LMFDB - Embedded newform 116.1.d.a.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,1,Mod(115,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("116.115");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	116.d (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:	$0.0578915414654$
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 3.1.116.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.53824.1

Embedding invariants

Embedding label			115.1
Character	$\chi$	$=$	116.115

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{19} -1.00000 q^{20} -1.00000 q^{22} -1.00000 q^{24} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{29} +1.00000 q^{30} +1.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +2.00000 q^{38} -1.00000 q^{39} +1.00000 q^{40} +1.00000 q^{43} +1.00000 q^{44} +1.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{52} -1.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -2.00000 q^{57} -1.00000 q^{58} -1.00000 q^{60} -1.00000 q^{62} +1.00000 q^{64} +1.00000 q^{65} -1.00000 q^{66} -2.00000 q^{76} +1.00000 q^{78} +1.00000 q^{79} -1.00000 q^{80} -1.00000 q^{81} -1.00000 q^{86} +1.00000 q^{87} -1.00000 q^{88} +1.00000 q^{93} -1.00000 q^{94} +2.00000 q^{95} -1.00000 q^{96} -1.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000	−1.00000
$2$	−1.00000	−1.00000
$3$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$3$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$4$	1.00000	1.00000
$5$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$6$	−1.00000	−1.00000
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−1.00000	−1.00000
$9$	0	0
$10$	1.00000	1.00000
$11$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$11$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$12$	1.00000	1.00000
$13$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$13$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$14$	0	0
$15$	−1.00000	−1.00000
$16$	1.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−2.00000	−2.00000	−1.00000			$\pi$
$19$	−2.00000	−2.00000	−1.00000			$\pi$
$20$	−1.00000	−1.00000
$21$	0	0
$22$	−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
$29$	1.00000	1.00000
$30$	1.00000	1.00000
$31$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$31$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$32$	−1.00000	−1.00000
$33$	1.00000	1.00000
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	2.00000	2.00000
$39$	−1.00000	−1.00000
$40$	1.00000	1.00000
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$43$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$44$	1.00000	1.00000
$45$	0	0
$46$	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
$52$	−1.00000	−1.00000
$53$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$53$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$54$	1.00000	1.00000
$55$	−1.00000	−1.00000
$56$	0	0
$57$	−2.00000	−2.00000
$58$	−1.00000	−1.00000
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−1.00000	−1.00000
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	−1.00000	−1.00000
$63$	0	0
$64$	1.00000	1.00000
$65$	1.00000	1.00000
$66$	−1.00000	−1.00000
$67$	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
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	−2.00000	−2.00000
$77$	0	0
$78$	1.00000	1.00000
$79$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$79$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$80$	−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
$86$	−1.00000	−1.00000
$87$	1.00000	1.00000
$88$	−1.00000	−1.00000
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	1.00000	1.00000
$94$	−1.00000	−1.00000
$95$	2.00000	2.00000
$96$	−1.00000	−1.00000
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.00000	−1.00000
$99$	0	0
$100$	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
$105$	0	0
$106$	1.00000	1.00000
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−1.00000	−1.00000
$109$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$109$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$110$	1.00000	1.00000
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	2.00000	2.00000
$115$	0	0
$116$	1.00000	1.00000
$117$	0	0
$118$	0	0
$119$	0	0
$120$	1.00000	1.00000
$121$	0	0
$122$	0	0
$123$	0	0
$124$	1.00000	1.00000
$125$	1.00000	1.00000
$126$	0	0
$127$	−2.00000	−2.00000	−1.00000			$\pi$
$127$	−2.00000	−2.00000	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	1.00000	1.00000
$130$	−1.00000	−1.00000
$131$	−2.00000	−2.00000	−1.00000			$\pi$
$131$	−2.00000	−2.00000	−1.00000			$\pi$
$132$	1.00000	1.00000
$133$	0	0
$134$	0	0
$135$	1.00000	1.00000
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	1.00000	1.00000
$142$	0	0
$143$	−1.00000	−1.00000
$144$	0	0
$145$	−1.00000	−1.00000
$146$	0	0
$147$	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			$\pi$
$152$	2.00000	2.00000
$153$	0	0
$154$	0	0
$155$	−1.00000	−1.00000
$156$	−1.00000	−1.00000
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−1.00000	−1.00000
$159$	−1.00000	−1.00000
$160$	1.00000	1.00000
$161$	0	0
$162$	1.00000	1.00000
$163$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$163$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$164$	0	0
$165$	−1.00000	−1.00000
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	0	0
$172$	1.00000	1.00000
$173$	2.00000	2.00000	1.00000			$0$
$173$	2.00000	2.00000	1.00000			$0$
$174$	−1.00000	−1.00000
$175$	0	0
$176$	1.00000	1.00000
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	−1.00000	−1.00000
$187$	0	0
$188$	1.00000	1.00000
$189$	0	0
$190$	−2.00000	−2.00000
$191$	−2.00000	−2.00000	−1.00000			$\pi$
$191$	−2.00000	−2.00000	−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
$196$	1.00000	1.00000
$197$	2.00000	2.00000	1.00000			$0$
$197$	2.00000	2.00000	1.00000			$0$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−1.00000	−1.00000
$209$	−2.00000	−2.00000
$210$	0	0
$211$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$211$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$212$	−1.00000	−1.00000
$213$	0	0
$214$	0	0
$215$	−1.00000	−1.00000
$216$	1.00000	1.00000
$217$	0	0
$218$	1.00000	1.00000
$219$	0	0
$220$	−1.00000	−1.00000
$221$	0	0
$222$	0	0
$223$	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			$\pi$
$228$	−2.00000	−2.00000
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	−1.00000	−1.00000
$233$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$233$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$234$	0	0
$235$	−1.00000	−1.00000
$236$	0	0
$237$	1.00000	1.00000
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−1.00000	−1.00000
$241$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$241$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−1.00000	−1.00000
$246$	0	0
$247$	2.00000	2.00000
$248$	−1.00000	−1.00000
$249$	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
$254$	2.00000	2.00000
$255$	0	0
$256$	1.00000	1.00000
$257$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$258$	−1.00000	−1.00000
$259$	0	0
$260$	1.00000	1.00000
$261$	0	0
$262$	2.00000	2.00000
$263$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$263$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$264$	−1.00000	−1.00000
$265$	1.00000	1.00000
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−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
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	2.00000	2.00000	1.00000			$0$
$277$	2.00000	2.00000	1.00000			$0$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−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
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	2.00000	2.00000
$286$	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
$295$	0	0
$296$	0	0
$297$	−1.00000	−1.00000
$298$	1.00000	1.00000
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−2.00000	−2.00000
$305$	0	0
$306$	0	0
$307$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$307$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$308$	0	0
$309$	0	0
$310$	1.00000	1.00000
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$312$	1.00000	1.00000
$313$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$313$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$314$	0	0
$315$	0	0
$316$	1.00000	1.00000
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	1.00000	1.00000
$319$	1.00000	1.00000
$320$	−1.00000	−1.00000
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−1.00000	−1.00000
$325$	0	0
$326$	−1.00000	−1.00000
$327$	−1.00000	−1.00000
$328$	0	0
$329$	0	0
$330$	1.00000	1.00000
$331$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$331$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	1.00000	1.00000
$342$	0	0
$343$	0	0
$344$	−1.00000	−1.00000
$345$	0	0
$346$	−2.00000	−2.00000
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	1.00000	1.00000
$349$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$350$	0	0
$351$	1.00000	1.00000
$352$	−1.00000	−1.00000
$353$	2.00000	2.00000	1.00000			$0$
$353$	2.00000	2.00000	1.00000			$0$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$359$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$360$	0	0
$361$	3.00000	3.00000
$362$	1.00000	1.00000
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−2.00000	−2.00000	−1.00000			$\pi$
$367$	−2.00000	−2.00000	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	1.00000	1.00000
$373$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$373$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$374$	0	0
$375$	1.00000	1.00000
$376$	−1.00000	−1.00000
$377$	−1.00000	−1.00000
$378$	0	0
$379$	−2.00000	−2.00000	−1.00000			$\pi$
$379$	−2.00000	−2.00000	−1.00000			$\pi$
$380$	2.00000	2.00000
$381$	−2.00000	−2.00000
$382$	2.00000	2.00000
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−1.00000	−1.00000
$385$	0	0
$386$	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
$393$	−2.00000	−2.00000
$394$	−2.00000	−2.00000
$395$	−1.00000	−1.00000
$396$	0	0
$397$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$402$	0	0
$403$	−1.00000	−1.00000
$404$	0	0
$405$	1.00000	1.00000
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	1.00000	1.00000
$417$	0	0
$418$	2.00000	2.00000
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	−1.00000	−1.00000
$423$	0	0
$424$	1.00000	1.00000
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−1.00000	−1.00000
$430$	1.00000	1.00000
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−1.00000	−1.00000
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	−1.00000	−1.00000
$436$	−1.00000	−1.00000
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	1.00000	1.00000
$441$	0	0
$442$	0	0
$443$	−2.00000	−2.00000	−1.00000			$\pi$
$443$	−2.00000	−2.00000	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−1.00000	−1.00000
$448$	0	0
$449$	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
$455$	0	0
$456$	2.00000	2.00000
$457$	2.00000	2.00000	1.00000			$0$
$457$	2.00000	2.00000	1.00000			$0$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	1.00000	1.00000
$465$	−1.00000	−1.00000
$466$	1.00000	1.00000
$467$	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
$469$	0	0
$470$	1.00000	1.00000
$471$	0	0
$472$	0	0
$473$	1.00000	1.00000
$474$	−1.00000	−1.00000
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$479$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$480$	1.00000	1.00000
$481$	0	0
$482$	1.00000	1.00000
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	1.00000	1.00000
$490$	1.00000	1.00000
$491$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$491$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$492$	0	0
$493$	0	0
$494$	−2.00000	−2.00000
$495$	0	0
$496$	1.00000	1.00000
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	1.00000	1.00000
$501$	0	0
$502$	−1.00000	−1.00000
$503$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$503$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−2.00000	−2.00000
$509$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$509$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−1.00000
$513$	2.00000	2.00000
$514$	1.00000	1.00000
$515$	0	0
$516$	1.00000	1.00000
$517$	1.00000	1.00000
$518$	0	0
$519$	2.00000	2.00000
$520$	−1.00000	−1.00000
$521$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$521$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	−2.00000	−2.00000
$525$	0	0
$526$	−1.00000	−1.00000
$527$	0	0
$528$	1.00000	1.00000
$529$	1.00000	1.00000
$530$	−1.00000	−1.00000
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	1.00000	1.00000
$540$	1.00000	1.00000
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	−1.00000	−1.00000
$543$	−1.00000	−1.00000
$544$	0	0
$545$	1.00000	1.00000
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	−2.00000	−2.00000
$552$	0	0
$553$	0	0
$554$	−2.00000	−2.00000
$555$	0	0
$556$	0	0
$557$	2.00000	2.00000	1.00000			$0$
$557$	2.00000	2.00000	1.00000			$0$
$558$	0	0
$559$	−1.00000	−1.00000
$560$	0	0
$561$	0	0
$562$	1.00000	1.00000
$563$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$563$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$564$	1.00000	1.00000
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	−2.00000	−2.00000
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	−1.00000	−1.00000
$573$	−2.00000	−2.00000
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−1.00000	−1.00000
$579$	0	0
$580$	−1.00000	−1.00000
$581$	0	0
$582$	0	0
$583$	−1.00000	−1.00000
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	1.00000	1.00000
$589$	−2.00000	−2.00000
$590$	0	0
$591$	2.00000	2.00000
$592$	0	0
$593$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$593$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$594$	1.00000	1.00000
$595$	0	0
$596$	−1.00000	−1.00000
$597$	0	0
$598$	0	0
$599$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$599$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$608$	2.00000	2.00000
$609$	0	0
$610$	0	0
$611$	−1.00000	−1.00000
$612$	0	0
$613$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$614$	−1.00000	−1.00000
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$619$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$620$	−1.00000	−1.00000
$621$	0	0
$622$	2.00000	2.00000
$623$	0	0
$624$	−1.00000	−1.00000
$625$	−1.00000	−1.00000
$626$	1.00000	1.00000
$627$	−2.00000	−2.00000
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	−1.00000	−1.00000
$633$	1.00000	1.00000
$634$	0	0
$635$	2.00000	2.00000
$636$	−1.00000	−1.00000
$637$	−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			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	−1.00000	−1.00000
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	1.00000	1.00000
$649$	0	0
$650$	0	0
$651$	0	0
$652$	1.00000	1.00000
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	1.00000	1.00000
$655$	2.00000	2.00000
$656$	0	0
$657$	0	0
$658$	0	0
$659$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$659$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$660$	−1.00000	−1.00000
$661$	2.00000	2.00000	1.00000			$0$
$661$	2.00000	2.00000	1.00000			$0$
$662$	−1.00000	−1.00000
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$674$	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
$682$	−1.00000	−1.00000
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	1.00000	1.00000
$689$	1.00000	1.00000
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	2.00000	2.00000
$693$	0	0
$694$	0	0
$695$	0	0
$696$	−1.00000	−1.00000
$697$	0	0
$698$	1.00000	1.00000
$699$	−1.00000	−1.00000
$700$	0	0
$701$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$701$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$702$	−1.00000	−1.00000
$703$	0	0
$704$	1.00000	1.00000
$705$	−1.00000	−1.00000
$706$	−2.00000	−2.00000
$707$	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
$712$	0	0
$713$	0	0
$714$	0	0
$715$	1.00000	1.00000
$716$	0	0
$717$	0	0
$718$	−1.00000	−1.00000
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	−3.00000	−3.00000
$723$	−1.00000	−1.00000
$724$	−1.00000	−1.00000
$725$	0	0
$726$	0	0
$727$	−2.00000	−2.00000	−1.00000			$\pi$
$727$	−2.00000	−2.00000	−1.00000			$\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	2.00000	2.00000
$735$	−1.00000	−1.00000
$736$	0	0
$737$	0	0
$738$	0	0
$739$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$739$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$740$	0	0
$741$	2.00000	2.00000
$742$	0	0
$743$	−2.00000	−2.00000	−1.00000			$\pi$
$743$	−2.00000	−2.00000	−1.00000			$\pi$
$744$	−1.00000	−1.00000
$745$	1.00000	1.00000
$746$	1.00000	1.00000
$747$	0	0
$748$	0	0
$749$	0	0
$750$	−1.00000	−1.00000
$751$	−2.00000	−2.00000	−1.00000			$\pi$
$751$	−2.00000	−2.00000	−1.00000			$\pi$
$752$	1.00000	1.00000
$753$	1.00000	1.00000
$754$	1.00000	1.00000
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	2.00000	2.00000
$759$	0	0
$760$	−2.00000	−2.00000
$761$	2.00000	2.00000	1.00000			$0$
$761$	2.00000	2.00000	1.00000			$0$
$762$	2.00000	2.00000
$763$	0	0
$764$	−2.00000	−2.00000
$765$	0	0
$766$	0	0
$767$	0	0
$768$	1.00000	1.00000
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	−1.00000	−1.00000
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	1.00000	1.00000
$781$	0	0
$782$	0	0
$783$	−1.00000	−1.00000
$784$	1.00000	1.00000
$785$	0	0
$786$	2.00000	2.00000
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	2.00000	2.00000
$789$	1.00000	1.00000
$790$	1.00000	1.00000
$791$	0	0
$792$	0	0
$793$	0	0
$794$	1.00000	1.00000
$795$	1.00000	1.00000
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	1.00000	1.00000
$803$	0	0
$804$	0	0
$805$	0	0
$806$	1.00000	1.00000
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	−1.00000	−1.00000
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	1.00000	1.00000
$814$	0	0
$815$	−1.00000	−1.00000
$816$	0	0
$817$	−2.00000	−2.00000
$818$	0	0
$819$	0	0
$820$	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
$823$	−2.00000	−2.00000	−1.00000			$\pi$
$823$	−2.00000	−2.00000	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$827$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	2.00000	2.00000
$832$	−1.00000	−1.00000
$833$	0	0
$834$	0	0
$835$	0	0
$836$	−2.00000	−2.00000
$837$	−1.00000	−1.00000
$838$	0	0
$839$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$839$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	−1.00000	−1.00000
$844$	1.00000	1.00000
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−1.00000	−1.00000
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$858$	1.00000	1.00000
$859$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$859$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$860$	−1.00000	−1.00000
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	1.00000	1.00000
$865$	−2.00000	−2.00000
$866$	0	0
$867$	1.00000	1.00000
$868$	0	0
$869$	1.00000	1.00000
$870$	1.00000	1.00000
$871$	0	0
$872$	1.00000	1.00000
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$878$	0	0
$879$	0	0
$880$	−1.00000	−1.00000
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	2.00000	2.00000
$887$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$887$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.00000	−1.00000
$892$	0	0
$893$	−2.00000	−2.00000
$894$	1.00000	1.00000
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	1.00000	1.00000
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	1.00000	1.00000
$906$	0	0
$907$	−2.00000	−2.00000	−1.00000			$\pi$
$907$	−2.00000	−2.00000	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$911$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$912$	−2.00000	−2.00000
$913$	0	0
$914$	−2.00000	−2.00000
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	1.00000	1.00000
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	−1.00000	−1.00000
$929$	2.00000	2.00000	1.00000			$0$
$929$	2.00000	2.00000	1.00000			$0$
$930$	1.00000	1.00000
$931$	−2.00000	−2.00000
$932$	−1.00000	−1.00000
$933$	−2.00000	−2.00000
$934$	−1.00000	−1.00000
$935$	0	0
$936$	0	0
$937$	2.00000	2.00000	1.00000			$0$
$937$	2.00000	2.00000	1.00000			$0$
$938$	0	0
$939$	−1.00000	−1.00000
$940$	−1.00000	−1.00000
$941$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$941$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	−1.00000	−1.00000
$947$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$947$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$948$	1.00000	1.00000
$949$	0	0
$950$	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
$955$	2.00000	2.00000
$956$	0	0
$957$	1.00000	1.00000
$958$	−1.00000	−1.00000
$959$	0	0
$960$	−1.00000	−1.00000
$961$	0	0
$962$	0	0
$963$	0	0
$964$	−1.00000	−1.00000
$965$	0	0
$966$	0	0
$967$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−2.00000	−2.00000	−1.00000			$\pi$
$971$	−2.00000	−2.00000	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$978$	−1.00000	−1.00000
$979$	0	0
$980$	−1.00000	−1.00000
$981$	0	0
$982$	−1.00000	−1.00000
$983$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$983$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$984$	0	0
$985$	−2.00000	−2.00000
$986$	0	0
$987$	0	0
$988$	2.00000	2.00000
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	−1.00000	−1.00000
$993$	1.00000	1.00000
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.1.d.a.115.1	✓	1
3.2	odd	2		1044.1.g.b.811.1		1
4.3	odd	2		116.1.d.b.115.1	yes	1
5.2	odd	4		2900.1.e.b.2899.1		2
5.3	odd	4		2900.1.e.b.2899.2		2
5.4	even	2		2900.1.g.d.2551.1		1
8.3	odd	2		1856.1.h.c.1855.1		1
8.5	even	2		1856.1.h.a.1855.1		1
12.11	even	2		1044.1.g.a.811.1		1
20.3	even	4		2900.1.e.a.2899.1		2
20.7	even	4		2900.1.e.a.2899.2		2
20.19	odd	2		2900.1.g.a.2551.1		1
29.2	odd	28		3364.1.j.f.2287.1		12
29.3	odd	28		3364.1.j.f.571.1		12
29.4	even	14		3364.1.h.a.651.1		6
29.5	even	14		3364.1.h.a.2759.1		6
29.6	even	14		3364.1.h.a.2719.1		6
29.7	even	7		3364.1.h.b.1111.1		6
29.8	odd	28		3364.1.j.f.1415.1		12
29.9	even	14		3364.1.h.a.267.1		6
29.10	odd	28		3364.1.j.f.1031.1		12
29.11	odd	28		3364.1.j.f.1619.1		12
29.12	odd	4		3364.1.b.a.1683.1		2
29.13	even	14		3364.1.h.a.63.1		6
29.14	odd	28		3364.1.j.f.2327.2		12
29.15	odd	28		3364.1.j.f.2327.1		12
29.16	even	7		3364.1.h.b.63.1		6
29.17	odd	4		3364.1.b.a.1683.2		2
29.18	odd	28		3364.1.j.f.1619.2		12
29.19	odd	28		3364.1.j.f.1031.2		12
29.20	even	7		3364.1.h.b.267.1		6
29.21	odd	28		3364.1.j.f.1415.2		12
29.22	even	14		3364.1.h.a.1111.1		6
29.23	even	7		3364.1.h.b.2719.1		6
29.24	even	7		3364.1.h.b.2759.1		6
29.25	even	7		3364.1.h.b.651.1		6
29.26	odd	28		3364.1.j.f.571.2		12
29.27	odd	28		3364.1.j.f.2287.2		12
29.28	even	2		116.1.d.b.115.1	yes	1
87.86	odd	2		1044.1.g.a.811.1		1
116.3	even	28		3364.1.j.f.571.2		12
116.7	odd	14		3364.1.h.a.1111.1		6
116.11	even	28		3364.1.j.f.1619.2		12
116.15	even	28		3364.1.j.f.2327.2		12
116.19	even	28		3364.1.j.f.1031.1		12
116.23	odd	14		3364.1.h.a.2719.1		6
116.27	even	28		3364.1.j.f.2287.1		12
116.31	even	28		3364.1.j.f.2287.2		12
116.35	odd	14		3364.1.h.b.2719.1		6
116.39	even	28		3364.1.j.f.1031.2		12
116.43	even	28		3364.1.j.f.2327.1		12
116.47	even	28		3364.1.j.f.1619.1		12
116.51	odd	14		3364.1.h.b.1111.1		6
116.55	even	28		3364.1.j.f.571.1		12
116.63	odd	14		3364.1.h.b.2759.1		6
116.67	odd	14		3364.1.h.b.267.1		6
116.71	odd	14		3364.1.h.b.63.1		6
116.75	even	4		3364.1.b.a.1683.1		2
116.79	even	28		3364.1.j.f.1415.1		12
116.83	odd	14		3364.1.h.a.651.1		6
116.91	odd	14		3364.1.h.b.651.1		6
116.95	even	28		3364.1.j.f.1415.2		12
116.99	even	4		3364.1.b.a.1683.2		2
116.103	odd	14		3364.1.h.a.63.1		6
116.107	odd	14		3364.1.h.a.267.1		6
116.111	odd	14		3364.1.h.a.2759.1		6
116.115	odd	2	CM	116.1.d.a.115.1	✓	1
145.28	odd	4		2900.1.e.a.2899.1		2
145.57	odd	4		2900.1.e.a.2899.2		2
145.144	even	2		2900.1.g.a.2551.1		1
232.115	odd	2		1856.1.h.a.1855.1		1
232.173	even	2		1856.1.h.c.1855.1		1
348.347	even	2		1044.1.g.b.811.1		1
580.347	even	4		2900.1.e.b.2899.1		2
580.463	even	4		2900.1.e.b.2899.2		2
580.579	odd	2		2900.1.g.d.2551.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.1.d.a.115.1	✓	1	1.1	even	1	trivial
116.1.d.a.115.1	✓	1	116.115	odd	2	CM
116.1.d.b.115.1	yes	1	4.3	odd	2
116.1.d.b.115.1	yes	1	29.28	even	2
1044.1.g.a.811.1		1	12.11	even	2
1044.1.g.a.811.1		1	87.86	odd	2
1044.1.g.b.811.1		1	3.2	odd	2
1044.1.g.b.811.1		1	348.347	even	2
1856.1.h.a.1855.1		1	8.5	even	2
1856.1.h.a.1855.1		1	232.115	odd	2
1856.1.h.c.1855.1		1	8.3	odd	2
1856.1.h.c.1855.1		1	232.173	even	2
2900.1.e.a.2899.1		2	20.3	even	4
2900.1.e.a.2899.1		2	145.28	odd	4
2900.1.e.a.2899.2		2	20.7	even	4
2900.1.e.a.2899.2		2	145.57	odd	4
2900.1.e.b.2899.1		2	5.2	odd	4
2900.1.e.b.2899.1		2	580.347	even	4
2900.1.e.b.2899.2		2	5.3	odd	4
2900.1.e.b.2899.2		2	580.463	even	4
2900.1.g.a.2551.1		1	20.19	odd	2
2900.1.g.a.2551.1		1	145.144	even	2
2900.1.g.d.2551.1		1	5.4	even	2
2900.1.g.d.2551.1		1	580.579	odd	2
3364.1.b.a.1683.1		2	29.12	odd	4
3364.1.b.a.1683.1		2	116.75	even	4
3364.1.b.a.1683.2		2	29.17	odd	4
3364.1.b.a.1683.2		2	116.99	even	4
3364.1.h.a.63.1		6	29.13	even	14
3364.1.h.a.63.1		6	116.103	odd	14
3364.1.h.a.267.1		6	29.9	even	14
3364.1.h.a.267.1		6	116.107	odd	14
3364.1.h.a.651.1		6	29.4	even	14
3364.1.h.a.651.1		6	116.83	odd	14
3364.1.h.a.1111.1		6	29.22	even	14
3364.1.h.a.1111.1		6	116.7	odd	14
3364.1.h.a.2719.1		6	29.6	even	14
3364.1.h.a.2719.1		6	116.23	odd	14
3364.1.h.a.2759.1		6	29.5	even	14
3364.1.h.a.2759.1		6	116.111	odd	14
3364.1.h.b.63.1		6	29.16	even	7
3364.1.h.b.63.1		6	116.71	odd	14
3364.1.h.b.267.1		6	29.20	even	7
3364.1.h.b.267.1		6	116.67	odd	14
3364.1.h.b.651.1		6	29.25	even	7
3364.1.h.b.651.1		6	116.91	odd	14
3364.1.h.b.1111.1		6	29.7	even	7
3364.1.h.b.1111.1		6	116.51	odd	14
3364.1.h.b.2719.1		6	29.23	even	7
3364.1.h.b.2719.1		6	116.35	odd	14
3364.1.h.b.2759.1		6	29.24	even	7
3364.1.h.b.2759.1		6	116.63	odd	14
3364.1.j.f.571.1		12	29.3	odd	28
3364.1.j.f.571.1		12	116.55	even	28
3364.1.j.f.571.2		12	29.26	odd	28
3364.1.j.f.571.2		12	116.3	even	28
3364.1.j.f.1031.1		12	29.10	odd	28
3364.1.j.f.1031.1		12	116.19	even	28
3364.1.j.f.1031.2		12	29.19	odd	28
3364.1.j.f.1031.2		12	116.39	even	28
3364.1.j.f.1415.1		12	29.8	odd	28
3364.1.j.f.1415.1		12	116.79	even	28
3364.1.j.f.1415.2		12	29.21	odd	28
3364.1.j.f.1415.2		12	116.95	even	28
3364.1.j.f.1619.1		12	29.11	odd	28
3364.1.j.f.1619.1		12	116.47	even	28
3364.1.j.f.1619.2		12	29.18	odd	28
3364.1.j.f.1619.2		12	116.11	even	28
3364.1.j.f.2287.1		12	29.2	odd	28
3364.1.j.f.2287.1		12	116.27	even	28
3364.1.j.f.2287.2		12	29.27	odd	28
3364.1.j.f.2287.2		12	116.31	even	28
3364.1.j.f.2327.1		12	29.15	odd	28
3364.1.j.f.2327.1		12	116.43	even	28
3364.1.j.f.2327.2		12	29.14	odd	28
3364.1.j.f.2327.2		12	116.15	even	28

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	116.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(59\)	\(89\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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