LMFDB - Embedded newform 2600.1.o.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2600,1,Mod(51,2600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2600.51");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2600 = 2^{3} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2600.o (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:	$1.29756903285$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.104.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.1352000.1

Embedding invariants

Embedding label			51.1
Character	$\chi$	$=$	2600.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{21} -1.00000 q^{24} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +2.00000 q^{31} -1.00000 q^{32} -1.00000 q^{34} +1.00000 q^{37} -1.00000 q^{39} -1.00000 q^{42} +1.00000 q^{43} +1.00000 q^{47} +1.00000 q^{48} +1.00000 q^{51} -1.00000 q^{52} +1.00000 q^{54} -1.00000 q^{56} -2.00000 q^{62} +1.00000 q^{64} +1.00000 q^{68} -1.00000 q^{71} -1.00000 q^{74} +1.00000 q^{78} -1.00000 q^{81} +1.00000 q^{84} -1.00000 q^{86} -1.00000 q^{91} +2.00000 q^{93} -1.00000 q^{94} -1.00000 q^{96} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2600\mathbb{Z}\right)^\times$.

$n$	$1301$	$1601$	$1951$	$1977$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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
$2$	−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
$5$	0	0
$5$	0	0
$6$	−1.00000	−1.00000
$7$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$7$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$8$	−1.00000	−1.00000
$9$	0	0
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	1.00000	1.00000
$13$	−1.00000	−1.00000
$13$	−1.00000	−1.00000
$14$	−1.00000	−1.00000
$15$	0	0
$16$	1.00000	1.00000
$17$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$17$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	1.00000	1.00000
$22$	0	0
$23$	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
$28$	1.00000	1.00000
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	2.00000	2.00000	1.00000			$0$
$31$	2.00000	2.00000	1.00000			$0$
$32$	−1.00000	−1.00000
$33$	0	0
$34$	−1.00000	−1.00000
$35$	0	0
$36$	0	0
$37$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$37$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$38$	0	0
$39$	−1.00000	−1.00000
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	−1.00000	−1.00000
$43$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$43$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$44$	0	0
$45$	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
$49$	0	0
$50$	0	0
$51$	1.00000	1.00000
$52$	−1.00000	−1.00000
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	1.00000	1.00000
$55$	0	0
$56$	−1.00000	−1.00000
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	−2.00000	−2.00000
$63$	0	0
$64$	1.00000	1.00000
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	1.00000	1.00000
$69$	0	0
$70$	0	0
$71$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−1.00000	−1.00000
$75$	0	0
$76$	0	0
$77$	0	0
$78$	1.00000	1.00000
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	−1.00000	−1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	1.00000	1.00000
$85$	0	0
$86$	−1.00000	−1.00000
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	−1.00000	−1.00000
$92$	0	0
$93$	2.00000	2.00000
$94$	−1.00000	−1.00000
$95$	0	0
$96$	−1.00000	−1.00000
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	−1.00000	−1.00000
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	1.00000	1.00000
$105$	0	0
$106$	0	0
$107$	−2.00000	−2.00000	−1.00000			$\pi$
$107$	−2.00000	−2.00000	−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	$0.666667\pi$
$110$	0	0
$111$	1.00000	1.00000
$112$	1.00000	1.00000
$113$	−2.00000	−2.00000	−1.00000			$\pi$
$113$	−2.00000	−2.00000	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	1.00000	1.00000
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	2.00000	2.00000
$125$	0	0
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	1.00000	1.00000
$130$	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
$136$	−1.00000	−1.00000
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−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
$141$	1.00000	1.00000
$142$	1.00000	1.00000
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	1.00000	1.00000
$149$	2.00000	2.00000	1.00000			$0$
$149$	2.00000	2.00000	1.00000			$0$
$150$	0	0
$151$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$151$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	−1.00000	−1.00000
$157$	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
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−2.00000	−2.00000	−1.00000			$\pi$
$167$	−2.00000	−2.00000	−1.00000			$\pi$
$168$	−1.00000	−1.00000
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	1.00000	1.00000
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$179$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	1.00000	1.00000
$183$	0	0
$184$	0	0
$185$	0	0
$186$	−2.00000	−2.00000
$187$	0	0
$188$	1.00000	1.00000
$189$	−1.00000	−1.00000
$190$	0	0
$191$	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
$195$	0	0
$196$	0	0
$197$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$197$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$198$	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
$204$	1.00000	1.00000
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−1.00000	−1.00000
$209$	0	0
$210$	0	0
$211$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$212$	0	0
$213$	−1.00000	−1.00000
$214$	2.00000	2.00000
$215$	0	0
$216$	1.00000	1.00000
$217$	2.00000	2.00000
$218$	1.00000	1.00000
$219$	0	0
$220$	0	0
$221$	−1.00000	−1.00000
$222$	−1.00000	−1.00000
$223$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$223$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$224$	−1.00000	−1.00000
$225$	0	0
$226$	2.00000	2.00000
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$229$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	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
$238$	−1.00000	−1.00000
$239$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−1.00000	−1.00000
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−2.00000	−2.00000
$249$	0	0
$250$	0	0
$251$	2.00000	2.00000	1.00000			$0$
$251$	2.00000	2.00000	1.00000			$0$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$258$	−1.00000	−1.00000
$259$	1.00000	1.00000
$260$	0	0
$261$	0	0
$262$	1.00000	1.00000
$263$	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
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$271$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$272$	1.00000	1.00000
$273$	−1.00000	−1.00000
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	1.00000	1.00000
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	−1.00000	−1.00000
$283$	−2.00000	−2.00000	−1.00000			$\pi$
$283$	−2.00000	−2.00000	−1.00000			$\pi$
$284$	−1.00000	−1.00000
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	0	0
$290$	0	0
$291$	0	0
$292$	0	0
$293$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$293$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$294$	0	0
$295$	0	0
$296$	−1.00000	−1.00000
$297$	0	0
$298$	−2.00000	−2.00000
$299$	0	0
$300$	0	0
$301$	1.00000	1.00000
$302$	1.00000	1.00000
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	1.00000	1.00000
$313$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$313$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−2.00000	−2.00000	−1.00000			$\pi$
$317$	−2.00000	−2.00000	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−2.00000	−2.00000
$322$	0	0
$323$	0	0
$324$	−1.00000	−1.00000
$325$	0	0
$326$	0	0
$327$	−1.00000	−1.00000
$328$	0	0
$329$	1.00000	1.00000
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	2.00000	2.00000
$335$	0	0
$336$	1.00000	1.00000
$337$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$337$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$338$	−1.00000	−1.00000
$339$	−2.00000	−2.00000
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−1.00000	−1.00000
$344$	−1.00000	−1.00000
$345$	0	0
$346$	0	0
$347$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$347$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$348$	0	0
$349$	−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
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	1.00000	1.00000
$358$	1.00000	1.00000
$359$	2.00000	2.00000	1.00000			$0$
$359$	2.00000	2.00000	1.00000			$0$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	1.00000	1.00000
$364$	−1.00000	−1.00000
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	2.00000	2.00000
$373$	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
$378$	1.00000	1.00000
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$383$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$384$	−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			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	−1.00000	−1.00000
$394$	−1.00000	−1.00000
$395$	0	0
$396$	0	0
$397$	−2.00000	−2.00000	−1.00000			$\pi$
$397$	−2.00000	−2.00000	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	−2.00000	−2.00000
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	−1.00000	−1.00000
$409$	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
$417$	−1.00000	−1.00000
$418$	0	0
$419$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$420$	0	0
$421$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$422$	1.00000	1.00000
$423$	0	0
$424$	0	0
$425$	0	0
$426$	1.00000	1.00000
$427$	0	0
$428$	−2.00000	−2.00000
$429$	0	0
$430$	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
$433$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$433$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$434$	−2.00000	−2.00000
$435$	0	0
$436$	−1.00000	−1.00000
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	1.00000	1.00000
$443$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$443$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$444$	1.00000	1.00000
$445$	0	0
$446$	−1.00000	−1.00000
$447$	2.00000	2.00000
$448$	1.00000	1.00000
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	−2.00000	−2.00000
$453$	−1.00000	−1.00000
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	1.00000	1.00000
$459$	−1.00000	−1.00000
$460$	0	0
$461$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$462$	0	0
$463$	−2.00000	−2.00000	−1.00000			$\pi$
$463$	−2.00000	−2.00000	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	−1.00000	−1.00000
$467$	−2.00000	−2.00000	−1.00000			$\pi$
$467$	−2.00000	−2.00000	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	1.00000	1.00000
$477$	0	0
$478$	1.00000	1.00000
$479$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$479$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$480$	0	0
$481$	−1.00000	−1.00000
$482$	0	0
$483$	0	0
$484$	1.00000	1.00000
$485$	0	0
$486$	0	0
$487$	−2.00000	−2.00000	−1.00000			$\pi$
$487$	−2.00000	−2.00000	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−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
$494$	0	0
$495$	0	0
$496$	2.00000	2.00000
$497$	−1.00000	−1.00000
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	−2.00000	−2.00000
$502$	−2.00000	−2.00000
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	1.00000	1.00000
$508$	0	0
$509$	2.00000	2.00000	1.00000			$0$
$509$	2.00000	2.00000	1.00000			$0$
$510$	0	0
$511$	0	0
$512$	−1.00000	−1.00000
$513$	0	0
$514$	−1.00000	−1.00000
$515$	0	0
$516$	1.00000	1.00000
$517$	0	0
$518$	−1.00000	−1.00000
$519$	0	0
$520$	0	0
$521$	−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
$523$	−2.00000	−2.00000	−1.00000			$\pi$
$523$	−2.00000	−2.00000	−1.00000			$\pi$
$524$	−1.00000	−1.00000
$525$	0	0
$526$	0	0
$527$	2.00000	2.00000
$528$	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
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$541$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$542$	1.00000	1.00000
$543$	0	0
$544$	−1.00000	−1.00000
$545$	0	0
$546$	1.00000	1.00000
$547$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$547$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	−1.00000	−1.00000
$557$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$557$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$558$	0	0
$559$	−1.00000	−1.00000
$560$	0	0
$561$	0	0
$562$	0	0
$563$	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
$566$	2.00000	2.00000
$567$	−1.00000	−1.00000
$568$	1.00000	1.00000
$569$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$570$	0	0
$571$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−1.00000	−1.00000
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	1.00000	1.00000
$592$	1.00000	1.00000
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	2.00000	2.00000
$597$	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	$-0.666667\pi$
$601$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$602$	−1.00000	−1.00000
$603$	0	0
$604$	−1.00000	−1.00000
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−1.00000	−1.00000
$612$	0	0
$613$	−2.00000	−2.00000	−1.00000			$\pi$
$613$	−2.00000	−2.00000	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	−1.00000	−1.00000
$625$	0	0
$626$	−1.00000	−1.00000
$627$	0	0
$628$	0	0
$629$	1.00000	1.00000
$630$	0	0
$631$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$632$	0	0
$633$	−1.00000	−1.00000
$634$	2.00000	2.00000
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	2.00000	2.00000	1.00000			$0$
$641$	2.00000	2.00000	1.00000			$0$
$642$	2.00000	2.00000
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	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
$651$	2.00000	2.00000
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	1.00000	1.00000
$655$	0	0
$656$	0	0
$657$	0	0
$658$	−1.00000	−1.00000
$659$	2.00000	2.00000	1.00000			$0$
$659$	2.00000	2.00000	1.00000			$0$
$660$	0	0
$661$	2.00000	2.00000	1.00000			$0$
$661$	2.00000	2.00000	1.00000			$0$
$662$	0	0
$663$	−1.00000	−1.00000
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−2.00000	−2.00000
$669$	1.00000	1.00000
$670$	0	0
$671$	0	0
$672$	−1.00000	−1.00000
$673$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$673$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$674$	−1.00000	−1.00000
$675$	0	0
$676$	1.00000	1.00000
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	2.00000	2.00000
$679$	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
$687$	−1.00000	−1.00000
$688$	1.00000	1.00000
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	−1.00000	−1.00000
$695$	0	0
$696$	0	0
$697$	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			$\pi$
$702$	−1.00000	−1.00000
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	2.00000	2.00000	1.00000			$0$
$709$	2.00000	2.00000	1.00000			$0$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	−1.00000	−1.00000
$715$	0	0
$716$	−1.00000	−1.00000
$717$	−1.00000	−1.00000
$718$	−2.00000	−2.00000
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	−1.00000	−1.00000
$723$	0	0
$724$	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
$730$	0	0
$731$	1.00000	1.00000
$732$	0	0
$733$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$733$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$744$	−2.00000	−2.00000
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−2.00000	−2.00000
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	1.00000	1.00000
$753$	2.00000	2.00000
$754$	0	0
$755$	0	0
$756$	−1.00000	−1.00000
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	−1.00000	−1.00000
$764$	0	0
$765$	0	0
$766$	−1.00000	−1.00000
$767$	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
$773$	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
$783$	0	0
$784$	0	0
$785$	0	0
$786$	1.00000	1.00000
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	1.00000	1.00000
$789$	0	0
$790$	0	0
$791$	−2.00000	−2.00000
$792$	0	0
$793$	0	0
$794$	2.00000	2.00000
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	1.00000	1.00000
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	2.00000	2.00000
$807$	0	0
$808$	0	0
$809$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	−1.00000	−1.00000
$814$	0	0
$815$	0	0
$816$	1.00000	1.00000
$817$	0	0
$818$	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
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	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
$834$	1.00000	1.00000
$835$	0	0
$836$	0	0
$837$	−2.00000	−2.00000
$838$	1.00000	1.00000
$839$	2.00000	2.00000	1.00000			$0$
$839$	2.00000	2.00000	1.00000			$0$
$840$	0	0
$841$	1.00000	1.00000
$842$	1.00000	1.00000
$843$	0	0
$844$	−1.00000	−1.00000
$845$	0	0
$846$	0	0
$847$	1.00000	1.00000
$848$	0	0
$849$	−2.00000	−2.00000
$850$	0	0
$851$	0	0
$852$	−1.00000	−1.00000
$853$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$853$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$854$	0	0
$855$	0	0
$856$	2.00000	2.00000
$857$	−2.00000	−2.00000	−1.00000			$\pi$
$857$	−2.00000	−2.00000	−1.00000			$\pi$
$858$	0	0
$859$	2.00000	2.00000	1.00000			$0$
$859$	2.00000	2.00000	1.00000			$0$
$860$	0	0
$861$	0	0
$862$	1.00000	1.00000
$863$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$863$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$864$	1.00000	1.00000
$865$	0	0
$866$	−1.00000	−1.00000
$867$	0	0
$868$	2.00000	2.00000
$869$	0	0
$870$	0	0
$871$	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	$-0.333333\pi$
$877$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$878$	0	0
$879$	1.00000	1.00000
$880$	0	0
$881$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$882$	0	0
$883$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$883$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$884$	−1.00000	−1.00000
$885$	0	0
$886$	−1.00000	−1.00000
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	−1.00000	−1.00000
$889$	0	0
$890$	0	0
$891$	0	0
$892$	1.00000	1.00000
$893$	0	0
$894$	−2.00000	−2.00000
$895$	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
$903$	1.00000	1.00000
$904$	2.00000	2.00000
$905$	0	0
$906$	1.00000	1.00000
$907$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$907$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$908$	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
$916$	−1.00000	−1.00000
$917$	−1.00000	−1.00000
$918$	1.00000	1.00000
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	1.00000	1.00000
$923$	1.00000	1.00000
$924$	0	0
$925$	0	0
$926$	2.00000	2.00000
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	1.00000	1.00000
$933$	0	0
$934$	2.00000	2.00000
$935$	0	0
$936$	0	0
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$938$	0	0
$939$	1.00000	1.00000
$940$	0	0
$941$	−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
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	−2.00000	−2.00000
$952$	−1.00000	−1.00000
$953$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$953$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$954$	0	0
$955$	0	0
$956$	−1.00000	−1.00000
$957$	0	0
$958$	1.00000	1.00000
$959$	0	0
$960$	0	0
$961$	3.00000	3.00000
$962$	1.00000	1.00000
$963$	0	0
$964$	0	0
$965$	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	$0.333333\pi$
$968$	−1.00000	−1.00000
$969$	0	0
$970$	0	0
$971$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$972$	0	0
$973$	−1.00000	−1.00000
$974$	2.00000	2.00000
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	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
$985$	0	0
$986$	0	0
$987$	1.00000	1.00000
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	−2.00000	−2.00000
$993$	0	0
$994$	1.00000	1.00000
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	−1.00000	−1.00000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2600.1.o.b.51.1		1
5.2	odd	4		2600.1.b.a.1299.1		2
5.3	odd	4		2600.1.b.a.1299.2		2
5.4	even	2		104.1.h.b.51.1	yes	1
8.3	odd	2		2600.1.o.d.51.1		1
13.12	even	2		2600.1.o.d.51.1		1
15.14	odd	2		936.1.o.a.883.1		1
20.19	odd	2		416.1.h.a.207.1		1
40.3	even	4		2600.1.b.b.1299.1		2
40.19	odd	2		104.1.h.a.51.1	✓	1
40.27	even	4		2600.1.b.b.1299.2		2
40.29	even	2		416.1.h.b.207.1		1
60.59	even	2		3744.1.o.b.2287.1		1
65.4	even	6		1352.1.p.b.699.1		2
65.9	even	6		1352.1.p.a.699.1		2
65.12	odd	4		2600.1.b.b.1299.2		2
65.19	odd	12		1352.1.n.a.315.1		4
65.24	odd	12		1352.1.n.a.867.1		4
65.29	even	6		1352.1.p.a.147.1		2
65.34	odd	4		1352.1.g.a.339.2		2
65.38	odd	4		2600.1.b.b.1299.1		2
65.44	odd	4		1352.1.g.a.339.1		2
65.49	even	6		1352.1.p.b.147.1		2
65.54	odd	12		1352.1.n.a.867.2		4
65.59	odd	12		1352.1.n.a.315.2		4
65.64	even	2		104.1.h.a.51.1	✓	1
80.19	odd	4		3328.1.c.a.3327.2		2
80.29	even	4		3328.1.c.e.3327.1		2
80.59	odd	4		3328.1.c.a.3327.1		2
80.69	even	4		3328.1.c.e.3327.2		2
104.51	odd	2	CM	2600.1.o.b.51.1		1
120.29	odd	2		3744.1.o.a.2287.1		1
120.59	even	2		936.1.o.b.883.1		1
195.194	odd	2		936.1.o.b.883.1		1
260.259	odd	2		416.1.h.b.207.1		1
520.19	even	12		1352.1.n.a.315.2		4
520.59	even	12		1352.1.n.a.315.1		4
520.99	even	4		1352.1.g.a.339.1		2
520.139	odd	6		1352.1.p.b.699.1		2
520.179	odd	6		1352.1.p.a.147.1		2
520.219	even	12		1352.1.n.a.867.2		4
520.259	odd	2		104.1.h.b.51.1	yes	1
520.363	even	4		2600.1.b.a.1299.2		2
520.379	even	12		1352.1.n.a.867.1		4
520.389	even	2		416.1.h.a.207.1		1
520.419	odd	6		1352.1.p.b.147.1		2
520.459	odd	6		1352.1.p.a.699.1		2
520.467	even	4		2600.1.b.a.1299.1		2
520.499	even	4		1352.1.g.a.339.2		2
780.779	even	2		3744.1.o.a.2287.1		1
1040.259	odd	4		3328.1.c.e.3327.2		2
1040.389	even	4		3328.1.c.a.3327.2		2
1040.779	odd	4		3328.1.c.e.3327.1		2
1040.909	even	4		3328.1.c.a.3327.1		2
1560.389	odd	2		3744.1.o.b.2287.1		1
1560.779	even	2		936.1.o.a.883.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.1.h.a.51.1	✓	1	40.19	odd	2
104.1.h.a.51.1	✓	1	65.64	even	2
104.1.h.b.51.1	yes	1	5.4	even	2
104.1.h.b.51.1	yes	1	520.259	odd	2
416.1.h.a.207.1		1	20.19	odd	2
416.1.h.a.207.1		1	520.389	even	2
416.1.h.b.207.1		1	40.29	even	2
416.1.h.b.207.1		1	260.259	odd	2
936.1.o.a.883.1		1	15.14	odd	2
936.1.o.a.883.1		1	1560.779	even	2
936.1.o.b.883.1		1	120.59	even	2
936.1.o.b.883.1		1	195.194	odd	2
1352.1.g.a.339.1		2	65.44	odd	4
1352.1.g.a.339.1		2	520.99	even	4
1352.1.g.a.339.2		2	65.34	odd	4
1352.1.g.a.339.2		2	520.499	even	4
1352.1.n.a.315.1		4	65.19	odd	12
1352.1.n.a.315.1		4	520.59	even	12
1352.1.n.a.315.2		4	65.59	odd	12
1352.1.n.a.315.2		4	520.19	even	12
1352.1.n.a.867.1		4	65.24	odd	12
1352.1.n.a.867.1		4	520.379	even	12
1352.1.n.a.867.2		4	65.54	odd	12
1352.1.n.a.867.2		4	520.219	even	12
1352.1.p.a.147.1		2	65.29	even	6
1352.1.p.a.147.1		2	520.179	odd	6
1352.1.p.a.699.1		2	65.9	even	6
1352.1.p.a.699.1		2	520.459	odd	6
1352.1.p.b.147.1		2	65.49	even	6
1352.1.p.b.147.1		2	520.419	odd	6
1352.1.p.b.699.1		2	65.4	even	6
1352.1.p.b.699.1		2	520.139	odd	6
2600.1.b.a.1299.1		2	5.2	odd	4
2600.1.b.a.1299.1		2	520.467	even	4
2600.1.b.a.1299.2		2	5.3	odd	4
2600.1.b.a.1299.2		2	520.363	even	4
2600.1.b.b.1299.1		2	40.3	even	4
2600.1.b.b.1299.1		2	65.38	odd	4
2600.1.b.b.1299.2		2	40.27	even	4
2600.1.b.b.1299.2		2	65.12	odd	4
2600.1.o.b.51.1		1	1.1	even	1	trivial
2600.1.o.b.51.1		1	104.51	odd	2	CM
2600.1.o.d.51.1		1	8.3	odd	2
2600.1.o.d.51.1		1	13.12	even	2
3328.1.c.a.3327.1		2	80.59	odd	4
3328.1.c.a.3327.1		2	1040.909	even	4
3328.1.c.a.3327.2		2	80.19	odd	4
3328.1.c.a.3327.2		2	1040.389	even	4
3328.1.c.e.3327.1		2	80.29	even	4
3328.1.c.e.3327.1		2	1040.779	odd	4
3328.1.c.e.3327.2		2	80.69	even	4
3328.1.c.e.3327.2		2	1040.259	odd	4
3744.1.o.a.2287.1		1	120.29	odd	2
3744.1.o.a.2287.1		1	780.779	even	2
3744.1.o.b.2287.1		1	60.59	even	2
3744.1.o.b.2287.1		1	1560.389	odd	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:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2600.o (of order \(2\), degree \(1\), minimal)

\(n\)	\(1301\)	\(1601\)	\(1951\)	\(1977\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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