LMFDB - Embedded newform 1440.2.f.i.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(289,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1440.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.f (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:	$11.4984578911$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			289.2
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	1440.289
Dual form			1440.2.f.i.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$-1$	$1$	$1$	$1$

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
$7$	0.763932i	0.288739i	0.989524	+	0.144370i	$0.0461154\pi$
$7$	0.763932i	0.288739i	−0.989524	+	0.144370i	$0.953885\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	− 5.70820i	− 1.19024i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	− 5.70820i	− 1.19024i	0.803636	−	0.595121i	$-0.202896\pi$
$24$	0	0
$25$	5.00000	1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	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
$35$	− 1.70820i	− 0.288739i
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	4.47214	0.698430	0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214	0.698430	0.349215	+	0.937043i	$0.386448\pi$
$42$	0	0
$43$	− 11.2361i	− 1.71348i	−0.515745	−	0.856742i	$-0.672485\pi$
$43$	− 11.2361i	− 1.71348i	0.515745	−	0.856742i	$-0.327515\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	− 13.7082i	− 1.99955i	−0.0212814	−	0.999774i	$-0.506775\pi$
$47$	− 13.7082i	− 1.99955i	0.0212814	−	0.999774i	$-0.493225\pi$
$48$	0	0
$49$	6.41641	0.916630
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−13.4164	−1.71780	−0.858898	−	0.512148i	$-0.828850\pi$
$61$	−13.4164	−1.71780	−0.858898	+	0.512148i	$0.828850\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	− 8.18034i	− 0.999388i	−0.866202	−	0.499694i	$-0.833446\pi$
$67$	− 8.18034i	− 0.999388i	0.866202	−	0.499694i	$-0.166554\pi$
$68$	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
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	− 17.7082i	− 1.94373i	−0.235543	−	0.971864i	$-0.575687\pi$
$83$	− 17.7082i	− 1.94373i	0.235543	−	0.971864i	$-0.424313\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	0	0
$103$	− 20.1803i	− 1.98843i	−0.107418	−	0.994214i	$-0.534258\pi$
$103$	− 20.1803i	− 1.98843i	0.107418	−	0.994214i	$-0.465742\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	6.29180i	0.608251i	0.952632	+	0.304125i	$0.0983642\pi$
$107$	6.29180i	0.608251i	−0.952632	+	0.304125i	$0.901636\pi$
$108$	0	0
$109$	−13.4164	−1.28506	−0.642529	−	0.766261i	$-0.722115\pi$
$109$	−13.4164	−1.28506	−0.642529	+	0.766261i	$0.722115\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	12.7639i	1.19024i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−11.1803	−1.00000
$126$	0	0
$127$	18.6525i	1.65514i	0.561363	+	0.827570i	$0.310277\pi$
$127$	18.6525i	1.65514i	−0.561363	+	0.827570i	$0.689723\pi$
$128$	0	0
$129$	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
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	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
$144$	0	0
$145$	13.4164	1.11417
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−4.47214	−0.366372	−0.183186	−	0.983078i	$-0.558641\pi$
$149$	−4.47214	−0.366372	−0.183186	+	0.983078i	$0.558641\pi$
$150$	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
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	4.36068	0.343670
$162$	0	0
$163$	6.65248i	0.521062i	0.965465	+	0.260531i	$0.0838976\pi$
$163$	6.65248i	0.521062i	−0.965465	+	0.260531i	$0.916102\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	10.2918i	0.796403i	0.917298	+	0.398202i	$0.130366\pi$
$167$	10.2918i	0.796403i	−0.917298	+	0.398202i	$0.869634\pi$
$168$	0	0
$169$	13.0000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	3.81966i	0.288739i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	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		−	1.00000i	$-0.5\pi$
$191$	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
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	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
$203$	− 4.58359i	− 0.321705i
$204$	0	0
$205$	−10.0000	−0.698430
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	25.1246i	1.71348i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 23.2361i	− 1.55600i	−0.628263	−	0.778001i	$-0.716234\pi$
$223$	− 23.2361i	− 1.55600i	0.628263	−	0.778001i	$-0.283766\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	13.1246i	0.871111i	0.900162	+	0.435556i	$0.143448\pi$
$227$	13.1246i	0.871111i	−0.900162	+	0.435556i	$0.856552\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	30.6525i	1.99955i
$236$	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
$241$	13.4164	0.864227	0.432113	−	0.901819i	$-0.357768\pi$
$241$	13.4164	0.864227	0.432113	+	0.901819i	$0.357768\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−14.3475	−0.916630
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	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			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	9.12461i	0.562648i	0.959613	+	0.281324i	$0.0907735\pi$
$263$	9.12461i	0.562648i	−0.959613	+	0.281324i	$0.909226\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−22.3607	−1.36335	−0.681677	−	0.731653i	$-0.738749\pi$
$269$	−22.3607	−1.36335	−0.681677	+	0.731653i	$0.738749\pi$
$270$	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
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−31.3050	−1.86750	−0.933748	−	0.357930i	$-0.883483\pi$
$281$	−31.3050	−1.86750	−0.933748	+	0.357930i	$0.883483\pi$
$282$	0	0
$283$	− 32.1803i	− 1.91292i	−0.291859	−	0.956461i	$-0.594274\pi$
$283$	− 32.1803i	− 1.91292i	0.291859	−	0.956461i	$-0.405726\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	3.41641i	0.201664i
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	8.58359	0.494750
$302$	0	0
$303$	0	0
$304$	0	0
$305$	30.0000	1.71780
$306$	0	0
$307$	27.5967i	1.57503i	0.616296	+	0.787515i	$0.288633\pi$
$307$	27.5967i	1.57503i	−0.616296	+	0.787515i	$0.711367\pi$
$308$	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
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	10.4721	0.577348
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	18.2918i	0.999388i
$336$	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
$343$	10.2492i	0.553406i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	37.1246i	1.99295i	0.0838690	+	0.996477i	$0.473272\pi$
$347$	37.1246i	1.99295i	−0.0838690	+	0.996477i	$0.526728\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	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
$361$	−19.0000	−1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	24.7639i	1.29267i	0.763055	+	0.646333i	$0.223698\pi$
$367$	24.7639i	1.29267i	−0.763055	+	0.646333i	$0.776302\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	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
$383$	1.12461i	0.0574650i	0.999587	+	0.0287325i	$0.00914709\pi$
$383$	1.12461i	0.0574650i	−0.999587	+	0.0287325i	$0.990853\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	31.3050	1.58722	0.793612	−	0.608424i	$-0.208198\pi$
$389$	31.3050	1.58722	0.793612	+	0.608424i	$0.208198\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−40.2492	−1.99020	−0.995098	−	0.0988936i	$-0.968470\pi$
$409$	−40.2492	−1.99020	−0.995098	+	0.0988936i	$0.968470\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	39.5967i	1.94373i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	40.2492	1.96163	0.980814	−	0.194948i	$-0.0624538\pi$
$421$	40.2492	1.96163	0.980814	+	0.194948i	$0.0624538\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	− 10.2492i	− 0.495995i
$428$	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
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	22.2918i	1.05912i	0.848274	+	0.529558i	$0.177642\pi$
$443$	22.2918i	1.05912i	−0.848274	+	0.529558i	$0.822358\pi$
$444$	0	0
$445$	−13.4164	−0.635999
$446$	0	0
$447$	0	0
$448$	0	0
$449$	22.3607	1.05527	0.527633	−	0.849473i	$-0.323080\pi$
$449$	22.3607	1.05527	0.527633	+	0.849473i	$0.323080\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	42.0000	1.95614	0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000	1.95614	0.978068	+	0.208288i	$0.0667892\pi$
$462$	0	0
$463$	− 38.0689i	− 1.76921i	−0.466340	−	0.884606i	$-0.654428\pi$
$463$	− 38.0689i	− 1.76921i	0.466340	−	0.884606i	$-0.345572\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 2.87539i	− 0.133057i	−0.997785	−	0.0665285i	$-0.978808\pi$
$467$	− 2.87539i	− 0.133057i	0.997785	−	0.0665285i	$-0.0211923\pi$
$468$	0	0
$469$	6.24922	0.288562
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	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
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	42.6525i	1.93277i	0.257103	+	0.966384i	$0.417232\pi$
$487$	42.6525i	1.93277i	−0.257103	+	0.966384i	$0.582768\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	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
$503$	− 37.7082i	− 1.68133i	−0.541559	−	0.840663i	$-0.682166\pi$
$503$	− 37.7082i	− 1.68133i	0.541559	−	0.840663i	$-0.317834\pi$
$504$	0	0
$505$	−40.2492	−1.79107
$506$	0	0
$507$	0	0
$508$	0	0
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	45.1246i	1.98843i
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	3.59675i	0.157275i	0.996903	+	0.0786374i	$0.0250569\pi$
$523$	3.59675i	0.157275i	−0.996903	+	0.0786374i	$0.974943\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−9.58359	−0.416678
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	− 14.0689i	− 0.608251i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	30.0000	1.28506
$546$	0	0
$547$	− 35.2361i	− 1.50659i	−0.657685	−	0.753293i	$-0.728464\pi$
$547$	− 35.2361i	− 1.50659i	0.657685	−	0.753293i	$-0.271536\pi$
$548$	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
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	− 32.5410i	− 1.37144i	−0.727865	−	0.685720i	$-0.759487\pi$
$563$	− 32.5410i	− 1.37144i	0.727865	−	0.685720i	$-0.240513\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−31.3050	−1.31237	−0.656186	−	0.754599i	$-0.727831\pi$
$569$	−31.3050	−1.31237	−0.656186	+	0.754599i	$0.727831\pi$
$570$	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
$575$	− 28.5410i	− 1.19024i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	13.5279	0.561230
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 40.5410i	− 1.67331i	−0.547733	−	0.836653i	$-0.684509\pi$
$587$	− 40.5410i	− 1.67331i	0.547733	−	0.836653i	$-0.315491\pi$
$588$	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
$601$	−40.2492	−1.64180	−0.820900	−	0.571072i	$-0.806528\pi$
$601$	−40.2492	−1.64180	−0.820900	+	0.571072i	$0.806528\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	24.5967	1.00000
$606$	0	0
$607$	− 44.1803i	− 1.79322i	−0.442816	−	0.896612i	$-0.646021\pi$
$607$	− 44.1803i	− 1.79322i	0.442816	−	0.896612i	$-0.353979\pi$
$608$	0	0
$609$	0	0
$610$	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
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	4.58359i	0.183638i
$624$	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
$635$	− 41.7082i	− 1.65514i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−49.1935	−1.94303	−0.971513	−	0.236986i	$-0.923841\pi$
$641$	−49.1935	−1.94303	−0.971513	+	0.236986i	$0.923841\pi$
$642$	0	0
$643$	− 50.0689i	− 1.97452i	−0.159103	−	0.987262i	$-0.550860\pi$
$643$	− 50.0689i	− 1.97452i	0.159103	−	0.987262i	$-0.449140\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	− 20.5410i	− 0.807551i	−0.914858	−	0.403775i	$-0.867698\pi$
$647$	− 20.5410i	− 0.807551i	0.914858	−	0.403775i	$-0.132302\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	40.2492	1.56551	0.782757	−	0.622328i	$-0.213813\pi$
$661$	40.2492	1.56551	0.782757	+	0.622328i	$0.213813\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	34.2492i	1.32614i
$668$	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
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	− 10.8754i	− 0.416135i	−0.978114	−	0.208068i	$-0.933283\pi$
$683$	− 10.8754i	− 0.416135i	0.978114	−	0.208068i	$-0.0667174\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	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
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−22.3607	−0.844551	−0.422276	−	0.906467i	$-0.638769\pi$
$701$	−22.3607	−0.844551	−0.422276	+	0.906467i	$0.638769\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	13.7508i	0.517151i
$708$	0	0
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	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
$721$	15.4164	0.574137
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−30.0000	−1.11417
$726$	0	0
$727$	− 35.0132i	− 1.29857i	−0.760547	−	0.649283i	$-0.775069\pi$
$727$	− 35.0132i	− 1.29857i	0.760547	−	0.649283i	$-0.224931\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	− 52.5410i	− 1.92754i	−0.266729	−	0.963772i	$-0.585943\pi$
$743$	− 52.5410i	− 1.92754i	0.266729	−	0.963772i	$-0.414057\pi$
$744$	0	0
$745$	10.0000	0.366372
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−4.80650	−0.175626
$750$	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
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	− 10.2492i	− 0.371047i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	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
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 2.06888i	− 0.0737477i	−0.999320	−	0.0368739i	$-0.988260\pi$
$787$	− 2.06888i	− 0.0737477i	0.999320	−	0.0368739i	$-0.0117400\pi$
$788$	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
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−9.75078	−0.343670
$806$	0	0
$807$	0	0
$808$	0	0
$809$	54.0000	1.89854	0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000	1.89854	0.949269	+	0.314464i	$0.101825\pi$
$810$	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
$815$	− 14.8754i	− 0.521062i
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	31.3050	1.09255	0.546275	−	0.837606i	$-0.316045\pi$
$821$	31.3050	1.09255	0.546275	+	0.837606i	$0.316045\pi$
$822$	0	0
$823$	27.8197i	0.969732i	0.874588	+	0.484866i	$0.161132\pi$
$823$	27.8197i	0.969732i	−0.874588	+	0.484866i	$0.838868\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 56.5410i	− 1.96612i	−0.183274	−	0.983062i	$-0.558669\pi$
$827$	− 56.5410i	− 1.96612i	0.183274	−	0.983062i	$-0.441331\pi$
$828$	0	0
$829$	−13.4164	−0.465971	−0.232986	−	0.972480i	$-0.574849\pi$
$829$	−13.4164	−0.465971	−0.232986	+	0.972480i	$0.574849\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	− 23.0132i	− 0.796403i
$836$	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
$841$	7.00000	0.241379
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−29.0689	−1.00000
$846$	0	0
$847$	− 8.40325i	− 0.288739i
$848$	0	0
$849$	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
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	34.2918i	1.16731i	0.812003	+	0.583653i	$0.198377\pi$
$863$	34.2918i	1.16731i	−0.812003	+	0.583653i	$0.801623\pi$
$864$	0	0
$865$	0	0
$866$	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
$875$	− 8.54102i	− 0.288739i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	58.1378	1.95871	0.979356	−	0.202145i	$-0.0647913\pi$
$881$	58.1378	1.95871	0.979356	+	0.202145i	$0.0647913\pi$
$882$	0	0
$883$	54.6525i	1.83920i	0.392853	+	0.919601i	$0.371488\pi$
$883$	54.6525i	1.83920i	−0.392853	+	0.919601i	$0.628512\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	57.1246i	1.91806i	0.283310	+	0.959028i	$0.408567\pi$
$887$	57.1246i	1.91806i	−0.283310	+	0.959028i	$0.591433\pi$
$888$	0	0
$889$	−14.2492	−0.477904
$890$	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
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	4.47214	0.148659
$906$	0	0
$907$	45.4853i	1.51031i	0.655544	+	0.755157i	$0.272439\pi$
$907$	45.4853i	1.51031i	−0.655544	+	0.755157i	$0.727561\pi$
$908$	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
$917$	0	0
$918$	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
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−49.1935	−1.61399	−0.806993	−	0.590561i	$-0.798907\pi$
$929$	−49.1935	−1.61399	−0.806993	+	0.590561i	$0.798907\pi$
$930$	0	0
$931$	0	0
$932$	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
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	0	0
$943$	− 25.5279i	− 0.831302i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	− 49.7082i	− 1.61530i	−0.589662	−	0.807650i	$-0.700739\pi$
$947$	− 49.7082i	− 1.61530i	0.589662	−	0.807650i	$-0.299261\pi$
$948$	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
$967$	− 62.0689i	− 1.99600i	−0.0632081	−	0.998000i	$-0.520133\pi$
$967$	− 62.0689i	− 1.99600i	0.0632081	−	0.998000i	$-0.479867\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	− 4.54102i	− 0.144836i	−0.997374	−	0.0724180i	$-0.976928\pi$
$983$	− 4.54102i	− 0.144836i	0.997374	−	0.0724180i	$-0.0230716\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−64.1378	−2.03946
$990$	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	1.00000			$0$
$997$	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	1440.2.f.i.289.2		4
3.2	odd	2		160.2.c.b.129.1	✓	4
4.3	odd	2	inner	1440.2.f.i.289.1		4
5.2	odd	4		7200.2.a.cb.1.2		2
5.3	odd	4		7200.2.a.cr.1.1		2
5.4	even	2	inner	1440.2.f.i.289.1		4
8.3	odd	2		2880.2.f.w.1729.3		4
8.5	even	2		2880.2.f.w.1729.4		4
12.11	even	2		160.2.c.b.129.4	yes	4
15.2	even	4		800.2.a.j.1.1		2
15.8	even	4		800.2.a.n.1.2		2
15.14	odd	2		160.2.c.b.129.4	yes	4
20.3	even	4		7200.2.a.cb.1.2		2
20.7	even	4		7200.2.a.cr.1.1		2
20.19	odd	2	CM	1440.2.f.i.289.2		4
24.5	odd	2		320.2.c.d.129.4		4
24.11	even	2		320.2.c.d.129.1		4
40.19	odd	2		2880.2.f.w.1729.4		4
40.29	even	2		2880.2.f.w.1729.3		4
48.5	odd	4		1280.2.f.g.129.2		4
48.11	even	4		1280.2.f.h.129.4		4
48.29	odd	4		1280.2.f.h.129.3		4
48.35	even	4		1280.2.f.g.129.1		4
60.23	odd	4		800.2.a.j.1.1		2
60.47	odd	4		800.2.a.n.1.2		2
60.59	even	2		160.2.c.b.129.1	✓	4
120.29	odd	2		320.2.c.d.129.1		4
120.53	even	4		1600.2.a.z.1.1		2
120.59	even	2		320.2.c.d.129.4		4
120.77	even	4		1600.2.a.bd.1.2		2
120.83	odd	4		1600.2.a.bd.1.2		2
120.107	odd	4		1600.2.a.z.1.1		2
240.29	odd	4		1280.2.f.g.129.1		4
240.59	even	4		1280.2.f.g.129.2		4
240.149	odd	4		1280.2.f.h.129.4		4
240.179	even	4		1280.2.f.h.129.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.c.b.129.1	✓	4	3.2	odd	2
160.2.c.b.129.1	✓	4	60.59	even	2
160.2.c.b.129.4	yes	4	12.11	even	2
160.2.c.b.129.4	yes	4	15.14	odd	2
320.2.c.d.129.1		4	24.11	even	2
320.2.c.d.129.1		4	120.29	odd	2
320.2.c.d.129.4		4	24.5	odd	2
320.2.c.d.129.4		4	120.59	even	2
800.2.a.j.1.1		2	15.2	even	4
800.2.a.j.1.1		2	60.23	odd	4
800.2.a.n.1.2		2	15.8	even	4
800.2.a.n.1.2		2	60.47	odd	4
1280.2.f.g.129.1		4	48.35	even	4
1280.2.f.g.129.1		4	240.29	odd	4
1280.2.f.g.129.2		4	48.5	odd	4
1280.2.f.g.129.2		4	240.59	even	4
1280.2.f.h.129.3		4	48.29	odd	4
1280.2.f.h.129.3		4	240.179	even	4
1280.2.f.h.129.4		4	48.11	even	4
1280.2.f.h.129.4		4	240.149	odd	4
1440.2.f.i.289.1		4	4.3	odd	2	inner
1440.2.f.i.289.1		4	5.4	even	2	inner
1440.2.f.i.289.2		4	1.1	even	1	trivial
1440.2.f.i.289.2		4	20.19	odd	2	CM
1600.2.a.z.1.1		2	120.53	even	4
1600.2.a.z.1.1		2	120.107	odd	4
1600.2.a.bd.1.2		2	120.77	even	4
1600.2.a.bd.1.2		2	120.83	odd	4
2880.2.f.w.1729.3		4	8.3	odd	2
2880.2.f.w.1729.3		4	40.29	even	2
2880.2.f.w.1729.4		4	8.5	even	2
2880.2.f.w.1729.4		4	40.19	odd	2
7200.2.a.cb.1.2		2	5.2	odd	4
7200.2.a.cb.1.2		2	20.3	even	4
7200.2.a.cr.1.1		2	5.3	odd	4
7200.2.a.cr.1.1		2	20.7	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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.23607 q^{5} +0.763932i q^{7} +O(q^{10})\)	\(q-2.23607 q^{5} +0.763932i q^{7} -5.70820i q^{23} +5.00000 q^{25} -6.00000 q^{29} -1.70820i q^{35} +4.47214 q^{41} -11.2361i q^{43} -13.7082i q^{47} +6.41641 q^{49} -13.4164 q^{61} -8.18034i q^{67} -17.7082i q^{83} +6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 20 q^{25} - 24 q^{29} - 28 q^{49} + 24 q^{89}+O(q^{100}) \) 4 * q + 20 * q^25 - 24 * q^29 - 28 * q^49 + 24 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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