LMFDB - Embedded newform 243.2.i.a.4.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	243.4
Dual form			243.2.i.a.61.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.03967 - 0.0791483i) q^{2} +(-0.137599 - 1.72658i) q^{3} +(2.15999 + 0.167888i) q^{4} +(1.00485 + 1.24581i) q^{5} +(0.144001 + 3.53253i) q^{6} +(2.22760 - 1.01257i) q^{7} +(-0.337568 - 0.0394561i) q^{8} +(-2.96213 + 0.475151i) q^{9} +(-1.95095 - 2.62057i) q^{10} +(0.101732 + 5.24528i) q^{11} +(-0.00734214 - 3.75249i) q^{12} +(3.45524 + 1.10788i) q^{13} +(-4.62371 + 1.88899i) q^{14} +(2.01273 - 1.90637i) q^{15} +(-3.59556 - 0.562336i) q^{16} +(-1.11860 - 3.73638i) q^{17} +(6.07937 - 0.734702i) q^{18} +(6.38307 - 1.51282i) q^{19} +(1.96130 + 2.85964i) q^{20} +(-2.05480 - 3.70680i) q^{21} +(0.207655 - 10.7067i) q^{22} +(2.65860 - 1.90025i) q^{23} +(-0.0216748 + 0.588266i) q^{24} +(0.516184 - 2.38297i) q^{25} +(-6.95986 - 2.53318i) q^{26} +(1.22797 + 5.04897i) q^{27} +(4.98160 - 1.81315i) q^{28} +(-0.186172 - 1.36302i) q^{29} +(-4.25617 + 3.72905i) q^{30} +(-4.51437 - 4.42766i) q^{31} +(7.95623 + 1.56255i) q^{32} +(9.04237 - 0.897394i) q^{33} +(1.98584 + 7.70951i) q^{34} +(3.49987 + 1.75770i) q^{35} +(-6.47794 + 0.529016i) q^{36} +(4.92352 + 3.23825i) q^{37} +(-13.1391 + 2.58043i) q^{38} +(1.43740 - 6.11819i) q^{39} +(-0.290049 - 0.460194i) q^{40} +(3.88267 - 7.37108i) q^{41} +(3.89771 + 7.72327i) q^{42} +(-3.43287 + 10.0329i) q^{43} +(-0.660877 + 11.3468i) q^{44} +(-3.56844 - 3.21281i) q^{45} +(-5.57305 + 3.66545i) q^{46} +(-3.59597 + 3.52690i) q^{47} +(-0.476169 + 6.28539i) q^{48} +(-0.665729 + 0.762841i) q^{49} +(-1.24145 + 4.81961i) q^{50} +(-6.29724 + 2.44547i) q^{51} +(7.27729 + 2.97310i) q^{52} +(-5.38254 - 4.51648i) q^{53} +(-2.10504 - 10.3954i) q^{54} +(-6.43241 + 5.39743i) q^{55} +(-0.791920 + 0.253919i) q^{56} +(-3.49030 - 10.8127i) q^{57} +(0.271848 + 2.79484i) q^{58} +(6.04488 - 3.33542i) q^{59} +(4.66752 - 3.77982i) q^{60} +(-3.69728 + 0.287376i) q^{61} +(8.85736 + 9.38825i) q^{62} +(-6.11733 + 4.05782i) q^{63} +(-9.02203 - 2.13826i) q^{64} +(2.09178 + 5.41783i) q^{65} +(-18.5144 + 1.11470i) q^{66} +(0.464082 - 3.39768i) q^{67} +(-1.78887 - 8.25835i) q^{68} +(-3.64675 - 4.32880i) q^{69} +(-6.99945 - 3.86213i) q^{70} +(-2.45599 + 5.69362i) q^{71} +(1.01867 - 0.0435219i) q^{72} +(2.70227 - 3.62977i) q^{73} +(-9.78604 - 6.99464i) q^{74} +(-4.18541 - 0.563336i) q^{75} +(14.0413 - 2.19603i) q^{76} +(5.53783 + 11.5814i) q^{77} +(-3.41606 + 12.3653i) q^{78} +(-6.98054 + 11.0754i) q^{79} +(-2.91242 - 5.04446i) q^{80} +(8.54846 - 2.81492i) q^{81} +(-8.50277 + 14.7272i) q^{82} +(2.89733 + 5.50045i) q^{83} +(-3.81601 - 8.35162i) q^{84} +(3.53082 - 5.14806i) q^{85} +(7.79601 - 20.1922i) q^{86} +(-2.32774 + 0.508991i) q^{87} +(0.172616 - 1.77465i) q^{88} +(0.529625 + 1.22781i) q^{89} +(7.02413 + 6.83550i) q^{90} +(8.81872 - 1.03076i) q^{91} +(6.06156 - 3.65817i) q^{92} +(-7.02352 + 8.40364i) q^{93} +(7.61373 - 6.90909i) q^{94} +(8.29869 + 6.43197i) q^{95} +(1.60310 - 13.9520i) q^{96} +(1.70401 - 2.11264i) q^{97} +(1.41824 - 1.50325i) q^{98} +(-2.79364 - 15.4889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{81}\right)$

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 $

$2$	−2.03967	−	0.0791483i	−1.44226	−	0.0559663i	−0.694289	−	0.719696i	$-0.744281\pi$
$2$	−2.03967	−	0.0791483i	−1.44226	−	0.0559663i	−0.747973	+	0.663730i	$0.768973\pi$
$3$	−0.137599	−	1.72658i	−0.0794430	−	0.996839i
$3$	−0.137599	−	1.72658i	−0.0794430	−	0.996839i
$4$	2.15999	+	0.167888i	1.07999	+	0.0839438i
$5$	1.00485	+	1.24581i	0.449381	+	0.557144i	0.951498	−	0.307655i	$-0.0995442\pi$
$5$	1.00485	+	1.24581i	0.449381	+	0.557144i	−0.502117	+	0.864799i	$0.667445\pi$
$6$	0.144001	+	3.53253i	0.0587882	+	1.44215i
$7$	2.22760	−	1.01257i	0.841955	−	0.382716i	0.0540695	−	0.998537i	$-0.482781\pi$
$7$	2.22760	−	1.01257i	0.841955	−	0.382716i	0.787886	+	0.615822i	$0.211176\pi$
$8$	−0.337568	−	0.0394561i	−0.119348	−	0.0139498i
$9$	−2.96213	+	0.475151i	−0.987378	+	0.158384i
$10$	−1.95095	−	2.62057i	−0.616943	−	0.828698i
$11$	0.101732	+	5.24528i	0.0306734	+	1.58151i	0.627162	+	0.778889i	$0.284216\pi$
$11$	0.101732	+	5.24528i	0.0306734	+	1.58151i	−0.596489	+	0.802621i	$0.703438\pi$
$12$	−0.00734214	−	3.75249i	−0.00211949	−	1.08325i
$13$	3.45524	+	1.10788i	0.958312	+	0.307270i	0.743012	−	0.669278i	$-0.233396\pi$
$13$	3.45524	+	1.10788i	0.958312	+	0.307270i	0.215300	+	0.976548i	$0.430927\pi$
$14$	−4.62371	+	1.88899i	−1.23574	+	0.504855i
$15$	2.01273	−	1.90637i	0.519683	−	0.492221i
$16$	−3.59556	−	0.562336i	−0.898891	−	0.140584i
$17$	−1.11860	−	3.73638i	−0.271300	−	0.906206i	−0.979713	−	0.200408i	$-0.935773\pi$
$17$	−1.11860	−	3.73638i	−0.271300	−	0.906206i	0.708412	−	0.705799i	$-0.249412\pi$
$18$	6.07937	−	0.734702i	1.43292	−	0.173171i
$19$	6.38307	−	1.51282i	1.46438	−	0.347064i	0.580300	−	0.814403i	$-0.302935\pi$
$19$	6.38307	−	1.51282i	1.46438	−	0.347064i	0.884078	+	0.467339i	$0.154787\pi$
$20$	1.96130	+	2.85964i	0.438560	+	0.639435i
$21$	−2.05480	−	3.70680i	−0.448393	−	0.808890i
$22$	0.207655	−	10.7067i	0.0442723	−	2.28267i
$23$	2.65860	−	1.90025i	0.554356	−	0.396230i	−0.269525	−	0.962993i	$-0.586867\pi$
$23$	2.65860	−	1.90025i	0.554356	−	0.396230i	0.823880	+	0.566764i	$0.191805\pi$
$24$	−0.0216748	+	0.588266i	−0.00442434	+	0.120079i
$25$	0.516184	−	2.38297i	0.103237	−	0.476594i
$26$	−6.95986	−	2.53318i	−1.36494	−	0.496798i
$27$	1.22797	+	5.04897i	0.236323	+	0.971674i
$28$	4.98160	−	1.81315i	0.941433	−	0.342654i
$29$	−0.186172	−	1.36302i	−0.0345713	−	0.253106i	0.965399	−	0.260776i	$-0.0839784\pi$
$29$	−0.186172	−	1.36302i	−0.0345713	−	0.253106i	−0.999971	+	0.00766965i	$0.997559\pi$
$30$	−4.25617	+	3.72905i	−0.777067	+	0.680828i
$31$	−4.51437	−	4.42766i	−0.810804	−	0.795231i	0.170971	−	0.985276i	$-0.445309\pi$
$31$	−4.51437	−	4.42766i	−0.810804	−	0.795231i	−0.981775	+	0.190045i	$0.939137\pi$
$32$	7.95623	+	1.56255i	1.40648	+	0.276223i
$33$	9.04237	−	0.897394i	1.57407	−	0.156216i
$34$	1.98584	+	7.70951i	0.340569	+	1.32217i
$35$	3.49987	+	1.75770i	0.591586	+	0.297106i
$36$	−6.47794	+	0.529016i	−1.07966	+	0.0881694i
$37$	4.92352	+	3.23825i	0.809422	+	0.532365i	0.885447	−	0.464741i	$-0.153852\pi$
$37$	4.92352	+	3.23825i	0.809422	+	0.532365i	−0.0760248	+	0.997106i	$0.524223\pi$
$38$	−13.1391	+	2.58043i	−2.13144	+	0.418601i
$39$	1.43740	−	6.11819i	0.230168	−	0.979694i
$40$	−0.290049	−	0.460194i	−0.0458608	−	0.0727631i
$41$	3.88267	−	7.37108i	0.606372	−	1.15117i	−0.368756	−	0.929526i	$-0.620216\pi$
$41$	3.88267	−	7.37108i	0.606372	−	1.15117i	0.975128	−	0.221643i	$-0.0711418\pi$
$42$	3.89771	+	7.72327i	0.601430	+	1.19173i
$43$	−3.43287	+	10.0329i	−0.523508	+	1.53001i	0.294989	+	0.955501i	$0.404684\pi$
$43$	−3.43287	+	10.0329i	−0.523508	+	1.53001i	−0.818498	+	0.574510i	$0.805193\pi$
$44$	−0.660877	+	11.3468i	−0.0996309	+	1.71060i
$45$	−3.56844	−	3.21281i	−0.531951	−	0.478937i
$46$	−5.57305	+	3.66545i	−0.821701	+	0.540442i
$47$	−3.59597	+	3.52690i	−0.524526	+	0.514452i	−0.913523	−	0.406787i	$-0.866649\pi$
$47$	−3.59597	+	3.52690i	−0.524526	+	0.514452i	0.388997	+	0.921239i	$0.372822\pi$
$48$	−0.476169	+	6.28539i	−0.0687290	+	0.907218i
$49$	−0.665729	+	0.762841i	−0.0951041	+	0.108977i
$50$	−1.24145	+	4.81961i	−0.175568	+	0.681596i
$51$	−6.29724	+	2.44547i	−0.881789	+	0.342435i
$52$	7.27729	+	2.97310i	1.00918	+	0.412295i
$53$	−5.38254	−	4.51648i	−0.739348	−	0.620387i	0.193314	−	0.981137i	$-0.438076\pi$
$53$	−5.38254	−	4.51648i	−0.739348	−	0.620387i	−0.932663	+	0.360750i	$0.882521\pi$
$54$	−2.10504	−	10.3954i	−0.286459	−	1.41464i
$55$	−6.43241	+	5.39743i	−0.867346	+	0.727789i
$56$	−0.791920	+	0.253919i	−0.105825	+	0.0339313i
$57$	−3.49030	−	10.8127i	−0.462301	−	1.43218i
$58$	0.271848	+	2.79484i	0.0356954	+	0.366980i
$59$	6.04488	−	3.33542i	0.786976	−	0.434235i	−0.0380878	−	0.999274i	$-0.512127\pi$
$59$	6.04488	−	3.33542i	0.786976	−	0.434235i	0.825064	+	0.565039i	$0.191139\pi$
$60$	4.66752	−	3.77982i	0.602574	−	0.487972i
$61$	−3.69728	+	0.287376i	−0.473389	+	0.0367947i	−0.311971	−	0.950092i	$-0.600989\pi$
$61$	−3.69728	+	0.287376i	−0.473389	+	0.0367947i	−0.161417	+	0.986886i	$0.551607\pi$
$62$	8.85736	+	9.38825i	1.12489	+	1.19231i
$63$	−6.11733	+	4.05782i	−0.770712	+	0.511237i
$64$	−9.02203	−	2.13826i	−1.12775	−	0.267283i
$65$	2.09178	+	5.41783i	0.259453	+	0.672000i
$66$	−18.5144	+	1.11470i	−2.27897	+	0.137210i
$67$	0.464082	−	3.39768i	0.0566966	−	0.415093i	−0.940471	−	0.339875i	$-0.889615\pi$
$67$	0.464082	−	3.39768i	0.0566966	−	0.415093i	0.997167	−	0.0752175i	$-0.0239651\pi$
$68$	−1.78887	−	8.25835i	−0.216932	−	1.00147i
$69$	−3.64675	−	4.32880i	−0.439017	−	0.521126i
$70$	−6.99945	−	3.86213i	−0.836594	−	0.461613i
$71$	−2.45599	+	5.69362i	−0.291472	+	0.675709i	−0.999537	−	0.0304392i	$-0.990309\pi$
$71$	−2.45599	+	5.69362i	−0.291472	+	0.675709i	0.708064	+	0.706148i	$0.249569\pi$
$72$	1.01867	−	0.0435219i	0.120051	−	0.00512911i
$73$	2.70227	−	3.62977i	0.316276	−	0.424833i	−0.615348	−	0.788256i	$-0.710984\pi$
$73$	2.70227	−	3.62977i	0.316276	−	0.424833i	0.931624	+	0.363423i	$0.118392\pi$
$74$	−9.78604	−	6.99464i	−1.13760	−	0.813111i
$75$	−4.18541	−	0.563336i	−0.483289	−	0.0650484i
$76$	14.0413	−	2.19603i	1.61065	−	0.251902i
$77$	5.53783	+	11.5814i	0.631094	+	1.31982i
$78$	−3.41606	+	12.3653i	−0.386792	+	1.40009i
$79$	−6.98054	+	11.0754i	−0.785372	+	1.24608i	0.179604	+	0.983739i	$0.442518\pi$
$79$	−6.98054	+	11.0754i	−0.785372	+	1.24608i	−0.964976	+	0.262339i	$0.915506\pi$
$80$	−2.91242	−	5.04446i	−0.325618	−	0.563988i
$81$	8.54846	−	2.81492i	0.949829	−	0.312769i
$82$	−8.50277	+	14.7272i	−0.938974	+	1.62635i
$83$	2.89733	+	5.50045i	0.318023	+	0.603753i	0.990681	−	0.136201i	$-0.0434893\pi$
$83$	2.89733	+	5.50045i	0.318023	+	0.603753i	−0.672658	+	0.739954i	$0.734847\pi$
$84$	−3.81601	−	8.35162i	−0.416361	−	0.911236i
$85$	3.53082	−	5.14806i	0.382971	−	0.558385i
$86$	7.79601	−	20.1922i	0.840665	−	2.17738i
$87$	−2.32774	+	0.508991i	−0.249560	+	0.0545695i
$88$	0.172616	−	1.77465i	0.0184010	−	0.189178i
$89$	0.529625	+	1.22781i	0.0561402	+	0.130148i	0.943977	−	0.330010i	$-0.107052\pi$
$89$	0.529625	+	1.22781i	0.0561402	+	0.130148i	−0.887837	+	0.460158i	$0.847793\pi$
$90$	7.02413	+	6.83550i	0.740408	+	0.720524i
$91$	8.81872	−	1.03076i	0.924453	−	0.108053i
$92$	6.06156	−	3.65817i	0.631962	−	0.381391i
$93$	−7.02352	+	8.40364i	−0.728305	+	0.871417i
$94$	7.61373	−	6.90909i	0.785296	−	0.712618i
$95$	8.29869	+	6.43197i	0.851428	+	0.659906i
$96$	1.60310	−	13.9520i	0.163615	−	1.42397i
$97$	1.70401	−	2.11264i	0.173016	−	0.214506i	−0.684432	−	0.729076i	$-0.739950\pi$
$97$	1.70401	−	2.11264i	0.173016	−	0.214506i	0.857448	+	0.514571i	$0.172049\pi$
$98$	1.41824	−	1.50325i	0.143264	−	0.151851i
$99$	−2.79364	−	15.4889i	−0.280772	−	1.55669i
$100$	1.51502	−	5.06053i	0.151502	−	0.506053i
$101$	5.41927	−	11.3334i	0.539237	−	1.12772i	−0.434632	−	0.900608i	$-0.643121\pi$
$101$	5.41927	−	11.3334i	0.539237	−	1.12772i	0.973869	−	0.227111i	$-0.0729280\pi$
$102$	13.0378	−	4.48953i	1.29094	−	0.444530i
$103$	11.3647	+	6.85862i	1.11980	+	0.675800i	0.950797	−	0.309816i	$-0.100267\pi$
$103$	11.3647	+	6.85862i	1.11980	+	0.675800i	0.168999	+	0.985616i	$0.445946\pi$
$104$	−1.12267	−	0.510315i	−0.110087	−	0.0500405i
$105$	2.55323	−	6.28465i	0.249169	−	0.613319i
$106$	10.6211	+	9.63814i	1.03161	+	0.936139i
$107$	−1.09985	−	6.23759i	−0.106327	−	0.603010i	−0.990682	−	0.136195i	$-0.956513\pi$
$107$	−1.09985	−	6.23759i	−0.106327	−	0.603010i	0.884355	−	0.466815i	$-0.154599\pi$
$108$	1.80475	+	11.1119i	0.173662	+	1.06924i
$109$	−2.05615	+	11.6610i	−0.196943	+	1.11692i	0.712681	+	0.701489i	$0.247481\pi$
$109$	−2.05615	+	11.6610i	−0.196943	+	1.11692i	−0.909624	+	0.415432i	$0.863630\pi$
$110$	13.5472	−	10.4998i	1.29167	−	1.00112i
$111$	4.91362	−	8.94642i	0.466380	−	0.849157i
$112$	−8.57889	+	2.38810i	−0.810629	+	0.225654i
$113$	3.31997	+	9.70298i	0.312317	+	0.912780i	0.984955	+	0.172809i	$0.0552842\pi$
$113$	3.31997	+	9.70298i	0.312317	+	0.912780i	−0.672639	+	0.739971i	$0.734839\pi$
$114$	6.26324	+	22.3306i	0.586606	+	2.09145i
$115$	5.03883	+	1.40266i	0.469874	+	0.130798i
$116$	−0.173295	−	2.97536i	−0.0160900	−	0.276255i
$117$	−10.7613	−	1.63992i	−0.994883	−	0.151611i
$118$	−12.5935	+	6.32471i	−1.15933	+	0.582237i
$119$	−6.27515	−	7.19052i	−0.575242	−	0.659154i
$120$	−0.754650	+	0.564114i	−0.0688898	+	0.0514963i
$121$	−16.5108	+	0.640696i	−1.50098	+	0.0582450i
$122$	7.56397	−	0.293516i	0.684810	−	0.0265737i
$123$	−13.2610	−	5.68948i	−1.19570	−	0.513003i
$124$	−9.00763	−	10.3216i	−0.808909	−	0.926907i
$125$	10.6389	−	5.34308i	0.951576	−	0.477899i
$126$	12.7985	−	7.79241i	1.14018	−	0.694203i
$127$	−0.509772	−	8.75245i	−0.0452350	−	0.776654i	−0.942303	−	0.334761i	$-0.891344\pi$
$127$	−0.509772	−	8.75245i	−0.0452350	−	0.776654i	0.897068	−	0.441893i	$-0.145693\pi$
$128$	2.61026	+	0.726616i	0.230717	+	0.0642244i
$129$	17.7950	+	4.54659i	1.56676	+	0.400305i
$130$	−3.83771	−	11.2161i	−0.336590	−	0.983720i
$131$	−13.7424	+	3.82545i	−1.20068	+	0.334231i	−0.810073	−	0.586328i	$-0.800573\pi$
$131$	−13.7424	+	3.82545i	−1.20068	+	0.334231i	−0.390602	+	0.920559i	$0.627733\pi$
$132$	19.6821	−	0.420259i	1.71310	−	0.0365789i
$133$	12.6871	−	9.83327i	1.10011	−	0.852652i
$134$	−1.21549	+	6.89340i	−0.105003	+	0.595499i
$135$	−5.05615	+	6.60326i	−0.435164	+	0.568318i
$136$	0.230181	+	1.30542i	0.0197378	+	0.111939i
$137$	−12.8641	−	11.6736i	−1.09906	−	0.997342i	−0.999997	−	0.00226085i	$-0.999280\pi$
$137$	−12.8641	−	11.6736i	−1.09906	−	0.997342i	−0.0990609	−	0.995081i	$-0.531584\pi$
$138$	7.09553	+	9.11793i	0.604012	+	0.776170i
$139$	−19.4551	−	8.84341i	−1.65016	−	0.750088i	−0.650204	−	0.759760i	$-0.725316\pi$
$139$	−19.4551	−	8.84341i	−1.65016	−	0.750088i	−0.999953	+	0.00967150i	$0.996921\pi$
$140$	7.26458	+	4.38420i	0.613969	+	0.370532i
$141$	6.58427	+	5.72342i	0.554496	+	0.481999i
$142$	5.46004	−	11.4187i	0.458196	−	0.958236i
$143$	−5.45962	+	18.2364i	−0.456557	+	1.52501i
$144$	10.9177	−	0.0427236i	0.909811	−	0.00356030i
$145$	1.51099	−	1.60156i	0.125481	−	0.133002i
$146$	−5.79901	+	7.18965i	−0.479930	+	0.595019i
$147$	1.40871	+	1.04447i	0.116188	+	0.0861461i
$148$	10.0911	+	7.82118i	0.829482	+	0.642897i
$149$	−13.0712	+	11.8615i	−1.07084	+	0.971734i	−0.999669	−	0.0257302i	$-0.991809\pi$
$149$	−13.0712	+	11.8615i	−1.07084	+	0.971734i	−0.0711695	+	0.997464i	$0.522673\pi$
$150$	8.49225	+	1.48029i	0.693389	+	0.120865i
$151$	−12.7924	+	7.72023i	−1.04103	+	0.628263i	−0.930757	−	0.365638i	$-0.880851\pi$
$151$	−12.7924	+	7.72023i	−1.04103	+	0.628263i	−0.110271	+	0.993902i	$0.535172\pi$
$152$	−2.21441	+	0.258828i	−0.179613	+	0.0209937i
$153$	5.08879	+	10.5362i	0.411404	+	0.851798i
$154$	−10.3787	−	24.0605i	−0.836337	−	1.93885i
$155$	0.979795	−	10.0732i	0.0786990	−	0.809096i
$156$	4.13193	−	12.9739i	0.330819	−	1.03874i
$157$	2.49997	−	6.47508i	0.199519	−	0.516768i	−0.796628	−	0.604471i	$-0.793385\pi$
$157$	2.49997	−	6.47508i	0.199519	−	0.516768i	0.996147	+	0.0877029i	$0.0279526\pi$
$158$	15.1146	−	22.0376i	1.20245	−	1.75322i
$159$	−7.05742	+	9.91483i	−0.559690	+	0.786297i
$160$	6.04813	+	11.4821i	0.478147	+	0.907740i
$161$	3.99816	−	6.92502i	0.315099	−	0.545768i
$162$	−17.6588	+	5.06491i	−1.38741	+	0.397937i
$163$	12.2117	+	21.1512i	0.956490	+	1.65669i	0.730920	+	0.682463i	$0.239091\pi$
$163$	12.2117	+	21.1512i	0.956490	+	1.65669i	0.225570	+	0.974227i	$0.427575\pi$
$164$	9.62404	−	15.2696i	0.751512	−	1.19235i
$165$	10.2042	+	10.3634i	0.794394	+	0.806786i
$166$	−5.47424	−	11.4484i	−0.424883	−	0.888568i
$167$	−8.99410	+	1.40665i	−0.695984	+	0.108850i	−0.492609	−	0.870251i	$-0.663957\pi$
$167$	−8.99410	+	1.40665i	−0.695984	+	0.108850i	−0.203375	+	0.979101i	$0.565191\pi$
$168$	0.547378	+	1.33237i	0.0422311	+	0.102795i
$169$	0.135133	+	0.0965874i	0.0103949	+	0.00742980i
$170$	−7.60915	+	10.2209i	−0.583595	+	0.783904i
$171$	−18.1887	+	7.51409i	−1.39092	+	0.574617i
$172$	−9.09937	+	21.0947i	−0.693821	+	1.60846i
$173$	−3.25915	−	1.79833i	−0.247789	−	0.136724i	0.354357	−	0.935110i	$-0.384700\pi$
$173$	−3.25915	−	1.79833i	−0.247789	−	0.136724i	−0.602146	+	0.798386i	$0.705687\pi$
$174$	4.78810	−	0.853934i	0.362985	−	0.0647366i
$175$	−1.26307	−	5.83099i	−0.0954792	−	0.440781i
$176$	2.58382	−	18.9169i	0.194763	−	1.42592i
$177$	−6.59063	−	9.97799i	−0.495382	−	0.749992i
$178$	−0.983080	−	2.54624i	−0.0736850	−	0.190849i
$179$	1.29159	+	0.306112i	0.0965379	+	0.0228799i	0.278601	−	0.960407i	$-0.410129\pi$
$179$	1.29159	+	0.306112i	0.0965379	+	0.0228799i	−0.182063	+	0.983287i	$0.558277\pi$
$180$	−7.16839	−	7.53873i	−0.534300	−	0.561904i
$181$	−4.33102	−	4.59062i	−0.321922	−	0.341218i	0.546121	−	0.837706i	$-0.316104\pi$
$181$	−4.33102	−	4.59062i	−0.321922	−	0.341218i	−0.868043	+	0.496489i	$0.834622\pi$
$182$	−18.0688	+	1.40442i	−1.33935	+	0.104103i
$183$	1.00492	+	6.34410i	0.0742858	+	0.468969i
$184$	−0.972434	+	0.536566i	−0.0716888	+	0.0395562i
$185$	0.913123	+	9.38773i	0.0671342	+	0.690200i
$186$	14.9908	−	16.5847i	1.09918	−	1.21605i
$187$	19.4846	−	6.24748i	1.42485	−	0.456861i
$188$	−8.35938	+	7.01435i	−0.609670	+	0.511574i
$189$	7.84787	+	10.0037i	0.570849	+	0.727662i
$190$	−16.4175	−	13.7759i	−1.19105	−	0.999409i
$191$	−5.19612	−	2.12285i	−0.375978	−	0.153604i	0.182331	−	0.983237i	$-0.441636\pi$
$191$	−5.19612	−	2.12285i	−0.375978	−	0.153604i	−0.558309	+	0.829633i	$0.688549\pi$
$192$	−2.45045	+	15.8715i	−0.176846	+	1.14542i
$193$	−1.57481	+	6.11378i	−0.113357	+	0.440080i	−0.999738	−	0.0228766i	$-0.992718\pi$
$193$	−1.57481	+	6.11378i	−0.113357	+	0.440080i	0.886381	+	0.462956i	$0.153211\pi$
$194$	−3.64282	+	4.17421i	−0.261539	+	0.299691i
$195$	9.06648	−	4.35710i	0.649264	−	0.312018i
$196$	−1.56604	+	1.53596i	−0.111860	+	0.109711i
$197$	9.22019	−	6.06421i	0.656911	−	0.432057i	−0.176808	−	0.984245i	$-0.556577\pi$
$197$	9.22019	−	6.06421i	0.656911	−	0.432057i	0.833720	+	0.552188i	$0.186207\pi$
$198$	4.47218	+	31.8132i	0.317824	+	2.26087i
$199$	0.760442	−	13.0563i	0.0539063	−	0.925535i	−0.857617	−	0.514288i	$-0.828056\pi$
$199$	0.760442	−	13.0563i	0.0539063	−	0.925535i	0.911524	−	0.411247i	$-0.134907\pi$
$200$	−0.268270	+	0.784048i	−0.0189695	+	0.0554406i
$201$	−5.93021	−	0.333754i	−0.418285	−	0.0235412i
$202$	−11.9505	+	22.6875i	−0.840836	+	1.59629i
$203$	−1.79487	−	2.84776i	−0.125975	−	0.199873i
$204$	−14.0125	+	4.22496i	−0.981073	+	0.295807i
$205$	13.0845	−	2.56971i	0.913859	−	0.179476i
$206$	−22.6373	−	14.8888i	−1.57722	−	1.03735i
$207$	−6.97221	+	6.89203i	−0.484602	+	0.479029i
$208$	−11.8005	−	5.92646i	−0.818220	−	0.410926i
$209$	8.58450	+	33.3271i	0.593802	+	2.30528i
$210$	−5.70515	+	12.6165i	−0.393693	+	0.870622i
$211$	0.804862	+	0.158070i	0.0554090	+	0.0108820i	0.220340	−	0.975423i	$-0.429283\pi$
$211$	0.804862	+	0.158070i	0.0554090	+	0.0108820i	−0.164931	+	0.986305i	$0.552740\pi$
$212$	−10.8680	−	10.6592i	−0.746414	−	0.732078i
$213$	10.1684	+	3.45702i	0.696729	+	0.236871i
$214$	1.74964	+	12.8096i	0.119603	+	0.875650i
$215$	−15.9487	+	5.80485i	−1.08769	+	0.395887i
$216$	−0.215312	−	1.75282i	−0.0146501	−	0.119264i
$217$	−14.5395	−	5.29196i	−0.987008	−	0.359241i
$218$	5.11680	−	23.6218i	0.346554	−	1.59987i
$219$	−6.63891	−	4.16622i	−0.448616	−	0.281527i
$220$	−14.8001	+	10.5785i	−0.997821	+	0.713200i
$221$	0.274427	−	14.1494i	0.0184600	−	0.951791i
$222$	−10.7302	+	17.8588i	−0.720166	+	1.19860i
$223$	0.847689	+	1.23596i	0.0567654	+	0.0827660i	0.852019	−	0.523511i	$-0.175378\pi$
$223$	0.847689	+	1.23596i	0.0567654	+	0.0827660i	−0.795253	+	0.606277i	$0.792662\pi$
$224$	19.3055	−	4.57549i	1.28990	−	0.305713i
$225$	−0.396734	+	7.30394i	−0.0264489	+	0.486929i
$226$	−6.00366	−	20.0536i	−0.399357	−	1.33395i
$227$	5.49625	+	0.859597i	0.364799	+	0.0570535i	0.334262	−	0.942480i	$-0.391513\pi$
$227$	5.49625	+	0.859597i	0.364799	+	0.0570535i	0.0305366	+	0.999534i	$0.490278\pi$
$228$	−5.72369	−	23.9413i	−0.379060	−	1.58555i
$229$	−13.6896	+	5.59283i	−0.904637	+	0.369585i	−0.782298	−	0.622904i	$-0.785953\pi$
$229$	−13.6896	+	5.59283i	−0.904637	+	0.369585i	−0.122338	+	0.992488i	$0.539039\pi$
$230$	−10.1665	−	3.25976i	−0.670361	−	0.214943i
$231$	19.2341	−	11.1551i	1.26551	−	0.733950i
$232$	0.00906633	+	0.467458i	0.000595234	+	0.0306901i
$233$	7.85582	+	10.5522i	0.514652	+	0.691297i	0.981155	−	0.193222i	$-0.0618939\pi$
$233$	7.85582	+	10.5522i	0.514652	+	0.691297i	−0.466503	+	0.884519i	$0.654486\pi$
$234$	21.8197	+	4.19663i	1.42640	+	0.274342i
$235$	−8.00726	−	0.935914i	−0.522336	−	0.0610523i
$236$	13.6168	−	6.18961i	0.886381	−	0.402910i
$237$	20.0830	+	10.5285i	1.30453	+	0.683898i
$238$	12.2301	+	15.1629i	0.792759	+	0.982867i
$239$	−11.1361	−	0.865566i	−0.720334	−	0.0559888i	−0.287908	−	0.957658i	$-0.592960\pi$
$239$	−11.1361	−	0.865566i	−0.720334	−	0.0559888i	−0.432426	+	0.901669i	$0.642342\pi$
$240$	−8.30890	+	5.72263i	−0.536337	+	0.369394i
$241$	−6.42186	−	0.249197i	−0.413668	−	0.0160522i	−0.168898	−	0.985633i	$-0.554021\pi$
$241$	−6.42186	−	0.249197i	−0.413668	−	0.0160522i	−0.244770	+	0.969581i	$0.578712\pi$
$242$	33.7273			2.16807
$243$	−6.03644	−	14.3722i	−0.387238	−	0.921980i
$244$	−8.03433			−0.514346
$245$	−1.61931	−	0.0628367i	−0.103454	−	0.00401449i
$246$	26.5977	+	12.6542i	1.69581	+	0.806804i
$247$	23.7311	+	1.84453i	1.50997	+	0.117364i
$248$	1.34921	+	1.67276i	0.0856748	+	0.106220i
$249$	9.09827	−	5.75932i	0.576580	−	0.364982i
$250$	−22.1228	+	10.0560i	−1.39917	+	0.636000i
$251$	−16.1845	−	1.89170i	−1.02156	−	0.119403i	−0.411213	−	0.911539i	$-0.634895\pi$
$251$	−16.1845	−	1.89170i	−1.02156	−	0.119403i	−0.610344	+	0.792136i	$0.708969\pi$
$252$	−13.8946	+	7.73781i	−0.875279	+	0.487436i
$253$	10.2378	+	13.7518i	0.643645	+	0.864565i
$254$	0.347023	+	17.8924i	0.0217742	+	1.12267i
$255$	−9.37435	−	5.38786i	−0.587045	−	0.337401i
$256$	12.3919	+	3.97329i	0.774491	+	0.248331i
$257$	−21.2658	+	8.68803i	−1.32652	+	0.541944i	−0.927097	−	0.374821i	$-0.877704\pi$
$257$	−21.2658	+	8.68803i	−1.32652	+	0.541944i	−0.399426	+	0.916765i	$0.630791\pi$
$258$	−35.9360	−	10.6820i	−2.23728	−	0.665031i
$259$	14.2466	+	2.22813i	0.885242	+	0.138449i
$260$	3.60862	+	12.0536i	0.223797	+	0.747535i
$261$	1.19911	+	3.94898i	0.0742228	+	0.244436i
$262$	28.3326	−	6.71495i	1.75039	−	0.414851i
$263$	−1.71024	−	2.49358i	−0.105458	−	0.153761i	0.768355	−	0.640024i	$-0.221076\pi$
$263$	−1.71024	−	2.49358i	−0.105458	−	0.153761i	−0.873812	+	0.486263i	$0.838360\pi$
$264$	−3.08782	−	0.0538446i	−0.190042	−	0.00331390i
$265$	0.218077	−	11.2440i	0.0133964	−	0.690714i
$266$	−26.6558	+	19.0524i	−1.63437	+	1.16818i
$267$	2.04703	−	1.08338i	0.125276	−	0.0663021i
$268$	1.57284	−	7.26104i	0.0960765	−	0.443538i
$269$	0.954769	+	0.347507i	0.0582133	+	0.0211879i	0.370963	−	0.928648i	$-0.379028\pi$
$269$	0.954769	+	0.347507i	0.0582133	+	0.0211879i	−0.312749	+	0.949836i	$0.601250\pi$
$270$	10.8355	−	13.0683i	0.659427	−	0.795309i
$271$	24.4563	−	8.90135i	1.48561	−	0.540718i	0.533321	−	0.845913i	$-0.320944\pi$
$271$	24.4563	−	8.90135i	1.48561	−	0.540718i	0.952290	+	0.305194i	$0.0987214\pi$
$272$	1.92089	+	14.0634i	0.116471	+	0.852721i
$273$	−2.99314	−	15.0844i	−0.181153	−	0.912947i
$274$	25.3146	+	24.8284i	1.52931	+	1.49994i
$275$	12.5518	+	2.46510i	0.756905	+	0.148651i
$276$	−7.15018	−	9.96239i	−0.430390	−	0.599666i
$277$	−5.46341	−	21.2102i	−0.328264	−	1.27440i	−0.893348	−	0.449366i	$-0.851650\pi$
$277$	−5.46341	−	21.2102i	−0.328264	−	1.27440i	0.565083	−	0.825034i	$-0.308844\pi$
$278$	38.9819	+	19.5774i	2.33798	+	1.17418i
$279$	15.4760	+	10.9703i	0.926521	+	0.656775i
$280$	−1.11209	−	0.731435i	−0.0664603	−	0.0437116i
$281$	−17.3873	+	3.41475i	−1.03724	+	0.203707i	−0.682215	−	0.731151i	$-0.738983\pi$
$281$	−17.3873	+	3.41475i	−1.03724	+	0.203707i	−0.355022	+	0.934858i	$0.615526\pi$
$282$	−12.9767	−	12.1950i	−0.772752	−	0.726202i
$283$	−13.0610	−	20.7226i	−0.776394	−	1.23183i	−0.968145	−	0.250389i	$-0.919441\pi$
$283$	−13.0610	−	20.7226i	−0.776394	−	1.23183i	0.191751	−	0.981444i	$-0.438583\pi$
$284$	−6.26080	+	11.8858i	−0.371510	+	0.705294i
$285$	9.96339	−	15.2134i	0.590181	−	0.901161i
$286$	12.5792	−	36.7641i	0.743823	−	2.17390i
$287$	1.18533	−	20.3513i	0.0699678	−	1.20130i
$288$	−24.3099	−	0.848075i	−1.43247	−	0.0499733i
$289$	1.49399	−	0.982611i	0.0878816	−	0.0578007i
$290$	−3.20868	+	3.14705i	−0.188420	+	0.184801i
$291$	−3.88210	−	2.65140i	−0.227573	−	0.155428i
$292$	6.44626	−	7.38659i	0.377239	−	0.432268i
$293$	1.77558	−	6.89323i	0.103731	−	0.402707i	−0.895360	−	0.445343i	$-0.853082\pi$
$293$	1.77558	−	6.89323i	0.103731	−	0.402707i	0.999091	+	0.0426362i	$0.0135756\pi$
$294$	−2.79062	−	2.24186i	−0.162752	−	0.130748i
$295$	10.2295	+	4.17920i	0.595584	+	0.243323i
$296$	−1.53426	−	1.28739i	−0.0891768	−	0.0748282i
$297$	−26.3583	+	6.95470i	−1.52946	+	0.403552i
$298$	27.5998	−	23.1590i	1.59881	−	1.34156i
$299$	11.2913	−	3.62042i	0.652995	−	0.209375i
$300$	−8.94585	−	1.91948i	−0.516489	−	0.110821i
$301$	2.51198	+	25.8255i	0.144788	+	1.48855i
$302$	26.7032	−	14.7342i	1.53660	−	0.847858i
$303$	−20.3137	−	7.79731i	−1.16699	−	0.447944i
$304$	−23.8015	+	1.85000i	−1.36511	+	0.106105i
$305$	−4.07321	−	4.31735i	−0.233232	−	0.247211i
$306$	−9.54552	−	21.8930i	−0.545681	−	1.25154i
$307$	−19.6068	−	4.64690i	−1.11902	−	0.265212i	−0.370832	−	0.928700i	$-0.620927\pi$
$307$	−19.6068	−	4.64690i	−1.11902	−	0.265212i	−0.748187	+	0.663488i	$0.769075\pi$
$308$	10.0173	+	25.9454i	0.570787	+	1.47838i
$309$	10.2782	−	20.5657i	0.584704	−	1.16994i
$310$	−2.79573	+	20.4684i	−0.158787	+	1.16252i
$311$	6.58521	+	30.4007i	0.373413	+	1.72387i	0.647415	+	0.762138i	$0.275850\pi$
$311$	6.58521	+	30.4007i	0.373413	+	1.72387i	−0.274002	+	0.961729i	$0.588347\pi$
$312$	−0.726620	+	2.00859i	−0.0411367	+	0.113714i
$313$	−11.9940	−	6.61803i	−0.677943	−	0.374073i	0.106466	−	0.994316i	$-0.466046\pi$
$313$	−11.9940	−	6.61803i	−0.677943	−	0.374073i	−0.784410	+	0.620243i	$0.787034\pi$
$314$	−5.61159	+	13.0091i	−0.316680	+	0.734148i
$315$	−11.2023	−	3.54358i	−0.631176	−	0.199658i
$316$	−16.9373	+	22.7507i	−0.952798	+	1.27983i
$317$	3.11831	+	2.22883i	0.175142	+	0.125184i	0.665684	−	0.746233i	$-0.268140\pi$
$317$	3.11831	+	2.22883i	0.175142	+	0.125184i	−0.490543	+	0.871417i	$0.663201\pi$
$318$	15.1795	−	19.6644i	0.851226	−	1.10272i
$319$	7.13047	−	1.11519i	0.399230	−	0.0624384i
$320$	−6.40188	−	13.3884i	−0.357876	−	0.748434i
$321$	−10.6183	+	2.75727i	−0.592658	+	0.153896i
$322$	−8.70302	+	13.8083i	−0.485000	+	0.769505i
$323$	−12.7926	−	22.1574i	−0.711798	−	1.23287i
$324$	18.9372	−	4.64502i	1.05206	−	0.258057i
$325$	4.42358	−	7.66187i	0.245376	−	0.425004i
$326$	−23.2336	−	44.1079i	−1.28679	−	2.44291i
$327$	20.4165	+	1.94555i	1.12904	+	0.107589i
$328$	−1.60150	+	2.33505i	−0.0884281	+	0.128931i
$329$	−4.43916	+	11.4977i	−0.244739	+	0.633890i
$330$	−19.9929	−	21.9454i	−1.10057	−	1.20806i
$331$	−1.31812	+	13.5514i	−0.0724503	+	0.744854i	0.886773	+	0.462205i	$0.152942\pi$
$331$	−1.31812	+	13.5514i	−0.0724503	+	0.744854i	−0.959223	+	0.282649i	$0.908787\pi$
$332$	5.33475	+	12.3673i	0.292782	+	0.678745i
$333$	−16.1228	−	7.25271i	−0.883523	−	0.397446i
$334$	18.4563	−	2.15723i	1.00988	−	0.118038i
$335$	4.69920	−	2.83598i	0.256745	−	0.154946i
$336$	5.30368	+	14.4835i	0.289340	+	0.790141i
$337$	−12.7165	+	11.5396i	−0.692712	+	0.628603i	−0.940334	−	0.340254i	$-0.889487\pi$
$337$	−12.7165	+	11.5396i	−0.692712	+	0.628603i	0.247621	+	0.968857i	$0.420351\pi$
$338$	−0.267982	−	0.207702i	−0.0145763	−	0.0112975i
$339$	16.2961	−	7.06731i	0.885083	−	0.383843i
$340$	8.49082	−	10.5270i	0.460479	−	0.570905i
$341$	22.7650	−	24.1295i	1.23280	−	1.30669i
$342$	37.6936	−	13.8866i	2.03824	−	0.750903i
$343$	−5.62308	+	18.7824i	−0.303618	+	1.01415i
$344$	1.55469	−	3.25136i	0.0838232	−	0.175301i
$345$	1.72845	−	8.89294i	0.0930567	−	0.478780i
$346$	6.50525	+	3.92594i	0.349725	+	0.211060i
$347$	−7.07154	−	3.21441i	−0.379620	−	0.172559i	0.214906	−	0.976635i	$-0.431055\pi$
$347$	−7.07154	−	3.21441i	−0.379620	−	0.172559i	−0.594526	+	0.804076i	$0.702660\pi$
$348$	−5.11334	+	0.708615i	−0.274104	+	0.0379857i
$349$	−0.216277	−	0.196261i	−0.0115771	−	0.0105056i	0.666199	−	0.745774i	$-0.267920\pi$
$349$	−0.216277	−	0.196261i	−0.0115771	−	0.0105056i	−0.677776	+	0.735269i	$0.737056\pi$
$350$	2.11473	+	11.9932i	0.113037	+	0.641065i
$351$	−1.35070	+	18.8059i	−0.0720952	+	1.00378i
$352$	−7.38662	+	41.8916i	−0.393708	+	2.23283i
$353$	23.6090	−	18.2984i	1.25658	−	0.973924i	0.256609	−	0.966515i	$-0.417395\pi$
$353$	23.6090	−	18.2984i	1.25658	−	0.973924i	0.999973	−	0.00740871i	$-0.00235829\pi$
$354$	12.6530	+	20.8734i	0.672497	+	1.10941i
$355$	−9.56108	+	2.66151i	−0.507449	+	0.141258i
$356$	0.937851	+	2.74097i	0.0497060	+	0.145271i
$357$	−11.5515	+	11.8239i	−0.611372	+	0.625789i
$358$	−2.61018	−	0.726594i	−0.137952	−	0.0384017i
$359$	1.00011	+	17.1712i	0.0527839	+	0.906264i	0.915937	+	0.401322i	$0.131449\pi$
$359$	1.00011	+	17.1712i	0.0527839	+	0.906264i	−0.863153	+	0.504942i	$0.831514\pi$
$360$	1.07783	+	1.22534i	0.0568064	+	0.0645810i
$361$	21.4760	−	10.7857i	1.13032	−	0.567666i
$362$	8.47050	+	9.70612i	0.445200	+	0.510142i
$363$	3.37809	+	28.4191i	0.177304	+	1.49161i
$364$	19.2214	−	0.745877i	1.00747	−	0.0390946i
$365$	7.23738	−	0.280843i	0.378822	−	0.0147000i
$366$	−1.54758	−	13.0194i	−0.0808931	−	0.680534i
$367$	8.81529	+	10.1012i	0.460155	+	0.527279i	0.935882	−	0.352314i	$-0.114605\pi$
$367$	8.81529	+	10.1012i	0.460155	+	0.527279i	−0.475727	+	0.879593i	$0.657815\pi$
$368$	−10.6277	+	5.33745i	−0.554009	+	0.278234i
$369$	−7.99862	+	23.6790i	−0.416392	+	1.23268i
$370$	−1.11944	−	19.2201i	−0.0581971	−	0.999206i
$371$	−16.5634	−	4.61074i	−0.859930	−	0.239378i
$372$	−16.5816	+	16.9726i	−0.859715	+	0.879989i
$373$	1.45916	+	4.26455i	0.0755524	+	0.220810i	0.977461	−	0.211117i	$-0.0677102\pi$
$373$	1.45916	+	4.26455i	0.0755524	+	0.220810i	−0.901908	+	0.431927i	$0.857834\pi$
$374$	−40.2365	+	11.2006i	−2.08058	+	0.579169i
$375$	−10.6891	−	17.6337i	−0.551985	−	0.910603i
$376$	1.35304	−	1.04869i	0.0697779	−	0.0540819i
$377$	0.866792	−	4.91582i	0.0446420	−	0.253178i
$378$	−15.2153	−	21.0253i	−0.782589	−	1.08143i
$379$	−0.140699	−	0.797946i	−0.00722724	−	0.0409877i	0.980981	−	0.194104i	$-0.0621801\pi$
$379$	−0.140699	−	0.797946i	−0.00722724	−	0.0409877i	−0.988208	+	0.153117i	$0.951069\pi$
$380$	16.8452	+	15.2862i	0.864142	+	0.784167i
$381$	−15.0416	+	2.08449i	−0.770606	+	0.106792i
$382$	10.4303	+	4.74117i	0.533662	+	0.242579i
$383$	27.1156	+	16.3643i	1.38554	+	0.836179i	0.996382	−	0.0849914i	$-0.0270863\pi$
$383$	27.1156	+	16.3643i	1.38554	+	0.836179i	0.389160	+	0.921170i	$0.372765\pi$
$384$	0.895387	−	4.60680i	0.0456926	−	0.235090i
$385$	−8.86358	+	18.5366i	−0.451730	+	0.944713i
$386$	3.69598	−	12.3454i	0.188120	−	0.628366i
$387$	5.40146	−	31.3501i	0.274571	−	1.59361i
$388$	4.03532	−	4.27719i	0.204862	−	0.217142i
$389$	15.5698	−	19.3036i	0.789421	−	0.978729i	−0.210578	−	0.977577i	$-0.567535\pi$
$389$	15.5698	−	19.3036i	0.789421	−	0.978729i	0.999999	−	0.00115183i	$-0.000366640\pi$
$390$	−18.8374	+	8.16943i	−0.953871	+	0.413675i
$391$	−10.0740	−	7.80792i	−0.509463	−	0.394863i
$392$	0.254828	−	0.231244i	0.0128707	−	0.0116796i
$393$	8.49587	+	23.2009i	0.428560	+	1.17033i
$394$	−19.2861	+	11.6392i	−0.971618	+	0.586375i
$395$	−20.8122	+	2.43260i	−1.04718	+	0.122397i
$396$	−3.43385	−	33.9248i	−0.172557	−	1.70478i
$397$	−14.1362	−	32.7713i	−0.709475	−	1.64475i	−0.763177	−	0.646190i	$-0.776361\pi$
$397$	−14.1362	−	32.7713i	−0.709475	−	1.64475i	0.0537021	−	0.998557i	$-0.482898\pi$
$398$	−2.58443	+	26.5703i	−0.129546	+	1.33185i
$399$	−18.7236	−	20.5522i	−0.937354	−	1.02890i
$400$	−3.19600	+	8.27785i	−0.159800	+	0.413892i
$401$	21.9235	−	31.9652i	1.09481	−	1.59627i	0.339863	−	0.940475i	$-0.389619\pi$
$401$	21.9235	−	31.9652i	1.09481	−	1.59627i	0.754942	−	0.655791i	$-0.227665\pi$
$402$	12.0692	+	1.15011i	0.601959	+	0.0573625i
$403$	−10.6929	−	20.3000i	−0.532652	−	1.01122i
$404$	13.6083	−	23.5703i	0.677038	−	1.17266i
$405$	12.0968	+	7.82122i	0.601092	+	0.388640i
$406$	3.43554	+	5.95053i	0.170503	+	0.295320i
$407$	−16.4846	+	26.1547i	−0.817113	+	1.29644i
$408$	2.22223	−	0.577050i	0.110017	−	0.0285682i
$409$	3.04884	+	6.37612i	0.150756	+	0.315279i	0.963666	−	0.267110i	$-0.0860687\pi$
$409$	3.04884	+	6.37612i	0.150756	+	0.315279i	−0.812910	+	0.582389i	$0.802118\pi$
$410$	−26.8913	+	4.20573i	−1.32807	+	0.207706i
$411$	−18.3853	+	23.8172i	−0.906878	+	1.17482i
$412$	23.3961	+	16.7225i	1.15264	+	0.823860i
$413$	10.0882	−	13.5509i	0.496410	−	0.666795i
$414$	14.7665	−	13.5056i	0.725732	−	0.663764i
$415$	−3.94116	+	9.13663i	−0.193464	+	0.448500i
$416$	25.7596	+	14.2135i	1.26297	+	0.696876i
$417$	−12.5918	+	34.8075i	−0.616624	+	1.70453i
$418$	−14.8717	−	68.6556i	−0.727400	−	3.35805i
$419$	−5.10858	+	37.4014i	−0.249570	+	1.82718i	0.258673	+	0.965965i	$0.416715\pi$
$419$	−5.10858	+	37.4014i	−0.249570	+	1.82718i	−0.508244	+	0.861213i	$0.669705\pi$
$420$	6.57005	−	13.1461i	0.320586	−	0.641465i
$421$	3.88589	+	10.0647i	0.189386	+	0.490523i	0.994759	−	0.102245i	$-0.0326027\pi$
$421$	3.88589	+	10.0647i	0.189386	+	0.490523i	−0.805373	+	0.592769i	$0.798035\pi$
$422$	−1.62914	−	0.386113i	−0.0793052	−	0.0187957i
$423$	8.97593	−	12.1558i	0.436425	−	0.591035i
$424$	1.63877	+	1.73699i	0.0795857	+	0.0843559i
$425$	−9.48110	+	0.736929i	−0.459901	+	0.0357463i
$426$	−20.4666	−	7.85597i	−0.991608	−	0.380623i
$427$	−7.94509	+	4.38392i	−0.384490	+	0.212153i
$428$	−1.32846	−	13.6578i	−0.0642136	−	0.660173i
$429$	32.2378	+	6.91714i	1.55646	+	0.333963i
$430$	32.9894	−	10.5776i	1.59089	−	0.510099i
$431$	−23.7275	+	19.9098i	−1.14292	+	0.959020i	−0.999530	−	0.0306467i	$-0.990243\pi$
$431$	−23.7275	+	19.9098i	−1.14292	+	0.959020i	−0.143385	+	0.989667i	$0.545799\pi$
$432$	−1.57604	−	18.8444i	−0.0758271	−	0.906652i
$433$	7.89284	+	6.62288i	0.379305	+	0.318275i	0.812430	−	0.583059i	$-0.198144\pi$
$433$	7.89284	+	6.62288i	0.379305	+	0.318275i	−0.433124	+	0.901334i	$0.642589\pi$
$434$	29.2369	+	11.9446i	1.40342	+	0.573360i
$435$	−2.97313	−	2.38847i	−0.142551	−	0.114518i
$436$	−6.39899	+	24.8424i	−0.306456	+	1.18974i
$437$	14.0953	−	16.1514i	0.674269	−	0.772627i
$438$	13.2114	+	9.02315i	0.631266	+	0.431143i
$439$	25.2633	−	24.7781i	1.20575	−	1.18259i	0.227812	−	0.973705i	$-0.426843\pi$
$439$	25.2633	−	24.7781i	1.20575	−	1.18259i	0.977940	−	0.208888i	$-0.0669843\pi$
$440$	2.38434	−	1.56820i	0.113669	−	0.0747611i
$441$	1.60951	−	2.57596i	0.0766435	−	0.122665i
$442$	−1.67964	+	28.8383i	−0.0798924	+	1.37170i
$443$	11.8151	−	34.5309i	0.561351	−	1.64061i	−0.190807	−	0.981628i	$-0.561110\pi$
$443$	11.8151	−	34.5309i	0.561351	−	1.64061i	0.752158	−	0.658983i	$-0.229013\pi$
$444$	12.1153	−	18.4992i	0.574969	−	0.877934i
$445$	−0.997430	+	1.89357i	−0.0472827	+	0.0897640i
$446$	−1.63118	−	2.58804i	−0.0772385	−	0.122547i
$447$	22.2784	+	20.9364i	1.05373	+	0.990256i
$448$	−22.2627	+	4.37224i	−1.05181	+	0.206569i
$449$	−13.4390	−	8.83897i	−0.634226	−	0.417137i	0.191276	−	0.981536i	$-0.438737\pi$
$449$	−13.4390	−	8.83897i	−0.634226	−	0.417137i	−0.825502	+	0.564399i	$0.809108\pi$
$450$	1.38730	−	14.8662i	0.0653979	−	0.700799i
$451$	39.0583	+	19.6158i	1.83918	+	0.923673i
$452$	5.54209	+	21.5157i	0.260678	+	1.01201i
$453$	15.0898	+	21.0247i	0.708980	+	0.987826i
$454$	−11.1425	−	2.18831i	−0.522942	−	0.102702i
$455$	10.1456	+	9.95072i	0.475632	+	0.466497i
$456$	0.751587	+	3.78774i	0.0351963	+	0.177377i
$457$	−3.98603	−	29.1829i	−0.186459	−	1.36512i	−0.811420	−	0.584463i	$-0.801305\pi$
$457$	−3.98603	−	29.1829i	−0.186459	−	1.36512i	0.624961	−	0.780656i	$-0.285115\pi$
$458$	28.3650	−	10.3240i	1.32541	−	0.482409i
$459$	17.4913	−	10.2360i	0.816423	−	0.477773i
$460$	10.6483	+	3.87568i	0.496481	+	0.180704i
$461$	−3.35349	+	15.4814i	−0.156187	+	0.721042i	0.830315	+	0.557295i	$0.188161\pi$
$461$	−3.35349	+	15.4814i	−0.156187	+	0.721042i	−0.986502	+	0.163747i	$0.947642\pi$
$462$	−40.1141	+	21.2303i	−1.86628	+	0.987722i
$463$	8.13784	−	5.81658i	0.378197	−	0.270319i	−0.376467	−	0.926430i	$-0.622861\pi$
$463$	8.13784	−	5.81658i	0.378197	−	0.270319i	0.754665	+	0.656111i	$0.227800\pi$
$464$	−0.0970818	+	5.00551i	−0.00450691	+	0.232375i
$465$	−17.5269	−	0.305629i	−0.812791	−	0.0141732i
$466$	−15.1881	−	22.1447i	−0.703573	−	1.02583i
$467$	2.33942	−	0.554454i	0.108256	−	0.0256571i	−0.176131	−	0.984367i	$-0.556358\pi$
$467$	2.33942	−	0.554454i	0.108256	−	0.0256571i	0.284387	+	0.958710i	$0.408210\pi$
$468$	−22.9690	−	5.34890i	−1.06174	−	0.247253i
$469$	−2.40660	−	8.03860i	−0.111126	−	0.371188i
$470$	16.2581	+	2.54271i	0.749928	+	0.117287i
$471$	−11.5237	−	3.42542i	−0.530985	−	0.157835i
$472$	−2.17216	+	0.887425i	−0.0999818	+	0.0408471i
$473$	−52.9748	−	16.9857i	−2.43578	−	0.781003i
$474$	−40.1293	−	23.0641i	−1.84320	−	1.05937i
$475$	−0.310156	−	15.9916i	−0.0142309	−	0.733743i
$476$	−12.3471	−	16.5850i	−0.565926	−	0.760171i
$477$	18.0898	+	10.8209i	0.828275	+	0.495455i
$478$	22.6454	+	2.64687i	1.03578	+	0.121065i
$479$	−8.37802	+	3.80828i	−0.382802	+	0.174005i	−0.595962	−	0.803012i	$-0.703229\pi$
$479$	−8.37802	+	3.80828i	−0.382802	+	0.174005i	0.213161	+	0.977017i	$0.431624\pi$
$480$	18.9925	−	12.0225i	0.866885	−	0.548749i
$481$	13.4244	+	16.6436i	0.612099	+	0.758884i
$482$	13.0787	+	1.01656i	0.595719	+	0.0463030i
$483$	−12.5067	−	5.95026i	−0.569076	−	0.270746i
$484$	−35.7708	−	1.38807i	−1.62594	−	0.0630940i
$485$	4.34422			0.197261
$486$	11.1748	+	29.7924i	0.506899	+	1.35141i
$487$	−13.1955			−0.597943			−0.298972	−	0.954262i	$-0.596644\pi$
$487$	−13.1955			−0.597943			−0.298972	+	0.954262i	$0.596644\pi$
$488$	1.25942	+	0.0488714i	0.0570114	+	0.00221230i
$489$	34.8389	−	23.9947i	1.57547	−	1.08508i
$490$	3.29788	+	0.256332i	0.148983	+	0.0115799i
$491$	−8.07499	−	10.0114i	−0.364419	−	0.451809i	0.562652	−	0.826694i	$-0.309781\pi$
$491$	−8.07499	−	10.0114i	−0.364419	−	0.451809i	−0.927071	+	0.374885i	$0.877682\pi$
$492$	−27.6884	−	14.5156i	−1.24829	−	0.654412i
$493$	−4.88451	+	2.22028i	−0.219987	+	0.0999965i
$494$	−48.2575	−	5.64049i	−2.17121	−	0.253778i
$495$	16.4890	−	19.0443i	0.741128	−	0.855976i
$496$	13.7419	+	18.4585i	0.617027	+	0.828812i
$497$	0.294222	+	15.1700i	0.0131977	+	0.680468i
$498$	−19.0133	+	11.0270i	−0.852006	+	0.494131i
$499$	−33.7089	−	10.8083i	−1.50902	−	0.483847i	−0.568237	−	0.822865i	$-0.692374\pi$
$499$	−33.7089	−	10.8083i	−1.50902	−	0.483847i	−0.940780	+	0.339018i	$0.889905\pi$
$500$	23.8770	−	9.75484i	1.06781	−	0.436250i
$501$	3.66627	+	15.3354i	0.163797	+	0.685137i
$502$	32.8613	+	5.13941i	1.46667	+	0.229383i
$503$	4.33940	+	14.4946i	0.193484	+	0.646282i	0.998587	+	0.0531463i	$0.0169250\pi$
$503$	4.33940	+	14.4946i	0.193484	+	0.646282i	−0.805103	+	0.593135i	$0.797890\pi$
$504$	2.22512	−	1.12842i	0.0991148	−	0.0502640i
$505$	19.5649	−	4.63696i	0.870625	−	0.206342i
$506$	−19.7933	−	28.8593i	−0.879918	−	1.28295i
$507$	0.148171	−	0.246608i	0.00658052	−	0.0109523i
$508$	0.368326	−	18.9908i	0.0163418	−	0.842579i
$509$	24.9514	−	17.8342i	1.10595	−	0.790488i	0.126461	−	0.991972i	$-0.459638\pi$
$509$	24.9514	−	17.8342i	1.10595	−	0.790488i	0.979492	+	0.201484i	$0.0645763\pi$
$510$	18.6941	+	11.7314i	0.827789	+	0.519475i
$511$	2.34418	−	10.8219i	0.103700	−	0.478734i
$512$	−30.0530	−	10.9384i	−1.32817	−	0.483413i
$513$	15.4764	+	30.3702i	0.683300	+	1.34088i
$514$	44.0627	−	16.0375i	1.94352	−	0.707385i
$515$	2.87519	+	21.0501i	0.126696	+	0.927580i
$516$	37.6737	+	12.8081i	1.65849	+	0.563847i
$517$	−18.8654	−	18.5031i	−0.829700	−	0.813764i
$518$	−28.8820	−	5.67224i	−1.26900	−	0.249224i
$519$	−2.65649	+	5.87463i	−0.116607	+	0.257868i
$520$	−0.492350	−	1.91142i	−0.0215910	−	0.0838214i
$521$	−4.81344	−	2.41740i	−0.210881	−	0.105908i	0.340224	−	0.940344i	$-0.389497\pi$
$521$	−4.81344	−	2.41740i	−0.210881	−	0.105908i	−0.551105	+	0.834436i	$0.685793\pi$
$522$	−2.13322	−	8.14952i	−0.0933686	−	0.356695i
$523$	15.9736	+	10.5060i	0.698477	+	0.459396i	0.848437	−	0.529296i	$-0.177544\pi$
$523$	15.9736	+	10.5060i	0.698477	+	0.459396i	−0.149960	+	0.988692i	$0.547914\pi$
$524$	−30.3256	+	5.95575i	−1.32478	+	0.260178i
$525$	−9.89385	+	2.98313i	−0.431803	+	0.130194i
$526$	3.29095	+	5.22144i	0.143492	+	0.227666i
$527$	−11.4937	+	21.8202i	−0.500672	+	0.950502i
$528$	−33.0170	−	1.85821i	−1.43688	−	0.0808682i
$529$	−3.98870	+	11.6574i	−0.173422	+	0.506844i
$530$	−1.33475	+	22.9168i	−0.0579778	+	0.995440i
$531$	−16.3209	+	12.7522i	−0.708267	+	0.553398i
$532$	29.0549	−	19.1097i	1.25969	−	0.828512i
$533$	21.5818	−	21.1673i	0.934814	−	0.916859i
$534$	−4.26101	+	2.04772i	−0.184392	+	0.0886137i
$535$	6.66568	−	7.63803i	0.288183	−	0.330221i
$536$	−0.290718	+	1.12864i	−0.0125571	+	0.0487497i
$537$	0.350804	−	2.27215i	0.0151383	−	0.0980504i
$538$	−1.91991	−	0.784368i	−0.0827730	−	0.0338165i
$539$	−4.06904	−	3.41433i	−0.175266	−	0.147065i
$540$	−12.0298	+	13.4141i	−0.517681	+	0.577251i
$541$	−20.6854	+	17.3571i	−0.889334	+	0.746240i	−0.968076	−	0.250655i	$-0.919354\pi$
$541$	−20.6854	+	17.3571i	−0.889334	+	0.746240i	0.0787424	+	0.996895i	$0.474910\pi$
$542$	−50.5871	+	16.2201i	−2.17290	+	0.696713i
$543$	−7.33011	+	8.10951i	−0.314565	+	0.348012i
$544$	−3.06154	−	31.4754i	−0.131263	−	1.34950i
$545$	−16.5935	+	9.15592i	−0.710789	+	0.392197i
$546$	4.91110	+	31.0040i	0.210176	+	1.32685i
$547$	7.63133	−	0.593154i	0.326292	−	0.0253614i	0.0866983	−	0.996235i	$-0.472368\pi$
$547$	7.63133	−	0.593154i	0.326292	−	0.0253614i	0.239594	+	0.970873i	$0.422986\pi$
$548$	−25.8266	−	27.3746i	−1.10326	−	1.16938i
$549$	10.8153	−	2.60801i	0.461586	−	0.111307i
$550$	−25.4065	−	6.02144i	−1.08334	−	0.256755i
$551$	−3.25035	−	8.41861i	−0.138469	−	0.358645i
$552$	1.06023	+	1.60515i	0.0451263	+	0.0683197i
$553$	−4.33528	+	31.7399i	−0.184355	+	1.34972i
$554$	9.46477	+	43.6942i	0.402120	+	1.85639i
$555$	16.0830	−	2.86832i	0.682685	−	0.121754i
$556$	−40.5380	−	22.3679i	−1.71919	−	0.948611i
$557$	−7.59294	+	17.6024i	−0.321723	+	0.745838i	0.678217	+	0.734862i	$0.262753\pi$
$557$	−7.59294	+	17.6024i	−0.321723	+	0.745838i	−0.999940	+	0.0109759i	$0.996506\pi$
$558$	−30.6975	−	23.6007i	−1.29953	−	0.999096i
$559$	−22.9767	+	30.8631i	−0.971811	+	1.30537i
$560$	−11.5956	−	8.28803i	−0.490003	−	0.350233i
$561$	−13.4678	−	32.7819i	−0.568611	−	1.38406i
$562$	35.7345	−	5.58877i	1.50737	−	0.235748i
$563$	14.7531	+	30.8536i	0.621771	+	1.30032i	0.936342	+	0.351090i	$0.114189\pi$
$563$	14.7531	+	30.8536i	0.621771	+	1.30032i	−0.314571	+	0.949234i	$0.601861\pi$
$564$	13.2611	+	13.4679i	0.558391	+	0.567102i
$565$	−8.75204	+	13.8861i	−0.368201	+	0.584191i
$566$	24.9999	+	43.3010i	1.05082	+	1.82008i
$567$	16.1923	−	14.9265i	0.680012	−	0.626852i
$568$	1.05371	−	1.82508i	0.0442128	−	0.0765787i
$569$	12.7703	+	24.2438i	0.535359	+	1.01635i	0.991944	+	0.126675i	$0.0404304\pi$
$569$	12.7703	+	24.2438i	0.535359	+	1.01635i	−0.456585	+	0.889680i	$0.650928\pi$
$570$	−21.5261	+	30.2416i	−0.901630	+	1.26668i
$571$	12.1745	−	17.7509i	0.509489	−	0.742853i	−0.481551	−	0.876418i	$-0.659926\pi$
$571$	12.1745	−	17.7509i	0.509489	−	0.742853i	0.991040	+	0.133565i	$0.0426425\pi$
$572$	−14.8544	+	38.4738i	−0.621093	+	1.60867i
$573$	−2.95028	+	9.26360i	−0.123250	+	0.386992i
$574$	−4.02845	+	41.4161i	−0.168144	+	1.72867i
$575$	−3.15592	−	7.31623i	−0.131611	−	0.305108i
$576$	27.7405	+	2.04698i	1.15585	+	0.0852909i
$577$	−31.5497	+	3.68763i	−1.31343	+	0.153518i	−0.743811	−	0.668390i	$-0.766984\pi$
$577$	−31.5497	+	3.68763i	−1.31343	+	0.153518i	−0.569620	+	0.821908i	$0.692910\pi$
$578$	−3.12501	+	1.88595i	−0.129983	+	0.0784453i
$579$	10.7726	+	1.87778i	0.447694	+	0.0780377i
$580$	3.53261	−	3.20567i	0.146684	−	0.133108i
$581$	12.0237	+	9.31907i	0.498827	+	0.386620i
$582$	7.70834	+	5.71524i	0.319521	+	0.236904i
$583$	23.1426	−	28.6924i	0.958470	−	1.18832i
$584$	−1.05542	+	1.11868i	−0.0436734	+	0.0462911i
$585$	−8.77041	−	15.0544i	−0.362612	−	0.622424i
$586$	−4.16718	+	13.9193i	−0.172145	+	0.575003i
$587$	−9.32074	+	19.4927i	−0.384708	+	0.804549i	0.615162	+	0.788401i	$0.289091\pi$
$587$	−9.32074	+	19.4927i	−0.384708	+	0.804549i	−0.999870	+	0.0161475i	$0.994860\pi$
$588$	2.86744	+	2.49254i	0.118251	+	0.102791i
$589$	−35.5138	−	21.4327i	−1.46332	−	0.883118i
$590$	−20.5340	−	9.33383i	−0.845370	−	0.384268i
$591$	−11.7390	−	15.0849i	−0.482879	−	0.620511i
$592$	−15.8818	−	14.4120i	−0.652740	−	0.592330i
$593$	−7.80646	−	44.2726i	−0.320573	−	1.81806i	−0.539115	−	0.842232i	$-0.681241\pi$
$593$	−7.80646	−	44.2726i	−0.320573	−	1.81806i	0.218542	−	0.975827i	$-0.429870\pi$
$594$	54.3126	−	12.0990i	2.22847	−	0.496430i
$595$	2.65249	−	15.0430i	0.108742	−	0.616704i
$596$	−30.2251	+	23.4263i	−1.23807	+	0.959577i
$597$	−22.6473	+	0.483574i	−0.926893	+	0.0197914i
$598$	−23.3171	+	6.49077i	−0.953508	+	0.265427i
$599$	−1.78999	−	5.23143i	−0.0731369	−	0.213751i	0.903524	−	0.428537i	$-0.140971\pi$
$599$	−1.78999	−	5.23143i	−0.0731369	−	0.213751i	−0.976661	+	0.214787i	$0.931094\pi$
$600$	1.39063	+	0.355304i	0.0567723	+	0.0145052i
$601$	−23.2331	−	6.46737i	−0.947697	−	0.263809i	−0.240358	−	0.970684i	$-0.577265\pi$
$601$	−23.2331	−	6.46737i	−0.947697	−	0.263809i	−0.707339	+	0.706875i	$0.750104\pi$
$602$	−3.07957	−	52.8741i	−0.125514	−	2.15499i
$603$	0.239741	+	10.2849i	0.00976299	+	0.418833i
$604$	−28.9275	+	14.5279i	−1.17704	+	0.591133i
$605$	−17.3890	−	19.9256i	−0.706964	−	0.810091i
$606$	40.8161	+	17.5117i	1.65804	+	0.711364i
$607$	13.0250	−	0.505431i	0.528670	−	0.0205148i	0.226941	−	0.973908i	$-0.427128\pi$
$607$	13.0250	−	0.505431i	0.528670	−	0.0205148i	0.301729	+	0.953394i	$0.402436\pi$
$608$	53.1491	−	2.06243i	2.15548	−	0.0836424i
$609$	−4.66989	+	3.49083i	−0.189234	+	0.141456i
$610$	7.96629	+	9.12835i	0.322546	+	0.369596i
$611$	−16.3323	+	8.20241i	−0.660736	+	0.331834i
$612$	9.22284	+	23.6123i	0.372811	+	0.954472i
$613$	0.894026	+	15.3498i	0.0361094	+	0.619974i	0.967016	+	0.254716i	$0.0819821\pi$
$613$	0.894026	+	15.3498i	0.0361094	+	0.619974i	−0.930906	+	0.365258i	$0.880981\pi$
$614$	39.6235	+	11.0300i	1.59908	+	0.445133i
$615$	−6.23721	−	22.2378i	−0.251509	−	0.896713i
$616$	−1.41244	−	4.12801i	−0.0569088	−	0.166322i
$617$	0.771362	−	0.214723i	0.0310538	−	0.00864443i	−0.252611	−	0.967568i	$-0.581289\pi$
$617$	0.771362	−	0.214723i	0.0310538	−	0.00864443i	0.283665	+	0.958924i	$0.408450\pi$
$618$	−22.5918	+	41.1338i	−0.908774	+	1.65464i
$619$	−26.5280	+	20.5608i	−1.06625	+	0.826406i	−0.985389	−	0.170319i	$-0.945520\pi$
$619$	−26.5280	+	20.5608i	−1.06625	+	0.826406i	−0.0808614	+	0.996725i	$0.525767\pi$
$620$	3.80750	−	21.5934i	0.152913	−	0.867213i
$621$	12.8590	+	11.0897i	0.516013	+	0.445015i
$622$	−11.0255	−	62.5285i	−0.442081	−	2.50717i
$623$	2.42304	+	2.19879i	0.0970770	+	0.0880927i
$624$	−8.60873	+	21.1900i	−0.344625	+	0.848280i
$625$	6.24858	+	2.84033i	0.249943	+	0.113613i
$626$	23.9400	+	14.4479i	0.956837	+	0.577454i
$627$	56.3605	−	19.4076i	2.25082	−	0.775064i
$628$	6.48699	−	13.5664i	0.258859	−	0.541358i
$629$	6.59190	−	22.0185i	0.262836	−	0.877934i
$630$	22.5684	+	8.11435i	0.899146	+	0.323284i
$631$	14.1697	−	15.0190i	0.564088	−	0.597899i	−0.381056	−	0.924552i	$-0.624439\pi$
$631$	14.1697	−	15.0190i	0.564088	−	0.597899i	0.945144	+	0.326653i	$0.105921\pi$
$632$	2.79340	−	3.46327i	0.111115	−	0.137762i
$633$	0.162171	−	1.41141i	0.00644572	−	0.0560984i
$634$	−6.18390	−	4.79288i	−0.245594	−	0.190350i
$635$	10.3917	−	9.42994i	0.412381	−	0.374216i
$636$	−16.9085	+	20.2311i	−0.670467	+	0.802214i
$637$	−3.14539	+	1.89825i	−0.124625	+	0.0752115i
$638$	−14.6320	+	1.71024i	−0.579288	+	0.0677091i
$639$	4.56963	−	18.0322i	0.180772	−	0.713344i
$640$	1.71768	+	3.98203i	0.0678973	+	0.157404i
$641$	1.89924	−	19.5259i	0.0750155	−	0.771227i	−0.880060	−	0.474863i	$-0.842498\pi$
$641$	1.89924	−	19.5259i	0.0750155	−	0.771227i	0.955075	−	0.296364i	$-0.0957741\pi$
$642$	21.8761	−	4.78349i	0.863380	−	0.188789i
$643$	1.32545	−	3.43301i	0.0522707	−	0.135385i	−0.904289	−	0.426921i	$-0.859598\pi$
$643$	1.32545	−	3.43301i	0.0522707	−	0.135385i	0.956560	+	0.291536i	$0.0941663\pi$
$644$	9.79861	−	14.2867i	0.386119	−	0.562976i
$645$	12.2170	+	26.7379i	0.481045	+	1.05280i
$646$	24.3389	+	46.2062i	0.957599	+	1.81796i
$647$	18.9601	−	32.8398i	0.745397	−	1.29107i	−0.204612	−	0.978843i	$-0.565593\pi$
$647$	18.9601	−	32.8398i	0.745397	−	1.29107i	0.950009	−	0.312222i	$-0.101073\pi$
$648$	−2.99675	+	0.612940i	−0.117724	+	0.0240785i
$649$	18.1102	+	31.3677i	0.710886	+	1.23129i
$650$	−9.62906	+	15.2775i	−0.377683	+	0.599235i
$651$	−7.13634	+	25.8318i	−0.279695	+	1.01243i
$652$	22.8260	+	47.7365i	0.893935	+	1.86951i
$653$	16.5394	−	2.58672i	0.647237	−	0.101226i	0.177624	−	0.984098i	$-0.443159\pi$
$653$	16.5394	−	2.58672i	0.647237	−	0.101226i	0.469613	+	0.882872i	$0.344393\pi$
$654$	−41.4889	−	5.58421i	−1.62234	−	0.218360i
$655$	−18.5747	−	13.2764i	−0.725775	−	0.518753i
$656$	−18.1054	+	24.3198i	−0.706898	+	0.949529i
$657$	−6.27978	+	12.0359i	−0.244998	+	0.469564i
$658$	9.96443	−	23.1002i	0.388454	−	0.900538i
$659$	38.4720	+	21.2280i	1.49866	+	0.826924i	0.999222	−	0.0394284i	$-0.0125537\pi$
$659$	38.4720	+	21.2280i	1.49866	+	0.826924i	0.499434	+	0.866352i	$0.333541\pi$
$660$	20.3010	+	24.0979i	0.790216	+	0.938009i
$661$	0.165067	+	0.762033i	0.00642035	+	0.0296396i	0.980432	−	0.196860i	$-0.0630744\pi$
$661$	0.165067	+	0.762033i	0.00642035	+	0.0296396i	−0.974011	+	0.226499i	$0.927272\pi$
$662$	3.76109	−	27.5361i	0.146179	−	1.07022i
$663$	−24.4678	+	1.47313i	−0.950249	+	0.0572115i
$664$	−0.761021	−	1.97109i	−0.0295333	−	0.0764933i
$665$	24.9990	+	5.92487i	0.969420	+	0.229757i
$666$	32.3111	+	16.0692i	1.25203	+	0.622669i
$667$	−3.08503	−	3.26995i	−0.119453	−	0.126613i
$668$	−19.6633	+	1.52835i	−0.760796	+	0.0591337i
$669$	2.01734	−	1.63367i	0.0779948	−	0.0631612i
$670$	−9.80927	+	5.41253i	−0.378965	+	0.209104i
$671$	−1.88350	−	19.3640i	−0.0727115	−	0.747540i
$672$	−10.5564	−	32.7029i	−0.407221	−	1.26154i
$673$	−23.3369	+	7.48268i	−0.899571	+	0.288436i	−0.718905	−	0.695108i	$-0.755356\pi$
$673$	−23.3369	+	7.48268i	−0.899571	+	0.288436i	−0.180667	+	0.983544i	$0.557825\pi$
$674$	26.8508	−	22.5305i	1.03425	−	0.867841i
$675$	12.6654	−	0.320026i	0.487492	−	0.0123178i
$676$	0.275670	+	0.231315i	0.0106027	+	0.00889673i
$677$	24.7397	+	10.1073i	0.950825	+	0.388455i	0.799929	−	0.600095i	$-0.204871\pi$
$677$	24.7397	+	10.1073i	0.950825	+	0.388455i	0.150896	+	0.988550i	$0.451784\pi$
$678$	−33.7980	+	13.1251i	−1.29800	+	0.504068i
$679$	1.65666	−	6.43155i	0.0635768	−	0.246820i
$680$	−1.39501	+	1.59851i	−0.0534963	+	0.0613000i
$681$	0.727881	−	9.60797i	0.0278924	−	0.368178i
$682$	−48.3429	+	47.4144i	−1.85114	+	1.81559i
$683$	22.4069	−	14.7372i	0.857376	−	0.563905i	−0.0429720	−	0.999076i	$-0.513683\pi$
$683$	22.4069	−	14.7372i	0.857376	−	0.563905i	0.900348	+	0.435171i	$0.143312\pi$
$684$	−40.5489	+	13.1767i	−1.55043	+	0.503823i
$685$	1.61663	−	27.7565i	0.0617683	−	1.06052i
$686$	12.9558	−	37.8648i	0.494655	−	1.44568i
$687$	11.5401	+	22.8666i	0.440284	+	0.872417i
$688$	17.9850	−	34.1437i	0.685672	−	1.30172i
$689$	−13.5943	−	21.5688i	−0.517900	−	0.821704i
$690$	−4.22933	+	18.0018i	−0.161008	+	0.685318i
$691$	14.2610	−	2.80076i	0.542513	−	0.106546i	0.0860537	−	0.996291i	$-0.472574\pi$
$691$	14.2610	−	2.80076i	0.542513	−	0.106546i	0.456459	+	0.889745i	$0.349118\pi$
$692$	−6.73782	−	4.43153i	−0.256133	−	0.168462i
$693$	−21.9067	−	31.6743i	−0.832166	−	1.20321i
$694$	14.1692	+	7.11602i	0.537854	+	0.270121i
$695$	−8.53210	−	33.1236i	−0.323641	−	1.25645i
$696$	0.805854	−	0.0799755i	0.0305458	−	0.00303146i
$697$	−31.8843	−	6.26188i	−1.20771	−	0.237186i
$698$	0.425599	+	0.417425i	0.0161092	+	0.0157998i
$699$	17.1382	−	15.0156i	0.648227	−	0.567944i
$700$	−1.74927	−	12.8069i	−0.0661162	−	0.484056i
$701$	1.50780	−	0.548796i	0.0569490	−	0.0207277i	−0.313389	−	0.949625i	$-0.601464\pi$
$701$	1.50780	−	0.548796i	0.0569490	−	0.0207277i	0.370338	+	0.928897i	$0.379242\pi$
$702$	4.24344	−	38.2508i	0.160158	−	1.44368i
$703$	36.3261	+	13.2216i	1.37006	+	0.498663i
$704$	10.2979	−	47.5406i	0.388118	−	1.79175i
$705$	−0.514134	+	13.9539i	−0.0193634	+	0.525535i
$706$	−49.6028	+	35.4540i	−1.86683	+	1.33433i
$707$	0.596081	−	30.7338i	0.0224179	−	1.15586i
$708$	−12.5605	−	22.6588i	−0.472053	−	0.851571i
$709$	−11.9898	−	17.4815i	−0.450285	−	0.656532i	0.531382	−	0.847132i	$-0.321673\pi$
$709$	−11.9898	−	17.4815i	−0.450285	−	0.656532i	−0.981668	+	0.190600i	$0.938957\pi$
$710$	19.7121	−	4.67185i	0.739781	−	0.175331i
$711$	15.4148	−	36.1236i	0.578100	−	1.35474i
$712$	−0.130340	−	0.435366i	−0.00488470	−	0.0163160i
$713$	−20.4155	−	3.19293i	−0.764568	−	0.119576i
$714$	24.4971	−	23.2026i	0.916782	−	0.868336i
$715$	−28.2052	+	11.5231i	−1.05482	+	0.430940i
$716$	2.73842	+	0.878040i	0.102340	+	0.0328139i
$717$	0.0378533	+	19.3464i	0.00141366	+	0.722505i
$718$	−0.680817	−	35.1028i	−0.0254079	−	1.31002i
$719$	−7.53586	−	10.1224i	−0.281040	−	0.377502i	0.639079	−	0.769141i	$-0.279316\pi$
$719$	−7.53586	−	10.1224i	−0.281040	−	0.377502i	−0.920119	+	0.391639i	$0.871908\pi$
$720$	11.0239	+	13.5585i	0.410835	+	0.505296i
$721$	32.2609	+	3.77075i	1.20146	+	0.140430i
$722$	−44.6575	+	20.2993i	−1.66198	+	0.755463i
$723$	0.453385	+	11.1221i	0.0168616	+	0.413636i
$724$	−8.58425	−	10.6428i	−0.319031	−	0.395537i
$725$	−3.34413	−	0.259927i	−0.124198	−	0.00965343i
$726$	−4.64085	−	58.2328i	−0.172238	−	2.16122i
$727$	17.8680	+	0.693362i	0.662689	+	0.0257154i	0.367926	−	0.929855i	$-0.380068\pi$
$727$	17.8680	+	0.693362i	0.662689	+	0.0257154i	0.294763	+	0.955570i	$0.404759\pi$
$728$	−3.01759			−0.111839
$729$	−23.9842	+	12.4000i	−0.888302	+	0.459259i
$730$	−14.7841			−0.547183
$731$	41.3270	+	1.60367i	1.52853	+	0.0593141i
$732$	1.10552	+	13.8719i	0.0408611	+	0.512720i
$733$	30.9720	+	2.40733i	1.14398	+	0.0889169i	0.635459	−	0.772135i	$-0.280811\pi$
$733$	30.9720	+	2.40733i	1.14398	+	0.0889169i	0.508517	+	0.861052i	$0.330194\pi$
$734$	−17.1808	−	21.3008i	−0.634154	−	0.786227i
$735$	0.114324	+	2.80451i	0.00421690	+	0.103446i
$736$	24.1216	−	10.9646i	0.889136	−	0.404162i
$737$	17.8690	+	2.08858i	0.658212	+	0.0769340i
$738$	18.1887	−	47.6641i	0.669534	−	1.75454i
$739$	−1.52810	−	2.05259i	−0.0562120	−	0.0755058i	0.773128	−	0.634250i	$-0.218691\pi$
$739$	−1.52810	−	2.05259i	−0.0562120	−	0.0755058i	−0.829340	+	0.558744i	$0.811283\pi$
$740$	0.396253	+	20.4307i	0.0145665	+	0.751047i
$741$	−0.0806657	−	41.2273i	−0.00296333	−	1.51452i
$742$	33.4189	+	10.7153i	1.22685	+	0.393373i
$743$	20.7192	−	8.46474i	0.760115	−	0.310541i	0.0352009	−	0.999380i	$-0.488793\pi$
$743$	20.7192	−	8.46474i	0.760115	−	0.310541i	0.724914	+	0.688839i	$0.241879\pi$
$744$	2.70249	−	2.55968i	0.0990781	−	0.0938425i
$745$	−27.9118	−	4.36533i	−1.02261	−	0.159933i
$746$	−2.63866	−	8.81375i	−0.0966084	−	0.322694i
$747$	−11.1958	−	14.9164i	−0.409634	−	0.545762i
$748$	43.1353	−	10.2233i	1.57718	−	0.373799i
$749$	−8.76604	−	12.7812i	−0.320304	−	0.467015i
$750$	20.4066	+	36.8130i	0.745144	+	1.34422i
$751$	−1.00564	+	51.8507i	−0.0366965	+	1.89206i	0.305149	+	0.952304i	$0.401294\pi$
$751$	−1.00564	+	51.8507i	−0.0366965	+	1.89206i	−0.341846	+	0.939756i	$0.611052\pi$
$752$	14.9128	−	10.6591i	0.543815	−	0.388696i
$753$	−1.03918	+	28.2041i	−0.0378700	+	1.02781i
$754$	−2.15704	+	9.95803i	−0.0785549	+	0.362650i
$755$	−22.4723	−	8.17925i	−0.817851	−	0.297673i
$756$	15.2718	+	22.9254i	0.555431	+	0.833789i
$757$	−9.59834	+	3.49351i	−0.348858	+	0.126974i	−0.510505	−	0.859875i	$-0.670542\pi$
$757$	−9.59834	+	3.49351i	−0.348858	+	0.126974i	0.161647	+	0.986849i	$0.448319\pi$
$758$	0.223824	+	1.63868i	0.00812964	+	0.0595195i
$759$	22.3347	−	19.5686i	0.810700	−	0.710294i
$760$	−2.54759	−	2.49866i	−0.0924109	−	0.0906360i
$761$	−26.9581	−	5.29440i	−0.977231	−	0.191922i	−0.321494	−	0.946912i	$-0.604185\pi$
$761$	−26.9581	−	5.29440i	−0.977231	−	0.191922i	−0.655737	+	0.754990i	$0.727642\pi$
$762$	30.8449	−	3.06115i	1.11739	−	0.110894i
$763$	7.22729	+	28.0581i	0.261646	+	1.01577i
$764$	−10.8672	−	5.45769i	−0.393160	−	0.197452i
$765$	−8.01264	+	16.9269i	−0.289698	+	0.611993i
$766$	−54.0115	−	35.5239i	−1.95152	−	1.28353i
$767$	24.5818	−	4.82770i	0.887596	−	0.174318i
$768$	5.15508	−	21.9422i	0.186018	−	0.791772i
$769$	−6.93460	−	11.0025i	−0.250068	−	0.396760i	0.697364	−	0.716717i	$-0.254356\pi$
$769$	−6.93460	−	11.0025i	−0.250068	−	0.396760i	−0.947432	+	0.319957i	$0.896331\pi$
$770$	19.5459	−	37.1069i	0.704385	−	1.33724i
$771$	17.9267	+	35.5215i	0.645614	+	1.27928i
$772$	−4.42800	+	12.9413i	−0.159367	+	0.465768i
$773$	−2.86580	+	49.2038i	−0.103076	+	1.76974i	0.410659	+	0.911789i	$0.365299\pi$
$773$	−2.86580	+	49.2038i	−0.103076	+	1.76974i	−0.513734	+	0.857949i	$0.671738\pi$
$774$	−13.4985	+	63.5162i	−0.485193	+	2.28304i
$775$	−12.8812	+	8.47211i	−0.462707	+	0.304327i
$776$	−0.658575	+	0.645926i	−0.0236415	+	0.0231874i
$777$	1.88671	−	24.9045i	0.0676854	−	0.893442i
$778$	−33.2851	+	38.1405i	−1.19333	+	1.36740i
$779$	13.6323	−	52.9239i	0.488428	−	1.89620i
$780$	20.3150	−	7.88914i	0.727393	−	0.282476i
$781$	−30.1145	−	12.3031i	−1.07758	−	0.440240i
$782$	19.9296	+	16.7229i	0.712680	+	0.598009i
$783$	6.65323	−	2.61373i	0.237767	−	0.0934070i
$784$	2.82264	−	2.36848i	0.100809	−	0.0845885i
$785$	10.5788	−	3.39196i	0.377574	−	0.121064i
$786$	−15.4924	−	47.9945i	−0.552597	−	1.71191i
$787$	3.61485	+	37.1640i	0.128856	+	1.32475i	0.807318	+	0.590117i	$0.200918\pi$
$787$	3.61485	+	37.1640i	0.128856	+	1.32475i	−0.678462	+	0.734635i	$0.737353\pi$
$788$	20.9336	−	11.5507i	0.745729	−	0.411476i
$789$	−4.07004	+	3.29597i	−0.144897	+	0.117340i
$790$	42.6425	−	3.31444i	1.51715	−	0.117922i
$791$	17.2205	+	18.2527i	0.612291	+	0.648991i
$792$	0.331916	+	5.33877i	0.0117941	+	0.189705i
$793$	−13.0934	−	3.10319i	−0.464960	−	0.110198i
$794$	26.2393	+	67.9615i	0.931198	+	2.41186i
$795$	−19.4436	+	1.17064i	−0.689595	+	0.0415183i
$796$	3.83453	−	28.0738i	0.135911	−	0.995048i
$797$	0.695772	+	3.21204i	0.0246455	+	0.113776i	0.988000	−	0.154457i	$-0.0493627\pi$
$797$	0.695772	+	3.21204i	0.0246455	+	0.113776i	−0.963354	+	0.268233i	$0.913560\pi$
$798$	36.5633	+	43.4017i	1.29433	+	1.53640i
$799$	17.2003	+	9.49074i	0.608504	+	0.335758i
$800$	7.83039	−	18.1529i	0.276846	−	0.641802i
$801$	−2.15222	−	3.38528i	−0.0760448	−	0.119613i
$802$	−47.2466	+	63.4631i	−1.66833	+	2.24096i
$803$	19.3141	+	13.8049i	0.681579	+	0.487163i
$804$	−12.7532	−	1.71651i	−0.449769	−	0.0605368i
$805$	12.6448	−	1.97761i	0.445671	−	0.0697017i
$806$	20.2033	+	42.2516i	0.711630	+	1.48825i
$807$	0.468623	−	1.69630i	0.0164963	−	0.0597125i
$808$	−2.27654	+	3.61198i	−0.0800886	+	0.127069i
$809$	9.21655	+	15.9635i	0.324037	+	0.561248i	0.981317	−	0.192398i	$-0.0616266\pi$
$809$	9.21655	+	15.9635i	0.324037	+	0.561248i	−0.657280	+	0.753646i	$0.728293\pi$
$810$	−24.0543	−	16.9101i	−0.845182	−	0.594161i
$811$	−18.3254	+	31.7406i	−0.643493	+	1.11456i	0.341154	+	0.940007i	$0.389182\pi$
$811$	−18.3254	+	31.7406i	−0.643493	+	1.11456i	−0.984647	+	0.174556i	$0.944151\pi$
$812$	−3.39880	−	6.45245i	−0.119274	−	0.226437i
$813$	−18.7340	−	41.0008i	−0.657031	−	1.43796i
$814$	35.6933	−	52.0421i	1.25105	−	1.82407i
$815$	−14.0796	+	36.4671i	−0.493187	+	1.27739i
$816$	24.0173	−	5.25169i	0.840773	−	0.183846i
$817$	−6.73427	+	69.2344i	−0.235602	+	2.42220i
$818$	−5.71397	−	13.2465i	−0.199784	−	0.463152i
$819$	−25.6324	+	7.24348i	−0.895670	+	0.253108i
$820$	28.6937	−	3.35382i	1.00203	−	0.117120i
$821$	25.7964	−	15.5682i	0.900302	−	0.543335i	0.0106339	−	0.999943i	$-0.496615\pi$
$821$	25.7964	−	15.5682i	0.900302	−	0.543335i	0.889668	+	0.456609i	$0.150936\pi$
$822$	39.3849	−	47.1240i	1.37371	−	1.64364i
$823$	26.6631	−	24.1955i	0.929417	−	0.843401i	−0.0585152	−	0.998287i	$-0.518637\pi$
$823$	26.6631	−	24.1955i	0.929417	−	0.843401i	0.987932	+	0.154885i	$0.0495008\pi$
$824$	−3.56574	−	2.76366i	−0.124218	−	0.0962766i
$825$	2.52906	−	22.0109i	0.0880507	−	0.766322i
$826$	−21.6492	+	26.8408i	−0.753271	+	0.933910i
$827$	18.0111	−	19.0907i	0.626308	−	0.663848i	−0.334070	−	0.942548i	$-0.608422\pi$
$827$	18.0111	−	19.0907i	0.626308	−	0.663848i	0.960378	+	0.278701i	$0.0899037\pi$
$828$	−16.2170	+	13.7162i	−0.563579	+	0.476669i
$829$	0.870287	−	2.90696i	0.0302263	−	0.100963i	−0.941545	−	0.336886i	$-0.890626\pi$
$829$	0.870287	−	2.90696i	0.0302263	−	0.100963i	0.971772	+	0.235923i	$0.0758114\pi$
$830$	8.76180	−	18.3237i	0.304127	−	0.636027i
$831$	−35.8694	+	12.3515i	−1.24429	+	0.428469i
$832$	−28.8044	−	17.3835i	−0.998613	−	0.602666i
$833$	3.59495	+	1.63411i	0.124558	+	0.0566184i
$834$	28.4381	−	69.9991i	0.984730	−	2.42387i
$835$	−10.7901	−	9.79150i	−0.373407	−	0.338849i
$836$	12.9472	+	73.4273i	0.447789	+	2.53954i
$837$	16.8116	−	28.2299i	0.581094	−	0.975769i
$838$	13.3801	−	75.8821i	0.462206	−	2.62130i
$839$	−9.92541	+	7.69278i	−0.342663	+	0.265584i	−0.769367	−	0.638808i	$-0.779428\pi$
$839$	−9.92541	+	7.69278i	−0.342663	+	0.265584i	0.426703	+	0.904392i	$0.359675\pi$
$840$	−1.10986	+	2.02076i	−0.0382936	+	0.0697228i
$841$	26.1146	−	7.26949i	0.900503	−	0.250672i
$842$	−7.12931	−	20.8362i	−0.245692	−	0.718062i
$843$	8.28829	+	29.5506i	0.285464	+	1.01778i
$844$	1.71195	+	0.476555i	0.0589279	+	0.0164037i
$845$	0.0154581	+	0.265406i	0.000531776	+	0.00913025i
$846$	−19.2700	+	24.0833i	−0.662517	+	0.828002i
$847$	−36.1308	+	18.1456i	−1.24147	+	0.623490i
$848$	16.8135	+	19.2661i	0.577377	+	0.661600i
$849$	−33.9820	+	25.4022i	−1.16626	+	0.871801i
$850$	19.3966	−	0.752676i	0.665298	−	0.0258166i
$851$	19.2431	−	0.746722i	0.659647	−	0.0255973i
$852$	21.3833	+	9.17426i	0.732579	+	0.314305i
$853$	3.99726	+	4.58036i	0.136864	+	0.156828i	0.817776	−	0.575536i	$-0.195207\pi$
$853$	3.99726	+	4.58036i	0.136864	+	0.156828i	−0.680912	+	0.732365i	$0.738417\pi$
$854$	16.5523	−	8.31289i	0.566409	−	0.284461i
$855$	−27.6380	−	15.1092i	−0.945199	−	0.516724i
$856$	0.125165	+	2.14901i	0.00427806	+	0.0734515i
$857$	8.59182	+	2.39170i	0.293491	+	0.0816988i	0.411789	−	0.911279i	$-0.364904\pi$
$857$	8.59182	+	2.39170i	0.293491	+	0.0816988i	−0.118298	+	0.992978i	$0.537744\pi$
$858$	−65.2069	−	16.6602i	−2.22613	−	0.568771i
$859$	9.65732	+	28.2246i	0.329504	+	0.963010i	0.979214	+	0.202829i	$0.0650135\pi$
$859$	9.65732	+	28.2246i	0.329504	+	0.963010i	−0.649711	+	0.760182i	$0.725110\pi$
$860$	−35.4235	+	9.86081i	−1.20793	+	0.336251i
$861$	−35.3012	+	0.753765i	−1.20306	+	0.0256883i
$862$	49.9721	−	38.7313i	1.70206	−	1.31919i
$863$	−2.79073	+	15.8270i	−0.0949975	+	0.538758i	0.899751	+	0.436404i	$0.143748\pi$
$863$	−2.79073	+	15.8270i	−0.0949975	+	0.538758i	−0.994748	+	0.102353i	$0.967363\pi$
$864$	1.88075	+	42.0895i	0.0639846	+	1.43191i
$865$	−1.03457	−	5.86734i	−0.0351764	−	0.199495i
$866$	−15.5746	−	14.1332i	−0.529245	−	0.480264i
$867$	−1.90213	−	2.44428i	−0.0645996	−	0.0830120i
$868$	−30.5168	−	13.8716i	−1.03581	−	0.470832i
$869$	−58.8036	−	35.4881i	−1.99477	−	1.20385i
$870$	5.87514	+	5.10700i	0.199186	+	0.173144i
$871$	5.36773	−	11.2257i	0.181879	−	0.380367i
$872$	1.15419	−	3.85525i	0.0390857	−	0.130555i
$873$	−4.04367	+	7.06758i	−0.136858	+	0.239201i
$874$	−30.0280	+	31.8279i	−1.01571	+	1.07659i
$875$	18.2891	−	22.6749i	0.618285	−	0.766553i
$876$	−13.6405	−	10.1136i	−0.460870	−	0.341706i
$877$	34.1702	+	26.4839i	1.15385	+	0.894299i	0.995656	−	0.0931093i	$-0.0296806\pi$
$877$	34.1702	+	26.4839i	1.15385	+	0.894299i	0.158191	+	0.987408i	$0.449434\pi$
$878$	−53.4898	+	48.5394i	−1.80519	+	1.63813i
$879$	−12.1460	−	2.11717i	−0.409674	−	0.0714104i
$880$	26.1633	−	15.7896i	0.881964	−	0.532268i
$881$	9.82711	−	1.14862i	0.331084	−	0.0386981i	0.0510728	−	0.998695i	$-0.483736\pi$
$881$	9.82711	−	1.14862i	0.331084	−	0.0386981i	0.280011	+	0.959997i	$0.409662\pi$
$882$	−3.48675	+	5.12670i	−0.117405	+	0.172625i
$883$	−11.7141	−	27.1563i	−0.394211	−	0.913883i	−0.993551	−	0.113389i	$-0.963830\pi$
$883$	−11.7141	−	27.1563i	−0.394211	−	0.913883i	0.599340	−	0.800495i	$-0.295430\pi$
$884$	2.96827	−	30.5164i	0.0998336	−	1.02638i
$885$	5.80815	−	18.2370i	0.195239	−	0.613031i
$886$	−26.8319	+	69.4963i	−0.901434	+	2.33477i
$887$	−6.87193	+	10.0195i	−0.230737	+	0.336423i	−0.922706	−	0.385505i	$-0.874027\pi$
$887$	−6.87193	+	10.0195i	−0.230737	+	0.336423i	0.691969	+	0.721927i	$0.256743\pi$
$888$	−2.01167	+	2.82615i	−0.0675072	+	0.0948395i
$889$	−9.99804	−	18.9808i	−0.335323	−	0.636596i
$890$	2.18430	−	3.78331i	0.0732178	−	0.126817i
$891$	15.6347	+	44.5527i	0.523782	+	1.49257i
$892$	1.62349	+	2.81198i	0.0543586	+	0.0941519i
$893$	−17.6178	+	27.9525i	−0.589557	+	0.935396i
$894$	−43.7835	−	44.4665i	−1.46434	−	1.48718i
$895$	0.916489	+	1.91667i	0.0306348	+	0.0640673i
$896$	6.55038	−	1.02446i	0.218833	−	0.0342248i
$897$	−7.80462	−	18.9972i	−0.260589	−	0.634298i
$898$	26.7115	+	19.0922i	0.891374	+	0.637116i
$899$	−5.19454	+	6.97747i	−0.173248	+	0.232712i
$900$	−2.08318	+	15.7098i	−0.0694394	+	0.523661i
$901$	−10.8544	+	25.1634i	−0.361613	+	0.838313i
$902$	−78.1134	−	43.1011i	−2.60089	−	1.43511i
$903$	44.2440	−	7.89070i	1.47235	−	0.262586i
$904$	−0.737875	−	3.40641i	−0.0245414	−	0.113295i
$905$	1.36704	−	10.0085i	0.0454420	−	0.332694i
$906$	−29.1141	−	44.0777i	−0.967250	−	1.46438i
$907$	6.41638	+	16.6188i	0.213052	+	0.551819i	0.997675	−	0.0681546i	$-0.0217111\pi$
$907$	6.41638	+	16.6188i	0.213052	+	0.551819i	−0.784623	+	0.619974i	$0.787143\pi$
$908$	11.7275	+	2.77947i	0.389191	+	0.0922400i
$909$	−10.6675	+	36.1461i	−0.353818	+	1.19889i
$910$	−19.9060	−	21.0992i	−0.659878	−	0.699430i
$911$	−21.0214	+	1.63392i	−0.696472	+	0.0541341i	−0.420847	−	0.907131i	$-0.638267\pi$
$911$	−21.0214	+	1.63392i	−0.696472	+	0.0541341i	−0.275624	+	0.961265i	$0.588885\pi$
$912$	6.46922	+	40.8405i	0.214217	+	1.35236i
$913$	−28.5566	+	15.7569i	−0.945086	+	0.521476i
$914$	5.82039	+	59.8389i	0.192522	+	1.97929i
$915$	−6.89377	+	7.62678i	−0.227901	+	0.252134i
$916$	−30.5084	+	9.78213i	−1.00803	+	0.323211i
$917$	−26.7390	+	22.4367i	−0.883000	+	0.740925i
$918$	−36.4865	+	19.4935i	−1.20423	+	0.643382i
$919$	−43.3283	−	36.3568i	−1.42927	−	1.19930i	−0.946143	−	0.323749i	$-0.895057\pi$
$919$	−43.3283	−	36.3568i	−1.42927	−	1.19930i	−0.483126	−	0.875551i	$-0.660499\pi$
$920$	−1.64561	−	0.672304i	−0.0542540	−	0.0221652i
$921$	−5.32534	+	34.4920i	−0.175476	+	1.13655i
$922$	8.06532	−	31.3115i	0.265617	−	1.03119i
$923$	−14.7939	+	16.9519i	−0.486947	+	0.557979i
$924$	43.4183	−	20.8657i	1.42836	−	0.686430i
$925$	10.2581	−	10.0611i	0.337284	−	0.330806i
$926$	−17.0588	+	11.2198i	−0.560588	+	0.368705i
$927$	−36.9226	−	14.9162i	−1.21270	−	0.489913i
$928$	0.648563	−	11.1354i	0.0212901	−	0.365537i
$929$	−4.42562	+	12.9344i	−0.145200	+	0.424363i	−0.994650	−	0.103307i	$-0.967058\pi$
$929$	−4.42562	+	12.9344i	−0.145200	+	0.424363i	0.849450	+	0.527670i	$0.176934\pi$
$930$	35.7249	+	2.01061i	1.17146	+	0.0659304i
$931$	−3.09536	+	5.87639i	−0.101446	+	0.192591i
$932$	15.1969	+	24.1115i	0.497791	+	0.789799i
$933$	51.5831	−	15.5530i	1.68875	−	0.509182i
$934$	−4.81553	+	0.945739i	−0.157569	+	0.0309455i
$935$	27.3622	+	17.9964i	0.894839	+	0.588545i
$936$	3.56797	+	0.978184i	0.116623	+	0.0319729i
$937$	−4.68517	−	2.35298i	−0.153058	−	0.0768685i	0.370622	−	0.928784i	$-0.379145\pi$
$937$	−4.68517	−	2.35298i	−0.153058	−	0.0768685i	−0.523679	+	0.851915i	$0.675441\pi$
$938$	4.27242	+	16.5865i	0.139499	+	0.541570i
$939$	−9.77617	+	21.6193i	−0.319033	+	0.705518i
$940$	−17.1385	−	3.36588i	−0.558995	−	0.109783i
$941$	−1.33767	−	1.31197i	−0.0436067	−	0.0427691i	0.678087	−	0.734981i	$-0.262809\pi$
$941$	−1.33767	−	1.31197i	−0.0436067	−	0.0427691i	−0.721694	+	0.692212i	$0.756636\pi$
$942$	23.2334	+	7.89880i	0.756986	+	0.257357i
$943$	−3.68443	−	26.9748i	−0.119981	−	0.878419i
$944$	−23.6104	+	8.59347i	−0.768452	+	0.279694i
$945$	−4.57683	+	19.8291i	−0.148884	+	0.645042i
$946$	106.707	+	38.8380i	3.46933	+	1.26273i
$947$	6.42874	−	29.6784i	0.208906	−	0.964418i	−0.745639	−	0.666350i	$-0.767856\pi$
$947$	6.42874	−	29.6784i	0.208906	−	0.964418i	0.954545	−	0.298067i	$-0.0963420\pi$
$948$	41.6115	+	26.1131i	1.35148	+	0.848113i
$949$	13.3583	−	9.54797i	0.433630	−	0.309940i
$950$	−0.633091	+	32.6420i	−0.0205402	+	1.05905i
$951$	3.41917	−	5.69068i	0.110874	−	0.184533i
$952$	1.83458	+	2.67488i	0.0594591	+	0.0866935i
$953$	−1.69751	+	0.402316i	−0.0549876	+	0.0130323i	−0.258018	−	0.966140i	$-0.583069\pi$
$953$	−1.69751	+	0.402316i	−0.0549876	+	0.0130323i	0.203030	+	0.979173i	$0.434921\pi$
$954$	−36.0407	−	23.5028i	−1.16686	−	0.760932i
$955$	−2.57663	−	8.60653i	−0.0833776	−	0.278501i
$956$	−23.9085	−	3.73922i	−0.773257	−	0.120935i
$957$	−2.90660	−	12.1579i	−0.0939571	−	0.393008i
$958$	17.3898	−	7.10451i	0.561839	−	0.229536i
$959$	−40.4766	−	12.9783i	−1.30706	−	0.419091i
$960$	−22.2352	+	12.8956i	−0.717638	+	0.416203i
$961$	0.174205	+	8.98197i	0.00561952	+	0.289741i
$962$	−26.0639	−	35.0099i	−0.840335	−	1.12877i
$963$	6.22172	+	17.9540i	0.200492	+	0.578558i
$964$	−13.8293	−	1.61641i	−0.445412	−	0.0520612i
$965$	−9.19907	+	4.18149i	−0.296129	+	0.134607i
$966$	25.0386	+	13.1264i	0.805603	+	0.422336i
$967$	−15.6603	−	19.4157i	−0.503600	−	0.624366i	0.461217	−	0.887287i	$-0.347413\pi$
$967$	−15.6603	−	19.4157i	−0.503600	−	0.624366i	−0.964817	+	0.262921i	$0.915314\pi$
$968$	5.59881	+	0.435174i	0.179953	+	0.0139870i
$969$	−36.4962	+	25.1362i	−1.17243	+	0.807491i
$970$	−8.86075	−	0.343838i	−0.284502	−	0.0110400i
$971$	14.3218			0.459608			0.229804	−	0.973237i	$-0.426191\pi$
$971$	14.3218			0.459608			0.229804	+	0.973237i	$0.426191\pi$
$972$	−10.6257	−	32.0573i	−0.340820	−	1.02824i
$973$	−52.2928			−1.67643
$974$	26.9143	+	1.04440i	0.862391	+	0.0334647i
$975$	−13.8375	−	6.58339i	−0.443154	−	0.210837i
$976$	13.4554	+	1.04584i	0.430697	+	0.0334764i
$977$	14.0672	+	17.4405i	0.450048	+	0.557972i	0.951673	−	0.307113i	$-0.0993630\pi$
$977$	14.0672	+	17.4405i	0.450048	+	0.557972i	−0.501625	+	0.865085i	$0.667264\pi$
$978$	−72.9588	+	46.1838i	−2.33296	+	1.47680i
$979$	−6.38632	+	2.90294i	−0.204108	+	0.0927783i
$980$	−3.48714	−	0.407589i	−0.111393	−	0.0130199i
$981$	0.549845	−	35.5184i	0.0175552	−	1.13402i
$982$	15.6779	+	21.0591i	0.500302	+	0.672022i
$983$	−0.353053	−	18.2033i	−0.0112606	−	0.580595i	−0.962370	−	0.271742i	$-0.912400\pi$
$983$	−0.353053	−	18.2033i	−0.0112606	−	0.580595i	0.951110	−	0.308854i	$-0.0999453\pi$
$984$	4.25200	+	2.44381i	0.135549	+	0.0779059i
$985$	16.8197	+	5.39303i	0.535921	+	0.171836i
$986$	10.1385	−	4.14204i	0.322876	−	0.131909i
$987$	20.4625	+	6.08247i	0.651329	+	0.193607i
$988$	50.9492	+	7.96831i	1.62091	+	0.253506i
$989$	9.93849	+	33.1969i	0.316026	+	1.05560i
$990$	−35.1395	+	37.5389i	−1.11681	+	1.19306i
$991$	39.3482	−	9.32570i	1.24994	−	0.296241i	0.448209	−	0.893929i	$-0.352062\pi$
$991$	39.3482	−	9.32570i	1.24994	−	0.296241i	0.801728	+	0.597689i	$0.203914\pi$
$992$	−28.9989	−	42.2814i	−0.920716	−	1.34244i
$993$	23.5790	+	0.411163i	0.748256	+	0.0130479i
$994$	0.600566	−	30.9650i	0.0190488	−	0.982151i
$995$	17.0298	−	12.1722i	0.539881	−	0.385884i
$996$	20.6191	−	10.9126i	0.653341	−	0.345778i
$997$	7.51178	−	34.6782i	0.237900	−	1.09827i	−0.689525	−	0.724262i	$-0.742181\pi$
$997$	7.51178	−	34.6782i	0.237900	−	1.09827i	0.927425	−	0.374009i	$-0.122017\pi$
$998$	67.8994	+	24.7134i	2.14932	+	0.782288i
$999$	−10.3039	+	28.8352i	−0.326000	+	0.912305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.4.5	✓	1404
3.2	odd	2		729.2.i.a.64.22		1404
243.61	even	81	inner	243.2.i.a.61.5	yes	1404
243.182	odd	162		729.2.i.a.262.22		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.5	✓	1404	1.1	even	1	trivial
243.2.i.a.61.5	yes	1404	243.61	even	81	inner
729.2.i.a.64.22		1404	3.2	odd	2
729.2.i.a.262.22		1404	243.182	odd	162

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03967 - 0.0791483i) q^{2} +(-0.137599 - 1.72658i) q^{3} +(2.15999 + 0.167888i) q^{4} +(1.00485 + 1.24581i) q^{5} +(0.144001 + 3.53253i) q^{6} +(2.22760 - 1.01257i) q^{7} +(-0.337568 - 0.0394561i) q^{8} +(-2.96213 + 0.475151i) q^{9} +(-1.95095 - 2.62057i) q^{10} +(0.101732 + 5.24528i) q^{11} +(-0.00734214 - 3.75249i) q^{12} +(3.45524 + 1.10788i) q^{13} +(-4.62371 + 1.88899i) q^{14} +(2.01273 - 1.90637i) q^{15} +(-3.59556 - 0.562336i) q^{16} +(-1.11860 - 3.73638i) q^{17} +(6.07937 - 0.734702i) q^{18} +(6.38307 - 1.51282i) q^{19} +(1.96130 + 2.85964i) q^{20} +(-2.05480 - 3.70680i) q^{21} +(0.207655 - 10.7067i) q^{22} +(2.65860 - 1.90025i) q^{23} +(-0.0216748 + 0.588266i) q^{24} +(0.516184 - 2.38297i) q^{25} +(-6.95986 - 2.53318i) q^{26} +(1.22797 + 5.04897i) q^{27} +(4.98160 - 1.81315i) q^{28} +(-0.186172 - 1.36302i) q^{29} +(-4.25617 + 3.72905i) q^{30} +(-4.51437 - 4.42766i) q^{31} +(7.95623 + 1.56255i) q^{32} +(9.04237 - 0.897394i) q^{33} +(1.98584 + 7.70951i) q^{34} +(3.49987 + 1.75770i) q^{35} +(-6.47794 + 0.529016i) q^{36} +(4.92352 + 3.23825i) q^{37} +(-13.1391 + 2.58043i) q^{38} +(1.43740 - 6.11819i) q^{39} +(-0.290049 - 0.460194i) q^{40} +(3.88267 - 7.37108i) q^{41} +(3.89771 + 7.72327i) q^{42} +(-3.43287 + 10.0329i) q^{43} +(-0.660877 + 11.3468i) q^{44} +(-3.56844 - 3.21281i) q^{45} +(-5.57305 + 3.66545i) q^{46} +(-3.59597 + 3.52690i) q^{47} +(-0.476169 + 6.28539i) q^{48} +(-0.665729 + 0.762841i) q^{49} +(-1.24145 + 4.81961i) q^{50} +(-6.29724 + 2.44547i) q^{51} +(7.27729 + 2.97310i) q^{52} +(-5.38254 - 4.51648i) q^{53} +(-2.10504 - 10.3954i) q^{54} +(-6.43241 + 5.39743i) q^{55} +(-0.791920 + 0.253919i) q^{56} +(-3.49030 - 10.8127i) q^{57} +(0.271848 + 2.79484i) q^{58} +(6.04488 - 3.33542i) q^{59} +(4.66752 - 3.77982i) q^{60} +(-3.69728 + 0.287376i) q^{61} +(8.85736 + 9.38825i) q^{62} +(-6.11733 + 4.05782i) q^{63} +(-9.02203 - 2.13826i) q^{64} +(2.09178 + 5.41783i) q^{65} +(-18.5144 + 1.11470i) q^{66} +(0.464082 - 3.39768i) q^{67} +(-1.78887 - 8.25835i) q^{68} +(-3.64675 - 4.32880i) q^{69} +(-6.99945 - 3.86213i) q^{70} +(-2.45599 + 5.69362i) q^{71} +(1.01867 - 0.0435219i) q^{72} +(2.70227 - 3.62977i) q^{73} +(-9.78604 - 6.99464i) q^{74} +(-4.18541 - 0.563336i) q^{75} +(14.0413 - 2.19603i) q^{76} +(5.53783 + 11.5814i) q^{77} +(-3.41606 + 12.3653i) q^{78} +(-6.98054 + 11.0754i) q^{79} +(-2.91242 - 5.04446i) q^{80} +(8.54846 - 2.81492i) q^{81} +(-8.50277 + 14.7272i) q^{82} +(2.89733 + 5.50045i) q^{83} +(-3.81601 - 8.35162i) q^{84} +(3.53082 - 5.14806i) q^{85} +(7.79601 - 20.1922i) q^{86} +(-2.32774 + 0.508991i) q^{87} +(0.172616 - 1.77465i) q^{88} +(0.529625 + 1.22781i) q^{89} +(7.02413 + 6.83550i) q^{90} +(8.81872 - 1.03076i) q^{91} +(6.06156 - 3.65817i) q^{92} +(-7.02352 + 8.40364i) q^{93} +(7.61373 - 6.90909i) q^{94} +(8.29869 + 6.43197i) q^{95} +(1.60310 - 13.9520i) q^{96} +(1.70401 - 2.11264i) q^{97} +(1.41824 - 1.50325i) q^{98} +(-2.79364 - 15.4889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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