LMFDB - Embedded newform 8281.2.a.bm.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.a (trivial)

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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.1
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.246980 q^{2} -1.93900 q^{4} +0.972853 q^{8} -3.00000 q^{9} -6.63102 q^{11} +3.63773 q^{16} +0.740939 q^{18} +1.63773 q^{22} -6.93900 q^{23} -5.00000 q^{25} -6.39373 q^{29} -2.84415 q^{32} +5.81700 q^{36} -11.6528 q^{37} +8.51573 q^{43} +12.8576 q^{44} +1.71379 q^{46} +1.23490 q^{50} -8.09246 q^{53} +1.57912 q^{58} -6.57301 q^{64} -14.5864 q^{67} +8.71917 q^{71} -2.91856 q^{72} +2.87800 q^{74} -7.42327 q^{79} +9.00000 q^{81} -2.10321 q^{86} -6.45101 q^{88} +13.4547 q^{92} +19.8931 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} + 4 q^{4} + 9 q^{8} - 9 q^{9} - 5 q^{11} + 18 q^{16} - 12 q^{18} + 12 q^{22} - 11 q^{23} - 15 q^{25} + 13 q^{29} + 27 q^{32} - 12 q^{36} - 17 q^{37} + 13 q^{43} + 47 q^{44} - 3 q^{46} - 20 q^{50}+ \cdots + 15 q^{99}+O(q^{100}) $ 3 * q + 4 * q^2 + 4 * q^4 + 9 * q^8 - 9 * q^9 - 5 * q^11 + 18 * q^16 - 12 * q^18 + 12 * q^22 - 11 * q^23 - 15 * q^25 + 13 * q^29 + 27 * q^32 - 12 * q^36 - 17 * q^37 + 13 * q^43 + 47 * q^44 - 3 * q^46 - 20 * q^50 - 9 * q^53 + 43 * q^58 + 49 * q^64 - 19 * q^67 + 15 * q^71 - 27 * q^72 - 11 * q^74 - 25 * q^79 + 27 * q^81 + 15 * q^86 + 69 * q^88 + 18 * q^92 + 15 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.246980	−0.174641	−0.0873205	−	0.996180i	$-0.527830\pi$
$2$	−0.246980	−0.174641	−0.0873205	+	0.996180i	$0.527830\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−1.93900	−0.969501
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0.972853	0.343955
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−6.63102	−1.99933	−0.999664	−	0.0259107i	$-0.991751\pi$
$11$	−6.63102	−1.99933	−0.999664	+	0.0259107i	$0.991751\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	0	0
$15$	0	0
$16$	3.63773	0.909432
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0.740939	0.174641
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	1.63773	0.349165
$23$	−6.93900	−1.44688	−0.723441	−	0.690386i	$-0.757441\pi$
$23$	−6.93900	−1.44688	−0.723441	+	0.690386i	$0.757441\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−6.39373	−1.18729	−0.593643	−	0.804728i	$-0.702311\pi$
$29$	−6.39373	−1.18729	−0.593643	+	0.804728i	$0.702311\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−2.84415	−0.502779
$33$	0	0
$34$	0	0
$35$	0	0
$36$	5.81700	0.969501
$37$	−11.6528	−1.91571	−0.957854	−	0.287257i	$-0.907257\pi$
$37$	−11.6528	−1.91571	−0.957854	+	0.287257i	$0.907257\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	8.51573	1.29864	0.649318	−	0.760517i	$-0.275054\pi$
$43$	8.51573	1.29864	0.649318	+	0.760517i	$0.275054\pi$
$44$	12.8576	1.93835
$45$	0	0
$46$	1.71379	0.252685
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	1.23490	0.174641
$51$	0	0
$52$	0	0
$53$	−8.09246	−1.11158	−0.555792	−	0.831321i	$-0.687585\pi$
$53$	−8.09246	−1.11158	−0.555792	+	0.831321i	$0.687585\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	1.57912	0.207349
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	−6.57301	−0.821626
$65$	0	0
$66$	0	0
$67$	−14.5864	−1.78201	−0.891007	−	0.453989i	$-0.850000\pi$
$67$	−14.5864	−1.78201	−0.891007	+	0.453989i	$0.850000\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	8.71917	1.03477	0.517387	−	0.855751i	$-0.326905\pi$
$71$	8.71917	1.03477	0.517387	+	0.855751i	$0.326905\pi$
$72$	−2.91856	−0.343955
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	2.87800	0.334561
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−7.42327	−0.835183	−0.417592	−	0.908635i	$-0.637126\pi$
$79$	−7.42327	−0.835183	−0.417592	+	0.908635i	$0.637126\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	−2.10321	−0.226795
$87$	0	0
$88$	−6.45101	−0.687680
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	13.4547	1.40275
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	0	0
$99$	19.8931	1.99933
$100$	9.69501	0.969501
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	1.99867	0.194128
$107$	−8.33273	−0.805556	−0.402778	−	0.915298i	$-0.631955\pi$
$107$	−8.33273	−0.805556	−0.402778	+	0.915298i	$0.631955\pi$
$108$	0	0
$109$	−2.94869	−0.282433	−0.141217	−	0.989979i	$-0.545101\pi$
$109$	−2.94869	−0.282433	−0.141217	+	0.989979i	$0.545101\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−15.3013	−1.43942	−0.719711	−	0.694273i	$-0.755726\pi$
$113$	−15.3013	−1.43942	−0.719711	+	0.694273i	$0.755726\pi$
$114$	0	0
$115$	0	0
$116$	12.3975	1.15107
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	32.9705	2.99731
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−21.3032	−1.89035	−0.945176	−	0.326560i	$-0.894110\pi$
$127$	−21.3032	−1.89035	−0.945176	+	0.326560i	$0.894110\pi$
$128$	7.31170	0.646269
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	3.60255	0.311213
$135$	0	0
$136$	0	0
$137$	−10.3134	−0.881129	−0.440565	−	0.897721i	$-0.645222\pi$
$137$	−10.3134	−0.881129	−0.440565	+	0.897721i	$0.645222\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	−2.15346	−0.180714
$143$	0	0
$144$	−10.9132	−0.909432
$145$	0	0
$146$	0	0
$147$	0	0
$148$	22.5948	1.85728
$149$	24.4131	2.00000	1.00000		0.000429442i	$-0.000136696\pi$
$149$	24.4131	2.00000	1.00000		0.000429442i	$0.000136696\pi$
$150$	0	0
$151$	−23.9191	−1.94651	−0.973256	−	0.229722i	$-0.926218\pi$
$151$	−23.9191	−1.94651	−0.973256	+	0.229722i	$0.926218\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	1.83340	0.145857
$159$	0	0
$160$	0	0
$161$	0	0
$162$	−2.22282	−0.174641
$163$	−24.9071	−1.95087	−0.975436	−	0.220283i	$-0.929302\pi$
$163$	−24.9071	−1.95087	−0.975436	+	0.220283i	$0.929302\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	0	0
$172$	−16.5120	−1.25903
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	−24.1219	−1.81825
$177$	0	0
$178$	0	0
$179$	23.1793	1.73250	0.866250	−	0.499610i	$-0.166523\pi$
$179$	23.1793	1.73250	0.866250	+	0.499610i	$0.166523\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	−6.75063	−0.497663
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	4.27173	0.309092	0.154546	−	0.987986i	$-0.450609\pi$
$191$	4.27173	0.309092	0.154546	+	0.987986i	$0.450609\pi$
$192$	0	0
$193$	25.4010	1.82841	0.914203	−	0.405257i	$-0.132818\pi$
$193$	25.4010	1.82841	0.914203	+	0.405257i	$0.132818\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	26.0000	1.85242	0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000	1.85242	0.926212	+	0.377004i	$0.123046\pi$
$198$	−4.91318	−0.349165
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−4.86426	−0.343955
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	20.8170	1.44688
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−23.1239	−1.59192	−0.795958	−	0.605352i	$-0.793032\pi$
$211$	−23.1239	−1.59192	−0.795958	+	0.605352i	$0.793032\pi$
$212$	15.6913	1.07768
$213$	0	0
$214$	2.05802	0.140683
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0.728266	0.0493244
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	15.0000	1.00000
$226$	3.77910	0.251382
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	0	0
$232$	−6.22016	−0.408374
$233$	−10.6377	−0.696901	−0.348450	−	0.937327i	$-0.613292\pi$
$233$	−10.6377	−0.696901	−0.348450	+	0.937327i	$0.613292\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	25.8950	1.67501	0.837504	−	0.546432i	$-0.184014\pi$
$239$	25.8950	1.67501	0.837504	+	0.546432i	$0.184014\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	−8.14303	−0.523454
$243$	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		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	46.0127	2.89279
$254$	5.26145	0.330133
$255$	0	0
$256$	11.3402	0.708761
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	19.1812	1.18729
$262$	0	0
$263$	24.0887	1.48538	0.742688	−	0.669638i	$-0.233551\pi$
$263$	24.0887	1.48538	0.742688	+	0.669638i	$0.233551\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	28.2831	1.72766
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	2.54719	0.153881
$275$	33.1551	1.99933
$276$	0	0
$277$	−31.0573	−1.86605	−0.933025	−	0.359810i	$-0.882841\pi$
$277$	−31.0573	−1.86605	−0.933025	+	0.359810i	$0.882841\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−16.9065	−1.00321
$285$	0	0
$286$	0	0
$287$	0	0
$288$	8.53245	0.502779
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	−11.3365	−0.658918
$297$	0	0
$298$	−6.02954	−0.349282
$299$	0	0
$300$	0	0
$301$	0	0
$302$	5.90754	0.339941
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	0	0
$315$	0	0
$316$	14.3937	0.809711
$317$	29.4728	1.65536	0.827678	−	0.561203i	$-0.189661\pi$
$317$	29.4728	1.65536	0.827678	+	0.561203i	$0.189661\pi$
$318$	0	0
$319$	42.3970	2.37378
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−17.4510	−0.969501
$325$	0	0
$326$	6.15154	0.340702
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	2.85192	0.156756	0.0783779	−	0.996924i	$-0.475026\pi$
$331$	2.85192	0.156756	0.0783779	+	0.996924i	$0.475026\pi$
$332$	0	0
$333$	34.9584	1.91571
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−36.2127	−1.97263	−0.986314	−	0.164875i	$-0.947278\pi$
$337$	−36.2127	−1.97263	−0.986314	+	0.164875i	$0.947278\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	8.28455	0.446673
$345$	0	0
$346$	0	0
$347$	−37.0019	−1.98637	−0.993184	−	0.116561i	$-0.962813\pi$
$347$	−37.0019	−1.98637	−0.993184	+	0.116561i	$0.962813\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	18.8596	1.00522
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	−5.72481	−0.302566
$359$	37.8920	1.99986	0.999932	−	0.0116868i	$-0.00372012\pi$
$359$	37.8920	1.99986	0.999932	+	0.0116868i	$0.00372012\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−25.2422	−1.31584
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−35.8485	−1.85616	−0.928082	−	0.372377i	$-0.878543\pi$
$373$	−35.8485	−1.85616	−0.928082	+	0.372377i	$0.878543\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−26.8829	−1.38088	−0.690441	−	0.723389i	$-0.742584\pi$
$379$	−26.8829	−1.38088	−0.690441	+	0.723389i	$0.742584\pi$
$380$	0	0
$381$	0	0
$382$	−1.05503	−0.0539801
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	−6.27354	−0.319315
$387$	−25.5472	−1.29864
$388$	0	0
$389$	−31.9667	−1.62078	−0.810389	−	0.585892i	$-0.800744\pi$
$389$	−31.9667	−1.62078	−0.810389	+	0.585892i	$0.800744\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−6.42147	−0.323509
$395$	0	0
$396$	−38.5727	−1.93835
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	−18.1886	−0.909432
$401$	−21.4494	−1.07113	−0.535565	−	0.844494i	$-0.679901\pi$
$401$	−21.4494	−1.07113	−0.535565	+	0.844494i	$0.679901\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	77.2699	3.83013
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	−5.14138	−0.252685
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	5.71114	0.278014
$423$	0	0
$424$	−7.87277	−0.382336
$425$	0	0
$426$	0	0
$427$	0	0
$428$	16.1572	0.780987
$429$	0	0
$430$	0	0
$431$	0.733643	0.0353383	0.0176692	−	0.999844i	$-0.494375\pi$
$431$	0.733643	0.0353383	0.0176692	+	0.999844i	$0.494375\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	5.71751	0.273819
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	34.0907	1.61970	0.809848	−	0.586640i	$-0.199550\pi$
$443$	34.0907	1.61970	0.809848	+	0.586640i	$0.199550\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−40.8256	−1.92668	−0.963340	−	0.268283i	$-0.913544\pi$
$449$	−40.8256	−1.92668	−0.963340	+	0.268283i	$0.913544\pi$
$450$	−3.70469	−0.174641
$451$	0	0
$452$	29.6692	1.39552
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	36.8374	1.72318	0.861592	−	0.507602i	$-0.169468\pi$
$457$	36.8374	1.72318	0.861592	+	0.507602i	$0.169468\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	12.5284	0.582244	0.291122	−	0.956686i	$-0.405971\pi$
$463$	12.5284	0.582244	0.291122	+	0.956686i	$0.405971\pi$
$464$	−23.2587	−1.07976
$465$	0	0
$466$	2.62730	0.121707
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−56.4680	−2.59640
$474$	0	0
$475$	0	0
$476$	0	0
$477$	24.2774	1.11158
$478$	−6.39553	−0.292525
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−63.9298	−2.90590
$485$	0	0
$486$	0	0
$487$	−13.9957	−0.634205	−0.317103	−	0.948391i	$-0.602710\pi$
$487$	−13.9957	−0.634205	−0.317103	+	0.948391i	$0.602710\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−4.63209	−0.209043	−0.104522	−	0.994523i	$-0.533331\pi$
$491$	−4.63209	−0.209043	−0.104522	+	0.994523i	$0.533331\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	20.9554	0.938092	0.469046	−	0.883174i	$-0.344598\pi$
$499$	20.9554	0.938092	0.469046	+	0.883174i	$0.344598\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	−11.3642	−0.505200
$507$	0	0
$508$	41.3069	1.83270
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	−17.4242	−0.770048
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	−4.73736	−0.207349
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	−5.94943	−0.259407
$527$	0	0
$528$	0	0
$529$	25.1497	1.09347
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−14.1904	−0.612934
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	23.3873	1.00550	0.502749	−	0.864432i	$-0.332322\pi$
$541$	23.3873	1.00550	0.502749	+	0.864432i	$0.332322\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	39.8447	1.70364	0.851819	−	0.523836i	$-0.175500\pi$
$547$	39.8447	1.70364	0.851819	+	0.523836i	$0.175500\pi$
$548$	19.9976	0.854255
$549$	0	0
$550$	−8.18864	−0.349165
$551$	0	0
$552$	0	0
$553$	0	0
$554$	7.67051	0.325889
$555$	0	0
$556$	0	0
$557$	−0.0817042	−0.00346192	−0.00173096	−	0.999999i	$-0.500551\pi$
$557$	−0.0817042	−0.00346192	−0.00173096	+	0.999999i	$0.500551\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−6.42147	−0.270873
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	8.48247	0.355916
$569$	46.8133	1.96251	0.981257	−	0.192701i	$-0.0617249\pi$
$569$	46.8133	1.96251	0.981257	+	0.192701i	$0.0617249\pi$
$570$	0	0
$571$	17.0592	0.713905	0.356953	−	0.934123i	$-0.383816\pi$
$571$	17.0592	0.713905	0.356953	+	0.934123i	$0.383816\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	34.6950	1.44688
$576$	19.7190	0.821626
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	4.19865	0.174641
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	53.6613	2.22242
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−42.3897	−1.74221
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−47.3370	−1.93900
$597$	0	0
$598$	0	0
$599$	−12.7597	−0.521348	−0.260674	−	0.965427i	$-0.583945\pi$
$599$	−12.7597	−0.521348	−0.260674	+	0.965427i	$0.583945\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	43.7593	1.78201
$604$	46.3793	1.88715
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−20.4614	−0.826430	−0.413215	−	0.910634i	$-0.635594\pi$
$613$	−20.4614	−0.826430	−0.413215	+	0.910634i	$0.635594\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	26.0000	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	27.2577	1.08511	0.542557	−	0.840019i	$-0.317456\pi$
$631$	27.2577	1.08511	0.542557	+	0.840019i	$0.317456\pi$
$632$	−7.22175	−0.287266
$633$	0	0
$634$	−7.27918	−0.289093
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−10.4712	−0.414558
$639$	−26.1575	−1.03477
$640$	0	0
$641$	10.3994	0.410750	0.205375	−	0.978683i	$-0.434159\pi$
$641$	10.3994	0.410750	0.205375	+	0.978683i	$0.434159\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	8.75568	0.343955
$649$	0	0
$650$	0	0
$651$	0	0
$652$	48.2948	1.89137
$653$	−40.4566	−1.58319	−0.791596	−	0.611045i	$-0.790749\pi$
$653$	−40.4566	−1.58319	−0.791596	+	0.611045i	$0.790749\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−51.1221	−1.99143	−0.995717	−	0.0924489i	$-0.970531\pi$
$659$	−51.1221	−1.99143	−0.995717	+	0.0924489i	$0.970531\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	−0.704366	−0.0273760
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−8.63401	−0.334561
$667$	44.3661	1.71786
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−14.3918	−0.554764	−0.277382	−	0.960760i	$-0.589467\pi$
$673$	−14.3918	−0.554764	−0.277382	+	0.960760i	$0.589467\pi$
$674$	8.94379	0.344502
$675$	0	0
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	52.0000	1.98972	0.994862	−	0.101237i	$-0.0322800\pi$
$683$	52.0000	1.98972	0.994862	+	0.101237i	$0.0322800\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	30.9779	1.18102
$689$	0	0
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	9.13872	0.346901
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−52.0334	−1.96527	−0.982637	−	0.185540i	$-0.940597\pi$
$701$	−52.0334	−1.96527	−0.982637	+	0.185540i	$0.940597\pi$
$702$	0	0
$703$	0	0
$704$	43.5858	1.64270
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−28.3648	−1.06526	−0.532631	−	0.846348i	$-0.678797\pi$
$709$	−28.3648	−1.06526	−0.532631	+	0.846348i	$0.678797\pi$
$710$	0	0
$711$	22.2698	0.835183
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−44.9446	−1.67966
$717$	0	0
$718$	−9.35855	−0.349258
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	4.69261	0.174641
$723$	0	0
$724$	0	0
$725$	31.9687	1.18729
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	19.7356	0.727462
$737$	96.7229	3.56283
$738$	0	0
$739$	52.0000	1.91285	0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000	1.91285	0.956425	+	0.291977i	$0.0943129\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−19.9675	−0.732536	−0.366268	−	0.930509i	$-0.619365\pi$
$743$	−19.9675	−0.732536	−0.366268	+	0.930509i	$0.619365\pi$
$744$	0	0
$745$	0	0
$746$	8.85384	0.324162
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−9.24219	−0.337252	−0.168626	−	0.985680i	$-0.553933\pi$
$751$	−9.24219	−0.337252	−0.168626	+	0.985680i	$0.553933\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	53.2441	1.93519	0.967595	−	0.252507i	$-0.0812550\pi$
$757$	53.2441	1.93519	0.967595	+	0.252507i	$0.0812550\pi$
$758$	6.63953	0.241159
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	0	0
$764$	−8.28290	−0.299665
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	0	0
$772$	−49.2526	−1.77264
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	6.30963	0.226795
$775$	0	0
$776$	0	0
$777$	0	0
$778$	7.89513	0.283054
$779$	0	0
$780$	0	0
$781$	−57.8170	−2.06886
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	−50.4140	−1.79593
$789$	0	0
$790$	0	0
$791$	0	0
$792$	19.3530	0.687680
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	14.2208	0.502779
$801$	0	0
$802$	5.29755	0.187063
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	49.7265	1.74829	0.874145	−	0.485666i	$-0.161423\pi$
$809$	49.7265	1.74829	0.874145	+	0.485666i	$0.161423\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	−19.0841	−0.668897
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−46.6929	−1.62959	−0.814796	−	0.579747i	$-0.803151\pi$
$821$	−46.6929	−1.62959	−0.814796	+	0.579747i	$0.803151\pi$
$822$	0	0
$823$	39.3088	1.37022	0.685110	−	0.728440i	$-0.259754\pi$
$823$	39.3088	1.37022	0.685110	+	0.728440i	$0.259754\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−26.3209	−0.915268	−0.457634	−	0.889141i	$-0.651303\pi$
$827$	−26.3209	−0.915268	−0.457634	+	0.889141i	$0.651303\pi$
$828$	−40.3642	−1.40275
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	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		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	11.8798	0.409648
$842$	−6.42147	−0.221298
$843$	0	0
$844$	44.8373	1.54336
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−29.4382	−1.01091
$849$	0	0
$850$	0	0
$851$	80.8587	2.77180
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−8.10652	−0.277075
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	0	0
$862$	−0.181195	−0.00617152
$863$	40.5198	1.37931	0.689655	−	0.724138i	$-0.257762\pi$
$863$	40.5198	1.37931	0.689655	+	0.724138i	$0.257762\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	49.2239	1.66981
$870$	0	0
$871$	0	0
$872$	−2.86864	−0.0971445
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−55.9969	−1.89088	−0.945440	−	0.325796i	$-0.894368\pi$
$877$	−55.9969	−1.89088	−0.945440	+	0.325796i	$0.894368\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	38.0258	1.27967	0.639835	−	0.768512i	$-0.279003\pi$
$883$	38.0258	1.27967	0.639835	+	0.768512i	$0.279003\pi$
$884$	0	0
$885$	0	0
$886$	−8.41970	−0.282865
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−59.6792	−1.99933
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	10.0831	0.336477
$899$	0	0
$900$	−29.0850	−0.969501
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−14.8859	−0.495097
$905$	0	0
$906$	0	0
$907$	−18.5101	−0.614617	−0.307309	−	0.951610i	$-0.599428\pi$
$907$	−18.5101	−0.614617	−0.307309	+	0.951610i	$0.599428\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	53.1868	1.76216	0.881079	−	0.472969i	$-0.156818\pi$
$911$	53.1868	1.76216	0.881079	+	0.472969i	$0.156818\pi$
$912$	0	0
$913$	0	0
$914$	−9.09810	−0.300938
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−25.4308	−0.838886	−0.419443	−	0.907782i	$-0.637775\pi$
$919$	−25.4308	−0.838886	−0.419443	+	0.907782i	$0.637775\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	58.2640	1.91571
$926$	−3.09426	−0.101684
$927$	0	0
$928$	18.1847	0.596943
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	20.6266	0.675646
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	13.9464	0.453438
$947$	−61.1976	−1.98865	−0.994327	−	0.106364i	$-0.966079\pi$
$947$	−61.1976	−1.98865	−0.994327	+	0.106364i	$0.966079\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−33.5415	−1.08652	−0.543259	−	0.839565i	$-0.682810\pi$
$953$	−33.5415	−1.08652	−0.543259	+	0.839565i	$0.682810\pi$
$954$	−5.99602	−0.194128
$955$	0	0
$956$	−50.2104	−1.62392
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	24.9982	0.805556
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−55.3303	−1.77930	−0.889652	−	0.456639i	$-0.849053\pi$
$967$	−55.3303	−1.77930	−0.889652	+	0.456639i	$0.849053\pi$
$968$	32.0754	1.03094
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	3.45665	0.110758
$975$	0	0
$976$	0	0
$977$	4.41598	0.141280	0.0706398	−	0.997502i	$-0.477496\pi$
$977$	4.41598	0.141280	0.0706398	+	0.997502i	$0.477496\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	8.84607	0.282433
$982$	1.14403	0.0365075
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−59.0907	−1.87897
$990$	0	0
$991$	46.8781	1.48913	0.744566	−	0.667549i	$-0.232656\pi$
$991$	46.8781	1.48913	0.744566	+	0.667549i	$0.232656\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	−5.17556	−0.163829
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.bm.1.1	yes	3
7.6	odd	2	CM	8281.2.a.bm.1.1	yes	3
13.12	even	2		8281.2.a.bc.1.3	✓	3
91.90	odd	2		8281.2.a.bc.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8281.2.a.bc.1.3	✓	3	13.12	even	2
8281.2.a.bc.1.3	✓	3	91.90	odd	2
8281.2.a.bm.1.1	yes	3	1.1	even	1	trivial
8281.2.a.bm.1.1	yes	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-0.246980 q^{2} -1.93900 q^{4} +0.972853 q^{8} -3.00000 q^{9} -6.63102 q^{11} +3.63773 q^{16} +0.740939 q^{18} +1.63773 q^{22} -6.93900 q^{23} -5.00000 q^{25} -6.39373 q^{29} -2.84415 q^{32} +5.81700 q^{36} -11.6528 q^{37} +8.51573 q^{43} +12.8576 q^{44} +1.71379 q^{46} +1.23490 q^{50} -8.09246 q^{53} +1.57912 q^{58} -6.57301 q^{64} -14.5864 q^{67} +8.71917 q^{71} -2.91856 q^{72} +2.87800 q^{74} -7.42327 q^{79} +9.00000 q^{81} -2.10321 q^{86} -6.45101 q^{88} +13.4547 q^{92} +19.8931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} + 4 q^{4} + 9 q^{8} - 9 q^{9} - 5 q^{11} + 18 q^{16} - 12 q^{18} + 12 q^{22} - 11 q^{23} - 15 q^{25} + 13 q^{29} + 27 q^{32} - 12 q^{36} - 17 q^{37} + 13 q^{43} + 47 q^{44} - 3 q^{46} - 20 q^{50}+ \cdots + 15 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 + 4 * q^4 + 9 * q^8 - 9 * q^9 - 5 * q^11 + 18 * q^16 - 12 * q^18 + 12 * q^22 - 11 * q^23 - 15 * q^25 + 13 * q^29 + 27 * q^32 - 12 * q^36 - 17 * q^37 + 13 * q^43 + 47 * q^44 - 3 * q^46 - 20 * q^50 - 9 * q^53 + 43 * q^58 + 49 * q^64 - 19 * q^67 + 15 * q^71 - 27 * q^72 - 11 * q^74 - 25 * q^79 + 27 * q^81 + 15 * q^86 + 69 * q^88 + 18 * q^92 + 15 * q^99

Introduction

L-functions

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Database

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