LMFDB - Embedded newform 3087.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3087,2,Mod(1,3087)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3087, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3087.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3087 = 3^{2} \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3087.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$24.6498191040$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 343)
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.3
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	3087.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.80194 q^{2} +5.85086 q^{4} +10.7899 q^{8} +O(q^{10})$	$q+2.80194 q^{2} +5.85086 q^{4} +10.7899 q^{8} +1.64310 q^{11} +18.5308 q^{16} +4.60388 q^{22} +4.91185 q^{23} -5.00000 q^{25} -2.78986 q^{29} +30.3424 q^{32} -12.0151 q^{37} -2.48858 q^{43} +9.61356 q^{44} +13.7627 q^{46} -14.0097 q^{50} +8.09246 q^{53} -7.81700 q^{58} +47.9560 q^{64} -10.4916 q^{67} +8.71917 q^{71} -33.6655 q^{74} +13.6963 q^{79} -6.97285 q^{86} +17.7289 q^{88} +28.7385 q^{92} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} + 4 q^{4} + 9 q^{8}+O(q^{10}) $ 3 * q + 4 * q^2 + 4 * q^4 + 9 * q^8	$ 3 q + 4 q^{2} + 4 q^{4} + 9 q^{8} + 9 q^{11} + 18 q^{16} + 5 q^{22} + 11 q^{23} - 15 q^{25} + 15 q^{29} + 27 q^{32} - 11 q^{37} - q^{43} - 2 q^{44} + 24 q^{46} - 20 q^{50} + 9 q^{53} + 6 q^{58} + 49 q^{64} + 19 q^{67} + 15 q^{71} - 17 q^{74} + 17 q^{79} - 27 q^{86} + 20 q^{88} + 31 q^{92}+O(q^{100}) $ 3 * q + 4 * q^2 + 4 * q^4 + 9 * q^8 + 9 * q^11 + 18 * q^16 + 5 * q^22 + 11 * q^23 - 15 * q^25 + 15 * q^29 + 27 * q^32 - 11 * q^37 - q^43 - 2 * q^44 + 24 * q^46 - 20 * q^50 + 9 * q^53 + 6 * q^58 + 49 * q^64 + 19 * q^67 + 15 * q^71 - 17 * q^74 + 17 * q^79 - 27 * q^86 + 20 * q^88 + 31 * q^92

Display 100 coefficients 10 coefficients

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 $

$2$	2.80194	1.98127	0.990635	−	0.136540i	$-0.0435982\pi$
$2$	2.80194	1.98127	0.990635	+	0.136540i	$0.0435982\pi$
$3$	0	0
$3$	0	0
$4$	5.85086	2.92543
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	10.7899	3.81479
$9$	0	0
$10$	0	0
$11$	1.64310	0.495415	0.247707	−	0.968835i	$-0.420323\pi$
$11$	1.64310	0.495415	0.247707	+	0.968835i	$0.420323\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	18.5308	4.63270
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	4.60388	0.981550
$23$	4.91185	1.02419	0.512096	−	0.858928i	$-0.328869\pi$
$23$	4.91185	1.02419	0.512096	+	0.858928i	$0.328869\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−2.78986	−0.518063	−0.259032	−	0.965869i	$-0.583403\pi$
$29$	−2.78986	−0.518063	−0.259032	+	0.965869i	$0.583403\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	30.3424	5.36383
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−12.0151	−1.97526	−0.987632	−	0.156788i	$-0.949886\pi$
$37$	−12.0151	−1.97526	−0.987632	+	0.156788i	$0.949886\pi$
$38$	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
$43$	−2.48858	−0.379505	−0.189753	−	0.981832i	$-0.560769\pi$
$43$	−2.48858	−0.379505	−0.189753	+	0.981832i	$0.560769\pi$
$44$	9.61356	1.44930
$45$	0	0
$46$	13.7627	2.02920
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	−14.0097	−1.98127
$51$	0	0
$52$	0	0
$53$	8.09246	1.11158	0.555792	−	0.831321i	$-0.312415\pi$
$53$	8.09246	1.11158	0.555792	+	0.831321i	$0.312415\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−7.81700	−1.02642
$59$	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
$64$	47.9560	5.99450
$65$	0	0
$66$	0	0
$67$	−10.4916	−1.28175	−0.640874	−	0.767646i	$-0.721428\pi$
$67$	−10.4916	−1.28175	−0.640874	+	0.767646i	$0.721428\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	8.71917	1.03477	0.517387	−	0.855751i	$-0.326905\pi$
$71$	8.71917	1.03477	0.517387	+	0.855751i	$0.326905\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−33.6655	−3.91353
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	13.6963	1.54096	0.770479	−	0.637465i	$-0.220017\pi$
$79$	13.6963	1.54096	0.770479	+	0.637465i	$0.220017\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	−6.97285	−0.751902
$87$	0	0
$88$	17.7289	1.88990
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	28.7385	2.99620
$93$	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
$100$	−29.2543	−2.92543
$101$	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
$106$	22.6746	2.20235
$107$	−20.3153	−1.96395	−0.981976	−	0.189006i	$-0.939473\pi$
$107$	−20.3153	−1.96395	−0.981976	+	0.189006i	$0.939473\pi$
$108$	0	0
$109$	−14.3230	−1.37190	−0.685949	−	0.727649i	$-0.740613\pi$
$109$	−14.3230	−1.37190	−0.685949	+	0.727649i	$0.740613\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	15.3013	1.43942	0.719711	−	0.694273i	$-0.244274\pi$
$113$	15.3013	1.43942	0.719711	+	0.694273i	$0.244274\pi$
$114$	0	0
$115$	0	0
$116$	−16.3230	−1.51556
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−8.30021	−0.754564
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	22.3870	1.98653	0.993264	−	0.115876i	$-0.0369675\pi$
$127$	22.3870	1.98653	0.993264	+	0.115876i	$0.0369675\pi$
$128$	73.6848	6.51288
$129$	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
$134$	−29.3967	−2.53949
$135$	0	0
$136$	0	0
$137$	−18.1933	−1.55436	−0.777178	−	0.629281i	$-0.783350\pi$
$137$	−18.1933	−1.55436	−0.777178	+	0.629281i	$0.783350\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	24.4306	2.05017
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−70.2984	−5.77849
$149$	−5.44265	−0.445879	−0.222940	−	0.974832i	$-0.571565\pi$
$149$	−5.44265	−0.445879	−0.222940	+	0.974832i	$0.571565\pi$
$150$	0	0
$151$	−19.1008	−1.55440	−0.777201	−	0.629252i	$-0.783361\pi$
$151$	−19.1008	−1.55440	−0.777201	+	0.629252i	$0.783361\pi$
$152$	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	$0.5\pi$
$158$	38.3763	3.05305
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	19.9269	1.56080	0.780398	−	0.625283i	$-0.215016\pi$
$163$	19.9269	1.56080	0.780398	+	0.625283i	$0.215016\pi$
$164$	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
$172$	−14.5603	−1.11022
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	30.4480	2.29511
$177$	0	0
$178$	0	0
$179$	−24.9041	−1.86142	−0.930709	−	0.365760i	$-0.880809\pi$
$179$	−24.9041	−1.86142	−0.930709	+	0.365760i	$0.880809\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	52.9982	3.90708
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−25.6732	−1.85765	−0.928825	−	0.370519i	$-0.879180\pi$
$191$	−25.6732	−1.85765	−0.928825	+	0.370519i	$0.879180\pi$
$192$	0	0
$193$	−7.03385	−0.506308	−0.253154	−	0.967426i	$-0.581468\pi$
$193$	−7.03385	−0.506308	−0.253154	+	0.967426i	$0.581468\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−28.0170	−1.99613	−0.998064	−	0.0621994i	$-0.980189\pi$
$197$	−28.0170	−1.99613	−0.998064	+	0.0621994i	$0.980189\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−53.9493	−3.81479
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−0.667858	−0.0459773	−0.0229886	−	0.999736i	$-0.507318\pi$
$211$	−0.667858	−0.0459773	−0.0229886	+	0.999736i	$0.507318\pi$
$212$	47.3478	3.25186
$213$	0	0
$214$	−56.9221	−3.89112
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−40.1323	−2.71810
$219$	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
$225$	0	0
$226$	42.8732	2.85188
$227$	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
$232$	−30.1021	−1.97630
$233$	25.5308	1.67258	0.836289	−	0.548289i	$-0.184721\pi$
$233$	25.5308	1.67258	0.836289	+	0.548289i	$0.184721\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	25.8950	1.67501	0.837504	−	0.546432i	$-0.184014\pi$
$239$	25.8950	1.67501	0.837504	+	0.546432i	$0.184014\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	−23.2567	−1.49500
$243$	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
$253$	8.07069	0.507400
$254$	62.7271	3.93585
$255$	0	0
$256$	110.548	6.90927
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−15.8146	−0.975171	−0.487585	−	0.873075i	$-0.662122\pi$
$263$	−15.8146	−0.975171	−0.487585	+	0.873075i	$0.662122\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−61.3846	−3.74966
$269$	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
$274$	−50.9764	−3.07960
$275$	−8.21552	−0.495415
$276$	0	0
$277$	18.5875	1.11681	0.558407	−	0.829567i	$-0.311413\pi$
$277$	18.5875	1.11681	0.558407	+	0.829567i	$0.311413\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	32.7590	1.95424	0.977119	−	0.212695i	$-0.0682240\pi$
$281$	32.7590	1.95424	0.977119	+	0.212695i	$0.0682240\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	51.0146	3.02716
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−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
$296$	−129.641	−7.53522
$297$	0	0
$298$	−15.2500	−0.883407
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−53.5193	−3.07969
$303$	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
$316$	80.1353	4.50796
$317$	29.4728	1.65536	0.827678	−	0.561203i	$-0.189661\pi$
$317$	29.4728	1.65536	0.827678	+	0.561203i	$0.189661\pi$
$318$	0	0
$319$	−4.58402	−0.256656
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	55.8340	3.09236
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−30.1390	−1.65659	−0.828294	−	0.560294i	$-0.810688\pi$
$331$	−30.1390	−1.65659	−0.828294	+	0.560294i	$0.810688\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	2.15644	0.117469	0.0587344	−	0.998274i	$-0.481293\pi$
$337$	2.15644	0.117469	0.0587344	+	0.998274i	$0.481293\pi$
$338$	−36.4252	−1.98127
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	−26.8514	−1.44773
$345$	0	0
$346$	0	0
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	49.8558	2.65732
$353$	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
$358$	−69.7797	−3.68797
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	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	$0.5\pi$
$368$	91.0206	4.74477
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−33.5967	−1.73957	−0.869786	−	0.493430i	$-0.835743\pi$
$373$	−33.5967	−1.73957	−0.869786	+	0.493430i	$0.835743\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	0	0
$381$	0	0
$382$	−71.9348	−3.68050
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	−19.7084	−1.00313
$387$	0	0
$388$	0	0
$389$	1.86187	0.0944006	0.0472003	−	0.998885i	$-0.484970\pi$
$389$	1.86187	0.0944006	0.0472003	+	0.998885i	$0.484970\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−78.5018	−3.95487
$395$	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
$400$	−92.6540	−4.63270
$401$	13.0696	0.652666	0.326333	−	0.945255i	$-0.394187\pi$
$401$	13.0696	0.652666	0.326333	+	0.945255i	$0.394187\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−19.7420	−0.978575
$408$	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
$414$	0	0
$415$	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
$421$	36.7385	1.79053	0.895264	−	0.445537i	$-0.146987\pi$
$421$	36.7385	1.79053	0.895264	+	0.445537i	$0.146987\pi$
$422$	−1.87130	−0.0910933
$423$	0	0
$424$	87.3165	4.24046
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−118.862	−5.74540
$429$	0	0
$430$	0	0
$431$	−18.6735	−0.899471	−0.449735	−	0.893162i	$-0.648482\pi$
$431$	−18.6735	−0.899471	−0.449735	+	0.893162i	$0.648482\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	−83.8021	−4.01339
$437$	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
$443$	20.0000	0.950229	0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000	0.950229	0.475114	+	0.879924i	$0.342407\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	41.7157	1.96869	0.984343	−	0.176263i	$-0.0564010\pi$
$449$	41.7157	1.96869	0.984343	+	0.176263i	$0.0564010\pi$
$450$	0	0
$451$	0	0
$452$	89.5255	4.21093
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	23.7730	1.11205	0.556027	−	0.831164i	$-0.312325\pi$
$457$	23.7730	1.11205	0.556027	+	0.831164i	$0.312325\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	−12.5284	−0.582244	−0.291122	−	0.956686i	$-0.594029\pi$
$463$	−12.5284	−0.582244	−0.291122	+	0.956686i	$0.594029\pi$
$464$	−51.6983	−2.40003
$465$	0	0
$466$	71.5357	3.31383
$467$	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
$473$	−4.08900	−0.188012
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	72.5561	3.31864
$479$	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
$484$	−48.5633	−2.20742
$485$	0	0
$486$	0	0
$487$	−24.0000	−1.08754	−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000	−1.08754	−0.543772	+	0.839233i	$0.683004\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	14.9498	0.674673	0.337336	−	0.941384i	$-0.390474\pi$
$491$	14.9498	0.674673	0.337336	+	0.941384i	$0.390474\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	43.1309	1.93081	0.965403	−	0.260762i	$-0.0839736\pi$
$499$	43.1309	1.93081	0.965403	+	0.260762i	$0.0839736\pi$
$500$	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
$506$	22.6136	1.00530
$507$	0	0
$508$	130.983	5.81144
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	162.380	7.17625
$513$	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	$0.5\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	−44.3116	−1.93208
$527$	0	0
$528$	0	0
$529$	1.12631	0.0489700
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−113.202	−4.88960
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	16.8576	0.724763	0.362382	−	0.932030i	$-0.381964\pi$
$541$	16.8576	0.724763	0.362382	+	0.932030i	$0.381964\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	39.8447	1.70364	0.851819	−	0.523836i	$-0.175500\pi$
$547$	39.8447	1.70364	0.851819	+	0.523836i	$0.175500\pi$
$548$	−106.446	−4.54716
$549$	0	0
$550$	−23.0194	−0.981550
$551$	0	0
$552$	0	0
$553$	0	0
$554$	52.0810	2.21271
$555$	0	0
$556$	0	0
$557$	20.5536	0.870885	0.435443	−	0.900216i	$-0.356592\pi$
$557$	20.5536	0.870885	0.435443	+	0.900216i	$0.356592\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	91.7886	3.87187
$563$	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
$568$	94.0786	3.94745
$569$	1.45414	0.0609607	0.0304804	−	0.999535i	$-0.490296\pi$
$569$	1.45414	0.0609607	0.0304804	+	0.999535i	$0.490296\pi$
$570$	0	0
$571$	−47.3196	−1.98026	−0.990132	−	0.140141i	$-0.955244\pi$
$571$	−47.3196	−1.98026	−0.990132	+	0.140141i	$0.955244\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−24.5593	−1.02419
$576$	0	0
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−47.6329	−1.98127
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	13.2968	0.550695
$584$	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
$592$	−222.649	−9.15081
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−31.8442	−1.30439
$597$	0	0
$598$	0	0
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	−111.756	−4.54729
$605$	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
$613$	1.12977	0.0456309	0.0228154	−	0.999740i	$-0.492737\pi$
$613$	1.12977	0.0456309	0.0228154	+	0.999740i	$0.492737\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	35.4851	1.42858	0.714289	−	0.699851i	$-0.246750\pi$
$617$	35.4851	1.42858	0.714289	+	0.699851i	$0.246750\pi$
$618$	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
$631$	6.24757	0.248712	0.124356	−	0.992238i	$-0.460314\pi$
$631$	6.24757	0.248712	0.124356	+	0.992238i	$0.460314\pi$
$632$	147.781	5.87843
$633$	0	0
$634$	82.5809	3.27971
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−12.8442	−0.508505
$639$	0	0
$640$	0	0
$641$	32.2610	1.27423	0.637116	−	0.770768i	$-0.280127\pi$
$641$	32.2610	1.27423	0.637116	+	0.770768i	$0.280127\pi$
$642$	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	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	116.590	4.56600
$653$	−22.9004	−0.896160	−0.448080	−	0.893993i	$-0.647892\pi$
$653$	−22.9004	−0.896160	−0.448080	+	0.893993i	$0.647892\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	51.1221	1.99143	0.995717	−	0.0924489i	$-0.0294695\pi$
$659$	51.1221	1.99143	0.995717	+	0.0924489i	$0.0294695\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	−84.4476	−3.28215
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−13.7034	−0.530596
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−47.9463	−1.84819	−0.924097	−	0.382158i	$-0.875181\pi$
$673$	−47.9463	−1.84819	−0.924097	+	0.382158i	$0.875181\pi$
$674$	6.04221	0.232737
$675$	0	0
$676$	−76.0611	−2.92543
$677$	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
$683$	36.5585	1.39887	0.699437	−	0.714695i	$-0.253434\pi$
$683$	36.5585	1.39887	0.699437	+	0.714695i	$0.253434\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−46.1154	−1.75813
$689$	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
$694$	−11.2078	−0.425440
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−42.6176	−1.60965	−0.804823	−	0.593516i	$-0.797740\pi$
$701$	−42.6176	−1.60965	−0.804823	+	0.593516i	$0.797740\pi$
$702$	0	0
$703$	0	0
$704$	78.7967	2.96976
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	52.9235	1.98758	0.993791	−	0.111262i	$-0.0354891\pi$
$709$	52.9235	1.98758	0.993791	+	0.111262i	$0.0354891\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−145.710	−5.44545
$717$	0	0
$718$	−22.4155	−0.836539
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	−53.2368	−1.98127
$723$	0	0
$724$	0	0
$725$	13.9493	0.518063
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	0	0
$730$	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
$736$	149.038	5.49360
$737$	−17.2387	−0.634997
$738$	0	0
$739$	39.9627	1.47005	0.735026	−	0.678039i	$-0.237170\pi$
$739$	39.9627	1.47005	0.735026	+	0.678039i	$0.237170\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	40.0000	1.46746	0.733729	−	0.679442i	$-0.237778\pi$
$743$	40.0000	1.46746	0.733729	+	0.679442i	$0.237778\pi$
$744$	0	0
$745$	0	0
$746$	−94.1359	−3.44656
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−9.24219	−0.337252	−0.168626	−	0.985680i	$-0.553933\pi$
$751$	−9.24219	−0.337252	−0.168626	+	0.985680i	$0.553933\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	53.2441	1.93519	0.967595	−	0.252507i	$-0.0812550\pi$
$757$	53.2441	1.93519	0.967595	+	0.252507i	$0.0812550\pi$
$758$	−33.6233	−1.22125
$759$	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
$764$	−150.210	−5.43442
$765$	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
$772$	−41.1540	−1.48117
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	5.21685	0.187033
$779$	0	0
$780$	0	0
$781$	14.3265	0.512643
$782$	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	$0.5\pi$
$788$	−163.923	−5.83953
$789$	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
$800$	−151.712	−5.36383
$801$	0	0
$802$	36.6203	1.29311
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	56.7891	1.99660	0.998300	−	0.0582924i	$-0.0185656\pi$
$809$	56.7891	1.99660	0.998300	+	0.0582924i	$0.0185656\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	−55.3159	−1.93882
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−46.6929	−1.62959	−0.814796	−	0.579747i	$-0.803151\pi$
$821$	−46.6929	−1.62959	−0.814796	+	0.579747i	$0.803151\pi$
$822$	0	0
$823$	−53.5502	−1.86664	−0.933321	−	0.359043i	$-0.883103\pi$
$823$	−53.5502	−1.86664	−0.933321	+	0.359043i	$0.883103\pi$
$824$	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	$0.777268\pi$
$828$	0	0
$829$	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
$841$	−21.2167	−0.731610
$842$	102.939	3.54752
$843$	0	0
$844$	−3.90754	−0.134503
$845$	0	0
$846$	0	0
$847$	0	0
$848$	149.960	5.14964
$849$	0	0
$850$	0	0
$851$	−59.0162	−2.02305
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−219.199	−7.49206
$857$	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
$862$	−52.3220	−1.78209
$863$	58.5273	1.99229	0.996147	−	0.0877008i	$-0.0279519\pi$
$863$	58.5273	1.99229	0.996147	+	0.0877008i	$0.0279519\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	22.5045	0.763413
$870$	0	0
$871$	0	0
$872$	−154.544	−5.23351
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−58.8238	−1.98634	−0.993170	−	0.116679i	$-0.962775\pi$
$877$	−58.8238	−1.98634	−0.993170	+	0.116679i	$0.962775\pi$
$878$	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
$883$	−52.9896	−1.78324	−0.891621	−	0.452783i	$-0.850431\pi$
$883$	−52.9896	−1.78324	−0.891621	+	0.452783i	$0.850431\pi$
$884$	0	0
$885$	0	0
$886$	56.0388	1.88266
$887$	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
$898$	116.885	3.90050
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	165.099	5.49110
$905$	0	0
$906$	0	0
$907$	33.2723	1.10479	0.552395	−	0.833583i	$-0.313714\pi$
$907$	33.2723	1.10479	0.552395	+	0.833583i	$0.313714\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	35.5319	1.17722	0.588612	−	0.808416i	$-0.299675\pi$
$911$	35.5319	1.17722	0.588612	+	0.808416i	$0.299675\pi$
$912$	0	0
$913$	0	0
$914$	66.6104	2.20328
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	60.0753	1.97526
$926$	−35.1038	−1.15358
$927$	0	0
$928$	−84.6510	−2.77880
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	149.377	4.89301
$933$	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
$946$	−11.4571	−0.372503
$947$	52.2968	1.69942	0.849708	−	0.527254i	$-0.176778\pi$
$947$	52.2968	1.69942	0.849708	+	0.527254i	$0.176778\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−19.6142	−0.635365	−0.317682	−	0.948197i	$-0.602905\pi$
$953$	−19.6142	−0.635365	−0.317682	+	0.948197i	$0.602905\pi$
$954$	0	0
$955$	0	0
$956$	151.508	4.90011
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	56.7018	1.82341	0.911704	−	0.410848i	$-0.134767\pi$
$967$	56.7018	1.82341	0.911704	+	0.410848i	$0.134767\pi$
$968$	−89.5581	−2.87851
$969$	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
$974$	−67.2465	−2.15472
$975$	0	0
$976$	0	0
$977$	4.41598	0.141280	0.0706398	−	0.997502i	$-0.477496\pi$
$977$	4.41598	0.141280	0.0706398	+	0.997502i	$0.477496\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	41.8883	1.33671
$983$	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
$989$	−12.2236	−0.388686
$990$	0	0
$991$	46.8781	1.48913	0.744566	−	0.667549i	$-0.232656\pi$
$991$	46.8781	1.48913	0.744566	+	0.667549i	$0.232656\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	120.850	3.82545
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3087.2.a.f.1.3		3
3.2	odd	2		343.2.a.a.1.1	✓	3
7.6	odd	2	CM	3087.2.a.f.1.3		3
12.11	even	2		5488.2.a.d.1.2		3
15.14	odd	2		8575.2.a.f.1.3		3
21.2	odd	6		343.2.c.b.18.3		6
21.5	even	6		343.2.c.b.18.3		6
21.11	odd	6		343.2.c.b.324.3		6
21.17	even	6		343.2.c.b.324.3		6
21.20	even	2		343.2.a.a.1.1	✓	3
84.83	odd	2		5488.2.a.d.1.2		3
105.104	even	2		8575.2.a.f.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.2.a.a.1.1	✓	3	3.2	odd	2
343.2.a.a.1.1	✓	3	21.20	even	2
343.2.c.b.18.3		6	21.2	odd	6
343.2.c.b.18.3		6	21.5	even	6
343.2.c.b.324.3		6	21.11	odd	6
343.2.c.b.324.3		6	21.17	even	6
3087.2.a.f.1.3		3	1.1	even	1	trivial
3087.2.a.f.1.3		3	7.6	odd	2	CM
5488.2.a.d.1.2		3	12.11	even	2
5488.2.a.d.1.2		3	84.83	odd	2
8575.2.a.f.1.3		3	15.14	odd	2
8575.2.a.f.1.3		3	105.104	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 3087 = 3^{2} \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3087.a (trivial)

\(f(q)\)	\(=\)	\(q+2.80194 q^{2} +5.85086 q^{4} +10.7899 q^{8} +O(q^{10})\)	\(q+2.80194 q^{2} +5.85086 q^{4} +10.7899 q^{8} +1.64310 q^{11} +18.5308 q^{16} +4.60388 q^{22} +4.91185 q^{23} -5.00000 q^{25} -2.78986 q^{29} +30.3424 q^{32} -12.0151 q^{37} -2.48858 q^{43} +9.61356 q^{44} +13.7627 q^{46} -14.0097 q^{50} +8.09246 q^{53} -7.81700 q^{58} +47.9560 q^{64} -10.4916 q^{67} +8.71917 q^{71} -33.6655 q^{74} +13.6963 q^{79} -6.97285 q^{86} +17.7289 q^{88} +28.7385 q^{92} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} + 4 q^{4} + 9 q^{8}+O(q^{10}) \) 3 * q + 4 * q^2 + 4 * q^4 + 9 * q^8	\( 3 q + 4 q^{2} + 4 q^{4} + 9 q^{8} + 9 q^{11} + 18 q^{16} + 5 q^{22} + 11 q^{23} - 15 q^{25} + 15 q^{29} + 27 q^{32} - 11 q^{37} - q^{43} - 2 q^{44} + 24 q^{46} - 20 q^{50} + 9 q^{53} + 6 q^{58} + 49 q^{64} + 19 q^{67} + 15 q^{71} - 17 q^{74} + 17 q^{79} - 27 q^{86} + 20 q^{88} + 31 q^{92}+O(q^{100}) \) 3 * q + 4 * q^2 + 4 * q^4 + 9 * q^8 + 9 * q^11 + 18 * q^16 + 5 * q^22 + 11 * q^23 - 15 * q^25 + 15 * q^29 + 27 * q^32 - 11 * q^37 - q^43 - 2 * q^44 + 24 * q^46 - 20 * q^50 + 9 * q^53 + 6 * q^58 + 49 * q^64 + 19 * q^67 + 15 * q^71 - 17 * q^74 + 17 * q^79 - 27 * q^86 + 20 * q^88 + 31 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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