LMFDB - Embedded newform 504.2.bk.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34646 - 0.432485i) q^{2} +(1.62591 + 1.16465i) q^{4} +(0.155280 - 0.268953i) q^{5} +(-2.58581 - 0.560001i) q^{7} +(-1.68554 - 2.27133i) q^{8} +O(q^{10})$	\(q+(-1.34646 - 0.432485i) q^{2} +(1.62591 + 1.16465i) q^{4} +(0.155280 - 0.268953i) q^{5} +(-2.58581 - 0.560001i) q^{7} +(-1.68554 - 2.27133i) q^{8} +(-0.325396 + 0.294978i) q^{10} +(0.622560 + 1.07831i) q^{11} -2.68845 q^{13} +(3.23950 + 1.87234i) q^{14} +(1.28719 + 3.78723i) q^{16} +(-1.93094 + 1.11483i) q^{17} +(-5.14286 - 2.96923i) q^{19} +(0.565707 - 0.256448i) q^{20} +(-0.371902 - 1.72114i) q^{22} +(-2.86149 - 1.65208i) q^{23} +(2.45178 + 4.24660i) q^{25} +(3.61989 + 1.16271i) q^{26} +(-3.55210 - 3.92207i) q^{28} +0.191829i q^{29} +(-1.95686 - 3.38939i) q^{31} +(-0.0952356 - 5.65605i) q^{32} +(3.08208 - 0.665971i) q^{34} +(-0.552137 + 0.608503i) q^{35} +(-0.643623 - 0.371596i) q^{37} +(5.64051 + 6.22216i) q^{38} +(-0.872611 + 0.100637i) q^{40} -9.28628i q^{41} -10.8775 q^{43} +(-0.243617 + 2.47830i) q^{44} +(3.13838 + 3.46201i) q^{46} +(-5.43928 + 9.42111i) q^{47} +(6.37280 + 2.89611i) q^{49} +(-1.46463 - 6.77824i) q^{50} +(-4.37119 - 3.13110i) q^{52} +(-10.8205 + 6.24721i) q^{53} +0.386684 q^{55} +(3.08653 + 6.81714i) q^{56} +(0.0829632 - 0.258290i) q^{58} +(-5.16549 + 2.98230i) q^{59} +(-4.58974 + 7.94967i) q^{61} +(1.16898 + 5.40999i) q^{62} +(-2.31792 + 7.65684i) q^{64} +(-0.417462 + 0.723066i) q^{65} +(-2.25830 - 3.91150i) q^{67} +(-4.43792 - 0.436248i) q^{68} +(1.00660 - 0.580534i) q^{70} -7.92636i q^{71} +(6.97675 - 4.02803i) q^{73} +(0.705903 + 0.778696i) q^{74} +(-4.90374 - 10.8173i) q^{76} +(-1.00597 - 3.13693i) q^{77} +(13.2839 + 7.66944i) q^{79} +(1.21846 + 0.241887i) q^{80} +(-4.01618 + 12.5036i) q^{82} -14.2247i q^{83} +0.692441i q^{85} +(14.6461 + 4.70435i) q^{86} +(1.39985 - 3.23157i) q^{88} +(5.53347 + 3.19475i) q^{89} +(6.95181 + 1.50553i) q^{91} +(-2.72844 - 6.01877i) q^{92} +(11.3983 - 10.3327i) q^{94} +(-1.59716 + 0.922123i) q^{95} -1.62950i q^{97} +(-7.32820 - 6.65563i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.34646	−	0.432485i	−0.952092	−	0.305813i
$2$	−1.34646	−	0.432485i	−0.952092	−	0.305813i
$3$		0			0
$3$		0			0
$4$	1.62591	+	1.16465i	0.812957	+	0.582324i
$5$	0.155280	−	0.268953i	0.0694432	−	0.120279i	−0.829213	−	0.558933i	$-0.811211\pi$
$5$	0.155280	−	0.268953i	0.0694432	−	0.120279i	0.898656	+	0.438653i	$0.144544\pi$
$6$		0			0
$7$	−2.58581	−	0.560001i	−0.977343	−	0.211660i
$7$	−2.58581	−	0.560001i	−0.977343	−	0.211660i
$8$	−1.68554	−	2.27133i	−0.595928	−	0.803038i
$9$		0			0
$10$	−0.325396	+	0.294978i	−0.102899	+	0.0932802i
$11$	0.622560	+	1.07831i	0.187709	+	0.325121i	0.944486	−	0.328552i	$-0.106560\pi$
$11$	0.622560	+	1.07831i	0.187709	+	0.325121i	−0.756777	+	0.653673i	$0.773227\pi$
$12$		0			0
$13$	−2.68845			−0.745642			−0.372821	−	0.927903i	$-0.621609\pi$
$13$	−2.68845			−0.745642			−0.372821	+	0.927903i	$0.621609\pi$
$14$	3.23950	+	1.87234i	0.865792	+	0.500404i
$15$		0			0
$16$	1.28719	+	3.78723i	0.321798	+	0.946808i
$17$	−1.93094	+	1.11483i	−0.468321	+	0.270386i	−0.715537	−	0.698575i	$-0.753818\pi$
$17$	−1.93094	+	1.11483i	−0.468321	+	0.270386i	0.247215	+	0.968961i	$0.420484\pi$
$18$		0			0
$19$	−5.14286	−	2.96923i	−1.17985	−	0.681188i	−0.223872	−	0.974619i	$-0.571870\pi$
$19$	−5.14286	−	2.96923i	−1.17985	−	0.681188i	−0.955980	+	0.293431i	$0.905203\pi$
$20$	0.565707	−	0.256448i	0.126496	−	0.0573434i
$21$		0			0
$22$	−0.371902	−	1.72114i	−0.0792898	−	0.366949i
$23$	−2.86149	−	1.65208i	−0.596662	−	0.344483i	0.171066	−	0.985260i	$-0.445279\pi$
$23$	−2.86149	−	1.65208i	−0.596662	−	0.344483i	−0.767727	+	0.640777i	$0.778612\pi$
$24$		0			0
$25$	2.45178	+	4.24660i	0.490355	+	0.849320i
$26$	3.61989	+	1.16271i	0.709920	+	0.228027i
$27$		0			0
$28$	−3.55210	−	3.92207i	−0.671283	−	0.741201i
$29$			0.191829i			0.0356218i	0.999841	+	0.0178109i	$0.00566968\pi$
$29$			0.191829i			0.0356218i	−0.999841	+	0.0178109i	$0.994330\pi$
$30$		0			0
$31$	−1.95686	−	3.38939i	−0.351463	−	0.608752i	0.635043	−	0.772477i	$-0.280982\pi$
$31$	−1.95686	−	3.38939i	−0.351463	−	0.608752i	−0.986506	+	0.163725i	$0.947649\pi$
$32$	−0.0952356	−	5.65605i	−0.0168354	−	0.999858i
$33$		0			0
$34$	3.08208	−	0.665971i	0.528572	−	0.114213i
$35$	−0.552137	+	0.608503i	−0.0933282	+	0.102856i
$36$		0			0
$37$	−0.643623	−	0.371596i	−0.105811	−	0.0610900i	0.446161	−	0.894953i	$-0.352791\pi$
$37$	−0.643623	−	0.371596i	−0.105811	−	0.0610900i	−0.551972	+	0.833863i	$0.686124\pi$
$38$	5.64051	+	6.22216i	0.915011	+	1.00937i
$39$		0			0
$40$	−0.872611	+	0.100637i	−0.137972	+	0.0159121i
$41$		−	9.28628i		−	1.45027i	−0.688605	−	0.725137i	$-0.741776\pi$
$41$		−	9.28628i		−	1.45027i	0.688605	−	0.725137i	$-0.258224\pi$
$42$		0			0
$43$	−10.8775			−1.65880			−0.829401	−	0.558654i	$-0.811318\pi$
$43$	−10.8775			−1.65880			−0.829401	+	0.558654i	$0.811318\pi$
$44$	−0.243617	+	2.47830i	−0.0367266	+	0.373617i
$45$		0			0
$46$	3.13838	+	3.46201i	0.462729	+	0.510446i
$47$	−5.43928	+	9.42111i	−0.793400	+	1.37421i	0.130450	+	0.991455i	$0.458358\pi$
$47$	−5.43928	+	9.42111i	−0.793400	+	1.37421i	−0.923850	+	0.382755i	$0.874975\pi$
$48$		0			0
$49$	6.37280	+	2.89611i	0.910400	+	0.413730i
$50$	−1.46463	−	6.77824i	−0.207130	−	0.958588i
$51$		0			0
$52$	−4.37119	−	3.13110i	−0.606175	−	0.434205i
$53$	−10.8205	+	6.24721i	−1.48631	+	0.858120i	−0.999878	−	0.0156002i	$-0.995034\pi$
$53$	−10.8205	+	6.24721i	−1.48631	+	0.858120i	−0.486429	+	0.873720i	$0.661701\pi$
$54$		0			0
$55$	0.386684			0.0521405
$56$	3.08653	+	6.81714i	0.412454	+	0.910978i
$57$		0			0
$58$	0.0829632	−	0.258290i	0.0108936	−	0.0339152i
$59$	−5.16549	+	2.98230i	−0.672490	+	0.388262i	−0.797019	−	0.603954i	$-0.793591\pi$
$59$	−5.16549	+	2.98230i	−0.672490	+	0.388262i	0.124530	+	0.992216i	$0.460258\pi$
$60$		0			0
$61$	−4.58974	+	7.94967i	−0.587656	+	1.01785i	0.406882	+	0.913481i	$0.366616\pi$
$61$	−4.58974	+	7.94967i	−0.587656	+	1.01785i	−0.994539	+	0.104370i	$0.966717\pi$
$62$	1.16898	+	5.40999i	0.148461	+	0.687069i
$63$		0			0
$64$	−2.31792	+	7.65684i	−0.289741	+	0.957105i
$65$	−0.417462	+	0.723066i	−0.0517798	+	0.0896852i
$66$		0			0
$67$	−2.25830	−	3.91150i	−0.275896	−	0.477865i	0.694465	−	0.719526i	$-0.255641\pi$
$67$	−2.25830	−	3.91150i	−0.275896	−	0.477865i	−0.970361	+	0.241661i	$0.922308\pi$
$68$	−4.43792	−	0.436248i	−0.538177	−	0.0529028i
$69$		0			0
$70$	1.00660	−	0.580534i	0.120312	−	0.0693871i
$71$		−	7.92636i		−	0.940686i	−0.882484	−	0.470343i	$-0.844130\pi$
$71$		−	7.92636i		−	0.940686i	0.882484	−	0.470343i	$-0.155870\pi$
$72$		0			0
$73$	6.97675	−	4.02803i	0.816567	−	0.471445i	−0.0326645	−	0.999466i	$-0.510399\pi$
$73$	6.97675	−	4.02803i	0.816567	−	0.471445i	0.849231	+	0.528021i	$0.177066\pi$
$74$	0.705903	+	0.778696i	0.0820596	+	0.0905216i
$75$		0			0
$76$	−4.90374	−	10.8173i	−0.562497	−	1.24083i
$77$	−1.00597	−	3.13693i	−0.114641	−	0.357486i
$78$		0			0
$79$	13.2839	+	7.66944i	1.49455	+	0.862880i	0.999980	−	0.00625715i	$-0.00199173\pi$
$79$	13.2839	+	7.66944i	1.49455	+	0.862880i	0.494571	+	0.869137i	$0.335325\pi$
$80$	1.21846	+	0.241887i	0.136228	+	0.0270438i
$81$		0			0
$82$	−4.01618	+	12.5036i	−0.443512	+	1.38079i
$83$		−	14.2247i		−	1.56137i	−0.624926	−	0.780684i	$-0.714871\pi$
$83$		−	14.2247i		−	1.56137i	0.624926	−	0.780684i	$-0.285129\pi$
$84$		0			0
$85$			0.692441i			0.0751058i
$86$	14.6461	+	4.70435i	1.57933	+	0.507283i
$87$		0			0
$88$	1.39985	−	3.23157i	0.149224	−	0.344486i
$89$	5.53347	+	3.19475i	0.586547	+	0.338643i	0.763731	−	0.645535i	$-0.223365\pi$
$89$	5.53347	+	3.19475i	0.586547	+	0.338643i	−0.177184	+	0.984178i	$0.556699\pi$
$90$		0			0
$91$	6.95181	+	1.50553i	0.728748	+	0.157823i
$92$	−2.72844	−	6.01877i	−0.284460	−	0.627500i
$93$		0			0
$94$	11.3983	−	10.3327i	1.17564	−	1.06574i
$95$	−1.59716	+	0.922123i	−0.163865	+	0.0946078i
$96$		0			0
$97$		−	1.62950i		−	0.165450i	−0.996572	−	0.0827252i	$-0.973638\pi$
$97$		−	1.62950i		−	0.165450i	0.996572	−	0.0827252i	$-0.0263624\pi$
$98$	−7.32820	−	6.65563i	−0.740260	−	0.672320i
$99$		0			0
$100$	−0.959415	+	9.76006i	−0.0959415	+	0.976006i
$101$	−1.08936	−	1.88683i	−0.108396	−	0.187747i	0.806725	−	0.590927i	$-0.201238\pi$
$101$	−1.08936	−	1.88683i	−0.108396	−	0.187747i	−0.915121	+	0.403180i	$0.867905\pi$
$102$		0			0
$103$	−1.59794	+	2.76772i	−0.157450	+	0.272711i	−0.933948	−	0.357408i	$-0.883661\pi$
$103$	−1.59794	+	2.76772i	−0.157450	+	0.272711i	0.776499	+	0.630119i	$0.216994\pi$
$104$	4.53148	+	6.10637i	0.444349	+	0.598779i
$105$		0			0
$106$	17.2712	−	3.73193i	1.67752	−	0.362477i
$107$	−1.10533	+	1.91448i	−0.106856	+	0.185080i	−0.914495	−	0.404597i	$-0.867412\pi$
$107$	−1.10533	+	1.91448i	−0.106856	+	0.185080i	0.807639	+	0.589677i	$0.200745\pi$
$108$		0			0
$109$	10.6676	−	6.15892i	1.02177	−	0.589918i	0.107152	−	0.994243i	$-0.465827\pi$
$109$	10.6676	−	6.15892i	1.02177	−	0.589918i	0.914615	+	0.404325i	$0.132493\pi$
$110$	−0.520655	−	0.167235i	−0.0496425	−	0.0159452i
$111$		0			0
$112$	−1.20758	−	10.5139i	−0.114106	−	0.993469i
$113$	10.3212			0.970936			0.485468	−	0.874254i	$-0.338649\pi$
$113$	10.3212			0.970936			0.485468	+	0.874254i	$0.338649\pi$
$114$		0			0
$115$	−0.888663	+	0.513070i	−0.0828682	+	0.0478440i
$116$	−0.223413	+	0.311898i	−0.0207434	+	0.0289590i
$117$		0			0
$118$	8.24493	−	1.78155i	0.759008	−	0.164005i
$119$	5.61734	−	1.80140i	0.514941	−	0.165134i
$120$		0			0
$121$	4.72484	−	8.18366i	0.429531	−	0.743969i
$122$	9.61802	−	8.71892i	0.870774	−	0.789374i
$123$		0			0
$124$	0.765748	−	7.78990i	0.0687662	−	0.699554i
$125$	3.07564			0.275094
$126$		0			0
$127$		−	15.9029i		−	1.41115i	−0.708634	−	0.705576i	$-0.750688\pi$
$127$		−	15.9029i		−	1.41115i	0.708634	−	0.705576i	$-0.249312\pi$
$128$	6.43246	−	9.30717i	0.568555	−	0.822646i
$129$		0			0
$130$	0.874811	−	0.793034i	0.0767260	−	0.0695536i
$131$	−13.0693	−	7.54554i	−1.14187	−	0.659257i	−0.194975	−	0.980808i	$-0.562462\pi$
$131$	−13.0693	−	7.54554i	−1.14187	−	0.659257i	−0.946892	+	0.321551i	$0.895796\pi$
$132$		0			0
$133$	11.6357	+	10.5579i	1.00894	+	0.915482i
$134$	1.34906	+	6.24336i	0.116541	+	0.539344i
$135$		0			0
$136$	5.78682	+	2.50672i	0.496216	+	0.214950i
$137$	7.41224	+	12.8384i	0.633270	+	1.09686i	0.986879	+	0.161463i	$0.0516212\pi$
$137$	7.41224	+	12.8384i	0.633270	+	1.09686i	−0.353608	+	0.935394i	$0.615045\pi$
$138$		0			0
$139$			0.758344i			0.0643219i	0.999483	+	0.0321610i	$0.0102389\pi$
$139$			0.758344i			0.0643219i	−0.999483	+	0.0321610i	$0.989761\pi$
$140$	−1.60642	+	0.346328i	−0.135767	+	0.0292700i
$141$		0			0
$142$	−3.42803	+	10.6725i	−0.287674	+	0.895620i
$143$	−1.67372	−	2.89897i	−0.139964	−	0.242424i
$144$		0			0
$145$	0.0515929	+	0.0297872i	0.00428456	+	0.00247369i
$146$	−11.1360	+	2.40625i	−0.921620	+	0.199142i
$147$		0			0
$148$	−0.613697	−	1.35378i	−0.0504456	−	0.111280i
$149$	15.0025	+	8.66168i	1.22905	+	0.709593i	0.966831	−	0.255416i	$-0.0822124\pi$
$149$	15.0025	+	8.66168i	1.22905	+	0.709593i	0.262219	+	0.965008i	$0.415546\pi$
$150$		0			0
$151$	−18.9094	+	10.9173i	−1.53882	+	0.888441i	−0.539917	+	0.841718i	$0.681544\pi$
$151$	−18.9094	+	10.9173i	−1.53882	+	0.888441i	−0.998908	+	0.0467227i	$0.985122\pi$
$152$	1.92436	+	16.6859i	0.156086	+	1.35340i
$153$		0			0
$154$	−0.00217451	+	4.65881i	−0.000175227	+	0.375418i
$155$	−1.21545			−0.0976269
$156$		0			0
$157$	−7.22291	−	12.5104i	−0.576451	−	0.998443i	−0.995882	−	0.0906554i	$-0.971104\pi$
$157$	−7.22291	−	12.5104i	−0.576451	−	0.998443i	0.419431	−	0.907787i	$-0.362230\pi$
$158$	−14.5693	−	16.0717i	−1.15907	−	1.27859i
$159$		0			0
$160$	−1.53600	−	0.852657i	−0.121431	−	0.0674085i
$161$	6.47409	+	5.87440i	0.510230	+	0.462967i
$162$		0			0
$163$	−3.09204	+	5.35558i	−0.242188	+	0.419481i	−0.961337	−	0.275374i	$-0.911198\pi$
$163$	−3.09204	+	5.35558i	−0.242188	+	0.419481i	0.719150	+	0.694855i	$0.244532\pi$
$164$	10.8152	−	15.0987i	0.844529	−	1.17901i
$165$		0			0
$166$	−6.15198	+	19.1531i	−0.477486	+	1.48657i
$167$	23.2344			1.79793			0.898965	−	0.438021i	$-0.144320\pi$
$167$	23.2344			1.79793			0.898965	+	0.438021i	$0.144320\pi$
$168$		0			0
$169$	−5.77223			−0.444018
$170$	0.299470	−	0.932345i	0.0229683	−	0.0715076i
$171$		0			0
$172$	−17.6859	−	12.6684i	−1.34853	−	0.965959i
$173$	8.94146	−	15.4871i	0.679807	−	1.17746i	−0.295232	−	0.955426i	$-0.595397\pi$
$173$	8.94146	−	15.4871i	0.679807	−	1.17746i	0.975039	−	0.222034i	$-0.0712697\pi$
$174$		0			0
$175$	−3.96172	−	12.3539i	−0.299478	−	0.933866i
$176$	−3.28244	+	3.74577i	−0.247423	+	0.282348i
$177$		0			0
$178$	−6.06892	−	6.69475i	−0.454885	−	0.501793i
$179$	8.46735	+	14.6659i	0.632879	+	1.09618i	0.986960	+	0.160964i	$0.0514604\pi$
$179$	8.46735	+	14.6659i	0.632879	+	1.09618i	−0.354081	+	0.935215i	$0.615206\pi$
$180$		0			0
$181$	−6.35921			−0.472676			−0.236338	−	0.971671i	$-0.575947\pi$
$181$	−6.35921			−0.472676			−0.236338	+	0.971671i	$0.575947\pi$
$182$	−8.70923	−	5.03370i	−0.645571	−	0.373122i
$183$		0			0
$184$	1.07072	+	9.28404i	0.0789343	+	0.684429i
$185$	−0.199883	+	0.115403i	−0.0146957	+	0.00848457i
$186$		0			0
$187$	−2.40425	−	1.38810i	−0.175816	−	0.101508i
$188$	−19.8161	+	8.98307i	−1.44524	+	0.655158i
$189$		0			0
$190$	2.54932	−	0.550854i	0.184947	−	0.0399631i
$191$	−2.20942	−	1.27561i	−0.159868	−	0.0922997i	0.417932	−	0.908478i	$-0.362755\pi$
$191$	−2.20942	−	1.27561i	−0.159868	−	0.0922997i	−0.577800	+	0.816179i	$0.696088\pi$
$192$		0			0
$193$	−1.47346	−	2.55211i	−0.106062	−	0.183705i	0.808110	−	0.589032i	$-0.200491\pi$
$193$	−1.47346	−	2.55211i	−0.106062	−	0.183705i	−0.914172	+	0.405327i	$0.867158\pi$
$194$	−0.704733	+	2.19406i	−0.0505969	+	0.157524i
$195$		0			0
$196$	6.98868	+	12.1309i	0.499191	+	0.866492i
$197$			17.6687i			1.25884i	0.777065	+	0.629420i	$0.216708\pi$
$197$			17.6687i			1.25884i	−0.777065	+	0.629420i	$0.783292\pi$
$198$		0			0
$199$	3.49007	+	6.04497i	0.247404	+	0.428517i	0.962805	−	0.270198i	$-0.0870891\pi$
$199$	3.49007	+	6.04497i	0.247404	+	0.428517i	−0.715401	+	0.698715i	$0.753756\pi$
$200$	5.51289	−	12.7266i	0.389820	−	0.899907i
$201$		0			0
$202$	0.650760	+	3.01168i	0.0457873	+	0.211901i
$203$	0.107424	−	0.496033i	0.00753972	−	0.0348147i
$204$		0			0
$205$	−2.49757	−	1.44197i	−0.174438	−	0.100712i
$206$	3.34856	−	3.03554i	0.233305	−	0.211496i
$207$		0			0
$208$	−3.46056	−	10.1818i	−0.239946	−	0.705980i
$209$		−	7.39410i		−	0.511460i
$210$		0			0
$211$	9.18555			0.632359			0.316180	−	0.948699i	$-0.397600\pi$
$211$	9.18555			0.632359			0.316180	+	0.948699i	$0.397600\pi$
$212$	−24.8690	−	2.44462i	−1.70801	−	0.167897i
$213$		0			0
$214$	2.31627	−	2.09974i	0.158337	−	0.143535i
$215$	−1.68905	+	2.92553i	−0.115193	+	0.199519i
$216$		0			0
$217$	3.16201	+	9.86014i	0.214651	+	0.669350i
$218$	−17.0271	+	3.67919i	−1.15322	+	0.249186i
$219$		0			0
$220$	0.628715	+	0.450351i	0.0423880	+	0.0303626i
$221$	5.19123	−	2.99716i	0.349200	−	0.201611i
$222$		0			0
$223$	10.0260			0.671389			0.335695	−	0.941971i	$-0.391029\pi$
$223$	10.0260			0.671389			0.335695	+	0.941971i	$0.391029\pi$
$224$	−2.92113	+	14.6788i	−0.195176	+	0.980768i
$225$		0			0
$226$	−13.8971	−	4.46376i	−0.924420	−	0.296925i
$227$	−5.79831	+	3.34766i	−0.384847	+	0.222192i	−0.679925	−	0.733281i	$-0.737988\pi$
$227$	−5.79831	+	3.34766i	−0.384847	+	0.222192i	0.295078	+	0.955473i	$0.404654\pi$
$228$		0			0
$229$	−1.61186	+	2.79182i	−0.106515	+	0.184489i	−0.914356	−	0.404911i	$-0.867302\pi$
$229$	−1.61186	+	2.79182i	−0.106515	+	0.184489i	0.807841	+	0.589400i	$0.200636\pi$
$230$	1.41844	−	0.306495i	0.0935295	−	0.0202097i
$231$		0			0
$232$	0.435708	−	0.323335i	0.0286056	−	0.0212280i
$233$	−7.24196	+	12.5435i	−0.474437	+	0.821749i	−0.999572	−	0.0292704i	$-0.990682\pi$
$233$	−7.24196	+	12.5435i	−0.474437	+	0.821749i	0.525135	+	0.851019i	$0.324015\pi$
$234$		0			0
$235$	1.68922	+	2.92582i	0.110193	+	0.190859i
$236$	−11.8720	−	1.16702i	−0.772800	−	0.0759663i
$237$		0			0
$238$	−8.34261	−	0.00389393i	−0.540771	−	0.000252406i
$239$		−	8.19957i		−	0.530386i	−0.964195	−	0.265193i	$-0.914564\pi$
$239$		−	8.19957i		−	0.530386i	0.964195	−	0.265193i	$-0.0854357\pi$
$240$		0			0
$241$	−5.82242	+	3.36158i	−0.375055	+	0.216538i	−0.675665	−	0.737209i	$-0.736143\pi$
$241$	−5.82242	+	3.36158i	−0.375055	+	0.216538i	0.300610	+	0.953747i	$0.402810\pi$
$242$	−9.90112	+	8.97556i	−0.636468	+	0.576971i
$243$		0			0
$244$	−16.7211	+	7.58004i	−1.07046	+	0.485263i
$245$	1.76848	−	1.26427i	0.112984	−	0.0807715i
$246$		0			0
$247$	13.8263	+	7.98262i	0.879747	+	0.507922i
$248$	−4.40006	+	10.1576i	−0.279404	+	0.645010i
$249$		0			0
$250$	−4.14123	−	1.33017i	−0.261915	−	0.0841273i
$251$		−	0.417637i		−	0.0263610i	−0.999913	−	0.0131805i	$-0.995804\pi$
$251$		−	0.417637i		−	0.0263610i	0.999913	−	0.0131805i	$-0.00419561\pi$
$252$		0			0
$253$		−	4.11408i		−	0.258650i
$254$	−6.87775	+	21.4126i	−0.431548	+	1.34355i
$255$		0			0
$256$	−12.6863	+	9.74980i	−0.792892	+	0.609363i
$257$	−12.6753	−	7.31810i	−0.790665	−	0.456490i	0.0495318	−	0.998773i	$-0.484227\pi$
$257$	−12.6753	−	7.31810i	−0.790665	−	0.456490i	−0.840196	+	0.542282i	$0.817560\pi$
$258$		0			0
$259$	1.45619	+	1.32130i	0.0904833	+	0.0821018i
$260$	−1.52087	+	0.689446i	−0.0943206	+	0.0427577i
$261$		0			0
$262$	14.3339	+	15.8120i	0.885553	+	0.976871i
$263$	12.4202	−	7.17081i	0.765863	−	0.442171i	−0.0655336	−	0.997850i	$-0.520875\pi$
$263$	12.4202	−	7.17081i	0.765863	−	0.442171i	0.831397	+	0.555679i	$0.187542\pi$
$264$		0			0
$265$			3.88026i			0.238363i
$266$	−11.1009	−	19.2480i	−0.680637	−	1.18017i
$267$		0			0
$268$	0.883706	−	8.98988i	0.0539809	−	0.549144i
$269$	−11.7294	−	20.3159i	−0.715152	−	1.23868i	−0.962901	−	0.269856i	$-0.913024\pi$
$269$	−11.7294	−	20.3159i	−0.715152	−	1.23868i	0.247748	−	0.968824i	$-0.420309\pi$
$270$		0			0
$271$	6.85210	−	11.8682i	0.416235	−	0.720941i	−0.579322	−	0.815099i	$-0.696683\pi$
$271$	6.85210	−	11.8682i	0.416235	−	0.720941i	0.995557	+	0.0941581i	$0.0300159\pi$
$272$	−6.70760	−	5.87792i	−0.406708	−	0.356401i
$273$		0			0
$274$	−4.42789	−	20.4921i	−0.267499	−	1.23797i
$275$	−3.05276	+	5.28753i	−0.184088	+	0.318850i
$276$		0			0
$277$	−5.66771	+	3.27225i	−0.340540	+	0.196611i	−0.660511	−	0.750817i	$-0.729660\pi$
$277$	−5.66771	+	3.27225i	−0.340540	+	0.196611i	0.319971	+	0.947427i	$0.396327\pi$
$278$	0.327972	−	1.02108i	0.0196705	−	0.0612404i
$279$		0			0
$280$	2.31276	+	0.228435i	0.138214	+	0.0136516i
$281$	−22.5178			−1.34330			−0.671650	−	0.740869i	$-0.734414\pi$
$281$	−22.5178			−1.34330			−0.671650	+	0.740869i	$0.734414\pi$
$282$		0			0
$283$	−11.9855	+	6.91985i	−0.712466	+	0.411343i	−0.811974	−	0.583694i	$-0.801607\pi$
$283$	−11.9855	+	6.91985i	−0.712466	+	0.411343i	0.0995073	+	0.995037i	$0.468273\pi$
$284$	9.23142	−	12.8876i	0.547784	−	0.764738i
$285$		0			0
$286$	0.999841	+	4.62721i	0.0591218	+	0.273613i
$287$	−5.20033	+	24.0125i	−0.306966	+	1.41742i
$288$		0			0
$289$	−6.01432	+	10.4171i	−0.353783	+	0.612771i
$290$	−0.0565854	−	0.0624204i	−0.00332281	−	0.00366545i
$291$		0			0
$292$	16.0348	+	1.57622i	0.938367	+	0.0922415i
$293$	−11.9348			−0.697238			−0.348619	−	0.937265i	$-0.613349\pi$
$293$	−11.9348			−0.697238			−0.348619	+	0.937265i	$0.613349\pi$
$294$		0			0
$295$			1.85236i			0.107849i
$296$	0.240832	+	2.08822i	0.0139981	+	0.121375i
$297$		0			0
$298$	−16.4542	−	18.1510i	−0.953166	−	1.05146i
$299$	7.69297	+	4.44154i	0.444896	+	0.256861i
$300$		0			0
$301$	28.1271	+	6.09140i	1.62122	+	0.351103i
$302$	30.1823	−	6.52176i	1.73680	−	0.375285i
$303$		0			0
$304$	4.62531	−	23.2992i	0.265280	−	1.33630i
$305$	1.42539	+	2.46885i	0.0816175	+	0.141366i
$306$		0			0
$307$		−	1.95782i		−	0.111739i	−0.998438	−	0.0558693i	$-0.982207\pi$
$307$		−	1.95782i		−	0.111739i	0.998438	−	0.0558693i	$-0.0177930\pi$
$308$	2.01779	−	6.27197i	0.114974	−	0.357379i
$309$		0			0
$310$	1.63655	+	0.525661i	0.0929498	+	0.0298556i
$311$	−10.9125	−	18.9010i	−0.618790	−	1.07178i	−0.989707	−	0.143110i	$-0.954290\pi$
$311$	−10.9125	−	18.9010i	−0.618790	−	1.07178i	0.370916	−	0.928666i	$-0.379044\pi$
$312$		0			0
$313$	−14.9776	−	8.64730i	−0.846582	−	0.488774i	0.0129144	−	0.999917i	$-0.495889\pi$
$313$	−14.9776	−	8.64730i	−0.846582	−	0.488774i	−0.859496	+	0.511142i	$0.829222\pi$
$314$	4.31479	+	19.9686i	0.243498	+	1.12689i
$315$		0			0
$316$	12.6662	+	27.9409i	0.712531	+	1.57180i
$317$	6.07528	+	3.50757i	0.341222	+	0.197005i	0.660812	−	0.750551i	$-0.270212\pi$
$317$	6.07528	+	3.50757i	0.341222	+	0.197005i	−0.319590	+	0.947556i	$0.603545\pi$
$318$		0			0
$319$	−0.206851	+	0.119425i	−0.0115814	+	0.00668653i
$320$	1.69940	+	1.81236i	0.0949994	+	0.101314i
$321$		0			0
$322$	−6.17652	−	10.7096i	−0.344204	−	0.596822i
$323$	13.2407			0.736733
$324$		0			0
$325$	−6.59148	−	11.4168i	−0.365629	−	0.633289i
$326$	6.47952	−	5.87382i	0.358868	−	0.325321i
$327$		0			0
$328$	−21.0923	+	15.6524i	−1.16463	+	0.864258i
$329$	19.3408	−	21.3152i	1.06629	−	1.17514i
$330$		0			0
$331$	−0.990108	+	1.71492i	−0.0544212	+	0.0942604i	−0.891953	−	0.452129i	$-0.850665\pi$
$331$	−0.990108	+	1.71492i	−0.0544212	+	0.0942604i	0.837531	+	0.546389i	$0.183998\pi$
$332$	16.5668	−	23.1282i	0.909222	−	1.26933i
$333$		0			0
$334$	−31.2842	−	10.0485i	−1.71179	−	0.549830i
$335$	−1.40268			−0.0766363
$336$		0			0
$337$	2.53342			0.138004			0.0690021	−	0.997617i	$-0.478018\pi$
$337$	2.53342			0.138004			0.0690021	+	0.997617i	$0.478018\pi$
$338$	7.77209	+	2.49640i	0.422746	+	0.135786i
$339$		0			0
$340$	−0.806450	+	1.12585i	−0.0437359	+	0.0610578i
$341$	2.43653	−	4.22019i	0.131945	−	0.228536i
$342$		0			0
$343$	−14.8570	−	11.0575i	−0.802203	−	0.597051i
$344$	18.3344	+	24.7064i	0.988526	+	1.33208i
$345$		0			0
$346$	−18.7372	+	16.9857i	−1.00732	+	0.913156i
$347$	5.46677	+	9.46873i	0.293472	+	0.508308i	0.974628	−	0.223830i	$-0.0718560\pi$
$347$	5.46677	+	9.46873i	0.293472	+	0.508308i	−0.681157	+	0.732138i	$0.738523\pi$
$348$		0			0
$349$	−12.1290			−0.649250			−0.324625	−	0.945843i	$-0.605238\pi$
$349$	−12.1290			−0.649250			−0.324625	+	0.945843i	$0.605238\pi$
$350$	−0.00856370	+	18.3474i	−0.000457749	+	0.980710i
$351$		0			0
$352$	6.03967	−	3.62393i	0.321915	−	0.193156i
$353$	−25.3752	+	14.6503i	−1.35058	+	0.779759i	−0.988331	−	0.152321i	$-0.951325\pi$
$353$	−25.3752	+	14.6503i	−1.35058	+	0.779759i	−0.362252	+	0.932080i	$0.617992\pi$
$354$		0			0
$355$	−2.13182	−	1.23080i	−0.113145	−	0.0653243i
$356$	5.27619	+	11.6389i	0.279638	+	0.616862i
$357$		0			0
$358$	−5.05819	−	23.4090i	−0.267333	−	1.23721i
$359$	−2.97798	−	1.71934i	−0.157172	−	0.0907431i	0.419351	−	0.907824i	$-0.362258\pi$
$359$	−2.97798	−	1.71934i	−0.157172	−	0.0907431i	−0.576523	+	0.817081i	$0.695591\pi$
$360$		0			0
$361$	8.13264	+	14.0861i	0.428034	+	0.741376i
$362$	8.56242	+	2.75026i	0.450031	+	0.144550i
$363$		0			0
$364$	9.54964	+	10.5443i	0.500537	+	0.552671i
$365$		−	2.50189i		−	0.130955i
$366$		0			0
$367$	5.72895	+	9.92283i	0.299049	+	0.517968i	0.975919	−	0.218135i	$-0.0699974\pi$
$367$	5.72895	+	9.92283i	0.299049	+	0.517968i	−0.676870	+	0.736103i	$0.736664\pi$
$368$	2.57353	−	12.9637i	0.134154	−	0.675778i
$369$		0			0
$370$	0.319045	−	0.0689387i	0.0165863	−	0.00358395i
$371$	31.4781	−	10.0946i	1.63426	−	0.524085i
$372$		0			0
$373$	−6.47611	−	3.73898i	−0.335320	−	0.193597i	0.322880	−	0.946440i	$-0.395349\pi$
$373$	−6.47611	−	3.73898i	−0.335320	−	0.193597i	−0.658201	+	0.752843i	$0.728682\pi$
$374$	2.63690	+	2.90882i	0.136351	+	0.150411i
$375$		0			0
$376$	30.5666	−	3.52521i	1.57635	−	0.181799i
$377$		−	0.515723i		−	0.0265611i
$378$		0			0
$379$	22.1705			1.13882			0.569412	−	0.822052i	$-0.307171\pi$
$379$	22.1705			1.13882			0.569412	+	0.822052i	$0.307171\pi$
$380$	−3.67080	−	0.360840i	−0.188308	−	0.0185107i
$381$		0			0
$382$	2.42321	+	2.67309i	0.123982	+	0.136767i
$383$	−8.74870	+	15.1532i	−0.447038	+	0.774292i	−0.998192	−	0.0601114i	$-0.980854\pi$
$383$	−8.74870	+	15.1532i	−0.447038	+	0.774292i	0.551154	+	0.834404i	$0.314188\pi$
$384$		0			0
$385$	−0.999891	−	0.216543i	−0.0509592	−	0.0110361i
$386$	0.880209	+	4.07356i	0.0448015	+	0.207339i
$387$		0			0
$388$	1.89779	−	2.64942i	0.0963457	−	0.134504i
$389$	−6.29925	+	3.63687i	−0.319384	+	0.184397i	−0.651118	−	0.758976i	$-0.725700\pi$
$389$	−6.29925	+	3.63687i	−0.319384	+	0.184397i	0.331734	+	0.943373i	$0.392366\pi$
$390$		0			0
$391$	7.36715			0.372573
$392$	−4.16356	−	19.3563i	−0.210292	−	0.977639i
$393$		0			0
$394$	7.64143	−	23.7902i	0.384970	−	1.19853i
$395$	4.12543	−	2.38182i	0.207573	−	0.119842i
$396$		0			0
$397$	16.6695	−	28.8724i	0.836616	−	1.44906i	−0.0560911	−	0.998426i	$-0.517864\pi$
$397$	16.6695	−	28.8724i	0.836616	−	1.44906i	0.892708	−	0.450637i	$-0.148803\pi$
$398$	−2.08488	−	9.64872i	−0.104506	−	0.483647i
$399$		0			0
$400$	−12.9270	+	14.7516i	−0.646348	+	0.737582i
$401$	16.5661	−	28.6934i	0.827272	−	1.43288i	−0.0728978	−	0.997339i	$-0.523225\pi$
$401$	16.5661	−	28.6934i	0.827272	−	1.43288i	0.900170	−	0.435538i	$-0.143442\pi$
$402$		0			0
$403$	5.26093	+	9.11219i	0.262065	+	0.453911i
$404$	0.426284	−	4.33656i	0.0212084	−	0.215752i
$405$		0			0
$406$	−0.359170	+	0.621430i	−0.0178253	+	0.0308410i
$407$		−	0.925363i		−	0.0458685i
$408$		0			0
$409$	−18.5838	+	10.7294i	−0.918911	+	0.530533i	−0.883287	−	0.468832i	$-0.844675\pi$
$409$	−18.5838	+	10.7294i	−0.918911	+	0.530533i	−0.0356233	+	0.999365i	$0.511342\pi$
$410$	2.73925	+	3.02172i	0.135282	+	0.149232i
$411$		0			0
$412$	−5.82153	+	2.63903i	−0.286806	+	0.130016i
$413$	15.0271	−	4.81897i	0.739433	−	0.237126i
$414$		0			0
$415$	−3.82578	−	2.20882i	−0.187800	−	0.108426i
$416$	0.256036	+	15.2060i	0.0125532	+	0.745536i
$417$		0			0
$418$	−3.19783	+	9.95586i	−0.156411	+	0.486957i
$419$			28.3797i			1.38644i	0.720727	+	0.693219i	$0.243808\pi$
$419$			28.3797i			1.38644i	−0.720727	+	0.693219i	$0.756192\pi$
$420$		0			0
$421$			35.8768i			1.74853i	0.485453	+	0.874263i	$0.338655\pi$
$421$			35.8768i			1.74853i	−0.485453	+	0.874263i	$0.661345\pi$
$422$	−12.3680	−	3.97261i	−0.602064	−	0.193384i
$423$		0			0
$424$	32.4278	+	14.0470i	1.57483	+	0.682184i
$425$	−9.46846	−	5.46662i	−0.459288	−	0.265170i
$426$		0			0
$427$	16.3200	−	17.9860i	0.789781	−	0.870406i
$428$	−4.02687	+	1.82547i	−0.194646	+	0.0882374i
$429$		0			0
$430$	3.53949	−	3.20862i	0.170689	−	0.154733i
$431$	−14.1992	+	8.19790i	−0.683950	+	0.394879i	−0.801342	−	0.598207i	$-0.795880\pi$
$431$	−14.1992	+	8.19790i	−0.683950	+	0.394879i	0.117392	+	0.993086i	$0.462547\pi$
$432$		0			0
$433$		−	33.3810i		−	1.60419i	−0.597198	−	0.802094i	$-0.703719\pi$
$433$		−	33.3810i		−	1.60419i	0.597198	−	0.802094i	$-0.296281\pi$
$434$	0.00683504	−	14.6438i	0.000328092	−	0.702926i
$435$		0			0
$436$	24.5175	+	2.41007i	1.17418	+	0.115422i
$437$	9.81081	+	16.9928i	0.469315	+	0.812877i
$438$		0			0
$439$	−16.7314	+	28.9796i	−0.798545	+	1.38312i	0.122018	+	0.992528i	$0.461063\pi$
$439$	−16.7314	+	28.9796i	−0.798545	+	1.38312i	−0.920564	+	0.390593i	$0.872270\pi$
$440$	−0.651771	−	0.878289i	−0.0310720	−	0.0418708i
$441$		0			0
$442$	−8.28602	+	1.79043i	−0.394126	+	0.0851621i
$443$	16.2807	−	28.1990i	0.773519	−	1.33977i	−0.162104	−	0.986774i	$-0.551828\pi$
$443$	16.2807	−	28.1990i	0.773519	−	1.33977i	0.935623	−	0.353001i	$-0.114839\pi$
$444$		0			0
$445$	1.71847	−	0.992161i	0.0814634	−	0.0470329i
$446$	−13.4996	−	4.33608i	−0.639224	−	0.205319i
$447$		0			0
$448$	10.2815	−	18.5011i	0.485757	−	0.874094i
$449$	−11.9136			−0.562238			−0.281119	−	0.959673i	$-0.590706\pi$
$449$	−11.9136			−0.562238			−0.281119	+	0.959673i	$0.590706\pi$
$450$		0			0
$451$	10.0135	−	5.78127i	0.471515	−	0.272229i
$452$	16.7814	+	12.0205i	0.789329	+	0.565399i
$453$		0			0
$454$	9.25501	−	1.99981i	0.434359	−	0.0938557i
$455$	1.48439	−	1.63593i	0.0695895	−	0.0766935i
$456$		0			0
$457$	3.04095	−	5.26709i	0.142250	−	0.246384i	−0.786094	−	0.618107i	$-0.787900\pi$
$457$	3.04095	−	5.26709i	0.142250	−	0.246384i	0.928344	+	0.371723i	$0.121233\pi$
$458$	3.37773	−	3.06198i	0.157831	−	0.143077i
$459$		0			0
$460$	−2.04243	−	0.200771i	−0.0952290	−	0.00936102i
$461$	−35.1038			−1.63495			−0.817474	−	0.575966i	$-0.804626\pi$
$461$	−35.1038			−1.63495			−0.817474	+	0.575966i	$0.804626\pi$
$462$		0			0
$463$		−	5.53696i		−	0.257324i	−0.991688	−	0.128662i	$-0.958932\pi$
$463$		−	5.53696i		−	0.257324i	0.991688	−	0.128662i	$-0.0410683\pi$
$464$	−0.726502	+	0.246921i	−0.0337270	+	0.0114630i
$465$		0			0
$466$	15.1759	−	13.7572i	0.703009	−	0.637291i
$467$	−13.4916	−	7.78937i	−0.624316	−	0.360449i	0.154232	−	0.988035i	$-0.450710\pi$
$467$	−13.4916	−	7.78937i	−0.624316	−	0.360449i	−0.778547	+	0.627586i	$0.784043\pi$
$468$		0			0
$469$	3.64910	+	11.3790i	0.168500	+	0.525435i
$470$	−1.00910	−	4.67006i	−0.0465463	−	0.215414i
$471$		0			0
$472$	15.4804	+	6.70579i	0.712545	+	0.308659i
$473$	−6.77189	−	11.7293i	−0.311372	−	0.539312i
$474$		0			0
$475$		−	29.1195i		−	1.33610i
$476$	11.2313	+	3.61329i	0.514786	+	0.165615i
$477$		0			0
$478$	−3.54619	+	11.0404i	−0.162199	+	0.504976i
$479$	7.56471	+	13.1025i	0.345641	+	0.598667i	0.985470	−	0.169850i	$-0.0543283\pi$
$479$	7.56471	+	13.1025i	0.345641	+	0.598667i	−0.639829	+	0.768517i	$0.720995\pi$
$480$		0			0
$481$	1.73035	+	0.999017i	0.0788970	+	0.0455512i
$482$	9.29349	−	2.00812i	0.423307	−	0.0914675i
$483$		0			0
$484$	17.2133	−	7.80316i	0.782421	−	0.354689i
$485$	−0.438258	−	0.253028i	−0.0199003	−	0.0114894i
$486$		0			0
$487$	−4.31159	+	2.48930i	−0.195377	+	0.112801i	−0.594497	−	0.804098i	$-0.702649\pi$
$487$	−4.31159	+	2.48930i	−0.195377	+	0.112801i	0.399120	+	0.916899i	$0.369316\pi$
$488$	25.7925	−	2.97462i	1.16757	−	0.134655i
$489$		0			0
$490$	−2.92797	+	0.937453i	−0.132272	+	0.0423498i
$491$	−12.9363			−0.583807			−0.291903	−	0.956448i	$-0.594289\pi$
$491$	−12.9363			−0.583807			−0.291903	+	0.956448i	$0.594289\pi$
$492$		0			0
$493$	−0.213857	−	0.370410i	−0.00963161	−	0.0166824i
$494$	−15.1642	−	16.7280i	−0.682271	−	0.752626i
$495$		0			0
$496$	10.3175	−	11.7739i	0.463271	−	0.528663i
$497$	−4.43877	+	20.4960i	−0.199106	+	0.919373i
$498$		0			0
$499$	4.01418	−	6.95277i	0.179700	−	0.311249i	−0.762078	−	0.647485i	$-0.775821\pi$
$499$	4.01418	−	6.95277i	0.179700	−	0.311249i	0.941778	+	0.336236i	$0.109154\pi$
$500$	5.00073	+	3.58204i	0.223640	+	0.160194i
$501$		0			0
$502$	−0.180622	+	0.562332i	−0.00806153	+	0.0250981i
$503$	3.41092			0.152085			0.0760427	−	0.997105i	$-0.475771\pi$
$503$	3.41092			0.152085			0.0760427	+	0.997105i	$0.475771\pi$
$504$		0			0
$505$	−0.676625			−0.0301094
$506$	−1.77928	+	5.53945i	−0.0790985	+	0.246259i
$507$		0			0
$508$	18.5212	−	25.8567i	0.821747	−	1.14721i
$509$	17.5417	−	30.3832i	0.777523	−	1.34671i	−0.155842	−	0.987782i	$-0.549809\pi$
$509$	17.5417	−	30.3832i	0.777523	−	1.34671i	0.933365	−	0.358928i	$-0.116858\pi$
$510$		0			0
$511$	−20.2962	+	6.50872i	−0.897852	+	0.287929i
$512$	21.2982	−	7.64111i	0.941256	−	0.337693i
$513$		0			0
$514$	13.9019	+	15.3354i	0.613185	+	0.676416i
$515$	0.496256	+	0.859541i	0.0218677	+	0.0378759i
$516$		0			0
$517$	−13.5451			−0.595713
$518$	−1.38926	−	2.40886i	−0.0610406	−	0.105839i
$519$		0			0
$520$	2.34597	−	0.270558i	0.102878	−	0.0118648i
$521$	−5.59051	+	3.22768i	−0.244925	+	0.141407i	−0.617438	−	0.786620i	$-0.711829\pi$
$521$	−5.59051	+	3.22768i	−0.244925	+	0.141407i	0.372513	+	0.928027i	$0.378496\pi$
$522$		0			0
$523$	11.2493	+	6.49478i	0.491897	+	0.283997i	0.725361	−	0.688368i	$-0.241673\pi$
$523$	11.2493	+	6.49478i	0.491897	+	0.283997i	−0.233464	+	0.972365i	$0.575006\pi$
$524$	−12.4616	−	27.4895i	−0.544388	−	1.20088i
$525$		0			0
$526$	−19.8246	+	4.28367i	−0.864394	+	0.186777i
$527$	7.55716	+	4.36313i	0.329195	+	0.190061i
$528$		0			0
$529$	−6.04126	−	10.4638i	−0.262663	−	0.454946i
$530$	1.67815	−	5.22462i	0.0728943	−	0.226943i
$531$		0			0
$532$	6.62241	+	30.7176i	0.287118	+	1.33178i
$533$			24.9657i			1.08139i
$534$		0			0
$535$	0.343270	+	0.594561i	0.0148409	+	0.0257051i
$536$	−5.07786	+	11.7223i	−0.219330	+	0.506328i
$537$		0			0
$538$	7.00684	+	32.4273i	0.302086	+	1.39804i
$539$	0.844561	+	8.67483i	0.0363778	+	0.373651i
$540$		0			0
$541$	−29.0331	−	16.7623i	−1.24823	−	0.720667i	−0.277475	−	0.960733i	$-0.589497\pi$
$541$	−29.0331	−	16.7623i	−1.24823	−	0.720667i	−0.970756	+	0.240066i	$0.922831\pi$
$542$	−14.3589	+	13.0166i	−0.616767	+	0.559112i
$543$		0			0
$544$	6.48942	+	10.8153i	0.278232	+	0.463703i
$545$		−	3.82543i		−	0.163863i
$546$		0			0
$547$	12.5739			0.537623			0.268811	−	0.963193i	$-0.413369\pi$
$547$	12.5739			0.537623			0.268811	+	0.963193i	$0.413369\pi$
$548$	−2.90051	+	29.5067i	−0.123904	+	1.26047i
$549$		0			0
$550$	6.39719	−	5.79918i	0.272777	−	0.247278i
$551$	0.569585	−	0.986549i	0.0242651	−	0.0420284i
$552$		0			0
$553$	−30.0546	−	27.2707i	−1.27805	−	1.15967i
$554$	9.04655	−	1.95476i	0.384351	−	0.0830500i
$555$		0			0
$556$	−0.883204	+	1.23300i	−0.0374562	+	0.0522910i
$557$	−6.60225	+	3.81181i	−0.279746	+	0.161512i	−0.633309	−	0.773899i	$-0.718304\pi$
$557$	−6.60225	+	3.81181i	−0.279746	+	0.161512i	0.353562	+	0.935411i	$0.384970\pi$
$558$		0			0
$559$	29.2436			1.23687
$560$	−3.01525	−	1.30781i	−0.127418	−	0.0552651i
$561$		0			0
$562$	30.3193	+	9.73860i	1.27894	+	0.410798i
$563$	−32.4941	+	18.7605i	−1.36946	+	0.790660i	−0.990859	−	0.134899i	$-0.956929\pi$
$563$	−32.4941	+	18.7605i	−1.36946	+	0.790660i	−0.378603	+	0.925559i	$0.623596\pi$
$564$		0			0
$565$	1.60267	−	2.77591i	0.0674249	−	0.116783i
$566$	19.1308	−	4.13375i	0.804127	−	0.173755i
$567$		0			0
$568$	−18.0034	+	13.3602i	−0.755407	+	0.560581i
$569$	−1.54166	+	2.67024i	−0.0646299	+	0.111942i	−0.896530	−	0.442984i	$-0.853920\pi$
$569$	−1.54166	+	2.67024i	−0.0646299	+	0.111942i	0.831900	+	0.554926i	$0.187253\pi$
$570$		0			0
$571$	14.4810	+	25.0818i	0.606011	+	1.04964i	0.991891	+	0.127093i	$0.0405646\pi$
$571$	14.4810	+	25.0818i	0.606011	+	1.04964i	−0.385880	+	0.922549i	$0.626102\pi$
$572$	0.654951	−	6.66278i	0.0273849	−	0.278585i
$573$		0			0
$574$	17.3871	−	30.0829i	0.725723	−	1.25564i
$575$		−	16.2021i		−	0.675676i
$576$		0			0
$577$	−6.94353	+	4.00885i	−0.289063	+	0.166890i	−0.637519	−	0.770435i	$-0.720039\pi$
$577$	−6.94353	+	4.00885i	−0.289063	+	0.166890i	0.348456	+	0.937325i	$0.386706\pi$
$578$	12.6033	−	11.4251i	0.524227	−	0.475222i
$579$		0			0
$580$	0.0491941	+	0.108519i	0.00204267	+	0.00450601i
$581$	−7.96587	+	36.7824i	−0.330480	+	1.52599i
$582$		0			0
$583$	−13.4728	−	7.77853i	−0.557986	−	0.322154i
$584$	−20.9086	−	9.05714i	−0.865203	−	0.374787i
$585$		0			0
$586$	16.0697	+	5.16161i	0.663834	+	0.213224i
$587$		−	27.9804i		−	1.15488i	−0.816434	−	0.577438i	$-0.804052\pi$
$587$		−	27.9804i		−	1.15488i	0.816434	−	0.577438i	$-0.195948\pi$
$588$		0			0
$589$			23.2415i			0.957649i
$590$	0.801119	−	2.49413i	0.0329815	−	0.102682i
$591$		0			0
$592$	0.578853	−	2.91586i	0.0237907	−	0.119841i
$593$	−6.88723	−	3.97634i	−0.282825	−	0.163289i	0.351877	−	0.936046i	$-0.385544\pi$
$593$	−6.88723	−	3.97634i	−0.282825	−	0.163289i	−0.634701	+	0.772757i	$0.718877\pi$
$594$		0			0
$595$	0.387768	−	1.79052i	0.0158969	−	0.0734041i
$596$	14.3049	+	31.5557i	0.585953	+	1.29257i
$597$		0			0
$598$	−8.43739	−	9.30745i	−0.345030	−	0.380610i
$599$	−29.4613	+	17.0095i	−1.20376	+	0.694989i	−0.961388	−	0.275195i	$-0.911257\pi$
$599$	−29.4613	+	17.0095i	−1.20376	+	0.694989i	−0.242368	+	0.970184i	$0.577924\pi$
$600$		0			0
$601$		−	21.9849i		−	0.896782i	−0.893837	−	0.448391i	$-0.851997\pi$
$601$		−	21.9849i		−	0.896782i	0.893837	−	0.448391i	$-0.148003\pi$
$602$	−35.2376	−	20.3664i	−1.43618	−	0.830071i
$603$		0			0
$604$	−43.4599	−	4.27211i	−1.76836	−	0.173830i
$605$	−1.46734	−	2.54151i	−0.0596560	−	0.103327i
$606$		0			0
$607$	−12.4261	+	21.5227i	−0.504361	+	0.873578i	0.495627	+	0.868536i	$0.334938\pi$
$607$	−12.4261	+	21.5227i	−0.504361	+	0.873578i	−0.999987	+	0.00504253i	$0.998395\pi$
$608$	−16.3043	+	29.3710i	−0.661228	+	1.19115i
$609$		0			0
$610$	−0.851492	−	3.94066i	−0.0344759	−	0.159553i
$611$	14.6232	−	25.3282i	0.591593	−	1.02467i
$612$		0			0
$613$	16.0142	−	9.24578i	0.646806	−	0.373434i	−0.140425	−	0.990091i	$-0.544847\pi$
$613$	16.0142	−	9.24578i	0.646806	−	0.373434i	0.787231	+	0.616658i	$0.211514\pi$
$614$	−0.846727	+	2.63613i	−0.0341711	+	0.106385i
$615$		0			0
$616$	−5.42941	+	7.57230i	−0.218757	+	0.305097i
$617$	4.59522			0.184997			0.0924983	−	0.995713i	$-0.470515\pi$
$617$	4.59522			0.184997			0.0924983	+	0.995713i	$0.470515\pi$
$618$		0			0
$619$	−7.77783	+	4.49053i	−0.312617	+	0.180490i	−0.648097	−	0.761558i	$-0.724435\pi$
$619$	−7.77783	+	4.49053i	−0.312617	+	0.180490i	0.335480	+	0.942047i	$0.391102\pi$
$620$	−1.97621	−	1.41556i	−0.0793665	−	0.0568505i
$621$		0			0
$622$	6.51885	+	30.1689i	0.261382	+	1.20966i
$623$	−12.5194	−	11.3598i	−0.501580	−	0.455119i
$624$		0			0
$625$	−11.7813	+	20.4058i	−0.471252	+	0.816232i
$626$	16.4269	+	18.1208i	0.656550	+	0.724253i
$627$		0			0
$628$	2.82643	−	28.7531i	0.112787	−	1.14737i
$629$	1.65706			0.0660714
$630$		0			0
$631$		−	19.3801i		−	0.771511i	−0.922601	−	0.385756i	$-0.873941\pi$
$631$		−	19.3801i		−	0.771511i	0.922601	−	0.385756i	$-0.126059\pi$
$632$	−4.97058	−	43.0992i	−0.197719	−	1.71440i
$633$		0			0
$634$	−6.66316	−	7.35027i	−0.264628	−	0.291916i
$635$	−4.27712	−	2.46940i	−0.169732	−	0.0979950i
$636$		0			0
$637$	−17.1330	−	7.78604i	−0.678832	−	0.308494i
$638$	0.330166	−	0.0713417i	0.0130714	−	0.00282444i
$639$		0			0
$640$	−1.50436	−	3.17524i	−0.0594649	−	0.125512i
$641$	16.2694	+	28.1793i	0.642601	+	1.11302i	0.984850	+	0.173408i	$0.0554779\pi$
$641$	16.2694	+	28.1793i	0.642601	+	1.11302i	−0.342249	+	0.939609i	$0.611189\pi$
$642$		0			0
$643$			41.5394i			1.63815i	0.573684	+	0.819077i	$0.305514\pi$
$643$			41.5394i			1.63815i	−0.573684	+	0.819077i	$0.694486\pi$
$644$	3.68471	+	17.0913i	0.145198	+	0.673492i
$645$		0			0
$646$	−17.8281	−	5.72641i	−0.701438	−	0.225302i
$647$	13.6161	+	23.5838i	0.535304	+	0.927174i	0.999149	+	0.0412571i	$0.0131363\pi$
$647$	13.6161	+	23.5838i	0.535304	+	0.927174i	−0.463845	+	0.885917i	$0.653530\pi$
$648$		0			0
$649$	−6.43166	−	3.71332i	−0.252465	−	0.145761i
$650$	3.93759	+	18.2230i	0.154445	+	0.714763i
$651$		0			0
$652$	−11.2648	+	5.10657i	−0.441162	+	0.199989i
$653$	−33.3010	−	19.2263i	−1.30317	−	0.752385i	−0.322222	−	0.946664i	$-0.604430\pi$
$653$	−33.3010	−	19.2263i	−1.30317	−	0.752385i	−0.980946	+	0.194279i	$0.937763\pi$
$654$		0			0
$655$	−4.05879	+	2.34334i	−0.158590	+	0.0915619i
$656$	35.1693	−	11.9532i	1.37313	−	0.466696i
$657$		0			0
$658$	−35.2600	+	20.3355i	−1.37458	+	0.792759i
$659$	0.588734			0.0229338			0.0114669	−	0.999934i	$-0.496350\pi$
$659$	0.588734			0.0229338			0.0114669	+	0.999934i	$0.496350\pi$
$660$		0			0
$661$	−5.80736	−	10.0586i	−0.225880	−	0.391236i	0.730703	−	0.682696i	$-0.239192\pi$
$661$	−5.80736	−	10.0586i	−0.225880	−	0.391236i	−0.956583	+	0.291459i	$0.905859\pi$
$662$	2.07482	−	1.88086i	0.0806400	−	0.0731018i
$663$		0			0
$664$	−32.3092	+	23.9763i	−1.25384	+	0.930462i
$665$	4.64635	−	1.49002i	0.180178	−	0.0577805i
$666$		0			0
$667$	0.316917	−	0.548917i	0.0122711	−	0.0212541i
$668$	37.7771	+	27.0599i	1.46164	+	1.04698i
$669$		0			0
$670$	1.88865	+	0.606636i	0.0729648	+	0.0234364i
$671$	−11.4296			−0.441233
$672$		0			0
$673$	−38.1246			−1.46960			−0.734798	−	0.678286i	$-0.762723\pi$
$673$	−38.1246			−1.46960			−0.734798	+	0.678286i	$0.762723\pi$
$674$	−3.41115	−	1.09566i	−0.131393	−	0.0422034i
$675$		0			0
$676$	−9.38516	−	6.72262i	−0.360968	−	0.258562i
$677$	−14.1674	+	24.5387i	−0.544498	+	0.943098i	0.454141	+	0.890930i	$0.349946\pi$
$677$	−14.1674	+	24.5387i	−0.544498	+	0.943098i	−0.998638	+	0.0521678i	$0.983387\pi$
$678$		0			0
$679$	−0.912520	+	4.21357i	−0.0350193	+	0.161702i
$680$	1.57277	−	1.16714i	0.0603128	−	0.0447576i
$681$		0			0
$682$	−5.10586	+	4.62856i	−0.195514	+	0.177237i
$683$	−16.3842	−	28.3783i	−0.626926	−	1.08587i	−0.988165	−	0.153394i	$-0.950980\pi$
$683$	−16.3842	−	28.3783i	−0.626926	−	1.08587i	0.361239	−	0.932473i	$-0.382354\pi$
$684$		0			0
$685$	4.60389			0.175905
$686$	15.2222	+	21.3140i	0.581185	+	0.813772i
$687$		0			0
$688$	−14.0014	−	41.1956i	−0.533800	−	1.57057i
$689$	29.0903	−	16.7953i	1.10825	−	0.639850i
$690$		0			0
$691$	14.7390	+	8.50955i	0.560697	+	0.323719i	0.753425	−	0.657534i	$-0.228400\pi$
$691$	14.7390	+	8.50955i	0.560697	+	0.323719i	−0.192728	+	0.981252i	$0.561734\pi$
$692$	32.5750	−	14.7670i	1.23832	−	0.561357i
$693$		0			0
$694$	−3.26572	−	15.1136i	−0.123965	−	0.573703i
$695$	0.203959	+	0.117756i	0.00773659	+	0.00446672i
$696$		0			0
$697$	10.3526	+	17.9312i	0.392133	+	0.679194i
$698$	16.3312	+	5.24560i	0.618145	+	0.198549i
$699$		0			0
$700$	7.94650	−	24.7004i	0.300350	−	0.933586i
$701$		−	30.8763i		−	1.16618i	−0.812406	−	0.583092i	$-0.801843\pi$
$701$		−	30.8763i		−	1.16618i	0.812406	−	0.583092i	$-0.198157\pi$
$702$		0			0
$703$	2.20671	+	3.82213i	0.0832275	+	0.144154i
$704$	−9.69947	+	2.26741i	−0.365562	+	0.0854564i
$705$		0			0
$706$	40.5027	−	8.75176i	1.52434	−	0.329377i
$707$	1.76026	+	5.48903i	0.0662013	+	0.206436i
$708$		0			0
$709$	12.1464	+	7.01270i	0.456166	+	0.263367i	0.710431	−	0.703767i	$-0.248500\pi$
$709$	12.1464	+	7.01270i	0.456166	+	0.263367i	−0.254265	+	0.967135i	$0.581833\pi$
$710$	2.33810	+	2.57921i	0.0877474	+	0.0967959i
$711$		0			0
$712$	−2.07053	−	17.9532i	−0.0775962	−	0.672826i
$713$			12.9316i			0.484292i
$714$		0			0
$715$	−1.03958			−0.0388781
$716$	−3.31339	+	33.7069i	−0.123827	+	1.25969i
$717$		0			0
$718$	3.26615	+	3.60295i	0.121891	+	0.134461i
$719$	18.8132	−	32.5854i	0.701613	−	1.21523i	−0.266288	−	0.963894i	$-0.585797\pi$
$719$	18.8132	−	32.5854i	0.701613	−	1.21523i	0.967900	−	0.251335i	$-0.0808696\pi$
$720$		0			0
$721$	5.68189	−	6.26193i	0.211605	−	0.233207i
$722$	−4.85824	−	22.4837i	−0.180805	−	0.836756i
$723$		0			0
$724$	−10.3395	−	7.40623i	−0.384265	−	0.275250i
$725$	−0.814622	+	0.470322i	−0.0302543	+	0.0174673i
$726$		0			0
$727$	39.3414			1.45909			0.729545	−	0.683933i	$-0.239732\pi$
$727$	39.3414			1.45909			0.729545	+	0.683933i	$0.239732\pi$
$728$	−8.29797	−	18.3275i	−0.307543	−	0.679264i
$729$		0			0
$730$	−1.08203	+	3.36869i	−0.0400476	+	0.124681i
$731$	21.0038	−	12.1265i	0.776852	−	0.448516i
$732$		0			0
$733$	20.2322	−	35.0431i	0.747292	−	1.29435i	−0.201824	−	0.979422i	$-0.564687\pi$
$733$	20.2322	−	35.0431i	0.747292	−	1.29435i	0.949116	−	0.314926i	$-0.101980\pi$
$734$	−3.42233	−	15.8384i	−0.126321	−	0.584605i
$735$		0			0
$736$	−9.07174	+	16.3421i	−0.334389	+	0.602377i
$737$	2.81186	−	4.87028i	0.103576	−	0.179399i
$738$		0			0
$739$	−4.18911	−	7.25575i	−0.154099	−	0.266907i	0.778632	−	0.627481i	$-0.215914\pi$
$739$	−4.18911	−	7.25575i	−0.154099	−	0.266907i	−0.932731	+	0.360574i	$0.882581\pi$
$740$	−0.459396	−	0.0451587i	−0.0168877	−	0.00166007i
$741$		0			0
$742$	−46.7498	−	0.0218206i	−1.71624	−	0.000801059i
$743$		−	16.9962i		−	0.623529i	−0.950159	−	0.311764i	$-0.899080\pi$
$743$		−	16.9962i		−	0.623529i	0.950159	−	0.311764i	$-0.100920\pi$
$744$		0			0
$745$	4.65916	−	2.68997i	0.170699	−	0.0985528i
$746$	7.10277	+	7.83521i	0.260051	+	0.286867i
$747$		0			0
$748$	−2.29247	−	5.05703i	−0.0838208	−	0.184903i
$749$	3.93028	−	4.33150i	0.143609	−	0.158270i
$750$		0			0
$751$	−11.0239	−	6.36463i	−0.402266	−	0.232249i	0.285195	−	0.958469i	$-0.407942\pi$
$751$	−11.0239	−	6.36463i	−0.402266	−	0.232249i	−0.687461	+	0.726221i	$0.741275\pi$
$752$	−42.6813	−	8.47303i	−1.55643	−	0.308980i
$753$		0			0
$754$	−0.223042	+	0.694401i	−0.00812272	+	0.0252886i
$755$			6.78097i			0.246785i
$756$		0			0
$757$			36.5299i			1.32770i	0.747864	+	0.663852i	$0.231079\pi$
$757$			36.5299i			1.32770i	−0.747864	+	0.663852i	$0.768921\pi$
$758$	−29.8518	−	9.58842i	−1.08426	−	0.348267i
$759$		0			0
$760$	4.78653	+	2.07342i	0.173626	+	0.0752109i
$761$	42.6597	+	24.6296i	1.54641	+	0.892822i	0.998411	+	0.0563444i	$0.0179445\pi$
$761$	42.6597	+	24.6296i	1.54641	+	0.892822i	0.548001	+	0.836477i	$0.315389\pi$
$762$		0			0
$763$	−31.0333	+	9.95194i	−1.12348	+	0.360284i
$764$	−2.10669	−	4.64722i	−0.0762173	−	0.168130i
$765$		0			0
$766$	18.3333	−	16.6195i	0.662410	−	0.600487i
$767$	13.8872	−	8.01776i	0.501437	−	0.289505i
$768$		0			0
$769$			19.8541i			0.715957i	0.933730	+	0.357979i	$0.116534\pi$
$769$			19.8541i			0.715957i	−0.933730	+	0.357979i	$0.883466\pi$
$770$	1.25266	+	0.724005i	0.0451428	+	0.0260913i
$771$		0			0
$772$	0.576586	−	5.86557i	0.0207518	−	0.211107i
$773$	−6.55810	−	11.3590i	−0.235879	−	0.408554i	0.723649	−	0.690168i	$-0.242463\pi$
$773$	−6.55810	−	11.3590i	−0.235879	−	0.408554i	−0.959528	+	0.281614i	$0.909130\pi$
$774$		0			0
$775$	9.59558	−	16.6200i	0.344683	−	0.597009i
$776$	−3.70114	+	2.74658i	−0.132863	+	0.0985965i
$777$		0			0
$778$	10.0546	−	2.17258i	0.360474	−	0.0778907i
$779$	−27.5731	+	47.7580i	−0.987909	+	1.71111i
$780$		0			0
$781$	8.54704	−	4.93464i	0.305837	−	0.176575i
$782$	−9.91957	−	3.18618i	−0.354723	−	0.113937i
$783$		0			0
$784$	−2.76521	+	27.8631i	−0.0987575	+	0.995112i
$785$	−4.48629			−0.160123
$786$		0			0
$787$	−12.9467	+	7.47476i	−0.461499	+	0.266447i	−0.712674	−	0.701495i	$-0.752516\pi$
$787$	−12.9467	+	7.47476i	−0.461499	+	0.266447i	0.251175	+	0.967942i	$0.419183\pi$
$788$	−20.5778	+	28.7277i	−0.733053	+	1.02338i
$789$		0			0
$790$	−6.58483	+	1.42284i	−0.234278	+	0.0506224i
$791$	−26.6886	−	5.77987i	−0.948938	−	0.205509i
$792$		0			0
$793$	12.3393	−	21.3723i	0.438181	−	0.758952i
$794$	−34.9316	+	31.6662i	−1.23968	+	1.12379i
$795$		0			0
$796$	−1.36571	+	13.8933i	−0.0484064	+	0.492435i
$797$	48.1132			1.70426			0.852128	−	0.523333i	$-0.175312\pi$
$797$	48.1132			1.70426			0.852128	+	0.523333i	$0.175312\pi$
$798$		0			0
$799$		−	24.2554i		−	0.858096i
$800$	23.7855	−	14.2718i	0.840945	−	0.504584i
$801$		0			0
$802$	−34.7151	+	31.4699i	−1.22583	+	1.11124i
$803$	8.68689	+	5.01538i	0.306554	+	0.176989i
$804$		0			0
$805$	2.58523	−	0.829048i	0.0911174	−	0.0292201i
$806$	−3.14275	−	14.5445i	−0.110699	−	0.512308i
$807$		0			0
$808$	−2.44947	+	5.65464i	−0.0861720	+	0.198930i
$809$	−16.0522	−	27.8032i	−0.564364	−	0.977508i	−0.997109	−	0.0759908i	$-0.975788\pi$
$809$	−16.0522	−	27.8032i	−0.564364	−	0.977508i	0.432744	−	0.901517i	$-0.357545\pi$
$810$		0			0
$811$		−	0.924758i		−	0.0324726i	−0.999868	−	0.0162363i	$-0.994832\pi$
$811$		−	0.924758i		−	0.0324726i	0.999868	−	0.0162363i	$-0.00516841\pi$
$812$	0.752367	−	0.681396i	0.0264029	−	0.0239123i
$813$		0			0
$814$	−0.400205	+	1.24596i	−0.0140272	+	0.0436710i
$815$	0.960264	+	1.66323i	0.0336366	+	0.0582603i
$816$		0			0
$817$	55.9414	+	32.2978i	1.95714	+	1.12996i
$818$	29.6627	−	6.40947i	1.03713	−	0.224102i
$819$		0			0
$820$	−2.38144	−	5.25331i	−0.0831637	−	0.183454i
$821$	−26.8884	−	15.5240i	−0.938413	−	0.541793i	−0.0489502	−	0.998801i	$-0.515588\pi$
$821$	−26.8884	−	15.5240i	−0.938413	−	0.541793i	−0.889462	+	0.457008i	$0.848921\pi$
$822$		0			0
$823$	4.91080	−	2.83525i	0.171180	−	0.0988307i	−0.411962	−	0.911201i	$-0.635156\pi$
$823$	4.91080	−	2.83525i	0.171180	−	0.0988307i	0.583142	+	0.812370i	$0.301823\pi$
$824$	8.97980	−	1.03563i	0.312826	−	0.0360779i
$825$		0			0
$826$	−22.3175	−	0.0104167i	−0.776524	−	0.000362445i
$827$	−15.9930			−0.556130			−0.278065	−	0.960562i	$-0.589693\pi$
$827$	−15.9930			−0.556130			−0.278065	+	0.960562i	$0.589693\pi$
$828$		0			0
$829$	−1.90039	−	3.29157i	−0.0660032	−	0.114321i	0.831135	−	0.556070i	$-0.187691\pi$
$829$	−1.90039	−	3.29157i	−0.0660032	−	0.114321i	−0.897139	+	0.441749i	$0.854358\pi$
$830$	4.19599	+	4.62868i	0.145645	+	0.160664i
$831$		0			0
$832$	6.23163	−	20.5850i	0.216043	−	0.713658i
$833$	−15.5341	+	1.51237i	−0.538226	+	0.0524004i
$834$		0			0
$835$	3.60783	−	6.24894i	0.124854	−	0.216254i
$836$	8.61151	−	12.0222i	0.297835	−	0.415795i
$837$		0			0
$838$	12.2738	−	38.2121i	0.423990	−	1.32002i
$839$	10.9412			0.377732			0.188866	−	0.982003i	$-0.439519\pi$
$839$	10.9412			0.377732			0.188866	+	0.982003i	$0.439519\pi$
$840$		0			0
$841$	28.9632			0.998731
$842$	15.5161	−	48.3066i	0.534722	−	1.66476i
$843$		0			0
$844$	14.9349	+	10.6979i	0.514081	+	0.368238i
$845$	−0.896312	+	1.55246i	−0.0308341	+	0.0534061i
$846$		0			0
$847$	−16.8004	+	18.5155i	−0.577268	+	0.636198i
$848$	−37.5877	−	32.9383i	−1.29077	−	1.13111i
$849$		0			0
$850$	10.3847	+	11.4556i	0.356192	+	0.392922i
$851$	1.22781	+	2.12663i	0.0420889	+	0.0729001i
$852$		0			0
$853$	−28.6102			−0.979594			−0.489797	−	0.871837i	$-0.662929\pi$
$853$	−28.6102			−0.979594			−0.489797	+	0.871837i	$0.662929\pi$
$854$	−29.7529	+	17.1594i	−1.01812	+	0.587181i
$855$		0			0
$856$	6.21151	−	0.716365i	0.212305	−	0.0244849i
$857$	−24.9796	+	14.4220i	−0.853287	+	0.492645i	−0.861758	−	0.507319i	$-0.830637\pi$
$857$	−24.9796	+	14.4220i	−0.853287	+	0.492645i	0.00847183	+	0.999964i	$0.497303\pi$
$858$		0			0
$859$	−13.6240	−	7.86585i	−0.464846	−	0.268379i	0.249233	−	0.968443i	$-0.419821\pi$
$859$	−13.6240	−	7.86585i	−0.464846	−	0.268379i	−0.714080	+	0.700064i	$0.753155\pi$
$860$	−6.15347	+	2.78951i	−0.209831	+	0.0951213i
$861$		0			0
$862$	22.6641	−	4.89722i	0.771942	−	0.166800i
$863$	12.1432	+	7.01089i	0.413360	+	0.238654i	0.692232	−	0.721675i	$-0.256627\pi$
$863$	12.1432	+	7.01089i	0.413360	+	0.238654i	−0.278872	+	0.960328i	$0.589961\pi$
$864$		0			0
$865$	−2.77686	−	4.80966i	−0.0944160	−	0.163533i
$866$	−14.4368	+	44.9462i	−0.490581	+	1.52733i
$867$		0			0
$868$	−6.34243	+	19.7144i	−0.215276	+	0.669149i
$869$			19.0988i			0.647881i
$870$		0			0
$871$	6.07134	+	10.5159i	0.205719	+	0.356316i
$872$	−31.9696	−	13.8485i	−1.08263	−	0.468970i
$873$		0			0
$874$	−5.86074	−	27.1232i	−0.198243	−	0.917456i
$875$	−7.95302	−	1.72236i	−0.268861	−	0.0582265i
$876$		0			0
$877$	26.6956	+	15.4127i	0.901446	+	0.520450i	0.877669	−	0.479267i	$-0.159097\pi$
$877$	26.6956	+	15.4127i	0.901446	+	0.520450i	0.0237773	+	0.999717i	$0.492431\pi$
$878$	35.0614	−	31.7838i	1.18326	−	1.07265i
$879$		0			0
$880$	0.497737	+	1.46446i	0.0167787	+	0.0493670i
$881$			9.33799i			0.314605i	0.987550	+	0.157302i	$0.0502797\pi$
$881$			9.33799i			0.314605i	−0.987550	+	0.157302i	$0.949720\pi$
$882$		0			0
$883$	−21.7043			−0.730408			−0.365204	−	0.930927i	$-0.619001\pi$
$883$	−21.7043			−0.730408			−0.365204	+	0.930927i	$0.619001\pi$
$884$	11.9311	+	1.17283i	0.401287	+	0.0394466i
$885$		0			0
$886$	−34.1169	+	30.9277i	−1.14618	+	1.03904i
$887$	−9.89190	+	17.1333i	−0.332138	+	0.575279i	−0.982931	−	0.183976i	$-0.941103\pi$
$887$	−9.89190	+	17.1333i	−0.332138	+	0.575279i	0.650793	+	0.759255i	$0.274436\pi$
$888$		0			0
$889$	−8.90562	+	41.1218i	−0.298685	+	1.37918i
$890$	−2.74295	+	0.592693i	−0.0919439	+	0.0198671i
$891$		0			0
$892$	16.3014	+	11.6767i	0.545810	+	0.390966i
$893$	55.9468	−	32.3009i	1.87219	−	1.08091i
$894$		0			0
$895$	5.25923			0.175797
$896$	−21.8451	+	20.4644i	−0.729795	+	0.683667i
$897$		0			0
$898$	16.0412	+	5.15245i	0.535302	+	0.171940i
$899$	0.650183	−	0.375383i	0.0216848	−	0.0125197i
$900$		0			0
$901$	13.9291	−	24.1259i	0.464046	−	0.803752i
$902$	−15.9830	+	3.45359i	−0.532177	+	0.114992i
$903$		0			0
$904$	−17.3968	−	23.4429i	−0.578607	−	0.779699i
$905$	−0.987456	+	1.71032i	−0.0328242	+	0.0568531i
$906$		0			0
$907$	−13.0878	−	22.6688i	−0.434574	−	0.752704i	0.562687	−	0.826670i	$-0.309768\pi$
$907$	−13.0878	−	22.6688i	−0.434574	−	0.752704i	−0.997261	+	0.0739661i	$0.976434\pi$
$908$	−13.3264	−	1.30999i	−0.442252	−	0.0434734i
$909$		0			0
$910$	−2.70619	+	1.56074i	−0.0897094	+	0.0517379i
$911$			0.701753i			0.0232501i	0.999932	+	0.0116251i	$0.00370045\pi$
$911$			0.701753i			0.0232501i	−0.999932	+	0.0116251i	$0.996300\pi$
$912$		0			0
$913$	15.3386	−	8.85576i	0.507634	−	0.293083i
$914$	−6.37246	+	5.77676i	−0.210782	+	0.191078i
$915$		0			0
$916$	−5.87224	+	2.66202i	−0.194024	+	0.0879555i
$917$	29.5691	+	26.8301i	0.976457	+	0.886009i
$918$		0			0
$919$	−24.7946	−	14.3152i	−0.817899	−	0.472214i	0.0317922	−	0.999494i	$-0.489879\pi$
$919$	−24.7946	−	14.3152i	−0.817899	−	0.472214i	−0.849692	+	0.527280i	$0.823212\pi$
$920$	2.66323	+	1.15365i	0.0878040	+	0.0380348i
$921$		0			0
$922$	47.2659	+	15.1819i	1.55662	+	0.499988i
$923$			21.3096i			0.701415i
$924$		0			0
$925$		−	3.64428i		−	0.119823i
$926$	−2.39465	+	7.45530i	−0.0786931	+	0.244996i
$927$		0			0
$928$	1.08500	−	0.0182690i	0.0356167	−	0.000599708i
$929$	−23.0348	−	13.2992i	−0.755747	−	0.436331i	0.0720194	−	0.997403i	$-0.477056\pi$
$929$	−23.0348	−	13.2992i	−0.755747	−	0.436331i	−0.827767	+	0.561072i	$0.810389\pi$
$930$		0			0
$931$	−24.1752	−	33.8166i	−0.792309	−	1.10829i
$932$	−26.3835	+	11.9602i	−0.864221	+	0.391771i
$933$		0			0
$934$	14.7971	+	16.3230i	0.484176	+	0.534104i
$935$	−0.746663	+	0.431086i	−0.0244185	+	0.0140980i
$936$		0			0
$937$			35.1395i			1.14796i	0.818870	+	0.573979i	$0.194601\pi$
$937$			35.1395i			1.14796i	−0.818870	+	0.573979i	$0.805399\pi$
$938$	0.00788793	−	16.8996i	0.000257550	−	0.551791i
$939$		0			0
$940$	−0.661016	+	6.72447i	−0.0215600	+	0.219328i
$941$	−10.5715	−	18.3104i	−0.344621	−	0.596902i	0.640663	−	0.767822i	$-0.278659\pi$
$941$	−10.5715	−	18.3104i	−0.344621	−	0.596902i	−0.985285	+	0.170920i	$0.945326\pi$
$942$		0			0
$943$	−15.3417	+	26.5726i	−0.499594	+	0.865323i
$944$	−17.9436	−	15.7241i	−0.584016	−	0.511777i
$945$		0			0
$946$	4.04536	+	18.7217i	0.131526	+	0.608696i
$947$	−2.51505	+	4.35619i	−0.0817280	+	0.141557i	−0.903992	−	0.427549i	$-0.859377\pi$
$947$	−2.51505	+	4.35619i	−0.0817280	+	0.141557i	0.822264	+	0.569106i	$0.192711\pi$
$948$		0			0
$949$	−18.7566	+	10.8292i	−0.608866	+	0.351529i
$950$	−12.5938	+	39.2083i	−0.408595	+	1.27209i
$951$		0			0
$952$	−13.5598	−	9.72253i	−0.439477	−	0.315109i
$953$	−7.79671			−0.252560			−0.126280	−	0.991995i	$-0.540304\pi$
$953$	−7.79671			−0.252560			−0.126280	+	0.991995i	$0.540304\pi$
$954$		0			0
$955$	−0.686156	+	0.396152i	−0.0222035	+	0.0128192i
$956$	9.54961	−	13.3318i	0.308856	−	0.431181i
$957$		0			0
$958$	−4.51898	−	20.9136i	−0.146001	−	0.675687i
$959$	−11.9771	−	37.3484i	−0.386762	−	1.20604i
$960$		0			0
$961$	7.84138	−	13.5817i	0.252948	−	0.438118i
$962$	−1.89779	−	2.09349i	−0.0611871	−	0.0674967i
$963$		0			0
$964$	−13.3818	−	1.31543i	−0.430999	−	0.0423672i
$965$	−0.915195			−0.0294612
$966$		0			0
$967$		−	43.5181i		−	1.39945i	−0.714413	−	0.699725i	$-0.753306\pi$
$967$		−	43.5181i		−	1.39945i	0.714413	−	0.699725i	$-0.246694\pi$
$968$	−26.5517	+	3.06218i	−0.853405	+	0.0984221i
$969$		0			0
$970$	0.480666	+	0.530232i	0.0154333	+	0.0170247i
$971$	40.4782	+	23.3701i	1.29901	+	0.749982i	0.980233	−	0.197849i	$-0.0633955\pi$
$971$	40.4782	+	23.3701i	1.29901	+	0.749982i	0.318774	+	0.947831i	$0.396729\pi$
$972$		0			0
$973$	0.424673	−	1.96093i	0.0136144	−	0.0628646i
$974$	6.88197	−	1.48705i	0.220513	−	0.0476480i
$975$		0			0
$976$	−36.0151	−	7.14966i	−1.15282	−	0.228855i
$977$	12.1197	+	20.9919i	0.387743	+	0.671591i	0.992146	−	0.125088i	$-0.0399214\pi$
$977$	12.1197	+	20.9919i	0.387743	+	0.671591i	−0.604402	+	0.796679i	$0.706588\pi$
$978$		0			0
$979$			7.95570i			0.254265i
$980$	4.34783	+	0.00405873i	0.138886	+	0.000129651i
$981$		0			0
$982$	17.4182	+	5.59475i	0.555837	+	0.178536i
$983$	15.9252	+	27.5832i	0.507934	+	0.879767i	0.999958	+	0.00918542i	$0.00292385\pi$
$983$	15.9252	+	27.5832i	0.507934	+	0.879767i	−0.492024	+	0.870582i	$0.663743\pi$
$984$		0			0
$985$	4.75203	+	2.74359i	0.151412	+	0.0874180i
$986$	0.127753	+	0.591233i	0.00406847	+	0.0188287i
$987$		0			0
$988$	13.1835	+	29.0818i	0.419421	+	0.925216i
$989$	31.1258	+	17.9705i	0.989743	+	0.571428i
$990$		0			0
$991$	3.32918	−	1.92210i	0.105755	−	0.0610575i	−0.446190	−	0.894938i	$-0.647219\pi$
$991$	3.32918	−	1.92210i	0.105755	−	0.0610575i	0.551945	+	0.833881i	$0.313886\pi$
$992$	−18.9842	+	11.3909i	−0.602748	+	0.361662i
$993$		0			0
$994$	14.8409	−	25.6774i	0.470723	−	0.814439i
$995$	2.16775			0.0687222
$996$		0			0
$997$	28.6326	+	49.5931i	0.906803	+	1.57063i	0.818479	+	0.574537i	$0.194818\pi$
$997$	28.6326	+	49.5931i	0.906803	+	1.57063i	0.0883239	+	0.996092i	$0.471849\pi$
$998$	−8.41191	+	7.62556i	−0.266274	+	0.241383i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.2		32
3.2	odd	2		168.2.t.a.19.15	yes	32
4.3	odd	2		2016.2.bs.c.271.10		32
7.3	odd	6	inner	504.2.bk.c.451.14		32
8.3	odd	2	inner	504.2.bk.c.19.14		32
8.5	even	2		2016.2.bs.c.271.7		32
12.11	even	2		672.2.bb.a.271.4		32
21.2	odd	6		1176.2.p.a.979.13		32
21.5	even	6		1176.2.p.a.979.14		32
21.17	even	6		168.2.t.a.115.3	yes	32
24.5	odd	2		672.2.bb.a.271.5		32
24.11	even	2		168.2.t.a.19.3	✓	32
28.3	even	6		2016.2.bs.c.1711.7		32
56.3	even	6	inner	504.2.bk.c.451.2		32
56.45	odd	6		2016.2.bs.c.1711.10		32
84.23	even	6		4704.2.p.a.3919.21		32
84.47	odd	6		4704.2.p.a.3919.14		32
84.59	odd	6		672.2.bb.a.367.5		32
168.5	even	6		4704.2.p.a.3919.22		32
168.59	odd	6		168.2.t.a.115.15	yes	32
168.101	even	6		672.2.bb.a.367.4		32
168.107	even	6		1176.2.p.a.979.16		32
168.131	odd	6		1176.2.p.a.979.15		32
168.149	odd	6		4704.2.p.a.3919.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.3	✓	32	24.11	even	2
168.2.t.a.19.15	yes	32	3.2	odd	2
168.2.t.a.115.3	yes	32	21.17	even	6
168.2.t.a.115.15	yes	32	168.59	odd	6
504.2.bk.c.19.2		32	1.1	even	1	trivial
504.2.bk.c.19.14		32	8.3	odd	2	inner
504.2.bk.c.451.2		32	56.3	even	6	inner
504.2.bk.c.451.14		32	7.3	odd	6	inner
672.2.bb.a.271.4		32	12.11	even	2
672.2.bb.a.271.5		32	24.5	odd	2
672.2.bb.a.367.4		32	168.101	even	6
672.2.bb.a.367.5		32	84.59	odd	6
1176.2.p.a.979.13		32	21.2	odd	6
1176.2.p.a.979.14		32	21.5	even	6
1176.2.p.a.979.15		32	168.131	odd	6
1176.2.p.a.979.16		32	168.107	even	6
2016.2.bs.c.271.7		32	8.5	even	2
2016.2.bs.c.271.10		32	4.3	odd	2
2016.2.bs.c.1711.7		32	28.3	even	6
2016.2.bs.c.1711.10		32	56.45	odd	6
4704.2.p.a.3919.13		32	168.149	odd	6
4704.2.p.a.3919.14		32	84.47	odd	6
4704.2.p.a.3919.21		32	84.23	even	6
4704.2.p.a.3919.22		32	168.5	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34646 - 0.432485i) q^{2} +(1.62591 + 1.16465i) q^{4} +(0.155280 - 0.268953i) q^{5} +(-2.58581 - 0.560001i) q^{7} +(-1.68554 - 2.27133i) q^{8} +O(q^{10})\)	\(q+(-1.34646 - 0.432485i) q^{2} +(1.62591 + 1.16465i) q^{4} +(0.155280 - 0.268953i) q^{5} +(-2.58581 - 0.560001i) q^{7} +(-1.68554 - 2.27133i) q^{8} +(-0.325396 + 0.294978i) q^{10} +(0.622560 + 1.07831i) q^{11} -2.68845 q^{13} +(3.23950 + 1.87234i) q^{14} +(1.28719 + 3.78723i) q^{16} +(-1.93094 + 1.11483i) q^{17} +(-5.14286 - 2.96923i) q^{19} +(0.565707 - 0.256448i) q^{20} +(-0.371902 - 1.72114i) q^{22} +(-2.86149 - 1.65208i) q^{23} +(2.45178 + 4.24660i) q^{25} +(3.61989 + 1.16271i) q^{26} +(-3.55210 - 3.92207i) q^{28} +0.191829i q^{29} +(-1.95686 - 3.38939i) q^{31} +(-0.0952356 - 5.65605i) q^{32} +(3.08208 - 0.665971i) q^{34} +(-0.552137 + 0.608503i) q^{35} +(-0.643623 - 0.371596i) q^{37} +(5.64051 + 6.22216i) q^{38} +(-0.872611 + 0.100637i) q^{40} -9.28628i q^{41} -10.8775 q^{43} +(-0.243617 + 2.47830i) q^{44} +(3.13838 + 3.46201i) q^{46} +(-5.43928 + 9.42111i) q^{47} +(6.37280 + 2.89611i) q^{49} +(-1.46463 - 6.77824i) q^{50} +(-4.37119 - 3.13110i) q^{52} +(-10.8205 + 6.24721i) q^{53} +0.386684 q^{55} +(3.08653 + 6.81714i) q^{56} +(0.0829632 - 0.258290i) q^{58} +(-5.16549 + 2.98230i) q^{59} +(-4.58974 + 7.94967i) q^{61} +(1.16898 + 5.40999i) q^{62} +(-2.31792 + 7.65684i) q^{64} +(-0.417462 + 0.723066i) q^{65} +(-2.25830 - 3.91150i) q^{67} +(-4.43792 - 0.436248i) q^{68} +(1.00660 - 0.580534i) q^{70} -7.92636i q^{71} +(6.97675 - 4.02803i) q^{73} +(0.705903 + 0.778696i) q^{74} +(-4.90374 - 10.8173i) q^{76} +(-1.00597 - 3.13693i) q^{77} +(13.2839 + 7.66944i) q^{79} +(1.21846 + 0.241887i) q^{80} +(-4.01618 + 12.5036i) q^{82} -14.2247i q^{83} +0.692441i q^{85} +(14.6461 + 4.70435i) q^{86} +(1.39985 - 3.23157i) q^{88} +(5.53347 + 3.19475i) q^{89} +(6.95181 + 1.50553i) q^{91} +(-2.72844 - 6.01877i) q^{92} +(11.3983 - 10.3327i) q^{94} +(-1.59716 + 0.922123i) q^{95} -1.62950i q^{97} +(-7.32820 - 6.65563i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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