LMFDB - Embedded newform 3887.1.c.a.3886.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3887,1,Mod(3886,3887)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3887, 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("3887.3886");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3887 = 13^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3887.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.93986570410$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.23.1
Artin image:	$C_4\times S_3$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{12} - \cdots)$

Embedding invariants

Embedding label			3886.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	3887.3886
Dual form			3887.1.c.a.3886.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{3} +1.00000i q^{6} -1.00000i q^{8} +O(q^{10})$	$q-1.00000i q^{2} -1.00000 q^{3} +1.00000i q^{6} -1.00000i q^{8} -1.00000 q^{16} -1.00000 q^{23} +1.00000i q^{24} -1.00000 q^{25} +1.00000 q^{27} -1.00000 q^{29} -1.00000i q^{31} -1.00000i q^{41} +1.00000i q^{46} +1.00000i q^{47} +1.00000 q^{48} -1.00000 q^{49} +1.00000i q^{50} -1.00000i q^{54} +1.00000i q^{58} -2.00000i q^{59} -1.00000 q^{62} -1.00000 q^{64} +1.00000 q^{69} -1.00000i q^{71} +1.00000i q^{73} +1.00000 q^{75} -1.00000 q^{81} -1.00000 q^{82} +1.00000 q^{87} +1.00000i q^{93} +1.00000 q^{94} +1.00000i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3}+O(q^{10}) $ 2 * q - 2 * q^3	$ 2 q - 2 q^{3} - 2 q^{16} - 2 q^{23} - 2 q^{25} + 2 q^{27} - 2 q^{29} + 2 q^{48} - 2 q^{49} - 2 q^{62} - 2 q^{64} + 2 q^{69} + 2 q^{75} - 2 q^{81} - 2 q^{82} + 2 q^{87} + 2 q^{94}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^16 - 2 * q^23 - 2 * q^25 + 2 * q^27 - 2 * q^29 + 2 * q^48 - 2 * q^49 - 2 * q^62 - 2 * q^64 + 2 * q^69 + 2 * q^75 - 2 * q^81 - 2 * q^82 + 2 * q^87 + 2 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3887\mathbb{Z}\right)^\times$.

$n$	$2029$	$3382$
$\chi(n)$	$-1$	$-1$

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 $

$2$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$3$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$4$	0	0
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	1.00000i	1.00000i
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	− 1.00000i	− 1.00000i
$9$	0	0
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	0	0
$15$	0	0
$16$	−1.00000	−1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−1.00000
$23$	−1.00000	−1.00000
$24$	1.00000i	1.00000i
$25$	−1.00000	−1.00000
$26$	0	0
$27$	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	$0.666667\pi$
$30$	0	0
$31$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$31$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$41$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	0	0
$46$	1.00000i	1.00000i
$47$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$47$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.00000	1.00000
$49$	−1.00000	−1.00000
$50$	1.00000i	1.00000i
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	− 1.00000i	− 1.00000i
$55$	0	0
$56$	0	0
$57$	0	0
$58$	1.00000i	1.00000i
$59$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$59$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	−1.00000	−1.00000
$63$	0	0
$64$	−1.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	1.00000	1.00000
$70$	0	0
$71$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$71$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$72$	0	0
$73$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$73$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$74$	0	0
$75$	1.00000	1.00000
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	−1.00000	−1.00000
$82$	−1.00000	−1.00000
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1.00000	1.00000
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	1.00000i	1.00000i
$94$	1.00000	1.00000
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	1.00000i	1.00000i
$99$	0	0
$100$	0	0
$101$	−2.00000	−2.00000	−1.00000			$\pi$
$101$	−2.00000	−2.00000	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	−2.00000	−2.00000
$119$	0	0
$120$	0	0
$121$	−1.00000	−1.00000
$122$	0	0
$123$	1.00000i	1.00000i
$124$	0	0
$125$	0	0
$126$	0	0
$127$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$127$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$128$	1.00000i	1.00000i
$129$	0	0
$130$	0	0
$131$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	− 1.00000i	− 1.00000i
$139$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$139$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$140$	0	0
$141$	− 1.00000i	− 1.00000i
$142$	−1.00000	−1.00000
$143$	0	0
$144$	0	0
$145$	0	0
$146$	1.00000	1.00000
$147$	1.00000	1.00000
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	− 1.00000i	− 1.00000i
$151$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$151$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	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
$162$	1.00000i	1.00000i
$163$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$163$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$167$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−2.00000	−2.00000	−1.00000			$\pi$
$173$	−2.00000	−2.00000	−1.00000			$\pi$
$174$	− 1.00000i	− 1.00000i
$175$	0	0
$176$	0	0
$177$	2.00000i	2.00000i
$178$	0	0
$179$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$179$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	1.00000i	1.00000i
$185$	0	0
$186$	1.00000	1.00000
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	1.00000	1.00000
$193$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$193$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$197$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	1.00000i	1.00000i
$201$	0	0
$202$	2.00000i	2.00000i
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	2.00000	2.00000	1.00000			$0$
$211$	2.00000	2.00000	1.00000			$0$
$212$	0	0
$213$	1.00000i	1.00000i
$214$	0	0
$215$	0	0
$216$	− 1.00000i	− 1.00000i
$217$	0	0
$218$	0	0
$219$	− 1.00000i	− 1.00000i
$220$	0	0
$221$	0	0
$222$	0	0
$223$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$223$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	0	0
$232$	1.00000i	1.00000i
$233$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$233$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$239$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	1.00000i	1.00000i
$243$	0	0
$244$	0	0
$245$	0	0
$246$	1.00000	1.00000
$247$	0	0
$248$	−1.00000	−1.00000
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	− 1.00000i	− 1.00000i
$255$	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
$259$	0	0
$260$	0	0
$261$	0	0
$262$	1.00000i	1.00000i
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$270$	0	0
$271$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$271$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$277$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$278$	1.00000i	1.00000i
$279$	0	0
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	−1.00000	−1.00000
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	− 1.00000i	− 1.00000i
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	1.00000	1.00000
$303$	2.00000	2.00000
$304$	0	0
$305$	0	0
$306$	0	0
$307$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$307$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$311$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$317$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	1.00000	1.00000
$327$	0	0
$328$	−1.00000	−1.00000
$329$	0	0
$330$	0	0
$331$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$331$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$332$	0	0
$333$	0	0
$334$	−2.00000	−2.00000
$335$	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
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	2.00000i	2.00000i
$347$	2.00000	2.00000	1.00000			$0$
$347$	2.00000	2.00000	1.00000			$0$
$348$	0	0
$349$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$349$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$353$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$354$	2.00000	2.00000
$355$	0	0
$356$	0	0
$357$	0	0
$358$	− 1.00000i	− 1.00000i
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−1.00000	−1.00000
$362$	0	0
$363$	1.00000	1.00000
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	1.00000	1.00000
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	1.00000	1.00000
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	−1.00000	−1.00000
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	− 1.00000i	− 1.00000i
$385$	0	0
$386$	1.00000	1.00000
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	1.00000i	1.00000i
$393$	1.00000	1.00000
$394$	−1.00000	−1.00000
$395$	0	0
$396$	0	0
$397$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$397$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	1.00000
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$409$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	1.00000	1.00000
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	− 2.00000i	− 2.00000i
$423$	0	0
$424$	0	0
$425$	0	0
$426$	1.00000	1.00000
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−1.00000
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	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	$0.333333\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$444$	0	0
$445$	0	0
$446$	2.00000	2.00000
$447$	0	0
$448$	0	0
$449$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$449$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	− 1.00000i	− 1.00000i
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$461$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$462$	0	0
$463$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$463$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$464$	1.00000	1.00000
$465$	0	0
$466$	− 1.00000i	− 1.00000i
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−2.00000	−2.00000
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	−1.00000	−1.00000
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$488$	0	0
$489$	− 1.00000i	− 1.00000i
$490$	0	0
$491$	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
$494$	0	0
$495$	0	0
$496$	1.00000i	1.00000i
$497$	0	0
$498$	0	0
$499$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$499$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$500$	0	0
$501$	2.00000i	2.00000i
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$509$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$510$	0	0
$511$	0	0
$512$	1.00000i	1.00000i
$513$	0	0
$514$	− 1.00000i	− 1.00000i
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	2.00000	2.00000
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−1.00000	−1.00000
$538$	1.00000i	1.00000i
$539$	0	0
$540$	0	0
$541$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$541$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$542$	−2.00000	−2.00000
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	− 1.00000i	− 1.00000i
$553$	0	0
$554$	− 1.00000i	− 1.00000i
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	−1.00000	−1.00000
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	1.00000	1.00000
$576$	0	0
$577$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$577$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$578$	− 1.00000i	− 1.00000i
$579$	− 1.00000i	− 1.00000i
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	1.00000	1.00000
$585$	0	0
$586$	0	0
$587$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$587$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	1.00000i	1.00000i
$592$	0	0
$593$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$593$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	2.00000	2.00000	1.00000			$0$
$599$	2.00000	2.00000	1.00000			$0$
$600$	− 1.00000i	− 1.00000i
$601$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	− 2.00000i	− 2.00000i
$607$	2.00000	2.00000	1.00000			$0$
$607$	2.00000	2.00000	1.00000			$0$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	−2.00000	−2.00000
$615$	0	0
$616$	0	0
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	−1.00000	−1.00000
$622$	− 1.00000i	− 1.00000i
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	−2.00000	−2.00000
$634$	2.00000	2.00000
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	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	$0.333333\pi$
$648$	1.00000i	1.00000i
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$654$	0	0
$655$	0	0
$656$	1.00000i	1.00000i
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	−1.00000	−1.00000
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.00000	1.00000
$668$	0	0
$669$	− 2.00000i	− 2.00000i
$670$	0	0
$671$	0	0
$672$	0	0
$673$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$673$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$674$	0	0
$675$	−1.00000	−1.00000
$676$	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
$683$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$683$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$691$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	− 2.00000i	− 2.00000i
$695$	0	0
$696$	− 1.00000i	− 1.00000i
$697$	0	0
$698$	1.00000	1.00000
$699$	−1.00000	−1.00000
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	−1.00000	−1.00000
$707$	0	0
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	1.00000i	1.00000i
$714$	0	0
$715$	0	0
$716$	0	0
$717$	1.00000i	1.00000i
$718$	0	0
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	1.00000i	1.00000i
$723$	0	0
$724$	0	0
$725$	1.00000	1.00000
$726$	− 1.00000i	− 1.00000i
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$739$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	1.00000	1.00000
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	− 1.00000i	− 1.00000i
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$761$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$762$	1.00000i	1.00000i
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	−1.00000	−1.00000
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	1.00000i	1.00000i
$776$	0	0
$777$	0	0
$778$	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
$786$	− 1.00000i	− 1.00000i
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	1.00000	1.00000
$795$	0	0
$796$	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
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	1.00000	1.00000
$808$	2.00000i	2.00000i
$809$	2.00000	2.00000	1.00000			$0$
$809$	2.00000	2.00000	1.00000			$0$
$810$	0	0
$811$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$811$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$812$	0	0
$813$	2.00000i	2.00000i
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	−1.00000	−1.00000
$819$	0	0
$820$	0	0
$821$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$821$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$822$	0	0
$823$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$823$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$830$	0	0
$831$	−1.00000	−1.00000
$832$	0	0
$833$	0	0
$834$	− 1.00000i	− 1.00000i
$835$	0	0
$836$	0	0
$837$	− 1.00000i	− 1.00000i
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	0	0
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$853$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$857$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$858$	0	0
$859$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$863$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−1.00000	−1.00000
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$877$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$878$	− 1.00000i	− 1.00000i
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	−2.00000	−2.00000	−1.00000			$\pi$
$883$	−2.00000	−2.00000	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	1.00000i	1.00000i
$887$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$887$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−2.00000	−2.00000
$899$	1.00000i	1.00000i
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	−1.00000	−1.00000
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	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
$921$	2.00000i	2.00000i
$922$	−1.00000	−1.00000
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−2.00000	−2.00000
$927$	0	0
$928$	0	0
$929$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$929$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−1.00000	−1.00000
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	1.00000i	1.00000i
$944$	2.00000i	2.00000i
$945$	0	0
$946$	0	0
$947$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$947$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	− 2.00000i	− 2.00000i
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	0	0
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$967$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$968$	1.00000i	1.00000i
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	−1.00000	−1.00000
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	−1.00000	−1.00000
$979$	0	0
$980$	0	0
$981$	0	0
$982$	− 1.00000i	− 1.00000i
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	1.00000	1.00000
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	2.00000	2.00000	1.00000			$0$
$991$	2.00000	2.00000	1.00000			$0$
$992$	0	0
$993$	1.00000i	1.00000i
$994$	0	0
$995$	0	0
$996$	0	0
$997$	2.00000	2.00000	1.00000			$0$
$997$	2.00000	2.00000	1.00000			$0$
$998$	−1.00000	−1.00000
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3887.1.c.a.3886.1		2
13.2	odd	12		3887.1.h.c.22.1		2
13.3	even	3		3887.1.j.e.2851.2		4
13.4	even	6		3887.1.j.e.3403.2		4
13.5	odd	4		23.1.b.a.22.1	✓	1
13.6	odd	12		3887.1.h.c.3357.1		2
13.7	odd	12		3887.1.h.a.3357.1		2
13.8	odd	4		3887.1.d.b.2874.1		1
13.9	even	3		3887.1.j.e.3403.1		4
13.10	even	6		3887.1.j.e.2851.1		4
13.11	odd	12		3887.1.h.a.22.1		2
13.12	even	2	inner	3887.1.c.a.3886.2		2
23.22	odd	2	CM	3887.1.c.a.3886.1		2
39.5	even	4		207.1.d.a.91.1		1
52.31	even	4		368.1.f.a.321.1		1
65.18	even	4		575.1.c.a.574.2		2
65.44	odd	4		575.1.d.a.551.1		1
65.57	even	4		575.1.c.a.574.1		2
91.5	even	12		1127.1.f.a.459.1		2
91.18	odd	12		1127.1.f.b.275.1		2
91.31	even	12		1127.1.f.a.275.1		2
91.44	odd	12		1127.1.f.b.459.1		2
91.83	even	4		1127.1.d.b.344.1		1
104.5	odd	4		1472.1.f.b.321.1		1
104.83	even	4		1472.1.f.a.321.1		1
117.5	even	12		1863.1.f.a.298.1		2
117.31	odd	12		1863.1.f.b.298.1		2
117.70	odd	12		1863.1.f.b.919.1		2
117.83	even	12		1863.1.f.a.919.1		2
143.5	odd	20		2783.1.f.c.850.1		4
143.18	even	20		2783.1.f.a.390.1		4
143.31	odd	20		2783.1.f.c.2138.1		4
143.57	even	20		2783.1.f.a.2138.1		4
143.70	odd	20		2783.1.f.c.390.1		4
143.83	even	20		2783.1.f.a.850.1		4
143.96	even	20		2783.1.f.a.735.1		4
143.109	even	4		2783.1.d.b.1816.1		1
143.135	odd	20		2783.1.f.c.735.1		4
156.83	odd	4		3312.1.c.a.2161.1		1
299.5	even	44		529.1.d.a.274.1		10
299.18	odd	44		529.1.d.a.274.1		10
299.22	odd	6		3887.1.j.e.3403.1		4
299.31	odd	44		529.1.d.a.28.1		10
299.44	even	44		529.1.d.a.42.1		10
299.45	even	12		3887.1.h.c.3357.1		2
299.57	even	44		529.1.d.a.63.1		10
299.68	odd	6		3887.1.j.e.2851.2		4
299.83	even	44		529.1.d.a.195.1		10
299.96	odd	44		529.1.d.a.352.1		10
299.109	even	44		529.1.d.a.263.1		10
299.114	odd	6		3887.1.j.e.2851.1		4
299.122	even	44		529.1.d.a.411.1		10
299.135	even	44		529.1.d.a.359.1		10
299.137	even	12		3887.1.h.a.3357.1		2
299.148	even	44		529.1.d.a.130.1		10
299.160	odd	6		3887.1.j.e.3403.2		4
299.174	odd	44		529.1.d.a.130.1		10
299.187	odd	44		529.1.d.a.359.1		10
299.200	odd	44		529.1.d.a.411.1		10
299.206	even	12		3887.1.h.a.22.1		2
299.213	odd	44		529.1.d.a.263.1		10
299.226	even	44		529.1.d.a.352.1		10
299.229	even	4		3887.1.d.b.2874.1		1
299.239	odd	44		529.1.d.a.195.1		10
299.252	even	4		23.1.b.a.22.1	✓	1
299.265	odd	44		529.1.d.a.63.1		10
299.275	even	12		3887.1.h.c.22.1		2
299.278	odd	44		529.1.d.a.42.1		10
299.291	even	44		529.1.d.a.28.1		10
299.298	odd	2	inner	3887.1.c.a.3886.2		2
897.551	odd	4		207.1.d.a.91.1		1
1196.551	odd	4		368.1.f.a.321.1		1
1495.252	odd	4		575.1.c.a.574.1		2
1495.1149	even	4		575.1.d.a.551.1		1
1495.1448	odd	4		575.1.c.a.574.2		2
2093.551	odd	12		1127.1.f.a.459.1		2
2093.850	odd	12		1127.1.f.a.275.1		2
2093.1448	odd	4		1127.1.d.b.344.1		1
2093.1747	even	12		1127.1.f.b.275.1		2
2093.2046	even	12		1127.1.f.b.459.1		2
2392.1149	even	4		1472.1.f.b.321.1		1
2392.1747	odd	4		1472.1.f.a.321.1		1
2691.551	odd	12		1863.1.f.a.919.1		2
2691.850	even	12		1863.1.f.b.298.1		2
2691.2345	odd	12		1863.1.f.a.298.1		2
2691.2644	even	12		1863.1.f.b.919.1		2
3289.252	odd	4		2783.1.d.b.1816.1		1
3289.850	even	20		2783.1.f.c.735.1		4
3289.1149	even	20		2783.1.f.c.850.1		4
3289.1448	odd	20		2783.1.f.a.390.1		4
3289.1747	even	20		2783.1.f.c.2138.1		4
3289.2345	odd	20		2783.1.f.a.2138.1		4
3289.2644	even	20		2783.1.f.c.390.1		4
3289.2943	odd	20		2783.1.f.a.850.1		4
3289.3242	odd	20		2783.1.f.a.735.1		4
3588.551	even	4		3312.1.c.a.2161.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.1.b.a.22.1	✓	1	13.5	odd	4
23.1.b.a.22.1	✓	1	299.252	even	4
207.1.d.a.91.1		1	39.5	even	4
207.1.d.a.91.1		1	897.551	odd	4
368.1.f.a.321.1		1	52.31	even	4
368.1.f.a.321.1		1	1196.551	odd	4
529.1.d.a.28.1		10	299.31	odd	44
529.1.d.a.28.1		10	299.291	even	44
529.1.d.a.42.1		10	299.44	even	44
529.1.d.a.42.1		10	299.278	odd	44
529.1.d.a.63.1		10	299.57	even	44
529.1.d.a.63.1		10	299.265	odd	44
529.1.d.a.130.1		10	299.148	even	44
529.1.d.a.130.1		10	299.174	odd	44
529.1.d.a.195.1		10	299.83	even	44
529.1.d.a.195.1		10	299.239	odd	44
529.1.d.a.263.1		10	299.109	even	44
529.1.d.a.263.1		10	299.213	odd	44
529.1.d.a.274.1		10	299.5	even	44
529.1.d.a.274.1		10	299.18	odd	44
529.1.d.a.352.1		10	299.96	odd	44
529.1.d.a.352.1		10	299.226	even	44
529.1.d.a.359.1		10	299.135	even	44
529.1.d.a.359.1		10	299.187	odd	44
529.1.d.a.411.1		10	299.122	even	44
529.1.d.a.411.1		10	299.200	odd	44
575.1.c.a.574.1		2	65.57	even	4
575.1.c.a.574.1		2	1495.252	odd	4
575.1.c.a.574.2		2	65.18	even	4
575.1.c.a.574.2		2	1495.1448	odd	4
575.1.d.a.551.1		1	65.44	odd	4
575.1.d.a.551.1		1	1495.1149	even	4
1127.1.d.b.344.1		1	91.83	even	4
1127.1.d.b.344.1		1	2093.1448	odd	4
1127.1.f.a.275.1		2	91.31	even	12
1127.1.f.a.275.1		2	2093.850	odd	12
1127.1.f.a.459.1		2	91.5	even	12
1127.1.f.a.459.1		2	2093.551	odd	12
1127.1.f.b.275.1		2	91.18	odd	12
1127.1.f.b.275.1		2	2093.1747	even	12
1127.1.f.b.459.1		2	91.44	odd	12
1127.1.f.b.459.1		2	2093.2046	even	12
1472.1.f.a.321.1		1	104.83	even	4
1472.1.f.a.321.1		1	2392.1747	odd	4
1472.1.f.b.321.1		1	104.5	odd	4
1472.1.f.b.321.1		1	2392.1149	even	4
1863.1.f.a.298.1		2	117.5	even	12
1863.1.f.a.298.1		2	2691.2345	odd	12
1863.1.f.a.919.1		2	117.83	even	12
1863.1.f.a.919.1		2	2691.551	odd	12
1863.1.f.b.298.1		2	117.31	odd	12
1863.1.f.b.298.1		2	2691.850	even	12
1863.1.f.b.919.1		2	117.70	odd	12
1863.1.f.b.919.1		2	2691.2644	even	12
2783.1.d.b.1816.1		1	143.109	even	4
2783.1.d.b.1816.1		1	3289.252	odd	4
2783.1.f.a.390.1		4	143.18	even	20
2783.1.f.a.390.1		4	3289.1448	odd	20
2783.1.f.a.735.1		4	143.96	even	20
2783.1.f.a.735.1		4	3289.3242	odd	20
2783.1.f.a.850.1		4	143.83	even	20
2783.1.f.a.850.1		4	3289.2943	odd	20
2783.1.f.a.2138.1		4	143.57	even	20
2783.1.f.a.2138.1		4	3289.2345	odd	20
2783.1.f.c.390.1		4	143.70	odd	20
2783.1.f.c.390.1		4	3289.2644	even	20
2783.1.f.c.735.1		4	143.135	odd	20
2783.1.f.c.735.1		4	3289.850	even	20
2783.1.f.c.850.1		4	143.5	odd	20
2783.1.f.c.850.1		4	3289.1149	even	20
2783.1.f.c.2138.1		4	143.31	odd	20
2783.1.f.c.2138.1		4	3289.1747	even	20
3312.1.c.a.2161.1		1	156.83	odd	4
3312.1.c.a.2161.1		1	3588.551	even	4
3887.1.c.a.3886.1		2	1.1	even	1	trivial
3887.1.c.a.3886.1		2	23.22	odd	2	CM
3887.1.c.a.3886.2		2	13.12	even	2	inner
3887.1.c.a.3886.2		2	299.298	odd	2	inner
3887.1.d.b.2874.1		1	13.8	odd	4
3887.1.d.b.2874.1		1	299.229	even	4
3887.1.h.a.22.1		2	13.11	odd	12
3887.1.h.a.22.1		2	299.206	even	12
3887.1.h.a.3357.1		2	13.7	odd	12
3887.1.h.a.3357.1		2	299.137	even	12
3887.1.h.c.22.1		2	13.2	odd	12
3887.1.h.c.22.1		2	299.275	even	12
3887.1.h.c.3357.1		2	13.6	odd	12
3887.1.h.c.3357.1		2	299.45	even	12
3887.1.j.e.2851.1		4	13.10	even	6
3887.1.j.e.2851.1		4	299.114	odd	6
3887.1.j.e.2851.2		4	13.3	even	3
3887.1.j.e.2851.2		4	299.68	odd	6
3887.1.j.e.3403.1		4	13.9	even	3
3887.1.j.e.3403.1		4	299.22	odd	6
3887.1.j.e.3403.2		4	13.4	even	6
3887.1.j.e.3403.2		4	299.160	odd	6

Overview	Random
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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:	\( N \)	\(=\)	\( 3887 = 13^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3887.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{3} +1.00000i q^{6} -1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{3} +1.00000i q^{6} -1.00000i q^{8} -1.00000 q^{16} -1.00000 q^{23} +1.00000i q^{24} -1.00000 q^{25} +1.00000 q^{27} -1.00000 q^{29} -1.00000i q^{31} -1.00000i q^{41} +1.00000i q^{46} +1.00000i q^{47} +1.00000 q^{48} -1.00000 q^{49} +1.00000i q^{50} -1.00000i q^{54} +1.00000i q^{58} -2.00000i q^{59} -1.00000 q^{62} -1.00000 q^{64} +1.00000 q^{69} -1.00000i q^{71} +1.00000i q^{73} +1.00000 q^{75} -1.00000 q^{81} -1.00000 q^{82} +1.00000 q^{87} +1.00000i q^{93} +1.00000 q^{94} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3}+O(q^{10}) \) 2 * q - 2 * q^3	\( 2 q - 2 q^{3} - 2 q^{16} - 2 q^{23} - 2 q^{25} + 2 q^{27} - 2 q^{29} + 2 q^{48} - 2 q^{49} - 2 q^{62} - 2 q^{64} + 2 q^{69} + 2 q^{75} - 2 q^{81} - 2 q^{82} + 2 q^{87} + 2 q^{94}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^16 - 2 * q^23 - 2 * q^25 + 2 * q^27 - 2 * q^29 + 2 * q^48 - 2 * q^49 - 2 * q^62 - 2 * q^64 + 2 * q^69 + 2 * q^75 - 2 * q^81 - 2 * q^82 + 2 * q^87 + 2 * q^94

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