LMFDB - Embedded newform 1620.2.r.h.1189.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(109,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("1620.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.r (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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} - 11x^{12} - 90x^{10} - 450x^{8} - 2250x^{6} - 6875x^{4} + 46875x^{2} + 390625 $ x^16 + 3x^14 - 11x^12 - 90x^10 - 450x^8 - 2250x^6 - 6875x^4 + 46875*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1189.5
Root			$-0.308893 + 2.21463i$ of defining polynomial
Character	$\chi$	$=$	1620.1189
Dual form			1620.2.r.h.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.308893 + 2.21463i) q^{5} +(4.27415 + 2.46768i) q^{7} +O(q^{10})$	$q+(0.308893 + 2.21463i) q^{5} +(4.27415 + 2.46768i) q^{7} +(1.20635 - 2.08945i) q^{11} +(2.51942 - 1.45459i) q^{13} -6.86869i q^{17} +4.17891 q^{19} +(2.90917 - 1.67961i) q^{23} +(-4.80917 + 1.36817i) q^{25} +(2.59808 - 4.50000i) q^{29} +(3.08945 + 5.35109i) q^{31} +(-4.14474 + 10.2279i) q^{35} -7.84453i q^{37} +(2.93840 + 5.08945i) q^{41} +(-4.27415 - 2.46768i) q^{43} +(-10.3122 - 5.95376i) q^{47} +(8.67891 + 15.0323i) q^{49} +8.54830i q^{53} +(5.00000 + 2.02619i) q^{55} +(-0.525704 - 0.910546i) q^{59} +(-4.58945 + 7.94917i) q^{61} +(3.99960 + 5.13026i) q^{65} +(-3.50947 + 2.02619i) q^{67} -14.1663 q^{71} +2.02619i q^{73} +(10.3122 - 5.95376i) q^{77} +(3.00000 - 5.19615i) q^{79} +(4.49387 + 2.59454i) q^{83} +(15.2116 - 2.12169i) q^{85} -3.09334 q^{89} +14.3578 q^{91} +(1.29084 + 9.25473i) q^{95} +(0.764681 + 0.441489i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91}+O(q^{100}) $ 16 * q - 24 * q^19 - 6 * q^25 + 4 * q^31 + 48 * q^49 + 80 * q^55 - 28 * q^61 + 48 * q^79 - 22 * q^85 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$5$	0.308893	+	2.21463i	0.138141	+	0.990413i
$5$	0.308893	+	2.21463i	0.138141	+	0.990413i
$6$		0			0
$7$	4.27415	+	2.46768i	1.61548	+	0.932696i	0.988070	+	0.154005i	$0.0492170\pi$
$7$	4.27415	+	2.46768i	1.61548	+	0.932696i	0.627407	+	0.778692i	$0.284116\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.20635	−	2.08945i	0.363727	−	0.629994i	−0.624844	−	0.780750i	$-0.714837\pi$
$11$	1.20635	−	2.08945i	0.363727	−	0.629994i	0.988571	+	0.150756i	$0.0481707\pi$
$12$		0			0
$13$	2.51942	−	1.45459i	0.698760	−	0.403429i	−0.108125	−	0.994137i	$-0.534485\pi$
$13$	2.51942	−	1.45459i	0.698760	−	0.403429i	0.806886	+	0.590708i	$0.201151\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.86869i		−	1.66590i	−0.553347	−	0.832951i	$-0.686650\pi$
$17$		−	6.86869i		−	1.66590i	0.553347	−	0.832951i	$-0.313350\pi$
$18$		0			0
$19$	4.17891			0.958707			0.479354	−	0.877622i	$-0.340871\pi$
$19$	4.17891			0.958707			0.479354	+	0.877622i	$0.340871\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.90917	−	1.67961i	0.606604	−	0.350223i	−0.165031	−	0.986288i	$-0.552772\pi$
$23$	2.90917	−	1.67961i	0.606604	−	0.350223i	0.771635	+	0.636065i	$0.219439\pi$
$24$		0			0
$25$	−4.80917	+	1.36817i	−0.961834	+	0.273634i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.59808	−	4.50000i	0.482451	−	0.835629i	−0.517346	−	0.855776i	$-0.673080\pi$
$29$	2.59808	−	4.50000i	0.482451	−	0.835629i	0.999797	+	0.0201471i	$0.00641344\pi$
$30$		0			0
$31$	3.08945	+	5.35109i	0.554882	+	0.961084i	0.997913	+	0.0645778i	$0.0205701\pi$
$31$	3.08945	+	5.35109i	0.554882	+	0.961084i	−0.443030	+	0.896507i	$0.646097\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.14474	+	10.2279i	−0.700590	+	1.72883i
$36$		0			0
$37$		−	7.84453i		−	1.28963i	−0.764337	−	0.644817i	$-0.776934\pi$
$37$		−	7.84453i		−	1.28963i	0.764337	−	0.644817i	$-0.223066\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.93840	+	5.08945i	0.458901	+	0.794839i	0.998903	−	0.0468242i	$-0.0149101\pi$
$41$	2.93840	+	5.08945i	0.458901	+	0.794839i	−0.540003	+	0.841663i	$0.681577\pi$
$42$		0			0
$43$	−4.27415	−	2.46768i	−0.651802	−	0.376318i	0.137344	−	0.990523i	$-0.456143\pi$
$43$	−4.27415	−	2.46768i	−0.651802	−	0.376318i	−0.789146	+	0.614205i	$0.789477\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.3122	−	5.95376i	−1.50419	−	0.868445i	−0.999988	−	0.00486027i	$-0.998453\pi$
$47$	−10.3122	−	5.95376i	−1.50419	−	0.868445i	−0.504203	−	0.863585i	$-0.668214\pi$
$48$		0			0
$49$	8.67891	+	15.0323i	1.23984	+	2.14747i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			8.54830i			1.17420i	0.809515	+	0.587100i	$0.199730\pi$
$53$			8.54830i			1.17420i	−0.809515	+	0.587100i	$0.800270\pi$
$54$		0			0
$55$	5.00000	+	2.02619i	0.674200	+	0.273212i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.525704	−	0.910546i	−0.0684408	−	0.118543i	0.829774	−	0.558099i	$-0.188469\pi$
$59$	−0.525704	−	0.910546i	−0.0684408	−	0.118543i	−0.898215	+	0.439556i	$0.855136\pi$
$60$		0			0
$61$	−4.58945	+	7.94917i	−0.587619	+	1.01779i	0.406924	+	0.913462i	$0.366601\pi$
$61$	−4.58945	+	7.94917i	−0.587619	+	1.01779i	−0.994543	+	0.104325i	$0.966732\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.99960	+	5.13026i	0.496089	+	0.636331i
$66$		0			0
$67$	−3.50947	+	2.02619i	−0.428750	+	0.247539i	−0.698814	−	0.715303i	$-0.746288\pi$
$67$	−3.50947	+	2.02619i	−0.428750	+	0.247539i	0.270064	+	0.962842i	$0.412955\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.1663			−1.68123			−0.840614	−	0.541634i	$-0.817806\pi$
$71$	−14.1663			−1.68123			−0.840614	+	0.541634i	$0.817806\pi$
$72$		0			0
$73$			2.02619i			0.237148i	0.992945	+	0.118574i	$0.0378323\pi$
$73$			2.02619i			0.237148i	−0.992945	+	0.118574i	$0.962168\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.3122	−	5.95376i	1.17519	−	0.678494i
$78$		0			0
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.49387	+	2.59454i	0.493267	+	0.284788i	0.725929	−	0.687770i	$-0.241410\pi$
$83$	4.49387	+	2.59454i	0.493267	+	0.284788i	−0.232662	+	0.972558i	$0.574744\pi$
$84$		0			0
$85$	15.2116	−	2.12169i	1.64993	−	0.230130i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.09334			−0.327893			−0.163947	−	0.986469i	$-0.552422\pi$
$89$	−3.09334			−0.327893			−0.163947	+	0.986469i	$0.552422\pi$
$90$		0			0
$91$	14.3578			1.50511
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.29084	+	9.25473i	0.132437	+	0.949516i
$96$		0			0
$97$	0.764681	+	0.441489i	0.0776416	+	0.0448264i	0.538318	−	0.842742i	$-0.319060\pi$
$97$	0.764681	+	0.441489i	0.0776416	+	0.0448264i	−0.460677	+	0.887568i	$0.652393\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.93840	+	5.08945i	−0.292382	+	0.506420i	−0.974372	−	0.224941i	$-0.927781\pi$
$101$	−2.93840	+	5.08945i	−0.292382	+	0.506420i	0.681991	+	0.731361i	$0.261114\pi$
$102$		0			0
$103$	8.54830	−	4.93536i	0.842289	−	0.486296i	−0.0157525	−	0.999876i	$-0.505014\pi$
$103$	8.54830	−	4.93536i	0.842289	−	0.486296i	0.858042	+	0.513580i	$0.171681\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.7668	+	6.79357i	−1.10693	+	0.639085i	−0.938032	−	0.346549i	$-0.887353\pi$
$113$	−11.7668	+	6.79357i	−1.10693	+	0.639085i	−0.168896	+	0.985634i	$0.554020\pi$
$114$		0			0
$115$	4.61834	+	5.92392i	0.430662	+	0.552408i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	16.9497	−	29.3578i	1.55378	−	2.69123i
$120$		0			0
$121$	2.58945	+	4.48507i	0.235405	+	0.407733i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.51551	−	10.2279i	−0.403879	−	0.914812i
$126$		0			0
$127$		−	4.93536i		−	0.437943i	−0.975731	−	0.218971i	$-0.929730\pi$
$127$		−	4.93536i		−	0.437943i	0.975731	−	0.218971i	$-0.0702701\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.08314	+	12.2684i	0.618857	+	1.07189i	0.989695	+	0.143194i	$0.0457373\pi$
$131$	7.08314	+	12.2684i	0.618857	+	1.07189i	−0.370838	+	0.928698i	$0.620929\pi$
$132$		0			0
$133$	17.8613	+	10.3122i	1.54877	+	0.894183i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.36376	+	2.51942i	0.372821	+	0.215248i	0.674690	−	0.738101i	$-0.264277\pi$
$137$	4.36376	+	2.51942i	0.372821	+	0.215248i	−0.301869	+	0.953349i	$0.597611\pi$
$138$		0			0
$139$	2.91055	+	5.04121i	0.246869	+	0.427590i	0.962656	−	0.270729i	$-0.0872648\pi$
$139$	2.91055	+	5.04121i	0.246869	+	0.427590i	−0.715786	+	0.698319i	$0.753932\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	7.01894i		−	0.586953i
$144$		0			0
$145$	10.7684	+	4.36376i	0.894264	+	0.362390i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.58788	−	11.4105i	−0.539700	−	0.934788i	−0.998920	−	0.0464656i	$-0.985204\pi$
$149$	−6.58788	−	11.4105i	−0.539700	−	0.934788i	0.459220	−	0.888323i	$-0.348129\pi$
$150$		0			0
$151$	3.08945	−	5.35109i	0.251416	−	0.435466i	−0.712500	−	0.701672i	$-0.752437\pi$
$151$	3.08945	−	5.35109i	0.251416	−	0.435466i	0.963916	+	0.266207i	$0.0857704\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.8964	+	8.49491i	−0.875218	+	0.682328i
$156$		0			0
$157$	6.79357	−	3.92227i	0.542186	−	0.313031i	−0.203779	−	0.979017i	$-0.565322\pi$
$157$	6.79357	−	3.92227i	0.542186	−	0.313031i	0.745964	+	0.665986i	$0.231989\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	16.5790			1.30661
$162$		0			0
$163$		−	10.7537i		−	0.842295i	−0.906992	−	0.421148i	$-0.861627\pi$
$163$		−	10.7537i		−	0.842295i	0.906992	−	0.421148i	$-0.138373\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.40305	+	4.27415i	−0.572865	+	0.330744i	−0.758293	−	0.651914i	$-0.773966\pi$
$167$	−7.40305	+	4.27415i	−0.572865	+	0.330744i	0.185428	+	0.982658i	$0.440633\pi$
$168$		0			0
$169$	−2.26836	+	3.92892i	−0.174489	+	0.302225i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−16.2607	−	9.38811i	−1.23628	−	0.713765i	−0.267945	−	0.963434i	$-0.586345\pi$
$173$	−16.2607	−	9.38811i	−1.23628	−	0.713765i	−0.968331	+	0.249670i	$0.919678\pi$
$174$		0			0
$175$	−23.9313	−	6.01974i	−1.80904	−	0.455050i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.97961			0.596424			0.298212	−	0.954500i	$-0.403610\pi$
$179$	7.97961			0.596424			0.298212	+	0.954500i	$0.403610\pi$
$180$		0			0
$181$	3.82109			0.284020			0.142010	−	0.989865i	$-0.454644\pi$
$181$	3.82109			0.284020			0.142010	+	0.989865i	$0.454644\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	17.3727	−	2.42313i	1.27727	−	0.178152i
$186$		0			0
$187$	−14.3518	−	8.28602i	−1.04951	−	0.605934i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.30916	+	5.73164i	−0.239443	+	0.414727i	−0.960554	−	0.278092i	$-0.910298\pi$
$191$	−3.30916	+	5.73164i	−0.239443	+	0.414727i	0.721112	+	0.692819i	$0.243631\pi$
$192$		0			0
$193$	−18.8513	+	10.8838i	−1.35695	+	0.783435i	−0.989211	−	0.146495i	$-0.953201\pi$
$193$	−18.8513	+	10.8838i	−1.35695	+	0.783435i	−0.367737	+	0.929930i	$0.619867\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			15.4170i			1.09842i	0.835686	+	0.549208i	$0.185070\pi$
$197$			15.4170i			1.09842i	−0.835686	+	0.549208i	$0.814930\pi$
$198$		0			0
$199$	−20.3578			−1.44313			−0.721564	−	0.692348i	$-0.756576\pi$
$199$	−20.3578			−1.44313			−0.721564	+	0.692348i	$0.756576\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	22.2091	−	12.8225i	1.55878	−	0.899960i
$204$		0			0
$205$	−10.3636	+	8.07956i	−0.723826	+	0.564301i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.04121	−	8.73164i	0.348708	−	0.603980i
$210$		0			0
$211$	−8.08945	−	14.0113i	−0.556901	−	0.964581i	−0.997753	−	0.0670010i	$-0.978657\pi$
$211$	−8.08945	−	14.0113i	−0.556901	−	0.964581i	0.440852	−	0.897580i	$-0.354676\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.14474	−	10.2279i	0.282669	−	0.697538i
$216$		0			0
$217$			30.4952i			2.07015i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.99110	−	17.3051i	−0.672074	−	1.16407i
$222$		0			0
$223$	−22.1354	−	12.7799i	−1.48230	−	0.855805i	−0.482500	−	0.875896i	$-0.660271\pi$
$223$	−22.1354	−	12.7799i	−1.48230	−	0.855805i	−0.999798	+	0.0200906i	$0.993605\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.3908	+	9.46323i	1.08790	+	0.628097i	0.933015	−	0.359837i	$-0.117168\pi$
$227$	16.3908	+	9.46323i	1.08790	+	0.628097i	0.154880	+	0.987933i	$0.450501\pi$
$228$		0			0
$229$	3.41055	+	5.90724i	0.225375	+	0.390361i	0.956432	−	0.291955i	$-0.0943059\pi$
$229$	3.41055	+	5.90724i	0.225375	+	0.390361i	−0.731057	+	0.682317i	$0.760973\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			0.150248i			0.00984309i	0.999988	+	0.00492154i	$0.00156658\pi$
$233$			0.150248i			0.00984309i	−0.999988	+	0.00492154i	$0.998433\pi$
$234$		0			0
$235$	10.0000	−	24.6768i	0.652328	−	1.60974i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.51551	−	7.82109i	−0.292084	−	0.505904i	0.682218	−	0.731149i	$-0.261015\pi$
$239$	−4.51551	−	7.82109i	−0.292084	−	0.505904i	−0.974302	+	0.225244i	$0.927682\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−30.6101	+	23.8640i	−1.95561	+	1.52461i
$246$		0			0
$247$	10.5284	−	6.07858i	0.669907	−	0.386771i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.3205			−1.09326			−0.546630	−	0.837374i	$-0.684090\pi$
$251$	−17.3205			−1.09326			−0.546630	+	0.837374i	$0.684090\pi$
$252$		0			0
$253$		−	8.10477i		−	0.509543i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−19.1698	+	11.0677i	−1.19578	+	0.690385i	−0.959612	−	0.281327i	$-0.909226\pi$
$257$	−19.1698	+	11.0677i	−1.19578	+	0.690385i	−0.236170	+	0.971712i	$0.575892\pi$
$258$		0			0
$259$	19.3578	−	33.5287i	1.20284	−	2.08337i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.81834	+	3.35922i	0.358774	+	0.207138i	0.668543	−	0.743674i	$-0.266918\pi$
$263$	5.81834	+	3.35922i	0.358774	+	0.207138i	−0.309769	+	0.950812i	$0.600252\pi$
$264$		0			0
$265$	−18.9313	+	2.64051i	−1.16294	+	0.162206i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	30.0646			1.83307			0.916536	−	0.399952i	$-0.130973\pi$
$269$	30.0646			1.83307			0.916536	+	0.399952i	$0.130973\pi$
$270$		0			0
$271$	−22.3578			−1.35814			−0.679070	−	0.734073i	$-0.737617\pi$
$271$	−22.3578			−1.35814			−0.679070	+	0.734073i	$0.737617\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.94280	+	11.6990i	−0.177458	+	0.705478i
$276$		0			0
$277$	9.31298	+	5.37685i	0.559563	+	0.323064i	0.752970	−	0.658055i	$-0.228620\pi$
$277$	9.31298	+	5.37685i	0.559563	+	0.323064i	−0.193407	+	0.981119i	$0.561954\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.21712	+	10.7684i	−0.370882	+	0.642387i	−0.989701	−	0.143147i	$-0.954278\pi$
$281$	−6.21712	+	10.7684i	−0.370882	+	0.642387i	0.618819	+	0.785533i	$0.287611\pi$
$282$		0			0
$283$	−1.52936	+	0.882978i	−0.0909112	+	0.0524876i	−0.544766	−	0.838588i	$-0.683382\pi$
$283$	−1.52936	+	0.882978i	−0.0909112	+	0.0524876i	0.453855	+	0.891075i	$0.350048\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			29.0041i			1.71206i
$288$		0			0
$289$	−30.1789			−1.77523
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−17.8454	+	10.3030i	−1.04254	+	0.601910i	−0.920551	−	0.390622i	$-0.872260\pi$
$293$	−17.8454	+	10.3030i	−1.04254	+	0.601910i	−0.121987	+	0.992532i	$0.538927\pi$
$294$		0			0
$295$	1.85414	−	1.44550i	0.107952	−	0.0841603i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.88627	−	8.46327i	0.282581	−	0.489444i
$300$		0			0
$301$	−12.1789	−	21.0945i	−0.701981	−	1.21587i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−19.0221	−	7.70850i	−1.08920	−	0.441387i
$306$		0			0
$307$			8.98775i			0.512958i	0.966550	+	0.256479i	$0.0825624\pi$
$307$			8.98775i			0.512958i	−0.966550	+	0.256479i	$0.917438\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.35109	+	9.26836i	0.303433	+	0.525561i	0.976911	−	0.213646i	$-0.0685340\pi$
$311$	5.35109	+	9.26836i	0.303433	+	0.525561i	−0.673479	+	0.739207i	$0.735201\pi$
$312$		0			0
$313$	6.02889	+	3.48078i	0.340773	+	0.196745i	0.660614	−	0.750726i	$-0.270296\pi$
$313$	6.02889	+	3.48078i	0.340773	+	0.196745i	−0.319841	+	0.947471i	$0.603629\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	29.4821	+	17.0215i	1.65588	+	0.956021i	0.974587	+	0.224008i	$0.0719143\pi$
$317$	29.4821	+	17.0215i	1.65588	+	0.956021i	0.681290	+	0.732013i	$0.261419\pi$
$318$		0			0
$319$	−6.26836	−	10.8571i	−0.350961	−	0.607882i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	28.7036i		−	1.59711i
$324$		0			0
$325$	−10.1262	+	10.4423i	−0.561699	+	0.579237i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−29.3840	−	50.8945i	−1.61999	−	2.80591i
$330$		0			0
$331$	16.2684	−	28.1776i	0.894190	−	1.54878i	0.0593863	−	0.998235i	$-0.481086\pi$
$331$	16.2684	−	28.1776i	0.894190	−	1.54878i	0.834804	−	0.550548i	$-0.185581\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.57132	−	7.14630i	−0.304394	−	0.390444i
$336$		0			0
$337$	8.54830	−	4.93536i	0.465656	−	0.268846i	−0.248764	−	0.968564i	$-0.580024\pi$
$337$	8.54830	−	4.93536i	0.465656	−	0.268846i	0.714419	+	0.699718i	$0.246691\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.9078			0.807303
$342$		0			0
$343$			51.1196i			2.76020i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.40305	+	4.27415i	−0.397416	+	0.229448i	−0.685369	−	0.728196i	$-0.740359\pi$
$347$	−7.40305	+	4.27415i	−0.397416	+	0.229448i	0.287952	+	0.957645i	$0.407026\pi$
$348$		0			0
$349$	10.0895	−	17.4754i	0.540076	−	0.935439i	−0.458823	−	0.888528i	$-0.651729\pi$
$349$	10.0895	−	17.4754i	0.540076	−	0.935439i	0.998899	−	0.0469115i	$-0.0149379\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	19.0397	+	10.9926i	1.01338	+	0.585077i	0.912180	−	0.409789i	$-0.134398\pi$
$353$	19.0397	+	10.9926i	1.01338	+	0.585077i	0.101202	+	0.994866i	$0.467731\pi$
$354$		0			0
$355$	−4.37587	−	31.3731i	−0.232247	−	1.66511i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.309878			−0.0163548			−0.00817738	−	0.999967i	$-0.502603\pi$
$359$	−0.309878			−0.0163548			−0.00817738	+	0.999967i	$0.502603\pi$
$360$		0			0
$361$	−1.53673			−0.0808803
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.48727	+	0.625878i	−0.234874	+	0.0327599i
$366$		0			0
$367$	−8.54830	−	4.93536i	−0.446218	−	0.257624i	0.260014	−	0.965605i	$-0.416273\pi$
$367$	−8.54830	−	4.93536i	−0.446218	−	0.257624i	−0.706231	+	0.707981i	$0.749606\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−21.0945	+	36.5367i	−1.09517	+	1.89689i
$372$		0			0
$373$	7.78362	−	4.49387i	0.403021	−	0.232684i	−0.284766	−	0.958597i	$-0.591916\pi$
$373$	7.78362	−	4.49387i	0.403021	−	0.232684i	0.687786	+	0.725913i	$0.258583\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	15.1165i		−	0.778539i
$378$		0			0
$379$	0.357817			0.0183798			0.00918990	−	0.999958i	$-0.497075\pi$
$379$	0.357817			0.0183798			0.00918990	+	0.999958i	$0.497075\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.8969	−	6.86869i	0.607904	−	0.350974i	−0.164241	−	0.986420i	$-0.552517\pi$
$383$	11.8969	−	6.86869i	0.607904	−	0.350974i	0.772145	+	0.635447i	$0.219184\pi$
$384$		0			0
$385$	16.3708	+	20.9987i	0.834331	+	1.07019i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.8050	−	22.1789i	0.649239	−	1.12452i	−0.334066	−	0.942550i	$-0.608421\pi$
$389$	12.8050	−	22.1789i	0.649239	−	1.12452i	0.983305	−	0.181966i	$-0.0582459\pi$
$390$		0			0
$391$	−11.5367	−	19.9822i	−0.583437	−	1.01054i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.4342	+	5.03883i	0.625634	+	0.253531i
$396$		0			0
$397$		−	11.0139i		−	0.552774i	−0.961046	−	0.276387i	$-0.910863\pi$
$397$		−	11.0139i		−	0.552774i	0.961046	−	0.276387i	$-0.0891371\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.3619	+	17.9473i	0.517447	+	0.896244i	0.999795	+	0.0202642i	$0.00645075\pi$
$401$	10.3619	+	17.9473i	0.517447	+	0.896244i	−0.482348	+	0.875980i	$0.660216\pi$
$402$		0			0
$403$	15.5672	+	8.98775i	0.775459	+	0.447712i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.3908	−	9.46323i	−0.812462	−	0.469075i
$408$		0			0
$409$	3.41055	+	5.90724i	0.168641	+	0.292094i	0.937942	−	0.346792i	$-0.112729\pi$
$409$	3.41055	+	5.90724i	0.168641	+	0.292094i	−0.769302	+	0.638886i	$0.779396\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	5.18908i		−	0.255338i
$414$		0			0
$415$	−4.35782	+	10.7537i	−0.213917	+	0.527879i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.28949	−	14.3578i	−0.404968	−	0.701425i	0.589350	−	0.807878i	$-0.299384\pi$
$419$	−8.28949	−	14.3578i	−0.404968	−	0.701425i	−0.994318	+	0.106453i	$0.966051\pi$
$420$		0			0
$421$	−14.8578	+	25.7345i	−0.724126	+	1.25422i	0.235207	+	0.971945i	$0.424423\pi$
$421$	−14.8578	+	25.7345i	−0.724126	+	1.25422i	−0.959333	+	0.282277i	$0.908910\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.39753	+	33.0327i	0.455847	+	1.60232i
$426$		0			0
$427$	−39.2320	+	22.6506i	−1.89857	+	1.09614i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.67116			0.0804972			0.0402486	−	0.999190i	$-0.487185\pi$
$431$	1.67116			0.0804972			0.0402486	+	0.999190i	$0.487185\pi$
$432$		0			0
$433$		−	36.5737i		−	1.75762i	−0.477170	−	0.878811i	$-0.658337\pi$
$433$		−	36.5737i		−	1.75762i	0.477170	−	0.878811i	$-0.341663\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.1572	−	7.01894i	0.581556	−	0.335761i
$438$		0			0
$439$	9.26836	−	16.0533i	0.442355	−	0.766181i	−0.555509	−	0.831511i	$-0.687477\pi$
$439$	9.26836	−	16.0533i	0.442355	−	0.766181i	0.997864	+	0.0653296i	$0.0208099\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.1306	−	9.31298i	−0.766386	−	0.442473i	0.0651979	−	0.997872i	$-0.479232\pi$
$443$	−16.1306	−	9.31298i	−0.766386	−	0.442473i	−0.831584	+	0.555399i	$0.812565\pi$
$444$		0			0
$445$	−0.955512	−	6.85060i	−0.0452956	−	0.324749i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	25.1783			1.18824			0.594120	−	0.804377i	$-0.297500\pi$
$449$	25.1783			1.18824			0.594120	+	0.804377i	$0.297500\pi$
$450$		0			0
$451$	14.1789			0.667659
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.43504	+	31.7972i	0.207918	+	1.49068i
$456$		0			0
$457$	−23.8902	−	13.7930i	−1.11753	−	0.645209i	−0.176764	−	0.984253i	$-0.556563\pi$
$457$	−23.8902	−	13.7930i	−1.11753	−	0.645209i	−0.940770	+	0.339044i	$0.889896\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.35109	+	9.26836i	−0.249225	+	0.431671i	−0.963311	−	0.268387i	$-0.913509\pi$
$461$	−5.35109	+	9.26836i	−0.249225	+	0.431671i	0.714086	+	0.700058i	$0.246843\pi$
$462$		0			0
$463$	−25.6449	+	14.8061i	−1.19182	+	0.688097i	−0.958719	−	0.284355i	$-0.908221\pi$
$463$	−25.6449	+	14.8061i	−1.19182	+	0.688097i	−0.233101	+	0.972453i	$0.574887\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	15.5672i		−	0.720366i	−0.932882	−	0.360183i	$-0.882714\pi$
$467$		−	15.5672i		−	0.720366i	0.932882	−	0.360183i	$-0.117286\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.3122	+	5.95376i	−0.474156	+	0.273754i
$474$		0			0
$475$	−20.0971	+	5.71745i	−0.922117	+	0.262335i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.6501	−	21.9105i	0.577996	−	1.00112i	−0.417713	−	0.908579i	$-0.637168\pi$
$479$	12.6501	−	21.9105i	0.577996	−	1.00112i	0.995709	−	0.0925394i	$-0.0294984\pi$
$480$		0			0
$481$	−11.4105	−	19.7636i	−0.520276	−	0.901145i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.741529	+	1.82986i	−0.0336711	+	0.0830896i
$486$		0			0
$487$		−	17.9755i		−	0.814548i	−0.913306	−	0.407274i	$-0.866479\pi$
$487$		−	17.9755i		−	0.814548i	0.913306	−	0.407274i	$-0.133521\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.7853	−	30.8051i	−0.802641	−	1.39021i	−0.917872	−	0.396876i	$-0.870094\pi$
$491$	−17.7853	−	30.8051i	−0.802641	−	1.39021i	0.115232	−	0.993339i	$-0.463239\pi$
$492$		0			0
$493$	−30.9091	−	17.8454i	−1.39208	−	0.803716i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−60.5488	−	34.9579i	−2.71599	−	1.56808i
$498$		0			0
$499$	2.08945	+	3.61904i	0.0935368	+	0.162011i	0.908997	−	0.416803i	$-0.136849\pi$
$499$	2.08945	+	3.61904i	0.0935368	+	0.162011i	−0.815460	+	0.578813i	$0.803516\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			37.2519i			1.66098i	0.557032	+	0.830491i	$0.311940\pi$
$503$			37.2519i			1.66098i	−0.557032	+	0.830491i	$0.688060\pi$
$504$		0			0
$505$	−12.1789	−	4.93536i	−0.541954	−	0.219621i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.77398	+	6.53673i	0.167279	+	0.289735i	0.937462	−	0.348087i	$-0.113169\pi$
$509$	3.77398	+	6.53673i	0.167279	+	0.289735i	−0.770183	+	0.637822i	$0.779835\pi$
$510$		0			0
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13.5705	+	17.4068i	0.597988	+	0.767036i
$516$		0			0
$517$	−24.8802	+	14.3646i	−1.09423	+	0.631755i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.03102			0.395656			0.197828	−	0.980237i	$-0.436611\pi$
$521$	9.03102			0.395656			0.197828	+	0.980237i	$0.436611\pi$
$522$		0			0
$523$		−	7.58430i		−	0.331638i	−0.986156	−	0.165819i	$-0.946973\pi$
$523$		−	7.58430i		−	0.331638i	0.986156	−	0.165819i	$-0.0530268\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	36.7550	−	21.2205i	1.60107	−	0.924380i
$528$		0			0
$529$	−5.85782	+	10.1460i	−0.254688	+	0.441132i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	14.8061	+	8.54830i	0.641323	+	0.370268i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	41.8791			1.80386
$540$		0			0
$541$	3.35782			0.144364			0.0721819	−	0.997391i	$-0.477004\pi$
$541$	3.35782			0.144364			0.0721819	+	0.997391i	$0.477004\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.16225	−	15.5024i	−0.0926208	−	0.664050i
$546$		0			0
$547$	17.0966	+	9.87073i	0.730998	+	0.422042i	0.818787	−	0.574097i	$-0.194647\pi$
$547$	17.0966	+	9.87073i	0.730998	+	0.422042i	−0.0877892	+	0.996139i	$0.527980\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.8571	−	18.8051i	0.462529	−	0.801124i
$552$		0			0
$553$	25.6449	−	14.8061i	1.09053	−	0.629619i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	39.2320i		−	1.66231i	−0.556037	−	0.831157i	$-0.687679\pi$
$557$		−	39.2320i		−	1.66231i	0.556037	−	0.831157i	$-0.312321\pi$
$558$		0			0
$559$	−14.3578			−0.607271
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.3122	+	5.95376i	−0.434608	+	0.250921i	−0.701308	−	0.712859i	$-0.747400\pi$
$563$	−10.3122	+	5.95376i	−0.434608	+	0.250921i	0.266700	+	0.963780i	$0.414067\pi$
$564$		0			0
$565$	−18.6799	−	23.9606i	−0.785870	−	1.00803i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.22731	+	3.85782i	−0.0933738	+	0.161728i	−0.908929	−	0.416952i	$-0.863098\pi$
$569$	−2.22731	+	3.85782i	−0.0933738	+	0.161728i	0.815555	+	0.578680i	$0.196432\pi$
$570$		0			0
$571$	9.08945	+	15.7434i	0.380382	+	0.658841i	0.991117	−	0.132994i	$-0.0424592\pi$
$571$	9.08945	+	15.7434i	0.380382	+	0.658841i	−0.610735	+	0.791835i	$0.709126\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−11.6927	+	12.0578i	−0.487619	+	0.502844i
$576$		0			0
$577$		−	7.84453i		−	0.326572i	−0.986579	−	0.163286i	$-0.947791\pi$
$577$		−	7.84453i		−	0.326572i	0.986579	−	0.163286i	$-0.0522094\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.8050	+	22.1789i	0.531241	+	0.920136i
$582$		0			0
$583$	17.8613	+	10.3122i	0.739739	+	0.427088i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.0520	+	5.80351i	0.414890	+	0.239537i	0.692888	−	0.721045i	$-0.256338\pi$
$587$	10.0520	+	5.80351i	0.414890	+	0.239537i	−0.277999	+	0.960581i	$0.589671\pi$
$588$		0			0
$589$	12.9105	+	22.3617i	0.531970	+	0.921399i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			5.03883i			0.206920i	0.994634	+	0.103460i	$0.0329914\pi$
$593$			5.03883i			0.206920i	−0.994634	+	0.103460i	$0.967009\pi$
$594$		0			0
$595$	70.2524	+	28.4690i	2.88007	+	1.16711i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.50531	−	14.7316i	−0.347518	−	0.601918i	0.638290	−	0.769796i	$-0.279642\pi$
$599$	−8.50531	−	14.7316i	−0.347518	−	0.601918i	−0.985808	+	0.167878i	$0.946309\pi$
$600$		0			0
$601$	1.67891	−	2.90795i	0.0684841	−	0.118618i	−0.829750	−	0.558135i	$-0.811517\pi$
$601$	1.67891	−	2.90795i	0.0684841	−	0.118618i	0.898234	+	0.439517i	$0.144850\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.13290	+	7.12009i	−0.371305	+	0.289473i
$606$		0			0
$607$	4.27415	−	2.46768i	0.173482	−	0.100160i	−0.410744	−	0.911751i	$-0.634731\pi$
$607$	4.27415	−	2.46768i	0.173482	−	0.100160i	0.584227	+	0.811590i	$0.301398\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−34.6410			−1.40143
$612$		0			0
$613$			37.7170i			1.52337i	0.647945	+	0.761687i	$0.275628\pi$
$613$			37.7170i			1.52337i	−0.647945	+	0.761687i	$0.724372\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.62399	+	2.66966i	−0.186155	+	0.107477i	−0.590181	−	0.807271i	$-0.700944\pi$
$617$	−4.62399	+	2.66966i	−0.186155	+	0.107477i	0.404026	+	0.914747i	$0.367610\pi$
$618$		0			0
$619$	5.82109	−	10.0824i	0.233969	−	0.405247i	−0.725003	−	0.688745i	$-0.758162\pi$
$619$	5.82109	−	10.0824i	0.233969	−	0.405247i	0.958973	+	0.283499i	$0.0914951\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−13.2214	−	7.63337i	−0.529704	−	0.305825i
$624$		0			0
$625$	21.2562	−	13.1595i	0.850249	−	0.526381i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−53.8817			−2.14840
$630$		0			0
$631$	−22.5367			−0.897173			−0.448586	−	0.893739i	$-0.648072\pi$
$631$	−22.5367			−0.897173			−0.448586	+	0.893739i	$0.648072\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.9300	−	1.52450i	0.433744	−	0.0604980i
$636$		0			0
$637$	43.7316	+	25.2484i	1.73271	+	1.00038i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.15551	−	15.8578i	0.361621	−	0.626346i	−0.626607	−	0.779336i	$-0.715557\pi$
$641$	9.15551	−	15.8578i	0.361621	−	0.626346i	0.988228	+	0.152990i	$0.0488901\pi$
$642$		0			0
$643$	17.8613	−	10.3122i	0.704380	−	0.406674i	−0.104597	−	0.994515i	$-0.533355\pi$
$643$	17.8613	−	10.3122i	0.704380	−	0.406674i	0.808977	+	0.587841i	$0.200022\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	44.2709i		−	1.74047i	−0.492639	−	0.870234i	$-0.663968\pi$
$647$		−	44.2709i		−	1.74047i	0.492639	−	0.870234i	$-0.336032\pi$
$648$		0			0
$649$	−2.53673			−0.0995752
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.260237	−	0.150248i	0.0101839	−	0.00587967i	−0.494899	−	0.868950i	$-0.664795\pi$
$653$	0.260237	−	0.150248i	0.0101839	−	0.00587967i	0.505083	+	0.863071i	$0.331462\pi$
$654$		0			0
$655$	−24.9819	+	19.4762i	−0.976125	+	0.760996i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	20.7237	−	35.8945i	0.807282	−	1.39825i	−0.107458	−	0.994210i	$-0.534271\pi$
$659$	20.7237	−	35.8945i	0.807282	−	1.39825i	0.914740	−	0.404043i	$-0.132395\pi$
$660$		0			0
$661$	23.2156	+	40.2107i	0.902983	+	1.56401i	0.823601	+	0.567169i	$0.191961\pi$
$661$	23.2156	+	40.2107i	0.902983	+	1.56401i	0.0793821	+	0.996844i	$0.474705\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.3205	+	42.7415i	−0.671660	+	1.65744i
$666$		0			0
$667$		−	17.4550i		−	0.675861i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.0729	+	19.1789i	0.427466	+	0.740394i
$672$		0			0
$673$	12.5971	+	7.27293i	0.485582	+	0.280351i	0.722740	−	0.691120i	$-0.242883\pi$
$673$	12.5971	+	7.27293i	0.485582	+	0.280351i	−0.237158	+	0.971471i	$0.576216\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.8724	+	17.2469i	1.14809	+	0.662850i	0.948421	−	0.317013i	$-0.102680\pi$
$677$	29.8724	+	17.2469i	1.14809	+	0.662850i	0.199669	+	0.979863i	$0.436013\pi$
$678$		0			0
$679$	2.17891	+	3.77398i	0.0836188	+	0.144832i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			44.5714i			1.70548i	0.522339	+	0.852738i	$0.325060\pi$
$683$			44.5714i			1.70548i	−0.522339	+	0.852738i	$0.674940\pi$
$684$		0			0
$685$	−4.23164	+	10.4423i	−0.161683	+	0.398981i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.4342	+	21.5367i	0.473707	+	0.820484i
$690$		0			0
$691$	15.3578	−	26.6005i	0.584239	−	1.01193i	−0.410731	−	0.911757i	$-0.634726\pi$
$691$	15.3578	−	26.6005i	0.584239	−	1.01193i	0.994970	−	0.100175i	$-0.0319402\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.2654	+	8.00298i	−0.389388	+	0.303570i
$696$		0			0
$697$	34.9579	−	20.1829i	1.32412	−	0.764484i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	27.3420			1.03269			0.516347	−	0.856379i	$-0.327291\pi$
$701$	27.3420			1.03269			0.516347	+	0.856379i	$0.327291\pi$
$702$		0			0
$703$		−	32.7816i		−	1.23638i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−25.1183	+	14.5021i	−0.944671	+	0.545406i
$708$		0			0
$709$	7.76836	−	13.4552i	0.291747	−	0.505321i	−0.682476	−	0.730908i	$-0.739097\pi$
$709$	7.76836	−	13.4552i	0.291747	−	0.505321i	0.974223	+	0.225587i	$0.0724301\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	17.9755	+	10.3782i	0.673188	+	0.388665i
$714$		0			0
$715$	15.5444	−	2.16810i	0.581326	−	0.0810825i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−40.3960			−1.50652			−0.753259	−	0.657724i	$-0.771519\pi$
$719$	−40.3960			−1.50652			−0.753259	+	0.657724i	$0.771519\pi$
$720$		0			0
$721$	48.7156			1.81426
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.33783	+	25.1959i	−0.235381	+	0.935751i
$726$		0			0
$727$	40.7614	+	23.5336i	1.51176	+	0.872813i	0.999906	+	0.0137388i	$0.00437333\pi$
$727$	40.7614	+	23.5336i	1.51176	+	0.872813i	0.511851	+	0.859074i	$0.328960\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.9497	+	29.3578i	−0.626909	+	1.08584i
$732$		0			0
$733$	−17.0966	+	9.87073i	−0.631477	+	0.364584i	−0.781324	−	0.624126i	$-0.785455\pi$
$733$	−17.0966	+	9.87073i	−0.631477	+	0.364584i	0.149847	+	0.988709i	$0.452122\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			9.77717i			0.360147i
$738$		0			0
$739$	22.8945			0.842189			0.421095	−	0.907017i	$-0.361646\pi$
$739$	22.8945			0.842189			0.421095	+	0.907017i	$0.361646\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−43.0938	+	24.8802i	−1.58096	+	0.912767i	−0.586239	+	0.810138i	$0.699392\pi$
$743$	−43.0938	+	24.8802i	−1.58096	+	0.912767i	−0.994720	+	0.102628i	$0.967275\pi$
$744$		0			0
$745$	23.2352	−	18.1144i	0.851271	−	0.663659i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	3.17891	+	5.50603i	0.116000	+	0.200918i	0.918179	−	0.396166i	$-0.129659\pi$
$751$	3.17891	+	5.50603i	0.116000	+	0.200918i	−0.802179	+	0.597084i	$0.796326\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	12.8050	+	5.18908i	0.466022	+	0.188850i
$756$		0			0
$757$		−	1.76596i		−	0.0641847i	−0.999485	−	0.0320924i	$-0.989783\pi$
$757$		−	1.76596i		−	0.0641847i	0.999485	−	0.0320924i	$-0.0102171\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.866025	−	1.50000i	−0.0313934	−	0.0543750i	0.849902	−	0.526941i	$-0.176661\pi$
$761$	−0.866025	−	1.50000i	−0.0313934	−	0.0543750i	−0.881295	+	0.472566i	$0.843328\pi$
$762$		0			0
$763$	−29.9191	−	17.2738i	−1.08314	−	0.625353i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.64893	−	1.52936i	−0.0956474	−	0.0552221i
$768$		0			0
$769$	12.8578	+	22.2704i	0.463665	+	0.803091i	0.999140	−	0.0414599i	$-0.0132009\pi$
$769$	12.8578	+	22.2704i	0.463665	+	0.803091i	−0.535475	+	0.844551i	$0.679868\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	30.6837i		−	1.10362i	−0.833971	−	0.551809i	$-0.813938\pi$
$773$		−	30.6837i		−	1.10362i	0.833971	−	0.551809i	$-0.186062\pi$
$774$		0			0
$775$	−22.1789	−	21.5074i	−0.796690	−	0.772569i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.2793	+	21.2684i	0.439951	+	0.762018i
$780$		0			0
$781$	−17.0895	+	29.5998i	−0.611509	+	1.05916i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.7849	+	13.8337i	0.384928	+	0.493745i
$786$		0			0
$787$	41.5261	−	23.9751i	1.48024	−	0.854620i	0.480495	−	0.876997i	$-0.340457\pi$
$787$	41.5261	−	23.9751i	1.48024	−	0.854620i	0.999750	+	0.0223775i	$0.00712359\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−67.0574			−2.38429
$792$		0			0
$793$			26.7030i			0.948252i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.1821	−	5.87864i	0.360668	−	0.208232i	−0.308706	−	0.951158i	$-0.599896\pi$
$797$	10.1821	−	5.87864i	0.360668	−	0.208232i	0.669374	+	0.742926i	$0.266562\pi$
$798$		0			0
$799$	−40.8945	+	70.8314i	−1.44674	+	2.50584i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.23364	+	2.44429i	0.149402	+	0.0862572i
$804$		0			0
$805$	5.12114	+	36.7163i	0.180496	+	1.29408i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.19615			−0.182687			−0.0913435	−	0.995819i	$-0.529116\pi$
$809$	−5.19615			−0.182687			−0.0913435	+	0.995819i	$0.529116\pi$
$810$		0			0
$811$	6.89454			0.242100			0.121050	−	0.992646i	$-0.461374\pi$
$811$	6.89454			0.242100			0.121050	+	0.992646i	$0.461374\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.8155	−	3.32175i	0.834220	−	0.116356i
$816$		0			0
$817$	−17.8613	−	10.3122i	−0.624887	−	0.360779i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.1053	−	45.2156i	0.911080	−	1.57804i	0.0985382	−	0.995133i	$-0.468583\pi$
$821$	26.1053	−	45.2156i	0.911080	−	1.57804i	0.812542	−	0.582903i	$-0.198083\pi$
$822$		0			0
$823$	10.0777	−	5.81834i	0.351285	−	0.202815i	−0.313966	−	0.949434i	$-0.601658\pi$
$823$	10.0777	−	5.81834i	0.351285	−	0.202815i	0.665251	+	0.746620i	$0.268324\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.7374i			0.477696i	0.971057	+	0.238848i	$0.0767697\pi$
$827$			13.7374i			0.477696i	−0.971057	+	0.238848i	$0.923230\pi$
$828$		0			0
$829$	4.17891			0.145139			0.0725697	−	0.997363i	$-0.476880\pi$
$829$	4.17891			0.145139			0.0725697	+	0.997363i	$0.476880\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	103.252	−	59.6127i	3.57748	−	2.06546i
$834$		0			0
$835$	−11.7524	−	15.0747i	−0.406709	−	0.521683i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.9085	−	20.6262i	0.411128	−	0.712095i	−0.583885	−	0.811836i	$-0.698468\pi$
$839$	11.9085	−	20.6262i	0.411128	−	0.712095i	0.995013	+	0.0997414i	$0.0318015\pi$
$840$		0			0
$841$	1.00000	+	1.73205i	0.0344828	+	0.0597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.40178	−	3.80997i	−0.323431	−	0.131067i
$846$		0			0
$847$			25.5598i			0.878245i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.1758	−	22.8211i	−0.451659	−	0.782297i
$852$		0			0
$853$	−10.8423	−	6.25983i	−0.371235	−	0.214333i	0.302763	−	0.953066i	$-0.402091\pi$
$853$	−10.8423	−	6.25983i	−0.371235	−	0.214333i	−0.673998	+	0.738733i	$0.735424\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−48.7820	−	28.1643i	−1.66636	−	0.962075i	−0.969574	−	0.244798i	$-0.921278\pi$
$857$	−48.7820	−	28.1643i	−1.66636	−	0.962075i	−0.696788	−	0.717277i	$-0.745388\pi$
$858$		0			0
$859$	19.2684	+	33.3738i	0.657428	+	1.13870i	0.981279	+	0.192591i	$0.0616890\pi$
$859$	19.2684	+	33.3738i	0.657428	+	1.13870i	−0.323851	+	0.946108i	$0.604978\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	8.54830i		−	0.290988i	−0.989359	−	0.145494i	$-0.953523\pi$
$863$		−	8.54830i		−	0.290988i	0.989359	−	0.145494i	$-0.0464771\pi$
$864$		0			0
$865$	15.7684	−	38.9113i	0.536140	−	1.32302i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.23808	−	12.5367i	−0.245535	−	0.425279i
$870$		0			0
$871$	−5.89454	+	10.2096i	−0.199729	+	0.345941i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.93927	−	54.8585i	0.200784	−	1.85455i
$876$		0			0
$877$	−41.7515	+	24.1052i	−1.40985	+	0.813975i	−0.995373	−	0.0960863i	$-0.969368\pi$
$877$	−41.7515	+	24.1052i	−1.40985	+	0.813975i	−0.414473	+	0.910061i	$0.636034\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.9388			0.806520			0.403260	−	0.915085i	$-0.367877\pi$
$881$	23.9388			0.806520			0.403260	+	0.915085i	$0.367877\pi$
$882$		0			0
$883$		−	50.2366i		−	1.69060i	−0.534295	−	0.845298i	$-0.679423\pi$
$883$		−	50.2366i		−	1.69060i	0.534295	−	0.845298i	$-0.320577\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.2091	−	12.8225i	0.745710	−	0.430536i	−0.0784318	−	0.996919i	$-0.524991\pi$
$887$	22.2091	−	12.8225i	0.745710	−	0.430536i	0.824142	+	0.566384i	$0.191658\pi$
$888$		0			0
$889$	12.1789	−	21.0945i	0.408467	−	0.707486i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−43.0938	−	24.8802i	−1.44208	−	0.832585i
$894$		0			0
$895$	2.46485	+	17.6719i	0.0823908	+	0.590706i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	32.1065			1.07081
$900$		0			0
$901$	58.7156			1.95610
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.18031	+	8.46230i	0.0392348	+	0.281296i
$906$		0			0
$907$	−51.2898	−	29.6122i	−1.70305	−	0.983256i	−0.942639	−	0.333815i	$-0.891664\pi$
$907$	−51.2898	−	29.6122i	−1.70305	−	0.983256i	−0.760411	−	0.649442i	$-0.775003\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−17.7853	+	30.8051i	−0.589254	+	1.02062i	0.405076	+	0.914283i	$0.367245\pi$
$911$	−17.7853	+	30.8051i	−0.589254	+	1.02062i	−0.994330	+	0.106335i	$0.966088\pi$
$912$		0			0
$913$	10.8423	−	6.25983i	0.358829	−	0.207170i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			69.9158i			2.30882i
$918$		0			0
$919$	19.8211			0.653837			0.326919	−	0.945052i	$-0.393990\pi$
$919$	19.8211			0.653837			0.326919	+	0.945052i	$0.393990\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−35.6908	+	20.6061i	−1.17478	+	0.678257i
$924$		0			0
$925$	10.7327	+	37.7257i	0.352887	+	1.24041i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.37206	−	11.0367i	0.209060	−	0.362103i	−0.742358	−	0.670003i	$-0.766293\pi$
$929$	6.37206	−	11.0367i	0.209060	−	0.362103i	0.951419	+	0.307900i	$0.0996261\pi$
$930$		0			0
$931$	36.2684	+	62.8186i	1.18865	+	2.05880i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13.9173	−	34.3435i	0.455144	−	1.12315i
$936$		0			0
$937$		−	12.7799i		−	0.417501i	−0.977969	−	0.208751i	$-0.933060\pi$
$937$		−	12.7799i		−	0.417501i	0.977969	−	0.208751i	$-0.0669397\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.9408	+	46.6629i	0.878246	+	1.52117i	0.853264	+	0.521479i	$0.174620\pi$
$941$	26.9408	+	46.6629i	0.878246	+	1.52117i	0.0249824	+	0.999688i	$0.492047\pi$
$942$		0			0
$943$	17.0966	+	9.87073i	0.556742	+	0.321435i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.07858	−	3.50947i	−0.197527	−	0.114042i	0.397974	−	0.917397i	$-0.369713\pi$
$947$	−6.07858	−	3.50947i	−0.197527	−	0.114042i	−0.595502	+	0.803354i	$0.703047\pi$
$948$		0			0
$949$	2.94727	+	5.10482i	0.0956725	+	0.165710i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			11.7573i			0.380855i	0.981701	+	0.190428i	$0.0609875\pi$
$953$			11.7573i			0.380855i	−0.981701	+	0.190428i	$0.939013\pi$
$954$		0			0
$955$	−13.7156	−	5.55810i	−0.443827	−	0.179856i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.4342	+	21.5367i	0.401522	+	0.695457i
$960$		0			0
$961$	−3.58945	+	6.21712i	−0.115789	+	0.200552i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−29.9267	−	38.3868i	−0.963374	−	1.23571i
$966$		0			0
$967$	−11.2931	+	6.52007i	−0.363161	+	0.209671i	−0.670467	−	0.741940i	$-0.733906\pi$
$967$	−11.2931	+	6.52007i	−0.363161	+	0.209671i	0.307305	+	0.951611i	$0.400573\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.7142			0.696843			0.348422	−	0.937338i	$-0.386718\pi$
$971$	21.7142			0.696843			0.348422	+	0.937338i	$0.386718\pi$
$972$		0			0
$973$			28.7292i			0.921016i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.5336	+	13.5871i	−0.752907	+	0.434691i	−0.826743	−	0.562579i	$-0.809809\pi$
$977$	−23.5336	+	13.5871i	−0.752907	+	0.434691i	0.0738365	+	0.997270i	$0.476476\pi$
$978$		0			0
$979$	−3.73164	+	6.46339i	−0.119264	+	0.206571i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.4694	+	12.9727i	0.716662	+	0.413765i	0.813523	−	0.581533i	$-0.197547\pi$
$983$	22.4694	+	12.9727i	0.716662	+	0.413765i	−0.0968610	+	0.995298i	$0.530880\pi$
$984$		0			0
$985$	−34.1429	+	4.76221i	−1.08788	+	0.151737i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.5790			−0.527181
$990$		0			0
$991$	−32.5367			−1.03356			−0.516782	−	0.856117i	$-0.672870\pi$
$991$	−32.5367			−1.03356			−0.516782	+	0.856117i	$0.672870\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.28840	−	45.0850i	−0.199356	−	1.42929i
$996$		0			0
$997$	−25.8703	−	14.9362i	−0.819320	−	0.473035i	0.0308620	−	0.999524i	$-0.490175\pi$
$997$	−25.8703	−	14.9362i	−0.819320	−	0.473035i	−0.850182	+	0.526489i	$0.823508\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.r.h.1189.5		16
3.2	odd	2	inner	1620.2.r.h.1189.4		16
5.4	even	2	inner	1620.2.r.h.1189.7		16
9.2	odd	6		1620.2.d.e.649.8	yes	8
9.4	even	3	inner	1620.2.r.h.109.7		16
9.5	odd	6	inner	1620.2.r.h.109.2		16
9.7	even	3		1620.2.d.e.649.1	✓	8
15.14	odd	2	inner	1620.2.r.h.1189.2		16
45.2	even	12		8100.2.a.be.1.8		8
45.4	even	6	inner	1620.2.r.h.109.5		16
45.7	odd	12		8100.2.a.be.1.7		8
45.14	odd	6	inner	1620.2.r.h.109.4		16
45.29	odd	6		1620.2.d.e.649.7	yes	8
45.34	even	6		1620.2.d.e.649.2	yes	8
45.38	even	12		8100.2.a.be.1.2		8
45.43	odd	12		8100.2.a.be.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.d.e.649.1	✓	8	9.7	even	3
1620.2.d.e.649.2	yes	8	45.34	even	6
1620.2.d.e.649.7	yes	8	45.29	odd	6
1620.2.d.e.649.8	yes	8	9.2	odd	6
1620.2.r.h.109.2		16	9.5	odd	6	inner
1620.2.r.h.109.4		16	45.14	odd	6	inner
1620.2.r.h.109.5		16	45.4	even	6	inner
1620.2.r.h.109.7		16	9.4	even	3	inner
1620.2.r.h.1189.2		16	15.14	odd	2	inner
1620.2.r.h.1189.4		16	3.2	odd	2	inner
1620.2.r.h.1189.5		16	1.1	even	1	trivial
1620.2.r.h.1189.7		16	5.4	even	2	inner
8100.2.a.be.1.1		8	45.43	odd	12
8100.2.a.be.1.2		8	45.38	even	12
8100.2.a.be.1.7		8	45.7	odd	12
8100.2.a.be.1.8		8	45.2	even	12

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.308893 + 2.21463i) q^{5} +(4.27415 + 2.46768i) q^{7} +O(q^{10})\)	\(q+(0.308893 + 2.21463i) q^{5} +(4.27415 + 2.46768i) q^{7} +(1.20635 - 2.08945i) q^{11} +(2.51942 - 1.45459i) q^{13} -6.86869i q^{17} +4.17891 q^{19} +(2.90917 - 1.67961i) q^{23} +(-4.80917 + 1.36817i) q^{25} +(2.59808 - 4.50000i) q^{29} +(3.08945 + 5.35109i) q^{31} +(-4.14474 + 10.2279i) q^{35} -7.84453i q^{37} +(2.93840 + 5.08945i) q^{41} +(-4.27415 - 2.46768i) q^{43} +(-10.3122 - 5.95376i) q^{47} +(8.67891 + 15.0323i) q^{49} +8.54830i q^{53} +(5.00000 + 2.02619i) q^{55} +(-0.525704 - 0.910546i) q^{59} +(-4.58945 + 7.94917i) q^{61} +(3.99960 + 5.13026i) q^{65} +(-3.50947 + 2.02619i) q^{67} -14.1663 q^{71} +2.02619i q^{73} +(10.3122 - 5.95376i) q^{77} +(3.00000 - 5.19615i) q^{79} +(4.49387 + 2.59454i) q^{83} +(15.2116 - 2.12169i) q^{85} -3.09334 q^{89} +14.3578 q^{91} +(1.29084 + 9.25473i) q^{95} +(0.764681 + 0.441489i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91}+O(q^{100}) \) 16 * q - 24 * q^19 - 6 * q^25 + 4 * q^31 + 48 * q^49 + 80 * q^55 - 28 * q^61 + 48 * q^79 - 22 * q^85 + 48 * q^91

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