LMFDB - Embedded newform 567.2.w.a.46.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 6]))

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

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

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.w (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	567.46
Dual form			567.2.w.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.306313 + 1.73719i) q^{2} +(-1.04461 - 0.380207i) q^{4} +(0.723302 + 4.10205i) q^{5} +(-1.55501 + 2.14055i) q^{7} +(-0.783518 + 1.35709i) q^{8} +O(q^{10})$	\(q+(-0.306313 + 1.73719i) q^{2} +(-1.04461 - 0.380207i) q^{4} +(0.723302 + 4.10205i) q^{5} +(-1.55501 + 2.14055i) q^{7} +(-0.783518 + 1.35709i) q^{8} -7.34759 q^{10} +(0.428940 - 2.43264i) q^{11} +(0.108160 - 0.0907572i) q^{13} +(-3.24222 - 3.35702i) q^{14} +(-3.82067 - 3.20592i) q^{16} -0.702677 q^{17} +6.46502 q^{19} +(0.804060 - 4.56005i) q^{20} +(4.09457 + 1.49030i) q^{22} +(4.27608 - 3.58805i) q^{23} +(-11.6052 + 4.22394i) q^{25} +(0.124532 + 0.215695i) q^{26} +(2.43823 - 1.64481i) q^{28} +(-0.100910 - 0.0846735i) q^{29} +(4.35670 + 1.58571i) q^{31} +(4.33878 - 3.64067i) q^{32} +(0.215239 - 1.22068i) q^{34} +(-9.90538 - 4.83046i) q^{35} +(-0.387945 + 0.671941i) q^{37} +(-1.98032 + 11.2310i) q^{38} +(-6.13358 - 2.23244i) q^{40} +(2.52108 - 2.11544i) q^{41} +(-5.66175 + 2.06071i) q^{43} +(-1.37298 + 2.37808i) q^{44} +(4.92331 + 8.52742i) q^{46} +(-5.59334 + 2.03581i) q^{47} +(-2.16389 - 6.65714i) q^{49} +(-3.78296 - 21.4542i) q^{50} +(-0.147492 + 0.0536827i) q^{52} +(-1.85992 + 3.22148i) q^{53} +10.2891 q^{55} +(-1.68654 - 3.78745i) q^{56} +(0.178004 - 0.149363i) q^{58} +(2.78047 - 2.33309i) q^{59} +(0.205027 - 0.0746237i) q^{61} +(-4.08919 + 7.08269i) q^{62} +(0.00796973 + 0.0138040i) q^{64} +(0.450523 + 0.378034i) q^{65} +(2.66458 + 15.1116i) q^{67} +(0.734024 + 0.267163i) q^{68} +(11.4256 - 15.7279i) q^{70} +(7.04066 + 12.1948i) q^{71} +(-6.36370 - 11.0222i) q^{73} +(-1.04845 - 0.879758i) q^{74} +(-6.75343 - 2.45805i) q^{76} +(4.54018 + 4.70095i) q^{77} +(1.00160 - 5.68035i) q^{79} +(10.3874 - 17.9914i) q^{80} +(2.90267 + 5.02758i) q^{82} +(1.84338 + 1.54678i) q^{83} +(-0.508248 - 2.88242i) q^{85} +(-1.84557 - 10.4667i) q^{86} +(2.96524 + 2.48813i) q^{88} -0.904179 q^{89} +(0.0260800 + 0.372651i) q^{91} +(-5.83104 + 2.12233i) q^{92} +(-1.82327 - 10.3403i) q^{94} +(4.67616 + 26.5198i) q^{95} +(-1.73081 + 0.629965i) q^{97} +(12.2275 - 1.71991i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.306313	+	1.73719i	−0.216596	+	1.22838i	0.661519	+	0.749928i	$0.269912\pi$
$2$	−0.306313	+	1.73719i	−0.216596	+	1.22838i	−0.878115	+	0.478449i	$0.841199\pi$
$3$		0			0
$3$		0			0
$4$	−1.04461	−	0.380207i	−0.522305	−	0.190104i
$5$	0.723302	+	4.10205i	0.323471	+	1.83449i	0.520212	+	0.854037i	$0.325853\pi$
$5$	0.723302	+	4.10205i	0.323471	+	1.83449i	−0.196741	+	0.980455i	$0.563036\pi$
$6$		0			0
$7$	−1.55501	+	2.14055i	−0.587738	+	0.809051i
$7$	−1.55501	+	2.14055i	−0.587738	+	0.809051i
$8$	−0.783518	+	1.35709i	−0.277015	+	0.479805i
$9$		0			0
$10$	−7.34759			−2.32351
$11$	0.428940	−	2.43264i	0.129330	−	0.733469i	−0.849311	−	0.527893i	$-0.822982\pi$
$11$	0.428940	−	2.43264i	0.129330	−	0.733469i	0.978641	−	0.205576i	$-0.0659068\pi$
$12$		0			0
$13$	0.108160	−	0.0907572i	0.0299983	−	0.0251715i	−0.627665	−	0.778483i	$-0.715989\pi$
$13$	0.108160	−	0.0907572i	0.0299983	−	0.0251715i	0.657664	+	0.753312i	$0.271545\pi$
$14$	−3.24222	−	3.35702i	−0.866518	−	0.897202i
$15$		0			0
$16$	−3.82067	−	3.20592i	−0.955168	−	0.801481i
$17$	−0.702677			−0.170424			−0.0852121	−	0.996363i	$-0.527157\pi$
$17$	−0.702677			−0.170424			−0.0852121	+	0.996363i	$0.527157\pi$
$18$		0			0
$19$	6.46502			1.48318			0.741588	−	0.670855i	$-0.234073\pi$
$19$	6.46502			1.48318			0.741588	+	0.670855i	$0.234073\pi$
$20$	0.804060	−	4.56005i	0.179793	−	1.01966i
$21$		0			0
$22$	4.09457	+	1.49030i	0.872965	+	0.317733i
$23$	4.27608	−	3.58805i	0.891624	−	0.748161i	−0.0769115	−	0.997038i	$-0.524506\pi$
$23$	4.27608	−	3.58805i	0.891624	−	0.748161i	0.968535	+	0.248877i	$0.0800614\pi$
$24$		0			0
$25$	−11.6052	+	4.22394i	−2.32104	+	0.844789i
$26$	0.124532	+	0.215695i	0.0244226	+	0.0423012i
$27$		0			0
$28$	2.43823	−	1.64481i	0.460783	−	0.310841i
$29$	−0.100910	−	0.0846735i	−0.0187385	−	0.0157235i	0.633370	−	0.773849i	$-0.281671\pi$
$29$	−0.100910	−	0.0846735i	−0.0187385	−	0.0157235i	−0.652109	+	0.758125i	$0.726115\pi$
$30$		0			0
$31$	4.35670	+	1.58571i	0.782487	+	0.284802i	0.702209	−	0.711971i	$-0.252197\pi$
$31$	4.35670	+	1.58571i	0.782487	+	0.284802i	0.0802776	+	0.996773i	$0.474419\pi$
$32$	4.33878	−	3.64067i	0.766995	−	0.643586i
$33$		0			0
$34$	0.215239	−	1.22068i	0.0369132	−	0.209345i
$35$	−9.90538	−	4.83046i	−1.67431	−	0.816498i
$36$		0			0
$37$	−0.387945	+	0.671941i	−0.0637778	+	0.110466i	−0.896151	−	0.443749i	$-0.853648\pi$
$37$	−0.387945	+	0.671941i	−0.0637778	+	0.110466i	0.832373	+	0.554215i	$0.186982\pi$
$38$	−1.98032	+	11.2310i	−0.321250	+	1.82190i
$39$		0			0
$40$	−6.13358	−	2.23244i	−0.969804	−	0.352980i
$41$	2.52108	−	2.11544i	0.393727	−	0.330376i	−0.424336	−	0.905505i	$-0.639493\pi$
$41$	2.52108	−	2.11544i	0.393727	−	0.330376i	0.818063	+	0.575129i	$0.195048\pi$
$42$		0			0
$43$	−5.66175	+	2.06071i	−0.863409	+	0.314255i	−0.735495	−	0.677530i	$-0.763050\pi$
$43$	−5.66175	+	2.06071i	−0.863409	+	0.314255i	−0.127914	+	0.991785i	$0.540828\pi$
$44$	−1.37298	+	2.37808i	−0.206985	+	0.358509i
$45$		0			0
$46$	4.92331	+	8.52742i	0.725902	+	1.25730i
$47$	−5.59334	+	2.03581i	−0.815873	+	0.296953i	−0.716048	−	0.698052i	$-0.754051\pi$
$47$	−5.59334	+	2.03581i	−0.815873	+	0.296953i	−0.0998253	+	0.995005i	$0.531828\pi$
$48$		0			0
$49$	−2.16389	−	6.65714i	−0.309127	−	0.951021i
$50$	−3.78296	−	21.4542i	−0.534992	−	3.03409i
$51$		0			0
$52$	−0.147492	+	0.0536827i	−0.0204535	+	0.00744445i
$53$	−1.85992	+	3.22148i	−0.255480	+	0.442504i	−0.965026	−	0.262155i	$-0.915567\pi$
$53$	−1.85992	+	3.22148i	−0.255480	+	0.442504i	0.709546	+	0.704659i	$0.248900\pi$
$54$		0			0
$55$	10.2891			1.38738
$56$	−1.68654	−	3.78745i	−0.225374	−	0.506119i
$57$		0			0
$58$	0.178004	−	0.149363i	0.0233731	−	0.0196123i
$59$	2.78047	−	2.33309i	0.361986	−	0.303742i	−0.443596	−	0.896227i	$-0.646297\pi$
$59$	2.78047	−	2.33309i	0.361986	−	0.303742i	0.805582	+	0.592485i	$0.201853\pi$
$60$		0			0
$61$	0.205027	−	0.0746237i	0.0262510	−	0.00955458i	−0.328861	−	0.944378i	$-0.606665\pi$
$61$	0.205027	−	0.0746237i	0.0262510	−	0.00955458i	0.355112	+	0.934824i	$0.384443\pi$
$62$	−4.08919	+	7.08269i	−0.519328	+	0.899502i
$63$		0			0
$64$	0.00796973	+	0.0138040i	0.000996216	+	0.00172550i
$65$	0.450523	+	0.378034i	0.0558805	+	0.0468893i
$66$		0			0
$67$	2.66458	+	15.1116i	0.325530	+	1.84617i	0.505925	+	0.862578i	$0.331151\pi$
$67$	2.66458	+	15.1116i	0.325530	+	1.84617i	−0.180395	+	0.983594i	$0.557738\pi$
$68$	0.734024	+	0.267163i	0.0890135	+	0.0323983i
$69$		0			0
$70$	11.4256	−	15.7279i	1.36562	−	1.87984i
$71$	7.04066	+	12.1948i	0.835573	+	1.44725i	0.893563	+	0.448937i	$0.148197\pi$
$71$	7.04066	+	12.1948i	0.835573	+	1.44725i	−0.0579909	+	0.998317i	$0.518469\pi$
$72$		0			0
$73$	−6.36370	−	11.0222i	−0.744815	−	1.29006i	−0.950281	−	0.311393i	$-0.899205\pi$
$73$	−6.36370	−	11.0222i	−0.744815	−	1.29006i	0.205467	−	0.978664i	$-0.434129\pi$
$74$	−1.04845	−	0.879758i	−0.121880	−	0.102270i
$75$		0			0
$76$	−6.75343	−	2.45805i	−0.774671	−	0.281957i
$77$	4.54018	+	4.70095i	0.517402	+	0.535723i
$78$		0			0
$79$	1.00160	−	5.68035i	0.112689	−	0.639090i	−0.875180	−	0.483798i	$-0.839257\pi$
$79$	1.00160	−	5.68035i	0.112689	−	0.639090i	0.987869	−	0.155292i	$-0.0496319\pi$
$80$	10.3874	−	17.9914i	1.16134	−	2.01150i
$81$		0			0
$82$	2.90267	+	5.02758i	0.320547	+	0.555203i
$83$	1.84338	+	1.54678i	0.202337	+	0.169781i	0.738326	−	0.674444i	$-0.235617\pi$
$83$	1.84338	+	1.54678i	0.202337	+	0.169781i	−0.535989	+	0.844225i	$0.680061\pi$
$84$		0			0
$85$	−0.508248	−	2.88242i	−0.0551272	−	0.312642i
$86$	−1.84557	−	10.4667i	−0.199013	−	1.12866i
$87$		0			0
$88$	2.96524	+	2.48813i	0.316095	+	0.265236i
$89$	−0.904179			−0.0958428			−0.0479214	−	0.998851i	$-0.515260\pi$
$89$	−0.904179			−0.0958428			−0.0479214	+	0.998851i	$0.515260\pi$
$90$		0			0
$91$	0.0260800	+	0.372651i	0.00273392	+	0.0390644i
$92$	−5.83104	+	2.12233i	−0.607928	+	0.221268i
$93$		0			0
$94$	−1.82327	−	10.3403i	−0.188056	−	1.06652i
$95$	4.67616	+	26.5198i	0.479764	+	2.72088i
$96$		0			0
$97$	−1.73081	+	0.629965i	−0.175737	+	0.0639632i	−0.428390	−	0.903594i	$-0.640919\pi$
$97$	−1.73081	+	0.629965i	−0.175737	+	0.0639632i	0.252653	+	0.967557i	$0.418697\pi$
$98$	12.2275	−	1.71991i	1.23517	−	0.173738i
$99$		0			0
$100$	13.7289			1.37289
$101$	6.23114	+	5.22855i	0.620021	+	0.520260i	0.897810	−	0.440382i	$-0.145157\pi$
$101$	6.23114	+	5.22855i	0.620021	+	0.520260i	−0.277789	+	0.960642i	$0.589602\pi$
$102$		0			0
$103$	−1.11235	−	6.30845i	−0.109603	−	0.621590i	−0.989281	−	0.146021i	$-0.953353\pi$
$103$	−1.11235	−	6.30845i	−0.109603	−	0.621590i	0.879678	−	0.475569i	$-0.157758\pi$
$104$	0.0384205	+	0.217893i	0.00376744	+	0.0213662i
$105$		0			0
$106$	−5.02660	−	4.21781i	−0.488226	−	0.409670i
$107$	5.96628	+	10.3339i	0.576782	+	0.999016i	0.995846	+	0.0910589i	$0.0290251\pi$
$107$	5.96628	+	10.3339i	0.576782	+	0.999016i	−0.419063	+	0.907957i	$0.637642\pi$
$108$		0			0
$109$	−0.160232	+	0.277531i	−0.0153475	+	0.0265826i	−0.873597	−	0.486650i	$-0.838219\pi$
$109$	−0.160232	+	0.277531i	−0.0153475	+	0.0265826i	0.858250	+	0.513232i	$0.171552\pi$
$110$	−3.15168	+	17.8741i	−0.300501	+	1.70422i
$111$		0			0
$112$	12.8036	−	3.19309i	1.20983	−	0.301718i
$113$	−1.98832	−	0.723688i	−0.187045	−	0.0680789i	0.246799	−	0.969067i	$-0.420621\pi$
$113$	−1.98832	−	0.723688i	−0.187045	−	0.0680789i	−0.433845	+	0.900988i	$0.642843\pi$
$114$		0			0
$115$	17.8113	+	14.9454i	1.66091	+	1.39367i
$116$	0.0732182	+	0.126818i	0.00679814	+	0.0117747i
$117$		0			0
$118$	3.20132	+	5.54485i	0.294705	+	0.510445i
$119$	1.09267	−	1.50411i	0.100165	−	0.137882i
$120$		0			0
$121$	4.60286	+	1.67530i	0.418442	+	0.152300i
$122$	0.0668330	+	0.379029i	0.00605077	+	0.0343156i
$123$		0			0
$124$	−3.94816	−	3.31290i	−0.354555	−	0.297507i
$125$	−15.3076	−	26.5135i	−1.36915	−	2.37144i
$126$		0			0
$127$	−5.21371	+	9.03041i	−0.462642	+	0.801320i	−0.999092	−	0.0426127i	$-0.986432\pi$
$127$	−5.21371	+	9.03041i	−0.462642	+	0.801320i	0.536450	+	0.843932i	$0.319765\pi$
$128$	10.6182	−	3.86470i	0.938524	−	0.341595i
$129$		0			0
$130$	−0.794717	+	0.666847i	−0.0697013	+	0.0584864i
$131$	−4.62719	+	3.88267i	−0.404279	+	0.339231i	−0.822145	−	0.569278i	$-0.807223\pi$
$131$	−4.62719	+	3.88267i	−0.404279	+	0.339231i	0.417866	+	0.908509i	$0.362778\pi$
$132$		0			0
$133$	−10.0532	+	13.8387i	−0.871720	+	1.19997i
$134$	−27.0678			−2.33831
$135$		0			0
$136$	0.550560	−	0.953598i	0.0472101	−	0.0817703i
$137$	−2.40899	+	0.876802i	−0.205814	+	0.0749103i	−0.442870	−	0.896586i	$-0.646040\pi$
$137$	−2.40899	+	0.876802i	−0.205814	+	0.0749103i	0.237056	+	0.971496i	$0.423818\pi$
$138$		0			0
$139$	−0.548284	−	3.10947i	−0.0465048	−	0.263742i	0.952686	−	0.303955i	$-0.0983074\pi$
$139$	−0.548284	−	3.10947i	−0.0465048	−	0.263742i	−0.999191	+	0.0402133i	$0.987196\pi$
$140$	8.51069	+	8.81205i	0.719284	+	0.744754i
$141$		0			0
$142$	−23.3413	+	8.49553i	−1.95876	+	0.712929i
$143$	−0.174386	−	0.302045i	−0.0145829	−	0.0252582i
$144$		0			0
$145$	0.274347	−	0.475182i	0.0227832	−	0.0394617i
$146$	21.0970	−	7.67868i	1.74600	−	0.635492i
$147$		0			0
$148$	0.660728	−	0.554417i	0.0543115	−	0.0455728i
$149$	−11.8471	−	4.31199i	−0.970551	−	0.353252i	−0.192392	−	0.981318i	$-0.561624\pi$
$149$	−11.8471	−	4.31199i	−0.970551	−	0.353252i	−0.778160	+	0.628066i	$0.783847\pi$
$150$		0			0
$151$	2.81699	−	15.9759i	0.229243	−	1.30010i	−0.625162	−	0.780495i	$-0.714967\pi$
$151$	2.81699	−	15.9759i	0.229243	−	1.30010i	0.854405	−	0.519607i	$-0.173922\pi$
$152$	−5.06546	+	8.77363i	−0.410863	+	0.711635i
$153$		0			0
$154$	−9.55715	+	6.44719i	−0.770137	+	0.519529i
$155$	−3.35345	+	19.0184i	−0.269356	+	1.52759i
$156$		0			0
$157$	6.45448	−	5.41595i	0.515124	−	0.432240i	−0.347804	−	0.937567i	$-0.613073\pi$
$157$	6.45448	−	5.41595i	0.515124	−	0.432240i	0.862928	+	0.505327i	$0.168628\pi$
$158$	9.56104	+	3.47994i	0.760636	+	0.276849i
$159$		0			0
$160$	18.0725	+	15.1646i	1.42875	+	1.19887i
$161$	1.03106	+	14.7326i	0.0812590	+	1.16109i
$162$		0			0
$163$	4.06419	+	7.03938i	0.318332	+	0.551367i	0.980140	−	0.198306i	$-0.0635440\pi$
$163$	4.06419	+	7.03938i	0.318332	+	0.551367i	−0.661808	+	0.749673i	$0.730211\pi$
$164$	−3.43785	+	1.25128i	−0.268451	+	0.0977083i
$165$		0			0
$166$	−3.25169	+	2.72849i	−0.252380	+	0.211772i
$167$	18.8324	+	6.85444i	1.45730	+	0.530412i	0.944619	−	0.328169i	$-0.106432\pi$
$167$	18.8324	+	6.85444i	1.45730	+	0.530412i	0.512677	+	0.858582i	$0.328654\pi$
$168$		0			0
$169$	−2.25396	+	12.7829i	−0.173382	+	0.983298i
$170$	5.16299			0.395983
$171$		0			0
$172$	6.69782			0.510704
$173$	19.8173	+	16.6287i	1.50668	+	1.26426i	0.869913	+	0.493206i	$0.164175\pi$
$173$	19.8173	+	16.6287i	1.50668	+	1.26426i	0.636772	+	0.771052i	$0.280269\pi$
$174$		0			0
$175$	9.00463	−	31.4097i	0.680686	−	2.37435i
$176$	−9.43771	+	7.91918i	−0.711394	+	0.596931i
$177$		0			0
$178$	0.276962	−	1.57073i	0.0207592	−	0.117731i
$179$	−19.5468			−1.46100			−0.730499	−	0.682914i	$-0.760712\pi$
$179$	−19.5468			−1.46100			−0.730499	+	0.682914i	$0.760712\pi$
$180$		0			0
$181$	1.41161	−	2.44499i	0.104924	−	0.181734i	−0.808783	−	0.588107i	$-0.799873\pi$
$181$	1.41161	−	2.44499i	0.104924	−	0.181734i	0.913707	+	0.406373i	$0.133207\pi$
$182$	−0.655353	−	0.0688420i	−0.0485780	−	0.00510291i
$183$		0			0
$184$	1.51894	+	8.61434i	0.111978	+	0.635057i
$185$	−3.03694	−	1.10535i	−0.223280	−	0.0812673i
$186$		0			0
$187$	−0.301407	+	1.70936i	−0.0220410	+	0.125001i
$188$	6.61690			0.482587
$189$		0			0
$190$	−47.5023			−3.44618
$191$	1.41634	−	8.03246i	0.102483	−	0.581208i	−0.889713	−	0.456520i	$-0.849096\pi$
$191$	1.41634	−	8.03246i	0.102483	−	0.581208i	0.992196	−	0.124688i	$-0.0397931\pi$
$192$		0			0
$193$	−2.78662	−	1.01425i	−0.200585	−	0.0730071i	0.239774	−	0.970829i	$-0.422927\pi$
$193$	−2.78662	−	1.01425i	−0.200585	−	0.0730071i	−0.440359	+	0.897822i	$0.645149\pi$
$194$	−0.564196	−	3.19972i	−0.0405069	−	0.229726i
$195$		0			0
$196$	−0.270672	+	7.77685i	−0.0193337	+	0.555489i
$197$	8.95897	−	15.5174i	0.638300	−	1.10557i	−0.347505	−	0.937678i	$-0.612971\pi$
$197$	8.95897	−	15.5174i	0.638300	−	1.10557i	0.985806	−	0.167891i	$-0.0536955\pi$
$198$		0			0
$199$	11.7675			0.834176			0.417088	−	0.908866i	$-0.363051\pi$
$199$	11.7675			0.834176			0.417088	+	0.908866i	$0.363051\pi$
$200$	3.36059	−	19.0588i	0.237629	−	1.34766i
$201$		0			0
$202$	−10.9916	+	9.22309i	−0.773370	+	0.648934i
$203$	0.338164	−	0.0843345i	0.0237344	−	0.00591912i
$204$		0			0
$205$	10.5011	+	8.81150i	0.733431	+	0.615422i
$206$	11.2997			0.787287
$207$		0			0
$208$	−0.704206			−0.0488279
$209$	2.77311	−	15.7271i	0.191820	−	1.08786i
$210$		0			0
$211$	4.57923	+	1.66670i	0.315247	+	0.114741i	0.494798	−	0.869008i	$-0.335242\pi$
$211$	4.57923	+	1.66670i	0.315247	+	0.114741i	−0.179550	+	0.983749i	$0.557464\pi$
$212$	3.16772	−	2.65804i	0.217560	−	0.182555i
$213$		0			0
$214$	−19.7795	+	7.19914i	−1.35210	+	0.492123i
$215$	−12.5483	−	21.7343i	−0.855786	−	1.48226i
$216$		0			0
$217$	−10.1690	+	6.85994i	−0.690317	+	0.465683i
$218$	−0.433042	−	0.363365i	−0.0293293	−	0.0246102i
$219$		0			0
$220$	−10.7481	−	3.91198i	−0.724635	−	0.263746i
$221$	−0.0760018	+	0.0637730i	−0.00511243	+	0.00428984i
$222$		0			0
$223$	3.39420	−	19.2495i	0.227292	−	1.28904i	−0.630962	−	0.775814i	$-0.717339\pi$
$223$	3.39420	−	19.2495i	0.227292	−	1.28904i	0.858254	−	0.513225i	$-0.171549\pi$
$224$	1.04618	+	14.9486i	0.0699009	+	0.998798i
$225$		0			0
$226$	1.86623	−	3.23241i	0.124140	−	0.215017i
$227$	2.13798	−	12.1251i	0.141902	−	0.804769i	−0.827900	−	0.560876i	$-0.810464\pi$
$227$	2.13798	−	12.1251i	0.141902	−	0.804769i	0.969802	−	0.243893i	$-0.0784245\pi$
$228$		0			0
$229$	24.0912	+	8.76849i	1.59199	+	0.579438i	0.977767	−	0.209693i	$-0.0672465\pi$
$229$	24.0912	+	8.76849i	1.59199	+	0.579438i	0.614225	+	0.789131i	$0.289469\pi$
$230$	−31.4189	+	26.3636i	−2.07170	+	1.73836i
$231$		0			0
$232$	0.193975	−	0.0706009i	0.0127351	−	0.00463518i
$233$	3.66677	−	6.35103i	0.240218	−	0.416070i	−0.720558	−	0.693395i	$-0.756114\pi$
$233$	3.66677	−	6.35103i	0.240218	−	0.416070i	0.960776	+	0.277324i	$0.0894477\pi$
$234$		0			0
$235$	−12.3967	−	21.4717i	−0.808670	−	1.40066i
$236$	−3.79156	+	1.38002i	−0.246810	+	0.0898314i
$237$		0			0
$238$	2.27823	+	2.35890i	0.147676	+	0.152905i
$239$	−2.57748	−	14.6176i	−0.166723	−	0.945536i	−0.947270	−	0.320438i	$-0.896170\pi$
$239$	−2.57748	−	14.6176i	−0.166723	−	0.945536i	0.780546	−	0.625098i	$-0.214941\pi$
$240$		0			0
$241$	16.4437	−	5.98501i	1.05923	−	0.385529i	0.247092	−	0.968992i	$-0.420525\pi$
$241$	16.4437	−	5.98501i	1.05923	−	0.385529i	0.812139	+	0.583464i	$0.198303\pi$
$242$	−4.32024	+	7.48287i	−0.277715	+	0.481017i
$243$		0			0
$244$	−0.242546			−0.0155274
$245$	25.7428	−	13.6915i	1.64465	−	0.874719i
$246$		0			0
$247$	0.699258	−	0.586747i	0.0444927	−	0.0373338i
$248$	−5.56551	+	4.67002i	−0.353410	+	0.296546i
$249$		0			0
$250$	50.7478	−	18.4707i	3.20957	−	1.16819i
$251$	6.62373	−	11.4726i	0.418086	−	0.724147i	−0.577661	−	0.816277i	$-0.696034\pi$
$251$	6.62373	−	11.4726i	0.418086	−	0.724147i	0.995747	+	0.0921303i	$0.0293676\pi$
$252$		0			0
$253$	−6.89427	−	11.9412i	−0.433439	−	0.750738i
$254$	−14.0905	−	11.8233i	−0.884117	−	0.741862i
$255$		0			0
$256$	3.46676	+	19.6610i	0.216673	+	1.22881i
$257$	−20.3970	−	7.42389i	−1.27233	−	0.463090i	−0.384441	−	0.923150i	$-0.625606\pi$
$257$	−20.3970	−	7.42389i	−1.27233	−	0.463090i	−0.887888	+	0.460060i	$0.847828\pi$
$258$		0			0
$259$	−0.835063	−	1.87529i	−0.0518883	−	0.116525i
$260$	−0.326890	−	0.566191i	−0.0202729	−	0.0351136i
$261$		0			0
$262$	−5.32756	−	9.22761i	−0.329138	−	0.570084i
$263$	−8.30629	−	6.96981i	−0.512188	−	0.429777i	0.349710	−	0.936858i	$-0.386280\pi$
$263$	−8.30629	−	6.96981i	−0.512188	−	0.429777i	−0.861898	+	0.507081i	$0.830724\pi$
$264$		0			0
$265$	−14.5599	−	5.29939i	−0.894410	−	0.325539i
$266$	−20.9610	−	21.7032i	−1.28520	−	1.33071i
$267$		0			0
$268$	2.96208	−	16.7988i	0.180938	−	1.02615i
$269$	6.69178	−	11.5905i	0.408005	−	0.706686i	−0.586661	−	0.809833i	$-0.699558\pi$
$269$	6.69178	−	11.5905i	0.408005	−	0.706686i	0.994666	+	0.103147i	$0.0328911\pi$
$270$		0			0
$271$	10.7152	+	18.5593i	0.650904	+	1.12740i	0.982904	+	0.184120i	$0.0589433\pi$
$271$	10.7152	+	18.5593i	0.650904	+	1.12740i	−0.332000	+	0.943279i	$0.607723\pi$
$272$	2.68470	+	2.25273i	0.162784	+	0.136592i
$273$		0			0
$274$	−0.785264	−	4.45345i	−0.0474395	−	0.269043i
$275$	5.29741	+	30.0431i	0.319446	+	1.81167i
$276$		0			0
$277$	4.19055	+	3.51628i	0.251785	+	0.211273i	0.759941	−	0.649992i	$-0.225228\pi$
$277$	4.19055	+	3.51628i	0.251785	+	0.211273i	−0.508155	+	0.861265i	$0.669672\pi$
$278$	5.56969			0.334048
$279$		0			0
$280$	14.3164	−	9.65776i	0.855570	−	0.577161i
$281$	−13.4765	+	4.90506i	−0.803942	+	0.292611i	−0.711119	−	0.703072i	$-0.751811\pi$
$281$	−13.4765	+	4.90506i	−0.803942	+	0.292611i	−0.0928232	+	0.995683i	$0.529589\pi$
$282$		0			0
$283$	−1.38317	−	7.84435i	−0.0822209	−	0.466298i	−0.997922	−	0.0644373i	$-0.979475\pi$
$283$	−1.38317	−	7.84435i	−0.0822209	−	0.466298i	0.915701	−	0.401861i	$-0.131636\pi$
$284$	−2.71821	−	15.4157i	−0.161296	−	0.914754i
$285$		0			0
$286$	0.578125	−	0.210420i	0.0341853	−	0.0124424i
$287$	0.607891	+	8.68602i	0.0358827	+	0.512720i
$288$		0			0
$289$	−16.5062			−0.970956
$290$	0.741445	+	0.622146i	0.0435392	+	0.0365337i
$291$		0			0
$292$	2.45685	+	13.9335i	0.143776	+	0.815396i
$293$	−3.09426	−	17.5484i	−0.180768	−	1.02519i	−0.931273	−	0.364323i	$-0.881300\pi$
$293$	−3.09426	−	17.5484i	−0.180768	−	1.02519i	0.750504	−	0.660866i	$-0.229811\pi$
$294$		0			0
$295$	11.5816	+	9.71809i	0.674305	+	0.565809i
$296$	−0.607924	−	1.05295i	−0.0353348	−	0.0612018i
$297$		0			0
$298$	11.1197	−	19.2598i	0.644144	−	1.11569i
$299$	0.136860	−	0.776170i	0.00791480	−	0.0448871i
$300$		0			0
$301$	4.39303	−	15.3237i	0.253210	−	0.883241i
$302$	26.8903	+	9.78727i	1.54736	+	0.563194i
$303$		0			0
$304$	−24.7007	−	20.7264i	−1.41668	−	1.18874i
$305$	0.454406	+	0.787055i	0.0260192	+	0.0450666i
$306$		0			0
$307$	−0.753447	−	1.30501i	−0.0430015	−	0.0744808i	0.843724	−	0.536778i	$-0.180359\pi$
$307$	−0.753447	−	1.30501i	−0.0430015	−	0.0744808i	−0.886725	+	0.462297i	$0.847025\pi$
$308$	−2.95539	−	6.63687i	−0.168399	−	0.378171i
$309$		0			0
$310$	−32.0113	−	11.6511i	−1.81812	−	0.661741i
$311$	1.01822	+	5.77462i	0.0577380	+	0.327449i	0.999972	−	0.00750727i	$-0.00238966\pi$
$311$	1.01822	+	5.77462i	0.0577380	+	0.327449i	−0.942234	+	0.334956i	$0.891279\pi$
$312$		0			0
$313$	−1.42966	−	1.19963i	−0.0808090	−	0.0678068i	0.601488	−	0.798882i	$-0.294575\pi$
$313$	−1.42966	−	1.19963i	−0.0808090	−	0.0678068i	−0.682297	+	0.731075i	$0.739019\pi$
$314$	7.43144	+	12.8716i	0.419380	+	0.726388i
$315$		0			0
$316$	−3.20599	+	5.55294i	−0.180351	+	0.312378i
$317$	−9.31341	+	3.38980i	−0.523093	+	0.190390i	−0.590052	−	0.807365i	$-0.700893\pi$
$317$	−9.31341	+	3.38980i	−0.523093	+	0.190390i	0.0669586	+	0.997756i	$0.478670\pi$
$318$		0			0
$319$	−0.249265	+	0.209158i	−0.0139561	+	0.0117106i
$320$	−0.0508601	+	0.0426767i	−0.00284316	+	0.00238570i
$321$		0			0
$322$	−25.9091	−	2.72164i	−1.44386	−	0.151671i
$323$	−4.54282			−0.252769
$324$		0			0
$325$	−0.871867	+	1.51012i	−0.0483625	+	0.0837662i
$326$	−13.4737	+	4.90401i	−0.746236	+	0.271608i
$327$		0			0
$328$	0.895534	+	5.07882i	0.0494476	+	0.280431i
$329$	4.33995	−	15.1385i	0.239269	−	0.834614i
$330$		0			0
$331$	−9.12572	+	3.32149i	−0.501595	+	0.182566i	−0.580411	−	0.814324i	$-0.697108\pi$
$331$	−9.12572	+	3.32149i	−0.501595	+	0.182566i	0.0788163	+	0.996889i	$0.474886\pi$
$332$	−1.33752	−	2.31664i	−0.0734057	−	0.127142i
$333$		0			0
$334$	−17.6761	+	30.6159i	−0.967192	+	1.67522i
$335$	−60.0611	+	21.8605i	−3.28149	+	1.19436i
$336$		0			0
$337$	−16.7483	+	14.0535i	−0.912339	+	0.765543i	−0.972562	−	0.232642i	$-0.925263\pi$
$337$	−16.7483	+	14.0535i	−0.912339	+	0.765543i	0.0602239	+	0.998185i	$0.480819\pi$
$338$	−21.5158	−	7.83112i	−1.17031	−	0.425957i
$339$		0			0
$340$	−0.564995	+	3.20424i	−0.0306411	+	0.173775i
$341$	5.72623	−	9.91812i	0.310093	−	0.537096i
$342$		0			0
$343$	17.6148	+	5.72001i	0.951110	+	0.308852i
$344$	1.63951	−	9.29812i	0.0883964	−	0.501321i
$345$		0			0
$346$	−34.9575	+	29.3329i	−1.87933	+	1.57694i
$347$	9.34786	+	3.40234i	0.501819	+	0.182647i	0.580512	−	0.814252i	$-0.302852\pi$
$347$	9.34786	+	3.40234i	0.501819	+	0.182647i	−0.0786928	+	0.996899i	$0.525075\pi$
$348$		0			0
$349$	−19.2188	−	16.1265i	−1.02876	−	0.863233i	−0.0380577	−	0.999276i	$-0.512117\pi$
$349$	−19.2188	−	16.1265i	−1.02876	−	0.863233i	−0.990703	+	0.136043i	$0.956562\pi$
$350$	51.8064	+	25.2639i	2.76917	+	1.35041i
$351$		0			0
$352$	−6.99537	−	12.1163i	−0.372854	−	0.645803i
$353$	−9.30697	+	3.38746i	−0.495360	+	0.180296i	−0.577606	−	0.816316i	$-0.696013\pi$
$353$	−9.30697	+	3.38746i	−0.495360	+	0.180296i	0.0822460	+	0.996612i	$0.473791\pi$
$354$		0			0
$355$	−44.9311	+	37.7016i	−2.38469	+	2.00100i
$356$	0.944515	+	0.343775i	0.0500592	+	0.0182201i
$357$		0			0
$358$	5.98745	−	33.9565i	0.316447	−	1.79466i
$359$	16.5248			0.872144			0.436072	−	0.899912i	$-0.356369\pi$
$359$	16.5248			0.872144			0.436072	+	0.899912i	$0.356369\pi$
$360$		0			0
$361$	22.7965			1.19981
$362$	3.81501	+	3.20117i	0.200512	+	0.168250i
$363$		0			0
$364$	0.114441	−	0.399191i	0.00599834	−	0.0209233i
$365$	40.6109	−	34.0766i	2.12567	−	1.78365i
$366$		0			0
$367$	−5.50999	+	31.2487i	−0.287619	+	1.63117i	0.408157	+	0.912912i	$0.366172\pi$
$367$	−5.50999	+	31.2487i	−0.287619	+	1.63117i	−0.695776	+	0.718259i	$0.744939\pi$
$368$	−27.8405			−1.45129
$369$		0			0
$370$	2.85046	−	4.93715i	0.148188	−	0.256670i
$371$	−4.00353	−	8.99068i	−0.207853	−	0.466773i
$372$		0			0
$373$	−4.16072	−	23.5966i	−0.215434	−	1.22179i	−0.880152	−	0.474692i	$-0.842559\pi$
$373$	−4.16072	−	23.5966i	−0.215434	−	1.22179i	0.664718	−	0.747094i	$-0.268552\pi$
$374$	−2.87716	−	1.04720i	−0.148774	−	0.0541494i
$375$		0			0
$376$	1.61970	−	9.18578i	0.0835296	−	0.473720i
$377$	−0.0185992			−0.000957907
$378$		0			0
$379$	18.5458			0.952632			0.476316	−	0.879274i	$-0.341972\pi$
$379$	18.5458			0.952632			0.476316	+	0.879274i	$0.341972\pi$
$380$	5.19826	−	29.4808i	0.266665	−	1.51233i
$381$		0			0
$382$	13.5200	+	4.92090i	0.691746	+	0.251775i
$383$	3.93094	+	22.2935i	0.200862	+	1.13914i	0.903820	+	0.427912i	$0.140751\pi$
$383$	3.93094	+	22.2935i	0.200862	+	1.13914i	−0.702959	+	0.711231i	$0.748138\pi$
$384$		0			0
$385$	−15.9996	+	22.0243i	−0.815416	+	1.12246i
$386$	2.61552	−	4.53021i	0.133126	−	0.230581i
$387$		0			0
$388$	2.04754			0.103948
$389$	−1.59902	+	9.06849i	−0.0810735	+	0.459791i	0.917061	+	0.398746i	$0.130554\pi$
$389$	−1.59902	+	9.06849i	−0.0810735	+	0.459791i	−0.998135	+	0.0610450i	$0.980557\pi$
$390$		0			0
$391$	−3.00470	+	2.52124i	−0.151954	+	0.127505i
$392$	10.7298	+	2.27939i	0.541937	+	0.115127i
$393$		0			0
$394$	24.2124	+	20.3166i	1.21980	+	1.02354i
$395$	24.0256			1.20886
$396$		0			0
$397$	−16.3534			−0.820753			−0.410376	−	0.911916i	$-0.634603\pi$
$397$	−16.3534			−0.820753			−0.410376	+	0.911916i	$0.634603\pi$
$398$	−3.60454	+	20.4424i	−0.180679	+	1.02468i
$399$		0			0
$400$	57.8813	+	21.0671i	2.89406	+	1.05335i
$401$	−28.0881	+	23.5687i	−1.40265	+	1.17697i	−0.442748	+	0.896646i	$0.645997\pi$
$401$	−28.0881	+	23.5687i	−1.40265	+	1.17697i	−0.959906	+	0.280321i	$0.909559\pi$
$402$		0			0
$403$	0.615137	−	0.223891i	0.0306421	−	0.0111528i
$404$	−4.52118	−	7.83092i	−0.224937	−	0.389603i
$405$		0			0
$406$	0.0429209	+	0.613287i	0.00213013	+	0.0304369i
$407$	1.46819	+	1.23195i	0.0727753	+	0.0610657i
$408$		0			0
$409$	−1.51858	−	0.552719i	−0.0750891	−	0.0273302i	0.304203	−	0.952607i	$-0.401610\pi$
$409$	−1.51858	−	0.552719i	−0.0750891	−	0.0273302i	−0.379292	+	0.925277i	$0.623832\pi$
$410$	−18.5239	+	15.5434i	−0.914829	+	0.767633i
$411$		0			0
$412$	−1.23655	+	7.01280i	−0.0609203	+	0.345496i
$413$	0.670435	+	9.57970i	0.0329900	+	0.471386i
$414$		0			0
$415$	−5.01164	+	8.68041i	−0.246012	+	0.426104i
$416$	0.138867	−	0.787552i	0.00680849	−	0.0386129i
$417$		0			0
$418$	26.4715	+	9.63482i	1.29476	+	0.471255i
$419$	−11.2741	+	9.46013i	−0.550778	+	0.462158i	−0.875204	−	0.483753i	$-0.839273\pi$
$419$	−11.2741	+	9.46013i	−0.550778	+	0.462158i	0.324426	+	0.945911i	$0.394829\pi$
$420$		0			0
$421$	12.7240	−	4.63116i	0.620130	−	0.225709i	−0.0127998	−	0.999918i	$-0.504074\pi$
$421$	12.7240	−	4.63116i	0.620130	−	0.225709i	0.632930	+	0.774209i	$0.281852\pi$
$422$	−4.29806	+	7.44446i	−0.209226	+	0.362390i
$423$		0			0
$424$	−2.91456	−	5.04817i	−0.141544	−	0.245161i
$425$	8.15470	−	2.96807i	0.395561	−	0.143972i
$426$		0			0
$427$	−0.159083	+	0.554910i	−0.00769858	+	0.0268540i
$428$	−2.30342	−	13.0633i	−0.111340	−	0.631440i
$429$		0			0
$430$	41.6002	−	15.1412i	2.00614	−	0.730176i
$431$	10.9091	−	18.8951i	0.525472	−	0.910145i	−0.474088	−	0.880478i	$-0.657222\pi$
$431$	10.9091	−	18.8951i	0.525472	−	0.910145i	0.999560	−	0.0296670i	$-0.00944470\pi$
$432$		0			0
$433$	10.1358			0.487096			0.243548	−	0.969889i	$-0.421689\pi$
$433$	10.1358			0.487096			0.243548	+	0.969889i	$0.421689\pi$
$434$	−8.80210	−	19.7668i	−0.422514	−	0.948835i
$435$		0			0
$436$	0.272900	−	0.228990i	0.0130695	−	0.0109666i
$437$	27.6449	−	23.1968i	1.32244	−	1.10966i
$438$		0			0
$439$	−2.67426	+	0.973350i	−0.127635	+	0.0464554i	−0.405048	−	0.914295i	$-0.632745\pi$
$439$	−2.67426	+	0.973350i	−0.127635	+	0.0464554i	0.277413	+	0.960751i	$0.410523\pi$
$440$	−8.06167	+	13.9632i	−0.384325	+	0.665671i
$441$		0			0
$442$	−0.0875055	−	0.151564i	−0.00416221	−	0.00720916i
$443$	4.88441	+	4.09850i	0.232065	+	0.194726i	0.751404	−	0.659843i	$-0.229377\pi$
$443$	4.88441	+	4.09850i	0.232065	+	0.194726i	−0.519339	+	0.854569i	$0.673822\pi$
$444$		0			0
$445$	−0.653995	−	3.70899i	−0.0310023	−	0.175823i
$446$	32.4003	+	11.7927i	1.53420	+	0.558402i
$447$		0			0
$448$	−0.0419411	−	0.00440573i	−0.00198153	−	0.000208151i
$449$	2.33757	+	4.04880i	0.110317	+	0.191074i	0.915898	−	0.401411i	$-0.131480\pi$
$449$	2.33757	+	4.04880i	0.110317	+	0.191074i	−0.805581	+	0.592485i	$0.798147\pi$
$450$		0			0
$451$	−4.06471	−	7.04029i	−0.191400	−	0.331514i
$452$	1.80187	+	1.51195i	0.0847527	+	0.0711159i
$453$		0			0
$454$	20.4086	+	7.42813i	0.957824	+	0.348620i
$455$	−1.50977	+	0.376520i	−0.0707790	+	0.0176515i
$456$		0			0
$457$	3.33384	−	18.9071i	0.155950	−	0.884438i	−0.801962	−	0.597375i	$-0.796210\pi$
$457$	3.33384	−	18.9071i	0.155950	−	0.884438i	0.957912	−	0.287062i	$-0.0926787\pi$
$458$	−22.6120	+	39.1651i	−1.05659	+	1.83006i
$459$		0			0
$460$	−12.9235	−	22.3841i	−0.602561	−	1.04367i
$461$	1.41824	+	1.19004i	0.0660540	+	0.0554259i	0.675217	−	0.737619i	$-0.264050\pi$
$461$	1.41824	+	1.19004i	0.0660540	+	0.0554259i	−0.609163	+	0.793045i	$0.708494\pi$
$462$		0			0
$463$	−2.62612	−	14.8935i	−0.122046	−	0.692158i	−0.983019	−	0.183506i	$-0.941255\pi$
$463$	−2.62612	−	14.8935i	−0.122046	−	0.692158i	0.860972	−	0.508652i	$-0.169856\pi$
$464$	0.114087	+	0.647020i	0.00529636	+	0.0300371i
$465$		0			0
$466$	9.90976	+	8.31528i	0.459061	+	0.385198i
$467$	24.7350			1.14460			0.572300	−	0.820044i	$-0.306051\pi$
$467$	24.7350			1.14460			0.572300	+	0.820044i	$0.306051\pi$
$468$		0			0
$469$	−36.4905	−	17.7950i	−1.68497	−	0.821696i
$470$	41.0976	−	14.9583i	1.89569	−	0.689975i
$471$		0			0
$472$	0.987672	+	5.60137i	0.0454613	+	0.257824i
$473$	2.58441	+	14.6569i	0.118831	+	0.673926i
$474$		0			0
$475$	−75.0277	+	27.3079i	−3.44251	+	1.25297i
$476$	−1.71329	+	1.15577i	−0.0785285	+	0.0529748i
$477$		0			0
$478$	26.1831			1.19759
$479$	−24.2765	−	20.3704i	−1.10922	−	0.930748i	−0.111211	−	0.993797i	$-0.535473\pi$
$479$	−24.2765	−	20.3704i	−1.10922	−	0.930748i	−0.998010	+	0.0630491i	$0.979918\pi$
$480$		0			0
$481$	0.0190232	+	0.107886i	0.000867385	+	0.00491918i
$482$	5.36018	+	30.3991i	0.244149	+	1.38464i
$483$		0			0
$484$	−4.17124	−	3.50008i	−0.189602	−	0.159095i
$485$	−3.83605	−	6.64423i	−0.174186	−	0.301699i
$486$		0			0
$487$	15.0234	−	26.0213i	0.680775	−	1.17914i	−0.293969	−	0.955815i	$-0.594976\pi$
$487$	15.0234	−	26.0213i	0.680775	−	1.17914i	0.974745	−	0.223323i	$-0.0716904\pi$
$488$	−0.0593709	+	0.336709i	−0.00268760	+	0.0152421i
$489$		0			0
$490$	15.8994	+	48.9140i	0.718261	+	2.20971i
$491$	−29.0255	−	10.5644i	−1.30990	−	0.476766i	−0.409695	−	0.912223i	$-0.634365\pi$
$491$	−29.0255	−	10.5644i	−1.30990	−	0.476766i	−0.900210	+	0.435456i	$0.856587\pi$
$492$		0			0
$493$	0.0709071	+	0.0594981i	0.00319350	+	0.00267966i
$494$	0.805098	+	1.39447i	0.0362231	+	0.0627402i
$495$		0			0
$496$	−11.5619	−	20.0257i	−0.519143	−	0.899182i
$497$	−37.0518	−	3.89213i	−1.66200	−	0.174586i
$498$		0			0
$499$	−14.5259	−	5.28698i	−0.650267	−	0.236678i	−0.00423824	−	0.999991i	$-0.501349\pi$
$499$	−14.5259	−	5.28698i	−0.650267	−	0.236678i	−0.646029	+	0.763313i	$0.723571\pi$
$500$	5.90983	+	33.5163i	0.264295	+	1.49889i
$501$		0			0
$502$	17.9012	+	15.0209i	0.798970	+	0.670415i
$503$	12.4023	+	21.4813i	0.552989	+	0.957806i	0.998057	+	0.0623088i	$0.0198464\pi$
$503$	12.4023	+	21.4813i	0.552989	+	0.957806i	−0.445067	+	0.895497i	$0.646820\pi$
$504$		0			0
$505$	−16.9408	+	29.3423i	−0.753854	+	1.30571i
$506$	22.8560	−	8.31889i	1.01607	−	0.369820i
$507$		0			0
$508$	8.87973	−	7.45098i	0.393974	−	0.330584i
$509$	−1.04593	+	0.877641i	−0.0463601	+	0.0389008i	−0.665673	−	0.746243i	$-0.731856\pi$
$509$	−1.04593	+	0.877641i	−0.0463601	+	0.0389008i	0.619313	+	0.785144i	$0.287411\pi$
$510$		0			0
$511$	33.4893	+	3.51790i	1.48148	+	0.155623i
$512$	−12.6175			−0.557620
$513$		0			0
$514$	19.1446	−	33.1594i	0.844430	−	1.46260i
$515$	25.0730	−	9.12584i	1.10485	−	0.402132i
$516$		0			0
$517$	2.55319	+	14.4798i	0.112289	+	0.636823i
$518$	3.51352	−	0.876236i	0.154375	−	0.0384996i
$519$		0			0
$520$	−0.866020	+	0.315205i	−0.0379775	+	0.0138227i
$521$	−13.2774	−	22.9971i	−0.581693	−	1.00752i	−0.995279	−	0.0970569i	$-0.969057\pi$
$521$	−13.2774	−	22.9971i	−0.581693	−	1.00752i	0.413586	−	0.910465i	$-0.364276\pi$
$522$		0			0
$523$	17.0005	−	29.4458i	0.743381	−	1.28757i	−0.207566	−	0.978221i	$-0.566554\pi$
$523$	17.0005	−	29.4458i	0.743381	−	1.28757i	0.950947	−	0.309353i	$-0.100113\pi$
$524$	6.30983	−	2.29659i	0.275646	−	0.100327i
$525$		0			0
$526$	14.6522	−	12.2947i	0.638866	−	0.536072i
$527$	−3.06136	−	1.11424i	−0.133355	−	0.0485372i
$528$		0			0
$529$	1.41679	−	8.03502i	0.0615996	−	0.349349i
$530$	13.6659	−	23.6701i	0.593610	−	1.02816i
$531$		0			0
$532$	15.7632	−	10.6337i	0.683422	−	0.461032i
$533$	0.0806895	−	0.457613i	0.00349505	−	0.0198214i
$534$		0			0
$535$	−38.0748	+	31.9485i	−1.64612	+	1.38125i
$536$	−22.5955	−	8.22410i	−0.975979	−	0.355227i
$537$		0			0
$538$	18.0851	+	15.1752i	0.779705	+	0.654250i
$539$	−17.1226	+	2.40845i	−0.737524	+	0.103739i
$540$		0			0
$541$	−1.17215	−	2.03023i	−0.0503948	−	0.0872863i	0.839728	−	0.543008i	$-0.182715\pi$
$541$	−1.17215	−	2.03023i	−0.0503948	−	0.0872863i	−0.890122	+	0.455722i	$0.849381\pi$
$542$	−35.5233	+	12.9294i	−1.52586	+	0.555366i
$543$		0			0
$544$	−3.04876	+	2.55822i	−0.130715	+	0.109683i
$545$	−1.25434	−	0.456543i	−0.0537300	−	0.0195561i
$546$		0			0
$547$	3.75899	−	21.3183i	0.160723	−	0.911504i	−0.792643	−	0.609686i	$-0.791296\pi$
$547$	3.75899	−	21.3183i	0.160723	−	0.911504i	0.953366	−	0.301818i	$-0.0975934\pi$
$548$	2.84983			0.121739
$549$		0			0
$550$	−53.8132			−2.29460
$551$	−0.652385	−	0.547416i	−0.0277925	−	0.0233207i
$552$		0			0
$553$	10.6016	+	10.9770i	0.450825	+	0.466789i
$554$	−7.39207	+	6.20268i	−0.314059	+	0.263527i
$555$		0			0
$556$	−0.609501	+	3.45665i	−0.0258486	+	0.146595i
$557$	9.14873			0.387644			0.193822	−	0.981037i	$-0.437912\pi$
$557$	9.14873			0.387644			0.193822	+	0.981037i	$0.437912\pi$
$558$		0			0
$559$	−0.425352	+	0.736731i	−0.0179905	+	0.0311604i
$560$	22.3591	+	50.2115i	0.944844	+	2.12182i
$561$		0			0
$562$	−4.39297	−	24.9138i	−0.185306	−	1.05092i
$563$	31.8857	+	11.6055i	1.34382	+	0.489111i	0.911014	−	0.412374i	$-0.135300\pi$
$563$	31.8857	+	11.6055i	1.34382	+	0.489111i	0.432808	+	0.901486i	$0.357523\pi$
$564$		0			0
$565$	1.53045	−	8.67962i	0.0643866	−	0.365155i
$566$	14.0508			0.590599
$567$		0			0
$568$	−22.0659			−0.925866
$569$	−3.23972	+	18.3734i	−0.135816	+	0.770251i	0.838472	+	0.544945i	$0.183449\pi$
$569$	−3.23972	+	18.3734i	−0.135816	+	0.770251i	−0.974288	+	0.225306i	$0.927662\pi$
$570$		0			0
$571$	−3.69402	−	1.34451i	−0.154590	−	0.0562661i	0.263566	−	0.964641i	$-0.415101\pi$
$571$	−3.69402	−	1.34451i	−0.154590	−	0.0562661i	−0.418156	+	0.908375i	$0.637323\pi$
$572$	0.0673255	+	0.381822i	0.00281502	+	0.0159648i
$573$		0			0
$574$	−15.2755	−	1.60462i	−0.637585	−	0.0669756i
$575$	−34.4689	+	59.7019i	−1.43745	+	2.48974i
$576$		0			0
$577$	7.95004			0.330965			0.165482	−	0.986213i	$-0.447082\pi$
$577$	7.95004			0.330965			0.165482	+	0.986213i	$0.447082\pi$
$578$	5.05608	−	28.6745i	0.210305	−	1.19270i
$579$		0			0
$580$	−0.467253	+	0.392072i	−0.0194016	+	0.0162799i
$581$	−6.17742	+	1.54058i	−0.256282	+	0.0639141i
$582$		0			0
$583$	7.03891	+	5.90634i	0.291522	+	0.244616i
$584$	19.9443			0.825300
$585$		0			0
$586$	31.4327			1.29847
$587$	3.92585	−	22.2646i	0.162037	−	0.918958i	−0.790030	−	0.613068i	$-0.789935\pi$
$587$	3.92585	−	22.2646i	0.162037	−	0.918958i	0.952067	−	0.305890i	$-0.0989538\pi$
$588$		0			0
$589$	28.1662	+	10.2516i	1.16057	+	0.422412i
$590$	−20.4297	+	17.1426i	−0.841079	+	0.705749i
$591$		0			0
$592$	3.63640	−	1.32354i	0.149455	−	0.0543973i
$593$	11.6835	+	20.2365i	0.479785	+	0.831011i	0.999731	−	0.0231874i	$-0.00738143\pi$
$593$	11.6835	+	20.2365i	0.479785	+	0.831011i	−0.519946	+	0.854199i	$0.674048\pi$
$594$		0			0
$595$	6.96028	+	3.39426i	0.285344	+	0.139151i
$596$	10.7361	+	9.00870i	0.439770	+	0.369011i
$597$		0			0
$598$	1.30643	+	0.475502i	0.0534240	+	0.0194447i
$599$	25.1192	−	21.0775i	1.02634	−	0.861204i	0.0359318	−	0.999354i	$-0.488560\pi$
$599$	25.1192	−	21.0775i	1.02634	−	0.861204i	0.990411	+	0.138150i	$0.0441156\pi$
$600$		0			0
$601$	6.43928	−	36.5190i	0.262664	−	1.48964i	−0.512943	−	0.858423i	$-0.671445\pi$
$601$	6.43928	−	36.5190i	0.262664	−	1.48964i	0.775606	−	0.631217i	$-0.217444\pi$
$602$	25.2745	+	12.3254i	1.03011	+	0.502344i
$603$		0			0
$604$	−9.01681	+	15.6176i	−0.366889	+	0.635470i
$605$	−3.54292	+	20.0929i	−0.144040	+	0.816893i
$606$		0			0
$607$	−14.1208	−	5.13953i	−0.573144	−	0.208607i	0.0391558	−	0.999233i	$-0.487533\pi$
$607$	−14.1208	−	5.13953i	−0.573144	−	0.208607i	−0.612300	+	0.790626i	$0.709755\pi$
$608$	28.0503	−	23.5370i	1.13759	−	0.954551i
$609$		0			0
$610$	−1.50645	+	0.548304i	−0.0609945	+	0.0222002i
$611$	−0.420213	+	0.727830i	−0.0170000	+	0.0294449i
$612$		0			0
$613$	14.0661	+	24.3632i	0.568125	+	0.984021i	0.996751	+	0.0805393i	$0.0256643\pi$
$613$	14.0661	+	24.3632i	0.568125	+	0.984021i	−0.428627	+	0.903482i	$0.641002\pi$
$614$	2.49784	−	0.909139i	0.100805	−	0.0366899i
$615$		0			0
$616$	−9.93693	+	2.47817i	−0.400370	+	0.0998482i
$617$	−0.135031	−	0.765797i	−0.00543613	−	0.0308298i	0.981969	−	0.189042i	$-0.0605382\pi$
$617$	−0.135031	−	0.765797i	−0.00543613	−	0.0308298i	−0.987405	+	0.158212i	$0.949427\pi$
$618$		0			0
$619$	10.3239	−	3.75760i	0.414953	−	0.151031i	−0.126103	−	0.992017i	$-0.540247\pi$
$619$	10.3239	−	3.75760i	0.414953	−	0.151031i	0.541056	+	0.840987i	$0.318025\pi$
$620$	10.7340	−	18.5918i	0.431087	−	0.746664i
$621$		0			0
$622$	−10.3435			−0.414737
$623$	1.40601	−	1.93544i	0.0563305	−	0.0775417i
$624$		0			0
$625$	50.3844	−	42.2775i	2.01538	−	1.69110i
$626$	2.52190	−	2.11612i	0.100795	−	0.0845773i
$627$		0			0
$628$	−8.80160	+	3.20352i	−0.351222	+	0.127834i
$629$	0.272600	−	0.472157i	0.0108693	−	0.0188262i
$630$		0			0
$631$	21.9799	+	38.0704i	0.875008	+	1.51556i	0.856755	+	0.515724i	$0.172477\pi$
$631$	21.9799	+	38.0704i	0.875008	+	1.51556i	0.0182532	+	0.999833i	$0.494190\pi$
$632$	6.92399	+	5.80992i	0.275422	+	0.231106i
$633$		0			0
$634$	−3.03591	−	17.2175i	−0.120571	−	0.683794i
$635$	−40.8143	−	14.8552i	−1.61967	−	0.589510i
$636$		0			0
$637$	−0.838231	−	0.523650i	−0.0332119	−	0.0207478i
$638$	−0.286994	−	0.497088i	−0.0113622	−	0.0196799i
$639$		0			0
$640$	23.5334	+	40.7610i	0.930238	+	1.61122i
$641$	25.0939	+	21.0563i	0.991149	+	0.831673i	0.985734	−	0.168312i	$-0.0538317\pi$
$641$	25.0939	+	21.0563i	0.991149	+	0.831673i	0.00541559	+	0.999985i	$0.498276\pi$
$642$		0			0
$643$	15.9951	+	5.82174i	0.630785	+	0.229587i	0.637573	−	0.770390i	$-0.279938\pi$
$643$	15.9951	+	5.82174i	0.630785	+	0.229587i	−0.00678774	+	0.999977i	$0.502161\pi$
$644$	4.52439	−	15.7819i	0.178286	−	0.621892i
$645$		0			0
$646$	1.39153	−	7.89174i	0.0547489	−	0.310496i
$647$	−14.6339	+	25.3466i	−0.575317	+	0.996479i	0.420690	+	0.907205i	$0.361788\pi$
$647$	−14.6339	+	25.3466i	−0.575317	+	0.996479i	−0.996007	+	0.0892745i	$0.971545\pi$
$648$		0			0
$649$	−4.48291	−	7.76464i	−0.175970	−	0.304789i
$650$	−2.35629	−	1.97717i	−0.0924215	−	0.0775508i
$651$		0			0
$652$	−1.56907	−	8.89865i	−0.0614496	−	0.348498i
$653$	−3.95607	−	22.4360i	−0.154813	−	0.877988i	−0.958957	−	0.283553i	$-0.908487\pi$
$653$	−3.95607	−	22.4360i	−0.154813	−	0.877988i	0.804144	−	0.594435i	$-0.202624\pi$
$654$		0			0
$655$	−19.2738	−	16.1726i	−0.753088	−	0.631916i
$656$	−16.4142			−0.640865
$657$		0			0
$658$	24.9691	+	12.1764i	0.973396	+	0.474687i
$659$	1.59882	−	0.581922i	0.0622810	−	0.0226684i	−0.310692	−	0.950511i	$-0.600561\pi$
$659$	1.59882	−	0.581922i	0.0622810	−	0.0226684i	0.372973	+	0.927842i	$0.378338\pi$
$660$		0			0
$661$	−2.71224	−	15.3819i	−0.105494	−	0.598285i	−0.991022	−	0.133699i	$-0.957314\pi$
$661$	−2.71224	−	15.3819i	−0.105494	−	0.598285i	0.885528	−	0.464586i	$-0.153797\pi$
$662$	−2.97473	−	16.8705i	−0.115616	−	0.655691i
$663$		0			0
$664$	−3.54344	+	1.28971i	−0.137512	+	0.0500503i
$665$	−64.0384	−	31.2290i	−2.48330	−	1.21101i
$666$		0			0
$667$	−0.735312			−0.0284714
$668$	−17.0664	−	14.3204i	−0.660320	−	0.554075i
$669$		0			0
$670$	−19.5782	−	111.034i	−0.756373	−	4.28960i
$671$	−0.0935884	−	0.530766i	−0.00361294	−	0.0204900i
$672$		0			0
$673$	−27.8478	−	23.3671i	−1.07346	−	0.900736i	−0.0780940	−	0.996946i	$-0.524883\pi$
$673$	−27.8478	−	23.3671i	−1.07346	−	0.900736i	−0.995361	+	0.0962102i	$0.969328\pi$
$674$	−19.2834	−	33.3997i	−0.742767	−	1.28651i
$675$		0			0
$676$	7.21466	−	12.4961i	0.277487	−	0.480621i
$677$	5.55448	−	31.5010i	0.213476	−	1.21068i	−0.670055	−	0.742311i	$-0.733730\pi$
$677$	5.55448	−	31.5010i	0.213476	−	1.21068i	0.883531	−	0.468372i	$-0.155159\pi$
$678$		0			0
$679$	1.34296	−	4.68449i	0.0515382	−	0.179774i
$680$	4.30993	+	1.56869i	0.165278	+	0.0601563i
$681$		0			0
$682$	15.4756	+	12.9856i	0.592592	+	0.497244i
$683$	−0.740434	−	1.28247i	−0.0283319	−	0.0490723i	0.851512	−	0.524335i	$-0.175686\pi$
$683$	−0.740434	−	1.28247i	−0.0283319	−	0.0490723i	−0.879844	+	0.475263i	$0.842353\pi$
$684$		0			0
$685$	−5.33912	−	9.24762i	−0.203997	−	0.353333i
$686$	−15.3324	+	28.8481i	−0.585393	+	1.10143i
$687$		0			0
$688$	28.2382	+	10.2779i	1.07657	+	0.391839i
$689$	0.0912029	+	0.517237i	0.00347455	+	0.0197052i
$690$		0			0
$691$	6.74135	+	5.65666i	0.256453	+	0.215190i	0.761945	−	0.647642i	$-0.224245\pi$
$691$	6.74135	+	5.65666i	0.256453	+	0.215190i	−0.505492	+	0.862831i	$0.668689\pi$
$692$	−14.3790	−	24.9052i	−0.546609	−	0.946755i
$693$		0			0
$694$	−8.77388	+	15.1968i	−0.333052	+	0.576863i
$695$	12.3586	−	4.49818i	0.468790	−	0.170626i
$696$		0			0
$697$	−1.77151	+	1.48647i	−0.0671006	+	0.0563041i
$698$	33.9018	−	28.4470i	1.28320	−	1.07673i
$699$		0			0
$700$	−21.3485	+	29.3873i	−0.806899	+	1.11074i
$701$	−1.01529			−0.0383469			−0.0191734	−	0.999816i	$-0.506103\pi$
$701$	−1.01529			−0.0383469			−0.0191734	+	0.999816i	$0.506103\pi$
$702$		0			0
$703$	−2.50807	+	4.34411i	−0.0945937	+	0.163841i
$704$	0.0369987	−	0.0134664i	0.00139444	−	0.000507534i
$705$		0			0
$706$	−3.03381	−	17.2056i	−0.114179	−	0.647540i
$707$	−20.8814	+	5.20761i	−0.785327	+	0.195852i
$708$		0			0
$709$	−42.0314	+	15.2982i	−1.57852	+	0.574535i	−0.974882	−	0.222723i	$-0.928505\pi$
$709$	−42.0314	+	15.2982i	−1.57852	+	0.574535i	−0.603639	+	0.797258i	$0.706283\pi$
$710$	−51.7319	−	89.6023i	−1.94146	−	3.36271i
$711$		0			0
$712$	0.708440	−	1.22705i	0.0265499	−	0.0459858i
$713$	24.3192	−	8.85147i	0.910762	−	0.331490i
$714$		0			0
$715$	1.11287	−	0.933808i	0.0416189	−	0.0349224i
$716$	20.4188	+	7.43184i	0.763087	+	0.277741i
$717$		0			0
$718$	−5.06175	+	28.7066i	−0.188903	+	1.07132i
$719$	2.63441	−	4.56292i	0.0982467	−	0.170168i	−0.812712	−	0.582665i	$-0.802010\pi$
$719$	2.63441	−	4.56292i	0.0982467	−	0.170168i	0.910959	+	0.412497i	$0.135343\pi$
$720$		0			0
$721$	15.2333	+	7.42867i	0.567316	+	0.276658i
$722$	−6.98286	+	39.6017i	−0.259875	+	1.47382i
$723$		0			0
$724$	−2.40419	+	2.01735i	−0.0893510	+	0.0749744i
$725$	1.52874	+	0.556414i	0.0567758	+	0.0206647i
$726$		0			0
$727$	31.0047	+	26.0161i	1.14990	+	0.964882i	0.999717	−	0.0237758i	$-0.00756878\pi$
$727$	31.0047	+	26.0161i	1.14990	+	0.964882i	0.150185	+	0.988658i	$0.452013\pi$
$728$	−0.526155	−	0.256585i	−0.0195006	−	0.00950969i
$729$		0			0
$730$	46.7579	+	80.9870i	1.73059	+	2.99746i
$731$	3.97838	−	1.44801i	0.147146	−	0.0535567i
$732$		0			0
$733$	−18.8382	+	15.8071i	−0.695804	+	0.583849i	−0.920577	−	0.390562i	$-0.872281\pi$
$733$	−18.8382	+	15.8071i	−0.695804	+	0.583849i	0.224772	+	0.974411i	$0.427836\pi$
$734$	−52.5972	−	19.1438i	−1.94140	−	0.706610i
$735$		0			0
$736$	5.49004	−	31.1356i	0.202366	−	1.14767i
$737$	37.9040			1.39621
$738$		0			0
$739$	41.2905			1.51890			0.759448	−	0.650568i	$-0.225469\pi$
$739$	41.2905			1.51890			0.759448	+	0.650568i	$0.225469\pi$
$740$	2.75215	+	2.30933i	0.101171	+	0.0848927i
$741$		0			0
$742$	16.8448	−	4.20093i	0.618393	−	0.154221i
$743$	8.19507	−	6.87648i	0.300648	−	0.252274i	−0.479966	−	0.877287i	$-0.659351\pi$
$743$	8.19507	−	6.87648i	0.300648	−	0.252274i	0.780614	+	0.625013i	$0.214907\pi$
$744$		0			0
$745$	9.11896	−	51.7162i	0.334093	−	1.89474i
$746$	42.2663			1.54748
$747$		0			0
$748$	0.964765	−	1.67102i	0.0352753	−	0.0610986i
$749$	−31.3978	−	3.29821i	−1.14725	−	0.120514i
$750$		0			0
$751$	2.25015	+	12.7612i	0.0821092	+	0.465664i	0.997943	+	0.0641070i	$0.0204199\pi$
$751$	2.25015	+	12.7612i	0.0821092	+	0.465664i	−0.915834	+	0.401557i	$0.868469\pi$
$752$	27.8970	+	10.1537i	1.01730	+	0.370266i
$753$		0			0
$754$	0.00569717	−	0.0323103i	0.000207479	−	0.00117667i
$755$	67.5716			2.45918
$756$		0			0
$757$	28.7036			1.04325			0.521625	−	0.853175i	$-0.325326\pi$
$757$	28.7036			1.04325			0.521625	+	0.853175i	$0.325326\pi$
$758$	−5.68081	+	32.2175i	−0.206336	+	1.17019i
$759$		0			0
$760$	−39.6537	−	14.4328i	−1.43839	−	0.523532i
$761$	6.50686	+	36.9023i	0.235874	+	1.33771i	0.840766	+	0.541399i	$0.182105\pi$
$761$	6.50686	+	36.9023i	0.235874	+	1.33771i	−0.604892	+	0.796307i	$0.706784\pi$
$762$		0			0
$763$	−0.344905	−	0.774548i	−0.0124864	−	0.0280405i
$764$	−4.53352	+	7.85229i	−0.164017	+	0.284086i
$765$		0			0
$766$	−39.9321			−1.44280
$767$	0.0889913	−	0.504695i	0.00321329	−	0.0182235i
$768$		0			0
$769$	−25.1958	+	21.1418i	−0.908584	+	0.762392i	−0.971849	−	0.235605i	$-0.924293\pi$
$769$	−25.1958	+	21.1418i	−0.908584	+	0.762392i	0.0632654	+	0.997997i	$0.479849\pi$
$770$	−33.3594	−	34.5407i	−1.20219	−	1.24476i
$771$		0			0
$772$	2.52531	+	2.11899i	0.0908879	+	0.0762640i
$773$	18.3980			0.661731			0.330866	−	0.943678i	$-0.392659\pi$
$773$	18.3980			0.661731			0.330866	+	0.943678i	$0.392659\pi$
$774$		0			0
$775$	−57.2583			−2.05678
$776$	0.501203	−	2.84246i	0.0179921	−	0.102038i
$777$		0			0
$778$	−15.2639	−	5.55560i	−0.547237	−	0.199178i
$779$	16.2988	−	13.6763i	0.583966	−	0.490006i
$780$		0			0
$781$	32.6856	−	11.8966i	1.16958	−	0.425693i
$782$	−3.45950	−	5.99202i	−0.123711	−	0.214274i
$783$		0			0
$784$	−13.0748	+	32.3720i	−0.466957	+	1.15614i
$785$	26.8850	+	22.5592i	0.959568	+	0.805174i
$786$		0			0
$787$	33.4128	+	12.1613i	1.19104	+	0.433503i	0.860088	−	0.510145i	$-0.170408\pi$
$787$	33.4128	+	12.1613i	1.19104	+	0.433503i	0.330951	+	0.943648i	$0.392631\pi$
$788$	−15.2585	+	12.8034i	−0.543560	+	0.456101i
$789$		0			0
$790$	−7.35935	+	41.7369i	−0.261834	+	1.48493i
$791$	4.64094	−	3.13075i	0.165013	−	0.111317i
$792$		0			0
$793$	0.0154031	−	0.0266790i	0.000546981	−	0.000947399i
$794$	5.00926	−	28.4089i	0.177772	−	1.00819i
$795$		0			0
$796$	−12.2925	−	4.47409i	−0.435695	−	0.158580i
$797$	7.71007	−	6.46952i	0.273105	−	0.229162i	−0.495940	−	0.868357i	$-0.665177\pi$
$797$	7.71007	−	6.46952i	0.273105	−	0.229162i	0.769045	+	0.639194i	$0.220732\pi$
$798$		0			0
$799$	3.93031	−	1.43052i	0.139045	−	0.0506081i
$800$	−34.9744	+	60.5774i	−1.23653	+	2.14174i
$801$		0			0
$802$	−32.3396	−	56.0138i	−1.14195	−	1.97792i
$803$	−29.5428	+	10.7527i	−1.04254	+	0.379455i
$804$		0			0
$805$	−59.6881	+	14.8856i	−2.10373	+	0.524648i
$806$	0.200517	+	1.13719i	0.00706292	+	0.0400558i
$807$		0			0
$808$	−11.9778	+	4.35957i	−0.421378	+	0.153369i
$809$	−14.1884	+	24.5750i	−0.498838	+	0.864012i	−0.999999	−	0.00134173i	$-0.999573\pi$
$809$	−14.1884	+	24.5750i	−0.498838	+	0.864012i	0.501162	+	0.865354i	$0.332906\pi$
$810$		0			0
$811$	−24.0856			−0.845758			−0.422879	−	0.906186i	$-0.638981\pi$
$811$	−24.0856			−0.845758			−0.422879	+	0.906186i	$0.638981\pi$
$812$	−0.385314	−	0.0404756i	−0.0135219	−	0.00142041i
$813$		0			0
$814$	−2.58986	+	2.17315i	−0.0907746	+	0.0761689i
$815$	−25.9363	+	21.7631i	−0.908508	+	0.762329i
$816$		0			0
$817$	−36.6033	+	13.3225i	−1.28059	+	0.466096i
$818$	1.42534	−	2.46876i	0.0498358	−	0.0863182i
$819$		0			0
$820$	−7.61941	−	13.1972i	−0.266081	−	0.460866i
$821$	21.4922	+	18.0341i	0.750083	+	0.629394i	0.935525	−	0.353261i	$-0.114927\pi$
$821$	21.4922	+	18.0341i	0.750083	+	0.629394i	−0.185442	+	0.982655i	$0.559372\pi$
$822$		0			0
$823$	4.95932	+	28.1257i	0.172871	+	0.980401i	0.940572	+	0.339593i	$0.110289\pi$
$823$	4.95932	+	28.1257i	0.172871	+	0.980401i	−0.767701	+	0.640808i	$0.778599\pi$
$824$	9.43270	+	3.43322i	0.328604	+	0.119602i
$825$		0			0
$826$	−16.8471	−	1.76972i	−0.586186	−	0.0615763i
$827$	−19.8973	−	34.4632i	−0.691897	−	1.19840i	−0.971215	−	0.238203i	$-0.923442\pi$
$827$	−19.8973	−	34.4632i	−0.691897	−	1.19840i	0.279318	−	0.960199i	$-0.409892\pi$
$828$		0			0
$829$	−17.7672	−	30.7737i	−0.617081	−	1.06882i	−0.990016	−	0.140958i	$-0.954982\pi$
$829$	−17.7672	−	30.7737i	−0.617081	−	1.06882i	0.372935	−	0.927858i	$-0.378352\pi$
$830$	−13.5444	−	11.3651i	−0.470132	−	0.394488i
$831$		0			0
$832$	0.00211482		0.000769731i	7.33181e−5		2.66856e-5i
$833$	1.52052	+	4.67782i	0.0526828	+	0.162077i
$834$		0			0
$835$	−14.4957	+	82.2093i	−0.501645	+	2.84497i
$836$	−8.87637	+	15.3743i	−0.306996	+	0.531732i
$837$		0			0
$838$	−12.9806	−	22.4831i	−0.448408	−	0.776665i
$839$	−6.42785	−	5.39360i	−0.221914	−	0.186208i	0.525052	−	0.851070i	$-0.324046\pi$
$839$	−6.42785	−	5.39360i	−0.221914	−	0.186208i	−0.746966	+	0.664862i	$0.768490\pi$
$840$		0			0
$841$	−5.03278	−	28.5423i	−0.173544	−	0.984218i
$842$	4.14766	+	23.5226i	0.142938	+	0.810642i
$843$		0			0
$844$	−4.14982	−	3.48212i	−0.142843	−	0.119859i
$845$	−54.0663			−1.85994
$846$		0			0
$847$	−10.7436	+	7.24753i	−0.369153	+	0.249028i
$848$	17.4340	−	6.34544i	0.598685	−	0.217903i
$849$		0			0
$850$	2.65820	+	15.0754i	0.0911756	+	0.517082i
$851$	0.752077	+	4.26524i	0.0257809	+	0.146210i
$852$		0			0
$853$	53.3397	−	19.4141i	1.82632	−	0.664725i	0.832456	−	0.554092i	$-0.186934\pi$
$853$	53.3397	−	19.4141i	1.82632	−	0.664725i	0.993861	−	0.110633i	$-0.0352878\pi$
$854$	−0.915255	−	0.446334i	−0.0313194	−	0.0152732i
$855$		0			0
$856$	−18.6987			−0.639110
$857$	−16.0477	−	13.4657i	−0.548181	−	0.459978i	0.326144	−	0.945320i	$-0.394251\pi$
$857$	−16.0477	−	13.4657i	−0.548181	−	0.459978i	−0.874324	+	0.485342i	$0.838695\pi$
$858$		0			0
$859$	4.95940	+	28.1262i	0.169213	+	0.959652i	0.944614	+	0.328184i	$0.106436\pi$
$859$	4.95940	+	28.1262i	0.169213	+	0.959652i	−0.775401	+	0.631469i	$0.782452\pi$
$860$	4.84455	+	27.4748i	0.165198	+	0.936883i
$861$		0			0
$862$	29.4827	+	24.7390i	1.00419	+	0.842612i
$863$	−23.8019	−	41.2262i	−0.810228	−	1.40336i	−0.912705	−	0.408620i	$-0.866010\pi$
$863$	−23.8019	−	41.2262i	−0.810228	−	1.40336i	0.102477	−	0.994735i	$-0.467323\pi$
$864$		0			0
$865$	−53.8779	+	93.3193i	−1.83190	+	3.17295i
$866$	−3.10473	+	17.6078i	−0.105503	+	0.598338i
$867$		0			0
$868$	13.2308	−	3.29963i	0.449084	−	0.111997i
$869$	−13.3886	−	4.87307i	−0.454179	−	0.165307i
$870$		0			0
$871$	1.65969	+	1.39264i	0.0562363	+	0.0471879i
$872$	−0.251090	−	0.434900i	−0.00850297	−	0.0147276i
$873$		0			0
$874$	31.8293	+	55.1299i	1.07664	+	1.86480i
$875$	80.5567	+	8.46214i	2.72331	+	0.286072i
$876$		0			0
$877$	−47.5513	−	17.3072i	−1.60569	−	0.584424i	−0.625111	−	0.780536i	$-0.714946\pi$
$877$	−47.5513	−	17.3072i	−1.60569	−	0.584424i	−0.980582	+	0.196112i	$0.937168\pi$
$878$	−0.871732	−	4.94384i	−0.0294195	−	0.166846i
$879$		0			0
$880$	−39.3112	−	32.9860i	−1.32518	−	1.11196i
$881$	10.1196	+	17.5276i	0.340937	+	0.590519i	0.984607	−	0.174783i	$-0.0559225\pi$
$881$	10.1196	+	17.5276i	0.340937	+	0.590519i	−0.643670	+	0.765303i	$0.722589\pi$
$882$		0			0
$883$	2.54791	−	4.41312i	0.0857441	−	0.148513i	−0.819964	−	0.572415i	$-0.806007\pi$
$883$	2.54791	−	4.41312i	0.0857441	−	0.148513i	0.905708	+	0.423902i	$0.139340\pi$
$884$	0.103639	−	0.0377216i	0.00348576	−	0.00126871i
$885$		0			0
$886$	−8.61603	+	7.22971i	−0.289461	+	0.242887i
$887$	0.672255	−	0.564089i	0.0225721	−	0.0189403i	−0.631432	−	0.775431i	$-0.717532\pi$
$887$	0.672255	−	0.564089i	0.0225721	−	0.0189403i	0.654004	+	0.756491i	$0.273088\pi$
$888$		0			0
$889$	−11.2227	−	25.2026i	−0.376396	−	0.845267i
$890$	6.64354			0.222692
$891$		0			0
$892$	−10.8644	+	18.8177i	−0.363767	+	0.630063i
$893$	−36.1611	+	13.1615i	−1.21008	+	0.440434i
$894$		0			0
$895$	−14.1383	−	80.1820i	−0.472590	−	2.68019i
$896$	−8.23880	+	28.7384i	−0.275239	+	0.960082i
$897$		0			0
$898$	−7.74955	+	2.82061i	−0.258606	+	0.0941248i
$899$	−0.305367	−	0.528911i	−0.0101846	−	0.0176402i
$900$		0			0
$901$	1.30692	−	2.26366i	0.0435400	−	0.0754134i
$902$	13.4754	−	4.90464i	0.448681	−	0.163307i
$903$		0			0
$904$	2.53999	−	2.13131i	0.0844789	−	0.0708862i
$905$	11.0505	+	4.02205i	0.367330	+	0.133697i
$906$		0			0
$907$	−1.74063	+	9.87160i	−0.0577966	+	0.327781i	−0.999973	−	0.00733616i	$-0.997665\pi$
$907$	−1.74063	+	9.87160i	−0.0577966	+	0.327781i	0.942176	+	0.335117i	$0.108776\pi$
$908$	−6.84339	+	11.8531i	−0.227106	+	0.393359i
$909$		0			0
$910$	−0.191625	−	2.73808i	−0.00635230	−	0.0907666i
$911$	−1.74967	+	9.92289i	−0.0579693	+	0.328760i	−0.999977	−	0.00683209i	$-0.997825\pi$
$911$	−1.74967	+	9.92289i	−0.0579693	+	0.328760i	0.942007	+	0.335592i	$0.108936\pi$
$912$		0			0
$913$	4.55345	−	3.82080i	0.150697	−	0.126450i
$914$	31.8240	+	11.5830i	1.05265	+	0.383132i
$915$		0			0
$916$	−21.8321	−	18.3193i	−0.721353	−	0.605287i
$917$	−1.11572	−	15.9423i	−0.0368444	−	0.526461i
$918$		0			0
$919$	−22.4955	−	38.9634i	−0.742059	−	1.28528i	−0.951556	−	0.307474i	$-0.900516\pi$
$919$	−22.4955	−	38.9634i	−0.742059	−	1.28528i	0.209498	−	0.977809i	$-0.432817\pi$
$920$	−34.2378	+	12.4615i	−1.12879	+	0.410845i
$921$		0			0
$922$	−2.50176	+	2.09922i	−0.0823910	+	0.0691342i
$923$	1.86828	+	0.680000i	0.0614953	+	0.0223825i
$924$		0			0
$925$	1.66394	−	9.43666i	0.0547099	−	0.310275i
$926$	26.6772			0.876666
$927$		0			0
$928$	−0.746095			−0.0244918
$929$	−19.2024	−	16.1127i	−0.630009	−	0.528640i	0.270923	−	0.962601i	$-0.412671\pi$
$929$	−19.2024	−	16.1127i	−0.630009	−	0.528640i	−0.900932	+	0.433961i	$0.857116\pi$
$930$		0			0
$931$	−13.9896	−	43.0386i	−0.458490	−	1.41053i
$932$	−6.24506	+	5.24023i	−0.204564	+	0.171649i
$933$		0			0
$934$	−7.57666	+	42.9694i	−0.247916	+	1.40600i
$935$	−7.22990			−0.236443
$936$		0			0
$937$	25.9068	−	44.8718i	0.846337	−	1.46590i	−0.0381183	−	0.999273i	$-0.512136\pi$
$937$	25.9068	−	44.8718i	0.846337	−	1.46590i	0.884455	−	0.466625i	$-0.154530\pi$
$938$	42.0907	−	57.9400i	1.37431	−	1.89181i
$939$		0			0
$940$	4.78602	+	27.1428i	0.156103	+	0.885302i
$941$	−10.7417	−	3.90966i	−0.350169	−	0.127451i	0.160946	−	0.986963i	$-0.448545\pi$
$941$	−10.7417	−	3.90966i	−0.350169	−	0.127451i	−0.511116	+	0.859512i	$0.670768\pi$
$942$		0			0
$943$	3.19003	−	18.0916i	0.103882	−	0.589142i
$944$	−18.1030			−0.589201
$945$		0			0
$946$	−26.2535			−0.853575
$947$	−3.19378	+	18.1128i	−0.103784	+	0.588587i	0.887915	+	0.460007i	$0.152153\pi$
$947$	−3.19378	+	18.1128i	−0.103784	+	0.588587i	−0.991699	+	0.128580i	$0.958958\pi$
$948$		0			0
$949$	−1.68865	−	0.614618i	−0.0548158	−	0.0199513i
$950$	−24.4569	−	138.702i	−0.793487	−	4.50009i
$951$		0			0
$952$	1.18510	+	2.66135i	0.0384092	+	0.0862550i
$953$	1.96945	−	3.41119i	0.0637968	−	0.110499i	−0.832363	−	0.554231i	$-0.813012\pi$
$953$	1.96945	−	3.41119i	0.0637968	−	0.110499i	0.896160	+	0.443732i	$0.146346\pi$
$954$		0			0
$955$	33.9740			1.09937
$956$	−2.86526	+	16.2497i	−0.0926692	+	0.525553i
$957$		0			0
$958$	42.8235	−	35.9331i	1.38356	−	1.16095i
$959$	1.86917	−	6.52000i	0.0603587	−	0.210542i
$960$		0			0
$961$	−7.28100	−	6.10948i	−0.234871	−	0.197080i
$962$	−0.193246			−0.00623049
$963$		0			0
$964$	−19.4528			−0.626533
$965$	2.14492	−	12.1645i	0.0690475	−	0.391588i
$966$		0			0
$967$	5.07490	+	1.84711i	0.163198	+	0.0593991i	0.422327	−	0.906444i	$-0.361213\pi$
$967$	5.07490	+	1.84711i	0.163198	+	0.0593991i	−0.259129	+	0.965843i	$0.583436\pi$
$968$	−5.87997	+	4.93388i	−0.188989	+	0.158581i
$969$		0			0
$970$	12.7173	−	4.62872i	0.408328	−	0.148619i
$971$	−23.7078	−	41.0631i	−0.760819	−	1.31778i	−0.942429	−	0.334407i	$-0.891464\pi$
$971$	−23.7078	−	41.0631i	−0.760819	−	1.31778i	0.181610	−	0.983371i	$-0.441869\pi$
$972$		0			0
$973$	7.50856	+	3.66163i	0.240713	+	0.117387i
$974$	40.6020	+	34.0692i	1.30097	+	1.09165i
$975$		0			0
$976$	−1.02258	−	0.372188i	−0.0327319	−	0.0119135i
$977$	44.2452	−	37.1261i	1.41553	−	1.18777i	0.461844	−	0.886961i	$-0.347188\pi$
$977$	44.2452	−	37.1261i	1.41553	−	1.18777i	0.953685	−	0.300809i	$-0.0972565\pi$
$978$		0			0
$979$	−0.387839	+	2.19954i	−0.0123954	+	0.0702977i
$980$	−32.0968	+	4.51471i	−1.02530	+	0.144217i
$981$		0			0
$982$	27.2433	−	47.1868i	0.869369	−	1.50579i
$983$	−7.20854	+	40.8817i	−0.229917	+	1.30392i	0.623142	+	0.782109i	$0.285856\pi$
$983$	−7.20854	+	40.8817i	−0.229917	+	1.30392i	−0.853059	+	0.521814i	$0.825255\pi$
$984$		0			0
$985$	70.1332	+	25.5264i	2.23463	+	0.813338i
$986$	−0.125079	+	0.104954i	−0.00398334	+	0.00334242i
$987$		0			0
$988$	−0.953538	+	0.347059i	−0.0303361	+	0.0110414i
$989$	−16.8161	+	29.1264i	−0.534722	+	0.926166i
$990$		0			0
$991$	25.3701	+	43.9423i	0.805908	+	1.39587i	0.915676	+	0.401917i	$0.131656\pi$
$991$	25.3701	+	43.9423i	0.805908	+	1.39587i	−0.109768	+	0.993957i	$0.535011\pi$
$992$	24.6758	−	8.98127i	0.783458	−	0.285155i
$993$		0			0
$994$	18.1108	−	63.1738i	0.574440	−	2.00375i
$995$	8.51146	+	48.2709i	0.269831	+	1.53029i
$996$		0			0
$997$	−30.2743	+	11.0190i	−0.958798	+	0.348974i	−0.773562	−	0.633720i	$-0.781527\pi$
$997$	−30.2743	+	11.0190i	−0.958798	+	0.348974i	−0.185236	+	0.982694i	$0.559305\pi$
$998$	13.6339	−	23.6147i	0.431575	−	0.747510i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.w.a.46.6		132
3.2	odd	2		189.2.w.a.151.17	yes	132
7.2	even	3		567.2.u.a.289.17		132
21.2	odd	6		189.2.u.a.16.6	✓	132
27.5	odd	18		189.2.u.a.130.6	yes	132
27.22	even	9		567.2.u.a.361.17		132
189.86	odd	18		189.2.w.a.184.17	yes	132
189.184	even	9	inner	567.2.w.a.37.6		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.6	✓	132	21.2	odd	6
189.2.u.a.130.6	yes	132	27.5	odd	18
189.2.w.a.151.17	yes	132	3.2	odd	2
189.2.w.a.184.17	yes	132	189.86	odd	18
567.2.u.a.289.17		132	7.2	even	3
567.2.u.a.361.17		132	27.22	even	9
567.2.w.a.37.6		132	189.184	even	9	inner
567.2.w.a.46.6		132	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.w (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.306313 + 1.73719i) q^{2} +(-1.04461 - 0.380207i) q^{4} +(0.723302 + 4.10205i) q^{5} +(-1.55501 + 2.14055i) q^{7} +(-0.783518 + 1.35709i) q^{8} +O(q^{10})\)	\(q+(-0.306313 + 1.73719i) q^{2} +(-1.04461 - 0.380207i) q^{4} +(0.723302 + 4.10205i) q^{5} +(-1.55501 + 2.14055i) q^{7} +(-0.783518 + 1.35709i) q^{8} -7.34759 q^{10} +(0.428940 - 2.43264i) q^{11} +(0.108160 - 0.0907572i) q^{13} +(-3.24222 - 3.35702i) q^{14} +(-3.82067 - 3.20592i) q^{16} -0.702677 q^{17} +6.46502 q^{19} +(0.804060 - 4.56005i) q^{20} +(4.09457 + 1.49030i) q^{22} +(4.27608 - 3.58805i) q^{23} +(-11.6052 + 4.22394i) q^{25} +(0.124532 + 0.215695i) q^{26} +(2.43823 - 1.64481i) q^{28} +(-0.100910 - 0.0846735i) q^{29} +(4.35670 + 1.58571i) q^{31} +(4.33878 - 3.64067i) q^{32} +(0.215239 - 1.22068i) q^{34} +(-9.90538 - 4.83046i) q^{35} +(-0.387945 + 0.671941i) q^{37} +(-1.98032 + 11.2310i) q^{38} +(-6.13358 - 2.23244i) q^{40} +(2.52108 - 2.11544i) q^{41} +(-5.66175 + 2.06071i) q^{43} +(-1.37298 + 2.37808i) q^{44} +(4.92331 + 8.52742i) q^{46} +(-5.59334 + 2.03581i) q^{47} +(-2.16389 - 6.65714i) q^{49} +(-3.78296 - 21.4542i) q^{50} +(-0.147492 + 0.0536827i) q^{52} +(-1.85992 + 3.22148i) q^{53} +10.2891 q^{55} +(-1.68654 - 3.78745i) q^{56} +(0.178004 - 0.149363i) q^{58} +(2.78047 - 2.33309i) q^{59} +(0.205027 - 0.0746237i) q^{61} +(-4.08919 + 7.08269i) q^{62} +(0.00796973 + 0.0138040i) q^{64} +(0.450523 + 0.378034i) q^{65} +(2.66458 + 15.1116i) q^{67} +(0.734024 + 0.267163i) q^{68} +(11.4256 - 15.7279i) q^{70} +(7.04066 + 12.1948i) q^{71} +(-6.36370 - 11.0222i) q^{73} +(-1.04845 - 0.879758i) q^{74} +(-6.75343 - 2.45805i) q^{76} +(4.54018 + 4.70095i) q^{77} +(1.00160 - 5.68035i) q^{79} +(10.3874 - 17.9914i) q^{80} +(2.90267 + 5.02758i) q^{82} +(1.84338 + 1.54678i) q^{83} +(-0.508248 - 2.88242i) q^{85} +(-1.84557 - 10.4667i) q^{86} +(2.96524 + 2.48813i) q^{88} -0.904179 q^{89} +(0.0260800 + 0.372651i) q^{91} +(-5.83104 + 2.12233i) q^{92} +(-1.82327 - 10.3403i) q^{94} +(4.67616 + 26.5198i) q^{95} +(-1.73081 + 0.629965i) q^{97} +(12.2275 - 1.71991i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

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