LMFDB - Embedded newform 832.4.e.a.545.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,4,Mod(545,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("832.545");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	832.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$49.0895891248$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			545.2
Root			$2.30278i$ of defining polynomial
Character	$\chi$	$=$	832.545
Dual form			832.4.e.a.545.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{3} +21.6333 q^{5} +36.0555i q^{7} +23.0000 q^{9} -46.8722 q^{13} -43.2666i q^{15} +114.000 q^{17} +72.1110 q^{21} +343.000 q^{25} -100.000i q^{27} +295.655i q^{31} +780.000i q^{35} -295.655 q^{37} +93.7443i q^{39} -218.000i q^{43} +497.566 q^{45} -281.233i q^{47} -957.000 q^{49} -228.000i q^{51} +829.277i q^{63} -1014.00 q^{65} +1016.77i q^{71} -686.000i q^{75} +421.000 q^{81} +2466.20 q^{85} -1690.00i q^{91} +591.310 q^{93} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 92 q^{9} + 456 q^{17} + 1372 q^{25} - 3828 q^{49} - 4056 q^{65} + 1684 q^{81}+O(q^{100}) $ 4 * q + 92 * q^9 + 456 * q^17 + 1372 * q^25 - 3828 * q^49 - 4056 * q^65 + 1684 * q^81

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	− 2.00000i	− 0.384900i	−0.981307	−	0.192450i	$-0.938357\pi$
$3$	− 2.00000i	− 0.384900i	0.981307	−	0.192450i	$-0.0616434\pi$
$4$	0	0
$5$	21.6333	1.93494	0.967471	−	0.252982i	$-0.0814114\pi$
$5$	21.6333	1.93494	0.967471	+	0.252982i	$0.0814114\pi$
$6$	0	0
$7$	36.0555i	1.94681i	0.229081	+	0.973407i	$0.426428\pi$
$7$	36.0555i	1.94681i	−0.229081	+	0.973407i	$0.573572\pi$
$8$	0	0
$9$	23.0000	0.851852
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−46.8722	−1.00000
$13$	−46.8722	−1.00000
$14$	0	0
$15$	− 43.2666i	− 0.744759i
$16$	0	0
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	72.1110	0.749329
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	343.000	2.74400
$26$	0	0
$27$	− 100.000i	− 0.712778i
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	295.655i	1.71294i	0.516194	+	0.856472i	$0.327348\pi$
$31$	295.655i	1.71294i	−0.516194	+	0.856472i	$0.672652\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	780.000i	3.76697i
$36$	0	0
$37$	−295.655	−1.31366	−0.656830	−	0.754039i	$-0.728103\pi$
$37$	−295.655	−1.31366	−0.656830	+	0.754039i	$0.728103\pi$
$38$	0	0
$39$	93.7443i	0.384900i
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	− 218.000i	− 0.773132i	−0.922262	−	0.386566i	$-0.873661\pi$
$43$	− 218.000i	− 0.773132i	0.922262	−	0.386566i	$-0.126339\pi$
$44$	0	0
$45$	497.566	1.64828
$46$	0	0
$47$	− 281.233i	− 0.872810i	−0.899750	−	0.436405i	$-0.856252\pi$
$47$	− 281.233i	− 0.872810i	0.899750	−	0.436405i	$-0.143748\pi$
$48$	0	0
$49$	−957.000	−2.79009
$50$	0	0
$51$	− 228.000i	− 0.626008i
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	829.277i	1.65840i
$64$	0	0
$65$	−1014.00	−1.93494
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	1016.77i	1.69955i	0.527148	+	0.849774i	$0.323261\pi$
$71$	1016.77i	1.69955i	−0.527148	+	0.849774i	$0.676739\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	− 686.000i	− 1.05617i
$76$	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
$81$	421.000	0.577503
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	2466.20	3.14702
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	− 1690.00i	− 1.94681i
$92$	0	0
$93$	591.310	0.659312
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	1560.00	1.44991
$106$	0	0
$107$	54.0000i	0.0487886i	0.999702	+	0.0243943i	$0.00776571\pi$
$107$	54.0000i	0.0487886i	−0.999702	+	0.0243943i	$0.992234\pi$
$108$	0	0
$109$	−93.7443	−0.0823769	−0.0411884	−	0.999151i	$-0.513114\pi$
$109$	−93.7443	−0.0823769	−0.0411884	+	0.999151i	$0.513114\pi$
$110$	0	0
$111$	591.310i	0.505628i
$112$	0	0
$113$	1818.00	1.51348	0.756739	−	0.653717i	$-0.226791\pi$
$113$	1818.00	1.51348	0.756739	+	0.653717i	$0.226791\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−1078.06	−0.851852
$118$	0	0
$119$	4110.33i	3.16633i
$120$	0	0
$121$	−1331.00	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	4716.06	3.37454
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	−436.000	−0.297579
$130$	0	0
$131$	2910.00i	1.94082i	0.241456	+	0.970412i	$0.422375\pi$
$131$	2910.00i	1.94082i	−0.241456	+	0.970412i	$0.577625\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	− 2163.33i	− 1.37918i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	− 3274.00i	− 1.99782i	−0.0466719	−	0.998910i	$-0.514862\pi$
$139$	− 3274.00i	− 1.99782i	0.0466719	−	0.998910i	$-0.485138\pi$
$140$	0	0
$141$	−562.466	−0.335945
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	1914.00i	1.07391i
$148$	0	0
$149$	454.299	0.249783	0.124891	−	0.992170i	$-0.460142\pi$
$149$	454.299	0.249783	0.124891	+	0.992170i	$0.460142\pi$
$150$	0	0
$151$	− 3540.65i	− 1.90817i	−0.299531	−	0.954086i	$-0.596830\pi$
$151$	− 3540.65i	− 1.90817i	0.299531	−	0.954086i	$-0.403170\pi$
$152$	0	0
$153$	2622.00	1.38546
$154$	0	0
$155$	6396.00i	3.31445i
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	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
$167$	− 713.899i	− 0.330797i	−0.986227	−	0.165399i	$-0.947109\pi$
$167$	− 713.899i	− 0.330797i	0.986227	−	0.165399i	$-0.0528911\pi$
$168$	0	0
$169$	2197.00	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
$175$	12367.0i	5.34206i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	510.000i	0.212956i	0.994315	+	0.106478i	$0.0339574\pi$
$179$	510.000i	0.212956i	−0.994315	+	0.106478i	$0.966043\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−6396.00	−2.54186
$186$	0	0
$187$	0	0
$188$	0	0
$189$	3605.55	1.38765
$190$	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
$195$	2028.00i	0.744759i
$196$	0	0
$197$	4434.83	1.60390	0.801950	−	0.597391i	$-0.203796\pi$
$197$	4434.83	1.60390	0.801950	+	0.597391i	$0.203796\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	− 6082.00i	− 1.98437i	−0.124774	−	0.992185i	$-0.539821\pi$
$211$	− 6082.00i	− 1.98437i	0.124774	−	0.992185i	$-0.460179\pi$
$212$	0	0
$213$	2033.53	0.654156
$214$	0	0
$215$	− 4716.06i	− 1.49597i
$216$	0	0
$217$	−10660.0	−3.33478
$218$	0	0
$219$	0	0
$220$	0	0
$221$	−5343.43	−1.62642
$222$	0	0
$223$	5026.14i	1.50931i	0.656124	+	0.754653i	$0.272195\pi$
$223$	5026.14i	1.50931i	−0.656124	+	0.754653i	$0.727805\pi$
$224$	0	0
$225$	7889.00	2.33748
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	4059.85	1.17154	0.585770	−	0.810478i	$-0.300792\pi$
$229$	4059.85	1.17154	0.585770	+	0.810478i	$0.300792\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	3858.00	1.08475	0.542373	−	0.840138i	$-0.317526\pi$
$233$	3858.00	1.08475	0.542373	+	0.840138i	$0.317526\pi$
$234$	0	0
$235$	− 6084.00i	− 1.68884i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 3223.36i	− 0.872393i	−0.899851	−	0.436197i	$-0.856325\pi$
$239$	− 3223.36i	− 0.872393i	0.899851	−	0.436197i	$-0.143675\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	− 3542.00i	− 0.935059i
$244$	0	0
$245$	−20703.1	−5.39866
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 4410.00i	− 1.10899i	−0.832187	−	0.554495i	$-0.812911\pi$
$251$	− 4410.00i	− 1.10899i	0.832187	−	0.554495i	$-0.187089\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	− 4932.39i	− 1.21129i
$256$	0	0
$257$	−4254.00	−1.03252	−0.516259	−	0.856432i	$-0.672676\pi$
$257$	−4254.00	−1.03252	−0.516259	+	0.856432i	$0.672676\pi$
$258$	0	0
$259$	− 10660.0i	− 2.55745i
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	− 7492.34i	− 1.67944i	−0.543023	−	0.839718i	$-0.682720\pi$
$271$	− 7492.34i	− 1.67944i	0.543023	−	0.839718i	$-0.317280\pi$
$272$	0	0
$273$	−3380.00	−0.749329
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	6800.07i	1.45917i
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	9142.00i	1.92027i	0.279542	+	0.960133i	$0.409817\pi$
$283$	9142.00i	1.92027i	−0.279542	+	0.960133i	$0.590183\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	8083.00	1.64523
$290$	0	0
$291$	0	0
$292$	0	0
$293$	9972.95	1.98849	0.994243	−	0.107151i	$-0.0341729\pi$
$293$	9972.95	1.98849	0.994243	+	0.107151i	$0.0341729\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	7860.10	1.50515
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	2.00000	0.000361172 0	0.000180586	−	1.00000i	$-0.499943\pi$
$313$	2.00000	0.000361172 0	0.000180586		1.00000i	$0.499943\pi$
$314$	0	0
$315$	17940.0i	3.20890i
$316$	0	0
$317$	−10448.9	−1.85132	−0.925659	−	0.378358i	$-0.876489\pi$
$317$	−10448.9	−1.85132	−0.925659	+	0.378358i	$0.876489\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	108.000	0.0187787
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−16077.2	−2.74400
$326$	0	0
$327$	187.489i	0.0317069i
$328$	0	0
$329$	10140.0	1.69920
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	−6800.07	−1.11904
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−6406.00	−1.03548	−0.517740	−	0.855538i	$-0.673227\pi$
$337$	−6406.00	−1.03548	−0.517740	+	0.855538i	$0.673227\pi$
$338$	0	0
$339$	− 3636.00i	− 0.582538i
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 22138.1i	− 3.48497i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	10086.0i	1.56036i	0.625555	+	0.780180i	$0.284872\pi$
$347$	10086.0i	1.56036i	−0.625555	+	0.780180i	$0.715128\pi$
$348$	0	0
$349$	−5026.14	−0.770897	−0.385448	−	0.922729i	$-0.625953\pi$
$349$	−5026.14	−0.770897	−0.385448	+	0.922729i	$0.625953\pi$
$350$	0	0
$351$	4687.22i	0.712778i
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	21996.0i	3.28853i
$356$	0	0
$357$	8220.66	1.21872
$358$	0	0
$359$	− 13174.7i	− 1.93686i	−0.249283	−	0.968431i	$-0.580195\pi$
$359$	− 13174.7i	− 1.93686i	0.249283	−	0.968431i	$-0.419805\pi$
$360$	0	0
$361$	−6859.00	−1.00000
$362$	0	0
$363$	2662.00i	0.384900i
$364$	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
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	− 9432.12i	− 1.29886i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	10275.8i	1.37094i	0.728101	+	0.685470i	$0.240403\pi$
$383$	10275.8i	1.37094i	−0.728101	+	0.685470i	$0.759597\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	− 5014.00i	− 0.658594i
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	5820.00	0.747023
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−3930.05	−0.496835	−0.248418	−	0.968653i	$-0.579911\pi$
$397$	−3930.05	−0.496835	−0.248418	+	0.968653i	$0.579911\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	− 13858.0i	− 1.71294i
$404$	0	0
$405$	9107.62	1.11744
$406$	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
$417$	−6548.00	−0.768961
$418$	0	0
$419$	− 17106.0i	− 1.99447i	−0.0743149	−	0.997235i	$-0.523677\pi$
$419$	− 17106.0i	− 1.99447i	0.0743149	−	0.997235i	$-0.476323\pi$
$420$	0	0
$421$	−17169.6	−1.98764	−0.993820	−	0.111000i	$-0.964595\pi$
$421$	−17169.6	−1.98764	−0.993820	+	0.111000i	$0.964595\pi$
$422$	0	0
$423$	− 6468.36i	− 0.743504i
$424$	0	0
$425$	39102.0	4.46288
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	3526.23i	0.394089i	0.980395	+	0.197045i	$0.0631344\pi$
$431$	3526.23i	0.394089i	−0.980395	+	0.197045i	$0.936866\pi$
$432$	0	0
$433$	−14758.0	−1.63793	−0.818966	−	0.573843i	$-0.805452\pi$
$433$	−14758.0	−1.63793	−0.818966	+	0.573843i	$0.805452\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−22011.0	−2.37674
$442$	0	0
$443$	− 16122.0i	− 1.72907i	−0.502570	−	0.864536i	$-0.667612\pi$
$443$	− 16122.0i	− 1.72907i	0.502570	−	0.864536i	$-0.332388\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	− 908.599i	− 0.0961415i
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−7081.30	−0.734456
$454$	0	0
$455$	− 36560.3i	− 3.76697i
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	− 11400.0i	− 1.15927i
$460$	0	0
$461$	−4824.23	−0.487390	−0.243695	−	0.969852i	$-0.578360\pi$
$461$	−4824.23	−0.487390	−0.243695	+	0.969852i	$0.578360\pi$
$462$	0	0
$463$	9641.24i	0.967746i	0.875138	+	0.483873i	$0.160770\pi$
$463$	9641.24i	0.967746i	−0.875138	+	0.483873i	$0.839230\pi$
$464$	0	0
$465$	12792.0	1.27573
$466$	0	0
$467$	15246.0i	1.51071i	0.655317	+	0.755354i	$0.272535\pi$
$467$	15246.0i	1.51071i	−0.655317	+	0.755354i	$0.727465\pi$
$468$	0	0
$469$	0	0
$470$	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
$479$	− 15164.9i	− 1.44656i	−0.690553	−	0.723282i	$-0.742633\pi$
$479$	− 15164.9i	− 1.44656i	0.690553	−	0.723282i	$-0.257367\pi$
$480$	0	0
$481$	13858.0	1.31366
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	5804.94i	0.540137i	0.962841	+	0.270069i	$0.0870464\pi$
$487$	5804.94i	0.540137i	−0.962841	+	0.270069i	$0.912954\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 12522.0i	− 1.15094i	−0.817824	−	0.575468i	$-0.804820\pi$
$491$	− 12522.0i	− 1.15094i	0.817824	−	0.575468i	$-0.195180\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−36660.0	−3.30870
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	−1427.80	−0.127324
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	− 4394.00i	− 0.384900i
$508$	0	0
$509$	−22909.7	−1.99500	−0.997498	−	0.0706887i	$-0.977480\pi$
$509$	−22909.7	−1.99500	−0.997498	+	0.0706887i	$0.977480\pi$
$510$	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
$521$	−1038.00	−0.0872852	−0.0436426	−	0.999047i	$-0.513896\pi$
$521$	−1038.00	−0.0872852	−0.0436426	+	0.999047i	$0.513896\pi$
$522$	0	0
$523$	− 14042.0i	− 1.17402i	−0.809579	−	0.587011i	$-0.800304\pi$
$523$	− 14042.0i	− 1.17402i	0.809579	−	0.587011i	$-0.199696\pi$
$524$	0	0
$525$	24734.1	2.05616
$526$	0	0
$527$	33704.7i	2.78596i
$528$	0	0
$529$	−12167.0	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	1168.20i	0.0944030i
$536$	0	0
$537$	1020.00	0.0819669
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−16650.4	−1.32321	−0.661606	−	0.749851i	$-0.730125\pi$
$541$	−16650.4	−1.32321	−0.661606	+	0.749851i	$0.730125\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−2028.00	−0.159394
$546$	0	0
$547$	25166.0i	1.96713i	0.180553	+	0.983565i	$0.442211\pi$
$547$	25166.0i	1.96713i	−0.180553	+	0.983565i	$0.557789\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	12792.0i	0.978361i
$556$	0	0
$557$	13520.8	1.02854	0.514269	−	0.857629i	$-0.328063\pi$
$557$	13520.8	1.02854	0.514269	+	0.857629i	$0.328063\pi$
$558$	0	0
$559$	10218.1i	0.773132i
$560$	0	0
$561$	0	0
$562$	0	0
$563$	− 26322.0i	− 1.97041i	−0.171384	−	0.985204i	$-0.554824\pi$
$563$	− 26322.0i	− 1.97041i	0.171384	−	0.985204i	$-0.445176\pi$
$564$	0	0
$565$	39329.4	2.92849
$566$	0	0
$567$	15179.4i	1.12429i
$568$	0	0
$569$	4794.00	0.353207	0.176604	−	0.984282i	$-0.443489\pi$
$569$	4794.00	0.353207	0.176604	+	0.984282i	$0.443489\pi$
$570$	0	0
$571$	− 20810.0i	− 1.52517i	−0.646889	−	0.762584i	$-0.723930\pi$
$571$	− 20810.0i	− 1.52517i	0.646889	−	0.762584i	$-0.276070\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−23322.0	−1.64828
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	− 8869.66i	− 0.617342i
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	88920.0i	6.12666i
$596$	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
$601$	−9830.00	−0.667178	−0.333589	−	0.942719i	$-0.608260\pi$
$601$	−9830.00	−0.667178	−0.333589	+	0.942719i	$0.608260\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−28793.9	−1.93494
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	13182.0i	0.872810i
$612$	0	0
$613$	19433.9	1.28047	0.640235	−	0.768179i	$-0.278837\pi$
$613$	19433.9	1.28047	0.640235	+	0.768179i	$0.278837\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	59149.0	3.78554
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−33704.7	−2.13656
$630$	0	0
$631$	− 3021.45i	− 0.190621i	−0.995448	−	0.0953107i	$-0.969616\pi$
$631$	− 3021.45i	− 0.190621i	0.995448	−	0.0953107i	$-0.0303845\pi$
$632$	0	0
$633$	−12164.0	−0.763785
$634$	0	0
$635$	0	0
$636$	0	0
$637$	44856.7	2.79009
$638$	0	0
$639$	23385.6i	1.44776i
$640$	0	0
$641$	30690.0	1.89108	0.945540	−	0.325506i	$-0.105535\pi$
$641$	30690.0	1.89108	0.945540	+	0.325506i	$0.105535\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0	0
$645$	−9432.12	−0.575798
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	21320.0i	1.28356i
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	62952.9i	3.75538i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	11646.0i	0.688412i	0.938894	+	0.344206i	$0.111852\pi$
$659$	11646.0i	0.688412i	−0.938894	+	0.344206i	$0.888148\pi$
$660$	0	0
$661$	13924.6	0.819373	0.409687	−	0.912226i	$-0.365638\pi$
$661$	13924.6	0.819373	0.409687	+	0.912226i	$0.365638\pi$
$662$	0	0
$663$	10686.9i	0.626008i
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	10052.3	0.580932
$670$	0	0
$671$	0	0
$672$	0	0
$673$	34882.0	1.99792	0.998962	−	0.0455605i	$-0.0145074\pi$
$673$	34882.0	1.99792	0.998962	+	0.0455605i	$0.0145074\pi$
$674$	0	0
$675$	− 34300.0i	− 1.95586i
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	− 8119.70i	− 0.450926i
$688$	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
$695$	− 70827.4i	− 3.86567i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	− 7716.00i	− 0.417519i
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	−12168.0	−0.650033
$706$	0	0
$707$	0	0
$708$	0	0
$709$	21251.1	1.12567	0.562837	−	0.826568i	$-0.309710\pi$
$709$	21251.1	1.12567	0.562837	+	0.826568i	$0.309710\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−6446.73	−0.335784
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	4283.00	0.217599
$730$	0	0
$731$	− 24852.0i	− 1.25743i
$732$	0	0
$733$	11126.7	0.560676	0.280338	−	0.959901i	$-0.409554\pi$
$733$	11126.7	0.560676	0.280338	+	0.959901i	$0.409554\pi$
$734$	0	0
$735$	41406.2i	2.07794i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	− 21308.8i	− 1.05215i	−0.850439	−	0.526073i	$-0.823664\pi$
$743$	− 21308.8i	− 1.05215i	0.850439	−	0.526073i	$-0.176336\pi$
$744$	0	0
$745$	9828.00	0.483316
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−1947.00	−0.0949823
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	−8820.00	−0.426851
$754$	0	0
$755$	− 76596.0i	− 3.69220i
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	− 3380.00i	− 0.160372i
$764$	0	0
$765$	56722.5	2.68079
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	8508.00i	0.397417i
$772$	0	0
$773$	11790.2	0.548593	0.274296	−	0.961645i	$-0.411555\pi$
$773$	11790.2	0.548593	0.274296	+	0.961645i	$0.411555\pi$
$774$	0	0
$775$	101410.i	4.70032i
$776$	0	0
$777$	−21320.0	−0.984364
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	65548.9i	2.94646i
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	− 32060.6i	− 1.41955i
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−22254.0	−0.967131	−0.483565	−	0.875308i	$-0.660659\pi$
$809$	−22254.0	−0.967131	−0.483565	+	0.875308i	$0.660659\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	−14984.7	−0.646415
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	− 38870.0i	− 1.65840i
$820$	0	0
$821$	43115.2	1.83280	0.916401	−	0.400262i	$-0.131081\pi$
$821$	43115.2	1.83280	0.916401	+	0.400262i	$0.131081\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	0	0
$826$	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
$831$	0	0
$832$	0	0
$833$	−109098.	−4.53784
$834$	0	0
$835$	− 15444.0i	− 0.640074i
$836$	0	0
$837$	29565.5	1.22095
$838$	0	0
$839$	− 44326.6i	− 1.82399i	−0.410204	−	0.911994i	$-0.634542\pi$
$839$	− 44326.6i	− 1.82399i	0.410204	−	0.911994i	$-0.365458\pi$
$840$	0	0
$841$	24389.0	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	47528.4	1.93494
$846$	0	0
$847$	− 47989.9i	− 1.94681i
$848$	0	0
$849$	18284.0	0.739111
$850$	0	0
$851$	0	0
$852$	0	0
$853$	9771.04	0.392209	0.196104	−	0.980583i	$-0.437171\pi$
$853$	9771.04	0.392209	0.196104	+	0.980583i	$0.437171\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−33894.0	−1.35099	−0.675494	−	0.737365i	$-0.736070\pi$
$857$	−33894.0	−1.35099	−0.675494	+	0.737365i	$0.736070\pi$
$858$	0	0
$859$	− 3850.00i	− 0.152922i	−0.997073	−	0.0764612i	$-0.975638\pi$
$859$	− 3850.00i	− 0.152922i	0.997073	−	0.0764612i	$-0.0243621\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	42812.3i	1.68870i	0.535792	+	0.844350i	$0.320013\pi$
$863$	42812.3i	1.68870i	−0.535792	+	0.844350i	$0.679987\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 16166.0i	− 0.633248i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	170040.i	6.56960i
$876$	0	0
$877$	−40274.0	−1.55069	−0.775346	−	0.631537i	$-0.782424\pi$
$877$	−40274.0	−1.55069	−0.775346	+	0.631537i	$0.782424\pi$
$878$	0	0
$879$	− 19945.9i	− 0.765368i
$880$	0	0
$881$	−31470.0	−1.20346	−0.601732	−	0.798698i	$-0.705522\pi$
$881$	−31470.0	−1.20346	−0.601732	+	0.798698i	$0.705522\pi$
$882$	0	0
$883$	51262.0i	1.95368i	0.213960	+	0.976842i	$0.431364\pi$
$883$	51262.0i	1.95368i	−0.213960	+	0.976842i	$0.568636\pi$
$884$	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
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	11033.0i	0.412058i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	− 15720.2i	− 0.579331i
$904$	0	0
$905$	0	0
$906$	0	0
$907$	− 36826.0i	− 1.34817i	−0.738655	−	0.674083i	$-0.764539\pi$
$907$	− 36826.0i	− 1.34817i	0.738655	−	0.674083i	$-0.235461\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−104922.	−3.77842
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	− 47658.0i	− 1.69955i
$924$	0	0
$925$	−101410.	−3.60468
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−5614.00	−0.195733	−0.0978663	−	0.995200i	$-0.531202\pi$
$937$	−5614.00	−0.195733	−0.0978663	+	0.995200i	$0.531202\pi$
$938$	0	0
$939$	− 4.00000i	0 0.000139015i
$940$	0	0
$941$	52720.4	1.82639	0.913196	−	0.407521i	$-0.133607\pi$
$941$	52720.4	1.82639	0.913196	+	0.407521i	$0.133607\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	78000.0	2.68502
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	20897.8i	0.712573i
$952$	0	0
$953$	58458.0	1.98703	0.993515	−	0.113698i	$-0.0362695\pi$
$953$	58458.0	1.98703	0.993515	+	0.113698i	$0.0362695\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−57621.0	−1.93417
$962$	0	0
$963$	1242.00i	0.0415606i
$964$	0	0
$965$	0	0
$966$	0	0
$967$	− 55518.3i	− 1.84627i	−0.384471	−	0.923137i	$-0.625616\pi$
$967$	− 55518.3i	− 1.84627i	0.384471	−	0.923137i	$-0.374384\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	41862.0i	1.38354i	0.722119	+	0.691769i	$0.243168\pi$
$971$	41862.0i	1.38354i	−0.722119	+	0.691769i	$0.756832\pi$
$972$	0	0
$973$	118046.	3.88939
$974$	0	0
$975$	32154.3i	1.05617i
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−2156.12	−0.0701729
$982$	0	0
$983$	− 19058.9i	− 0.618399i	−0.950997	−	0.309199i	$-0.899939\pi$
$983$	− 19058.9i	− 0.618399i	0.950997	−	0.309199i	$-0.100061\pi$
$984$	0	0
$985$	95940.0	3.10345
$986$	0	0
$987$	− 20280.0i	− 0.654022i
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	29565.5i	0.936348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.4.e.a.545.2	yes	4
4.3	odd	2	inner	832.4.e.a.545.4	yes	4
8.3	odd	2	inner	832.4.e.a.545.1	✓	4
8.5	even	2	inner	832.4.e.a.545.3	yes	4
13.12	even	2	inner	832.4.e.a.545.1	✓	4
52.51	odd	2	inner	832.4.e.a.545.3	yes	4
104.51	odd	2	CM	832.4.e.a.545.2	yes	4
104.77	even	2	inner	832.4.e.a.545.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
832.4.e.a.545.1	✓	4	8.3	odd	2	inner
832.4.e.a.545.1	✓	4	13.12	even	2	inner
832.4.e.a.545.2	yes	4	1.1	even	1	trivial
832.4.e.a.545.2	yes	4	104.51	odd	2	CM
832.4.e.a.545.3	yes	4	8.5	even	2	inner
832.4.e.a.545.3	yes	4	52.51	odd	2	inner
832.4.e.a.545.4	yes	4	4.3	odd	2	inner
832.4.e.a.545.4	yes	4	104.77	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	832.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{3} +21.6333 q^{5} +36.0555i q^{7} +23.0000 q^{9} -46.8722 q^{13} -43.2666i q^{15} +114.000 q^{17} +72.1110 q^{21} +343.000 q^{25} -100.000i q^{27} +295.655i q^{31} +780.000i q^{35} -295.655 q^{37} +93.7443i q^{39} -218.000i q^{43} +497.566 q^{45} -281.233i q^{47} -957.000 q^{49} -228.000i q^{51} +829.277i q^{63} -1014.00 q^{65} +1016.77i q^{71} -686.000i q^{75} +421.000 q^{81} +2466.20 q^{85} -1690.00i q^{91} +591.310 q^{93} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 92 q^{9} + 456 q^{17} + 1372 q^{25} - 3828 q^{49} - 4056 q^{65} + 1684 q^{81}+O(q^{100}) \) 4 * q + 92 * q^9 + 456 * q^17 + 1372 * q^25 - 3828 * q^49 - 4056 * q^65 + 1684 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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