LMFDB - Embedded newform 35.3.c.a.34.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,3,Mod(34,35)] 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("35.34"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [1,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			34.1
Character	$\chi$	$=$	35.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -7.00000 q^{7} -8.00000 q^{9} -13.0000 q^{11} -4.00000 q^{12} +19.0000 q^{13} -5.00000 q^{15} +16.0000 q^{16} -29.0000 q^{17} +20.0000 q^{20} +7.00000 q^{21} +25.0000 q^{25} +17.0000 q^{27} -28.0000 q^{28} +23.0000 q^{29} +13.0000 q^{33} -35.0000 q^{35} -32.0000 q^{36} -19.0000 q^{39} -52.0000 q^{44} -40.0000 q^{45} +31.0000 q^{47} -16.0000 q^{48} +49.0000 q^{49} +29.0000 q^{51} +76.0000 q^{52} -65.0000 q^{55} -20.0000 q^{60} +56.0000 q^{63} +64.0000 q^{64} +95.0000 q^{65} -116.000 q^{68} +2.00000 q^{71} +34.0000 q^{73} -25.0000 q^{75} +91.0000 q^{77} -157.000 q^{79} +80.0000 q^{80} +55.0000 q^{81} -86.0000 q^{83} +28.0000 q^{84} -145.000 q^{85} -23.0000 q^{87} -133.000 q^{91} -149.000 q^{97} +104.000 q^{99} +O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

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	0	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	−1.00000	−0.333333	−0.166667	−	0.986013i	$-0.553300\pi$
$3$	−1.00000	−0.333333	−0.166667	+	0.986013i	$0.553300\pi$
$4$	4.00000	1.00000
$5$	5.00000	1.00000
$5$	5.00000	1.00000
$6$	0	0
$7$	−7.00000	−1.00000
$7$	−7.00000	−1.00000
$8$	0	0
$9$	−8.00000	−0.888889
$10$	0	0
$11$	−13.0000	−1.18182	−0.590909	−	0.806738i	$-0.701231\pi$
$11$	−13.0000	−1.18182	−0.590909	+	0.806738i	$0.701231\pi$
$12$	−4.00000	−0.333333
$13$	19.0000	1.46154	0.730769	−	0.682625i	$-0.239162\pi$
$13$	19.0000	1.46154	0.730769	+	0.682625i	$0.239162\pi$
$14$	0	0
$15$	−5.00000	−0.333333
$16$	16.0000	1.00000
$17$	−29.0000	−1.70588	−0.852941	−	0.522007i	$-0.825183\pi$
$17$	−29.0000	−1.70588	−0.852941	+	0.522007i	$0.825183\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	20.0000	1.00000
$21$	7.00000	0.333333
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	25.0000	1.00000
$26$	0	0
$27$	17.0000	0.629630
$28$	−28.0000	−1.00000
$29$	23.0000	0.793103	0.396552	−	0.918012i	$-0.370207\pi$
$29$	23.0000	0.793103	0.396552	+	0.918012i	$0.370207\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	13.0000	0.393939
$34$	0	0
$35$	−35.0000	−1.00000
$36$	−32.0000	−0.888889
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−19.0000	−0.487179
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−52.0000	−1.18182
$45$	−40.0000	−0.888889
$46$	0	0
$47$	31.0000	0.659574	0.329787	−	0.944055i	$-0.393023\pi$
$47$	31.0000	0.659574	0.329787	+	0.944055i	$0.393023\pi$
$48$	−16.0000	−0.333333
$49$	49.0000	1.00000
$50$	0	0
$51$	29.0000	0.568627
$52$	76.0000	1.46154
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	−65.0000	−1.18182
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−20.0000	−0.333333
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	56.0000	0.888889
$64$	64.0000	1.00000
$65$	95.0000	1.46154
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−116.000	−1.70588
$69$	0	0
$70$	0	0
$71$	2.00000	0.0281690	0.0140845	−	0.999901i	$-0.495517\pi$
$71$	2.00000	0.0281690	0.0140845	+	0.999901i	$0.495517\pi$
$72$	0	0
$73$	34.0000	0.465753	0.232877	−	0.972506i	$-0.425186\pi$
$73$	34.0000	0.465753	0.232877	+	0.972506i	$0.425186\pi$
$74$	0	0
$75$	−25.0000	−0.333333
$76$	0	0
$77$	91.0000	1.18182
$78$	0	0
$79$	−157.000	−1.98734	−0.993671	−	0.112331i	$-0.964168\pi$
$79$	−157.000	−1.98734	−0.993671	+	0.112331i	$0.964168\pi$
$80$	80.0000	1.00000
$81$	55.0000	0.679012
$82$	0	0
$83$	−86.0000	−1.03614	−0.518072	−	0.855337i	$-0.673350\pi$
$83$	−86.0000	−1.03614	−0.518072	+	0.855337i	$0.673350\pi$
$84$	28.0000	0.333333
$85$	−145.000	−1.70588
$86$	0	0
$87$	−23.0000	−0.264368
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	−133.000	−1.46154
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−149.000	−1.53608	−0.768041	−	0.640400i	$-0.778768\pi$
$97$	−149.000	−1.53608	−0.768041	+	0.640400i	$0.778768\pi$
$98$	0	0
$99$	104.000	1.05051
$100$	100.000	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	199.000	1.93204	0.966019	−	0.258470i	$-0.0832182\pi$
$103$	199.000	1.93204	0.966019	+	0.258470i	$0.0832182\pi$
$104$	0	0
$105$	35.0000	0.333333
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	68.0000	0.629630
$109$	−97.0000	−0.889908	−0.444954	−	0.895553i	$-0.646780\pi$
$109$	−97.0000	−0.889908	−0.444954	+	0.895553i	$0.646780\pi$
$110$	0	0
$111$	0	0
$112$	−112.000	−1.00000
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	92.0000	0.793103
$117$	−152.000	−1.29915
$118$	0	0
$119$	203.000	1.70588
$120$	0	0
$121$	48.0000	0.396694
$122$	0	0
$123$	0	0
$124$	0	0
$125$	125.000	1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	52.0000	0.393939
$133$	0	0
$134$	0	0
$135$	85.0000	0.629630
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	−140.000	−1.00000
$141$	−31.0000	−0.219858
$142$	0	0
$143$	−247.000	−1.72727
$144$	−128.000	−0.888889
$145$	115.000	0.793103
$146$	0	0
$147$	−49.0000	−0.333333
$148$	0	0
$149$	−262.000	−1.75839	−0.879195	−	0.476463i	$-0.841919\pi$
$149$	−262.000	−1.75839	−0.879195	+	0.476463i	$0.841919\pi$
$150$	0	0
$151$	−13.0000	−0.0860927	−0.0430464	−	0.999073i	$-0.513706\pi$
$151$	−13.0000	−0.0860927	−0.0430464	+	0.999073i	$0.513706\pi$
$152$	0	0
$153$	232.000	1.51634
$154$	0	0
$155$	0	0
$156$	−76.0000	−0.487179
$157$	−134.000	−0.853503	−0.426752	−	0.904369i	$-0.640342\pi$
$157$	−134.000	−0.853503	−0.426752	+	0.904369i	$0.640342\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	65.0000	0.393939
$166$	0	0
$167$	271.000	1.62275	0.811377	−	0.584523i	$-0.198718\pi$
$167$	271.000	1.62275	0.811377	+	0.584523i	$0.198718\pi$
$168$	0	0
$169$	192.000	1.13609
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−221.000	−1.27746	−0.638728	−	0.769432i	$-0.720539\pi$
$173$	−221.000	−1.27746	−0.638728	+	0.769432i	$0.720539\pi$
$174$	0	0
$175$	−175.000	−1.00000
$176$	−208.000	−1.18182
$177$	0	0
$178$	0	0
$179$	218.000	1.21788	0.608939	−	0.793217i	$-0.291596\pi$
$179$	218.000	1.21788	0.608939	+	0.793217i	$0.291596\pi$
$180$	−160.000	−0.888889
$181$	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
$187$	377.000	2.01604
$188$	124.000	0.659574
$189$	−119.000	−0.629630
$190$	0	0
$191$	347.000	1.81675	0.908377	−	0.418152i	$-0.137322\pi$
$191$	347.000	1.81675	0.908377	+	0.418152i	$0.137322\pi$
$192$	−64.0000	−0.333333
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	−95.0000	−0.487179
$196$	196.000	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−161.000	−0.793103
$204$	116.000	0.568627
$205$	0	0
$206$	0	0
$207$	0	0
$208$	304.000	1.46154
$209$	0	0
$210$	0	0
$211$	107.000	0.507109	0.253555	−	0.967321i	$-0.418400\pi$
$211$	107.000	0.507109	0.253555	+	0.967321i	$0.418400\pi$
$212$	0	0
$213$	−2.00000	−0.00938967
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−34.0000	−0.155251
$220$	−260.000	−1.18182
$221$	−551.000	−2.49321
$222$	0	0
$223$	−401.000	−1.79821	−0.899103	−	0.437737i	$-0.855780\pi$
$223$	−401.000	−1.79821	−0.899103	+	0.437737i	$0.855780\pi$
$224$	0	0
$225$	−200.000	−0.888889
$226$	0	0
$227$	391.000	1.72247	0.861233	−	0.508209i	$-0.169692\pi$
$227$	391.000	1.72247	0.861233	+	0.508209i	$0.169692\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−91.0000	−0.393939
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	155.000	0.659574
$236$	0	0
$237$	157.000	0.662447
$238$	0	0
$239$	−397.000	−1.66109	−0.830544	−	0.556953i	$-0.811970\pi$
$239$	−397.000	−1.66109	−0.830544	+	0.556953i	$0.811970\pi$
$240$	−80.0000	−0.333333
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−208.000	−0.855967
$244$	0	0
$245$	245.000	1.00000
$246$	0	0
$247$	0	0
$248$	0	0
$249$	86.0000	0.345382
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	224.000	0.888889
$253$	0	0
$254$	0	0
$255$	145.000	0.568627
$256$	256.000	1.00000
$257$	−494.000	−1.92218	−0.961089	−	0.276237i	$-0.910912\pi$
$257$	−494.000	−1.92218	−0.961089	+	0.276237i	$0.910912\pi$
$258$	0	0
$259$	0	0
$260$	380.000	1.46154
$261$	−184.000	−0.704981
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	−464.000	−1.70588
$273$	133.000	0.487179
$274$	0	0
$275$	−325.000	−1.18182
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	527.000	1.87544	0.937722	−	0.347385i	$-0.112930\pi$
$281$	527.000	1.87544	0.937722	+	0.347385i	$0.112930\pi$
$282$	0	0
$283$	559.000	1.97527	0.987633	−	0.156787i	$-0.0501135\pi$
$283$	559.000	1.97527	0.987633	+	0.156787i	$0.0501135\pi$
$284$	8.00000	0.0281690
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	552.000	1.91003
$290$	0	0
$291$	149.000	0.512027
$292$	136.000	0.465753
$293$	19.0000	0.0648464	0.0324232	−	0.999474i	$-0.489678\pi$
$293$	19.0000	0.0648464	0.0324232	+	0.999474i	$0.489678\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−221.000	−0.744108
$298$	0	0
$299$	0	0
$300$	−100.000	−0.333333
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−569.000	−1.85342	−0.926710	−	0.375777i	$-0.877376\pi$
$307$	−569.000	−1.85342	−0.926710	+	0.375777i	$0.877376\pi$
$308$	364.000	1.18182
$309$	−199.000	−0.644013
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	−221.000	−0.706070	−0.353035	−	0.935610i	$-0.614850\pi$
$313$	−221.000	−0.706070	−0.353035	+	0.935610i	$0.614850\pi$
$314$	0	0
$315$	280.000	0.888889
$316$	−628.000	−1.98734
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	−299.000	−0.937304
$320$	320.000	1.00000
$321$	0	0
$322$	0	0
$323$	0	0
$324$	220.000	0.679012
$325$	475.000	1.46154
$326$	0	0
$327$	97.0000	0.296636
$328$	0	0
$329$	−217.000	−0.659574
$330$	0	0
$331$	−598.000	−1.80665	−0.903323	−	0.428960i	$-0.858880\pi$
$331$	−598.000	−1.80665	−0.903323	+	0.428960i	$0.858880\pi$
$332$	−344.000	−1.03614
$333$	0	0
$334$	0	0
$335$	0	0
$336$	112.000	0.333333
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	−580.000	−1.70588
$341$	0	0
$342$	0	0
$343$	−343.000	−1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	−92.0000	−0.264368
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	323.000	0.920228
$352$	0	0
$353$	139.000	0.393768	0.196884	−	0.980427i	$-0.436918\pi$
$353$	139.000	0.393768	0.196884	+	0.980427i	$0.436918\pi$
$354$	0	0
$355$	10.0000	0.0281690
$356$	0	0
$357$	−203.000	−0.568627
$358$	0	0
$359$	578.000	1.61003	0.805014	−	0.593256i	$-0.202158\pi$
$359$	578.000	1.61003	0.805014	+	0.593256i	$0.202158\pi$
$360$	0	0
$361$	361.000	1.00000
$362$	0	0
$363$	−48.0000	−0.132231
$364$	−532.000	−1.46154
$365$	170.000	0.465753
$366$	0	0
$367$	391.000	1.06540	0.532698	−	0.846306i	$-0.321178\pi$
$367$	391.000	1.06540	0.532698	+	0.846306i	$0.321178\pi$
$368$	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
$375$	−125.000	−0.333333
$376$	0	0
$377$	437.000	1.15915
$378$	0	0
$379$	−502.000	−1.32454	−0.662269	−	0.749266i	$-0.730406\pi$
$379$	−502.000	−1.32454	−0.662269	+	0.749266i	$0.730406\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	514.000	1.34204	0.671018	−	0.741441i	$-0.265857\pi$
$383$	514.000	1.34204	0.671018	+	0.741441i	$0.265857\pi$
$384$	0	0
$385$	455.000	1.18182
$386$	0	0
$387$	0	0
$388$	−596.000	−1.53608
$389$	743.000	1.91003	0.955013	−	0.296564i	$-0.0958409\pi$
$389$	743.000	1.91003	0.955013	+	0.296564i	$0.0958409\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−785.000	−1.98734
$396$	416.000	1.05051
$397$	−389.000	−0.979849	−0.489924	−	0.871765i	$-0.662976\pi$
$397$	−389.000	−0.979849	−0.489924	+	0.871765i	$0.662976\pi$
$398$	0	0
$399$	0	0
$400$	400.000	1.00000
$401$	−73.0000	−0.182045	−0.0910224	−	0.995849i	$-0.529014\pi$
$401$	−73.0000	−0.182045	−0.0910224	+	0.995849i	$0.529014\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	275.000	0.679012
$406$	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
$412$	796.000	1.93204
$413$	0	0
$414$	0	0
$415$	−430.000	−1.03614
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	140.000	0.333333
$421$	527.000	1.25178	0.625891	−	0.779911i	$-0.284736\pi$
$421$	527.000	1.25178	0.625891	+	0.779911i	$0.284736\pi$
$422$	0	0
$423$	−248.000	−0.586288
$424$	0	0
$425$	−725.000	−1.70588
$426$	0	0
$427$	0	0
$428$	0	0
$429$	247.000	0.575758
$430$	0	0
$431$	−853.000	−1.97912	−0.989559	−	0.144127i	$-0.953963\pi$
$431$	−853.000	−1.97912	−0.989559	+	0.144127i	$0.953963\pi$
$432$	272.000	0.629630
$433$	754.000	1.74134	0.870670	−	0.491868i	$-0.163686\pi$
$433$	754.000	1.74134	0.870670	+	0.491868i	$0.163686\pi$
$434$	0	0
$435$	−115.000	−0.264368
$436$	−388.000	−0.889908
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−392.000	−0.888889
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	262.000	0.586130
$448$	−448.000	−1.00000
$449$	−817.000	−1.81960	−0.909800	−	0.415048i	$-0.863765\pi$
$449$	−817.000	−1.81960	−0.909800	+	0.415048i	$0.863765\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	13.0000	0.0286976
$454$	0	0
$455$	−665.000	−1.46154
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	−493.000	−1.07407
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	368.000	0.793103
$465$	0	0
$466$	0	0
$467$	871.000	1.86510	0.932548	−	0.361046i	$-0.117580\pi$
$467$	871.000	1.86510	0.932548	+	0.361046i	$0.117580\pi$
$468$	−608.000	−1.29915
$469$	0	0
$470$	0	0
$471$	134.000	0.284501
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	812.000	1.70588
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	192.000	0.396694
$485$	−745.000	−1.53608
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	107.000	0.217923	0.108961	−	0.994046i	$-0.465248\pi$
$491$	107.000	0.217923	0.108961	+	0.994046i	$0.465248\pi$
$492$	0	0
$493$	−667.000	−1.35294
$494$	0	0
$495$	520.000	1.05051
$496$	0	0
$497$	−14.0000	−0.0281690
$498$	0	0
$499$	683.000	1.36874	0.684369	−	0.729136i	$-0.260078\pi$
$499$	683.000	1.36874	0.684369	+	0.729136i	$0.260078\pi$
$500$	500.000	1.00000
$501$	−271.000	−0.540918
$502$	0	0
$503$	439.000	0.872763	0.436382	−	0.899762i	$-0.356260\pi$
$503$	439.000	0.872763	0.436382	+	0.899762i	$0.356260\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−192.000	−0.378698
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	−238.000	−0.465753
$512$	0	0
$513$	0	0
$514$	0	0
$515$	995.000	1.93204
$516$	0	0
$517$	−403.000	−0.779497
$518$	0	0
$519$	221.000	0.425819
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	−326.000	−0.623327	−0.311663	−	0.950193i	$-0.600886\pi$
$523$	−326.000	−0.623327	−0.311663	+	0.950193i	$0.600886\pi$
$524$	0	0
$525$	175.000	0.333333
$526$	0	0
$527$	0	0
$528$	208.000	0.393939
$529$	529.000	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−218.000	−0.405959
$538$	0	0
$539$	−637.000	−1.18182
$540$	340.000	0.629630
$541$	767.000	1.41774	0.708872	−	0.705337i	$-0.249204\pi$
$541$	767.000	1.41774	0.708872	+	0.705337i	$0.249204\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−485.000	−0.889908
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	1099.00	1.98734
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−560.000	−1.00000
$561$	−377.000	−0.672014
$562$	0	0
$563$	874.000	1.55240	0.776199	−	0.630488i	$-0.217145\pi$
$563$	874.000	1.55240	0.776199	+	0.630488i	$0.217145\pi$
$564$	−124.000	−0.219858
$565$	0	0
$566$	0	0
$567$	−385.000	−0.679012
$568$	0	0
$569$	−1102.00	−1.93673	−0.968366	−	0.249536i	$-0.919722\pi$
$569$	−1102.00	−1.93673	−0.968366	+	0.249536i	$0.919722\pi$
$570$	0	0
$571$	−118.000	−0.206655	−0.103327	−	0.994647i	$-0.532949\pi$
$571$	−118.000	−0.206655	−0.103327	+	0.994647i	$0.532949\pi$
$572$	−988.000	−1.72727
$573$	−347.000	−0.605585
$574$	0	0
$575$	0	0
$576$	−512.000	−0.888889
$577$	−29.0000	−0.0502600	−0.0251300	−	0.999684i	$-0.508000\pi$
$577$	−29.0000	−0.0502600	−0.0251300	+	0.999684i	$0.508000\pi$
$578$	0	0
$579$	0	0
$580$	460.000	0.793103
$581$	602.000	1.03614
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−760.000	−1.29915
$586$	0	0
$587$	−1094.00	−1.86371	−0.931857	−	0.362826i	$-0.881812\pi$
$587$	−1094.00	−1.86371	−0.931857	+	0.362826i	$0.881812\pi$
$588$	−196.000	−0.333333
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	619.000	1.04384	0.521922	−	0.852993i	$-0.325215\pi$
$593$	619.000	1.04384	0.521922	+	0.852993i	$0.325215\pi$
$594$	0	0
$595$	1015.00	1.70588
$596$	−1048.00	−1.75839
$597$	0	0
$598$	0	0
$599$	323.000	0.539232	0.269616	−	0.962968i	$-0.413103\pi$
$599$	323.000	0.539232	0.269616	+	0.962968i	$0.413103\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	−52.0000	−0.0860927
$605$	240.000	0.396694
$606$	0	0
$607$	−809.000	−1.33278	−0.666392	−	0.745601i	$-0.732162\pi$
$607$	−809.000	−1.33278	−0.666392	+	0.745601i	$0.732162\pi$
$608$	0	0
$609$	161.000	0.264368
$610$	0	0
$611$	589.000	0.963993
$612$	928.000	1.51634
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	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	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	−304.000	−0.487179
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	−536.000	−0.853503
$629$	0	0
$630$	0	0
$631$	947.000	1.50079	0.750396	−	0.660988i	$-0.229863\pi$
$631$	947.000	1.50079	0.750396	+	0.660988i	$0.229863\pi$
$632$	0	0
$633$	−107.000	−0.169036
$634$	0	0
$635$	0	0
$636$	0	0
$637$	931.000	1.46154
$638$	0	0
$639$	−16.0000	−0.0250391
$640$	0	0
$641$	−958.000	−1.49454	−0.747270	−	0.664521i	$-0.768636\pi$
$641$	−958.000	−1.49454	−0.747270	+	0.664521i	$0.768636\pi$
$642$	0	0
$643$	−1241.00	−1.93002	−0.965008	−	0.262221i	$-0.915545\pi$
$643$	−1241.00	−1.93002	−0.965008	+	0.262221i	$0.915545\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−974.000	−1.50541	−0.752705	−	0.658358i	$-0.771251\pi$
$647$	−974.000	−1.50541	−0.752705	+	0.658358i	$0.771251\pi$
$648$	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
$657$	−272.000	−0.414003
$658$	0	0
$659$	1283.00	1.94689	0.973445	−	0.228923i	$-0.0735203\pi$
$659$	1283.00	1.94689	0.973445	+	0.228923i	$0.0735203\pi$
$660$	260.000	0.393939
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	551.000	0.831071
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	1084.00	1.62275
$669$	401.000	0.599402
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	425.000	0.629630
$676$	768.000	1.13609
$677$	1291.00	1.90694	0.953471	−	0.301484i	$-0.0974820\pi$
$677$	1291.00	1.90694	0.953471	+	0.301484i	$0.0974820\pi$
$678$	0	0
$679$	1043.00	1.53608
$680$	0	0
$681$	−391.000	−0.574156
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	−884.000	−1.27746
$693$	−728.000	−1.05051
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−700.000	−1.00000
$701$	−313.000	−0.446505	−0.223252	−	0.974761i	$-0.571667\pi$
$701$	−313.000	−0.446505	−0.223252	+	0.974761i	$0.571667\pi$
$702$	0	0
$703$	0	0
$704$	−832.000	−1.18182
$705$	−155.000	−0.219858
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−1417.00	−1.99859	−0.999295	−	0.0375492i	$-0.988045\pi$
$709$	−1417.00	−1.99859	−0.999295	+	0.0375492i	$0.988045\pi$
$710$	0	0
$711$	1256.00	1.76653
$712$	0	0
$713$	0	0
$714$	0	0
$715$	−1235.00	−1.72727
$716$	872.000	1.21788
$717$	397.000	0.553696
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−640.000	−0.888889
$721$	−1393.00	−1.93204
$722$	0	0
$723$	0	0
$724$	0	0
$725$	575.000	0.793103
$726$	0	0
$727$	1426.00	1.96149	0.980743	−	0.195304i	$-0.0625693\pi$
$727$	1426.00	1.96149	0.980743	+	0.195304i	$0.0625693\pi$
$728$	0	0
$729$	−287.000	−0.393690
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−1061.00	−1.44748	−0.723738	−	0.690075i	$-0.757578\pi$
$733$	−1061.00	−1.44748	−0.723738	+	0.690075i	$0.757578\pi$
$734$	0	0
$735$	−245.000	−0.333333
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−1357.00	−1.83627	−0.918133	−	0.396273i	$-0.870303\pi$
$739$	−1357.00	−1.83627	−0.918133	+	0.396273i	$0.870303\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	−1310.00	−1.75839
$746$	0	0
$747$	688.000	0.921017
$748$	1508.00	2.01604
$749$	0	0
$750$	0	0
$751$	−1333.00	−1.77497	−0.887483	−	0.460840i	$-0.847548\pi$
$751$	−1333.00	−1.77497	−0.887483	+	0.460840i	$0.847548\pi$
$752$	496.000	0.659574
$753$	0	0
$754$	0	0
$755$	−65.0000	−0.0860927
$756$	−476.000	−0.629630
$757$	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
$763$	679.000	0.889908
$764$	1388.00	1.81675
$765$	1160.00	1.51634
$766$	0	0
$767$	0	0
$768$	−256.000	−0.333333
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	494.000	0.640726
$772$	0	0
$773$	−1541.00	−1.99353	−0.996766	−	0.0803607i	$-0.974393\pi$
$773$	−1541.00	−1.99353	−0.996766	+	0.0803607i	$0.974393\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	−380.000	−0.487179
$781$	−26.0000	−0.0332907
$782$	0	0
$783$	391.000	0.499361
$784$	784.000	1.00000
$785$	−670.000	−0.853503
$786$	0	0
$787$	−449.000	−0.570521	−0.285260	−	0.958450i	$-0.592080\pi$
$787$	−449.000	−0.570521	−0.285260	+	0.958450i	$0.592080\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	1531.00	1.92095	0.960477	−	0.278360i	$-0.0897909\pi$
$797$	1531.00	1.92095	0.960477	+	0.278360i	$0.0897909\pi$
$798$	0	0
$799$	−899.000	−1.12516
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−442.000	−0.550436
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−97.0000	−0.119901	−0.0599506	−	0.998201i	$-0.519094\pi$
$809$	−97.0000	−0.119901	−0.0599506	+	0.998201i	$0.519094\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	−644.000	−0.793103
$813$	0	0
$814$	0	0
$815$	0	0
$816$	464.000	0.568627
$817$	0	0
$818$	0	0
$819$	1064.00	1.29915
$820$	0	0
$821$	1607.00	1.95737	0.978685	−	0.205369i	$-0.0658396\pi$
$821$	1607.00	1.95737	0.978685	+	0.205369i	$0.0658396\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	325.000	0.393939
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	1216.00	1.46154
$833$	−1421.00	−1.70588
$834$	0	0
$835$	1355.00	1.62275
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−312.000	−0.370987
$842$	0	0
$843$	−527.000	−0.625148
$844$	428.000	0.507109
$845$	960.000	1.13609
$846$	0	0
$847$	−336.000	−0.396694
$848$	0	0
$849$	−559.000	−0.658422
$850$	0	0
$851$	0	0
$852$	−8.00000	−0.00938967
$853$	−86.0000	−0.100821	−0.0504103	−	0.998729i	$-0.516053\pi$
$853$	−86.0000	−0.100821	−0.0504103	+	0.998729i	$0.516053\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	706.000	0.823804	0.411902	−	0.911228i	$-0.364865\pi$
$857$	706.000	0.823804	0.411902	+	0.911228i	$0.364865\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	−1105.00	−1.27746
$866$	0	0
$867$	−552.000	−0.636678
$868$	0	0
$869$	2041.00	2.34868
$870$	0	0
$871$	0	0
$872$	0	0
$873$	1192.00	1.36541
$874$	0	0
$875$	−875.000	−1.00000
$876$	−136.000	−0.155251
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	−19.0000	−0.0216155
$880$	−1040.00	−1.18182
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	−2204.00	−2.49321
$885$	0	0
$886$	0	0
$887$	−494.000	−0.556933	−0.278467	−	0.960446i	$-0.589826\pi$
$887$	−494.000	−0.556933	−0.278467	+	0.960446i	$0.589826\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−715.000	−0.802469
$892$	−1604.00	−1.79821
$893$	0	0
$894$	0	0
$895$	1090.00	1.21788
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−800.000	−0.888889
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	1564.00	1.72247
$909$	0	0
$910$	0	0
$911$	−1678.00	−1.84193	−0.920966	−	0.389643i	$-0.872598\pi$
$911$	−1678.00	−1.84193	−0.920966	+	0.389643i	$0.872598\pi$
$912$	0	0
$913$	1118.00	1.22453
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−997.000	−1.08487	−0.542437	−	0.840096i	$-0.682498\pi$
$919$	−997.000	−1.08487	−0.542437	+	0.840096i	$0.682498\pi$
$920$	0	0
$921$	569.000	0.617807
$922$	0	0
$923$	38.0000	0.0411701
$924$	−364.000	−0.393939
$925$	0	0
$926$	0	0
$927$	−1592.00	−1.71737
$928$	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
$935$	1885.00	2.01604
$936$	0	0
$937$	−1829.00	−1.95197	−0.975987	−	0.217828i	$-0.930103\pi$
$937$	−1829.00	−1.95197	−0.975987	+	0.217828i	$0.930103\pi$
$938$	0	0
$939$	221.000	0.235357
$940$	620.000	0.659574
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	−595.000	−0.629630
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	628.000	0.662447
$949$	646.000	0.680717
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	1735.00	1.81675
$956$	−1588.00	−1.66109
$957$	299.000	0.312435
$958$	0	0
$959$	0	0
$960$	−320.000	−0.333333
$961$	961.000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−832.000	−0.855967
$973$	0	0
$974$	0	0
$975$	−475.000	−0.487179
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	980.000	1.00000
$981$	776.000	0.791030
$982$	0	0
$983$	−1121.00	−1.14039	−0.570193	−	0.821511i	$-0.693132\pi$
$983$	−1121.00	−1.14039	−0.570193	+	0.821511i	$0.693132\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	217.000	0.219858
$988$	0	0
$989$	0	0
$990$	0	0
$991$	722.000	0.728557	0.364279	−	0.931290i	$-0.381316\pi$
$991$	722.000	0.728557	0.364279	+	0.931290i	$0.381316\pi$
$992$	0	0
$993$	598.000	0.602216
$994$	0	0
$995$	0	0
$996$	344.000	0.345382
$997$	1651.00	1.65597	0.827984	−	0.560752i	$-0.189488\pi$
$997$	1651.00	1.65597	0.827984	+	0.560752i	$0.189488\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.c.a.34.1	✓	1
3.2	odd	2		315.3.e.a.244.1		1
4.3	odd	2		560.3.p.b.209.1		1
5.2	odd	4		175.3.d.e.76.2		2
5.3	odd	4		175.3.d.e.76.1		2
5.4	even	2		35.3.c.b.34.1	yes	1
7.2	even	3		245.3.i.b.129.1		2
7.3	odd	6		245.3.i.a.19.1		2
7.4	even	3		245.3.i.b.19.1		2
7.5	odd	6		245.3.i.a.129.1		2
7.6	odd	2		35.3.c.b.34.1	yes	1
15.14	odd	2		315.3.e.b.244.1		1
20.19	odd	2		560.3.p.a.209.1		1
21.20	even	2		315.3.e.b.244.1		1
28.27	even	2		560.3.p.a.209.1		1
35.4	even	6		245.3.i.a.19.1		2
35.9	even	6		245.3.i.a.129.1		2
35.13	even	4		175.3.d.e.76.2		2
35.19	odd	6		245.3.i.b.129.1		2
35.24	odd	6		245.3.i.b.19.1		2
35.27	even	4		175.3.d.e.76.1		2
35.34	odd	2	CM	35.3.c.a.34.1	✓	1
105.104	even	2		315.3.e.a.244.1		1
140.139	even	2		560.3.p.b.209.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.c.a.34.1	✓	1	1.1	even	1	trivial
35.3.c.a.34.1	✓	1	35.34	odd	2	CM
35.3.c.b.34.1	yes	1	5.4	even	2
35.3.c.b.34.1	yes	1	7.6	odd	2
175.3.d.e.76.1		2	5.3	odd	4
175.3.d.e.76.1		2	35.27	even	4
175.3.d.e.76.2		2	5.2	odd	4
175.3.d.e.76.2		2	35.13	even	4
245.3.i.a.19.1		2	7.3	odd	6
245.3.i.a.19.1		2	35.4	even	6
245.3.i.a.129.1		2	7.5	odd	6
245.3.i.a.129.1		2	35.9	even	6
245.3.i.b.19.1		2	7.4	even	3
245.3.i.b.19.1		2	35.24	odd	6
245.3.i.b.129.1		2	7.2	even	3
245.3.i.b.129.1		2	35.19	odd	6
315.3.e.a.244.1		1	3.2	odd	2
315.3.e.a.244.1		1	105.104	even	2
315.3.e.b.244.1		1	15.14	odd	2
315.3.e.b.244.1		1	21.20	even	2
560.3.p.a.209.1		1	20.19	odd	2
560.3.p.a.209.1		1	28.27	even	2
560.3.p.b.209.1		1	4.3	odd	2
560.3.p.b.209.1		1	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(n\)	\(22\)	\(31\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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