LMFDB - Embedded newform 1700.1.d.b.1699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1700,1,Mod(1699,1700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1700, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1700.1699");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$1700 = 2^{2} \cdot 5^{2} \cdot 17$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1700.d (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:	$0.848410521476$
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 68)
Projective image:	$D_{2}$
Projective field:	Galois closure of $\Q(i, \sqrt{17})$
Artin image:	$D_4:C_2$
Artin field:	Galois closure of 8.0.1156000000.2

Embedding invariants

Embedding label			1699.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1700.1699
Dual form			1700.1.d.b.1699.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +1.00000i q^{8} +1.00000 q^{9} +2.00000i q^{13} +1.00000 q^{16} +1.00000i q^{17} -1.00000i q^{18} +2.00000 q^{26} -1.00000i q^{32} +1.00000 q^{34} -1.00000 q^{36} +1.00000 q^{49} -2.00000i q^{52} -2.00000i q^{53} -1.00000 q^{64} -1.00000i q^{68} +1.00000i q^{72} +1.00000 q^{81} +2.00000 q^{89} -1.00000i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 2 q^{4} + 2 q^{9} + 2 q^{16} + 4 q^{26} + 2 q^{34} - 2 q^{36} + 2 q^{49} - 2 q^{64} + 2 q^{81} + 4 q^{89}+O(q^{100})$ 2 * q - 2 * q^4 + 2 * q^9 + 2 * q^16 + 4 * q^26 + 2 * q^34 - 2 * q^36 + 2 * q^49 - 2 * q^64 + 2 * q^81 + 4 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1700\mathbb{Z}\right)^\times$ .

$n$	$477$	$851$	$1601$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	− 1.00000i	− 1.00000i
$2$	− 1.00000i	− 1.00000i
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	−1.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	1.00000i	1.00000i
$9$	1.00000	1.00000
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$13$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	1.00000
$17$	1.00000i	1.00000i
$17$	1.00000i	1.00000i
$18$	− 1.00000i	− 1.00000i
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	0	0
$26$	2.00000	2.00000
$27$	0	0
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	− 1.00000i	− 1.00000i
$33$	0	0
$34$	1.00000	1.00000
$35$	0	0
$36$	−1.00000	−1.00000
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	1.00000	1.00000
$50$	0	0
$51$	0	0
$52$	− 2.00000i	− 2.00000i
$53$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$53$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	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			$\pi$
$62$	0	0
$63$	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	$0.5\pi$
$68$	− 1.00000i	− 1.00000i
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000i	1.00000i
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	2.00000	2.00000	1.00000			$0$
$89$	2.00000	2.00000	1.00000			$0$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	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		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−2.00000	−2.00000
$105$	0	0
$106$	−2.00000	−2.00000
$107$	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
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	2.00000i	2.00000i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−1.00000	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000i	1.00000i
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	−1.00000	−1.00000
$137$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$137$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	1.00000	1.00000
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−2.00000	−2.00000	−1.00000			$\pi$
$149$	−2.00000	−2.00000	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	1.00000i	1.00000i
$154$	0	0
$155$	0	0
$156$	0	0
$157$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$157$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	− 1.00000i	− 1.00000i
$163$	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			$\pi$
$168$	0	0
$169$	−3.00000	−3.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	− 2.00000i	− 2.00000i
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	−1.00000	−1.00000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	2.00000i	2.00000i
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	2.00000i	2.00000i
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	2.00000i	2.00000i
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	−2.00000	−2.00000
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	2.00000	2.00000	1.00000			$0$
$229$	2.00000	2.00000	1.00000			$0$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	2.00000	2.00000
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	1.00000i	1.00000i
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$257$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	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
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	1.00000i	1.00000i
$273$	0	0
$274$	−2.00000	−2.00000
$275$	0	0
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	2.00000	2.00000	1.00000			$0$
$281$	2.00000	2.00000	1.00000			$0$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	− 1.00000i	− 1.00000i
$289$	−1.00000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$293$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	2.00000i	2.00000i
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	1.00000	1.00000
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	2.00000	2.00000
$315$	0	0
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−1.00000	−1.00000
$325$	0	0
$326$	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
$335$	0	0
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	3.00000i	3.00000i
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	−2.00000	−2.00000	−1.00000			$\pi$
$349$	−2.00000	−2.00000	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$353$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$354$	0	0
$355$	0	0
$356$	−2.00000	−2.00000
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	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
$372$	0	0
$373$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$373$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	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			$0$
$390$	0	0
$391$	0	0
$392$	1.00000i	1.00000i
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	2.00000	2.00000
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−2.00000	−2.00000	−1.00000			$\pi$
$409$	−2.00000	−2.00000	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	2.00000	2.00000
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−2.00000	−2.00000	−1.00000			$\pi$
$421$	−2.00000	−2.00000	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	2.00000	2.00000
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$433$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	1.00000	1.00000
$442$	2.00000i	2.00000i
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$457$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$458$	− 2.00000i	− 2.00000i
$459$	0	0
$460$	0	0
$461$	2.00000	2.00000	1.00000			$0$
$461$	2.00000	2.00000	1.00000			$0$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	− 2.00000i	− 2.00000i
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	− 2.00000i	− 2.00000i
$478$	0	0
$479$	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
$484$	1.00000	1.00000
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	0	0
$502$	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
$509$	−2.00000	−2.00000	−1.00000			$\pi$
$509$	−2.00000	−2.00000	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	− 1.00000i	− 1.00000i
$513$	0	0
$514$	−2.00000	−2.00000
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	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
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	1.00000	1.00000
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	2.00000i	2.00000i
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$557$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	− 2.00000i	− 2.00000i
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−2.00000	−2.00000	−1.00000			$\pi$
$569$	−2.00000	−2.00000	−1.00000			$\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	−1.00000	−1.00000
$577$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$577$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$578$	1.00000i	1.00000i
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−2.00000	−2.00000
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	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
$596$	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
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	− 1.00000i	− 1.00000i
$613$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$613$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$614$	0	0
$615$	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
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	− 2.00000i	− 2.00000i
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	2.00000i	2.00000i
$638$	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	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	1.00000i	1.00000i
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	2.00000	2.00000	1.00000			$0$
$661$	2.00000	2.00000	1.00000			$0$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	0	0
$675$	0	0
$676$	3.00000	3.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	4.00000	4.00000
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	2.00000i	2.00000i
$699$	0	0
$700$	0	0
$701$	−2.00000	−2.00000	−1.00000			$\pi$
$701$	−2.00000	−2.00000	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	−2.00000	−2.00000
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	2.00000i	2.00000i
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	− 1.00000i	− 1.00000i
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$733$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$734$	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
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	2.00000	2.00000
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$757$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−2.00000	−2.00000	−1.00000			$\pi$
$761$	−2.00000	−2.00000	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	2.00000	2.00000	1.00000			$0$
$769$	2.00000	2.00000	1.00000			$0$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$773$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	− 2.00000i	− 2.00000i
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	1.00000
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$797$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	2.00000	2.00000
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	− 2.00000i	− 2.00000i
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	2.00000i	2.00000i
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	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
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	− 2.00000i	− 2.00000i
$833$	1.00000i	1.00000i
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	2.00000i	2.00000i
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	− 2.00000i	− 2.00000i
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	2.00000	2.00000
$867$	0	0
$868$	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
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	− 1.00000i	− 1.00000i
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	2.00000	2.00000
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	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
$898$	0	0
$899$	0	0
$900$	0	0
$901$	2.00000	2.00000
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	−2.00000	−2.00000
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	−2.00000	−2.00000
$915$	0	0
$916$	−2.00000	−2.00000
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	− 2.00000i	− 2.00000i
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	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
$936$	−2.00000	−2.00000
$937$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$937$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	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
$951$	0	0
$952$	0	0
$953$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$953$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$954$	−2.00000	−2.00000
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−1.00000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	− 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
$974$	0	0
$975$	0	0
$976$	0	0
$977$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$977$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1700.1.d.b.1699.1		2
4.3	odd	2	CM	1700.1.d.b.1699.1		2
5.2	odd	4		1700.1.h.d.951.1		1
5.3	odd	4		68.1.d.a.67.1	✓	1
5.4	even	2	inner	1700.1.d.b.1699.2		2
15.8	even	4		612.1.e.a.271.1		1
17.16	even	2	RM	1700.1.d.b.1699.1		2
20.3	even	4		68.1.d.a.67.1	✓	1
20.7	even	4		1700.1.h.d.951.1		1
20.19	odd	2	inner	1700.1.d.b.1699.2		2
35.3	even	12		3332.1.o.d.2039.1		2
35.13	even	4		3332.1.g.a.883.1		1
35.18	odd	12		3332.1.o.c.2039.1		2
35.23	odd	12		3332.1.o.c.67.1		2
35.33	even	12		3332.1.o.d.67.1		2
40.3	even	4		1088.1.g.a.1087.1		1
40.13	odd	4		1088.1.g.a.1087.1		1
60.23	odd	4		612.1.e.a.271.1		1
68.67	odd	2	CM	1700.1.d.b.1699.1		2
85.3	even	16		1156.1.g.a.399.1		4
85.8	odd	8		1156.1.f.a.327.1		2
85.13	odd	4		1156.1.c.a.579.1		1
85.23	even	16		1156.1.g.a.423.1		4
85.28	even	16		1156.1.g.a.423.1		4
85.33	odd	4		68.1.d.a.67.1	✓	1
85.38	odd	4		1156.1.c.a.579.1		1
85.43	odd	8		1156.1.f.a.327.1		2
85.48	even	16		1156.1.g.a.399.1		4
85.53	odd	8		1156.1.f.a.251.1		2
85.58	even	16		1156.1.g.a.155.1		4
85.63	even	16		1156.1.g.a.179.1		4
85.67	odd	4		1700.1.h.d.951.1		1
85.73	even	16		1156.1.g.a.179.1		4
85.78	even	16		1156.1.g.a.155.1		4
85.83	odd	8		1156.1.f.a.251.1		2
85.84	even	2	inner	1700.1.d.b.1699.2		2
140.3	odd	12		3332.1.o.d.2039.1		2
140.23	even	12		3332.1.o.c.67.1		2
140.83	odd	4		3332.1.g.a.883.1		1
140.103	odd	12		3332.1.o.d.67.1		2
140.123	even	12		3332.1.o.c.2039.1		2
255.203	even	4		612.1.e.a.271.1		1
340.3	odd	16		1156.1.g.a.399.1		4
340.23	odd	16		1156.1.g.a.423.1		4
340.43	even	8		1156.1.f.a.327.1		2
340.63	odd	16		1156.1.g.a.179.1		4
340.67	even	4		1700.1.h.d.951.1		1
340.83	even	8		1156.1.f.a.251.1		2
340.123	even	4		1156.1.c.a.579.1		1
340.143	odd	16		1156.1.g.a.155.1		4
340.163	odd	16		1156.1.g.a.155.1		4
340.183	even	4		1156.1.c.a.579.1		1
340.203	even	4		68.1.d.a.67.1	✓	1
340.223	even	8		1156.1.f.a.251.1		2
340.243	odd	16		1156.1.g.a.179.1		4
340.263	even	8		1156.1.f.a.327.1		2
340.283	odd	16		1156.1.g.a.423.1		4
340.303	odd	16		1156.1.g.a.399.1		4
340.339	odd	2	inner	1700.1.d.b.1699.2		2
595.33	even	12		3332.1.o.d.67.1		2
595.118	even	4		3332.1.g.a.883.1		1
595.373	odd	12		3332.1.o.c.67.1		2
595.458	even	12		3332.1.o.d.2039.1		2
595.543	odd	12		3332.1.o.c.2039.1		2
680.203	even	4		1088.1.g.a.1087.1		1
680.373	odd	4		1088.1.g.a.1087.1		1
1020.203	odd	4		612.1.e.a.271.1		1
2380.543	even	12		3332.1.o.c.2039.1		2
2380.1223	odd	12		3332.1.o.d.67.1		2
2380.1563	even	12		3332.1.o.c.67.1		2
2380.1903	odd	4		3332.1.g.a.883.1		1
2380.2243	odd	12		3332.1.o.d.2039.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.1.d.a.67.1	✓	1	5.3	odd	4
68.1.d.a.67.1	✓	1	20.3	even	4
68.1.d.a.67.1	✓	1	85.33	odd	4
68.1.d.a.67.1	✓	1	340.203	even	4
612.1.e.a.271.1		1	15.8	even	4
612.1.e.a.271.1		1	60.23	odd	4
612.1.e.a.271.1		1	255.203	even	4
612.1.e.a.271.1		1	1020.203	odd	4
1088.1.g.a.1087.1		1	40.3	even	4
1088.1.g.a.1087.1		1	40.13	odd	4
1088.1.g.a.1087.1		1	680.203	even	4
1088.1.g.a.1087.1		1	680.373	odd	4
1156.1.c.a.579.1		1	85.13	odd	4
1156.1.c.a.579.1		1	85.38	odd	4
1156.1.c.a.579.1		1	340.123	even	4
1156.1.c.a.579.1		1	340.183	even	4
1156.1.f.a.251.1		2	85.53	odd	8
1156.1.f.a.251.1		2	85.83	odd	8
1156.1.f.a.251.1		2	340.83	even	8
1156.1.f.a.251.1		2	340.223	even	8
1156.1.f.a.327.1		2	85.8	odd	8
1156.1.f.a.327.1		2	85.43	odd	8
1156.1.f.a.327.1		2	340.43	even	8
1156.1.f.a.327.1		2	340.263	even	8
1156.1.g.a.155.1		4	85.58	even	16
1156.1.g.a.155.1		4	85.78	even	16
1156.1.g.a.155.1		4	340.143	odd	16
1156.1.g.a.155.1		4	340.163	odd	16
1156.1.g.a.179.1		4	85.63	even	16
1156.1.g.a.179.1		4	85.73	even	16
1156.1.g.a.179.1		4	340.63	odd	16
1156.1.g.a.179.1		4	340.243	odd	16
1156.1.g.a.399.1		4	85.3	even	16
1156.1.g.a.399.1		4	85.48	even	16
1156.1.g.a.399.1		4	340.3	odd	16
1156.1.g.a.399.1		4	340.303	odd	16
1156.1.g.a.423.1		4	85.23	even	16
1156.1.g.a.423.1		4	85.28	even	16
1156.1.g.a.423.1		4	340.23	odd	16
1156.1.g.a.423.1		4	340.283	odd	16
1700.1.d.b.1699.1		2	1.1	even	1	trivial
1700.1.d.b.1699.1		2	4.3	odd	2	CM
1700.1.d.b.1699.1		2	17.16	even	2	RM
1700.1.d.b.1699.1		2	68.67	odd	2	CM
1700.1.d.b.1699.2		2	5.4	even	2	inner
1700.1.d.b.1699.2		2	20.19	odd	2	inner
1700.1.d.b.1699.2		2	85.84	even	2	inner
1700.1.d.b.1699.2		2	340.339	odd	2	inner
1700.1.h.d.951.1		1	5.2	odd	4
1700.1.h.d.951.1		1	20.7	even	4
1700.1.h.d.951.1		1	85.67	odd	4
1700.1.h.d.951.1		1	340.67	even	4
3332.1.g.a.883.1		1	35.13	even	4
3332.1.g.a.883.1		1	140.83	odd	4
3332.1.g.a.883.1		1	595.118	even	4
3332.1.g.a.883.1		1	2380.1903	odd	4
3332.1.o.c.67.1		2	35.23	odd	12
3332.1.o.c.67.1		2	140.23	even	12
3332.1.o.c.67.1		2	595.373	odd	12
3332.1.o.c.67.1		2	2380.1563	even	12
3332.1.o.c.2039.1		2	35.18	odd	12
3332.1.o.c.2039.1		2	140.123	even	12
3332.1.o.c.2039.1		2	595.543	odd	12
3332.1.o.c.2039.1		2	2380.543	even	12
3332.1.o.d.67.1		2	35.33	even	12
3332.1.o.d.67.1		2	140.103	odd	12
3332.1.o.d.67.1		2	595.33	even	12
3332.1.o.d.67.1		2	2380.1223	odd	12
3332.1.o.d.2039.1		2	35.3	even	12
3332.1.o.d.2039.1		2	140.3	odd	12
3332.1.o.d.2039.1		2	595.458	even	12
3332.1.o.d.2039.1		2	2380.2243	odd	12

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1700.1.d.b.1699.1

Level	$1700$
Weight	$1$
Character	1700.1699
Analytic conductor	$0.848$
Analytic rank	$0$
Dimension	$2$
Projective image	$D_{2}$
CM/RM discs	-4, -68, 17
Inner twists	$8$