LMFDB - Embedded newform 108.2.h.a.71.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,2,Mod(35,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.170772624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.3
Root			$0.774115 - 1.18353i$ of defining polynomial
Character	$\chi$	$=$	108.71
Dual form			108.2.h.a.35.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.774115 - 1.18353i) q^{2} +(-0.801492 - 1.83238i) q^{4} +(-0.686141 - 0.396143i) q^{5} +(2.35143 - 1.35760i) q^{7} +(-2.78912 - 0.469882i) q^{8} +(-1.00000 + 0.505408i) q^{10} +(1.71352 + 2.96790i) q^{11} +(-1.68614 + 2.92048i) q^{13} +(0.213517 - 3.83392i) q^{14} +(-2.71522 + 2.93727i) q^{16} +2.52434i q^{17} +2.20979i q^{19} +(-0.175949 + 1.57478i) q^{20} +(4.83906 + 0.269495i) q^{22} +(1.07561 - 1.86301i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(2.15121 + 4.25639i) q^{26} +(-4.37228 - 3.22060i) q^{28} +(0.686141 - 0.396143i) q^{29} +(-1.47603 - 0.852189i) q^{31} +(1.37446 + 5.48734i) q^{32} +(2.98763 + 1.95413i) q^{34} -2.15121 q^{35} +4.74456 q^{37} +(2.61535 + 1.71063i) q^{38} +(1.72759 + 1.42730i) q^{40} +(-0.127719 - 0.0737384i) q^{41} +(-6.01594 + 3.47331i) q^{43} +(4.06494 - 5.51856i) q^{44} +(-1.37228 - 2.71519i) q^{46} +(-5.77846 - 10.0086i) q^{47} +(0.186141 - 0.322405i) q^{49} +(-6.17377 - 0.343827i) q^{50} +(6.70285 + 0.748907i) q^{52} -8.51278i q^{53} -2.71519i q^{55} +(-7.19633 + 2.68161i) q^{56} +(0.0623037 - 1.11873i) q^{58} +(-2.58891 + 4.48412i) q^{59} +(-1.68614 - 2.92048i) q^{61} +(-2.15121 + 1.08724i) q^{62} +(7.55842 + 2.62112i) q^{64} +(2.31386 - 1.33591i) q^{65} +(-6.01594 - 3.47331i) q^{67} +(4.62554 - 2.02324i) q^{68} +(-1.66529 + 2.54603i) q^{70} +1.75079 q^{71} -2.37228 q^{73} +(3.67284 - 5.61534i) q^{74} +(4.04917 - 1.77113i) q^{76} +(8.05842 + 4.65253i) q^{77} +(8.80507 - 5.08361i) q^{79} +(3.02661 - 0.939764i) q^{80} +(-0.186141 + 0.0940770i) q^{82} +(3.62725 + 6.28258i) q^{83} +(1.00000 - 1.73205i) q^{85} +(-0.546267 + 9.80880i) q^{86} +(-3.38465 - 9.08299i) q^{88} +5.34363i q^{89} +9.15640i q^{91} +(-4.27582 - 0.477736i) q^{92} +(-16.3187 - 0.908812i) q^{94} +(0.875393 - 1.51622i) q^{95} +(6.24456 + 10.8159i) q^{97} +(-0.237482 - 0.469882i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41}+ \cdots + 4 q^{97}+O(q^{100}) $ 8 * q + 3 * q^2 - q^4 + 6 * q^5 - 8 * q^10 - 2 * q^13 - 12 * q^14 - q^16 - 18 * q^20 + 3 * q^22 - 6 * q^25 - 12 * q^28 - 6 * q^29 + 33 * q^32 + 7 * q^34 - 8 * q^37 + 27 * q^38 + 10 * q^40 - 24 * q^41 + 12 * q^46 - 10 * q^49 - 21 * q^50 + 16 * q^52 - 18 * q^56 + 4 * q^58 - 2 * q^61 + 26 * q^64 + 30 * q^65 + 15 * q^68 - 6 * q^70 + 4 * q^73 + 30 * q^74 - 3 * q^76 + 30 * q^77 + 10 * q^82 + 8 * q^85 - 21 * q^86 - 21 * q^88 - 24 * q^92 - 18 * q^94 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.774115	−	1.18353i	0.547382	−	0.836883i
$2$	0.774115	−	1.18353i	0.547382	−	0.836883i
$3$		0			0
$3$		0			0
$4$	−0.801492	−	1.83238i	−0.400746	−	0.916189i
$5$	−0.686141	−	0.396143i	−0.306851	−	0.177161i	0.338665	−	0.940907i	$-0.390025\pi$
$5$	−0.686141	−	0.396143i	−0.306851	−	0.177161i	−0.645517	+	0.763746i	$0.723358\pi$
$6$		0			0
$7$	2.35143	−	1.35760i	0.888756	−	0.513124i	0.0152206	−	0.999884i	$-0.495155\pi$
$7$	2.35143	−	1.35760i	0.888756	−	0.513124i	0.873535	+	0.486761i	$0.161822\pi$
$8$	−2.78912	−	0.469882i	−0.986104	−	0.166128i
$9$		0			0
$10$	−1.00000	+	0.505408i	−0.316228	+	0.159824i
$11$	1.71352	+	2.96790i	0.516645	+	0.894855i	0.999813	+	0.0193276i	$0.00615256\pi$
$11$	1.71352	+	2.96790i	0.516645	+	0.894855i	−0.483168	+	0.875527i	$0.660514\pi$
$12$		0			0
$13$	−1.68614	+	2.92048i	−0.467651	+	0.809996i	−0.999317	−	0.0369586i	$-0.988233\pi$
$13$	−1.68614	+	2.92048i	−0.467651	+	0.809996i	0.531666	+	0.846954i	$0.321566\pi$
$14$	0.213517	−	3.83392i	0.0570648	−	1.02466i
$15$		0			0
$16$	−2.71522	+	2.93727i	−0.678806	+	0.734318i
$17$			2.52434i			0.612242i	0.951993	+	0.306121i	$0.0990312\pi$
$17$			2.52434i			0.612242i	−0.951993	+	0.306121i	$0.900969\pi$
$18$		0			0
$19$			2.20979i			0.506960i	0.967341	+	0.253480i	$0.0815752\pi$
$19$			2.20979i			0.506960i	−0.967341	+	0.253480i	$0.918425\pi$
$20$	−0.175949	+	1.57478i	−0.0393434	+	0.352130i
$21$		0			0
$22$	4.83906	+	0.269495i	1.03169	+	0.0574564i
$23$	1.07561	−	1.86301i	0.224279	−	0.388463i	−0.731824	−	0.681494i	$-0.761330\pi$
$23$	1.07561	−	1.86301i	0.224279	−	0.388463i	0.956103	+	0.293031i	$0.0946638\pi$
$24$		0			0
$25$	−2.18614	−	3.78651i	−0.437228	−	0.757301i
$26$	2.15121	+	4.25639i	0.421888	+	0.834746i
$27$		0			0
$28$	−4.37228	−	3.22060i	−0.826284	−	0.608637i
$29$	0.686141	−	0.396143i	0.127413	−	0.0735620i	−0.434939	−	0.900460i	$-0.643230\pi$
$29$	0.686141	−	0.396143i	0.127413	−	0.0735620i	0.562352	+	0.826898i	$0.309897\pi$
$30$		0			0
$31$	−1.47603	−	0.852189i	−0.265104	−	0.153058i	0.361557	−	0.932350i	$-0.382245\pi$
$31$	−1.47603	−	0.852189i	−0.265104	−	0.153058i	−0.626660	+	0.779292i	$0.715579\pi$
$32$	1.37446	+	5.48734i	0.242972	+	0.970033i
$33$		0			0
$34$	2.98763	+	1.95413i	0.512375	+	0.335130i
$35$	−2.15121			−0.363621
$36$		0			0
$37$	4.74456			0.780001			0.390001	−	0.920815i	$-0.372475\pi$
$37$	4.74456			0.780001			0.390001	+	0.920815i	$0.372475\pi$
$38$	2.61535	+	1.71063i	0.424266	+	0.277501i
$39$		0			0
$40$	1.72759	+	1.42730i	0.273156	+	0.225676i
$41$	−0.127719	−	0.0737384i	−0.0199463	−	0.0115160i	0.489994	−	0.871726i	$-0.336999\pi$
$41$	−0.127719	−	0.0737384i	−0.0199463	−	0.0115160i	−0.509940	+	0.860210i	$0.670332\pi$
$42$		0			0
$43$	−6.01594	+	3.47331i	−0.917423	+	0.529674i	−0.882812	−	0.469727i	$-0.844353\pi$
$43$	−6.01594	+	3.47331i	−0.917423	+	0.529674i	−0.0346108	+	0.999401i	$0.511019\pi$
$44$	4.06494	−	5.51856i	0.612813	−	0.831954i
$45$		0			0
$46$	−1.37228	−	2.71519i	−0.202332	−	0.400334i
$47$	−5.77846	−	10.0086i	−0.842875	−	1.45990i	−0.887454	−	0.460897i	$-0.847528\pi$
$47$	−5.77846	−	10.0086i	−0.842875	−	1.45990i	0.0445785	−	0.999006i	$-0.485806\pi$
$48$		0			0
$49$	0.186141	−	0.322405i	0.0265915	−	0.0460579i
$50$	−6.17377	−	0.343827i	−0.873103	−	0.0486244i
$51$		0			0
$52$	6.70285	+	0.748907i	0.929519	+	0.103855i
$53$		−	8.51278i		−	1.16932i	−0.811278	−	0.584660i	$-0.801228\pi$
$53$		−	8.51278i		−	1.16932i	0.811278	−	0.584660i	$-0.198772\pi$
$54$		0			0
$55$		−	2.71519i		−	0.366117i
$56$	−7.19633	+	2.68161i	−0.961650	+	0.358346i
$57$		0			0
$58$	0.0623037	−	1.11873i	0.00818088	−	0.146896i
$59$	−2.58891	+	4.48412i	−0.337047	+	0.583783i	−0.983876	−	0.178852i	$-0.942762\pi$
$59$	−2.58891	+	4.48412i	−0.337047	+	0.583783i	0.646829	+	0.762635i	$0.276095\pi$
$60$		0			0
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	0.737659	−	0.675174i	$-0.235931\pi$
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	−0.953547	+	0.301244i	$0.902598\pi$
$62$	−2.15121	+	1.08724i	−0.273204	+	0.138080i
$63$		0			0
$64$	7.55842	+	2.62112i	0.944803	+	0.327640i
$65$	2.31386	−	1.33591i	0.286999	−	0.165699i
$66$		0			0
$67$	−6.01594	−	3.47331i	−0.734964	−	0.424332i	0.0852711	−	0.996358i	$-0.472824\pi$
$67$	−6.01594	−	3.47331i	−0.734964	−	0.424332i	−0.820236	+	0.572026i	$0.806158\pi$
$68$	4.62554	−	2.02324i	0.560929	−	0.245353i
$69$		0			0
$70$	−1.66529	+	2.54603i	−0.199040	+	0.304309i
$71$	1.75079			0.207780			0.103890	−	0.994589i	$-0.466871\pi$
$71$	1.75079			0.207780			0.103890	+	0.994589i	$0.466871\pi$
$72$		0			0
$73$	−2.37228			−0.277655			−0.138827	−	0.990317i	$-0.544333\pi$
$73$	−2.37228			−0.277655			−0.138827	+	0.990317i	$0.544333\pi$
$74$	3.67284	−	5.61534i	0.426959	−	0.652770i
$75$		0			0
$76$	4.04917	−	1.77113i	0.464471	−	0.203162i
$77$	8.05842	+	4.65253i	0.918342	+	0.530205i
$78$		0			0
$79$	8.80507	−	5.08361i	0.990647	−	0.571951i	0.0851797	−	0.996366i	$-0.472854\pi$
$79$	8.80507	−	5.08361i	0.990647	−	0.571951i	0.905468	+	0.424415i	$0.139520\pi$
$80$	3.02661	−	0.939764i	0.338385	−	0.105069i
$81$		0			0
$82$	−0.186141	+	0.0940770i	−0.0205558	+	0.0103891i
$83$	3.62725	+	6.28258i	0.398142	+	0.689603i	0.993497	−	0.113861i	$-0.0363217\pi$
$83$	3.62725	+	6.28258i	0.398142	+	0.689603i	−0.595355	+	0.803463i	$0.702988\pi$
$84$		0			0
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	−0.546267	+	9.80880i	−0.0589055	+	1.05771i
$87$		0			0
$88$	−3.38465	−	9.08299i	−0.360805	−	0.968250i
$89$			5.34363i			0.566424i	0.959057	+	0.283212i	$0.0913999\pi$
$89$			5.34363i			0.566424i	−0.959057	+	0.283212i	$0.908600\pi$
$90$		0			0
$91$			9.15640i			0.959852i
$92$	−4.27582	−	0.477736i	−0.445785	−	0.0498074i
$93$		0			0
$94$	−16.3187	−	0.908812i	−1.68314	−	0.0937368i
$95$	0.875393	−	1.51622i	0.0898134	−	0.155561i
$96$		0			0
$97$	6.24456	+	10.8159i	0.634039	+	1.09819i	0.986718	+	0.162444i	$0.0519376\pi$
$97$	6.24456	+	10.8159i	0.634039	+	1.09819i	−0.352679	+	0.935745i	$0.614729\pi$
$98$	−0.237482	−	0.469882i	−0.0239893	−	0.0474652i
$99$		0			0
$100$	−5.18614	+	7.04069i	−0.518614	+	0.704069i
$101$	−15.4307	+	8.90892i	−1.53541	+	0.886471i	−0.536314	+	0.844019i	$0.680184\pi$
$101$	−15.4307	+	8.90892i	−1.53541	+	0.886471i	−0.999099	+	0.0424521i	$0.986483\pi$
$102$		0			0
$103$	12.6325	+	7.29339i	1.24472	+	0.718640i	0.970051	−	0.242899i	$-0.0780985\pi$
$103$	12.6325	+	7.29339i	1.24472	+	0.718640i	0.274669	+	0.961539i	$0.411432\pi$
$104$	6.07514	−	7.35330i	0.595716	−	0.721050i
$105$		0			0
$106$	−10.0751	−	6.58987i	−0.978584	−	0.640065i
$107$	13.2332			1.27930			0.639650	−	0.768667i	$-0.279080\pi$
$107$	13.2332			1.27930			0.639650	+	0.768667i	$0.279080\pi$
$108$		0			0
$109$	−9.48913			−0.908893			−0.454447	−	0.890774i	$-0.650163\pi$
$109$	−9.48913			−0.908893			−0.454447	+	0.890774i	$0.650163\pi$
$110$	−3.21352	−	2.10187i	−0.306397	−	0.200406i
$111$		0			0
$112$	−2.39702	+	10.5930i	−0.226497	+	1.00094i
$113$	−13.8030	−	7.96916i	−1.29848	−	0.749675i	−0.318335	−	0.947978i	$-0.603124\pi$
$113$	−13.8030	−	7.96916i	−1.29848	−	0.749675i	−0.980141	+	0.198303i	$0.936457\pi$
$114$		0			0
$115$	−1.47603	+	0.852189i	−0.137641	+	0.0794670i
$116$	−1.27582	−	0.939764i	−0.118457	−	0.0872549i
$117$		0			0
$118$	3.30298	+	6.53528i	0.304064	+	0.601621i
$119$	3.42703	+	5.93580i	0.314156	+	0.544134i
$120$		0			0
$121$	−0.372281	+	0.644810i	−0.0338438	+	0.0586191i
$122$	−4.76175	−	0.265189i	−0.431108	−	0.0240091i
$123$		0			0
$124$	−0.378504	+	3.38768i	−0.0339906	+	0.304222i
$125$			7.42554i			0.664160i
$126$		0			0
$127$		−	16.2912i		−	1.44561i	−0.691053	−	0.722804i	$-0.742853\pi$
$127$		−	16.2912i		−	1.44561i	0.691053	−	0.722804i	$-0.257147\pi$
$128$	8.95326	−	6.91658i	0.791364	−	0.611345i
$129$		0			0
$130$	0.210106	−	3.77267i	0.0184275	−	0.330885i
$131$	−3.62725	+	6.28258i	−0.316914	+	0.548911i	−0.979843	−	0.199771i	$-0.935980\pi$
$131$	−3.62725	+	6.28258i	−0.316914	+	0.548911i	0.662928	+	0.748683i	$0.269313\pi$
$132$		0			0
$133$	3.00000	+	5.19615i	0.260133	+	0.450564i
$134$	−8.76780	+	4.43132i	−0.757423	+	0.382807i
$135$		0			0
$136$	1.18614	−	7.04069i	0.101711	−	0.603734i
$137$	16.2446	−	9.37880i	1.38787	−	0.801285i	0.394792	−	0.918771i	$-0.370817\pi$
$137$	16.2446	−	9.37880i	1.38787	−	0.801285i	0.993075	+	0.117485i	$0.0374833\pi$
$138$		0			0
$139$	8.09262	+	4.67228i	0.686407	+	0.396297i	0.802265	−	0.596968i	$-0.203628\pi$
$139$	8.09262	+	4.67228i	0.686407	+	0.396297i	−0.115858	+	0.993266i	$0.536962\pi$
$140$	1.72418	+	3.94184i	0.145720	+	0.333146i
$141$		0			0
$142$	1.35531	−	2.07211i	0.113735	−	0.173887i
$143$	−11.5569			−0.966438
$144$		0			0
$145$	−0.627719			−0.0521292
$146$	−1.83642	+	2.80767i	−0.151983	+	0.232364i
$147$		0			0
$148$	−3.80273	−	8.69384i	−0.312582	−	0.714629i
$149$	8.31386	+	4.80001i	0.681098	+	0.393232i	0.800269	−	0.599642i	$-0.204690\pi$
$149$	8.31386	+	4.80001i	0.681098	+	0.393232i	−0.119171	+	0.992874i	$0.538024\pi$
$150$		0			0
$151$	−7.92967	+	4.57820i	−0.645308	+	0.372569i	−0.786656	−	0.617391i	$-0.788190\pi$
$151$	−7.92967	+	4.57820i	−0.645308	+	0.372569i	0.141348	+	0.989960i	$0.454856\pi$
$152$	1.03834	−	6.16337i	0.0842204	−	0.499915i
$153$		0			0
$154$	11.7446	−	5.93580i	0.946404	−	0.478320i
$155$	0.675178	+	1.16944i	0.0542316	+	0.0939319i
$156$		0			0
$157$	8.43070	−	14.6024i	0.672843	−	1.16540i	−0.304251	−	0.952592i	$-0.598406\pi$
$157$	8.43070	−	14.6024i	0.672843	−	1.16540i	0.977094	−	0.212807i	$-0.0682605\pi$
$158$	0.799528	−	14.3564i	0.0636070	−	1.14213i
$159$		0			0
$160$	1.23070	−	4.30957i	0.0972955	−	0.340701i
$161$		−	5.84096i		−	0.460332i
$162$		0			0
$163$		−	11.8716i		−	0.929855i	−0.885349	−	0.464928i	$-0.846080\pi$
$163$		−	11.8716i		−	0.929855i	0.885349	−	0.464928i	$-0.153920\pi$
$164$	−0.0327513	+	0.293130i	−0.00255744	+	0.0228896i
$165$		0			0
$166$	10.2435	+	0.570478i	0.795052	+	0.0442777i
$167$	9.60592	−	16.6379i	0.743329	−	1.28748i	−0.207643	−	0.978205i	$-0.566579\pi$
$167$	9.60592	−	16.6379i	0.743329	−	1.28748i	0.950972	−	0.309278i	$-0.100087\pi$
$168$		0			0
$169$	0.813859	+	1.40965i	0.0626046	+	0.108434i
$170$	−1.27582	−	2.52434i	−0.0978510	−	0.193608i
$171$		0			0
$172$	11.1861	+	8.23966i	0.852935	+	0.628268i
$173$	4.80298	−	2.77300i	0.365164	−	0.210828i	−0.306180	−	0.951974i	$-0.599051\pi$
$173$	4.80298	−	2.77300i	0.365164	−	0.210828i	0.671344	+	0.741146i	$0.265717\pi$
$174$		0			0
$175$	−10.2811	−	5.93580i	−0.777178	−	0.448704i
$176$	−13.3701	−	3.02544i	−1.00781	−	0.228051i
$177$		0			0
$178$	6.32435	+	4.13658i	0.474030	+	0.310050i
$179$	−18.8114			−1.40603			−0.703016	−	0.711174i	$-0.748164\pi$
$179$	−18.8114			−1.40603			−0.703016	+	0.711174i	$0.748164\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	10.8369	+	7.08811i	0.803283	+	0.525405i
$183$		0			0
$184$	−3.87539	+	4.69074i	−0.285698	+	0.345806i
$185$	−3.25544	−	1.87953i	−0.239345	−	0.138186i
$186$		0			0
$187$	−7.49198	+	4.32550i	−0.547868	+	0.316312i
$188$	−13.7081	+	18.6101i	−0.999769	+	1.35728i
$189$		0			0
$190$	−1.11684	−	2.20979i	−0.0810244	−	0.160315i
$191$	−1.95100	−	3.37923i	−0.141169	−	0.244512i	0.786768	−	0.617249i	$-0.211753\pi$
$191$	−1.95100	−	3.37923i	−0.141169	−	0.244512i	−0.927937	+	0.372736i	$0.878420\pi$
$192$		0			0
$193$	1.87228	−	3.24289i	0.134770	−	0.233428i	−0.790740	−	0.612153i	$-0.790304\pi$
$193$	1.87228	−	3.24289i	0.134770	−	0.233428i	0.925509	+	0.378724i	$0.123637\pi$
$194$	17.6350	+	0.982118i	1.26612	+	0.0705120i
$195$		0			0
$196$	−0.739958	−	0.0826752i	−0.0528542	−	0.00590537i
$197$		−	10.6873i		−	0.761436i	−0.924691	−	0.380718i	$-0.875677\pi$
$197$		−	10.6873i		−	0.761436i	0.924691	−	0.380718i	$-0.124323\pi$
$198$		0			0
$199$			19.3236i			1.36981i	0.728630	+	0.684907i	$0.240157\pi$
$199$			19.3236i			1.36981i	−0.728630	+	0.684907i	$0.759843\pi$
$200$	4.31821	+	11.5883i	0.305343	+	0.819414i
$201$		0			0
$202$	−1.40116	+	25.1592i	−0.0985850	+	1.77020i
$203$	1.07561	−	1.86301i	0.0754928	−	0.130757i
$204$		0			0
$205$	0.0584220	+	0.101190i	0.00408037	+	0.00706741i
$206$	18.4110	−	9.30506i	1.28275	−	0.648315i
$207$		0			0
$208$	−4.00000	−	12.8824i	−0.277350	−	0.893234i
$209$	−6.55842	+	3.78651i	−0.453656	+	0.261918i
$210$		0			0
$211$	−5.30350	−	3.06198i	−0.365108	−	0.210795i	0.306211	−	0.951964i	$-0.400939\pi$
$211$	−5.30350	−	3.06198i	−0.365108	−	0.210795i	−0.671319	+	0.741169i	$0.734272\pi$
$212$	−15.5986	+	6.82292i	−1.07132	+	0.468600i
$213$		0			0
$214$	10.2440	−	15.6619i	0.700265	−	1.07062i
$215$	5.50371			0.375350
$216$		0			0
$217$	−4.62772			−0.314150
$218$	−7.34568	+	11.2307i	−0.497512	+	0.760637i
$219$		0			0
$220$	−4.97526	+	2.17621i	−0.335432	+	0.146720i
$221$	−7.37228	−	4.25639i	−0.495913	−	0.286316i
$222$		0			0
$223$	−1.47603	+	0.852189i	−0.0988426	+	0.0570668i	−0.548606	−	0.836081i	$-0.684841\pi$
$223$	−1.47603	+	0.852189i	−0.0988426	+	0.0570668i	0.449764	+	0.893147i	$0.351508\pi$
$224$	10.6815	+	11.0371i	0.713690	+	0.737448i
$225$		0			0
$226$	−20.1168	+	10.1672i	−1.33815	+	0.676313i
$227$	−9.44298	−	16.3557i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951050\pi$
$227$	−9.44298	−	16.3557i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$228$		0			0
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	−0.978290	−	0.207241i	$-0.933552\pi$
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	0.668621	+	0.743603i	$0.266885\pi$
$230$	−0.134029	+	2.40663i	−0.00883759	+	0.158688i
$231$		0			0
$232$	−2.09987	+	0.782488i	−0.137863	+	0.0513729i
$233$			28.0627i			1.83845i	0.393737	+	0.919223i	$0.371182\pi$
$233$			28.0627i			1.83845i	−0.393737	+	0.919223i	$0.628818\pi$
$234$		0			0
$235$			9.15640i			0.597298i
$236$	10.2916	+	1.14988i	0.669926	+	0.0748506i
$237$		0			0
$238$	9.67812	+	0.538989i	0.627339	+	0.0349375i
$239$	−8.33010	+	14.4282i	−0.538830	+	0.933280i	0.460138	+	0.887847i	$0.347800\pi$
$239$	−8.33010	+	14.4282i	−0.538830	+	0.933280i	−0.998967	+	0.0454327i	$0.985533\pi$
$240$		0			0
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	−0.999342	−	0.0362667i	$-0.988453\pi$
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	0.468263	−	0.883589i	$-0.344880\pi$
$242$	0.474964	+	0.939764i	0.0305319	+	0.0604103i
$243$		0			0
$244$	−4.00000	+	5.43039i	−0.256074	+	0.347645i
$245$	−0.255437	+	0.147477i	−0.0163193	+	0.00942195i
$246$		0			0
$247$	−6.45364	−	3.72601i	−0.410635	−	0.237080i
$248$	3.71642	+	3.07042i	0.235993	+	0.194972i
$249$		0			0
$250$	8.78835	+	5.74822i	0.555824	+	0.363549i
$251$	16.7347			1.05629			0.528144	−	0.849155i	$-0.322888\pi$
$251$	16.7347			1.05629			0.528144	+	0.849155i	$0.322888\pi$
$252$		0			0
$253$	7.37228			0.463491
$254$	−19.2811	−	12.6112i	−1.20980	−	0.791300i
$255$		0			0
$256$	−1.25513	−	15.9507i	−0.0784457	−	0.996918i
$257$	9.98913	+	5.76722i	0.623105	+	0.359750i	0.778077	−	0.628169i	$-0.216195\pi$
$257$	9.98913	+	5.76722i	0.623105	+	0.359750i	−0.154972	+	0.987919i	$0.549529\pi$
$258$		0			0
$259$	11.1565	−	6.44121i	0.693231	−	0.400237i
$260$	−4.30243	−	3.16915i	−0.266825	−	0.196542i
$261$		0			0
$262$	4.62772	+	9.15640i	0.285901	+	0.565684i
$263$	6.25343	+	10.8313i	0.385603	+	0.667884i	0.991853	−	0.127391i	$-0.0406602\pi$
$263$	6.25343	+	10.8313i	0.385603	+	0.667884i	−0.606250	+	0.795274i	$0.707327\pi$
$264$		0			0
$265$	−3.37228	+	5.84096i	−0.207158	+	0.358807i
$266$	8.47215	+	0.471827i	0.519461	+	0.0289296i
$267$		0			0
$268$	−1.54269	+	13.8073i	−0.0942345	+	0.843416i
$269$		−	24.9484i		−	1.52113i	−0.649260	−	0.760566i	$-0.724921\pi$
$269$		−	24.9484i		−	1.52113i	0.649260	−	0.760566i	$-0.275079\pi$
$270$		0			0
$271$			1.38712i			0.0842618i	0.999112	+	0.0421309i	$0.0134147\pi$
$271$			1.38712i			0.0842618i	−0.999112	+	0.0421309i	$0.986585\pi$
$272$	−7.41467	−	6.85414i	−0.449580	−	0.415593i
$273$		0			0
$274$	1.47506	−	26.4862i	0.0891115	−	1.60009i
$275$	7.49198	−	12.9765i	0.451783	−	0.782512i
$276$		0			0
$277$	−0.313859	−	0.543620i	−0.0188580	−	0.0326630i	0.856442	−	0.516243i	$-0.172670\pi$
$277$	−0.313859	−	0.543620i	−0.0188580	−	0.0326630i	−0.875300	+	0.483580i	$0.839336\pi$
$278$	11.7944	−	5.96099i	0.707381	−	0.357516i
$279$		0			0
$280$	6.00000	+	1.01082i	0.358569	+	0.0604078i
$281$	5.56930	−	3.21543i	0.332236	−	0.191817i	−0.324597	−	0.945852i	$-0.605229\pi$
$281$	5.56930	−	3.21543i	0.332236	−	0.191817i	0.656834	+	0.754036i	$0.271895\pi$
$282$		0			0
$283$	8.80507	+	5.08361i	0.523407	+	0.302189i	0.738327	−	0.674442i	$-0.235616\pi$
$283$	8.80507	+	5.08361i	0.523407	+	0.302189i	−0.214921	+	0.976632i	$0.568949\pi$
$284$	−1.40324	−	3.20810i	−0.0832669	−	0.190366i
$285$		0			0
$286$	−8.94639	+	13.6780i	−0.529011	+	0.808796i
$287$	−0.400428			−0.0236365
$288$		0			0
$289$	10.6277			0.625160
$290$	−0.485927	+	0.742925i	−0.0285346	+	0.0436260i
$291$		0			0
$292$	1.90136	+	4.34692i	0.111269	+	0.254384i
$293$	17.3139	+	9.99616i	1.01149	+	0.583982i	0.911627	−	0.411020i	$-0.134827\pi$
$293$	17.3139	+	9.99616i	1.01149	+	0.583982i	0.0998599	+	0.995002i	$0.468161\pi$
$294$		0			0
$295$	3.55271	−	2.05116i	0.206847	−	0.119423i
$296$	−13.2332	−	2.22938i	−0.769163	−	0.129580i
$297$		0			0
$298$	12.1168	−	6.12395i	0.701910	−	0.354751i
$299$	3.62725	+	6.28258i	0.209769	+	0.363331i
$300$		0			0
$301$	−9.43070	+	16.3345i	−0.543577	+	0.941502i
$302$	−0.720040	+	12.9291i	−0.0414336	+	0.743984i
$303$		0			0
$304$	−6.49074	−	6.00006i	−0.372270	−	0.344127i
$305$			2.67181i			0.152988i
$306$		0			0
$307$		−	25.9530i		−	1.48121i	−0.671938	−	0.740607i	$-0.734538\pi$
$307$		−	25.9530i		−	1.48121i	0.671938	−	0.740607i	$-0.265462\pi$
$308$	2.06644	−	18.4950i	0.117747	−	1.05385i
$309$		0			0
$310$	1.90674	+	0.106189i	0.108295	+	0.00603114i
$311$	−15.6591	+	27.1224i	−0.887948	+	1.53797i	−0.0456512	+	0.998957i	$0.514536\pi$
$311$	−15.6591	+	27.1224i	−0.887948	+	1.53797i	−0.842297	+	0.539014i	$0.818797\pi$
$312$		0			0
$313$	−2.24456	−	3.88770i	−0.126870	−	0.219746i	0.795592	−	0.605832i	$-0.207160\pi$
$313$	−2.24456	−	3.88770i	−0.126870	−	0.219746i	−0.922462	+	0.386087i	$0.873826\pi$
$314$	−10.7561	−	21.2819i	−0.607000	−	1.20101i
$315$		0			0
$316$	−16.3723	−	12.0597i	−0.921013	−	0.678414i
$317$	−20.6644	+	11.9306i	−1.16063	+	0.670089i	−0.951454	−	0.307790i	$-0.900411\pi$
$317$	−20.6644	+	11.9306i	−1.16063	+	0.670089i	−0.209173	+	0.977879i	$0.567077\pi$
$318$		0			0
$319$	2.35143	+	1.35760i	0.131655	+	0.0760109i
$320$	−4.14780	−	4.79268i	−0.231869	−	0.267919i
$321$		0			0
$322$	−6.91296	−	4.52158i	−0.385244	−	0.251978i
$323$	−5.57825			−0.310382
$324$		0			0
$325$	14.7446			0.817881
$326$	−14.0504	−	9.18998i	−0.778180	−	0.508986i
$327$		0			0
$328$	0.321575	+	0.265678i	0.0177560	+	0.0146696i
$329$	−27.1753	−	15.6896i	−1.49822	−	0.864998i
$330$		0			0
$331$	24.1149	−	13.9228i	1.32548	−	0.765264i	0.340879	−	0.940107i	$-0.389275\pi$
$331$	24.1149	−	13.9228i	1.32548	−	0.765264i	0.984596	+	0.174843i	$0.0559419\pi$
$332$	8.60485	−	11.6819i	0.472253	−	0.641129i
$333$		0			0
$334$	−12.2554	−	24.2486i	−0.670588	−	1.32682i
$335$	2.75186	+	4.76635i	0.150350	+	0.260414i
$336$		0			0
$337$	2.12772	−	3.68532i	0.115904	−	0.200752i	−0.802237	−	0.597006i	$-0.796357\pi$
$337$	2.12772	−	3.68532i	0.115904	−	0.200752i	0.918141	+	0.396254i	$0.129690\pi$
$338$	2.29838	+	0.128000i	0.125015	+	0.00696230i
$339$		0			0
$340$	−3.97526	−	0.444155i	−0.215589	−	0.0240877i
$341$		−	5.84096i		−	0.316306i
$342$		0			0
$343$			17.9955i			0.971668i
$344$	18.4113	−	6.86070i	0.992668	−	0.369904i
$345$		0			0
$346$	0.436126	−	7.83111i	0.0234463	−	0.421003i
$347$	3.86473	−	6.69391i	0.207470	−	0.359348i	−0.743447	−	0.668795i	$-0.766811\pi$
$347$	3.86473	−	6.69391i	0.207470	−	0.359348i	0.950917	+	0.309447i	$0.100144\pi$
$348$		0			0
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	0.977121	−	0.212683i	$-0.0682200\pi$
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	−0.672749	+	0.739871i	$0.734887\pi$
$350$	−14.9840	+	7.57301i	−0.800926	+	0.404795i
$351$		0			0
$352$	−13.9307	+	13.4819i	−0.742509	+	0.718587i
$353$	4.24456	−	2.45060i	0.225915	−	0.130432i	−0.382771	−	0.923843i	$-0.625030\pi$
$353$	4.24456	−	2.45060i	0.225915	−	0.130432i	0.608686	+	0.793411i	$0.291697\pi$
$354$		0			0
$355$	−1.20128	−	0.693562i	−0.0637576	−	0.0368105i
$356$	9.79155	−	4.28287i	0.518951	−	0.226992i
$357$		0			0
$358$	−14.5622	+	22.2639i	−0.769636	+	1.17668i
$359$	29.9679			1.58165			0.790823	−	0.612045i	$-0.209653\pi$
$359$	29.9679			1.58165			0.790823	+	0.612045i	$0.209653\pi$
$360$		0			0
$361$	14.1168			0.742992
$362$	−3.09646	+	4.73412i	−0.162746	+	0.248820i
$363$		0			0
$364$	16.7780	−	7.33878i	0.879406	−	0.384656i
$365$	1.62772	+	0.939764i	0.0851987	+	0.0491895i
$366$		0			0
$367$	−11.7571	+	6.78799i	−0.613718	+	0.354330i	−0.774419	−	0.632673i	$-0.781958\pi$
$367$	−11.7571	+	6.78799i	−0.613718	+	0.354330i	0.160701	+	0.987003i	$0.448624\pi$
$368$	2.55164	+	8.21782i	0.133014	+	0.428384i
$369$		0			0
$370$	−4.74456	+	2.39794i	−0.246658	+	0.124663i
$371$	−11.5569	−	20.0172i	−0.600006	−	1.03924i
$372$		0			0
$373$	−4.43070	+	7.67420i	−0.229413	+	0.397355i	−0.957634	−	0.287987i	$-0.907014\pi$
$373$	−4.43070	+	7.67420i	−0.229413	+	0.397355i	0.728221	+	0.685342i	$0.240347\pi$
$374$	−0.680295	+	12.2154i	−0.0351772	+	0.631644i
$375$		0			0
$376$	11.4140	+	30.6304i	0.588632	+	1.57964i
$377$			2.67181i			0.137605i
$378$		0			0
$379$			9.66181i			0.496294i	0.968722	+	0.248147i	$0.0798216\pi$
$379$			9.66181i			0.496294i	−0.968722	+	0.248147i	$0.920178\pi$
$380$	−3.47992	−	0.388810i	−0.178516	−	0.0199455i
$381$		0			0
$382$	−5.50972	−	0.306845i	−0.281902	−	0.0156995i
$383$	0.200214	−	0.346781i	0.0102305	−	0.0177197i	−0.860865	−	0.508834i	$-0.830077\pi$
$383$	0.200214	−	0.346781i	0.0102305	−	0.0177197i	0.871095	+	0.491114i	$0.163410\pi$
$384$		0			0
$385$	−3.68614	−	6.38458i	−0.187863	−	0.325388i
$386$	−2.38870	−	4.72627i	−0.121581	−	0.240561i
$387$		0			0
$388$	14.8139	−	20.1113i	0.752060	−	1.02099i
$389$	−7.19702	+	4.15520i	−0.364903	+	0.210677i	−0.671229	−	0.741250i	$-0.734233\pi$
$389$	−7.19702	+	4.15520i	−0.364903	+	0.210677i	0.306326	+	0.951927i	$0.400900\pi$
$390$		0			0
$391$	4.70285	+	2.71519i	0.237834	+	0.137313i
$392$	−0.670662	+	0.811764i	−0.0338735	+	0.0410002i
$393$		0			0
$394$	−12.6487	−	8.27317i	−0.637232	−	0.416796i
$395$	−8.05535			−0.405309
$396$		0			0
$397$	−7.25544			−0.364140			−0.182070	−	0.983286i	$-0.558280\pi$
$397$	−7.25544			−0.364140			−0.182070	+	0.983286i	$0.558280\pi$
$398$	22.8701	+	14.9587i	1.14637	+	0.749812i
$399$		0			0
$400$	17.0579	+	3.85992i	0.852893	+	0.192996i
$401$	18.9891	+	10.9634i	0.948272	+	0.547485i	0.892544	−	0.450961i	$-0.148919\pi$
$401$	18.9891	+	10.9634i	0.948272	+	0.547485i	0.0557281	+	0.998446i	$0.482252\pi$
$402$		0			0
$403$	4.97760	−	2.87382i	0.247952	−	0.143155i
$404$	28.6921	+	21.1345i	1.42749	+	1.05148i
$405$		0			0
$406$	−1.37228	−	2.71519i	−0.0681052	−	0.134753i
$407$	8.12989	+	14.0814i	0.402984	+	0.697988i
$408$		0			0
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	−0.892559	−	0.450931i	$-0.851092\pi$
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	0.836797	+	0.547513i	$0.184426\pi$
$410$	0.164987	+	0.00918836i	0.00814811	+	0.000453781i
$411$		0			0
$412$	3.23939	−	28.9932i	0.159594	−	1.42839i
$413$			14.0588i			0.691788i
$414$		0			0
$415$		−	5.74764i		−	0.282141i
$416$	−18.3432	−	5.23834i	−0.899349	−	0.256831i
$417$		0			0
$418$	−0.595525	+	10.6933i	−0.0291281	+	0.523026i
$419$	2.82639	−	4.89545i	0.138078	−	0.239159i	−0.788691	−	0.614790i	$-0.789241\pi$
$419$	2.82639	−	4.89545i	0.138078	−	0.239159i	0.926769	+	0.375631i	$0.122574\pi$
$420$		0			0
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	−0.960417	−	0.278565i	$-0.910141\pi$
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	0.238964	−	0.971028i	$-0.423192\pi$
$422$	−7.72946	+	3.90653i	−0.376264	+	0.190167i
$423$		0			0
$424$	−4.00000	+	23.7432i	−0.194257	+	1.15307i
$425$	9.55842	−	5.51856i	0.463652	−	0.267689i
$426$		0			0
$427$	−7.92967	−	4.57820i	−0.383744	−	0.221555i
$428$	−10.6063	−	24.2482i	−0.512674	−	1.17208i
$429$		0			0
$430$	4.26051	−	6.51381i	0.205460	−	0.314124i
$431$	−14.6581			−0.706054			−0.353027	−	0.935613i	$-0.614848\pi$
$431$	−14.6581			−0.706054			−0.353027	+	0.935613i	$0.614848\pi$
$432$		0			0
$433$	−14.3723			−0.690688			−0.345344	−	0.938476i	$-0.612238\pi$
$433$	−14.3723			−0.690688			−0.345344	+	0.938476i	$0.612238\pi$
$434$	−3.58239	+	5.47705i	−0.171960	+	0.262907i
$435$		0			0
$436$	7.60545	+	17.3877i	0.364235	+	0.832718i
$437$	4.11684	+	2.37686i	0.196935	+	0.113701i
$438$		0			0
$439$	−28.4919	+	16.4498i	−1.35984	+	0.785106i	−0.989602	−	0.143830i	$-0.954058\pi$
$439$	−28.4919	+	16.4498i	−1.35984	+	0.785106i	−0.370241	+	0.928936i	$0.620725\pi$
$440$	−1.27582	+	7.57301i	−0.0608224	+	0.361029i
$441$		0			0
$442$	−10.7446	+	5.43039i	−0.511067	+	0.258297i
$443$	2.58891	+	4.48412i	0.123003	+	0.213047i	0.920950	−	0.389680i	$-0.127414\pi$
$443$	2.58891	+	4.48412i	0.123003	+	0.213047i	−0.797948	+	0.602727i	$0.794081\pi$
$444$		0			0
$445$	2.11684	−	3.66648i	0.100348	−	0.173808i
$446$	−0.134029	+	2.40663i	−0.00634644	+	0.113957i
$447$		0			0
$448$	21.3315	−	4.09793i	1.00782	−	0.193609i
$449$			3.81396i			0.179992i	0.995942	+	0.0899959i	$0.0286854\pi$
$449$			3.81396i			0.179992i	−0.995942	+	0.0899959i	$0.971315\pi$
$450$		0			0
$451$		−	0.505408i		−	0.0237987i
$452$	−3.53954	+	31.6795i	−0.166486	+	1.49008i
$453$		0			0
$454$	−26.6675	−	1.48515i	−1.25157	−	0.0697016i
$455$	3.62725	−	6.28258i	0.170048	−	0.294532i
$456$		0			0
$457$	2.98913	+	5.17732i	0.139825	+	0.242185i	0.927430	−	0.373996i	$-0.122013\pi$
$457$	2.98913	+	5.17732i	0.139825	+	0.242185i	−0.787605	+	0.616180i	$0.788679\pi$
$458$	5.97868	+	11.8294i	0.279365	+	0.552752i
$459$		0			0
$460$	2.74456	+	2.02163i	0.127966	+	0.0942591i
$461$	19.8030	−	11.4333i	0.922317	−	0.532500i	0.0379435	−	0.999280i	$-0.487919\pi$
$461$	19.8030	−	11.4333i	0.922317	−	0.532500i	0.884373	+	0.466780i	$0.154586\pi$
$462$		0			0
$463$	−18.2108	−	10.5140i	−0.846327	−	0.488627i	0.0130831	−	0.999914i	$-0.495835\pi$
$463$	−18.2108	−	10.5140i	−0.846327	−	0.488627i	−0.859410	+	0.511288i	$0.829169\pi$
$464$	−0.699444	+	3.09100i	−0.0324709	+	0.143496i
$465$		0			0
$466$	33.2130	+	21.7237i	1.53856	+	1.00633i
$467$	−24.3897			−1.12862			−0.564310	−	0.825563i	$-0.690858\pi$
$467$	−24.3897			−1.12862			−0.564310	+	0.825563i	$0.690858\pi$
$468$		0			0
$469$	−18.8614			−0.870939
$470$	10.8369	+	7.08811i	0.499868	+	0.326950i
$471$		0			0
$472$	9.32780	−	11.2903i	0.429347	−	0.519678i
$473$	−20.6168	−	11.9031i	−0.947963	−	0.547307i
$474$		0			0
$475$	8.36737	−	4.83090i	0.383921	−	0.221657i
$476$	8.12989	−	11.0371i	0.372633	−	0.505885i
$477$		0			0
$478$	10.6277	+	21.0280i	0.486101	+	0.961798i
$479$	−4.90307	−	8.49236i	−0.224027	−	0.388026i	0.732000	−	0.681304i	$-0.238587\pi$
$479$	−4.90307	−	8.49236i	−0.224027	−	0.388026i	−0.956027	+	0.293278i	$0.905254\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−23.2831	−	1.29667i	−1.06051	−	0.0590617i
$483$		0			0
$484$	1.47992	+	0.165350i	0.0672689	+	0.00751593i
$485$		−	9.89497i		−	0.449308i
$486$		0			0
$487$			17.9365i			0.812780i	0.913700	+	0.406390i	$0.133213\pi$
$487$			17.9365i			0.812780i	−0.913700	+	0.406390i	$0.866787\pi$
$488$	3.33057	+	8.93787i	0.150768	+	0.404598i
$489$		0			0
$490$	−0.0231945	+	0.416482i	−0.00104782	+	0.0188147i
$491$	12.3950	−	21.4689i	0.559381	−	0.968876i	−0.438168	−	0.898893i	$-0.644372\pi$
$491$	12.3950	−	21.4689i	0.559381	−	0.968876i	0.997548	−	0.0699824i	$-0.0222943\pi$
$492$		0			0
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	−9.40571	+	4.75372i	−0.423183	+	0.213880i
$495$		0			0
$496$	6.51087	−	2.02163i	0.292347	−	0.0907740i
$497$	4.11684	−	2.37686i	0.184666	−	0.106617i
$498$		0			0
$499$	0.437696	+	0.252704i	0.0195940	+	0.0113126i	0.509765	−	0.860314i	$-0.329732\pi$
$499$	0.437696	+	0.252704i	0.0195940	+	0.0113126i	−0.490171	+	0.871626i	$0.663066\pi$
$500$	13.6064	−	5.95150i	0.608496	−	0.266159i
$501$		0			0
$502$	12.9546	−	19.8061i	0.578193	−	0.883989i
$503$	−12.9073			−0.575507			−0.287754	−	0.957704i	$-0.592908\pi$
$503$	−12.9073			−0.575507			−0.287754	+	0.957704i	$0.592908\pi$
$504$		0			0
$505$	14.1168			0.628191
$506$	5.70699	−	8.72532i	0.253707	−	0.387888i
$507$		0			0
$508$	−29.8516	+	13.0572i	−1.32445	+	0.579321i
$509$	−15.6861	−	9.05640i	−0.695276	−	0.401418i	0.110310	−	0.993897i	$-0.464816\pi$
$509$	−15.6861	−	9.05640i	−0.695276	−	0.401418i	−0.805586	+	0.592480i	$0.798149\pi$
$510$		0			0
$511$	−5.57825	+	3.22060i	−0.246767	+	0.142471i
$512$	−19.8498	−	10.8622i	−0.877244	−	0.480045i
$513$		0			0
$514$	14.5584	−	7.35794i	0.642144	−	0.324545i
$515$	−5.77846	−	10.0086i	−0.254629	−	0.441031i
$516$		0			0
$517$	19.8030	−	34.2998i	0.870934	−	1.50850i
$518$	1.01304	−	18.1903i	0.0445106	−	0.799236i
$519$		0			0
$520$	−7.08136	+	2.63877i	−0.310538	+	0.115718i
$521$		−	10.4472i		−	0.457700i	−0.973462	−	0.228850i	$-0.926503\pi$
$521$		−	10.4472i		−	0.457700i	0.973462	−	0.228850i	$-0.0734966\pi$
$522$		0			0
$523$		−	4.41957i		−	0.193254i	−0.995321	−	0.0966272i	$-0.969195\pi$
$523$		−	4.41957i		−	0.193254i	0.995321	−	0.0966272i	$-0.0308055\pi$
$524$	14.4193	+	1.61106i	0.629909	+	0.0703794i
$525$		0			0
$526$	17.6600	+	0.983512i	0.770012	+	0.0428832i
$527$	2.15121	−	3.72601i	0.0937083	−	0.162308i
$528$		0			0
$529$	9.18614	+	15.9109i	0.399397	+	0.691777i
$530$	4.30243	+	8.51278i	0.186885	+	0.369771i
$531$		0			0
$532$	7.11684	−	9.66181i	0.308554	−	0.418892i
$533$	0.430703	−	0.248667i	0.0186558	−	0.0107709i
$534$		0			0
$535$	−9.07982	−	5.24224i	−0.392555	−	0.226642i
$536$	15.1472	+	12.5143i	0.654258	+	0.540534i
$537$		0			0
$538$	−29.5272	−	19.3130i	−1.27301	−	0.832641i
$539$	1.27582			0.0549535
$540$		0			0
$541$	36.9783			1.58982			0.794910	−	0.606728i	$-0.207518\pi$
$541$	36.9783			1.58982			0.794910	+	0.606728i	$0.207518\pi$
$542$	1.64170	+	1.07379i	0.0705172	+	0.0461234i
$543$		0			0
$544$	−13.8519	+	3.46959i	−0.593895	+	0.148758i
$545$	6.51087	+	3.75906i	0.278895	+	0.161020i
$546$		0			0
$547$	−7.21723	+	4.16687i	−0.308586	+	0.178162i	−0.646294	−	0.763089i	$-0.723682\pi$
$547$	−7.21723	+	4.16687i	−0.308586	+	0.178162i	0.337707	+	0.941251i	$0.390349\pi$
$548$	−30.2054	−	22.2492i	−1.29031	−	0.950437i
$549$		0			0
$550$	−9.55842	−	18.9123i	−0.407572	−	0.806423i
$551$	0.875393	+	1.51622i	0.0372930	+	0.0645933i
$552$		0			0
$553$	13.8030	−	23.9075i	0.586963	−	1.01665i
$554$	−0.886355	−	0.0493624i	−0.0376576	−	0.00209721i
$555$		0			0
$556$	2.07521	−	18.5735i	0.0880086	−	0.787693i
$557$			20.4897i			0.868175i	0.900871	+	0.434087i	$0.142929\pi$
$557$			20.4897i			0.868175i	−0.900871	+	0.434087i	$0.857071\pi$
$558$		0			0
$559$		−	23.4259i		−	0.990811i
$560$	5.84102	−	6.31870i	0.246828	−	0.267014i
$561$		0			0
$562$	0.505710	−	9.08055i	0.0213321	−	0.383040i
$563$	−5.54098	+	9.59726i	−0.233524	+	0.404476i	−0.958843	−	0.283937i	$-0.908359\pi$
$563$	−5.54098	+	9.59726i	−0.233524	+	0.404476i	0.725318	+	0.688414i	$0.241693\pi$
$564$		0			0
$565$	6.31386	+	10.9359i	0.265626	+	0.460078i
$566$	12.8327	−	6.48577i	0.539400	−	0.272617i
$567$		0			0
$568$	−4.88316	−	0.822662i	−0.204893	−	0.0345181i
$569$	−0.989125	+	0.571072i	−0.0414663	+	0.0239406i	−0.520590	−	0.853807i	$-0.674288\pi$
$569$	−0.989125	+	0.571072i	−0.0414663	+	0.0239406i	0.479124	+	0.877747i	$0.340955\pi$
$570$		0			0
$571$	14.5463	+	8.39829i	0.608742	+	0.351457i	0.772473	−	0.635048i	$-0.219020\pi$
$571$	14.5463	+	8.39829i	0.608742	+	0.351457i	−0.163731	+	0.986505i	$0.552353\pi$
$572$	9.26278	+	21.1767i	0.387296	+	0.885441i
$573$		0			0
$574$	−0.309978	+	0.473919i	−0.0129382	+	0.0197810i
$575$	−9.40571			−0.392245
$576$		0			0
$577$	−42.8397			−1.78344			−0.891719	−	0.452589i	$-0.850500\pi$
$577$	−42.8397			−1.78344			−0.891719	+	0.452589i	$0.850500\pi$
$578$	8.22708	−	12.5782i	0.342201	−	0.523186i
$579$		0			0
$580$	0.503111	+	1.15022i	0.0208906	+	0.0477602i
$581$	17.0584	+	9.84868i	0.707703	+	0.408592i
$582$		0			0
$583$	25.2651	−	14.5868i	1.04637	−	0.604123i
$584$	6.61659	+	1.11469i	0.273796	+	0.0461263i
$585$		0			0
$586$	25.2337	−	12.7533i	1.04239	−	0.526834i
$587$	6.41637	+	11.1135i	0.264832	+	0.458702i	0.967520	−	0.252796i	$-0.0813502\pi$
$587$	6.41637	+	11.1135i	0.264832	+	0.458702i	−0.702688	+	0.711499i	$0.748017\pi$
$588$		0			0
$589$	1.88316	−	3.26172i	0.0775941	−	0.134397i
$590$	0.322598	−	5.79258i	0.0132811	−	0.238477i
$591$		0			0
$592$	−12.8825	+	13.9361i	−0.529469	+	0.572769i
$593$		−	15.4410i		−	0.634085i	−0.948411	−	0.317043i	$-0.897310\pi$
$593$		−	15.4410i		−	0.634085i	0.948411	−	0.317043i	$-0.102690\pi$
$594$		0			0
$595$		−	5.43039i		−	0.222624i
$596$	2.13195	−	19.0813i	0.0873279	−	0.781601i
$597$		0			0
$598$	10.2435	+	0.570478i	0.418889	+	0.0233286i
$599$	−9.20550	+	15.9444i	−0.376126	+	0.651470i	−0.990495	−	0.137549i	$-0.956077\pi$
$599$	−9.20550	+	15.9444i	−0.376126	+	0.651470i	0.614369	+	0.789019i	$0.289411\pi$
$600$		0			0
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	0.991001	+	0.133851i	$0.0427344\pi$
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	−0.379582	+	0.925158i	$0.623932\pi$
$602$	12.0319	+	23.8063i	0.490383	+	0.970272i
$603$		0			0
$604$	14.7446	+	10.8608i	0.599948	+	0.441919i
$605$	0.510875	−	0.294954i	0.0207700	−	0.0119916i
$606$		0			0
$607$	33.1947	+	19.1650i	1.34733	+	0.777883i	0.987871	−	0.155277i	$-0.0496270\pi$
$607$	33.1947	+	19.1650i	1.34733	+	0.777883i	0.359462	+	0.933160i	$0.382960\pi$
$608$	−12.1258	+	3.03726i	−0.491768	+	0.123177i
$609$		0			0
$610$	3.16218	+	2.06829i	0.128033	+	0.0837427i
$611$	38.9732			1.57669
$612$		0			0
$613$	−30.2337			−1.22113			−0.610564	−	0.791967i	$-0.709057\pi$
$613$	−30.2337			−1.22113			−0.610564	+	0.791967i	$0.709057\pi$
$614$	−30.7162	−	20.0906i	−1.23960	−	0.810790i
$615$		0			0
$616$	−20.2898	−	16.7630i	−0.817499	−	0.675400i
$617$	−7.24456	−	4.18265i	−0.291655	−	0.168387i	0.347033	−	0.937853i	$-0.387189\pi$
$617$	−7.24456	−	4.18265i	−0.291655	−	0.168387i	−0.638688	+	0.769466i	$0.720523\pi$
$618$		0			0
$619$	−23.9520	+	13.8287i	−0.962711	+	0.555821i	−0.897006	−	0.442018i	$-0.854263\pi$
$619$	−23.9520	+	13.8287i	−0.962711	+	0.555821i	−0.0657046	+	0.997839i	$0.520930\pi$
$620$	1.60171	−	2.17448i	0.0643263	−	0.0873293i
$621$		0			0
$622$	19.9783	+	39.5289i	0.801055	+	1.58497i
$623$	7.25450	+	12.5652i	0.290645	+	0.503412i
$624$		0			0
$625$	−7.98913	+	13.8376i	−0.319565	+	0.553503i
$626$	−6.33876	−	0.353015i	−0.253348	−	0.0141093i
$627$		0			0
$628$	−33.5143	−	3.74454i	−1.33737	−	0.149423i
$629$			11.9769i			0.477549i
$630$		0			0
$631$		−	17.9365i		−	0.714040i	−0.934097	−	0.357020i	$-0.883793\pi$
$631$		−	17.9365i		−	0.714040i	0.934097	−	0.357020i	$-0.116207\pi$
$632$	−26.9471	+	10.0415i	−1.07190	+	0.399428i
$633$		0			0
$634$	−1.87639	+	33.6926i	−0.0745210	+	1.33810i
$635$	−6.45364	+	11.1780i	−0.256105	+	0.443587i
$636$		0			0
$637$	0.627719	+	1.08724i	0.0248711	+	0.0430780i
$638$	3.42703	−	1.73205i	0.135678	−	0.0685725i
$639$		0			0
$640$	−8.88316	+	1.19897i	−0.351138	+	0.0473935i
$641$	−23.8723	+	13.7827i	−0.942898	+	0.544383i	−0.890868	−	0.454263i	$-0.849903\pi$
$641$	−23.8723	+	13.7827i	−0.942898	+	0.544383i	−0.0520307	+	0.998645i	$0.516569\pi$
$642$		0			0
$643$	5.46644	+	3.15605i	0.215575	+	0.124463i	0.603900	−	0.797060i	$-0.293613\pi$
$643$	5.46644	+	3.15605i	0.215575	+	0.124463i	−0.388324	+	0.921523i	$0.626946\pi$
$644$	−10.7029	+	4.68148i	−0.421752	+	0.184476i
$645$		0			0
$646$	−4.31821	+	6.60203i	−0.169898	+	0.259753i
$647$	36.9711			1.45348			0.726741	−	0.686912i	$-0.241034\pi$
$647$	36.9711			1.45348			0.726741	+	0.686912i	$0.241034\pi$
$648$		0			0
$649$	−17.7446			−0.696535
$650$	11.4140	−	17.4506i	0.447693	−	0.684471i
$651$		0			0
$652$	−21.7533	+	9.51498i	−0.851923	+	0.372635i
$653$	−6.68614	−	3.86025i	−0.261649	−	0.151063i	0.363438	−	0.931619i	$-0.381603\pi$
$653$	−6.68614	−	3.86025i	−0.261649	−	0.151063i	−0.625087	+	0.780555i	$0.714936\pi$
$654$		0			0
$655$	4.97760	−	2.87382i	0.194491	−	0.112290i
$656$	0.563374	−	0.174928i	0.0219961	−	0.00682980i
$657$		0			0
$658$	−39.6060	+	20.0172i	−1.54400	+	0.780351i
$659$	8.33010	+	14.4282i	0.324495	+	0.562041i	0.981410	−	0.191923i	$-0.0614724\pi$
$659$	8.33010	+	14.4282i	0.324495	+	0.562041i	−0.656915	+	0.753964i	$0.728139\pi$
$660$		0			0
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	−0.995496	−	0.0948069i	$-0.969777\pi$
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	0.579853	+	0.814721i	$0.303110\pi$
$662$	2.18971	−	39.3186i	0.0851055	−	1.52816i
$663$		0			0
$664$	−7.16477	−	19.2273i	−0.278047	−	0.746163i
$665$		−	4.75372i		−	0.184341i
$666$		0			0
$667$		−	1.70438i		−	0.0659938i
$668$	−38.1861	−	4.26652i	−1.47746	−	0.165076i
$669$		0			0
$670$	7.77138	+	0.432800i	0.300235	+	0.0167205i
$671$	5.77846	−	10.0086i	0.223075	−	0.386377i
$672$		0			0
$673$	−0.569297	−	0.986051i	−0.0219448	−	0.0380095i	0.854844	−	0.518884i	$-0.173652\pi$
$673$	−0.569297	−	0.986051i	−0.0219448	−	0.0380095i	−0.876789	+	0.480875i	$0.840319\pi$
$674$	−2.71459	−	5.37108i	−0.104562	−	0.206886i
$675$		0			0
$676$	1.93070	−	2.62112i	0.0742578	−	0.100812i
$677$	−28.5475	+	16.4819i	−1.09717	+	0.633452i	−0.935477	−	0.353389i	$-0.885029\pi$
$677$	−28.5475	+	16.4819i	−1.09717	+	0.633452i	−0.161695	+	0.986841i	$0.551696\pi$
$678$		0			0
$679$	29.3673	+	16.9552i	1.12701	+	0.650681i
$680$	−3.60298	+	4.36102i	−0.138168	+	0.167238i
$681$		0			0
$682$	−6.91296	−	4.52158i	−0.264711	−	0.173140i
$683$	2.07668			0.0794618			0.0397309	−	0.999210i	$-0.487350\pi$
$683$	2.07668			0.0794618			0.0397309	+	0.999210i	$0.487350\pi$
$684$		0			0
$685$	−14.8614			−0.567825
$686$	21.2983	+	13.9306i	0.813172	+	0.531874i
$687$		0			0
$688$	6.13258	−	27.1013i	0.233802	−	1.03323i
$689$	24.8614	+	14.3537i	0.947144	+	0.546834i
$690$		0			0
$691$	10.0064	−	5.77717i	0.380660	−	0.219774i	−0.297446	−	0.954739i	$-0.596135\pi$
$691$	10.0064	−	5.77717i	0.380660	−	0.219774i	0.678105	+	0.734965i	$0.262801\pi$
$692$	−8.93075	−	6.57835i	−0.339496	−	0.250071i
$693$		0			0
$694$	−4.93070	−	9.75588i	−0.187167	−	0.370328i
$695$	−3.70178	−	6.41168i	−0.140417	−	0.243209i
$696$		0			0
$697$	0.186141	−	0.322405i	0.00705058	−	0.0122120i
$698$	16.0580	+	0.894292i	0.607802	+	0.0338494i
$699$		0			0
$700$	−2.63641	+	23.5964i	−0.0996470	+	0.891859i
$701$			26.1282i			0.986850i	0.869788	+	0.493425i	$0.164255\pi$
$701$			26.1282i			0.986850i	−0.869788	+	0.493425i	$0.835745\pi$
$702$		0			0
$703$			10.4845i			0.395429i
$704$	5.17227	+	26.9240i	0.194937	+	1.01473i
$705$		0			0
$706$	0.385420	−	6.92062i	0.0145055	−	0.260461i
$707$	−24.1895	+	41.8974i	−0.909738	+	1.57571i
$708$		0			0
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	0.908053	−	0.418855i	$-0.137569\pi$
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	−0.816766	+	0.576969i	$0.804235\pi$
$710$	−1.75079	+	0.884861i	−0.0657058	+	0.0332082i
$711$		0			0
$712$	2.51087	−	14.9040i	0.0940990	−	0.558553i
$713$	−3.17527	+	1.83324i	−0.118915	+	0.0686554i
$714$		0			0
$715$	7.92967	+	4.57820i	0.296553	+	0.171215i
$716$	15.0772	+	34.4696i	0.563461	+	1.28819i
$717$		0			0
$718$	23.1986	−	35.4680i	0.865765	−	1.32365i
$719$	−7.65492			−0.285481			−0.142740	−	0.989760i	$-0.545591\pi$
$719$	−7.65492			−0.285481			−0.142740	+	0.989760i	$0.545591\pi$
$720$		0			0
$721$	39.6060			1.47500
$722$	10.9281	−	16.7077i	0.406700	−	0.621797i
$723$		0			0
$724$	3.20597	+	7.32951i	0.119149	+	0.272399i
$725$	−3.00000	−	1.73205i	−0.111417	−	0.0643268i
$726$		0			0
$727$	−2.67732	+	1.54575i	−0.0992963	+	0.0573287i	−0.548826	−	0.835937i	$-0.684925\pi$
$727$	−2.67732	+	1.54575i	−0.0992963	+	0.0573287i	0.449530	+	0.893265i	$0.351592\pi$
$728$	4.30243	−	25.5383i	0.159459	−	0.946514i
$729$		0			0
$730$	2.37228	−	1.19897i	0.0878021	−	0.0443759i
$731$	−8.76780	−	15.1863i	−0.324289	−	0.561685i
$732$		0			0
$733$	2.68614	−	4.65253i	0.0992149	−	0.171845i	−0.812145	−	0.583456i	$-0.801700\pi$
$733$	2.68614	−	4.65253i	0.0992149	−	0.171845i	0.911360	+	0.411610i	$0.135034\pi$
$734$	−1.06759	+	19.1696i	−0.0394053	+	0.707564i
$735$		0			0
$736$	11.7013	+	3.34159i	0.431316	+	0.123173i
$737$		−	23.8063i		−	0.876916i
$738$		0			0
$739$		−	9.66181i		−	0.355415i	−0.984083	−	0.177708i	$-0.943132\pi$
$739$		−	9.66181i		−	0.355415i	0.984083	−	0.177708i	$-0.0568681\pi$
$740$	−0.834801	+	7.47162i	−0.0306879	+	0.274662i
$741$		0			0
$742$	−32.6373	−	1.81762i	−1.19815	−	0.0667270i
$743$	22.5132	−	38.9940i	0.825929	−	1.43055i	−0.0752776	−	0.997163i	$-0.523984\pi$
$743$	22.5132	−	38.9940i	0.825929	−	1.43055i	0.901207	−	0.433389i	$-0.142682\pi$
$744$		0			0
$745$	−3.80298	−	6.58696i	−0.139331	−	0.241328i
$746$	5.65278	+	11.1846i	0.206963	+	0.409497i
$747$		0			0
$748$	13.9307	+	10.2613i	0.509357	+	0.375190i
$749$	31.1168	−	17.9653i	1.13698	−	0.656438i
$750$		0			0
$751$	−39.9743	−	23.0792i	−1.45868	−	0.842170i	−0.459735	−	0.888056i	$-0.652056\pi$
$751$	−39.9743	−	23.0792i	−1.45868	−	0.842170i	−0.998947	+	0.0458859i	$0.985389\pi$
$752$	45.0878	+	10.2026i	1.64418	+	0.372052i
$753$		0			0
$754$	3.16218	+	2.06829i	0.115160	+	0.0753228i
$755$	7.25450			0.264018
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	11.4350	+	7.47935i	0.415340	+	0.271662i
$759$		0			0
$760$	−3.15402	+	3.81761i	−0.114408	+	0.138479i
$761$	16.5475	+	9.55373i	0.599848	+	0.346322i	0.768982	−	0.639271i	$-0.220764\pi$
$761$	16.5475	+	9.55373i	0.599848	+	0.346322i	−0.169134	+	0.985593i	$0.554097\pi$
$762$		0			0
$763$	−22.3130	+	12.8824i	−0.807784	+	0.466375i
$764$	−4.62832	+	6.28339i	−0.167447	+	0.227325i
$765$		0			0
$766$	−0.255437	−	0.505408i	−0.00922933	−	0.0182611i
$767$	−8.73053	−	15.1217i	−0.315241	−	0.546014i
$768$		0			0
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.397285	−	0.917695i	$-0.369952\pi$
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.596105	−	0.802907i	$-0.296714\pi$
$770$	−10.4098	−	0.579740i	−0.375145	−	0.0208924i
$771$		0			0
$772$	−7.44281	−	0.831582i	−0.267873	−	0.0299293i
$773$		−	45.7330i		−	1.64490i	−0.568835	−	0.822451i	$-0.692606\pi$
$773$		−	45.7330i		−	1.64490i	0.568835	−	0.822451i	$-0.307394\pi$
$774$		0			0
$775$			7.45202i			0.267685i
$776$	−12.3347	−	33.1011i	−0.442789	−	1.18826i
$777$		0			0
$778$	−0.653512	+	11.7345i	−0.0234295	+	0.420702i
$779$	0.162946	−	0.282231i	0.00583815	−	0.0101120i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	6.85407	−	3.46410i	0.245101	−	0.123876i
$783$		0			0
$784$	0.441578	+	1.42215i	0.0157706	+	0.0507910i
$785$	−11.5693	+	6.67954i	−0.412926	+	0.238403i
$786$		0			0
$787$	−17.0095	−	9.82043i	−0.606323	−	0.350061i	0.165202	−	0.986260i	$-0.447172\pi$
$787$	−17.0095	−	9.82043i	−0.606323	−	0.350061i	−0.771525	+	0.636199i	$0.780506\pi$
$788$	−19.5831	+	8.56575i	−0.697619	+	0.305142i
$789$		0			0
$790$	−6.23577	+	9.53376i	−0.221859	+	0.339196i
$791$	−43.2756			−1.53870
$792$		0			0
$793$	11.3723			0.403842
$794$	−5.61654	+	8.58704i	−0.199324	+	0.304742i
$795$		0			0
$796$	35.4082	−	15.4877i	1.25501	−	0.548947i
$797$	−40.8030	−	23.5576i	−1.44532	−	0.834454i	−0.447119	−	0.894475i	$-0.647550\pi$
$797$	−40.8030	−	23.5576i	−1.44532	−	0.834454i	−0.998197	+	0.0600211i	$0.980883\pi$
$798$		0			0
$799$	25.2651	−	14.5868i	0.893814	−	0.516043i
$800$	17.7731	−	17.2005i	0.628373	−	0.608129i
$801$		0			0
$802$	27.6753	−	13.9873i	0.977248	−	0.493909i
$803$	−4.06494	−	7.04069i	−0.143449	−	0.248461i
$804$		0			0
$805$	−2.31386	+	4.00772i	−0.0815528	+	0.141254i
$806$	0.451982	−	8.11582i	0.0159204	−	0.285868i
$807$		0			0
$808$	47.2243	−	17.5975i	1.66134	−	0.619077i
$809$			27.1778i			0.955521i	0.878490	+	0.477760i	$0.158551\pi$
$809$			27.1778i			0.955521i	−0.878490	+	0.477760i	$0.841449\pi$
$810$		0			0
$811$			25.9530i			0.911332i	0.890151	+	0.455666i	$0.150599\pi$
$811$			25.9530i			0.911332i	−0.890151	+	0.455666i	$0.849401\pi$
$812$	−4.27582	−	0.477736i	−0.150052	−	0.0167652i
$813$		0			0
$814$	22.9592	+	1.27863i	0.804720	+	0.0448161i
$815$	−4.70285	+	8.14558i	−0.164734	+	0.285327i
$816$		0			0
$817$	−7.67527	−	13.2940i	−0.268524	−	0.465096i
$818$	1.43877	+	2.84674i	0.0503053	+	0.0995340i
$819$		0			0
$820$	0.138593	−	0.188154i	0.00483989	−	0.00657062i
$821$	18.6861	−	10.7884i	0.652151	−	0.376519i	−0.137129	−	0.990553i	$-0.543787\pi$
$821$	18.6861	−	10.7884i	0.652151	−	0.376519i	0.789280	+	0.614034i	$0.210454\pi$
$822$		0			0
$823$	−25.8657	−	14.9336i	−0.901622	−	0.520552i	−0.0238957	−	0.999714i	$-0.507607\pi$
$823$	−25.8657	−	14.9336i	−0.901622	−	0.520552i	−0.877726	+	0.479163i	$0.840940\pi$
$824$	−31.8067	−	26.2780i	−1.10804	−	0.915437i
$825$		0			0
$826$	16.6390	+	10.8831i	0.578945	+	0.378672i
$827$	−7.00314			−0.243523			−0.121762	−	0.992559i	$-0.538854\pi$
$827$	−7.00314			−0.243523			−0.121762	+	0.992559i	$0.538854\pi$
$828$		0			0
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$	−6.80251	−	4.44934i	−0.236119	−	0.154439i
$831$		0			0
$832$	−20.3995	+	17.6547i	−0.707225	+	0.612065i
$833$	0.813859	+	0.469882i	0.0281986	+	0.0162804i
$834$		0			0
$835$	−13.1820	+	7.61065i	−0.456183	+	0.263377i
$836$	12.1948	+	8.98266i	0.421767	+	0.310672i
$837$		0			0
$838$	−3.60597	−	7.13477i	−0.124566	−	0.246466i
$839$	−22.8391	−	39.5585i	−0.788493	−	1.36571i	−0.926890	−	0.375333i	$-0.877528\pi$
$839$	−22.8391	−	39.5585i	−0.788493	−	1.36571i	0.138397	−	0.990377i	$-0.455805\pi$
$840$		0			0
$841$	−14.1861	+	24.5711i	−0.489177	+	0.847280i
$842$	−41.8044	−	2.32815i	−1.44067	−	0.0802333i
$843$		0			0
$844$	−1.35999	+	12.1722i	−0.0468128	+	0.418983i
$845$		−	1.28962i		−	0.0443643i
$846$		0			0
$847$			2.02163i			0.0694641i
$848$	25.0043	+	23.1141i	0.858653	+	0.793741i
$849$		0			0
$850$	0.867935	−	15.5847i	0.0297699	−	0.534550i
$851$	5.10328	−	8.83915i	0.174938	−	0.303002i
$852$		0			0
$853$	−2.19702	−	3.80534i	−0.0752244	−	0.130292i	0.825959	−	0.563730i	$-0.190634\pi$
$853$	−2.19702	−	3.80534i	−0.0752244	−	0.130292i	−0.901184	+	0.433437i	$0.857301\pi$
$854$	−11.5569	+	5.84096i	−0.395470	+	0.199874i
$855$		0			0
$856$	−36.9090	−	6.21803i	−1.26152	−	0.212528i
$857$	22.0367	−	12.7229i	0.752758	−	0.434605i	−0.0739313	−	0.997263i	$-0.523555\pi$
$857$	22.0367	−	12.7229i	0.752758	−	0.434605i	0.826690	+	0.562658i	$0.190221\pi$
$858$		0			0
$859$	−30.4056	−	17.5547i	−1.03743	−	0.598958i	−0.118323	−	0.992975i	$-0.537752\pi$
$859$	−30.4056	−	17.5547i	−1.03743	−	0.598958i	−0.919103	+	0.394017i	$0.871085\pi$
$860$	−4.41118	−	10.0849i	−0.150420	−	0.343892i
$861$		0			0
$862$	−11.3470	+	17.3483i	−0.386481	+	0.590885i
$863$	−4.15335			−0.141382			−0.0706909	−	0.997498i	$-0.522520\pi$
$863$	−4.15335			−0.141382			−0.0706909	+	0.997498i	$0.522520\pi$
$864$		0			0
$865$	−4.39403			−0.149402
$866$	−11.1258	+	17.0100i	−0.378070	+	0.578025i
$867$		0			0
$868$	3.70908	+	8.47973i	0.125894	+	0.287821i
$869$	30.1753	+	17.4217i	1.02363	+	0.590991i
$870$		0			0
$871$	20.2875	−	11.7130i	0.687414	−	0.396879i
$872$	26.4663	+	4.45877i	0.896264	+	0.150993i
$873$		0			0
$874$	6.00000	−	3.03245i	0.202953	−	0.102574i
$875$	10.0809	+	17.4606i	0.340796	+	0.590276i
$876$		0			0
$877$	−13.6861	+	23.7051i	−0.462148	+	0.800464i	−0.999068	−	0.0431693i	$-0.986254\pi$
$877$	−13.6861	+	23.7051i	−0.462148	+	0.800464i	0.536920	+	0.843633i	$0.319588\pi$
$878$	−2.58715	+	46.4551i	−0.0873122	+	1.56778i
$879$		0			0
$880$	7.97526	+	7.37236i	0.268846	+	0.248522i
$881$		−	19.7899i		−	0.666740i	−0.942796	−	0.333370i	$-0.891814\pi$
$881$		−	19.7899i		−	0.666740i	0.942796	−	0.333370i	$-0.108186\pi$
$882$		0			0
$883$			34.7921i			1.17085i	0.810727	+	0.585424i	$0.199072\pi$
$883$			34.7921i			1.17085i	−0.810727	+	0.585424i	$0.800928\pi$
$884$	−1.89049	+	16.9203i	−0.0635842	+	0.569090i
$885$		0			0
$886$	7.31121	+	0.407173i	0.245625	+	0.0136792i
$887$	−2.75186	+	4.76635i	−0.0923983	+	0.160039i	−0.908520	−	0.417842i	$-0.862787\pi$
$887$	−2.75186	+	4.76635i	−0.0923983	+	0.160039i	0.816122	+	0.577880i	$0.196120\pi$
$888$		0			0
$889$	−22.1168	−	38.3075i	−0.741775	−	1.28479i
$890$	−2.70071	−	5.34363i	−0.0905281	−	0.179119i
$891$		0			0
$892$	2.74456	+	2.02163i	0.0918948	+	0.0676893i
$893$	22.1168	−	12.7692i	0.740112	−	0.427304i
$894$		0			0
$895$	12.9073	+	7.45202i	0.431443	+	0.249094i
$896$	11.6630	−	28.4188i	0.389634	−	0.949404i
$897$		0			0
$898$	4.51394	+	2.95244i	0.150632	+	0.0985243i
$899$	−1.35036			−0.0450369
$900$		0			0
$901$	21.4891			0.715907
$902$	−0.598166	−	0.391244i	−0.0199168	−	0.0130270i
$903$		0			0
$904$	34.7537	+	28.7127i	1.15589	+	0.954971i
$905$	2.74456	+	1.58457i	0.0912323	+	0.0526730i
$906$		0			0
$907$	−21.3258	+	12.3125i	−0.708111	+	0.408828i	−0.810361	−	0.585930i	$-0.800729\pi$
$907$	−21.3258	+	12.3125i	−0.708111	+	0.408828i	0.102250	+	0.994759i	$0.467396\pi$
$908$	−22.4014	+	30.4121i	−0.743417	+	1.00926i
$909$		0			0
$910$	−4.62772	−	9.15640i	−0.153407	−	0.303532i
$911$	6.57932	+	11.3957i	0.217983	+	0.377557i	0.954191	−	0.299198i	$-0.0967191\pi$
$911$	6.57932	+	11.3957i	0.217983	+	0.377557i	−0.736209	+	0.676755i	$0.763386\pi$
$912$		0			0
$913$	−12.4307	+	21.5306i	−0.411396	+	0.712559i
$914$	8.44144	+	0.470117i	0.279218	+	0.0155501i
$915$		0			0
$916$	18.6286	+	2.08137i	0.615508	+	0.0687704i
$917$			19.6974i			0.650464i
$918$		0			0
$919$		−	46.0993i		−	1.52067i	−0.649529	−	0.760337i	$-0.725034\pi$
$919$		−	46.0993i		−	1.52067i	0.649529	−	0.760337i	$-0.274966\pi$
$920$	4.51727	−	1.68330i	0.148930	−	0.0554967i
$921$		0			0
$922$	1.79817	−	32.2881i	0.0592197	−	1.06335i
$923$	−2.95207	+	5.11313i	−0.0971686	+	0.168301i
$924$		0			0
$925$	−10.3723	−	17.9653i	−0.341039	−	0.590696i
$926$	−26.5409	+	13.4140i	−0.872187	+	0.440811i
$927$		0			0
$928$	3.11684	+	3.22060i	0.102315	+	0.105721i
$929$	−30.4307	+	17.5692i	−0.998399	+	0.576426i	−0.907774	−	0.419459i	$-0.862220\pi$
$929$	−30.4307	+	17.5692i	−0.998399	+	0.576426i	−0.0906248	+	0.995885i	$0.528886\pi$
$930$		0			0
$931$	0.712446	+	0.411331i	0.0233495	+	0.0134808i
$932$	51.4214	−	22.4920i	1.68437	−	0.736750i
$933$		0			0
$934$	−18.8804	+	28.8659i	−0.617786	+	0.944522i
$935$	6.85407			0.224152
$936$		0			0
$937$	−11.7228			−0.382968			−0.191484	−	0.981496i	$-0.561330\pi$
$937$	−11.7228			−0.382968			−0.191484	+	0.981496i	$0.561330\pi$
$938$	−14.6009	+	22.3231i	−0.476736	+	0.728874i
$939$		0			0
$940$	16.7780	−	7.33878i	0.547238	−	0.239365i
$941$	−31.8030	−	18.3615i	−1.03675	−	0.598567i	−0.117837	−	0.993033i	$-0.537596\pi$
$941$	−31.8030	−	18.3615i	−1.03675	−	0.598567i	−0.918910	+	0.394466i	$0.870929\pi$
$942$		0			0
$943$	−0.274750	+	0.158627i	−0.00894709	+	0.00516561i
$944$	−6.14162	−	19.7797i	−0.199893	−	0.643775i
$945$		0			0
$946$	−30.0475	+	15.1863i	−0.976930	+	0.493748i
$947$	22.2757	+	38.5827i	0.723864	+	1.25377i	0.959440	+	0.281913i	$0.0909689\pi$
$947$	22.2757	+	38.5827i	0.723864	+	1.25377i	−0.235576	+	0.971856i	$0.575698\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	0.759784	−	13.6427i	0.0246506	−	0.442628i
$951$		0			0
$952$	−6.76930	−	18.1660i	−0.219394	−	0.588763i
$953$			32.8164i			1.06303i	0.847050	+	0.531514i	$0.178377\pi$
$953$			32.8164i			1.06303i	−0.847050	+	0.531514i	$0.821623\pi$
$954$		0			0
$955$			3.09150i			0.100039i
$956$	33.1144	+	3.69985i	1.07100	+	0.119662i
$957$		0			0
$958$	−13.8465	−	0.771134i	−0.447361	−	0.0249142i
$959$	25.4653	−	44.1071i	0.822317	−	1.42429i
$960$		0			0
$961$	−14.0475	−	24.3311i	−0.453147	−	0.784873i
$962$	10.2066	+	20.1947i	0.329073	+	0.651103i
$963$		0			0
$964$	−19.5584	+	26.5525i	−0.629934	+	0.855197i
$965$	−2.56930	+	1.48338i	−0.0827086	+	0.0477518i
$966$		0			0
$967$	48.7282	+	28.1332i	1.56699	+	0.904704i	0.996517	+	0.0833895i	$0.0265746\pi$
$967$	48.7282	+	28.1332i	1.56699	+	0.904704i	0.570476	+	0.821314i	$0.306759\pi$
$968$	1.34132	−	1.62353i	0.0431118	−	0.0521821i
$969$		0			0
$970$	−11.7110	−	7.65985i	−0.376018	−	0.245943i
$971$	−24.7156			−0.793160			−0.396580	−	0.918000i	$-0.629803\pi$
$971$	−24.7156			−0.793160			−0.396580	+	0.918000i	$0.629803\pi$
$972$		0			0
$973$	25.3723			0.813398
$974$	21.2284	+	13.8849i	0.680202	+	0.444901i
$975$		0			0
$976$	13.1565	+	2.97710i	0.421129	+	0.0952948i
$977$	18.6386	+	10.7610i	0.596301	+	0.344275i	0.767585	−	0.640947i	$-0.221458\pi$
$977$	18.6386	+	10.7610i	0.596301	+	0.344275i	−0.171284	+	0.985222i	$0.554791\pi$
$978$		0			0
$979$	−15.8593	+	9.15640i	−0.506867	+	0.292640i
$980$	0.474964	+	0.349857i	0.0151722	+	0.0111758i
$981$		0			0
$982$	−15.8139	−	31.2893i	−0.504641	−	0.998481i
$983$	−8.40464	−	14.5573i	−0.268066	−	0.464305i	0.700296	−	0.713852i	$-0.253051\pi$
$983$	−8.40464	−	14.5573i	−0.268066	−	0.464305i	−0.968362	+	0.249548i	$0.919718\pi$
$984$		0			0
$985$	−4.23369	+	7.33296i	−0.134897	+	0.233648i
$986$	2.82405	+	0.157276i	0.0899361	+	0.00500868i
$987$		0			0
$988$	−1.65492	+	14.8119i	−0.0526502	+	0.471229i
$989$			14.9436i			0.475180i
$990$		0			0
$991$			16.2912i			0.517506i	0.965944	+	0.258753i	$0.0833116\pi$
$991$			16.2912i			0.517506i	−0.965944	+	0.258753i	$0.916688\pi$
$992$	2.64750	−	9.27080i	0.0840583	−	0.294348i
$993$		0			0
$994$	0.373822	−	6.71238i	0.0118569	−	0.212904i
$995$	7.65492	−	13.2587i	0.242677	−	0.420330i
$996$		0			0
$997$	26.4307	+	45.7793i	0.837069	+	1.44985i	0.892335	+	0.451374i	$0.149066\pi$
$997$	26.4307	+	45.7793i	0.837069	+	1.44985i	−0.0552661	+	0.998472i	$0.517601\pi$
$998$	0.637910	−	0.322405i	0.0201927	−	0.0102056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.h.a.71.3		8
3.2	odd	2		36.2.h.a.23.2	yes	8
4.3	odd	2	inner	108.2.h.a.71.4		8
8.3	odd	2		1728.2.s.f.1151.3		8
8.5	even	2		1728.2.s.f.1151.4		8
9.2	odd	6	inner	108.2.h.a.35.4		8
9.4	even	3		324.2.b.b.323.6		8
9.5	odd	6		324.2.b.b.323.3		8
9.7	even	3		36.2.h.a.11.1	✓	8
12.11	even	2		36.2.h.a.23.1	yes	8
15.2	even	4		900.2.o.a.599.2		16
15.8	even	4		900.2.o.a.599.7		16
15.14	odd	2		900.2.r.c.851.3		8
24.5	odd	2		576.2.s.f.383.3		8
24.11	even	2		576.2.s.f.383.2		8
36.7	odd	6		36.2.h.a.11.2	yes	8
36.11	even	6	inner	108.2.h.a.35.3		8
36.23	even	6		324.2.b.b.323.5		8
36.31	odd	6		324.2.b.b.323.4		8
45.7	odd	12		900.2.o.a.299.5		16
45.34	even	6		900.2.r.c.551.4		8
45.43	odd	12		900.2.o.a.299.4		16
60.23	odd	4		900.2.o.a.599.5		16
60.47	odd	4		900.2.o.a.599.4		16
60.59	even	2		900.2.r.c.851.4		8
72.5	odd	6		5184.2.c.j.5183.6		8
72.11	even	6		1728.2.s.f.575.4		8
72.13	even	6		5184.2.c.j.5183.4		8
72.29	odd	6		1728.2.s.f.575.3		8
72.43	odd	6		576.2.s.f.191.3		8
72.59	even	6		5184.2.c.j.5183.5		8
72.61	even	6		576.2.s.f.191.2		8
72.67	odd	6		5184.2.c.j.5183.3		8
180.7	even	12		900.2.o.a.299.7		16
180.43	even	12		900.2.o.a.299.2		16
180.79	odd	6		900.2.r.c.551.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.1	✓	8	9.7	even	3
36.2.h.a.11.2	yes	8	36.7	odd	6
36.2.h.a.23.1	yes	8	12.11	even	2
36.2.h.a.23.2	yes	8	3.2	odd	2
108.2.h.a.35.3		8	36.11	even	6	inner
108.2.h.a.35.4		8	9.2	odd	6	inner
108.2.h.a.71.3		8	1.1	even	1	trivial
108.2.h.a.71.4		8	4.3	odd	2	inner
324.2.b.b.323.3		8	9.5	odd	6
324.2.b.b.323.4		8	36.31	odd	6
324.2.b.b.323.5		8	36.23	even	6
324.2.b.b.323.6		8	9.4	even	3
576.2.s.f.191.2		8	72.61	even	6
576.2.s.f.191.3		8	72.43	odd	6
576.2.s.f.383.2		8	24.11	even	2
576.2.s.f.383.3		8	24.5	odd	2
900.2.o.a.299.2		16	180.43	even	12
900.2.o.a.299.4		16	45.43	odd	12
900.2.o.a.299.5		16	45.7	odd	12
900.2.o.a.299.7		16	180.7	even	12
900.2.o.a.599.2		16	15.2	even	4
900.2.o.a.599.4		16	60.47	odd	4
900.2.o.a.599.5		16	60.23	odd	4
900.2.o.a.599.7		16	15.8	even	4
900.2.r.c.551.3		8	180.79	odd	6
900.2.r.c.551.4		8	45.34	even	6
900.2.r.c.851.3		8	15.14	odd	2
900.2.r.c.851.4		8	60.59	even	2
1728.2.s.f.575.3		8	72.29	odd	6
1728.2.s.f.575.4		8	72.11	even	6
1728.2.s.f.1151.3		8	8.3	odd	2
1728.2.s.f.1151.4		8	8.5	even	2
5184.2.c.j.5183.3		8	72.67	odd	6
5184.2.c.j.5183.4		8	72.13	even	6
5184.2.c.j.5183.5		8	72.59	even	6
5184.2.c.j.5183.6		8	72.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.774115 - 1.18353i) q^{2} +(-0.801492 - 1.83238i) q^{4} +(-0.686141 - 0.396143i) q^{5} +(2.35143 - 1.35760i) q^{7} +(-2.78912 - 0.469882i) q^{8} +(-1.00000 + 0.505408i) q^{10} +(1.71352 + 2.96790i) q^{11} +(-1.68614 + 2.92048i) q^{13} +(0.213517 - 3.83392i) q^{14} +(-2.71522 + 2.93727i) q^{16} +2.52434i q^{17} +2.20979i q^{19} +(-0.175949 + 1.57478i) q^{20} +(4.83906 + 0.269495i) q^{22} +(1.07561 - 1.86301i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(2.15121 + 4.25639i) q^{26} +(-4.37228 - 3.22060i) q^{28} +(0.686141 - 0.396143i) q^{29} +(-1.47603 - 0.852189i) q^{31} +(1.37446 + 5.48734i) q^{32} +(2.98763 + 1.95413i) q^{34} -2.15121 q^{35} +4.74456 q^{37} +(2.61535 + 1.71063i) q^{38} +(1.72759 + 1.42730i) q^{40} +(-0.127719 - 0.0737384i) q^{41} +(-6.01594 + 3.47331i) q^{43} +(4.06494 - 5.51856i) q^{44} +(-1.37228 - 2.71519i) q^{46} +(-5.77846 - 10.0086i) q^{47} +(0.186141 - 0.322405i) q^{49} +(-6.17377 - 0.343827i) q^{50} +(6.70285 + 0.748907i) q^{52} -8.51278i q^{53} -2.71519i q^{55} +(-7.19633 + 2.68161i) q^{56} +(0.0623037 - 1.11873i) q^{58} +(-2.58891 + 4.48412i) q^{59} +(-1.68614 - 2.92048i) q^{61} +(-2.15121 + 1.08724i) q^{62} +(7.55842 + 2.62112i) q^{64} +(2.31386 - 1.33591i) q^{65} +(-6.01594 - 3.47331i) q^{67} +(4.62554 - 2.02324i) q^{68} +(-1.66529 + 2.54603i) q^{70} +1.75079 q^{71} -2.37228 q^{73} +(3.67284 - 5.61534i) q^{74} +(4.04917 - 1.77113i) q^{76} +(8.05842 + 4.65253i) q^{77} +(8.80507 - 5.08361i) q^{79} +(3.02661 - 0.939764i) q^{80} +(-0.186141 + 0.0940770i) q^{82} +(3.62725 + 6.28258i) q^{83} +(1.00000 - 1.73205i) q^{85} +(-0.546267 + 9.80880i) q^{86} +(-3.38465 - 9.08299i) q^{88} +5.34363i q^{89} +9.15640i q^{91} +(-4.27582 - 0.477736i) q^{92} +(-16.3187 - 0.908812i) q^{94} +(0.875393 - 1.51622i) q^{95} +(6.24456 + 10.8159i) q^{97} +(-0.237482 - 0.469882i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41}+ \cdots + 4 q^{97}+O(q^{100}) \) 8 * q + 3 * q^2 - q^4 + 6 * q^5 - 8 * q^10 - 2 * q^13 - 12 * q^14 - q^16 - 18 * q^20 + 3 * q^22 - 6 * q^25 - 12 * q^28 - 6 * q^29 + 33 * q^32 + 7 * q^34 - 8 * q^37 + 27 * q^38 + 10 * q^40 - 24 * q^41 + 12 * q^46 - 10 * q^49 - 21 * q^50 + 16 * q^52 - 18 * q^56 + 4 * q^58 - 2 * q^61 + 26 * q^64 + 30 * q^65 + 15 * q^68 - 6 * q^70 + 4 * q^73 + 30 * q^74 - 3 * q^76 + 30 * q^77 + 10 * q^82 + 8 * q^85 - 21 * q^86 - 21 * q^88 - 24 * q^92 - 18 * q^94 + 4 * q^97

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