LMFDB - Embedded newform 1728.2.z.a.1007.13

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)

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")

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);

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			1007.13
Character	$\chi$	$=$	1728.1007
Dual form			1728.2.z.a.719.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.206232 - 0.769670i) q^{5} +(2.17574 - 3.76849i) q^{7} +(1.05570 + 3.93991i) q^{11} +(-0.454903 + 1.69772i) q^{13} +6.68683i q^{17} +(0.708282 - 0.708282i) q^{19} +(3.88191 - 2.24122i) q^{23} +(3.78027 + 2.18254i) q^{25} +(1.06907 + 3.98981i) q^{29} +(4.94177 - 2.85313i) q^{31} +(-2.45179 - 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(-1.36389 - 2.36233i) q^{41} +(8.60436 - 2.30553i) q^{43} +(1.23164 - 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(-1.68291 - 1.68291i) q^{53} +3.25015 q^{55} +(-1.00516 - 0.269331i) q^{59} +(1.97401 - 0.528935i) q^{61} +(1.21287 + 0.700250i) q^{65} +(-8.01120 - 2.14659i) q^{67} -8.05218i q^{71} -9.73126i q^{73} +(17.1444 + 4.59383i) q^{77} +(-11.9835 - 6.91865i) q^{79} +(3.05012 - 0.817277i) q^{83} +(5.14666 + 1.37904i) q^{85} -1.71120 q^{89} +(5.40809 + 5.40809i) q^{91} +(-0.399073 - 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.206232	−	0.769670i	0.0922300	−	0.344207i	−0.904355	−	0.426781i	$-0.859647\pi$
$5$	0.206232	−	0.769670i	0.0922300	−	0.344207i	0.996585	+	0.0825742i	$0.0263142\pi$
$6$		0			0
$7$	2.17574	−	3.76849i	0.822352	−	1.42436i	−0.0815745	−	0.996667i	$-0.525995\pi$
$7$	2.17574	−	3.76849i	0.822352	−	1.42436i	0.903926	−	0.427688i	$-0.140672\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.05570	+	3.93991i	0.318304	+	1.18793i	0.920874	+	0.389861i	$0.127477\pi$
$11$	1.05570	+	3.93991i	0.318304	+	1.18793i	−0.602570	+	0.798066i	$0.705856\pi$
$12$		0			0
$13$	−0.454903	+	1.69772i	−0.126167	+	0.470863i	−0.999879	−	0.0155820i	$-0.995040\pi$
$13$	−0.454903	+	1.69772i	−0.126167	+	0.470863i	0.873711	+	0.486445i	$0.161707\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			6.68683i			1.62180i	0.585188	+	0.810898i	$0.301021\pi$
$17$			6.68683i			1.62180i	−0.585188	+	0.810898i	$0.698979\pi$
$18$		0			0
$19$	0.708282	−	0.708282i	0.162491	−	0.162491i	−0.621178	−	0.783669i	$-0.713346\pi$
$19$	0.708282	−	0.708282i	0.162491	−	0.162491i	0.783669	+	0.621178i	$0.213346\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.88191	−	2.24122i	0.809433	−	0.467327i	−0.0373258	−	0.999303i	$-0.511884\pi$
$23$	3.88191	−	2.24122i	0.809433	−	0.467327i	0.846759	+	0.531977i	$0.178551\pi$
$24$		0			0
$25$	3.78027	+	2.18254i	0.756053	+	0.436508i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.06907	+	3.98981i	0.198520	+	0.740888i	0.991327	+	0.131415i	$0.0419522\pi$
$29$	1.06907	+	3.98981i	0.198520	+	0.740888i	−0.792807	+	0.609473i	$0.791381\pi$
$30$		0			0
$31$	4.94177	−	2.85313i	0.887568	−	0.512437i	0.0144215	−	0.999896i	$-0.495409\pi$
$31$	4.94177	−	2.85313i	0.887568	−	0.512437i	0.873146	+	0.487459i	$0.162076\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.45179	−	2.45179i	−0.414427	−	0.414427i
$36$		0			0
$37$	−1.51665	+	1.51665i	−0.249335	+	0.249335i	−0.820698	−	0.571363i	$-0.806415\pi$
$37$	−1.51665	+	1.51665i	−0.249335	+	0.249335i	0.571363	+	0.820698i	$0.306415\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.36389	−	2.36233i	−0.213005	−	0.368935i	0.739649	−	0.672993i	$-0.234992\pi$
$41$	−1.36389	−	2.36233i	−0.213005	−	0.368935i	−0.952653	+	0.304058i	$0.901658\pi$
$42$		0			0
$43$	8.60436	−	2.30553i	1.31215	−	0.351590i	0.466120	−	0.884722i	$-0.345652\pi$
$43$	8.60436	−	2.30553i	1.31215	−	0.351590i	0.846033	+	0.533131i	$0.178985\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.23164	−	2.13327i	0.179654	−	0.311169i	−0.762108	−	0.647449i	$-0.775836\pi$
$47$	1.23164	−	2.13327i	0.179654	−	0.311169i	0.941762	+	0.336280i	$0.109169\pi$
$48$		0			0
$49$	−5.96768	−	10.3363i	−0.852525	−	1.47662i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.68291	−	1.68291i	−0.231165	−	0.231165i	0.582014	−	0.813179i	$-0.302265\pi$
$53$	−1.68291	−	1.68291i	−0.231165	−	0.231165i	−0.813179	+	0.582014i	$0.802265\pi$
$54$		0			0
$55$	3.25015			0.438250
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.00516	−	0.269331i	−0.130860	−	0.0350640i	0.192794	−	0.981239i	$-0.438245\pi$
$59$	−1.00516	−	0.269331i	−0.130860	−	0.0350640i	−0.323655	+	0.946175i	$0.604912\pi$
$60$		0			0
$61$	1.97401	−	0.528935i	0.252747	−	0.0677232i	−0.130221	−	0.991485i	$-0.541569\pi$
$61$	1.97401	−	0.528935i	0.252747	−	0.0677232i	0.382968	+	0.923762i	$0.374902\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.21287	+	0.700250i	0.150438	+	0.0868553i
$66$		0			0
$67$	−8.01120	−	2.14659i	−0.978723	−	0.262248i	−0.266217	−	0.963913i	$-0.585774\pi$
$67$	−8.01120	−	2.14659i	−0.978723	−	0.262248i	−0.712507	+	0.701665i	$0.752440\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.05218i		−	0.955618i	−0.878464	−	0.477809i	$-0.841431\pi$
$71$		−	8.05218i		−	0.955618i	0.878464	−	0.477809i	$-0.158569\pi$
$72$		0			0
$73$		−	9.73126i		−	1.13896i	−0.822006	−	0.569479i	$-0.807145\pi$
$73$		−	9.73126i		−	1.13896i	0.822006	−	0.569479i	$-0.192855\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	17.1444	+	4.59383i	1.95379	+	0.523516i
$78$		0			0
$79$	−11.9835	−	6.91865i	−1.34824	−	0.778409i	−0.360243	−	0.932858i	$-0.617306\pi$
$79$	−11.9835	−	6.91865i	−1.34824	−	0.778409i	−0.988001	+	0.154449i	$0.950640\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.05012	−	0.817277i	0.334794	−	0.0897078i	−0.0875058	−	0.996164i	$-0.527890\pi$
$83$	3.05012	−	0.817277i	0.334794	−	0.0897078i	0.422300	+	0.906456i	$0.361223\pi$
$84$		0			0
$85$	5.14666	+	1.37904i	0.558233	+	0.149578i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.71120			−0.181386			−0.0906932	−	0.995879i	$-0.528908\pi$
$89$	−1.71120			−0.181386			−0.0906932	+	0.995879i	$0.528908\pi$
$90$		0			0
$91$	5.40809	+	5.40809i	0.566922	+	0.566922i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.399073	−	0.691214i	−0.0409440	−	0.0709171i
$96$		0			0
$97$	3.66561	−	6.34903i	0.372187	−	0.644646i	−0.617715	−	0.786402i	$-0.711941\pi$
$97$	3.66561	−	6.34903i	0.372187	−	0.644646i	0.989902	+	0.141756i	$0.0452748\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	14.0255	−	3.75813i	1.39559	−	0.373948i	0.518833	−	0.854876i	$-0.326367\pi$
$101$	14.0255	−	3.75813i	1.39559	−	0.373948i	0.876760	+	0.480928i	$0.159700\pi$
$102$		0			0
$103$	7.43866	+	12.8841i	0.732953	+	1.26951i	0.955616	+	0.294616i	$0.0951917\pi$
$103$	7.43866	+	12.8841i	0.732953	+	1.26951i	−0.222663	+	0.974895i	$0.571475\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0974799	+	0.0974799i	−0.00942374	+	0.00942374i	−0.711803	−	0.702379i	$-0.752121\pi$
$107$	−0.0974799	+	0.0974799i	−0.00942374	+	0.00942374i	0.702379	+	0.711803i	$0.252121\pi$
$108$		0			0
$109$	8.80665	+	8.80665i	0.843524	+	0.843524i	0.989315	−	0.145791i	$-0.0465728\pi$
$109$	8.80665	+	8.80665i	0.843524	+	0.843524i	−0.145791	+	0.989315i	$0.546573\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.22037	+	4.16868i	−0.679235	+	0.392157i	−0.799567	−	0.600577i	$-0.794938\pi$
$113$	−7.22037	+	4.16868i	−0.679235	+	0.392157i	0.120331	+	0.992734i	$0.461604\pi$
$114$		0			0
$115$	−0.924424	−	3.45000i	−0.0862030	−	0.321714i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	25.1993	+	14.5488i	2.31001	+	1.33369i
$120$		0			0
$121$	−4.88210	+	2.81868i	−0.443827	+	0.256244i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.27664	−	5.27664i	0.471957	−	0.471957i
$126$		0			0
$127$			4.84829i			0.430216i	0.976590	+	0.215108i	$0.0690103\pi$
$127$			4.84829i			0.430216i	−0.976590	+	0.215108i	$0.930990\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.49193	+	20.4961i	−0.479832	+	1.79076i	0.122452	+	0.992474i	$0.460924\pi$
$131$	−5.49193	+	20.4961i	−0.479832	+	1.79076i	−0.602284	+	0.798282i	$0.705742\pi$
$132$		0			0
$133$	−1.12812	−	4.21019i	−0.0978201	−	0.365070i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.93860	−	5.08981i	0.251062	−	0.434852i	−0.712757	−	0.701411i	$-0.752554\pi$
$137$	2.93860	−	5.08981i	0.251062	−	0.434852i	0.963818	+	0.266560i	$0.0858869\pi$
$138$		0			0
$139$	1.86863	−	6.97384i	0.158496	−	0.591513i	−0.840285	−	0.542145i	$-0.817612\pi$
$139$	1.86863	−	6.97384i	0.158496	−	0.591513i	0.998781	−	0.0493686i	$-0.0157209\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.16910			−0.599510
$144$		0			0
$145$	3.29131			0.273328
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.16425	+	4.34504i	−0.0953792	+	0.355960i	−0.997077	−	0.0764076i	$-0.975655\pi$
$149$	−1.16425	+	4.34504i	−0.0953792	+	0.355960i	0.901698	+	0.432367i	$0.142322\pi$
$150$		0			0
$151$	4.23499	−	7.33521i	0.344638	−	0.596931i	−0.640650	−	0.767833i	$-0.721335\pi$
$151$	4.23499	−	7.33521i	0.344638	−	0.596931i	0.985288	+	0.170902i	$0.0546683\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.17682	−	4.39194i	−0.0945241	−	0.352769i
$156$		0			0
$157$	−4.38117	+	16.3507i	−0.349655	+	1.30493i	0.537423	+	0.843313i	$0.319398\pi$
$157$	−4.38117	+	16.3507i	−0.349655	+	1.30493i	−0.887079	+	0.461618i	$0.847269\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	19.5052i		−	1.53723i
$162$		0			0
$163$	−13.6982	+	13.6982i	−1.07293	+	1.07293i	−0.0758059	+	0.997123i	$0.524153\pi$
$163$	−13.6982	+	13.6982i	−1.07293	+	1.07293i	−0.997123	+	0.0758059i	$0.975847\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.11859	+	4.10992i	−0.550853	+	0.318035i	−0.749466	−	0.662043i	$-0.769690\pi$
$167$	−7.11859	+	4.10992i	−0.550853	+	0.318035i	0.198613	+	0.980078i	$0.436356\pi$
$168$		0			0
$169$	8.58301	+	4.95540i	0.660232	+	0.381185i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.52258	+	9.41440i	0.191788	+	0.715764i	0.993075	+	0.117483i	$0.0374826\pi$
$173$	2.52258	+	9.41440i	0.191788	+	0.715764i	−0.801287	+	0.598281i	$0.795851\pi$
$174$		0			0
$175$	16.4497	−	9.49727i	1.24348	−	0.717926i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.59887	+	2.59887i	0.194248	+	0.194248i	0.797529	−	0.603281i	$-0.206140\pi$
$179$	2.59887	+	2.59887i	0.194248	+	0.194248i	−0.603281	+	0.797529i	$0.706140\pi$
$180$		0			0
$181$	6.92926	−	6.92926i	0.515048	−	0.515048i	−0.401021	−	0.916069i	$-0.631345\pi$
$181$	6.92926	−	6.92926i	0.515048	−	0.515048i	0.916069	+	0.401021i	$0.131345\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.854536	+	1.48010i	0.0628267	+	0.108819i
$186$		0			0
$187$	−26.3455	+	7.05926i	−1.92657	+	0.516224i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.96728	−	12.0677i	0.504135	−	0.873187i	−0.495854	−	0.868406i	$-0.665145\pi$
$191$	6.96728	−	12.0677i	0.504135	−	0.873187i	0.999989	−	0.00478132i	$-0.00152195\pi$
$192$		0			0
$193$	−1.34094	−	2.32257i	−0.0965226	−	0.167182i	0.813720	−	0.581256i	$-0.197439\pi$
$193$	−1.34094	−	2.32257i	−0.0965226	−	0.167182i	−0.910243	+	0.414074i	$0.864105\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.2363	−	14.2363i	−1.01430	−	1.01430i	−0.999896	−	0.0144009i	$-0.995416\pi$
$197$	−14.2363	−	14.2363i	−1.01430	−	1.01430i	−0.0144009	−	0.999896i	$-0.504584\pi$
$198$		0			0
$199$	−7.90078			−0.560072			−0.280036	−	0.959990i	$-0.590346\pi$
$199$	−7.90078			−0.560072			−0.280036	+	0.959990i	$0.590346\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	17.3615	+	4.65201i	1.21854	+	0.326507i
$204$		0			0
$205$	−2.09950	+	0.562559i	−0.146635	+	0.0392908i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.53830	+	2.04284i	0.244749	+	0.141306i
$210$		0			0
$211$	−13.2108	−	3.53982i	−0.909469	−	0.243691i	−0.226391	−	0.974037i	$-0.572693\pi$
$211$	−13.2108	−	3.53982i	−0.909469	−	0.243691i	−0.683078	+	0.730345i	$0.739359\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	7.09799i		−	0.484079i
$216$		0			0
$217$		−	24.8307i		−	1.68562i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.3524	−	3.04186i	−0.763643	−	0.204618i
$222$		0			0
$223$	24.3372	+	14.0511i	1.62974	+	0.940931i	0.984169	+	0.177230i	$0.0567136\pi$
$223$	24.3372	+	14.0511i	1.62974	+	0.940931i	0.645570	+	0.763701i	$0.276620\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.489998	−	0.131295i	0.0325223	−	0.00871433i	−0.242521	−	0.970146i	$-0.577974\pi$
$227$	0.489998	−	0.131295i	0.0325223	−	0.00871433i	0.275044	+	0.961432i	$0.411308\pi$
$228$		0			0
$229$	−14.6181	−	3.91690i	−0.965988	−	0.258836i	−0.258855	−	0.965916i	$-0.583345\pi$
$229$	−14.6181	−	3.91690i	−0.965988	−	0.258836i	−0.707133	+	0.707080i	$0.750012\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.4968			−1.01523			−0.507614	−	0.861584i	$-0.669473\pi$
$233$	−15.4968			−1.01523			−0.507614	+	0.861584i	$0.669473\pi$
$234$		0			0
$235$	−1.38791	−	1.38791i	−0.0905371	−	0.0905371i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.61709	−	13.1932i	−0.492709	−	0.853397i	0.507256	−	0.861796i	$-0.330660\pi$
$239$	−7.61709	−	13.1932i	−0.492709	−	0.853397i	−0.999965	+	0.00839869i	$0.997327\pi$
$240$		0			0
$241$	−9.10697	+	15.7737i	−0.586632	+	1.01608i	0.408038	+	0.912965i	$0.366213\pi$
$241$	−9.10697	+	15.7737i	−0.586632	+	1.01608i	−0.994670	+	0.103111i	$0.967120\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.18628	+	2.46146i	−0.586890	+	0.157257i
$246$		0			0
$247$	0.880265	+	1.52466i	0.0560099	+	0.0970121i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.18418	−	2.18418i	0.137864	−	0.137864i	−0.634807	−	0.772671i	$-0.718920\pi$
$251$	2.18418	−	2.18418i	0.137864	−	0.137864i	0.772671	+	0.634807i	$0.218920\pi$
$252$		0			0
$253$	12.9283	+	12.9283i	0.812796	+	0.812796i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.6777	+	9.62887i	−1.04033	+	0.600633i	−0.919926	−	0.392093i	$-0.871751\pi$
$257$	−16.6777	+	9.62887i	−1.04033	+	0.600633i	−0.120400	+	0.992725i	$0.538418\pi$
$258$		0			0
$259$	2.41564	+	9.01529i	0.150101	+	0.560183i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−22.8254	−	13.1782i	−1.40747	−	0.812605i	−0.412329	−	0.911035i	$-0.635285\pi$
$263$	−22.8254	−	13.1782i	−1.40747	−	0.812605i	−0.995144	+	0.0984300i	$0.968618\pi$
$264$		0			0
$265$	−1.64235	+	0.948214i	−0.100889	+	0.0582483i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.605506	−	0.605506i	0.0369184	−	0.0369184i	−0.688407	−	0.725325i	$-0.741690\pi$
$269$	0.605506	−	0.605506i	0.0369184	−	0.0369184i	0.725325	+	0.688407i	$0.241690\pi$
$270$		0			0
$271$		−	19.1084i		−	1.16075i	−0.814349	−	0.580376i	$-0.802906\pi$
$271$		−	19.1084i		−	1.16075i	0.814349	−	0.580376i	$-0.197094\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.60819	+	17.1980i	−0.277884	+	1.03708i
$276$		0			0
$277$	−1.82792	−	6.82191i	−0.109829	−	0.409889i	0.889019	−	0.457871i	$-0.151388\pi$
$277$	−1.82792	−	6.82191i	−0.109829	−	0.409889i	−0.998848	+	0.0479819i	$0.984721\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.8490	−	20.5230i	0.706849	−	1.22430i	−0.259171	−	0.965831i	$-0.583449\pi$
$281$	11.8490	−	20.5230i	0.706849	−	1.22430i	0.966020	−	0.258467i	$-0.0832174\pi$
$282$		0			0
$283$	0.194826	−	0.727099i	0.0115812	−	0.0432215i	−0.959893	−	0.280365i	$-0.909544\pi$
$283$	0.194826	−	0.727099i	0.0115812	−	0.0432215i	0.971475	+	0.237143i	$0.0762112\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.8699			−0.700659
$288$		0			0
$289$	−27.7137			−1.63022
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.31070	+	19.8198i	−0.310255	+	1.15789i	0.618072	+	0.786121i	$0.287914\pi$
$293$	−5.31070	+	19.8198i	−0.310255	+	1.15789i	−0.928327	+	0.371765i	$0.878753\pi$
$294$		0			0
$295$	−0.414592	+	0.718095i	−0.0241385	+	0.0418091i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.03907	+	7.60993i	0.117923	+	0.440093i
$300$		0			0
$301$	10.0325	−	37.4417i	0.578262	−	2.15810i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	1.62842i		−	0.0932432i
$306$		0			0
$307$	15.3450	−	15.3450i	0.875783	−	0.875783i	−0.117312	−	0.993095i	$-0.537428\pi$
$307$	15.3450	−	15.3450i	0.875783	−	0.875783i	0.993095	+	0.117312i	$0.0374277\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.576605	−	0.332903i	0.0326963	−	0.0188772i	−0.483563	−	0.875310i	$-0.660658\pi$
$311$	0.576605	−	0.332903i	0.0326963	−	0.0188772i	0.516259	+	0.856432i	$0.327324\pi$
$312$		0			0
$313$	14.3283	+	8.27244i	0.809882	+	0.467586i	0.846915	−	0.531728i	$-0.178457\pi$
$313$	14.3283	+	8.27244i	0.809882	+	0.467586i	−0.0370327	+	0.999314i	$0.511791\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.75927	+	6.56570i	0.0988107	+	0.368767i	0.997570	−	0.0696766i	$-0.0221967\pi$
$317$	1.75927	+	6.56570i	0.0988107	+	0.368767i	−0.898759	+	0.438443i	$0.855530\pi$
$318$		0			0
$319$	−14.5909	+	8.42404i	−0.816931	+	0.471656i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.73616	+	4.73616i	0.263527	+	0.263527i
$324$		0			0
$325$	−5.42499	+	5.42499i	−0.300924	+	0.300924i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.35946	−	9.28286i	−0.295477	−	0.511781i
$330$		0			0
$331$	−9.39568	+	2.51757i	−0.516434	+	0.138378i	−0.507616	−	0.861583i	$-0.669473\pi$
$331$	−9.39568	+	2.51757i	−0.516434	+	0.138378i	−0.00881711	+	0.999961i	$0.502807\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.30434	+	5.72328i	−0.180535	+	0.312696i
$336$		0			0
$337$	13.5580	+	23.4832i	0.738553	+	1.27921i	0.953147	+	0.302509i	$0.0978241\pi$
$337$	13.5580	+	23.4832i	0.738553	+	1.27921i	−0.214593	+	0.976704i	$0.568843\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	16.4581	+	16.4581i	0.891254	+	0.891254i
$342$		0			0
$343$	−21.4761			−1.15960
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−30.1679	−	8.08347i	−1.61950	−	0.433944i	−0.668645	−	0.743582i	$-0.733125\pi$
$347$	−30.1679	−	8.08347i	−1.61950	−	0.433944i	−0.950854	+	0.309638i	$0.899792\pi$
$348$		0			0
$349$	−31.6714	+	8.48634i	−1.69533	+	0.454263i	−0.971757	−	0.235982i	$-0.924169\pi$
$349$	−31.6714	+	8.48634i	−1.69533	+	0.454263i	−0.723576	+	0.690245i	$0.757503\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.48989	+	2.01489i	0.185748	+	0.107242i	0.589990	−	0.807410i	$-0.299131\pi$
$353$	3.48989	+	2.01489i	0.185748	+	0.107242i	−0.404243	+	0.914652i	$0.632465\pi$
$354$		0			0
$355$	−6.19752	−	1.66062i	−0.328930	−	0.0881366i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			14.8043i			0.781342i	0.920530	+	0.390671i	$0.127757\pi$
$359$			14.8043i			0.781342i	−0.920530	+	0.390671i	$0.872243\pi$
$360$		0			0
$361$			17.9967i			0.947193i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.48986	−	2.00690i	−0.392037	−	0.105046i
$366$		0			0
$367$	2.66934	+	1.54114i	0.139338	+	0.0804470i	0.568049	−	0.822995i	$-0.307699\pi$
$367$	2.66934	+	1.54114i	0.139338	+	0.0804470i	−0.428710	+	0.903442i	$0.641032\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.0036	+	2.68045i	−0.519361	+	0.139162i
$372$		0			0
$373$	28.2816	+	7.57804i	1.46437	+	0.392376i	0.900996	−	0.433828i	$-0.142837\pi$
$373$	28.2816	+	7.57804i	1.46437	+	0.392376i	0.563372	+	0.826204i	$0.309504\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.25990			−0.373904
$378$		0			0
$379$	13.0654	+	13.0654i	0.671124	+	0.671124i	0.957975	−	0.286851i	$-0.0926085\pi$
$379$	13.0654	+	13.0654i	0.671124	+	0.671124i	−0.286851	+	0.957975i	$0.592608\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.66394	+	2.88203i	0.0850235	+	0.147265i	0.905401	−	0.424557i	$-0.139570\pi$
$383$	1.66394	+	2.88203i	0.0850235	+	0.147265i	−0.820378	+	0.571822i	$0.806237\pi$
$384$		0			0
$385$	7.07147	−	12.2481i	0.360396	−	0.624223i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.62255	−	1.77451i	0.335777	−	0.0899711i	−0.0869912	−	0.996209i	$-0.527725\pi$
$389$	6.62255	−	1.77451i	0.335777	−	0.0899711i	0.422768	+	0.906238i	$0.361059\pi$
$390$		0			0
$391$	14.9867	+	25.9577i	0.757908	+	1.31274i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.79645	+	7.79645i	−0.392282	+	0.392282i
$396$		0			0
$397$	2.33820	+	2.33820i	0.117351	+	0.117351i	0.763344	−	0.645993i	$-0.223556\pi$
$397$	2.33820	+	2.33820i	0.117351	+	0.117351i	−0.645993	+	0.763344i	$0.723556\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.32787	+	1.92135i	−0.166186	+	0.0959474i	−0.580786	−	0.814056i	$-0.697255\pi$
$401$	−3.32787	+	1.92135i	−0.166186	+	0.0959474i	0.414600	+	0.910004i	$0.363921\pi$
$402$		0			0
$403$	2.59579	+	9.68764i	0.129306	+	0.482575i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.57656	−	4.37433i	−0.375556	−	0.216828i
$408$		0			0
$409$	4.36888	−	2.52237i	0.216027	−	0.124723i	−0.388082	−	0.921625i	$-0.626862\pi$
$409$	4.36888	−	2.52237i	0.216027	−	0.124723i	0.604109	+	0.796901i	$0.293529\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.20193	+	3.20193i	−0.157557	+	0.157557i
$414$		0			0
$415$		−	2.51613i		−	0.123512i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.72083	−	21.3504i	0.279481	−	1.04304i	−0.673298	−	0.739371i	$-0.735123\pi$
$419$	5.72083	−	21.3504i	0.279481	−	1.04304i	0.952779	−	0.303665i	$-0.0982103\pi$
$420$		0			0
$421$	2.13099	+	7.95298i	0.103858	+	0.387604i	0.998213	−	0.0597538i	$-0.0190316\pi$
$421$	2.13099	+	7.95298i	0.103858	+	0.387604i	−0.894355	+	0.447358i	$0.852365\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−14.5943	+	25.2780i	−0.707926	+	1.22616i
$426$		0			0
$427$	2.30165	−	8.58988i	0.111385	−	0.415693i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.08094			−0.0520671			−0.0260336	−	0.999661i	$-0.508288\pi$
$431$	−1.08094			−0.0520671			−0.0260336	+	0.999661i	$0.508288\pi$
$432$		0			0
$433$	−15.5307			−0.746359			−0.373179	−	0.927759i	$-0.621732\pi$
$433$	−15.5307			−0.746359			−0.373179	+	0.927759i	$0.621732\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.16207	−	4.33690i	0.0555893	−	0.207462i
$438$		0			0
$439$	2.26321	−	3.91999i	0.108017	−	0.187091i	−0.806950	−	0.590620i	$-0.798883\pi$
$439$	2.26321	−	3.91999i	0.108017	−	0.187091i	0.914967	+	0.403529i	$0.132217\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.82958	−	25.4883i	−0.324483	−	1.21099i	−0.914830	−	0.403838i	$-0.867676\pi$
$443$	−6.82958	−	25.4883i	−0.324483	−	1.21099i	0.590347	−	0.807149i	$-0.298991\pi$
$444$		0			0
$445$	−0.352904	+	1.31706i	−0.0167293	+	0.0624345i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	5.94688i		−	0.280650i	−0.990105	−	0.140325i	$-0.955185\pi$
$449$		−	5.94688i		−	0.280650i	0.990105	−	0.140325i	$-0.0448148\pi$
$450$		0			0
$451$	7.86752	−	7.86752i	0.370467	−	0.370467i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.27777	−	3.04712i	0.247426	−	0.142851i
$456$		0			0
$457$	−18.2318	−	10.5261i	−0.852846	−	0.492391i	0.00876413	−	0.999962i	$-0.497210\pi$
$457$	−18.2318	−	10.5261i	−0.852846	−	0.492391i	−0.861610	+	0.507571i	$0.830544\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.2518	−	38.2603i	−0.477475	−	1.78196i	−0.611788	−	0.791021i	$-0.709550\pi$
$461$	−10.2518	−	38.2603i	−0.477475	−	1.78196i	0.134314	−	0.990939i	$-0.457117\pi$
$462$		0			0
$463$	−9.98020	+	5.76207i	−0.463819	+	0.267786i	−0.713649	−	0.700504i	$-0.752959\pi$
$463$	−9.98020	+	5.76207i	−0.463819	+	0.267786i	0.249829	+	0.968290i	$0.419625\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.1476	−	25.1476i	−1.16369	−	1.16369i	−0.983661	−	0.180032i	$-0.942380\pi$
$467$	−25.1476	−	25.1476i	−1.16369	−	1.16369i	−0.180032	−	0.983661i	$-0.557620\pi$
$468$		0			0
$469$	−25.5197	+	25.5197i	−1.17839	+	1.17839i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.1672	+	31.4664i	0.835327	+	1.44683i
$474$		0			0
$475$	4.22335	−	1.13164i	0.193780	−	0.0519233i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.64784	−	4.58619i	0.120983	−	0.209548i	−0.799173	−	0.601101i	$-0.794729\pi$
$479$	2.64784	−	4.58619i	0.120983	−	0.209548i	0.920155	+	0.391553i	$0.128062\pi$
$480$		0			0
$481$	−1.88491	−	3.26477i	−0.0859447	−	0.148861i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.13069	−	4.13069i	−0.187565	−	0.187565i
$486$		0			0
$487$	−1.85543			−0.0840775			−0.0420387	−	0.999116i	$-0.513385\pi$
$487$	−1.85543			−0.0840775			−0.0420387	+	0.999116i	$0.513385\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.49505	−	0.936497i	−0.157730	−	0.0422635i	0.179090	−	0.983833i	$-0.442685\pi$
$491$	−3.49505	−	0.936497i	−0.157730	−	0.0422635i	−0.336820	+	0.941569i	$0.609351\pi$
$492$		0			0
$493$	−26.6792	+	7.14866i	−1.20157	+	0.321960i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−30.3446	−	17.5194i	−1.36114	−	0.785854i
$498$		0			0
$499$	12.0253	+	3.22216i	0.538325	+	0.144244i	0.517730	−	0.855544i	$-0.326777\pi$
$499$	12.0253	+	3.22216i	0.538325	+	0.144244i	0.0205953	+	0.999788i	$0.493444\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	16.6233i		−	0.741198i	−0.928793	−	0.370599i	$-0.879152\pi$
$503$		−	16.6233i		−	0.741198i	0.928793	−	0.370599i	$-0.120848\pi$
$504$		0			0
$505$		−	11.5701i		−	0.514862i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.1091	−	4.04848i	−0.669700	−	0.179446i	−0.0920802	−	0.995752i	$-0.529352\pi$
$509$	−15.1091	−	4.04848i	−0.669700	−	0.179446i	−0.577620	+	0.816306i	$0.696018\pi$
$510$		0			0
$511$	−36.6722	−	21.1727i	−1.62228	−	0.936624i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.4506	−	3.06819i	0.504575	−	0.135200i
$516$		0			0
$517$	9.70511	+	2.60048i	0.426830	+	0.114369i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	40.4461			1.77198			0.885988	−	0.463709i	$-0.153482\pi$
$521$	40.4461			1.77198			0.885988	+	0.463709i	$0.153482\pi$
$522$		0			0
$523$	−7.69126	−	7.69126i	−0.336315	−	0.336315i	0.518663	−	0.854979i	$-0.326430\pi$
$523$	−7.69126	−	7.69126i	−0.336315	−	0.336315i	−0.854979	+	0.518663i	$0.826430\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	19.0784	+	33.0448i	0.831069	+	1.43945i
$528$		0			0
$529$	−1.45387	+	2.51818i	−0.0632119	+	0.109486i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.63102	−	1.24088i	0.200592	−	0.0537484i
$534$		0			0
$535$	0.0549239	+	0.0951309i	0.00237457	+	0.00411287i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	34.4241	−	34.4241i	1.48275	−	1.48275i
$540$		0			0
$541$	−17.0176	−	17.0176i	−0.731643	−	0.731643i	0.239302	−	0.970945i	$-0.423081\pi$
$541$	−17.0176	−	17.0176i	−0.731643	−	0.731643i	−0.970945	+	0.239302i	$0.923081\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.59443	−	4.96200i	0.368145	−	0.212549i
$546$		0			0
$547$	5.77510	+	21.5530i	0.246926	+	0.921539i	0.972406	+	0.233296i	$0.0749511\pi$
$547$	5.77510	+	21.5530i	0.246926	+	0.921539i	−0.725480	+	0.688243i	$0.758382\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.58311	+	2.06871i	0.152645	+	0.0881299i
$552$		0			0
$553$	−52.1457	+	30.1064i	−2.21746	+	1.28025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.6516	−	11.6516i	0.493695	−	0.493695i	−0.415773	−	0.909468i	$-0.636489\pi$
$557$	11.6516	−	11.6516i	0.493695	−	0.493695i	0.909468	+	0.415773i	$0.136489\pi$
$558$		0			0
$559$			15.6566i			0.662203i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.30826	+	4.88249i	−0.0551365	+	0.205772i	−0.987999	−	0.154460i	$-0.950636\pi$
$563$	−1.30826	+	4.88249i	−0.0551365	+	0.205772i	0.932862	+	0.360233i	$0.117303\pi$
$564$		0			0
$565$	1.71944	+	6.41702i	0.0723372	+	0.269966i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.79764	+	4.84565i	−0.117283	+	0.203140i	−0.918690	−	0.394979i	$-0.870752\pi$
$569$	−2.79764	+	4.84565i	−0.117283	+	0.203140i	0.801407	+	0.598119i	$0.204085\pi$
$570$		0			0
$571$	2.31993	−	8.65808i	0.0970859	−	0.362329i	−0.900242	−	0.435391i	$-0.856610\pi$
$571$	2.31993	−	8.65808i	0.0970859	−	0.362329i	0.997327	+	0.0730613i	$0.0232769\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	19.5662			0.815966
$576$		0			0
$577$	16.6893			0.694785			0.347393	−	0.937720i	$-0.387067\pi$
$577$	16.6893			0.694785			0.347393	+	0.937720i	$0.387067\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.55636	−	13.2725i	0.147543	−	0.550637i
$582$		0			0
$583$	4.85387	−	8.40714i	0.201027	−	0.348188i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.34545	+	5.02128i	0.0555325	+	0.207250i	0.988118	−	0.153700i	$-0.0491190\pi$
$587$	1.34545	+	5.02128i	0.0555325	+	0.207250i	−0.932585	+	0.360950i	$0.882452\pi$
$588$		0			0
$589$	1.47934	−	5.52099i	0.0609553	−	0.227488i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			44.7927i			1.83942i	0.392602	+	0.919708i	$0.371575\pi$
$593$			44.7927i			1.83942i	−0.392602	+	0.919708i	$0.628425\pi$
$594$		0			0
$595$	16.3947	−	16.3947i	0.672116	−	0.672116i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−27.1165	+	15.6557i	−1.10795	+	0.639674i	−0.938297	−	0.345830i	$-0.887597\pi$
$599$	−27.1165	+	15.6557i	−1.10795	+	0.639674i	−0.169651	+	0.985504i	$0.554264\pi$
$600$		0			0
$601$	15.4248	+	8.90549i	0.629189	+	0.363262i	0.780438	−	0.625233i	$-0.214996\pi$
$601$	15.4248	+	8.90549i	0.629189	+	0.363262i	−0.151249	+	0.988496i	$0.548330\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.16261	+	4.33891i	0.0472667	+	0.176402i
$606$		0			0
$607$	−29.3159	+	16.9255i	−1.18989	+	0.686986i	−0.958283	−	0.285823i	$-0.907733\pi$
$607$	−29.3159	+	16.9255i	−1.18989	+	0.686986i	−0.231612	+	0.972808i	$0.574400\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.06141	+	3.06141i	0.123852	+	0.123852i
$612$		0			0
$613$	−11.3734	+	11.3734i	−0.459367	+	0.459367i	−0.898448	−	0.439081i	$-0.855304\pi$
$613$	−11.3734	+	11.3734i	−0.459367	+	0.459367i	0.439081	+	0.898448i	$0.355304\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.0269	−	31.2236i	−0.725738	−	1.25701i	−0.958670	−	0.284521i	$-0.908165\pi$
$617$	−18.0269	−	31.2236i	−0.725738	−	1.25701i	0.232932	−	0.972493i	$-0.425168\pi$
$618$		0			0
$619$	−16.0209	+	4.29280i	−0.643936	+	0.172542i	−0.565986	−	0.824415i	$-0.691504\pi$
$619$	−16.0209	+	4.29280i	−0.643936	+	0.172542i	−0.0779503	+	0.996957i	$0.524838\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.72312	+	6.44863i	−0.149163	+	0.258359i
$624$		0			0
$625$	7.93964	+	13.7519i	0.317585	+	0.550074i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−10.1416	−	10.1416i	−0.404371	−	0.404371i
$630$		0			0
$631$	−24.4330			−0.972664			−0.486332	−	0.873774i	$-0.661665\pi$
$631$	−24.4330			−0.972664			−0.486332	+	0.873774i	$0.661665\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.73158	+	0.999874i	0.148083	+	0.0396788i
$636$		0			0
$637$	20.2629	−	5.42943i	0.802845	−	0.215122i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	40.0952	+	23.1490i	1.58366	+	0.914329i	0.994318	+	0.106448i	$0.0339479\pi$
$641$	40.0952	+	23.1490i	1.58366	+	0.914329i	0.589346	+	0.807881i	$0.299385\pi$
$642$		0			0
$643$	−10.5870	−	2.83678i	−0.417511	−	0.111872i	0.0439466	−	0.999034i	$-0.486007\pi$
$643$	−10.5870	−	2.83678i	−0.417511	−	0.111872i	−0.461458	+	0.887162i	$0.652674\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	10.0479i		−	0.395025i	−0.980300	−	0.197512i	$-0.936714\pi$
$647$		−	10.0479i		−	0.395025i	0.980300	−	0.197512i	$-0.0632863\pi$
$648$		0			0
$649$		−	4.24456i		−	0.166614i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	25.5935	+	6.85777i	1.00155	+	0.268365i	0.722096	−	0.691793i	$-0.243179\pi$
$653$	25.5935	+	6.85777i	1.00155	+	0.268365i	0.279457	+	0.960158i	$0.409846\pi$
$654$		0			0
$655$	14.6427	+	8.45394i	0.572136	+	0.330323i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.76233	−	1.81196i	0.263423	−	0.0705840i	−0.124690	−	0.992196i	$-0.539794\pi$
$659$	6.76233	−	1.81196i	0.263423	−	0.0705840i	0.388113	+	0.921612i	$0.373127\pi$
$660$		0			0
$661$	20.1902	+	5.40993i	0.785306	+	0.210422i	0.629123	−	0.777306i	$-0.283414\pi$
$661$	20.1902	+	5.40993i	0.785306	+	0.210422i	0.156183	+	0.987728i	$0.450081\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.47311			−0.134681
$666$		0			0
$667$	13.0920	+	13.0920i	0.506926	+	0.506926i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.16791	+	7.21904i	0.160901	+	0.278688i
$672$		0			0
$673$	3.86200	−	6.68918i	0.148869	−	0.257849i	−0.781941	−	0.623353i	$-0.785770\pi$
$673$	3.86200	−	6.68918i	0.148869	−	0.257849i	0.930810	+	0.365504i	$0.119103\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.62160	+	2.04220i	−0.292922	+	0.0784882i	−0.402287	−	0.915513i	$-0.631785\pi$
$677$	−7.62160	+	2.04220i	−0.292922	+	0.0784882i	0.109366	+	0.994002i	$0.465118\pi$
$678$		0			0
$679$	−15.9508	−	27.6277i	−0.612137	−	1.06025i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23.0318	+	23.0318i	−0.881288	+	0.881288i	−0.993666	−	0.112378i	$-0.964153\pi$
$683$	−23.0318	+	23.0318i	−0.881288	+	0.881288i	0.112378	+	0.993666i	$0.464153\pi$
$684$		0			0
$685$	−3.31144	−	3.31144i	−0.126524	−	0.126524i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.62267	−	2.09155i	0.138013	−	0.0796816i
$690$		0			0
$691$	6.66520	+	24.8749i	0.253556	+	0.946285i	0.968888	+	0.247500i	$0.0796089\pi$
$691$	6.66520	+	24.8749i	0.253556	+	0.946285i	−0.715332	+	0.698785i	$0.753724\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.98218	−	2.87646i	−0.188985	−	0.109111i
$696$		0			0
$697$	15.7965	−	9.12014i	0.598337	−	0.345450i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−35.0396	+	35.0396i	−1.32343	+	1.32343i	−0.412443	+	0.910983i	$0.635325\pi$
$701$	−35.0396	+	35.0396i	−1.32343	+	1.32343i	−0.910983	+	0.412443i	$0.864675\pi$
$702$		0			0
$703$			2.14843i			0.0810295i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.3534	−	61.0318i	0.615034	−	2.29534i
$708$		0			0
$709$	−12.2110	−	45.5722i	−0.458595	−	1.71150i	−0.677297	−	0.735710i	$-0.736849\pi$
$709$	−12.2110	−	45.5722i	−0.458595	−	1.71150i	0.218702	−	0.975792i	$-0.429818\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.7890	−	22.1512i	0.478951	−	0.829568i
$714$		0			0
$715$	−1.47850	+	5.51784i	−0.0552928	+	0.206356i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	26.0582			0.971806			0.485903	−	0.874013i	$-0.338491\pi$
$719$	26.0582			0.971806			0.485903	+	0.874013i	$0.338491\pi$
$720$		0			0
$721$	64.7383			2.41098
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.66655	+	17.4158i	−0.173311	+	0.646807i
$726$		0			0
$727$	4.96698	−	8.60307i	0.184215	−	0.319070i	−0.759097	−	0.650978i	$-0.774359\pi$
$727$	4.96698	−	8.60307i	0.184215	−	0.319070i	0.943312	+	0.331908i	$0.107692\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.4167	+	57.5359i	0.570207	+	2.12804i
$732$		0			0
$733$	3.40512	−	12.7081i	0.125771	−	0.469384i	−0.874095	−	0.485755i	$-0.838545\pi$
$733$	3.40512	−	12.7081i	0.125771	−	0.469384i	0.999866	+	0.0163712i	$0.00521135\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	33.8295i		−	1.24613i
$738$		0			0
$739$	32.6637	−	32.6637i	1.20155	−	1.20155i	0.227861	−	0.973694i	$-0.426827\pi$
$739$	32.6637	−	32.6637i	1.20155	−	1.20155i	0.973694	−	0.227861i	$-0.0731732\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.76936	+	5.06299i	−0.321717	+	0.185743i	−0.652157	−	0.758084i	$-0.726136\pi$
$743$	−8.76936	+	5.06299i	−0.321717	+	0.185743i	0.330441	+	0.943827i	$0.392803\pi$
$744$		0			0
$745$	3.10414	+	1.79218i	0.113727	+	0.0656603i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.155261	+	0.579443i	0.00567312	+	0.0211724i
$750$		0			0
$751$	22.6187	−	13.0589i	0.825368	−	0.476526i	−0.0268964	−	0.999638i	$-0.508562\pi$
$751$	22.6187	−	13.0589i	0.825368	−	0.476526i	0.852264	+	0.523112i	$0.175229\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.77230	−	4.77230i	−0.173682	−	0.173682i
$756$		0			0
$757$	2.39808	−	2.39808i	0.0871596	−	0.0871596i	−0.662183	−	0.749342i	$-0.730370\pi$
$757$	2.39808	−	2.39808i	0.0871596	−	0.0871596i	0.749342	+	0.662183i	$0.230370\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.1857	+	40.1589i	0.840482	+	1.45576i	0.889488	+	0.456959i	$0.151061\pi$
$761$	23.1857	+	40.1589i	0.840482	+	1.45576i	−0.0490055	+	0.998799i	$0.515605\pi$
$762$		0			0
$763$	52.3487	−	14.0268i	1.89515	−	0.507804i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.914499	−	1.58396i	0.0330206	−	0.0571934i
$768$		0			0
$769$	−7.38255	−	12.7870i	−0.266222	−	0.461109i	0.701661	−	0.712511i	$-0.252442\pi$
$769$	−7.38255	−	12.7870i	−0.266222	−	0.461109i	−0.967883	+	0.251401i	$0.919109\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−22.1409	−	22.1409i	−0.796353	−	0.796353i	0.186165	−	0.982518i	$-0.440394\pi$
$773$	−22.1409	−	22.1409i	−0.796353	−	0.796353i	−0.982518	+	0.186165i	$0.940394\pi$
$774$		0			0
$775$	24.9083			0.894731
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.63922	−	0.707177i	−0.0945599	−	0.0253372i
$780$		0			0
$781$	31.7248	−	8.50064i	1.13520	−	0.304177i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	11.6811	+	6.74410i	0.416917	+	0.240707i
$786$		0			0
$787$	4.18136	+	1.12039i	0.149050	+	0.0399377i	0.332572	−	0.943078i	$-0.392083\pi$
$787$	4.18136	+	1.12039i	0.149050	+	0.0399377i	−0.183523	+	0.983015i	$0.558750\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			36.2799i			1.28996i
$792$		0			0
$793$			3.59194i			0.127553i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−51.5141	−	13.8032i	−1.82472	−	0.488933i	−0.827370	−	0.561657i	$-0.810164\pi$
$797$	−51.5141	−	13.8032i	−1.82472	−	0.488933i	−0.997352	+	0.0727237i	$0.976831\pi$
$798$		0			0
$799$	14.2648	+	8.23579i	0.504652	+	0.291361i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	38.3403	−	10.2732i	1.35300	−	0.362535i
$804$		0			0
$805$	−15.0126	−	4.02261i	−0.529124	−	0.141778i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−30.1140			−1.05875			−0.529375	−	0.848388i	$-0.677574\pi$
$809$	−30.1140			−1.05875			−0.529375	+	0.848388i	$0.677574\pi$
$810$		0			0
$811$	−20.5672	−	20.5672i	−0.722214	−	0.722214i	0.246842	−	0.969056i	$-0.420607\pi$
$811$	−20.5672	−	20.5672i	−0.722214	−	0.722214i	−0.969056	+	0.246842i	$0.920607\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.71810	+	13.3681i	0.270353	+	0.468265i
$816$		0			0
$817$	4.46135	−	7.72728i	0.156083	−	0.270343i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−31.8546	+	8.53541i	−1.11173	+	0.297888i	−0.767533	−	0.641009i	$-0.778516\pi$
$821$	−31.8546	+	8.53541i	−1.11173	+	0.297888i	−0.344199	+	0.938897i	$0.611849\pi$
$822$		0			0
$823$	−4.71220	−	8.16178i	−0.164257	−	0.284502i	0.772134	−	0.635460i	$-0.219189\pi$
$823$	−4.71220	−	8.16178i	−0.164257	−	0.284502i	−0.936391	+	0.350958i	$0.885856\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.7468	+	38.7468i	−1.34736	+	1.34736i	−0.458841	+	0.888518i	$0.651735\pi$
$827$	−38.7468	+	38.7468i	−1.34736	+	1.34736i	−0.888518	+	0.458841i	$0.848265\pi$
$828$		0			0
$829$	11.0569	+	11.0569i	0.384021	+	0.384021i	0.872548	−	0.488528i	$-0.162466\pi$
$829$	11.0569	+	11.0569i	0.384021	+	0.384021i	−0.488528	+	0.872548i	$0.662466\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	69.1173	−	39.9049i	2.39477	−	1.38262i
$834$		0			0
$835$	1.69520	+	6.32656i	0.0586647	+	0.218940i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.3695	+	14.6471i	0.875853	+	0.505674i	0.869289	−	0.494305i	$-0.164577\pi$
$839$	25.3695	+	14.6471i	0.875853	+	0.505674i	0.00656388	+	0.999978i	$0.497911\pi$
$840$		0			0
$841$	10.3391	−	5.96927i	0.356520	−	0.205837i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.58412	−	5.58412i	0.192100	−	0.192100i
$846$		0			0
$847$			24.5309i			0.842891i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.48834	+	9.28662i	−0.0852992	+	0.318341i
$852$		0			0
$853$	−10.9035	−	40.6922i	−0.373327	−	1.39328i	−0.855774	−	0.517350i	$-0.826918\pi$
$853$	−10.9035	−	40.6922i	−0.373327	−	1.39328i	0.482447	−	0.875925i	$-0.339748\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.2207	+	24.6310i	−0.485769	+	0.841377i	−0.999866	−	0.0163548i	$-0.994794\pi$
$857$	−14.2207	+	24.6310i	−0.485769	+	0.841377i	0.514097	+	0.857732i	$0.328127\pi$
$858$		0			0
$859$	0.896437	−	3.34555i	0.0305860	−	0.114149i	−0.948945	−	0.315441i	$-0.897848\pi$
$859$	0.896437	−	3.34555i	0.0305860	−	0.114149i	0.979531	+	0.201293i	$0.0645142\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.1356			−0.379062			−0.189531	−	0.981875i	$-0.560697\pi$
$863$	−11.1356			−0.379062			−0.189531	+	0.981875i	$0.560697\pi$
$864$		0			0
$865$	7.76622			0.264059
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.6080	−	54.5177i	0.495541	−	1.84939i
$870$		0			0
$871$	7.28863	−	12.6243i	0.246966	−	0.427757i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.40437	−	31.3655i	−0.284119	−	1.06035i
$876$		0			0
$877$	7.32539	−	27.3387i	0.247361	−	0.923163i	−0.724821	−	0.688937i	$-0.758078\pi$
$877$	7.32539	−	27.3387i	0.247361	−	0.923163i	0.972182	−	0.234226i	$-0.0752557\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	4.86363i		−	0.163860i	−0.996638	−	0.0819299i	$-0.973892\pi$
$881$		−	4.86363i		−	0.163860i	0.996638	−	0.0819299i	$-0.0261084\pi$
$882$		0			0
$883$	−8.56478	+	8.56478i	−0.288228	+	0.288228i	−0.836379	−	0.548151i	$-0.815332\pi$
$883$	−8.56478	+	8.56478i	−0.288228	+	0.288228i	0.548151	+	0.836379i	$0.315332\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.99885	−	2.30874i	0.134268	−	0.0775199i	−0.431361	−	0.902179i	$-0.641967\pi$
$887$	3.99885	−	2.30874i	0.134268	−	0.0775199i	0.565630	+	0.824659i	$0.308633\pi$
$888$		0			0
$889$	18.2707	+	10.5486i	0.612780	+	0.353789i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.638605	−	2.38330i	−0.0213701	−	0.0797543i
$894$		0			0
$895$	2.53624	−	1.46430i	0.0847772	−	0.0489461i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	16.6665	+	16.6665i	0.555859	+	0.555859i
$900$		0			0
$901$	11.2533	−	11.2533i	0.374903	−	0.374903i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.90421	−	6.76228i	−0.129780	−	0.224786i
$906$		0			0
$907$	−8.35931	+	2.23987i	−0.277566	+	0.0743737i	−0.394917	−	0.918717i	$-0.629227\pi$
$907$	−8.35931	+	2.23987i	−0.277566	+	0.0743737i	0.117350	+	0.993091i	$0.462560\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.9969	+	41.5638i	−0.795052	+	1.37707i	0.127755	+	0.991806i	$0.459223\pi$
$911$	−23.9969	+	41.5638i	−0.795052	+	1.37707i	−0.922806	+	0.385264i	$0.874110\pi$
$912$		0			0
$913$	6.43999	+	11.1544i	0.213133	+	0.369156i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	65.2905	+	65.2905i	2.15608	+	2.15608i
$918$		0			0
$919$	−51.8939			−1.71182			−0.855910	−	0.517124i	$-0.827003\pi$
$919$	−51.8939			−1.71182			−0.855910	+	0.517124i	$0.827003\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.6703	+	3.66296i	0.449965	+	0.120568i
$924$		0			0
$925$	−9.04347	+	2.42319i	−0.297347	+	0.0796740i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−8.80130	−	5.08143i	−0.288761	−	0.166716i	0.348622	−	0.937263i	$-0.386650\pi$
$929$	−8.80130	−	5.08143i	−0.288761	−	0.166716i	−0.637383	+	0.770547i	$0.719983\pi$
$930$		0			0
$931$	−11.5478	−	3.09423i	−0.378465	−	0.101409i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			21.7332i			0.710751i
$936$		0			0
$937$			37.8157i			1.23539i	0.786420	+	0.617693i	$0.211932\pi$
$937$			37.8157i			1.23539i	−0.786420	+	0.617693i	$0.788068\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	34.3731	+	9.21025i	1.12053	+	0.300246i	0.771099	−	0.636716i	$-0.219707\pi$
$941$	34.3731	+	9.21025i	1.12053	+	0.300246i	0.349433	+	0.936961i	$0.386374\pi$
$942$		0			0
$943$	−10.5890	−	6.11357i	−0.344826	−	0.199085i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.0399	+	2.69018i	−0.326253	+	0.0874191i	−0.418228	−	0.908342i	$-0.637349\pi$
$947$	−10.0399	+	2.69018i	−0.326253	+	0.0874191i	0.0919752	+	0.995761i	$0.470682\pi$
$948$		0			0
$949$	16.5210	+	4.42678i	0.536293	+	0.143699i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	24.6743			0.799280			0.399640	−	0.916672i	$-0.369135\pi$
$953$	24.6743			0.799280			0.399640	+	0.916672i	$0.369135\pi$
$954$		0			0
$955$	−7.85126	−	7.85126i	−0.254061	−	0.254061i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−12.7873	−	22.1482i	−0.412922	−	0.715203i
$960$		0			0
$961$	0.780708	−	1.35223i	0.0251841	−	0.0436202i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.06416	+	0.553089i	−0.0664475	+	0.0178046i
$966$		0			0
$967$	−12.5371	−	21.7150i	−0.403167	−	0.698306i	0.590939	−	0.806716i	$-0.298757\pi$
$967$	−12.5371	−	21.7150i	−0.403167	−	0.698306i	−0.994106	+	0.108410i	$0.965424\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.9203	−	18.9203i	0.607180	−	0.607180i	−0.335028	−	0.942208i	$-0.608746\pi$
$971$	18.9203	−	18.9203i	0.607180	−	0.607180i	0.942208	+	0.335028i	$0.108746\pi$
$972$		0			0
$973$	−22.2152	−	22.2152i	−0.712186	−	0.712186i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.1897	−	7.03771i	0.389982	−	0.225156i	−0.292170	−	0.956366i	$-0.594377\pi$
$977$	12.1897	−	7.03771i	0.389982	−	0.225156i	0.682152	+	0.731210i	$0.261044\pi$
$978$		0			0
$979$	−1.80650	−	6.74196i	−0.0577360	−	0.215474i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.562149	−	0.324557i	−0.0179298	−	0.0103518i	0.491008	−	0.871155i	$-0.336628\pi$
$983$	−0.562149	−	0.324557i	−0.0179298	−	0.0103518i	−0.508938	+	0.860803i	$0.669962\pi$
$984$		0			0
$985$	−13.8933	+	8.02129i	−0.442677	+	0.255579i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	28.2341	−	28.2341i	0.897792	−	0.897792i
$990$		0			0
$991$			36.5529i			1.16114i	0.814210	+	0.580571i	$0.197171\pi$
$991$			36.5529i			1.16114i	−0.814210	+	0.580571i	$0.802829\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.62940	+	6.08100i	−0.0516554	+	0.192781i
$996$		0			0
$997$	−2.07498	−	7.74395i	−0.0657154	−	0.245253i	0.925253	−	0.379352i	$-0.123853\pi$
$997$	−2.07498	−	7.74395i	−0.0657154	−	0.245253i	−0.990968	+	0.134098i	$0.957186\pi$
$998$		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.1007.13		88
3.2	odd	2		576.2.y.a.47.8		88
4.3	odd	2		432.2.v.a.35.3		88
9.4	even	3		576.2.y.a.239.4		88
9.5	odd	6	inner	1728.2.z.a.1583.13		88
12.11	even	2		144.2.u.a.83.20	yes	88
16.5	even	4		432.2.v.a.251.11		88
16.11	odd	4	inner	1728.2.z.a.143.13		88
36.23	even	6		432.2.v.a.179.11		88
36.31	odd	6		144.2.u.a.131.12	yes	88
48.5	odd	4		144.2.u.a.11.12	✓	88
48.11	even	4		576.2.y.a.335.4		88
144.5	odd	12		432.2.v.a.395.3		88
144.59	even	12	inner	1728.2.z.a.719.13		88
144.85	even	12		144.2.u.a.59.20	yes	88
144.139	odd	12		576.2.y.a.527.8		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.12	✓	88	48.5	odd	4
144.2.u.a.59.20	yes	88	144.85	even	12
144.2.u.a.83.20	yes	88	12.11	even	2
144.2.u.a.131.12	yes	88	36.31	odd	6
432.2.v.a.35.3		88	4.3	odd	2
432.2.v.a.179.11		88	36.23	even	6
432.2.v.a.251.11		88	16.5	even	4
432.2.v.a.395.3		88	144.5	odd	12
576.2.y.a.47.8		88	3.2	odd	2
576.2.y.a.239.4		88	9.4	even	3
576.2.y.a.335.4		88	48.11	even	4
576.2.y.a.527.8		88	144.139	odd	12
1728.2.z.a.143.13		88	16.11	odd	4	inner
1728.2.z.a.719.13		88	144.59	even	12	inner
1728.2.z.a.1007.13		88	1.1	even	1	trivial
1728.2.z.a.1583.13		88	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.206232 - 0.769670i) q^{5} +(2.17574 - 3.76849i) q^{7} +(1.05570 + 3.93991i) q^{11} +(-0.454903 + 1.69772i) q^{13} +6.68683i q^{17} +(0.708282 - 0.708282i) q^{19} +(3.88191 - 2.24122i) q^{23} +(3.78027 + 2.18254i) q^{25} +(1.06907 + 3.98981i) q^{29} +(4.94177 - 2.85313i) q^{31} +(-2.45179 - 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(-1.36389 - 2.36233i) q^{41} +(8.60436 - 2.30553i) q^{43} +(1.23164 - 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(-1.68291 - 1.68291i) q^{53} +3.25015 q^{55} +(-1.00516 - 0.269331i) q^{59} +(1.97401 - 0.528935i) q^{61} +(1.21287 + 0.700250i) q^{65} +(-8.01120 - 2.14659i) q^{67} -8.05218i q^{71} -9.73126i q^{73} +(17.1444 + 4.59383i) q^{77} +(-11.9835 - 6.91865i) q^{79} +(3.05012 - 0.817277i) q^{83} +(5.14666 + 1.37904i) q^{85} -1.71120 q^{89} +(5.40809 + 5.40809i) q^{91} +(-0.399073 - 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 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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