LMFDB - Embedded newform 637.2.c.b.246.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(246,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("637.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.c (of order $2$, degree $1$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 13 $ x^2 + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			246.2
Root			$3.60555i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.b.246.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{4} +3.60555i q^{5} -3.00000 q^{9} +O(q^{10})$	$q+2.00000 q^{4} +3.60555i q^{5} -3.00000 q^{9} +3.60555i q^{13} +4.00000 q^{16} +3.60555i q^{19} +7.21110i q^{20} +1.00000 q^{23} -8.00000 q^{25} -5.00000 q^{29} -10.8167i q^{31} -6.00000 q^{36} +7.21110i q^{41} +9.00000 q^{43} -10.8167i q^{45} +3.60555i q^{47} +7.21110i q^{52} +11.0000 q^{53} +14.4222i q^{59} +8.00000 q^{64} -13.0000 q^{65} -10.8167i q^{73} +7.21110i q^{76} +15.0000 q^{79} +14.4222i q^{80} +9.00000 q^{81} -18.0278i q^{83} +3.60555i q^{89} +2.00000 q^{92} -13.0000 q^{95} -18.0278i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{4} - 6 q^{9}+O(q^{10}) $ 2 * q + 4 * q^4 - 6 * q^9	$ 2 q + 4 q^{4} - 6 q^{9} + 8 q^{16} + 2 q^{23} - 16 q^{25} - 10 q^{29} - 12 q^{36} + 18 q^{43} + 22 q^{53} + 16 q^{64} - 26 q^{65} + 30 q^{79} + 18 q^{81} + 4 q^{92} - 26 q^{95}+O(q^{100}) $ 2 * q + 4 * q^4 - 6 * q^9 + 8 * q^16 + 2 * q^23 - 16 * q^25 - 10 * q^29 - 12 * q^36 + 18 * q^43 + 22 * q^53 + 16 * q^64 - 26 * q^65 + 30 * q^79 + 18 * q^81 + 4 * q^92 - 26 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$1$

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	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	2.00000	1.00000
$5$	3.60555i	1.61245i	0.591608	+	0.806226i	$0.298493\pi$
$5$	3.60555i	1.61245i	−0.591608	+	0.806226i	$0.701507\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	3.60555i	1.00000i
$13$	3.60555i	1.00000i
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	3.60555i	0.827170i	0.910465	+	0.413585i	$0.135724\pi$
$19$	3.60555i	0.827170i	−0.910465	+	0.413585i	$0.864276\pi$
$20$	7.21110i	1.61245i
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	−8.00000	−1.60000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	− 10.8167i	− 1.94273i	−0.237595	−	0.971364i	$-0.576359\pi$
$31$	− 10.8167i	− 1.94273i	0.237595	−	0.971364i	$-0.423641\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−6.00000	−1.00000
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	7.21110i	1.12619i	0.826394	+	0.563093i	$0.190389\pi$
$41$	7.21110i	1.12619i	−0.826394	+	0.563093i	$0.809611\pi$
$42$	0	0
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	0	0
$45$	− 10.8167i	− 1.61245i
$46$	0	0
$47$	3.60555i	0.525924i	0.964806	+	0.262962i	$0.0846993\pi$
$47$	3.60555i	0.525924i	−0.964806	+	0.262962i	$0.915301\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	0	0
$52$	7.21110i	1.00000i
$53$	11.0000	1.51097	0.755483	−	0.655168i	$-0.227402\pi$
$53$	11.0000	1.51097	0.755483	+	0.655168i	$0.227402\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	14.4222i	1.87761i	0.344447	+	0.938806i	$0.388066\pi$
$59$	14.4222i	1.87761i	−0.344447	+	0.938806i	$0.611934\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	8.00000	1.00000
$65$	−13.0000	−1.61245
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	− 10.8167i	− 1.26599i	−0.774154	−	0.632997i	$-0.781825\pi$
$73$	− 10.8167i	− 1.26599i	0.774154	−	0.632997i	$-0.218175\pi$
$74$	0	0
$75$	0	0
$76$	7.21110i	0.827170i
$77$	0	0
$78$	0	0
$79$	15.0000	1.68763	0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000	1.68763	0.843816	+	0.536633i	$0.180304\pi$
$80$	14.4222i	1.61245i
$81$	9.00000	1.00000
$82$	0	0
$83$	− 18.0278i	− 1.97880i	−0.145204	−	0.989402i	$-0.546384\pi$
$83$	− 18.0278i	− 1.97880i	0.145204	−	0.989402i	$-0.453616\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	3.60555i	0.382188i	0.981572	+	0.191094i	$0.0612035\pi$
$89$	3.60555i	0.382188i	−0.981572	+	0.191094i	$0.938797\pi$
$90$	0	0
$91$	0	0
$92$	2.00000	0.208514
$93$	0	0
$94$	0	0
$95$	−13.0000	−1.33377
$96$	0	0
$97$	− 18.0278i	− 1.83044i	−0.402953	−	0.915221i	$-0.632016\pi$
$97$	− 18.0278i	− 1.83044i	0.402953	−	0.915221i	$-0.367984\pi$
$98$	0	0
$99$	0	0
$100$	−16.0000	−1.60000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−19.0000	−1.78737	−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000	−1.78737	−0.893685	+	0.448695i	$0.851889\pi$
$114$	0	0
$115$	3.60555i	0.336219i
$116$	−10.0000	−0.928477
$117$	− 10.8167i	− 1.00000i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.0000	1.00000
$122$	0	0
$123$	0	0
$124$	− 21.6333i	− 1.94273i
$125$	− 10.8167i	− 0.967471i
$126$	0	0
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−12.0000	−1.00000
$145$	− 18.0278i	− 1.49712i
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	39.0000	3.13256
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	14.4222i	1.12619i
$165$	0	0
$166$	0	0
$167$	− 18.0278i	− 1.39503i	−0.716570	−	0.697515i	$-0.754289\pi$
$167$	− 18.0278i	− 1.39503i	0.716570	−	0.697515i	$-0.245711\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	− 10.8167i	− 0.827170i
$172$	18.0000	1.37249
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	25.0000	1.86859	0.934294	−	0.356504i	$-0.116031\pi$
$179$	25.0000	1.86859	0.934294	+	0.356504i	$0.116031\pi$
$180$	− 21.6333i	− 1.61245i
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	7.21110i	0.525924i
$189$	0	0
$190$	0	0
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−26.0000	−1.81592
$206$	0	0
$207$	−3.00000	−0.208514
$208$	14.4222i	1.00000i
$209$	0	0
$210$	0	0
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	22.0000	1.51097
$213$	0	0
$214$	0	0
$215$	32.4500i	2.21307i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 18.0278i	− 1.20723i	−0.797277	−	0.603614i	$-0.793727\pi$
$223$	− 18.0278i	− 1.20723i	0.797277	−	0.603614i	$-0.206273\pi$
$224$	0	0
$225$	24.0000	1.60000
$226$	0	0
$227$	14.4222i	0.957235i	0.878023	+	0.478618i	$0.158862\pi$
$227$	14.4222i	0.957235i	−0.878023	+	0.478618i	$0.841138\pi$
$228$	0	0
$229$	− 21.6333i	− 1.42957i	−0.699345	−	0.714785i	$-0.746525\pi$
$229$	− 21.6333i	− 1.42957i	0.699345	−	0.714785i	$-0.253475\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	29.0000	1.89985	0.949927	−	0.312473i	$-0.101157\pi$
$233$	29.0000	1.89985	0.949927	+	0.312473i	$0.101157\pi$
$234$	0	0
$235$	−13.0000	−0.848026
$236$	28.8444i	1.87761i
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	− 10.8167i	− 0.696762i	−0.937353	−	0.348381i	$-0.886732\pi$
$241$	− 10.8167i	− 0.696762i	0.937353	−	0.348381i	$-0.113268\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−13.0000	−0.827170
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	−26.0000	−1.61245
$261$	15.0000	0.928477
$262$	0	0
$263$	−31.0000	−1.91154	−0.955771	−	0.294112i	$-0.904976\pi$
$263$	−31.0000	−1.91154	−0.955771	+	0.294112i	$0.904976\pi$
$264$	0	0
$265$	39.6611i	2.43636i
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	28.8444i	1.75217i	0.482154	+	0.876087i	$0.339855\pi$
$271$	28.8444i	1.75217i	−0.482154	+	0.876087i	$0.660145\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−17.0000	−1.02143	−0.510716	−	0.859750i	$-0.670619\pi$
$277$	−17.0000	−1.02143	−0.510716	+	0.859750i	$0.670619\pi$
$278$	0	0
$279$	32.4500i	1.94273i
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	− 21.6333i	− 1.26599i
$293$	− 18.0278i	− 1.05319i	−0.850115	−	0.526596i	$-0.823468\pi$
$293$	− 18.0278i	− 1.05319i	0.850115	−	0.526596i	$-0.176532\pi$
$294$	0	0
$295$	−52.0000	−3.02756
$296$	0	0
$297$	0	0
$298$	0	0
$299$	3.60555i	0.208514i
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	14.4222i	0.827170i
$305$	0	0
$306$	0	0
$307$	32.4500i	1.85202i	0.377503	+	0.926009i	$0.376783\pi$
$307$	32.4500i	1.85202i	−0.377503	+	0.926009i	$0.623217\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	0	0
$315$	0	0
$316$	30.0000	1.68763
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	28.8444i	1.61245i
$321$	0	0
$322$	0	0
$323$	0	0
$324$	18.0000	1.00000
$325$	− 28.8444i	− 1.60000i
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	− 36.0555i	− 1.97880i
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	23.0000	1.25289	0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000	1.25289	0.626445	+	0.779466i	$0.284509\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	32.4500i	1.73701i	0.495683	+	0.868503i	$0.334918\pi$
$349$	32.4500i	1.73701i	−0.495683	+	0.868503i	$0.665082\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 36.0555i	− 1.91904i	−0.281638	−	0.959521i	$-0.590878\pi$
$353$	− 36.0555i	− 1.91904i	0.281638	−	0.959521i	$-0.409122\pi$
$354$	0	0
$355$	0	0
$356$	7.21110i	0.382188i
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	0	0
$363$	0	0
$364$	0	0
$365$	39.0000	2.04135
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	4.00000	0.208514
$369$	− 21.6333i	− 1.12619i
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	− 18.0278i	− 0.928477i
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	−26.0000	−1.33377
$381$	0	0
$382$	0	0
$383$	28.8444i	1.47388i	0.675958	+	0.736940i	$0.263730\pi$
$383$	28.8444i	1.47388i	−0.675958	+	0.736940i	$0.736270\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−27.0000	−1.37249
$388$	− 36.0555i	− 1.83044i
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	54.0833i	2.72122i
$396$	0	0
$397$	3.60555i	0.180957i	0.995898	+	0.0904787i	$0.0288397\pi$
$397$	3.60555i	0.180957i	−0.995898	+	0.0904787i	$0.971160\pi$
$398$	0	0
$399$	0	0
$400$	−32.0000	−1.60000
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	39.0000	1.94273
$404$	0	0
$405$	32.4500i	1.61245i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	39.6611i	1.96111i	0.196236	+	0.980557i	$0.437128\pi$
$409$	39.6611i	1.96111i	−0.196236	+	0.980557i	$0.562872\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	65.0000	3.19072
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	− 10.8167i	− 0.525924i
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	16.0000	0.773389
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	3.60555i	0.172477i
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−41.0000	−1.94797	−0.973984	−	0.226615i	$-0.927234\pi$
$443$	−41.0000	−1.94797	−0.973984	+	0.226615i	$0.927234\pi$
$444$	0	0
$445$	−13.0000	−0.616259
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	−38.0000	−1.78737
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	7.21110i	0.336219i
$461$	7.21110i	0.335855i	0.985799	+	0.167927i	$0.0537074\pi$
$461$	7.21110i	0.335855i	−0.985799	+	0.167927i	$0.946293\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	−20.0000	−0.928477
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	− 21.6333i	− 1.00000i
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	− 28.8444i	− 1.32347i
$476$	0	0
$477$	−33.0000	−1.51097
$478$	0	0
$479$	39.6611i	1.81216i	0.423106	+	0.906080i	$0.360940\pi$
$479$	39.6611i	1.81216i	−0.423106	+	0.906080i	$0.639060\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	22.0000	1.00000
$485$	65.0000	2.95150
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−40.0000	−1.80517	−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000	−1.80517	−0.902587	+	0.430507i	$0.858335\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	− 43.2666i	− 1.94273i
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	− 21.6333i	− 0.967471i
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−24.0000	−1.06483
$509$	3.60555i	0.159813i	0.996802	+	0.0799066i	$0.0254622\pi$
$509$	3.60555i	0.159813i	−0.996802	+	0.0799066i	$0.974538\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	− 43.2666i	− 1.87761i
$532$	0	0
$533$	−26.0000	−1.12619
$534$	0	0
$535$	28.8444i	1.24705i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	37.0000	1.58201	0.791003	−	0.611812i	$-0.209559\pi$
$547$	37.0000	1.58201	0.791003	+	0.611812i	$0.209559\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	− 18.0278i	− 0.768008i
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	32.4500i	1.37249i
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	− 68.5055i	− 2.88205i
$566$	0	0
$567$	0	0
$568$	0	0
$569$	1.00000	0.0419222	0.0209611	−	0.999780i	$-0.493327\pi$
$569$	1.00000	0.0419222	0.0209611	+	0.999780i	$0.493327\pi$
$570$	0	0
$571$	−3.00000	−0.125546	−0.0627730	−	0.998028i	$-0.519994\pi$
$571$	−3.00000	−0.125546	−0.0627730	+	0.998028i	$0.519994\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−8.00000	−0.333623
$576$	−24.0000	−1.00000
$577$	− 36.0555i	− 1.50101i	−0.660864	−	0.750505i	$-0.729810\pi$
$577$	− 36.0555i	− 1.50101i	0.660864	−	0.750505i	$-0.270190\pi$
$578$	0	0
$579$	0	0
$580$	− 36.0555i	− 1.49712i
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	39.0000	1.61245
$586$	0	0
$587$	− 18.0278i	− 0.744085i	−0.928216	−	0.372043i	$-0.878658\pi$
$587$	− 18.0278i	− 0.744085i	0.928216	−	0.372043i	$-0.121342\pi$
$588$	0	0
$589$	39.0000	1.60697
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 46.8722i	− 1.92481i	−0.271620	−	0.962405i	$-0.587559\pi$
$593$	− 46.8722i	− 1.92481i	0.271620	−	0.962405i	$-0.412441\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	11.0000	0.449448	0.224724	−	0.974422i	$-0.427852\pi$
$599$	11.0000	0.449448	0.224724	+	0.974422i	$0.427852\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	39.6611i	1.61245i
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−13.0000	−0.525924
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	14.4222i	0.579677i	0.957076	+	0.289839i	$0.0936017\pi$
$619$	14.4222i	0.579677i	−0.957076	+	0.289839i	$0.906398\pi$
$620$	78.0000	3.13256
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−1.00000	−0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	− 43.2666i	− 1.71698i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−17.0000	−0.671460	−0.335730	−	0.941958i	$-0.608983\pi$
$641$	−17.0000	−0.671460	−0.335730	+	0.941958i	$0.608983\pi$
$642$	0	0
$643$	− 43.2666i	− 1.70627i	−0.521691	−	0.853134i	$-0.674699\pi$
$643$	− 43.2666i	− 1.70627i	0.521691	−	0.853134i	$-0.325301\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−34.0000	−1.33052	−0.665261	−	0.746611i	$-0.731680\pi$
$653$	−34.0000	−1.33052	−0.665261	+	0.746611i	$0.731680\pi$
$654$	0	0
$655$	0	0
$656$	28.8444i	1.12619i
$657$	32.4500i	1.26599i
$658$	0	0
$659$	−19.0000	−0.740135	−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000	−0.740135	−0.370067	+	0.929005i	$0.620665\pi$
$660$	0	0
$661$	− 10.8167i	− 0.420719i	−0.977624	−	0.210360i	$-0.932537\pi$
$661$	− 10.8167i	− 0.420719i	0.977624	−	0.210360i	$-0.0674635\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−5.00000	−0.193601
$668$	− 36.0555i	− 1.39503i
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	51.0000	1.96591	0.982953	−	0.183858i	$-0.0588587\pi$
$673$	51.0000	1.96591	0.982953	+	0.183858i	$0.0588587\pi$
$674$	0	0
$675$	0	0
$676$	−26.0000	−1.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	− 21.6333i	− 0.827170i
$685$	0	0
$686$	0	0
$687$	0	0
$688$	36.0000	1.37249
$689$	39.6611i	1.51097i
$690$	0	0
$691$	− 46.8722i	− 1.78310i	−0.452921	−	0.891551i	$-0.649618\pi$
$691$	− 46.8722i	− 1.78310i	0.452921	−	0.891551i	$-0.350382\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	23.0000	0.868698	0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000	0.868698	0.434349	+	0.900745i	$0.356978\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	−45.0000	−1.68763
$712$	0	0
$713$	− 10.8167i	− 0.405087i
$714$	0	0
$715$	0	0
$716$	50.0000	1.86859
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	− 43.2666i	− 1.61245i
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	40.0000	1.48556
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	54.0833i	1.99761i	0.0488615	+	0.998806i	$0.484441\pi$
$733$	54.0833i	1.99761i	−0.0488615	+	0.998806i	$0.515559\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	54.0833i	1.97880i
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−27.0000	−0.985244	−0.492622	−	0.870243i	$-0.663961\pi$
$751$	−27.0000	−0.985244	−0.492622	+	0.870243i	$0.663961\pi$
$752$	14.4222i	0.525924i
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−47.0000	−1.70824	−0.854122	−	0.520073i	$-0.825905\pi$
$757$	−47.0000	−1.70824	−0.854122	+	0.520073i	$0.825905\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	− 46.8722i	− 1.69911i	−0.527496	−	0.849557i	$-0.676869\pi$
$761$	− 46.8722i	− 1.69911i	0.527496	−	0.849557i	$-0.323131\pi$
$762$	0	0
$763$	0	0
$764$	−40.0000	−1.44715
$765$	0	0
$766$	0	0
$767$	−52.0000	−1.87761
$768$	0	0
$769$	32.4500i	1.17018i	0.810970	+	0.585088i	$0.198940\pi$
$769$	32.4500i	1.17018i	−0.810970	+	0.585088i	$0.801060\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	− 36.0555i	− 1.29683i	−0.761288	−	0.648413i	$-0.775433\pi$
$773$	− 36.0555i	− 1.29683i	0.761288	−	0.648413i	$-0.224567\pi$
$774$	0	0
$775$	86.5332i	3.10837i
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−26.0000	−0.931547
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	39.6611i	1.41376i	0.707331	+	0.706882i	$0.249899\pi$
$787$	39.6611i	1.41376i	−0.707331	+	0.706882i	$0.750101\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	− 10.8167i	− 0.382188i
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−31.0000	−1.08990	−0.544951	−	0.838468i	$-0.683452\pi$
$809$	−31.0000	−1.08990	−0.544951	+	0.838468i	$0.683452\pi$
$810$	0	0
$811$	− 43.2666i	− 1.51930i	−0.650334	−	0.759648i	$-0.725371\pi$
$811$	− 43.2666i	− 1.51930i	0.650334	−	0.759648i	$-0.274629\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	32.4500i	1.13528i
$818$	0	0
$819$	0	0
$820$	−52.0000	−1.81592
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−6.00000	−0.208514
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	28.8444i	1.00000i
$833$	0	0
$834$	0	0
$835$	65.0000	2.24942
$836$	0	0
$837$	0	0
$838$	0	0
$839$	57.6888i	1.99164i	0.0913415	+	0.995820i	$0.470885\pi$
$839$	57.6888i	1.99164i	−0.0913415	+	0.995820i	$0.529115\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	0	0
$844$	−10.0000	−0.344214
$845$	− 46.8722i	− 1.61245i
$846$	0	0
$847$	0	0
$848$	44.0000	1.51097
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 18.0278i	− 0.617259i	−0.951182	−	0.308629i	$-0.900130\pi$
$853$	− 18.0278i	− 0.617259i	0.951182	−	0.308629i	$-0.0998703\pi$
$854$	0	0
$855$	39.0000	1.33377
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	64.8999i	2.21307i
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	54.0833i	1.83044i
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	− 36.0555i	− 1.20723i
$893$	−13.0000	−0.435028
$894$	0	0
$895$	90.1388i	3.01301i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	54.0833i	1.80378i
$900$	48.0000	1.60000
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	53.0000	1.75984	0.879918	−	0.475125i	$-0.157597\pi$
$907$	53.0000	1.75984	0.879918	+	0.475125i	$0.157597\pi$
$908$	28.8444i	0.957235i
$909$	0	0
$910$	0	0
$911$	37.0000	1.22586	0.612932	−	0.790135i	$-0.289990\pi$
$911$	37.0000	1.22586	0.612932	+	0.790135i	$0.289990\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	− 43.2666i	− 1.42957i
$917$	0	0
$918$	0	0
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	3.60555i	0.118294i	0.998249	+	0.0591472i	$0.0188381\pi$
$929$	3.60555i	0.118294i	−0.998249	+	0.0591472i	$0.981162\pi$
$930$	0	0
$931$	0	0
$932$	58.0000	1.89985
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	0	0
$939$	0	0
$940$	−26.0000	−0.848026
$941$	− 61.2944i	− 1.99814i	−0.0431245	−	0.999070i	$-0.513731\pi$
$941$	− 61.2944i	− 1.99814i	0.0431245	−	0.999070i	$-0.486269\pi$
$942$	0	0
$943$	7.21110i	0.234826i
$944$	57.6888i	1.87761i
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	39.0000	1.26599
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−61.0000	−1.97598	−0.987992	−	0.154506i	$-0.950622\pi$
$953$	−61.0000	−1.97598	−0.987992	+	0.154506i	$0.950622\pi$
$954$	0	0
$955$	− 72.1110i	− 2.33346i
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−86.0000	−2.77419
$962$	0	0
$963$	−24.0000	−0.773389
$964$	− 21.6333i	− 0.696762i
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	− 61.2944i	− 1.95499i	−0.210966	−	0.977493i	$-0.567661\pi$
$983$	− 61.2944i	− 1.95499i	0.210966	−	0.977493i	$-0.432339\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−26.0000	−0.827170
$989$	9.00000	0.286183
$990$	0	0
$991$	60.0000	1.90596	0.952981	−	0.303029i	$-0.0979978\pi$
$991$	60.0000	1.90596	0.952981	+	0.303029i	$0.0979978\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.b.246.2	yes	2
7.2	even	3		637.2.r.b.116.2		4
7.3	odd	6		637.2.r.b.324.2		4
7.4	even	3		637.2.r.b.324.1		4
7.5	odd	6		637.2.r.b.116.1		4
7.6	odd	2	inner	637.2.c.b.246.1	✓	2
13.5	odd	4		8281.2.a.u.1.2		2
13.8	odd	4		8281.2.a.u.1.1		2
13.12	even	2	inner	637.2.c.b.246.1	✓	2
91.12	odd	6		637.2.r.b.116.2		4
91.25	even	6		637.2.r.b.324.2		4
91.34	even	4		8281.2.a.u.1.2		2
91.38	odd	6		637.2.r.b.324.1		4
91.51	even	6		637.2.r.b.116.1		4
91.83	even	4		8281.2.a.u.1.1		2
91.90	odd	2	CM	637.2.c.b.246.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.b.246.1	✓	2	7.6	odd	2	inner
637.2.c.b.246.1	✓	2	13.12	even	2	inner
637.2.c.b.246.2	yes	2	1.1	even	1	trivial
637.2.c.b.246.2	yes	2	91.90	odd	2	CM
637.2.r.b.116.1		4	7.5	odd	6
637.2.r.b.116.1		4	91.51	even	6
637.2.r.b.116.2		4	7.2	even	3
637.2.r.b.116.2		4	91.12	odd	6
637.2.r.b.324.1		4	7.4	even	3
637.2.r.b.324.1		4	91.38	odd	6
637.2.r.b.324.2		4	7.3	odd	6
637.2.r.b.324.2		4	91.25	even	6
8281.2.a.u.1.1		2	13.8	odd	4
8281.2.a.u.1.1		2	91.83	even	4
8281.2.a.u.1.2		2	13.5	odd	4
8281.2.a.u.1.2		2	91.34	even	4

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{4} +3.60555i q^{5} -3.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{4} +3.60555i q^{5} -3.00000 q^{9} +3.60555i q^{13} +4.00000 q^{16} +3.60555i q^{19} +7.21110i q^{20} +1.00000 q^{23} -8.00000 q^{25} -5.00000 q^{29} -10.8167i q^{31} -6.00000 q^{36} +7.21110i q^{41} +9.00000 q^{43} -10.8167i q^{45} +3.60555i q^{47} +7.21110i q^{52} +11.0000 q^{53} +14.4222i q^{59} +8.00000 q^{64} -13.0000 q^{65} -10.8167i q^{73} +7.21110i q^{76} +15.0000 q^{79} +14.4222i q^{80} +9.00000 q^{81} -18.0278i q^{83} +3.60555i q^{89} +2.00000 q^{92} -13.0000 q^{95} -18.0278i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{4} - 6 q^{9}+O(q^{10}) \) 2 * q + 4 * q^4 - 6 * q^9	\( 2 q + 4 q^{4} - 6 q^{9} + 8 q^{16} + 2 q^{23} - 16 q^{25} - 10 q^{29} - 12 q^{36} + 18 q^{43} + 22 q^{53} + 16 q^{64} - 26 q^{65} + 30 q^{79} + 18 q^{81} + 4 q^{92} - 26 q^{95}+O(q^{100}) \) 2 * q + 4 * q^4 - 6 * q^9 + 8 * q^16 + 2 * q^23 - 16 * q^25 - 10 * q^29 - 12 * q^36 + 18 * q^43 + 22 * q^53 + 16 * q^64 - 26 * q^65 + 30 * q^79 + 18 * q^81 + 4 * q^92 - 26 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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