LMFDB - Embedded newform 5929.2.a.bg.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5929,2,Mod(1,5929)] 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("5929.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5929, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,1,0,11,0,0,0,-3,-12,0,0,0,0,0,0,21,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

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

Self dual:	yes
Analytic conductor:	$47.3433033584$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.6125.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 9x + 11 $ x^4 - x^3 - 9x^2 + 9x + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 539)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.4
Root			$2.36415$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.36415 q^{2} +3.58921 q^{4} +3.75713 q^{8} -3.00000 q^{9} +1.70400 q^{16} -7.09245 q^{18} -9.58240 q^{23} -5.00000 q^{25} -10.6831 q^{29} -3.48575 q^{32} -10.7676 q^{36} -1.36643 q^{37} +8.74072 q^{43} -22.6542 q^{46} -11.8208 q^{50} -13.1552 q^{53} -25.2564 q^{58} -11.6488 q^{64} +16.3336 q^{67} +9.97679 q^{71} -11.2714 q^{72} -3.23045 q^{74} +12.6254 q^{79} +9.00000 q^{81} +20.6644 q^{86} -34.3932 q^{92} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 11 q^{4} - 3 q^{8} - 12 q^{9} + 21 q^{16} - 3 q^{18} - 8 q^{23} - 20 q^{25} + 2 q^{29} - 50 q^{32} - 33 q^{36} + 6 q^{37} - 12 q^{43} - 47 q^{46} - 5 q^{50} + 10 q^{53} - 2 q^{58} + 33 q^{64}+ \cdots + 8 q^{92}+O(q^{100}) $ 4 * q + q^2 + 11 * q^4 - 3 * q^8 - 12 * q^9 + 21 * q^16 - 3 * q^18 - 8 * q^23 - 20 * q^25 + 2 * q^29 - 50 * q^32 - 33 * q^36 + 6 * q^37 - 12 * q^43 - 47 * q^46 - 5 * q^50 + 10 * q^53 - 2 * q^58 + 33 * q^64 - 4 * q^67 - 16 * q^71 + 9 * q^72 - 61 * q^74 + 8 * q^79 + 36 * q^81 + 12 * q^86 + 8 * q^92

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 $

$2$	2.36415	1.67171	0.835853	−	0.548953i	$-0.184973\pi$
$2$	2.36415	1.67171	0.835853	+	0.548953i	$0.184973\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	3.58921	1.79460
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	3.75713	1.32835
$9$	−3.00000	−1.00000
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	1.70400	0.426000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−7.09245	−1.67171
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−9.58240	−1.99807	−0.999035	−	0.0439305i	$-0.986012\pi$
$23$	−9.58240	−1.99807	−0.999035	+	0.0439305i	$0.986012\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−10.6831	−1.98380	−0.991898	−	0.127036i	$-0.959454\pi$
$29$	−10.6831	−1.98380	−0.991898	+	0.127036i	$0.959454\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−3.48575	−0.616199
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−10.7676	−1.79460
$37$	−1.36643	−0.224640	−0.112320	−	0.993672i	$-0.535828\pi$
$37$	−1.36643	−0.224640	−0.112320	+	0.993672i	$0.535828\pi$
$38$	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
$43$	8.74072	1.33295	0.666474	−	0.745528i	$-0.267803\pi$
$43$	8.74072	1.33295	0.666474	+	0.745528i	$0.267803\pi$
$44$	0	0
$45$	0	0
$46$	−22.6542	−3.34019
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	−11.8208	−1.67171
$51$	0	0
$52$	0	0
$53$	−13.1552	−1.80701	−0.903503	−	0.428581i	$-0.859014\pi$
$53$	−13.1552	−1.80701	−0.903503	+	0.428581i	$0.859014\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−25.2564	−3.31633
$59$	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
$64$	−11.6488	−1.45610
$65$	0	0
$66$	0	0
$67$	16.3336	1.99547	0.997735	−	0.0672706i	$-0.0214291\pi$
$67$	16.3336	1.99547	0.997735	+	0.0672706i	$0.0214291\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	9.97679	1.18403	0.592014	−	0.805928i	$-0.298333\pi$
$71$	9.97679	1.18403	0.592014	+	0.805928i	$0.298333\pi$
$72$	−11.2714	−1.32835
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−3.23045	−0.375532
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	12.6254	1.42047	0.710235	−	0.703964i	$-0.248589\pi$
$79$	12.6254	1.42047	0.710235	+	0.703964i	$0.248589\pi$
$80$	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
$86$	20.6644	2.22830
$87$	0	0
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	−34.3932	−3.58574
$93$	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
$99$	0	0
$100$	−17.9460	−1.79460
$101$	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
$106$	−31.1009	−3.02079
$107$	−13.0701	−1.26353	−0.631766	−	0.775159i	$-0.717670\pi$
$107$	−13.0701	−1.26353	−0.631766	+	0.775159i	$0.717670\pi$
$108$	0	0
$109$	8.34177	0.798997	0.399498	−	0.916734i	$-0.369184\pi$
$109$	8.34177	0.798997	0.399498	+	0.916734i	$0.369184\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−19.5120	−1.83554	−0.917769	−	0.397114i	$-0.870012\pi$
$113$	−19.5120	−1.83554	−0.917769	+	0.397114i	$0.870012\pi$
$114$	0	0
$115$	0	0
$116$	−38.3438	−3.56013
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	0	0
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	3.61347	0.320644	0.160322	−	0.987065i	$-0.448747\pi$
$127$	3.61347	0.320644	0.160322	+	0.987065i	$0.448747\pi$
$128$	−20.5681	−1.81798
$129$	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
$134$	38.6151	3.33584
$135$	0	0
$136$	0	0
$137$	20.5312	1.75410	0.877051	−	0.480397i	$-0.159507\pi$
$137$	20.5312	1.75410	0.877051	+	0.480397i	$0.159507\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	23.5866	1.97935
$143$	0	0
$144$	−5.11199	−0.426000
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−4.90441	−0.403140
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	0	0
$151$	−22.5267	−1.83319	−0.916597	−	0.399811i	$-0.869076\pi$
$151$	−22.5267	−1.83319	−0.916597	+	0.399811i	$0.869076\pi$
$152$	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	$0.5\pi$
$158$	29.8484	2.37461
$159$	0	0
$160$	0	0
$161$	0	0
$162$	21.2774	1.67171
$163$	6.84954	0.536497	0.268249	−	0.963350i	$-0.413555\pi$
$163$	6.84954	0.536497	0.268249	+	0.963350i	$0.413555\pi$
$164$	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
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	31.3723	2.39211
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	12.3153	0.920486	0.460243	−	0.887793i	$-0.347762\pi$
$179$	12.3153	0.920486	0.460243	+	0.887793i	$0.347762\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	−36.0023	−2.65413
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−22.6905	−1.64182	−0.820912	−	0.571055i	$-0.806534\pi$
$191$	−22.6905	−1.64182	−0.820912	+	0.571055i	$0.806534\pi$
$192$	0	0
$193$	14.5678	1.04861	0.524305	−	0.851530i	$-0.324325\pi$
$193$	14.5678	1.04861	0.524305	+	0.851530i	$0.324325\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−27.2550	−1.94184	−0.970918	−	0.239411i	$-0.923046\pi$
$197$	−27.2550	−1.94184	−0.970918	+	0.239411i	$0.923046\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−18.7856	−1.32835
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	28.7472	1.99807
$208$	0	0
$209$	0	0
$210$	0	0
$211$	5.84313	0.402258	0.201129	−	0.979565i	$-0.435539\pi$
$211$	5.84313	0.402258	0.201129	+	0.979565i	$0.435539\pi$
$212$	−47.2168	−3.24286
$213$	0	0
$214$	−30.8996	−2.11225
$215$	0	0
$216$	0	0
$217$	0	0
$218$	19.7212	1.33569
$219$	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
$226$	−46.1294	−3.06848
$227$	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
$232$	−40.1377	−2.63517
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−30.1069	−1.94745	−0.973726	−	0.227725i	$-0.926871\pi$
$239$	−30.1069	−1.94745	−0.973726	+	0.227725i	$0.926871\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	0	0
$243$	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
$253$	0	0
$254$	8.54279	0.536022
$255$	0	0
$256$	−25.3284	−1.58302
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	32.0492	1.98380
$262$	0	0
$263$	−4.85603	−0.299435	−0.149718	−	0.988729i	$-0.547836\pi$
$263$	−4.85603	−0.299435	−0.149718	+	0.988729i	$0.547836\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	58.6248	3.58108
$269$	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
$274$	48.5389	2.93234
$275$	0	0
$276$	0	0
$277$	10.5714	0.635176	0.317588	−	0.948229i	$-0.397127\pi$
$277$	10.5714	0.635176	0.317588	+	0.948229i	$0.397127\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	28.1645	1.68015	0.840077	−	0.542467i	$-0.182510\pi$
$281$	28.1645	1.68015	0.840077	+	0.542467i	$0.182510\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	35.8088	2.12486
$285$	0	0
$286$	0	0
$287$	0	0
$288$	10.4572	0.616199
$289$	−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
$296$	−5.13386	−0.298400
$297$	0	0
$298$	−52.0113	−3.01293
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−53.2565	−3.06456
$303$	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
$316$	45.3153	2.54918
$317$	−0.441542	−0.0247995	−0.0123997	−	0.999923i	$-0.503947\pi$
$317$	−0.441542	−0.0247995	−0.0123997	+	0.999923i	$0.503947\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	32.3029	1.79460
$325$	0	0
$326$	16.1933	0.896866
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−26.0143	−1.42988	−0.714939	−	0.699187i	$-0.753545\pi$
$331$	−26.0143	−1.42988	−0.714939	+	0.699187i	$0.753545\pi$
$332$	0	0
$333$	4.09930	0.224640
$334$	0	0
$335$	0	0
$336$	0	0
$337$	36.7116	1.99981	0.999904	−	0.0138879i	$-0.00442079\pi$
$337$	36.7116	1.99981	0.999904	+	0.0138879i	$0.00442079\pi$
$338$	−30.7340	−1.67171
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	32.8400	1.77061
$345$	0	0
$346$	0	0
$347$	33.9916	1.82476	0.912381	−	0.409342i	$-0.134242\pi$
$347$	33.9916	1.82476	0.912381	+	0.409342i	$0.134242\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	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
$358$	29.1151	1.53878
$359$	−15.2997	−0.807489	−0.403745	−	0.914872i	$-0.632292\pi$
$359$	−15.2997	−0.807489	−0.403745	+	0.914872i	$0.632292\pi$
$360$	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	$0.5\pi$
$368$	−16.3284	−0.851177
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	31.4801	1.61702	0.808511	−	0.588481i	$-0.200274\pi$
$379$	31.4801	1.61702	0.808511	+	0.588481i	$0.200274\pi$
$380$	0	0
$381$	0	0
$382$	−53.6437	−2.74465
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	34.4404	1.75297
$387$	−26.2222	−1.33295
$388$	0	0
$389$	36.9632	1.87411	0.937054	−	0.349185i	$-0.113542\pi$
$389$	36.9632	1.87411	0.937054	+	0.349185i	$0.113542\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−64.4349	−3.24618
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	−8.51999	−0.426000
$401$	15.0655	0.752336	0.376168	−	0.926552i	$-0.377242\pi$
$401$	15.0655	0.752336	0.376168	+	0.926552i	$0.377242\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	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
$414$	67.9627	3.34019
$415$	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
$421$	39.6960	1.93467	0.967333	−	0.253507i	$-0.0815842\pi$
$421$	39.6960	1.93467	0.967333	+	0.253507i	$0.0815842\pi$
$422$	13.8140	0.672457
$423$	0	0
$424$	−49.4258	−2.40033
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−46.9112	−2.26754
$429$	0	0
$430$	0	0
$431$	41.4399	1.99609	0.998044	−	0.0625092i	$-0.0199103\pi$
$431$	41.4399	1.99609	0.998044	+	0.0625092i	$0.0199103\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	29.9404	1.43388
$437$	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
$443$	29.0473	1.38008	0.690039	−	0.723772i	$-0.257593\pi$
$443$	29.0473	1.38008	0.690039	+	0.723772i	$0.257593\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	23.2641	1.09790	0.548950	−	0.835855i	$-0.315028\pi$
$449$	23.2641	1.09790	0.548950	+	0.835855i	$0.315028\pi$
$450$	35.4623	1.67171
$451$	0	0
$452$	−70.0328	−3.29406
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	20.0280	0.936872	0.468436	−	0.883497i	$-0.344818\pi$
$457$	20.0280	0.936872	0.468436	+	0.883497i	$0.344818\pi$
$458$	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
$463$	2.73687	0.127193	0.0635967	−	0.997976i	$-0.479743\pi$
$463$	2.73687	0.127193	0.0635967	+	0.997976i	$0.479743\pi$
$464$	−18.2039	−0.845096
$465$	0	0
$466$	−52.0113	−2.40938
$467$	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
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	39.4656	1.80701
$478$	−71.1772	−3.25557
$479$	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
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−42.6440	−1.93239	−0.966193	−	0.257821i	$-0.916996\pi$
$487$	−42.6440	−1.93239	−0.966193	+	0.257821i	$0.916996\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−44.0000	−1.98569	−0.992846	−	0.119401i	$-0.961903\pi$
$491$	−44.0000	−1.98569	−0.992846	+	0.119401i	$0.961903\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	36.2872	1.62444	0.812219	−	0.583352i	$-0.198259\pi$
$499$	36.2872	1.62444	0.812219	+	0.583352i	$0.198259\pi$
$500$	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
$506$	0	0
$507$	0	0
$508$	12.9695	0.575428
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	−18.7440	−0.828375
$513$	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	$0.5\pi$
$522$	75.7692	3.31633
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	−11.4804	−0.500568
$527$	0	0
$528$	0	0
$529$	68.8225	2.99228
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	61.3675	2.65067
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−46.1682	−1.98493	−0.992463	−	0.122548i	$-0.960893\pi$
$541$	−46.1682	−1.98493	−0.992463	+	0.122548i	$0.960893\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	73.6909	3.14792
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	24.9925	1.06183
$555$	0	0
$556$	0	0
$557$	−24.2798	−1.02877	−0.514384	−	0.857560i	$-0.671980\pi$
$557$	−24.2798	−1.02877	−0.514384	+	0.857560i	$0.671980\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	66.5852	2.80873
$563$	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
$568$	37.4841	1.57280
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	−24.7563	−1.03602	−0.518010	−	0.855374i	$-0.673327\pi$
$571$	−24.7563	−1.03602	−0.518010	+	0.855374i	$0.673327\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	47.9120	1.99807
$576$	34.9465	1.45610
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−40.1906	−1.67171
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	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
$592$	−2.32840	−0.0956966
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−78.9626	−3.23443
$597$	0	0
$598$	0	0
$599$	−4.11667	−0.168203	−0.0841014	−	0.996457i	$-0.526802\pi$
$599$	−4.11667	−0.168203	−0.0841014	+	0.996457i	$0.526802\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	−49.0009	−1.99547
$604$	−80.8529	−3.28986
$605$	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
$613$	−18.4525	−0.745288	−0.372644	−	0.927974i	$-0.621549\pi$
$613$	−18.4525	−0.745288	−0.372644	+	0.927974i	$0.621549\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	32.2257	1.29736	0.648679	−	0.761062i	$-0.275322\pi$
$617$	32.2257	1.29736	0.648679	+	0.761062i	$0.275322\pi$
$618$	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
$631$	15.0481	0.599057	0.299528	−	0.954087i	$-0.403171\pi$
$631$	15.0481	0.599057	0.299528	+	0.954087i	$0.403171\pi$
$632$	47.4353	1.88687
$633$	0	0
$634$	−1.04387	−0.0414574
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−29.9304	−1.18403
$640$	0	0
$641$	−5.91529	−0.233640	−0.116820	−	0.993153i	$-0.537270\pi$
$641$	−5.91529	−0.233640	−0.116820	+	0.993153i	$0.537270\pi$
$642$	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	$0.5\pi$
$648$	33.8141	1.32835
$649$	0	0
$650$	0	0
$651$	0	0
$652$	24.5844	0.962800
$653$	−34.2303	−1.33954	−0.669768	−	0.742571i	$-0.733606\pi$
$653$	−34.2303	−1.33954	−0.669768	+	0.742571i	$0.733606\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−44.0000	−1.71400	−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000	−1.71400	−0.856998	+	0.515319i	$0.827673\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	−61.5018	−2.39034
$663$	0	0
$664$	0	0
$665$	0	0
$666$	9.69136	0.375532
$667$	102.369	3.96376
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−49.5307	−1.90927	−0.954633	−	0.297784i	$-0.903752\pi$
$673$	−49.5307	−1.90927	−0.954633	+	0.297784i	$0.903752\pi$
$674$	86.7917	3.34309
$675$	0	0
$676$	−46.6597	−1.79460
$677$	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
$683$	45.1792	1.72873	0.864366	−	0.502863i	$-0.167720\pi$
$683$	45.1792	1.72873	0.864366	+	0.502863i	$0.167720\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	14.8942	0.567835
$689$	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
$694$	80.3612	3.05047
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−29.4846	−1.11362	−0.556810	−	0.830640i	$-0.687975\pi$
$701$	−29.4846	−1.11362	−0.556810	+	0.830640i	$0.687975\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−52.1793	−1.95963	−0.979817	−	0.199896i	$-0.935939\pi$
$709$	−52.1793	−1.95963	−0.979817	+	0.199896i	$0.935939\pi$
$710$	0	0
$711$	−37.8763	−1.42047
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	44.2021	1.65191
$717$	0	0
$718$	−36.1709	−1.34989
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	−44.9189	−1.67171
$723$	0	0
$724$	0	0
$725$	53.4154	1.98380
$726$	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
$736$	33.4018	1.23121
$737$	0	0
$738$	0	0
$739$	0.971330	0.0357309	0.0178655	−	0.999840i	$-0.494313\pi$
$739$	0.971330	0.0357309	0.0178655	+	0.999840i	$0.494313\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	47.5883	1.74585	0.872923	−	0.487858i	$-0.162222\pi$
$743$	47.5883	1.74585	0.872923	+	0.487858i	$0.162222\pi$
$744$	0	0
$745$	0	0
$746$	−52.0113	−1.90427
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	23.2815	0.849553	0.424777	−	0.905298i	$-0.360353\pi$
$751$	23.2815	0.849553	0.424777	+	0.905298i	$0.360353\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−26.7520	−0.972316	−0.486158	−	0.873871i	$-0.661602\pi$
$757$	−26.7520	−0.972316	−0.486158	+	0.873871i	$0.661602\pi$
$758$	74.4236	2.70319
$759$	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
$764$	−81.4408	−2.94642
$765$	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
$772$	52.2867	1.88184
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	−61.9931	−2.22830
$775$	0	0
$776$	0	0
$777$	0	0
$778$	87.3865	3.13296
$779$	0	0
$780$	0	0
$781$	0	0
$782$	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	$0.5\pi$
$788$	−97.8238	−3.48483
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	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
$800$	17.4287	0.616199
$801$	0	0
$802$	35.6171	1.25768
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−55.6248	−1.95566	−0.977832	−	0.209393i	$-0.932851\pi$
$809$	−55.6248	−1.95566	−0.977832	+	0.209393i	$0.932851\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−22.0000	−0.767805	−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000	−0.767805	−0.383903	+	0.923374i	$0.625420\pi$
$822$	0	0
$823$	−35.4041	−1.23411	−0.617055	−	0.786920i	$-0.711674\pi$
$823$	−35.4041	−1.23411	−0.617055	+	0.786920i	$0.711674\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−44.0000	−1.53003	−0.765015	−	0.644013i	$-0.777268\pi$
$827$	−44.0000	−1.53003	−0.765015	+	0.644013i	$0.777268\pi$
$828$	103.180	3.58574
$829$	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
$841$	85.1280	2.93545
$842$	93.8474	3.23420
$843$	0	0
$844$	20.9722	0.721893
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−22.4164	−0.769784
$849$	0	0
$850$	0	0
$851$	13.0937	0.448846
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−49.1059	−1.67841
$857$	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
$862$	97.9701	3.33688
$863$	8.00000	0.272323	0.136162	−	0.990687i	$-0.456523\pi$
$863$	8.00000	0.272323	0.136162	+	0.990687i	$0.456523\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	31.3411	1.06134
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−45.6460	−1.54135	−0.770677	−	0.637226i	$-0.780082\pi$
$877$	−45.6460	−1.54135	−0.770677	+	0.637226i	$0.780082\pi$
$878$	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
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	0	0
$885$	0	0
$886$	68.6722	2.30709
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	54.9998	1.83537
$899$	0	0
$900$	53.8381	1.79460
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−73.3092	−2.43823
$905$	0	0
$906$	0	0
$907$	23.5735	0.782746	0.391373	−	0.920232i	$-0.372000\pi$
$907$	23.5735	0.782746	0.391373	+	0.920232i	$0.372000\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	0	0
$913$	0	0
$914$	47.3493	1.56618
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−20.3948	−0.672763	−0.336381	−	0.941726i	$-0.609203\pi$
$919$	−20.3948	−0.672763	−0.336381	+	0.941726i	$0.609203\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	6.83216	0.224640
$926$	6.47038	0.212630
$927$	0	0
$928$	37.2385	1.22241
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	−78.9626	−2.58651
$933$	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
$946$	0	0
$947$	−20.0000	−0.649913	−0.324956	−	0.945729i	$-0.605350\pi$
$947$	−20.0000	−0.649913	−0.324956	+	0.945729i	$0.605350\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	34.4819	1.11698	0.558489	−	0.829512i	$-0.311381\pi$
$953$	34.4819	1.11698	0.558489	+	0.829512i	$0.311381\pi$
$954$	93.3027	3.02079
$955$	0	0
$956$	−108.060	−3.49490
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	39.2102	1.26353
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−60.3531	−1.94082	−0.970412	−	0.241454i	$-0.922376\pi$
$967$	−60.3531	−1.94082	−0.970412	+	0.241454i	$0.922376\pi$
$968$	0	0
$969$	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
$974$	−100.817	−3.23038
$975$	0	0
$976$	0	0
$977$	−12.3326	−0.394556	−0.197278	−	0.980348i	$-0.563210\pi$
$977$	−12.3326	−0.394556	−0.197278	+	0.980348i	$0.563210\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−25.0253	−0.798997
$982$	−104.023	−3.31950
$983$	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
$989$	−83.7571	−2.66332
$990$	0	0
$991$	−24.0000	−0.762385	−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000	−0.762385	−0.381193	+	0.924496i	$0.624487\pi$
$992$	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	$0.5\pi$
$998$	85.7884	2.71558
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bg.1.4		4
7.6	odd	2	CM	5929.2.a.bg.1.4		4
11.7	odd	10		539.2.f.c.148.1	✓	8
11.8	odd	10		539.2.f.c.295.1	yes	8
11.10	odd	2		5929.2.a.bc.1.1		4
77.18	odd	30		539.2.q.d.324.2		16
77.19	even	30		539.2.q.d.361.2		16
77.30	odd	30		539.2.q.d.361.2		16
77.40	even	30		539.2.q.d.214.1		16
77.41	even	10		539.2.f.c.295.1	yes	8
77.51	odd	30		539.2.q.d.214.1		16
77.52	even	30		539.2.q.d.471.1		16
77.62	even	10		539.2.f.c.148.1	✓	8
77.73	even	30		539.2.q.d.324.2		16
77.74	odd	30		539.2.q.d.471.1		16
77.76	even	2		5929.2.a.bc.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.f.c.148.1	✓	8	11.7	odd	10
539.2.f.c.148.1	✓	8	77.62	even	10
539.2.f.c.295.1	yes	8	11.8	odd	10
539.2.f.c.295.1	yes	8	77.41	even	10
539.2.q.d.214.1		16	77.40	even	30
539.2.q.d.214.1		16	77.51	odd	30
539.2.q.d.324.2		16	77.18	odd	30
539.2.q.d.324.2		16	77.73	even	30
539.2.q.d.361.2		16	77.19	even	30
539.2.q.d.361.2		16	77.30	odd	30
539.2.q.d.471.1		16	77.52	even	30
539.2.q.d.471.1		16	77.74	odd	30
5929.2.a.bc.1.1		4	11.10	odd	2
5929.2.a.bc.1.1		4	77.76	even	2
5929.2.a.bg.1.4		4	1.1	even	1	trivial
5929.2.a.bg.1.4		4	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+2.36415 q^{2} +3.58921 q^{4} +3.75713 q^{8} -3.00000 q^{9} +1.70400 q^{16} -7.09245 q^{18} -9.58240 q^{23} -5.00000 q^{25} -10.6831 q^{29} -3.48575 q^{32} -10.7676 q^{36} -1.36643 q^{37} +8.74072 q^{43} -22.6542 q^{46} -11.8208 q^{50} -13.1552 q^{53} -25.2564 q^{58} -11.6488 q^{64} +16.3336 q^{67} +9.97679 q^{71} -11.2714 q^{72} -3.23045 q^{74} +12.6254 q^{79} +9.00000 q^{81} +20.6644 q^{86} -34.3932 q^{92} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 11 q^{4} - 3 q^{8} - 12 q^{9} + 21 q^{16} - 3 q^{18} - 8 q^{23} - 20 q^{25} + 2 q^{29} - 50 q^{32} - 33 q^{36} + 6 q^{37} - 12 q^{43} - 47 q^{46} - 5 q^{50} + 10 q^{53} - 2 q^{58} + 33 q^{64}+ \cdots + 8 q^{92}+O(q^{100}) \) 4 * q + q^2 + 11 * q^4 - 3 * q^8 - 12 * q^9 + 21 * q^16 - 3 * q^18 - 8 * q^23 - 20 * q^25 + 2 * q^29 - 50 * q^32 - 33 * q^36 + 6 * q^37 - 12 * q^43 - 47 * q^46 - 5 * q^50 + 10 * q^53 - 2 * q^58 + 33 * q^64 - 4 * q^67 - 16 * q^71 + 9 * q^72 - 61 * q^74 + 8 * q^79 + 36 * q^81 + 12 * q^86 + 8 * q^92

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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