LMFDB - Embedded newform 1840.2.m.c.1839.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1840,2,Mod(1839,1840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1840.1839"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1840 = 2^{4} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1840.m (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$14.6924739719$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 9 $ x^4 - 4*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1839.3
Root			$1.58114 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1840.1839
Dual form			1840.2.m.c.1839.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+3.16228 q^{3} -2.23607i q^{5} -4.24264i q^{7} +7.00000 q^{9} -7.07107i q^{15} -13.4164i q^{21} +(-4.74342 + 0.707107i) q^{23} -5.00000 q^{25} +12.6491 q^{27} -6.00000 q^{29} -9.48683 q^{35} +12.0000 q^{41} +12.7279i q^{43} -15.6525i q^{45} +9.48683 q^{47} -11.0000 q^{49} +13.4164i q^{61} -29.6985i q^{63} -4.24264i q^{67} +(-15.0000 + 2.23607i) q^{69} -15.8114 q^{75} +19.0000 q^{81} -15.5563i q^{83} -18.9737 q^{87} +17.8885i q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 28 q^{9} - 20 q^{25} - 24 q^{29} + 48 q^{41} - 44 q^{49} - 60 q^{69} + 76 q^{81}+O(q^{100}) $ 4 * q + 28 * q^9 - 20 * q^25 - 24 * q^29 + 48 * q^41 - 44 * q^49 - 60 * q^69 + 76 * q^81

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times$.

$n$	$737$	$1151$	$1201$	$1381$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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
$3$	3.16228			1.82574			0.912871	−	0.408248i	$-0.133860\pi$
$3$	3.16228			1.82574			0.912871	+	0.408248i	$0.133860\pi$
$4$		0			0
$5$		−	2.23607i		−	1.00000i
$5$		−	2.23607i		−	1.00000i
$6$		0			0
$7$		−	4.24264i		−	1.60357i	−0.597614	−	0.801784i	$-0.703885\pi$
$7$		−	4.24264i		−	1.60357i	0.597614	−	0.801784i	$-0.296115\pi$
$8$		0			0
$9$	7.00000			2.33333
$10$		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
$15$		−	7.07107i		−	1.82574i
$16$		0			0
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		0			0
$21$		−	13.4164i		−	2.92770i
$22$		0			0
$23$	−4.74342	+	0.707107i	−0.989071	+	0.147442i
$23$	−4.74342	+	0.707107i	−0.989071	+	0.147442i
$24$		0			0
$25$	−5.00000			−1.00000
$26$		0			0
$27$	12.6491			2.43432
$28$		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		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9.48683			−1.60357
$36$		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
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$		0			0
$43$			12.7279i			1.94099i	0.241121	+	0.970495i	$0.422485\pi$
$43$			12.7279i			1.94099i	−0.241121	+	0.970495i	$0.577515\pi$
$44$		0			0
$45$		−	15.6525i		−	2.33333i
$46$		0			0
$47$	9.48683			1.38380			0.691898	−	0.721995i	$-0.256775\pi$
$47$	9.48683			1.38380			0.691898	+	0.721995i	$0.256775\pi$
$48$		0			0
$49$	−11.0000			−1.57143
$50$		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
$61$			13.4164i			1.71780i	0.512148	+	0.858898i	$0.328850\pi$
$61$			13.4164i			1.71780i	−0.512148	+	0.858898i	$0.671150\pi$
$62$		0			0
$63$		−	29.6985i		−	3.74166i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	4.24264i		−	0.518321i	−0.965834	−	0.259161i	$-0.916554\pi$
$67$		−	4.24264i		−	0.518321i	0.965834	−	0.259161i	$-0.0834459\pi$
$68$		0			0
$69$	−15.0000	+	2.23607i	−1.80579	+	0.269191i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−15.8114			−1.82574
$76$		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
$81$	19.0000			2.11111
$82$		0			0
$83$		−	15.5563i		−	1.70753i	−0.520658	−	0.853766i	$-0.674313\pi$
$83$		−	15.5563i		−	1.70753i	0.520658	−	0.853766i	$-0.325687\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−18.9737			−2.03419
$88$		0			0
$89$			17.8885i			1.89618i	0.317999	+	0.948091i	$0.396989\pi$
$89$			17.8885i			1.89618i	−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		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
$103$		−	12.7279i		−	1.25412i	−0.778971	−	0.627060i	$-0.784258\pi$
$103$		−	12.7279i		−	1.25412i	0.778971	−	0.627060i	$-0.215742\pi$
$104$		0			0
$105$	−30.0000			−2.92770
$106$		0			0
$107$		−	18.3848i		−	1.77732i	−0.458563	−	0.888662i	$-0.651636\pi$
$107$		−	18.3848i		−	1.77732i	0.458563	−	0.888662i	$-0.348364\pi$
$108$		0			0
$109$		−	13.4164i		−	1.28506i	−0.766261	−	0.642529i	$-0.777885\pi$
$109$		−	13.4164i		−	1.28506i	0.766261	−	0.642529i	$-0.222115\pi$
$110$		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
$115$	1.58114	+	10.6066i	0.147442	+	0.989071i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−11.0000			−1.00000
$122$		0			0
$123$	37.9473			3.42160
$124$		0			0
$125$			11.1803i			1.00000i
$126$		0			0
$127$	22.1359			1.96425			0.982124	−	0.188237i	$-0.0602772\pi$
$127$	22.1359			1.96425			0.982124	+	0.188237i	$0.0602772\pi$
$128$		0			0
$129$			40.2492i			3.54375i
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		−	28.2843i		−	2.43432i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$	30.0000			2.52646
$142$		0			0
$143$		0			0
$144$		0			0
$145$			13.4164i			1.11417i
$146$		0			0
$147$	−34.7851			−2.86902
$148$		0			0
$149$			4.47214i			0.366372i	0.983078	+	0.183186i	$0.0586410\pi$
$149$			4.47214i			0.366372i	−0.983078	+	0.183186i	$0.941359\pi$
$150$		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
$161$	3.00000	+	20.1246i	0.236433	+	1.58604i
$162$		0			0
$163$	22.1359			1.73382			0.866910	−	0.498464i	$-0.166102\pi$
$163$	22.1359			1.73382			0.866910	+	0.498464i	$0.166102\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.48683			−0.734113			−0.367057	−	0.930199i	$-0.619634\pi$
$167$	−9.48683			−0.734113			−0.367057	+	0.930199i	$0.619634\pi$
$168$		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
$175$			21.2132i			1.60357i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$			26.8328i			1.99447i	0.0743294	+	0.997234i	$0.476318\pi$
$181$			26.8328i			1.99447i	−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$			42.4264i			3.13625i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		−	53.6656i		−	3.90360i
$190$		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
$201$		−	13.4164i		−	0.946320i
$202$		0			0
$203$			25.4558i			1.78665i
$204$		0			0
$205$		−	26.8328i		−	1.87409i
$206$		0			0
$207$	−33.2039	+	4.94975i	−2.30783	+	0.344031i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	28.4605			1.94099
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	3.16228			0.211762			0.105881	−	0.994379i	$-0.466234\pi$
$223$	3.16228			0.211762			0.105881	+	0.994379i	$0.466234\pi$
$224$		0			0
$225$	−35.0000			−2.33333
$226$		0			0
$227$		−	9.89949i		−	0.657053i	−0.944495	−	0.328526i	$-0.893448\pi$
$227$		−	9.89949i		−	0.657053i	0.944495	−	0.328526i	$-0.106552\pi$
$228$		0			0
$229$			26.8328i			1.77316i	0.462573	+	0.886581i	$0.346926\pi$
$229$			26.8328i			1.77316i	−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		−	21.2132i		−	1.38380i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$			13.4164i			0.864227i	0.901819	+	0.432113i	$0.142232\pi$
$241$			13.4164i			0.864227i	−0.901819	+	0.432113i	$0.857768\pi$
$242$		0			0
$243$	22.1359			1.42002
$244$		0			0
$245$			24.5967i			1.57143i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		−	49.1935i		−	3.11751i
$250$		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
$261$	−42.0000			−2.59973
$262$		0			0
$263$		−	15.5563i		−	0.959246i	−0.877475	−	0.479623i	$-0.840774\pi$
$263$		−	15.5563i		−	0.959246i	0.877475	−	0.479623i	$-0.159226\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			56.5685i			3.46194i
$268$		0			0
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		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
$281$		−	31.3050i		−	1.86750i	−0.357930	−	0.933748i	$-0.616517\pi$
$281$		−	31.3050i		−	1.86750i	0.357930	−	0.933748i	$-0.383483\pi$
$282$		0			0
$283$			29.6985i			1.76539i	0.469945	+	0.882696i	$0.344274\pi$
$283$			29.6985i			1.76539i	−0.469945	+	0.882696i	$0.655726\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	50.9117i		−	3.00522i
$288$		0			0
$289$	−17.0000			−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
$301$	54.0000			3.11251
$302$		0			0
$303$	56.9210			3.27003
$304$		0			0
$305$	30.0000			1.71780
$306$		0			0
$307$	−34.7851			−1.98529			−0.992644	−	0.121070i	$-0.961367\pi$
$307$	−34.7851			−1.98529			−0.992644	+	0.121070i	$0.961367\pi$
$308$		0			0
$309$		−	40.2492i		−	2.28970i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$	−66.4078			−3.74166
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		−	58.1378i		−	3.24493i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	42.4264i		−	2.34619i
$328$		0			0
$329$		−	40.2492i		−	2.21901i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.48683			−0.518321
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$			16.9706i			0.916324i
$344$		0			0
$345$	5.00000	+	33.5410i	0.269191	+	1.80579i
$346$		0			0
$347$	−28.4605			−1.52784			−0.763920	−	0.645311i	$-0.776728\pi$
$347$	−28.4605			−1.52784			−0.763920	+	0.645311i	$0.776728\pi$
$348$		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
$363$	−34.7851			−1.82574
$364$		0			0
$365$		0			0
$366$		0			0
$367$			38.1838i			1.99318i	0.0825348	+	0.996588i	$0.473698\pi$
$367$			38.1838i			1.99318i	−0.0825348	+	0.996588i	$0.526302\pi$
$368$		0			0
$369$	84.0000			4.37287
$370$		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
$375$			35.3553i			1.82574i
$376$		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
$381$	70.0000			3.58621
$382$		0			0
$383$		−	26.8701i		−	1.37300i	−0.727132	−	0.686498i	$-0.759147\pi$
$383$		−	26.8701i		−	1.37300i	0.727132	−	0.686498i	$-0.240853\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			89.0955i			4.52898i
$388$		0			0
$389$			31.3050i			1.58722i	0.608424	+	0.793612i	$0.291802\pi$
$389$			31.3050i			1.58722i	−0.608424	+	0.793612i	$0.708198\pi$
$390$		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
$401$			35.7771i			1.78662i	0.449439	+	0.893311i	$0.351624\pi$
$401$			35.7771i			1.78662i	−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		−	42.4853i		−	2.11111i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	4.00000			0.197787			0.0988936	−	0.995098i	$-0.468470\pi$
$409$	4.00000			0.197787			0.0988936	+	0.995098i	$0.468470\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−34.7851			−1.70753
$416$		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
$421$			40.2492i			1.96163i	0.194948	+	0.980814i	$0.437546\pi$
$421$			40.2492i			1.96163i	−0.194948	+	0.980814i	$0.562454\pi$
$422$		0			0
$423$	66.4078			3.22886
$424$		0			0
$425$		0			0
$426$		0			0
$427$	56.9210			2.75460
$428$		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			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$			42.4264i			2.03419i
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	−77.0000			−3.66667
$442$		0			0
$443$	9.48683			0.450733			0.225367	−	0.974274i	$-0.427642\pi$
$443$	9.48683			0.450733			0.225367	+	0.974274i	$0.427642\pi$
$444$		0			0
$445$	40.0000			1.89618
$446$		0			0
$447$			14.1421i			0.668900i
$448$		0			0
$449$	−36.0000			−1.69895			−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000			−1.69895			−0.849473	+	0.527633i	$0.823080\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$		0			0
$463$	−41.1096			−1.91053			−0.955263	−	0.295758i	$-0.904428\pi$
$463$	−41.1096			−1.91053			−0.955263	+	0.295758i	$0.904428\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			32.5269i			1.50517i	0.658497	+	0.752583i	$0.271192\pi$
$467$			32.5269i			1.50517i	−0.658497	+	0.752583i	$0.728808\pi$
$468$		0			0
$469$	−18.0000			−0.831163
$470$		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
$483$	9.48683	+	63.6396i	0.431666	+	2.89570i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−22.1359			−1.00308			−0.501538	−	0.865136i	$-0.667232\pi$
$487$	−22.1359			−1.00308			−0.501538	+	0.865136i	$0.667232\pi$
$488$		0			0
$489$	70.0000			3.16551
$490$		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
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	−30.0000			−1.34030
$502$		0			0
$503$		−	43.8406i		−	1.95476i	−0.211498	−	0.977378i	$-0.567834\pi$
$503$		−	43.8406i		−	1.95476i	0.211498	−	0.977378i	$-0.432166\pi$
$504$		0			0
$505$		−	40.2492i		−	1.79107i
$506$		0			0
$507$	41.1096			1.82574
$508$		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
$515$	−28.4605			−1.25412
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	17.8885i		−	0.783711i	−0.920027	−	0.391856i	$-0.871833\pi$
$521$		−	17.8885i		−	0.783711i	0.920027	−	0.391856i	$-0.128167\pi$
$522$		0			0
$523$		−	29.6985i		−	1.29862i	−0.760522	−	0.649312i	$-0.775057\pi$
$523$		−	29.6985i		−	1.29862i	0.760522	−	0.649312i	$-0.224943\pi$
$524$		0			0
$525$			67.0820i			2.92770i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	22.0000	−	6.70820i	0.956522	−	0.291661i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−41.1096			−1.77732
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$		0			0
$543$			84.8528i			3.64138i
$544$		0			0
$545$	−30.0000			−1.28506
$546$		0			0
$547$	3.16228			0.135209			0.0676046	−	0.997712i	$-0.478464\pi$
$547$	3.16228			0.135209			0.0676046	+	0.997712i	$0.478464\pi$
$548$		0			0
$549$			93.9149i			4.00819i
$550$		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
$563$			1.41421i			0.0596020i	0.999556	+	0.0298010i	$0.00948736\pi$
$563$			1.41421i			0.0596020i	−0.999556	+	0.0298010i	$0.990513\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	80.6102i		−	3.38531i
$568$		0			0
$569$			31.3050i			1.31237i	0.754599	+	0.656186i	$0.227831\pi$
$569$			31.3050i			1.31237i	−0.754599	+	0.656186i	$0.772169\pi$
$570$		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
$575$	23.7171	−	3.53553i	0.989071	−	0.147442i
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−66.0000			−2.73814
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	47.4342			1.95782			0.978909	−	0.204298i	$-0.0654911\pi$
$587$	47.4342			1.95782			0.978909	+	0.204298i	$0.0654911\pi$
$588$		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		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	28.0000			1.14214			0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000			1.14214			0.571072	+	0.820900i	$0.306528\pi$
$602$		0			0
$603$		−	29.6985i		−	1.20942i
$604$		0			0
$605$			24.5967i			1.00000i
$606$		0			0
$607$	15.8114			0.641764			0.320882	−	0.947119i	$-0.396021\pi$
$607$	15.8114			0.641764			0.320882	+	0.947119i	$0.396021\pi$
$608$		0			0
$609$			80.4984i			3.26196i
$610$		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
$615$		−	84.8528i		−	3.42160i
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$	−60.0000	+	8.94427i	−2.40772	+	0.358921i
$622$		0			0
$623$	75.8947			3.04066
$624$		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
$635$		−	49.4975i		−	1.96425i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	49.1935i		−	1.94303i	−0.236986	−	0.971513i	$-0.576159\pi$
$641$		−	49.1935i		−	1.94303i	0.236986	−	0.971513i	$-0.423841\pi$
$642$		0			0
$643$			29.6985i			1.17119i	0.810602	+	0.585597i	$0.199140\pi$
$643$			29.6985i			1.17119i	−0.810602	+	0.585597i	$0.800860\pi$
$644$		0			0
$645$	90.0000			3.54375
$646$		0			0
$647$	−47.4342			−1.86483			−0.932415	−	0.361390i	$-0.882302\pi$
$647$	−47.4342			−1.86483			−0.932415	+	0.361390i	$0.882302\pi$
$648$		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
$661$			40.2492i			1.56551i	0.622328	+	0.782757i	$0.286187\pi$
$661$			40.2492i			1.56551i	−0.622328	+	0.782757i	$0.713813\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	28.4605	−	4.24264i	1.10199	−	0.164276i
$668$		0			0
$669$	10.0000			0.386622
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$	−63.2456			−2.43432
$676$		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
$681$		−	31.3050i		−	1.19961i
$682$		0			0
$683$	28.4605			1.08901			0.544505	−	0.838757i	$-0.316717\pi$
$683$	28.4605			1.08901			0.544505	+	0.838757i	$0.316717\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			84.8528i			3.23734i
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		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
$701$		−	22.3607i		−	0.844551i	−0.906467	−	0.422276i	$-0.861231\pi$
$701$		−	22.3607i		−	0.844551i	0.906467	−	0.422276i	$-0.138769\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		−	67.0820i		−	2.52646i
$706$		0			0
$707$		−	76.3675i		−	2.87210i
$708$		0			0
$709$			26.8328i			1.00773i	0.863783	+	0.503864i	$0.168089\pi$
$709$			26.8328i			1.00773i	−0.863783	+	0.503864i	$0.831911\pi$
$710$		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
$721$	−54.0000			−2.01107
$722$		0			0
$723$			42.4264i			1.57786i
$724$		0			0
$725$	30.0000			1.11417
$726$		0			0
$727$			4.24264i			0.157351i	0.996900	+	0.0786754i	$0.0250691\pi$
$727$			4.24264i			0.157351i	−0.996900	+	0.0786754i	$0.974931\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$		0			0
$735$			77.7817i			2.86902i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	26.8701i		−	0.985767i	−0.870095	−	0.492883i	$-0.835943\pi$
$743$		−	26.8701i		−	0.985767i	0.870095	−	0.492883i	$-0.164057\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$		0			0
$747$		−	108.894i		−	3.98424i
$748$		0			0
$749$	−78.0000			−2.85006
$750$		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			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	42.0000			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$762$		0			0
$763$	−56.9210			−2.06068
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	53.6656i		−	1.93523i	−0.252426	−	0.967616i	$-0.581229\pi$
$769$		−	53.6656i		−	1.93523i	0.252426	−	0.967616i	$-0.418771\pi$
$770$		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
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−75.8947			−2.71225
$784$		0			0
$785$		0			0
$786$		0			0
$787$			38.1838i			1.36110i	0.732700	+	0.680552i	$0.238260\pi$
$787$			38.1838i			1.36110i	−0.732700	+	0.680552i	$0.761740\pi$
$788$		0			0
$789$		−	49.1935i		−	1.75133i
$790$		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
$801$			125.220i			4.42442i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	45.0000	−	6.70820i	1.58604	−	0.236433i
$806$		0			0
$807$	−75.8947			−2.67162
$808$		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		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	49.4975i		−	1.73382i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	48.0000			1.67521			0.837606	−	0.546275i	$-0.183955\pi$
$821$	48.0000			1.67521			0.837606	+	0.546275i	$0.183955\pi$
$822$		0			0
$823$	15.8114			0.551150			0.275575	−	0.961280i	$-0.411132\pi$
$823$	15.8114			0.551150			0.275575	+	0.961280i	$0.411132\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			32.5269i			1.13107i	0.824724	+	0.565536i	$0.191331\pi$
$827$			32.5269i			1.13107i	−0.824724	+	0.565536i	$0.808669\pi$
$828$		0			0
$829$	−56.0000			−1.94496			−0.972480	−	0.232986i	$-0.925151\pi$
$829$	−56.0000			−1.94496			−0.972480	+	0.232986i	$0.925151\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$			21.2132i			0.734113i
$836$		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
$843$		−	98.9949i		−	3.40957i
$844$		0			0
$845$		−	29.0689i		−	1.00000i
$846$		0			0
$847$			46.6690i			1.60357i
$848$		0			0
$849$			93.9149i			3.22315i
$850$		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		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		−	160.997i		−	5.48676i
$862$		0			0
$863$	9.48683			0.322936			0.161468	−	0.986878i	$-0.448377\pi$
$863$	9.48683			0.322936			0.161468	+	0.986878i	$0.448377\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−53.7587			−1.82574
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	47.4342			1.60357
$876$		0			0
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	58.1378i		−	1.95871i	−0.202145	−	0.979356i	$-0.564791\pi$
$881$		−	58.1378i		−	1.95871i	0.202145	−	0.979356i	$-0.435209\pi$
$882$		0			0
$883$	22.1359			0.744934			0.372467	−	0.928045i	$-0.378512\pi$
$883$	22.1359			0.744934			0.372467	+	0.928045i	$0.378512\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−28.4605			−0.955610			−0.477805	−	0.878466i	$-0.658567\pi$
$887$	−28.4605			−0.955610			−0.477805	+	0.878466i	$0.658567\pi$
$888$		0			0
$889$		−	93.9149i		−	3.14980i
$890$		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
$903$	170.763			5.68264
$904$		0			0
$905$	60.0000			1.99447
$906$		0			0
$907$			4.24264i			0.140875i	0.997516	+	0.0704373i	$0.0224395\pi$
$907$			4.24264i			0.140875i	−0.997516	+	0.0704373i	$0.977561\pi$
$908$		0			0
$909$	126.000			4.17916
$910$		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
$915$	94.8683			3.13625
$916$		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
$921$	−110.000			−3.62462
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	89.0955i		−	2.92628i
$928$		0			0
$929$	36.0000			1.18112			0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000			1.18112			0.590561	+	0.806993i	$0.298907\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			44.7214i			1.45787i	0.684580	+	0.728937i	$0.259985\pi$
$941$			44.7214i			1.45787i	−0.684580	+	0.728937i	$0.740015\pi$
$942$		0			0
$943$	−56.9210	+	8.48528i	−1.85360	+	0.276319i
$944$		0			0
$945$	−120.000			−3.90360
$946$		0			0
$947$	−9.48683			−0.308281			−0.154140	−	0.988049i	$-0.549261\pi$
$947$	−9.48683			−0.308281			−0.154140	+	0.988049i	$0.549261\pi$
$948$		0			0
$949$		0			0
$950$		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
$961$	31.0000			1.00000
$962$		0			0
$963$		−	128.693i		−	4.14709i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−41.1096			−1.32200			−0.660998	−	0.750388i	$-0.729867\pi$
$967$	−41.1096			−1.32200			−0.660998	+	0.750388i	$0.729867\pi$
$968$		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			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		−	93.9149i		−	2.99847i
$982$		0			0
$983$		−	41.0122i		−	1.30809i	−0.756457	−	0.654043i	$-0.773072\pi$
$983$		−	41.0122i		−	1.30809i	0.756457	−	0.654043i	$-0.226928\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	127.279i		−	4.05134i
$988$		0			0
$989$	−9.00000	−	60.3738i	−0.286183	−	1.91978i
$990$		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		1.00000			$0$
$997$		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	1840.2.m.c.1839.3	yes	4
4.3	odd	2	inner	1840.2.m.c.1839.1	✓	4
5.4	even	2	inner	1840.2.m.c.1839.1	✓	4
20.19	odd	2	CM	1840.2.m.c.1839.3	yes	4
23.22	odd	2	inner	1840.2.m.c.1839.4	yes	4
92.91	even	2	inner	1840.2.m.c.1839.2	yes	4
115.114	odd	2	inner	1840.2.m.c.1839.2	yes	4
460.459	even	2	inner	1840.2.m.c.1839.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1840.2.m.c.1839.1	✓	4	4.3	odd	2	inner
1840.2.m.c.1839.1	✓	4	5.4	even	2	inner
1840.2.m.c.1839.2	yes	4	92.91	even	2	inner
1840.2.m.c.1839.2	yes	4	115.114	odd	2	inner
1840.2.m.c.1839.3	yes	4	1.1	even	1	trivial
1840.2.m.c.1839.3	yes	4	20.19	odd	2	CM
1840.2.m.c.1839.4	yes	4	23.22	odd	2	inner
1840.2.m.c.1839.4	yes	4	460.459	even	2	inner

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:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.16228 q^{3} -2.23607i q^{5} -4.24264i q^{7} +7.00000 q^{9} -7.07107i q^{15} -13.4164i q^{21} +(-4.74342 + 0.707107i) q^{23} -5.00000 q^{25} +12.6491 q^{27} -6.00000 q^{29} -9.48683 q^{35} +12.0000 q^{41} +12.7279i q^{43} -15.6525i q^{45} +9.48683 q^{47} -11.0000 q^{49} +13.4164i q^{61} -29.6985i q^{63} -4.24264i q^{67} +(-15.0000 + 2.23607i) q^{69} -15.8114 q^{75} +19.0000 q^{81} -15.5563i q^{83} -18.9737 q^{87} +17.8885i q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 28 q^{9} - 20 q^{25} - 24 q^{29} + 48 q^{41} - 44 q^{49} - 60 q^{69} + 76 q^{81}+O(q^{100}) \) 4 * q + 28 * q^9 - 20 * q^25 - 24 * q^29 + 48 * q^41 - 44 * q^49 - 60 * q^69 + 76 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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