LMFDB - Embedded newform 1728.2.z.a.1583.1

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			1583.1
Character	$\chi$	$=$	1728.1583
Dual form			1728.2.z.a.143.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$	−3.73424	+	1.00059i	−1.67000	+	0.447476i	−0.965111	−	0.261839i	$-0.915671\pi$
$5$	−3.73424	+	1.00059i	−1.67000	+	0.447476i	−0.704891	+	0.709315i	$0.749004\pi$
$6$		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
$11$	0.211428	+	0.0566521i	0.0637480	+	0.0170812i	0.290552	−	0.956859i	$-0.406161\pi$
$11$	0.211428	+	0.0566521i	0.0637480	+	0.0170812i	−0.226804	+	0.973940i	$0.572828\pi$
$12$		0			0
$13$	−2.71526	+	0.727551i	−0.753076	+	0.201786i	−0.614882	−	0.788619i	$-0.710796\pi$
$13$	−2.71526	+	0.727551i	−0.753076	+	0.201786i	−0.138194	+	0.990405i	$0.544130\pi$
$14$		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	−0.566369	−	0.824152i	$-0.691652\pi$
$19$	1.12365	−	1.12365i	0.257782	−	0.257782i	0.824152	+	0.566369i	$0.191652\pi$
$20$		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
$29$	−2.03634	−	0.545635i	−0.378138	−	0.101322i	0.0647434	−	0.997902i	$-0.479377\pi$
$29$	−2.03634	−	0.545635i	−0.378138	−	0.101322i	−0.442882	+	0.896580i	$0.646044\pi$
$30$		0			0
$31$	−7.21206	−	4.16388i	−1.29532	−	0.747856i	−0.315731	−	0.948849i	$-0.602250\pi$
$31$	−7.21206	−	4.16388i	−1.29532	−	0.747856i	−0.979593	+	0.200993i	$0.935583\pi$
$32$		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	−0.891416	−	0.453187i	$-0.850287\pi$
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	0.453187	+	0.891416i	$0.350287\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.70386	+	2.95117i	−0.266098	+	0.460895i	−0.967851	−	0.251526i	$-0.919068\pi$
$41$	−1.70386	+	2.95117i	−0.266098	+	0.460895i	0.701753	+	0.712420i	$0.252401\pi$
$42$		0			0
$43$	1.25664	−	4.68985i	0.191636	−	0.715195i	−0.801476	−	0.598027i	$-0.795952\pi$
$43$	1.25664	−	4.68985i	0.191636	−	0.715195i	0.993112	−	0.117168i	$-0.0373817\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.34998	−	4.07028i	−0.342779	−	0.593711i	0.642168	−	0.766564i	$-0.278035\pi$
$47$	−2.34998	−	4.07028i	−0.342779	−	0.593711i	−0.984948	+	0.172852i	$0.944702\pi$
$48$		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	−0.999098	−	0.0424680i	$-0.986478\pi$
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.0424680	−	0.999098i	$-0.513522\pi$
$54$		0			0
$55$	−0.846209			−0.114103
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.43167	−	5.34305i	−0.186387	−	0.695605i	−0.994329	−	0.106344i	$-0.966085\pi$
$59$	−1.43167	−	5.34305i	−0.186387	−	0.695605i	0.807942	−	0.589261i	$-0.200581\pi$
$60$		0			0
$61$	−2.33105	+	8.69958i	−0.298460	+	1.11387i	0.639971	+	0.768399i	$0.278946\pi$
$61$	−2.33105	+	8.69958i	−0.298460	+	1.11387i	−0.938431	+	0.345468i	$0.887720\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.41144	−	5.43370i	1.16735	−	0.673967i
$66$		0			0
$67$	−1.38665	−	5.17504i	−0.169406	−	0.632231i	−0.997437	−	0.0715493i	$-0.977206\pi$
$67$	−1.38665	−	5.17504i	−0.169406	−	0.632231i	0.828031	−	0.560682i	$-0.189461\pi$
$68$		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	$-0.939536\pi$
$73$		−	3.22646i		−	0.377629i	0.982013	−	0.188814i	$-0.0604644\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.190618	+	0.711397i	0.0217230	+	0.0810712i
$78$		0			0
$79$	−4.98587	+	2.87859i	−0.560954	+	0.323867i	−0.753528	−	0.657415i	$-0.771650\pi$
$79$	−4.98587	+	2.87859i	−0.560954	+	0.323867i	0.192574	+	0.981282i	$0.438316\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.20739	−	4.50604i	0.132528	−	0.494602i	−0.867468	−	0.497494i	$-0.834254\pi$
$83$	1.20739	−	4.50604i	0.132528	−	0.494602i	0.999996	+	0.00289160i	$0.000920425\pi$
$84$		0			0
$85$	−4.24186	−	15.8308i	−0.460094	−	1.71710i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.96157			−0.313926			−0.156963	−	0.987605i	$-0.550170\pi$
$89$	−2.96157			−0.313926			−0.156963	+	0.987605i	$0.550170\pi$
$90$		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
$101$	−0.0347486	+	0.129684i	−0.00345762	+	0.0129040i	−0.967633	−	0.252361i	$-0.918793\pi$
$101$	−0.0347486	+	0.129684i	−0.00345762	+	0.0129040i	0.964175	+	0.265265i	$0.0854595\pi$
$102$		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	$-0.941734\pi$
$107$	−8.28837	+	8.28837i	−0.801267	+	0.801267i	0.182027	+	0.983294i	$0.441734\pi$
$108$		0			0
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	0.941547	−	0.336881i	$-0.109372\pi$
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	−0.336881	+	0.941547i	$0.609372\pi$
$110$		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
$115$	−14.3746	−	3.85167i	−1.34044	−	0.359171i
$116$		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	$-0.797289\pi$
$127$		−	13.4028i		−	1.18931i	0.803981	−	0.594654i	$-0.202711\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.632708	−	0.169534i	0.0552800	−	0.0148122i	−0.231073	−	0.972936i	$-0.574224\pi$
$131$	0.632708	−	0.169534i	0.0552800	−	0.0148122i	0.286353	+	0.958124i	$0.407557\pi$
$132$		0			0
$133$	5.16461	+	1.38385i	0.447829	+	0.119995i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.5230	+	18.2263i	0.899037	+	1.55718i	0.828727	+	0.559652i	$0.189065\pi$
$137$	10.5230	+	18.2263i	0.899037	+	1.55718i	0.0703095	+	0.997525i	$0.477601\pi$
$138$		0			0
$139$	−6.44400	+	1.72666i	−0.546573	+	0.146454i	−0.521530	−	0.853233i	$-0.674639\pi$
$139$	−6.44400	+	1.72666i	−0.546573	+	0.146454i	−0.0250423	+	0.999686i	$0.507972\pi$
$140$		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
$149$	21.5773	−	5.78161i	1.76768	−	0.473648i	0.779428	−	0.626492i	$-0.215510\pi$
$149$	21.5773	−	5.78161i	1.76768	−	0.473648i	0.988250	+	0.152844i	$0.0488431\pi$
$150$		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
$155$	31.0979	+	8.33265i	2.49784	+	0.669295i
$156$		0			0
$157$	−14.3943	+	3.85693i	−1.14879	+	0.307817i	−0.782479	−	0.622677i	$-0.786045\pi$
$157$	−14.3943	+	3.85693i	−1.14879	+	0.307817i	−0.366308	+	0.930494i	$0.619378\pi$
$158$		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	−0.515545	−	0.856863i	$-0.672410\pi$
$163$	4.35766	−	4.35766i	0.341318	−	0.341318i	0.856863	+	0.515545i	$0.172410\pi$
$164$		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
$173$	−5.24342	−	1.40497i	−0.398650	−	0.106818i	0.0539235	−	0.998545i	$-0.482827\pi$
$173$	−5.24342	−	1.40497i	−0.398650	−	0.106818i	−0.452573	+	0.891727i	$0.649494\pi$
$174$		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	$-0.256395\pi$
$179$	−0.380130	−	0.380130i	−0.0284123	−	0.0284123i	−0.721170	+	0.692758i	$0.756395\pi$
$180$		0			0
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	−0.867804	−	0.496906i	$-0.834469\pi$
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	0.496906	+	0.867804i	$0.334469\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.28695	−	12.6214i	0.535747	−	0.927941i
$186$		0			0
$187$	−0.240169	+	0.896324i	−0.0175629	+	0.0655457i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.40555	+	9.36269i	0.391132	+	0.677461i	0.992599	−	0.121437i	$-0.0387502\pi$
$191$	5.40555	+	9.36269i	0.391132	+	0.677461i	−0.601467	+	0.798898i	$0.705417\pi$
$192$		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	$-0.297410\pi$
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	−0.804207	+	0.594349i	$0.797410\pi$
$198$		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
$203$	−1.83591	−	6.85170i	−0.128856	−	0.480895i
$204$		0			0
$205$	3.40971	−	12.7252i	0.238145	−	0.888768i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.301228	−	0.173914i	0.0208364	−	0.0120299i
$210$		0			0
$211$	4.70786	+	17.5700i	0.324103	+	1.20957i	0.915211	+	0.402975i	$0.132024\pi$
$211$	4.70786	+	17.5700i	0.324103	+	1.20957i	−0.591108	+	0.806592i	$0.701309\pi$
$212$		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
$221$	−3.08436	−	11.5110i	−0.207476	−	0.774312i
$222$		0			0
$223$	2.82059	−	1.62847i	0.188881	−	0.109050i	−0.402578	−	0.915386i	$-0.631886\pi$
$223$	2.82059	−	1.62847i	0.188881	−	0.109050i	0.591458	+	0.806336i	$0.298552\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.36663	+	8.83238i	−0.157079	+	0.586226i	0.841840	+	0.539728i	$0.181473\pi$
$227$	−2.36663	+	8.83238i	−0.157079	+	0.586226i	−0.998918	+	0.0464979i	$0.985194\pi$
$228$		0			0
$229$	1.36053	+	5.07755i	0.0899061	+	0.335534i	0.996198	−	0.0871183i	$-0.0277658\pi$
$229$	1.36053	+	5.07755i	0.0899061	+	0.335534i	−0.906292	+	0.422652i	$0.861099\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.1506			0.927034			0.463517	−	0.886088i	$-0.346587\pi$
$233$	14.1506			0.927034			0.463517	+	0.886088i	$0.346587\pi$
$234$		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	−0.513745	−	0.857943i	$-0.671742\pi$
$239$	7.51536	−	13.0170i	0.486128	−	0.841999i	0.999873	+	0.0159444i	$0.00507546\pi$
$240$		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
$245$	4.32388	−	16.1369i	0.276242	−	1.03095i
$246$		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	$-0.698667\pi$
$251$	3.59758	−	3.59758i	0.227077	−	0.227077i	0.811471	+	0.584393i	$0.198667\pi$
$252$		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
$259$	−12.2521	−	3.28294i	−0.761307	−	0.203992i
$260$		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	$-0.853861\pi$
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	0.443148	+	0.896448i	$0.353861\pi$
$270$		0			0
$271$		−	11.8875i		−	0.722111i	−0.932544	−	0.361056i	$-0.882416\pi$
$271$		−	11.8875i		−	0.722111i	0.932544	−	0.361056i	$-0.117584\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.10281	−	0.563445i	0.126804	−	0.0339770i
$276$		0			0
$277$	−10.0081	−	2.68166i	−0.601329	−	0.161126i	−0.0547032	−	0.998503i	$-0.517421\pi$
$277$	−10.0081	−	2.68166i	−0.601329	−	0.161126i	−0.546626	+	0.837377i	$0.684088\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.05630	−	12.2219i	−0.420944	−	0.729096i	0.575088	−	0.818091i	$-0.304968\pi$
$281$	−7.05630	−	12.2219i	−0.420944	−	0.729096i	−0.996032	+	0.0889955i	$0.971634\pi$
$282$		0			0
$283$	12.7951	−	3.42843i	0.760588	−	0.203799i	0.142378	−	0.989812i	$-0.454525\pi$
$283$	12.7951	−	3.42843i	0.760588	−	0.203799i	0.618209	+	0.786013i	$0.287858\pi$
$284$		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
$293$	−29.7073	+	7.96005i	−1.73552	+	0.465031i	−0.981443	−	0.191756i	$-0.938582\pi$
$293$	−29.7073	+	7.96005i	−1.73552	+	0.465031i	−0.754077	+	0.656787i	$0.771915\pi$
$294$		0			0
$295$	10.6924	+	18.5197i	0.622533	+	1.07826i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.4522	−	2.80065i	−0.604463	−	0.161965i
$300$		0			0
$301$	15.7800	−	4.22825i	0.909546	−	0.243712i
$302$		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	−0.483758	+	0.875202i	$0.660728\pi$
$307$	−23.8109	+	23.8109i	−1.35896	+	1.35896i	−0.875202	+	0.483758i	$0.839272\pi$
$308$		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	−0.886990	−	0.461788i	$-0.847208\pi$
$313$	−16.4634	+	9.50514i	−0.930565	+	0.537262i	−0.0435750	+	0.999050i	$0.513875\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.8751	+	3.18193i	0.666972	+	0.178715i	0.576391	−	0.817174i	$-0.304461\pi$
$317$	11.8751	+	3.18193i	0.666972	+	0.178715i	0.0905818	+	0.995889i	$0.471127\pi$
$318$		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
$331$	8.94844	−	33.3960i	0.491851	−	1.83561i	−0.0551468	−	0.998478i	$-0.517563\pi$
$331$	8.94844	−	33.3960i	0.491851	−	1.83561i	0.546998	−	0.837134i	$-0.315771\pi$
$332$		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
$347$	−2.92992	−	10.9346i	−0.157287	−	0.587002i	−0.998899	−	0.0469191i	$-0.985060\pi$
$347$	−2.92992	−	10.9346i	−0.157287	−	0.587002i	0.841612	−	0.540082i	$-0.181607\pi$
$348$		0			0
$349$	−2.90715	+	10.8496i	−0.155616	+	0.580767i	0.843436	+	0.537230i	$0.180529\pi$
$349$	−2.90715	+	10.8496i	−0.155616	+	0.580767i	−0.999052	+	0.0435372i	$0.986137\pi$
$350$		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
$355$	−7.54056	−	28.1417i	−0.400211	−	1.49361i
$356$		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
$365$	3.22835	+	12.0484i	0.168980	+	0.630641i
$366$		0			0
$367$	−20.1365	+	11.6258i	−1.05112	+	0.606863i	−0.922962	−	0.384891i	$-0.874239\pi$
$367$	−20.1365	+	11.6258i	−1.05112	+	0.606863i	−0.128156	+	0.991754i	$0.540906\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.33867	−	34.8524i	0.484839	−	1.80945i
$372$		0			0
$373$	−2.66079	−	9.93021i	−0.137771	−	0.514167i	−0.999971	−	0.00759967i	$-0.997581\pi$
$373$	−2.66079	−	9.93021i	−0.137771	−	0.514167i	0.862201	−	0.506567i	$-0.169086\pi$
$374$		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	0.847156	−	0.531345i	$-0.178313\pi$
$379$	6.14819	+	6.14819i	0.315811	+	0.315811i	−0.531345	+	0.847156i	$0.678313\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.40170	−	2.42782i	0.0716238	−	0.124056i	−0.827989	−	0.560744i	$-0.810515\pi$
$383$	1.40170	−	2.42782i	0.0716238	−	0.124056i	0.899613	+	0.436688i	$0.143849\pi$
$384$		0			0
$385$	−1.42363	−	2.46580i	−0.0725548	−	0.125669i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.82350	+	29.1977i	−0.396667	+	1.48038i	0.422255	+	0.906477i	$0.361239\pi$
$389$	−7.82350	+	29.1977i	−0.396667	+	1.48038i	−0.818922	+	0.573905i	$0.805428\pi$
$390$		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	0.754530	−	0.656266i	$-0.227865\pi$
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	−0.656266	+	0.754530i	$0.727865\pi$
$398$		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
$403$	22.6120	+	6.05887i	1.12638	+	0.301814i
$404$		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	0.944470	−	0.328598i	$-0.106576\pi$
$409$	22.8959	+	13.2190i	1.13213	+	0.653636i	0.187660	+	0.982234i	$0.439910\pi$
$410$		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
$419$	−0.499479	+	0.133835i	−0.0244012	+	0.00653827i	−0.270999	−	0.962580i	$-0.587354\pi$
$419$	−0.499479	+	0.133835i	−0.0244012	+	0.00653827i	0.246598	+	0.969118i	$0.420687\pi$
$420$		0			0
$421$	12.8514	+	3.44352i	0.626339	+	0.167827i	0.558008	−	0.829836i	$-0.311566\pi$
$421$	12.8514	+	3.44352i	0.626339	+	0.167827i	0.0683313	+	0.997663i	$0.478233\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	21.0818	+	36.5148i	1.02262	+	1.77123i
$426$		0			0
$427$	−29.2717	+	7.84332i	−1.41655	+	0.379565i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.61129			−0.414791			−0.207396	−	0.978257i	$-0.566499\pi$
$431$	−8.61129			−0.414791			−0.207396	+	0.978257i	$0.566499\pi$
$432$		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
$437$	5.90859	−	1.58320i	0.282646	−	0.0757348i
$438$		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
$443$	−31.1860	−	8.35627i	−1.48169	−	0.397018i	−0.574770	−	0.818315i	$-0.694908\pi$
$443$	−31.1860	−	8.35627i	−1.48169	−	0.397018i	−0.906923	+	0.421297i	$0.861575\pi$
$444$		0			0
$445$	11.0592	−	2.96330i	0.524257	−	0.140474i
$446$		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	−0.160246	−	0.987077i	$-0.551229\pi$
$457$	13.1358	−	7.58393i	0.614465	−	0.354761i	0.774711	+	0.632316i	$0.217895\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.5696	+	3.10006i	0.538849	+	0.144384i	0.517971	−	0.855398i	$-0.326687\pi$
$461$	11.5696	+	3.10006i	0.538849	+	0.144384i	0.0208774	+	0.999782i	$0.493354\pi$
$462$		0			0
$463$	2.03363	+	1.17412i	0.0945107	+	0.0545658i	0.546510	−	0.837452i	$-0.315956\pi$
$463$	2.03363	+	1.17412i	0.0945107	+	0.0545658i	−0.452000	+	0.892018i	$0.649289\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.1509	+	24.1509i	1.11757	+	1.11757i	0.992097	+	0.125473i	$0.0400449\pi$
$467$	24.1509	+	24.1509i	1.11757	+	1.11757i	0.125473	+	0.992097i	$0.459955\pi$
$468$		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
$475$	4.09051	−	15.2660i	0.187685	−	0.700452i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.40917	−	4.17281i	−0.110078	−	0.190660i	0.805724	−	0.592292i	$-0.201777\pi$
$479$	−2.40917	−	4.17281i	−0.110078	−	0.190660i	−0.915801	+	0.401631i	$0.868443\pi$
$480$		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
$491$	−0.504576	−	1.88310i	−0.0227712	−	0.0849832i	0.953605	−	0.301060i	$-0.0973405\pi$
$491$	−0.504576	−	1.88310i	−0.0227712	−	0.0849832i	−0.976376	+	0.216077i	$0.930674\pi$
$492$		0			0
$493$	2.31315	−	8.63279i	0.104179	−	0.388801i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.9598	+	12.6785i	−0.985032	+	0.568708i
$498$		0			0
$499$	2.91509	+	10.8793i	0.130497	+	0.487023i	0.999976	−	0.00694794i	$-0.00221162\pi$
$499$	2.91509	+	10.8793i	0.130497	+	0.487023i	−0.869478	+	0.493971i	$0.835545\pi$
$500$		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
$509$	−8.59758	−	32.0866i	−0.381081	−	1.42221i	−0.844253	−	0.535945i	$-0.819955\pi$
$509$	−8.59758	−	32.0866i	−0.381081	−	1.42221i	0.463172	−	0.886269i	$-0.346711\pi$
$510$		0			0
$511$	9.40169	−	5.42807i	0.415906	−	0.240124i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.18713	+	30.5548i	−0.360768	+	1.34641i
$516$		0			0
$517$	−0.266262	−	0.993703i	−0.0117102	−	0.0437030i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.5032			−0.898262			−0.449131	−	0.893466i	$-0.648266\pi$
$521$	−20.5032			−0.898262			−0.449131	+	0.893466i	$0.648266\pi$
$522$		0			0
$523$	29.2406	+	29.2406i	1.27860	+	1.27860i	0.941451	+	0.337151i	$0.109463\pi$
$523$	29.2406	+	29.2406i	1.27860	+	1.27860i	0.337151	+	0.941451i	$0.390537\pi$
$524$		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
$533$	2.47928	−	9.25281i	0.107390	−	0.400784i
$534$		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	0.994033	−	0.109077i	$-0.0347895\pi$
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	−0.109077	+	0.994033i	$0.534790\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−29.8905	−	17.2573i	−1.28037	−	0.739221i
$546$		0			0
$547$	38.0779	+	10.2029i	1.62809	+	0.436246i	0.953365	−	0.301821i	$-0.0975945\pi$
$547$	38.0779	+	10.2029i	1.62809	+	0.436246i	0.674728	+	0.738067i	$0.264261\pi$
$548$		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	$-0.764529\pi$
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	0.674107	+	0.738634i	$0.264529\pi$
$558$		0			0
$559$			13.6484i			0.577266i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.85715	+	1.30147i	−0.204705	+	0.0548504i	−0.359714	−	0.933063i	$-0.617126\pi$
$563$	−4.85715	+	1.30147i	−0.204705	+	0.0548504i	0.155010	+	0.987913i	$0.450459\pi$
$564$		0			0
$565$	63.1966	+	16.9335i	2.65870	+	0.712397i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.4710	−	30.2606i	−0.732421	−	1.26859i	−0.955846	−	0.293869i	$-0.905057\pi$
$569$	−17.4710	−	30.2606i	−0.732421	−	1.26859i	0.223425	−	0.974721i	$-0.428276\pi$
$570$		0			0
$571$	−34.1869	+	9.16034i	−1.43068	+	0.383348i	−0.889258	−	0.457406i	$-0.848779\pi$
$571$	−34.1869	+	9.16034i	−1.43068	+	0.383348i	−0.541417	+	0.840754i	$0.682112\pi$
$572$		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
$581$	15.1616	−	4.06253i	0.629008	−	0.168542i
$582$		0			0
$583$	−1.17362	−	2.03278i	−0.0486065	−	0.0841890i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.3561	+	3.31081i	0.509991	+	0.136652i	0.504633	−	0.863334i	$-0.331628\pi$
$587$	12.3561	+	3.31081i	0.509991	+	0.136652i	0.00535825	+	0.999986i	$0.498294\pi$
$588$		0			0
$589$	−12.7825	+	3.42507i	−0.526696	+	0.141128i
$590$		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	−0.894136	−	0.447796i	$-0.852209\pi$
$601$	−23.3729	+	13.4944i	−0.953401	+	0.550447i	−0.0592656	+	0.998242i	$0.518876\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	40.8977	+	10.9585i	1.66273	+	0.445527i
$606$		0			0
$607$	−21.2314	−	12.2579i	−0.861755	−	0.497534i	0.00284471	−	0.999996i	$-0.499095\pi$
$607$	−21.2314	−	12.2579i	−0.861755	−	0.497534i	−0.864600	+	0.502462i	$0.832428\pi$
$608$		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	−0.262481	+	0.964937i	$0.584541\pi$
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.964937	+	0.262481i	$0.915459\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.8393	+	27.4345i	−0.637668	+	1.10447i	0.348275	+	0.937392i	$0.386767\pi$
$617$	−15.8393	+	27.4345i	−0.637668	+	1.10447i	−0.985943	+	0.167081i	$0.946566\pi$
$618$		0			0
$619$	−5.39413	+	20.1312i	−0.216809	+	0.809141i	0.768713	+	0.639593i	$0.220897\pi$
$619$	−5.39413	+	20.1312i	−0.216809	+	0.809141i	−0.985522	+	0.169547i	$0.945769\pi$
$620$		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
$635$	13.4107	+	50.0494i	0.532187	+	1.98615i
$636$		0			0
$637$	3.14400	−	11.7335i	0.124570	−	0.464900i
$638$		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
$643$	3.45056	+	12.8777i	0.136077	+	0.507846i	0.999991	+	0.00420705i	$0.00133915\pi$
$643$	3.45056	+	12.8777i	0.136077	+	0.507846i	−0.863914	+	0.503639i	$0.831994\pi$
$644$		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
$653$	−5.39824	−	20.1465i	−0.211249	−	0.788394i	−0.987453	−	0.157912i	$-0.949524\pi$
$653$	−5.39824	−	20.1465i	−0.211249	−	0.788394i	0.776204	−	0.630482i	$-0.217143\pi$
$654$		0			0
$655$	−2.19305	+	1.26616i	−0.0856896	+	0.0494729i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.90477	+	14.5728i	−0.152108	+	0.567676i	0.847227	+	0.531230i	$0.178270\pi$
$659$	−3.90477	+	14.5728i	−0.152108	+	0.567676i	−0.999336	+	0.0364452i	$0.988397\pi$
$660$		0			0
$661$	2.44325	+	9.11835i	0.0950316	+	0.354663i	0.997024	−	0.0770887i	$-0.0245625\pi$
$661$	2.44325	+	9.11835i	0.0950316	+	0.354663i	−0.901993	+	0.431751i	$0.857896\pi$
$662$		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
$677$	4.16296	−	15.5364i	0.159996	−	0.597111i	−0.838630	−	0.544701i	$-0.816643\pi$
$677$	4.16296	−	15.5364i	0.159996	−	0.597111i	0.998626	−	0.0524101i	$-0.0166903\pi$
$678$		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	−0.102416	+	0.994742i	$0.532657\pi$
$683$	−28.6734	+	28.6734i	−1.09716	+	1.09716i	−0.994742	+	0.102416i	$0.967343\pi$
$684$		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
$691$	−44.0504	−	11.8033i	−1.67575	−	0.449017i	−0.709102	−	0.705106i	$-0.750899\pi$
$691$	−44.0504	−	11.8033i	−1.67575	−	0.449017i	−0.966653	+	0.256089i	$0.917566\pi$
$692$		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	$-0.636974\pi$
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	0.908834	+	0.417158i	$0.136974\pi$
$702$		0			0
$703$			5.99049i			0.225935i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.436349	+	0.116919i	−0.0164106	+	0.00439721i
$708$		0			0
$709$	−16.3841	−	4.39011i	−0.615319	−	0.164874i	−0.0623199	−	0.998056i	$-0.519850\pi$
$709$	−16.3841	−	4.39011i	−0.615319	−	0.164874i	−0.552999	+	0.833182i	$0.686517\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.0285	−	27.7622i	−0.600273	−	1.03970i
$714$		0			0
$715$	2.29767	−	0.615660i	0.0859282	−	0.0230244i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−43.0731			−1.60635			−0.803177	−	0.595740i	$-0.796859\pi$
$719$	−43.0731			−1.60635			−0.803177	+	0.595740i	$0.796859\pi$
$720$		0			0
$721$	27.5313			1.02532
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−20.2528	+	5.42673i	−0.752171	+	0.201544i
$726$		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
$731$	19.8820	+	5.32737i	0.735363	+	0.197040i
$732$		0			0
$733$	−2.53658	+	0.679676i	−0.0936909	+	0.0251044i	−0.305360	−	0.952237i	$-0.598777\pi$
$733$	−2.53658	+	0.679676i	−0.0936909	+	0.0251044i	0.211669	+	0.977341i	$0.432110\pi$
$734$		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	−0.906206	−	0.422836i	$-0.861035\pi$
$739$	−13.1402	+	13.1402i	−0.483370	+	0.483370i	0.422836	+	0.906206i	$0.361035\pi$
$740$		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
$749$	−38.0958	−	10.2077i	−1.39199	−	0.372982i
$750$		0			0
$751$	−7.86676	−	4.54188i	−0.287062	−	0.165735i	0.349554	−	0.936916i	$-0.386333\pi$
$751$	−7.86676	−	4.54188i	−0.287062	−	0.165735i	−0.636616	+	0.771181i	$0.719666\pi$
$752$		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	−0.288920	−	0.957353i	$-0.593296\pi$
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	0.957353	+	0.288920i	$0.0932961\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.1080	+	24.4358i	−0.511415	+	0.885797i	0.488497	+	0.872565i	$0.337545\pi$
$761$	−14.1080	+	24.4358i	−0.511415	+	0.885797i	−0.999912	+	0.0132318i	$0.995788\pi$
$762$		0			0
$763$	−7.77481	+	29.0160i	−0.281467	+	1.05045i
$764$		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	$-0.336460\pi$
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	−0.870895	+	0.491470i	$0.836460\pi$
$774$		0			0
$775$	−82.8256			−2.97518
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.40154	+	5.23060i	0.0502152	+	0.187406i
$780$		0			0
$781$	−0.426938	+	1.59335i	−0.0152770	+	0.0570146i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	49.8924	−	28.8054i	1.78074	−	1.02811i
$786$		0			0
$787$	9.05729	+	33.8023i	0.322857	+	1.20492i	0.916448	+	0.400153i	$0.131043\pi$
$787$	9.05729	+	33.8023i	0.322857	+	1.20492i	−0.593591	+	0.804767i	$0.702290\pi$
$788$		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
$797$	7.41329	+	27.6668i	0.262592	+	0.980007i	0.963708	+	0.266959i	$0.0860190\pi$
$797$	7.41329	+	27.6668i	0.262592	+	0.980007i	−0.701116	+	0.713048i	$0.747314\pi$
$798$		0			0
$799$	17.2554	−	9.96243i	0.610453	−	0.352445i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.182786	−	0.682165i	0.00645036	−	0.0240731i
$804$		0			0
$805$	−12.9598	−	48.3667i	−0.456773	−	1.70470i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.9831			−1.40573			−0.702865	−	0.711323i	$-0.748096\pi$
$809$	−39.9831			−1.40573			−0.702865	+	0.711323i	$0.748096\pi$
$810$		0			0
$811$	33.5121	+	33.5121i	1.17677	+	1.17677i	0.980563	+	0.196204i	$0.0628616\pi$
$811$	33.5121	+	33.5121i	1.17677	+	1.17677i	0.196204	+	0.980563i	$0.437138\pi$
$812$		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
$821$	2.91908	−	10.8942i	0.101877	−	0.380209i	−0.896096	−	0.443861i	$-0.853608\pi$
$821$	2.91908	−	10.8942i	0.101877	−	0.380209i	0.997972	+	0.0636527i	$0.0202750\pi$
$822$		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	$-0.863619\pi$
$827$	−14.2104	+	14.2104i	−0.494144	+	0.494144i	0.415465	+	0.909609i	$0.363619\pi$
$828$		0			0
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	0.805869	−	0.592093i	$-0.201698\pi$
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	−0.592093	+	0.805869i	$0.701698\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.8654	−	9.15989i	−0.549704	−	0.317371i
$834$		0			0
$835$	51.2913	+	13.7435i	1.77501	+	0.475612i
$836$		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
$851$	−14.0170	+	3.75585i	−0.480497	+	0.128749i
$852$		0			0
$853$	18.8477	+	5.05023i	0.645334	+	0.172917i	0.566618	−	0.823980i	$-0.308251\pi$
$853$	18.8477	+	5.05023i	0.645334	+	0.172917i	0.0787157	+	0.996897i	$0.474918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.6982	−	32.3862i	−0.638717	−	1.10629i	−0.985715	−	0.168424i	$-0.946132\pi$
$857$	−18.6982	−	32.3862i	−0.638717	−	1.10629i	0.346998	−	0.937866i	$-0.387201\pi$
$858$		0			0
$859$	−26.5180	+	7.10549i	−0.904784	+	0.242436i	−0.681070	−	0.732219i	$-0.738485\pi$
$859$	−26.5180	+	7.10549i	−0.904784	+	0.242436i	−0.223714	+	0.974655i	$0.571818\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.1797			0.346520			0.173260	−	0.984876i	$-0.444570\pi$
$863$	10.1797			0.346520			0.173260	+	0.984876i	$0.444570\pi$
$864$		0			0
$865$	20.9860			0.713545
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.21723	+	0.326156i	−0.0412918	+	0.0110641i
$870$		0			0
$871$	7.53020	+	13.0427i	0.255151	+	0.441935i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−62.1414	−	16.6507i	−2.10076	−	0.562897i
$876$		0			0
$877$	25.7779	−	6.90717i	0.870458	−	0.233239i	0.204172	−	0.978935i	$-0.434550\pi$
$877$	25.7779	−	6.90717i	0.870458	−	0.233239i	0.666286	+	0.745696i	$0.267883\pi$
$878$		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	−0.290310	−	0.956933i	$-0.593759\pi$
$883$	19.8089	−	19.8089i	0.666622	−	0.666622i	0.956933	+	0.290310i	$0.0937586\pi$
$884$		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
$893$	−7.21410	−	1.93301i	−0.241411	−	0.0646858i
$894$		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
$907$	15.0239	−	56.0698i	0.498859	−	1.86177i	−0.00838605	−	0.999965i	$-0.502669\pi$
$907$	15.0239	−	56.0698i	0.498859	−	1.86177i	0.507245	−	0.861802i	$-0.330664\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.9347	−	20.6715i	−0.395414	−	0.684877i	0.597740	−	0.801690i	$-0.296066\pi$
$911$	−11.9347	−	20.6715i	−0.395414	−	0.684877i	−0.993154	+	0.116813i	$0.962732\pi$
$912$		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
$923$	−5.48292	−	20.4625i	−0.180473	−	0.673533i
$924$		0			0
$925$	−9.70397	+	36.2157i	−0.319065	+	1.19077i
$926$		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
$931$	1.77730	+	6.63296i	0.0582485	+	0.217387i
$932$		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	$0.0308775\pi$
$937$			5.92940i			0.193705i	−0.995299	+	0.0968526i	$0.969122\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.52232	+	20.6096i	0.180022	+	0.671853i	0.995641	+	0.0932635i	$0.0297299\pi$
$941$	5.52232	+	20.6096i	0.180022	+	0.671853i	−0.815619	+	0.578589i	$0.803603\pi$
$942$		0			0
$943$	−11.3603	+	6.55886i	−0.369941	+	0.213586i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.57071	+	31.9863i	−0.278511	+	1.03942i	0.674941	+	0.737871i	$0.264169\pi$
$947$	−8.57071	+	31.9863i	−0.278511	+	1.03942i	−0.953452	+	0.301545i	$0.902498\pi$
$948$		0			0
$949$	2.34741	+	8.76066i	0.0762002	+	0.284383i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.546564			−0.0177049			−0.00885247	−	0.999961i	$-0.502818\pi$
$953$	−0.546564			−0.0177049			−0.00885247	+	0.999961i	$0.502818\pi$
$954$		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
$965$	−5.20393	+	19.4213i	−0.167521	+	0.625195i
$966$		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	$-0.516811\pi$
$971$	29.4725	−	29.4725i	0.945816	−	0.945816i	0.998606	+	0.0527896i	$0.0168113\pi$
$972$		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
$979$	−0.626159	−	0.167779i	−0.0200121	−	0.00536224i
$980$		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	$-0.963899\pi$
$991$		−	7.12527i		−	0.226342i	0.993576	−	0.113171i	$-0.0361008\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.60763	−	2.57436i	0.304582	−	0.0816126i
$996$		0			0
$997$	−47.5897	−	12.7516i	−1.50718	−	0.403848i	−0.591684	−	0.806170i	$-0.701537\pi$
$997$	−47.5897	−	12.7516i	−1.50718	−	0.403848i	−0.915498	+	0.402322i	$0.868203\pi$
$998$		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.1583.1		88
3.2	odd	2		576.2.y.a.239.15		88
4.3	odd	2		432.2.v.a.179.16		88
9.2	odd	6	inner	1728.2.z.a.1007.1		88
9.7	even	3		576.2.y.a.47.3		88
12.11	even	2		144.2.u.a.131.7	yes	88
16.5	even	4		432.2.v.a.395.9		88
16.11	odd	4	inner	1728.2.z.a.719.1		88
36.7	odd	6		144.2.u.a.83.14	yes	88
36.11	even	6		432.2.v.a.35.9		88
48.5	odd	4		144.2.u.a.59.14	yes	88
48.11	even	4		576.2.y.a.527.3		88
144.11	even	12	inner	1728.2.z.a.143.1		88
144.43	odd	12		576.2.y.a.335.15		88
144.101	odd	12		432.2.v.a.251.16		88
144.133	even	12		144.2.u.a.11.7	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	144.133	even	12
144.2.u.a.59.14	yes	88	48.5	odd	4
144.2.u.a.83.14	yes	88	36.7	odd	6
144.2.u.a.131.7	yes	88	12.11	even	2
432.2.v.a.35.9		88	36.11	even	6
432.2.v.a.179.16		88	4.3	odd	2
432.2.v.a.251.16		88	144.101	odd	12
432.2.v.a.395.9		88	16.5	even	4
576.2.y.a.47.3		88	9.7	even	3
576.2.y.a.239.15		88	3.2	odd	2
576.2.y.a.335.15		88	144.43	odd	12
576.2.y.a.527.3		88	48.11	even	4
1728.2.z.a.143.1		88	144.11	even	12	inner
1728.2.z.a.719.1		88	16.11	odd	4	inner
1728.2.z.a.1007.1		88	9.2	odd	6	inner
1728.2.z.a.1583.1		88	1.1	even	1	trivial

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)

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

L-functions

Modular forms

Varieties

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Database

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