LMFDB - Embedded newform 2592.2.p.f.2159.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2592,2,Mod(431,2592)] 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("2592.431"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2592, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-32,0,0,0,0,0,-8,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(41)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2159.3
Root			$-1.32661 + 0.490008i$ of defining polynomial
Character	$\chi$	$=$	2592.2159
Dual form			2592.2.p.f.431.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796225 + 1.37910i) q^{5} +(-1.24653 + 0.719687i) q^{7} +(4.27718 - 2.46943i) q^{11} +(-4.65213 - 2.68591i) q^{13} +1.32336i q^{17} -0.267949 q^{19} +(-2.97155 + 5.14688i) q^{23} +(1.23205 + 2.13397i) q^{25} +(-4.35066 - 7.53556i) q^{29} +(6.81119 + 3.93244i) q^{31} -2.29213i q^{35} -2.49307i q^{37} +(-8.55435 - 4.93886i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-4.56400 - 7.90509i) q^{47} +(-2.46410 + 4.26795i) q^{49} -5.51641 q^{53} +7.86488i q^{55} +(-4.27718 - 2.46943i) q^{59} +(-4.65213 + 2.68591i) q^{61} +(7.40828 - 4.27718i) q^{65} +(0.598076 - 1.03590i) q^{67} -5.51641 q^{71} -7.92820 q^{73} +(-3.55443 + 6.15645i) q^{77} +(10.5508 - 6.09150i) q^{79} +(6.26222 - 3.61549i) q^{83} +(-1.82505 - 1.05369i) q^{85} -15.7853i q^{89} +7.73205 q^{91} +(0.213348 - 0.369529i) q^{95} +(-4.69615 - 8.13397i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{19} - 8 q^{25} + 16 q^{43} + 16 q^{49} - 32 q^{67} - 16 q^{73} + 96 q^{91} + 8 q^{97}+O(q^{100}) $ 16 * q - 32 * q^19 - 8 * q^25 + 16 * q^43 + 16 * q^49 - 32 * q^67 - 16 * q^73 + 96 * q^91 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−0.796225	+	1.37910i	−0.356083	+	0.616753i	−0.987303	−	0.158851i	$-0.949221\pi$
$5$	−0.796225	+	1.37910i	−0.356083	+	0.616753i	0.631220	+	0.775604i	$0.282555\pi$
$6$		0			0
$7$	−1.24653	+	0.719687i	−0.471146	+	0.272016i	−0.716719	−	0.697362i	$-0.754357\pi$
$7$	−1.24653	+	0.719687i	−0.471146	+	0.272016i	0.245574	+	0.969378i	$0.421024\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.27718	−	2.46943i	1.28962	−	0.744561i	0.311031	−	0.950400i	$-0.399326\pi$
$11$	4.27718	−	2.46943i	1.28962	−	0.744561i	0.978586	+	0.205839i	$0.0659924\pi$
$12$		0			0
$13$	−4.65213	−	2.68591i	−1.29027	−	0.744937i	−0.311567	−	0.950224i	$-0.600854\pi$
$13$	−4.65213	−	2.68591i	−1.29027	−	0.744937i	−0.978702	+	0.205287i	$0.934187\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.32336i			0.320963i	0.987039	+	0.160481i	$0.0513046\pi$
$17$			1.32336i			0.320963i	−0.987039	+	0.160481i	$0.948695\pi$
$18$		0			0
$19$	−0.267949			−0.0614718			−0.0307359	−	0.999528i	$-0.509785\pi$
$19$	−0.267949			−0.0614718			−0.0307359	+	0.999528i	$0.509785\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.97155	+	5.14688i	−0.619612	+	1.07320i	0.369945	+	0.929054i	$0.379377\pi$
$23$	−2.97155	+	5.14688i	−0.619612	+	1.07320i	−0.989557	+	0.144145i	$0.953957\pi$
$24$		0			0
$25$	1.23205	+	2.13397i	0.246410	+	0.426795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.35066	−	7.53556i	−0.807896	−	1.39932i	−0.914318	−	0.404997i	$-0.867273\pi$
$29$	−4.35066	−	7.53556i	−0.807896	−	1.39932i	0.106422	−	0.994321i	$-0.466061\pi$
$30$		0			0
$31$	6.81119	+	3.93244i	1.22333	+	0.706287i	0.965625	−	0.259937i	$-0.0837019\pi$
$31$	6.81119	+	3.93244i	1.22333	+	0.706287i	0.257700	+	0.966225i	$0.417035\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	2.29213i		−	0.387441i
$36$		0			0
$37$		−	2.49307i		−	0.409858i	−0.978777	−	0.204929i	$-0.934304\pi$
$37$		−	2.49307i		−	0.409858i	0.978777	−	0.204929i	$-0.0656963\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.55435	−	4.93886i	−1.33597	−	0.771320i	−0.349759	−	0.936840i	$-0.613736\pi$
$41$	−8.55435	−	4.93886i	−1.33597	−	0.771320i	−0.986206	+	0.165520i	$0.947070\pi$
$42$		0			0
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.56400	−	7.90509i	−0.665728	−	1.15308i	−0.979087	−	0.203441i	$-0.934788\pi$
$47$	−4.56400	−	7.90509i	−0.665728	−	1.15308i	0.313359	−	0.949635i	$-0.398546\pi$
$48$		0			0
$49$	−2.46410	+	4.26795i	−0.352015	+	0.609707i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.51641			−0.757737			−0.378869	−	0.925450i	$-0.623687\pi$
$53$	−5.51641			−0.757737			−0.378869	+	0.925450i	$0.623687\pi$
$54$		0			0
$55$			7.86488i			1.06050i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.27718	−	2.46943i	−0.556841	−	0.321492i	0.195036	−	0.980796i	$-0.437518\pi$
$59$	−4.27718	−	2.46943i	−0.556841	−	0.321492i	−0.751877	+	0.659304i	$0.770851\pi$
$60$		0			0
$61$	−4.65213	+	2.68591i	−0.595644	+	0.343895i	−0.767326	−	0.641257i	$-0.778413\pi$
$61$	−4.65213	+	2.68591i	−0.595644	+	0.343895i	0.171682	+	0.985152i	$0.445080\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.40828	−	4.27718i	0.918885	−	0.530518i
$66$		0			0
$67$	0.598076	−	1.03590i	0.0730666	−	0.126555i	−0.827177	−	0.561941i	$-0.810055\pi$
$67$	0.598076	−	1.03590i	0.0730666	−	0.126555i	0.900244	+	0.435386i	$0.143388\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.51641			−0.654677			−0.327339	−	0.944907i	$-0.606152\pi$
$71$	−5.51641			−0.654677			−0.327339	+	0.944907i	$0.606152\pi$
$72$		0			0
$73$	−7.92820			−0.927926			−0.463963	−	0.885855i	$-0.653573\pi$
$73$	−7.92820			−0.927926			−0.463963	+	0.885855i	$0.653573\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.55443	+	6.15645i	−0.405065	+	0.701593i
$78$		0			0
$79$	10.5508	−	6.09150i	1.18706	−	0.685348i	0.229420	−	0.973327i	$-0.426317\pi$
$79$	10.5508	−	6.09150i	1.18706	−	0.685348i	0.957636	+	0.287980i	$0.0929836\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.26222	−	3.61549i	0.687368	−	0.396852i	−0.115257	−	0.993336i	$-0.536769\pi$
$83$	6.26222	−	3.61549i	0.687368	−	0.396852i	0.802625	+	0.596484i	$0.203436\pi$
$84$		0			0
$85$	−1.82505	−	1.05369i	−0.197955	−	0.114289i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	15.7853i		−	1.67324i	−0.547782	−	0.836621i	$-0.684528\pi$
$89$		−	15.7853i		−	1.67324i	0.547782	−	0.836621i	$-0.315472\pi$
$90$		0			0
$91$	7.73205			0.810539
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.213348	−	0.369529i	0.0218890	−	0.0379129i
$96$		0			0
$97$	−4.69615	−	8.13397i	−0.476822	−	0.825880i	0.522825	−	0.852440i	$-0.324878\pi$
$97$	−4.69615	−	8.13397i	−0.476822	−	0.825880i	−0.999647	+	0.0265599i	$0.991545\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.59245	−	2.75821i	−0.158455	−	0.274452i	0.775857	−	0.630909i	$-0.217318\pi$
$101$	−1.59245	−	2.75821i	−0.158455	−	0.274452i	−0.934312	+	0.356457i	$0.883985\pi$
$102$		0			0
$103$	−1.24653	−	0.719687i	−0.122825	−	0.0709129i	0.437329	−	0.899302i	$-0.355925\pi$
$103$	−1.24653	−	0.719687i	−0.122825	−	0.0709129i	−0.560154	+	0.828389i	$0.689258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	12.1698i		−	1.17650i	−0.808678	−	0.588252i	$-0.799816\pi$
$107$		−	12.1698i		−	1.17650i	0.808678	−	0.588252i	$-0.200184\pi$
$108$		0			0
$109$		−	13.6224i		−	1.30479i	−0.757880	−	0.652394i	$-0.773765\pi$
$109$		−	13.6224i		−	1.30479i	0.757880	−	0.652394i	$-0.226235\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.70042	+	5.60054i	0.912538	+	0.526854i	0.881247	−	0.472656i	$-0.156705\pi$
$113$	9.70042	+	5.60054i	0.912538	+	0.526854i	0.0312914	+	0.999510i	$0.490038\pi$
$114$		0			0
$115$	−4.73205	−	8.19615i	−0.441266	−	0.764295i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.952407	−	1.64962i	−0.0873070	−	0.151220i
$120$		0			0
$121$	6.69615	−	11.5981i	0.608741	−	1.05437i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.8862			−1.06314
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.26222	−	3.61549i	−0.547133	−	0.315887i	0.200832	−	0.979626i	$-0.435635\pi$
$131$	−6.26222	−	3.61549i	−0.547133	−	0.315887i	−0.747965	+	0.663739i	$0.768969\pi$
$132$		0			0
$133$	0.334008	−	0.192840i	0.0289622	−	0.0167213i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.11615	−	2.95381i	0.437103	−	0.252361i	−0.265265	−	0.964175i	$-0.585460\pi$
$137$	5.11615	−	2.95381i	0.437103	−	0.252361i	0.702368	+	0.711814i	$0.252126\pi$
$138$		0			0
$139$	3.59808	−	6.23205i	0.305185	−	0.528596i	−0.672118	−	0.740444i	$-0.734615\pi$
$139$	3.59808	−	6.23205i	0.305185	−	0.528596i	0.977302	+	0.211849i	$0.0679484\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−26.5306			−2.21860
$144$		0			0
$145$	13.8564			1.15071
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.59245	−	2.75821i	0.130459	−	0.225961i	−0.793395	−	0.608707i	$-0.791688\pi$
$149$	1.59245	−	2.75821i	0.130459	−	0.225961i	0.923853	+	0.382746i	$0.125022\pi$
$150$		0			0
$151$	−5.56466	+	3.21276i	−0.452845	+	0.261450i	−0.709031	−	0.705177i	$-0.750867\pi$
$151$	−5.56466	+	3.21276i	−0.452845	+	0.261450i	0.256186	+	0.966628i	$0.417534\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.8465	+	6.26222i	−0.871210	+	0.502994i
$156$		0			0
$157$	1.82505	+	1.05369i	0.145655	+	0.0840940i	0.571056	−	0.820911i	$-0.306534\pi$
$157$	1.82505	+	1.05369i	0.145655	+	0.0840940i	−0.425401	+	0.905005i	$0.639867\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	8.55435i		−	0.674177i
$162$		0			0
$163$	−19.1962			−1.50356			−0.751779	−	0.659415i	$-0.770804\pi$
$163$	−19.1962			−1.50356			−0.751779	+	0.659415i	$0.770804\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.54486	−	4.40782i	0.196927	−	0.341087i	−0.750604	−	0.660753i	$-0.770237\pi$
$167$	2.54486	−	4.40782i	0.196927	−	0.341087i	0.947531	+	0.319665i	$0.103570\pi$
$168$		0			0
$169$	7.92820	+	13.7321i	0.609862	+	1.05631i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.94311	+	10.2938i	0.451846	+	0.782620i	0.998501	−	0.0547379i	$-0.0174323\pi$
$173$	5.94311	+	10.2938i	0.451846	+	0.782620i	−0.546655	+	0.837358i	$0.684099\pi$
$174$		0			0
$175$	−3.07159	−	1.77338i	−0.232190	−	0.134055i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	9.87771i		−	0.738295i	−0.929371	−	0.369147i	$-0.879650\pi$
$179$		−	9.87771i		−	0.738295i	0.929371	−	0.369147i	$-0.120350\pi$
$180$		0			0
$181$			16.1154i			1.19785i	0.800804	+	0.598926i	$0.204406\pi$
$181$			16.1154i			1.19785i	−0.800804	+	0.598926i	$0.795594\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.43820	+	1.98504i	0.252781	+	0.145943i
$186$		0			0
$187$	3.26795	+	5.66025i	0.238976	+	0.413919i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.56400	−	7.90509i	−0.330240	−	0.571992i	0.652319	−	0.757945i	$-0.273796\pi$
$191$	−4.56400	−	7.90509i	−0.330240	−	0.571992i	−0.982559	+	0.185953i	$0.940463\pi$
$192$		0			0
$193$	−7.69615	+	13.3301i	−0.553981	+	0.959524i	0.444001	+	0.896026i	$0.353559\pi$
$193$	−7.69615	+	13.3301i	−0.553981	+	0.959524i	−0.997982	+	0.0634972i	$0.979775\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.8485			−1.41414			−0.707072	−	0.707141i	$-0.749984\pi$
$197$	−19.8485			−1.41414			−0.707072	+	0.707141i	$0.749984\pi$
$198$		0			0
$199$		−	14.2904i		−	1.01302i	−0.862234	−	0.506510i	$-0.830935\pi$
$199$		−	14.2904i		−	1.01302i	0.862234	−	0.506510i	$-0.169065\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.8465	+	6.26222i	0.761274	+	0.439522i
$204$		0			0
$205$	13.6224	−	7.86488i	0.951428	−	0.549307i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.14607	+	0.661681i	−0.0792750	+	0.0457695i
$210$		0			0
$211$	−8.52628	+	14.7679i	−0.586973	+	1.01667i	0.407653	+	0.913137i	$0.366347\pi$
$211$	−8.52628	+	14.7679i	−0.586973	+	1.01667i	−0.994626	+	0.103531i	$0.966986\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.18490			−0.217208
$216$		0			0
$217$	−11.3205			−0.768486
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.55443	−	6.15645i	0.239097	−	0.414128i
$222$		0			0
$223$	−16.7835	+	9.68994i	−1.12390	+	0.648886i	−0.942395	−	0.334503i	$-0.891432\pi$
$223$	−16.7835	+	9.68994i	−1.12390	+	0.648886i	−0.181509	+	0.983389i	$0.558098\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.55435	+	4.93886i	−0.567772	+	0.327803i	−0.756259	−	0.654272i	$-0.772975\pi$
$227$	−8.55435	+	4.93886i	−0.567772	+	0.327803i	0.188487	+	0.982076i	$0.439642\pi$
$228$		0			0
$229$	13.6224	+	7.86488i	0.900192	+	0.519726i	0.877263	−	0.480011i	$-0.159367\pi$
$229$	13.6224	+	7.86488i	0.900192	+	0.519726i	0.0229296	+	0.999737i	$0.492701\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	2.64673i		−	0.173393i	−0.996235	−	0.0866964i	$-0.972369\pi$
$233$		−	2.64673i		−	0.173393i	0.996235	−	0.0866964i	$-0.0276310\pi$
$234$		0			0
$235$	14.5359			0.948217
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.18490	−	5.51641i	0.206014	−	0.356827i	−0.744441	−	0.667688i	$-0.767284\pi$
$239$	3.18490	−	5.51641i	0.206014	−	0.356827i	0.950455	+	0.310861i	$0.100617\pi$
$240$		0			0
$241$	−7.69615	−	13.3301i	−0.495753	−	0.858669i	0.504235	−	0.863566i	$-0.331774\pi$
$241$	−7.69615	−	13.3301i	−0.495753	−	0.858669i	−0.999988	+	0.00489737i	$0.998441\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.92396	−	6.79650i	−0.250693	−	0.434212i
$246$		0			0
$247$	1.24653	+	0.719687i	0.0793151	+	0.0457926i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			2.64673i			0.167060i	0.996505	+	0.0835299i	$0.0266194\pi$
$251$			2.64673i			0.167060i	−0.996505	+	0.0835299i	$0.973381\pi$
$252$		0			0
$253$			29.3521i			1.84535i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.55435	−	4.93886i	−0.533606	−	0.308077i	0.208878	−	0.977942i	$-0.433019\pi$
$257$	−8.55435	−	4.93886i	−0.533606	−	0.308077i	−0.742484	+	0.669864i	$0.766352\pi$
$258$		0			0
$259$	1.79423	+	3.10770i	0.111488	+	0.193103i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.8862	+	20.5875i	0.732935	+	1.26948i	0.955623	+	0.294591i	$0.0951835\pi$
$263$	11.8862	+	20.5875i	0.732935	+	1.26948i	−0.222688	+	0.974890i	$0.571483\pi$
$264$		0			0
$265$	4.39230	−	7.60770i	0.269817	−	0.467337i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.739059			−0.0450612			−0.0225306	−	0.999746i	$-0.507172\pi$
$269$	−0.739059			−0.0450612			−0.0225306	+	0.999746i	$0.507172\pi$
$270$		0			0
$271$		−	4.31812i		−	0.262307i	−0.991362	−	0.131154i	$-0.958132\pi$
$271$		−	4.31812i		−	0.262307i	0.991362	−	0.131154i	$-0.0418681\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.5394	+	6.08492i	0.635549	+	0.366935i
$276$		0			0
$277$	1.82505	−	1.05369i	0.109657	−	0.0633104i	−0.444169	−	0.895943i	$-0.646501\pi$
$277$	1.82505	−	1.05369i	0.109657	−	0.0633104i	0.553825	+	0.832633i	$0.313168\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.26222	+	3.61549i	−0.373573	+	0.215682i	−0.675018	−	0.737801i	$-0.735864\pi$
$281$	−6.26222	+	3.61549i	−0.373573	+	0.215682i	0.301445	+	0.953483i	$0.402531\pi$
$282$		0			0
$283$	0.0717968	−	0.124356i	0.00426787	−	0.00739218i	−0.863884	−	0.503692i	$-0.831975\pi$
$283$	0.0717968	−	0.124356i	0.00426787	−	0.00739218i	0.868151	+	0.496299i	$0.165308\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.2177			0.839246
$288$		0			0
$289$	15.2487			0.896983
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.55443	+	6.15645i	−0.207652	+	0.359664i	−0.950974	−	0.309269i	$-0.899916\pi$
$293$	−3.55443	+	6.15645i	−0.207652	+	0.359664i	0.743322	+	0.668933i	$0.233249\pi$
$294$		0			0
$295$	6.81119	−	3.93244i	0.396563	−	0.228956i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	27.6481	−	15.9626i	1.59893	−	0.923143i
$300$		0			0
$301$	−2.49307	−	1.43937i	−0.143698	−	0.0829641i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	8.55435i		−	0.489821i
$306$		0			0
$307$	−7.07180			−0.403609			−0.201804	−	0.979426i	$-0.564681\pi$
$307$	−7.07180			−0.403609			−0.201804	+	0.979426i	$0.564681\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.48796	+	14.7016i	−0.481308	+	0.833650i	−0.999770	−	0.0214506i	$-0.993172\pi$
$311$	−8.48796	+	14.7016i	−0.481308	+	0.833650i	0.518462	+	0.855101i	$0.326505\pi$
$312$		0			0
$313$	5.69615	+	9.86603i	0.321966	+	0.557661i	0.980894	−	0.194545i	$-0.0623231\pi$
$313$	5.69615	+	9.86603i	0.321966	+	0.557661i	−0.658928	+	0.752206i	$0.728990\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.16575	+	2.01915i	0.0654753	+	0.113407i	0.896905	−	0.442224i	$-0.145810\pi$
$317$	1.16575	+	2.01915i	0.0654753	+	0.113407i	−0.831429	+	0.555630i	$0.812477\pi$
$318$		0			0
$319$	−37.2170	−	21.4873i	−2.08375	−	1.20306i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	0.354594i		−	0.0197301i
$324$		0			0
$325$		−	13.2367i		−	0.734240i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.3784	+	6.56931i	0.627310	+	0.362178i
$330$		0			0
$331$	13.0622	+	22.6244i	0.717962	+	1.24355i	0.961806	+	0.273732i	$0.0882583\pi$
$331$	13.0622	+	22.6244i	0.717962	+	1.24355i	−0.243844	+	0.969815i	$0.578408\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.952407	+	1.64962i	0.0520355	+	0.0901282i
$336$		0			0
$337$	−4.69615	+	8.13397i	−0.255816	+	0.443086i	−0.965117	−	0.261820i	$-0.915677\pi$
$337$	−4.69615	+	8.13397i	−0.255816	+	0.443086i	0.709301	+	0.704906i	$0.249011\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	38.8435			2.10350
$342$		0			0
$343$		−	17.1691i		−	0.927047i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.1087	−	9.87771i	−0.918443	−	0.530263i	−0.0353051	−	0.999377i	$-0.511240\pi$
$347$	−17.1087	−	9.87771i	−0.918443	−	0.530263i	−0.883138	+	0.469113i	$0.844574\pi$
$348$		0			0
$349$	−20.7676	+	11.9902i	−1.11166	+	0.641819i	−0.939260	−	0.343208i	$-0.888487\pi$
$349$	−20.7676	+	11.9902i	−1.11166	+	0.641819i	−0.172403	+	0.985026i	$0.555153\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.1087	+	9.87771i	−0.910604	+	0.525738i	−0.880626	−	0.473813i	$-0.842877\pi$
$353$	−17.1087	+	9.87771i	−0.910604	+	0.525738i	−0.0299788	+	0.999551i	$0.509544\pi$
$354$		0			0
$355$	4.39230	−	7.60770i	0.233119	−	0.403775i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.79650			0.358705			0.179353	−	0.983785i	$-0.442600\pi$
$359$	6.79650			0.358705			0.179353	+	0.983785i	$0.442600\pi$
$360$		0			0
$361$	−18.9282			−0.996221
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.31264	−	10.9338i	0.330418	−	0.572302i
$366$		0			0
$367$	−14.2009	+	8.19889i	−0.741281	+	0.427979i	−0.822535	−	0.568715i	$-0.807441\pi$
$367$	−14.2009	+	8.19889i	−0.741281	+	0.427979i	0.0812540	+	0.996693i	$0.474108\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.87639	−	3.97009i	0.357005	−	0.206117i
$372$		0			0
$373$	15.7814	+	9.11142i	0.817132	+	0.471771i	0.849426	−	0.527707i	$-0.176948\pi$
$373$	15.7814	+	9.11142i	0.817132	+	0.471771i	−0.0322945	+	0.999478i	$0.510281\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			46.7418i			2.40733i
$378$		0			0
$379$	29.7321			1.52723			0.763616	−	0.645670i	$-0.223422\pi$
$379$	29.7321			1.52723			0.763616	+	0.645670i	$0.223422\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.94311	−	10.2938i	0.303679	−	0.525987i	−0.673288	−	0.739381i	$-0.735118\pi$
$383$	5.94311	−	10.2938i	0.303679	−	0.525987i	0.976966	+	0.213394i	$0.0684518\pi$
$384$		0			0
$385$	−5.66025	−	9.80385i	−0.288473	−	0.499650i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.98113	−	6.89551i	−0.201851	−	0.349616i	0.747274	−	0.664516i	$-0.231362\pi$
$389$	−3.98113	−	6.89551i	−0.201851	−	0.349616i	−0.949125	+	0.314900i	$0.898029\pi$
$390$		0			0
$391$	−6.81119	−	3.93244i	−0.344457	−	0.198872i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			19.4008i			0.976162i
$396$		0			0
$397$		−	13.6224i		−	0.683688i	−0.939757	−	0.341844i	$-0.888949\pi$
$397$		−	13.6224i		−	0.683688i	0.939757	−	0.341844i	$-0.111051\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−34.2174	−	19.7554i	−1.70874	−	0.986539i	−0.936131	−	0.351651i	$-0.885620\pi$
$401$	−34.2174	−	19.7554i	−1.70874	−	0.986539i	−0.772604	−	0.634888i	$-0.781046\pi$
$402$		0			0
$403$	−21.1244	−	36.5885i	−1.05228	−	1.82260i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.15645	−	10.6633i	−0.305164	−	0.528560i
$408$		0			0
$409$	14.6962	−	25.4545i	0.726678	−	1.25864i	−0.231602	−	0.972811i	$-0.574397\pi$
$409$	14.6962	−	25.4545i	0.726678	−	1.25864i	0.958280	−	0.285832i	$-0.0922701\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.10886			0.349804
$414$		0			0
$415$			11.5150i			0.565249i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.307087	−	0.177297i	−0.0150022	−	0.00866152i	0.492480	−	0.870324i	$-0.336090\pi$
$419$	−0.307087	−	0.177297i	−0.0150022	−	0.00866152i	−0.507482	+	0.861662i	$0.669424\pi$
$420$		0			0
$421$	11.4633	−	6.61835i	0.558688	−	0.322559i	−0.193931	−	0.981015i	$-0.562124\pi$
$421$	11.4633	−	6.61835i	0.558688	−	0.322559i	0.752619	+	0.658457i	$0.228790\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.82402	+	1.63045i	−0.136985	+	0.0790884i
$426$		0			0
$427$	3.86603	−	6.69615i	0.187090	−	0.324050i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	38.4168			1.85047			0.925237	−	0.379390i	$-0.123866\pi$
$431$	38.4168			1.85047			0.925237	+	0.379390i	$0.123866\pi$
$432$		0			0
$433$	11.4641			0.550930			0.275465	−	0.961311i	$-0.411168\pi$
$433$	11.4641			0.550930			0.275465	+	0.961311i	$0.411168\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.796225	−	1.37910i	0.0380886	−	0.0659714i
$438$		0			0
$439$	30.4058	−	17.5548i	1.45119	−	0.837846i	0.452642	−	0.891692i	$-0.350481\pi$
$439$	30.4058	−	17.5548i	1.45119	−	0.837846i	0.998549	+	0.0538462i	$0.0171481\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−27.3410	+	15.7853i	−1.29901	+	0.749984i	−0.980233	−	0.197846i	$-0.936606\pi$
$443$	−27.3410	+	15.7853i	−1.29901	+	0.749984i	−0.318777	+	0.947830i	$0.603272\pi$
$444$		0			0
$445$	21.7696	+	12.5687i	1.03198	+	0.595813i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			23.0163i			1.08621i	0.839666	+	0.543104i	$0.182751\pi$
$449$			23.0163i			1.08621i	−0.839666	+	0.543104i	$0.817249\pi$
$450$		0			0
$451$	−48.7846			−2.29718
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.15645	+	10.6633i	−0.288619	+	0.499903i
$456$		0			0
$457$	7.19615	+	12.4641i	0.336622	+	0.583046i	0.983795	−	0.179297i	$-0.0573823\pi$
$457$	7.19615	+	12.4641i	0.336622	+	0.583046i	−0.647173	+	0.762343i	$0.724049\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.49754	−	16.4502i	−0.442344	−	0.766163i	0.555519	−	0.831504i	$-0.312520\pi$
$461$	−9.49754	−	16.4502i	−0.442344	−	0.766163i	−0.997863	+	0.0653412i	$0.979186\pi$
$462$		0			0
$463$	26.6662	+	15.3958i	1.23929	+	0.715502i	0.968948	−	0.247264i	$-0.0795315\pi$
$463$	26.6662	+	15.3958i	1.23929	+	0.715502i	0.270337	+	0.962766i	$0.412865\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			17.4633i			0.808105i	0.914736	+	0.404052i	$0.132399\pi$
$467$			17.4633i			0.808105i	−0.914736	+	0.404052i	$0.867601\pi$
$468$		0			0
$469$			1.72171i			0.0795012i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.55435	+	4.93886i	0.393329	+	0.227089i
$474$		0			0
$475$	−0.330127	−	0.571797i	−0.0151473	−	0.0262358i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.59245	+	2.75821i	0.0727609	+	0.126026i	0.900110	−	0.435662i	$-0.143486\pi$
$479$	1.59245	+	2.75821i	0.0727609	+	0.126026i	−0.827349	+	0.561688i	$0.810152\pi$
$480$		0			0
$481$	−6.69615	+	11.5981i	−0.305318	+	0.528827i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	14.9568			0.679152
$486$		0			0
$487$			37.8850i			1.71674i	0.513035	+	0.858368i	$0.328521\pi$
$487$			37.8850i			1.71674i	−0.513035	+	0.858368i	$0.671479\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	14.5095	+	8.37705i	0.654804	+	0.378051i	0.790294	−	0.612728i	$-0.209928\pi$
$491$	14.5095	+	8.37705i	0.654804	+	0.378051i	−0.135490	+	0.990779i	$0.543261\pi$
$492$		0			0
$493$	9.97227	−	5.75749i	0.449129	−	0.259305i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.87639	−	3.97009i	0.308448	−	0.178083i
$498$		0			0
$499$	−13.1962	+	22.8564i	−0.590741	+	1.02319i	0.403392	+	0.915027i	$0.367831\pi$
$499$	−13.1962	+	22.8564i	−0.590741	+	1.02319i	−0.994133	+	0.108166i	$0.965502\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.3785			1.53286			0.766432	−	0.642326i	$-0.222030\pi$
$503$	34.3785			1.53286			0.766432	+	0.642326i	$0.222030\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.0900	+	19.2084i	−0.491555	+	0.851398i	−0.999953	−	0.00972413i	$-0.996905\pi$
$509$	−11.0900	+	19.2084i	−0.491555	+	0.851398i	0.508398	+	0.861122i	$0.330238\pi$
$510$		0			0
$511$	9.88278	−	5.70582i	0.437188	−	0.252411i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.98504	−	1.14607i	0.0874715	−	0.0505017i
$516$		0			0
$517$	−39.0421	−	22.5410i	−1.71707	−	0.991350i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			1.32336i			0.0579776i	0.999580	+	0.0289888i	$0.00922871\pi$
$521$			1.32336i			0.0579776i	−0.999580	+	0.0289888i	$0.990771\pi$
$522$		0			0
$523$	6.41154			0.280357			0.140179	−	0.990126i	$-0.455232\pi$
$523$	6.41154			0.280357			0.140179	+	0.990126i	$0.455232\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.20405	+	9.01367i	−0.226692	+	0.392642i
$528$		0			0
$529$	−6.16025	−	10.6699i	−0.267837	−	0.463908i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	26.5306	+	45.9524i	1.14917	+	1.99042i
$534$		0			0
$535$	16.7835	+	9.68994i	0.725612	+	0.418933i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			24.3397i			1.04838i
$540$		0			0
$541$		−	12.4653i		−	0.535927i	−0.963429	−	0.267963i	$-0.913649\pi$
$541$		−	12.4653i		−	0.535927i	0.963429	−	0.267963i	$-0.0863506\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	18.7867	+	10.8465i	0.804732	+	0.464612i
$546$		0			0
$547$	−0.205771	−	0.356406i	−0.00879815	−	0.0152388i	0.861593	−	0.507600i	$-0.169467\pi$
$547$	−0.205771	−	0.356406i	−0.00879815	−	0.0152388i	−0.870391	+	0.492361i	$0.836134\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.16575	+	2.01915i	0.0496628	+	0.0860185i
$552$		0			0
$553$	−8.76795	+	15.1865i	−0.372851	+	0.645797i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	36.3977			1.54222			0.771110	−	0.636702i	$-0.219702\pi$
$557$	36.3977			1.54222			0.771110	+	0.636702i	$0.219702\pi$
$558$		0			0
$559$		−	10.7436i		−	0.454407i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.2323	−	5.90763i	−0.431240	−	0.248977i	0.268635	−	0.963242i	$-0.413428\pi$
$563$	−10.2323	−	5.90763i	−0.431240	−	0.248977i	−0.699875	+	0.714265i	$0.746761\pi$
$564$		0			0
$565$	−15.4474	+	8.91858i	−0.649878	+	0.375207i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	30.7792	−	17.7704i	1.29033	−	0.744973i	0.311619	−	0.950207i	$-0.399129\pi$
$569$	30.7792	−	17.7704i	1.29033	−	0.744973i	0.978713	+	0.205234i	$0.0657956\pi$
$570$		0			0
$571$	3.59808	−	6.23205i	0.150575	−	0.260803i	−0.780864	−	0.624701i	$-0.785221\pi$
$571$	3.59808	−	6.23205i	0.150575	−	0.260803i	0.931439	+	0.363898i	$0.118554\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−14.6444			−0.610714
$576$		0			0
$577$	−1.92820			−0.0802722			−0.0401361	−	0.999194i	$-0.512779\pi$
$577$	−1.92820			−0.0802722			−0.0401361	+	0.999194i	$0.512779\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.20405	+	9.01367i	−0.215900	+	0.373950i
$582$		0			0
$583$	−23.5947	+	13.6224i	−0.977191	+	0.564181i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.5095	+	8.37705i	−0.598870	+	0.345758i	−0.768597	−	0.639733i	$-0.779045\pi$
$587$	−14.5095	+	8.37705i	−0.598870	+	0.345758i	0.169727	+	0.985491i	$0.445712\pi$
$588$		0			0
$589$	−1.82505	−	1.05369i	−0.0752000	−	0.0434167i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.93754i			0.0795651i	0.999208	+	0.0397826i	$0.0126665\pi$
$593$			1.93754i			0.0795651i	−0.999208	+	0.0397826i	$0.987333\pi$
$594$		0			0
$595$	3.03332			0.124354
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.7533	−	37.6778i	0.888815	−	1.53947i	0.0475370	−	0.998869i	$-0.484863\pi$
$599$	21.7533	−	37.6778i	0.888815	−	1.53947i	0.841278	−	0.540603i	$-0.181804\pi$
$600$		0			0
$601$	−4.80385	−	8.32051i	−0.195953	−	0.339401i	0.751259	−	0.660007i	$-0.229447\pi$
$601$	−4.80385	−	8.32051i	−0.195953	−	0.339401i	−0.947213	+	0.320606i	$0.896113\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.6633	+	18.4694i	0.433524	+	0.750886i
$606$		0			0
$607$	23.5052	+	13.5707i	0.954045	+	0.550818i	0.894335	−	0.447398i	$-0.147649\pi$
$607$	23.5052	+	13.5707i	0.954045	+	0.550818i	0.0597098	+	0.998216i	$0.480982\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			49.0340i			1.98370i
$612$		0			0
$613$			2.49307i			0.100694i	0.998732	+	0.0503470i	$0.0160327\pi$
$613$			2.49307i			0.100694i	−0.998732	+	0.0503470i	$0.983967\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.5469	+	11.8628i	0.827187	+	0.477577i	0.852889	−	0.522093i	$-0.174849\pi$
$617$	20.5469	+	11.8628i	0.827187	+	0.477577i	−0.0257016	+	0.999670i	$0.508182\pi$
$618$		0			0
$619$	13.4019	+	23.2128i	0.538669	+	0.933002i	0.998976	+	0.0452421i	$0.0144059\pi$
$619$	13.4019	+	23.2128i	0.538669	+	0.933002i	−0.460307	+	0.887760i	$0.652261\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.3605	+	19.6770i	0.455149	+	0.788341i
$624$		0			0
$625$	3.30385	−	5.72243i	0.132154	−	0.228897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.29923			0.131549
$630$		0			0
$631$		−	17.9405i		−	0.714200i	−0.934066	−	0.357100i	$-0.883766\pi$
$631$		−	17.9405i		−	0.714200i	0.934066	−	0.357100i	$-0.116234\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	22.9266	−	13.2367i	0.908386	−	0.524457i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.2323	+	5.90763i	−0.404152	+	0.233337i	−0.688274	−	0.725451i	$-0.741631\pi$
$641$	−10.2323	+	5.90763i	−0.404152	+	0.233337i	0.284122	+	0.958788i	$0.408298\pi$
$642$		0			0
$643$	11.3923	−	19.7321i	0.449269	−	0.778156i	−0.549070	−	0.835776i	$-0.685018\pi$
$643$	11.3923	−	19.7321i	0.449269	−	0.778156i	0.998339	+	0.0576203i	$0.0183513\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.47812			0.0581108			0.0290554	−	0.999578i	$-0.490750\pi$
$647$	1.47812			0.0581108			0.0290554	+	0.999578i	$0.490750\pi$
$648$		0			0
$649$	−24.3923			−0.957482
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.9054	−	24.0848i	0.544159	−	0.942511i	−0.454501	−	0.890746i	$-0.650182\pi$
$653$	13.9054	−	24.0848i	0.544159	−	0.942511i	0.998659	−	0.0517641i	$-0.0164844\pi$
$654$		0			0
$655$	9.97227	−	5.75749i	0.389649	−	0.224964i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.4008	+	11.2011i	−0.755749	+	0.436332i	−0.827767	−	0.561071i	$-0.810389\pi$
$659$	−19.4008	+	11.2011i	−0.755749	+	0.436332i	0.0720183	+	0.997403i	$0.477056\pi$
$660$		0			0
$661$	−35.7260	−	20.6264i	−1.38958	−	0.802274i	−0.396312	−	0.918116i	$-0.629710\pi$
$661$	−35.7260	−	20.6264i	−1.38958	−	0.802274i	−0.993268	+	0.115842i	$0.963044\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			0.614175i			0.0238167i
$666$		0			0
$667$	51.7128			2.00233
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−13.2653	+	22.9762i	−0.512102	+	0.886986i
$672$		0			0
$673$	6.62436	+	11.4737i	0.255350	+	0.442279i	0.964991	−	0.262285i	$-0.0844759\pi$
$673$	6.62436	+	11.4737i	0.255350	+	0.442279i	−0.709640	+	0.704564i	$0.751143\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.00027	−	10.3928i	−0.230609	−	0.399427i	0.727378	−	0.686237i	$-0.240739\pi$
$677$	−6.00027	−	10.3928i	−0.230609	−	0.399427i	−0.957988	+	0.286810i	$0.907405\pi$
$678$		0			0
$679$	11.7078	+	6.75952i	0.449305	+	0.259407i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	34.9266i		−	1.33643i	−0.743969	−	0.668214i	$-0.767059\pi$
$683$		−	34.9266i		−	1.33643i	0.743969	−	0.668214i	$-0.232941\pi$
$684$		0			0
$685$			9.40760i			0.359446i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	25.6631	+	14.8166i	0.977684	+	0.564466i
$690$		0			0
$691$	−11.9282	−	20.6603i	−0.453770	−	0.785953i	0.544846	−	0.838536i	$-0.316588\pi$
$691$	−11.9282	−	20.6603i	−0.453770	−	0.785953i	−0.998617	+	0.0525828i	$0.983255\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.72976	+	9.92423i	0.217342	+	0.376448i
$696$		0			0
$697$	6.53590	−	11.3205i	0.247565	−	0.428795i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	17.2883			0.652970			0.326485	−	0.945202i	$-0.394136\pi$
$701$	17.2883			0.652970			0.326485	+	0.945202i	$0.394136\pi$
$702$		0			0
$703$			0.668016i			0.0251947i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.97009	+	2.29213i	0.149311	+	0.0862045i
$708$		0			0
$709$	−23.9287	+	13.8152i	−0.898660	+	0.518841i	−0.876765	−	0.480919i	$-0.840303\pi$
$709$	−23.9287	+	13.8152i	−0.898660	+	0.518841i	−0.0218946	+	0.999760i	$0.506970\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−40.4796	+	23.3709i	−1.51597	+	0.875248i
$714$		0			0
$715$	21.1244	−	36.5885i	0.790006	−	1.36833i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.0711			0.562058			0.281029	−	0.959699i	$-0.409324\pi$
$719$	15.0711			0.562058			0.281029	+	0.959699i	$0.409324\pi$
$720$		0			0
$721$	2.07180			0.0771577
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.7205	−	18.5684i	0.398148	−	0.689612i
$726$		0			0
$727$	−16.7835	+	9.68994i	−0.622464	+	0.359380i	−0.777828	−	0.628477i	$-0.783678\pi$
$727$	−16.7835	+	9.68994i	−0.622464	+	0.359380i	0.155364	+	0.987857i	$0.450345\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.29213	+	1.32336i	−0.0847775	+	0.0489463i
$732$		0			0
$733$	−39.0421	−	22.5410i	−1.44205	−	0.832569i	−0.444066	−	0.895994i	$-0.646464\pi$
$733$	−39.0421	−	22.5410i	−1.44205	−	0.832569i	−0.997987	+	0.0634249i	$0.979798\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	5.90763i		−	0.217610i
$738$		0			0
$739$	−48.6410			−1.78929			−0.894644	−	0.446779i	$-0.852571\pi$
$739$	−48.6410			−1.78929			−0.894644	+	0.446779i	$0.852571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.6543	−	37.5063i	0.794418	−	1.37597i	−0.128790	−	0.991672i	$-0.541109\pi$
$743$	21.6543	−	37.5063i	0.794418	−	1.37597i	0.923208	−	0.384300i	$-0.125557\pi$
$744$		0			0
$745$	2.53590	+	4.39230i	0.0929081	+	0.160922i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.75848	+	15.1701i	0.320028	+	0.554304i
$750$		0			0
$751$	6.23267	+	3.59843i	0.227433	+	0.131309i	0.609387	−	0.792873i	$-0.291415\pi$
$751$	6.23267	+	3.59843i	0.227433	+	0.131309i	−0.381954	+	0.924181i	$0.624749\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	10.2323i		−	0.372392i
$756$		0			0
$757$		−	36.0600i		−	1.31062i	−0.755359	−	0.655311i	$-0.772537\pi$
$757$		−	36.0600i		−	1.31062i	0.755359	−	0.655311i	$-0.227463\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−22.8390	−	13.1861i	−0.827914	−	0.477996i	0.0252238	−	0.999682i	$-0.491970\pi$
$761$	−22.8390	−	13.1861i	−0.827914	−	0.477996i	−0.853138	+	0.521685i	$0.825304\pi$
$762$		0			0
$763$	9.80385	+	16.9808i	0.354923	+	0.614745i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.2653	+	22.9762i	0.478983	+	0.829622i
$768$		0			0
$769$	−8.96410	+	15.5263i	−0.323254	+	0.559892i	−0.981157	−	0.193210i	$-0.938110\pi$
$769$	−8.96410	+	15.5263i	−0.323254	+	0.559892i	0.657904	+	0.753102i	$0.271443\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−34.1805			−1.22939			−0.614694	−	0.788766i	$-0.710720\pi$
$773$	−34.1805			−1.22939			−0.614694	+	0.788766i	$0.710720\pi$
$774$		0			0
$775$			19.3799i			0.696146i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.29213	+	1.32336i	0.0821241	+	0.0474144i
$780$		0			0
$781$	−23.5947	+	13.6224i	−0.844283	+	0.487447i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.90631	+	1.67796i	−0.103731	+	0.0598888i
$786$		0			0
$787$	−25.7224	+	44.5526i	−0.916906	+	1.58813i	−0.112819	+	0.993616i	$0.535988\pi$
$787$	−25.7224	+	44.5526i	−0.916906	+	1.58813i	−0.804087	+	0.594512i	$0.797345\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−16.1225			−0.573251
$792$		0			0
$793$	28.8564			1.02472
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.92396	+	6.79650i	−0.138994	+	0.240744i	−0.927116	−	0.374774i	$-0.877720\pi$
$797$	−3.92396	+	6.79650i	−0.138994	+	0.240744i	0.788122	+	0.615519i	$0.211053\pi$
$798$		0			0
$799$	10.4613	−	6.03983i	0.370094	−	0.213674i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−33.9103	+	19.5781i	−1.19667	+	0.690897i
$804$		0			0
$805$	11.7973	+	6.81119i	0.415801	+	0.240063i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	2.64673i		−	0.0930539i	−0.998917	−	0.0465270i	$-0.985185\pi$
$809$		−	2.64673i		−	0.0930539i	0.998917	−	0.0465270i	$-0.0148153\pi$
$810$		0			0
$811$	40.9282			1.43718			0.718592	−	0.695432i	$-0.244787\pi$
$811$	40.9282			1.43718			0.718592	+	0.695432i	$0.244787\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.2845	−	26.4735i	0.535391	−	0.927325i
$816$		0			0
$817$	−0.267949	−	0.464102i	−0.00937436	−	0.0162369i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.33178	+	14.4311i	0.290781	+	0.503648i	0.973995	−	0.226571i	$-0.0727515\pi$
$821$	8.33178	+	14.4311i	0.290781	+	0.503648i	−0.683213	+	0.730219i	$0.739418\pi$
$822$		0			0
$823$	−24.8412	−	14.3421i	−0.865909	−	0.499933i	7.73618e−5	−	1.00000i	$-0.499975\pi$
$823$	−24.8412	−	14.3421i	−0.865909	−	0.499933i	−0.865987	+	0.500067i	$0.833309\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	3.00132i		−	0.104366i	−0.998638	−	0.0521830i	$-0.983382\pi$
$827$		−	3.00132i		−	0.104366i	0.998638	−	0.0521830i	$-0.0166179\pi$
$828$		0			0
$829$			12.4653i			0.432939i	0.976289	+	0.216470i	$0.0694542\pi$
$829$			12.4653i			0.432939i	−0.976289	+	0.216470i	$0.930546\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.64804	−	3.26090i	−0.195693	−	0.112983i
$834$		0			0
$835$	4.05256	+	7.01924i	0.140245	+	0.242911i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−28.5498	−	49.4497i	−0.985648	−	1.70719i	−0.639022	−	0.769188i	$-0.720661\pi$
$839$	−28.5498	−	49.4497i	−0.985648	−	1.70719i	−0.346625	−	0.938004i	$-0.612673\pi$
$840$		0			0
$841$	−23.3564	+	40.4545i	−0.805393	+	1.39498i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−25.2505			−0.868645
$846$		0			0
$847$			19.2765i			0.662349i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.8315	+	7.40828i	0.439859	+	0.253953i
$852$		0			0
$853$	−0.334008	+	0.192840i	−0.0114362	+	0.00660270i	−0.505707	−	0.862705i	$-0.668768\pi$
$853$	−0.334008	+	0.192840i	−0.0114362	+	0.00660270i	0.494271	+	0.869308i	$0.335435\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.9253	+	18.4321i	−1.09055	+	0.629627i	−0.933722	−	0.357999i	$-0.883459\pi$
$857$	−31.9253	+	18.4321i	−1.09055	+	0.629627i	−0.156825	+	0.987626i	$0.550126\pi$
$858$		0			0
$859$	−9.79423	+	16.9641i	−0.334175	+	0.578808i	−0.983326	−	0.181852i	$-0.941791\pi$
$859$	−9.79423	+	16.9641i	−0.334175	+	0.578808i	0.649151	+	0.760659i	$0.275124\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.27462			−0.281671			−0.140836	−	0.990033i	$-0.544979\pi$
$863$	−8.27462			−0.281671			−0.140836	+	0.990033i	$0.544979\pi$
$864$		0			0
$865$	−18.9282			−0.643578
$866$		0			0
$867$		0			0
$868$		0			0
$869$	30.0851	−	52.1089i	1.02057	−	1.76767i
$870$		0			0
$871$	−5.56466	+	3.21276i	−0.188551	+	0.108860i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	14.8166	−	8.55435i	0.500891	−	0.289190i
$876$		0			0
$877$	18.9425	+	10.9365i	0.639644	+	0.369298i	0.784477	−	0.620158i	$-0.212931\pi$
$877$	18.9425	+	10.9365i	0.639644	+	0.369298i	−0.144834	+	0.989456i	$0.546265\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			35.5408i			1.19740i	0.800974	+	0.598699i	$0.204316\pi$
$881$			35.5408i			1.19740i	−0.800974	+	0.598699i	$0.795684\pi$
$882$		0			0
$883$	−19.8756			−0.668869			−0.334434	−	0.942419i	$-0.608545\pi$
$883$	−19.8756			−0.668869			−0.334434	+	0.942419i	$0.608545\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.86707	+	17.0903i	−0.331304	+	0.573835i	−0.982768	−	0.184845i	$-0.940822\pi$
$887$	−9.86707	+	17.0903i	−0.331304	+	0.573835i	0.651464	+	0.758679i	$0.274155\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.22292	+	2.11816i	0.0409235	+	0.0708816i
$894$		0			0
$895$	13.6224	+	7.86488i	0.455346	+	0.262894i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	68.4348i		−	2.28243i
$900$		0			0
$901$		−	7.30021i		−	0.243205i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−22.2249	−	12.8315i	−0.738779	−	0.426534i
$906$		0			0
$907$	13.1865	+	22.8397i	0.437852	+	0.758381i	0.997524	−	0.0703330i	$-0.0224062\pi$
$907$	13.1865	+	22.8397i	0.437852	+	0.758381i	−0.559672	+	0.828714i	$0.689073\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.1800	+	38.4168i	0.734855	+	1.27281i	0.954787	+	0.297291i	$0.0960833\pi$
$911$	22.1800	+	38.4168i	0.734855	+	1.27281i	−0.219931	+	0.975515i	$0.570583\pi$
$912$		0			0
$913$	17.8564	−	30.9282i	0.590961	−	1.02357i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.4081			0.343706
$918$		0			0
$919$			30.8949i			1.01913i	0.860433	+	0.509564i	$0.170193\pi$
$919$			30.8949i			1.01913i	−0.860433	+	0.509564i	$0.829807\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	25.6631	+	14.8166i	0.844710	+	0.487693i
$924$		0			0
$925$	5.32014	−	3.07159i	0.174925	−	0.100993i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.5244	−	7.23099i	0.410913	−	0.237241i	−0.280269	−	0.959922i	$-0.590424\pi$
$929$	12.5244	−	7.23099i	0.410913	−	0.237241i	0.691182	+	0.722681i	$0.257090\pi$
$930$		0			0
$931$	0.660254	−	1.14359i	0.0216390	−	0.0374798i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−10.4081			−0.340381
$936$		0			0
$937$	−2.60770			−0.0851897			−0.0425948	−	0.999092i	$-0.513562\pi$
$937$	−2.60770			−0.0851897			−0.0425948	+	0.999092i	$0.513562\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.8673	+	27.4830i	−0.517260	+	0.895921i	0.482539	+	0.875875i	$0.339715\pi$
$941$	−15.8673	+	27.4830i	−0.517260	+	0.895921i	−0.999799	+	0.0200467i	$0.993619\pi$
$942$		0			0
$943$	50.8394	−	29.3521i	1.65556	−	0.955837i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.0638	−	13.3159i	0.749474	−	0.432709i	−0.0760299	−	0.997106i	$-0.524224\pi$
$947$	23.0638	−	13.3159i	0.749474	−	0.432709i	0.825504	+	0.564397i	$0.190891\pi$
$948$		0			0
$949$	36.8830	+	21.2944i	1.19727	+	0.691246i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	57.9429i		−	1.87696i	−0.345340	−	0.938478i	$-0.612236\pi$
$953$		−	57.9429i		−	1.87696i	0.345340	−	0.938478i	$-0.387764\pi$
$954$		0			0
$955$	14.5359			0.470371
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.25164	+	7.36406i	−0.137293	+	0.237798i
$960$		0			0
$961$	15.4282	+	26.7224i	0.497684	+	0.862014i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.2557	−	21.2276i	−0.394526	−	0.683340i
$966$		0			0
$967$	−5.56466	−	3.21276i	−0.178947	−	0.103315i	0.407851	−	0.913049i	$-0.366278\pi$
$967$	−5.56466	−	3.21276i	−0.178947	−	0.103315i	−0.586798	+	0.809733i	$0.699612\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			42.5122i			1.36428i	0.731221	+	0.682140i	$0.238951\pi$
$971$			42.5122i			1.36428i	−0.731221	+	0.682140i	$0.761049\pi$
$972$		0			0
$973$			10.3580i			0.332061i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	35.8954	+	20.7242i	1.14839	+	0.663026i	0.948495	−	0.316791i	$-0.102605\pi$
$977$	35.8954	+	20.7242i	1.14839	+	0.663026i	0.199899	+	0.979817i	$0.435939\pi$
$978$		0			0
$979$	−38.9808	−	67.5167i	−1.24583	−	2.15784i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.0563	+	46.8630i	0.862963	+	1.49470i	0.869055	+	0.494715i	$0.164727\pi$
$983$	27.0563	+	46.8630i	0.862963	+	1.49470i	−0.00609223	+	0.999981i	$0.501939\pi$
$984$		0			0
$985$	15.8038	−	27.3731i	0.503552	−	0.872178i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.8862			−0.377960
$990$		0			0
$991$		−	0.668016i		−	0.0212202i	−0.999944	−	0.0106101i	$-0.996623\pi$
$991$		−	0.668016i		−	0.0212202i	0.999944	−	0.0106101i	$-0.00337737\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	19.7079	+	11.3784i	0.624783	+	0.360719i
$996$		0			0
$997$	25.4197	−	14.6761i	0.805050	−	0.464796i	−0.0401838	−	0.999192i	$-0.512794\pi$
$997$	25.4197	−	14.6761i	0.805050	−	0.464796i	0.845234	+	0.534396i	$0.179461\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.p.f.2159.3		16
3.2	odd	2	inner	2592.2.p.f.2159.5		16
4.3	odd	2		648.2.l.f.539.2		16
8.3	odd	2	inner	2592.2.p.f.2159.6		16
8.5	even	2		648.2.l.f.539.4		16
9.2	odd	6	inner	2592.2.p.f.431.6		16
9.4	even	3		864.2.f.a.431.5		8
9.5	odd	6		864.2.f.a.431.3		8
9.7	even	3	inner	2592.2.p.f.431.4		16
12.11	even	2		648.2.l.f.539.7		16
24.5	odd	2		648.2.l.f.539.5		16
24.11	even	2	inner	2592.2.p.f.2159.4		16
36.7	odd	6		648.2.l.f.107.5		16
36.11	even	6		648.2.l.f.107.4		16
36.23	even	6		216.2.f.a.107.2	yes	8
36.31	odd	6		216.2.f.a.107.7	yes	8
72.5	odd	6		216.2.f.a.107.8	yes	8
72.11	even	6	inner	2592.2.p.f.431.3		16
72.13	even	6		216.2.f.a.107.1	✓	8
72.29	odd	6		648.2.l.f.107.2		16
72.43	odd	6	inner	2592.2.p.f.431.5		16
72.59	even	6		864.2.f.a.431.6		8
72.61	even	6		648.2.l.f.107.7		16
72.67	odd	6		864.2.f.a.431.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.a.107.1	✓	8	72.13	even	6
216.2.f.a.107.2	yes	8	36.23	even	6
216.2.f.a.107.7	yes	8	36.31	odd	6
216.2.f.a.107.8	yes	8	72.5	odd	6
648.2.l.f.107.2		16	72.29	odd	6
648.2.l.f.107.4		16	36.11	even	6
648.2.l.f.107.5		16	36.7	odd	6
648.2.l.f.107.7		16	72.61	even	6
648.2.l.f.539.2		16	4.3	odd	2
648.2.l.f.539.4		16	8.5	even	2
648.2.l.f.539.5		16	24.5	odd	2
648.2.l.f.539.7		16	12.11	even	2
864.2.f.a.431.3		8	9.5	odd	6
864.2.f.a.431.4		8	72.67	odd	6
864.2.f.a.431.5		8	9.4	even	3
864.2.f.a.431.6		8	72.59	even	6
2592.2.p.f.431.3		16	72.11	even	6	inner
2592.2.p.f.431.4		16	9.7	even	3	inner
2592.2.p.f.431.5		16	72.43	odd	6	inner
2592.2.p.f.431.6		16	9.2	odd	6	inner
2592.2.p.f.2159.3		16	1.1	even	1	trivial
2592.2.p.f.2159.4		16	24.11	even	2	inner
2592.2.p.f.2159.5		16	3.2	odd	2	inner
2592.2.p.f.2159.6		16	8.3	odd	2	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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.796225 + 1.37910i) q^{5} +(-1.24653 + 0.719687i) q^{7} +(4.27718 - 2.46943i) q^{11} +(-4.65213 - 2.68591i) q^{13} +1.32336i q^{17} -0.267949 q^{19} +(-2.97155 + 5.14688i) q^{23} +(1.23205 + 2.13397i) q^{25} +(-4.35066 - 7.53556i) q^{29} +(6.81119 + 3.93244i) q^{31} -2.29213i q^{35} -2.49307i q^{37} +(-8.55435 - 4.93886i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-4.56400 - 7.90509i) q^{47} +(-2.46410 + 4.26795i) q^{49} -5.51641 q^{53} +7.86488i q^{55} +(-4.27718 - 2.46943i) q^{59} +(-4.65213 + 2.68591i) q^{61} +(7.40828 - 4.27718i) q^{65} +(0.598076 - 1.03590i) q^{67} -5.51641 q^{71} -7.92820 q^{73} +(-3.55443 + 6.15645i) q^{77} +(10.5508 - 6.09150i) q^{79} +(6.26222 - 3.61549i) q^{83} +(-1.82505 - 1.05369i) q^{85} -15.7853i q^{89} +7.73205 q^{91} +(0.213348 - 0.369529i) q^{95} +(-4.69615 - 8.13397i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{19} - 8 q^{25} + 16 q^{43} + 16 q^{49} - 32 q^{67} - 16 q^{73} + 96 q^{91} + 8 q^{97}+O(q^{100}) \) 16 * q - 32 * q^19 - 8 * q^25 + 16 * q^43 + 16 * q^49 - 32 * q^67 - 16 * q^73 + 96 * q^91 + 8 * q^97

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