LMFDB - Embedded newform 2304.3.g.j.1279.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2304,3,Mod(1279,2304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2304, 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("2304.1279");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 2304 = 2^{8} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2304.g (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:	$62.7794529086$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1279.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	2304.1279
Dual form			2304.3.g.j.1279.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+O(q^{10})$	$q+14.0000i q^{11} -2.00000 q^{17} -34.0000i q^{19} -25.0000 q^{25} -46.0000 q^{41} -14.0000i q^{43} +49.0000 q^{49} -82.0000i q^{59} +62.0000i q^{67} +142.000 q^{73} -158.000i q^{83} +146.000 q^{89} -94.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q+O(q^{10}) $ 2 * q	$ 2 q - 4 q^{17} - 50 q^{25} - 92 q^{41} + 98 q^{49} + 284 q^{73} + 292 q^{89} - 188 q^{97}+O(q^{100}) $ 2 * q - 4 * q^17 - 50 * q^25 - 92 * q^41 + 98 * q^49 + 284 * q^73 + 292 * q^89 - 188 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times$.

$n$	$1279$	$1793$	$2053$
$\chi(n)$	$-1$	$1$	$1$

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
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	14.0000i	1.27273i	0.771389	+	0.636364i	$0.219562\pi$
$11$	14.0000i	1.27273i	−0.771389	+	0.636364i	$0.780438\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−2.00000	−0.117647	−0.0588235	−	0.998268i	$-0.518735\pi$
$17$	−2.00000	−0.117647	−0.0588235	+	0.998268i	$0.518735\pi$
$18$	0	0
$19$	− 34.0000i	− 1.78947i	−0.446594	−	0.894737i	$-0.647363\pi$
$19$	− 34.0000i	− 1.78947i	0.446594	−	0.894737i	$-0.352637\pi$
$20$	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
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−46.0000	−1.12195	−0.560976	−	0.827832i	$-0.689574\pi$
$41$	−46.0000	−1.12195	−0.560976	+	0.827832i	$0.689574\pi$
$42$	0	0
$43$	− 14.0000i	− 0.325581i	−0.986661	−	0.162791i	$-0.947950\pi$
$43$	− 14.0000i	− 0.325581i	0.986661	−	0.162791i	$-0.0520495\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	49.0000	1.00000
$50$	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
$59$	− 82.0000i	− 1.38983i	−0.719092	−	0.694915i	$-0.755442\pi$
$59$	− 82.0000i	− 1.38983i	0.719092	−	0.694915i	$-0.244558\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	62.0000i	0.925373i	0.886522	+	0.462687i	$0.153114\pi$
$67$	62.0000i	0.925373i	−0.886522	+	0.462687i	$0.846886\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	142.000	1.94521	0.972603	−	0.232473i	$-0.0746819\pi$
$73$	142.000	1.94521	0.972603	+	0.232473i	$0.0746819\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	− 158.000i	− 1.90361i	−0.306697	−	0.951807i	$-0.599224\pi$
$83$	− 158.000i	− 1.90361i	0.306697	−	0.951807i	$-0.400776\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	146.000	1.64045	0.820225	−	0.572041i	$-0.193848\pi$
$89$	146.000	1.64045	0.820225	+	0.572041i	$0.193848\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−94.0000	−0.969072	−0.484536	−	0.874771i	$-0.661012\pi$
$97$	−94.0000	−0.969072	−0.484536	+	0.874771i	$0.661012\pi$
$98$	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
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 178.000i	− 1.66355i	−0.555112	−	0.831776i	$-0.687325\pi$
$107$	− 178.000i	− 1.66355i	0.555112	−	0.831776i	$-0.312675\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−98.0000	−0.867257	−0.433628	−	0.901092i	$-0.642767\pi$
$113$	−98.0000	−0.867257	−0.433628	+	0.901092i	$0.642767\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−75.0000	−0.619835
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	− 62.0000i	− 0.473282i	−0.971597	−	0.236641i	$-0.923953\pi$
$131$	− 62.0000i	− 0.473282i	0.971597	−	0.236641i	$-0.0760466\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−238.000	−1.73723	−0.868613	−	0.495491i	$-0.834988\pi$
$137$	−238.000	−1.73723	−0.868613	+	0.495491i	$0.834988\pi$
$138$	0	0
$139$	− 206.000i	− 1.48201i	−0.671497	−	0.741007i	$-0.734348\pi$
$139$	− 206.000i	− 1.48201i	0.671497	−	0.741007i	$-0.265652\pi$
$140$	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
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	− 322.000i	− 1.97546i	−0.156171	−	0.987730i	$-0.549915\pi$
$163$	− 322.000i	− 1.97546i	0.156171	−	0.987730i	$-0.450085\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	−169.000	−1.00000
$170$	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
$178$	0	0
$179$	34.0000i	0.189944i	0.995480	+	0.0949721i	$0.0302762\pi$
$179$	34.0000i	0.189944i	−0.995480	+	0.0949721i	$0.969724\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	− 28.0000i	− 0.149733i
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	98.0000	0.507772	0.253886	−	0.967234i	$-0.418291\pi$
$193$	98.0000	0.507772	0.253886	+	0.967234i	$0.418291\pi$
$194$	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
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	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
$209$	476.000	2.27751
$210$	0	0
$211$	− 226.000i	− 1.07109i	−0.844507	−	0.535545i	$-0.820106\pi$
$211$	− 226.000i	− 1.07109i	0.844507	−	0.535545i	$-0.179894\pi$
$212$	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
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	− 446.000i	− 1.96476i	−0.186900	−	0.982379i	$-0.559844\pi$
$227$	− 446.000i	− 1.96476i	0.186900	−	0.982379i	$-0.440156\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	434.000	1.86266	0.931330	−	0.364175i	$-0.118649\pi$
$233$	434.000	1.86266	0.931330	+	0.364175i	$0.118649\pi$
$234$	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
$241$	194.000	0.804979	0.402490	−	0.915425i	$-0.368145\pi$
$241$	194.000	0.804979	0.402490	+	0.915425i	$0.368145\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 466.000i	− 1.85657i	−0.371865	−	0.928287i	$-0.621282\pi$
$251$	− 466.000i	− 1.85657i	0.371865	−	0.928287i	$-0.378718\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−386.000	−1.50195	−0.750973	−	0.660333i	$-0.770415\pi$
$257$	−386.000	−1.50195	−0.750973	+	0.660333i	$0.770415\pi$
$258$	0	0
$259$	0	0
$260$	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
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	− 350.000i	− 1.27273i
$276$	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
$281$	−238.000	−0.846975	−0.423488	−	0.905902i	$-0.639194\pi$
$281$	−238.000	−0.846975	−0.423488	+	0.905902i	$0.639194\pi$
$282$	0	0
$283$	82.0000i	0.289753i	0.989450	+	0.144876i	$0.0462784\pi$
$283$	82.0000i	0.289753i	−0.989450	+	0.144876i	$0.953722\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−285.000	−0.986159
$290$	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
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	542.000i	1.76547i	0.469869	+	0.882736i	$0.344301\pi$
$307$	542.000i	1.76547i	−0.469869	+	0.882736i	$0.655699\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	526.000	1.68051	0.840256	−	0.542191i	$-0.182405\pi$
$313$	526.000	1.68051	0.840256	+	0.542191i	$0.182405\pi$
$314$	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
$323$	68.0000i	0.210526i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	− 14.0000i	− 0.0422961i	−0.999776	−	0.0211480i	$-0.993268\pi$
$331$	− 14.0000i	− 0.0422961i	0.999776	−	0.0211480i	$-0.00673213\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−478.000	−1.41840	−0.709199	−	0.705009i	$-0.750943\pi$
$337$	−478.000	−1.41840	−0.709199	+	0.705009i	$0.750943\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	− 658.000i	− 1.89625i	−0.317892	−	0.948127i	$-0.602975\pi$
$347$	− 658.000i	− 1.89625i	0.317892	−	0.948127i	$-0.397025\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−194.000	−0.549575	−0.274788	−	0.961505i	$-0.588608\pi$
$353$	−194.000	−0.549575	−0.274788	+	0.961505i	$0.588608\pi$
$354$	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
$361$	−795.000	−2.20222
$362$	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
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	− 686.000i	− 1.81003i	−0.425383	−	0.905013i	$-0.639861\pi$
$379$	− 686.000i	− 1.81003i	0.425383	−	0.905013i	$-0.360139\pi$
$380$	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
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	766.000	1.91022	0.955112	−	0.296244i	$-0.0957342\pi$
$401$	766.000	1.91022	0.955112	+	0.296244i	$0.0957342\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	334.000	0.816626	0.408313	−	0.912842i	$-0.366117\pi$
$409$	334.000	0.816626	0.408313	+	0.912842i	$0.366117\pi$
$410$	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
$419$	514.000i	1.22673i	0.789799	+	0.613365i	$0.210185\pi$
$419$	514.000i	1.22673i	−0.789799	+	0.613365i	$0.789815\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	50.0000	0.117647
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	578.000	1.33487	0.667436	−	0.744667i	$-0.267392\pi$
$433$	578.000	1.33487	0.667436	+	0.744667i	$0.267392\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	878.000i	1.98194i	0.134079	+	0.990971i	$0.457192\pi$
$443$	878.000i	1.98194i	−0.134079	+	0.990971i	$0.542808\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−866.000	−1.92873	−0.964365	−	0.264574i	$-0.914769\pi$
$449$	−866.000	−1.92873	−0.964365	+	0.264574i	$0.914769\pi$
$450$	0	0
$451$	− 644.000i	− 1.42794i
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	238.000	0.520788	0.260394	−	0.965502i	$-0.416148\pi$
$457$	238.000	0.520788	0.260394	+	0.965502i	$0.416148\pi$
$458$	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
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	34.0000i	0.0728051i	0.999337	+	0.0364026i	$0.0115899\pi$
$467$	34.0000i	0.0728051i	−0.999337	+	0.0364026i	$0.988410\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	196.000	0.414376
$474$	0	0
$475$	850.000i	1.78947i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	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
$491$	782.000i	1.59267i	0.604857	+	0.796334i	$0.293230\pi$
$491$	782.000i	1.59267i	−0.604857	+	0.796334i	$0.706770\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	− 802.000i	− 1.60721i	−0.595160	−	0.803607i	$-0.702911\pi$
$499$	− 802.000i	− 1.60721i	0.595160	−	0.803607i	$-0.297089\pi$
$500$	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
$511$	0	0
$512$	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
$521$	−1006.00	−1.93090	−0.965451	−	0.260584i	$-0.916085\pi$
$521$	−1006.00	−1.93090	−0.965451	+	0.260584i	$0.916085\pi$
$522$	0	0
$523$	− 398.000i	− 0.760994i	−0.924782	−	0.380497i	$-0.875753\pi$
$523$	− 398.000i	− 0.760994i	0.924782	−	0.380497i	$-0.124247\pi$
$524$	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
$539$	686.000i	1.27273i
$540$	0	0
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	1022.00i	1.86837i	0.356785	+	0.934186i	$0.383873\pi$
$547$	1022.00i	1.86837i	−0.356785	+	0.934186i	$0.616127\pi$
$548$	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		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	226.000i	0.401421i	0.979651	+	0.200710i	$0.0643251\pi$
$563$	226.000i	0.401421i	−0.979651	+	0.200710i	$0.935675\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	626.000	1.10018	0.550088	−	0.835107i	$-0.314594\pi$
$569$	626.000	1.10018	0.550088	+	0.835107i	$0.314594\pi$
$570$	0	0
$571$	658.000i	1.15236i	0.817321	+	0.576182i	$0.195458\pi$
$571$	658.000i	1.15236i	−0.817321	+	0.576182i	$0.804542\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	2.00000	0.00346620	0.00173310	−	0.999998i	$-0.499448\pi$
$577$	2.00000	0.00346620	0.00173310	+	0.999998i	$0.499448\pi$
$578$	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
$587$	− 1138.00i	− 1.93867i	−0.245741	−	0.969336i	$-0.579031\pi$
$587$	− 1138.00i	− 1.93867i	0.245741	−	0.969336i	$-0.420969\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	862.000	1.45363	0.726813	−	0.686836i	$-0.241001\pi$
$593$	862.000	1.45363	0.726813	+	0.686836i	$0.241001\pi$
$594$	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
$601$	−914.000	−1.52080	−0.760399	−	0.649456i	$-0.774997\pi$
$601$	−914.000	−1.52080	−0.760399	+	0.649456i	$0.774997\pi$
$602$	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
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−334.000	−0.541329	−0.270665	−	0.962674i	$-0.587243\pi$
$617$	−334.000	−0.541329	−0.270665	+	0.962674i	$0.587243\pi$
$618$	0	0
$619$	562.000i	0.907916i	0.891023	+	0.453958i	$0.149988\pi$
$619$	562.000i	0.907916i	−0.891023	+	0.453958i	$0.850012\pi$
$620$	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
$631$	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
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−482.000	−0.751950	−0.375975	−	0.926630i	$-0.622692\pi$
$641$	−482.000	−0.751950	−0.375975	+	0.926630i	$0.622692\pi$
$642$	0	0
$643$	1214.00i	1.88802i	0.329910	+	0.944012i	$0.392982\pi$
$643$	1214.00i	1.88802i	−0.329910	+	0.944012i	$0.607018\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	1148.00	1.76888
$650$	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
$659$	994.000i	1.50835i	0.656676	+	0.754173i	$0.271962\pi$
$659$	994.000i	1.50835i	−0.656676	+	0.754173i	$0.728038\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	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
$673$	−1246.00	−1.85141	−0.925706	−	0.378244i	$-0.876528\pi$
$673$	−1246.00	−1.85141	−0.925706	+	0.378244i	$0.876528\pi$
$674$	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
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	398.000i	0.582723i	0.956613	+	0.291362i	$0.0941083\pi$
$683$	398.000i	0.582723i	−0.956613	+	0.291362i	$0.905892\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	734.000i	1.06223i	0.847300	+	0.531114i	$0.178227\pi$
$691$	734.000i	1.06223i	−0.847300	+	0.531114i	$0.821773\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	92.0000	0.131994
$698$	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
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	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
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	28.0000i	0.0383037i
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−868.000	−1.17775
$738$	0	0
$739$	− 322.000i	− 0.435724i	−0.975980	−	0.217862i	$-0.930092\pi$
$739$	− 322.000i	− 0.435724i	0.975980	−	0.217862i	$-0.0699083\pi$
$740$	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
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	1394.00	1.83180	0.915900	−	0.401406i	$-0.131478\pi$
$761$	1394.00	1.83180	0.915900	+	0.401406i	$0.131478\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−1054.00	−1.37061	−0.685306	−	0.728256i	$-0.740331\pi$
$769$	−1054.00	−1.37061	−0.685306	+	0.728256i	$0.740331\pi$
$770$	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
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	1564.00i	2.00770i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	926.000i	1.17662i	0.808635	+	0.588310i	$0.200207\pi$
$787$	926.000i	1.17662i	−0.808635	+	0.588310i	$0.799793\pi$
$788$	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		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	1988.00i	2.47572i
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1582.00	−1.95550	−0.977750	−	0.209772i	$-0.932728\pi$
$809$	−1582.00	−1.95550	−0.977750	+	0.209772i	$0.932728\pi$
$810$	0	0
$811$	178.000i	0.219482i	0.993960	+	0.109741i	$0.0350022\pi$
$811$	178.000i	0.219482i	−0.993960	+	0.109741i	$0.964998\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−476.000	−0.582619
$818$	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
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	1262.00i	1.52600i	0.646400	+	0.762999i	$0.276274\pi$
$827$	1262.00i	1.52600i	−0.646400	+	0.762999i	$0.723726\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−98.0000	−0.117647
$834$	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
$847$	0	0
$848$	0	0
$849$	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
$857$	1202.00	1.40257	0.701284	−	0.712882i	$-0.252611\pi$
$857$	1202.00	1.40257	0.701284	+	0.712882i	$0.252611\pi$
$858$	0	0
$859$	− 1646.00i	− 1.91618i	−0.286465	−	0.958091i	$-0.592480\pi$
$859$	− 1646.00i	− 1.91618i	0.286465	−	0.958091i	$-0.407520\pi$
$860$	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
$871$	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
$881$	1438.00	1.63224	0.816118	−	0.577885i	$-0.196122\pi$
$881$	1438.00	1.63224	0.816118	+	0.577885i	$0.196122\pi$
$882$	0	0
$883$	− 1762.00i	− 1.99547i	−0.0672672	−	0.997735i	$-0.521428\pi$
$883$	− 1762.00i	− 1.99547i	0.0672672	−	0.997735i	$-0.478572\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	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
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	1714.00i	1.88975i	0.327436	+	0.944873i	$0.393815\pi$
$907$	1714.00i	1.88975i	−0.327436	+	0.944873i	$0.606185\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	2212.00	2.42278
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−1058.00	−1.13886	−0.569429	−	0.822040i	$-0.692836\pi$
$929$	−1058.00	−1.13886	−0.569429	+	0.822040i	$0.692836\pi$
$930$	0	0
$931$	− 1666.00i	− 1.78947i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	718.000	0.766275	0.383138	−	0.923691i	$-0.374843\pi$
$937$	718.000	0.766275	0.383138	+	0.923691i	$0.374843\pi$
$938$	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
$947$	994.000i	1.04963i	0.851216	+	0.524815i	$0.175866\pi$
$947$	994.000i	1.04963i	−0.851216	+	0.524815i	$0.824134\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−142.000	−0.149003	−0.0745016	−	0.997221i	$-0.523737\pi$
$953$	−142.000	−0.149003	−0.0745016	+	0.997221i	$0.523737\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	974.000i	1.00309i	0.865132	+	0.501545i	$0.167235\pi$
$971$	974.000i	1.00309i	−0.865132	+	0.501545i	$0.832765\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1918.00	1.96315	0.981576	−	0.191071i	$-0.0611960\pi$
$977$	1918.00	1.96315	0.981576	+	0.191071i	$0.0611960\pi$
$978$	0	0
$979$	2044.00i	2.08784i
$980$	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	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2304.3.g.j.1279.2		2
3.2	odd	2		256.3.c.e.255.1		2
4.3	odd	2	inner	2304.3.g.j.1279.1		2
8.3	odd	2	CM	2304.3.g.j.1279.2		2
8.5	even	2	inner	2304.3.g.j.1279.1		2
12.11	even	2		256.3.c.e.255.2		2
16.3	odd	4		72.3.b.a.19.1		1
16.5	even	4		72.3.b.a.19.1		1
16.11	odd	4		288.3.b.a.271.1		1
16.13	even	4		288.3.b.a.271.1		1
24.5	odd	2		256.3.c.e.255.2		2
24.11	even	2		256.3.c.e.255.1		2
48.5	odd	4		8.3.d.a.3.1	✓	1
48.11	even	4		32.3.d.a.15.1		1
48.29	odd	4		32.3.d.a.15.1		1
48.35	even	4		8.3.d.a.3.1	✓	1
240.29	odd	4		800.3.g.a.751.1		1
240.53	even	4		200.3.e.a.99.2		2
240.59	even	4		800.3.g.a.751.1		1
240.77	even	4		800.3.e.a.399.1		2
240.83	odd	4		200.3.e.a.99.2		2
240.107	odd	4		800.3.e.a.399.1		2
240.149	odd	4		200.3.g.a.51.1		1
240.173	even	4		800.3.e.a.399.2		2
240.179	even	4		200.3.g.a.51.1		1
240.197	even	4		200.3.e.a.99.1		2
240.203	odd	4		800.3.e.a.399.2		2
240.227	odd	4		200.3.e.a.99.1		2
336.5	even	12		392.3.k.b.67.1		2
336.53	odd	12		392.3.k.d.275.1		2
336.83	odd	4		392.3.g.a.99.1		1
336.101	even	12		392.3.k.b.275.1		2
336.125	even	4		1568.3.g.a.687.1		1
336.131	odd	12		392.3.k.b.67.1		2
336.149	odd	12		392.3.k.d.67.1		2
336.179	even	12		392.3.k.d.275.1		2
336.227	odd	12		392.3.k.b.275.1		2
336.251	odd	4		1568.3.g.a.687.1		1
336.275	even	12		392.3.k.d.67.1		2
336.293	even	4		392.3.g.a.99.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.3.d.a.3.1	✓	1	48.5	odd	4
8.3.d.a.3.1	✓	1	48.35	even	4
32.3.d.a.15.1		1	48.11	even	4
32.3.d.a.15.1		1	48.29	odd	4
72.3.b.a.19.1		1	16.3	odd	4
72.3.b.a.19.1		1	16.5	even	4
200.3.e.a.99.1		2	240.197	even	4
200.3.e.a.99.1		2	240.227	odd	4
200.3.e.a.99.2		2	240.53	even	4
200.3.e.a.99.2		2	240.83	odd	4
200.3.g.a.51.1		1	240.149	odd	4
200.3.g.a.51.1		1	240.179	even	4
256.3.c.e.255.1		2	3.2	odd	2
256.3.c.e.255.1		2	24.11	even	2
256.3.c.e.255.2		2	12.11	even	2
256.3.c.e.255.2		2	24.5	odd	2
288.3.b.a.271.1		1	16.11	odd	4
288.3.b.a.271.1		1	16.13	even	4
392.3.g.a.99.1		1	336.83	odd	4
392.3.g.a.99.1		1	336.293	even	4
392.3.k.b.67.1		2	336.5	even	12
392.3.k.b.67.1		2	336.131	odd	12
392.3.k.b.275.1		2	336.101	even	12
392.3.k.b.275.1		2	336.227	odd	12
392.3.k.d.67.1		2	336.149	odd	12
392.3.k.d.67.1		2	336.275	even	12
392.3.k.d.275.1		2	336.53	odd	12
392.3.k.d.275.1		2	336.179	even	12
800.3.e.a.399.1		2	240.77	even	4
800.3.e.a.399.1		2	240.107	odd	4
800.3.e.a.399.2		2	240.173	even	4
800.3.e.a.399.2		2	240.203	odd	4
800.3.g.a.751.1		1	240.29	odd	4
800.3.g.a.751.1		1	240.59	even	4
1568.3.g.a.687.1		1	336.125	even	4
1568.3.g.a.687.1		1	336.251	odd	4
2304.3.g.j.1279.1		2	4.3	odd	2	inner
2304.3.g.j.1279.1		2	8.5	even	2	inner
2304.3.g.j.1279.2		2	1.1	even	1	trivial
2304.3.g.j.1279.2		2	8.3	odd	2	CM

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:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2304.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+O(q^{10})\)	\(q+14.0000i q^{11} -2.00000 q^{17} -34.0000i q^{19} -25.0000 q^{25} -46.0000 q^{41} -14.0000i q^{43} +49.0000 q^{49} -82.0000i q^{59} +62.0000i q^{67} +142.000 q^{73} -158.000i q^{83} +146.000 q^{89} -94.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q+O(q^{10}) \) 2 * q	\( 2 q - 4 q^{17} - 50 q^{25} - 92 q^{41} + 98 q^{49} + 284 q^{73} + 292 q^{89} - 188 q^{97}+O(q^{100}) \) 2 * q - 4 * q^17 - 50 * q^25 - 92 * q^41 + 98 * q^49 + 284 * q^73 + 292 * q^89 - 188 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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