LMFDB - Embedded newform 335.1.d.b.334.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [335,1,Mod(334,335)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(335, 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("335.334");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 335 = 5 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	335.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:	$0.167186779232$
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 3.1.335.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.561125.1

Embedding invariants

Embedding label			334.1
Character	$\chi$	$=$	335.334

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} -2.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} -1.00000 q^{16} +2.00000 q^{19} +1.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -1.00000 q^{29} -1.00000 q^{30} -1.00000 q^{35} +2.00000 q^{38} -2.00000 q^{39} +1.00000 q^{40} +1.00000 q^{42} +1.00000 q^{43} -1.00000 q^{48} +1.00000 q^{50} +1.00000 q^{53} -1.00000 q^{54} -1.00000 q^{56} +2.00000 q^{57} -1.00000 q^{58} -1.00000 q^{59} +1.00000 q^{64} +2.00000 q^{65} -1.00000 q^{67} -1.00000 q^{70} +2.00000 q^{71} +1.00000 q^{75} -2.00000 q^{78} +1.00000 q^{80} -1.00000 q^{81} +1.00000 q^{86} -1.00000 q^{87} -1.00000 q^{89} -2.00000 q^{91} -2.00000 q^{95} +1.00000 q^{97} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/335\mathbb{Z}\right)^\times$.

$n$	$136$	$202$
$\chi(n)$	$-1$	$-1$

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	0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$3$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$3$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$4$	0	0
$5$	−1.00000	−1.00000
$5$	−1.00000	−1.00000
$6$	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
$10$	−1.00000	−1.00000
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	−2.00000	−2.00000	−1.00000			$\pi$
$13$	−2.00000	−2.00000	−1.00000			$\pi$
$14$	1.00000	1.00000
$15$	−1.00000	−1.00000
$16$	−1.00000	−1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	2.00000	2.00000	1.00000			$0$
$19$	2.00000	2.00000	1.00000			$0$
$20$	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
$25$	1.00000	1.00000
$26$	−2.00000	−2.00000
$27$	−1.00000	−1.00000
$28$	0	0
$29$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$30$	−1.00000	−1.00000
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−1.00000	−1.00000
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	2.00000	2.00000
$39$	−2.00000	−2.00000
$40$	1.00000	1.00000
$41$	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
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−1.00000	−1.00000
$49$	0	0
$50$	1.00000	1.00000
$51$	0	0
$52$	0	0
$53$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$53$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$54$	−1.00000	−1.00000
$55$	0	0
$56$	−1.00000	−1.00000
$57$	2.00000	2.00000
$58$	−1.00000	−1.00000
$59$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$59$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	1.00000
$65$	2.00000	2.00000
$66$	0	0
$67$	−1.00000	−1.00000
$67$	−1.00000	−1.00000
$68$	0	0
$69$	0	0
$70$	−1.00000	−1.00000
$71$	2.00000	2.00000	1.00000			$0$
$71$	2.00000	2.00000	1.00000			$0$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	1.00000	1.00000
$76$	0	0
$77$	0	0
$78$	−2.00000	−2.00000
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	1.00000	1.00000
$81$	−1.00000	−1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	1.00000	1.00000
$87$	−1.00000	−1.00000
$88$	0	0
$89$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$89$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$90$	0	0
$91$	−2.00000	−2.00000
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−2.00000	−2.00000
$96$	0	0
$97$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$97$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$98$	0	0
$99$	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			$\pi$
$104$	2.00000	2.00000
$105$	−1.00000	−1.00000
$106$	1.00000	1.00000
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−1.00000
$113$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$113$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$114$	2.00000	2.00000
$115$	0	0
$116$	0	0
$117$	0	0
$118$	−1.00000	−1.00000
$119$	0	0
$120$	1.00000	1.00000
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−1.00000	−1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	1.00000	1.00000
$129$	1.00000	1.00000
$130$	2.00000	2.00000
$131$	−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
$133$	2.00000	2.00000
$134$	−1.00000	−1.00000
$135$	1.00000	1.00000
$136$	0	0
$137$	−2.00000	−2.00000	−1.00000			$\pi$
$137$	−2.00000	−2.00000	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	2.00000	2.00000
$143$	0	0
$144$	0	0
$145$	1.00000	1.00000
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$150$	1.00000	1.00000
$151$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$151$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$152$	−2.00000	−2.00000
$153$	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
$159$	1.00000	1.00000
$160$	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
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	−1.00000	−1.00000
$169$	3.00000	3.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	−1.00000	−1.00000
$175$	1.00000	1.00000
$176$	0	0
$177$	−1.00000	−1.00000
$178$	−1.00000	−1.00000
$179$	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	$0.666667\pi$
$182$	−2.00000	−2.00000
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−1.00000	−1.00000
$190$	−2.00000	−2.00000
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	1.00000	1.00000
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	1.00000	1.00000
$195$	2.00000	2.00000
$196$	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
$199$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$199$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$200$	−1.00000	−1.00000
$201$	−1.00000	−1.00000
$202$	0	0
$203$	−1.00000	−1.00000
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	2.00000	2.00000
$209$	0	0
$210$	−1.00000	−1.00000
$211$	−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
$213$	2.00000	2.00000
$214$	0	0
$215$	−1.00000	−1.00000
$216$	1.00000	1.00000
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	0	0
$226$	1.00000	1.00000
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	1.00000	1.00000
$233$	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
$239$	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	$0.666667\pi$
$242$	1.00000	1.00000
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−4.00000	−4.00000
$248$	0	0
$249$	0	0
$250$	−1.00000	−1.00000
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	1.00000	1.00000
$259$	0	0
$260$	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
$265$	−1.00000	−1.00000
$266$	2.00000	2.00000
$267$	−1.00000	−1.00000
$268$	0	0
$269$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$270$	1.00000	1.00000
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	−2.00000	−2.00000
$274$	−2.00000	−2.00000
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	1.00000	1.00000
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	−2.00000	−2.00000
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.00000	1.00000
$290$	1.00000	1.00000
$291$	1.00000	1.00000
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	1.00000	1.00000
$296$	0	0
$297$	0	0
$298$	−1.00000	−1.00000
$299$	0	0
$300$	0	0
$301$	1.00000	1.00000
$302$	−1.00000	−1.00000
$303$	0	0
$304$	−2.00000	−2.00000
$305$	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			$\pi$
$312$	2.00000	2.00000
$313$	−2.00000	−2.00000	−1.00000			$\pi$
$313$	−2.00000	−2.00000	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	1.00000	1.00000
$319$	0	0
$320$	−1.00000	−1.00000
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−2.00000	−2.00000
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	1.00000	1.00000
$336$	−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	$0.333333\pi$
$338$	3.00000	3.00000
$339$	1.00000	1.00000
$340$	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	$0.666667\pi$
$350$	1.00000	1.00000
$351$	2.00000	2.00000
$352$	0	0
$353$	−2.00000	−2.00000	−1.00000			$\pi$
$353$	−2.00000	−2.00000	−1.00000			$\pi$
$354$	−1.00000	−1.00000
$355$	−2.00000	−2.00000
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$359$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$360$	0	0
$361$	3.00000	3.00000
$362$	−1.00000	−1.00000
$363$	1.00000	1.00000
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$367$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	1.00000	1.00000
$372$	0	0
$373$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$373$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$374$	0	0
$375$	−1.00000	−1.00000
$376$	0	0
$377$	2.00000	2.00000
$378$	−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
$389$	2.00000	2.00000	1.00000			$0$
$389$	2.00000	2.00000	1.00000			$0$
$390$	2.00000	2.00000
$391$	0	0
$392$	0	0
$393$	−1.00000	−1.00000
$394$	1.00000	1.00000
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	−1.00000	−1.00000
$399$	2.00000	2.00000
$400$	−1.00000	−1.00000
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	−1.00000	−1.00000
$403$	0	0
$404$	0	0
$405$	1.00000	1.00000
$406$	−1.00000	−1.00000
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−2.00000	−2.00000
$412$	0	0
$413$	−1.00000	−1.00000
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	2.00000	2.00000	1.00000			$0$
$419$	2.00000	2.00000	1.00000			$0$
$420$	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
$424$	−1.00000	−1.00000
$425$	0	0
$426$	2.00000	2.00000
$427$	0	0
$428$	0	0
$429$	0	0
$430$	−1.00000	−1.00000
$431$	−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	$0.333333\pi$
$434$	0	0
$435$	1.00000	1.00000
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$443$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$444$	0	0
$445$	1.00000	1.00000
$446$	0	0
$447$	−1.00000	−1.00000
$448$	1.00000	1.00000
$449$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−1.00000	−1.00000
$454$	0	0
$455$	2.00000	2.00000
$456$	−2.00000	−2.00000
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	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
$463$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$463$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$464$	1.00000	1.00000
$465$	0	0
$466$	1.00000	1.00000
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	−1.00000	−1.00000
$470$	0	0
$471$	0	0
$472$	1.00000	1.00000
$473$	0	0
$474$	0	0
$475$	2.00000	2.00000
$476$	0	0
$477$	0	0
$478$	0	0
$479$	2.00000	2.00000	1.00000			$0$
$479$	2.00000	2.00000	1.00000			$0$
$480$	0	0
$481$	0	0
$482$	−1.00000	−1.00000
$483$	0	0
$484$	0	0
$485$	−1.00000	−1.00000
$486$	0	0
$487$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$487$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	2.00000	2.00000	1.00000			$0$
$491$	2.00000	2.00000	1.00000			$0$
$492$	0	0
$493$	0	0
$494$	−4.00000	−4.00000
$495$	0	0
$496$	0	0
$497$	2.00000	2.00000
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	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
$507$	3.00000	3.00000
$508$	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
$513$	−2.00000	−2.00000
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−2.00000	−2.00000
$521$	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
$525$	1.00000	1.00000
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	1.00000
$530$	−1.00000	−1.00000
$531$	0	0
$532$	0	0
$533$	0	0
$534$	−1.00000	−1.00000
$535$	0	0
$536$	1.00000	1.00000
$537$	0	0
$538$	−1.00000	−1.00000
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	−1.00000	−1.00000
$544$	0	0
$545$	0	0
$546$	−2.00000	−2.00000
$547$	−2.00000	−2.00000	−1.00000			$\pi$
$547$	−2.00000	−2.00000	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	−2.00000	−2.00000
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−2.00000	−2.00000
$560$	1.00000	1.00000
$561$	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	$0.333333\pi$
$564$	0	0
$565$	−1.00000	−1.00000
$566$	0	0
$567$	−1.00000	−1.00000
$568$	−2.00000	−2.00000
$569$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$570$	−2.00000	−2.00000
$571$	−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
$577$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$577$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$578$	1.00000	1.00000
$579$	0	0
$580$	0	0
$581$	0	0
$582$	1.00000	1.00000
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$587$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$588$	0	0
$589$	0	0
$590$	1.00000	1.00000
$591$	1.00000	1.00000
$592$	0	0
$593$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$593$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−1.00000	−1.00000
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	−1.00000	−1.00000
$601$	−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
$604$	0	0
$605$	−1.00000	−1.00000
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	−1.00000	−1.00000
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$619$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−1.00000	−1.00000
$624$	2.00000	2.00000
$625$	1.00000	1.00000
$626$	−2.00000	−2.00000
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	−1.00000	−1.00000
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	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
$647$	−2.00000	−2.00000	−1.00000			$\pi$
$647$	−2.00000	−2.00000	−1.00000			$\pi$
$648$	1.00000	1.00000
$649$	0	0
$650$	−2.00000	−2.00000
$651$	0	0
$652$	0	0
$653$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$653$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$654$	0	0
$655$	1.00000	1.00000
$656$	0	0
$657$	0	0
$658$	0	0
$659$	2.00000	2.00000	1.00000			$0$
$659$	2.00000	2.00000	1.00000			$0$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−2.00000	−2.00000
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	1.00000	1.00000
$671$	0	0
$672$	0	0
$673$	−2.00000	−2.00000	−1.00000			$\pi$
$673$	−2.00000	−2.00000	−1.00000			$\pi$
$674$	1.00000	1.00000
$675$	−1.00000	−1.00000
$676$	0	0
$677$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$677$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$678$	1.00000	1.00000
$679$	1.00000	1.00000
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−2.00000	−2.00000	−1.00000			$\pi$
$683$	−2.00000	−2.00000	−1.00000			$\pi$
$684$	0	0
$685$	2.00000	2.00000
$686$	−1.00000	−1.00000
$687$	0	0
$688$	−1.00000	−1.00000
$689$	−2.00000	−2.00000
$690$	0	0
$691$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$692$	0	0
$693$	0	0
$694$	1.00000	1.00000
$695$	0	0
$696$	1.00000	1.00000
$697$	0	0
$698$	−1.00000	−1.00000
$699$	1.00000	1.00000
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	2.00000	2.00000
$703$	0	0
$704$	0	0
$705$	0	0
$706$	−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	$0.666667\pi$
$710$	−2.00000	−2.00000
$711$	0	0
$712$	1.00000	1.00000
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−1.00000	−1.00000
$719$	2.00000	2.00000	1.00000			$0$
$719$	2.00000	2.00000	1.00000			$0$
$720$	0	0
$721$	0	0
$722$	3.00000	3.00000
$723$	−1.00000	−1.00000
$724$	0	0
$725$	−1.00000	−1.00000
$726$	1.00000	1.00000
$727$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$727$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$728$	2.00000	2.00000
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$733$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$734$	1.00000	1.00000
$735$	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
$741$	−4.00000	−4.00000
$742$	1.00000	1.00000
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	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			$0$
$751$	2.00000	2.00000	1.00000			$0$
$752$	0	0
$753$	0	0
$754$	2.00000	2.00000
$755$	1.00000	1.00000
$756$	0	0
$757$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$757$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$758$	0	0
$759$	0	0
$760$	2.00000	2.00000
$761$	2.00000	2.00000	1.00000			$0$
$761$	2.00000	2.00000	1.00000			$0$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	1.00000	1.00000
$767$	2.00000	2.00000
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	−1.00000	−1.00000
$777$	0	0
$778$	2.00000	2.00000
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	1.00000	1.00000
$784$	0	0
$785$	0	0
$786$	−1.00000	−1.00000
$787$	−2.00000	−2.00000	−1.00000			$\pi$
$787$	−2.00000	−2.00000	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	1.00000	1.00000
$792$	0	0
$793$	0	0
$794$	0	0
$795$	−1.00000	−1.00000
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	2.00000	2.00000
$799$	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
$808$	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
$813$	0	0
$814$	0	0
$815$	0	0
$816$	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	$0.666667\pi$
$822$	−2.00000	−2.00000
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	−1.00000	−1.00000
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$830$	0	0
$831$	0	0
$832$	−2.00000	−2.00000
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	2.00000	2.00000
$839$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$839$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$840$	1.00000	1.00000
$841$	0	0
$842$	−1.00000	−1.00000
$843$	0	0
$844$	0	0
$845$	−3.00000	−3.00000
$846$	0	0
$847$	1.00000	1.00000
$848$	−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
$857$	−2.00000	−2.00000	−1.00000			$\pi$
$857$	−2.00000	−2.00000	−1.00000			$\pi$
$858$	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
$862$	−1.00000	−1.00000
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	1.00000	1.00000
$867$	1.00000	1.00000
$868$	0	0
$869$	0	0
$870$	1.00000	1.00000
$871$	2.00000	2.00000
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−1.00000	−1.00000
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	−1.00000	−1.00000
$879$	0	0
$880$	0	0
$881$	2.00000	2.00000	1.00000			$0$
$881$	2.00000	2.00000	1.00000			$0$
$882$	0	0
$883$	−2.00000	−2.00000	−1.00000			$\pi$
$883$	−2.00000	−2.00000	−1.00000			$\pi$
$884$	0	0
$885$	1.00000	1.00000
$886$	1.00000	1.00000
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	1.00000	1.00000
$891$	0	0
$892$	0	0
$893$	0	0
$894$	−1.00000	−1.00000
$895$	0	0
$896$	1.00000	1.00000
$897$	0	0
$898$	−1.00000	−1.00000
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	1.00000	1.00000
$904$	−1.00000	−1.00000
$905$	1.00000	1.00000
$906$	−1.00000	−1.00000
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	2.00000	2.00000
$911$	2.00000	2.00000	1.00000			$0$
$911$	2.00000	2.00000	1.00000			$0$
$912$	−2.00000	−2.00000
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−1.00000	−1.00000
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	−1.00000	−1.00000
$923$	−4.00000	−4.00000
$924$	0	0
$925$	0	0
$926$	1.00000	1.00000
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$938$	−1.00000	−1.00000
$939$	−2.00000	−2.00000
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	1.00000	1.00000
$945$	1.00000	1.00000
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	2.00000	2.00000
$951$	0	0
$952$	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
$958$	2.00000	2.00000
$959$	−2.00000	−2.00000
$960$	−1.00000	−1.00000
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−1.00000	−1.00000
$969$	0	0
$970$	−1.00000	−1.00000
$971$	−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
$973$	0	0
$974$	1.00000	1.00000
$975$	−2.00000	−2.00000
$976$	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
$982$	2.00000	2.00000
$983$	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
$985$	−1.00000	−1.00000
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	2.00000	2.00000
$995$	1.00000	1.00000
$996$	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	335.1.d.b.334.1	yes	1
3.2	odd	2		3015.1.h.a.334.1		1
5.2	odd	4		1675.1.b.c.401.2		2
5.3	odd	4		1675.1.b.c.401.1		2
5.4	even	2		335.1.d.a.334.1	✓	1
15.14	odd	2		3015.1.h.b.334.1		1
67.66	odd	2		335.1.d.a.334.1	✓	1
201.200	even	2		3015.1.h.b.334.1		1
335.133	even	4		1675.1.b.c.401.2		2
335.267	even	4		1675.1.b.c.401.1		2
335.334	odd	2	CM	335.1.d.b.334.1	yes	1
1005.1004	even	2		3015.1.h.a.334.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
335.1.d.a.334.1	✓	1	5.4	even	2
335.1.d.a.334.1	✓	1	67.66	odd	2
335.1.d.b.334.1	yes	1	1.1	even	1	trivial
335.1.d.b.334.1	yes	1	335.334	odd	2	CM
1675.1.b.c.401.1		2	5.3	odd	4
1675.1.b.c.401.1		2	335.267	even	4
1675.1.b.c.401.2		2	5.2	odd	4
1675.1.b.c.401.2		2	335.133	even	4
3015.1.h.a.334.1		1	3.2	odd	2
3015.1.h.a.334.1		1	1005.1004	even	2
3015.1.h.b.334.1		1	15.14	odd	2
3015.1.h.b.334.1		1	201.200	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 335 = 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	335.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(136\)	\(202\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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