LMFDB - Embedded newform 216.2.n.b.181.2

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			181.2
Root			$-1.34532 - 0.436011i$ of defining polynomial
Character	$\chi$	$=$	216.181
Dual form			216.2.n.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05026 - 0.947078i) q^{2} +(0.206086 + 1.98935i) q^{4} +(-0.602794 + 0.348023i) q^{5} +(0.795065 - 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +O(q^{10})$	\(q+(-1.05026 - 0.947078i) q^{2} +(0.206086 + 1.98935i) q^{4} +(-0.602794 + 0.348023i) q^{5} +(0.795065 - 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +(0.962695 + 0.205379i) q^{10} +(2.37222 + 1.36960i) q^{11} +(4.76780 - 2.75269i) q^{13} +(-2.13924 + 0.693314i) q^{14} +(-3.91506 + 0.819955i) q^{16} +5.65175 q^{17} -0.963328i q^{19} +(-0.816569 - 1.12745i) q^{20} +(-1.19433 - 3.68512i) q^{22} +(-3.28857 - 5.69597i) q^{23} +(-2.25776 + 3.91055i) q^{25} +(-7.61444 - 1.62444i) q^{26} +(2.90338 + 1.29787i) q^{28} +(2.85076 + 1.64589i) q^{29} +(-3.69844 - 6.40589i) q^{31} +(4.88838 + 2.84670i) q^{32} +(-5.93580 - 5.35265i) q^{34} +1.10680i q^{35} +6.25538i q^{37} +(-0.912347 + 1.01174i) q^{38} +(-0.210173 + 1.95747i) q^{40} +(0.931886 + 1.61407i) q^{41} +(2.99838 + 1.73111i) q^{43} +(-2.23574 + 5.00145i) q^{44} +(-1.94068 + 9.09677i) q^{46} +(-3.85668 + 6.67997i) q^{47} +(2.23574 + 3.87242i) q^{49} +(6.07483 - 1.96882i) q^{50} +(6.45866 + 8.91756i) q^{52} -2.54179i q^{53} -1.90662 q^{55} +(-1.82011 - 4.11282i) q^{56} +(-1.43525 - 4.42850i) q^{58} +(-4.62019 + 2.66747i) q^{59} +(-7.93715 - 4.58252i) q^{61} +(-2.18256 + 10.2305i) q^{62} +(-2.43802 - 7.61945i) q^{64} +(-1.91600 + 3.31861i) q^{65} +(-5.95780 + 3.43974i) q^{67} +(1.16474 + 11.2433i) q^{68} +(1.04823 - 1.16243i) q^{70} -3.68351 q^{71} +2.83201 q^{73} +(5.92433 - 6.56976i) q^{74} +(1.91640 - 0.198528i) q^{76} +(3.77214 - 2.17785i) q^{77} +(2.87870 - 4.98605i) q^{79} +(2.07461 - 1.85680i) q^{80} +(0.549933 - 2.57776i) q^{82} +(-5.74968 - 3.31958i) q^{83} +(-3.40684 + 1.96694i) q^{85} +(-1.50957 - 4.65781i) q^{86} +(7.08487 - 3.13539i) q^{88} +2.98701 q^{89} -8.75427i q^{91} +(10.6536 - 7.71598i) q^{92} +(10.3770 - 3.36312i) q^{94} +(0.335261 + 0.580689i) q^{95} +(-1.24837 + 2.16224i) q^{97} +(1.31938 - 6.18447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.05026	−	0.947078i	−0.742645	−	0.669685i
$2$	−1.05026	−	0.947078i	−0.742645	−	0.669685i
$3$		0			0
$3$		0			0
$4$	0.206086	+	1.98935i	0.103043	+	0.994677i
$5$	−0.602794	+	0.348023i	−0.269578	+	0.155641i	−0.628696	−	0.777651i	$-0.716411\pi$
$5$	−0.602794	+	0.348023i	−0.269578	+	0.155641i	0.359118	+	0.933292i	$0.383078\pi$
$6$		0			0
$7$	0.795065	−	1.37709i	0.300506	−	0.520492i	−0.675745	−	0.737136i	$-0.736178\pi$
$7$	0.795065	−	1.37709i	0.300506	−	0.520492i	0.976251	+	0.216644i	$0.0695111\pi$
$8$	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	$-0.197831\pi$
$11$	2.37222	+	1.36960i	0.715252	+	0.412951i	−0.0977506	+	0.995211i	$0.531165\pi$
$12$		0			0
$13$	4.76780	−	2.75269i	1.32235	−	0.763460i	0.338248	−	0.941057i	$-0.390166\pi$
$13$	4.76780	−	2.75269i	1.32235	−	0.763460i	0.984103	+	0.177597i	$0.0568325\pi$
$14$	−2.13924	+	0.693314i	−0.571735	+	0.185296i
$15$		0			0
$16$	−3.91506	+	0.819955i	−0.978764	+	0.204989i
$17$	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	$-0.0352457\pi$
$20$	−0.816569	−	1.12745i	−0.182590	−	0.252105i
$21$		0			0
$22$	−1.19433	−	3.68512i	−0.254631	−	0.785670i
$23$	−3.28857	−	5.69597i	−0.685714	−	1.18769i	−0.973212	−	0.229910i	$-0.926157\pi$
$23$	−3.28857	−	5.69597i	−0.685714	−	1.18769i	0.287498	−	0.957781i	$-0.407177\pi$
$24$		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	$-0.234465\pi$
$29$	2.85076	+	1.64589i	0.529373	+	0.305634i	−0.211388	+	0.977402i	$0.567798\pi$
$30$		0			0
$31$	−3.69844	−	6.40589i	−0.664259	−	1.15053i	−0.979486	−	0.201514i	$-0.935414\pi$
$31$	−3.69844	−	6.40589i	−0.664259	−	1.15053i	0.315226	−	0.949017i	$-0.397920\pi$
$32$	4.88838	+	2.84670i	0.864152	+	0.503230i
$33$		0			0
$34$	−5.93580	−	5.35265i	−1.01798	−	0.917971i
$35$			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	$0.828093\pi$
$38$	−0.912347	+	1.01174i	−0.148002	+	0.164127i
$39$		0			0
$40$	−0.210173	+	1.95747i	−0.0332313	+	0.309503i
$41$	0.931886	+	1.61407i	0.145536	+	0.252076i	0.929573	−	0.368639i	$-0.120176\pi$
$41$	0.931886	+	1.61407i	0.145536	+	0.252076i	−0.784037	+	0.620714i	$0.786843\pi$
$42$		0			0
$43$	2.99838	+	1.73111i	0.457248	+	0.263992i	0.710886	−	0.703307i	$-0.248294\pi$
$43$	2.99838	+	1.73111i	0.457248	+	0.263992i	−0.253638	+	0.967299i	$0.581627\pi$
$44$	−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	0.434717	+	0.900567i	$0.356848\pi$
$47$	−3.85668	+	6.67997i	−0.562555	+	0.974374i	−0.997273	+	0.0738070i	$0.976485\pi$
$48$		0			0
$49$	2.23574	+	3.87242i	0.319392	+	0.553203i
$50$	6.07483	−	1.96882i	0.859111	−	0.278433i
$51$		0			0
$52$	6.45866	+	8.91756i	0.895655	+	1.23664i
$53$		−	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
$56$	−1.82011	−	4.11282i	−0.243223	−	0.549598i
$57$		0			0
$58$	−1.43525	−	4.42850i	−0.188458	−	0.581491i
$59$	−4.62019	+	2.66747i	−0.601498	+	0.347275i	−0.769631	−	0.638489i	$-0.779560\pi$
$59$	−4.62019	+	2.66747i	−0.601498	+	0.347275i	0.168133	+	0.985764i	$0.446226\pi$
$60$		0			0
$61$	−7.93715	−	4.58252i	−1.01625	−	0.586731i	−0.103233	−	0.994657i	$-0.532919\pi$
$61$	−7.93715	−	4.58252i	−1.01625	−	0.586731i	−0.913015	+	0.407926i	$0.866252\pi$
$62$	−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	$-0.804717\pi$
$67$	−5.95780	+	3.43974i	−0.727861	+	0.420231i	0.0897783	+	0.995962i	$0.471384\pi$
$68$	1.16474	+	11.2433i	0.141246	+	1.36345i
$69$		0			0
$70$	1.04823	−	1.16243i	0.125287	−	0.138937i
$71$	−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	$0.447002\pi$
$74$	5.92433	−	6.56976i	0.688690	−	0.763719i
$75$		0			0
$76$	1.91640	−	0.198528i	0.219826	−	0.0227728i
$77$	3.77214	−	2.17785i	0.429875	−	0.248189i
$78$		0			0
$79$	2.87870	−	4.98605i	0.323879	−	0.560975i	−0.657406	−	0.753537i	$-0.728346\pi$
$79$	2.87870	−	4.98605i	0.323879	−	0.560975i	0.981285	+	0.192562i	$0.0616797\pi$
$80$	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	$-0.452049\pi$
$83$	−5.74968	−	3.31958i	−0.631110	−	0.364371i	−0.781182	+	0.624304i	$0.785383\pi$
$84$		0			0
$85$	−3.40684	+	1.96694i	−0.369524	+	0.213345i
$86$	−1.50957	−	4.65781i	−0.162781	−	0.502265i
$87$		0			0
$88$	7.08487	−	3.13539i	0.755250	−	0.334233i
$89$	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
$92$	10.6536	−	7.71598i	1.11071	−	0.804447i
$93$		0			0
$94$	10.3770	−	3.36312i	1.07030	−	0.346879i
$95$	0.335261	+	0.580689i	0.0343970	+	0.0595774i
$96$		0			0
$97$	−1.24837	+	2.16224i	−0.126753	+	0.219543i	−0.922417	−	0.386196i	$-0.873789\pi$
$97$	−1.24837	+	2.16224i	−0.126753	+	0.219543i	0.795664	+	0.605738i	$0.207122\pi$
$98$	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	$-0.489911\pi$
$101$	−8.22136	−	4.74661i	−0.818056	−	0.472305i	−0.849746	+	0.527193i	$0.823245\pi$
$102$		0			0
$103$	7.37220	+	12.7690i	0.726405	+	1.25817i	0.958393	+	0.285451i	$0.0921435\pi$
$103$	7.37220	+	12.7690i	0.726405	+	1.25817i	−0.231989	+	0.972719i	$0.574523\pi$
$104$	1.66237	−	15.4826i	0.163008	−	1.51819i
$105$		0			0
$106$	−2.40727	+	2.66953i	−0.233815	+	0.259288i
$107$		−	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	$-0.00369529\pi$
$110$	2.00244	+	1.80571i	0.190925	+	0.172168i
$111$		0			0
$112$	−1.98357	+	6.04331i	−0.187430	+	0.571039i
$113$	−4.34789	−	7.53076i	−0.409015	−	0.708435i	0.585765	−	0.810481i	$-0.300794\pi$
$113$	−4.34789	−	7.53076i	−0.409015	−	0.708435i	−0.994780	+	0.102046i	$0.967461\pi$
$114$		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
$122$	3.99606	+	12.3299i	0.361786	+	1.11630i
$123$		0			0
$124$	11.9814	−	8.67767i	1.07596	−	0.779277i
$125$		−	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	$0.524422\pi$
$128$	−4.65567	+	10.3114i	−0.411507	+	0.911407i
$129$		0			0
$130$	5.15529	−	1.67080i	0.452148	−	0.146539i
$131$	5.74968	−	3.31958i	0.502352	−	0.290033i	−0.227332	−	0.973817i	$-0.573000\pi$
$131$	5.74968	−	3.31958i	0.502352	−	0.290033i	0.729684	+	0.683784i	$0.239667\pi$
$132$		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	−0.933028	−	0.359803i	$-0.882844\pi$
$137$	−1.81325	+	3.14063i	−0.154916	+	0.268322i	0.778112	+	0.628125i	$0.216177\pi$
$138$		0			0
$139$	−14.9919	+	8.65556i	−1.27159	+	0.734155i	−0.975288	−	0.220937i	$-0.929088\pi$
$139$	−14.9919	+	8.65556i	−1.27159	+	0.734155i	−0.296307	+	0.955093i	$0.595755\pi$
$140$	−2.20182	+	0.228097i	−0.186088	+	0.0192777i
$141$		0			0
$142$	3.86864	+	3.48858i	0.324649	+	0.292755i
$143$	15.0804			1.26109
$144$		0			0
$145$	−2.29123			−0.190276
$146$	−2.97434	−	2.68213i	−0.246158	−	0.221975i
$147$		0			0
$148$	−12.4442	+	1.28914i	−1.02290	+	0.105967i
$149$	−18.7251	+	10.8109i	−1.53402	+	0.885665i	−0.534846	+	0.844949i	$0.679631\pi$
$149$	−18.7251	+	10.8109i	−1.53402	+	0.885665i	−0.999171	+	0.0407158i	$0.987036\pi$
$150$		0			0
$151$	−6.35019	+	10.9988i	−0.516771	+	0.895073i	0.483039	+	0.875599i	$0.339533\pi$
$151$	−6.35019	+	10.9988i	−0.516771	+	0.895073i	−0.999810	+	0.0194749i	$0.993801\pi$
$152$	−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	$-0.421147\pi$
$157$	15.1285	−	8.73443i	1.20738	−	0.697083i	0.962187	+	0.272390i	$0.0878140\pi$
$158$	−7.74556	+	2.51029i	−0.616203	+	0.199708i
$159$		0			0
$160$	−3.93741	−	0.0147030i	−0.311279	−	0.00116238i
$161$	−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	$-0.108915\pi$
$164$	−3.01891	+	2.18649i	−0.235738	+	0.170736i
$165$		0			0
$166$	2.89475	+	8.93182i	0.224676	+	0.693244i
$167$	5.97532	+	10.3496i	0.462384	+	0.800873i	0.999079	−	0.0429032i	$-0.0136607\pi$
$167$	5.97532	+	10.3496i	0.462384	+	0.800873i	−0.536695	+	0.843776i	$0.680327\pi$
$168$		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	$-0.168173\pi$
$173$	11.2973	+	6.52248i	0.858916	+	0.495895i	−0.00473326	+	0.999989i	$0.501507\pi$
$174$		0			0
$175$	3.59013	+	6.21829i	0.271388	+	0.470058i
$176$	−10.4104	−	3.41696i	−0.784714	−	0.257563i
$177$		0			0
$178$	−3.13713	−	2.82893i	−0.235138	−	0.212037i
$179$			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	$0.813013\pi$
$182$	−8.29098	+	9.19425i	−0.614569	+	0.681523i
$183$		0			0
$184$	−18.4966	−	1.98598i	−1.36359	−	0.146409i
$185$	−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	−0.967497	−	0.252884i	$-0.918621\pi$
$191$	−3.65884	+	6.33729i	−0.264744	+	0.458550i	0.702752	+	0.711434i	$0.251954\pi$
$192$		0			0
$193$	−10.2354	−	17.7282i	−0.736759	−	1.27610i	−0.953947	−	0.299974i	$-0.903022\pi$
$193$	−10.2354	−	17.7282i	−0.736759	−	1.27610i	0.217189	−	0.976130i	$-0.430311\pi$
$194$	3.35893	−	1.08861i	0.241157	−	0.0781576i
$195$		0			0
$196$	−7.24287	+	5.24574i	−0.517348	+	0.374696i
$197$			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	$0.477915\pi$
$200$	5.16861	+	11.6792i	0.365476	+	0.825847i
$201$		0			0
$202$	4.13915	+	12.7714i	0.291229	+	0.898595i
$203$	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	$-0.548733\pi$
$211$	9.10981	−	5.25955i	0.627145	−	0.362082i	0.779646	+	0.626221i	$0.215399\pi$
$212$	5.05651	−	0.523826i	0.347283	−	0.0359765i
$213$		0			0
$214$	−7.41926	+	8.22755i	−0.507170	+	0.562424i
$215$	−2.40987			−0.164352
$216$		0			0
$217$	−11.7620			−0.798456
$218$	−0.229572	+	0.254583i	−0.0155486	+	0.0172425i
$219$		0			0
$220$	−0.392926	−	3.79293i	−0.0264911	−	0.255720i
$221$	26.9464	−	15.5575i	1.81261	−	1.04651i
$222$		0			0
$223$	1.93129	−	3.34510i	0.129329	−	0.224004i	−0.794088	−	0.607803i	$-0.792051\pi$
$223$	1.93129	−	3.34510i	0.129329	−	0.224004i	0.923417	+	0.383799i	$0.125384\pi$
$224$	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	$-0.154266\pi$
$227$	13.9183	+	8.03574i	0.923790	+	0.533351i	0.0389481	+	0.999241i	$0.487599\pi$
$228$		0			0
$229$	−7.46319	+	4.30888i	−0.493182	+	0.284739i	−0.725893	−	0.687807i	$-0.758573\pi$
$229$	−7.46319	+	4.30888i	−0.493182	+	0.284739i	0.232712	+	0.972546i	$0.425240\pi$
$230$	−1.99606	−	6.15888i	−0.131616	−	0.406105i
$231$		0			0
$232$	8.51408	−	3.76788i	0.558977	−	0.247373i
$233$	−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
$236$	−6.25870	−	8.64147i	−0.407406	−	0.562512i
$237$		0			0
$238$	−12.0904	+	3.91844i	−0.783706	+	0.253995i
$239$	2.01493	+	3.48996i	0.130335	+	0.225746i	0.923806	−	0.382862i	$-0.125061\pi$
$239$	2.01493	+	3.48996i	0.130335	+	0.225746i	−0.793471	+	0.608608i	$0.791728\pi$
$240$		0			0
$241$	2.81649	−	4.87830i	0.181426	−	0.314239i	−0.760940	−	0.648822i	$-0.775262\pi$
$241$	2.81649	−	4.87830i	0.181426	−	0.314239i	0.942366	+	0.334583i	$0.108595\pi$
$242$	−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
$248$	−20.8020	−	2.23351i	−1.32093	−	0.141828i
$249$		0			0
$250$	−6.27273	+	6.95612i	−0.396722	+	0.439944i
$251$			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
$254$	1.81437	+	1.63612i	0.113843	+	0.102659i
$255$		0			0
$256$	14.6553	−	6.42034i	0.915959	−	0.401271i
$257$	5.42539	+	9.39705i	0.338427	+	0.586172i	0.984137	−	0.177410i	$-0.0567720\pi$
$257$	5.42539	+	9.39705i	0.338427	+	0.586172i	−0.645710	+	0.763582i	$0.723439\pi$
$258$		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	−0.247130	−	0.968982i	$-0.579487\pi$
$263$	11.6051	−	20.1005i	0.715598	−	1.23945i	0.962728	−	0.270470i	$-0.0871792\pi$
$264$		0			0
$265$	0.884601	+	1.53217i	0.0543406	+	0.0941207i
$266$	0.667890	+	2.06079i	0.0409509	+	0.126355i
$267$		0			0
$268$	−8.07067	−	11.1433i	−0.492995	−	0.680685i
$269$			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	$0.565786\pi$
$272$	−22.1269	+	4.63418i	−1.34164	+	0.280988i
$273$		0			0
$274$	4.87880	−	1.58119i	0.294739	−	0.0955233i
$275$	−10.7118	+	6.18447i	−0.645947	+	0.372938i
$276$		0			0
$277$	−1.83595	−	1.05999i	−0.110312	−	0.0636885i	0.443829	−	0.896111i	$-0.353620\pi$
$277$	−1.83595	−	1.05999i	−0.110312	−	0.0636885i	−0.554141	+	0.832423i	$0.686953\pi$
$278$	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	−0.153557	−	0.988140i	$-0.549073\pi$
$281$	13.0580	−	22.6171i	0.778976	−	1.34923i	0.932533	−	0.361086i	$-0.117594\pi$
$282$		0			0
$283$	16.5376	−	9.54799i	0.983058	−	0.567569i	0.0798661	−	0.996806i	$-0.474551\pi$
$283$	16.5376	−	9.54799i	0.983058	−	0.567569i	0.903192	+	0.429237i	$0.141217\pi$
$284$	−0.759119	−	7.32781i	−0.0450455	−	0.434826i
$285$		0			0
$286$	−15.8383	−	14.2823i	−0.936539	−	0.844531i
$287$	2.96364			0.174938
$288$		0			0
$289$	14.9423			0.878956
$290$	2.40638	+	2.16998i	0.141308	+	0.127425i
$291$		0			0
$292$	0.583636	+	5.63386i	0.0341547	+	0.329697i
$293$	−5.07116	+	2.92784i	−0.296261	+	0.171046i	−0.640762	−	0.767740i	$-0.721381\pi$
$293$	−5.07116	+	2.92784i	−0.296261	+	0.171046i	0.344501	+	0.938786i	$0.388048\pi$
$294$		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
$302$	17.0861	−	5.53751i	0.983195	−	0.318648i
$303$		0			0
$304$	0.789886	+	3.77149i	0.0453031	+	0.216310i
$305$	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	$0.872077\pi$
$308$	5.10989	+	7.05530i	0.291163	+	0.402013i
$309$		0			0
$310$	−2.24484	−	6.92649i	−0.127498	−	0.393398i
$311$	9.57980	+	16.5927i	0.543221	+	0.940886i	0.998717	+	0.0506479i	$0.0161286\pi$
$311$	9.57980	+	16.5927i	0.543221	+	0.940886i	−0.455496	+	0.890238i	$0.650538\pi$
$312$		0			0
$313$	−12.6102	+	21.8416i	−0.712773	+	1.23456i	0.251039	+	0.967977i	$0.419228\pi$
$313$	−12.6102	+	21.8416i	−0.712773	+	1.23456i	−0.963812	+	0.266582i	$0.914106\pi$
$314$	−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	$-0.311234\pi$
$317$	2.13931	+	1.23513i	0.120156	+	0.0693719i	−0.438718	+	0.898625i	$0.644567\pi$
$318$		0			0
$319$	4.50843	+	7.80883i	0.252424	+	0.437211i
$320$	4.12137	+	3.74447i	0.230392	+	0.209322i
$321$		0			0
$322$	10.9841	+	9.90502i	0.612121	+	0.551985i
$323$		−	5.44449i		−	0.302939i
$324$		0			0
$325$			24.8597i			1.37897i
$326$	−8.11408	+	8.99807i	−0.449397	+	0.498357i
$327$		0			0
$328$	5.24142	+	0.562771i	0.289409	+	0.0310738i
$329$	6.13262	+	10.6220i	0.338103	+	0.585611i
$330$		0			0
$331$	−24.4404	−	14.1107i	−1.34336	−	0.775592i	−0.356065	−	0.934461i	$-0.615882\pi$
$331$	−24.4404	−	14.1107i	−1.34336	−	0.775592i	−0.987300	+	0.158869i	$0.949215\pi$
$332$	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	0.977341	−	0.211670i	$-0.0678902\pi$
$337$	5.60565	+	9.70927i	0.305359	+	0.528897i	−0.671982	+	0.740567i	$0.734557\pi$
$338$	−23.2866	+	7.54704i	−1.26662	+	0.410505i
$339$		0			0
$340$	−4.61504	−	6.37205i	−0.250286	−	0.345573i
$341$		−	20.2616i		−	1.09723i
$342$		0			0
$343$	18.2411			0.984929
$344$	8.95494	−	3.96298i	0.482818	−	0.213669i
$345$		0			0
$346$	−5.68775	−	17.5497i	−0.305776	−	0.943477i
$347$	17.8303	−	10.2943i	0.957180	−	0.552628i	0.0618763	−	0.998084i	$-0.480292\pi$
$347$	17.8303	−	10.2943i	0.957180	−	0.552628i	0.895304	+	0.445455i	$0.146958\pi$
$348$		0			0
$349$	−2.93968	−	1.69723i	−0.157358	−	0.0908505i	0.419253	−	0.907869i	$-0.362292\pi$
$349$	−2.93968	−	1.69723i	−0.157358	−	0.0908505i	−0.576611	+	0.817019i	$0.695625\pi$
$350$	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	−0.852322	−	0.523017i	$-0.824806\pi$
$353$	0.503241	−	0.871639i	0.0267848	−	0.0463926i	0.879107	+	0.476624i	$0.158140\pi$
$354$		0			0
$355$	2.22040	−	1.28195i	0.117847	−	0.0680388i
$356$	0.615580	+	5.94222i	0.0326257	+	0.314937i
$357$		0			0
$358$	3.14312	−	3.48555i	0.166119	−	0.184217i
$359$	−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
$362$	14.1236	−	15.6623i	0.742320	−	0.823193i
$363$		0			0
$364$	17.4154	−	1.80413i	0.912812	−	0.0945622i
$365$	−1.70712	+	0.985604i	−0.0893546	+	0.0515889i
$366$		0			0
$367$	−8.66667	+	15.0111i	−0.452397	+	0.783574i	−0.998534	−	0.0541214i	$-0.982764\pi$
$367$	−8.66667	+	15.0111i	−0.452397	+	0.783574i	0.546138	+	0.837695i	$0.316098\pi$
$368$	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	$-0.776090\pi$
$373$	−11.2742	+	6.50917i	−0.583757	+	0.337032i	0.178868	+	0.983873i	$0.442756\pi$
$374$	−6.75003	−	20.8274i	−0.349036	−	1.07696i
$375$		0			0
$376$	8.82897	+	19.9504i	0.455319	+	1.02886i
$377$	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	$0.800219\pi$
$380$	−1.08610	+	0.786624i	−0.0557159	+	0.0403530i
$381$		0			0
$382$	9.84463	−	3.19059i	0.503695	−	0.163245i
$383$	−15.0117	−	26.0010i	−0.767061	−	1.32859i	−0.939150	−	0.343508i	$-0.888385\pi$
$383$	−15.0117	−	26.0010i	−0.767061	−	1.32859i	0.172089	−	0.985081i	$-0.444948\pi$
$384$		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	−0.967358	−	0.253412i	$-0.918447\pi$
$389$	−32.9474	−	19.0222i	−1.67050	−	0.964463i	−0.703140	−	0.711051i	$-0.748220\pi$
$390$		0			0
$391$	−18.5862	−	32.1922i	−0.939943	−	1.62803i
$392$	12.5750	+	1.35018i	0.635134	+	0.0681943i
$393$		0			0
$394$	19.4565	−	21.5762i	0.980203	−	1.08699i
$395$			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	$-0.388994\pi$
$398$	−2.05427	−	1.85246i	−0.102971	−	0.0928553i
$399$		0			0
$400$	5.63278	−	17.1613i	0.281639	−	0.858065i
$401$	2.35402	+	4.07728i	0.117554	+	0.203610i	0.918798	−	0.394728i	$-0.129161\pi$
$401$	2.35402	+	4.07728i	0.117554	+	0.203610i	−0.801244	+	0.598338i	$0.795828\pi$
$402$		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	0.967622	−	0.252405i	$-0.0812216\pi$
$409$	5.36377	+	9.29032i	0.265221	+	0.459377i	−0.702400	+	0.711782i	$0.747888\pi$
$410$	0.565625	+	1.74525i	0.0279342	+	0.0861917i
$411$		0			0
$412$	−23.8828	+	17.2974i	−1.17662	+	0.852183i
$413$			8.48324i			0.417433i
$414$		0			0
$415$	4.62117			0.226844
$416$	31.1430	+	0.116294i	1.52691	+	0.00570177i
$417$		0			0
$418$	−3.54998	+	1.15053i	−0.173635	+	0.0562742i
$419$	−3.57600	+	2.06460i	−0.174699	+	0.100863i	−0.584800	−	0.811178i	$-0.698827\pi$
$419$	−3.57600	+	2.06460i	−0.174699	+	0.100863i	0.410101	+	0.912040i	$0.365494\pi$
$420$		0			0
$421$	13.7321	+	7.92824i	0.669262	+	0.386399i	0.795797	−	0.605563i	$-0.207052\pi$
$421$	13.7321	+	7.92824i	0.669262	+	0.386399i	−0.126535	+	0.991962i	$0.540386\pi$
$422$	−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
$428$	15.5843	−	1.61444i	0.753294	−	0.0780370i
$429$		0			0
$430$	2.53099	+	2.28234i	0.122055	+	0.110064i
$431$	−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	$0.789332\pi$
$434$	12.3531	+	11.1395i	0.592969	+	0.534714i
$435$		0			0
$436$	0.482219	−	0.0499552i	0.0230941	−	0.00239242i
$437$	−5.48709	+	3.16797i	−0.262483	+	0.151545i
$438$		0			0
$439$	10.9273	−	18.9267i	0.521533	−	0.903321i	−0.478154	−	0.878276i	$-0.658694\pi$
$439$	10.9273	−	18.9267i	0.521533	−	0.903321i	0.999686	−	0.0250450i	$-0.00797290\pi$
$440$	−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	$-0.0186477\pi$
$443$	30.4500	+	17.5803i	1.44672	+	0.835265i	0.448436	+	0.893815i	$0.351981\pi$
$444$		0			0
$445$	−1.80055	+	1.03955i	−0.0853543	+	0.0492793i
$446$	−5.19643	+	1.68413i	−0.246058	+	0.0797459i
$447$		0			0
$448$	−12.4311	−	2.70058i	−0.587313	−	0.127591i
$449$	−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
$452$	14.0853	−	10.2015i	0.662518	−	0.479837i
$453$		0			0
$454$	−7.00735	−	21.6213i	−0.328871	−	1.01474i
$455$	3.04669	+	5.27703i	0.142831	+	0.247391i
$456$		0			0
$457$	4.05512	−	7.02368i	0.189691	−	0.328554i	−0.755456	−	0.655199i	$-0.772585\pi$
$457$	4.05512	−	7.02368i	0.189691	−	0.328554i	0.945147	+	0.326645i	$0.105918\pi$
$458$	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	$-0.170734\pi$
$461$	18.1813	+	10.4970i	0.846789	+	0.488894i	−0.0127771	+	0.999918i	$0.504067\pi$
$462$		0			0
$463$	−4.45005	−	7.70772i	−0.206812	−	0.358208i	0.743897	−	0.668294i	$-0.232975\pi$
$463$	−4.45005	−	7.70772i	−0.206812	−	0.358208i	−0.950708	+	0.310086i	$0.899642\pi$
$464$	−12.5105	−	4.10625i	−0.580783	−	0.190628i
$465$		0			0
$466$	25.3675	+	22.8753i	1.17513	+	1.05968i
$467$		−	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
$470$	−5.08473	+	5.63869i	−0.234541	+	0.260094i
$471$		0			0
$472$	−1.61090	+	15.0033i	−0.0741477	+	0.690581i
$473$	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	−0.993483	−	0.113976i	$-0.963641\pi$
$479$	−8.71143	+	15.0886i	−0.398035	+	0.689418i	0.595448	+	0.803394i	$0.296975\pi$
$480$		0			0
$481$	17.2191	+	29.8244i	0.785125	+	1.35988i
$482$	−7.57817	+	2.45604i	−0.345176	+	0.111870i
$483$		0			0
$484$	5.66399	−	4.10221i	0.257454	−	0.186464i
$485$		−	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	$0.735318\pi$
$488$	−23.7051	+	10.4906i	−1.07308	+	0.474887i
$489$		0			0
$490$	1.35703	+	4.18714i	0.0613042	+	0.189156i
$491$	−20.6346	+	11.9134i	−0.931229	+	0.537645i	−0.887200	−	0.461385i	$-0.847353\pi$
$491$	−20.6346	+	11.9134i	−0.931229	+	0.537645i	−0.0440286	+	0.999030i	$0.514019\pi$
$492$		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	$-0.810207\pi$
$499$	−16.8622	+	9.73540i	−0.754856	+	0.435816i	0.0725899	+	0.997362i	$0.476874\pi$
$500$	13.1760	−	1.36496i	0.589248	−	0.0610427i
$501$		0			0
$502$	13.1481	−	14.5806i	0.586830	−	0.650762i
$503$	−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
$506$	−17.0627	+	18.9216i	−0.758529	+	0.841168i
$507$		0			0
$508$	−0.356022	−	3.43669i	−0.0157959	−	0.152479i
$509$	−0.392870	+	0.226823i	−0.0174136	+	0.0100538i	−0.508682	−	0.860955i	$-0.669867\pi$
$509$	−0.392870	+	0.226823i	−0.0174136	+	0.0100538i	0.491268	+	0.871009i	$0.336534\pi$
$510$		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
$518$	−4.33694	−	13.3817i	−0.190554	−	0.587960i
$519$		0			0
$520$	4.38624	+	9.91136i	0.192349	+	0.434642i
$521$	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	$0.979395\pi$
$524$	7.78875	+	10.7540i	0.340253	+	0.469792i
$525$		0			0
$526$	−31.2251	+	10.1199i	−1.36148	+	0.441247i
$527$	−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
$536$	−2.07728	+	19.3469i	−0.0897246	+	0.835658i
$537$		0			0
$538$	3.80693	−	4.22168i	0.164128	−	0.182010i
$539$			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	$-0.104328\pi$
$542$	7.09577	+	6.39866i	0.304789	+	0.274846i
$543$		0			0
$544$	27.6279	+	16.0888i	1.18454	+	0.689803i
$545$	0.0843608	+	0.146117i	0.00361362	+	0.00625897i
$546$		0			0
$547$	15.7731	+	9.10661i	0.674409	+	0.389370i	0.797745	−	0.602995i	$-0.206026\pi$
$547$	15.7731	+	9.10661i	0.674409	+	0.389370i	−0.123336	+	0.992365i	$0.539359\pi$
$548$	−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
$554$	0.924333	+	2.85205i	0.0392711	+	0.121172i
$555$		0			0
$556$	−20.3086	−	28.0404i	−0.861276	−	1.18918i
$557$		−	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
$560$	−0.907529	−	4.33320i	−0.0383501	−	0.183111i
$561$		0			0
$562$	−35.1345	+	11.3869i	−1.48206	+	0.480327i
$563$	8.04256	−	4.64337i	0.338953	−	0.195695i	−0.320856	−	0.947128i	$-0.603970\pi$
$563$	8.04256	−	4.64337i	0.338953	−	0.195695i	0.659809	+	0.751433i	$0.270637\pi$
$564$		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	−0.722436	−	0.691437i	$-0.756978\pi$
$569$	5.66727	−	9.81599i	0.237584	−	0.411508i	0.960021	+	0.279930i	$0.0903111\pi$
$570$		0			0
$571$	37.7843	−	21.8148i	1.58122	−	0.912920i	0.586543	−	0.809918i	$-0.300489\pi$
$571$	37.7843	−	21.8148i	1.58122	−	0.912920i	0.994681	−	0.103002i	$-0.0328448\pi$
$572$	3.10785	+	30.0002i	0.129946	+	1.25437i
$573$		0			0
$574$	−3.11258	−	2.80680i	−0.129917	−	0.117153i
$575$	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	$0.453580\pi$
$578$	−15.6932	−	14.1515i	−0.652752	−	0.588624i
$579$		0			0
$580$	−0.472190	−	4.55807i	−0.0196066	−	0.189264i
$581$	−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	$-0.389341\pi$
$587$	−7.34574	−	4.24107i	−0.303191	−	0.175048i	−0.643876	+	0.765130i	$0.722675\pi$
$588$		0			0
$589$	−6.17097	+	3.56281i	−0.254270	+	0.146803i
$590$	−4.99568	+	1.61907i	−0.205669	+	0.0666561i
$591$		0			0
$592$	−5.12913	−	24.4902i	−0.210806	−	1.00654i
$593$	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
$596$	−25.3657	−	35.0228i	−1.03902	−	1.43459i
$597$		0			0
$598$	15.7878	+	48.7137i	0.645613	+	1.99205i
$599$	14.9623	+	25.9155i	0.611344	+	1.05888i	0.991014	+	0.133757i	$0.0427043\pi$
$599$	14.9623	+	25.9155i	0.611344	+	1.05888i	−0.379670	+	0.925122i	$0.623962\pi$
$600$		0			0
$601$	1.81973	−	3.15186i	0.0742282	−	0.128567i	−0.826522	−	0.562904i	$-0.809684\pi$
$601$	1.81973	−	3.15186i	0.0742282	−	0.128567i	0.900750	+	0.434337i	$0.143017\pi$
$602$	−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	0.930296	−	0.366809i	$-0.119550\pi$
$607$	3.63358	+	6.29355i	0.147482	+	0.255447i	−0.782814	+	0.622256i	$0.786216\pi$
$608$	2.74231	−	4.70912i	0.111215	−	0.190980i
$609$		0			0
$610$	−6.69990	−	6.04169i	−0.271271	−	0.244621i
$611$			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	$-0.229146\pi$
$614$	12.9817	−	14.3960i	0.523898	−	0.580975i
$615$		0			0
$616$	1.31521	−	12.2494i	0.0529915	−	0.493541i
$617$	−15.6751	−	27.1501i	−0.631056	−	1.09302i	−0.987336	−	0.158642i	$-0.949288\pi$
$617$	−15.6751	−	27.1501i	−0.631056	−	1.09302i	0.356280	−	0.934379i	$-0.384045\pi$
$618$		0			0
$619$	1.72589	+	0.996445i	0.0693695	+	0.0400505i	0.534284	−	0.845305i	$-0.320581\pi$
$619$	1.72589	+	0.996445i	0.0693695	+	0.0400505i	−0.464914	+	0.885356i	$0.653915\pi$
$620$	−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
$626$	33.9297	−	10.9964i	1.35610	−	0.439505i
$627$		0			0
$628$	20.4936	+	28.2959i	0.817785	+	1.12913i
$629$			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	$0.599597\pi$
$632$	−6.59010	−	14.8913i	−0.262140	−	0.592345i
$633$		0			0
$634$	−1.07706	−	3.32330i	−0.0427756	−	0.131985i
$635$	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	−0.511570	−	0.859241i	$-0.670936\pi$
$641$	12.3638	−	21.4147i	0.488340	−	0.845829i	0.999910	+	0.0134123i	$0.00426940\pi$
$642$		0			0
$643$	40.0176	−	23.1042i	1.57814	−	0.911141i	0.583023	−	0.812456i	$-0.301870\pi$
$643$	40.0176	−	23.1042i	1.57814	−	0.911141i	0.995119	−	0.0986850i	$-0.0314636\pi$
$644$	−2.15535	−	20.8057i	−0.0849326	−	0.819858i
$645$		0			0
$646$	−5.15636	+	5.71812i	−0.202874	+	0.224976i
$647$	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
$650$	23.5441	−	26.1091i	0.923474	−	1.02408i
$651$		0			0
$652$	17.0438	−	1.76564i	0.667485	−	0.0691476i
$653$	31.8848	−	18.4087i	1.24775	−	0.720389i	0.277090	−	0.960844i	$-0.410630\pi$
$653$	31.8848	−	18.4087i	1.24775	−	0.720389i	0.970660	+	0.240455i	$0.0772968\pi$
$654$		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	$-0.286882\pi$
$659$	6.46565	+	3.73294i	0.251866	+	0.145415i	−0.368752	+	0.929528i	$0.620215\pi$
$660$		0			0
$661$	−2.51984	+	1.45483i	−0.0980102	+	0.0565862i	−0.548204	−	0.836345i	$-0.684688\pi$
$661$	−2.51984	+	1.45483i	−0.0980102	+	0.0565862i	0.450194	+	0.892931i	$0.351355\pi$
$662$	12.3048	+	37.9668i	0.478240	+	1.47562i
$663$		0			0
$664$	−17.1720	+	7.59940i	−0.666402	+	0.294914i
$665$	1.06622			0.0413461
$666$		0			0
$667$		−	21.6505i		−	0.838310i
$668$	−19.3575	+	14.0199i	−0.748965	+	0.542447i
$669$		0			0
$670$	−6.44199	+	2.08781i	−0.248876	+	0.0806592i
$671$	−12.5525	−	21.7415i	−0.484582	−	0.839321i
$672$		0			0
$673$	21.0527	−	36.4643i	0.811522	−	1.40560i	−0.100277	−	0.994960i	$-0.531973\pi$
$673$	21.0527	−	36.4643i	0.811522	−	1.40560i	0.911799	−	0.410637i	$-0.134694\pi$
$674$	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	$-0.0718650\pi$
$677$	32.9941	+	19.0492i	1.26807	+	0.732119i	0.293445	+	0.955976i	$0.405198\pi$
$678$		0			0
$679$	1.98507	+	3.43825i	0.0761801	+	0.131948i
$680$	−1.18785	+	11.0631i	−0.0455518	+	0.424251i
$681$		0			0
$682$	−19.1893	+	21.2799i	−0.734796	+	0.814849i
$683$		−	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
$686$	−19.1579	−	17.2758i	−0.731453	−	0.659593i
$687$		0			0
$688$	−13.1582	−	4.31887i	−0.501653	−	0.164656i
$689$	−6.99676	−	12.1187i	−0.266555	−	0.461687i
$690$		0			0
$691$	−3.38522	−	1.95446i	−0.128780	−	0.0743512i	0.434226	−	0.900804i	$-0.357022\pi$
$691$	−3.38522	−	1.95446i	−0.128780	−	0.0743512i	−0.563006	+	0.826453i	$0.690355\pi$
$692$	−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
$698$	1.48002	+	4.56664i	0.0560196	+	0.172850i
$699$		0			0
$700$	−11.6305	+	8.42354i	−0.439591	+	0.318380i
$701$			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
$704$	4.65211	−	21.4142i	0.175333	−	0.807076i
$705$		0			0
$706$	−1.35404	+	0.438838i	−0.0509601	+	0.0165159i
$707$	−13.0730	+	7.54772i	−0.491662	+	0.283861i
$708$		0			0
$709$	6.84805	+	3.95372i	0.257184	+	0.148485i	0.623049	−	0.782183i	$-0.285894\pi$
$709$	6.84805	+	3.95372i	0.257184	+	0.148485i	−0.365865	+	0.930668i	$0.619227\pi$
$710$	−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
$716$	−6.60217	+	0.683947i	−0.246735	+	0.0255603i
$717$		0			0
$718$	33.0592	+	29.8114i	1.23376	+	1.11255i
$719$	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
$722$	−18.9803	−	17.1156i	−0.706372	−	0.636977i
$723$		0			0
$724$	−29.6669	+	3.07332i	−1.10256	+	0.114219i
$725$	−12.8727	+	7.43204i	−0.478079	+	0.276019i
$726$		0			0
$727$	2.83467	−	4.90979i	0.105132	−	0.182094i	−0.808660	−	0.588276i	$-0.799807\pi$
$727$	2.83467	−	4.90979i	0.105132	−	0.182094i	0.913792	+	0.406182i	$0.133140\pi$
$728$	−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	$-0.741020\pi$
$733$	−10.8544	+	6.26677i	−0.400915	+	0.231469i	0.285964	+	0.958240i	$0.407686\pi$
$734$	23.3190	−	7.55754i	0.860718	−	0.278954i
$735$		0			0
$736$	0.138933	−	37.2056i	0.00512114	−	1.37142i
$737$	−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	$-0.0107369\pi$
$740$	7.05261	−	5.10795i	0.259259	−	0.187772i
$741$		0			0
$742$	1.76226	+	5.43749i	0.0646945	+	0.199616i
$743$	15.6588	+	27.1219i	0.574467	+	0.995006i	0.996099	+	0.0882391i	$0.0281240\pi$
$743$	15.6588	+	27.1219i	0.574467	+	0.995006i	−0.421632	+	0.906767i	$0.638543\pi$
$744$		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	0.924830	−	0.380381i	$-0.124207\pi$
$751$	3.64466	+	6.31274i	0.132996	+	0.230355i	−0.791834	+	0.610736i	$0.790874\pi$
$752$	9.62186	−	29.3148i	0.350873	−	1.06900i
$753$		0			0
$754$	−19.0333	−	17.1634i	−0.693153	−	0.625055i
$755$		−	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	$-0.0748202\pi$
$758$	21.6542	−	24.0134i	0.786518	−	0.872206i
$759$		0			0
$760$	1.88568	+	0.202466i	0.0684009	+	0.00734421i
$761$	−12.5800	−	21.7892i	−0.456025	−	0.789859i	0.542721	−	0.839913i	$-0.317394\pi$
$761$	−12.5800	−	21.7892i	−0.456025	−	0.789859i	−0.998747	+	0.0500541i	$0.984061\pi$
$762$		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	0.605046	−	0.796190i	$-0.293155\pi$
$769$	−10.7318	−	18.5880i	−0.386998	−	0.670300i	−0.992044	+	0.125890i	$0.959821\pi$
$770$	4.07870	−	1.32188i	0.146986	−	0.0476374i
$771$		0			0
$772$	33.1583	−	24.0153i	1.19339	−	0.864330i
$773$		−	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
$776$	2.85786	+	6.45775i	0.102591	+	0.231820i
$777$		0			0
$778$	16.5878	+	51.1820i	0.594701	+	1.83496i
$779$	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	$-0.784453\pi$
$787$	−17.5726	+	10.1455i	−0.626395	+	0.361649i	0.152960	+	0.988232i	$0.451120\pi$
$788$	−40.8686	+	4.23376i	−1.45588	+	0.150821i
$789$		0			0
$790$	3.79534	−	4.20882i	0.135032	−	0.149743i
$791$	−13.8274			−0.491646
$792$		0			0
$793$	−50.4570			−1.79178
$794$	−35.4690	+	39.3332i	−1.25875	+	1.39588i
$795$		0			0
$796$	0.403098	+	3.89112i	0.0142874	+	0.137917i
$797$	−28.8758	+	16.6715i	−1.02283	+	0.590533i	−0.914924	−	0.403627i	$-0.867749\pi$
$797$	−28.8758	+	16.6715i	−1.02283	+	0.590533i	−0.107910	+	0.994161i	$0.534416\pi$
$798$		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
$806$	17.7556	+	54.7852i	0.625413	+	1.92972i
$807$		0			0
$808$	−24.5539	+	10.8662i	−0.863803	+	0.382273i
$809$	−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	$0.664188\pi$
$812$	6.14069	+	8.47854i	0.215496	+	0.297538i
$813$		0			0
$814$	23.0518	−	7.47096i	0.807965	−	0.261857i
$815$	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	$-0.564652\pi$
$821$	−32.9739	−	19.0375i	−1.15080	−	0.664414i	−0.949082	+	0.315030i	$0.897985\pi$
$822$		0			0
$823$	11.2626	+	19.5074i	0.392589	+	0.679984i	0.992790	−	0.119865i	$-0.0382461\pi$
$823$	11.2626	+	19.5074i	0.392589	+	0.679984i	−0.600201	+	0.799849i	$0.704913\pi$
$824$	41.4651	+	4.45211i	1.44451	+	0.155097i
$825$		0			0
$826$	8.03429	−	8.90960i	0.279549	−	0.310004i
$827$			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	$0.772391\pi$
$830$	−4.85342	−	4.37661i	−0.168465	−	0.151914i
$831$		0			0
$832$	−32.5980	−	29.6169i	−1.13013	−	1.02678i
$833$	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	−0.642809	−	0.766027i	$-0.722231\pi$
$839$	9.90604	−	17.1578i	0.341994	−	0.592352i	0.984803	+	0.173675i	$0.0555643\pi$
$840$		0			0
$841$	−9.08210	−	15.7307i	−0.313176	−	0.542436i
$842$	−6.91361	−	21.3321i	−0.238259	−	0.735152i
$843$		0			0
$844$	12.3405	+	17.0387i	0.424778	+	0.586497i
$845$			12.0481i			0.414466i
$846$		0			0
$847$	−5.56028			−0.191053
$848$	2.08415	+	9.95124i	0.0715700	+	0.341727i
$849$		0			0
$850$	34.3334	−	11.1273i	1.17763	−	0.381662i
$851$	35.6304	−	20.5712i	1.22140	−	0.705173i
$852$		0			0
$853$	5.95424	+	3.43768i	0.203869	+	0.117704i	0.598459	−	0.801153i	$-0.295780\pi$
$853$	5.95424	+	3.43768i	0.203869	+	0.117704i	−0.394590	+	0.918857i	$0.629113\pi$
$854$	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	−0.792260	−	0.610184i	$-0.791096\pi$
$857$	3.87316	−	6.70851i	0.132305	−	0.229158i	0.924565	+	0.381025i	$0.124429\pi$
$858$		0			0
$859$	−0.594592	+	0.343288i	−0.0202872	+	0.0117128i	−0.510109	−	0.860110i	$-0.670395\pi$
$859$	−0.594592	+	0.343288i	−0.0202872	+	0.0117128i	0.489822	+	0.871822i	$0.337062\pi$
$860$	−0.496640	−	4.79409i	−0.0169353	−	0.163477i
$861$		0			0
$862$	16.9988	+	15.3288i	0.578980	+	0.522100i
$863$	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
$866$	34.4806	+	31.0931i	1.17170	+	1.05659i
$867$		0			0
$868$	−2.42398	−	23.3988i	−0.0822752	−	0.794206i
$869$	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	$-0.759517\pi$
$877$	−14.7508	+	8.51640i	−0.498100	+	0.287578i	0.229828	+	0.973231i	$0.426183\pi$
$878$	−29.4016	+	9.52888i	−0.992255	+	0.321584i
$879$		0			0
$880$	7.46451	−	1.56334i	0.251629	−	0.0527001i
$881$	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	$0.959545\pi$
$884$	36.5027	+	50.3998i	1.22772	+	1.69513i
$885$		0			0
$886$	−15.3304	−	47.3023i	−0.515035	−	1.58915i
$887$	−7.02719	−	12.1715i	−0.235950	−	0.408677i	0.723598	−	0.690221i	$-0.242487\pi$
$887$	−7.02719	−	12.1715i	−0.235950	−	0.408677i	−0.959548	+	0.281544i	$0.909153\pi$
$888$		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
$896$	10.4982	+	14.6095i	0.350719	+	0.488069i
$897$		0			0
$898$	3.38026	+	3.04818i	0.112801	+	0.101719i
$899$		−	24.3489i		−	0.812081i
$900$		0			0
$901$		−	14.3655i		−	0.478585i
$902$	4.83508	−	5.36184i	0.160990	−	0.178530i
$903$		0			0
$904$	−24.4548	−	2.62571i	−0.813355	−	0.0873300i
$905$	−5.19001	−	8.98936i	−0.172522	−	0.298816i
$906$		0			0
$907$	−39.7958	−	22.9761i	−1.32140	−	0.762910i	−0.337447	−	0.941345i	$-0.609563\pi$
$907$	−39.7958	−	22.9761i	−1.32140	−	0.762910i	−0.983952	+	0.178435i	$0.942897\pi$
$908$	−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	0.0226136	+	0.999744i	$0.492801\pi$
$911$	−25.7911	+	44.6715i	−0.854497	+	1.48003i	−0.877111	+	0.480288i	$0.840532\pi$
$912$		0			0
$913$	−9.09302	−	15.7496i	−0.300935	−	0.521235i
$914$	−10.9109	+	3.53616i	−0.360900	+	0.116966i
$915$		0			0
$916$	−10.1099	−	13.9589i	−0.334042	−	0.461216i
$917$		−	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	$0.613730\pi$
$920$	11.8408	−	5.24012i	0.390381	−	0.172762i
$921$		0			0
$922$	−9.15362	−	28.2437i	−0.301458	−	0.930157i
$923$	−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	−0.892641	−	0.450767i	$-0.851150\pi$
$929$	−1.70516	+	2.95343i	−0.0559446	+	0.0968989i	0.836697	+	0.547666i	$0.184484\pi$
$930$		0			0
$931$	3.73042	−	2.15376i	0.122259	−	0.0705865i
$932$	−4.97770	−	48.0500i	−0.163050	−	1.57393i
$933$		0			0
$934$	−24.6739	+	27.3621i	−0.807356	+	0.895314i
$935$	−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	$0.340288\pi$
$938$	10.3603	−	11.4890i	0.338277	−	0.375130i
$939$		0			0
$940$	10.6806	−	1.10645i	0.348362	−	0.0360883i
$941$	−40.5880	+	23.4335i	−1.32313	+	0.763910i	−0.984227	−	0.176911i	$-0.943389\pi$
$941$	−40.5880	+	23.4335i	−1.32313	+	0.763910i	−0.338904	+	0.940821i	$0.610056\pi$
$942$		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	$-0.535202\pi$
$947$	−31.5821	−	18.2340i	−1.02628	−	0.592524i	−0.915917	+	0.401367i	$0.868535\pi$
$948$		0			0
$949$	13.5024	−	7.79564i	0.438308	−	0.253057i
$950$	−1.89662	−	5.85206i	−0.0615344	−	0.189866i
$951$		0			0
$952$	−10.2868	−	23.2446i	−0.333398	−	0.753362i
$953$	−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
$956$	−6.52751	+	4.72763i	−0.211115	+	0.152903i
$957$		0			0
$958$	23.4394	−	7.59657i	0.757292	−	0.245434i
$959$	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	0.989468	−	0.144749i	$-0.0462374\pi$
$967$	11.4864	+	19.8951i	0.369378	+	0.639782i	−0.620090	+	0.784531i	$0.712904\pi$
$968$	−9.83377	−	1.05585i	−0.316069	−	0.0339364i
$969$		0			0
$970$	−1.64588	+	1.82519i	−0.0528461	+	0.0586034i
$971$		−	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
$974$	31.2313	+	28.1630i	1.00071	+	0.902401i
$975$		0			0
$976$	34.8319	+	11.4327i	1.11494	+	0.365952i
$977$	−19.1024	−	33.0863i	−0.611140	−	1.05853i	−0.991049	−	0.133501i	$-0.957378\pi$
$977$	−19.1024	−	33.0863i	−0.611140	−	1.05853i	0.379909	−	0.925024i	$-0.375955\pi$
$978$		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	−0.158186	−	0.987409i	$-0.550565\pi$
$983$	24.3307	−	42.1420i	0.776028	−	1.34412i	0.934215	−	0.356711i	$-0.116102\pi$
$984$		0			0
$985$	−7.14968	−	12.3836i	−0.227808	−	0.394574i
$986$	−8.11169	−	25.0288i	−0.258329	−	0.797079i
$987$		0			0
$988$	8.59054	−	6.22181i	0.273301	−	0.197942i
$989$		−	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	$0.565076\pi$
$992$	0.156249	−	41.8428i	0.00496091	−	1.32851i
$993$		0			0
$994$	7.87991	−	2.55383i	0.249936	−	0.0810027i
$995$	−1.17905	+	0.680723i	−0.0373783	+	0.0215804i
$996$		0			0
$997$	−21.1161	−	12.1914i	−0.668752	−	0.386104i	0.126851	−	0.991922i	$-0.459513\pi$
$997$	−21.1161	−	12.1914i	−0.668752	−	0.386104i	−0.795604	+	0.605817i	$0.792846\pi$
$998$	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.181.2		16
3.2	odd	2		72.2.n.b.61.7	yes	16
4.3	odd	2		864.2.r.b.721.4		16
8.3	odd	2		864.2.r.b.721.5		16
8.5	even	2	inner	216.2.n.b.181.8		16
9.2	odd	6		648.2.d.j.325.5		8
9.4	even	3	inner	216.2.n.b.37.8		16
9.5	odd	6		72.2.n.b.13.1	✓	16
9.7	even	3		648.2.d.k.325.4		8
12.11	even	2		288.2.r.b.241.7		16
24.5	odd	2		72.2.n.b.61.1	yes	16
24.11	even	2		288.2.r.b.241.2		16
36.7	odd	6		2592.2.d.k.1297.4		8
36.11	even	6		2592.2.d.j.1297.5		8
36.23	even	6		288.2.r.b.49.2		16
36.31	odd	6		864.2.r.b.145.5		16
72.5	odd	6		72.2.n.b.13.7	yes	16
72.11	even	6		2592.2.d.j.1297.4		8
72.13	even	6	inner	216.2.n.b.37.2		16
72.29	odd	6		648.2.d.j.325.6		8
72.43	odd	6		2592.2.d.k.1297.5		8
72.59	even	6		288.2.r.b.49.7		16
72.61	even	6		648.2.d.k.325.3		8
72.67	odd	6		864.2.r.b.145.4		16

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

\(f(q)\)	\(=\)	\(q+(-1.05026 - 0.947078i) q^{2} +(0.206086 + 1.98935i) q^{4} +(-0.602794 + 0.348023i) q^{5} +(0.795065 - 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +O(q^{10})\)	\(q+(-1.05026 - 0.947078i) q^{2} +(0.206086 + 1.98935i) q^{4} +(-0.602794 + 0.348023i) q^{5} +(0.795065 - 1.37709i) q^{7} +(1.66763 - 2.28452i) q^{8} +(0.962695 + 0.205379i) q^{10} +(2.37222 + 1.36960i) q^{11} +(4.76780 - 2.75269i) q^{13} +(-2.13924 + 0.693314i) q^{14} +(-3.91506 + 0.819955i) q^{16} +5.65175 q^{17} -0.963328i q^{19} +(-0.816569 - 1.12745i) q^{20} +(-1.19433 - 3.68512i) q^{22} +(-3.28857 - 5.69597i) q^{23} +(-2.25776 + 3.91055i) q^{25} +(-7.61444 - 1.62444i) q^{26} +(2.90338 + 1.29787i) q^{28} +(2.85076 + 1.64589i) q^{29} +(-3.69844 - 6.40589i) q^{31} +(4.88838 + 2.84670i) q^{32} +(-5.93580 - 5.35265i) q^{34} +1.10680i q^{35} +6.25538i q^{37} +(-0.912347 + 1.01174i) q^{38} +(-0.210173 + 1.95747i) q^{40} +(0.931886 + 1.61407i) q^{41} +(2.99838 + 1.73111i) q^{43} +(-2.23574 + 5.00145i) q^{44} +(-1.94068 + 9.09677i) q^{46} +(-3.85668 + 6.67997i) q^{47} +(2.23574 + 3.87242i) q^{49} +(6.07483 - 1.96882i) q^{50} +(6.45866 + 8.91756i) q^{52} -2.54179i q^{53} -1.90662 q^{55} +(-1.82011 - 4.11282i) q^{56} +(-1.43525 - 4.42850i) q^{58} +(-4.62019 + 2.66747i) q^{59} +(-7.93715 - 4.58252i) q^{61} +(-2.18256 + 10.2305i) q^{62} +(-2.43802 - 7.61945i) q^{64} +(-1.91600 + 3.31861i) q^{65} +(-5.95780 + 3.43974i) q^{67} +(1.16474 + 11.2433i) q^{68} +(1.04823 - 1.16243i) q^{70} -3.68351 q^{71} +2.83201 q^{73} +(5.92433 - 6.56976i) q^{74} +(1.91640 - 0.198528i) q^{76} +(3.77214 - 2.17785i) q^{77} +(2.87870 - 4.98605i) q^{79} +(2.07461 - 1.85680i) q^{80} +(0.549933 - 2.57776i) q^{82} +(-5.74968 - 3.31958i) q^{83} +(-3.40684 + 1.96694i) q^{85} +(-1.50957 - 4.65781i) q^{86} +(7.08487 - 3.13539i) q^{88} +2.98701 q^{89} -8.75427i q^{91} +(10.6536 - 7.71598i) q^{92} +(10.3770 - 3.36312i) q^{94} +(0.335261 + 0.580689i) q^{95} +(-1.24837 + 2.16224i) q^{97} +(1.31938 - 6.18447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) \) 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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