LMFDB - Embedded newform 3703.1.b.b.1588.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3703,1,Mod(1588,3703)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3703, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3703.1588");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3703 = 7 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3703.b (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:	yes
Analytic conductor:	$1.84803774178$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 161)
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			1588.4
Root			$1.91899$ of defining polynomial
Character	$\chi$	$=$	3703.1588

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.830830 q^{2} -0.309721 q^{4} -1.00000 q^{7} -1.08816 q^{8} +1.00000 q^{9} +0.284630 q^{11} -0.830830 q^{14} -0.594351 q^{16} +0.830830 q^{18} +0.236479 q^{22} +1.00000 q^{25} +0.309721 q^{28} +1.68251 q^{29} +0.594351 q^{32} -0.309721 q^{36} +1.30972 q^{37} +1.91899 q^{43} -0.0881559 q^{44} +1.00000 q^{49} +0.830830 q^{50} -1.68251 q^{53} +1.08816 q^{56} +1.39788 q^{58} -1.00000 q^{63} +1.08816 q^{64} -0.830830 q^{67} -0.284630 q^{71} -1.08816 q^{72} +1.08816 q^{74} -0.284630 q^{77} -1.68251 q^{79} +1.00000 q^{81} +1.59435 q^{86} -0.309721 q^{88} +0.830830 q^{98} +0.284630 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} + 4 q^{4} - 5 q^{7} - 2 q^{8} + 5 q^{9} + q^{11} + q^{14} + 3 q^{16} - q^{18} + 2 q^{22} + 5 q^{25} - 4 q^{28} - q^{29} - 3 q^{32} + 4 q^{36} + q^{37} + q^{43} + 3 q^{44} + 5 q^{49} - q^{50}+ \cdots + q^{99}+O(q^{100}) $ 5 * q - q^2 + 4 * q^4 - 5 * q^7 - 2 * q^8 + 5 * q^9 + q^11 + q^14 + 3 * q^16 - q^18 + 2 * q^22 + 5 * q^25 - 4 * q^28 - q^29 - 3 * q^32 + 4 * q^36 + q^37 + q^43 + 3 * q^44 + 5 * q^49 - q^50 + q^53 + 2 * q^56 - 2 * q^58 - 5 * q^63 + 2 * q^64 + q^67 - q^71 - 2 * q^72 + 2 * q^74 - q^77 + q^79 + 5 * q^81 + 2 * q^86 + 4 * q^88 - q^98 + q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3703\mathbb{Z}\right)^\times$.

$n$	$2117$	$3179$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$2$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	−0.309721	−0.309721
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	−1.00000	−1.00000
$7$	−1.00000	−1.00000
$8$	−1.08816	−1.08816
$9$	1.00000	1.00000
$10$	0	0
$11$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$11$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−0.830830	−0.830830
$15$	0	0
$16$	−0.594351	−0.594351
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0.830830	0.830830
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0.236479	0.236479
$23$	0	0
$23$	0	0
$24$	0	0
$25$	1.00000	1.00000
$26$	0	0
$27$	0	0
$28$	0.309721	0.309721
$29$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$29$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0.594351	0.594351
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−0.309721	−0.309721
$37$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$37$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$43$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$44$	−0.0881559	−0.0881559
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	1.00000	1.00000
$50$	0.830830	0.830830
$51$	0	0
$52$	0	0
$53$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$53$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$54$	0	0
$55$	0	0
$56$	1.08816	1.08816
$57$	0	0
$58$	1.39788	1.39788
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−1.00000	−1.00000
$64$	1.08816	1.08816
$65$	0	0
$66$	0	0
$67$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$67$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$71$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$72$	−1.08816	−1.08816
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	1.08816	1.08816
$75$	0	0
$76$	0	0
$77$	−0.284630	−0.284630
$78$	0	0
$79$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$79$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$80$	0	0
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	1.59435	1.59435
$87$	0	0
$88$	−0.309721	−0.309721
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0.830830	0.830830
$99$	0.284630	0.284630
$100$	−0.309721	−0.309721
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	−1.39788	−1.39788
$107$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$107$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$108$	0	0
$109$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$109$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$110$	0	0
$111$	0	0
$112$	0.594351	0.594351
$113$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$113$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$114$	0	0
$115$	0	0
$116$	−0.521109	−0.521109
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−0.918986	−0.918986
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	−0.830830	−0.830830
$127$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$127$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$128$	0.309721	0.309721
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−0.690279	−0.690279
$135$	0	0
$136$	0	0
$137$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$137$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	−0.236479	−0.236479
$143$	0	0
$144$	−0.594351	−0.594351
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−0.405649	−0.405649
$149$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$149$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$150$	0	0
$151$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$151$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$152$	0	0
$153$	0	0
$154$	−0.236479	−0.236479
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−1.39788	−1.39788
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0.830830	0.830830
$163$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$163$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	−0.594351	−0.594351
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	−1.00000	−1.00000
$176$	−0.169170	−0.169170
$177$	0	0
$178$	0	0
$179$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$179$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$191$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$192$	0	0
$193$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$193$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$194$	0	0
$195$	0	0
$196$	−0.309721	−0.309721
$197$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$197$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$198$	0.236479	0.236479
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−1.08816	−1.08816
$201$	0	0
$202$	0	0
$203$	−1.68251	−1.68251
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$211$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$212$	0.521109	0.521109
$213$	0	0
$214$	1.08816	1.08816
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−0.690279	−0.690279
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	−0.594351	−0.594351
$225$	1.00000	1.00000
$226$	1.59435	1.59435
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	−1.83083	−1.83083
$233$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$233$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$239$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−0.763521	−0.763521
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0.309721	0.309721
$253$	0	0
$254$	−1.59435	−1.59435
$255$	0	0
$256$	−0.830830	−0.830830
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−1.30972	−1.30972
$260$	0	0
$261$	1.68251	1.68251
$262$	0	0
$263$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$263$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0.257326	0.257326
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	−0.690279	−0.690279
$275$	0.284630	0.284630
$276$	0	0
$277$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$277$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$281$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0.0881559	0.0881559
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0.594351	0.594351
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	−1.42518	−1.42518
$297$	0	0
$298$	1.59435	1.59435
$299$	0	0
$300$	0	0
$301$	−1.91899	−1.91899
$302$	1.39788	1.39788
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0.0881559	0.0881559
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0.521109	0.521109
$317$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$317$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$318$	0	0
$319$	0.478891	0.478891
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−0.309721	−0.309721
$325$	0	0
$326$	1.39788	1.39788
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$331$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$332$	0	0
$333$	1.30972	1.30972
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$337$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$338$	0.830830	0.830830
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−1.00000	−1.00000
$344$	−2.08816	−2.08816
$345$	0	0
$346$	0	0
$347$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$347$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−0.830830	−0.830830
$351$	0	0
$352$	0.169170	0.169170
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	−1.59435	−1.59435
$359$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$359$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	1.68251	1.68251
$372$	0	0
$373$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$373$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$379$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$380$	0	0
$381$	0	0
$382$	1.08816	1.08816
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	−0.236479	−0.236479
$387$	1.91899	1.91899
$388$	0	0
$389$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$389$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$390$	0	0
$391$	0	0
$392$	−1.08816	−1.08816
$393$	0	0
$394$	−1.59435	−1.59435
$395$	0	0
$396$	−0.0881559	−0.0881559
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	−0.594351	−0.594351
$401$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$401$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	−1.39788	−1.39788
$407$	0.372786	0.372786
$408$	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
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$421$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$422$	−0.236479	−0.236479
$423$	0	0
$424$	1.83083	1.83083
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−0.405649	−0.405649
$429$	0	0
$430$	0	0
$431$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$431$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0.257326	0.257326
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	1.00000	1.00000
$442$	0	0
$443$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$443$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−1.08816	−1.08816
$449$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$449$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$450$	0.830830	0.830830
$451$	0	0
$452$	−0.594351	−0.594351
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$457$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$463$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$464$	−1.00000	−1.00000
$465$	0	0
$466$	−1.08816	−1.08816
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	0.830830	0.830830
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0.546200	0.546200
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1.68251	−1.68251
$478$	−1.08816	−1.08816
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0.284630	0.284630
$485$	0	0
$486$	0	0
$487$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$487$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$491$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0.284630	0.284630
$498$	0	0
$499$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$499$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	1.08816	1.08816
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0.594351	0.594351
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−1.00000
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−1.08816	−1.08816
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	1.39788	1.39788
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	−0.690279	−0.690279
$527$	0	0
$528$	0	0
$529$	0	0
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0.904073	0.904073
$537$	0	0
$538$	0	0
$539$	0.284630	0.284630
$540$	0	0
$541$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$541$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$547$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$548$	0.257326	0.257326
$549$	0	0
$550$	0.236479	0.236479
$551$	0	0
$552$	0	0
$553$	1.68251	1.68251
$554$	−1.08816	−1.08816
$555$	0	0
$556$	0	0
$557$	−2.00000	−2.00000	−1.00000			$\pi$
$557$	−2.00000	−2.00000	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−1.39788	−1.39788
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−1.00000	−1.00000
$568$	0.309721	0.309721
$569$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$569$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$570$	0	0
$571$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$571$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.08816	1.08816
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0.830830	0.830830
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−0.478891	−0.478891
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−0.778434	−0.778434
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	−0.594351	−0.594351
$597$	0	0
$598$	0	0
$599$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$599$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	−1.59435	−1.59435
$603$	−0.830830	−0.830830
$604$	−0.521109	−0.521109
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$613$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$614$	0	0
$615$	0	0
$616$	0.309721	0.309721
$617$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$617$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$631$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$632$	1.83083	1.83083
$633$	0	0
$634$	−1.08816	−1.08816
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0.397877	0.397877
$639$	−0.284630	−0.284630
$640$	0	0
$641$	−2.00000	−2.00000	−1.00000			$\pi$
$641$	−2.00000	−2.00000	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−1.08816	−1.08816
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−0.521109	−0.521109
$653$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$653$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$659$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−1.59435	−1.59435
$663$	0	0
$664$	0	0
$665$	0	0
$666$	1.08816	1.08816
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$673$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$674$	0.236479	0.236479
$675$	0	0
$676$	−0.309721	−0.309721
$677$	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
$683$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$683$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$684$	0	0
$685$	0	0
$686$	−0.830830	−0.830830
$687$	0	0
$688$	−1.14055	−1.14055
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	−0.284630	−0.284630
$694$	−1.08816	−1.08816
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0.309721	0.309721
$701$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$701$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$702$	0	0
$703$	0	0
$704$	0.309721	0.309721
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$709$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$710$	0	0
$711$	−1.68251	−1.68251
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0.594351	0.594351
$717$	0	0
$718$	1.59435	1.59435
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	0.830830	0.830830
$723$	0	0
$724$	0	0
$725$	1.68251	1.68251
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−0.236479	−0.236479
$738$	0	0
$739$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$739$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$740$	0	0
$741$	0	0
$742$	1.39788	1.39788
$743$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$743$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$744$	0	0
$745$	0	0
$746$	0.236479	0.236479
$747$	0	0
$748$	0	0
$749$	−1.30972	−1.30972
$750$	0	0
$751$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$751$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$757$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$758$	−1.39788	−1.39788
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0.830830	0.830830
$764$	−0.405649	−0.405649
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0.0881559	0.0881559
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	1.59435	1.59435
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0.236479	0.236479
$779$	0	0
$780$	0	0
$781$	−0.0810141	−0.0810141
$782$	0	0
$783$	0	0
$784$	−0.594351	−0.594351
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0.594351	0.594351
$789$	0	0
$790$	0	0
$791$	−1.91899	−1.91899
$792$	−0.309721	−0.309721
$793$	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
$799$	0	0
$800$	0.594351	0.594351
$801$	0	0
$802$	1.08816	1.08816
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$809$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0.521109	0.521109
$813$	0	0
$814$	0.309721	0.309721
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$821$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$822$	0	0
$823$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$823$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$827$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.83083	1.83083
$842$	1.59435	1.59435
$843$	0	0
$844$	0.0881559	0.0881559
$845$	0	0
$846$	0	0
$847$	0.918986	0.918986
$848$	1.00000	1.00000
$849$	0	0
$850$	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
$856$	−1.42518	−1.42518
$857$	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
$861$	0	0
$862$	1.59435	1.59435
$863$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$863$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−0.478891	−0.478891
$870$	0	0
$871$	0	0
$872$	0.904073	0.904073
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$877$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0.830830	0.830830
$883$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$883$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$884$	0	0
$885$	0	0
$886$	−0.236479	−0.236479
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	1.91899	1.91899
$890$	0	0
$891$	0.284630	0.284630
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−0.309721	−0.309721
$897$	0	0
$898$	−1.08816	−1.08816
$899$	0	0
$900$	−0.309721	−0.309721
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−2.08816	−2.08816
$905$	0	0
$906$	0	0
$907$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$907$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$911$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$912$	0	0
$913$	0	0
$914$	−1.39788	−1.39788
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$919$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	1.30972	1.30972
$926$	0.690279	0.690279
$927$	0	0
$928$	1.00000	1.00000
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0.405649	0.405649
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0.690279	0.690279
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0.453800	0.453800
$947$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$947$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$953$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$954$	−1.39788	−1.39788
$955$	0	0
$956$	0.405649	0.405649
$957$	0	0
$958$	0	0
$959$	0.830830	0.830830
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	1.30972	1.30972
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$967$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$968$	1.00000	1.00000
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	−1.59435	−1.59435
$975$	0	0
$976$	0	0
$977$	−2.00000	−2.00000	−1.00000			$\pi$
$977$	−2.00000	−2.00000	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−0.830830	−0.830830
$982$	0.690279	0.690279
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$991$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$992$	0	0
$993$	0	0
$994$	0.236479	0.236479
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0.690279	0.690279
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3703.1.b.b.1588.4		5
7.6	odd	2	CM	3703.1.b.b.1588.4		5
23.2	even	11		3703.1.l.i.2603.1		10
23.3	even	11		3703.1.l.e.699.1		10
23.4	even	11		3703.1.l.d.706.1		10
23.5	odd	22		161.1.l.a.48.1	✓	10
23.6	even	11		3703.1.l.d.2911.1		10
23.7	odd	22		3703.1.l.c.118.1		10
23.8	even	11		3703.1.l.e.2617.1		10
23.9	even	11		3703.1.l.f.1392.1		10
23.10	odd	22		3703.1.l.c.3044.1		10
23.11	odd	22		3703.1.l.h.2582.1		10
23.12	even	11		3703.1.l.i.2582.1		10
23.13	even	11		3703.1.l.g.3044.1		10
23.14	odd	22		161.1.l.a.104.1	yes	10
23.15	odd	22		3703.1.l.a.2617.1		10
23.16	even	11		3703.1.l.g.118.1		10
23.17	odd	22		3703.1.l.b.2911.1		10
23.18	even	11		3703.1.l.f.3429.1		10
23.19	odd	22		3703.1.l.b.706.1		10
23.20	odd	22		3703.1.l.a.699.1		10
23.21	odd	22		3703.1.l.h.2603.1		10
23.22	odd	2		3703.1.b.c.1588.4		5
69.5	even	22		1449.1.bq.a.370.1		10
69.14	even	22		1449.1.bq.a.748.1		10
92.51	even	22		2576.1.cj.a.209.1		10
92.83	even	22		2576.1.cj.a.1553.1		10
161.5	even	66		1127.1.v.a.1060.1		20
161.6	odd	22		3703.1.l.d.2911.1		10
161.13	odd	22		3703.1.l.g.3044.1		10
161.20	even	22		3703.1.l.a.699.1		10
161.27	odd	22		3703.1.l.d.706.1		10
161.34	even	22		3703.1.l.h.2582.1		10
161.37	odd	66		1127.1.v.a.472.1		20
161.41	odd	22		3703.1.l.f.3429.1		10
161.48	odd	22		3703.1.l.i.2603.1		10
161.51	odd	66		1127.1.v.a.1060.1		20
161.55	odd	22		3703.1.l.f.1392.1		10
161.60	odd	66		1127.1.v.a.656.1		20
161.62	odd	22		3703.1.l.g.118.1		10
161.74	odd	66		1127.1.v.a.117.1		20
161.76	even	22		3703.1.l.c.118.1		10
161.83	even	22		161.1.l.a.104.1	yes	10
161.90	even	22		3703.1.l.h.2603.1		10
161.97	even	22		161.1.l.a.48.1	✓	10
161.104	odd	22		3703.1.l.i.2582.1		10
161.111	even	22		3703.1.l.b.706.1		10
161.118	odd	22		3703.1.l.e.699.1		10
161.125	even	22		3703.1.l.c.3044.1		10
161.129	even	66		1127.1.v.a.656.1		20
161.132	even	22		3703.1.l.b.2911.1		10
161.143	even	66		1127.1.v.a.117.1		20
161.146	odd	22		3703.1.l.e.2617.1		10
161.152	even	66		1127.1.v.a.472.1		20
161.153	even	22		3703.1.l.a.2617.1		10
161.160	even	2		3703.1.b.c.1588.4		5
483.83	odd	22		1449.1.bq.a.748.1		10
483.419	odd	22		1449.1.bq.a.370.1		10
644.83	odd	22		2576.1.cj.a.1553.1		10
644.419	odd	22		2576.1.cj.a.209.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.1.l.a.48.1	✓	10	23.5	odd	22
161.1.l.a.48.1	✓	10	161.97	even	22
161.1.l.a.104.1	yes	10	23.14	odd	22
161.1.l.a.104.1	yes	10	161.83	even	22
1127.1.v.a.117.1		20	161.74	odd	66
1127.1.v.a.117.1		20	161.143	even	66
1127.1.v.a.472.1		20	161.37	odd	66
1127.1.v.a.472.1		20	161.152	even	66
1127.1.v.a.656.1		20	161.60	odd	66
1127.1.v.a.656.1		20	161.129	even	66
1127.1.v.a.1060.1		20	161.5	even	66
1127.1.v.a.1060.1		20	161.51	odd	66
1449.1.bq.a.370.1		10	69.5	even	22
1449.1.bq.a.370.1		10	483.419	odd	22
1449.1.bq.a.748.1		10	69.14	even	22
1449.1.bq.a.748.1		10	483.83	odd	22
2576.1.cj.a.209.1		10	92.51	even	22
2576.1.cj.a.209.1		10	644.419	odd	22
2576.1.cj.a.1553.1		10	92.83	even	22
2576.1.cj.a.1553.1		10	644.83	odd	22
3703.1.b.b.1588.4		5	1.1	even	1	trivial
3703.1.b.b.1588.4		5	7.6	odd	2	CM
3703.1.b.c.1588.4		5	23.22	odd	2
3703.1.b.c.1588.4		5	161.160	even	2
3703.1.l.a.699.1		10	23.20	odd	22
3703.1.l.a.699.1		10	161.20	even	22
3703.1.l.a.2617.1		10	23.15	odd	22
3703.1.l.a.2617.1		10	161.153	even	22
3703.1.l.b.706.1		10	23.19	odd	22
3703.1.l.b.706.1		10	161.111	even	22
3703.1.l.b.2911.1		10	23.17	odd	22
3703.1.l.b.2911.1		10	161.132	even	22
3703.1.l.c.118.1		10	23.7	odd	22
3703.1.l.c.118.1		10	161.76	even	22
3703.1.l.c.3044.1		10	23.10	odd	22
3703.1.l.c.3044.1		10	161.125	even	22
3703.1.l.d.706.1		10	23.4	even	11
3703.1.l.d.706.1		10	161.27	odd	22
3703.1.l.d.2911.1		10	23.6	even	11
3703.1.l.d.2911.1		10	161.6	odd	22
3703.1.l.e.699.1		10	23.3	even	11
3703.1.l.e.699.1		10	161.118	odd	22
3703.1.l.e.2617.1		10	23.8	even	11
3703.1.l.e.2617.1		10	161.146	odd	22
3703.1.l.f.1392.1		10	23.9	even	11
3703.1.l.f.1392.1		10	161.55	odd	22
3703.1.l.f.3429.1		10	23.18	even	11
3703.1.l.f.3429.1		10	161.41	odd	22
3703.1.l.g.118.1		10	23.16	even	11
3703.1.l.g.118.1		10	161.62	odd	22
3703.1.l.g.3044.1		10	23.13	even	11
3703.1.l.g.3044.1		10	161.13	odd	22
3703.1.l.h.2582.1		10	23.11	odd	22
3703.1.l.h.2582.1		10	161.34	even	22
3703.1.l.h.2603.1		10	23.21	odd	22
3703.1.l.h.2603.1		10	161.90	even	22
3703.1.l.i.2582.1		10	23.12	even	11
3703.1.l.i.2582.1		10	161.104	odd	22
3703.1.l.i.2603.1		10	23.2	even	11
3703.1.l.i.2603.1		10	161.48	odd	22

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:	\( N \)	\(=\)	\( 3703 = 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3703.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.830830 q^{2} -0.309721 q^{4} -1.00000 q^{7} -1.08816 q^{8} +1.00000 q^{9} +0.284630 q^{11} -0.830830 q^{14} -0.594351 q^{16} +0.830830 q^{18} +0.236479 q^{22} +1.00000 q^{25} +0.309721 q^{28} +1.68251 q^{29} +0.594351 q^{32} -0.309721 q^{36} +1.30972 q^{37} +1.91899 q^{43} -0.0881559 q^{44} +1.00000 q^{49} +0.830830 q^{50} -1.68251 q^{53} +1.08816 q^{56} +1.39788 q^{58} -1.00000 q^{63} +1.08816 q^{64} -0.830830 q^{67} -0.284630 q^{71} -1.08816 q^{72} +1.08816 q^{74} -0.284630 q^{77} -1.68251 q^{79} +1.00000 q^{81} +1.59435 q^{86} -0.309721 q^{88} +0.830830 q^{98} +0.284630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} + 4 q^{4} - 5 q^{7} - 2 q^{8} + 5 q^{9} + q^{11} + q^{14} + 3 q^{16} - q^{18} + 2 q^{22} + 5 q^{25} - 4 q^{28} - q^{29} - 3 q^{32} + 4 q^{36} + q^{37} + q^{43} + 3 q^{44} + 5 q^{49} - q^{50}+ \cdots + q^{99}+O(q^{100}) \) 5 * q - q^2 + 4 * q^4 - 5 * q^7 - 2 * q^8 + 5 * q^9 + q^11 + q^14 + 3 * q^16 - q^18 + 2 * q^22 + 5 * q^25 - 4 * q^28 - q^29 - 3 * q^32 + 4 * q^36 + q^37 + q^43 + 3 * q^44 + 5 * q^49 - q^50 + q^53 + 2 * q^56 - 2 * q^58 - 5 * q^63 + 2 * q^64 + q^67 - q^71 - 2 * q^72 + 2 * q^74 - q^77 + q^79 + 5 * q^81 + 2 * q^86 + 4 * q^88 - q^98 + q^99

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