LMFDB - Embedded newform 162.2.g.b.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			103.2
Character	$\chi$	$=$	162.103
Dual form			162.2.g.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 - 0.727374i) q^{2} +(0.224505 - 1.71744i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.24355 - 0.262233i) q^{5} +(-1.40328 + 1.01528i) q^{6} +(3.76235 + 1.88952i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-2.89919 - 0.771149i) q^{9} +O(q^{10})$	\(q+(-0.686242 - 0.727374i) q^{2} +(0.224505 - 1.71744i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.24355 - 0.262233i) q^{5} +(-1.40328 + 1.01528i) q^{6} +(3.76235 + 1.88952i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-2.89919 - 0.771149i) q^{9} +(-1.73036 - 1.45194i) q^{10} +(-1.42253 - 3.29779i) q^{11} +(1.70148 + 0.323986i) q^{12} +(-4.26836 - 1.01162i) q^{13} +(-1.20749 - 4.03330i) q^{14} +(0.0533189 - 3.91203i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.241347 + 1.36875i) q^{17} +(1.42864 + 2.63799i) q^{18} +(0.883044 + 5.00799i) q^{19} +(0.131339 + 2.25500i) q^{20} +(4.08981 - 6.03740i) q^{21} +(-1.42253 + 3.29779i) q^{22} +(-0.261895 + 0.131529i) q^{23} +(-0.931968 - 1.45994i) q^{24} +(0.0995059 - 0.0235833i) q^{25} +(2.19330 + 3.79891i) q^{26} +(-1.97529 + 4.80606i) q^{27} +(-2.10509 + 3.64612i) q^{28} +(2.13741 - 7.13946i) q^{29} +(-2.88209 + 2.64581i) q^{30} +(6.75905 + 4.44550i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-5.98313 + 1.70274i) q^{33} +(1.16121 - 0.763743i) q^{34} +(8.93649 + 3.25262i) q^{35} +(0.938417 - 2.84945i) q^{36} +(-2.90034 + 1.05564i) q^{37} +(3.03670 - 4.07900i) q^{38} +(-2.69567 + 7.10354i) q^{39} +(1.55010 - 1.64301i) q^{40} +(-5.07095 + 5.37489i) q^{41} +(-7.19804 + 1.16830i) q^{42} +(1.66067 - 2.23066i) q^{43} +(3.37493 - 1.22837i) q^{44} +(-6.70670 - 0.969843i) q^{45} +(0.275394 + 0.100235i) q^{46} +(-0.834413 + 0.548802i) q^{47} +(-0.422370 + 1.67976i) q^{48} +(6.40486 + 8.60322i) q^{49} +(-0.0854390 - 0.0561941i) q^{50} +(2.29656 + 0.721791i) q^{51} +(1.25809 - 4.20232i) q^{52} +(-5.96257 + 10.3275i) q^{53} +(4.85133 - 1.86135i) q^{54} +(-4.05630 - 7.02572i) q^{55} +(4.09669 - 0.970933i) q^{56} +(8.79917 - 0.392254i) q^{57} +(-6.65983 + 3.34469i) q^{58} +(-3.66592 + 8.49856i) q^{59} +(3.90231 + 0.280693i) q^{60} +(-0.863013 - 14.8174i) q^{61} +(-1.40481 - 7.96705i) q^{62} +(-9.45068 - 8.37942i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-9.84155 - 1.15031i) q^{65} +(5.34440 + 3.18348i) q^{66} +(-1.60063 - 5.34648i) q^{67} +(-1.35240 - 0.320525i) q^{68} +(0.167096 + 0.479318i) q^{69} +(-3.76673 - 8.73225i) q^{70} +(4.88985 + 4.10307i) q^{71} +(-2.71660 + 1.27283i) q^{72} +(4.66440 - 3.91389i) q^{73} +(2.75818 + 1.38521i) q^{74} +(-0.0181633 - 0.176190i) q^{75} +(-5.05086 + 0.590361i) q^{76} +(0.879204 - 15.0954i) q^{77} +(7.01681 - 2.91399i) q^{78} +(8.31655 + 8.81503i) q^{79} -2.25882 q^{80} +(7.81066 + 4.47142i) q^{81} +7.38945 q^{82} +(2.12671 + 2.25418i) q^{83} +(5.78938 + 4.43393i) q^{84} +(-0.182543 + 3.13414i) q^{85} +(-2.76214 + 0.322848i) q^{86} +(-11.7817 - 5.27372i) q^{87} +(-3.20950 - 1.61187i) q^{88} +(-0.706078 + 0.592470i) q^{89} +(3.89698 + 5.54382i) q^{90} +(-14.1476 - 11.8712i) q^{91} +(-0.116078 - 0.269100i) q^{92} +(9.15232 - 10.6102i) q^{93} +(0.971793 + 0.230319i) q^{94} +(3.29441 + 11.0041i) q^{95} +(1.51166 - 0.845503i) q^{96} +(1.85410 + 0.216713i) q^{97} +(1.86247 - 10.5626i) q^{98} +(1.58110 + 10.6579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$3$	0.224505	−	1.71744i	0.129618	−	0.991564i
$3$	0.224505	−	1.71744i	0.129618	−	0.991564i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	2.24355	−	0.262233i	1.00334	−	0.117274i	0.401476	−	0.915870i	$-0.368497\pi$
$5$	2.24355	−	0.262233i	1.00334	−	0.117274i	0.601868	+	0.798595i	$0.294423\pi$
$6$	−1.40328	+	1.01528i	−0.572889	+	0.414486i
$7$	3.76235	+	1.88952i	1.42203	+	0.714172i	0.982881	−	0.184240i	$-0.0589824\pi$
$7$	3.76235	+	1.88952i	1.42203	+	0.714172i	0.439153	+	0.898412i	$0.355279\pi$
$8$	0.766044	−	0.642788i	0.270838	−	0.227260i
$9$	−2.89919	−	0.771149i	−0.966398	−	0.257050i
$10$	−1.73036	−	1.45194i	−0.547186	−	0.459144i
$11$	−1.42253	−	3.29779i	−0.428909	−	0.994323i	−0.986433	−	0.164162i	$-0.947508\pi$
$11$	−1.42253	−	3.29779i	−0.428909	−	0.994323i	0.557524	−	0.830160i	$-0.311751\pi$
$12$	1.70148	+	0.323986i	0.491175	+	0.0935266i
$13$	−4.26836	−	1.01162i	−1.18383	−	0.280573i	−0.408876	−	0.912590i	$-0.634079\pi$
$13$	−4.26836	−	1.01162i	−1.18383	−	0.280573i	−0.774955	+	0.632017i	$0.782227\pi$
$14$	−1.20749	−	4.03330i	−0.322716	−	1.07795i
$15$	0.0533189	−	3.91203i	0.0137669	−	1.01008i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	−0.241347	+	1.36875i	−0.0585354	+	0.331970i	−0.999987	−	0.00517869i	$-0.998352\pi$
$17$	−0.241347	+	1.36875i	−0.0585354	+	0.331970i	0.941451	+	0.337149i	$0.109463\pi$
$18$	1.42864	+	2.63799i	0.336733	+	0.621781i
$19$	0.883044	+	5.00799i	0.202584	+	1.14891i	0.901196	+	0.433411i	$0.142690\pi$
$19$	0.883044	+	5.00799i	0.202584	+	1.14891i	−0.698612	+	0.715501i	$0.746199\pi$
$20$	0.131339	+	2.25500i	0.0293682	+	0.504233i
$21$	4.08981	−	6.03740i	0.892469	−	1.31747i
$22$	−1.42253	+	3.29779i	−0.303284	+	0.703092i
$23$	−0.261895	+	0.131529i	−0.0546090	+	0.0274257i	−0.475894	−	0.879503i	$-0.657875\pi$
$23$	−0.261895	+	0.131529i	−0.0546090	+	0.0274257i	0.421285	+	0.906928i	$0.361579\pi$
$24$	−0.931968	−	1.45994i	−0.190237	−	0.298010i
$25$	0.0995059	−	0.0235833i	0.0199012	−	0.00471667i
$26$	2.19330	+	3.79891i	0.430142	+	0.745028i
$27$	−1.97529	+	4.80606i	−0.380144	+	0.924927i
$28$	−2.10509	+	3.64612i	−0.397824	+	0.689051i
$29$	2.13741	−	7.13946i	0.396908	−	1.32576i	−0.493161	−	0.869938i	$-0.664159\pi$
$29$	2.13741	−	7.13946i	0.396908	−	1.32576i	0.890069	−	0.455826i	$-0.150656\pi$
$30$	−2.88209	+	2.64581i	−0.526196	+	0.483057i
$31$	6.75905	+	4.44550i	1.21396	+	0.798435i	0.984586	−	0.174902i	$-0.0559610\pi$
$31$	6.75905	+	4.44550i	1.21396	+	0.798435i	0.229376	+	0.973338i	$0.426331\pi$
$32$	0.597159	+	0.802123i	0.105564	+	0.141797i
$33$	−5.98313	+	1.70274i	−1.04153	+	0.296408i
$34$	1.16121	−	0.763743i	0.199147	−	0.130981i
$35$	8.93649	+	3.25262i	1.51054	+	0.549793i
$36$	0.938417	−	2.84945i	0.156403	−	0.474909i
$37$	−2.90034	+	1.05564i	−0.476813	+	0.173546i	−0.569236	−	0.822174i	$-0.692761\pi$
$37$	−2.90034	+	1.05564i	−0.476813	+	0.173546i	0.0924230	+	0.995720i	$0.470539\pi$
$38$	3.03670	−	4.07900i	0.492618	−	0.661700i
$39$	−2.69567	+	7.10354i	−0.431652	+	1.13748i
$40$	1.55010	−	1.64301i	0.245092	−	0.259782i
$41$	−5.07095	+	5.37489i	−0.791949	+	0.839417i	−0.990043	−	0.140766i	$-0.955043\pi$
$41$	−5.07095	+	5.37489i	−0.791949	+	0.839417i	0.198094	+	0.980183i	$0.436525\pi$
$42$	−7.19804	+	1.16830i	−1.11068	+	0.180272i
$43$	1.66067	−	2.23066i	0.253249	−	0.340173i	−0.657258	−	0.753666i	$-0.728284\pi$
$43$	1.66067	−	2.23066i	0.253249	−	0.340173i	0.910507	+	0.413493i	$0.135691\pi$
$44$	3.37493	−	1.22837i	0.508790	−	0.185184i
$45$	−6.70670	−	0.969843i	−0.999775	−	0.144576i
$46$	0.275394	+	0.100235i	0.0406046	+	0.0147789i
$47$	−0.834413	+	0.548802i	−0.121712	+	0.0800510i	−0.608905	−	0.793243i	$-0.708391\pi$
$47$	−0.834413	+	0.548802i	−0.121712	+	0.0800510i	0.487194	+	0.873294i	$0.338021\pi$
$48$	−0.422370	+	1.67976i	−0.0609638	+	0.242453i
$49$	6.40486	+	8.60322i	0.914980	+	1.22903i
$50$	−0.0854390	−	0.0561941i	−0.0120829	−	0.00794705i
$51$	2.29656	+	0.721791i	0.321583	+	0.101071i
$52$	1.25809	−	4.20232i	0.174466	−	0.582757i
$53$	−5.96257	+	10.3275i	−0.819022	+	1.41859i	0.0873808	+	0.996175i	$0.472150\pi$
$53$	−5.96257	+	10.3275i	−0.819022	+	1.41859i	−0.906403	+	0.422413i	$0.861183\pi$
$54$	4.85133	−	1.86135i	0.660182	−	0.253298i
$55$	−4.05630	−	7.02572i	−0.546951	−	0.947348i
$56$	4.09669	−	0.970933i	0.547443	−	0.129746i
$57$	8.79917	−	0.392254i	1.16548	−	0.0519553i
$58$	−6.65983	+	3.34469i	−0.874479	+	0.439180i
$59$	−3.66592	+	8.49856i	−0.477262	+	1.10642i	0.494226	+	0.869333i	$0.335451\pi$
$59$	−3.66592	+	8.49856i	−0.477262	+	1.10642i	−0.971489	+	0.237085i	$0.923808\pi$
$60$	3.90231	+	0.280693i	0.503786	+	0.0362373i
$61$	−0.863013	−	14.8174i	−0.110498	−	1.89717i	−0.366386	−	0.930463i	$-0.619405\pi$
$61$	−0.863013	−	14.8174i	−0.110498	−	1.89717i	0.255888	−	0.966706i	$-0.417632\pi$
$62$	−1.40481	−	7.96705i	−0.178410	−	1.01182i
$63$	−9.45068	−	8.37942i	−1.19067	−	1.05571i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	−9.84155	−	1.15031i	−1.22069	−	0.142679i
$66$	5.34440	+	3.18348i	0.657850	+	0.391859i
$67$	−1.60063	−	5.34648i	−0.195548	−	0.653177i	−0.998376	−	0.0569657i	$-0.981857\pi$
$67$	−1.60063	−	5.34648i	−0.195548	−	0.653177i	0.802828	−	0.596211i	$-0.203328\pi$
$68$	−1.35240	−	0.320525i	−0.164003	−	0.0388693i
$69$	0.167096	+	0.479318i	0.0201160	+	0.0577031i
$70$	−3.76673	−	8.73225i	−0.450210	−	1.04370i
$71$	4.88985	+	4.10307i	0.580319	+	0.486945i	0.885052	−	0.465493i	$-0.154123\pi$
$71$	4.88985	+	4.10307i	0.580319	+	0.486945i	−0.304733	+	0.952438i	$0.598567\pi$
$72$	−2.71660	+	1.27283i	−0.320154	+	0.150005i
$73$	4.66440	−	3.91389i	0.545926	−	0.458087i	−0.327632	−	0.944805i	$-0.606251\pi$
$73$	4.66440	−	3.91389i	0.545926	−	0.458087i	0.873559	+	0.486719i	$0.161806\pi$
$74$	2.75818	+	1.38521i	0.320632	+	0.161027i
$75$	−0.0181633	−	0.176190i	−0.00209732	−	0.0203447i
$76$	−5.05086	+	0.590361i	−0.579374	+	0.0677191i
$77$	0.879204	−	15.0954i	0.100195	−	1.72028i
$78$	7.01681	−	2.91399i	0.794497	−	0.329944i
$79$	8.31655	+	8.81503i	0.935685	+	0.991768i	0.999981	−	0.00616298i	$-0.00196175\pi$
$79$	8.31655	+	8.81503i	0.935685	+	0.991768i	−0.0642963	+	0.997931i	$0.520480\pi$
$80$	−2.25882			−0.252544
$81$	7.81066	+	4.47142i	0.867851	+	0.496824i
$82$	7.38945			0.816028
$83$	2.12671	+	2.25418i	0.233436	+	0.247428i	0.833494	−	0.552529i	$-0.186337\pi$
$83$	2.12671	+	2.25418i	0.233436	+	0.247428i	−0.600057	+	0.799957i	$0.704856\pi$
$84$	5.78938	+	4.43393i	0.631673	+	0.483781i
$85$	−0.182543	+	3.13414i	−0.0197996	+	0.339945i
$86$	−2.76214	+	0.322848i	−0.297850	+	0.0348136i
$87$	−11.7817	−	5.27372i	−1.26313	−	0.565402i
$88$	−3.20950	−	1.61187i	−0.342134	−	0.171826i
$89$	−0.706078	+	0.592470i	−0.0748441	+	0.0628017i	−0.679442	−	0.733729i	$-0.737778\pi$
$89$	−0.706078	+	0.592470i	−0.0748441	+	0.0628017i	0.604598	+	0.796531i	$0.293334\pi$
$90$	3.89698	+	5.54382i	0.410777	+	0.584370i
$91$	−14.1476	−	11.8712i	−1.48307	−	1.24444i
$92$	−0.116078	−	0.269100i	−0.0121020	−	0.0280556i
$93$	9.15232	−	10.6102i	0.949051	−	1.10023i
$94$	0.971793	+	0.230319i	0.100233	+	0.0237556i
$95$	3.29441	+	11.0041i	0.337999	+	1.12900i
$96$	1.51166	−	0.845503i	0.154283	−	0.0862938i
$97$	1.85410	+	0.216713i	0.188256	+	0.0220039i	0.209698	−	0.977766i	$-0.432752\pi$
$97$	1.85410	+	0.216713i	0.188256	+	0.0220039i	−0.0214426	+	0.999770i	$0.506826\pi$
$98$	1.86247	−	10.5626i	0.188138	−	1.06698i
$99$	1.58110	+	10.6579i	0.158907	+	1.07116i
$100$	0.0177577	+	0.100709i	0.00177577	+	0.0100709i
$101$	−0.417028	−	7.16010i	−0.0414959	−	0.712457i	−0.953336	−	0.301911i	$-0.902375\pi$
$101$	−0.417028	−	7.16010i	−0.0414959	−	0.712457i	0.911840	−	0.410545i	$-0.134662\pi$
$102$	−1.05098	−	2.16578i	−0.104063	−	0.214444i
$103$	2.16352	−	5.01560i	0.213178	−	0.494202i	−0.777754	−	0.628569i	$-0.783641\pi$
$103$	2.16352	−	5.01560i	0.213178	−	0.494202i	0.990932	+	0.134367i	$0.0429002\pi$
$104$	−3.92001	+	1.96870i	−0.384389	+	0.193047i
$105$	7.59246	−	14.6177i	0.740949	−	1.42654i
$106$	11.6037	−	2.75013i	1.12705	−	0.267116i
$107$	−6.91374	−	11.9750i	−0.668377	−	1.15766i	−0.978358	−	0.206920i	$-0.933656\pi$
$107$	−6.91374	−	11.9750i	−0.668377	−	1.15766i	0.309981	−	0.950743i	$-0.399677\pi$
$108$	−4.68308	−	2.25139i	−0.450630	−	0.216640i
$109$	−8.52071	+	14.7583i	−0.816136	+	1.41359i	0.0923739	+	0.995724i	$0.470554\pi$
$109$	−8.52071	+	14.7583i	−0.816136	+	1.41359i	−0.908510	+	0.417864i	$0.862779\pi$
$110$	−2.32672	+	7.77179i	−0.221844	+	0.741011i
$111$	1.16185	+	5.21816i	0.110278	+	0.495285i
$112$	−3.51755	−	2.31353i	−0.332377	−	0.218608i
$113$	−5.25309	−	7.05612i	−0.494169	−	0.663784i	0.483155	−	0.875535i	$-0.339491\pi$
$113$	−5.25309	−	7.05612i	−0.494169	−	0.663784i	−0.977324	+	0.211751i	$0.932084\pi$
$114$	−6.32367	−	6.13110i	−0.592266	−	0.574230i
$115$	−0.553083	+	0.363768i	−0.0515753	+	0.0339216i
$116$	7.00310	+	2.54892i	0.650221	+	0.236661i
$117$	11.5947	+	6.22443i	1.07193	+	0.575448i
$118$	8.69734	−	3.16557i	0.800655	−	0.291415i
$119$	−3.49432	+	4.69368i	−0.320323	+	0.430269i
$120$	−2.47376	−	3.03106i	−0.225822	−	0.276696i
$121$	−1.30320	+	1.38131i	−0.118473	+	0.125574i
$122$	−10.1855	+	10.7960i	−0.922154	+	0.977426i
$123$	8.09259	+	9.91573i	0.729684	+	0.894071i
$124$	−4.83098	+	6.48914i	−0.433835	+	0.582742i
$125$	−10.3959	+	3.78380i	−0.929839	+	0.338434i
$126$	0.390478	+	12.6245i	0.0347865	+	1.12468i
$127$	−19.3394	−	7.03896i	−1.71609	−	0.624607i	−0.718603	−	0.695420i	$-0.755218\pi$
$127$	−19.3394	−	7.03896i	−1.71609	−	0.624607i	−0.997490	+	0.0708135i	$0.977440\pi$
$128$	−0.835488	+	0.549509i	−0.0738474	+	0.0485702i
$129$	−3.45820	−	3.35289i	−0.304477	−	0.295206i
$130$	5.91697	+	7.94787i	0.518953	+	0.697075i
$131$	4.90387	+	3.22533i	0.428453	+	0.281798i	0.745365	−	0.666657i	$-0.232275\pi$
$131$	4.90387	+	3.22533i	0.428453	+	0.281798i	−0.316912	+	0.948455i	$0.602646\pi$
$132$	−1.35197	−	6.07201i	−0.117674	−	0.528501i
$133$	−6.14039	+	20.5103i	−0.532440	+	1.77847i
$134$	−2.79047	+	4.83323i	−0.241060	+	0.417528i
$135$	−3.17133	+	11.3006i	−0.272945	+	0.972601i
$136$	0.694932	+	1.20366i	0.0595900	+	0.103213i
$137$	−2.87536	+	0.681474i	−0.245659	+	0.0582222i	−0.351601	−	0.936150i	$-0.614362\pi$
$137$	−2.87536	+	0.681474i	−0.245659	+	0.0582222i	0.105942	+	0.994372i	$0.466214\pi$
$138$	0.233975	−	0.450469i	0.0199173	−	0.0383465i
$139$	13.7117	−	6.88629i	1.16301	−	0.584088i	0.240727	−	0.970593i	$-0.422614\pi$
$139$	13.7117	−	6.88629i	1.16301	−	0.584088i	0.922287	+	0.386505i	$0.126318\pi$
$140$	−3.76673	+	8.73225i	−0.318346	+	0.738010i
$141$	0.755204	+	1.55626i	0.0635996	+	0.131061i
$142$	−0.371153	−	6.37245i	−0.0311465	−	0.534764i
$143$	2.73576	+	15.5152i	0.228775	+	1.29745i
$144$	2.79007	+	1.10251i	0.232506	+	0.0918759i
$145$	2.92318	−	16.5782i	0.242757	−	1.37674i
$146$	−6.04777	−	0.706882i	−0.500517	−	0.0585020i
$147$	16.2134	−	9.06849i	1.33726	−	0.747956i
$148$	−0.885212	−	2.95681i	−0.0727640	−	0.243049i
$149$	13.2332	+	3.13632i	1.08410	+	0.256937i	0.733570	−	0.679614i	$-0.237853\pi$
$149$	13.2332	+	3.13632i	1.08410	+	0.256937i	0.350532	+	0.936551i	$0.386001\pi$
$150$	−0.115691	+	0.134120i	−0.00944617	+	0.0109509i
$151$	−1.72891	−	4.00806i	−0.140697	−	0.326172i	0.833269	−	0.552868i	$-0.186467\pi$
$151$	−1.72891	−	4.00806i	−0.140697	−	0.326172i	−0.973965	+	0.226697i	$0.927207\pi$
$152$	3.89553	+	3.26873i	0.315969	+	0.265129i
$153$	1.75522	−	3.78216i	0.141901	−	0.305769i
$154$	−11.5833	+	9.71955i	−0.933410	+	0.783224i
$155$	16.3300	+	8.20124i	1.31166	+	0.658739i
$156$	−6.93478	−	3.10414i	−0.555227	−	0.248530i
$157$	1.90125	−	0.222225i	0.151736	−	0.0177355i	−0.0398855	−	0.999204i	$-0.512699\pi$
$157$	1.90125	−	0.222225i	0.151736	−	0.0177355i	0.191622	+	0.981469i	$0.438625\pi$
$158$	0.704656	−	12.0985i	0.0560594	−	0.962503i
$159$	16.3982	+	12.5589i	1.30046	+	0.995988i
$160$	1.55010	+	1.64301i	0.122546	+	0.129891i
$161$	−1.23387			−0.0972424
$162$	−2.10761	−	8.74974i	−0.165589	−	0.687445i
$163$	10.0794			0.789479			0.394739	−	0.918793i	$-0.370835\pi$
$163$	10.0794			0.789479			0.394739	+	0.918793i	$0.370835\pi$
$164$	−5.07095	−	5.37489i	−0.395974	−	0.419708i
$165$	−12.9769	+	5.38914i	−1.01025	+	0.419544i
$166$	0.180195	−	3.09382i	0.0139858	−	0.240127i
$167$	−16.2485	+	1.89918i	−1.25735	+	0.146963i	−0.718552	−	0.695474i	$-0.755195\pi$
$167$	−16.2485	+	1.89918i	−1.25735	+	0.146963i	−0.538796	+	0.842436i	$0.681121\pi$
$168$	−0.747790	−	7.25379i	−0.0576932	−	0.559642i
$169$	5.57832	+	2.80154i	0.429101	+	0.215503i
$170$	2.40496	−	2.01800i	0.184452	−	0.154774i
$171$	1.30179	−	15.2001i	0.0995503	−	1.16238i
$172$	2.13033	+	1.78756i	0.162436	+	0.136300i
$173$	−8.48647	−	19.6739i	−0.645214	−	1.49578i	−0.855322	−	0.518097i	$-0.826641\pi$
$173$	−8.48647	−	19.6739i	−0.645214	−	1.49578i	0.210107	−	0.977678i	$-0.432619\pi$
$174$	4.24914	+	12.1888i	0.322127	+	0.924028i
$175$	0.418937	+	0.0992899i	0.0316687	+	0.00750561i
$176$	1.03006	+	3.44064i	0.0776437	+	0.259348i
$177$	13.7727	+	8.20397i	1.03522	+	0.616648i
$178$	0.915487	+	0.107005i	0.0686187	+	0.00802037i
$179$	1.49127	−	8.45738i	0.111462	−	0.632135i	−0.876979	−	0.480529i	$-0.840445\pi$
$179$	1.49127	−	8.45738i	0.111462	−	0.632135i	0.988441	−	0.151605i	$-0.0484443\pi$
$180$	1.35816	−	6.63896i	0.101231	−	0.494839i
$181$	−0.0323020	−	0.183193i	−0.00240099	−	0.0136167i	0.983584	−	0.180452i	$-0.0577562\pi$
$181$	−0.0323020	−	0.183193i	−0.00240099	−	0.0136167i	−0.985985	+	0.166836i	$0.946645\pi$
$182$	1.07384	+	18.4371i	0.0795983	+	1.36665i
$183$	−25.6417	−	1.84440i	−1.89549	−	0.136342i
$184$	−0.116078	+	0.269100i	−0.00855741	+	0.0198383i
$185$	−6.23022	+	3.12894i	−0.458055	+	0.230044i
$186$	−13.9983	+	0.624023i	−1.02641	+	0.0457556i
$187$	4.85718	−	1.15117i	0.355192	−	0.0841821i
$188$	−0.499357	−	0.864911i	−0.0364193	−	0.0630801i
$189$	−16.5129	+	14.3497i	−1.20113	+	1.04379i
$190$	5.74333	−	9.94773i	0.416665	−	0.721685i
$191$	2.10629	−	7.03551i	0.152406	−	0.509072i	−0.847353	−	0.531030i	$-0.821805\pi$
$191$	2.10629	−	7.03551i	0.152406	−	0.509072i	0.999759	+	0.0219585i	$0.00699017\pi$
$192$	−1.65236	−	0.519325i	−0.119249	−	0.0374790i
$193$	−0.408383	−	0.268598i	−0.0293961	−	0.0193341i	0.534726	−	0.845026i	$-0.320415\pi$
$193$	−0.408383	−	0.268598i	−0.0293961	−	0.0193341i	−0.564122	+	0.825691i	$0.690785\pi$
$194$	−1.11473	−	1.49734i	−0.0800330	−	0.107503i
$195$	−4.18507	+	16.6440i	−0.299699	+	1.19190i
$196$	−8.96107	+	5.89379i	−0.640076	+	0.420985i
$197$	7.84299	+	2.85462i	0.558790	+	0.203383i	0.605948	−	0.795505i	$-0.292794\pi$
$197$	7.84299	+	2.85462i	0.558790	+	0.203383i	−0.0471576	+	0.998887i	$0.515016\pi$
$198$	6.66728	−	8.46397i	0.473823	−	0.601508i
$199$	−6.56743	+	2.39035i	−0.465553	+	0.169447i	−0.564137	−	0.825681i	$-0.690791\pi$
$199$	−6.56743	+	2.39035i	−0.465553	+	0.169447i	0.0985841	+	0.995129i	$0.468569\pi$
$200$	0.0610669	−	0.0820270i	0.00431808	−	0.00580019i
$201$	−9.54161	+	1.54867i	−0.673013	+	0.109235i
$202$	−4.92189	+	5.21690i	−0.346303	+	0.367060i
$203$	21.5318	−	22.8224i	1.51124	−	1.60182i
$204$	−0.854103	+	2.25071i	−0.0597992	+	0.157581i
$205$	−9.96743	+	13.3886i	−0.696155	+	0.935099i
$206$	−5.13291	+	1.86823i	−0.357627	+	0.130166i
$207$	0.860714	−	0.179367i	0.0598238	−	0.0124669i
$208$	4.12206	+	1.50031i	0.285813	+	0.104028i
$209$	15.2592	−	10.0361i	1.05550	−	0.694213i
$210$	−15.8428	+	4.50869i	−1.09325	+	0.311129i
$211$	−3.48773	−	4.68484i	−0.240105	−	0.322518i	0.665694	−	0.746225i	$-0.268136\pi$
$211$	−3.48773	−	4.68484i	−0.240105	−	0.322518i	−0.905799	+	0.423708i	$0.860728\pi$
$212$	−9.96331	−	6.55298i	−0.684283	−	0.450060i
$213$	8.14458	−	7.47686i	0.558057	−	0.512306i
$214$	−3.96577	+	13.2466i	−0.271094	+	0.905518i
$215$	3.14083	−	5.44008i	0.214203	−	0.371010i
$216$	1.57612	+	4.95135i	0.107242	+	0.336897i
$217$	17.0300	+	29.4969i	1.15607	+	2.00238i
$218$	16.5821	−	3.93002i	1.12308	−	0.266175i
$219$	−5.67469	−	8.88951i	−0.383460	−	0.600697i
$220$	7.24969	−	3.64093i	0.488774	−	0.245471i
$221$	2.41481	−	5.59817i	0.162438	−	0.376573i
$222$	2.99824	−	4.42602i	0.201229	−	0.297055i
$223$	−0.622088	−	10.6808i	−0.0416581	−	0.715242i	−0.952884	−	0.303335i	$-0.901900\pi$
$223$	−0.622088	−	10.6808i	−0.0416581	−	0.715242i	0.911226	−	0.411907i	$-0.135137\pi$
$224$	0.731089	+	4.14621i	0.0488479	+	0.277030i
$225$	−0.306673	−	0.00836116i	−0.0204449	−	0.000557410i
$226$	−1.52755	+	8.66317i	−0.101611	+	0.576265i
$227$	−3.82548	−	0.447134i	−0.253906	−	0.0296773i	−0.0118122	−	0.999930i	$-0.503760\pi$
$227$	−3.82548	−	0.447134i	−0.253906	−	0.0296773i	−0.242094	+	0.970253i	$0.577834\pi$
$228$	−0.120036	+	8.80709i	−0.00794959	+	0.583264i
$229$	−4.10527	−	13.7126i	−0.271284	−	0.906151i	−0.979719	−	0.200375i	$-0.935784\pi$
$229$	−4.10527	−	13.7126i	−0.271284	−	0.906151i	0.708435	−	0.705776i	$-0.249401\pi$
$230$	0.644144	+	0.152665i	0.0424736	+	0.0100664i
$231$	−25.7280	−	4.89897i	−1.69278	−	0.322328i
$232$	−2.95180	−	6.84304i	−0.193795	−	0.449268i
$233$	−13.0394	−	10.9414i	−0.854241	−	0.716793i	0.106478	−	0.994315i	$-0.466043\pi$
$233$	−13.0394	−	10.9414i	−0.854241	−	0.716793i	−0.960719	+	0.277522i	$0.910487\pi$
$234$	−3.42929	−	12.7051i	−0.224179	−	0.830561i
$235$	−1.72813	+	1.45007i	−0.112731	+	0.0945923i
$236$	−8.27103	−	4.15387i	−0.538398	−	0.270394i
$237$	17.0064	−	12.3041i	1.10468	−	0.799240i
$238$	5.81200	−	0.679326i	0.376736	−	0.0440342i
$239$	0.489375	−	8.40225i	0.0316551	−	0.543496i	−0.944783	−	0.327697i	$-0.893727\pi$
$239$	0.489375	−	8.40225i	0.0316551	−	0.543496i	0.976438	−	0.215799i	$-0.0692356\pi$
$240$	−0.507117	+	3.87938i	−0.0327343	+	0.250413i
$241$	−9.97509	−	10.5730i	−0.642552	−	0.681065i	0.321460	−	0.946923i	$-0.395826\pi$
$241$	−9.97509	−	10.5730i	−0.642552	−	0.681065i	−0.964012	+	0.265858i	$0.914345\pi$
$242$	1.89904			0.122075
$243$	9.43293	−	12.4105i	0.605122	−	0.796132i
$244$	14.8425			0.950192
$245$	16.6256	+	17.6221i	1.06217	+	1.12584i
$246$	1.65897	−	12.6909i	0.105772	−	0.809144i
$247$	1.29703	−	22.2692i	0.0825284	−	1.41696i
$248$	8.03525	−	0.939186i	0.510239	−	0.0596384i
$249$	4.34887	−	3.14641i	0.275598	−	0.199396i
$250$	9.88635	+	4.96511i	0.625268	+	0.314021i
$251$	22.1883	−	18.6182i	1.40052	−	1.17517i	0.439647	−	0.898171i	$-0.355104\pi$
$251$	22.1883	−	18.6182i	1.40052	−	1.17517i	0.960869	−	0.277002i	$-0.0893408\pi$
$252$	8.91475	−	8.94747i	0.561577	−	0.563637i
$253$	0.806309	+	0.676574i	0.0506922	+	0.0425358i
$254$	8.15154	+	18.8974i	0.511473	+	1.18573i
$255$	5.34171	+	1.01714i	0.334511	+	0.0636956i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	4.68564	+	15.6511i	0.292282	+	0.976290i	0.970434	+	0.241368i	$0.0775960\pi$
$257$	4.68564	+	15.6511i	0.292282	+	0.976290i	−0.678152	+	0.734922i	$0.737219\pi$
$258$	−0.0656437	+	4.81630i	−0.00408680	+	0.299849i
$259$	−12.9067	−	1.50858i	−0.801986	−	0.0937387i
$260$	1.72060	−	9.75801i	0.106707	−	0.605166i
$261$	−11.7024	+	19.0504i	−0.724358	+	1.17919i
$262$	−1.01922	−	5.78030i	−0.0629678	−	0.357108i
$263$	0.882761	+	15.1564i	0.0544333	+	0.934584i	0.909406	+	0.415911i	$0.136537\pi$
$263$	0.882761	+	15.1564i	0.0544333	+	0.934584i	−0.854972	+	0.518674i	$0.826426\pi$
$264$	−3.48884	+	5.15025i	−0.214724	+	0.316976i
$265$	−10.6691	+	24.7338i	−0.655398	+	1.51938i
$266$	19.1325	−	9.60869i	1.17309	−	0.589147i
$267$	0.859013	+	1.34566i	0.0525707	+	0.0823530i
$268$	5.43050	−	1.28705i	0.331721	−	0.0786193i
$269$	4.66091	+	8.07293i	0.284181	+	0.492215i	0.972410	−	0.233278i	$-0.0749451\pi$
$269$	4.66091	+	8.07293i	0.284181	+	0.492215i	−0.688229	+	0.725493i	$0.741612\pi$
$270$	10.3961	−	5.44820i	0.632684	−	0.331567i
$271$	8.84975	−	15.3282i	0.537584	−	0.931123i	−0.461449	−	0.887167i	$-0.652670\pi$
$271$	8.84975	−	15.3282i	0.537584	−	0.931123i	0.999033	−	0.0439566i	$-0.0139963\pi$
$272$	0.398618	−	1.33148i	0.0241697	−	0.0807326i
$273$	−23.5643	+	21.6325i	−1.42618	+	1.30926i
$274$	2.46888	+	1.62381i	0.149150	+	0.0980978i
$275$	−0.219323	−	0.294602i	−0.0132257	−	0.0177652i
$276$	−0.488223	+	0.138943i	−0.0293876	+	0.00836340i
$277$	−15.4213	+	10.1427i	−0.926576	+	0.609419i	−0.920576	−	0.390563i	$-0.872280\pi$
$277$	−15.4213	+	10.1427i	−0.926576	+	0.609419i	−0.00600004	+	0.999982i	$0.501910\pi$
$278$	−14.4185	−	5.24789i	−0.864762	−	0.314748i
$279$	−16.1677	−	18.1006i	−0.967933	−	1.08365i
$280$	8.93649	−	3.25262i	0.534058	−	0.194381i
$281$	0.416337	−	0.559238i	0.0248366	−	0.0333614i	−0.789531	−	0.613710i	$-0.789676\pi$
$281$	0.416337	−	0.559238i	0.0248366	−	0.0333614i	0.814368	+	0.580349i	$0.197084\pi$
$282$	0.613732	−	1.61729i	0.0365472	−	0.0963081i
$283$	−8.93228	+	9.46767i	−0.530969	+	0.562794i	−0.936221	−	0.351411i	$-0.885702\pi$
$283$	−8.93228	+	9.46767i	−0.530969	+	0.562794i	0.405252	+	0.914205i	$0.367184\pi$
$284$	−4.38045	+	4.64301i	−0.259932	+	0.275512i
$285$	19.6385	−	3.18747i	1.16328	−	0.188809i
$286$	9.40799	−	12.6371i	0.556306	−	0.747249i
$287$	−29.2346	+	10.6405i	−1.72567	+	0.628091i
$288$	−1.11272	−	2.78601i	−0.0655678	−	0.164167i
$289$	14.1595	+	5.15365i	0.832915	+	0.303156i
$290$	−14.0646	+	9.25040i	−0.825899	+	0.543202i
$291$	0.788448	−	3.13565i	0.0462196	−	0.183815i
$292$	3.63606	+	4.88408i	0.212784	+	0.285819i
$293$	24.9319	+	16.3980i	1.45654	+	0.957980i	0.997580	+	0.0695225i	$0.0221476\pi$
$293$	24.9319	+	16.3980i	1.45654	+	0.957980i	0.458958	+	0.888458i	$0.348223\pi$
$294$	−17.7225	−	5.57005i	−1.03360	−	0.324852i
$295$	−5.99606	+	20.0282i	−0.349104	+	1.16609i
$296$	−1.54324	+	2.67297i	−0.0896990	+	0.155363i
$297$	18.6593	−	0.322683i	1.08272	−	0.0187240i
$298$	−6.79987	−	11.7777i	−0.393906	−	0.682265i
$299$	1.25092	−	0.296474i	0.0723427	−	0.0171455i
$300$	0.176948	−	0.00788807i	0.0102161	−	0.000455418i
$301$	10.4629	−	5.25466i	0.603071	−	0.302874i
$302$	−1.72891	+	4.00806i	−0.0994876	+	0.230638i
$303$	−12.3907	−	0.891260i	−0.711825	−	0.0512016i
$304$	−0.295681	−	5.07665i	−0.0169585	−	0.291166i
$305$	−5.82181	−	33.0171i	−0.333356	−	1.89055i
$306$	−3.95555	+	1.31877i	−0.226124	+	0.0753891i
$307$	1.01743	−	5.77016i	0.0580680	−	0.329320i	−0.941911	−	0.335864i	$-0.890972\pi$
$307$	1.01743	−	5.77016i	0.0580680	−	0.329320i	0.999979	+	0.00654360i	$0.00208291\pi$
$308$	15.0187	+	1.75543i	0.855769	+	0.100025i
$309$	−8.12827	−	4.84174i	−0.462401	−	0.275437i
$310$	−5.24096	−	17.5060i	−0.297667	−	0.994276i
$311$	6.95655	+	1.64873i	0.394470	+	0.0934910i	0.423063	−	0.906100i	$-0.360955\pi$
$311$	6.95655	+	1.64873i	0.394470	+	0.0934910i	−0.0285938	+	0.999591i	$0.509103\pi$
$312$	2.50107	+	7.17437i	0.141595	+	0.406169i
$313$	4.96810	+	11.5173i	0.280813	+	0.650999i	0.998993	−	0.0448588i	$-0.0142838\pi$
$313$	4.96810	+	11.5173i	0.280813	+	0.650999i	−0.718180	+	0.695857i	$0.755025\pi$
$314$	−1.46636	−	1.23042i	−0.0827514	−	0.0694367i
$315$	−23.4004	−	16.3213i	−1.31846	−	0.919603i
$316$	−9.28368	+	7.78993i	−0.522248	+	0.438218i
$317$	−13.9405	−	7.00116i	−0.782974	−	0.393224i	0.0119537	−	0.999929i	$-0.496195\pi$
$317$	−13.9405	−	7.00116i	−0.782974	−	0.393224i	−0.794928	+	0.606704i	$0.792491\pi$
$318$	−2.11808	−	20.5461i	−0.118776	−	1.15217i
$319$	−26.5850	+	3.10734i	−1.48847	+	0.173978i
$320$	0.131339	−	2.25500i	0.00734205	−	0.126058i
$321$	−22.1184	+	9.18549i	−1.23453	+	0.512684i
$322$	0.846732	+	0.897483i	0.0471865	+	0.0500148i
$323$	−7.06781			−0.393263
$324$	−4.91800	+	7.53746i	−0.273222	+	0.418748i
$325$	−0.448585			−0.0248830
$326$	−6.91690	−	7.33148i	−0.383092	−	0.406053i
$327$	23.4335	+	17.9471i	1.29588	+	0.992478i
$328$	−0.429658	+	7.37694i	−0.0237239	+	0.407324i
$329$	−4.17633	+	0.488142i	−0.230248	+	0.0269122i
$330$	12.8252	+	5.74081i	0.706005	+	0.316021i
$331$	30.0560	+	15.0947i	1.65203	+	0.829680i	0.997270	+	0.0738429i	$0.0235263\pi$
$331$	30.0560	+	15.0947i	1.65203	+	0.829680i	0.654759	+	0.755837i	$0.272770\pi$
$332$	−2.37402	+	1.99204i	−0.130291	+	0.109327i
$333$	9.22271	−	0.823906i	0.505401	−	0.0451498i
$334$	12.5318	+	10.5154i	0.685711	+	0.575379i
$335$	−4.99311	−	11.5753i	−0.272803	−	0.632428i
$336$	−4.76305	+	5.52178i	−0.259846	+	0.301238i
$337$	−9.34707	−	2.21530i	−0.509168	−	0.120675i	−0.0320011	−	0.999488i	$-0.510188\pi$
$337$	−9.34707	−	2.21530i	−0.509168	−	0.120675i	−0.477167	+	0.878813i	$0.658336\pi$
$338$	−1.79031	−	5.98005i	−0.0973800	−	0.325272i
$339$	−13.2978	+	7.43773i	−0.722238	+	0.403962i
$340$	−3.11822	−	0.364468i	−0.169109	−	0.0197661i
$341$	5.04539	−	28.6138i	0.273223	−	1.54953i
$342$	−11.9495	+	9.48406i	−0.646155	+	0.512839i
$343$	2.72371	+	15.4469i	0.147067	+	0.834056i
$344$	−0.161698	−	2.77624i	−0.00871816	−	0.149685i
$345$	0.500580	+	1.03155i	0.0269503	+	0.0555370i
$346$	−8.48647	+	19.6739i	−0.456236	+	1.05767i
$347$	2.62462	−	1.31813i	0.140897	−	0.0707610i	−0.376954	−	0.926232i	$-0.623029\pi$
$347$	2.62462	−	1.31813i	0.140897	−	0.0707610i	0.517851	+	0.855471i	$0.326732\pi$
$348$	5.94985	−	11.4551i	0.318945	−	0.614060i
$349$	0.0832690	−	0.0197351i	0.00445728	−	0.00105640i	−0.228387	−	0.973571i	$-0.573345\pi$
$349$	0.0832690	−	0.0197351i	0.00445728	−	0.00105640i	0.232844	+	0.972514i	$0.425197\pi$
$350$	−0.215271	−	0.372861i	−0.0115067	−	0.0199302i
$351$	13.2931	−	18.5158i	0.709536	−	0.988299i
$352$	1.79576	−	3.11035i	0.0957144	−	0.165782i
$353$	−5.58667	+	18.6608i	−0.297348	+	0.993212i	0.670549	+	0.741865i	$0.266059\pi$
$353$	−5.58667	+	18.6608i	−0.297348	+	0.993212i	−0.967897	+	0.251347i	$0.919127\pi$
$354$	−3.48408	−	15.6478i	−0.185177	−	0.831673i
$355$	12.0466	+	7.92315i	0.639365	+	0.420517i
$356$	−0.550413	−	0.739333i	−0.0291718	−	0.0391846i
$357$	7.27662	+	7.05503i	0.385119	+	0.373392i
$358$	−7.17505	+	4.71910i	−0.379213	+	0.249412i
$359$	3.65287	+	1.32954i	0.192791	+	0.0701702i	0.436611	−	0.899650i	$-0.356178\pi$
$359$	3.65287	+	1.32954i	0.192791	+	0.0701702i	−0.243820	+	0.969820i	$0.578401\pi$
$360$	−5.76103	+	3.56804i	−0.303633	+	0.188052i
$361$	−6.44606	+	2.34617i	−0.339266	+	0.123483i
$362$	−0.111083	+	0.149211i	−0.00583840	+	0.00784233i
$363$	2.07975	+	2.54828i	0.109158	+	0.133750i
$364$	12.6738	−	13.4334i	0.664285	−	0.704101i
$365$	9.43843	−	10.0042i	0.494030	−	0.523641i
$366$	16.2548	+	19.9168i	0.849653	+	1.04107i
$367$	−13.3298	+	17.9050i	−0.695809	+	0.934634i	−0.999837	−	0.0180288i	$-0.994261\pi$
$367$	−13.3298	+	17.9050i	−0.695809	+	0.934634i	0.304028	+	0.952663i	$0.401668\pi$
$368$	0.275394	−	0.100235i	0.0143559	−	0.00522512i
$369$	18.8465	−	11.6724i	0.981109	−	0.607641i
$370$	6.55135	+	2.38449i	0.340588	+	0.123964i
$371$	−41.9473	+	27.5892i	−2.17779	+	1.43236i
$372$	10.0601	+	9.75377i	0.521593	+	0.505709i
$373$	−3.99625	−	5.36789i	−0.206918	−	0.277939i	0.686534	−	0.727097i	$-0.259131\pi$
$373$	−3.99625	−	5.36789i	−0.206918	−	0.277939i	−0.893452	+	0.449159i	$0.851724\pi$
$374$	−4.17053	−	2.74300i	−0.215653	−	0.141837i
$375$	4.16451	+	18.7038i	0.215055	+	0.965862i
$376$	−0.286434	+	0.956757i	−0.0147717	+	0.0493410i
$377$	−16.3457	+	28.3115i	−0.841845	+	1.45812i
$378$	21.7694	+	2.16364i	1.11970	+	0.111286i
$379$	14.2265	+	24.6411i	0.730767	+	1.26573i	0.956556	+	0.291550i	$0.0941708\pi$
$379$	14.2265	+	24.6411i	0.730767	+	1.26573i	−0.225788	+	0.974176i	$0.572496\pi$
$380$	−11.1770	+	2.64900i	−0.573370	+	0.135891i
$381$	−16.4308	+	31.6339i	−0.841774	+	1.62066i
$382$	−6.56287	+	3.29600i	−0.335786	+	0.168638i
$383$	13.7800	−	31.9456i	0.704124	−	1.63234i	−0.0686342	−	0.997642i	$-0.521864\pi$
$383$	13.7800	−	31.9456i	0.704124	−	1.63234i	0.772758	−	0.634701i	$-0.218877\pi$
$384$	0.756177	+	1.55827i	0.0385885	+	0.0795200i
$385$	−1.98596	−	34.0977i	−0.101214	−	1.73778i
$386$	0.0848786	+	0.481371i	0.00432021	+	0.0245011i
$387$	−6.53477	+	5.18651i	−0.332181	+	0.263645i
$388$	−0.324153	+	1.83836i	−0.0164564	+	0.0933288i
$389$	−20.5578	−	2.40286i	−1.04232	−	0.121830i	−0.422334	−	0.906440i	$-0.638789\pi$
$389$	−20.5578	−	2.40286i	−1.04232	−	0.121830i	−0.619989	+	0.784610i	$0.712863\pi$
$390$	14.9784	−	8.37770i	0.758460	−	0.424221i
$391$	−0.116822	−	0.390213i	−0.00590795	−	0.0197339i
$392$	10.4364	+	2.47348i	0.527120	+	0.124930i
$393$	6.64024	−	7.69799i	0.334956	−	0.388312i
$394$	−3.30582	−	7.66374i	−0.166545	−	0.386094i
$395$	20.9701	+	17.5960i	1.05512	+	0.885353i
$396$	−10.7318	+	0.958723i	−0.539295	+	0.0481776i
$397$	2.81853	−	2.36502i	0.141458	−	0.118697i	−0.569313	−	0.822121i	$-0.692791\pi$
$397$	2.81853	−	2.36502i	0.141458	−	0.118697i	0.710771	+	0.703424i	$0.248346\pi$
$398$	6.24552	+	3.13662i	0.313060	+	0.157224i
$399$	33.8467	+	15.1504i	1.69445	+	0.758470i
$400$	−0.101571	+	0.0118719i	−0.00507855	+	0.000593597i
$401$	−1.22319	+	21.0013i	−0.0610830	+	1.04875i	0.818957	+	0.573855i	$0.194553\pi$
$401$	−1.22319	+	21.0013i	−0.0610830	+	1.04875i	−0.880040	+	0.474899i	$0.842484\pi$
$402$	7.67431	+	5.87755i	0.382760	+	0.293145i
$403$	−24.3529	−	25.8126i	−1.21311	−	1.28582i
$404$	7.17224			0.356832
$405$	18.6961	+	7.98362i	0.929018	+	0.396709i
$406$	−31.3765			−1.55719
$407$	7.60710	+	8.06305i	0.377070	+	0.399671i
$408$	2.22323	−	0.923276i	0.110066	−	0.0457090i
$409$	0.106998	−	1.83708i	0.00529069	−	0.0908376i	−0.994629	−	0.103503i	$-0.966995\pi$
$409$	0.106998	−	1.83708i	0.00529069	−	0.0908376i	0.999920	+	0.0126658i	$0.00403177\pi$
$410$	16.5786	−	1.93776i	0.818757	−	0.0956989i
$411$	0.524855	+	5.09126i	0.0258892	+	0.251133i
$412$	4.88132	+	2.45149i	0.240485	+	0.120776i
$413$	−29.8507	+	25.0477i	−1.46886	+	1.23252i
$414$	−0.721125	−	0.502971i	−0.0354414	−	0.0247197i
$415$	5.36248	+	4.49966i	0.263234	+	0.220879i
$416$	−1.73744	−	4.02785i	−0.0851852	−	0.197482i
$417$	−8.74843	−	25.0951i	−0.428412	−	1.22891i
$418$	−17.7715	−	4.21192i	−0.869232	−	0.206012i
$419$	−3.70575	−	12.3781i	−0.181038	−	0.604709i	−0.999544	−	0.0302103i	$-0.990382\pi$
$419$	−3.70575	−	12.3781i	−0.181038	−	0.604709i	0.818506	−	0.574499i	$-0.194803\pi$
$420$	14.1515	+	8.42956i	0.690521	+	0.411320i
$421$	12.4210	+	1.45181i	0.605365	+	0.0707570i	0.413253	−	0.910616i	$-0.364392\pi$
$421$	12.4210	+	1.45181i	0.605365	+	0.0707570i	0.192112	+	0.981373i	$0.438466\pi$
$422$	−1.01420	+	5.75182i	−0.0493705	+	0.279994i
$423$	2.84233	−	0.947628i	0.138199	−	0.0460752i
$424$	2.07078	+	11.7440i	0.100566	+	0.570338i
$425$	0.00826418	+	0.141890i	0.000400871	+	0.00688270i
$426$	−11.0276	−	0.793216i	−0.534290	−	0.0384314i
$427$	24.7508	−	57.3788i	1.19777	−	2.77675i
$428$	12.3567	−	6.20576i	0.597283	−	0.299967i
$429$	27.2607	−	1.21524i	1.31616	−	0.0586723i
$430$	−6.11233	+	1.44865i	−0.294763	+	0.0698601i
$431$	2.34564	+	4.06276i	0.112985	+	0.195696i	0.916973	−	0.398950i	$-0.130625\pi$
$431$	2.34564	+	4.06276i	0.112985	+	0.195696i	−0.803987	+	0.594647i	$0.797292\pi$
$432$	2.51988	−	4.54425i	0.121238	−	0.218635i
$433$	11.1994	−	19.3979i	0.538209	−	0.932205i	−0.460792	−	0.887508i	$-0.652434\pi$
$433$	11.1994	−	19.3979i	0.538209	−	0.932205i	0.999001	−	0.0446970i	$-0.0142322\pi$
$434$	9.76854	−	32.6292i	0.468905	−	1.56625i
$435$	−27.8158	−	8.74228i	−1.33366	−	0.419160i
$436$	−14.2379	−	9.36441i	−0.681871	−	0.448474i
$437$	−0.889960	−	1.19542i	−0.0425726	−	0.0571849i
$438$	−2.57178	+	10.2280i	−0.122885	+	0.488711i
$439$	−1.97929	+	1.30180i	−0.0944663	+	0.0621314i	−0.595863	−	0.803086i	$-0.703190\pi$
$439$	−1.97929	+	1.30180i	−0.0944663	+	0.0621314i	0.501397	+	0.865217i	$0.332820\pi$
$440$	−7.62335	−	2.77467i	−0.363429	−	0.132277i
$441$	−11.9346	−	29.8815i	−0.568313	−	1.42293i
$442$	−5.72910	+	2.08522i	−0.272506	+	0.0991840i
$443$	−13.1297	+	17.6362i	−0.623809	+	0.837921i	−0.995917	−	0.0902682i	$-0.971228\pi$
$443$	−13.1297	+	17.6362i	−0.623809	+	0.837921i	0.372108	+	0.928189i	$0.378635\pi$
$444$	−5.27688	+	0.856477i	−0.250430	+	0.0406466i
$445$	−1.42875	+	1.51439i	−0.0677294	+	0.0717890i
$446$	−7.34206	+	7.78212i	−0.347656	+	0.368494i
$447$	8.35734	−	22.0230i	0.395289	−	1.04165i
$448$	2.51414	−	3.37708i	0.118782	−	0.159552i
$449$	−6.42022	+	2.33677i	−0.302989	+	0.110279i	−0.489041	−	0.872261i	$-0.662653\pi$
$449$	−6.42022	+	2.33677i	−0.302989	+	0.110279i	0.186052	+	0.982540i	$0.440431\pi$
$450$	0.204370	+	0.228804i	0.00963411	+	0.0107859i
$451$	24.9389	+	9.07700i	1.17432	+	0.427419i
$452$	7.34963	−	4.83393i	0.345697	−	0.227369i
$453$	−7.27175	+	2.06947i	−0.341657	+	0.0972320i
$454$	2.29997	+	3.08939i	0.107943	+	0.144992i
$455$	−34.8538	−	22.9237i	−1.63397	−	1.07468i
$456$	6.48842	−	5.95648i	0.303848	−	0.278938i
$457$	6.91767	−	23.1066i	0.323595	−	1.08088i	−0.629193	−	0.777249i	$-0.716615\pi$
$457$	6.91767	−	23.1066i	0.323595	−	1.08088i	0.952789	−	0.303634i	$-0.0982001\pi$
$458$	−7.15694	+	12.3962i	−0.334422	+	0.579236i
$459$	−6.10157	−	3.86360i	−0.284797	−	0.180337i
$460$	−0.330994	−	0.573299i	−0.0154327	−	0.0267302i
$461$	23.2660	−	5.51415i	1.08361	−	0.256820i	0.350245	−	0.936658i	$-0.386098\pi$
$461$	23.2660	−	5.51415i	1.08361	−	0.256820i	0.733362	+	0.679839i	$0.237950\pi$
$462$	14.0922	+	22.0757i	0.655629	+	1.02706i
$463$	−1.04020	+	0.522406i	−0.0483420	+	0.0242783i	−0.472806	−	0.881167i	$-0.656759\pi$
$463$	−1.04020	+	0.522406i	−0.0483420	+	0.0242783i	0.424464	+	0.905445i	$0.360463\pi$
$464$	−2.95180	+	6.84304i	−0.137034	+	0.317680i
$465$	17.7513	−	26.2046i	0.823197	−	1.21521i
$466$	0.989727	+	16.9930i	0.0458482	+	0.787184i
$467$	5.51838	+	31.2963i	0.255360	+	1.44822i	0.795146	+	0.606418i	$0.207394\pi$
$467$	5.51838	+	31.2963i	0.255360	+	1.44822i	−0.539786	+	0.841802i	$0.681495\pi$
$468$	−6.88807	+	11.2132i	−0.318401	+	0.518329i
$469$	4.08016	−	23.1397i	0.188404	−	1.06849i
$470$	2.24066	+	0.261895i	0.103354	+	0.0120803i
$471$	0.0451842	−	3.31518i	0.00208198	−	0.152755i
$472$	2.65451	+	8.86669i	0.122184	+	0.408122i
$473$	−9.71862	−	2.30335i	−0.446862	−	0.105908i
$474$	−20.6202	−	3.92638i	−0.947117	−	0.180344i
$475$	0.205973	+	0.477500i	0.00945070	+	0.0219092i
$476$	−4.48256	−	3.76132i	−0.205458	−	0.172400i
$477$	25.2507	−	25.3433i	1.15615	−	1.16039i
$478$	−6.44740	+	5.41001i	−0.294897	+	0.247448i
$479$	−0.572276	−	0.287408i	−0.0261479	−	0.0131320i	0.435677	−	0.900103i	$-0.356509\pi$
$479$	−0.572276	−	0.287408i	−0.0261479	−	0.0131320i	−0.461825	+	0.886971i	$0.652805\pi$
$480$	3.16977	−	2.29333i	0.144679	−	0.104676i
$481$	13.4476	−	1.57180i	0.613158	−	0.0716679i
$482$	−0.845183	+	14.5112i	−0.0384970	+	0.660969i
$483$	−0.277010	+	2.11909i	−0.0126044	+	0.0964221i
$484$	−1.30320	−	1.38131i	−0.0592365	−	0.0627870i
$485$	4.21659			0.191466
$486$	−15.5003	+	1.65532i	−0.703109	+	0.0750870i
$487$	−32.1652			−1.45754			−0.728772	−	0.684756i	$-0.759909\pi$
$487$	−32.1652			−1.45754			−0.728772	+	0.684756i	$0.759909\pi$
$488$	−10.1855	−	10.7960i	−0.461077	−	0.488713i
$489$	2.26288	−	17.3107i	0.102331	−	0.782819i
$490$	1.40868	−	24.1861i	0.0636377	−	1.09262i
$491$	−12.3627	+	1.44500i	−0.557923	+	0.0652118i	−0.390381	−	0.920653i	$-0.627657\pi$
$491$	−12.3627	+	1.44500i	−0.557923	+	0.0652118i	−0.167541	+	0.985865i	$0.553583\pi$
$492$	−10.3695	+	7.50235i	−0.467493	+	0.338232i
$493$	9.25627	+	4.64867i	0.416881	+	0.209366i
$494$	−17.0881	+	14.3386i	−0.768831	+	0.645126i
$495$	6.34213	+	23.4969i	0.285058	+	1.05611i
$496$	−6.19726	−	5.20012i	−0.278265	−	0.233492i
$497$	10.6445	+	24.6767i	0.477470	+	1.10690i
$498$	−5.27299	−	1.00405i	−0.236289	−	0.0449927i
$499$	−6.71533	−	1.59156i	−0.300619	−	0.0712481i	0.0775381	−	0.996989i	$-0.475294\pi$
$499$	−6.71533	−	1.59156i	−0.300619	−	0.0712481i	−0.378157	+	0.925741i	$0.623442\pi$
$500$	−3.17293	−	10.5983i	−0.141898	−	0.473972i
$501$	−0.386154	+	28.3322i	−0.0172521	+	1.26579i
$502$	−28.7690	−	3.36261i	−1.28402	−	0.150081i
$503$	3.29830	−	18.7056i	0.147064	−	0.834040i	−0.818623	−	0.574331i	$-0.805262\pi$
$503$	3.29830	−	18.7056i	0.147064	−	0.834040i	0.965687	−	0.259709i	$-0.0836267\pi$
$504$	−12.6258	−	0.344231i	−0.562399	−	0.0153333i
$505$	−2.81324	−	15.9547i	−0.125187	−	0.709973i
$506$	−0.0612010	−	1.05078i	−0.00272072	−	0.0467129i
$507$	6.06383	−	8.95146i	0.269304	−	0.397548i
$508$	8.15154	−	18.8974i	0.361666	−	0.838436i
$509$	9.82955	−	4.93658i	0.435687	−	0.218810i	−0.217416	−	0.976079i	$-0.569763\pi$
$509$	9.82955	−	4.93658i	0.435687	−	0.218810i	0.653103	+	0.757269i	$0.273467\pi$
$510$	−2.92587	−	4.58342i	−0.129560	−	0.202957i
$511$	24.9445	−	5.91195i	1.10348	−	0.261529i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	−25.8130	−	5.64825i	−1.13967	−	0.249376i
$514$	8.16873	−	14.1487i	0.360307	−	0.624070i
$515$	3.53870	−	11.8201i	0.155934	−	0.520855i
$516$	3.54829	−	3.25740i	0.156205	−	0.143399i
$517$	2.99681	+	1.97104i	0.131800	+	0.0866860i
$518$	7.75984	+	10.4233i	0.340948	+	0.457973i
$519$	−35.6939	+	10.1581i	−1.56679	+	0.445892i
$520$	−8.27847	+	5.44483i	−0.363035	+	0.238772i
$521$	20.7976	+	7.56971i	0.911159	+	0.331635i	0.754716	−	0.656052i	$-0.227775\pi$
$521$	20.7976	+	7.56971i	0.911159	+	0.331635i	0.156444	+	0.987687i	$0.449997\pi$
$522$	21.8874	−	4.56120i	0.957986	−	0.199638i
$523$	17.2973	−	6.29571i	0.756359	−	0.275292i	0.0650798	−	0.997880i	$-0.479270\pi$
$523$	17.2973	−	6.29571i	0.756359	−	0.275292i	0.691279	+	0.722588i	$0.257048\pi$
$524$	−3.50500	+	4.70804i	−0.153117	+	0.205672i
$525$	0.264578	−	0.697208i	0.0115471	−	0.0304286i
$526$	10.4186	−	11.0431i	0.454272	−	0.481500i
$527$	−7.71606	+	8.17854i	−0.336117	+	0.356263i
$528$	6.14035	−	0.996624i	0.267224	−	0.0433725i
$529$	−13.6834	+	18.3799i	−0.594929	+	0.799128i
$530$	25.3123	−	9.21291i	1.09949	−	0.400183i
$531$	17.1819	−	21.8120i	0.745630	−	0.946561i
$532$	−20.1186	−	7.32257i	−0.872252	−	0.317474i
$533$	27.0820	−	17.8121i	1.17305	−	0.771528i
$534$	0.389307	−	1.54827i	0.0168469	−	0.0670002i
$535$	−18.6515	−	25.0533i	−0.806375	−	1.08315i
$536$	−4.66281	−	3.06678i	−0.201403	−	0.132465i
$537$	−14.1902	−	4.45989i	−0.612354	−	0.192458i
$538$	2.67353	−	8.93021i	0.115264	−	0.385008i
$539$	19.2605	−	33.3602i	0.829610	−	1.43693i
$540$	−11.0971	−	3.82304i	−0.477543	−	0.164517i
$541$	−8.09100	−	14.0140i	−0.347859	−	0.602510i	0.638010	−	0.770028i	$-0.279758\pi$
$541$	−8.09100	−	14.0140i	−0.347859	−	0.602510i	−0.985869	+	0.167518i	$0.946425\pi$
$542$	−17.2224	+	4.08179i	−0.739766	+	0.175328i
$543$	−0.321876	+	0.0143487i	−0.0138130	+	0.000615763i
$544$	−1.24203	+	0.623770i	−0.0532515	+	0.0267439i
$545$	−15.2465	+	35.3453i	−0.653088	+	1.51403i
$546$	31.9057	+	2.29498i	1.36544	+	0.0982159i
$547$	−2.59023	−	44.4725i	−0.110750	−	1.90151i	−0.359821	−	0.933021i	$-0.617162\pi$
$547$	−2.59023	−	44.4725i	−0.110750	−	1.90151i	0.249071	−	0.968485i	$-0.419875\pi$
$548$	−0.513133	−	2.91012i	−0.0219200	−	0.124314i
$549$	−8.92435	+	43.6239i	−0.380882	+	1.86182i
$550$	−0.0637771	+	0.361698i	−0.00271947	+	0.0154229i
$551$	37.6418	+	4.39969i	1.60359	+	0.187433i
$552$	0.436103	+	0.259772i	0.0185618	+	0.0110566i
$553$	14.6336	+	48.8795i	0.622282	+	2.07857i
$554$	17.9603	+	4.25667i	0.763060	+	0.180849i
$555$	3.97504	+	11.4025i	0.168731	+	0.484009i
$556$	6.07737	+	14.0889i	0.257738	+	0.597504i
$557$	−10.0552	−	8.43728i	−0.426051	−	0.357499i	0.404409	−	0.914578i	$-0.367477\pi$
$557$	−10.0552	−	8.43728i	−0.426051	−	0.357499i	−0.830459	+	0.557080i	$0.811922\pi$
$558$	−2.07097	+	24.1813i	−0.0876712	+	1.02368i
$559$	−9.34491	+	7.84131i	−0.395248	+	0.331652i
$560$	−8.49846	−	4.26809i	−0.359126	−	0.180360i
$561$	−0.886606	−	8.60035i	−0.0374325	−	0.363107i
$562$	−0.692483	+	0.0809397i	−0.0292106	+	0.00341423i
$563$	−1.95829	+	33.6226i	−0.0825322	+	1.41702i	0.662034	+	0.749474i	$0.269694\pi$
$563$	−1.95829	+	33.6226i	−0.0825322	+	1.41702i	−0.744566	+	0.667549i	$0.767343\pi$
$564$	−1.59754	+	0.663438i	−0.0672686	+	0.0279358i
$565$	−13.6359	−	14.4532i	−0.573666	−	0.608051i
$566$	13.0162			0.547113
$567$	20.9376	+	31.5814i	0.879295	+	1.32630i
$568$	6.38325			0.267835
$569$	−24.8075	−	26.2944i	−1.03998	−	1.10232i	−0.994645	−	0.103346i	$-0.967045\pi$
$569$	−24.8075	−	26.2944i	−1.03998	−	1.10232i	−0.0453375	−	0.998972i	$-0.514436\pi$
$570$	−15.7952	−	12.0971i	−0.661589	−	0.506693i
$571$	−1.96662	+	33.7656i	−0.0823005	+	1.41305i	0.664148	+	0.747601i	$0.268795\pi$
$571$	−1.96662	+	33.7656i	−0.0823005	+	1.41305i	−0.746448	+	0.665444i	$0.768242\pi$
$572$	−15.6481	+	1.82900i	−0.654278	+	0.0764742i
$573$	−11.6102	−	5.19694i	−0.485023	−	0.217105i
$574$	27.8017	+	13.9625i	1.16042	+	0.582784i
$575$	−0.0229582	+	0.0192643i	−0.000957425	+	0.000803375i
$576$	−1.26287	+	2.72124i	−0.0526197	+	0.113385i
$577$	21.3204	+	17.8899i	0.887580	+	0.744768i	0.967723	−	0.252016i	$-0.0810935\pi$
$577$	21.3204	+	17.8899i	0.887580	+	0.744768i	−0.0801436	+	0.996783i	$0.525538\pi$
$578$	−5.96824	−	13.8359i	−0.248246	−	0.575499i
$579$	−0.552985	+	0.641072i	−0.0229813	+	0.0266420i
$580$	16.3802	+	3.88217i	0.680150	+	0.161198i
$581$	3.74209	+	12.4995i	0.155248	+	0.518565i
$582$	−2.82186	+	1.57832i	−0.116970	+	0.0654235i
$583$	42.5398	+	4.97220i	1.76182	+	0.205927i
$584$	1.05733	−	5.99643i	0.0437527	−	0.248134i
$585$	27.6455	+	10.9243i	1.14300	+	0.451663i
$586$	−5.18186	−	29.3878i	−0.214061	−	1.21400i
$587$	0.518114	+	8.89568i	0.0213849	+	0.367164i	0.991976	+	0.126429i	$0.0403515\pi$
$587$	0.518114	+	8.89568i	0.0213849	+	0.367164i	−0.970591	+	0.240735i	$0.922611\pi$
$588$	8.11042	+	16.7133i	0.334468	+	0.689244i
$589$	−16.2945	+	37.7749i	−0.671403	+	1.55649i
$590$	18.6828	−	9.38283i	0.769157	−	0.386285i
$591$	6.66342	−	12.8290i	0.274097	−	0.527714i
$592$	3.00328	−	0.711791i	0.123434	−	0.0292544i
$593$	−17.5496	−	30.3968i	−0.720675	−	1.24825i	−0.960729	−	0.277487i	$-0.910499\pi$
$593$	−17.5496	−	30.3968i	−0.720675	−	1.24825i	0.240054	−	0.970760i	$-0.422835\pi$
$594$	−13.0395	−	13.3509i	−0.535018	−	0.547792i
$595$	−6.60882	+	11.4468i	−0.270935	+	0.469273i
$596$	−3.90045	+	13.0284i	−0.159769	+	0.533664i
$597$	2.63085	+	11.8158i	0.107674	+	0.483589i
$598$	−1.07408	−	0.706435i	−0.0439225	−	0.0288883i
$599$	1.20379	+	1.61697i	0.0491855	+	0.0660675i	0.826035	−	0.563618i	$-0.190591\pi$
$599$	1.20379	+	1.61697i	0.0491855	+	0.0660675i	−0.776850	+	0.629686i	$0.783184\pi$
$600$	−0.127167	−	0.123294i	−0.00519156	−	0.00503346i
$601$	9.97324	−	6.55950i	0.406817	−	0.267568i	−0.329566	−	0.944132i	$-0.606902\pi$
$601$	9.97324	−	6.55950i	0.406817	−	0.267568i	0.736383	+	0.676565i	$0.236532\pi$
$602$	−11.0022	−	4.00446i	−0.448415	−	0.163210i
$603$	0.517611	+	16.7348i	0.0210788	+	0.681494i
$604$	4.10181	−	1.49294i	0.166900	−	0.0607467i
$605$	−2.56157	+	3.44078i	−0.104143	+	0.139888i
$606$	7.85471	+	9.62426i	0.319076	+	0.390959i
$607$	−5.73034	+	6.07381i	−0.232587	+	0.246528i	−0.833147	−	0.553052i	$-0.813463\pi$
$607$	−5.73034	+	6.07381i	−0.232587	+	0.246528i	0.600559	+	0.799580i	$0.294945\pi$
$608$	−3.48971	+	3.69888i	−0.141526	+	0.150009i
$609$	−34.3621	−	42.1034i	−1.39242	−	1.70612i
$610$	−20.0206	+	26.8924i	−0.810611	+	1.08884i
$611$	4.11676	−	1.49838i	0.166546	−	0.0606178i
$612$	3.67370	+	1.97217i	0.148501	+	0.0797201i
$613$	−24.8380	−	9.04029i	−1.00320	−	0.365134i	−0.212381	−	0.977187i	$-0.568122\pi$
$613$	−24.8380	−	9.04029i	−1.00320	−	0.365134i	−0.790817	+	0.612053i	$0.790344\pi$
$614$	−4.89527	+	3.21967i	−0.197557	+	0.129935i
$615$	20.7563	+	20.1243i	0.836976	+	0.811488i
$616$	−9.02960	−	12.1289i	−0.363813	−	0.488685i
$617$	12.6415	+	8.31444i	0.508927	+	0.334727i	0.777866	−	0.628431i	$-0.216302\pi$
$617$	12.6415	+	8.31444i	0.508927	+	0.334727i	−0.268938	+	0.963157i	$0.586673\pi$
$618$	2.05620	+	9.23489i	0.0827125	+	0.371482i
$619$	−11.0904	+	37.0446i	−0.445762	+	1.48895i	0.380031	+	0.924974i	$0.375913\pi$
$619$	−11.0904	+	37.0446i	−0.445762	+	1.48895i	−0.825793	+	0.563974i	$0.809272\pi$
$620$	−9.13687	+	15.8255i	−0.366945	+	0.635568i
$621$	−0.114818	−	1.51849i	−0.00460748	−	0.0609350i
$622$	−3.57463	−	6.19144i	−0.143330	−	0.248254i
$623$	−3.77600	+	0.894928i	−0.151282	+	0.0358545i
$624$	3.50211	−	6.74256i	0.140197	−	0.269918i
$625$	−22.7884	+	11.4448i	−0.911536	+	0.457791i
$626$	4.96810	−	11.5173i	0.198565	−	0.460326i
$627$	−13.8107	−	28.4599i	−0.551544	−	1.13658i
$628$	0.111301	+	1.91096i	0.00444138	+	0.0762555i
$629$	−0.744914	−	4.22462i	−0.0297017	−	0.168446i
$630$	4.18661	+	28.2212i	0.166798	+	1.12436i
$631$	−4.17190	+	23.6600i	−0.166081	+	0.941892i	0.781862	+	0.623451i	$0.214270\pi$
$631$	−4.17190	+	23.6600i	−0.166081	+	0.941892i	−0.947943	+	0.318440i	$0.896841\pi$
$632$	12.0370	+	1.40693i	0.478808	+	0.0559646i
$633$	−8.82894	+	4.93820i	−0.350919	+	0.196276i
$634$	4.47406	+	14.9444i	0.177688	+	0.593518i
$635$	−45.2346	−	10.7208i	−1.79508	−	0.425442i
$636$	−13.4912	+	15.6402i	−0.534959	+	0.620175i
$637$	−18.6351	−	43.2009i	−0.738348	−	1.71168i
$638$	20.5039	+	17.2048i	0.811758	+	0.681146i
$639$	−11.0126	−	15.6664i	−0.435650	−	0.619754i
$640$	−1.73036	+	1.45194i	−0.0683983	+	0.0573930i
$641$	5.31254	+	2.66806i	0.209833	+	0.105382i	0.550612	−	0.834762i	$-0.314395\pi$
$641$	5.31254	+	2.66806i	0.209833	+	0.105382i	−0.340779	+	0.940143i	$0.610691\pi$
$642$	21.8599	+	9.78489i	0.862740	+	0.386179i
$643$	14.6766	−	1.71545i	0.578788	−	0.0676507i	0.178338	−	0.983969i	$-0.442928\pi$
$643$	14.6766	−	1.71545i	0.578788	−	0.0676507i	0.400450	+	0.916319i	$0.368854\pi$
$644$	0.0717430	−	1.23178i	0.00282707	−	0.0485390i
$645$	−8.63787	−	6.61551i	−0.340116	−	0.260485i
$646$	4.85022	+	5.14094i	0.190829	+	0.202267i
$647$	19.6797			0.773690			0.386845	−	0.922145i	$-0.373565\pi$
$647$	19.6797			0.773690			0.386845	+	0.922145i	$0.373565\pi$
$648$	8.85749	−	1.59529i	0.347955	−	0.0626689i
$649$	33.2414			1.30484
$650$	0.307837	+	0.326289i	0.0120744	+	0.0127981i
$651$	54.4825	−	22.6259i	2.13534	−	0.886777i
$652$	−0.586065	+	10.0623i	−0.0229521	+	0.394072i
$653$	−33.4217	+	3.90644i	−1.30789	+	0.152871i	−0.741326	−	0.671145i	$-0.765803\pi$
$653$	−33.4217	+	3.90644i	−1.30789	+	0.152871i	−0.566566	+	0.824016i	$0.691729\pi$
$654$	−3.02681	−	29.3610i	−0.118358	−	1.14811i
$655$	11.8478	+	5.95021i	0.462933	+	0.232494i
$656$	5.66064	−	4.74984i	0.221011	−	0.185450i
$657$	−16.5412	+	7.75020i	−0.645333	+	0.302364i
$658$	3.22103	+	2.70277i	0.125569	+	0.105365i
$659$	17.9088	+	41.5172i	0.697626	+	1.61728i	0.783811	+	0.621000i	$0.213273\pi$
$659$	17.9088	+	41.5172i	0.697626	+	1.61728i	−0.0861849	+	0.996279i	$0.527468\pi$
$660$	−4.62548	−	13.2683i	−0.180047	−	0.516468i
$661$	−12.5188	−	2.96701i	−0.486926	−	0.115403i	−0.0201823	−	0.999796i	$-0.506425\pi$
$661$	−12.5188	−	2.96701i	−0.486926	−	0.115403i	−0.466743	+	0.884393i	$0.654573\pi$
$662$	−9.64621	−	32.2206i	−0.374911	−	1.25229i
$663$	−9.07237	−	5.40411i	−0.352342	−	0.209878i
$664$	3.07811	+	0.359779i	0.119454	+	0.0139621i
$665$	−8.39777	+	47.6261i	−0.325651	+	1.84686i
$666$	−6.92829	−	6.14296i	−0.268466	−	0.238035i
$667$	0.379266	+	2.15092i	0.0146852	+	0.0832840i
$668$	−0.951199	−	16.3314i	−0.0368030	−	0.631883i
$669$	−18.4833	−	1.32951i	−0.714608	−	0.0514017i
$670$	−4.99311	+	11.5753i	−0.192901	+	0.447194i
$671$	−47.6370	+	23.9242i	−1.83900	+	0.923583i
$672$	7.28500	−	0.324754i	0.281025	−	0.0125277i
$673$	8.59055	−	2.03600i	0.331141	−	0.0784819i	−0.0616821	−	0.998096i	$-0.519646\pi$
$673$	8.59055	−	2.03600i	0.331141	−	0.0784819i	0.392823	+	0.919614i	$0.371498\pi$
$674$	4.80300	+	8.31904i	0.185005	+	0.320438i
$675$	−0.0832096	+	0.524815i	−0.00320274	+	0.0202002i
$676$	−3.12115	+	5.40598i	−0.120044	+	0.207922i
$677$	−4.78789	+	15.9927i	−0.184013	+	0.614648i	0.815350	+	0.578969i	$0.196545\pi$
$677$	−4.78789	+	15.9927i	−0.184013	+	0.614648i	−0.999363	+	0.0356792i	$0.988641\pi$
$678$	14.5355	+	4.56840i	0.558233	+	0.175448i
$679$	6.56629	+	4.31872i	0.251991	+	0.165737i
$680$	1.87475	+	2.51823i	0.0718934	+	0.0965696i
$681$	−1.62677	+	6.46964i	−0.0623378	+	0.247917i
$682$	−24.2753	+	15.9661i	−0.929549	+	0.611374i
$683$	−2.56187	−	0.932444i	−0.0980272	−	0.0356790i	0.292541	−	0.956253i	$-0.405499\pi$
$683$	−2.56187	−	0.932444i	−0.0980272	−	0.0356790i	−0.390568	+	0.920574i	$0.627721\pi$
$684$	15.0987	+	2.18339i	0.577313	+	0.0834841i
$685$	−6.27230	+	2.28293i	−0.239652	+	0.0872263i
$686$	9.36657	−	12.5815i	0.357617	−	0.480363i
$687$	−24.4721	+	3.97201i	−0.933670	+	0.151542i
$688$	−1.90840	+	2.02279i	−0.0727572	+	0.0771181i
$689$	35.8979	−	38.0496i	1.36760	−	1.44957i
$690$	0.406807	−	1.07200i	0.0154869	−	0.0408105i
$691$	−2.78748	+	3.74424i	−0.106041	+	0.142437i	−0.851976	−	0.523581i	$-0.824596\pi$
$691$	−2.78748	+	3.74424i	−0.106041	+	0.142437i	0.745935	+	0.666019i	$0.232003\pi$
$692$	20.1340	−	7.32818i	0.765380	−	0.278576i
$693$	−14.1897	+	43.0864i	−0.539024	+	1.63672i
$694$	−2.75990	−	1.00452i	−0.104764	−	0.0381311i
$695$	28.9571	−	19.0454i	1.09840	−	0.722432i
$696$	−12.4152	+	3.53324i	−0.470597	+	0.133927i
$697$	−6.13302	−	8.23807i	−0.232305	−	0.312039i
$698$	−0.0714974	−	0.0470246i	−0.00270622	−	0.00177991i
$699$	−21.7186	+	19.9380i	−0.821472	+	0.754125i
$700$	−0.123481	+	0.412455i	−0.00466714	+	0.0155893i
$701$	25.3003	−	43.8213i	0.955577	−	1.65511i	0.222536	−	0.974925i	$-0.428567\pi$
$701$	25.3003	−	43.8213i	0.955577	−	1.65511i	0.733042	−	0.680184i	$-0.238100\pi$
$702$	−22.5902	+	3.03722i	−0.852612	+	0.114632i
$703$	−7.84776	−	13.5927i	−0.295984	−	0.512659i
$704$	−3.49471	+	0.828262i	−0.131712	+	0.0312163i
$705$	2.10244	+	3.29351i	0.0791824	+	0.124041i
$706$	17.4072	−	8.74220i	0.655127	−	0.329017i
$707$	11.9602	−	27.7268i	0.449808	−	1.04277i
$708$	−8.99091	+	13.2724i	−0.337899	+	0.498808i
$709$	−0.865531	−	14.8606i	−0.0325057	−	0.558101i	−0.974767	−	0.223224i	$-0.928342\pi$
$709$	−0.865531	−	14.8606i	−0.0325057	−	0.558101i	0.942262	−	0.334878i	$-0.108695\pi$
$710$	−2.50376	−	14.1995i	−0.0939646	−	0.532900i
$711$	−17.3136	−	31.9698i	−0.649311	−	1.19896i
$712$	−0.160055	+	0.907717i	−0.00599831	+	0.0340181i
$713$	−2.35488	−	0.275246i	−0.0881908	−	0.0103080i
$714$	0.138125	−	10.1343i	0.00516920	−	0.379266i
$715$	10.2064	+	34.0917i	0.381698	+	1.27496i
$716$	8.35637	+	1.98050i	0.312292	+	0.0740146i
$717$	−14.3205	−	2.72682i	−0.534808	−	0.101835i
$718$	−1.53968	−	3.56938i	−0.0574604	−	0.133208i
$719$	−10.0350	−	8.42040i	−0.374244	−	0.314028i	0.436194	−	0.899853i	$-0.356326\pi$
$719$	−10.0350	−	8.42040i	−0.374244	−	0.314028i	−0.810438	+	0.585825i	$0.800771\pi$
$720$	6.54876	+	1.74188i	0.244058	+	0.0649162i
$721$	17.6170	−	14.7824i	0.656091	−	0.550526i
$722$	6.13010	+	3.07865i	0.228139	+	0.114576i
$723$	−20.3979	+	14.7579i	−0.758606	+	0.548853i
$724$	0.184762	−	0.0215955i	0.00686662	−	0.000802592i
$725$	0.0443130	−	0.760825i	0.00164574	−	0.0282563i
$726$	0.426345	−	3.26149i	0.0158232	−	0.121045i
$727$	21.5371	+	22.8280i	0.798768	+	0.846645i	0.990883	−	0.134728i	$-0.0430160\pi$
$727$	21.5371	+	22.8280i	0.798768	+	0.846645i	−0.192115	+	0.981372i	$0.561535\pi$
$728$	−18.4684			−0.684483
$729$	−19.1965	−	18.9867i	−0.710981	−	0.703211i
$730$	−13.7538			−0.509051
$731$	2.65242	+	2.81140i	0.0981033	+	0.103983i
$732$	3.33222	−	25.4911i	0.123162	−	0.942176i
$733$	−1.84946	+	31.7541i	−0.0683115	+	1.17286i	0.773753	+	0.633487i	$0.218377\pi$
$733$	−1.84946	+	31.7541i	−0.0683115	+	1.17286i	−0.842065	+	0.539377i	$0.818660\pi$
$734$	22.1711	−	2.59143i	0.818350	−	0.0956514i
$735$	33.9975	−	24.5973i	1.25402	−	0.907283i
$736$	−0.261895	−	0.131529i	−0.00965359	−	0.00484822i
$737$	−15.3547	+	12.8841i	−0.565596	+	0.474591i
$738$	−21.4234	−	5.69836i	−0.788608	−	0.209760i
$739$	−13.0781	−	10.9738i	−0.481086	−	0.403679i	0.369733	−	0.929138i	$-0.379449\pi$
$739$	−13.0781	−	10.9738i	−0.481086	−	0.403679i	−0.850819	+	0.525459i	$0.823894\pi$
$740$	−2.76139	−	6.40162i	−0.101511	−	0.235328i
$741$	−37.9549	−	7.22714i	−1.39431	−	0.265496i
$742$	48.8536	+	11.5785i	1.79347	+	0.425061i
$743$	11.7045	+	39.0957i	0.429396	+	1.43428i	0.849877	+	0.526981i	$0.176676\pi$
$743$	11.7045	+	39.0957i	0.429396	+	1.43428i	−0.420481	+	0.907301i	$0.638139\pi$
$744$	0.190962	−	14.0109i	0.00700099	−	0.513665i
$745$	30.5116	+	3.56630i	1.11786	+	0.130659i
$746$	−1.16207	+	6.59043i	−0.0425464	+	0.241293i
$747$	−4.42743	−	8.17531i	−0.161991	−	0.299119i
$748$	0.866805	+	4.91590i	0.0316935	+	0.179743i
$749$	−3.38496	−	58.1176i	−0.123684	−	2.12357i
$750$	10.7468	−	15.8645i	0.392418	−	0.579290i
$751$	−4.37209	+	10.1356i	−0.159540	+	0.369855i	−0.979171	−	0.203036i	$-0.934919\pi$
$751$	−4.37209	+	10.1356i	−0.159540	+	0.369855i	0.819631	+	0.572891i	$0.194178\pi$
$752$	0.892483	−	0.448222i	0.0325455	−	0.0163450i
$753$	−26.9943	−	42.2870i	−0.983726	−	1.54103i
$754$	31.8101	−	7.53914i	1.15846	−	0.274559i
$755$	−4.92993	−	8.53889i	−0.179419	−	0.310762i
$756$	−13.3653	−	17.3193i	−0.486092	−	0.629897i
$757$	−10.2741	+	17.7953i	−0.373419	+	0.646780i	−0.990089	−	0.140441i	$-0.955148\pi$
$757$	−10.2741	+	17.7953i	−0.373419	+	0.646780i	0.616670	+	0.787222i	$0.288481\pi$
$758$	8.16042	−	27.2577i	0.296400	−	0.990045i
$759$	1.34299	−	1.23289i	0.0487476	−	0.0447512i
$760$	9.59696	+	6.31202i	0.348118	+	0.228961i
$761$	6.46390	+	8.68252i	0.234316	+	0.314741i	0.903692	−	0.428183i	$-0.140846\pi$
$761$	6.46390	+	8.68252i	0.234316	+	0.314741i	−0.669376	+	0.742924i	$0.733439\pi$
$762$	34.2852	−	9.75720i	1.24202	−	0.353466i
$763$	−59.9440	+	39.4258i	−2.17012	+	1.42731i
$764$	6.90114	+	2.51181i	0.249675	+	0.0908741i
$765$	2.94612	−	8.94572i	0.106517	−	0.323433i
$766$	−32.6928	+	11.8992i	−1.18124	+	0.429935i
$767$	24.2448	−	32.5664i	0.875429	−	1.17591i
$768$	0.614522	−	1.61937i	0.0221747	−	0.0584340i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.224505 - 1.71744i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.24355 - 0.262233i) q^{5} +(-1.40328 + 1.01528i) q^{6} +(3.76235 + 1.88952i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-2.89919 - 0.771149i) q^{9} +O(q^{10})\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.224505 - 1.71744i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.24355 - 0.262233i) q^{5} +(-1.40328 + 1.01528i) q^{6} +(3.76235 + 1.88952i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-2.89919 - 0.771149i) q^{9} +(-1.73036 - 1.45194i) q^{10} +(-1.42253 - 3.29779i) q^{11} +(1.70148 + 0.323986i) q^{12} +(-4.26836 - 1.01162i) q^{13} +(-1.20749 - 4.03330i) q^{14} +(0.0533189 - 3.91203i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.241347 + 1.36875i) q^{17} +(1.42864 + 2.63799i) q^{18} +(0.883044 + 5.00799i) q^{19} +(0.131339 + 2.25500i) q^{20} +(4.08981 - 6.03740i) q^{21} +(-1.42253 + 3.29779i) q^{22} +(-0.261895 + 0.131529i) q^{23} +(-0.931968 - 1.45994i) q^{24} +(0.0995059 - 0.0235833i) q^{25} +(2.19330 + 3.79891i) q^{26} +(-1.97529 + 4.80606i) q^{27} +(-2.10509 + 3.64612i) q^{28} +(2.13741 - 7.13946i) q^{29} +(-2.88209 + 2.64581i) q^{30} +(6.75905 + 4.44550i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-5.98313 + 1.70274i) q^{33} +(1.16121 - 0.763743i) q^{34} +(8.93649 + 3.25262i) q^{35} +(0.938417 - 2.84945i) q^{36} +(-2.90034 + 1.05564i) q^{37} +(3.03670 - 4.07900i) q^{38} +(-2.69567 + 7.10354i) q^{39} +(1.55010 - 1.64301i) q^{40} +(-5.07095 + 5.37489i) q^{41} +(-7.19804 + 1.16830i) q^{42} +(1.66067 - 2.23066i) q^{43} +(3.37493 - 1.22837i) q^{44} +(-6.70670 - 0.969843i) q^{45} +(0.275394 + 0.100235i) q^{46} +(-0.834413 + 0.548802i) q^{47} +(-0.422370 + 1.67976i) q^{48} +(6.40486 + 8.60322i) q^{49} +(-0.0854390 - 0.0561941i) q^{50} +(2.29656 + 0.721791i) q^{51} +(1.25809 - 4.20232i) q^{52} +(-5.96257 + 10.3275i) q^{53} +(4.85133 - 1.86135i) q^{54} +(-4.05630 - 7.02572i) q^{55} +(4.09669 - 0.970933i) q^{56} +(8.79917 - 0.392254i) q^{57} +(-6.65983 + 3.34469i) q^{58} +(-3.66592 + 8.49856i) q^{59} +(3.90231 + 0.280693i) q^{60} +(-0.863013 - 14.8174i) q^{61} +(-1.40481 - 7.96705i) q^{62} +(-9.45068 - 8.37942i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-9.84155 - 1.15031i) q^{65} +(5.34440 + 3.18348i) q^{66} +(-1.60063 - 5.34648i) q^{67} +(-1.35240 - 0.320525i) q^{68} +(0.167096 + 0.479318i) q^{69} +(-3.76673 - 8.73225i) q^{70} +(4.88985 + 4.10307i) q^{71} +(-2.71660 + 1.27283i) q^{72} +(4.66440 - 3.91389i) q^{73} +(2.75818 + 1.38521i) q^{74} +(-0.0181633 - 0.176190i) q^{75} +(-5.05086 + 0.590361i) q^{76} +(0.879204 - 15.0954i) q^{77} +(7.01681 - 2.91399i) q^{78} +(8.31655 + 8.81503i) q^{79} -2.25882 q^{80} +(7.81066 + 4.47142i) q^{81} +7.38945 q^{82} +(2.12671 + 2.25418i) q^{83} +(5.78938 + 4.43393i) q^{84} +(-0.182543 + 3.13414i) q^{85} +(-2.76214 + 0.322848i) q^{86} +(-11.7817 - 5.27372i) q^{87} +(-3.20950 - 1.61187i) q^{88} +(-0.706078 + 0.592470i) q^{89} +(3.89698 + 5.54382i) q^{90} +(-14.1476 - 11.8712i) q^{91} +(-0.116078 - 0.269100i) q^{92} +(9.15232 - 10.6102i) q^{93} +(0.971793 + 0.230319i) q^{94} +(3.29441 + 11.0041i) q^{95} +(1.51166 - 0.845503i) q^{96} +(1.85410 + 0.216713i) q^{97} +(1.86247 - 10.5626i) q^{98} +(1.58110 + 10.6579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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