LMFDB - Embedded newform 7.19.b.a.6.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,19,Mod(6,7)] 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("7.6"); S:= CuspForms(chi, 19); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 19, names="a")

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	7.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$14.3770296397$
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			6.1
Character	$\chi$	$=$	7.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-999.000 q^{2} +735857. q^{4} -4.03536e7 q^{7} -4.73239e8 q^{8} +3.87420e8 q^{9} -2.87480e9 q^{11} +4.03133e10 q^{14} +2.79866e11 q^{16} -3.87033e11 q^{18} +2.87192e12 q^{22} -1.65338e12 q^{23} +3.81470e12 q^{25} -2.96945e13 q^{28} +2.83122e13 q^{29} -1.55529e14 q^{32} +2.85086e14 q^{36} +2.57341e14 q^{37} +3.71357e14 q^{43} -2.11544e15 q^{44} +1.65172e15 q^{46} +1.62841e15 q^{49} -3.81088e15 q^{50} -3.22005e15 q^{53} +1.90969e16 q^{56} -2.82839e16 q^{58} -1.56338e16 q^{63} +8.20082e16 q^{64} +1.44774e16 q^{67} +7.89279e16 q^{71} -1.83343e17 q^{72} -2.57084e17 q^{74} +1.16009e17 q^{77} +1.24984e17 q^{79} +1.50095e17 q^{81} -3.70985e17 q^{86} +1.36047e18 q^{88} -1.21665e18 q^{92} -1.62679e18 q^{98} -1.11376e18 q^{99} +O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−999.000	−1.95117	−0.975586	−	0.219618i	$-0.929519\pi$
$2$	−999.000	−1.95117	−0.975586	+	0.219618i	$0.929519\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	735857.	2.80707
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	−4.03536e7	−1.00000
$7$	−4.03536e7	−1.00000
$8$	−4.73239e8	−3.52591
$9$	3.87420e8	1.00000
$10$	0	0
$11$	−2.87480e9	−1.21920	−0.609598	−	0.792711i	$-0.708669\pi$
$11$	−2.87480e9	−1.21920	−0.609598	+	0.792711i	$0.708669\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	4.03133e10	1.95117
$15$	0	0
$16$	2.79866e11	4.07258
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−3.87033e11	−1.95117
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	2.87192e12	2.37886
$23$	−1.65338e12	−0.917955	−0.458978	−	0.888448i	$-0.651784\pi$
$23$	−1.65338e12	−0.917955	−0.458978	+	0.888448i	$0.651784\pi$
$24$	0	0
$25$	3.81470e12	1.00000
$26$	0	0
$27$	0	0
$28$	−2.96945e13	−2.80707
$29$	2.83122e13	1.95160	0.975802	−	0.218657i	$-0.0701675\pi$
$29$	2.83122e13	1.95160	0.975802	+	0.218657i	$0.0701675\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−1.55529e14	−4.42040
$33$	0	0
$34$	0	0
$35$	0	0
$36$	2.85086e14	2.80707
$37$	2.57341e14	1.98013	0.990065	−	0.140613i	$-0.0449074\pi$
$37$	2.57341e14	1.98013	0.990065	+	0.140613i	$0.0449074\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	3.71357e14	0.738882	0.369441	−	0.929254i	$-0.379549\pi$
$43$	3.71357e14	0.738882	0.369441	+	0.929254i	$0.379549\pi$
$44$	−2.11544e15	−3.42237
$45$	0	0
$46$	1.65172e15	1.79109
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	1.62841e15	1.00000
$50$	−3.81088e15	−1.95117
$51$	0	0
$52$	0	0
$53$	−3.22005e15	−0.975842	−0.487921	−	0.872888i	$-0.662245\pi$
$53$	−3.22005e15	−0.975842	−0.487921	+	0.872888i	$0.662245\pi$
$54$	0	0
$55$	0	0
$56$	1.90969e16	3.52591
$57$	0	0
$58$	−2.82839e16	−3.80791
$59$	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
$63$	−1.56338e16	−1.00000
$64$	8.20082e16	4.55237
$65$	0	0
$66$	0	0
$67$	1.44774e16	0.532128	0.266064	−	0.963955i	$-0.414277\pi$
$67$	1.44774e16	0.532128	0.266064	+	0.963955i	$0.414277\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	7.89279e16	1.72149	0.860746	−	0.509034i	$-0.169997\pi$
$71$	7.89279e16	1.72149	0.860746	+	0.509034i	$0.169997\pi$
$72$	−1.83343e17	−3.52591
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−2.57084e17	−3.86357
$75$	0	0
$76$	0	0
$77$	1.16009e17	1.21920
$78$	0	0
$79$	1.24984e17	1.04282	0.521411	−	0.853306i	$-0.325406\pi$
$79$	1.24984e17	1.04282	0.521411	+	0.853306i	$0.325406\pi$
$80$	0	0
$81$	1.50095e17	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	−3.70985e17	−1.44169
$87$	0	0
$88$	1.36047e18	4.29877
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	−1.21665e18	−2.57677
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.62679e18	−1.95117
$99$	−1.11376e18	−1.21920
$100$	2.80707e18	2.80707
$101$	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
$106$	3.21683e18	1.90404
$107$	−2.08415e17	−0.113364	−0.0566820	−	0.998392i	$-0.518052\pi$
$107$	−2.08415e17	−0.113364	−0.0566820	+	0.998392i	$0.518052\pi$
$108$	0	0
$109$	−4.29984e18	−1.97977	−0.989883	−	0.141889i	$-0.954682\pi$
$109$	−4.29984e18	−1.97977	−0.989883	+	0.141889i	$0.954682\pi$
$110$	0	0
$111$	0	0
$112$	−1.12936e19	−4.07258
$113$	7.49108e17	0.249367	0.124683	−	0.992197i	$-0.460208\pi$
$113$	7.49108e17	0.249367	0.124683	+	0.992197i	$0.460208\pi$
$114$	0	0
$115$	0	0
$116$	2.08337e19	5.47829
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	2.70455e18	0.486437
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	1.56182e19	1.95117
$127$	1.21715e18	0.141615	0.0708076	−	0.997490i	$-0.477442\pi$
$127$	1.21715e18	0.141615	0.0708076	+	0.997490i	$0.477442\pi$
$128$	−4.11553e19	−4.46206
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−1.44629e19	−1.03827
$135$	0	0
$136$	0	0
$137$	3.07927e18	0.181118	0.0905592	−	0.995891i	$-0.471135\pi$
$137$	3.07927e18	0.181118	0.0905592	+	0.995891i	$0.471135\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	−7.88489e19	−3.35893
$143$	0	0
$144$	1.08426e20	4.07258
$145$	0	0
$146$	0	0
$147$	0	0
$148$	1.89366e20	5.55836
$149$	−1.55633e19	−0.429956	−0.214978	−	0.976619i	$-0.568968\pi$
$149$	−1.55633e19	−0.429956	−0.214978	+	0.976619i	$0.568968\pi$
$150$	0	0
$151$	−5.89087e19	−1.44340	−0.721700	−	0.692206i	$-0.756639\pi$
$151$	−5.89087e19	−1.44340	−0.721700	+	0.692206i	$0.756639\pi$
$152$	0	0
$153$	0	0
$154$	−1.15892e20	−2.37886
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−1.24859e20	−2.03472
$159$	0	0
$160$	0	0
$161$	6.67198e19	0.917955
$162$	−1.49945e20	−1.95117
$163$	1.43326e20	1.76456	0.882280	−	0.470725i	$-0.156008\pi$
$163$	1.43326e20	1.76456	0.882280	+	0.470725i	$0.156008\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	1.12455e20	1.00000
$170$	0	0
$171$	0	0
$172$	2.73266e20	2.07410
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	−1.53937e20	−1.00000
$176$	−8.04557e20	−4.96527
$177$	0	0
$178$	0	0
$179$	3.41266e20	1.80890	0.904452	−	0.426575i	$-0.140280\pi$
$179$	3.41266e20	1.80890	0.904452	+	0.426575i	$0.140280\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	7.82443e20	3.23663
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−3.66805e20	−1.08426	−0.542131	−	0.840294i	$-0.682382\pi$
$191$	−3.66805e20	−1.08426	−0.542131	+	0.840294i	$0.682382\pi$
$192$	0	0
$193$	−7.37850e20	−1.98588	−0.992938	−	0.118631i	$-0.962149\pi$
$193$	−7.37850e20	−1.98588	−0.992938	+	0.118631i	$0.962149\pi$
$194$	0	0
$195$	0	0
$196$	1.19828e21	2.80707
$197$	6.97837e20	1.56156	0.780779	−	0.624807i	$-0.214822\pi$
$197$	6.97837e20	1.56156	0.780779	+	0.624807i	$0.214822\pi$
$198$	1.11264e21	2.37886
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−1.80526e21	−3.52591
$201$	0	0
$202$	0	0
$203$	−1.14250e21	−1.95160
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−6.40552e20	−0.917955
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−3.12195e20	−0.376603	−0.188301	−	0.982111i	$-0.560298\pi$
$211$	−3.12195e20	−0.376603	−0.188301	+	0.982111i	$0.560298\pi$
$212$	−2.36949e21	−2.73926
$213$	0	0
$214$	2.08207e20	0.221193
$215$	0	0
$216$	0	0
$217$	0	0
$218$	4.29554e21	3.86286
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	6.27615e21	4.42040
$225$	1.47789e21	1.00000
$226$	−7.48359e20	−0.486557
$227$	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
$232$	−1.33984e22	−6.88117
$233$	1.37938e21	0.681522	0.340761	−	0.940150i	$-0.389315\pi$
$233$	1.37938e21	0.681522	0.340761	+	0.940150i	$0.389315\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	4.75276e21	1.86795	0.933974	−	0.357340i	$-0.116316\pi$
$239$	4.75276e21	1.86795	0.933974	+	0.357340i	$0.116316\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−2.70185e21	−0.949123
$243$	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			$\pi$
$252$	−1.15043e22	−2.80707
$253$	4.75313e21	1.11917
$254$	−1.21593e21	−0.276315
$255$	0	0
$256$	1.96162e22	4.15388
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−1.03846e22	−1.98013
$260$	0	0
$261$	1.09687e22	1.95160
$262$	0	0
$263$	−1.18193e22	−1.96332	−0.981660	−	0.190641i	$-0.938943\pi$
$263$	−1.18193e22	−1.96332	−0.981660	+	0.190641i	$0.938943\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	1.06533e22	1.49372
$269$	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
$274$	−3.07619e21	−0.353393
$275$	−1.09665e22	−1.21920
$276$	0	0
$277$	−1.35047e22	−1.40659	−0.703294	−	0.710899i	$-0.748288\pi$
$277$	−1.35047e22	−1.40659	−0.703294	+	0.710899i	$0.748288\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	2.10693e22	1.92883	0.964413	−	0.264402i	$-0.0851746\pi$
$281$	2.10693e22	1.92883	0.964413	+	0.264402i	$0.0851746\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	5.80796e22	4.83235
$285$	0	0
$286$	0	0
$287$	0	0
$288$	−6.02551e22	−4.42040
$289$	1.40631e22	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
$296$	−1.21784e23	−6.98175
$297$	0	0
$298$	1.55477e22	0.838919
$299$	0	0
$300$	0	0
$301$	−1.49856e22	−0.738882
$302$	5.88498e22	2.81632
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	8.53657e22	3.42237
$309$	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
$316$	9.19702e22	2.92727
$317$	4.25936e22	1.31768	0.658841	−	0.752282i	$-0.271047\pi$
$317$	4.25936e22	1.31768	0.658841	+	0.752282i	$0.271047\pi$
$318$	0	0
$319$	−8.13919e22	−2.37939
$320$	0	0
$321$	0	0
$322$	−6.66530e22	−1.79109
$323$	0	0
$324$	1.10448e23	2.80707
$325$	0	0
$326$	−1.43183e23	−3.44296
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−8.30296e22	−1.74093	−0.870464	−	0.492232i	$-0.836181\pi$
$331$	−8.30296e22	−1.74093	−0.870464	+	0.492232i	$0.836181\pi$
$332$	0	0
$333$	9.96992e22	1.98013
$334$	0	0
$335$	0	0
$336$	0	0
$337$	7.18999e21	0.128251	0.0641253	−	0.997942i	$-0.479574\pi$
$337$	7.18999e21	0.128251	0.0641253	+	0.997942i	$0.479574\pi$
$338$	−1.12343e23	−1.95117
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−6.57124e22	−1.00000
$344$	−1.75741e23	−2.60523
$345$	0	0
$346$	0	0
$347$	5.21422e22	0.714865	0.357432	−	0.933939i	$-0.383652\pi$
$347$	5.21422e22	0.714865	0.357432	+	0.933939i	$0.383652\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	1.53783e23	1.95117
$351$	0	0
$352$	4.47114e23	5.38933
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	−3.40925e23	−3.52948
$359$	1.53131e23	1.54601	0.773006	−	0.634399i	$-0.218752\pi$
$359$	1.53131e23	1.54601	0.773006	+	0.634399i	$0.218752\pi$
$360$	0	0
$361$	1.04127e23	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			$\pi$
$368$	−4.62723e23	−3.73845
$369$	0	0
$370$	0	0
$371$	1.29941e23	0.975842
$372$	0	0
$373$	2.46051e22	0.176054	0.0880270	−	0.996118i	$-0.471944\pi$
$373$	2.46051e22	0.176054	0.0880270	+	0.996118i	$0.471944\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−2.58094e23	−1.59965	−0.799825	−	0.600233i	$-0.795075\pi$
$379$	−2.58094e23	−1.59965	−0.799825	+	0.600233i	$0.795075\pi$
$380$	0	0
$381$	0	0
$382$	3.66438e23	2.11558
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	7.37112e23	3.87479
$387$	1.43871e23	0.738882
$388$	0	0
$389$	7.17145e22	0.351609	0.175805	−	0.984425i	$-0.443747\pi$
$389$	7.17145e22	0.351609	0.175805	+	0.984425i	$0.443747\pi$
$390$	0	0
$391$	0	0
$392$	−7.70629e23	−3.52591
$393$	0	0
$394$	−6.97140e23	−3.04687
$395$	0	0
$396$	−8.19565e23	−3.42237
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	1.06760e24	4.07258
$401$	−4.43152e23	−1.65293	−0.826464	−	0.562990i	$-0.809651\pi$
$401$	−4.43152e23	−1.65293	−0.826464	+	0.562990i	$0.809651\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	1.14136e24	3.80791
$407$	−7.39804e23	−2.41416
$408$	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
$414$	6.39912e23	1.79109
$415$	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
$421$	−8.11763e23	−1.95385	−0.976923	−	0.213592i	$-0.931484\pi$
$421$	−8.11763e23	−1.95385	−0.976923	+	0.213592i	$0.931484\pi$
$422$	3.11883e23	0.734817
$423$	0	0
$424$	1.52385e24	3.44073
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−1.53364e23	−0.318221
$429$	0	0
$430$	0	0
$431$	1.01766e24	1.98293	0.991466	−	0.130365i	$-0.0416150\pi$
$431$	1.01766e24	1.98293	0.991466	+	0.130365i	$0.0416150\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	−3.16407e24	−5.55734
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	6.30881e23	1.00000
$442$	0	0
$443$	1.14498e24	1.74247	0.871234	−	0.490869i	$-0.163321\pi$
$443$	1.14498e24	1.74247	0.871234	+	0.490869i	$0.163321\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−3.30933e24	−4.55237
$449$	−9.79230e23	−1.32028	−0.660142	−	0.751141i	$-0.729504\pi$
$449$	−9.79230e23	−1.32028	−0.660142	+	0.751141i	$0.729504\pi$
$450$	−1.47641e24	−1.95117
$451$	0	0
$452$	5.51237e23	0.699990
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	1.42806e24	1.64248	0.821241	−	0.570582i	$-0.193282\pi$
$457$	1.42806e24	1.64248	0.821241	+	0.570582i	$0.193282\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	1.69974e24	1.73842	0.869210	−	0.494444i	$-0.164628\pi$
$463$	1.69974e24	1.73842	0.869210	+	0.494444i	$0.164628\pi$
$464$	7.92361e24	7.94806
$465$	0	0
$466$	−1.37800e24	−1.32977
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	−5.84214e23	−0.532128
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−1.06758e24	−0.900842
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1.24751e24	−0.975842
$478$	−4.74801e24	−3.64469
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	1.99016e24	1.36546
$485$	0	0
$486$	0	0
$487$	1.85745e24	1.20547	0.602734	−	0.797942i	$-0.294078\pi$
$487$	1.85745e24	1.20547	0.602734	+	0.797942i	$0.294078\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−1.82775e24	−1.10200	−0.551001	−	0.834505i	$-0.685754\pi$
$491$	−1.82775e24	−1.10200	−0.551001	+	0.834505i	$0.685754\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−3.18502e24	−1.72149
$498$	0	0
$499$	1.53837e24	0.801968	0.400984	−	0.916085i	$-0.368668\pi$
$499$	1.53837e24	0.801968	0.400984	+	0.916085i	$0.368668\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	7.39854e24	3.52591
$505$	0	0
$506$	−4.74838e24	−2.18369
$507$	0	0
$508$	8.95646e23	0.397524
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	−8.80793e24	−3.64287
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	1.03743e25	3.86357
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	−1.09578e25	−3.80791
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	1.18075e25	3.83077
$527$	0	0
$528$	0	0
$529$	−5.10493e23	−0.157358
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−6.85125e24	−1.87623
$537$	0	0
$538$	0	0
$539$	−4.68136e24	−1.21920
$540$	0	0
$541$	4.58742e24	1.15556	0.577781	−	0.816192i	$-0.303919\pi$
$541$	4.58742e24	1.15556	0.577781	+	0.816192i	$0.303919\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	8.75705e24	1.99743	0.998715	−	0.0506691i	$-0.0161354\pi$
$547$	8.75705e24	1.99743	0.998715	+	0.0506691i	$0.0161354\pi$
$548$	2.26590e24	0.508412
$549$	0	0
$550$	1.09555e25	2.37886
$551$	0	0
$552$	0	0
$553$	−5.04355e24	−1.04282
$554$	1.34912e25	2.74450
$555$	0	0
$556$	0	0
$557$	−6.18061e24	−1.19766	−0.598831	−	0.800875i	$-0.704368\pi$
$557$	−6.18061e24	−1.19766	−0.598831	+	0.800875i	$0.704368\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−2.10482e25	−3.76347
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−6.05686e24	−1.00000
$568$	−3.73518e25	−6.06982
$569$	8.73236e24	1.39676	0.698379	−	0.715728i	$-0.253905\pi$
$569$	8.73236e24	1.39676	0.698379	+	0.715728i	$0.253905\pi$
$570$	0	0
$571$	−8.05757e23	−0.124876	−0.0624380	−	0.998049i	$-0.519888\pi$
$571$	−8.05757e23	−0.124876	−0.0624380	+	0.998049i	$0.519888\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−6.30714e24	−0.917955
$576$	3.17717e25	4.55237
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−1.40490e25	−1.95117
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	9.25699e24	1.18974
$584$	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
$592$	7.20209e25	8.06423
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	−1.14523e25	−1.20692
$597$	0	0
$598$	0	0
$599$	−1.91929e25	−1.93330	−0.966652	−	0.256092i	$-0.917565\pi$
$599$	−1.91929e25	−1.93330	−0.966652	+	0.256092i	$0.917565\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	1.49706e25	1.44169
$603$	5.60883e24	0.532128
$604$	−4.33484e25	−4.05173
$605$	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
$613$	2.44264e25	1.99855	0.999275	−	0.0380762i	$-0.0121230\pi$
$613$	2.44264e25	1.99855	0.999275	+	0.0380762i	$0.0121230\pi$
$614$	0	0
$615$	0	0
$616$	−5.48998e25	−4.29877
$617$	2.28749e25	1.76520	0.882598	−	0.470129i	$-0.155792\pi$
$617$	2.28749e25	1.76520	0.882598	+	0.470129i	$0.155792\pi$
$618$	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
$625$	1.45519e25	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−2.85731e25	−1.80175	−0.900873	−	0.434084i	$-0.857072\pi$
$631$	−2.85731e25	−1.80175	−0.900873	+	0.434084i	$0.857072\pi$
$632$	−5.91472e25	−3.67689
$633$	0	0
$634$	−4.25510e25	−2.57102
$635$	0	0
$636$	0	0
$637$	0	0
$638$	8.13105e25	4.64259
$639$	3.05783e25	1.72149
$640$	0	0
$641$	3.34019e24	0.182831	0.0914154	−	0.995813i	$-0.470861\pi$
$641$	3.34019e24	0.182831	0.0914154	+	0.995813i	$0.470861\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	4.90962e25	2.57677
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−7.10307e25	−3.52591
$649$	0	0
$650$	0	0
$651$	0	0
$652$	1.05467e26	4.95325
$653$	−3.53183e25	−1.63599	−0.817996	−	0.575223i	$-0.804915\pi$
$653$	−3.53183e25	−1.63599	−0.817996	+	0.575223i	$0.804915\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−4.45004e25	−1.89843	−0.949216	−	0.314626i	$-0.898121\pi$
$659$	−4.45004e25	−1.89843	−0.949216	+	0.314626i	$0.898121\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	8.29465e25	3.39685
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−9.95995e25	−3.86357
$667$	−4.68108e25	−1.79148
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−5.76590e24	−0.203578	−0.101789	−	0.994806i	$-0.532457\pi$
$673$	−5.76590e24	−0.203578	−0.101789	+	0.994806i	$0.532457\pi$
$674$	−7.18280e24	−0.250239
$675$	0	0
$676$	8.27511e25	2.80707
$677$	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
$683$	−1.62916e25	−0.503706	−0.251853	−	0.967766i	$-0.581040\pi$
$683$	−1.62916e25	−0.503706	−0.251853	+	0.967766i	$0.581040\pi$
$684$	0	0
$685$	0	0
$686$	6.56467e25	1.95117
$687$	0	0
$688$	1.03930e26	3.00916
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	4.49441e25	1.21920
$694$	−5.20900e25	−1.39482
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−1.13275e26	−2.80707
$701$	−6.35666e25	−1.55513	−0.777565	−	0.628803i	$-0.783545\pi$
$701$	−6.35666e25	−1.55513	−0.777565	+	0.628803i	$0.783545\pi$
$702$	0	0
$703$	0	0
$704$	−2.35757e26	−5.55023
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	4.03198e25	0.890640	0.445320	−	0.895372i	$-0.353090\pi$
$709$	4.03198e25	0.890640	0.445320	+	0.895372i	$0.353090\pi$
$710$	0	0
$711$	4.84213e25	1.04282
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	2.51123e26	5.07772
$717$	0	0
$718$	−1.52978e26	−3.01654
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	−1.04023e26	−1.95117
$723$	0	0
$724$	0	0
$725$	1.08002e26	1.95160
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	5.81497e25	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
$736$	2.57148e26	4.05773
$737$	−4.16195e25	−0.648768
$738$	0	0
$739$	7.64836e25	1.16351	0.581753	−	0.813366i	$-0.302367\pi$
$739$	7.64836e25	1.16351	0.581753	+	0.813366i	$0.302367\pi$
$740$	0	0
$741$	0	0
$742$	−1.29811e26	−1.90404
$743$	8.79718e25	1.27481	0.637403	−	0.770531i	$-0.280009\pi$
$743$	8.79718e25	1.27481	0.637403	+	0.770531i	$0.280009\pi$
$744$	0	0
$745$	0	0
$746$	−2.45805e25	−0.343512
$747$	0	0
$748$	0	0
$749$	8.41030e24	0.113364
$750$	0	0
$751$	−1.42396e26	−1.87386	−0.936932	−	0.349512i	$-0.886347\pi$
$751$	−1.42396e26	−1.87386	−0.936932	+	0.349512i	$0.886347\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−1.53814e26	−1.88422	−0.942111	−	0.335301i	$-0.891162\pi$
$757$	−1.53814e26	−1.88422	−0.942111	+	0.335301i	$0.891162\pi$
$758$	2.57836e26	3.12119
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	1.73514e26	1.97977
$764$	−2.69916e26	−3.04360
$765$	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
$772$	−5.42952e26	−5.57450
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−1.43727e26	−1.44169
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−7.16428e25	−0.686050
$779$	0	0
$780$	0	0
$781$	−2.26902e26	−2.09884
$782$	0	0
$783$	0	0
$784$	4.55737e26	4.07258
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	5.13509e26	4.38341
$789$	0	0
$790$	0	0
$791$	−3.02292e25	−0.249367
$792$	5.27073e26	4.29877
$793$	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
$800$	−5.93295e26	−4.42040
$801$	0	0
$802$	4.42709e26	3.22515
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−2.44840e26	−1.64947	−0.824737	−	0.565517i	$-0.808677\pi$
$809$	−2.44840e26	−1.64947	−0.824737	+	0.565517i	$0.808677\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	−8.40716e26	−5.47829
$813$	0	0
$814$	7.39064e26	4.71045
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−2.33903e26	−1.38022	−0.690108	−	0.723707i	$-0.742437\pi$
$821$	−2.33903e26	−1.38022	−0.690108	+	0.723707i	$0.742437\pi$
$822$	0	0
$823$	1.17495e26	0.678299	0.339149	−	0.940733i	$-0.389861\pi$
$823$	1.17495e26	0.678299	0.339149	+	0.940733i	$0.389861\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	3.61742e26	1.99917	0.999585	−	0.0287973i	$-0.00916774\pi$
$827$	3.61742e26	1.99917	0.999585	+	0.0287973i	$0.00916774\pi$
$828$	−4.71355e26	−2.57677
$829$	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
$841$	5.91123e26	2.80876
$842$	8.10951e26	3.81229
$843$	0	0
$844$	−2.29731e26	−1.05715
$845$	0	0
$846$	0	0
$847$	−1.09138e26	−0.486437
$848$	−9.01180e26	−3.97419
$849$	0	0
$850$	0	0
$851$	−4.25482e26	−1.81767
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	9.86302e25	0.399711
$857$	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
$862$	−1.01664e27	−3.86904
$863$	4.11903e26	1.55131	0.775653	−	0.631159i	$-0.217421\pi$
$863$	4.11903e26	1.55131	0.775653	+	0.631159i	$0.217421\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−3.59303e26	−1.27140
$870$	0	0
$871$	0	0
$872$	2.03485e27	6.98047
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−4.45489e26	−1.45158	−0.725790	−	0.687916i	$-0.758526\pi$
$877$	−4.45489e26	−1.45158	−0.725790	+	0.687916i	$0.758526\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−6.30250e26	−1.95117
$883$	5.67006e26	1.73757	0.868783	−	0.495194i	$-0.164903\pi$
$883$	5.67006e26	1.73757	0.868783	+	0.495194i	$0.164903\pi$
$884$	0	0
$885$	0	0
$886$	−1.14384e27	−3.39985
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	−4.91163e25	−0.141615
$890$	0	0
$891$	−4.31492e26	−1.21920
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.66076e27	4.46206
$897$	0	0
$898$	9.78251e26	2.57610
$899$	0	0
$900$	1.08752e27	2.80707
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−3.54507e26	−0.879244
$905$	0	0
$906$	0	0
$907$	−1.04328e25	−0.0251152	−0.0125576	−	0.999921i	$-0.503997\pi$
$907$	−1.04328e25	−0.0251152	−0.0125576	+	0.999921i	$0.503997\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−1.00255e26	−0.231975	−0.115987	−	0.993251i	$-0.537003\pi$
$911$	−1.00255e26	−0.231975	−0.115987	+	0.993251i	$0.537003\pi$
$912$	0	0
$913$	0	0
$914$	−1.42663e27	−3.20476
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	6.92943e26	1.48203	0.741016	−	0.671487i	$-0.234344\pi$
$919$	6.92943e26	1.48203	0.741016	+	0.671487i	$0.234344\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	9.81678e26	1.98013
$926$	−1.69804e27	−3.39196
$927$	0	0
$928$	−4.40336e27	−8.62686
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	1.01502e27	1.91308
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	5.83629e26	1.03827
$939$	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
$946$	1.06651e27	1.75770
$947$	−1.16067e27	−1.89479	−0.947393	−	0.320072i	$-0.896293\pi$
$947$	−1.16067e27	−1.89479	−0.947393	+	0.320072i	$0.896293\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	1.29663e27	1.99977	0.999883	−	0.0152689i	$-0.00486043\pi$
$953$	1.29663e27	1.99977	0.999883	+	0.0152689i	$0.00486043\pi$
$954$	1.24626e27	1.90404
$955$	0	0
$956$	3.49735e27	5.24347
$957$	0	0
$958$	0	0
$959$	−1.24260e26	−0.181118
$960$	0	0
$961$	6.99054e26	1.00000
$962$	0	0
$963$	−8.07443e25	−0.113364
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−1.47860e27	−1.99992	−0.999962	−	0.00867290i	$-0.997239\pi$
$967$	−1.47860e27	−1.99992	−0.999962	+	0.00867290i	$0.997239\pi$
$968$	−1.27990e27	−1.71513
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	−1.85559e27	−2.35208
$975$	0	0
$976$	0	0
$977$	1.10215e27	1.35891	0.679455	−	0.733717i	$-0.262216\pi$
$977$	1.10215e27	1.35891	0.679455	+	0.733717i	$0.262216\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−1.66585e27	−1.97977
$982$	1.82592e27	2.15019
$983$	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
$989$	−6.13993e26	−0.678261
$990$	0	0
$991$	−1.34100e27	−1.45468	−0.727338	−	0.686279i	$-0.759243\pi$
$991$	−1.34100e27	−1.45468	−0.727338	+	0.686279i	$0.759243\pi$
$992$	0	0
$993$	0	0
$994$	3.18184e27	3.35893
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	−1.53684e27	−1.56478
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.19.b.a.6.1	✓	1
3.2	odd	2		63.19.d.a.55.1		1
7.6	odd	2	CM	7.19.b.a.6.1	✓	1
21.20	even	2		63.19.d.a.55.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.19.b.a.6.1	✓	1	1.1	even	1	trivial
7.19.b.a.6.1	✓	1	7.6	odd	2	CM
63.19.d.a.55.1		1	3.2	odd	2
63.19.d.a.55.1		1	21.20	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(n\)	\(3\)
\(\chi(n)\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more