LMFDB - Embedded newform 31.19.b.a.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,19,Mod(30,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("31.30");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$N$	$=$	$31$
Weight:	$k$	$=$	$19$
Character orbit:	$[\chi]$	$=$	31.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:	$63.6697026900$
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			30.1
Character	$\chi$	$=$	31.30

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

f(q)

=

q-495.000 q^{2} -17119.0 q^{4} -3.35569e6 q^{5} +7.22602e7 q^{7} +1.38235e8 q^{8} +3.87420e8 q^{9} +1.66106e9 q^{10} -3.57688e10 q^{14} -6.39388e10 q^{16} -1.91773e11 q^{18} -3.01506e11 q^{19} +5.74460e10 q^{20} +7.44593e12 q^{25} -1.23702e12 q^{28} -2.64396e13 q^{31} -4.58783e12 q^{32} -2.42483e14 q^{35} -6.63225e12 q^{36} +1.49245e14 q^{38} -4.63874e14 q^{40} +6.40888e14 q^{41} -1.30006e15 q^{45} -4.84327e14 q^{47} +3.59312e15 q^{49} -3.68574e15 q^{50} +9.98890e15 q^{56} -1.47537e16 q^{59} +1.30876e16 q^{62} +2.79951e16 q^{63} +1.90321e16 q^{64} +3.38863e16 q^{67} +1.20029e17 q^{70} -8.62604e16 q^{71} +5.35551e16 q^{72} +5.16148e15 q^{76} +2.14558e17 q^{80} +1.50095e17 q^{81} -3.17239e17 q^{82} +6.43530e17 q^{90} +2.39742e17 q^{94} +1.01176e18 q^{95} +1.38834e18 q^{97} -1.77860e18 q^{98} +O(q^{100})

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$ .

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

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

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	−495.000	−0.966797	−0.483398	−	0.875400i	$-0.660598\pi$
$2$	−495.000	−0.966797	−0.483398	+	0.875400i	$0.660598\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	−17119.0	−0.0653038
$5$	−3.35569e6	−1.71811	−0.859056	−	0.511882i	$-0.828948\pi$
$5$	−3.35569e6	−1.71811	−0.859056	+	0.511882i	$0.828948\pi$
$6$	0	0
$7$	7.22602e7	1.79068	0.895338	−	0.445388i	$-0.146934\pi$
$7$	7.22602e7	1.79068	0.895338	+	0.445388i	$0.146934\pi$
$8$	1.38235e8	1.02993
$9$	3.87420e8	1.00000
$10$	1.66106e9	1.66106
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−3.57688e10	−1.73122
$15$	0	0
$16$	−6.39388e10	−0.930432
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−1.91773e11	−0.966797
$19$	−3.01506e11	−0.934358	−0.467179	−	0.884163i	$-0.654730\pi$
$19$	−3.01506e11	−0.934358	−0.467179	+	0.884163i	$0.654730\pi$
$20$	5.74460e10	0.112199
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	7.44593e12	1.95191
$26$	0	0
$27$	0	0
$28$	−1.23702e12	−0.116938
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	−2.64396e13	−1.00000
$31$	−2.64396e13	−1.00000
$32$	−4.58783e12	−0.130394
$33$	0	0
$34$	0	0
$35$	−2.42483e14	−3.07658
$36$	−6.63225e12	−0.0653038
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	1.49245e14	0.903334
$39$	0	0
$40$	−4.63874e14	−1.76954
$41$	6.40888e14	1.95762	0.978808	−	0.204782i	$-0.0656486\pi$
$41$	6.40888e14	1.95762	0.978808	+	0.204782i	$0.0656486\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	−1.30006e15	−1.71811
$46$	0	0
$47$	−4.84327e14	−0.432771	−0.216386	−	0.976308i	$-0.569427\pi$
$47$	−4.84327e14	−0.432771	−0.216386	+	0.976308i	$0.569427\pi$
$48$	0	0
$49$	3.59312e15	2.20652
$50$	−3.68574e15	−1.88710
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	9.98890e15	1.84427
$57$	0	0
$58$	0	0
$59$	−1.47537e16	−1.70308	−0.851538	−	0.524293i	$-0.824330\pi$
$59$	−1.47537e16	−1.70308	−0.851538	+	0.524293i	$0.824330\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	1.30876e16	0.966797
$63$	2.79951e16	1.79068
$64$	1.90321e16	1.05650
$65$	0	0
$66$	0	0
$67$	3.38863e16	1.24552	0.622761	−	0.782412i	$-0.286011\pi$
$67$	3.38863e16	1.24552	0.622761	+	0.782412i	$0.286011\pi$
$68$	0	0
$69$	0	0
$70$	1.20029e17	2.97443
$71$	−8.62604e16	−1.88142	−0.940712	−	0.339207i	$-0.889841\pi$
$71$	−8.62604e16	−1.88142	−0.940712	+	0.339207i	$0.889841\pi$
$72$	5.35551e16	1.02993
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	5.16148e15	0.0610171
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	2.14558e17	1.59859
$81$	1.50095e17	1.00000
$82$	−3.17239e17	−1.89262
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	6.43530e17	1.66106
$91$	0	0
$92$	0	0
$93$	0	0
$94$	2.39742e17	0.418402
$95$	1.01176e18	1.60533
$96$	0	0
$97$	1.38834e18	1.82621	0.913104	−	0.407726i	$-0.133678\pi$
$97$	1.38834e18	1.82621	0.913104	+	0.407726i	$0.133678\pi$
$98$	−1.77860e18	−2.13325
$99$	0	0
$100$	−1.27467e17	−0.127467
$101$	−2.14631e18	−1.96246	−0.981230	−	0.192839i	$-0.938231\pi$
$101$	−2.14631e18	−1.96246	−0.981230	+	0.192839i	$0.938231\pi$
$102$	0	0
$103$	1.85003e18	1.41789	0.708946	−	0.705262i	$-0.249171\pi$
$103$	1.85003e18	1.41789	0.708946	+	0.705262i	$0.249171\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−5.50705e17	−0.299547	−0.149774	−	0.988720i	$-0.547854\pi$
$107$	−5.50705e17	−0.299547	−0.149774	+	0.988720i	$0.547854\pi$
$108$	0	0
$109$	9.97975e17	0.459496	0.229748	−	0.973250i	$-0.426210\pi$
$109$	9.97975e17	0.459496	0.229748	+	0.973250i	$0.426210\pi$
$110$	0	0
$111$	0	0
$112$	−4.62023e18	−1.66610
$113$	5.97094e18	1.98764	0.993818	−	0.111020i	$-0.0354119\pi$
$113$	5.97094e18	1.98764	0.993818	+	0.111020i	$0.0354119\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	7.30310e18	1.64653
$119$	0	0
$120$	0	0
$121$	5.55992e18	1.00000
$122$	0	0
$123$	0	0
$124$	4.52620e17	0.0653038
$125$	−1.21853e19	−1.63548
$126$	−1.38576e19	−1.73122
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−8.21824e18	−0.891023
$129$	0	0
$130$	0	0
$131$	−2.18370e19	−1.92199	−0.960994	−	0.276568i	$-0.910803\pi$
$131$	−2.18370e19	−1.92199	−0.960994	+	0.276568i	$0.910803\pi$
$132$	0	0
$133$	−2.17869e19	−1.67313
$134$	−1.67737e19	−1.20417
$135$	0	0
$136$	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			$\pi$
$140$	4.15106e18	0.200912
$141$	0	0
$142$	4.26989e19	1.81895
$143$	0	0
$144$	−2.47712e19	−0.930432
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−1.84284e19	−0.509109	−0.254554	−	0.967058i	$-0.581929\pi$
$149$	−1.84284e19	−0.509109	−0.254554	+	0.967058i	$0.581929\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	−4.16787e19	−0.962325
$153$	0	0
$154$	0	0
$155$	8.87231e19	1.71811
$156$	0	0
$157$	2.33197e19	0.402371	0.201185	−	0.979553i	$-0.435521\pi$
$157$	2.33197e19	0.402371	0.201185	+	0.979553i	$0.435521\pi$
$158$	0	0
$159$	0	0
$160$	1.53953e19	0.224031
$161$	0	0
$162$	−7.42968e19	−0.966797
$163$	9.72517e19	1.19732	0.598658	−	0.801005i	$-0.295701\pi$
$163$	9.72517e19	1.19732	0.598658	+	0.801005i	$0.295701\pi$
$164$	−1.09714e19	−0.127840
$165$	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
$171$	−1.16810e20	−0.934358
$172$	0	0
$173$	2.16429e20	1.55920	0.779599	−	0.626279i	$-0.215423\pi$
$173$	2.16429e20	1.55920	0.779599	+	0.626279i	$0.215423\pi$
$174$	0	0
$175$	5.38045e20	3.49523
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	2.22558e19	0.112199
$181$	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
$188$	8.29120e18	0.0282616
$189$	0	0
$190$	−5.00821e20	−1.55203
$191$	6.42984e20	1.90064	0.950319	−	0.311277i	$-0.100757\pi$
$191$	6.42984e20	1.90064	0.950319	+	0.311277i	$0.100757\pi$
$192$	0	0
$193$	−7.24969e20	−1.95121	−0.975605	−	0.219534i	$-0.929546\pi$
$193$	−7.24969e20	−1.95121	−0.975605	+	0.219534i	$0.929546\pi$
$194$	−6.87229e20	−1.76557
$195$	0	0
$196$	−6.15107e19	−0.144094
$197$	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			$\pi$
$200$	1.02929e21	2.01033
$201$	0	0
$202$	1.06243e21	1.89730
$203$	0	0
$204$	0	0
$205$	−2.15062e21	−3.36340
$206$	−9.15764e20	−1.37081
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	1.38850e21	1.67496	0.837480	−	0.546469i	$-0.184028\pi$
$211$	1.38850e21	1.67496	0.837480	+	0.546469i	$0.184028\pi$
$212$	0	0
$213$	0	0
$214$	2.72599e20	0.289601
$215$	0	0
$216$	0	0
$217$	−1.91053e21	−1.79068
$218$	−4.93998e20	−0.444239
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	−3.31518e20	−0.233493
$225$	2.88471e21	1.95191
$226$	−2.95562e21	−1.92164
$227$	2.76142e21	1.72544	0.862720	−	0.505682i	$-0.168759\pi$
$227$	2.76142e21	1.72544	0.862720	+	0.505682i	$0.168759\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−1.78653e21	−0.882685	−0.441343	−	0.897339i	$-0.645498\pi$
$233$	−1.78653e21	−0.882685	−0.441343	+	0.897339i	$0.645498\pi$
$234$	0	0
$235$	1.62525e21	0.743549
$236$	2.52569e20	0.111217
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−2.75216e21	−0.966797
$243$	0	0
$244$	0	0
$245$	−1.20574e22	−3.79104
$246$	0	0
$247$	0	0
$248$	−3.65489e21	−1.02993
$249$	0	0
$250$	6.03171e21	1.58118
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−4.79248e20	−0.116938
$253$	0	0
$254$	0	0
$255$	0	0
$256$	−9.21134e20	−0.195058
$257$	9.68560e21	1.98029	0.990144	−	0.140053i	$-0.0447274\pi$
$257$	9.68560e21	1.98029	0.990144	+	0.140053i	$0.0447274\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	1.08093e22	1.85817
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	1.07845e22	1.61758
$267$	0	0
$268$	−5.80100e20	−0.0813373
$269$	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	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	−1.02433e22	−1.00000
$280$	−3.35196e22	−3.16867
$281$	−1.99984e22	−1.83079	−0.915396	−	0.402554i	$-0.868123\pi$
$281$	−1.99984e22	−1.83079	−0.915396	+	0.402554i	$0.868123\pi$
$282$	0	0
$283$	1.26496e22	1.08642	0.543209	−	0.839597i	$-0.317209\pi$
$283$	1.26496e22	1.08642	0.543209	+	0.839597i	$0.317209\pi$
$284$	1.47669e21	0.122864
$285$	0	0
$286$	0	0
$287$	4.63107e22	3.50545
$288$	−1.77742e21	−0.130394
$289$	1.40631e22	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	3.12984e22	1.96659	0.983293	−	0.182031i	$-0.0582670\pi$
$293$	3.12984e22	1.96659	0.983293	+	0.182031i	$0.0582670\pi$
$294$	0	0
$295$	4.95089e22	2.92607
$296$	0	0
$297$	0	0
$298$	9.12204e21	0.492205
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	1.92779e22	0.869356
$305$	0	0
$306$	0	0
$307$	−3.50067e22	−1.44512	−0.722562	−	0.691306i	$-0.757036\pi$
$307$	−3.50067e22	−1.44512	−0.722562	+	0.691306i	$0.757036\pi$
$308$	0	0
$309$	0	0
$310$	−4.39179e22	−1.66106
$311$	−3.25646e22	−1.19647	−0.598236	−	0.801320i	$-0.704131\pi$
$311$	−3.25646e22	−1.19647	−0.598236	+	0.801320i	$0.704131\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	−1.15433e22	−0.389011
$315$	−9.39427e22	−3.07658
$316$	0	0
$317$	4.84386e22	1.49850	0.749252	−	0.662285i	$-0.230413\pi$
$317$	4.84386e22	1.49850	0.749252	+	0.662285i	$0.230413\pi$
$318$	0	0
$319$	0	0
$320$	−6.38659e22	−1.81518
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−2.56947e21	−0.0653038
$325$	0	0
$326$	−4.81396e22	−1.15756
$327$	0	0
$328$	8.85932e22	2.01621
$329$	−3.49976e22	−0.774952
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−1.13712e23	−2.13995
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−5.56654e22	−0.966797
$339$	0	0
$340$	0	0
$341$	0	0
$342$	5.78207e22	0.903334
$343$	1.41970e23	2.16048
$344$	0	0
$345$	0	0
$346$	−1.07132e23	−1.50743
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	7.35446e22	0.957463	0.478731	−	0.877961i	$-0.341097\pi$
$349$	7.35446e22	0.957463	0.478731	+	0.877961i	$0.341097\pi$
$350$	−2.66332e23	−3.37918
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	2.89463e23	3.23249
$356$	0	0
$357$	0	0
$358$	0	0
$359$	5.17272e22	0.522238	0.261119	−	0.965307i	$-0.415908\pi$
$359$	5.17272e22	0.522238	0.261119	+	0.965307i	$0.415908\pi$
$360$	−1.79714e23	−1.76954
$361$	−1.32216e22	−0.126976
$362$	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
$369$	2.48293e23	1.95762
$370$	0	0
$371$	0	0
$372$	0	0
$373$	1.81191e23	1.29645	0.648226	−	0.761448i	$-0.275511\pi$
$373$	1.81191e23	1.29645	0.648226	+	0.761448i	$0.275511\pi$
$374$	0	0
$375$	0	0
$376$	−6.69511e22	−0.445725
$377$	0	0
$378$	0	0
$379$	3.09640e23	1.91913	0.959563	−	0.281493i	$-0.0908297\pi$
$379$	3.09640e23	1.91913	0.959563	+	0.281493i	$0.0908297\pi$
$380$	−1.73203e22	−0.104834
$381$	0	0
$382$	−3.18277e23	−1.83753
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	3.58860e23	1.88642
$387$	0	0
$388$	−2.37670e22	−0.119258
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	4.96696e23	2.27256
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	2.88400e23	1.17728	0.588642	−	0.808394i	$-0.299663\pi$
$397$	2.88400e23	1.17728	0.588642	+	0.808394i	$0.299663\pi$
$398$	0	0
$399$	0	0
$400$	−4.76084e23	−1.81612
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	3.67428e22	0.128156
$405$	−5.03670e23	−1.71811
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	1.06456e24	3.25173
$411$	0	0
$412$	−3.16706e22	−0.0925938
$413$	−1.06611e24	−3.04966
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−3.97712e23	−0.999177	−0.499588	−	0.866263i	$-0.666515\pi$
$419$	−3.97712e23	−0.999177	−0.499588	+	0.866263i	$0.666515\pi$
$420$	0	0
$421$	1.51229e23	0.363995	0.181998	−	0.983299i	$-0.441744\pi$
$421$	1.51229e23	0.363995	0.181998	+	0.983299i	$0.441744\pi$
$422$	−6.87308e23	−1.61935
$423$	−1.87638e23	−0.432771
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	9.42752e21	0.0195616
$429$	0	0
$430$	0	0
$431$	1.78560e23	0.347928	0.173964	−	0.984752i	$-0.444342\pi$
$431$	1.78560e23	0.347928	0.173964	+	0.984752i	$0.444342\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	9.45714e23	1.73122
$435$	0	0
$436$	−1.70843e22	−0.0300068
$437$	0	0
$438$	0	0
$439$	−9.80551e23	−1.61916	−0.809580	−	0.587010i	$-0.800305\pi$
$439$	−9.80551e23	−1.61916	−0.809580	+	0.587010i	$0.800305\pi$
$440$	0	0
$441$	1.39205e24	2.20652
$442$	0	0
$443$	−9.29782e23	−1.41497	−0.707486	−	0.706728i	$-0.750171\pi$
$443$	−9.29782e23	−1.41497	−0.707486	+	0.706728i	$0.750171\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	1.37527e24	1.89184
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	−1.42793e24	−1.88710
$451$	0	0
$452$	−1.02217e23	−0.129800
$453$	0	0
$454$	−1.36690e24	−1.66815
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	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	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	8.84330e23	0.853377
$467$	1.82772e24	1.73005	0.865025	−	0.501729i	$-0.167302\pi$
$467$	1.82772e24	1.73005	0.865025	+	0.501729i	$0.167302\pi$
$468$	0	0
$469$	2.44863e24	2.23033
$470$	−8.04499e23	−0.718861
$471$	0	0
$472$	−2.03949e24	−1.75405
$473$	0	0
$474$	0	0
$475$	−2.24499e24	−1.82378
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−2.26203e24	−1.70403	−0.852017	−	0.523514i	$-0.824621\pi$
$479$	−2.26203e24	−1.70403	−0.852017	+	0.523514i	$0.824621\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−9.51802e22	−0.0653038
$485$	−4.65883e24	−3.13763
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	5.96841e24	3.66517
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	1.69052e24	0.930432
$497$	−6.23320e24	−3.36902
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	2.08600e23	0.106803
$501$	0	0
$502$	0	0
$503$	4.05523e24	1.96745	0.983724	−	0.179684i	$-0.0575077\pi$
$503$	4.05523e24	1.96745	0.983724	+	0.179684i	$0.0575077\pi$
$504$	3.86991e24	1.84427
$505$	7.20236e24	3.37173
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	2.61032e24	1.07960
$513$	0	0
$514$	−4.79437e24	−1.91454
$515$	−6.20812e24	−2.43610
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	3.80252e24	1.34441	0.672205	−	0.740365i	$-0.265347\pi$
$521$	3.80252e24	1.34441	0.672205	+	0.740365i	$0.265347\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	3.73827e23	0.125513
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	3.24415e24	1.00000
$530$	0	0
$531$	−5.71590e24	−1.70308
$532$	3.72969e23	0.109262
$533$	0	0
$534$	0	0
$535$	1.84799e24	0.514655
$536$	4.68429e24	1.28280
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	4.79616e24	1.20814	0.604071	−	0.796931i	$-0.293544\pi$
$541$	4.79616e24	1.20814	0.604071	+	0.796931i	$0.293544\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−3.34889e24	−0.789464
$546$	0	0
$547$	−1.64032e24	−0.374148	−0.187074	−	0.982346i	$-0.559900\pi$
$547$	−1.64032e24	−0.374148	−0.187074	+	0.982346i	$0.559900\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	5.07041e24	0.966797
$559$	0	0
$560$	1.55040e25	2.86255
$561$	0	0
$562$	9.89923e24	1.77000
$563$	1.07900e25	1.89865	0.949327	−	0.314289i	$-0.101766\pi$
$563$	1.07900e25	1.89865	0.949327	+	0.314289i	$0.101766\pi$
$564$	0	0
$565$	−2.00366e25	−3.41498
$566$	−6.26153e24	−1.05035
$567$	1.08459e25	1.79068
$568$	−1.19242e25	−1.93774
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	−2.29238e25	−3.38906
$575$	0	0
$576$	7.37344e24	1.05650
$577$	−1.14591e25	−1.61647	−0.808237	−	0.588858i	$-0.799578\pi$
$577$	−1.14591e25	−1.61647	−0.808237	+	0.588858i	$0.799578\pi$
$578$	−6.96123e24	−0.966797
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−1.54927e25	−1.90129
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	7.97170e24	0.934358
$590$	−2.45069e25	−2.82892
$591$	0	0
$592$	0	0
$593$	−1.79575e25	−1.98040	−0.990202	−	0.139640i	$-0.955406\pi$
$593$	−1.79575e25	−1.98040	−0.990202	+	0.139640i	$0.955406\pi$
$594$	0	0
$595$	0	0
$596$	3.15475e23	0.0332467
$597$	0	0
$598$	0	0
$599$	1.60900e25	1.62074	0.810372	−	0.585915i	$-0.199265\pi$
$599$	1.60900e25	1.62074	0.810372	+	0.585915i	$0.199265\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	1.31283e25	1.24552
$604$	0	0
$605$	−1.86573e25	−1.71811
$606$	0	0
$607$	−1.28013e25	−1.14434	−0.572170	−	0.820135i	$-0.693898\pi$
$607$	−1.28013e25	−1.14434	−0.572170	+	0.820135i	$0.693898\pi$
$608$	1.38326e24	0.121835
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	1.73283e25	1.39714
$615$	0	0
$616$	0	0
$617$	1.01842e25	0.785890	0.392945	−	0.919562i	$-0.371456\pi$
$617$	1.01842e25	0.785890	0.392945	+	0.919562i	$0.371456\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	−1.51885e24	−0.112199
$621$	0	0
$622$	1.61195e25	1.15674
$623$	0	0
$624$	0	0
$625$	1.24860e25	0.858032
$626$	0	0
$627$	0	0
$628$	−3.99210e23	−0.0262763
$629$	0	0
$630$	4.65016e25	2.97443
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	−2.39771e25	−1.44875
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−3.34191e25	−1.88142
$640$	2.75778e25	1.53088
$641$	0	0	1.00000			$0$
$641$	0	0	−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			$\pi$
$648$	2.07484e25	1.02993
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−1.66485e24	−0.0781893
$653$	−1.11850e25	−0.518106	−0.259053	−	0.965863i	$-0.583410\pi$
$653$	−1.11850e25	−0.518106	−0.259053	+	0.965863i	$0.583410\pi$
$654$	0	0
$655$	7.32780e25	3.30219
$656$	−4.09776e25	−1.82143
$657$	0	0
$658$	1.73238e25	0.749222
$659$	−4.49960e25	−1.91958	−0.959788	−	0.280727i	$-0.909425\pi$
$659$	−4.49960e25	−1.91958	−0.959788	+	0.280727i	$0.909425\pi$
$660$	0	0
$661$	−4.54205e25	−1.88555	−0.942776	−	0.333427i	$-0.891795\pi$
$661$	−4.54205e25	−1.88555	−0.942776	+	0.333427i	$0.891795\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	7.31099e25	2.87463
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	5.62874e25	2.06889
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	−1.92512e24	−0.0653038
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	1.00322e26	3.27015
$680$	0	0
$681$	0	0
$682$	0	0
$683$	2.07431e24	0.0641339	0.0320669	−	0.999486i	$-0.489791\pi$
$683$	2.07431e24	0.0641339	0.0320669	+	0.999486i	$0.489791\pi$
$684$	1.99966e24	0.0610171
$685$	0	0
$686$	−7.02754e25	−2.08875
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−7.17238e25	−1.99692	−0.998461	−	0.0554562i	$-0.982339\pi$
$691$	−7.17238e25	−1.99692	−0.998461	+	0.0554562i	$0.982339\pi$
$692$	−3.70505e24	−0.101822
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−3.64046e25	−0.925672
$699$	0	0
$700$	−9.21078e24	−0.228252
$701$	8.07205e25	1.97479	0.987396	−	0.158268i	$-0.0505909\pi$
$701$	8.07205e25	1.97479	0.987396	+	0.158268i	$0.0505909\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−1.55093e26	−3.51413
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	−1.43284e26	−3.12517
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−2.56050e25	−0.504899
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	8.31243e25	1.59859
$721$	1.33683e26	2.53899
$722$	6.54471e24	0.122760
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−9.21230e25	−1.62390	−0.811948	−	0.583729i	$-0.801593\pi$
$727$	−9.21230e25	−1.62390	−0.811948	+	0.583729i	$0.801593\pi$
$728$	0	0
$729$	5.81497e25	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	2.51738e25	0.412109	0.206055	−	0.978541i	$-0.433938\pi$
$733$	2.51738e25	0.412109	0.206055	+	0.978541i	$0.433938\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−1.22905e26	−1.89262
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	6.18398e25	0.874705
$746$	−8.96894e25	−1.25341
$747$	0	0
$748$	0	0
$749$	−3.97941e25	−0.536392
$750$	0	0
$751$	6.55355e25	0.862417	0.431208	−	0.902252i	$-0.358087\pi$
$751$	6.55355e25	0.862417	0.431208	+	0.902252i	$0.358087\pi$
$752$	3.09673e25	0.402664
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−1.53272e26	−1.85541
$759$	0	0
$760$	1.39861e26	1.65338
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	7.21139e25	0.822807
$764$	−1.10072e25	−0.124119
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	1.50203e26	1.59713	0.798565	−	0.601908i	$-0.205593\pi$
$769$	1.50203e26	1.59713	0.798565	+	0.601908i	$0.205593\pi$
$770$	0	0
$771$	0	0
$772$	1.24108e25	0.127421
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	−1.96868e26	−1.95191
$776$	1.91917e26	1.88087
$777$	0	0
$778$	0	0
$779$	−1.93231e26	−1.82911
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−2.29740e26	−2.05301
$785$	−7.82537e25	−0.691318
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	4.31462e26	3.55921
$792$	0	0
$793$	0	0
$794$	−1.42758e26	−1.13819
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−3.41607e25	−0.254517
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−2.96696e26	−2.02120
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	2.49317e26	1.66106
$811$	2.36134e26	1.55586	0.777929	−	0.628352i	$-0.216270\pi$
$811$	2.36134e26	1.55586	0.777929	+	0.628352i	$0.216270\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−3.26346e26	−2.05712
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	3.68164e25	0.219643
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	2.55739e26	1.46033
$825$	0	0
$826$	5.27724e26	2.94840
$827$	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
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	1.96867e26	0.966001
$839$	−1.31365e26	−0.637710	−0.318855	−	0.947804i	$-0.603298\pi$
$839$	−1.31365e26	−0.637710	−0.318855	+	0.947804i	$0.603298\pi$
$840$	0	0
$841$	2.10457e26	1.00000
$842$	−7.48582e25	−0.351909
$843$	0	0
$844$	−2.37698e25	−0.109381
$845$	−3.77365e26	−1.71811
$846$	9.28810e25	0.418402
$847$	4.01761e26	1.79068
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	3.47267e26	1.45252	0.726259	−	0.687421i	$-0.241257\pi$
$853$	3.47267e26	1.45252	0.726259	+	0.687421i	$0.241257\pi$
$854$	0	0
$855$	3.91976e26	1.60533
$856$	−7.61268e25	−0.308513
$857$	−4.93332e26	−1.97839	−0.989196	−	0.146600i	$-0.953167\pi$
$857$	−4.93332e26	−1.97839	−0.989196	+	0.146600i	$0.953167\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	−8.83873e25	−0.336376
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	−7.26269e26	−2.67887
$866$	0	0
$867$	0	0
$868$	3.27064e25	0.116938
$869$	0	0
$870$	0	0
$871$	0	0
$872$	1.37955e26	0.473249
$873$	5.37872e26	1.82621
$874$	0	0
$875$	−8.80511e26	−2.92862
$876$	0	0
$877$	−1.92960e26	−0.628740	−0.314370	−	0.949300i	$-0.601793\pi$
$877$	−1.92960e26	−0.628740	−0.314370	+	0.949300i	$0.601793\pi$
$878$	4.85373e26	1.56540
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−6.89065e26	−2.13325
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	4.60242e26	1.36799
$887$	1.87744e26	0.552400	0.276200	−	0.961100i	$-0.410925\pi$
$887$	1.87744e26	0.552400	0.276200	+	0.961100i	$0.410925\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	1.46027e26	0.404363
$894$	0	0
$895$	0	0
$896$	−5.93852e26	−1.59553
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−4.93833e25	−0.127467
$901$	0	0
$902$	0	0
$903$	0	0
$904$	8.25394e26	2.04713
$905$	0	0
$906$	0	0
$907$	5.17762e26	1.24642	0.623211	−	0.782054i	$-0.285828\pi$
$907$	5.17762e26	1.24642	0.623211	+	0.782054i	$0.285828\pi$
$908$	−4.72728e25	−0.112678
$909$	−8.31526e26	−1.96246
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−1.57794e27	−3.44166
$918$	0	0
$919$	−4.71308e26	−1.00801	−0.504006	−	0.863700i	$-0.668141\pi$
$919$	−4.71308e26	−1.00801	−0.504006	+	0.863700i	$0.668141\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	7.16739e26	1.41789
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	−1.08335e27	−2.06168
$932$	3.05835e25	0.0576427
$933$	0	0
$934$	−9.04723e26	−1.67261
$935$	0	0
$936$	0	0
$937$	−5.61547e26	−1.00862	−0.504312	−	0.863521i	$-0.668254\pi$
$937$	−5.61547e26	−1.00862	−0.504312	+	0.863521i	$0.668254\pi$
$938$	−1.21207e27	−2.15627
$939$	0	0
$940$	−2.78227e25	−0.0485566
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	9.43336e26	1.58460
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	1.11127e27	1.76322
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	−2.15765e27	−3.26551
$956$	0	0
$957$	0	0
$958$	1.11970e27	1.64745
$959$	0	0
$960$	0	0
$961$	6.99054e26	1.00000
$962$	0	0
$963$	−2.13355e26	−0.299547
$964$	0	0
$965$	2.43277e27	3.35240
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	7.68576e26	1.02993
$969$	0	0
$970$	2.30612e27	3.03345
$971$	7.80188e26	1.01678	0.508389	−	0.861128i	$-0.330241\pi$
$971$	7.80188e26	1.01678	0.508389	+	0.861128i	$0.330241\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1.13144e27	1.39502	0.697510	−	0.716575i	$-0.254291\pi$
$977$	1.13144e27	1.39502	0.697510	+	0.716575i	$0.254291\pi$
$978$	0	0
$979$	0	0
$980$	2.06411e26	0.247570
$981$	3.86636e26	0.459496
$982$	0	0
$983$	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	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	1.21301e26	0.130394
$993$	0	0
$994$	3.08543e27	3.25716
$995$	0	0
$996$	0	0
$997$	−1.94573e27	−1.99906	−0.999531	−	0.0306324i	$-0.990248\pi$
$997$	−1.94573e27	−1.99906	−0.999531	+	0.0306324i	$0.990248\pi$
$998$	0	0
$999$	0	0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.19.b.a.30.1	✓	1
31.30	odd	2	CM	31.19.b.a.30.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.19.b.a.30.1	✓	1	1.1	even	1	trivial
31.19.b.a.30.1	✓	1	31.30	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	31.19.b.a.30.1

Level	$31$
Weight	$19$
Character	31.30
Self dual	yes
Analytic conductor	$63.670$
Analytic rank	$0$
Dimension	$1$
CM discriminant	-31
Inner twists	$2$