LMFDB - Embedded newform 1260.2.ej.a.737.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(53,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("1260.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.ej (of order $12$, degree $4$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			737.12
Character	$\chi$	$=$	1260.737
Dual form			1260.2.ej.a.53.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36627 + 1.77012i) q^{5} +(-1.95909 - 1.77819i) q^{7} +O(q^{10})$	$q+(1.36627 + 1.77012i) q^{5} +(-1.95909 - 1.77819i) q^{7} +(0.278831 - 0.160983i) q^{11} +(-3.06571 + 3.06571i) q^{13} +(-7.47871 - 2.00391i) q^{17} +(-6.65273 - 3.84096i) q^{19} +(0.170057 - 0.0455667i) q^{23} +(-1.26663 + 4.83691i) q^{25} +3.35013 q^{29} +(3.49948 + 6.06127i) q^{31} +(0.470975 - 5.89730i) q^{35} +(-6.27756 + 1.68207i) q^{37} -9.24208i q^{41} +(3.35424 - 3.35424i) q^{43} +(-1.48099 - 5.52713i) q^{47} +(0.676046 + 6.96728i) q^{49} +(-2.18813 + 8.16621i) q^{53} +(0.665917 + 0.273617i) q^{55} +(-6.20011 - 10.7389i) q^{59} +(-4.19920 + 7.27323i) q^{61} +(-9.61524 - 1.23808i) q^{65} +(-1.54517 + 5.76666i) q^{67} +1.74397i q^{71} +(-14.4421 - 3.86976i) q^{73} +(-0.832514 - 0.180436i) q^{77} +(-0.747636 - 0.431648i) q^{79} +(10.4381 + 10.4381i) q^{83} +(-6.67075 - 15.9761i) q^{85} +(3.91069 - 6.77352i) q^{89} +(11.4574 - 0.554564i) q^{91} +(-2.29047 - 17.0239i) q^{95} +(5.08584 + 5.08584i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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
$5$	1.36627	+	1.77012i	0.611013	+	0.791620i
$5$	1.36627	+	1.77012i	0.611013	+	0.791620i
$6$		0			0
$7$	−1.95909	−	1.77819i	−0.740465	−	0.672094i
$7$	−1.95909	−	1.77819i	−0.740465	−	0.672094i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.278831	−	0.160983i	0.0840707	−	0.0485383i	−0.457375	−	0.889274i	$-0.651210\pi$
$11$	0.278831	−	0.160983i	0.0840707	−	0.0485383i	0.541446	+	0.840736i	$0.317877\pi$
$12$		0			0
$13$	−3.06571	+	3.06571i	−0.850275	+	0.850275i	−0.990167	−	0.139892i	$-0.955324\pi$
$13$	−3.06571	+	3.06571i	−0.850275	+	0.850275i	0.139892	+	0.990167i	$0.455324\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.47871	−	2.00391i	−1.81385	−	0.486020i	−0.817857	−	0.575422i	$-0.804838\pi$
$17$	−7.47871	−	2.00391i	−1.81385	−	0.486020i	−0.995996	+	0.0894013i	$0.971505\pi$
$18$		0			0
$19$	−6.65273	−	3.84096i	−1.52624	−	0.881176i	−0.999515	−	0.0311416i	$-0.990086\pi$
$19$	−6.65273	−	3.84096i	−1.52624	−	0.881176i	−0.526727	−	0.850035i	$-0.676581\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.170057	−	0.0455667i	0.0354594	−	0.00950131i	−0.241046	−	0.970514i	$-0.577490\pi$
$23$	0.170057	−	0.0455667i	0.0354594	−	0.00950131i	0.276505	+	0.961012i	$0.410824\pi$
$24$		0			0
$25$	−1.26663	+	4.83691i	−0.253325	+	0.967381i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.35013			0.622103			0.311052	−	0.950393i	$-0.399319\pi$
$29$	3.35013			0.622103			0.311052	+	0.950393i	$0.399319\pi$
$30$		0			0
$31$	3.49948	+	6.06127i	0.628525	+	1.08864i	0.987848	+	0.155424i	$0.0496743\pi$
$31$	3.49948	+	6.06127i	0.628525	+	1.08864i	−0.359323	+	0.933213i	$0.616992\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.470975	−	5.89730i	0.0796093	−	0.996826i
$36$		0			0
$37$	−6.27756	+	1.68207i	−1.03202	+	0.276530i	−0.734804	−	0.678279i	$-0.762726\pi$
$37$	−6.27756	+	1.68207i	−1.03202	+	0.276530i	−0.297220	+	0.954809i	$0.596059\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	9.24208i		−	1.44337i	−0.692221	−	0.721686i	$-0.743368\pi$
$41$		−	9.24208i		−	1.44337i	0.692221	−	0.721686i	$-0.256632\pi$
$42$		0			0
$43$	3.35424	−	3.35424i	0.511517	−	0.511517i	−0.403474	−	0.914991i	$-0.632197\pi$
$43$	3.35424	−	3.35424i	0.511517	−	0.511517i	0.914991	+	0.403474i	$0.132197\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.48099	−	5.52713i	−0.216024	−	0.806214i	−0.985803	−	0.167904i	$-0.946300\pi$
$47$	−1.48099	−	5.52713i	−0.216024	−	0.806214i	0.769779	−	0.638311i	$-0.220366\pi$
$48$		0			0
$49$	0.676046	+	6.96728i	0.0965780	+	0.995325i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.18813	+	8.16621i	−0.300563	+	1.12172i	0.636135	+	0.771578i	$0.280532\pi$
$53$	−2.18813	+	8.16621i	−0.300563	+	1.12172i	−0.936698	+	0.350138i	$0.886135\pi$
$54$		0			0
$55$	0.665917	+	0.273617i	0.0897922	+	0.0368946i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.20011	−	10.7389i	−0.807186	−	1.39809i	−0.914806	−	0.403894i	$-0.867656\pi$
$59$	−6.20011	−	10.7389i	−0.807186	−	1.39809i	0.107620	−	0.994192i	$-0.465677\pi$
$60$		0			0
$61$	−4.19920	+	7.27323i	−0.537653	+	0.931242i	0.461377	+	0.887204i	$0.347356\pi$
$61$	−4.19920	+	7.27323i	−0.537653	+	0.931242i	−0.999030	+	0.0440377i	$0.985978\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.61524	−	1.23808i	−1.19262	−	0.153565i
$66$		0			0
$67$	−1.54517	+	5.76666i	−0.188773	+	0.704509i	0.805019	+	0.593250i	$0.202155\pi$
$67$	−1.54517	+	5.76666i	−0.188773	+	0.704509i	−0.993791	+	0.111260i	$0.964511\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.74397i			0.206971i	0.994631	+	0.103485i	$0.0329995\pi$
$71$			1.74397i			0.206971i	−0.994631	+	0.103485i	$0.967000\pi$
$72$		0			0
$73$	−14.4421	−	3.86976i	−1.69032	−	0.452921i	−0.719850	−	0.694129i	$-0.755790\pi$
$73$	−14.4421	−	3.86976i	−1.69032	−	0.452921i	−0.970473	+	0.241208i	$0.922456\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.832514	−	0.180436i	−0.0948737	−	0.0205626i
$78$		0			0
$79$	−0.747636	−	0.431648i	−0.0841157	−	0.0485642i	0.457352	−	0.889286i	$-0.348798\pi$
$79$	−0.747636	−	0.431648i	−0.0841157	−	0.0485642i	−0.541468	+	0.840721i	$0.682131\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	10.4381	+	10.4381i	1.14573	+	1.14573i	0.987383	+	0.158352i	$0.0506181\pi$
$83$	10.4381	+	10.4381i	1.14573	+	1.14573i	0.158352	+	0.987383i	$0.449382\pi$
$84$		0			0
$85$	−6.67075	−	15.9761i	−0.723545	−	1.73285i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.91069	−	6.77352i	0.414533	−	0.717992i	−0.580847	−	0.814013i	$-0.697278\pi$
$89$	3.91069	−	6.77352i	0.414533	−	0.717992i	0.995379	+	0.0960214i	$0.0306117\pi$
$90$		0			0
$91$	11.4574	−	0.554564i	1.20106	−	0.0581341i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.29047	−	17.0239i	−0.234997	−	1.74661i
$96$		0			0
$97$	5.08584	+	5.08584i	0.516389	+	0.516389i	0.916477	−	0.400088i	$-0.131020\pi$
$97$	5.08584	+	5.08584i	0.516389	+	0.516389i	−0.400088	+	0.916477i	$0.631020\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.1209	−	5.84333i	1.00707	−	0.581433i	0.0967388	−	0.995310i	$-0.469159\pi$
$101$	10.1209	−	5.84333i	1.00707	−	0.581433i	0.910333	+	0.413877i	$0.135826\pi$
$102$		0			0
$103$	−3.20407	−	11.9578i	−0.315707	−	1.17823i	−0.923330	−	0.384008i	$-0.874544\pi$
$103$	−3.20407	−	11.9578i	−0.315707	−	1.17823i	0.607623	−	0.794225i	$-0.292123\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.21078	+	11.9828i	0.310398	+	1.15842i	0.928198	+	0.372086i	$0.121357\pi$
$107$	3.21078	+	11.9828i	0.310398	+	1.15842i	−0.617800	+	0.786335i	$0.711976\pi$
$108$		0			0
$109$	−5.49933	+	3.17504i	−0.526741	+	0.304114i	−0.739688	−	0.672950i	$-0.765027\pi$
$109$	−5.49933	+	3.17504i	−0.526741	+	0.304114i	0.212948	+	0.977064i	$0.431694\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.24152	−	1.24152i	−0.116792	−	0.116792i	0.646295	−	0.763088i	$-0.276317\pi$
$113$	−1.24152	−	1.24152i	−0.116792	−	0.116792i	−0.763088	+	0.646295i	$0.776317\pi$
$114$		0			0
$115$	0.313002	+	0.238765i	0.0291876	+	0.0222649i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.0881	+	17.2244i	1.01644	+	1.57896i
$120$		0			0
$121$	−5.44817	+	9.43651i	−0.495288	+	0.857864i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.2924	+	4.36643i	−0.920584	+	0.390546i
$126$		0			0
$127$	−6.87309	−	6.87309i	−0.609888	−	0.609888i	0.333029	−	0.942917i	$-0.391929\pi$
$127$	−6.87309	−	6.87309i	−0.609888	−	0.609888i	−0.942917	+	0.333029i	$0.891929\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.36666	−	4.25314i	−0.643628	−	0.371599i	0.142383	−	0.989812i	$-0.454524\pi$
$131$	−7.36666	−	4.25314i	−0.643628	−	0.371599i	−0.786011	+	0.618213i	$0.787857\pi$
$132$		0			0
$133$	6.20332	+	19.3546i	0.537896	+	1.67826i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.0595	−	3.23133i	−1.03031	−	0.276071i	−0.296219	−	0.955120i	$-0.595726\pi$
$137$	−12.0595	−	3.23133i	−1.03031	−	0.276071i	−0.734093	+	0.679049i	$0.762392\pi$
$138$		0			0
$139$			1.37920i			0.116982i	0.998288	+	0.0584909i	$0.0186289\pi$
$139$			1.37920i			0.116982i	−0.998288	+	0.0584909i	$0.981371\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.361287	+	1.34834i	−0.0302124	+	0.112754i
$144$		0			0
$145$	4.57717	+	5.93012i	0.380113	+	0.492470i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.85741	+	6.68124i	−0.316012	+	0.547348i	−0.979652	−	0.200703i	$-0.935677\pi$
$149$	−3.85741	+	6.68124i	−0.316012	+	0.547348i	0.663640	+	0.748052i	$0.269011\pi$
$150$		0			0
$151$	−6.42732	−	11.1324i	−0.523048	−	0.905946i	−0.999640	−	0.0268213i	$-0.991461\pi$
$151$	−6.42732	−	11.1324i	−0.523048	−	0.905946i	0.476592	−	0.879124i	$-0.341872\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.94794	+	14.4758i	−0.477750	+	1.16272i
$156$		0			0
$157$	1.35285	−	5.04892i	0.107969	−	0.402947i	−0.890696	−	0.454600i	$-0.849782\pi$
$157$	1.35285	−	5.04892i	0.107969	−	0.402947i	0.998665	+	0.0516527i	$0.0164489\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.414183	−	0.213126i	−0.0326422	−	0.0167967i
$162$		0			0
$163$	1.70181	+	6.35124i	0.133296	+	0.497468i	0.999999	−	0.00135680i	$-0.000431884\pi$
$163$	1.70181	+	6.35124i	0.133296	+	0.497468i	−0.866703	+	0.498825i	$0.833765\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.229235	−	0.229235i	0.0177387	−	0.0177387i	−0.698182	−	0.715921i	$-0.746007\pi$
$167$	0.229235	−	0.229235i	0.0177387	−	0.0177387i	0.715921	+	0.698182i	$0.246007\pi$
$168$		0			0
$169$		−	5.79715i		−	0.445935i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.591523	−	0.158498i	0.0449726	−	0.0120504i	−0.236263	−	0.971689i	$-0.575923\pi$
$173$	0.591523	−	0.158498i	0.0449726	−	0.0120504i	0.281235	+	0.959639i	$0.409256\pi$
$174$		0			0
$175$	11.0824	−	7.22361i	0.837750	−	0.546054i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.4705	+	19.8674i	0.857342	+	1.48496i	0.874455	+	0.485107i	$0.161219\pi$
$179$	11.4705	+	19.8674i	0.857342	+	1.48496i	−0.0171129	+	0.999854i	$0.505447\pi$
$180$		0			0
$181$	10.2071			0.758684			0.379342	−	0.925256i	$-0.376150\pi$
$181$	10.2071			0.758684			0.379342	+	0.925256i	$0.376150\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.5543	−	8.81386i	−0.849488	−	0.648008i
$186$		0			0
$187$	−2.40789	+	0.645193i	−0.176082	+	0.0471812i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.68304	+	3.28111i	0.411210	+	0.237412i	0.691310	−	0.722559i	$-0.257034\pi$
$191$	5.68304	+	3.28111i	0.411210	+	0.237412i	−0.280099	+	0.959971i	$0.590367\pi$
$192$		0			0
$193$	−1.31063	−	0.351181i	−0.0943409	−	0.0252786i	0.211340	−	0.977413i	$-0.432217\pi$
$193$	−1.31063	−	0.351181i	−0.0943409	−	0.0252786i	−0.305681	+	0.952134i	$0.598884\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.1064	−	17.1064i	1.21878	−	1.21878i	0.250721	−	0.968059i	$-0.419332\pi$
$197$	17.1064	−	17.1064i	1.21878	−	1.21878i	0.968059	−	0.250721i	$-0.0806675\pi$
$198$		0			0
$199$	−19.5841	+	11.3069i	−1.38828	+	0.801526i	−0.993122	−	0.117086i	$-0.962645\pi$
$199$	−19.5841	+	11.3069i	−1.38828	+	0.801526i	−0.395161	+	0.918612i	$0.629311\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.56319	−	5.95718i	−0.460646	−	0.418112i
$204$		0			0
$205$	16.3596	−	12.6272i	1.14260	−	0.881919i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.47332			−0.171083
$210$		0			0
$211$	24.2008			1.66605			0.833025	−	0.553236i	$-0.186607\pi$
$211$	24.2008			1.66605			0.833025	+	0.553236i	$0.186607\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	10.5202	+	1.35461i	0.717471	+	0.0923834i
$216$		0			0
$217$	3.92234	−	18.0973i	0.266266	−	1.22853i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	29.0710	−	16.7841i	1.95552	−	1.12902i
$222$		0			0
$223$	−5.12211	+	5.12211i	−0.343002	+	0.343002i	−0.857495	−	0.514493i	$-0.827980\pi$
$223$	−5.12211	+	5.12211i	−0.343002	+	0.343002i	0.514493	+	0.857495i	$0.327980\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.3782	−	3.04878i	−0.755199	−	0.202355i	−0.139376	−	0.990240i	$-0.544510\pi$
$227$	−11.3782	−	3.04878i	−0.755199	−	0.202355i	−0.615823	+	0.787885i	$0.711176\pi$
$228$		0			0
$229$	1.80857	+	1.04418i	0.119514	+	0.0690014i	0.558565	−	0.829461i	$-0.311352\pi$
$229$	1.80857	+	1.04418i	0.119514	+	0.0690014i	−0.439051	+	0.898462i	$0.644685\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.3691	+	2.77840i	−0.679305	+	0.182019i	−0.581943	−	0.813230i	$-0.697707\pi$
$233$	−10.3691	+	2.77840i	−0.679305	+	0.182019i	−0.0973625	+	0.995249i	$0.531041\pi$
$234$		0			0
$235$	7.76023	−	10.1731i	0.506222	−	0.663617i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	26.0584			1.68558			0.842788	−	0.538246i	$-0.180913\pi$
$239$	26.0584			1.68558			0.842788	+	0.538246i	$0.180913\pi$
$240$		0			0
$241$	4.48517	+	7.76855i	0.288915	+	0.500416i	0.973551	−	0.228469i	$-0.0733721\pi$
$241$	4.48517	+	7.76855i	0.288915	+	0.500416i	−0.684636	+	0.728885i	$0.740039\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.4092	+	10.7158i	−0.728909	+	0.684610i
$246$		0			0
$247$	32.1706	−	8.62009i	2.04697	−	0.548483i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	14.5007i		−	0.915278i	−0.889138	−	0.457639i	$-0.848695\pi$
$251$		−	14.5007i		−	0.915278i	0.889138	−	0.457639i	$-0.151305\pi$
$252$		0			0
$253$	0.0400817	−	0.0400817i	0.00251992	−	0.00251992i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.59463	+	28.3436i	0.473740	+	1.76802i	0.626147	+	0.779705i	$0.284631\pi$
$257$	7.59463	+	28.3436i	0.473740	+	1.76802i	−0.152407	+	0.988318i	$0.548703\pi$
$258$		0			0
$259$	15.2893	+	7.86741i	0.950033	+	0.488857i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.27191	+	4.74681i	−0.0784290	+	0.292701i	−0.993989	−	0.109480i	$-0.965081\pi$
$263$	−1.27191	+	4.74681i	−0.0784290	+	0.292701i	0.915560	+	0.402182i	$0.131748\pi$
$264$		0			0
$265$	−17.4447	+	7.28399i	−1.07162	+	0.447452i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.35997	+	12.7478i	0.448745	+	0.777249i	0.998305	−	0.0582054i	$-0.0185378\pi$
$269$	7.35997	+	12.7478i	0.448745	+	0.777249i	−0.549560	+	0.835454i	$0.685204\pi$
$270$		0			0
$271$	10.3860	−	17.9890i	0.630902	−	1.09275i	−0.356466	−	0.934308i	$-0.616018\pi$
$271$	10.3860	−	17.9890i	0.630902	−	1.09275i	0.987368	−	0.158446i	$-0.0506482\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.425486	+	1.55258i	0.0256578	+	0.0936244i
$276$		0			0
$277$	3.82780	−	14.2855i	0.229990	−	0.858335i	−0.750353	−	0.661037i	$-0.770117\pi$
$277$	3.82780	−	14.2855i	0.229990	−	0.858335i	0.980344	−	0.197298i	$-0.0632167\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	4.15459i		−	0.247842i	−0.992292	−	0.123921i	$-0.960453\pi$
$281$		−	4.15459i		−	0.247842i	0.992292	−	0.123921i	$-0.0395470\pi$
$282$		0			0
$283$	−8.73826	−	2.34141i	−0.519435	−	0.139182i	−0.0104300	−	0.999946i	$-0.503320\pi$
$283$	−8.73826	−	2.34141i	−0.519435	−	0.139182i	−0.509005	+	0.860763i	$0.669987\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−16.4342	+	18.1060i	−0.970082	+	1.06877i
$288$		0			0
$289$	37.1929	+	21.4734i	2.18782	+	1.26314i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.70315	−	8.70315i	−0.508443	−	0.508443i	0.405605	−	0.914048i	$-0.367061\pi$
$293$	−8.70315	−	8.70315i	−0.508443	−	0.508443i	−0.914048	+	0.405605i	$0.867061\pi$
$294$		0			0
$295$	10.5381	−	25.6471i	0.613552	−	1.49323i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.381652	+	0.661040i	−0.0220715	+	0.0382289i
$300$		0			0
$301$	−12.5357	+	0.606757i	−0.722548	+	0.0349729i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−18.6117	+	2.50410i	−1.06570	+	0.143384i
$306$		0			0
$307$	−4.91008	−	4.91008i	−0.280233	−	0.280233i	0.552969	−	0.833202i	$-0.313495\pi$
$307$	−4.91008	−	4.91008i	−0.280233	−	0.280233i	−0.833202	+	0.552969i	$0.813495\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	25.7894	−	14.8895i	1.46238	−	0.844308i	0.463263	−	0.886221i	$-0.346678\pi$
$311$	25.7894	−	14.8895i	1.46238	−	0.844308i	0.999121	+	0.0419126i	$0.0133451\pi$
$312$		0			0
$313$	−3.75297	−	14.0063i	−0.212130	−	0.791681i	−0.987157	−	0.159753i	$-0.948930\pi$
$313$	−3.75297	−	14.0063i	−0.212130	−	0.791681i	0.775027	−	0.631928i	$-0.217736\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.43868	+	5.36924i	0.0808046	+	0.301567i	0.994487	−	0.104863i	$-0.0334403\pi$
$317$	1.43868	+	5.36924i	0.0808046	+	0.301567i	−0.913682	+	0.406430i	$0.866774\pi$
$318$		0			0
$319$	0.934120	−	0.539314i	0.0523007	−	0.0301958i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	42.0569	+	42.0569i	2.34011	+	2.34011i
$324$		0			0
$325$	−10.9454	−	18.7117i	−0.607144	−	1.03794i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.92692	+	13.4616i	−0.381894	+	0.742163i
$330$		0			0
$331$	0.770935	−	1.33530i	0.0423744	−	0.0733946i	−0.844060	−	0.536248i	$-0.819841\pi$
$331$	0.770935	−	1.33530i	0.0423744	−	0.0733946i	0.886435	+	0.462854i	$0.153174\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.3188	+	5.14366i	−0.673047	+	0.281028i
$336$		0			0
$337$	−0.152014	−	0.152014i	−0.00828071	−	0.00828071i	0.702954	−	0.711235i	$-0.251864\pi$
$337$	−0.152014	−	0.152014i	−0.00828071	−	0.00828071i	−0.711235	+	0.702954i	$0.751864\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.95153	+	1.12671i	0.105681	+	0.0610150i
$342$		0			0
$343$	11.0647	−	14.8516i	0.597440	−	0.801914i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.02782	+	1.34720i	0.269908	+	0.0723215i	0.391234	−	0.920291i	$-0.372048\pi$
$347$	5.02782	+	1.34720i	0.269908	+	0.0723215i	−0.121327	+	0.992613i	$0.538715\pi$
$348$		0			0
$349$			14.7301i			0.788482i	0.919007	+	0.394241i	$0.128992\pi$
$349$			14.7301i			0.788482i	−0.919007	+	0.394241i	$0.871008\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.806987	+	3.01172i	−0.0429516	+	0.160298i	−0.984071	−	0.177778i	$-0.943109\pi$
$353$	−0.806987	+	3.01172i	−0.0429516	+	0.160298i	0.941119	+	0.338075i	$0.109776\pi$
$354$		0			0
$355$	−3.08703	+	2.38273i	−0.163842	+	0.126462i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.879880	+	1.52400i	−0.0464383	+	0.0804335i	−0.888310	−	0.459244i	$-0.848120\pi$
$359$	−0.879880	+	1.52400i	−0.0464383	+	0.0804335i	0.841872	+	0.539677i	$0.181454\pi$
$360$		0			0
$361$	20.0059	+	34.6513i	1.05294	+	1.82375i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.8819	−	30.8514i	−0.674269	−	1.61484i
$366$		0			0
$367$	−2.56464	+	9.57136i	−0.133873	+	0.499621i	−1.00000		0.000203056i	$-0.999935\pi$
$367$	−2.56464	+	9.57136i	−0.133873	+	0.499621i	0.866127	+	0.499824i	$0.166602\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.8079	−	12.1074i	0.976455	−	0.628585i
$372$		0			0
$373$	6.40047	+	23.8869i	0.331404	+	1.23682i	0.907716	+	0.419585i	$0.137825\pi$
$373$	6.40047	+	23.8869i	0.331404	+	1.23682i	−0.576312	+	0.817230i	$0.695509\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.2705	+	10.2705i	−0.528959	+	0.528959i
$378$		0			0
$379$		−	34.8419i		−	1.78971i	−0.446357	−	0.894855i	$-0.647279\pi$
$379$		−	34.8419i		−	1.78971i	0.446357	−	0.894855i	$-0.352721\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.14784	−	0.575511i	0.109749	−	0.0294072i	−0.203526	−	0.979069i	$-0.565240\pi$
$383$	2.14784	−	0.575511i	0.109749	−	0.0294072i	0.313276	+	0.949662i	$0.398574\pi$
$384$		0			0
$385$	−0.818044	−	1.72017i	−0.0416914	−	0.0876680i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.01837	−	12.1562i	−0.355845	−	0.616342i	0.631417	−	0.775444i	$-0.282474\pi$
$389$	−7.01837	−	12.1562i	−0.355845	−	0.616342i	−0.987262	+	0.159101i	$0.949140\pi$
$390$		0			0
$391$	−1.36312			−0.0689359
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.257404	−	1.91315i	−0.0129514	−	0.0962611i
$396$		0			0
$397$	−19.1356	+	5.12736i	−0.960387	+	0.257335i	−0.704764	−	0.709442i	$-0.748947\pi$
$397$	−19.1356	+	5.12736i	−0.960387	+	0.257335i	−0.255623	+	0.966777i	$0.582281\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.14707	−	0.662260i	−0.0572818	−	0.0330717i	0.471086	−	0.882088i	$-0.343862\pi$
$401$	−1.14707	−	0.662260i	−0.0572818	−	0.0330717i	−0.528367	+	0.849016i	$0.677196\pi$
$402$		0			0
$403$	−29.3105	−	7.85372i	−1.46006	−	0.391222i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.47959	+	1.47959i	−0.0733407	+	0.0733407i
$408$		0			0
$409$	−26.0613	+	15.0465i	−1.28865	+	0.744001i	−0.978413	−	0.206659i	$-0.933741\pi$
$409$	−26.0613	+	15.0465i	−1.28865	+	0.744001i	−0.310234	+	0.950660i	$0.600408\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.94931	+	32.0635i	−0.341953	+	1.57774i
$414$		0			0
$415$	−4.21543	+	32.7380i	−0.206928	+	1.60705i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−22.4361			−1.09608			−0.548039	−	0.836453i	$-0.684625\pi$
$419$	−22.4361			−1.09608			−0.548039	+	0.836453i	$0.684625\pi$
$420$		0			0
$421$	−25.1845			−1.22742			−0.613708	−	0.789533i	$-0.710323\pi$
$421$	−25.1845			−1.22742			−0.613708	+	0.789533i	$0.710323\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	19.1655	−	33.6356i	0.929662	−	1.63157i
$426$		0			0
$427$	21.1598	−	6.78190i	1.02400	−	0.328199i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−25.8306	+	14.9133i	−1.24422	+	0.718348i	−0.969950	−	0.243306i	$-0.921768\pi$
$431$	−25.8306	+	14.9133i	−1.24422	+	0.718348i	−0.274266	+	0.961654i	$0.588435\pi$
$432$		0			0
$433$	−12.5115	+	12.5115i	−0.601263	+	0.601263i	−0.940648	−	0.339385i	$-0.889781\pi$
$433$	−12.5115	+	12.5115i	−0.601263	+	0.601263i	0.339385	+	0.940648i	$0.389781\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.30636	−	0.350039i	−0.0624919	−	0.0167447i
$438$		0			0
$439$	−1.53770	−	0.887790i	−0.0733903	−	0.0423719i	0.462856	−	0.886434i	$-0.346825\pi$
$439$	−1.53770	−	0.887790i	−0.0733903	−	0.0423719i	−0.536246	+	0.844062i	$0.680158\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−17.4352	+	4.67175i	−0.828371	+	0.221961i	−0.648003	−	0.761638i	$-0.724396\pi$
$443$	−17.4352	+	4.67175i	−0.828371	+	0.221961i	−0.180368	+	0.983599i	$0.557729\pi$
$444$		0			0
$445$	17.3330	−	2.33206i	0.821662	−	0.110550i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.668727			0.0315592			0.0157796	−	0.999875i	$-0.494977\pi$
$449$	0.668727			0.0315592			0.0157796	+	0.999875i	$0.494977\pi$
$450$		0			0
$451$	−1.48782	−	2.57698i	−0.0700587	−	0.121345i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	16.6355	+	19.5233i	0.779886	+	0.915266i
$456$		0			0
$457$	0.194824	−	0.0522029i	0.00911347	−	0.00244195i	−0.254259	−	0.967136i	$-0.581832\pi$
$457$	0.194824	−	0.0522029i	0.00911347	−	0.00244195i	0.263373	+	0.964694i	$0.415165\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			11.3093i			0.526728i	0.964697	+	0.263364i	$0.0848320\pi$
$461$			11.3093i			0.526728i	−0.964697	+	0.263364i	$0.915168\pi$
$462$		0			0
$463$	1.50277	−	1.50277i	0.0698395	−	0.0698395i	−0.671324	−	0.741164i	$-0.734274\pi$
$463$	1.50277	−	1.50277i	0.0698395	−	0.0698395i	0.741164	+	0.671324i	$0.234274\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.30522	−	19.7994i	−0.245496	−	0.916205i	−0.973133	−	0.230242i	$-0.926048\pi$
$467$	−5.30522	−	19.7994i	−0.245496	−	0.916205i	0.727637	−	0.685962i	$-0.240619\pi$
$468$		0			0
$469$	13.2814	−	8.54977i	0.613277	−	0.394792i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.395290	−	1.47524i	0.0181755	−	0.0678317i
$474$		0			0
$475$	27.0049	−	27.3136i	1.23907	−	1.25323i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.8722	+	20.5632i	0.542453	+	0.939557i	0.998762	+	0.0497352i	$0.0158378\pi$
$479$	11.8722	+	20.5632i	0.542453	+	0.939557i	−0.456309	+	0.889821i	$0.650829\pi$
$480$		0			0
$481$	14.0884	−	24.4019i	0.642378	−	1.11263i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.05391	+	15.9512i	−0.0932634	+	0.724305i
$486$		0			0
$487$	3.54832	−	13.2425i	0.160790	−	0.600075i	−0.837750	−	0.546054i	$-0.816129\pi$
$487$	3.54832	−	13.2425i	0.160790	−	0.600075i	0.998540	−	0.0540215i	$-0.0172040\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	12.7800i		−	0.576751i	−0.957517	−	0.288376i	$-0.906885\pi$
$491$		−	12.7800i		−	0.576751i	0.957517	−	0.288376i	$-0.0931152\pi$
$492$		0			0
$493$	−25.0546	−	6.71337i	−1.12840	−	0.302355i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.10112	−	3.41659i	0.139104	−	0.153255i
$498$		0			0
$499$	−18.2619	−	10.5435i	−0.817516	−	0.471993i	0.0320430	−	0.999486i	$-0.489799\pi$
$499$	−18.2619	−	10.5435i	−0.817516	−	0.471993i	−0.849559	+	0.527493i	$0.823132\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.45863	−	2.45863i	−0.109625	−	0.109625i	0.650167	−	0.759791i	$-0.274699\pi$
$503$	−2.45863	−	2.45863i	−0.109625	−	0.109625i	−0.759791	+	0.650167i	$0.774699\pi$
$504$		0			0
$505$	24.1713	+	9.93170i	1.07561	+	0.441955i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	13.4216	−	23.2468i	0.594900	−	1.03040i	−0.398661	−	0.917098i	$-0.630525\pi$
$509$	13.4216	−	23.2468i	0.594900	−	1.03040i	0.993561	−	0.113298i	$-0.0361416\pi$
$510$		0			0
$511$	21.4122	+	33.2621i	0.947221	+	1.47143i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.7890	−	22.0091i	0.739812	−	0.969836i
$516$		0			0
$517$	−1.30272	−	1.30272i	−0.0572936	−	0.0572936i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.4336	−	6.60117i	0.500913	−	0.289202i	−0.228177	−	0.973620i	$-0.573277\pi$
$521$	11.4336	−	6.60117i	0.500913	−	0.289202i	0.729091	+	0.684417i	$0.239943\pi$
$522$		0			0
$523$	3.32822	+	12.4211i	0.145533	+	0.543136i	0.999731	+	0.0231888i	$0.00738189\pi$
$523$	3.32822	+	12.4211i	0.145533	+	0.543136i	−0.854198	+	0.519948i	$0.825951\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.0253	−	52.3431i	−0.610952	−	2.28010i
$528$		0			0
$529$	−19.8917	+	11.4845i	−0.864858	+	0.499326i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	28.3335	+	28.3335i	1.22726	+	1.22726i
$534$		0			0
$535$	−16.8242	+	22.0552i	−0.727372	+	0.953528i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.31012	+	1.83386i	0.0564307	+	0.0789900i
$540$		0			0
$541$	3.92367	−	6.79600i	0.168692	−	0.292183i	−0.769268	−	0.638926i	$-0.779379\pi$
$541$	3.92367	−	6.79600i	0.168692	−	0.292183i	0.937960	+	0.346743i	$0.112712\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.1338	−	5.39650i	−0.562588	−	0.231161i
$546$		0			0
$547$	−8.08493	−	8.08493i	−0.345687	−	0.345687i	0.512813	−	0.858500i	$-0.328603\pi$
$547$	−8.08493	−	8.08493i	−0.345687	−	0.345687i	−0.858500	+	0.512813i	$0.828603\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−22.2875	−	12.8677i	−0.949480	−	0.548183i
$552$		0			0
$553$	0.697131	+	2.17508i	0.0296450	+	0.0924938i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.91997	+	0.514455i	0.0813518	+	0.0217982i	0.299265	−	0.954170i	$-0.403258\pi$
$557$	1.91997	+	0.514455i	0.0813518	+	0.0217982i	−0.217914	+	0.975968i	$0.569925\pi$
$558$		0			0
$559$			20.5663i			0.869860i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.5333	−	39.3107i	0.443925	−	1.65675i	−0.274835	−	0.961492i	$-0.588623\pi$
$563$	10.5333	−	39.3107i	0.443925	−	1.65675i	0.718759	−	0.695259i	$-0.244710\pi$
$564$		0			0
$565$	0.501387	−	3.89388i	0.0210935	−	0.163817i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.82483	−	3.16070i	0.0765009	−	0.132504i	−0.825237	−	0.564787i	$-0.808959\pi$
$569$	1.82483	−	3.16070i	0.0765009	−	0.132504i	0.901738	+	0.432283i	$0.142292\pi$
$570$		0			0
$571$	−2.55485	−	4.42512i	−0.106917	−	0.185186i	0.807603	−	0.589727i	$-0.200765\pi$
$571$	−2.55485	−	4.42512i	−0.106917	−	0.185186i	−0.914520	+	0.404541i	$0.867431\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.00500292	+	0.880266i	0.000208636	+	0.0367096i
$576$		0			0
$577$	−8.70185	+	32.4757i	−0.362263	+	1.35198i	0.508831	+	0.860866i	$0.330078\pi$
$577$	−8.70185	+	32.4757i	−0.362263	+	1.35198i	−0.871094	+	0.491116i	$0.836589\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.88818	−	39.0103i	−0.0783349	−	1.61842i
$582$		0			0
$583$	0.704504	+	2.62925i	0.0291776	+	0.108892i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.35665	+	3.35665i	−0.138544	+	0.138544i	−0.772977	−	0.634434i	$-0.781233\pi$
$587$	−3.35665	+	3.35665i	−0.138544	+	0.138544i	0.634434	+	0.772977i	$0.281233\pi$
$588$		0			0
$589$		−	53.7654i		−	2.21536i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−25.0849	+	6.72147i	−1.03011	+	0.276018i	−0.734010	−	0.679139i	$-0.762353\pi$
$593$	−25.0849	+	6.72147i	−1.03011	+	0.276018i	−0.296102	+	0.955156i	$0.595687\pi$
$594$		0			0
$595$	−15.3400	+	43.1604i	−0.628877	+	1.76940i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.3005	−	28.2332i	−0.666019	−	1.15358i	−0.979008	−	0.203821i	$-0.934664\pi$
$599$	−16.3005	−	28.2332i	−0.666019	−	1.15358i	0.312990	−	0.949757i	$-0.398670\pi$
$600$		0			0
$601$	14.8937			0.607525			0.303763	−	0.952748i	$-0.401757\pi$
$601$	14.8937			0.607525			0.303763	+	0.952748i	$0.401757\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.1474	+	3.24890i	−0.981730	+	0.132086i
$606$		0			0
$607$	−36.5614	+	9.79659i	−1.48398	+	0.397631i	−0.907699	−	0.419621i	$-0.862163\pi$
$607$	−36.5614	+	9.79659i	−1.48398	+	0.397631i	−0.576280	+	0.817252i	$0.695496\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	21.4848	+	12.4043i	0.869184	+	0.501824i
$612$		0			0
$613$	−10.2876	−	2.75655i	−0.415511	−	0.111336i	0.0450059	−	0.998987i	$-0.485669\pi$
$613$	−10.2876	−	2.75655i	−0.415511	−	0.111336i	−0.460517	+	0.887651i	$0.652336\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.06591	−	4.06591i	0.163687	−	0.163687i	−0.620511	−	0.784198i	$-0.713075\pi$
$617$	4.06591	−	4.06591i	0.163687	−	0.163687i	0.784198	+	0.620511i	$0.213075\pi$
$618$		0			0
$619$	−30.7260	+	17.7397i	−1.23498	+	0.713018i	−0.968064	−	0.250701i	$-0.919339\pi$
$619$	−30.7260	+	17.7397i	−1.23498	+	0.713018i	−0.266918	+	0.963719i	$0.586005\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−19.7060	+	6.31594i	−0.789505	+	0.253043i
$624$		0			0
$625$	−21.7913	−	12.2531i	−0.871653	−	0.490124i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	50.3187			2.00634
$630$		0			0
$631$	−1.55056			−0.0617269			−0.0308634	−	0.999524i	$-0.509826\pi$
$631$	−1.55056			−0.0617269			−0.0308634	+	0.999524i	$0.509826\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.77569	−	21.5566i	0.110150	−	0.855449i
$636$		0			0
$637$	−23.4322	−	19.2871i	−0.928418	−	0.764182i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.3821	+	10.6129i	−0.726051	+	0.419186i	−0.816976	−	0.576672i	$-0.804351\pi$
$641$	−18.3821	+	10.6129i	−0.726051	+	0.419186i	0.0909246	+	0.995858i	$0.471018\pi$
$642$		0			0
$643$	−10.5608	+	10.5608i	−0.416479	+	0.416479i	−0.883988	−	0.467509i	$-0.845151\pi$
$643$	−10.5608	+	10.5608i	−0.416479	+	0.416479i	0.467509	+	0.883988i	$0.345151\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−42.9849	−	11.5178i	−1.68991	−	0.452811i	−0.719545	−	0.694446i	$-0.755650\pi$
$647$	−42.9849	−	11.5178i	−1.68991	−	0.452811i	−0.970367	+	0.241635i	$0.922316\pi$
$648$		0			0
$649$	−3.45757	−	1.99623i	−0.135721	−	0.0783588i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15.8609	−	4.24992i	0.620686	−	0.166312i	0.0652462	−	0.997869i	$-0.479217\pi$
$653$	15.8609	−	4.24992i	0.620686	−	0.166312i	0.555439	+	0.831557i	$0.312550\pi$
$654$		0			0
$655$	−2.53627	−	18.8508i	−0.0991002	−	0.736560i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.66201			0.220561			0.110280	−	0.993901i	$-0.464825\pi$
$659$	5.66201			0.220561			0.110280	+	0.993901i	$0.464825\pi$
$660$		0			0
$661$	6.34525	+	10.9903i	0.246802	+	0.427473i	0.962637	−	0.270796i	$-0.0872870\pi$
$661$	6.34525	+	10.9903i	0.246802	+	0.427473i	−0.715835	+	0.698270i	$0.753954\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−25.7846	+	37.4242i	−0.999882	+	1.45125i
$666$		0			0
$667$	0.569713	−	0.152654i	0.0220594	−	0.00591080i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			2.70400i			0.104387i
$672$		0			0
$673$	8.99194	−	8.99194i	0.346614	−	0.346614i	−0.512233	−	0.858847i	$-0.671181\pi$
$673$	8.99194	−	8.99194i	0.346614	−	0.346614i	0.858847	+	0.512233i	$0.171181\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.6588	+	39.7793i	0.409652	+	1.52884i	0.795311	+	0.606202i	$0.207308\pi$
$677$	10.6588	+	39.7793i	0.409652	+	1.52884i	−0.385659	+	0.922642i	$0.626026\pi$
$678$		0			0
$679$	−0.919990	−	19.0072i	−0.0353060	−	0.729430i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.30499	−	12.3344i	0.126462	−	0.471963i	−0.873425	−	0.486958i	$-0.838107\pi$
$683$	3.30499	−	12.3344i	0.126462	−	0.471963i	0.999888	+	0.0149949i	$0.00477320\pi$
$684$		0			0
$685$	−10.7567	−	25.7616i	−0.410991	−	0.984299i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−18.3271	−	31.7434i	−0.698206	−	1.20933i
$690$		0			0
$691$	−18.0250	+	31.2202i	−0.685703	+	1.18767i	0.287512	+	0.957777i	$0.407172\pi$
$691$	−18.0250	+	31.2202i	−0.685703	+	1.18767i	−0.973215	+	0.229895i	$0.926162\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.44134	+	1.88435i	−0.0926052	+	0.0714775i
$696$		0			0
$697$	−18.5203	+	69.1188i	−0.701508	+	2.61806i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			6.11174i			0.230837i	0.993317	+	0.115419i	$0.0368210\pi$
$701$			6.11174i			0.230837i	−0.993317	+	0.115419i	$0.963179\pi$
$702$		0			0
$703$	48.2237	+	12.9215i	1.81879	+	0.487343i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.2184	−	6.54942i	−1.13648	−	0.246316i
$708$		0			0
$709$	18.3061	+	10.5691i	0.687502	+	0.396929i	0.802675	−	0.596416i	$-0.203409\pi$
$709$	18.3061	+	10.5691i	0.687502	+	0.396929i	−0.115174	+	0.993345i	$0.536743\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.871303	+	0.871303i	0.0326306	+	0.0326306i
$714$		0			0
$715$	−2.88034	+	1.20268i	−0.107719	+	0.0449775i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.43130	+	11.1393i	−0.239847	+	0.415428i	−0.960670	−	0.277692i	$-0.910431\pi$
$719$	−6.43130	+	11.1393i	−0.239847	+	0.415428i	0.720823	+	0.693119i	$0.243764\pi$
$720$		0			0
$721$	−14.9862	+	29.1238i	−0.558114	+	1.08463i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.24336	+	16.2043i	−0.157594	+	0.601811i
$726$		0			0
$727$	7.62693	+	7.62693i	0.282867	+	0.282867i	0.834251	−	0.551384i	$-0.185900\pi$
$727$	7.62693	+	7.62693i	0.282867	+	0.282867i	−0.551384	+	0.834251i	$0.685900\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−31.8070	+	18.3638i	−1.17642	+	0.679209i
$732$		0			0
$733$	−5.72503	−	21.3661i	−0.211459	−	0.789175i	−0.987383	−	0.158349i	$-0.949383\pi$
$733$	−5.72503	−	21.3661i	−0.211459	−	0.789175i	0.775924	−	0.630826i	$-0.217284\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.497493	+	1.85667i	0.0183254	+	0.0683913i
$738$		0			0
$739$	−22.3351	+	12.8952i	−0.821610	+	0.474357i	−0.850971	−	0.525212i	$-0.823986\pi$
$739$	−22.3351	+	12.8952i	−0.821610	+	0.474357i	0.0293614	+	0.999569i	$0.490653\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.8981	−	11.8981i	−0.436498	−	0.436498i	0.454334	−	0.890831i	$-0.349877\pi$
$743$	−11.8981	−	11.8981i	−0.436498	−	0.436498i	−0.890831	+	0.454334i	$0.849877\pi$
$744$		0			0
$745$	−17.0968	+	2.30028i	−0.626379	+	0.0842759i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.0176	−	29.1848i	0.548730	−	1.06639i
$750$		0			0
$751$	−7.47887	+	12.9538i	−0.272908	+	0.472690i	−0.969605	−	0.244675i	$-0.921319\pi$
$751$	−7.47887	+	12.9538i	−0.272908	+	0.472690i	0.696697	+	0.717365i	$0.254652\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10.9243	−	26.5870i	0.397576	−	0.967600i
$756$		0			0
$757$	0.791273	+	0.791273i	0.0287593	+	0.0287593i	0.721340	−	0.692581i	$-0.243526\pi$
$757$	0.791273	+	0.791273i	0.0287593	+	0.0287593i	−0.692581	+	0.721340i	$0.743526\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	31.6532	+	18.2750i	1.14743	+	0.662468i	0.948259	−	0.317497i	$-0.102842\pi$
$761$	31.6532	+	18.2750i	1.14743	+	0.662468i	0.199169	+	0.979965i	$0.436176\pi$
$762$		0			0
$763$	16.4195	+	3.55870i	0.594426	+	0.128834i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	51.9301	+	13.9146i	1.87509	+	0.502428i
$768$		0			0
$769$			5.20875i			0.187832i	0.995580	+	0.0939161i	$0.0299386\pi$
$769$			5.20875i			0.187832i	−0.995580	+	0.0939161i	$0.970061\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.08551	−	22.7114i	0.218881	−	0.816873i	−0.765884	−	0.642979i	$-0.777698\pi$
$773$	6.08551	−	22.7114i	0.218881	−	0.816873i	0.984764	−	0.173894i	$-0.0556351\pi$
$774$		0			0
$775$	−33.7503	+	9.24928i	−1.21235	+	0.332244i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−35.4985	+	61.4851i	−1.27186	+	2.20293i
$780$		0			0
$781$	0.280750	+	0.486272i	0.0100460	+	0.0174002i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.7855	−	4.50346i	0.384952	−	0.160735i
$786$		0			0
$787$	11.3116	−	42.2153i	0.403214	−	1.50481i	−0.404113	−	0.914709i	$-0.632420\pi$
$787$	11.3116	−	42.2153i	0.403214	−	1.50481i	0.807327	−	0.590105i	$-0.200914\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.224582	+	4.63991i	0.00798520	+	0.164976i
$792$		0			0
$793$	−9.42408	−	35.1712i	−0.334659	−	1.24896i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.15958	−	4.15958i	0.147340	−	0.147340i	−0.629589	−	0.776929i	$-0.716777\pi$
$797$	4.15958	−	4.15958i	0.147340	−	0.147340i	0.776929	+	0.629589i	$0.216777\pi$
$798$		0			0
$799$			44.3035i			1.56735i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.64988	+	1.24593i	−0.164091	+	0.0439680i
$804$		0			0
$805$	−0.188628	−	1.02434i	−0.00664826	−	0.0361032i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−20.9157	−	36.2270i	−0.735357	−	1.27368i	−0.954567	−	0.297997i	$-0.903681\pi$
$809$	−20.9157	−	36.2270i	−0.735357	−	1.27368i	0.219210	−	0.975678i	$-0.429652\pi$
$810$		0			0
$811$	−37.5510			−1.31860			−0.659298	−	0.751882i	$-0.729146\pi$
$811$	−37.5510			−1.31860			−0.659298	+	0.751882i	$0.729146\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.91731	+	11.6899i	−0.312360	+	0.409479i
$816$		0			0
$817$	−35.1984	+	9.43138i	−1.23144	+	0.329962i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−29.4988	−	17.0312i	−1.02952	−	0.594391i	−0.112670	−	0.993632i	$-0.535940\pi$
$821$	−29.4988	−	17.0312i	−1.02952	−	0.594391i	−0.916846	+	0.399241i	$0.869274\pi$
$822$		0			0
$823$	−7.35355	−	1.97038i	−0.256329	−	0.0686830i	0.128366	−	0.991727i	$-0.459027\pi$
$823$	−7.35355	−	1.97038i	−0.256329	−	0.0686830i	−0.384695	+	0.923044i	$0.625693\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.4533	−	13.4533i	0.467818	−	0.467818i	−0.433389	−	0.901207i	$-0.642682\pi$
$827$	13.4533	−	13.4533i	0.467818	−	0.467818i	0.901207	+	0.433389i	$0.142682\pi$
$828$		0			0
$829$	17.9305	−	10.3522i	0.622754	−	0.359547i	−0.155187	−	0.987885i	$-0.549598\pi$
$829$	17.9305	−	10.3522i	0.622754	−	0.359547i	0.777940	+	0.628338i	$0.216265\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.90587	−	53.4610i	0.308570	−	1.85231i
$834$		0			0
$835$	0.718968	+	0.0925763i	0.0248809	+	0.00320373i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.41181			−0.290408			−0.145204	−	0.989402i	$-0.546384\pi$
$839$	−8.41181			−0.290408			−0.145204	+	0.989402i	$0.546384\pi$
$840$		0			0
$841$	−17.7766			−0.612988
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.2616	−	7.92046i	0.353011	−	0.272472i
$846$		0			0
$847$	27.4534	−	8.79903i	0.943309	−	0.302338i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.990898	+	0.572095i	−0.0339675	+	0.0196112i
$852$		0			0
$853$	30.2271	−	30.2271i	1.03496	−	1.03496i	0.0355907	−	0.999366i	$-0.488669\pi$
$853$	30.2271	−	30.2271i	1.03496	−	1.03496i	0.999366	−	0.0355907i	$-0.0113313\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−32.3738	−	8.67454i	−1.10587	−	0.296317i	−0.340716	−	0.940166i	$-0.610670\pi$
$857$	−32.3738	−	8.67454i	−1.10587	−	0.296317i	−0.765152	+	0.643850i	$0.777336\pi$
$858$		0			0
$859$	−5.78830	−	3.34188i	−0.197494	−	0.114023i	0.397992	−	0.917389i	$-0.369707\pi$
$859$	−5.78830	−	3.34188i	−0.197494	−	0.114023i	−0.595486	+	0.803366i	$0.703041\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.6365	−	8.20902i	1.04288	−	0.279438i	0.303573	−	0.952808i	$-0.401821\pi$
$863$	30.6365	−	8.20902i	1.04288	−	0.279438i	0.739306	+	0.673370i	$0.235154\pi$
$864$		0			0
$865$	1.08874	+	0.830514i	0.0370182	+	0.0282383i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.277952			−0.00942889
$870$		0			0
$871$	−12.9419	−	22.4159i	−0.438518	−	0.759535i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	27.9282	+	9.74774i	0.944144	+	0.329534i
$876$		0			0
$877$	15.6314	−	4.18842i	0.527835	−	0.141433i	0.0149468	−	0.999888i	$-0.495242\pi$
$877$	15.6314	−	4.18842i	0.527835	−	0.141433i	0.512888	+	0.858455i	$0.328575\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			31.4844i			1.06073i	0.847768	+	0.530367i	$0.177946\pi$
$881$			31.4844i			1.06073i	−0.847768	+	0.530367i	$0.822054\pi$
$882$		0			0
$883$	14.3228	−	14.3228i	0.482001	−	0.482001i	−0.423769	−	0.905770i	$-0.639293\pi$
$883$	14.3228	−	14.3228i	0.482001	−	0.482001i	0.905770	+	0.423769i	$0.139293\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.261132	+	0.974559i	0.00876797	+	0.0327225i	0.970171	−	0.242421i	$-0.0779414\pi$
$887$	0.261132	+	0.974559i	0.00876797	+	0.0327225i	−0.961403	+	0.275143i	$0.911275\pi$
$888$		0			0
$889$	1.24329	+	25.6867i	0.0416986	+	0.861503i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−11.3768	+	42.4589i	−0.380711	+	1.42083i
$894$		0			0
$895$	−19.4959	+	47.4482i	−0.651677	+	1.58602i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.7237	+	20.3060i	0.391007	+	0.677245i
$900$		0			0
$901$	32.7288	−	56.6879i	1.09035	−	1.88855i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13.9456	+	18.0677i	0.463566	+	0.600590i
$906$		0			0
$907$	−2.97483	+	11.1022i	−0.0987776	+	0.368643i	−0.997565	−	0.0697415i	$-0.977783\pi$
$907$	−2.97483	+	11.1022i	−0.0987776	+	0.368643i	0.898787	+	0.438385i	$0.144449\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			44.1423i			1.46250i	0.682110	+	0.731249i	$0.261062\pi$
$911$			44.1423i			1.46250i	−0.682110	+	0.731249i	$0.738938\pi$
$912$		0			0
$913$	4.59084	+	1.23011i	0.151935	+	0.0407108i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.86901	+	21.4316i	0.226835	+	0.707735i
$918$		0			0
$919$	−44.0140	−	25.4115i	−1.45189	−	0.838248i	−0.453299	−	0.891359i	$-0.649753\pi$
$919$	−44.0140	−	25.4115i	−1.45189	−	0.838248i	−0.998589	+	0.0531110i	$0.983086\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.34650	−	5.34650i	−0.175982	−	0.175982i
$924$		0			0
$925$	−0.184680	−	32.4945i	−0.00607223	−	1.06841i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.6686	−	21.9426i	0.415643	−	0.719914i	−0.579853	−	0.814721i	$-0.696890\pi$
$929$	12.6686	−	21.9426i	0.415643	−	0.719914i	0.995496	+	0.0948069i	$0.0302234\pi$
$930$		0			0
$931$	22.2635	−	48.9481i	0.729656	−	1.60421i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.43189	−	3.38074i	−0.144938	−	0.110562i
$936$		0			0
$937$	27.2110	+	27.2110i	0.888943	+	0.888943i	0.994422	−	0.105478i	$-0.0336373\pi$
$937$	27.2110	+	27.2110i	0.888943	+	0.888943i	−0.105478	+	0.994422i	$0.533637\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.7628	−	17.7609i	1.00284	−	0.578990i	0.0937521	−	0.995596i	$-0.470114\pi$
$941$	30.7628	−	17.7609i	1.00284	−	0.578990i	0.909087	+	0.416606i	$0.136781\pi$
$942$		0			0
$943$	−0.421131	−	1.57168i	−0.0137139	−	0.0511810i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.279063	−	1.04148i	−0.00906831	−	0.0338434i	0.961243	−	0.275701i	$-0.0889100\pi$
$947$	−0.279063	−	1.04148i	−0.00906831	−	0.0338434i	−0.970312	+	0.241858i	$0.922243\pi$
$948$		0			0
$949$	56.1389	−	32.4118i	1.82235	−	1.05213i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−16.2557	−	16.2557i	−0.526573	−	0.526573i	0.392976	−	0.919549i	$-0.371446\pi$
$953$	−16.2557	−	16.2557i	−0.526573	−	0.526573i	−0.919549	+	0.392976i	$0.871446\pi$
$954$		0			0
$955$	1.95662	+	14.5425i	0.0633146	+	0.470585i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.8797	+	27.7746i	0.577364	+	0.896888i
$960$		0			0
$961$	−8.99270	+	15.5758i	−0.290087	+	0.502445i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.16903	−	2.79977i	−0.0376325	−	0.0901277i
$966$		0			0
$967$	35.0813	+	35.0813i	1.12814	+	1.12814i	0.990480	+	0.137658i	$0.0439576\pi$
$967$	35.0813	+	35.0813i	1.12814	+	1.12814i	0.137658	+	0.990480i	$0.456042\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−52.5751	−	30.3543i	−1.68722	−	0.974115i	−0.956635	−	0.291288i	$-0.905916\pi$
$971$	−52.5751	−	30.3543i	−1.68722	−	0.974115i	−0.730581	−	0.682826i	$-0.760751\pi$
$972$		0			0
$973$	2.45248	−	2.70196i	0.0786229	−	0.0866210i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.7582	+	8.24162i	0.984041	+	0.263673i	0.714745	−	0.699385i	$-0.246543\pi$
$977$	30.7582	+	8.24162i	0.984041	+	0.263673i	0.269295	+	0.963058i	$0.413209\pi$
$978$		0			0
$979$		−	2.51822i		−	0.0804828i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.83528	−	32.9737i	0.281802	−	1.05170i	−0.669343	−	0.742953i	$-0.733424\pi$
$983$	8.83528	−	32.9737i	0.281802	−	1.05170i	0.951145	−	0.308745i	$-0.0999089\pi$
$984$		0			0
$985$	53.6522	+	6.90840i	1.70950	+	0.220120i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.417571	−	0.723254i	0.0132780	−	0.0229981i
$990$		0			0
$991$	−15.8771	−	27.5000i	−0.504354	−	0.873566i	−0.999987	−	0.00503449i	$-0.998397\pi$
$991$	−15.8771	−	27.5000i	−0.504354	−	0.873566i	0.495634	−	0.868532i	$-0.334936\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−46.7717	−	19.2180i	−1.48276	−	0.609250i
$996$		0			0
$997$	14.2337	−	53.1208i	0.450785	−	1.68235i	−0.249409	−	0.968398i	$-0.580236\pi$
$997$	14.2337	−	53.1208i	0.450785	−	1.68235i	0.700193	−	0.713953i	$-0.253097\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.ej.a.737.12	yes	64
3.2	odd	2	inner	1260.2.ej.a.737.5	yes	64
5.3	odd	4	inner	1260.2.ej.a.233.15	yes	64
7.4	even	3	inner	1260.2.ej.a.557.2	yes	64
15.8	even	4	inner	1260.2.ej.a.233.2	yes	64
21.11	odd	6	inner	1260.2.ej.a.557.15	yes	64
35.18	odd	12	inner	1260.2.ej.a.53.5	✓	64
105.53	even	12	inner	1260.2.ej.a.53.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.5	✓	64	35.18	odd	12	inner
1260.2.ej.a.53.12	yes	64	105.53	even	12	inner
1260.2.ej.a.233.2	yes	64	15.8	even	4	inner
1260.2.ej.a.233.15	yes	64	5.3	odd	4	inner
1260.2.ej.a.557.2	yes	64	7.4	even	3	inner
1260.2.ej.a.557.15	yes	64	21.11	odd	6	inner
1260.2.ej.a.737.5	yes	64	3.2	odd	2	inner
1260.2.ej.a.737.12	yes	64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.ej (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36627 + 1.77012i) q^{5} +(-1.95909 - 1.77819i) q^{7} +O(q^{10})\)	\(q+(1.36627 + 1.77012i) q^{5} +(-1.95909 - 1.77819i) q^{7} +(0.278831 - 0.160983i) q^{11} +(-3.06571 + 3.06571i) q^{13} +(-7.47871 - 2.00391i) q^{17} +(-6.65273 - 3.84096i) q^{19} +(0.170057 - 0.0455667i) q^{23} +(-1.26663 + 4.83691i) q^{25} +3.35013 q^{29} +(3.49948 + 6.06127i) q^{31} +(0.470975 - 5.89730i) q^{35} +(-6.27756 + 1.68207i) q^{37} -9.24208i q^{41} +(3.35424 - 3.35424i) q^{43} +(-1.48099 - 5.52713i) q^{47} +(0.676046 + 6.96728i) q^{49} +(-2.18813 + 8.16621i) q^{53} +(0.665917 + 0.273617i) q^{55} +(-6.20011 - 10.7389i) q^{59} +(-4.19920 + 7.27323i) q^{61} +(-9.61524 - 1.23808i) q^{65} +(-1.54517 + 5.76666i) q^{67} +1.74397i q^{71} +(-14.4421 - 3.86976i) q^{73} +(-0.832514 - 0.180436i) q^{77} +(-0.747636 - 0.431648i) q^{79} +(10.4381 + 10.4381i) q^{83} +(-6.67075 - 15.9761i) q^{85} +(3.91069 - 6.77352i) q^{89} +(11.4574 - 0.554564i) q^{91} +(-2.29047 - 17.0239i) q^{95} +(5.08584 + 5.08584i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

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