LMFDB - Embedded newform 5929.2.a.bg.1.3

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			1.3
Root			$2.20724$ 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)

$f(q)$	$=$	$q+2.20724 q^{2} +2.87192 q^{4} +1.92453 q^{8} -3.00000 q^{9} -1.49593 q^{16} -6.62173 q^{18} -2.56038 q^{23} -5.00000 q^{25} +7.83857 q^{29} -7.15093 q^{32} -8.61575 q^{36} -11.9191 q^{37} -12.8185 q^{43} -5.65138 q^{46} -11.0362 q^{50} +14.3107 q^{53} +17.3016 q^{58} -12.7920 q^{64} -12.5669 q^{67} -16.0545 q^{71} -5.77360 q^{72} -26.3084 q^{74} -2.85867 q^{79} +9.00000 q^{81} -28.2935 q^{86} -7.35321 q^{92} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.20724	1.56076	0.780378	−	0.625308i	$-0.215027\pi$
$2$	2.20724	1.56076	0.780378	+	0.625308i	$0.215027\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	2.87192	1.43596
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.92453	0.680425
$9$	−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
$16$	−1.49593	−0.373981
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−6.62173	−1.56076
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−2.56038	−0.533877	−0.266938	−	0.963714i	$-0.586012\pi$
$23$	−2.56038	−0.533877	−0.266938	+	0.963714i	$0.586012\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	7.83857	1.45559	0.727793	−	0.685797i	$-0.240546\pi$
$29$	7.83857	1.45559	0.727793	+	0.685797i	$0.240546\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−7.15093	−1.26412
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−8.61575	−1.43596
$37$	−11.9191	−1.95949	−0.979747	−	0.200239i	$-0.935828\pi$
$37$	−11.9191	−1.95949	−0.979747	+	0.200239i	$0.935828\pi$
$38$	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
$43$	−12.8185	−1.95480	−0.977399	−	0.211402i	$-0.932197\pi$
$43$	−12.8185	−1.95480	−0.977399	+	0.211402i	$0.932197\pi$
$44$	0	0
$45$	0	0
$46$	−5.65138	−0.833251
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	−11.0362	−1.56076
$51$	0	0
$52$	0	0
$53$	14.3107	1.96573	0.982863	−	0.184336i	$-0.0590136\pi$
$53$	14.3107	1.96573	0.982863	+	0.184336i	$0.0590136\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	17.3016	2.27181
$59$	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
$64$	−12.7920	−1.59900
$65$	0	0
$66$	0	0
$67$	−12.5669	−1.53529	−0.767644	−	0.640877i	$-0.778571\pi$
$67$	−12.5669	−1.53529	−0.767644	+	0.640877i	$0.778571\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−16.0545	−1.90532	−0.952662	−	0.304033i	$-0.901667\pi$
$71$	−16.0545	−1.90532	−0.952662	+	0.304033i	$0.901667\pi$
$72$	−5.77360	−0.680425
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−26.3084	−3.05829
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−2.85867	−0.321625	−0.160813	−	0.986985i	$-0.551411\pi$
$79$	−2.85867	−0.321625	−0.160813	+	0.986985i	$0.551411\pi$
$80$	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
$86$	−28.2935	−3.05096
$87$	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
$92$	−7.35321	−0.766625
$93$	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
$100$	−14.3596	−1.43596
$101$	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
$106$	31.5872	3.06802
$107$	11.2129	1.08399	0.541994	−	0.840382i	$-0.317670\pi$
$107$	11.2129	1.08399	0.541994	+	0.840382i	$0.317670\pi$
$108$	0	0
$109$	−15.6273	−1.49683	−0.748414	−	0.663232i	$-0.769184\pi$
$109$	−15.6273	−1.49683	−0.748414	+	0.663232i	$0.769184\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	10.8230	1.01815	0.509073	−	0.860724i	$-0.329988\pi$
$113$	10.8230	1.01815	0.509073	+	0.860724i	$0.329988\pi$
$114$	0	0
$115$	0	0
$116$	22.5117	2.09016
$117$	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
$127$	−20.0418	−1.77842	−0.889212	−	0.457495i	$-0.848747\pi$
$127$	−20.0418	−1.77842	−0.889212	+	0.457495i	$0.848747\pi$
$128$	−13.9332	−1.23153
$129$	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
$134$	−27.7381	−2.39621
$135$	0	0
$136$	0	0
$137$	17.0399	1.45582	0.727909	−	0.685674i	$-0.240493\pi$
$137$	17.0399	1.45582	0.727909	+	0.685674i	$0.240493\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	−35.4363	−2.97374
$143$	0	0
$144$	4.48778	0.373981
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−34.2308	−2.81375
$149$	−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
$151$	2.38389	0.193998	0.0969991	−	0.995284i	$-0.469076\pi$
$151$	2.38389	0.193998	0.0969991	+	0.995284i	$0.469076\pi$
$152$	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	$0.5\pi$
$158$	−6.30977	−0.501978
$159$	0	0
$160$	0	0
$161$	0	0
$162$	19.8652	1.56076
$163$	−21.2779	−1.66661	−0.833307	−	0.552811i	$-0.813555\pi$
$163$	−21.2779	−1.66661	−0.833307	+	0.552811i	$0.813555\pi$
$164$	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
$172$	−36.8136	−2.80701
$173$	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
$179$	26.3987	1.97313	0.986564	−	0.163374i	$-0.0522378\pi$
$179$	26.3987	1.97313	0.986564	+	0.163374i	$0.0522378\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	−4.92754	−0.363263
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	9.07920	0.656948	0.328474	−	0.944513i	$-0.393466\pi$
$191$	9.07920	0.656948	0.328474	+	0.944513i	$0.393466\pi$
$192$	0	0
$193$	2.12124	0.152690	0.0763450	−	0.997081i	$-0.475675\pi$
$193$	2.12124	0.152690	0.0763450	+	0.997081i	$0.475675\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−2.03059	−0.144674	−0.0723369	−	0.997380i	$-0.523046\pi$
$197$	−2.03059	−0.144674	−0.0723369	+	0.997380i	$0.523046\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−9.62266	−0.680425
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	7.68115	0.533877
$208$	0	0
$209$	0	0
$210$	0	0
$211$	28.8708	1.98755	0.993774	−	0.111417i	$-0.0355390\pi$
$211$	28.8708	1.98755	0.993774	+	0.111417i	$0.0355390\pi$
$212$	41.0992	2.82270
$213$	0	0
$214$	24.7495	1.69184
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−34.4933	−2.33618
$219$	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
$226$	23.8891	1.58908
$227$	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
$232$	15.0856	0.990417
$233$	−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
$239$	28.4956	1.84323	0.921614	−	0.388108i	$-0.126871\pi$
$239$	28.4956	1.84323	0.921614	+	0.388108i	$0.126871\pi$
$240$	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
$254$	−44.2372	−2.77569
$255$	0	0
$256$	−5.16986	−0.323116
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−23.5157	−1.45559
$262$	0	0
$263$	22.7783	1.40457	0.702284	−	0.711897i	$-0.252164\pi$
$263$	22.7783	1.40457	0.702284	+	0.711897i	$0.252164\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−36.0910	−2.20461
$269$	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
$274$	37.6112	2.27217
$275$	0	0
$276$	0	0
$277$	33.2853	1.99992	0.999959	−	0.00902525i	$-0.00287287\pi$
$277$	33.2853	1.99992	0.999959	+	0.00902525i	$0.00287287\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−33.4755	−1.99698	−0.998491	−	0.0549198i	$-0.982510\pi$
$281$	−33.4755	−1.99698	−0.998491	+	0.0549198i	$0.982510\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−46.1073	−2.73597
$285$	0	0
$286$	0	0
$287$	0	0
$288$	21.4528	1.26412
$289$	−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
$296$	−22.9388	−1.33329
$297$	0	0
$298$	−48.5593	−2.81297
$299$	0	0
$300$	0	0
$301$	0	0
$302$	5.26182	0.302784
$303$	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
$316$	−8.20985	−0.461840
$317$	21.2860	1.19554	0.597772	−	0.801666i	$-0.296053\pi$
$317$	21.2860	1.19554	0.597772	+	0.801666i	$0.296053\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	25.8473	1.43596
$325$	0	0
$326$	−46.9655	−2.60118
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	16.1571	0.888076	0.444038	−	0.896008i	$-0.353545\pi$
$331$	16.1571	0.888076	0.444038	+	0.896008i	$0.353545\pi$
$332$	0	0
$333$	35.7574	1.95949
$334$	0	0
$335$	0	0
$336$	0	0
$337$	10.8596	0.591558	0.295779	−	0.955256i	$-0.404421\pi$
$337$	10.8596	0.591558	0.295779	+	0.955256i	$0.404421\pi$
$338$	−28.6941	−1.56076
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	−24.6696	−1.33009
$345$	0	0
$346$	0	0
$347$	−18.5358	−0.995054	−0.497527	−	0.867448i	$-0.665758\pi$
$347$	−18.5358	−0.995054	−0.497527	+	0.867448i	$0.665758\pi$
$348$	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
$358$	58.2682	3.07957
$359$	−37.6998	−1.98972	−0.994859	−	0.101273i	$-0.967708\pi$
$359$	−37.6998	−1.98972	−0.994859	+	0.101273i	$0.967708\pi$
$360$	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	$0.5\pi$
$368$	3.83014	0.199660
$369$	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
$379$	31.5194	1.61904	0.809522	−	0.587090i	$-0.199726\pi$
$379$	31.5194	1.61904	0.809522	+	0.587090i	$0.199726\pi$
$380$	0	0
$381$	0	0
$382$	20.0400	1.02534
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	4.68208	0.238312
$387$	38.4554	1.95480
$388$	0	0
$389$	−1.67761	−0.0850582	−0.0425291	−	0.999095i	$-0.513542\pi$
$389$	−1.67761	−0.0850582	−0.0425291	+	0.999095i	$0.513542\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−4.48201	−0.225801
$395$	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
$400$	7.47963	0.373981
$401$	−30.6367	−1.52992	−0.764961	−	0.644077i	$-0.777242\pi$
$401$	−30.6367	−1.52992	−0.764961	+	0.644077i	$0.777242\pi$
$402$	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
$414$	16.9541	0.833251
$415$	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
$421$	22.1607	1.08004	0.540022	−	0.841651i	$-0.318416\pi$
$421$	22.1607	1.08004	0.540022	+	0.841651i	$0.318416\pi$
$422$	63.7248	3.10208
$423$	0	0
$424$	27.5414	1.33753
$425$	0	0
$426$	0	0
$427$	0	0
$428$	32.2024	1.55656
$429$	0	0
$430$	0	0
$431$	15.2740	0.735725	0.367862	−	0.929880i	$-0.380090\pi$
$431$	15.2740	0.735725	0.367862	+	0.929880i	$0.380090\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	−44.8804	−2.14938
$437$	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
$443$	−5.59153	−0.265662	−0.132831	−	0.991139i	$-0.542407\pi$
$443$	−5.59153	−0.265662	−0.132831	+	0.991139i	$0.542407\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	40.8782	1.92916	0.964580	−	0.263790i	$-0.0849724\pi$
$449$	40.8782	1.92916	0.964580	+	0.263790i	$0.0849724\pi$
$450$	33.1086	1.56076
$451$	0	0
$452$	31.0829	1.46201
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	42.1142	1.97002	0.985011	−	0.172493i	$-0.0551823\pi$
$457$	42.1142	1.97002	0.985011	+	0.172493i	$0.0551823\pi$
$458$	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
$463$	23.0299	1.07029	0.535145	−	0.844760i	$-0.320257\pi$
$463$	23.0299	1.07029	0.535145	+	0.844760i	$0.320257\pi$
$464$	−11.7259	−0.544362
$465$	0	0
$466$	−48.5593	−2.24947
$467$	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
$477$	−42.9321	−1.96573
$478$	62.8967	2.87683
$479$	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
$487$	41.1883	1.86642	0.933210	−	0.359333i	$-0.116996\pi$
$487$	41.1883	1.86642	0.933210	+	0.359333i	$0.116996\pi$
$488$	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
$499$	−44.6759	−1.99997	−0.999985	−	0.00546838i	$-0.998259\pi$
$499$	−44.6759	−1.99997	−0.999985	+	0.00546838i	$0.998259\pi$
$500$	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
$508$	−57.5585	−2.55374
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	16.4552	0.727223
$513$	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	$0.5\pi$
$522$	−51.9049	−2.27181
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	50.2772	2.19219
$527$	0	0
$528$	0	0
$529$	−16.4444	−0.714976
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−24.1854	−1.04465
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−19.6885	−0.846476	−0.423238	−	0.906019i	$-0.639107\pi$
$541$	−19.6885	−0.846476	−0.423238	+	0.906019i	$0.639107\pi$
$542$	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	$0.889785\pi$
$548$	48.9372	2.09049
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	73.4687	3.12138
$555$	0	0
$556$	0	0
$557$	43.4353	1.84041	0.920207	−	0.391433i	$-0.128020\pi$
$557$	43.4353	1.84041	0.920207	+	0.391433i	$0.128020\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−73.8886	−3.11680
$563$	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
$568$	−30.8975	−1.29643
$569$	−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
$571$	−46.5287	−1.94717	−0.973583	−	0.228332i	$-0.926673\pi$
$571$	−46.5287	−1.94717	−0.973583	+	0.228332i	$0.926673\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	12.8019	0.533877
$576$	38.3760	1.59900
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−37.5231	−1.56076
$579$	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
$592$	17.8301	0.732814
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−63.1822	−2.58804
$597$	0	0
$598$	0	0
$599$	45.1162	1.84340	0.921698	−	0.387907i	$-0.126802\pi$
$599$	45.1162	1.84340	0.921698	+	0.387907i	$0.126802\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	37.7006	1.53529
$604$	6.84633	0.278573
$605$	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
$613$	−12.0810	−0.487949	−0.243974	−	0.969782i	$-0.578451\pi$
$613$	−12.0810	−0.487949	−0.243974	+	0.969782i	$0.578451\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−3.84770	−0.154902	−0.0774512	−	0.996996i	$-0.524678\pi$
$617$	−3.84770	−0.154902	−0.0774512	+	0.996996i	$0.524678\pi$
$618$	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
$631$	50.2369	1.99990	0.999950	−	0.00996082i	$-0.00317068\pi$
$631$	50.2369	1.99990	0.999950	+	0.00996082i	$0.00317068\pi$
$632$	−5.50160	−0.218842
$633$	0	0
$634$	46.9834	1.86595
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	48.1636	1.90532
$640$	0	0
$641$	−24.7737	−0.978503	−0.489251	−	0.872143i	$-0.662730\pi$
$641$	−24.7737	−0.978503	−0.489251	+	0.872143i	$0.662730\pi$
$642$	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	$0.5\pi$
$648$	17.3208	0.680425
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−61.1084	−2.39319
$653$	25.5159	0.998514	0.499257	−	0.866454i	$-0.333606\pi$
$653$	25.5159	0.998514	0.499257	+	0.866454i	$0.333606\pi$
$654$	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	$0.5\pi$
$662$	35.6627	1.38607
$663$	0	0
$664$	0	0
$665$	0	0
$666$	78.9253	3.05829
$667$	−20.0697	−0.777103
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	49.1526	1.89470	0.947348	−	0.320207i	$-0.103752\pi$
$673$	49.1526	1.89470	0.947348	+	0.320207i	$0.103752\pi$
$674$	23.9697	0.923278
$675$	0	0
$676$	−37.3349	−1.43596
$677$	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
$683$	−11.0364	−0.422295	−0.211147	−	0.977454i	$-0.567720\pi$
$683$	−11.0364	−0.422295	−0.211147	+	0.977454i	$0.567720\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	19.1755	0.731058
$689$	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
$694$	−40.9130	−1.55304
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−50.9432	−1.92410	−0.962049	−	0.272876i	$-0.912025\pi$
$701$	−50.9432	−1.92410	−0.962049	+	0.272876i	$0.912025\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	35.9568	1.35038	0.675192	−	0.737642i	$-0.264061\pi$
$709$	35.9568	1.35038	0.675192	+	0.737642i	$0.264061\pi$
$710$	0	0
$711$	8.57600	0.321625
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	75.8148	2.83333
$717$	0	0
$718$	−83.2125	−3.10546
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	−41.9376	−1.56076
$723$	0	0
$724$	0	0
$725$	−39.1928	−1.45559
$726$	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
$736$	18.3091	0.674883
$737$	0	0
$738$	0	0
$739$	−32.7381	−1.20429	−0.602145	−	0.798387i	$-0.705687\pi$
$739$	−32.7381	−1.20429	−0.602145	+	0.798387i	$0.705687\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−54.1326	−1.98593	−0.992965	−	0.118405i	$-0.962222\pi$
$743$	−54.1326	−1.98593	−0.992965	+	0.118405i	$0.962222\pi$
$744$	0	0
$745$	0	0
$746$	−48.5593	−1.77788
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−39.9954	−1.45945	−0.729727	−	0.683739i	$-0.760353\pi$
$751$	−39.9954	−1.45945	−0.729727	+	0.683739i	$0.760353\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	49.9075	1.81392	0.906959	−	0.421220i	$-0.138398\pi$
$757$	49.9075	1.81392	0.906959	+	0.421220i	$0.138398\pi$
$758$	69.5710	2.52693
$759$	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
$764$	26.0747	0.943350
$765$	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
$772$	6.09202	0.219257
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	84.8804	3.05096
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−3.70289	−0.132755
$779$	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	$0.5\pi$
$788$	−5.83170	−0.207746
$789$	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
$800$	35.7547	1.26412
$801$	0	0
$802$	−67.6225	−2.38783
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−28.5175	−1.00262	−0.501311	−	0.865267i	$-0.667149\pi$
$809$	−28.5175	−1.00262	−0.501311	+	0.865267i	$0.667149\pi$
$810$	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
$823$	2.10386	0.0733360	0.0366680	−	0.999328i	$-0.488326\pi$
$823$	2.10386	0.0733360	0.0366680	+	0.999328i	$0.488326\pi$
$824$	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	$0.777268\pi$
$828$	22.0596	0.766625
$829$	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
$841$	32.4432	1.11873
$842$	48.9140	1.68569
$843$	0	0
$844$	82.9145	2.85404
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−21.4077	−0.735145
$849$	0	0
$850$	0	0
$851$	30.5175	1.04613
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	21.5795	0.737573
$857$	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
$862$	33.7135	1.14829
$863$	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
$872$	−30.0753	−1.01848
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	59.1125	1.99609	0.998043	−	0.0625337i	$-0.0199181\pi$
$877$	59.1125	1.99609	0.998043	+	0.0625337i	$0.0199181\pi$
$878$	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
$886$	−12.3419	−0.414633
$887$	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
$898$	90.2280	3.01095
$899$	0	0
$900$	43.0788	1.43596
$901$	0	0
$902$	0	0
$903$	0	0
$904$	20.8293	0.692772
$905$	0	0
$906$	0	0
$907$	−51.6513	−1.71505	−0.857526	−	0.514440i	$-0.828000\pi$
$907$	−51.6513	−1.71505	−0.857526	+	0.514440i	$0.828000\pi$
$908$	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
$914$	92.9563	3.07472
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−17.0609	−0.562789	−0.281394	−	0.959592i	$-0.590797\pi$
$919$	−17.0609	−0.562789	−0.281394	+	0.959592i	$0.590797\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	59.5957	1.95949
$926$	50.8325	1.67046
$927$	0	0
$928$	−56.0531	−1.84003
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	−63.1822	−2.06960
$933$	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
$953$	−38.0531	−1.23266	−0.616330	−	0.787488i	$-0.711381\pi$
$953$	−38.0531	−1.23266	−0.616330	+	0.787488i	$0.711381\pi$
$954$	−94.7616	−3.06802
$955$	0	0
$956$	81.8370	2.64680
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	−33.6386	−1.08399
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−32.9320	−1.05902	−0.529511	−	0.848303i	$-0.677624\pi$
$967$	−32.9320	−1.05902	−0.529511	+	0.848303i	$0.677624\pi$
$968$	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
$974$	90.9125	2.91302
$975$	0	0
$976$	0	0
$977$	54.4749	1.74281	0.871404	−	0.490567i	$-0.163210\pi$
$977$	54.4749	1.74281	0.871404	+	0.490567i	$0.163210\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	46.8820	1.49683
$982$	−97.1186	−3.09918
$983$	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
$989$	32.8202	1.04362
$990$	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	$0.5\pi$
$998$	−98.6106	−3.12146
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bg.1.3		4
7.6	odd	2	CM	5929.2.a.bg.1.3		4
11.2	odd	10		539.2.f.c.246.2	✓	8
11.6	odd	10		539.2.f.c.344.2	yes	8
11.10	odd	2		5929.2.a.bc.1.2		4
77.2	odd	30		539.2.q.d.312.2		16
77.6	even	10		539.2.f.c.344.2	yes	8
77.13	even	10		539.2.f.c.246.2	✓	8
77.17	even	30		539.2.q.d.520.2		16
77.24	even	30		539.2.q.d.422.1		16
77.39	odd	30		539.2.q.d.520.2		16
77.46	odd	30		539.2.q.d.422.1		16
77.61	even	30		539.2.q.d.410.1		16
77.68	even	30		539.2.q.d.312.2		16
77.72	odd	30		539.2.q.d.410.1		16
77.76	even	2		5929.2.a.bc.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.f.c.246.2	✓	8	11.2	odd	10
539.2.f.c.246.2	✓	8	77.13	even	10
539.2.f.c.344.2	yes	8	11.6	odd	10
539.2.f.c.344.2	yes	8	77.6	even	10
539.2.q.d.312.2		16	77.2	odd	30
539.2.q.d.312.2		16	77.68	even	30
539.2.q.d.410.1		16	77.61	even	30
539.2.q.d.410.1		16	77.72	odd	30
539.2.q.d.422.1		16	77.24	even	30
539.2.q.d.422.1		16	77.46	odd	30
539.2.q.d.520.2		16	77.17	even	30
539.2.q.d.520.2		16	77.39	odd	30
5929.2.a.bc.1.2		4	11.10	odd	2
5929.2.a.bc.1.2		4	77.76	even	2
5929.2.a.bg.1.3		4	1.1	even	1	trivial
5929.2.a.bg.1.3		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)

\(f(q)\)	\(=\)	\(q+2.20724 q^{2} +2.87192 q^{4} +1.92453 q^{8} -3.00000 q^{9} -1.49593 q^{16} -6.62173 q^{18} -2.56038 q^{23} -5.00000 q^{25} +7.83857 q^{29} -7.15093 q^{32} -8.61575 q^{36} -11.9191 q^{37} -12.8185 q^{43} -5.65138 q^{46} -11.0362 q^{50} +14.3107 q^{53} +17.3016 q^{58} -12.7920 q^{64} -12.5669 q^{67} -16.0545 q^{71} -5.77360 q^{72} -26.3084 q^{74} -2.85867 q^{79} +9.00000 q^{81} -28.2935 q^{86} -7.35321 q^{92} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 11 q^{4} - 3 q^{8} - 12 q^{9} + 21 q^{16} - 3 q^{18} - 8 q^{23} - 20 q^{25} + 2 q^{29} - 50 q^{32} - 33 q^{36} + 6 q^{37} - 12 q^{43} - 47 q^{46} - 5 q^{50} + 10 q^{53} - 2 q^{58} + 33 q^{64}+ \cdots + 8 q^{92}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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