LMFDB - Embedded newform 7.49.b.a.6.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,49,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, 49); 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, 49, names="a")

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 49 $
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:	$102.146525701$
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)

$f(q)$

$=$

$q+2.24186e6 q^{2} -2.76449e14 q^{4} +1.91581e20 q^{7} -1.25079e21 q^{8} +7.97664e22 q^{9} +1.85303e25 q^{11} +4.29498e26 q^{14} +7.50094e28 q^{16} +1.78825e29 q^{18} +4.15423e31 q^{22} -9.36422e32 q^{23} +3.55271e33 q^{25} -5.29625e34 q^{28} -2.24415e35 q^{29} +5.20225e35 q^{32} -2.20514e37 q^{36} +8.06089e37 q^{37} +1.49024e39 q^{43} -5.12269e39 q^{44} -2.09933e39 q^{46} +3.67034e40 q^{49} +7.96468e39 q^{50} +1.01363e41 q^{53} -2.39627e41 q^{56} -5.03107e41 q^{58} +1.52818e43 q^{63} -1.99470e43 q^{64} +1.00840e44 q^{67} -5.00741e44 q^{71} -9.97707e43 q^{72} +1.80714e44 q^{74} +3.55006e45 q^{77} -6.38947e45 q^{79} +6.36269e45 q^{81} +3.34090e45 q^{86} -2.31775e46 q^{88} +2.58873e47 q^{92} +8.22837e46 q^{98} +1.47810e48 q^{99} +O(q^{100})$

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 $

$2$	2.24186e6	0.133625	0.0668125	−	0.997766i	$-0.478717\pi$
$2$	2.24186e6	0.133625	0.0668125	+	0.997766i	$0.478717\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	−2.76449e14	−0.982144
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	1.91581e20	1.00000
$7$	1.91581e20	1.00000
$8$	−1.25079e21	−0.264864
$9$	7.97664e22	1.00000
$10$	0	0
$11$	1.85303e25	1.88130	0.940651	−	0.339376i	$-0.110216\pi$
$11$	1.85303e25	1.88130	0.940651	+	0.339376i	$0.110216\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	4.29498e26	0.133625
$15$	0	0
$16$	7.50094e28	0.946752
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	1.78825e29	0.133625
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	4.15423e31	0.251389
$23$	−9.36422e32	−1.94986	−0.974931	−	0.222509i	$-0.928575\pi$
$23$	−9.36422e32	−1.94986	−0.974931	+	0.222509i	$0.928575\pi$
$24$	0	0
$25$	3.55271e33	1.00000
$26$	0	0
$27$	0	0
$28$	−5.29625e34	−0.982144
$29$	−2.24415e35	−1.79267	−0.896335	−	0.443378i	$-0.853780\pi$
$29$	−2.24415e35	−1.79267	−0.896335	+	0.443378i	$0.853780\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	5.20225e35	0.391374
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−2.20514e37	−0.982144
$37$	8.06089e37	1.86012	0.930062	−	0.367403i	$-0.119753\pi$
$37$	8.06089e37	1.86012	0.930062	+	0.367403i	$0.119753\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	1.49024e39	0.933280	0.466640	−	0.884447i	$-0.345464\pi$
$43$	1.49024e39	0.933280	0.466640	+	0.884447i	$0.345464\pi$
$44$	−5.12269e39	−1.84771
$45$	0	0
$46$	−2.09933e39	−0.260550
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	3.67034e40	1.00000
$50$	7.96468e39	0.133625
$51$	0	0
$52$	0	0
$53$	1.01363e41	0.420008	0.210004	−	0.977700i	$-0.432652\pi$
$53$	1.01363e41	0.420008	0.210004	+	0.977700i	$0.432652\pi$
$54$	0	0
$55$	0	0
$56$	−2.39627e41	−0.264864
$57$	0	0
$58$	−5.03107e41	−0.239546
$59$	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
$63$	1.52818e43	1.00000
$64$	−1.99470e43	−0.894454
$65$	0	0
$66$	0	0
$67$	1.00840e44	1.50604	0.753022	−	0.657995i	$-0.228595\pi$
$67$	1.00840e44	1.50604	0.753022	+	0.657995i	$0.228595\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−5.00741e44	−1.85957	−0.929785	−	0.368103i	$-0.880007\pi$
$71$	−5.00741e44	−1.85957	−0.929785	+	0.368103i	$0.880007\pi$
$72$	−9.97707e43	−0.264864
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	1.80714e44	0.248559
$75$	0	0
$76$	0	0
$77$	3.55006e45	1.88130
$78$	0	0
$79$	−6.38947e45	−1.82985	−0.914924	−	0.403627i	$-0.867749\pi$
$79$	−6.38947e45	−1.82985	−0.914924	+	0.403627i	$0.867749\pi$
$80$	0	0
$81$	6.36269e45	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	3.34090e45	0.124710
$87$	0	0
$88$	−2.31775e46	−0.498289
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	2.58873e47	1.91505
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	8.22837e46	0.133625
$99$	1.47810e48	1.88130
$100$	−9.82144e47	−0.982144
$101$	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
$106$	2.27241e47	0.0561237
$107$	1.00289e49	1.97717	0.988586	−	0.150657i	$-0.0481390\pi$
$107$	1.00289e49	1.97717	0.988586	+	0.150657i	$0.0481390\pi$
$108$	0	0
$109$	1.46955e49	1.85759	0.928794	−	0.370597i	$-0.120847\pi$
$109$	1.46955e49	1.85759	0.928794	+	0.370597i	$0.120847\pi$
$110$	0	0
$111$	0	0
$112$	1.43704e49	0.946752
$113$	−7.10553e48	−0.378193	−0.189097	−	0.981958i	$-0.560556\pi$
$113$	−7.10553e48	−0.378193	−0.189097	+	0.981958i	$0.560556\pi$
$114$	0	0
$115$	0	0
$116$	6.20394e49	1.76066
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	2.46355e50	2.53929
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	3.42595e49	0.133625
$127$	6.08860e50	1.96439	0.982197	−	0.187856i	$-0.0601537\pi$
$127$	6.08860e50	1.96439	0.982197	+	0.187856i	$0.0601537\pi$
$128$	−1.91149e50	−0.510896
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	2.26069e50	0.201245
$135$	0	0
$136$	0	0
$137$	−2.64824e51	−1.38568	−0.692841	−	0.721091i	$-0.743641\pi$
$137$	−2.64824e51	−1.38568	−0.692841	+	0.721091i	$0.743641\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	−1.12259e51	−0.248485
$143$	0	0
$144$	5.98323e51	0.946752
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−2.22843e52	−1.82691
$149$	−2.55732e52	−1.78367	−0.891834	−	0.452362i	$-0.850581\pi$
$149$	−2.55732e52	−1.78367	−0.891834	+	0.452362i	$0.850581\pi$
$150$	0	0
$151$	−2.16151e52	−1.09474	−0.547370	−	0.836891i	$-0.684371\pi$
$151$	−2.16151e52	−1.09474	−0.547370	+	0.836891i	$0.684371\pi$
$152$	0	0
$153$	0	0
$154$	7.95873e51	0.251389
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−1.43243e52	−0.244514
$159$	0	0
$160$	0	0
$161$	−1.79401e53	−1.94986
$162$	1.42642e52	0.133625
$163$	1.74636e53	1.41134	0.705669	−	0.708541i	$-0.250646\pi$
$163$	1.74636e53	1.41134	0.705669	+	0.708541i	$0.250646\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	2.94633e53	1.00000
$170$	0	0
$171$	0	0
$172$	−4.11974e53	−0.916616
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	6.80633e53	1.00000
$176$	1.38995e54	1.78113
$177$	0	0
$178$	0	0
$179$	1.42007e54	1.21293	0.606466	−	0.795109i	$-0.292587\pi$
$179$	1.42007e54	1.21293	0.606466	+	0.795109i	$0.292587\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	1.17126e54	0.516449
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	4.76297e53	0.0857190	0.0428595	−	0.999081i	$-0.486353\pi$
$191$	4.76297e53	0.0857190	0.0428595	+	0.999081i	$0.486353\pi$
$192$	0	0
$193$	−1.06322e55	−1.49021	−0.745107	−	0.666945i	$-0.767602\pi$
$193$	−1.06322e55	−1.49021	−0.745107	+	0.666945i	$0.767602\pi$
$194$	0	0
$195$	0	0
$196$	−1.01466e55	−0.982144
$197$	2.23399e55	1.91378	0.956888	−	0.290456i	$-0.0938070\pi$
$197$	2.23399e55	1.91378	0.956888	+	0.290456i	$0.0938070\pi$
$198$	3.31368e54	0.251389
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−4.44368e54	−0.264864
$201$	0	0
$202$	0	0
$203$	−4.29937e55	−1.79267
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−7.46951e55	−1.94986
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−2.23709e54	−0.0368897	−0.0184448	−	0.999830i	$-0.505872\pi$
$211$	−2.23709e54	−0.0368897	−0.0184448	+	0.999830i	$0.505872\pi$
$212$	−2.80217e55	−0.412509
$213$	0	0
$214$	2.24835e55	0.264200
$215$	0	0
$216$	0	0
$217$	0	0
$218$	3.29453e55	0.248220
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	9.96654e55	0.391374
$225$	2.83387e56	1.00000
$226$	−1.59296e55	−0.0505361
$227$	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
$232$	2.80695e56	0.474814
$233$	7.86572e56	1.20004	0.600021	−	0.799984i	$-0.295159\pi$
$233$	7.86572e56	1.20004	0.600021	+	0.799984i	$0.295159\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	1.35527e57	1.12325	0.561623	−	0.827393i	$-0.310177\pi$
$239$	1.35527e57	1.12325	0.561623	+	0.827393i	$0.310177\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	5.52293e56	0.339313
$243$	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			$\pi$
$252$	−4.22463e57	−0.982144
$253$	−1.73522e58	−3.66828
$254$	1.36498e57	0.262492
$255$	0	0
$256$	5.18605e57	0.826186
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	1.54432e58	1.86012
$260$	0	0
$261$	−1.79008e58	−1.79267
$262$	0	0
$263$	−2.90032e56	−0.0241829	−0.0120914	−	0.999927i	$-0.503849\pi$
$263$	−2.90032e56	−0.0241829	−0.0120914	+	0.999927i	$0.503849\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−2.78771e58	−1.47915
$269$	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
$274$	−5.93697e57	−0.185162
$275$	6.58329e58	1.88130
$276$	0	0
$277$	−4.06019e58	−0.975062	−0.487531	−	0.873106i	$-0.662102\pi$
$277$	−4.06019e58	−0.975062	−0.487531	+	0.873106i	$0.662102\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	2.21832e58	0.377636	0.188818	−	0.982012i	$-0.439534\pi$
$281$	2.21832e58	0.377636	0.188818	+	0.982012i	$0.439534\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	1.38429e59	1.82637
$285$	0	0
$286$	0	0
$287$	0	0
$288$	4.14965e58	0.391374
$289$	1.15225e59	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
$296$	−1.00825e59	−0.492680
$297$	0	0
$298$	−5.73314e58	−0.238343
$299$	0	0
$300$	0	0
$301$	2.85501e59	0.933280
$302$	−4.84580e58	−0.146285
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	−9.81411e59	−1.84771
$309$	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
$316$	1.76636e60	1.79717
$317$	−7.21709e59	−0.680675	−0.340337	−	0.940303i	$-0.610541\pi$
$317$	−7.21709e59	−0.680675	−0.340337	+	0.940303i	$0.610541\pi$
$318$	0	0
$319$	−4.15848e60	−3.37255
$320$	0	0
$321$	0	0
$322$	−4.02191e59	−0.260550
$323$	0	0
$324$	−1.75896e60	−0.982144
$325$	0	0
$326$	3.91509e59	0.188590
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	4.49002e60	1.50098	0.750492	−	0.660880i	$-0.229817\pi$
$331$	4.49002e60	1.50098	0.750492	+	0.660880i	$0.229817\pi$
$332$	0	0
$333$	6.42989e60	1.86012
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−3.17872e60	−0.690454	−0.345227	−	0.938519i	$-0.612198\pi$
$337$	−3.17872e60	−0.690454	−0.345227	+	0.938519i	$0.612198\pi$
$338$	6.60524e59	0.133625
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	7.03168e60	1.00000
$344$	−1.86397e60	−0.247193
$345$	0	0
$346$	0	0
$347$	8.09827e60	0.871937	0.435968	−	0.899962i	$-0.356406\pi$
$347$	8.09827e60	0.871937	0.435968	+	0.899962i	$0.356406\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	1.52588e60	0.133625
$351$	0	0
$352$	9.63994e60	0.736292
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	3.18359e60	0.162078
$359$	−2.97012e61	−1.41419	−0.707094	−	0.707120i	$-0.749994\pi$
$359$	−2.97012e61	−1.41419	−0.707094	+	0.707120i	$0.749994\pi$
$360$	0	0
$361$	2.39979e61	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			$\pi$
$368$	−7.02405e61	−1.84603
$369$	0	0
$370$	0	0
$371$	1.94192e61	0.420008
$372$	0	0
$373$	−7.23753e61	−1.37587	−0.687936	−	0.725771i	$-0.741483\pi$
$373$	−7.23753e61	−1.37587	−0.687936	+	0.725771i	$0.741483\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−1.20985e62	−1.56816	−0.784081	−	0.620658i	$-0.786865\pi$
$379$	−1.20985e62	−1.56816	−0.784081	+	0.620658i	$0.786865\pi$
$380$	0	0
$381$	0	0
$382$	1.06779e60	0.0114542
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	−2.38359e61	−0.199130
$387$	1.18871e62	0.933280
$388$	0	0
$389$	2.56860e62	1.78199	0.890996	−	0.454011i	$-0.150007\pi$
$389$	2.56860e62	1.78199	0.890996	+	0.454011i	$0.150007\pi$
$390$	0	0
$391$	0	0
$392$	−4.59081e61	−0.264864
$393$	0	0
$394$	5.00828e61	0.255729
$395$	0	0
$396$	−4.08619e62	−1.84771
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	2.66487e62	0.946752
$401$	−1.42653e61	−0.0477327	−0.0238663	−	0.999715i	$-0.507598\pi$
$401$	−1.42653e61	−0.0477327	−0.0238663	+	0.999715i	$0.507598\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	−9.63858e61	−0.239546
$407$	1.49371e63	3.49945
$408$	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
$414$	−1.67456e62	−0.260550
$415$	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
$421$	9.68432e61	0.100762	0.0503812	−	0.998730i	$-0.483956\pi$
$421$	9.68432e61	0.100762	0.0503812	+	0.998730i	$0.483956\pi$
$422$	−5.01524e60	−0.00492939
$423$	0	0
$424$	−1.26783e62	−0.111245
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−2.77249e63	−1.94187
$429$	0	0
$430$	0	0
$431$	−5.87787e62	−0.348149	−0.174075	−	0.984732i	$-0.555693\pi$
$431$	−5.87787e62	−0.348149	−0.174075	+	0.984732i	$0.555693\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	−4.06257e63	−1.82442
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	2.92770e63	1.00000
$442$	0	0
$443$	1.31314e63	0.402366	0.201183	−	0.979554i	$-0.435521\pi$
$443$	1.31314e63	0.402366	0.201183	+	0.979554i	$0.435521\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−3.82147e63	−0.894454
$449$	−5.77488e63	−1.28124	−0.640620	−	0.767858i	$-0.721323\pi$
$449$	−5.77488e63	−1.28124	−0.640620	+	0.767858i	$0.721323\pi$
$450$	6.35314e62	0.133625
$451$	0	0
$452$	1.96432e63	0.371441
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	1.22470e64	1.77844	0.889220	−	0.457479i	$-0.151248\pi$
$457$	1.22470e64	1.77844	0.889220	+	0.457479i	$0.151248\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	1.42199e64	1.50991	0.754956	−	0.655776i	$-0.227658\pi$
$463$	1.42199e64	1.50991	0.754956	+	0.655776i	$0.227658\pi$
$464$	−1.68332e64	−1.69721
$465$	0	0
$466$	1.76338e63	0.160356
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	1.93191e64	1.50604
$470$	0	0
$471$	0	0
$472$	0	0
$473$	2.76145e64	1.75578
$474$	0	0
$475$	0	0
$476$	0	0
$477$	8.08536e63	0.420008
$478$	3.03831e63	0.150094
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−6.81047e64	−2.49395
$485$	0	0
$486$	0	0
$487$	−4.93391e64	−1.55774	−0.778872	−	0.627183i	$-0.784208\pi$
$487$	−4.93391e64	−1.55774	−0.778872	+	0.627183i	$0.784208\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	6.61891e64	1.71724	0.858619	−	0.512615i	$-0.171323\pi$
$491$	6.61891e64	1.71724	0.858619	+	0.512615i	$0.171323\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−9.59325e64	−1.85957
$498$	0	0
$499$	6.19454e64	1.09043	0.545213	−	0.838298i	$-0.316449\pi$
$499$	6.19454e64	1.09043	0.545213	+	0.838298i	$0.316449\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	−1.91142e64	−0.264864
$505$	0	0
$506$	−3.89012e64	−0.490174
$507$	0	0
$508$	−1.68319e65	−1.92932
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	6.54300e64	0.621295
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	3.46214e64	0.248559
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	−4.01310e64	−0.239546
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	−6.50211e62	−0.00323144
$527$	0	0
$528$	0	0
$529$	6.46246e65	2.80196
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−1.26129e65	−0.398897
$537$	0	0
$538$	0	0
$539$	6.80125e65	1.88130
$540$	0	0
$541$	−5.67627e64	−0.143658	−0.0718289	−	0.997417i	$-0.522884\pi$
$541$	−5.67627e64	−0.143658	−0.0718289	+	0.997417i	$0.522884\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−6.30351e65	−1.22430	−0.612148	−	0.790743i	$-0.709694\pi$
$547$	−6.30351e65	−1.22430	−0.612148	+	0.790743i	$0.709694\pi$
$548$	7.32103e65	1.36094
$549$	0	0
$550$	1.47588e65	0.251389
$551$	0	0
$552$	0	0
$553$	−1.22410e66	−1.82985
$554$	−9.10237e64	−0.130293
$555$	0	0
$556$	0	0
$557$	−2.24022e65	−0.281687	−0.140843	−	0.990032i	$-0.544981\pi$
$557$	−2.24022e65	−0.281687	−0.140843	+	0.990032i	$0.544981\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	4.97316e64	0.0504616
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1.21897e66	1.00000
$568$	6.26319e65	0.492534
$569$	−1.40090e66	−1.05612	−0.528058	−	0.849208i	$-0.677080\pi$
$569$	−1.40090e66	−1.05612	−0.528058	+	0.849208i	$0.677080\pi$
$570$	0	0
$571$	−1.83751e66	−1.27340	−0.636698	−	0.771113i	$-0.719700\pi$
$571$	−1.83751e66	−1.27340	−0.636698	+	0.771113i	$0.719700\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−3.32684e66	−1.94986
$576$	−1.59110e66	−0.894454
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	2.58319e65	0.133625
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1.87829e66	0.790162
$584$	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
$592$	6.04643e66	1.76108
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	7.06968e66	1.75182
$597$	0	0
$598$	0	0
$599$	−8.53210e66	−1.87418	−0.937092	−	0.349081i	$-0.886494\pi$
$599$	−8.53210e66	−1.87418	−0.937092	+	0.349081i	$0.886494\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	6.40053e65	0.124710
$603$	8.04365e66	1.50604
$604$	5.97548e66	1.07519
$605$	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
$613$	−6.49326e66	−0.819241	−0.409620	−	0.912256i	$-0.634339\pi$
$613$	−6.49326e66	−0.819241	−0.409620	+	0.912256i	$0.634339\pi$
$614$	0	0
$615$	0	0
$616$	−4.44037e66	−0.498289
$617$	4.86447e66	0.525039	0.262520	−	0.964927i	$-0.415447\pi$
$617$	4.86447e66	0.525039	0.262520	+	0.964927i	$0.415447\pi$
$618$	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
$625$	1.26218e67	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−3.13919e67	−1.97749	−0.988743	−	0.149627i	$-0.952193\pi$
$631$	−3.13919e67	−1.97749	−0.988743	+	0.149627i	$0.952193\pi$
$632$	7.99186e66	0.484661
$633$	0	0
$634$	−1.61797e66	−0.0909552
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−9.32273e66	−0.450657
$639$	−3.99423e67	−1.85957
$640$	0	0
$641$	−1.27735e67	−0.551718	−0.275859	−	0.961198i	$-0.588962\pi$
$641$	−1.27735e67	−0.551718	−0.275859	+	0.961198i	$0.588962\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	4.95952e67	1.91505
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−7.95836e66	−0.264864
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−4.82780e67	−1.38614
$653$	−6.01652e67	−1.66506	−0.832528	−	0.553983i	$-0.813107\pi$
$653$	−6.01652e67	−1.66506	−0.832528	+	0.553983i	$0.813107\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	5.91665e67	1.31470	0.657348	−	0.753587i	$-0.271678\pi$
$659$	5.91665e67	1.31470	0.657348	+	0.753587i	$0.271678\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	1.00660e67	0.200569
$663$	0	0
$664$	0	0
$665$	0	0
$666$	1.44149e67	0.248559
$667$	2.10147e68	3.49546
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−3.71247e67	−0.498083	−0.249041	−	0.968493i	$-0.580116\pi$
$673$	−3.71247e67	−0.498083	−0.249041	+	0.968493i	$0.580116\pi$
$674$	−7.12624e66	−0.0922620
$675$	0	0
$676$	−8.14509e67	−0.982144
$677$	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
$683$	3.28553e67	0.309391	0.154696	−	0.987962i	$-0.450560\pi$
$683$	3.28553e67	0.309391	0.154696	+	0.987962i	$0.450560\pi$
$684$	0	0
$685$	0	0
$686$	1.57640e67	0.133625
$687$	0	0
$688$	1.11782e68	0.883585
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	2.83176e68	1.88130
$694$	1.81552e67	0.116513
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−1.88160e68	−0.982144
$701$	−9.52428e67	−0.480396	−0.240198	−	0.970724i	$-0.577212\pi$
$701$	−9.52428e67	−0.480396	−0.240198	+	0.970724i	$0.577212\pi$
$702$	0	0
$703$	0	0
$704$	−3.69624e68	−1.68274
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	3.38246e68	1.29934	0.649671	−	0.760215i	$-0.274907\pi$
$709$	3.38246e68	1.29934	0.649671	+	0.760215i	$0.274907\pi$
$710$	0	0
$711$	−5.09666e68	−1.82985
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−3.92577e68	−1.19127
$717$	0	0
$718$	−6.65858e67	−0.188971
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	5.37998e67	0.133625
$723$	0	0
$724$	0	0
$725$	−7.97283e68	−1.79267
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	5.07529e68	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
$736$	−4.87151e68	−0.763125
$737$	1.86860e69	2.83332
$738$	0	0
$739$	−1.19352e68	−0.169576	−0.0847878	−	0.996399i	$-0.527021\pi$
$739$	−1.19352e68	−0.169576	−0.0847878	+	0.996399i	$0.527021\pi$
$740$	0	0
$741$	0	0
$742$	4.35351e67	0.0561237
$743$	−4.30796e68	−0.537700	−0.268850	−	0.963182i	$-0.586644\pi$
$743$	−4.30796e68	−0.537700	−0.268850	+	0.963182i	$0.586644\pi$
$744$	0	0
$745$	0	0
$746$	−1.62255e68	−0.183851
$747$	0	0
$748$	0	0
$749$	1.92136e69	1.97717
$750$	0	0
$751$	1.20165e69	1.15989	0.579946	−	0.814655i	$-0.303074\pi$
$751$	1.20165e69	1.15989	0.579946	+	0.814655i	$0.303074\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−2.48507e69	−1.98170	−0.990848	−	0.134986i	$-0.956901\pi$
$757$	−2.48507e69	−1.98170	−0.990848	+	0.134986i	$0.956901\pi$
$758$	−2.71231e68	−0.209546
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	2.81539e69	1.85759
$764$	−1.31672e68	−0.0841884
$765$	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
$772$	2.93927e69	1.46361
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	2.66491e68	0.124710
$775$	0	0
$776$	0	0
$777$	0	0
$778$	5.75843e68	0.238119
$779$	0	0
$780$	0	0
$781$	−9.27888e69	−3.49841
$782$	0	0
$783$	0	0
$784$	2.75310e69	0.946752
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−6.17584e69	−1.87960
$789$	0	0
$790$	0	0
$791$	−1.36129e69	−0.378193
$792$	−1.84878e69	−0.498289
$793$	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
$800$	1.84821e69	0.391374
$801$	0	0
$802$	−3.19808e67	−0.00637829
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1.04953e70	−1.69914	−0.849570	−	0.527477i	$-0.823138\pi$
$809$	−1.04953e70	−1.69914	−0.849570	+	0.527477i	$0.823138\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	1.18856e70	1.76066
$813$	0	0
$814$	3.34868e69	0.467615
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	1.75547e70	1.99599	0.997993	−	0.0633190i	$-0.0201686\pi$
$821$	1.75547e70	1.99599	0.997993	+	0.0633190i	$0.0201686\pi$
$822$	0	0
$823$	−1.85034e70	−1.98452	−0.992260	−	0.124176i	$-0.960371\pi$
$823$	−1.85034e70	−1.98452	−0.992260	+	0.124176i	$0.960371\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−1.18356e70	−1.12995	−0.564974	−	0.825108i	$-0.691114\pi$
$827$	−1.18356e70	−1.12995	−0.564974	+	0.825108i	$0.691114\pi$
$828$	2.06494e70	1.91505
$829$	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
$841$	3.46909e70	2.21366
$842$	2.17109e68	0.0134644
$843$	0	0
$844$	6.18442e68	0.0362310
$845$	0	0
$846$	0	0
$847$	4.71971e70	2.53929
$848$	7.60317e69	0.397644
$849$	0	0
$850$	0	0
$851$	−7.54840e70	−3.62698
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	−1.25441e70	−0.523682
$857$	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
$862$	−1.31773e69	−0.0465215
$863$	5.60929e70	1.92597	0.962983	−	0.269560i	$-0.0868784\pi$
$863$	5.60929e70	1.92597	0.962983	+	0.269560i	$0.0868784\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−1.18399e71	−3.44249
$870$	0	0
$871$	0	0
$872$	−1.83810e70	−0.492009
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−3.74477e70	−0.873845	−0.436923	−	0.899499i	$-0.643932\pi$
$877$	−3.74477e70	−0.873845	−0.436923	+	0.899499i	$0.643932\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	6.56348e69	0.133625
$883$	−9.53575e70	−1.88929	−0.944644	−	0.328098i	$-0.893592\pi$
$883$	−9.53575e70	−1.88929	−0.944644	+	0.328098i	$0.893592\pi$
$884$	0	0
$885$	0	0
$886$	2.94387e69	0.0537662
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	1.16646e71	1.96439
$890$	0	0
$891$	1.17903e71	1.88130
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−3.66205e70	−0.510896
$897$	0	0
$898$	−1.29464e70	−0.171206
$899$	0	0
$900$	−7.83422e70	−0.982144
$901$	0	0
$902$	0	0
$903$	0	0
$904$	8.88750e69	0.100170
$905$	0	0
$906$	0	0
$907$	−9.04422e70	−0.941448	−0.470724	−	0.882281i	$-0.656007\pi$
$907$	−9.04422e70	−0.941448	−0.470724	+	0.882281i	$0.656007\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	2.03358e71	1.90467	0.952334	−	0.305056i	$-0.0986753\pi$
$911$	2.03358e71	1.90467	0.952334	+	0.305056i	$0.0986753\pi$
$912$	0	0
$913$	0	0
$914$	2.74559e70	0.237644
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	2.61130e71	1.98282	0.991411	−	0.130784i	$-0.0417493\pi$
$919$	2.61130e71	1.98282	0.991411	+	0.130784i	$0.0417493\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	2.86380e71	1.86012
$926$	3.18789e70	0.201762
$927$	0	0
$928$	−1.16746e71	−0.701604
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	−2.17447e71	−1.17861
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	4.33106e70	0.201245
$939$	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
$946$	6.19079e70	0.234616
$947$	−5.32700e71	−1.96826	−0.984132	−	0.177439i	$-0.943219\pi$
$947$	−5.32700e71	−1.96826	−0.984132	+	0.177439i	$0.943219\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−2.92475e71	−0.928664	−0.464332	−	0.885661i	$-0.653706\pi$
$953$	−2.92475e71	−0.928664	−0.464332	+	0.885661i	$0.653706\pi$
$954$	1.81262e70	0.0561237
$955$	0	0
$956$	−3.74662e71	−1.10319
$957$	0	0
$958$	0	0
$959$	−5.07353e71	−1.38568
$960$	0	0
$961$	3.84912e71	1.00000
$962$	0	0
$963$	7.99973e71	1.97717
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−4.64708e71	−1.03979	−0.519894	−	0.854231i	$-0.674029\pi$
$967$	−4.64708e71	−1.03979	−0.519894	+	0.854231i	$0.674029\pi$
$968$	−3.08138e71	−0.672568
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	−1.10611e71	−0.208154
$975$	0	0
$976$	0	0
$977$	−4.67867e71	−0.817812	−0.408906	−	0.912577i	$-0.634090\pi$
$977$	−4.67867e71	−0.817812	−0.408906	+	0.912577i	$0.634090\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	1.17221e72	1.85759
$982$	1.48386e71	0.229466
$983$	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
$989$	−1.39549e72	−1.81977
$990$	0	0
$991$	1.60507e72	1.99401	0.997004	−	0.0773547i	$-0.0246474\pi$
$991$	1.60507e72	1.99401	0.997004	+	0.0773547i	$0.0246474\pi$
$992$	0	0
$993$	0	0
$994$	−2.15067e71	−0.248485
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1.38873e71	0.145708
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.49.b.a.6.1	✓	1
7.6	odd	2	CM	7.49.b.a.6.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.49.b.a.6.1	✓	1	1.1	even	1	trivial
7.49.b.a.6.1	✓	1	7.6	odd	2	CM

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:	\( k \)	\(=\)	\( 49 \)
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

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