LMFDB - Embedded newform 5929.2.a.bg.1.2

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			1.2
Root			$-0.746117$ 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)

$f(q)$	$=$	$q-0.746117 q^{2} -1.44331 q^{4} +2.56911 q^{8} -3.00000 q^{9} +0.969764 q^{16} +2.23835 q^{18} -3.36187 q^{23} -5.00000 q^{25} +9.44700 q^{29} -5.86178 q^{32} +4.32993 q^{36} +11.0746 q^{37} -1.32431 q^{43} +2.50835 q^{46} +3.73058 q^{50} +6.97487 q^{53} -7.04857 q^{58} +2.43404 q^{64} -13.8615 q^{67} -0.0882461 q^{71} -7.70733 q^{72} -8.26297 q^{74} -17.5697 q^{79} +9.00000 q^{81} +0.988093 q^{86} +4.85222 q^{92} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.746117	−0.527584	−0.263792	−	0.964580i	$-0.584973\pi$
$2$	−0.746117	−0.527584	−0.263792	+	0.964580i	$0.584973\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−1.44331	−0.721655
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	2.56911	0.908318
$9$	−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
$16$	0.969764	0.242441
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	2.23835	0.527584
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−3.36187	−0.700998	−0.350499	−	0.936563i	$-0.613988\pi$
$23$	−3.36187	−0.700998	−0.350499	+	0.936563i	$0.613988\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	9.44700	1.75426	0.877132	−	0.480249i	$-0.159454\pi$
$29$	9.44700	1.75426	0.877132	+	0.480249i	$0.159454\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−5.86178	−1.03623
$33$	0	0
$34$	0	0
$35$	0	0
$36$	4.32993	0.721655
$37$	11.0746	1.82066	0.910330	−	0.413884i	$-0.135828\pi$
$37$	11.0746	1.82066	0.910330	+	0.413884i	$0.135828\pi$
$38$	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
$43$	−1.32431	−0.201956	−0.100978	−	0.994889i	$-0.532197\pi$
$43$	−1.32431	−0.201956	−0.100978	+	0.994889i	$0.532197\pi$
$44$	0	0
$45$	0	0
$46$	2.50835	0.369835
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	3.73058	0.527584
$51$	0	0
$52$	0	0
$53$	6.97487	0.958072	0.479036	−	0.877795i	$-0.340986\pi$
$53$	6.97487	0.958072	0.479036	+	0.877795i	$0.340986\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−7.04857	−0.925522
$59$	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
$64$	2.43404	0.304255
$65$	0	0
$66$	0	0
$67$	−13.8615	−1.69345	−0.846725	−	0.532031i	$-0.821429\pi$
$67$	−13.8615	−1.69345	−0.846725	+	0.532031i	$0.821429\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−0.0882461	−0.0104729	−0.00523645	−	0.999986i	$-0.501667\pi$
$71$	−0.0882461	−0.0104729	−0.00523645	+	0.999986i	$0.501667\pi$
$72$	−7.70733	−0.908318
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−8.26297	−0.960551
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−17.5697	−1.97674	−0.988372	−	0.152053i	$-0.951411\pi$
$79$	−17.5697	−1.97674	−0.988372	+	0.152053i	$0.951411\pi$
$80$	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
$86$	0.988093	0.106549
$87$	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
$92$	4.85222	0.505879
$93$	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
$100$	7.21655	0.721655
$101$	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
$106$	−5.20406	−0.505463
$107$	−19.2906	−1.86489	−0.932447	−	0.361308i	$-0.882330\pi$
$107$	−19.2906	−1.86489	−0.932447	+	0.361308i	$0.882330\pi$
$108$	0	0
$109$	20.7828	1.99064	0.995318	−	0.0966592i	$-0.0308157\pi$
$109$	20.7828	1.99064	0.995318	+	0.0966592i	$0.0308157\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	20.7481	1.95182	0.975909	−	0.218179i	$-0.0700116\pi$
$113$	20.7481	1.95182	0.975909	+	0.218179i	$0.0700116\pi$
$114$	0	0
$115$	0	0
$116$	−13.6350	−1.26597
$117$	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
$127$	22.2751	1.97659	0.988297	−	0.152545i	$-0.0487468\pi$
$127$	22.2751	1.97659	0.988297	+	0.152545i	$0.0487468\pi$
$128$	9.90748	0.875706
$129$	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
$134$	10.3423	0.893437
$135$	0	0
$136$	0	0
$137$	−4.35090	−0.371722	−0.185861	−	0.982576i	$-0.559507\pi$
$137$	−4.35090	−0.371722	−0.185861	+	0.982576i	$0.559507\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0.0658419	0.00552533
$143$	0	0
$144$	−2.90929	−0.242441
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−15.9841	−1.31389
$149$	−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
$151$	−16.3061	−1.32697	−0.663487	−	0.748187i	$-0.730924\pi$
$151$	−16.3061	−1.32697	−0.663487	+	0.748187i	$0.730924\pi$
$152$	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	$0.5\pi$
$158$	13.1090	1.04290
$159$	0	0
$160$	0	0
$161$	0	0
$162$	−6.71505	−0.527584
$163$	25.5111	1.99819	0.999093	−	0.0425718i	$-0.0135551\pi$
$163$	25.5111	1.99819	0.999093	+	0.0425718i	$0.0135551\pi$
$164$	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
$172$	1.91140	0.145743
$173$	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
$179$	−18.7874	−1.40424	−0.702118	−	0.712060i	$-0.747762\pi$
$179$	−18.7874	−1.40424	−0.702118	+	0.712060i	$0.747762\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	−8.63701	−0.636729
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	27.6347	1.99958	0.999789	−	0.0205267i	$-0.00653431\pi$
$191$	27.6347	1.99958	0.999789	+	0.0205267i	$0.00653431\pi$
$192$	0	0
$193$	−25.6924	−1.84938	−0.924689	−	0.380724i	$-0.875675\pi$
$193$	−25.6924	−1.84938	−0.924689	+	0.380724i	$0.875675\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−14.8139	−1.05545	−0.527724	−	0.849416i	$-0.676954\pi$
$197$	−14.8139	−1.05545	−0.527724	+	0.849416i	$0.676954\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−12.8456	−0.908318
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	10.0856	0.700998
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−25.2595	−1.73894	−0.869469	−	0.493987i	$-0.835539\pi$
$211$	−25.2595	−1.73894	−0.869469	+	0.493987i	$0.835539\pi$
$212$	−10.0669	−0.691397
$213$	0	0
$214$	14.3930	0.983888
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−15.5064	−1.05023
$219$	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
$226$	−15.4805	−1.02975
$227$	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
$232$	24.2704	1.59343
$233$	−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
$239$	20.2183	1.30781	0.653907	−	0.756575i	$-0.273129\pi$
$239$	20.2183	1.30781	0.653907	+	0.756575i	$0.273129\pi$
$240$	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
$254$	−16.6198	−1.04282
$255$	0	0
$256$	−12.2602	−0.766264
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−28.3410	−1.75426
$262$	0	0
$263$	−14.9211	−0.920072	−0.460036	−	0.887900i	$-0.652164\pi$
$263$	−14.9211	−0.920072	−0.460036	+	0.887900i	$0.652164\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	20.0064	1.22209
$269$	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
$274$	3.24628	0.196115
$275$	0	0
$276$	0	0
$277$	−26.7518	−1.60736	−0.803679	−	0.595063i	$-0.797127\pi$
$277$	−26.7518	−1.60736	−0.803679	+	0.595063i	$0.797127\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−12.0956	−0.721565	−0.360782	−	0.932650i	$-0.617490\pi$
$281$	−12.0956	−0.721565	−0.360782	+	0.932650i	$0.617490\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0.127367	0.00755781
$285$	0	0
$286$	0	0
$287$	0	0
$288$	17.5853	1.03623
$289$	−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
$296$	28.4520	1.65374
$297$	0	0
$298$	16.4146	0.950870
$299$	0	0
$300$	0	0
$301$	0	0
$302$	12.1663	0.700091
$303$	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
$316$	25.3585	1.42653
$317$	−20.5716	−1.15542	−0.577708	−	0.816243i	$-0.696053\pi$
$317$	−20.5716	−1.15542	−0.577708	+	0.816243i	$0.696053\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−12.9898	−0.721655
$325$	0	0
$326$	−19.0343	−1.05421
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−32.2349	−1.77179	−0.885895	−	0.463887i	$-0.846455\pi$
$331$	−32.2349	−1.77179	−0.885895	+	0.463887i	$0.846455\pi$
$332$	0	0
$333$	−33.2239	−1.82066
$334$	0	0
$335$	0	0
$336$	0	0
$337$	11.8294	0.644391	0.322195	−	0.946673i	$-0.395579\pi$
$337$	11.8294	0.644391	0.322195	+	0.946673i	$0.395579\pi$
$338$	9.69952	0.527584
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	−3.40231	−0.183440
$345$	0	0
$346$	0	0
$347$	−36.4637	−1.95747	−0.978737	−	0.205120i	$-0.934242\pi$
$347$	−36.4637	−1.95747	−0.978737	+	0.205120i	$0.934242\pi$
$348$	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
$358$	14.0176	0.740853
$359$	28.2440	1.49066	0.745331	−	0.666695i	$-0.232292\pi$
$359$	28.2440	1.49066	0.745331	+	0.666695i	$0.232292\pi$
$360$	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	$0.5\pi$
$368$	−3.26022	−0.169951
$369$	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
$379$	−12.0637	−0.619669	−0.309834	−	0.950791i	$-0.600274\pi$
$379$	−12.0637	−0.619669	−0.309834	+	0.950791i	$0.600274\pi$
$380$	0	0
$381$	0	0
$382$	−20.6187	−1.05495
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	19.1695	0.975702
$387$	3.97294	0.201956
$388$	0	0
$389$	24.5221	1.24332	0.621660	−	0.783287i	$-0.286458\pi$
$389$	24.5221	1.24332	0.621660	+	0.783287i	$0.286458\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	11.0529	0.556837
$395$	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
$400$	−4.84882	−0.242441
$401$	39.9476	1.99489	0.997445	−	0.0714367i	$-0.0227584\pi$
$401$	39.9476	1.99489	0.997445	+	0.0714367i	$0.0227584\pi$
$402$	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
$414$	−7.52504	−0.369835
$415$	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
$421$	2.37284	0.115645	0.0578225	−	0.998327i	$-0.481584\pi$
$421$	2.37284	0.115645	0.0578225	+	0.998327i	$0.481584\pi$
$422$	18.8466	0.917436
$423$	0	0
$424$	17.9192	0.870233
$425$	0	0
$426$	0	0
$427$	0	0
$428$	27.8423	1.34581
$429$	0	0
$430$	0	0
$431$	10.3372	0.497926	0.248963	−	0.968513i	$-0.419910\pi$
$431$	10.3372	0.497926	0.248963	+	0.968513i	$0.419910\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	−29.9961	−1.43655
$437$	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
$443$	−41.4080	−1.96735	−0.983676	−	0.179949i	$-0.942407\pi$
$443$	−41.4080	−1.96735	−0.983676	+	0.179949i	$0.942407\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−26.5002	−1.25062	−0.625310	−	0.780376i	$-0.715028\pi$
$449$	−26.5002	−1.25062	−0.625310	+	0.780376i	$0.715028\pi$
$450$	−11.1917	−0.527584
$451$	0	0
$452$	−29.9459	−1.40854
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−29.7362	−1.39100	−0.695501	−	0.718525i	$-0.744818\pi$
$457$	−29.7362	−1.39100	−0.695501	+	0.718525i	$0.744818\pi$
$458$	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
$463$	−27.4582	−1.27609	−0.638046	−	0.769998i	$-0.720257\pi$
$463$	−27.4582	−1.27609	−0.638046	+	0.769998i	$0.720257\pi$
$464$	9.16136	0.425305
$465$	0	0
$466$	16.4146	0.760390
$467$	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
$477$	−20.9246	−0.958072
$478$	−15.0852	−0.689982
$479$	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
$487$	27.8112	1.26025	0.630123	−	0.776495i	$-0.283004\pi$
$487$	27.8112	1.26025	0.630123	+	0.776495i	$0.283004\pi$
$488$	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
$499$	−14.0380	−0.628426	−0.314213	−	0.949352i	$-0.601741\pi$
$499$	−14.0380	−0.628426	−0.314213	+	0.949352i	$0.601741\pi$
$500$	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
$508$	−32.1498	−1.42642
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	−10.6674	−0.471437
$513$	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	$0.5\pi$
$522$	21.1457	0.925522
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	11.1329	0.485415
$527$	0	0
$528$	0	0
$529$	−11.6978	−0.508602
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−35.6117	−1.53819
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−8.84497	−0.380275	−0.190138	−	0.981757i	$-0.560893\pi$
$541$	−8.84497	−0.380275	−0.190138	+	0.981757i	$0.560893\pi$
$542$	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	$0.889785\pi$
$548$	6.27970	0.268255
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	19.9599	0.848017
$555$	0	0
$556$	0	0
$557$	−4.14975	−0.175830	−0.0879152	−	0.996128i	$-0.528020\pi$
$557$	−4.14975	−0.175830	−0.0879152	+	0.996128i	$0.528020\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	9.02475	0.380686
$563$	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
$568$	−0.226714	−0.00951271
$569$	−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
$571$	31.2285	1.30687	0.653435	−	0.756982i	$-0.273327\pi$
$571$	31.2285	1.30687	0.653435	+	0.756982i	$0.273327\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	16.8093	0.700998
$576$	−7.30213	−0.304255
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	12.6840	0.527584
$579$	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
$592$	10.7398	0.441402
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	31.7528	1.30065
$597$	0	0
$598$	0	0
$599$	−47.6604	−1.94735	−0.973676	−	0.227937i	$-0.926802\pi$
$599$	−47.6604	−1.94735	−0.973676	+	0.227937i	$0.926802\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	41.5845	1.69345
$604$	23.5348	0.957618
$605$	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
$613$	41.9378	1.69385	0.846925	−	0.531712i	$-0.178451\pi$
$613$	41.9378	1.69385	0.846925	+	0.531712i	$0.178451\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−48.2946	−1.94427	−0.972133	−	0.234428i	$-0.924678\pi$
$617$	−48.2946	−1.94427	−0.972133	+	0.234428i	$0.924678\pi$
$618$	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
$631$	−40.9367	−1.62966	−0.814832	−	0.579698i	$-0.803171\pi$
$631$	−40.9367	−1.62966	−0.814832	+	0.579698i	$0.803171\pi$
$632$	−45.1385	−1.79551
$633$	0	0
$634$	15.3488	0.609580
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0.264738	0.0104729
$640$	0	0
$641$	34.3449	1.35654	0.678270	−	0.734813i	$-0.262730\pi$
$641$	34.3449	1.35654	0.678270	+	0.734813i	$0.262730\pi$
$642$	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	$0.5\pi$
$648$	23.1220	0.908318
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−36.8205	−1.44200
$653$	−46.6714	−1.82639	−0.913196	−	0.407520i	$-0.866394\pi$
$653$	−46.6714	−1.82639	−0.913196	+	0.407520i	$0.866394\pi$
$654$	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	$0.5\pi$
$662$	24.0510	0.934768
$663$	0	0
$664$	0	0
$665$	0	0
$666$	24.7889	0.960551
$667$	−31.7596	−1.22974
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	30.9896	1.19456	0.597281	−	0.802032i	$-0.296248\pi$
$673$	30.9896	1.19456	0.597281	+	0.802032i	$0.296248\pi$
$674$	−8.82614	−0.339970
$675$	0	0
$676$	18.7630	0.721655
$677$	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
$683$	38.9586	1.49071	0.745355	−	0.666668i	$-0.232280\pi$
$683$	38.9586	1.49071	0.745355	+	0.666668i	$0.232280\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−1.28427	−0.0489624
$689$	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
$694$	27.2062	1.03273
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	32.7207	1.23584	0.617922	−	0.786239i	$-0.287975\pi$
$701$	32.7207	1.23584	0.617922	+	0.786239i	$0.287975\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	48.4711	1.82037	0.910185	−	0.414202i	$-0.135939\pi$
$709$	48.4711	1.82037	0.910185	+	0.414202i	$0.135939\pi$
$710$	0	0
$711$	52.7091	1.97674
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	27.1160	1.01337
$717$	0	0
$718$	−21.0733	−0.786449
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	14.1762	0.527584
$723$	0	0
$724$	0	0
$725$	−47.2350	−1.75426
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	19.7065	0.726392
$737$	0	0
$738$	0	0
$739$	31.1664	1.14648	0.573238	−	0.819389i	$-0.305687\pi$
$739$	31.1664	1.14648	0.573238	+	0.819389i	$0.305687\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−22.8669	−0.838907	−0.419453	−	0.907777i	$-0.637778\pi$
$743$	−22.8669	−0.838907	−0.419453	+	0.907777i	$0.637778\pi$
$744$	0	0
$745$	0	0
$746$	16.4146	0.600980
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	54.3842	1.98451	0.992253	−	0.124234i	$-0.0396474\pi$
$751$	54.3842	1.98451	0.992253	+	0.124234i	$0.0396474\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−6.62188	−0.240676	−0.120338	−	0.992733i	$-0.538398\pi$
$757$	−6.62188	−0.240676	−0.120338	+	0.992733i	$0.538398\pi$
$758$	9.00090	0.326927
$759$	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
$764$	−39.8855	−1.44301
$765$	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
$772$	37.0821	1.33461
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	−2.96428	−0.106549
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−18.2964	−0.655956
$779$	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	$0.5\pi$
$788$	21.3811	0.761669
$789$	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
$800$	29.3089	1.03623
$801$	0	0
$802$	−29.8056	−1.05247
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−5.86051	−0.206044	−0.103022	−	0.994679i	$-0.532851\pi$
$809$	−5.86051	−0.206044	−0.103022	+	0.994679i	$0.532851\pi$
$810$	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
$823$	55.1812	1.92350	0.961748	−	0.273936i	$-0.0883256\pi$
$823$	55.1812	1.92350	0.961748	+	0.273936i	$0.0883256\pi$
$824$	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	$0.777268\pi$
$828$	−14.5567	−0.505879
$829$	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
$841$	60.2458	2.07744
$842$	−1.77041	−0.0610125
$843$	0	0
$844$	36.4573	1.25491
$845$	0	0
$846$	0	0
$847$	0	0
$848$	6.76397	0.232276
$849$	0	0
$850$	0	0
$851$	−37.2315	−1.27628
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−49.5597	−1.69392
$857$	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
$862$	−7.71276	−0.262698
$863$	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
$872$	53.3934	1.80813
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	14.7443	0.497878	0.248939	−	0.968519i	$-0.419918\pi$
$877$	14.7443	0.497878	0.248939	+	0.968519i	$0.419918\pi$
$878$	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
$886$	30.8952	1.03794
$887$	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
$898$	19.7722	0.659807
$899$	0	0
$900$	−21.6497	−0.721655
$901$	0	0
$902$	0	0
$903$	0	0
$904$	53.3042	1.77287
$905$	0	0
$906$	0	0
$907$	13.5085	0.448542	0.224271	−	0.974527i	$-0.428000\pi$
$907$	13.5085	0.448542	0.224271	+	0.974527i	$0.428000\pi$
$908$	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
$914$	22.1867	0.733871
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	50.0604	1.65134	0.825671	−	0.564152i	$-0.190797\pi$
$919$	50.0604	1.65134	0.825671	+	0.564152i	$0.190797\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−55.3732	−1.82066
$926$	20.4870	0.673246
$927$	0	0
$928$	−55.3762	−1.81781
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	31.7528	1.04010
$933$	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
$953$	59.3641	1.92299	0.961495	−	0.274822i	$-0.0886189\pi$
$953$	59.3641	1.92299	0.961495	+	0.274822i	$0.0886189\pi$
$954$	15.6122	0.505463
$955$	0	0
$956$	−29.1813	−0.943791
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	57.8718	1.86489
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−4.36827	−0.140474	−0.0702371	−	0.997530i	$-0.522376\pi$
$967$	−4.36827	−0.140474	−0.0702371	+	0.997530i	$0.522376\pi$
$968$	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
$974$	−20.7504	−0.664886
$975$	0	0
$976$	0	0
$977$	−62.0969	−1.98666	−0.993328	−	0.115321i	$-0.963210\pi$
$977$	−62.0969	−1.98666	−0.993328	+	0.115321i	$0.963210\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−62.3485	−1.99064
$982$	32.8291	1.04762
$983$	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
$989$	4.45217	0.141571
$990$	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	$0.5\pi$
$998$	10.4740	0.331548
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bg.1.2		4
7.6	odd	2	CM	5929.2.a.bg.1.2		4
11.7	odd	10		539.2.f.c.148.2	✓	8
11.8	odd	10		539.2.f.c.295.2	yes	8
11.10	odd	2		5929.2.a.bc.1.3		4
77.18	odd	30		539.2.q.d.324.1		16
77.19	even	30		539.2.q.d.361.1		16
77.30	odd	30		539.2.q.d.361.1		16
77.40	even	30		539.2.q.d.214.2		16
77.41	even	10		539.2.f.c.295.2	yes	8
77.51	odd	30		539.2.q.d.214.2		16
77.52	even	30		539.2.q.d.471.2		16
77.62	even	10		539.2.f.c.148.2	✓	8
77.73	even	30		539.2.q.d.324.1		16
77.74	odd	30		539.2.q.d.471.2		16
77.76	even	2		5929.2.a.bc.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.f.c.148.2	✓	8	11.7	odd	10
539.2.f.c.148.2	✓	8	77.62	even	10
539.2.f.c.295.2	yes	8	11.8	odd	10
539.2.f.c.295.2	yes	8	77.41	even	10
539.2.q.d.214.2		16	77.40	even	30
539.2.q.d.214.2		16	77.51	odd	30
539.2.q.d.324.1		16	77.18	odd	30
539.2.q.d.324.1		16	77.73	even	30
539.2.q.d.361.1		16	77.19	even	30
539.2.q.d.361.1		16	77.30	odd	30
539.2.q.d.471.2		16	77.52	even	30
539.2.q.d.471.2		16	77.74	odd	30
5929.2.a.bc.1.3		4	11.10	odd	2
5929.2.a.bc.1.3		4	77.76	even	2
5929.2.a.bg.1.2		4	1.1	even	1	trivial
5929.2.a.bg.1.2		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)

\(f(q)\)	\(=\)	\(q-0.746117 q^{2} -1.44331 q^{4} +2.56911 q^{8} -3.00000 q^{9} +0.969764 q^{16} +2.23835 q^{18} -3.36187 q^{23} -5.00000 q^{25} +9.44700 q^{29} -5.86178 q^{32} +4.32993 q^{36} +11.0746 q^{37} -1.32431 q^{43} +2.50835 q^{46} +3.73058 q^{50} +6.97487 q^{53} -7.04857 q^{58} +2.43404 q^{64} -13.8615 q^{67} -0.0882461 q^{71} -7.70733 q^{72} -8.26297 q^{74} -17.5697 q^{79} +9.00000 q^{81} +0.988093 q^{86} +4.85222 q^{92} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 11 q^{4} - 3 q^{8} - 12 q^{9} + 21 q^{16} - 3 q^{18} - 8 q^{23} - 20 q^{25} + 2 q^{29} - 50 q^{32} - 33 q^{36} + 6 q^{37} - 12 q^{43} - 47 q^{46} - 5 q^{50} + 10 q^{53} - 2 q^{58} + 33 q^{64}+ \cdots + 8 q^{92}+O(q^{100}) \) 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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