LMFDB - Embedded newform 144.3.g.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(127,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.g (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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			127.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	144.127
Dual form			144.3.g.c.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.8564i q^{7} +O(q^{10})$	$q-13.8564i q^{7} +22.0000 q^{13} -27.7128i q^{19} -25.0000 q^{25} +41.5692i q^{31} +26.0000 q^{37} +83.1384i q^{43} -143.000 q^{49} +74.0000 q^{61} +55.4256i q^{67} +46.0000 q^{73} -69.2820i q^{79} -304.841i q^{91} -2.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q+O(q^{10}) $ 2 * q	$ 2 q + 44 q^{13} - 50 q^{25} + 52 q^{37} - 286 q^{49} + 148 q^{61} + 92 q^{73} - 4 q^{97}+O(q^{100}) $ 2 * q + 44 * q^13 - 50 * q^25 + 52 * q^37 - 286 * q^49 + 148 * q^61 + 92 * q^73 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	0	0
$2$	0	0
$3$	0	0
$3$	0	0
$4$	0	0
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	− 13.8564i	− 1.97949i	−0.142857	−	0.989743i	$-0.545629\pi$
$7$	− 13.8564i	− 1.97949i	0.142857	−	0.989743i	$-0.454371\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	22.0000	1.69231	0.846154	−	0.532939i	$-0.178912\pi$
$13$	22.0000	1.69231	0.846154	+	0.532939i	$0.178912\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	− 27.7128i	− 1.45857i	−0.684211	−	0.729285i	$-0.739853\pi$
$19$	− 27.7128i	− 1.45857i	0.684211	−	0.729285i	$-0.260147\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	−25.0000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	41.5692i	1.34094i	0.741935	+	0.670471i	$0.233908\pi$
$31$	41.5692i	1.34094i	−0.741935	+	0.670471i	$0.766092\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	26.0000	0.702703	0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000	0.702703	0.351351	+	0.936244i	$0.385722\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	83.1384i	1.93345i	0.255814	+	0.966726i	$0.417657\pi$
$43$	83.1384i	1.93345i	−0.255814	+	0.966726i	$0.582343\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	−143.000	−2.91837
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			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
$61$	74.0000	1.21311	0.606557	−	0.795040i	$-0.292550\pi$
$61$	74.0000	1.21311	0.606557	+	0.795040i	$0.292550\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	55.4256i	0.827248i	0.910448	+	0.413624i	$0.135737\pi$
$67$	55.4256i	0.827248i	−0.910448	+	0.413624i	$0.864263\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	46.0000	0.630137	0.315068	−	0.949069i	$-0.397973\pi$
$73$	46.0000	0.630137	0.315068	+	0.949069i	$0.397973\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	− 69.2820i	− 0.876988i	−0.898734	−	0.438494i	$-0.855512\pi$
$79$	− 69.2820i	− 0.876988i	0.898734	−	0.438494i	$-0.144488\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	− 304.841i	− 3.34990i
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.0206186	−0.0103093	−	0.999947i	$-0.503282\pi$
$97$	−2.00000	−0.0206186	−0.0103093	+	0.999947i	$0.503282\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	69.2820i	0.672641i	0.941748	+	0.336321i	$0.109183\pi$
$103$	69.2820i	0.672641i	−0.941748	+	0.336321i	$0.890817\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	214.000	1.96330	0.981651	−	0.190684i	$-0.0610707\pi$
$109$	214.000	1.96330	0.981651	+	0.190684i	$0.0610707\pi$
$110$	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
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	121.000	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	− 207.846i	− 1.63658i	−0.574803	−	0.818292i	$-0.694921\pi$
$127$	− 207.846i	− 1.63658i	0.574803	−	0.818292i	$-0.305079\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	−384.000	−2.88722
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	277.128i	1.99373i	0.0791367	+	0.996864i	$0.474784\pi$
$139$	277.128i	1.99373i	−0.0791367	+	0.996864i	$0.525216\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	96.9948i	0.642350i	0.947020	+	0.321175i	$0.104078\pi$
$151$	96.9948i	0.642350i	−0.947020	+	0.321175i	$0.895922\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−118.000	−0.751592	−0.375796	−	0.926702i	$-0.622631\pi$
$157$	−118.000	−0.751592	−0.375796	+	0.926702i	$0.622631\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	193.990i	1.19012i	0.803681	+	0.595060i	$0.202872\pi$
$163$	193.990i	1.19012i	−0.803681	+	0.595060i	$0.797128\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	315.000	1.86391
$170$	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
$175$	346.410i	1.97949i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−314.000	−1.73481	−0.867403	−	0.497606i	$-0.834213\pi$
$181$	−314.000	−1.73481	−0.867403	+	0.497606i	$0.834213\pi$
$182$	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
$193$	−382.000	−1.97927	−0.989637	−	0.143590i	$-0.954135\pi$
$193$	−382.000	−1.97927	−0.989637	+	0.143590i	$0.954135\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	− 96.9948i	− 0.487411i	−0.969849	−	0.243706i	$-0.921637\pi$
$199$	− 96.9948i	− 0.487411i	0.969849	−	0.243706i	$-0.0783631\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	− 387.979i	− 1.83876i	−0.393365	−	0.919382i	$-0.628689\pi$
$211$	− 387.979i	− 1.83876i	0.393365	−	0.919382i	$-0.371311\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	576.000	2.65438
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	290.985i	1.30486i	0.757848	+	0.652432i	$0.226251\pi$
$223$	290.985i	1.30486i	−0.757848	+	0.652432i	$0.773749\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	−26.0000	−0.113537	−0.0567686	−	0.998387i	$-0.518080\pi$
$229$	−26.0000	−0.113537	−0.0567686	+	0.998387i	$0.518080\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	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			$\pi$
$240$	0	0
$241$	286.000	1.18672	0.593361	−	0.804936i	$-0.297801\pi$
$241$	286.000	1.18672	0.593361	+	0.804936i	$0.297801\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	− 609.682i	− 2.46835i
$248$	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
$256$	0	0
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	− 360.267i	− 1.39099i
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	− 484.974i	− 1.78957i	−0.446494	−	0.894786i	$-0.647328\pi$
$271$	− 484.974i	− 1.78957i	0.446494	−	0.894786i	$-0.352672\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−122.000	−0.440433	−0.220217	−	0.975451i	$-0.570676\pi$
$277$	−122.000	−0.440433	−0.220217	+	0.975451i	$0.570676\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	332.554i	1.17510i	0.809187	+	0.587551i	$0.199908\pi$
$283$	332.554i	1.17510i	−0.809187	+	0.587551i	$0.800092\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−289.000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	1152.00	3.82724
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	498.831i	1.62486i	0.583062	+	0.812428i	$0.301855\pi$
$307$	498.831i	1.62486i	−0.583062	+	0.812428i	$0.698145\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	−142.000	−0.453674	−0.226837	−	0.973933i	$-0.572838\pi$
$313$	−142.000	−0.453674	−0.226837	+	0.973933i	$0.572838\pi$
$314$	0	0
$315$	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
$324$	0	0
$325$	−550.000	−1.69231
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	− 554.256i	− 1.67449i	−0.546828	−	0.837245i	$-0.684165\pi$
$331$	− 554.256i	− 1.67449i	0.546828	−	0.837245i	$-0.315835\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−482.000	−1.43027	−0.715134	−	0.698988i	$-0.753634\pi$
$337$	−482.000	−1.43027	−0.715134	+	0.698988i	$0.753634\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	1302.50i	3.79738i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	−502.000	−1.43840	−0.719198	−	0.694805i	$-0.755490\pi$
$349$	−502.000	−1.43840	−0.719198	+	0.694805i	$0.755490\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	−407.000	−1.12742
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	152.420i	0.415315i	0.978202	+	0.207657i	$0.0665839\pi$
$367$	152.420i	0.415315i	−0.978202	+	0.207657i	$0.933416\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	698.000	1.87131	0.935657	−	0.352911i	$-0.114808\pi$
$373$	698.000	1.87131	0.935657	+	0.352911i	$0.114808\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	304.841i	0.804330i	0.915567	+	0.402165i	$0.131742\pi$
$379$	304.841i	0.804330i	−0.915567	+	0.402165i	$0.868258\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	362.000	0.911839	0.455919	−	0.890021i	$-0.349311\pi$
$397$	362.000	0.911839	0.455919	+	0.890021i	$0.349311\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	914.523i	2.26929i
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−626.000	−1.53056	−0.765281	−	0.643696i	$-0.777400\pi$
$409$	−626.000	−1.53056	−0.765281	+	0.643696i	$0.777400\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	358.000	0.850356	0.425178	−	0.905110i	$-0.360211\pi$
$421$	358.000	0.850356	0.425178	+	0.905110i	$0.360211\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	− 1025.37i	− 2.40134i
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	−862.000	−1.99076	−0.995381	−	0.0960028i	$-0.969394\pi$
$433$	−862.000	−1.99076	−0.995381	+	0.0960028i	$0.969394\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	− 872.954i	− 1.98850i	−0.107062	−	0.994252i	$-0.534144\pi$
$439$	− 872.954i	− 1.98850i	0.107062	−	0.994252i	$-0.465856\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	814.000	1.78118	0.890591	−	0.454805i	$-0.150291\pi$
$457$	814.000	1.78118	0.890591	+	0.454805i	$0.150291\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	− 762.102i	− 1.64601i	−0.568035	−	0.823005i	$-0.692296\pi$
$463$	− 762.102i	− 1.64601i	0.568035	−	0.823005i	$-0.307704\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	768.000	1.63753
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	692.820i	1.45857i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	572.000	1.18919
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	152.420i	0.312978i	0.987680	+	0.156489i	$0.0500176\pi$
$487$	152.420i	0.312978i	−0.987680	+	0.156489i	$0.949982\pi$
$488$	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
$499$	− 997.661i	− 1.99932i	−0.0260521	−	0.999661i	$-0.508294\pi$
$499$	− 997.661i	− 1.99932i	0.0260521	−	0.999661i	$-0.491706\pi$
$500$	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
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	− 637.395i	− 1.24735i
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	− 360.267i	− 0.688846i	−0.938815	−	0.344423i	$-0.888075\pi$
$523$	− 360.267i	− 0.688846i	0.938815	−	0.344423i	$-0.111925\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	529.000	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
$541$	−1034.00	−1.91128	−0.955638	−	0.294545i	$-0.904832\pi$
$541$	−1034.00	−1.91128	−0.955638	+	0.294545i	$0.904832\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 969.948i	− 1.77321i	−0.462523	−	0.886607i	$-0.653056\pi$
$547$	− 969.948i	− 1.77321i	0.462523	−	0.886607i	$-0.346944\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−960.000	−1.73599
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	1829.05i	3.27200i
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	720.533i	1.26188i	0.775832	+	0.630940i	$0.217330\pi$
$571$	720.533i	1.26188i	−0.775832	+	0.630940i	$0.782670\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	962.000	1.66724	0.833622	−	0.552335i	$-0.186263\pi$
$577$	962.000	1.66724	0.833622	+	0.552335i	$0.186263\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	1152.00	1.95586
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	−526.000	−0.875208	−0.437604	−	0.899168i	$-0.644173\pi$
$601$	−526.000	−0.875208	−0.437604	+	0.899168i	$0.644173\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	900.666i	1.48380i	0.670511	+	0.741900i	$0.266075\pi$
$607$	900.666i	1.48380i	−0.670511	+	0.741900i	$0.733925\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−1126.00	−1.83687	−0.918434	−	0.395574i	$-0.870546\pi$
$613$	−1126.00	−1.83687	−0.918434	+	0.395574i	$0.870546\pi$
$614$	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
$619$	1219.36i	1.96989i	0.172859	+	0.984947i	$0.444699\pi$
$619$	1219.36i	1.96989i	−0.172859	+	0.984947i	$0.555301\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	− 1066.94i	− 1.69088i	−0.534073	−	0.845438i	$-0.679339\pi$
$631$	− 1066.94i	− 1.69088i	0.534073	−	0.845438i	$-0.320661\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−3146.00	−4.93878
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	1247.08i	1.93947i	0.244168	+	0.969733i	$0.421485\pi$
$643$	1247.08i	1.93947i	−0.244168	+	0.969733i	$0.578515\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	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
$661$	122.000	0.184569	0.0922844	−	0.995733i	$-0.470583\pi$
$661$	122.000	0.184569	0.0922844	+	0.995733i	$0.470583\pi$
$662$	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
$673$	1154.00	1.71471	0.857355	−	0.514725i	$-0.172106\pi$
$673$	1154.00	1.71471	0.857355	+	0.514725i	$0.172106\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	27.7128i	0.0408142i
$680$	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
$689$	0	0
$690$	0	0
$691$	415.692i	0.601581i	0.953690	+	0.300790i	$0.0972504\pi$
$691$	415.692i	0.601581i	−0.953690	+	0.300790i	$0.902750\pi$
$692$	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
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	− 720.533i	− 1.02494i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	934.000	1.31735	0.658674	−	0.752428i	$-0.271118\pi$
$709$	934.000	1.31735	0.658674	+	0.752428i	$0.271118\pi$
$710$	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	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	960.000	1.33148
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	1371.78i	1.88691i	0.331499	+	0.943455i	$0.392446\pi$
$727$	1371.78i	1.88691i	−0.331499	+	0.943455i	$0.607554\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−1034.00	−1.41064	−0.705321	−	0.708888i	$-0.749197\pi$
$733$	−1034.00	−1.41064	−0.705321	+	0.708888i	$0.749197\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	− 831.384i	− 1.12501i	−0.826793	−	0.562506i	$-0.809837\pi$
$739$	− 831.384i	− 1.12501i	0.826793	−	0.562506i	$-0.190163\pi$
$740$	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
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	− 900.666i	− 1.19929i	−0.800266	−	0.599645i	$-0.795309\pi$
$751$	− 900.666i	− 1.19929i	0.800266	−	0.599645i	$-0.204691\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	838.000	1.10700	0.553501	−	0.832849i	$-0.313292\pi$
$757$	838.000	1.10700	0.553501	+	0.832849i	$0.313292\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	− 2965.27i	− 3.88633i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−1534.00	−1.99480	−0.997399	−	0.0720749i	$-0.977038\pi$
$769$	−1534.00	−1.99480	−0.997399	+	0.0720749i	$0.977038\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	− 1039.23i	− 1.34094i
$776$	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
$787$	− 193.990i	− 0.246493i	−0.992376	−	0.123246i	$-0.960669\pi$
$787$	− 193.990i	− 0.246493i	0.992376	−	0.123246i	$-0.0393305\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	1628.00	2.05296
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	581.969i	0.717594i	0.933416	+	0.358797i	$0.116813\pi$
$811$	581.969i	0.717594i	−0.933416	+	0.358797i	$0.883187\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	2304.00	2.82007
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	1260.93i	1.53212i	0.642770	+	0.766059i	$0.277785\pi$
$823$	1260.93i	1.53212i	−0.642770	+	0.766059i	$0.722215\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−458.000	−0.552473	−0.276236	−	0.961090i	$-0.589087\pi$
$829$	−458.000	−0.552473	−0.276236	+	0.961090i	$0.589087\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−841.000	−1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	− 1676.63i	− 1.97949i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	1658.00	1.94373	0.971864	−	0.235543i	$-0.0756867\pi$
$853$	1658.00	1.94373	0.971864	+	0.235543i	$0.0756867\pi$
$854$	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
$859$	− 969.948i	− 1.12916i	−0.825378	−	0.564580i	$-0.809038\pi$
$859$	− 969.948i	− 1.12916i	0.825378	−	0.564580i	$-0.190962\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	1219.36i	1.39996i
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−598.000	−0.681870	−0.340935	−	0.940087i	$-0.610744\pi$
$877$	−598.000	−0.681870	−0.340935	+	0.940087i	$0.610744\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	− 471.118i	− 0.533542i	−0.963760	−	0.266771i	$-0.914043\pi$
$883$	− 471.118i	− 0.533542i	0.963760	−	0.266771i	$-0.0859568\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	−2880.00	−3.23960
$890$	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
$905$	0	0
$906$	0	0
$907$	1801.33i	1.98603i	0.117971	+	0.993017i	$0.462361\pi$
$907$	1801.33i	1.98603i	−0.117971	+	0.993017i	$0.537639\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	− 1621.20i	− 1.76409i	−0.471164	−	0.882045i	$-0.656166\pi$
$919$	− 1621.20i	− 1.76409i	0.471164	−	0.882045i	$-0.343834\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−650.000	−0.702703
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	3962.93i	4.25664i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−1198.00	−1.27855	−0.639274	−	0.768979i	$-0.720765\pi$
$937$	−1198.00	−1.27855	−0.639274	+	0.768979i	$0.720765\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	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
$949$	1012.00	1.06639
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−767.000	−0.798127
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	1177.79i	1.21799i	0.793175	+	0.608994i	$0.208427\pi$
$967$	1177.79i	1.21799i	−0.793175	+	0.608994i	$0.791573\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	3840.00	3.94656
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			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
$991$	1981.47i	1.99946i	0.0232089	+	0.999731i	$0.492612\pi$
$991$	1981.47i	1.99946i	−0.0232089	+	0.999731i	$0.507388\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−1894.00	−1.89970	−0.949850	−	0.312707i	$-0.898764\pi$
$997$	−1894.00	−1.89970	−0.949850	+	0.312707i	$0.898764\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.g.c.127.1	✓	2
3.2	odd	2	CM	144.3.g.c.127.1	✓	2
4.3	odd	2	inner	144.3.g.c.127.2	yes	2
5.2	odd	4		3600.3.j.e.1999.3		4
5.3	odd	4		3600.3.j.e.1999.2		4
5.4	even	2		3600.3.e.h.3151.2		2
8.3	odd	2		576.3.g.f.127.2		2
8.5	even	2		576.3.g.f.127.1		2
9.2	odd	6		1296.3.o.f.271.1		2
9.4	even	3		1296.3.o.k.703.1		2
9.5	odd	6		1296.3.o.k.703.1		2
9.7	even	3		1296.3.o.f.271.1		2
12.11	even	2	inner	144.3.g.c.127.2	yes	2
15.2	even	4		3600.3.j.e.1999.3		4
15.8	even	4		3600.3.j.e.1999.2		4
15.14	odd	2		3600.3.e.h.3151.2		2
16.3	odd	4		2304.3.b.m.127.2		4
16.5	even	4		2304.3.b.m.127.3		4
16.11	odd	4		2304.3.b.m.127.1		4
16.13	even	4		2304.3.b.m.127.4		4
20.3	even	4		3600.3.j.e.1999.4		4
20.7	even	4		3600.3.j.e.1999.1		4
20.19	odd	2		3600.3.e.h.3151.1		2
24.5	odd	2		576.3.g.f.127.1		2
24.11	even	2		576.3.g.f.127.2		2
36.7	odd	6		1296.3.o.k.271.1		2
36.11	even	6		1296.3.o.k.271.1		2
36.23	even	6		1296.3.o.f.703.1		2
36.31	odd	6		1296.3.o.f.703.1		2
48.5	odd	4		2304.3.b.m.127.3		4
48.11	even	4		2304.3.b.m.127.1		4
48.29	odd	4		2304.3.b.m.127.4		4
48.35	even	4		2304.3.b.m.127.2		4
60.23	odd	4		3600.3.j.e.1999.4		4
60.47	odd	4		3600.3.j.e.1999.1		4
60.59	even	2		3600.3.e.h.3151.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.g.c.127.1	✓	2	1.1	even	1	trivial
144.3.g.c.127.1	✓	2	3.2	odd	2	CM
144.3.g.c.127.2	yes	2	4.3	odd	2	inner
144.3.g.c.127.2	yes	2	12.11	even	2	inner
576.3.g.f.127.1		2	8.5	even	2
576.3.g.f.127.1		2	24.5	odd	2
576.3.g.f.127.2		2	8.3	odd	2
576.3.g.f.127.2		2	24.11	even	2
1296.3.o.f.271.1		2	9.2	odd	6
1296.3.o.f.271.1		2	9.7	even	3
1296.3.o.f.703.1		2	36.23	even	6
1296.3.o.f.703.1		2	36.31	odd	6
1296.3.o.k.271.1		2	36.7	odd	6
1296.3.o.k.271.1		2	36.11	even	6
1296.3.o.k.703.1		2	9.4	even	3
1296.3.o.k.703.1		2	9.5	odd	6
2304.3.b.m.127.1		4	16.11	odd	4
2304.3.b.m.127.1		4	48.11	even	4
2304.3.b.m.127.2		4	16.3	odd	4
2304.3.b.m.127.2		4	48.35	even	4
2304.3.b.m.127.3		4	16.5	even	4
2304.3.b.m.127.3		4	48.5	odd	4
2304.3.b.m.127.4		4	16.13	even	4
2304.3.b.m.127.4		4	48.29	odd	4
3600.3.e.h.3151.1		2	20.19	odd	2
3600.3.e.h.3151.1		2	60.59	even	2
3600.3.e.h.3151.2		2	5.4	even	2
3600.3.e.h.3151.2		2	15.14	odd	2
3600.3.j.e.1999.1		4	20.7	even	4
3600.3.j.e.1999.1		4	60.47	odd	4
3600.3.j.e.1999.2		4	5.3	odd	4
3600.3.j.e.1999.2		4	15.8	even	4
3600.3.j.e.1999.3		4	5.2	odd	4
3600.3.j.e.1999.3		4	15.2	even	4
3600.3.j.e.1999.4		4	20.3	even	4
3600.3.j.e.1999.4		4	60.23	odd	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-13.8564i q^{7} +O(q^{10})\)	\(q-13.8564i q^{7} +22.0000 q^{13} -27.7128i q^{19} -25.0000 q^{25} +41.5692i q^{31} +26.0000 q^{37} +83.1384i q^{43} -143.000 q^{49} +74.0000 q^{61} +55.4256i q^{67} +46.0000 q^{73} -69.2820i q^{79} -304.841i q^{91} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q+O(q^{10}) \) 2 * q	\( 2 q + 44 q^{13} - 50 q^{25} + 52 q^{37} - 286 q^{49} + 148 q^{61} + 92 q^{73} - 4 q^{97}+O(q^{100}) \) 2 * q + 44 * q^13 - 50 * q^25 + 52 * q^37 - 286 * q^49 + 148 * q^61 + 92 * q^73 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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