LMFDB - Embedded newform 162.2.g.b.13.4

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			13.4
Character	$\chi$	$=$	162.13
Dual form			162.2.g.b.25.4

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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	0.968066	+	0.250694i	$0.0806589\pi$
$5$	0.664151	+	2.21842i	0.297017	+	0.992107i	−0.671049	+	0.741413i	$0.734156\pi$
$6$	1.54272	−	0.787412i	0.629812	−	0.321460i
$7$	−0.590051	−	1.36789i	−0.223018	−	0.517014i	0.769567	−	0.638566i	$-0.220472\pi$
$7$	−0.590051	−	1.36789i	−0.223018	−	0.517014i	−0.992585	+	0.121552i	$0.961213\pi$
$8$	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	−0.817938	−	0.575306i	$-0.804883\pi$
$11$	−4.28069	+	1.01454i	−1.29068	+	0.305896i	−0.472739	+	0.881202i	$0.656735\pi$
$12$	1.73201	−	0.0112858i	0.499989	−	0.00325792i
$13$	0.407438	+	0.267976i	0.113003	+	0.0743233i	0.604752	−	0.796413i	$-0.293272\pi$
$13$	0.407438	+	0.267976i	0.113003	+	0.0743233i	−0.491749	+	0.870737i	$0.663642\pi$
$14$	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	0.543323	−	0.839524i	$-0.317166\pi$
$17$	6.18123	−	2.24978i	1.49917	−	0.545653i	0.955845	+	0.293871i	$0.0949435\pi$
$18$	0.482400	−	2.96096i	0.113703	−	0.697905i
$19$	−6.76026	−	2.46053i	−1.55091	−	0.564485i	−0.582279	−	0.812989i	$-0.697839\pi$
$19$	−6.76026	−	2.46053i	−1.55091	−	0.564485i	−0.968631	+	0.248504i	$0.920061\pi$
$20$	−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	−0.995128	−	0.0985910i	$-0.968566\pi$
$23$	−1.15348	+	2.67407i	−0.240517	+	0.557582i	0.754611	+	0.656173i	$0.227826\pi$
$24$	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	0.825428	+	0.564508i	$0.190934\pi$
$29$	0.382974	+	6.57542i	0.0711166	+	1.22102i	−0.754311	+	0.656517i	$0.772029\pi$
$30$	2.77141	+	2.89944i	0.505988	+	0.529363i
$31$	−1.78001	+	0.208053i	−0.319699	+	0.0373674i	−0.274429	−	0.961607i	$-0.588489\pi$
$31$	−1.78001	+	0.208053i	−0.319699	+	0.0373674i	−0.0452698	+	0.998975i	$0.514415\pi$
$32$	−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	0.306742	−	0.951793i	$-0.400761\pi$
$37$	−3.51174	−	2.94670i	−0.577326	−	0.484434i	−0.884068	+	0.467359i	$0.845206\pi$
$38$	−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	−0.903483	−	0.428625i	$-0.858998\pi$
$41$	−7.03828	+	3.53476i	−1.09920	+	0.552037i	−0.195713	+	0.980661i	$0.562702\pi$
$42$	−1.98738	−	1.64566i	−0.306659	−	0.253931i
$43$	−0.304424	−	0.322671i	−0.0464243	−	0.0492069i	0.703745	−	0.710452i	$-0.251510\pi$
$43$	−0.304424	−	0.322671i	−0.0464243	−	0.0492069i	−0.750170	+	0.661246i	$0.770028\pi$
$44$	−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	0.661922	−	0.749573i	$-0.269741\pi$
$47$	7.76840	+	0.907996i	1.13314	+	0.132445i	0.471216	+	0.882018i	$0.343815\pi$
$48$	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	−0.790468	−	0.612503i	$-0.790163\pi$
$53$	0.984340	−	1.70493i	0.135209	−	0.234190i	0.925677	+	0.378314i	$0.123496\pi$
$54$	−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	0.934450	−	0.356095i	$-0.115892\pi$
$59$	12.3643	+	2.93038i	1.60969	+	0.381503i	0.675240	+	0.737598i	$0.264040\pi$
$60$	1.17536	+	3.83484i	0.151738	+	0.495076i
$61$	4.60541	−	6.18613i	0.589662	−	0.792053i	−0.402711	−	0.915327i	$-0.631932\pi$
$61$	4.60541	−	6.18613i	0.589662	−	0.792053i	0.992373	+	0.123274i	$0.0393394\pi$
$62$	−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	0.957231	+	0.289324i	$0.0934305\pi$
$67$	−0.221954	+	3.81081i	−0.0271160	+	0.465564i	−0.984347	+	0.176240i	$0.943606\pi$
$68$	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	−0.794841	−	0.606818i	$-0.792446\pi$
$71$	1.34489	−	7.62726i	0.159609	−	0.905189i	0.954450	−	0.298371i	$-0.0964433\pi$
$72$	2.66312	−	1.38122i	0.313852	−	0.162778i
$73$	1.74940	+	9.92135i	0.204752	+	1.16121i	0.897830	+	0.440343i	$0.145143\pi$
$73$	1.74940	+	9.92135i	0.204752	+	1.16121i	−0.693078	+	0.720863i	$0.743746\pi$
$74$	−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	0.991481	+	0.130252i	$0.0415787\pi$
$79$	15.0035	+	7.53506i	1.68803	+	0.847761i	0.696550	+	0.717509i	$0.254718\pi$
$80$	−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	0.174698	−	0.984622i	$-0.444105\pi$
$83$	−4.65331	−	2.33698i	−0.510767	−	0.256517i	−0.685465	+	0.728105i	$0.740401\pi$
$84$	−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	0.942934	−	0.332980i	$-0.108054\pi$
$89$	−0.537926	−	3.05073i	−0.0570200	−	0.323377i	−0.999954	+	0.00960343i	$0.996943\pi$
$90$	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	−0.935035	−	0.354555i	$-0.884633\pi$
$97$	0.403864	−	1.34900i	0.0410062	−	0.136970i	0.976042	+	0.217584i	$0.0698177\pi$
$98$	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	−0.993242	−	0.116064i	$-0.962972\pi$
$101$	−6.00167	+	8.06164i	−0.597188	+	0.802163i	0.396053	+	0.918228i	$0.370380\pi$
$102$	7.76440	−	8.33796i	0.768790	−	0.825581i
$103$	−1.63242	−	0.386890i	−0.160847	−	0.0381214i	0.149403	−	0.988776i	$-0.452265\pi$
$103$	−1.63242	−	0.386890i	−0.160847	−	0.0381214i	−0.310250	+	0.950655i	$0.600413\pi$
$104$	−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	−0.993445	−	0.114309i	$-0.963535\pi$
$107$	−6.16214	−	10.6731i	−0.595717	−	1.03181i	0.397728	−	0.917503i	$-0.369799\pi$
$108$	−1.58729	−	4.94778i	−0.152737	−	0.476100i
$109$	9.54562	−	16.5335i	0.914305	−	1.58362i	0.106389	−	0.994325i	$-0.466071\pi$
$109$	9.54562	−	16.5335i	0.914305	−	1.58362i	0.807916	−	0.589298i	$-0.200595\pi$
$110$	−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	−0.933186	−	0.359393i	$-0.882984\pi$
$113$	−5.52918	+	5.86059i	−0.520142	+	0.551318i	0.413045	+	0.910711i	$0.364465\pi$
$114$	−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	0.287382	−	0.957816i	$-0.407215\pi$
$127$	14.4311	−	12.1091i	1.28055	−	1.07451i	0.993168	−	0.116693i	$-0.0372293\pi$
$128$	−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	−0.676461	−	0.736479i	$-0.736487\pi$
$131$	−13.3322	+	1.55832i	−1.16484	+	0.136151i	−0.488383	+	0.872629i	$0.662413\pi$
$132$	−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	−0.346036	−	0.938221i	$-0.612472\pi$
$137$	4.42901	−	2.91301i	0.378396	−	0.248875i	0.724432	+	0.689346i	$0.242102\pi$
$138$	0.326096	+	5.03360i	0.0277592	+	0.428488i
$139$	−7.14865	+	16.5724i	−0.606340	+	1.40565i	0.287723	+	0.957714i	$0.407102\pi$
$139$	−7.14865	+	16.5724i	−0.606340	+	1.40565i	−0.894063	+	0.447941i	$0.852157\pi$
$140$	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	−0.228030	−	0.973654i	$-0.573229\pi$
$149$	−14.7989	−	9.73339i	−1.21237	−	0.797390i	−0.984343	+	0.176264i	$0.943599\pi$
$150$	−0.310370	+	0.545759i	−0.0253416	+	0.0445610i
$151$	−2.32779	+	0.551696i	−0.189433	+	0.0448964i	−0.324237	−	0.945976i	$-0.605108\pi$
$151$	−2.32779	+	0.551696i	−0.189433	+	0.0448964i	0.134804	+	0.990872i	$0.456959\pi$
$152$	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	0.990698	+	0.136078i	$0.0434498\pi$
$157$	2.97910	+	9.95089i	0.237758	+	0.794167i	−0.752940	+	0.658089i	$0.771365\pi$
$158$	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	0.999799	−	0.0200284i	$-0.00637567\pi$
$167$	1.98331	+	6.62473i	0.153473	+	0.512637i	−0.846326	+	0.532665i	$0.821190\pi$
$168$	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	−0.670734	−	0.741698i	$-0.734021\pi$
$173$	−12.3276	+	2.92169i	−0.937249	+	0.222132i	−0.266516	+	0.963831i	$0.585872\pi$
$174$	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	−0.377333	−	0.926078i	$-0.623159\pi$
$179$	−0.951462	+	0.346304i	−0.0711156	+	0.0258840i	0.306217	+	0.951962i	$0.400937\pi$
$180$	6.55856	+	2.29078i	0.488846	+	0.170745i
$181$	14.7137	+	5.35534i	1.09366	+	0.398059i	0.824975	−	0.565169i	$-0.191189\pi$
$181$	14.7137	+	5.35534i	1.09366	+	0.398059i	0.268684	+	0.963228i	$0.413411\pi$
$182$	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	−0.994732	−	0.102513i	$-0.967312\pi$
$191$	−0.257431	−	4.41992i	−0.0186271	−	0.319814i	0.976105	−	0.217301i	$-0.0697254\pi$
$192$	−0.485936	+	1.66249i	−0.0350694	+	0.119980i
$193$	−18.8735	+	2.20600i	−1.35855	+	0.158791i	−0.763972	−	0.645250i	$-0.776753\pi$
$193$	−18.8735	+	2.20600i	−1.35855	+	0.158791i	−0.594574	+	0.804041i	$0.702679\pi$
$194$	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	−0.239637	+	0.970863i	$0.577028\pi$
$197$	−17.3672	+	14.5728i	−1.23736	+	1.03827i	−0.997726	+	0.0674075i	$0.978527\pi$
$198$	0.939015	+	13.1644i	0.0667329	+	0.935552i
$199$	−2.88695	−	2.42244i	−0.204650	−	0.171722i	0.534702	−	0.845041i	$-0.320424\pi$
$199$	−2.88695	−	2.42244i	−0.204650	−	0.171722i	−0.739352	+	0.673319i	$0.764868\pi$
$200$	−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	−0.336606	−	0.941646i	$-0.609279\pi$
$211$	9.04987	−	9.59230i	0.623019	−	0.660361i	0.959624	+	0.281284i	$0.0907604\pi$
$212$	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	−0.921171	−	0.389157i	$-0.872766\pi$
$223$	−4.24353	+	5.70006i	−0.284168	+	0.381704i	0.637003	+	0.770861i	$0.280174\pi$
$224$	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	−0.934011	−	0.357246i	$-0.883716\pi$
$227$	0.642640	−	2.14657i	0.0426535	−	0.142473i	0.976664	+	0.214773i	$0.0689011\pi$
$228$	−11.7366	−	4.18538i	−0.777277	−	0.277184i
$229$	0.903744	−	15.5167i	0.0597211	−	1.02537i	−0.826745	−	0.562577i	$-0.809810\pi$
$229$	0.903744	−	15.5167i	0.0597211	−	1.02537i	0.886466	−	0.462794i	$-0.153153\pi$
$230$	−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	−0.906482	−	0.422244i	$-0.861243\pi$
$233$	1.36995	−	7.76937i	0.0897483	−	0.508988i	0.996231	−	0.0867442i	$-0.0276463\pi$
$234$	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	0.890466	−	0.455049i	$-0.150378\pi$
$239$	3.07871	+	4.13542i	0.199145	+	0.267498i	−0.691321	+	0.722548i	$0.742971\pi$
$240$	−2.37414	+	3.23279i	−0.153250	+	0.208676i
$241$	−1.85788	−	0.933061i	−0.119676	−	0.0601038i	0.387954	−	0.921679i	$-0.373182\pi$
$241$	−1.85788	−	0.933061i	−0.119676	−	0.0601038i	−0.507630	+	0.861575i	$0.669478\pi$
$242$	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	0.825311	+	0.564678i	$0.191000\pi$
$251$	3.84832	+	21.8249i	0.242904	+	1.37757i	−0.582408	+	0.812897i	$0.697889\pi$
$252$	−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	0.914574	+	0.404418i	$0.132526\pi$
$257$	−0.653529	+	11.2207i	−0.0407660	+	0.699925i	−0.955340	+	0.295507i	$0.904511\pi$
$258$	−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	−0.777775	−	0.628543i	$-0.783651\pi$
$263$	0.769213	−	1.03323i	0.0474317	−	0.0637118i	0.825206	+	0.564832i	$0.191059\pi$
$264$	−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	−0.999923	−	0.0124213i	$-0.996046\pi$
$269$	−8.37641	−	14.5084i	−0.510719	−	0.884591i	0.489204	−	0.872169i	$-0.337287\pi$
$270$	5.81154	−	10.5363i	0.353679	−	0.641217i
$271$	−13.9516	+	24.1649i	−0.847502	+	1.46792i	0.0359290	+	0.999354i	$0.488561\pi$
$271$	−13.9516	+	24.1649i	−0.847502	+	1.46792i	−0.883431	+	0.468562i	$0.844772\pi$
$272$	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	0.209567	−	0.977794i	$-0.432795\pi$
$277$	3.12877	+	0.365701i	0.187990	+	0.0219728i	−0.0215771	+	0.999767i	$0.506869\pi$
$278$	−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	0.704403	−	0.709800i	$-0.251215\pi$
$281$	−0.756901	−	0.802268i	−0.0451529	−	0.0478593i	−0.749556	+	0.661941i	$0.769733\pi$
$282$	12.6994	−	4.71615i	0.756240	−	0.280842i
$283$	28.2064	−	14.1658i	1.67670	−	0.842068i	0.682941	−	0.730473i	$-0.260700\pi$
$283$	28.2064	−	14.1658i	1.67670	−	0.842068i	0.993754	−	0.111595i	$-0.0355959\pi$
$284$	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	−0.888874	−	0.458151i	$-0.848512\pi$
$293$	−28.2115	+	3.29745i	−1.64813	+	0.192639i	−0.759258	+	0.650790i	$0.774438\pi$
$294$	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	−0.979692	−	0.200507i	$-0.935741\pi$
$307$	−28.0570	+	10.2119i	−1.60130	+	0.582824i	−0.621604	+	0.783332i	$0.713519\pi$
$308$	−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	0.591928	−	0.805991i	$-0.298367\pi$
$311$	1.52200	+	1.00103i	0.0863046	+	0.0567634i	−0.505623	+	0.862754i	$0.668737\pi$
$312$	0.427088	+	0.728730i	0.0241791	+	0.0412562i
$313$	−4.20142	+	0.995754i	−0.237478	+	0.0562833i	−0.347631	−	0.937631i	$-0.613014\pi$
$313$	−4.20142	+	0.995754i	−0.237478	+	0.0562833i	0.110153	+	0.993915i	$0.464866\pi$
$314$	−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	0.731152	+	0.682215i	$0.238983\pi$
$317$	12.9195	+	29.9507i	0.725630	+	1.68220i	−0.00552184	+	0.999985i	$0.501758\pi$
$318$	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	0.781834	−	0.623487i	$-0.214284\pi$
$331$	−3.78788	−	8.78130i	−0.208201	−	0.482664i	−0.990035	+	0.140823i	$0.955025\pi$
$332$	−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	0.111232	−	0.993794i	$-0.464520\pi$
$337$	−13.9009	−	9.14276i	−0.757230	−	0.498038i	−0.868461	+	0.495757i	$0.834891\pi$
$338$	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	−0.415429	−	0.909626i	$-0.636368\pi$
$347$	9.89690	−	22.9436i	0.531294	−	1.23168i	0.946722	−	0.322051i	$-0.104372\pi$
$348$	0.737526	+	11.3844i	0.0395355	+	0.610268i
$349$	17.1526	−	11.2815i	0.918160	−	0.603884i	−3.99838e−5	−	1.00000i	$-0.500013\pi$
$349$	17.1526	−	11.2815i	0.918160	−	0.603884i	0.918200	+	0.396116i	$0.129642\pi$
$350$	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	−0.903046	−	0.429544i	$-0.858674\pi$
$353$	−1.05164	−	18.0559i	−0.0559731	−	0.961021i	0.847073	−	0.531477i	$-0.178363\pi$
$354$	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	0.255607	−	0.966781i	$-0.417725\pi$
$359$	23.7236	−	19.9065i	1.25209	−	1.05062i	0.996479	−	0.0838438i	$-0.0267197\pi$
$360$	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	0.567776	−	0.823183i	$-0.307804\pi$
$367$	−5.49865	−	5.82823i	−0.287027	−	0.304231i	−0.854803	+	0.518952i	$0.826322\pi$
$368$	−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	−0.990294	−	0.138987i	$-0.955615\pi$
$373$	−15.3339	+	16.2530i	−0.793962	+	0.841550i	0.196332	+	0.980537i	$0.437097\pi$
$374$	−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	0.999633	+	0.0270727i	$0.00861857\pi$
$379$	10.1868	+	17.6441i	0.523262	+	0.906317i	−0.476371	+	0.879244i	$0.658048\pi$
$380$	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	0.292987	−	0.956116i	$-0.405351\pi$
$383$	2.46010	+	0.583054i	0.125705	+	0.0297927i	−0.167282	+	0.985909i	$0.553499\pi$
$384$	−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	−0.761832	−	0.647775i	$-0.775700\pi$
$389$	4.54869	−	15.1937i	0.230628	−	0.770350i	0.992459	−	0.122575i	$-0.0391152\pi$
$390$	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	0.781319	+	0.624132i	$0.214547\pi$
$397$	5.19212	+	29.4460i	0.260585	+	1.47785i	−0.520734	+	0.853719i	$0.674341\pi$
$398$	−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	0.640618	−	0.767860i	$-0.278678\pi$
$401$	−5.58127	−	7.49695i	−0.278715	−	0.374380i	−0.919333	+	0.393480i	$0.871271\pi$
$402$	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	0.792646	−	0.609683i	$-0.208703\pi$
$409$	−0.379338	−	0.509540i	−0.0187571	−	0.0251951i	−0.811403	+	0.584487i	$0.801296\pi$
$410$	−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	−0.974479	−	0.224477i	$-0.927933\pi$
$419$	0.398563	−	6.84305i	0.0194711	−	0.334305i	0.993951	−	0.109829i	$-0.0350302\pi$
$420$	4.55212	−	3.87051i	0.222121	−	0.188862i
$421$	6.42595	−	21.4642i	0.313182	−	1.04610i	−0.646007	−	0.763332i	$-0.723562\pi$
$421$	6.42595	−	21.4642i	0.313182	−	1.04610i	0.959188	−	0.282768i	$-0.0912526\pi$
$422$	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	0.989155	−	0.146876i	$-0.0469217\pi$
$431$	7.62700	+	13.2103i	0.367379	+	0.636320i	−0.621776	+	0.783196i	$0.713588\pi$
$432$	3.02087	−	4.22781i	0.145341	−	0.203411i
$433$	8.83327	−	15.2997i	0.424500	−	0.735255i	−0.571874	−	0.820342i	$-0.693783\pi$
$433$	8.83327	−	15.2997i	0.424500	−	0.735255i	0.996374	+	0.0850866i	$0.0271167\pi$
$434$	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	0.660146	−	0.751137i	$-0.270494\pi$
$439$	23.6609	+	2.76556i	1.12927	+	0.131993i	0.469127	+	0.883131i	$0.344569\pi$
$440$	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	0.921858	−	0.387527i	$-0.126671\pi$
$443$	10.1320	+	10.7393i	0.481385	+	0.510239i	−0.440473	+	0.897766i	$0.645189\pi$
$444$	−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	0.426558	−	0.904460i	$-0.359726\pi$
$449$	−8.26585	−	6.93587i	−0.390090	−	0.327324i	−0.816648	+	0.577136i	$0.804170\pi$
$450$	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	−0.748368	−	0.663284i	$-0.769162\pi$
$457$	−1.75430	−	30.1202i	−0.0820627	−	1.40896i	0.666305	−	0.745679i	$-0.267875\pi$
$458$	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	−0.879611	−	0.475693i	$-0.842197\pi$
$461$	−16.9882	+	11.1733i	−0.791219	+	0.520393i	0.0883926	+	0.996086i	$0.471827\pi$
$462$	10.1769	+	5.02828i	0.473474	+	0.233937i
$463$	8.36162	−	19.3844i	0.388597	−	0.900870i	−0.605845	−	0.795583i	$-0.707165\pi$
$463$	8.36162	−	19.3844i	0.388597	−	0.900870i	0.994442	−	0.105287i	$-0.0335760\pi$
$464$	−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	0.689098	−	0.724668i	$-0.258007\pi$
$467$	16.2329	+	5.90831i	0.751171	+	0.273404i	0.0620726	+	0.998072i	$0.480229\pi$
$468$	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	−0.994723	−	0.102594i	$-0.967286\pi$
$479$	−8.46394	−	19.6216i	−0.386727	−	0.896534i	0.607996	−	0.793940i	$-0.291974\pi$
$480$	−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	0.879890	−	0.475177i	$-0.157616\pi$
$491$	−2.57840	−	8.61245i	−0.116361	−	0.388674i	−0.996252	+	0.0865028i	$0.972431\pi$
$492$	−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	0.520287	−	0.853992i	$-0.325825\pi$
$499$	−1.29086	−	0.849012i	−0.0577868	−	0.0380070i	−0.578074	+	0.815985i	$0.696195\pi$
$500$	−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	−0.521632	−	0.853171i	$-0.674676\pi$
$503$	−8.36142	+	3.04331i	−0.372817	+	0.135694i	0.148815	+	0.988865i	$0.452454\pi$
$504$	−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	−0.769146	−	0.639073i	$-0.779318\pi$
$509$	5.04282	−	11.6906i	0.223519	−	0.518176i	0.992665	+	0.120898i	$0.0385773\pi$
$510$	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	−0.310724	−	0.950500i	$-0.600571\pi$
$521$	13.0420	−	10.9435i	0.571380	−	0.479445i	0.882104	+	0.471056i	$0.156127\pi$
$522$	19.6543	+	2.03801i	0.860245	+	0.0892013i
$523$	−12.6277	−	10.5959i	−0.552172	−	0.463327i	0.323504	−	0.946227i	$-0.395139\pi$
$523$	−12.6277	−	10.5959i	−0.552172	−	0.463327i	−0.875676	+	0.482900i	$0.839584\pi$
$524$	−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	0.734490	+	0.678620i	$0.237422\pi$
$541$	22.2115	+	38.4714i	0.954947	+	1.65402i	0.220457	+	0.975397i	$0.429245\pi$
$542$	−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	−0.615513	−	0.788127i	$-0.711051\pi$
$547$	7.39145	−	9.92844i	0.316036	−	0.424509i	0.931548	+	0.363617i	$0.118458\pi$
$548$	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	−0.956112	−	0.293000i	$-0.905346\pi$
$557$	1.00425	−	5.69536i	0.0425512	−	0.241320i	0.998664	+	0.0516799i	$0.0164575\pi$
$558$	−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	0.794763	−	0.606920i	$-0.207595\pi$
$563$	−0.346453	−	0.465367i	−0.0146013	−	0.0196129i	−0.809364	+	0.587308i	$0.800188\pi$
$564$	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	0.304680	−	0.952455i	$-0.401451\pi$
$569$	−6.61617	−	3.32276i	−0.277364	−	0.139298i	−0.582044	+	0.813157i	$0.697747\pi$
$570$	−11.6013	−	26.4201i	−0.485924	−	1.10662i
$571$	−13.5093	−	18.1461i	−0.565346	−	0.759391i	0.423891	−	0.905713i	$-0.360664\pi$
$571$	−13.5093	−	18.1461i	−0.565346	−	0.759391i	−0.989237	+	0.146322i	$0.953256\pi$
$572$	−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	−0.900154	−	0.435572i	$-0.856546\pi$
$577$	2.27449	−	12.8993i	0.0946884	−	0.537004i	0.994842	−	0.101433i	$-0.0323427\pi$
$578$	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	−0.306386	−	0.951907i	$-0.599120\pi$
$587$	16.7999	−	22.5661i	0.693404	−	0.931403i	0.999790	+	0.0205040i	$0.00652710\pi$
$588$	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	0.856613	−	0.515960i	$-0.172565\pi$
$593$	−0.451178	−	0.781463i	−0.0185276	−	0.0320908i	−0.875141	+	0.483869i	$0.839231\pi$
$594$	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	−0.929510	−	0.368796i	$-0.879770\pi$
$599$	−12.4157	+	13.1599i	−0.507292	+	0.537698i	0.422218	+	0.906494i	$0.361252\pi$
$600$	−0.623106	+	0.0769494i	−0.0254382	+	0.00314145i
$601$	−33.5660	−	3.92330i	−1.36918	−	0.160035i	−0.600480	−	0.799640i	$-0.705024\pi$
$601$	−33.5660	−	3.92330i	−1.36918	−	0.160035i	−0.768704	+	0.639605i	$0.779098\pi$
$602$	−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	−0.726819	−	0.686829i	$-0.759002\pi$
$607$	−15.0269	+	7.54680i	−0.609924	+	0.306315i	0.116895	+	0.993144i	$0.462706\pi$
$608$	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	−0.427287	−	0.904116i	$-0.640530\pi$
$613$	9.62863	−	8.07938i	0.388897	−	0.326323i	0.816183	+	0.577793i	$0.196086\pi$
$614$	−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	0.279381	−	0.960180i	$-0.409871\pi$
$617$	19.1926	−	2.24329i	0.772663	−	0.0903114i	0.493283	+	0.869869i	$0.335797\pi$
$618$	−2.82300	+	0.688522i	−0.113558	+	0.0276964i
$619$	−0.922443	−	15.8377i	−0.0370761	−	0.636572i	−0.964748	−	0.263176i	$-0.915230\pi$
$619$	−0.922443	−	15.8377i	−0.0370761	−	0.636572i	0.927672	−	0.373397i	$-0.121807\pi$
$620$	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	−0.672343	−	0.740240i	$-0.734712\pi$
$631$	−17.8744	+	6.50576i	−0.711570	+	0.258990i	−0.0392270	+	0.999230i	$0.512490\pi$
$632$	−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	0.973409	−	0.229072i	$-0.0735693\pi$
$641$	3.51399	+	8.14633i	0.138794	+	0.321761i	−0.834615	+	0.550833i	$0.814310\pi$
$642$	−17.9106	−	11.6135i	−0.706876	−	0.458349i
$643$	12.9312	+	43.1932i	0.509957	+	1.70337i	0.693582	+	0.720378i	$0.256031\pi$
$643$	12.9312	+	43.1932i	0.509957	+	1.70337i	−0.183625	+	0.982996i	$0.558783\pi$
$644$	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	0.829161	+	0.559010i	$0.188819\pi$
$653$	11.3354	+	37.8629i	0.443588	+	1.48169i	−0.385572	+	0.922678i	$0.625996\pi$
$654$	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	−0.735913	−	0.677077i	$-0.763247\pi$
$659$	−27.9731	+	6.62974i	−1.08968	+	0.258258i	−0.353764	+	0.935335i	$0.615098\pi$
$660$	−8.92194	−	15.2233i	−0.347286	−	0.592567i
$661$	11.3890	+	7.49066i	0.442981	+	0.291353i	0.751338	−	0.659918i	$-0.229409\pi$
$661$	11.3890	+	7.49066i	0.442981	+	0.291353i	−0.308357	+	0.951271i	$0.599779\pi$
$662$	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	−0.00683660	−	0.999977i	$-0.502176\pi$
$673$	23.5724	−	15.5038i	0.908650	−	0.597629i	0.915487	+	0.402348i	$0.131806\pi$
$674$	−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	0.998223	−	0.0595952i	$-0.0189810\pi$
$677$	−0.00439596	−	0.0754757i	−0.000168951	−	0.00290077i	−0.998392	+	0.0566944i	$0.981944\pi$
$678$	−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	−0.875713	−	0.482831i	$-0.839608\pi$
$683$	−14.4335	+	12.1112i	−0.552283	+	0.463421i	0.323430	+	0.946252i	$0.395164\pi$
$684$	−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	0.964189	−	0.265218i	$-0.0854439\pi$
$691$	16.9118	+	17.9255i	0.643357	+	0.681918i	−0.320832	+	0.947136i	$0.603962\pi$
$692$	−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	−0.832749	−	0.553650i	$-0.813234\pi$
$701$	1.67068	−	2.89370i	0.0631007	−	0.109294i	0.895850	+	0.444357i	$0.146568\pi$
$702$	−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	−0.660447	−	0.750873i	$-0.729633\pi$
$709$	6.61150	−	8.88078i	0.248300	−	0.333525i	0.908747	+	0.417348i	$0.137040\pi$
$710$	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	0.649802	+	0.760104i	$0.274852\pi$
$719$	−5.92011	+	33.5746i	−0.220783	+	1.25212i	−0.870585	+	0.492019i	$0.836259\pi$
$720$	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	0.994261	−	0.106981i	$-0.0341185\pi$
$727$	40.5032	+	20.3415i	1.50218	+	0.754423i	0.507919	+	0.861405i	$0.330415\pi$
$728$	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	0.779889	−	0.625917i	$-0.215275\pi$
$733$	−1.17522	−	1.57859i	−0.0434077	−	0.0583067i	−0.823297	+	0.567611i	$0.807868\pi$
$734$	−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	−0.730069	−	0.683373i	$-0.760512\pi$
$739$	5.15688	−	29.2461i	0.189699	−	1.07584i	0.919768	−	0.392463i	$-0.128377\pi$
$740$	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	0.990220	+	0.139514i	$0.0445541\pi$
$743$	−0.258982	+	4.44654i	−0.00950111	+	0.163128i	−0.999721	+	0.0236135i	$0.992483\pi$
$744$	−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	0.443729	−	0.896161i	$-0.353655\pi$
$751$	12.0048	+	2.84520i	0.438063	+	0.103823i	−0.00566597	+	0.999984i	$0.501804\pi$
$752$	−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	−0.995060	−	0.0992801i	$-0.968346\pi$
$757$	−11.3233	+	19.6125i	−0.411551	+	0.712827i	0.583509	+	0.812107i	$0.301679\pi$
$758$	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	−0.845215	−	0.534426i	$-0.820528\pi$
$761$	−7.24273	+	7.67684i	−0.262549	+	0.278285i	0.582667	+	0.812711i	$0.302009\pi$
$762$	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	+	0.162748i
$768$	−1.62370	+	0.602989i	−0.0585903	+	0.0217585i
$769$	−36.5243	+	18.3432i	−1.31710	+	0.661473i	−0.961922	−	0.273326i	$-0.911876\pi$
$769$	−36.5243	+	18.3432i	−1.31710	+	0.661473i	−0.355179	+	0.934798i	$0.615580\pi$
$770$	−13.5622	+	6.81119i	−0.488747	+	0.245458i
$771$	14.9943	+	12.4161i	0.540007	+	0.447156i
$772$	−13.0400	−	13.8216i	−0.469319	−	0.497449i
$773$	24.8151	+	20.8223i	0.892537	+	0.748928i	0.968717	−	0.248167i	$-0.0798280\pi$
$773$	24.8151	+	20.8223i	0.892537	+	0.748928i	−0.0761803	+	0.997094i	$0.524272\pi$
$774$	−1.10227	+	0.745732i	−0.0396203	+	0.0268048i
$775$	0.497634	−	0.417565i	0.0178756	−	0.0149994i
$776$	1.39864	+	0.163477i	0.0502081	+	0.00586848i
$777$	7.12526	+	9.44182i	0.255617	+	0.338723i
$778$	10.8838	−	11.5361i	0.390202	−	0.413590i
$779$	56.2780	−	6.57795i	2.01637	−	0.235680i
$780$	−0.548761	+	1.87743i	−0.0196488	+	0.0672227i
$781$	1.98111	+	34.0144i	0.0708898	+	1.21713i
$782$	−9.57826	+	16.5900i	−0.342518	+	0.593258i
$783$	9.17303	−	32.9726i	0.327817	−	1.17834i
$784$	2.39036	+	4.14022i	0.0853699	+	0.147865i
$785$	−20.0967	+	13.2178i	−0.717281	+	0.471763i
$786$	−19.3409	+	12.9020i	−0.689866	+	0.460199i
$787$	4.22566	−	9.79619i	0.150629	−	0.349196i	−0.826149	−	0.563452i	$-0.809473\pi$
$787$	4.22566	−	9.79619i	0.150629	−	0.349196i	0.976778	+	0.214255i	$0.0687324\pi$
$788$	−22.0602	−	5.22836i	−0.785861	−	0.186252i
$789$	−0.653797	−	2.13315i	−0.0232758	−	0.0759421i
$790$	−23.2171	+	31.1859i	−0.826026	+	1.10955i
$791$	11.2791	+	4.10527i	0.401040	+	0.145967i
$792$	−9.99871	+	8.61443i	−0.355289	+	0.306100i
$793$	3.53416	−	1.28633i	0.125502	−	0.0456788i
$794$	−8.57548	+	28.6441i	−0.304333	+	1.01654i
$795$	6.01565	−	5.11489i	0.213353	−	0.181406i
$796$	0.219127	−	3.76227i	0.00776675	−	0.133350i
$797$	15.7578	+	10.3641i	0.558169	+	0.367114i	0.797030	−	0.603940i	$-0.206403\pi$
$797$	15.7578	+	10.3641i	0.558169	+	0.367114i	−0.238860	+	0.971054i	$0.576774\pi$
$798$	9.38598	+	16.0151i	0.332260	+	0.566928i
$799$	50.0611	−	11.8647i	1.77103	−	0.419743i
$800$	0.0629446	−	0.356976i	0.00222543	−	0.0126210i
$801$	−8.24981	+	4.27873i	−0.291493	+	0.151181i
$802$	−1.62298	−	9.20438i	−0.0573095	−	0.325018i
$803$	−17.5543	−	40.6954i	−0.619477	−	1.43611i
$804$	−0.341420	+	6.60288i	−0.0120410	+	0.232866i
$805$	2.88138	+	9.62449i	0.101555	+	0.339219i
$806$	−0.521891	−	0.701021i	−0.0183828	−	0.0246924i
$807$	−28.8419	−	3.18078i	−1.01528	−	0.111969i
$808$	−8.98134	−	4.51060i	−0.315963	−	0.158682i
$809$	42.8188			1.50543			0.752715	−	0.658347i	$-0.228744\pi$
$809$	42.8188			1.50543			0.752715	+	0.658347i	$0.228744\pi$
$810$	−8.75074	−	18.9152i	−0.307470	−	0.664613i
$811$	12.5236			0.439761			0.219881	−	0.975527i	$-0.429433\pi$
$811$	12.5236			0.439761			0.219881	+	0.975527i	$0.429433\pi$
$812$	8.76848	+	4.40370i	0.307713	+	0.154540i
$813$	19.4312	+	44.2516i	0.681483	+	1.55197i
$814$	12.0431	+	16.1767i	0.422111	+	0.566994i
$815$	−4.38777	−	14.6562i	−0.153697	−	0.513384i
$816$	9.55956	+	6.19857i	0.334652	+	0.216993i
$817$	1.26404	+	2.93039i	0.0442233	+	0.102521i
$818$	−0.110308	−	0.625588i	−0.00385683	−	0.0218732i
$819$	−2.16125	+	0.281208i	−0.0755200	+	0.00982621i
$820$	3.16709	−	17.9615i	0.110600	−	0.627242i
$821$	21.5050	−	5.09678i	0.750530	−	0.177879i	0.162490	−	0.986710i	$-0.448048\pi$
$821$	21.5050	−	5.09678i	0.750530	−	0.177879i	0.588041	+	0.808831i	$0.299899\pi$
$822$	4.53899	−	7.98141i	0.158315	−	0.278384i
$823$	−0.0154692	−	0.0101742i	−0.000539222	−	0.000354652i	0.549239	−	0.835665i	$-0.314918\pi$
$823$	−0.0154692	−	0.0101742i	−0.000539222	−	0.000354652i	−0.549779	+	0.835310i	$0.685288\pi$
$824$	0.0975460	−	1.67480i	0.00339818	−	0.0583444i
$825$	−0.497336	−	2.71689i	−0.0173150	−	0.0945901i
$826$	5.42908	−	18.1344i	0.188902	−	0.630976i
$827$	−5.05612	+	1.84028i	−0.175819	+	0.0639927i	−0.428429	−	0.903575i	$-0.640933\pi$
$827$	−5.05612	+	1.84028i	−0.175819	+	0.0639927i	0.252611	+	0.967568i	$0.418711\pi$
$828$	4.46659	+	7.50866i	0.155225	+	0.260944i
$829$	−21.3345	−	7.76512i	−0.740978	−	0.269694i	−0.0561737	−	0.998421i	$-0.517890\pi$
$829$	−21.3345	−	7.76512i	−0.740978	−	0.269694i	−0.684804	+	0.728727i	$0.740112\pi$
$830$	7.20071	−	9.67224i	0.249940	−	0.335728i
$831$	3.71825	−	3.99292i	0.128985	−	0.138513i
$832$	−0.474520	−	0.112463i	−0.0164510	−	0.00389896i
$833$	12.4556	−	28.8753i	0.431561	−	1.00047i
$834$	2.02097	+	31.1955i	0.0699804	+	1.08021i
$835$	−13.3792	+	8.79964i	−0.463007	+	0.304524i
$836$	15.8244	+	27.4087i	0.547300	+	0.947951i
$837$	9.10139	+	1.97001i	0.314590	+	0.0680935i
$838$	3.42733	−	5.93630i	0.118395	−	0.205066i
$839$	1.28480	+	22.0592i	0.0443564	+	0.761569i	0.945012	+	0.327036i	$0.106050\pi$
$839$	1.28480	+	22.0592i	0.0443564	+	0.761569i	−0.900656	+	0.434534i	$0.856913\pi$
$840$	5.80501	−	1.41582i	0.200292	−	0.0488506i
$841$	−14.2855	+	1.66974i	−0.492605	+	0.0575772i
$842$	15.3755	−	16.2971i	0.529876	−	0.561636i
$843$	−1.89599	+	0.234142i	−0.0653014	+	0.00806428i
$844$	13.0984	+	1.53099i	0.450866	+	0.0526987i
$845$	22.6392	−	18.9966i	0.778814	−	0.653502i
$846$	6.43602	−	22.5639i	0.221275	−	0.775763i
$847$	−9.53313	−	7.99924i	−0.327562	−	0.274857i
$848$	1.35099	+	1.43197i	0.0463932	+	0.0491739i
$849$	9.14233	−	53.9001i	0.313764	−	1.84985i
$850$	−2.13077	+	1.07011i	−0.0730847	+	0.0367045i
$851$	11.9304	−	5.99167i	0.408968	−	0.205392i
$852$	2.24329	−	13.2257i	0.0768539	−	0.453105i
$853$	−5.27828	−	5.59465i	−0.180725	−	0.191557i	0.630678	−	0.776045i	$-0.282777\pi$
$853$	−5.27828	−	5.59465i	−0.180725	−	0.191557i	−0.811403	+	0.584488i	$0.801295\pi$
$854$	−8.80114	−	7.38503i	−0.301169	−	0.252711i
$855$	−48.4768	+	12.1585i	−1.65787	+	0.415814i
$856$	9.44095	−	7.92190i	0.322685	−	0.270765i
$857$	−17.3892	−	2.03251i	−0.594004	−	0.0694291i	−0.186221	−	0.982508i	$-0.559624\pi$
$857$	−17.3892	−	2.03251i	−0.594004	−	0.0694291i	−0.407783	+	0.913079i	$0.633698\pi$
$858$	−3.68788	+	0.455428i	−0.125902	+	0.0155481i
$859$	−5.20412	+	5.51605i	−0.177562	+	0.188205i	−0.810042	−	0.586372i	$-0.800556\pi$
$859$	−5.20412	+	5.51605i	−0.177562	+	0.188205i	0.632480	+	0.774577i	$0.282037\pi$
$860$	1.02033	−	0.119259i	0.0347928	−	0.00406670i
$861$	19.7437	−	4.81542i	0.672862	−	0.164109i
$862$	0.886941	+	15.2282i	0.0302093	+	0.518674i
$863$	13.9025	−	24.0798i	0.473245	−	0.819685i	−0.526286	−	0.850308i	$-0.676416\pi$
$863$	13.9025	−	24.0798i	0.473245	−	0.819685i	0.999531	+	0.0306232i	$0.00974918\pi$
$864$	4.59698	−	2.42235i	0.156392	−	0.0824099i
$865$	−14.6689	−	25.4073i	−0.498758	−	0.863875i
$866$	14.7602	−	9.70792i	0.501571	−	0.329888i
$867$	−2.94147	−	45.4043i	−0.0998975	−	1.54201i
$868$	−1.05745	+	2.45143i	−0.0358920	+	0.0832071i
$869$	−71.8702	−	17.0335i	−2.43803	−	0.577824i
$870$	−18.0036	+	19.3336i	−0.610381	+	0.655470i
$871$	−1.11164	+	1.49319i	−0.0376664	+	0.0505948i
$872$	17.9399	+	6.52959i	0.607522	+	0.221120i
$873$	−4.22411	+	0.0550507i	−0.142965	+	0.00186318i
$874$	19.6875	−	7.16567i	0.665940	−	0.242382i
$875$	4.58838	−	15.3263i	0.155116	−	0.518122i
$876$	3.14196	+	17.1642i	0.106157	+	0.579924i
$877$	−2.12328	+	36.4552i	−0.0716979	+	1.23101i	0.750138	+	0.661282i	$0.229987\pi$
$877$	−2.12328	+	36.4552i	−0.0716979	+	1.23101i	−0.821836	+	0.569725i	$0.807050\pi$
$878$	19.9030	+	13.0904i	0.671693	+	0.441779i
$879$	−24.3200	+	42.7647i	−0.820295	+	1.44242i
$880$	9.91281	−	2.34938i	0.334161	−	0.0791976i
$881$	6.68482	−	37.9115i	0.225217	−	1.27727i	−0.637052	−	0.770821i	$-0.719846\pi$
$881$	6.68482	−	37.9115i	0.225217	−	1.27727i	0.862269	−	0.506450i	$-0.169043\pi$
$882$	−8.71372	−	11.3916i	−0.293406	−	0.383574i
$883$	1.47794	+	8.38181i	0.0497366	+	0.282070i	0.999525	−	0.0308231i	$-0.00981285\pi$
$883$	1.47794	+	8.38181i	0.0497366	+	0.282070i	−0.949788	+	0.312893i	$0.898702\pi$
$884$	1.27055	+	2.94548i	0.0427334	+	0.0990671i
$885$	42.7629	+	27.7281i	1.43746	+	0.932071i
$886$	4.23449	+	14.1442i	0.142261	+	0.475184i
$887$	23.2390	+	31.2154i	0.780289	+	1.04811i	0.997407	+	0.0719647i	$0.0229269\pi$
$887$	23.2390	+	31.2154i	0.780289	+	1.04811i	−0.217118	+	0.976145i	$0.569666\pi$
$888$	−3.19237	−	7.27013i	−0.107129	−	0.243970i
$889$	−25.0790	−	12.5951i	−0.841123	−	0.422428i
$890$	7.17357			0.240459
$891$	26.4109	−	29.4976i	0.884800	−	0.988205i
$892$	−7.10621			−0.237933
$893$	−50.2822	−	25.2527i	−1.68263	−	0.845049i
$894$	−30.4947	−	3.36306i	−1.01990	−	0.112478i
$895$	−1.40016	−	1.88074i	−0.0468023	−	0.0628663i
$896$	0.427259	+	1.42714i	0.0142737	+	0.0476775i
$897$	−0.127024	+	2.45657i	−0.00424121	+	0.0820226i
$898$	−4.27382	−	9.90783i	−0.142619	−	0.330629i
$899$	−2.04973	−	11.6246i	−0.0683624	−	0.387703i
$900$	−0.0490772	+	1.08634i	−0.00163591	+	0.0362114i
$901$	2.24871	−	12.7531i	0.0749155	−	0.424867i
$902$	33.7149	−	7.99058i	1.12258	−	0.266057i
$903$	0.578768	+	0.987539i	0.0192602	+	0.0328632i
$904$	−6.73169	−	4.42750i	−0.223893	−	0.147256i
$905$	−2.10829	+	36.1979i	−0.0700818	+	1.20326i
$906$	−3.15671	+	2.68404i	−0.104875	+	0.0891712i
$907$	0.490184	−	1.63733i	0.0162763	−	0.0543666i	−0.949466	−	0.313871i	$-0.898374\pi$
$907$	0.490184	−	1.63733i	0.0162763	−	0.0543666i	0.965742	+	0.259504i	$0.0835592\pi$
$908$	2.10557	−	0.766364i	0.0698757	−	0.0254327i
$909$	28.4648	+	9.94220i	0.944117	+	0.329762i
$910$	1.58087	+	0.575391i	0.0524055	+	0.0190740i
$911$	−9.37413	+	12.5916i	−0.310579	+	0.417180i	−0.929816	−	0.368024i	$-0.880034\pi$
$911$	−9.37413	+	12.5916i	−0.310579	+	0.417180i	0.619238	+	0.785204i	$0.287442\pi$
$912$	−3.65144	−	11.9136i	−0.120911	−	0.394497i
$913$	22.2903	+	5.28291i	0.737703	+	0.174839i
$914$	11.9502	−	27.7037i	0.395278	−	0.916357i
$915$	25.7328	−	17.1660i	0.850701	−	0.567490i
$916$	12.9860	−	8.54101i	0.429069	−	0.282203i
$917$	9.99831	+	17.3176i	0.330173	+	0.571877i
$918$	−30.8383	−	14.7400i	−1.01782	−	0.486491i
$919$	−11.2459	+	19.4785i	−0.370969	+	0.642537i	−0.989715	−	0.143054i	$-0.954308\pi$
$919$	−11.2459	+	19.4785i	−0.370969	+	0.642537i	0.618746	+	0.785591i	$0.287641\pi$
$920$	−0.392122	−	6.73248i	−0.0129279	−	0.221963i
$921$	−14.5089	+	49.6379i	−0.478084	+	1.63563i
$922$	−20.1958	+	2.36055i	−0.665112	+	0.0777405i
$923$	2.59189	−	2.74724i	0.0853130	−	0.0904265i
$924$	6.83776	+	9.06084i	0.224946	+	0.298080i
$925$	1.65048	+	0.192913i	0.0542674	+	0.00634294i
$926$	16.1719	−	13.5699i	0.531442	−	0.445933i
$927$	0.358088	+	5.02016i	0.0117612	+	0.164884i
$928$	−5.04560	−	4.23376i	−0.165630	−	0.138980i
$929$	37.6794	+	39.9379i	1.23622	+	1.31032i	0.934084	+	0.357055i	$0.116219\pi$
$929$	37.6794	+	39.9379i	1.23622	+	1.31032i	0.302138	+	0.953264i	$0.402300\pi$
$930$	−5.53637	−	4.58442i	−0.181545	−	0.150329i
$931$	−30.7347	+	15.4356i	−1.00729	+	0.505880i
$932$	7.05007	−	3.54068i	0.230933	−	0.115979i
$933$	2.95788	−	1.09846i	0.0968365	−	0.0359619i
$934$	11.8546	+	12.5652i	0.387896	+	0.411146i
$935$	−51.3342	−	43.0745i	−1.67881	−	1.40869i
$936$	1.45519	+	0.150893i	0.0475645	+	0.00493209i
$937$	−7.52251	+	6.31214i	−0.245750	+	0.206209i	−0.757340	−	0.653021i	$-0.773501\pi$
$937$	−7.52251	+	6.31214i	−0.245750	+	0.206209i	0.511590	+	0.859230i	$0.329057\pi$
$938$	5.64823	+	0.660184i	0.184421	+	0.0215558i
$939$	−2.91734	+	6.88617i	−0.0952037	+	0.224722i
$940$	−12.4291	+	13.1740i	−0.405391	+	0.429689i
$941$	−22.4201	+	2.62054i	−0.730875	+	0.0854271i	−0.473387	−	0.880854i	$-0.656969\pi$
$941$	−22.4201	+	2.62054i	−0.730875	+	0.0854271i	−0.257488	+	0.966281i	$0.582895\pi$
$942$	12.4314	+	13.0056i	0.405036	+	0.423747i
$943$	−1.33366	−	22.8981i	−0.0434301	−	0.745665i
$944$	−6.35339	+	11.0044i	−0.206785	+	0.358162i
$945$	−16.7214	+	6.45896i	−0.543948	+	0.210110i
$946$	0.975784	+	1.69011i	0.0317255	+	0.0549501i
$947$	−36.6967	+	24.1358i	−1.19248	+	0.784308i	−0.981177	−	0.193112i	$-0.938142\pi$
$947$	−36.6967	+	24.1358i	−1.19248	+	0.784308i	−0.211305	+	0.977420i	$0.567771\pi$
$948$	26.0714	+	12.8815i	0.846759	+	0.418372i
$949$	−1.94591	+	4.51113i	−0.0631670	+	0.146438i
$950$	2.53745	+	0.601388i	0.0823259	+	0.0195116i
$951$	55.0575	+	12.6706i	1.78536	+	0.410871i
$952$	5.85175	−	7.86026i	0.189656	−	0.254753i
$953$	−26.3447	−	9.58870i	−0.853389	−	0.310608i	−0.121968	−	0.992534i	$-0.538921\pi$
$953$	−26.3447	−	9.58870i	−0.853389	−	0.310608i	−0.731421	+	0.681926i	$0.761143\pi$
$954$	−4.57338	−	3.73705i	−0.148068	−	0.120991i
$955$	9.63427	−	3.50659i	0.311758	−	0.113471i
$956$	−1.47864	+	4.93901i	−0.0478227	+	0.159739i
$957$	−47.2722	−	16.8577i	−1.52809	−	0.544931i
$958$	1.24251	−	21.3331i	0.0401438	−	0.689242i
$959$	−6.59802	−	4.33959i	−0.213061	−	0.140133i
$960$	−4.01083	+	0.0261345i	−0.129449	+	0.000843486i
$961$	−27.0392	+	6.40842i	−0.872234	+	0.206723i
$962$	0.388204	−	2.20161i	0.0125162	−	0.0709829i
$963$	−25.0197	+	27.2214i	−0.806249	+	0.877199i
$964$	−0.361018	−	2.04743i	−0.0116276	−	0.0659434i
$965$	−17.4287	−	40.4043i	−0.561050	−	1.30066i
$966$	6.69300	−	3.41614i	0.215344	−	0.109913i
$967$	4.56167	+	15.2370i	0.146693	+	0.489990i	0.999479	−	0.0322708i	$-0.0102739\pi$
$967$	4.56167	+	15.2370i	0.146693	+	0.489990i	−0.852786	+	0.522261i	$0.825089\pi$
$968$	4.98844	+	6.70063i	0.160334	+	0.215366i
$969$	−48.5165	+	66.0634i	−1.55858	+	2.12226i
$970$	2.91402	+	1.46348i	0.0935637	+	0.0469894i
$971$	15.4071			0.494438			0.247219	−	0.968960i	$-0.420483\pi$
$971$	15.4071			0.494438			0.247219	+	0.968960i	$0.420483\pi$
$972$	−12.7380	+	8.98569i	−0.408572	+	0.288216i
$973$	26.8873			0.861969
$974$	−10.0079	−	5.02617i	−0.320674	−	0.161049i
$975$	−0.181231	+	0.246776i	−0.00580404	+	0.00790317i
$976$	4.60541	+	6.18613i	0.147415	+	0.198013i
$977$	−8.32046	−	27.7923i	−0.266195	−	0.889154i	−0.981682	−	0.190527i	$-0.938980\pi$
$977$	−8.32046	−	27.7923i	−0.266195	−	0.889154i	0.715487	−	0.698626i	$-0.246205\pi$
$978$	−10.1921	+	5.20211i	−0.325908	+	0.166345i
$979$	5.39779	+	12.5135i	0.172514	+	0.399933i
$980$	1.92241	+	10.9025i	0.0614091	+	0.348268i
$981$	−55.8973	−	12.4809i	−1.78466	−	0.398484i
$982$	1.56112	−	8.85355i	0.0498173	−	0.282528i
$983$	−28.8192	+	6.83027i	−0.919189	+	0.217852i	−0.662865	−	0.748739i	$-0.730660\pi$
$983$	−28.8192	+	6.83027i	−0.919189	+	0.217852i	−0.256324	+	0.966591i	$0.582511\pi$
$984$	−13.6414	+	0.0888870i	−0.434872	+	0.00283361i
$985$	−43.8631	−	28.8492i	−1.39759	−	0.919212i
$986$	−2.51918	+	43.2526i	−0.0802270	+	1.37744i
$987$	−19.0086	−	6.77864i	−0.605051	−	0.215766i
$988$	1.00620	−	3.36093i	0.0320114	−	0.106926i
$989$	1.21399	−	0.441857i	0.0386027	−	0.0140502i
$990$	−28.5805	+	10.8263i	−0.908347	+	0.344081i
$991$	−34.5253	−	12.5662i	−1.09673	−	0.399178i	−0.270622	−	0.962686i	$-0.587229\pi$
$991$	−34.5253	−	12.5662i	−1.09673	−	0.399178i	−0.826111	+	0.563508i	$0.809452\pi$
$992$	1.07018	−	1.43751i	0.0339784	−	0.0456408i
$993$	−16.1424	−	3.71490i	−0.512264	−	0.117889i
$994$	−11.2268	−	2.66081i	−0.356093	−	0.0843956i
$995$	3.45661	−	8.01332i	0.109582	−	0.254039i
$996$	−8.08597	−	3.99516i	−0.256214	−	0.126592i
$997$	30.2226	−	19.8777i	0.957158	−	0.629533i	0.0281546	−	0.999604i	$-0.491037\pi$
$997$	30.2226	−	19.8777i	0.957158	−	0.629533i	0.929004	+	0.370071i	$0.120667\pi$
$998$	−0.772519	−	1.33804i	−0.0244537	−	0.0423550i
$999$	12.3112	+	20.3924i	0.389508	+	0.645186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.13.4	✓	90
3.2	odd	2		486.2.g.b.253.2		90
81.25	even	27	inner	162.2.g.b.25.4	yes	90
81.56	odd	54		486.2.g.b.73.2		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.4	✓	90	1.1	even	1	trivial
162.2.g.b.25.4	yes	90	81.25	even	27	inner
486.2.g.b.73.2		90	81.56	odd	54
486.2.g.b.253.2		90	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
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

Introduction

L-functions

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