LMFDB - Embedded newform 162.2.g.b.97.5

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			97.5
Character	$\chi$	$=$	162.97
Dual form			162.2.g.b.157.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973045 + 0.230616i) q^{2} +(1.70747 + 0.290767i) q^{3} +(0.893633 + 0.448799i) q^{4} +(0.537372 - 0.721815i) q^{5} +(1.59439 + 0.676699i) q^{6} +(-3.95679 - 2.60242i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.83091 + 0.992953i) q^{9} +O(q^{10})$	\(q+(0.973045 + 0.230616i) q^{2} +(1.70747 + 0.290767i) q^{3} +(0.893633 + 0.448799i) q^{4} +(0.537372 - 0.721815i) q^{5} +(1.59439 + 0.676699i) q^{6} +(-3.95679 - 2.60242i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.83091 + 0.992953i) q^{9} +(0.689349 - 0.578432i) q^{10} +(-4.21098 + 0.492194i) q^{11} +(1.39536 + 1.02615i) q^{12} +(-1.75605 + 5.86562i) q^{13} +(-3.24997 - 3.44477i) q^{14} +(1.12743 - 1.07623i) q^{15} +(0.597159 + 0.802123i) q^{16} +(-0.432180 - 2.45101i) q^{17} +(2.52561 + 1.61904i) q^{18} +(-0.284021 + 1.61076i) q^{19} +(0.804163 - 0.403866i) q^{20} +(-5.99940 - 5.59406i) q^{21} +(-4.21098 - 0.492194i) q^{22} +(6.35325 - 4.17860i) q^{23} +(1.12110 + 1.32028i) q^{24} +(1.20177 + 4.01418i) q^{25} +(-3.06142 + 5.30254i) q^{26} +(4.54497 + 2.51857i) q^{27} +(-2.36795 - 4.10141i) q^{28} +(2.09368 - 2.21918i) q^{29} +(1.34523 - 0.787216i) q^{30} +(-0.107618 - 1.84773i) q^{31} +(0.396080 + 0.918216i) q^{32} +(-7.33324 - 0.384010i) q^{33} +(0.144712 - 2.48461i) q^{34} +(-4.00473 + 1.45760i) q^{35} +(2.08416 + 2.15784i) q^{36} +(-8.42259 - 3.06557i) q^{37} +(-0.647833 + 1.50184i) q^{38} +(-4.70394 + 9.50478i) q^{39} +(0.875624 - 0.207527i) q^{40} +(5.04755 - 1.19629i) q^{41} +(-4.54760 - 6.82682i) q^{42} +(1.06337 - 2.46516i) q^{43} +(-3.98397 - 1.45005i) q^{44} +(2.23798 - 1.50981i) q^{45} +(7.14564 - 2.60080i) q^{46} +(0.486795 - 8.35794i) q^{47} +(0.786399 + 1.54324i) q^{48} +(6.11101 + 14.1669i) q^{49} +(0.243639 + 4.18313i) q^{50} +(-0.0252598 - 4.31070i) q^{51} +(-4.20175 + 4.45360i) q^{52} +(-1.11544 - 1.93201i) q^{53} +(3.84164 + 3.49883i) q^{54} +(-1.90759 + 3.30404i) q^{55} +(-1.35827 - 4.53694i) q^{56} +(-0.953314 + 2.66775i) q^{57} +(2.54903 - 1.67652i) q^{58} +(-3.71218 - 0.433892i) q^{59} +(1.49051 - 0.455765i) q^{60} +(2.81018 - 1.41133i) q^{61} +(0.321399 - 1.82275i) q^{62} +(-8.61722 - 11.2961i) q^{63} +(0.173648 + 0.984808i) q^{64} +(3.29024 + 4.41957i) q^{65} +(-7.04702 - 2.06482i) q^{66} +(3.28793 + 3.48500i) q^{67} +(0.713803 - 2.38427i) q^{68} +(12.0630 - 5.28751i) q^{69} +(-4.23293 + 0.494758i) q^{70} +(-3.18551 + 2.67296i) q^{71} +(1.53034 + 2.58032i) q^{72} +(1.09995 + 0.922965i) q^{73} +(-7.48859 - 4.92532i) q^{74} +(0.884789 + 7.20353i) q^{75} +(-0.976720 + 1.31196i) q^{76} +(17.9429 + 9.01124i) q^{77} +(-6.76910 + 8.16377i) q^{78} +(-5.03759 - 1.19393i) q^{79} +0.899881 q^{80} +(7.02809 + 5.62192i) q^{81} +5.18737 q^{82} +(-2.63513 - 0.624537i) q^{83} +(-2.85065 - 7.69155i) q^{84} +(-2.00142 - 1.00515i) q^{85} +(1.60321 - 2.15349i) q^{86} +(4.22017 - 3.18040i) q^{87} +(-3.54218 - 2.32973i) q^{88} +(12.5970 + 10.5701i) q^{89} +(2.52584 - 0.952998i) q^{90} +(22.2131 - 18.6390i) q^{91} +(7.55282 - 0.882798i) q^{92} +(0.353505 - 3.18624i) q^{93} +(2.40115 - 8.02039i) q^{94} +(1.01005 + 1.07059i) q^{95} +(0.409307 + 1.68299i) q^{96} +(2.79423 + 3.75330i) q^{97} +(2.67917 + 15.1943i) q^{98} +(-12.4096 - 2.78795i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

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 $

$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$3$	1.70747	+	0.290767i	0.985808	+	0.167875i
$3$	1.70747	+	0.290767i	0.985808	+	0.167875i
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	0.537372	−	0.721815i	0.240320	−	0.322806i	−0.665557	−	0.746347i	$-0.731806\pi$
$5$	0.537372	−	0.721815i	0.240320	−	0.322806i	0.905877	+	0.423542i	$0.139213\pi$
$6$	1.59439	+	0.676699i	0.650907	+	0.276261i
$7$	−3.95679	−	2.60242i	−1.49552	−	0.983622i	−0.992879	−	0.119129i	$-0.961990\pi$
$7$	−3.95679	−	2.60242i	−1.49552	−	0.983622i	−0.502646	−	0.864493i	$-0.667640\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$	2.83091	+	0.992953i	0.943636	+	0.330984i
$10$	0.689349	−	0.578432i	0.217991	−	0.182916i
$11$	−4.21098	+	0.492194i	−1.26966	+	0.148402i	−0.724115	−	0.689680i	$-0.757751\pi$
$11$	−4.21098	+	0.492194i	−1.26966	+	0.148402i	−0.545545	+	0.838082i	$0.683677\pi$
$12$	1.39536	+	1.02615i	0.402804	+	0.296224i
$13$	−1.75605	+	5.86562i	−0.487041	+	1.62683i	0.262541	+	0.964921i	$0.415439\pi$
$13$	−1.75605	+	5.86562i	−0.487041	+	1.62683i	−0.749583	+	0.661911i	$0.769746\pi$
$14$	−3.24997	−	3.44477i	−0.868591	−	0.920653i
$15$	1.12743	−	1.07623i	0.291100	−	0.277881i
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	−0.432180	−	2.45101i	−0.104819	−	0.594458i	−0.991292	−	0.131679i	$-0.957963\pi$
$17$	−0.432180	−	2.45101i	−0.104819	−	0.594458i	0.886473	−	0.462780i	$-0.153148\pi$
$18$	2.52561	+	1.61904i	0.595292	+	0.381611i
$19$	−0.284021	+	1.61076i	−0.0651589	+	0.369534i	0.934740	+	0.355332i	$0.115632\pi$
$19$	−0.284021	+	1.61076i	−0.0651589	+	0.369534i	−0.999899	+	0.0142026i	$0.995479\pi$
$20$	0.804163	−	0.403866i	0.179816	−	0.0903071i
$21$	−5.99940	−	5.59406i	−1.30918	−	1.22072i
$22$	−4.21098	−	0.492194i	−0.897785	−	0.104936i
$23$	6.35325	−	4.17860i	1.32474	−	0.871297i	0.327453	−	0.944867i	$-0.393810\pi$
$23$	6.35325	−	4.17860i	1.32474	−	0.871297i	0.997290	+	0.0735700i	$0.0234392\pi$
$24$	1.12110	+	1.32028i	0.228843	+	0.269501i
$25$	1.20177	+	4.01418i	0.240353	+	0.802836i
$26$	−3.06142	+	5.30254i	−0.600395	+	1.03991i
$27$	4.54497	+	2.51857i	0.874681	+	0.484699i
$28$	−2.36795	−	4.10141i	−0.447500	−	0.775093i
$29$	2.09368	−	2.21918i	0.388787	−	0.412091i	−0.503186	−	0.864178i	$-0.667839\pi$
$29$	2.09368	−	2.21918i	0.388787	−	0.412091i	0.891974	+	0.452087i	$0.149321\pi$
$30$	1.34523	−	0.787216i	0.245605	−	0.143725i
$31$	−0.107618	−	1.84773i	−0.0193288	−	0.331863i	−0.994086	−	0.108595i	$-0.965365\pi$
$31$	−0.107618	−	1.84773i	−0.0193288	−	0.331863i	0.974757	−	0.223267i	$-0.0716723\pi$
$32$	0.396080	+	0.918216i	0.0700177	+	0.162319i
$33$	−7.33324	−	0.384010i	−1.27655	−	0.0668476i
$34$	0.144712	−	2.48461i	0.0248180	−	0.426108i
$35$	−4.00473	+	1.45760i	−0.676923	+	0.246380i
$36$	2.08416	+	2.15784i	0.347359	+	0.359641i
$37$	−8.42259	−	3.06557i	−1.38467	−	0.503977i	−0.461076	−	0.887361i	$-0.652537\pi$
$37$	−8.42259	−	3.06557i	−1.38467	−	0.503977i	−0.923589	+	0.383384i	$0.874759\pi$
$38$	−0.647833	+	1.50184i	−0.105092	+	0.243631i
$39$	−4.70394	+	9.50478i	−0.753233	+	1.52198i
$40$	0.875624	−	0.207527i	0.138448	−	0.0328129i
$41$	5.04755	−	1.19629i	0.788295	−	0.186829i	0.183298	−	0.983057i	$-0.441323\pi$
$41$	5.04755	−	1.19629i	0.788295	−	0.186829i	0.604996	+	0.796228i	$0.293175\pi$
$42$	−4.54760	−	6.82682i	−0.701710	−	1.05340i
$43$	1.06337	−	2.46516i	0.162162	−	0.375934i	−0.817690	−	0.575659i	$-0.804746\pi$
$43$	1.06337	−	2.46516i	0.162162	−	0.375934i	0.979852	+	0.199725i	$0.0640049\pi$
$44$	−3.98397	−	1.45005i	−0.600606	−	0.218603i
$45$	2.23798	−	1.50981i	0.333618	−	0.225069i
$46$	7.14564	−	2.60080i	1.05357	−	0.383467i
$47$	0.486795	−	8.35794i	0.0710063	−	1.21913i	−0.755097	−	0.655613i	$-0.772410\pi$
$47$	0.486795	−	8.35794i	0.0710063	−	1.21913i	0.826103	−	0.563519i	$-0.190553\pi$
$48$	0.786399	+	1.54324i	0.113507	+	0.222747i
$49$	6.11101	+	14.1669i	0.873002	+	2.02384i
$50$	0.243639	+	4.18313i	0.0344558	+	0.591583i
$51$	−0.0252598	−	4.31070i	−0.00353708	−	0.603618i
$52$	−4.20175	+	4.45360i	−0.582678	+	0.617603i
$53$	−1.11544	−	1.93201i	−0.153218	−	0.265381i	0.779191	−	0.626787i	$-0.215630\pi$
$53$	−1.11544	−	1.93201i	−0.153218	−	0.265381i	−0.932409	+	0.361406i	$0.882297\pi$
$54$	3.84164	+	3.49883i	0.522781	+	0.476130i
$55$	−1.90759	+	3.30404i	−0.257219	+	0.445517i
$56$	−1.35827	−	4.53694i	−0.181507	−	0.606274i
$57$	−0.953314	+	2.66775i	−0.126270	+	0.353352i
$58$	2.54903	−	1.67652i	0.334703	−	0.220138i
$59$	−3.71218	−	0.433892i	−0.483285	−	0.0564879i	−0.129038	−	0.991640i	$-0.541189\pi$
$59$	−3.71218	−	0.433892i	−0.483285	−	0.0564879i	−0.354247	+	0.935152i	$0.615263\pi$
$60$	1.49051	−	0.455765i	0.192425	−	0.0588390i
$61$	2.81018	−	1.41133i	0.359807	−	0.180702i	−0.259707	−	0.965687i	$-0.583626\pi$
$61$	2.81018	−	1.41133i	0.359807	−	0.180702i	0.619514	+	0.784986i	$0.287330\pi$
$62$	0.321399	−	1.82275i	0.0408178	−	0.231489i
$63$	−8.61722	−	11.2961i	−1.08567	−	1.42318i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	3.29024	+	4.41957i	0.408105	+	0.548180i
$66$	−7.04702	−	2.06482i	−0.867428	−	0.254162i
$67$	3.28793	+	3.48500i	0.401685	+	0.425761i	0.896367	−	0.443313i	$-0.146197\pi$
$67$	3.28793	+	3.48500i	0.401685	+	0.425761i	−0.494682	+	0.869074i	$0.664716\pi$
$68$	0.713803	−	2.38427i	0.0865614	−	0.289135i
$69$	12.0630	−	5.28751i	1.45221	−	0.636542i
$70$	−4.23293	+	0.494758i	−0.505932	+	0.0591349i
$71$	−3.18551	+	2.67296i	−0.378051	+	0.317222i	−0.811937	−	0.583746i	$-0.801587\pi$
$71$	−3.18551	+	2.67296i	−0.378051	+	0.317222i	0.433886	+	0.900968i	$0.357142\pi$
$72$	1.53034	+	2.58032i	0.180353	+	0.304094i
$73$	1.09995	+	0.922965i	0.128739	+	0.108025i	0.704884	−	0.709323i	$-0.250999\pi$
$73$	1.09995	+	0.922965i	0.128739	+	0.108025i	−0.576145	+	0.817348i	$0.695444\pi$
$74$	−7.48859	−	4.92532i	−0.870531	−	0.572557i
$75$	0.884789	+	7.20353i	0.102167	+	0.831792i
$76$	−0.976720	+	1.31196i	−0.112037	+	0.150492i
$77$	17.9429	+	9.01124i	2.04478	+	1.02693i
$78$	−6.76910	+	8.16377i	−0.766449	+	0.924365i
$79$	−5.03759	−	1.19393i	−0.566773	−	0.134328i	−0.0627675	−	0.998028i	$-0.519993\pi$
$79$	−5.03759	−	1.19393i	−0.566773	−	0.134328i	−0.504005	+	0.863701i	$0.668141\pi$
$80$	0.899881			0.100610
$81$	7.02809	+	5.62192i	0.780899	+	0.624657i
$82$	5.18737			0.572850
$83$	−2.63513	−	0.624537i	−0.289243	−	0.0685519i	0.0834329	−	0.996513i	$-0.473412\pi$
$83$	−2.63513	−	0.624537i	−0.289243	−	0.0685519i	−0.372676	+	0.927962i	$0.621560\pi$
$84$	−2.85065	−	7.69155i	−0.311031	−	0.839217i
$85$	−2.00142	−	1.00515i	−0.217085	−	0.109024i
$86$	1.60321	−	2.15349i	0.172879	−	0.232216i
$87$	4.22017	−	3.18040i	0.452449	−	0.340975i
$88$	−3.54218	−	2.32973i	−0.377597	−	0.248350i
$89$	12.5970	+	10.5701i	1.33528	+	1.12043i	0.982813	+	0.184604i	$0.0591003\pi$
$89$	12.5970	+	10.5701i	1.33528	+	1.12043i	0.352463	+	0.935826i	$0.385344\pi$
$90$	2.52584	−	0.952998i	0.266247	−	0.100455i
$91$	22.2131	−	18.6390i	2.32857	−	1.95390i
$92$	7.55282	−	0.882798i	0.787436	−	0.0920380i
$93$	0.353505	−	3.18624i	0.0366568	−	0.330398i
$94$	2.40115	−	8.02039i	0.247659	−	0.827240i
$95$	1.01005	+	1.07059i	0.103629	+	0.109840i
$96$	0.409307	+	1.68299i	0.0417747	+	0.171770i
$97$	2.79423	+	3.75330i	0.283711	+	0.381090i	0.921018	−	0.389520i	$-0.127359\pi$
$97$	2.79423	+	3.75330i	0.283711	+	0.381090i	−0.637307	+	0.770610i	$0.719952\pi$
$98$	2.67917	+	15.1943i	0.270637	+	1.53486i
$99$	−12.4096	−	2.78795i	−1.24722	−	0.280200i
$100$	−0.727623	+	4.12656i	−0.0727623	+	0.412656i
$101$	−10.7240	+	5.38577i	−1.06707	+	0.535904i	−0.893568	−	0.448928i	$-0.851806\pi$
$101$	−10.7240	+	5.38577i	−1.06707	+	0.535904i	−0.173506	+	0.984833i	$0.555510\pi$
$102$	0.969536	−	4.20033i	0.0959984	−	0.415894i
$103$	7.07350	+	0.826773i	0.696972	+	0.0814644i	0.457199	−	0.889364i	$-0.348853\pi$
$103$	7.07350	+	0.826773i	0.696972	+	0.0814644i	0.239774	+	0.970829i	$0.422927\pi$
$104$	−5.11557	+	3.36456i	−0.501622	+	0.329922i
$105$	−7.26178	+	1.32437i	−0.708677	+	0.129245i
$106$	−0.639826	−	2.13717i	−0.0621454	−	0.207580i
$107$	−4.54371	+	7.86994i	−0.439257	+	0.760816i	−0.997632	−	0.0687727i	$-0.978092\pi$
$107$	−4.54371	+	7.86994i	−0.439257	+	0.760816i	0.558375	+	0.829589i	$0.311425\pi$
$108$	2.93120	+	4.29046i	0.282055	+	0.412850i
$109$	−4.27740	−	7.40867i	−0.409700	−	0.709622i	0.585156	−	0.810921i	$-0.301033\pi$
$109$	−4.27740	−	7.40867i	−0.409700	−	0.709622i	−0.994856	+	0.101299i	$0.967700\pi$
$110$	−2.61814	+	2.77506i	−0.249629	+	0.264592i
$111$	−13.4900	−	7.68339i	−1.28041	−	0.729275i
$112$	−0.275368	−	4.72789i	−0.0260198	−	0.446743i
$113$	−2.11058	−	4.89288i	−0.198547	−	0.460284i	0.789633	−	0.613579i	$-0.210271\pi$
$113$	−2.11058	−	4.89288i	−0.198547	−	0.460284i	−0.988180	+	0.153295i	$0.951011\pi$
$114$	−1.54284	+	2.37599i	−0.144500	+	0.222532i
$115$	0.397880	−	6.83133i	0.0371025	−	0.637025i
$116$	2.86695	−	1.04348i	0.266189	−	0.0968850i
$117$	−10.7955	+	14.8614i	−0.998046	+	1.37393i
$118$	−3.51206	−	1.27828i	−0.323311	−	0.117676i
$119$	−4.66852	+	10.8229i	−0.427963	+	0.992129i
$120$	1.55544	−	0.0997430i	0.141992	−	0.00910524i
$121$	6.78664	−	1.60846i	0.616968	−	0.146224i
$122$	3.05991	−	0.725211i	0.277031	−	0.0656576i
$123$	8.96638	−	0.574970i	0.808471	−	0.0518433i
$124$	0.733090	−	1.69949i	0.0658334	−	0.152619i
$125$	7.77135	+	2.82854i	0.695091	+	0.252992i
$126$	−5.77988	−	12.9789i	−0.514913	−	1.15625i
$127$	−2.08699	+	0.759602i	−0.185190	+	0.0674038i	−0.432951	−	0.901418i	$-0.642528\pi$
$127$	−2.08699	+	0.759602i	−0.185190	+	0.0674038i	0.247760	+	0.968821i	$0.420305\pi$
$128$	−0.0581448	+	0.998308i	−0.00513933	+	0.0882388i
$129$	2.53246	−	3.90000i	0.222970	−	0.343376i
$130$	2.18233	+	5.05922i	0.191403	+	0.443723i
$131$	0.0633149	+	1.08707i	0.00553185	+	0.0949781i	0.999944	−	0.0105899i	$-0.00337094\pi$
$131$	0.0633149	+	1.08707i	0.00553185	+	0.0949781i	−0.994412	+	0.105568i	$0.966334\pi$
$132$	−6.38088	−	3.63432i	−0.555385	−	0.316327i
$133$	5.31569	−	5.63430i	0.460929	−	0.488556i
$134$	2.39561	+	4.14931i	0.206949	+	0.358446i
$135$	4.26028	−	1.92722i	0.366667	−	0.165869i
$136$	1.24441	−	2.15539i	0.106708	−	0.184823i
$137$	−1.73952	−	5.81040i	−0.148617	−	0.496416i	0.850968	−	0.525218i	$-0.176016\pi$
$137$	−1.73952	−	5.81040i	−0.148617	−	0.496416i	−0.999585	+	0.0288015i	$0.990831\pi$
$138$	12.9572	−	2.36307i	1.10299	−	0.201158i
$139$	−11.7886	+	7.75350i	−0.999898	+	0.657644i	−0.940218	−	0.340574i	$-0.889379\pi$
$139$	−11.7886	+	7.75350i	−0.999898	+	0.657644i	−0.0596807	+	0.998218i	$0.519008\pi$
$140$	−4.23293	−	0.494758i	−0.357748	−	0.0418147i
$141$	3.26140	−	14.1294i	0.274660	−	1.18991i
$142$	−3.71607	+	1.86628i	−0.311846	+	0.156615i
$143$	4.50769	−	25.5644i	0.376952	−	2.13780i
$144$	0.894031	+	2.86369i	0.0745026	+	0.238641i
$145$	−0.476748	−	2.70377i	−0.0395918	−	0.224536i
$146$	0.857447	+	1.15175i	0.0709628	+	0.0953196i
$147$	6.31509	+	25.9665i	0.520860	+	2.14168i
$148$	−6.15088	−	6.51955i	−0.505599	−	0.535903i
$149$	−0.589967	+	1.97063i	−0.0483319	+	0.161440i	−0.978749	−	0.205063i	$-0.934260\pi$
$149$	−0.589967	+	1.97063i	−0.0483319	+	0.161440i	0.930417	+	0.366503i	$0.119445\pi$
$150$	−0.800309	+	7.21340i	−0.0653449	+	0.588972i
$151$	−8.84148	+	1.03342i	−0.719509	+	0.0840986i	−0.467965	−	0.883747i	$-0.655013\pi$
$151$	−8.84148	+	1.03342i	−0.719509	+	0.0840986i	−0.251545	+	0.967846i	$0.580939\pi$
$152$	−1.25295	+	1.05135i	−0.101628	+	0.0852758i
$153$	1.21028	−	7.36773i	0.0978453	−	0.595646i
$154$	15.3811	+	12.9063i	1.23944	+	1.04002i
$155$	−1.39155	−	0.915239i	−0.111772	−	0.0735138i
$156$	−8.46933	+	6.38265i	−0.678089	+	0.511021i
$157$	−2.34792	+	3.15381i	−0.187385	+	0.251701i	−0.885881	−	0.463912i	$-0.846445\pi$
$157$	−2.34792	+	3.15381i	−0.187385	+	0.251701i	0.698496	+	0.715613i	$0.253853\pi$
$158$	−4.62646	−	2.32349i	−0.368061	−	0.184847i
$159$	−1.34282	−	3.62318i	−0.106493	−	0.287337i
$160$	0.875624	+	0.207527i	0.0692242	+	0.0164064i
$161$	−36.0129			−2.83821
$162$	5.54214	+	7.09117i	0.435432	+	0.557135i
$163$	−10.9972			−0.861367			−0.430683	−	0.902503i	$-0.641727\pi$
$163$	−10.9972			−0.861367			−0.430683	+	0.902503i	$0.641727\pi$
$164$	5.04755	+	1.19629i	0.394147	+	0.0934146i
$165$	−4.21786	+	5.08689i	−0.328360	+	0.396014i
$166$	−2.42007	−	1.21541i	−0.187834	−	0.0943338i
$167$	−9.59118	+	12.8832i	−0.742188	+	0.996931i	0.257343	+	0.966320i	$0.417153\pi$
$167$	−9.59118	+	12.8832i	−0.742188	+	0.996931i	−0.999531	+	0.0306113i	$0.990255\pi$
$168$	−1.00001	−	8.14163i	−0.0771527	−	0.628141i
$169$	−20.4605	−	13.4571i	−1.57388	−	1.03516i
$170$	−1.71567	−	1.43962i	−0.131586	−	0.110414i
$171$	−2.40345	+	4.27790i	−0.183796	+	0.327139i
$172$	2.05662	−	1.72571i	0.156816	−	0.131584i
$173$	−11.5069	+	1.34497i	−0.874855	+	0.102256i	−0.541655	−	0.840601i	$-0.682202\pi$
$173$	−11.5069	+	1.34497i	−0.874855	+	0.102256i	−0.333199	+	0.942856i	$0.608128\pi$
$174$	4.83986	−	2.12144i	0.366909	−	0.160826i
$175$	5.69145	−	19.0108i	0.430233	−	1.43708i
$176$	−2.90943	−	3.08381i	−0.219306	−	0.232451i
$177$	−6.21228	−	1.82024i	−0.466943	−	0.136817i
$178$	9.81978	+	13.1903i	0.736024	+	0.988651i
$179$	1.19249	+	6.76294i	0.0891308	+	0.505486i	0.996389	+	0.0849109i	$0.0270605\pi$
$179$	1.19249	+	6.76294i	0.0891308	+	0.505486i	−0.907258	+	0.420575i	$0.861828\pi$
$180$	2.67753	−	0.344812i	0.199571	−	0.0257007i
$181$	−4.15485	+	23.5633i	−0.308827	+	1.75145i	0.296092	+	0.955159i	$0.404316\pi$
$181$	−4.15485	+	23.5633i	−0.308827	+	1.75145i	−0.604919	+	0.796287i	$0.706795\pi$
$182$	25.9128	−	13.0139i	1.92079	−	0.964656i
$183$	5.20867	−	1.59269i	0.385036	−	0.117735i
$184$	7.55282	+	0.882798i	0.556801	+	0.0650807i
$185$	−6.73884	+	4.43220i	−0.495449	+	0.325862i
$186$	1.07877	−	3.01883i	0.0790996	−	0.221352i
$187$	3.02628	+	10.1085i	0.221303	+	0.739204i
$188$	4.18605	−	7.25046i	0.305299	−	0.528794i
$189$	−11.4291	−	21.7934i	−0.831345	−	1.58524i
$190$	0.735928	+	1.27466i	0.0533898	+	0.0924739i
$191$	6.80578	−	7.21370i	0.492449	−	0.521965i	−0.432716	−	0.901530i	$-0.642445\pi$
$191$	6.80578	−	7.21370i	0.492449	−	0.521965i	0.925165	+	0.379565i	$0.123926\pi$
$192$	0.0101493	+	1.73202i	0.000732462	+	0.124998i
$193$	−1.01279	−	17.3890i	−0.0729023	−	1.25168i	−0.814231	−	0.580542i	$-0.802841\pi$
$193$	−1.01279	−	17.3890i	−0.0729023	−	1.25168i	0.741328	−	0.671143i	$-0.234196\pi$
$194$	1.85334	+	4.29653i	0.133062	+	0.308473i
$195$	4.33293	+	8.50297i	0.310288	+	0.608910i
$196$	−0.897101	+	15.4026i	−0.0640787	+	1.10019i
$197$	19.0553	−	6.93558i	1.35764	−	0.494140i	0.442314	−	0.896860i	$-0.354158\pi$
$197$	19.0553	−	6.93558i	1.35764	−	0.494140i	0.915323	+	0.402720i	$0.131935\pi$
$198$	−11.4322	−	5.57466i	−0.812450	−	0.396174i
$199$	4.91031	+	1.78721i	0.348083	+	0.126692i	0.510144	−	0.860089i	$-0.329592\pi$
$199$	4.91031	+	1.78721i	0.348083	+	0.126692i	−0.162062	+	0.986781i	$0.551814\pi$
$200$	−1.65966	+	3.84752i	−0.117356	+	0.272061i
$201$	4.60072	+	6.90656i	0.324510	+	0.487151i
$202$	−11.6769	+	2.76748i	−0.821586	+	0.194720i
$203$	−14.0595	+	3.33216i	−0.986782	+	0.233872i
$204$	1.91206	−	3.86352i	0.133871	−	0.270500i
$205$	1.84891	−	4.28625i	0.129133	−	0.299365i
$206$	6.69216	+	2.43575i	0.466265	+	0.169707i
$207$	22.1346	−	5.52075i	1.53846	−	0.383719i
$208$	−5.75360	+	2.09414i	−0.398940	+	0.145202i
$209$	0.403201	−	6.92269i	0.0278900	−	0.478853i
$210$	−7.37146	−	0.386012i	−0.508679	−	0.0266373i
$211$	−3.96517	−	9.19229i	−0.272973	−	0.632823i	0.725490	−	0.688232i	$-0.241613\pi$
$211$	−3.96517	−	9.19229i	−0.272973	−	0.632823i	−0.998464	+	0.0554089i	$0.982354\pi$
$212$	−0.129715	−	2.22711i	−0.00890884	−	0.152959i
$213$	−6.21637	+	3.63776i	−0.425939	+	0.249255i
$214$	−6.23617	+	6.60995i	−0.426296	+	0.451847i
$215$	−1.20797	−	2.09226i	−0.0823828	−	0.142691i
$216$	1.86275	+	4.85079i	0.126744	+	0.330055i
$217$	−4.38275	+	7.59115i	−0.297521	+	0.515321i
$218$	−2.45354	−	8.19540i	−0.166175	−	0.555063i
$219$	1.60976	+	1.89576i	0.108777	+	0.128104i
$220$	−3.18754	+	2.09648i	−0.214904	+	0.141344i
$221$	15.1357	+	1.76911i	1.01813	+	0.119003i
$222$	−11.3544	−	10.5873i	−0.762059	−	0.710572i
$223$	20.2555	−	10.1727i	1.35641	−	0.681215i	0.385961	−	0.922515i	$-0.373870\pi$
$223$	20.2555	−	10.1727i	1.35641	−	0.681215i	0.970451	+	0.241300i	$0.0775738\pi$
$224$	0.822380	−	4.66395i	0.0549476	−	0.311623i
$225$	−0.583799	+	12.5571i	−0.0389199	+	0.837139i
$226$	−0.925316	−	5.24773i	−0.0615511	−	0.349074i
$227$	1.72373	+	2.31537i	0.114408	+	0.153677i	0.855638	−	0.517574i	$-0.173165\pi$
$227$	1.72373	+	2.31537i	0.114408	+	0.153677i	−0.741230	+	0.671251i	$0.765757\pi$
$228$	−2.04919	+	1.95614i	−0.135711	+	0.129548i
$229$	13.2406	+	14.0343i	0.874967	+	0.927410i	0.997885	−	0.0650064i	$-0.0207068\pi$
$229$	13.2406	+	14.0343i	0.874967	+	0.927410i	−0.122918	+	0.992417i	$0.539225\pi$
$230$	1.96257	−	6.55543i	0.129408	−	0.432252i
$231$	28.0167	+	20.6036i	1.84336	+	1.35562i
$232$	3.03031	−	0.354193i	0.198950	−	0.0232539i
$233$	20.8609	−	17.5044i	1.36664	−	1.14675i	0.392777	−	0.919634i	$-0.371515\pi$
$233$	20.8609	−	17.5044i	1.36664	−	1.14675i	0.973868	−	0.227117i	$-0.0729299\pi$
$234$	−13.9318	+	11.9712i	−0.910749	+	0.782580i
$235$	−5.77130	−	4.84270i	−0.376478	−	0.315903i
$236$	−3.12260	−	2.05376i	−0.203264	−	0.133689i
$237$	−8.25437	−	3.50336i	−0.536179	−	0.227568i
$238$	−7.03860	+	9.45449i	−0.456245	+	0.612843i
$239$	7.06865	+	3.55001i	0.457233	+	0.229631i	0.662481	−	0.749079i	$-0.269504\pi$
$239$	7.06865	+	3.55001i	0.457233	+	0.229631i	−0.205248	+	0.978710i	$0.565800\pi$
$240$	1.53652	+	0.261656i	0.0991819	+	0.0168898i
$241$	−0.421799	−	0.0999681i	−0.0271704	−	0.00643951i	0.217008	−	0.976170i	$-0.430370\pi$
$241$	−0.421799	−	0.0999681i	−0.0271704	−	0.00643951i	−0.244179	+	0.969730i	$0.578518\pi$
$242$	6.97465			0.448347
$243$	10.3656	+	11.6428i	0.664953	+	0.746886i
$244$	3.14467			0.201317
$245$	13.5098	+	3.20188i	0.863108	+	0.204560i
$246$	8.85729	+	1.50832i	0.564720	+	0.0961669i
$247$	−8.94938	−	4.49455i	−0.569435	−	0.285981i
$248$	1.10526	−	1.48462i	0.0701841	−	0.0942736i
$249$	−4.31781	−	1.83259i	−0.273630	−	0.116136i
$250$	6.90957	+	4.54449i	0.436999	+	0.287419i
$251$	−4.62180	−	3.87815i	−0.291725	−	0.244787i	0.485165	−	0.874423i	$-0.338760\pi$
$251$	−4.62180	−	3.87815i	−0.291725	−	0.244787i	−0.776890	+	0.629636i	$0.783204\pi$
$252$	−2.63094	−	13.9620i	−0.165734	−	0.879522i
$253$	−24.6967	+	20.7230i	−1.55267	+	1.30285i
$254$	−2.20591	+	0.257834i	−0.138411	+	0.0161780i
$255$	−3.12510	−	2.29821i	−0.195701	−	0.143920i
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	−11.6285	−	12.3254i	−0.725363	−	0.768840i	0.254808	−	0.966992i	$-0.417988\pi$
$257$	−11.6285	−	12.3254i	−0.725363	−	0.768840i	−0.980171	+	0.198152i	$0.936506\pi$
$258$	3.36360	−	3.21085i	0.209408	−	0.199899i
$259$	25.3485	+	34.0489i	1.57508	+	2.11570i
$260$	0.956773	+	5.42613i	0.0593365	+	0.336514i
$261$	8.13056	−	4.20335i	0.503269	−	0.260181i
$262$	−0.189088	+	1.07237i	−0.0116819	+	0.0662515i
$263$	−20.4228	+	10.2567i	−1.25933	+	0.632458i	−0.948128	−	0.317887i	$-0.897027\pi$
$263$	−20.4228	+	10.2567i	−1.25933	+	0.632458i	−0.311198	+	0.950345i	$0.600730\pi$
$264$	−5.37075	−	5.00789i	−0.330547	−	0.308214i
$265$	−1.99396	−	0.233060i	−0.122488	−	0.0143168i
$266$	6.47176	−	4.25655i	0.396809	−	0.260986i
$267$	18.4355	+	21.7109i	1.12823	+	1.32869i
$268$	1.37414	+	4.58993i	0.0839387	+	0.280375i
$269$	11.0727	−	19.1784i	0.675113	−	1.16933i	−0.301323	−	0.953522i	$-0.597428\pi$
$269$	11.0727	−	19.1784i	0.675113	−	1.16933i	0.976436	−	0.215808i	$-0.0692385\pi$
$270$	4.58990	−	0.892785i	0.279332	−	0.0543332i
$271$	8.46422	+	14.6605i	0.514165	+	0.890559i	0.999865	+	0.0164339i	$0.00523130\pi$
$271$	8.46422	+	14.6605i	0.514165	+	0.890559i	−0.485700	+	0.874125i	$0.661435\pi$
$272$	1.70794	−	1.81031i	0.103559	−	0.109766i
$273$	43.3479	−	25.3667i	2.62353	−	1.53527i
$274$	−0.352660	−	6.05494i	−0.0213050	−	0.365793i
$275$	−7.03638	−	16.3122i	−0.424309	−	0.983660i
$276$	13.1529	+	0.688761i	0.791712	+	0.0414585i
$277$	1.38639	−	23.8035i	0.0833004	−	1.43021i	−0.654943	−	0.755678i	$-0.727307\pi$
$277$	1.38639	−	23.8035i	0.0833004	−	1.43021i	0.738244	−	0.674534i	$-0.235655\pi$
$278$	−13.2589	+	4.82586i	−0.795219	+	0.289436i
$279$	1.53005	−	5.33762i	0.0916020	−	0.319555i
$280$	−4.00473	−	1.45760i	−0.239328	−	0.0871084i
$281$	2.40187	−	5.56816i	0.143284	−	0.332169i	−0.831429	−	0.555631i	$-0.812477\pi$
$281$	2.40187	−	5.56816i	0.143284	−	0.332169i	0.974713	+	0.223462i	$0.0717360\pi$
$282$	6.43196	−	12.9964i	0.383017	−	0.773925i
$283$	6.35030	−	1.50505i	0.377486	−	0.0894659i	−0.0374926	−	0.999297i	$-0.511937\pi$
$283$	6.35030	−	1.50505i	0.377486	−	0.0894659i	0.414979	+	0.909831i	$0.363789\pi$
$284$	−4.04630	+	0.958991i	−0.240104	+	0.0569056i
$285$	1.41334	+	2.12169i	0.0837188	+	0.125678i
$286$	10.2817	−	23.8357i	0.607972	−	1.40944i
$287$	−23.0853	−	8.40237i	−1.36268	−	0.495976i
$288$	0.209521	+	2.99267i	0.0123461	+	0.176345i
$289$	10.1541	−	3.69578i	0.597299	−	0.217399i
$290$	0.159636	−	2.74084i	0.00937413	−	0.160948i
$291$	3.67973	+	7.22112i	0.215709	+	0.423310i
$292$	0.568723	+	1.31845i	0.0332820	+	0.0771563i
$293$	0.343009	+	5.88924i	0.0200388	+	0.344053i	0.993394	+	0.114751i	$0.0366072\pi$
$293$	0.343009	+	5.88924i	0.0200388	+	0.344053i	−0.973355	+	0.229302i	$0.926356\pi$
$294$	0.156591	+	26.7229i	0.00913256	+	1.55851i
$295$	−2.30801	+	2.44635i	−0.134378	+	0.142432i
$296$	−4.48157	−	7.76230i	−0.260486	−	0.451175i
$297$	−20.3784	−	8.36866i	−1.18248	−	0.485599i
$298$	−1.02852	+	1.78145i	−0.0595806	+	0.103197i
$299$	13.3534	+	44.6036i	0.772249	+	2.57949i
$300$	−2.44226	+	6.83440i	−0.141004	+	0.394584i
$301$	−10.6229	+	6.98680i	−0.612294	+	0.402712i
$302$	−8.84148	−	1.03342i	−0.508770	−	0.0594667i
$303$	−19.8768	+	6.07787i	−1.14189	+	0.349165i
$304$	−1.46164	+	0.734061i	−0.0838306	+	0.0421013i
$305$	0.491395	−	2.78684i	0.0281372	−	0.159574i
$306$	2.87677	−	6.89003i	0.164454	−	0.393877i
$307$	−2.40217	−	13.6234i	−0.137099	−	0.777527i	−0.973375	−	0.229219i	$-0.926383\pi$
$307$	−2.40217	−	13.6234i	−0.137099	−	0.777527i	0.836276	−	0.548309i	$-0.184728\pi$
$308$	11.9901	+	16.1055i	0.683199	+	0.917695i
$309$	11.8374	+	3.46843i	0.673405	+	0.197312i
$310$	−1.14297	−	1.21148i	−0.0649166	−	0.0688076i
$311$	6.10565	−	20.3943i	0.346220	−	1.15645i	−0.590695	−	0.806895i	$-0.701146\pi$
$311$	6.10565	−	20.3943i	0.346220	−	1.15645i	0.936914	−	0.349559i	$-0.113669\pi$
$312$	−9.71298	+	4.25745i	−0.549889	+	0.241031i
$313$	−13.4077	+	1.56714i	−0.757849	+	0.0885799i	−0.486237	−	0.873827i	$-0.661631\pi$
$313$	−13.4077	+	1.56714i	−0.757849	+	0.0885799i	−0.271612	+	0.962407i	$0.587557\pi$
$314$	−3.01195	+	2.52733i	−0.169974	+	0.142625i
$315$	−12.7844	+	0.149833i	−0.720317	+	0.00844211i
$316$	−3.96592	−	3.32780i	−0.223100	−	0.187203i
$317$	−7.36594	−	4.84465i	−0.413712	−	0.272103i	0.325544	−	0.945527i	$-0.394452\pi$
$317$	−7.36594	−	4.84465i	−0.413712	−	0.272103i	−0.739256	+	0.673424i	$0.764823\pi$
$318$	−0.471065	−	3.83519i	−0.0264160	−	0.215067i
$319$	−7.72421	+	10.3754i	−0.432473	+	0.580912i
$320$	0.804163	+	0.403866i	0.0449541	+	0.0225768i
$321$	−10.0466	+	12.1165i	−0.560745	+	0.676279i
$322$	−35.0422	−	8.30514i	−1.95282	−	0.462828i
$323$	4.07075			0.226503
$324$	3.75742	+	8.17813i	0.208746	+	0.454341i
$325$	−25.6560			−1.42314
$326$	−10.7008	−	2.53613i	−0.592660	−	0.140463i
$327$	−5.14933	−	13.8938i	−0.284759	−	0.768329i
$328$	4.63561	+	2.32809i	0.255959	+	0.128547i
$329$	−23.6770	+	31.8038i	−1.30536	+	1.75340i
$330$	−5.27729	+	3.97707i	−0.290505	+	0.218930i
$331$	−2.52570	−	1.66118i	−0.138825	−	0.0913066i	0.478197	−	0.878253i	$-0.341291\pi$
$331$	−2.52570	−	1.66118i	−0.138825	−	0.0913066i	−0.617022	+	0.786946i	$0.711661\pi$
$332$	−2.07455	−	1.74075i	−0.113856	−	0.0955361i
$333$	−20.7996	−	17.0416i	−1.13981	−	0.933873i
$334$	−12.3037	+	10.3240i	−0.673230	+	0.564907i
$335$	4.28237	−	0.500537i	0.233971	−	0.0273473i
$336$	0.904532	−	8.15279i	0.0493462	−	0.444771i
$337$	−0.618666	+	2.06649i	−0.0337009	+	0.112569i	−0.973185	−	0.230023i	$-0.926120\pi$
$337$	−0.618666	+	2.06649i	−0.0337009	+	0.112569i	0.939484	+	0.342592i	$0.111305\pi$
$338$	−16.8056	−	17.8129i	−0.914102	−	0.968891i
$339$	−2.18107	−	8.96814i	−0.118459	−	0.487082i
$340$	−1.33742	−	1.79647i	−0.0725320	−	0.0974274i
$341$	1.36262	+	7.72781i	0.0737901	+	0.418484i
$342$	−3.32522	+	3.60832i	−0.179807	+	0.195116i
$343$	6.93163	−	39.3112i	0.374273	−	2.12261i
$344$	2.39916	−	1.20491i	0.129354	−	0.0649641i
$345$	2.66569	−	11.5486i	0.143516	−	0.621756i
$346$	−11.5069	−	1.34497i	−0.618616	−	0.0723058i
$347$	24.2348	−	15.9395i	1.30099	−	0.855677i	0.305658	−	0.952141i	$-0.401124\pi$
$347$	24.2348	−	15.9395i	1.30099	−	0.855677i	0.995336	+	0.0964641i	$0.0307533\pi$
$348$	5.19864	−	0.948103i	0.278676	−	0.0508237i
$349$	7.51624	+	25.1060i	0.402335	+	1.34389i	0.883980	+	0.467525i	$0.154854\pi$
$349$	7.51624	+	25.1060i	0.402335	+	1.34389i	−0.481645	+	0.876367i	$0.659960\pi$
$350$	9.92222	−	17.1858i	0.530365	−	0.918619i
$351$	−22.7542	+	22.2364i	−1.21453	+	1.18689i
$352$	−2.11983	−	3.67165i	−0.112987	−	0.195699i
$353$	10.1452	−	10.7533i	0.539974	−	0.572339i	−0.398728	−	0.917069i	$-0.630548\pi$
$353$	10.1452	−	10.7533i	0.539974	−	0.572339i	0.938702	+	0.344731i	$0.112030\pi$
$354$	−5.62505	−	3.20382i	−0.298968	−	0.170281i
$355$	0.217581	+	3.73572i	0.0115480	+	0.198272i
$356$	6.51321	+	15.0993i	0.345199	+	0.800262i
$357$	−11.1183	+	17.1222i	−0.588443	+	0.906205i
$358$	−0.399296	+	6.85565i	−0.0211035	+	0.362332i
$359$	−22.1228	+	8.05203i	−1.16760	+	0.424970i	−0.851805	−	0.523859i	$-0.824492\pi$
$359$	−22.1228	+	8.05203i	−1.16760	+	0.424970i	−0.315790	+	0.948829i	$0.602270\pi$
$360$	2.68488	+	0.281964i	0.141505	+	0.0148608i
$361$	15.3403	+	5.58340i	0.807383	+	0.293863i
$362$	−9.47692	+	21.9700i	−0.498096	+	1.15472i
$363$	12.0557	−	0.773071i	0.632759	−	0.0405757i
$364$	28.2156	−	6.68721i	1.47890	−	0.350505i
$365$	1.25729	−	0.297983i	0.0658096	−	0.0155972i
$366$	5.43557	−	0.348556i	0.284122	−	0.0182193i
$367$	11.0697	−	25.6624i	0.577833	−	1.33957i	−0.339184	−	0.940720i	$-0.610151\pi$
$367$	11.0697	−	25.6624i	0.577833	−	1.33957i	0.917017	−	0.398848i	$-0.130590\pi$
$368$	7.14564	+	2.60080i	0.372492	+	0.135576i
$369$	15.4770	+	1.62539i	0.805701	+	0.0846142i
$370$	−7.57933	+	2.75865i	−0.394030	+	0.143415i
$371$	−0.614315	+	10.5474i	−0.0318937	+	0.547593i
$372$	1.74589	−	2.68868i	0.0905200	−	0.139401i
$373$	−5.01904	−	11.6354i	−0.259876	−	0.602460i	0.737461	−	0.675389i	$-0.236024\pi$
$373$	−5.01904	−	11.6354i	−0.259876	−	0.602460i	−0.997337	+	0.0729295i	$0.976765\pi$
$374$	0.613530	+	10.5339i	0.0317249	+	0.544695i
$375$	12.4469	+	7.08930i	0.642755	+	0.366090i
$376$	5.74529	−	6.08965i	0.296291	−	0.314050i
$377$	9.34023	+	16.1778i	0.481046	+	0.833197i
$378$	−6.09514	−	23.8417i	−0.313500	−	1.22628i
$379$	−4.98552	+	8.63517i	−0.256089	+	0.443559i	−0.965191	−	0.261547i	$-0.915767\pi$
$379$	−4.98552	+	8.63517i	−0.256089	+	0.443559i	0.709102	+	0.705106i	$0.249101\pi$
$380$	0.422133	+	1.41002i	0.0216550	+	0.0723326i
$381$	−3.78434	+	0.690170i	−0.193878	+	0.0353585i
$382$	8.28592	−	5.44974i	0.423945	−	0.278833i
$383$	−31.6256	−	3.69650i	−1.61599	−	0.188882i	−0.740479	−	0.672079i	$-0.765401\pi$
$383$	−31.6256	−	3.69650i	−1.61599	−	0.188882i	−0.875512	+	0.483197i	$0.839476\pi$
$384$	−0.389556	+	1.68767i	−0.0198794	+	0.0861238i
$385$	16.1464	−	8.10904i	0.822898	−	0.413275i
$386$	3.02468	−	17.1538i	0.153952	−	0.873105i
$387$	5.45809	−	5.92278i	0.277450	−	0.301072i
$388$	0.812536	+	4.60812i	0.0412503	+	0.233942i
$389$	−12.8269	−	17.2296i	−0.650351	−	0.873573i	0.347594	−	0.937645i	$-0.386999\pi$
$389$	−12.8269	−	17.2296i	−0.650351	−	0.873573i	−0.997945	+	0.0640717i	$0.979591\pi$
$390$	2.25521	+	9.27301i	0.114197	+	0.469557i
$391$	−12.9875	−	13.7660i	−0.656808	−	0.696176i
$392$	−4.42501	+	14.7806i	−0.223497	+	0.746531i
$393$	−0.207977	+	1.87456i	−0.0104911	+	0.0945589i
$394$	20.1412	−	2.35416i	1.01470	−	0.118601i
$395$	−3.56885	+	2.99462i	−0.179568	+	0.150676i
$396$	−9.83843	−	8.06084i	−0.494400	−	0.405073i
$397$	3.00463	+	2.52118i	0.150798	+	0.126535i	0.715065	−	0.699058i	$-0.246397\pi$
$397$	3.00463	+	2.52118i	0.150798	+	0.126535i	−0.564267	+	0.825592i	$0.690841\pi$
$398$	4.36579	+	2.87143i	0.218837	+	0.143932i
$399$	10.7147	−	8.07478i	0.536404	−	0.404244i
$400$	−2.50222	+	3.36107i	−0.125111	+	0.168053i
$401$	−22.9043	−	11.5030i	−1.14378	−	0.574430i	−0.227032	−	0.973887i	$-0.572902\pi$
$401$	−22.9043	−	11.5030i	−1.14378	−	0.574430i	−0.916752	+	0.399457i	$0.869199\pi$
$402$	2.88394	+	7.78139i	0.143838	+	0.388100i
$403$	11.0271	+	2.61347i	0.549299	+	0.130186i
$404$	−12.0004			−0.597043
$405$	7.83468	−	2.05192i	0.389308	−	0.101961i
$406$	−14.4490			−0.717090
$407$	36.9763	+	8.76353i	1.83284	+	0.434392i
$408$	2.75151	−	3.31842i	0.136220	−	0.164286i
$409$	−12.5591	−	6.30740i	−0.621006	−	0.311881i	0.110333	−	0.993895i	$-0.464808\pi$
$409$	−12.5591	−	6.30740i	−0.621006	−	0.311881i	−0.731339	+	0.682014i	$0.761104\pi$
$410$	2.78755	−	3.74433i	0.137667	−	0.184919i
$411$	−1.28070	−	10.4269i	−0.0631725	−	0.514320i
$412$	5.95005	+	3.91341i	0.293138	+	0.192800i
$413$	13.5591	+	11.3775i	0.667202	+	0.559849i
$414$	22.8111	−	0.267347i	1.12111	−	0.0131394i
$415$	−1.86684	+	1.56647i	−0.0916398	+	0.0768949i
$416$	−6.08145	+	0.710819i	−0.298168	+	0.0348508i
$417$	−22.3832	+	9.81113i	−1.09611	+	0.480453i
$418$	1.98882	−	6.64310i	0.0972761	−	0.324925i
$419$	27.6612	+	29.3192i	1.35134	+	1.43234i	0.802854	+	0.596176i	$0.203314\pi$
$419$	27.6612	+	29.3192i	1.35134	+	1.43234i	0.548485	+	0.836160i	$0.315205\pi$
$420$	−7.08374	−	2.07558i	−0.345651	−	0.101278i
$421$	10.5011	+	14.1054i	0.511791	+	0.687455i	0.980639	−	0.195824i	$-0.0627382\pi$
$421$	10.5011	+	14.1054i	0.511791	+	0.687455i	−0.468848	+	0.883279i	$0.655331\pi$
$422$	−1.73840	−	9.85894i	−0.0846239	−	0.479926i
$423$	9.67712	−	23.1772i	0.470517	−	1.12691i
$424$	0.387390	−	2.19700i	0.0188133	−	0.106696i
$425$	9.31944	−	4.68040i	0.452059	−	0.227033i
$426$	−6.88774	+	2.10611i	−0.333712	+	0.102041i
$427$	−14.7922	−	1.72895i	−0.715842	−	0.0836700i
$428$	−7.59243	+	4.99362i	−0.366994	+	0.241376i
$429$	15.1300	−	42.3397i	0.730485	−	2.04418i
$430$	−0.692899	−	2.31444i	−0.0334146	−	0.111612i
$431$	−12.3193	+	21.3377i	−0.593402	+	1.02780i	0.400368	+	0.916354i	$0.368882\pi$
$431$	−12.3193	+	21.3377i	−0.593402	+	1.02780i	−0.993770	+	0.111448i	$0.964451\pi$
$432$	0.693865	+	5.14962i	0.0333836	+	0.247761i
$433$	7.80606	+	13.5205i	0.375135	+	0.649754i	0.990347	−	0.138608i	$-0.0442629\pi$
$433$	7.80606	+	13.5205i	0.375135	+	0.649754i	−0.615212	+	0.788362i	$0.710930\pi$
$434$	−6.01526	+	6.37580i	−0.288742	+	0.306048i
$435$	−0.0278647	−	4.75524i	−0.00133601	−	0.227996i
$436$	−0.497417	−	8.54032i	−0.0238220	−	0.409007i
$437$	4.92627	+	11.4204i	0.235656	+	0.546311i
$438$	1.12917	+	2.21590i	0.0539540	+	0.105880i
$439$	−1.84393	+	31.6591i	−0.0880062	+	1.51101i	0.608556	+	0.793511i	$0.291749\pi$
$439$	−1.84393	+	31.6591i	−0.0880062	+	1.51101i	−0.696562	+	0.717497i	$0.745288\pi$
$440$	−3.58510	+	1.30487i	−0.170913	+	0.0622072i
$441$	3.23264	+	46.1732i	0.153935	+	2.19872i
$442$	14.3197	+	5.21194i	0.681118	+	0.247907i
$443$	6.05206	−	14.0302i	0.287542	−	0.666597i	−0.711818	−	0.702364i	$-0.752128\pi$
$443$	6.05206	−	14.0302i	0.287542	−	0.666597i	0.999360	+	0.0357667i	$0.0113873\pi$
$444$	−8.60677	−	12.9204i	−0.408459	−	0.613175i
$445$	14.3989	−	3.41261i	0.682574	−	0.161773i
$446$	22.0555	−	5.22726i	1.04436	−	0.247518i
$447$	−1.58034	+	3.19324i	−0.0747477	+	0.151035i
$448$	1.87579	−	4.34858i	0.0886229	−	0.205451i
$449$	−6.40822	−	2.33240i	−0.302423	−	0.110073i	0.186352	−	0.982483i	$-0.440334\pi$
$449$	−6.40822	−	2.33240i	−0.302423	−	0.110073i	−0.488774	+	0.872410i	$0.662556\pi$
$450$	−3.46392	+	12.0840i	−0.163291	+	0.569644i
$451$	−20.6663	+	7.52193i	−0.973140	+	0.354194i
$452$	0.309835	−	5.31967i	0.0145734	−	0.250216i
$453$	−15.3970	−	0.806277i	−0.723416	−	0.0378822i
$454$	1.14331	+	2.65048i	0.0536580	+	0.124393i
$455$	−1.51723	−	26.0499i	−0.0711289	−	1.22124i
$456$	−2.44508	+	1.43083i	−0.114501	+	0.0670049i
$457$	4.39074	−	4.65391i	0.205390	−	0.217701i	−0.616488	−	0.787364i	$-0.711445\pi$
$457$	4.39074	−	4.65391i	0.205390	−	0.217701i	0.821878	+	0.569664i	$0.192927\pi$
$458$	9.64722	+	16.7095i	0.450785	+	0.780782i
$459$	4.20881	−	12.2283i	0.196450	−	0.570767i
$460$	3.42145	−	5.92613i	0.159526	−	0.276307i
$461$	−0.513842	−	1.71635i	−0.0239320	−	0.0799385i	0.945189	−	0.326523i	$-0.105877\pi$
$461$	−0.513842	−	1.71635i	−0.0239320	−	0.0799385i	−0.969121	+	0.246584i	$0.920692\pi$
$462$	22.5100	+	26.5093i	1.04726	+	1.23333i
$463$	15.9861	−	10.5142i	0.742936	−	0.488637i	−0.120740	−	0.992684i	$-0.538527\pi$
$463$	15.9861	−	10.5142i	0.742936	−	0.488637i	0.863676	+	0.504047i	$0.168156\pi$
$464$	3.03031	+	0.354193i	0.140679	+	0.0164430i
$465$	−2.10991	−	1.96736i	−0.0978449	−	0.0912342i
$466$	24.3354	−	12.2217i	1.12732	−	0.566159i
$467$	−0.191366	+	1.08529i	−0.00885536	+	0.0502212i	−0.988915	−	0.148481i	$-0.952562\pi$
$467$	−0.191366	+	1.08529i	−0.00885536	+	0.0502212i	0.980060	+	0.198702i	$0.0636727\pi$
$468$	−16.3170	+	8.43559i	−0.754253	+	0.389935i
$469$	−3.94020	−	22.3460i	−0.181941	−	1.03184i
$470$	−4.49893	−	6.04312i	−0.207520	−	0.278748i
$471$	−4.92604	+	4.70234i	−0.226980	+	0.216672i
$472$	−2.56480	−	2.71852i	−0.118054	−	0.125130i
$473$	−3.26449	+	10.9041i	−0.150101	+	0.501373i
$474$	−7.22394	−	5.31252i	−0.331807	−	0.244012i
$475$	−6.80722	+	0.795650i	−0.312337	+	0.0365069i
$476$	−9.02923	+	7.57643i	−0.413854	+	0.347265i
$477$	−1.23933	−	6.57691i	−0.0567450	−	0.301136i
$478$	6.05943	+	5.08446i	0.277152	+	0.232558i
$479$	28.4725	+	18.7266i	1.30094	+	0.855642i	0.995331	−	0.0965158i	$-0.0307698\pi$
$479$	28.4725	+	18.7266i	1.30094	+	0.855642i	0.305608	+	0.952157i	$0.401140\pi$
$480$	1.43476	+	0.608949i	0.0654876	+	0.0277946i
$481$	32.7720	−	44.0204i	1.49428	−	2.00716i
$482$	−0.387375	−	0.194547i	−0.0176444	−	0.00886137i
$483$	−61.4909	−	10.4714i	−2.79793	−	0.476464i
$484$	6.78664	+	1.60846i	0.308484	+	0.0731120i
$485$	4.21073			0.191199
$486$	7.40117	+	13.7194i	0.335724	+	0.622326i
$487$	−6.28526			−0.284812			−0.142406	−	0.989808i	$-0.545484\pi$
$487$	−6.28526			−0.284812			−0.142406	+	0.989808i	$0.545484\pi$
$488$	3.05991	+	0.725211i	0.138515	+	0.0328288i
$489$	−18.7774	−	3.19762i	−0.849142	−	0.144602i
$490$	12.4072	+	6.23114i	0.560501	+	0.281494i
$491$	24.0769	−	32.3409i	1.08658	−	1.45952i	0.210348	−	0.977627i	$-0.432540\pi$
$491$	24.0769	−	32.3409i	1.08658	−	1.45952i	0.876227	−	0.481898i	$-0.160052\pi$
$492$	8.27070	+	3.51029i	0.372872	+	0.158256i
$493$	−6.34408	−	4.17257i	−0.285723	−	0.187923i
$494$	−7.67163	−	6.43726i	−0.345163	−	0.289626i
$495$	−8.68097	+	7.45930i	−0.390181	+	0.335271i
$496$	1.41784	−	1.18971i	0.0636631	−	0.0534197i
$497$	19.5605	−	2.28630i	0.877411	−	0.102555i
$498$	−3.77880	−	2.77895i	−0.169332	−	0.124528i
$499$	−6.22942	+	20.8077i	−0.278867	+	0.931481i	0.697722	+	0.716368i	$0.254197\pi$
$499$	−6.22942	+	20.8077i	−0.278867	+	0.931481i	−0.976589	+	0.215112i	$0.930988\pi$
$500$	5.67529	+	6.01545i	0.253806	+	0.269019i
$501$	−20.1227	+	19.2089i	−0.899014	+	0.858189i
$502$	−3.60285	−	4.83947i	−0.160803	−	0.215996i
$503$	2.83726	+	16.0909i	0.126507	+	0.717457i	0.980401	+	0.197011i	$0.0631234\pi$
$503$	2.83726	+	16.0909i	0.126507	+	0.717457i	−0.853894	+	0.520447i	$0.825766\pi$
$504$	0.659826	−	14.1924i	0.0293910	−	0.632178i
$505$	−1.87522	+	10.6349i	−0.0834460	+	0.473246i
$506$	−28.8101	+	14.4690i	−1.28077	+	0.643224i
$507$	−31.0228	−	28.9268i	−1.37777	−	1.28468i
$508$	−2.20591	−	0.257834i	−0.0978715	−	0.0114395i
$509$	−23.8891	+	15.7121i	−1.05887	+	0.696428i	−0.954530	−	0.298115i	$-0.903642\pi$
$509$	−23.8891	+	15.7121i	−1.05887	+	0.696428i	−0.104337	+	0.994542i	$0.533272\pi$
$510$	−2.51086	−	2.95696i	−0.111183	−	0.130937i
$511$	−1.95031	−	6.51450i	−0.0862768	−	0.288184i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−5.34769	+	6.60555i	−0.236106	+	0.291642i
$514$	−8.47257	−	14.6749i	−0.373709	−	0.647283i
$515$	4.39787	−	4.66147i	0.193793	−	0.205409i
$516$	4.01340	−	2.34860i	0.176680	−	0.103392i
$517$	2.06384	+	35.4348i	0.0907676	+	1.55842i
$518$	16.8130	+	38.9769i	0.738720	+	1.71255i
$519$	−20.0388	−	1.04935i	−0.879605	−	0.0460611i
$520$	−0.320368	+	5.50051i	−0.0140491	+	0.241213i
$521$	6.35056	−	2.31141i	0.278223	−	0.101265i	−0.199140	−	0.979971i	$-0.563815\pi$
$521$	6.35056	−	2.31141i	0.278223	−	0.101265i	0.477363	+	0.878706i	$0.341593\pi$
$522$	8.88076	−	2.21502i	0.388701	−	0.0969486i
$523$	41.5732	+	15.1314i	1.81787	+	0.661650i	0.995725	+	0.0923727i	$0.0294451\pi$
$523$	41.5732	+	15.1314i	1.81787	+	0.661650i	0.822145	+	0.569278i	$0.192777\pi$
$524$	−0.431298	+	0.999861i	−0.0188413	+	0.0436791i
$525$	15.2457	−	30.8054i	0.665376	−	1.34446i
$526$	−22.2377	+	5.27044i	−0.969610	+	0.229802i
$527$	−4.48231	+	1.06233i	−0.195253	+	0.0462757i
$528$	−4.07109	−	6.11148i	−0.177171	−	0.265968i
$529$	13.7932	−	31.9763i	0.599706	−	1.39027i
$530$	−1.88646	−	0.686617i	−0.0819428	−	0.0298247i
$531$	−10.0780	−	4.91433i	−0.437349	−	0.213264i
$532$	7.27894	−	2.64932i	0.315582	−	0.114863i
$533$	−1.84677	+	31.7078i	−0.0799924	+	1.37342i
$534$	12.9317	+	25.3772i	0.559609	+	1.09818i
$535$	3.23898	+	7.50880i	0.140033	+	0.324634i
$536$	0.278584	+	4.78311i	0.0120330	+	0.206599i
$537$	0.0696979	+	11.8943i	0.00300769	+	0.513275i
$538$	15.1971	−	16.1079i	0.655192	−	0.694463i
$539$	−32.7062	−	56.6489i	−1.40876	−	2.44004i
$540$	4.67206	+	0.189783i	0.201054	+	0.00816695i
$541$	2.15840	−	3.73845i	0.0927967	−	0.160729i	−0.815890	−	0.578207i	$-0.803753\pi$
$541$	2.15840	−	3.73845i	0.0927967	−	0.160729i	0.908687	+	0.417478i	$0.137086\pi$
$542$	4.85513	+	16.2173i	0.208546	+	0.696591i
$543$	−13.9457	+	39.0255i	−0.598468	+	1.67475i
$544$	2.07938	−	1.36763i	0.0891528	−	0.0586367i
$545$	−7.64624	−	0.893718i	−0.327529	−	0.0382827i
$546$	48.0294	−	14.6863i	2.05547	−	0.628514i
$547$	−29.0025	+	14.5656i	−1.24006	+	0.622779i	−0.943226	−	0.332151i	$-0.892226\pi$
$547$	−29.0025	+	14.5656i	−1.24006	+	0.622779i	−0.296829	+	0.954931i	$0.595929\pi$
$548$	1.05321	−	5.97306i	0.0449910	−	0.255157i
$549$	9.35675	−	1.20496i	0.399336	−	0.0514264i
$550$	−3.08487	−	17.4952i	−0.131539	−	0.745996i
$551$	2.97992	+	4.00272i	0.126949	+	0.170522i
$552$	12.6395	+	3.70346i	0.537974	+	0.157630i
$553$	16.8255	+	17.8340i	0.715495	+	0.758380i
$554$	6.83848	−	22.8421i	0.290539	−	0.970469i
$555$	−12.7951	+	5.60842i	−0.543122	+	0.238064i
$556$	−14.0145	+	1.63806i	−0.594346	+	0.0694691i
$557$	27.5704	−	23.1343i	1.16820	−	0.980233i	0.168212	−	0.985751i	$-0.446201\pi$
$557$	27.5704	−	23.1343i	1.16820	−	0.980233i	0.999985	+	0.00551749i	$0.00175628\pi$
$558$	2.71975	−	4.84089i	0.115136	−	0.204931i
$559$	12.5924	+	10.5663i	0.532602	+	0.446906i
$560$	−3.56064	−	2.34187i	−0.150464	−	0.0989619i
$561$	2.22807	+	18.1399i	0.0940690	+	0.765865i
$562$	3.62123	−	4.86416i	0.152753	−	0.205182i
$563$	10.7328	+	5.39023i	0.452335	+	0.227171i	0.660355	−	0.750953i	$-0.270406\pi$
$563$	10.7328	+	5.39023i	0.452335	+	0.227171i	−0.208020	+	0.978125i	$0.566702\pi$
$564$	9.25576	−	11.1628i	0.389738	−	0.470038i
$565$	−4.66592	−	1.10584i	−0.196297	−	0.0465232i
$566$	6.52622			0.274317
$567$	−13.1781	−	40.5348i	−0.553427	−	1.70230i
$568$	−4.15839			−0.174482
$569$	−29.2471	−	6.93169i	−1.22610	−	0.290592i	−0.433963	−	0.900931i	$-0.642885\pi$
$569$	−29.2471	−	6.93169i	−1.22610	−	0.290592i	−0.792140	+	0.610339i	$0.791033\pi$
$570$	0.885944	+	2.39043i	0.0371081	+	0.100124i
$571$	−18.7127	−	9.39786i	−0.783101	−	0.393288i	0.0118744	−	0.999929i	$-0.496220\pi$
$571$	−18.7127	−	9.39786i	−0.783101	−	0.393288i	−0.794976	+	0.606641i	$0.792516\pi$
$572$	15.5015	−	20.8221i	0.648150	−	0.870616i
$573$	13.7182	−	10.3383i	0.573085	−	0.431888i
$574$	−20.5253	−	13.4997i	−0.856711	−	0.563467i
$575$	24.4088	+	20.4814i	1.01792	+	0.854133i
$576$	−0.486285	+	2.96033i	−0.0202619	+	0.123347i
$577$	25.8767	−	21.7131i	1.07726	−	0.903928i	0.0815689	−	0.996668i	$-0.474007\pi$
$577$	25.8767	−	21.7131i	1.07726	−	0.903928i	0.995690	+	0.0927399i	$0.0295625\pi$
$578$	10.7327	−	1.25447i	0.446421	−	0.0521791i
$579$	3.32683	−	29.9856i	0.138258	−	1.24616i
$580$	0.787414	−	2.63015i	0.0326956	−	0.109211i
$581$	8.80134	+	9.32887i	0.365141	+	0.387027i
$582$	1.91523	+	7.87508i	0.0793890	+	0.326433i
$583$	5.64804	+	7.58663i	0.233918	+	0.314206i
$584$	0.249338	+	1.41406i	0.0103177	+	0.0585144i
$585$	4.92596	+	15.7784i	0.203664	+	0.652358i
$586$	−1.02439	+	5.80960i	−0.0423171	+	0.239992i
$587$	−5.91286	+	2.96955i	−0.244050	+	0.122567i	−0.566620	−	0.823979i	$-0.691749\pi$
$587$	−5.91286	+	2.96955i	−0.244050	+	0.122567i	0.322570	+	0.946545i	$0.395453\pi$
$588$	−6.01035	+	26.0387i	−0.247863	+	1.07382i
$589$	3.00683	+	0.351448i	0.123894	+	0.0144811i
$590$	−2.80996	+	1.84814i	−0.115684	+	0.0760868i
$591$	34.5531	−	6.30163i	1.42132	−	0.259214i
$592$	−2.57066	−	8.58659i	−0.105653	−	0.352907i
$593$	−0.624047	+	1.08088i	−0.0256266	+	0.0443865i	−0.878554	−	0.477643i	$-0.841491\pi$
$593$	−0.624047	+	1.08088i	−0.0256266	+	0.0443865i	0.852928	+	0.522029i	$0.174825\pi$
$594$	−17.8992	−	12.8427i	−0.734413	−	0.526941i
$595$	5.30337	+	9.18570i	0.217417	+	0.376577i
$596$	−1.41163	+	1.49624i	−0.0578226	+	0.0612883i
$597$	7.86454	+	4.47936i	0.321874	+	0.183328i
$598$	2.70720	+	46.4808i	0.110706	+	1.90074i
$599$	−16.0453	−	37.1971i	−0.655592	−	1.51983i	−0.843207	−	0.537590i	$-0.819335\pi$
$599$	−16.0453	−	37.1971i	−0.655592	−	1.51983i	0.187615	−	0.982243i	$-0.439924\pi$
$600$	−3.95255	+	6.08696i	−0.161362	+	0.248499i
$601$	−2.24413	+	38.5302i	−0.0915399	+	1.57168i	0.569921	+	0.821700i	$0.306974\pi$
$601$	−2.24413	+	38.5302i	−0.0915399	+	1.57168i	−0.661461	+	0.749980i	$0.730063\pi$
$602$	−11.9478	+	4.34866i	−0.486957	+	0.177238i
$603$	5.84739	+	13.1305i	0.238124	+	0.534714i
$604$	−8.36483	−	3.04455i	−0.340360	−	0.123881i
$605$	2.48594	−	5.76305i	0.101068	−	0.234301i
$606$	−20.7427	+	1.33013i	−0.842615	+	0.0540327i
$607$	−27.8613	+	6.60324i	−1.13085	+	0.268017i	−0.753111	−	0.657893i	$-0.771448\pi$
$607$	−27.8613	+	6.60324i	−1.13085	+	0.268017i	−0.377743	+	0.925910i	$0.623300\pi$
$608$	−1.59152	+	0.377198i	−0.0645448	+	0.0152974i
$609$	−24.9750	+	1.60153i	−1.01204	+	0.0648971i
$610$	1.12084	−	2.59840i	0.0453814	−	0.105206i
$611$	48.1697	+	17.5323i	1.94874	+	0.709283i
$612$	4.38818	−	6.04087i	0.177382	−	0.244188i
$613$	−3.45856	+	1.25881i	−0.139690	+	0.0508429i	−0.410919	−	0.911672i	$-0.634792\pi$
$613$	−3.45856	+	1.25881i	−0.139690	+	0.0508429i	0.271229	+	0.962515i	$0.412570\pi$
$614$	0.804349	−	13.8101i	0.0324609	−	0.557332i
$615$	4.40326	−	6.78104i	0.177556	−	0.273438i
$616$	7.95271	+	18.4365i	0.320424	+	0.742826i
$617$	−0.480387	−	8.24792i	−0.0193396	−	0.332049i	−0.994076	−	0.108689i	$-0.965335\pi$
$617$	−0.480387	−	8.24792i	−0.0193396	−	0.332049i	0.974736	−	0.223359i	$-0.0717024\pi$
$618$	10.7184	+	6.10483i	0.431159	+	0.245572i
$619$	−10.8014	+	11.4488i	−0.434143	+	0.460165i	−0.907097	−	0.420923i	$-0.861706\pi$
$619$	−10.8014	+	11.4488i	−0.434143	+	0.460165i	0.472953	+	0.881087i	$0.343188\pi$
$620$	−0.832779	−	1.44242i	−0.0334452	−	0.0579288i
$621$	39.3994	−	2.99050i	1.58104	−	0.120005i
$622$	10.6443	−	18.4365i	0.426798	−	0.739236i
$623$	−22.3356	−	74.6063i	−0.894859	−	2.98904i
$624$	−10.4330	+	1.90272i	−0.417654	+	0.0761698i
$625$	−11.2866	+	7.42330i	−0.451463	+	0.296932i
$626$	−13.4077	−	1.56714i	−0.535880	−	0.0626354i
$627$	2.70135	−	11.7031i	0.107881	−	0.467375i
$628$	−3.51361	+	1.76460i	−0.140208	+	0.0704152i
$629$	−3.87369	+	21.9688i	−0.154454	+	0.875952i
$630$	−12.4743	−	2.80248i	−0.496988	−	0.111654i
$631$	6.42930	+	36.4624i	0.255947	+	1.45155i	0.793631	+	0.608399i	$0.208188\pi$
$631$	6.42930	+	36.4624i	0.255947	+	1.45155i	−0.537685	+	0.843146i	$0.680701\pi$
$632$	−3.09157	−	4.15270i	−0.122976	−	0.165186i
$633$	−4.09759	−	16.8485i	−0.162865	−	0.669668i
$634$	−6.05013	−	6.41277i	−0.240281	−	0.254683i
$635$	−0.573197	+	1.91461i	−0.0227466	+	0.0759790i
$636$	0.426088	−	3.84045i	0.0168955	−	0.152284i
$637$	−93.8291	+	10.9670i	−3.71764	+	0.434530i
$638$	−9.90873	+	8.31442i	−0.392291	+	0.329171i
$639$	−11.6720	+	4.40385i	−0.461738	+	0.174214i
$640$	0.689349	+	0.578432i	0.0272489	+	0.0228645i
$641$	−39.3612	−	25.8883i	−1.55467	−	1.02253i	−0.978758	−	0.205017i	$-0.934275\pi$
$641$	−39.3612	−	25.8883i	−1.55467	−	1.02253i	−0.575916	−	0.817509i	$-0.695355\pi$
$642$	−12.5700	+	9.47303i	−0.496100	+	0.373871i
$643$	3.24751	−	4.36216i	0.128069	−	0.172027i	−0.733464	−	0.679729i	$-0.762097\pi$
$643$	3.24751	−	4.36216i	0.128069	−	0.172027i	0.861533	+	0.507702i	$0.169505\pi$
$644$	−32.1823	−	16.1626i	−1.26816	−	0.636894i
$645$	−1.45421	−	3.92372i	−0.0572594	−	0.154496i
$646$	3.96102	+	0.938780i	0.155844	+	0.0369358i
$647$	25.2978			0.994557			0.497279	−	0.867591i	$-0.334333\pi$
$647$	25.2978			0.994557			0.497279	+	0.867591i	$0.334333\pi$
$648$	1.77013	+	8.82421i	0.0695373	+	0.346648i
$649$	15.8455			0.621990
$650$	−24.9645	−	5.91669i	−0.979188	−	0.232072i
$651$	−9.69068	+	11.6873i	−0.379808	+	0.458062i
$652$	−9.82745	−	4.93553i	−0.384873	−	0.193290i
$653$	−18.2201	+	24.4739i	−0.713008	+	0.957736i	−1.00000		0.000197051i	$-0.999937\pi$
$653$	−18.2201	+	24.4739i	−0.713008	+	0.957736i	0.286992	+	0.957933i	$0.407345\pi$
$654$	−1.80640	−	14.7068i	−0.0706357	−	0.575082i
$655$	0.818691	+	0.538461i	0.0319889	+	0.0210394i
$656$	3.97376	+	3.33438i	0.155149	+	0.130186i
$657$	2.19739	+	3.70503i	0.0857283	+	0.144547i
$658$	−30.3732	+	25.4862i	−1.18407	+	0.993555i
$659$	−18.6840	+	2.18385i	−0.727826	+	0.0850706i	−0.471933	−	0.881635i	$-0.656443\pi$
$659$	−18.6840	+	2.18385i	−0.727826	+	0.0850706i	−0.255893	+	0.966705i	$0.582369\pi$
$660$	−6.05221	+	2.65284i	−0.235582	+	0.103262i
$661$	−0.384072	+	1.28289i	−0.0149387	+	0.0498987i	−0.965134	−	0.261757i	$-0.915698\pi$
$661$	−0.384072	+	1.28289i	−0.0149387	+	0.0498987i	0.950195	+	0.311655i	$0.100883\pi$
$662$	−2.07452	−	2.19887i	−0.0806286	−	0.0854613i
$663$	25.3293	+	7.42165i	0.983708	+	0.288233i
$664$	−1.61718	−	2.17225i	−0.0627588	−	0.0842997i
$665$	−1.21042	−	6.86466i	−0.0469383	−	0.266200i
$666$	−16.3089	−	21.3790i	−0.631957	−	0.828418i
$667$	4.02865	−	22.8476i	0.155990	−	0.884664i
$668$	−14.3530	+	7.20833i	−0.555333	+	0.278899i
$669$	37.5436	−	11.4800i	1.45152	−	0.443841i
$670$	4.28237	+	0.500537i	0.165442	+	0.0193374i
$671$	−11.1390	+	7.32623i	−0.430016	+	0.282826i
$672$	2.76031	−	7.72443i	0.106481	−	0.297977i
$673$	−8.59506	−	28.7095i	−0.331315	−	1.10667i	−0.947683	−	0.319212i	$-0.896582\pi$
$673$	−8.59506	−	28.7095i	−0.331315	−	1.10667i	0.616368	−	0.787458i	$-0.288603\pi$
$674$	−1.07856	+	1.86811i	−0.0415444	+	0.0719570i
$675$	−4.64801	+	21.2711i	−0.178902	+	0.818725i
$676$	−12.2446	−	21.2083i	−0.470948	−	0.815705i
$677$	−10.4366	+	11.0621i	−0.401110	+	0.425152i	−0.896173	−	0.443705i	$-0.853664\pi$
$677$	−10.4366	+	11.0621i	−0.401110	+	0.425152i	0.495062	+	0.868857i	$0.335145\pi$
$678$	−0.0540824	−	9.22939i	−0.00207702	−	0.354453i
$679$	−1.28850	−	22.1228i	−0.0494483	−	0.848994i
$680$	−0.887079	−	2.05648i	−0.0340179	−	0.0788624i
$681$	2.26999	+	4.45464i	0.0869861	+	0.170702i
$682$	−0.456264	+	7.83375i	−0.0174712	+	0.299970i
$683$	−32.1031	+	11.6846i	−1.22839	+	0.447098i	−0.873047	−	0.487637i	$-0.837859\pi$
$683$	−32.1031	+	11.6846i	−1.22839	+	0.447098i	−0.355346	+	0.934735i	$0.615637\pi$
$684$	−4.06772	+	2.74421i	−0.155533	+	0.104927i
$685$	−5.12881	−	1.86673i	−0.195962	−	0.0713242i
$686$	15.8106	−	36.6530i	0.603650	−	1.39942i
$687$	18.5273	+	27.8130i	0.706861	+	1.06113i
$688$	2.61236	−	0.619142i	0.0995955	−	0.0236046i
$689$	13.2912	−	3.15007i	0.506354	−	0.120008i
$690$	5.25713	−	10.6226i	0.200135	−	0.404394i
$691$	−3.28549	+	7.61662i	−0.124986	+	0.289750i	−0.969208	−	0.246244i	$-0.920804\pi$
$691$	−3.28549	+	7.61662i	−0.124986	+	0.289750i	0.844222	+	0.535994i	$0.180063\pi$
$692$	−10.8866	−	3.96239i	−0.413845	−	0.150627i
$693$	41.8469	+	43.3264i	1.58963	+	1.64583i
$694$	27.2575	−	9.92091i	1.03468	−	0.376593i
$695$	−0.738277	+	12.6757i	−0.0280044	+	0.480818i
$696$	5.27716	+	0.276342i	0.200030	+	0.0104747i
$697$	−5.11358	−	11.8546i	−0.193690	−	0.449025i
$698$	1.52380	+	26.1626i	0.0576766	+	0.990269i
$699$	40.7091	−	23.8226i	1.53976	−	0.901052i
$700$	13.6181	−	14.4343i	0.514715	−	0.545566i
$701$	20.0087	+	34.6561i	0.755718	+	1.30894i	0.945016	+	0.327023i	$0.106045\pi$
$701$	20.0087	+	34.6561i	0.755718	+	1.30894i	−0.189298	+	0.981920i	$0.560621\pi$
$702$	−27.2689	+	16.3895i	−1.02920	+	0.618582i
$703$	7.33010	−	12.6961i	0.276460	−	0.478843i
$704$	−1.21595	−	4.06154i	−0.0458277	−	0.153075i
$705$	−8.44623	−	9.94687i	−0.318103	−	0.374621i
$706$	12.3516	−	8.12377i	0.464858	−	0.305742i
$707$	56.4484	+	6.59788i	2.12296	+	0.248139i
$708$	−4.73457	−	4.41469i	−0.177936	−	0.165914i
$709$	26.9452	−	13.5324i	1.01195	−	0.508219i	0.136043	−	0.990703i	$-0.456561\pi$
$709$	26.9452	−	13.5324i	1.01195	−	0.508219i	0.875905	+	0.482483i	$0.160265\pi$
$710$	−0.649801	+	3.68520i	−0.0243866	+	0.138303i
$711$	−13.0754	−	8.38199i	−0.490367	−	0.314349i
$712$	2.85550	+	16.1944i	0.107014	+	0.606909i
$713$	−8.40466	−	11.2894i	−0.314757	−	0.422792i
$714$	−14.7673	+	14.0967i	−0.552651	+	0.527554i
$715$	−16.0305	−	16.9913i	−0.599505	−	0.635438i
$716$	−1.96956	+	6.57877i	−0.0736057	+	0.245860i
$717$	11.0373	+	8.11687i	0.412195	+	0.303130i
$718$	−23.3834	+	2.73313i	−0.872660	+	0.101999i
$719$	−20.1751	+	16.9289i	−0.752404	+	0.631342i	−0.936138	−	0.351634i	$-0.885626\pi$
$719$	−20.1751	+	16.9289i	−0.752404	+	0.631342i	0.183733	+	0.982976i	$0.441182\pi$
$720$	2.54748	+	0.893539i	0.0949390	+	0.0333002i
$721$	−25.8367	−	21.6796i	−0.962209	−	0.807389i
$722$	13.6392	+	8.97061i	0.507597	+	0.333852i
$723$	−0.691141	−	0.293338i	−0.0257038	−	0.0109094i
$724$	−14.2881	+	19.1922i	−0.531013	+	0.713274i
$725$	11.4243	+	5.73750i	0.424288	+	0.213085i
$726$	11.9090	+	2.02800i	0.441984	+	0.0752661i
$727$	−37.7796	−	8.95394i	−1.40117	−	0.332083i	−0.540542	−	0.841317i	$-0.681781\pi$
$727$	−37.7796	−	8.95394i	−1.40117	−	0.332083i	−0.860628	+	0.509234i	$0.829929\pi$
$728$	28.9972			1.07471
$729$	14.3136	+	22.8937i	0.530133	+	0.847915i
$730$	1.29212			0.0478235
$731$	−6.50172	−	1.54094i	−0.240475	−	0.0569936i
$732$	5.36943	+	0.914368i	0.198460	+	0.0337960i
$733$	23.1712	+	11.6370i	0.855849	+	0.429823i	0.821921	−	0.569601i	$-0.192902\pi$
$733$	23.1712	+	11.6370i	0.855849	+	0.429823i	0.0339274	+	0.999424i	$0.489198\pi$
$734$	16.6895	−	22.4178i	0.616019	−	0.827458i
$735$	22.1365	+	9.39531i	0.816519	+	0.346551i
$736$	6.35325	+	4.17860i	0.234184	+	0.154025i
$737$	−15.5607	−	13.0570i	−0.573186	−	0.480960i
$738$	14.6850	+	5.15082i	0.540562	+	0.189604i
$739$	15.3874	−	12.9116i	0.566034	−	0.474959i	−0.314293	−	0.949326i	$-0.601767\pi$
$739$	15.3874	−	12.9116i	0.566034	−	0.474959i	0.880327	+	0.474367i	$0.157323\pi$
$740$	−8.01121	+	0.936377i	−0.294498	+	0.0344219i
$741$	−13.9739	−	10.2765i	−0.513345	−	0.377516i
$742$	−3.03015	+	10.1214i	−0.111240	+	0.371569i
$743$	10.1530	+	10.7616i	0.372478	+	0.394804i	0.886314	−	0.463085i	$-0.153257\pi$
$743$	10.1530	+	10.7616i	0.372478	+	0.394804i	−0.513836	+	0.857889i	$0.671776\pi$
$744$	2.31888	−	2.21357i	0.0850142	−	0.0811536i
$745$	1.10540	+	1.48480i	0.0404986	+	0.0543990i
$746$	−2.20043	−	12.4793i	−0.0805635	−	0.456899i
$747$	−6.83968	−	4.38457i	−0.250251	−	0.160423i
$748$	−1.83229	+	10.3914i	−0.0669953	+	0.379949i
$749$	38.4594	−	19.3150i	1.40528	−	0.705756i
$750$	10.4765	+	9.76866i	0.382547	+	0.356701i
$751$	16.2830	+	1.90321i	0.594176	+	0.0694492i	0.407866	−	0.913042i	$-0.366273\pi$
$751$	16.2830	+	1.90321i	0.594176	+	0.0694492i	0.186310	+	0.982491i	$0.440347\pi$
$752$	6.99479	−	4.60055i	0.255074	−	0.167765i
$753$	−6.76394	−	7.96569i	−0.246492	−	0.290286i
$754$	5.35762	+	17.8957i	0.195113	+	0.651722i
$755$	−4.00522	+	6.93725i	−0.145765	+	0.252472i
$756$	−0.432575	−	24.6046i	−0.0157326	−	0.894862i
$757$	−0.252679	−	0.437653i	−0.00918377	−	0.0159068i	0.861397	−	0.507932i	$-0.169590\pi$
$757$	−0.252679	−	0.437653i	−0.00918377	−	0.0159068i	−0.870581	+	0.492026i	$0.836257\pi$
$758$	−6.84254	+	7.25267i	−0.248532	+	0.263429i
$759$	−48.1945	+	28.2029i	−1.74935	+	1.02370i
$760$	0.0855808	+	1.46937i	0.00310434	+	0.0532995i
$761$	−7.50717	−	17.4036i	−0.272135	−	0.630879i	0.726266	−	0.687414i	$-0.241254\pi$
$761$	−7.50717	−	17.4036i	−0.272135	−	0.630879i	−0.998401	+	0.0565345i	$0.981995\pi$
$762$	−3.84150	−	0.201163i	−0.139163	−	0.00728736i
$763$	−2.35572	+	40.4461i	−0.0852827	+	1.46425i
$764$	9.31937	−	3.39197i	0.337163	−	0.122717i
$765$	−4.66777	−	4.83281i	−0.168764	−	0.174731i
$766$	−29.9206	−	10.8902i	−1.08108	−	0.393480i
$767$	9.06383	−	21.0123i	0.327276	−	0.758711i

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)

\(f(q)\)	\(=\)	\(q+(0.973045 + 0.230616i) q^{2} +(1.70747 + 0.290767i) q^{3} +(0.893633 + 0.448799i) q^{4} +(0.537372 - 0.721815i) q^{5} +(1.59439 + 0.676699i) q^{6} +(-3.95679 - 2.60242i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.83091 + 0.992953i) q^{9} +O(q^{10})\)	\(q+(0.973045 + 0.230616i) q^{2} +(1.70747 + 0.290767i) q^{3} +(0.893633 + 0.448799i) q^{4} +(0.537372 - 0.721815i) q^{5} +(1.59439 + 0.676699i) q^{6} +(-3.95679 - 2.60242i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.83091 + 0.992953i) q^{9} +(0.689349 - 0.578432i) q^{10} +(-4.21098 + 0.492194i) q^{11} +(1.39536 + 1.02615i) q^{12} +(-1.75605 + 5.86562i) q^{13} +(-3.24997 - 3.44477i) q^{14} +(1.12743 - 1.07623i) q^{15} +(0.597159 + 0.802123i) q^{16} +(-0.432180 - 2.45101i) q^{17} +(2.52561 + 1.61904i) q^{18} +(-0.284021 + 1.61076i) q^{19} +(0.804163 - 0.403866i) q^{20} +(-5.99940 - 5.59406i) q^{21} +(-4.21098 - 0.492194i) q^{22} +(6.35325 - 4.17860i) q^{23} +(1.12110 + 1.32028i) q^{24} +(1.20177 + 4.01418i) q^{25} +(-3.06142 + 5.30254i) q^{26} +(4.54497 + 2.51857i) q^{27} +(-2.36795 - 4.10141i) q^{28} +(2.09368 - 2.21918i) q^{29} +(1.34523 - 0.787216i) q^{30} +(-0.107618 - 1.84773i) q^{31} +(0.396080 + 0.918216i) q^{32} +(-7.33324 - 0.384010i) q^{33} +(0.144712 - 2.48461i) q^{34} +(-4.00473 + 1.45760i) q^{35} +(2.08416 + 2.15784i) q^{36} +(-8.42259 - 3.06557i) q^{37} +(-0.647833 + 1.50184i) q^{38} +(-4.70394 + 9.50478i) q^{39} +(0.875624 - 0.207527i) q^{40} +(5.04755 - 1.19629i) q^{41} +(-4.54760 - 6.82682i) q^{42} +(1.06337 - 2.46516i) q^{43} +(-3.98397 - 1.45005i) q^{44} +(2.23798 - 1.50981i) q^{45} +(7.14564 - 2.60080i) q^{46} +(0.486795 - 8.35794i) q^{47} +(0.786399 + 1.54324i) q^{48} +(6.11101 + 14.1669i) q^{49} +(0.243639 + 4.18313i) q^{50} +(-0.0252598 - 4.31070i) q^{51} +(-4.20175 + 4.45360i) q^{52} +(-1.11544 - 1.93201i) q^{53} +(3.84164 + 3.49883i) q^{54} +(-1.90759 + 3.30404i) q^{55} +(-1.35827 - 4.53694i) q^{56} +(-0.953314 + 2.66775i) q^{57} +(2.54903 - 1.67652i) q^{58} +(-3.71218 - 0.433892i) q^{59} +(1.49051 - 0.455765i) q^{60} +(2.81018 - 1.41133i) q^{61} +(0.321399 - 1.82275i) q^{62} +(-8.61722 - 11.2961i) q^{63} +(0.173648 + 0.984808i) q^{64} +(3.29024 + 4.41957i) q^{65} +(-7.04702 - 2.06482i) q^{66} +(3.28793 + 3.48500i) q^{67} +(0.713803 - 2.38427i) q^{68} +(12.0630 - 5.28751i) q^{69} +(-4.23293 + 0.494758i) q^{70} +(-3.18551 + 2.67296i) q^{71} +(1.53034 + 2.58032i) q^{72} +(1.09995 + 0.922965i) q^{73} +(-7.48859 - 4.92532i) q^{74} +(0.884789 + 7.20353i) q^{75} +(-0.976720 + 1.31196i) q^{76} +(17.9429 + 9.01124i) q^{77} +(-6.76910 + 8.16377i) q^{78} +(-5.03759 - 1.19393i) q^{79} +0.899881 q^{80} +(7.02809 + 5.62192i) q^{81} +5.18737 q^{82} +(-2.63513 - 0.624537i) q^{83} +(-2.85065 - 7.69155i) q^{84} +(-2.00142 - 1.00515i) q^{85} +(1.60321 - 2.15349i) q^{86} +(4.22017 - 3.18040i) q^{87} +(-3.54218 - 2.32973i) q^{88} +(12.5970 + 10.5701i) q^{89} +(2.52584 - 0.952998i) q^{90} +(22.2131 - 18.6390i) q^{91} +(7.55282 - 0.882798i) q^{92} +(0.353505 - 3.18624i) q^{93} +(2.40115 - 8.02039i) q^{94} +(1.01005 + 1.07059i) q^{95} +(0.409307 + 1.68299i) q^{96} +(2.79423 + 3.75330i) q^{97} +(2.67917 + 15.1943i) q^{98} +(-12.4096 - 2.78795i) 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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