LMFDB - Embedded newform 162.2.g.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	162.25
Dual form			162.2.g.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 - 0.448799i) q^{2} +(-1.57770 + 0.714739i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.891212 - 2.97686i) q^{5} +(-1.08911 + 1.34679i) q^{6} +(0.275210 - 0.638009i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.97830 - 2.25529i) q^{9} +O(q^{10})$	\(q+(0.893633 - 0.448799i) q^{2} +(-1.57770 + 0.714739i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.891212 - 2.97686i) q^{5} +(-1.08911 + 1.34679i) q^{6} +(0.275210 - 0.638009i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.97830 - 2.25529i) q^{9} +(-0.539594 - 3.06019i) q^{10} +(5.37847 + 1.27472i) q^{11} +(-0.368831 + 1.69232i) q^{12} +(-2.73022 + 1.79570i) q^{13} +(-0.0404011 - 0.693660i) q^{14} +(0.721605 + 5.33358i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(-4.35745 - 1.58598i) q^{17} +(0.755699 - 2.90326i) q^{18} +(-2.23534 + 0.813599i) q^{19} +(-1.85561 - 2.49252i) q^{20} +(0.0218094 + 1.20329i) q^{21} +(5.37847 - 1.27472i) q^{22} +(2.79341 + 6.47585i) q^{23} +(0.429915 + 1.67785i) q^{24} +(-3.88998 - 2.55848i) q^{25} +(-1.63391 + 2.83001i) q^{26} +(-1.50922 + 4.97215i) q^{27} +(-0.347418 - 0.601745i) q^{28} +(0.0802101 - 1.37715i) q^{29} +(3.03856 + 4.44241i) q^{30} +(-3.53161 - 0.412786i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-9.39673 + 1.83307i) q^{33} +(-4.60574 + 0.538334i) q^{34} +(-1.65399 - 1.38786i) q^{35} +(-0.627664 - 2.93360i) q^{36} +(-0.935772 + 0.785206i) q^{37} +(-1.63243 + 1.73028i) q^{38} +(3.02403 - 4.78447i) q^{39} +(-2.77687 - 1.39460i) q^{40} +(10.1420 + 5.09352i) q^{41} +(0.559527 + 1.06551i) q^{42} +(-6.37841 + 6.76072i) q^{43} +(4.23428 - 3.55299i) q^{44} +(-4.95059 - 7.89905i) q^{45} +(5.40264 + 4.53335i) q^{46} +(10.4074 - 1.21645i) q^{47} +(1.13720 + 1.30643i) q^{48} +(4.47238 + 4.74044i) q^{49} +(-4.62445 - 0.540521i) q^{50} +(8.00832 - 0.612227i) q^{51} +(-0.190007 + 3.26229i) q^{52} +(-2.11764 - 3.66786i) q^{53} +(0.882803 + 5.12061i) q^{54} +(8.58802 - 14.8749i) q^{55} +(-0.580527 - 0.381818i) q^{56} +(2.94520 - 2.88130i) q^{57} +(-0.546388 - 1.26667i) q^{58} +(-5.60397 + 1.32817i) q^{59} +(4.70910 + 2.60618i) q^{60} +(1.03387 + 1.38873i) q^{61} +(-3.34122 + 1.21611i) q^{62} +(-0.894449 - 1.88285i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(2.91232 + 9.72783i) q^{65} +(-7.57454 + 5.85533i) q^{66} +(-0.0594932 - 1.02146i) q^{67} +(-3.87424 + 2.54813i) q^{68} +(-9.03571 - 8.22041i) q^{69} +(-2.10093 - 0.497930i) q^{70} +(-2.04677 - 11.6078i) q^{71} +(-1.87750 - 2.33987i) q^{72} +(1.49312 - 8.46788i) q^{73} +(-0.483836 + 1.12166i) q^{74} +(7.96587 + 1.25620i) q^{75} +(-0.682248 + 2.27887i) q^{76} +(2.29349 - 3.08070i) q^{77} +(0.555105 - 5.63274i) q^{78} +(-7.86088 + 3.94788i) q^{79} -3.10740 q^{80} +(-1.17268 - 8.92327i) q^{81} +11.3492 q^{82} +(-8.11371 + 4.07486i) q^{83} +(0.978213 + 0.701063i) q^{84} +(-8.60465 + 11.5580i) q^{85} +(-2.66575 + 8.90423i) q^{86} +(0.857758 + 2.23007i) q^{87} +(2.18932 - 5.07541i) q^{88} +(-0.642803 + 3.64552i) q^{89} +(-7.96910 - 4.83703i) q^{90} +(0.394285 + 2.23610i) q^{91} +(6.86253 + 1.62645i) q^{92} +(5.86687 - 1.87293i) q^{93} +(8.75447 - 5.75790i) q^{94} +(0.429800 + 7.37939i) q^{95} +(1.60257 + 0.657097i) q^{96} +(0.260981 + 0.871736i) q^{97} +(6.12417 + 2.22901i) q^{98} +(13.5151 - 9.60824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$	−1.57770	+	0.714739i	−0.910888	+	0.412654i
$3$	−1.57770	+	0.714739i	−0.910888	+	0.412654i
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	0.891212	−	2.97686i	0.398562	−	1.33129i	−0.489675	−	0.871905i	$-0.662884\pi$
$5$	0.891212	−	2.97686i	0.398562	−	1.33129i	0.888237	−	0.459385i	$-0.151930\pi$
$6$	−1.08911	+	1.34679i	−0.444629	+	0.549823i
$7$	0.275210	−	0.638009i	0.104020	−	0.241145i	−0.858256	−	0.513223i	$-0.828452\pi$
$7$	0.275210	−	0.638009i	0.104020	−	0.241145i	0.962275	+	0.272078i	$0.0877108\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$	1.97830	−	2.25529i	0.659433	−	0.751764i
$10$	−0.539594	−	3.06019i	−0.170635	−	0.967717i
$11$	5.37847	+	1.27472i	1.62167	+	0.384343i	0.938325	−	0.345753i	$-0.112377\pi$
$11$	5.37847	+	1.27472i	1.62167	+	0.384343i	0.683345	+	0.730096i	$0.260525\pi$
$12$	−0.368831	+	1.69232i	−0.106472	+	0.488532i
$13$	−2.73022	+	1.79570i	−0.757227	+	0.498036i	−0.868461	−	0.495758i	$-0.834890\pi$
$13$	−2.73022	+	1.79570i	−0.757227	+	0.498036i	0.111233	+	0.993794i	$0.464520\pi$
$14$	−0.0404011	−	0.693660i	−0.0107976	−	0.185388i
$15$	0.721605	+	5.33358i	0.186318	+	1.37712i
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	−4.35745	−	1.58598i	−1.05684	−	0.384657i	−0.245597	−	0.969372i	$-0.578984\pi$
$17$	−4.35745	−	1.58598i	−1.05684	−	0.384657i	−0.811239	+	0.584715i	$0.801206\pi$
$18$	0.755699	−	2.90326i	0.178120	−	0.684305i
$19$	−2.23534	+	0.813599i	−0.512823	+	0.186652i	−0.585453	−	0.810707i	$-0.699083\pi$
$19$	−2.23534	+	0.813599i	−0.512823	+	0.186652i	0.0726295	+	0.997359i	$0.476861\pi$
$20$	−1.85561	−	2.49252i	−0.414927	−	0.557344i
$21$	0.0218094	+	1.20329i	0.00475921	+	0.262580i
$22$	5.37847	−	1.27472i	1.14669	−	0.271771i
$23$	2.79341	+	6.47585i	0.582466	+	1.35031i	0.913558	+	0.406709i	$0.133324\pi$
$23$	2.79341	+	6.47585i	0.582466	+	1.35031i	−0.331092	+	0.943598i	$0.607417\pi$
$24$	0.429915	+	1.67785i	0.0877560	+	0.342489i
$25$	−3.88998	−	2.55848i	−0.777995	−	0.511695i
$26$	−1.63391	+	2.83001i	−0.320436	+	0.555011i
$27$	−1.50922	+	4.97215i	−0.290450	+	0.956890i
$28$	−0.347418	−	0.601745i	−0.0656558	−	0.113719i
$29$	0.0802101	−	1.37715i	0.0148946	−	0.255731i	−0.982638	−	0.185532i	$-0.940599\pi$
$29$	0.0802101	−	1.37715i	0.0148946	−	0.255731i	0.997533	−	0.0701997i	$-0.0223637\pi$
$30$	3.03856	+	4.44241i	0.554762	+	0.811069i
$31$	−3.53161	−	0.412786i	−0.634296	−	0.0741386i	−0.207133	−	0.978313i	$-0.566413\pi$
$31$	−3.53161	−	0.412786i	−0.634296	−	0.0741386i	−0.427164	+	0.904174i	$0.640487\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$	−9.39673	+	1.83307i	−1.63576	+	0.319096i
$34$	−4.60574	+	0.538334i	−0.789879	+	0.0923236i
$35$	−1.65399	−	1.38786i	−0.279576	−	0.234592i
$36$	−0.627664	−	2.93360i	−0.104611	−	0.488934i
$37$	−0.935772	+	0.785206i	−0.153840	+	0.129087i	−0.716459	−	0.697629i	$-0.754238\pi$
$37$	−0.935772	+	0.785206i	−0.153840	+	0.129087i	0.562619	+	0.826716i	$0.309794\pi$
$38$	−1.63243	+	1.73028i	−0.264816	+	0.280688i
$39$	3.02403	−	4.78447i	0.484232	−	0.766128i
$40$	−2.77687	−	1.39460i	−0.439062	−	0.220505i
$41$	10.1420	+	5.09352i	1.58392	+	0.795474i	0.999868	−	0.0162419i	$-0.00517017\pi$
$41$	10.1420	+	5.09352i	1.58392	+	0.795474i	0.584052	+	0.811716i	$0.301466\pi$
$42$	0.559527	+	1.06551i	0.0863368	+	0.164412i
$43$	−6.37841	+	6.76072i	−0.972699	+	1.03100i	0.0268093	+	0.999641i	$0.491465\pi$
$43$	−6.37841	+	6.76072i	−0.972699	+	1.03100i	−0.999508	+	0.0313600i	$0.990016\pi$
$44$	4.23428	−	3.55299i	0.638342	−	0.535633i
$45$	−4.95059	−	7.89905i	−0.737991	−	1.17752i
$46$	5.40264	+	4.53335i	0.796575	+	0.668406i
$47$	10.4074	−	1.21645i	1.51808	−	0.177438i	0.684162	−	0.729330i	$-0.260168\pi$
$47$	10.4074	−	1.21645i	1.51808	−	0.177438i	0.833916	+	0.551892i	$0.186094\pi$
$48$	1.13720	+	1.30643i	0.164141	+	0.188568i
$49$	4.47238	+	4.74044i	0.638911	+	0.677206i
$50$	−4.62445	−	0.540521i	−0.653996	−	0.0764412i
$51$	8.00832	−	0.612227i	1.12139	−	0.0857289i
$52$	−0.190007	+	3.26229i	−0.0263492	+	0.452398i
$53$	−2.11764	−	3.66786i	−0.290880	−	0.503819i	0.683138	−	0.730289i	$-0.260615\pi$
$53$	−2.11764	−	3.66786i	−0.290880	−	0.503819i	−0.974018	+	0.226470i	$0.927281\pi$
$54$	0.882803	+	5.12061i	0.120134	+	0.696827i
$55$	8.58802	−	14.8749i	1.15801	−	2.00573i
$56$	−0.580527	−	0.381818i	−0.0775762	−	0.0510226i
$57$	2.94520	−	2.88130i	0.390101	−	0.381638i
$58$	−0.546388	−	1.26667i	−0.0717442	−	0.166322i
$59$	−5.60397	+	1.32817i	−0.729575	+	0.172913i	−0.578584	−	0.815623i	$-0.696395\pi$
$59$	−5.60397	+	1.32817i	−0.729575	+	0.172913i	−0.150991	+	0.988535i	$0.548246\pi$
$60$	4.70910	+	2.60618i	0.607942	+	0.336456i
$61$	1.03387	+	1.38873i	0.132374	+	0.177809i	0.863368	−	0.504575i	$-0.168351\pi$
$61$	1.03387	+	1.38873i	0.132374	+	0.177809i	−0.730994	+	0.682384i	$0.760943\pi$
$62$	−3.34122	+	1.21611i	−0.424336	+	0.154446i
$63$	−0.894449	−	1.88285i	−0.112690	−	0.237217i
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	2.91232	+	9.72783i	0.361229	+	1.20659i
$66$	−7.57454	+	5.85533i	−0.932362	+	0.720742i
$67$	−0.0594932	−	1.02146i	−0.00726825	−	0.124791i	−0.999990	−	0.00436439i	$-0.998611\pi$
$67$	−0.0594932	−	1.02146i	−0.00726825	−	0.124791i	0.992722	−	0.120427i	$-0.0384263\pi$
$68$	−3.87424	+	2.54813i	−0.469821	+	0.309006i
$69$	−9.03571	−	8.22041i	−1.08777	−	0.989621i
$70$	−2.10093	−	0.497930i	−0.251109	−	0.0595140i
$71$	−2.04677	−	11.6078i	−0.242907	−	1.37759i	−0.825304	−	0.564688i	$-0.808996\pi$
$71$	−2.04677	−	11.6078i	−0.242907	−	1.37759i	0.582397	−	0.812904i	$-0.302115\pi$
$72$	−1.87750	−	2.33987i	−0.221266	−	0.275756i
$73$	1.49312	−	8.46788i	0.174756	−	0.991090i	−0.763669	−	0.645608i	$-0.776604\pi$
$73$	1.49312	−	8.46788i	0.174756	−	0.991090i	0.938425	−	0.345482i	$-0.112285\pi$
$74$	−0.483836	+	1.12166i	−0.0562448	+	0.130390i
$75$	7.96587	+	1.25620i	0.919819	+	0.145054i
$76$	−0.682248	+	2.27887i	−0.0782593	+	0.261404i
$77$	2.29349	−	3.08070i	0.261368	−	0.351078i
$78$	0.555105	−	5.63274i	0.0628532	−	0.637782i
$79$	−7.86088	+	3.94788i	−0.884418	+	0.444171i	−0.832207	−	0.554465i	$-0.812923\pi$
$79$	−7.86088	+	3.94788i	−0.884418	+	0.444171i	−0.0522107	+	0.998636i	$0.516627\pi$
$80$	−3.10740			−0.347418
$81$	−1.17268	−	8.92327i	−0.130297	−	0.991475i
$82$	11.3492			1.25331
$83$	−8.11371	+	4.07486i	−0.890596	+	0.447274i	−0.834409	−	0.551146i	$-0.814191\pi$
$83$	−8.11371	+	4.07486i	−0.890596	+	0.447274i	−0.0561870	+	0.998420i	$0.517894\pi$
$84$	0.978213	+	0.701063i	0.106732	+	0.0764922i
$85$	−8.60465	+	11.5580i	−0.933305	+	1.25365i
$86$	−2.66575	+	8.90423i	−0.287455	+	0.960168i
$87$	0.857758	+	2.23007i	0.0919613	+	0.239089i
$88$	2.18932	−	5.07541i	0.233382	−	0.541040i
$89$	−0.642803	+	3.64552i	−0.0681370	+	0.386424i	0.931600	+	0.363485i	$0.118413\pi$
$89$	−0.642803	+	3.64552i	−0.0681370	+	0.386424i	−0.999737	+	0.0229387i	$0.992698\pi$
$90$	−7.96910	−	4.83703i	−0.840017	−	0.509867i
$91$	0.394285	+	2.23610i	0.0413323	+	0.234407i
$92$	6.86253	+	1.62645i	0.715469	+	0.169569i
$93$	5.86687	−	1.87293i	0.608366	−	0.194213i
$94$	8.75447	−	5.75790i	0.902954	−	0.593882i
$95$	0.429800	+	7.37939i	0.0440966	+	0.757109i
$96$	1.60257	+	0.657097i	0.163561	+	0.0670647i
$97$	0.260981	+	0.871736i	0.0264986	+	0.0885113i	0.970216	−	0.242241i	$-0.0778826\pi$
$97$	0.260981	+	0.871736i	0.0264986	+	0.0885113i	−0.943717	+	0.330753i	$0.892697\pi$
$98$	6.12417	+	2.22901i	0.618634	+	0.225165i
$99$	13.5151	−	9.60824i	1.35832	−	0.965664i
$100$	−4.37515	+	1.59242i	−0.437515	+	0.159242i
$101$	−11.7954	−	15.8440i	−1.17368	−	1.57653i	−0.735294	−	0.677748i	$-0.762956\pi$
$101$	−11.7954	−	15.8440i	−1.17368	−	1.57653i	−0.438391	−	0.898785i	$-0.644451\pi$
$102$	6.88173	−	4.14123i	0.681393	−	0.410043i
$103$	5.78007	−	1.36990i	0.569527	−	0.134980i	0.0642442	−	0.997934i	$-0.479536\pi$
$103$	5.78007	−	1.36990i	0.569527	−	0.134980i	0.505283	+	0.862954i	$0.331388\pi$
$104$	1.29432	+	3.00056i	0.126918	+	0.294229i
$105$	3.60147	+	1.00747i	0.351467	+	0.0983186i
$106$	−3.53852	−	2.32732i	−0.343692	−	0.226050i
$107$	−1.62313	+	2.81135i	−0.156914	+	0.271783i	−0.933754	−	0.357914i	$-0.883488\pi$
$107$	−1.62313	+	2.81135i	−0.156914	+	0.271783i	0.776840	+	0.629698i	$0.216821\pi$
$108$	3.08703	+	4.17974i	0.297049	+	0.402196i
$109$	4.22282	+	7.31415i	0.404473	+	0.700568i	0.994260	−	0.106991i	$-0.0341215\pi$
$109$	4.22282	+	7.31415i	0.404473	+	0.700568i	−0.589787	+	0.807559i	$0.700788\pi$
$110$	0.998698	−	17.1470i	0.0952221	−	1.63490i
$111$	0.915154	−	1.90765i	0.0868625	−	0.181067i
$112$	−0.690137	−	0.0806655i	−0.0652119	−	0.00762217i
$113$	−7.98089	−	8.45925i	−0.750779	−	0.795779i	0.233508	−	0.972355i	$-0.424980\pi$
$113$	−7.98089	−	8.45925i	−0.750779	−	0.795779i	−0.984287	+	0.176576i	$0.943498\pi$
$114$	1.33880	−	3.89663i	0.125390	−	0.364953i
$115$	21.7672	−	2.54422i	2.02980	−	0.237250i
$116$	−1.05675	−	0.886718i	−0.0981168	−	0.0823297i
$117$	−1.35138	+	9.70987i	−0.124935	+	0.897677i
$118$	−4.41181	+	3.70195i	−0.406140	+	0.340792i
$119$	−2.21109	+	2.34361i	−0.202690	+	0.214839i
$120$	5.37786	+	0.215524i	0.490929	+	0.0196746i
$121$	17.4731	+	8.77531i	1.58846	+	0.797755i
$122$	1.54717	+	0.777016i	0.140074	+	0.0703478i
$123$	−19.6417	−	0.787165i	−1.77103	−	0.0709762i
$124$	−2.44004	+	2.58629i	−0.219122	+	0.232256i
$125$	0.819020	−	0.687239i	0.0732553	−	0.0614685i
$126$	−1.64433	−	1.28115i	−0.146489	−	0.114134i
$127$	−7.51805	−	6.30840i	−0.667119	−	0.559780i	0.245092	−	0.969500i	$-0.421182\pi$
$127$	−7.51805	−	6.30840i	−0.667119	−	0.559780i	−0.912211	+	0.409720i	$0.865626\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$	5.23110	−	15.2253i	0.460572	−	1.34051i
$130$	6.96838	+	7.38606i	0.611168	+	0.647800i
$131$	−18.3590	−	2.14586i	−1.60403	−	0.187484i	−0.733533	−	0.679654i	$-0.762130\pi$
$131$	−18.3590	−	2.14586i	−1.60403	−	0.187484i	−0.870499	+	0.492169i	$0.836204\pi$
$132$	−4.14099	+	8.63196i	−0.360427	+	0.751316i
$133$	−0.0961063	+	1.65008i	−0.00833347	+	0.143080i
$134$	−0.511595	−	0.886109i	−0.0441951	−	0.0765481i
$135$	13.4563	+	8.92398i	1.15814	+	0.768054i
$136$	−2.31855	+	4.01585i	−0.198814	+	0.344356i
$137$	12.2593	+	8.06304i	1.04738	+	0.688872i	0.951853	−	0.306555i	$-0.0991764\pi$
$137$	12.2593	+	8.06304i	1.04738	+	0.688872i	0.0955257	+	0.995427i	$0.469547\pi$
$138$	−11.7639	−	3.29081i	−1.00141	−	0.280132i
$139$	5.07402	+	11.7629i	0.430373	+	0.997716i	0.986070	+	0.166331i	$0.0531921\pi$
$139$	5.07402	+	11.7629i	0.430373	+	0.997716i	−0.555697	+	0.831385i	$0.687549\pi$
$140$	−2.10093	+	0.497930i	−0.177561	+	0.0420828i
$141$	−15.5504	+	9.35779i	−1.30958	+	0.788068i
$142$	−7.03863	−	9.45452i	−0.590669	−	0.793406i
$143$	−16.9734	+	6.17782i	−1.41939	+	0.516616i
$144$	−2.72793	−	1.24836i	−0.227327	−	0.104030i
$145$	−4.02811	−	1.46611i	−0.334516	−	0.121754i
$146$	−2.46608	−	8.23728i	−0.204094	−	0.681722i
$147$	−10.4443	−	4.28243i	−0.861428	−	0.353209i
$148$	0.0710276	+	1.21950i	0.00583843	+	0.100242i
$149$	14.8005	−	9.73443i	1.21250	−	0.797476i	0.228140	−	0.973628i	$-0.426736\pi$
$149$	14.8005	−	9.73443i	1.21250	−	0.797476i	0.984363	+	0.176153i	$0.0563652\pi$
$150$	7.68234	−	2.45249i	0.627261	−	0.200245i
$151$	15.3504	+	3.63812i	1.24920	+	0.296066i	0.801434	−	0.598084i	$-0.204071\pi$
$151$	15.3504	+	3.63812i	1.24920	+	0.296066i	0.447768	+	0.894150i	$0.352219\pi$
$152$	0.413075	+	2.34266i	0.0335048	+	0.190015i
$153$	−12.1972	+	6.68977i	−0.986083	+	0.540836i
$154$	0.666927	−	3.78233i	0.0537425	−	0.304789i
$155$	−4.37622	+	10.1452i	−0.351507	+	0.814884i
$156$	−2.03191	−	5.28273i	−0.162683	−	0.422957i
$157$	0.902664	−	3.01511i	0.0720404	−	0.240632i	−0.914384	−	0.404848i	$-0.867324\pi$
$157$	0.902664	−	3.01511i	0.0720404	−	0.240632i	0.986424	+	0.164216i	$0.0525096\pi$
$158$	−5.25293	+	7.05591i	−0.417901	+	0.561338i
$159$	5.96257	+	4.27324i	0.472863	+	0.338890i
$160$	−2.77687	+	1.39460i	−0.219531	+	0.110253i
$161$	4.90043			0.386208
$162$	−5.05270	−	7.44783i	−0.396978	−	0.585157i
$163$	−10.6732			−0.835986			−0.417993	−	0.908450i	$-0.637266\pi$
$163$	−10.6732			−0.835986			−0.417993	+	0.908450i	$0.637266\pi$
$164$	10.1420	−	5.09352i	0.791960	−	0.397737i
$165$	−2.91770	+	29.6064i	−0.227142	+	2.30485i
$166$	−5.42188	+	7.28285i	−0.420820	+	0.565259i
$167$	−0.546468	+	1.82533i	−0.0422870	+	0.141248i	−0.976526	−	0.215399i	$-0.930895\pi$
$167$	−0.546468	+	1.82533i	−0.0422870	+	0.141248i	0.934239	+	0.356647i	$0.116080\pi$
$168$	1.18880	+	0.187472i	0.0917179	+	0.0144637i
$169$	−0.919445	+	2.13151i	−0.0707265	+	0.163963i
$170$	−2.50215	+	14.1904i	−0.191906	+	1.08835i
$171$	−2.58727	+	6.65089i	−0.197854	+	0.508606i
$172$	1.61401	+	9.15350i	0.123067	+	0.697948i
$173$	1.41829	+	0.336142i	0.107831	+	0.0255564i	0.284177	−	0.958772i	$-0.408280\pi$
$173$	1.41829	+	0.336142i	0.107831	+	0.0255564i	−0.176346	+	0.984328i	$0.556428\pi$
$174$	1.76737	+	1.60790i	0.133984	+	0.121895i
$175$	−2.70289	+	1.77772i	−0.204320	+	0.134383i
$176$	−0.321393	−	5.51811i	−0.0242259	−	0.415943i
$177$	7.89212	−	6.10083i	0.593208	−	0.458566i
$178$	1.06168	+	3.54624i	0.0795759	+	0.265802i
$179$	3.40456	+	1.23916i	0.254469	+	0.0926191i	0.466105	−	0.884729i	$-0.345657\pi$
$179$	3.40456	+	1.23916i	0.254469	+	0.0926191i	−0.211636	+	0.977349i	$0.567879\pi$
$180$	−9.29230	−	0.746000i	−0.692607	−	0.0556035i
$181$	−20.8444	+	7.58675i	−1.54935	+	0.563919i	−0.968266	−	0.249922i	$-0.919595\pi$
$181$	−20.8444	+	7.58675i	−1.54935	+	0.563919i	−0.581088	+	0.813841i	$0.697373\pi$
$182$	1.35591	+	1.82130i	0.100506	+	0.135004i
$183$	−2.62373	−	1.45206i	−0.193952	−	0.107339i
$184$	6.86253	−	1.62645i	0.505913	−	0.119904i
$185$	1.50347	+	3.48544i	0.110538	+	0.256255i
$186$	4.40226	−	4.30675i	0.322790	−	0.315787i
$187$	−21.4147	−	14.0847i	−1.56600	−	1.02997i
$188$	5.23914	−	9.07445i	0.382103	−	0.661822i
$189$	2.75692	+	2.33129i	0.200537	+	0.169576i
$190$	3.69595	+	6.40157i	0.268132	+	0.464418i
$191$	0.340269	−	5.84219i	0.0246210	−	0.422726i	−0.963366	−	0.268190i	$-0.913575\pi$
$191$	0.340269	−	5.84219i	0.0246210	−	0.422726i	0.987987	−	0.154536i	$-0.0493883\pi$
$192$	1.72701	−	0.132028i	0.124636	−	0.00952830i
$193$	−14.3530	−	1.67762i	−1.03315	−	0.120758i	−0.417418	−	0.908714i	$-0.637065\pi$
$193$	−14.3530	−	1.67762i	−1.03315	−	0.120758i	−0.615731	+	0.787957i	$0.711139\pi$
$194$	0.624455	+	0.661884i	0.0448333	+	0.0475205i
$195$	−11.5476	−	13.2661i	−0.826943	−	0.950004i
$196$	6.47314	−	0.756601i	0.462367	−	0.0540429i
$197$	−3.66493	−	3.07525i	−0.261116	−	0.219102i	0.502825	−	0.864388i	$-0.332294\pi$
$197$	−3.66493	−	3.07525i	−0.261116	−	0.219102i	−0.763941	+	0.645286i	$0.776738\pi$
$198$	7.76535	−	14.6518i	0.551859	−	1.04126i
$199$	11.9225	−	10.0042i	0.845166	−	0.709178i	−0.113554	−	0.993532i	$-0.536223\pi$
$199$	11.9225	−	10.0042i	0.845166	−	0.709178i	0.958719	+	0.284354i	$0.0917790\pi$
$200$	−3.19509	+	3.38660i	−0.225927	+	0.239469i
$201$	0.823939	+	1.56904i	0.0581162	+	0.110671i
$202$	−17.6515	−	8.86492i	−1.24196	−	0.623733i
$203$	−0.856563	−	0.430182i	−0.0601189	−	0.0301929i
$204$	4.29116	−	6.78926i	0.300441	−	0.475343i
$205$	24.2014	−	25.6520i	1.69030	−	1.79161i
$206$	4.55045	−	3.81828i	0.317045	−	0.266032i
$207$	20.1311	+	6.51121i	1.39921	+	0.452560i
$208$	2.50329	+	2.10051i	0.173572	+	0.145644i
$209$	−13.0598	+	1.52648i	−0.903368	+	0.105589i
$210$	3.67054	−	0.716031i	0.253291	−	0.0494108i
$211$	−10.1033	−	10.7089i	−0.695542	−	0.737231i	0.279282	−	0.960209i	$-0.409904\pi$
$211$	−10.1033	−	10.7089i	−0.695542	−	0.737231i	−0.974824	+	0.222978i	$0.928422\pi$
$212$	−4.20664	−	0.491686i	−0.288913	−	0.0337691i
$213$	11.5257	+	16.8508i	0.789731	+	1.15460i
$214$	−0.188754	+	3.24077i	−0.0129029	+	0.221535i
$215$	14.4412	+	25.0129i	0.984880	+	1.70586i
$216$	4.63453	+	2.34970i	0.315340	+	0.159877i
$217$	−1.23530	+	2.13960i	−0.0838575	+	0.145245i
$218$	7.05624	+	4.64096i	0.477909	+	0.314325i
$219$	3.69662	+	14.4270i	0.249795	+	0.974886i
$220$	−6.80308	−	15.7713i	−0.458664	−	1.06330i
$221$	14.7447	−	3.49457i	0.991838	−	0.235070i
$222$	−0.0383423	−	2.11546i	−0.00257337	−	0.141981i
$223$	6.19591	+	8.32255i	0.414909	+	0.557319i	0.959618	−	0.281306i	$-0.0907675\pi$
$223$	6.19591	+	8.32255i	0.414909	+	0.557319i	−0.544710	+	0.838625i	$0.683360\pi$
$224$	−0.652932	+	0.237648i	−0.0436259	+	0.0158785i
$225$	−13.4656	+	3.71160i	−0.897709	+	0.247440i
$226$	−10.9285	−	3.97765i	−0.726952	−	0.264589i
$227$	2.85714	+	9.54350i	0.189635	+	0.633424i	0.998940	+	0.0460357i	$0.0146588\pi$
$227$	2.85714	+	9.54350i	0.189635	+	0.633424i	−0.809305	+	0.587389i	$0.800156\pi$
$228$	−0.552409	−	4.08301i	−0.0365842	−	0.270404i
$229$	−1.21402	−	20.8439i	−0.0802247	−	1.37740i	−0.762821	−	0.646609i	$-0.776186\pi$
$229$	−1.21402	−	20.8439i	−0.0802247	−	1.37740i	0.682597	−	0.730795i	$-0.260851\pi$
$230$	18.3100	−	12.0427i	1.20733	−	0.794072i
$231$	−1.41656	+	6.49968i	−0.0932029	+	0.427647i
$232$	−1.34230	−	0.318132i	−0.0881266	−	0.0208864i
$233$	−2.00393	−	11.3648i	−0.131282	−	0.744535i	−0.977377	−	0.211504i	$-0.932164\pi$
$233$	−2.00393	−	11.3648i	−0.131282	−	0.744535i	0.846095	−	0.533031i	$-0.178947\pi$
$234$	3.15015	+	9.28355i	0.205931	+	0.606885i
$235$	5.65402	−	32.0655i	0.368827	−	2.09172i
$236$	−2.28111	+	5.28820i	−0.148488	+	0.344233i
$237$	9.58043	−	11.8471i	0.622316	−	0.769549i
$238$	−0.924086	+	3.08666i	−0.0598996	+	0.200079i
$239$	1.72538	−	2.31759i	0.111606	−	0.149913i	−0.742810	−	0.669502i	$-0.766508\pi$
$239$	1.72538	−	2.31759i	0.111606	−	0.149913i	0.854416	+	0.519589i	$0.173915\pi$
$240$	4.90256	−	2.22098i	0.316459	−	0.143364i
$241$	0.0473887	−	0.0237995i	0.00305257	−	0.00153306i	−0.447272	−	0.894398i	$-0.647604\pi$
$241$	0.0473887	−	0.0237995i	0.00305257	−	0.00153306i	0.450325	+	0.892865i	$0.351308\pi$
$242$	19.5529			1.25691
$243$	8.22794	+	13.2401i	0.527823	+	0.849355i
$244$	1.73132			0.110837
$245$	18.0975	−	9.08888i	1.15620	−	0.580667i
$246$	−17.9057	+	8.11173i	−1.14163	+	0.517185i
$247$	4.64201	−	6.23530i	0.295364	−	0.396743i
$248$	−1.01977	+	3.40628i	−0.0647557	+	0.216299i
$249$	9.88857	−	12.2281i	0.626663	−	0.774925i
$250$	0.423470	−	0.981715i	0.0267826	−	0.0620891i
$251$	1.45888	−	8.27374i	0.0920839	−	0.522234i	−0.903518	−	0.428550i	$-0.859025\pi$
$251$	1.45888	−	8.27374i	0.0920839	−	0.522234i	0.995602	−	0.0936838i	$-0.0298643\pi$
$252$	−2.04441	−	0.406903i	−0.128786	−	0.0256325i
$253$	6.76936	+	38.3910i	0.425586	+	2.41362i
$254$	−9.54958	−	2.26329i	−0.599194	−	0.142012i
$255$	5.31460	−	24.3852i	0.332813	−	1.52706i
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	0.825207	+	14.1683i	0.0514750	+	0.883792i	0.920917	+	0.389758i	$0.127441\pi$
$257$	0.825207	+	14.1683i	0.0514750	+	0.883792i	−0.869442	+	0.494034i	$0.835522\pi$
$258$	−2.15843	−	15.9535i	−0.134378	−	0.993225i
$259$	0.243434	+	0.813128i	0.0151263	+	0.0505253i
$260$	9.54203	+	3.47302i	0.591772	+	0.215387i
$261$	−2.94721	−	2.90532i	−0.182427	−	0.179835i
$262$	−17.3693	+	6.32189i	−1.07308	+	0.390568i
$263$	−14.3710	−	19.3035i	−0.886151	−	1.19031i	−0.980843	−	0.194801i	$-0.937594\pi$
$263$	−14.3710	−	19.3035i	−0.886151	−	1.19031i	0.0946919	−	0.995507i	$-0.469813\pi$
$264$	0.173496	+	9.57228i	0.0106779	+	0.589133i
$265$	−12.8060	+	3.03507i	−0.786664	+	0.186443i
$266$	0.654671	+	1.51770i	0.0401405	+	0.0930561i
$267$	−1.59144	−	6.21098i	−0.0973945	−	0.380106i
$268$	−0.854863	−	0.562252i	−0.0522191	−	0.0343450i
$269$	4.00049	−	6.92906i	0.243914	−	0.422472i	−0.717911	−	0.696134i	$-0.754902\pi$
$269$	4.00049	−	6.92906i	0.243914	−	0.422472i	0.961826	+	0.273662i	$0.0882351\pi$
$270$	16.0301	+	1.93557i	0.975560	+	0.117795i
$271$	1.88940	+	3.27253i	0.114773	+	0.198792i	0.917689	−	0.397300i	$-0.130053\pi$
$271$	1.88940	+	3.27253i	0.114773	+	0.198792i	−0.802916	+	0.596092i	$0.796719\pi$
$272$	−0.269623	+	4.62925i	−0.0163483	+	0.280690i
$273$	−2.22029	−	3.24609i	−0.134378	−	0.196463i
$274$	14.5740	+	1.70345i	0.880445	+	0.102909i
$275$	−17.6608	−	18.7193i	−1.06498	−	1.12882i
$276$	−11.9895	+	2.33886i	−0.721685	+	0.140783i
$277$	−9.30469	+	1.08756i	−0.559064	+	0.0653453i	−0.390933	−	0.920419i	$-0.627847\pi$
$277$	−9.30469	+	1.08756i	−0.559064	+	0.0653453i	−0.168132	+	0.985765i	$0.553773\pi$
$278$	9.81349	+	8.23449i	0.588574	+	0.493872i
$279$	−7.91754	+	7.14820i	−0.474010	+	0.427952i
$280$	−1.65399	+	1.38786i	−0.0988449	+	0.0829407i
$281$	−5.32890	+	5.64830i	−0.317895	+	0.336949i	−0.866541	−	0.499105i	$-0.833662\pi$
$281$	−5.32890	+	5.64830i	−0.317895	+	0.336949i	0.548646	+	0.836055i	$0.315144\pi$
$282$	−9.69656	+	15.3414i	−0.577422	+	0.913568i
$283$	−17.1311	−	8.60354i	−1.01834	−	0.511427i	−0.140344	−	0.990103i	$-0.544821\pi$
$283$	−17.1311	−	8.60354i	−1.01834	−	0.511427i	−0.877992	+	0.478676i	$0.841117\pi$
$284$	−10.5331	−	5.28994i	−0.625026	−	0.313900i
$285$	−5.95243	−	11.3353i	−0.352591	−	0.671445i
$286$	−12.3954	+	13.1384i	−0.732956	+	0.776888i
$287$	6.04091	−	5.06892i	0.356584	−	0.299209i
$288$	−2.99803	+	0.108713i	−0.176661	+	0.00640598i
$289$	3.44925	+	2.89427i	0.202897	+	0.170251i
$290$	−4.25764	+	0.497647i	−0.250017	+	0.0292228i
$291$	−1.03481	−	1.18881i	−0.0606618	−	0.0696891i
$292$	−5.90065	−	6.25433i	−0.345310	−	0.366007i
$293$	17.5250	+	2.04838i	1.02382	+	0.119668i	0.611398	−	0.791324i	$-0.290608\pi$
$293$	17.5250	+	2.04838i	1.02382	+	0.119668i	0.412425	+	0.910991i	$0.364682\pi$
$294$	−11.2553	+	0.860454i	−0.656422	+	0.0501827i
$295$	−1.04057	+	17.8659i	−0.0605844	+	1.04019i
$296$	0.610782	+	1.05790i	0.0355010	+	0.0614895i
$297$	−14.4554	+	24.8187i	−0.838788	+	1.44013i
$298$	8.85739	−	15.3415i	0.513095	−	0.888706i
$299$	−19.2553	−	12.6644i	−1.11356	−	0.732401i
$300$	5.76452	−	5.63946i	0.332815	−	0.325594i
$301$	2.55800	+	5.93011i	0.147441	+	0.341806i
$302$	15.3504	−	3.63812i	0.883319	−	0.209350i
$303$	29.9339	+	16.5664i	1.71966	+	0.951718i
$304$	1.42052	+	1.90809i	0.0814726	+	0.109437i
$305$	5.05546	−	1.84004i	0.289475	−	0.105360i
$306$	−7.89743	+	11.4523i	−0.451466	+	0.654683i
$307$	−12.9189	−	4.70209i	−0.737320	−	0.268363i	−0.0540601	−	0.998538i	$-0.517216\pi$
$307$	−12.9189	−	4.70209i	−0.737320	−	0.268363i	−0.683260	+	0.730175i	$0.739438\pi$
$308$	−1.10152	−	3.67933i	−0.0627649	−	0.209649i
$309$	−8.14011	+	6.29254i	−0.463075	+	0.357970i
$310$	0.642433	+	11.0301i	0.0364877	+	0.626470i
$311$	14.9898	−	9.85896i	0.849995	−	0.559050i	−0.0481050	−	0.998842i	$-0.515318\pi$
$311$	14.9898	−	9.85896i	0.849995	−	0.559050i	0.898100	+	0.439792i	$0.144948\pi$
$312$	−4.18667	−	3.80890i	−0.237023	−	0.215637i
$313$	4.64166	+	1.10009i	0.262362	+	0.0621810i	0.359692	−	0.933071i	$-0.382882\pi$
$313$	4.64166	+	1.10009i	0.262362	+	0.0621810i	−0.0973294	+	0.995252i	$0.531030\pi$
$314$	−0.546528	−	3.09951i	−0.0308423	−	0.174916i
$315$	−6.40212	+	0.984625i	−0.360719	+	0.0554773i
$316$	−1.52750	+	8.66290i	−0.0859288	+	0.487326i
$317$	−1.95397	+	4.52981i	−0.109746	+	0.254420i	−0.964235	−	0.265050i	$-0.914611\pi$
$317$	−1.95397	+	4.52981i	−0.109746	+	0.254420i	0.854489	+	0.519470i	$0.173871\pi$
$318$	7.24617	+	1.14271i	0.406345	+	0.0640799i
$319$	2.18690	−	7.30474i	0.122443	−	0.408987i
$320$	−1.85561	+	2.49252i	−0.103732	+	0.139336i
$321$	0.551444	−	5.59559i	0.0307786	−	0.312315i
$322$	4.37918	−	2.19931i	0.244042	−	0.122563i
$323$	11.0307			0.613767
$324$	−7.85784	−	4.38798i	−0.436547	−	0.243777i
$325$	15.2147			0.843962
$326$	−9.53788	+	4.79010i	−0.528254	+	0.265299i
$327$	−11.8901	−	8.52134i	−0.657522	−	0.471231i
$328$	6.77729	−	9.10348i	0.374213	−	0.502655i
$329$	2.08812	−	6.97481i	0.115122	−	0.384534i
$330$	10.6800	+	27.7667i	0.587912	+	1.52850i
$331$	8.20945	−	19.0316i	0.451232	−	1.04607i	−0.529071	−	0.848577i	$-0.677460\pi$
$331$	8.20945	−	19.0316i	0.451232	−	1.04607i	0.980304	−	0.197497i	$-0.0632812\pi$
$332$	−1.57663	+	8.94153i	−0.0865290	+	0.490730i
$333$	−0.0803676	+	3.66381i	−0.00440412	+	0.200775i
$334$	0.330865	+	1.87643i	0.0181041	+	0.102674i
$335$	−3.09376	−	0.733234i	−0.169030	−	0.0400609i
$336$	1.14649	−	0.366002i	0.0625460	−	0.0199670i
$337$	23.4132	−	15.3991i	1.27540	−	0.838843i	0.282670	−	0.959217i	$-0.408780\pi$
$337$	23.4132	−	15.3991i	1.27540	−	0.838843i	0.992729	+	0.120374i	$0.0384095\pi$
$338$	0.134975	+	2.31744i	0.00734169	+	0.126052i
$339$	18.6376	+	7.64194i	1.01226	+	0.415053i
$340$	4.13264	+	13.8040i	0.224124	+	0.748626i
$341$	−18.4685	−	6.72198i	−1.00012	−	0.364016i
$342$	0.672842	+	7.10462i	0.0363831	+	0.384174i
$343$	8.82581	−	3.21233i	0.476549	−	0.173450i
$344$	5.55041	+	7.45550i	0.299258	+	0.401973i
$345$	−32.5237	+	19.5719i	−1.75102	+	1.05371i
$346$	1.41829	−	0.336142i	0.0762480	−	0.0180711i
$347$	4.31805	+	10.0104i	0.231805	+	0.537384i	0.993926	−	0.110050i	$-0.0351011\pi$
$347$	4.31805	+	10.0104i	0.231805	+	0.537384i	−0.762121	+	0.647435i	$0.775842\pi$
$348$	2.30101	+	0.643679i	0.123347	+	0.0345048i
$349$	13.5397	+	8.90522i	0.724765	+	0.476685i	0.857512	−	0.514465i	$-0.172009\pi$
$349$	13.5397	+	8.90522i	0.724765	+	0.476685i	−0.132747	+	0.991150i	$0.542380\pi$
$350$	−1.61755	+	2.80169i	−0.0864619	+	0.149756i
$351$	−4.80794	−	16.2852i	−0.256629	−	0.869238i
$352$	−2.76373	−	4.78692i	−0.147307	−	0.255144i
$353$	−1.59059	+	27.3094i	−0.0846586	+	1.45353i	0.642090	+	0.766629i	$0.278067\pi$
$353$	−1.59059	+	27.3094i	−0.0846586	+	1.45353i	−0.726749	+	0.686903i	$0.758970\pi$
$354$	4.31461	−	8.99388i	0.229319	−	0.478019i
$355$	−36.3789	−	4.25208i	−1.93079	−	0.225677i
$356$	2.54030	+	2.69256i	0.134636	+	0.142705i
$357$	1.81337	−	5.27788i	0.0959735	−	0.279335i
$358$	3.59856	−	0.420611i	0.190190	−	0.0222300i
$359$	−4.66035	−	3.91050i	−0.245964	−	0.206388i	0.511468	−	0.859302i	$-0.329102\pi$
$359$	−4.66035	−	3.91050i	−0.245964	−	0.206388i	−0.757432	+	0.652914i	$0.773546\pi$
$360$	−8.63871	+	3.50373i	−0.455300	+	0.184663i
$361$	−10.2200	+	8.57562i	−0.537896	+	0.451348i
$362$	−15.2223	+	16.1347i	−0.800068	+	0.848023i
$363$	−33.8394	−	1.35616i	−1.77611	−	0.0711798i
$364$	2.02908	+	1.01904i	0.106353	+	0.0534123i
$365$	−23.8770	−	11.9915i	−1.24978	−	0.627662i
$366$	−2.99633	−	0.120082i	−0.156621	−	0.00627678i
$367$	−12.3462	+	13.0862i	−0.644468	+	0.683096i	−0.964431	−	0.264334i	$-0.914848\pi$
$367$	−12.3462	+	13.0862i	−0.644468	+	0.683096i	0.319963	+	0.947430i	$0.396329\pi$
$368$	5.40264	−	4.53335i	0.281632	−	0.236317i
$369$	31.5513	−	12.7967i	1.64250	−	0.666172i
$370$	2.90782	+	2.43995i	0.151170	+	0.126847i
$371$	−2.92293	+	0.341641i	−0.151751	+	0.0177371i
$372$	2.00114	−	5.82439i	0.103754	−	0.301980i
$373$	16.3827	+	17.3646i	0.848262	+	0.899106i	0.995948	−	0.0899288i	$-0.0286639\pi$
$373$	16.3827	+	17.3646i	0.848262	+	0.899106i	−0.147686	+	0.989034i	$0.547182\pi$
$374$	−25.4581	−	2.97562i	−1.31641	−	0.153866i
$375$	−0.800974	+	1.66964i	−0.0413621	+	0.0862201i
$376$	0.609257	−	10.4605i	0.0314200	−	0.539461i
$377$	2.25396	+	3.90397i	0.116085	+	0.201065i
$378$	3.50995	+	0.846008i	0.180533	+	0.0435140i
$379$	−11.8242	+	20.4801i	−0.607367	+	1.05199i	0.384305	+	0.923206i	$0.374441\pi$
$379$	−11.8242	+	20.4801i	−0.607367	+	1.05199i	−0.991673	+	0.128785i	$0.958892\pi$
$380$	6.17584	+	4.06191i	0.316814	+	0.208372i
$381$	16.3701	+	4.57934i	0.838666	+	0.234607i
$382$	−2.31789	−	5.37348i	−0.118594	−	0.274931i
$383$	−13.8773	+	3.28898i	−0.709097	+	0.168059i	−0.569311	−	0.822123i	$-0.692790\pi$
$383$	−13.8773	+	3.28898i	−0.709097	+	0.168059i	−0.139787	+	0.990182i	$0.544642\pi$
$384$	1.48406	−	0.893066i	0.0757331	−	0.0455741i
$385$	−7.12681	−	9.57296i	−0.363216	−	0.487883i
$386$	−13.5792	+	4.94242i	−0.691163	+	0.251563i
$387$	2.62900	+	27.7599i	0.133639	+	1.41112i
$388$	0.855086	+	0.311226i	0.0434104	+	0.0158001i
$389$	10.2329	+	34.1803i	0.518829	+	1.73301i	0.667964	+	0.744193i	$0.267166\pi$
$389$	10.2329	+	34.1803i	0.518829	+	1.73301i	−0.149135	+	0.988817i	$0.547649\pi$
$390$	−16.2731	−	6.67243i	−0.824023	−	0.337872i
$391$	−1.90156	−	32.6485i	−0.0961658	−	1.65110i
$392$	5.44504	−	3.58126i	0.275016	−	0.180881i
$393$	30.4988	−	9.73635i	1.53846	−	0.491134i
$394$	−4.65527	−	1.10332i	−0.234529	−	0.0555845i
$395$	4.74656	+	26.9191i	0.238826	+	1.35445i
$396$	0.363656	−	16.5784i	0.0182744	−	0.833096i
$397$	4.23676	−	24.0278i	0.212637	−	1.20592i	−0.672324	−	0.740257i	$-0.734704\pi$
$397$	4.23676	−	24.0278i	0.212637	−	1.20592i	0.884961	−	0.465666i	$-0.154185\pi$
$398$	6.16449	−	14.2909i	0.308998	−	0.716338i
$399$	−1.02775	−	2.67203i	−0.0514518	−	0.133769i
$400$	−1.33534	+	4.46033i	−0.0667668	+	0.223017i
$401$	23.3072	−	31.3070i	1.16391	−	1.56340i	0.402093	−	0.915599i	$-0.368283\pi$
$401$	23.3072	−	31.3070i	1.16391	−	1.56340i	0.761812	−	0.647798i	$-0.224310\pi$
$402$	1.44048	+	1.03236i	0.0718447	+	0.0514894i
$403$	10.3833	−	5.21470i	0.517230	−	0.259763i
$404$	−19.7525			−0.982725
$405$	−27.6084	−	4.46164i	−1.37187	−	0.221701i
$406$	−0.958518			−0.0475705
$407$	−6.03394	+	3.03036i	−0.299091	+	0.150209i
$408$	0.787705	−	7.99297i	0.0389972	−	0.395711i
$409$	−10.6428	+	14.2958i	−0.526254	+	0.706882i	−0.983183	−	0.182621i	$-0.941542\pi$
$409$	−10.6428	+	14.2958i	−0.526254	+	0.706882i	0.456929	+	0.889503i	$0.348949\pi$
$410$	10.1146	−	33.7850i	0.499523	−	1.66852i
$411$	−25.1044	−	3.95892i	−1.23831	−	0.195279i
$412$	2.35279	−	5.45437i	0.115914	−	0.268718i
$413$	−0.694889	+	3.94091i	−0.0341933	+	0.193920i
$414$	20.9120	−	3.21620i	1.02777	−	0.158068i
$415$	4.89923	+	27.7849i	0.240494	+	1.36391i
$416$	3.17973	+	0.753611i	0.155899	+	0.0369488i
$417$	−16.4127	−	14.9318i	−0.803733	−	0.731212i
$418$	−10.9856	+	7.22536i	−0.537324	+	0.353404i
$419$	−0.463457	−	7.95725i	−0.0226414	−	0.388737i	−0.990524	−	0.137336i	$-0.956146\pi$
$419$	−0.463457	−	7.95725i	−0.0226414	−	0.388737i	0.967883	−	0.251401i	$-0.0808912\pi$
$420$	2.95876	−	2.28720i	0.144373	−	0.111604i
$421$	8.16468	+	27.2719i	0.397922	+	1.32915i	0.888948	+	0.458008i	$0.151437\pi$
$421$	8.16468	+	27.2719i	0.397922	+	1.32915i	−0.491026	+	0.871145i	$0.663378\pi$
$422$	−13.8348	−	5.03546i	−0.673468	−	0.245122i
$423$	17.8455	−	25.8783i	0.867679	−	1.25824i
$424$	−3.97986	+	1.44855i	−0.193279	+	0.0703479i
$425$	12.8927	+	17.3179i	0.625386	+	0.840039i
$426$	17.8624	+	9.88565i	0.865435	+	0.478962i
$427$	1.17056	−	0.277427i	0.0566473	−	0.0134257i
$428$	1.28578	+	2.98077i	0.0621505	+	0.144081i
$429$	22.3635	−	21.8783i	1.07972	−	1.05630i
$430$	24.1309	+	15.8711i	1.16369	+	0.765373i
$431$	−13.7252	+	23.7728i	−0.661122	+	1.14510i	0.319200	+	0.947688i	$0.396586\pi$
$431$	−13.7252	+	23.7728i	−0.661122	+	1.14510i	−0.980321	+	0.197409i	$0.936747\pi$
$432$	5.19611	+	0.0197932i	0.249998	+	0.000952301i
$433$	1.90681	+	3.30270i	0.0916356	+	0.158717i	0.908199	−	0.418538i	$-0.137457\pi$
$433$	1.90681	+	3.30270i	0.0916356	+	0.158717i	−0.816564	+	0.577255i	$0.804124\pi$
$434$	−0.143652	+	2.46642i	−0.00689553	+	0.118392i
$435$	7.40305	−	0.565955i	0.354949	−	0.0271354i
$436$	8.38854	+	0.980480i	0.401738	+	0.0469565i
$437$	−11.5130	−	12.2030i	−0.550740	−	0.583750i
$438$	9.77825	+	11.2334i	0.467223	+	0.536752i
$439$	−5.47284	+	0.639683i	−0.261204	+	0.0305304i	−0.245687	−	0.969349i	$-0.579014\pi$
$439$	−5.47284	+	0.639683i	−0.261204	+	0.0305304i	−0.0155172	+	0.999880i	$0.504939\pi$
$440$	−13.1576	−	11.0405i	−0.627265	−	0.526337i
$441$	19.5388	−	0.708505i	0.930418	−	0.0337383i
$442$	11.6080	−	9.74029i	0.552137	−	0.463298i
$443$	17.7115	−	18.7731i	0.841499	−	0.891937i	−0.153868	−	0.988091i	$-0.549173\pi$
$443$	17.7115	−	18.7731i	0.841499	−	0.891937i	0.995366	+	0.0961548i	$0.0306544\pi$
$444$	−0.983682	−	1.87324i	−0.0466835	−	0.0888999i
$445$	10.2793	+	5.16246i	0.487286	+	0.244724i
$446$	9.27202	+	4.65658i	0.439043	+	0.220496i
$447$	−16.3932	+	25.9365i	−0.775372	+	1.22676i
$448$	−0.476825	+	0.505405i	−0.0225279	+	0.0238781i
$449$	−7.95557	+	6.67552i	−0.375447	+	0.315037i	−0.810912	−	0.585168i	$-0.801028\pi$
$449$	−7.95557	+	6.67552i	−0.375447	+	0.315037i	0.435465	+	0.900206i	$0.356584\pi$
$450$	−10.3676	+	9.36017i	−0.488732	+	0.441243i
$451$	48.0558	+	40.3236i	2.26286	+	1.89877i
$452$	−11.5512	+	1.35014i	−0.543324	+	0.0635054i
$453$	−26.8188	+	5.23167i	−1.26005	+	0.245805i
$454$	6.83635	+	7.24610i	0.320846	+	0.340076i
$455$	7.00794	+	0.819111i	0.328537	+	0.0384005i
$456$	−2.32610	−	3.40079i	−0.108930	−	0.159257i
$457$	2.03404	−	34.9231i	0.0951485	−	1.63364i	−0.526384	−	0.850247i	$-0.676452\pi$
$457$	2.03404	−	34.9231i	0.0951485	−	1.63364i	0.621532	−	0.783389i	$-0.286511\pi$
$458$	−10.4396	−	18.0819i	−0.487811	−	0.844914i
$459$	14.4621	−	19.2723i	0.675033	−	0.899552i
$460$	10.9577	−	18.9793i	0.510905	−	0.884913i
$461$	−13.1697	−	8.66185i	−0.613374	−	0.403423i	0.204461	−	0.978875i	$-0.434456\pi$
$461$	−13.1697	−	8.66185i	−0.613374	−	0.403423i	−0.817836	+	0.575452i	$0.804826\pi$
$462$	1.65116	+	6.44408i	0.0768191	+	0.299806i
$463$	1.50290	+	3.48411i	0.0698456	+	0.161920i	0.949563	−	0.313577i	$-0.101527\pi$
$463$	1.50290	+	3.48411i	0.0698456	+	0.161920i	−0.879717	+	0.475497i	$0.842268\pi$
$464$	−1.34230	+	0.318132i	−0.0623149	+	0.0147689i
$465$	−0.346800	−	19.1340i	−0.0160825	−	0.887319i
$466$	−6.89131	−	9.25663i	−0.319234	−	0.428805i
$467$	37.6811	−	13.7148i	1.74367	−	0.634645i	0.744226	−	0.667928i	$-0.232819\pi$
$467$	37.6811	−	13.7148i	1.74367	−	0.634645i	0.999446	+	0.0332831i	$0.0105963\pi$
$468$	6.98152	+	6.88230i	0.322721	+	0.318134i
$469$	−0.668073	−	0.243159i	−0.0308488	−	0.0112280i
$470$	−9.33836	−	31.1923i	−0.430747	−	1.43879i
$471$	0.730877	+	5.40211i	0.0336770	+	0.248916i
$472$	0.334869	+	5.74947i	0.0154136	+	0.264641i
$473$	−42.9241	+	28.2317i	−1.97365	+	1.29809i
$474$	3.24444	−	14.8866i	0.149022	−	0.683765i
$475$	10.7770	+	2.55420i	0.494483	+	0.117195i
$476$	0.559498	+	3.17307i	0.0256446	+	0.145438i
$477$	−12.4614	−	2.48022i	−0.570569	−	0.113562i
$478$	0.501726	−	2.84543i	0.0229484	−	0.130147i
$479$	8.98549	−	20.8307i	0.410558	−	0.951780i	−0.579992	−	0.814622i	$-0.696944\pi$
$479$	8.98549	−	20.8307i	0.410558	−	0.951780i	0.990549	−	0.137157i	$-0.0437966\pi$
$480$	3.38431	−	4.18500i	0.154472	−	0.191018i
$481$	1.14487	−	3.82415i	0.0522018	−	0.174366i
$482$	0.0316669	−	0.0425360i	0.00144239	−	0.00193746i
$483$	−7.73142	+	3.50252i	−0.351792	+	0.159370i
$484$	17.4731	−	8.77531i	0.794231	−	0.398878i
$485$	2.82762			0.128396
$486$	13.2949	+	8.13911i	0.603070	+	0.369198i
$487$	−27.0825			−1.22723			−0.613613	−	0.789607i	$-0.710285\pi$
$487$	−27.0825			−1.22723			−0.613613	+	0.789607i	$0.710285\pi$
$488$	1.54717	−	0.777016i	0.0700369	−	0.0351739i
$489$	16.8391	−	7.62852i	0.761490	−	0.344973i
$490$	12.0934	−	16.2442i	0.546324	−	0.733840i
$491$	−2.03944	+	6.81222i	−0.0920388	+	0.307431i	−0.991596	−	0.129372i	$-0.958704\pi$
$491$	−2.03944	+	6.81222i	−0.0920388	+	0.307431i	0.899557	+	0.436803i	$0.143889\pi$
$492$	−12.3606	+	15.2850i	−0.557258	+	0.689100i
$493$	−2.53365	+	5.87367i	−0.114110	+	0.264537i
$494$	1.34985	−	7.65540i	0.0607328	−	0.344433i
$495$	−16.5575	−	48.7954i	−0.744206	−	2.19319i
$496$	0.617433	+	3.50164i	0.0277236	+	0.157228i
$497$	−7.96918	−	1.88873i	−0.357466	−	0.0847211i
$498$	3.34879	−	15.3654i	0.150063	−	0.688541i
$499$	−24.8765	+	16.3615i	−1.11362	+	0.732442i	−0.966498	−	0.256676i	$-0.917373\pi$
$499$	−24.8765	+	16.3615i	−1.11362	+	0.732442i	−0.147127	+	0.989118i	$0.547002\pi$
$500$	−0.0621658	−	1.06735i	−0.00278014	−	0.0477331i
$501$	−0.442469	−	3.27041i	−0.0197681	−	0.146111i
$502$	−2.40954	−	8.04843i	−0.107543	−	0.359219i
$503$	0.405417	+	0.147560i	0.0180767	+	0.00657936i	0.351043	−	0.936359i	$-0.385827\pi$
$503$	0.405417	+	0.147560i	0.0180767	+	0.00657936i	−0.332966	+	0.942939i	$0.608049\pi$
$504$	−2.00957	+	0.553906i	−0.0895132	+	0.0246729i
$505$	−57.6774	+	20.9928i	−2.56661	+	0.934169i
$506$	23.2792	+	31.2693i	1.03488	+	1.39009i
$507$	−0.0728627	−	4.02006i	−0.00323595	−	0.178537i
$508$	−9.54958	+	2.26329i	−0.423694	+	0.100417i
$509$	8.75229	+	20.2901i	0.387939	+	0.899343i	0.994542	+	0.104338i	$0.0332724\pi$
$509$	8.75229	+	20.2901i	0.387939	+	0.899343i	−0.606603	+	0.795005i	$0.707468\pi$
$510$	−6.19478	−	24.1766i	−0.274309	−	1.07056i
$511$	−4.99166	−	3.28307i	−0.220818	−	0.145234i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−0.671697	−	12.3424i	−0.0296561	−	0.544928i
$514$	7.09614	+	12.2909i	0.312997	+	0.542127i
$515$	1.07327	−	18.4273i	0.0472939	−	0.812004i
$516$	−9.08878	−	13.2879i	−0.400111	−	0.584968i
$517$	57.5266	+	6.72390i	2.53002	+	0.295717i
$518$	0.582472	+	0.617384i	0.0255924	+	0.0271263i
$519$	−2.47790	+	0.483377i	−0.108768	+	0.0212179i
$520$	10.0858	−	1.17886i	0.442290	−	0.0516963i
$521$	0.934191	+	0.783879i	0.0409276	+	0.0343424i	0.663022	−	0.748600i	$-0.269274\pi$
$521$	0.934191	+	0.783879i	0.0409276	+	0.0343424i	−0.622094	+	0.782942i	$0.713718\pi$
$522$	−3.93762	−	1.27359i	−0.172345	−	0.0557433i
$523$	7.65711	−	6.42508i	0.334822	−	0.280949i	−0.459839	−	0.888002i	$-0.652093\pi$
$523$	7.65711	−	6.42508i	0.334822	−	0.280949i	0.794661	+	0.607053i	$0.207648\pi$
$524$	−12.6845	+	13.4448i	−0.554124	+	0.587337i
$525$	2.99376	−	4.73658i	0.130658	−	0.206721i
$526$	−21.5058	−	10.8006i	−0.937696	−	0.470929i
$527$	14.7341	+	7.39977i	0.641829	+	0.322339i
$528$	4.45107	+	8.47623i	0.193708	+	0.368881i
$529$	−18.3499	+	19.4498i	−0.797822	+	0.845642i
$530$	−10.0817	+	8.45954i	−0.437921	+	0.367459i
$531$	−8.09093	+	15.2661i	−0.351116	+	0.662492i
$532$	1.26618	+	1.06245i	0.0548958	+	0.0460630i
$533$	−36.8364	+	4.30556i	−1.59556	+	0.186495i
$534$	−4.20965	−	4.83610i	−0.182169	−	0.209279i
$535$	6.92243	+	7.33734i	0.299283	+	0.317221i
$536$	−1.01627	−	0.118785i	−0.0438962	−	0.00513074i
$537$	−6.25706	+	0.478345i	−0.270012	+	0.0206421i
$538$	0.465216	−	7.98745i	0.0200569	−	0.344363i
$539$	18.0118	+	31.1974i	0.775823	+	1.34377i
$540$	15.1937	−	5.46460i	0.653832	−	0.235159i
$541$	−1.46755	+	2.54188i	−0.0630951	+	0.109284i	−0.895847	−	0.444362i	$-0.853430\pi$
$541$	−1.46755	+	2.54188i	−0.0630951	+	0.109284i	0.832752	+	0.553646i	$0.186764\pi$
$542$	3.15714	+	2.07648i	0.135611	+	0.0891925i
$543$	27.4638	−	26.8680i	1.17858	−	1.15301i
$544$	1.83666	+	4.25786i	0.0787462	+	0.182554i
$545$	25.5366	−	6.05228i	1.09387	−	0.259251i
$546$	−3.44097	−	1.90435i	−0.147260	−	0.0814987i
$547$	9.40820	+	12.6374i	0.402266	+	0.540336i	0.956388	−	0.292099i	$-0.0943535\pi$
$547$	9.40820	+	12.6374i	0.402266	+	0.540336i	−0.554123	+	0.832435i	$0.686946\pi$
$548$	13.7883	−	5.01852i	0.589006	−	0.214380i
$549$	5.17731	+	0.415642i	0.220962	+	0.0177392i
$550$	−24.1835	−	8.80206i	−1.03119	−	0.375321i
$551$	0.941154	+	3.14367i	0.0400945	+	0.133925i
$552$	−9.66456	+	7.47097i	−0.411351	+	0.317986i
$553$	0.355390	+	6.10181i	0.0151127	+	0.259475i
$554$	−7.82687	+	5.14782i	−0.332532	+	0.218710i
$555$	−4.86322	−	4.42441i	−0.206432	−	0.187806i
$556$	12.4653	+	2.95433i	0.528646	+	0.125291i
$557$	−2.45674	−	13.9329i	−0.104095	−	0.590354i	−0.991578	−	0.129512i	$-0.958659\pi$
$557$	−2.45674	−	13.9329i	−0.104095	−	0.590354i	0.887482	−	0.460841i	$-0.152452\pi$
$558$	−3.86726	+	9.94125i	−0.163714	+	0.420847i
$559$	5.27429	−	29.9120i	0.223079	−	1.26514i
$560$	−0.855189	+	1.98255i	−0.0361383	+	0.0837780i
$561$	43.8529	+	6.91553i	1.85147	+	0.291974i
$562$	−2.22712	+	7.43911i	−0.0939455	+	0.313800i
$563$	−14.2152	+	19.0944i	−0.599101	+	0.804732i	−0.993455	−	0.114226i	$-0.963561\pi$
$563$	−14.2152	+	19.0944i	−0.599101	+	0.804732i	0.394354	+	0.918959i	$0.370968\pi$
$564$	−1.77995	+	18.0614i	−0.0749492	+	0.760522i
$565$	−32.2946	+	16.2190i	−1.35865	+	0.682338i
$566$	−19.1701			−0.805781
$567$	−6.01587	−	1.70760i	−0.252643	−	0.0717124i
$568$	−11.7869			−0.494566
$569$	−1.76778	+	0.887811i	−0.0741091	+	0.0372190i	−0.485468	−	0.874255i	$-0.661351\pi$
$569$	−1.76778	+	0.887811i	−0.0741091	+	0.0372190i	0.411359	+	0.911474i	$0.365054\pi$
$570$	−10.4066	−	7.45814i	−0.435883	−	0.312387i
$571$	5.08064	−	6.82448i	0.212618	−	0.285596i	−0.683001	−	0.730417i	$-0.739326\pi$
$571$	5.08064	−	6.82448i	0.212618	−	0.285596i	0.895619	+	0.444822i	$0.146733\pi$
$572$	−5.18046	+	17.3039i	−0.216606	+	0.723513i
$573$	3.63879	+	9.46044i	0.152013	+	0.395216i
$574$	3.12342	−	7.24091i	0.130369	−	0.302230i
$575$	5.70202	−	32.3378i	0.237791	−	1.34858i
$576$	−2.63035	+	1.44266i	−0.109598	+	0.0601109i
$577$	−6.90467	−	39.1583i	−0.287445	−	1.63018i	−0.696418	−	0.717636i	$-0.745224\pi$
$577$	−6.90467	−	39.1583i	−0.287445	−	1.63018i	0.408973	−	0.912546i	$-0.365887\pi$
$578$	4.38131	+	1.03839i	0.182239	+	0.0431913i
$579$	23.8438	−	7.61183i	0.990914	−	0.316337i
$580$	−3.58142	+	2.35554i	−0.148710	+	0.0978084i
$581$	0.366821	+	6.29807i	0.0152183	+	0.261288i
$582$	−1.45828	−	0.597934i	−0.0604476	−	0.0247852i
$583$	−6.71417	−	22.4269i	−0.278072	−	0.928826i
$584$	−8.07995	−	2.94086i	−0.334351	−	0.121694i
$585$	27.7005	+	12.6764i	1.14528	+	0.524105i
$586$	16.5802	−	6.03472i	0.684924	−	0.249292i
$587$	6.53316	+	8.77555i	0.269652	+	0.362206i	0.916237	−	0.400636i	$-0.131211\pi$
$587$	6.53316	+	8.77555i	0.269652	+	0.362206i	−0.646585	+	0.762842i	$0.723803\pi$
$588$	−9.67192	+	5.82029i	−0.398863	+	0.240025i
$589$	8.23021	−	1.95060i	0.339120	−	0.0803729i
$590$	7.08832	+	16.4326i	0.291821	+	0.676518i
$591$	7.98018	+	2.23236i	0.328261	+	0.0918268i
$592$	1.02060	+	0.671260i	0.0419465	+	0.0275886i
$593$	−6.95035	+	12.0384i	−0.285417	+	0.494356i	−0.972710	−	0.232024i	$-0.925465\pi$
$593$	−6.95035	+	12.0384i	−0.285417	+	0.494356i	0.687293	+	0.726380i	$0.258799\pi$
$594$	−1.77922	+	28.6664i	−0.0730022	+	1.17620i
$595$	5.00605	+	8.67074i	0.205228	+	0.355466i
$596$	1.03002	−	17.6848i	0.0421914	−	0.724398i
$597$	−11.6598	+	24.3051i	−0.477205	+	0.994743i
$598$	−22.8909	−	2.67556i	−0.936079	−	0.109412i
$599$	8.55657	+	9.06943i	0.349612	+	0.370567i	0.878185	−	0.478321i	$-0.158754\pi$
$599$	8.55657	+	9.06943i	0.349612	+	0.370567i	−0.528573	+	0.848888i	$0.677273\pi$
$600$	2.62038	−	7.62671i	0.106976	−	0.311359i
$601$	−33.8011	+	3.95078i	−1.37877	+	0.161156i	−0.772962	−	0.634452i	$-0.781226\pi$
$601$	−33.8011	+	3.95078i	−1.37877	+	0.161156i	−0.605813	+	0.795607i	$0.707152\pi$
$602$	4.94734	+	4.15131i	0.201638	+	0.169195i
$603$	−2.42138	−	1.88658i	−0.0986063	−	0.0768273i
$604$	12.0849	−	10.1404i	0.491726	−	0.412607i
$605$	41.6951	−	44.1942i	1.69515	−	1.79675i
$606$	34.1849	+	1.37000i	1.38867	+	0.0556526i
$607$	−0.126803	−	0.0636828i	−0.00514677	−	0.00258481i	0.446224	−	0.894921i	$-0.352768\pi$
$607$	−0.126803	−	0.0636828i	−0.00514677	−	0.00258481i	−0.451371	+	0.892337i	$0.649065\pi$
$608$	2.12578	+	1.06760i	0.0862116	+	0.0432971i
$609$	1.65887	+	0.0664813i	0.0672208	+	0.00269396i
$610$	3.69192	−	3.91321i	0.149481	−	0.158441i
$611$	−26.2302	+	22.0097i	−1.06116	+	0.890419i
$612$	−1.91763	+	13.7785i	−0.0775156	+	0.556963i
$613$	5.46537	+	4.58599i	0.220744	+	0.185226i	0.746453	−	0.665438i	$-0.231755\pi$
$613$	5.46537	+	4.58599i	0.220744	+	0.185226i	−0.525709	+	0.850665i	$0.676200\pi$
$614$	−13.6550	+	1.59605i	−0.551073	+	0.0644111i
$615$	−19.8482	+	57.7689i	−0.800355	+	2.32947i
$616$	−2.63563	−	2.79361i	−0.106193	−	0.112558i
$617$	−12.3620	−	1.44491i	−0.497674	−	0.0581698i	−0.136447	−	0.990647i	$-0.543568\pi$
$617$	−12.3620	−	1.44491i	−0.497674	−	0.0581698i	−0.361228	+	0.932478i	$0.617642\pi$
$618$	−4.45019	+	9.27649i	−0.179013	+	0.373155i
$619$	−0.942223	+	16.1773i	−0.0378711	+	0.650222i	0.924951	+	0.380086i	$0.124106\pi$
$619$	−0.942223	+	16.1773i	−0.0378711	+	0.650222i	−0.962822	+	0.270136i	$0.912931\pi$
$620$	5.52442	+	9.56858i	0.221866	+	0.384283i
$621$	−36.4147	+	4.11573i	−1.46127	+	0.165158i
$622$	8.97070	−	15.5377i	0.359692	−	0.623005i
$623$	2.14897	+	1.41340i	0.0860966	+	0.0566266i
$624$	−5.45077	−	1.52479i	−0.218206	−	0.0610403i
$625$	−10.5365	−	24.4263i	−0.421460	−	0.977054i
$626$	4.64166	−	1.10009i	0.185518	−	0.0439686i
$627$	19.5135	−	11.7427i	0.779295	−	0.468958i
$628$	−1.87945	−	2.52454i	−0.0749984	−	0.100740i
$629$	5.32290	−	1.93738i	0.212238	−	0.0772482i
$630$	−5.27925	+	3.75316i	−0.210330	+	0.149529i
$631$	30.2871	+	11.0236i	1.20571	+	0.438843i	0.865214	−	0.501402i	$-0.167182\pi$
$631$	30.2871	+	11.0236i	1.20571	+	0.438843i	0.340497	+	0.940246i	$0.389405\pi$
$632$	2.52288	+	8.42700i	0.100355	+	0.335208i
$633$	23.5941	+	9.67424i	0.937782	+	0.384517i
$634$	0.286844	+	4.92493i	0.0113920	+	0.195594i
$635$	−25.4794	+	16.7580i	−1.01112	+	0.665023i
$636$	6.98826	−	2.23091i	0.277103	−	0.0884615i
$637$	−20.7230	−	4.91143i	−0.821074	−	0.194598i
$638$	−1.32408	−	7.50923i	−0.0524208	−	0.297293i
$639$	−30.2281	−	18.3476i	−1.19580	−	0.725821i
$640$	−0.539594	+	3.06019i	−0.0213293	+	0.120965i
$641$	2.93257	−	6.79846i	0.115829	−	0.268523i	−0.850432	−	0.526084i	$-0.823660\pi$
$641$	2.93257	−	6.79846i	0.115829	−	0.268523i	0.966262	+	0.257561i	$0.0829189\pi$
$642$	−2.01851	−	5.24789i	−0.0796642	−	0.207118i
$643$	−2.09220	+	6.98845i	−0.0825085	+	0.275597i	−0.989281	−	0.146022i	$-0.953353\pi$
$643$	−2.09220	+	6.98845i	−0.0825085	+	0.275597i	0.906773	+	0.421619i	$0.138538\pi$
$644$	2.92633	−	3.93074i	0.115314	−	0.154893i
$645$	−40.6616	−	29.1412i	−1.60105	−	1.14743i
$646$	9.85743	−	4.95059i	0.387835	−	0.194778i
$647$	25.8659			1.01689			0.508446	−	0.861094i	$-0.330220\pi$
$647$	25.8659			1.01689			0.508446	+	0.861094i	$0.330220\pi$
$648$	−8.99134	−	0.394650i	−0.353213	−	0.0155033i
$649$	−31.8339			−1.24959
$650$	13.5964	−	6.82836i	0.533294	−	0.267830i
$651$	0.419680	−	4.25857i	0.0164486	−	0.166906i
$652$	−6.37357	+	8.56119i	−0.249608	+	0.335282i
$653$	0.658203	−	2.19855i	0.0257575	−	0.0860360i	−0.944144	−	0.329532i	$-0.893109\pi$
$653$	0.658203	−	2.19855i	0.0257575	−	0.0860360i	0.969902	+	0.243496i	$0.0782943\pi$
$654$	−14.4497	−	2.27870i	−0.565029	−	0.0891040i
$655$	−22.7497	+	52.7397i	−0.888903	+	2.06071i
$656$	1.97077	−	11.1768i	0.0769457	−	0.436381i
$657$	−16.1437	−	20.1194i	−0.629826	−	0.784932i
$658$	−1.26428	−	7.17007i	−0.0492866	−	0.279518i
$659$	−32.6804	−	7.74540i	−1.27305	−	0.301718i	−0.462095	−	0.886830i	$-0.652902\pi$
$659$	−32.6804	−	7.74540i	−1.27305	−	0.301718i	−0.810952	+	0.585113i	$0.801050\pi$
$660$	22.0056	+	20.0200i	0.856567	+	0.779279i
$661$	15.0448	−	9.89512i	0.585175	−	0.384875i	−0.222124	−	0.975018i	$-0.571299\pi$
$661$	15.0448	−	9.89512i	0.585175	−	0.384875i	0.807299	+	0.590143i	$0.200929\pi$
$662$	−1.20515	−	20.6917i	−0.0468396	−	0.804206i
$663$	−20.7651	+	16.0520i	−0.806451	+	0.623409i
$664$	2.60402	+	8.69804i	0.101056	+	0.337549i
$665$	4.82640	+	1.75667i	0.187160	+	0.0681206i
$666$	1.57250	+	3.31017i	0.0609329	+	0.128266i
$667$	9.14230	−	3.32753i	0.353991	−	0.128842i
$668$	1.13781	+	1.52835i	0.0440232	+	0.0591335i
$669$	−15.7238	−	8.70206i	−0.607915	−	0.336441i
$670$	−3.09376	+	0.733234i	−0.119522	+	0.0283273i
$671$	3.79041	+	8.78717i	0.146327	+	0.339225i
$672$	0.860277	−	0.841613i	0.0331859	−	0.0324659i
$673$	7.51146	+	4.94036i	0.289545	+	0.190437i	0.685969	−	0.727631i	$-0.259378\pi$
$673$	7.51146	+	4.94036i	0.289545	+	0.190437i	−0.396424	+	0.918068i	$0.629749\pi$
$674$	14.0117	−	24.2690i	0.539710	−	0.934806i
$675$	18.5920	−	15.4802i	0.715605	−	0.595834i
$676$	1.16068	+	2.01036i	0.0446416	+	0.0773215i
$677$	−1.07919	+	18.5289i	−0.0414765	+	0.712124i	0.911913	+	0.410383i	$0.134605\pi$
$677$	−1.07919	+	18.5289i	−0.0414765	+	0.712124i	−0.953390	+	0.301741i	$0.902432\pi$
$678$	20.0849	−	1.53547i	0.771356	−	0.0589693i
$679$	0.628000	+	0.0734027i	0.0241004	+	0.00281694i
$680$	9.88827	+	10.4810i	0.379198	+	0.401926i
$681$	−11.3288	−	13.0147i	−0.434121	−	0.498725i
$682$	−19.5209	+	2.28166i	−0.747493	+	0.0873694i
$683$	6.63544	+	5.56779i	0.253898	+	0.213046i	0.760849	−	0.648929i	$-0.224783\pi$
$683$	6.63544	+	5.56779i	0.253898	+	0.213046i	−0.506951	+	0.861975i	$0.669227\pi$
$684$	3.78982	+	6.04695i	0.144907	+	0.231211i
$685$	34.9281	−	29.3082i	1.33453	−	1.11981i
$686$	6.44534	−	6.83166i	0.246084	−	0.260834i
$687$	16.8133	+	32.0178i	0.641468	+	1.22156i
$688$	8.30605	+	4.17146i	0.316665	+	0.159035i
$689$	12.3680	+	6.21144i	0.471183	+	0.236637i
$690$	−20.2804	+	32.0867i	−0.772062	+	1.22152i
$691$	25.2925	−	26.8085i	0.962172	−	1.01984i	−0.0376168	−	0.999292i	$-0.511977\pi$
$691$	25.2925	−	26.8085i	0.962172	−	1.01984i	0.999789	−	0.0205505i	$-0.00654189\pi$
$692$	1.11657	−	0.936917i	0.0424458	−	0.0356162i
$693$	−2.41066	−	11.2670i	−0.0915732	−	0.427999i
$694$	8.35139	+	7.00765i	0.317015	+	0.266007i
$695$	39.5385	−	4.62139i	1.49978	−	0.175299i
$696$	2.34514	−	0.457479i	0.0888923	−	0.0173407i
$697$	−36.1152	−	38.2798i	−1.36796	−	1.44995i
$698$	16.0962	+	1.88138i	0.609250	+	0.0712111i
$699$	11.2845	+	16.4981i	0.426819	+	0.624014i
$700$	−0.188105	+	3.22964i	−0.00710969	+	0.122069i
$701$	−18.8835	−	32.7071i	−0.713218	−	1.23533i	−0.963643	−	0.267194i	$-0.913904\pi$
$701$	−18.8835	−	32.7071i	−0.713218	−	1.23533i	0.250425	−	0.968136i	$-0.419430\pi$
$702$	−11.6053	−	12.3952i	−0.438014	−	0.467825i
$703$	1.45293	−	2.51655i	0.0547983	−	0.0949134i
$704$	−4.61813	−	3.03739i	−0.174052	−	0.114476i
$705$	13.9981	+	54.6310i	0.527199	+	2.05752i
$706$	10.8350	+	25.1184i	0.407782	+	0.945344i
$707$	−13.3548	+	3.16515i	−0.502259	+	0.119038i
$708$	−0.180770	−	9.97361i	−0.00679374	−	0.374831i
$709$	−9.95354	−	13.3699i	−0.373813	−	0.502118i	0.574914	−	0.818214i	$-0.305035\pi$
$709$	−9.95354	−	13.3699i	−0.373813	−	0.502118i	−0.948727	+	0.316096i	$0.897628\pi$
$710$	−34.4177	+	12.5270i	−1.29167	+	0.470130i
$711$	−6.64754	+	25.5387i	−0.249302	+	0.957774i
$712$	3.47851	+	1.26608i	0.130363	+	0.0474482i
$713$	−7.19209	−	24.0233i	−0.269346	−	0.899678i
$714$	−0.748223	−	5.53032i	−0.0280015	−	0.206967i
$715$	3.26356	+	56.0332i	0.122050	+	2.09552i
$716$	3.02702	−	1.99090i	0.113125	−	0.0744035i
$717$	−1.06567	+	4.88967i	−0.0397983	+	0.182608i
$718$	−5.91967	−	1.40299i	−0.220920	−	0.0523590i
$719$	−0.219237	−	1.24336i	−0.00817617	−	0.0463694i	0.980447	−	0.196785i	$-0.0630500\pi$
$719$	−0.219237	−	1.24336i	−0.00817617	−	0.0463694i	−0.988623	+	0.150415i	$0.951939\pi$
$720$	−6.14736	+	7.00809i	−0.229099	+	0.261176i
$721$	0.716725	−	4.06475i	0.0266922	−	0.151379i
$722$	−5.28422	+	12.2502i	−0.196658	+	0.455905i
$723$	−0.0577549	+	0.0714191i	−0.00214793	+	0.00265610i
$724$	−6.36192	+	21.2503i	−0.236439	+	0.789761i
$725$	−3.83543	+	5.15188i	−0.142444	+	0.191336i
$726$	−30.8486	+	13.9752i	−1.14490	+	0.518668i
$727$	5.85101	−	2.93849i	0.217002	−	0.108982i	−0.336978	−	0.941513i	$-0.609405\pi$
$727$	5.85101	−	2.93849i	0.217002	−	0.108982i	0.553980	+	0.832530i	$0.313108\pi$
$728$	2.27060			0.0841539
$729$	−22.4445	−	15.0082i	−0.831277	−	0.555858i
$730$	−26.7190			−0.988915
$731$	38.5160	−	19.3434i	1.42456	−	0.715443i
$732$	−2.73151	+	1.23744i	−0.100960	+	0.0457372i
$733$	4.97694	−	6.68519i	0.183827	−	0.246923i	−0.700651	−	0.713504i	$-0.747107\pi$
$733$	4.97694	−	6.68519i	0.183827	−	0.246923i	0.884478	+	0.466581i	$0.154514\pi$
$734$	−5.15990	+	17.2353i	−0.190455	+	0.636166i
$735$	−22.0562	+	27.2745i	−0.813557	+	1.00604i
$736$	2.79341	−	6.47585i	0.102966	−	0.238703i
$737$	0.982093	−	5.56972i	0.0361759	−	0.205163i
$738$	22.4521	−	25.5958i	0.826475	−	0.942194i
$739$	2.08267	+	11.8114i	0.0766121	+	0.434489i	0.998853	+	0.0478740i	$0.0152446\pi$
$739$	2.08267	+	11.8114i	0.0766121	+	0.434489i	−0.922241	+	0.386615i	$0.873644\pi$
$740$	3.69357	+	0.875391i	0.135778	+	0.0321800i
$741$	−2.86711	+	13.1553i	−0.105326	+	0.483271i
$742$	−2.45869	+	1.61711i	−0.0902615	+	0.0593659i
$743$	−1.67970	−	28.8393i	−0.0616222	−	1.05801i	−0.877435	−	0.479696i	$-0.840747\pi$
$743$	−1.67970	−	28.8393i	−0.0616222	−	1.05801i	0.815813	−	0.578316i	$-0.196290\pi$
$744$	−0.825699	−	6.10297i	−0.0302716	−	0.223746i
$745$	−15.7876	−	52.7344i	−0.578414	−	1.93204i
$746$	22.4333	+	8.16506i	0.821342	+	0.298944i
$747$	−6.86134	+	26.3601i	−0.251043	+	0.964464i
$748$	−24.0856	+	8.76645i	−0.880658	+	0.320533i
$749$	1.34696	+	1.80929i	0.0492170	+	0.0661099i
$750$	0.0335585	+	1.85153i	0.00122538	+	0.0676081i
$751$	−6.59190	+	1.56231i	−0.240542	+	0.0570094i	−0.349118	−	0.937079i	$-0.613519\pi$
$751$	−6.59190	+	1.56231i	−0.240542	+	0.0570094i	0.108577	+	0.994088i	$0.465371\pi$
$752$	−4.15023	−	9.62132i	−0.151343	−	0.350853i
$753$	3.61187	+	14.0962i	0.131624	+	0.513695i
$754$	3.76631	+	2.47714i	0.137161	+	0.0902122i
$755$	24.5107	−	42.4537i	0.892034	−	1.54505i
$756$	3.51630	−	0.819244i	0.127887	−	0.0297956i
$757$	−10.9210	−	18.9158i	−0.396932	−	0.687506i	0.596414	−	0.802677i	$-0.296592\pi$
$757$	−10.9210	−	18.9158i	−0.396932	−	0.687506i	−0.993346	+	0.115171i	$0.963258\pi$
$758$	−1.37503	+	23.6084i	−0.0499433	+	0.857494i
$759$	−38.1196	−	55.7313i	−1.38365	−	2.02292i
$760$	7.34191	+	0.858146i	0.266319	+	0.0311282i
$761$	16.0381	+	16.9994i	0.581381	+	0.616228i	0.949582	−	0.313518i	$-0.101508\pi$
$761$	16.0381	+	16.9994i	0.581381	+	0.616228i	−0.368201	+	0.929746i	$0.620026\pi$
$762$	16.6841	−	3.25465i	0.604400	−	0.117903i
$763$	5.82866	−	0.681273i	0.211012	−	0.0246637i
$764$	−4.48296	−	3.76165i	−0.162188	−	0.136092i
$765$	9.04421	+	42.2712i	0.326994	+	1.52832i
$766$	−10.9251	+	9.16727i	−0.394741	+	0.331227i
$767$	12.9151	−	13.6892i	0.466338	−	0.494289i
$768$	0.925397	−	1.46412i	0.0333924	−	0.0528318i
$769$	34.6714	+	17.4126i	1.25028	+	0.627915i	0.945846	−	0.324617i	$-0.105235\pi$
$769$	34.6714	+	17.4126i	1.25028	+	0.627915i	0.304437	+	0.952532i	$0.401532\pi$
$770$	−10.6651	−	5.35621i	−0.384343	−	0.193024i
$771$	−11.4285	−	21.7635i	−0.411589	−	0.783794i
$772$	−9.91666	+	10.5110i	−0.356908	+	0.378301i
$773$	32.0265	−	26.8735i	1.15191	−	0.966571i	0.152152	−	0.988357i	$-0.451380\pi$
$773$	32.0265	−	26.8735i	1.15191	−	0.966571i	0.999763	+	0.0217863i	$0.00693535\pi$
$774$	14.8080	+	23.6273i	0.532262	+	0.849264i
$775$	12.6818	+	10.6413i	0.455543	+	0.382246i
$776$	0.903811	−	0.105640i	0.0324449	−	0.00379227i
$777$	−0.965241	−	1.10888i	−0.0346278	−	0.0397809i
$778$	24.4846	+	25.9521i	0.877814	+	0.930428i
$779$	−26.8150	−	3.13423i	−0.960748	−	0.112295i
$780$	−17.5368	+	1.34067i	−0.627918	+	0.0480036i
$781$	3.78822	−	65.0413i	0.135553	−	2.32736i
$782$	−16.3519	−	28.3223i	−0.584742	−	1.01280i
$783$	6.72636	+	2.47725i	0.240381	+	0.0885298i
$784$	3.25860	−	5.64406i	0.116379	−	0.201574i
$785$	−8.17107	−	5.37420i	−0.291638	−	0.191813i
$786$	22.8850	−	22.3885i	0.816282	−	0.798573i
$787$	13.6882	+	31.7327i	0.487930	+	1.13115i	0.967323	+	0.253549i	$0.0815977\pi$
$787$	13.6882	+	31.7327i	0.487930	+	1.13115i	−0.479393	+	0.877601i	$0.659143\pi$
$788$	−4.65527	+	1.10332i	−0.165837	+	0.0393041i
$789$	36.4701	+	20.1838i	1.29837	+	0.718562i
$790$	16.3230	+	21.9255i	0.580745	+	0.780076i
$791$	−7.59350	+	2.76381i	−0.269994	+	0.0982698i
$792$	−7.11540	−	14.9782i	−0.252835	−	0.532228i
$793$	−5.31645	−	1.93503i	−0.188793	−	0.0687149i
$794$	−6.99757	−	23.3735i	−0.248335	−	0.829495i
$795$	18.0347	−	13.9414i	0.639626	−	0.494449i
$796$	−0.904952	−	15.5374i	−0.0320752	−	0.550709i
$797$	2.47748	−	1.62946i	0.0877569	−	0.0577186i	−0.504872	−	0.863194i	$-0.668460\pi$
$797$	2.47748	−	1.62946i	0.0877569	−	0.0577186i	0.592629	+	0.805476i	$0.298090\pi$
$798$	−2.11763	−	1.92656i	−0.0749635	−	0.0681995i
$799$	−47.2791	−	11.2053i	−1.67261	−	0.396417i
$800$	0.808494	+	4.58520i	0.0285846	+	0.162111i
$801$	6.95005	+	8.66163i	0.245568	+	0.306044i
$802$	6.77751	−	38.4372i	0.239322	−	1.35726i
$803$	18.8249	−	43.6409i	0.664315	−	1.54005i
$804$	1.75058	+	0.276064i	0.0617383	+	0.00973602i
$805$	4.36732	−	14.5879i	0.153928	−	0.514155i
$806$	6.93853	−	9.32006i	0.244399	−	0.328285i
$807$	−1.35913	+	13.7913i	−0.0478436	+	0.485477i
$808$	−17.6515	+	8.86492i	−0.620978	+	0.311867i
$809$	−49.0772			−1.72546			−0.862731	−	0.505663i	$-0.831248\pi$
$809$	−49.0772			−1.72546			−0.862731	+	0.505663i	$0.831248\pi$
$810$	−26.6742	+	8.40356i	−0.937234	+	0.295271i
$811$	−19.4023			−0.681307			−0.340654	−	0.940189i	$-0.610648\pi$
$811$	−19.4023			−0.681307			−0.340654	+	0.940189i	$0.610648\pi$
$812$	−0.856563	+	0.430182i	−0.0300595	+	0.0150964i
$813$	−5.31991	−	3.81266i	−0.186577	−	0.133716i
$814$	−4.03210	+	5.41605i	−0.141325	+	0.189833i
$815$	−9.51205	+	31.7725i	−0.333193	+	1.11294i
$816$	−2.88332	−	7.49630i	−0.100936	−	0.262423i
$817$	8.75743	−	20.3020i	0.306384	−	0.710277i
$818$	−3.09484	+	17.5517i	−0.108208	+	0.613681i
$819$	5.82307	+	3.53445i	0.203475	+	0.123504i
$820$	−6.12398	−	34.7308i	−0.213859	−	1.21285i
$821$	0.0542400	+	0.0128551i	0.00189299	+	0.000448646i	0.231562	−	0.972820i	$-0.425616\pi$
$821$	0.0542400	+	0.0128551i	0.00189299	+	0.000448646i	−0.229669	+	0.973269i	$0.573764\pi$
$822$	−24.2109	+	7.72902i	−0.844452	+	0.269581i
$823$	24.4081	−	16.0535i	0.850813	−	0.559588i	−0.0475370	−	0.998869i	$-0.515137\pi$
$823$	24.4081	−	16.0535i	0.850813	−	0.559588i	0.898350	+	0.439281i	$0.144767\pi$
$824$	−0.345391	−	5.93014i	−0.0120323	−	0.206586i
$825$	41.2429	+	16.9107i	1.43589	+	0.588756i
$826$	1.14770	+	3.83359i	0.0399337	+	0.133388i
$827$	39.4672	+	14.3649i	1.37241	+	0.499516i	0.919868	−	0.392227i	$-0.128295\pi$
$827$	39.4672	+	14.3649i	1.37241	+	0.499516i	0.452541	+	0.891744i	$0.350518\pi$
$828$	17.2443	−	12.2594i	0.599279	−	0.426044i
$829$	−11.8020	+	4.29559i	−0.409902	+	0.149192i	−0.538737	−	0.842474i	$-0.681098\pi$
$829$	−11.8020	+	4.29559i	−0.409902	+	0.149192i	0.128835	+	0.991666i	$0.458876\pi$
$830$	16.8480	+	22.6307i	0.584801	+	0.785524i
$831$	13.9027	−	8.36627i	0.482280	−	0.290223i
$832$	3.17973	−	0.753611i	0.110237	−	0.0261268i
$833$	−11.9699	−	27.7493i	−0.414732	−	0.961457i
$834$	−21.3683	−	5.97751i	−0.739923	−	0.206984i
$835$	4.94673	+	3.25351i	0.171189	+	0.112592i
$836$	−6.57437	+	11.3872i	−0.227380	+	0.393833i
$837$	7.38243	−	16.9367i	0.255174	−	0.585418i
$838$	−3.98537	−	6.90286i	−0.137672	−	0.238455i
$839$	−2.36536	+	40.6117i	−0.0816613	+	1.40207i	0.669922	+	0.742432i	$0.266328\pi$
$839$	−2.36536	+	40.6117i	−0.0816613	+	1.40207i	−0.751583	+	0.659638i	$0.770709\pi$
$840$	1.61755	−	3.37181i	0.0558107	−	0.116338i
$841$	26.9138	+	3.14577i	0.928062	+	0.108475i
$842$	19.5358	+	20.7068i	0.673250	+	0.713603i
$843$	4.37036	−	12.7201i	0.150523	−	0.438104i
$844$	−14.6232	+	1.70920i	−0.503350	+	0.0588331i
$845$	5.52579	+	4.63669i	0.190093	+	0.159507i
$846$	4.33319	−	31.1347i	0.148978	−	1.07043i
$847$	10.4075	−	8.73293i	0.357606	−	0.300067i
$848$	−2.90643	+	3.08063i	−0.0998071	+	0.105789i
$849$	33.1770	+	1.32961i	1.13863	+	0.0456321i
$850$	19.2935	+	9.68958i	0.661763	+	0.332350i
$851$	−7.69886	−	3.86651i	−0.263914	−	0.132542i
$852$	20.3991	+	0.817519i	0.698861	+	0.0280077i
$853$	17.4593	−	18.5058i	0.597795	−	0.633625i	−0.355856	−	0.934541i	$-0.615811\pi$
$853$	17.4593	−	18.5058i	0.597795	−	0.633625i	0.953651	+	0.300916i	$0.0972922\pi$
$854$	0.921540	−	0.773264i	0.0315344	−	0.0264605i
$855$	17.4929	+	13.6293i	0.598246	+	0.466112i
$856$	2.48678	+	2.08666i	0.0849965	+	0.0713206i
$857$	45.3387	−	5.29934i	1.54874	−	0.181022i	0.701670	−	0.712502i	$-0.252438\pi$
$857$	45.3387	−	5.29934i	1.54874	−	0.181022i	0.847071	+	0.531480i	$0.178364\pi$
$858$	10.1658	−	29.5879i	0.347054	−	1.01012i
$859$	−11.0934	−	11.7583i	−0.378501	−	0.401188i	0.509916	−	0.860224i	$-0.329676\pi$
$859$	−11.0934	−	11.7583i	−0.378501	−	0.401188i	−0.888418	+	0.459036i	$0.848195\pi$
$860$	28.6871	+	3.35304i	0.978221	+	0.114338i
$861$	−5.90781	+	12.3149i	−0.201338	+	0.419692i
$862$	−1.59610	+	27.4040i	−0.0543635	+	0.933385i
$863$	−20.5808	−	35.6470i	−0.700578	−	1.21344i	−0.968264	−	0.249931i	$-0.919592\pi$
$863$	−20.5808	−	35.6470i	−0.700578	−	1.21344i	0.267685	−	0.963506i	$-0.413741\pi$
$864$	4.65230	−	2.31432i	0.158274	−	0.0787349i
$865$	2.26465	−	3.92248i	0.0770003	−	0.133368i
$866$	3.18624	+	2.09562i	0.108273	+	0.0712121i
$867$	−7.51055	−	2.10098i	−0.255072	−	0.0713531i
$868$	0.978553	+	2.26854i	0.0332143	+	0.0769993i
$869$	−47.3120	+	11.2131i	−1.60495	+	0.380380i
$870$	6.36160	−	3.82824i	0.215679	−	0.129789i
$871$	1.99666	+	2.68198i	0.0676542	+	0.0908754i
$872$	7.93631	−	2.88858i	0.268758	−	0.0978197i
$873$	2.48231	+	1.13597i	0.0840136	+	0.0384466i
$874$	−15.7651	−	5.73802i	−0.533262	−	0.194091i
$875$	−0.213062	−	0.711677i	−0.00720282	−	0.0240591i
$876$	13.7797	+	5.65005i	0.465573	+	0.190898i
$877$	1.27082	+	21.8191i	0.0429125	+	0.736778i	0.949308	+	0.314348i	$0.101786\pi$
$877$	1.27082	+	21.8191i	0.0429125	+	0.736778i	−0.906395	+	0.422430i	$0.861177\pi$
$878$	−4.60362	+	3.02785i	−0.155365	+	0.102185i
$879$	−29.1134	+	9.29407i	−0.981969	+	0.313481i
$880$	−16.7131	−	3.96107i	−0.563397	−	0.133528i
$881$	9.44504	+	53.5655i	0.318212	+	1.80467i	0.553619	+	0.832770i	$0.313247\pi$
$881$	9.44504	+	53.5655i	0.318212	+	1.80467i	−0.235407	+	0.971897i	$0.575642\pi$
$882$	17.1425	−	9.40213i	0.577218	−	0.316586i
$883$	7.67767	−	43.5423i	0.258374	−	1.46531i	−0.528886	−	0.848693i	$-0.677390\pi$
$883$	7.67767	−	43.5423i	0.258374	−	1.46531i	0.787260	−	0.616621i	$-0.211499\pi$
$884$	6.00187	−	13.9139i	0.201865	−	0.467975i
$885$	−11.1277	−	28.9308i	−0.374055	−	0.972499i
$886$	7.40223	−	24.7252i	0.248683	−	0.830658i
$887$	12.8442	−	17.2527i	0.431265	−	0.579290i	−0.532370	−	0.846512i	$-0.678698\pi$
$887$	12.8442	−	17.2527i	0.431265	−	0.579290i	0.963635	+	0.267222i	$0.0861057\pi$
$888$	−1.71976	−	1.23251i	−0.0577113	−	0.0413604i
$889$	−6.09386	+	3.06045i	−0.204382	+	0.102644i
$890$	11.5028			0.385576
$891$	5.06748	−	49.4884i	0.169767	−	1.65792i
$892$	10.3756			0.347402
$893$	−22.2745	+	11.1867i	−0.745386	+	0.374347i
$894$	−3.00921	+	30.5350i	−0.100643	+	1.02124i
$895$	6.72299	−	9.03054i	0.224725	−	0.301858i
$896$	−0.199281	+	0.665645i	−0.00665752	+	0.0222376i
$897$	39.4308	+	6.21817i	1.31656	+	0.207619i
$898$	−4.11339	+	9.53592i	−0.137266	+	0.318218i
$899$	−0.851742	+	4.83047i	−0.0284072	+	0.161105i
$900$	−5.06396	+	13.0175i	−0.168799	+	0.433917i
$901$	3.41035	+	19.3410i	0.113615	+	0.644344i
$902$	61.0415	+	14.4671i	2.03246	+	0.481702i
$903$	−8.27424	−	7.52765i	−0.275349	−	0.250505i
$904$	−9.71660	+	6.39071i	−0.323169	+	0.212552i
$905$	4.00786	+	68.8123i	0.133226	+	2.28740i
$906$	−21.6181	+	16.7114i	−0.718215	+	0.555200i
$907$	0.0159538	+	0.0532895i	0.000529738	+	0.00176945i	0.958254	−	0.285918i	$-0.0922986\pi$
$907$	0.0159538	+	0.0532895i	0.000529738	+	0.00176945i	−0.957724	+	0.287688i	$0.907113\pi$
$908$	9.36123	+	3.40721i	0.310663	+	0.113072i
$909$	−59.0675	−	4.74203i	−1.95915	−	0.157283i
$910$	6.63014	−	2.41318i	0.219787	−	0.0799960i
$911$	−5.46199	−	7.33672i	−0.180964	−	0.243076i	0.702380	−	0.711802i	$-0.252121\pi$
$911$	−5.46199	−	7.33672i	−0.180964	−	0.243076i	−0.883344	+	0.468726i	$0.844713\pi$
$912$	−3.60495	−	1.99510i	−0.119372	−	0.0660645i
$913$	−48.8337	+	11.5738i	−1.61616	+	0.383037i
$914$	−13.8558	−	32.1213i	−0.458309	−	1.06248i
$915$	−6.66088	+	6.51637i	−0.220202	+	0.215425i
$916$	−17.4443	−	11.4733i	−0.576377	−	0.379089i
$917$	−6.42166	+	11.1226i	−0.212062	+	0.367302i
$918$	4.27442	−	23.7129i	0.141077	−	0.782642i
$919$	1.08222	+	1.87445i	0.0356990	+	0.0618325i	0.883323	−	0.468765i	$-0.155301\pi$
$919$	1.08222	+	1.87445i	0.0356990	+	0.0618325i	−0.847624	+	0.530598i	$0.821968\pi$
$920$	1.27427	−	21.8783i	0.0420113	−	0.721306i
$921$	23.7429	−	1.81512i	0.782357	−	0.0598103i
$922$	−15.6563	−	1.82996i	−0.515613	−	0.0602665i
$923$	26.4322	+	28.0165i	0.870027	+	0.922175i
$924$	4.36763	+	5.01760i	0.143684	+	0.165067i
$925$	5.64906	−	0.660280i	0.185740	−	0.0217099i
$926$	2.90671	+	2.43902i	0.0955203	+	0.0801510i
$927$	8.34517	−	15.7458i	0.274091	−	0.517160i
$928$	−1.05675	+	0.886718i	−0.0346895	+	0.0291080i
$929$	1.40707	−	1.49140i	0.0461643	−	0.0489313i	−0.703880	−	0.710319i	$-0.748551\pi$
$929$	1.40707	−	1.49140i	0.0461643	−	0.0489313i	0.750044	+	0.661388i	$0.230032\pi$
$930$	−8.89724	−	16.9431i	−0.291752	−	0.555587i
$931$	−13.8541	−	6.95780i	−0.454050	−	0.228033i
$932$	−10.3127	−	5.17921i	−0.337803	−	0.169651i
$933$	−16.6029	+	26.2683i	−0.543555	+	0.859986i
$934$	27.5178	−	29.1672i	0.900412	−	0.954380i
$935$	−61.0131	+	51.1961i	−1.99534	+	1.67429i
$936$	9.32769	+	3.01695i	0.304885	+	0.0986120i
$937$	34.7783	+	29.1825i	1.13616	+	0.953350i	0.999306	−	0.0372415i	$-0.0118571\pi$
$937$	34.7783	+	29.1825i	1.13616	+	0.953350i	0.136852	+	0.990592i	$0.456302\pi$
$938$	−0.706142	+	0.0825361i	−0.0230563	+	0.00269490i
$939$	−8.10945	+	1.58195i	−0.264642	+	0.0516251i
$940$	−22.3441	−	23.6834i	−0.728786	−	0.772468i
$941$	3.74125	+	0.437289i	0.121961	+	0.0142552i	0.176855	−	0.984237i	$-0.443408\pi$
$941$	3.74125	+	0.437289i	0.121961	+	0.0142552i	−0.0548933	+	0.998492i	$0.517482\pi$
$942$	3.07760	+	4.49949i	0.100274	+	0.146601i
$943$	−4.65403	+	79.9066i	−0.151556	+	2.60212i
$944$	2.87961	+	4.98763i	0.0937232	+	0.162333i
$945$	9.39690	−	6.12929i	0.305681	−	0.199386i
$946$	−25.6881	+	44.4930i	−0.835191	+	1.44659i
$947$	−13.4364	−	8.83729i	−0.436626	−	0.287173i	0.312105	−	0.950048i	$-0.398966\pi$
$947$	−13.4364	−	8.83729i	−0.436626	−	0.287173i	−0.748731	+	0.662874i	$0.769336\pi$
$948$	−3.78176	−	14.7593i	−0.122826	−	0.479359i
$949$	11.1292	+	25.8004i	0.361269	+	0.837515i
$950$	10.7770	−	2.55420i	0.349652	−	0.0828691i
$951$	−0.154845	−	8.54328i	−0.00502120	−	0.277035i
$952$	1.92406	+	2.58446i	0.0623591	+	0.0837628i
$953$	−22.6638	+	8.24893i	−0.734151	+	0.267209i	−0.681921	−	0.731426i	$-0.738855\pi$
$953$	−22.6638	+	8.24893i	−0.734151	+	0.267209i	−0.0522302	+	0.998635i	$0.516633\pi$
$954$	−12.2491	+	3.37626i	−0.396578	+	0.109311i
$955$	−17.0881	−	6.21956i	−0.552958	−	0.201260i
$956$	−0.828667	−	2.76794i	−0.0268010	−	0.0895216i
$957$	1.77071	+	13.0878i	0.0572388	+	0.423068i
$958$	−1.31908	−	22.6477i	−0.0426175	−	0.731714i
$959$	8.51817	−	5.60249i	0.275066	−	0.180914i
$960$	1.14611	−	5.25873i	0.0369904	−	0.169725i
$961$	−17.8625	−	4.23349i	−0.576209	−	0.136564i
$962$	−0.693177	−	3.93120i	−0.0223489	−	0.126747i
$963$	3.12937	+	9.22232i	0.100843	+	0.297185i
$964$	0.00920844	−	0.0522236i	0.000296584	−	0.00168201i
$965$	−17.7856	+	41.2316i	−0.572538	+	1.32729i
$966$	−5.33712	+	6.59982i	−0.171719	+	0.212346i
$967$	−5.39397	+	18.0171i	−0.173458	+	0.579392i	0.826408	+	0.563071i	$0.190380\pi$
$967$	−5.39397	+	18.0171i	−0.173458	+	0.579392i	−0.999867	+	0.0163204i	$0.994805\pi$
$968$	11.6762	−	15.6838i	0.375286	−	0.504097i
$969$	−17.4032	+	7.88410i	−0.559073	+	0.253274i
$970$	2.52685	−	1.26903i	0.0811324	−	0.0407462i
$971$	−29.0121			−0.931043			−0.465522	−	0.885036i	$-0.654133\pi$
$971$	−29.0121			−0.931043			−0.465522	+	0.885036i	$0.654133\pi$
$972$	15.5336	+	1.30663i	0.498240	+	0.0419102i
$973$	8.90126			0.285361
$974$	−24.2018	+	12.1546i	−0.775477	+	0.389459i
$975$	−24.0044	+	10.8746i	−0.768755	+	0.348265i
$976$	1.03387	−	1.38873i	0.0330935	−	0.0444523i
$977$	0.146593	−	0.489655i	0.00468993	−	0.0156655i	−0.955613	−	0.294626i	$-0.904805\pi$
$977$	0.146593	−	0.489655i	0.00468993	−	0.0156655i	0.960302	+	0.278961i	$0.0899900\pi$
$978$	11.6243	−	14.3745i	0.371703	−	0.459644i
$979$	−8.10432	+	18.7879i	−0.259015	+	0.600464i
$980$	3.51665	−	19.9439i	0.112335	−	0.637084i
$981$	24.8495	+	4.94586i	0.793385	+	0.157909i
$982$	1.23480	+	7.00292i	0.0394042	+	0.223472i
$983$	−34.0298	−	8.06522i	−1.08538	−	0.257241i	−0.351275	−	0.936272i	$-0.614252\pi$
$983$	−34.0298	−	8.06522i	−1.08538	−	0.257241i	−0.734109	+	0.679032i	$0.762400\pi$
$984$	−4.18594	+	19.2066i	−0.133443	+	0.612283i
$985$	−12.4208	+	8.16929i	−0.395760	+	0.260295i
$986$	0.371942	+	6.38600i	0.0118451	+	0.203372i
$987$	1.69073	+	12.4966i	0.0538165	+	0.397773i
$988$	−2.22946	−	7.44693i	−0.0709287	−	0.236918i
$989$	−61.5989	−	22.4202i	−1.95873	−	0.712920i
$990$	−36.6957	−	36.1742i	−1.16627	−	1.14969i
$991$	−7.26164	+	2.64302i	−0.230674	+	0.0839583i	−0.454771	−	0.890608i	$-0.650279\pi$
$991$	−7.26164	+	2.64302i	−0.230674	+	0.0839583i	0.224097	+	0.974567i	$0.428057\pi$
$992$	2.12329	+	2.85207i	0.0674145	+	0.0905534i
$993$	0.650570	+	35.8939i	0.0206452	+	1.13906i
$994$	−7.96918	+	1.88873i	−0.252767	+	0.0599069i
$995$	−19.1555	−	44.4075i	−0.607271	−	1.40781i
$996$	−3.90340	−	15.2340i	−0.123684	−	0.482707i
$997$	2.97274	+	1.95520i	0.0941476	+	0.0619218i	0.595710	−	0.803200i	$-0.296871\pi$
$997$	2.97274	+	1.95520i	0.0941476	+	0.0619218i	−0.501562	+	0.865122i	$0.667241\pi$
$998$	−14.8874	+	25.7857i	−0.471252	+	0.816233i
$999$	−2.49187	−	5.83785i	−0.0788392	−	0.184701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.25.1	yes	90
3.2	odd	2		486.2.g.b.73.1		90
81.13	even	27	inner	162.2.g.b.13.1	✓	90
81.68	odd	54		486.2.g.b.253.1		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.1	✓	90	81.13	even	27	inner
162.2.g.b.25.1	yes	90	1.1	even	1	trivial
486.2.g.b.73.1		90	3.2	odd	2
486.2.g.b.253.1		90	81.68	odd	54

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)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(-1.57770 + 0.714739i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.891212 - 2.97686i) q^{5} +(-1.08911 + 1.34679i) q^{6} +(0.275210 - 0.638009i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.97830 - 2.25529i) q^{9} +O(q^{10})\)	\(q+(0.893633 - 0.448799i) q^{2} +(-1.57770 + 0.714739i) q^{3} +(0.597159 - 0.802123i) q^{4} +(0.891212 - 2.97686i) q^{5} +(-1.08911 + 1.34679i) q^{6} +(0.275210 - 0.638009i) q^{7} +(0.173648 - 0.984808i) q^{8} +(1.97830 - 2.25529i) q^{9} +(-0.539594 - 3.06019i) q^{10} +(5.37847 + 1.27472i) q^{11} +(-0.368831 + 1.69232i) q^{12} +(-2.73022 + 1.79570i) q^{13} +(-0.0404011 - 0.693660i) q^{14} +(0.721605 + 5.33358i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(-4.35745 - 1.58598i) q^{17} +(0.755699 - 2.90326i) q^{18} +(-2.23534 + 0.813599i) q^{19} +(-1.85561 - 2.49252i) q^{20} +(0.0218094 + 1.20329i) q^{21} +(5.37847 - 1.27472i) q^{22} +(2.79341 + 6.47585i) q^{23} +(0.429915 + 1.67785i) q^{24} +(-3.88998 - 2.55848i) q^{25} +(-1.63391 + 2.83001i) q^{26} +(-1.50922 + 4.97215i) q^{27} +(-0.347418 - 0.601745i) q^{28} +(0.0802101 - 1.37715i) q^{29} +(3.03856 + 4.44241i) q^{30} +(-3.53161 - 0.412786i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-9.39673 + 1.83307i) q^{33} +(-4.60574 + 0.538334i) q^{34} +(-1.65399 - 1.38786i) q^{35} +(-0.627664 - 2.93360i) q^{36} +(-0.935772 + 0.785206i) q^{37} +(-1.63243 + 1.73028i) q^{38} +(3.02403 - 4.78447i) q^{39} +(-2.77687 - 1.39460i) q^{40} +(10.1420 + 5.09352i) q^{41} +(0.559527 + 1.06551i) q^{42} +(-6.37841 + 6.76072i) q^{43} +(4.23428 - 3.55299i) q^{44} +(-4.95059 - 7.89905i) q^{45} +(5.40264 + 4.53335i) q^{46} +(10.4074 - 1.21645i) q^{47} +(1.13720 + 1.30643i) q^{48} +(4.47238 + 4.74044i) q^{49} +(-4.62445 - 0.540521i) q^{50} +(8.00832 - 0.612227i) q^{51} +(-0.190007 + 3.26229i) q^{52} +(-2.11764 - 3.66786i) q^{53} +(0.882803 + 5.12061i) q^{54} +(8.58802 - 14.8749i) q^{55} +(-0.580527 - 0.381818i) q^{56} +(2.94520 - 2.88130i) q^{57} +(-0.546388 - 1.26667i) q^{58} +(-5.60397 + 1.32817i) q^{59} +(4.70910 + 2.60618i) q^{60} +(1.03387 + 1.38873i) q^{61} +(-3.34122 + 1.21611i) q^{62} +(-0.894449 - 1.88285i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(2.91232 + 9.72783i) q^{65} +(-7.57454 + 5.85533i) q^{66} +(-0.0594932 - 1.02146i) q^{67} +(-3.87424 + 2.54813i) q^{68} +(-9.03571 - 8.22041i) q^{69} +(-2.10093 - 0.497930i) q^{70} +(-2.04677 - 11.6078i) q^{71} +(-1.87750 - 2.33987i) q^{72} +(1.49312 - 8.46788i) q^{73} +(-0.483836 + 1.12166i) q^{74} +(7.96587 + 1.25620i) q^{75} +(-0.682248 + 2.27887i) q^{76} +(2.29349 - 3.08070i) q^{77} +(0.555105 - 5.63274i) q^{78} +(-7.86088 + 3.94788i) q^{79} -3.10740 q^{80} +(-1.17268 - 8.92327i) q^{81} +11.3492 q^{82} +(-8.11371 + 4.07486i) q^{83} +(0.978213 + 0.701063i) q^{84} +(-8.60465 + 11.5580i) q^{85} +(-2.66575 + 8.90423i) q^{86} +(0.857758 + 2.23007i) q^{87} +(2.18932 - 5.07541i) q^{88} +(-0.642803 + 3.64552i) q^{89} +(-7.96910 - 4.83703i) q^{90} +(0.394285 + 2.23610i) q^{91} +(6.86253 + 1.62645i) q^{92} +(5.86687 - 1.87293i) q^{93} +(8.75447 - 5.75790i) q^{94} +(0.429800 + 7.37939i) q^{95} +(1.60257 + 0.657097i) q^{96} +(0.260981 + 0.871736i) q^{97} +(6.12417 + 2.22901i) q^{98} +(13.5151 - 9.60824i) 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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