LMFDB - Embedded newform 1824.2.f.b.1025.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(1025,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.1025"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,0,0,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(29)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1025.1
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1824.1025
Dual form			1824.2.f.b.1025.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} -3.00000 q^{9} -2.62685i q^{11} +4.35890i q^{19} -9.55505i q^{23} +5.00000 q^{25} +5.19615i q^{27} -8.54983 q^{29} -8.71780i q^{31} -4.54983 q^{33} -12.5498 q^{41} +4.30136i q^{47} -7.00000 q^{49} -0.549834 q^{53} +7.54983 q^{57} -15.0997 q^{61} +8.71780i q^{67} -16.5498 q^{69} +15.0997 q^{73} -8.66025i q^{75} +3.46410i q^{79} +9.00000 q^{81} -16.4833i q^{83} +14.8087i q^{87} +3.45017 q^{89} -15.0997 q^{93} +7.88054i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{9} + 20 q^{25} - 4 q^{29} + 12 q^{33} - 20 q^{41} - 28 q^{49} + 28 q^{53} - 36 q^{69} + 36 q^{81} + 44 q^{89}+O(q^{100}) $ 4 * q - 12 * q^9 + 20 * q^25 - 4 * q^29 + 12 * q^33 - 20 * q^41 - 28 * q^49 + 28 * q^53 - 36 * q^69 + 36 * q^81 + 44 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$-1$	$1$	$1$	$-1$

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
$3$	− 1.73205i	− 1.00000i
$3$	− 1.73205i	− 1.00000i
$4$	0	0
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	− 2.62685i	− 0.792025i	−0.918245	−	0.396012i	$-0.870394\pi$
$11$	− 2.62685i	− 0.792025i	0.918245	−	0.396012i	$-0.129606\pi$
$12$	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
$19$	4.35890i	1.00000i
$19$	4.35890i	1.00000i
$20$	0	0
$21$	0	0
$22$	0	0
$23$	− 9.55505i	− 1.99237i	−0.0872897	−	0.996183i	$-0.527821\pi$
$23$	− 9.55505i	− 1.99237i	0.0872897	−	0.996183i	$-0.472179\pi$
$24$	0	0
$25$	5.00000	1.00000
$26$	0	0
$27$	5.19615i	1.00000i
$28$	0	0
$29$	−8.54983	−1.58766	−0.793832	−	0.608137i	$-0.791917\pi$
$29$	−8.54983	−1.58766	−0.793832	+	0.608137i	$0.791917\pi$
$30$	0	0
$31$	− 8.71780i	− 1.56576i	−0.622171	−	0.782881i	$-0.713749\pi$
$31$	− 8.71780i	− 1.56576i	0.622171	−	0.782881i	$-0.286251\pi$
$32$	0	0
$33$	−4.54983	−0.792025
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−12.5498	−1.95995	−0.979977	−	0.199109i	$-0.936195\pi$
$41$	−12.5498	−1.95995	−0.979977	+	0.199109i	$0.936195\pi$
$42$	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
$47$	4.30136i	0.627417i	0.949519	+	0.313709i	$0.101571\pi$
$47$	4.30136i	0.627417i	−0.949519	+	0.313709i	$0.898429\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−0.549834	−0.0755256	−0.0377628	−	0.999287i	$-0.512023\pi$
$53$	−0.549834	−0.0755256	−0.0377628	+	0.999287i	$0.512023\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	7.54983	1.00000
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−15.0997	−1.93331	−0.966657	−	0.256074i	$-0.917571\pi$
$61$	−15.0997	−1.93331	−0.966657	+	0.256074i	$0.917571\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	8.71780i	1.06505i	0.846415	+	0.532524i	$0.178756\pi$
$67$	8.71780i	1.06505i	−0.846415	+	0.532524i	$0.821244\pi$
$68$	0	0
$69$	−16.5498	−1.99237
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	15.0997	1.76728	0.883641	−	0.468165i	$-0.155085\pi$
$73$	15.0997	1.76728	0.883641	+	0.468165i	$0.155085\pi$
$74$	0	0
$75$	− 8.66025i	− 1.00000i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	3.46410i	0.389742i	0.980829	+	0.194871i	$0.0624288\pi$
$79$	3.46410i	0.389742i	−0.980829	+	0.194871i	$0.937571\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	− 16.4833i	− 1.80927i	−0.426185	−	0.904636i	$-0.640143\pi$
$83$	− 16.4833i	− 1.80927i	0.426185	−	0.904636i	$-0.359857\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	14.8087i	1.58766i
$88$	0	0
$89$	3.45017	0.365717	0.182858	−	0.983139i	$-0.441465\pi$
$89$	3.45017	0.365717	0.182858	+	0.983139i	$0.441465\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−15.0997	−1.56576
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	7.88054i	0.792025i
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	− 10.3923i	− 1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$	− 10.3923i	− 1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$	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
$113$	−20.5498	−1.93317	−0.966583	−	0.256354i	$-0.917479\pi$
$113$	−20.5498	−1.93317	−0.966583	+	0.256354i	$0.917479\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	4.09967	0.372697
$122$	0	0
$123$	21.7370i	1.95995i
$124$	0	0
$125$	0	0
$126$	0	0
$127$	− 8.71780i	− 0.773579i	−0.922168	−	0.386790i	$-0.873584\pi$
$127$	− 8.71780i	− 0.773579i	0.922168	−	0.386790i	$-0.126416\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	11.2296i	0.981131i	0.871404	+	0.490566i	$0.163210\pi$
$131$	11.2296i	0.981131i	−0.871404	+	0.490566i	$0.836790\pi$
$132$	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
$141$	7.45017	0.627417
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	12.1244i	1.00000i
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	17.3205i	1.40952i	0.709444	+	0.704761i	$0.248946\pi$
$151$	17.3205i	1.40952i	−0.709444	+	0.704761i	$0.751054\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−15.0997	−1.20508	−0.602542	−	0.798087i	$-0.705846\pi$
$157$	−15.0997	−1.20508	−0.602542	+	0.798087i	$0.705846\pi$
$158$	0	0
$159$	0.952341i	0.0755256i
$160$	0	0
$161$	0	0
$162$	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
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	13.0000	1.00000
$170$	0	0
$171$	− 13.0767i	− 1.00000i
$172$	0	0
$173$	−24.5498	−1.86649	−0.933245	−	0.359241i	$-0.883035\pi$
$173$	−24.5498	−1.86649	−0.933245	+	0.359241i	$0.883035\pi$
$174$	0	0
$175$	0	0
$176$	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
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	26.1534i	1.93331i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	− 23.4115i	− 1.69399i	−0.531598	−	0.846997i	$-0.678408\pi$
$191$	− 23.4115i	− 1.69399i	0.531598	−	0.846997i	$-0.321592\pi$
$192$	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
$201$	15.0997	1.06505
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	28.6652i	1.99237i
$208$	0	0
$209$	11.4502	0.792025
$210$	0	0
$211$	8.71780i	0.600158i	0.953914	+	0.300079i	$0.0970130\pi$
$211$	8.71780i	0.600158i	−0.953914	+	0.300079i	$0.902987\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	− 26.1534i	− 1.76728i
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 24.2487i	− 1.62381i	−0.583787	−	0.811907i	$-0.698430\pi$
$223$	− 24.2487i	− 1.62381i	0.583787	−	0.811907i	$-0.301570\pi$
$224$	0	0
$225$	−15.0000	−1.00000
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	6.00000	0.389742
$238$	0	0
$239$	− 20.0624i	− 1.29773i	−0.760903	−	0.648866i	$-0.775244\pi$
$239$	− 20.0624i	− 1.29773i	0.760903	−	0.648866i	$-0.224756\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	− 15.5885i	− 1.00000i
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−28.5498	−1.80927
$250$	0	0
$251$	− 26.9906i	− 1.70363i	−0.523839	−	0.851817i	$-0.675501\pi$
$251$	− 26.9906i	− 1.70363i	0.523839	−	0.851817i	$-0.324499\pi$
$252$	0	0
$253$	−25.0997	−1.57800
$254$	0	0
$255$	0	0
$256$	0	0
$257$	21.6495	1.35046	0.675229	−	0.737608i	$-0.264045\pi$
$257$	21.6495	1.35046	0.675229	+	0.737608i	$0.264045\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	25.6495	1.58766
$262$	0	0
$263$	18.1578i	1.11966i	0.828609	+	0.559828i	$0.189133\pi$
$263$	18.1578i	1.11966i	−0.828609	+	0.559828i	$0.810867\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	− 5.97586i	− 0.365717i
$268$	0	0
$269$	17.6495	1.07611	0.538055	−	0.842910i	$-0.319159\pi$
$269$	17.6495	1.07611	0.538055	+	0.842910i	$0.319159\pi$
$270$	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
$275$	− 13.1342i	− 0.792025i
$276$	0	0
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	0	0
$279$	26.1534i	1.56576i
$280$	0	0
$281$	29.6495	1.76874	0.884371	−	0.466786i	$-0.154588\pi$
$281$	29.6495	1.76874	0.884371	+	0.466786i	$0.154588\pi$
$282$	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
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	15.4502	0.902608	0.451304	−	0.892370i	$-0.350959\pi$
$293$	15.4502	0.902608	0.451304	+	0.892370i	$0.350959\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	13.6495	0.792025
$298$	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
$307$	− 3.46410i	− 0.197707i	−0.995102	−	0.0988534i	$-0.968483\pi$
$307$	− 3.46410i	− 0.197707i	0.995102	−	0.0988534i	$-0.0315175\pi$
$308$	0	0
$309$	−18.0000	−1.02398
$310$	0	0
$311$	− 33.9189i	− 1.92336i	−0.274172	−	0.961681i	$-0.588404\pi$
$311$	− 33.9189i	− 1.92336i	0.274172	−	0.961681i	$-0.411596\pi$
$312$	0	0
$313$	15.0997	0.853484	0.426742	−	0.904373i	$-0.359661\pi$
$313$	15.0997	0.853484	0.426742	+	0.904373i	$0.359661\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	33.6495	1.88994	0.944972	−	0.327151i	$-0.106088\pi$
$317$	33.6495	1.88994	0.944972	+	0.327151i	$0.106088\pi$
$318$	0	0
$319$	22.4591i	1.25747i
$320$	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
$329$	0	0
$330$	0	0
$331$	10.3923i	0.571213i	0.958347	+	0.285606i	$0.0921950\pi$
$331$	10.3923i	0.571213i	−0.958347	+	0.285606i	$0.907805\pi$
$332$	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
$339$	35.5934i	1.93317i
$340$	0	0
$341$	−22.9003	−1.24012
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	− 30.3397i	− 1.62872i	−0.580361	−	0.814359i	$-0.697089\pi$
$347$	− 30.3397i	− 1.62872i	0.580361	−	0.814359i	$-0.302911\pi$
$348$	0	0
$349$	22.0000	1.17763	0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000	1.17763	0.588817	+	0.808267i	$0.299594\pi$
$350$	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
$359$	− 6.20604i	− 0.327542i	−0.986498	−	0.163771i	$-0.947634\pi$
$359$	− 6.20604i	− 0.327542i	0.986498	−	0.163771i	$-0.0523658\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	− 7.10083i	− 0.372697i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	37.6495	1.95995
$370$	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
$379$	− 17.3205i	− 0.889695i	−0.895606	−	0.444847i	$-0.853258\pi$
$379$	− 17.3205i	− 0.889695i	0.895606	−	0.444847i	$-0.146742\pi$
$380$	0	0
$381$	−15.0997	−0.773579
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	19.4502	0.981131
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−26.0000	−1.30490	−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000	−1.30490	−0.652451	+	0.757831i	$0.726259\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	5.64950	0.282123	0.141061	−	0.990001i	$-0.454949\pi$
$401$	5.64950	0.282123	0.141061	+	0.990001i	$0.454949\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	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
$419$	− 40.8471i	− 1.99551i	−0.0669762	−	0.997755i	$-0.521335\pi$
$419$	− 40.8471i	− 1.99551i	0.0669762	−	0.997755i	$-0.478665\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	− 12.9041i	− 0.627417i
$424$	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
$437$	41.6495	1.99237
$438$	0	0
$439$	− 38.1051i	− 1.81866i	−0.416078	−	0.909329i	$-0.636596\pi$
$439$	− 38.1051i	− 1.81866i	0.416078	−	0.909329i	$-0.363404\pi$
$440$	0	0
$441$	21.0000	1.00000
$442$	0	0
$443$	25.0860i	1.19187i	0.803033	+	0.595935i	$0.203218\pi$
$443$	25.0860i	1.19187i	−0.803033	+	0.595935i	$0.796782\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−36.5498	−1.72489	−0.862447	−	0.506148i	$-0.831069\pi$
$449$	−36.5498	−1.72489	−0.862447	+	0.506148i	$0.831069\pi$
$450$	0	0
$451$	32.9665i	1.55233i
$452$	0	0
$453$	30.0000	1.40952
$454$	0	0
$455$	0	0
$456$	0	0
$457$	15.0997	0.706333	0.353166	−	0.935561i	$-0.385105\pi$
$457$	15.0997	0.706333	0.353166	+	0.935561i	$0.385105\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	32.2443i	1.49209i	0.665895	+	0.746045i	$0.268050\pi$
$467$	32.2443i	1.49209i	−0.665895	+	0.746045i	$0.731950\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	26.1534i	1.20508i
$472$	0	0
$473$	0	0
$474$	0	0
$475$	21.7945i	1.00000i
$476$	0	0
$477$	1.64950	0.0755256
$478$	0	0
$479$	25.3161i	1.15672i	0.815780	+	0.578362i	$0.196308\pi$
$479$	25.3161i	1.15672i	−0.815780	+	0.578362i	$0.803692\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	− 43.5890i	− 1.97521i	−0.156973	−	0.987603i	$-0.550174\pi$
$487$	− 43.5890i	− 1.97521i	0.156973	−	0.987603i	$-0.449826\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0.722166i	0.0325909i	0.999867	+	0.0162954i	$0.00518723\pi$
$491$	0.722166i	0.0325909i	−0.999867	+	0.0162954i	$0.994813\pi$
$492$	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
$503$	39.1725i	1.74662i	0.487167	+	0.873309i	$0.338030\pi$
$503$	39.1725i	1.74662i	−0.487167	+	0.873309i	$0.661970\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	− 22.5167i	− 1.00000i
$508$	0	0
$509$	23.4502	1.03941	0.519705	−	0.854346i	$-0.326042\pi$
$509$	23.4502	1.03941	0.519705	+	0.854346i	$0.326042\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−22.6495	−1.00000
$514$	0	0
$515$	0	0
$516$	0	0
$517$	11.2990	0.496930
$518$	0	0
$519$	42.5216i	1.86649i
$520$	0	0
$521$	45.6495	1.99994	0.999971	−	0.00767777i	$-0.00244393\pi$
$521$	45.6495	1.99994	0.999971	+	0.00767777i	$0.00244393\pi$
$522$	0	0
$523$	43.5890i	1.90601i	0.302949	+	0.953007i	$0.402029\pi$
$523$	43.5890i	1.90601i	−0.302949	+	0.953007i	$0.597971\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−68.2990	−2.96952
$530$	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
$539$	18.3879i	0.792025i
$540$	0	0
$541$	−15.0997	−0.649185	−0.324593	−	0.945854i	$-0.605227\pi$
$541$	−15.0997	−0.649185	−0.324593	+	0.945854i	$0.605227\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 31.1769i	− 1.33303i	−0.745492	−	0.666514i	$-0.767786\pi$
$547$	− 31.1769i	− 1.33303i	0.745492	−	0.666514i	$-0.232214\pi$
$548$	0	0
$549$	45.2990	1.93331
$550$	0	0
$551$	− 37.2679i	− 1.58766i
$552$	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
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−2.35050	−0.0985379	−0.0492690	−	0.998786i	$-0.515689\pi$
$569$	−2.35050	−0.0985379	−0.0492690	+	0.998786i	$0.515689\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	−40.5498	−1.69399
$574$	0	0
$575$	− 47.7753i	− 1.99237i
$576$	0	0
$577$	−45.2990	−1.88582	−0.942911	−	0.333044i	$-0.891924\pi$
$577$	−45.2990	−1.88582	−0.942911	+	0.333044i	$0.891924\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1.44433i	0.0598181i
$584$	0	0
$585$	0	0
$586$	0	0
$587$	46.1007i	1.90278i	0.307986	+	0.951391i	$0.400345\pi$
$587$	46.1007i	1.90278i	−0.307986	+	0.951391i	$0.599655\pi$
$588$	0	0
$589$	38.0000	1.56576
$590$	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
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	− 26.1534i	− 1.06505i
$604$	0	0
$605$	0	0
$606$	0	0
$607$	− 8.71780i	− 0.353845i	−0.984225	−	0.176922i	$-0.943386\pi$
$607$	− 8.71780i	− 0.353845i	0.984225	−	0.176922i	$-0.0566141\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	45.2990	1.82961	0.914805	−	0.403896i	$-0.132344\pi$
$613$	45.2990	1.82961	0.914805	+	0.403896i	$0.132344\pi$
$614$	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
$621$	49.6495	1.99237
$622$	0	0
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	− 19.8323i	− 0.792025i
$628$	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
$633$	15.0997	0.600158
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	27.4502	1.08422	0.542108	−	0.840309i	$-0.317626\pi$
$641$	27.4502	1.08422	0.542108	+	0.840309i	$0.317626\pi$
$642$	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
$647$	11.4597i	0.450529i	0.974298	+	0.225264i	$0.0723246\pi$
$647$	11.4597i	0.450529i	−0.974298	+	0.225264i	$0.927675\pi$
$648$	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
$657$	−45.2990	−1.76728
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	81.6941i	3.16321i
$668$	0	0
$669$	−42.0000	−1.62381
$670$	0	0
$671$	39.6645i	1.53123i
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	25.9808i	1.00000i
$676$	0	0
$677$	−6.35050	−0.244069	−0.122035	−	0.992526i	$-0.538942\pi$
$677$	−6.35050	−0.244069	−0.122035	+	0.992526i	$0.538942\pi$
$678$	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
$687$	3.46410i	0.132164i
$688$	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
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	45.2990	1.70124	0.850620	−	0.525781i	$-0.176227\pi$
$709$	45.2990	1.70124	0.850620	+	0.525781i	$0.176227\pi$
$710$	0	0
$711$	− 10.3923i	− 0.389742i
$712$	0	0
$713$	−83.2990	−3.11957
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−34.7492	−1.29773
$718$	0	0
$719$	53.0290i	1.97765i	0.149093	+	0.988823i	$0.452364\pi$
$719$	53.0290i	1.97765i	−0.149093	+	0.988823i	$0.547636\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−42.7492	−1.58766
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−15.0997	−0.557719	−0.278859	−	0.960332i	$-0.589956\pi$
$733$	−15.0997	−0.557719	−0.278859	+	0.960332i	$0.589956\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	22.9003	0.843545
$738$	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
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	49.4498i	1.80927i
$748$	0	0
$749$	0	0
$750$	0	0
$751$	− 51.9615i	− 1.89610i	−0.318117	−	0.948051i	$-0.603050\pi$
$751$	− 51.9615i	− 1.89610i	0.318117	−	0.948051i	$-0.396950\pi$
$752$	0	0
$753$	−46.7492	−1.70363
$754$	0	0
$755$	0	0
$756$	0	0
$757$	46.0000	1.67190	0.835949	−	0.548807i	$-0.184918\pi$
$757$	46.0000	1.67190	0.835949	+	0.548807i	$0.184918\pi$
$758$	0	0
$759$	43.4739i	1.57800i
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−45.2990	−1.63352	−0.816762	−	0.576975i	$-0.804233\pi$
$769$	−45.2990	−1.63352	−0.816762	+	0.576975i	$0.804233\pi$
$770$	0	0
$771$	− 37.4980i	− 1.35046i
$772$	0	0
$773$	−26.7492	−0.962101	−0.481050	−	0.876693i	$-0.659745\pi$
$773$	−26.7492	−0.962101	−0.481050	+	0.876693i	$0.659745\pi$
$774$	0	0
$775$	− 43.5890i	− 1.56576i
$776$	0	0
$777$	0	0
$778$	0	0
$779$	− 54.7035i	− 1.95995i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	− 44.4262i	− 1.58766i
$784$	0	0
$785$	0	0
$786$	0	0
$787$	8.71780i	0.310756i	0.987855	+	0.155378i	$0.0496595\pi$
$787$	8.71780i	0.310756i	−0.987855	+	0.155378i	$0.950340\pi$
$788$	0	0
$789$	31.4502	1.11966
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−50.7492	−1.79763	−0.898814	−	0.438330i	$-0.855570\pi$
$797$	−50.7492	−1.79763	−0.898814	+	0.438330i	$0.855570\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−10.3505	−0.365717
$802$	0	0
$803$	− 39.6645i	− 1.39973i
$804$	0	0
$805$	0	0
$806$	0	0
$807$	− 30.5698i	− 1.07611i
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	− 45.0333i	− 1.58133i	−0.612247	−	0.790667i	$-0.709734\pi$
$811$	− 45.0333i	− 1.58133i	0.612247	−	0.790667i	$-0.290266\pi$
$812$	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
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	−22.7492	−0.792025
$826$	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
$831$	− 24.2487i	− 0.841178i
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	45.2990	1.56576
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	44.0997	1.52068
$842$	0	0
$843$	− 51.3544i	− 1.76874i
$844$	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
$853$	−50.0000	−1.71197	−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000	−1.71197	−0.855984	+	0.517003i	$0.827048\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−54.7492	−1.87020	−0.935098	−	0.354389i	$-0.884689\pi$
$857$	−54.7492	−1.87020	−0.935098	+	0.354389i	$0.884689\pi$
$858$	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
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 29.4449i	− 1.00000i
$868$	0	0
$869$	9.09967	0.308685
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	− 26.7605i	− 0.902608i
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	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
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	− 23.6416i	− 0.792025i
$892$	0	0
$893$	−18.7492	−0.627417
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	74.5357i	2.48591i
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	43.5890i	1.44735i	0.690142	+	0.723674i	$0.257548\pi$
$907$	43.5890i	1.44735i	−0.690142	+	0.723674i	$0.742452\pi$
$908$	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
$913$	−43.2990	−1.43299
$914$	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
$921$	−6.00000	−0.197707
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	31.1769i	1.02398i
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	− 30.5123i	− 1.00000i
$932$	0	0
$933$	−58.7492	−1.92336
$934$	0	0
$935$	0	0
$936$	0	0
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	0	0
$939$	− 26.1534i	− 0.853484i
$940$	0	0
$941$	−14.3505	−0.467813	−0.233906	−	0.972259i	$-0.575151\pi$
$941$	−14.3505	−0.467813	−0.233906	+	0.972259i	$0.575151\pi$
$942$	0	0
$943$	119.914i	3.90495i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	38.9424i	1.26546i	0.774374	+	0.632729i	$0.218065\pi$
$947$	38.9424i	1.26546i	−0.774374	+	0.632729i	$0.781935\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	− 58.2826i	− 1.88994i
$952$	0	0
$953$	35.4502	1.14834	0.574172	−	0.818735i	$-0.305324\pi$
$953$	35.4502	1.14834	0.574172	+	0.818735i	$0.305324\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	38.9003	1.25747
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−45.0000	−1.45161
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	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
$977$	−14.7492	−0.471868	−0.235934	−	0.971769i	$-0.575815\pi$
$977$	−14.7492	−0.471868	−0.235934	+	0.971769i	$0.575815\pi$
$978$	0	0
$979$	− 9.06306i	− 0.289657i
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	− 8.71780i	− 0.276930i	−0.990367	−	0.138465i	$-0.955783\pi$
$991$	− 8.71780i	− 0.276930i	0.990367	−	0.138465i	$-0.0442168\pi$
$992$	0	0
$993$	18.0000	0.571213
$994$	0	0
$995$	0	0
$996$	0	0
$997$	45.2990	1.43463	0.717317	−	0.696747i	$-0.245370\pi$
$997$	45.2990	1.43463	0.717317	+	0.696747i	$0.245370\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.f.b.1025.1	✓	4
3.2	odd	2		1824.2.f.c.1025.2	yes	4
4.3	odd	2	inner	1824.2.f.b.1025.4	yes	4
12.11	even	2		1824.2.f.c.1025.3	yes	4
19.18	odd	2		1824.2.f.c.1025.3	yes	4
57.56	even	2	inner	1824.2.f.b.1025.4	yes	4
76.75	even	2		1824.2.f.c.1025.2	yes	4
228.227	odd	2	CM	1824.2.f.b.1025.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.f.b.1025.1	✓	4	1.1	even	1	trivial
1824.2.f.b.1025.1	✓	4	228.227	odd	2	CM
1824.2.f.b.1025.4	yes	4	4.3	odd	2	inner
1824.2.f.b.1025.4	yes	4	57.56	even	2	inner
1824.2.f.c.1025.2	yes	4	3.2	odd	2
1824.2.f.c.1025.2	yes	4	76.75	even	2
1824.2.f.c.1025.3	yes	4	12.11	even	2
1824.2.f.c.1025.3	yes	4	19.18	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} -3.00000 q^{9} -2.62685i q^{11} +4.35890i q^{19} -9.55505i q^{23} +5.00000 q^{25} +5.19615i q^{27} -8.54983 q^{29} -8.71780i q^{31} -4.54983 q^{33} -12.5498 q^{41} +4.30136i q^{47} -7.00000 q^{49} -0.549834 q^{53} +7.54983 q^{57} -15.0997 q^{61} +8.71780i q^{67} -16.5498 q^{69} +15.0997 q^{73} -8.66025i q^{75} +3.46410i q^{79} +9.00000 q^{81} -16.4833i q^{83} +14.8087i q^{87} +3.45017 q^{89} -15.0997 q^{93} +7.88054i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{9} + 20 q^{25} - 4 q^{29} + 12 q^{33} - 20 q^{41} - 28 q^{49} + 28 q^{53} - 36 q^{69} + 36 q^{81} + 44 q^{89}+O(q^{100}) \) 4 * q - 12 * q^9 + 20 * q^25 - 4 * q^29 + 12 * q^33 - 20 * q^41 - 28 * q^49 + 28 * q^53 - 36 * q^69 + 36 * q^81 + 44 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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