LMFDB - Embedded newform 216.2.n.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(37,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("216.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.n (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:	$1.72476868366$
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} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.8
Root			$1.05026 - 0.947078i$ of defining polynomial
Character	$\chi$	$=$	216.37
Dual form			216.2.n.b.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34532 - 0.436011i) q^{2} +(1.61979 - 1.17315i) q^{4} +(0.602794 + 0.348023i) q^{5} +(0.795065 + 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +O(q^{10})$	\(q+(1.34532 - 0.436011i) q^{2} +(1.61979 - 1.17315i) q^{4} +(0.602794 + 0.348023i) q^{5} +(0.795065 + 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +(0.962695 + 0.205379i) q^{10} +(-2.37222 + 1.36960i) q^{11} +(-4.76780 - 2.75269i) q^{13} +(1.67005 + 1.50598i) q^{14} +(1.24743 - 3.80052i) q^{16} +5.65175 q^{17} -0.963328i q^{19} +(1.38468 - 0.143445i) q^{20} +(-2.59424 + 2.87688i) q^{22} +(-3.28857 + 5.69597i) q^{23} +(-2.25776 - 3.91055i) q^{25} +(-7.61444 - 1.62444i) q^{26} +(2.90338 + 1.29787i) q^{28} +(-2.85076 + 1.64589i) q^{29} +(-3.69844 + 6.40589i) q^{31} +(0.0211236 - 5.65681i) q^{32} +(7.60343 - 2.46423i) q^{34} +1.10680i q^{35} +6.25538i q^{37} +(-0.420022 - 1.29599i) q^{38} +(1.80030 - 0.796718i) q^{40} +(0.931886 - 1.61407i) q^{41} +(-2.99838 + 1.73111i) q^{43} +(-2.23574 + 5.00145i) q^{44} +(-1.94068 + 9.09677i) q^{46} +(-3.85668 - 6.67997i) q^{47} +(2.23574 - 3.87242i) q^{49} +(-4.74246 - 4.27655i) q^{50} +(-10.9522 + 1.13458i) q^{52} -2.54179i q^{53} -1.90662 q^{55} +(4.47186 + 0.480144i) q^{56} +(-3.11757 + 3.45722i) q^{58} +(4.62019 + 2.66747i) q^{59} +(7.93715 - 4.58252i) q^{61} +(-2.18256 + 10.2305i) q^{62} +(-2.43802 - 7.61945i) q^{64} +(-1.91600 - 3.31861i) q^{65} +(5.95780 + 3.43974i) q^{67} +(9.15463 - 6.63036i) q^{68} +(0.482579 + 1.48901i) q^{70} -3.68351 q^{71} +2.83201 q^{73} +(2.72742 + 8.41550i) q^{74} +(-1.13013 - 1.56039i) q^{76} +(-3.77214 - 2.17785i) q^{77} +(2.87870 + 4.98605i) q^{79} +(2.07461 - 1.85680i) q^{80} +(0.549933 - 2.57776i) q^{82} +(5.74968 - 3.31958i) q^{83} +(3.40684 + 1.96694i) q^{85} +(-3.27900 + 3.63623i) q^{86} +(-0.827111 + 7.70337i) q^{88} +2.98701 q^{89} -8.75427i q^{91} +(1.35545 + 13.0843i) q^{92} +(-8.10103 - 7.30516i) q^{94} +(0.335261 - 0.580689i) q^{95} +(-1.24837 - 2.16224i) q^{97} +(1.31938 - 6.18447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.34532	−	0.436011i	0.951287	−	0.308307i
$2$	1.34532	−	0.436011i	0.951287	−	0.308307i
$3$		0			0
$3$		0			0
$4$	1.61979	−	1.17315i	0.809894	−	0.586576i
$5$	0.602794	+	0.348023i	0.269578	+	0.155641i	0.628696	−	0.777651i	$-0.283589\pi$
$5$	0.602794	+	0.348023i	0.269578	+	0.155641i	−0.359118	+	0.933292i	$0.616922\pi$
$6$		0			0
$7$	0.795065	+	1.37709i	0.300506	+	0.520492i	0.976251	−	0.216644i	$-0.0695111\pi$
$7$	0.795065	+	1.37709i	0.300506	+	0.520492i	−0.675745	+	0.737136i	$0.736178\pi$
$8$	1.66763	−	2.28452i	0.589596	−	0.807698i
$9$		0			0
$10$	0.962695	+	0.205379i	0.304431	+	0.0649464i
$11$	−2.37222	+	1.36960i	−0.715252	+	0.412951i	−0.813003	−	0.582260i	$-0.802169\pi$
$11$	−2.37222	+	1.36960i	−0.715252	+	0.412951i	0.0977506	+	0.995211i	$0.468835\pi$
$12$		0			0
$13$	−4.76780	−	2.75269i	−1.32235	−	0.763460i	−0.338248	−	0.941057i	$-0.609834\pi$
$13$	−4.76780	−	2.75269i	−1.32235	−	0.763460i	−0.984103	+	0.177597i	$0.943168\pi$
$14$	1.67005	+	1.50598i	0.446339	+	0.402489i
$15$		0			0
$16$	1.24743	−	3.80052i	0.311857	−	0.950129i
$17$	5.65175			1.37075			0.685375	−	0.728190i	$-0.259638\pi$
$17$	5.65175			1.37075			0.685375	+	0.728190i	$0.259638\pi$
$18$		0			0
$19$		−	0.963328i		−	0.221003i	−0.993876	−	0.110501i	$-0.964754\pi$
$19$		−	0.963328i		−	0.221003i	0.993876	−	0.110501i	$-0.0352457\pi$
$20$	1.38468	−	0.143445i	0.309625	−	0.0320753i
$21$		0			0
$22$	−2.59424	+	2.87688i	−0.553095	+	0.613352i
$23$	−3.28857	+	5.69597i	−0.685714	+	1.18769i	0.287498	+	0.957781i	$0.407177\pi$
$23$	−3.28857	+	5.69597i	−0.685714	+	1.18769i	−0.973212	+	0.229910i	$0.926157\pi$
$24$		0			0
$25$	−2.25776	−	3.91055i	−0.451552	−	0.782111i
$26$	−7.61444	−	1.62444i	−1.49332	−	0.318580i
$27$		0			0
$28$	2.90338	+	1.29787i	0.548686	+	0.245274i
$29$	−2.85076	+	1.64589i	−0.529373	+	0.305634i	−0.740761	−	0.671768i	$-0.765535\pi$
$29$	−2.85076	+	1.64589i	−0.529373	+	0.305634i	0.211388	+	0.977402i	$0.432202\pi$
$30$		0			0
$31$	−3.69844	+	6.40589i	−0.664259	+	1.15053i	0.315226	+	0.949017i	$0.397920\pi$
$31$	−3.69844	+	6.40589i	−0.664259	+	1.15053i	−0.979486	+	0.201514i	$0.935414\pi$
$32$	0.0211236	−	5.65681i	0.00373416	−	0.999993i
$33$		0			0
$34$	7.60343	−	2.46423i	1.30398	−	0.422611i
$35$			1.10680i			0.187084i
$36$		0			0
$37$			6.25538i			1.02838i	0.857677	+	0.514189i	$0.171907\pi$
$37$			6.25538i			1.02838i	−0.857677	+	0.514189i	$0.828093\pi$
$38$	−0.420022	−	1.29599i	−0.0681366	−	0.210237i
$39$		0			0
$40$	1.80030	−	0.796718i	0.284653	−	0.125972i
$41$	0.931886	−	1.61407i	0.145536	−	0.252076i	−0.784037	−	0.620714i	$-0.786843\pi$
$41$	0.931886	−	1.61407i	0.145536	−	0.252076i	0.929573	+	0.368639i	$0.120176\pi$
$42$		0			0
$43$	−2.99838	+	1.73111i	−0.457248	+	0.263992i	−0.710886	−	0.703307i	$-0.751706\pi$
$43$	−2.99838	+	1.73111i	−0.457248	+	0.263992i	0.253638	+	0.967299i	$0.418373\pi$
$44$	−2.23574	+	5.00145i	−0.337051	+	0.753996i
$45$		0			0
$46$	−1.94068	+	9.09677i	−0.286138	+	1.34125i
$47$	−3.85668	−	6.67997i	−0.562555	−	0.974374i	−0.997273	−	0.0738070i	$-0.976485\pi$
$47$	−3.85668	−	6.67997i	−0.562555	−	0.974374i	0.434717	−	0.900567i	$-0.356848\pi$
$48$		0			0
$49$	2.23574	−	3.87242i	0.319392	−	0.553203i
$50$	−4.74246	−	4.27655i	−0.670685	−	0.604795i
$51$		0			0
$52$	−10.9522	+	1.13458i	−1.51879	+	0.157338i
$53$		−	2.54179i		−	0.349141i	−0.984645	−	0.174571i	$-0.944146\pi$
$53$		−	2.54179i		−	0.349141i	0.984645	−	0.174571i	$-0.0558537\pi$
$54$		0			0
$55$	−1.90662			−0.257088
$56$	4.47186	+	0.480144i	0.597578	+	0.0641619i
$57$		0			0
$58$	−3.11757	+	3.45722i	−0.409357	+	0.453955i
$59$	4.62019	+	2.66747i	0.601498	+	0.347275i	0.769631	−	0.638489i	$-0.220440\pi$
$59$	4.62019	+	2.66747i	0.601498	+	0.347275i	−0.168133	+	0.985764i	$0.553774\pi$
$60$		0			0
$61$	7.93715	−	4.58252i	1.01625	−	0.586731i	0.103233	−	0.994657i	$-0.467081\pi$
$61$	7.93715	−	4.58252i	1.01625	−	0.586731i	0.913015	+	0.407926i	$0.133748\pi$
$62$	−2.18256	+	10.2305i	−0.277185	+	1.29928i
$63$		0			0
$64$	−2.43802	−	7.61945i	−0.304752	−	0.952432i
$65$	−1.91600	−	3.31861i	−0.237651	−	0.411623i
$66$		0			0
$67$	5.95780	+	3.43974i	0.727861	+	0.420231i	0.817639	−	0.575731i	$-0.195283\pi$
$67$	5.95780	+	3.43974i	0.727861	+	0.420231i	−0.0897783	+	0.995962i	$0.528616\pi$
$68$	9.15463	−	6.63036i	1.11016	−	0.804049i
$69$		0			0
$70$	0.482579	+	1.48901i	0.0576792	+	0.177971i
$71$	−3.68351			−0.437153			−0.218576	−	0.975820i	$-0.570141\pi$
$71$	−3.68351			−0.437153			−0.218576	+	0.975820i	$0.570141\pi$
$72$		0			0
$73$	2.83201			0.331461			0.165731	−	0.986171i	$-0.447002\pi$
$73$	2.83201			0.331461			0.165731	+	0.986171i	$0.447002\pi$
$74$	2.72742	+	8.41550i	0.317056	+	0.978282i
$75$		0			0
$76$	−1.13013	−	1.56039i	−0.129635	−	0.178989i
$77$	−3.77214	−	2.17785i	−0.429875	−	0.248189i
$78$		0			0
$79$	2.87870	+	4.98605i	0.323879	+	0.560975i	0.981285	−	0.192562i	$-0.0616797\pi$
$79$	2.87870	+	4.98605i	0.323879	+	0.560975i	−0.657406	+	0.753537i	$0.728346\pi$
$80$	2.07461	−	1.85680i	0.231948	−	0.207596i
$81$		0			0
$82$	0.549933	−	2.57776i	0.0607299	−	0.284666i
$83$	5.74968	−	3.31958i	0.631110	−	0.364371i	−0.150072	−	0.988675i	$-0.547951\pi$
$83$	5.74968	−	3.31958i	0.631110	−	0.364371i	0.781182	+	0.624304i	$0.214617\pi$
$84$		0			0
$85$	3.40684	+	1.96694i	0.369524	+	0.213345i
$86$	−3.27900	+	3.63623i	−0.353584	+	0.392105i
$87$		0			0
$88$	−0.827111	+	7.70337i	−0.0881703	+	0.821182i
$89$	2.98701			0.316622			0.158311	−	0.987389i	$-0.449395\pi$
$89$	2.98701			0.316622			0.158311	+	0.987389i	$0.449395\pi$
$90$		0			0
$91$		−	8.75427i		−	0.917697i
$92$	1.35545	+	13.0843i	0.141316	+	1.36413i
$93$		0			0
$94$	−8.10103	−	7.30516i	−0.835557	−	0.753470i
$95$	0.335261	−	0.580689i	0.0343970	−	0.0595774i
$96$		0			0
$97$	−1.24837	−	2.16224i	−0.126753	−	0.219543i	0.795664	−	0.605738i	$-0.207122\pi$
$97$	−1.24837	−	2.16224i	−0.126753	−	0.219543i	−0.922417	+	0.386196i	$0.873789\pi$
$98$	1.31938	−	6.18447i	0.133277	−	0.624726i
$99$		0			0
$100$	−8.24477	−	3.68557i	−0.824477	−	0.368557i
$101$	8.22136	−	4.74661i	0.818056	−	0.472305i	−0.0316896	−	0.999498i	$-0.510089\pi$
$101$	8.22136	−	4.74661i	0.818056	−	0.472305i	0.849746	+	0.527193i	$0.176755\pi$
$102$		0			0
$103$	7.37220	−	12.7690i	0.726405	−	1.25817i	−0.231989	−	0.972719i	$-0.574523\pi$
$103$	7.37220	−	12.7690i	0.726405	−	1.25817i	0.958393	−	0.285451i	$-0.0921435\pi$
$104$	−14.2395	+	6.30165i	−1.39630	+	0.617927i
$105$		0			0
$106$	−1.10825	−	3.41952i	−0.107643	−	0.332134i
$107$		−	7.83384i		−	0.757325i	−0.925535	−	0.378663i	$-0.876384\pi$
$107$		−	7.83384i		−	0.757325i	0.925535	−	0.378663i	$-0.123616\pi$
$108$		0			0
$109$		−	0.242400i		−	0.0232177i	−0.999933	−	0.0116089i	$-0.996305\pi$
$109$		−	0.242400i		−	0.0232177i	0.999933	−	0.0116089i	$-0.00369529\pi$
$110$	−2.56501	+	0.831306i	−0.244565	+	0.0792619i
$111$		0			0
$112$	6.22545	−	1.30383i	0.588249	−	0.123201i
$113$	−4.34789	+	7.53076i	−0.409015	+	0.708435i	−0.994780	−	0.102046i	$-0.967461\pi$
$113$	−4.34789	+	7.53076i	−0.409015	+	0.708435i	0.585765	+	0.810481i	$0.300794\pi$
$114$		0			0
$115$	−3.96466	+	2.28900i	−0.369706	+	0.213450i
$116$	−2.68675	+	6.01037i	−0.249459	+	0.558049i
$117$		0			0
$118$	7.37870	+	1.57415i	0.679264	+	0.144912i
$119$	4.49350	+	7.78298i	0.411919	+	0.713464i
$120$		0			0
$121$	−1.74837	+	3.02827i	−0.158943	+	0.275297i
$122$	8.68000	−	9.62565i	0.785850	−	0.871466i
$123$		0			0
$124$	1.52439	+	14.7150i	0.136894	+	1.32145i
$125$		−	6.62325i		−	0.592401i
$126$		0			0
$127$	−1.72754			−0.153295			−0.0766473	−	0.997058i	$-0.524422\pi$
$127$	−1.72754			−0.153295			−0.0766473	+	0.997058i	$0.524422\pi$
$128$	−6.60209	−	9.18762i	−0.583548	−	0.812079i
$129$		0			0
$130$	−4.02460	−	3.62921i	−0.352980	−	0.318303i
$131$	−5.74968	−	3.31958i	−0.502352	−	0.290033i	0.227332	−	0.973817i	$-0.427000\pi$
$131$	−5.74968	−	3.31958i	−0.502352	−	0.290033i	−0.729684	+	0.683784i	$0.760333\pi$
$132$		0			0
$133$	1.32659	−	0.765908i	0.115030	−	0.0664127i
$134$	9.51493	+	2.02989i	0.821964	+	0.175356i
$135$		0			0
$136$	9.42503	−	12.9115i	0.808189	−	1.10715i
$137$	−1.81325	−	3.14063i	−0.154916	−	0.268322i	0.778112	−	0.628125i	$-0.216177\pi$
$137$	−1.81325	−	3.14063i	−0.154916	−	0.268322i	−0.933028	+	0.359803i	$0.882844\pi$
$138$		0			0
$139$	14.9919	+	8.65556i	1.27159	+	0.734155i	0.975288	−	0.220937i	$-0.0709117\pi$
$139$	14.9919	+	8.65556i	1.27159	+	0.734155i	0.296307	+	0.955093i	$0.404245\pi$
$140$	1.29845	+	1.79279i	0.109739	+	0.151518i
$141$		0			0
$142$	−4.95552	+	1.60605i	−0.415858	+	0.134777i
$143$	15.0804			1.26109
$144$		0			0
$145$	−2.29123			−0.190276
$146$	3.80996	−	1.23479i	0.315315	−	0.102192i
$147$		0			0
$148$	7.33851	+	10.1324i	0.603222	+	0.832877i
$149$	18.7251	+	10.8109i	1.53402	+	0.885665i	0.999171	+	0.0407158i	$0.0129638\pi$
$149$	18.7251	+	10.8109i	1.53402	+	0.885665i	0.534846	+	0.844949i	$0.320369\pi$
$150$		0			0
$151$	−6.35019	−	10.9988i	−0.516771	−	0.895073i	−0.999810	−	0.0194749i	$-0.993801\pi$
$151$	−6.35019	−	10.9988i	−0.516771	−	0.895073i	0.483039	−	0.875599i	$-0.339533\pi$
$152$	−2.20074	−	1.60648i	−0.178503	−	0.130302i
$153$		0			0
$154$	−6.02431	−	1.28521i	−0.485453	−	0.103565i
$155$	−4.45880	+	2.57429i	−0.358139	+	0.206772i
$156$		0			0
$157$	−15.1285	−	8.73443i	−1.20738	−	0.697083i	−0.245197	−	0.969473i	$-0.578853\pi$
$157$	−15.1285	−	8.73443i	−1.20738	−	0.697083i	−0.962187	+	0.272390i	$0.912186\pi$
$158$	6.04675	+	5.45270i	0.481054	+	0.433794i
$159$		0			0
$160$	1.98144	−	3.40254i	0.156646	−	0.268995i
$161$	−10.4585			−0.824245
$162$		0			0
$163$		−	8.56748i		−	0.671057i	−0.942030	−	0.335528i	$-0.891085\pi$
$163$		−	8.56748i		−	0.671057i	0.942030	−	0.335528i	$-0.108915\pi$
$164$	−0.384097	−	3.70770i	−0.0299929	−	0.289523i
$165$		0			0
$166$	6.28781	−	6.97284i	0.488028	−	0.541197i
$167$	5.97532	−	10.3496i	0.462384	−	0.800873i	−0.536695	−	0.843776i	$-0.680327\pi$
$167$	5.97532	−	10.3496i	0.462384	−	0.800873i	0.999079	+	0.0429032i	$0.0136607\pi$
$168$		0			0
$169$	8.65464	+	14.9903i	0.665741	+	1.15310i
$170$	5.44091	+	1.16075i	0.417299	+	0.0890254i
$171$		0			0
$172$	−2.82587	+	6.32159i	−0.215471	+	0.482017i
$173$	−11.2973	+	6.52248i	−0.858916	+	0.495895i	−0.863649	−	0.504094i	$-0.831827\pi$
$173$	−11.2973	+	6.52248i	−0.858916	+	0.495895i	0.00473326	+	0.999989i	$0.498493\pi$
$174$		0			0
$175$	3.59013	−	6.21829i	0.271388	−	0.470058i
$176$	2.24603	+	10.7242i	0.169301	+	0.808363i
$177$		0			0
$178$	4.01849	−	1.30237i	0.301199	−	0.0976167i
$179$			3.31875i			0.248055i	0.992279	+	0.124028i	$0.0395811\pi$
$179$			3.31875i			0.248055i	−0.992279	+	0.124028i	$0.960419\pi$
$180$		0			0
$181$			14.9128i			1.10846i	0.832363	+	0.554231i	$0.186987\pi$
$181$			14.9128i			1.10846i	−0.832363	+	0.554231i	$0.813013\pi$
$182$	−3.81696	−	11.7773i	−0.282932	−	0.872994i
$183$		0			0
$184$	7.52841	+	17.0116i	0.555002	+	1.25411i
$185$	−2.17702	+	3.77070i	−0.160058	+	0.277228i
$186$		0			0
$187$	−13.4072	+	7.74065i	−0.980432	+	0.566053i
$188$	−14.0836	−	6.29566i	−1.02715	−	0.459158i
$189$		0			0
$190$	0.197847	−	0.927391i	0.0143533	−	0.0672800i
$191$	−3.65884	−	6.33729i	−0.264744	−	0.458550i	0.702752	−	0.711434i	$-0.251954\pi$
$191$	−3.65884	−	6.33729i	−0.264744	−	0.458550i	−0.967497	+	0.252884i	$0.918621\pi$
$192$		0			0
$193$	−10.2354	+	17.7282i	−0.736759	+	1.27610i	0.217189	+	0.976130i	$0.430311\pi$
$193$	−10.2354	+	17.7282i	−0.736759	+	1.27610i	−0.953947	+	0.299974i	$0.903022\pi$
$194$	−2.62223	−	2.36461i	−0.188265	−	0.169769i
$195$		0			0
$196$	−0.921510	−	8.89537i	−0.0658222	−	0.635384i
$197$			20.5437i			1.46368i	0.681479	+	0.731838i	$0.261337\pi$
$197$			20.5437i			1.46368i	−0.681479	+	0.731838i	$0.738663\pi$
$198$		0			0
$199$	1.95597			0.138655			0.0693275	−	0.997594i	$-0.477915\pi$
$199$	1.95597			0.138655			0.0693275	+	0.997594i	$0.477915\pi$
$200$	−12.6988	−	1.36347i	−0.897943	−	0.0964121i
$201$		0			0
$202$	8.99081	−	9.97033i	0.632591	−	0.701510i
$203$	−4.53308	−	2.61718i	−0.318160	−	0.183690i
$204$		0			0
$205$	1.12347	−	0.648636i	0.0784666	−	0.0453027i
$206$	4.35055	−	20.3928i	0.303117	−	1.42084i
$207$		0			0
$208$	−16.4091	+	14.6863i	−1.13777	+	1.01831i
$209$	1.31938	+	2.28523i	0.0912633	+	0.158073i
$210$		0			0
$211$	−9.10981	−	5.25955i	−0.627145	−	0.362082i	0.152501	−	0.988303i	$-0.451267\pi$
$211$	−9.10981	−	5.25955i	−0.627145	−	0.362082i	−0.779646	+	0.626221i	$0.784601\pi$
$212$	−2.98190	−	4.11716i	−0.204798	−	0.282767i
$213$		0			0
$214$	−3.41564	−	10.5390i	−0.233488	−	0.720434i
$215$	−2.40987			−0.164352
$216$		0			0
$217$	−11.7620			−0.798456
$218$	−0.105689	−	0.326106i	−0.00715817	−	0.0220867i
$219$		0			0
$220$	−3.08831	+	2.23675i	−0.208214	+	0.150802i
$221$	−26.9464	−	15.5575i	−1.81261	−	1.04651i
$222$		0			0
$223$	1.93129	+	3.34510i	0.129329	+	0.224004i	0.923417	−	0.383799i	$-0.125384\pi$
$223$	1.93129	+	3.34510i	0.129329	+	0.224004i	−0.794088	+	0.607803i	$0.792051\pi$
$224$	7.80675	−	4.46844i	0.521610	−	0.298560i
$225$		0			0
$226$	−2.56582	+	12.0270i	−0.170676	+	0.800027i
$227$	−13.9183	+	8.03574i	−0.923790	+	0.533351i	−0.884842	−	0.465891i	$-0.845734\pi$
$227$	−13.9183	+	8.03574i	−0.923790	+	0.533351i	−0.0389481	+	0.999241i	$0.512401\pi$
$228$		0			0
$229$	7.46319	+	4.30888i	0.493182	+	0.284739i	0.725893	−	0.687807i	$-0.241427\pi$
$229$	7.46319	+	4.30888i	0.493182	+	0.284739i	−0.232712	+	0.972546i	$0.574760\pi$
$230$	−4.33572	+	4.80808i	−0.285889	+	0.317035i
$231$		0			0
$232$	−0.993962	+	9.25735i	−0.0652568	+	0.607775i
$233$	−24.1535			−1.58235			−0.791176	−	0.611589i	$-0.790531\pi$
$233$	−24.1535			−1.58235			−0.791176	+	0.611589i	$0.790531\pi$
$234$		0			0
$235$		−	5.36886i		−	0.350226i
$236$	10.6131	−	1.09945i	0.690853	−	0.0715684i
$237$		0			0
$238$	9.43868	+	8.51140i	0.611819	+	0.551712i
$239$	2.01493	−	3.48996i	0.130335	−	0.225746i	−0.793471	−	0.608608i	$-0.791728\pi$
$239$	2.01493	−	3.48996i	0.130335	−	0.225746i	0.923806	+	0.382862i	$0.125061\pi$
$240$		0			0
$241$	2.81649	+	4.87830i	0.181426	+	0.314239i	0.942366	−	0.334583i	$-0.108595\pi$
$241$	2.81649	+	4.87830i	0.181426	+	0.314239i	−0.760940	+	0.648822i	$0.775262\pi$
$242$	−1.03177	+	4.83631i	−0.0663244	+	0.310890i
$243$		0			0
$244$	7.48051	−	16.7342i	0.478891	−	1.07130i
$245$	2.69539	−	1.55618i	0.172202	−	0.0994209i
$246$		0			0
$247$	−2.65175	+	4.59296i	−0.168727	+	0.292243i
$248$	8.46671	+	19.1318i	0.537637	+	1.21487i
$249$		0			0
$250$	−2.88781	−	8.91040i	−0.182641	−	0.563543i
$251$			13.8828i			0.876276i	0.898908	+	0.438138i	$0.144362\pi$
$251$			13.8828i			0.876276i	−0.898908	+	0.438138i	$0.855638\pi$
$252$		0			0
$253$		−	18.0161i		−	1.13267i
$254$	−2.32410	+	0.753228i	−0.145827	+	0.0472618i
$255$		0			0
$256$	−12.8879	−	9.48173i	−0.805491	−	0.592608i
$257$	5.42539	−	9.39705i	0.338427	−	0.586172i	−0.645710	−	0.763582i	$-0.723439\pi$
$257$	5.42539	−	9.39705i	0.338427	−	0.586172i	0.984137	+	0.177410i	$0.0567720\pi$
$258$		0			0
$259$	−8.61423	+	4.97343i	−0.535262	+	0.309034i
$260$	−6.99676	−	3.12769i	−0.433921	−	0.193971i
$261$		0			0
$262$	−9.18256	−	1.95898i	−0.567300	−	0.121026i
$263$	11.6051	+	20.1005i	0.715598	+	1.23945i	0.962728	+	0.270470i	$0.0871792\pi$
$263$	11.6051	+	20.1005i	0.715598	+	1.23945i	−0.247130	+	0.968982i	$0.579487\pi$
$264$		0			0
$265$	0.884601	−	1.53217i	0.0543406	−	0.0941207i
$266$	1.45075	−	1.60880i	0.0889512	−	0.0986421i
$267$		0			0
$268$	13.6857	−	1.41776i	0.835987	−	0.0866035i
$269$			4.01966i			0.245083i	0.992463	+	0.122541i	$0.0391044\pi$
$269$			4.01966i			0.245083i	−0.992463	+	0.122541i	$0.960896\pi$
$270$		0			0
$271$	−6.75621			−0.410411			−0.205205	−	0.978719i	$-0.565786\pi$
$271$	−6.75621			−0.410411			−0.205205	+	0.978719i	$0.565786\pi$
$272$	7.05014	−	21.4796i	0.427478	−	1.30239i
$273$		0			0
$274$	−3.80875	−	3.43457i	−0.230095	−	0.207490i
$275$	10.7118	+	6.18447i	0.645947	+	0.372938i
$276$		0			0
$277$	1.83595	−	1.05999i	0.110312	−	0.0636885i	−0.443829	−	0.896111i	$-0.646380\pi$
$277$	1.83595	−	1.05999i	0.110312	−	0.0636885i	0.554141	+	0.832423i	$0.313047\pi$
$278$	23.9428	+	5.10790i	1.43600	+	0.306352i
$279$		0			0
$280$	2.52851	+	1.84574i	0.151107	+	0.110304i
$281$	13.0580	+	22.6171i	0.778976	+	1.34923i	0.932533	+	0.361086i	$0.117594\pi$
$281$	13.0580	+	22.6171i	0.778976	+	1.34923i	−0.153557	+	0.988140i	$0.549073\pi$
$282$		0			0
$283$	−16.5376	−	9.54799i	−0.983058	−	0.567569i	−0.0798661	−	0.996806i	$-0.525449\pi$
$283$	−16.5376	−	9.54799i	−0.983058	−	0.567569i	−0.903192	+	0.429237i	$0.858783\pi$
$284$	−5.96651	+	4.32132i	−0.354047	+	0.256423i
$285$		0			0
$286$	20.2880	−	6.57522i	1.19965	−	0.388801i
$287$	2.96364			0.174938
$288$		0			0
$289$	14.9423			0.878956
$290$	−3.08245	+	0.999003i	−0.181007	+	0.0586635i
$291$		0			0
$292$	4.58725	−	3.32237i	0.268448	−	0.194427i
$293$	5.07116	+	2.92784i	0.296261	+	0.171046i	0.640762	−	0.767740i	$-0.278619\pi$
$293$	5.07116	+	2.92784i	0.296261	+	0.171046i	−0.344501	+	0.938786i	$0.611952\pi$
$294$		0			0
$295$	1.85668	+	3.21587i	0.108100	+	0.187235i
$296$	14.2905	+	10.4317i	0.830619	+	0.606328i
$297$		0			0
$298$	29.9049	+	6.37984i	1.73235	+	0.369574i
$299$	31.3585	−	18.1048i	1.81351	−	1.04703i
$300$		0			0
$301$	−4.76780	−	2.75269i	−0.274812	−	0.158663i
$302$	−13.3387	−	12.0282i	−0.767555	−	0.692148i
$303$		0			0
$304$	−3.66115	−	1.20168i	−0.209981	−	0.0689212i
$305$	6.37929			0.365277
$306$		0			0
$307$			13.7071i			0.782305i	0.920326	+	0.391152i	$0.127923\pi$
$307$			13.7071i			0.782305i	−0.920326	+	0.391152i	$0.872077\pi$
$308$	−8.66501	+	0.897646i	−0.493735	+	0.0511481i
$309$		0			0
$310$	−4.87610	+	5.40733i	−0.276944	+	0.307116i
$311$	9.57980	−	16.5927i	0.543221	−	0.940886i	−0.455496	−	0.890238i	$-0.650538\pi$
$311$	9.57980	−	16.5927i	0.543221	−	0.940886i	0.998717	−	0.0506479i	$-0.0161286\pi$
$312$		0			0
$313$	−12.6102	−	21.8416i	−0.712773	−	1.23456i	−0.963812	−	0.266582i	$-0.914106\pi$
$313$	−12.6102	−	21.8416i	−0.712773	−	1.23456i	0.251039	−	0.967977i	$-0.419228\pi$
$314$	−24.1610	−	5.15444i	−1.36348	−	0.290882i
$315$		0			0
$316$	10.5123	+	4.69919i	0.591362	+	0.264350i
$317$	−2.13931	+	1.23513i	−0.120156	+	0.0693719i	−0.558873	−	0.829253i	$-0.688766\pi$
$317$	−2.13931	+	1.23513i	−0.120156	+	0.0693719i	0.438718	+	0.898625i	$0.355433\pi$
$318$		0			0
$319$	4.50843	−	7.80883i	0.252424	−	0.437211i
$320$	1.18212	−	5.44145i	0.0660828	−	0.304186i
$321$		0			0
$322$	−14.0701	+	4.56002i	−0.784094	+	0.254120i
$323$		−	5.44449i		−	0.302939i
$324$		0			0
$325$			24.8597i			1.37897i
$326$	−3.73552	−	11.5260i	−0.206891	−	0.638368i
$327$		0			0
$328$	−2.13333	−	4.82058i	−0.117794	−	0.266172i
$329$	6.13262	−	10.6220i	0.338103	−	0.585611i
$330$		0			0
$331$	24.4404	−	14.1107i	1.34336	−	0.775592i	0.356065	−	0.934461i	$-0.384118\pi$
$331$	24.4404	−	14.1107i	1.34336	−	0.775592i	0.987300	+	0.158869i	$0.0507848\pi$
$332$	5.41889	−	12.1223i	0.297400	−	0.665296i
$333$		0			0
$334$	3.52621	−	16.5288i	0.192946	−	0.904416i
$335$	2.39422	+	4.14691i	0.130810	+	0.226570i
$336$		0			0
$337$	5.60565	−	9.70927i	0.305359	−	0.528897i	−0.671982	−	0.740567i	$-0.734557\pi$
$337$	5.60565	−	9.70927i	0.305359	−	0.528897i	0.977341	+	0.211670i	$0.0678902\pi$
$338$	18.1792	+	16.3932i	0.988819	+	0.891675i
$339$		0			0
$340$	7.82588	−	0.810717i	0.424418	−	0.0439673i
$341$		−	20.2616i		−	1.09723i
$342$		0			0
$343$	18.2411			0.984929
$344$	−1.04543	+	9.73669i	−0.0563657	+	0.524967i
$345$		0			0
$346$	−12.3546	+	13.7006i	−0.664188	+	0.736548i
$347$	−17.8303	−	10.2943i	−0.957180	−	0.552628i	−0.0618763	−	0.998084i	$-0.519708\pi$
$347$	−17.8303	−	10.2943i	−0.957180	−	0.552628i	−0.895304	+	0.445455i	$0.853042\pi$
$348$		0			0
$349$	2.93968	−	1.69723i	0.157358	−	0.0908505i	−0.419253	−	0.907869i	$-0.637708\pi$
$349$	2.93968	−	1.69723i	0.157358	−	0.0908505i	0.576611	+	0.817019i	$0.304375\pi$
$350$	2.11864	−	9.93094i	0.113246	−	0.530831i
$351$		0			0
$352$	7.69748	+	13.4482i	0.410277	+	0.716789i
$353$	0.503241	+	0.871639i	0.0267848	+	0.0463926i	0.879107	−	0.476624i	$-0.158140\pi$
$353$	0.503241	+	0.871639i	0.0267848	+	0.0463926i	−0.852322	+	0.523017i	$0.824806\pi$
$354$		0			0
$355$	−2.22040	−	1.28195i	−0.117847	−	0.0680388i
$356$	4.83832	−	3.50422i	0.256430	−	0.185723i
$357$		0			0
$358$	1.44701	+	4.46479i	0.0764770	+	0.235972i
$359$	−31.4772			−1.66131			−0.830653	−	0.556791i	$-0.812032\pi$
$359$	−31.4772			−1.66131			−0.830653	+	0.556791i	$0.812032\pi$
$360$		0			0
$361$	18.0720			0.951158
$362$	6.50216	+	20.0626i	0.341746	+	1.05446i
$363$		0			0
$364$	−10.2701	−	14.1801i	−0.538299	−	0.743238i
$365$	1.70712	+	0.985604i	0.0893546	+	0.0515889i
$366$		0			0
$367$	−8.66667	−	15.0111i	−0.452397	−	0.783574i	0.546138	−	0.837695i	$-0.316098\pi$
$367$	−8.66667	−	15.0111i	−0.452397	−	0.783574i	−0.998534	+	0.0541214i	$0.982764\pi$
$368$	17.5454	+	19.6036i	0.914616	+	1.02191i
$369$		0			0
$370$	−1.28472	+	6.02202i	−0.0667895	+	0.313070i
$371$	3.50027	−	2.02088i	0.181725	−	0.104919i
$372$		0			0
$373$	11.2742	+	6.50917i	0.583757	+	0.337032i	0.762625	−	0.646841i	$-0.223910\pi$
$373$	11.2742	+	6.50917i	0.583757	+	0.337032i	−0.178868	+	0.983873i	$0.557244\pi$
$374$	−14.6620	+	16.2594i	−0.758154	+	0.840752i
$375$		0			0
$376$	−21.6920	−	2.32907i	−1.11868	−	0.120113i
$377$	18.1225			0.933357
$378$		0			0
$379$			22.8643i			1.17446i	0.809421	+	0.587229i	$0.199781\pi$
$379$			22.8643i			1.17446i	−0.809421	+	0.587229i	$0.800219\pi$
$380$	−0.138185	−	1.33390i	−0.00708874	−	0.0684279i
$381$		0			0
$382$	−7.68545	−	6.93041i	−0.393222	−	0.354590i
$383$	−15.0117	+	26.0010i	−0.767061	+	1.32859i	0.172089	+	0.985081i	$0.444948\pi$
$383$	−15.0117	+	26.0010i	−0.767061	+	1.32859i	−0.939150	+	0.343508i	$0.888385\pi$
$384$		0			0
$385$	−1.51588	−	2.62559i	−0.0772565	−	0.133812i
$386$	−6.04020	+	28.3129i	−0.307438	+	1.44109i
$387$		0			0
$388$	−4.55874	−	2.03785i	−0.231435	−	0.103456i
$389$	32.9474	−	19.0222i	1.67050	−	0.964463i	0.703140	−	0.711051i	$-0.251780\pi$
$389$	32.9474	−	19.0222i	1.67050	−	0.964463i	0.967358	−	0.253412i	$-0.0815528\pi$
$390$		0			0
$391$	−18.5862	+	32.1922i	−0.939943	+	1.62803i
$392$	−5.11821	−	11.5654i	−0.258509	−	0.584139i
$393$		0			0
$394$	8.95728	+	27.6379i	0.451261	+	1.39238i
$395$			4.00742i			0.201635i
$396$		0			0
$397$		−	37.4510i		−	1.87961i	−0.341709	−	0.939806i	$-0.611006\pi$
$397$		−	37.4510i		−	1.87961i	0.341709	−	0.939806i	$-0.388994\pi$
$398$	2.63141	−	0.852825i	0.131901	−	0.0427483i
$399$		0			0
$400$	−17.6785	+	3.70252i	−0.883926	+	0.185126i
$401$	2.35402	−	4.07728i	0.117554	−	0.203610i	−0.801244	−	0.598338i	$-0.795828\pi$
$401$	2.35402	−	4.07728i	0.117554	−	0.203610i	0.918798	+	0.394728i	$0.129161\pi$
$402$		0			0
$403$	35.2669	−	20.3613i	1.75677	−	1.01427i
$404$	7.74837	−	17.3334i	0.385496	−	0.862369i
$405$		0			0
$406$	−7.23958	−	1.54447i	−0.359294	−	0.0766508i
$407$	−8.56739	−	14.8391i	−0.424670	−	0.735549i
$408$		0			0
$409$	5.36377	−	9.29032i	0.265221	−	0.459377i	−0.702400	−	0.711782i	$-0.747888\pi$
$409$	5.36377	−	9.29032i	0.265221	−	0.459377i	0.967622	+	0.252405i	$0.0812216\pi$
$410$	1.22862	−	1.36247i	0.0606771	−	0.0672876i
$411$		0			0
$412$	−3.03861	−	29.3318i	−0.149702	−	1.44508i
$413$			8.48324i			0.417433i
$414$		0			0
$415$	4.62117			0.226844
$416$	−15.6722	+	26.9124i	−0.768392	+	1.31949i
$417$		0			0
$418$	2.77138	+	2.49911i	0.135552	+	0.122235i
$419$	3.57600	+	2.06460i	0.174699	+	0.100863i	0.584800	−	0.811178i	$-0.301173\pi$
$419$	3.57600	+	2.06460i	0.174699	+	0.100863i	−0.410101	+	0.912040i	$0.634506\pi$
$420$		0			0
$421$	−13.7321	+	7.92824i	−0.669262	+	0.386399i	−0.795797	−	0.605563i	$-0.792948\pi$
$421$	−13.7321	+	7.92824i	−0.669262	+	0.386399i	0.126535	+	0.991962i	$0.459614\pi$
$422$	−14.5489	−	3.10381i	−0.708227	−	0.151091i
$423$		0			0
$424$	−5.80675	−	4.23876i	−0.282001	−	0.205852i
$425$	−12.7603	−	22.1015i	−0.618965	−	1.07208i
$426$		0			0
$427$	12.6211	+	7.28679i	0.610778	+	0.352633i
$428$	−9.19028	−	12.6892i	−0.444229	−	0.613353i
$429$		0			0
$430$	−3.24205	+	1.05073i	−0.156346	+	0.0506708i
$431$	−16.1853			−0.779619			−0.389810	−	0.920895i	$-0.627459\pi$
$431$	−16.1853			−0.779619			−0.389810	+	0.920895i	$0.627459\pi$
$432$		0			0
$433$	−32.8306			−1.57774			−0.788868	−	0.614563i	$-0.789332\pi$
$433$	−32.8306			−1.57774			−0.788868	+	0.614563i	$0.789332\pi$
$434$	−15.8237	+	5.12836i	−0.759561	+	0.246169i
$435$		0			0
$436$	−0.284372	−	0.392636i	−0.0136190	−	0.0188039i
$437$	5.48709	+	3.16797i	0.262483	+	0.151545i
$438$		0			0
$439$	10.9273	+	18.9267i	0.521533	+	0.903321i	0.999686	+	0.0250450i	$0.00797290\pi$
$439$	10.9273	+	18.9267i	0.521533	+	0.903321i	−0.478154	+	0.878276i	$0.658694\pi$
$440$	−3.17953	+	4.35569i	−0.151578	+	0.207650i
$441$		0			0
$442$	−43.0349	−	9.18095i	−2.04696	−	0.436693i
$443$	−30.4500	+	17.5803i	−1.44672	+	0.835265i	−0.998284	−	0.0585501i	$-0.981352\pi$
$443$	−30.4500	+	17.5803i	−1.44672	+	0.835265i	−0.448436	+	0.893815i	$0.648019\pi$
$444$		0			0
$445$	1.80055	+	1.03955i	0.0853543	+	0.0492793i
$446$	4.05671	+	3.65817i	0.192091	+	0.173219i
$447$		0			0
$448$	8.55431	−	9.41533i	0.404153	−	0.444833i
$449$	−3.21851			−0.151891			−0.0759453	−	0.997112i	$-0.524197\pi$
$449$	−3.21851			−0.151891			−0.0759453	+	0.997112i	$0.524197\pi$
$450$		0			0
$451$			5.10526i			0.240397i
$452$	1.79208	+	17.2990i	0.0842921	+	0.813675i
$453$		0			0
$454$	−15.2209	+	16.8792i	−0.714354	+	0.792180i
$455$	3.04669	−	5.27703i	0.142831	−	0.247391i
$456$		0			0
$457$	4.05512	+	7.02368i	0.189691	+	0.328554i	0.945147	−	0.326645i	$-0.105918\pi$
$457$	4.05512	+	7.02368i	0.189691	+	0.328554i	−0.755456	+	0.655199i	$0.772585\pi$
$458$	11.9191	+	2.54279i	0.556944	+	0.118817i
$459$		0			0
$460$	−3.73657	+	8.35884i	−0.174218	+	0.389733i
$461$	−18.1813	+	10.4970i	−0.846789	+	0.488894i	−0.859566	−	0.511024i	$-0.829266\pi$
$461$	−18.1813	+	10.4970i	−0.846789	+	0.488894i	0.0127771	+	0.999918i	$0.495933\pi$
$462$		0			0
$463$	−4.45005	+	7.70772i	−0.206812	+	0.358208i	−0.950708	−	0.310086i	$-0.899642\pi$
$463$	−4.45005	+	7.70772i	−0.206812	+	0.358208i	0.743897	+	0.668294i	$0.232975\pi$
$464$	2.69911	+	12.8875i	0.125303	+	0.598287i
$465$		0			0
$466$	−32.4943	+	10.5312i	−1.50527	+	0.487849i
$467$		−	26.0527i		−	1.20557i	−0.797902	−	0.602787i	$-0.794057\pi$
$467$		−	26.0527i		−	1.20557i	0.797902	−	0.602787i	$-0.205943\pi$
$468$		0			0
$469$			10.9392i			0.505128i
$470$	−2.34089	−	7.22285i	−0.107977	−	0.333165i
$471$		0			0
$472$	13.7986	−	6.10655i	0.635134	−	0.281077i
$473$	4.74188	−	8.21317i	0.218032	−	0.377642i
$474$		0			0
$475$	−3.76715	+	2.17496i	−0.172849	+	0.0997942i
$476$	16.4091	+	7.33521i	0.752112	+	0.336209i
$477$		0			0
$478$	1.18907	−	5.57365i	0.0543866	−	0.254933i
$479$	−8.71143	−	15.0886i	−0.398035	−	0.689418i	0.595448	−	0.803394i	$-0.296975\pi$
$479$	−8.71143	−	15.0886i	−0.398035	−	0.689418i	−0.993483	+	0.113976i	$0.963641\pi$
$480$		0			0
$481$	17.2191	−	29.8244i	0.785125	−	1.35988i
$482$	5.91608	+	5.33487i	0.269470	+	0.242997i
$483$		0			0
$484$	0.720629	+	6.95626i	0.0327559	+	0.316194i
$485$		−	1.73785i		−	0.0789118i
$486$		0			0
$487$	−29.7367			−1.34750			−0.673750	−	0.738959i	$-0.735318\pi$
$487$	−29.7367			−1.34750			−0.673750	+	0.738959i	$0.735318\pi$
$488$	2.76741	−	25.7745i	0.125275	−	1.16676i
$489$		0			0
$490$	2.94765	−	3.26879i	0.133161	−	0.147669i
$491$	20.6346	+	11.9134i	0.931229	+	0.537645i	0.887200	−	0.461385i	$-0.152647\pi$
$491$	20.6346	+	11.9134i	0.931229	+	0.537645i	0.0440286	+	0.999030i	$0.485981\pi$
$492$		0			0
$493$	−16.1118	+	9.30215i	−0.725639	+	0.418948i
$494$	−1.56487	+	7.33521i	−0.0704070	+	0.330027i
$495$		0			0
$496$	19.7321	+	22.0469i	0.885999	+	0.989933i
$497$	−2.92863	−	5.07254i	−0.131367	−	0.227534i
$498$		0			0
$499$	16.8622	+	9.73540i	0.754856	+	0.435816i	0.827446	−	0.561546i	$-0.189793\pi$
$499$	16.8622	+	9.73540i	0.754856	+	0.435816i	−0.0725899	+	0.997362i	$0.523126\pi$
$500$	−7.77008	−	10.7283i	−0.347488	−	0.479782i
$501$		0			0
$502$	6.05307	+	18.6769i	0.270162	+	0.833590i
$503$	−1.23494			−0.0550631			−0.0275316	−	0.999621i	$-0.508765\pi$
$503$	−1.23494			−0.0550631			−0.0275316	+	0.999621i	$0.508765\pi$
$504$		0			0
$505$	6.60772			0.294040
$506$	−7.85524	−	24.2375i	−0.349208	−	1.07749i
$507$		0			0
$508$	−2.79825	+	2.02667i	−0.124152	+	0.0899190i
$509$	0.392870	+	0.226823i	0.0174136	+	0.0100538i	0.508682	−	0.860955i	$-0.330133\pi$
$509$	0.392870	+	0.226823i	0.0174136	+	0.0100538i	−0.491268	+	0.871009i	$0.663466\pi$
$510$		0			0
$511$	2.25163	+	3.89993i	0.0996061	+	0.172523i
$512$	−21.4725	−	7.13674i	−0.948958	−	0.315403i
$513$		0			0
$514$	3.20168	−	15.0076i	0.141220	−	0.661957i
$515$	8.88784	−	5.13140i	0.391645	−	0.226116i
$516$		0			0
$517$	18.2978	+	10.5643i	0.804737	+	0.464615i
$518$	−9.42045	+	10.4468i	−0.413911	+	0.459005i
$519$		0			0
$520$	−10.7766	−	1.15708i	−0.472586	−	0.0507415i
$521$	29.0873			1.27434			0.637170	−	0.770724i	$-0.280105\pi$
$521$	29.0873			1.27434			0.637170	+	0.770724i	$0.280105\pi$
$522$		0			0
$523$			2.95874i			0.129377i	0.997906	+	0.0646883i	$0.0206053\pi$
$523$			2.95874i			0.129377i	−0.997906	+	0.0646883i	$0.979395\pi$
$524$	−13.2076	+	1.36824i	−0.576979	+	0.0597717i
$525$		0			0
$526$	24.3766	+	21.9818i	1.06287	+	0.958452i
$527$	−20.9026	+	36.2044i	−0.910534	+	1.57709i
$528$		0			0
$529$	−10.1294	−	17.5446i	−0.440407	−	0.762808i
$530$	0.522029	−	2.44697i	0.0226755	−	0.106289i
$531$		0			0
$532$	1.25027	−	2.79690i	0.0542061	−	0.121261i
$533$	−8.88610	+	5.13039i	−0.384900	+	0.222222i
$534$		0			0
$535$	2.72636	−	4.72219i	0.117871	−	0.204158i
$536$	17.7935	−	7.87447i	0.768564	−	0.340125i
$537$		0			0
$538$	1.75262	+	5.40774i	0.0755607	+	0.233144i
$539$			12.2483i			0.527573i
$540$		0			0
$541$		−	14.9753i		−	0.643838i	−0.946767	−	0.321919i	$-0.895672\pi$
$541$		−	14.9753i		−	0.643838i	0.946767	−	0.321919i	$-0.104328\pi$
$542$	−9.08929	+	2.94578i	−0.390418	+	0.126532i
$543$		0			0
$544$	0.119385	−	31.9709i	0.00511861	−	1.37074i
$545$	0.0843608	−	0.146117i	0.00361362	−	0.00625897i
$546$		0			0
$547$	−15.7731	+	9.10661i	−0.674409	+	0.389370i	−0.797745	−	0.602995i	$-0.793974\pi$
$547$	−15.7731	+	9.10661i	−0.674409	+	0.389370i	0.123336	+	0.992365i	$0.460641\pi$
$548$	−6.62152	−	2.95995i	−0.282857	−	0.126443i
$549$		0			0
$550$	17.1074	+	3.64964i	0.729460	+	0.155621i
$551$	1.58553	+	2.74622i	0.0675459	+	0.116993i
$552$		0			0
$553$	−4.57750	+	7.92846i	−0.194655	+	0.337153i
$554$	2.00778	−	2.22652i	0.0853025	−	0.0945958i
$555$		0			0
$556$	34.4380	−	3.56758i	1.46049	−	0.151299i
$557$		−	35.7359i		−	1.51418i	−0.653310	−	0.757090i	$-0.726620\pi$
$557$		−	35.7359i		−	1.51418i	0.653310	−	0.757090i	$-0.273380\pi$
$558$		0			0
$559$	19.0609			0.806190
$560$	4.20643	+	1.38066i	0.177754	+	0.0583434i
$561$		0			0
$562$	27.4286	+	24.7339i	1.15700	+	1.04334i
$563$	−8.04256	−	4.64337i	−0.338953	−	0.195695i	0.320856	−	0.947128i	$-0.396030\pi$
$563$	−8.04256	−	4.64337i	−0.338953	−	0.195695i	−0.659809	+	0.751433i	$0.729363\pi$
$564$		0			0
$565$	−5.24176	+	3.02633i	−0.220523	+	0.127319i
$566$	−26.4114	−	5.63454i	−1.11016	−	0.236838i
$567$		0			0
$568$	−6.14274	+	8.41504i	−0.257744	+	0.353087i
$569$	5.66727	+	9.81599i	0.237584	+	0.411508i	0.960021	−	0.279930i	$-0.0903111\pi$
$569$	5.66727	+	9.81599i	0.237584	+	0.411508i	−0.722436	+	0.691437i	$0.756978\pi$
$570$		0			0
$571$	−37.7843	−	21.8148i	−1.58122	−	0.912920i	−0.994681	−	0.103002i	$-0.967155\pi$
$571$	−37.7843	−	21.8148i	−1.58122	−	0.912920i	−0.586543	−	0.809918i	$-0.699511\pi$
$572$	24.4270	−	17.6916i	1.02135	−	0.739723i
$573$		0			0
$574$	3.98705	−	1.29218i	0.166416	−	0.0539345i
$575$	29.6992			1.23854
$576$		0			0
$577$	6.98123			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$577$	6.98123			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$578$	20.1022	−	6.51499i	0.836139	−	0.270988i
$579$		0			0
$580$	−3.71131	+	2.68796i	−0.154104	+	0.111612i
$581$	9.14274	+	5.27856i	0.379305	+	0.218992i
$582$		0			0
$583$	3.48124	+	6.02968i	0.144178	+	0.249724i
$584$	4.72274	−	6.46976i	0.195428	−	0.267721i
$585$		0			0
$586$	8.09892	+	1.72780i	0.334563	+	0.0713749i
$587$	7.34574	−	4.24107i	0.303191	−	0.175048i	−0.340684	−	0.940178i	$-0.610659\pi$
$587$	7.34574	−	4.24107i	0.303191	−	0.175048i	0.643876	+	0.765130i	$0.277325\pi$
$588$		0			0
$589$	6.17097	+	3.56281i	0.254270	+	0.146803i
$590$	3.89999	+	3.51685i	0.160560	+	0.144786i
$591$		0			0
$592$	23.7737	+	7.80313i	0.977092	+	0.320707i
$593$	9.40869			0.386368			0.193184	−	0.981163i	$-0.438119\pi$
$593$	9.40869			0.386368			0.193184	+	0.981163i	$0.438119\pi$
$594$		0			0
$595$			6.25538i			0.256445i
$596$	43.0135	−	4.45595i	1.76190	−	0.182523i
$597$		0			0
$598$	34.2934	−	38.0295i	1.40236	−	1.55514i
$599$	14.9623	−	25.9155i	0.611344	−	1.05888i	−0.379670	−	0.925122i	$-0.623962\pi$
$599$	14.9623	−	25.9155i	0.611344	−	1.05888i	0.991014	−	0.133757i	$-0.0427043\pi$
$600$		0			0
$601$	1.81973	+	3.15186i	0.0742282	+	0.128567i	0.900750	−	0.434337i	$-0.143017\pi$
$601$	1.81973	+	3.15186i	0.0742282	+	0.128567i	−0.826522	+	0.562904i	$0.809684\pi$
$602$	−7.61444	−	1.62444i	−0.310342	−	0.0662074i
$603$		0			0
$604$	−23.1893	−	10.3661i	−0.943558	−	0.421789i
$605$	−2.10782	+	1.21695i	−0.0856950	+	0.0494760i
$606$		0			0
$607$	3.63358	−	6.29355i	0.147482	−	0.255447i	−0.782814	−	0.622256i	$-0.786216\pi$
$607$	3.63358	−	6.29355i	0.147482	−	0.255447i	0.930296	+	0.366809i	$0.119550\pi$
$608$	−5.44937	−	0.0203490i	−0.221001	−	0.000825260i
$609$		0			0
$610$	8.58221	−	2.78144i	0.347483	−	0.112617i
$611$			42.4651i			1.71795i
$612$		0			0
$613$		−	32.6469i		−	1.31859i	−0.751882	−	0.659297i	$-0.770854\pi$
$613$		−	32.6469i		−	1.31859i	0.751882	−	0.659297i	$-0.229146\pi$
$614$	5.97645	+	18.4405i	0.241190	+	0.744197i
$615$		0			0
$616$	−11.2659	+	4.98567i	−0.453914	+	0.200878i
$617$	−15.6751	+	27.1501i	−0.631056	+	1.09302i	0.356280	+	0.934379i	$0.384045\pi$
$617$	−15.6751	+	27.1501i	−0.631056	+	1.09302i	−0.987336	+	0.158642i	$0.949288\pi$
$618$		0			0
$619$	−1.72589	+	0.996445i	−0.0693695	+	0.0400505i	−0.534284	−	0.845305i	$-0.679419\pi$
$619$	−1.72589	+	0.996445i	−0.0693695	+	0.0400505i	0.464914	+	0.885356i	$0.346085\pi$
$620$	−4.20227	+	9.40065i	−0.168767	+	0.377539i
$621$		0			0
$622$	5.65332	−	26.4994i	0.226677	−	1.06253i
$623$	2.37486	+	4.11339i	0.0951469	+	0.164799i
$624$		0			0
$625$	−8.98375	+	15.5603i	−0.359350	+	0.622413i
$626$	−26.4880	−	23.8858i	−1.05867	−	0.954668i
$627$		0			0
$628$	−34.7517	+	3.60008i	−1.38675	+	0.143659i
$629$			35.3538i			1.40965i
$630$		0			0
$631$	−15.4643			−0.615623			−0.307812	−	0.951447i	$-0.599597\pi$
$631$	−15.4643			−0.615623			−0.307812	+	0.951447i	$0.599597\pi$
$632$	16.1913	+	1.73846i	0.644056	+	0.0691523i
$633$		0			0
$634$	−2.33953	+	2.59441i	−0.0929147	+	0.103037i
$635$	−1.04135	−	0.601225i	−0.0413248	−	0.0238589i
$636$		0			0
$637$	−21.3192	+	12.3086i	−0.844697	+	0.487686i
$638$	2.66056	−	12.4711i	0.105332	−	0.493737i
$639$		0			0
$640$	−0.782194	−	7.83593i	−0.0309189	−	0.309742i
$641$	12.3638	+	21.4147i	0.488340	+	0.845829i	0.999910	−	0.0134123i	$-0.00426940\pi$
$641$	12.3638	+	21.4147i	0.488340	+	0.845829i	−0.511570	+	0.859241i	$0.670936\pi$
$642$		0			0
$643$	−40.0176	−	23.1042i	−1.57814	−	0.911141i	−0.995119	−	0.0986850i	$-0.968536\pi$
$643$	−40.0176	−	23.1042i	−1.57814	−	0.911141i	−0.583023	−	0.812456i	$-0.698130\pi$
$644$	−16.9406	+	12.2694i	−0.667551	+	0.483483i
$645$		0			0
$646$	−2.37386	−	7.32460i	−0.0933983	−	0.288182i
$647$	6.36971			0.250419			0.125210	−	0.992130i	$-0.460040\pi$
$647$	6.36971			0.250419			0.125210	+	0.992130i	$0.460040\pi$
$648$		0			0
$649$	−14.6135			−0.573630
$650$	10.8391	+	33.4443i	0.425145	+	1.31179i
$651$		0			0
$652$	−10.0510	−	13.8775i	−0.393626	−	0.543485i
$653$	−31.8848	−	18.4087i	−1.24775	−	0.720389i	−0.277090	−	0.960844i	$-0.589370\pi$
$653$	−31.8848	−	18.4087i	−1.24775	−	0.720389i	−0.970660	+	0.240455i	$0.922703\pi$
$654$		0			0
$655$	−2.31058	−	4.00205i	−0.0902820	−	0.156373i
$656$	−4.97185	−	5.55509i	−0.194118	−	0.216890i
$657$		0			0
$658$	3.61904	−	16.9639i	0.141085	−	0.661323i
$659$	−6.46565	+	3.73294i	−0.251866	+	0.145415i	−0.620618	−	0.784113i	$-0.713118\pi$
$659$	−6.46565	+	3.73294i	−0.251866	+	0.145415i	0.368752	+	0.929528i	$0.379785\pi$
$660$		0			0
$661$	2.51984	+	1.45483i	0.0980102	+	0.0565862i	0.548204	−	0.836345i	$-0.315312\pi$
$661$	2.51984	+	1.45483i	0.0980102	+	0.0565862i	−0.450194	+	0.892931i	$0.648645\pi$
$662$	26.7278	−	29.6397i	1.03881	−	1.15198i
$663$		0			0
$664$	2.00471	−	18.6711i	0.0777980	−	0.724578i
$665$	1.06622			0.0413461
$666$		0			0
$667$		−	21.6505i		−	0.838310i
$668$	−2.46286	−	23.7741i	−0.0952908	−	0.919846i
$669$		0			0
$670$	5.02909	+	4.53502i	0.194291	+	0.175203i
$671$	−12.5525	+	21.7415i	−0.484582	+	0.839321i
$672$		0			0
$673$	21.0527	+	36.4643i	0.811522	+	1.40560i	0.911799	+	0.410637i	$0.134694\pi$
$673$	21.0527	+	36.4643i	0.811522	+	1.40560i	−0.100277	+	0.994960i	$0.531973\pi$
$674$	3.30806	−	15.5062i	0.127422	−	0.597278i
$675$		0			0
$676$	31.6046	+	14.1279i	1.21556	+	0.543379i
$677$	−32.9941	+	19.0492i	−1.26807	+	0.732119i	−0.974622	−	0.223858i	$-0.928135\pi$
$677$	−32.9941	+	19.0492i	−1.26807	+	0.732119i	−0.293445	+	0.955976i	$0.594802\pi$
$678$		0			0
$679$	1.98507	−	3.43825i	0.0761801	−	0.131948i
$680$	10.1749	−	4.50285i	0.390188	−	0.172676i
$681$		0			0
$682$	−8.83428	−	27.2584i	−0.338282	−	1.04378i
$683$		−	47.0728i		−	1.80119i	−0.434659	−	0.900595i	$-0.643131\pi$
$683$		−	47.0728i		−	1.80119i	0.434659	−	0.900595i	$-0.356869\pi$
$684$		0			0
$685$		−	2.52421i		−	0.0964450i
$686$	24.5402	−	7.95335i	0.936951	−	0.303660i
$687$		0			0
$688$	2.83887	+	13.5548i	0.108231	+	0.516772i
$689$	−6.99676	+	12.1187i	−0.266555	+	0.461687i
$690$		0			0
$691$	3.38522	−	1.95446i	0.128780	−	0.0743512i	−0.434226	−	0.900804i	$-0.642978\pi$
$691$	3.38522	−	1.95446i	0.128780	−	0.0743512i	0.563006	+	0.826453i	$0.309645\pi$
$692$	−10.6473	+	23.8185i	−0.404750	+	0.905442i
$693$		0			0
$694$	−28.4760	−	6.07498i	−1.08093	−	0.230603i
$695$	6.02468	+	10.4350i	0.228529	+	0.395824i
$696$		0			0
$697$	5.26678	−	9.12234i	0.199494	−	0.345533i
$698$	3.21481	−	3.56505i	0.121683	−	0.134939i
$699$		0			0
$700$	−1.47975	−	14.2841i	−0.0559292	−	0.539887i
$701$			16.4480i			0.621231i	0.950536	+	0.310615i	$0.100535\pi$
$701$			16.4480i			0.621231i	−0.950536	+	0.310615i	$0.899465\pi$
$702$		0			0
$703$	6.02598			0.227274
$704$	16.2192	+	14.7359i	0.611282	+	0.555381i
$705$		0			0
$706$	1.05707	+	0.953217i	0.0397832	+	0.0358748i
$707$	13.0730	+	7.54772i	0.491662	+	0.283861i
$708$		0			0
$709$	−6.84805	+	3.95372i	−0.257184	+	0.148485i	−0.623049	−	0.782183i	$-0.714106\pi$
$709$	−6.84805	+	3.95372i	−0.257184	+	0.148485i	0.365865	+	0.930668i	$0.380773\pi$
$710$	−3.54610	−	0.756515i	−0.133083	−	0.0283915i
$711$		0			0
$712$	4.98123	−	6.82387i	0.186679	−	0.255735i
$713$	−24.3251	−	42.1324i	−0.910984	−	1.57787i
$714$		0			0
$715$	9.09037	+	5.24833i	0.339961	+	0.196276i
$716$	3.89340	+	5.37567i	0.145503	+	0.200898i
$717$		0			0
$718$	−42.3471	+	13.7244i	−1.58038	+	0.512191i
$719$	37.0556			1.38194			0.690970	−	0.722884i	$-0.257184\pi$
$719$	37.0556			1.38194			0.690970	+	0.722884i	$0.257184\pi$
$720$		0			0
$721$	23.4455			0.873156
$722$	24.3127	−	7.87960i	0.904824	−	0.293248i
$723$		0			0
$724$	17.4950	+	24.1556i	0.650197	+	0.897736i
$725$	12.8727	+	7.43204i	0.478079	+	0.276019i
$726$		0			0
$727$	2.83467	+	4.90979i	0.105132	+	0.182094i	0.913792	−	0.406182i	$-0.133140\pi$
$727$	2.83467	+	4.90979i	0.105132	+	0.182094i	−0.808660	+	0.588276i	$0.799807\pi$
$728$	−19.9993	−	14.5989i	−0.741222	−	0.541071i
$729$		0			0
$730$	2.72636	+	0.581634i	0.100907	+	0.0215272i
$731$	−16.9461	+	9.78381i	−0.626773	+	0.361867i
$732$		0			0
$733$	10.8544	+	6.26677i	0.400915	+	0.231469i	0.686879	−	0.726772i	$-0.258980\pi$
$733$	10.8544	+	6.26677i	0.400915	+	0.231469i	−0.285964	+	0.958240i	$0.592314\pi$
$734$	−18.2045	−	16.4160i	−0.671940	−	0.605927i
$735$		0			0
$736$	32.1516	+	18.7231i	1.18512	+	0.690144i
$737$	−18.8443			−0.694139
$738$		0			0
$739$		−	1.83358i		−	0.0674492i	−0.999431	−	0.0337246i	$-0.989263\pi$
$739$		−	1.83358i		−	0.0674492i	0.999431	−	0.0337246i	$-0.0107369\pi$
$740$	0.897304	+	8.66172i	0.0329856	+	0.318411i
$741$		0			0
$742$	3.82787	−	4.24490i	0.140526	−	0.155835i
$743$	15.6588	−	27.1219i	0.574467	−	0.995006i	−0.421632	−	0.906767i	$-0.638543\pi$
$743$	15.6588	−	27.1219i	0.574467	−	0.995006i	0.996099	−	0.0882391i	$-0.0281240\pi$
$744$		0			0
$745$	7.52491	+	13.0335i	0.275691	+	0.477511i
$746$	18.0055	+	3.84125i	0.659230	+	0.140638i
$747$		0			0
$748$	−12.6359	+	28.2669i	−0.462013	+	1.03354i
$749$	10.7879	−	6.22841i	0.394182	−	0.227581i
$750$		0			0
$751$	3.64466	−	6.31274i	0.132996	−	0.230355i	−0.791834	−	0.610736i	$-0.790874\pi$
$751$	3.64466	−	6.31274i	0.132996	−	0.230355i	0.924830	+	0.380381i	$0.124207\pi$
$752$	−30.1983	+	6.32461i	−1.10122	+	0.230635i
$753$		0			0
$754$	24.3806	−	7.90162i	0.887890	−	0.287760i
$755$		−	8.84005i		−	0.321722i
$756$		0			0
$757$		−	12.8156i		−	0.465792i	−0.972502	−	0.232896i	$-0.925180\pi$
$757$		−	12.8156i		−	0.465792i	0.972502	−	0.232896i	$-0.0748202\pi$
$758$	9.96908	+	30.7598i	0.362093	+	1.11725i
$759$		0			0
$760$	−0.767501	−	1.73428i	−0.0278402	−	0.0629090i
$761$	−12.5800	+	21.7892i	−0.456025	+	0.789859i	−0.998747	−	0.0500541i	$-0.984061\pi$
$761$	−12.5800	+	21.7892i	−0.456025	+	0.789859i	0.542721	+	0.839913i	$0.317394\pi$
$762$		0			0
$763$	0.333807	−	0.192724i	0.0120846	−	0.00697706i
$764$	−13.3611	−	5.97269i	−0.483389	−	0.216084i
$765$		0			0
$766$	−8.85883	+	41.5250i	−0.320083	+	1.50036i
$767$	−14.6854	−	25.4359i	−0.530261	−	0.918439i
$768$		0			0
$769$	−10.7318	+	18.5880i	−0.386998	+	0.670300i	−0.992044	−	0.125890i	$-0.959821\pi$
$769$	−10.7318	+	18.5880i	−0.386998	+	0.670300i	0.605046	+	0.796190i	$0.293155\pi$
$770$	−3.18414	−	2.87132i	−0.114748	−	0.103475i
$771$		0			0
$772$	4.21873	+	40.7236i	0.151835	+	1.46567i
$773$		−	20.2122i		−	0.726981i	−0.931598	−	0.363491i	$-0.881585\pi$
$773$		−	20.2122i		−	0.726981i	0.931598	−	0.363491i	$-0.118415\pi$
$774$		0			0
$775$	33.4007			1.19979
$776$	−7.02150	−	0.753899i	−0.252057	−	0.0270634i
$777$		0			0
$778$	36.0310	−	39.9564i	1.29177	−	1.43251i
$779$	−1.55488	−	0.897712i	−0.0557095	−	0.0321639i
$780$		0			0
$781$	8.73811	−	5.04495i	0.312674	−	0.180523i
$782$	−10.9682	+	51.4127i	−0.392223	+	1.83851i
$783$		0			0
$784$	−11.9283	−	13.3276i	−0.426010	−	0.475984i
$785$	−6.07957	−	10.5301i	−0.216989	−	0.375836i
$786$		0			0
$787$	17.5726	+	10.1455i	0.626395	+	0.361649i	0.779355	−	0.626583i	$-0.215547\pi$
$787$	17.5726	+	10.1455i	0.626395	+	0.361649i	−0.152960	+	0.988232i	$0.548880\pi$
$788$	24.1009	+	33.2764i	0.858558	+	1.18542i
$789$		0			0
$790$	1.74728	+	5.39127i	0.0621654	+	0.191813i
$791$	−13.8274			−0.491646
$792$		0			0
$793$	−50.4570			−1.79178
$794$	−16.3291	−	50.3837i	−0.579497	−	1.78805i
$795$		0			0
$796$	3.16826	−	2.29465i	0.112296	−	0.0813318i
$797$	28.8758	+	16.6715i	1.02283	+	0.590533i	0.914924	−	0.403627i	$-0.132251\pi$
$797$	28.8758	+	16.6715i	1.02283	+	0.590533i	0.107910	+	0.994161i	$0.465584\pi$
$798$		0			0
$799$	−21.7970	−	37.7535i	−0.771122	−	1.33562i
$800$	−22.1690	+	12.6891i	−0.783792	+	0.448628i
$801$		0			0
$802$	1.38918	−	6.51164i	0.0490535	−	0.229934i
$803$	−6.71815	+	3.87873i	−0.237078	+	0.136877i
$804$		0			0
$805$	−6.30432	−	3.63980i	−0.222198	−	0.128286i
$806$	38.5676	−	42.7693i	1.35848	−	1.50649i
$807$		0			0
$808$	2.86650	−	26.6974i	0.100843	−	0.939212i
$809$	−30.6920			−1.07907			−0.539536	−	0.841962i	$-0.681400\pi$
$809$	−30.6920			−1.07907			−0.539536	+	0.841962i	$0.681400\pi$
$810$		0			0
$811$			49.5457i			1.73978i	0.493241	+	0.869892i	$0.335812\pi$
$811$			49.5457i			1.73978i	−0.493241	+	0.869892i	$0.664188\pi$
$812$	−10.4130	+	1.07873i	−0.365424	+	0.0378558i
$813$		0			0
$814$	−17.9959	−	16.2280i	−0.630757	−	0.568790i
$815$	2.98168	−	5.16443i	0.104444	−	0.180902i
$816$		0			0
$817$	1.66763	+	2.88842i	0.0583430	+	0.101053i
$818$	3.16532	−	14.8372i	0.110673	−	0.518769i
$819$		0			0
$820$	1.05884	−	2.36865i	0.0369761	−	0.0827170i
$821$	32.9739	−	19.0375i	1.15080	−	0.664414i	0.201716	−	0.979444i	$-0.435348\pi$
$821$	32.9739	−	19.0375i	1.15080	−	0.664414i	0.949082	+	0.315030i	$0.102015\pi$
$822$		0			0
$823$	11.2626	−	19.5074i	0.392589	−	0.679984i	−0.600201	−	0.799849i	$-0.704913\pi$
$823$	11.2626	−	19.5074i	0.392589	−	0.679984i	0.992790	+	0.119865i	$0.0382461\pi$
$824$	−16.8769	−	38.1359i	−0.587936	−	1.32853i
$825$		0			0
$826$	3.69879	+	11.4127i	0.128697	+	0.397099i
$827$			33.5317i			1.16601i	0.812468	+	0.583006i	$0.198124\pi$
$827$			33.5317i			1.16601i	−0.812468	+	0.583006i	$0.801876\pi$
$828$		0			0
$829$			37.7559i			1.31132i	0.755058	+	0.655658i	$0.227609\pi$
$829$			37.7559i			1.31132i	−0.755058	+	0.655658i	$0.772391\pi$
$830$	6.21696	−	2.01488i	0.215794	−	0.0699376i
$831$		0			0
$832$	−9.35003	+	43.0392i	−0.324154	+	1.49212i
$833$	12.6359	−	21.8860i	0.437807	−	0.758304i
$834$		0			0
$835$	7.20378	−	4.15910i	0.249297	−	0.143932i
$836$	4.81804	+	2.15376i	0.166635	+	0.0744892i
$837$		0			0
$838$	5.71107	+	1.21838i	0.197286	+	0.0420884i
$839$	9.90604	+	17.1578i	0.341994	+	0.592352i	0.984803	−	0.173675i	$-0.0555643\pi$
$839$	9.90604	+	17.1578i	0.341994	+	0.592352i	−0.642809	+	0.766027i	$0.722231\pi$
$840$		0			0
$841$	−9.08210	+	15.7307i	−0.313176	+	0.542436i
$842$	−15.0173	+	16.6534i	−0.517531	+	0.573914i
$843$		0			0
$844$	−20.9262	+	2.16784i	−0.720310	+	0.0746200i
$845$			12.0481i			0.414466i
$846$		0			0
$847$	−5.56028			−0.191053
$848$	−9.66010	−	3.17069i	−0.331729	−	0.108882i
$849$		0			0
$850$	−26.8032	−	24.1700i	−0.919342	−	0.829023i
$851$	−35.6304	−	20.5712i	−1.22140	−	0.705173i
$852$		0			0
$853$	−5.95424	+	3.43768i	−0.203869	+	0.117704i	−0.598459	−	0.801153i	$-0.704220\pi$
$853$	−5.95424	+	3.43768i	−0.203869	+	0.117704i	0.394590	+	0.918857i	$0.370887\pi$
$854$	20.1566	+	4.30015i	0.689744	+	0.147148i
$855$		0			0
$856$	−17.8965	−	13.0639i	−0.611690	−	0.446516i
$857$	3.87316	+	6.70851i	0.132305	+	0.229158i	0.924565	−	0.381025i	$-0.124429\pi$
$857$	3.87316	+	6.70851i	0.132305	+	0.229158i	−0.792260	+	0.610184i	$0.791096\pi$
$858$		0			0
$859$	0.594592	+	0.343288i	0.0202872	+	0.0117128i	0.510109	−	0.860110i	$-0.329605\pi$
$859$	0.594592	+	0.343288i	0.0202872	+	0.0117128i	−0.489822	+	0.871822i	$0.662938\pi$
$860$	−3.90348	+	2.82715i	−0.133108	+	0.0964049i
$861$		0			0
$862$	−21.7745	+	7.05698i	−0.741642	+	0.240362i
$863$	42.9194			1.46099			0.730496	−	0.682917i	$-0.239289\pi$
$863$	42.9194			1.46099			0.730496	+	0.682917i	$0.239289\pi$
$864$		0			0
$865$	−9.07991			−0.308726
$866$	−44.1677	+	14.3145i	−1.50088	+	0.486426i
$867$		0			0
$868$	−19.0519	+	13.7986i	−0.646665	+	0.468355i
$869$	−13.6578	−	7.88535i	−0.463310	−	0.267492i
$870$		0			0
$871$	−18.9371	−	32.8000i	−0.641658	−	1.11138i
$872$	−0.553766	−	0.404233i	−0.0187529	−	0.0136891i
$873$		0			0
$874$	8.76318	+	1.86951i	0.296419	+	0.0632372i
$875$	9.12082	−	5.26591i	0.308340	−	0.178020i
$876$		0			0
$877$	14.7508	+	8.51640i	0.498100	+	0.287578i	0.727929	−	0.685653i	$-0.240483\pi$
$877$	14.7508	+	8.51640i	0.498100	+	0.287578i	−0.229828	+	0.973231i	$0.573817\pi$
$878$	22.9530	+	20.6981i	0.774627	+	0.698526i
$879$		0			0
$880$	−2.37836	+	7.24613i	−0.0801746	+	0.244267i
$881$	7.90546			0.266342			0.133171	−	0.991093i	$-0.457484\pi$
$881$	7.90546			0.266342			0.133171	+	0.991093i	$0.457484\pi$
$882$		0			0
$883$			7.53298i			0.253505i	0.991934	+	0.126752i	$0.0404554\pi$
$883$			7.53298i			0.253505i	−0.991934	+	0.126752i	$0.959545\pi$
$884$	−61.8989	+	6.41237i	−2.08188	+	0.215671i
$885$		0			0
$886$	−33.2998	+	36.9277i	−1.11873	+	1.24061i
$887$	−7.02719	+	12.1715i	−0.235950	+	0.408677i	−0.959548	−	0.281544i	$-0.909153\pi$
$887$	−7.02719	+	12.1715i	−0.235950	+	0.408677i	0.723598	+	0.690221i	$0.242487\pi$
$888$		0			0
$889$	−1.37351	−	2.37899i	−0.0460660	−	0.0797886i
$890$	2.87558	+	0.613468i	0.0963896	+	0.0205635i
$891$		0			0
$892$	7.05260	+	3.15265i	0.236138	+	0.105558i
$893$	−6.43501	+	3.71525i	−0.215339	+	0.124326i
$894$		0			0
$895$	−1.15500	+	2.00052i	−0.0386075	+	0.0668701i
$896$	7.40312	−	16.3964i	0.247321	−	0.547767i
$897$		0			0
$898$	−4.32993	+	1.40331i	−0.144492	+	0.0468289i
$899$		−	24.3489i		−	0.812081i
$900$		0			0
$901$		−	14.3655i		−	0.478585i
$902$	2.22595	+	6.86822i	0.0741160	+	0.228687i
$903$		0			0
$904$	9.95347	+	22.4913i	0.331048	+	0.748051i
$905$	−5.19001	+	8.98936i	−0.172522	+	0.298816i
$906$		0			0
$907$	39.7958	−	22.9761i	1.32140	−	0.762910i	0.337447	−	0.941345i	$-0.390437\pi$
$907$	39.7958	−	22.9761i	1.32140	−	0.762910i	0.983952	+	0.178435i	$0.0571034\pi$
$908$	−13.1176	+	29.3445i	−0.435322	+	0.973831i
$909$		0			0
$910$	1.79794	−	8.42770i	0.0596012	−	0.279375i
$911$	−25.7911	−	44.6715i	−0.854497	−	1.48003i	−0.877111	−	0.480288i	$-0.840532\pi$
$911$	−25.7911	−	44.6715i	−0.854497	−	1.48003i	0.0226136	−	0.999744i	$-0.492801\pi$
$912$		0			0
$913$	−9.09302	+	15.7496i	−0.300935	+	0.521235i
$914$	8.51785	+	7.68104i	0.281746	+	0.254066i
$915$		0			0
$916$	17.1438	−	1.77600i	0.566446	−	0.0586805i
$917$		−	10.5571i		−	0.348627i
$918$		0			0
$919$	−21.2048			−0.699481			−0.349741	−	0.936847i	$-0.613730\pi$
$919$	−21.2048			−0.699481			−0.349741	+	0.936847i	$0.613730\pi$
$920$	−1.38234	+	12.8745i	−0.0455743	+	0.424461i
$921$		0			0
$922$	−19.8830	+	22.0491i	−0.654810	+	0.726149i
$923$	17.5623	+	10.1396i	0.578069	+	0.333748i
$924$		0			0
$925$	24.4620	−	14.1231i	0.804305	−	0.464366i
$926$	−2.62611	+	12.3096i	−0.0862992	+	0.404520i
$927$		0			0
$928$	9.25027	+	16.1610i	0.303655	+	0.530511i
$929$	−1.70516	−	2.95343i	−0.0559446	−	0.0968989i	0.836697	−	0.547666i	$-0.184484\pi$
$929$	−1.70516	−	2.95343i	−0.0559446	−	0.0968989i	−0.892641	+	0.450767i	$0.851150\pi$
$930$		0			0
$931$	−3.73042	−	2.15376i	−0.122259	−	0.0705865i
$932$	−39.1236	+	28.3358i	−1.28154	+	0.928170i
$933$		0			0
$934$	−11.3593	−	35.0493i	−0.371687	−	1.14685i
$935$	−10.7757			−0.352403
$936$		0			0
$937$	29.4448			0.961919			0.480959	−	0.876743i	$-0.340288\pi$
$937$	29.4448			0.961919			0.480959	+	0.876743i	$0.340288\pi$
$938$	4.76964	+	14.7168i	0.155734	+	0.480521i
$939$		0			0
$940$	−6.29849	−	8.69642i	−0.205434	−	0.283646i
$941$	40.5880	+	23.4335i	1.32313	+	0.763910i	0.984227	−	0.176911i	$-0.0566106\pi$
$941$	40.5880	+	23.4335i	1.32313	+	0.763910i	0.338904	+	0.940821i	$0.389944\pi$
$942$		0			0
$943$	6.12914	+	10.6160i	0.199592	+	0.345704i
$944$	15.9011	−	14.2316i	0.517537	−	0.463201i
$945$		0			0
$946$	2.79832	−	13.1169i	0.0909812	−	0.426467i
$947$	31.5821	−	18.2340i	1.02628	−	0.592524i	0.110365	−	0.993891i	$-0.464798\pi$
$947$	31.5821	−	18.2340i	1.02628	−	0.592524i	0.915917	+	0.401367i	$0.131465\pi$
$948$		0			0
$949$	−13.5024	−	7.79564i	−0.438308	−	0.253057i
$950$	−4.11972	+	4.56855i	−0.133661	+	0.148223i
$951$		0			0
$952$	25.2738	+	2.71365i	0.819130	+	0.0879500i
$953$	−38.0590			−1.23285			−0.616426	−	0.787413i	$-0.711420\pi$
$953$	−38.0590			−1.23285			−0.616426	+	0.787413i	$0.711420\pi$
$954$		0			0
$955$		−	5.09344i		−	0.164820i
$956$	−0.830495	−	8.01680i	−0.0268601	−	0.259282i
$957$		0			0
$958$	−18.2985	−	16.5008i	−0.591198	−	0.533117i
$959$	2.88330	−	4.99401i	0.0931065	−	0.161265i
$960$		0			0
$961$	−11.8569	−	20.5368i	−0.382481	−	0.662477i
$962$	10.1615	−	47.6312i	0.327620	−	1.53569i
$963$		0			0
$964$	10.2851	+	4.59764i	0.331261	+	0.148080i
$965$	−12.3397	+	7.12430i	−0.397228	+	0.229339i
$966$		0			0
$967$	11.4864	−	19.8951i	0.369378	−	0.639782i	−0.620090	−	0.784531i	$-0.712904\pi$
$967$	11.4864	−	19.8951i	0.369378	−	0.639782i	0.989468	+	0.144749i	$0.0462374\pi$
$968$	4.00249	+	9.04422i	0.128645	+	0.290692i
$969$		0			0
$970$	−0.757723	−	2.33797i	−0.0243290	−	0.0750677i
$971$		−	53.8829i		−	1.72919i	−0.502474	−	0.864593i	$-0.667577\pi$
$971$		−	53.8829i		−	1.72919i	0.502474	−	0.864593i	$-0.332423\pi$
$972$		0			0
$973$			27.5269i			0.882473i
$974$	−40.0055	+	12.9656i	−1.28186	+	0.415443i
$975$		0			0
$976$	−7.51491	−	35.8816i	−0.240546	−	1.14854i
$977$	−19.1024	+	33.0863i	−0.611140	+	1.05853i	0.379909	+	0.925024i	$0.375955\pi$
$977$	−19.1024	+	33.0863i	−0.611140	+	1.05853i	−0.991049	+	0.133501i	$0.957378\pi$
$978$		0			0
$979$	−7.08585	+	4.09102i	−0.226465	+	0.130749i
$980$	2.54032	−	5.68279i	0.0811475	−	0.181530i
$981$		0			0
$982$	32.9547	+	7.03045i	1.05163	+	0.224351i
$983$	24.3307	+	42.1420i	0.776028	+	1.34412i	0.934215	+	0.356711i	$0.116102\pi$
$983$	24.3307	+	42.1420i	0.776028	+	1.34412i	−0.158186	+	0.987409i	$0.550565\pi$
$984$		0			0
$985$	−7.14968	+	12.3836i	−0.227808	+	0.394574i
$986$	−17.6197	+	19.5393i	−0.561126	+	0.622259i
$987$		0			0
$988$	1.09297	+	10.5505i	0.0347722	+	0.335657i
$989$		−	22.7715i		−	0.724093i
$990$		0			0
$991$	−12.7822			−0.406040			−0.203020	−	0.979175i	$-0.565076\pi$
$991$	−12.7822			−0.406040			−0.203020	+	0.979175i	$0.565076\pi$
$992$	36.1588	+	21.0567i	1.14804	+	0.668551i
$993$		0			0
$994$	−6.15164	−	5.54728i	−0.195118	−	0.175949i
$995$	1.17905	+	0.680723i	0.0373783	+	0.0215804i
$996$		0			0
$997$	21.1161	−	12.1914i	0.668752	−	0.386104i	−0.126851	−	0.991922i	$-0.540487\pi$
$997$	21.1161	−	12.1914i	0.668752	−	0.386104i	0.795604	+	0.605817i	$0.207154\pi$
$998$	26.9299	+	5.74514i	0.852450	+	0.181859i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.n.b.37.8		16
3.2	odd	2		72.2.n.b.13.1	✓	16
4.3	odd	2		864.2.r.b.145.5		16
8.3	odd	2		864.2.r.b.145.4		16
8.5	even	2	inner	216.2.n.b.37.2		16
9.2	odd	6		72.2.n.b.61.7	yes	16
9.4	even	3		648.2.d.k.325.4		8
9.5	odd	6		648.2.d.j.325.5		8
9.7	even	3	inner	216.2.n.b.181.2		16
12.11	even	2		288.2.r.b.49.2		16
24.5	odd	2		72.2.n.b.13.7	yes	16
24.11	even	2		288.2.r.b.49.7		16
36.7	odd	6		864.2.r.b.721.4		16
36.11	even	6		288.2.r.b.241.7		16
36.23	even	6		2592.2.d.j.1297.5		8
36.31	odd	6		2592.2.d.k.1297.4		8
72.5	odd	6		648.2.d.j.325.6		8
72.11	even	6		288.2.r.b.241.2		16
72.13	even	6		648.2.d.k.325.3		8
72.29	odd	6		72.2.n.b.61.1	yes	16
72.43	odd	6		864.2.r.b.721.5		16
72.59	even	6		2592.2.d.j.1297.4		8
72.61	even	6	inner	216.2.n.b.181.8		16
72.67	odd	6		2592.2.d.k.1297.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.1	✓	16	3.2	odd	2
72.2.n.b.13.7	yes	16	24.5	odd	2
72.2.n.b.61.1	yes	16	72.29	odd	6
72.2.n.b.61.7	yes	16	9.2	odd	6
216.2.n.b.37.2		16	8.5	even	2	inner
216.2.n.b.37.8		16	1.1	even	1	trivial
216.2.n.b.181.2		16	9.7	even	3	inner
216.2.n.b.181.8		16	72.61	even	6	inner
288.2.r.b.49.2		16	12.11	even	2
288.2.r.b.49.7		16	24.11	even	2
288.2.r.b.241.2		16	72.11	even	6
288.2.r.b.241.7		16	36.11	even	6
648.2.d.j.325.5		8	9.5	odd	6
648.2.d.j.325.6		8	72.5	odd	6
648.2.d.k.325.3		8	72.13	even	6
648.2.d.k.325.4		8	9.4	even	3
864.2.r.b.145.4		16	8.3	odd	2
864.2.r.b.145.5		16	4.3	odd	2
864.2.r.b.721.4		16	36.7	odd	6
864.2.r.b.721.5		16	72.43	odd	6
2592.2.d.j.1297.4		8	72.59	even	6
2592.2.d.j.1297.5		8	36.23	even	6
2592.2.d.k.1297.4		8	36.31	odd	6
2592.2.d.k.1297.5		8	72.67	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.34532 - 0.436011i) q^{2} +(1.61979 - 1.17315i) q^{4} +(0.602794 + 0.348023i) q^{5} +(0.795065 + 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +O(q^{10})\)	\(q+(1.34532 - 0.436011i) q^{2} +(1.61979 - 1.17315i) q^{4} +(0.602794 + 0.348023i) q^{5} +(0.795065 + 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +(0.962695 + 0.205379i) q^{10} +(-2.37222 + 1.36960i) q^{11} +(-4.76780 - 2.75269i) q^{13} +(1.67005 + 1.50598i) q^{14} +(1.24743 - 3.80052i) q^{16} +5.65175 q^{17} -0.963328i q^{19} +(1.38468 - 0.143445i) q^{20} +(-2.59424 + 2.87688i) q^{22} +(-3.28857 + 5.69597i) q^{23} +(-2.25776 - 3.91055i) q^{25} +(-7.61444 - 1.62444i) q^{26} +(2.90338 + 1.29787i) q^{28} +(-2.85076 + 1.64589i) q^{29} +(-3.69844 + 6.40589i) q^{31} +(0.0211236 - 5.65681i) q^{32} +(7.60343 - 2.46423i) q^{34} +1.10680i q^{35} +6.25538i q^{37} +(-0.420022 - 1.29599i) q^{38} +(1.80030 - 0.796718i) q^{40} +(0.931886 - 1.61407i) q^{41} +(-2.99838 + 1.73111i) q^{43} +(-2.23574 + 5.00145i) q^{44} +(-1.94068 + 9.09677i) q^{46} +(-3.85668 - 6.67997i) q^{47} +(2.23574 - 3.87242i) q^{49} +(-4.74246 - 4.27655i) q^{50} +(-10.9522 + 1.13458i) q^{52} -2.54179i q^{53} -1.90662 q^{55} +(4.47186 + 0.480144i) q^{56} +(-3.11757 + 3.45722i) q^{58} +(4.62019 + 2.66747i) q^{59} +(7.93715 - 4.58252i) q^{61} +(-2.18256 + 10.2305i) q^{62} +(-2.43802 - 7.61945i) q^{64} +(-1.91600 - 3.31861i) q^{65} +(5.95780 + 3.43974i) q^{67} +(9.15463 - 6.63036i) q^{68} +(0.482579 + 1.48901i) q^{70} -3.68351 q^{71} +2.83201 q^{73} +(2.72742 + 8.41550i) q^{74} +(-1.13013 - 1.56039i) q^{76} +(-3.77214 - 2.17785i) q^{77} +(2.87870 + 4.98605i) q^{79} +(2.07461 - 1.85680i) q^{80} +(0.549933 - 2.57776i) q^{82} +(5.74968 - 3.31958i) q^{83} +(3.40684 + 1.96694i) q^{85} +(-3.27900 + 3.63623i) q^{86} +(-0.827111 + 7.70337i) q^{88} +2.98701 q^{89} -8.75427i q^{91} +(1.35545 + 13.0843i) q^{92} +(-8.10103 - 7.30516i) q^{94} +(0.335261 - 0.580689i) q^{95} +(-1.24837 - 2.16224i) q^{97} +(1.31938 - 6.18447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

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