LMFDB - Embedded newform 2880.2.d.e.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(289,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2880.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.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:	no
Analytic conductor:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 320)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			289.3
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	2880.289
Dual form			2880.2.d.e.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23607 q^{5} -4.47214i q^{7} +O(q^{10})$	$q+2.23607 q^{5} -4.47214i q^{7} -2.00000i q^{11} -4.47214 q^{13} -6.00000i q^{19} +4.47214i q^{23} +5.00000 q^{25} -10.0000i q^{35} -4.47214 q^{37} -2.00000 q^{41} -13.4164i q^{47} -13.0000 q^{49} -13.4164 q^{53} -4.47214i q^{55} +14.0000i q^{59} -10.0000 q^{65} -8.94427 q^{77} +14.0000 q^{89} +20.0000i q^{91} -13.4164i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 20 q^{25} - 8 q^{41} - 52 q^{49} - 40 q^{65} + 56 q^{89}+O(q^{100}) $ 4 * q + 20 * q^25 - 8 * q^41 - 52 * q^49 - 40 * q^65 + 56 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0	0
$2$	0	0
$3$	0	0
$3$	0	0
$4$	0	0
$5$	2.23607	1.00000
$5$	2.23607	1.00000
$6$	0	0
$7$	− 4.47214i	− 1.69031i	−0.534522	−	0.845154i	$-0.679509\pi$
$7$	− 4.47214i	− 1.69031i	0.534522	−	0.845154i	$-0.320491\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	− 2.00000i	− 0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$	− 2.00000i	− 0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	0	0
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	− 6.00000i	− 1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$	− 6.00000i	− 1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	4.47214i	0.932505i	0.884652	+	0.466252i	$0.154396\pi$
$23$	4.47214i	0.932505i	−0.884652	+	0.466252i	$0.845604\pi$
$24$	0	0
$25$	5.00000	1.00000
$26$	0	0
$27$	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	$0.5\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 10.0000i	− 1.69031i
$36$	0	0
$37$	−4.47214	−0.735215	−0.367607	−	0.929981i	$-0.619823\pi$
$37$	−4.47214	−0.735215	−0.367607	+	0.929981i	$0.619823\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	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
$47$	− 13.4164i	− 1.95698i	−0.206284	−	0.978492i	$-0.566137\pi$
$47$	− 13.4164i	− 1.95698i	0.206284	−	0.978492i	$-0.433863\pi$
$48$	0	0
$49$	−13.0000	−1.85714
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−13.4164	−1.84289	−0.921443	−	0.388514i	$-0.872988\pi$
$53$	−13.4164	−1.84289	−0.921443	+	0.388514i	$0.872988\pi$
$54$	0	0
$55$	− 4.47214i	− 0.603023i
$56$	0	0
$57$	0	0
$58$	0	0
$59$	14.0000i	1.82264i	0.411693	+	0.911322i	$0.364937\pi$
$59$	14.0000i	1.82264i	−0.411693	+	0.911322i	$0.635063\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−10.0000	−1.24035
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−8.94427	−1.01929
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	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
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	20.0000i	2.09657i
$92$	0	0
$93$	0	0
$94$	0	0
$95$	− 13.4164i	− 1.37649i
$96$	0	0
$97$	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			$\pi$
$102$	0	0
$103$	− 4.47214i	− 0.440653i	−0.975426	−	0.220326i	$-0.929288\pi$
$103$	− 4.47214i	− 0.440653i	0.975426	−	0.220326i	$-0.0707122\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	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	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	10.0000i	0.932505i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	7.00000	0.636364
$122$	0	0
$123$	0	0
$124$	0	0
$125$	11.1803	1.00000
$126$	0	0
$127$	− 22.3607i	− 1.98419i	−0.125491	−	0.992095i	$-0.540051\pi$
$127$	− 22.3607i	− 1.98419i	0.125491	−	0.992095i	$-0.459949\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	22.0000i	1.92215i	0.276289	+	0.961074i	$0.410895\pi$
$131$	22.0000i	1.92215i	−0.276289	+	0.961074i	$0.589105\pi$
$132$	0	0
$133$	−26.8328	−2.32670
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	− 14.0000i	− 1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$	− 14.0000i	− 1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	8.94427i	0.747958i
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−22.3607	−1.78458	−0.892288	−	0.451466i	$-0.850901\pi$
$157$	−22.3607	−1.78458	−0.892288	+	0.451466i	$0.850901\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	20.0000	1.57622
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	4.47214i	0.346064i	0.984916	+	0.173032i	$0.0553564\pi$
$167$	4.47214i	0.346064i	−0.984916	+	0.173032i	$0.944644\pi$
$168$	0	0
$169$	7.00000	0.538462
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−13.4164	−1.02003	−0.510015	−	0.860165i	$-0.670360\pi$
$173$	−13.4164	−1.02003	−0.510015	+	0.860165i	$0.670360\pi$
$174$	0	0
$175$	− 22.3607i	− 1.69031i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	− 26.0000i	− 1.94333i	−0.236360	−	0.971666i	$-0.575954\pi$
$179$	− 26.0000i	− 1.94333i	0.236360	−	0.971666i	$-0.424046\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−10.0000	−0.735215
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	22.3607	1.59313	0.796566	−	0.604551i	$-0.206648\pi$
$197$	22.3607	1.59313	0.796566	+	0.604551i	$0.206648\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−4.47214	−0.312348
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−12.0000	−0.830057
$210$	0	0
$211$	− 22.0000i	− 1.51454i	−0.653101	−	0.757271i	$-0.726532\pi$
$211$	− 22.0000i	− 1.51454i	0.653101	−	0.757271i	$-0.273468\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 22.3607i	− 1.49738i	−0.662919	−	0.748691i	$-0.730683\pi$
$223$	− 22.3607i	− 1.49738i	0.662919	−	0.748691i	$-0.269317\pi$
$224$	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	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	− 30.0000i	− 1.95698i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−29.0689	−1.85714
$246$	0	0
$247$	26.8328i	1.70733i
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 2.00000i	− 0.126239i	−0.998006	−	0.0631194i	$-0.979895\pi$
$251$	− 2.00000i	− 0.126239i	0.998006	−	0.0631194i	$-0.0201049\pi$
$252$	0	0
$253$	8.94427	0.562322
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	20.0000i	1.24274i
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 31.3050i	− 1.93035i	−0.261612	−	0.965173i	$-0.584254\pi$
$263$	− 31.3050i	− 1.93035i	0.261612	−	0.965173i	$-0.415746\pi$
$264$	0	0
$265$	−30.0000	−1.84289
$266$	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		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	− 10.0000i	− 0.603023i
$276$	0	0
$277$	31.3050	1.88093	0.940466	−	0.339887i	$-0.110389\pi$
$277$	31.3050	1.88093	0.940466	+	0.339887i	$0.110389\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	8.94427i	0.527964i
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	4.47214	0.261265	0.130632	−	0.991431i	$-0.458299\pi$
$293$	4.47214	0.261265	0.130632	+	0.991431i	$0.458299\pi$
$294$	0	0
$295$	31.3050i	1.82264i
$296$	0	0
$297$	0	0
$298$	0	0
$299$	− 20.0000i	− 1.15663i
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	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	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−31.3050	−1.75826	−0.879131	−	0.476581i	$-0.841876\pi$
$317$	−31.3050	−1.75826	−0.879131	+	0.476581i	$0.841876\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−22.3607	−1.24035
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−60.0000	−3.30791
$330$	0	0
$331$	18.0000i	0.989369i	0.869072	+	0.494685i	$0.164716\pi$
$331$	18.0000i	0.989369i	−0.869072	+	0.494685i	$0.835284\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	26.8328i	1.44884i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−17.0000	−0.894737
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	− 22.3607i	− 1.16722i	−0.812035	−	0.583609i	$-0.801640\pi$
$367$	− 22.3607i	− 1.16722i	0.812035	−	0.583609i	$-0.198360\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	60.0000i	3.11504i
$372$	0	0
$373$	31.3050	1.62091	0.810454	−	0.585802i	$-0.199220\pi$
$373$	31.3050	1.62091	0.810454	+	0.585802i	$0.199220\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	34.0000i	1.74646i	0.487306	+	0.873231i	$0.337980\pi$
$379$	34.0000i	1.74646i	−0.487306	+	0.873231i	$0.662020\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	− 13.4164i	− 0.685546i	−0.939418	−	0.342773i	$-0.888634\pi$
$383$	− 13.4164i	− 0.685546i	0.939418	−	0.342773i	$-0.111366\pi$
$384$	0	0
$385$	−20.0000	−1.01929
$386$	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
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−4.47214	−0.224450	−0.112225	−	0.993683i	$-0.535798\pi$
$397$	−4.47214	−0.224450	−0.112225	+	0.993683i	$0.535798\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	38.0000	1.89763	0.948815	−	0.315833i	$-0.102284\pi$
$401$	38.0000	1.89763	0.948815	+	0.315833i	$0.102284\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	8.94427i	0.443351i
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	62.6099	3.08083
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 26.0000i	− 1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$	− 26.0000i	− 1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	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
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	26.8328	1.28359
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	31.3050	1.48400
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	0	0
$451$	4.00000i	0.188353i
$452$	0	0
$453$	0	0
$454$	0	0
$455$	44.7214i	2.09657i
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	− 22.3607i	− 1.03919i	−0.854413	−	0.519594i	$-0.826083\pi$
$463$	− 22.3607i	− 1.03919i	0.854413	−	0.519594i	$-0.173917\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	− 30.0000i	− 1.37649i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	31.3050i	1.41856i	0.704925	+	0.709281i	$0.250980\pi$
$487$	31.3050i	1.41856i	−0.704925	+	0.709281i	$0.749020\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 2.00000i	− 0.0902587i	−0.998981	−	0.0451294i	$-0.985630\pi$
$491$	− 2.00000i	− 0.0902587i	0.998981	−	0.0451294i	$-0.0143700\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	− 6.00000i	− 0.268597i	−0.990941	−	0.134298i	$-0.957122\pi$
$499$	− 6.00000i	− 0.268597i	0.990941	−	0.134298i	$-0.0428781\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	40.2492i	1.79462i	0.441397	+	0.897312i	$0.354483\pi$
$503$	40.2492i	1.79462i	−0.441397	+	0.897312i	$0.645517\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	− 10.0000i	− 0.440653i
$516$	0	0
$517$	−26.8328	−1.18011
$518$	0	0
$519$	0	0
$520$	0	0
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	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
$529$	3.00000	0.130435
$530$	0	0
$531$	0	0
$532$	0	0
$533$	8.94427	0.387419
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	26.0000i	1.11990i
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−13.4164	−0.568471	−0.284236	−	0.958754i	$-0.591740\pi$
$557$	−13.4164	−0.568471	−0.284236	+	0.958754i	$0.591740\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	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
$569$	46.0000	1.92842	0.964210	−	0.265139i	$-0.0854179\pi$
$569$	46.0000	1.92842	0.964210	+	0.265139i	$0.0854179\pi$
$570$	0	0
$571$	18.0000i	0.753277i	0.926360	+	0.376638i	$0.122920\pi$
$571$	18.0000i	0.753277i	−0.926360	+	0.376638i	$0.877080\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	22.3607i	0.932505i
$576$	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
$583$	26.8328i	1.11130i
$584$	0	0
$585$	0	0
$586$	0	0
$587$	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
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	15.6525	0.636364
$606$	0	0
$607$	49.1935i	1.99670i	0.0574012	+	0.998351i	$0.481719\pi$
$607$	49.1935i	1.99670i	−0.0574012	+	0.998351i	$0.518281\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	60.0000i	2.42734i
$612$	0	0
$613$	49.1935	1.98691	0.993453	−	0.114239i	$-0.0364430\pi$
$613$	49.1935	1.98691	0.993453	+	0.114239i	$0.0364430\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	− 46.0000i	− 1.84890i	−0.381308	−	0.924448i	$-0.624526\pi$
$619$	− 46.0000i	− 1.84890i	0.381308	−	0.924448i	$-0.375474\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	− 62.6099i	− 2.50841i
$624$	0	0
$625$	25.0000	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
$633$	0	0
$634$	0	0
$635$	− 50.0000i	− 1.98419i
$636$	0	0
$637$	58.1378	2.30350
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	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
$647$	40.2492i	1.58236i	0.611583	+	0.791180i	$0.290533\pi$
$647$	40.2492i	1.58236i	−0.611583	+	0.791180i	$0.709467\pi$
$648$	0	0
$649$	28.0000	1.09910
$650$	0	0
$651$	0	0
$652$	0	0
$653$	4.47214	0.175008	0.0875041	−	0.996164i	$-0.472111\pi$
$653$	4.47214	0.175008	0.0875041	+	0.996164i	$0.472111\pi$
$654$	0	0
$655$	49.1935i	1.92215i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 26.0000i	− 1.01282i	−0.862294	−	0.506408i	$-0.830973\pi$
$659$	− 26.0000i	− 1.01282i	0.862294	−	0.506408i	$-0.169027\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−60.0000	−2.32670
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−49.1935	−1.89066	−0.945330	−	0.326116i	$-0.894260\pi$
$677$	−49.1935	−1.89066	−0.945330	+	0.326116i	$0.894260\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	60.0000	2.28582
$690$	0	0
$691$	42.0000i	1.59776i	0.601494	+	0.798878i	$0.294573\pi$
$691$	42.0000i	1.59776i	−0.601494	+	0.798878i	$0.705427\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	− 31.3050i	− 1.18746i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	26.8328i	1.01202i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	20.0000i	0.747958i
$716$	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
$721$	−20.0000	−0.744839
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	− 4.47214i	− 0.165862i	−0.996555	−	0.0829312i	$-0.973572\pi$
$727$	− 4.47214i	− 0.165862i	0.996555	−	0.0829312i	$-0.0264282\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	49.1935	1.81700	0.908502	−	0.417881i	$-0.137227\pi$
$733$	49.1935	1.81700	0.908502	+	0.417881i	$0.137227\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	− 54.0000i	− 1.98642i	−0.116326	−	0.993211i	$-0.537112\pi$
$739$	− 54.0000i	− 1.98642i	0.116326	−	0.993211i	$-0.462888\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	40.2492i	1.47660i	0.674472	+	0.738300i	$0.264371\pi$
$743$	40.2492i	1.47660i	−0.674472	+	0.738300i	$0.735629\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	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
$757$	31.3050	1.13780	0.568899	−	0.822407i	$-0.307370\pi$
$757$	31.3050	1.13780	0.568899	+	0.822407i	$0.307370\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	− 62.6099i	− 2.26071i
$768$	0	0
$769$	−54.0000	−1.94729	−0.973645	−	0.228069i	$-0.926759\pi$
$769$	−54.0000	−1.94729	−0.973645	+	0.228069i	$0.926759\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	22.3607	0.804258	0.402129	−	0.915583i	$-0.368270\pi$
$773$	22.3607	0.804258	0.402129	+	0.915583i	$0.368270\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	12.0000i	0.429945i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−50.0000	−1.78458
$786$	0	0
$787$	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
$794$	0	0
$795$	0	0
$796$	0	0
$797$	40.2492	1.42570	0.712850	−	0.701316i	$-0.247404\pi$
$797$	40.2492	1.42570	0.712850	+	0.701316i	$0.247404\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	44.7214	1.57622
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−26.0000	−0.914111	−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000	−0.914111	−0.457056	+	0.889438i	$0.651096\pi$
$810$	0	0
$811$	2.00000i	0.0702295i	0.999383	+	0.0351147i	$0.0111797\pi$
$811$	2.00000i	0.0702295i	−0.999383	+	0.0351147i	$0.988820\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	31.3050i	1.09122i	0.838039	+	0.545611i	$0.183702\pi$
$823$	31.3050i	1.09122i	−0.838039	+	0.545611i	$0.816298\pi$
$824$	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
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	10.0000i	0.346064i
$836$	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
$841$	29.0000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	15.6525	0.538462
$846$	0	0
$847$	− 31.3050i	− 1.07565i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	− 20.0000i	− 0.685591i
$852$	0	0
$853$	−58.1378	−1.99060	−0.995300	−	0.0968435i	$-0.969125\pi$
$853$	−58.1378	−1.99060	−0.995300	+	0.0968435i	$0.969125\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	− 14.0000i	− 0.477674i	−0.971060	−	0.238837i	$-0.923234\pi$
$859$	− 14.0000i	− 0.477674i	0.971060	−	0.238837i	$-0.0767661\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	58.1378i	1.97903i	0.144421	+	0.989516i	$0.453868\pi$
$863$	58.1378i	1.97903i	−0.144421	+	0.989516i	$0.546132\pi$
$864$	0	0
$865$	−30.0000	−1.02003
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	− 50.0000i	− 1.69031i
$876$	0	0
$877$	−58.1378	−1.96317	−0.981586	−	0.191018i	$-0.938821\pi$
$877$	−58.1378	−1.96317	−0.981586	+	0.191018i	$0.938821\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−58.0000	−1.95407	−0.977035	−	0.213080i	$-0.931651\pi$
$881$	−58.0000	−1.95407	−0.977035	+	0.213080i	$0.931651\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	4.47214i	0.150160i	0.997178	+	0.0750798i	$0.0239212\pi$
$887$	4.47214i	0.150160i	−0.997178	+	0.0750798i	$0.976079\pi$
$888$	0	0
$889$	−100.000	−3.35389
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−80.4984	−2.69378
$894$	0	0
$895$	− 58.1378i	− 1.94333i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	98.3870	3.24902
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−22.3607	−0.735215
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	0	0
$931$	78.0000i	2.55635i
$932$	0	0
$933$	0	0
$934$	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	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	− 8.94427i	− 0.291266i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	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
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	31.3050i	1.00670i	0.864083	+	0.503350i	$0.167899\pi$
$967$	31.3050i	1.00670i	−0.864083	+	0.503350i	$0.832101\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	62.0000i	1.98967i	0.101482	+	0.994837i	$0.467641\pi$
$971$	62.0000i	1.98967i	−0.101482	+	0.994837i	$0.532359\pi$
$972$	0	0
$973$	−62.6099	−2.00718
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	− 28.0000i	− 0.894884i
$980$	0	0
$981$	0	0
$982$	0	0
$983$	40.2492i	1.28375i	0.766809	+	0.641875i	$0.221843\pi$
$983$	40.2492i	1.28375i	−0.766809	+	0.641875i	$0.778157\pi$
$984$	0	0
$985$	50.0000	1.59313
$986$	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
$997$	49.1935	1.55797	0.778987	−	0.627040i	$-0.215734\pi$
$997$	49.1935	1.55797	0.778987	+	0.627040i	$0.215734\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.d.e.289.3		4
3.2	odd	2		320.2.f.a.289.1	✓	4
4.3	odd	2	inner	2880.2.d.e.289.4		4
5.4	even	2	inner	2880.2.d.e.289.2		4
8.3	odd	2	inner	2880.2.d.e.289.2		4
8.5	even	2	inner	2880.2.d.e.289.1		4
12.11	even	2		320.2.f.a.289.2	yes	4
15.2	even	4		1600.2.d.g.801.4		4
15.8	even	4		1600.2.d.g.801.2		4
15.14	odd	2		320.2.f.a.289.4	yes	4
20.19	odd	2	inner	2880.2.d.e.289.1		4
24.5	odd	2		320.2.f.a.289.3	yes	4
24.11	even	2		320.2.f.a.289.4	yes	4
40.19	odd	2	CM	2880.2.d.e.289.3		4
40.29	even	2	inner	2880.2.d.e.289.4		4
48.5	odd	4		1280.2.c.b.769.1		2
48.11	even	4		1280.2.c.c.769.1		2
48.29	odd	4		1280.2.c.c.769.2		2
48.35	even	4		1280.2.c.b.769.2		2
60.23	odd	4		1600.2.d.g.801.3		4
60.47	odd	4		1600.2.d.g.801.1		4
60.59	even	2		320.2.f.a.289.3	yes	4
120.29	odd	2		320.2.f.a.289.2	yes	4
120.53	even	4		1600.2.d.g.801.1		4
120.59	even	2		320.2.f.a.289.1	✓	4
120.77	even	4		1600.2.d.g.801.3		4
120.83	odd	4		1600.2.d.g.801.4		4
120.107	odd	4		1600.2.d.g.801.2		4
240.29	odd	4		1280.2.c.c.769.1		2
240.53	even	4		6400.2.a.bi.1.2		2
240.59	even	4		1280.2.c.c.769.2		2
240.77	even	4		6400.2.a.bj.1.1		2
240.83	odd	4		6400.2.a.bi.1.1		2
240.107	odd	4		6400.2.a.bj.1.2		2
240.149	odd	4		1280.2.c.b.769.2		2
240.173	even	4		6400.2.a.bj.1.2		2
240.179	even	4		1280.2.c.b.769.1		2
240.197	even	4		6400.2.a.bi.1.1		2
240.203	odd	4		6400.2.a.bj.1.1		2
240.227	odd	4		6400.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
320.2.f.a.289.1	✓	4	3.2	odd	2
320.2.f.a.289.1	✓	4	120.59	even	2
320.2.f.a.289.2	yes	4	12.11	even	2
320.2.f.a.289.2	yes	4	120.29	odd	2
320.2.f.a.289.3	yes	4	24.5	odd	2
320.2.f.a.289.3	yes	4	60.59	even	2
320.2.f.a.289.4	yes	4	15.14	odd	2
320.2.f.a.289.4	yes	4	24.11	even	2
1280.2.c.b.769.1		2	48.5	odd	4
1280.2.c.b.769.1		2	240.179	even	4
1280.2.c.b.769.2		2	48.35	even	4
1280.2.c.b.769.2		2	240.149	odd	4
1280.2.c.c.769.1		2	48.11	even	4
1280.2.c.c.769.1		2	240.29	odd	4
1280.2.c.c.769.2		2	48.29	odd	4
1280.2.c.c.769.2		2	240.59	even	4
1600.2.d.g.801.1		4	60.47	odd	4
1600.2.d.g.801.1		4	120.53	even	4
1600.2.d.g.801.2		4	15.8	even	4
1600.2.d.g.801.2		4	120.107	odd	4
1600.2.d.g.801.3		4	60.23	odd	4
1600.2.d.g.801.3		4	120.77	even	4
1600.2.d.g.801.4		4	15.2	even	4
1600.2.d.g.801.4		4	120.83	odd	4
2880.2.d.e.289.1		4	8.5	even	2	inner
2880.2.d.e.289.1		4	20.19	odd	2	inner
2880.2.d.e.289.2		4	5.4	even	2	inner
2880.2.d.e.289.2		4	8.3	odd	2	inner
2880.2.d.e.289.3		4	1.1	even	1	trivial
2880.2.d.e.289.3		4	40.19	odd	2	CM
2880.2.d.e.289.4		4	4.3	odd	2	inner
2880.2.d.e.289.4		4	40.29	even	2	inner
6400.2.a.bi.1.1		2	240.83	odd	4
6400.2.a.bi.1.1		2	240.197	even	4
6400.2.a.bi.1.2		2	240.53	even	4
6400.2.a.bi.1.2		2	240.227	odd	4
6400.2.a.bj.1.1		2	240.77	even	4
6400.2.a.bj.1.1		2	240.203	odd	4
6400.2.a.bj.1.2		2	240.107	odd	4
6400.2.a.bj.1.2		2	240.173	even	4

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:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.23607 q^{5} -4.47214i q^{7} +O(q^{10})\)	\(q+2.23607 q^{5} -4.47214i q^{7} -2.00000i q^{11} -4.47214 q^{13} -6.00000i q^{19} +4.47214i q^{23} +5.00000 q^{25} -10.0000i q^{35} -4.47214 q^{37} -2.00000 q^{41} -13.4164i q^{47} -13.0000 q^{49} -13.4164 q^{53} -4.47214i q^{55} +14.0000i q^{59} -10.0000 q^{65} -8.94427 q^{77} +14.0000 q^{89} +20.0000i q^{91} -13.4164i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 20 q^{25} - 8 q^{41} - 52 q^{49} - 40 q^{65} + 56 q^{89}+O(q^{100}) \) 4 * q + 20 * q^25 - 8 * q^41 - 52 * q^49 - 40 * q^65 + 56 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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