LMFDB - Embedded newform 2268.2.t.b.2105.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1781,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("2268.1781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2105.3
Root			$-0.268067 - 1.71118i$ of defining polynomial
Character	$\chi$	$=$	2268.2105
Dual form			2268.2.t.b.1781.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.842869 + 1.45989i) q^{5} +(2.30301 - 1.30235i) q^{7} +O(q^{10})$	$q+(-0.842869 + 1.45989i) q^{5} +(2.30301 - 1.30235i) q^{7} +(-3.38216 + 1.95269i) q^{11} +6.05515i q^{13} +(-0.201244 - 0.348565i) q^{17} +(-0.145617 - 0.0840718i) q^{19} +(-7.69373 - 4.44198i) q^{23} +(1.07914 + 1.86913i) q^{25} -7.10580i q^{29} +(-5.44527 + 3.14383i) q^{31} +(-0.0398441 + 4.45986i) q^{35} +(3.13257 - 5.42578i) q^{37} -3.29414 q^{41} -3.60947 q^{43} +(-4.38482 + 7.59474i) q^{47} +(3.60775 - 5.99868i) q^{49} +(4.94628 - 2.85574i) q^{53} -6.58345i q^{55} +(-2.25163 - 3.89994i) q^{59} +(-4.43678 - 2.56157i) q^{61} +(-8.83986 - 5.10369i) q^{65} +(2.95521 + 5.11857i) q^{67} +11.4308i q^{71} +(-6.05559 + 3.49620i) q^{73} +(-5.24607 + 8.90184i) q^{77} +(-0.603968 + 1.04610i) q^{79} -0.362701 q^{83} +0.678488 q^{85} +(-1.38526 + 2.39934i) q^{89} +(7.88594 + 13.9451i) q^{91} +(0.245471 - 0.141723i) q^{95} -0.587643i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{7}+O(q^{10}) $ 16 * q + 2 * q^7	$ 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95}+O(q^{100}) $ 16 * q + 2 * q^7 + 6 * q^11 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^31 - 15 * q^35 + q^37 + 12 * q^41 + 4 * q^43 + 18 * q^47 - 8 * q^49 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - 48 * q^77 - q^79 - 12 * q^85 + 21 * q^89 + 9 * q^91 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$5$	−0.842869	+	1.45989i	−0.376942	+	0.652883i	−0.990616	−	0.136677i	$-0.956358\pi$
$5$	−0.842869	+	1.45989i	−0.376942	+	0.652883i	0.613673	+	0.789560i	$0.289691\pi$
$6$		0			0
$7$	2.30301	−	1.30235i	0.870458	−	0.492243i
$7$	2.30301	−	1.30235i	0.870458	−	0.492243i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.38216	+	1.95269i	−1.01976	+	0.588758i	−0.914034	−	0.405637i	$-0.867050\pi$
$11$	−3.38216	+	1.95269i	−1.01976	+	0.588758i	−0.105725	+	0.994395i	$0.533716\pi$
$12$		0			0
$13$			6.05515i			1.67940i	0.543054	+	0.839698i	$0.317268\pi$
$13$			6.05515i			1.67940i	−0.543054	+	0.839698i	$0.682732\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.201244	−	0.348565i	−0.0488088	−	0.0845393i	0.840589	−	0.541674i	$-0.182209\pi$
$17$	−0.201244	−	0.348565i	−0.0488088	−	0.0845393i	−0.889398	+	0.457134i	$0.848876\pi$
$18$		0			0
$19$	−0.145617	−	0.0840718i	−0.0334067	−	0.0192874i	0.483204	−	0.875508i	$-0.339473\pi$
$19$	−0.145617	−	0.0840718i	−0.0334067	−	0.0192874i	−0.516610	+	0.856221i	$0.672806\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.69373	−	4.44198i	−1.60425	−	0.926216i	−0.990623	−	0.136623i	$-0.956375\pi$
$23$	−7.69373	−	4.44198i	−1.60425	−	0.926216i	−0.613630	−	0.789593i	$-0.710291\pi$
$24$		0			0
$25$	1.07914	+	1.86913i	0.215829	+	0.373827i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	7.10580i		−	1.31951i	−0.751479	−	0.659757i	$-0.770659\pi$
$29$		−	7.10580i		−	1.31951i	0.751479	−	0.659757i	$-0.229341\pi$
$30$		0			0
$31$	−5.44527	+	3.14383i	−0.978000	+	0.564649i	−0.901666	−	0.432434i	$-0.857655\pi$
$31$	−5.44527	+	3.14383i	−0.978000	+	0.564649i	−0.0763342	+	0.997082i	$0.524322\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0398441	+	4.45986i	−0.00673488	+	0.753855i
$36$		0			0
$37$	3.13257	−	5.42578i	0.514992	−	0.891992i	−0.484857	−	0.874594i	$-0.661128\pi$
$37$	3.13257	−	5.42578i	0.514992	−	0.891992i	0.999849	−	0.0173987i	$-0.00553846\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.29414			−0.514458			−0.257229	−	0.966350i	$-0.582810\pi$
$41$	−3.29414			−0.514458			−0.257229	+	0.966350i	$0.582810\pi$
$42$		0			0
$43$	−3.60947			−0.550439			−0.275220	−	0.961381i	$-0.588751\pi$
$43$	−3.60947			−0.550439			−0.275220	+	0.961381i	$0.588751\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.38482	+	7.59474i	−0.639592	+	1.10781i	0.345930	+	0.938260i	$0.387563\pi$
$47$	−4.38482	+	7.59474i	−0.639592	+	1.10781i	−0.985522	+	0.169546i	$0.945770\pi$
$48$		0			0
$49$	3.60775	−	5.99868i	0.515393	−	0.856954i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.94628	−	2.85574i	0.679424	−	0.392266i	−0.120214	−	0.992748i	$-0.538358\pi$
$53$	4.94628	−	2.85574i	0.679424	−	0.392266i	0.799638	+	0.600482i	$0.205025\pi$
$54$		0			0
$55$		−	6.58345i		−	0.887712i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.25163	−	3.89994i	−0.293138	−	0.507729i	0.681412	−	0.731900i	$-0.261366\pi$
$59$	−2.25163	−	3.89994i	−0.293138	−	0.507729i	−0.974550	+	0.224171i	$0.928033\pi$
$60$		0			0
$61$	−4.43678	−	2.56157i	−0.568071	−	0.327976i	0.188308	−	0.982110i	$-0.439700\pi$
$61$	−4.43678	−	2.56157i	−0.568071	−	0.327976i	−0.756379	+	0.654134i	$0.773033\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.83986	−	5.10369i	−1.09645	−	0.633035i
$66$		0			0
$67$	2.95521	+	5.11857i	0.361036	+	0.625332i	0.988132	−	0.153610i	$-0.0490899\pi$
$67$	2.95521	+	5.11857i	0.361036	+	0.625332i	−0.627096	+	0.778942i	$0.715757\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			11.4308i			1.35658i	0.734792	+	0.678292i	$0.237280\pi$
$71$			11.4308i			1.35658i	−0.734792	+	0.678292i	$0.762720\pi$
$72$		0			0
$73$	−6.05559	+	3.49620i	−0.708753	+	0.409199i	−0.810599	−	0.585601i	$-0.800858\pi$
$73$	−6.05559	+	3.49620i	−0.708753	+	0.409199i	0.101846	+	0.994800i	$0.467525\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.24607	+	8.90184i	−0.597845	+	1.01446i
$78$		0			0
$79$	−0.603968	+	1.04610i	−0.0679517	+	0.117696i	−0.898000	−	0.439996i	$-0.854980\pi$
$79$	−0.603968	+	1.04610i	−0.0679517	+	0.117696i	0.830048	+	0.557692i	$0.188313\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.362701			−0.0398116			−0.0199058	−	0.999802i	$-0.506337\pi$
$83$	−0.362701			−0.0398116			−0.0199058	+	0.999802i	$0.506337\pi$
$84$		0			0
$85$	0.678488			0.0735924
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.38526	+	2.39934i	−0.146837	+	0.254329i	−0.930057	−	0.367416i	$-0.880243\pi$
$89$	−1.38526	+	2.39934i	−0.146837	+	0.254329i	0.783220	+	0.621745i	$0.213576\pi$
$90$		0			0
$91$	7.88594	+	13.9451i	0.826671	+	1.46184i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.245471	−	0.141723i	0.0251848	−	0.0145405i
$96$		0			0
$97$		−	0.587643i		−	0.0596661i	−0.999555	−	0.0298330i	$-0.990502\pi$
$97$		−	0.587643i		−	0.0596661i	0.999555	−	0.0298330i	$-0.00949756\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.92329	+	11.9915i	0.688893	+	1.19320i	0.972196	+	0.234167i	$0.0752364\pi$
$101$	6.92329	+	11.9915i	0.688893	+	1.19320i	−0.283303	+	0.959030i	$0.591430\pi$
$102$		0			0
$103$	−10.4610	−	6.03967i	−1.03075	−	0.595106i	−0.113554	−	0.993532i	$-0.536223\pi$
$103$	−10.4610	−	6.03967i	−1.03075	−	0.595106i	−0.917201	+	0.398425i	$0.869557\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.9299	−	9.19711i	−1.54000	−	0.889118i	−0.998838	−	0.0481978i	$-0.984652\pi$
$107$	−15.9299	−	9.19711i	−1.54000	−	0.889118i	−0.541159	−	0.840920i	$-0.682014\pi$
$108$		0			0
$109$	−5.51036	−	9.54422i	−0.527796	−	0.914170i	−0.999475	−	0.0323997i	$-0.989685\pi$
$109$	−5.51036	−	9.54422i	−0.527796	−	0.914170i	0.471679	−	0.881771i	$-0.343648\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.50796i			0.800361i	0.916436	+	0.400181i	$0.131053\pi$
$113$			8.50796i			0.800361i	−0.916436	+	0.400181i	$0.868947\pi$
$114$		0			0
$115$	12.9696	−	7.48801i	1.20942	−	0.698260i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.917422	−	0.540659i	−0.0840999	−	0.0495621i
$120$		0			0
$121$	2.12600	−	3.68234i	0.193273	−	0.334758i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0670			−1.07930
$126$		0			0
$127$	−10.6312			−0.943365			−0.471682	−	0.881769i	$-0.656353\pi$
$127$	−10.6312			−0.943365			−0.471682	+	0.881769i	$0.656353\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.16740	−	5.48610i	0.276737	−	0.479322i	−0.693835	−	0.720134i	$-0.744080\pi$
$131$	3.16740	−	5.48610i	0.276737	−	0.479322i	0.970572	+	0.240812i	$0.0774136\pi$
$132$		0			0
$133$	−0.444848	−	0.00397424i	−0.0385732	−	0.000344611i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.4158	+	8.32296i	−1.23162	+	0.711078i	−0.967368	−	0.253375i	$-0.918459\pi$
$137$	−14.4158	+	8.32296i	−1.23162	+	0.711078i	−0.264255	+	0.964453i	$0.585126\pi$
$138$		0			0
$139$		−	4.89601i		−	0.415274i	−0.978206	−	0.207637i	$-0.933423\pi$
$139$		−	4.89601i		−	0.415274i	0.978206	−	0.207637i	$-0.0665773\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−11.8238	−	20.4795i	−0.988758	−	1.71258i
$144$		0			0
$145$	10.3737	+	5.98926i	0.861489	+	0.497381i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.57864	+	2.64348i	0.375097	+	0.216562i	0.675683	−	0.737192i	$-0.263849\pi$
$149$	4.57864	+	2.64348i	0.375097	+	0.216562i	−0.300586	+	0.953755i	$0.597182\pi$
$150$		0			0
$151$	7.29163	+	12.6295i	0.593385	+	1.02777i	0.993773	+	0.111427i	$0.0355421\pi$
$151$	7.29163	+	12.6295i	0.593385	+	1.02777i	−0.400388	+	0.916346i	$0.631125\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	10.5993i		−	0.851360i
$156$		0			0
$157$	15.4160	−	8.90044i	1.23033	−	0.710332i	0.263232	−	0.964732i	$-0.415211\pi$
$157$	15.4160	−	8.90044i	1.23033	−	0.710332i	0.967099	+	0.254400i	$0.0818781\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−23.5038	−	0.209981i	−1.85236	−	0.0165488i
$162$		0			0
$163$	0.0482228	−	0.0835243i	0.00377710	−	0.00654213i	−0.864131	−	0.503267i	$-0.832131\pi$
$163$	0.0482228	−	0.0835243i	0.00377710	−	0.00654213i	0.867908	+	0.496725i	$0.165464\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.95745			−0.383619			−0.191809	−	0.981432i	$-0.561436\pi$
$167$	−4.95745			−0.383619			−0.191809	+	0.981432i	$0.561436\pi$
$168$		0			0
$169$	−23.6648			−1.82037
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.40033	−	12.8177i	0.562637	−	0.974515i	−0.434629	−	0.900610i	$-0.643120\pi$
$173$	7.40033	−	12.8177i	0.562637	−	0.974515i	0.997265	−	0.0739055i	$-0.0235463\pi$
$174$		0			0
$175$	4.91956	+	2.89921i	0.371884	+	0.219160i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.592751	+	0.342225i	−0.0443043	+	0.0255791i	−0.521989	−	0.852952i	$-0.674810\pi$
$179$	−0.592751	+	0.342225i	−0.0443043	+	0.0255791i	0.477684	+	0.878532i	$0.341476\pi$
$180$		0			0
$181$			7.84745i			0.583297i	0.956526	+	0.291648i	$0.0942037\pi$
$181$			7.84745i			0.583297i	−0.956526	+	0.291648i	$0.905796\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.28070	+	9.14644i	0.388245	+	0.672459i
$186$		0			0
$187$	1.36128	+	0.785934i	0.0995464	+	0.0574732i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.9694	−	9.79729i	−1.22786	−	0.708907i	−0.261281	−	0.965263i	$-0.584145\pi$
$191$	−16.9694	−	9.79729i	−1.22786	−	0.708907i	−0.966582	+	0.256356i	$0.917478\pi$
$192$		0			0
$193$	−9.18116	−	15.9022i	−0.660875	−	1.14467i	−0.980386	−	0.197086i	$-0.936852\pi$
$193$	−9.18116	−	15.9022i	−0.660875	−	1.14467i	0.319512	−	0.947582i	$-0.396481\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.92313i			0.422006i	0.977485	+	0.211003i	$0.0676730\pi$
$197$			5.92313i			0.422006i	−0.977485	+	0.211003i	$0.932327\pi$
$198$		0			0
$199$	−13.6268	+	7.86741i	−0.965975	+	0.557706i	−0.898007	−	0.439982i	$-0.854985\pi$
$199$	−13.6268	+	7.86741i	−0.965975	+	0.557706i	−0.0679681	+	0.997687i	$0.521652\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.25426	−	16.3648i	−0.649522	−	1.14858i
$204$		0			0
$205$	2.77653	−	4.80909i	0.193921	−	0.335881i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.656665			0.0454225
$210$		0			0
$211$	−10.1324			−0.697541			−0.348771	−	0.937208i	$-0.613401\pi$
$211$	−10.1324			−0.697541			−0.348771	+	0.937208i	$0.613401\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.04231	−	5.26944i	0.207484	−	0.359373i
$216$		0			0
$217$	−8.44616	+	14.3320i	−0.573363	+	0.972917i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.11061	−	1.21856i	0.141975	−	0.0819693i
$222$		0			0
$223$			15.4665i			1.03571i	0.855467	+	0.517857i	$0.173270\pi$
$223$			15.4665i			1.03571i	−0.855467	+	0.517857i	$0.826730\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.0360	+	24.3110i	0.931600	+	1.61358i	0.780588	+	0.625046i	$0.214920\pi$
$227$	14.0360	+	24.3110i	0.931600	+	1.61358i	0.151011	+	0.988532i	$0.451747\pi$
$228$		0			0
$229$	14.7453	+	8.51319i	0.974396	+	0.562568i	0.900573	−	0.434704i	$-0.143147\pi$
$229$	14.7453	+	8.51319i	0.974396	+	0.562568i	0.0738222	+	0.997271i	$0.476480\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.0015	+	9.23847i	1.04829	+	0.605233i	0.922171	−	0.386782i	$-0.126413\pi$
$233$	16.0015	+	9.23847i	1.04829	+	0.605233i	0.126122	+	0.992015i	$0.459747\pi$
$234$		0			0
$235$	−7.39166	−	12.8027i	−0.482179	−	0.835158i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			7.00506i			0.453120i	0.973997	+	0.226560i	$0.0727479\pi$
$239$			7.00506i			0.453120i	−0.973997	+	0.226560i	$0.927252\pi$
$240$		0			0
$241$	−5.38459	+	3.10879i	−0.346852	+	0.200255i	−0.663298	−	0.748355i	$-0.730844\pi$
$241$	−5.38459	+	3.10879i	−0.346852	+	0.200255i	0.316446	+	0.948611i	$0.397510\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.71656	+	10.3230i	0.365217	+	0.659514i
$246$		0			0
$247$	0.509067	−	0.881730i	0.0323912	−	0.0561031i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.81844			0.619734			0.309867	−	0.950780i	$-0.399715\pi$
$251$	9.81844			0.619734			0.309867	+	0.950780i	$0.399715\pi$
$252$		0			0
$253$	34.6952			2.18127
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.667904	+	1.15684i	−0.0416627	+	0.0721619i	−0.886105	−	0.463485i	$-0.846599\pi$
$257$	−0.667904	+	1.15684i	−0.0416627	+	0.0721619i	0.844442	+	0.535647i	$0.179932\pi$
$258$		0			0
$259$	0.148083	−	16.5754i	0.00920144	−	1.02994i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−17.6238	+	10.1751i	−1.08673	+	0.627424i	−0.932704	−	0.360643i	$-0.882557\pi$
$263$	−17.6238	+	10.1751i	−1.08673	+	0.627424i	−0.154026	+	0.988067i	$0.549224\pi$
$264$		0			0
$265$			9.62805i			0.591446i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.3614	+	23.1426i	0.814659	+	1.41103i	0.909572	+	0.415546i	$0.136409\pi$
$269$	13.3614	+	23.1426i	0.814659	+	1.41103i	−0.0949131	+	0.995486i	$0.530257\pi$
$270$		0			0
$271$	3.76517	+	2.17382i	0.228718	+	0.132050i	0.609980	−	0.792417i	$-0.291177\pi$
$271$	3.76517	+	2.17382i	0.228718	+	0.132050i	−0.381263	+	0.924467i	$0.624511\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.29968	−	4.21447i	−0.440187	−	0.254142i
$276$		0			0
$277$	2.19901	+	3.80880i	0.132126	+	0.228849i	0.924496	−	0.381192i	$-0.124486\pi$
$277$	2.19901	+	3.80880i	0.132126	+	0.228849i	−0.792370	+	0.610041i	$0.791153\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			5.33787i			0.318430i	0.987244	+	0.159215i	$0.0508964\pi$
$281$			5.33787i			0.318430i	−0.987244	+	0.159215i	$0.949104\pi$
$282$		0			0
$283$	15.5431	−	8.97381i	0.923941	−	0.533437i	0.0390505	−	0.999237i	$-0.487567\pi$
$283$	15.5431	−	8.97381i	0.923941	−	0.533437i	0.884890	+	0.465800i	$0.154233\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.58645	+	4.29014i	−0.447814	+	0.253239i
$288$		0			0
$289$	8.41900	−	14.5821i	0.495235	−	0.857773i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	26.2253			1.53210			0.766048	−	0.642783i	$-0.222220\pi$
$293$	26.2253			1.53210			0.766048	+	0.642783i	$0.222220\pi$
$294$		0			0
$295$	7.59132			0.441984
$296$		0			0
$297$		0			0
$298$		0			0
$299$	26.8968	−	46.5867i	1.55548	−	2.69418i
$300$		0			0
$301$	−8.31267	+	4.70081i	−0.479134	+	0.270950i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.47924	−	4.31814i	0.428260	−	0.247256i
$306$		0			0
$307$			7.19520i			0.410652i	0.978694	+	0.205326i	$0.0658254\pi$
$307$			7.19520i			0.410652i	−0.978694	+	0.205326i	$0.934175\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.08721	−	1.88311i	−0.0616503	−	0.106781i	0.833553	−	0.552440i	$-0.186303\pi$
$311$	−1.08721	−	1.88311i	−0.0616503	−	0.106781i	−0.895203	+	0.445658i	$0.852970\pi$
$312$		0			0
$313$	10.2870	+	5.93922i	0.581457	+	0.335704i	0.761712	−	0.647916i	$-0.224359\pi$
$313$	10.2870	+	5.93922i	0.581457	+	0.335704i	−0.180255	+	0.983620i	$0.557692\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.09969	+	4.09901i	0.398758	+	0.230223i	0.685948	−	0.727651i	$-0.259388\pi$
$317$	7.09969	+	4.09901i	0.398758	+	0.230223i	−0.287190	+	0.957874i	$0.592721\pi$
$318$		0			0
$319$	13.8754	+	24.0329i	0.776875	+	1.34559i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			0.0676757i			0.00376558i
$324$		0			0
$325$	−11.3179	+	6.53438i	−0.627803	+	0.362462i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.207279	+	23.2014i	−0.0114277	+	1.27913i
$330$		0			0
$331$	−8.58540	+	14.8704i	−0.471897	+	0.817349i	−0.999483	−	0.0321526i	$-0.989764\pi$
$331$	−8.58540	+	14.8704i	−0.471897	+	0.817349i	0.527586	+	0.849501i	$0.323097\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.96340			−0.544359
$336$		0			0
$337$	−7.90797			−0.430775			−0.215387	−	0.976529i	$-0.569101\pi$
$337$	−7.90797			−0.430775			−0.215387	+	0.976529i	$0.569101\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.2779	−	21.2659i	0.664883	−	1.15161i
$342$		0			0
$343$	0.496303	−	18.5136i	0.0267979	−	0.999641i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.443850	+	0.256257i	−0.0238271	+	0.0137566i	−0.511866	−	0.859065i	$-0.671046\pi$
$347$	−0.443850	+	0.256257i	−0.0238271	+	0.0137566i	0.488039	+	0.872822i	$0.337712\pi$
$348$		0			0
$349$			6.63505i			0.355166i	0.984106	+	0.177583i	$0.0568278\pi$
$349$			6.63505i			0.355166i	−0.984106	+	0.177583i	$0.943172\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.03437	+	15.6480i	0.480851	+	0.832858i	0.999759	−	0.0219721i	$-0.00699449\pi$
$353$	9.03437	+	15.6480i	0.480851	+	0.832858i	−0.518908	+	0.854830i	$0.673661\pi$
$354$		0			0
$355$	−16.6877	−	9.63465i	−0.885691	−	0.511354i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.52677	+	0.881479i	0.0805796	+	0.0465227i	0.539748	−	0.841826i	$-0.318519\pi$
$359$	1.52677	+	0.881479i	0.0805796	+	0.0465227i	−0.459169	+	0.888349i	$0.651853\pi$
$360$		0			0
$361$	−9.48586	−	16.4300i	−0.499256	−	0.864737i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	11.7873i		−	0.616977i
$366$		0			0
$367$	28.9614	−	16.7209i	1.51177	−	0.872822i	0.511867	−	0.859065i	$-0.328954\pi$
$367$	28.9614	−	16.7209i	1.51177	−	0.872822i	0.999905	−	0.0137576i	$-0.00437931\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.67218	−	13.0186i	0.398320	−	0.675893i
$372$		0			0
$373$	−12.7844	+	22.1433i	−0.661952	+	1.14653i	0.318150	+	0.948040i	$0.396938\pi$
$373$	−12.7844	+	22.1433i	−0.661952	+	1.14653i	−0.980102	+	0.198494i	$0.936395\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	43.0267			2.21599
$378$		0			0
$379$	25.7920			1.32485			0.662423	−	0.749130i	$-0.269528\pi$
$379$	25.7920			1.32485			0.662423	+	0.749130i	$0.269528\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.4158	−	28.4330i	0.838808	−	1.45286i	−0.0520838	−	0.998643i	$-0.516586\pi$
$383$	16.4158	−	28.4330i	0.838808	−	1.45286i	0.890892	−	0.454215i	$-0.150080\pi$
$384$		0			0
$385$	−8.57397	−	15.1618i	−0.436970	−	0.772715i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	17.4542	−	10.0772i	0.884965	−	0.510935i	0.0126730	−	0.999920i	$-0.495966\pi$
$389$	17.4542	−	10.0772i	0.884965	−	0.510935i	0.872292	+	0.488985i	$0.162633\pi$
$390$		0			0
$391$			3.57568i			0.180830i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.01813	−	1.76346i	−0.0512278	−	0.0887291i
$396$		0			0
$397$	−30.2125	−	17.4432i	−1.51632	−	0.875449i	−0.999816	−	0.0191652i	$-0.993899\pi$
$397$	−30.2125	−	17.4432i	−1.51632	−	0.875449i	−0.516506	−	0.856284i	$-0.672768\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.36793	−	4.83122i	−0.417874	−	0.241260i	0.276293	−	0.961073i	$-0.410894\pi$
$401$	−8.36793	−	4.83122i	−0.417874	−	0.241260i	−0.694167	+	0.719814i	$0.744227\pi$
$402$		0			0
$403$	−19.0364	−	32.9719i	−0.948268	−	1.64245i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			24.4678i			1.21282i
$408$		0			0
$409$	−32.1202	+	18.5446i	−1.58824	+	0.916973i	−0.594647	+	0.803987i	$0.702708\pi$
$409$	−32.1202	+	18.5446i	−1.58824	+	0.916973i	−0.993597	+	0.112986i	$0.963958\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.2646	−	6.04920i	−0.505090	−	0.297662i
$414$		0			0
$415$	0.305709	−	0.529504i	0.0150067	−	0.0259923i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.68386			−0.179968			−0.0899841	−	0.995943i	$-0.528682\pi$
$419$	−3.68386			−0.179968			−0.0899841	+	0.995943i	$0.528682\pi$
$420$		0			0
$421$	17.1028			0.833539			0.416769	−	0.909012i	$-0.363162\pi$
$421$	17.1028			0.833539			0.416769	+	0.909012i	$0.363162\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.434342	−	0.752303i	0.0210687	−	0.0364921i
$426$		0			0
$427$	−13.5540	−	0.121091i	−0.655926	−	0.00585999i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	27.3242	−	15.7756i	1.31616	−	0.759885i	0.333051	−	0.942909i	$-0.391922\pi$
$431$	27.3242	−	15.7756i	1.31616	−	0.759885i	0.983108	+	0.183024i	$0.0585887\pi$
$432$		0			0
$433$			10.0692i			0.483893i	0.970290	+	0.241947i	$0.0777859\pi$
$433$			10.0692i			0.483893i	−0.970290	+	0.241947i	$0.922214\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.746890	+	1.29365i	0.0357286	+	0.0618837i
$438$		0			0
$439$	−24.1966	−	13.9699i	−1.15484	−	0.666748i	−0.204779	−	0.978808i	$-0.565648\pi$
$439$	−24.1966	−	13.9699i	−1.15484	−	0.666748i	−0.950062	+	0.312060i	$0.898981\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−30.1930	−	17.4319i	−1.43451	−	0.828215i	−0.437050	−	0.899437i	$-0.643977\pi$
$443$	−30.1930	−	17.4319i	−1.43451	−	0.828215i	−0.997460	+	0.0712223i	$0.977310\pi$
$444$		0			0
$445$	−2.33518	−	4.04466i	−0.110698	−	0.191735i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			23.2411i			1.09682i	0.836211	+	0.548408i	$0.184766\pi$
$449$			23.2411i			1.09682i	−0.836211	+	0.548408i	$0.815234\pi$
$450$		0			0
$451$	11.1413	−	6.43244i	0.524624	−	0.302892i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−27.0051	−	0.241262i	−1.26602	−	0.0113105i
$456$		0			0
$457$	3.10938	−	5.38560i	0.145451	−	0.251928i	−0.784090	−	0.620647i	$-0.786870\pi$
$457$	3.10938	−	5.38560i	0.145451	−	0.251928i	0.929541	+	0.368719i	$0.120203\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.34329			0.202287			0.101144	−	0.994872i	$-0.467750\pi$
$461$	4.34329			0.202287			0.101144	+	0.994872i	$0.467750\pi$
$462$		0			0
$463$	−7.14903			−0.332243			−0.166122	−	0.986105i	$-0.553124\pi$
$463$	−7.14903			−0.332243			−0.166122	+	0.986105i	$0.553124\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.944451	−	1.63584i	0.0437040	−	0.0756975i	−0.843346	−	0.537371i	$-0.819417\pi$
$467$	0.944451	−	1.63584i	0.0437040	−	0.0756975i	0.887050	+	0.461673i	$0.152751\pi$
$468$		0			0
$469$	13.4721	+	7.93941i	0.622082	+	0.366608i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.2078	−	7.04818i	0.561316	−	0.324076i
$474$		0			0
$475$		−	0.362903i		−	0.0166511i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.22491	−	9.04981i	−0.238732	−	0.413497i	0.721618	−	0.692291i	$-0.243399\pi$
$479$	−5.22491	−	9.04981i	−0.238732	−	0.413497i	−0.960351	+	0.278794i	$0.910065\pi$
$480$		0			0
$481$	32.8539	+	18.9682i	1.49801	+	0.864875i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.857895	+	0.495306i	0.0389550	+	0.0224907i
$486$		0			0
$487$	−11.8298	−	20.4898i	−0.536060	−	0.928483i	−0.999111	−	0.0421513i	$-0.986579\pi$
$487$	−11.8298	−	20.4898i	−0.536060	−	0.928483i	0.463052	−	0.886331i	$-0.346754\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			13.4830i			0.608481i	0.952595	+	0.304241i	$0.0984027\pi$
$491$			13.4830i			0.608481i	−0.952595	+	0.304241i	$0.901597\pi$
$492$		0			0
$493$	−2.47683	+	1.43000i	−0.111551	+	0.0644039i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.8869	+	26.3253i	0.667770	+	1.18085i
$498$		0			0
$499$	6.04035	−	10.4622i	0.270403	−	0.468352i	−0.698562	−	0.715550i	$-0.746176\pi$
$499$	6.04035	−	10.4622i	0.270403	−	0.468352i	0.968965	+	0.247197i	$0.0795096\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.5283			0.915310			0.457655	−	0.889130i	$-0.348690\pi$
$503$	20.5283			0.915310			0.457655	+	0.889130i	$0.348690\pi$
$504$		0			0
$505$	−23.3417			−1.03869
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.09043	−	7.08483i	0.181305	−	0.314029i	−0.761020	−	0.648728i	$-0.775301\pi$
$509$	4.09043	−	7.08483i	0.181305	−	0.314029i	0.942325	+	0.334699i	$0.108635\pi$
$510$		0			0
$511$	−9.39282	+	15.9383i	−0.415514	+	0.705069i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	17.6345	−	10.1813i	0.777070	−	0.448642i
$516$		0			0
$517$		−	34.2488i		−	1.50626i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.8746	+	24.0314i	0.607856	+	1.05284i	0.991593	+	0.129395i	$0.0413034\pi$
$521$	13.8746	+	24.0314i	0.607856	+	1.05284i	−0.383738	+	0.923442i	$0.625363\pi$
$522$		0			0
$523$	19.8843	+	11.4802i	0.869478	+	0.501993i	0.867175	−	0.498004i	$-0.165934\pi$
$523$	19.8843	+	11.4802i	0.869478	+	0.501993i	0.00230311	+	0.999997i	$0.499267\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.19166	+	1.26535i	0.0954700	+	0.0551196i
$528$		0			0
$529$	27.9623	+	48.4322i	1.21575	+	2.10575i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	19.9465i		−	0.863979i
$534$		0			0
$535$	26.8536	−	15.5039i	1.16098	−	0.670292i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.488426	+	27.3333i	−0.0210380	+	1.17733i
$540$		0			0
$541$	−2.60405	+	4.51035i	−0.111957	+	0.193915i	−0.916559	−	0.399899i	$-0.869045\pi$
$541$	−2.60405	+	4.51035i	−0.111957	+	0.193915i	0.804602	+	0.593814i	$0.202379\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	18.5780			0.795795
$546$		0			0
$547$	−21.2448			−0.908361			−0.454181	−	0.890910i	$-0.650068\pi$
$547$	−21.2448			−0.908361			−0.454181	+	0.890910i	$0.650068\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.597397	+	1.03472i	−0.0254500	+	0.0440807i
$552$		0			0
$553$	−0.0285508	+	3.19577i	−0.00121410	+	0.135898i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.0945	−	6.40543i	0.470090	−	0.271407i	−0.246187	−	0.969222i	$-0.579178\pi$
$557$	11.0945	−	6.40543i	0.470090	−	0.271407i	0.716277	+	0.697816i	$0.245844\pi$
$558$		0			0
$559$		−	21.8559i		−	0.924406i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.7396	+	32.4580i	0.789781	+	1.36794i	0.926101	+	0.377277i	$0.123139\pi$
$563$	18.7396	+	32.4580i	0.789781	+	1.36794i	−0.136319	+	0.990665i	$0.543527\pi$
$564$		0			0
$565$	−12.4207	−	7.17109i	−0.522542	−	0.301690i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.94906	+	3.43469i	0.249397	+	0.143990i	0.619488	−	0.785006i	$-0.287340\pi$
$569$	5.94906	+	3.43469i	0.249397	+	0.143990i	−0.370091	+	0.928996i	$0.620673\pi$
$570$		0			0
$571$	−0.0847909	−	0.146862i	−0.00354839	−	0.00614599i	0.864246	−	0.503070i	$-0.167796\pi$
$571$	−0.0847909	−	0.146862i	−0.00354839	−	0.00614599i	−0.867794	+	0.496924i	$0.834463\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	19.1741i		−	0.799617i
$576$		0			0
$577$	−5.41193	+	3.12458i	−0.225302	+	0.130078i	−0.608403	−	0.793628i	$-0.708189\pi$
$577$	−5.41193	+	3.12458i	−0.225302	+	0.130078i	0.383101	+	0.923706i	$0.374856\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.835305	+	0.472365i	−0.0346543	+	0.0195970i
$582$		0			0
$583$	−11.1527	+	19.3171i	−0.461900	+	0.800033i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.5762			0.890545			0.445273	−	0.895395i	$-0.353107\pi$
$587$	21.5762			0.890545			0.445273	+	0.895395i	$0.353107\pi$
$588$		0			0
$589$	1.05723			0.0435624
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.13036	+	7.15399i	−0.169613	+	0.293779i	−0.938284	−	0.345866i	$-0.887585\pi$
$593$	−4.13036	+	7.15399i	−0.169613	+	0.293779i	0.768671	+	0.639645i	$0.220919\pi$
$594$		0			0
$595$	1.56257	−	0.883632i	0.0640591	−	0.0362254i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	30.7618	−	17.7603i	1.25689	−	0.725667i	0.284422	−	0.958699i	$-0.408198\pi$
$599$	30.7618	−	17.7603i	1.25689	−	0.725667i	0.972469	+	0.233033i	$0.0748649\pi$
$600$		0			0
$601$		−	41.4516i		−	1.69085i	−0.534098	−	0.845423i	$-0.679349\pi$
$601$		−	41.4516i		−	1.69085i	0.534098	−	0.845423i	$-0.320651\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.58388	+	6.20746i	0.145705	+	0.252369i
$606$		0			0
$607$	2.09569	+	1.20995i	0.0850616	+	0.0491103i	0.541927	−	0.840425i	$-0.317695\pi$
$607$	2.09569	+	1.20995i	0.0850616	+	0.0491103i	−0.456866	+	0.889536i	$0.651028\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−45.9873	−	26.5508i	−1.86045	−	1.07413i
$612$		0			0
$613$	21.3228	+	36.9321i	0.861219	+	1.49168i	0.870753	+	0.491720i	$0.163632\pi$
$613$	21.3228	+	36.9321i	0.861219	+	1.49168i	−0.00953416	+	0.999955i	$0.503035\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	15.3039i		−	0.616110i	−0.951369	−	0.308055i	$-0.900322\pi$
$617$		−	15.3039i		−	0.616110i	0.951369	−	0.308055i	$-0.0996781\pi$
$618$		0			0
$619$	−23.9177	+	13.8089i	−0.961334	+	0.555026i	−0.896583	−	0.442875i	$-0.853958\pi$
$619$	−23.9177	+	13.8089i	−0.961334	+	0.555026i	−0.0647505	+	0.997901i	$0.520625\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.0654840	+	7.32981i	−0.00262356	+	0.293663i
$624$		0			0
$625$	4.77517	−	8.27084i	0.191007	−	0.330834i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.52164			−0.100545
$630$		0			0
$631$	8.28775			0.329930			0.164965	−	0.986299i	$-0.447249\pi$
$631$	8.28775			0.329930			0.164965	+	0.986299i	$0.447249\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.96069	−	15.5204i	0.355594	−	0.615907i
$636$		0			0
$637$	36.3229	+	21.8455i	1.43916	+	0.865549i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.58307	−	4.95544i	0.339011	−	0.195728i	−0.320824	−	0.947139i	$-0.603960\pi$
$641$	8.58307	−	4.95544i	0.339011	−	0.195728i	0.659835	+	0.751411i	$0.270626\pi$
$642$		0			0
$643$			7.89432i			0.311321i	0.987811	+	0.155661i	$0.0497507\pi$
$643$			7.89432i			0.311321i	−0.987811	+	0.155661i	$0.950249\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.15966	−	3.74063i	−0.0849049	−	0.147060i	0.820446	−	0.571724i	$-0.193725\pi$
$647$	−2.15966	−	3.74063i	−0.0849049	−	0.147060i	−0.905351	+	0.424665i	$0.860392\pi$
$648$		0			0
$649$	15.2308	+	8.79348i	0.597859	+	0.345174i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−37.5853	−	21.6999i	−1.47082	−	0.849181i	−0.471361	−	0.881940i	$-0.656237\pi$
$653$	−37.5853	−	21.6999i	−1.47082	−	0.849181i	−0.999463	+	0.0327591i	$0.989571\pi$
$654$		0			0
$655$	5.33940	+	9.24812i	0.208628	+	0.361354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	10.7952i		−	0.420522i	−0.977645	−	0.210261i	$-0.932569\pi$
$659$		−	10.7952i		−	0.420522i	0.977645	−	0.210261i	$-0.0674314\pi$
$660$		0			0
$661$	−3.39495	+	1.96008i	−0.132048	+	0.0762381i	−0.564569	−	0.825386i	$-0.690958\pi$
$661$	−3.39495	+	1.96008i	−0.132048	+	0.0762381i	0.432521	+	0.901624i	$0.357624\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.380751	−	0.646081i	0.0147649	−	0.0250539i
$666$		0			0
$667$	−31.5638	+	54.6701i	−1.22216	+	2.11683i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	20.0078			0.772394
$672$		0			0
$673$	24.6808			0.951375			0.475687	−	0.879614i	$-0.342199\pi$
$673$	24.6808			0.951375			0.475687	+	0.879614i	$0.342199\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.36327	+	12.7536i	−0.282994	+	0.490159i	−0.972121	−	0.234481i	$-0.924661\pi$
$677$	−7.36327	+	12.7536i	−0.282994	+	0.490159i	0.689127	+	0.724641i	$0.257994\pi$
$678$		0			0
$679$	−0.765319	−	1.35335i	−0.0293702	−	0.0519368i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.60128	−	0.924499i	0.0612712	−	0.0353750i	−0.469051	−	0.883171i	$-0.655404\pi$
$683$	1.60128	−	0.924499i	0.0612712	−	0.0353750i	0.530323	+	0.847796i	$0.322071\pi$
$684$		0			0
$685$		−	28.0606i		−	1.07214i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	17.2919	+	29.9505i	0.658769	+	1.14102i
$690$		0			0
$691$	33.7613	+	19.4921i	1.28434	+	0.741514i	0.977639	−	0.210292i	$-0.0674415\pi$
$691$	33.7613	+	19.4921i	1.28434	+	0.741514i	0.306701	+	0.951806i	$0.400775\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.14764	+	4.12669i	0.271126	+	0.156534i
$696$		0			0
$697$	0.662926	+	1.14822i	0.0251101	+	0.0434920i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	25.4389i		−	0.960813i	−0.877046	−	0.480406i	$-0.840489\pi$
$701$		−	25.4389i		−	0.960813i	0.877046	−	0.480406i	$-0.159511\pi$
$702$		0			0
$703$	−0.912310	+	0.526722i	−0.0344084	+	0.0198657i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	31.5616	+	18.6000i	1.18700	+	0.699525i
$708$		0			0
$709$	7.14517	−	12.3758i	0.268342	−	0.464783i	−0.700092	−	0.714053i	$-0.746857\pi$
$709$	7.14517	−	12.3758i	0.268342	−	0.464783i	0.968434	+	0.249270i	$0.0801908\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	55.8593			2.09195
$714$		0			0
$715$	39.8637			1.49082
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.7344	−	28.9848i	0.624088	−	1.08095i	−0.364629	−	0.931153i	$-0.618804\pi$
$719$	16.7344	−	28.9848i	0.624088	−	1.08095i	0.988716	−	0.149799i	$-0.0478626\pi$
$720$		0			0
$721$	−31.9577	−	0.285507i	−1.19017	−	0.0106329i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.2817	−	7.66819i	0.493269	−	0.284789i
$726$		0			0
$727$		−	14.0127i		−	0.519703i	−0.965649	−	0.259851i	$-0.916326\pi$
$727$		−	14.0127i		−	0.519703i	0.965649	−	0.259851i	$-0.0836736\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.726384	+	1.25813i	0.0268663	+	0.0465338i
$732$		0			0
$733$	−23.6491	−	13.6538i	−0.873501	−	0.504316i	−0.00499085	−	0.999988i	$-0.501589\pi$
$733$	−23.6491	−	13.6538i	−0.873501	−	0.504316i	−0.868510	+	0.495672i	$0.834922\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.9899	−	11.5412i	−0.736339	−	0.425126i
$738$		0			0
$739$	26.3157	+	45.5801i	0.968039	+	1.67669i	0.701220	+	0.712945i	$0.252639\pi$
$739$	26.3157	+	45.5801i	0.968039	+	1.67669i	0.266819	+	0.963747i	$0.414027\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			35.7407i			1.31120i	0.755109	+	0.655599i	$0.227584\pi$
$743$			35.7407i			1.31120i	−0.755109	+	0.655599i	$0.772416\pi$
$744$		0			0
$745$	−7.71839	+	4.45621i	−0.282780	+	0.163263i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−48.6646	−	0.434766i	−1.77816	−	0.0158860i
$750$		0			0
$751$	16.5641	−	28.6899i	0.604433	−	1.04691i	−0.387708	−	0.921782i	$-0.626733\pi$
$751$	16.5641	−	28.6899i	0.604433	−	1.04691i	0.992141	−	0.125126i	$-0.0399336\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−24.5836			−0.894687
$756$		0			0
$757$	−13.6903			−0.497584			−0.248792	−	0.968557i	$-0.580034\pi$
$757$	−13.6903			−0.497584			−0.248792	+	0.968557i	$0.580034\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.51737	+	11.2884i	−0.236255	+	0.409205i	−0.959637	−	0.281243i	$-0.909253\pi$
$761$	−6.51737	+	11.2884i	−0.236255	+	0.409205i	0.723382	+	0.690448i	$0.242587\pi$
$762$		0			0
$763$	−25.1204	−	14.8040i	−0.909419	−	0.535942i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	23.6147	−	13.6340i	0.852678	−	0.492294i
$768$		0			0
$769$		−	21.3464i		−	0.769772i	−0.922964	−	0.384886i	$-0.874241\pi$
$769$		−	21.3464i		−	0.769772i	0.922964	−	0.384886i	$-0.125759\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.73940	+	9.94093i	0.206432	+	0.357550i	0.950588	−	0.310455i	$-0.100482\pi$
$773$	5.73940	+	9.94093i	0.206432	+	0.357550i	−0.744156	+	0.668006i	$0.767148\pi$
$774$		0			0
$775$	−11.7525	−	6.78529i	−0.422161	−	0.243735i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.479682	+	0.276944i	0.0171864	+	0.00992256i
$780$		0			0
$781$	−22.3208	−	38.6607i	−0.798701	−	1.38339i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			30.0076i			1.07102i
$786$		0			0
$787$	−35.6808	+	20.6003i	−1.27188	+	0.734322i	−0.975342	−	0.220698i	$-0.929166\pi$
$787$	−35.6808	+	20.6003i	−1.27188	+	0.734322i	−0.296541	+	0.955020i	$0.595833\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.0804	+	19.5939i	0.393972	+	0.696681i
$792$		0			0
$793$	15.5107	−	26.8653i	0.550801	−	0.954016i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	50.0132			1.77156			0.885779	−	0.464108i	$-0.153625\pi$
$797$	50.0132			1.77156			0.885779	+	0.464108i	$0.153625\pi$
$798$		0			0
$799$	3.52967			0.124871
$800$		0			0
$801$		0			0
$802$		0			0
$803$	13.6540	−	23.6494i	0.481838	−	0.834568i
$804$		0			0
$805$	20.1172	−	34.1360i	0.709037	−	1.20314i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−43.8995	+	25.3454i	−1.54343	+	0.891097i	−0.544807	+	0.838562i	$0.683397\pi$
$809$	−43.8995	+	25.3454i	−1.54343	+	0.891097i	−0.998619	+	0.0525356i	$0.983270\pi$
$810$		0			0
$811$			8.96566i			0.314827i	0.987533	+	0.157413i	$0.0503155\pi$
$811$			8.96566i			0.314827i	−0.987533	+	0.157413i	$0.949684\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.0812910	+	0.140800i	0.00284750	+	0.00493201i
$816$		0			0
$817$	0.525599	+	0.303455i	0.0183884	+	0.0106165i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−28.2190	−	16.2922i	−0.984849	−	0.568603i	−0.0811184	−	0.996704i	$-0.525849\pi$
$821$	−28.2190	−	16.2922i	−0.984849	−	0.568603i	−0.903731	+	0.428102i	$0.859183\pi$
$822$		0			0
$823$	10.0877	+	17.4724i	0.351636	+	0.609051i	0.986536	−	0.163543i	$-0.0522923\pi$
$823$	10.0877	+	17.4724i	0.351636	+	0.609051i	−0.634901	+	0.772594i	$0.718959\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	0.253288i		−	0.00880770i	−0.999990	−	0.00440385i	$-0.998598\pi$
$827$		−	0.253288i		−	0.00880770i	0.999990	−	0.00440385i	$-0.00140179\pi$
$828$		0			0
$829$	−6.10909	+	3.52708i	−0.212177	+	0.122501i	−0.602323	−	0.798253i	$-0.705758\pi$
$829$	−6.10909	+	3.52708i	−0.212177	+	0.122501i	0.390146	+	0.920753i	$0.372425\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.81696	−	0.0503371i	−0.0976020	−	0.00174408i
$834$		0			0
$835$	4.17848	−	7.23733i	0.144602	−	0.250458i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−34.1871			−1.18027			−0.590136	−	0.807304i	$-0.700926\pi$
$839$	−34.1871			−1.18027			−0.590136	+	0.807304i	$0.700926\pi$
$840$		0			0
$841$	−21.4924			−0.741117
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19.9463	−	34.5480i	0.686174	−	1.18849i
$846$		0			0
$847$	0.100500	−	11.2493i	0.00345323	−	0.386530i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−48.2024	+	27.8296i	−1.65236	+	0.953988i
$852$		0			0
$853$			25.1247i			0.860252i	0.902769	+	0.430126i	$0.141531\pi$
$853$			25.1247i			0.860252i	−0.902769	+	0.430126i	$0.858469\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0954	+	36.5383i	0.720604	+	1.24812i	0.960758	+	0.277388i	$0.0894688\pi$
$857$	21.0954	+	36.5383i	0.720604	+	1.24812i	−0.240154	+	0.970735i	$0.577198\pi$
$858$		0			0
$859$	−4.08139	−	2.35639i	−0.139255	−	0.0803990i	0.428754	−	0.903421i	$-0.358953\pi$
$859$	−4.08139	−	2.35639i	−0.139255	−	0.0803990i	−0.568009	+	0.823022i	$0.692286\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−30.8409	−	17.8060i	−1.04984	−	0.606123i	−0.127232	−	0.991873i	$-0.540609\pi$
$863$	−30.8409	−	17.8060i	−1.04984	−	0.606123i	−0.922603	+	0.385750i	$0.873943\pi$
$864$		0			0
$865$	12.4750	+	21.6074i	0.424163	+	0.734672i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	4.71745i		−	0.160029i
$870$		0			0
$871$	−30.9937	+	17.8942i	−1.05018	+	0.606322i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−27.7905	+	15.7155i	−0.939489	+	0.531281i
$876$		0			0
$877$	−20.4532	+	35.4260i	−0.690655	+	1.19625i	0.280969	+	0.959717i	$0.409344\pi$
$877$	−20.4532	+	35.4260i	−0.690655	+	1.19625i	−0.971624	+	0.236532i	$0.923989\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37.4443			−1.26153			−0.630765	−	0.775974i	$-0.717259\pi$
$881$	−37.4443			−1.26153			−0.630765	+	0.775974i	$0.717259\pi$
$882$		0			0
$883$	−49.8357			−1.67711			−0.838553	−	0.544821i	$-0.816598\pi$
$883$	−49.8357			−1.67711			−0.838553	+	0.544821i	$0.816598\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.4482	−	25.0251i	0.485124	−	0.840260i	−0.514730	−	0.857352i	$-0.672108\pi$
$887$	14.4482	−	25.0251i	0.485124	−	0.840260i	0.999854	+	0.0170929i	$0.00544110\pi$
$888$		0			0
$889$	−24.4838	+	13.8456i	−0.821159	+	0.464365i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.27701	−	0.737280i	0.0427334	−	0.0246721i
$894$		0			0
$895$		−	1.15380i		−	0.0385674i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	22.3394	+	38.6930i	0.745062	+	1.29048i
$900$		0			0
$901$	−1.99082	−	1.14940i	−0.0663238	−	0.0382920i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.4564	−	6.61437i	−0.380825	−	0.219869i
$906$		0			0
$907$	7.43498	+	12.8778i	0.246874	+	0.427599i	0.962657	−	0.270724i	$-0.0872632\pi$
$907$	7.43498	+	12.8778i	0.246874	+	0.427599i	−0.715783	+	0.698323i	$0.753930\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			9.02533i			0.299022i	0.988760	+	0.149511i	$0.0477700\pi$
$911$			9.02533i			0.299022i	−0.988760	+	0.149511i	$0.952230\pi$
$912$		0			0
$913$	1.22671	−	0.708243i	0.0405982	−	0.0234394i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.149729	−	16.7596i	0.00494450	−	0.553452i
$918$		0			0
$919$	13.2083	−	22.8774i	0.435702	−	0.754657i	−0.561651	−	0.827374i	$-0.689834\pi$
$919$	13.2083	−	22.8774i	0.435702	−	0.754657i	0.997353	+	0.0727170i	$0.0231670\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−69.2151			−2.27824
$924$		0			0
$925$	13.5220			0.444601
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.1259	+	19.2706i	−0.365029	+	0.632249i	−0.988781	−	0.149373i	$-0.952274\pi$
$929$	−11.1259	+	19.2706i	−0.365029	+	0.632249i	0.623752	+	0.781623i	$0.285608\pi$
$930$		0			0
$931$	−1.02967	+	0.570197i	−0.0337460	+	0.0186875i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.29476	+	1.32488i	−0.0750465	+	0.0433281i
$936$		0			0
$937$		−	14.6822i		−	0.479647i	−0.970817	−	0.239823i	$-0.922910\pi$
$937$		−	14.6822i		−	0.479647i	0.970817	−	0.239823i	$-0.0770896\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.0396	−	39.9058i	−0.751070	−	1.30089i	−0.947305	−	0.320334i	$-0.896205\pi$
$941$	−23.0396	−	39.9058i	−0.751070	−	1.30089i	0.196235	−	0.980557i	$-0.437129\pi$
$942$		0			0
$943$	25.3442	+	14.6325i	0.825322	+	0.476500i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.96116	+	4.01903i	0.226207	+	0.130601i	0.608821	−	0.793308i	$-0.291643\pi$
$947$	6.96116	+	4.01903i	0.226207	+	0.130601i	−0.382614	+	0.923908i	$0.624976\pi$
$948$		0			0
$949$	−21.1700	−	36.6675i	−0.687206	−	1.19028i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			54.9348i			1.77951i	0.456437	+	0.889756i	$0.349125\pi$
$953$			54.9348i			1.77951i	−0.456437	+	0.889756i	$0.650875\pi$
$954$		0			0
$955$	28.6060	−	16.5157i	0.925667	−	0.534434i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.3603	+	37.9423i	−0.722053	+	1.22522i
$960$		0			0
$961$	4.26733	−	7.39124i	0.137656	−	0.238427i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	30.9541			0.996446
$966$		0			0
$967$	53.1835			1.71026			0.855132	−	0.518410i	$-0.173476\pi$
$967$	53.1835			1.71026			0.855132	+	0.518410i	$0.173476\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.61403	+	13.1879i	−0.244346	+	0.423219i	−0.961947	−	0.273234i	$-0.911907\pi$
$971$	−7.61403	+	13.1879i	−0.244346	+	0.423219i	0.717602	+	0.696454i	$0.245240\pi$
$972$		0			0
$973$	−6.37634	−	11.2756i	−0.204416	−	0.361479i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.49418	−	0.862667i	0.0478031	−	0.0275992i	−0.475908	−	0.879495i	$-0.657880\pi$
$977$	1.49418	−	0.862667i	0.0478031	−	0.0275992i	0.523711	+	0.851896i	$0.324547\pi$
$978$		0			0
$979$		−	10.8199i		−	0.345806i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−30.1191	−	52.1679i	−0.960651	−	1.66390i	−0.720871	−	0.693070i	$-0.756258\pi$
$983$	−30.1191	−	52.1679i	−0.960651	−	1.66390i	−0.239780	−	0.970827i	$-0.577075\pi$
$984$		0			0
$985$	−8.64713	−	4.99242i	−0.275521	−	0.159072i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.7703	+	16.0332i	0.883044	+	0.509826i
$990$		0			0
$991$	−2.87312	−	4.97639i	−0.0912676	−	0.158080i	0.816777	−	0.576953i	$-0.195759\pi$
$991$	−2.87312	−	4.97639i	−0.0912676	−	0.158080i	−0.908045	+	0.418873i	$0.862425\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	26.5248i		−	0.840892i
$996$		0			0
$997$	−0.0224508	+	0.0129620i	−0.000711024	+	0.000410510i	−0.500355	−	0.865820i	$-0.666797\pi$
$997$	−0.0224508	+	0.0129620i	−0.000711024	+	0.000410510i	0.499644	+	0.866231i	$0.333464\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.b.2105.3		16
3.2	odd	2		2268.2.t.a.2105.6		16
7.3	odd	6		2268.2.t.a.1781.6		16
9.2	odd	6		756.2.w.a.341.6		16
9.4	even	3		756.2.bm.a.89.6		16
9.5	odd	6		252.2.bm.a.173.7	yes	16
9.7	even	3		252.2.w.a.5.4	✓	16
21.17	even	6	inner	2268.2.t.b.1781.3		16
36.7	odd	6		1008.2.ca.d.257.5		16
36.11	even	6		3024.2.ca.d.2609.6		16
36.23	even	6		1008.2.df.d.929.2		16
36.31	odd	6		3024.2.df.d.1601.6		16
63.2	odd	6		5292.2.x.a.881.6		16
63.4	even	3		5292.2.w.b.521.3		16
63.5	even	6		1764.2.x.a.1469.8		16
63.11	odd	6		5292.2.bm.a.2285.3		16
63.13	odd	6		5292.2.bm.a.4625.3		16
63.16	even	3		1764.2.x.a.293.8		16
63.20	even	6		5292.2.w.b.1097.3		16
63.23	odd	6		1764.2.x.b.1469.1		16
63.25	even	3		1764.2.bm.a.1697.2		16
63.31	odd	6		756.2.w.a.521.6		16
63.32	odd	6		1764.2.w.b.1109.5		16
63.34	odd	6		1764.2.w.b.509.5		16
63.38	even	6		756.2.bm.a.17.6		16
63.40	odd	6		5292.2.x.a.4409.6		16
63.41	even	6		1764.2.bm.a.1685.2		16
63.47	even	6		5292.2.x.b.881.3		16
63.52	odd	6		252.2.bm.a.185.7	yes	16
63.58	even	3		5292.2.x.b.4409.3		16
63.59	even	6		252.2.w.a.101.4	yes	16
63.61	odd	6		1764.2.x.b.293.1		16
252.31	even	6		3024.2.ca.d.2033.6		16
252.59	odd	6		1008.2.ca.d.353.5		16
252.115	even	6		1008.2.df.d.689.2		16
252.227	odd	6		3024.2.df.d.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.4	✓	16	9.7	even	3
252.2.w.a.101.4	yes	16	63.59	even	6
252.2.bm.a.173.7	yes	16	9.5	odd	6
252.2.bm.a.185.7	yes	16	63.52	odd	6
756.2.w.a.341.6		16	9.2	odd	6
756.2.w.a.521.6		16	63.31	odd	6
756.2.bm.a.17.6		16	63.38	even	6
756.2.bm.a.89.6		16	9.4	even	3
1008.2.ca.d.257.5		16	36.7	odd	6
1008.2.ca.d.353.5		16	252.59	odd	6
1008.2.df.d.689.2		16	252.115	even	6
1008.2.df.d.929.2		16	36.23	even	6
1764.2.w.b.509.5		16	63.34	odd	6
1764.2.w.b.1109.5		16	63.32	odd	6
1764.2.x.a.293.8		16	63.16	even	3
1764.2.x.a.1469.8		16	63.5	even	6
1764.2.x.b.293.1		16	63.61	odd	6
1764.2.x.b.1469.1		16	63.23	odd	6
1764.2.bm.a.1685.2		16	63.41	even	6
1764.2.bm.a.1697.2		16	63.25	even	3
2268.2.t.a.1781.6		16	7.3	odd	6
2268.2.t.a.2105.6		16	3.2	odd	2
2268.2.t.b.1781.3		16	21.17	even	6	inner
2268.2.t.b.2105.3		16	1.1	even	1	trivial
3024.2.ca.d.2033.6		16	252.31	even	6
3024.2.ca.d.2609.6		16	36.11	even	6
3024.2.df.d.17.6		16	252.227	odd	6
3024.2.df.d.1601.6		16	36.31	odd	6
5292.2.w.b.521.3		16	63.4	even	3
5292.2.w.b.1097.3		16	63.20	even	6
5292.2.x.a.881.6		16	63.2	odd	6
5292.2.x.a.4409.6		16	63.40	odd	6
5292.2.x.b.881.3		16	63.47	even	6
5292.2.x.b.4409.3		16	63.58	even	3
5292.2.bm.a.2285.3		16	63.11	odd	6
5292.2.bm.a.4625.3		16	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.842869 + 1.45989i) q^{5} +(2.30301 - 1.30235i) q^{7} +O(q^{10})\)	\(q+(-0.842869 + 1.45989i) q^{5} +(2.30301 - 1.30235i) q^{7} +(-3.38216 + 1.95269i) q^{11} +6.05515i q^{13} +(-0.201244 - 0.348565i) q^{17} +(-0.145617 - 0.0840718i) q^{19} +(-7.69373 - 4.44198i) q^{23} +(1.07914 + 1.86913i) q^{25} -7.10580i q^{29} +(-5.44527 + 3.14383i) q^{31} +(-0.0398441 + 4.45986i) q^{35} +(3.13257 - 5.42578i) q^{37} -3.29414 q^{41} -3.60947 q^{43} +(-4.38482 + 7.59474i) q^{47} +(3.60775 - 5.99868i) q^{49} +(4.94628 - 2.85574i) q^{53} -6.58345i q^{55} +(-2.25163 - 3.89994i) q^{59} +(-4.43678 - 2.56157i) q^{61} +(-8.83986 - 5.10369i) q^{65} +(2.95521 + 5.11857i) q^{67} +11.4308i q^{71} +(-6.05559 + 3.49620i) q^{73} +(-5.24607 + 8.90184i) q^{77} +(-0.603968 + 1.04610i) q^{79} -0.362701 q^{83} +0.678488 q^{85} +(-1.38526 + 2.39934i) q^{89} +(7.88594 + 13.9451i) q^{91} +(0.245471 - 0.141723i) q^{95} -0.587643i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{7}+O(q^{10}) \) 16 * q + 2 * q^7	\( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95}+O(q^{100}) \) 16 * q + 2 * q^7 + 6 * q^11 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^31 - 15 * q^35 + q^37 + 12 * q^41 + 4 * q^43 + 18 * q^47 - 8 * q^49 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - 48 * q^77 - q^79 - 12 * q^85 + 21 * q^89 + 9 * q^91 + 6 * q^95

Introduction

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