LMFDB - Embedded newform 31.13.b.a.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,13,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, 13, names="a")

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

chi := DirichletCharacter("31.30");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 13 $
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:	$28.3338083356$
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)

$f(q)$

$=$

$q+97.0000 q^{2} +5313.00 q^{4} +29266.0 q^{5} -50398.0 q^{7} +118049. q^{8} +531441. q^{9} +O(q^{10})$

$q+97.0000 q^{2} +5313.00 q^{4} +29266.0 q^{5} -50398.0 q^{7} +118049. q^{8} +531441. q^{9} +2.83880e6 q^{10} -4.88861e6 q^{14} -1.03113e7 q^{16} +5.15498e7 q^{18} +1.86502e7 q^{19} +1.55490e8 q^{20} +6.12358e8 q^{25} -2.67765e8 q^{28} +8.87504e8 q^{31} -1.48372e9 q^{32} -1.47495e9 q^{35} +2.82355e9 q^{36} +1.80907e9 q^{38} +3.45482e9 q^{40} -5.83294e9 q^{41} +1.55532e10 q^{45} +7.96025e9 q^{47} -1.13013e10 q^{49} +5.93987e10 q^{50} -5.94943e9 q^{56} -6.56353e10 q^{59} +8.60879e10 q^{62} -2.67836e10 q^{63} -1.01686e11 q^{64} -1.63049e11 q^{67} -1.43070e11 q^{70} -1.75443e11 q^{71} +6.27361e10 q^{72} +9.90883e10 q^{76} -3.01770e11 q^{80} +2.82430e11 q^{81} -5.65795e11 q^{82} +1.50866e12 q^{90} +7.72144e11 q^{94} +5.45816e11 q^{95} +1.60108e12 q^{97} -1.09623e12 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

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 $

$2$	97.0000	1.51562	0.757812	−	0.652472i	$-0.226268\pi$
$2$	97.0000	1.51562	0.757813	+	0.652472i	$0.226268\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	5313.00	1.29712
$5$	29266.0	1.87302	0.936512	−	0.350636i	$-0.114034\pi$
$5$	29266.0	1.87302	0.936512	+	0.350636i	$0.114034\pi$
$6$	0	0
$7$	−50398.0	−0.428376	−0.214188	−	0.976792i	$-0.568711\pi$
$7$	−50398.0	−0.428376	−0.214188	+	0.976792i	$0.568711\pi$
$8$	118049.	0.450321
$9$	531441.	1.00000
$10$	2.83880e6	2.83880
$11$	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			$\pi$
$14$	−4.88861e6	−0.649257
$15$	0	0
$16$	−1.03113e7	−0.614601
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	5.15498e7	1.51562
$19$	1.86502e7	0.396425	0.198212	−	0.980159i	$-0.436486\pi$
$19$	1.86502e7	0.396425	0.198212	+	0.980159i	$0.436486\pi$
$20$	1.55490e8	2.42954
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	6.12358e8	2.50822
$26$	0	0
$27$	0	0
$28$	−2.67765e8	−0.555655
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	8.87504e8	1.00000
$31$	8.87504e8	1.00000
$32$	−1.48372e9	−1.38183
$33$	0	0
$34$	0	0
$35$	−1.47495e9	−0.802358
$36$	2.82355e9	1.29712
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	1.80907e9	0.600832
$39$	0	0
$40$	3.45482e9	0.843462
$41$	−5.83294e9	−1.22796	−0.613980	−	0.789322i	$-0.710432\pi$
$41$	−5.83294e9	−1.22796	−0.613980	+	0.789322i	$0.710432\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	1.55532e10	1.87302
$46$	0	0
$47$	7.96025e9	0.738481	0.369240	−	0.929334i	$-0.379618\pi$
$47$	7.96025e9	0.738481	0.369240	+	0.929334i	$0.379618\pi$
$48$	0	0
$49$	−1.13013e10	−0.816494
$50$	5.93987e10	3.80152
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	−5.94943e9	−0.192907
$57$	0	0
$58$	0	0
$59$	−6.56353e10	−1.55606	−0.778029	−	0.628229i	$-0.783780\pi$
$59$	−6.56353e10	−1.55606	−0.778029	+	0.628229i	$0.783780\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	8.60879e10	1.51562
$63$	−2.67836e10	−0.428376
$64$	−1.01686e11	−1.47973
$65$	0	0
$66$	0	0
$67$	−1.63049e11	−1.80248	−0.901238	−	0.433324i	$-0.857341\pi$
$67$	−1.63049e11	−1.80248	−0.901238	+	0.433324i	$0.857341\pi$
$68$	0	0
$69$	0	0
$70$	−1.43070e11	−1.21607
$71$	−1.75443e11	−1.36958	−0.684789	−	0.728741i	$-0.740106\pi$
$71$	−1.75443e11	−1.36958	−0.684789	+	0.728741i	$0.740106\pi$
$72$	6.27361e10	0.450321
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	9.90883e10	0.514210
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−3.01770e11	−1.15116
$81$	2.82430e11	1.00000
$82$	−5.65795e11	−1.86113
$83$	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			$\pi$
$90$	1.50866e12	2.83880
$91$	0	0
$92$	0	0
$93$	0	0
$94$	7.72144e11	1.11926
$95$	5.45816e11	0.742513
$96$	0	0
$97$	1.60108e12	1.92212	0.961062	−	0.276332i	$-0.0891188\pi$
$97$	1.60108e12	1.92212	0.961062	+	0.276332i	$0.0891188\pi$
$98$	−1.09623e12	−1.23750
$99$	0	0
$100$	3.25346e12	3.25346
$101$	−8.15453e11	−0.768193	−0.384097	−	0.923293i	$-0.625487\pi$
$101$	−8.15453e11	−0.768193	−0.384097	+	0.923293i	$0.625487\pi$
$102$	0	0
$103$	−2.06608e12	−1.73031	−0.865156	−	0.501503i	$-0.832781\pi$
$103$	−2.06608e12	−1.73031	−0.865156	+	0.501503i	$0.832781\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−2.98640e12	−1.98996	−0.994982	−	0.100058i	$-0.968097\pi$
$107$	−2.98640e12	−1.98996	−0.994982	+	0.100058i	$0.968097\pi$
$108$	0	0
$109$	−3.31422e12	−1.97616	−0.988082	−	0.153931i	$-0.950807\pi$
$109$	−3.31422e12	−1.97616	−0.988082	+	0.153931i	$0.950807\pi$
$110$	0	0
$111$	0	0
$112$	5.19669e11	0.263280
$113$	4.15246e12	1.99450	0.997251	−	0.0740986i	$-0.0236079\pi$
$113$	4.15246e12	1.99450	0.997251	+	0.0740986i	$0.0236079\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	−6.36663e12	−2.35840
$119$	0	0
$120$	0	0
$121$	3.13843e12	1.00000
$122$	0	0
$123$	0	0
$124$	4.71531e12	1.29712
$125$	1.07763e13	2.82493
$126$	−2.59801e12	−0.649257
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−3.78623e12	−0.860888
$129$	0	0
$130$	0	0
$131$	9.93196e12	1.96520	0.982601	−	0.185729i	$-0.0594647\pi$
$131$	9.93196e12	1.96520	0.982601	+	0.185729i	$0.0594647\pi$
$132$	0	0
$133$	−9.39931e11	−0.169819
$134$	−1.58158e13	−2.73188
$135$	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			$\pi$
$140$	−7.83640e12	−1.04075
$141$	0	0
$142$	−1.70180e13	−2.07577
$143$	0	0
$144$	−5.47984e12	−0.614601
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	7.54559e12	0.689566	0.344783	−	0.938682i	$-0.387953\pi$
$149$	7.54559e12	0.689566	0.344783	+	0.938682i	$0.387953\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	2.20163e12	0.178519
$153$	0	0
$154$	0	0
$155$	2.59737e13	1.87302
$156$	0	0
$157$	1.13474e13	0.757700	0.378850	−	0.925458i	$-0.376320\pi$
$157$	1.13474e13	0.757700	0.378850	+	0.925458i	$0.376320\pi$
$158$	0	0
$159$	0	0
$160$	−4.34227e13	−2.58819
$161$	0	0
$162$	2.73957e13	1.51562
$163$	−3.41290e13	−1.81969	−0.909846	−	0.414946i	$-0.863801\pi$
$163$	−3.41290e13	−1.81969	−0.909846	+	0.414946i	$0.863801\pi$
$164$	−3.09904e13	−1.59281
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	2.32981e13	1.00000
$170$	0	0
$171$	9.91146e12	0.396425
$172$	0	0
$173$	4.82522e13	1.79987	0.899933	−	0.436029i	$-0.143615\pi$
$173$	4.82522e13	1.79987	0.899933	+	0.436029i	$0.143615\pi$
$174$	0	0
$175$	−3.08616e13	−1.07446
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	8.26339e13	2.42954
$181$	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
$188$	4.22928e13	0.957898
$189$	0	0
$190$	5.29441e13	1.12537
$191$	9.49484e13	1.95563	0.977817	−	0.209461i	$-0.0671711\pi$
$191$	9.49484e13	1.95563	0.977817	+	0.209461i	$0.0671711\pi$
$192$	0	0
$193$	−6.42820e13	−1.24378	−0.621892	−	0.783103i	$-0.713636\pi$
$193$	−6.42820e13	−1.24378	−0.621892	+	0.783103i	$0.713636\pi$
$194$	1.55304e14	2.91322
$195$	0	0
$196$	−6.00440e13	−1.05909
$197$	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			$\pi$
$200$	7.22883e13	1.12950
$201$	0	0
$202$	−7.90989e13	−1.16429
$203$	0	0
$204$	0	0
$205$	−1.70707e14	−2.30000
$206$	−2.00410e14	−2.62250
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−2.43085e13	−0.275463	−0.137732	−	0.990470i	$-0.543981\pi$
$211$	−2.43085e13	−0.275463	−0.137732	+	0.990470i	$0.543981\pi$
$212$	0	0
$213$	0	0
$214$	−2.89681e14	−3.01604
$215$	0	0
$216$	0	0
$217$	−4.47284e13	−0.428376
$218$	−3.21480e14	−2.99512
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	7.47767e13	0.591941
$225$	3.25432e14	2.50822
$226$	4.02788e14	3.02292
$227$	−4.63363e13	−0.338662	−0.169331	−	0.985559i	$-0.554161\pi$
$227$	−4.63363e13	−0.338662	−0.169331	+	0.985559i	$0.554161\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−3.05268e14	−1.90786	−0.953928	−	0.300035i	$-0.903002\pi$
$233$	−3.05268e14	−1.90786	−0.953928	+	0.300035i	$0.903002\pi$
$234$	0	0
$235$	2.32965e14	1.38319
$236$	−3.48721e14	−2.01839
$237$	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			$\pi$
$242$	3.04428e14	1.51562
$243$	0	0
$244$	0	0
$245$	−3.30745e14	−1.52931
$246$	0	0
$247$	0	0
$248$	1.04769e14	0.450321
$249$	0	0
$250$	1.04530e15	4.28153
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−1.42301e14	−0.555655
$253$	0	0
$254$	0	0
$255$	0	0
$256$	4.92427e13	0.174945
$257$	−3.33556e14	−1.15763	−0.578816	−	0.815458i	$-0.696485\pi$
$257$	−3.33556e14	−1.15763	−0.578816	+	0.815458i	$0.696485\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	9.63400e14	2.97851
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	−9.11733e13	−0.257382
$267$	0	0
$268$	−8.66280e14	−2.33803
$269$	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
$279$	4.71656e14	1.00000
$280$	−1.74116e14	−0.361319
$281$	9.47299e14	1.92420	0.962098	−	0.272705i	$-0.0879183\pi$
$281$	9.47299e14	1.92420	0.962098	+	0.272705i	$0.0879183\pi$
$282$	0	0
$283$	1.44145e14	0.280595	0.140298	−	0.990109i	$-0.455194\pi$
$283$	1.44145e14	0.280595	0.140298	+	0.990109i	$0.455194\pi$
$284$	−9.32131e14	−1.77651
$285$	0	0
$286$	0	0
$287$	2.93968e14	0.526028
$288$	−7.88512e14	−1.38183
$289$	5.82622e14	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−7.61410e14	−1.20341	−0.601704	−	0.798719i	$-0.705511\pi$
$293$	−7.61410e14	−1.20341	−0.601704	+	0.798719i	$0.705511\pi$
$294$	0	0
$295$	−1.92088e15	−2.91453
$296$	0	0
$297$	0	0
$298$	7.31923e14	1.04512
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−1.92307e14	−0.243643
$305$	0	0
$306$	0	0
$307$	−2.46722e13	−0.0294699	−0.0147349	−	0.999891i	$-0.504690\pi$
$307$	−2.46722e13	−0.0294699	−0.0147349	+	0.999891i	$0.504690\pi$
$308$	0	0
$309$	0	0
$310$	2.51945e15	2.83880
$311$	1.73580e14	0.191839	0.0959195	−	0.995389i	$-0.469421\pi$
$311$	1.73580e14	0.191839	0.0959195	+	0.995389i	$0.469421\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	1.10070e15	1.14839
$315$	−7.83848e14	−0.802358
$316$	0	0
$317$	1.79772e15	1.77160	0.885802	−	0.464063i	$-0.153609\pi$
$317$	1.79772e15	1.77160	0.885802	+	0.464063i	$0.153609\pi$
$318$	0	0
$319$	0	0
$320$	−2.97595e15	−2.77157
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.50055e15	1.29712
$325$	0	0
$326$	−3.31051e15	−2.75797
$327$	0	0
$328$	−6.88572e14	−0.552976
$329$	−4.01180e14	−0.316347
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−4.77179e15	−3.37608
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	2.25991e15	1.51562
$339$	0	0
$340$	0	0
$341$	0	0
$342$	9.61412e14	0.600832
$343$	1.26714e15	0.778142
$344$	0	0
$345$	0	0
$346$	4.68046e15	2.72792
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	6.85340e14	0.379274	0.189637	−	0.981854i	$-0.439269\pi$
$349$	6.85340e14	0.379274	0.189637	+	0.981854i	$0.439269\pi$
$350$	−2.99358e15	−1.62848
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	−5.13453e15	−2.56525
$356$	0	0
$357$	0	0
$358$	0	0
$359$	1.45797e15	0.681055	0.340527	−	0.940235i	$-0.389394\pi$
$359$	1.45797e15	0.681055	0.340527	+	0.940235i	$0.389394\pi$
$360$	1.83603e15	0.843462
$361$	−1.86549e15	−0.842847
$362$	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
$369$	−3.09986e15	−1.22796
$370$	0	0
$371$	0	0
$372$	0	0
$373$	4.51411e15	1.67617	0.838087	−	0.545537i	$-0.183674\pi$
$373$	4.51411e15	1.67617	0.838087	+	0.545537i	$0.183674\pi$
$374$	0	0
$375$	0	0
$376$	9.39699e14	0.332554
$377$	0	0
$378$	0	0
$379$	5.82048e15	1.96392	0.981960	−	0.189088i	$-0.0605531\pi$
$379$	5.82048e15	1.96392	0.981960	+	0.189088i	$0.0605531\pi$
$380$	2.89992e15	0.963128
$381$	0	0
$382$	9.21000e15	2.96401
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	−6.23535e15	−1.88511
$387$	0	0
$388$	8.50652e15	2.49322
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	−1.33411e15	−0.367685
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	6.33802e15	1.61886	0.809432	−	0.587214i	$-0.199775\pi$
$397$	6.33802e15	1.61886	0.809432	+	0.587214i	$0.199775\pi$
$398$	0	0
$399$	0	0
$400$	−6.31421e15	−1.54155
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	−4.33250e15	−0.996438
$405$	8.26558e15	1.87302
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	−1.65586e16	−3.48593
$411$	0	0
$412$	−1.09771e16	−2.24442
$413$	3.30789e15	0.666578
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	8.28806e15	1.53168	0.765841	−	0.643030i	$-0.222323\pi$
$419$	8.28806e15	1.53168	0.765841	+	0.643030i	$0.222323\pi$
$420$	0	0
$421$	−1.10530e16	−1.98513	−0.992566	−	0.121709i	$-0.961162\pi$
$421$	−1.10530e16	−1.98513	−0.992566	+	0.121709i	$0.961162\pi$
$422$	−2.35793e15	−0.417499
$423$	4.23040e15	0.738481
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−1.58667e16	−2.58122
$429$	0	0
$430$	0	0
$431$	−1.27332e16	−1.98643	−0.993214	−	0.116305i	$-0.962895\pi$
$431$	−1.27332e16	−1.98643	−0.993214	+	0.116305i	$0.962895\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	−4.33866e15	−0.649257
$435$	0	0
$436$	−1.76085e16	−2.56332
$437$	0	0
$438$	0	0
$439$	1.30819e16	1.82761	0.913805	−	0.406153i	$-0.133130\pi$
$439$	1.30819e16	1.82761	0.913805	+	0.406153i	$0.133130\pi$
$440$	0	0
$441$	−6.00599e15	−0.816494
$442$	0	0
$443$	−5.40015e12	−0.000714470 0	−0.000357235	−	1.00000i	$-0.500114\pi$
$443$	−5.40015e12	−0.000714470 0	−0.000357235		1.00000i	$0.500114\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	5.12478e15	0.633880
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	3.15669e16	3.80152
$451$	0	0
$452$	2.20620e16	2.58711
$453$	0	0
$454$	−4.49462e15	−0.513284
$455$	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
$466$	−2.96110e16	−2.89159
$467$	−3.57527e15	−0.344674	−0.172337	−	0.985038i	$-0.555132\pi$
$467$	−3.57527e15	−0.344674	−0.172337	+	0.985038i	$0.555132\pi$
$468$	0	0
$469$	8.21735e15	0.772137
$470$	2.25976e16	2.09640
$471$	0	0
$472$	−7.74819e15	−0.700726
$473$	0	0
$474$	0	0
$475$	1.14206e16	0.994321
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−1.87856e16	−1.55529	−0.777646	−	0.628703i	$-0.783586\pi$
$479$	−1.87856e16	−1.55529	−0.777646	+	0.628703i	$0.783586\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	1.66745e16	1.29712
$485$	4.68571e16	3.60019
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	−3.20822e16	−2.31786
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−9.15131e15	−0.614601
$497$	8.84200e15	0.586695
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	5.72542e16	3.66427
$501$	0	0
$502$	0	0
$503$	3.21573e16	1.98551	0.992755	−	0.120153i	$-0.0383384\pi$
$503$	3.21573e16	1.98551	0.992755	+	0.120153i	$0.0383384\pi$
$504$	−3.16177e15	−0.192907
$505$	−2.38650e16	−1.43884
$506$	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
$512$	2.02849e16	1.12604
$513$	0	0
$514$	−3.23550e16	−1.75454
$515$	−6.04660e16	−3.24091
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−3.52656e16	−1.76329	−0.881647	−	0.471909i	$-0.843565\pi$
$521$	−3.52656e16	−1.76329	−0.881647	+	0.471909i	$0.843565\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	5.27685e16	2.54910
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	2.19146e16	1.00000
$530$	0	0
$531$	−3.48813e16	−1.55606
$532$	−4.99385e15	−0.220275
$533$	0	0
$534$	0	0
$535$	−8.73999e16	−3.72725
$536$	−1.92478e16	−0.811693
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	4.09616e16	1.63378	0.816890	−	0.576793i	$-0.195696\pi$
$541$	4.09616e16	1.63378	0.816890	+	0.576793i	$0.195696\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−9.69941e16	−3.70140
$546$	0	0
$547$	3.23819e16	1.20887	0.604433	−	0.796656i	$-0.293400\pi$
$547$	3.23819e16	1.20887	0.604433	+	0.796656i	$0.293400\pi$
$548$	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			$\pi$
$558$	4.57506e16	1.51562
$559$	0	0
$560$	1.52086e16	0.493130
$561$	0	0
$562$	9.18880e16	2.91636
$563$	−4.27926e16	−1.34375	−0.671875	−	0.740665i	$-0.734511\pi$
$563$	−4.27926e16	−1.34375	−0.671875	+	0.740665i	$0.734511\pi$
$564$	0	0
$565$	1.21526e17	3.73575
$566$	1.39821e16	0.425277
$567$	−1.42339e16	−0.428376
$568$	−2.07109e16	−0.616750
$569$	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
$574$	2.85149e16	0.797262
$575$	0	0
$576$	−5.40402e16	−1.47973
$577$	−7.64981e15	−0.207298	−0.103649	−	0.994614i	$-0.533052\pi$
$577$	−7.64981e15	−0.207298	−0.103649	+	0.994614i	$0.533052\pi$
$578$	5.65144e16	1.51562
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−7.38568e16	−1.82392
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	1.65521e16	0.396425
$590$	−1.86326e17	−4.41734
$591$	0	0
$592$	0	0
$593$	−3.62701e16	−0.834106	−0.417053	−	0.908882i	$-0.636937\pi$
$593$	−3.62701e16	−0.834106	−0.417053	+	0.908882i	$0.636937\pi$
$594$	0	0
$595$	0	0
$596$	4.00897e16	0.894449
$597$	0	0
$598$	0	0
$599$	−9.79808e15	−0.212119	−0.106060	−	0.994360i	$-0.533823\pi$
$599$	−9.79808e15	−0.212119	−0.106060	+	0.994360i	$0.533823\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	−8.66510e16	−1.80248
$604$	0	0
$605$	9.18492e16	1.87302
$606$	0	0
$607$	−9.19012e16	−1.83734	−0.918669	−	0.395029i	$-0.870734\pi$
$607$	−9.19012e16	−1.83734	−0.918669	+	0.395029i	$0.870734\pi$
$608$	−2.76717e16	−0.547790
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	−2.39321e15	−0.0446653
$615$	0	0
$616$	0	0
$617$	7.86005e16	1.42467	0.712335	−	0.701839i	$-0.247637\pi$
$617$	7.86005e16	1.42467	0.712335	+	0.701839i	$0.247637\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	1.37998e17	2.42954
$621$	0	0
$622$	1.68372e16	0.290756
$623$	0	0
$624$	0	0
$625$	1.65876e17	2.78294
$626$	0	0
$627$	0	0
$628$	6.02886e16	0.982827
$629$	0	0
$630$	−7.60332e16	−1.21607
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	1.74379e17	2.68509
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−9.32378e16	−1.36958
$640$	−1.10808e17	−1.61246
$641$	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			$\pi$
$648$	3.33405e16	0.450321
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−1.81327e17	−2.36036
$653$	9.96919e16	1.28582	0.642911	−	0.765941i	$-0.277726\pi$
$653$	9.96919e16	1.28582	0.642911	+	0.765941i	$0.277726\pi$
$654$	0	0
$655$	2.90669e17	3.68087
$656$	6.01451e16	0.754705
$657$	0	0
$658$	−3.89145e16	−0.479464
$659$	1.60872e17	1.96412	0.982061	−	0.188565i	$-0.0603836\pi$
$659$	1.60872e17	1.96412	0.982061	+	0.188565i	$0.0603836\pi$
$660$	0	0
$661$	−4.88153e16	−0.585257	−0.292629	−	0.956226i	$-0.594530\pi$
$661$	−4.88153e16	−0.585257	−0.292629	+	0.956226i	$0.594530\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−2.75080e16	−0.318075
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	−4.62864e17	−5.11687
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	1.23783e17	1.29712
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	−8.06910e16	−0.823392
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−2.02981e17	−1.99954	−0.999771	−	0.0213800i	$-0.993194\pi$
$683$	−2.02981e17	−1.99954	−0.999771	+	0.0213800i	$0.993194\pi$
$684$	5.26596e16	0.514210
$685$	0	0
$686$	1.22912e17	1.17937
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−1.01813e17	−0.935262	−0.467631	−	0.883924i	$-0.654892\pi$
$691$	−1.01813e17	−0.935262	−0.467631	+	0.883924i	$0.654892\pi$
$692$	2.56364e17	2.33464
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	6.64780e16	0.574838
$699$	0	0
$700$	−1.63968e17	−1.39370
$701$	−9.62592e16	−0.811211	−0.405606	−	0.914048i	$-0.632939\pi$
$701$	−9.62592e16	−0.811211	−0.405606	+	0.914048i	$0.632939\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	4.10972e16	0.329076
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	−4.98049e17	−3.88796
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	1.41423e17	1.03222
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−1.60373e17	−1.15116
$721$	1.04126e17	0.741224
$722$	−1.80952e17	−1.27744
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−2.38308e17	−1.61410	−0.807052	−	0.590481i	$-0.798938\pi$
$727$	−2.38308e17	−1.61410	−0.807052	+	0.590481i	$0.798938\pi$
$728$	0	0
$729$	1.50095e17	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−3.07244e17	−1.98089	−0.990443	−	0.137920i	$-0.955958\pi$
$733$	−3.07244e17	−1.98089	−0.990443	+	0.137920i	$0.955958\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−3.00687e17	−1.86113
$739$	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
$745$	2.20829e17	1.29157
$746$	4.37869e17	2.54045
$747$	0	0
$748$	0	0
$749$	1.50508e17	0.852452
$750$	0	0
$751$	2.62546e17	1.46341	0.731705	−	0.681622i	$-0.238725\pi$
$751$	2.62546e17	1.46341	0.731705	+	0.681622i	$0.238725\pi$
$752$	−8.20804e16	−0.453871
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	5.64587e17	2.97657
$759$	0	0
$760$	6.44330e16	0.334370
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	1.67030e17	0.846541
$764$	5.04461e17	2.53669
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−3.37440e17	−1.63169	−0.815846	−	0.578269i	$-0.803728\pi$
$769$	−3.37440e17	−1.63169	−0.815846	+	0.578269i	$0.803728\pi$
$770$	0	0
$771$	0	0
$772$	−3.41530e17	−1.61334
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	5.43470e17	2.50822
$776$	1.89005e17	0.865574
$777$	0	0
$778$	0	0
$779$	−1.08785e17	−0.486794
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.16531e17	0.501818
$785$	3.32092e17	1.41919
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	−2.09276e17	−0.854397
$792$	0	0
$793$	0	0
$794$	6.14788e17	2.45359
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−9.08571e17	−3.46592
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−9.62634e16	−0.345934
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	8.01762e17	2.83880
$811$	−4.71505e17	−1.65715	−0.828573	−	0.559881i	$-0.810847\pi$
$811$	−4.71505e17	−1.65715	−0.828573	+	0.559881i	$0.810847\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−9.98819e17	−3.40833
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	−9.06965e17	−2.98337
$821$	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			$\pi$
$824$	−2.43899e17	−0.779196
$825$	0	0
$826$	3.20865e17	1.01028
$827$	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
$838$	8.03941e17	2.32145
$839$	−6.81330e17	−1.95338	−0.976688	−	0.214664i	$-0.931134\pi$
$839$	−6.81330e17	−1.95338	−0.976688	+	0.214664i	$0.931134\pi$
$840$	0	0
$841$	3.53815e17	1.00000
$842$	−1.07215e18	−3.00872
$843$	0	0
$844$	−1.29151e17	−0.357309
$845$	6.81842e17	1.87302
$846$	4.10349e17	1.11926
$847$	−1.58171e17	−0.428376
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−1.41061e16	−0.0366195	−0.0183097	−	0.999832i	$-0.505828\pi$
$853$	−1.41061e16	−0.0366195	−0.0183097	+	0.999832i	$0.505828\pi$
$854$	0	0
$855$	2.90069e17	0.742513
$856$	−3.52541e17	−0.896123
$857$	−4.61467e17	−1.16481	−0.582406	−	0.812898i	$-0.697889\pi$
$857$	−4.61467e17	−1.16481	−0.582406	+	0.812898i	$0.697889\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	−1.23512e18	−3.01068
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	1.41215e18	3.37119
$866$	0	0
$867$	0	0
$868$	−2.37642e17	−0.555655
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−3.91241e17	−0.889908
$873$	8.50877e17	1.92212
$874$	0	0
$875$	−5.43102e17	−1.21013
$876$	0	0
$877$	−8.89369e17	−1.95472	−0.977360	−	0.211584i	$-0.932138\pi$
$877$	−8.89369e17	−1.95472	−0.977360	+	0.211584i	$0.932138\pi$
$878$	1.26894e18	2.76997
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−5.82581e17	−1.23750
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	−5.23815e14	−0.00108287
$887$	6.35021e17	1.30391	0.651953	−	0.758259i	$-0.273950\pi$
$887$	6.35021e17	1.30391	0.651953	+	0.758259i	$0.273950\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	1.48460e17	0.292752
$894$	0	0
$895$	0	0
$896$	1.90818e17	0.368784
$897$	0	0
$898$	0	0
$899$	0	0
$900$	1.72902e18	3.25346
$901$	0	0
$902$	0	0
$903$	0	0
$904$	4.90193e17	0.898166
$905$	0	0
$906$	0	0
$907$	8.34732e16	0.149935	0.0749675	−	0.997186i	$-0.476115\pi$
$907$	8.34732e16	0.149935	0.0749675	+	0.997186i	$0.476115\pi$
$908$	−2.46185e17	−0.439285
$909$	−4.33365e17	−0.768193
$910$	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
$917$	−5.00551e17	−0.841845
$918$	0	0
$919$	2.05550e17	0.341213	0.170606	−	0.985339i	$-0.445427\pi$
$919$	2.05550e17	0.341213	0.170606	+	0.985339i	$0.445427\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−1.09800e18	−1.73031
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	−2.10772e17	−0.323679
$932$	−1.62189e18	−2.47472
$933$	0	0
$934$	−3.46802e17	−0.522396
$935$	0	0
$936$	0	0
$937$	−1.27036e18	−1.87710	−0.938550	−	0.345142i	$-0.887831\pi$
$937$	−1.27036e18	−1.87710	−0.938550	+	0.345142i	$0.887831\pi$
$938$	7.97083e17	1.17027
$939$	0	0
$940$	1.23774e18	1.79417
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	6.76785e17	0.956355
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	1.10780e18	1.50702
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	2.77876e18	3.66295
$956$	0	0
$957$	0	0
$958$	−1.82220e18	−2.35724
$959$	0	0
$960$	0	0
$961$	7.87663e17	1.00000
$962$	0	0
$963$	−1.58709e18	−1.98996
$964$	0	0
$965$	−1.88128e18	−2.32964
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	3.70488e17	0.450321
$969$	0	0
$970$	4.54514e18	5.45653
$971$	1.29105e18	1.54038	0.770191	−	0.637813i	$-0.220161\pi$
$971$	1.29105e18	1.54038	0.770191	+	0.637813i	$0.220161\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1.56323e16	0.0179744	0.00898720	−	0.999960i	$-0.497139\pi$
$977$	1.56323e16	0.0179744	0.00898720	+	0.999960i	$0.497139\pi$
$978$	0	0
$979$	0	0
$980$	−1.75725e18	−1.98370
$981$	−1.76131e18	−1.97616
$982$	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			$\pi$
$992$	−1.31681e18	−1.38183
$993$	0	0
$994$	8.57674e17	0.889209
$995$	0	0
$996$	0	0
$997$	−9.47187e17	−0.964417	−0.482209	−	0.876056i	$-0.660165\pi$
$997$	−9.47187e17	−0.964417	−0.482209	+	0.876056i	$0.660165\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.13.b.a.30.1	✓	1
31.30	odd	2	CM	31.13.b.a.30.1	✓	1

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

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	31.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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