LMFDB - Embedded newform 792.2.r.f.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(289,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.r (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,1,0,-5,0,0,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.185640625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 264)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			289.1
Root			$-0.245684 - 1.71454i$ of defining polynomial
Character	$\chi$	$=$	792.289
Dual form			792.2.r.f.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95223 - 1.41838i) q^{5} +(-1.46086 + 4.49606i) q^{7} +(-0.960858 - 3.17439i) q^{11} +(4.86531 - 3.53486i) q^{13} +(0.720508 + 0.523480i) q^{17} +(-1.02419 - 3.15214i) q^{19} -0.204948 q^{23} +(0.254316 + 0.782703i) q^{25} +(2.95756 - 9.10244i) q^{29} +(7.37928 - 5.36136i) q^{31} +(9.22903 - 6.70528i) q^{35} +(0.445299 - 1.37049i) q^{37} +(-1.09445 - 3.36838i) q^{41} -7.79505 q^{43} +(2.83419 + 8.72275i) q^{47} +(-12.4173 - 9.02172i) q^{49} +(-3.76124 + 2.73270i) q^{53} +(-2.62667 + 7.55999i) q^{55} +(0.305720 - 0.940910i) q^{59} +(-5.20386 - 3.78082i) q^{61} -14.5120 q^{65} +6.17505 q^{67} +(5.50435 + 3.99914i) q^{71} +(1.19363 - 3.67361i) q^{73} +(15.6759 + 0.317257i) q^{77} +(3.67274 - 2.66840i) q^{79} +(-8.08582 - 5.87469i) q^{83} +(-0.664104 - 2.04390i) q^{85} +0.930414 q^{89} +(8.78539 + 27.0387i) q^{91} +(-2.47146 + 7.60637i) q^{95} +(-2.36531 + 1.71850i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{5} - 5 q^{7} - q^{11} - q^{13} + 4 q^{17} - 2 q^{19} - 16 q^{23} + 7 q^{25} + 7 q^{29} + 29 q^{31} + 20 q^{35} + 13 q^{37} + 23 q^{41} - 48 q^{43} + 15 q^{47} - 11 q^{49} - 9 q^{53} - 22 q^{55}+ \cdots + 21 q^{97}+O(q^{100}) $ 8 * q + q^5 - 5 * q^7 - q^11 - q^13 + 4 * q^17 - 2 * q^19 - 16 * q^23 + 7 * q^25 + 7 * q^29 + 29 * q^31 + 20 * q^35 + 13 * q^37 + 23 * q^41 - 48 * q^43 + 15 * q^47 - 11 * q^49 - 9 * q^53 - 22 * q^55 - 12 * q^59 + 9 * q^61 - 42 * q^65 + 38 * q^67 + 41 * q^71 - 25 * q^73 + 55 * q^77 + 11 * q^79 - 23 * q^83 + 23 * q^85 - 12 * q^89 - 35 * q^91 - 29 * q^95 + 21 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$1$

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
$5$	−1.95223	−	1.41838i	−0.873063	−	0.634317i	0.0583444	−	0.998297i	$-0.481418\pi$
$5$	−1.95223	−	1.41838i	−0.873063	−	0.634317i	−0.931407	+	0.363979i	$0.881418\pi$
$6$		0			0
$7$	−1.46086	+	4.49606i	−0.552153	+	1.69935i	0.151194	+	0.988504i	$0.451688\pi$
$7$	−1.46086	+	4.49606i	−0.552153	+	1.69935i	−0.703347	+	0.710847i	$0.748312\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.960858	−	3.17439i	−0.289710	−	0.957115i
$11$	−0.960858	−	3.17439i	−0.289710	−	0.957115i
$12$		0			0
$13$	4.86531	−	3.53486i	1.34940	−	0.980393i	0.350354	−	0.936617i	$-0.386061\pi$
$13$	4.86531	−	3.53486i	1.34940	−	0.980393i	0.999041	−	0.0437754i	$-0.0139386\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.720508	+	0.523480i	0.174749	+	0.126963i	0.671722	−	0.740804i	$-0.265555\pi$
$17$	0.720508	+	0.523480i	0.174749	+	0.126963i	−0.496973	+	0.867766i	$0.665555\pi$
$18$		0			0
$19$	−1.02419	−	3.15214i	−0.234966	−	0.723149i	−0.997126	−	0.0757613i	$-0.975861\pi$
$19$	−1.02419	−	3.15214i	−0.234966	−	0.723149i	0.762160	−	0.647388i	$-0.224139\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.204948			−0.0427347			−0.0213673	−	0.999772i	$-0.506802\pi$
$23$	−0.204948			−0.0427347			−0.0213673	+	0.999772i	$0.506802\pi$
$24$		0			0
$25$	0.254316	+	0.782703i	0.0508631	+	0.156541i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.95756	−	9.10244i	0.549205	−	1.69028i	−0.161570	−	0.986861i	$-0.551656\pi$
$29$	2.95756	−	9.10244i	0.549205	−	1.69028i	0.710775	−	0.703419i	$-0.248344\pi$
$30$		0			0
$31$	7.37928	−	5.36136i	1.32536	−	0.962929i	0.325509	−	0.945539i	$-0.394464\pi$
$31$	7.37928	−	5.36136i	1.32536	−	0.962929i	0.999849	−	0.0173896i	$-0.00553554\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.22903	−	6.70528i	1.55999	−	1.13340i
$36$		0			0
$37$	0.445299	−	1.37049i	0.0732066	−	0.225307i	−0.907758	−	0.419495i	$-0.862207\pi$
$37$	0.445299	−	1.37049i	0.0732066	−	0.225307i	0.980964	+	0.194188i	$0.0622072\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.09445	−	3.36838i	−0.170925	−	0.526052i	0.828499	−	0.559990i	$-0.189195\pi$
$41$	−1.09445	−	3.36838i	−0.170925	−	0.526052i	−0.999424	+	0.0339380i	$0.989195\pi$
$42$		0			0
$43$	−7.79505			−1.18873			−0.594367	−	0.804194i	$-0.702597\pi$
$43$	−7.79505			−1.18873			−0.594367	+	0.804194i	$0.702597\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.83419	+	8.72275i	0.413410	+	1.27234i	0.913666	+	0.406466i	$0.133239\pi$
$47$	2.83419	+	8.72275i	0.413410	+	1.27234i	−0.500256	+	0.865877i	$0.666761\pi$
$48$		0			0
$49$	−12.4173	−	9.02172i	−1.77390	−	1.28882i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.76124	+	2.73270i	−0.516647	+	0.375366i	−0.815339	−	0.578984i	$-0.803450\pi$
$53$	−3.76124	+	2.73270i	−0.516647	+	0.375366i	0.298693	+	0.954349i	$0.403450\pi$
$54$		0			0
$55$	−2.62667	+	7.55999i	−0.354179	+	1.01939i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.305720	−	0.940910i	0.0398014	−	0.122496i	−0.929182	−	0.369624i	$-0.879487\pi$
$59$	0.305720	−	0.940910i	0.0398014	−	0.122496i	0.968983	+	0.247127i	$0.0794867\pi$
$60$		0			0
$61$	−5.20386	−	3.78082i	−0.666285	−	0.484085i	0.202494	−	0.979283i	$-0.435095\pi$
$61$	−5.20386	−	3.78082i	−0.666285	−	0.484085i	−0.868780	+	0.495199i	$0.835095\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−14.5120			−1.79999
$66$		0			0
$67$	6.17505			0.754402			0.377201	−	0.926131i	$-0.376887\pi$
$67$	6.17505			0.754402			0.377201	+	0.926131i	$0.376887\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.50435	+	3.99914i	0.653246	+	0.474611i	0.864375	−	0.502847i	$-0.167714\pi$
$71$	5.50435	+	3.99914i	0.653246	+	0.474611i	−0.211129	+	0.977458i	$0.567714\pi$
$72$		0			0
$73$	1.19363	−	3.67361i	0.139704	−	0.429964i	−0.856588	−	0.516001i	$-0.827420\pi$
$73$	1.19363	−	3.67361i	0.139704	−	0.429964i	0.996292	+	0.0860366i	$0.0274202\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.6759	+	0.317257i	1.78644	+	0.0361548i
$78$		0			0
$79$	3.67274	−	2.66840i	0.413215	−	0.300218i	−0.361687	−	0.932300i	$-0.617799\pi$
$79$	3.67274	−	2.66840i	0.413215	−	0.300218i	0.774902	+	0.632081i	$0.217799\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.08582	−	5.87469i	−0.887534	−	0.644831i	0.0476997	−	0.998862i	$-0.484811\pi$
$83$	−8.08582	−	5.87469i	−0.887534	−	0.644831i	−0.935234	+	0.354030i	$0.884811\pi$
$84$		0			0
$85$	−0.664104	−	2.04390i	−0.0720322	−	0.221692i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.930414			0.0986237			0.0493119	−	0.998783i	$-0.484297\pi$
$89$	0.930414			0.0986237			0.0493119	+	0.998783i	$0.484297\pi$
$90$		0			0
$91$	8.78539	+	27.0387i	0.920960	+	2.83442i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.47146	+	7.60637i	−0.253566	+	0.780397i
$96$		0			0
$97$	−2.36531	+	1.71850i	−0.240161	+	0.174487i	−0.701355	−	0.712812i	$-0.747421\pi$
$97$	−2.36531	+	1.71850i	−0.240161	+	0.174487i	0.461194	+	0.887299i	$0.347421\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.9399	−	7.94832i	1.08856	−	0.790887i	0.109407	−	0.993997i	$-0.465105\pi$
$101$	10.9399	−	7.94832i	1.08856	−	0.790887i	0.979156	+	0.203110i	$0.0651048\pi$
$102$		0			0
$103$	3.96718	−	12.2097i	0.390898	−	1.20306i	−0.541213	−	0.840886i	$-0.682035\pi$
$103$	3.96718	−	12.2097i	0.390898	−	1.20306i	0.932111	−	0.362174i	$-0.117965\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.03051	+	9.32695i	0.292971	+	0.901671i	0.983896	+	0.178744i	$0.0572034\pi$
$107$	3.03051	+	9.32695i	0.292971	+	0.901671i	−0.690925	+	0.722926i	$0.742797\pi$
$108$		0			0
$109$	10.5344			1.00901			0.504505	−	0.863409i	$-0.331675\pi$
$109$	10.5344			1.00901			0.504505	+	0.863409i	$0.331675\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.221117	+	0.680529i	0.0208010	+	0.0640188i	0.960918	−	0.276833i	$-0.0892847\pi$
$113$	0.221117	+	0.680529i	0.0208010	+	0.0640188i	−0.940117	+	0.340851i	$0.889285\pi$
$114$		0			0
$115$	0.400106	+	0.290694i	0.0373101	+	0.0271073i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.40616	+	2.47472i	−0.312242	+	0.226857i
$120$		0			0
$121$	−9.15350	+	6.10028i	−0.832137	+	0.554571i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.11474	+	9.58618i	−0.278591	+	0.857414i
$126$		0			0
$127$	−0.536562	−	0.389835i	−0.0476122	−	0.0345923i	0.563725	−	0.825963i	$-0.309368\pi$
$127$	−0.536562	−	0.389835i	−0.0476122	−	0.0345923i	−0.611337	+	0.791371i	$0.709368\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.41309			−0.123462			−0.0617309	−	0.998093i	$-0.519662\pi$
$131$	−1.41309			−0.123462			−0.0617309	+	0.998093i	$0.519662\pi$
$132$		0			0
$133$	15.6684			1.35862
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.57889	+	2.60022i	0.305765	+	0.222152i	0.730077	−	0.683365i	$-0.239484\pi$
$137$	3.57889	+	2.60022i	0.305765	+	0.222152i	−0.424312	+	0.905516i	$0.639484\pi$
$138$		0			0
$139$	−3.62068	+	11.1433i	−0.307102	+	0.945163i	0.671782	+	0.740749i	$0.265529\pi$
$139$	−3.62068	+	11.1433i	−0.307102	+	0.945163i	−0.978884	+	0.204414i	$0.934471\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−15.8959	−	12.0479i	−1.32928	−	1.00750i
$144$		0			0
$145$	−18.6845	+	13.5751i	−1.55166	+	1.12735i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−14.0745	−	10.2257i	−1.15303	−	0.837724i	−0.164148	−	0.986436i	$-0.552487\pi$
$149$	−14.0745	−	10.2257i	−1.15303	−	0.837724i	−0.988881	+	0.148712i	$0.952487\pi$
$150$		0			0
$151$	−0.653879	−	2.01243i	−0.0532119	−	0.163769i	0.920919	−	0.389754i	$-0.127440\pi$
$151$	−0.653879	−	2.01243i	−0.0532119	−	0.163769i	−0.974131	+	0.225985i	$0.927440\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−22.0105			−1.76792
$156$		0			0
$157$	−0.988113	−	3.04110i	−0.0788600	−	0.242706i	0.903853	−	0.427844i	$-0.140727\pi$
$157$	−0.988113	−	3.04110i	−0.0788600	−	0.242706i	−0.982713	+	0.185138i	$0.940727\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.299400	−	0.921460i	0.0235961	−	0.0726212i
$162$		0			0
$163$	−3.36966	+	2.44820i	−0.263932	+	0.191758i	−0.711879	−	0.702302i	$-0.752155\pi$
$163$	−3.36966	+	2.44820i	−0.263932	+	0.191758i	0.447947	+	0.894060i	$0.352155\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.7263	+	9.97277i	−1.06218	+	0.771716i	−0.974490	−	0.224432i	$-0.927947\pi$
$167$	−13.7263	+	9.97277i	−1.06218	+	0.771716i	−0.0876866	+	0.996148i	$0.527947\pi$
$168$		0			0
$169$	7.15884	−	22.0326i	0.550680	−	1.69482i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.75652	+	23.8721i	0.589717	+	1.81496i	0.579439	+	0.815016i	$0.303272\pi$
$173$	7.75652	+	23.8721i	0.589717	+	1.81496i	0.0102785	+	0.999947i	$0.496728\pi$
$174$		0			0
$175$	−3.89060			−0.294101
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.577907	−	1.77861i	−0.0431948	−	0.132940i	0.927133	−	0.374731i	$-0.122265\pi$
$179$	−0.577907	−	1.77861i	−0.0431948	−	0.132940i	−0.970328	+	0.241791i	$0.922265\pi$
$180$		0			0
$181$	10.7418	+	7.80440i	0.798434	+	0.580097i	0.910454	−	0.413609i	$-0.135732\pi$
$181$	10.7418	+	7.80440i	0.798434	+	0.580097i	−0.112020	+	0.993706i	$0.535732\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.81319	+	2.04390i	−0.206830	+	0.150271i
$186$		0			0
$187$	0.969423	−	2.79016i	0.0708912	−	0.204037i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.36702	−	7.28492i	0.171271	−	0.527119i	−0.828172	−	0.560473i	$-0.810619\pi$
$191$	2.36702	−	7.28492i	0.171271	−	0.527119i	0.999444	+	0.0333549i	$0.0106192\pi$
$192$		0			0
$193$	−12.2193	−	8.87785i	−0.879565	−	0.639041i	0.0535714	−	0.998564i	$-0.482940\pi$
$193$	−12.2193	−	8.87785i	−0.879565	−	0.639041i	−0.933136	+	0.359523i	$0.882940\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.48280			−0.461881			−0.230940	−	0.972968i	$-0.574180\pi$
$197$	−6.48280			−0.461881			−0.230940	+	0.972968i	$0.574180\pi$
$198$		0			0
$199$	7.03322			0.498572			0.249286	−	0.968430i	$-0.419804\pi$
$199$	7.03322			0.498572			0.249286	+	0.968430i	$0.419804\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	36.6045	+	26.5947i	2.56913	+	1.86659i
$204$		0			0
$205$	−2.64101	+	8.12818i	−0.184456	+	0.567697i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.02200	+	6.27994i	−0.624065	+	0.434392i
$210$		0			0
$211$	−4.47037	+	3.24791i	−0.307753	+	0.223595i	−0.730932	−	0.682451i	$-0.760914\pi$
$211$	−4.47037	+	3.24791i	−0.307753	+	0.223595i	0.423179	+	0.906046i	$0.360914\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.2177	+	11.0563i	1.03784	+	0.754034i
$216$		0			0
$217$	13.3249	+	41.0099i	0.904554	+	2.78393i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.35592			0.360278
$222$		0			0
$223$	−2.59911	−	7.99924i	−0.174049	−	0.535669i	0.825539	−	0.564344i	$-0.190871\pi$
$223$	−2.59911	−	7.99924i	−0.174049	−	0.535669i	−0.999589	+	0.0286757i	$0.990871\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.35570	−	10.3278i	0.222725	−	0.685478i	−0.775789	−	0.630992i	$-0.782648\pi$
$227$	3.35570	−	10.3278i	0.222725	−	0.685478i	0.998515	−	0.0544860i	$-0.0173520\pi$
$228$		0			0
$229$	−18.3090	+	13.3022i	−1.20989	+	0.879037i	−0.995221	−	0.0976492i	$-0.968868\pi$
$229$	−18.3090	+	13.3022i	−1.20989	+	0.879037i	−0.214670	+	0.976687i	$0.568868\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.995718	−	0.723431i	0.0652316	−	0.0473936i	−0.554692	−	0.832056i	$-0.687164\pi$
$233$	0.995718	−	0.723431i	0.0652316	−	0.0473936i	0.619923	+	0.784662i	$0.287164\pi$
$234$		0			0
$235$	6.83915	−	21.0487i	0.446137	−	1.37307i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.11205	−	9.57790i	−0.201302	−	0.619543i	−0.999845	−	0.0176057i	$-0.994396\pi$
$239$	−3.11205	−	9.57790i	−0.201302	−	0.619543i	0.798543	−	0.601937i	$-0.205604\pi$
$240$		0			0
$241$	−4.56095			−0.293797			−0.146898	−	0.989152i	$-0.546929\pi$
$241$	−4.56095			−0.293797			−0.146898	+	0.989152i	$0.546929\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.4453	+	35.2249i	0.731211	+	2.25044i
$246$		0			0
$247$	−16.1254	−	11.7158i	−1.02603	−	0.745456i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.46032	+	3.96715i	−0.344652	+	0.250404i	−0.746622	−	0.665248i	$-0.768326\pi$
$251$	−5.46032	+	3.96715i	−0.344652	+	0.250404i	0.401970	+	0.915653i	$0.368326\pi$
$252$		0			0
$253$	0.196926	+	0.650586i	0.0123807	+	0.0409020i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.67213	−	5.14628i	0.104304	−	0.321016i	−0.885262	−	0.465092i	$-0.846021\pi$
$257$	1.67213	−	5.14628i	0.104304	−	0.321016i	0.989567	+	0.144076i	$0.0460211\pi$
$258$		0			0
$259$	5.51128	+	4.00418i	0.342454	+	0.248807i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.3831			1.38020			0.690101	−	0.723713i	$-0.257566\pi$
$263$	22.3831			1.38020			0.690101	+	0.723713i	$0.257566\pi$
$264$		0			0
$265$	11.2188			0.689166
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.9163	−	13.7435i	−1.15335	−	0.837958i	−0.164427	−	0.986389i	$-0.552578\pi$
$269$	−18.9163	−	13.7435i	−1.15335	−	0.837958i	−0.988923	+	0.148432i	$0.952578\pi$
$270$		0			0
$271$	−5.37163	+	16.5322i	−0.326303	+	1.00426i	0.644545	+	0.764566i	$0.277047\pi$
$271$	−5.37163	+	16.5322i	−0.326303	+	1.00426i	−0.970849	+	0.239693i	$0.922953\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.24024	−	1.55936i	0.135092	−	0.0940331i
$276$		0			0
$277$	7.50149	−	5.45015i	0.450721	−	0.327468i	−0.339160	−	0.940729i	$-0.610143\pi$
$277$	7.50149	−	5.45015i	0.450721	−	0.327468i	0.789880	+	0.613261i	$0.210143\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.09533	+	2.97543i	0.244307	+	0.177499i	0.703200	−	0.710992i	$-0.251754\pi$
$281$	4.09533	+	2.97543i	0.244307	+	0.177499i	−0.458893	+	0.888492i	$0.651754\pi$
$282$		0			0
$283$	−2.88522	−	8.87980i	−0.171509	−	0.527849i	0.827948	−	0.560805i	$-0.189508\pi$
$283$	−2.88522	−	8.87980i	−0.171509	−	0.527849i	−0.999457	+	0.0329553i	$0.989508\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.7433			0.988324
$288$		0			0
$289$	−5.00819	−	15.4136i	−0.294599	−	0.906683i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.70352	−	5.24290i	0.0995207	−	0.306293i	−0.888885	−	0.458131i	$-0.848519\pi$
$293$	1.70352	−	5.24290i	0.0995207	−	0.306293i	0.988405	+	0.151838i	$0.0485191\pi$
$294$		0			0
$295$	−1.93140	+	1.40324i	−0.112450	+	0.0817000i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.997138	+	0.724463i	−0.0576660	+	0.0418968i
$300$		0			0
$301$	11.3875	−	35.0470i	0.656363	−	2.02008i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.79648	+	14.7620i	0.274646	+	0.845272i
$306$		0			0
$307$	−18.5988			−1.06149			−0.530745	−	0.847532i	$-0.678088\pi$
$307$	−18.5988			−1.06149			−0.530745	+	0.847532i	$0.678088\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.76813	−	30.0632i	−0.553900	−	1.70473i	−0.698831	−	0.715287i	$-0.746296\pi$
$311$	−9.76813	−	30.0632i	−0.553900	−	1.70473i	0.144931	−	0.989442i	$-0.453704\pi$
$312$		0			0
$313$	13.3046	+	9.66638i	0.752022	+	0.546376i	0.896453	−	0.443139i	$-0.146135\pi$
$313$	13.3046	+	9.66638i	0.752022	+	0.546376i	−0.144431	+	0.989515i	$0.546135\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.4189	−	15.5618i	1.20301	−	0.874035i	0.208429	−	0.978037i	$-0.433165\pi$
$317$	21.4189	−	15.5618i	1.20301	−	0.874035i	0.994577	+	0.104002i	$0.0331649\pi$
$318$		0			0
$319$	−31.7365	−	0.642299i	−1.77690	−	0.0359619i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.912141	−	2.80728i	0.0507529	−	0.156201i
$324$		0			0
$325$	4.00407	+	2.90912i	0.222106	+	0.161369i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−43.3584			−2.39042
$330$		0			0
$331$	−18.4301			−1.01301			−0.506506	−	0.862237i	$-0.669063\pi$
$331$	−18.4301			−1.01301			−0.506506	+	0.862237i	$0.669063\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.0551	−	8.75854i	−0.658640	−	0.478530i
$336$		0			0
$337$	−0.106081	+	0.326483i	−0.00577858	+	0.0177847i	−0.953904	−	0.300111i	$-0.902976\pi$
$337$	−0.106081	+	0.326483i	−0.00577858	+	0.0177847i	0.948126	+	0.317896i	$0.102976\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−24.1095	−	18.2732i	−1.30560	−	0.989549i
$342$		0			0
$343$	31.9301	−	23.1986i	1.72406	−	1.25260i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.17807	−	5.21517i	−0.385339	−	0.279965i	0.378204	−	0.925722i	$-0.376542\pi$
$347$	−7.17807	−	5.21517i	−0.385339	−	0.279965i	−0.763543	+	0.645757i	$0.776542\pi$
$348$		0			0
$349$	10.6415	+	32.7513i	0.569629	+	1.75314i	0.653780	+	0.756685i	$0.273182\pi$
$349$	10.6415	+	32.7513i	0.569629	+	1.75314i	−0.0841506	+	0.996453i	$0.526818\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	35.5171			1.89039			0.945193	−	0.326513i	$-0.105874\pi$
$353$	35.5171			1.89039			0.945193	+	0.326513i	$0.105874\pi$
$354$		0			0
$355$	−5.07345	−	15.6145i	−0.269271	−	0.828730i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.00659	+	18.4864i	−0.317016	+	0.975675i	0.657901	+	0.753105i	$0.271445\pi$
$359$	−6.00659	+	18.4864i	−0.317016	+	0.975675i	−0.974917	+	0.222570i	$0.928555\pi$
$360$		0			0
$361$	6.48433	−	4.71114i	0.341281	−	0.247955i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.54080	+	5.47871i	−0.394704	+	0.286769i
$366$		0			0
$367$	−4.12228	+	12.6871i	−0.215181	+	0.662259i	0.783960	+	0.620812i	$0.213197\pi$
$367$	−4.12228	+	12.6871i	−0.215181	+	0.662259i	−0.999141	+	0.0414473i	$0.986803\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.79175	−	20.9029i	−0.352610	−	1.08522i
$372$		0			0
$373$	19.4513			1.00715			0.503576	−	0.863951i	$-0.332017\pi$
$373$	19.4513			1.00715			0.503576	+	0.863951i	$0.332017\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.7864	−	54.7408i	−0.916044	−	2.81929i
$378$		0			0
$379$	19.9382	+	14.4860i	1.02416	+	0.744094i	0.967131	−	0.254279i	$-0.0818380\pi$
$379$	19.9382	+	14.4860i	1.02416	+	0.744094i	0.0570266	+	0.998373i	$0.481838\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−21.9642	+	15.9579i	−1.12232	+	0.815411i	−0.984559	−	0.175055i	$-0.943990\pi$
$383$	−21.9642	+	15.9579i	−1.12232	+	0.815411i	−0.137758	+	0.990466i	$0.543990\pi$
$384$		0			0
$385$	−30.1530	−	22.8537i	−1.53674	−	1.16473i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.71085	−	5.26546i	0.0867436	−	0.266969i	−0.898271	−	0.439443i	$-0.855176\pi$
$389$	1.71085	−	5.26546i	0.0867436	−	0.266969i	0.985014	+	0.172474i	$0.0551759\pi$
$390$		0			0
$391$	−0.147667	−	0.107286i	−0.00746784	−	0.00542570i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−10.9548			−0.551196
$396$		0			0
$397$	26.4130			1.32563			0.662815	−	0.748783i	$-0.269361\pi$
$397$	26.4130			1.32563			0.662815	+	0.748783i	$0.269361\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	21.7322	+	15.7894i	1.08525	+	0.788483i	0.978591	−	0.205813i	$-0.0659838\pi$
$401$	21.7322	+	15.7894i	1.08525	+	0.788483i	0.106662	+	0.994295i	$0.465984\pi$
$402$		0			0
$403$	16.9509	−	52.1694i	0.844382	−	2.59874i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.77833	−	0.0967064i	−0.236853	−	0.00479356i
$408$		0			0
$409$	−4.95113	+	3.59721i	−0.244818	+	0.177871i	−0.703427	−	0.710768i	$-0.748348\pi$
$409$	−4.95113	+	3.59721i	−0.244818	+	0.177871i	0.458609	+	0.888638i	$0.348348\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.78377	+	2.74907i	0.186187	+	0.135273i
$414$		0			0
$415$	7.45284	+	22.9375i	0.365845	+	1.12596i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.1984			0.547075			0.273538	−	0.961861i	$-0.411806\pi$
$419$	11.1984			0.547075			0.273538	+	0.961861i	$0.411806\pi$
$420$		0			0
$421$	6.38155	+	19.6404i	0.311018	+	0.957214i	0.977363	+	0.211570i	$0.0678578\pi$
$421$	6.38155	+	19.6404i	0.311018	+	0.957214i	−0.666345	+	0.745643i	$0.732142\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.226493	+	0.697073i	−0.0109865	+	0.0338130i
$426$		0			0
$427$	24.6009	−	17.8736i	1.19052	−	0.864964i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	25.2600	−	18.3525i	1.21673	−	0.884009i	0.220909	−	0.975294i	$-0.429098\pi$
$431$	25.2600	−	18.3525i	1.21673	−	0.884009i	0.995825	+	0.0912859i	$0.0290977\pi$
$432$		0			0
$433$	−11.9458	+	36.7655i	−0.574080	+	1.76684i	0.0652087	+	0.997872i	$0.479229\pi$
$433$	−11.9458	+	36.7655i	−0.574080	+	1.76684i	−0.639289	+	0.768966i	$0.720771\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.209906	+	0.646025i	0.0100412	+	0.0309036i
$438$		0			0
$439$	−10.5363			−0.502872			−0.251436	−	0.967874i	$-0.580903\pi$
$439$	−10.5363			−0.502872			−0.251436	+	0.967874i	$0.580903\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.35771	−	7.25628i	−0.112018	−	0.344756i	0.879295	−	0.476277i	$-0.158014\pi$
$443$	−2.35771	−	7.25628i	−0.112018	−	0.344756i	−0.991313	+	0.131521i	$0.958014\pi$
$444$		0			0
$445$	−1.81638	−	1.31968i	−0.0861047	−	0.0625587i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	32.3712	−	23.5191i	1.52769	−	1.10993i	0.570188	−	0.821514i	$-0.306870\pi$
$449$	32.3712	−	23.5191i	1.52769	−	1.10993i	0.957504	−	0.288419i	$-0.0931296\pi$
$450$		0			0
$451$	−9.64093	+	6.71075i	−0.453974	+	0.315997i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	21.1999	−	65.2466i	0.993867	−	3.05881i
$456$		0			0
$457$	−19.5709	−	14.2191i	−0.915490	−	0.665142i	0.0269075	−	0.999638i	$-0.491434\pi$
$457$	−19.5709	−	14.2191i	−0.915490	−	0.665142i	−0.942397	+	0.334496i	$0.891434\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	31.9494			1.48803			0.744017	−	0.668161i	$-0.232918\pi$
$461$	31.9494			1.48803			0.744017	+	0.668161i	$0.232918\pi$
$462$		0			0
$463$	22.5612			1.04851			0.524254	−	0.851562i	$-0.324344\pi$
$463$	22.5612			1.04851			0.524254	+	0.851562i	$0.324344\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.1681	−	13.1999i	−0.840718	−	0.610818i	0.0818529	−	0.996644i	$-0.473916\pi$
$467$	−18.1681	−	13.1999i	−0.840718	−	0.610818i	−0.922571	+	0.385827i	$0.873916\pi$
$468$		0			0
$469$	−9.02087	+	27.7634i	−0.416545	+	1.28199i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.48994	+	24.7445i	0.344388	+	1.13775i
$474$		0			0
$475$	2.20672	−	1.60327i	0.101251	−	0.0735633i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.64222	+	1.19315i	0.0750352	+	0.0545162i	0.624670	−	0.780888i	$-0.285233\pi$
$479$	1.64222	+	1.19315i	0.0750352	+	0.0545162i	−0.549635	+	0.835405i	$0.685233\pi$
$480$		0			0
$481$	−2.67796	−	8.24192i	−0.122105	−	0.375799i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.05511			0.320356
$486$		0			0
$487$	6.94156	+	21.3639i	0.314552	+	0.968092i	0.975938	+	0.218046i	$0.0699684\pi$
$487$	6.94156	+	21.3639i	0.314552	+	0.968092i	−0.661386	+	0.750045i	$0.730032\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.20427	−	16.0171i	0.234866	−	0.722842i	−0.762274	−	0.647255i	$-0.775917\pi$
$491$	5.20427	−	16.0171i	0.234866	−	0.722842i	0.997139	−	0.0755869i	$-0.0240830\pi$
$492$		0			0
$493$	6.89589	−	5.01016i	0.310575	−	0.225646i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−26.0215	+	18.9057i	−1.16722	+	0.848036i
$498$		0			0
$499$	12.3245	−	37.9308i	0.551719	−	1.69802i	−0.152735	−	0.988267i	$-0.548808\pi$
$499$	12.3245	−	37.9308i	0.551719	−	1.69802i	0.704454	−	0.709749i	$-0.251192\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.08685	+	18.7334i	0.271399	+	0.835281i	0.990150	+	0.140013i	$0.0447143\pi$
$503$	6.08685	+	18.7334i	0.271399	+	0.835281i	−0.718751	+	0.695268i	$0.755286\pi$
$504$		0			0
$505$	−32.6309			−1.45206
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.8047	+	39.4088i	0.567558	+	1.74676i	0.660226	+	0.751067i	$0.270461\pi$
$509$	12.8047	+	39.4088i	0.567558	+	1.74676i	−0.0926679	+	0.995697i	$0.529539\pi$
$510$		0			0
$511$	14.7731	+	10.7333i	0.653522	+	0.474811i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.0628	+	18.2092i	−1.10440	+	0.802393i
$516$		0			0
$517$	24.9662	−	17.3782i	1.09801	−	0.764291i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.62870	+	14.2457i	−0.202787	+	0.624115i	0.797010	+	0.603966i	$0.206414\pi$
$521$	−4.62870	+	14.2457i	−0.202787	+	0.624115i	−0.999797	+	0.0201484i	$0.993586\pi$
$522$		0			0
$523$	−13.7706	−	10.0050i	−0.602148	−	0.437486i	0.244492	−	0.969651i	$-0.421379\pi$
$523$	−13.7706	−	10.0050i	−0.602148	−	0.437486i	−0.846641	+	0.532165i	$0.821379\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.12339			0.353861
$528$		0			0
$529$	−22.9580			−0.998174
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−17.2316	−	12.5195i	−0.746383	−	0.542279i
$534$		0			0
$535$	7.31288	−	22.5067i	0.316163	−	0.973051i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−16.7072	+	48.0860i	−0.719628	+	2.07121i
$540$		0			0
$541$	7.07203	−	5.13813i	0.304050	−	0.220905i	−0.425289	−	0.905058i	$-0.639828\pi$
$541$	7.07203	−	5.13813i	0.304050	−	0.220905i	0.729339	+	0.684152i	$0.239828\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−20.5655	−	14.9417i	−0.880929	−	0.640032i
$546$		0			0
$547$	−3.46411	−	10.6614i	−0.148115	−	0.455851i	0.849284	−	0.527937i	$-0.177034\pi$
$547$	−3.46411	−	10.6614i	−0.148115	−	0.455851i	−0.997398	+	0.0720864i	$0.977034\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−31.7212			−1.35137
$552$		0			0
$553$	6.63193	+	20.4110i	0.282018	+	0.867964i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.64712	+	5.06930i	−0.0697905	+	0.214793i	−0.979869	−	0.199644i	$-0.936021\pi$
$557$	−1.64712	+	5.06930i	−0.0697905	+	0.214793i	0.910078	+	0.414437i	$0.136021\pi$
$558$		0			0
$559$	−37.9254	+	27.5544i	−1.60407	+	1.16543i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.27521	+	4.55921i	−0.264469	+	0.192148i	−0.712115	−	0.702063i	$-0.752262\pi$
$563$	−6.27521	+	4.55921i	−0.264469	+	0.192148i	0.447646	+	0.894211i	$0.352262\pi$
$564$		0			0
$565$	0.533575	−	1.64217i	0.0224477	−	0.0690868i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.40452	−	7.40036i	−0.100803	−	0.310239i	0.887920	−	0.459999i	$-0.152150\pi$
$569$	−2.40452	−	7.40036i	−0.100803	−	0.310239i	−0.988722	+	0.149759i	$0.952150\pi$
$570$		0			0
$571$	−46.6962			−1.95418			−0.977088	−	0.212834i	$-0.931731\pi$
$571$	−46.6962			−1.95418			−0.977088	+	0.212834i	$0.931731\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.0521215	−	0.160414i	−0.00217362	−	0.00668971i
$576$		0			0
$577$	13.5333	+	9.83253i	0.563400	+	0.409334i	0.832702	−	0.553722i	$-0.186793\pi$
$577$	13.5333	+	9.83253i	0.563400	+	0.409334i	−0.269302	+	0.963056i	$0.586793\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	38.2252	−	27.7722i	1.58585	−	1.15219i
$582$		0			0
$583$	12.2887	+	9.31391i	0.508946	+	0.385743i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.63485	−	14.2646i	0.191301	−	0.588764i	−0.808699	−	0.588223i	$-0.799828\pi$
$587$	4.63485	−	14.2646i	0.191301	−	0.588764i	1.00000		0.000540811i	$-0.000172146\pi$
$588$		0			0
$589$	−24.4575	−	17.7694i	−1.00775	−	0.732177i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.84235			−0.404177			−0.202088	−	0.979367i	$-0.564773\pi$
$593$	−9.84235			−0.404177			−0.202088	+	0.979367i	$0.564773\pi$
$594$		0			0
$595$	10.1597			0.416506
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.51930	−	1.10384i	−0.0620769	−	0.0451015i	0.556314	−	0.830972i	$-0.312215\pi$
$599$	−1.51930	−	1.10384i	−0.0620769	−	0.0451015i	−0.618391	+	0.785871i	$0.712215\pi$
$600$		0			0
$601$	8.51453	−	26.2050i	0.347315	−	1.06893i	−0.613018	−	0.790069i	$-0.710045\pi$
$601$	8.51453	−	26.2050i	0.347315	−	1.06893i	0.960333	−	0.278857i	$-0.0899554\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	26.5222	+	1.07398i	1.07828	+	0.0436635i
$606$		0			0
$607$	−10.9756	+	7.97424i	−0.445486	+	0.323664i	−0.787811	−	0.615917i	$-0.788786\pi$
$607$	−10.9756	+	7.97424i	−0.445486	+	0.323664i	0.342325	+	0.939582i	$0.388786\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	44.6229	+	32.4204i	1.80525	+	1.31159i
$612$		0			0
$613$	−13.1565	−	40.4915i	−0.531385	−	1.63544i	−0.751332	−	0.659924i	$-0.770588\pi$
$613$	−13.1565	−	40.4915i	−0.531385	−	1.63544i	0.219947	−	0.975512i	$-0.429412\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.95843			0.239877			0.119939	−	0.992781i	$-0.461730\pi$
$617$	5.95843			0.239877			0.119939	+	0.992781i	$0.461730\pi$
$618$		0			0
$619$	6.93986	+	21.3587i	0.278936	+	0.858478i	0.988151	+	0.153485i	$0.0490497\pi$
$619$	6.93986	+	21.3587i	0.278936	+	0.858478i	−0.709215	+	0.704993i	$0.750950\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.35920	+	4.18320i	−0.0544553	+	0.167596i
$624$		0			0
$625$	23.0065	−	16.7152i	0.920260	−	0.668608i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.03826	−	0.754343i	0.0413983	−	0.0300776i
$630$		0			0
$631$	0.328317	−	1.01045i	0.0130701	−	0.0402256i	−0.944309	−	0.329061i	$-0.893268\pi$
$631$	0.328317	−	1.01045i	0.0130701	−	0.0402256i	0.957379	+	0.288835i	$0.0932679\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.494558	+	1.52209i	0.0196259	+	0.0604024i
$636$		0			0
$637$	−92.3047			−3.65724
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.66138	+	29.7347i	0.381601	+	1.17445i	0.938916	+	0.344147i	$0.111832\pi$
$641$	9.66138	+	29.7347i	0.381601	+	1.17445i	−0.557314	+	0.830302i	$0.688168\pi$
$642$		0			0
$643$	19.3052	+	14.0261i	0.761324	+	0.553134i	0.899316	−	0.437299i	$-0.144065\pi$
$643$	19.3052	+	14.0261i	0.761324	+	0.553134i	−0.137992	+	0.990433i	$0.544065\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.07454	−	4.41341i	0.238815	−	0.173509i	−0.461940	−	0.886911i	$-0.652847\pi$
$647$	6.07454	−	4.41341i	0.238815	−	0.173509i	0.700755	+	0.713402i	$0.252847\pi$
$648$		0			0
$649$	−3.28057	−	0.0663939i	−0.128774	−	0.00260619i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.71150	−	17.5782i	0.223508	−	0.687888i	−0.774931	−	0.632045i	$-0.782216\pi$
$653$	5.71150	−	17.5782i	0.223508	−	0.687888i	0.998440	−	0.0558423i	$-0.0177844\pi$
$654$		0			0
$655$	2.75866	+	2.00429i	0.107790	+	0.0783140i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.0641			−0.937403			−0.468702	−	0.883357i	$-0.655278\pi$
$659$	−24.0641			−0.937403			−0.468702	+	0.883357i	$0.655278\pi$
$660$		0			0
$661$	10.9489			0.425863			0.212931	−	0.977067i	$-0.431699\pi$
$661$	10.9489			0.425863			0.212931	+	0.977067i	$0.431699\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−30.5883	−	22.2237i	−1.18616	−	0.861797i
$666$		0			0
$667$	−0.606147	+	1.86553i	−0.0234701	+	0.0722336i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.00164	+	20.1519i	−0.270295	+	0.777955i
$672$		0			0
$673$	14.8164	−	10.7648i	0.571132	−	0.414952i	−0.264384	−	0.964417i	$-0.585169\pi$
$673$	14.8164	−	10.7648i	0.571132	−	0.414952i	0.835516	+	0.549466i	$0.185169\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−26.4379	−	19.2083i	−1.01609	−	0.738234i	−0.0506135	−	0.998718i	$-0.516118\pi$
$677$	−26.4379	−	19.2083i	−1.01609	−	0.738234i	−0.965478	+	0.260485i	$0.916118\pi$
$678$		0			0
$679$	−4.27109	−	13.1451i	−0.163910	−	0.504462i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	42.7468			1.63566			0.817831	−	0.575458i	$-0.195176\pi$
$683$	42.7468			1.63566			0.817831	+	0.575458i	$0.195176\pi$
$684$		0			0
$685$	−3.29872	−	10.1524i	−0.126038	−	0.387904i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.63991	+	26.5909i	−0.329154	+	1.01303i
$690$		0			0
$691$	−13.5847	+	9.86988i	−0.516787	+	0.375468i	−0.815392	−	0.578909i	$-0.803479\pi$
$691$	−13.5847	+	9.86988i	−0.516787	+	0.375468i	0.298605	+	0.954377i	$0.403479\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.8738	−	16.6188i	0.867652	−	0.630386i
$696$		0			0
$697$	0.974716	−	2.99987i	0.0369200	−	0.113628i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.85906	+	11.8770i	0.145755	+	0.448587i	0.997107	−	0.0760071i	$-0.0242172\pi$
$701$	3.85906	+	11.8770i	0.145755	+	0.448587i	−0.851353	+	0.524594i	$0.824217\pi$
$702$		0			0
$703$	−4.77603			−0.180132
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19.7544	+	60.7979i	0.742942	+	2.28654i
$708$		0			0
$709$	31.5048	+	22.8896i	1.18319	+	0.859636i	0.992528	−	0.122020i	$-0.0389371\pi$
$709$	31.5048	+	22.8896i	1.18319	+	0.859636i	0.190660	+	0.981656i	$0.438937\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.51237	+	1.09880i	−0.0566387	+	0.0411504i
$714$		0			0
$715$	13.9439	+	46.0666i	0.521473	+	1.72279i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.4849	+	35.3469i	−0.428315	+	1.31822i	0.471470	+	0.881882i	$0.343724\pi$
$719$	−11.4849	+	35.3469i	−0.428315	+	1.31822i	−0.899785	+	0.436334i	$0.856276\pi$
$720$		0			0
$721$	49.1001	+	35.6733i	1.82858	+	1.32854i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.87666			0.292532
$726$		0			0
$727$	−1.69543			−0.0628801			−0.0314400	−	0.999506i	$-0.510009\pi$
$727$	−1.69543			−0.0628801			−0.0314400	+	0.999506i	$0.510009\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.61640	−	4.08055i	−0.207730	−	0.150925i
$732$		0			0
$733$	−4.64378	+	14.2921i	−0.171522	+	0.527890i	−0.999458	−	0.0329330i	$-0.989515\pi$
$733$	−4.64378	+	14.2921i	−0.171522	+	0.527890i	0.827936	+	0.560823i	$0.189515\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.93335	−	19.6020i	−0.218558	−	0.722049i
$738$		0			0
$739$	25.0145	−	18.1741i	0.920174	−	0.668546i	−0.0233930	−	0.999726i	$-0.507447\pi$
$739$	25.0145	−	18.1741i	0.920174	−	0.668546i	0.943567	+	0.331180i	$0.107447\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.26114	−	3.09590i	−0.156326	−	0.113577i	0.506873	−	0.862021i	$-0.330801\pi$
$743$	−4.26114	−	3.09590i	−0.156326	−	0.113577i	−0.663198	+	0.748444i	$0.730801\pi$
$744$		0			0
$745$	12.9727	+	39.9259i	0.475283	+	1.46277i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−46.3617			−1.69402
$750$		0			0
$751$	10.0487	+	30.9268i	0.366683	+	1.12853i	0.948921	+	0.315515i	$0.102177\pi$
$751$	10.0487	+	30.9268i	0.366683	+	1.12853i	−0.582238	+	0.813019i	$0.697823\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.57787	+	4.85617i	−0.0574244	+	0.176734i
$756$		0			0
$757$	30.7000	−	22.3048i	1.11581	−	0.810683i	0.132241	−	0.991218i	$-0.457783\pi$
$757$	30.7000	−	22.3048i	1.11581	−	0.810683i	0.983569	+	0.180535i	$0.0577828\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−40.4447	+	29.3848i	−1.46612	+	1.06520i	−0.484402	+	0.874846i	$0.660963\pi$
$761$	−40.4447	+	29.3848i	−1.46612	+	1.06520i	−0.981716	+	0.190352i	$0.939037\pi$
$762$		0			0
$763$	−15.3892	+	47.3632i	−0.557128	+	1.71466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.83856	−	5.65850i	−0.0663865	−	0.204317i
$768$		0			0
$769$	21.4620			0.773940			0.386970	−	0.922092i	$-0.373522\pi$
$769$	21.4620			0.773940			0.386970	+	0.922092i	$0.373522\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.57912	+	7.93773i	0.0927647	+	0.285500i	0.986665	−	0.162766i	$-0.0520416\pi$
$773$	2.57912	+	7.93773i	0.0927647	+	0.285500i	−0.893900	+	0.448266i	$0.852042\pi$
$774$		0			0
$775$	6.07302	+	4.41230i	0.218149	+	0.158495i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.49665	+	6.89972i	−0.340253	+	0.247208i
$780$		0			0
$781$	7.40594	−	21.3156i	0.265005	−	0.762731i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.38440	+	7.33844i	−0.0851030	+	0.261920i
$786$		0			0
$787$	−16.3990	−	11.9146i	−0.584562	−	0.424709i	0.255804	−	0.966729i	$-0.417660\pi$
$787$	−16.3990	−	11.9146i	−0.584562	−	0.424709i	−0.840366	+	0.542020i	$0.817660\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.38272			−0.120276
$792$		0			0
$793$	−38.6830			−1.37368
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.7487	−	21.6137i	−1.05375	−	0.765597i	−0.0808312	−	0.996728i	$-0.525757\pi$
$797$	−29.7487	−	21.6137i	−1.05375	−	0.765597i	−0.972923	+	0.231131i	$0.925757\pi$
$798$		0			0
$799$	−2.52412	+	7.76846i	−0.0892971	+	0.274828i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−12.8084	−	0.259223i	−0.451998	−	0.00914778i
$804$		0			0
$805$	−1.89147	+	1.37424i	−0.0666657	+	0.0484355i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.410774	−	0.298445i	−0.0144421	−	0.0104928i	0.580541	−	0.814231i	$-0.302841\pi$
$809$	−0.410774	−	0.298445i	−0.0144421	−	0.0104928i	−0.594983	+	0.803738i	$0.702841\pi$
$810$		0			0
$811$	13.1816	+	40.5689i	0.462870	+	1.42457i	0.861642	+	0.507517i	$0.169436\pi$
$811$	13.1816	+	40.5689i	0.462870	+	1.42457i	−0.398772	+	0.917050i	$0.630564\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.0508			0.352065
$816$		0			0
$817$	7.98362	+	24.5711i	0.279312	+	0.859633i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.88658	+	30.4278i	−0.345044	+	1.06194i	0.616516	+	0.787342i	$0.288544\pi$
$821$	−9.88658	+	30.4278i	−0.345044	+	1.06194i	−0.961560	+	0.274594i	$0.911456\pi$
$822$		0			0
$823$	−21.9348	+	15.9365i	−0.764598	+	0.555513i	−0.900317	−	0.435235i	$-0.856665\pi$
$823$	−21.9348	+	15.9365i	−0.764598	+	0.555513i	0.135719	+	0.990747i	$0.456665\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.9539	−	7.95847i	0.380904	−	0.276743i	−0.380814	−	0.924652i	$-0.624356\pi$
$827$	10.9539	−	7.95847i	0.380904	−	0.276743i	0.761718	+	0.647909i	$0.224356\pi$
$828$		0			0
$829$	−3.84608	+	11.8370i	−0.133580	+	0.411117i	−0.995366	−	0.0961545i	$-0.969346\pi$
$829$	−3.84608	+	11.8370i	−0.133580	+	0.411117i	0.861787	+	0.507271i	$0.169346\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.22410	−	13.0004i	−0.146356	−	0.450439i
$834$		0			0
$835$	40.9421			1.41686
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.341189	−	1.05007i	−0.0117791	−	0.0362525i	0.944994	−	0.327087i	$-0.106067\pi$
$839$	−0.341189	−	1.05007i	−0.0117791	−	0.0362525i	−0.956773	+	0.290835i	$0.906067\pi$
$840$		0			0
$841$	−50.6457	−	36.7963i	−1.74640	−	1.26884i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−45.2262	+	32.8588i	−1.55583	+	1.13038i
$846$		0			0
$847$	−14.0552	−	50.0663i	−0.482944	−	1.72030i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.0912632	+	0.280879i	−0.00312846	+	0.00962842i
$852$		0			0
$853$	−16.2816	−	11.8293i	−0.557471	−	0.405026i	0.273062	−	0.961997i	$-0.411964\pi$
$853$	−16.2816	−	11.8293i	−0.557471	−	0.405026i	−0.830532	+	0.556970i	$0.811964\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.5205			0.905924			0.452962	−	0.891530i	$-0.350367\pi$
$857$	26.5205			0.905924			0.452962	+	0.891530i	$0.350367\pi$
$858$		0			0
$859$	−40.3123			−1.37544			−0.687719	−	0.725977i	$-0.741388\pi$
$859$	−40.3123			−1.37544			−0.687719	+	0.725977i	$0.741388\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	41.6384	+	30.2521i	1.41739	+	1.02979i	0.992196	+	0.124689i	$0.0397934\pi$
$863$	41.6384	+	30.2521i	1.41739	+	1.02979i	0.425192	+	0.905103i	$0.360207\pi$
$864$		0			0
$865$	18.7171	−	57.6054i	0.636402	−	1.95864i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.9995	−	9.09474i	−0.407056	−	0.308518i
$870$		0			0
$871$	30.0435	−	21.8279i	1.01799	−	0.739610i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−38.5498	−	28.0081i	−1.30322	−	0.946846i
$876$		0			0
$877$	12.9505	+	39.8576i	0.437308	+	1.34590i	0.890703	+	0.454586i	$0.150213\pi$
$877$	12.9505	+	39.8576i	0.437308	+	1.34590i	−0.453395	+	0.891310i	$0.649787\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.6635			1.03308			0.516539	−	0.856263i	$-0.327220\pi$
$881$	30.6635			1.03308			0.516539	+	0.856263i	$0.327220\pi$
$882$		0			0
$883$	5.54832	+	17.0760i	0.186716	+	0.574652i	0.999974	−	0.00725148i	$-0.00230824\pi$
$883$	5.54832	+	17.0760i	0.186716	+	0.574652i	−0.813258	+	0.581903i	$0.802308\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.48830	+	23.0466i	−0.251433	+	0.773830i	0.743079	+	0.669204i	$0.233365\pi$
$887$	−7.48830	+	23.0466i	−0.251433	+	0.773830i	−0.994512	+	0.104626i	$0.966635\pi$
$888$		0			0
$889$	2.53656	−	1.84292i	0.0850735	−	0.0618096i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	24.5925	−	17.8675i	0.822958	−	0.597914i
$894$		0			0
$895$	−1.39454	+	4.29195i	−0.0466143	+	0.143464i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−26.9768	−	83.0260i	−0.899726	−	2.76907i
$900$		0			0
$901$	−4.14052			−0.137941
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.90093	−	30.4719i	−0.329118	−	1.01292i
$906$		0			0
$907$	12.1932	+	8.85887i	0.404868	+	0.294154i	0.771521	−	0.636204i	$-0.219496\pi$
$907$	12.1932	+	8.85887i	0.404868	+	0.294154i	−0.366653	+	0.930358i	$0.619496\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−39.4415	+	28.6559i	−1.30675	+	0.949413i	−0.999997	−	0.00237514i	$-0.999244\pi$
$911$	−39.4415	+	28.6559i	−1.30675	+	0.949413i	−0.306757	+	0.951788i	$0.599244\pi$
$912$		0			0
$913$	−10.8792	+	31.3123i	−0.360050	+	1.03629i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.06432	−	6.35332i	0.0681698	−	0.209805i
$918$		0			0
$919$	−21.1984	−	15.4015i	−0.699271	−	0.508050i	0.180424	−	0.983589i	$-0.442253\pi$
$919$	−21.1984	−	15.4015i	−0.699271	−	0.508050i	−0.879695	+	0.475539i	$0.842253\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	40.9168			1.34679
$924$		0			0
$925$	1.18593			0.0389932
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.79770	+	7.11844i	0.321452	+	0.233549i	0.736795	−	0.676116i	$-0.236338\pi$
$929$	9.79770	+	7.11844i	0.321452	+	0.233549i	−0.415343	+	0.909665i	$0.636338\pi$
$930$		0			0
$931$	−15.7200	+	48.3811i	−0.515201	+	1.58562i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.85004	+	4.07203i	−0.191317	+	0.133170i
$936$		0			0
$937$	−7.99643	+	5.80975i	−0.261232	+	0.189796i	−0.710690	−	0.703505i	$-0.751617\pi$
$937$	−7.99643	+	5.80975i	−0.261232	+	0.189796i	0.449458	+	0.893301i	$0.351617\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.46167	+	4.69468i	0.210644	+	0.153042i	0.688105	−	0.725611i	$-0.258443\pi$
$941$	6.46167	+	4.69468i	0.210644	+	0.153042i	−0.477461	+	0.878653i	$0.658443\pi$
$942$		0			0
$943$	0.224306	+	0.690343i	0.00730441	+	0.0224807i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.3817			0.954776			0.477388	−	0.878693i	$-0.341584\pi$
$947$	29.3817			0.954776			0.477388	+	0.878693i	$0.341584\pi$
$948$		0			0
$949$	−7.17832	−	22.0926i	−0.233018	−	0.717156i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−12.2804	+	37.7951i	−0.397800	+	1.22430i	0.528959	+	0.848648i	$0.322583\pi$
$953$	−12.2804	+	37.7951i	−0.397800	+	1.22430i	−0.926759	+	0.375656i	$0.877417\pi$
$954$		0			0
$955$	−14.9537	+	10.8645i	−0.483891	+	0.351567i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.9190	+	12.2924i	−0.546343	+	0.396941i
$960$		0			0
$961$	16.1300	−	49.6432i	0.520324	−	1.60139i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.2627	+	34.6631i	0.362560	+	1.11585i
$966$		0			0
$967$	35.5630			1.14363			0.571814	−	0.820383i	$-0.306240\pi$
$967$	35.5630			1.14363			0.571814	+	0.820383i	$0.306240\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.28310	+	16.2597i	0.169543	+	0.521799i	0.999342	−	0.0362627i	$-0.0115453\pi$
$971$	5.28310	+	16.2597i	0.169543	+	0.521799i	−0.829800	+	0.558061i	$0.811545\pi$
$972$		0			0
$973$	−44.8117	−	32.5576i	−1.43660	−	1.04375i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.4671	−	17.7764i	0.782771	−	0.568717i	−0.123038	−	0.992402i	$-0.539264\pi$
$977$	24.4671	−	17.7764i	0.782771	−	0.568717i	0.905810	+	0.423685i	$0.139264\pi$
$978$		0			0
$979$	−0.893996	−	2.95350i	−0.0285722	−	0.0943942i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.61476	−	17.2805i	0.179083	−	0.551161i	−0.820713	−	0.571340i	$-0.806424\pi$
$983$	5.61476	−	17.2805i	0.179083	−	0.551161i	0.999796	+	0.0201791i	$0.00642366\pi$
$984$		0			0
$985$	12.6559	+	9.19506i	0.403251	+	0.292979i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.59758			0.0508002
$990$		0			0
$991$	19.2500			0.611497			0.305748	−	0.952112i	$-0.401093\pi$
$991$	19.2500			0.611497			0.305748	+	0.952112i	$0.401093\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−13.7305	−	9.97576i	−0.435285	−	0.316253i
$996$		0			0
$997$	−2.06598	+	6.35843i	−0.0654302	+	0.201373i	−0.978427	−	0.206594i	$-0.933762\pi$
$997$	−2.06598	+	6.35843i	−0.0654302	+	0.201373i	0.912997	+	0.407967i	$0.133762\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.r.f.289.1		8
3.2	odd	2		264.2.q.e.25.2	✓	8
11.2	odd	10		8712.2.a.cc.1.4		4
11.4	even	5	inner	792.2.r.f.433.1		8
11.9	even	5		8712.2.a.bz.1.4		4
12.11	even	2		528.2.y.k.289.2		8
33.2	even	10		2904.2.a.be.1.1		4
33.20	odd	10		2904.2.a.bb.1.1		4
33.26	odd	10		264.2.q.e.169.2	yes	8
132.35	odd	10		5808.2.a.cl.1.1		4
132.59	even	10		528.2.y.k.433.2		8
132.119	even	10		5808.2.a.co.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.e.25.2	✓	8	3.2	odd	2
264.2.q.e.169.2	yes	8	33.26	odd	10
528.2.y.k.289.2		8	12.11	even	2
528.2.y.k.433.2		8	132.59	even	10
792.2.r.f.289.1		8	1.1	even	1	trivial
792.2.r.f.433.1		8	11.4	even	5	inner
2904.2.a.bb.1.1		4	33.20	odd	10
2904.2.a.be.1.1		4	33.2	even	10
5808.2.a.cl.1.1		4	132.35	odd	10
5808.2.a.co.1.1		4	132.119	even	10
8712.2.a.bz.1.4		4	11.9	even	5
8712.2.a.cc.1.4		4	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95223 - 1.41838i) q^{5} +(-1.46086 + 4.49606i) q^{7} +(-0.960858 - 3.17439i) q^{11} +(4.86531 - 3.53486i) q^{13} +(0.720508 + 0.523480i) q^{17} +(-1.02419 - 3.15214i) q^{19} -0.204948 q^{23} +(0.254316 + 0.782703i) q^{25} +(2.95756 - 9.10244i) q^{29} +(7.37928 - 5.36136i) q^{31} +(9.22903 - 6.70528i) q^{35} +(0.445299 - 1.37049i) q^{37} +(-1.09445 - 3.36838i) q^{41} -7.79505 q^{43} +(2.83419 + 8.72275i) q^{47} +(-12.4173 - 9.02172i) q^{49} +(-3.76124 + 2.73270i) q^{53} +(-2.62667 + 7.55999i) q^{55} +(0.305720 - 0.940910i) q^{59} +(-5.20386 - 3.78082i) q^{61} -14.5120 q^{65} +6.17505 q^{67} +(5.50435 + 3.99914i) q^{71} +(1.19363 - 3.67361i) q^{73} +(15.6759 + 0.317257i) q^{77} +(3.67274 - 2.66840i) q^{79} +(-8.08582 - 5.87469i) q^{83} +(-0.664104 - 2.04390i) q^{85} +0.930414 q^{89} +(8.78539 + 27.0387i) q^{91} +(-2.47146 + 7.60637i) q^{95} +(-2.36531 + 1.71850i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{5} - 5 q^{7} - q^{11} - q^{13} + 4 q^{17} - 2 q^{19} - 16 q^{23} + 7 q^{25} + 7 q^{29} + 29 q^{31} + 20 q^{35} + 13 q^{37} + 23 q^{41} - 48 q^{43} + 15 q^{47} - 11 q^{49} - 9 q^{53} - 22 q^{55}+ \cdots + 21 q^{97}+O(q^{100}) \) 8 * q + q^5 - 5 * q^7 - q^11 - q^13 + 4 * q^17 - 2 * q^19 - 16 * q^23 + 7 * q^25 + 7 * q^29 + 29 * q^31 + 20 * q^35 + 13 * q^37 + 23 * q^41 - 48 * q^43 + 15 * q^47 - 11 * q^49 - 9 * q^53 - 22 * q^55 - 12 * q^59 + 9 * q^61 - 42 * q^65 + 38 * q^67 + 41 * q^71 - 25 * q^73 + 55 * q^77 + 11 * q^79 - 23 * q^83 + 23 * q^85 - 12 * q^89 - 35 * q^91 - 29 * q^95 + 21 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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