LMFDB - Embedded newform 720.2.z.g.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.2
Root			$0.482716 - 1.32928i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19301 - 0.759419i) q^{2} +(0.846564 + 1.81200i) q^{4} +(-2.17104 - 0.535339i) q^{5} +(-2.13436 - 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} +O(q^{10})$	\(q+(-1.19301 - 0.759419i) q^{2} +(0.846564 + 1.81200i) q^{4} +(-2.17104 - 0.535339i) q^{5} +(-2.13436 - 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} +(2.18353 + 2.28740i) q^{10} +(-2.17074 + 2.17074i) q^{11} -1.54663i q^{13} +(0.925449 + 4.16720i) q^{14} +(-2.56666 + 3.06794i) q^{16} +(3.86386 + 3.86386i) q^{17} +(0.0136865 - 0.0136865i) q^{19} +(-0.867892 - 4.38711i) q^{20} +(4.23822 - 0.941219i) q^{22} +(3.15240 - 3.15240i) q^{23} +(4.42682 + 2.32449i) q^{25} +(-1.17454 + 1.84515i) q^{26} +(2.06058 - 5.67434i) q^{28} +(-3.33787 - 3.33787i) q^{29} +8.92639i q^{31} +(5.39191 - 1.71093i) q^{32} +(-1.67535 - 7.54394i) q^{34} +(3.49118 + 5.77640i) q^{35} +7.24737i q^{37} +(-0.0267220 + 0.00593441i) q^{38} +(-2.29625 + 5.89298i) q^{40} +10.3771i q^{41} +2.02975i q^{43} +(-5.77103 - 2.09570i) q^{44} +(-6.15484 + 1.36686i) q^{46} +(-3.34313 + 3.34313i) q^{47} +2.11103i q^{49} +(-3.51600 - 6.13496i) q^{50} +(2.80249 - 1.30932i) q^{52} +7.30702 q^{53} +(5.87483 - 3.55067i) q^{55} +(-6.76751 + 5.20472i) q^{56} +(1.44728 + 6.51696i) q^{58} +(3.52732 + 3.52732i) q^{59} +(1.41629 - 1.41629i) q^{61} +(6.77887 - 10.6493i) q^{62} +(-7.73194 - 2.05356i) q^{64} +(-0.827973 + 3.35780i) q^{65} +0.748197i q^{67} +(-3.73030 + 10.2723i) q^{68} +(0.221682 - 9.54260i) q^{70} +0.269603 q^{71} +(0.811870 + 0.811870i) q^{73} +(5.50380 - 8.64622i) q^{74} +(0.0363865 + 0.0132134i) q^{76} +9.26628 q^{77} -2.80567 q^{79} +(7.21470 - 5.28659i) q^{80} +(7.88056 - 12.3800i) q^{82} -12.8279 q^{83} +(-6.32012 - 10.4571i) q^{85} +(1.54143 - 2.42152i) q^{86} +(5.29341 + 6.88283i) q^{88} +13.3732 q^{89} +(-3.30108 + 3.30108i) q^{91} +(8.38083 + 3.04342i) q^{92} +(6.52724 - 1.44956i) q^{94} +(-0.0370409 + 0.0223871i) q^{95} +(6.33466 + 6.33466i) q^{97} +(1.60315 - 2.51848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.19301	−	0.759419i	−0.843588	−	0.536991i
$2$	−1.19301	−	0.759419i	−0.843588	−	0.536991i
$3$		0			0
$3$		0			0
$4$	0.846564	+	1.81200i	0.423282	+	0.905998i
$5$	−2.17104	−	0.535339i	−0.970918	−	0.239411i
$5$	−2.17104	−	0.535339i	−0.970918	−	0.239411i
$6$		0			0
$7$	−2.13436	−	2.13436i	−0.806714	−	0.806714i	0.177421	−	0.984135i	$-0.443225\pi$
$7$	−2.13436	−	2.13436i	−0.806714	−	0.806714i	−0.984135	+	0.177421i	$0.943225\pi$
$8$	0.366101	−	2.80463i	0.129436	−	0.991588i
$9$		0			0
$10$	2.18353	+	2.28740i	0.690494	+	0.723338i
$11$	−2.17074	+	2.17074i	−0.654501	+	0.654501i	−0.954074	−	0.299572i	$-0.903156\pi$
$11$	−2.17074	+	2.17074i	−0.654501	+	0.654501i	0.299572	+	0.954074i	$0.403156\pi$
$12$		0			0
$13$		−	1.54663i		−	0.428958i	−0.976729	−	0.214479i	$-0.931195\pi$
$13$		−	1.54663i		−	0.428958i	0.976729	−	0.214479i	$-0.0688054\pi$
$14$	0.925449	+	4.16720i	0.247337	+	1.11373i
$15$		0			0
$16$	−2.56666	+	3.06794i	−0.641664	+	0.766986i
$17$	3.86386	+	3.86386i	0.937125	+	0.937125i	0.998137	−	0.0610123i	$-0.0194329\pi$
$17$	3.86386	+	3.86386i	0.937125	+	0.937125i	−0.0610123	+	0.998137i	$0.519433\pi$
$18$		0			0
$19$	0.0136865	−	0.0136865i	0.00313991	−	0.00313991i	−0.705535	−	0.708675i	$-0.749293\pi$
$19$	0.0136865	−	0.0136865i	0.00313991	−	0.00313991i	0.708675	+	0.705535i	$0.249293\pi$
$20$	−0.867892	−	4.38711i	−0.194067	−	0.980988i
$21$		0			0
$22$	4.23822	−	0.941219i	0.903591	−	0.200669i
$23$	3.15240	−	3.15240i	0.657320	−	0.657320i	−0.297425	−	0.954745i	$-0.596128\pi$
$23$	3.15240	−	3.15240i	0.657320	−	0.657320i	0.954745	+	0.297425i	$0.0961279\pi$
$24$		0			0
$25$	4.42682	+	2.32449i	0.885365	+	0.464897i
$26$	−1.17454	+	1.84515i	−0.230347	+	0.361864i
$27$		0			0
$28$	2.06058	−	5.67434i	0.389413	−	1.07235i
$29$	−3.33787	−	3.33787i	−0.619826	−	0.619826i	0.325660	−	0.945487i	$-0.394413\pi$
$29$	−3.33787	−	3.33787i	−0.619826	−	0.619826i	−0.945487	+	0.325660i	$0.894413\pi$
$30$		0			0
$31$			8.92639i			1.60323i	0.597843	+	0.801613i	$0.296025\pi$
$31$			8.92639i			1.60323i	−0.597843	+	0.801613i	$0.703975\pi$
$32$	5.39191	−	1.71093i	0.953164	−	0.302452i
$33$		0			0
$34$	−1.67535	−	7.54394i	−0.287320	−	1.29377i
$35$	3.49118	+	5.77640i	0.590117	+	0.976390i
$36$		0			0
$37$			7.24737i			1.19146i	0.803184	+	0.595730i	$0.203137\pi$
$37$			7.24737i			1.19146i	−0.803184	+	0.595730i	$0.796863\pi$
$38$	−0.0267220	+	0.00593441i	−0.00433489	+	0.000962688i
$39$		0			0
$40$	−2.29625	+	5.89298i	−0.363069	+	0.931762i
$41$			10.3771i			1.62063i	0.585996	+	0.810314i	$0.300704\pi$
$41$			10.3771i			1.62063i	−0.585996	+	0.810314i	$0.699296\pi$
$42$		0			0
$43$			2.02975i			0.309534i	0.987951	+	0.154767i	$0.0494627\pi$
$43$			2.02975i			0.309534i	−0.987951	+	0.154767i	$0.950537\pi$
$44$	−5.77103	−	2.09570i	−0.870015	−	0.315938i
$45$		0			0
$46$	−6.15484	+	1.36686i	−0.907482	+	0.201533i
$47$	−3.34313	+	3.34313i	−0.487646	+	0.487646i	−0.907563	−	0.419917i	$-0.862059\pi$
$47$	−3.34313	+	3.34313i	−0.487646	+	0.487646i	0.419917	+	0.907563i	$0.362059\pi$
$48$		0			0
$49$			2.11103i			0.301575i
$50$	−3.51600	−	6.13496i	−0.497238	−	0.867614i
$51$		0			0
$52$	2.80249	−	1.30932i	0.388635	−	0.181570i
$53$	7.30702			1.00370			0.501848	−	0.864956i	$-0.332654\pi$
$53$	7.30702			1.00370			0.501848	+	0.864956i	$0.332654\pi$
$54$		0			0
$55$	5.87483	−	3.55067i	0.792162	−	0.478772i
$56$	−6.76751	+	5.20472i	−0.904346	+	0.695510i
$57$		0			0
$58$	1.44728	+	6.51696i	0.190037	+	0.855719i
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	0.898399	−	0.439181i	$-0.144731\pi$
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	−0.439181	+	0.898399i	$0.644731\pi$
$60$		0			0
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	−0.610601	−	0.791939i	$-0.709072\pi$
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	0.791939	+	0.610601i	$0.209072\pi$
$62$	6.77887	−	10.6493i	0.860918	−	1.35246i
$63$		0			0
$64$	−7.73194	−	2.05356i	−0.966492	−	0.256695i
$65$	−0.827973	+	3.35780i	−0.102697	+	0.416484i
$66$		0			0
$67$			0.748197i			0.0914068i	0.998955	+	0.0457034i	$0.0145529\pi$
$67$			0.748197i			0.0914068i	−0.998955	+	0.0457034i	$0.985447\pi$
$68$	−3.73030	+	10.2723i	−0.452365	+	1.24570i
$69$		0			0
$70$	0.221682	−	9.54260i	0.0264961	−	1.14056i
$71$	0.269603			0.0319960			0.0159980	−	0.999872i	$-0.494907\pi$
$71$	0.269603			0.0319960			0.0159980	+	0.999872i	$0.494907\pi$
$72$		0			0
$73$	0.811870	+	0.811870i	0.0950222	+	0.0950222i	0.753020	−	0.657998i	$-0.228596\pi$
$73$	0.811870	+	0.811870i	0.0950222	+	0.0950222i	−0.657998	+	0.753020i	$0.728596\pi$
$74$	5.50380	−	8.64622i	0.639803	−	1.00510i
$75$		0			0
$76$	0.0363865	+	0.0132134i	0.00417381	+	0.00151568i
$77$	9.26628			1.05599
$78$		0			0
$79$	−2.80567			−0.315662			−0.157831	−	0.987466i	$-0.550450\pi$
$79$	−2.80567			−0.315662			−0.157831	+	0.987466i	$0.550450\pi$
$80$	7.21470	−	5.28659i	0.806628	−	0.591059i
$81$		0			0
$82$	7.88056	−	12.3800i	0.870262	−	1.36714i
$83$	−12.8279			−1.40804			−0.704022	−	0.710178i	$-0.748614\pi$
$83$	−12.8279			−1.40804			−0.704022	+	0.710178i	$0.748614\pi$
$84$		0			0
$85$	−6.32012	−	10.4571i	−0.685514	−	1.13423i
$86$	1.54143	−	2.42152i	0.166217	−	0.261119i
$87$		0			0
$88$	5.29341	+	6.88283i	0.564279	+	0.733712i
$89$	13.3732			1.41755			0.708777	−	0.705432i	$-0.249247\pi$
$89$	13.3732			1.41755			0.708777	+	0.705432i	$0.249247\pi$
$90$		0			0
$91$	−3.30108	+	3.30108i	−0.346047	+	0.346047i
$92$	8.38083	+	3.04342i	0.873762	+	0.317299i
$93$		0			0
$94$	6.52724	−	1.44956i	0.673233	−	0.149511i
$95$	−0.0370409	+	0.0223871i	−0.00380032	+	0.00229686i
$96$		0			0
$97$	6.33466	+	6.33466i	0.643187	+	0.643187i	0.951338	−	0.308151i	$-0.0997101\pi$
$97$	6.33466	+	6.33466i	0.643187	+	0.643187i	−0.308151	+	0.951338i	$0.599710\pi$
$98$	1.60315	−	2.51848i	0.161943	−	0.254405i
$99$		0			0
$100$	−0.464366	+	9.98921i	−0.0464366	+	0.998921i
$101$	3.78129	+	3.78129i	0.376252	+	0.376252i	0.869748	−	0.493496i	$-0.164281\pi$
$101$	3.78129	+	3.78129i	0.376252	+	0.376252i	−0.493496	+	0.869748i	$0.664281\pi$
$102$		0			0
$103$	10.7199	−	10.7199i	1.05626	−	1.05626i	0.0579430	−	0.998320i	$-0.481546\pi$
$103$	10.7199	−	10.7199i	1.05626	−	1.05626i	0.998320	−	0.0579430i	$-0.0184542\pi$
$104$	−4.33774	−	0.566224i	−0.425350	−	0.0555228i
$105$		0			0
$106$	−8.71737	−	5.54909i	−0.846706	−	0.538975i
$107$	−10.9109			−1.05479			−0.527397	−	0.849619i	$-0.676832\pi$
$107$	−10.9109			−1.05479			−0.527397	+	0.849619i	$0.676832\pi$
$108$		0			0
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	0.992870	−	0.119200i	$-0.0380329\pi$
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	−0.119200	+	0.992870i	$0.538033\pi$
$110$	−9.70520	−	0.225460i	−0.925355	−	0.0214968i
$111$		0			0
$112$	12.0263	−	1.06993i	1.13638	−	0.101098i
$113$	−4.88810	+	4.88810i	−0.459834	+	0.459834i	−0.898601	−	0.438767i	$-0.855415\pi$
$113$	−4.88810	+	4.88810i	−0.459834	+	0.459834i	0.438767	+	0.898601i	$0.355415\pi$
$114$		0			0
$115$	−8.53157	+	5.15637i	−0.795573	+	0.480834i
$116$	3.22248	−	8.87392i	0.299200	−	0.823923i
$117$		0			0
$118$	−1.52943	−	6.88685i	−0.140795	−	0.633986i
$119$		−	16.4938i		−	1.51198i
$120$		0			0
$121$			1.57582i			0.143256i
$122$	−2.76522	+	0.614097i	−0.250351	+	0.0555978i
$123$		0			0
$124$	−16.1746	+	7.55676i	−1.45252	+	0.678617i
$125$	−8.36642	−	7.41640i	−0.748315	−	0.663343i
$126$		0			0
$127$	1.38586	−	1.38586i	0.122975	−	0.122975i	−0.642941	−	0.765916i	$-0.722286\pi$
$127$	1.38586	−	1.38586i	0.122975	−	0.122975i	0.765916	+	0.642941i	$0.222286\pi$
$128$	7.66480	+	8.32171i	0.677479	+	0.735542i
$129$		0			0
$130$	3.53776	−	3.37712i	0.310282	−	0.296193i
$131$	3.52096	+	3.52096i	0.307627	+	0.307627i	0.843989	−	0.536361i	$-0.180202\pi$
$131$	3.52096	+	3.52096i	0.307627	+	0.307627i	−0.536361	+	0.843989i	$0.680202\pi$
$132$		0			0
$133$	−0.0584241			−0.00506601
$134$	0.568195	−	0.892609i	0.0490846	−	0.0771097i
$135$		0			0
$136$	12.2513	−	9.42216i	1.05054	−	0.807943i
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	−0.424732	−	0.905319i	$-0.639632\pi$
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	0.905319	+	0.424732i	$0.139632\pi$
$138$		0			0
$139$	−12.1022	−	12.1022i	−1.02650	−	1.02650i	−0.999639	−	0.0268584i	$-0.991450\pi$
$139$	−12.1022	−	12.1022i	−1.02650	−	1.02650i	−0.0268584	−	0.999639i	$-0.508550\pi$
$140$	−7.51130	+	11.2161i	−0.634821	+	0.947933i
$141$		0			0
$142$	−0.321641	−	0.204742i	−0.0269915	−	0.0171816i
$143$	3.35733	+	3.35733i	0.280754	+	0.280754i
$144$		0			0
$145$	5.45975	+	9.03353i	0.453408	+	0.750194i
$146$	−0.352023	−	1.58512i	−0.0291336	−	0.131186i
$147$		0			0
$148$	−13.1322	+	6.13537i	−1.07946	+	0.504324i
$149$	−13.5590	+	13.5590i	−1.11080	+	1.11080i	−0.117757	+	0.993042i	$0.537570\pi$
$149$	−13.5590	+	13.5590i	−1.11080	+	1.11080i	−0.993042	+	0.117757i	$0.962430\pi$
$150$		0			0
$151$	−20.7185			−1.68605			−0.843025	−	0.537874i	$-0.819228\pi$
$151$	−20.7185			−1.68605			−0.843025	+	0.537874i	$0.819228\pi$
$152$	−0.0333751	−	0.0433964i	−0.00270707	−	0.00351991i
$153$		0			0
$154$	−11.0548	−	7.03699i	−0.890821	−	0.567057i
$155$	4.77865	−	19.3795i	0.383830	−	1.55660i
$156$		0			0
$157$	−5.72312			−0.456755			−0.228377	−	0.973573i	$-0.573342\pi$
$157$	−5.72312			−0.456755			−0.228377	+	0.973573i	$0.573342\pi$
$158$	3.34720	+	2.13068i	0.266289	+	0.169508i
$159$		0			0
$160$	−12.6220	+	0.827992i	−0.997855	+	0.0654585i
$161$	−13.4567			−1.06054
$162$		0			0
$163$	−17.9900			−1.40909			−0.704543	−	0.709662i	$-0.748848\pi$
$163$	−17.9900			−1.40909			−0.704543	+	0.709662i	$0.748848\pi$
$164$	−18.8032	+	8.78487i	−1.46829	+	0.685983i
$165$		0			0
$166$	15.3039	+	9.74175i	1.18781	+	0.756106i
$167$	−2.39642	−	2.39642i	−0.185441	−	0.185441i	0.608281	−	0.793722i	$-0.291859\pi$
$167$	−2.39642	−	2.39642i	−0.185441	−	0.185441i	−0.793722	+	0.608281i	$0.791859\pi$
$168$		0			0
$169$	10.6079			0.815995
$170$	−0.401314	+	17.2751i	−0.0307794	+	1.32494i
$171$		0			0
$172$	−3.67790	+	1.71832i	−0.280437	+	0.131020i
$173$		−	9.45205i		−	0.718626i	−0.933217	−	0.359313i	$-0.883011\pi$
$173$		−	9.45205i		−	0.718626i	0.933217	−	0.359313i	$-0.116989\pi$
$174$		0			0
$175$	−4.48716	−	14.4098i	−0.339197	−	1.08928i
$176$	−1.08816	−	12.2312i	−0.0820230	−	0.921963i
$177$		0			0
$178$	−15.9544	−	10.1559i	−1.19583	−	0.761213i
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	−0.993728	−	0.111824i	$-0.964331\pi$
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	0.111824	+	0.993728i	$0.464331\pi$
$180$		0			0
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	0.795225	−	0.606314i	$-0.207352\pi$
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	−0.606314	+	0.795225i	$0.707352\pi$
$182$	6.44513	−	1.43133i	0.477745	−	0.106097i
$183$		0			0
$184$	−7.68722	−	9.99541i	−0.566709	−	0.736871i
$185$	3.87980	−	15.7343i	0.285249	−	1.15681i
$186$		0			0
$187$	−16.7748			−1.22670
$188$	−8.88791	−	3.22756i	−0.648217	−	0.235394i
$189$		0			0
$190$	0.0611915	+	0.00142153i	0.00443930	+	0.000103129i
$191$			5.46421i			0.395376i	0.980265	+	0.197688i	$0.0633433\pi$
$191$			5.46421i			0.395376i	−0.980265	+	0.197688i	$0.936657\pi$
$192$		0			0
$193$	4.82485	−	4.82485i	0.347300	−	0.347300i	−0.511803	−	0.859103i	$-0.671022\pi$
$193$	4.82485	−	4.82485i	0.347300	−	0.347300i	0.859103	+	0.511803i	$0.171022\pi$
$194$	−2.74667	−	12.3680i	−0.197200	−	0.887970i
$195$		0			0
$196$	−3.82517	+	1.78712i	−0.273226	+	0.127651i
$197$		−	2.94582i		−	0.209881i	−0.994478	−	0.104941i	$-0.966535\pi$
$197$		−	2.94582i		−	0.209881i	0.994478	−	0.104941i	$-0.0334653\pi$
$198$		0			0
$199$			2.14620i			0.152140i	0.997102	+	0.0760700i	$0.0242372\pi$
$199$			2.14620i			0.152140i	−0.997102	+	0.0760700i	$0.975763\pi$
$200$	8.14000	−	11.5646i	0.575585	−	0.817742i
$201$		0			0
$202$	−1.63955	−	7.38271i	−0.115358	−	0.519446i
$203$			14.2485i			1.00005i
$204$		0			0
$205$	5.55526	−	22.5291i	0.387996	−	1.57350i
$206$	−20.9299	+	4.64809i	−1.45825	+	0.323848i
$207$		0			0
$208$	4.74498	+	3.96967i	0.329005	+	0.275247i
$209$			0.0594197i			0.00411014i
$210$		0			0
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	0.871708	−	0.490025i	$-0.163012\pi$
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	−0.490025	+	0.871708i	$0.663012\pi$
$212$	6.18586	+	13.2403i	0.424847	+	0.909346i
$213$		0			0
$214$	13.0168	+	8.28593i	0.889812	+	0.566414i
$215$	1.08661	−	4.40667i	0.0741059	−	0.300532i
$216$		0			0
$217$	19.0522	−	19.0522i	1.29335	−	1.29335i
$218$	−3.95498	−	17.8089i	−0.267865	−	1.20617i
$219$		0			0
$220$	11.4072	+	7.63930i	0.769075	+	0.515041i
$221$	5.97597	−	5.97597i	0.401988	−	0.401988i
$222$		0			0
$223$	1.16163	+	1.16163i	0.0777882	+	0.0777882i	0.744930	−	0.667142i	$-0.232483\pi$
$223$	1.16163	+	1.16163i	0.0777882	+	0.0777882i	−0.667142	+	0.744930i	$0.732483\pi$
$224$	−15.1601	−	7.85656i	−1.01292	−	0.524939i
$225$		0			0
$226$	9.54369	−	2.11945i	0.634837	−	0.140984i
$227$		−	12.8161i		−	0.850632i	−0.905045	−	0.425316i	$-0.860163\pi$
$227$		−	12.8161i		−	0.850632i	0.905045	−	0.425316i	$-0.139837\pi$
$228$		0			0
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	−0.674093	−	0.738647i	$-0.735465\pi$
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	0.738647	+	0.674093i	$0.235465\pi$
$230$	14.0941	+	0.327418i	0.929340	+	0.0215893i
$231$		0			0
$232$	−10.5835	+	8.13950i	−0.694840	+	0.534384i
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	0.716990	−	0.697083i	$-0.245519\pi$
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	−0.697083	+	0.716990i	$0.745519\pi$
$234$		0			0
$235$	9.04777	−	5.46836i	0.590212	−	0.356716i
$236$	−3.40538	+	9.37758i	−0.221671	+	0.610429i
$237$		0			0
$238$	−12.5257	+	19.6773i	−0.811921	+	1.27549i
$239$	12.5096			0.809178			0.404589	−	0.914499i	$-0.367415\pi$
$239$	12.5096			0.809178			0.404589	+	0.914499i	$0.367415\pi$
$240$		0			0
$241$	−19.5775			−1.26110			−0.630548	−	0.776150i	$-0.717170\pi$
$241$	−19.5775			−1.26110			−0.630548	+	0.776150i	$0.717170\pi$
$242$	1.19671	−	1.87997i	0.0769273	−	0.120849i
$243$		0			0
$244$	3.76530	+	1.36733i	0.241049	+	0.0875346i
$245$	1.13012	−	4.58312i	0.0722004	−	0.292805i
$246$		0			0
$247$	−0.0211680	−	0.0211680i	−0.00134689	−	0.00134689i
$248$	25.0352	+	3.26796i	1.58974	+	0.207516i
$249$		0			0
$250$	4.34910	+	15.2015i	0.275061	+	0.961427i
$251$	−5.17763	+	5.17763i	−0.326809	+	0.326809i	−0.851372	−	0.524563i	$-0.824229\pi$
$251$	−5.17763	+	5.17763i	−0.326809	+	0.326809i	0.524563	+	0.851372i	$0.324229\pi$
$252$		0			0
$253$			13.6860i			0.860433i
$254$	−2.70580	+	0.600902i	−0.169777	+	0.0377040i
$255$		0			0
$256$	−2.82454	−	15.7487i	−0.176534	−	0.984295i
$257$	14.7989	+	14.7989i	0.923131	+	0.923131i	0.997249	−	0.0741183i	$-0.0236142\pi$
$257$	14.7989	+	14.7989i	0.923131	+	0.923131i	−0.0741183	+	0.997249i	$0.523614\pi$
$258$		0			0
$259$	15.4685	−	15.4685i	0.961168	−	0.961168i
$260$	−6.78525	+	1.34231i	−0.420803	+	0.0832465i
$261$		0			0
$262$	−1.52667	−	6.87443i	−0.0943178	−	0.424704i
$263$	−11.7906	+	11.7906i	−0.727038	+	0.727038i	−0.970029	−	0.242991i	$-0.921871\pi$
$263$	−11.7906	+	11.7906i	−0.727038	+	0.727038i	0.242991	+	0.970029i	$0.421871\pi$
$264$		0			0
$265$	−15.8638	−	3.91173i	−0.974507	−	0.240296i
$266$	0.0697008	+	0.0443684i	0.00427363	+	0.00272040i
$267$		0			0
$268$	−1.35573	+	0.633397i	−0.0828144	+	0.0386909i
$269$	−2.10121	−	2.10121i	−0.128113	−	0.128113i	0.640143	−	0.768256i	$-0.278875\pi$
$269$	−2.10121	−	2.10121i	−0.128113	−	0.128113i	−0.768256	+	0.640143i	$0.778875\pi$
$270$		0			0
$271$			18.8596i			1.14564i	0.819683	+	0.572818i	$0.194150\pi$
$271$			18.8596i			1.14564i	−0.819683	+	0.572818i	$0.805850\pi$
$272$	−21.7713	+	1.93690i	−1.32008	+	0.117442i
$273$		0			0
$274$	−10.9827	+	2.43902i	−0.663488	+	0.147347i
$275$	−14.6553	+	4.56362i	−0.883748	+	0.275197i
$276$		0			0
$277$			9.91909i			0.595980i	0.954569	+	0.297990i	$0.0963162\pi$
$277$			9.91909i			0.595980i	−0.954569	+	0.297990i	$0.903684\pi$
$278$	5.24746	+	23.6288i	0.314722	+	1.41716i
$279$		0			0
$280$	17.4788	−	7.67673i	1.04456	−	0.458773i
$281$			9.31434i			0.555647i	0.960632	+	0.277823i	$0.0896130\pi$
$281$			9.31434i			0.555647i	−0.960632	+	0.277823i	$0.910387\pi$
$282$		0			0
$283$			3.42364i			0.203514i	0.994809	+	0.101757i	$0.0324465\pi$
$283$			3.42364i			0.203514i	−0.994809	+	0.101757i	$0.967554\pi$
$284$	0.228237	+	0.488520i	0.0135434	+	0.0289883i
$285$		0			0
$286$	−1.45572	−	6.55496i	−0.0860785	−	0.387603i
$287$	22.1485	−	22.1485i	1.30738	−	1.30738i
$288$		0			0
$289$			12.8589i			0.756405i
$290$	0.346682	−	14.9234i	0.0203579	−	0.876330i
$291$		0			0
$292$	−0.783805	+	2.15841i	−0.0458687	+	0.126311i
$293$	−2.66471			−0.155674			−0.0778369	−	0.996966i	$-0.524801\pi$
$293$	−2.66471			−0.155674			−0.0778369	+	0.996966i	$0.524801\pi$
$294$		0			0
$295$	−5.76963	−	9.54626i	−0.335921	−	0.555804i
$296$	20.3262	+	2.65327i	1.18144	+	0.154218i
$297$		0			0
$298$	26.4731	−	5.87912i	1.53355	−	0.340568i
$299$	−4.87559	−	4.87559i	−0.281963	−	0.281963i
$300$		0			0
$301$	4.33223	−	4.33223i	0.249706	−	0.249706i
$302$	24.7175	+	15.7341i	1.42233	+	0.905393i
$303$		0			0
$304$	0.00686086	+	0.0771181i	0.000393497	+	0.00442303i
$305$	−3.83303	+	2.31663i	−0.219478	+	0.132650i
$306$		0			0
$307$			10.5554i			0.602430i	0.953556	+	0.301215i	$0.0973922\pi$
$307$			10.5554i			0.602430i	−0.953556	+	0.301215i	$0.902608\pi$
$308$	7.84450	+	16.7905i	0.446982	+	0.956725i
$309$		0			0
$310$	−20.4182	+	19.4911i	−1.15968	+	1.10702i
$311$	20.4762			1.16110			0.580550	−	0.814225i	$-0.302838\pi$
$311$	20.4762			1.16110			0.580550	+	0.814225i	$0.302838\pi$
$312$		0			0
$313$	−2.82393	−	2.82393i	−0.159618	−	0.159618i	0.622780	−	0.782397i	$-0.286003\pi$
$313$	−2.82393	−	2.82393i	−0.159618	−	0.159618i	−0.782397	+	0.622780i	$0.786003\pi$
$314$	6.82776	+	4.34625i	0.385313	+	0.245273i
$315$		0			0
$316$	−2.37518	−	5.08385i	−0.133614	−	0.285989i
$317$	−20.2533			−1.13754			−0.568769	−	0.822497i	$-0.692580\pi$
$317$	−20.2533			−1.13754			−0.568769	+	0.822497i	$0.692580\pi$
$318$		0			0
$319$	14.4913			0.811354
$320$	15.6870	+	8.59757i	0.876930	+	0.480619i
$321$		0			0
$322$	16.0541	+	10.2193i	0.894658	+	0.569499i
$323$	0.105766			0.00588497
$324$		0			0
$325$	3.59512	−	6.84667i	0.199422	−	0.379785i
$326$	21.4623	+	13.6620i	1.18869	+	0.756666i
$327$		0			0
$328$	29.1039	+	3.79907i	1.60700	+	0.209768i
$329$	14.2709			0.786781
$330$		0			0
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.0741908	−	0.997244i	$-0.476363\pi$
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.997244	−	0.0741908i	$-0.0236374\pi$
$332$	−10.8596	−	23.2441i	−0.596000	−	1.27569i
$333$		0			0
$334$	1.03908	+	4.67885i	0.0568557	+	0.256016i
$335$	0.400539	−	1.62437i	0.0218838	−	0.0887485i
$336$		0			0
$337$	−5.89449	−	5.89449i	−0.321093	−	0.321093i	0.528093	−	0.849186i	$-0.322907\pi$
$337$	−5.89449	−	5.89449i	−0.321093	−	0.321093i	−0.849186	+	0.528093i	$0.822907\pi$
$338$	−12.6554	−	8.05587i	−0.688364	−	0.438181i
$339$		0			0
$340$	13.5978	−	20.3046i	0.737444	−	1.10117i
$341$	−19.3768	−	19.3768i	−1.04931	−	1.04931i
$342$		0			0
$343$	−10.4349	+	10.4349i	−0.563429	+	0.563429i
$344$	5.69271	+	0.743095i	0.306930	+	0.0400650i
$345$		0			0
$346$	−7.17807	+	11.2764i	−0.385895	+	0.606225i
$347$	11.4626			0.615346			0.307673	−	0.951492i	$-0.400450\pi$
$347$	11.4626			0.615346			0.307673	+	0.951492i	$0.400450\pi$
$348$		0			0
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	0.715563	−	0.698548i	$-0.246170\pi$
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	−0.698548	+	0.715563i	$0.746170\pi$
$350$	−5.58981	+	20.5987i	−0.298788	+	1.10105i
$351$		0			0
$352$	−7.99044	+	15.4184i	−0.425892	+	0.821803i
$353$	18.4551	−	18.4551i	0.982266	−	0.982266i	−0.0175800	−	0.999845i	$-0.505596\pi$
$353$	18.4551	−	18.4551i	0.982266	−	0.982266i	0.999845	+	0.0175800i	$0.00559616\pi$
$354$		0			0
$355$	−0.585320	−	0.144329i	−0.0310655	−	0.00766020i
$356$	11.3213	+	24.2321i	0.600026	+	1.28430i
$357$		0			0
$358$	23.0369	−	5.11602i	1.21754	−	0.270390i
$359$		−	15.5802i		−	0.822292i	−0.911569	−	0.411146i	$-0.865129\pi$
$359$		−	15.5802i		−	0.822292i	0.911569	−	0.411146i	$-0.134871\pi$
$360$		0			0
$361$			18.9996i			0.999980i
$362$	−1.10200	−	4.96220i	−0.0579199	−	0.260808i
$363$		0			0
$364$	−8.77611	−	3.18696i	−0.459993	−	0.167042i
$365$	−1.32798	−	2.19723i	−0.0695095	−	0.115008i
$366$		0			0
$367$	−5.37489	+	5.37489i	−0.280567	+	0.280567i	−0.833335	−	0.552768i	$-0.813572\pi$
$367$	−5.37489	+	5.37489i	−0.280567	+	0.280567i	0.552768	+	0.833335i	$0.313572\pi$
$368$	1.58025	+	17.7625i	0.0823762	+	0.925933i
$369$		0			0
$370$	−16.5776	+	15.8249i	−0.861829	+	0.822696i
$371$	−15.5958	−	15.5958i	−0.809696	−	0.809696i
$372$		0			0
$373$	3.24424			0.167980			0.0839902	−	0.996467i	$-0.473234\pi$
$373$	3.24424			0.167980			0.0839902	+	0.996467i	$0.473234\pi$
$374$	20.0126	+	12.7391i	1.03483	+	0.658726i
$375$		0			0
$376$	8.15233	+	10.6002i	0.420424	+	0.546662i
$377$	−5.16245	+	5.16245i	−0.265880	+	0.265880i
$378$		0			0
$379$	25.7690	+	25.7690i	1.32367	+	1.32367i	0.910785	+	0.412882i	$0.135478\pi$
$379$	25.7690	+	25.7690i	1.32367	+	1.32367i	0.412882	+	0.910785i	$0.364522\pi$
$380$	−0.0719228	−	0.0481659i	−0.00368956	−	0.00247086i
$381$		0			0
$382$	4.14962	−	6.51888i	0.212313	−	0.333535i
$383$	0.418091	+	0.418091i	0.0213634	+	0.0213634i	0.717708	−	0.696344i	$-0.245191\pi$
$383$	0.418091	+	0.418091i	0.0213634	+	0.0213634i	−0.696344	+	0.717708i	$0.745191\pi$
$384$		0			0
$385$	−20.1175	−	4.96060i	−1.02528	−	0.252816i
$386$	−9.42019	+	2.09203i	−0.479475	+	0.106481i
$387$		0			0
$388$	−6.11568	+	16.8411i	−0.310476	+	0.854976i
$389$	13.3626	−	13.3626i	0.677508	−	0.677508i	−0.281927	−	0.959436i	$-0.590974\pi$
$389$	13.3626	−	13.3626i	0.677508	−	0.677508i	0.959436	+	0.281927i	$0.0909737\pi$
$390$		0			0
$391$	24.3609			1.23198
$392$	5.92066	+	0.772850i	0.299038	+	0.0390348i
$393$		0			0
$394$	−2.23712	+	3.51441i	−0.112704	+	0.177053i
$395$	6.09121	+	1.50198i	0.306482	+	0.0755730i
$396$		0			0
$397$	−13.8391			−0.694564			−0.347282	−	0.937761i	$-0.612895\pi$
$397$	−13.8391			−0.694564			−0.347282	+	0.937761i	$0.612895\pi$
$398$	1.62986	−	2.56044i	0.0816977	−	0.128343i
$399$		0			0
$400$	−18.4935	+	7.61508i	−0.924676	+	0.380754i
$401$	−20.3112			−1.01430			−0.507148	−	0.861859i	$-0.669300\pi$
$401$	−20.3112			−1.01430			−0.507148	+	0.861859i	$0.669300\pi$
$402$		0			0
$403$	13.8058			0.687718
$404$	−3.65057	+	10.0528i	−0.181623	+	0.500144i
$405$		0			0
$406$	10.8206	−	16.9986i	0.537015	−	0.843626i
$407$	−15.7321	−	15.7321i	−0.779813	−	0.779813i
$408$		0			0
$409$	18.2875			0.904259			0.452130	−	0.891952i	$-0.350664\pi$
$409$	18.2875			0.904259			0.452130	+	0.891952i	$0.350664\pi$
$410$	−23.7365	+	22.6587i	−1.17226	+	1.11903i
$411$		0			0
$412$	28.4995	+	10.3493i	1.40407	+	0.509875i
$413$		−	15.0572i		−	0.740915i
$414$		0			0
$415$	27.8499	+	6.86728i	1.36710	+	0.337101i
$416$	−2.64618	−	8.33930i	−0.129740	−	0.408868i
$417$		0			0
$418$	0.0451245	−	0.0708885i	0.00220711	−	0.00346727i
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	−0.143563	−	0.989641i	$-0.545856\pi$
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	0.989641	+	0.143563i	$0.0458558\pi$
$420$		0			0
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	0.930074	−	0.367372i	$-0.119742\pi$
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	−0.367372	+	0.930074i	$0.619742\pi$
$422$	−2.40397	−	10.8248i	−0.117023	−	0.526944i
$423$		0			0
$424$	2.67511	−	20.4935i	0.129915	−	0.995252i
$425$	8.12315	+	26.0861i	0.394031	+	1.26536i
$426$		0			0
$427$	−6.04577			−0.292576
$428$	−9.23676	−	19.7705i	−0.446475	−	0.955641i
$429$		0			0
$430$	−4.64285	+	4.43203i	−0.223898	+	0.213732i
$431$			15.9479i			0.768185i	0.923295	+	0.384093i	$0.125486\pi$
$431$			15.9479i			0.768185i	−0.923295	+	0.384093i	$0.874514\pi$
$432$		0			0
$433$	3.52109	−	3.52109i	0.169213	−	0.169213i	−0.617420	−	0.786633i	$-0.711822\pi$
$433$	3.52109	−	3.52109i	0.169213	−	0.169213i	0.786633	+	0.617420i	$0.211822\pi$
$434$	−37.1981	+	8.26092i	−1.78557	+	0.396537i
$435$		0			0
$436$	−8.80607	+	24.2498i	−0.421734	+	1.16135i
$437$		−	0.0862907i		−	0.00412784i
$438$		0			0
$439$		−	6.45840i		−	0.308242i	−0.988052	−	0.154121i	$-0.950745\pi$
$439$		−	6.45840i		−	0.308242i	0.988052	−	0.154121i	$-0.0492546\pi$
$440$	−7.80755	−	17.7767i	−0.372210	−	0.847469i
$441$		0			0
$442$	−11.6677	+	2.59115i	−0.554975	+	0.123248i
$443$			27.0992i			1.28752i	0.765226	+	0.643761i	$0.222627\pi$
$443$			27.0992i			1.28752i	−0.765226	+	0.643761i	$0.777373\pi$
$444$		0			0
$445$	−29.0337	−	7.15919i	−1.37633	−	0.339378i
$446$	−0.503675	−	2.26800i	−0.0238497	−	0.107393i
$447$		0			0
$448$	12.1197	+	20.8858i	0.572604	+	0.986763i
$449$			41.0879i			1.93906i	0.244976	+	0.969529i	$0.421220\pi$
$449$			41.0879i			1.93906i	−0.244976	+	0.969529i	$0.578780\pi$
$450$		0			0
$451$	−22.5259	−	22.5259i	−1.06070	−	1.06070i
$452$	−12.9953	−	4.71913i	−0.611248	−	0.221969i
$453$		0			0
$454$	−9.73276	+	15.2897i	−0.456781	+	0.717583i
$455$	8.93396	−	5.39957i	0.418831	−	0.253136i
$456$		0			0
$457$	−18.2449	+	18.2449i	−0.853462	+	0.853462i	−0.990558	−	0.137096i	$-0.956223\pi$
$457$	−18.2449	+	18.2449i	−0.853462	+	0.853462i	0.137096	+	0.990558i	$0.456223\pi$
$458$	−1.90730	+	0.423571i	−0.0891221	+	0.0197922i
$459$		0			0
$460$	−16.5659	−	11.0940i	−0.772387	−	0.517259i
$461$	−6.68802	+	6.68802i	−0.311492	+	0.311492i	−0.845488	−	0.533995i	$-0.820690\pi$
$461$	−6.68802	+	6.68802i	−0.311492	+	0.311492i	0.533995	+	0.845488i	$0.320690\pi$
$462$		0			0
$463$	−28.6926	−	28.6926i	−1.33346	−	1.33346i	−0.902254	−	0.431205i	$-0.858089\pi$
$463$	−28.6926	−	28.6926i	−1.33346	−	1.33346i	−0.431205	−	0.902254i	$-0.641911\pi$
$464$	18.8075	−	1.67322i	0.873118	−	0.0776775i
$465$		0			0
$466$	−0.131756	−	0.593286i	−0.00610349	−	0.0274834i
$467$			32.4161i			1.50004i	0.661417	+	0.750018i	$0.269955\pi$
$467$			32.4161i			1.50004i	−0.661417	+	0.750018i	$0.730045\pi$
$468$		0			0
$469$	1.59693	−	1.59693i	0.0737392	−	0.0737392i
$470$	−14.9469	−	0.347229i	−0.689449	−	0.0160165i
$471$		0			0
$472$	11.1842	−	8.60148i	0.514794	−	0.395915i
$473$	−4.40605	−	4.40605i	−0.202591	−	0.202591i
$474$		0			0
$475$	0.0924020	−	0.0287737i	0.00423970	−	0.00132023i
$476$	29.8867	−	13.9631i	1.36985	−	0.639996i
$477$		0			0
$478$	−14.9241	−	9.50003i	−0.682613	−	0.434521i
$479$	7.33117			0.334970			0.167485	−	0.985875i	$-0.446435\pi$
$479$	7.33117			0.334970			0.167485	+	0.985875i	$0.446435\pi$
$480$		0			0
$481$	11.2090			0.511087
$482$	23.3562	+	14.8675i	1.06385	+	0.677197i
$483$		0			0
$484$	−2.85538	+	1.33403i	−0.129790	+	0.0606378i
$485$	−10.3616	−	17.1440i	−0.470496	−	0.778468i
$486$		0			0
$487$	−11.7773	−	11.7773i	−0.533681	−	0.533681i	0.387985	−	0.921666i	$-0.373171\pi$
$487$	−11.7773	−	11.7773i	−0.533681	−	0.533681i	−0.921666	+	0.387985i	$0.873171\pi$
$488$	−3.45368	−	4.49069i	−0.156341	−	0.203284i
$489$		0			0
$490$	−4.82875	+	4.60950i	−0.218141	+	0.208236i
$491$	27.3556	−	27.3556i	1.23454	−	1.23454i	0.272343	−	0.962200i	$-0.412202\pi$
$491$	27.3556	−	27.3556i	1.23454	−	1.23454i	0.962200	−	0.272343i	$-0.0877985\pi$
$492$		0			0
$493$		−	25.7941i		−	1.16171i
$494$	0.00917834	+	0.0413292i	0.000412953	+	0.00185949i
$495$		0			0
$496$	−27.3856	−	22.9110i	−1.22965	−	1.02873i
$497$	−0.575432	−	0.575432i	−0.0258117	−	0.0258117i
$498$		0			0
$499$	−12.1629	+	12.1629i	−0.544488	+	0.544488i	−0.924841	−	0.380353i	$-0.875802\pi$
$499$	−12.1629	+	12.1629i	−0.544488	+	0.544488i	0.380353	+	0.924841i	$0.375802\pi$
$500$	6.35577	−	21.4384i	0.284239	−	0.958753i
$501$		0			0
$502$	10.1090	−	2.24499i	0.451185	−	0.100199i
$503$	13.2748	−	13.2748i	0.591892	−	0.591892i	−0.346250	−	0.938142i	$-0.612545\pi$
$503$	13.2748	−	13.2748i	0.591892	−	0.591892i	0.938142	+	0.346250i	$0.112545\pi$
$504$		0			0
$505$	−6.18505	−	10.2336i	−0.275231	−	0.455389i
$506$	10.3934	−	16.3276i	0.462045	−	0.725851i
$507$		0			0
$508$	3.68440	+	1.33795i	0.163469	+	0.0593621i
$509$	9.29995	+	9.29995i	0.412213	+	0.412213i	0.882509	−	0.470296i	$-0.155853\pi$
$509$	9.29995	+	9.29995i	0.412213	+	0.412213i	−0.470296	+	0.882509i	$0.655853\pi$
$510$		0			0
$511$		−	3.46565i		−	0.153312i
$512$	−8.59016	+	20.9334i	−0.379635	+	0.925136i
$513$		0			0
$514$	−6.41673	−	28.8939i	−0.283030	−	1.27446i
$515$	−29.0121	+	17.5345i	−1.27843	+	0.772664i
$516$		0			0
$517$		−	14.5141i		−	0.638329i
$518$	−30.2013	+	6.70708i	−1.32697	+	0.294692i
$519$		0			0
$520$	9.11427	+	3.55145i	0.399687	+	0.155742i
$521$		−	33.5279i		−	1.46888i	−0.678671	−	0.734442i	$-0.737444\pi$
$521$		−	33.5279i		−	1.46888i	0.678671	−	0.734442i	$-0.262556\pi$
$522$		0			0
$523$			25.9463i			1.13455i	0.823528	+	0.567276i	$0.192003\pi$
$523$			25.9463i			1.13455i	−0.823528	+	0.567276i	$0.807997\pi$
$524$	−3.39924	+	9.36067i	−0.148497	+	0.408923i
$525$		0			0
$526$	23.0203	−	5.11233i	1.00373	−	0.222908i
$527$	−34.4903	+	34.4903i	−1.50242	+	1.50242i
$528$		0			0
$529$			3.12481i			0.135861i
$530$	15.9551	+	16.7140i	0.693046	+	0.726012i
$531$		0			0
$532$	−0.0494598	−	0.105864i	−0.00214435	−	0.00458980i
$533$	16.0495			0.695182
$534$		0			0
$535$	23.6879	+	5.84102i	1.02412	+	0.252529i
$536$	2.09842	+	0.273916i	0.0906379	+	0.0118314i
$537$		0			0
$538$	0.911073	+	4.10247i	0.0392792	+	0.176870i
$539$	−4.58248	−	4.58248i	−0.197381	−	0.197381i
$540$		0			0
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	−0.604428	−	0.796660i	$-0.706598\pi$
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	0.796660	+	0.604428i	$0.206598\pi$
$542$	14.3223	−	22.4997i	0.615196	−	0.966445i
$543$		0			0
$544$	27.4444	+	14.2228i	1.17667	+	0.609798i
$545$	−14.9199	−	24.6859i	−0.639096	−	1.05743i
$546$		0			0
$547$			15.5964i			0.666853i	0.942776	+	0.333426i	$0.108205\pi$
$547$			15.5964i			0.666853i	−0.942776	+	0.333426i	$0.891795\pi$
$548$	14.9547	+	5.43067i	0.638835	+	0.231987i
$549$		0			0
$550$	20.9497	+	5.68506i	0.893297	+	0.242412i
$551$	−0.0913677			−0.00389239
$552$		0			0
$553$	5.98831	+	5.98831i	0.254649	+	0.254649i
$554$	7.53275	−	11.8336i	0.320036	−	0.502762i
$555$		0			0
$556$	11.6839	−	32.1745i	0.495506	−	1.36450i
$557$	−15.5348			−0.658231			−0.329116	−	0.944290i	$-0.606751\pi$
$557$	−15.5348			−0.658231			−0.329116	+	0.944290i	$0.606751\pi$
$558$		0			0
$559$	3.13928			0.132777
$560$	−26.6823	−	4.11530i	−1.12753	−	0.173903i
$561$		0			0
$562$	7.07349	−	11.1121i	0.298377	−	0.468737i
$563$	−24.3087			−1.02449			−0.512245	−	0.858839i	$-0.671186\pi$
$563$	−24.3087			−1.02449			−0.512245	+	0.858839i	$0.671186\pi$
$564$		0			0
$565$	13.2291	−	7.99547i	0.556550	−	0.336372i
$566$	2.59998	−	4.08445i	0.109285	−	0.171682i
$567$		0			0
$568$	0.0987022	−	0.756139i	0.00414145	−	0.0317269i
$569$	0.187259			0.00785029			0.00392515	−	0.999992i	$-0.498751\pi$
$569$	0.187259			0.00785029			0.00392515	+	0.999992i	$0.498751\pi$
$570$		0			0
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	−0.870974	−	0.491328i	$-0.836511\pi$
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	0.491328	+	0.870974i	$0.336511\pi$
$572$	−3.24127	+	8.92566i	−0.135524	+	0.373200i
$573$		0			0
$574$	−43.2434	+	9.60346i	−1.80495	+	0.400841i
$575$	21.2828	−	6.62740i	0.887554	−	0.276382i
$576$		0			0
$577$	−1.53648	−	1.53648i	−0.0639645	−	0.0639645i	0.674401	−	0.738365i	$-0.264402\pi$
$577$	−1.53648	−	1.53648i	−0.0639645	−	0.0639645i	−0.738365	+	0.674401i	$0.764402\pi$
$578$	9.76529	−	15.3408i	0.406183	−	0.638095i
$579$		0			0
$580$	−11.7467	+	17.5405i	−0.487755	+	0.728330i
$581$	27.3794	+	27.3794i	1.13589	+	1.13589i
$582$		0			0
$583$	−15.8616	+	15.8616i	−0.656920	+	0.656920i
$584$	2.57423	−	1.97977i	0.106522	−	0.0819235i
$585$		0			0
$586$	3.17903	+	2.02363i	0.131325	+	0.0835954i
$587$	3.06150			0.126362			0.0631808	−	0.998002i	$-0.479876\pi$
$587$	3.06150			0.126362			0.0631808	+	0.998002i	$0.479876\pi$
$588$		0			0
$589$	0.122171	+	0.122171i	0.00503398	+	0.00503398i
$590$	−0.366359	+	15.7704i	−0.0150828	+	0.649257i
$591$		0			0
$592$	−22.2345	−	18.6015i	−0.913833	−	0.764518i
$593$	20.8213	−	20.8213i	0.855029	−	0.855029i	−0.135718	−	0.990747i	$-0.543334\pi$
$593$	20.8213	−	20.8213i	0.855029	−	0.855029i	0.990747	+	0.135718i	$0.0433342\pi$
$594$		0			0
$595$	−8.82977	+	35.8087i	−0.361985	+	1.46801i
$596$	−36.0475	−	13.0903i	−1.47656	−	0.536200i
$597$		0			0
$598$	2.11403	+	9.51927i	0.0864492	+	0.389272i
$599$			27.8866i			1.13942i	0.821847	+	0.569709i	$0.192944\pi$
$599$			27.8866i			1.13942i	−0.821847	+	0.569709i	$0.807056\pi$
$600$		0			0
$601$			4.70260i			0.191823i	0.995390	+	0.0959115i	$0.0305766\pi$
$601$			4.70260i			0.191823i	−0.995390	+	0.0959115i	$0.969423\pi$
$602$	−8.45839	+	1.87843i	−0.344738	+	0.0765592i
$603$		0			0
$604$	−17.5396	−	37.5419i	−0.713675	−	1.52756i
$605$	0.843598	−	3.42116i	0.0342971	−	0.139090i
$606$		0			0
$607$	28.8294	−	28.8294i	1.17015	−	1.17015i	0.187975	−	0.982174i	$-0.439807\pi$
$607$	28.8294	−	28.8294i	1.17015	−	1.17015i	0.982174	−	0.187975i	$-0.0601925\pi$
$608$	0.0503799	−	0.0972133i	0.00204317	−	0.00394252i
$609$		0			0
$610$	6.33215	+	0.147101i	0.256381	+	0.00595595i
$611$	5.17059	+	5.17059i	0.209180	+	0.209180i
$612$		0			0
$613$	−38.7980			−1.56704			−0.783518	−	0.621369i	$-0.786577\pi$
$613$	−38.7980			−1.56704			−0.783518	+	0.621369i	$0.786577\pi$
$614$	8.01599	−	12.5928i	0.323499	−	0.508203i
$615$		0			0
$616$	3.39240	−	25.9885i	0.136684	−	1.04711i
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	−0.834907	−	0.550391i	$-0.814479\pi$
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	0.550391	+	0.834907i	$0.314479\pi$
$618$		0			0
$619$	28.1001	+	28.1001i	1.12944	+	1.12944i	0.990268	+	0.139172i	$0.0444440\pi$
$619$	28.1001	+	28.1001i	1.12944	+	1.12944i	0.139172	+	0.990268i	$0.455556\pi$
$620$	39.1611	−	7.74714i	1.57275	−	0.311133i
$621$		0			0
$622$	−24.4284	−	15.5500i	−0.979490	−	0.623500i
$623$	−28.5432	−	28.5432i	−1.14356	−	1.14356i
$624$		0			0
$625$	14.1935	+	20.5802i	0.567741	+	0.823207i
$626$	1.22444	+	5.51353i	0.0489384	+	0.220365i
$627$		0			0
$628$	−4.84499	−	10.3703i	−0.193336	−	0.413819i
$629$	−28.0029	+	28.0029i	−1.11655	+	1.11655i
$630$		0			0
$631$	38.2613			1.52316			0.761580	−	0.648071i	$-0.224424\pi$
$631$	38.2613			1.52316			0.761580	+	0.648071i	$0.224424\pi$
$632$	−1.02716	+	7.86886i	−0.0408582	+	0.313007i
$633$		0			0
$634$	24.1625	+	15.3807i	0.959614	+	0.610847i
$635$	−3.75067	+	2.26685i	−0.148841	+	0.0899574i
$636$		0			0
$637$	3.26498			0.129363
$638$	−17.2883	−	11.0049i	−0.684449	−	0.435690i
$639$		0			0
$640$	−12.1856	−	22.1700i	−0.481680	−	0.876347i
$641$	−7.15922			−0.282772			−0.141386	−	0.989955i	$-0.545156\pi$
$641$	−7.15922			−0.282772			−0.141386	+	0.989955i	$0.545156\pi$
$642$		0			0
$643$	8.74864			0.345013			0.172506	−	0.985008i	$-0.444813\pi$
$643$	8.74864			0.345013			0.172506	+	0.985008i	$0.444813\pi$
$644$	−11.3920	−	24.3835i	−0.448907	−	0.960845i
$645$		0			0
$646$	−0.126180	−	0.0803206i	−0.00496449	−	0.00316017i
$647$	−8.84125	−	8.84125i	−0.347585	−	0.347585i	0.511624	−	0.859209i	$-0.329044\pi$
$647$	−8.84125	−	8.84125i	−0.347585	−	0.347585i	−0.859209	+	0.511624i	$0.829044\pi$
$648$		0			0
$649$	−15.3137			−0.601117
$650$	−9.48852	+	5.43796i	−0.372170	+	0.213294i
$651$		0			0
$652$	−15.2297	−	32.5978i	−0.596441	−	1.27663i
$653$		−	20.7854i		−	0.813396i	−0.913563	−	0.406698i	$-0.866680\pi$
$653$		−	20.7854i		−	0.813396i	0.913563	−	0.406698i	$-0.133320\pi$
$654$		0			0
$655$	−5.75923	−	9.52904i	−0.225032	−	0.372330i
$656$	−31.8363	−	26.6344i	−1.24300	−	1.03990i
$657$		0			0
$658$	−17.0254	−	10.8376i	−0.663719	−	0.422494i
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	−0.398003	−	0.917384i	$-0.630297\pi$
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	0.917384	+	0.398003i	$0.130297\pi$
$660$		0			0
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.977194	−	0.212350i	$-0.931888\pi$
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.212350	−	0.977194i	$-0.568112\pi$
$662$	−38.0589	+	8.45208i	−1.47920	+	0.328499i
$663$		0			0
$664$	−4.69631	+	35.9775i	−0.182252	+	1.39620i
$665$	0.126841	+	0.0312767i	0.00491868	+	0.00121286i
$666$		0			0
$667$	−21.0446			−0.814848
$668$	2.31358	−	6.37103i	0.0895151	−	0.246503i
$669$		0			0
$670$	−1.71142	+	1.63371i	−0.0661180	+	0.0631158i
$671$			6.14880i			0.237372i
$672$		0			0
$673$	29.9888	−	29.9888i	1.15598	−	1.15598i	0.170652	−	0.985331i	$-0.445413\pi$
$673$	29.9888	−	29.9888i	1.15598	−	1.15598i	0.985331	−	0.170652i	$-0.0545873\pi$
$674$	2.55582	+	11.5086i	0.0984464	+	0.443295i
$675$		0			0
$676$	8.98030	+	19.2215i	0.345396	+	0.739289i
$677$			33.4274i			1.28472i	0.766403	+	0.642360i	$0.222044\pi$
$677$			33.4274i			1.28472i	−0.766403	+	0.642360i	$0.777956\pi$
$678$		0			0
$679$		−	27.0409i		−	1.03774i
$680$	−31.6421	+	13.8973i	−1.21342	+	0.532936i
$681$		0			0
$682$	8.40169	+	37.8320i	0.321717	+	1.44866i
$683$		−	4.07583i		−	0.155957i	−0.996955	−	0.0779787i	$-0.975153\pi$
$683$		−	4.07583i		−	0.155957i	0.996955	−	0.0779787i	$-0.0248466\pi$
$684$		0			0
$685$	−15.2237	+	9.20102i	−0.581668	+	0.351553i
$686$	20.3734	−	4.52450i	0.777858	−	0.172746i
$687$		0			0
$688$	−6.22716	−	5.20968i	−0.237408	−	0.198617i
$689$		−	11.3013i		−	0.430544i
$690$		0			0
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	0.522044	−	0.852919i	$-0.325170\pi$
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	−0.852919	+	0.522044i	$0.825170\pi$
$692$	17.1271	−	8.00177i	0.651074	−	0.304182i
$693$		0			0
$694$	−13.6751	−	8.70494i	−0.519098	−	0.330435i
$695$	19.7956	+	32.7532i	0.750890	+	1.24240i
$696$		0			0
$697$	−40.0956	+	40.0956i	−1.51873	+	1.51873i
$698$	−0.137828	−	0.620624i	−0.00521685	−	0.0234910i
$699$		0			0
$700$	22.3117	−	20.3295i	0.843305	−	0.768383i
$701$	−11.8325	+	11.8325i	−0.446908	+	0.446908i	−0.894325	−	0.447418i	$-0.852344\pi$
$701$	−11.8325	+	11.8325i	−0.446908	+	0.446908i	0.447418	+	0.894325i	$0.352344\pi$
$702$		0			0
$703$	0.0991914	+	0.0991914i	0.00374108	+	0.00374108i
$704$	21.2417	−	12.3263i	0.800578	−	0.464563i
$705$		0			0
$706$	−36.0323	+	8.00203i	−1.35609	+	0.301160i
$707$		−	16.1413i		−	0.607056i
$708$		0			0
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.247563	+	0.968872i	$0.579630\pi$
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.968872	+	0.247563i	$0.920370\pi$
$710$	0.588688	+	0.616690i	0.0220931	+	0.0231440i
$711$		0			0
$712$	4.89594	−	37.5069i	0.183483	−	1.40563i
$713$	28.1395	+	28.1395i	1.05383	+	1.05383i
$714$		0			0
$715$	−5.49158	−	9.08620i	−0.205373	−	0.339805i
$716$	−31.3686	−	11.3912i	−1.17230	−	0.425709i
$717$		0			0
$718$	−11.8319	+	18.5874i	−0.441563	+	0.693676i
$719$	−4.16893			−0.155475			−0.0777374	−	0.996974i	$-0.524770\pi$
$719$	−4.16893			−0.155475			−0.0777374	+	0.996974i	$0.524770\pi$
$720$		0			0
$721$	−45.7603			−1.70420
$722$	14.4287	−	22.6668i	0.536980	−	0.843572i
$723$		0			0
$724$	−2.45369	+	6.75686i	−0.0911906	+	0.251117i
$725$	−7.01733	−	22.5350i	−0.260617	−	0.836928i
$726$		0			0
$727$	28.6014	+	28.6014i	1.06077	+	1.06077i	0.998030	+	0.0627368i	$0.0199829\pi$
$727$	28.6014	+	28.6014i	1.06077	+	1.06077i	0.0627368	+	0.998030i	$0.480017\pi$
$728$	8.04978	+	10.4668i	0.298345	+	0.387927i
$729$		0			0
$730$	−0.0843236	+	3.62982i	−0.00312096	+	0.134345i
$731$	−7.84269	+	7.84269i	−0.290072	+	0.290072i
$732$		0			0
$733$		−	18.7069i		−	0.690956i	−0.938427	−	0.345478i	$-0.887717\pi$
$733$		−	18.7069i		−	0.690956i	0.938427	−	0.345478i	$-0.112283\pi$
$734$	10.4941	−	2.33052i	0.387345	−	0.0860212i
$735$		0			0
$736$	11.6039	−	22.3910i	0.427726	−	0.825342i
$737$	−1.62414	−	1.62414i	−0.0598259	−	0.0598259i
$738$		0			0
$739$	34.6914	−	34.6914i	1.27614	−	1.27614i	0.333337	−	0.942808i	$-0.391825\pi$
$739$	34.6914	−	34.6914i	1.27614	−	1.27614i	0.942808	−	0.333337i	$-0.108175\pi$
$740$	31.7951	−	6.28994i	1.16881	−	0.231223i
$741$		0			0
$742$	6.76227	+	30.4498i	0.248251	+	1.11785i
$743$	−24.7660	+	24.7660i	−0.908577	+	0.908577i	−0.996157	−	0.0875803i	$-0.972087\pi$
$743$	−24.7660	+	24.7660i	−0.908577	+	0.908577i	0.0875803	+	0.996157i	$0.472087\pi$
$744$		0			0
$745$	36.6959	−	22.1785i	1.34443	−	0.812558i
$746$	−3.87042	−	2.46374i	−0.141706	−	0.0902039i
$747$		0			0
$748$	−14.2010	−	30.3960i	−0.519240	−	1.11139i
$749$	23.2878	+	23.2878i	0.850917	+	0.850917i
$750$		0			0
$751$			45.2370i			1.65072i	0.564606	+	0.825361i	$0.309028\pi$
$751$			45.2370i			1.65072i	−0.564606	+	0.825361i	$0.690972\pi$
$752$	−1.67586	−	18.8372i	−0.0611124	−	0.686922i
$753$		0			0
$754$	10.0793	−	2.23841i	0.367068	−	0.0815181i
$755$	44.9808	+	11.0914i	1.63702	+	0.403659i
$756$		0			0
$757$			6.44058i			0.234087i	0.993127	+	0.117044i	$0.0373417\pi$
$757$			6.44058i			0.234087i	−0.993127	+	0.117044i	$0.962658\pi$
$758$	−11.1733	−	50.3123i	−0.405833	−	1.82743i
$759$		0			0
$760$	0.0492268	+	0.112082i	0.00178564	+	0.00406565i
$761$			9.50571i			0.344582i	0.985046	+	0.172291i	$0.0551169\pi$
$761$			9.50571i			0.344582i	−0.985046	+	0.172291i	$0.944883\pi$
$762$		0			0
$763$		−	38.9367i		−	1.40960i
$764$	−9.90112	+	4.62580i	−0.358210	+	0.167356i
$765$		0			0
$766$	−0.181282	−	0.816294i	−0.00654998	−	0.0294939i
$767$	5.45546	−	5.45546i	0.196985	−	0.196985i
$768$		0			0
$769$		−	46.8513i		−	1.68950i	−0.535159	−	0.844751i	$-0.679748\pi$
$769$		−	46.8513i		−	1.68950i	0.535159	−	0.844751i	$-0.320252\pi$
$770$	20.2332	+	21.1957i	0.729155	+	0.763839i
$771$		0			0
$772$	12.8271	+	4.65806i	0.461659	+	0.167647i
$773$	−10.9964			−0.395513			−0.197756	−	0.980251i	$-0.563365\pi$
$773$	−10.9964			−0.395513			−0.197756	+	0.980251i	$0.563365\pi$
$774$		0			0
$775$	−20.7493	+	39.5155i	−0.745335	+	1.41944i
$776$	20.0855	−	15.4473i	0.721028	−	0.554524i
$777$		0			0
$778$	−26.0895	+	5.79393i	−0.935354	+	0.207723i
$779$	0.142026	+	0.142026i	0.00508862	+	0.00508862i
$780$		0			0
$781$	−0.585238	+	0.585238i	−0.0209414	+	0.0209414i
$782$	−29.0628	−	18.5001i	−1.03928	−	0.661562i
$783$		0			0
$784$	−6.47651	−	5.41828i	−0.231304	−	0.193510i
$785$	12.4251	+	3.06381i	0.443472	+	0.109352i
$786$		0			0
$787$		−	25.5190i		−	0.909653i	−0.890580	−	0.454826i	$-0.849701\pi$
$787$		−	25.5190i		−	0.909653i	0.890580	−	0.454826i	$-0.150299\pi$
$788$	5.33782	−	2.49383i	0.190152	−	0.0888390i
$789$		0			0
$790$	−6.12626	−	6.41767i	−0.217963	−	0.228330i
$791$	20.8660			0.741909
$792$		0			0
$793$	−2.19048	−	2.19048i	−0.0777864	−	0.0777864i
$794$	16.5102	+	10.5097i	0.585926	+	0.372974i
$795$		0			0
$796$	−3.88890	+	1.81690i	−0.137838	+	0.0643981i
$797$	13.3808			0.473972			0.236986	−	0.971513i	$-0.423840\pi$
$797$	13.3808			0.473972			0.236986	+	0.971513i	$0.423840\pi$
$798$		0			0
$799$	−25.8348			−0.913969
$800$	27.8461	+	4.95944i	0.984507	+	0.175343i
$801$		0			0
$802$	24.2316	+	15.4248i	0.855648	+	0.544667i
$803$	−3.52471			−0.124384
$804$		0			0
$805$	29.2151	+	7.20391i	1.02970	+	0.253905i
$806$	−16.4706	−	10.4844i	−0.580150	−	0.369298i
$807$		0			0
$808$	11.9895	−	9.22079i	0.421788	−	0.324386i
$809$	−52.7958			−1.85620			−0.928102	−	0.372327i	$-0.878560\pi$
$809$	−52.7958			−1.85620			−0.928102	+	0.372327i	$0.878560\pi$
$810$		0			0
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	−0.678929	−	0.734204i	$-0.737556\pi$
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	0.734204	+	0.678929i	$0.237556\pi$
$812$	−25.8181	+	12.0622i	−0.906039	+	0.423301i
$813$		0			0
$814$	6.82137	+	30.7159i	0.239089	+	1.07659i
$815$	39.0570	+	9.63075i	1.36811	+	0.337351i
$816$		0			0
$817$	0.0277803	+	0.0277803i	0.000971909	+	0.000971909i
$818$	−21.8173	−	13.8879i	−0.762822	−	0.485579i
$819$		0			0
$820$	45.5255	−	9.00619i	1.58982	−	0.314510i
$821$	25.7715	+	25.7715i	0.899431	+	0.899431i	0.995386	−	0.0959548i	$-0.0305904\pi$
$821$	25.7715	+	25.7715i	0.899431	+	0.899431i	−0.0959548	+	0.995386i	$0.530590\pi$
$822$		0			0
$823$	−17.5565	+	17.5565i	−0.611982	+	0.611982i	−0.943462	−	0.331480i	$-0.892452\pi$
$823$	−17.5565	+	17.5565i	−0.611982	+	0.611982i	0.331480	+	0.943462i	$0.392452\pi$
$824$	−26.1408	−	33.9900i	−0.910658	−	1.18410i
$825$		0			0
$826$	−11.4347	+	17.9634i	−0.397864	+	0.625027i
$827$	−14.8548			−0.516551			−0.258276	−	0.966071i	$-0.583154\pi$
$827$	−14.8548			−0.516551			−0.258276	+	0.966071i	$0.583154\pi$
$828$		0			0
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	0.855387	−	0.517990i	$-0.173320\pi$
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	−0.517990	+	0.855387i	$0.673320\pi$
$830$	−28.0101	−	29.3425i	−0.972246	−	1.01849i
$831$		0			0
$832$	−3.17610	+	11.9585i	−0.110112	+	0.414585i
$833$	−8.15672	+	8.15672i	−0.282614	+	0.282614i
$834$		0			0
$835$	3.91983	+	6.48563i	0.135651	+	0.224444i
$836$	−0.107668	+	0.0503026i	−0.00372378	+	0.00173975i
$837$		0			0
$838$	−33.8138	+	7.50934i	−1.16808	+	0.259406i
$839$			4.54484i			0.156905i	0.996918	+	0.0784527i	$0.0249979\pi$
$839$			4.54484i			0.156905i	−0.996918	+	0.0784527i	$0.975002\pi$
$840$		0			0
$841$		−	6.71729i		−	0.231631i
$842$	−5.00615	−	22.5422i	−0.172523	−	0.776855i
$843$		0			0
$844$	−5.35262	+	14.7398i	−0.184245	+	0.507364i
$845$	−23.0302	−	5.67884i	−0.792264	−	0.195358i
$846$		0			0
$847$	3.36337	−	3.36337i	0.115567	−	0.115567i
$848$	−18.7546	+	22.4175i	−0.644036	+	0.769820i
$849$		0			0
$850$	10.1193	−	37.2900i	0.347089	−	1.27904i
$851$	22.8466	+	22.8466i	0.783171	+	0.783171i
$852$		0			0
$853$	37.3745			1.27968			0.639839	−	0.768509i	$-0.279001\pi$
$853$	37.3745			1.27968			0.639839	+	0.768509i	$0.279001\pi$
$854$	7.21269	+	4.59128i	0.246813	+	0.157110i
$855$		0			0
$856$	−3.99449	+	30.6010i	−0.136529	+	1.04592i
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	−0.929893	−	0.367831i	$-0.880101\pi$
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$858$		0			0
$859$	−15.7662	−	15.7662i	−0.537935	−	0.537935i	0.384987	−	0.922922i	$-0.374206\pi$
$859$	−15.7662	−	15.7662i	−0.537935	−	0.537935i	−0.922922	+	0.384987i	$0.874206\pi$
$860$	8.90475	−	1.76161i	0.303650	−	0.0600703i
$861$		0			0
$862$	12.1112	−	19.0261i	0.412508	−	0.648032i
$863$	22.6395	+	22.6395i	0.770659	+	0.770659i	0.978222	−	0.207563i	$-0.0665532\pi$
$863$	22.6395	+	22.6395i	0.770659	+	0.770659i	−0.207563	+	0.978222i	$0.566553\pi$
$864$		0			0
$865$	−5.06005	+	20.5208i	−0.172047	+	0.697727i
$866$	−6.87470	+	1.52673i	−0.233612	+	0.0518803i
$867$		0			0
$868$	50.6513	+	18.3936i	1.71922	+	0.624318i
$869$	6.09036	−	6.09036i	0.206601	−	0.206601i
$870$		0			0
$871$	1.15719			0.0392097
$872$	28.9215	−	22.2428i	0.979406	−	0.753236i
$873$		0			0
$874$	−0.0655308	+	0.102946i	−0.00221661	+	0.00348220i
$875$	2.02769	+	33.6863i	0.0685483	+	1.13880i
$876$		0			0
$877$	−30.0542			−1.01486			−0.507429	−	0.861694i	$-0.669404\pi$
$877$	−30.0542			−1.01486			−0.507429	+	0.861694i	$0.669404\pi$
$878$	−4.90463	+	7.70496i	−0.165523	+	0.260030i
$879$		0			0
$880$	−4.18542	+	27.1370i	−0.141091	+	0.914788i
$881$	3.86747			0.130298			0.0651492	−	0.997876i	$-0.479248\pi$
$881$	3.86747			0.130298			0.0651492	+	0.997876i	$0.479248\pi$
$882$		0			0
$883$	−0.485919			−0.0163525			−0.00817624	−	0.999967i	$-0.502603\pi$
$883$	−0.485919			−0.0163525			−0.00817624	+	0.999967i	$0.502603\pi$
$884$	15.8875	+	5.76939i	0.534354	+	0.194046i
$885$		0			0
$886$	20.5797	−	32.3297i	0.691388	−	1.08614i
$887$	−12.9762	−	12.9762i	−0.435699	−	0.435699i	0.454863	−	0.890561i	$-0.349688\pi$
$887$	−12.9762	−	12.9762i	−0.435699	−	0.435699i	−0.890561	+	0.454863i	$0.849688\pi$
$888$		0			0
$889$	−5.91587			−0.198412
$890$	29.2008	+	30.5898i	0.978812	+	1.02537i
$891$		0			0
$892$	−1.12147	+	3.08825i	−0.0375496	+	0.103402i
$893$			0.0915117i			0.00306232i
$894$		0			0
$895$	31.9328	−	19.2998i	1.06739	−	0.645120i
$896$	1.40209	−	34.1210i	0.0468406	−	1.13990i
$897$		0			0
$898$	31.2030	−	49.0184i	1.04126	−	1.63577i
$899$	29.7951	−	29.7951i	0.993722	−	0.993722i
$900$		0			0
$901$	28.2333	+	28.2333i	0.940588	+	0.940588i
$902$	9.76711	+	43.9803i	0.325209	+	1.46438i
$903$		0			0
$904$	11.9198	+	15.4989i	0.396446	+	0.515485i
$905$	−4.15721	−	6.87839i	−0.138190	−	0.228645i
$906$		0			0
$907$	54.3645			1.80514			0.902571	−	0.430540i	$-0.141677\pi$
$907$	54.3645			1.80514			0.902571	+	0.430540i	$0.141677\pi$
$908$	23.2226	−	10.8496i	0.770670	−	0.360057i
$909$		0			0
$910$	−14.7589	−	0.342861i	−0.489252	−	0.0113657i
$911$		−	40.0402i		−	1.32659i	−0.748358	−	0.663295i	$-0.769157\pi$
$911$		−	40.0402i		−	1.32659i	0.748358	−	0.663295i	$-0.230843\pi$
$912$		0			0
$913$	27.8460	−	27.8460i	0.921567	−	0.921567i
$914$	35.6220	−	7.91090i	1.17827	−	0.261669i
$915$		0			0
$916$	2.59710	+	0.943112i	0.0858106	+	0.0311613i
$917$		−	15.0300i		−	0.496335i
$918$		0			0
$919$			8.81475i			0.290772i	0.989375	+	0.145386i	$0.0464423\pi$
$919$			8.81475i			0.290772i	−0.989375	+	0.145386i	$0.953558\pi$
$920$	11.3383	+	25.8157i	0.373813	+	0.851118i
$921$		0			0
$922$	13.0579	−	2.89989i	0.430040	−	0.0955028i
$923$		−	0.416977i		−	0.0137250i
$924$		0			0
$925$	−16.8464	+	32.0828i	−0.553907	+	1.05488i
$926$	12.4410	+	56.0204i	0.408835	+	1.84095i
$927$		0			0
$928$	−23.7083	−	12.2866i	−0.778264	−	0.403329i
$929$		−	47.9673i		−	1.57376i	−0.617109	−	0.786878i	$-0.711696\pi$
$929$		−	47.9673i		−	1.57376i	0.617109	−	0.786878i	$-0.288304\pi$
$930$		0			0
$931$	0.0288926	+	0.0288926i	0.000946918	+	0.000946918i
$932$	−0.293365	+	0.807856i	−0.00960951	+	0.0264622i
$933$		0			0
$934$	24.6174	−	38.6728i	0.805506	−	1.26541i
$935$	36.4189	+	8.98024i	1.19102	+	0.293685i
$936$		0			0
$937$	13.8299	−	13.8299i	0.451803	−	0.451803i	−0.444150	−	0.895953i	$-0.646494\pi$
$937$	13.8299	−	13.8299i	0.451803	−	0.451803i	0.895953	+	0.444150i	$0.146494\pi$
$938$	−3.11789	+	0.692418i	−0.101803	+	0.0226083i
$939$		0			0
$940$	17.5682	+	11.7652i	0.573010	+	0.383739i
$941$	5.19108	−	5.19108i	0.169224	−	0.169224i	−0.617414	−	0.786638i	$-0.711820\pi$
$941$	5.19108	−	5.19108i	0.169224	−	0.169224i	0.786638	+	0.617414i	$0.211820\pi$
$942$		0			0
$943$	32.7127	+	32.7127i	1.06527	+	1.06527i
$944$	−19.8750	+	1.76819i	−0.646877	+	0.0575498i
$945$		0			0
$946$	1.91044	+	8.60253i	0.0621138	+	0.279692i
$947$			24.1342i			0.784255i	0.919911	+	0.392128i	$0.128261\pi$
$947$			24.1342i			0.784255i	−0.919911	+	0.392128i	$0.871739\pi$
$948$		0			0
$949$	1.25566	−	1.25566i	0.0407606	−	0.0407606i
$950$	−0.132088	−	0.0358444i	−0.00428551	−	0.00116295i
$951$		0			0
$952$	−46.2590	−	6.03840i	−1.49926	−	0.195706i
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	0.232430	−	0.972613i	$-0.425332\pi$
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	−0.972613	+	0.232430i	$0.925332\pi$
$954$		0			0
$955$	2.92521	−	11.8630i	0.0946574	−	0.383878i
$956$	10.5902	+	22.6673i	0.342511	+	0.733114i
$957$		0			0
$958$	−8.74618	−	5.56743i	−0.282576	−	0.179876i
$959$	−24.0121			−0.775392
$960$		0			0
$961$	−48.6804			−1.57034
$962$	−13.3725	−	8.51235i	−0.431147	−	0.274449i
$963$		0			0
$964$	−16.5736	−	35.4743i	−0.533799	−	1.14255i
$965$	−13.0579	+	7.89200i	−0.420347	+	0.254052i
$966$		0			0
$967$	−21.4211	−	21.4211i	−0.688855	−	0.688855i	0.273124	−	0.961979i	$-0.411943\pi$
$967$	−21.4211	−	21.4211i	−0.688855	−	0.688855i	−0.961979	+	0.273124i	$0.911943\pi$
$968$	4.41959	+	0.576910i	0.142051	+	0.0185426i
$969$		0			0
$970$	−0.657939	+	28.3218i	−0.0211251	+	0.909358i
$971$	11.7978	−	11.7978i	0.378609	−	0.378609i	−0.491991	−	0.870600i	$-0.663731\pi$
$971$	11.7978	−	11.7978i	0.378609	−	0.378609i	0.870600	+	0.491991i	$0.163731\pi$
$972$		0			0
$973$			51.6611i			1.65618i
$974$	5.10658	+	22.9944i	0.163625	+	0.736788i
$975$		0			0
$976$	0.709967	+	7.98025i	0.0227255	+	0.255442i
$977$	−2.15703	−	2.15703i	−0.0690096	−	0.0690096i	0.671760	−	0.740769i	$-0.265539\pi$
$977$	−2.15703	−	2.15703i	−0.0690096	−	0.0690096i	−0.740769	+	0.671760i	$0.765539\pi$
$978$		0			0
$979$	−29.0296	+	29.0296i	−0.927791	+	0.927791i
$980$	9.26131	−	1.83214i	0.295842	−	0.0585257i
$981$		0			0
$982$	−53.4101	+	11.8613i	−1.70438	+	0.378508i
$983$	−19.9712	+	19.9712i	−0.636983	+	0.636983i	−0.949810	−	0.312827i	$-0.898724\pi$
$983$	−19.9712	+	19.9712i	−0.636983	+	0.636983i	0.312827	+	0.949810i	$0.398724\pi$
$984$		0			0
$985$	−1.57702	+	6.39550i	−0.0502479	+	0.203778i
$986$	−19.5886	+	30.7728i	−0.623827	+	0.980004i
$987$		0			0
$988$	0.0204363	−	0.0562765i	0.000650164	−	0.00179039i
$989$	6.39858	+	6.39858i	0.203463	+	0.203463i
$990$		0			0
$991$		−	19.2270i		−	0.610767i	−0.952230	−	0.305383i	$-0.901215\pi$
$991$		−	19.2270i		−	0.610767i	0.952230	−	0.305383i	$-0.0987846\pi$
$992$	15.2724	+	48.1303i	0.484900	+	1.52814i
$993$		0			0
$994$	0.249504	+	1.12349i	0.00791379	+	0.0356350i
$995$	1.14894	−	4.65948i	0.0364240	−	0.147715i
$996$		0			0
$997$		−	2.01694i		−	0.0638771i	−0.999490	−	0.0319385i	$-0.989832\pi$
$997$		−	2.01694i		−	0.0638771i	0.999490	−	0.0319385i	$-0.0101681\pi$
$998$	23.7473	−	5.27379i	0.751709	−	0.166939i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.667.2		18
3.2	odd	2		80.2.s.b.27.8	yes	18
5.3	odd	4		720.2.bd.g.523.2		18
12.11	even	2		320.2.s.b.207.7		18
15.2	even	4		400.2.j.d.43.2		18
15.8	even	4		80.2.j.b.43.8	✓	18
15.14	odd	2		400.2.s.d.107.2		18
16.3	odd	4		720.2.bd.g.307.2		18
24.5	odd	2		640.2.s.d.287.7		18
24.11	even	2		640.2.s.c.287.3		18
48.5	odd	4		640.2.j.c.607.7		18
48.11	even	4		640.2.j.d.607.3		18
48.29	odd	4		320.2.j.b.47.3		18
48.35	even	4		80.2.j.b.67.8	yes	18
60.23	odd	4		320.2.j.b.143.7		18
60.47	odd	4		1600.2.j.d.143.3		18
60.59	even	2		1600.2.s.d.207.3		18
80.3	even	4	inner	720.2.z.g.163.2		18
120.53	even	4		640.2.j.d.543.7		18
120.83	odd	4		640.2.j.c.543.3		18
240.29	odd	4		1600.2.j.d.1007.7		18
240.53	even	4		640.2.s.c.223.3		18
240.77	even	4		1600.2.s.d.943.3		18
240.83	odd	4		80.2.s.b.3.8	yes	18
240.173	even	4		320.2.s.b.303.7		18
240.179	even	4		400.2.j.d.307.2		18
240.203	odd	4		640.2.s.d.223.7		18
240.227	odd	4		400.2.s.d.243.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	15.8	even	4
80.2.j.b.67.8	yes	18	48.35	even	4
80.2.s.b.3.8	yes	18	240.83	odd	4
80.2.s.b.27.8	yes	18	3.2	odd	2
320.2.j.b.47.3		18	48.29	odd	4
320.2.j.b.143.7		18	60.23	odd	4
320.2.s.b.207.7		18	12.11	even	2
320.2.s.b.303.7		18	240.173	even	4
400.2.j.d.43.2		18	15.2	even	4
400.2.j.d.307.2		18	240.179	even	4
400.2.s.d.107.2		18	15.14	odd	2
400.2.s.d.243.2		18	240.227	odd	4
640.2.j.c.543.3		18	120.83	odd	4
640.2.j.c.607.7		18	48.5	odd	4
640.2.j.d.543.7		18	120.53	even	4
640.2.j.d.607.3		18	48.11	even	4
640.2.s.c.223.3		18	240.53	even	4
640.2.s.c.287.3		18	24.11	even	2
640.2.s.d.223.7		18	240.203	odd	4
640.2.s.d.287.7		18	24.5	odd	2
720.2.z.g.163.2		18	80.3	even	4	inner
720.2.z.g.667.2		18	1.1	even	1	trivial
720.2.bd.g.307.2		18	16.3	odd	4
720.2.bd.g.523.2		18	5.3	odd	4
1600.2.j.d.143.3		18	60.47	odd	4
1600.2.j.d.1007.7		18	240.29	odd	4
1600.2.s.d.207.3		18	60.59	even	2
1600.2.s.d.943.3		18	240.77	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19301 - 0.759419i) q^{2} +(0.846564 + 1.81200i) q^{4} +(-2.17104 - 0.535339i) q^{5} +(-2.13436 - 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} +O(q^{10})\)	\(q+(-1.19301 - 0.759419i) q^{2} +(0.846564 + 1.81200i) q^{4} +(-2.17104 - 0.535339i) q^{5} +(-2.13436 - 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} +(2.18353 + 2.28740i) q^{10} +(-2.17074 + 2.17074i) q^{11} -1.54663i q^{13} +(0.925449 + 4.16720i) q^{14} +(-2.56666 + 3.06794i) q^{16} +(3.86386 + 3.86386i) q^{17} +(0.0136865 - 0.0136865i) q^{19} +(-0.867892 - 4.38711i) q^{20} +(4.23822 - 0.941219i) q^{22} +(3.15240 - 3.15240i) q^{23} +(4.42682 + 2.32449i) q^{25} +(-1.17454 + 1.84515i) q^{26} +(2.06058 - 5.67434i) q^{28} +(-3.33787 - 3.33787i) q^{29} +8.92639i q^{31} +(5.39191 - 1.71093i) q^{32} +(-1.67535 - 7.54394i) q^{34} +(3.49118 + 5.77640i) q^{35} +7.24737i q^{37} +(-0.0267220 + 0.00593441i) q^{38} +(-2.29625 + 5.89298i) q^{40} +10.3771i q^{41} +2.02975i q^{43} +(-5.77103 - 2.09570i) q^{44} +(-6.15484 + 1.36686i) q^{46} +(-3.34313 + 3.34313i) q^{47} +2.11103i q^{49} +(-3.51600 - 6.13496i) q^{50} +(2.80249 - 1.30932i) q^{52} +7.30702 q^{53} +(5.87483 - 3.55067i) q^{55} +(-6.76751 + 5.20472i) q^{56} +(1.44728 + 6.51696i) q^{58} +(3.52732 + 3.52732i) q^{59} +(1.41629 - 1.41629i) q^{61} +(6.77887 - 10.6493i) q^{62} +(-7.73194 - 2.05356i) q^{64} +(-0.827973 + 3.35780i) q^{65} +0.748197i q^{67} +(-3.73030 + 10.2723i) q^{68} +(0.221682 - 9.54260i) q^{70} +0.269603 q^{71} +(0.811870 + 0.811870i) q^{73} +(5.50380 - 8.64622i) q^{74} +(0.0363865 + 0.0132134i) q^{76} +9.26628 q^{77} -2.80567 q^{79} +(7.21470 - 5.28659i) q^{80} +(7.88056 - 12.3800i) q^{82} -12.8279 q^{83} +(-6.32012 - 10.4571i) q^{85} +(1.54143 - 2.42152i) q^{86} +(5.29341 + 6.88283i) q^{88} +13.3732 q^{89} +(-3.30108 + 3.30108i) q^{91} +(8.38083 + 3.04342i) q^{92} +(6.52724 - 1.44956i) q^{94} +(-0.0370409 + 0.0223871i) q^{95} +(6.33466 + 6.33466i) q^{97} +(1.60315 - 2.51848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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