LMFDB - Embedded newform 1728.2.z.a.719.1

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			719.1
Character	$\chi$	$=$	1728.719
Dual form			1728.2.z.a.1007.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00059 - 3.73424i) q^{5} +(1.68236 + 2.91393i) q^{7} +(0.0566521 - 0.211428i) q^{11} +(0.727551 + 2.71526i) q^{13} +4.23937i q^{17} +(1.12365 + 1.12365i) q^{19} +(3.33369 + 1.92471i) q^{23} +(-8.61325 + 4.97286i) q^{25} +(-0.545635 + 2.03634i) q^{29} +(7.21206 + 4.16388i) q^{31} +(9.19798 - 9.19798i) q^{35} +(-2.66564 - 2.66564i) q^{37} +(1.70386 - 2.95117i) q^{41} +(-4.68985 - 1.25664i) q^{43} +(2.34998 + 4.07028i) q^{47} +(-2.16067 + 3.74239i) q^{49} +(7.58271 - 7.58271i) q^{53} -0.846209 q^{55} +(-5.34305 + 1.43167i) q^{59} +(8.69958 + 2.33105i) q^{61} +(9.41144 - 5.43370i) q^{65} +(5.17504 - 1.38665i) q^{67} +7.53614i q^{71} +3.22646i q^{73} +(0.711397 - 0.190618i) q^{77} +(4.98587 - 2.87859i) q^{79} +(4.50604 + 1.20739i) q^{83} +(15.8308 - 4.24186i) q^{85} +2.96157 q^{89} +(-6.68807 + 6.68807i) q^{91} +(3.07166 - 5.32027i) q^{95} +(-7.63883 - 13.2308i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$	−1.00059	−	3.73424i	−0.447476	−	1.67000i	−0.709315	−	0.704891i	$-0.750996\pi$
$5$	−1.00059	−	3.73424i	−0.447476	−	1.67000i	0.261839	−	0.965111i	$-0.415671\pi$
$6$		0			0
$7$	1.68236	+	2.91393i	0.635872	+	1.10136i	0.986330	+	0.164785i	$0.0526929\pi$
$7$	1.68236	+	2.91393i	0.635872	+	1.10136i	−0.350457	+	0.936579i	$0.613974\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.0566521	−	0.211428i	0.0170812	−	0.0637480i	−0.956859	−	0.290552i	$-0.906161\pi$
$11$	0.0566521	−	0.211428i	0.0170812	−	0.0637480i	0.973940	+	0.226804i	$0.0728277\pi$
$12$		0			0
$13$	0.727551	+	2.71526i	0.201786	+	0.753076i	0.990405	+	0.138194i	$0.0441298\pi$
$13$	0.727551	+	2.71526i	0.201786	+	0.753076i	−0.788619	+	0.614882i	$0.789204\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.23937i			1.02820i	0.857731	+	0.514100i	$0.171874\pi$
$17$			4.23937i			1.02820i	−0.857731	+	0.514100i	$0.828126\pi$
$18$		0			0
$19$	1.12365	+	1.12365i	0.257782	+	0.257782i	0.824152	−	0.566369i	$-0.191652\pi$
$19$	1.12365	+	1.12365i	0.257782	+	0.257782i	−0.566369	+	0.824152i	$0.691652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.33369	+	1.92471i	0.695123	+	0.401329i	0.805528	−	0.592557i	$-0.201882\pi$
$23$	3.33369	+	1.92471i	0.695123	+	0.401329i	−0.110405	+	0.993887i	$0.535215\pi$
$24$		0			0
$25$	−8.61325	+	4.97286i	−1.72265	+	0.994572i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.545635	+	2.03634i	−0.101322	+	0.378138i	−0.997902	−	0.0647434i	$-0.979377\pi$
$29$	−0.545635	+	2.03634i	−0.101322	+	0.378138i	0.896580	+	0.442882i	$0.146044\pi$
$30$		0			0
$31$	7.21206	+	4.16388i	1.29532	+	0.747856i	0.979593	−	0.200993i	$-0.0644169\pi$
$31$	7.21206	+	4.16388i	1.29532	+	0.747856i	0.315731	+	0.948849i	$0.397750\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.19798	−	9.19798i	1.55474	−	1.55474i
$36$		0			0
$37$	−2.66564	−	2.66564i	−0.438229	−	0.438229i	0.453187	−	0.891416i	$-0.350287\pi$
$37$	−2.66564	−	2.66564i	−0.438229	−	0.438229i	−0.891416	+	0.453187i	$0.850287\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.70386	−	2.95117i	0.266098	−	0.460895i	−0.701753	−	0.712420i	$-0.747599\pi$
$41$	1.70386	−	2.95117i	0.266098	−	0.460895i	0.967851	+	0.251526i	$0.0809323\pi$
$42$		0			0
$43$	−4.68985	−	1.25664i	−0.715195	−	0.191636i	−0.117168	−	0.993112i	$-0.537382\pi$
$43$	−4.68985	−	1.25664i	−0.715195	−	0.191636i	−0.598027	+	0.801476i	$0.704048\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.34998	+	4.07028i	0.342779	+	0.593711i	0.984948	−	0.172852i	$-0.0552984\pi$
$47$	2.34998	+	4.07028i	0.342779	+	0.593711i	−0.642168	+	0.766564i	$0.721965\pi$
$48$		0			0
$49$	−2.16067	+	3.74239i	−0.308667	+	0.534628i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.58271	−	7.58271i	1.04157	−	1.04157i	0.0424680	−	0.999098i	$-0.486478\pi$
$53$	7.58271	−	7.58271i	1.04157	−	1.04157i	0.999098	−	0.0424680i	$-0.0135220\pi$
$54$		0			0
$55$	−0.846209			−0.114103
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.34305	+	1.43167i	−0.695605	+	0.186387i	−0.589261	−	0.807942i	$-0.700581\pi$
$59$	−5.34305	+	1.43167i	−0.695605	+	0.186387i	−0.106344	+	0.994329i	$0.533915\pi$
$60$		0			0
$61$	8.69958	+	2.33105i	1.11387	+	0.298460i	0.768399	−	0.639971i	$-0.221054\pi$
$61$	8.69958	+	2.33105i	1.11387	+	0.298460i	0.345468	+	0.938431i	$0.387720\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.41144	−	5.43370i	1.16735	−	0.673967i
$66$		0			0
$67$	5.17504	−	1.38665i	0.632231	−	0.169406i	0.0715493	−	0.997437i	$-0.477206\pi$
$67$	5.17504	−	1.38665i	0.632231	−	0.169406i	0.560682	+	0.828031i	$0.310539\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.53614i			0.894375i	0.894440	+	0.447187i	$0.147574\pi$
$71$			7.53614i			0.894375i	−0.894440	+	0.447187i	$0.852426\pi$
$72$		0			0
$73$			3.22646i			0.377629i	0.982013	+	0.188814i	$0.0604644\pi$
$73$			3.22646i			0.377629i	−0.982013	+	0.188814i	$0.939536\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.711397	−	0.190618i	0.0810712	−	0.0217230i
$78$		0			0
$79$	4.98587	−	2.87859i	0.560954	−	0.323867i	−0.192574	−	0.981282i	$-0.561684\pi$
$79$	4.98587	−	2.87859i	0.560954	−	0.323867i	0.753528	+	0.657415i	$0.228350\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.50604	+	1.20739i	0.494602	+	0.132528i	0.497494	−	0.867468i	$-0.334254\pi$
$83$	4.50604	+	1.20739i	0.494602	+	0.132528i	−0.00289160	+	0.999996i	$0.500920\pi$
$84$		0			0
$85$	15.8308	−	4.24186i	1.71710	−	0.460094i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.96157			0.313926			0.156963	−	0.987605i	$-0.449830\pi$
$89$	2.96157			0.313926			0.156963	+	0.987605i	$0.449830\pi$
$90$		0			0
$91$	−6.68807	+	6.68807i	−0.701100	+	0.701100i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.07166	−	5.32027i	0.315146	−	0.545849i
$96$		0			0
$97$	−7.63883	−	13.2308i	−0.775606	−	1.34339i	−0.934453	−	0.356085i	$-0.884111\pi$
$97$	−7.63883	−	13.2308i	−0.775606	−	1.34339i	0.158848	−	0.987303i	$-0.449222\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.129684	−	0.0347486i	−0.0129040	−	0.00345762i	0.252361	−	0.967633i	$-0.418793\pi$
$101$	−0.129684	−	0.0347486i	−0.0129040	−	0.00345762i	−0.265265	+	0.964175i	$0.585460\pi$
$102$		0			0
$103$	4.09117	−	7.08611i	0.403115	−	0.698215i	−0.590985	−	0.806682i	$-0.701261\pi$
$103$	4.09117	−	7.08611i	0.403115	−	0.698215i	0.994100	+	0.108467i	$0.0345942\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.28837	+	8.28837i	0.801267	+	0.801267i	0.983294	−	0.182027i	$-0.0582658\pi$
$107$	8.28837	+	8.28837i	0.801267	+	0.801267i	−0.182027	+	0.983294i	$0.558266\pi$
$108$		0			0
$109$	6.31291	−	6.31291i	0.604667	−	0.604667i	−0.336881	−	0.941547i	$-0.609372\pi$
$109$	6.31291	−	6.31291i	0.604667	−	0.604667i	0.941547	+	0.336881i	$0.109372\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.6562	−	8.46178i	−1.37874	−	0.796017i	−0.386735	−	0.922191i	$-0.626397\pi$
$113$	−14.6562	−	8.46178i	−1.37874	−	0.796017i	−0.992008	+	0.126174i	$0.959730\pi$
$114$		0			0
$115$	3.85167	−	14.3746i	0.359171	−	1.34044i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.3533	+	7.13215i	−1.13242	+	0.653803i
$120$		0			0
$121$	9.48479	+	5.47604i	0.862253	+	0.497822i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	13.5199	+	13.5199i	1.20926	+	1.20926i
$126$		0			0
$127$			13.4028i			1.18931i	0.803981	+	0.594654i	$0.202711\pi$
$127$			13.4028i			1.18931i	−0.803981	+	0.594654i	$0.797289\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.169534	+	0.632708i	0.0148122	+	0.0552800i	0.972936	−	0.231073i	$-0.0742236\pi$
$131$	0.169534	+	0.632708i	0.0148122	+	0.0552800i	−0.958124	+	0.286353i	$0.907557\pi$
$132$		0			0
$133$	−1.38385	+	5.16461i	−0.119995	+	0.447829i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.5230	−	18.2263i	−0.899037	−	1.55718i	−0.828727	−	0.559652i	$-0.810935\pi$
$137$	−10.5230	−	18.2263i	−0.899037	−	1.55718i	−0.0703095	−	0.997525i	$-0.522399\pi$
$138$		0			0
$139$	1.72666	+	6.44400i	0.146454	+	0.546573i	0.999686	+	0.0250423i	$0.00797204\pi$
$139$	1.72666	+	6.44400i	0.146454	+	0.546573i	−0.853233	+	0.521530i	$0.825361\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.615299			0.0514539
$144$		0			0
$145$	8.15012			0.676831
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.78161	+	21.5773i	0.473648	+	1.76768i	0.626492	+	0.779428i	$0.284490\pi$
$149$	5.78161	+	21.5773i	0.473648	+	1.76768i	−0.152844	+	0.988250i	$0.548843\pi$
$150$		0			0
$151$	9.97506	+	17.2773i	0.811759	+	1.40601i	0.911632	+	0.411007i	$0.134823\pi$
$151$	9.97506	+	17.2773i	0.811759	+	1.40601i	−0.0998734	+	0.995000i	$0.531844\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.33265	−	31.0979i	0.669295	−	2.49784i
$156$		0			0
$157$	3.85693	+	14.3943i	0.307817	+	1.14879i	0.930494	+	0.366308i	$0.119378\pi$
$157$	3.85693	+	14.3943i	0.307817	+	1.14879i	−0.622677	+	0.782479i	$0.713955\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			12.9522i			1.02078i
$162$		0			0
$163$	4.35766	+	4.35766i	0.341318	+	0.341318i	0.856863	−	0.515545i	$-0.172410\pi$
$163$	4.35766	+	4.35766i	0.341318	+	0.341318i	−0.515545	+	0.856863i	$0.672410\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.8952	−	6.86770i	−0.920479	−	0.531439i	−0.0366910	−	0.999327i	$-0.511682\pi$
$167$	−11.8952	−	6.86770i	−0.920479	−	0.531439i	−0.883788	+	0.467888i	$0.845015\pi$
$168$		0			0
$169$	4.41505	−	2.54903i	0.339619	−	0.196079i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.40497	+	5.24342i	−0.106818	+	0.398650i	−0.998545	−	0.0539235i	$-0.982827\pi$
$173$	−1.40497	+	5.24342i	−0.106818	+	0.398650i	0.891727	+	0.452573i	$0.149494\pi$
$174$		0			0
$175$	−28.9812	−	16.7323i	−2.19077	−	1.26484i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.380130	−	0.380130i	0.0284123	−	0.0284123i	−0.692758	−	0.721170i	$-0.743605\pi$
$179$	0.380130	−	0.380130i	0.0284123	−	0.0284123i	0.721170	+	0.692758i	$0.243605\pi$
$180$		0			0
$181$	−4.98992	−	4.98992i	−0.370898	−	0.370898i	0.496906	−	0.867804i	$-0.334469\pi$
$181$	−4.98992	−	4.98992i	−0.370898	−	0.370898i	−0.867804	+	0.496906i	$0.834469\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.28695	+	12.6214i	−0.535747	+	0.927941i
$186$		0			0
$187$	0.896324	+	0.240169i	0.0655457	+	0.0175629i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.40555	−	9.36269i	−0.391132	−	0.677461i	0.601467	−	0.798898i	$-0.294583\pi$
$191$	−5.40555	−	9.36269i	−0.391132	−	0.677461i	−0.992599	+	0.121437i	$0.961250\pi$
$192$		0			0
$193$	2.60044	−	4.50410i	0.187184	−	0.324212i	−0.757126	−	0.653268i	$-0.773397\pi$
$193$	2.60044	−	4.50410i	0.187184	−	0.324212i	0.944310	+	0.329056i	$0.106731\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.94550	−	2.94550i	0.209858	−	0.209858i	−0.594349	−	0.804207i	$-0.702590\pi$
$197$	2.94550	−	2.94550i	0.209858	−	0.209858i	0.804207	+	0.594349i	$0.202590\pi$
$198$		0			0
$199$	−2.57285			−0.182384			−0.0911921	−	0.995833i	$-0.529068\pi$
$199$	−2.57285			−0.182384			−0.0911921	+	0.995833i	$0.529068\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.85170	+	1.83591i	−0.480895	+	0.128856i
$204$		0			0
$205$	−12.7252	−	3.40971i	−0.888768	−	0.238145i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.301228	−	0.173914i	0.0208364	−	0.0120299i
$210$		0			0
$211$	−17.5700	+	4.70786i	−1.20957	+	0.324103i	−0.806592	−	0.591108i	$-0.798691\pi$
$211$	−17.5700	+	4.70786i	−1.20957	+	0.324103i	−0.402975	+	0.915211i	$0.632024\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			18.7704i			1.28013i
$216$		0			0
$217$			28.0206i			1.90216i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.5110	+	3.08436i	−0.774312	+	0.207476i
$222$		0			0
$223$	−2.82059	+	1.62847i	−0.188881	+	0.109050i	−0.591458	−	0.806336i	$-0.701448\pi$
$223$	−2.82059	+	1.62847i	−0.188881	+	0.109050i	0.402578	+	0.915386i	$0.368114\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.83238	−	2.36663i	−0.586226	−	0.157079i	−0.0464979	−	0.998918i	$-0.514806\pi$
$227$	−8.83238	−	2.36663i	−0.586226	−	0.157079i	−0.539728	+	0.841840i	$0.681473\pi$
$228$		0			0
$229$	−5.07755	+	1.36053i	−0.335534	+	0.0899061i	−0.422652	−	0.906292i	$-0.638901\pi$
$229$	−5.07755	+	1.36053i	−0.335534	+	0.0899061i	0.0871183	+	0.996198i	$0.472234\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.1506			−0.927034			−0.463517	−	0.886088i	$-0.653413\pi$
$233$	−14.1506			−0.927034			−0.463517	+	0.886088i	$0.653413\pi$
$234$		0			0
$235$	12.8480	−	12.8480i	0.838114	−	0.838114i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.51536	+	13.0170i	−0.486128	+	0.841999i	−0.999873	−	0.0159444i	$-0.994925\pi$
$239$	−7.51536	+	13.0170i	−0.486128	+	0.841999i	0.513745	+	0.857943i	$0.328258\pi$
$240$		0			0
$241$	7.18920	+	12.4521i	0.463097	+	0.802108i	0.999113	−	0.0420996i	$-0.0134047\pi$
$241$	7.18920	+	12.4521i	0.463097	+	0.802108i	−0.536016	+	0.844208i	$0.680071\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	16.1369	+	4.32388i	1.03095	+	0.276242i
$246$		0			0
$247$	−2.23348	+	3.86850i	−0.142113	+	0.246147i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.59758	−	3.59758i	−0.227077	−	0.227077i	0.584393	−	0.811471i	$-0.301333\pi$
$251$	−3.59758	−	3.59758i	−0.227077	−	0.227077i	−0.811471	+	0.584393i	$0.801333\pi$
$252$		0			0
$253$	0.595798	−	0.595798i	0.0374575	−	0.0374575i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.92640	+	2.84426i	0.307300	+	0.177420i	0.645718	−	0.763576i	$-0.276558\pi$
$257$	4.92640	+	2.84426i	0.307300	+	0.177420i	−0.338418	+	0.940996i	$0.609892\pi$
$258$		0			0
$259$	3.28294	−	12.2521i	0.203992	−	0.761307i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	18.8392	−	10.8768i	1.16167	−	0.670693i	0.209970	−	0.977708i	$-0.432663\pi$
$263$	18.8392	−	10.8768i	1.16167	−	0.670693i	0.951705	+	0.307015i	$0.0993300\pi$
$264$		0			0
$265$	−35.9028	−	20.7285i	−2.20549	−	1.27334i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.43467	+	7.43467i	0.453300	+	0.453300i	0.896448	−	0.443148i	$-0.146139\pi$
$269$	7.43467	+	7.43467i	0.453300	+	0.453300i	−0.443148	+	0.896448i	$0.646139\pi$
$270$		0			0
$271$			11.8875i			0.722111i	0.932544	+	0.361056i	$0.117584\pi$
$271$			11.8875i			0.722111i	−0.932544	+	0.361056i	$0.882416\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.563445	+	2.10281i	0.0339770	+	0.126804i
$276$		0			0
$277$	2.68166	−	10.0081i	0.161126	−	0.601329i	−0.837377	−	0.546626i	$-0.815912\pi$
$277$	2.68166	−	10.0081i	0.161126	−	0.601329i	0.998503	−	0.0547032i	$-0.0174213\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.05630	+	12.2219i	0.420944	+	0.729096i	0.996032	−	0.0889955i	$-0.0283657\pi$
$281$	7.05630	+	12.2219i	0.420944	+	0.729096i	−0.575088	+	0.818091i	$0.695032\pi$
$282$		0			0
$283$	−3.42843	−	12.7951i	−0.203799	−	0.760588i	−0.989812	−	0.142378i	$-0.954525\pi$
$283$	−3.42843	−	12.7951i	−0.203799	−	0.760588i	0.786013	−	0.618209i	$-0.212142\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.4660			0.676817
$288$		0			0
$289$	−0.972286			−0.0571933
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.96005	−	29.7073i	−0.465031	−	1.73552i	−0.656787	−	0.754077i	$-0.728085\pi$
$293$	−7.96005	−	29.7073i	−0.465031	−	1.73552i	0.191756	−	0.981443i	$-0.438582\pi$
$294$		0			0
$295$	10.6924	+	18.5197i	0.622533	+	1.07826i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.80065	+	10.4522i	−0.161965	+	0.604463i
$300$		0			0
$301$	−4.22825	−	15.7800i	−0.243712	−	0.909546i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	34.8187i		−	1.99371i
$306$		0			0
$307$	−23.8109	−	23.8109i	−1.35896	−	1.35896i	−0.875202	−	0.483758i	$-0.839272\pi$
$307$	−23.8109	−	23.8109i	−1.35896	−	1.35896i	−0.483758	−	0.875202i	$-0.660728\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.20941	−	5.31706i	−0.522218	−	0.301503i	0.215624	−	0.976477i	$-0.430822\pi$
$311$	−9.20941	−	5.31706i	−0.522218	−	0.301503i	−0.737842	+	0.674974i	$0.764155\pi$
$312$		0			0
$313$	16.4634	−	9.50514i	0.930565	−	0.537262i	0.0435750	−	0.999050i	$-0.486125\pi$
$313$	16.4634	−	9.50514i	0.930565	−	0.537262i	0.886990	+	0.461788i	$0.152792\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.18193	−	11.8751i	0.178715	−	0.666972i	−0.817174	−	0.576391i	$-0.804461\pi$
$317$	3.18193	−	11.8751i	0.178715	−	0.666972i	0.995889	−	0.0905818i	$-0.0288727\pi$
$318$		0			0
$319$	0.399628	+	0.230725i	0.0223749	+	0.0129181i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.76356	+	4.76356i	−0.265052	+	0.265052i
$324$		0			0
$325$	−19.7692	−	19.7692i	−1.09660	−	1.09660i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.90701	+	13.6953i	−0.435928	+	0.755049i
$330$		0			0
$331$	−33.3960	−	8.94844i	−1.83561	−	0.491851i	−0.837134	−	0.546998i	$-0.815771\pi$
$331$	−33.3960	−	8.94844i	−1.83561	−	0.491851i	−0.998478	+	0.0551468i	$0.982437\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−10.3561	−	17.9374i	−0.565817	−	0.980023i
$336$		0			0
$337$	−14.3693	+	24.8884i	−0.782746	+	1.35576i	0.147591	+	0.989049i	$0.452848\pi$
$337$	−14.3693	+	24.8884i	−0.782746	+	1.35576i	−0.930336	+	0.366707i	$0.880485\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.28894	−	1.28894i	0.0698001	−	0.0698001i
$342$		0			0
$343$	9.01293			0.486653
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.9346	+	2.92992i	−0.587002	+	0.157287i	−0.540082	−	0.841612i	$-0.681607\pi$
$347$	−10.9346	+	2.92992i	−0.587002	+	0.157287i	−0.0469191	+	0.998899i	$0.514940\pi$
$348$		0			0
$349$	10.8496	+	2.90715i	0.580767	+	0.155616i	0.537230	−	0.843436i	$-0.319471\pi$
$349$	10.8496	+	2.90715i	0.580767	+	0.155616i	0.0435372	+	0.999052i	$0.486137\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.85946	+	1.07356i	−0.0989689	+	0.0571397i	−0.548668	−	0.836041i	$-0.684865\pi$
$353$	−1.85946	+	1.07356i	−0.0989689	+	0.0571397i	0.449699	+	0.893180i	$0.351531\pi$
$354$		0			0
$355$	28.1417	−	7.54056i	1.49361	−	0.400211i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	11.0166i		−	0.581435i	−0.956809	−	0.290718i	$-0.906106\pi$
$359$		−	11.0166i		−	0.581435i	0.956809	−	0.290718i	$-0.0938941\pi$
$360$		0			0
$361$		−	16.4748i		−	0.867097i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.0484	−	3.22835i	0.630641	−	0.168980i
$366$		0			0
$367$	20.1365	−	11.6258i	1.05112	−	0.606863i	0.128156	−	0.991754i	$-0.459094\pi$
$367$	20.1365	−	11.6258i	1.05112	−	0.606863i	0.922962	+	0.384891i	$0.125761\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	34.8524	+	9.33867i	1.80945	+	0.484839i
$372$		0			0
$373$	9.93021	−	2.66079i	0.514167	−	0.137771i	0.00759967	−	0.999971i	$-0.497581\pi$
$373$	9.93021	−	2.66079i	0.514167	−	0.137771i	0.506567	+	0.862201i	$0.330914\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.92615			−0.305212
$378$		0			0
$379$	6.14819	−	6.14819i	0.315811	−	0.315811i	−0.531345	−	0.847156i	$-0.678313\pi$
$379$	6.14819	−	6.14819i	0.315811	−	0.315811i	0.847156	+	0.531345i	$0.178313\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.40170	+	2.42782i	−0.0716238	+	0.124056i	−0.899613	−	0.436688i	$-0.856151\pi$
$383$	−1.40170	+	2.42782i	−0.0716238	+	0.124056i	0.827989	+	0.560744i	$0.189485\pi$
$384$		0			0
$385$	−1.42363	−	2.46580i	−0.0725548	−	0.125669i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−29.1977	−	7.82350i	−1.48038	−	0.396667i	−0.573905	−	0.818922i	$-0.694572\pi$
$389$	−29.1977	−	7.82350i	−1.48038	−	0.396667i	−0.906477	+	0.422255i	$0.861239\pi$
$390$		0			0
$391$	−8.15956	+	14.1328i	−0.412647	+	0.714725i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−15.7382	−	15.7382i	−0.791873	−	0.791873i
$396$		0			0
$397$	1.95789	−	1.95789i	0.0982636	−	0.0982636i	−0.656266	−	0.754530i	$-0.727865\pi$
$397$	1.95789	−	1.95789i	0.0982636	−	0.0982636i	0.754530	+	0.656266i	$0.227865\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	28.7356	+	16.5905i	1.43499	+	0.828489i	0.997495	−	0.0707337i	$-0.0225340\pi$
$401$	28.7356	+	16.5905i	1.43499	+	0.828489i	0.437490	+	0.899223i	$0.355867\pi$
$402$		0			0
$403$	−6.05887	+	22.6120i	−0.301814	+	1.12638i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.714607	+	0.412578i	−0.0354217	+	0.0204508i
$408$		0			0
$409$	−22.8959	−	13.2190i	−1.13213	−	0.653636i	−0.187660	−	0.982234i	$-0.560090\pi$
$409$	−22.8959	−	13.2190i	−1.13213	−	0.653636i	−0.944470	+	0.328598i	$0.893424\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.1607	−	13.1607i	−0.647596	−	0.647596i
$414$		0			0
$415$		−	18.0347i		−	0.885290i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.133835	−	0.499479i	−0.00653827	−	0.0244012i	0.962580	−	0.270999i	$-0.0873540\pi$
$419$	−0.133835	−	0.499479i	−0.00653827	−	0.0244012i	−0.969118	+	0.246598i	$0.920687\pi$
$420$		0			0
$421$	−3.44352	+	12.8514i	−0.167827	+	0.626339i	0.829836	+	0.558008i	$0.188434\pi$
$421$	−3.44352	+	12.8514i	−0.167827	+	0.626339i	−0.997663	+	0.0683313i	$0.978233\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−21.0818	−	36.5148i	−1.02262	−	1.77123i
$426$		0			0
$427$	7.84332	+	29.2717i	0.379565	+	1.41655i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.61129			0.414791			0.207396	−	0.978257i	$-0.433501\pi$
$431$	8.61129			0.414791			0.207396	+	0.978257i	$0.433501\pi$
$432$		0			0
$433$	6.43973			0.309474			0.154737	−	0.987956i	$-0.450547\pi$
$433$	6.43973			0.309474			0.154737	+	0.987956i	$0.450547\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.58320	+	5.90859i	0.0757348	+	0.282646i
$438$		0			0
$439$	−14.4510	−	25.0298i	−0.689707	−	1.19461i	−0.971933	−	0.235260i	$-0.924406\pi$
$439$	−14.4510	−	25.0298i	−0.689707	−	1.19461i	0.282225	−	0.959348i	$-0.408927\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.35627	+	31.1860i	−0.397018	+	1.48169i	0.421297	+	0.906923i	$0.361575\pi$
$443$	−8.35627	+	31.1860i	−0.397018	+	1.48169i	−0.818315	+	0.574770i	$0.805092\pi$
$444$		0			0
$445$	−2.96330	−	11.0592i	−0.140474	−	0.524257i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			10.7097i			0.505423i	0.967542	+	0.252711i	$0.0813223\pi$
$449$			10.7097i			0.505423i	−0.967542	+	0.252711i	$0.918678\pi$
$450$		0			0
$451$	−0.527433	−	0.527433i	−0.0248359	−	0.0248359i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	31.6669	+	18.2829i	1.48457	+	0.857114i
$456$		0			0
$457$	−13.1358	+	7.58393i	−0.614465	+	0.354761i	−0.774711	−	0.632316i	$-0.782105\pi$
$457$	−13.1358	+	7.58393i	−0.614465	+	0.354761i	0.160246	+	0.987077i	$0.448771\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.10006	−	11.5696i	0.144384	−	0.538849i	−0.855398	−	0.517971i	$-0.826687\pi$
$461$	3.10006	−	11.5696i	0.144384	−	0.538849i	0.999782	−	0.0208774i	$-0.00664596\pi$
$462$		0			0
$463$	−2.03363	−	1.17412i	−0.0945107	−	0.0545658i	0.452000	−	0.892018i	$-0.350711\pi$
$463$	−2.03363	−	1.17412i	−0.0945107	−	0.0545658i	−0.546510	+	0.837452i	$0.684044\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.1509	+	24.1509i	−1.11757	+	1.11757i	−0.125473	+	0.992097i	$0.540045\pi$
$467$	−24.1509	+	24.1509i	−1.11757	+	1.11757i	−0.992097	+	0.125473i	$0.959955\pi$
$468$		0			0
$469$	12.7469	+	12.7469i	0.588596	+	0.588596i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.531379	+	0.920376i	−0.0244328	+	0.0423189i
$474$		0			0
$475$	−15.2660	−	4.09051i	−0.700452	−	0.187685i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.40917	+	4.17281i	0.110078	+	0.190660i	0.915801	−	0.401631i	$-0.131557\pi$
$479$	2.40917	+	4.17281i	0.110078	+	0.190660i	−0.805724	+	0.592292i	$0.798223\pi$
$480$		0			0
$481$	5.29851	−	9.17730i	0.241591	−	0.418449i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−41.7638	+	41.7638i	−1.89640	+	1.89640i
$486$		0			0
$487$	−37.5042			−1.69948			−0.849739	−	0.527204i	$-0.823240\pi$
$487$	−37.5042			−1.69948			−0.849739	+	0.527204i	$0.823240\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.88310	+	0.504576i	−0.0849832	+	0.0227712i	−0.301060	−	0.953605i	$-0.597340\pi$
$491$	−1.88310	+	0.504576i	−0.0849832	+	0.0227712i	0.216077	+	0.976376i	$0.430674\pi$
$492$		0			0
$493$	−8.63279	−	2.31315i	−0.388801	−	0.104179i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.9598	+	12.6785i	−0.985032	+	0.568708i
$498$		0			0
$499$	−10.8793	+	2.91509i	−0.487023	+	0.130497i	−0.493971	−	0.869478i	$-0.664455\pi$
$499$	−10.8793	+	2.91509i	−0.487023	+	0.130497i	0.00694794	+	0.999976i	$0.497788\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			15.3339i			0.683706i	0.939753	+	0.341853i	$0.111055\pi$
$503$			15.3339i			0.683706i	−0.939753	+	0.341853i	$0.888945\pi$
$504$		0			0
$505$			0.519039i			0.0230969i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−32.0866	+	8.59758i	−1.42221	+	0.381081i	−0.886269	−	0.463172i	$-0.846711\pi$
$509$	−32.0866	+	8.59758i	−1.42221	+	0.381081i	−0.535945	+	0.844253i	$0.680045\pi$
$510$		0			0
$511$	−9.40169	+	5.42807i	−0.415906	+	0.240124i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−30.5548	−	8.18713i	−1.34641	−	0.360768i
$516$		0			0
$517$	0.993703	−	0.266262i	0.0437030	−	0.0117102i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.5032			0.898262			0.449131	−	0.893466i	$-0.351734\pi$
$521$	20.5032			0.898262			0.449131	+	0.893466i	$0.351734\pi$
$522$		0			0
$523$	29.2406	−	29.2406i	1.27860	−	1.27860i	0.337151	−	0.941451i	$-0.390537\pi$
$523$	29.2406	−	29.2406i	1.27860	−	1.27860i	0.941451	−	0.337151i	$-0.109463\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−17.6523	+	30.5746i	−0.768944	+	1.33185i
$528$		0			0
$529$	−4.09099	−	7.08581i	−0.177869	−	0.308079i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.25281	+	2.47928i	0.400784	+	0.107390i
$534$		0			0
$535$	22.6575	−	39.2440i	0.979570	−	1.69667i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.668841	+	0.668841i	0.0288090	+	0.0288090i
$540$		0			0
$541$	20.5836	−	20.5836i	0.884956	−	0.884956i	−0.109077	−	0.994033i	$-0.534790\pi$
$541$	20.5836	−	20.5836i	0.884956	−	0.884956i	0.994033	+	0.109077i	$0.0347895\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−29.8905	−	17.2573i	−1.28037	−	0.739221i
$546$		0			0
$547$	−10.2029	+	38.0779i	−0.436246	+	1.62809i	0.301821	+	0.953365i	$0.402406\pi$
$547$	−10.2029	+	38.0779i	−0.436246	+	1.62809i	−0.738067	+	0.674728i	$0.764261\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.90122	+	1.67502i	−0.123596	+	0.0713584i
$552$		0			0
$553$	16.7761	+	9.68566i	0.713391	+	0.411876i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.52288	+	1.52288i	0.0645265	+	0.0645265i	0.738634	−	0.674107i	$-0.235471\pi$
$557$	1.52288	+	1.52288i	0.0645265	+	0.0645265i	−0.674107	+	0.738634i	$0.735471\pi$
$558$		0			0
$559$		−	13.6484i		−	0.577266i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.30147	−	4.85715i	−0.0548504	−	0.204705i	0.933063	−	0.359714i	$-0.117126\pi$
$563$	−1.30147	−	4.85715i	−0.0548504	−	0.204705i	−0.987913	+	0.155010i	$0.950459\pi$
$564$		0			0
$565$	−16.9335	+	63.1966i	−0.712397	+	2.65870i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.4710	+	30.2606i	0.732421	+	1.26859i	0.955846	+	0.293869i	$0.0949430\pi$
$569$	17.4710	+	30.2606i	0.732421	+	1.26859i	−0.223425	+	0.974721i	$0.571724\pi$
$570$		0			0
$571$	9.16034	+	34.1869i	0.383348	+	1.43068i	0.840754	+	0.541417i	$0.182112\pi$
$571$	9.16034	+	34.1869i	0.383348	+	1.43068i	−0.457406	+	0.889258i	$0.651221\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−38.2852			−1.59660
$576$		0			0
$577$	−17.4865			−0.727972			−0.363986	−	0.931404i	$-0.618584\pi$
$577$	−17.4865			−0.727972			−0.363986	+	0.931404i	$0.618584\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.06253	+	15.1616i	0.168542	+	0.629008i
$582$		0			0
$583$	−1.17362	−	2.03278i	−0.0486065	−	0.0841890i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.31081	−	12.3561i	0.136652	−	0.509991i	−0.863334	−	0.504633i	$-0.831628\pi$
$587$	3.31081	−	12.3561i	0.136652	−	0.509991i	0.999986	−	0.00535825i	$-0.00170559\pi$
$588$		0			0
$589$	3.42507	+	12.7825i	0.141128	+	0.526696i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			25.7816i			1.05872i	0.848397	+	0.529361i	$0.177568\pi$
$593$			25.7816i			1.05872i	−0.848397	+	0.529361i	$0.822432\pi$
$594$		0			0
$595$	38.9937	+	38.9937i	1.59858	+	1.59858i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−27.3647	−	15.7990i	−1.11809	−	0.645531i	−0.177180	−	0.984179i	$-0.556697\pi$
$599$	−27.3647	−	15.7990i	−1.11809	−	0.645531i	−0.940913	+	0.338647i	$0.890031\pi$
$600$		0			0
$601$	23.3729	−	13.4944i	0.953401	−	0.550447i	0.0592656	−	0.998242i	$-0.481124\pi$
$601$	23.3729	−	13.4944i	0.953401	−	0.550447i	0.894136	+	0.447796i	$0.147791\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.9585	−	40.8977i	0.445527	−	1.66273i
$606$		0			0
$607$	21.2314	+	12.2579i	0.861755	+	0.497534i	0.864600	−	0.502462i	$-0.167572\pi$
$607$	21.2314	+	12.2579i	0.861755	+	0.497534i	−0.00284471	+	0.999996i	$0.500905\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.34212	+	9.34212i	−0.377942	+	0.377942i
$612$		0			0
$613$	−30.3894	−	30.3894i	−1.22742	−	1.22742i	−0.964937	−	0.262481i	$-0.915459\pi$
$613$	−30.3894	−	30.3894i	−1.22742	−	1.22742i	−0.262481	−	0.964937i	$-0.584541\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.8393	−	27.4345i	0.637668	−	1.10447i	−0.348275	−	0.937392i	$-0.613233\pi$
$617$	15.8393	−	27.4345i	0.637668	−	1.10447i	0.985943	−	0.167081i	$-0.0534341\pi$
$618$		0			0
$619$	20.1312	+	5.39413i	0.809141	+	0.216809i	0.639593	−	0.768713i	$-0.279103\pi$
$619$	20.1312	+	5.39413i	0.809141	+	0.216809i	0.169547	+	0.985522i	$0.445769\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.98242	+	8.62981i	0.199617	+	0.345746i
$624$		0			0
$625$	12.0944	−	20.9481i	0.483775	−	0.837923i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	11.3007	−	11.3007i	0.450587	−	0.450587i
$630$		0			0
$631$	19.9953			0.796002			0.398001	−	0.917385i	$-0.369704\pi$
$631$	19.9953			0.796002			0.398001	+	0.917385i	$0.369704\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	50.0494	−	13.4107i	1.98615	−	0.532187i
$636$		0			0
$637$	−11.7335	−	3.14400i	−0.464900	−	0.124570i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.6976	+	7.33098i	−0.501526	+	0.289556i	−0.729344	−	0.684148i	$-0.760174\pi$
$641$	−12.6976	+	7.33098i	−0.501526	+	0.289556i	0.227818	+	0.973704i	$0.426841\pi$
$642$		0			0
$643$	−12.8777	+	3.45056i	−0.507846	+	0.136077i	−0.503639	−	0.863914i	$-0.668006\pi$
$643$	−12.8777	+	3.45056i	−0.507846	+	0.136077i	−0.00420705	+	0.999991i	$0.501339\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	30.5078i		−	1.19939i	−0.800231	−	0.599693i	$-0.795290\pi$
$647$		−	30.5078i		−	1.19939i	0.800231	−	0.599693i	$-0.204710\pi$
$648$		0			0
$649$			1.21078i			0.0475272i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.1465	+	5.39824i	−0.788394	+	0.211249i	−0.630482	−	0.776204i	$-0.717143\pi$
$653$	−20.1465	+	5.39824i	−0.788394	+	0.211249i	−0.157912	+	0.987453i	$0.550476\pi$
$654$		0			0
$655$	2.19305	−	1.26616i	0.0856896	−	0.0494729i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.5728	−	3.90477i	−0.567676	−	0.152108i	−0.0364452	−	0.999336i	$-0.511603\pi$
$659$	−14.5728	−	3.90477i	−0.567676	−	0.152108i	−0.531230	+	0.847227i	$0.678270\pi$
$660$		0			0
$661$	−9.11835	+	2.44325i	−0.354663	+	0.0950316i	−0.431751	−	0.901993i	$-0.642104\pi$
$661$	−9.11835	+	2.44325i	−0.354663	+	0.0950316i	0.0770887	+	0.997024i	$0.475438\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	20.6706			0.801570
$666$		0			0
$667$	−5.73833	+	5.73833i	−0.222189	+	0.222189i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.985698	−	1.70728i	0.0380525	−	0.0659088i
$672$		0			0
$673$	−16.1140	−	27.9103i	−0.621149	−	1.07586i	−0.989272	−	0.146085i	$-0.953333\pi$
$673$	−16.1140	−	27.9103i	−0.621149	−	1.07586i	0.368123	−	0.929777i	$-0.380001\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.5364	+	4.16296i	0.597111	+	0.159996i	0.544701	−	0.838630i	$-0.316643\pi$
$677$	15.5364	+	4.16296i	0.597111	+	0.159996i	0.0524101	+	0.998626i	$0.483310\pi$
$678$		0			0
$679$	25.7025	−	44.5181i	0.986372	−	1.70845i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	28.6734	+	28.6734i	1.09716	+	1.09716i	0.994742	+	0.102416i	$0.0326571\pi$
$683$	28.6734	+	28.6734i	1.09716	+	1.09716i	0.102416	+	0.994742i	$0.467343\pi$
$684$		0			0
$685$	−57.5322	+	57.5322i	−2.19819	+	2.19819i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	26.1058	+	15.0722i	0.994552	+	0.574205i
$690$		0			0
$691$	11.8033	−	44.0504i	0.449017	−	1.67575i	−0.256089	−	0.966653i	$-0.582434\pi$
$691$	11.8033	−	44.0504i	0.449017	−	1.67575i	0.705106	−	0.709102i	$-0.250899\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.3358	−	12.8956i	0.847243	−	0.489156i
$696$		0			0
$697$	12.5111	+	7.22328i	0.473892	+	0.273601i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−13.0178	−	13.0178i	−0.491676	−	0.491676i	0.417158	−	0.908834i	$-0.363026\pi$
$701$	−13.0178	−	13.0178i	−0.491676	−	0.491676i	−0.908834	+	0.417158i	$0.863026\pi$
$702$		0			0
$703$		−	5.99049i		−	0.225935i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.116919	−	0.436349i	−0.00439721	−	0.0164106i
$708$		0			0
$709$	4.39011	−	16.3841i	0.164874	−	0.615319i	−0.833182	−	0.552999i	$-0.813483\pi$
$709$	4.39011	−	16.3841i	0.164874	−	0.615319i	0.998056	−	0.0623199i	$-0.0198499\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.0285	+	27.7622i	0.600273	+	1.03970i
$714$		0			0
$715$	−0.615660	−	2.29767i	−0.0230244	−	0.0859282i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	43.0731			1.60635			0.803177	−	0.595740i	$-0.203141\pi$
$719$	43.0731			1.60635			0.803177	+	0.595740i	$0.203141\pi$
$720$		0			0
$721$	27.5313			1.02532
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.42673	−	20.2528i	−0.201544	−	0.752171i
$726$		0			0
$727$	−15.3101	−	26.5179i	−0.567821	−	0.983495i	−0.996781	−	0.0801716i	$-0.974453\pi$
$727$	−15.3101	−	26.5179i	−0.567821	−	0.983495i	0.428960	−	0.903324i	$-0.358880\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.32737	−	19.8820i	0.197040	−	0.735363i
$732$		0			0
$733$	0.679676	+	2.53658i	0.0251044	+	0.0936909i	0.977341	−	0.211669i	$-0.0678899\pi$
$733$	0.679676	+	2.53658i	0.0251044	+	0.0936909i	−0.952237	+	0.305360i	$0.901223\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1.17271i		−	0.0431972i
$738$		0			0
$739$	−13.1402	−	13.1402i	−0.483370	−	0.483370i	0.422836	−	0.906206i	$-0.361035\pi$
$739$	−13.1402	−	13.1402i	−0.483370	−	0.483370i	−0.906206	+	0.422836i	$0.861035\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.79055	−	1.03378i	−0.0656890	−	0.0379255i	0.466796	−	0.884365i	$-0.345408\pi$
$743$	−1.79055	−	1.03378i	−0.0656890	−	0.0379255i	−0.532485	+	0.846440i	$0.678742\pi$
$744$		0			0
$745$	74.7897	−	43.1798i	2.74008	−	1.58199i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.2077	+	38.0958i	−0.372982	+	1.39199i
$750$		0			0
$751$	7.86676	+	4.54188i	0.287062	+	0.165735i	0.636616	−	0.771181i	$-0.280334\pi$
$751$	7.86676	+	4.54188i	0.287062	+	0.165735i	−0.349554	+	0.936916i	$0.613667\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	54.5367	−	54.5367i	1.98479	−	1.98479i
$756$		0			0
$757$	18.3910	+	18.3910i	0.668433	+	0.668433i	0.957353	−	0.288920i	$-0.0932961\pi$
$757$	18.3910	+	18.3910i	0.668433	+	0.668433i	−0.288920	+	0.957353i	$0.593296\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.1080	−	24.4358i	0.511415	−	0.885797i	−0.488497	−	0.872565i	$-0.662455\pi$
$761$	14.1080	−	24.4358i	0.511415	−	0.885797i	0.999912	−	0.0132318i	$-0.00421194\pi$
$762$		0			0
$763$	29.0160	+	7.77481i	1.05045	+	0.281467i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.77467	−	13.4661i	−0.280727	−	0.486234i
$768$		0			0
$769$	−14.6064	+	25.2991i	−0.526722	+	0.912309i	0.472794	+	0.881173i	$0.343246\pi$
$769$	−14.6064	+	25.2991i	−0.526722	+	0.912309i	−0.999515	+	0.0311354i	$0.990088\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.5491	−	10.5491i	0.379425	−	0.379425i	−0.491470	−	0.870895i	$-0.663540\pi$
$773$	10.5491	−	10.5491i	0.379425	−	0.379425i	0.870895	+	0.491470i	$0.163540\pi$
$774$		0			0
$775$	−82.8256			−2.97518
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.23060	−	1.40154i	0.187406	−	0.0502152i
$780$		0			0
$781$	1.59335	+	0.426938i	0.0570146	+	0.0152770i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	49.8924	−	28.8054i	1.78074	−	1.02811i
$786$		0			0
$787$	−33.8023	+	9.05729i	−1.20492	+	0.322857i	−0.804767	−	0.593591i	$-0.797710\pi$
$787$	−33.8023	+	9.05729i	−1.20492	+	0.322857i	−0.400153	+	0.916448i	$0.631043\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	56.9431i		−	2.02466i
$792$		0			0
$793$			25.3175i			0.899052i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	27.6668	−	7.41329i	0.980007	−	0.262592i	0.266959	−	0.963708i	$-0.413981\pi$
$797$	27.6668	−	7.41329i	0.980007	−	0.262592i	0.713048	+	0.701116i	$0.247314\pi$
$798$		0			0
$799$	−17.2554	+	9.96243i	−0.610453	+	0.352445i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.682165	+	0.182786i	0.0240731	+	0.00645036i
$804$		0			0
$805$	48.3667	−	12.9598i	1.70470	−	0.456773i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	39.9831			1.40573			0.702865	−	0.711323i	$-0.251904\pi$
$809$	39.9831			1.40573			0.702865	+	0.711323i	$0.251904\pi$
$810$		0			0
$811$	33.5121	−	33.5121i	1.17677	−	1.17677i	0.196204	−	0.980563i	$-0.437138\pi$
$811$	33.5121	−	33.5121i	1.17677	−	1.17677i	0.980563	−	0.196204i	$-0.0628616\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.9123	−	20.6328i	0.417271	−	0.722734i
$816$		0			0
$817$	−3.85771	−	6.68176i	−0.134964	−	0.233765i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.8942	+	2.91908i	0.380209	+	0.101877i	0.443861	−	0.896096i	$-0.353608\pi$
$821$	10.8942	+	2.91908i	0.380209	+	0.101877i	−0.0636527	+	0.997972i	$0.520275\pi$
$822$		0			0
$823$	−27.4702	+	47.5798i	−0.957551	+	1.65853i	−0.229131	+	0.973396i	$0.573588\pi$
$823$	−27.4702	+	47.5798i	−0.957551	+	1.65853i	−0.728420	+	0.685131i	$0.759745\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.2104	+	14.2104i	0.494144	+	0.494144i	0.909609	−	0.415465i	$-0.136381\pi$
$827$	14.2104	+	14.2104i	0.494144	+	0.494144i	−0.415465	+	0.909609i	$0.636381\pi$
$828$		0			0
$829$	6.15512	−	6.15512i	0.213776	−	0.213776i	−0.592093	−	0.805869i	$-0.701698\pi$
$829$	6.15512	−	6.15512i	0.213776	−	0.213776i	0.805869	+	0.592093i	$0.201698\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.8654	−	9.15989i	−0.549704	−	0.317371i
$834$		0			0
$835$	−13.7435	+	51.2913i	−0.475612	+	1.77501i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.5384	+	12.4352i	−0.743590	+	0.429312i	−0.823373	−	0.567500i	$-0.807911\pi$
$839$	−21.5384	+	12.4352i	−0.743590	+	0.429312i	0.0797833	+	0.996812i	$0.474577\pi$
$840$		0			0
$841$	21.2658	+	12.2778i	0.733303	+	0.423373i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.9363	−	13.9363i	−0.479424	−	0.479424i
$846$		0			0
$847$			36.8507i			1.26621i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.75585	−	14.0170i	−0.128749	−	0.480497i
$852$		0			0
$853$	−5.05023	+	18.8477i	−0.172917	+	0.645334i	0.823980	+	0.566618i	$0.191749\pi$
$853$	−5.05023	+	18.8477i	−0.172917	+	0.645334i	−0.996897	+	0.0787157i	$0.974918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	18.6982	+	32.3862i	0.638717	+	1.10629i	0.985715	+	0.168424i	$0.0538679\pi$
$857$	18.6982	+	32.3862i	0.638717	+	1.10629i	−0.346998	+	0.937866i	$0.612799\pi$
$858$		0			0
$859$	7.10549	+	26.5180i	0.242436	+	0.904784i	0.974655	+	0.223714i	$0.0718182\pi$
$859$	7.10549	+	26.5180i	0.242436	+	0.904784i	−0.732219	+	0.681070i	$0.761515\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.1797			−0.346520			−0.173260	−	0.984876i	$-0.555430\pi$
$863$	−10.1797			−0.346520			−0.173260	+	0.984876i	$0.555430\pi$
$864$		0			0
$865$	20.9860			0.713545
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.326156	−	1.21723i	−0.0110641	−	0.0412918i
$870$		0			0
$871$	7.53020	+	13.0427i	0.255151	+	0.441935i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−16.6507	+	62.1414i	−0.562897	+	2.10076i
$876$		0			0
$877$	−6.90717	−	25.7779i	−0.233239	−	0.870458i	−0.978935	−	0.204172i	$-0.934550\pi$
$877$	−6.90717	−	25.7779i	−0.233239	−	0.870458i	0.745696	−	0.666286i	$-0.232117\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	30.7798i		−	1.03700i	−0.855078	−	0.518499i	$-0.826491\pi$
$881$		−	30.7798i		−	1.03700i	0.855078	−	0.518499i	$-0.173509\pi$
$882$		0			0
$883$	19.8089	+	19.8089i	0.666622	+	0.666622i	0.956933	−	0.290310i	$-0.0937586\pi$
$883$	19.8089	+	19.8089i	0.666622	+	0.666622i	−0.290310	+	0.956933i	$0.593759\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.0940	+	12.1786i	0.708266	+	0.408918i	0.810419	−	0.585851i	$-0.199240\pi$
$887$	21.0940	+	12.1786i	0.708266	+	0.408918i	−0.102153	+	0.994769i	$0.532573\pi$
$888$		0			0
$889$	−39.0550	+	22.5484i	−1.30986	+	0.756249i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.93301	+	7.21410i	−0.0646858	+	0.241411i
$894$		0			0
$895$	−1.79985	−	1.03914i	−0.0601624	−	0.0347348i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.4142	+	12.4142i	−0.414037	+	0.414037i
$900$		0			0
$901$	32.1460	+	32.1460i	1.07094	+	1.07094i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13.6407	+	23.6264i	−0.453433	+	0.785369i
$906$		0			0
$907$	−56.0698	−	15.0239i	−1.86177	−	0.498859i	−0.861802	−	0.507245i	$-0.830664\pi$
$907$	−56.0698	−	15.0239i	−1.86177	−	0.498859i	−0.999965	+	0.00838605i	$0.997331\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.9347	+	20.6715i	0.395414	+	0.684877i	0.993154	−	0.116813i	$-0.0372678\pi$
$911$	11.9347	+	20.6715i	0.395414	+	0.684877i	−0.597740	+	0.801690i	$0.703934\pi$
$912$		0			0
$913$	0.510553	−	0.884303i	0.0168968	−	0.0292662i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.55845	+	1.55845i	−0.0514646	+	0.0514646i
$918$		0			0
$919$	15.7779			0.520466			0.260233	−	0.965546i	$-0.416201\pi$
$919$	15.7779			0.520466			0.260233	+	0.965546i	$0.416201\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−20.4625	+	5.48292i	−0.673533	+	0.180473i
$924$		0			0
$925$	36.2157	+	9.70397i	1.19077	+	0.319065i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.3132	+	8.26371i	−0.469600	+	0.271123i	−0.716072	−	0.698026i	$-0.754062\pi$
$929$	−14.3132	+	8.26371i	−0.469600	+	0.271123i	0.246472	+	0.969150i	$0.420729\pi$
$930$		0			0
$931$	−6.63296	+	1.77730i	−0.217387	+	0.0582485i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	3.58740i		−	0.117320i
$936$		0			0
$937$		−	5.92940i		−	0.193705i	−0.995299	−	0.0968526i	$-0.969122\pi$
$937$		−	5.92940i		−	0.193705i	0.995299	−	0.0968526i	$-0.0308775\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.6096	−	5.52232i	0.671853	−	0.180022i	0.0932635	−	0.995641i	$-0.470270\pi$
$941$	20.6096	−	5.52232i	0.671853	−	0.180022i	0.578589	+	0.815619i	$0.303603\pi$
$942$		0			0
$943$	11.3603	−	6.55886i	0.369941	−	0.213586i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.9863	−	8.57071i	−1.03942	−	0.278511i	−0.301545	−	0.953452i	$-0.597502\pi$
$947$	−31.9863	−	8.57071i	−1.03942	−	0.278511i	−0.737871	+	0.674941i	$0.764169\pi$
$948$		0			0
$949$	−8.76066	+	2.34741i	−0.284383	+	0.0762002i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.546564			0.0177049			0.00885247	−	0.999961i	$-0.497182\pi$
$953$	0.546564			0.0177049			0.00885247	+	0.999961i	$0.497182\pi$
$954$		0			0
$955$	−29.5538	+	29.5538i	−0.956339	+	0.956339i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	35.4068	−	61.3264i	1.14335	−	1.98033i
$960$		0			0
$961$	19.1758	+	33.2135i	0.618576	+	1.07140i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−19.4213	−	5.20393i	−0.625195	−	0.167521i
$966$		0			0
$967$	7.49046	−	12.9739i	0.240877	−	0.417211i	−0.720087	−	0.693883i	$-0.755898\pi$
$967$	7.49046	−	12.9739i	0.240877	−	0.417211i	0.960964	+	0.276672i	$0.0892316\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−29.4725	−	29.4725i	−0.945816	−	0.945816i	0.0527896	−	0.998606i	$-0.483189\pi$
$971$	−29.4725	−	29.4725i	−0.945816	−	0.945816i	−0.998606	+	0.0527896i	$0.983189\pi$
$972$		0			0
$973$	−15.8725	+	15.8725i	−0.508849	+	0.508849i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.02199	−	1.16740i	−0.0646892	−	0.0373483i	0.467307	−	0.884095i	$-0.345224\pi$
$977$	−2.02199	−	1.16740i	−0.0646892	−	0.0373483i	−0.531996	+	0.846747i	$0.678558\pi$
$978$		0			0
$979$	0.167779	−	0.626159i	0.00536224	−	0.0200121i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.5089	−	12.4182i	0.686029	−	0.396079i	−0.116094	−	0.993238i	$-0.537037\pi$
$983$	21.5089	−	12.4182i	0.686029	−	0.396079i	0.802123	+	0.597159i	$0.203704\pi$
$984$		0			0
$985$	−13.9464	−	8.05197i	−0.444370	−	0.256557i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.2158	−	13.2158i	−0.420240	−	0.420240i
$990$		0			0
$991$			7.12527i			0.226342i	0.993576	+	0.113171i	$0.0361008\pi$
$991$			7.12527i			0.226342i	−0.993576	+	0.113171i	$0.963899\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.57436	+	9.60763i	0.0816126	+	0.304582i
$996$		0			0
$997$	12.7516	−	47.5897i	0.403848	−	1.50718i	−0.402322	−	0.915498i	$-0.631797\pi$
$997$	12.7516	−	47.5897i	0.403848	−	1.50718i	0.806170	−	0.591684i	$-0.201537\pi$
$998$		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.719.1		88
3.2	odd	2		576.2.y.a.527.3		88
4.3	odd	2		432.2.v.a.395.9		88
9.2	odd	6	inner	1728.2.z.a.143.1		88
9.7	even	3		576.2.y.a.335.15		88
12.11	even	2		144.2.u.a.59.14	yes	88
16.3	odd	4	inner	1728.2.z.a.1583.1		88
16.13	even	4		432.2.v.a.179.16		88
36.7	odd	6		144.2.u.a.11.7	✓	88
36.11	even	6		432.2.v.a.251.16		88
48.29	odd	4		144.2.u.a.131.7	yes	88
48.35	even	4		576.2.y.a.239.15		88
144.29	odd	12		432.2.v.a.35.9		88
144.61	even	12		144.2.u.a.83.14	yes	88
144.83	even	12	inner	1728.2.z.a.1007.1		88
144.115	odd	12		576.2.y.a.47.3		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	36.7	odd	6
144.2.u.a.59.14	yes	88	12.11	even	2
144.2.u.a.83.14	yes	88	144.61	even	12
144.2.u.a.131.7	yes	88	48.29	odd	4
432.2.v.a.35.9		88	144.29	odd	12
432.2.v.a.179.16		88	16.13	even	4
432.2.v.a.251.16		88	36.11	even	6
432.2.v.a.395.9		88	4.3	odd	2
576.2.y.a.47.3		88	144.115	odd	12
576.2.y.a.239.15		88	48.35	even	4
576.2.y.a.335.15		88	9.7	even	3
576.2.y.a.527.3		88	3.2	odd	2
1728.2.z.a.143.1		88	9.2	odd	6	inner
1728.2.z.a.719.1		88	1.1	even	1	trivial
1728.2.z.a.1007.1		88	144.83	even	12	inner
1728.2.z.a.1583.1		88	16.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(-1.00059 - 3.73424i) q^{5} +(1.68236 + 2.91393i) q^{7} +(0.0566521 - 0.211428i) q^{11} +(0.727551 + 2.71526i) q^{13} +4.23937i q^{17} +(1.12365 + 1.12365i) q^{19} +(3.33369 + 1.92471i) q^{23} +(-8.61325 + 4.97286i) q^{25} +(-0.545635 + 2.03634i) q^{29} +(7.21206 + 4.16388i) q^{31} +(9.19798 - 9.19798i) q^{35} +(-2.66564 - 2.66564i) q^{37} +(1.70386 - 2.95117i) q^{41} +(-4.68985 - 1.25664i) q^{43} +(2.34998 + 4.07028i) q^{47} +(-2.16067 + 3.74239i) q^{49} +(7.58271 - 7.58271i) q^{53} -0.846209 q^{55} +(-5.34305 + 1.43167i) q^{59} +(8.69958 + 2.33105i) q^{61} +(9.41144 - 5.43370i) q^{65} +(5.17504 - 1.38665i) q^{67} +7.53614i q^{71} +3.22646i q^{73} +(0.711397 - 0.190618i) q^{77} +(4.98587 - 2.87859i) q^{79} +(4.50604 + 1.20739i) q^{83} +(15.8308 - 4.24186i) q^{85} +2.96157 q^{89} +(-6.68807 + 6.68807i) q^{91} +(3.07166 - 5.32027i) q^{95} +(-7.63883 - 13.2308i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 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

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