LMFDB - Embedded newform 162.2.g.b.25.4

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			25.4
Character	$\chi$	$=$	162.25
Dual form			162.2.g.b.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 - 0.448799i) q^{2} +(1.02523 + 1.39603i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.664151 - 2.21842i) q^{5} +(1.54272 + 0.787412i) q^{6} +(-0.590051 + 1.36789i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.897788 + 2.86251i) q^{9} +O(q^{10})$	\(q+(0.893633 - 0.448799i) q^{2} +(1.02523 + 1.39603i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.664151 - 2.21842i) q^{5} +(1.54272 + 0.787412i) q^{6} +(-0.590051 + 1.36789i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.897788 + 2.86251i) q^{9} +(-0.402118 - 2.28052i) q^{10} +(-4.28069 - 1.01454i) q^{11} +(1.73201 + 0.0112858i) q^{12} +(0.407438 - 0.267976i) q^{13} +(0.0866199 + 1.48721i) q^{14} +(3.77789 - 1.34723i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(6.18123 + 2.24978i) q^{17} +(0.482400 + 2.96096i) q^{18} +(-6.76026 + 2.46053i) q^{19} +(-1.38284 - 1.85748i) q^{20} +(-2.51456 + 0.578682i) q^{21} +(-4.28069 + 1.01454i) q^{22} +(-1.15348 - 2.67407i) q^{23} +(1.55285 - 0.767241i) q^{24} +(-0.302850 - 0.199188i) q^{25} +(0.243833 - 0.422330i) q^{26} +(-4.91659 + 1.68141i) q^{27} +(0.744864 + 1.29014i) q^{28} +(0.382974 - 6.57542i) q^{29} +(2.77141 - 2.89944i) q^{30} +(-1.78001 - 0.208053i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-2.97238 - 7.01611i) q^{33} +(6.53345 - 0.763651i) q^{34} +(2.64267 + 2.21747i) q^{35} +(1.75997 + 2.42951i) q^{36} +(-3.51174 + 2.94670i) q^{37} +(-4.93690 + 5.23281i) q^{38} +(0.791822 + 0.294057i) q^{39} +(-2.06939 - 1.03929i) q^{40} +(-7.03828 - 3.53476i) q^{41} +(-1.98738 + 1.64566i) q^{42} +(-0.304424 + 0.322671i) q^{43} +(-3.37004 + 2.82780i) q^{44} +(5.75399 + 3.89281i) q^{45} +(-2.23091 - 1.87195i) q^{46} +(7.76840 - 0.907996i) q^{47} +(1.04334 - 1.38255i) q^{48} +(3.28072 + 3.47736i) q^{49} +(-0.360032 - 0.0420817i) q^{50} +(3.19645 + 10.9357i) q^{51} +(0.0283552 - 0.486840i) q^{52} +(0.984340 + 1.70493i) q^{53} +(-3.63901 + 3.70912i) q^{54} +(-5.09371 + 8.82256i) q^{55} +(1.24465 + 0.818618i) q^{56} +(-10.3658 - 6.91489i) q^{57} +(-2.60880 - 6.04789i) q^{58} +(12.3643 - 2.93038i) q^{59} +(1.17536 - 3.83484i) q^{60} +(4.60541 + 6.18613i) q^{61} +(-1.68405 + 0.612943i) q^{62} +(-3.38587 - 2.91710i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(-0.323883 - 1.08185i) q^{65} +(-5.80504 - 4.93582i) q^{66} +(-0.221954 - 3.81081i) q^{67} +(5.49578 - 3.61463i) q^{68} +(2.55049 - 4.35184i) q^{69} +(3.35678 + 0.795571i) q^{70} +(1.34489 + 7.62726i) q^{71} +(2.66312 + 1.38122i) q^{72} +(1.74940 - 9.92135i) q^{73} +(-1.81573 + 4.20933i) q^{74} +(-0.0324209 - 0.627002i) q^{75} +(-2.06330 + 6.89189i) q^{76} +(3.91361 - 5.25689i) q^{77} +(0.839570 - 0.0925906i) q^{78} +(15.0035 - 7.53506i) q^{79} -2.31570 q^{80} +(-7.38795 - 5.13986i) q^{81} -7.87604 q^{82} +(-4.65331 + 2.33698i) q^{83} +(-1.03741 + 2.36255i) q^{84} +(9.09624 - 12.2184i) q^{85} +(-0.127229 + 0.424975i) q^{86} +(9.57211 - 6.20670i) q^{87} +(-1.74246 + 4.03949i) q^{88} +(-0.537926 + 3.05073i) q^{89} +(6.88904 + 0.896360i) q^{90} +(0.126153 + 0.715451i) q^{91} +(-2.83374 - 0.671609i) q^{92} +(-1.53448 - 2.69824i) q^{93} +(6.53459 - 4.29787i) q^{94} +(0.968660 + 16.6313i) q^{95} +(0.311875 - 1.70374i) q^{96} +(0.403864 + 1.34900i) q^{97} +(4.49240 + 1.63510i) q^{98} +(6.74730 - 11.3427i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$	1.02523	+	1.39603i	0.591919	+	0.805997i
$3$	1.02523	+	1.39603i	0.591919	+	0.805997i
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	0.664151	−	2.21842i	0.297017	−	0.992107i	−0.671049	−	0.741413i	$-0.734156\pi$
$5$	0.664151	−	2.21842i	0.297017	−	0.992107i	0.968066	−	0.250694i	$-0.0806589\pi$
$6$	1.54272	+	0.787412i	0.629812	+	0.321460i
$7$	−0.590051	+	1.36789i	−0.223018	+	0.517014i	−0.992585	−	0.121552i	$-0.961213\pi$
$7$	−0.590051	+	1.36789i	−0.223018	+	0.517014i	0.769567	+	0.638566i	$0.220472\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$	−0.897788	+	2.86251i	−0.299263	+	0.954171i
$10$	−0.402118	−	2.28052i	−0.127161	−	0.721165i
$11$	−4.28069	−	1.01454i	−1.29068	−	0.305896i	−0.472739	−	0.881202i	$-0.656735\pi$
$11$	−4.28069	−	1.01454i	−1.29068	−	0.305896i	−0.817938	+	0.575306i	$0.804883\pi$
$12$	1.73201	+	0.0112858i	0.499989	+	0.00325792i
$13$	0.407438	−	0.267976i	0.113003	−	0.0743233i	−0.491749	−	0.870737i	$-0.663642\pi$
$13$	0.407438	−	0.267976i	0.113003	−	0.0743233i	0.604752	+	0.796413i	$0.293272\pi$
$14$	0.0866199	+	1.48721i	0.0231502	+	0.397473i
$15$	3.77789	−	1.34723i	0.975446	−	0.347852i
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	6.18123	+	2.24978i	1.49917	+	0.545653i	0.955845	−	0.293871i	$-0.0949435\pi$
$17$	6.18123	+	2.24978i	1.49917	+	0.545653i	0.543323	+	0.839524i	$0.317166\pi$
$18$	0.482400	+	2.96096i	0.113703	+	0.697905i
$19$	−6.76026	+	2.46053i	−1.55091	+	0.564485i	−0.968631	−	0.248504i	$-0.920061\pi$
$19$	−6.76026	+	2.46053i	−1.55091	+	0.564485i	−0.582279	+	0.812989i	$0.697839\pi$
$20$	−1.38284	−	1.85748i	−0.309213	−	0.415345i
$21$	−2.51456	+	0.578682i	−0.548721	+	0.126279i
$22$	−4.28069	+	1.01454i	−0.912647	+	0.216301i
$23$	−1.15348	−	2.67407i	−0.240517	−	0.557582i	0.754611	−	0.656173i	$-0.227826\pi$
$23$	−1.15348	−	2.67407i	−0.240517	−	0.557582i	−0.995128	+	0.0985910i	$0.968566\pi$
$24$	1.55285	−	0.767241i	0.316974	−	0.156612i
$25$	−0.302850	−	0.199188i	−0.0605701	−	0.0398376i
$26$	0.243833	−	0.422330i	0.0478195	−	0.0828258i
$27$	−4.91659	+	1.68141i	−0.946198	+	0.323587i
$28$	0.744864	+	1.29014i	0.140766	+	0.243814i
$29$	0.382974	−	6.57542i	0.0711166	−	1.22102i	−0.754311	−	0.656517i	$-0.772029\pi$
$29$	0.382974	−	6.57542i	0.0711166	−	1.22102i	0.825428	−	0.564508i	$-0.190934\pi$
$30$	2.77141	−	2.89944i	0.505988	−	0.529363i
$31$	−1.78001	−	0.208053i	−0.319699	−	0.0373674i	−0.0452698	−	0.998975i	$-0.514415\pi$
$31$	−1.78001	−	0.208053i	−0.319699	−	0.0373674i	−0.274429	+	0.961607i	$0.588489\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$	−2.97238	−	7.01611i	−0.517425	−	1.22135i
$34$	6.53345	−	0.763651i	1.12048	−	0.130965i
$35$	2.64267	+	2.21747i	0.446694	+	0.374820i
$36$	1.75997	+	2.42951i	0.293328	+	0.404918i
$37$	−3.51174	+	2.94670i	−0.577326	+	0.484434i	−0.884068	−	0.467359i	$-0.845206\pi$
$37$	−3.51174	+	2.94670i	−0.577326	+	0.484434i	0.306742	+	0.951793i	$0.400761\pi$
$38$	−4.93690	+	5.23281i	−0.800871	+	0.848874i
$39$	0.791822	+	0.294057i	0.126793	+	0.0470867i
$40$	−2.06939	−	1.03929i	−0.327199	−	0.164326i
$41$	−7.03828	−	3.53476i	−1.09920	−	0.552037i	−0.195713	−	0.980661i	$-0.562702\pi$
$41$	−7.03828	−	3.53476i	−1.09920	−	0.552037i	−0.903483	+	0.428625i	$0.858998\pi$
$42$	−1.98738	+	1.64566i	−0.306659	+	0.253931i
$43$	−0.304424	+	0.322671i	−0.0464243	+	0.0492069i	−0.750170	−	0.661246i	$-0.770028\pi$
$43$	−0.304424	+	0.322671i	−0.0464243	+	0.0492069i	0.703745	+	0.710452i	$0.251510\pi$
$44$	−3.37004	+	2.82780i	−0.508053	+	0.426307i
$45$	5.75399	+	3.89281i	0.857754	+	0.580306i
$46$	−2.23091	−	1.87195i	−0.328929	−	0.276004i
$47$	7.76840	−	0.907996i	1.13314	−	0.132445i	0.471216	−	0.882018i	$-0.343815\pi$
$47$	7.76840	−	0.907996i	1.13314	−	0.132445i	0.661922	+	0.749573i	$0.269741\pi$
$48$	1.04334	−	1.38255i	0.150593	−	0.199554i
$49$	3.28072	+	3.47736i	0.468675	+	0.496766i
$50$	−0.360032	−	0.0420817i	−0.0509162	−	0.00595126i
$51$	3.19645	+	10.9357i	0.447592	+	1.53131i
$52$	0.0283552	−	0.486840i	0.00393216	−	0.0675126i
$53$	0.984340	+	1.70493i	0.135209	+	0.234190i	0.925677	−	0.378314i	$-0.123496\pi$
$53$	0.984340	+	1.70493i	0.135209	+	0.234190i	−0.790468	+	0.612503i	$0.790163\pi$
$54$	−3.63901	+	3.70912i	−0.495207	+	0.504748i
$55$	−5.09371	+	8.82256i	−0.686836	+	1.18963i
$56$	1.24465	+	0.818618i	0.166323	+	0.109392i
$57$	−10.3658	−	6.91489i	−1.37299	−	0.915899i
$58$	−2.60880	−	6.04789i	−0.342553	−	0.794126i
$59$	12.3643	−	2.93038i	1.60969	−	0.381503i	0.675240	−	0.737598i	$-0.264040\pi$
$59$	12.3643	−	2.93038i	1.60969	−	0.381503i	0.934450	+	0.356095i	$0.115892\pi$
$60$	1.17536	−	3.83484i	0.151738	−	0.495076i
$61$	4.60541	+	6.18613i	0.589662	+	0.792053i	0.992373	−	0.123274i	$-0.0393394\pi$
$61$	4.60541	+	6.18613i	0.589662	+	0.792053i	−0.402711	+	0.915327i	$0.631932\pi$
$62$	−1.68405	+	0.612943i	−0.213874	+	0.0778439i
$63$	−3.38587	−	2.91710i	−0.426579	−	0.367521i
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	−0.323883	−	1.08185i	−0.0401728	−	0.134186i
$66$	−5.80504	−	4.93582i	−0.714551	−	0.607558i
$67$	−0.221954	−	3.81081i	−0.0271160	−	0.465564i	−0.984347	−	0.176240i	$-0.943606\pi$
$67$	−0.221954	−	3.81081i	−0.0271160	−	0.465564i	0.957231	−	0.289324i	$-0.0934305\pi$
$68$	5.49578	−	3.61463i	0.666461	−	0.438338i
$69$	2.55049	−	4.35184i	0.307042	−	0.523900i
$70$	3.35678	+	0.795571i	0.401212	+	0.0950889i
$71$	1.34489	+	7.62726i	0.159609	+	0.905189i	0.954450	+	0.298371i	$0.0964433\pi$
$71$	1.34489	+	7.62726i	0.159609	+	0.905189i	−0.794841	+	0.606818i	$0.792446\pi$
$72$	2.66312	+	1.38122i	0.313852	+	0.162778i
$73$	1.74940	−	9.92135i	0.204752	−	1.16121i	−0.693078	−	0.720863i	$-0.743746\pi$
$73$	1.74940	−	9.92135i	0.204752	−	1.16121i	0.897830	−	0.440343i	$-0.145143\pi$
$74$	−1.81573	+	4.20933i	−0.211074	+	0.489325i
$75$	−0.0324209	−	0.627002i	−0.00374364	−	0.0723999i
$76$	−2.06330	+	6.89189i	−0.236676	+	0.790554i
$77$	3.91361	−	5.25689i	0.445997	−	0.599078i
$78$	0.839570	−	0.0925906i	0.0950626	−	0.0104838i
$79$	15.0035	−	7.53506i	1.68803	−	0.847761i	0.696550	−	0.717509i	$-0.254718\pi$
$79$	15.0035	−	7.53506i	1.68803	−	0.847761i	0.991481	−	0.130252i	$-0.0415787\pi$
$80$	−2.31570			−0.258904
$81$	−7.38795	−	5.13986i	−0.820884	−	0.571096i
$82$	−7.87604			−0.869763
$83$	−4.65331	+	2.33698i	−0.510767	+	0.256517i	−0.685465	−	0.728105i	$-0.740401\pi$
$83$	−4.65331	+	2.33698i	−0.510767	+	0.256517i	0.174698	+	0.984622i	$0.444105\pi$
$84$	−1.03741	+	2.36255i	−0.113191	+	0.257775i
$85$	9.09624	−	12.2184i	0.986625	−	1.32527i
$86$	−0.127229	+	0.424975i	−0.0137195	+	0.0458262i
$87$	9.57211	−	6.20670i	1.02624	−	0.665428i
$88$	−1.74246	+	4.03949i	−0.185747	+	0.430611i
$89$	−0.537926	+	3.05073i	−0.0570200	+	0.323377i	−0.999954	−	0.00960343i	$-0.996943\pi$
$89$	−0.537926	+	3.05073i	−0.0570200	+	0.323377i	0.942934	+	0.332980i	$0.108054\pi$
$90$	6.88904	+	0.896360i	0.726169	+	0.0944847i
$91$	0.126153	+	0.715451i	0.0132245	+	0.0749996i
$92$	−2.83374	−	0.671609i	−0.295438	−	0.0700201i
$93$	−1.53448	−	2.69824i	−0.159118	−	0.279795i
$94$	6.53459	−	4.29787i	0.673991	−	0.443291i
$95$	0.968660	+	16.6313i	0.0993825	+	1.70633i
$96$	0.311875	−	1.70374i	0.0318306	−	0.173887i
$97$	0.403864	+	1.34900i	0.0410062	+	0.136970i	0.976042	−	0.217584i	$-0.0698177\pi$
$97$	0.403864	+	1.34900i	0.0410062	+	0.136970i	−0.935035	+	0.354555i	$0.884633\pi$
$98$	4.49240	+	1.63510i	0.453801	+	0.165170i
$99$	6.74730	−	11.3427i	0.678129	−	1.13998i
$100$	−0.340623	+	0.123977i	−0.0340623	+	0.0123977i
$101$	−6.00167	−	8.06164i	−0.597188	−	0.802163i	0.396053	−	0.918228i	$-0.370380\pi$
$101$	−6.00167	−	8.06164i	−0.597188	−	0.802163i	−0.993242	+	0.116064i	$0.962972\pi$
$102$	7.76440	+	8.33796i	0.768790	+	0.825581i
$103$	−1.63242	+	0.386890i	−0.160847	+	0.0381214i	−0.310250	−	0.950655i	$-0.600413\pi$
$103$	−1.63242	+	0.386890i	−0.160847	+	0.0381214i	0.149403	+	0.988776i	$0.452265\pi$
$104$	−0.193154	−	0.447782i	−0.0189403	−	0.0439086i
$105$	−0.386285	+	5.96267i	−0.0376976	+	0.581897i
$106$	1.64481	+	1.08181i	0.159758	+	0.105074i
$107$	−6.16214	+	10.6731i	−0.595717	+	1.03181i	0.397728	+	0.917503i	$0.369799\pi$
$107$	−6.16214	+	10.6731i	−0.595717	+	1.03181i	−0.993445	+	0.114309i	$0.963535\pi$
$108$	−1.58729	+	4.94778i	−0.152737	+	0.476100i
$109$	9.54562	+	16.5335i	0.914305	+	1.58362i	0.807916	+	0.589298i	$0.200595\pi$
$109$	9.54562	+	16.5335i	0.914305	+	1.58362i	0.106389	+	0.994325i	$0.466071\pi$
$110$	−0.592346	+	10.1702i	−0.0564779	+	0.969689i
$111$	−7.71403	−	1.88143i	−0.732183	−	0.178577i
$112$	1.47965	+	0.172947i	0.139814	+	0.0163419i
$113$	−5.52918	−	5.86059i	−0.520142	−	0.551318i	0.413045	−	0.910711i	$-0.364465\pi$
$113$	−5.52918	−	5.86059i	−0.520142	−	0.551318i	−0.933186	+	0.359393i	$0.882984\pi$
$114$	−12.3666	−	1.52720i	−1.15824	−	0.143035i
$115$	−6.69829	+	0.782918i	−0.624619	+	0.0730075i
$116$	−5.04560	−	4.23376i	−0.468472	−	0.393095i
$117$	0.401292	+	1.40688i	0.0370995	+	0.130066i
$118$	9.73395	−	8.16776i	0.896083	−	0.751903i
$119$	−6.72470	+	7.12777i	−0.616452	+	0.653401i
$120$	−0.670736	−	3.95444i	−0.0612295	−	0.360989i
$121$	7.46507	+	3.74910i	0.678643	+	0.340827i
$122$	6.89187	+	3.46123i	0.623961	+	0.313365i
$123$	−2.28127	−	13.4496i	−0.205695	−	1.21271i
$124$	−1.22983	+	1.30355i	−0.110442	+	0.117062i
$125$	8.22664	−	6.90297i	0.735813	−	0.617420i
$126$	−4.33491	−	1.08725i	−0.386185	−	0.0968596i
$127$	14.4311	+	12.1091i	1.28055	+	1.07451i	0.993168	+	0.116693i	$0.0372293\pi$
$127$	14.4311	+	12.1091i	1.28055	+	1.07451i	0.287382	+	0.957816i	$0.407215\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$	−0.762564	−	0.0941715i	−0.0671400	−	0.00829134i
$130$	−0.774964	−	0.821414i	−0.0679689	−	0.0720428i
$131$	−13.3322	−	1.55832i	−1.16484	−	0.136151i	−0.488383	−	0.872629i	$-0.662413\pi$
$131$	−13.3322	−	1.55832i	−1.16484	−	0.136151i	−0.676461	+	0.736479i	$0.736487\pi$
$132$	−7.40277	−	1.80551i	−0.644328	−	0.157150i
$133$	0.623154	−	10.6991i	0.0540343	−	0.927733i
$134$	−1.90863	−	3.30585i	−0.164881	−	0.285582i
$135$	0.464710	+	12.0238i	0.0399958	+	1.03484i
$136$	3.28896	−	5.69665i	0.282026	−	0.488484i
$137$	4.42901	+	2.91301i	0.378396	+	0.248875i	0.724432	−	0.689346i	$-0.242102\pi$
$137$	4.42901	+	2.91301i	0.378396	+	0.248875i	−0.346036	+	0.938221i	$0.612472\pi$
$138$	0.326096	−	5.03360i	0.0277592	−	0.428488i
$139$	−7.14865	−	16.5724i	−0.606340	−	1.40565i	−0.894063	−	0.447941i	$-0.852157\pi$
$139$	−7.14865	−	16.5724i	−0.606340	−	1.40565i	0.287723	−	0.957714i	$-0.407102\pi$
$140$	3.35678	−	0.795571i	0.283700	−	0.0672380i
$141$	9.23202	+	9.91400i	0.777476	+	0.834909i
$142$	4.62495	+	6.21238i	0.388117	+	0.521332i
$143$	−2.01599	+	0.733761i	−0.168586	+	0.0613601i
$144$	2.99975	+	0.0390942i	0.249979	+	0.00325785i
$145$	−14.3327	−	5.21667i	−1.19026	−	0.433221i
$146$	−2.88937	−	9.65117i	−0.239126	−	0.798737i
$147$	−1.49099	+	8.14510i	−0.122975	+	0.671796i
$148$	0.266550	+	4.57649i	0.0219103	+	0.376185i
$149$	−14.7989	+	9.73339i	−1.21237	+	0.797390i	−0.984343	−	0.176264i	$-0.943599\pi$
$149$	−14.7989	+	9.73339i	−1.21237	+	0.797390i	−0.228030	+	0.973654i	$0.573229\pi$
$150$	−0.310370	−	0.545759i	−0.0253416	−	0.0445610i
$151$	−2.32779	−	0.551696i	−0.189433	−	0.0448964i	0.134804	−	0.990872i	$-0.456959\pi$
$151$	−2.32779	−	0.551696i	−0.189433	−	0.0448964i	−0.324237	+	0.945976i	$0.605108\pi$
$152$	1.24925	+	7.08482i	0.101327	+	0.574655i
$153$	−11.9895	+	15.6740i	−0.969291	+	1.26717i
$154$	1.13804	−	6.45415i	0.0917060	−	0.520091i
$155$	−1.64374	+	3.81063i	−0.132029	+	0.306077i
$156$	0.708713	−	0.459540i	0.0567424	−	0.0367927i
$157$	2.97910	−	9.95089i	0.237758	−	0.794167i	−0.752940	−	0.658089i	$-0.771365\pi$
$157$	2.97910	−	9.95089i	0.237758	−	0.794167i	0.990698	−	0.136078i	$-0.0434498\pi$
$158$	10.0259	−	13.4672i	0.797620	−	1.07139i
$159$	−1.37095	+	3.12212i	−0.108723	+	0.247600i
$160$	−2.06939	+	1.03929i	−0.163600	+	0.0821628i
$161$	4.33845			0.341917
$162$	−8.90888	−	1.27744i	−0.699948	−	0.100365i
$163$	−6.60659			−0.517468			−0.258734	−	0.965949i	$-0.583305\pi$
$163$	−6.60659			−0.517468			−0.258734	+	0.965949i	$0.583305\pi$
$164$	−7.03828	+	3.53476i	−0.549598	+	0.276018i
$165$	−17.5388	+	1.93424i	−1.36539	+	0.150580i
$166$	−3.10951	+	4.17680i	−0.241345	+	0.324183i
$167$	1.98331	−	6.62473i	0.153473	−	0.512637i	−0.846326	−	0.532665i	$-0.821190\pi$
$167$	1.98331	−	6.62473i	0.153473	−	0.512637i	0.999799	+	0.0200284i	$0.00637567\pi$
$168$	0.133243	+	2.57684i	0.0102799	+	0.198808i
$169$	−5.05484	+	11.7184i	−0.388834	+	0.901419i
$170$	2.64510	−	15.0011i	0.202870	−	1.15053i
$171$	−0.974023	−	21.5604i	−0.0744854	−	1.64876i
$172$	0.0770323	+	0.436872i	0.00587365	+	0.0333112i
$173$	−12.3276	−	2.92169i	−0.937249	−	0.222132i	−0.266516	−	0.963831i	$-0.585872\pi$
$173$	−12.3276	−	2.92169i	−0.937249	−	0.222132i	−0.670734	+	0.741698i	$0.734021\pi$
$174$	5.76838	−	9.84247i	0.437300	−	0.746155i
$175$	0.451164	−	0.296735i	0.0341048	−	0.0224311i
$176$	0.255795	+	4.39183i	0.0192813	+	0.331047i
$177$	16.7672	+	14.2565i	1.26030	+	1.07159i
$178$	0.888457	+	2.96765i	0.0665926	+	0.222435i
$179$	−0.951462	−	0.346304i	−0.0711156	−	0.0258840i	0.306217	−	0.951962i	$-0.400937\pi$
$179$	−0.951462	−	0.346304i	−0.0711156	−	0.0258840i	−0.377333	+	0.926078i	$0.623159\pi$
$180$	6.55856	−	2.29078i	0.488846	−	0.170745i
$181$	14.7137	−	5.35534i	1.09366	−	0.398059i	0.268684	−	0.963228i	$-0.413411\pi$
$181$	14.7137	−	5.35534i	1.09366	−	0.398059i	0.824975	+	0.565169i	$0.191189\pi$
$182$	0.433828	+	0.582733i	0.0321575	+	0.0431950i
$183$	−3.91439	+	12.7715i	−0.289360	+	0.944097i
$184$	−2.83374	+	0.671609i	−0.208906	+	0.0495117i
$185$	4.20469	+	9.74756i	0.309135	+	0.716655i
$186$	−2.58223	−	1.72257i	−0.189338	−	0.126305i
$187$	−24.1774	−	15.9018i	−1.76803	−	1.16285i
$188$	3.91064	−	6.77343i	0.285213	−	0.494003i
$189$	0.601054	−	7.71748i	0.0437203	−	0.561364i
$190$	8.32972	+	14.4275i	0.604301	+	1.04668i
$191$	−0.257431	+	4.41992i	−0.0186271	+	0.319814i	0.976105	+	0.217301i	$0.0697254\pi$
$191$	−0.257431	+	4.41992i	−0.0186271	+	0.319814i	−0.994732	+	0.102513i	$0.967312\pi$
$192$	−0.485936	−	1.66249i	−0.0350694	−	0.119980i
$193$	−18.8735	−	2.20600i	−1.35855	−	0.158791i	−0.594574	−	0.804041i	$-0.702679\pi$
$193$	−18.8735	−	2.20600i	−1.35855	−	0.158791i	−0.763972	+	0.645250i	$0.776753\pi$
$194$	0.966336	+	1.02426i	0.0693789	+	0.0735373i
$195$	1.17823	−	1.56130i	0.0843748	−	0.111807i
$196$	4.74839	−	0.555007i	0.339171	−	0.0396433i
$197$	−17.3672	−	14.5728i	−1.23736	−	1.03827i	−0.997726	−	0.0674075i	$-0.978527\pi$
$197$	−17.3672	−	14.5728i	−1.23736	−	1.03827i	−0.239637	−	0.970863i	$-0.577028\pi$
$198$	0.939015	−	13.1644i	0.0667329	−	0.935552i
$199$	−2.88695	+	2.42244i	−0.204650	+	0.171722i	−0.739352	−	0.673319i	$-0.764868\pi$
$199$	−2.88695	+	2.42244i	−0.204650	+	0.171722i	0.534702	+	0.845041i	$0.320424\pi$
$200$	−0.248751	+	0.263661i	−0.0175894	+	0.0186436i
$201$	5.09244	−	4.21683i	0.359193	−	0.297432i
$202$	−8.98134	−	4.51060i	−0.631925	−	0.317365i
$203$	8.76848	+	4.40370i	0.615427	+	0.309079i
$204$	10.6806	+	3.96642i	0.747791	+	0.277705i
$205$	−12.5161	+	13.2663i	−0.874160	+	0.926555i
$206$	−1.28515	+	1.07837i	−0.0895403	+	0.0751333i
$207$	8.69013	−	0.901104i	0.604006	−	0.0626311i
$208$	−0.373573	−	0.313465i	−0.0259026	−	0.0217349i
$209$	31.4349	−	3.67421i	2.17440	−	0.254151i
$210$	2.33085	+	5.50180i	0.160844	+	0.379660i
$211$	9.04987	+	9.59230i	0.623019	+	0.660361i	0.959624	−	0.281284i	$-0.0907604\pi$
$211$	9.04987	+	9.59230i	0.623019	+	0.660361i	−0.336606	+	0.941646i	$0.609279\pi$
$212$	1.95537	+	0.228550i	0.134295	+	0.0156969i
$213$	−9.26904	+	9.69724i	−0.635104	+	0.664444i
$214$	−0.716594	+	12.3034i	−0.0489853	+	0.841046i
$215$	0.513636	+	0.889644i	0.0350297	+	0.0606732i
$216$	0.802107	+	5.13387i	0.0545765	+	0.349316i
$217$	1.33489	−	2.31210i	0.0906182	−	0.156955i
$218$	15.9505	+	10.4908i	1.08030	+	0.710527i
$219$	15.6440	−	7.72950i	1.05713	−	0.522311i
$220$	4.03503	+	9.35425i	0.272042	+	0.630663i
$221$	3.12136	−	0.739775i	0.209965	−	0.0497627i
$222$	−7.73789	+	1.78074i	−0.519333	+	0.119516i
$223$	−4.24353	−	5.70006i	−0.284168	−	0.381704i	0.637003	−	0.770861i	$-0.280174\pi$
$223$	−4.24353	−	5.70006i	−0.284168	−	0.381704i	−0.921171	+	0.389157i	$0.872766\pi$
$224$	1.39989	−	0.509517i	0.0935338	−	0.0340435i
$225$	0.842073	−	0.688084i	0.0561382	−	0.0458723i
$226$	−7.57128	−	2.75572i	−0.503634	−	0.183308i
$227$	0.642640	+	2.14657i	0.0426535	+	0.142473i	0.976664	−	0.214773i	$-0.0689011\pi$
$227$	0.642640	+	2.14657i	0.0426535	+	0.142473i	−0.934011	+	0.357246i	$0.883716\pi$
$228$	−11.7366	+	4.18538i	−0.777277	+	0.277184i
$229$	0.903744	+	15.5167i	0.0597211	+	1.02537i	0.886466	+	0.462794i	$0.153153\pi$
$229$	0.903744	+	15.5167i	0.0597211	+	1.02537i	−0.826745	+	0.562577i	$0.809810\pi$
$230$	−5.63444	+	3.70583i	−0.371524	+	0.244355i
$231$	11.3511	+	0.0739637i	0.746850	+	0.00486645i
$232$	−6.40902	−	1.51897i	−0.420773	−	0.0997250i
$233$	1.36995	+	7.76937i	0.0897483	+	0.508988i	0.996231	+	0.0867442i	$0.0276463\pi$
$233$	1.36995	+	7.76937i	0.0897483	+	0.508988i	−0.906482	+	0.422244i	$0.861243\pi$
$234$	0.990016	+	1.07714i	0.0647193	+	0.0704146i
$235$	3.14508	−	17.8366i	0.205162	−	1.16353i
$236$	5.03290	−	11.6676i	0.327614	−	0.759494i
$237$	25.9013	+	13.2202i	1.68247	+	0.858742i
$238$	−2.81048	+	9.38764i	−0.182176	+	0.608511i
$239$	3.07871	−	4.13542i	0.199145	−	0.267498i	−0.691321	−	0.722548i	$-0.742971\pi$
$239$	3.07871	−	4.13542i	0.199145	−	0.267498i	0.890466	+	0.455049i	$0.150378\pi$
$240$	−2.37414	−	3.23279i	−0.153250	−	0.208676i
$241$	−1.85788	+	0.933061i	−0.119676	+	0.0601038i	−0.507630	−	0.861575i	$-0.669478\pi$
$241$	−1.85788	+	0.933061i	−0.119676	+	0.0601038i	0.387954	+	0.921679i	$0.373182\pi$
$242$	8.35362			0.536991
$243$	−0.398994	−	15.5834i	−0.0255955	−	0.999672i
$244$	7.71220			0.493723
$245$	9.89315	−	4.96853i	0.632050	−	0.317428i
$246$	−8.07478	−	10.9952i	−0.514829	−	0.701026i
$247$	−2.09502	+	2.81410i	−0.133303	+	0.179057i
$248$	−0.513987	+	1.71684i	−0.0326382	+	0.109019i
$249$	−8.03322	−	4.10020i	−0.509085	−	0.259839i
$250$	4.25355	−	9.86083i	0.269018	−	0.623654i
$251$	3.84832	−	21.8249i	0.242904	−	1.37757i	−0.582408	−	0.812897i	$-0.697889\pi$
$251$	3.84832	−	21.8249i	0.242904	−	1.37757i	0.825311	−	0.564678i	$-0.191000\pi$
$252$	−4.36178	+	0.973907i	−0.274766	+	0.0613504i
$253$	2.22474	+	12.6171i	0.139868	+	0.793231i
$254$	18.3306	+	4.34444i	1.15017	+	0.272594i
$255$	26.3830	+	0.171911i	1.65216	+	0.0107655i
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	−0.653529	−	11.2207i	−0.0407660	−	0.699925i	−0.955340	−	0.295507i	$-0.904511\pi$
$257$	−0.653529	−	11.2207i	−0.0407660	−	0.699925i	0.914574	−	0.404418i	$-0.132526\pi$
$258$	−0.723716	+	0.258083i	−0.0450566	+	0.0160676i
$259$	−1.95866	−	6.54238i	−0.121705	−	0.406524i
$260$	−1.06118	−	0.386239i	−0.0658118	−	0.0239535i
$261$	18.4784	+	6.99960i	1.14378	+	0.433265i
$262$	−12.6135	+	4.59094i	−0.779264	+	0.283629i
$263$	0.769213	+	1.03323i	0.0474317	+	0.0637118i	0.825206	−	0.564832i	$-0.191059\pi$
$263$	0.769213	+	1.03323i	0.0474317	+	0.0637118i	−0.777775	+	0.628543i	$0.783651\pi$
$264$	−7.42567	+	1.70889i	−0.457018	+	0.105175i
$265$	4.43599	−	1.05135i	0.272501	−	0.0645839i
$266$	−4.24489	−	9.84077i	−0.260271	−	0.603376i
$267$	−4.81040	+	2.37675i	−0.294392	+	0.145455i
$268$	−3.18928	−	2.09762i	−0.194816	−	0.128133i
$269$	−8.37641	+	14.5084i	−0.510719	+	0.884591i	0.489204	+	0.872169i	$0.337287\pi$
$269$	−8.37641	+	14.5084i	−0.510719	+	0.884591i	−0.999923	+	0.0124213i	$0.996046\pi$
$270$	5.81154	+	10.5363i	0.353679	+	0.641217i
$271$	−13.9516	−	24.1649i	−0.847502	−	1.46792i	−0.883431	−	0.468562i	$-0.844772\pi$
$271$	−13.9516	−	24.1649i	−0.847502	−	1.46792i	0.0359290	−	0.999354i	$-0.488561\pi$
$272$	0.382472	−	6.56680i	0.0231908	−	0.398171i
$273$	−0.869453	+	0.909618i	−0.0526217	+	0.0550526i
$274$	5.26526	+	0.615421i	0.318086	+	0.0371790i
$275$	1.09432	+	1.15992i	0.0659902	+	0.0699456i
$276$	−1.96766	−	4.64454i	−0.118439	−	0.279568i
$277$	3.12877	−	0.365701i	0.187990	−	0.0219728i	−0.0215771	−	0.999767i	$-0.506869\pi$
$277$	3.12877	−	0.365701i	0.187990	−	0.0219728i	0.209567	+	0.977794i	$0.432795\pi$
$278$	−13.8260	−	11.6014i	−0.829226	−	0.695803i
$279$	2.19363	−	4.90851i	0.131329	−	0.293865i
$280$	2.64267	−	2.21747i	0.157930	−	0.132519i
$281$	−0.756901	+	0.802268i	−0.0451529	+	0.0478593i	−0.749556	−	0.661941i	$-0.769733\pi$
$281$	−0.756901	+	0.802268i	−0.0451529	+	0.0478593i	0.704403	+	0.709800i	$0.251215\pi$
$282$	12.6994	+	4.71615i	0.756240	+	0.280842i
$283$	28.2064	+	14.1658i	1.67670	+	0.842068i	0.993754	+	0.111595i	$0.0355959\pi$
$283$	28.2064	+	14.1658i	1.67670	+	0.842068i	0.682941	+	0.730473i	$0.260700\pi$
$284$	6.92112	+	3.47592i	0.410693	+	0.206258i
$285$	−22.2246	+	18.4032i	−1.31647	+	1.09011i
$286$	−1.47224	+	1.56049i	−0.0870556	+	0.0922736i
$287$	8.98811	−	7.54192i	0.530551	−	0.445186i
$288$	2.69822	−	1.31135i	0.158994	−	0.0772719i
$289$	20.1233	+	16.8855i	1.18372	+	0.993263i
$290$	−15.1494	+	1.77071i	−0.889603	+	0.103980i
$291$	−1.46919	+	1.94685i	−0.0861252	+	0.114126i
$292$	−6.91347	−	7.32785i	−0.404580	−	0.428830i
$293$	−28.2115	−	3.29745i	−1.64813	−	0.192639i	−0.759258	−	0.650790i	$-0.774438\pi$
$293$	−28.2115	−	3.29745i	−1.64813	−	0.192639i	−0.888874	+	0.458151i	$0.848512\pi$
$294$	2.32312	+	7.94788i	0.135487	+	0.463530i
$295$	1.71092	−	29.3753i	0.0996135	−	1.71030i
$296$	2.29212	+	3.97008i	0.133227	+	0.230756i
$297$	22.7523	−	2.20950i	1.32022	−	0.128208i
$298$	−8.85644	+	15.3398i	−0.513040	+	0.888611i
$299$	−1.18656	−	0.780412i	−0.0686204	−	0.0451324i
$300$	−0.522293	−	0.348414i	−0.0301546	−	0.0201157i
$301$	−0.261753	−	0.606812i	−0.0150872	−	0.0349761i
$302$	−2.32779	+	0.551696i	−0.133949	+	0.0317465i
$303$	5.10116	−	16.6436i	0.293054	−	0.956148i
$304$	4.29603	+	5.77057i	0.246394	+	0.330965i
$305$	16.7821	−	6.10819i	0.960942	−	0.349754i
$306$	−3.67970	+	19.3877i	−0.210354	+	1.10832i
$307$	−28.0570	−	10.2119i	−1.60130	−	0.582824i	−0.621604	−	0.783332i	$-0.713519\pi$
$307$	−28.0570	−	10.2119i	−1.60130	−	0.582824i	−0.979692	+	0.200507i	$0.935741\pi$
$308$	−1.87963	−	6.27839i	−0.107102	−	0.357745i
$309$	−2.21372	−	1.88225i	−0.125934	−	0.107077i
$310$	0.241303	+	4.14301i	0.0137051	+	0.235307i
$311$	1.52200	−	1.00103i	0.0863046	−	0.0567634i	−0.505623	−	0.862754i	$-0.668737\pi$
$311$	1.52200	−	1.00103i	0.0863046	−	0.0567634i	0.591928	+	0.805991i	$0.298367\pi$
$312$	0.427088	−	0.728730i	0.0241791	−	0.0412562i
$313$	−4.20142	−	0.995754i	−0.237478	−	0.0562833i	0.110153	−	0.993915i	$-0.464866\pi$
$313$	−4.20142	−	0.995754i	−0.237478	−	0.0562833i	−0.347631	+	0.937631i	$0.613014\pi$
$314$	−1.80373	−	10.2295i	−0.101790	−	0.577282i
$315$	−8.72009	+	5.57387i	−0.491321	+	0.314052i
$316$	2.91545	−	16.5343i	0.164007	−	0.930128i
$317$	12.9195	−	29.9507i	0.725630	−	1.68220i	−0.00552184	−	0.999985i	$-0.501758\pi$
$317$	12.9195	−	29.9507i	0.725630	−	1.68220i	0.731152	−	0.682215i	$-0.238983\pi$
$318$	0.176081	+	3.40530i	0.00987411	+	0.190960i
$319$	−8.31044	+	27.7588i	−0.465295	+	1.55419i
$320$	−1.38284	+	1.85748i	−0.0773032	+	0.103836i
$321$	−21.2177	+	2.33995i	−1.18425	+	0.130603i
$322$	3.87698	−	1.94709i	0.216055	−	0.108507i
$323$	−47.3224			−2.63309
$324$	−8.53458	+	2.85674i	−0.474143	+	0.158708i
$325$	−0.176770			−0.00980546
$326$	−5.90386	+	2.96503i	−0.326985	+	0.164218i
$327$	−13.2947	+	30.2767i	−0.735200	+	1.67430i
$328$	−4.70324	+	6.31755i	−0.259693	+	0.348828i
$329$	−3.34171	+	11.1621i	−0.184234	+	0.615386i
$330$	−14.8052	+	9.59989i	−0.814997	+	0.528457i
$331$	−3.78788	+	8.78130i	−0.208201	+	0.482664i	−0.990035	−	0.140823i	$-0.955025\pi$
$331$	−3.78788	+	8.78130i	−0.208201	+	0.482664i	0.781834	+	0.623487i	$0.214284\pi$
$332$	−0.904218	+	5.12807i	−0.0496254	+	0.281440i
$333$	−5.28216	−	12.6979i	−0.289461	−	0.695841i
$334$	−1.20082	−	6.81018i	−0.0657059	−	0.372637i
$335$	−8.60138	−	2.03856i	−0.469944	−	0.111379i
$336$	1.27555	+	2.24295i	0.0695872	+	0.122363i
$337$	−13.9009	+	9.14276i	−0.757230	+	0.498038i	−0.868461	−	0.495757i	$-0.834891\pi$
$337$	−13.9009	+	9.14276i	−0.757230	+	0.498038i	0.111232	+	0.993794i	$0.464520\pi$
$338$	0.742055	+	12.7406i	0.0403625	+	0.692997i
$339$	2.51284	−	13.7274i	0.136479	−	0.745568i
$340$	−4.36874	−	14.5926i	−0.236928	−	0.791395i
$341$	7.40859	+	2.69651i	0.401198	+	0.146024i
$342$	−10.5467	−	18.8299i	−0.570300	−	1.01820i
$343$	−16.4917	+	6.00247i	−0.890465	+	0.324103i
$344$	0.264906	+	0.355831i	0.0142828	+	0.0191851i
$345$	−7.96029	−	8.54832i	−0.428568	−	0.460226i
$346$	−12.3276	+	2.92169i	−0.662735	+	0.157071i
$347$	9.89690	+	22.9436i	0.531294	+	1.23168i	0.946722	+	0.322051i	$0.104372\pi$
$347$	9.89690	+	22.9436i	0.531294	+	1.23168i	−0.415429	+	0.909626i	$0.636368\pi$
$348$	0.737526	−	11.3844i	0.0395355	−	0.610268i
$349$	17.1526	+	11.2815i	0.918160	+	0.603884i	0.918200	−	0.396116i	$-0.129642\pi$
$349$	17.1526	+	11.2815i	0.918160	+	0.603884i	−3.99838e−5		1.00000i	$0.500013\pi$
$350$	0.270001	−	0.467655i	0.0144321	−	0.0249972i
$351$	−1.55263	+	2.00260i	−0.0828732	+	0.106891i
$352$	2.19964	+	3.80988i	0.117241	+	0.203067i
$353$	−1.05164	+	18.0559i	−0.0559731	+	0.961021i	0.847073	+	0.531477i	$0.178363\pi$
$353$	−1.05164	+	18.0559i	−0.0559731	+	0.961021i	−0.903046	+	0.429544i	$0.858674\pi$
$354$	21.3820	+	5.21501i	1.13644	+	0.277174i
$355$	17.8137	+	2.08212i	0.945452	+	0.110507i
$356$	2.12583	+	2.25325i	0.112669	+	0.119422i
$357$	−16.8450	−	2.08024i	−0.891530	−	0.110098i
$358$	−1.00568	+	0.117547i	−0.0531518	+	0.00621255i
$359$	23.7236	+	19.9065i	1.25209	+	1.05062i	0.996479	+	0.0838438i	$0.0267197\pi$
$359$	23.7236	+	19.9065i	1.25209	+	1.05062i	0.255607	+	0.966781i	$0.417725\pi$
$360$	4.83284	−	4.99059i	0.254713	−	0.263027i
$361$	25.0920	−	21.0547i	1.32063	−	1.10814i
$362$	10.7452	−	11.3892i	0.564753	−	0.598603i
$363$	2.41960	+	14.2651i	0.126996	+	0.748726i
$364$	0.649213	+	0.326047i	0.0340280	+	0.0170895i
$365$	−20.8479	−	10.4702i	−1.09123	−	0.548034i
$366$	2.23381	+	13.1698i	0.116763	+	0.688397i
$367$	−5.49865	+	5.82823i	−0.287027	+	0.304231i	−0.854803	−	0.518952i	$-0.826322\pi$
$367$	−5.49865	+	5.82823i	−0.287027	+	0.304231i	0.567776	+	0.823183i	$0.307804\pi$
$368$	−2.23091	+	1.87195i	−0.116294	+	0.0975823i
$369$	16.4372	−	16.9737i	0.855685	−	0.883616i
$370$	8.13214	+	6.82368i	0.422770	+	0.354746i
$371$	−2.91296	+	0.340477i	−0.151234	+	0.0176767i
$372$	−3.08065	−	0.380440i	−0.159724	−	0.0197249i
$373$	−15.3339	−	16.2530i	−0.793962	−	0.841550i	0.196332	−	0.980537i	$-0.437097\pi$
$373$	−15.3339	−	16.2530i	−0.793962	−	0.841550i	−0.990294	+	0.138987i	$0.955615\pi$
$374$	−28.7424	−	3.35951i	−1.48624	−	0.173716i
$375$	18.0710	+	4.40746i	0.933181	+	0.227600i
$376$	0.454767	−	7.80805i	0.0234528	−	0.402670i
$377$	−1.60602	−	2.78170i	−0.0827141	−	0.143265i
$378$	−2.92648	−	7.16634i	−0.150522	−	0.368597i
$379$	10.1868	−	17.6441i	0.523262	−	0.906317i	−0.476371	−	0.879244i	$-0.658048\pi$
$379$	10.1868	−	17.6441i	0.523262	−	0.906317i	0.999633	−	0.0270727i	$-0.00861857\pi$
$380$	13.9188	+	9.15451i	0.714017	+	0.469617i
$381$	−2.10942	+	32.5608i	−0.108069	+	1.66814i
$382$	1.75361	+	4.06532i	0.0897224	+	0.208000i
$383$	2.46010	−	0.583054i	0.125705	−	0.0297927i	−0.167282	−	0.985909i	$-0.553499\pi$
$383$	2.46010	−	0.583054i	0.125705	−	0.0297927i	0.292987	+	0.956116i	$0.405351\pi$
$384$	−1.18037	−	1.26757i	−0.0602356	−	0.0646852i
$385$	−9.06276	−	12.1734i	−0.461881	−	0.620414i
$386$	−17.8560	+	6.49907i	−0.908848	+	0.330794i
$387$	−0.650341	−	1.16111i	−0.0330587	−	0.0590225i
$388$	1.32323	+	0.481618i	0.0671771	+	0.0244505i
$389$	4.54869	+	15.1937i	0.230628	+	0.770350i	0.992459	+	0.122575i	$0.0391152\pi$
$389$	4.54869	+	15.1937i	0.230628	+	0.770350i	−0.761832	+	0.647775i	$0.775700\pi$
$390$	0.352197	−	1.92401i	0.0178342	−	0.0974262i
$391$	−1.11385	−	19.1241i	−0.0563299	−	0.967148i
$392$	3.99423	−	2.62704i	0.201739	−	0.132686i
$393$	−11.4932	−	20.2098i	−0.579756	−	1.01945i
$394$	−22.0602	−	5.22836i	−1.11138	−	0.263401i
$395$	−6.75131	−	38.2886i	−0.339695	−	1.92651i
$396$	−5.06903	−	12.1855i	−0.254728	−	0.612347i
$397$	5.19212	−	29.4460i	0.260585	−	1.47785i	−0.520734	−	0.853719i	$-0.674341\pi$
$397$	5.19212	−	29.4460i	0.260585	−	1.47785i	0.781319	−	0.624132i	$-0.214547\pi$
$398$	−1.49268	+	3.46043i	−0.0748214	+	0.173456i
$399$	15.5752	−	10.0992i	0.779734	−	0.505592i
$400$	−0.103961	+	0.347255i	−0.00519807	+	0.0173628i
$401$	−5.58127	+	7.49695i	−0.278715	+	0.374380i	−0.919333	−	0.393480i	$-0.871271\pi$
$401$	−5.58127	+	7.49695i	−0.278715	+	0.374380i	0.640618	+	0.767860i	$0.278678\pi$
$402$	2.65826	−	6.05378i	0.132582	−	0.301935i
$403$	−0.780997	+	0.392231i	−0.0389042	+	0.0195384i
$404$	−10.0504			−0.500025
$405$	−16.3091	+	12.9759i	−0.810405	+	0.644779i
$406$	9.81218			0.486970
$407$	18.0222	−	9.05110i	0.893328	−	0.448646i
$408$	11.3246	−	1.24892i	0.560654	−	0.0618307i
$409$	−0.379338	+	0.509540i	−0.0187571	+	0.0251951i	−0.811403	−	0.584487i	$-0.801296\pi$
$409$	−0.379338	+	0.509540i	−0.0187571	+	0.0251951i	0.792646	+	0.609683i	$0.208703\pi$
$410$	−5.23088	+	17.4724i	−0.258335	+	0.862898i
$411$	0.474136	+	9.16954i	0.0233874	+	0.452300i
$412$	−0.664479	+	1.54043i	−0.0327365	+	0.0758918i
$413$	−3.28709	+	18.6420i	−0.161747	+	0.917315i
$414$	7.36137	−	4.70538i	0.361792	−	0.231257i
$415$	2.09390	+	11.8751i	0.102786	+	0.582926i
$416$	−0.474520	−	0.112463i	−0.0232653	−	0.00551397i
$417$	15.8065	−	26.9703i	0.774049	−	1.32074i
$418$	26.4423	−	17.3914i	1.29333	−	0.850639i
$419$	0.398563	+	6.84305i	0.0194711	+	0.334305i	0.993951	+	0.109829i	$0.0350302\pi$
$419$	0.398563	+	6.84305i	0.0194711	+	0.334305i	−0.974479	+	0.224477i	$0.927933\pi$
$420$	4.55212	+	3.87051i	0.222121	+	0.188862i
$421$	6.42595	+	21.4642i	0.313182	+	1.04610i	0.959188	+	0.282768i	$0.0912526\pi$
$421$	6.42595	+	21.4642i	0.313182	+	1.04610i	−0.646007	+	0.763332i	$0.723562\pi$
$422$	12.3923	+	4.51042i	0.603247	+	0.219564i
$423$	−4.37523	+	23.0523i	−0.212731	+	1.12084i
$424$	1.84995	−	0.673328i	0.0898417	−	0.0326997i
$425$	−1.42386	−	1.91257i	−0.0690673	−	0.0927734i
$426$	−3.93101	+	12.8257i	−0.190458	+	0.621408i
$427$	−11.1794	+	2.64956i	−0.541008	+	0.128221i
$428$	4.88140	+	11.3164i	0.235951	+	0.546997i
$429$	−3.09121	−	2.06210i	−0.149245	−	0.0995593i
$430$	0.858273	+	0.564495i	0.0413896	+	0.0272224i
$431$	7.62700	−	13.2103i	0.367379	−	0.636320i	−0.621776	−	0.783196i	$-0.713588\pi$
$431$	7.62700	−	13.2103i	0.367379	−	0.636320i	0.989155	+	0.146876i	$0.0469217\pi$
$432$	3.02087	+	4.22781i	0.145341	+	0.203411i
$433$	8.83327	+	15.2997i	0.424500	+	0.735255i	0.996374	−	0.0850866i	$-0.0271167\pi$
$433$	8.83327	+	15.2997i	0.424500	+	0.735255i	−0.571874	+	0.820342i	$0.693783\pi$
$434$	0.155234	−	2.66526i	0.00745146	−	0.127937i
$435$	−7.41174	−	25.3571i	−0.355366	−	1.21578i
$436$	18.9622	+	2.21636i	0.908123	+	0.106144i
$437$	14.3775	+	15.2392i	0.687767	+	0.728990i
$438$	10.5110	−	13.9284i	0.502236	−	0.665523i
$439$	23.6609	−	2.76556i	1.12927	−	0.131993i	0.469127	−	0.883131i	$-0.344569\pi$
$439$	23.6609	−	2.76556i	1.12927	−	0.131993i	0.660146	+	0.751137i	$0.270494\pi$
$440$	7.80401	+	6.54835i	0.372042	+	0.312180i
$441$	−12.8994	+	6.26918i	−0.614257	+	0.298532i
$442$	2.45734	−	2.06195i	0.116884	−	0.0980770i
$443$	10.1320	−	10.7393i	0.481385	−	0.510239i	−0.440473	−	0.897766i	$-0.645189\pi$
$443$	10.1320	−	10.7393i	0.481385	−	0.510239i	0.921858	+	0.387527i	$0.126671\pi$
$444$	−6.11564	+	5.06409i	−0.290235	+	0.240331i
$445$	6.41053	+	3.21949i	0.303888	+	0.152619i
$446$	−6.35034	−	3.18926i	−0.300697	−	0.151016i
$447$	−28.7604	−	10.6807i	−1.36032	−	0.505179i
$448$	1.02231	−	1.08359i	0.0482997	−	0.0511947i
$449$	−8.26585	+	6.93587i	−0.390090	+	0.327324i	−0.816648	−	0.577136i	$-0.804170\pi$
$449$	−8.26585	+	6.93587i	−0.390090	+	0.327324i	0.426558	+	0.904460i	$0.359726\pi$
$450$	0.443692	−	0.992816i	0.0209159	−	0.0468018i
$451$	26.5426	+	22.2719i	1.24984	+	1.04874i
$452$	−8.00271	+	0.935383i	−0.376416	+	0.0439967i
$453$	−1.61635	−	3.81527i	−0.0759425	−	0.179257i
$454$	1.53766	+	1.62983i	0.0721660	+	0.0764915i
$455$	1.67096	+	0.195307i	0.0783356	+	0.00915612i
$456$	−8.60984	+	9.00758i	−0.403193	+	0.421819i
$457$	−1.75430	+	30.1202i	−0.0820627	+	1.40896i	0.666305	+	0.745679i	$0.267875\pi$
$457$	−1.75430	+	30.1202i	−0.0820627	+	1.40896i	−0.748368	+	0.663284i	$0.769162\pi$
$458$	7.77149	+	13.4606i	0.363138	+	0.628974i
$459$	−34.1734	−	0.668094i	−1.59508	−	0.0311840i
$460$	−3.37194	+	5.84038i	−0.157218	+	0.272309i
$461$	−16.9882	−	11.1733i	−0.791219	−	0.520393i	0.0883926	−	0.996086i	$-0.471827\pi$
$461$	−16.9882	−	11.1733i	−0.791219	−	0.520393i	−0.879611	+	0.475693i	$0.842197\pi$
$462$	10.1769	−	5.02828i	0.473474	−	0.233937i
$463$	8.36162	+	19.3844i	0.388597	+	0.900870i	0.994442	+	0.105287i	$0.0335760\pi$
$463$	8.36162	+	19.3844i	0.388597	+	0.900870i	−0.605845	+	0.795583i	$0.707165\pi$
$464$	−6.40902	+	1.51897i	−0.297531	+	0.0705162i
$465$	−7.00496	+	1.61207i	−0.324847	+	0.0747581i
$466$	4.71112	+	6.32813i	0.218238	+	0.293145i
$467$	16.2329	−	5.90831i	0.751171	−	0.273404i	0.0620726	−	0.998072i	$-0.480229\pi$
$467$	16.2329	−	5.90831i	0.751171	−	0.273404i	0.689098	+	0.724668i	$0.258007\pi$
$468$	1.36813	+	0.518246i	0.0632418	+	0.0239559i
$469$	5.34374	+	1.94496i	0.246751	+	0.0898099i
$470$	−5.19452	−	17.3509i	−0.239605	−	0.800337i
$471$	16.9460	−	6.04309i	0.780830	−	0.278451i
$472$	−0.738833	−	12.6853i	−0.0340076	−	0.583887i
$473$	1.63051	−	1.07240i	0.0749710	−	0.0493092i
$474$	29.0795	+	0.189481i	1.33566	+	0.00870314i
$475$	2.53745	+	0.601388i	0.116426	+	0.0275936i
$476$	1.70163	+	9.65044i	0.0779943	+	0.442327i
$477$	−5.76410	+	1.28702i	−0.263920	+	0.0589287i
$478$	0.895260	−	5.07727i	0.0409482	−	0.232229i
$479$	−8.46394	+	19.6216i	−0.386727	+	0.896534i	0.607996	+	0.793940i	$0.291974\pi$
$479$	−8.46394	+	19.6216i	−0.386727	+	0.896534i	−0.994723	+	0.102594i	$0.967286\pi$
$480$	−3.57248	−	1.82341i	−0.163061	−	0.0832270i
$481$	−0.641171	+	2.14166i	−0.0292349	+	0.0976513i
$482$	−1.24150	+	1.66763i	−0.0565489	+	0.0759584i
$483$	4.44792	+	6.05659i	0.202388	+	0.275584i
$484$	7.46507	−	3.74910i	0.339321	−	0.170414i
$485$	3.26087			0.148069
$486$	−7.35035	−	13.7467i	−0.333419	−	0.623564i
$487$	−11.1991			−0.507482			−0.253741	−	0.967272i	$-0.581661\pi$
$487$	−11.1991			−0.507482			−0.253741	+	0.967272i	$0.581661\pi$
$488$	6.89187	−	3.46123i	0.311980	−	0.156682i
$489$	−6.77330	−	9.22298i	−0.306299	−	0.417078i
$490$	6.61097	−	8.88008i	0.298653	−	0.401161i
$491$	−2.57840	+	8.61245i	−0.116361	+	0.388674i	−0.996252	−	0.0865028i	$-0.972431\pi$
$491$	−2.57840	+	8.61245i	−0.116361	+	0.388674i	0.879890	+	0.475177i	$0.157616\pi$
$492$	−12.1505	−	6.20168i	−0.547787	−	0.279594i
$493$	17.1605	−	39.7826i	0.772871	−	1.79172i
$494$	−0.609213	+	3.45502i	−0.0274098	+	0.155449i
$495$	−20.6816	−	22.5016i	−0.929570	−	1.01137i
$496$	0.311199	+	1.76490i	0.0139733	+	0.0792463i
$497$	−11.2268	−	2.66081i	−0.503592	−	0.119353i
$498$	−9.01891	−	0.0587670i	−0.404147	−	0.00263341i
$499$	−1.29086	+	0.849012i	−0.0577868	+	0.0380070i	−0.578074	−	0.815985i	$-0.696195\pi$
$499$	−1.29086	+	0.849012i	−0.0577868	+	0.0380070i	0.520287	+	0.853992i	$0.325825\pi$
$500$	−0.624424	−	10.7209i	−0.0279251	−	0.479455i
$501$	11.2817	−	4.02314i	0.504028	−	0.179741i
$502$	−6.35601	−	21.2306i	−0.283683	−	0.947566i
$503$	−8.36142	−	3.04331i	−0.372817	−	0.135694i	0.148815	−	0.988865i	$-0.452454\pi$
$503$	−8.36142	−	3.04331i	−0.372817	−	0.135694i	−0.521632	+	0.853171i	$0.674676\pi$
$504$	−3.46074	+	2.82788i	−0.154153	+	0.125964i
$505$	−21.8701	+	7.96007i	−0.973207	+	0.354219i
$506$	7.65065	+	10.2766i	0.340113	+	0.456851i
$507$	−21.5417	+	4.95745i	−0.956699	+	0.220168i
$508$	18.3306	−	4.34444i	0.813290	−	0.192753i
$509$	5.04282	+	11.6906i	0.223519	+	0.518176i	0.992665	−	0.120898i	$-0.0385773\pi$
$509$	5.04282	+	11.6906i	0.223519	+	0.518176i	−0.769146	+	0.639073i	$0.779318\pi$
$510$	23.6538	−	11.6870i	1.04741	−	0.517510i
$511$	12.5391	+	8.24709i	0.554697	+	0.364830i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	29.1003	−	23.4642i	1.28481	−	1.03597i
$514$	−5.61983	−	9.73384i	−0.247880	−	0.429341i
$515$	−0.225888	+	3.87834i	−0.00995380	+	0.170900i
$516$	−0.530909	+	0.555435i	−0.0233720	+	0.0244517i
$517$	−34.1753	−	3.99452i	−1.50303	−	0.175679i
$518$	−4.68654	−	4.96744i	−0.205915	−	0.218257i
$519$	−8.55991	−	20.2051i	−0.375738	−	0.886905i
$520$	−1.12165	+	0.131102i	−0.0491877	+	0.00574922i
$521$	13.0420	+	10.9435i	0.571380	+	0.479445i	0.882104	−	0.471056i	$-0.156127\pi$
$521$	13.0420	+	10.9435i	0.571380	+	0.479445i	−0.310724	+	0.950500i	$0.600571\pi$
$522$	19.6543	−	2.03801i	0.860245	−	0.0892013i
$523$	−12.6277	+	10.5959i	−0.552172	+	0.463327i	−0.875676	−	0.482900i	$-0.839584\pi$
$523$	−12.6277	+	10.5959i	−0.552172	+	0.463327i	0.323504	+	0.946227i	$0.395139\pi$
$524$	−9.21142	+	9.76354i	−0.402403	+	0.426522i
$525$	0.876800	+	0.325615i	0.0382667	+	0.0142110i
$526$	1.15111	+	0.578108i	0.0501907	+	0.0252067i
$527$	−10.5346	−	5.29066i	−0.458893	−	0.230465i
$528$	−5.86887	+	4.85975i	−0.255410	+	0.211494i
$529$	9.96344	−	10.5606i	0.433193	−	0.459158i
$530$	3.49230	−	2.93039i	0.151696	−	0.127288i
$531$	−2.71223	+	38.0237i	−0.117701	+	1.65009i
$532$	−8.20991	−	6.88893i	−0.355945	−	0.298673i
$533$	−3.81490	+	0.445898i	−0.165242	+	0.0193140i
$534$	−3.23205	+	4.28285i	−0.139864	+	0.185337i
$535$	19.5849	+	20.7588i	0.846730	+	0.897482i
$536$	−3.79145	−	0.443157i	−0.163766	−	0.0191415i
$537$	−0.492022	−	1.68331i	−0.0212323	−	0.0726402i
$538$	−0.974090	+	16.7245i	−0.0419960	+	0.721043i
$539$	−10.5158	−	18.2140i	−0.452949	−	0.784531i
$540$	9.92205	+	6.80734i	0.426977	+	0.292941i
$541$	22.2115	−	38.4714i	0.954947	−	1.65402i	0.220457	−	0.975397i	$-0.429245\pi$
$541$	22.2115	−	38.4714i	0.954947	−	1.65402i	0.734490	−	0.678620i	$-0.237422\pi$
$542$	−23.3128	−	15.3331i	−1.00137	−	0.658613i
$543$	22.5612	+	15.0502i	0.968193	+	0.645867i
$544$	−2.60538	−	6.03996i	−0.111705	−	0.258961i
$545$	43.0180	−	10.1954i	1.84269	−	0.436725i
$546$	−0.368735	+	1.20307i	−0.0157804	+	0.0514868i
$547$	7.39145	+	9.92844i	0.316036	+	0.424509i	0.931548	−	0.363617i	$-0.118458\pi$
$547$	7.39145	+	9.92844i	0.316036	+	0.424509i	−0.615513	+	0.788127i	$0.711051\pi$
$548$	4.98141	−	1.81309i	0.212795	−	0.0774512i
$549$	−21.8426	+	7.62919i	−0.932218	+	0.325606i
$550$	1.49849	+	0.545407i	0.0638960	+	0.0232562i
$551$	13.5900	+	45.3938i	0.578954	+	1.93384i
$552$	−3.84284	−	3.26743i	−0.163562	−	0.139071i
$553$	1.45430	+	24.9693i	0.0618429	+	1.06180i
$554$	2.63185	−	1.73099i	0.111816	−	0.0735428i
$555$	−9.29708	+	15.8634i	−0.394639	+	0.673364i
$556$	−17.5620	−	4.16227i	−0.744795	−	0.176520i
$557$	1.00425	+	5.69536i	0.0425512	+	0.241320i	0.998664	−	0.0516799i	$-0.0164575\pi$
$557$	1.00425	+	5.69536i	0.0425512	+	0.241320i	−0.956112	+	0.293000i	$0.905346\pi$
$558$	−0.242639	−	5.37090i	−0.0102717	−	0.227368i
$559$	−0.0375659	+	0.213047i	−0.00158887	+	0.00901093i
$560$	1.36638	−	3.16763i	0.0577402	−	0.133857i
$561$	−2.58825	−	50.0554i	−0.109276	−	2.11334i
$562$	−0.316334	+	1.05663i	−0.0133438	+	0.0445712i
$563$	−0.346453	+	0.465367i	−0.0146013	+	0.0196129i	−0.809364	−	0.587308i	$-0.800188\pi$
$563$	−0.346453	+	0.465367i	−0.0146013	+	0.0196129i	0.794763	+	0.606920i	$0.207595\pi$
$564$	13.4652	−	1.48499i	0.566988	−	0.0625293i
$565$	−16.6735	+	8.37373i	−0.701458	+	0.352285i
$566$	31.5637			1.32672
$567$	11.3900	−	7.07314i	0.478337	−	0.297044i
$568$	7.74492			0.324970
$569$	−6.61617	+	3.32276i	−0.277364	+	0.139298i	−0.582044	−	0.813157i	$-0.697747\pi$
$569$	−6.61617	+	3.32276i	−0.277364	+	0.139298i	0.304680	+	0.952455i	$0.401451\pi$
$570$	−11.6013	+	26.4201i	−0.485924	+	1.10662i
$571$	−13.5093	+	18.1461i	−0.565346	+	0.759391i	−0.989237	−	0.146322i	$-0.953256\pi$
$571$	−13.5093	+	18.1461i	−0.565346	+	0.759391i	0.423891	+	0.905713i	$0.360664\pi$
$572$	−0.615300	+	2.05524i	−0.0257270	+	0.0859341i
$573$	−6.43426	+	4.17208i	−0.268795	+	0.174291i
$574$	4.64726	−	10.7736i	0.193973	−	0.449680i
$575$	−0.183310	+	1.03960i	−0.00764455	+	0.0433544i
$576$	1.82268	−	2.38282i	0.0759451	−	0.0992842i
$577$	2.27449	+	12.8993i	0.0946884	+	0.537004i	0.994842	+	0.101433i	$0.0323427\pi$
$577$	2.27449	+	12.8993i	0.0946884	+	0.537004i	−0.900154	+	0.435572i	$0.856546\pi$
$578$	25.5610	+	6.05808i	1.06320	+	0.251983i
$579$	−16.2701	−	28.6096i	−0.676164	−	1.18898i
$580$	−12.7433	+	8.38140i	−0.529137	+	0.348019i
$581$	−0.451046	−	7.74416i	−0.0187125	−	0.321282i
$582$	−0.439169	+	2.39913i	−0.0182042	+	0.0994473i
$583$	−2.48393	−	8.29692i	−0.102874	−	0.343623i
$584$	−9.46684	−	3.44565i	−0.391741	−	0.142582i
$585$	3.38758	+	0.0441486i	0.140059	+	0.00182532i
$586$	−26.6906	+	9.71458i	−1.10258	+	0.401306i
$587$	16.7999	+	22.5661i	0.693404	+	0.931403i	0.999790	−	0.0205040i	$-0.00652710\pi$
$587$	16.7999	+	22.5661i	0.693404	+	0.931403i	−0.306386	+	0.951907i	$0.599120\pi$
$588$	5.64302	+	6.05987i	0.232714	+	0.249905i
$589$	12.5452	−	2.97328i	0.516917	−	0.122512i
$590$	−11.6547	−	27.0186i	−0.479816	−	1.11234i
$591$	2.53860	−	39.1857i	0.104424	−	1.61188i
$592$	3.83008	+	2.51909i	0.157415	+	0.103534i
$593$	−0.451178	+	0.781463i	−0.0185276	+	0.0320908i	−0.875141	−	0.483869i	$-0.839231\pi$
$593$	−0.451178	+	0.781463i	−0.0185276	+	0.0320908i	0.856613	+	0.515960i	$0.172565\pi$
$594$	19.3406	−	12.1857i	0.793552	−	0.499985i
$595$	11.3462	+	19.6521i	0.465147	+	0.805658i
$596$	−1.02991	+	17.6829i	−0.0421869	+	0.724321i
$597$	−6.34159	−	1.54669i	−0.259544	−	0.0633020i
$598$	−1.41060	−	0.164875i	−0.0576835	−	0.00674224i
$599$	−12.4157	−	13.1599i	−0.507292	−	0.537698i	0.422218	−	0.906494i	$-0.361252\pi$
$599$	−12.4157	−	13.1599i	−0.507292	−	0.537698i	−0.929510	+	0.368796i	$0.879770\pi$
$600$	−0.623106	−	0.0769494i	−0.0254382	−	0.00314145i
$601$	−33.5660	+	3.92330i	−1.36918	+	0.160035i	−0.768704	−	0.639605i	$-0.779098\pi$
$601$	−33.5660	+	3.92330i	−1.36918	+	0.160035i	−0.600480	+	0.799640i	$0.705024\pi$
$602$	−0.506248	−	0.424792i	−0.0206331	−	0.0173132i
$603$	11.1078	+	2.78595i	0.452343	+	0.113453i
$604$	−1.83259	+	1.53772i	−0.0745669	+	0.0625690i
$605$	13.2750	−	14.0707i	0.539706	−	0.572055i
$606$	−2.91106	−	17.1626i	−0.118254	−	0.697184i
$607$	−15.0269	−	7.54680i	−0.609924	−	0.306315i	0.116895	−	0.993144i	$-0.462706\pi$
$607$	−15.0269	−	7.54680i	−0.609924	−	0.306315i	−0.726819	+	0.686829i	$0.759002\pi$
$608$	6.42890	+	3.22871i	0.260726	+	0.130942i
$609$	2.84207	+	16.7559i	0.115166	+	0.678982i
$610$	12.2557	−	12.9903i	0.496219	−	0.525961i
$611$	2.92182	−	2.45170i	0.118204	−	0.0991851i
$612$	5.41288	+	18.9769i	0.218803	+	0.767096i
$613$	9.62863	+	8.07938i	0.388897	+	0.326323i	0.816183	−	0.577793i	$-0.196086\pi$
$613$	9.62863	+	8.07938i	0.388897	+	0.326323i	−0.427287	+	0.904116i	$0.640530\pi$
$614$	−29.6557	+	3.46626i	−1.19681	+	0.139887i
$615$	−31.3520	−	3.87176i	−1.26423	−	0.156124i
$616$	−4.49744	−	4.76700i	−0.181207	−	0.192068i
$617$	19.1926	+	2.24329i	0.772663	+	0.0903114i	0.493283	−	0.869869i	$-0.335797\pi$
$617$	19.1926	+	2.24329i	0.772663	+	0.0903114i	0.279381	+	0.960180i	$0.409871\pi$
$618$	−2.82300	−	0.688522i	−0.113558	−	0.0276964i
$619$	−0.922443	+	15.8377i	−0.0370761	+	0.636572i	0.927672	+	0.373397i	$0.121807\pi$
$619$	−0.922443	+	15.8377i	−0.0370761	+	0.636572i	−0.964748	+	0.263176i	$0.915230\pi$
$620$	2.07502	+	3.59403i	0.0833347	+	0.144340i
$621$	10.1674	+	11.2078i	0.408003	+	0.449754i
$622$	0.910844	−	1.57763i	0.0365215	−	0.0632571i
$623$	−3.85566	−	2.53591i	−0.154474	−	0.101599i
$624$	0.0546060	−	0.842894i	0.00218599	−	0.0337428i
$625$	−10.5678	−	24.4989i	−0.422713	−	0.979958i
$626$	−4.20142	+	0.995754i	−0.167922	+	0.0397983i
$627$	37.3574	+	40.1171i	1.49191	+	1.60212i
$628$	−6.20284	−	8.33186i	−0.247520	−	0.332478i
$629$	−28.3363	+	10.3136i	−1.12984	+	0.411229i
$630$	−5.29101	+	8.89456i	−0.210799	+	0.354368i
$631$	−17.8744	−	6.50576i	−0.711570	−	0.258990i	−0.0392270	−	0.999230i	$-0.512490\pi$
$631$	−17.8744	−	6.50576i	−0.711570	−	0.258990i	−0.672343	+	0.740240i	$0.734712\pi$
$632$	−4.81525	−	16.0841i	−0.191540	−	0.639789i
$633$	−4.11288	+	22.4682i	−0.163472	+	0.893032i
$634$	−1.89659	−	32.5632i	−0.0753232	−	1.29325i
$635$	36.4475	−	23.9719i	1.44637	−	0.951295i
$636$	1.68565	+	2.96407i	0.0668403	+	0.117533i
$637$	2.26854	+	0.537655i	0.0898830	+	0.0213027i
$638$	5.03165	+	28.5359i	0.199205	+	1.12975i
$639$	−23.0406	−	2.99790i	−0.911470	−	0.118595i
$640$	−0.402118	+	2.28052i	−0.0158951	+	0.0901456i
$641$	3.51399	−	8.14633i	0.138794	−	0.321761i	−0.834615	−	0.550833i	$-0.814310\pi$
$641$	3.51399	−	8.14633i	0.138794	−	0.321761i	0.973409	+	0.229072i	$0.0735693\pi$
$642$	−17.9106	+	11.6135i	−0.706876	+	0.458349i
$643$	12.9312	−	43.1932i	0.509957	−	1.70337i	−0.183625	−	0.982996i	$-0.558783\pi$
$643$	12.9312	−	43.1932i	0.509957	−	1.70337i	0.693582	−	0.720378i	$-0.256031\pi$
$644$	2.59074	−	3.47997i	0.102089	−	0.137130i
$645$	−0.715370	+	1.62914i	−0.0281677	+	0.0641475i
$646$	−42.2888	+	21.2382i	−1.66383	+	0.835608i
$647$	3.10784			0.122182			0.0610909	−	0.998132i	$-0.480542\pi$
$647$	3.10784			0.122182			0.0610909	+	0.998132i	$0.480542\pi$
$648$	−6.34468	+	6.38318i	−0.249243	+	0.250755i
$649$	−55.9006			−2.19429
$650$	−0.157968	+	0.0793344i	−0.00619601	+	0.00311175i
$651$	4.59633	−	0.506898i	0.180144	−	0.0198669i
$652$	−3.94518	+	5.29930i	−0.154505	+	0.207537i
$653$	11.3354	−	37.8629i	0.443588	−	1.48169i	−0.385572	−	0.922678i	$-0.625996\pi$
$653$	11.3354	−	37.8629i	0.443588	−	1.48169i	0.829161	−	0.559010i	$-0.188819\pi$
$654$	1.70754	+	33.0229i	0.0667701	+	1.29130i
$655$	−12.3116	+	28.5416i	−0.481055	+	1.11521i
$656$	−1.36766	+	7.75638i	−0.0533981	+	0.302836i
$657$	26.8294	+	13.9150i	1.04671	+	0.542874i
$658$	2.02328	+	11.4746i	0.0788755	+	0.447325i
$659$	−27.9731	−	6.62974i	−1.08968	−	0.258258i	−0.353764	−	0.935335i	$-0.615098\pi$
$659$	−27.9731	−	6.62974i	−1.08968	−	0.258258i	−0.735913	+	0.677077i	$0.763247\pi$
$660$	−8.92194	+	15.2233i	−0.347286	+	0.592567i
$661$	11.3890	−	7.49066i	0.442981	−	0.291353i	−0.308357	−	0.951271i	$-0.599779\pi$
$661$	11.3890	−	7.49066i	0.442981	−	0.291353i	0.751338	+	0.659918i	$0.229409\pi$
$662$	0.556064	+	9.54726i	0.0216121	+	0.371065i
$663$	4.23287	+	3.59906i	0.164391	+	0.139776i
$664$	1.49344	+	4.98843i	0.0579566	+	0.193588i
$665$	−23.3213	−	8.48826i	−0.904362	−	0.329161i
$666$	−10.4191	−	8.97663i	−0.403733	−	0.347837i
$667$	−18.0249	+	6.56051i	−0.697926	+	0.254024i
$668$	−4.12950	−	5.54687i	−0.159775	−	0.214615i
$669$	3.60682	−	11.7680i	0.139448	−	0.454977i
$670$	−8.60138	+	2.03856i	−0.332300	+	0.0787566i
$671$	−13.4382	−	31.1533i	−0.518777	−	1.20266i
$672$	2.14651	+	1.43191i	0.0828034	+	0.0552370i
$673$	23.5724	+	15.5038i	0.908650	+	0.597629i	0.915487	−	0.402348i	$-0.131806\pi$
$673$	23.5724	+	15.5038i	0.908650	+	0.597629i	−0.00683660	+	0.999977i	$0.502176\pi$
$674$	−8.31903	+	14.4090i	−0.320437	+	0.555013i
$675$	1.82391	+	0.470110i	0.0702022	+	0.0180945i
$676$	6.38109	+	11.0524i	0.245427	+	0.425091i
$677$	−0.00439596	+	0.0754757i	−0.000168951	+	0.00290077i	−0.998392	−	0.0566944i	$-0.981944\pi$
$677$	−0.00439596	+	0.0754757i	−0.000168951	+	0.00290077i	0.998223	+	0.0595952i	$0.0189810\pi$
$678$	−3.91528	−	13.3950i	−0.150365	−	0.514431i
$679$	−2.08359	−	0.243536i	−0.0799607	−	0.00934606i
$680$	−10.4532	−	11.0797i	−0.400862	−	0.424889i
$681$	−2.33781	+	3.09788i	−0.0895851	+	0.118711i
$682$	7.83074	−	0.915283i	0.299855	−	0.0350480i
$683$	−14.4335	−	12.1112i	−0.552283	−	0.463421i	0.323430	−	0.946252i	$-0.395164\pi$
$683$	−14.4335	−	12.1112i	−0.552283	−	0.463421i	−0.875713	+	0.482831i	$0.839608\pi$
$684$	−17.8757	−	12.0937i	−0.683495	−	0.462413i
$685$	9.40381	−	7.89073i	0.359301	−	0.301489i
$686$	−12.0436	+	12.7654i	−0.459826	+	0.487387i
$687$	−20.7352	+	17.1699i	−0.791097	+	0.655073i
$688$	0.396425	+	0.199092i	0.0151136	+	0.00759032i
$689$	0.857937	+	0.430872i	0.0326848	+	0.0164149i
$690$	−10.9501	−	4.06649i	−0.416862	−	0.154809i
$691$	16.9118	−	17.9255i	0.643357	−	0.681918i	−0.320832	−	0.947136i	$-0.603962\pi$
$691$	16.9118	−	17.9255i	0.643357	−	0.681918i	0.964189	+	0.265218i	$0.0854439\pi$
$692$	−9.70508	+	8.14353i	−0.368932	+	0.309571i
$693$	11.5343	+	15.9223i	0.438153	+	0.604839i
$694$	19.1413	+	16.0614i	0.726592	+	0.609683i
$695$	−41.5124	+	4.85210i	−1.57465	+	0.184051i
$696$	−4.45023	−	10.5045i	−0.168686	−	0.398171i
$697$	−35.5528	−	37.6838i	−1.34666	−	1.42737i
$698$	20.3913	+	2.38340i	0.771821	+	0.0902130i
$699$	−9.44173	+	9.87791i	−0.357119	+	0.373617i
$700$	0.0313983	−	0.539088i	0.00118674	−	0.0203756i
$701$	1.67068	+	2.89370i	0.0631007	+	0.109294i	0.895850	−	0.444357i	$-0.146568\pi$
$701$	1.67068	+	2.89370i	0.0631007	+	0.109294i	−0.832749	+	0.553650i	$0.813234\pi$
$702$	−0.488715	+	2.48641i	−0.0184454	+	0.0938434i
$703$	16.4898	−	28.5612i	0.621925	−	1.07721i
$704$	3.67554	+	2.41744i	0.138527	+	0.0911107i
$705$	28.1249	−	13.8961i	1.05924	−	0.523357i
$706$	7.16371	+	16.6074i	0.269610	+	0.625026i
$707$	14.5687	−	3.45285i	0.547914	−	0.129858i
$708$	21.4481	−	4.93593i	0.806071	−	0.185503i
$709$	6.61150	+	8.88078i	0.248300	+	0.333525i	0.908747	−	0.417348i	$-0.137040\pi$
$709$	6.61150	+	8.88078i	0.248300	+	0.333525i	−0.660447	+	0.750873i	$0.729633\pi$
$710$	16.8533	−	6.13411i	0.632495	−	0.230209i
$711$	8.09920	+	49.7127i	0.303744	+	1.86437i
$712$	2.91097	+	1.05951i	0.109093	+	0.0397067i
$713$	1.49686	+	4.99985i	0.0560577	+	0.187246i
$714$	−15.9868	+	5.70103i	−0.598291	+	0.213356i
$715$	0.288866	+	4.95964i	0.0108030	+	0.185480i
$716$	−0.845952	+	0.556392i	−0.0316147	+	0.0207933i
$717$	8.92956	+	0.0581848i	0.333481	+	0.00217295i
$718$	30.1342	+	7.14194i	1.12460	+	0.266535i
$719$	−5.92011	−	33.5746i	−0.220783	−	1.25212i	−0.870585	−	0.492019i	$-0.836259\pi$
$719$	−5.92011	−	33.5746i	−0.220783	−	1.25212i	0.649802	−	0.760104i	$-0.274852\pi$
$720$	2.07901	−	6.62873i	0.0774802	−	0.247038i
$721$	0.433986	−	2.46125i	0.0161625	−	0.0916619i
$722$	12.9737	−	30.0764i	0.482832	−	1.11933i
$723$	−3.20734	−	1.63704i	−0.119282	−	0.0608823i
$724$	4.49076	−	15.0002i	0.166898	−	0.557477i
$725$	−1.42573	+	1.91508i	−0.0529502	+	0.0711244i
$726$	8.56442	+	11.6619i	0.317855	+	0.432813i
$727$	40.5032	−	20.3415i	1.50218	−	0.754423i	0.507919	−	0.861405i	$-0.330415\pi$
$727$	40.5032	−	20.3415i	1.50218	−	0.754423i	0.994261	+	0.106981i	$0.0341185\pi$
$728$	0.726488			0.0269254
$729$	21.3457	−	16.5336i	0.790583	−	0.612355i
$730$	−23.3293			−0.863457
$731$	−2.60766	+	1.30961i	−0.0964477	+	0.0484379i
$732$	7.90681	+	10.7664i	0.292244	+	0.397939i
$733$	−1.17522	+	1.57859i	−0.0434077	+	0.0583067i	−0.823297	−	0.567611i	$-0.807868\pi$
$733$	−1.17522	+	1.57859i	−0.0434077	+	0.0583067i	0.779889	+	0.625917i	$0.215275\pi$
$734$	−2.29807	+	7.67608i	−0.0848232	+	0.283329i
$735$	17.0790	+	8.71721i	0.629969	+	0.321539i
$736$	−1.15348	+	2.67407i	−0.0425178	+	0.0985674i
$737$	−2.91611	+	16.5381i	−0.107416	+	0.609188i
$738$	7.07101	−	22.5453i	0.260288	−	0.829902i
$739$	5.15688	+	29.2461i	0.189699	+	1.07584i	0.919768	+	0.392463i	$0.128377\pi$
$739$	5.15688	+	29.2461i	0.189699	+	1.07584i	−0.730069	+	0.683373i	$0.760512\pi$
$740$	10.3296	+	2.44816i	0.379724	+	0.0899963i
$741$	−6.07646	−	0.0395940i	−0.223224	−	0.00145452i
$742$	−2.45031	+	1.61160i	−0.0899539	+	0.0591636i
$743$	−0.258982	−	4.44654i	−0.00950111	−	0.163128i	−0.999721	−	0.0236135i	$-0.992483\pi$
$743$	−0.258982	−	4.44654i	−0.00950111	−	0.163128i	0.990220	−	0.139514i	$-0.0445541\pi$
$744$	−2.92371	+	1.04262i	−0.107188	+	0.0382243i
$745$	11.7640	+	39.2946i	0.431001	+	1.43964i
$746$	−20.9973	−	7.64238i	−0.768765	−	0.279807i
$747$	−2.51195	−	15.4183i	−0.0919073	−	0.564125i
$748$	−27.1929	+	9.89742i	−0.994272	+	0.361885i
$749$	−10.9637	−	14.7268i	−0.400606	−	0.538107i
$750$	18.1269	−	4.17159i	0.661900	−	0.152325i
$751$	12.0048	−	2.84520i	0.438063	−	0.103823i	−0.00566597	−	0.999984i	$-0.501804\pi$
$751$	12.0048	−	2.84520i	0.438063	−	0.103823i	0.443729	+	0.896161i	$0.353655\pi$
$752$	−3.09785	−	7.18163i	−0.112967	−	0.261887i
$753$	34.4136	−	17.0033i	1.25410	−	0.619634i
$754$	−2.68362	−	1.76504i	−0.0977316	−	0.0642791i
$755$	−2.76990	+	4.79760i	−0.100807	+	0.174603i
$756$	−5.83144	−	5.09068i	−0.212088	−	0.185146i
$757$	−11.3233	−	19.6125i	−0.411551	−	0.712827i	0.583509	−	0.812107i	$-0.301679\pi$
$757$	−11.3233	−	19.6125i	−0.411551	−	0.712827i	−0.995060	+	0.0992801i	$0.968346\pi$
$758$	1.18462	−	20.3392i	0.0430275	−	0.738753i
$759$	−15.3330	+	16.0413i	−0.556551	+	0.582262i
$760$	16.5468	+	1.93404i	0.600215	+	0.0701551i
$761$	−7.24273	−	7.67684i	−0.262549	−	0.278285i	0.582667	−	0.812711i	$-0.302009\pi$
$761$	−7.24273	−	7.67684i	−0.262549	−	0.278285i	−0.845215	+	0.534426i	$0.820528\pi$
$762$	12.7282	+	30.0441i	0.461095	+	1.08838i
$763$	−28.2484	+	3.30177i	−1.02266	+	0.119532i
$764$	3.39160	+	2.84589i	0.122704	+	0.102961i
$765$	26.8087	+	37.0076i	0.969272	+	1.33801i
$766$	1.93675	−	1.62513i	0.0699776	−	0.0587182i
$767$	4.25240	−	4.50728i	0.153545	−

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)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(1.02523 + 1.39603i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.664151 - 2.21842i) q^{5} +(1.54272 + 0.787412i) q^{6} +(-0.590051 + 1.36789i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.897788 + 2.86251i) q^{9} +O(q^{10})\)	\(q+(0.893633 - 0.448799i) q^{2} +(1.02523 + 1.39603i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.664151 - 2.21842i) q^{5} +(1.54272 + 0.787412i) q^{6} +(-0.590051 + 1.36789i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.897788 + 2.86251i) q^{9} +(-0.402118 - 2.28052i) q^{10} +(-4.28069 - 1.01454i) q^{11} +(1.73201 + 0.0112858i) q^{12} +(0.407438 - 0.267976i) q^{13} +(0.0866199 + 1.48721i) q^{14} +(3.77789 - 1.34723i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(6.18123 + 2.24978i) q^{17} +(0.482400 + 2.96096i) q^{18} +(-6.76026 + 2.46053i) q^{19} +(-1.38284 - 1.85748i) q^{20} +(-2.51456 + 0.578682i) q^{21} +(-4.28069 + 1.01454i) q^{22} +(-1.15348 - 2.67407i) q^{23} +(1.55285 - 0.767241i) q^{24} +(-0.302850 - 0.199188i) q^{25} +(0.243833 - 0.422330i) q^{26} +(-4.91659 + 1.68141i) q^{27} +(0.744864 + 1.29014i) q^{28} +(0.382974 - 6.57542i) q^{29} +(2.77141 - 2.89944i) q^{30} +(-1.78001 - 0.208053i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-2.97238 - 7.01611i) q^{33} +(6.53345 - 0.763651i) q^{34} +(2.64267 + 2.21747i) q^{35} +(1.75997 + 2.42951i) q^{36} +(-3.51174 + 2.94670i) q^{37} +(-4.93690 + 5.23281i) q^{38} +(0.791822 + 0.294057i) q^{39} +(-2.06939 - 1.03929i) q^{40} +(-7.03828 - 3.53476i) q^{41} +(-1.98738 + 1.64566i) q^{42} +(-0.304424 + 0.322671i) q^{43} +(-3.37004 + 2.82780i) q^{44} +(5.75399 + 3.89281i) q^{45} +(-2.23091 - 1.87195i) q^{46} +(7.76840 - 0.907996i) q^{47} +(1.04334 - 1.38255i) q^{48} +(3.28072 + 3.47736i) q^{49} +(-0.360032 - 0.0420817i) q^{50} +(3.19645 + 10.9357i) q^{51} +(0.0283552 - 0.486840i) q^{52} +(0.984340 + 1.70493i) q^{53} +(-3.63901 + 3.70912i) q^{54} +(-5.09371 + 8.82256i) q^{55} +(1.24465 + 0.818618i) q^{56} +(-10.3658 - 6.91489i) q^{57} +(-2.60880 - 6.04789i) q^{58} +(12.3643 - 2.93038i) q^{59} +(1.17536 - 3.83484i) q^{60} +(4.60541 + 6.18613i) q^{61} +(-1.68405 + 0.612943i) q^{62} +(-3.38587 - 2.91710i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(-0.323883 - 1.08185i) q^{65} +(-5.80504 - 4.93582i) q^{66} +(-0.221954 - 3.81081i) q^{67} +(5.49578 - 3.61463i) q^{68} +(2.55049 - 4.35184i) q^{69} +(3.35678 + 0.795571i) q^{70} +(1.34489 + 7.62726i) q^{71} +(2.66312 + 1.38122i) q^{72} +(1.74940 - 9.92135i) q^{73} +(-1.81573 + 4.20933i) q^{74} +(-0.0324209 - 0.627002i) q^{75} +(-2.06330 + 6.89189i) q^{76} +(3.91361 - 5.25689i) q^{77} +(0.839570 - 0.0925906i) q^{78} +(15.0035 - 7.53506i) q^{79} -2.31570 q^{80} +(-7.38795 - 5.13986i) q^{81} -7.87604 q^{82} +(-4.65331 + 2.33698i) q^{83} +(-1.03741 + 2.36255i) q^{84} +(9.09624 - 12.2184i) q^{85} +(-0.127229 + 0.424975i) q^{86} +(9.57211 - 6.20670i) q^{87} +(-1.74246 + 4.03949i) q^{88} +(-0.537926 + 3.05073i) q^{89} +(6.88904 + 0.896360i) q^{90} +(0.126153 + 0.715451i) q^{91} +(-2.83374 - 0.671609i) q^{92} +(-1.53448 - 2.69824i) q^{93} +(6.53459 - 4.29787i) q^{94} +(0.968660 + 16.6313i) q^{95} +(0.311875 - 1.70374i) q^{96} +(0.403864 + 1.34900i) q^{97} +(4.49240 + 1.63510i) q^{98} +(6.74730 - 11.3427i) 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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