LMFDB - Embedded newform 504.2.bk.c.19.14

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			19.14
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04777 + 0.949827i) q^{2} +(0.195657 + 1.99041i) q^{4} +(-0.155280 + 0.268953i) q^{5} +(2.58581 + 0.560001i) q^{7} +(-1.68554 + 2.27133i) q^{8} +O(q^{10})$	\(q+(1.04777 + 0.949827i) q^{2} +(0.195657 + 1.99041i) q^{4} +(-0.155280 + 0.268953i) q^{5} +(2.58581 + 0.560001i) q^{7} +(-1.68554 + 2.27133i) q^{8} +(-0.418156 + 0.134312i) q^{10} +(0.622560 + 1.07831i) q^{11} +2.68845 q^{13} +(2.17744 + 3.04282i) q^{14} +(-3.92344 + 0.778874i) q^{16} +(-1.93094 + 1.11483i) q^{17} +(-5.14286 - 2.96923i) q^{19} +(-0.565707 - 0.256448i) q^{20} +(-0.371902 + 1.72114i) q^{22} +(2.86149 + 1.65208i) q^{23} +(2.45178 + 4.24660i) q^{25} +(2.81689 + 2.55356i) q^{26} +(-0.608698 + 5.25638i) q^{28} -0.191829i q^{29} +(1.95686 + 3.38939i) q^{31} +(-4.85067 - 2.91050i) q^{32} +(-3.08208 - 0.665971i) q^{34} +(-0.552137 + 0.608503i) q^{35} +(0.643623 + 0.371596i) q^{37} +(-2.56829 - 7.99590i) q^{38} +(-0.349151 - 0.806022i) q^{40} -9.28628i q^{41} -10.8775 q^{43} +(-2.02446 + 1.45013i) q^{44} +(1.42900 + 4.44893i) q^{46} +(5.43928 - 9.42111i) q^{47} +(6.37280 + 2.89611i) q^{49} +(-1.46463 + 6.77824i) q^{50} +(0.526014 + 5.35111i) q^{52} +(10.8205 - 6.24721i) q^{53} -0.386684 q^{55} +(-5.63043 + 4.92933i) q^{56} +(0.182205 - 0.200993i) q^{58} +(-5.16549 + 2.98230i) q^{59} +(4.58974 - 7.94967i) q^{61} +(-1.16898 + 5.40999i) q^{62} +(-2.31792 - 7.65684i) q^{64} +(-0.417462 + 0.723066i) q^{65} +(-2.25830 - 3.91150i) q^{67} +(-2.59676 - 3.62523i) q^{68} +(-1.15649 + 0.113138i) q^{70} +7.92636i q^{71} +(6.97675 - 4.02803i) q^{73} +(0.321419 + 1.00068i) q^{74} +(4.90374 - 10.8173i) q^{76} +(1.00597 + 3.13693i) q^{77} +(-13.2839 - 7.66944i) q^{79} +(0.399750 - 1.17616i) q^{80} +(8.82036 - 9.72992i) q^{82} -14.2247i q^{83} -0.692441i q^{85} +(-11.3971 - 10.3317i) q^{86} +(-3.49854 - 0.403483i) q^{88} +(5.53347 + 3.19475i) q^{89} +(6.95181 + 1.50553i) q^{91} +(-2.72844 + 6.01877i) q^{92} +(14.6476 - 4.70481i) q^{94} +(1.59716 - 0.922123i) q^{95} -1.62950i q^{97} +(3.92645 + 9.08752i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.04777	+	0.949827i	0.740887	+	0.671629i
$2$	1.04777	+	0.949827i	0.740887	+	0.671629i
$3$		0			0
$3$		0			0
$4$	0.195657	+	1.99041i	0.0978285	+	0.995203i
$5$	−0.155280	+	0.268953i	−0.0694432	+	0.120279i	−0.898656	−	0.438653i	$-0.855456\pi$
$5$	−0.155280	+	0.268953i	−0.0694432	+	0.120279i	0.829213	+	0.558933i	$0.188789\pi$
$6$		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
$10$	−0.418156	+	0.134312i	−0.132233	+	0.0424733i
$11$	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	$-0.378391\pi$
$13$	2.68845			0.745642			0.372821	+	0.927903i	$0.378391\pi$
$14$	2.17744	+	3.04282i	0.581944	+	0.813229i
$15$		0			0
$16$	−3.92344	+	0.778874i	−0.980859	+	0.194719i
$17$	−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	0.767727	−	0.640777i	$-0.221388\pi$
$23$	2.86149	+	1.65208i	0.596662	+	0.344483i	−0.171066	+	0.985260i	$0.554721\pi$
$24$		0			0
$25$	2.45178	+	4.24660i	0.490355	+	0.849320i
$26$	2.81689	+	2.55356i	0.552437	+	0.500795i
$27$		0			0
$28$	−0.608698	+	5.25638i	−0.115033	+	0.993362i
$29$		−	0.191829i		−	0.0356218i	−0.999841	−	0.0178109i	$-0.994330\pi$
$29$		−	0.191829i		−	0.0356218i	0.999841	−	0.0178109i	$-0.00566968\pi$
$30$		0			0
$31$	1.95686	+	3.38939i	0.351463	+	0.608752i	0.986506	−	0.163725i	$-0.0523510\pi$
$31$	1.95686	+	3.38939i	0.351463	+	0.608752i	−0.635043	+	0.772477i	$0.719018\pi$
$32$	−4.85067	−	2.91050i	−0.857485	−	0.514509i
$33$		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	0.551972	−	0.833863i	$-0.313876\pi$
$37$	0.643623	+	0.371596i	0.105811	+	0.0610900i	−0.446161	+	0.894953i	$0.647209\pi$
$38$	−2.56829	−	7.99590i	−0.416632	−	1.29711i
$39$		0			0
$40$	−0.349151	−	0.806022i	−0.0552057	−	0.127443i
$41$		−	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	$0.811318\pi$
$44$	−2.02446	+	1.45013i	−0.305199	+	0.218615i
$45$		0			0
$46$	1.42900	+	4.44893i	0.210694	+	0.655958i
$47$	5.43928	−	9.42111i	0.793400	−	1.37421i	−0.130450	−	0.991455i	$-0.541642\pi$
$47$	5.43928	−	9.42111i	0.793400	−	1.37421i	0.923850	−	0.382755i	$-0.125025\pi$
$48$		0			0
$49$	6.37280	+	2.89611i	0.910400	+	0.413730i
$50$	−1.46463	+	6.77824i	−0.207130	+	0.958588i
$51$		0			0
$52$	0.526014	+	5.35111i	0.0729451	+	0.742065i
$53$	10.8205	−	6.24721i	1.48631	−	0.858120i	0.486429	−	0.873720i	$-0.338299\pi$
$53$	10.8205	−	6.24721i	1.48631	−	0.858120i	0.999878	+	0.0156002i	$0.00496591\pi$
$54$		0			0
$55$	−0.386684			−0.0521405
$56$	−5.63043	+	4.92933i	−0.752397	+	0.658710i
$57$		0			0
$58$	0.182205	−	0.200993i	0.0239246	−	0.0263917i
$59$	−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	$-0.633384\pi$
$61$	4.58974	−	7.94967i	0.587656	−	1.01785i	0.994539	−	0.104370i	$-0.0332826\pi$
$62$	−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	$0.922308\pi$
$68$	−2.59676	−	3.62523i	−0.314904	−	0.439624i
$69$		0			0
$70$	−1.15649	+	0.113138i	−0.138227	+	0.0135225i
$71$			7.92636i			0.940686i	0.882484	+	0.470343i	$0.155870\pi$
$71$			7.92636i			0.940686i	−0.882484	+	0.470343i	$0.844130\pi$
$72$		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	$0.177066\pi$
$74$	0.321419	+	1.00068i	0.0373642	+	0.116326i
$75$		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	−0.494571	−	0.869137i	$-0.664675\pi$
$79$	−13.2839	−	7.66944i	−1.49455	−	0.862880i	−0.999980	+	0.00625715i	$0.998008\pi$
$80$	0.399750	−	1.17616i	0.0446934	−	0.131499i
$81$		0			0
$82$	8.82036	−	9.72992i	0.974046	−	1.07449i
$83$		−	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
$86$	−11.3971	−	10.3317i	−1.22899	−	1.11410i
$87$		0			0
$88$	−3.49854	−	0.403483i	−0.372946	−	0.0430114i
$89$	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
$94$	14.6476	−	4.70481i	1.51078	−	0.485264i
$95$	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	$-0.0263624\pi$
$98$	3.92645	+	9.08752i	0.396631	+	0.917978i
$99$		0			0
$100$	−7.97276	+	5.71091i	−0.797276	+	0.571091i
$101$	1.08936	+	1.88683i	0.108396	+	0.187747i	0.915121	−	0.403180i	$-0.132095\pi$
$101$	1.08936	+	1.88683i	0.108396	+	0.187747i	−0.806725	+	0.590927i	$0.798762\pi$
$102$		0			0
$103$	1.59794	−	2.76772i	0.157450	−	0.272711i	−0.776499	−	0.630119i	$-0.783006\pi$
$103$	1.59794	−	2.76772i	0.157450	−	0.272711i	0.933948	+	0.357408i	$0.116339\pi$
$104$	−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	−0.914615	−	0.404325i	$-0.867507\pi$
$109$	−10.6676	+	6.15892i	−1.02177	+	0.589918i	−0.107152	+	0.994243i	$0.534173\pi$
$110$	−0.405157	−	0.367283i	−0.0386302	−	0.0350191i
$111$		0			0
$112$	−10.5814	−	0.183108i	−0.999850	−	0.0173021i
$113$	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
$116$	0.381818	−	0.0375327i	0.0354509	−	0.00348483i
$117$		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
$122$	12.3598	−	3.96999i	1.11901	−	0.359426i
$123$		0			0
$124$	−6.36338	+	4.55811i	−0.571448	+	0.409330i
$125$	−3.07564			−0.275094
$126$		0			0
$127$			15.9029i			1.41115i	0.708634	+	0.705576i	$0.249312\pi$
$127$			15.9029i			1.41115i	−0.708634	+	0.705576i	$0.750688\pi$
$128$	4.84402	−	10.2243i	0.428155	−	0.903706i
$129$		0			0
$130$	−1.12419	+	0.361092i	−0.0985982	+	0.0316699i
$131$	−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
$136$	0.722522	−	6.26489i	0.0619558	−	0.537210i
$137$	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	$0.989761\pi$
$140$	−1.31920	−	0.979920i	−0.111493	−	0.0828183i
$141$		0			0
$142$	−7.52867	+	8.30503i	−0.631792	+	0.696943i
$143$	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	−0.262219	−	0.965008i	$-0.584454\pi$
$149$	−15.0025	−	8.66168i	−1.22905	−	0.709593i	−0.966831	+	0.255416i	$0.917788\pi$
$150$		0			0
$151$	18.9094	−	10.9173i	1.53882	−	0.888441i	0.539917	−	0.841718i	$-0.318456\pi$
$151$	18.9094	−	10.9173i	1.53882	−	0.888441i	0.998908	−	0.0467227i	$-0.0148777\pi$
$152$	15.4126	−	6.67640i	1.25013	−	0.541527i
$153$		0			0
$154$	−1.92551	+	4.24228i	−0.155162	+	0.341853i
$155$	−1.21545			−0.0976269
$156$		0			0
$157$	7.22291	+	12.5104i	0.576451	+	0.998443i	0.995882	+	0.0906554i	$0.0288962\pi$
$157$	7.22291	+	12.5104i	0.576451	+	0.998443i	−0.419431	+	0.907787i	$0.637770\pi$
$158$	−6.63383	−	20.6532i	−0.527759	−	1.64308i
$159$		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	$0.244532\pi$
$164$	18.4835	−	1.81693i	1.44332	−	0.141878i
$165$		0			0
$166$	13.5110	−	14.9043i	1.04866	−	1.15680i
$167$	−23.2344			−1.79793			−0.898965	−	0.438021i	$-0.855680\pi$
$167$	−23.2344			−1.79793			−0.898965	+	0.438021i	$0.855680\pi$
$168$		0			0
$169$	−5.77223			−0.444018
$170$	0.657699	−	0.725521i	0.0504432	−	0.0556449i
$171$		0			0
$172$	−2.12826	−	21.6506i	−0.162278	−	1.65084i
$173$	−8.94146	+	15.4871i	−0.679807	+	1.17746i	0.295232	+	0.955426i	$0.404603\pi$
$173$	−8.94146	+	15.4871i	−0.679807	+	1.17746i	−0.975039	+	0.222034i	$0.928730\pi$
$174$		0			0
$175$	3.96172	+	12.3539i	0.299478	+	0.933866i
$176$	−3.28244	−	3.74577i	−0.247423	−	0.282348i
$177$		0			0
$178$	2.76336	+	8.60322i	0.207123	+	0.644838i
$179$	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	$-0.424053\pi$
$181$	6.35921			0.472676			0.236338	+	0.971671i	$0.424053\pi$
$182$	5.85393	+	8.18048i	0.433922	+	0.606378i
$183$		0			0
$184$	−8.57558	+	3.71475i	−0.632200	+	0.273855i
$185$	−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	0.577800	−	0.816179i	$-0.303912\pi$
$191$	2.20942	+	1.27561i	0.159868	+	0.0922997i	−0.417932	+	0.908478i	$0.637245\pi$
$192$		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	$0.867158\pi$
$194$	1.54774	−	1.70734i	0.111121	−	0.122580i
$195$		0			0
$196$	−4.51755	+	13.2511i	−0.322682	+	0.946507i
$197$		−	17.6687i		−	1.25884i	−0.777065	−	0.629420i	$-0.783292\pi$
$197$		−	17.6687i		−	1.25884i	0.777065	−	0.629420i	$-0.216708\pi$
$198$		0			0
$199$	−3.49007	−	6.04497i	−0.247404	−	0.428517i	0.715401	−	0.698715i	$-0.246244\pi$
$199$	−3.49007	−	6.04497i	−0.247404	−	0.428517i	−0.962805	+	0.270198i	$0.912911\pi$
$200$	−13.7780	−	1.58900i	−0.974253	−	0.112359i
$201$		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
$206$	4.30313	−	1.38217i	0.299813	−	0.0963004i
$207$		0			0
$208$	−10.5480	+	2.09396i	−0.731370	+	0.145190i
$209$		−	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	$0.397600\pi$
$212$	14.5516	+	20.3148i	0.999407	+	1.39523i
$213$		0			0
$214$	−2.97656	+	0.956075i	−0.203474	+	0.0653559i
$215$	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
$220$	−0.0756575	−	0.769659i	−0.00510083	−	0.0518904i
$221$	−5.19123	+	2.99716i	−0.349200	+	0.201611i
$222$		0			0
$223$	−10.0260			−0.671389			−0.335695	−	0.941971i	$-0.608971\pi$
$223$	−10.0260			−0.671389			−0.335695	+	0.941971i	$0.608971\pi$
$224$	−10.9130	−	10.2424i	−0.729156	−	0.684348i
$225$		0			0
$226$	10.8143	+	9.80335i	0.719354	+	0.652109i
$227$	−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	−0.807841	−	0.589400i	$-0.799364\pi$
$229$	1.61186	−	2.79182i	0.106515	−	0.184489i	0.914356	+	0.404911i	$0.132698\pi$
$230$	−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
$236$	−6.94665	−	9.69792i	−0.452189	−	0.631281i
$237$		0			0
$238$	−7.59672	−	3.44804i	−0.492422	−	0.223503i
$239$			8.19957i			0.530386i	0.964195	+	0.265193i	$0.0854357\pi$
$239$			8.19957i			0.530386i	−0.964195	+	0.265193i	$0.914564\pi$
$240$		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	$0.402810\pi$
$242$	12.7236	−	4.08684i	0.817905	−	0.262712i
$243$		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
$248$	−10.9968	−	1.26825i	−0.698297	−	0.0805338i
$249$		0			0
$250$	−3.22258	−	2.92133i	−0.203814	−	0.184761i
$251$		−	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
$254$	−15.1050	+	16.6626i	−0.947771	+	1.04550i
$255$		0			0
$256$	14.7867	−	6.11173i	0.924169	−	0.381983i
$257$	−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
$262$	−6.52666	−	20.3196i	−0.403219	−	1.25535i
$263$	−12.4202	+	7.17081i	−0.765863	+	0.442171i	−0.831397	−	0.555679i	$-0.812458\pi$
$263$	−12.4202	+	7.17081i	−0.765863	+	0.442171i	0.0655336	+	0.997850i	$0.479125\pi$
$264$		0			0
$265$			3.88026i			0.238363i
$266$	−2.16340	−	22.1141i	−0.132646	−	1.35590i
$267$		0			0
$268$	7.34361	−	5.26025i	0.448583	−	0.321321i
$269$	11.7294	+	20.3159i	0.715152	+	1.23868i	0.962901	+	0.269856i	$0.0869760\pi$
$269$	11.7294	+	20.3159i	0.715152	+	1.23868i	−0.247748	+	0.968824i	$0.579691\pi$
$270$		0			0
$271$	−6.85210	+	11.8682i	−0.416235	+	0.720941i	−0.995557	−	0.0941581i	$-0.969984\pi$
$271$	−6.85210	+	11.8682i	−0.416235	+	0.720941i	0.579322	+	0.815099i	$0.303317\pi$
$272$	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	−0.319971	−	0.947427i	$-0.603673\pi$
$277$	5.66771	−	3.27225i	0.340540	−	0.196611i	0.660511	+	0.750817i	$0.270340\pi$
$278$	−0.720296	+	0.794573i	−0.0432005	+	0.0476553i
$279$		0			0
$280$	−0.451465	−	2.27974i	−0.0269802	−	0.136241i
$281$	−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	$0.468273\pi$
$284$	−15.7767	+	1.55085i	−0.936174	+	0.0920260i
$285$		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
$290$	0.0257650	+	0.0802146i	0.00151297	+	0.00471036i
$291$		0			0
$292$	9.38246	+	13.0985i	0.549067	+	0.766529i
$293$	11.9348			0.697238			0.348619	−	0.937265i	$-0.386651\pi$
$293$	11.9348			0.697238			0.348619	+	0.937265i	$0.386651\pi$
$294$		0			0
$295$		−	1.85236i		−	0.107849i
$296$	−1.92887	+	0.835544i	−0.112113	+	0.0485650i
$297$		0			0
$298$	−7.49209	−	23.3252i	−0.434005	−	1.35119i
$299$	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
$304$	22.4903	+	7.64394i	1.28991	+	0.438410i
$305$	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	$-0.0177930\pi$
$308$	−6.04693	+	2.61605i	−0.344556	+	0.149063i
$309$		0			0
$310$	−1.27351	−	1.15446i	−0.0723305	−	0.0655691i
$311$	10.9125	+	18.9010i	0.618790	+	1.07178i	0.989707	+	0.143110i	$0.0457103\pi$
$311$	10.9125	+	18.9010i	0.618790	+	1.07178i	−0.370916	+	0.928666i	$0.620956\pi$
$312$		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	0.319590	−	0.947556i	$-0.396455\pi$
$317$	−6.07528	−	3.50757i	−0.341222	−	0.197005i	−0.660812	+	0.750551i	$0.729788\pi$
$318$		0			0
$319$	0.206851	−	0.119425i	0.0115814	−	0.00668653i
$320$	2.41925	+	0.565541i	0.135240	+	0.0316147i
$321$		0			0
$322$	1.20372	+	12.3043i	0.0670804	+	0.685692i
$323$	13.2407			0.736733
$324$		0			0
$325$	6.59148	+	11.4168i	0.365629	+	0.633289i
$326$	−8.32663	+	2.67452i	−0.461170	+	0.148128i
$327$		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	$0.183998\pi$
$332$	28.3130	−	2.78317i	1.55388	−	0.152746i
$333$		0			0
$334$	−24.3444	−	22.0686i	−1.33206	−	1.20754i
$335$	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	$0.478018\pi$
$338$	−6.04799	−	5.48262i	−0.328967	−	0.298215i
$339$		0			0
$340$	1.37824	−	0.135481i	0.0747455	−	0.00734749i
$341$	−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
$346$	−24.0787	+	7.73409i	−1.29448	+	0.415787i
$347$	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	$-0.394762\pi$
$349$	12.1290			0.649250			0.324625	+	0.945843i	$0.394762\pi$
$350$	−7.58307	+	16.7070i	−0.405332	+	0.893028i
$351$		0			0
$352$	0.118580	−	7.04247i	0.00632032	−	0.375365i
$353$	−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	0.576523	−	0.817081i	$-0.304409\pi$
$359$	2.97798	+	1.71934i	0.157172	+	0.0907431i	−0.419351	+	0.907824i	$0.637742\pi$
$360$		0			0
$361$	8.13264	+	14.0861i	0.428034	+	0.741376i
$362$	6.66300	+	6.04015i	0.350200	+	0.317463i
$363$		0			0
$364$	−1.63645	+	14.1315i	−0.0857735	+	0.740692i
$365$			2.50189i			0.130955i
$366$		0			0
$367$	−5.72895	−	9.92283i	−0.299049	−	0.517968i	0.676870	−	0.736103i	$-0.263336\pi$
$367$	−5.72895	−	9.92283i	−0.299049	−	0.517968i	−0.975919	+	0.218135i	$0.930003\pi$
$368$	−12.5136	−	4.25310i	−0.652318	−	0.221708i
$369$		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	0.658201	−	0.752843i	$-0.271318\pi$
$373$	6.47611	+	3.73898i	0.335320	+	0.193597i	−0.322880	+	0.946440i	$0.604651\pi$
$374$	−1.20066	−	3.73803i	−0.0620846	−	0.193289i
$375$		0			0
$376$	12.2304	+	28.2341i	0.630734	+	1.45606i
$377$		−	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	$0.307171\pi$
$380$	2.14790	+	2.99858i	0.110185	+	0.153824i
$381$		0			0
$382$	1.10336	+	3.43511i	0.0564529	+	0.175756i
$383$	8.74870	−	15.1532i	0.447038	−	0.774292i	−0.551154	−	0.834404i	$-0.685812\pi$
$383$	8.74870	−	15.1532i	0.447038	−	0.774292i	0.998192	+	0.0601114i	$0.0191456\pi$
$384$		0			0
$385$	−0.999891	−	0.216543i	−0.0509592	−	0.0110361i
$386$	0.880209	−	4.07356i	0.0448015	−	0.207339i
$387$		0			0
$388$	3.24336	−	0.318823i	0.164657	−	0.0161858i
$389$	6.29925	−	3.63687i	0.319384	−	0.184397i	−0.331734	−	0.943373i	$-0.607634\pi$
$389$	6.29925	−	3.63687i	0.319384	−	0.184397i	0.651118	+	0.758976i	$0.274300\pi$
$390$		0			0
$391$	−7.36715			−0.372573
$392$	−17.3196	+	9.59326i	−0.874773	+	0.484533i
$393$		0			0
$394$	16.7822	−	18.5128i	0.845474	−	0.932659i
$395$	4.12543	−	2.38182i	0.207573	−	0.119842i
$396$		0			0
$397$	−16.6695	+	28.8724i	−0.836616	+	1.44906i	0.0560911	+	0.998426i	$0.482136\pi$
$397$	−16.6695	+	28.8724i	−0.836616	+	1.44906i	−0.892708	+	0.450637i	$0.851197\pi$
$398$	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
$404$	−3.54243	+	2.53745i	−0.176242	+	0.126243i
$405$		0			0
$406$	0.583702	−	0.417696i	0.0289687	−	0.0207299i
$407$			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	$0.511342\pi$
$410$	1.24726	+	3.88312i	0.0615979	+	0.191774i
$411$		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
$416$	−13.0408	−	7.82474i	−0.639377	−	0.383640i
$417$		0			0
$418$	7.02311	−	7.74733i	0.343512	−	0.378935i
$419$			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	$-0.661345\pi$
$421$		−	35.8768i		−	1.74853i	0.485453	−	0.874263i	$-0.338655\pi$
$422$	9.62437	+	8.72468i	0.468507	+	0.424711i
$423$		0			0
$424$	−4.04883	+	35.1068i	−0.196628	+	1.70494i
$425$	−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
$430$	4.54849	−	1.46098i	0.219348	−	0.0704547i
$431$	14.1992	−	8.19790i	0.683950	−	0.394879i	−0.117392	−	0.993086i	$-0.537453\pi$
$431$	14.1992	−	8.19790i	0.683950	−	0.394879i	0.801342	+	0.598207i	$0.204120\pi$
$432$		0			0
$433$		−	33.3810i		−	1.60419i	−0.597198	−	0.802094i	$-0.703719\pi$
$433$		−	33.3810i		−	1.60419i	0.597198	−	0.802094i	$-0.296281\pi$
$434$	−6.05236	+	13.3346i	−0.290523	+	0.640079i
$435$		0			0
$436$	−14.3459	−	20.0278i	−0.687046	−	0.959156i
$437$	−9.81081	−	16.9928i	−0.469315	−	0.812877i
$438$		0			0
$439$	16.7314	−	28.9796i	0.798545	−	1.38312i	−0.122018	−	0.992528i	$-0.538937\pi$
$439$	16.7314	−	28.9796i	0.798545	−	1.38312i	0.920564	−	0.390593i	$-0.127730\pi$
$440$	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
$446$	−10.5049	−	9.52294i	−0.497424	−	0.450924i
$447$		0			0
$448$	−1.70587	−	21.0972i	−0.0805948	−	0.996747i
$449$	−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
$452$	2.01941	+	20.5434i	0.0949852	+	0.966279i
$453$		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	$0.121233\pi$
$458$	4.34061	−	1.39421i	0.202824	−	0.0651471i
$459$		0			0
$460$	−1.19509	−	1.66841i	−0.0557214	−	0.0777902i
$461$	35.1038			1.63495			0.817474	−	0.575966i	$-0.195374\pi$
$461$	35.1038			1.63495			0.817474	+	0.575966i	$0.195374\pi$
$462$		0			0
$463$			5.53696i			0.257324i	0.991688	+	0.128662i	$0.0410683\pi$
$463$			5.53696i			0.257324i	−0.991688	+	0.128662i	$0.958932\pi$
$464$	0.149411	+	0.752629i	0.00693622	+	0.0349399i
$465$		0			0
$466$	−19.5020	+	6.26408i	−0.903415	+	0.290178i
$467$	−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
$472$	1.93283	−	16.7593i	0.0889659	−	0.771411i
$473$	−6.77189	−	11.7293i	−0.311372	−	0.539312i
$474$		0			0
$475$		−	29.1195i		−	1.33610i
$476$	−4.68460	−	10.8283i	−0.214718	−	0.496316i
$477$		0			0
$478$	−7.78818	+	8.59129i	−0.356223	+	0.392956i
$479$	−7.56471	−	13.1025i	−0.345641	−	0.598667i	0.639829	−	0.768517i	$-0.279005\pi$
$479$	−7.56471	−	13.1025i	−0.345641	−	0.598667i	−0.985470	+	0.169850i	$0.945672\pi$
$480$		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	−0.399120	−	0.916899i	$-0.630684\pi$
$487$	4.31159	−	2.48930i	0.195377	−	0.112801i	0.594497	+	0.804098i	$0.297351\pi$
$488$	10.3202	+	23.8243i	0.467172	+	1.07848i
$489$		0			0
$490$	−3.05381	−	0.355081i	−0.137957	−	0.0160409i
$491$	−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
$494$	−6.90472	−	21.4966i	−0.310658	−	0.967177i
$495$		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	$0.109154\pi$
$500$	−0.601772	−	6.12178i	−0.0269120	−	0.273774i
$501$		0			0
$502$	0.396683	−	0.437589i	0.0177048	−	0.0195305i
$503$	−3.41092			−0.152085			−0.0760427	−	0.997105i	$-0.524229\pi$
$503$	−3.41092			−0.152085			−0.0760427	+	0.997105i	$0.524229\pi$
$504$		0			0
$505$	−0.676625			−0.0301094
$506$	−3.90766	+	4.31062i	−0.173717	+	0.191631i
$507$		0			0
$508$	−31.6532	+	3.11151i	−1.40438	+	0.138051i
$509$	−17.5417	+	30.3832i	−0.777523	+	1.34671i	0.155842	+	0.987782i	$0.450191\pi$
$509$	−17.5417	+	30.3832i	−0.777523	+	1.34671i	−0.933365	+	0.358928i	$0.883142\pi$
$510$		0			0
$511$	20.2962	−	6.50872i	0.897852	−	0.287929i
$512$	21.2982	+	7.64111i	0.941256	+	0.337693i
$513$		0			0
$514$	−6.32993	−	19.7071i	−0.279201	−	0.869242i
$515$	0.496256	+	0.859541i	0.0218677	+	0.0378759i
$516$		0			0
$517$	13.5451			0.595713
$518$	0.270747	+	2.76756i	0.0118959	+	0.121599i
$519$		0			0
$520$	−0.938676	−	2.16695i	−0.0411637	−	0.0950271i
$521$	−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
$530$	−3.68558	+	4.06563i	−0.160091	+	0.176600i
$531$		0			0
$532$	18.7378	−	25.2254i	0.812388	−	1.09366i
$533$		−	24.9657i		−	1.08139i
$534$		0			0
$535$	−0.343270	−	0.594561i	−0.0148409	−	0.0257051i
$536$	12.6908	+	1.46361i	0.548158	+	0.0632184i
$537$		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	0.970756	−	0.240066i	$-0.0771692\pi$
$541$	29.0331	+	16.7623i	1.24823	+	0.720667i	0.277475	+	0.960733i	$0.410503\pi$
$542$	−18.4522	+	5.92685i	−0.792588	+	0.254580i
$543$		0			0
$544$	12.6111	+	0.212343i	0.540694	+	0.00910411i
$545$		−	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	$0.413369\pi$
$548$	−24.1033	+	17.2653i	−1.02964	+	0.737537i
$549$		0			0
$550$	−8.22084	+	2.64054i	−0.350538	+	0.112593i
$551$	−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
$556$	−1.50941	+	0.148375i	−0.0640134	+	0.00629252i
$557$	6.60225	−	3.81181i	0.279746	−	0.161512i	−0.353562	−	0.935411i	$-0.615030\pi$
$557$	6.60225	−	3.81181i	0.279746	−	0.161512i	0.633309	+	0.773899i	$0.281696\pi$
$558$		0			0
$559$	−29.2436			−1.23687
$560$	1.69233	−	2.81747i	0.0715139	−	0.119060i
$561$		0			0
$562$	−23.5935	−	21.3880i	−0.995234	−	0.902199i
$563$	−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	$0.626102\pi$
$572$	−5.44266	+	3.89859i	−0.227569	+	0.163008i
$573$		0			0
$574$	28.2565	−	20.2203i	1.17940	−	0.843978i
$575$			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	$0.386706\pi$
$578$	−16.1961	+	5.20220i	−0.673668	+	0.216383i
$579$		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
$584$	−2.61057	+	22.6359i	−0.108026	+	0.936681i
$585$		0			0
$586$	12.5049	+	11.3360i	0.516575	+	0.468285i
$587$		−	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
$590$	1.75942	−	1.94086i	0.0724344	−	0.0799038i
$591$		0			0
$592$	−2.81464	−	0.956631i	−0.115681	−	0.0393173i
$593$	−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
$598$	3.84179	+	11.9607i	0.157103	+	0.489110i
$599$	29.4613	−	17.0095i	1.20376	−	0.694989i	0.242368	−	0.970184i	$-0.422076\pi$
$599$	29.4613	−	17.0095i	1.20376	−	0.694989i	0.961388	+	0.275195i	$0.0887425\pi$
$600$		0			0
$601$		−	21.9849i		−	0.896782i	−0.893837	−	0.448391i	$-0.851997\pi$
$601$		−	21.9849i		−	0.896782i	0.893837	−	0.448391i	$-0.148003\pi$
$602$	−23.6850	−	33.0983i	−0.965330	−	1.34899i
$603$		0			0
$604$	25.4297	+	35.5013i	1.03472	+	1.44453i
$605$	1.46734	+	2.54151i	0.0596560	+	0.103327i
$606$		0			0
$607$	12.4261	−	21.5227i	0.504361	−	0.873578i	−0.495627	−	0.868536i	$-0.665062\pi$
$607$	12.4261	−	21.5227i	0.504361	−	0.873578i	0.999987	−	0.00504253i	$-0.00160509\pi$
$608$	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	−0.787231	−	0.616658i	$-0.788486\pi$
$613$	−16.0142	+	9.24578i	−0.646806	+	0.373434i	0.140425	+	0.990091i	$0.455153\pi$
$614$	1.85959	−	2.05135i	0.0750469	−	0.0827858i
$615$		0			0
$616$	−8.82061	−	3.00251i	−0.355392	−	0.120975i
$617$	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	$0.391102\pi$
$620$	−0.237810	−	2.41923i	−0.00955070	−	0.0971586i
$621$		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
$626$	−7.47965	−	23.2865i	−0.298947	−	0.930716i
$627$		0			0
$628$	−23.4877	+	16.8243i	−0.937260	+	0.671362i
$629$	−1.65706			−0.0660714
$630$		0			0
$631$			19.3801i			0.771511i	0.922601	+	0.385756i	$0.126059\pi$
$631$			19.3801i			0.771511i	−0.922601	+	0.385756i	$0.873941\pi$
$632$	39.8103	−	17.2450i	1.58357	−	0.685968i
$633$		0			0
$634$	−3.03394	−	9.44560i	−0.120493	−	0.375133i
$635$	−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
$640$	1.99766	+	2.89043i	0.0789646	+	0.114254i
$641$	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	$0.694486\pi$
$644$	−10.4257	+	14.0354i	−0.410832	+	0.553074i
$645$		0			0
$646$	13.8733	+	12.5764i	0.545836	+	0.494812i
$647$	−13.6161	−	23.5838i	−0.535304	−	0.927174i	−0.999149	−	0.0412571i	$-0.986864\pi$
$647$	−13.6161	−	23.5838i	−0.535304	−	0.927174i	0.463845	−	0.885917i	$-0.346470\pi$
$648$		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	0.980946	−	0.194279i	$-0.0622368\pi$
$653$	33.3010	+	19.2263i	1.30317	+	0.752385i	0.322222	+	0.946664i	$0.395570\pi$
$654$		0			0
$655$	4.05879	−	2.34334i	0.158590	−	0.0915619i
$656$	7.23285	+	36.4341i	0.282395	+	1.42251i
$657$		0			0
$658$	40.5104	−	3.96309i	1.57926	−	0.154497i
$659$	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	0.956583	−	0.291459i	$-0.0941408\pi$
$661$	5.80736	+	10.0586i	0.225880	+	0.391236i	−0.730703	+	0.682696i	$0.760808\pi$
$662$	−2.66628	+	0.856413i	−0.103628	+	0.0332854i
$663$		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
$668$	−4.54597	−	46.2459i	−0.175889	−	1.78931i
$669$		0			0
$670$	1.46969	+	1.33230i	0.0567789	+	0.0514712i
$671$	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	$0.762723\pi$
$674$	2.65445	+	2.40631i	0.102246	+	0.0926876i
$675$		0			0
$676$	−1.12938	−	11.4891i	−0.0434376	−	0.441888i
$677$	14.1674	−	24.5387i	0.544498	−	0.943098i	−0.454141	−	0.890930i	$-0.650054\pi$
$677$	14.1674	−	24.5387i	0.544498	−	0.943098i	0.998638	−	0.0521678i	$-0.0166131\pi$
$678$		0			0
$679$	0.912520	−	4.21357i	0.0350193	−	0.161702i
$680$	1.57277	+	1.16714i	0.0603128	+	0.0447576i
$681$		0			0
$682$	−6.56138	+	2.10752i	−0.251248	+	0.0807012i
$683$	−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
$686$	5.06401	+	25.6974i	0.193345	+	0.981131i
$687$		0			0
$688$	42.6771	−	8.47220i	1.62705	−	0.322999i
$689$	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
$698$	12.7084	+	11.5204i	0.481021	+	0.436055i
$699$		0			0
$700$	−23.8141	+	10.3026i	−0.900089	+	0.389400i
$701$			30.8763i			1.16618i	0.812406	+	0.583092i	$0.198157\pi$
$701$			30.8763i			1.16618i	−0.812406	+	0.583092i	$0.801843\pi$
$702$		0			0
$703$	−2.20671	−	3.82213i	−0.0832275	−	0.144154i
$704$	6.81337	−	7.26628i	0.256789	−	0.273858i
$705$		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	0.254265	−	0.967135i	$-0.418167\pi$
$709$	−12.1464	−	7.01270i	−0.456166	−	0.263367i	−0.710431	+	0.703767i	$0.751500\pi$
$710$	−1.06461	−	3.31446i	−0.0399540	−	0.124389i
$711$		0			0
$712$	−16.5832	+	7.18349i	−0.621483	+	0.269213i
$713$			12.9316i			0.484292i
$714$		0			0
$715$	−1.03958			−0.0388781
$716$	−27.5344	+	19.7229i	−1.02901	+	0.737081i
$717$		0			0
$718$	1.48717	+	4.63004i	0.0555008	+	0.172792i
$719$	−18.8132	+	32.5854i	−0.701613	+	1.21523i	0.266288	+	0.963894i	$0.414203\pi$
$719$	−18.8132	+	32.5854i	−0.701613	+	1.21523i	−0.967900	+	0.251335i	$0.919130\pi$
$720$		0			0
$721$	5.68189	−	6.26193i	0.211605	−	0.233207i
$722$	−4.85824	+	22.4837i	−0.180805	+	0.836756i
$723$		0			0
$724$	1.24422	+	12.6574i	0.0462412	+	0.470409i
$725$	0.814622	−	0.470322i	0.0302543	−	0.0174673i
$726$		0			0
$727$	−39.3414			−1.45909			−0.729545	−	0.683933i	$-0.760268\pi$
$727$	−39.3414			−1.45909			−0.729545	+	0.683933i	$0.760268\pi$
$728$	−15.1371	+	13.2523i	−0.561019	+	0.491162i
$729$		0			0
$730$	−2.37636	+	2.62141i	−0.0879530	+	0.0970227i
$731$	21.0038	−	12.1265i	0.776852	−	0.448516i
$732$		0			0
$733$	−20.2322	+	35.0431i	−0.747292	+	1.29435i	0.201824	+	0.979422i	$0.435313\pi$
$733$	−20.2322	+	35.0431i	−0.747292	+	1.29435i	−0.949116	+	0.314926i	$0.898020\pi$
$734$	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	$0.882581\pi$
$740$	−0.268807	−	0.375269i	−0.00988153	−	0.0137952i
$741$		0			0
$742$	42.5700	+	19.3219i	1.56280	+	0.709330i
$743$			16.9962i			0.623529i	0.950159	+	0.311764i	$0.100920\pi$
$743$			16.9962i			0.623529i	−0.950159	+	0.311764i	$0.899080\pi$
$744$		0			0
$745$	4.65916	−	2.68997i	0.170699	−	0.0985528i
$746$	3.23410	+	10.0688i	0.118409	+	0.368644i
$747$		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	0.687461	−	0.726221i	$-0.258725\pi$
$751$	11.0239	+	6.36463i	0.402266	+	0.232249i	−0.285195	+	0.958469i	$0.592058\pi$
$752$	−14.0028	+	41.1996i	−0.510630	+	1.50240i
$753$		0			0
$754$	0.489848	−	0.540361i	0.0178392	−	0.0196788i
$755$			6.78097i			0.246785i
$756$		0			0
$757$		−	36.5299i		−	1.32770i	−0.747864	−	0.663852i	$-0.768921\pi$
$757$		−	36.5299i		−	1.32770i	0.747864	−	0.663852i	$-0.231079\pi$
$758$	23.2297	+	21.0582i	0.843741	+	0.764867i
$759$		0			0
$760$	−0.597630	+	5.18197i	−0.0216783	+	0.187970i
$761$	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
$766$	23.5596	−	7.56736i	0.851242	−	0.273420i
$767$	−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	$0.883466\pi$
$770$	−0.841980	−	1.17661i	−0.0303428	−	0.0424021i
$771$		0			0
$772$	4.79144	−	3.43212i	0.172448	−	0.123525i
$773$	6.55810	+	11.3590i	0.235879	+	0.408554i	0.959528	−	0.281614i	$-0.0908699\pi$
$773$	6.55810	+	11.3590i	0.235879	+	0.408554i	−0.723649	+	0.690168i	$0.757537\pi$
$774$		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
$782$	−7.71910	−	6.99751i	−0.276034	−	0.250231i
$783$		0			0
$784$	−27.2590	−	6.39909i	−0.973535	−	0.228539i
$785$	−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	$0.419183\pi$
$788$	35.1678	−	3.45700i	1.25280	−	0.123151i
$789$		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
$794$	−44.8896	+	14.4186i	−1.59307	+	0.511696i
$795$		0			0
$796$	11.3491	−	8.12939i	0.402258	−	0.288139i
$797$	−48.1132			−1.70426			−0.852128	−	0.523333i	$-0.824688\pi$
$797$	−48.1132			−1.70426			−0.852128	+	0.523333i	$0.824688\pi$
$798$		0			0
$799$			24.2554i			0.858096i
$800$	0.466993	−	27.7348i	0.0165107	−	0.980572i
$801$		0			0
$802$	44.6113	−	14.3292i	1.57528	−	0.505981i
$803$	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
$808$	−6.12180	−	0.706019i	−0.215364	−	0.0248377i
$809$	−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	$-0.00516841\pi$
$812$	1.00833	+	0.116766i	0.0353853	+	0.00409768i
$813$		0			0
$814$	−0.878935	+	0.969570i	−0.0308066	+	0.0339834i
$815$	−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	0.889462	−	0.457008i	$-0.151079\pi$
$821$	26.8884	+	15.5240i	0.938413	+	0.541793i	0.0489502	+	0.998801i	$0.484412\pi$
$822$		0			0
$823$	−4.91080	+	2.83525i	−0.171180	+	0.0988307i	−0.583142	−	0.812370i	$-0.698177\pi$
$823$	−4.91080	+	2.83525i	−0.171180	+	0.0988307i	0.411962	+	0.911201i	$0.364844\pi$
$824$	3.59302	+	8.29455i	0.125169	+	0.288954i
$825$		0			0
$826$	−20.3221	−	9.22392i	−0.707098	−	0.320941i
$827$	−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	0.897139	−	0.441749i	$-0.145642\pi$
$829$	1.90039	+	3.29157i	0.0660032	+	0.114321i	−0.831135	+	0.556070i	$0.812309\pi$
$830$	1.91056	+	5.94817i	0.0663164	+	0.206464i
$831$		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
$836$	14.7173	−	1.44671i	0.509007	−	0.0500354i
$837$		0			0
$838$	−26.9558	+	29.7355i	−0.931172	+	1.02719i
$839$	−10.9412			−0.377732			−0.188866	−	0.982003i	$-0.560481\pi$
$839$	−10.9412			−0.377732			−0.188866	+	0.982003i	$0.560481\pi$
$840$		0			0
$841$	28.9632			0.998731
$842$	34.0767	−	37.5907i	1.17436	−	1.29546i
$843$		0			0
$844$	1.79722	+	18.2830i	0.0618628	+	0.629326i
$845$	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
$850$	−4.72846	−	14.7212i	−0.162185	−	0.504932i
$851$	1.22781	+	2.12663i	0.0420889	+	0.0729001i
$852$		0			0
$853$	28.6102			0.979594			0.489797	−	0.871837i	$-0.337071\pi$
$853$	28.6102			0.979594			0.489797	+	0.871837i	$0.337071\pi$
$854$	34.1833	−	3.34411i	1.16973	−	0.114433i
$855$		0			0
$856$	−2.48536	−	5.73750i	−0.0849479	−	0.196104i
$857$	−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	0.278872	−	0.960328i	$-0.410039\pi$
$863$	−12.1432	−	7.01089i	−0.413360	−	0.238654i	−0.692232	+	0.721675i	$0.743373\pi$
$864$		0			0
$865$	−2.77686	−	4.80966i	−0.0944160	−	0.163533i
$866$	31.7062	−	34.9757i	1.07742	−	1.18852i
$867$		0			0
$868$	−19.0070	+	8.22289i	−0.645140	+	0.279103i
$869$		−	19.0988i		−	0.647881i
$870$		0			0
$871$	−6.07134	−	10.5159i	−0.205719	−	0.356316i
$872$	3.99161	−	34.6107i	0.135173	−	1.17207i
$873$		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	−0.0237773	−	0.999717i	$-0.507569\pi$
$877$	−26.6956	−	15.4127i	−0.901446	−	0.520450i	−0.877669	+	0.479267i	$0.840903\pi$
$878$	45.0563	−	14.4721i	1.52058	−	0.488411i
$879$		0			0
$880$	1.51713	−	0.301178i	0.0511425	−	0.0101527i
$881$			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	$0.619001\pi$
$884$	−6.98127	−	9.74625i	−0.234805	−	0.327802i
$885$		0			0
$886$	43.8426	−	14.0823i	1.47292	−	0.473104i
$887$	9.89190	−	17.1333i	0.332138	−	0.575279i	−0.650793	−	0.759255i	$-0.725564\pi$
$887$	9.89190	−	17.1333i	0.332138	−	0.575279i	0.982931	+	0.183976i	$0.0588969\pi$
$888$		0			0
$889$	−8.90562	+	41.1218i	−0.298685	+	1.37918i
$890$	−2.74295	−	0.592693i	−0.0919439	−	0.0198671i
$891$		0			0
$892$	−1.96165	−	19.9558i	−0.0656810	−	0.668169i
$893$	−55.9468	+	32.3009i	−1.87219	+	1.08091i
$894$		0			0
$895$	−5.25923			−0.175797
$896$	18.2513	−	23.7253i	0.609733	−	0.792607i
$897$		0			0
$898$	−12.4828	−	11.3159i	−0.416555	−	0.377616i
$899$	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	$0.976434\pi$
$908$	−7.79768	−	10.8860i	−0.258775	−	0.361265i
$909$		0			0
$910$	−3.10916	+	0.304165i	−0.103068	+	0.0100830i
$911$		−	0.701753i		−	0.0232501i	−0.999932	−	0.0116251i	$-0.996300\pi$
$911$		−	0.701753i		−	0.0232501i	0.999932	−	0.0116251i	$-0.00370045\pi$
$912$		0			0
$913$	15.3386	−	8.85576i	0.507634	−	0.293083i
$914$	8.18905	−	2.63033i	0.270870	−	0.0870037i
$915$		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	0.849692	−	0.527280i	$-0.176788\pi$
$919$	24.7946	+	14.3152i	0.817899	+	0.472214i	−0.0317922	+	0.999494i	$0.510121\pi$
$920$	0.332522	−	2.88325i	0.0109629	−	0.0950579i
$921$		0			0
$922$	36.7808	+	33.3426i	1.21131	+	1.09808i
$923$			21.3096i			0.701415i
$924$		0			0
$925$			3.64428i			0.119823i
$926$	−5.25915	+	5.80148i	−0.172827	+	0.190648i
$927$		0			0
$928$	−0.558319	+	0.930499i	−0.0183277	+	0.0305451i
$929$	−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
$934$	−6.73756	−	20.9762i	−0.220460	−	0.686361i
$935$	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	$0.805399\pi$
$938$	6.98468	−	15.3886i	0.228058	−	0.502457i
$939$		0			0
$940$	−5.49305	+	3.93469i	−0.179164	+	0.128335i
$941$	10.5715	+	18.3104i	0.344621	+	0.596902i	0.985285	−	0.170920i	$-0.0546739\pi$
$941$	10.5715	+	18.3104i	0.344621	+	0.596902i	−0.640663	+	0.767822i	$0.721341\pi$
$942$		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
$950$	27.6585	−	30.5107i	0.897361	−	0.989897i
$951$		0			0
$952$	5.37665	−	15.7952i	0.174258	−	0.511925i
$953$	−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
$956$	−16.3205	+	1.60430i	−0.527842	+	0.0518869i
$957$		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
$962$	0.864119	+	2.69027i	0.0278603	+	0.0867379i
$963$		0			0
$964$	−7.83010	−	10.9313i	−0.252191	−	0.352072i
$965$	0.915195			0.0294612
$966$		0			0
$967$			43.5181i			1.39945i	0.714413	+	0.699725i	$0.246694\pi$
$967$			43.5181i			1.39945i	−0.714413	+	0.699725i	$0.753306\pi$
$968$	10.6239	+	24.5256i	0.341466	+	0.788281i
$969$		0			0
$970$	0.218862	+	0.681385i	0.00702722	+	0.0218780i
$971$	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
$976$	−11.8158	+	34.7648i	−0.378214	+	1.11280i
$977$	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
$980$	−2.86243	−	3.27264i	−0.0914371	−	0.104540i
$981$		0			0
$982$	−13.5543	−	12.2872i	−0.432535	−	0.392102i
$983$	−15.9252	−	27.5832i	−0.507934	−	0.879767i	−0.999958	−	0.00918542i	$-0.997076\pi$
$983$	−15.9252	−	27.5832i	−0.507934	−	0.879767i	0.492024	−	0.870582i	$-0.336257\pi$
$984$		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	−0.551945	−	0.833881i	$-0.686114\pi$
$991$	−3.32918	+	1.92210i	−0.105755	+	0.0610575i	0.446190	+	0.894938i	$0.352781\pi$
$992$	0.372726	−	22.1362i	0.0118341	−	0.702826i
$993$		0			0
$994$	−24.1185	+	17.2591i	−0.764993	+	0.547427i
$995$	2.16775			0.0687222
$996$		0			0
$997$	−28.6326	−	49.5931i	−0.906803	−	1.57063i	−0.818479	−	0.574537i	$-0.805182\pi$
$997$	−28.6326	−	49.5931i	−0.906803	−	1.57063i	−0.0883239	−	0.996092i	$-0.528151\pi$
$998$	10.8099	−	3.47215i	0.342181	−	0.109909i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04777 + 0.949827i) q^{2} +(0.195657 + 1.99041i) q^{4} +(-0.155280 + 0.268953i) q^{5} +(2.58581 + 0.560001i) q^{7} +(-1.68554 + 2.27133i) q^{8} +O(q^{10})\)	\(q+(1.04777 + 0.949827i) q^{2} +(0.195657 + 1.99041i) q^{4} +(-0.155280 + 0.268953i) q^{5} +(2.58581 + 0.560001i) q^{7} +(-1.68554 + 2.27133i) q^{8} +(-0.418156 + 0.134312i) q^{10} +(0.622560 + 1.07831i) q^{11} +2.68845 q^{13} +(2.17744 + 3.04282i) q^{14} +(-3.92344 + 0.778874i) q^{16} +(-1.93094 + 1.11483i) q^{17} +(-5.14286 - 2.96923i) q^{19} +(-0.565707 - 0.256448i) q^{20} +(-0.371902 + 1.72114i) q^{22} +(2.86149 + 1.65208i) q^{23} +(2.45178 + 4.24660i) q^{25} +(2.81689 + 2.55356i) q^{26} +(-0.608698 + 5.25638i) q^{28} -0.191829i q^{29} +(1.95686 + 3.38939i) q^{31} +(-4.85067 - 2.91050i) q^{32} +(-3.08208 - 0.665971i) q^{34} +(-0.552137 + 0.608503i) q^{35} +(0.643623 + 0.371596i) q^{37} +(-2.56829 - 7.99590i) q^{38} +(-0.349151 - 0.806022i) q^{40} -9.28628i q^{41} -10.8775 q^{43} +(-2.02446 + 1.45013i) q^{44} +(1.42900 + 4.44893i) q^{46} +(5.43928 - 9.42111i) q^{47} +(6.37280 + 2.89611i) q^{49} +(-1.46463 + 6.77824i) q^{50} +(0.526014 + 5.35111i) q^{52} +(10.8205 - 6.24721i) q^{53} -0.386684 q^{55} +(-5.63043 + 4.92933i) q^{56} +(0.182205 - 0.200993i) q^{58} +(-5.16549 + 2.98230i) q^{59} +(4.58974 - 7.94967i) q^{61} +(-1.16898 + 5.40999i) q^{62} +(-2.31792 - 7.65684i) q^{64} +(-0.417462 + 0.723066i) q^{65} +(-2.25830 - 3.91150i) q^{67} +(-2.59676 - 3.62523i) q^{68} +(-1.15649 + 0.113138i) q^{70} +7.92636i q^{71} +(6.97675 - 4.02803i) q^{73} +(0.321419 + 1.00068i) q^{74} +(4.90374 - 10.8173i) q^{76} +(1.00597 + 3.13693i) q^{77} +(-13.2839 - 7.66944i) q^{79} +(0.399750 - 1.17616i) q^{80} +(8.82036 - 9.72992i) q^{82} -14.2247i q^{83} -0.692441i q^{85} +(-11.3971 - 10.3317i) q^{86} +(-3.49854 - 0.403483i) q^{88} +(5.53347 + 3.19475i) q^{89} +(6.95181 + 1.50553i) q^{91} +(-2.72844 + 6.01877i) q^{92} +(14.6476 - 4.70481i) q^{94} +(1.59716 - 0.922123i) q^{95} -1.62950i q^{97} +(3.92645 + 9.08752i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 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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