LMFDB - Embedded newform 1024.2.e.p.257.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(257,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1024.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 512)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1024.257
Dual form			1024.2.e.p.769.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.73205i) q^{3} +(2.44949 - 2.44949i) q^{5} -2.82843i q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(1.73205 + 1.73205i) q^{3} +(2.44949 - 2.44949i) q^{5} -2.82843i q^{7} +3.00000i q^{9} +(1.73205 - 1.73205i) q^{11} +(-2.44949 - 2.44949i) q^{13} +8.48528 q^{15} -4.00000 q^{17} +(1.73205 + 1.73205i) q^{19} +(4.89898 - 4.89898i) q^{21} +2.82843i q^{23} -7.00000i q^{25} +(-2.44949 - 2.44949i) q^{29} +5.65685 q^{31} +6.00000 q^{33} +(-6.92820 - 6.92820i) q^{35} +(-2.44949 + 2.44949i) q^{37} -8.48528i q^{39} -2.00000i q^{41} +(-8.66025 + 8.66025i) q^{43} +(7.34847 + 7.34847i) q^{45} +11.3137 q^{47} -1.00000 q^{49} +(-6.92820 - 6.92820i) q^{51} +(-7.34847 + 7.34847i) q^{53} -8.48528i q^{55} +6.00000i q^{57} +(1.73205 - 1.73205i) q^{59} +(2.44949 + 2.44949i) q^{61} +8.48528 q^{63} -12.0000 q^{65} +(5.19615 + 5.19615i) q^{67} +(-4.89898 + 4.89898i) q^{69} +2.82843i q^{71} +8.00000i q^{73} +(12.1244 - 12.1244i) q^{75} +(-4.89898 - 4.89898i) q^{77} -5.65685 q^{79} +9.00000 q^{81} +(5.19615 + 5.19615i) q^{83} +(-9.79796 + 9.79796i) q^{85} -8.48528i q^{87} +8.00000i q^{89} +(-6.92820 + 6.92820i) q^{91} +(9.79796 + 9.79796i) q^{93} +8.48528 q^{95} +12.0000 q^{97} +(5.19615 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 32 q^{17} + 48 q^{33} - 8 q^{49} - 96 q^{65} + 72 q^{81} + 96 q^{97}+O(q^{100}) $ 8 * q - 32 * q^17 + 48 * q^33 - 8 * q^49 - 96 * q^65 + 72 * q^81 + 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.73205	+	1.73205i	1.00000	+	1.00000i	1.00000			$0$
$3$	1.73205	+	1.73205i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$4$		0			0
$5$	2.44949	−	2.44949i	1.09545	−	1.09545i	0.100509	−	0.994936i	$-0.467953\pi$
$5$	2.44949	−	2.44949i	1.09545	−	1.09545i	0.994936	−	0.100509i	$-0.0320471\pi$
$6$		0			0
$7$		−	2.82843i		−	1.06904i	−0.845154	−	0.534522i	$-0.820491\pi$
$7$		−	2.82843i		−	1.06904i	0.845154	−	0.534522i	$-0.179509\pi$
$8$		0			0
$9$			3.00000i			1.00000i
$10$		0			0
$11$	1.73205	−	1.73205i	0.522233	−	0.522233i	−0.396012	−	0.918245i	$-0.629606\pi$
$11$	1.73205	−	1.73205i	0.522233	−	0.522233i	0.918245	+	0.396012i	$0.129606\pi$
$12$		0			0
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	0.280491	−	0.959857i	$-0.409503\pi$
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	−0.959857	+	0.280491i	$0.909503\pi$
$14$		0			0
$15$	8.48528			2.19089
$16$		0			0
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	1.73205	+	1.73205i	0.397360	+	0.397360i	0.877301	−	0.479941i	$-0.159342\pi$
$19$	1.73205	+	1.73205i	0.397360	+	0.397360i	−0.479941	+	0.877301i	$0.659342\pi$
$20$		0			0
$21$	4.89898	−	4.89898i	1.06904	−	1.06904i
$22$		0			0
$23$			2.82843i			0.589768i	0.955533	+	0.294884i	$0.0952810\pi$
$23$			2.82843i			0.589768i	−0.955533	+	0.294884i	$0.904719\pi$
$24$		0			0
$25$		−	7.00000i		−	1.40000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.44949	−	2.44949i	−0.454859	−	0.454859i	0.442105	−	0.896963i	$-0.354232\pi$
$29$	−2.44949	−	2.44949i	−0.454859	−	0.454859i	−0.896963	+	0.442105i	$0.854232\pi$
$30$		0			0
$31$	5.65685			1.01600			0.508001	−	0.861357i	$-0.330385\pi$
$31$	5.65685			1.01600			0.508001	+	0.861357i	$0.330385\pi$
$32$		0			0
$33$	6.00000			1.04447
$34$		0			0
$35$	−6.92820	−	6.92820i	−1.17108	−	1.17108i
$36$		0			0
$37$	−2.44949	+	2.44949i	−0.402694	+	0.402694i	−0.879181	−	0.476488i	$-0.841910\pi$
$37$	−2.44949	+	2.44949i	−0.402694	+	0.402694i	0.476488	+	0.879181i	$0.341910\pi$
$38$		0			0
$39$		−	8.48528i		−	1.35873i
$40$		0			0
$41$		−	2.00000i		−	0.312348i	−0.987730	−	0.156174i	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$		0			0
$43$	−8.66025	+	8.66025i	−1.32068	+	1.32068i	−0.407448	+	0.913228i	$0.633581\pi$
$43$	−8.66025	+	8.66025i	−1.32068	+	1.32068i	−0.913228	+	0.407448i	$0.866419\pi$
$44$		0			0
$45$	7.34847	+	7.34847i	1.09545	+	1.09545i
$46$		0			0
$47$	11.3137			1.65027			0.825137	−	0.564933i	$-0.191098\pi$
$47$	11.3137			1.65027			0.825137	+	0.564933i	$0.191098\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−6.92820	−	6.92820i	−0.970143	−	0.970143i
$52$		0			0
$53$	−7.34847	+	7.34847i	−1.00939	+	1.00939i	−0.00943438	+	0.999955i	$0.503003\pi$
$53$	−7.34847	+	7.34847i	−1.00939	+	1.00939i	−0.999955	+	0.00943438i	$0.996997\pi$
$54$		0			0
$55$		−	8.48528i		−	1.14416i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	1.73205	−	1.73205i	0.225494	−	0.225494i	−0.585313	−	0.810807i	$-0.699029\pi$
$59$	1.73205	−	1.73205i	0.225494	−	0.225494i	0.810807	+	0.585313i	$0.199029\pi$
$60$		0			0
$61$	2.44949	+	2.44949i	0.313625	+	0.313625i	0.846312	−	0.532687i	$-0.178818\pi$
$61$	2.44949	+	2.44949i	0.313625	+	0.313625i	−0.532687	+	0.846312i	$0.678818\pi$
$62$		0			0
$63$	8.48528			1.06904
$64$		0			0
$65$	−12.0000			−1.48842
$66$		0			0
$67$	5.19615	+	5.19615i	0.634811	+	0.634811i	0.949271	−	0.314460i	$-0.101823\pi$
$67$	5.19615	+	5.19615i	0.634811	+	0.634811i	−0.314460	+	0.949271i	$0.601823\pi$
$68$		0			0
$69$	−4.89898	+	4.89898i	−0.589768	+	0.589768i
$70$		0			0
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$		0			0
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$		0			0
$75$	12.1244	−	12.1244i	1.40000	−	1.40000i
$76$		0			0
$77$	−4.89898	−	4.89898i	−0.558291	−	0.558291i
$78$		0			0
$79$	−5.65685			−0.636446			−0.318223	−	0.948016i	$-0.603086\pi$
$79$	−5.65685			−0.636446			−0.318223	+	0.948016i	$0.603086\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	5.19615	+	5.19615i	0.570352	+	0.570352i	0.932227	−	0.361875i	$-0.117863\pi$
$83$	5.19615	+	5.19615i	0.570352	+	0.570352i	−0.361875	+	0.932227i	$0.617863\pi$
$84$		0			0
$85$	−9.79796	+	9.79796i	−1.06274	+	1.06274i
$86$		0			0
$87$		−	8.48528i		−	0.909718i
$88$		0			0
$89$			8.00000i			0.847998i	0.905663	+	0.423999i	$0.139374\pi$
$89$			8.00000i			0.847998i	−0.905663	+	0.423999i	$0.860626\pi$
$90$		0			0
$91$	−6.92820	+	6.92820i	−0.726273	+	0.726273i
$92$		0			0
$93$	9.79796	+	9.79796i	1.01600	+	1.01600i
$94$		0			0
$95$	8.48528			0.870572
$96$		0			0
$97$	12.0000			1.21842			0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000			1.21842			0.609208	+	0.793011i	$0.291488\pi$
$98$		0			0
$99$	5.19615	+	5.19615i	0.522233	+	0.522233i
$100$		0			0
$101$	−2.44949	+	2.44949i	−0.243733	+	0.243733i	−0.818393	−	0.574659i	$-0.805135\pi$
$101$	−2.44949	+	2.44949i	−0.243733	+	0.243733i	0.574659	+	0.818393i	$0.305135\pi$
$102$		0			0
$103$			14.1421i			1.39347i	0.717331	+	0.696733i	$0.245364\pi$
$103$			14.1421i			1.39347i	−0.717331	+	0.696733i	$0.754636\pi$
$104$		0			0
$105$		−	24.0000i		−	2.34216i
$106$		0			0
$107$	1.73205	−	1.73205i	0.167444	−	0.167444i	−0.618411	−	0.785855i	$-0.712223\pi$
$107$	1.73205	−	1.73205i	0.167444	−	0.167444i	0.785855	+	0.618411i	$0.212223\pi$
$108$		0			0
$109$	−7.34847	−	7.34847i	−0.703856	−	0.703856i	0.261380	−	0.965236i	$-0.415822\pi$
$109$	−7.34847	−	7.34847i	−0.703856	−	0.703856i	−0.965236	+	0.261380i	$0.915822\pi$
$110$		0			0
$111$	−8.48528			−0.805387
$112$		0			0
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$		0			0
$115$	6.92820	+	6.92820i	0.646058	+	0.646058i
$116$		0			0
$117$	7.34847	−	7.34847i	0.679366	−	0.679366i
$118$		0			0
$119$			11.3137i			1.03713i
$120$		0			0
$121$			5.00000i			0.454545i
$122$		0			0
$123$	3.46410	−	3.46410i	0.312348	−	0.312348i
$124$		0			0
$125$	−4.89898	−	4.89898i	−0.438178	−	0.438178i
$126$		0			0
$127$	5.65685			0.501965			0.250982	−	0.967992i	$-0.419246\pi$
$127$	5.65685			0.501965			0.250982	+	0.967992i	$0.419246\pi$
$128$		0			0
$129$	−30.0000			−2.64135
$130$		0			0
$131$	5.19615	+	5.19615i	0.453990	+	0.453990i	0.896676	−	0.442687i	$-0.145975\pi$
$131$	5.19615	+	5.19615i	0.453990	+	0.453990i	−0.442687	+	0.896676i	$0.645975\pi$
$132$		0			0
$133$	4.89898	−	4.89898i	0.424795	−	0.424795i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			2.00000i			0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$			2.00000i			0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$		0			0
$139$	−8.66025	+	8.66025i	−0.734553	+	0.734553i	−0.971518	−	0.236965i	$-0.923847\pi$
$139$	−8.66025	+	8.66025i	−0.734553	+	0.734553i	0.236965	+	0.971518i	$0.423847\pi$
$140$		0			0
$141$	19.5959	+	19.5959i	1.65027	+	1.65027i
$142$		0			0
$143$	−8.48528			−0.709575
$144$		0			0
$145$	−12.0000			−0.996546
$146$		0			0
$147$	−1.73205	−	1.73205i	−0.142857	−	0.142857i
$148$		0			0
$149$	7.34847	−	7.34847i	0.602010	−	0.602010i	−0.338836	−	0.940846i	$-0.610033\pi$
$149$	7.34847	−	7.34847i	0.602010	−	0.602010i	0.940846	+	0.338836i	$0.110033\pi$
$150$		0			0
$151$		−	19.7990i		−	1.61122i	−0.592447	−	0.805609i	$-0.701838\pi$
$151$		−	19.7990i		−	1.61122i	0.592447	−	0.805609i	$-0.298162\pi$
$152$		0			0
$153$		−	12.0000i		−	0.970143i
$154$		0			0
$155$	13.8564	−	13.8564i	1.11297	−	1.11297i
$156$		0			0
$157$	−17.1464	−	17.1464i	−1.36843	−	1.36843i	−0.862675	−	0.505759i	$-0.831212\pi$
$157$	−17.1464	−	17.1464i	−1.36843	−	1.36843i	−0.505759	−	0.862675i	$-0.668788\pi$
$158$		0			0
$159$	−25.4558			−2.01878
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$	−12.1244	−	12.1244i	−0.949653	−	0.949653i	0.0491391	−	0.998792i	$-0.484352\pi$
$163$	−12.1244	−	12.1244i	−0.949653	−	0.949653i	−0.998792	+	0.0491391i	$0.984352\pi$
$164$		0			0
$165$	14.6969	−	14.6969i	1.14416	−	1.14416i
$166$		0			0
$167$			8.48528i			0.656611i	0.944572	+	0.328305i	$0.106478\pi$
$167$			8.48528i			0.656611i	−0.944572	+	0.328305i	$0.893522\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$	−5.19615	+	5.19615i	−0.397360	+	0.397360i
$172$		0			0
$173$	−12.2474	−	12.2474i	−0.931156	−	0.931156i	0.0666220	−	0.997778i	$-0.478778\pi$
$173$	−12.2474	−	12.2474i	−0.931156	−	0.931156i	−0.997778	+	0.0666220i	$0.978778\pi$
$174$		0			0
$175$	−19.7990			−1.49666
$176$		0			0
$177$	6.00000			0.450988
$178$		0			0
$179$	−8.66025	−	8.66025i	−0.647298	−	0.647298i	0.305041	−	0.952339i	$-0.401330\pi$
$179$	−8.66025	−	8.66025i	−0.647298	−	0.647298i	−0.952339	+	0.305041i	$0.901330\pi$
$180$		0			0
$181$	17.1464	−	17.1464i	1.27448	−	1.27448i	0.330774	−	0.943710i	$-0.392690\pi$
$181$	17.1464	−	17.1464i	1.27448	−	1.27448i	0.943710	−	0.330774i	$-0.107310\pi$
$182$		0			0
$183$			8.48528i			0.627250i
$184$		0			0
$185$			12.0000i			0.882258i
$186$		0			0
$187$	−6.92820	+	6.92820i	−0.506640	+	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.9706			−1.22795			−0.613973	−	0.789327i	$-0.710430\pi$
$191$	−16.9706			−1.22795			−0.613973	+	0.789327i	$0.710430\pi$
$192$		0			0
$193$	12.0000			0.863779			0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000			0.863779			0.431889	+	0.901927i	$0.357847\pi$
$194$		0			0
$195$	−20.7846	−	20.7846i	−1.48842	−	1.48842i
$196$		0			0
$197$	−7.34847	+	7.34847i	−0.523557	+	0.523557i	−0.918644	−	0.395087i	$-0.870714\pi$
$197$	−7.34847	+	7.34847i	−0.523557	+	0.523557i	0.395087	+	0.918644i	$0.370714\pi$
$198$		0			0
$199$		−	2.82843i		−	0.200502i	−0.994962	−	0.100251i	$-0.968035\pi$
$199$		−	2.82843i		−	0.200502i	0.994962	−	0.100251i	$-0.0319646\pi$
$200$		0			0
$201$			18.0000i			1.26962i
$202$		0			0
$203$	−6.92820	+	6.92820i	−0.486265	+	0.486265i
$204$		0			0
$205$	−4.89898	−	4.89898i	−0.342160	−	0.342160i
$206$		0			0
$207$	−8.48528			−0.589768
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	−8.66025	−	8.66025i	−0.596196	−	0.596196i	0.343102	−	0.939298i	$-0.388522\pi$
$211$	−8.66025	−	8.66025i	−0.596196	−	0.596196i	−0.939298	+	0.343102i	$0.888522\pi$
$212$		0			0
$213$	−4.89898	+	4.89898i	−0.335673	+	0.335673i
$214$		0			0
$215$			42.4264i			2.89346i
$216$		0			0
$217$		−	16.0000i		−	1.08615i
$218$		0			0
$219$	−13.8564	+	13.8564i	−0.936329	+	0.936329i
$220$		0			0
$221$	9.79796	+	9.79796i	0.659082	+	0.659082i
$222$		0			0
$223$	−5.65685			−0.378811			−0.189405	−	0.981899i	$-0.560656\pi$
$223$	−5.65685			−0.378811			−0.189405	+	0.981899i	$0.560656\pi$
$224$		0			0
$225$	21.0000			1.40000
$226$		0			0
$227$	15.5885	+	15.5885i	1.03464	+	1.03464i	0.999378	+	0.0352642i	$0.0112273\pi$
$227$	15.5885	+	15.5885i	1.03464	+	1.03464i	0.0352642	+	0.999378i	$0.488773\pi$
$228$		0			0
$229$	2.44949	−	2.44949i	0.161867	−	0.161867i	−0.621526	−	0.783393i	$-0.713487\pi$
$229$	2.44949	−	2.44949i	0.161867	−	0.161867i	0.783393	+	0.621526i	$0.213487\pi$
$230$		0			0
$231$		−	16.9706i		−	1.11658i
$232$		0			0
$233$		−	8.00000i		−	0.524097i	−0.965055	−	0.262049i	$-0.915602\pi$
$233$		−	8.00000i		−	0.524097i	0.965055	−	0.262049i	$-0.0843981\pi$
$234$		0			0
$235$	27.7128	−	27.7128i	1.80778	−	1.80778i
$236$		0			0
$237$	−9.79796	−	9.79796i	−0.636446	−	0.636446i
$238$		0			0
$239$	16.9706			1.09773			0.548867	−	0.835910i	$-0.315059\pi$
$239$	16.9706			1.09773			0.548867	+	0.835910i	$0.315059\pi$
$240$		0			0
$241$	−20.0000			−1.28831			−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000			−1.28831			−0.644157	+	0.764894i	$0.722792\pi$
$242$		0			0
$243$	15.5885	+	15.5885i	1.00000	+	1.00000i
$244$		0			0
$245$	−2.44949	+	2.44949i	−0.156492	+	0.156492i
$246$		0			0
$247$		−	8.48528i		−	0.539906i
$248$		0			0
$249$			18.0000i			1.14070i
$250$		0			0
$251$	−12.1244	+	12.1244i	−0.765283	+	0.765283i	−0.977272	−	0.211989i	$-0.932006\pi$
$251$	−12.1244	+	12.1244i	−0.765283	+	0.765283i	0.211989	+	0.977272i	$0.432006\pi$
$252$		0			0
$253$	4.89898	+	4.89898i	0.307996	+	0.307996i
$254$		0			0
$255$	−33.9411			−2.12548
$256$		0			0
$257$	−10.0000			−0.623783			−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000			−0.623783			−0.311891	+	0.950118i	$0.600963\pi$
$258$		0			0
$259$	6.92820	+	6.92820i	0.430498	+	0.430498i
$260$		0			0
$261$	7.34847	−	7.34847i	0.454859	−	0.454859i
$262$		0			0
$263$			25.4558i			1.56967i	0.619702	+	0.784837i	$0.287254\pi$
$263$			25.4558i			1.56967i	−0.619702	+	0.784837i	$0.712746\pi$
$264$		0			0
$265$			36.0000i			2.21146i
$266$		0			0
$267$	−13.8564	+	13.8564i	−0.847998	+	0.847998i
$268$		0			0
$269$	2.44949	+	2.44949i	0.149348	+	0.149348i	0.777827	−	0.628479i	$-0.216322\pi$
$269$	2.44949	+	2.44949i	0.149348	+	0.149348i	−0.628479	+	0.777827i	$0.716322\pi$
$270$		0			0
$271$	−11.3137			−0.687259			−0.343629	−	0.939105i	$-0.611656\pi$
$271$	−11.3137			−0.687259			−0.343629	+	0.939105i	$0.611656\pi$
$272$		0			0
$273$	−24.0000			−1.45255
$274$		0			0
$275$	−12.1244	−	12.1244i	−0.731126	−	0.731126i
$276$		0			0
$277$	−17.1464	+	17.1464i	−1.03023	+	1.03023i	−0.0307004	+	0.999529i	$0.509774\pi$
$277$	−17.1464	+	17.1464i	−1.03023	+	1.03023i	−0.999529	+	0.0307004i	$0.990226\pi$
$278$		0			0
$279$			16.9706i			1.01600i
$280$		0			0
$281$		−	32.0000i		−	1.90896i	−0.298275	−	0.954480i	$-0.596411\pi$
$281$		−	32.0000i		−	1.90896i	0.298275	−	0.954480i	$-0.403589\pi$
$282$		0			0
$283$	19.0526	−	19.0526i	1.13256	−	1.13256i	0.142806	−	0.989751i	$-0.454387\pi$
$283$	19.0526	−	19.0526i	1.13256	−	1.13256i	0.989751	−	0.142806i	$-0.0456126\pi$
$284$		0			0
$285$	14.6969	+	14.6969i	0.870572	+	0.870572i
$286$		0			0
$287$	−5.65685			−0.333914
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	20.7846	+	20.7846i	1.21842	+	1.21842i
$292$		0			0
$293$	−7.34847	+	7.34847i	−0.429302	+	0.429302i	−0.888391	−	0.459088i	$-0.848176\pi$
$293$	−7.34847	+	7.34847i	−0.429302	+	0.429302i	0.459088	+	0.888391i	$0.348176\pi$
$294$		0			0
$295$		−	8.48528i		−	0.494032i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.92820	−	6.92820i	0.400668	−	0.400668i
$300$		0			0
$301$	24.4949	+	24.4949i	1.41186	+	1.41186i
$302$		0			0
$303$	−8.48528			−0.487467
$304$		0			0
$305$	12.0000			0.687118
$306$		0			0
$307$	1.73205	+	1.73205i	0.0988534	+	0.0988534i	0.754804	−	0.655951i	$-0.227732\pi$
$307$	1.73205	+	1.73205i	0.0988534	+	0.0988534i	−0.655951	+	0.754804i	$0.727732\pi$
$308$		0			0
$309$	−24.4949	+	24.4949i	−1.39347	+	1.39347i
$310$		0			0
$311$			8.48528i			0.481156i	0.970630	+	0.240578i	$0.0773370\pi$
$311$			8.48528i			0.481156i	−0.970630	+	0.240578i	$0.922663\pi$
$312$		0			0
$313$		−	30.0000i		−	1.69570i	−0.530236	−	0.847850i	$-0.677897\pi$
$313$		−	30.0000i		−	1.69570i	0.530236	−	0.847850i	$-0.322103\pi$
$314$		0			0
$315$	20.7846	−	20.7846i	1.17108	−	1.17108i
$316$		0			0
$317$	−12.2474	−	12.2474i	−0.687885	−	0.687885i	0.273879	−	0.961764i	$-0.411693\pi$
$317$	−12.2474	−	12.2474i	−0.687885	−	0.687885i	−0.961764	+	0.273879i	$0.911693\pi$
$318$		0			0
$319$	−8.48528			−0.475085
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$	−6.92820	−	6.92820i	−0.385496	−	0.385496i
$324$		0			0
$325$	−17.1464	+	17.1464i	−0.951113	+	0.951113i
$326$		0			0
$327$		−	25.4558i		−	1.40771i
$328$		0			0
$329$		−	32.0000i		−	1.76422i
$330$		0			0
$331$	1.73205	−	1.73205i	0.0952021	−	0.0952021i	−0.657902	−	0.753104i	$-0.728556\pi$
$331$	1.73205	−	1.73205i	0.0952021	−	0.0952021i	0.753104	+	0.657902i	$0.228556\pi$
$332$		0			0
$333$	−7.34847	−	7.34847i	−0.402694	−	0.402694i
$334$		0			0
$335$	25.4558			1.39080
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	17.3205	+	17.3205i	0.940721	+	0.940721i
$340$		0			0
$341$	9.79796	−	9.79796i	0.530589	−	0.530589i
$342$		0			0
$343$		−	16.9706i		−	0.916324i
$344$		0			0
$345$			24.0000i			1.29212i
$346$		0			0
$347$	−12.1244	+	12.1244i	−0.650870	+	0.650870i	−0.953202	−	0.302333i	$-0.902235\pi$
$347$	−12.1244	+	12.1244i	−0.650870	+	0.650870i	0.302333	+	0.953202i	$0.402235\pi$
$348$		0			0
$349$	−12.2474	−	12.2474i	−0.655591	−	0.655591i	0.298743	−	0.954334i	$-0.403433\pi$
$349$	−12.2474	−	12.2474i	−0.655591	−	0.655591i	−0.954334	+	0.298743i	$0.903433\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	26.0000			1.38384			0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000			1.38384			0.691920	+	0.721974i	$0.256765\pi$
$354$		0			0
$355$	6.92820	+	6.92820i	0.367711	+	0.367711i
$356$		0			0
$357$	−19.5959	+	19.5959i	−1.03713	+	1.03713i
$358$		0			0
$359$			2.82843i			0.149279i	0.997211	+	0.0746393i	$0.0237806\pi$
$359$			2.82843i			0.149279i	−0.997211	+	0.0746393i	$0.976219\pi$
$360$		0			0
$361$		−	13.0000i		−	0.684211i
$362$		0			0
$363$	−8.66025	+	8.66025i	−0.454545	+	0.454545i
$364$		0			0
$365$	19.5959	+	19.5959i	1.02570	+	1.02570i
$366$		0			0
$367$	−22.6274			−1.18114			−0.590571	−	0.806986i	$-0.701097\pi$
$367$	−22.6274			−1.18114			−0.590571	+	0.806986i	$0.701097\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	20.7846	+	20.7846i	1.07908	+	1.07908i
$372$		0			0
$373$	2.44949	−	2.44949i	0.126830	−	0.126830i	−0.640843	−	0.767672i	$-0.721415\pi$
$373$	2.44949	−	2.44949i	0.126830	−	0.126830i	0.767672	+	0.640843i	$0.221415\pi$
$374$		0			0
$375$		−	16.9706i		−	0.876356i
$376$		0			0
$377$			12.0000i			0.618031i
$378$		0			0
$379$	1.73205	−	1.73205i	0.0889695	−	0.0889695i	−0.661221	−	0.750191i	$-0.729962\pi$
$379$	1.73205	−	1.73205i	0.0889695	−	0.0889695i	0.750191	+	0.661221i	$0.229962\pi$
$380$		0			0
$381$	9.79796	+	9.79796i	0.501965	+	0.501965i
$382$		0			0
$383$	33.9411			1.73431			0.867155	−	0.498038i	$-0.165946\pi$
$383$	33.9411			1.73431			0.867155	+	0.498038i	$0.165946\pi$
$384$		0			0
$385$	−24.0000			−1.22315
$386$		0			0
$387$	−25.9808	−	25.9808i	−1.32068	−	1.32068i
$388$		0			0
$389$	−2.44949	+	2.44949i	−0.124194	+	0.124194i	−0.766472	−	0.642278i	$-0.777990\pi$
$389$	−2.44949	+	2.44949i	−0.124194	+	0.124194i	0.642278	+	0.766472i	$0.277990\pi$
$390$		0			0
$391$		−	11.3137i		−	0.572159i
$392$		0			0
$393$			18.0000i			0.907980i
$394$		0			0
$395$	−13.8564	+	13.8564i	−0.697191	+	0.697191i
$396$		0			0
$397$	−17.1464	−	17.1464i	−0.860555	−	0.860555i	0.130848	−	0.991402i	$-0.458230\pi$
$397$	−17.1464	−	17.1464i	−0.860555	−	0.860555i	−0.991402	+	0.130848i	$0.958230\pi$
$398$		0			0
$399$	16.9706			0.849591
$400$		0			0
$401$	−4.00000			−0.199750			−0.0998752	−	0.995000i	$-0.531844\pi$
$401$	−4.00000			−0.199750			−0.0998752	+	0.995000i	$0.531844\pi$
$402$		0			0
$403$	−13.8564	−	13.8564i	−0.690237	−	0.690237i
$404$		0			0
$405$	22.0454	−	22.0454i	1.09545	−	1.09545i
$406$		0			0
$407$			8.48528i			0.420600i
$408$		0			0
$409$			18.0000i			0.890043i	0.895520	+	0.445021i	$0.146804\pi$
$409$			18.0000i			0.890043i	−0.895520	+	0.445021i	$0.853196\pi$
$410$		0			0
$411$	−3.46410	+	3.46410i	−0.170872	+	0.170872i
$412$		0			0
$413$	−4.89898	−	4.89898i	−0.241063	−	0.241063i
$414$		0			0
$415$	25.4558			1.24958
$416$		0			0
$417$	−30.0000			−1.46911
$418$		0			0
$419$	−22.5167	−	22.5167i	−1.10001	−	1.10001i	−0.994408	−	0.105602i	$-0.966323\pi$
$419$	−22.5167	−	22.5167i	−1.10001	−	1.10001i	−0.105602	−	0.994408i	$-0.533677\pi$
$420$		0			0
$421$	−7.34847	+	7.34847i	−0.358142	+	0.358142i	−0.863128	−	0.504985i	$-0.831498\pi$
$421$	−7.34847	+	7.34847i	−0.358142	+	0.358142i	0.504985	+	0.863128i	$0.331498\pi$
$422$		0			0
$423$			33.9411i			1.65027i
$424$		0			0
$425$			28.0000i			1.35820i
$426$		0			0
$427$	6.92820	−	6.92820i	0.335279	−	0.335279i
$428$		0			0
$429$	−14.6969	−	14.6969i	−0.709575	−	0.709575i
$430$		0			0
$431$	5.65685			0.272481			0.136241	−	0.990676i	$-0.456498\pi$
$431$	5.65685			0.272481			0.136241	+	0.990676i	$0.456498\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$		0			0
$435$	−20.7846	−	20.7846i	−0.996546	−	0.996546i
$436$		0			0
$437$	−4.89898	+	4.89898i	−0.234350	+	0.234350i
$438$		0			0
$439$		−	2.82843i		−	0.134993i	−0.997719	−	0.0674967i	$-0.978499\pi$
$439$		−	2.82843i		−	0.134993i	0.997719	−	0.0674967i	$-0.0215012\pi$
$440$		0			0
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	−22.5167	+	22.5167i	−1.06980	+	1.06980i	−0.0724250	+	0.997374i	$0.523074\pi$
$443$	−22.5167	+	22.5167i	−1.06980	+	1.06980i	−0.997374	+	0.0724250i	$0.976926\pi$
$444$		0			0
$445$	19.5959	+	19.5959i	0.928936	+	0.928936i
$446$		0			0
$447$	25.4558			1.20402
$448$		0			0
$449$	−4.00000			−0.188772			−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$		0			0
$451$	−3.46410	−	3.46410i	−0.163118	−	0.163118i
$452$		0			0
$453$	34.2929	−	34.2929i	1.61122	−	1.61122i
$454$		0			0
$455$			33.9411i			1.59118i
$456$		0			0
$457$		−	18.0000i		−	0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$		−	18.0000i		−	0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.2474	+	12.2474i	0.570421	+	0.570421i	0.932246	−	0.361825i	$-0.117846\pi$
$461$	12.2474	+	12.2474i	0.570421	+	0.570421i	−0.361825	+	0.932246i	$0.617846\pi$
$462$		0			0
$463$	5.65685			0.262896			0.131448	−	0.991323i	$-0.458037\pi$
$463$	5.65685			0.262896			0.131448	+	0.991323i	$0.458037\pi$
$464$		0			0
$465$	48.0000			2.22595
$466$		0			0
$467$	−12.1244	−	12.1244i	−0.561048	−	0.561048i	0.368557	−	0.929605i	$-0.379852\pi$
$467$	−12.1244	−	12.1244i	−0.561048	−	0.561048i	−0.929605	+	0.368557i	$0.879852\pi$
$468$		0			0
$469$	14.6969	−	14.6969i	0.678642	−	0.678642i
$470$		0			0
$471$		−	59.3970i		−	2.73687i
$472$		0			0
$473$			30.0000i			1.37940i
$474$		0			0
$475$	12.1244	−	12.1244i	0.556304	−	0.556304i
$476$		0			0
$477$	−22.0454	−	22.0454i	−1.00939	−	1.00939i
$478$		0			0
$479$	5.65685			0.258468			0.129234	−	0.991614i	$-0.458748\pi$
$479$	5.65685			0.258468			0.129234	+	0.991614i	$0.458748\pi$
$480$		0			0
$481$	12.0000			0.547153
$482$		0			0
$483$	13.8564	+	13.8564i	0.630488	+	0.630488i
$484$		0			0
$485$	29.3939	−	29.3939i	1.33471	−	1.33471i
$486$		0			0
$487$		−	14.1421i		−	0.640841i	−0.947275	−	0.320421i	$-0.896176\pi$
$487$		−	14.1421i		−	0.640841i	0.947275	−	0.320421i	$-0.103824\pi$
$488$		0			0
$489$		−	42.0000i		−	1.89931i
$490$		0			0
$491$	5.19615	−	5.19615i	0.234499	−	0.234499i	−0.580069	−	0.814568i	$-0.696974\pi$
$491$	5.19615	−	5.19615i	0.234499	−	0.234499i	0.814568	+	0.580069i	$0.196974\pi$
$492$		0			0
$493$	9.79796	+	9.79796i	0.441278	+	0.441278i
$494$		0			0
$495$	25.4558			1.14416
$496$		0			0
$497$	8.00000			0.358849
$498$		0			0
$499$	−22.5167	−	22.5167i	−1.00798	−	1.00798i	−0.999968	−	0.00801629i	$-0.997448\pi$
$499$	−22.5167	−	22.5167i	−1.00798	−	1.00798i	−0.00801629	−	0.999968i	$-0.502552\pi$
$500$		0			0
$501$	−14.6969	+	14.6969i	−0.656611	+	0.656611i
$502$		0			0
$503$			14.1421i			0.630567i	0.948998	+	0.315283i	$0.102100\pi$
$503$			14.1421i			0.630567i	−0.948998	+	0.315283i	$0.897900\pi$
$504$		0			0
$505$			12.0000i			0.533993i
$506$		0			0
$507$	1.73205	−	1.73205i	0.0769231	−	0.0769231i
$508$		0			0
$509$	−7.34847	−	7.34847i	−0.325715	−	0.325715i	0.525239	−	0.850955i	$-0.323976\pi$
$509$	−7.34847	−	7.34847i	−0.325715	−	0.325715i	−0.850955	+	0.525239i	$0.823976\pi$
$510$		0			0
$511$	22.6274			1.00098
$512$		0			0
$513$		0			0
$514$		0			0
$515$	34.6410	+	34.6410i	1.52647	+	1.52647i
$516$		0			0
$517$	19.5959	−	19.5959i	0.861827	−	0.861827i
$518$		0			0
$519$		−	42.4264i		−	1.86231i
$520$		0			0
$521$		−	14.0000i		−	0.613351i	−0.951814	−	0.306676i	$-0.900783\pi$
$521$		−	14.0000i		−	0.613351i	0.951814	−	0.306676i	$-0.0992167\pi$
$522$		0			0
$523$	15.5885	−	15.5885i	0.681636	−	0.681636i	−0.278733	−	0.960369i	$-0.589914\pi$
$523$	15.5885	−	15.5885i	0.681636	−	0.681636i	0.960369	+	0.278733i	$0.0899144\pi$
$524$		0			0
$525$	−34.2929	−	34.2929i	−1.49666	−	1.49666i
$526$		0			0
$527$	−22.6274			−0.985666
$528$		0			0
$529$	15.0000			0.652174
$530$		0			0
$531$	5.19615	+	5.19615i	0.225494	+	0.225494i
$532$		0			0
$533$	−4.89898	+	4.89898i	−0.212198	+	0.212198i
$534$		0			0
$535$		−	8.48528i		−	0.366851i
$536$		0			0
$537$		−	30.0000i		−	1.29460i
$538$		0			0
$539$	−1.73205	+	1.73205i	−0.0746047	+	0.0746047i
$540$		0			0
$541$	22.0454	+	22.0454i	0.947806	+	0.947806i	0.998704	−	0.0508978i	$-0.0162083\pi$
$541$	22.0454	+	22.0454i	0.947806	+	0.947806i	−0.0508978	+	0.998704i	$0.516208\pi$
$542$		0			0
$543$	59.3970			2.54897
$544$		0			0
$545$	−36.0000			−1.54207
$546$		0			0
$547$	−8.66025	−	8.66025i	−0.370286	−	0.370286i	0.497296	−	0.867581i	$-0.334326\pi$
$547$	−8.66025	−	8.66025i	−0.370286	−	0.370286i	−0.867581	+	0.497296i	$0.834326\pi$
$548$		0			0
$549$	−7.34847	+	7.34847i	−0.313625	+	0.313625i
$550$		0			0
$551$		−	8.48528i		−	0.361485i
$552$		0			0
$553$			16.0000i			0.680389i
$554$		0			0
$555$	−20.7846	+	20.7846i	−0.882258	+	0.882258i
$556$		0			0
$557$	−12.2474	−	12.2474i	−0.518941	−	0.518941i	0.398310	−	0.917251i	$-0.369597\pi$
$557$	−12.2474	−	12.2474i	−0.518941	−	0.518941i	−0.917251	+	0.398310i	$0.869597\pi$
$558$		0			0
$559$	42.4264			1.79445
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	15.5885	+	15.5885i	0.656975	+	0.656975i	0.954663	−	0.297688i	$-0.0962155\pi$
$563$	15.5885	+	15.5885i	0.656975	+	0.656975i	−0.297688	+	0.954663i	$0.596216\pi$
$564$		0			0
$565$	24.4949	−	24.4949i	1.03051	−	1.03051i
$566$		0			0
$567$		−	25.4558i		−	1.06904i
$568$		0			0
$569$		−	2.00000i		−	0.0838444i	−0.999121	−	0.0419222i	$-0.986652\pi$
$569$		−	2.00000i		−	0.0838444i	0.999121	−	0.0419222i	$-0.0133482\pi$
$570$		0			0
$571$	5.19615	−	5.19615i	0.217452	−	0.217452i	−0.589972	−	0.807424i	$-0.700861\pi$
$571$	5.19615	−	5.19615i	0.217452	−	0.217452i	0.807424	+	0.589972i	$0.200861\pi$
$572$		0			0
$573$	−29.3939	−	29.3939i	−1.22795	−	1.22795i
$574$		0			0
$575$	19.7990			0.825675
$576$		0			0
$577$	30.0000			1.24892			0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000			1.24892			0.624458	+	0.781058i	$0.285320\pi$
$578$		0			0
$579$	20.7846	+	20.7846i	0.863779	+	0.863779i
$580$		0			0
$581$	14.6969	−	14.6969i	0.609732	−	0.609732i
$582$		0			0
$583$			25.4558i			1.05427i
$584$		0			0
$585$		−	36.0000i		−	1.48842i
$586$		0			0
$587$	15.5885	−	15.5885i	0.643404	−	0.643404i	−0.307986	−	0.951391i	$-0.599655\pi$
$587$	15.5885	−	15.5885i	0.643404	−	0.643404i	0.951391	+	0.307986i	$0.0996551\pi$
$588$		0			0
$589$	9.79796	+	9.79796i	0.403718	+	0.403718i
$590$		0			0
$591$	−25.4558			−1.04711
$592$		0			0
$593$	−34.0000			−1.39621			−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$		0			0
$595$	27.7128	+	27.7128i	1.13611	+	1.13611i
$596$		0			0
$597$	4.89898	−	4.89898i	0.200502	−	0.200502i
$598$		0			0
$599$		−	2.82843i		−	0.115566i	−0.998329	−	0.0577832i	$-0.981597\pi$
$599$		−	2.82843i		−	0.115566i	0.998329	−	0.0577832i	$-0.0184032\pi$
$600$		0			0
$601$			24.0000i			0.978980i	0.872009	+	0.489490i	$0.162817\pi$
$601$			24.0000i			0.978980i	−0.872009	+	0.489490i	$0.837183\pi$
$602$		0			0
$603$	−15.5885	+	15.5885i	−0.634811	+	0.634811i
$604$		0			0
$605$	12.2474	+	12.2474i	0.497930	+	0.497930i
$606$		0			0
$607$	−45.2548			−1.83684			−0.918419	−	0.395610i	$-0.870533\pi$
$607$	−45.2548			−1.83684			−0.918419	+	0.395610i	$0.870533\pi$
$608$		0			0
$609$	−24.0000			−0.972529
$610$		0			0
$611$	−27.7128	−	27.7128i	−1.12114	−	1.12114i
$612$		0			0
$613$	−7.34847	+	7.34847i	−0.296802	+	0.296802i	−0.839760	−	0.542958i	$-0.817304\pi$
$613$	−7.34847	+	7.34847i	−0.296802	+	0.296802i	0.542958	+	0.839760i	$0.317304\pi$
$614$		0			0
$615$		−	16.9706i		−	0.684319i
$616$		0			0
$617$			32.0000i			1.28827i	0.764911	+	0.644136i	$0.222783\pi$
$617$			32.0000i			1.28827i	−0.764911	+	0.644136i	$0.777217\pi$
$618$		0			0
$619$	−12.1244	+	12.1244i	−0.487319	+	0.487319i	−0.907459	−	0.420140i	$-0.861981\pi$
$619$	−12.1244	+	12.1244i	−0.487319	+	0.487319i	0.420140	+	0.907459i	$0.361981\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.6274			0.906548
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	10.3923	+	10.3923i	0.415029	+	0.415029i
$628$		0			0
$629$	9.79796	−	9.79796i	0.390670	−	0.390670i
$630$		0			0
$631$		−	19.7990i		−	0.788185i	−0.919071	−	0.394093i	$-0.871059\pi$
$631$		−	19.7990i		−	0.788185i	0.919071	−	0.394093i	$-0.128941\pi$
$632$		0			0
$633$		−	30.0000i		−	1.19239i
$634$		0			0
$635$	13.8564	−	13.8564i	0.549875	−	0.549875i
$636$		0			0
$637$	2.44949	+	2.44949i	0.0970523	+	0.0970523i
$638$		0			0
$639$	−8.48528			−0.335673
$640$		0			0
$641$	−4.00000			−0.157991			−0.0789953	−	0.996875i	$-0.525171\pi$
$641$	−4.00000			−0.157991			−0.0789953	+	0.996875i	$0.525171\pi$
$642$		0			0
$643$	5.19615	+	5.19615i	0.204916	+	0.204916i	0.802103	−	0.597186i	$-0.203715\pi$
$643$	5.19615	+	5.19615i	0.204916	+	0.204916i	−0.597186	+	0.802103i	$0.703715\pi$
$644$		0			0
$645$	−73.4847	+	73.4847i	−2.89346	+	2.89346i
$646$		0			0
$647$			14.1421i			0.555985i	0.960583	+	0.277992i	$0.0896690\pi$
$647$			14.1421i			0.555985i	−0.960583	+	0.277992i	$0.910331\pi$
$648$		0			0
$649$		−	6.00000i		−	0.235521i
$650$		0			0
$651$	27.7128	−	27.7128i	1.08615	−	1.08615i
$652$		0			0
$653$	22.0454	+	22.0454i	0.862703	+	0.862703i	0.991651	−	0.128948i	$-0.0411600\pi$
$653$	22.0454	+	22.0454i	0.862703	+	0.862703i	−0.128948	+	0.991651i	$0.541160\pi$
$654$		0			0
$655$	25.4558			0.994642
$656$		0			0
$657$	−24.0000			−0.936329
$658$		0			0
$659$	32.9090	+	32.9090i	1.28195	+	1.28195i	0.939556	+	0.342395i	$0.111238\pi$
$659$	32.9090	+	32.9090i	1.28195	+	1.28195i	0.342395	+	0.939556i	$0.388762\pi$
$660$		0			0
$661$	−22.0454	+	22.0454i	−0.857467	+	0.857467i	−0.991039	−	0.133572i	$-0.957355\pi$
$661$	−22.0454	+	22.0454i	−0.857467	+	0.857467i	0.133572	+	0.991039i	$0.457355\pi$
$662$		0			0
$663$			33.9411i			1.31816i
$664$		0			0
$665$		−	24.0000i		−	0.930680i
$666$		0			0
$667$	6.92820	−	6.92820i	0.268261	−	0.268261i
$668$		0			0
$669$	−9.79796	−	9.79796i	−0.378811	−	0.378811i
$670$		0			0
$671$	8.48528			0.327571
$672$		0			0
$673$	−20.0000			−0.770943			−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000			−0.770943			−0.385472	+	0.922720i	$0.625961\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.44949	+	2.44949i	−0.0941415	+	0.0941415i	−0.752609	−	0.658468i	$-0.771205\pi$
$677$	−2.44949	+	2.44949i	−0.0941415	+	0.0941415i	0.658468	+	0.752609i	$0.271205\pi$
$678$		0			0
$679$		−	33.9411i		−	1.30254i
$680$		0			0
$681$			54.0000i			2.06928i
$682$		0			0
$683$	−8.66025	+	8.66025i	−0.331375	+	0.331375i	−0.853109	−	0.521733i	$-0.825286\pi$
$683$	−8.66025	+	8.66025i	−0.331375	+	0.331375i	0.521733	+	0.853109i	$0.325286\pi$
$684$		0			0
$685$	4.89898	+	4.89898i	0.187180	+	0.187180i
$686$		0			0
$687$	8.48528			0.323734
$688$		0			0
$689$	36.0000			1.37149
$690$		0			0
$691$	5.19615	+	5.19615i	0.197671	+	0.197671i	0.799001	−	0.601330i	$-0.205362\pi$
$691$	5.19615	+	5.19615i	0.197671	+	0.197671i	−0.601330	+	0.799001i	$0.705362\pi$
$692$		0			0
$693$	14.6969	−	14.6969i	0.558291	−	0.558291i
$694$		0			0
$695$			42.4264i			1.60933i
$696$		0			0
$697$			8.00000i			0.303022i
$698$		0			0
$699$	13.8564	−	13.8564i	0.524097	−	0.524097i
$700$		0			0
$701$	31.8434	+	31.8434i	1.20271	+	1.20271i	0.973340	+	0.229367i	$0.0736657\pi$
$701$	31.8434	+	31.8434i	1.20271	+	1.20271i	0.229367	+	0.973340i	$0.426334\pi$
$702$		0			0
$703$	−8.48528			−0.320028
$704$		0			0
$705$	96.0000			3.61557
$706$		0			0
$707$	6.92820	+	6.92820i	0.260562	+	0.260562i
$708$		0			0
$709$	7.34847	−	7.34847i	0.275978	−	0.275978i	−0.555523	−	0.831501i	$-0.687482\pi$
$709$	7.34847	−	7.34847i	0.275978	−	0.275978i	0.831501	+	0.555523i	$0.187482\pi$
$710$		0			0
$711$		−	16.9706i		−	0.636446i
$712$		0			0
$713$			16.0000i			0.599205i
$714$		0			0
$715$	−20.7846	+	20.7846i	−0.777300	+	0.777300i
$716$		0			0
$717$	29.3939	+	29.3939i	1.09773	+	1.09773i
$718$		0			0
$719$	39.5980			1.47676			0.738378	−	0.674387i	$-0.235592\pi$
$719$	39.5980			1.47676			0.738378	+	0.674387i	$0.235592\pi$
$720$		0			0
$721$	40.0000			1.48968
$722$		0			0
$723$	−34.6410	−	34.6410i	−1.28831	−	1.28831i
$724$		0			0
$725$	−17.1464	+	17.1464i	−0.636802	+	0.636802i
$726$		0			0
$727$			19.7990i			0.734304i	0.930161	+	0.367152i	$0.119667\pi$
$727$			19.7990i			0.734304i	−0.930161	+	0.367152i	$0.880333\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	34.6410	−	34.6410i	1.28124	−	1.28124i
$732$		0			0
$733$	−12.2474	−	12.2474i	−0.452370	−	0.452370i	0.443771	−	0.896140i	$-0.353641\pi$
$733$	−12.2474	−	12.2474i	−0.452370	−	0.452370i	−0.896140	+	0.443771i	$0.853641\pi$
$734$		0			0
$735$	−8.48528			−0.312984
$736$		0			0
$737$	18.0000			0.663039
$738$		0			0
$739$	−25.9808	−	25.9808i	−0.955718	−	0.955718i	0.0433425	−	0.999060i	$-0.486199\pi$
$739$	−25.9808	−	25.9808i	−0.955718	−	0.955718i	−0.999060	+	0.0433425i	$0.986199\pi$
$740$		0			0
$741$	14.6969	−	14.6969i	0.539906	−	0.539906i
$742$		0			0
$743$			42.4264i			1.55647i	0.627971	+	0.778237i	$0.283886\pi$
$743$			42.4264i			1.55647i	−0.627971	+	0.778237i	$0.716114\pi$
$744$		0			0
$745$		−	36.0000i		−	1.31894i
$746$		0			0
$747$	−15.5885	+	15.5885i	−0.570352	+	0.570352i
$748$		0			0
$749$	−4.89898	−	4.89898i	−0.179005	−	0.179005i
$750$		0			0
$751$	−28.2843			−1.03211			−0.516054	−	0.856556i	$-0.672600\pi$
$751$	−28.2843			−1.03211			−0.516054	+	0.856556i	$0.672600\pi$
$752$		0			0
$753$	−42.0000			−1.53057
$754$		0			0
$755$	−48.4974	−	48.4974i	−1.76500	−	1.76500i
$756$		0			0
$757$	−31.8434	+	31.8434i	−1.15737	+	1.15737i	−0.172327	+	0.985040i	$0.555129\pi$
$757$	−31.8434	+	31.8434i	−1.15737	+	1.15737i	−0.985040	+	0.172327i	$0.944871\pi$
$758$		0			0
$759$			16.9706i			0.615992i
$760$		0			0
$761$		−	14.0000i		−	0.507500i	−0.967270	−	0.253750i	$-0.918336\pi$
$761$		−	14.0000i		−	0.507500i	0.967270	−	0.253750i	$-0.0816640\pi$
$762$		0			0
$763$	−20.7846	+	20.7846i	−0.752453	+	0.752453i
$764$		0			0
$765$	−29.3939	−	29.3939i	−1.06274	−	1.06274i
$766$		0			0
$767$	−8.48528			−0.306386
$768$		0			0
$769$	12.0000			0.432731			0.216366	−	0.976312i	$-0.430580\pi$
$769$	12.0000			0.432731			0.216366	+	0.976312i	$0.430580\pi$
$770$		0			0
$771$	−17.3205	−	17.3205i	−0.623783	−	0.623783i
$772$		0			0
$773$	−31.8434	+	31.8434i	−1.14533	+	1.14533i	−0.157866	+	0.987461i	$0.550461\pi$
$773$	−31.8434	+	31.8434i	−1.14533	+	1.14533i	−0.987461	+	0.157866i	$0.949539\pi$
$774$		0			0
$775$		−	39.5980i		−	1.42240i
$776$		0			0
$777$			24.0000i			0.860995i
$778$		0			0
$779$	3.46410	−	3.46410i	0.124114	−	0.124114i
$780$		0			0
$781$	4.89898	+	4.89898i	0.175299	+	0.175299i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−84.0000			−2.99809
$786$		0			0
$787$	5.19615	+	5.19615i	0.185223	+	0.185223i	0.793627	−	0.608404i	$-0.208190\pi$
$787$	5.19615	+	5.19615i	0.185223	+	0.185223i	−0.608404	+	0.793627i	$0.708190\pi$
$788$		0			0
$789$	−44.0908	+	44.0908i	−1.56967	+	1.56967i
$790$		0			0
$791$		−	28.2843i		−	1.00567i
$792$		0			0
$793$		−	12.0000i		−	0.426132i
$794$		0			0
$795$	−62.3538	+	62.3538i	−2.21146	+	2.21146i
$796$		0			0
$797$	31.8434	+	31.8434i	1.12795	+	1.12795i	0.990510	+	0.137440i	$0.0438874\pi$
$797$	31.8434	+	31.8434i	1.12795	+	1.12795i	0.137440	+	0.990510i	$0.456113\pi$
$798$		0			0
$799$	−45.2548			−1.60100
$800$		0			0
$801$	−24.0000			−0.847998
$802$		0			0
$803$	13.8564	+	13.8564i	0.488982	+	0.488982i
$804$		0			0
$805$	19.5959	−	19.5959i	0.690665	−	0.690665i
$806$		0			0
$807$			8.48528i			0.298696i
$808$		0			0
$809$			46.0000i			1.61727i	0.588308	+	0.808637i	$0.299794\pi$
$809$			46.0000i			1.61727i	−0.588308	+	0.808637i	$0.700206\pi$
$810$		0			0
$811$	−25.9808	+	25.9808i	−0.912308	+	0.912308i	−0.996453	−	0.0841455i	$-0.973184\pi$
$811$	−25.9808	+	25.9808i	−0.912308	+	0.912308i	0.0841455	+	0.996453i	$0.473184\pi$
$812$		0			0
$813$	−19.5959	−	19.5959i	−0.687259	−	0.687259i
$814$		0			0
$815$	−59.3970			−2.08059
$816$		0			0
$817$	−30.0000			−1.04957
$818$		0			0
$819$	−20.7846	−	20.7846i	−0.726273	−	0.726273i
$820$		0			0
$821$	2.44949	−	2.44949i	0.0854878	−	0.0854878i	−0.663070	−	0.748558i	$-0.730747\pi$
$821$	2.44949	−	2.44949i	0.0854878	−	0.0854878i	0.748558	+	0.663070i	$0.230747\pi$
$822$		0			0
$823$			19.7990i			0.690149i	0.938575	+	0.345075i	$0.112146\pi$
$823$			19.7990i			0.690149i	−0.938575	+	0.345075i	$0.887854\pi$
$824$		0			0
$825$		−	42.0000i		−	1.46225i
$826$		0			0
$827$	5.19615	−	5.19615i	0.180688	−	0.180688i	−0.610968	−	0.791656i	$-0.709219\pi$
$827$	5.19615	−	5.19615i	0.180688	−	0.180688i	0.791656	+	0.610968i	$0.209219\pi$
$828$		0			0
$829$	12.2474	+	12.2474i	0.425371	+	0.425371i	0.887048	−	0.461677i	$-0.152752\pi$
$829$	12.2474	+	12.2474i	0.425371	+	0.425371i	−0.461677	+	0.887048i	$0.652752\pi$
$830$		0			0
$831$	−59.3970			−2.06046
$832$		0			0
$833$	4.00000			0.138592
$834$		0			0
$835$	20.7846	+	20.7846i	0.719281	+	0.719281i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	36.7696i		−	1.26943i	−0.772748	−	0.634713i	$-0.781118\pi$
$839$		−	36.7696i		−	1.26943i	0.772748	−	0.634713i	$-0.218882\pi$
$840$		0			0
$841$		−	17.0000i		−	0.586207i
$842$		0			0
$843$	55.4256	−	55.4256i	1.90896	−	1.90896i
$844$		0			0
$845$	−2.44949	−	2.44949i	−0.0842650	−	0.0842650i
$846$		0			0
$847$	14.1421			0.485930
$848$		0			0
$849$	66.0000			2.26511
$850$		0			0
$851$	−6.92820	−	6.92820i	−0.237496	−	0.237496i
$852$		0			0
$853$	12.2474	−	12.2474i	0.419345	−	0.419345i	−0.465633	−	0.884978i	$-0.654173\pi$
$853$	12.2474	−	12.2474i	0.419345	−	0.419345i	0.884978	+	0.465633i	$0.154173\pi$
$854$		0			0
$855$			25.4558i			0.870572i
$856$		0			0
$857$			14.0000i			0.478231i	0.970991	+	0.239115i	$0.0768574\pi$
$857$			14.0000i			0.478231i	−0.970991	+	0.239115i	$0.923143\pi$
$858$		0			0
$859$	−12.1244	+	12.1244i	−0.413678	+	0.413678i	−0.883018	−	0.469340i	$-0.844492\pi$
$859$	−12.1244	+	12.1244i	−0.413678	+	0.413678i	0.469340	+	0.883018i	$0.344492\pi$
$860$		0			0
$861$	−9.79796	−	9.79796i	−0.333914	−	0.333914i
$862$		0			0
$863$	16.9706			0.577685			0.288842	−	0.957377i	$-0.406730\pi$
$863$	16.9706			0.577685			0.288842	+	0.957377i	$0.406730\pi$
$864$		0			0
$865$	−60.0000			−2.04006
$866$		0			0
$867$	−1.73205	−	1.73205i	−0.0588235	−	0.0588235i
$868$		0			0
$869$	−9.79796	+	9.79796i	−0.332373	+	0.332373i
$870$		0			0
$871$		−	25.4558i		−	0.862538i
$872$		0			0
$873$			36.0000i			1.21842i
$874$		0			0
$875$	−13.8564	+	13.8564i	−0.468432	+	0.468432i
$876$		0			0
$877$	−26.9444	−	26.9444i	−0.909847	−	0.909847i	0.0864122	−	0.996259i	$-0.472460\pi$
$877$	−26.9444	−	26.9444i	−0.909847	−	0.909847i	−0.996259	+	0.0864122i	$0.972460\pi$
$878$		0			0
$879$	−25.4558			−0.858604
$880$		0			0
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$		0			0
$883$	1.73205	+	1.73205i	0.0582882	+	0.0582882i	0.735650	−	0.677362i	$-0.236877\pi$
$883$	1.73205	+	1.73205i	0.0582882	+	0.0582882i	−0.677362	+	0.735650i	$0.736877\pi$
$884$		0			0
$885$	14.6969	−	14.6969i	0.494032	−	0.494032i
$886$		0			0
$887$		−	25.4558i		−	0.854724i	−0.904081	−	0.427362i	$-0.859443\pi$
$887$		−	25.4558i		−	0.854724i	0.904081	−	0.427362i	$-0.140557\pi$
$888$		0			0
$889$		−	16.0000i		−	0.536623i
$890$		0			0
$891$	15.5885	−	15.5885i	0.522233	−	0.522233i
$892$		0			0
$893$	19.5959	+	19.5959i	0.655752	+	0.655752i
$894$		0			0
$895$	−42.4264			−1.41816
$896$		0			0
$897$	24.0000			0.801337
$898$		0			0
$899$	−13.8564	−	13.8564i	−0.462137	−	0.462137i
$900$		0			0
$901$	29.3939	−	29.3939i	0.979252	−	0.979252i
$902$		0			0
$903$			84.8528i			2.82372i
$904$		0			0
$905$		−	84.0000i		−	2.79225i
$906$		0			0
$907$	5.19615	−	5.19615i	0.172535	−	0.172535i	−0.615557	−	0.788092i	$-0.711069\pi$
$907$	5.19615	−	5.19615i	0.172535	−	0.172535i	0.788092	+	0.615557i	$0.211069\pi$
$908$		0			0
$909$	−7.34847	−	7.34847i	−0.243733	−	0.243733i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	18.0000			0.595713
$914$		0			0
$915$	20.7846	+	20.7846i	0.687118	+	0.687118i
$916$		0			0
$917$	14.6969	−	14.6969i	0.485336	−	0.485336i
$918$		0			0
$919$			36.7696i			1.21292i	0.795116	+	0.606458i	$0.207410\pi$
$919$			36.7696i			1.21292i	−0.795116	+	0.606458i	$0.792590\pi$
$920$		0			0
$921$			6.00000i			0.197707i
$922$		0			0
$923$	6.92820	−	6.92820i	0.228045	−	0.228045i
$924$		0			0
$925$	17.1464	+	17.1464i	0.563771	+	0.563771i
$926$		0			0
$927$	−42.4264			−1.39347
$928$		0			0
$929$	28.0000			0.918650			0.459325	−	0.888268i	$-0.348091\pi$
$929$	28.0000			0.918650			0.459325	+	0.888268i	$0.348091\pi$
$930$		0			0
$931$	−1.73205	−	1.73205i	−0.0567657	−	0.0567657i
$932$		0			0
$933$	−14.6969	+	14.6969i	−0.481156	+	0.481156i
$934$		0			0
$935$			33.9411i			1.10999i
$936$		0			0
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$		0			0
$939$	51.9615	−	51.9615i	1.69570	−	1.69570i
$940$		0			0
$941$	−26.9444	−	26.9444i	−0.878362	−	0.878362i	0.115003	−	0.993365i	$-0.463312\pi$
$941$	−26.9444	−	26.9444i	−0.878362	−	0.878362i	−0.993365	+	0.115003i	$0.963312\pi$
$942$		0			0
$943$	5.65685			0.184213
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.4449	+	29.4449i	0.956830	+	0.956830i	0.999106	−	0.0422764i	$-0.0134610\pi$
$947$	29.4449	+	29.4449i	0.956830	+	0.956830i	−0.0422764	+	0.999106i	$0.513461\pi$
$948$		0			0
$949$	19.5959	−	19.5959i	0.636110	−	0.636110i
$950$		0			0
$951$		−	42.4264i		−	1.37577i
$952$		0			0
$953$		−	34.0000i		−	1.10137i	−0.834714	−	0.550684i	$-0.814367\pi$
$953$		−	34.0000i		−	1.10137i	0.834714	−	0.550684i	$-0.185633\pi$
$954$		0			0
$955$	−41.5692	+	41.5692i	−1.34515	+	1.34515i
$956$		0			0
$957$	−14.6969	−	14.6969i	−0.475085	−	0.475085i
$958$		0			0
$959$	5.65685			0.182669
$960$		0			0
$961$	1.00000			0.0322581
$962$		0			0
$963$	5.19615	+	5.19615i	0.167444	+	0.167444i
$964$		0			0
$965$	29.3939	−	29.3939i	0.946222	−	0.946222i
$966$		0			0
$967$		−	14.1421i		−	0.454780i	−0.973804	−	0.227390i	$-0.926981\pi$
$967$		−	14.1421i		−	0.454780i	0.973804	−	0.227390i	$-0.0730193\pi$
$968$		0			0
$969$		−	24.0000i		−	0.770991i
$970$		0			0
$971$	−36.3731	+	36.3731i	−1.16727	+	1.16727i	−0.184420	+	0.982848i	$0.559041\pi$
$971$	−36.3731	+	36.3731i	−1.16727	+	1.16727i	−0.982848	+	0.184420i	$0.940959\pi$
$972$		0			0
$973$	24.4949	+	24.4949i	0.785270	+	0.785270i
$974$		0			0
$975$	−59.3970			−1.90223
$976$		0			0
$977$	28.0000			0.895799			0.447900	−	0.894084i	$-0.352172\pi$
$977$	28.0000			0.895799			0.447900	+	0.894084i	$0.352172\pi$
$978$		0			0
$979$	13.8564	+	13.8564i	0.442853	+	0.442853i
$980$		0			0
$981$	22.0454	−	22.0454i	0.703856	−	0.703856i
$982$		0			0
$983$			42.4264i			1.35319i	0.736354	+	0.676596i	$0.236546\pi$
$983$			42.4264i			1.35319i	−0.736354	+	0.676596i	$0.763454\pi$
$984$		0			0
$985$			36.0000i			1.14706i
$986$		0			0
$987$	55.4256	−	55.4256i	1.76422	−	1.76422i
$988$		0			0
$989$	−24.4949	−	24.4949i	−0.778892	−	0.778892i
$990$		0			0
$991$	45.2548			1.43757			0.718784	−	0.695234i	$-0.244699\pi$
$991$	45.2548			1.43757			0.718784	+	0.695234i	$0.244699\pi$
$992$		0			0
$993$	6.00000			0.190404
$994$		0			0
$995$	−6.92820	−	6.92820i	−0.219639	−	0.219639i
$996$		0			0
$997$	7.34847	−	7.34847i	0.232728	−	0.232728i	−0.581102	−	0.813831i	$-0.697378\pi$
$997$	7.34847	−	7.34847i	0.232728	−	0.232728i	0.813831	+	0.581102i	$0.197378\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.e.p.257.4		8
4.3	odd	2	inner	1024.2.e.p.257.2		8
8.3	odd	2	inner	1024.2.e.p.257.3		8
8.5	even	2	inner	1024.2.e.p.257.1		8
16.3	odd	4	inner	1024.2.e.p.769.3		8
16.5	even	4	inner	1024.2.e.p.769.4		8
16.11	odd	4	inner	1024.2.e.p.769.2		8
16.13	even	4	inner	1024.2.e.p.769.1		8
32.3	odd	8		512.2.b.d.257.2		4
32.5	even	8		512.2.a.g.1.2	yes	4
32.11	odd	8		512.2.a.g.1.1	✓	4
32.13	even	8		512.2.b.d.257.1		4
32.19	odd	8		512.2.b.d.257.3		4
32.21	even	8		512.2.a.g.1.3	yes	4
32.27	odd	8		512.2.a.g.1.4	yes	4
32.29	even	8		512.2.b.d.257.4		4
96.5	odd	8		4608.2.a.w.1.2		4
96.11	even	8		4608.2.a.w.1.3		4
96.29	odd	8		4608.2.d.d.2305.1		4
96.35	even	8		4608.2.d.d.2305.2		4
96.53	odd	8		4608.2.a.w.1.4		4
96.59	even	8		4608.2.a.w.1.1		4
96.77	odd	8		4608.2.d.d.2305.3		4
96.83	even	8		4608.2.d.d.2305.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.a.g.1.1	✓	4	32.11	odd	8
512.2.a.g.1.2	yes	4	32.5	even	8
512.2.a.g.1.3	yes	4	32.21	even	8
512.2.a.g.1.4	yes	4	32.27	odd	8
512.2.b.d.257.1		4	32.13	even	8
512.2.b.d.257.2		4	32.3	odd	8
512.2.b.d.257.3		4	32.19	odd	8
512.2.b.d.257.4		4	32.29	even	8
1024.2.e.p.257.1		8	8.5	even	2	inner
1024.2.e.p.257.2		8	4.3	odd	2	inner
1024.2.e.p.257.3		8	8.3	odd	2	inner
1024.2.e.p.257.4		8	1.1	even	1	trivial
1024.2.e.p.769.1		8	16.13	even	4	inner
1024.2.e.p.769.2		8	16.11	odd	4	inner
1024.2.e.p.769.3		8	16.3	odd	4	inner
1024.2.e.p.769.4		8	16.5	even	4	inner
4608.2.a.w.1.1		4	96.59	even	8
4608.2.a.w.1.2		4	96.5	odd	8
4608.2.a.w.1.3		4	96.11	even	8
4608.2.a.w.1.4		4	96.53	odd	8
4608.2.d.d.2305.1		4	96.29	odd	8
4608.2.d.d.2305.2		4	96.35	even	8
4608.2.d.d.2305.3		4	96.77	odd	8
4608.2.d.d.2305.4		4	96.83	even	8

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.73205i) q^{3} +(2.44949 - 2.44949i) q^{5} -2.82843i q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.73205i) q^{3} +(2.44949 - 2.44949i) q^{5} -2.82843i q^{7} +3.00000i q^{9} +(1.73205 - 1.73205i) q^{11} +(-2.44949 - 2.44949i) q^{13} +8.48528 q^{15} -4.00000 q^{17} +(1.73205 + 1.73205i) q^{19} +(4.89898 - 4.89898i) q^{21} +2.82843i q^{23} -7.00000i q^{25} +(-2.44949 - 2.44949i) q^{29} +5.65685 q^{31} +6.00000 q^{33} +(-6.92820 - 6.92820i) q^{35} +(-2.44949 + 2.44949i) q^{37} -8.48528i q^{39} -2.00000i q^{41} +(-8.66025 + 8.66025i) q^{43} +(7.34847 + 7.34847i) q^{45} +11.3137 q^{47} -1.00000 q^{49} +(-6.92820 - 6.92820i) q^{51} +(-7.34847 + 7.34847i) q^{53} -8.48528i q^{55} +6.00000i q^{57} +(1.73205 - 1.73205i) q^{59} +(2.44949 + 2.44949i) q^{61} +8.48528 q^{63} -12.0000 q^{65} +(5.19615 + 5.19615i) q^{67} +(-4.89898 + 4.89898i) q^{69} +2.82843i q^{71} +8.00000i q^{73} +(12.1244 - 12.1244i) q^{75} +(-4.89898 - 4.89898i) q^{77} -5.65685 q^{79} +9.00000 q^{81} +(5.19615 + 5.19615i) q^{83} +(-9.79796 + 9.79796i) q^{85} -8.48528i q^{87} +8.00000i q^{89} +(-6.92820 + 6.92820i) q^{91} +(9.79796 + 9.79796i) q^{93} +8.48528 q^{95} +12.0000 q^{97} +(5.19615 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 32 q^{17} + 48 q^{33} - 8 q^{49} - 96 q^{65} + 72 q^{81} + 96 q^{97}+O(q^{100}) \) 8 * q - 32 * q^17 + 48 * q^33 - 8 * q^49 - 96 * q^65 + 72 * q^81 + 96 * q^97

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