LMFDB - Embedded newform 1728.2.z.a.143.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1728,2,Mod(143,1728)] 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("1728.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.10
Character	$\chi$	$=$	1728.143
Dual form			1728.2.z.a.1583.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.664471 - 0.178044i) q^{5} +(-0.645693 + 1.11837i) q^{7} +(3.21069 - 0.860301i) q^{11} +(-4.74727 - 1.27203i) q^{13} -5.58523i q^{17} +(2.49649 + 2.49649i) q^{19} +(-2.36529 + 1.36560i) q^{23} +(-3.92031 - 2.26339i) q^{25} +(2.95682 - 0.792277i) q^{29} +(-5.28160 + 3.04933i) q^{31} +(0.628165 - 0.628165i) q^{35} +(0.507420 + 0.507420i) q^{37} +(-4.89892 - 8.48518i) q^{41} +(-0.254540 - 0.949956i) q^{43} +(6.13774 - 10.6309i) q^{47} +(2.66616 + 4.61793i) q^{49} +(0.601793 - 0.601793i) q^{53} -2.28658 q^{55} +(1.28003 - 4.77715i) q^{59} +(-2.90167 - 10.8292i) q^{61} +(2.92795 + 1.69045i) q^{65} +(0.0295686 - 0.110351i) q^{67} -0.0447904i q^{71} -13.2931i q^{73} +(-1.11098 + 4.14624i) q^{77} +(-2.50052 - 1.44368i) q^{79} +(1.01705 + 3.79568i) q^{83} +(-0.994419 + 3.71122i) q^{85} -12.7362 q^{89} +(4.48788 - 4.48788i) q^{91} +(-1.21436 - 2.10333i) q^{95} +(4.41066 - 7.63949i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.664471	−	0.178044i	−0.297161	−	0.0796239i	0.107158	−	0.994242i	$-0.465825\pi$
$5$	−0.664471	−	0.178044i	−0.297161	−	0.0796239i	−0.404319	+	0.914618i	$0.632491\pi$
$6$		0			0
$7$	−0.645693	+	1.11837i	−0.244049	+	0.422705i	−0.961864	−	0.273529i	$-0.911809\pi$
$7$	−0.645693	+	1.11837i	−0.244049	+	0.422705i	0.717815	+	0.696234i	$0.245142\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.21069	−	0.860301i	0.968058	−	0.259390i	0.260051	−	0.965595i	$-0.416261\pi$
$11$	3.21069	−	0.860301i	0.968058	−	0.259390i	0.708008	+	0.706205i	$0.249594\pi$
$12$		0			0
$13$	−4.74727	−	1.27203i	−1.31666	−	0.352797i	−0.468933	−	0.883234i	$-0.655361\pi$
$13$	−4.74727	−	1.27203i	−1.31666	−	0.352797i	−0.847725	+	0.530437i	$0.822028\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	5.58523i		−	1.35462i	−0.735699	−	0.677308i	$-0.763146\pi$
$17$		−	5.58523i		−	1.35462i	0.735699	−	0.677308i	$-0.236854\pi$
$18$		0			0
$19$	2.49649	+	2.49649i	0.572733	+	0.572733i	0.932891	−	0.360158i	$-0.117277\pi$
$19$	2.49649	+	2.49649i	0.572733	+	0.572733i	−0.360158	+	0.932891i	$0.617277\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.36529	+	1.36560i	−0.493197	+	0.284747i	−0.725900	−	0.687801i	$-0.758576\pi$
$23$	−2.36529	+	1.36560i	−0.493197	+	0.284747i	0.232703	+	0.972548i	$0.425243\pi$
$24$		0			0
$25$	−3.92031	−	2.26339i	−0.784061	−	0.452678i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.95682	−	0.792277i	0.549067	−	0.147122i	0.0263884	−	0.999652i	$-0.491599\pi$
$29$	2.95682	−	0.792277i	0.549067	−	0.147122i	0.522679	+	0.852530i	$0.324933\pi$
$30$		0			0
$31$	−5.28160	+	3.04933i	−0.948604	+	0.547677i	−0.892647	−	0.450757i	$-0.851154\pi$
$31$	−5.28160	+	3.04933i	−0.948604	+	0.547677i	−0.0559568	+	0.998433i	$0.517821\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.628165	−	0.628165i	0.106179	−	0.106179i
$36$		0			0
$37$	0.507420	+	0.507420i	0.0834193	+	0.0834193i	0.747585	−	0.664166i	$-0.231213\pi$
$37$	0.507420	+	0.507420i	0.0834193	+	0.0834193i	−0.664166	+	0.747585i	$0.731213\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.89892	−	8.48518i	−0.765083	−	1.32516i	−0.940203	−	0.340616i	$-0.889365\pi$
$41$	−4.89892	−	8.48518i	−0.765083	−	1.32516i	0.175120	−	0.984547i	$-0.443969\pi$
$42$		0			0
$43$	−0.254540	−	0.949956i	−0.0388170	−	0.144867i	0.943798	−	0.330524i	$-0.107225\pi$
$43$	−0.254540	−	0.949956i	−0.0388170	−	0.144867i	−0.982615	+	0.185657i	$0.940559\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.13774	−	10.6309i	0.895281	−	1.55067i	0.0618250	−	0.998087i	$-0.480308\pi$
$47$	6.13774	−	10.6309i	0.895281	−	1.55067i	0.833456	−	0.552586i	$-0.186359\pi$
$48$		0			0
$49$	2.66616	+	4.61793i	0.380880	+	0.659704i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.601793	−	0.601793i	0.0826626	−	0.0826626i	−0.664567	−	0.747229i	$-0.731384\pi$
$53$	0.601793	−	0.601793i	0.0826626	−	0.0826626i	0.747229	+	0.664567i	$0.231384\pi$
$54$		0			0
$55$	−2.28658			−0.308322
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.28003	−	4.77715i	0.166646	−	0.621932i	−0.831178	−	0.556006i	$-0.812333\pi$
$59$	1.28003	−	4.77715i	0.166646	−	0.621932i	0.997824	−	0.0659263i	$-0.0210002\pi$
$60$		0			0
$61$	−2.90167	−	10.8292i	−0.371520	−	1.38653i	−0.858363	−	0.513043i	$-0.828518\pi$
$61$	−2.90167	−	10.8292i	−0.371520	−	1.38653i	0.486842	−	0.873490i	$-0.338149\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.92795	+	1.69045i	0.363167	+	0.209675i
$66$		0			0
$67$	0.0295686	−	0.110351i	0.00361238	−	0.0134816i	−0.964096	−	0.265554i	$-0.914445\pi$
$67$	0.0295686	−	0.110351i	0.00361238	−	0.0134816i	0.967708	+	0.252072i	$0.0811120\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.0447904i		−	0.00531565i	−0.999996	−	0.00265782i	$-0.999154\pi$
$71$		−	0.0447904i		−	0.00531565i	0.999996	−	0.00265782i	$-0.000846013\pi$
$72$		0			0
$73$		−	13.2931i		−	1.55585i	−0.628360	−	0.777923i	$-0.716274\pi$
$73$		−	13.2931i		−	1.55585i	0.628360	−	0.777923i	$-0.283726\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.11098	+	4.14624i	−0.126608	+	0.472507i
$78$		0			0
$79$	−2.50052	−	1.44368i	−0.281331	−	0.162426i	0.352695	−	0.935738i	$-0.385265\pi$
$79$	−2.50052	−	1.44368i	−0.281331	−	0.162426i	−0.634026	+	0.773312i	$0.718599\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.01705	+	3.79568i	0.111636	+	0.416630i	0.999013	−	0.0444135i	$-0.0141419\pi$
$83$	1.01705	+	3.79568i	0.111636	+	0.416630i	−0.887378	+	0.461043i	$0.847475\pi$
$84$		0			0
$85$	−0.994419	+	3.71122i	−0.107860	+	0.402539i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.7362			−1.35003			−0.675017	−	0.737802i	$-0.735864\pi$
$89$	−12.7362			−1.35003			−0.675017	+	0.737802i	$0.735864\pi$
$90$		0			0
$91$	4.48788	−	4.48788i	0.470458	−	0.470458i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.21436	−	2.10333i	−0.124590	−	0.215797i
$96$		0			0
$97$	4.41066	−	7.63949i	0.447835	−	0.775673i	−0.550410	−	0.834895i	$-0.685529\pi$
$97$	4.41066	−	7.63949i	0.447835	−	0.775673i	0.998245	+	0.0592215i	$0.0188618\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.88240	+	7.02523i	0.187306	+	0.699037i	0.994125	+	0.108238i	$0.0345207\pi$
$101$	1.88240	+	7.02523i	0.187306	+	0.699037i	−0.806819	+	0.590799i	$0.798813\pi$
$102$		0			0
$103$	−9.50698	−	16.4666i	−0.936750	−	1.62250i	−0.771483	−	0.636250i	$-0.780485\pi$
$103$	−9.50698	−	16.4666i	−0.936750	−	1.62250i	−0.165267	−	0.986249i	$-0.552849\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.28797	−	8.28797i	−0.801228	−	0.801228i	0.182060	−	0.983287i	$-0.441724\pi$
$107$	−8.28797	−	8.28797i	−0.801228	−	0.801228i	−0.983287	+	0.182060i	$0.941724\pi$
$108$		0			0
$109$	−14.3799	+	14.3799i	−1.37735	+	1.37735i	−0.528273	+	0.849074i	$0.677160\pi$
$109$	−14.3799	+	14.3799i	−1.37735	+	1.37735i	−0.849074	+	0.528273i	$0.822840\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.18778	−	1.26312i	0.205809	−	0.118824i	−0.393553	−	0.919302i	$-0.628754\pi$
$113$	2.18778	−	1.26312i	0.205809	−	0.118824i	0.599362	+	0.800478i	$0.295421\pi$
$114$		0			0
$115$	1.81480	−	0.486275i	0.169231	−	0.0453454i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.24637	+	3.60634i	0.572604	+	0.330593i
$120$		0			0
$121$	0.0421101	−	0.0243123i	0.00382819	−	0.00221021i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.63408	+	4.63408i	0.414485	+	0.414485i
$126$		0			0
$127$		−	17.5157i		−	1.55427i	−0.629333	−	0.777135i	$-0.716672\pi$
$127$		−	17.5157i		−	1.55427i	0.629333	−	0.777135i	$-0.283328\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	11.9889	+	3.21241i	1.04747	+	0.280669i	0.741207	−	0.671277i	$-0.234254\pi$
$131$	11.9889	+	3.21241i	1.04747	+	0.280669i	0.306266	+	0.951946i	$0.400920\pi$
$132$		0			0
$133$	−4.40397	+	1.18004i	−0.381872	+	0.102322i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.00063	−	8.66134i	0.427232	−	0.739988i	−0.569394	−	0.822065i	$-0.692822\pi$
$137$	5.00063	−	8.66134i	0.427232	−	0.739988i	0.996626	+	0.0820768i	$0.0261553\pi$
$138$		0			0
$139$	−1.37583	−	0.368654i	−0.116697	−	0.0312688i	0.199998	−	0.979796i	$-0.435906\pi$
$139$	−1.37583	−	0.368654i	−0.116697	−	0.0312688i	−0.316695	+	0.948528i	$0.602573\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−16.3363			−1.36611
$144$		0			0
$145$	−2.10578			−0.174876
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.52986	−	1.48172i	−0.453024	−	0.121387i	0.0250901	−	0.999685i	$-0.492013\pi$
$149$	−5.52986	−	1.48172i	−0.453024	−	0.121387i	−0.478114	+	0.878298i	$0.658679\pi$
$150$		0			0
$151$	−8.10127	+	14.0318i	−0.659272	+	1.14189i	0.321533	+	0.946899i	$0.395802\pi$
$151$	−8.10127	+	14.0318i	−0.659272	+	1.14189i	−0.980804	+	0.194994i	$0.937531\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.05239	−	1.08583i	0.325496	−	0.0872163i
$156$		0			0
$157$	7.56718	+	2.02762i	0.603927	+	0.161822i	0.547810	−	0.836602i	$-0.315462\pi$
$157$	7.56718	+	2.02762i	0.603927	+	0.161822i	0.0561165	+	0.998424i	$0.482128\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	3.52703i		−	0.277969i
$162$		0			0
$163$	4.89763	+	4.89763i	0.383612	+	0.383612i	0.872402	−	0.488789i	$-0.162561\pi$
$163$	4.89763	+	4.89763i	0.383612	+	0.383612i	−0.488789	+	0.872402i	$0.662561\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.7832	+	10.8445i	−1.45349	+	0.839174i	−0.998677	−	0.0514129i	$-0.983628\pi$
$167$	−18.7832	+	10.8445i	−1.45349	+	0.839174i	−0.454814	+	0.890587i	$0.650294\pi$
$168$		0			0
$169$	9.66023	+	5.57734i	0.743095	+	0.429026i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.68601	−	2.05946i	0.584356	−	0.156578i	0.0454836	−	0.998965i	$-0.485517\pi$
$173$	7.68601	−	2.05946i	0.584356	−	0.156578i	0.538873	+	0.842387i	$0.318850\pi$
$174$		0			0
$175$	5.06263	−	2.92291i	0.382699	−	0.220951i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.47991	−	9.47991i	0.708562	−	0.708562i	−0.257671	−	0.966233i	$-0.582955\pi$
$179$	9.47991	−	9.47991i	0.708562	−	0.708562i	0.966233	+	0.257671i	$0.0829551\pi$
$180$		0			0
$181$	8.00075	+	8.00075i	0.594691	+	0.594691i	0.938895	−	0.344204i	$-0.111851\pi$
$181$	8.00075	+	8.00075i	0.594691	+	0.594691i	−0.344204	+	0.938895i	$0.611851\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.246822	−	0.427509i	−0.0181467	−	0.0314311i
$186$		0			0
$187$	−4.80498	−	17.9324i	−0.351375	−	1.31135i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.22986	+	15.9866i	−0.667850	+	1.15675i	0.310655	+	0.950523i	$0.399452\pi$
$191$	−9.22986	+	15.9866i	−0.667850	+	1.15675i	−0.978504	+	0.206227i	$0.933882\pi$
$192$		0			0
$193$	2.61643	+	4.53179i	0.188335	+	0.326205i	0.944695	−	0.327950i	$-0.106358\pi$
$193$	2.61643	+	4.53179i	0.188335	+	0.326205i	−0.756360	+	0.654155i	$0.773024\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.3573	−	14.3573i	1.02292	−	1.02292i	0.0231869	−	0.999731i	$-0.492619\pi$
$197$	14.3573	−	14.3573i	1.02292	−	1.02292i	0.999731	−	0.0231869i	$-0.00738128\pi$
$198$		0			0
$199$	13.8358			0.980797			0.490399	−	0.871498i	$-0.336851\pi$
$199$	13.8358			0.980797			0.490399	+	0.871498i	$0.336851\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.02314	+	3.81839i	−0.0718100	+	0.267999i
$204$		0			0
$205$	1.74445	+	6.51038i	0.121838	+	0.454705i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.1632	+	5.86770i	0.703001	+	0.405878i
$210$		0			0
$211$	−6.87239	+	25.6481i	−0.473115	+	1.76569i	0.155358	+	0.987858i	$0.450347\pi$
$211$	−6.87239	+	25.6481i	−0.473115	+	1.76569i	−0.628473	+	0.777831i	$0.716320\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			0.676538i			0.0461395i
$216$		0			0
$217$		−	7.87574i		−	0.534640i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.10457	+	26.5146i	−0.477905	+	1.78357i
$222$		0			0
$223$	2.77266	+	1.60079i	0.185671	+	0.107197i	0.589954	−	0.807437i	$-0.299146\pi$
$223$	2.77266	+	1.60079i	0.185671	+	0.107197i	−0.404284	+	0.914634i	$0.632479\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.745680	+	2.78291i	0.0494925	+	0.184708i	0.986247	−	0.165279i	$-0.0528525\pi$
$227$	0.745680	+	2.78291i	0.0494925	+	0.184708i	−0.936754	+	0.349988i	$0.886186\pi$
$228$		0			0
$229$	4.72334	−	17.6277i	0.312127	−	1.16487i	−0.614508	−	0.788911i	$-0.710645\pi$
$229$	4.72334	−	17.6277i	0.312127	−	1.16487i	0.926635	−	0.375963i	$-0.122688\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00585			0.393456			0.196728	−	0.980458i	$-0.436968\pi$
$233$	6.00585			0.393456			0.196728	+	0.980458i	$0.436968\pi$
$234$		0			0
$235$	−5.97112	+	5.97112i	−0.389513	+	0.389513i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00788	−	10.4059i	−0.388617	−	0.673105i	0.603647	−	0.797252i	$-0.293714\pi$
$239$	−6.00788	−	10.4059i	−0.388617	−	0.673105i	−0.992264	+	0.124147i	$0.960381\pi$
$240$		0			0
$241$	1.51923	−	2.63138i	0.0978622	−	0.169502i	−0.812937	−	0.582351i	$-0.802133\pi$
$241$	1.51923	−	2.63138i	0.0978622	−	0.169502i	0.910800	+	0.412849i	$0.135466\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.949391	−	3.54317i	−0.0606543	−	0.226365i
$246$		0			0
$247$	−8.67590	−	15.0271i	−0.552034	−	0.956152i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.95387	−	2.95387i	−0.186447	−	0.186447i	0.607711	−	0.794158i	$-0.292088\pi$
$251$	−2.95387	−	2.95387i	−0.186447	−	0.186447i	−0.794158	+	0.607711i	$0.792088\pi$
$252$		0			0
$253$	−6.41937	+	6.41937i	−0.403582	+	0.403582i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.67398	+	0.966474i	−0.104420	+	0.0602870i	−0.551301	−	0.834307i	$-0.685868\pi$
$257$	−1.67398	+	0.966474i	−0.104420	+	0.0602870i	0.446880	+	0.894594i	$0.352535\pi$
$258$		0			0
$259$	−0.895122	+	0.239847i	−0.0556202	+	0.0149034i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.51993	−	0.877533i	−0.0937230	−	0.0541110i	0.452406	−	0.891812i	$-0.350566\pi$
$263$	−1.51993	−	0.877533i	−0.0937230	−	0.0541110i	−0.546129	+	0.837701i	$0.683899\pi$
$264$		0			0
$265$	−0.507020	+	0.292728i	−0.0311460	+	0.0179821i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.2013	−	14.2013i	−0.865871	−	0.865871i	0.126141	−	0.992012i	$-0.459741\pi$
$269$	−14.2013	−	14.2013i	−0.865871	−	0.865871i	−0.992012	+	0.126141i	$0.959741\pi$
$270$		0			0
$271$			11.3712i			0.690754i	0.938464	+	0.345377i	$0.112249\pi$
$271$			11.3712i			0.690754i	−0.938464	+	0.345377i	$0.887751\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−14.5341	−	3.89439i	−0.876437	−	0.234841i
$276$		0			0
$277$	−6.77138	+	1.81439i	−0.406853	+	0.109016i	−0.456441	−	0.889754i	$-0.650876\pi$
$277$	−6.77138	+	1.81439i	−0.406853	+	0.109016i	0.0495877	+	0.998770i	$0.484209\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.16379	−	8.94395i	0.308046	−	0.533552i	−0.669889	−	0.742461i	$-0.733658\pi$
$281$	5.16379	−	8.94395i	0.308046	−	0.533552i	0.977935	+	0.208910i	$0.0669916\pi$
$282$		0			0
$283$	23.3260	+	6.25018i	1.38659	+	0.371535i	0.873509	−	0.486807i	$-0.161839\pi$
$283$	23.3260	+	6.25018i	1.38659	+	0.371535i	0.513078	+	0.858342i	$0.328505\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.6528			0.746871
$288$		0			0
$289$	−14.1948			−0.834987
$290$		0			0
$291$		0			0
$292$		0			0
$293$	18.8302	+	5.04554i	1.10007	+	0.294763i	0.762794	−	0.646642i	$-0.223827\pi$
$293$	18.8302	+	5.04554i	1.10007	+	0.294763i	0.337278	+	0.941405i	$0.390494\pi$
$294$		0			0
$295$	−1.70109	+	2.94638i	−0.0990414	+	0.171545i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.9658	−	3.47416i	0.749829	−	0.200916i
$300$		0			0
$301$	1.22676	+	0.328709i	0.0707093	+	0.0189465i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			7.71230i			0.441605i
$306$		0			0
$307$	4.37646	+	4.37646i	0.249778	+	0.249778i	0.820879	−	0.571101i	$-0.193484\pi$
$307$	4.37646	+	4.37646i	0.249778	+	0.249778i	−0.571101	+	0.820879i	$0.693484\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.65273	+	1.53155i	−0.150423	+	0.0868465i	−0.573322	−	0.819330i	$-0.694346\pi$
$311$	−2.65273	+	1.53155i	−0.150423	+	0.0868465i	0.422900	+	0.906177i	$0.361012\pi$
$312$		0			0
$313$	2.59526	+	1.49837i	0.146693	+	0.0846930i	0.571550	−	0.820567i	$-0.306342\pi$
$313$	2.59526	+	1.49837i	0.146693	+	0.0846930i	−0.424857	+	0.905260i	$0.639676\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.24401	+	2.47692i	−0.519195	+	0.139118i	−0.508894	−	0.860829i	$-0.669946\pi$
$317$	−9.24401	+	2.47692i	−0.519195	+	0.139118i	−0.0103009	+	0.999947i	$0.503279\pi$
$318$		0			0
$319$	8.81182	−	5.08751i	0.493367	−	0.284846i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	13.9434	−	13.9434i	0.775834	−	0.775834i
$324$		0			0
$325$	15.7317	+	15.7317i	0.872636	+	0.872636i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.92619	+	13.7286i	0.436985	+	0.756880i
$330$		0			0
$331$	3.90856	+	14.5870i	0.214834	+	0.801772i	0.986225	+	0.165410i	$0.0528947\pi$
$331$	3.90856	+	14.5870i	0.214834	+	0.801772i	−0.771391	+	0.636362i	$0.780439\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.0392949	+	0.0680608i	−0.00214691	+	0.00371856i
$336$		0			0
$337$	1.09448	+	1.89569i	0.0596200	+	0.103265i	0.894295	−	0.447478i	$-0.147678\pi$
$337$	1.09448	+	1.89569i	0.0596200	+	0.103265i	−0.834675	+	0.550743i	$0.814344\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.3342	+	14.3342i	−0.776242	+	0.776242i
$342$		0			0
$343$	−15.9258			−0.859912
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.41711	+	27.6810i	−0.398171	+	1.48599i	0.418140	+	0.908382i	$0.362682\pi$
$347$	−7.41711	+	27.6810i	−0.398171	+	1.48599i	−0.816311	+	0.577612i	$0.803985\pi$
$348$		0			0
$349$	6.18561	+	23.0850i	0.331108	+	1.23571i	0.908027	+	0.418911i	$0.137588\pi$
$349$	6.18561	+	23.0850i	0.331108	+	1.23571i	−0.576919	+	0.816801i	$0.695745\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.355770	+	0.205404i	0.0189357	+	0.0109325i	0.509438	−	0.860507i	$-0.329853\pi$
$353$	0.355770	+	0.205404i	0.0189357	+	0.0109325i	−0.490502	+	0.871440i	$0.663187\pi$
$354$		0			0
$355$	−0.00797469	+	0.0297620i	−0.000423253	+	0.00157960i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			1.19383i			0.0630078i	0.999504	+	0.0315039i	$0.0100297\pi$
$359$			1.19383i			0.0630078i	−0.999504	+	0.0315039i	$0.989970\pi$
$360$		0			0
$361$		−	6.53512i		−	0.343954i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.36677	+	8.83291i	−0.123883	+	0.462336i
$366$		0			0
$367$	16.1698	+	9.33562i	0.844055	+	0.487316i	0.858641	−	0.512578i	$-0.171310\pi$
$367$	16.1698	+	9.33562i	0.844055	+	0.487316i	−0.0145854	+	0.999894i	$0.504643\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.284455	+	1.06160i	0.0147682	+	0.0551156i
$372$		0			0
$373$	−3.09325	+	11.5442i	−0.160163	+	0.597735i	0.838445	+	0.544986i	$0.183465\pi$
$373$	−3.09325	+	11.5442i	−0.160163	+	0.597735i	−0.998608	+	0.0527491i	$0.983202\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.0446			−0.774838
$378$		0			0
$379$	−15.3650	+	15.3650i	−0.789248	+	0.789248i	−0.981371	−	0.192123i	$-0.938463\pi$
$379$	−15.3650	+	15.3650i	−0.789248	+	0.789248i	0.192123	+	0.981371i	$0.438463\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.1162	+	19.2539i	0.568013	+	0.983827i	0.996762	+	0.0804037i	$0.0256210\pi$
$383$	11.1162	+	19.2539i	0.568013	+	0.983827i	−0.428750	+	0.903423i	$0.641046\pi$
$384$		0			0
$385$	1.47643	−	2.55725i	0.0752458	−	0.130330i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.18905	−	15.6338i	−0.212393	−	0.792663i	−0.987068	−	0.160303i	$-0.948753\pi$
$389$	−4.18905	−	15.6338i	−0.212393	−	0.792663i	0.774675	−	0.632360i	$-0.217914\pi$
$390$		0			0
$391$	7.62718	+	13.2107i	0.385723	+	0.668092i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.40449	+	1.40449i	0.0706674	+	0.0706674i
$396$		0			0
$397$	14.5828	−	14.5828i	0.731887	−	0.731887i	−0.239106	−	0.970993i	$-0.576854\pi$
$397$	14.5828	−	14.5828i	0.731887	−	0.731887i	0.970993	+	0.239106i	$0.0768543\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−27.9585	+	16.1418i	−1.39618	+	0.806085i	−0.993990	−	0.109470i	$-0.965085\pi$
$401$	−27.9585	+	16.1418i	−1.39618	+	0.806085i	−0.402191	+	0.915556i	$0.631751\pi$
$402$		0			0
$403$	28.9521	−	7.75768i	1.44220	−	0.386438i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.06570	+	1.19263i	0.102393	+	0.0591166i
$408$		0			0
$409$	−12.9975	+	7.50409i	−0.642683	+	0.371053i	−0.785647	−	0.618674i	$-0.787670\pi$
$409$	−12.9975	+	7.50409i	−0.642683	+	0.371053i	0.142964	+	0.989728i	$0.454337\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.51613	+	4.51613i	0.222224	+	0.222224i
$414$		0			0
$415$		−	2.70320i		−	0.132695i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	22.4191	+	6.00718i	1.09525	+	0.293470i	0.760827	−	0.648955i	$-0.224794\pi$
$419$	22.4191	+	6.00718i	1.09525	+	0.293470i	0.334418	+	0.942425i	$0.391460\pi$
$420$		0			0
$421$	−15.1189	+	4.05109i	−0.736849	+	0.197438i	−0.607677	−	0.794184i	$-0.707899\pi$
$421$	−15.1189	+	4.05109i	−0.736849	+	0.197438i	−0.129172	+	0.991622i	$0.541232\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.6415	+	21.8958i	−0.613205	+	1.06210i
$426$		0			0
$427$	13.9846	+	3.74717i	0.676764	+	0.181338i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.63818			0.0789082			0.0394541	−	0.999221i	$-0.487438\pi$
$431$	1.63818			0.0789082			0.0394541	+	0.999221i	$0.487438\pi$
$432$		0			0
$433$	24.1284			1.15954			0.579769	−	0.814781i	$-0.303143\pi$
$433$	24.1284			1.15954			0.579769	+	0.814781i	$0.303143\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.31411	−	2.49571i	−0.445554	−	0.119386i
$438$		0			0
$439$	−6.04546	+	10.4711i	−0.288534	+	0.499756i	−0.973460	−	0.228857i	$-0.926501\pi$
$439$	−6.04546	+	10.4711i	−0.288534	+	0.499756i	0.684926	+	0.728613i	$0.259835\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.2512	+	4.35450i	−0.772119	+	0.206889i	−0.623307	−	0.781977i	$-0.714211\pi$
$443$	−16.2512	+	4.35450i	−0.772119	+	0.206889i	−0.148811	+	0.988866i	$0.547545\pi$
$444$		0			0
$445$	8.46284	+	2.26761i	0.401177	+	0.107495i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	31.8270i		−	1.50201i	−0.660298	−	0.751004i	$-0.729570\pi$
$449$		−	31.8270i		−	1.50201i	0.660298	−	0.751004i	$-0.270430\pi$
$450$		0			0
$451$	−23.0287	−	23.0287i	−1.08438	−	1.08438i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.78111	+	2.18303i	−0.177261	+	0.102342i
$456$		0			0
$457$	24.8553	+	14.3502i	1.16268	+	0.671275i	0.951945	−	0.306268i	$-0.0990803\pi$
$457$	24.8553	+	14.3502i	1.16268	+	0.671275i	0.210737	+	0.977543i	$0.432414\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.80601	+	0.483918i	−0.0841141	+	0.0225383i	−0.300631	−	0.953741i	$-0.597197\pi$
$461$	−1.80601	+	0.483918i	−0.0841141	+	0.0225383i	0.216517	+	0.976279i	$0.430530\pi$
$462$		0			0
$463$	−4.71990	+	2.72503i	−0.219352	+	0.126643i	−0.605650	−	0.795731i	$-0.707087\pi$
$463$	−4.71990	+	2.72503i	−0.219352	+	0.126643i	0.386298	+	0.922374i	$0.373754\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.95228	+	8.95228i	−0.414262	+	0.414262i	−0.883220	−	0.468958i	$-0.844630\pi$
$467$	−8.95228	+	8.95228i	−0.414262	+	0.414262i	0.468958	+	0.883220i	$0.344630\pi$
$468$		0			0
$469$	0.104322	+	0.104322i	0.00481713	+	0.00481713i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.63450	−	2.83103i	−0.0751542	−	0.130171i
$474$		0			0
$475$	−4.13647	−	15.4375i	−0.189794	−	0.708321i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.27809	−	7.40987i	0.195471	−	0.338566i	−0.751584	−	0.659638i	$-0.770710\pi$
$479$	4.27809	−	7.40987i	0.195471	−	0.338566i	0.947055	+	0.321072i	$0.104043\pi$
$480$		0			0
$481$	−1.76341	−	3.05431i	−0.0804045	−	0.139265i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.29093	+	4.29093i	−0.194841	+	0.194841i
$486$		0			0
$487$	13.1689			0.596738			0.298369	−	0.954451i	$-0.403557\pi$
$487$	13.1689			0.596738			0.298369	+	0.954451i	$0.403557\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.16956	−	8.09692i	0.0979110	−	0.365409i	−0.899534	−	0.436851i	$-0.856094\pi$
$491$	2.16956	−	8.09692i	0.0979110	−	0.365409i	0.997445	+	0.0714425i	$0.0227602\pi$
$492$		0			0
$493$	−4.42505	−	16.5145i	−0.199294	−	0.743776i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0500924	+	0.0289209i	0.00224695	+	0.00129728i
$498$		0			0
$499$	8.38567	−	31.2957i	0.375394	−	1.40099i	−0.477374	−	0.878700i	$-0.658411\pi$
$499$	8.38567	−	31.2957i	0.375394	−	1.40099i	0.852768	−	0.522289i	$-0.174922\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	20.8126i		−	0.927989i	−0.885838	−	0.463994i	$-0.846416\pi$
$503$		−	20.8126i		−	0.927989i	0.885838	−	0.463994i	$-0.153584\pi$
$504$		0			0
$505$		−	5.00321i		−	0.222640i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.54865	−	20.7078i	0.245940	−	0.917859i	−0.726969	−	0.686670i	$-0.759072\pi$
$509$	5.54865	−	20.7078i	0.245940	−	0.917859i	0.972909	−	0.231189i	$-0.0742616\pi$
$510$		0			0
$511$	14.8667	+	8.58329i	0.657664	+	0.379703i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.38533	+	12.6342i	0.149175	+	0.556730i
$516$		0			0
$517$	10.5606	−	39.4127i	0.464455	−	1.73337i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.1534			0.882938			0.441469	−	0.897277i	$-0.354458\pi$
$521$	20.1534			0.882938			0.441469	+	0.897277i	$0.354458\pi$
$522$		0			0
$523$	−14.7713	+	14.7713i	−0.645905	+	0.645905i	−0.952001	−	0.306096i	$-0.900977\pi$
$523$	−14.7713	+	14.7713i	−0.645905	+	0.645905i	0.306096	+	0.952001i	$0.400977\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.0312	+	29.4990i	0.741892	+	1.28499i
$528$		0			0
$529$	−7.77028	+	13.4585i	−0.337838	+	0.585153i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.4631	+	46.5131i	0.539838	+	2.01470i
$534$		0			0
$535$	4.03149	+	6.98274i	0.174296	+	0.301890i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	12.5330	+	12.5330i	0.539835	+	0.539835i
$540$		0			0
$541$	11.1739	−	11.1739i	0.480403	−	0.480403i	−0.424857	−	0.905260i	$-0.639676\pi$
$541$	11.1739	−	11.1739i	0.480403	−	0.480403i	0.905260	+	0.424857i	$0.139676\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	12.1153	−	6.99478i	0.518963	−	0.299624i
$546$		0			0
$547$	−12.0633	+	3.23236i	−0.515791	+	0.138206i	−0.507319	−	0.861758i	$-0.669363\pi$
$547$	−12.0633	+	3.23236i	−0.515791	+	0.138206i	−0.00847177	+	0.999964i	$0.502697\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.35956	+	5.40375i	0.398731	+	0.230207i
$552$		0			0
$553$	3.22914	−	1.86435i	0.137317	−	0.0792800i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.41323	−	4.41323i	−0.186995	−	0.186995i	0.607401	−	0.794395i	$-0.292212\pi$
$557$	−4.41323	−	4.41323i	−0.186995	−	0.186995i	−0.794395	+	0.607401i	$0.792212\pi$
$558$		0			0
$559$			4.83349i			0.204435i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−33.9300	−	9.09152i	−1.42998	−	0.383162i	−0.540967	−	0.841044i	$-0.681942\pi$
$563$	−33.9300	−	9.09152i	−1.42998	−	0.383162i	−0.889013	+	0.457882i	$0.848608\pi$
$564$		0			0
$565$	−1.67861	+	0.449782i	−0.0706197	+	0.0189225i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.8432	+	18.7810i	−0.454572	+	0.787342i	−0.998663	−	0.0516841i	$-0.983541\pi$
$569$	−10.8432	+	18.7810i	−0.454572	+	0.787342i	0.544091	+	0.839026i	$0.316874\pi$
$570$		0			0
$571$	10.0422	+	2.69081i	0.420255	+	0.112607i	0.462748	−	0.886490i	$-0.346863\pi$
$571$	10.0422	+	2.69081i	0.420255	+	0.112607i	−0.0424934	+	0.999097i	$0.513530\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.3635			0.515595
$576$		0			0
$577$	−33.2014			−1.38219			−0.691096	−	0.722763i	$-0.742872\pi$
$577$	−33.2014			−1.38219			−0.691096	+	0.722763i	$0.742872\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.90169	−	1.31340i	−0.203356	−	0.0544891i
$582$		0			0
$583$	1.41444	−	2.44989i	0.0585803	−	0.101464i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.06941	+	0.554497i	−0.0854137	+	0.0228865i	−0.301273	−	0.953538i	$-0.597411\pi$
$587$	−2.06941	+	0.554497i	−0.0854137	+	0.0228865i	0.215859	+	0.976425i	$0.430745\pi$
$588$		0			0
$589$	−20.7981	−	5.57282i	−0.856969	−	0.229624i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			13.9278i			0.571945i	0.958238	+	0.285973i	$0.0923166\pi$
$593$			13.9278i			0.571945i	−0.958238	+	0.285973i	$0.907683\pi$
$594$		0			0
$595$	−3.50844	−	3.50844i	−0.143832	−	0.143832i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	20.2130	−	11.6700i	0.825881	−	0.476823i	−0.0265594	−	0.999647i	$-0.508455\pi$
$599$	20.2130	−	11.6700i	0.825881	−	0.476823i	0.852440	+	0.522825i	$0.175122\pi$
$600$		0			0
$601$	10.3379	+	5.96857i	0.421691	+	0.243463i	0.695800	−	0.718235i	$-0.255050\pi$
$601$	10.3379	+	5.96857i	0.421691	+	0.243463i	−0.274110	+	0.961698i	$0.588383\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.0323096	+	0.00865733i	−0.00131357	+	0.000351971i
$606$		0			0
$607$	−10.3919	+	5.99979i	−0.421796	+	0.243524i	−0.695845	−	0.718192i	$-0.744970\pi$
$607$	−10.3919	+	5.99979i	−0.421796	+	0.243524i	0.274050	+	0.961716i	$0.411637\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−42.6603	+	42.6603i	−1.72585	+	1.72585i
$612$		0			0
$613$	−18.1803	−	18.1803i	−0.734296	−	0.734296i	0.237172	−	0.971468i	$-0.423780\pi$
$613$	−18.1803	−	18.1803i	−0.734296	−	0.734296i	−0.971468	+	0.237172i	$0.923780\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.9672	+	32.8521i	0.763589	+	1.32257i	0.940989	+	0.338436i	$0.109898\pi$
$617$	18.9672	+	32.8521i	0.763589	+	1.32257i	−0.177401	+	0.984139i	$0.556769\pi$
$618$		0			0
$619$	−0.000616823	−	0.00230201i	−2.47922e−5	−	9.25258e-5i	0.965913	−	0.258865i	$-0.0833486\pi$
$619$	−0.000616823	−	0.00230201i	−2.47922e−5	−	9.25258e-5i	−0.965938	+	0.258773i	$0.916682\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.22368	−	14.2438i	0.329475	−	0.570667i
$624$		0			0
$625$	9.06281	+	15.6972i	0.362512	+	0.627890i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.83406	−	2.83406i	0.113001	−	0.113001i
$630$		0			0
$631$	39.2643			1.56309			0.781543	−	0.623852i	$-0.214433\pi$
$631$	39.2643			1.56309			0.781543	+	0.623852i	$0.214433\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.11858	+	11.6387i	−0.123757	+	0.461868i
$636$		0			0
$637$	−6.78286	−	25.3140i	−0.268747	−	1.00298i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.2983	−	8.83246i	−0.604245	−	0.348861i	0.166465	−	0.986047i	$-0.446765\pi$
$641$	−15.2983	−	8.83246i	−0.604245	−	0.348861i	−0.770710	+	0.637186i	$0.780098\pi$
$642$		0			0
$643$	−1.76926	+	6.60298i	−0.0697729	+	0.260396i	−0.991997	−	0.126259i	$-0.959703\pi$
$643$	−1.76926	+	6.60298i	−0.0697729	+	0.260396i	0.922224	+	0.386655i	$0.126370\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	4.24252i		−	0.166791i	−0.996517	−	0.0833953i	$-0.973424\pi$
$647$		−	4.24252i		−	0.166791i	0.996517	−	0.0833953i	$-0.0265764\pi$
$648$		0			0
$649$		−	16.4392i		−	0.645293i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.14041	−	26.6484i	0.279426	−	1.04283i	−0.673391	−	0.739286i	$-0.735163\pi$
$653$	7.14041	−	26.6484i	0.279426	−	1.04283i	0.952817	−	0.303545i	$-0.0981703\pi$
$654$		0			0
$655$	−7.39431	−	4.26911i	−0.288919	−	0.166808i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.71978	−	10.1504i	−0.105948	−	0.395402i	0.892503	−	0.451041i	$-0.148947\pi$
$659$	−2.71978	−	10.1504i	−0.105948	−	0.395402i	−0.998451	+	0.0556391i	$0.982280\pi$
$660$		0			0
$661$	7.59396	−	28.3410i	0.295371	−	1.10234i	−0.645552	−	0.763717i	$-0.723372\pi$
$661$	7.59396	−	28.3410i	0.295371	−	1.10234i	0.940922	−	0.338622i	$-0.109961\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.13641			0.121625
$666$		0			0
$667$	−5.91179	+	5.91179i	−0.228905	+	0.228905i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.6327	−	32.2728i	−0.719307	−	1.24588i
$672$		0			0
$673$	−5.32418	+	9.22175i	−0.205232	+	0.355472i	−0.950207	−	0.311621i	$-0.899128\pi$
$673$	−5.32418	+	9.22175i	−0.205232	+	0.355472i	0.744975	+	0.667093i	$0.232462\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.70565	−	21.2938i	−0.219286	−	0.818387i	−0.984614	−	0.174746i	$-0.944090\pi$
$677$	−5.70565	−	21.2938i	−0.219286	−	0.818387i	0.765327	−	0.643641i	$-0.222577\pi$
$678$		0			0
$679$	5.69587	+	9.86554i	0.218587	+	0.378605i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.68202	−	1.68202i	−0.0643609	−	0.0643609i	0.674194	−	0.738555i	$-0.264491\pi$
$683$	−1.68202	−	1.68202i	−0.0643609	−	0.0643609i	−0.738555	+	0.674194i	$0.764491\pi$
$684$		0			0
$685$	−4.86488	+	4.86488i	−0.185877	+	0.185877i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.62237	+	2.09138i	−0.138001	+	0.0796751i
$690$		0			0
$691$	−2.22350	+	0.595784i	−0.0845858	+	0.0226647i	−0.300864	−	0.953667i	$-0.597275\pi$
$691$	−2.22350	+	0.595784i	−0.0845858	+	0.0226647i	0.216278	+	0.976332i	$0.430608\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.848565	+	0.489919i	0.0321879	+	0.0185837i
$696$		0			0
$697$	−47.3917	+	27.3616i	−1.79509	+	1.03639i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.2728	+	10.2728i	0.387997	+	0.387997i	0.873972	−	0.485976i	$-0.161536\pi$
$701$	10.2728	+	10.2728i	0.387997	+	0.387997i	−0.485976	+	0.873972i	$0.661536\pi$
$702$		0			0
$703$			2.53353i			0.0955540i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.07228	−	2.43091i	−0.341198	−	0.0914238i
$708$		0			0
$709$	−4.88619	+	1.30925i	−0.183505	+	0.0491700i	−0.349401	−	0.936973i	$-0.613615\pi$
$709$	−4.88619	+	1.30925i	−0.183505	+	0.0491700i	0.165896	+	0.986143i	$0.446948\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.32834	−	14.4251i	0.311899	−	0.540224i
$714$		0			0
$715$	10.8550	+	2.90859i	0.405955	+	0.108775i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.73858			−0.251307			−0.125653	−	0.992074i	$-0.540103\pi$
$719$	−6.73858			−0.251307			−0.125653	+	0.992074i	$0.540103\pi$
$720$		0			0
$721$	24.5544			0.914452
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.3849	−	3.58646i	−0.497101	−	0.133198i
$726$		0			0
$727$	4.14056	−	7.17166i	0.153565	−	0.265982i	−0.778971	−	0.627060i	$-0.784258\pi$
$727$	4.14056	−	7.17166i	0.153565	−	0.265982i	0.932536	+	0.361078i	$0.117591\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.30572	+	1.42166i	−0.196239	+	0.0525821i
$732$		0			0
$733$	43.6909	+	11.7070i	1.61376	+	0.432406i	0.949161	−	0.314792i	$-0.101935\pi$
$733$	43.6909	+	11.7070i	1.61376	+	0.432406i	0.664601	+	0.747198i	$0.268601\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	0.379742i		−	0.0139880i
$738$		0			0
$739$	−22.0530	−	22.0530i	−0.811234	−	0.811234i	0.173585	−	0.984819i	$-0.444465\pi$
$739$	−22.0530	−	22.0530i	−0.811234	−	0.811234i	−0.984819	+	0.173585i	$0.944465\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	29.9386	−	17.2851i	1.09834	−	0.634128i	0.162557	−	0.986699i	$-0.448026\pi$
$743$	29.9386	−	17.2851i	1.09834	−	0.634128i	0.935785	+	0.352571i	$0.114693\pi$
$744$		0			0
$745$	3.41062	+	1.96912i	0.124955	+	0.0721431i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	14.6205	−	3.91756i	0.534222	−	0.143144i
$750$		0			0
$751$	−38.8676	+	22.4402i	−1.41830	+	0.818855i	−0.996149	−	0.0876713i	$-0.972057\pi$
$751$	−38.8676	+	22.4402i	−1.41830	+	0.818855i	−0.422149	+	0.906526i	$0.638724\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.88134	−	7.88134i	0.286832	−	0.286832i
$756$		0			0
$757$	27.6111	+	27.6111i	1.00354	+	1.00354i	0.999994	+	0.00354931i	$0.00112978\pi$
$757$	27.6111	+	27.6111i	1.00354	+	1.00354i	0.00354931	+	0.999994i	$0.498870\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−17.8578	−	30.9307i	−0.647346	−	1.12124i	−0.983754	−	0.179520i	$-0.942545\pi$
$761$	−17.8578	−	30.9307i	−0.647346	−	1.12124i	0.336408	−	0.941716i	$-0.390788\pi$
$762$		0			0
$763$	−6.79711	−	25.3672i	−0.246072	−	0.918353i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.1534	+	21.0502i	−0.438832	+	0.760079i
$768$		0			0
$769$	−22.6077	−	39.1577i	−0.815254	−	1.41206i	−0.909145	−	0.416479i	$-0.863264\pi$
$769$	−22.6077	−	39.1577i	−0.815254	−	1.41206i	0.0938910	−	0.995582i	$-0.470069\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.57961	−	5.57961i	0.200685	−	0.200685i	−0.599609	−	0.800293i	$-0.704677\pi$
$773$	5.57961	−	5.57961i	0.200685	−	0.200685i	0.800293	+	0.599609i	$0.204677\pi$
$774$		0			0
$775$	27.6073			0.991684
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.95305	−	33.4132i	0.320776	−	1.19715i
$780$		0			0
$781$	−0.0385333	−	0.143808i	−0.00137883	−	0.00514586i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.66717	−	2.69459i	−0.166578	−	0.0961741i
$786$		0			0
$787$	2.39956	−	8.95529i	0.0855351	−	0.319221i	−0.909880	−	0.414872i	$-0.863826\pi$
$787$	2.39956	−	8.95529i	0.0855351	−	0.319221i	0.995415	+	0.0956504i	$0.0304931\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			3.26235i			0.115996i
$792$		0			0
$793$			55.1001i			1.95666i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.57307	−	24.5310i	0.232830	−	0.868934i	−0.746285	−	0.665627i	$-0.768164\pi$
$797$	6.57307	−	24.5310i	0.232830	−	0.868934i	0.979115	−	0.203307i	$-0.0651690\pi$
$798$		0			0
$799$	−59.3759	−	34.2807i	−2.10057	−	1.21276i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.4361	−	42.6801i	−0.403571	−	1.50615i
$804$		0			0
$805$	−0.627969	+	2.34361i	−0.0221330	+	0.0826014i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	33.1931			1.16701			0.583503	−	0.812111i	$-0.301682\pi$
$809$	33.1931			1.16701			0.583503	+	0.812111i	$0.301682\pi$
$810$		0			0
$811$	−7.35128	+	7.35128i	−0.258138	+	0.258138i	−0.824297	−	0.566158i	$-0.808429\pi$
$811$	−7.35128	+	7.35128i	−0.258138	+	0.258138i	0.566158	+	0.824297i	$0.308429\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.38234	−	4.12633i	−0.0834497	−	0.144539i
$816$		0			0
$817$	1.73610	−	3.00701i	0.0607383	−	0.105202i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.3476	−	38.6179i	−0.361135	−	1.34777i	−0.872585	−	0.488462i	$-0.837558\pi$
$821$	−10.3476	−	38.6179i	−0.361135	−	1.34777i	0.511450	−	0.859313i	$-0.329109\pi$
$822$		0			0
$823$	−11.8717	−	20.5623i	−0.413821	−	0.716758i	0.581483	−	0.813558i	$-0.302473\pi$
$823$	−11.8717	−	20.5623i	−0.413821	−	0.716758i	−0.995304	+	0.0968000i	$0.969139\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.1545	−	25.1545i	−0.874708	−	0.874708i	0.118273	−	0.992981i	$-0.462264\pi$
$827$	−25.1545	−	25.1545i	−0.874708	−	0.874708i	−0.992981	+	0.118273i	$0.962264\pi$
$828$		0			0
$829$	6.12372	−	6.12372i	0.212686	−	0.212686i	−0.592722	−	0.805407i	$-0.701947\pi$
$829$	6.12372	−	6.12372i	0.212686	−	0.212686i	0.805407	+	0.592722i	$0.201947\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	25.7922	−	14.8911i	0.893646	−	0.515947i
$834$		0			0
$835$	14.4117	−	3.86161i	0.498739	−	0.133637i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−35.2084	−	20.3276i	−1.21553	−	0.701786i	−0.251570	−	0.967839i	$-0.580947\pi$
$839$	−35.2084	−	20.3276i	−1.21553	−	0.701786i	−0.963958	+	0.266054i	$0.914280\pi$
$840$		0			0
$841$	−16.9997	+	9.81476i	−0.586195	+	0.338440i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.42593	−	5.42593i	−0.186658	−	0.186658i
$846$		0			0
$847$			0.0627931i			0.00215760i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.89313	−	0.507262i	−0.0648955	−	0.0173887i
$852$		0			0
$853$	−41.6120	+	11.1499i	−1.42477	+	0.381765i	−0.887173	−	0.461437i	$-0.847334\pi$
$853$	−41.6120	+	11.1499i	−1.42477	+	0.381765i	−0.537595	+	0.843203i	$0.680667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.72246	−	8.17953i	0.161316	−	0.279408i	−0.774025	−	0.633155i	$-0.781759\pi$
$857$	4.72246	−	8.17953i	0.161316	−	0.279408i	0.935341	+	0.353748i	$0.115093\pi$
$858$		0			0
$859$	−21.9088	−	5.87045i	−0.747519	−	0.200297i	−0.135102	−	0.990832i	$-0.543136\pi$
$859$	−21.9088	−	5.87045i	−0.747519	−	0.200297i	−0.612417	+	0.790535i	$0.709803\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.58147			0.121915			0.0609573	−	0.998140i	$-0.480585\pi$
$863$	3.58147			0.121915			0.0609573	+	0.998140i	$0.480585\pi$
$864$		0			0
$865$	−5.47380			−0.186115
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.27039	−	2.48399i	−0.314476	−	0.0842637i
$870$		0			0
$871$	−0.280740	+	0.486256i	−0.00951252	+	0.0164762i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.17482	+	2.19044i	−0.276359	+	0.0740503i
$876$		0			0
$877$	−16.8966	−	4.52743i	−0.570558	−	0.152881i	−0.0380056	−	0.999278i	$-0.512100\pi$
$877$	−16.8966	−	4.52743i	−0.570558	−	0.152881i	−0.532553	+	0.846397i	$0.678767\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			46.1363i			1.55437i	0.629272	+	0.777185i	$0.283353\pi$
$881$			46.1363i			1.55437i	−0.629272	+	0.777185i	$0.716647\pi$
$882$		0			0
$883$	−19.7311	−	19.7311i	−0.664003	−	0.664003i	0.292318	−	0.956321i	$-0.405573\pi$
$883$	−19.7311	−	19.7311i	−0.664003	−	0.664003i	−0.956321	+	0.292318i	$0.905573\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.7760	−	17.1912i	0.999780	−	0.577223i	0.0915965	−	0.995796i	$-0.470803\pi$
$887$	29.7760	−	17.1912i	0.999780	−	0.577223i	0.908183	+	0.418573i	$0.137470\pi$
$888$		0			0
$889$	19.5891	+	11.3098i	0.656999	+	0.379318i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	41.8626	−	11.2171i	1.40088	−	0.375364i
$894$		0			0
$895$	−7.98697	+	4.61128i	−0.266975	+	0.154138i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.2008	+	13.2008i	−0.440272	+	0.440272i
$900$		0			0
$901$	−3.36115	−	3.36115i	−0.111976	−	0.111976i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.89178	−	6.74076i	−0.129367	−	0.224070i
$906$		0			0
$907$	−14.3921	−	53.7121i	−0.477883	−	1.78348i	−0.610170	−	0.792271i	$-0.708899\pi$
$907$	−14.3921	−	53.7121i	−0.477883	−	1.78348i	0.132287	−	0.991211i	$-0.457768\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.01435	−	10.4172i	0.199264	−	0.345136i	−0.749026	−	0.662541i	$-0.769478\pi$
$911$	6.01435	−	10.4172i	0.199264	−	0.345136i	0.948290	+	0.317405i	$0.102811\pi$
$912$		0			0
$913$	6.53085	+	11.3118i	0.216140	+	0.374365i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.3338	+	11.3338i	−0.374275	+	0.374275i
$918$		0			0
$919$	11.8860			0.392084			0.196042	−	0.980595i	$-0.437191\pi$
$919$	11.8860			0.392084			0.196042	+	0.980595i	$0.437191\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.0569747	+	0.212633i	−0.00187535	+	0.00699889i
$924$		0			0
$925$	−0.840752	−	3.13773i	−0.0276438	−	0.103168i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.44934	+	1.99148i	0.113169	+	0.0653382i	0.555516	−	0.831506i	$-0.312521\pi$
$929$	3.44934	+	1.99148i	0.113169	+	0.0653382i	−0.442347	+	0.896844i	$0.645854\pi$
$930$		0			0
$931$	−4.87255	+	18.1846i	−0.159692	+	0.595977i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			12.7711i			0.417659i
$936$		0			0
$937$		−	26.0017i		−	0.849438i	−0.905325	−	0.424719i	$-0.860373\pi$
$937$		−	26.0017i		−	0.849438i	0.905325	−	0.424719i	$-0.139627\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.0855	−	41.3717i	0.361378	−	1.34868i	−0.510888	−	0.859648i	$-0.670683\pi$
$941$	11.0855	−	41.3717i	0.361378	−	1.34868i	0.872265	−	0.489033i	$-0.162650\pi$
$942$		0			0
$943$	23.1747	+	13.3799i	0.754673	+	0.435710i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.71769	+	17.6066i	0.153304	+	0.572139i	0.999245	+	0.0388617i	$0.0123732\pi$
$947$	4.71769	+	17.6066i	0.153304	+	0.572139i	−0.845940	+	0.533277i	$0.820960\pi$
$948$		0			0
$949$	−16.9093	+	63.1062i	−0.548898	+	2.04851i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.9031			0.547545			0.273772	−	0.961795i	$-0.411729\pi$
$953$	16.9031			0.547545			0.273772	+	0.961795i	$0.411729\pi$
$954$		0			0
$955$	8.97930	−	8.97930i	0.290563	−	0.290563i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.45774	+	11.1851i	0.208531	+	0.361187i
$960$		0			0
$961$	3.09688	−	5.36395i	0.0998993	−	0.173031i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.931682	−	3.47708i	−0.0299919	−	0.111931i
$966$		0			0
$967$	−1.50617	−	2.60876i	−0.0484351	−	0.0838921i	0.840791	−	0.541359i	$-0.182090\pi$
$967$	−1.50617	−	2.60876i	−0.0484351	−	0.0838921i	−0.889227	+	0.457467i	$0.848757\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	35.4934	+	35.4934i	1.13904	+	1.13904i	0.988623	+	0.150413i	$0.0480604\pi$
$971$	35.4934	+	35.4934i	1.13904	+	1.13904i	0.150413	+	0.988623i	$0.451940\pi$
$972$		0			0
$973$	1.30066	−	1.30066i	0.0416972	−	0.0416972i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.03784	+	4.64065i	−0.257153	+	0.148467i	−0.623035	−	0.782194i	$-0.714101\pi$
$977$	−8.03784	+	4.64065i	−0.257153	+	0.148467i	0.365882	+	0.930661i	$0.380767\pi$
$978$		0			0
$979$	−40.8920	+	10.9570i	−1.30691	+	0.350186i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.0480	+	6.37856i	0.352376	+	0.203444i	0.665731	−	0.746192i	$-0.268120\pi$
$983$	11.0480	+	6.37856i	0.352376	+	0.203444i	−0.313355	+	0.949636i	$0.601453\pi$
$984$		0			0
$985$	−12.0963	+	6.98379i	−0.385420	+	0.222522i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.89932	+	1.89932i	0.0603949	+	0.0603949i
$990$		0			0
$991$		−	6.60967i		−	0.209963i	−0.994474	−	0.104982i	$-0.966522\pi$
$991$		−	6.60967i		−	0.209963i	0.994474	−	0.104982i	$-0.0334784\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.19352	−	2.46340i	−0.291454	−	0.0780949i
$996$		0			0
$997$	36.5814	−	9.80194i	1.15854	−	0.310431i	0.372159	−	0.928169i	$-0.378618\pi$
$997$	36.5814	−	9.80194i	1.15854	−	0.310431i	0.786384	+	0.617738i	$0.211951\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.z.a.143.10		88
3.2	odd	2		576.2.y.a.335.7		88
4.3	odd	2		432.2.v.a.251.8		88
9.4	even	3		576.2.y.a.527.5		88
9.5	odd	6	inner	1728.2.z.a.719.10		88
12.11	even	2		144.2.u.a.11.15	✓	88
16.3	odd	4	inner	1728.2.z.a.1007.10		88
16.13	even	4		432.2.v.a.35.15		88
36.23	even	6		432.2.v.a.395.15		88
36.31	odd	6		144.2.u.a.59.8	yes	88
48.29	odd	4		144.2.u.a.83.8	yes	88
48.35	even	4		576.2.y.a.47.5		88
144.13	even	12		144.2.u.a.131.15	yes	88
144.67	odd	12		576.2.y.a.239.7		88
144.77	odd	12		432.2.v.a.179.8		88
144.131	even	12	inner	1728.2.z.a.1583.10		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.15	✓	88	12.11	even	2
144.2.u.a.59.8	yes	88	36.31	odd	6
144.2.u.a.83.8	yes	88	48.29	odd	4
144.2.u.a.131.15	yes	88	144.13	even	12
432.2.v.a.35.15		88	16.13	even	4
432.2.v.a.179.8		88	144.77	odd	12
432.2.v.a.251.8		88	4.3	odd	2
432.2.v.a.395.15		88	36.23	even	6
576.2.y.a.47.5		88	48.35	even	4
576.2.y.a.239.7		88	144.67	odd	12
576.2.y.a.335.7		88	3.2	odd	2
576.2.y.a.527.5		88	9.4	even	3
1728.2.z.a.143.10		88	1.1	even	1	trivial
1728.2.z.a.719.10		88	9.5	odd	6	inner
1728.2.z.a.1007.10		88	16.3	odd	4	inner
1728.2.z.a.1583.10		88	144.131	even	12	inner

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.664471 - 0.178044i) q^{5} +(-0.645693 + 1.11837i) q^{7} +(3.21069 - 0.860301i) q^{11} +(-4.74727 - 1.27203i) q^{13} -5.58523i q^{17} +(2.49649 + 2.49649i) q^{19} +(-2.36529 + 1.36560i) q^{23} +(-3.92031 - 2.26339i) q^{25} +(2.95682 - 0.792277i) q^{29} +(-5.28160 + 3.04933i) q^{31} +(0.628165 - 0.628165i) q^{35} +(0.507420 + 0.507420i) q^{37} +(-4.89892 - 8.48518i) q^{41} +(-0.254540 - 0.949956i) q^{43} +(6.13774 - 10.6309i) q^{47} +(2.66616 + 4.61793i) q^{49} +(0.601793 - 0.601793i) q^{53} -2.28658 q^{55} +(1.28003 - 4.77715i) q^{59} +(-2.90167 - 10.8292i) q^{61} +(2.92795 + 1.69045i) q^{65} +(0.0295686 - 0.110351i) q^{67} -0.0447904i q^{71} -13.2931i q^{73} +(-1.11098 + 4.14624i) q^{77} +(-2.50052 - 1.44368i) q^{79} +(1.01705 + 3.79568i) q^{83} +(-0.994419 + 3.71122i) q^{85} -12.7362 q^{89} +(4.48788 - 4.48788i) q^{91} +(-1.21436 - 2.10333i) q^{95} +(4.41066 - 7.63949i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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