LMFDB - Embedded newform 231.1.h.a.230.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,1,Mod(230,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("231.230");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	231.h (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:	yes
Analytic conductor:	$0.115284017918$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.231.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.373527.1

Embedding invariants

Embedding label			230.1
Character	$\chi$	$=$	231.230

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} -1.00000 q^{16} -1.00000 q^{18} +1.00000 q^{19} +1.00000 q^{21} -1.00000 q^{22} -1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} -1.00000 q^{29} +1.00000 q^{30} -1.00000 q^{33} -1.00000 q^{35} -1.00000 q^{37} -1.00000 q^{38} -1.00000 q^{39} +1.00000 q^{40} -1.00000 q^{42} +1.00000 q^{45} +1.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{54} +1.00000 q^{55} -1.00000 q^{56} -1.00000 q^{57} +1.00000 q^{58} +1.00000 q^{59} -2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} +1.00000 q^{66} -1.00000 q^{67} +1.00000 q^{70} +1.00000 q^{72} +1.00000 q^{73} +1.00000 q^{74} -1.00000 q^{77} +1.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} +1.00000 q^{87} +1.00000 q^{88} -2.00000 q^{89} -1.00000 q^{90} -1.00000 q^{91} -1.00000 q^{94} +1.00000 q^{95} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−1.00000	−1.00000
$3$	−1.00000	−1.00000
$4$	0	0
$5$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$5$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$6$	1.00000	1.00000
$7$	−1.00000	−1.00000
$7$	−1.00000	−1.00000
$8$	1.00000	1.00000
$9$	1.00000	1.00000
$10$	−1.00000	−1.00000
$11$	1.00000	1.00000
$11$	1.00000	1.00000
$12$	0	0
$13$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$13$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$14$	1.00000	1.00000
$15$	−1.00000	−1.00000
$16$	−1.00000	−1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−1.00000	−1.00000
$19$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$19$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$20$	0	0
$21$	1.00000	1.00000
$22$	−1.00000	−1.00000
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−1.00000	−1.00000
$25$	0	0
$26$	−1.00000	−1.00000
$27$	−1.00000	−1.00000
$28$	0	0
$29$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$30$	1.00000	1.00000
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	−1.00000	−1.00000
$34$	0	0
$35$	−1.00000	−1.00000
$36$	0	0
$37$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$38$	−1.00000	−1.00000
$39$	−1.00000	−1.00000
$40$	1.00000	1.00000
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	−1.00000	−1.00000
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	1.00000	1.00000
$46$	0	0
$47$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$47$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$48$	1.00000	1.00000
$49$	1.00000	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	1.00000	1.00000
$55$	1.00000	1.00000
$56$	−1.00000	−1.00000
$57$	−1.00000	−1.00000
$58$	1.00000	1.00000
$59$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$59$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$60$	0	0
$61$	−2.00000	−2.00000	−1.00000			$\pi$
$61$	−2.00000	−2.00000	−1.00000			$\pi$
$62$	0	0
$63$	−1.00000	−1.00000
$64$	1.00000	1.00000
$65$	1.00000	1.00000
$66$	1.00000	1.00000
$67$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$68$	0	0
$69$	0	0
$70$	1.00000	1.00000
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	1.00000	1.00000
$73$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$73$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$74$	1.00000	1.00000
$75$	0	0
$76$	0	0
$77$	−1.00000	−1.00000
$78$	1.00000	1.00000
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−1.00000	−1.00000
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1.00000	1.00000
$88$	1.00000	1.00000
$89$	−2.00000	−2.00000	−1.00000			$\pi$
$89$	−2.00000	−2.00000	−1.00000			$\pi$
$90$	−1.00000	−1.00000
$91$	−1.00000	−1.00000
$92$	0	0
$93$	0	0
$94$	−1.00000	−1.00000
$95$	1.00000	1.00000
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.00000	−1.00000
$99$	1.00000	1.00000
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	1.00000	1.00000
$105$	1.00000	1.00000
$106$	0	0
$107$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	−1.00000	−1.00000
$111$	1.00000	1.00000
$112$	1.00000	1.00000
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	1.00000	1.00000
$115$	0	0
$116$	0	0
$117$	1.00000	1.00000
$118$	−1.00000	−1.00000
$119$	0	0
$120$	−1.00000	−1.00000
$121$	1.00000	1.00000
$122$	2.00000	2.00000
$123$	0	0
$124$	0	0
$125$	−1.00000	−1.00000
$126$	1.00000	1.00000
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	0	0
$130$	−1.00000	−1.00000
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	−1.00000	−1.00000
$134$	1.00000	1.00000
$135$	−1.00000	−1.00000
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−2.00000	−2.00000	−1.00000			$\pi$
$139$	−2.00000	−2.00000	−1.00000			$\pi$
$140$	0	0
$141$	−1.00000	−1.00000
$142$	0	0
$143$	1.00000	1.00000
$144$	−1.00000	−1.00000
$145$	−1.00000	−1.00000
$146$	−1.00000	−1.00000
$147$	−1.00000	−1.00000
$148$	0	0
$149$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	1.00000	1.00000
$153$	0	0
$154$	1.00000	1.00000
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	−1.00000	−1.00000
$163$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$163$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$164$	0	0
$165$	−1.00000	−1.00000
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	1.00000	1.00000
$169$	0	0
$170$	0	0
$171$	1.00000	1.00000
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	−1.00000	−1.00000
$175$	0	0
$176$	−1.00000	−1.00000
$177$	−1.00000	−1.00000
$178$	2.00000	2.00000
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	1.00000	1.00000
$183$	2.00000	2.00000
$184$	0	0
$185$	−1.00000	−1.00000
$186$	0	0
$187$	0	0
$188$	0	0
$189$	1.00000	1.00000
$190$	−1.00000	−1.00000
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−1.00000	−1.00000
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	−1.00000	−1.00000
$196$	0	0
$197$	2.00000	2.00000	1.00000			$0$
$197$	2.00000	2.00000	1.00000			$0$
$198$	−1.00000	−1.00000
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	1.00000	1.00000
$202$	0	0
$203$	1.00000	1.00000
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−1.00000	−1.00000
$209$	1.00000	1.00000
$210$	−1.00000	−1.00000
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	1.00000	1.00000
$215$	0	0
$216$	−1.00000	−1.00000
$217$	0	0
$218$	0	0
$219$	−1.00000	−1.00000
$220$	0	0
$221$	0	0
$222$	−1.00000	−1.00000
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	1.00000	1.00000
$232$	−1.00000	−1.00000
$233$	2.00000	2.00000	1.00000			$0$
$233$	2.00000	2.00000	1.00000			$0$
$234$	−1.00000	−1.00000
$235$	1.00000	1.00000
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$240$	1.00000	1.00000
$241$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$241$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$242$	−1.00000	−1.00000
$243$	−1.00000	−1.00000
$244$	0	0
$245$	1.00000	1.00000
$246$	0	0
$247$	1.00000	1.00000
$248$	0	0
$249$	0	0
$250$	1.00000	1.00000
$251$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$251$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$258$	0	0
$259$	1.00000	1.00000
$260$	0	0
$261$	−1.00000	−1.00000
$262$	0	0
$263$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$264$	−1.00000	−1.00000
$265$	0	0
$266$	1.00000	1.00000
$267$	2.00000	2.00000
$268$	0	0
$269$	−2.00000	−2.00000	−1.00000			$\pi$
$269$	−2.00000	−2.00000	−1.00000			$\pi$
$270$	1.00000	1.00000
$271$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$271$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$272$	0	0
$273$	1.00000	1.00000
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	2.00000	2.00000
$279$	0	0
$280$	−1.00000	−1.00000
$281$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$282$	1.00000	1.00000
$283$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$283$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$284$	0	0
$285$	−1.00000	−1.00000
$286$	−1.00000	−1.00000
$287$	0	0
$288$	0	0
$289$	1.00000	1.00000
$290$	1.00000	1.00000
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	1.00000	1.00000
$295$	1.00000	1.00000
$296$	−1.00000	−1.00000
$297$	−1.00000	−1.00000
$298$	1.00000	1.00000
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−1.00000	−1.00000
$305$	−2.00000	−2.00000
$306$	0	0
$307$	−2.00000	−2.00000	−1.00000			$\pi$
$307$	−2.00000	−2.00000	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$312$	−1.00000	−1.00000
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	−1.00000	−1.00000
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	−1.00000	−1.00000
$320$	1.00000	1.00000
$321$	1.00000	1.00000
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	1.00000	1.00000
$327$	0	0
$328$	0	0
$329$	−1.00000	−1.00000
$330$	1.00000	1.00000
$331$	2.00000	2.00000	1.00000			$0$
$331$	2.00000	2.00000	1.00000			$0$
$332$	0	0
$333$	−1.00000	−1.00000
$334$	0	0
$335$	−1.00000	−1.00000
$336$	−1.00000	−1.00000
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	−1.00000	−1.00000
$343$	−1.00000	−1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	2.00000	2.00000	1.00000			$0$
$347$	2.00000	2.00000	1.00000			$0$
$348$	0	0
$349$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$349$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$350$	0	0
$351$	−1.00000	−1.00000
$352$	0	0
$353$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$353$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$354$	1.00000	1.00000
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	2.00000	2.00000	1.00000			$0$
$359$	2.00000	2.00000	1.00000			$0$
$360$	1.00000	1.00000
$361$	0	0
$362$	0	0
$363$	−1.00000	−1.00000
$364$	0	0
$365$	1.00000	1.00000
$366$	−2.00000	−2.00000
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	1.00000	1.00000
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	1.00000	1.00000
$376$	1.00000	1.00000
$377$	−1.00000	−1.00000
$378$	−1.00000	−1.00000
$379$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$379$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−2.00000	−2.00000	−1.00000			$\pi$
$383$	−2.00000	−2.00000	−1.00000			$\pi$
$384$	1.00000	1.00000
$385$	−1.00000	−1.00000
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	1.00000	1.00000
$391$	0	0
$392$	1.00000	1.00000
$393$	0	0
$394$	−2.00000	−2.00000
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	1.00000	1.00000
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	−1.00000	−1.00000
$403$	0	0
$404$	0	0
$405$	1.00000	1.00000
$406$	−1.00000	−1.00000
$407$	−1.00000	−1.00000
$408$	0	0
$409$	−2.00000	−2.00000	−1.00000			$\pi$
$409$	−2.00000	−2.00000	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−1.00000	−1.00000
$414$	0	0
$415$	0	0
$416$	0	0
$417$	2.00000	2.00000
$418$	−1.00000	−1.00000
$419$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$419$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$420$	0	0
$421$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$422$	0	0
$423$	1.00000	1.00000
$424$	0	0
$425$	0	0
$426$	0	0
$427$	2.00000	2.00000
$428$	0	0
$429$	−1.00000	−1.00000
$430$	0	0
$431$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$431$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$432$	1.00000	1.00000
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	1.00000	1.00000
$436$	0	0
$437$	0	0
$438$	1.00000	1.00000
$439$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$439$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$440$	1.00000	1.00000
$441$	1.00000	1.00000
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	−2.00000	−2.00000
$446$	0	0
$447$	1.00000	1.00000
$448$	−1.00000	−1.00000
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−1.00000	−1.00000
$456$	−1.00000	−1.00000
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	−1.00000	−1.00000
$463$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$464$	1.00000	1.00000
$465$	0	0
$466$	−2.00000	−2.00000
$467$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$467$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$468$	0	0
$469$	1.00000	1.00000
$470$	−1.00000	−1.00000
$471$	0	0
$472$	1.00000	1.00000
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	1.00000	1.00000
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	−1.00000	−1.00000
$482$	−1.00000	−1.00000
$483$	0	0
$484$	0	0
$485$	0	0
$486$	1.00000	1.00000
$487$	2.00000	2.00000	1.00000			$0$
$487$	2.00000	2.00000	1.00000			$0$
$488$	−2.00000	−2.00000
$489$	1.00000	1.00000
$490$	−1.00000	−1.00000
$491$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$492$	0	0
$493$	0	0
$494$	−1.00000	−1.00000
$495$	1.00000	1.00000
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$500$	0	0
$501$	0	0
$502$	−1.00000	−1.00000
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	−1.00000	−1.00000
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	−2.00000	−2.00000	−1.00000			$\pi$
$509$	−2.00000	−2.00000	−1.00000			$\pi$
$510$	0	0
$511$	−1.00000	−1.00000
$512$	1.00000	1.00000
$513$	−1.00000	−1.00000
$514$	−1.00000	−1.00000
$515$	0	0
$516$	0	0
$517$	1.00000	1.00000
$518$	−1.00000	−1.00000
$519$	0	0
$520$	1.00000	1.00000
$521$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$521$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$522$	1.00000	1.00000
$523$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$523$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$524$	0	0
$525$	0	0
$526$	1.00000	1.00000
$527$	0	0
$528$	1.00000	1.00000
$529$	1.00000	1.00000
$530$	0	0
$531$	1.00000	1.00000
$532$	0	0
$533$	0	0
$534$	−2.00000	−2.00000
$535$	−1.00000	−1.00000
$536$	−1.00000	−1.00000
$537$	0	0
$538$	2.00000	2.00000
$539$	1.00000	1.00000
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	−1.00000	−1.00000
$543$	0	0
$544$	0	0
$545$	0	0
$546$	−1.00000	−1.00000
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	−2.00000	−2.00000
$550$	0	0
$551$	−1.00000	−1.00000
$552$	0	0
$553$	0	0
$554$	0	0
$555$	1.00000	1.00000
$556$	0	0
$557$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$557$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$558$	0	0
$559$	0	0
$560$	1.00000	1.00000
$561$	0	0
$562$	1.00000	1.00000
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	−1.00000	−1.00000
$567$	−1.00000	−1.00000
$568$	0	0
$569$	2.00000	2.00000	1.00000			$0$
$569$	2.00000	2.00000	1.00000			$0$
$570$	1.00000	1.00000
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.00000	1.00000
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−1.00000	−1.00000
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	1.00000	1.00000
$585$	1.00000	1.00000
$586$	0	0
$587$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$587$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$588$	0	0
$589$	0	0
$590$	−1.00000	−1.00000
$591$	−2.00000	−2.00000
$592$	1.00000	1.00000
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	1.00000	1.00000
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$601$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$602$	0	0
$603$	−1.00000	−1.00000
$604$	0	0
$605$	1.00000	1.00000
$606$	0	0
$607$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$608$	0	0
$609$	−1.00000	−1.00000
$610$	2.00000	2.00000
$611$	1.00000	1.00000
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	2.00000	2.00000
$615$	0	0
$616$	−1.00000	−1.00000
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	2.00000	2.00000
$623$	2.00000	2.00000
$624$	1.00000	1.00000
$625$	−1.00000	−1.00000
$626$	0	0
$627$	−1.00000	−1.00000
$628$	0	0
$629$	0	0
$630$	1.00000	1.00000
$631$	2.00000	2.00000	1.00000			$0$
$631$	2.00000	2.00000	1.00000			$0$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	1.00000	1.00000
$638$	1.00000	1.00000
$639$	0	0
$640$	−1.00000	−1.00000
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	−1.00000	−1.00000
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$647$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$648$	1.00000	1.00000
$649$	1.00000	1.00000
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	1.00000	1.00000
$658$	1.00000	1.00000
$659$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$659$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−2.00000	−2.00000
$663$	0	0
$664$	0	0
$665$	−1.00000	−1.00000
$666$	1.00000	1.00000
$667$	0	0
$668$	0	0
$669$	0	0
$670$	1.00000	1.00000
$671$	−2.00000	−2.00000
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	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			$\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	1.00000
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	−1.00000	−1.00000
$694$	−2.00000	−2.00000
$695$	−2.00000	−2.00000
$696$	1.00000	1.00000
$697$	0	0
$698$	−1.00000	−1.00000
$699$	−2.00000	−2.00000
$700$	0	0
$701$	2.00000	2.00000	1.00000			$0$
$701$	2.00000	2.00000	1.00000			$0$
$702$	1.00000	1.00000
$703$	−1.00000	−1.00000
$704$	1.00000	1.00000
$705$	−1.00000	−1.00000
$706$	−1.00000	−1.00000
$707$	0	0
$708$	0	0
$709$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$709$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$710$	0	0
$711$	0	0
$712$	−2.00000	−2.00000
$713$	0	0
$714$	0	0
$715$	1.00000	1.00000
$716$	0	0
$717$	1.00000	1.00000
$718$	−2.00000	−2.00000
$719$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$719$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$720$	−1.00000	−1.00000
$721$	0	0
$722$	0	0
$723$	−1.00000	−1.00000
$724$	0	0
$725$	0	0
$726$	1.00000	1.00000
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	−1.00000	−1.00000
$729$	1.00000	1.00000
$730$	−1.00000	−1.00000
$731$	0	0
$732$	0	0
$733$	−2.00000	−2.00000	−1.00000			$\pi$
$733$	−2.00000	−2.00000	−1.00000			$\pi$
$734$	0	0
$735$	−1.00000	−1.00000
$736$	0	0
$737$	−1.00000	−1.00000
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	−1.00000	−1.00000
$742$	0	0
$743$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$744$	0	0
$745$	−1.00000	−1.00000
$746$	0	0
$747$	0	0
$748$	0	0
$749$	1.00000	1.00000
$750$	−1.00000	−1.00000
$751$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$752$	−1.00000	−1.00000
$753$	−1.00000	−1.00000
$754$	1.00000	1.00000
$755$	0	0
$756$	0	0
$757$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$757$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$758$	1.00000	1.00000
$759$	0	0
$760$	1.00000	1.00000
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	2.00000	2.00000
$767$	1.00000	1.00000
$768$	0	0
$769$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$769$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$770$	1.00000	1.00000
$771$	−1.00000	−1.00000
$772$	0	0
$773$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$773$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−1.00000	−1.00000
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	1.00000	1.00000
$784$	−1.00000	−1.00000
$785$	0	0
$786$	0	0
$787$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$787$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$788$	0	0
$789$	1.00000	1.00000
$790$	0	0
$791$	0	0
$792$	1.00000	1.00000
$793$	−2.00000	−2.00000
$794$	0	0
$795$	0	0
$796$	0	0
$797$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$797$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$798$	−1.00000	−1.00000
$799$	0	0
$800$	0	0
$801$	−2.00000	−2.00000
$802$	0	0
$803$	1.00000	1.00000
$804$	0	0
$805$	0	0
$806$	0	0
$807$	2.00000	2.00000
$808$	0	0
$809$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$810$	−1.00000	−1.00000
$811$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$811$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$812$	0	0
$813$	−1.00000	−1.00000
$814$	1.00000	1.00000
$815$	−1.00000	−1.00000
$816$	0	0
$817$	0	0
$818$	2.00000	2.00000
$819$	−1.00000	−1.00000
$820$	0	0
$821$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$821$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$822$	0	0
$823$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$823$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$824$	0	0
$825$	0	0
$826$	1.00000	1.00000
$827$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$827$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	1.00000	1.00000
$833$	0	0
$834$	−2.00000	−2.00000
$835$	0	0
$836$	0	0
$837$	0	0
$838$	−1.00000	−1.00000
$839$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$839$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$840$	1.00000	1.00000
$841$	0	0
$842$	1.00000	1.00000
$843$	1.00000	1.00000
$844$	0	0
$845$	0	0
$846$	−1.00000	−1.00000
$847$	−1.00000	−1.00000
$848$	0	0
$849$	−1.00000	−1.00000
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−2.00000	−2.00000	−1.00000			$\pi$
$853$	−2.00000	−2.00000	−1.00000			$\pi$
$854$	−2.00000	−2.00000
$855$	1.00000	1.00000
$856$	−1.00000	−1.00000
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	1.00000	1.00000
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	1.00000	1.00000
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−1.00000	−1.00000
$868$	0	0
$869$	0	0
$870$	−1.00000	−1.00000
$871$	−1.00000	−1.00000
$872$	0	0
$873$	0	0
$874$	0	0
$875$	1.00000	1.00000
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	−1.00000	−1.00000
$879$	0	0
$880$	−1.00000	−1.00000
$881$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$881$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$882$	−1.00000	−1.00000
$883$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$883$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$884$	0	0
$885$	−1.00000	−1.00000
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	1.00000	1.00000
$889$	0	0
$890$	2.00000	2.00000
$891$	1.00000	1.00000
$892$	0	0
$893$	1.00000	1.00000
$894$	−1.00000	−1.00000
$895$	0	0
$896$	1.00000	1.00000
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	2.00000	2.00000	1.00000			$0$
$907$	2.00000	2.00000	1.00000			$0$
$908$	0	0
$909$	0	0
$910$	1.00000	1.00000
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	1.00000	1.00000
$913$	0	0
$914$	0	0
$915$	2.00000	2.00000
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	2.00000	2.00000
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	1.00000	1.00000
$927$	0	0
$928$	0	0
$929$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$929$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$930$	0	0
$931$	1.00000	1.00000
$932$	0	0
$933$	2.00000	2.00000
$934$	−1.00000	−1.00000
$935$	0	0
$936$	1.00000	1.00000
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$938$	−1.00000	−1.00000
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	−1.00000	−1.00000
$945$	1.00000	1.00000
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	1.00000	1.00000
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	1.00000	1.00000
$958$	0	0
$959$	0	0
$960$	−1.00000	−1.00000
$961$	1.00000	1.00000
$962$	1.00000	1.00000
$963$	−1.00000	−1.00000
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	1.00000	1.00000
$969$	0	0
$970$	0	0
$971$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$971$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$972$	0	0
$973$	2.00000	2.00000
$974$	−2.00000	−2.00000
$975$	0	0
$976$	2.00000	2.00000
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−1.00000	−1.00000
$979$	−2.00000	−2.00000
$980$	0	0
$981$	0	0
$982$	1.00000	1.00000
$983$	−2.00000	−2.00000	−1.00000			$\pi$
$983$	−2.00000	−2.00000	−1.00000			$\pi$
$984$	0	0
$985$	2.00000	2.00000
$986$	0	0
$987$	1.00000	1.00000
$988$	0	0
$989$	0	0
$990$	−1.00000	−1.00000
$991$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$992$	0	0
$993$	−2.00000	−2.00000
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−2.00000	−2.00000	−1.00000			$\pi$
$997$	−2.00000	−2.00000	−1.00000			$\pi$
$998$	1.00000	1.00000
$999$	1.00000	1.00000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.1.h.a.230.1	✓	1
3.2	odd	2		231.1.h.d.230.1	yes	1
4.3	odd	2		3696.1.bb.d.3233.1		1
7.2	even	3		1617.1.k.d.1550.1		2
7.3	odd	6		1617.1.k.c.362.1		2
7.4	even	3		1617.1.k.d.362.1		2
7.5	odd	6		1617.1.k.c.1550.1		2
7.6	odd	2		231.1.h.b.230.1	yes	1
11.2	odd	10		2541.1.r.b.524.1		4
11.3	even	5		2541.1.r.d.1322.1		4
11.4	even	5		2541.1.r.d.2393.1		4
11.5	even	5		2541.1.r.d.965.1		4
11.6	odd	10		2541.1.r.b.965.1		4
11.7	odd	10		2541.1.r.b.2393.1		4
11.8	odd	10		2541.1.r.b.1322.1		4
11.9	even	5		2541.1.r.d.524.1		4
11.10	odd	2		231.1.h.c.230.1	yes	1
12.11	even	2		3696.1.bb.b.3233.1		1
21.2	odd	6		1617.1.k.a.1550.1		2
21.5	even	6		1617.1.k.b.1550.1		2
21.11	odd	6		1617.1.k.a.362.1		2
21.17	even	6		1617.1.k.b.362.1		2
21.20	even	2		231.1.h.c.230.1	yes	1
28.27	even	2		3696.1.bb.a.3233.1		1
33.2	even	10		2541.1.r.c.524.1		4
33.5	odd	10		2541.1.r.a.965.1		4
33.8	even	10		2541.1.r.c.1322.1		4
33.14	odd	10		2541.1.r.a.1322.1		4
33.17	even	10		2541.1.r.c.965.1		4
33.20	odd	10		2541.1.r.a.524.1		4
33.26	odd	10		2541.1.r.a.2393.1		4
33.29	even	10		2541.1.r.c.2393.1		4
33.32	even	2		231.1.h.b.230.1	yes	1
44.43	even	2		3696.1.bb.c.3233.1		1
77.6	even	10		2541.1.r.a.965.1		4
77.10	even	6		1617.1.k.a.362.1		2
77.13	even	10		2541.1.r.a.524.1		4
77.20	odd	10		2541.1.r.c.524.1		4
77.27	odd	10		2541.1.r.c.965.1		4
77.32	odd	6		1617.1.k.b.362.1		2
77.41	even	10		2541.1.r.a.1322.1		4
77.48	odd	10		2541.1.r.c.2393.1		4
77.54	even	6		1617.1.k.a.1550.1		2
77.62	even	10		2541.1.r.a.2393.1		4
77.65	odd	6		1617.1.k.b.1550.1		2
77.69	odd	10		2541.1.r.c.1322.1		4
77.76	even	2		231.1.h.d.230.1	yes	1
84.83	odd	2		3696.1.bb.c.3233.1		1
132.131	odd	2		3696.1.bb.a.3233.1		1
231.20	even	10		2541.1.r.b.524.1		4
231.32	even	6		1617.1.k.c.362.1		2
231.41	odd	10		2541.1.r.d.1322.1		4
231.62	odd	10		2541.1.r.d.2393.1		4
231.65	even	6		1617.1.k.c.1550.1		2
231.83	odd	10		2541.1.r.d.965.1		4
231.104	even	10		2541.1.r.b.965.1		4
231.125	even	10		2541.1.r.b.2393.1		4
231.131	odd	6		1617.1.k.d.1550.1		2
231.146	even	10		2541.1.r.b.1322.1		4
231.164	odd	6		1617.1.k.d.362.1		2
231.167	odd	10		2541.1.r.d.524.1		4
231.230	odd	2	CM	231.1.h.a.230.1	✓	1
308.307	odd	2		3696.1.bb.b.3233.1		1
924.923	even	2		3696.1.bb.d.3233.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.1.h.a.230.1	✓	1	1.1	even	1	trivial
231.1.h.a.230.1	✓	1	231.230	odd	2	CM
231.1.h.b.230.1	yes	1	7.6	odd	2
231.1.h.b.230.1	yes	1	33.32	even	2
231.1.h.c.230.1	yes	1	11.10	odd	2
231.1.h.c.230.1	yes	1	21.20	even	2
231.1.h.d.230.1	yes	1	3.2	odd	2
231.1.h.d.230.1	yes	1	77.76	even	2
1617.1.k.a.362.1		2	21.11	odd	6
1617.1.k.a.362.1		2	77.10	even	6
1617.1.k.a.1550.1		2	21.2	odd	6
1617.1.k.a.1550.1		2	77.54	even	6
1617.1.k.b.362.1		2	21.17	even	6
1617.1.k.b.362.1		2	77.32	odd	6
1617.1.k.b.1550.1		2	21.5	even	6
1617.1.k.b.1550.1		2	77.65	odd	6
1617.1.k.c.362.1		2	7.3	odd	6
1617.1.k.c.362.1		2	231.32	even	6
1617.1.k.c.1550.1		2	7.5	odd	6
1617.1.k.c.1550.1		2	231.65	even	6
1617.1.k.d.362.1		2	7.4	even	3
1617.1.k.d.362.1		2	231.164	odd	6
1617.1.k.d.1550.1		2	7.2	even	3
1617.1.k.d.1550.1		2	231.131	odd	6
2541.1.r.a.524.1		4	33.20	odd	10
2541.1.r.a.524.1		4	77.13	even	10
2541.1.r.a.965.1		4	33.5	odd	10
2541.1.r.a.965.1		4	77.6	even	10
2541.1.r.a.1322.1		4	33.14	odd	10
2541.1.r.a.1322.1		4	77.41	even	10
2541.1.r.a.2393.1		4	33.26	odd	10
2541.1.r.a.2393.1		4	77.62	even	10
2541.1.r.b.524.1		4	11.2	odd	10
2541.1.r.b.524.1		4	231.20	even	10
2541.1.r.b.965.1		4	11.6	odd	10
2541.1.r.b.965.1		4	231.104	even	10
2541.1.r.b.1322.1		4	11.8	odd	10
2541.1.r.b.1322.1		4	231.146	even	10
2541.1.r.b.2393.1		4	11.7	odd	10
2541.1.r.b.2393.1		4	231.125	even	10
2541.1.r.c.524.1		4	33.2	even	10
2541.1.r.c.524.1		4	77.20	odd	10
2541.1.r.c.965.1		4	33.17	even	10
2541.1.r.c.965.1		4	77.27	odd	10
2541.1.r.c.1322.1		4	33.8	even	10
2541.1.r.c.1322.1		4	77.69	odd	10
2541.1.r.c.2393.1		4	33.29	even	10
2541.1.r.c.2393.1		4	77.48	odd	10
2541.1.r.d.524.1		4	11.9	even	5
2541.1.r.d.524.1		4	231.167	odd	10
2541.1.r.d.965.1		4	11.5	even	5
2541.1.r.d.965.1		4	231.83	odd	10
2541.1.r.d.1322.1		4	11.3	even	5
2541.1.r.d.1322.1		4	231.41	odd	10
2541.1.r.d.2393.1		4	11.4	even	5
2541.1.r.d.2393.1		4	231.62	odd	10
3696.1.bb.a.3233.1		1	28.27	even	2
3696.1.bb.a.3233.1		1	132.131	odd	2
3696.1.bb.b.3233.1		1	12.11	even	2
3696.1.bb.b.3233.1		1	308.307	odd	2
3696.1.bb.c.3233.1		1	44.43	even	2
3696.1.bb.c.3233.1		1	84.83	odd	2
3696.1.bb.d.3233.1		1	4.3	odd	2
3696.1.bb.d.3233.1		1	924.923	even	2

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	231.h (of order \(2\), degree \(1\), minimal)

\(n\)	\(155\)	\(199\)	\(211\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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