LMFDB - Embedded newform 2592.2.s.j.863.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 $ x^16 - 12x^14 + 49x^12 - 12x^10 - 600x^8 + 108x^6 + 4057x^4 + 18252*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			863.1
Root			$-2.13219 + 1.08896i$ of defining polynomial
Character	$\chi$	$=$	2592.863
Dual form			2592.2.s.j.1727.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.47996 - 2.00916i) q^{5} +(2.66739 - 1.54002i) q^{7} +O(q^{10})$	$q+(-3.47996 - 2.00916i) q^{5} +(2.66739 - 1.54002i) q^{7} +(2.97508 + 5.15300i) q^{11} +(0.673991 - 1.16739i) q^{13} -4.87346i q^{17} +7.49484i q^{19} +(-1.28929 + 2.23312i) q^{23} +(5.57343 + 9.65346i) q^{25} +(-5.60128 + 3.23390i) q^{29} +(-1.28744 - 0.743302i) q^{31} -12.3765 q^{35} +1.91997 q^{37} +(1.69513 + 0.978684i) q^{41} +(6.79671 - 3.92409i) q^{43} +(-1.14264 - 1.97910i) q^{47} +(1.24330 - 2.15346i) q^{49} +0.871059i q^{53} -23.9096i q^{55} +(-0.650515 + 1.12672i) q^{59} +(3.29671 + 5.71008i) q^{61} +(-4.69093 + 2.70831i) q^{65} +(8.44338 + 4.87479i) q^{67} +4.64914 q^{71} -2.14686 q^{73} +(15.8714 + 9.16336i) q^{77} +(8.08415 - 4.66739i) q^{79} +(5.09779 + 8.82963i) q^{83} +(-9.79155 + 16.9595i) q^{85} -0.947609i q^{89} -4.15183i q^{91} +(15.0583 - 26.0818i) q^{95} +(-5.15811 - 8.93411i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

Display 100 coefficients 10 coefficients

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
$5$	−3.47996	−	2.00916i	−1.55629	−	0.898523i	−0.997607	−	0.0691392i	$-0.977975\pi$
$5$	−3.47996	−	2.00916i	−1.55629	−	0.898523i	−0.558680	−	0.829383i	$-0.688692\pi$
$6$		0			0
$7$	2.66739	−	1.54002i	1.00818	−	0.582072i	0.0975199	−	0.995234i	$-0.468909\pi$
$7$	2.66739	−	1.54002i	1.00818	−	0.582072i	0.910658	+	0.413162i	$0.135576\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.97508	+	5.15300i	0.897021	+	1.55369i	0.831283	+	0.555850i	$0.187607\pi$
$11$	2.97508	+	5.15300i	0.897021	+	1.55369i	0.0657387	+	0.997837i	$0.479060\pi$
$12$		0			0
$13$	0.673991	−	1.16739i	0.186932	−	0.323775i	−0.757294	−	0.653074i	$-0.773479\pi$
$13$	0.673991	−	1.16739i	0.186932	−	0.323775i	0.944226	+	0.329299i	$0.106812\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	4.87346i		−	1.18199i	−0.806676	−	0.590994i	$-0.798736\pi$
$17$		−	4.87346i		−	1.18199i	0.806676	−	0.590994i	$-0.201264\pi$
$18$		0			0
$19$			7.49484i			1.71943i	0.510771	+	0.859717i	$0.329360\pi$
$19$			7.49484i			1.71943i	−0.510771	+	0.859717i	$0.670640\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.28929	+	2.23312i	−0.268836	+	0.465638i	−0.968562	−	0.248774i	$-0.919972\pi$
$23$	−1.28929	+	2.23312i	−0.268836	+	0.465638i	0.699725	+	0.714412i	$0.253306\pi$
$24$		0			0
$25$	5.57343	+	9.65346i	1.11469	+	1.93069i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.60128	+	3.23390i	−1.04013	+	0.600521i	−0.919871	−	0.392222i	$-0.871707\pi$
$29$	−5.60128	+	3.23390i	−1.04013	+	0.600521i	−0.120261	+	0.992742i	$0.538373\pi$
$30$		0			0
$31$	−1.28744	−	0.743302i	−0.231230	−	0.133501i	0.379909	−	0.925024i	$-0.375955\pi$
$31$	−1.28744	−	0.743302i	−0.231230	−	0.133501i	−0.611140	+	0.791523i	$0.709289\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−12.3765			−2.09202
$36$		0			0
$37$	1.91997			0.315641			0.157820	−	0.987468i	$-0.449553\pi$
$37$	1.91997			0.315641			0.157820	+	0.987468i	$0.449553\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.69513	+	0.978684i	0.264735	+	0.152845i	0.626493	−	0.779427i	$-0.284490\pi$
$41$	1.69513	+	0.978684i	0.264735	+	0.152845i	−0.361758	+	0.932272i	$0.617823\pi$
$42$		0			0
$43$	6.79671	−	3.92409i	1.03649	−	0.598417i	0.117652	−	0.993055i	$-0.462463\pi$
$43$	6.79671	−	3.92409i	1.03649	−	0.598417i	0.918837	+	0.394637i	$0.129130\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.14264	−	1.97910i	−0.166671	−	0.288682i	0.770577	−	0.637347i	$-0.219968\pi$
$47$	−1.14264	−	1.97910i	−0.166671	−	0.288682i	−0.937247	+	0.348665i	$0.886635\pi$
$48$		0			0
$49$	1.24330	−	2.15346i	0.177615	−	0.307637i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			0.871059i			0.119649i	0.998209	+	0.0598245i	$0.0190541\pi$
$53$			0.871059i			0.119649i	−0.998209	+	0.0598245i	$0.980946\pi$
$54$		0			0
$55$		−	23.9096i		−	3.22398i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.650515	+	1.12672i	−0.0846898	+	0.146687i	−0.905259	−	0.424860i	$-0.860323\pi$
$59$	−0.650515	+	1.12672i	−0.0846898	+	0.146687i	0.820569	+	0.571547i	$0.193657\pi$
$60$		0			0
$61$	3.29671	+	5.71008i	0.422101	+	0.731101i	0.996145	−	0.0877241i	$-0.0279594\pi$
$61$	3.29671	+	5.71008i	0.422101	+	0.731101i	−0.574044	+	0.818825i	$0.694626\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.69093	+	2.70831i	−0.581838	+	0.335924i
$66$		0			0
$67$	8.44338	+	4.87479i	1.03152	+	0.595550i	0.917421	−	0.397919i	$-0.130267\pi$
$67$	8.44338	+	4.87479i	1.03152	+	0.595550i	0.114103	+	0.993469i	$0.463601\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.64914			0.551751			0.275876	−	0.961193i	$-0.411032\pi$
$71$	4.64914			0.551751			0.275876	+	0.961193i	$0.411032\pi$
$72$		0			0
$73$	−2.14686			−0.251271			−0.125635	−	0.992076i	$-0.540097\pi$
$73$	−2.14686			−0.251271			−0.125635	+	0.992076i	$0.540097\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.8714	+	9.16336i	1.80871	+	1.04426i
$78$		0			0
$79$	8.08415	−	4.66739i	0.909538	−	0.525122i	0.0292556	−	0.999572i	$-0.490686\pi$
$79$	8.08415	−	4.66739i	0.909538	−	0.525122i	0.880282	+	0.474450i	$0.157353\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.09779	+	8.82963i	0.559555	+	0.969178i	0.997533	+	0.0701921i	$0.0223612\pi$
$83$	5.09779	+	8.82963i	0.559555	+	0.969178i	−0.437979	+	0.898985i	$0.644305\pi$
$84$		0			0
$85$	−9.79155	+	16.9595i	−1.06204	+	1.83951i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	0.947609i		−	0.100446i	−0.998738	−	0.0502232i	$-0.984007\pi$
$89$		−	0.947609i		−	0.100446i	0.998738	−	0.0502232i	$-0.0159933\pi$
$90$		0			0
$91$		−	4.15183i		−	0.435230i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.0583	−	26.0818i	1.54495	−	2.67593i
$96$		0			0
$97$	−5.15811	−	8.93411i	−0.523727	−	0.907121i	−0.999619	−	0.0276173i	$-0.991208\pi$
$97$	−5.15811	−	8.93411i	−0.523727	−	0.907121i	0.475892	−	0.879504i	$-0.342125\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.85352	+	1.07013i	−0.184433	+	0.106482i	−0.589374	−	0.807861i	$-0.700625\pi$
$101$	−1.85352	+	1.07013i	−0.184433	+	0.106482i	0.404941	+	0.914343i	$0.367292\pi$
$102$		0			0
$103$	8.53590	+	4.92820i	0.841067	+	0.485590i	0.857627	−	0.514273i	$-0.171938\pi$
$103$	8.53590	+	4.92820i	0.841067	+	0.485590i	−0.0165597	+	0.999863i	$0.505271\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.38765			0.424170			0.212085	−	0.977251i	$-0.431975\pi$
$107$	4.38765			0.424170			0.212085	+	0.977251i	$0.431975\pi$
$108$		0			0
$109$	16.4588			1.57646			0.788231	−	0.615379i	$-0.210997\pi$
$109$	16.4588			1.57646			0.788231	+	0.615379i	$0.210997\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.5032	+	7.21875i	1.17621	+	0.679082i	0.955134	−	0.296175i	$-0.0957112\pi$
$113$	12.5032	+	7.21875i	1.17621	+	0.679082i	0.221072	+	0.975258i	$0.429045\pi$
$114$		0			0
$115$	8.97338	−	5.18078i	0.836772	−	0.483111i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.50521	−	12.9994i	−0.688002	−	1.19165i
$120$		0			0
$121$	−12.2022	+	21.1349i	−1.10929	+	1.92136i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	24.7000i		−	2.20924i
$126$		0			0
$127$		−	1.17862i		−	0.104586i	−0.998632	−	0.0522929i	$-0.983347\pi$
$127$		−	1.17862i		−	0.104586i	0.998632	−	0.0522929i	$-0.0166530\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.0552077	−	0.0956225i	0.00482352	−	0.00835458i	−0.863604	−	0.504171i	$-0.831798\pi$
$131$	0.0552077	−	0.0956225i	0.00482352	−	0.00835458i	0.868427	+	0.495817i	$0.165131\pi$
$132$		0			0
$133$	11.5422	+	19.9916i	1.00083	+	1.73349i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.05915	−	5.23030i	0.773975	−	0.446855i	−0.0603156	−	0.998179i	$-0.519211\pi$
$137$	9.05915	−	5.23030i	0.773975	−	0.446855i	0.834291	+	0.551325i	$0.185877\pi$
$138$		0			0
$139$	−12.7042	−	7.33477i	−1.07756	−	0.622127i	−0.147320	−	0.989089i	$-0.547065\pi$
$139$	−12.7042	−	7.33477i	−1.07756	−	0.622127i	−0.930236	+	0.366961i	$0.880398\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.02072			0.670726
$144$		0			0
$145$	25.9897			2.15833
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.95575	+	1.70651i	0.242145	+	0.139802i	0.616162	−	0.787619i	$-0.288687\pi$
$149$	2.95575	+	1.70651i	0.242145	+	0.139802i	−0.374017	+	0.927422i	$0.622020\pi$
$150$		0			0
$151$	−7.64667	+	4.41481i	−0.622277	+	0.359272i	−0.777755	−	0.628567i	$-0.783642\pi$
$151$	−7.64667	+	4.41481i	−0.622277	+	0.359272i	0.155478	+	0.987839i	$0.450308\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.98682	+	5.17333i	0.239907	+	0.415531i
$156$		0			0
$157$	10.1981	−	17.6637i	0.813899	−	1.40971i	−0.0962168	−	0.995360i	$-0.530674\pi$
$157$	10.1981	−	17.6637i	0.813899	−	1.40971i	0.910116	−	0.414354i	$-0.135992\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			7.94213i			0.625927i
$162$		0			0
$163$		−	11.3880i		−	0.891978i	−0.895038	−	0.445989i	$-0.852852\pi$
$163$		−	11.3880i		−	0.891978i	0.895038	−	0.445989i	$-0.147148\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.6463	−	20.1720i	0.901219	−	1.56096i	0.0753056	−	0.997161i	$-0.476007\pi$
$167$	11.6463	−	20.1720i	0.901219	−	1.56096i	0.825914	−	0.563797i	$-0.190660\pi$
$168$		0			0
$169$	5.59147	+	9.68471i	0.430113	+	0.744978i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.6270	−	6.71284i	0.883984	−	0.510368i	0.0120137	−	0.999928i	$-0.496176\pi$
$173$	11.6270	−	6.71284i	0.883984	−	0.510368i	0.871970	+	0.489560i	$0.162842\pi$
$174$		0			0
$175$	29.7330	+	17.1663i	2.24760	+	1.29765i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−20.7141			−1.54824			−0.774120	−	0.633038i	$-0.781808\pi$
$179$	−20.7141			−1.54824			−0.774120	+	0.633038i	$0.781808\pi$
$180$		0			0
$181$	−8.06148			−0.599205			−0.299602	−	0.954064i	$-0.596854\pi$
$181$	−8.06148			−0.599205			−0.299602	+	0.954064i	$0.596854\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.68141	−	3.85752i	−0.491227	−	0.283610i
$186$		0			0
$187$	25.1129	−	14.4990i	1.83644	−	1.06027i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.3965	+	19.7393i	0.824620	+	1.42828i	0.902209	+	0.431298i	$0.141944\pi$
$191$	11.3965	+	19.7393i	0.824620	+	1.42828i	−0.0775893	+	0.996985i	$0.524722\pi$
$192$		0			0
$193$	8.22670	−	14.2491i	0.592171	−	1.02567i	−0.401768	−	0.915741i	$-0.631604\pi$
$193$	8.22670	−	14.2491i	0.592171	−	1.02567i	0.993939	−	0.109929i	$-0.0350623\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			21.9544i			1.56419i	0.623160	+	0.782095i	$0.285849\pi$
$197$			21.9544i			1.56419i	−0.623160	+	0.782095i	$0.714151\pi$
$198$		0			0
$199$			11.2933i			0.800564i	0.916392	+	0.400282i	$0.131088\pi$
$199$			11.2933i			0.800564i	−0.916392	+	0.400282i	$0.868912\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.96053	+	17.2521i	−0.699092	+	1.21086i
$204$		0			0
$205$	−3.93266	−	6.81157i	−0.274669	−	0.475741i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−38.6209	+	22.2978i	−2.67146	+	1.54237i
$210$		0			0
$211$	−12.2667	−	7.08219i	−0.844476	−	0.487558i	0.0143073	−	0.999898i	$-0.495446\pi$
$211$	−12.2667	−	7.08219i	−0.844476	−	0.487558i	−0.858783	+	0.512339i	$0.828779\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−31.5364			−2.15077
$216$		0			0
$217$	−4.57879			−0.310828
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.68922	−	3.28467i	−0.382698	−	0.220951i
$222$		0			0
$223$	−15.9548	+	9.21152i	−1.06841	+	0.616849i	−0.927748	−	0.373208i	$-0.878258\pi$
$223$	−15.9548	+	9.21152i	−1.06841	+	0.616849i	−0.140666	+	0.990057i	$0.544924\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.53415	+	6.12133i	0.234570	+	0.406287i	0.959148	−	0.282906i	$-0.0912985\pi$
$227$	3.53415	+	6.12133i	0.234570	+	0.406287i	−0.724578	+	0.689193i	$0.757965\pi$
$228$		0			0
$229$	−5.13614	+	8.89605i	−0.339405	+	0.587867i	−0.984321	−	0.176386i	$-0.943559\pi$
$229$	−5.13614	+	8.89605i	−0.339405	+	0.587867i	0.644916	+	0.764254i	$0.276892\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	7.49420i		−	0.490961i	−0.969401	−	0.245481i	$-0.921054\pi$
$233$		−	7.49420i		−	0.490961i	0.969401	−	0.245481i	$-0.0789458\pi$
$234$		0			0
$235$			9.18294i			0.599029i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.309224	+	0.535592i	−0.0200020	+	0.0346445i	−0.875853	−	0.482578i	$-0.839701\pi$
$239$	−0.309224	+	0.535592i	−0.0200020	+	0.0346445i	0.855851	+	0.517222i	$0.173034\pi$
$240$		0			0
$241$	12.4521	+	21.5678i	0.802113	+	1.38930i	0.918223	+	0.396065i	$0.129624\pi$
$241$	12.4521	+	21.5678i	0.802113	+	1.38930i	−0.116109	+	0.993236i	$0.537042\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.65329	+	4.99598i	−0.552838	+	0.319181i
$246$		0			0
$247$	8.74938	+	5.05146i	0.556710	+	0.321416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.54676			−0.160750			−0.0803751	−	0.996765i	$-0.525612\pi$
$251$	−2.54676			−0.160750			−0.0803751	+	0.996765i	$0.525612\pi$
$252$		0			0
$253$	−15.3430			−0.964607
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.74647	−	4.47243i	−0.483212	−	0.278982i	0.238542	−	0.971132i	$-0.423330\pi$
$257$	−7.74647	−	4.47243i	−0.483212	−	0.278982i	−0.721754	+	0.692150i	$0.756664\pi$
$258$		0			0
$259$	5.12129	−	2.95678i	0.318222	−	0.183725i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.43595	+	2.48714i	0.0885444	+	0.153363i	0.906896	−	0.421354i	$-0.138445\pi$
$263$	1.43595	+	2.48714i	0.0885444	+	0.153363i	−0.818352	+	0.574718i	$0.805112\pi$
$264$		0			0
$265$	1.75009	−	3.03125i	0.107507	−	0.186208i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	4.51044i		−	0.275006i	−0.990501	−	0.137503i	$-0.956092\pi$
$269$		−	4.51044i		−	0.275006i	0.990501	−	0.137503i	$-0.0439077\pi$
$270$		0			0
$271$			2.72670i			0.165635i	0.996565	+	0.0828177i	$0.0263919\pi$
$271$			2.72670i			0.165635i	−0.996565	+	0.0828177i	$0.973608\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−33.1628	+	57.4397i	−1.99979	+	3.46374i
$276$		0			0
$277$	−2.76814	−	4.79455i	−0.166321	−	0.288077i	0.770802	−	0.637074i	$-0.219856\pi$
$277$	−2.76814	−	4.79455i	−0.166321	−	0.288077i	−0.937124	+	0.348997i	$0.886522\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	17.0968	−	9.87083i	1.01991	−	0.588844i	0.105831	−	0.994384i	$-0.466250\pi$
$281$	17.0968	−	9.87083i	1.01991	−	0.588844i	0.914077	+	0.405540i	$0.132917\pi$
$282$		0			0
$283$	−11.3348	−	6.54413i	−0.673782	−	0.389008i	0.123726	−	0.992316i	$-0.460516\pi$
$283$	−11.3348	−	6.54413i	−0.673782	−	0.389008i	−0.797508	+	0.603308i	$0.793849\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.02876			0.355866
$288$		0			0
$289$	−6.75064			−0.397096
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−19.5916	−	11.3112i	−1.14455	−	0.660808i	−0.196999	−	0.980404i	$-0.563120\pi$
$293$	−19.5916	−	11.3112i	−1.14455	−	0.660808i	−0.947554	+	0.319595i	$0.896453\pi$
$294$		0			0
$295$	4.52754	−	2.61397i	0.263603	−	0.152191i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.73794	+	3.01021i	0.100508	+	0.174085i
$300$		0			0
$301$	12.0863	−	20.9341i	0.696643	−	1.20662i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	26.4945i		−	1.51707i
$306$		0			0
$307$		−	7.64667i		−	0.436418i	−0.975902	−	0.218209i	$-0.929978\pi$
$307$		−	7.64667i		−	0.436418i	0.975902	−	0.218209i	$-0.0700215\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.6632	−	18.4692i	0.604654	−	1.04729i	−0.387452	−	0.921890i	$-0.626645\pi$
$311$	10.6632	−	18.4692i	0.604654	−	1.04729i	0.992106	−	0.125402i	$-0.0400220\pi$
$312$		0			0
$313$	8.86747	+	15.3589i	0.501219	+	0.868137i	0.999999	+	0.00140816i	$0.000448232\pi$
$313$	8.86747	+	15.3589i	0.501219	+	0.868137i	−0.498780	+	0.866729i	$0.666218\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.80699	+	1.62061i	−0.157656	+	0.0910228i	−0.576752	−	0.816919i	$-0.695680\pi$
$317$	−2.80699	+	1.62061i	−0.157656	+	0.0910228i	0.419096	+	0.907942i	$0.362347\pi$
$318$		0			0
$319$	−33.3286	−	19.2423i	−1.86604	−	1.07736i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	36.5258			2.03235
$324$		0			0
$325$	15.0258			0.833480
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.09570	−	3.51936i	−0.336067	−	0.194028i
$330$		0			0
$331$	8.08415	−	4.66739i	0.444345	−	0.256543i	−0.261094	−	0.965313i	$-0.584083\pi$
$331$	8.08415	−	4.66739i	0.444345	−	0.256543i	0.705439	+	0.708771i	$0.250750\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−19.5884	−	33.9282i	−1.07023	−	1.85369i
$336$		0			0
$337$	−7.03270	+	12.1810i	−0.383095	+	0.663541i	−0.991503	−	0.130084i	$-0.958475\pi$
$337$	−7.03270	+	12.1810i	−0.383095	+	0.663541i	0.608408	+	0.793625i	$0.291809\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	8.84554i		−	0.479013i
$342$		0			0
$343$			13.9014i			0.750606i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.28431	−	5.68859i	0.176311	−	0.305379i	−0.764303	−	0.644857i	$-0.776917\pi$
$347$	3.28431	−	5.68859i	0.176311	−	0.305379i	0.940614	+	0.339478i	$0.110250\pi$
$348$		0			0
$349$	−6.12737	−	10.6129i	−0.327991	−	0.568096i	0.654122	−	0.756389i	$-0.273038\pi$
$349$	−6.12737	−	10.6129i	−0.327991	−	0.568096i	−0.982113	+	0.188292i	$0.939705\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.37831	−	2.52782i	0.233034	−	0.134542i	−0.378937	−	0.925422i	$-0.623710\pi$
$353$	4.37831	−	2.52782i	0.233034	−	0.134542i	0.611971	+	0.790880i	$0.290377\pi$
$354$		0			0
$355$	−16.1788	−	9.34085i	−0.858683	−	0.495761i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	31.8214			1.67947			0.839734	−	0.542998i	$-0.182711\pi$
$359$	31.8214			1.67947			0.839734	+	0.542998i	$0.182711\pi$
$360$		0			0
$361$	−37.1726			−1.95645
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.47099	+	4.31338i	0.391049	+	0.225772i
$366$		0			0
$367$	−2.17667	+	1.25670i	−0.113621	+	0.0655991i	−0.555734	−	0.831360i	$-0.687563\pi$
$367$	−2.17667	+	1.25670i	−0.113621	+	0.0655991i	0.442113	+	0.896960i	$0.354229\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.34144	+	2.32345i	0.0696443	+	0.120628i
$372$		0			0
$373$	−15.9589	+	27.6417i	−0.826323	+	1.43123i	0.0745816	+	0.997215i	$0.476238\pi$
$373$	−15.9589	+	27.6417i	−0.826323	+	1.43123i	−0.900904	+	0.434018i	$0.857095\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			8.71849i			0.449025i
$378$		0			0
$379$			23.9053i			1.22793i	0.789332	+	0.613967i	$0.210427\pi$
$379$			23.9053i			1.22793i	−0.789332	+	0.613967i	$0.789573\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.63058	+	2.82425i	−0.0833189	+	0.144313i	−0.904674	−	0.426105i	$-0.859885\pi$
$383$	−1.63058	+	2.82425i	−0.0833189	+	0.144313i	0.821355	+	0.570418i	$0.193219\pi$
$384$		0			0
$385$	−36.8213	−	63.7763i	−1.87658	−	3.25034i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.1379	+	7.58519i	−0.666120	+	0.384584i	−0.794605	−	0.607127i	$-0.792322\pi$
$389$	−13.1379	+	7.58519i	−0.666120	+	0.384584i	0.128485	+	0.991711i	$0.458989\pi$
$390$		0			0
$391$	10.8830	+	6.28332i	0.550378	+	0.317761i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−37.5101			−1.88734
$396$		0			0
$397$	−25.1683			−1.26316			−0.631580	−	0.775310i	$-0.717593\pi$
$397$	−25.1683			−1.26316			−0.631580	+	0.775310i	$0.717593\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.58225	+	3.22291i	0.278764	+	0.160945i	0.632864	−	0.774263i	$-0.281879\pi$
$401$	5.58225	+	3.22291i	0.278764	+	0.160945i	−0.354100	+	0.935208i	$0.615213\pi$
$402$		0			0
$403$	−1.73544	+	1.00196i	−0.0864485	+	0.0499111i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.71206	+	9.89358i	0.283136	+	0.490407i
$408$		0			0
$409$	13.2583	−	22.9641i	0.655582	−	1.13550i	−0.326165	−	0.945313i	$-0.605757\pi$
$409$	13.2583	−	22.9641i	0.655582	−	1.13550i	0.981747	−	0.190189i	$-0.0609101\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			4.00721i			0.197182i
$414$		0			0
$415$		−	40.9690i		−	2.01109i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.3635	−	28.3424i	0.799410	−	1.38462i	−0.120591	−	0.992702i	$-0.538479\pi$
$419$	16.3635	−	28.3424i	0.799410	−	1.38462i	0.920001	−	0.391917i	$-0.128188\pi$
$420$		0			0
$421$	−11.8096	−	20.4548i	−0.575565	−	0.996907i	−0.995980	−	0.0895754i	$-0.971449\pi$
$421$	−11.8096	−	20.4548i	−0.575565	−	0.996907i	0.420415	−	0.907332i	$-0.361884\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	47.0458	−	27.1619i	2.28206	−	1.31755i
$426$		0			0
$427$	17.5872	+	10.1540i	0.851106	+	0.491386i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	28.7052			1.38268			0.691340	−	0.722530i	$-0.257021\pi$
$431$	28.7052			1.38268			0.691340	+	0.722530i	$0.257021\pi$
$432$		0			0
$433$	10.2444			0.492315			0.246158	−	0.969230i	$-0.420832\pi$
$433$	10.2444			0.492315			0.246158	+	0.969230i	$0.420832\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.7369	−	9.66304i	−0.800633	−	0.462246i
$438$		0			0
$439$	−34.0720	+	19.6715i	−1.62617	+	0.938870i	−0.640949	+	0.767584i	$0.721459\pi$
$439$	−34.0720	+	19.6715i	−1.62617	+	0.938870i	−0.985221	+	0.171286i	$0.945208\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.18611	+	2.05440i	0.0563536	+	0.0976073i	0.892826	−	0.450402i	$-0.148719\pi$
$443$	1.18611	+	2.05440i	0.0563536	+	0.0976073i	−0.836472	+	0.548009i	$0.815386\pi$
$444$		0			0
$445$	−1.90390	+	3.29765i	−0.0902533	+	0.156323i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			33.6097i			1.58614i	0.609129	+	0.793071i	$0.291519\pi$
$449$			33.6097i			1.58614i	−0.609129	+	0.793071i	$0.708481\pi$
$450$		0			0
$451$			11.6467i			0.548420i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.34168	+	14.4482i	−0.391064	+	0.677343i
$456$		0			0
$457$	−13.9768	−	24.2085i	−0.653807	−	1.13243i	−0.982191	−	0.187883i	$-0.939838\pi$
$457$	−13.9768	−	24.2085i	−0.653807	−	1.13243i	0.328384	−	0.944544i	$-0.393496\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.63590	−	1.52184i	0.122766	−	0.0708791i	−0.437359	−	0.899287i	$-0.644086\pi$
$461$	2.63590	−	1.52184i	0.122766	−	0.0708791i	0.560126	+	0.828408i	$0.310753\pi$
$462$		0			0
$463$	17.2385	+	9.95266i	0.801142	+	0.462539i	0.843870	−	0.536547i	$-0.180272\pi$
$463$	17.2385	+	9.95266i	0.801142	+	0.462539i	−0.0427284	+	0.999087i	$0.513605\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.82289			−0.130628			−0.0653139	−	0.997865i	$-0.520805\pi$
$467$	−2.82289			−0.130628			−0.0653139	+	0.997865i	$0.520805\pi$
$468$		0			0
$469$	30.0290			1.38661
$470$		0			0
$471$		0			0
$472$		0			0
$473$	40.4416	+	23.3490i	1.85951	+	1.07359i
$474$		0			0
$475$	−72.3511	+	41.7720i	−3.31970	+	1.91663i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.1687	−	26.2730i	−0.693077	−	1.20044i	−0.970825	−	0.239790i	$-0.922921\pi$
$479$	−15.1687	−	26.2730i	−0.693077	−	1.20044i	0.277748	−	0.960654i	$-0.410412\pi$
$480$		0			0
$481$	1.29404	−	2.24134i	0.0590032	−	0.102196i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			41.4538i			1.88232i
$486$		0			0
$487$		−	11.9668i		−	0.542268i	−0.962542	−	0.271134i	$-0.912601\pi$
$487$		−	11.9668i		−	0.542268i	0.962542	−	0.271134i	$-0.0873986\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.10953	+	8.84996i	−0.230590	+	0.399393i	−0.957982	−	0.286829i	$-0.907399\pi$
$491$	−5.10953	+	8.84996i	−0.230590	+	0.399393i	0.727392	+	0.686222i	$0.240732\pi$
$492$		0			0
$493$	15.7603	+	27.2976i	0.709808	+	1.22942i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.4010	−	7.15975i	0.556263	−	0.321159i
$498$		0			0
$499$	−9.72060	−	5.61219i	−0.435154	−	0.251236i	0.266386	−	0.963866i	$-0.414170\pi$
$499$	−9.72060	−	5.61219i	−0.435154	−	0.251236i	−0.701540	+	0.712630i	$0.747504\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.4842			0.913346			0.456673	−	0.889635i	$-0.349041\pi$
$503$	20.4842			0.913346			0.456673	+	0.889635i	$0.349041\pi$
$504$		0			0
$505$	8.60026			0.382707
$506$		0			0
$507$		0			0
$508$		0			0
$509$	27.9102	+	16.1139i	1.23710	+	0.714238i	0.968500	−	0.249015i	$-0.0801068\pi$
$509$	27.9102	+	16.1139i	1.23710	+	0.714238i	0.268597	+	0.963253i	$0.413440\pi$
$510$		0			0
$511$	−5.72650	+	3.30620i	−0.253325	+	0.146258i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−19.8031	−	34.2999i	−0.872628	−	1.51144i
$516$		0			0
$517$	6.79888	−	11.7760i	0.299014	−	0.517908i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			27.2971i			1.19591i	0.801531	+	0.597953i	$0.204019\pi$
$521$			27.2971i			1.19591i	−0.801531	+	0.597953i	$0.795981\pi$
$522$		0			0
$523$			26.4845i			1.15809i	0.815297	+	0.579044i	$0.196574\pi$
$523$			26.4845i			1.15809i	−0.815297	+	0.579044i	$0.803426\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.62245	+	6.27427i	−0.157797	+	0.273312i
$528$		0			0
$529$	8.17545	+	14.1603i	0.355454	+	0.615665i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.28501	−	1.31925i	0.0989746	−	0.0571430i
$534$		0			0
$535$	−15.2688	−	8.81547i	−0.660130	−	0.381126i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	14.7957			0.637296
$540$		0			0
$541$	7.15472			0.307605			0.153803	−	0.988102i	$-0.450848\pi$
$541$	7.15472			0.307605			0.153803	+	0.988102i	$0.450848\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−57.2759	−	33.0682i	−2.45343	−	1.41649i
$546$		0			0
$547$	−8.89513	+	5.13561i	−0.380328	+	0.219583i	−0.677961	−	0.735098i	$-0.737136\pi$
$547$	−8.89513	+	5.13561i	−0.380328	+	0.219583i	0.297633	+	0.954680i	$0.403803\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−24.2376	−	41.9807i	−1.03256	−	1.78844i
$552$		0			0
$553$	14.3757	−	24.8995i	0.611317	−	1.05883i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			9.44585i			0.400234i	0.979772	+	0.200117i	$0.0641322\pi$
$557$			9.44585i			0.400234i	−0.979772	+	0.200117i	$0.935868\pi$
$558$		0			0
$559$		−	10.5792i		−	0.447452i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.0784	−	26.1166i	0.635479	−	1.10068i	−0.350935	−	0.936400i	$-0.614136\pi$
$563$	15.0784	−	26.1166i	0.635479	−	1.10068i	0.986413	−	0.164282i	$-0.0525306\pi$
$564$		0			0
$565$	−29.0072	−	50.2419i	−1.22034	−	2.11369i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.8243	+	12.6002i	−0.914920	+	0.528230i	−0.882011	−	0.471229i	$-0.843811\pi$
$569$	−21.8243	+	12.6002i	−0.914920	+	0.528230i	−0.0329094	+	0.999458i	$0.510477\pi$
$570$		0			0
$571$	32.3079	+	18.6529i	1.35204	+	0.780602i	0.988535	−	0.150990i	$-0.0482462\pi$
$571$	32.3079	+	18.6529i	1.35204	+	0.780602i	0.363506	+	0.931592i	$0.381580\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−28.7431			−1.19867
$576$		0			0
$577$	−17.7799			−0.740189			−0.370094	−	0.928994i	$-0.620675\pi$
$577$	−17.7799			−0.740189			−0.370094	+	0.928994i	$0.620675\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	27.1955	+	15.7014i	1.12826	+	0.651402i
$582$		0			0
$583$	−4.48856	+	2.59147i	−0.185897	+	0.107328i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.2653	+	24.7083i	0.588793	+	1.01982i	0.994391	+	0.105767i	$0.0337299\pi$
$587$	14.2653	+	24.7083i	0.588793	+	1.01982i	−0.405598	+	0.914051i	$0.632937\pi$
$588$		0			0
$589$	5.57093	−	9.64913i	0.229546	−	0.397585i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			31.3024i			1.28544i	0.766102	+	0.642718i	$0.222193\pi$
$593$			31.3024i			1.28544i	−0.766102	+	0.642718i	$0.777807\pi$
$594$		0			0
$595$			60.3166i			2.47274i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.72926	−	2.99517i	0.0706557	−	0.122379i	−0.828533	−	0.559940i	$-0.810824\pi$
$599$	1.72926	−	2.99517i	0.0706557	−	0.122379i	0.899189	+	0.437561i	$0.144158\pi$
$600$		0			0
$601$	6.78744	+	11.7562i	0.276865	+	0.479545i	0.970604	−	0.240682i	$-0.0773711\pi$
$601$	6.78744	+	11.7562i	0.276865	+	0.479545i	−0.693739	+	0.720227i	$0.744038\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	84.9267	−	49.0325i	3.45276	−	1.99345i
$606$		0			0
$607$	−30.8069	−	17.7864i	−1.25042	−	0.721927i	−0.279223	−	0.960226i	$-0.590077\pi$
$607$	−30.8069	−	17.7864i	−1.25042	−	0.721927i	−0.971192	+	0.238299i	$0.923410\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.08051			−0.124624
$612$		0			0
$613$	−23.5978			−0.953104			−0.476552	−	0.879146i	$-0.658114\pi$
$613$	−23.5978			−0.953104			−0.476552	+	0.879146i	$0.658114\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.5804	−	6.68594i	−0.466209	−	0.269166i	0.248442	−	0.968647i	$-0.420081\pi$
$617$	−11.5804	−	6.68594i	−0.466209	−	0.269166i	−0.714651	+	0.699481i	$0.753415\pi$
$618$		0			0
$619$	−32.2014	+	18.5915i	−1.29428	+	0.747254i	−0.979410	−	0.201880i	$-0.935295\pi$
$619$	−32.2014	+	18.5915i	−1.29428	+	0.747254i	−0.314872	+	0.949134i	$0.601962\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.45933	−	2.52764i	−0.0584670	−	0.101268i
$624$		0			0
$625$	−21.7591	+	37.6878i	−0.870363	+	1.50751i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	9.35689i		−	0.373084i
$630$		0			0
$631$			37.8564i			1.50704i	0.657425	+	0.753520i	$0.271646\pi$
$631$			37.8564i			1.50704i	−0.657425	+	0.753520i	$0.728354\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.36804	+	4.10156i	−0.0939728	+	0.162766i
$636$		0			0
$637$	−1.67595	−	2.90283i	−0.0664035	−	0.115014i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.54689	+	4.35720i	−0.298084	+	0.172099i	−0.641582	−	0.767054i	$-0.721722\pi$
$641$	−7.54689	+	4.35720i	−0.298084	+	0.172099i	0.343498	+	0.939154i	$0.388388\pi$
$642$		0			0
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.895025	−	0.446016i	$-0.147158\pi$
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.0612510	+	0.998122i	$0.480491\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.9855			0.864339			0.432169	−	0.901792i	$-0.357748\pi$
$647$	21.9855			0.864339			0.432169	+	0.901792i	$0.357748\pi$
$648$		0			0
$649$	−7.74134			−0.303874
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−41.0423	−	23.6958i	−1.60611	−	0.927289i	−0.990229	−	0.139450i	$-0.955466\pi$
$653$	−41.0423	−	23.6958i	−1.60611	−	0.927289i	−0.615882	−	0.787838i	$-0.711200\pi$
$654$		0			0
$655$	−0.384241	+	0.221842i	−0.0150136	+	0.00866808i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.4752	+	21.6077i	0.485966	+	0.841717i	0.999870	−	0.0161304i	$-0.00513468\pi$
$659$	12.4752	+	21.6077i	0.485966	+	0.841717i	−0.513904	+	0.857848i	$0.671801\pi$
$660$		0			0
$661$	21.0029	−	36.3781i	0.816918	−	1.41494i	−0.0910240	−	0.995849i	$-0.529014\pi$
$661$	21.0029	−	36.3781i	0.816918	−	1.41494i	0.907942	−	0.419095i	$-0.137653\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	92.7602i		−	3.59709i
$666$		0			0
$667$		−	16.6778i		−	0.645766i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−19.6160	+	33.9759i	−0.757267	+	1.31163i
$672$		0			0
$673$	−22.5926	−	39.1315i	−0.870880	−	1.50841i	−0.861087	−	0.508457i	$-0.830216\pi$
$673$	−22.5926	−	39.1315i	−0.870880	−	1.50841i	−0.00979297	−	0.999952i	$-0.503117\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−24.7614	+	14.2960i	−0.951658	+	0.549440i	−0.893596	−	0.448873i	$-0.851826\pi$
$677$	−24.7614	+	14.2960i	−0.951658	+	0.549440i	−0.0580623	+	0.998313i	$0.518492\pi$
$678$		0			0
$679$	−27.5173	−	15.8871i	−1.05602	−	0.609693i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	25.4357			0.973269			0.486634	−	0.873606i	$-0.338224\pi$
$683$	25.4357			0.973269			0.486634	+	0.873606i	$0.338224\pi$
$684$		0			0
$685$	−42.0340			−1.60604
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.01686	+	0.587086i	0.0387394	+	0.0223662i
$690$		0			0
$691$	29.1105	−	16.8069i	1.10741	−	0.639366i	0.169256	−	0.985572i	$-0.445864\pi$
$691$	29.1105	−	16.8069i	1.10741	−	0.639366i	0.938159	+	0.346206i	$0.112530\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	29.4734	+	51.0495i	1.11799	+	1.93642i
$696$		0			0
$697$	4.76958	−	8.26116i	0.180661	−	0.312914i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	12.1433i		−	0.458648i	−0.973350	−	0.229324i	$-0.926349\pi$
$701$		−	12.1433i		−	0.458648i	0.973350	−	0.229324i	$-0.0736515\pi$
$702$		0			0
$703$			14.3898i			0.542723i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.29604	+	5.70892i	−0.123961	+	0.214706i
$708$		0			0
$709$	−17.1361	−	29.6807i	−0.643561	−	1.11468i	−0.984632	−	0.174643i	$-0.944123\pi$
$709$	−17.1361	−	29.6807i	−0.643561	−	1.11468i	0.341071	−	0.940038i	$-0.389210\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.31976	−	1.91667i	0.124326	−	0.0717797i
$714$		0			0
$715$	−27.9118	−	16.1149i	−1.04384	−	0.602663i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−28.4119			−1.05958			−0.529792	−	0.848128i	$-0.677730\pi$
$719$	−28.4119			−1.05958			−0.529792	+	0.848128i	$0.677730\pi$
$720$		0			0
$721$	30.3581			1.13059
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−62.4367	−	36.0479i	−2.31884	−	1.33878i
$726$		0			0
$727$	22.9650	−	13.2589i	0.851725	−	0.491744i	−0.00950728	−	0.999955i	$-0.503026\pi$
$727$	22.9650	−	13.2589i	0.851725	−	0.491744i	0.861233	+	0.508211i	$0.169693\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−19.1239	−	33.1235i	−0.707322	−	1.22512i
$732$		0			0
$733$	−12.0307	+	20.8378i	−0.444365	+	0.769664i	−0.998008	−	0.0630910i	$-0.979904\pi$
$733$	−12.0307	+	20.8378i	−0.444365	+	0.769664i	0.553642	+	0.832755i	$0.313237\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			58.0116i			2.13689i
$738$		0			0
$739$		−	20.9740i		−	0.771540i	−0.922595	−	0.385770i	$-0.873936\pi$
$739$		−	20.9740i		−	0.771540i	0.922595	−	0.385770i	$-0.126064\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−19.3620	+	33.5359i	−0.710322	+	1.23031i	0.254414	+	0.967095i	$0.418118\pi$
$743$	−19.3620	+	33.5359i	−0.710322	+	1.23031i	−0.964736	+	0.263219i	$0.915216\pi$
$744$		0			0
$745$	−6.85728	−	11.8771i	−0.251231	−	0.435145i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.7036	−	6.75705i	0.427638	−	0.246897i
$750$		0			0
$751$	−15.3784	−	8.87871i	−0.561165	−	0.323989i	0.192448	−	0.981307i	$-0.438357\pi$
$751$	−15.3784	−	8.87871i	−0.561165	−	0.323989i	−0.753613	+	0.657319i	$0.771691\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	35.4802			1.29126
$756$		0			0
$757$	−26.7760			−0.973191			−0.486596	−	0.873627i	$-0.661761\pi$
$757$	−26.7760			−0.973191			−0.486596	+	0.873627i	$0.661761\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.81297	−	2.77877i	−0.174470	−	0.100730i	0.410222	−	0.911986i	$-0.365451\pi$
$761$	−4.81297	−	2.77877i	−0.174470	−	0.100730i	−0.584692	+	0.811255i	$0.698785\pi$
$762$		0			0
$763$	43.9019	−	25.3468i	1.58935	−	0.917614i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.876882	+	1.51881i	0.0316624	+	0.0548409i
$768$		0			0
$769$	1.58003	−	2.73670i	0.0569774	−	0.0986878i	−0.836130	−	0.548532i	$-0.815187\pi$
$769$	1.58003	−	2.73670i	0.0569774	−	0.0986878i	0.893107	+	0.449844i	$0.148520\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			8.55146i			0.307575i	0.988104	+	0.153787i	$0.0491471\pi$
$773$			8.55146i			0.307575i	−0.988104	+	0.153787i	$0.950853\pi$
$774$		0			0
$775$		−	16.5710i		−	0.595246i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.33508	+	12.7047i	−0.262807	+	0.455194i
$780$		0			0
$781$	13.8316	+	23.9570i	0.494933	+	0.857248i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−70.9782	+	40.9793i	−2.53332	+	1.46261i
$786$		0			0
$787$	−40.2138	−	23.2174i	−1.43347	−	0.827612i	−0.436082	−	0.899907i	$-0.643634\pi$
$787$	−40.2138	−	23.2174i	−1.43347	−	0.827612i	−0.997383	+	0.0722950i	$0.976968\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	44.4679			1.58110
$792$		0			0
$793$	8.88783			0.315616
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.84163	−	4.52737i	−0.277765	−	0.160368i	0.354646	−	0.935001i	$-0.384601\pi$
$797$	−7.84163	−	4.52737i	−0.277765	−	0.160368i	−0.632411	+	0.774633i	$0.717935\pi$
$798$		0			0
$799$	−9.64509	+	5.56859i	−0.341219	+	0.197003i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.38708	−	11.0627i	−0.225395	−	0.390396i
$804$		0			0
$805$	15.9570	−	27.6383i	0.562410	−	0.974122i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	33.0623i		−	1.16241i	−0.813758	−	0.581204i	$-0.802582\pi$
$809$		−	33.0623i		−	1.16241i	0.813758	−	0.581204i	$-0.197418\pi$
$810$		0			0
$811$		−	20.5874i		−	0.722922i	−0.932387	−	0.361461i	$-0.882278\pi$
$811$		−	20.5874i		−	0.722922i	0.932387	−	0.361461i	$-0.117722\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−22.8803	+	39.6299i	−0.801462	+	1.38817i
$816$		0			0
$817$	29.4104	+	50.9403i	1.02894	+	1.78218i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.6299	+	24.6124i	−1.48779	+	0.858978i	−0.999903	−	0.0139273i	$-0.995567\pi$
$821$	−42.6299	+	24.6124i	−1.48779	+	0.858978i	−0.487890	+	0.872905i	$0.662233\pi$
$822$		0			0
$823$	−23.4802	−	13.5563i	−0.818469	−	0.472543i	0.0314190	−	0.999506i	$-0.489997\pi$
$823$	−23.4802	−	13.5563i	−0.818469	−	0.472543i	−0.849888	+	0.526963i	$0.823331\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.5040			−1.30414			−0.652070	−	0.758159i	$-0.726099\pi$
$827$	−37.5040			−1.30414			−0.652070	+	0.758159i	$0.726099\pi$
$828$		0			0
$829$	−6.78386			−0.235613			−0.117807	−	0.993037i	$-0.537586\pi$
$829$	−6.78386			−0.235613			−0.117807	+	0.993037i	$0.537586\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.4948	−	6.05918i	−0.363624	−	0.209938i
$834$		0			0
$835$	−81.0575	+	46.7986i	−2.80511	+	1.61953i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	20.0402	+	34.7106i	0.691863	+	1.19834i	0.971227	+	0.238156i	$0.0765430\pi$
$839$	20.0402	+	34.7106i	0.691863	+	1.19834i	−0.279364	+	0.960185i	$0.590124\pi$
$840$		0			0
$841$	6.41625	−	11.1133i	0.221250	−	0.383216i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	44.9366i		−	1.54587i
$846$		0			0
$847$			75.1666i			2.58276i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.47540	+	4.28752i	−0.0848556	+	0.146974i
$852$		0			0
$853$	7.71847	+	13.3688i	0.264275	+	0.457738i	0.967373	−	0.253355i	$-0.0815339\pi$
$853$	7.71847	+	13.3688i	0.264275	+	0.457738i	−0.703098	+	0.711093i	$0.748201\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.6520	−	7.30464i	0.432184	−	0.249522i	−0.268093	−	0.963393i	$-0.586393\pi$
$857$	12.6520	−	7.30464i	0.432184	−	0.249522i	0.700277	+	0.713872i	$0.253060\pi$
$858$		0			0
$859$	−5.02878	−	2.90337i	−0.171580	−	0.0990616i	0.411751	−	0.911297i	$-0.364917\pi$
$859$	−5.02878	−	2.90337i	−0.171580	−	0.0990616i	−0.583331	+	0.812235i	$0.698251\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.5724			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$863$	−19.5724			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$864$		0			0
$865$	−53.9487			−1.83431
$866$		0			0
$867$		0			0
$868$		0			0
$869$	48.1020	+	27.7717i	1.63175	+	0.942091i
$870$		0			0
$871$	11.3815	−	6.57113i	0.385649	−	0.222654i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−38.0384	−	65.8845i	−1.28593	−	2.22730i
$876$		0			0
$877$	2.64809	−	4.58662i	0.0894196	−	0.154879i	−0.817846	−	0.575437i	$-0.804832\pi$
$877$	2.64809	−	4.58662i	0.0894196	−	0.154879i	0.907266	+	0.420557i	$0.138165\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			16.5467i			0.557473i	0.960368	+	0.278736i	$0.0899155\pi$
$881$			16.5467i			0.557473i	−0.960368	+	0.278736i	$0.910084\pi$
$882$		0			0
$883$		−	24.9361i		−	0.839166i	−0.907717	−	0.419583i	$-0.862176\pi$
$883$		−	24.9361i		−	0.839166i	0.907717	−	0.419583i	$-0.137824\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.50506	+	11.2671i	−0.218419	+	0.378312i	−0.954325	−	0.298772i	$-0.903423\pi$
$887$	−6.50506	+	11.2671i	−0.218419	+	0.378312i	0.735906	+	0.677084i	$0.236756\pi$
$888$		0			0
$889$	−1.81510	−	3.14384i	−0.0608765	−	0.105441i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.8331	−	8.56387i	0.496370	−	0.286579i
$894$		0			0
$895$	72.0841	+	41.6178i	2.40951	+	1.39113i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.61506			0.320680
$900$		0			0
$901$	4.24507			0.141424
$902$		0			0
$903$		0			0
$904$		0			0
$905$	28.0536	+	16.1968i	0.932535	+	0.538399i
$906$		0			0
$907$	30.7534	−	17.7555i	1.02115	−	0.589561i	0.106713	−	0.994290i	$-0.465967\pi$
$907$	30.7534	−	17.7555i	1.02115	−	0.589561i	0.914437	+	0.404729i	$0.132634\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	21.2073	+	36.7321i	0.702629	+	1.21699i	0.967540	+	0.252716i	$0.0813239\pi$
$911$	21.2073	+	36.7321i	0.702629	+	1.21699i	−0.264912	+	0.964273i	$0.585343\pi$
$912$		0			0
$913$	−30.3327	+	52.5378i	−1.00387	+	1.73875i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	0.340083i		−	0.0112305i
$918$		0			0
$919$		−	3.12106i		−	0.102954i	−0.998674	−	0.0514772i	$-0.983607\pi$
$919$		−	3.12106i		−	0.102954i	0.998674	−	0.0514772i	$-0.0163929\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.13348	−	5.42734i	0.103140	−	0.178643i
$924$		0			0
$925$	10.7008	+	18.5343i	0.351840	+	0.609405i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	51.7148	−	29.8576i	1.69671	−	0.979595i	0.747863	−	0.663853i	$-0.231080\pi$
$929$	51.7148	−	29.8576i	1.69671	−	0.979595i	0.948845	−	0.315742i	$-0.102253\pi$
$930$		0			0
$931$	16.1399	+	9.31835i	0.528962	+	0.305397i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−116.523			−3.81070
$936$		0			0
$937$	−19.8793			−0.649428			−0.324714	−	0.945812i	$-0.605268\pi$
$937$	−19.8793			−0.649428			−0.324714	+	0.945812i	$0.605268\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.37354	+	5.41181i	0.305569	+	0.176420i	0.644942	−	0.764232i	$-0.276882\pi$
$941$	9.37354	+	5.41181i	0.305569	+	0.176420i	−0.339373	+	0.940652i	$0.610215\pi$
$942$		0			0
$943$	−4.37104	+	2.52362i	−0.142341	+	0.0821804i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.5953	+	20.0836i	0.376796	+	0.652630i	0.990594	−	0.136833i	$-0.0436924\pi$
$947$	11.5953	+	20.0836i	0.376796	+	0.652630i	−0.613798	+	0.789463i	$0.710359\pi$
$948$		0			0
$949$	−1.44696	+	2.50621i	−0.0469704	+	0.0813551i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			17.7414i			0.574700i	0.957826	+	0.287350i	$0.0927743\pi$
$953$			17.7414i			0.574700i	−0.957826	+	0.287350i	$0.907226\pi$
$954$		0			0
$955$		−	91.5893i		−	2.96376i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.1095	−	27.9025i	0.520203	−	0.901018i
$960$		0			0
$961$	−14.3950	−	24.9329i	−0.464355	−	0.804286i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−57.2572	+	33.0575i	−1.84318	+	1.06416i
$966$		0			0
$967$	11.6547	+	6.72886i	0.374791	+	0.216386i	0.675549	−	0.737315i	$-0.263906\pi$
$967$	11.6547	+	6.72886i	0.374791	+	0.216386i	−0.300759	+	0.953700i	$0.597240\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.8995			0.574423			0.287211	−	0.957867i	$-0.407272\pi$
$971$	17.8995			0.574423			0.287211	+	0.957867i	$0.407272\pi$
$972$		0			0
$973$	−45.1827			−1.44849
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.0208	−	9.82699i	−0.544545	−	0.314393i	0.202374	−	0.979308i	$-0.435134\pi$
$977$	−17.0208	−	9.82699i	−0.544545	−	0.314393i	−0.746919	+	0.664915i	$0.768468\pi$
$978$		0			0
$979$	4.88303	−	2.81922i	0.156062	−	0.0901026i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−29.8264	−	51.6608i	−0.951314	−	1.64772i	−0.742587	−	0.669749i	$-0.766402\pi$
$983$	−29.8264	−	51.6608i	−0.951314	−	1.64772i	−0.208726	−	0.977974i	$-0.566932\pi$
$984$		0			0
$985$	44.1099	−	76.4006i	1.40546	−	2.43433i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			20.2372i			0.643505i
$990$		0			0
$991$			48.0373i			1.52595i	0.646426	+	0.762977i	$0.276263\pi$
$991$			48.0373i			1.52595i	−0.646426	+	0.762977i	$0.723737\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	22.6901	−	39.3004i	0.719324	−	1.24591i
$996$		0			0
$997$	3.19614	+	5.53587i	0.101223	+	0.175323i	0.912189	−	0.409770i	$-0.134391\pi$
$997$	3.19614	+	5.53587i	0.101223	+	0.175323i	−0.810966	+	0.585093i	$0.801058\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.j.863.1		16
3.2	odd	2	inner	2592.2.s.j.863.8		16
4.3	odd	2		2592.2.s.i.863.1		16
9.2	odd	6		2592.2.s.i.1727.1		16
9.4	even	3		2592.2.c.b.2591.16	yes	16
9.5	odd	6		2592.2.c.b.2591.2	yes	16
9.7	even	3		2592.2.s.i.1727.8		16
12.11	even	2		2592.2.s.i.863.8		16
36.7	odd	6	inner	2592.2.s.j.1727.8		16
36.11	even	6	inner	2592.2.s.j.1727.1		16
36.23	even	6		2592.2.c.b.2591.1	✓	16
36.31	odd	6		2592.2.c.b.2591.15	yes	16
72.5	odd	6		5184.2.c.l.5183.16		16
72.13	even	6		5184.2.c.l.5183.2		16
72.59	even	6		5184.2.c.l.5183.15		16
72.67	odd	6		5184.2.c.l.5183.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2592.2.c.b.2591.1	✓	16	36.23	even	6
2592.2.c.b.2591.2	yes	16	9.5	odd	6
2592.2.c.b.2591.15	yes	16	36.31	odd	6
2592.2.c.b.2591.16	yes	16	9.4	even	3
2592.2.s.i.863.1		16	4.3	odd	2
2592.2.s.i.863.8		16	12.11	even	2
2592.2.s.i.1727.1		16	9.2	odd	6
2592.2.s.i.1727.8		16	9.7	even	3
2592.2.s.j.863.1		16	1.1	even	1	trivial
2592.2.s.j.863.8		16	3.2	odd	2	inner
2592.2.s.j.1727.1		16	36.11	even	6	inner
2592.2.s.j.1727.8		16	36.7	odd	6	inner
5184.2.c.l.5183.1		16	72.67	odd	6
5184.2.c.l.5183.2		16	72.13	even	6
5184.2.c.l.5183.15		16	72.59	even	6
5184.2.c.l.5183.16		16	72.5	odd	6

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-3.47996 - 2.00916i) q^{5} +(2.66739 - 1.54002i) q^{7} +O(q^{10})\)	\(q+(-3.47996 - 2.00916i) q^{5} +(2.66739 - 1.54002i) q^{7} +(2.97508 + 5.15300i) q^{11} +(0.673991 - 1.16739i) q^{13} -4.87346i q^{17} +7.49484i q^{19} +(-1.28929 + 2.23312i) q^{23} +(5.57343 + 9.65346i) q^{25} +(-5.60128 + 3.23390i) q^{29} +(-1.28744 - 0.743302i) q^{31} -12.3765 q^{35} +1.91997 q^{37} +(1.69513 + 0.978684i) q^{41} +(6.79671 - 3.92409i) q^{43} +(-1.14264 - 1.97910i) q^{47} +(1.24330 - 2.15346i) q^{49} +0.871059i q^{53} -23.9096i q^{55} +(-0.650515 + 1.12672i) q^{59} +(3.29671 + 5.71008i) q^{61} +(-4.69093 + 2.70831i) q^{65} +(8.44338 + 4.87479i) q^{67} +4.64914 q^{71} -2.14686 q^{73} +(15.8714 + 9.16336i) q^{77} +(8.08415 - 4.66739i) q^{79} +(5.09779 + 8.82963i) q^{83} +(-9.79155 + 16.9595i) q^{85} -0.947609i q^{89} -4.15183i q^{91} +(15.0583 - 26.0818i) q^{95} +(-5.15811 - 8.93411i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

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