LMFDB - Embedded newform 5929.2.a.bc.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:	$0$
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)

$f(q)$	$=$	$q+2.82528 q^{2} +5.98218 q^{4} +11.2508 q^{8} -3.00000 q^{9} +19.8222 q^{16} -8.47583 q^{18} +7.50465 q^{23} -5.00000 q^{25} +4.60250 q^{29} +33.5015 q^{32} -17.9466 q^{36} +8.21093 q^{37} +6.59794 q^{43} +21.2027 q^{46} -14.1264 q^{50} +1.86964 q^{53} +13.0033 q^{58} +55.0068 q^{64} +6.09473 q^{67} -9.83400 q^{71} -33.7523 q^{72} +23.1982 q^{74} -15.8029 q^{79} +9.00000 q^{81} +18.6410 q^{86} +44.8942 q^{92} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.82528	1.99777	0.998886	−	0.0471903i	$-0.0150267\pi$
$2$	2.82528	1.99777	0.998886	+	0.0471903i	$0.0150267\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	5.98218	2.99109
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	11.2508	3.97775
$9$	−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
$16$	19.8222	4.95554
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−8.47583	−1.99777
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	7.50465	1.56483	0.782414	−	0.622758i	$-0.213988\pi$
$23$	7.50465	1.56483	0.782414	+	0.622758i	$0.213988\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	4.60250	0.854663	0.427331	−	0.904095i	$-0.359454\pi$
$29$	4.60250	0.854663	0.427331	+	0.904095i	$0.359454\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	33.5015	5.92229
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−17.9466	−2.99109
$37$	8.21093	1.34987	0.674935	−	0.737878i	$-0.264172\pi$
$37$	8.21093	1.34987	0.674935	+	0.737878i	$0.264172\pi$
$38$	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
$43$	6.59794	1.00618	0.503088	−	0.864235i	$-0.332197\pi$
$43$	6.59794	1.00618	0.503088	+	0.864235i	$0.332197\pi$
$44$	0	0
$45$	0	0
$46$	21.2027	3.12617
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	−14.1264	−1.99777
$51$	0	0
$52$	0	0
$53$	1.86964	0.256814	0.128407	−	0.991722i	$-0.459014\pi$
$53$	1.86964	0.256814	0.128407	+	0.991722i	$0.459014\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	13.0033	1.70742
$59$	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
$64$	55.0068	6.87585
$65$	0	0
$66$	0	0
$67$	6.09473	0.744590	0.372295	−	0.928114i	$-0.378571\pi$
$67$	6.09473	0.744590	0.372295	+	0.928114i	$0.378571\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−9.83400	−1.16708	−0.583541	−	0.812084i	$-0.698333\pi$
$71$	−9.83400	−1.16708	−0.583541	+	0.812084i	$0.698333\pi$
$72$	−33.7523	−3.97775
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	23.1982	2.69673
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−15.8029	−1.77797	−0.888985	−	0.457937i	$-0.848589\pi$
$79$	−15.8029	−1.77797	−0.888985	+	0.457937i	$0.848589\pi$
$80$	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
$86$	18.6410	2.01011
$87$	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
$92$	44.8942	4.68055
$93$	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
$100$	−29.9109	−2.99109
$101$	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
$106$	5.28224	0.513056
$107$	−1.14782	−0.110964	−0.0554821	−	0.998460i	$-0.517670\pi$
$107$	−1.14782	−0.110964	−0.0554821	+	0.998460i	$0.517670\pi$
$108$	0	0
$109$	−4.50273	−0.431283	−0.215642	−	0.976473i	$-0.569184\pi$
$109$	−4.50273	−0.431283	−0.215642	+	0.976473i	$0.569184\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−14.0591	−1.32257	−0.661285	−	0.750135i	$-0.729988\pi$
$113$	−14.0591	−1.32257	−0.661285	+	0.750135i	$0.729988\pi$
$114$	0	0
$115$	0	0
$116$	27.5330	2.55638
$117$	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
$127$	−10.1533	−0.900958	−0.450479	−	0.892787i	$-0.648747\pi$
$127$	−10.1533	−0.900958	−0.450479	+	0.892787i	$0.648747\pi$
$128$	88.4062	7.81408
$129$	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
$134$	17.2193	1.48752
$135$	0	0
$136$	0	0
$137$	−23.2202	−1.98384	−0.991920	−	0.126868i	$-0.959507\pi$
$137$	−23.2202	−1.98384	−0.991920	+	0.126868i	$0.959507\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	−27.7838	−2.33156
$143$	0	0
$144$	−59.4665	−4.95554
$145$	0	0
$146$	0	0
$147$	0	0
$148$	49.1193	4.03758
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	0	0
$151$	−12.4489	−1.01308	−0.506540	−	0.862217i	$-0.669076\pi$
$151$	−12.4489	−1.01308	−0.506540	+	0.862217i	$0.669076\pi$
$152$	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	$0.5\pi$
$158$	−44.6477	−3.55198
$159$	0	0
$160$	0	0
$161$	0	0
$162$	25.4275	1.99777
$163$	8.91721	0.698450	0.349225	−	0.937039i	$-0.386445\pi$
$163$	8.91721	0.698450	0.349225	+	0.937039i	$0.386445\pi$
$164$	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
$172$	39.4701	3.00957
$173$	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
$179$	−23.9265	−1.78835	−0.894176	−	0.447715i	$-0.852238\pi$
$179$	−23.9265	−1.78835	−0.894176	+	0.447715i	$0.852238\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	84.4331	6.22449
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−22.0235	−1.59356	−0.796781	−	0.604268i	$-0.793466\pi$
$191$	−22.0235	−1.59356	−0.796781	+	0.604268i	$0.793466\pi$
$192$	0	0
$193$	−27.0034	−1.94375	−0.971873	−	0.235507i	$-0.924325\pi$
$193$	−27.0034	−1.94375	−0.971873	+	0.235507i	$0.924325\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−18.0995	−1.28953	−0.644767	−	0.764379i	$-0.723046\pi$
$197$	−18.0995	−1.28953	−0.644767	+	0.764379i	$0.723046\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−56.2539	−3.97775
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−22.5140	−1.56483
$208$	0	0
$209$	0	0
$210$	0	0
$211$	21.4544	1.47698	0.738490	−	0.674264i	$-0.235539\pi$
$211$	21.4544	1.47698	0.738490	+	0.674264i	$0.235539\pi$
$212$	11.1845	0.768155
$213$	0	0
$214$	−3.24291	−0.221681
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−12.7215	−0.861606
$219$	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
$226$	−39.7208	−2.64219
$227$	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
$232$	51.7817	3.39963
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	2.60706	0.168637	0.0843185	−	0.996439i	$-0.473129\pi$
$239$	2.60706	0.168637	0.0843185	+	0.996439i	$0.473129\pi$
$240$	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
$254$	−28.6858	−1.79991
$255$	0	0
$256$	139.758	8.73490
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−13.8075	−0.854663
$262$	0	0
$263$	−28.9988	−1.78814	−0.894072	−	0.447924i	$-0.852164\pi$
$263$	−28.9988	−1.78814	−0.894072	+	0.447924i	$0.852164\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	36.4598	2.22714
$269$	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
$274$	−65.6036	−3.96326
$275$	0	0
$276$	0	0
$277$	27.1049	1.62858	0.814289	−	0.580460i	$-0.197127\pi$
$277$	27.1049	1.62858	0.814289	+	0.580460i	$0.197127\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	8.59337	0.512638	0.256319	−	0.966592i	$-0.417490\pi$
$281$	8.59337	0.512638	0.256319	+	0.966592i	$0.417490\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−58.8288	−3.49085
$285$	0	0
$286$	0	0
$287$	0	0
$288$	−100.505	−5.92229
$289$	−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
$296$	92.3793	5.36944
$297$	0	0
$298$	62.1561	3.60060
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−35.1717	−2.02390
$303$	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
$316$	−94.5361	−5.31807
$317$	33.7271	1.89430	0.947152	−	0.320786i	$-0.103947\pi$
$317$	33.7271	1.89430	0.947152	+	0.320786i	$0.103947\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	53.8397	2.99109
$325$	0	0
$326$	25.1936	1.39534
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	6.09209	0.334852	0.167426	−	0.985885i	$-0.446455\pi$
$331$	6.09209	0.334852	0.167426	+	0.985885i	$0.446455\pi$
$332$	0	0
$333$	−24.6328	−1.34987
$334$	0	0
$335$	0	0
$336$	0	0
$337$	29.4006	1.60155	0.800776	−	0.598964i	$-0.204421\pi$
$337$	29.4006	1.60155	0.800776	+	0.598964i	$0.204421\pi$
$338$	−36.7286	−1.99777
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	74.2319	4.00231
$345$	0	0
$346$	0	0
$347$	−25.0079	−1.34250	−0.671248	−	0.741233i	$-0.734242\pi$
$347$	−25.0079	−1.34250	−0.671248	+	0.741233i	$0.734242\pi$
$348$	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
$358$	−67.5990	−3.57272
$359$	−32.7555	−1.72877	−0.864384	−	0.502832i	$-0.832292\pi$
$359$	−32.7555	−1.72877	−0.864384	+	0.502832i	$0.832292\pi$
$360$	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	$0.5\pi$
$368$	148.758	7.75457
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−38.9358	−2.00000	−1.00000		0.000859657i	$-0.999726\pi$
$379$	−38.9358	−2.00000	−1.00000		0.000859657i	$0.999726\pi$
$380$	0	0
$381$	0	0
$382$	−62.2224	−3.18357
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	−76.2920	−3.88316
$387$	−19.7938	−1.00618
$388$	0	0
$389$	−21.8077	−1.10569	−0.552847	−	0.833283i	$-0.686458\pi$
$389$	−21.8077	−1.10569	−0.552847	+	0.833283i	$0.686458\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−51.1360	−2.57620
$395$	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
$400$	−99.1108	−4.95554
$401$	9.62349	0.480574	0.240287	−	0.970702i	$-0.422758\pi$
$401$	9.62349	0.480574	0.240287	+	0.970702i	$0.422758\pi$
$402$	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
$414$	−63.6082	−3.12617
$415$	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
$421$	−38.2296	−1.86319	−0.931597	−	0.363492i	$-0.881584\pi$
$421$	−38.2296	−1.86319	−0.931597	+	0.363492i	$0.881584\pi$
$422$	60.6146	2.95067
$423$	0	0
$424$	21.0348	1.02154
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−6.86648	−0.331904
$429$	0	0
$430$	0	0
$431$	35.0511	1.68835	0.844177	−	0.536065i	$-0.180090\pi$
$431$	35.0511	1.68835	0.844177	+	0.536065i	$0.180090\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	−26.9362	−1.29001
$437$	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
$443$	37.9522	1.80316	0.901582	−	0.432608i	$-0.142407\pi$
$443$	37.9522	1.80316	0.901582	+	0.432608i	$0.142407\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−39.6421	−1.87083	−0.935413	−	0.353556i	$-0.884972\pi$
$449$	−39.6421	−1.87083	−0.935413	+	0.353556i	$0.884972\pi$
$450$	42.3791	1.99777
$451$	0	0
$452$	−84.1041	−3.95593
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	38.4060	1.79656	0.898279	−	0.439425i	$-0.144818\pi$
$457$	38.4060	1.79656	0.898279	+	0.439425i	$0.144818\pi$
$458$	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
$463$	41.6915	1.93757	0.968784	−	0.247907i	$-0.0797429\pi$
$463$	41.6915	1.93757	0.968784	+	0.247907i	$0.0797429\pi$
$464$	91.2315	4.23532
$465$	0	0
$466$	62.1561	2.87932
$467$	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
$477$	−5.60891	−0.256814
$478$	7.36568	0.336898
$479$	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
$487$	−2.35546	−0.106736	−0.0533681	−	0.998575i	$-0.516996\pi$
$487$	−2.35546	−0.106736	−0.0533681	+	0.998575i	$0.516996\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	44.0000	1.98569	0.992846	−	0.119401i	$-0.0380974\pi$
$491$	44.0000	1.98569	0.992846	+	0.119401i	$0.0380974\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−13.5733	−0.607623	−0.303812	−	0.952732i	$-0.598259\pi$
$499$	−13.5733	−0.607623	−0.303812	+	0.952732i	$0.598259\pi$
$500$	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
$508$	−60.7388	−2.69485
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	218.044	9.63627
$513$	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	$0.5\pi$
$522$	−39.0100	−1.70742
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	−81.9296	−3.57230
$527$	0	0
$528$	0	0
$529$	33.3198	1.44869
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	68.5705	2.96179
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−40.7017	−1.74990	−0.874951	−	0.484211i	$-0.839107\pi$
$541$	−40.7017	−1.74990	−0.874951	+	0.484211i	$0.839107\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	−138.908	−5.93385
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	76.5789	3.25353
$555$	0	0
$556$	0	0
$557$	−30.9942	−1.31327	−0.656634	−	0.754209i	$-0.728020\pi$
$557$	−30.9942	−1.31327	−0.656634	+	0.754209i	$0.728020\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	24.2787	1.02413
$563$	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
$568$	−110.640	−4.64236
$569$	22.0000	0.922288	0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000	0.922288	0.461144	+	0.887325i	$0.347439\pi$
$570$	0	0
$571$	−44.0566	−1.84371	−0.921856	−	0.387534i	$-0.873327\pi$
$571$	−44.0566	−1.84371	−0.921856	+	0.387534i	$0.873327\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−37.5233	−1.56483
$576$	−165.020	−6.87585
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−48.0297	−1.99777
$579$	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
$592$	162.758	6.68933
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	131.608	5.39088
$597$	0	0
$598$	0	0
$599$	−25.3391	−1.03533	−0.517663	−	0.855584i	$-0.673198\pi$
$599$	−25.3391	−1.03533	−0.517663	+	0.855584i	$0.673198\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	−18.2842	−0.744590
$604$	−74.4718	−3.03021
$605$	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
$613$	49.4042	1.99542	0.997709	−	0.0676456i	$-0.0215487\pi$
$613$	49.4042	1.99542	0.997709	+	0.0676456i	$0.0215487\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	45.9166	1.84853	0.924266	−	0.381749i	$-0.124678\pi$
$617$	45.9166	1.84853	0.924266	+	0.381749i	$0.124678\pi$
$618$	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
$631$	−40.3484	−1.60624	−0.803122	−	0.595815i	$-0.796829\pi$
$631$	−40.3484	−1.60624	−0.803122	+	0.595815i	$0.796829\pi$
$632$	−177.795	−7.07231
$633$	0	0
$634$	95.2884	3.78439
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	29.5020	1.16708
$640$	0	0
$641$	−49.6559	−1.96129	−0.980644	−	0.195799i	$-0.937270\pi$
$641$	−49.6559	−1.96129	−0.980644	+	0.195799i	$0.937270\pi$
$642$	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	$0.5\pi$
$648$	101.257	3.97775
$649$	0	0
$650$	0	0
$651$	0	0
$652$	53.3444	2.08913
$653$	5.38581	0.210763	0.105382	−	0.994432i	$-0.466394\pi$
$653$	5.38581	0.210763	0.105382	+	0.994432i	$0.466394\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	44.0000	1.71400	0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000	1.71400	0.856998	+	0.515319i	$0.172327\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	17.2118	0.668957
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−69.5945	−2.69673
$667$	34.5402	1.33740
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0.611628	0.0235765	0.0117883	−	0.999931i	$-0.496248\pi$
$673$	0.611628	0.0235765	0.0117883	+	0.999931i	$0.496248\pi$
$674$	83.0648	3.19953
$675$	0	0
$676$	−77.7684	−2.99109
$677$	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
$683$	−21.1014	−0.807423	−0.403711	−	0.914886i	$-0.632280\pi$
$683$	−21.1014	−0.807423	−0.403711	+	0.914886i	$0.632280\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	130.785	4.98615
$689$	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
$694$	−70.6543	−2.68200
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−49.7071	−1.87741	−0.938707	−	0.344717i	$-0.887975\pi$
$701$	−49.7071	−1.87741	−0.938707	+	0.344717i	$0.887975\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−26.2486	−0.985786	−0.492893	−	0.870090i	$-0.664061\pi$
$709$	−26.2486	−0.985786	−0.492893	+	0.870090i	$0.664061\pi$
$710$	0	0
$711$	47.4088	1.77797
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−143.133	−5.34913
$717$	0	0
$718$	−92.5433	−3.45369
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	−53.6802	−1.99777
$723$	0	0
$724$	0	0
$725$	−23.0125	−0.854663
$726$	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
$736$	251.417	9.26737
$737$	0	0
$738$	0	0
$739$	51.3997	1.89077	0.945384	−	0.325959i	$-0.105687\pi$
$739$	51.3997	1.89077	0.945384	+	0.325959i	$0.105687\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	10.5888	0.388466	0.194233	−	0.980955i	$-0.437778\pi$
$743$	10.5888	0.388466	0.194233	+	0.980955i	$0.437778\pi$
$744$	0	0
$745$	0	0
$746$	62.1561	2.27570
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	10.3298	0.376939	0.188469	−	0.982079i	$-0.439647\pi$
$751$	10.3298	0.376939	0.188469	+	0.982079i	$0.439647\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	37.4664	1.36174	0.680869	−	0.732405i	$-0.261602\pi$
$757$	37.4664	1.36174	0.680869	+	0.732405i	$0.261602\pi$
$758$	−110.004	−3.99554
$759$	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
$764$	−131.748	−4.76649
$765$	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
$772$	−161.539	−5.81392
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	−55.9230	−2.01011
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−61.6127	−2.20892
$779$	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	$0.5\pi$
$788$	−108.274	−3.85712
$789$	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
$800$	−167.508	−5.92229
$801$	0	0
$802$	27.1890	0.960078
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−52.0028	−1.82832	−0.914160	−	0.405353i	$-0.867149\pi$
$809$	−52.0028	−1.82832	−0.914160	+	0.405353i	$0.867149\pi$
$810$	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	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	0	0
$823$	−53.8809	−1.87817	−0.939086	−	0.343683i	$-0.888326\pi$
$823$	−53.8809	−1.87817	−0.939086	+	0.343683i	$0.888326\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	−134.683	−4.68055
$829$	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
$841$	−7.81699	−0.269551
$842$	−108.009	−3.72224
$843$	0	0
$844$	128.344	4.41779
$845$	0	0
$846$	0	0
$847$	0	0
$848$	37.0602	1.27265
$849$	0	0
$850$	0	0
$851$	61.6202	2.11231
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−12.9139	−0.441387
$857$	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
$862$	99.0291	3.37295
$863$	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
$872$	−50.6592	−1.71554
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−21.7892	−0.735771	−0.367885	−	0.929871i	$-0.619918\pi$
$877$	−21.7892	−0.735771	−0.367885	+	0.929871i	$0.619918\pi$
$878$	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
$886$	107.225	3.60231
$887$	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
$898$	−112.000	−3.73749
$899$	0	0
$900$	89.7328	2.99109
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−158.176	−5.26085
$905$	0	0
$906$	0	0
$907$	−45.4308	−1.50850	−0.754252	−	0.656585i	$-0.772000\pi$
$907$	−45.4308	−1.50850	−0.754252	+	0.656585i	$0.772000\pi$
$908$	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
$914$	108.508	3.58911
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	60.6047	1.99916	0.999582	−	0.0289084i	$-0.00920311\pi$
$919$	60.6047	1.99916	0.999582	+	0.0289084i	$0.00920311\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−41.0547	−1.34987
$926$	117.790	3.87082
$927$	0	0
$928$	154.191	5.06156
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	131.608	4.31097
$933$	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
$953$	−2.20709	−0.0714945	−0.0357473	−	0.999361i	$-0.511381\pi$
$953$	−2.20709	−0.0714945	−0.0357473	+	0.999361i	$0.511381\pi$
$954$	−15.8467	−0.513056
$955$	0	0
$956$	15.5959	0.504409
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	3.44347	0.110964
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−57.6533	−1.85401	−0.927003	−	0.375053i	$-0.877624\pi$
$967$	−57.6533	−1.85401	−0.927003	+	0.375053i	$0.877624\pi$
$968$	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
$974$	−6.65483	−0.213235
$975$	0	0
$976$	0	0
$977$	−26.0454	−0.833265	−0.416632	−	0.909075i	$-0.636790\pi$
$977$	−26.0454	−0.833265	−0.416632	+	0.909075i	$0.636790\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	13.5082	0.431283
$982$	124.312	3.96696
$983$	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
$989$	49.5152	1.57449
$990$	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	$0.5\pi$
$998$	−38.3483	−1.21389
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bc.1.4		4
7.6	odd	2	CM	5929.2.a.bc.1.4		4
11.5	even	5		539.2.f.c.344.1	yes	8
11.9	even	5		539.2.f.c.246.1	✓	8
11.10	odd	2		5929.2.a.bg.1.1		4
77.5	odd	30		539.2.q.d.410.2		16
77.9	even	15		539.2.q.d.312.1		16
77.16	even	15		539.2.q.d.410.2		16
77.20	odd	10		539.2.f.c.246.1	✓	8
77.27	odd	10		539.2.f.c.344.1	yes	8
77.31	odd	30		539.2.q.d.422.2		16
77.38	odd	30		539.2.q.d.520.1		16
77.53	even	15		539.2.q.d.422.2		16
77.60	even	15		539.2.q.d.520.1		16
77.75	odd	30		539.2.q.d.312.1		16
77.76	even	2		5929.2.a.bg.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.f.c.246.1	✓	8	11.9	even	5
539.2.f.c.246.1	✓	8	77.20	odd	10
539.2.f.c.344.1	yes	8	11.5	even	5
539.2.f.c.344.1	yes	8	77.27	odd	10
539.2.q.d.312.1		16	77.9	even	15
539.2.q.d.312.1		16	77.75	odd	30
539.2.q.d.410.2		16	77.5	odd	30
539.2.q.d.410.2		16	77.16	even	15
539.2.q.d.422.2		16	77.31	odd	30
539.2.q.d.422.2		16	77.53	even	15
539.2.q.d.520.1		16	77.38	odd	30
539.2.q.d.520.1		16	77.60	even	15
5929.2.a.bc.1.4		4	1.1	even	1	trivial
5929.2.a.bc.1.4		4	7.6	odd	2	CM
5929.2.a.bg.1.1		4	11.10	odd	2
5929.2.a.bg.1.1		4	77.76	even	2

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)

\(f(q)\)	\(=\)	\(q+2.82528 q^{2} +5.98218 q^{4} +11.2508 q^{8} -3.00000 q^{9} +19.8222 q^{16} -8.47583 q^{18} +7.50465 q^{23} -5.00000 q^{25} +4.60250 q^{29} +33.5015 q^{32} -17.9466 q^{36} +8.21093 q^{37} +6.59794 q^{43} +21.2027 q^{46} -14.1264 q^{50} +1.86964 q^{53} +13.0033 q^{58} +55.0068 q^{64} +6.09473 q^{67} -9.83400 q^{71} -33.7523 q^{72} +23.1982 q^{74} -15.8029 q^{79} +9.00000 q^{81} +18.6410 q^{86} +44.8942 q^{92} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 11 q^{4} + 3 q^{8} - 12 q^{9} + 21 q^{16} + 3 q^{18} - 8 q^{23} - 20 q^{25} - 2 q^{29} + 50 q^{32} - 33 q^{36} + 6 q^{37} + 12 q^{43} + 47 q^{46} + 5 q^{50} + 10 q^{53} - 2 q^{58} + 33 q^{64}+ \cdots + 8 q^{92}+O(q^{100}) \) 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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Database

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