0.818826	+	0.574042i	$0.805375\pi$
$948$		0			0
$949$	−8.36126	−	14.4821i	−0.271418	−	0.470110i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	38.7615			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$953$	38.7615			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$954$		0			0
$955$	−22.0179	+	8.54737i	−0.712482	+	0.276586i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	29.6177	+	51.2994i	0.956407	+	1.65655i
$960$		0			0
$961$	30.7982	−	53.3440i	0.993490	−	1.72077i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	34.9227	+	5.39616i	1.12420	+	0.173709i
$966$		0			0
$967$	19.5551	+	33.8704i	0.628849	+	1.08920i	0.987783	+	0.155835i	$0.0498068\pi$
$967$	19.5551	+	33.8704i	0.628849	+	1.08920i	−0.358934	+	0.933363i	$0.616860\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.5132			−0.754574			−0.377287	−	0.926096i	$-0.623143\pi$
$971$	−23.5132			−0.754574			−0.377287	+	0.926096i	$0.623143\pi$
$972$		0			0
$973$			90.0371i			2.88646i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.9499	−	34.5542i	−0.638253	−	1.10549i	−0.985816	−	0.167830i	$-0.946324\pi$
$977$	−19.9499	−	34.5542i	−0.638253	−	1.10549i	0.347563	−	0.937657i	$-0.387009\pi$
$978$		0			0
$979$	2.67724	+	1.54571i	0.0855651	+	0.0494010i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	43.2536	+	24.9725i	1.37958	+	0.796499i	0.992108	−	0.125384i	$-0.0400162\pi$
$983$	43.2536	+	24.9725i	1.37958	+	0.796499i	0.387469	+	0.921883i	$0.373350\pi$
$984$		0			0
$985$	−33.1580	−	26.6442i	−1.05650	−	0.848956i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	1.43180i		−	0.0455285i
$990$		0			0
$991$			37.3553i			1.18663i	0.804971	+	0.593315i	$0.202181\pi$
$991$			37.3553i			1.18663i	−0.804971	+	0.593315i	$0.797819\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.01488	+	2.50747i	−0.0638761	+	0.0794921i
$996$		0			0
$997$	44.6518	+	25.7797i	1.41414	+	0.816452i	0.995775	−	0.0918294i	$-0.0292714\pi$
$997$	44.6518	+	25.7797i	1.41414	+	0.816452i	0.418361	+	0.908281i	$0.362605\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.2.br.d.1439.3		24
3.2	odd	2		720.2.br.c.479.11	yes	24
4.3	odd	2		2160.2.br.c.1439.3		24
5.4	even	2	inner	2160.2.br.d.1439.7		24
9.4	even	3		720.2.br.d.239.11	yes	24
9.5	odd	6		2160.2.br.c.719.7		24
12.11	even	2		720.2.br.d.479.2	yes	24
15.14	odd	2		720.2.br.c.479.2	yes	24
20.19	odd	2		2160.2.br.c.1439.7		24
36.23	even	6	inner	2160.2.br.d.719.7		24
36.31	odd	6		720.2.br.c.239.2	✓	24
45.4	even	6		720.2.br.d.239.2	yes	24
45.14	odd	6		2160.2.br.c.719.3		24
60.59	even	2		720.2.br.d.479.11	yes	24
180.59	even	6	inner	2160.2.br.d.719.3		24
180.139	odd	6		720.2.br.c.239.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.br.c.239.2	✓	24	36.31	odd	6
720.2.br.c.239.11	yes	24	180.139	odd	6
720.2.br.c.479.2	yes	24	15.14	odd	2
720.2.br.c.479.11	yes	24	3.2	odd	2
720.2.br.d.239.2	yes	24	45.4	even	6
720.2.br.d.239.11	yes	24	9.4	even	3
720.2.br.d.479.2	yes	24	12.11	even	2
720.2.br.d.479.11	yes	24	60.59	even	2
2160.2.br.c.719.3		24	45.14	odd	6
2160.2.br.c.719.7		24	9.5	odd	6
2160.2.br.c.1439.3		24	4.3	odd	2
2160.2.br.c.1439.7		24	20.19	odd	2
2160.2.br.d.719.3		24	180.59	even	6	inner
2160.2.br.d.719.7		24	36.23	even	6	inner
2160.2.br.d.1439.3		24	1.1	even	1	trivial
2160.2.br.d.1439.7		24	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.br (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.74305 - 1.40063i) q^{5} +(-2.45766 + 4.25679i) q^{7} +O(q^{10})\)	\(q+(-1.74305 - 1.40063i) q^{5} +(-2.45766 + 4.25679i) q^{7} +(-1.62292 + 2.81098i) q^{11} +(3.94659 - 2.27856i) q^{13} +4.68147 q^{17} -2.29982i q^{19} +(2.41968 - 1.39700i) q^{23} +(1.07645 + 4.88275i) q^{25} +(-0.841610 - 0.485904i) q^{29} +(-8.33350 + 4.81135i) q^{31} +(10.2460 - 3.97752i) q^{35} -2.32167i q^{37} +(-8.23509 + 4.75453i) q^{41} +(0.256227 - 0.443798i) q^{43} +(-7.37017 - 4.25517i) q^{47} +(-8.58018 - 14.8613i) q^{49} -9.90660 q^{53} +(6.76598 - 2.62656i) q^{55} +(1.48077 + 2.56476i) q^{59} +(1.67840 - 2.90707i) q^{61} +(-10.0705 - 1.55607i) q^{65} +(-4.05210 - 7.01844i) q^{67} -8.66662 q^{71} -3.66953i q^{73} +(-7.97717 - 13.8169i) q^{77} +(0.00584899 + 0.00337691i) q^{79} +(-2.41968 - 1.39700i) q^{83} +(-8.16004 - 6.55703i) q^{85} -0.952424i q^{89} +22.3997i q^{91} +(-3.22120 + 4.00870i) q^{95} +(-3.07057 - 1.77279i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{5}+O(q^{10}) \) 24 * q - 3 * q^5	\( 24 q - 3 q^{5} + 6 q^{11} + 3 q^{25} - 12 q^{29} - 18 q^{31} + 30 q^{35} + 12 q^{41} - 12 q^{49} - 6 q^{59} - 3 q^{65} - 96 q^{71} - 18 q^{79} - 24 q^{95}+O(q^{100}) \) 24 * q - 3 * q^5 + 6 * q^11 + 3 * q^25 - 12 * q^29 - 18 * q^31 + 30 * q^35 + 12 * q^41 - 12 * q^49 - 6 * q^59 - 3 * q^65 - 96 * q^71 - 18 * q^79 - 24 * q^95

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