LMFDB - Embedded newform 720.2.u.a.179.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.6
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(1.65197 + 1.50698i) q^{5} +4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +O(q^{10})$	\(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(1.65197 + 1.50698i) q^{5} +4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +(-1.36208 - 2.85390i) q^{10} +(4.26649 - 4.26649i) q^{11} +(2.10930 - 2.10930i) q^{13} +(2.29324 - 5.64362i) q^{14} +(0.107775 + 3.99855i) q^{16} -3.59142 q^{17} +(0.954870 - 0.954870i) q^{19} +(0.265210 + 4.46427i) q^{20} +(-7.86127 + 3.31847i) q^{22} +6.53188 q^{23} +(0.457999 + 4.97898i) q^{25} +(-3.88652 + 1.64061i) q^{26} +(-6.00912 + 6.17327i) q^{28} +(-1.84857 + 1.84857i) q^{29} +7.64329i q^{31} +(1.98755 - 5.29619i) q^{32} +(4.70541 + 1.91201i) q^{34} +(-6.49135 + 7.11588i) q^{35} +(1.90965 + 1.90965i) q^{37} +(-1.75941 + 0.742695i) q^{38} +(2.02922 - 5.99018i) q^{40} -7.67058 q^{41} +(5.43308 - 5.43308i) q^{43} +(12.0664 - 0.162586i) q^{44} +(-8.55794 - 3.47746i) q^{46} +3.24864i q^{47} -11.5547 q^{49} +(2.05066 - 6.76719i) q^{50} +(5.96546 - 0.0803806i) q^{52} +(-6.08323 + 6.08323i) q^{53} +(13.4776 - 0.618574i) q^{55} +(11.1596 - 4.88894i) q^{56} +(3.40610 - 1.43781i) q^{58} +(2.97848 - 2.97848i) q^{59} +(-0.157020 - 0.157020i) q^{61} +(4.06915 - 10.0141i) q^{62} +(-5.42364 + 5.88082i) q^{64} +(6.66318 - 0.305816i) q^{65} +(0.305394 + 0.305394i) q^{67} +(-5.14701 - 5.01014i) q^{68} +(12.2932 - 5.86719i) q^{70} +1.61808i q^{71} +6.90696 q^{73} +(-1.48532 - 3.51865i) q^{74} +(2.70053 - 0.0363879i) q^{76} +(18.3780 + 18.3780i) q^{77} -5.39306i q^{79} +(-5.84771 + 6.76789i) q^{80} +(10.0498 + 4.08368i) q^{82} +(-5.82210 + 5.82210i) q^{83} +(-5.93291 - 5.41221i) q^{85} +(-10.0108 + 4.22584i) q^{86} +(-15.8957 - 6.21090i) q^{88} +7.74878 q^{89} +(9.08585 + 9.08585i) q^{91} +(9.36110 + 9.11218i) q^{92} +(1.72952 - 4.25630i) q^{94} +(3.01639 - 0.138441i) q^{95} +9.34141i q^{97} +(15.1387 + 6.15150i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.31018	−	0.532382i	−0.926437	−	0.376451i
$2$	−1.31018	−	0.532382i	−0.926437	−	0.376451i
$3$		0			0
$3$		0			0
$4$	1.43314	+	1.39503i	0.716570	+	0.697516i
$5$	1.65197	+	1.50698i	0.738783	+	0.673944i
$5$	1.65197	+	1.50698i	0.738783	+	0.673944i
$6$		0			0
$7$			4.30751i			1.62809i	0.580804	+	0.814044i	$0.302738\pi$
$7$			4.30751i			1.62809i	−0.580804	+	0.814044i	$0.697262\pi$
$8$	−1.13498	−	2.59072i	−0.401276	−	0.915957i
$9$		0			0
$10$	−1.36208	−	2.85390i	−0.430729	−	0.902481i
$11$	4.26649	−	4.26649i	1.28640	−	1.28640i	0.349435	−	0.936961i	$-0.386374\pi$
$11$	4.26649	−	4.26649i	1.28640	−	1.28640i	0.936961	−	0.349435i	$-0.113626\pi$
$12$		0			0
$13$	2.10930	−	2.10930i	0.585015	−	0.585015i	−0.351262	−	0.936277i	$-0.614247\pi$
$13$	2.10930	−	2.10930i	0.585015	−	0.585015i	0.936277	+	0.351262i	$0.114247\pi$
$14$	2.29324	−	5.64362i	0.612895	−	1.50832i
$15$		0			0
$16$	0.107775	+	3.99855i	0.0269438	+	0.999637i
$17$	−3.59142			−0.871048			−0.435524	−	0.900177i	$-0.643437\pi$
$17$	−3.59142			−0.871048			−0.435524	+	0.900177i	$0.643437\pi$
$18$		0			0
$19$	0.954870	−	0.954870i	0.219062	−	0.219062i	−0.589041	−	0.808103i	$-0.700494\pi$
$19$	0.954870	−	0.954870i	0.219062	−	0.219062i	0.808103	+	0.589041i	$0.200494\pi$
$20$	0.265210	+	4.46427i	0.0593028	+	0.998240i
$21$		0			0
$22$	−7.86127	+	3.31847i	−1.67603	+	0.707499i
$23$	6.53188			1.36199			0.680996	−	0.732287i	$-0.261547\pi$
$23$	6.53188			1.36199			0.680996	+	0.732287i	$0.261547\pi$
$24$		0			0
$25$	0.457999	+	4.97898i	0.0915997	+	0.995796i
$26$	−3.88652	+	1.64061i	−0.762209	+	0.321750i
$27$		0			0
$28$	−6.00912	+	6.17327i	−1.13562	+	1.16664i
$29$	−1.84857	+	1.84857i	−0.343270	+	0.343270i	−0.857595	−	0.514325i	$-0.828042\pi$
$29$	−1.84857	+	1.84857i	−0.343270	+	0.343270i	0.514325	+	0.857595i	$0.328042\pi$
$30$		0			0
$31$			7.64329i			1.37278i	0.727236	+	0.686388i	$0.240805\pi$
$31$			7.64329i			1.37278i	−0.727236	+	0.686388i	$0.759195\pi$
$32$	1.98755	−	5.29619i	0.351352	−	0.936243i
$33$		0			0
$34$	4.70541	+	1.91201i	0.806970	+	0.327907i
$35$	−6.49135	+	7.11588i	−1.09724	+	1.20280i
$36$		0			0
$37$	1.90965	+	1.90965i	0.313945	+	0.313945i	0.846436	−	0.532491i	$-0.178744\pi$
$37$	1.90965	+	1.90965i	0.313945	+	0.313945i	−0.532491	+	0.846436i	$0.678744\pi$
$38$	−1.75941	+	0.742695i	−0.285413	+	0.120481i
$39$		0			0
$40$	2.02922	−	5.99018i	0.320848	−	0.947131i
$41$	−7.67058			−1.19794			−0.598972	−	0.800770i	$-0.704424\pi$
$41$	−7.67058			−1.19794			−0.598972	+	0.800770i	$0.704424\pi$
$42$		0			0
$43$	5.43308	−	5.43308i	0.828537	−	0.828537i	−0.158777	−	0.987314i	$-0.550755\pi$
$43$	5.43308	−	5.43308i	0.828537	−	0.828537i	0.987314	+	0.158777i	$0.0507552\pi$
$44$	12.0664	−	0.162586i	1.81907	−	0.0245108i
$45$		0			0
$46$	−8.55794	−	3.47746i	−1.26180	−	0.512723i
$47$			3.24864i			0.473863i	0.971526	+	0.236932i	$0.0761417\pi$
$47$			3.24864i			0.473863i	−0.971526	+	0.236932i	$0.923858\pi$
$48$		0			0
$49$	−11.5547			−1.65067
$50$	2.05066	−	6.76719i	0.290007	−	0.957025i
$51$		0			0
$52$	5.96546	−	0.0803806i	0.827261	−	0.0111468i
$53$	−6.08323	+	6.08323i	−0.835596	+	0.835596i	−0.988276	−	0.152680i	$-0.951210\pi$
$53$	−6.08323	+	6.08323i	−0.835596	+	0.835596i	0.152680	+	0.988276i	$0.451210\pi$
$54$		0			0
$55$	13.4776	−	0.618574i	1.81732	−	0.0834085i
$56$	11.1596	−	4.88894i	1.49126	−	0.653312i
$57$		0			0
$58$	3.40610	−	1.43781i	0.447243	−	0.188794i
$59$	2.97848	−	2.97848i	0.387765	−	0.387765i	−0.486125	−	0.873889i	$-0.661590\pi$
$59$	2.97848	−	2.97848i	0.387765	−	0.387765i	0.873889	+	0.486125i	$0.161590\pi$
$60$		0			0
$61$	−0.157020	−	0.157020i	−0.0201044	−	0.0201044i	0.696983	−	0.717088i	$-0.254525\pi$
$61$	−0.157020	−	0.157020i	−0.0201044	−	0.0201044i	−0.717088	+	0.696983i	$0.754525\pi$
$62$	4.06915	−	10.0141i	0.516782	−	1.27179i
$63$		0			0
$64$	−5.42364	+	5.88082i	−0.677955	+	0.735103i
$65$	6.66318	−	0.305816i	0.826466	−	0.0379318i
$66$		0			0
$67$	0.305394	+	0.305394i	0.0373098	+	0.0373098i	0.725516	−	0.688206i	$-0.241601\pi$
$67$	0.305394	+	0.305394i	0.0373098	+	0.0373098i	−0.688206	+	0.725516i	$0.741601\pi$
$68$	−5.14701	−	5.01014i	−0.624166	−	0.607569i
$69$		0			0
$70$	12.2932	−	5.86719i	1.46932	−	0.701264i
$71$			1.61808i			0.192030i	0.995380	+	0.0960152i	$0.0306097\pi$
$71$			1.61808i			0.192030i	−0.995380	+	0.0960152i	$0.969390\pi$
$72$		0			0
$73$	6.90696			0.808399			0.404199	−	0.914671i	$-0.367550\pi$
$73$	6.90696			0.808399			0.404199	+	0.914671i	$0.367550\pi$
$74$	−1.48532	−	3.51865i	−0.172665	−	0.409035i
$75$		0			0
$76$	2.70053	−	0.0363879i	0.309773	−	0.00417398i
$77$	18.3780	+	18.3780i	2.09436	+	2.09436i
$78$		0			0
$79$		−	5.39306i		−	0.606767i	−0.952869	−	0.303383i	$-0.901884\pi$
$79$		−	5.39306i		−	0.606767i	0.952869	−	0.303383i	$-0.0981163\pi$
$80$	−5.84771	+	6.76789i	−0.653793	+	0.756673i
$81$		0			0
$82$	10.0498	+	4.08368i	1.10982	+	0.450967i
$83$	−5.82210	+	5.82210i	−0.639059	+	0.639059i	−0.950323	−	0.311265i	$-0.899247\pi$
$83$	−5.82210	+	5.82210i	−0.639059	+	0.639059i	0.311265	+	0.950323i	$0.399247\pi$
$84$		0			0
$85$	−5.93291	−	5.41221i	−0.643515	−	0.587037i
$86$	−10.0108	+	4.22584i	−1.07949	+	0.455684i
$87$		0			0
$88$	−15.8957	−	6.21090i	−1.69448	−	0.662084i
$89$	7.74878			0.821369			0.410684	−	0.911778i	$-0.365290\pi$
$89$	7.74878			0.821369			0.410684	+	0.911778i	$0.365290\pi$
$90$		0			0
$91$	9.08585	+	9.08585i	0.952455	+	0.952455i
$92$	9.36110	+	9.11218i	0.975962	+	0.950011i
$93$		0			0
$94$	1.72952	−	4.25630i	0.178386	−	0.439004i
$95$	3.01639	−	0.138441i	0.309475	−	0.0142038i
$96$		0			0
$97$			9.34141i			0.948476i	0.880397	+	0.474238i	$0.157276\pi$
$97$			9.34141i			0.948476i	−0.880397	+	0.474238i	$0.842724\pi$
$98$	15.1387	+	6.15150i	1.52924	+	0.621396i
$99$		0			0
$100$	−6.28946	+	7.77449i	−0.628946	+	0.777449i
$101$	7.91178	+	7.91178i	0.787251	+	0.787251i	0.981043	−	0.193792i	$-0.0620786\pi$
$101$	7.91178	+	7.91178i	0.787251	+	0.787251i	−0.193792	+	0.981043i	$0.562079\pi$
$102$		0			0
$103$		−	16.1744i		−	1.59371i	−0.604172	−	0.796854i	$-0.706496\pi$
$103$		−	16.1744i		−	1.59371i	0.604172	−	0.796854i	$-0.293504\pi$
$104$	−7.85862	−	3.07059i	−0.770601	−	0.301096i
$105$		0			0
$106$	11.2087	−	4.73152i	1.08869	−	0.459566i
$107$	5.26603	+	5.26603i	0.509086	+	0.509086i	0.914246	−	0.405160i	$-0.132784\pi$
$107$	5.26603	+	5.26603i	0.509086	+	0.509086i	−0.405160	+	0.914246i	$0.632784\pi$
$108$		0			0
$109$	−11.9434	−	11.9434i	−1.14397	−	1.14397i	−0.987718	−	0.156248i	$-0.950060\pi$
$109$	−11.9434	−	11.9434i	−1.14397	−	1.14397i	−0.156248	−	0.987718i	$-0.549940\pi$
$110$	−17.9874	−	6.36481i	−1.71504	−	0.606861i
$111$		0			0
$112$	−17.2238	+	0.464243i	−1.62750	+	0.0438668i
$113$	−18.0886			−1.70163			−0.850815	−	0.525466i	$-0.823891\pi$
$113$	−18.0886			−1.70163			−0.850815	+	0.525466i	$0.823891\pi$
$114$		0			0
$115$	10.7905	+	9.84344i	1.00622	+	0.917906i
$116$	−5.22806	+	0.0704446i	−0.485413	+	0.00654062i
$117$		0			0
$118$	−5.48802	+	2.31665i	−0.505214	+	0.213265i
$119$		−	15.4701i		−	1.41814i
$120$		0			0
$121$		−	25.4059i		−	2.30963i
$122$	0.122130	+	0.289319i	0.0110571	+	0.0261937i
$123$		0			0
$124$	−10.6626	+	10.9539i	−0.957532	+	0.983689i
$125$	−6.74664	+	8.91531i	−0.603438	+	0.797410i
$126$		0			0
$127$	7.28333			0.646291			0.323145	−	0.946349i	$-0.395260\pi$
$127$	7.28333			0.646291			0.323145	+	0.946349i	$0.395260\pi$
$128$	10.2368	−	4.81748i	0.904813	−	0.425810i
$129$		0			0
$130$	−8.89277	−	3.14668i	−0.779948	−	0.275982i
$131$	−9.89718	−	9.89718i	−0.864721	−	0.864721i	0.127161	−	0.991882i	$-0.459413\pi$
$131$	−9.89718	−	9.89718i	−0.864721	−	0.864721i	−0.991882	+	0.127161i	$0.959413\pi$
$132$		0			0
$133$	4.11312	+	4.11312i	0.356652	+	0.356652i
$134$	−0.237535	−	0.562707i	−0.0205199	−	0.0486105i
$135$		0			0
$136$	4.07619	+	9.30436i	0.349530	+	0.797842i
$137$		−	17.7974i		−	1.52054i	−0.649608	−	0.760269i	$-0.725067\pi$
$137$		−	17.7974i		−	1.52054i	0.649608	−	0.760269i	$-0.274933\pi$
$138$		0			0
$139$	4.98268	+	4.98268i	0.422625	+	0.422625i	0.886107	−	0.463481i	$-0.153400\pi$
$139$	4.98268	+	4.98268i	0.422625	+	0.422625i	−0.463481	+	0.886107i	$0.653400\pi$
$140$	−19.2299	+	1.14240i	−1.62522	+	0.0965502i
$141$		0			0
$142$	0.861435	−	2.11997i	0.0722900	−	0.177904i
$143$		−	17.9986i		−	1.50512i
$144$		0			0
$145$	−5.83953	+	0.268013i	−0.484947	+	0.0222573i
$146$	−9.04936	−	3.67714i	−0.748930	−	0.304322i
$147$		0			0
$148$	0.0727725	+	5.40082i	0.00598186	+	0.443945i
$149$	−9.78188	−	9.78188i	−0.801363	−	0.801363i	0.181946	−	0.983309i	$-0.441760\pi$
$149$	−9.78188	−	9.78188i	−0.801363	−	0.801363i	−0.983309	+	0.181946i	$0.941760\pi$
$150$		0			0
$151$	−12.0108			−0.977422			−0.488711	−	0.872446i	$-0.662533\pi$
$151$	−12.0108			−0.977422			−0.488711	+	0.872446i	$0.662533\pi$
$152$	−3.55756	−	1.39004i	−0.288556	−	0.112747i
$153$		0			0
$154$	−14.2943	−	33.8625i	−1.15187	−	2.72872i
$155$	−11.5183	+	12.6265i	−0.925173	+	1.01418i
$156$		0			0
$157$	8.81467	−	8.81467i	0.703488	−	0.703488i	−0.261670	−	0.965157i	$-0.584273\pi$
$157$	8.81467	−	8.81467i	0.703488	−	0.703488i	0.965157	+	0.261670i	$0.0842732\pi$
$158$	−2.87117	+	7.06588i	−0.228418	+	0.562131i
$159$		0			0
$160$	11.2646	−	5.75394i	0.890548	−	0.454889i
$161$			28.1362i			2.21744i
$162$		0			0
$163$	8.90000	+	8.90000i	0.697102	+	0.697102i	0.963784	−	0.266682i	$-0.0859275\pi$
$163$	8.90000	+	8.90000i	0.697102	+	0.697102i	−0.266682	+	0.963784i	$0.585927\pi$
$164$	−10.9930	−	10.7007i	−0.858410	−	0.835584i
$165$		0			0
$166$	10.7276	−	4.52841i	0.832621	−	0.351473i
$167$	4.24306			0.328338			0.164169	−	0.986432i	$-0.447506\pi$
$167$	4.24306			0.328338			0.164169	+	0.986432i	$0.447506\pi$
$168$		0			0
$169$			4.10170i			0.315515i
$170$	4.89182	+	10.2495i	0.375185	+	0.786104i
$171$		0			0
$172$	15.3657	−	0.207042i	1.17162	−	0.0157868i
$173$	−4.03165	−	4.03165i	−0.306521	−	0.306521i	0.537037	−	0.843558i	$-0.319543\pi$
$173$	−4.03165	−	4.03165i	−0.306521	−	0.306521i	−0.843558	+	0.537037i	$0.819543\pi$
$174$		0			0
$175$	−21.4470	+	1.97284i	−1.62124	+	0.149132i
$176$	17.5196	+	16.5999i	1.32059	+	1.25127i
$177$		0			0
$178$	−10.1523	−	4.12531i	−0.760946	−	0.309205i
$179$	−0.833880	−	0.833880i	−0.0623272	−	0.0623272i	0.675256	−	0.737583i	$-0.264033\pi$
$179$	−0.833880	−	0.833880i	−0.0623272	−	0.0623272i	−0.737583	+	0.675256i	$0.764033\pi$
$180$		0			0
$181$	−10.5947	+	10.5947i	−0.787501	+	0.787501i	−0.981084	−	0.193583i	$-0.937989\pi$
$181$	−10.5947	+	10.5947i	−0.787501	+	0.787501i	0.193583	+	0.981084i	$0.437989\pi$
$182$	−7.06695	−	16.7412i	−0.523837	−	1.24094i
$183$		0			0
$184$	−7.41355	−	16.9223i	−0.546534	−	1.24753i
$185$	0.276870	+	6.03250i	0.0203559	+	0.443518i
$186$		0			0
$187$	−15.3228	+	15.3228i	−1.12051	+	1.12051i
$188$	−4.53196	+	4.65575i	−0.330527	+	0.339556i
$189$		0			0
$190$	−4.02571	−	1.42449i	−0.292056	−	0.103343i
$191$	−3.83158			−0.277244			−0.138622	−	0.990345i	$-0.544267\pi$
$191$	−3.83158			−0.277244			−0.138622	+	0.990345i	$0.544267\pi$
$192$		0			0
$193$			5.03272i			0.362263i	0.983459	+	0.181132i	$0.0579760\pi$
$193$			5.03272i			0.362263i	−0.983459	+	0.181132i	$0.942024\pi$
$194$	4.97320	−	12.2389i	0.357055	−	0.878703i
$195$		0			0
$196$	−16.5595	−	16.1191i	−1.18282	−	1.15137i
$197$	7.01759	−	7.01759i	0.499982	−	0.499982i	−0.411450	−	0.911432i	$-0.634978\pi$
$197$	7.01759	−	7.01759i	0.499982	−	0.499982i	0.911432	+	0.411450i	$0.134978\pi$
$198$		0			0
$199$	13.7542			0.975009			0.487504	−	0.873121i	$-0.337907\pi$
$199$	13.7542			0.975009			0.487504	+	0.873121i	$0.337907\pi$
$200$	12.3793	−	6.83759i	0.875350	−	0.483490i
$201$		0			0
$202$	−6.15376	−	14.5779i	−0.432977	−	1.02570i
$203$	−7.96273	−	7.96273i	−0.558874	−	0.558874i
$204$		0			0
$205$	−12.6716	−	11.5594i	−0.885020	−	0.807346i
$206$	−8.61094	+	21.1913i	−0.599953	+	1.47647i
$207$		0			0
$208$	8.66147	+	8.20681i	0.600565	+	0.569040i
$209$		−	8.14789i		−	0.563601i
$210$		0			0
$211$	12.8000	−	12.8000i	0.881190	−	0.881190i	−0.112466	−	0.993656i	$-0.535875\pi$
$211$	12.8000	−	12.8000i	0.881190	−	0.881190i	0.993656	+	0.112466i	$0.0358748\pi$
$212$	−17.2044	+	0.231818i	−1.18160	+	0.0159213i
$213$		0			0
$214$	−4.09590	−	9.70298i	−0.279990	−	0.663282i
$215$	17.1628	−	0.787712i	1.17050	−	0.0537215i
$216$		0			0
$217$	−32.9236			−2.23500
$218$	9.28951	+	22.0064i	0.629165	+	1.49046i
$219$		0			0
$220$	20.1783	+	17.9152i	1.36042	+	1.20784i
$221$	−7.57539	+	7.57539i	−0.509576	+	0.509576i
$222$		0			0
$223$	−12.7040			−0.850723			−0.425362	−	0.905023i	$-0.639853\pi$
$223$	−12.7040			−0.850723			−0.425362	+	0.905023i	$0.639853\pi$
$224$	22.8134	+	8.56140i	1.52429	+	0.572033i
$225$		0			0
$226$	23.6993	+	9.63002i	1.57645	+	0.640580i
$227$	−13.3440	+	13.3440i	−0.885675	+	0.885675i	−0.994104	−	0.108429i	$-0.965418\pi$
$227$	−13.3440	+	13.3440i	−0.885675	+	0.885675i	0.108429	+	0.994104i	$0.465418\pi$
$228$		0			0
$229$	−1.09552	+	1.09552i	−0.0723941	+	0.0723941i	−0.742377	−	0.669983i	$-0.766302\pi$
$229$	−1.09552	+	1.09552i	−0.0723941	+	0.0723941i	0.669983	+	0.742377i	$0.266302\pi$
$230$	−8.89697	−	18.6413i	−0.586649	−	1.22917i
$231$		0			0
$232$	6.88720	+	2.69103i	0.452167	+	0.176675i
$233$		−	17.1156i		−	1.12128i	−0.828060	−	0.560640i	$-0.810555\pi$
$233$		−	17.1156i		−	1.12128i	0.828060	−	0.560640i	$-0.189445\pi$
$234$		0			0
$235$	−4.89565	+	5.36665i	−0.319357	+	0.350082i
$236$	8.42364	−	0.113503i	0.548332	−	0.00738841i
$237$		0			0
$238$	−8.23600	+	20.2686i	−0.533861	+	1.31382i
$239$	17.8555			1.15498			0.577488	−	0.816399i	$-0.304033\pi$
$239$	17.8555			1.15498			0.577488	+	0.816399i	$0.304033\pi$
$240$		0			0
$241$	5.11525			0.329502			0.164751	−	0.986335i	$-0.447318\pi$
$241$	5.11525			0.329502			0.164751	+	0.986335i	$0.447318\pi$
$242$	−13.5256	+	33.2863i	−0.869461	+	2.13972i
$243$		0			0
$244$	−0.00598368	−	0.444080i	−0.000383066	−	0.0284293i
$245$	−19.0880	−	17.4127i	−1.21949	−	1.11246i
$246$		0			0
$247$		−	4.02822i		−	0.256309i
$248$	19.8016	−	8.67498i	1.25740	−	0.550862i
$249$		0			0
$250$	13.5857	−	8.08887i	0.859233	−	0.511585i
$251$	4.02622	−	4.02622i	0.254133	−	0.254133i	−0.568530	−	0.822663i	$-0.692488\pi$
$251$	4.02622	−	4.02622i	0.254133	−	0.254133i	0.822663	+	0.568530i	$0.192488\pi$
$252$		0			0
$253$	27.8682	−	27.8682i	1.75206	−	1.75206i
$254$	−9.54246	−	3.87751i	−0.598747	−	0.243297i
$255$		0			0
$256$	−15.9768	+	0.861887i	−0.998548	+	0.0538680i
$257$	−29.1773			−1.82003			−0.910016	−	0.414573i	$-0.863931\pi$
$257$	−29.1773			−1.82003			−0.910016	+	0.414573i	$0.863931\pi$
$258$		0			0
$259$	−8.22585	+	8.22585i	−0.511130	+	0.511130i
$260$	9.97589	+	8.85707i	0.618678	+	0.549292i
$261$		0			0
$262$	7.69800	+	18.2362i	0.475584	+	1.12663i
$263$	1.92706			0.118828			0.0594139	−	0.998233i	$-0.481077\pi$
$263$	1.92706			0.118828			0.0594139	+	0.998233i	$0.481077\pi$
$264$		0			0
$265$	−19.2166	+	0.881973i	−1.18047	+	0.0541792i
$266$	−3.19917	−	7.57867i	−0.196154	−	0.464678i
$267$		0			0
$268$	0.0116379	+	0.863706i	0.000710895	+	0.0527592i
$269$	9.93701	−	9.93701i	0.605870	−	0.605870i	−0.335994	−	0.941864i	$-0.609072\pi$
$269$	9.93701	−	9.93701i	0.605870	−	0.605870i	0.941864	+	0.335994i	$0.109072\pi$
$270$		0			0
$271$		−	15.0777i		−	0.915907i	−0.888976	−	0.457954i	$-0.848583\pi$
$271$		−	15.0777i		−	0.915907i	0.888976	−	0.457954i	$-0.151417\pi$
$272$	−0.387066	−	14.3605i	−0.0234693	−	0.870731i
$273$		0			0
$274$	−9.47504	+	23.3178i	−0.572408	+	1.40868i
$275$	23.1968	+	19.2887i	1.39882	+	1.16315i
$276$		0			0
$277$	4.33837	+	4.33837i	0.260667	+	0.260667i	0.825325	−	0.564658i	$-0.190992\pi$
$277$	4.33837	+	4.33837i	0.260667	+	0.260667i	−0.564658	+	0.825325i	$0.690992\pi$
$278$	−3.87551	−	9.18089i	−0.232438	−	0.550633i
$279$		0			0
$280$	25.8028	+	8.74090i	1.54201	+	0.522369i
$281$	2.93138			0.174871			0.0874357	−	0.996170i	$-0.472133\pi$
$281$	2.93138			0.174871			0.0874357	+	0.996170i	$0.472133\pi$
$282$		0			0
$283$	12.3064	−	12.3064i	0.731542	−	0.731542i	−0.239383	−	0.970925i	$-0.576945\pi$
$283$	12.3064	−	12.3064i	0.731542	−	0.731542i	0.970925	+	0.239383i	$0.0769452\pi$
$284$	−2.25727	+	2.31893i	−0.133944	+	0.137603i
$285$		0			0
$286$	−9.58215	+	23.5814i	−0.566604	+	1.39440i
$287$		−	33.0411i		−	1.95036i
$288$		0			0
$289$	−4.10170			−0.241276
$290$	7.79352	+	2.75772i	0.457651	+	0.161939i
$291$		0			0
$292$	9.89863	+	9.63543i	0.579274	+	0.563871i
$293$	15.2191	−	15.2191i	0.889109	−	0.889109i	−0.105328	−	0.994437i	$-0.533589\pi$
$293$	15.2191	−	15.2191i	0.889109	−	0.889109i	0.994437	+	0.105328i	$0.0335894\pi$
$294$		0			0
$295$	9.40886	−	0.431832i	0.547805	−	0.0251422i
$296$	2.77996	−	7.11479i	0.161582	−	0.413539i
$297$		0			0
$298$	7.60832	+	18.0237i	0.440738	+	1.04409i
$299$	13.7777	−	13.7777i	0.796786	−	0.796786i
$300$		0			0
$301$	23.4031	+	23.4031i	1.34893	+	1.34893i
$302$	15.7363	+	6.39432i	0.905520	+	0.367952i
$303$		0			0
$304$	3.92100	+	3.71518i	0.224885	+	0.213080i
$305$	−0.0227655	−	0.496019i	−0.00130355	−	0.0284020i
$306$		0			0
$307$	−3.79402	−	3.79402i	−0.216536	−	0.216536i	0.590501	−	0.807037i	$-0.298930\pi$
$307$	−3.79402	−	3.79402i	−0.216536	−	0.216536i	−0.807037	+	0.590501i	$0.798930\pi$
$308$	0.700342	+	51.9760i	0.0399057	+	2.96161i
$309$		0			0
$310$	21.8132	−	10.4108i	1.23890	−	0.591294i
$311$		−	18.1916i		−	1.03155i	−0.856724	−	0.515775i	$-0.827504\pi$
$311$		−	18.1916i		−	1.03155i	0.856724	−	0.515775i	$-0.172496\pi$
$312$		0			0
$313$	−16.7785			−0.948377			−0.474188	−	0.880423i	$-0.657258\pi$
$313$	−16.7785			−0.948377			−0.474188	+	0.880423i	$0.657258\pi$
$314$	−16.2416	+	6.85603i	−0.916565	+	0.386908i
$315$		0			0
$316$	7.52349	−	7.72901i	0.423229	−	0.434791i
$317$	−0.103425	−	0.103425i	−0.00580894	−	0.00580894i	0.704196	−	0.710005i	$-0.251307\pi$
$317$	−0.103425	−	0.103425i	−0.00580894	−	0.00580894i	−0.710005	+	0.704196i	$0.751307\pi$
$318$		0			0
$319$			15.7738i			0.883163i
$320$	−17.8220	+	1.54159i	−0.996280	+	0.0861777i
$321$		0			0
$322$	14.9792	−	36.8634i	0.834758	−	2.05432i
$323$	−3.42934	+	3.42934i	−0.190814	+	0.190814i
$324$		0			0
$325$	11.4682	+	9.53611i	0.636143	+	0.528968i
$326$	−6.92240	−	16.3988i	−0.383396	−	0.908246i
$327$		0			0
$328$	8.70595	+	19.8723i	0.480706	+	1.09726i
$329$	−13.9936			−0.771490
$330$		0			0
$331$	2.18428	+	2.18428i	0.120059	+	0.120059i	0.764583	−	0.644525i	$-0.222945\pi$
$331$	2.18428	+	2.18428i	0.120059	+	0.120059i	−0.644525	+	0.764583i	$0.722945\pi$
$332$	−16.4659	+	0.221867i	−0.903683	+	0.0121765i
$333$		0			0
$334$	−5.55917	−	2.25893i	−0.304184	−	0.123603i
$335$	0.0442773	+	0.964725i	0.00241913	+	0.0527085i
$336$		0			0
$337$		−	20.9206i		−	1.13962i	−0.821778	−	0.569808i	$-0.807018\pi$
$337$		−	20.9206i		−	1.13962i	0.821778	−	0.569808i	$-0.192982\pi$
$338$	2.18367	−	5.37396i	0.118776	−	0.292305i
$339$		0			0
$340$	−0.952482	−	16.0331i	−0.0516556	−	0.869515i
$341$	32.6100	+	32.6100i	1.76593	+	1.76593i
$342$		0			0
$343$		−	19.6193i		−	1.05934i
$344$	−20.2420	−	7.90915i	−1.09138	−	0.426433i
$345$		0			0
$346$	3.13581	+	7.42857i	0.168582	+	0.399362i
$347$	4.34853	+	4.34853i	0.233441	+	0.233441i	0.814127	−	0.580686i	$-0.197216\pi$
$347$	4.34853	+	4.34853i	0.233441	+	0.233441i	−0.580686	+	0.814127i	$0.697216\pi$
$348$		0			0
$349$	3.70979	+	3.70979i	0.198580	+	0.198580i	0.799391	−	0.600811i	$-0.205155\pi$
$349$	3.70979	+	3.70979i	0.198580	+	0.198580i	−0.600811	+	0.799391i	$0.705155\pi$
$350$	29.1497	+	8.83324i	1.55812	+	0.472157i
$351$		0			0
$352$	−14.1163	−	31.0760i	−0.752401	−	1.65636i
$353$	16.3398			0.869681			0.434840	−	0.900508i	$-0.356805\pi$
$353$	16.3398			0.869681			0.434840	+	0.900508i	$0.356805\pi$
$354$		0			0
$355$	−2.43842	+	2.67301i	−0.129418	+	0.141869i
$356$	11.1051	+	10.8098i	0.588568	+	0.572917i
$357$		0			0
$358$	0.648590	+	1.53648i	0.0342790	+	0.0812053i
$359$			24.6929i			1.30324i	0.758545	+	0.651621i	$0.225911\pi$
$359$			24.6929i			1.30324i	−0.758545	+	0.651621i	$0.774089\pi$
$360$		0			0
$361$			17.1764i			0.904024i
$362$	19.5215	−	8.24056i	1.02603	−	0.433114i
$363$		0			0
$364$	0.346241	+	25.6963i	0.0181479	+	1.34685i
$365$	11.4101	+	10.4087i	0.597231	+	0.544815i
$366$		0			0
$367$	−6.68177			−0.348786			−0.174393	−	0.984676i	$-0.555796\pi$
$367$	−6.68177			−0.348786			−0.174393	+	0.984676i	$0.555796\pi$
$368$	0.703974	+	26.1180i	0.0366972	+	1.36150i
$369$		0			0
$370$	2.84885	−	8.05106i	0.148104	−	0.418555i
$371$	−26.2036	−	26.2036i	−1.36042	−	1.36042i
$372$		0			0
$373$	−18.9638	−	18.9638i	−0.981911	−	0.981911i	0.0179284	−	0.999839i	$-0.494293\pi$
$373$	−18.9638	−	18.9638i	−0.981911	−	0.981911i	−0.999839	+	0.0179284i	$0.994293\pi$
$374$	28.2331	−	11.9180i	1.45990	−	0.616265i
$375$		0			0
$376$	8.41631	−	3.68714i	0.434038	−	0.190150i
$377$			7.79837i			0.401636i
$378$		0			0
$379$	−17.4207	−	17.4207i	−0.894843	−	0.894843i	0.100131	−	0.994974i	$-0.468074\pi$
$379$	−17.4207	−	17.4207i	−0.894843	−	0.894843i	−0.994974	+	0.100131i	$0.968074\pi$
$380$	4.51603	+	4.00955i	0.231668	+	0.205686i
$381$		0			0
$382$	5.02006	+	2.03986i	0.256849	+	0.104369i
$383$		−	10.4542i		−	0.534182i	−0.963671	−	0.267091i	$-0.913938\pi$
$383$		−	10.4542i		−	0.534182i	0.963671	−	0.267091i	$-0.0860625\pi$
$384$		0			0
$385$	2.66452	+	58.0551i	0.135796	+	2.95876i
$386$	2.67933	−	6.59376i	0.136374	−	0.335614i
$387$		0			0
$388$	−13.0316	+	13.3875i	−0.661577	+	0.679649i
$389$	6.71454	+	6.71454i	0.340441	+	0.340441i	0.856533	−	0.516092i	$-0.172614\pi$
$389$	6.71454	+	6.71454i	0.340441	+	0.340441i	−0.516092	+	0.856533i	$0.672614\pi$
$390$		0			0
$391$	−23.4587			−1.18636
$392$	13.1143	+	29.9349i	0.662373	+	1.51194i
$393$		0			0
$394$	−12.9303	+	5.45826i	−0.651421	+	0.274983i
$395$	8.12726	−	8.90917i	0.408927	−	0.448269i
$396$		0			0
$397$	−25.8345	+	25.8345i	−1.29660	+	1.29660i	−0.365968	+	0.930628i	$0.619262\pi$
$397$	−25.8345	+	25.8345i	−1.29660	+	1.29660i	−0.930628	+	0.365968i	$0.880738\pi$
$398$	−18.0205	−	7.32248i	−0.903284	−	0.367043i
$399$		0			0
$400$	−19.8593	+	2.36794i	−0.992966	+	0.118397i
$401$		−	18.5375i		−	0.925717i	−0.886432	−	0.462858i	$-0.846824\pi$
$401$		−	18.5375i		−	0.925717i	0.886432	−	0.462858i	$-0.153176\pi$
$402$		0			0
$403$	16.1220	+	16.1220i	0.803094	+	0.803094i
$404$	0.301500	+	22.3759i	0.0150002	+	1.11324i
$405$		0			0
$406$	6.19339	+	14.6718i	0.307373	+	0.728150i
$407$	16.2950			0.807715
$408$		0			0
$409$			6.45252i			0.319057i	0.987193	+	0.159528i	$0.0509973\pi$
$409$			6.45252i			0.319057i	−0.987193	+	0.159528i	$0.949003\pi$
$410$	10.4480	+	21.8910i	0.515988	+	1.08112i
$411$		0			0
$412$	22.5638	−	23.1801i	1.11164	−	1.14200i
$413$	12.8298	+	12.8298i	0.631315	+	0.631315i
$414$		0			0
$415$	−18.3917	+	0.844113i	−0.902815	+	0.0414359i
$416$	−6.97892	−	15.3636i	−0.342170	−	0.753263i
$417$		0			0
$418$	−4.33779	+	10.6752i	−0.212168	+	0.522141i
$419$	12.0000	+	12.0000i	0.586236	+	0.586236i	0.936610	−	0.350374i	$-0.113945\pi$
$419$	12.0000	+	12.0000i	0.586236	+	0.586236i	−0.350374	+	0.936610i	$0.613945\pi$
$420$		0			0
$421$	23.9012	−	23.9012i	1.16487	−	1.16487i	0.181478	−	0.983395i	$-0.441912\pi$
$421$	23.9012	−	23.9012i	1.16487	−	1.16487i	0.983395	−	0.181478i	$-0.0580882\pi$
$422$	−23.5848	+	9.95582i	−1.14809	+	0.484642i
$423$		0			0
$424$	22.6643	+	8.85560i	1.10067	+	0.430066i
$425$	−1.64487	−	17.8816i	−0.0797877	−	0.867386i
$426$		0			0
$427$	0.676366	−	0.676366i	0.0327317	−	0.0327317i
$428$	0.200676	+	14.8932i	0.00970005	+	0.719891i
$429$		0			0
$430$	−22.9058	−	8.10515i	−1.10461	−	0.390865i
$431$	−12.5590			−0.604944			−0.302472	−	0.953158i	$-0.597812\pi$
$431$	−12.5590			−0.604944			−0.302472	+	0.953158i	$0.597812\pi$
$432$		0			0
$433$		−	4.64837i		−	0.223386i	−0.993743	−	0.111693i	$-0.964373\pi$
$433$		−	4.64837i		−	0.223386i	0.993743	−	0.111693i	$-0.0356274\pi$
$434$	43.1358	+	17.5279i	2.07058	+	0.841367i
$435$		0			0
$436$	−0.455134	−	33.7778i	−0.0217970	−	1.61767i
$437$	6.23710	−	6.23710i	0.298361	−	0.298361i
$438$		0			0
$439$	7.09686			0.338715			0.169357	−	0.985555i	$-0.445831\pi$
$439$	7.09686			0.338715			0.169357	+	0.985555i	$0.445831\pi$
$440$	−16.8994	−	34.2147i	−0.805647	−	1.63112i
$441$		0			0
$442$	13.9581	−	5.89212i	0.663920	−	0.280259i
$443$	−16.7044	−	16.7044i	−0.793649	−	0.793649i	0.188436	−	0.982085i	$-0.439658\pi$
$443$	−16.7044	−	16.7044i	−0.793649	−	0.793649i	−0.982085	+	0.188436i	$0.939658\pi$
$444$		0			0
$445$	12.8007	+	11.6773i	0.606813	+	0.553556i
$446$	16.6445	+	6.76338i	0.788141	+	0.320255i
$447$		0			0
$448$	−25.3317	−	23.3624i	−1.19681	−	1.10377i
$449$		−	22.3540i		−	1.05495i	−0.849571	−	0.527475i	$-0.823139\pi$
$449$		−	22.3540i		−	1.05495i	0.849571	−	0.527475i	$-0.176861\pi$
$450$		0			0
$451$	−32.7265	+	32.7265i	−1.54103	+	1.54103i
$452$	−25.9234	−	25.2341i	−1.21934	−	1.18691i
$453$		0			0
$454$	24.5872	−	10.3790i	1.15393	−	0.487109i
$455$	1.31731	+	28.7018i	0.0617562	+	1.34556i
$456$		0			0
$457$	28.9883			1.35602			0.678008	−	0.735055i	$-0.262844\pi$
$457$	28.9883			1.35602			0.678008	+	0.735055i	$0.262844\pi$
$458$	2.01856	−	0.852093i	0.0943213	−	0.0398157i
$459$		0			0
$460$	1.73232	+	29.1601i	0.0807700	+	1.35959i
$461$	3.75610	−	3.75610i	0.174939	−	0.174939i	−0.614206	−	0.789146i	$-0.710524\pi$
$461$	3.75610	−	3.75610i	0.174939	−	0.174939i	0.789146	+	0.614206i	$0.210524\pi$
$462$		0			0
$463$	18.4896			0.859286			0.429643	−	0.902999i	$-0.358639\pi$
$463$	18.4896			0.859286			0.429643	+	0.902999i	$0.358639\pi$
$464$	−7.59081	−	7.19235i	−0.352395	−	0.333897i
$465$		0			0
$466$	−9.11203	+	22.4245i	−0.422107	+	1.03879i
$467$	−17.8623	+	17.8623i	−0.826570	+	0.826570i	−0.987041	−	0.160471i	$-0.948699\pi$
$467$	−17.8623	+	17.8623i	−0.826570	+	0.826570i	0.160471	+	0.987041i	$0.448699\pi$
$468$		0			0
$469$	−1.31549	+	1.31549i	−0.0607436	+	0.0607436i
$470$	9.27129	−	4.42492i	0.427653	−	0.204106i
$471$		0			0
$472$	−11.0969	−	4.33588i	−0.510776	−	0.199575i
$473$		−	46.3604i		−	2.13165i
$474$		0			0
$475$	5.19161	+	4.31695i	0.238207	+	0.198075i
$476$	21.5813	−	22.1708i	0.989176	−	1.01620i
$477$		0			0
$478$	−23.3939	−	9.50594i	−1.07001	−	0.434792i
$479$	−21.2617			−0.971474			−0.485737	−	0.874105i	$-0.661449\pi$
$479$	−21.2617			−0.971474			−0.485737	+	0.874105i	$0.661449\pi$
$480$		0			0
$481$	8.05606			0.367325
$482$	−6.70190	−	2.72327i	−0.305263	−	0.124041i
$483$		0			0
$484$	35.4420	−	36.4102i	1.61100	−	1.65501i
$485$	−14.0773	+	15.4317i	−0.639219	+	0.700718i
$486$		0			0
$487$		−	38.2041i		−	1.73119i	−0.500744	−	0.865595i	$-0.666940\pi$
$487$		−	38.2041i		−	1.73119i	0.500744	−	0.865595i	$-0.333060\pi$
$488$	−0.228580	+	0.585010i	−0.0103473	+	0.0264821i
$489$		0			0
$490$	15.7384	+	32.9759i	0.710990	+	1.48970i
$491$	11.2555	−	11.2555i	0.507953	−	0.507953i	−0.405945	−	0.913898i	$-0.633057\pi$
$491$	11.2555	−	11.2555i	0.507953	−	0.507953i	0.913898	+	0.405945i	$0.133057\pi$
$492$		0			0
$493$	6.63898	−	6.63898i	0.299005	−	0.299005i
$494$	−2.14455	+	5.27769i	−0.0964879	+	0.237454i
$495$		0			0
$496$	−30.5621	+	0.823756i	−1.37228	+	0.0369877i
$497$	−6.96989			−0.312642
$498$		0			0
$499$	19.2924	−	19.2924i	0.863646	−	0.863646i	−0.128114	−	0.991759i	$-0.540892\pi$
$499$	19.2924	−	19.2924i	0.863646	−	0.863646i	0.991759	+	0.128114i	$0.0408923\pi$
$500$	−22.1060	+	3.36510i	−0.988611	+	0.150492i
$501$		0			0
$502$	−7.41856	+	3.13159i	−0.331107	+	0.139770i
$503$	−27.8587			−1.24216			−0.621078	−	0.783748i	$-0.713305\pi$
$503$	−27.8587			−1.24216			−0.621078	+	0.783748i	$0.713305\pi$
$504$		0			0
$505$	1.14708	+	24.9929i	0.0510445	+	1.11217i
$506$	−51.3489	+	21.6758i	−2.28274	+	0.963608i
$507$		0			0
$508$	10.4380	+	10.1605i	0.463112	+	0.450798i
$509$	−0.475925	+	0.475925i	−0.0210950	+	0.0210950i	−0.717576	−	0.696481i	$-0.754748\pi$
$509$	−0.475925	+	0.475925i	−0.0210950	+	0.0210950i	0.696481	+	0.717576i	$0.254748\pi$
$510$		0			0
$511$			29.7518i			1.31614i
$512$	21.3913	+	7.37652i	0.945370	+	0.325999i
$513$		0			0
$514$	38.2275	+	15.5335i	1.68614	+	0.685153i
$515$	24.3745	−	26.7196i	1.07407	−	1.17740i
$516$		0			0
$517$	13.8603	+	13.8603i	0.609575	+	0.609575i
$518$	15.1566	−	6.39805i	0.665945	−	0.281114i
$519$		0			0
$520$	−8.35486	−	16.9153i	−0.366385	−	0.741786i
$521$	28.2023			1.23557			0.617783	−	0.786348i	$-0.288031\pi$
$521$	28.2023			1.23557			0.617783	+	0.786348i	$0.288031\pi$
$522$		0			0
$523$	−10.5066	+	10.5066i	−0.459420	+	0.459420i	−0.898465	−	0.439045i	$-0.855317\pi$
$523$	−10.5066	+	10.5066i	−0.459420	+	0.459420i	0.439045	+	0.898465i	$0.355317\pi$
$524$	−0.377159	−	27.9909i	−0.0164763	−	1.22279i
$525$		0			0
$526$	−2.52480	−	1.02593i	−0.110086	−	0.0447328i
$527$		−	27.4503i		−	1.19575i
$528$		0			0
$529$	19.6655			0.855022
$530$	25.6468	+	9.07505i	1.11403	+	0.394195i
$531$		0			0
$532$	0.156741	+	11.6326i	0.00679560	+	0.504337i
$533$	−16.1796	+	16.1796i	−0.700815	+	0.700815i
$534$		0			0
$535$	0.763491	+	16.6351i	0.0330086	+	0.719199i
$536$	0.444574	−	1.13781i	0.0192027	−	0.0491457i
$537$		0			0
$538$	−18.3095	+	7.72898i	−0.789380	+	0.333220i
$539$	−49.2979	+	49.2979i	−2.12341	+	2.12341i
$540$		0			0
$541$	−12.4368	−	12.4368i	−0.534698	−	0.534698i	0.387269	−	0.921967i	$-0.373419\pi$
$541$	−12.4368	−	12.4368i	−0.534698	−	0.534698i	−0.921967	+	0.387269i	$0.873419\pi$
$542$	−8.02711	+	19.7545i	−0.344794	+	0.848530i
$543$		0			0
$544$	−7.13813	+	19.0209i	−0.306045	+	0.815512i
$545$	−1.73160	−	37.7285i	−0.0741736	−	1.61611i
$546$		0			0
$547$	−5.78283	−	5.78283i	−0.247256	−	0.247256i	0.572588	−	0.819844i	$-0.305940\pi$
$547$	−5.78283	−	5.78283i	−0.247256	−	0.247256i	−0.819844	+	0.572588i	$0.805940\pi$
$548$	24.8280	−	25.5062i	1.06060	−	1.08957i
$549$		0			0
$550$	−20.1230	−	37.6213i	−0.858049	−	1.60418i
$551$			3.53028i			0.150395i
$552$		0			0
$553$	23.2307			0.987870
$554$	−3.37437	−	7.99371i	−0.143363	−	0.339620i
$555$		0			0
$556$	0.189878	+	14.0919i	0.00805264	+	0.597628i
$557$	12.9551	+	12.9551i	0.548924	+	0.548924i	0.926130	−	0.377205i	$-0.123115\pi$
$557$	12.9551	+	12.9551i	0.548924	+	0.548924i	−0.377205	+	0.926130i	$0.623115\pi$
$558$		0			0
$559$		−	22.9200i		−	0.969413i
$560$	−29.1528	−	25.1891i	−1.23193	−	1.06443i
$561$		0			0
$562$	−3.84063	−	1.56061i	−0.162007	−	0.0658305i
$563$	−14.1388	+	14.1388i	−0.595881	+	0.595881i	−0.939214	−	0.343333i	$-0.888444\pi$
$563$	−14.1388	+	14.1388i	−0.595881	+	0.595881i	0.343333	+	0.939214i	$0.388444\pi$
$564$		0			0
$565$	−29.8817	−	27.2592i	−1.25713	−	1.14680i
$566$	−22.6754	+	9.57192i	−0.953117	+	0.402338i
$567$		0			0
$568$	4.19198	−	1.83648i	0.175892	−	0.0770572i
$569$	−1.34936			−0.0565679			−0.0282840	−	0.999600i	$-0.509004\pi$
$569$	−1.34936			−0.0565679			−0.0282840	+	0.999600i	$0.509004\pi$
$570$		0			0
$571$	−32.6417	−	32.6417i	−1.36601	−	1.36601i	−0.866045	−	0.499967i	$-0.833346\pi$
$571$	−32.6417	−	32.6417i	−1.36601	−	1.36601i	−0.499967	−	0.866045i	$-0.666654\pi$
$572$	25.1087	−	25.7945i	1.04985	−	1.07852i
$573$		0			0
$574$	−17.5905	+	43.2898i	−0.734213	+	1.80688i
$575$	2.99159	+	32.5221i	0.124758	+	1.35627i
$576$		0			0
$577$		−	40.3389i		−	1.67933i	−0.543104	−	0.839665i	$-0.682751\pi$
$577$		−	40.3389i		−	1.67933i	0.543104	−	0.839665i	$-0.317249\pi$
$578$	5.37396	+	2.18367i	0.223527	+	0.0908286i
$579$		0			0
$580$	−8.74275	−	7.76223i	−0.363023	−	0.322309i
$581$	−25.0788	−	25.0788i	−1.04044	−	1.04044i
$582$		0			0
$583$			51.9081i			2.14981i
$584$	−7.83926	−	17.8940i	−0.324391	−	0.740459i
$585$		0			0
$586$	−28.0421	+	11.8374i	−1.15841	+	0.488997i
$587$	9.96452	+	9.96452i	0.411280	+	0.411280i	0.882184	−	0.470905i	$-0.156072\pi$
$587$	9.96452	+	9.96452i	0.411280	+	0.411280i	−0.470905	+	0.882184i	$0.656072\pi$
$588$		0			0
$589$	7.29835	+	7.29835i	0.300723	+	0.300723i
$590$	−12.5572	−	4.44333i	−0.516972	−	0.182929i
$591$		0			0
$592$	−7.43002	+	7.84165i	−0.305372	+	0.322290i
$593$	−19.4892			−0.800324			−0.400162	−	0.916444i	$-0.631046\pi$
$593$	−19.4892			−0.800324			−0.400162	+	0.916444i	$0.631046\pi$
$594$		0			0
$595$	23.3132	−	25.5561i	0.955748	−	1.04770i
$596$	−0.372765	−	27.6648i	−0.0152690	−	1.13320i
$597$		0			0
$598$	−25.3863	+	10.7163i	−1.03812	+	0.438221i
$599$			16.4963i			0.674020i	0.941501	+	0.337010i	$0.109416\pi$
$599$			16.4963i			0.674020i	−0.941501	+	0.337010i	$0.890584\pi$
$600$		0			0
$601$		−	8.09948i		−	0.330385i	−0.986261	−	0.165192i	$-0.947176\pi$
$601$		−	8.09948i		−	0.330385i	0.986261	−	0.165192i	$-0.0528245\pi$
$602$	−18.2029	−	43.1216i	−0.741893	−	1.75751i
$603$		0			0
$604$	−17.2131	−	16.7554i	−0.700391	−	0.681768i
$605$	38.2863	−	41.9697i	1.55656	−	1.70631i
$606$		0			0
$607$	−0.975144			−0.0395799			−0.0197899	−	0.999804i	$-0.506300\pi$
$607$	−0.975144			−0.0395799			−0.0197899	+	0.999804i	$0.506300\pi$
$608$	−3.15932	−	6.95503i	−0.128127	−	0.282064i
$609$		0			0
$610$	−0.234245	+	0.661994i	−0.00948429	+	0.0268033i
$611$	6.85236	+	6.85236i	0.277217	+	0.277217i
$612$		0			0
$613$	−7.41162	−	7.41162i	−0.299353	−	0.299353i	0.541408	−	0.840760i	$-0.317892\pi$
$613$	−7.41162	−	7.41162i	−0.299353	−	0.299353i	−0.840760	+	0.541408i	$0.817892\pi$
$614$	2.95098	+	6.99072i	0.119092	+	0.282122i
$615$		0			0
$616$	26.7535	−	68.4708i	1.07793	−	2.75877i
$617$			15.5875i			0.627531i	0.949501	+	0.313765i	$0.101591\pi$
$617$			15.5875i			0.627531i	−0.949501	+	0.313765i	$0.898409\pi$
$618$		0			0
$619$	−3.34655	−	3.34655i	−0.134509	−	0.134509i	0.636647	−	0.771156i	$-0.280321\pi$
$619$	−3.34655	−	3.34655i	−0.134509	−	0.134509i	−0.771156	+	0.636647i	$0.780321\pi$
$620$	−34.1217	+	2.02708i	−1.37036	+	0.0814095i
$621$		0			0
$622$	−9.68486	+	23.8342i	−0.388328	+	0.955665i
$623$			33.3780i			1.33726i
$624$		0			0
$625$	−24.5805	+	4.56073i	−0.983219	+	0.182429i
$626$	21.9828	+	8.93257i	0.878611	+	0.357017i
$627$		0			0
$628$	24.9294	−	0.335907i	0.994791	−	0.0134041i
$629$	−6.85837	−	6.85837i	−0.273461	−	0.273461i
$630$		0			0
$631$	−17.5464			−0.698510			−0.349255	−	0.937028i	$-0.613565\pi$
$631$	−17.5464			−0.698510			−0.349255	+	0.937028i	$0.613565\pi$
$632$	−13.9719	+	6.12102i	−0.555773	+	0.243481i
$633$		0			0
$634$	0.0804439	+	0.190567i	0.00319483	+	0.00756840i
$635$	12.0318	+	10.9759i	0.477468	+	0.435564i
$636$		0			0
$637$	−24.3723	+	24.3723i	−0.965666	+	0.965666i
$638$	8.39768	−	20.6665i	0.332467	−	0.818194i
$639$		0			0
$640$	24.1707	+	7.46834i	0.955432	+	0.295212i
$641$			30.7369i			1.21403i	0.794689	+	0.607016i	$0.207634\pi$
$641$			30.7369i			1.21403i	−0.794689	+	0.607016i	$0.792366\pi$
$642$		0			0
$643$	−2.00487	−	2.00487i	−0.0790643	−	0.0790643i	0.666469	−	0.745533i	$-0.267805\pi$
$643$	−2.00487	−	2.00487i	−0.0790643	−	0.0790643i	−0.745533	+	0.666469i	$0.767805\pi$
$644$	−39.2509	+	40.3231i	−1.54670	+	1.58895i
$645$		0			0
$646$	6.31877	−	2.66733i	0.248609	−	0.104945i
$647$	41.0262			1.61291			0.806453	−	0.591298i	$-0.201384\pi$
$647$	41.0262			1.61291			0.806453	+	0.591298i	$0.201384\pi$
$648$		0			0
$649$		−	25.4153i		−	0.997637i
$650$	−9.94858	−	18.5995i	−0.390215	−	0.729532i
$651$		0			0
$652$	0.339159	+	25.1707i	0.0132825	+	0.985762i
$653$	−10.2034	−	10.2034i	−0.399291	−	0.399291i	0.478692	−	0.877983i	$-0.341111\pi$
$653$	−10.2034	−	10.2034i	−0.399291	−	0.399291i	−0.877983	+	0.478692i	$0.841111\pi$
$654$		0			0
$655$	−1.43494	−	31.2647i	−0.0560676	−	1.22161i
$656$	−0.826697	−	30.6712i	−0.0322771	−	1.19751i
$657$		0			0
$658$	18.3341	+	7.44992i	0.714737	+	0.290428i
$659$	14.6544	+	14.6544i	0.570853	+	0.570853i	0.932367	−	0.361514i	$-0.117740\pi$
$659$	14.6544	+	14.6544i	0.570853	+	0.570853i	−0.361514	+	0.932367i	$0.617740\pi$
$660$		0			0
$661$	31.9191	−	31.9191i	1.24151	−	1.24151i	0.282131	−	0.959376i	$-0.408959\pi$
$661$	31.9191	−	31.9191i	1.24151	−	1.24151i	0.959376	−	0.282131i	$-0.0910414\pi$
$662$	−1.69892	−	4.02466i	−0.0660306	−	0.156423i
$663$		0			0
$664$	21.6914	+	8.47546i	0.841789	+	0.328912i
$665$	0.596337	+	12.9931i	0.0231250	+	0.503852i
$666$		0			0
$667$	−12.0746	+	12.0746i	−0.467531	+	0.467531i
$668$	6.08089	+	5.91920i	0.235277	+	0.229021i
$669$		0			0
$670$	0.455591	−	1.28753i	0.0176010	−	0.0497418i
$671$	−1.33985			−0.0517243
$672$		0			0
$673$			3.74068i			0.144193i	0.997398	+	0.0720963i	$0.0229689\pi$
$673$			3.74068i			0.144193i	−0.997398	+	0.0720963i	$0.977031\pi$
$674$	−11.1377	+	27.4097i	−0.429009	+	1.05578i
$675$		0			0
$676$	−5.72199	+	5.87830i	−0.220077	+	0.226088i
$677$	−14.8520	+	14.8520i	−0.570808	+	0.570808i	−0.932354	−	0.361546i	$-0.882249\pi$
$677$	−14.8520	+	14.8520i	−0.570808	+	0.570808i	0.361546	+	0.932354i	$0.382249\pi$
$678$		0			0
$679$	−40.2382			−1.54420
$680$	−7.28779	+	21.5133i	−0.279474	+	0.824996i
$681$		0			0
$682$	−25.3640	−	60.0860i	−0.971237	−	2.30081i
$683$	0.704118	+	0.704118i	0.0269423	+	0.0269423i	0.720450	−	0.693507i	$-0.243935\pi$
$683$	0.704118	+	0.704118i	0.0269423	+	0.0269423i	−0.693507	+	0.720450i	$0.743935\pi$
$684$		0			0
$685$	26.8205	−	29.4008i	1.02476	−	1.12335i
$686$	−10.4450	+	25.7049i	−0.398791	+	0.981416i
$687$		0			0
$688$	22.3100	+	21.1389i	0.850560	+	0.805913i
$689$			25.6627i			0.977672i
$690$		0			0
$691$	−27.9600	+	27.9600i	−1.06365	+	1.06365i	−0.0658160	+	0.997832i	$0.520965\pi$
$691$	−27.9600	+	27.9600i	−1.06365	+	1.06365i	−0.997832	+	0.0658160i	$0.979035\pi$
$692$	−0.153637	−	11.4022i	−0.00584040	−	0.433447i
$693$		0			0
$694$	−3.38227	−	8.01243i	−0.128389	−	0.304148i
$695$	0.722410	+	15.7400i	0.0274026	+	0.597054i
$696$		0			0
$697$	27.5483			1.04347
$698$	−2.88546	−	6.83551i	−0.109216	−	0.258728i
$699$		0			0
$700$	−33.4887	−	27.0919i	−1.26576	−	1.02398i
$701$	−3.89364	+	3.89364i	−0.147061	+	0.147061i	−0.776804	−	0.629743i	$-0.783160\pi$
$701$	−3.89364	+	3.89364i	−0.147061	+	0.147061i	0.629743	+	0.776804i	$0.283160\pi$
$702$		0			0
$703$	3.64694			0.137547
$704$	1.95056	+	48.2304i	0.0735146	+	1.81775i
$705$		0			0
$706$	−21.4081	−	8.69902i	−0.805704	−	0.327392i
$707$	−34.0801	+	34.0801i	−1.28171	+	1.28171i
$708$		0			0
$709$	−24.4875	+	24.4875i	−0.919648	+	0.919648i	−0.997004	−	0.0773555i	$-0.975352\pi$
$709$	−24.4875	+	24.4875i	−0.919648	+	0.919648i	0.0773555	+	0.997004i	$0.475352\pi$
$710$	4.61783	−	2.20396i	0.173304	−	0.0827130i
$711$		0			0
$712$	−8.79470	−	20.0749i	−0.329595	−	0.752338i
$713$			49.9251i			1.86971i
$714$		0			0
$715$	27.1236	−	29.7332i	1.01437	−	1.11196i
$716$	−0.0317773	−	2.35836i	−0.00118757	−	0.0881359i
$717$		0			0
$718$	13.1461	−	32.3521i	0.490606	−	1.20737i
$719$	−16.1711			−0.603079			−0.301540	−	0.953454i	$-0.597501\pi$
$719$	−16.1711			−0.603079			−0.301540	+	0.953454i	$0.597501\pi$
$720$		0			0
$721$	69.6714			2.59470
$722$	9.14443	−	22.5042i	0.340320	−	0.837520i
$723$		0			0
$724$	−29.9637	+	0.403741i	−1.11359	+	0.0150049i
$725$	−10.0506	−	8.35734i	−0.373271	−	0.310384i
$726$		0			0
$727$			37.5868i			1.39402i	0.717063	+	0.697008i	$0.245486\pi$
$727$			37.5868i			1.39402i	−0.717063	+	0.697008i	$0.754514\pi$
$728$	13.2266	−	33.8511i	0.490211	−	1.25461i
$729$		0			0
$730$	−9.40786	−	19.7118i	−0.348200	−	0.729565i
$731$	−19.5125	+	19.5125i	−0.721695	+	0.721695i
$732$		0			0
$733$	10.5565	−	10.5565i	0.389913	−	0.389913i	−0.484744	−	0.874656i	$-0.661087\pi$
$733$	10.5565	−	10.5565i	0.389913	−	0.389913i	0.874656	+	0.484744i	$0.161087\pi$
$734$	8.75432	+	3.55726i	0.323128	+	0.131301i
$735$		0			0
$736$	12.9824	−	34.5941i	0.478539	−	1.27516i
$737$	2.60592			0.0959903
$738$		0			0
$739$	−5.50334	+	5.50334i	−0.202444	+	0.202444i	−0.801046	−	0.598603i	$-0.795723\pi$
$739$	−5.50334	+	5.50334i	−0.202444	+	0.202444i	0.598603	+	0.801046i	$0.295723\pi$
$740$	−8.01874	+	9.03165i	−0.294775	+	0.332010i
$741$		0			0
$742$	20.3811	+	48.2817i	0.748214	+	1.77248i
$743$	5.53668			0.203121			0.101561	−	0.994829i	$-0.467616\pi$
$743$	5.53668			0.203121			0.101561	+	0.994829i	$0.467616\pi$
$744$		0			0
$745$	−1.41822	−	30.9005i	−0.0519595	−	1.13211i
$746$	14.7500	+	34.9421i	0.540037	+	1.27932i
$747$		0			0
$748$	−43.3354	+	0.583915i	−1.58450	+	0.0213501i
$749$	−22.6835	+	22.6835i	−0.828837	+	0.828837i
$750$		0			0
$751$		−	30.2295i		−	1.10309i	−0.834145	−	0.551546i	$-0.814038\pi$
$751$		−	30.2295i		−	1.10309i	0.834145	−	0.551546i	$-0.185962\pi$
$752$	−12.9898	+	0.350123i	−0.473691	+	0.0127677i
$753$		0			0
$754$	4.15171	−	10.2173i	0.151196	−	0.372091i
$755$	−19.8414	−	18.1000i	−0.722103	−	0.658728i
$756$		0			0
$757$	25.8317	+	25.8317i	0.938870	+	0.938870i	0.998236	−	0.0593667i	$-0.0189081\pi$
$757$	25.8317	+	25.8317i	0.938870	+	0.938870i	−0.0593667	+	0.998236i	$0.518908\pi$
$758$	13.5498	+	32.0988i	0.492151	+	1.16588i
$759$		0			0
$760$	−3.78220	−	7.65749i	−0.137195	−	0.277766i
$761$	−6.93351			−0.251340			−0.125670	−	0.992072i	$-0.540108\pi$
$761$	−6.93351			−0.251340			−0.125670	+	0.992072i	$0.540108\pi$
$762$		0			0
$763$	51.4462	−	51.4462i	1.86248	−	1.86248i
$764$	−5.49119	−	5.34518i	−0.198664	−	0.193382i
$765$		0			0
$766$	−5.56560	+	13.6968i	−0.201093	+	0.494886i
$767$		−	12.5650i		−	0.453696i
$768$		0			0
$769$	18.4481			0.665257			0.332629	−	0.943058i	$-0.392064\pi$
$769$	18.4481			0.665257			0.332629	+	0.943058i	$0.392064\pi$
$770$	27.4165	−	77.4812i	0.988022	−	2.79223i
$771$		0			0
$772$	−7.02080	+	7.21259i	−0.252684	+	0.259587i
$773$	8.74138	−	8.74138i	0.314405	−	0.314405i	−0.532208	−	0.846614i	$-0.678638\pi$
$773$	8.74138	−	8.74138i	0.314405	−	0.314405i	0.846614	+	0.532208i	$0.178638\pi$
$774$		0			0
$775$	−38.0558	+	3.50062i	−1.36700	+	0.125746i
$776$	24.2010	−	10.6023i	0.868763	−	0.380601i
$777$		0			0
$778$	−5.22255	−	12.3719i	−0.187237	−	0.443556i
$779$	−7.32440	+	7.32440i	−0.262424	+	0.262424i
$780$		0			0
$781$	6.90351	+	6.90351i	0.247027	+	0.247027i
$782$	30.7352	+	12.4890i	1.09909	+	0.446606i
$783$		0			0
$784$	−1.24531	−	46.2019i	−0.0444752	−	1.65007i
$785$	27.8451	−	1.27799i	0.993836	−	0.0456134i
$786$		0			0
$787$	−16.3355	−	16.3355i	−0.582299	−	0.582299i	0.353235	−	0.935534i	$-0.385081\pi$
$787$	−16.3355	−	16.3355i	−0.582299	−	0.582299i	−0.935534	+	0.353235i	$0.885081\pi$
$788$	19.8469	−	0.267424i	0.707018	−	0.00952659i
$789$		0			0
$790$	−15.3912	+	7.34580i	−0.547596	+	0.261352i
$791$		−	77.9168i		−	2.77040i
$792$		0			0
$793$	−0.662406			−0.0235227
$794$	47.6016	−	20.0940i	1.68932	−	0.713109i
$795$		0			0
$796$	19.7117	+	19.1875i	0.698662	+	0.680084i
$797$	−11.3444	−	11.3444i	−0.401841	−	0.401841i	0.477040	−	0.878881i	$-0.341710\pi$
$797$	−11.3444	−	11.3444i	−0.401841	−	0.401841i	−0.878881	+	0.477040i	$0.841710\pi$
$798$		0			0
$799$		−	11.6672i		−	0.412757i
$800$	27.2799	+	7.47032i	0.964491	+	0.264116i
$801$		0			0
$802$	−9.86901	+	24.2874i	−0.348487	+	0.857618i
$803$	29.4685	−	29.4685i	1.03992	−	1.03992i
$804$		0			0
$805$	−42.4008	+	46.4801i	−1.49443	+	1.63821i
$806$	−12.5396	−	29.7058i	−0.441690	−	1.04634i
$807$		0			0
$808$	11.5175	−	29.4769i	0.405184	−	1.03699i
$809$	14.8157			0.520893			0.260446	−	0.965488i	$-0.416130\pi$
$809$	14.8157			0.520893			0.260446	+	0.965488i	$0.416130\pi$
$810$		0			0
$811$	−9.73571	−	9.73571i	−0.341867	−	0.341867i	0.515202	−	0.857069i	$-0.327717\pi$
$811$	−9.73571	−	9.73571i	−0.341867	−	0.341867i	−0.857069	+	0.515202i	$0.827717\pi$
$812$	−0.303441	−	22.5200i	−0.0106487	−	0.790295i
$813$		0			0
$814$	−21.3494	−	8.67518i	−0.748296	−	0.304065i
$815$	1.29036	+	28.1147i	0.0451994	+	0.984815i
$816$		0			0
$817$		−	10.3758i		−	0.363002i
$818$	3.43520	−	8.45396i	0.120109	−	0.295586i
$819$		0			0
$820$	−2.03432	−	34.2435i	−0.0710414	−	1.19583i
$821$	0.499371	+	0.499371i	0.0174282	+	0.0174282i	0.715767	−	0.698339i	$-0.246077\pi$
$821$	0.499371	+	0.499371i	0.0174282	+	0.0174282i	−0.698339	+	0.715767i	$0.746077\pi$
$822$		0			0
$823$		−	33.6494i		−	1.17295i	−0.809969	−	0.586473i	$-0.800516\pi$
$823$		−	33.6494i		−	1.17295i	0.809969	−	0.586473i	$-0.199484\pi$
$824$	−41.9033	+	18.3576i	−1.45977	+	0.639517i
$825$		0			0
$826$	−9.97900	−	23.6397i	−0.347214	−	0.822532i
$827$	11.7750	+	11.7750i	0.409456	+	0.409456i	0.881549	−	0.472093i	$-0.156501\pi$
$827$	11.7750	+	11.7750i	0.409456	+	0.409456i	−0.472093	+	0.881549i	$0.656501\pi$
$828$		0			0
$829$	35.3882	+	35.3882i	1.22908	+	1.22908i	0.964311	+	0.264772i	$0.0852968\pi$
$829$	35.3882	+	35.3882i	1.22908	+	1.22908i	0.264772	+	0.964311i	$0.414703\pi$
$830$	24.5459	+	8.68549i	0.851999	+	0.301478i
$831$		0			0
$832$	0.964334	+	23.8445i	0.0334323	+	0.826660i
$833$	41.4977			1.43781
$834$		0			0
$835$	7.00940	+	6.39422i	0.242570	+	0.221281i
$836$	11.3666	−	11.6771i	0.393121	−	0.403859i
$837$		0			0
$838$	−9.33354	−	22.1107i	−0.322422	−	0.763800i
$839$			20.9084i			0.721838i	0.932597	+	0.360919i	$0.117537\pi$
$839$			20.9084i			0.721838i	−0.932597	+	0.360919i	$0.882463\pi$
$840$		0			0
$841$			22.1656i			0.764331i
$842$	−44.0394	+	18.5903i	−1.51770	+	0.640664i
$843$		0			0
$844$	36.2007	−	0.487779i	1.24608	−	0.0167901i
$845$	−6.18119	+	6.77587i	−0.212639	+	0.233097i
$846$		0			0
$847$	109.436			3.76027
$848$	−24.9797	−	23.6685i	−0.857807	−	0.812779i
$849$		0			0
$850$	−7.36478	+	24.3038i	−0.252610	+	0.833614i
$851$	12.4736	+	12.4736i	0.427590	+	0.427590i
$852$		0			0
$853$	33.7697	+	33.7697i	1.15625	+	1.15625i	0.985275	+	0.170976i	$0.0546920\pi$
$853$	33.7697	+	33.7697i	1.15625	+	1.15625i	0.170976	+	0.985275i	$0.445308\pi$
$854$	−1.24625	+	0.526076i	−0.0426457	+	0.0180020i
$855$		0			0
$856$	7.66596	−	19.6196i	0.262017	−	0.670585i
$857$			44.3305i			1.51430i	0.653241	+	0.757150i	$0.273409\pi$
$857$			44.3305i			1.51430i	−0.653241	+	0.757150i	$0.726591\pi$
$858$		0			0
$859$	31.2008	+	31.2008i	1.06456	+	1.06456i	0.997767	+	0.0667892i	$0.0212755\pi$
$859$	31.2008	+	31.2008i	1.06456	+	1.06456i	0.0667892	+	0.997767i	$0.478724\pi$
$860$	25.6956	+	22.8138i	0.876214	+	0.777944i
$861$		0			0
$862$	16.4545	+	6.68616i	0.560442	+	0.227732i
$863$			47.7067i			1.62396i	0.583689	+	0.811978i	$0.301609\pi$
$863$			47.7067i			1.62396i	−0.583689	+	0.811978i	$0.698391\pi$
$864$		0			0
$865$	−0.584527	−	12.7358i	−0.0198745	−	0.433030i
$866$	−2.47471	+	6.09019i	−0.0840940	+	0.206953i
$867$		0			0
$868$	−47.1841	−	45.9294i	−1.60153	−	1.55895i
$869$	−23.0095	−	23.0095i	−0.780542	−	0.780542i
$870$		0			0
$871$	1.28834			0.0436536
$872$	−17.3864	+	44.4973i	−0.588778	+	1.50687i
$873$		0			0
$874$	−11.4922	+	4.85120i	−0.388731	+	0.164094i
$875$	−38.4028	−	29.0613i	−1.29825	−	0.982450i
$876$		0			0
$877$	−11.6792	+	11.6792i	−0.394379	+	0.394379i	−0.876245	−	0.481866i	$-0.839959\pi$
$877$	−11.6792	+	11.6792i	−0.394379	+	0.394379i	0.481866	+	0.876245i	$0.339959\pi$
$878$	−9.29816	−	3.77824i	−0.313798	−	0.127509i
$879$		0			0
$880$	3.92595	+	53.8243i	0.132344	+	1.81442i
$881$			26.5637i			0.894953i	0.894296	+	0.447477i	$0.147677\pi$
$881$			26.5637i			0.894953i	−0.894296	+	0.447477i	$0.852323\pi$
$882$		0			0
$883$	−23.1556	−	23.1556i	−0.779249	−	0.779249i	0.200454	−	0.979703i	$-0.435758\pi$
$883$	−23.1556	−	23.1556i	−0.779249	−	0.779249i	−0.979703	+	0.200454i	$0.935758\pi$
$884$	−21.4245	+	0.288681i	−0.720584	+	0.00970938i
$885$		0			0
$886$	12.9926	+	30.7788i	0.436496	+	1.03404i
$887$	−44.2415			−1.48549			−0.742743	−	0.669577i	$-0.766475\pi$
$887$	−44.2415			−1.48549			−0.742743	+	0.669577i	$0.766475\pi$
$888$		0			0
$889$			31.3730i			1.05222i
$890$	−10.5545	−	22.1142i	−0.353787	−	0.741270i
$891$		0			0
$892$	−18.2066	−	17.7225i	−0.609602	−	0.593393i
$893$	3.10203	+	3.10203i	0.103805	+	0.103805i
$894$		0			0
$895$	−0.120900	−	2.63419i	−0.00404123	−	0.0880512i
$896$	20.7514	+	44.0951i	0.693255	+	1.47311i
$897$		0			0
$898$	−11.9009	+	29.2877i	−0.397137	+	0.977344i
$899$	−14.1291	−	14.1291i	−0.471233	−	0.471233i
$900$		0			0
$901$	21.8474	−	21.8474i	0.727844	−	0.727844i
$902$	60.3005	−	25.4545i	2.00779	−	0.847544i
$903$		0			0
$904$	20.5302	+	46.8624i	0.682823	+	1.55862i
$905$	−33.4683	+	1.53607i	−1.11252	+	0.0510607i
$906$		0			0
$907$	−36.0867	+	36.0867i	−1.19824	+	1.19824i	−0.223545	+	0.974694i	$0.571763\pi$
$907$	−36.0867	+	36.0867i	−1.19824	+	1.19824i	−0.974694	+	0.223545i	$0.928237\pi$
$908$	−37.7392	+	0.508511i	−1.25242	+	0.0168755i
$909$		0			0
$910$	13.5544	−	38.3057i	0.449324	−	1.26982i
$911$	4.93520			0.163510			0.0817552	−	0.996652i	$-0.473947\pi$
$911$	4.93520			0.163510			0.0817552	+	0.996652i	$0.473947\pi$
$912$		0			0
$913$			49.6799i			1.64416i
$914$	−37.9799	−	15.4328i	−1.25626	−	0.510473i
$915$		0			0
$916$	−3.09832	+	0.0417478i	−0.102371	+	0.00137939i
$917$	42.6323	−	42.6323i	1.40784	−	1.40784i
$918$		0			0
$919$	28.2846			0.933023			0.466511	−	0.884515i	$-0.345511\pi$
$919$	28.2846			0.933023			0.466511	+	0.884515i	$0.345511\pi$
$920$	13.2546	−	39.1272i	0.436992	−	1.28998i
$921$		0			0
$922$	−6.92085	+	2.92149i	−0.227926	+	0.0962141i
$923$	3.41301	+	3.41301i	0.112341	+	0.112341i
$924$		0			0
$925$	−8.63350	+	10.3827i	−0.283868	+	0.341382i
$926$	−24.2247	−	9.84355i	−0.796074	−	0.323479i
$927$		0			0
$928$	6.11625	+	13.4645i	0.200776	+	0.441993i
$929$		−	27.7896i		−	0.911746i	−0.890045	−	0.455873i	$-0.849327\pi$
$929$		−	27.7896i		−	0.911746i	0.890045	−	0.455873i	$-0.150673\pi$
$930$		0			0
$931$	−11.0332	+	11.0332i	−0.361599	+	0.361599i
$932$	23.8768	−	24.5290i	0.782110	−	0.803475i
$933$		0			0
$934$	32.9124	−	13.8933i	1.07693	−	0.454602i
$935$	−48.4039	+	2.22156i	−1.58298	+	0.0726528i
$936$		0			0
$937$	−39.5362			−1.29159			−0.645796	−	0.763510i	$-0.723474\pi$
$937$	−39.5362			−1.29159			−0.645796	+	0.763510i	$0.723474\pi$
$938$	2.42387	−	1.02318i	0.0791421	−	0.0334081i
$939$		0			0
$940$	−14.5028	+	0.861573i	−0.473029	+	0.0281014i
$941$	−12.9497	+	12.9497i	−0.422149	+	0.422149i	−0.885943	−	0.463794i	$-0.846488\pi$
$941$	−12.9497	+	12.9497i	−0.422149	+	0.422149i	0.463794	+	0.885943i	$0.346488\pi$
$942$		0			0
$943$	−50.1033			−1.63159
$944$	12.2306	+	11.5886i	0.398072	+	0.377176i
$945$		0			0
$946$	−24.6814	+	60.7404i	−0.802463	+	1.97484i
$947$	21.0330	−	21.0330i	0.683481	−	0.683481i	−0.277302	−	0.960783i	$-0.589440\pi$
$947$	21.0330	−	21.0330i	0.683481	−	0.683481i	0.960783	+	0.277302i	$0.0894401\pi$
$948$		0			0
$949$	14.5689	−	14.5689i	0.472925	−	0.472925i
$950$	−4.50367	−	8.41989i	−0.146118	−	0.273177i
$951$		0			0
$952$	−40.0787	+	17.5582i	−1.29896	+	0.569066i
$953$			25.8627i			0.837774i	0.908038	+	0.418887i	$0.137580\pi$
$953$			25.8627i			0.837774i	−0.908038	+	0.418887i	$0.862420\pi$
$954$		0			0
$955$	−6.32965	−	5.77413i	−0.204823	−	0.186847i
$956$	25.5894	+	24.9090i	0.827621	+	0.805614i
$957$		0			0
$958$	27.8567	+	11.3194i	0.900009	+	0.365712i
$959$	76.6628			2.47557
$960$		0			0
$961$	−27.4199			−0.884512
$962$	−10.5549	−	4.28890i	−0.340303	−	0.138280i
$963$		0			0
$964$	7.33087	+	7.13594i	0.236111	+	0.229833i
$965$	−7.58423	+	8.31389i	−0.244145	+	0.267634i
$966$		0			0
$967$			29.5467i			0.950157i	0.879943	+	0.475079i	$0.157580\pi$
$967$			29.5467i			0.950157i	−0.879943	+	0.475079i	$0.842420\pi$
$968$	−65.8195	+	28.8352i	−2.11552	+	0.926797i
$969$		0			0
$970$	26.6594	−	12.7238i	0.855982	−	0.408536i
$971$	4.28841	−	4.28841i	0.137621	−	0.137621i	−0.634940	−	0.772561i	$-0.718975\pi$
$971$	4.28841	−	4.28841i	0.137621	−	0.137621i	0.772561	+	0.634940i	$0.218975\pi$
$972$		0			0
$973$	−21.4630	+	21.4630i	−0.688071	+	0.688071i
$974$	−20.3391	+	50.0542i	−0.651708	+	1.60384i
$975$		0			0
$976$	0.610930	−	0.644775i	0.0195554	−	0.0206388i
$977$	14.9714			0.478976			0.239488	−	0.970899i	$-0.423020\pi$
$977$	14.9714			0.478976			0.239488	+	0.970899i	$0.423020\pi$
$978$		0			0
$979$	33.0601	−	33.0601i	1.05660	−	1.05660i
$980$	−3.06442	−	51.5831i	−0.0978893	−	1.64776i
$981$		0			0
$982$	−20.7389	+	8.75449i	−0.661806	+	0.279367i
$983$	9.58755			0.305795			0.152898	−	0.988242i	$-0.451139\pi$
$983$	9.58755			0.305795			0.152898	+	0.988242i	$0.451139\pi$
$984$		0			0
$985$	22.1682	−	1.01744i	0.706338	−	0.0324183i
$986$	−12.2327	+	5.16378i	−0.389569	+	0.164448i
$987$		0			0
$988$	5.61949	−	5.77299i	0.178780	−	0.183663i
$989$	35.4883	−	35.4883i	1.12846	−	1.12846i
$990$		0			0
$991$			43.4685i			1.38082i	0.723417	+	0.690412i	$0.242571\pi$
$991$			43.4685i			1.38082i	−0.723417	+	0.690412i	$0.757429\pi$
$992$	40.4803	+	15.1914i	1.28525	+	0.482328i
$993$		0			0
$994$	9.13181	+	3.71064i	0.289643	+	0.117694i
$995$	22.7215	+	20.7273i	0.720320	+	0.657101i
$996$		0			0
$997$	1.90040	+	1.90040i	0.0601862	+	0.0601862i	0.736559	−	0.676373i	$-0.236449\pi$
$997$	1.90040	+	1.90040i	0.0601862	+	0.0601862i	−0.676373	+	0.736559i	$0.736449\pi$
$998$	−35.5474	+	15.0056i	−1.12523	+	0.474993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.6	yes	96
3.2	odd	2	inner	720.2.u.a.179.43	yes	96
4.3	odd	2		2880.2.u.a.2159.37		96
5.4	even	2	inner	720.2.u.a.179.44	yes	96
12.11	even	2		2880.2.u.a.2159.12		96
15.14	odd	2	inner	720.2.u.a.179.5	✓	96
16.5	even	4		2880.2.u.a.719.13		96
16.11	odd	4	inner	720.2.u.a.539.5	yes	96
20.19	odd	2		2880.2.u.a.2159.36		96
48.5	odd	4		2880.2.u.a.719.36		96
48.11	even	4	inner	720.2.u.a.539.44	yes	96
60.59	even	2		2880.2.u.a.2159.13		96
80.59	odd	4	inner	720.2.u.a.539.43	yes	96
80.69	even	4		2880.2.u.a.719.12		96
240.59	even	4	inner	720.2.u.a.539.6	yes	96
240.149	odd	4		2880.2.u.a.719.37		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.5	✓	96	15.14	odd	2	inner
720.2.u.a.179.6	yes	96	1.1	even	1	trivial
720.2.u.a.179.43	yes	96	3.2	odd	2	inner
720.2.u.a.179.44	yes	96	5.4	even	2	inner
720.2.u.a.539.5	yes	96	16.11	odd	4	inner
720.2.u.a.539.6	yes	96	240.59	even	4	inner
720.2.u.a.539.43	yes	96	80.59	odd	4	inner
720.2.u.a.539.44	yes	96	48.11	even	4	inner
2880.2.u.a.719.12		96	80.69	even	4
2880.2.u.a.719.13		96	16.5	even	4
2880.2.u.a.719.36		96	48.5	odd	4
2880.2.u.a.719.37		96	240.149	odd	4
2880.2.u.a.2159.12		96	12.11	even	2
2880.2.u.a.2159.13		96	60.59	even	2
2880.2.u.a.2159.36		96	20.19	odd	2
2880.2.u.a.2159.37		96	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(1.65197 + 1.50698i) q^{5} +4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +O(q^{10})\)	\(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(1.65197 + 1.50698i) q^{5} +4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +(-1.36208 - 2.85390i) q^{10} +(4.26649 - 4.26649i) q^{11} +(2.10930 - 2.10930i) q^{13} +(2.29324 - 5.64362i) q^{14} +(0.107775 + 3.99855i) q^{16} -3.59142 q^{17} +(0.954870 - 0.954870i) q^{19} +(0.265210 + 4.46427i) q^{20} +(-7.86127 + 3.31847i) q^{22} +6.53188 q^{23} +(0.457999 + 4.97898i) q^{25} +(-3.88652 + 1.64061i) q^{26} +(-6.00912 + 6.17327i) q^{28} +(-1.84857 + 1.84857i) q^{29} +7.64329i q^{31} +(1.98755 - 5.29619i) q^{32} +(4.70541 + 1.91201i) q^{34} +(-6.49135 + 7.11588i) q^{35} +(1.90965 + 1.90965i) q^{37} +(-1.75941 + 0.742695i) q^{38} +(2.02922 - 5.99018i) q^{40} -7.67058 q^{41} +(5.43308 - 5.43308i) q^{43} +(12.0664 - 0.162586i) q^{44} +(-8.55794 - 3.47746i) q^{46} +3.24864i q^{47} -11.5547 q^{49} +(2.05066 - 6.76719i) q^{50} +(5.96546 - 0.0803806i) q^{52} +(-6.08323 + 6.08323i) q^{53} +(13.4776 - 0.618574i) q^{55} +(11.1596 - 4.88894i) q^{56} +(3.40610 - 1.43781i) q^{58} +(2.97848 - 2.97848i) q^{59} +(-0.157020 - 0.157020i) q^{61} +(4.06915 - 10.0141i) q^{62} +(-5.42364 + 5.88082i) q^{64} +(6.66318 - 0.305816i) q^{65} +(0.305394 + 0.305394i) q^{67} +(-5.14701 - 5.01014i) q^{68} +(12.2932 - 5.86719i) q^{70} +1.61808i q^{71} +6.90696 q^{73} +(-1.48532 - 3.51865i) q^{74} +(2.70053 - 0.0363879i) q^{76} +(18.3780 + 18.3780i) q^{77} -5.39306i q^{79} +(-5.84771 + 6.76789i) q^{80} +(10.0498 + 4.08368i) q^{82} +(-5.82210 + 5.82210i) q^{83} +(-5.93291 - 5.41221i) q^{85} +(-10.0108 + 4.22584i) q^{86} +(-15.8957 - 6.21090i) q^{88} +7.74878 q^{89} +(9.08585 + 9.08585i) q^{91} +(9.36110 + 9.11218i) q^{92} +(1.72952 - 4.25630i) q^{94} +(3.01639 - 0.138441i) q^{95} +9.34141i q^{97} +(15.1387 + 6.15150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

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