LMFDB - Embedded newform 189.2.u.a.4.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.20
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.373934 + 2.12069i) q^{2} +(-1.62126 + 0.609530i) q^{3} +(-2.47810 + 0.901956i) q^{4} +(-1.18205 + 0.430229i) q^{5} +(-1.89887 - 3.21026i) q^{6} +(-2.62839 - 0.302569i) q^{7} +(-0.686013 - 1.18821i) q^{8} +(2.25695 - 1.97641i) q^{9} +O(q^{10})$	\(q+(0.373934 + 2.12069i) q^{2} +(-1.62126 + 0.609530i) q^{3} +(-2.47810 + 0.901956i) q^{4} +(-1.18205 + 0.430229i) q^{5} +(-1.89887 - 3.21026i) q^{6} +(-2.62839 - 0.302569i) q^{7} +(-0.686013 - 1.18821i) q^{8} +(2.25695 - 1.97641i) q^{9} +(-1.35439 - 2.34587i) q^{10} +(0.527955 + 0.192160i) q^{11} +(3.46787 - 2.97278i) q^{12} +(-3.76711 + 1.37111i) q^{13} +(-0.341193 - 5.68714i) q^{14} +(1.65416 - 1.41800i) q^{15} +(-1.77704 + 1.49111i) q^{16} +(1.82298 + 3.15749i) q^{17} +(5.03529 + 4.04723i) q^{18} +(1.32067 - 2.28747i) q^{19} +(2.54118 - 2.13231i) q^{20} +(4.44573 - 1.11154i) q^{21} +(-0.210090 + 1.19148i) q^{22} +(-0.669703 + 3.79808i) q^{23} +(1.83645 + 1.50825i) q^{24} +(-2.61809 + 2.19684i) q^{25} +(-4.31636 - 7.47615i) q^{26} +(-2.45441 + 4.57994i) q^{27} +(6.78634 - 1.62090i) q^{28} +(7.38407 + 2.68758i) q^{29} +(3.62569 + 2.97772i) q^{30} +(-7.43614 + 2.70653i) q^{31} +(-5.92875 - 4.97481i) q^{32} +(-0.973077 + 0.0102636i) q^{33} +(-6.01437 + 5.04666i) q^{34} +(3.23705 - 0.773162i) q^{35} +(-3.81032 + 6.93341i) q^{36} +6.30064 q^{37} +(5.34485 + 1.94537i) q^{38} +(5.27171 - 4.51909i) q^{39} +(1.32210 + 1.10938i) q^{40} +(2.95635 - 1.07602i) q^{41} +(4.01964 + 9.01235i) q^{42} +(0.190954 + 1.08296i) q^{43} -1.48165 q^{44} +(-1.81751 + 3.30721i) q^{45} -8.30496 q^{46} +(-7.72021 - 2.80993i) q^{47} +(1.97216 - 3.50064i) q^{48} +(6.81690 + 1.59054i) q^{49} +(-5.63780 - 4.73067i) q^{50} +(-4.88010 - 4.00794i) q^{51} +(8.09860 - 6.79553i) q^{52} +(-2.59291 + 4.49105i) q^{53} +(-10.6304 - 3.49245i) q^{54} -0.706739 q^{55} +(1.44360 + 3.33065i) q^{56} +(-0.746866 + 4.51356i) q^{57} +(-2.93836 + 16.6643i) q^{58} +(6.22586 + 5.22411i) q^{59} +(-2.82021 + 5.00594i) q^{60} +(9.96675 + 3.62760i) q^{61} +(-8.52034 - 14.7577i) q^{62} +(-6.53015 + 4.51190i) q^{63} +(6.01330 - 10.4153i) q^{64} +(3.86300 - 3.24144i) q^{65} +(-0.385633 - 2.05975i) q^{66} +(1.78355 - 10.1150i) q^{67} +(-7.36544 - 6.18034i) q^{68} +(-1.22928 - 6.56586i) q^{69} +(2.85008 + 6.57567i) q^{70} +(-4.01075 + 6.94683i) q^{71} +(-3.89668 - 1.32589i) q^{72} +3.24640 q^{73} +(2.35603 + 13.3617i) q^{74} +(2.90556 - 5.15744i) q^{75} +(-1.20956 + 6.85977i) q^{76} +(-1.32953 - 0.664814i) q^{77} +(11.5549 + 9.48981i) q^{78} +(-2.46342 - 13.9708i) q^{79} +(1.45902 - 2.52710i) q^{80} +(1.18762 - 8.92130i) q^{81} +(3.38739 + 5.86714i) q^{82} +(13.4275 + 4.88722i) q^{83} +(-10.0144 + 6.76437i) q^{84} +(-3.51329 - 2.94800i) q^{85} +(-2.22521 + 0.809909i) q^{86} +(-13.6096 + 0.143548i) q^{87} +(-0.133858 - 0.759145i) q^{88} +(3.34480 - 5.79337i) q^{89} +(-7.69319 - 2.61768i) q^{90} +(10.3163 - 2.46402i) q^{91} +(-1.76610 - 10.0161i) q^{92} +(10.4062 - 8.92053i) q^{93} +(3.07212 - 17.4229i) q^{94} +(-0.576956 + 3.27208i) q^{95} +(12.6443 + 4.45170i) q^{96} +(-0.378721 - 2.14784i) q^{97} +(-0.823964 + 15.0513i) q^{98} +(1.57135 - 0.609759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.373934	+	2.12069i	0.264412	+	1.49955i	0.770705	+	0.637192i	$0.219904\pi$
$2$	0.373934	+	2.12069i	0.264412	+	1.49955i	−0.506294	+	0.862361i	$0.668985\pi$
$3$	−1.62126	+	0.609530i	−0.936033	+	0.351912i
$3$	−1.62126	+	0.609530i	−0.936033	+	0.351912i
$4$	−2.47810	+	0.901956i	−1.23905	+	0.450978i
$5$	−1.18205	+	0.430229i	−0.528627	+	0.192404i	−0.592525	−	0.805552i	$-0.701869\pi$
$5$	−1.18205	+	0.430229i	−0.528627	+	0.192404i	0.0638983	+	0.997956i	$0.479647\pi$
$6$	−1.89887	−	3.21026i	−0.775209	−	1.31058i
$7$	−2.62839	−	0.302569i	−0.993439	−	0.114360i
$7$	−2.62839	−	0.302569i	−0.993439	−	0.114360i
$8$	−0.686013	−	1.18821i	−0.242542	−	0.420096i
$9$	2.25695	−	1.97641i	0.752316	−	0.658803i
$10$	−1.35439	−	2.34587i	−0.428296	−	0.741830i
$11$	0.527955	+	0.192160i	0.159184	+	0.0579384i	0.420383	−	0.907347i	$-0.361896\pi$
$11$	0.527955	+	0.192160i	0.159184	+	0.0579384i	−0.261199	+	0.965285i	$0.584118\pi$
$12$	3.46787	−	2.97278i	1.00109	−	0.858168i
$13$	−3.76711	+	1.37111i	−1.04481	+	0.380279i	−0.806701	−	0.590960i	$-0.798749\pi$
$13$	−3.76711	+	1.37111i	−1.04481	+	0.380279i	−0.238107	+	0.971239i	$0.576527\pi$
$14$	−0.341193	−	5.68714i	−0.0911876	−	1.51995i
$15$	1.65416	−	1.41800i	0.427103	−	0.366127i
$16$	−1.77704	+	1.49111i	−0.444260	+	0.372778i
$17$	1.82298	+	3.15749i	0.442137	+	0.765803i	0.997848	−	0.0655721i	$-0.0208872\pi$
$17$	1.82298	+	3.15749i	0.442137	+	0.765803i	−0.555711	+	0.831376i	$0.687554\pi$
$18$	5.03529	+	4.04723i	1.18683	+	0.953942i
$19$	1.32067	−	2.28747i	0.302982	−	0.524781i	−0.673828	−	0.738889i	$-0.735351\pi$
$19$	1.32067	−	2.28747i	0.302982	−	0.524781i	0.976810	+	0.214108i	$0.0686843\pi$
$20$	2.54118	−	2.13231i	0.568226	−	0.476798i
$21$	4.44573	−	1.11154i	0.970137	−	0.242558i
$22$	−0.210090	+	1.19148i	−0.0447914	+	0.254025i
$23$	−0.669703	+	3.79808i	−0.139643	+	0.791953i	0.831871	+	0.554969i	$0.187270\pi$
$23$	−0.669703	+	3.79808i	−0.139643	+	0.791953i	−0.971514	+	0.236984i	$0.923841\pi$
$24$	1.83645	+	1.50825i	0.374864	+	0.307870i
$25$	−2.61809	+	2.19684i	−0.523618	+	0.439367i
$26$	−4.31636	−	7.47615i	−0.846507	−	1.46619i
$27$	−2.45441	+	4.57994i	−0.472352	+	0.881410i
$28$	6.78634	−	1.62090i	1.28250	−	0.306321i
$29$	7.38407	+	2.68758i	1.37119	+	0.499071i	0.919495	−	0.393102i	$-0.128598\pi$
$29$	7.38407	+	2.68758i	1.37119	+	0.499071i	0.451693	+	0.892174i	$0.350820\pi$
$30$	3.62569	+	2.97772i	0.661958	+	0.543655i
$31$	−7.43614	+	2.70653i	−1.33557	+	0.486107i	−0.908414	−	0.418071i	$-0.862706\pi$
$31$	−7.43614	+	2.70653i	−1.33557	+	0.486107i	−0.427155	+	0.904178i	$0.640484\pi$
$32$	−5.92875	−	4.97481i	−1.04806	−	0.879431i
$33$	−0.973077	+	0.0102636i	−0.169391	+	0.00178666i
$34$	−6.01437	+	5.04666i	−1.03146	+	0.865495i
$35$	3.23705	−	0.773162i	0.547162	−	0.130688i
$36$	−3.81032	+	6.93341i	−0.635053	+	1.15557i
$37$	6.30064			1.03582			0.517910	−	0.855435i	$-0.326710\pi$
$37$	6.30064			1.03582			0.517910	+	0.855435i	$0.326710\pi$
$38$	5.34485	+	1.94537i	0.867049	+	0.315580i
$39$	5.27171	−	4.51909i	0.844150	−	0.723634i
$40$	1.32210	+	1.10938i	0.209043	+	0.175408i
$41$	2.95635	−	1.07602i	0.461705	−	0.168047i	−0.100686	−	0.994918i	$-0.532104\pi$
$41$	2.95635	−	1.07602i	0.461705	−	0.168047i	0.562391	+	0.826871i	$0.309882\pi$
$42$	4.01964	+	9.01235i	0.620244	+	1.39064i
$43$	0.190954	+	1.08296i	0.0291203	+	0.165149i	0.995900	−	0.0904620i	$-0.0288344\pi$
$43$	0.190954	+	1.08296i	0.0291203	+	0.165149i	−0.966780	+	0.255611i	$0.917723\pi$
$44$	−1.48165			−0.223367
$45$	−1.81751	+	3.30721i	−0.270938	+	0.493010i
$46$	−8.30496			−1.22450
$47$	−7.72021	−	2.80993i	−1.12611	−	0.409870i	−0.289230	−	0.957260i	$-0.593399\pi$
$47$	−7.72021	−	2.80993i	−1.12611	−	0.409870i	−0.836878	+	0.547390i	$0.815622\pi$
$48$	1.97216	−	3.50064i	0.284657	−	0.505273i
$49$	6.81690	+	1.59054i	0.973843	+	0.227220i
$50$	−5.63780	−	4.73067i	−0.797305	−	0.669018i
$51$	−4.88010	−	4.00794i	−0.683350	−	0.561224i
$52$	8.09860	−	6.79553i	1.12307	−	0.942370i
$53$	−2.59291	+	4.49105i	−0.356163	+	0.616893i	−0.987316	−	0.158765i	$-0.949249\pi$
$53$	−2.59291	+	4.49105i	−0.356163	+	0.616893i	0.631153	+	0.775658i	$0.282582\pi$
$54$	−10.6304	−	3.49245i	−1.44662	−	0.475262i
$55$	−0.706739			−0.0952967
$56$	1.44360	+	3.33065i	0.192909	+	0.445077i
$57$	−0.746866	+	4.51356i	−0.0989248	+	0.597835i
$58$	−2.93836	+	16.6643i	−0.385826	+	2.18813i
$59$	6.22586	+	5.22411i	0.810538	+	0.680122i	0.950736	−	0.310002i	$-0.100330\pi$
$59$	6.22586	+	5.22411i	0.810538	+	0.680122i	−0.140198	+	0.990123i	$0.544774\pi$
$60$	−2.82021	+	5.00594i	−0.364087	+	0.646264i
$61$	9.96675	+	3.62760i	1.27611	+	0.464466i	0.889144	−	0.457627i	$-0.151301\pi$
$61$	9.96675	+	3.62760i	1.27611	+	0.464466i	0.386967	+	0.922094i	$0.373523\pi$
$62$	−8.52034	−	14.7577i	−1.08208	−	1.87422i
$63$	−6.53015	+	4.51190i	−0.822721	+	0.568445i
$64$	6.01330	−	10.4153i	0.751662	−	1.30192i
$65$	3.86300	−	3.24144i	0.479146	−	0.402051i
$66$	−0.385633	−	2.05975i	−0.0474681	−	0.253538i
$67$	1.78355	−	10.1150i	0.217896	−	1.23575i	−0.657914	−	0.753093i	$-0.728561\pi$
$67$	1.78355	−	10.1150i	0.217896	−	1.23575i	0.875810	−	0.482656i	$-0.160328\pi$
$68$	−7.36544	−	6.18034i	−0.893191	−	0.749476i
$69$	−1.22928	−	6.56586i	−0.147988	−	0.790437i
$70$	2.85008	+	6.57567i	0.340650	+	0.785943i
$71$	−4.01075	+	6.94683i	−0.475989	+	0.824437i	−0.999622	−	0.0275070i	$-0.991243\pi$
$71$	−4.01075	+	6.94683i	−0.475989	+	0.824437i	0.523633	+	0.851944i	$0.324576\pi$
$72$	−3.89668	−	1.32589i	−0.459229	−	0.156257i
$73$	3.24640			0.379963			0.189981	−	0.981788i	$-0.439157\pi$
$73$	3.24640			0.379963			0.189981	+	0.981788i	$0.439157\pi$
$74$	2.35603	+	13.3617i	0.273883	+	1.55327i
$75$	2.90556	−	5.15744i	0.335505	−	0.595530i
$76$	−1.20956	+	6.85977i	−0.138746	+	0.786869i
$77$	−1.32953	−	0.664814i	−0.151514	−	0.0757626i
$78$	11.5549	+	9.48981i	1.30833	+	1.07451i
$79$	−2.46342	−	13.9708i	−0.277156	−	1.57183i	−0.732027	−	0.681275i	$-0.761426\pi$
$79$	−2.46342	−	13.9708i	−0.277156	−	1.57183i	0.454871	−	0.890557i	$-0.349685\pi$
$80$	1.45902	−	2.52710i	0.163124	−	0.282538i
$81$	1.18762	−	8.92130i	0.131958	−	0.991255i
$82$	3.38739	+	5.86714i	0.374075	+	0.647917i
$83$	13.4275	+	4.88722i	1.47386	+	0.536442i	0.949146	−	0.314835i	$-0.101949\pi$
$83$	13.4275	+	4.88722i	1.47386	+	0.536442i	0.524716	+	0.851277i	$0.324172\pi$
$84$	−10.0144	+	6.76437i	−1.09266	+	0.738053i
$85$	−3.51329	−	2.94800i	−0.381069	−	0.319755i
$86$	−2.22521	+	0.809909i	−0.239950	+	0.0873348i
$87$	−13.6096	+	0.143548i	−1.45911	+	0.0153900i
$88$	−0.133858	−	0.759145i	−0.0142693	−	0.0809251i
$89$	3.34480	−	5.79337i	0.354549	−	0.614096i	−0.632492	−	0.774567i	$-0.717968\pi$
$89$	3.34480	−	5.79337i	0.354549	−	0.614096i	0.987041	+	0.160471i	$0.0513012\pi$
$90$	−7.69319	−	2.61768i	−0.810933	−	0.275928i
$91$	10.3163	−	2.46402i	1.08144	−	0.258299i
$92$	−1.76610	−	10.0161i	−0.184129	−	1.04425i
$93$	10.4062	−	8.92053i	1.07907	−	0.925016i
$94$	3.07212	−	17.4229i	0.316865	−	1.79703i
$95$	−0.576956	+	3.27208i	−0.0591944	+	0.335708i
$96$	12.6443	+	4.45170i	1.29051	+	0.454350i
$97$	−0.378721	−	2.14784i	−0.0384533	−	0.218080i	0.959526	−	0.281620i	$-0.0908719\pi$
$97$	−0.378721	−	2.14784i	−0.0384533	−	0.218080i	−0.997979	+	0.0635407i	$0.979761\pi$
$98$	−0.823964	+	15.0513i	−0.0832329	+	1.52041i
$99$	1.57135	−	0.609759i	0.157927	−	0.0612831i
$100$	4.50644	−	7.80539i	0.450644	−	0.780539i
$101$	−2.18580	−	12.3963i	−0.217495	−	1.23347i	−0.876524	−	0.481358i	$-0.840144\pi$
$101$	−2.18580	−	12.3963i	−0.217495	−	1.23347i	0.659030	−	0.752117i	$-0.270967\pi$
$102$	6.67476	−	11.8479i	0.660899	−	1.17311i
$103$	0.0637281	−	0.0231951i	0.00627932	−	0.00228548i	−0.338879	−	0.940830i	$-0.610048\pi$
$103$	0.0637281	−	0.0231951i	0.00627932	−	0.00228548i	0.345158	+	0.938545i	$0.387825\pi$
$104$	4.21346	+	3.53551i	0.413163	+	0.346685i
$105$	−4.77683	+	3.22657i	−0.466171	+	0.314881i
$106$	−10.4937	−	3.81939i	−1.01924	−	0.370972i
$107$	2.34433	+	4.06050i	0.226635	+	0.392543i	0.956809	−	0.290718i	$-0.0938943\pi$
$107$	2.34433	+	4.06050i	0.226635	+	0.392543i	−0.730174	+	0.683261i	$0.760561\pi$
$108$	1.95138	−	13.5633i	0.187772	−	1.30513i
$109$	−7.09903	+	12.2959i	−0.679964	+	1.17773i	0.295027	+	0.955489i	$0.404671\pi$
$109$	−7.09903	+	12.2959i	−0.679964	+	1.17773i	−0.974991	+	0.222243i	$0.928662\pi$
$110$	−0.264274	−	1.49877i	−0.0251976	−	0.142902i
$111$	−10.2150	+	3.84043i	−0.969561	+	0.364517i
$112$	5.12193	−	3.38156i	0.483976	−	0.319527i
$113$	−0.270466	+	1.53389i	−0.0254433	+	0.144296i	−0.994883	−	0.101033i	$-0.967785\pi$
$113$	−0.270466	+	1.53389i	−0.0254433	+	0.144296i	0.969440	+	0.245330i	$0.0788962\pi$
$114$	−9.85113	+	0.103905i	−0.922643	+	0.00973163i
$115$	−0.842424	−	4.77762i	−0.0785564	−	0.445516i
$116$	−20.7226			−1.92404
$117$	−5.79228	+	10.5399i	−0.535496	+	0.974412i
$118$	−8.75065	+	15.1566i	−0.805563	+	1.39528i
$119$	−3.83614	−	8.85070i	−0.351659	−	0.811342i
$120$	−2.81966	−	0.992722i	−0.257399	−	0.0906227i
$121$	−8.18468	−	6.86776i	−0.744062	−	0.624342i
$122$	−3.96609	+	22.4928i	−0.359073	+	2.03641i
$123$	−4.13714	+	3.54650i	−0.373033	+	0.319777i
$124$	15.9863	−	13.4141i	1.43562	−	1.20463i
$125$	5.29432	−	9.17003i	0.473539	−	0.820193i
$126$	−12.0102	−	12.1612i	−1.06995	−	1.08341i
$127$	4.37260	+	7.57356i	0.388005	+	0.672045i	0.992181	−	0.124806i	$-0.0398309\pi$
$127$	4.37260	+	7.57356i	0.388005	+	0.672045i	−0.604176	+	0.796851i	$0.706498\pi$
$128$	9.79088	+	3.56359i	0.865400	+	0.314980i
$129$	−0.969680	−	1.63936i	−0.0853756	−	0.144337i
$130$	8.31859	+	6.98012i	0.729588	+	0.612197i
$131$	−3.14989	+	17.8639i	−0.275207	+	1.56078i	0.463096	+	0.886308i	$0.346739\pi$
$131$	−3.14989	+	17.8639i	−0.275207	+	1.56078i	−0.738303	+	0.674469i	$0.764372\pi$
$132$	2.40213	−	0.903107i	0.209079	−	0.0786054i
$133$	−4.16336	+	5.61277i	−0.361009	+	0.486689i
$134$	22.1178			1.91068
$135$	0.930802	−	6.46966i	0.0801107	−	0.556820i
$136$	2.50117	−	4.33216i	0.214474	−	0.371479i
$137$	−13.8684	+	11.6370i	−1.18486	+	0.994215i	−0.184925	+	0.982753i	$0.559204\pi$
$137$	−13.8684	+	11.6370i	−1.18486	+	0.994215i	−0.999934	+	0.0114625i	$0.996351\pi$
$138$	13.4645	−	5.06212i	1.14617	−	0.430916i
$139$	−1.87847	−	1.57622i	−0.159330	−	0.133693i	0.559637	−	0.828738i	$-0.310940\pi$
$139$	−1.87847	−	1.57622i	−0.159330	−	0.133693i	−0.718967	+	0.695044i	$0.755385\pi$
$140$	−7.32440	+	4.83566i	−0.619025	+	0.408688i
$141$	14.2292	−	0.150083i	1.19831	−	0.0126393i
$142$	−16.2318	−	5.90790i	−1.36214	−	0.495780i
$143$	−2.25233			−0.188350
$144$	−1.06364	+	6.87752i	−0.0886365	+	0.573127i
$145$	−9.88458			−0.820870
$146$	1.21394	+	6.88461i	0.100467	+	0.569774i
$147$	−12.0214	+	1.57643i	−0.991511	+	0.130022i
$148$	−15.6136	+	5.68290i	−1.28343	+	0.467132i
$149$	9.39990	+	7.88746i	0.770070	+	0.646166i	0.940727	−	0.339165i	$-0.110144\pi$
$149$	9.39990	+	7.88746i	0.770070	+	0.646166i	−0.170657	+	0.985331i	$0.554589\pi$
$150$	12.0238	+	4.23323i	0.981740	+	0.345642i
$151$	−22.2462	−	8.09696i	−1.81037	−	0.658921i	−0.997020	−	0.0771470i	$-0.975419\pi$
$151$	−22.2462	−	8.09696i	−1.81037	−	0.658921i	−0.813351	−	0.581774i	$-0.802359\pi$
$152$	−3.62399			−0.293944
$153$	10.3548	+	3.52334i	0.837140	+	0.284845i
$154$	0.912706	−	3.06812i	0.0735479	−	0.247236i
$155$	7.62542	−	6.39849i	0.612488	−	0.513939i
$156$	−8.98783	+	15.9536i	−0.719602	+	1.27731i
$157$	6.34814	+	5.32672i	0.506637	+	0.425119i	0.859944	−	0.510389i	$-0.170498\pi$
$157$	6.34814	+	5.32672i	0.506637	+	0.425119i	−0.353307	+	0.935507i	$0.614943\pi$
$158$	28.7064	−	10.4483i	2.28376	−	0.831222i
$159$	1.46634	−	8.86160i	0.116289	−	0.702770i
$160$	9.14836	+	3.32973i	0.723241	+	0.263238i
$161$	2.90942	−	9.78020i	0.229295	−	0.770788i
$162$	19.3634	−	0.817400i	1.52133	−	0.0642210i
$163$	−9.36043	−	16.2127i	−0.733165	−	1.26988i	−0.955524	−	0.294915i	$-0.904709\pi$
$163$	−9.36043	−	16.2127i	−0.733165	−	1.26988i	0.222358	−	0.974965i	$-0.428625\pi$
$164$	−6.35562	+	5.33300i	−0.496291	+	0.416437i
$165$	1.14581	−	0.430778i	0.0892009	−	0.0335361i
$166$	−5.34325	+	30.3031i	−0.414717	+	2.35198i
$167$	−3.09189	+	17.5350i	−0.239258	+	1.35690i	0.594201	+	0.804316i	$0.297468\pi$
$167$	−3.09189	+	17.5350i	−0.239258	+	1.35690i	−0.833459	+	0.552581i	$0.813643\pi$
$168$	−4.37057	−	4.51992i	−0.337197	−	0.348720i
$169$	2.35256	−	1.97403i	0.180966	−	0.151848i
$170$	4.93804	−	8.55294i	0.378730	−	0.655980i
$171$	−1.54029	−	7.77287i	−0.117789	−	0.594407i
$172$	−1.44998	−	2.51145i	−0.110560	−	0.191496i
$173$	−12.0380	+	10.1011i	−0.915231	+	0.767970i	−0.973107	−	0.230354i	$-0.926012\pi$
$173$	−12.0380	+	10.1011i	−0.915231	+	0.767970i	0.0578763	+	0.998324i	$0.481567\pi$
$174$	−5.39353	−	28.8081i	−0.408883	−	2.18394i
$175$	7.54606	−	4.98200i	0.570429	−	0.376604i
$176$	−1.22473	+	0.445765i	−0.0923174	+	0.0336008i
$177$	−13.2780	−	4.67479i	−0.998033	−	0.351379i
$178$	13.5367	+	4.92694i	1.01462	+	0.369290i
$179$	3.21640	+	5.57097i	0.240405	+	0.416394i	0.960830	−	0.277139i	$-0.0893863\pi$
$179$	3.21640	+	5.57097i	0.240405	+	0.416394i	−0.720424	+	0.693533i	$0.756053\pi$
$180$	1.52101	−	9.83492i	0.113370	−	0.733052i
$181$	4.24299	+	7.34908i	0.315379	+	0.546253i	0.979518	−	0.201357i	$-0.0645350\pi$
$181$	4.24299	+	7.34908i	0.315379	+	0.546253i	−0.664139	+	0.747609i	$0.731202\pi$
$182$	9.08303	+	20.9563i	0.673279	+	1.55338i
$183$	−18.3698	+	0.193756i	−1.35793	+	0.0143229i
$184$	4.97234	−	1.80978i	0.366565	−	0.133419i
$185$	−7.44764	+	2.71072i	−0.547562	+	0.199296i
$186$	22.8089	+	18.7326i	1.67243	+	1.37354i
$187$	0.355707	+	2.01731i	0.0260119	+	0.147521i
$188$	21.6659			1.58015
$189$	7.83691	−	11.2953i	0.570051	−	0.821609i
$190$	−7.15480			−0.519064
$191$	−2.76767	−	15.6962i	−0.200262	−	1.13574i	−0.904724	−	0.425999i	$-0.859923\pi$
$191$	−2.76767	−	15.6962i	−0.200262	−	1.13574i	0.704462	−	0.709742i	$-0.251188\pi$
$192$	−3.40064	+	20.5512i	−0.245420	+	1.48316i
$193$	19.0137	−	6.92041i	1.36863	−	0.498142i	0.449922	−	0.893068i	$-0.351452\pi$
$193$	19.0137	−	6.92041i	1.36863	−	0.498142i	0.918713	+	0.394926i	$0.129230\pi$
$194$	4.41327	−	1.60630i	0.316854	−	0.115326i
$195$	−4.28716	+	7.60982i	−0.307010	+	0.544950i
$196$	−18.3276	+	2.20702i	−1.30911	+	0.157645i
$197$	0.836616	+	1.44906i	0.0596065	+	0.103241i	0.894289	−	0.447490i	$-0.147682\pi$
$197$	0.836616	+	1.44906i	0.0596065	+	0.103241i	−0.834682	+	0.550732i	$0.814349\pi$
$198$	1.88069	+	3.10434i	0.133655	+	0.220616i
$199$	9.34464	+	16.1854i	0.662424	+	1.14735i	0.979977	+	0.199112i	$0.0638057\pi$
$199$	9.34464	+	16.1854i	0.662424	+	1.14735i	−0.317553	+	0.948241i	$0.602861\pi$
$200$	4.40635	+	1.60378i	0.311576	+	0.113404i
$201$	3.27381	+	17.4862i	0.230917	+	1.23338i
$202$	25.4713	−	9.27078i	1.79215	−	0.652290i
$203$	−18.5951	−	9.29821i	−1.30512	−	0.652607i
$204$	15.7084	+	5.53046i	1.09981	+	0.387210i
$205$	−3.03161	+	2.54382i	−0.211736	+	0.177668i
$206$	0.0730198	+	0.126474i	0.00508753	+	0.00881186i
$207$	5.99506	+	9.89566i	0.416686	+	0.687796i
$208$	4.64981	−	8.05371i	0.322406	−	0.558424i
$209$	1.13681	−	0.953899i	0.0786350	−	0.0659826i
$210$	−8.62878	−	8.92364i	−0.595442	−	0.615790i
$211$	−1.23023	+	6.97695i	−0.0846922	+	0.480313i	0.912730	+	0.408562i	$0.133970\pi$
$211$	−1.23023	+	6.97695i	−0.0846922	+	0.480313i	−0.997423	+	0.0717509i	$0.977141\pi$
$212$	2.37477	−	13.4680i	0.163100	−	0.924984i
$213$	2.26817	−	13.7073i	0.155412	−	0.939207i
$214$	−7.73442	+	6.48995i	−0.528714	+	0.443644i
$215$	−0.691636	−	1.19795i	−0.0471692	−	0.0816995i
$216$	7.12569	−	0.225543i	0.484842	−	0.0153462i
$217$	20.3640	−	4.86389i	1.38240	−	0.330182i
$218$	−28.7303	−	10.4570i	−1.94586	−	0.708236i
$219$	−5.26325	+	1.97878i	−0.355658	+	0.133713i
$220$	1.75137	−	0.637448i	0.118078	−	0.0429767i
$221$	−11.1966	−	9.39508i	−0.753167	−	0.631982i
$222$	−11.9641	−	20.2267i	−0.802976	−	1.35753i
$223$	18.1735	−	15.2493i	1.21698	−	1.02117i	0.218008	−	0.975947i	$-0.430044\pi$
$223$	18.1735	−	15.2493i	1.21698	−	1.02117i	0.998977	−	0.0452241i	$-0.0144002\pi$
$224$	14.0779	+	14.8696i	0.940617	+	0.993518i
$225$	−1.56704	+	10.1326i	−0.104469	+	0.675504i
$226$	−3.35404			−0.223107
$227$	1.43364	+	0.521804i	0.0951543	+	0.0346333i	0.389159	−	0.921171i	$-0.372766\pi$
$227$	1.43364	+	0.521804i	0.0951543	+	0.0346333i	−0.294004	+	0.955804i	$0.594988\pi$
$228$	−2.22022	−	11.8587i	−0.147038	−	0.785362i
$229$	1.52233	+	1.27739i	0.100599	+	0.0844123i	0.691700	−	0.722185i	$-0.256862\pi$
$229$	1.52233	+	1.27739i	0.100599	+	0.0844123i	−0.591101	+	0.806597i	$0.701307\pi$
$230$	9.81684	−	3.57304i	0.647303	−	0.235599i
$231$	2.56074	+	0.267446i	0.168484	+	0.0175967i
$232$	−1.87216	−	10.6175i	−0.122913	−	0.697076i
$233$	10.2291			0.670128			0.335064	−	0.942195i	$-0.391242\pi$
$233$	10.2291			0.670128			0.335064	+	0.942195i	$0.391242\pi$
$234$	−24.5177	−	8.34240i	−1.60277	−	0.545359i
$235$	10.3345			0.674152
$236$	−20.1402	−	7.33045i	−1.31102	−	0.477172i
$237$	12.5094	+	21.1487i	0.812574	+	1.37375i
$238$	17.3351	−	11.4448i	1.12367	−	0.741859i
$239$	4.61717	+	3.87426i	0.298660	+	0.250605i	0.779786	−	0.626046i	$-0.215328\pi$
$239$	4.61717	+	3.87426i	0.298660	+	0.250605i	−0.481126	+	0.876651i	$0.659772\pi$
$240$	−0.825107	+	4.98639i	−0.0532604	+	0.321870i
$241$	−7.48242	+	6.27849i	−0.481985	+	0.404433i	−0.851143	−	0.524933i	$-0.824090\pi$
$241$	−7.48242	+	6.27849i	−0.481985	+	0.404433i	0.369159	+	0.929366i	$0.379646\pi$
$242$	11.5038	−	19.9252i	0.739495	−	1.28084i
$243$	3.51235	+	15.1876i	0.225317	+	0.974285i
$244$	−27.9706			−1.79063
$245$	−8.74219	+	1.05274i	−0.558518	+	0.0672572i
$246$	−9.06803	−	7.44742i	−0.578156	−	0.474830i
$247$	−1.83872	+	10.4279i	−0.116995	+	0.663513i
$248$	8.31722	+	6.97897i	0.528144	+	0.443165i
$249$	−24.7484	+	0.261035i	−1.56836	+	0.0165424i
$250$	21.4265	+	7.79861i	1.35513	+	0.493227i
$251$	−8.67976	−	15.0338i	−0.547862	−	0.948924i	−0.998421	−	0.0561775i	$-0.982109\pi$
$251$	−8.67976	−	15.0338i	−0.547862	−	0.948924i	0.450559	−	0.892747i	$-0.351225\pi$
$252$	12.1129	−	17.0709i	0.763038	−	1.07536i
$253$	−1.08341	+	1.87652i	−0.0681134	+	0.117976i
$254$	−14.4261	+	12.1049i	−0.905174	+	0.759531i
$255$	7.49283	+	2.63801i	0.469219	+	0.165198i
$256$	0.280681	−	1.59182i	0.0175426	−	0.0994888i
$257$	−1.53786	−	1.29042i	−0.0959292	−	0.0804942i	0.593562	−	0.804788i	$-0.297721\pi$
$257$	−1.53786	−	1.29042i	−0.0959292	−	0.0804942i	−0.689491	+	0.724294i	$0.742166\pi$
$258$	3.11397	−	2.66940i	0.193867	−	0.166190i
$259$	−16.5606	−	1.90638i	−1.02902	−	0.118457i
$260$	−6.64927	+	11.5169i	−0.412370	+	0.714247i
$261$	21.9772	−	8.52820i	1.36036	−	0.527883i
$262$	−39.0616			−2.41324
$263$	0.152054	+	0.862344i	0.00937608	+	0.0531744i	0.989137	−	0.146998i	$-0.0469610\pi$
$263$	0.152054	+	0.862344i	0.00937608	+	0.0531744i	−0.979761	+	0.200172i	$0.935850\pi$
$264$	0.679739	+	1.14918i	0.0418351	+	0.0707271i
$265$	1.13275	−	6.42417i	0.0695845	−	0.394633i
$266$	−13.4598	−	6.73037i	−0.825270	−	0.412665i
$267$	−1.89156	+	11.4313i	−0.115761	+	0.699584i
$268$	4.70349	+	26.6748i	0.287311	+	1.62942i
$269$	1.56979	−	2.71895i	0.0957115	−	0.165777i	−0.814194	−	0.580593i	$-0.802821\pi$
$269$	1.56979	−	2.71895i	0.0957115	−	0.165777i	0.909905	+	0.414816i	$0.136154\pi$
$270$	14.0682	−	0.445287i	0.856162	−	0.0270993i
$271$	7.48337	+	12.9616i	0.454582	+	0.787360i	0.998664	−	0.0516725i	$-0.0164552\pi$
$271$	7.48337	+	12.9616i	0.454582	+	0.787360i	−0.544082	+	0.839032i	$0.683122\pi$
$272$	−7.94768	−	2.89272i	−0.481899	−	0.175397i
$273$	−15.2235	+	10.2829i	−0.921366	+	0.622349i
$274$	−29.8643	−	25.0591i	−1.80417	−	1.51388i
$275$	−1.80438	+	0.656739i	−0.108808	+	0.0396029i
$276$	8.96840	+	15.1621i	0.539834	+	0.912653i
$277$	−2.72267	−	15.4410i	−0.163589	−	0.927760i	−0.950507	−	0.310703i	$-0.899436\pi$
$277$	−2.72267	−	15.4410i	−0.163589	−	0.927760i	0.786918	−	0.617058i	$-0.211675\pi$
$278$	2.64025	−	4.57305i	0.158352	−	0.274273i
$279$	−11.4338	+	20.8053i	−0.684521	+	1.24558i
$280$	−3.13934	−	3.31590i	−0.187612	−	0.198163i
$281$	−3.33633	−	18.9213i	−0.199029	−	1.12875i	−0.906563	−	0.422070i	$-0.861304\pi$
$281$	−3.33633	−	18.9213i	−0.199029	−	1.12875i	0.707535	−	0.706679i	$-0.249807\pi$
$282$	5.63906	+	30.1195i	0.335801	+	1.79359i
$283$	−0.775260	+	4.39672i	−0.0460844	+	0.261358i	−0.999141	−	0.0414337i	$-0.986807\pi$
$283$	−0.775260	+	4.39672i	−0.0460844	+	0.261358i	0.953057	+	0.302791i	$0.0979186\pi$
$284$	3.67333	−	20.8325i	0.217972	−	1.23618i
$285$	−1.05904	−	5.65655i	−0.0627319	−	0.335065i
$286$	−0.842225	−	4.77650i	−0.0498018	−	0.282440i
$287$	−8.09603	+	1.93371i	−0.477893	+	0.114144i
$288$	−23.2131	+	0.489738i	−1.36785	+	0.0288581i
$289$	1.85351	−	3.21038i	0.109030	−	0.188846i
$290$	−3.69619	−	20.9621i	−0.217048	−	1.23094i
$291$	1.92317	+	3.25135i	0.112738	+	0.190598i
$292$	−8.04492	+	2.92811i	−0.470794	+	0.171355i
$293$	−18.4319	−	15.4662i	−1.07681	−	0.903547i	−0.0811537	−	0.996702i	$-0.525860\pi$
$293$	−18.4319	−	15.4662i	−1.07681	−	0.903547i	−0.995652	+	0.0931547i	$0.970305\pi$
$294$	−7.83834	−	24.9042i	−0.457142	−	1.45244i
$295$	−9.60681	−	3.49659i	−0.559330	−	0.203580i
$296$	−4.32232	−	7.48649i	−0.251230	−	0.435143i
$297$	−2.17590	+	1.94636i	−0.126258	+	0.112939i
$298$	−13.2119	+	22.8837i	−0.765344	+	1.32561i
$299$	−2.68475	−	15.2260i	−0.155263	−	0.880542i
$300$	−2.54849	+	15.4014i	−0.147137	+	0.889198i
$301$	−0.174234	−	2.90421i	−0.0100427	−	0.167396i
$302$	8.85249	−	50.2050i	0.509404	−	2.88897i
$303$	11.0996	+	18.7652i	0.637657	+	1.07803i
$304$	1.06399	+	6.03419i	0.0610240	+	0.346084i
$305$	−13.3418			−0.763952
$306$	−3.59987	+	23.2769i	−0.205791	+	1.33065i
$307$	6.54938	−	11.3439i	0.373793	−	0.647428i	−0.616353	−	0.787470i	$-0.711390\pi$
$307$	6.54938	−	11.3439i	0.373793	−	0.647428i	0.990146	+	0.140042i	$0.0447238\pi$
$308$	3.89435	+	0.448300i	0.221901	+	0.0255443i
$309$	−0.0891815	+	0.0764494i	−0.00507336	+	0.00434906i
$310$	16.4206	+	13.7785i	0.932627	+	0.782567i
$311$	0.323474	−	1.83451i	0.0183425	−	0.104026i	−0.974262	−	0.225419i	$-0.927625\pi$
$311$	0.323474	−	1.83451i	0.0183425	−	0.104026i	0.992605	+	0.121393i	$0.0387361\pi$
$312$	−8.98609	−	3.16374i	−0.508737	−	0.179112i
$313$	−16.3079	+	13.6840i	−0.921778	+	0.773464i	−0.974323	−	0.225155i	$-0.927711\pi$
$313$	−16.3079	+	13.6840i	−0.921778	+	0.773464i	0.0525448	+	0.998619i	$0.483267\pi$
$314$	−8.92253	+	15.4543i	−0.503528	+	0.872135i
$315$	5.77778	−	8.14273i	0.325541	−	0.458791i
$316$	18.7056	+	32.3991i	1.05227	+	1.82259i
$317$	16.7454	+	6.09481i	0.940513	+	0.342319i	0.766368	−	0.642401i	$-0.222062\pi$
$317$	16.7454	+	6.09481i	0.940513	+	0.342319i	0.174144	+	0.984720i	$0.444284\pi$
$318$	19.3410	−	0.204000i	1.08459	−	0.0114398i
$319$	3.38201	+	2.83784i	0.189356	+	0.158889i
$320$	−2.62701	+	14.8985i	−0.146854	+	0.832851i
$321$	−6.27575	−	5.15417i	−0.350278	−	0.287678i
$322$	21.8287	+	2.51282i	1.21647	+	0.140034i
$323$	9.63020			0.535839
$324$	5.10356	+	23.1791i	0.283531	+	1.28773i
$325$	6.85050	−	11.8654i	0.379997	−	0.658175i
$326$	30.8820	−	25.9130i	1.71039	−	1.43519i
$327$	4.01465	−	24.2619i	0.222011	−	1.34168i
$328$	−3.30664	−	2.77460i	−0.182579	−	0.153202i
$329$	19.4415	+	9.72148i	1.07185	+	0.535963i
$330$	1.34200	+	2.26881i	0.0738748	+	0.124894i
$331$	22.7316	+	8.27362i	1.24944	+	0.454759i	0.880213	−	0.474579i	$-0.157400\pi$
$331$	22.7316	+	8.27362i	1.24944	+	0.454759i	0.369228	+	0.929339i	$0.379622\pi$
$332$	−37.6829			−2.06812
$333$	14.2202	−	12.4526i	0.779263	−	0.682400i
$334$	−38.3424			−2.09800
$335$	2.24354	+	12.7238i	0.122578	+	0.695174i
$336$	−6.24280	+	8.60434i	−0.340573	+	0.469405i
$337$	−22.1062	+	8.04599i	−1.20420	+	0.438293i	−0.864689	−	0.502308i	$-0.832484\pi$
$337$	−22.1062	+	8.04599i	−1.20420	+	0.438293i	−0.339512	+	0.940602i	$0.610262\pi$
$338$	5.06600	+	4.25088i	0.275554	+	0.231217i
$339$	−0.496456	−	2.65169i	−0.0269638	−	0.144020i
$340$	11.3653	+	4.13661i	0.616367	+	0.224339i
$341$	−4.44603			−0.240766
$342$	15.9079	−	6.17301i	0.860199	−	0.333798i
$343$	−17.4363	−	6.24315i	−0.941469	−	0.337098i
$344$	1.15578	−	0.969816i	0.0623156	−	0.0522890i
$345$	4.27789	+	7.23227i	0.230314	+	0.389372i
$346$	−25.9226	−	21.7517i	−1.39361	−	1.16938i
$347$	20.9104	−	7.61076i	1.12253	−	0.408567i	0.286954	−	0.957944i	$-0.407357\pi$
$347$	20.9104	−	7.61076i	1.12253	−	0.408567i	0.835574	+	0.549377i	$0.185135\pi$
$348$	33.5966	−	12.6310i	1.80097	−	0.677094i
$349$	−7.49093	−	2.72647i	−0.400980	−	0.145945i	0.133655	−	0.991028i	$-0.457329\pi$
$349$	−7.49093	−	2.72647i	−0.400980	−	0.145945i	−0.534635	+	0.845083i	$0.679551\pi$
$350$	13.3870	+	14.1399i	0.715565	+	0.755809i
$351$	2.96641	−	20.6184i	0.158335	−	1.10053i
$352$	−2.17415	−	3.76574i	−0.115883	−	0.200715i
$353$	22.9621	−	19.2675i	1.22215	−	1.02550i	0.223438	−	0.974718i	$-0.428272\pi$
$353$	22.9621	−	19.2675i	1.22215	−	1.02550i	0.998710	−	0.0507858i	$-0.0161726\pi$
$354$	4.94868	−	29.9065i	0.263019	−	1.58951i
$355$	1.75216	−	9.93701i	0.0929952	−	0.527402i
$356$	−3.06341	+	17.3734i	−0.162360	+	0.920791i
$357$	11.6141	+	12.0110i	0.614685	+	0.635690i
$358$	−10.6116	+	8.90417i	−0.560839	+	0.470600i
$359$	−3.88481	+	6.72868i	−0.205032	+	0.355126i	−0.950143	−	0.311814i	$-0.899063\pi$
$359$	−3.88481	+	6.72868i	−0.205032	+	0.355126i	0.745111	+	0.666941i	$0.232397\pi$
$360$	5.17649	−	0.109211i	0.272825	−	0.00575592i
$361$	6.01166	+	10.4125i	0.316403	+	0.548027i
$362$	−13.9985	+	11.7461i	−0.735745	+	0.617363i
$363$	17.4556	+	6.14560i	0.916180	+	0.322560i
$364$	−23.3424	+	15.4109i	−1.22347	+	0.807753i
$365$	−3.83739	+	1.39670i	−0.200858	+	0.0731065i
$366$	−7.27999	−	38.8841i	−0.380531	−	2.03251i
$367$	30.1778	+	10.9838i	1.57527	+	0.573352i	0.974169	−	0.225821i	$-0.0725064\pi$
$367$	30.1778	+	10.9838i	1.57527	+	0.573352i	0.601102	+	0.799173i	$0.294729\pi$
$368$	−4.47327	−	7.74794i	−0.233185	−	0.403889i
$369$	4.54567	−	8.27149i	0.236638	−	0.430596i
$370$	−8.53352	−	14.7805i	−0.443637	−	0.768401i
$371$	8.17403	−	11.0197i	0.424375	−	0.572115i
$372$	−17.7417	+	31.4919i	−0.919862	+	1.63278i
$373$	9.31908	−	3.39187i	0.482524	−	0.175624i	−0.0892935	−	0.996005i	$-0.528461\pi$
$373$	9.31908	−	3.39187i	0.482524	−	0.175624i	0.571817	+	0.820381i	$0.306239\pi$
$374$	−4.14508	+	1.50869i	−0.214337	+	0.0780123i
$375$	−2.99405	+	18.0940i	−0.154612	+	0.934371i
$376$	1.95738	+	11.1009i	0.100944	+	0.572484i
$377$	−31.5016			−1.62241
$378$	26.8842	+	12.3960i	1.38277	+	0.637579i
$379$	20.2706			1.04123			0.520614	−	0.853792i	$-0.325703\pi$
$379$	20.2706			1.04123			0.520614	+	0.853792i	$0.325703\pi$
$380$	−1.52152	−	8.62895i	−0.0780521	−	0.442656i
$381$	−11.7054	−	9.61346i	−0.599686	−	0.492512i
$382$	32.2519	−	11.7387i	1.65015	−	0.600606i
$383$	33.5257	−	12.2024i	1.71308	−	0.623511i	0.715879	−	0.698225i	$-0.246026\pi$
$383$	33.5257	−	12.2024i	1.71308	−	0.623511i	0.997205	+	0.0747134i	$0.0238042\pi$
$384$	−18.0456	+	0.190337i	−0.920888	+	0.00971312i
$385$	1.85759	+	0.213837i	0.0946715	+	0.0108982i
$386$	21.7859	+	37.7343i	1.10887	+	1.92063i
$387$	2.57134	+	2.06677i	0.130708	+	0.105060i
$388$	2.87576	+	4.98097i	0.145995	+	0.252870i
$389$	8.00687	+	2.91426i	0.405964	+	0.147759i	0.536928	−	0.843628i	$-0.319585\pi$
$389$	8.00687	+	2.91426i	0.405964	+	0.147759i	−0.130963	+	0.991387i	$0.541807\pi$
$390$	−17.7412	−	6.24615i	−0.898359	−	0.316286i
$391$	−13.2132	+	4.80922i	−0.668222	+	0.243213i
$392$	−2.78659	−	9.19104i	−0.140744	−	0.464218i
$393$	−5.78180	−	30.8820i	−0.291653	−	1.55779i
$394$	−2.76017	+	2.31606i	−0.139055	+	0.116681i
$395$	8.92250	+	15.4542i	0.448940	+	0.777587i
$396$	−3.34400	+	2.92834i	−0.168042	+	0.147155i
$397$	−5.28373	+	9.15168i	−0.265183	+	0.459310i	−0.967611	−	0.252444i	$-0.918766\pi$
$397$	−5.28373	+	9.15168i	−0.265183	+	0.459310i	0.702429	+	0.711754i	$0.252099\pi$
$398$	−30.8299	+	25.8693i	−1.54536	+	1.29671i
$399$	3.32872	−	11.6374i	0.166644	−	0.582600i
$400$	1.37671	−	7.80773i	0.0688357	−	0.390387i
$401$	−2.24904	+	12.7549i	−0.112312	+	0.636951i	0.875735	+	0.482793i	$0.160378\pi$
$401$	−2.24904	+	12.7549i	−0.112312	+	0.636951i	−0.988046	+	0.154158i	$0.950733\pi$
$402$	−35.8586	+	13.4814i	−1.78846	+	0.672393i
$403$	24.3017	−	20.3916i	1.21056	−	1.01578i
$404$	16.5975	+	28.7477i	0.825757	+	1.43025i
$405$	2.43438	+	11.0563i	0.120965	+	0.549393i
$406$	12.7653	−	42.9113i	0.633530	−	2.12965i
$407$	3.32645	+	1.21073i	0.164886	+	0.0600137i
$408$	−1.41447	+	8.54808i	−0.0700265	+	0.423193i
$409$	−2.79886	+	1.01870i	−0.138395	+	0.0503715i	−0.410289	−	0.911956i	$-0.634572\pi$
$409$	−2.79886	+	1.01870i	−0.138395	+	0.0503715i	0.271894	+	0.962327i	$0.412350\pi$
$410$	−6.52827	−	5.47787i	−0.322408	−	0.270533i
$411$	15.3912	−	27.3198i	0.759191	−	1.34758i
$412$	−0.137004	+	0.114960i	−0.00674970	+	0.00566367i
$413$	−14.7833	−	15.6148i	−0.727441	−	0.768353i
$414$	−18.7439	+	16.4140i	−0.921210	+	0.806703i
$415$	−17.9746			−0.882337
$416$	29.1553	+	10.6116i	1.42945	+	0.520279i
$417$	4.00623	+	1.41048i	0.196186	+	0.0690715i
$418$	2.44802	+	2.05413i	0.119736	+	0.100471i
$419$	28.4030	−	10.3378i	1.38758	−	0.505036i	0.463110	−	0.886301i	$-0.346734\pi$
$419$	28.4030	−	10.3378i	1.38758	−	0.505036i	0.924466	+	0.381265i	$0.124511\pi$
$420$	8.92726	−	12.3043i	0.435606	−	0.600387i
$421$	2.47000	+	14.0081i	0.120380	+	0.682711i	0.983945	+	0.178473i	$0.0571156\pi$
$421$	2.47000	+	14.0081i	0.120380	+	0.682711i	−0.863564	+	0.504238i	$0.831773\pi$
$422$	−15.2560			−0.742649
$423$	−22.9777	+	8.91642i	−1.11721	+	0.433531i
$424$	7.11508			0.345539
$425$	−11.7092	−	4.26180i	−0.567980	−	0.206728i
$426$	29.9170	−	0.315551i	1.44948	−	0.0152885i
$427$	−25.0989	−	12.5504i	−1.21462	−	0.607356i
$428$	−9.47188	−	7.94785i	−0.457841	−	0.384174i
$429$	3.65161	−	1.37286i	0.176302	−	0.0662825i
$430$	2.28185	−	1.91470i	0.110041	−	0.0923350i
$431$	−6.53397	+	11.3172i	−0.314730	+	0.545129i	−0.979380	−	0.202026i	$-0.935247\pi$
$431$	−6.53397	+	11.3172i	−0.314730	+	0.545129i	0.664650	+	0.747155i	$0.268581\pi$
$432$	−2.46762	−	11.7985i	−0.118724	−	0.567658i
$433$	−4.56247			−0.219258			−0.109629	−	0.993973i	$-0.534966\pi$
$433$	−4.56247			−0.219258			−0.109629	+	0.993973i	$0.534966\pi$
$434$	17.9296	+	41.3669i	0.860648	+	1.98568i
$435$	16.0254	−	6.02495i	0.768361	−	0.288874i
$436$	6.50179	−	36.8735i	0.311379	−	1.76592i
$437$	7.80351	+	6.54793i	0.373293	+	0.313230i
$438$	−6.16448	−	10.4218i	−0.294550	−	0.497972i
$439$	−4.12263	−	1.50051i	−0.196762	−	0.0716156i	0.241759	−	0.970336i	$-0.422276\pi$
$439$	−4.12263	−	1.50051i	−0.196762	−	0.0716156i	−0.438522	+	0.898721i	$0.644498\pi$
$440$	0.484832	+	0.839754i	0.0231135	+	0.0400337i
$441$	18.5290	−	9.88322i	0.882331	−	0.470629i
$442$	15.7372	−	27.2577i	0.748544	−	1.29652i
$443$	−23.1955	+	19.4633i	−1.10205	+	0.924730i	−0.997561	−	0.0697956i	$-0.977765\pi$
$443$	−23.1955	+	19.4633i	−1.10205	+	0.924730i	−0.104489	+	0.994526i	$0.533321\pi$
$444$	21.8498	−	18.7304i	1.03695	−	0.888907i
$445$	−1.46123	+	8.28706i	−0.0692691	+	0.392844i
$446$	39.1348	+	32.8380i	1.85308	+	1.55492i
$447$	−20.0473	−	7.05807i	−0.948205	−	0.333835i
$448$	−18.9567	+	25.5562i	−0.895618	+	1.20742i
$449$	−8.20302	+	14.2081i	−0.387125	+	0.670519i	−0.992061	−	0.125754i	$-0.959865\pi$
$449$	−8.20302	+	14.2081i	−0.387125	+	0.670519i	0.604937	+	0.796273i	$0.293198\pi$
$450$	−22.0740	+	0.465704i	−1.04058	+	0.0219535i
$451$	1.76759			0.0832325
$452$	−0.713258	−	4.04509i	−0.0335488	−	0.190265i
$453$	41.0021	−	0.432472i	1.92645	−	0.0203193i
$454$	−0.570494	+	3.23543i	−0.0267746	+	0.151846i
$455$	−11.1342	+	7.35096i	−0.521981	+	0.344618i
$456$	5.87541	−	2.20893i	0.275142	−	0.103443i
$457$	−2.35879	−	13.3774i	−0.110340	−	0.625767i	−0.988953	−	0.148232i	$-0.952642\pi$
$457$	−2.35879	−	13.3774i	−0.110340	−	0.625767i	0.878613	−	0.477534i	$-0.158469\pi$
$458$	−2.13969	+	3.70606i	−0.0999813	+	0.173173i
$459$	−18.9354	+	0.599346i	−0.883831	+	0.0279751i
$460$	6.39682	+	11.0796i	0.298253	+	0.516590i
$461$	−0.559614	−	0.203683i	−0.0260638	−	0.00948646i	0.328955	−	0.944345i	$-0.393303\pi$
$461$	−0.559614	−	0.203683i	−0.0260638	−	0.00948646i	−0.355019	+	0.934859i	$0.615526\pi$
$462$	0.390377	+	5.53053i	0.0181620	+	0.257303i
$463$	−5.41109	−	4.54044i	−0.251475	−	0.211012i	0.508332	−	0.861161i	$-0.330262\pi$
$463$	−5.41109	−	4.54044i	−0.251475	−	0.211012i	−0.759807	+	0.650149i	$0.774707\pi$
$464$	−17.1293	+	6.23455i	−0.795207	+	0.289432i
$465$	−8.46270	+	15.0215i	−0.392448	+	0.696606i
$466$	3.82500	+	21.6926i	0.177190	+	1.00489i
$467$	−6.15178	+	10.6552i	−0.284670	+	0.493063i	−0.972529	−	0.232781i	$-0.925217\pi$
$467$	−6.15178	+	10.6552i	−0.284670	+	0.493063i	0.687859	+	0.725844i	$0.258551\pi$
$468$	4.84737	−	31.3433i	0.224070	−	1.44884i
$469$	−7.74838	+	26.0467i	−0.357787	+	1.20272i
$470$	3.86444	+	21.9163i	0.178253	+	1.01093i
$471$	−13.5388	−	4.76661i	−0.623833	−	0.219634i
$472$	1.93632	−	10.9814i	0.0891265	−	0.505462i
$473$	−0.107285	+	0.608446i	−0.00493299	+	0.0279764i
$474$	−40.1720	+	34.4368i	−1.84516	+	1.58173i
$475$	1.56756	+	8.89009i	0.0719247	+	0.407905i
$476$	17.4893	+	18.4729i	0.801621	+	0.846705i
$477$	3.02409	+	15.2607i	0.138463	+	0.698740i
$478$	−6.48959	+	11.2403i	−0.296827	+	0.514119i
$479$	−1.22758	−	6.96196i	−0.0560896	−	0.318100i	0.943834	−	0.330419i	$-0.107190\pi$
$479$	−1.22758	−	6.96196i	−0.0560896	−	0.318100i	−0.999924	+	0.0123185i	$0.996079\pi$
$480$	−16.8614	+	0.177847i	−0.769615	+	0.00811756i
$481$	−23.7352	+	8.63890i	−1.08223	+	0.393900i
$482$	−16.1127	−	13.5201i	−0.733911	−	0.615825i
$483$	1.24440	+	17.6296i	0.0566222	+	0.802175i
$484$	26.4769	+	9.63681i	1.20350	+	0.438037i
$485$	1.37173	+	2.37590i	0.0622869	+	0.107884i
$486$	−30.8948	+	13.1278i	−1.40142	+	0.595488i
$487$	−12.5927	+	21.8113i	−0.570632	+	0.988363i	0.425869	+	0.904785i	$0.359968\pi$
$487$	−12.5927	+	21.8113i	−0.570632	+	0.988363i	−0.996501	+	0.0835787i	$0.973365\pi$
$488$	−2.52697	−	14.3312i	−0.114391	−	0.648741i
$489$	25.0578	+	20.5796i	1.13315	+	0.930640i
$490$	−5.50154	−	18.1458i	−0.248534	−	0.819743i
$491$	0.552850	−	3.13537i	0.0249498	−	0.141497i	−0.969788	−	0.243948i	$-0.921557\pi$
$491$	0.552850	−	3.13537i	0.0249498	−	0.141497i	0.994738	+	0.102451i	$0.0326685\pi$
$492$	7.05347	−	12.5201i	0.317995	−	0.564450i
$493$	4.97498	+	28.2145i	0.224062	+	1.27072i
$494$	−22.8019			−1.02591
$495$	−1.59507	+	1.39680i	−0.0716932	+	0.0627817i
$496$	9.17856	−	15.8977i	0.412130	−	0.713830i
$497$	12.6437	−	17.0455i	0.567149	−	0.764594i
$498$	−9.80784	−	52.3860i	−0.439500	−	2.34747i
$499$	11.3551	+	9.52808i	0.508325	+	0.426536i	0.860539	−	0.509384i	$-0.170127\pi$
$499$	11.3551	+	9.52808i	0.508325	+	0.426536i	−0.352214	+	0.935919i	$0.614571\pi$
$500$	−4.84891	+	27.4995i	−0.216850	+	1.22982i
$501$	−5.67534	−	30.3133i	−0.253556	−	1.35430i
$502$	28.6363	−	24.0287i	1.27810	−	1.07245i
$503$	−10.8253	+	18.7499i	−0.482674	+	0.836017i	−0.999802	−	0.0198916i	$-0.993668\pi$
$503$	−10.8253	+	18.7499i	−0.482674	+	0.836017i	0.517128	+	0.855908i	$0.327001\pi$
$504$	9.84085	+	4.66396i	0.438346	+	0.207749i
$505$	7.91695	+	13.7126i	0.352300	+	0.610201i
$506$	−4.38464	−	1.59588i	−0.194921	−	0.0709455i
$507$	−2.61087	+	4.63436i	−0.115953	+	0.205819i
$508$	−17.6668	−	14.8242i	−0.783836	−	0.657717i
$509$	−1.60162	+	9.08323i	−0.0709905	+	0.402607i	0.928519	+	0.371285i	$0.121083\pi$
$509$	−1.60162	+	9.08323i	−0.0709905	+	0.402607i	−0.999509	+	0.0313219i	$0.990028\pi$
$510$	−2.79256	+	16.8764i	−0.123657	+	0.747299i
$511$	−8.53282	−	0.982260i	−0.377470	−	0.0434526i
$512$	24.3192			1.07477
$513$	7.23499	+	11.6630i	0.319433	+	0.514933i
$514$	2.16152	−	3.74386i	0.0953405	−	0.165135i
$515$	−0.0653503	+	0.0548354i	−0.00287968	+	0.00241634i
$516$	3.88160	+	3.18789i	0.170878	+	0.140339i
$517$	−3.53596	−	2.96703i	−0.155512	−	0.130490i
$518$	−2.14973	−	35.8327i	−0.0944539	−	1.57440i
$519$	13.3598	−	23.7139i	0.586428	−	1.04093i
$520$	−6.50158	−	2.36638i	−0.285113	−	0.103773i
$521$	13.1565			0.576397			0.288199	−	0.957571i	$-0.406944\pi$
$521$	13.1565			0.576397			0.288199	+	0.957571i	$0.406944\pi$
$522$	26.3037	+	43.4178i	1.15128	+	1.90035i
$523$	−25.5674			−1.11799			−0.558993	−	0.829172i	$-0.688812\pi$
$523$	−25.5674			−1.11799			−0.558993	+	0.829172i	$0.688812\pi$
$524$	−8.30671	−	47.1097i	−0.362880	−	2.05800i
$525$	−9.19743	+	12.6766i	−0.401409	+	0.553254i
$526$	−1.77190	+	0.644920i	−0.0772587	+	0.0281199i
$527$	−22.1017	−	18.5456i	−0.962767	−	0.807857i
$528$	1.71389	−	1.46921i	0.0745876	−	0.0639390i
$529$	7.63606	+	2.77930i	0.332002	+	0.120839i
$530$	14.0472			0.610173
$531$	24.3764	−	0.514280i	1.05785	−	0.0223179i
$532$	5.25476	−	17.6642i	0.227823	−	0.765840i
$533$	−9.66154	+	8.10699i	−0.418488	+	0.351153i
$534$	−24.9495	+	0.263157i	−1.07967	+	0.0113879i
$535$	−4.51805	−	3.79109i	−0.195332	−	0.163903i
$536$	−13.2423	+	4.81981i	−0.571982	+	0.208184i
$537$	−8.61029	−	7.07149i	−0.371561	−	0.305157i
$538$	6.35304	+	2.31232i	0.273899	+	0.0996910i
$539$	3.29338	+	2.14967i	0.141856	+	0.0925928i
$540$	3.52872	+	16.8720i	0.151852	+	0.726057i
$541$	−16.0161	−	27.7407i	−0.688587	−	1.19267i	−0.972295	−	0.233757i	$-0.924898\pi$
$541$	−16.0161	−	27.7407i	−0.688587	−	1.19267i	0.283708	−	0.958911i	$-0.408435\pi$
$542$	−24.6892	+	20.7167i	−1.06049	+	0.889857i
$543$	−11.3585	−	9.32851i	−0.487438	−	0.400325i
$544$	4.89994	−	27.7889i	0.210083	−	1.19144i
$545$	3.10133	−	17.5885i	0.132846	−	0.753409i
$546$	−27.4994	−	28.4391i	−1.17687	−	1.21708i
$547$	2.92116	−	2.45114i	0.124900	−	0.104803i	−0.578198	−	0.815896i	$-0.696244\pi$
$547$	2.92116	−	2.45114i	0.124900	−	0.104803i	0.703098	+	0.711093i	$0.251800\pi$
$548$	23.8713	−	41.3464i	1.01973	−	1.76623i
$549$	29.6640	−	11.5111i	1.26603	−	0.491280i
$550$	−2.06746	−	3.58094i	−0.0881566	−	0.152692i
$551$	15.8997	−	13.3414i	0.677349	−	0.568363i
$552$	−6.95832	+	5.96491i	−0.296166	+	0.253883i
$553$	2.24772	+	37.4660i	0.0955829	+	1.59322i
$554$	31.7275	−	11.5478i	1.34797	−	0.490621i
$555$	10.4223	−	8.93433i	0.442401	−	0.379241i
$556$	6.07672	+	2.21175i	0.257710	+	0.0937989i
$557$	−20.8040	−	36.0337i	−0.881495	−	1.52679i	−0.849679	−	0.527301i	$-0.823204\pi$
$557$	−20.8040	−	36.0337i	−0.881495	−	1.52679i	−0.0318169	−	0.999494i	$-0.510129\pi$
$558$	−48.3971	−	16.4676i	−2.04881	−	0.697129i
$559$	−2.20420	−	3.81779i	−0.0932278	−	0.161475i
$560$	−4.59950	+	6.20076i	−0.194364	+	0.262030i
$561$	−1.80630	−	3.05377i	−0.0762622	−	0.128930i
$562$	38.8785	−	14.1506i	1.63999	−	0.596908i
$563$	38.6210	−	14.0569i	1.62768	−	0.592428i	0.642858	−	0.765985i	$-0.277749\pi$
$563$	38.6210	−	14.0569i	1.62768	−	0.592428i	0.984824	+	0.173558i	$0.0555263\pi$
$564$	−35.1260	+	13.2060i	−1.47907	+	0.556073i
$565$	−0.340221	−	1.92949i	−0.0143132	−	0.0811742i
$566$	−9.61396			−0.404105
$567$	−5.82085	+	23.0893i	−0.244453	+	0.969661i
$568$	11.0057			0.461790
$569$	4.09993	+	23.2519i	0.171878	+	0.974769i	0.941686	+	0.336493i	$0.109241\pi$
$569$	4.09993	+	23.2519i	0.171878	+	0.974769i	−0.769808	+	0.638276i	$0.779648\pi$
$570$	11.5998	−	4.36106i	0.485861	−	0.182665i
$571$	−19.2801	+	7.01738i	−0.806847	+	0.293668i	−0.712321	−	0.701854i	$-0.752356\pi$
$571$	−19.2801	+	7.01738i	−0.806847	+	0.293668i	−0.0945261	+	0.995522i	$0.530134\pi$
$572$	5.58152	−	2.03151i	0.233375	−	0.0849416i
$573$	14.0544	+	23.7607i	0.587132	+	0.992616i
$574$	−7.12819	−	16.4461i	−0.297525	−	0.686445i
$575$	−6.59041	−	11.4149i	−0.274839	−	0.476035i
$576$	−7.01326	−	35.3916i	−0.292219	−	1.47465i
$577$	−15.2320	−	26.3826i	−0.634116	−	1.09832i	−0.986702	−	0.162541i	$-0.948031\pi$
$577$	−15.2320	−	26.3826i	−0.634116	−	1.09832i	0.352586	−	0.935779i	$-0.385302\pi$
$578$	7.50130	+	2.73025i	0.312013	+	0.113563i
$579$	−26.6079	+	22.8092i	−1.10579	+	0.947917i
$580$	24.4950	−	8.91546i	1.01710	−	0.370194i
$581$	−33.8141	−	16.9083i	−1.40285	−	0.701474i
$582$	−6.17596	+	5.29424i	−0.256002	+	0.219453i
$583$	−2.23194	+	1.87282i	−0.0924374	+	0.0775642i
$584$	−2.22708	−	3.85741i	−0.0921570	−	0.159621i
$585$	2.31218	−	14.9506i	0.0955967	−	0.618132i
$586$	25.9067	−	44.8717i	1.07020	−	1.85363i
$587$	−1.75988	+	1.47672i	−0.0726382	+	0.0609507i	−0.678384	−	0.734708i	$-0.737319\pi$
$587$	−1.75988	+	1.47672i	−0.0726382	+	0.0609507i	0.605746	+	0.795658i	$0.292875\pi$
$588$	28.3685	−	14.7494i	1.16990	−	0.608254i
$589$	−3.62958	+	20.5843i	−0.149554	+	0.848163i
$590$	3.82287	−	21.6805i	0.157385	−	0.892574i
$591$	−2.23962	−	1.83936i	−0.0921255	−	0.0756611i
$592$	−11.1965	+	9.39497i	−0.460173	+	0.386131i
$593$	−5.24746	−	9.08887i	−0.215487	−	0.373235i	0.737936	−	0.674871i	$-0.235801\pi$
$593$	−5.24746	−	9.08887i	−0.215487	−	0.373235i	−0.953423	+	0.301636i	$0.902467\pi$
$594$	−4.94127	−	3.88659i	−0.202743	−	0.159469i
$595$	8.34232	+	8.81151i	0.342002	+	0.361236i
$596$	−30.4081	−	11.0676i	−1.24556	−	0.453348i
$597$	−25.0155	−	20.5448i	−1.02382	−	0.840845i
$598$	31.2857	−	11.3870i	1.27937	−	0.465651i
$599$	19.4788	+	16.3447i	0.795883	+	0.667825i	0.947194	−	0.320661i	$-0.103905\pi$
$599$	19.4788	+	16.3447i	0.795883	+	0.667825i	−0.151311	+	0.988486i	$0.548349\pi$
$600$	−8.12137	+	0.0856606i	−0.331554	+	0.00349708i
$601$	−8.19333	+	6.87502i	−0.334213	+	0.280438i	−0.794414	−	0.607377i	$-0.792222\pi$
$601$	−8.19333	+	6.87502i	−0.334213	+	0.280438i	0.460201	+	0.887815i	$0.347777\pi$
$602$	6.09377	−	1.45548i	0.248364	−	0.0593210i
$603$	−15.9661	−	26.3541i	−0.650188	−	1.07322i
$604$	62.4315			2.54030
$605$	12.6294	+	4.59672i	0.513457	+	0.186883i
$606$	−35.6446	+	30.5558i	−1.44796	+	1.24124i
$607$	12.5731	+	10.5501i	0.510325	+	0.428214i	0.861244	−	0.508192i	$-0.169686\pi$
$607$	12.5731	+	10.5501i	0.510325	+	0.428214i	−0.350918	+	0.936406i	$0.614131\pi$
$608$	−19.2096	+	6.99174i	−0.779054	+	0.283552i
$609$	35.8149	+	3.74055i	1.45129	+	0.151575i
$610$	−4.98898	−	28.2939i	−0.201998	−	1.14559i
$611$	32.9356			1.33243
$612$	−28.8383	+	0.608415i	−1.16572	+	0.0245937i
$613$	28.6417			1.15683			0.578413	−	0.815744i	$-0.303672\pi$
$613$	28.6417			1.15683			0.578413	+	0.815744i	$0.303672\pi$
$614$	26.5058	+	9.64733i	1.06969	+	0.389335i
$615$	3.36448	−	5.97204i	0.135669	−	0.240816i
$616$	0.122137	+	2.03583i	0.00492105	+	0.0820261i
$617$	−1.12125	−	0.940841i	−0.0451399	−	0.0378768i	0.619939	−	0.784650i	$-0.287157\pi$
$617$	−1.12125	−	0.940841i	−0.0451399	−	0.0378768i	−0.665078	+	0.746773i	$0.731602\pi$
$618$	−0.195473	−	0.160539i	−0.00786309	−	0.00645783i
$619$	11.9651	−	10.0399i	0.480917	−	0.403537i	−0.369841	−	0.929095i	$-0.620588\pi$
$619$	11.9651	−	10.0399i	0.480917	−	0.403537i	0.850758	+	0.525558i	$0.176143\pi$
$620$	−13.1254	+	22.7339i	−0.527130	+	0.913016i
$621$	−15.7512	−	12.3892i	−0.632075	−	0.497163i
$622$	4.01139			0.160842
$623$	−10.5444	+	14.2152i	−0.422451	+	0.569521i
$624$	−2.62956	+	15.8913i	−0.105267	+	0.636162i
$625$	0.654451	−	3.71158i	0.0261781	−	0.148463i
$626$	−35.1175	−	29.4671i	−1.40358	−	1.17774i
$627$	−1.26164	+	2.23944i	−0.0503849	+	0.0894345i
$628$	−20.5358	−	7.47443i	−0.819469	−	0.298262i
$629$	11.4859	+	19.8942i	0.457974	+	0.793234i
$630$	19.4287	+	9.20802i	0.774057	+	0.366856i
$631$	15.8431	−	27.4411i	0.630705	−	1.09241i	−0.356703	−	0.934218i	$-0.616099\pi$
$631$	15.8431	−	27.4411i	0.630705	−	1.09241i	0.987408	−	0.158195i	$-0.0505673\pi$
$632$	−14.9102	+	12.5112i	−0.593098	+	0.497668i
$633$	−2.25815	−	12.0613i	−0.0897533	−	0.479393i
$634$	−6.66352	+	37.7907i	−0.264642	+	1.50086i
$635$	−8.42698	−	7.07107i	−0.334414	−	0.280607i
$636$	4.35902	+	23.2825i	0.172846	+	0.923213i
$637$	−27.8608	+	3.35502i	−1.10389	+	0.132931i
$638$	−4.75353	+	8.23335i	−0.188194	+	0.325962i
$639$	4.67771	+	23.6055i	0.185047	+	0.933820i
$640$	−13.1064			−0.518077
$641$	5.56536	+	31.5627i	0.219819	+	1.24665i	0.872346	+	0.488888i	$0.162597\pi$
$641$	5.56536	+	31.5627i	0.219819	+	1.24665i	−0.652528	+	0.757765i	$0.726291\pi$
$642$	8.58367	−	15.2362i	0.338770	−	0.601326i
$643$	4.23474	−	24.0164i	0.167002	−	0.947115i	−0.779974	−	0.625811i	$-0.784768\pi$
$643$	4.23474	−	24.0164i	0.167002	−	0.947115i	0.946976	−	0.321303i	$-0.104121\pi$
$644$	1.61146	+	26.8605i	0.0635006	+	1.05845i
$645$	1.85151	+	1.52061i	0.0729030	+	0.0598740i
$646$	3.60106	+	20.4226i	0.141682	+	0.803518i
$647$	−2.24162	+	3.88259i	−0.0881271	+	0.152641i	−0.906719	−	0.421734i	$-0.861421\pi$
$647$	−2.24162	+	3.88259i	−0.0881271	+	0.152641i	0.818592	+	0.574375i	$0.194755\pi$
$648$	−11.4151	+	4.70898i	−0.448427	+	0.184986i
$649$	2.28311	+	3.95445i	0.0896197	+	0.155226i
$650$	27.7245	+	10.0909i	1.08744	+	0.395797i
$651$	−30.0506	+	20.2981i	−1.17778	+	0.795544i
$652$	37.8193	+	31.7342i	1.48112	+	1.24281i
$653$	−33.5381	+	12.2069i	−1.31245	+	0.477692i	−0.901031	−	0.433755i	$-0.857188\pi$
$653$	−33.5381	+	12.2069i	−1.31245	+	0.477692i	−0.411417	+	0.911447i	$0.634966\pi$
$654$	52.9530	−	0.558525i	2.07063	−	0.0218401i
$655$	−3.96227	−	22.4711i	−0.154819	−	0.878020i
$656$	−3.64908	+	6.32039i	−0.142473	+	0.246770i
$657$	7.32696	−	6.41621i	0.285852	−	0.250320i
$658$	−13.3464	+	44.8646i	−0.520296	+	1.74901i
$659$	4.96812	+	28.1756i	0.193531	+	1.09757i	0.914496	+	0.404595i	$0.132588\pi$
$659$	4.96812	+	28.1756i	0.193531	+	1.09757i	−0.720965	+	0.692971i	$0.756301\pi$
$660$	−2.45088	+	2.10098i	−0.0954005	+	0.0817805i
$661$	−2.79990	+	15.8790i	−0.108903	+	0.617622i	0.880686	+	0.473701i	$0.157082\pi$
$661$	−2.79990	+	15.8790i	−0.108903	+	0.617622i	−0.989589	+	0.143921i	$0.954029\pi$
$662$	−9.04564	+	51.3004i	−0.351569	+	1.99385i
$663$	23.8792	+	8.40717i	0.927391	+	0.326507i
$664$	−3.40442	−	19.3074i	−0.132117	−	0.749273i
$665$	2.50650	−	8.42575i	0.0971978	−	0.326736i
$666$	31.7256	+	25.5002i	1.22934	+	0.988112i
$667$	−15.1528	+	26.2454i	−0.586718	+	1.01623i
$668$	−8.15376	−	46.2423i	−0.315478	−	1.78917i
$669$	−20.1689	+	35.8003i	−0.779775	+	1.38412i
$670$	−26.1442	+	9.51571i	−1.01004	+	0.367624i
$671$	4.56491	+	3.83042i	0.176226	+	0.147872i
$672$	−31.8873	−	15.5266i	−1.23008	−	0.598951i
$673$	−11.1747	−	4.06725i	−0.430752	−	0.156781i	0.117539	−	0.993068i	$-0.462499\pi$
$673$	−11.1747	−	4.06725i	−0.430752	−	0.156781i	−0.548292	+	0.836287i	$0.684722\pi$
$674$	−25.3293	−	43.8716i	−0.975648	−	1.68987i
$675$	−3.63551	−	17.3826i	−0.139931	−	0.669058i
$676$	−4.04939	+	7.01375i	−0.155746	+	0.269760i
$677$	0.695464	+	3.94417i	0.0267288	+	0.151587i	0.995251	−	0.0973397i	$-0.0310333\pi$
$677$	0.695464	+	3.94417i	0.0267288	+	0.151587i	−0.968522	+	0.248927i	$0.919922\pi$
$678$	5.43775	−	2.04438i	0.208836	−	0.0785141i
$679$	0.345560	+	5.75995i	0.0132614	+	0.221046i
$680$	−1.09268	+	6.19689i	−0.0419023	+	0.237640i
$681$	−2.64236	+	0.0278704i	−0.101255	+	0.00106800i
$682$	−1.66252	−	9.42864i	−0.0636613	−	0.361041i
$683$	21.1456			0.809112			0.404556	−	0.914513i	$-0.367426\pi$
$683$	21.1456			0.809112			0.404556	+	0.914513i	$0.367426\pi$
$684$	10.8278	+	17.8727i	0.414011	+	0.683381i
$685$	11.3865	−	19.7221i	0.435057	−	0.753541i
$686$	6.71975	−	39.3114i	0.256561	−	1.50092i
$687$	−3.24670	−	1.14307i	−0.123869	−	0.0436108i
$688$	−1.95414	−	1.63972i	−0.0745011	−	0.0625138i
$689$	3.61002	−	20.4734i	0.137531	−	0.779975i
$690$	−13.7377	+	11.7765i	−0.522987	+	0.448322i
$691$	4.34782	−	3.64825i	0.165399	−	0.138786i	−0.556332	−	0.830960i	$-0.687792\pi$
$691$	4.34782	−	3.64825i	0.165399	−	0.138786i	0.721730	+	0.692174i	$0.243347\pi$
$692$	20.7207	−	35.8892i	0.787681	−	1.36430i
$693$	−4.31463	+	1.12724i	−0.163899	+	0.0428205i
$694$	23.9592	+	41.4985i	0.909477	+	1.57526i
$695$	2.89857	+	1.05499i	0.109949	+	0.0400182i
$696$	9.50696	+	16.0726i	0.360360	+	0.609231i
$697$	8.78689	+	7.37308i	0.332827	+	0.279275i
$698$	2.98089	−	16.9054i	0.112828	−	0.639880i
$699$	−16.5839	+	6.23492i	−0.627262	+	0.235826i
$700$	−14.2064	+	19.1521i	−0.536951	+	0.723882i
$701$	−30.0373			−1.13449			−0.567246	−	0.823548i	$-0.691991\pi$
$701$	−30.0373			−1.13449			−0.567246	+	0.823548i	$0.691991\pi$
$702$	44.8344	−	1.41910i	1.69217	−	0.0535606i
$703$	8.32107	−	14.4125i	0.313835	−	0.543578i
$704$	5.17616	−	4.34331i	0.195084	−	0.163695i
$705$	−16.7550	+	6.29921i	−0.631028	+	0.237242i
$706$	49.4466	+	41.4906i	1.86095	+	1.56152i
$707$	1.99441	+	33.2436i	0.0750074	+	1.25025i
$708$	37.1206	−	0.391532i	1.39508	−	0.0147147i
$709$	27.2178	+	9.90647i	1.02219	+	0.372045i	0.798101	−	0.602524i	$-0.205838\pi$
$709$	27.2178	+	9.90647i	1.02219	+	0.372045i	0.224086	+	0.974569i	$0.428060\pi$
$710$	21.7285			0.815456
$711$	−33.1717	−	26.6625i	−1.24404	−	0.999923i
$712$	−9.17832			−0.343972
$713$	−5.29961	−	30.0556i	−0.198472	−	1.12559i
$714$	−21.1287	+	29.1213i	−0.790721	+	1.08984i
$715$	2.66236	−	0.969020i	0.0995667	−	0.0362393i
$716$	−12.9954	−	10.9044i	−0.485659	−	0.407517i
$717$	−9.84709	−	3.46688i	−0.367746	−	0.129473i
$718$	−15.7221	−	5.72238i	−0.586744	−	0.213557i
$719$	−11.3334			−0.422663			−0.211331	−	0.977414i	$-0.567780\pi$
$719$	−11.3334			−0.422663			−0.211331	+	0.977414i	$0.567780\pi$
$720$	−1.70164	−	8.58715i	−0.0634165	−	0.320024i
$721$	−0.174521	+	0.0416838i	−0.00649949	+	0.00155239i
$722$	−19.8337	+	16.6425i	−0.738134	+	0.619368i
$723$	8.30399	−	14.7398i	0.308829	−	0.548179i
$724$	−17.1431	−	14.3848i	−0.637119	−	0.534606i
$725$	−25.2363	+	9.18527i	−0.937254	+	0.341132i
$726$	−6.50566	+	39.3159i	−0.241448	+	1.45915i
$727$	−15.0125	−	5.46412i	−0.556785	−	0.202653i	0.0482737	−	0.998834i	$-0.484628\pi$
$727$	−15.0125	−	5.46412i	−0.556785	−	0.202653i	−0.605058	+	0.796181i	$0.706850\pi$
$728$	−10.0049	−	10.5676i	−0.370806	−	0.391660i
$729$	−14.9517	−	22.4821i	−0.553767	−	0.832671i
$730$	−4.39689	−	7.61564i	−0.162736	−	0.281868i
$731$	−3.07132	+	2.57714i	−0.113597	+	0.0953190i
$732$	45.3475	−	17.0489i	1.67609	−	0.630145i
$733$	2.71416	−	15.3928i	0.100250	−	0.568546i	−0.892762	−	0.450529i	$-0.851235\pi$
$733$	2.71416	−	15.3928i	0.100250	−	0.568546i	0.993012	−	0.118017i	$-0.0376536\pi$
$734$	−12.0088	+	68.1050i	−0.443251	+	2.51380i
$735$	13.5317	−	7.03539i	0.499123	−	0.259504i
$736$	22.8652	−	19.1862i	0.842823	−	0.707212i
$737$	2.88534	−	4.99755i	0.106283	−	0.184087i
$738$	19.2410	+	6.54695i	0.708272	+	0.240997i
$739$	3.91928	+	6.78840i	0.144173	+	0.249715i	0.929064	−	0.369919i	$-0.120614\pi$
$739$	3.91928	+	6.78840i	0.144173	+	0.249715i	−0.784891	+	0.619634i	$0.787281\pi$
$740$	16.0111	−	13.4349i	0.588579	−	0.493877i
$741$	−3.37508	−	18.0271i	−0.123987	−	0.662242i
$742$	26.4259	+	13.2139i	0.970126	+	0.485098i
$743$	−15.2292	+	5.54298i	−0.558705	+	0.203352i	−0.605910	−	0.795533i	$-0.707191\pi$
$743$	−15.2292	+	5.54298i	−0.558705	+	0.203352i	0.0472049	+	0.998885i	$0.484969\pi$
$744$	−17.7382	−	6.24512i	−0.650315	−	0.228957i
$745$	−14.5045	−	5.27922i	−0.531405	−	0.193416i
$746$	10.6778	+	18.4945i	0.390943	+	0.677132i
$747$	39.9644	−	15.5081i	1.46222	−	0.567410i
$748$	−2.70101	−	4.67828i	−0.0987586	−	0.171055i
$749$	−4.93324	−	11.3819i	−0.180257	−	0.415886i
$750$	−39.4914	+	0.416537i	−1.44202	+	0.0152098i
$751$	−31.5364	+	11.4783i	−1.15078	+	0.418850i	−0.845795	−	0.533507i	$-0.820874\pi$
$751$	−31.5364	+	11.4783i	−1.15078	+	0.418850i	−0.304985	+	0.952357i	$0.598651\pi$
$752$	17.9090	−	6.51836i	0.653075	−	0.237700i
$753$	23.2357	+	19.0831i	0.846754	+	0.695425i
$754$	−11.7795	−	66.8050i	−0.428985	−	2.43289i
$755$	29.7796			1.08379
$756$	−9.23285	+	35.0594i	−0.335796	+	1.27510i
$757$	−45.5849			−1.65681			−0.828405	−	0.560129i	$-0.810752\pi$
$757$	−45.5849			−1.65681			−0.828405	+	0.560129i	$0.810752\pi$
$758$	7.57986	+	42.9875i	0.275313	+	1.56138i
$759$	0.612691	−	3.70269i	0.0222393	−	0.134399i
$760$	4.28372	−	1.55915i	0.155387	−	0.0565562i
$761$	1.89014	−	0.687955i	0.0685175	−	0.0249383i	−0.307534	−	0.951537i	$-0.599504\pi$
$761$	1.89014	−	0.687955i	0.0685175	−	0.0249383i	0.376052	+	0.926599i	$0.377282\pi$
$762$	16.0101	−	28.4183i	0.579984	−	1.02949i
$763$	22.3794	−	30.1705i	0.810189	−	1.09224i
$764$	21.0159	+	36.4006i	0.760329	+	1.31693i
$765$	−13.7557	+	0.290211i	−0.497340	+	0.0104926i
$766$	38.4138	+	66.5347i	1.38795	+	2.40400i
$767$	−30.6163	−	11.1434i	−1.10549	−	0.402366i
$768$	0.515206	+	2.75183i	0.0185909	+	0.0992983i
$769$	−5.02496	+	1.82893i	−0.181205	+	0.0659531i	−0.431029	−	0.902338i	$-0.641849\pi$
$769$	−5.02496	+	1.82893i	−0.181205	+	0.0659531i	0.249824	+	0.968291i	$0.419627\pi$
$770$	0.241134	+	4.01933i	0.00868988	+	0.144846i
$771$	3.27982	+	1.15473i	0.118120	+	0.0415866i
$772$	−40.8760	+	34.2990i	−1.47116	+	1.23445i
$773$	−23.9689	−	41.5154i	−0.862102	−	1.49320i	−0.869896	−	0.493235i	$-0.835814\pi$
$773$	−23.9689	−	41.5154i	−0.862102	−	1.49320i	0.00779362	−	0.999970i	$-0.497519\pi$
$774$	−3.42147	+	6.22584i	−0.122982	+	0.223783i
$775$	13.5226	−	23.4219i	0.485748	−	0.841340i
$776$	−2.29227	+	1.92344i	−0.0822877	+	0.0690476i
$777$	28.0109	−	7.00343i	1.00489	−	0.251246i
$778$	−3.18619	+	18.0698i	−0.114231	+	0.647834i
$779$	1.44299	−	8.18363i	0.0517006	−	0.293209i
$780$	3.76030	−	22.7247i	0.134640	−	0.813676i
$781$	−3.45240	+	2.89691i	−0.123537	+	0.103659i
$782$	−15.1397	−	26.2228i	−0.541396	−	0.937726i
$783$	−30.4325	+	27.2222i	−1.08757	+	0.972841i
$784$	−14.4856	+	7.33833i	−0.517342	+	0.262083i
$785$	−9.79551	−	3.56527i	−0.349617	−	0.127250i
$786$	63.3290	−	23.8092i	2.25887	−	0.849247i
$787$	1.63063	−	0.593501i	0.0581257	−	0.0211560i	−0.312794	−	0.949821i	$-0.601265\pi$
$787$	1.63063	−	0.593501i	0.0581257	−	0.0211560i	0.370919	+	0.928665i	$0.379043\pi$
$788$	−3.38021	−	2.83634i	−0.120415	−	0.101040i
$789$	−0.772143	−	1.30540i	−0.0274890	−	0.0464734i
$790$	−29.4372	+	24.7007i	−1.04733	+	0.878812i
$791$	1.17500	−	3.94983i	0.0417781	−	0.140440i
$792$	−1.80249	−	1.44879i	−0.0640487	−	0.0514806i
$793$	−42.5196			−1.50992
$794$	−21.3836	−	7.78300i	−0.758877	−	0.276209i
$795$	2.07923	+	11.1057i	0.0737428	+	0.393878i
$796$	−37.7555	−	31.6806i	−1.33821	−	1.12289i
$797$	29.7151	−	10.8154i	1.05256	−	0.383102i	0.242934	−	0.970043i	$-0.421890\pi$
$797$	29.7151	−	10.8154i	1.05256	−	0.383102i	0.809630	+	0.586941i	$0.199668\pi$
$798$	25.9241	+	2.70754i	0.917702	+	0.0958459i
$799$	−5.20145	−	29.4989i	−0.184014	−	1.04360i
$800$	26.4508			0.935178
$801$	−3.90102	−	19.6860i	−0.137836	−	0.695572i
$802$	−27.8902			−0.984838
$803$	1.71395	+	0.623828i	0.0604841	+	0.0220144i
$804$	−23.8846	−	40.3798i	−0.842346	−	1.42409i
$805$	0.768661	+	12.8124i	0.0270918	+	0.451577i
$806$	52.3314	+	43.9113i	1.84330	+	1.54671i
$807$	−0.887746	+	5.36494i	−0.0312502	+	0.188855i
$808$	−13.2299	+	11.1012i	−0.465426	+	0.390538i
$809$	8.18791	−	14.1819i	0.287872	−	0.498608i	−0.685430	−	0.728139i	$-0.740386\pi$
$809$	8.18791	−	14.1819i	0.287872	−	0.498608i	0.973301	+	0.229530i	$0.0737190\pi$
$810$	−22.5367	+	9.29690i	−0.791860	+	0.326660i
$811$	0.558614			0.0196156			0.00980780	−	0.999952i	$-0.496878\pi$
$811$	0.558614			0.0196156			0.00980780	+	0.999952i	$0.496878\pi$
$812$	54.4671	+	6.27001i	1.91142	+	0.220034i
$813$	−20.0329	−	16.4527i	−0.702585	−	0.577022i
$814$	−1.32370	+	7.50710i	−0.0463958	+	0.263124i
$815$	18.0396	+	15.1371i	0.631901	+	0.530228i
$816$	14.6484	−	0.154505i	0.512797	−	0.00540876i
$817$	2.72941	+	0.993426i	0.0954901	+	0.0347556i
$818$	−3.20694	−	5.55458i	−0.112128	−	0.194211i
$819$	18.4134	−	25.9504i	0.643417	−	0.906779i
$820$	5.21822	−	9.03822i	0.182228	−	0.315628i
$821$	25.4781	−	21.3787i	0.889193	−	0.746122i	−0.0788547	−	0.996886i	$-0.525126\pi$
$821$	25.4781	−	21.3787i	0.889193	−	0.746122i	0.968048	+	0.250764i	$0.0806819\pi$
$822$	63.6920	+	22.4241i	2.22151	+	0.782130i
$823$	5.24776	−	29.7616i	0.182926	−	1.03742i	−0.745666	−	0.666320i	$-0.767869\pi$
$823$	5.24776	−	29.7616i	0.182926	−	1.03742i	0.928592	−	0.371103i	$-0.121020\pi$
$824$	−0.0712790	−	0.0598102i	−0.00248312	−	0.00208359i
$825$	2.52505	−	2.16456i	0.0879111	−	0.0753604i
$826$	27.5861	−	37.1898i	0.959842	−	1.29400i
$827$	8.28426	−	14.3488i	0.288072	−	0.498955i	−0.685278	−	0.728282i	$-0.740319\pi$
$827$	8.28426	−	14.3488i	0.288072	−	0.498955i	0.973349	+	0.229327i	$0.0736525\pi$
$828$	−23.7818	−	19.1152i	−0.826476	−	0.664299i
$829$	−52.7772			−1.83303			−0.916514	−	0.400002i	$-0.869009\pi$
$829$	−52.7772			−1.83303			−0.916514	+	0.400002i	$0.869009\pi$
$830$	−6.72131	−	38.1184i	−0.233300	−	1.32311i
$831$	13.8259	+	23.3743i	0.479615	+	0.810845i
$832$	−8.37211	+	47.4806i	−0.290251	+	1.64609i
$833$	7.40495	+	24.4238i	0.256566	+	0.846235i
$834$	−1.49312	+	9.02340i	−0.0517024	+	0.312455i
$835$	−3.88931	−	22.0574i	−0.134595	−	0.763327i
$836$	−1.95677	+	3.38922i	−0.0676761	+	0.117219i
$837$	5.85559	−	40.7000i	0.202399	−	1.40680i
$838$	32.5442	+	56.3682i	1.12422	+	1.94721i
$839$	16.3710	+	5.95857i	0.565191	+	0.205713i	0.608783	−	0.793337i	$-0.291658\pi$
$839$	16.3710	+	5.95857i	0.565191	+	0.205713i	−0.0435921	+	0.999049i	$0.513880\pi$
$840$	7.11082	+	3.46241i	0.245347	+	0.119464i
$841$	25.0861	+	21.0498i	0.865039	+	0.725854i
$842$	−28.7831	+	10.4762i	−0.991932	+	0.361034i
$843$	16.9421	+	28.6427i	0.583518	+	0.986505i
$844$	−3.24428	−	18.3992i	−0.111673	−	0.633328i
$845$	−1.93154	+	3.34553i	−0.0664471	+	0.115090i
$846$	−27.5011	−	45.3943i	−0.945507	−	1.56069i
$847$	19.4346	+	20.5276i	0.667780	+	0.705337i
$848$	−2.08896	−	11.8471i	−0.0717352	−	0.406831i
$849$	−1.42303	−	7.60075i	−0.0488384	−	0.260857i
$850$	4.65947	−	26.4252i	0.159819	−	0.906377i
$851$	−4.21956	+	23.9303i	−0.144645	+	0.820321i
$852$	6.74261	+	36.0138i	0.230998	+	1.23381i
$853$	5.45394	+	30.9308i	0.186739	+	1.05905i	0.923700	+	0.383116i	$0.125149\pi$
$853$	5.45394	+	30.9308i	0.186739	+	1.05905i	−0.736961	+	0.675935i	$0.763740\pi$
$854$	17.2301	−	57.9200i	0.589602	−	1.98198i
$855$	5.16481	+	8.52521i	0.176633	+	0.291556i
$856$	3.21648	−	5.57111i	0.109937	−	0.190417i
$857$	4.01483	+	22.7692i	0.137144	+	0.777783i	0.973343	+	0.229356i	$0.0736620\pi$
$857$	4.01483	+	22.7692i	0.137144	+	0.777783i	−0.836199	+	0.548427i	$0.815227\pi$
$858$	4.27688	+	7.23057i	0.146010	+	0.246848i
$859$	4.18867	−	1.52455i	0.142916	−	0.0520170i	−0.269572	−	0.962980i	$-0.586882\pi$
$859$	4.18867	−	1.52455i	0.142916	−	0.0520170i	0.412488	+	0.910963i	$0.364660\pi$
$860$	2.79444	+	2.34482i	0.0952898	+	0.0799576i
$861$	11.9471	−	8.06982i	0.407156	−	0.275019i
$862$	−26.4435	−	9.62463i	−0.900668	−	0.327816i
$863$	19.4918	+	33.7607i	0.663507	+	1.14923i	0.979688	+	0.200529i	$0.0642660\pi$
$863$	19.4918	+	33.7607i	0.663507	+	1.14923i	−0.316181	+	0.948699i	$0.602401\pi$
$864$	37.3359	−	14.9431i	1.27019	−	0.508374i
$865$	9.88366	−	17.1190i	0.336055	−	0.582064i
$866$	−1.70606	−	9.67557i	−0.0579744	−	0.328789i
$867$	−1.04820	+	6.33462i	−0.0355987	+	0.215135i
$868$	−46.0771	+	30.4207i	−1.56396	+	1.03254i
$869$	1.38404	−	7.84929i	0.0469504	−	0.266269i
$870$	18.7695	+	31.7320i	0.636346	+	1.07582i
$871$	7.15004	+	40.5499i	0.242270	+	1.37398i
$872$	19.4801			0.659680
$873$	−5.09975	−	4.09904i	−0.172600	−	0.138732i
$874$	−10.9681	+	18.9973i	−0.371002	+	0.642594i
$875$	−16.6901	+	22.5006i	−0.564229	+	0.760658i
$876$	11.2581	−	9.65084i	0.380376	−	0.326072i
$877$	14.7127	+	12.3454i	0.496811	+	0.416874i	0.856460	−	0.516214i	$-0.172659\pi$
$877$	14.7127	+	12.3454i	0.496811	+	0.416874i	−0.359649	+	0.933088i	$0.617103\pi$
$878$	1.64053	−	9.30389i	0.0553651	−	0.313991i
$879$	39.3100	+	13.8399i	1.32589	+	0.466809i
$880$	1.25590	−	1.05383i	0.0423365	−	0.0355245i
$881$	−1.55565	+	2.69447i	−0.0524113	+	0.0907791i	−0.891041	−	0.453923i	$-0.850024\pi$
$881$	−1.55565	+	2.69447i	−0.0524113	+	0.0907791i	0.838629	+	0.544702i	$0.183357\pi$
$882$	27.8878	+	35.5984i	0.939032	+	1.19866i
$883$	3.39560	+	5.88134i	0.114271	+	0.197923i	0.917488	−	0.397763i	$-0.130213\pi$
$883$	3.39560	+	5.88134i	0.114271	+	0.197923i	−0.803217	+	0.595686i	$0.796880\pi$
$884$	36.2204	+	13.1831i	1.21822	+	0.443397i
$885$	17.7064	−	0.186759i	0.595194	−	0.00627784i
$886$	−49.9492	−	41.9124i	−1.67808	−	1.40807i
$887$	5.14942	−	29.2038i	0.172901	−	0.980568i	−0.767639	−	0.640883i	$-0.778568\pi$
$887$	5.14942	−	29.2038i	0.172901	−	0.980568i	0.940539	−	0.339685i	$-0.110320\pi$
$888$	11.5708	+	9.50293i	0.388292	+	0.318897i
$889$	−9.20138	−	21.2293i	−0.308604	−	0.712008i
$890$	−18.1207			−0.607406
$891$	2.34133	−	4.48183i	0.0784374	−	0.150147i
$892$	−31.2815	+	54.1811i	−1.04738	+	1.81412i
$893$	−16.6235	+	13.9487i	−0.556283	+	0.466777i
$894$	7.47159	−	45.1533i	0.249887	−	1.51015i
$895$	−6.19873	−	5.20135i	−0.207201	−	0.173862i
$896$	−24.6561	−	12.3289i	−0.823701	−	0.411881i
$897$	13.6334	+	23.0488i	0.455205	+	0.769577i
$898$	−33.1982	−	12.0832i	−1.10784	−	0.403221i
$899$	−62.1830			−2.07392
$900$	−5.25583	−	26.5229i	−0.175194	−	0.884098i
$901$	−18.9072			−0.629892
$902$	0.660962	+	3.74850i	0.0220076	+	0.124811i
$903$	2.05268	+	4.60227i	0.0683090	+	0.153154i
$904$	2.00813	−	0.730898i	0.0667893	−	0.0243093i
$905$	−8.17720	−	6.86148i	−0.271819	−	0.228083i
$906$	16.2493	+	86.7910i	0.539845	+	2.88344i
$907$	30.2347	+	11.0045i	1.00393	+	0.365399i	0.791098	−	0.611690i	$-0.209510\pi$
$907$	30.2347	+	11.0045i	1.00393	+	0.365399i	0.212829	+	0.977089i	$0.431732\pi$
$908$	−4.02336			−0.133520
$909$	−29.4333	−	23.6577i	−0.976241	−	0.784676i
$910$	−19.7526	−	20.8635i	−0.654791	−	0.691617i
$911$	32.3136	−	27.1143i	1.07060	−	0.898338i	0.0754913	−	0.997146i	$-0.475948\pi$
$911$	32.3136	−	27.1143i	1.07060	−	0.898338i	0.995106	+	0.0988083i	$0.0315031\pi$
$912$	−5.40302	−	9.13444i	−0.178912	−	0.302471i
$913$	6.15000	+	5.16046i	0.203535	+	0.170786i
$914$	27.4872	−	10.0045i	0.909195	−	0.330920i
$915$	21.6306	−	8.13225i	0.715084	−	0.268844i
$916$	−4.92465	−	1.79243i	−0.162715	−	0.0592235i
$917$	13.6842	−	46.0003i	0.451893	−	1.51907i
$918$	−8.35164	−	39.9321i	−0.275645	−	1.31795i
$919$	−1.74885	−	3.02910i	−0.0576893	−	0.0999207i	0.835738	−	0.549128i	$-0.185040\pi$
$919$	−1.74885	−	3.02910i	−0.0576893	−	0.0999207i	−0.893428	+	0.449207i	$0.851707\pi$
$920$	−5.09891	+	4.27849i	−0.168106	+	0.141058i
$921$	−3.70381	+	22.3833i	−0.122045	+	0.737556i
$922$	0.222689	−	1.26293i	0.00733387	−	0.0415924i
$923$	5.58404	−	31.6687i	0.183801	−	1.04239i
$924$	−6.58699	+	1.64691i	−0.216696	+	0.0541794i
$925$	−16.4956	+	13.8415i	−0.542373	+	0.455105i
$926$	7.60547	−	13.1731i	0.249931	−	0.432894i
$927$	0.0979880	−	0.178303i	0.00321835	−	0.00585624i
$928$	−30.4081	−	52.6684i	−0.998195	−	1.72892i
$929$	9.85847	−	8.27224i	0.323446	−	0.271403i	−0.466577	−	0.884481i	$-0.654513\pi$
$929$	9.85847	−	8.27224i	0.323446	−	0.271403i	0.790023	+	0.613077i	$0.210069\pi$
$930$	−35.0204	−	12.3297i	−1.14836	−	0.404306i
$931$	12.6412	−	13.4929i	0.414298	−	0.442211i
$932$	−25.3487	+	9.22617i	−0.830324	+	0.302213i
$933$	0.593755	+	3.17138i	0.0194387	+	0.103826i
$934$	−24.8967	−	9.06165i	−0.814644	−	0.296506i
$935$	−1.28837	−	2.23152i	−0.0421342	−	0.0729785i
$936$	16.4972	−	0.348048i	0.539227	−	0.0113763i
$937$	−11.2756	−	19.5299i	−0.368358	−	0.638015i	0.620951	−	0.783849i	$-0.286747\pi$
$937$	−11.2756	−	19.5299i	−0.368358	−	0.638015i	−0.989309	+	0.145835i	$0.953413\pi$
$938$	−58.1342	−	6.69215i	−1.89815	−	0.218506i
$939$	18.0985	−	32.1254i	0.590624	−	1.04837i
$940$	−25.6101	+	9.32131i	−0.835309	+	0.304028i
$941$	−48.1800	+	17.5361i	−1.57062	+	0.571660i	−0.973138	−	0.230221i	$-0.926055\pi$
$941$	−48.1800	+	17.5361i	−1.57062	+	0.571660i	−0.597484	+	0.801881i	$0.703833\pi$
$942$	5.04588	−	30.4939i	0.164404	−	0.993545i
$943$	2.10694	+	11.9491i	0.0686115	+	0.389115i
$944$	−18.8533			−0.613624
$945$	−4.40403	+	16.7232i	−0.143263	+	0.544005i
$946$	−1.33044			−0.0432564
$947$	−7.07615	−	40.1308i	−0.229944	−	1.30408i	−0.853005	−	0.521903i	$-0.825222\pi$
$947$	−7.07615	−	40.1308i	−0.229944	−	1.30408i	0.623061	−	0.782173i	$-0.285889\pi$
$948$	−50.0748	−	41.1256i	−1.62635	−	1.33570i
$949$	−12.2295	+	4.45119i	−0.396988	+	0.144492i
$950$	−18.2669	+	6.64862i	−0.592657	+	0.215710i
$951$	−30.8635	+	0.325534i	−1.00082	+	0.0105562i
$952$	−7.88484	+	10.6298i	−0.255549	+	0.344515i
$953$	9.89160	+	17.1328i	0.320420	+	0.554984i	0.980575	−	0.196145i	$-0.0628425\pi$
$953$	9.89160	+	17.1328i	0.320420	+	0.554984i	−0.660154	+	0.751130i	$0.729509\pi$
$954$	−31.2324	+	12.1196i	−1.01119	+	0.392388i
$955$	10.0245	+	17.3629i	0.324385	+	0.561851i
$956$	−14.9362	−	5.43635i	−0.483073	−	0.175824i
$957$	−7.21286	−	2.53944i	−0.233159	−	0.0820884i
$958$	14.3051	−	5.20663i	0.462177	−	0.168219i
$959$	39.9727	−	26.3904i	1.29078	−	0.852192i
$960$	−4.82202	−	25.7555i	−0.155630	−	0.831256i
$961$	24.2234	−	20.3259i	0.781400	−	0.655673i
$962$	−27.1958	−	47.1045i	−0.876828	−	1.51871i
$963$	13.3162	+	4.53098i	0.429109	+	0.146009i
$964$	12.8793	−	22.3076i	0.414814	−	0.718478i
$965$	−19.4977	+	16.3605i	−0.627652	+	0.526663i
$966$	−36.9216	+	9.23130i	−1.18793	+	0.297012i
$967$	−0.846087	+	4.79840i	−0.0272083	+	0.154306i	−0.995385	−	0.0959614i	$-0.969407\pi$
$967$	−0.846087	+	4.79840i	−0.0272083	+	0.154306i	0.968177	+	0.250268i	$0.0805186\pi$
$968$	−2.54554	+	14.4365i	−0.0818168	+	0.464006i
$969$	−15.6130	+	5.86989i	−0.501563	+	0.188568i
$970$	−4.52561	+	3.79744i	−0.145309	+	0.121928i
$971$	10.5651	+	18.2994i	0.339052	+	0.587255i	0.984255	−	0.176756i	$-0.0565605\pi$
$971$	10.5651	+	18.2994i	0.339052	+	0.587255i	−0.645203	+	0.764011i	$0.723227\pi$
$972$	−22.4025	−	34.4685i	−0.718561	−	1.10558i
$973$	4.46044	+	4.71130i	0.142995	+	0.151037i
$974$	−50.9638	−	18.5493i	−1.63298	−	0.594358i
$975$	−3.87410	+	23.4125i	−0.124071	+	0.749799i
$976$	−23.1205	+	8.41516i	−0.740068	+	0.269363i
$977$	31.1920	+	26.1732i	0.997921	+	0.837355i	0.986695	−	0.162582i	$-0.0519822\pi$
$977$	31.1920	+	26.1732i	0.997921	+	0.837355i	0.0112257	+	0.999937i	$0.496427\pi$
$978$	−34.2728	+	60.8352i	−1.09592	+	1.94529i
$979$	2.87916	−	2.41590i	0.0920183	−	0.0772125i
$980$	20.7145	−	10.4939i	0.661701	−	0.335214i
$981$	8.27954	+	41.7817i	0.264345	+	1.33399i
$982$	6.85586			0.218779
$983$	−1.06476	−	0.387542i	−0.0339607	−	0.0123607i	0.324984	−	0.945720i	$-0.394641\pi$
$983$	−1.06476	−	0.387542i	−0.0339607	−	0.0123607i	−0.358945	+	0.933359i	$0.616863\pi$
$984$	7.05211	+	2.48284i	0.224813	+	0.0791502i
$985$	−1.61235	−	1.35292i	−0.0513737	−	0.0431076i
$986$	−57.9739	+	21.1008i	−1.84626	+	0.671985i
$987$	−37.4453	−	3.91083i	−1.19190	−	0.124483i
$988$	−4.84898	−	27.4999i	−0.154267	−	0.874889i
$989$	−4.24103			−0.134857
$990$	−3.55864	−	2.86034i	−0.113101	−	0.0909075i
$991$	25.2948			0.803516			0.401758	−	0.915746i	$-0.368399\pi$
$991$	25.2948			0.803516			0.401758	+	0.915746i	$0.368399\pi$
$992$	57.5515	+	20.9470i	1.82726	+	0.665069i
$993$	−41.8968	+	0.441908i	−1.32955	+	0.0140235i
$994$	40.8761	+	20.4395i	1.29651	+	0.648302i
$995$	−18.0092	−	15.1115i	−0.570931	−	0.479068i
$996$	61.0936	−	22.9688i	1.93582	−	0.727795i
$997$	−5.06605	+	4.25092i	−0.160444	+	0.134628i	−0.719475	−	0.694518i	$-0.755618\pi$
$997$	−5.06605	+	4.25092i	−0.160444	+	0.134628i	0.559031	+	0.829146i	$0.311173\pi$
$998$	−15.9600	+	27.6436i	−0.505206	+	0.875042i
$999$	−15.4644	+	28.8566i	−0.489271	+	0.912981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.20	✓	132
3.2	odd	2		567.2.u.a.550.3		132
7.2	even	3		189.2.w.a.58.20	yes	132
21.2	odd	6		567.2.w.a.226.3		132
27.7	even	9		189.2.w.a.88.20	yes	132
27.20	odd	18		567.2.w.a.424.3		132
189.128	odd	18		567.2.u.a.100.3		132
189.142	even	9	inner	189.2.u.a.142.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.20	✓	132	1.1	even	1	trivial
189.2.u.a.142.20	yes	132	189.142	even	9	inner
189.2.w.a.58.20	yes	132	7.2	even	3
189.2.w.a.88.20	yes	132	27.7	even	9
567.2.u.a.100.3		132	189.128	odd	18
567.2.u.a.550.3		132	3.2	odd	2
567.2.w.a.226.3		132	21.2	odd	6
567.2.w.a.424.3		132	27.20	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.373934 + 2.12069i) q^{2} +(-1.62126 + 0.609530i) q^{3} +(-2.47810 + 0.901956i) q^{4} +(-1.18205 + 0.430229i) q^{5} +(-1.89887 - 3.21026i) q^{6} +(-2.62839 - 0.302569i) q^{7} +(-0.686013 - 1.18821i) q^{8} +(2.25695 - 1.97641i) q^{9} +O(q^{10})\)	\(q+(0.373934 + 2.12069i) q^{2} +(-1.62126 + 0.609530i) q^{3} +(-2.47810 + 0.901956i) q^{4} +(-1.18205 + 0.430229i) q^{5} +(-1.89887 - 3.21026i) q^{6} +(-2.62839 - 0.302569i) q^{7} +(-0.686013 - 1.18821i) q^{8} +(2.25695 - 1.97641i) q^{9} +(-1.35439 - 2.34587i) q^{10} +(0.527955 + 0.192160i) q^{11} +(3.46787 - 2.97278i) q^{12} +(-3.76711 + 1.37111i) q^{13} +(-0.341193 - 5.68714i) q^{14} +(1.65416 - 1.41800i) q^{15} +(-1.77704 + 1.49111i) q^{16} +(1.82298 + 3.15749i) q^{17} +(5.03529 + 4.04723i) q^{18} +(1.32067 - 2.28747i) q^{19} +(2.54118 - 2.13231i) q^{20} +(4.44573 - 1.11154i) q^{21} +(-0.210090 + 1.19148i) q^{22} +(-0.669703 + 3.79808i) q^{23} +(1.83645 + 1.50825i) q^{24} +(-2.61809 + 2.19684i) q^{25} +(-4.31636 - 7.47615i) q^{26} +(-2.45441 + 4.57994i) q^{27} +(6.78634 - 1.62090i) q^{28} +(7.38407 + 2.68758i) q^{29} +(3.62569 + 2.97772i) q^{30} +(-7.43614 + 2.70653i) q^{31} +(-5.92875 - 4.97481i) q^{32} +(-0.973077 + 0.0102636i) q^{33} +(-6.01437 + 5.04666i) q^{34} +(3.23705 - 0.773162i) q^{35} +(-3.81032 + 6.93341i) q^{36} +6.30064 q^{37} +(5.34485 + 1.94537i) q^{38} +(5.27171 - 4.51909i) q^{39} +(1.32210 + 1.10938i) q^{40} +(2.95635 - 1.07602i) q^{41} +(4.01964 + 9.01235i) q^{42} +(0.190954 + 1.08296i) q^{43} -1.48165 q^{44} +(-1.81751 + 3.30721i) q^{45} -8.30496 q^{46} +(-7.72021 - 2.80993i) q^{47} +(1.97216 - 3.50064i) q^{48} +(6.81690 + 1.59054i) q^{49} +(-5.63780 - 4.73067i) q^{50} +(-4.88010 - 4.00794i) q^{51} +(8.09860 - 6.79553i) q^{52} +(-2.59291 + 4.49105i) q^{53} +(-10.6304 - 3.49245i) q^{54} -0.706739 q^{55} +(1.44360 + 3.33065i) q^{56} +(-0.746866 + 4.51356i) q^{57} +(-2.93836 + 16.6643i) q^{58} +(6.22586 + 5.22411i) q^{59} +(-2.82021 + 5.00594i) q^{60} +(9.96675 + 3.62760i) q^{61} +(-8.52034 - 14.7577i) q^{62} +(-6.53015 + 4.51190i) q^{63} +(6.01330 - 10.4153i) q^{64} +(3.86300 - 3.24144i) q^{65} +(-0.385633 - 2.05975i) q^{66} +(1.78355 - 10.1150i) q^{67} +(-7.36544 - 6.18034i) q^{68} +(-1.22928 - 6.56586i) q^{69} +(2.85008 + 6.57567i) q^{70} +(-4.01075 + 6.94683i) q^{71} +(-3.89668 - 1.32589i) q^{72} +3.24640 q^{73} +(2.35603 + 13.3617i) q^{74} +(2.90556 - 5.15744i) q^{75} +(-1.20956 + 6.85977i) q^{76} +(-1.32953 - 0.664814i) q^{77} +(11.5549 + 9.48981i) q^{78} +(-2.46342 - 13.9708i) q^{79} +(1.45902 - 2.52710i) q^{80} +(1.18762 - 8.92130i) q^{81} +(3.38739 + 5.86714i) q^{82} +(13.4275 + 4.88722i) q^{83} +(-10.0144 + 6.76437i) q^{84} +(-3.51329 - 2.94800i) q^{85} +(-2.22521 + 0.809909i) q^{86} +(-13.6096 + 0.143548i) q^{87} +(-0.133858 - 0.759145i) q^{88} +(3.34480 - 5.79337i) q^{89} +(-7.69319 - 2.61768i) q^{90} +(10.3163 - 2.46402i) q^{91} +(-1.76610 - 10.0161i) q^{92} +(10.4062 - 8.92053i) q^{93} +(3.07212 - 17.4229i) q^{94} +(-0.576956 + 3.27208i) q^{95} +(12.6443 + 4.45170i) q^{96} +(-0.378721 - 2.14784i) q^{97} +(-0.823964 + 15.0513i) q^{98} +(1.57135 - 0.609759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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