LMFDB - Embedded newform 936.2.cl.a.779.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(155,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.cl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			779.6
Character	$\chi$	$=$	936.779
Dual form			936.2.cl.a.155.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.72159 + 0.190107i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.00993 - 0.583083i) q^{5} +(-2.24293 + 0.984512i) q^{6} +(-0.658612 - 1.14075i) q^{7} +2.82843i q^{8} +(2.92772 + 0.654573i) q^{9} +1.64921 q^{10} +(2.05086 - 2.79177i) q^{12} +(1.80278 - 3.12250i) q^{13} +(1.61326 + 0.931418i) q^{14} +(-1.62783 - 1.19582i) q^{15} +(-2.00000 - 3.46410i) q^{16} -1.16715i q^{17} +(-4.04856 + 1.26852i) q^{18} +(-2.01986 + 1.16617i) q^{20} +(-0.916993 - 2.08911i) q^{21} +(-0.537705 + 4.86938i) q^{24} +(-1.82003 - 3.15238i) q^{25} +5.09902i q^{26} +(4.91588 + 1.68348i) q^{27} -2.63445 q^{28} +(2.83925 + 0.313527i) q^{30} +(1.87146 - 3.24146i) q^{31} +(4.89898 + 2.82843i) q^{32} +(0.825300 + 1.42946i) q^{34} +1.53610i q^{35} +(4.06147 - 4.41638i) q^{36} +5.39282 q^{37} +(3.69724 - 5.03293i) q^{39} +(1.64921 - 2.85651i) q^{40} +(2.60030 + 1.91021i) q^{42} +(-3.03604 - 5.25858i) q^{43} +(-2.57512 - 2.36817i) q^{45} +(3.79232 - 2.18950i) q^{47} +(-2.78462 - 6.34396i) q^{48} +(2.63246 - 4.55955i) q^{49} +(4.45814 + 2.57391i) q^{50} +(0.221884 - 2.00935i) q^{51} +(-3.60555 - 6.24500i) q^{52} +(-7.21110 + 1.41421i) q^{54} +(3.22653 - 1.86284i) q^{56} +(-3.69906 + 1.62366i) q^{60} +5.29329i q^{62} +(-1.18153 - 3.77090i) q^{63} -8.00000 q^{64} +(-3.64135 + 2.10234i) q^{65} +(-2.02156 - 1.16715i) q^{68} +(-1.08619 - 1.88133i) q^{70} -2.75117i q^{71} +(-1.85141 + 8.28084i) q^{72} +(-6.60483 + 3.81330i) q^{74} +(-2.53405 - 5.77310i) q^{75} +(-0.969362 + 8.77840i) q^{78} +4.66466i q^{80} +(8.14307 + 3.83281i) q^{81} +(-4.53543 - 0.500828i) q^{84} +(-0.680545 + 1.17874i) q^{85} +(7.43675 + 4.29361i) q^{86} +(4.82841 + 1.07953i) q^{90} -4.74932 q^{91} +(3.83810 - 5.22468i) q^{93} +(-3.09642 + 5.36316i) q^{94} +(7.89631 + 5.80071i) q^{96} +7.44572i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 48 q^{16} + 60 q^{25} + 12 q^{27} + 48 q^{30} + 48 q^{42} - 84 q^{49} - 60 q^{51} - 192 q^{64} - 168 q^{75} - 96 q^{90}+O(q^{100}) $ 24 * q + 24 * q^4 - 48 * q^16 + 60 * q^25 + 12 * q^27 + 48 * q^30 + 48 * q^42 - 84 * q^49 - 60 * q^51 - 192 * q^64 - 168 * q^75 - 96 * q^90

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	1.72159	+	0.190107i	0.993958	+	0.109759i
$3$	1.72159	+	0.190107i	0.993958	+	0.109759i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.00993	−	0.583083i	−0.451654	−	0.260763i	0.256874	−	0.966445i	$-0.417307\pi$
$5$	−1.00993	−	0.583083i	−0.451654	−	0.260763i	−0.708528	+	0.705682i	$0.750641\pi$
$6$	−2.24293	+	0.984512i	−0.915672	+	0.401925i
$7$	−0.658612	−	1.14075i	−0.248932	−	0.431163i	0.714298	−	0.699842i	$-0.246746\pi$
$7$	−0.658612	−	1.14075i	−0.248932	−	0.431163i	−0.963230	+	0.268679i	$0.913413\pi$
$8$			2.82843i			1.00000i
$9$	2.92772	+	0.654573i	0.975906	+	0.218191i
$10$	1.64921			0.521525
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	2.05086	−	2.79177i	0.592033	−	0.805914i
$13$	1.80278	−	3.12250i	0.500000	−	0.866025i
$13$	1.80278	−	3.12250i	0.500000	−	0.866025i
$14$	1.61326	+	0.931418i	0.431163	+	0.248932i
$15$	−1.62783	−	1.19582i	−0.420304	−	0.308760i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		−	1.16715i		−	0.283076i	−0.989933	−	0.141538i	$-0.954795\pi$
$17$		−	1.16715i		−	0.283076i	0.989933	−	0.141538i	$-0.0452047\pi$
$18$	−4.04856	+	1.26852i	−0.954255	+	0.298994i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−2.01986	+	1.16617i	−0.451654	+	0.260763i
$21$	−0.916993	−	2.08911i	−0.200104	−	0.455880i
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.537705	+	4.86938i	−0.109759	+	0.993958i
$25$	−1.82003	−	3.15238i	−0.364006	−	0.630476i
$26$			5.09902i			1.00000i
$27$	4.91588	+	1.68348i	0.946062	+	0.323987i
$28$	−2.63445			−0.497864
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	2.83925	+	0.313527i	0.518374	+	0.0572419i
$31$	1.87146	−	3.24146i	0.336124	−	0.582184i	−0.647576	−	0.762001i	$-0.724217\pi$
$31$	1.87146	−	3.24146i	0.336124	−	0.582184i	0.983700	+	0.179817i	$0.0575506\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$		0			0
$34$	0.825300	+	1.42946i	0.141538	+	0.245151i
$35$			1.53610i			0.259649i
$36$	4.06147	−	4.41638i	0.676912	−	0.736064i
$37$	5.39282			0.886575			0.443287	−	0.896380i	$-0.353812\pi$
$37$	5.39282			0.886575			0.443287	+	0.896380i	$0.353812\pi$
$38$		0			0
$39$	3.69724	−	5.03293i	0.592033	−	0.805914i
$40$	1.64921	−	2.85651i	0.260763	−	0.451654i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	2.60030	+	1.91021i	0.401236	+	0.294752i
$43$	−3.03604	−	5.25858i	−0.462992	−	0.801925i	0.536117	−	0.844144i	$-0.319891\pi$
$43$	−3.03604	−	5.25858i	−0.462992	−	0.801925i	−0.999108	+	0.0422186i	$0.986557\pi$
$44$		0			0
$45$	−2.57512	−	2.36817i	−0.383876	−	0.353027i
$46$		0			0
$47$	3.79232	−	2.18950i	0.553167	−	0.319371i	−0.197231	−	0.980357i	$-0.563195\pi$
$47$	3.79232	−	2.18950i	0.553167	−	0.319371i	0.750398	+	0.660986i	$0.229862\pi$
$48$	−2.78462	−	6.34396i	−0.401925	−	0.915672i
$49$	2.63246	−	4.55955i	0.376066	−	0.651365i
$50$	4.45814	+	2.57391i	0.630476	+	0.364006i
$51$	0.221884	−	2.00935i	0.0310700	−	0.281365i
$52$	−3.60555	−	6.24500i	−0.500000	−	0.866025i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−7.21110	+	1.41421i	−0.981307	+	0.192450i
$55$		0			0
$56$	3.22653	−	1.86284i	0.431163	−	0.248932i
$57$		0			0
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−3.69906	+	1.62366i	−0.477546	+	0.209614i
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$			5.29329i			0.672248i
$63$	−1.18153	−	3.77090i	−0.148858	−	0.475089i
$64$	−8.00000			−1.00000
$65$	−3.64135	+	2.10234i	−0.451654	+	0.260763i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−2.02156	−	1.16715i	−0.245151	−	0.141538i
$69$		0			0
$70$	−1.08619	−	1.88133i	−0.129824	−	0.224862i
$71$		−	2.75117i		−	0.326503i	−0.986584	−	0.163252i	$-0.947802\pi$
$71$		−	2.75117i		−	0.326503i	0.986584	−	0.163252i	$-0.0521983\pi$
$72$	−1.85141	+	8.28084i	−0.218191	+	0.975906i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−6.60483	+	3.81330i	−0.767796	+	0.443287i
$75$	−2.53405	−	5.77310i	−0.292606	−	0.666620i
$76$		0			0
$77$		0			0
$78$	−0.969362	+	8.77840i	−0.109759	+	0.993958i
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$			4.66466i			0.521525i
$81$	8.14307	+	3.83281i	0.904785	+	0.425868i
$82$		0			0
$83$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$83$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$84$	−4.53543	−	0.500828i	−0.494856	−	0.0546449i
$85$	−0.680545	+	1.17874i	−0.0738155	+	0.127852i
$86$	7.43675	+	4.29361i	0.801925	+	0.462992i
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	4.82841	+	1.07953i	0.508960	+	0.113792i
$91$	−4.74932			−0.497864
$92$		0			0
$93$	3.83810	−	5.22468i	0.397993	−	0.541774i
$94$	−3.09642	+	5.36316i	−0.319371	+	0.553167i
$95$		0			0
$96$	7.89631	+	5.80071i	0.805914	+	0.592033i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$			7.44572i			0.752131i
$99$		0			0
$100$	−7.28012			−0.728012
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	1.14907	+	2.61784i	0.113775	+	0.259205i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	8.83176	+	5.09902i	0.866025	+	0.500000i
$105$	−0.292024	+	2.64453i	−0.0284987	+	0.258080i
$106$		0			0
$107$			10.1980i			0.985882i	0.870063	+	0.492941i	$0.164078\pi$
$107$			10.1980i			0.985882i	−0.870063	+	0.492941i	$0.835922\pi$
$108$	7.83176	−	6.83107i	0.753612	−	0.657320i
$109$	13.6402			1.30649			0.653247	−	0.757145i	$-0.273406\pi$
$109$	13.6402			1.30649			0.653247	+	0.757145i	$0.273406\pi$
$110$		0			0
$111$	9.28421	+	1.02522i	0.881218	+	0.0973092i
$112$	−2.63445	+	4.56300i	−0.248932	+	0.431163i
$113$	−4.33176	−	2.50094i	−0.407498	−	0.235269i	0.282216	−	0.959351i	$-0.408930\pi$
$113$	−4.33176	−	2.50094i	−0.407498	−	0.235269i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	7.32192	−	7.96175i	0.676912	−	0.736064i
$118$		0			0
$119$	−1.33143	+	0.768700i	−0.122052	+	0.0704666i
$120$	3.38230	−	4.60420i	0.308760	−	0.420304i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$	−3.74292	−	6.48292i	−0.336124	−	0.582184i
$125$			10.0757i			0.901201i
$126$	4.11350	+	3.78293i	0.366460	+	0.337010i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$	−4.22711	−	9.63027i	−0.372176	−	0.847898i
$130$	2.97315	−	5.14965i	0.260763	−	0.451654i
$131$	19.7381	+	11.3958i	1.72453	+	0.995656i	0.908818	+	0.417193i	$0.136986\pi$
$131$	19.7381	+	11.3958i	1.72453	+	0.995656i	0.815709	+	0.578463i	$0.196347\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.98308	−	4.56657i	−0.342809	−	0.393027i
$136$	3.30120			0.283076
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$		0			0
$139$	−11.0147	+	19.0781i	−0.934256	+	1.61818i	−0.158301	+	0.987391i	$0.550602\pi$
$139$	−11.0147	+	19.0781i	−0.934256	+	1.61818i	−0.775955	+	0.630788i	$0.782732\pi$
$140$	2.66061	+	1.53610i	0.224862	+	0.129824i
$141$	6.94505	−	3.04846i	0.584879	−	0.256727i
$142$	1.94537	+	3.36948i	0.163252	+	0.282760i
$143$		0			0
$144$	−3.58793	−	11.4511i	−0.298994	−	0.954255i
$145$		0			0
$146$		0			0
$147$	5.39881	−	7.34922i	0.445286	−	0.606153i
$148$	5.39282	−	9.34064i	0.443287	−	0.767796i
$149$	−21.1240	−	12.1959i	−1.73054	−	0.999129i	−0.886135	−	0.463428i	$-0.846619\pi$
$149$	−21.1240	−	12.1959i	−1.73054	−	0.999129i	−0.844407	−	0.535701i	$-0.820047\pi$
$150$	7.18576	+	5.27873i	0.586715	+	0.431007i
$151$	11.0624	+	19.1606i	0.900244	+	1.55927i	0.827177	+	0.561942i	$0.189945\pi$
$151$	11.0624	+	19.1606i	0.900244	+	1.55927i	0.0730673	+	0.997327i	$0.476721\pi$
$152$		0			0
$153$	0.763985	−	3.41709i	0.0617645	−	0.276255i
$154$		0			0
$155$	−3.78008	+	2.18243i	−0.303623	+	0.175297i
$156$	−5.02005	−	11.4367i	−0.401925	−	0.915672i
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$		0			0
$160$	−3.29841	−	5.71302i	−0.260763	−	0.451654i
$161$		0			0
$162$	−12.6834	+	1.06381i	−0.996501	+	0.0835805i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.1013	−	5.83196i	−0.781659	−	0.451291i	0.0553591	−	0.998467i	$-0.482370\pi$
$167$	−10.1013	−	5.83196i	−0.781659	−	0.451291i	−0.837018	+	0.547176i	$0.815703\pi$
$168$	5.90889	−	2.59365i	0.455880	−	0.200104i
$169$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$170$		−	1.92487i		−	0.147631i
$171$		0			0
$172$	−12.1442			−0.925984
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	−2.39739	+	4.15240i	−0.181225	+	0.313892i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			21.0965i			1.57683i	0.615146	+	0.788413i	$0.289097\pi$
$179$			21.0965i			1.57683i	−0.615146	+	0.788413i	$0.710903\pi$
$180$	−6.67692	+	2.09206i	−0.497668	+	0.155933i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	5.81671	−	3.35828i	0.431163	−	0.248932i
$183$		0			0
$184$		0			0
$185$	−5.44637	−	3.14446i	−0.400425	−	0.231185i
$186$	−1.00629	+	9.11285i	−0.0737850	+	0.668186i
$187$		0			0
$188$		−	8.75800i		−	0.638743i
$189$	−1.31722	−	6.71655i	−0.0958140	−	0.488557i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−13.7727	−	1.52086i	−0.993958	−	0.109759i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$	−6.66857	+	2.92710i	−0.477546	+	0.209614i
$196$	−5.26492	−	9.11911i	−0.376066	−	0.651365i
$197$			14.9701i			1.06657i	0.845935	+	0.533286i	$0.179043\pi$
$197$			14.9701i			1.06657i	−0.845935	+	0.533286i	$0.820957\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	8.91628	−	5.14782i	0.630476	−	0.364006i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−3.25841	−	2.39366i	−0.228135	−	0.167590i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−14.4222			−1.00000
$209$		0			0
$210$	−1.51231	−	3.44537i	−0.104359	−	0.237753i
$211$	−13.8451	+	23.9804i	−0.953134	+	1.65088i	−0.214552	+	0.976713i	$0.568829\pi$
$211$	−13.8451	+	23.9804i	−0.953134	+	1.65088i	−0.738582	+	0.674164i	$0.764504\pi$
$212$		0			0
$213$	0.523017	−	4.73637i	0.0358365	−	0.324531i
$214$	−7.21110	−	12.4900i	−0.492941	−	0.853799i
$215$			7.08105i			0.482924i
$216$	−4.76161	+	13.9042i	−0.323987	+	0.946062i
$217$	−4.93026			−0.334688
$218$	−16.7058	+	9.64508i	−1.13146	+	0.653247i
$219$		0			0
$220$		0			0
$221$	−3.64443	−	2.10411i	−0.245151	−	0.141538i
$222$	−12.0957	+	5.30930i	−0.811812	+	0.356337i
$223$	5.99480	+	10.3833i	0.401441	+	0.695317i	0.993900	−	0.110284i	$-0.0351760\pi$
$223$	5.99480	+	10.3833i	0.401441	+	0.695317i	−0.592459	+	0.805601i	$0.701843\pi$
$224$		−	7.45135i		−	0.497864i
$225$	−3.26507	−	10.4206i	−0.217671	−	0.694709i
$226$	7.07374			0.470538
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$	−14.0355	+	24.3103i	−0.927494	+	1.60647i	−0.139995	+	0.990152i	$0.544709\pi$
$229$	−14.0355	+	24.3103i	−0.927494	+	1.60647i	−0.787500	+	0.616315i	$0.788625\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	19.2337i		−	1.26004i	−0.776579	−	0.630019i	$-0.783047\pi$
$233$		−	19.2337i		−	1.26004i	0.776579	−	0.630019i	$-0.216953\pi$
$234$	−3.33768	+	14.9285i	−0.218191	+	0.975906i
$235$	−5.10664			−0.333120
$236$		0			0
$237$		0			0
$238$	1.08711	−	1.88292i	0.0704666	−	0.122052i
$239$	−26.2505	−	15.1557i	−1.69800	−	0.980342i	−0.947654	−	0.319298i	$-0.896553\pi$
$239$	−26.2505	−	15.1557i	−1.69800	−	0.980342i	−0.750347	−	0.661044i	$-0.770114\pi$
$240$	−0.886787	+	8.03062i	−0.0572419	+	0.518374i
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$			15.5563i			1.00000i
$243$	13.2904	+	8.14657i	0.852576	+	0.522603i
$244$		0			0
$245$	−5.31720	+	3.06988i	−0.339703	+	0.196128i
$246$		0			0
$247$		0			0
$248$	9.16824	+	5.29329i	0.582184	+	0.336124i
$249$		0			0
$250$	−7.12462	−	12.3402i	−0.450601	−	0.780463i
$251$			20.8817i			1.31804i	0.752124	+	0.659022i	$0.229030\pi$
$251$			20.8817i			1.31804i	−0.752124	+	0.659022i	$0.770970\pi$
$252$	−7.71293	−	1.72444i	−0.485869	−	0.108629i
$253$		0			0
$254$		0			0
$255$	−1.39570	+	1.89992i	−0.0874024	+	0.118978i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−24.1337	−	13.9336i	−1.50542	−	0.869155i	−0.999980	−	0.00629280i	$-0.997997\pi$
$257$	−24.1337	−	13.9336i	−1.50542	−	0.869155i	−0.505440	−	0.862862i	$-0.668670\pi$
$258$	11.9868	+	8.80560i	0.746263	+	0.548213i
$259$	−3.55178	−	6.15186i	−0.220697	−	0.382258i
$260$			8.40934i			0.521525i
$261$		0			0
$262$	−32.2322			−1.99131
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	8.10731	+	2.77641i	0.493395	+	0.168967i
$271$	0.553478			0.0336214			0.0168107	−	0.999859i	$-0.494649\pi$
$271$	0.553478			0.0336214			0.0168107	+	0.999859i	$0.494649\pi$
$272$	−4.04313	+	2.33430i	−0.245151	+	0.141538i
$273$	−8.17637	−	0.902881i	−0.494856	−	0.0546449i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		−	31.1543i		−	1.86851i
$279$	7.60088	−	8.26508i	0.455053	−	0.494818i
$280$	−4.34475			−0.259649
$281$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$281$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$282$	−6.35033	+	8.64448i	−0.378157	+	0.514771i
$283$	−9.74764	+	16.8834i	−0.579437	+	1.00361i	0.416107	+	0.909316i	$0.363394\pi$
$283$	−9.74764	+	16.8834i	−0.579437	+	1.00361i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$	−4.76516	−	2.75117i	−0.282760	−	0.163252i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	12.4914	+	11.4876i	0.736064	+	0.676912i
$289$	15.6378			0.919868
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−29.3630	−	16.9527i	−1.71541	−	0.990390i	−0.926854	−	0.375422i	$-0.877498\pi$
$293$	−29.3630	−	16.9527i	−1.71541	−	0.990390i	−0.788552	−	0.614968i	$-0.789169\pi$
$294$	−1.41549	+	12.8184i	−0.0825529	+	0.747587i
$295$		0			0
$296$			15.2532i			0.886575i
$297$		0			0
$298$	34.4953			1.99826
$299$		0			0
$300$	−12.5333	−	1.38400i	−0.723613	−	0.0799055i
$301$	−3.99915	+	6.92673i	−0.230507	+	0.399250i
$302$	−27.0972	−	15.6446i	−1.55927	−	0.900244i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	1.48056	+	4.72528i	0.0846380	+	0.270126i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	3.08642	−	5.34584i	0.175297	−	0.303623i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	14.2353	+	10.4574i	0.805914	+	0.592033i
$313$	−11.3713	−	19.6956i	−0.642741	−	1.11326i	−0.984818	−	0.173589i	$-0.944464\pi$
$313$	−11.3713	−	19.6956i	−0.642741	−	1.11326i	0.342077	−	0.939672i	$-0.388870\pi$
$314$		0			0
$315$	−1.00549	+	4.49727i	−0.0566530	+	0.253393i
$316$		0			0
$317$	28.4724	−	16.4386i	1.59917	−	0.923282i	0.607524	−	0.794301i	$-0.292163\pi$
$317$	28.4724	−	16.4386i	1.59917	−	0.923282i	0.991647	−	0.128980i	$-0.0411704\pi$
$318$		0			0
$319$		0			0
$320$	8.07943	+	4.66466i	0.451654	+	0.260763i
$321$	−1.93872	+	17.5568i	−0.108209	+	0.979925i
$322$		0			0
$323$		0			0
$324$	14.7817	−	10.2714i	0.821205	−	0.570633i
$325$	−13.1244			−0.728012
$326$		0			0
$327$	23.4828	+	2.59310i	1.29860	+	0.143399i
$328$		0			0
$329$	−4.99534	−	2.88406i	−0.275402	−	0.159003i
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	15.7887	+	3.52999i	0.865214	+	0.193443i
$334$	16.4953			0.902582
$335$		0			0
$336$	−5.40289	+	7.35477i	−0.294752	+	0.401236i
$337$	9.06935	−	15.7086i	0.494039	−	0.855701i	−0.505937	−	0.862570i	$-0.668853\pi$
$337$	9.06935	−	15.7086i	0.494039	−	0.855701i	0.999976	+	0.00686960i	$0.00218668\pi$
$338$	15.9217	+	9.19239i	0.866025	+	0.500000i
$339$	−6.98205	−	5.12909i	−0.379213	−	0.278574i
$340$	1.36109	+	2.35748i	0.0738155	+	0.127852i
$341$		0			0
$342$		0			0
$343$	−16.1557			−0.872323
$344$	14.8735	−	8.58722i	0.801925	−	0.462992i
$345$		0			0
$346$		0			0
$347$	17.5289	+	10.1203i	0.941000	+	0.543287i	0.890274	−	0.455426i	$-0.150513\pi$
$347$	17.5289	+	10.1203i	0.941000	+	0.543287i	0.0507263	+	0.998713i	$0.483846\pi$
$348$		0			0
$349$	8.64271	+	14.9696i	0.462634	+	0.801305i	0.999091	−	0.0426221i	$-0.0135711\pi$
$349$	8.64271	+	14.9696i	0.462634	+	0.801305i	−0.536457	+	0.843927i	$0.680238\pi$
$350$		−	6.78083i		−	0.362451i
$351$	14.1189	−	12.3149i	0.753612	−	0.657320i
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$	−1.60416	+	2.77848i	−0.0851399	+	0.147467i
$356$		0			0
$357$	−2.43830	+	1.07027i	−0.129049	+	0.0566446i
$358$	−14.9175	−	25.8378i	−0.788413	−	1.36557i
$359$			3.17864i			0.167762i	0.996476	+	0.0838812i	$0.0267316\pi$
$359$			3.17864i			0.167762i	−0.996476	+	0.0838812i	$0.973268\pi$
$360$	6.69821	−	7.28353i	0.353027	−	0.383876i
$361$	19.0000			1.00000
$362$		0			0
$363$	11.2797	−	15.3547i	0.592033	−	0.805914i
$364$	−4.74932	+	8.22606i	−0.248932	+	0.431163i
$365$		0			0
$366$		0			0
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		0			0
$369$		0			0
$370$	8.89388			0.462371
$371$		0			0
$372$	−5.21130	−	11.8725i	−0.270194	−	0.615559i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−1.91547	+	17.3463i	−0.0989146	+	0.895757i
$376$	6.19284	+	10.7263i	0.319371	+	0.553167i
$377$		0			0
$378$	6.36258	+	7.29465i	0.327256	+	0.375196i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.0160	−	8.09214i	−0.716184	−	0.413489i	0.0971627	−	0.995269i	$-0.469023\pi$
$383$	−14.0160	−	8.09214i	−0.716184	−	0.413489i	−0.813346	+	0.581780i	$0.802357\pi$
$384$	17.9434	−	7.87610i	0.915672	−	0.401925i
$385$		0			0
$386$		0			0
$387$	−5.44655	−	17.3829i	−0.276864	−	0.883624i
$388$		0			0
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$	6.09752	−	8.30035i	0.308760	−	0.420304i
$391$		0			0
$392$	12.8964	+	7.44572i	0.651365	+	0.376066i
$393$	31.8144	+	23.3712i	1.60483	+	1.17892i
$394$	−10.5854	−	18.3345i	−0.533286	−	0.923679i
$395$		0			0
$396$		0			0
$397$	−3.33082			−0.167169			−0.0835845	−	0.996501i	$-0.526637\pi$
$397$	−3.33082			−0.167169			−0.0835845	+	0.996501i	$0.526637\pi$
$398$		0			0
$399$		0			0
$400$	−7.28012	+	12.6095i	−0.364006	+	0.630476i
$401$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$401$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$402$		0			0
$403$	−6.74764	−	11.6873i	−0.336124	−	0.582184i
$404$		0			0
$405$	−5.98908	−	8.61895i	−0.297600	−	0.428279i
$406$		0			0
$407$		0			0
$408$	5.68330	+	0.627583i	0.281365	+	0.0310700i
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	17.6635	−	10.1980i	0.866025	−	0.500000i
$417$	−22.5897	+	30.7505i	−1.10622	+	1.50586i
$418$		0			0
$419$	23.4558	+	13.5422i	1.14589	+	0.661582i	0.947883	−	0.318618i	$-0.103219\pi$
$419$	23.4558	+	13.5422i	1.14589	+	0.661582i	0.198010	+	0.980200i	$0.436552\pi$
$420$	4.28844	+	3.15033i	0.209254	+	0.153721i
$421$	19.5278	+	33.8231i	0.951725	+	1.64844i	0.741691	+	0.670741i	$0.234024\pi$
$421$	19.5278	+	33.8231i	0.951725	+	1.64844i	0.210033	+	0.977694i	$0.432643\pi$
$422$		−	39.1598i		−	1.90627i
$423$	12.5360	−	3.92788i	0.609523	−	0.190980i
$424$		0			0
$425$	−3.67930	+	2.12425i	−0.178473	+	0.103041i
$426$	2.70856	+	6.17067i	0.131230	+	0.298970i
$427$		0			0
$428$	17.6635	+	10.1980i	0.853799	+	0.492941i
$429$		0			0
$430$	−5.00706	−	8.67248i	−0.241462	−	0.418224i
$431$			37.9936i			1.83009i	0.403355	+	0.915044i	$0.367844\pi$
$431$			37.9936i			1.83009i	−0.403355	+	0.915044i	$0.632156\pi$
$432$	−4.00000	−	20.3961i	−0.192450	−	0.981307i
$433$	35.4188			1.70212			0.851060	−	0.525069i	$-0.175960\pi$
$433$	35.4188			1.70212			0.851060	+	0.525069i	$0.175960\pi$
$434$	6.03832	−	3.48622i	0.289848	−	0.167344i
$435$		0			0
$436$	13.6402	−	23.6255i	0.653247	−	1.13146i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	10.6917	−	11.6260i	0.509127	−	0.553617i
$442$	5.95132			0.283076
$443$	27.9497	−	16.1368i	1.32793	−	0.766680i	0.342950	−	0.939354i	$-0.388574\pi$
$443$	27.9497	−	16.1368i	1.32793	−	0.766680i	0.984979	+	0.172673i	$0.0552404\pi$
$444$	11.0599	−	15.0555i	0.524881	−	0.714503i
$445$		0			0
$446$	−14.6842	−	8.47793i	−0.695317	−	0.401441i
$447$	−34.0482	−	25.0122i	−1.61042	−	1.18303i
$448$	5.26890	+	9.12600i	0.248932	+	0.431163i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	11.3674	+	10.4539i	0.535863	+	0.492800i
$451$		0			0
$452$	−8.66352	+	5.00189i	−0.407498	+	0.235269i
$453$	15.4023	+	35.0897i	0.723662	+	1.64866i
$454$		0			0
$455$	4.79648	+	2.76925i	0.224862	+	0.129824i
$456$		0			0
$457$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$457$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$458$		−	39.6985i		−	1.85499i
$459$	1.96488	−	5.73757i	0.0917127	−	0.267807i
$460$		0			0
$461$	−3.43413	+	1.98269i	−0.159943	+	0.0923433i	−0.577835	−	0.816153i	$-0.696102\pi$
$461$	−3.43413	+	1.98269i	−0.159943	+	0.0923433i	0.417892	+	0.908497i	$0.362769\pi$
$462$		0			0
$463$	−20.1739	+	34.9423i	−0.937563	+	1.62391i	−0.167564	+	0.985861i	$0.553590\pi$
$463$	−20.1739	+	34.9423i	−0.937563	+	1.62391i	−0.769999	+	0.638045i	$0.779743\pi$
$464$		0			0
$465$	−6.92263	+	3.03862i	−0.321029	+	0.140913i
$466$	13.6002	+	23.5563i	0.630019	+	1.09123i
$467$		−	41.4721i		−	1.91910i	−0.281539	−	0.959550i	$-0.590845\pi$
$467$		−	41.4721i		−	1.91910i	0.281539	−	0.959550i	$-0.409155\pi$
$468$	−6.46823	−	20.6437i	−0.298994	−	0.954255i
$469$		0			0
$470$	6.25433	−	3.61094i	0.288491	−	0.166560i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$			3.07480i			0.140933i
$477$		0			0
$478$	42.8668			1.96068
$479$	−30.8836	+	17.8306i	−1.41111	+	0.814703i	−0.995493	−	0.0948388i	$-0.969766\pi$
$479$	−30.8836	+	17.8306i	−1.41111	+	0.814703i	−0.415614	+	0.909541i	$0.636433\pi$
$480$	−4.59242	−	10.4625i	−0.209614	−	0.477546i
$481$	9.72205	−	16.8391i	0.443287	−	0.767796i
$482$		0			0
$483$		0			0
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	−22.0378	−	0.579772i	−0.999654	−	0.0262990i
$487$	36.0555			1.63383			0.816916	−	0.576757i	$-0.195682\pi$
$487$	36.0555			1.63383			0.816916	+	0.576757i	$0.195682\pi$
$488$		0			0
$489$		0			0
$490$	4.34147	−	7.51965i	0.196128	−	0.339703i
$491$	−23.7812	−	13.7301i	−1.07323	−	0.619631i	−0.144169	−	0.989553i	$-0.546051\pi$
$491$	−23.7812	−	13.7301i	−1.07323	−	0.619631i	−0.929063	+	0.369922i	$0.879384\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−14.9717			−0.672248
$497$	−3.13839	+	1.81195i	−0.140776	+	0.0812772i
$498$		0			0
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	17.4517	+	10.0757i	0.780463	+	0.450601i
$501$	−16.2815	−	11.9606i	−0.727403	−	0.534358i
$502$	−14.7656	−	25.5748i	−0.659022	−	1.14146i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	10.6657	−	3.34186i	0.475089	−	0.148858i
$505$		0			0
$506$		0			0
$507$	−9.05002	−	20.6179i	−0.401925	−	0.915672i
$508$		0			0
$509$	0.921447	+	0.531998i	0.0408424	+	0.0235804i	0.520282	−	0.853994i	$-0.325827\pi$
$509$	0.921447	+	0.531998i	0.0408424	+	0.0235804i	−0.479440	+	0.877575i	$0.659160\pi$
$510$	0.365933	−	3.31384i	0.0162038	−	0.146739i
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$	39.4102			1.73831
$515$		0			0
$516$	−20.9072	−	2.30870i	−0.920389	−	0.101635i
$517$		0			0
$518$	8.70005	+	5.02298i	0.382258	+	0.220697i
$519$		0			0
$520$	−5.94630	−	10.2993i	−0.260763	−	0.451654i
$521$		−	43.1204i		−	1.88914i	−0.328310	−	0.944570i	$-0.606479\pi$
$521$		−	43.1204i		−	1.88914i	0.328310	−	0.944570i	$-0.393521\pi$
$522$		0			0
$523$	43.4953			1.90192			0.950958	−	0.309320i	$-0.100101\pi$
$523$	43.4953			1.90192			0.950958	+	0.309320i	$0.100101\pi$
$524$	39.4762	−	22.7916i	1.72453	−	0.995656i
$525$	−4.91671	+	6.69295i	−0.214583	+	0.292104i
$526$		0			0
$527$	−3.78327	−	2.18427i	−0.164802	−	0.0951485i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	5.94630	−	10.2993i	0.257081	−	0.445277i
$536$		0			0
$537$	−4.01060	+	36.3194i	−0.173070	+	1.56730i
$538$		0			0
$539$		0			0
$540$	−11.8926	+	2.33233i	−0.511776	+	0.100368i
$541$	25.8833			1.11281			0.556404	−	0.830912i	$-0.312181\pi$
$541$	25.8833			1.11281			0.556404	+	0.830912i	$0.312181\pi$
$542$	−0.677869	+	0.391368i	−0.0291170	+	0.0168107i
$543$		0			0
$544$	3.30120	−	5.71785i	0.141538	−	0.245151i
$545$	−13.7756	−	7.95337i	−0.590083	−	0.340685i
$546$	10.6524	−	4.67576i	0.455880	−	0.200104i
$547$	−18.7927	−	32.5499i	−0.803517	−	1.39173i	−0.917287	−	0.398226i	$-0.869626\pi$
$547$	−18.7927	−	32.5499i	−0.803517	−	1.39173i	0.113770	−	0.993507i	$-0.463707\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−8.77861	−	6.44886i	−0.372631	−	0.273739i
$556$	22.0294	+	38.1561i	0.934256	+	1.61818i
$557$			30.1407i			1.27710i	0.769580	+	0.638550i	$0.220466\pi$
$557$			30.1407i			1.27710i	−0.769580	+	0.638550i	$0.779534\pi$
$558$	−3.46484	+	15.4972i	−0.146678	+	0.656051i
$559$	−21.8932			−0.925984
$560$	5.32121	−	3.07220i	0.224862	−	0.129824i
$561$		0			0
$562$		0			0
$563$	11.8170	+	6.82257i	0.498029	+	0.287537i	0.727899	−	0.685684i	$-0.240497\pi$
$563$	11.8170	+	6.82257i	0.498029	+	0.287537i	−0.229870	+	0.973221i	$0.573830\pi$
$564$	1.66496	−	15.0776i	0.0701075	−	0.634883i
$565$	2.91651	+	5.05155i	0.122699	+	0.212520i
$566$		−	27.5705i		−	1.15887i
$567$	−0.990849	−	11.8135i	−0.0416117	−	0.496122i
$568$	7.78147			0.326503
$569$	−9.56831	+	5.52427i	−0.401125	+	0.231589i	−0.686969	−	0.726687i	$-0.741059\pi$
$569$	−9.56831	+	5.52427i	−0.401125	+	0.231589i	0.285845	+	0.958276i	$0.407726\pi$
$570$		0			0
$571$	−21.3730	+	37.0192i	−0.894434	+	1.54920i	−0.0599303	+	0.998203i	$0.519088\pi$
$571$	−21.3730	+	37.0192i	−0.894434	+	1.54920i	−0.834504	+	0.551002i	$0.814245\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−23.4217	−	5.23658i	−0.975906	−	0.218191i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−19.1523	+	11.0576i	−0.796629	+	0.459934i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−12.0370	+	3.77152i	−0.497668	+	0.155933i
$586$	47.9496			1.98078
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	−7.33040	−	16.7002i	−0.302301	−	0.688706i
$589$		0			0
$590$		0			0
$591$	−2.84592	+	25.7722i	−0.117065	+	1.06013i
$592$	−10.7856	−	18.6813i	−0.443287	−	0.767796i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	1.79286			0.0735002
$596$	−42.2479	+	24.3918i	−1.73054	+	0.999129i
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	16.3288	−	7.16736i	0.666620	−	0.292606i
$601$	24.4695	+	42.3823i	0.998130	+	1.72881i	0.552001	+	0.833843i	$0.313864\pi$
$601$	24.4695	+	42.3823i	0.998130	+	1.72881i	0.446129	+	0.894969i	$0.352802\pi$
$602$		−	11.3113i		−	0.461014i
$603$		0			0
$604$	44.2495			1.80049
$605$	−11.1092	+	6.41391i	−0.451654	+	0.260763i
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	15.7887i		−	0.638743i
$612$	−5.15459	−	4.74035i	−0.208362	−	0.191617i
$613$	−47.4216			−1.91534			−0.957671	−	0.287865i	$-0.907054\pi$
$613$	−47.4216			−1.91534			−0.957671	+	0.287865i	$0.907054\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$617$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$618$		0			0
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$			8.72972i			0.350594i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−24.8291	−	2.74177i	−0.993958	−	0.109759i
$625$	−3.22515	+	5.58613i	−0.129006	+	0.223445i
$626$	27.8538	+	16.0814i	1.11326	+	0.642741i
$627$		0			0
$628$		0			0
$629$		−	6.29424i		−	0.250968i
$630$	−1.94858	−	6.21900i	−0.0776334	−	0.247771i
$631$	49.1736			1.95757			0.978785	−	0.204890i	$-0.0656837\pi$
$631$	49.1736			1.95757			0.978785	+	0.204890i	$0.0656837\pi$
$632$		0			0
$633$	−28.3943	+	38.6522i	−1.12857	+	1.53629i
$634$	−23.2476	+	40.2661i	−0.923282	+	1.59917i
$635$		0			0
$636$		0			0
$637$	−9.49147	−	16.4397i	−0.376066	−	0.651365i
$638$		0			0
$639$	1.80084	−	8.05464i	0.0712401	−	0.318637i
$640$	−13.1937			−0.521525
$641$	4.83648	−	2.79234i	0.191029	−	0.110291i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	4.83648	−	2.79234i	0.191029	−	0.110291i	0.592464	+	0.805597i	$0.298155\pi$
$642$	−10.0401	−	22.8735i	−0.396251	−	0.902745i
$643$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$643$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$644$		0			0
$645$	−1.34616	+	12.1906i	−0.0530050	+	0.480006i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−10.8408	+	23.0321i	−0.425868	+	0.904785i
$649$		0			0
$650$	16.0741	−	9.28036i	0.630476	−	0.364006i
$651$	−8.48787	−	0.937280i	−0.332666	−	0.0367349i
$652$		0			0
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	−30.5940	+	13.4289i	−1.19632	+	0.525113i
$655$	−13.2894	−	23.0179i	−0.519260	−	0.899384i
$656$		0			0
$657$		0			0
$658$	8.15736			0.318007
$659$	17.5794	−	10.1495i	0.684796	−	0.395367i	−0.116863	−	0.993148i	$-0.537284\pi$
$659$	17.5794	−	10.1495i	0.684796	−	0.395367i	0.801660	+	0.597781i	$0.203951\pi$
$660$		0			0
$661$	3.60555	−	6.24500i	0.140240	−	0.242902i	−0.787347	−	0.616510i	$-0.788546\pi$
$661$	3.60555	−	6.24500i	0.140240	−	0.242902i	0.927587	+	0.373608i	$0.121879\pi$
$662$		0			0
$663$	−5.87419	−	4.31524i	−0.228135	−	0.167590i
$664$		0			0
$665$		0			0
$666$	−21.8332	+	6.84093i	−0.846018	+	0.265081i
$667$		0			0
$668$	−20.2025	+	11.6639i	−0.781659	+	0.451291i
$669$	8.34662	+	19.0154i	0.322699	+	0.735178i
$670$		0			0
$671$		0			0
$672$	1.41656	−	12.8281i	0.0546449	−	0.494856i
$673$	19.6173	+	33.9782i	0.756191	+	1.30976i	0.944780	+	0.327705i	$0.106275\pi$
$673$	19.6173	+	33.9782i	0.756191	+	1.30976i	−0.188589	+	0.982056i	$0.560391\pi$
$674$			25.6520i			0.988078i
$675$	−3.64006	−	18.5607i	−0.140106	−	0.714403i
$676$	−26.0000			−1.00000
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$	12.1780	+	1.34477i	0.467695	+	0.0516456i
$679$		0			0
$680$	−3.33398	−	1.92487i	−0.127852	−	0.0738155i
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$		0			0
$686$	19.7866	−	11.4238i	0.755454	−	0.436162i
$687$	−28.7849	+	39.1840i	−1.09821	+	1.49496i
$688$	−12.1442	+	21.0343i	−0.462992	+	0.801925i
$689$		0			0
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$		0			0
$694$	−28.6246			−1.08657
$695$	22.2482	−	12.8450i	0.843921	−	0.487238i
$696$		0			0
$697$		0			0
$698$	−21.1702	−	12.2226i	−0.801305	−	0.462634i
$699$	3.65646	−	33.1124i	0.138300	−	1.25243i
$700$	4.79477	+	8.30479i	0.181225	+	0.313892i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−8.58412	+	25.0662i	−0.323987	+	0.946062i
$703$		0			0
$704$		0			0
$705$	−8.79152	−	0.970810i	−0.331108	−	0.0365628i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.9679	−	34.5854i	−0.749910	−	1.29888i	−0.947865	−	0.318671i	$-0.896763\pi$
$709$	−19.9679	−	34.5854i	−0.749910	−	1.29888i	0.197955	−	0.980211i	$-0.436570\pi$
$710$		−	4.53724i		−	0.170280i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	2.22950	−	3.03495i	0.0834371	−	0.113580i
$715$		0			0
$716$	36.5402	+	21.0965i	1.36557	+	0.788413i
$717$	−42.3112	−	31.0823i	−1.58014	−	1.16079i
$718$	−2.24764	−	3.89303i	−0.0838812	−	0.145287i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−3.05336	+	13.6568i	−0.113792	+	0.508960i
$721$		0			0
$722$	−23.2702	+	13.4350i	−0.866025	+	0.500000i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−2.95738	+	26.7816i	−0.109759	+	0.993958i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$		−	13.4331i		−	0.497864i
$729$	21.3318	+	16.5516i	0.790065	+	0.613023i
$730$		0			0
$731$	−6.13755	+	3.54352i	−0.227006	+	0.131062i
$732$		0			0
$733$	11.6244	−	20.1341i	0.429357	−	0.743669i	−0.567459	−	0.823402i	$-0.692073\pi$
$733$	11.6244	−	20.1341i	0.429357	−	0.743669i	0.996816	+	0.0797329i	$0.0254067\pi$
$734$		0			0
$735$	−9.73762	+	4.27423i	−0.359177	+	0.157657i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$	−10.8927	+	6.28893i	−0.400425	+	0.231185i
$741$		0			0
$742$		0			0
$743$	41.1240	+	23.7429i	1.50869	+	0.871044i	0.999949	+	0.0101256i	$0.00322315\pi$
$743$	41.1240	+	23.7429i	1.50869	+	0.871044i	0.508743	+	0.860918i	$0.330110\pi$
$744$	14.7776	+	10.8558i	0.541774	+	0.397993i
$745$	14.2225	+	24.6340i	0.521071	+	0.902521i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.6334	−	6.71655i	0.425076	−	0.245418i
$750$	−9.91969	−	22.5992i	−0.362216	−	0.825205i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	−15.1693	−	8.75800i	−0.553167	−	0.319371i
$753$	−3.96977	+	35.9497i	−0.144667	+	1.31008i
$754$		0			0
$755$		−	25.8011i		−	0.939000i
$756$	−12.9506	−	4.43505i	−0.471010	−	0.161301i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$		0			0
$763$	−8.98360	−	15.5601i	−0.325228	−	0.563312i
$764$		0			0
$765$	−2.76402	+	3.00555i	−0.0999332	+	0.108666i
$766$	22.8880			0.826978
$767$		0			0
$768$	−16.4069	+	22.3341i	−0.592033	+	0.805914i
$769$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$769$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−38.8994	−	28.5759i	−1.40093	−	1.02914i
$772$		0			0
$773$			4.54977i			0.163644i	0.996647	+	0.0818220i	$0.0260739\pi$
$773$			4.54977i			0.163644i	−0.996647	+	0.0818220i	$0.973926\pi$
$774$	18.9622	+	17.4384i	0.681583	+	0.626809i
$775$	−13.6244			−0.489404
$776$		0			0
$777$	−4.94518	−	11.2662i	−0.177407	−	0.404172i
$778$		0			0
$779$		0			0
$780$	−1.59868	+	14.4774i	−0.0572419	+	0.518374i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−21.0597			−0.752131
$785$		0			0
$786$	−55.4905	−	6.12758i	−1.97928	−	0.218564i
$787$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$787$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$788$	25.9289	+	14.9701i	0.923679	+	0.533286i
$789$		0			0
$790$		0			0
$791$			6.58861i			0.234264i
$792$		0			0
$793$		0			0
$794$	4.07940	−	2.35524i	0.144773	−	0.0835845i
$795$		0			0
$796$		0			0
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$	−2.55548	−	4.42621i	−0.0904062	−	0.156588i
$800$		−	20.5913i		−	0.728012i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	16.5283	+	9.54261i	0.582184	+	0.336124i
$807$		0			0
$808$		0			0
$809$			49.0847i			1.72572i	0.505439	+	0.862862i	$0.331331\pi$
$809$			49.0847i			1.72572i	−0.505439	+	0.862862i	$0.668669\pi$
$810$	13.4296	+	6.32110i	0.471868	+	0.222101i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	0.952860	+	0.105220i	0.0334183	+	0.00369024i
$814$		0			0
$815$		0			0
$816$	−7.40436	+	3.25007i	−0.259205	+	0.113775i
$817$		0			0
$818$		0			0
$819$	−13.9047	−	3.10878i	−0.485869	−	0.108629i
$820$		0			0
$821$	26.3984	−	15.2411i	0.921309	−	0.531918i	0.0372568	−	0.999306i	$-0.488138\pi$
$821$	26.3984	−	15.2411i	0.921309	−	0.531918i	0.884053	+	0.467388i	$0.154805\pi$
$822$		0			0
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	−14.4222	+	24.9800i	−0.500000	+	0.866025i
$833$	−5.32169	−	3.07248i	−0.184385	−	0.106455i
$834$	5.92267	−	53.6349i	0.205085	−	1.85722i
$835$	6.80104	+	11.7797i	0.235360	+	0.407655i
$836$		0			0
$837$	14.6568	−	12.7841i	0.506614	−	0.441882i
$838$	−38.3032			−1.32316
$839$	39.4951	−	22.8025i	1.36352	−	0.787231i	0.373432	−	0.927657i	$-0.378181\pi$
$839$	39.4951	−	22.8025i	1.36352	−	0.787231i	0.990091	+	0.140427i	$0.0448475\pi$
$840$	−7.47987	−	0.825970i	−0.258080	−	0.0284987i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−47.8330	−	27.6164i	−1.64844	−	0.951725i
$843$		0			0
$844$	27.6901	+	47.9607i	0.953134	+	1.65088i
$845$			15.1602i			0.521525i
$846$	−12.5760	+	13.6750i	−0.432372	+	0.470155i
$847$	−14.4895			−0.497864
$848$		0			0
$849$	−19.9911	+	27.2131i	−0.686092	+	0.933953i
$850$	3.00414	−	5.20332i	0.103041	−	0.178473i
$851$		0			0
$852$	−7.68062	−	5.64226i	−0.263134	−	0.193301i
$853$	−11.7719	−	20.3895i	−0.403062	−	0.698124i	0.591032	−	0.806648i	$-0.298721\pi$
$853$	−11.7719	−	20.3895i	−0.403062	−	0.698124i	−0.994094	+	0.108524i	$0.965387\pi$
$854$		0			0
$855$		0			0
$856$	−28.8444			−0.985882
$857$	−49.1635	+	28.3846i	−1.67939	+	0.969599i	−0.717346	+	0.696717i	$0.754643\pi$
$857$	−49.1635	+	28.3846i	−1.67939	+	0.969599i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	−0.747641	+	1.29495i	−0.0255092	+	0.0441832i	−0.878498	−	0.477746i	$-0.841454\pi$
$859$	−0.747641	+	1.29495i	−0.0255092	+	0.0441832i	0.852989	+	0.521929i	$0.174787\pi$
$860$	12.2647	+	7.08105i	0.418224	+	0.241462i
$861$		0			0
$862$	−26.8655	−	46.5325i	−0.915044	−	1.58490i
$863$		−	28.6643i		−	0.975743i	−0.872915	−	0.487872i	$-0.837773\pi$
$863$		−	28.6643i		−	0.975743i	0.872915	−	0.487872i	$-0.162227\pi$
$864$	19.3212	+	22.1516i	0.657320	+	0.753612i
$865$		0			0
$866$	−43.3790	+	25.0449i	−1.47408	+	0.851060i
$867$	26.9218	+	2.97285i	0.914311	+	0.100963i
$868$	−4.93026	+	8.53947i	−0.167344	+	0.289848i
$869$		0			0
$870$		0			0
$871$		0			0
$872$			38.5803i			1.30649i
$873$		0			0
$874$		0			0
$875$	11.4939	−	6.63601i	0.388565	−	0.224338i
$876$		0			0
$877$	24.8212	−	42.9916i	0.838152	−	1.45172i	−0.0532864	−	0.998579i	$-0.516970\pi$
$877$	24.8212	−	42.9916i	0.838152	−	1.45172i	0.891438	−	0.453142i	$-0.149697\pi$
$878$		0			0
$879$	−47.3281	−	34.7677i	−1.59634	−	1.17269i
$880$		0			0
$881$		−	36.2766i		−	1.22219i	−0.791558	−	0.611094i	$-0.790730\pi$
$881$		−	36.2766i		−	1.22219i	0.791558	−	0.611094i	$-0.209270\pi$
$882$	−4.87377	+	21.7990i	−0.164108	+	0.734010i
$883$	−14.4965			−0.487845			−0.243923	−	0.969795i	$-0.578434\pi$
$883$	−14.4965			−0.487845			−0.243923	+	0.969795i	$0.578434\pi$
$884$	−7.28885	+	4.20822i	−0.245151	+	0.141538i
$885$		0			0
$886$	−22.8208	+	39.5268i	−0.766680	+	1.32793i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$	−2.89975	+	26.2597i	−0.0973092	+	0.881218i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	23.9792			0.802883
$893$		0			0
$894$	59.3866	+	6.55781i	1.98619	+	0.219326i
$895$	12.3010	−	21.3060i	0.411177	−	0.712180i
$896$	−12.9061	−	7.45135i	−0.431163	−	0.248932i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−21.3141	−	4.76536i	−0.710471	−	0.158845i
$901$		0			0
$902$		0			0
$903$	−8.20170	+	11.1647i	−0.272935	+	0.371538i
$904$	7.07374	−	12.2521i	0.235269	−	0.407498i
$905$		0			0
$906$	−43.6760	−	32.0849i	−1.45104	−	1.06595i
$907$	−24.4041	−	42.2691i	−0.810325	−	1.40352i	−0.912637	−	0.408771i	$-0.865957\pi$
$907$	−24.4041	−	42.2691i	−0.810325	−	1.40352i	0.102312	−	0.994752i	$-0.467376\pi$
$908$		0			0
$909$		0			0
$910$	−7.83261			−0.259649
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	28.0711	+	48.6205i	0.927494	+	1.60647i
$917$		−	30.0217i		−	0.991403i
$918$	1.65060	+	8.41644i	0.0544779	+	0.277784i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	2.80395	−	4.85659i	0.0923433	−	0.159943i
$923$	−8.59051	−	4.95974i	−0.282760	−	0.163252i
$924$		0			0
$925$	−9.81509	−	17.0002i	−0.322718	−	0.558964i
$926$		−	57.0605i		−	1.87513i
$927$		0			0
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$	6.32983	−	8.61658i	0.207563	−	0.282549i
$931$		0			0
$932$	−33.3137	−	19.2337i	−1.09123	−	0.630019i
$933$		0			0
$934$	29.3252	+	50.7927i	0.959550	+	1.66199i
$935$		0			0
$936$	22.5192	+	20.7095i	0.736064	+	0.676912i
$937$	−53.9906			−1.76379			−0.881897	−	0.471441i	$-0.843734\pi$
$937$	−53.9906			−1.76379			−0.881897	+	0.471441i	$0.843734\pi$
$938$		0			0
$939$	−15.8323	−	36.0694i	−0.516668	−	1.17708i
$940$	−5.10664	+	8.84495i	−0.166560	+	0.288491i
$941$	50.5268	+	29.1716i	1.64713	+	0.950968i	0.978207	+	0.207632i	$0.0665756\pi$
$941$	50.5268	+	29.1716i	1.64713	+	0.950968i	0.668918	+	0.743336i	$0.266758\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−2.58600	+	7.55129i	−0.0841227	+	0.245644i
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	52.1428	−	22.8876i	1.69085	−	0.742181i
$952$	−2.17421	−	3.76584i	−0.0704666	−	0.122052i
$953$			37.8620i			1.22647i	0.789900	+	0.613236i	$0.210132\pi$
$953$			37.8620i			1.22647i	−0.789900	+	0.613236i	$0.789868\pi$
$954$		0			0
$955$		0			0
$956$	−52.5009	+	30.3114i	−1.69800	+	0.980342i
$957$		0			0
$958$	25.2163	−	43.6760i	0.814703	−	1.41111i
$959$		0			0
$960$	13.0227	+	9.56658i	0.420304	+	0.308760i
$961$	8.49528	+	14.7143i	0.274041	+	0.474654i
$962$			27.4981i			0.886575i
$963$	−6.67536	+	29.8570i	−0.215110	+	0.962128i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	26.2374	−	45.4445i	0.843738	−	1.46140i	−0.0429750	−	0.999076i	$-0.513684\pi$
$967$	26.2374	−	45.4445i	0.843738	−	1.46140i	0.886713	−	0.462321i	$-0.152983\pi$
$968$	26.9444	+	15.5563i	0.866025	+	0.500000i
$969$		0			0
$970$		0			0
$971$			4.98741i			0.160053i	0.996793	+	0.0800267i	$0.0255006\pi$
$971$			4.98741i			0.160053i	−0.996793	+	0.0800267i	$0.974499\pi$
$972$	27.4006	−	14.8730i	0.878875	−	0.477051i
$973$	29.0177			0.930265
$974$	−44.1588	+	25.4951i	−1.41494	+	0.816916i
$975$	−22.5948	−	2.49505i	−0.723613	−	0.0799055i
$976$		0			0
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$		0			0
$979$		0			0
$980$			12.2795i			0.392255i
$981$	39.9347	+	8.92850i	1.27502	+	0.285065i
$982$	38.8346			1.23926
$983$	45.0226	−	25.9938i	1.43600	−	0.829073i	0.438429	−	0.898766i	$-0.355535\pi$
$983$	45.0226	−	25.9938i	1.43600	−	0.829073i	0.997569	+	0.0696927i	$0.0222019\pi$
$984$		0			0
$985$	8.72878	−	15.1187i	0.278122	−	0.481722i
$986$		0			0
$987$	−8.05163	−	5.91481i	−0.256286	−	0.188271i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	18.3365	−	10.5866i	0.582184	−	0.336124i
$993$		0			0
$994$	2.56249	−	4.43836i	0.0812772	−	0.140776i
$995$		0			0
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$	26.5105	+	9.07873i	0.838754	+	0.287238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cl.a.779.6	yes	24
8.3	odd	2	inner	936.2.cl.a.779.12	yes	24
9.2	odd	6	inner	936.2.cl.a.155.6	✓	24
13.12	even	2	inner	936.2.cl.a.779.12	yes	24
72.11	even	6	inner	936.2.cl.a.155.12	yes	24
104.51	odd	2	CM	936.2.cl.a.779.6	yes	24
117.38	odd	6	inner	936.2.cl.a.155.12	yes	24
936.155	even	6	inner	936.2.cl.a.155.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cl.a.155.6	✓	24	9.2	odd	6	inner
936.2.cl.a.155.6	✓	24	936.155	even	6	inner
936.2.cl.a.155.12	yes	24	72.11	even	6	inner
936.2.cl.a.155.12	yes	24	117.38	odd	6	inner
936.2.cl.a.779.6	yes	24	1.1	even	1	trivial
936.2.cl.a.779.6	yes	24	104.51	odd	2	CM
936.2.cl.a.779.12	yes	24	8.3	odd	2	inner
936.2.cl.a.779.12	yes	24	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.72159 + 0.190107i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.00993 - 0.583083i) q^{5} +(-2.24293 + 0.984512i) q^{6} +(-0.658612 - 1.14075i) q^{7} +2.82843i q^{8} +(2.92772 + 0.654573i) q^{9} +1.64921 q^{10} +(2.05086 - 2.79177i) q^{12} +(1.80278 - 3.12250i) q^{13} +(1.61326 + 0.931418i) q^{14} +(-1.62783 - 1.19582i) q^{15} +(-2.00000 - 3.46410i) q^{16} -1.16715i q^{17} +(-4.04856 + 1.26852i) q^{18} +(-2.01986 + 1.16617i) q^{20} +(-0.916993 - 2.08911i) q^{21} +(-0.537705 + 4.86938i) q^{24} +(-1.82003 - 3.15238i) q^{25} +5.09902i q^{26} +(4.91588 + 1.68348i) q^{27} -2.63445 q^{28} +(2.83925 + 0.313527i) q^{30} +(1.87146 - 3.24146i) q^{31} +(4.89898 + 2.82843i) q^{32} +(0.825300 + 1.42946i) q^{34} +1.53610i q^{35} +(4.06147 - 4.41638i) q^{36} +5.39282 q^{37} +(3.69724 - 5.03293i) q^{39} +(1.64921 - 2.85651i) q^{40} +(2.60030 + 1.91021i) q^{42} +(-3.03604 - 5.25858i) q^{43} +(-2.57512 - 2.36817i) q^{45} +(3.79232 - 2.18950i) q^{47} +(-2.78462 - 6.34396i) q^{48} +(2.63246 - 4.55955i) q^{49} +(4.45814 + 2.57391i) q^{50} +(0.221884 - 2.00935i) q^{51} +(-3.60555 - 6.24500i) q^{52} +(-7.21110 + 1.41421i) q^{54} +(3.22653 - 1.86284i) q^{56} +(-3.69906 + 1.62366i) q^{60} +5.29329i q^{62} +(-1.18153 - 3.77090i) q^{63} -8.00000 q^{64} +(-3.64135 + 2.10234i) q^{65} +(-2.02156 - 1.16715i) q^{68} +(-1.08619 - 1.88133i) q^{70} -2.75117i q^{71} +(-1.85141 + 8.28084i) q^{72} +(-6.60483 + 3.81330i) q^{74} +(-2.53405 - 5.77310i) q^{75} +(-0.969362 + 8.77840i) q^{78} +4.66466i q^{80} +(8.14307 + 3.83281i) q^{81} +(-4.53543 - 0.500828i) q^{84} +(-0.680545 + 1.17874i) q^{85} +(7.43675 + 4.29361i) q^{86} +(4.82841 + 1.07953i) q^{90} -4.74932 q^{91} +(3.83810 - 5.22468i) q^{93} +(-3.09642 + 5.36316i) q^{94} +(7.89631 + 5.80071i) q^{96} +7.44572i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 48 q^{16} + 60 q^{25} + 12 q^{27} + 48 q^{30} + 48 q^{42} - 84 q^{49} - 60 q^{51} - 192 q^{64} - 168 q^{75} - 96 q^{90}+O(q^{100}) \) 24 * q + 24 * q^4 - 48 * q^16 + 60 * q^25 + 12 * q^27 + 48 * q^30 + 48 * q^42 - 84 * q^49 - 60 * q^51 - 192 * q^64 - 168 * q^75 - 96 * q^90

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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