LMFDB - Embedded newform 117.2.h.a.16.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(16,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.h (of order $3$, degree $2$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	117.16
Dual form			117.2.h.a.22.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.163365 q^{2} +(0.725052 - 1.57299i) q^{3} -1.97331 q^{4} +(-1.55806 - 2.69863i) q^{5} +(-0.118448 + 0.256972i) q^{6} +(0.0682144 + 0.118151i) q^{7} +0.649100 q^{8} +(-1.94860 - 2.28100i) q^{9} +(0.254532 + 0.440862i) q^{10} +4.17771 q^{11} +(-1.43075 + 3.10400i) q^{12} +(0.300890 + 3.59297i) q^{13} +(-0.0111438 - 0.0193017i) q^{14} +(-5.37459 + 0.494158i) q^{15} +3.84058 q^{16} +(2.67892 - 4.64002i) q^{17} +(0.318333 + 0.372636i) q^{18} +(-0.154748 + 0.268032i) q^{19} +(3.07453 + 5.32524i) q^{20} +(0.235309 - 0.0216351i) q^{21} -0.682491 q^{22} +(0.961735 - 1.66577i) q^{23} +(0.470632 - 1.02103i) q^{24} +(-2.35507 + 4.07910i) q^{25} +(-0.0491549 - 0.586967i) q^{26} +(-5.00083 + 1.41128i) q^{27} +(-0.134608 - 0.233148i) q^{28} -2.75870 q^{29} +(0.878021 - 0.0807282i) q^{30} +(2.28432 + 3.95657i) q^{31} -1.92562 q^{32} +(3.02905 - 6.57149i) q^{33} +(-0.437642 + 0.758018i) q^{34} +(0.212564 - 0.368171i) q^{35} +(3.84519 + 4.50112i) q^{36} +(4.48902 + 7.77522i) q^{37} +(0.0252804 - 0.0437870i) q^{38} +(5.86988 + 2.13180i) q^{39} +(-1.01133 - 1.75168i) q^{40} +(-3.56877 + 6.18129i) q^{41} +(-0.0384413 + 0.00353442i) q^{42} +(-5.32209 - 9.21812i) q^{43} -8.24392 q^{44} +(-3.11955 + 8.81247i) q^{45} +(-0.157114 + 0.272129i) q^{46} +(-0.663436 + 1.14910i) q^{47} +(2.78462 - 6.04120i) q^{48} +(3.49069 - 6.04606i) q^{49} +(0.384737 - 0.666383i) q^{50} +(-5.35636 - 7.57817i) q^{51} +(-0.593749 - 7.09006i) q^{52} +7.10873 q^{53} +(0.816961 - 0.230555i) q^{54} +(-6.50910 - 11.2741i) q^{55} +(0.0442780 + 0.0766917i) q^{56} +(0.309411 + 0.437754i) q^{57} +0.450675 q^{58} -4.80940 q^{59} +(10.6057 - 0.975129i) q^{60} +(3.61647 + 6.26392i) q^{61} +(-0.373179 - 0.646365i) q^{62} +(0.136579 - 0.385825i) q^{63} -7.36659 q^{64} +(9.22731 - 6.41004i) q^{65} +(-0.494842 + 1.07355i) q^{66} +(6.53369 - 11.3167i) q^{67} +(-5.28634 + 9.15621i) q^{68} +(-1.92294 - 2.72057i) q^{69} +(-0.0347255 + 0.0601463i) q^{70} +(2.24787 - 3.89343i) q^{71} +(-1.26484 - 1.48060i) q^{72} +1.18478 q^{73} +(-0.733350 - 1.27020i) q^{74} +(4.70884 + 6.66207i) q^{75} +(0.305366 - 0.528910i) q^{76} +(0.284980 + 0.493599i) q^{77} +(-0.958933 - 0.348261i) q^{78} +(-1.41978 + 2.45913i) q^{79} +(-5.98384 - 10.3643i) q^{80} +(-1.40592 + 8.88951i) q^{81} +(0.583013 - 1.00981i) q^{82} +(-5.19008 + 8.98948i) q^{83} +(-0.464338 + 0.0426928i) q^{84} -16.6956 q^{85} +(0.869443 + 1.50592i) q^{86} +(-2.00020 + 4.33941i) q^{87} +2.71175 q^{88} +(6.17396 + 10.6936i) q^{89} +(0.509626 - 1.43965i) q^{90} +(-0.403988 + 0.280643i) q^{91} +(-1.89780 + 3.28709i) q^{92} +(7.87989 - 0.724505i) q^{93} +(0.108382 - 0.187723i) q^{94} +0.964425 q^{95} +(-1.39617 + 3.02898i) q^{96} +(8.05756 + 13.9561i) q^{97} +(-0.570257 + 0.987715i) q^{98} +(-8.14068 - 9.52935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.163365			−0.115517			−0.0577583	−	0.998331i	$-0.518395\pi$
$2$	−0.163365			−0.115517			−0.0577583	+	0.998331i	$0.518395\pi$
$3$	0.725052	−	1.57299i	0.418609	−	0.908167i
$3$	0.725052	−	1.57299i	0.418609	−	0.908167i
$4$	−1.97331			−0.986656
$5$	−1.55806	−	2.69863i	−0.696783	−	1.20686i	−0.969576	−	0.244791i	$-0.921281\pi$
$5$	−1.55806	−	2.69863i	−0.696783	−	1.20686i	0.272792	−	0.962073i	$-0.412053\pi$
$6$	−0.118448	+	0.256972i	−0.0483563	+	0.104908i
$7$	0.0682144	+	0.118151i	0.0257826	+	0.0446568i	0.878629	−	0.477505i	$-0.158459\pi$
$7$	0.0682144	+	0.118151i	0.0257826	+	0.0446568i	−0.852846	+	0.522162i	$0.825126\pi$
$8$	0.649100			0.229492
$9$	−1.94860	−	2.28100i	−0.649533	−	0.760333i
$10$	0.254532	+	0.440862i	0.0804900	+	0.139413i
$11$	4.17771			1.25963			0.629813	−	0.776747i	$-0.283132\pi$
$11$	4.17771			1.25963			0.629813	+	0.776747i	$0.283132\pi$
$12$	−1.43075	+	3.10400i	−0.413023	+	0.896048i
$13$	0.300890	+	3.59297i	0.0834518	+	0.996512i
$13$	0.300890	+	3.59297i	0.0834518	+	0.996512i
$14$	−0.0111438	−	0.0193017i	−0.00297832	−	0.00515860i
$15$	−5.37459	+	0.494158i	−1.38771	+	0.127591i
$16$	3.84058			0.960146
$17$	2.67892	−	4.64002i	0.649733	−	1.12537i	−0.333453	−	0.942767i	$-0.608214\pi$
$17$	2.67892	−	4.64002i	0.649733	−	1.12537i	0.983186	−	0.182604i	$-0.0584528\pi$
$18$	0.318333	+	0.372636i	0.0750318	+	0.0878311i
$19$	−0.154748	+	0.268032i	−0.0355017	+	0.0614907i	−0.883230	−	0.468939i	$-0.844636\pi$
$19$	−0.154748	+	0.268032i	−0.0355017	+	0.0614907i	0.847729	+	0.530430i	$0.177970\pi$
$20$	3.07453	+	5.32524i	0.687486	+	1.19076i
$21$	0.235309	−	0.0216351i	0.0513486	−	0.00472117i
$22$	−0.682491			−0.145508
$23$	0.961735	−	1.66577i	0.200536	−	0.347338i	−0.748166	−	0.663512i	$-0.769065\pi$
$23$	0.961735	−	1.66577i	0.200536	−	0.347338i	0.948701	+	0.316174i	$0.102398\pi$
$24$	0.470632	−	1.02103i	0.0960673	−	0.208417i
$25$	−2.35507	+	4.07910i	−0.471014	+	0.815821i
$26$	−0.0491549	−	0.586967i	−0.00964007	−	0.115114i
$27$	−5.00083	+	1.41128i	−0.962410	+	0.271602i
$28$	−0.134608	−	0.233148i	−0.0254386	−	0.0440609i
$29$	−2.75870			−0.512278			−0.256139	−	0.966640i	$-0.582450\pi$
$29$	−2.75870			−0.512278			−0.256139	+	0.966640i	$0.582450\pi$
$30$	0.878021	−	0.0807282i	0.160304	−	0.0147389i
$31$	2.28432	+	3.95657i	0.410277	+	0.710620i	0.994920	−	0.100670i	$-0.0320988\pi$
$31$	2.28432	+	3.95657i	0.410277	+	0.710620i	−0.584643	+	0.811291i	$0.698765\pi$
$32$	−1.92562			−0.340404
$33$	3.02905	−	6.57149i	0.527291	−	1.14395i
$34$	−0.437642	+	0.758018i	−0.0750550	+	0.129999i
$35$	0.212564	−	0.368171i	0.0359298	−	0.0622322i
$36$	3.84519	+	4.50112i	0.640866	+	0.750187i
$37$	4.48902	+	7.77522i	0.737991	+	1.27824i	0.953399	+	0.301713i	$0.0975586\pi$
$37$	4.48902	+	7.77522i	0.737991	+	1.27824i	−0.215408	+	0.976524i	$0.569108\pi$
$38$	0.0252804	−	0.0437870i	0.00410103	−	0.00710319i
$39$	5.86988	+	2.13180i	0.939932	+	0.341361i
$40$	−1.01133	−	1.75168i	−0.159906	−	0.276965i
$41$	−3.56877	+	6.18129i	−0.557349	+	0.965356i	0.440368	+	0.897817i	$0.354848\pi$
$41$	−3.56877	+	6.18129i	−0.557349	+	0.965356i	−0.997717	+	0.0675387i	$0.978485\pi$
$42$	−0.0384413	+	0.00353442i	−0.00593162	+	0.000545373i
$43$	−5.32209	−	9.21812i	−0.811610	−	1.40575i	−0.911736	−	0.410776i	$-0.865258\pi$
$43$	−5.32209	−	9.21812i	−0.811610	−	1.40575i	0.100126	−	0.994975i	$-0.468075\pi$
$44$	−8.24392			−1.24282
$45$	−3.11955	+	8.81247i	−0.465035	+	1.31369i
$46$	−0.157114	+	0.272129i	−0.0231652	+	0.0401233i
$47$	−0.663436	+	1.14910i	−0.0967720	+	0.167614i	−0.910347	−	0.413846i	$-0.864185\pi$
$47$	−0.663436	+	1.14910i	−0.0967720	+	0.167614i	0.813575	+	0.581460i	$0.197518\pi$
$48$	2.78462	−	6.04120i	0.401926	−	0.871972i
$49$	3.49069	−	6.04606i	0.498671	−	0.863723i
$50$	0.384737	−	0.666383i	0.0544100	−	0.0942408i
$51$	−5.35636	−	7.57817i	−0.750040	−	1.06116i
$52$	−0.593749	−	7.09006i	−0.0823382	−	0.983214i
$53$	7.10873			0.976459			0.488230	−	0.872715i	$-0.337643\pi$
$53$	7.10873			0.976459			0.488230	+	0.872715i	$0.337643\pi$
$54$	0.816961	−	0.230555i	0.111174	−	0.0313745i
$55$	−6.50910	−	11.2741i	−0.877687	−	1.52020i
$56$	0.0442780	+	0.0766917i	0.00591689	+	0.0102484i
$57$	0.309411	+	0.437754i	0.0409825	+	0.0579820i
$58$	0.450675			0.0591765
$59$	−4.80940			−0.626131			−0.313066	−	0.949732i	$-0.601356\pi$
$59$	−4.80940			−0.626131			−0.313066	+	0.949732i	$0.601356\pi$
$60$	10.6057	−	0.975129i	1.36920	−	0.125889i
$61$	3.61647	+	6.26392i	0.463042	+	0.802012i	0.999111	−	0.0421621i	$-0.0134246\pi$
$61$	3.61647	+	6.26392i	0.463042	+	0.802012i	−0.536069	+	0.844174i	$0.680091\pi$
$62$	−0.373179	−	0.646365i	−0.0473938	−	0.0820884i
$63$	0.136579	−	0.385825i	0.0172074	−	0.0486094i
$64$	−7.36659			−0.920823
$65$	9.22731	−	6.41004i	1.14451	−	0.795068i
$66$	−0.494842	+	1.07355i	−0.0609108	+	0.132145i
$67$	6.53369	−	11.3167i	0.798218	−	1.38255i	−0.122558	−	0.992461i	$-0.539110\pi$
$67$	6.53369	−	11.3167i	0.798218	−	1.38255i	0.920776	−	0.390092i	$-0.127557\pi$
$68$	−5.28634	+	9.15621i	−0.641063	+	1.11035i
$69$	−1.92294	−	2.72057i	−0.231495	−	0.327518i
$70$	−0.0347255	+	0.0601463i	−0.00415049	+	0.00718885i
$71$	2.24787	−	3.89343i	0.266773	−	0.462065i	−0.701253	−	0.712912i	$-0.747376\pi$
$71$	2.24787	−	3.89343i	0.266773	−	0.462065i	0.968027	+	0.250847i	$0.0807092\pi$
$72$	−1.26484	−	1.48060i	−0.149062	−	0.174490i
$73$	1.18478			0.138668			0.0693340	−	0.997594i	$-0.477913\pi$
$73$	1.18478			0.138668			0.0693340	+	0.997594i	$0.477913\pi$
$74$	−0.733350	−	1.27020i	−0.0852502	−	0.147658i
$75$	4.70884	+	6.66207i	0.543730	+	0.769270i
$76$	0.305366	−	0.528910i	0.0350279	−	0.0606702i
$77$	0.284980	+	0.493599i	0.0324764	+	0.0562509i
$78$	−0.958933	−	0.348261i	−0.108578	−	0.0394328i
$79$	−1.41978	+	2.45913i	−0.159737	+	0.276673i	−0.934774	−	0.355243i	$-0.884398\pi$
$79$	−1.41978	+	2.45913i	−0.159737	+	0.276673i	0.775037	+	0.631916i	$0.217731\pi$
$80$	−5.98384	−	10.3643i	−0.669014	−	1.15877i
$81$	−1.40592	+	8.88951i	−0.156214	+	0.987723i
$82$	0.583013	−	1.00981i	0.0643830	−	0.111515i
$83$	−5.19008	+	8.98948i	−0.569685	+	0.986724i	0.426912	+	0.904293i	$0.359601\pi$
$83$	−5.19008	+	8.98948i	−0.569685	+	0.986724i	−0.996597	+	0.0824302i	$0.973732\pi$
$84$	−0.464338	+	0.0426928i	−0.0506634	+	0.00465817i
$85$	−16.6956			−1.81089
$86$	0.869443	+	1.50592i	0.0937545	+	0.162387i
$87$	−2.00020	+	4.33941i	−0.214444	+	0.465233i
$88$	2.71175			0.289074
$89$	6.17396	+	10.6936i	0.654439	+	1.13352i	0.982034	+	0.188703i	$0.0604284\pi$
$89$	6.17396	+	10.6936i	0.654439	+	1.13352i	−0.327595	+	0.944818i	$0.606238\pi$
$90$	0.509626	−	1.43965i	0.0537193	−	0.151752i
$91$	−0.403988	+	0.280643i	−0.0423494	+	0.0294194i
$92$	−1.89780	+	3.28709i	−0.197860	+	0.342703i
$93$	7.87989	−	0.724505i	0.817107	−	0.0751276i
$94$	0.108382	−	0.187723i	0.0111788	−	0.0193622i
$95$	0.964425			0.0989479
$96$	−1.39617	+	3.02898i	−0.142496	+	0.309144i
$97$	8.05756	+	13.9561i	0.818121	+	1.41703i	0.907065	+	0.420990i	$0.138317\pi$
$97$	8.05756	+	13.9561i	0.818121	+	1.41703i	−0.0889443	+	0.996037i	$0.528349\pi$
$98$	−0.570257	+	0.987715i	−0.0576047	+	0.0997743i
$99$	−8.14068	−	9.52935i	−0.818169	−	0.957736i
$100$	4.64729	−	8.04935i	0.464729	−	0.804935i
$101$	−17.4488			−1.73622			−0.868110	−	0.496373i	$-0.834665\pi$
$101$	−17.4488			−1.73622			−0.868110	+	0.496373i	$0.834665\pi$
$102$	0.875042	+	1.23801i	0.0866421	+	0.122581i
$103$	7.28512	+	12.6182i	0.717824	+	1.24331i	0.961860	+	0.273542i	$0.0881953\pi$
$103$	7.28512	+	12.6182i	0.717824	+	1.24331i	−0.244036	+	0.969766i	$0.578471\pi$
$104$	0.195308	+	2.33220i	0.0191515	+	0.228691i
$105$	−0.425010	−	0.601303i	−0.0414767	−	0.0586812i
$106$	−1.16132			−0.112797
$107$	−2.71632	−	4.70481i	−0.262597	−	0.454831i	0.704334	−	0.709868i	$-0.251246\pi$
$107$	−2.71632	−	4.70481i	−0.262597	−	0.454831i	−0.966931	+	0.255037i	$0.917912\pi$
$108$	9.86819	−	2.78490i	0.949567	−	0.267977i
$109$	−3.10914			−0.297802			−0.148901	−	0.988852i	$-0.547574\pi$
$109$	−3.10914			−0.297802			−0.148901	+	0.988852i	$0.547574\pi$
$110$	1.06336	+	1.84179i	0.101387	+	0.175608i
$111$	15.4851	−	1.42375i	1.46978	−	0.135137i
$112$	0.261983	+	0.453768i	0.0247551	+	0.0428770i
$113$	7.02864			0.661198			0.330599	−	0.943771i	$-0.392749\pi$
$113$	7.02864			0.661198			0.330599	+	0.943771i	$0.392749\pi$
$114$	−0.0505469	−	0.0715138i	−0.00473415	−	0.00669788i
$115$	−5.99374			−0.558919
$116$	5.44377			0.505442
$117$	7.60926	−	7.68760i	0.703477	−	0.710719i
$118$	0.785689			0.0723285
$119$	0.730963			0.0670073
$120$	−3.48865	+	0.320758i	−0.318469	+	0.0292811i
$121$	6.45323			0.586658
$122$	−0.590805	−	1.02331i	−0.0534890	−	0.0926457i
$123$	7.13557	+	10.0954i	0.643393	+	0.910272i
$124$	−4.50768	−	7.80754i	−0.404802	−	0.701138i
$125$	−0.903222			−0.0807866
$126$	−0.0223123	+	0.0630304i	−0.00198774	+	0.00561520i
$127$	0.669477	+	1.15957i	0.0594065	+	0.102895i	0.894199	−	0.447669i	$-0.147746\pi$
$127$	0.669477	+	1.15957i	0.0594065	+	0.102895i	−0.834793	+	0.550564i	$0.814413\pi$
$128$	5.05468			0.446775
$129$	−18.3588	+	1.68797i	−1.61640	+	0.148618i
$130$	−1.50742	+	1.04718i	−0.132209	+	0.0918435i
$131$	−6.59535	−	11.4235i	−0.576238	−	0.998074i	−0.995906	−	0.0903959i	$-0.971187\pi$
$131$	−6.59535	−	11.4235i	−0.576238	−	0.998074i	0.419668	−	0.907678i	$-0.362147\pi$
$132$	−5.97727	+	12.9676i	−0.520255	+	1.12869i
$133$	−0.0422242			−0.00366130
$134$	−1.06738	+	1.84875i	−0.0922074	+	0.159708i
$135$	11.6001	+	11.2965i	0.998378	+	0.972250i
$136$	1.73889	−	3.01184i	0.149108	−	0.258263i
$137$	4.14439	+	7.17829i	0.354079	+	0.613283i	0.986960	−	0.160966i	$-0.0514611\pi$
$137$	4.14439	+	7.17829i	0.354079	+	0.613283i	−0.632881	+	0.774249i	$0.718128\pi$
$138$	0.314141	+	0.444446i	0.0267415	+	0.0378338i
$139$	−6.15797			−0.522313			−0.261156	−	0.965297i	$-0.584104\pi$
$139$	−6.15797			−0.522313			−0.261156	+	0.965297i	$0.584104\pi$
$140$	−0.419454	+	0.726516i	−0.0354503	+	0.0614018i
$141$	1.32650	+	1.87674i	0.111712	+	0.158050i
$142$	−0.367224	+	0.636050i	−0.0308167	+	0.0533761i
$143$	1.25703	+	15.0104i	0.105118	+	1.25523i
$144$	−7.48376	−	8.76037i	−0.623646	−	0.730031i
$145$	4.29821	+	7.44471i	0.356947	+	0.618250i
$146$	−0.193552			−0.0160185
$147$	−6.97946	−	9.87454i	−0.575656	−	0.814438i
$148$	−8.85824	−	15.3429i	−0.728143	−	1.26118i
$149$	−3.97159			−0.325365			−0.162683	−	0.986678i	$-0.552015\pi$
$149$	−3.97159			−0.325365			−0.162683	+	0.986678i	$0.552015\pi$
$150$	−0.769261	−	1.08835i	−0.0628099	−	0.0888634i
$151$	4.38546	−	7.59584i	0.356884	−	0.618141i	−0.630555	−	0.776145i	$-0.717173\pi$
$151$	4.38546	−	7.59584i	0.356884	−	0.618141i	0.987438	+	0.158004i	$0.0505059\pi$
$152$	−0.100447	+	0.173979i	−0.00814734	+	0.0141116i
$153$	−15.8040	+	2.93093i	−1.27768	+	0.236952i
$154$	−0.0465557	−	0.0806369i	−0.00375157	−	0.00649791i
$155$	7.11821	−	12.3291i	0.571748	−	0.990297i
$156$	−11.5831	−	4.20670i	−0.927390	−	0.336806i
$157$	6.29755	+	10.9077i	0.502599	+	0.870527i	0.999995	+	0.00300365i	$0.000956092\pi$
$157$	6.29755	+	10.9077i	0.502599	+	0.870527i	−0.497397	+	0.867523i	$0.665711\pi$
$158$	0.231942	−	0.401735i	0.0184523	−	0.0319604i
$159$	5.15420	−	11.1820i	0.408755	−	0.886787i
$160$	3.00022	+	5.19653i	0.237188	+	0.410822i
$161$	0.262417			0.0206813
$162$	0.229679	−	1.45224i	0.0180453	−	0.114098i
$163$	1.05864	−	1.83361i	0.0829188	−	0.143620i	−0.821584	−	0.570088i	$-0.806909\pi$
$163$	1.05864	−	1.83361i	0.0829188	−	0.143620i	0.904502	+	0.426468i	$0.140242\pi$
$164$	7.04230	−	12.1976i	0.549911	−	0.952474i
$165$	−22.4535	+	2.06445i	−1.74800	+	0.160717i
$166$	0.847878	−	1.46857i	0.0658081	−	0.113983i
$167$	4.66281	−	8.07622i	0.360819	−	0.624956i	−0.627277	−	0.778796i	$-0.715831\pi$
$167$	4.66281	−	8.07622i	0.360819	−	0.624956i	0.988096	+	0.153840i	$0.0491640\pi$
$168$	0.152739	−	0.0140434i	0.0117841	−	0.00108347i
$169$	−12.8189	+	2.16218i	−0.986072	+	0.166321i
$170$	2.72748			0.209188
$171$	0.912923	−	0.169306i	0.0698129	−	0.0129471i
$172$	10.5021	+	18.1902i	0.800780	+	1.38699i
$173$	4.27403	+	7.40284i	0.324948	+	0.562827i	0.981502	−	0.191452i	$-0.0613197\pi$
$173$	4.27403	+	7.40284i	0.324948	+	0.562827i	−0.656553	+	0.754279i	$0.727986\pi$
$174$	0.326763	−	0.708908i	0.0247718	−	0.0537422i
$175$	−0.642599			−0.0485759
$176$	16.0448			1.20942
$177$	−3.48707	+	7.56515i	−0.262104	+	0.568631i
$178$	−1.00861	−	1.74696i	−0.0755985	−	0.130941i
$179$	1.59537	+	2.76327i	0.119244	+	0.206536i	0.919468	−	0.393164i	$-0.128620\pi$
$179$	1.59537	+	2.76327i	0.119244	+	0.206536i	−0.800224	+	0.599701i	$0.795286\pi$
$180$	6.15585	−	17.3898i	0.458830	−	1.29616i
$181$	−1.50392			−0.111786			−0.0558928	−	0.998437i	$-0.517801\pi$
$181$	−1.50392			−0.111786			−0.0558928	+	0.998437i	$0.517801\pi$
$182$	0.0659975	−	0.0458472i	0.00489206	−	0.00339842i
$183$	12.4752	−	1.14701i	0.922194	−	0.0847897i
$184$	0.624262	−	1.08125i	0.0460212	−	0.0797111i
$185$	13.9883	−	24.2284i	1.02844	−	1.78131i
$186$	−1.28730	+	0.118359i	−0.0943894	+	0.00867848i
$187$	11.1917	−	19.3847i	0.818421	−	1.41755i
$188$	1.30917	−	2.26754i	0.0954807	−	0.165377i
$189$	−0.507873	−	0.494582i	−0.0369423	−	0.0359755i
$190$	−0.157553			−0.0114301
$191$	−10.0559	−	17.4174i	−0.727621	−	1.26028i	−0.957886	−	0.287149i	$-0.907292\pi$
$191$	−10.0559	−	17.4174i	−0.727621	−	1.26028i	0.230264	−	0.973128i	$-0.426041\pi$
$192$	−5.34116	+	11.5876i	−0.385465	+	0.836261i
$193$	−3.94854	+	6.83908i	−0.284222	+	0.492287i	−0.972420	−	0.233235i	$-0.925069\pi$
$193$	−3.94854	+	6.83908i	−0.284222	+	0.492287i	0.688198	+	0.725523i	$0.258402\pi$
$194$	−1.31632	−	2.27994i	−0.0945065	−	0.163690i
$195$	−3.39266	−	19.1621i	−0.242953	−	1.37223i
$196$	−6.88823	+	11.9308i	−0.492016	+	0.852197i
$197$	−11.6325	−	20.1482i	−0.828785	−	1.43550i	−0.898992	−	0.437965i	$-0.855699\pi$
$197$	−11.6325	−	20.1482i	−0.828785	−	1.43550i	0.0702072	−	0.997532i	$-0.477634\pi$
$198$	1.32990	+	1.55676i	0.0945120	+	0.110634i
$199$	−4.59323	+	7.95571i	−0.325605	+	0.563965i	−0.981635	−	0.190770i	$-0.938901\pi$
$199$	−4.59323	+	7.95571i	−0.325605	+	0.563965i	0.656029	+	0.754735i	$0.272235\pi$
$200$	−1.52868	+	2.64775i	−0.108094	+	0.187224i
$201$	−13.0638	−	18.4826i	−0.921448	−	1.30366i
$202$	2.85052			0.200562
$203$	−0.188183	−	0.325942i	−0.0132079	−	0.0228767i
$204$	10.5698	+	14.9541i	0.740032	+	1.04700i
$205$	22.2414			1.55340
$206$	−1.19013	−	2.06137i	−0.0829206	−	0.143623i
$207$	−5.67366	+	1.05221i	−0.394347	+	0.0731335i
$208$	1.15559	+	13.7991i	0.0801259	+	0.956797i
$209$	−0.646493	+	1.11976i	−0.0447188	+	0.0774553i
$210$	0.0694317	+	0.0982320i	0.00479125	+	0.00677865i
$211$	−6.24157	+	10.8107i	−0.429687	+	0.744241i	−0.996845	−	0.0793686i	$-0.974710\pi$
$211$	−6.24157	+	10.8107i	−0.429687	+	0.744241i	0.567158	+	0.823609i	$0.308043\pi$
$212$	−14.0277			−0.963429
$213$	−4.49450	−	6.35882i	−0.307958	−	0.435699i
$214$	0.443752	+	0.768602i	0.0303343	+	0.0525405i
$215$	−16.5842	+	28.7247i	−1.13103	+	1.95901i
$216$	−3.24604	+	0.916065i	−0.220865	+	0.0623303i
$217$	−0.311647	+	0.539789i	−0.0211560	+	0.0366433i
$218$	0.507925			0.0344010
$219$	0.859027	−	1.86365i	0.0580477	−	0.125934i
$220$	12.8445	+	22.2473i	0.865975	+	1.49991i
$221$	17.4775	+	8.22915i	1.17567	+	0.553553i
$222$	−2.52973	+	0.232592i	−0.169784	+	0.0156105i
$223$	−9.88798			−0.662148			−0.331074	−	0.943605i	$-0.607411\pi$
$223$	−9.88798			−0.662148			−0.331074	+	0.943605i	$0.607411\pi$
$224$	−0.131355	−	0.227513i	−0.00877651	−	0.0152014i
$225$	13.8935	−	2.57662i	0.926235	−	0.171775i
$226$	−1.14823			−0.0763794
$227$	−5.01892	−	8.69303i	−0.333118	−	0.576977i	0.650004	−	0.759931i	$-0.274767\pi$
$227$	−5.01892	−	8.69303i	−0.333118	−	0.576977i	−0.983121	+	0.182954i	$0.941434\pi$
$228$	−0.610564	−	0.863826i	−0.0404356	−	0.0572083i
$229$	−2.85730	−	4.94899i	−0.188816	−	0.327039i	0.756040	−	0.654526i	$-0.227132\pi$
$229$	−2.85730	−	4.94899i	−0.188816	−	0.327039i	−0.944856	+	0.327487i	$0.893798\pi$
$230$	0.979168			0.0645644
$231$	0.983052	−	0.0903852i	0.0646801	−	0.00594691i
$232$	−1.79067			−0.117563
$233$	20.4987			1.34292			0.671458	−	0.741043i	$-0.265669\pi$
$233$	20.4987			1.34292			0.671458	+	0.741043i	$0.265669\pi$
$234$	−1.24309	+	1.25588i	−0.0812632	+	0.0820998i
$235$	4.13468			0.269717
$236$	9.49046			0.617776
$237$	2.83877	+	4.01629i	0.184398	+	0.260886i
$238$	−0.119414			−0.00774045
$239$	14.9837	+	25.9525i	0.969212	+	1.67872i	0.697845	+	0.716249i	$0.254143\pi$
$239$	14.9837	+	25.9525i	0.969212	+	1.67872i	0.271368	+	0.962476i	$0.412524\pi$
$240$	−20.6416	+	1.89786i	−1.33241	+	0.122506i
$241$	−7.66471	−	13.2757i	−0.493727	−	0.855161i	0.506247	−	0.862389i	$-0.331033\pi$
$241$	−7.66471	−	13.2757i	−0.493727	−	0.855161i	−0.999974	+	0.00722792i	$0.997699\pi$
$242$	−1.05423			−0.0677687
$243$	12.9637	+	8.65686i	0.831625	+	0.555338i
$244$	−7.13643	−	12.3607i	−0.456863	−	0.791310i
$245$	−21.7548			−1.38986
$246$	−1.16570	−	1.64924i	−0.0743225	−	0.105151i
$247$	−1.00959	−	0.475358i	−0.0642389	−	0.0302463i
$248$	1.48276	+	2.56821i	0.0941551	+	0.163081i
$249$	10.3773	+	14.6818i	0.657634	+	0.930420i
$250$	0.147555			0.00933219
$251$	−10.1509	+	17.5818i	−0.640718	+	1.10976i	0.344555	+	0.938766i	$0.388030\pi$
$251$	−10.1509	+	17.5818i	−0.640718	+	1.10976i	−0.985273	+	0.170990i	$0.945304\pi$
$252$	−0.269514	+	0.761354i	−0.0169778	+	0.0479608i
$253$	4.01785	−	6.95911i	0.252600	−	0.437516i
$254$	−0.109369	−	0.189433i	−0.00686243	−	0.0118861i
$255$	−12.1052	+	26.2620i	−0.758056	+	1.64459i
$256$	13.9074			0.869214
$257$	13.9975	−	24.2444i	0.873140	−	1.51232i	0.0144089	−	0.999896i	$-0.495413\pi$
$257$	13.9975	−	24.2444i	0.873140	−	1.51232i	0.858731	−	0.512427i	$-0.171253\pi$
$258$	2.99919	−	0.275756i	0.186721	−	0.0171678i
$259$	−0.612432	+	1.06076i	−0.0380547	+	0.0659126i
$260$	−18.2084	+	12.6490i	−1.12923	+	0.784459i
$261$	5.37560	+	6.29259i	0.332741	+	0.389502i
$262$	1.07745	+	1.86620i	0.0665650	+	0.115294i
$263$	−2.63843			−0.162693			−0.0813464	−	0.996686i	$-0.525922\pi$
$263$	−2.63843			−0.162693			−0.0813464	+	0.996686i	$0.525922\pi$
$264$	1.96616	−	4.26556i	0.121009	−	0.262527i
$265$	−11.0758	−	19.1838i	−0.680381	−	1.17845i
$266$	0.00689796			0.000422941
$267$	21.2974	−	1.95816i	1.30338	−	0.119837i
$268$	−12.8930	+	22.3314i	−0.787566	+	1.36410i
$269$	−1.95848	+	3.39219i	−0.119411	+	0.206826i	−0.919534	−	0.393010i	$-0.871434\pi$
$269$	−1.95848	+	3.39219i	−0.119411	+	0.206826i	0.800124	+	0.599835i	$0.204767\pi$
$270$	−1.89505	−	1.84546i	−0.115329	−	0.112311i
$271$	−9.54824	−	16.5380i	−0.580015	−	1.00461i	−0.995477	−	0.0950042i	$-0.969714\pi$
$271$	−9.54824	−	16.5380i	−0.580015	−	1.00461i	0.415462	−	0.909610i	$-0.363620\pi$
$272$	10.2886	−	17.8204i	0.623839	−	1.08052i
$273$	0.148537	+	0.838950i	0.00898984	+	0.0507755i
$274$	−0.677048	−	1.17268i	−0.0409020	−	0.0708443i
$275$	−9.83880	+	17.0413i	−0.593302	+	1.02763i
$276$	3.79456	+	5.36854i	0.228405	+	0.323148i
$277$	1.48070	+	2.56464i	0.0889664	+	0.154094i	0.907074	−	0.420970i	$-0.138310\pi$
$277$	1.48070	+	2.56464i	0.0889664	+	0.154094i	−0.818108	+	0.575064i	$0.804977\pi$
$278$	1.00600			0.0603358
$279$	4.57369	−	12.9203i	0.273820	−	0.773518i
$280$	0.137975	−	0.238980i	0.00824559	−	0.0142818i
$281$	−2.16169	+	3.74415i	−0.128955	+	0.223357i	−0.923272	−	0.384147i	$-0.874496\pi$
$281$	−2.16169	+	3.74415i	−0.128955	+	0.223357i	0.794317	+	0.607504i	$0.207829\pi$
$282$	−0.216705	−	0.306593i	−0.0129046	−	0.0182574i
$283$	10.8996	−	18.8787i	0.647916	−	1.12222i	−0.335704	−	0.941968i	$-0.608974\pi$
$283$	10.8996	−	18.8787i	0.647916	−	1.12222i	0.983620	−	0.180256i	$-0.0576926\pi$
$284$	−4.43575	+	7.68295i	−0.263213	+	0.455899i
$285$	0.699258	−	1.51703i	0.0414205	−	0.0898612i
$286$	−0.205355	−	2.45217i	−0.0121429	−	0.145000i
$287$	−0.973766			−0.0574796
$288$	3.75226	+	4.39234i	0.221104	+	0.258821i
$289$	−5.85322	−	10.1381i	−0.344307	−	0.596357i
$290$	−0.702177	−	1.21621i	−0.0412332	−	0.0714181i
$291$	27.7950	−	2.55556i	1.62937	−	0.149810i
$292$	−2.33794			−0.136818
$293$	−10.6414			−0.621679			−0.310839	−	0.950462i	$-0.600610\pi$
$293$	−10.6414			−0.621679			−0.310839	+	0.950462i	$0.600610\pi$
$294$	1.14020	+	1.61315i	0.0664978	+	0.0940811i
$295$	7.49332	+	12.9788i	0.436278	+	0.755655i
$296$	2.91383	+	5.04690i	0.169363	+	0.293345i
$297$	−20.8920	+	5.89593i	−1.21228	+	0.342117i
$298$	0.648819			0.0375851
$299$	6.27446	+	2.95427i	0.362861	+	0.170850i
$300$	−9.29202	−	13.1463i	−0.536475	−	0.759004i
$301$	0.726086	−	1.25762i	0.0418509	−	0.0724878i
$302$	−0.716431	+	1.24089i	−0.0412260	+	0.0714055i
$303$	−12.6513	+	27.4468i	−0.726797	+	1.57678i
$304$	−0.594323	+	1.02940i	−0.0340868	+	0.0590400i
$305$	11.2693	−	19.5191i	0.645280	−	1.11766i
$306$	2.58183	−	0.478812i	0.147593	−	0.0273719i
$307$	10.9099			0.622662			0.311331	−	0.950302i	$-0.399225\pi$
$307$	10.9099			0.622662			0.311331	+	0.950302i	$0.399225\pi$
$308$	−0.562354	−	0.974025i	−0.0320431	−	0.0555002i
$309$	25.1304	−	2.31058i	1.42962	−	0.131444i
$310$	−1.16287	+	2.01414i	−0.0660464	+	0.114396i
$311$	−0.145889	−	0.252687i	−0.00827259	−	0.0143285i	0.861859	−	0.507147i	$-0.169300\pi$
$311$	−0.145889	−	0.252687i	−0.00827259	−	0.0143285i	−0.870132	+	0.492819i	$0.835967\pi$
$312$	3.81014	+	1.38375i	0.215707	+	0.0783394i
$313$	4.12641	−	7.14715i	0.233239	−	0.403981i	−0.725521	−	0.688200i	$-0.758401\pi$
$313$	4.12641	−	7.14715i	0.233239	−	0.403981i	0.958759	+	0.284219i	$0.0917344\pi$
$314$	−1.02880	−	1.78193i	−0.0580585	−	0.100560i
$315$	−1.25400	+	0.232560i	−0.0706548	+	0.0131033i
$316$	2.80166	−	4.85262i	0.157606	−	0.272981i
$317$	−7.08881	+	12.2782i	−0.398147	+	0.689611i	−0.993497	−	0.113855i	$-0.963680\pi$
$317$	−7.08881	+	12.2782i	−0.398147	+	0.689611i	0.595350	+	0.803466i	$0.297013\pi$
$318$	−0.842016	+	1.82674i	−0.0472179	+	0.102439i
$319$	−11.5250			−0.645278
$320$	11.4776	+	19.8797i	0.641615	+	1.11131i
$321$	−9.37010	+	0.861519i	−0.522988	+	0.0480853i
$322$	−0.0428697			−0.00238903
$323$	0.829116	+	1.43607i	0.0461332	+	0.0799051i
$324$	2.77433	−	17.5418i	0.154129	−	0.974543i
$325$	−15.3647	−	7.23435i	−0.852282	−	0.401290i
$326$	−0.172944	+	0.299548i	−0.00957849	+	0.0165904i
$327$	−2.25429	+	4.89065i	−0.124662	+	0.270454i
$328$	−2.31649	+	4.01228i	−0.127907	+	0.221541i
$329$	−0.181023			−0.00998014
$330$	3.66811	−	0.337259i	0.201923	−	0.0185655i
$331$	−5.75482	−	9.96765i	−0.316314	−	0.547872i	0.663402	−	0.748263i	$-0.269112\pi$
$331$	−5.75482	−	9.96765i	−0.316314	−	0.547872i	−0.979716	+	0.200392i	$0.935779\pi$
$332$	10.2416	−	17.7390i	0.562083	−	0.973557i
$333$	8.98796	−	25.3902i	0.492537	−	1.39138i
$334$	−0.761740	+	1.31937i	−0.0416805	+	0.0721928i
$335$	−40.7194			−2.22474
$336$	0.903724	−	0.0830915i	0.0493022	−	0.00453301i
$337$	−6.72098	−	11.6411i	−0.366115	−	0.634130i	0.622839	−	0.782350i	$-0.285979\pi$
$337$	−6.72098	−	11.6411i	−0.366115	−	0.634130i	−0.988954	+	0.148220i	$0.952646\pi$
$338$	2.09417	−	0.353224i	0.113908	−	0.0192129i
$339$	5.09613	−	11.0560i	0.276784	−	0.600478i
$340$	32.9457			1.78673
$341$	9.54324	+	16.5294i	0.516795	+	0.895116i
$342$	−0.149140	+	0.0276586i	−0.00806455	+	0.00149561i
$343$	1.90746			0.102993
$344$	−3.45457	−	5.98349i	−0.186258	−	0.322608i
$345$	−4.34578	+	9.42810i	−0.233969	+	0.507592i
$346$	−0.698227	−	1.20937i	−0.0375369	−	0.0650159i
$347$	−8.51438			−0.457076			−0.228538	−	0.973535i	$-0.573394\pi$
$347$	−8.51438			−0.457076			−0.228538	+	0.973535i	$0.573394\pi$
$348$	3.94702	−	8.56301i	0.211582	−	0.459025i
$349$	−10.5936			−0.567064			−0.283532	−	0.958963i	$-0.591506\pi$
$349$	−10.5936			−0.567064			−0.283532	+	0.958963i	$0.591506\pi$
$350$	0.104978			0.00561132
$351$	−6.57541	−	17.5432i	−0.350969	−	0.936387i
$352$	−8.04467			−0.428782
$353$	−1.69055			−0.0899790			−0.0449895	−	0.998987i	$-0.514325\pi$
$353$	−1.69055			−0.0899790			−0.0449895	+	0.998987i	$0.514325\pi$
$354$	0.569665	−	1.23588i	0.0302774	−	0.0656863i
$355$	−14.0092			−0.743533
$356$	−12.1832	−	21.1018i	−0.645706	−	1.11840i
$357$	0.529986	−	1.14980i	0.0280499	−	0.0608538i
$358$	−0.260628	−	0.451421i	−0.0137746	−	0.0238584i
$359$	−31.9604			−1.68680			−0.843402	−	0.537282i	$-0.819451\pi$
$359$	−31.9604			−1.68680			−0.843402	+	0.537282i	$0.819451\pi$
$360$	−2.02490	+	5.72018i	−0.106722	+	0.301480i
$361$	9.45211	+	16.3715i	0.497479	+	0.861659i
$362$	0.245688			0.0129131
$363$	4.67893	−	10.1509i	0.245580	−	0.532783i
$364$	0.797194	−	0.553796i	0.0417843	−	0.0290268i
$365$	−1.84595	−	3.19728i	−0.0966216	−	0.167353i
$366$	−2.03801	+	0.187382i	−0.106529	+	0.00979461i
$367$	18.8213			0.982465			0.491232	−	0.871029i	$-0.336547\pi$
$367$	18.8213			0.982465			0.491232	+	0.871029i	$0.336547\pi$
$368$	3.69362	−	6.39754i	0.192543	−	0.333495i
$369$	21.0536	−	3.90449i	1.09601	−	0.203260i
$370$	−2.28520	+	3.95808i	−0.118802	+	0.205771i
$371$	0.484918	+	0.839902i	0.0251757	+	0.0436055i
$372$	−15.5495	+	1.42967i	−0.806203	+	0.0741251i
$373$	14.5944			0.755671			0.377835	−	0.925873i	$-0.376669\pi$
$373$	14.5944			0.755671			0.377835	+	0.925873i	$0.376669\pi$
$374$	−1.82834	+	3.16678i	−0.0945412	+	0.163750i
$375$	−0.654883	+	1.42076i	−0.0338180	+	0.0733677i
$376$	−0.430636	+	0.745884i	−0.0222084	+	0.0384660i
$377$	−0.830064	−	9.91194i	−0.0427505	−	0.510491i
$378$	0.0829687	+	0.0807974i	0.00426745	+	0.00415577i
$379$	−9.71303	−	16.8235i	−0.498925	−	0.864164i	0.501074	−	0.865404i	$-0.332938\pi$
$379$	−9.71303	−	16.8235i	−0.498925	−	0.864164i	−0.999999	+	0.00124079i	$0.999605\pi$
$380$	−1.90311			−0.0976275
$381$	2.30939	−	0.212334i	0.118314	−	0.0108782i
$382$	1.64279	+	2.84539i	0.0840523	+	0.145583i
$383$	−8.25957			−0.422044			−0.211022	−	0.977481i	$-0.567679\pi$
$383$	−8.25957			−0.422044			−0.211022	+	0.977481i	$0.567679\pi$
$384$	3.66491	−	7.95096i	0.187024	−	0.405746i
$385$	0.888028	−	1.53811i	0.0452581	−	0.0783893i
$386$	0.645054	−	1.11727i	0.0328324	−	0.0568674i
$387$	−10.6559	+	30.1021i	−0.541671	+	1.53018i
$388$	−15.9001	−	27.5397i	−0.807204	−	1.39812i
$389$	3.64491	−	6.31318i	0.184805	−	0.320091i	−0.758706	−	0.651433i	$-0.774168\pi$
$389$	3.64491	−	6.31318i	0.184805	−	0.320091i	0.943511	+	0.331342i	$0.107501\pi$
$390$	0.554242	+	3.13042i	0.0280651	+	0.158515i
$391$	−5.15282	−	8.92494i	−0.260589	−	0.451354i
$392$	2.26581	−	3.92450i	0.114441	−	0.198217i
$393$	−22.7510	+	2.09180i	−1.14764	+	0.105518i
$394$	1.90035	+	3.29151i	0.0957384	+	0.165824i
$395$	8.84837			0.445210
$396$	16.0641	+	18.8044i	0.807251	+	0.944956i
$397$	−4.03967	+	6.99691i	−0.202745	+	0.351165i	−0.949412	−	0.314033i	$-0.898320\pi$
$397$	−4.03967	+	6.99691i	−0.202745	+	0.351165i	0.746667	+	0.665198i	$0.231653\pi$
$398$	0.750373	−	1.29968i	0.0376128	−	0.0651473i
$399$	−0.0306147	+	0.0664183i	−0.00153265	+	0.00332507i
$400$	−9.04485	+	15.6661i	−0.452243	+	0.783307i
$401$	0.0564213	−	0.0977246i	0.00281755	−	0.00488013i	−0.864613	−	0.502438i	$-0.832436\pi$
$401$	0.0564213	−	0.0977246i	0.00281755	−	0.00488013i	0.867431	+	0.497558i	$0.165770\pi$
$402$	2.13417	+	3.01942i	0.106442	+	0.150595i
$403$	−13.5285	+	9.39801i	−0.673903	+	0.468148i
$404$	34.4319			1.71305
$405$	26.1800	−	10.0563i	1.30090	−	0.499700i
$406$	0.0307425	+	0.0532476i	0.00152573	+	0.00264263i
$407$	18.7538	+	32.4826i	0.929592	+	1.61010i
$408$	−3.47681	−	4.91900i	−0.172128	−	0.243527i
$409$	25.5211			1.26194			0.630969	−	0.775808i	$-0.282657\pi$
$409$	25.5211			1.26194			0.630969	+	0.775808i	$0.282657\pi$
$410$	−3.63346			−0.179444
$411$	14.2963	−	1.31445i	0.705183	−	0.0648370i
$412$	−14.3758	−	24.8996i	−0.708246	−	1.22672i
$413$	−0.328071	−	0.568235i	−0.0161433	−	0.0279610i
$414$	0.926879	−	0.171894i	0.0455536	−	0.00844813i
$415$	32.3457			1.58779
$416$	−0.579399	−	6.91870i	−0.0284074	−	0.339217i
$417$	−4.46485	+	9.68644i	−0.218645	+	0.474347i
$418$	0.105614	−	0.182929i	0.00516576	−	0.00894737i
$419$	−7.80239	+	13.5141i	−0.381171	+	0.660208i	−0.991230	−	0.132148i	$-0.957813\pi$
$419$	−7.80239	+	13.5141i	−0.381171	+	0.660208i	0.610059	+	0.792356i	$0.291146\pi$
$420$	0.838677	+	1.18656i	0.0409232	+	0.0578982i
$421$	−4.15567	+	7.19784i	−0.202535	+	0.350801i	−0.949345	−	0.314237i	$-0.898251\pi$
$421$	−4.15567	+	7.19784i	−0.202535	+	0.350801i	0.746809	+	0.665038i	$0.231585\pi$
$422$	1.01965	−	1.76609i	0.0496360	−	0.0859721i
$423$	3.91388	−	0.725846i	0.190299	−	0.0352919i
$424$	4.61428			0.224089
$425$	12.6181	+	21.8552i	0.612068	+	1.06013i
$426$	0.734245	+	1.03881i	0.0355743	+	0.0503305i
$427$	−0.493391	+	0.854578i	−0.0238769	+	0.0413559i
$428$	5.36015	+	9.28406i	0.259093	+	0.448762i
$429$	24.5226	+	8.90602i	1.18396	+	0.429987i
$430$	2.70928	−	4.69261i	0.130653	−	0.226298i
$431$	9.43395	+	16.3401i	0.454417	+	0.787074i	0.998655	−	0.0518573i	$-0.0165141\pi$
$431$	9.43395	+	16.3401i	0.454417	+	0.787074i	−0.544237	+	0.838932i	$0.683181\pi$
$432$	−19.2061	+	5.42015i	−0.924054	+	0.260777i
$433$	−5.44393	+	9.42916i	−0.261619	+	0.453137i	−0.966672	−	0.256017i	$-0.917590\pi$
$433$	−5.44393	+	9.42916i	−0.261619	+	0.453137i	0.705054	+	0.709154i	$0.250923\pi$
$434$	0.0509123	−	0.0881827i	0.00244387	−	0.00423291i
$435$	14.8269	−	1.36323i	0.710895	−	0.0653621i
$436$	6.13531			0.293828
$437$	0.297653	+	0.515551i	0.0142387	+	0.0246621i
$438$	−0.140335	+	0.304455i	−0.00670547	+	0.0145474i
$439$	−35.3376			−1.68657			−0.843285	−	0.537466i	$-0.819382\pi$
$439$	−35.3376			−1.68657			−0.843285	+	0.537466i	$0.819382\pi$
$440$	−4.22506	−	7.31802i	−0.201422	−	0.348873i
$441$	−20.5930	+	3.81907i	−0.980620	+	0.181861i
$442$	−2.85522	−	1.34436i	−0.135809	−	0.0639445i
$443$	4.71029	−	8.15846i	0.223793	−	0.387620i	−0.732164	−	0.681129i	$-0.761489\pi$
$443$	4.71029	−	8.15846i	0.223793	−	0.387620i	0.955957	+	0.293508i	$0.0948228\pi$
$444$	−30.5570	+	2.80951i	−1.45017	+	0.133334i
$445$	19.2388	−	33.3225i	0.912004	−	1.57964i
$446$	1.61535			0.0764891
$447$	−2.87961	+	6.24728i	−0.136201	+	0.295486i
$448$	−0.502507	−	0.870368i	−0.0237412	−	0.0411210i
$449$	−10.8122	+	18.7273i	−0.510259	+	0.883795i	0.489670	+	0.871908i	$0.337117\pi$
$449$	−10.8122	+	18.7273i	−0.510259	+	0.883795i	−0.999929	+	0.0118874i	$0.996216\pi$
$450$	−2.26972	+	0.420930i	−0.106996	+	0.0198428i
$451$	−14.9093	+	25.8236i	−0.702051	+	1.21599i
$452$	−13.8697			−0.652375
$453$	−8.76850	−	12.4057i	−0.411980	−	0.582869i
$454$	0.819917	+	1.42014i	0.0384806	+	0.0666503i
$455$	1.38679	+	0.652957i	0.0650136	+	0.0306111i
$456$	0.200839	+	0.284147i	0.00940514	+	0.0133064i
$457$	21.9147			1.02512			0.512562	−	0.858650i	$-0.328696\pi$
$457$	21.9147			1.02512			0.512562	+	0.858650i	$0.328696\pi$
$458$	0.466784	+	0.808493i	0.0218114	+	0.0377784i
$459$	−6.84842	+	26.9847i	−0.319657	+	1.25954i
$460$	11.8275			0.551461
$461$	16.2574	+	28.1586i	0.757182	+	1.31148i	0.944282	+	0.329136i	$0.106758\pi$
$461$	16.2574	+	28.1586i	0.757182	+	1.31148i	−0.187101	+	0.982341i	$0.559909\pi$
$462$	−0.160596	+	0.0147658i	−0.00747162	+	0.000686966i
$463$	5.55585	+	9.62301i	0.258202	+	0.447219i	0.965760	−	0.259436i	$-0.0835366\pi$
$463$	5.55585	+	9.62301i	0.258202	+	0.447219i	−0.707558	+	0.706655i	$0.750203\pi$
$464$	−10.5950			−0.491861
$465$	−14.2325	−	20.1361i	−0.660015	−	0.933790i
$466$	−3.34877			−0.155129
$467$	−22.2399			−1.02914			−0.514571	−	0.857448i	$-0.672049\pi$
$467$	−22.2399			−1.02914			−0.514571	+	0.857448i	$0.672049\pi$
$468$	−15.0154	+	15.1700i	−0.694089	+	0.701235i
$469$	1.78277			0.0823206
$470$	−0.675462			−0.0311567
$471$	21.7237	−	1.99735i	1.00098	−	0.0920332i
$472$	−3.12179			−0.143692
$473$	−22.2341	−	38.5106i	−1.02233	−	1.77072i
$474$	−0.463756	−	0.656122i	−0.0213010	−	0.0301367i
$475$	−0.728886	−	1.26247i	−0.0334436	−	0.0579260i
$476$	−1.44242			−0.0661131
$477$	−13.8521	−	16.2150i	−0.634242	−	0.742434i
$478$	−2.44781	−	4.23973i	−0.111960	−	0.193921i
$479$	20.0436			0.915814			0.457907	−	0.889000i	$-0.348599\pi$
$479$	20.0436			0.915814			0.457907	+	0.889000i	$0.348599\pi$
$480$	10.3494	−	0.951560i	0.472384	−	0.0434326i
$481$	−26.5854	+	18.4684i	−1.21219	+	0.842088i
$482$	1.25215	+	2.16878i	0.0570337	+	0.0987852i
$483$	0.190266	−	0.412779i	0.00865739	−	0.0187821i
$484$	−12.7342			−0.578829
$485$	25.1082	−	43.4887i	1.14011	−	1.97472i
$486$	−2.11782	−	1.41423i	−0.0960664	−	0.0641507i
$487$	−0.356440	+	0.617373i	−0.0161519	+	0.0279758i	−0.873988	−	0.485947i	$-0.838475\pi$
$487$	−0.356440	+	0.617373i	−0.0161519	+	0.0279758i	0.857837	+	0.513923i	$0.171808\pi$
$488$	2.34745	+	4.06591i	0.106264	+	0.184055i
$489$	−2.11669	−	2.99469i	−0.0957199	−	0.135424i
$490$	3.55397			0.160552
$491$	5.09385	−	8.82281i	0.229882	−	0.398168i	−0.727891	−	0.685693i	$-0.759499\pi$
$491$	5.09385	−	8.82281i	0.229882	−	0.398168i	0.957773	+	0.287525i	$0.0928325\pi$
$492$	−14.0807	−	19.9214i	−0.634807	−	0.898125i
$493$	−7.39033	+	12.8004i	−0.332844	+	0.576502i
$494$	0.164932	+	0.0776569i	0.00742065	+	0.00349395i
$495$	−13.0326	+	36.8159i	−0.585771	+	1.65475i
$496$	8.77314	+	15.1955i	0.393925	+	0.682299i
$497$	0.613349			0.0275124
$498$	−1.69529	−	2.39849i	−0.0759676	−	0.107479i
$499$	19.9631	+	34.5772i	0.893673	+	1.54789i	0.835438	+	0.549584i	$0.185214\pi$
$499$	19.9631	+	34.5772i	0.893673	+	1.54789i	0.0582348	+	0.998303i	$0.481453\pi$
$500$	1.78234			0.0797086
$501$	−9.32303	−	13.1902i	−0.416522	−	0.589296i
$502$	1.65830	−	2.87226i	0.0740135	−	0.128195i
$503$	11.9792	−	20.7485i	0.534125	−	0.925132i	−0.465080	−	0.885269i	$-0.653975\pi$
$503$	11.9792	−	20.7485i	0.534125	−	0.925132i	0.999205	−	0.0398630i	$-0.0126922\pi$
$504$	0.0886538	−	0.250439i	0.00394895	−	0.0111555i
$505$	27.1862	+	47.0878i	1.20977	+	2.09538i
$506$	−0.656376	+	1.13688i	−0.0291795	+	0.0505403i
$507$	−5.89331	+	21.7317i	−0.261731	+	0.965141i
$508$	−1.32109	−	2.28819i	−0.0586137	−	0.101522i
$509$	−7.55690	+	13.0889i	−0.334954	+	0.580157i	−0.983476	−	0.181039i	$-0.942054\pi$
$509$	−7.55690	+	13.0889i	−0.334954	+	0.580157i	0.648522	+	0.761196i	$0.275387\pi$
$510$	1.97757	−	4.29030i	0.0875681	−	0.189978i
$511$	0.0808190	+	0.139983i	0.00357522	+	0.00619247i
$512$	−12.3813			−0.547183
$513$	0.395600	−	1.55877i	0.0174662	−	0.0688216i
$514$	−2.28670	+	3.96068i	−0.100862	+	0.174698i
$515$	22.7012	−	39.3197i	1.00034	−	1.73263i
$516$	36.2277	−	3.33090i	1.59483	−	0.146634i
$517$	−2.77164	+	4.80062i	−0.121897	+	0.211131i
$518$	0.100050	−	0.173292i	0.00439594	−	0.00761400i
$519$	14.7435	−	1.35557i	0.647167	−	0.0595028i
$520$	5.98945	−	4.16076i	0.262655	−	0.182461i
$521$	−19.9265			−0.872994			−0.436497	−	0.899706i	$-0.643781\pi$
$521$	−19.9265			−0.872994			−0.436497	+	0.899706i	$0.643781\pi$
$522$	−0.878185	−	1.02799i	−0.0384371	−	0.0449939i
$523$	7.52452	+	13.0328i	0.329024	+	0.569887i	0.982319	−	0.187217i	$-0.0599469\pi$
$523$	7.52452	+	13.0328i	0.329024	+	0.569887i	−0.653294	+	0.757104i	$0.726614\pi$
$524$	13.0147	+	22.5421i	0.568549	+	0.984755i
$525$	−0.465918	+	1.01080i	−0.0203343	+	0.0441150i
$526$	0.431028			0.0187937
$527$	24.4781			1.06628
$528$	11.6333	−	25.2384i	0.506276	−	1.09836i
$529$	9.65013	+	16.7145i	0.419571	+	0.726718i
$530$	1.80940	+	3.13397i	0.0785952	+	0.136131i
$531$	9.37160	+	10.9703i	0.406693	+	0.476068i
$532$	0.0833215			0.00361245
$533$	−23.2830	−	10.9626i	−1.00850	−	0.474844i
$534$	−3.47925	+	0.319894i	−0.150562	+	0.0138432i
$535$	−8.46436	+	14.6607i	−0.365946	+	0.633838i
$536$	4.24102	−	7.34567i	0.183184	−	0.317285i
$537$	5.50332	−	0.505994i	0.237486	−	0.0218353i
$538$	0.319948	−	0.554166i	0.0137939	−	0.0238918i
$539$	14.5831	−	25.2587i	0.628138	−	1.08797i
$540$	−22.8906	−	22.2916i	−0.985055	−	0.959277i
$541$	−34.9072			−1.50078			−0.750389	−	0.660997i	$-0.770134\pi$
$541$	−34.9072			−1.50078			−0.750389	+	0.660997i	$0.770134\pi$
$542$	1.55985	+	2.70174i	0.0670013	+	0.116050i
$543$	−1.09042	+	2.36566i	−0.0467945	+	0.101520i
$544$	−5.15858	+	8.93491i	−0.221172	+	0.383081i
$545$	4.84421	+	8.39042i	0.207503	+	0.359406i
$546$	−0.0242657	−	0.137055i	−0.00103848	−	0.00586542i
$547$	6.34298	−	10.9864i	0.271206	−	0.469743i	−0.697965	−	0.716132i	$-0.745911\pi$
$547$	6.34298	−	10.9864i	0.271206	−	0.469743i	0.969171	+	0.246389i	$0.0792441\pi$
$548$	−8.17817	−	14.1650i	−0.349354	−	0.605099i
$549$	7.24094	−	20.4550i	0.309036	−	0.873000i
$550$	1.60732	−	2.78395i	0.0685362	−	0.118708i
$551$	0.426904	−	0.739419i	0.0181867	−	0.0315003i
$552$	−1.24818	−	1.76592i	−0.0531261	−	0.0751627i
$553$	−0.387397			−0.0164738
$554$	−0.241894	−	0.418973i	−0.0102771	−	0.0178005i
$555$	−27.9689	−	39.5703i	−1.18721	−	1.67967i
$556$	12.1516			0.515343
$557$	−3.74325	−	6.48350i	−0.158607	−	0.274715i	0.775760	−	0.631028i	$-0.217367\pi$
$557$	−3.74325	−	6.48350i	−0.158607	−	0.274715i	−0.934366	+	0.356314i	$0.884033\pi$
$558$	−0.747182	+	2.11073i	−0.0316307	+	0.0893542i
$559$	31.5191	−	21.8958i	1.33312	−	0.926092i
$560$	0.816368	−	1.41399i	0.0344978	−	0.0597520i
$561$	−22.3773	−	31.6594i	−0.944770	−	1.33666i
$562$	0.353144	−	0.611664i	0.0148965	−	0.0258015i
$563$	−18.5788			−0.783003			−0.391501	−	0.920178i	$-0.628044\pi$
$563$	−18.5788			−0.783003			−0.391501	+	0.920178i	$0.628044\pi$
$564$	−2.61761	−	3.70339i	−0.110221	−	0.155941i
$565$	−10.9510	−	18.9677i	−0.460712	−	0.797977i
$566$	−1.78062	+	3.08412i	−0.0748450	+	0.129635i
$567$	−1.14621	+	0.440281i	−0.0481362	+	0.0184901i
$568$	1.45909	−	2.52723i	0.0612222	−	0.106040i
$569$	26.1468			1.09613			0.548066	−	0.836435i	$-0.315364\pi$
$569$	26.1468			1.09613			0.548066	+	0.836435i	$0.315364\pi$
$570$	−0.114234	+	0.247830i	−0.00478475	+	0.0103805i
$571$	−13.5880	−	23.5351i	−0.568640	−	0.984913i	−0.996701	−	0.0811634i	$-0.974136\pi$
$571$	−13.5880	−	23.5351i	−0.568640	−	0.984913i	0.428061	−	0.903750i	$-0.359197\pi$
$572$	−2.48051	−	29.6202i	−0.103715	−	1.23848i
$573$	−34.6884	+	3.18937i	−1.44913	+	0.133238i
$574$	0.159079			0.00663985
$575$	4.52991	+	7.84603i	0.188910	+	0.327202i
$576$	14.3545	+	16.8032i	0.598105	+	0.700133i
$577$	6.97981			0.290573			0.145287	−	0.989390i	$-0.453590\pi$
$577$	6.97981			0.290573			0.145287	+	0.989390i	$0.453590\pi$
$578$	0.956211	+	1.65621i	0.0397731	+	0.0688891i
$579$	7.89490	+	11.1697i	0.328101	+	0.464197i
$580$	−8.48170	−	14.6907i	−0.352183	−	0.610000i
$581$	−1.41615			−0.0587519
$582$	−4.54073	+	0.417490i	−0.188219	+	0.0173055i
$583$	29.6982			1.22997
$584$	0.769041			0.0318232
$585$	−32.6016	−	8.55689i	−1.34791	−	0.353784i
$586$	1.73844			0.0718142
$587$	45.7017			1.88631			0.943155	−	0.332353i	$-0.107843\pi$
$587$	45.7017			1.88631			0.943155	+	0.332353i	$0.107843\pi$
$588$	13.7726	+	19.4855i	0.567974	+	0.803570i
$589$	−1.41398			−0.0582620
$590$	−1.22415	−	2.12028i	−0.0503973	−	0.0872907i
$591$	−40.1271	+	3.68942i	−1.65061	+	0.151763i
$592$	17.2405	+	29.8614i	0.708579	+	1.22729i
$593$	−18.9869			−0.779700			−0.389850	−	0.920878i	$-0.627473\pi$
$593$	−18.9869			−0.779700			−0.389850	+	0.920878i	$0.627473\pi$
$594$	3.41302	−	0.963189i	0.140038	−	0.0395201i
$595$	−1.13888	−	1.97260i	−0.0466896	−	0.0808687i
$596$	7.83719			0.321024
$597$	9.18392	+	12.9934i	0.375873	+	0.531785i
$598$	−1.02503	−	0.482625i	−0.0419165	−	0.0197360i
$599$	6.44845	+	11.1690i	0.263477	+	0.456355i	0.967163	−	0.254155i	$-0.0817975\pi$
$599$	6.44845	+	11.1690i	0.263477	+	0.456355i	−0.703687	+	0.710510i	$0.748464\pi$
$600$	3.05651	+	4.32435i	0.124782	+	0.176541i
$601$	−23.8355			−0.972269			−0.486135	−	0.873884i	$-0.661593\pi$
$601$	−23.8355			−0.972269			−0.486135	+	0.873884i	$0.661593\pi$
$602$	−0.118617	+	0.205451i	−0.00483447	+	0.00837355i
$603$	−38.5449	+	7.14833i	−1.56967	+	0.291103i
$604$	−8.65388	+	14.9890i	−0.352121	+	0.609892i
$605$	−10.0545	−	17.4149i	−0.408773	−	0.708016i
$606$	2.06678	−	4.48385i	0.0839571	−	0.182144i
$607$	−34.7796			−1.41166			−0.705831	−	0.708380i	$-0.749426\pi$
$607$	−34.7796			−1.41166			−0.705831	+	0.708380i	$0.749426\pi$
$608$	0.297986	−	0.516127i	0.0120849	−	0.0209317i
$609$	−0.649147	+	0.0596848i	−0.0263048	+	0.00241855i
$610$	−1.84102	+	3.18873i	−0.0745405	+	0.129108i
$611$	−4.32832	−	2.03795i	−0.175105	−	0.0824468i
$612$	31.1863	−	5.78364i	1.26063	−	0.233790i
$613$	−20.8146	−	36.0519i	−0.840694	−	1.45612i	−0.889309	−	0.457307i	$-0.848814\pi$
$613$	−20.8146	−	36.0519i	−0.840694	−	1.45612i	0.0486150	−	0.998818i	$-0.484519\pi$
$614$	−1.78230			−0.0719277
$615$	16.1262	−	34.9855i	0.650269	−	1.41075i
$616$	0.184980	+	0.320396i	0.00745307	+	0.0129091i
$617$	−39.2398			−1.57974			−0.789868	−	0.613277i	$-0.789851\pi$
$617$	−39.2398			−1.57974			−0.789868	+	0.613277i	$0.789851\pi$
$618$	−4.10543	+	0.377467i	−0.165145	+	0.0151840i
$619$	15.9718	−	27.6639i	0.641959	−	1.11191i	−0.343035	−	0.939322i	$-0.611455\pi$
$619$	15.9718	−	27.6639i	0.641959	−	1.11191i	0.984995	−	0.172584i	$-0.0552116\pi$
$620$	−14.0464	+	24.3291i	−0.564119	+	0.977082i
$621$	−2.45859	+	9.68753i	−0.0986598	+	0.388747i
$622$	0.0238331	+	0.0412802i	0.000955621	+	0.00165518i
$623$	−0.842306	+	1.45892i	−0.0337463	+	0.0584503i
$624$	22.5437	+	8.18734i	0.902472	+	0.327756i
$625$	13.1826	+	22.8330i	0.527305	+	0.913319i
$626$	−0.674112	+	1.16760i	−0.0269429	+	0.0466665i
$627$	1.29263	+	1.82881i	0.0516226	+	0.0730356i
$628$	−12.4270	−	21.5242i	−0.495892	−	0.858911i
$629$	48.1029			1.91799
$630$	0.204860	−	0.0379922i	0.00816180	−	0.00151364i
$631$	15.2846	−	26.4736i	0.608469	−	1.05390i	−0.383024	−	0.923738i	$-0.625117\pi$
$631$	15.2846	−	26.4736i	0.608469	−	1.05390i	0.991493	−	0.130160i	$-0.0415493\pi$
$632$	−0.921578	+	1.59622i	−0.0366584	+	0.0634942i
$633$	12.4797	+	17.6563i	0.496023	+	0.701774i
$634$	1.15806	−	2.00583i	0.0459926	−	0.0796615i
$635$	2.08616	−	3.61334i	0.0827869	−	0.143391i
$636$	−10.1708	+	22.0655i	−0.403300	+	0.874954i
$637$	22.7736	+	10.7228i	0.902325	+	0.424852i
$638$	1.88279			0.0745403
$639$	−13.2611	+	2.45933i	−0.524601	+	0.0972898i
$640$	−7.87547	−	13.6407i	−0.311305	−	0.539197i
$641$	−18.0877	−	31.3288i	−0.714421	−	1.23741i	−0.963182	−	0.268849i	$-0.913357\pi$
$641$	−18.0877	−	31.3288i	−0.714421	−	1.23741i	0.248761	−	0.968565i	$-0.419977\pi$
$642$	1.53075	−	0.140742i	0.0604138	−	0.00555465i
$643$	−8.27644			−0.326391			−0.163195	−	0.986594i	$-0.552180\pi$
$643$	−8.27644			−0.326391			−0.163195	+	0.986594i	$0.552180\pi$
$644$	−0.517830			−0.0204053
$645$	33.1593	+	46.9137i	1.30564	+	1.84723i
$646$	−0.135449	−	0.234604i	−0.00532915	−	0.00923036i
$647$	6.67339	+	11.5586i	0.262358	+	0.454417i	0.966868	−	0.255277i	$-0.0821666\pi$
$647$	6.67339	+	11.5586i	0.262358	+	0.454417i	−0.704510	+	0.709694i	$0.748833\pi$
$648$	−0.912586	+	5.77018i	−0.0358497	+	0.226674i
$649$	−20.0923			−0.788691
$650$	2.51006	+	1.18184i	0.0984527	+	0.0463556i
$651$	0.623123	+	0.881594i	0.0244221	+	0.0345524i
$652$	−2.08902	+	3.61829i	−0.0818123	+	0.141703i
$653$	−4.85882	+	8.41572i	−0.190140	+	0.329333i	−0.945297	−	0.326212i	$-0.894228\pi$
$653$	−4.85882	+	8.41572i	−0.190140	+	0.329333i	0.755156	+	0.655545i	$0.227561\pi$
$654$	0.368272	−	0.798961i	0.0144006	−	0.0312419i
$655$	−20.5518	+	35.5968i	−0.803026	+	1.39088i
$656$	−13.7062	+	23.7398i	−0.535136	+	0.926883i
$657$	−2.30866	−	2.70248i	−0.0900695	−	0.105434i
$658$	0.0295729			0.00115287
$659$	11.8520	+	20.5283i	0.461689	+	0.799669i	0.999045	−	0.0436865i	$-0.0139103\pi$
$659$	11.8520	+	20.5283i	0.461689	+	0.799669i	−0.537356	+	0.843355i	$0.680577\pi$
$660$	44.3077	−	4.07380i	1.72467	−	0.158573i
$661$	9.86814	−	17.0921i	0.383826	−	0.664807i	−0.607779	−	0.794106i	$-0.707939\pi$
$661$	9.86814	−	17.0921i	0.383826	−	0.664807i	0.991606	+	0.129299i	$0.0412728\pi$
$662$	0.940137	+	1.62837i	0.0365395	+	0.0632882i
$663$	25.6165	−	21.5255i	0.994863	−	0.835979i
$664$	−3.36888	+	5.83507i	−0.130738	+	0.226445i
$665$	0.0657876	+	0.113948i	0.00255114	+	0.00441870i
$666$	−1.46832	+	4.14788i	−0.0568962	+	0.160727i
$667$	−2.65314	+	4.59537i	−0.102730	+	0.177933i
$668$	−9.20117	+	15.9369i	−0.356004	+	0.616617i
$669$	−7.16930	+	15.5537i	−0.277181	+	0.601341i
$670$	6.65213			0.256994
$671$	15.1086	+	26.1688i	0.583260	+	1.01024i
$672$	−0.453115	+	0.0416610i	−0.0174793	+	0.00160711i
$673$	7.08528			0.273117			0.136559	−	0.990632i	$-0.456396\pi$
$673$	7.08528			0.273117			0.136559	+	0.990632i	$0.456396\pi$
$674$	1.09797	+	1.90174i	0.0422923	+	0.0732525i
$675$	6.02053	−	23.7226i	0.231730	−	0.913082i
$676$	25.2957	−	4.26665i	0.972913	−	0.164102i
$677$	−16.5344	+	28.6383i	−0.635467	+	1.10066i	0.350949	+	0.936394i	$0.385859\pi$
$677$	−16.5344	+	28.6383i	−0.635467	+	1.10066i	−0.986416	+	0.164266i	$0.947474\pi$
$678$	−0.832529	+	1.80616i	−0.0319731	+	0.0693652i
$679$	−1.09928	+	1.90401i	−0.0421866	+	0.0730693i
$680$	−10.8371			−0.415585
$681$	−17.3130	+	1.59182i	−0.663437	+	0.0609987i
$682$	−1.55903	−	2.70032i	−0.0596984	−	0.103401i
$683$	6.21557	−	10.7657i	0.237832	−	0.411937i	−0.722260	−	0.691622i	$-0.756896\pi$
$683$	6.21557	−	10.7657i	0.237832	−	0.411937i	0.960092	+	0.279684i	$0.0902298\pi$
$684$	−1.80148	+	0.334093i	−0.0688813	+	0.0127744i
$685$	12.9144	−	22.3683i	0.493433	−	0.854651i
$686$	−0.311613			−0.0118974
$687$	−9.85642	+	0.906233i	−0.376046	+	0.0345749i
$688$	−20.4399	−	35.4030i	−0.779264	−	1.34973i
$689$	2.13894	+	25.5415i	0.0814873	+	0.973053i
$690$	0.709948	−	1.54022i	0.0270273	−	0.0586353i
$691$	−31.8087			−1.21006			−0.605030	−	0.796203i	$-0.706839\pi$
$691$	−31.8087			−1.21006			−0.605030	+	0.796203i	$0.706839\pi$
$692$	−8.43399	−	14.6081i	−0.320612	−	0.555317i
$693$	0.570589	−	1.61187i	0.0216749	−	0.0612297i
$694$	1.39095			0.0527998
$695$	9.59447	+	16.6181i	0.363939	+	0.630361i
$696$	−1.29833	+	2.81671i	−0.0492131	+	0.106767i
$697$	19.1209	+	33.1184i	0.724256	+	1.25445i
$698$	1.73063			0.0655053
$699$	14.8626	−	32.2443i	0.562156	−	1.21959i
$700$	1.26805			0.0479277
$701$	−21.3043			−0.804652			−0.402326	−	0.915496i	$-0.631798\pi$
$701$	−21.3043			−0.804652			−0.402326	+	0.915496i	$0.631798\pi$
$702$	1.07419	+	2.86595i	0.0405428	+	0.108168i
$703$	−2.77867			−0.104800
$704$	−30.7754			−1.15989
$705$	2.99786	−	6.50381i	0.112906	−	0.244948i
$706$	0.276177			0.0103941
$707$	−1.19026	−	2.06159i	−0.0447643	−	0.0775340i
$708$	6.88107	−	14.9284i	0.258607	−	0.561044i
$709$	−3.70329	−	6.41429i	−0.139080	−	0.240894i	0.788069	−	0.615587i	$-0.211081\pi$
$709$	−3.70329	−	6.41429i	−0.139080	−	0.240894i	−0.927149	+	0.374694i	$0.877748\pi$
$710$	2.28862			0.0858904
$711$	8.37584	−	1.55334i	0.314119	−	0.0582548i
$712$	4.00752	+	6.94123i	0.150188	+	0.260134i
$713$	8.78765			0.329100
$714$	−0.0865813	+	0.187837i	−0.00324022	+	0.00702962i
$715$	38.5490	−	26.7793i	1.44165	−	1.00149i
$716$	−3.14817	−	5.45279i	−0.117653	−	0.203780i
$717$	51.6869	−	4.75227i	1.93028	−	0.177477i
$718$	5.22121			0.194854
$719$	19.8553	−	34.3905i	0.740479	−	1.28255i	−0.211798	−	0.977313i	$-0.567932\pi$
$719$	19.8553	−	34.3905i	0.740479	−	1.28255i	0.952277	−	0.305234i	$-0.0987348\pi$
$720$	−11.9809	+	33.8450i	−0.446502	+	1.26133i
$721$	−0.993900	+	1.72149i	−0.0370148	+	0.0641115i
$722$	−1.54414	−	2.67454i	−0.0574671	−	0.0995359i
$723$	−26.4398	+	2.43097i	−0.983307	+	0.0904086i
$724$	2.96771			0.110294
$725$	6.49694	−	11.2530i	0.241290	−	0.417927i
$726$	−0.764374	+	1.65830i	−0.0283686	+	0.0615452i
$727$	−7.16724	+	12.4140i	−0.265818	+	0.460411i	−0.967778	−	0.251806i	$-0.918975\pi$
$727$	−7.16724	+	12.4140i	−0.265818	+	0.460411i	0.701959	+	0.712217i	$0.252309\pi$
$728$	−0.262229	+	0.182165i	−0.00971884	+	0.00675150i
$729$	23.0166	−	14.1152i	0.852465	−	0.522784i
$730$	0.301564	+	0.522325i	0.0111614	+	0.0193321i
$731$	−57.0297			−2.10932
$732$	−24.6175	+	2.26342i	−0.909888	+	0.0836583i
$733$	−3.57055	−	6.18437i	−0.131881	−	0.228425i	0.792521	−	0.609845i	$-0.208768\pi$
$733$	−3.57055	−	6.18437i	−0.131881	−	0.228425i	−0.924402	+	0.381420i	$0.875435\pi$
$734$	−3.07475			−0.113491
$735$	−15.7733	+	34.2201i	−0.581809	+	1.26223i
$736$	−1.85193	+	3.20764i	−0.0682632	+	0.118235i
$737$	27.2959	−	47.2778i	1.00546	−	1.74150i
$738$	−3.43943	+	0.637858i	−0.126607	+	0.0234799i
$739$	−0.0763939	−	0.132318i	−0.00281019	−	0.00486740i	0.864617	−	0.502432i	$-0.167561\pi$
$739$	−0.0763939	−	0.132318i	−0.00281019	−	0.00486740i	−0.867427	+	0.497564i	$0.834228\pi$
$740$	−27.6033	+	47.8102i	−1.01472	+	1.75754i
$741$	−1.47974	+	1.24342i	−0.0543597	+	0.0456782i
$742$	−0.0792186	−	0.137211i	−0.00290821	−	0.00503716i
$743$	−12.0334	+	20.8424i	−0.441462	+	0.764634i	−0.997798	−	0.0663228i	$-0.978873\pi$
$743$	−12.0334	+	20.8424i	−0.441462	+	0.764634i	0.556336	+	0.830957i	$0.312207\pi$
$744$	5.11484	−	0.470276i	0.187519	−	0.0172412i
$745$	6.18796	+	10.7179i	0.226709	+	0.392672i
$746$	−2.38422			−0.0872925
$747$	30.6184	−	5.67832i	1.12027	−	0.207759i
$748$	−22.0848	+	38.2520i	−0.807500	+	1.39863i
$749$	0.370585	−	0.641871i	0.0135409	−	0.0234535i
$750$	0.106985	−	0.232103i	0.00390654	−	0.00847519i
$751$	0.999421	−	1.73105i	0.0364694	−	0.0631669i	−0.847215	−	0.531251i	$-0.821722\pi$
$751$	0.999421	−	1.73105i	0.0364694	−	0.0631669i	0.883684	+	0.468084i	$0.155056\pi$
$752$	−2.54798	+	4.41323i	−0.0929153	+	0.160934i
$753$	20.2961	+	28.7150i	0.739633	+	1.04643i
$754$	0.135604	+	1.61926i	0.00493839	+	0.0589701i
$755$	−27.3312			−0.994683
$756$	1.00219	+	0.975964i	0.0364493	+	0.0354955i
$757$	3.61667	+	6.26425i	0.131450	+	0.227678i	0.924236	−	0.381822i	$-0.124703\pi$
$757$	3.61667	+	6.26425i	0.131450	+	0.227678i	−0.792786	+	0.609500i	$0.791370\pi$
$758$	1.58677	+	2.74837i	0.0576341	+	0.0998252i
$759$	−8.03347	−	11.3658i	−0.291597	−	0.412551i
$760$	0.626009			0.0227077
$761$	18.4602			0.669181			0.334591	−	0.942364i	$-0.391402\pi$
$761$	18.4602			0.669181			0.334591	+	0.942364i	$0.391402\pi$
$762$	−0.377275	+	0.0346879i	−0.0136672	+	0.00125661i
$763$	−0.212088	−	0.367347i	−0.00767811	−	0.0132989i
$764$	19.8435	+	34.3699i	0.717912	+	1.24346i
$765$	32.5331	+	38.0827i	1.17624	+	1.37688i
$766$	1.34932			0.0487531
$767$	−1.44710	−	17.2801i	−0.0522518	−	0.623947i
$768$	10.0836	−	21.8762i	0.363861	−	0.789391i
$769$	−14.4442	+	25.0181i	−0.520872	+	0.902177i	0.478833	+	0.877906i	$0.341060\pi$
$769$	−14.4442	+	25.0181i	−0.520872	+	0.902177i	−0.999705	+	0.0242713i	$0.992273\pi$
$770$	−0.145073	+	0.251273i	−0.00522806	+	0.00905527i
$771$	−27.9873	−	39.5964i	−1.00794	−	1.42603i
$772$	7.79171	−	13.4956i	0.280430	−	0.485718i
$773$	−10.7888	+	18.6867i	−0.388045	+	0.672113i	−0.992186	−	0.124764i	$-0.960183\pi$
$773$	−10.7888	+	18.6867i	−0.388045	+	0.672113i	0.604142	+	0.796877i	$0.293516\pi$
$774$	1.74081	−	4.91763i	0.0625720	−	0.176761i
$775$	−21.5190			−0.772985
$776$	5.23016	+	9.05891i	0.187752	+	0.325196i
$777$	1.22453	+	1.73246i	0.0439296	+	0.0621516i
$778$	−0.595452	+	1.03135i	−0.0213480	+	0.0369758i
$779$	−1.10452	−	1.91309i	−0.0395736	−	0.0685435i
$780$	6.69477	+	37.8128i	0.239711	+	1.35391i
$781$	9.39095	−	16.2656i	0.336035	−	0.582029i
$782$	0.841791	+	1.45802i	0.0301024	+	0.0521388i
$783$	13.7958	−	3.89331i	0.493021	−	0.139136i
$784$	13.4063	−	23.2204i	0.478796	−	0.829300i
$785$	19.6239	−	33.9895i	0.700405	−	1.21314i
$786$	3.71672	−	0.341728i	0.132571	−	0.0121890i
$787$	27.8276			0.991946			0.495973	−	0.868338i	$-0.334811\pi$
$787$	27.8276			0.991946			0.495973	+	0.868338i	$0.334811\pi$
$788$	22.9546	+	39.7586i	0.817725	+	1.41634i
$789$	−1.91300	+	4.15023i	−0.0681047	+	0.147752i
$790$	−1.44551			−0.0514291
$791$	0.479454	+	0.830439i	0.0170474	+	0.0295270i
$792$	−5.28412	−	6.18551i	−0.187763	−	0.219792i
$793$	−21.4179	+	14.8786i	−0.760573	+	0.528356i
$794$	0.659941	−	1.14305i	0.0234204	−	0.0405654i
$795$	−38.2065	+	3.51284i	−1.35505	+	0.124588i
$796$	9.06387	−	15.6991i	0.321260	−	0.556439i
$797$	−38.9009			−1.37794			−0.688970	−	0.724790i	$-0.741937\pi$
$797$	−38.9009			−1.37794			−0.688970	+	0.724790i	$0.741937\pi$
$798$	0.00500138	−	0.0108504i	0.000177047	−	0.000384101i
$799$	3.55458	+	6.15671i	0.125752	+	0.217809i
$800$	4.53497	−	7.85480i	0.160335	−	0.277709i
$801$	12.3616	−	34.9204i	0.436775	−	1.23385i
$802$	−0.00921727	+	0.0159648i	−0.000325473	+	0.000563736i
$803$	4.94966			0.174670
$804$	25.7789	+	36.4720i	0.909152	+	1.28627i
$805$	−0.408859	−	0.708165i	−0.0144104	−	0.0249595i
$806$	2.21009	−	1.53531i	0.0778470	−	0.0540789i
$807$	3.91588	+	5.54019i	0.137846	+	0.195024i
$808$	−11.3260			−0.398448
$809$	11.2678	+	19.5163i	0.396153	+	0.686157i	0.993248	−	0.116013i	$-0.0370116\pi$
$809$	11.2678	+	19.5163i	0.396153	+	0.686157i	−0.597094	+	0.802171i	$0.703678\pi$
$810$	−4.27690	+	1.64284i	−0.150275	+	0.0577237i
$811$	−26.2480			−0.921692			−0.460846	−	0.887480i	$-0.652454\pi$
$811$	−26.2480			−0.921692			−0.460846	+	0.887480i	$0.652454\pi$
$812$	0.371344	+	0.643186i	0.0130316	+	0.0225714i
$813$	−32.9372	+	3.02836i	−1.15516	+	0.106209i
$814$	−3.06372	−	5.30652i	−0.107383	−	0.185993i
$815$	−6.59765			−0.231106
$816$	−20.5715	−	29.1046i	−0.720148	−	1.01887i
$817$	3.29433			0.115254
$818$	−4.16926			−0.145775
$819$	1.42736	+	0.374636i	0.0498759	+	0.0130908i
$820$	−43.8892			−1.53268
$821$	−3.38370			−0.118092			−0.0590460	−	0.998255i	$-0.518806\pi$
$821$	−3.38370			−0.118092			−0.0590460	+	0.998255i	$0.518806\pi$
$822$	−2.33551	+	0.214735i	−0.0814604	+	0.00748975i
$823$	38.6239			1.34634			0.673172	−	0.739486i	$-0.264931\pi$
$823$	38.6239			1.34634			0.673172	+	0.739486i	$0.264931\pi$
$824$	4.72878	+	8.19048i	0.164735	+	0.285329i
$825$	19.6722	+	27.8322i	0.684897	+	0.968992i
$826$	0.0535953	+	0.0928297i	0.00186482	+	0.00322996i
$827$	−11.8393			−0.411694			−0.205847	−	0.978584i	$-0.565995\pi$
$827$	−11.8393			−0.411694			−0.205847	+	0.978584i	$0.565995\pi$
$828$	11.1959	−	2.07633i	0.389085	−	0.0721576i
$829$	−7.44930	−	12.9026i	−0.258725	−	0.448125i	0.707176	−	0.707038i	$-0.249969\pi$
$829$	−7.44930	−	12.9026i	−0.258725	−	0.448125i	−0.965901	+	0.258913i	$0.916636\pi$
$830$	−5.28416			−0.183416
$831$	5.10774	−	0.469623i	0.177185	−	0.0162910i
$832$	−2.21653	−	26.4680i	−0.0768444	−	0.917611i
$833$	−18.7026	−	32.3938i	−0.648006	−	1.12238i
$834$	0.729401	−	1.58243i	0.0252571	−	0.0547949i
$835$	−29.0596			−1.00565
$836$	1.27573	−	2.20963i	0.0441221	−	0.0764217i
$837$	−17.0073	−	16.5623i	−0.587860	−	0.572476i
$838$	1.27464	−	2.20774i	0.0440316	−	0.0762650i
$839$	−26.4068	−	45.7380i	−0.911665	−	1.57905i	−0.811712	−	0.584057i	$-0.801464\pi$
$839$	−26.4068	−	45.7380i	−0.911665	−	1.57905i	−0.0999523	−	0.994992i	$-0.531869\pi$
$840$	−0.275874	−	0.390306i	−0.00951856	−	0.0134668i
$841$	−21.3896			−0.737572
$842$	0.678892	−	1.17588i	0.0233962	−	0.0405233i
$843$	4.32218	+	6.11502i	0.148864	+	0.210612i
$844$	12.3166	−	21.3329i	0.423954	−	0.734309i
$845$	25.8075	+	31.2248i	0.887806	+	1.07416i
$846$	−0.639391	+	0.118578i	−0.0219827	+	0.00407679i
$847$	0.440203	+	0.762455i	0.0151256	+	0.0261982i
$848$	27.3017			0.937543
$849$	−21.7933	−	30.8331i	−0.747942	−	1.05819i
$850$	−2.06136	−	3.57037i	−0.0707039	−	0.122463i
$851$	17.2690			0.591973
$852$	8.86905	+	12.5479i	0.303849	+	0.429885i
$853$	11.5316	−	19.9733i	0.394834	−	0.683873i	−0.598246	−	0.801313i	$-0.704135\pi$
$853$	11.5316	−	19.9733i	0.394834	−	0.683873i	0.993080	+	0.117440i	$0.0374686\pi$
$854$	0.0806029	−	0.139608i	0.00275817	−	0.00477730i
$855$	−1.87928	−	2.19985i	−0.0642699	−	0.0752334i
$856$	−1.76317	−	3.05389i	−0.0602638	−	0.104380i
$857$	−13.4357	+	23.2713i	−0.458955	+	0.794933i	−0.998906	−	0.0467630i	$-0.985109\pi$
$857$	−13.4357	+	23.2713i	−0.458955	+	0.794933i	0.539951	+	0.841696i	$0.318443\pi$
$858$	−4.00614	−	1.45493i	−0.136767	−	0.0496706i
$859$	−15.1421	−	26.2269i	−0.516642	−	0.894850i	−0.999813	−	0.0193240i	$-0.993849\pi$
$859$	−15.1421	−	26.2269i	−0.516642	−	0.894850i	0.483172	−	0.875526i	$-0.339485\pi$
$860$	32.7258	−	56.6828i	1.11594	−	1.93287i
$861$	−0.706031	+	1.53173i	−0.0240615	+	0.0522011i
$862$	−1.54118	−	2.66940i	−0.0524927	−	0.0909201i
$863$	−4.43659			−0.151023			−0.0755116	−	0.997145i	$-0.524059\pi$
$863$	−4.43659			−0.151023			−0.0755116	+	0.997145i	$0.524059\pi$
$864$	9.62968	−	2.71759i	0.327609	−	0.0924544i
$865$	13.3183	−	23.0681i	0.452837	−	0.784337i
$866$	0.889348	−	1.54040i	0.0302213	−	0.0523448i
$867$	−20.1910	+	1.85643i	−0.685721	+	0.0630476i
$868$	0.614978	−	1.06517i	0.0208737	−	0.0361543i
$869$	−5.93141	+	10.2735i	−0.201209	+	0.348505i
$870$	−2.42220	+	0.222705i	−0.0821201	+	0.00755040i
$871$	42.6265	+	20.0703i	1.44434	+	0.680057i
$872$	−2.01814			−0.0683430
$873$	16.1329	−	45.5741i	0.546016	−	1.54245i
$874$	−0.0486262	−	0.0842230i	−0.00164480	−	0.00284889i
$875$	−0.0616127	−	0.106716i	−0.00208289	−	0.00360767i
$876$	−1.69513	+	3.67756i	−0.0572731	+	0.124253i
$877$	8.62930			0.291391			0.145695	−	0.989329i	$-0.453458\pi$
$877$	8.62930			0.291391			0.145695	+	0.989329i	$0.453458\pi$
$878$	5.77293			0.194827
$879$	−7.71559	+	16.7389i	−0.260240	+	0.564588i
$880$	−24.9987	−	43.2991i	−0.842707	−	1.45961i
$881$	16.9018	+	29.2748i	0.569436	+	0.986292i	0.996622	+	0.0821281i	$0.0261717\pi$
$881$	16.9018	+	29.2748i	0.569436	+	0.986292i	−0.427186	+	0.904164i	$0.640495\pi$
$882$	3.36418	−	0.623903i	0.113278	−	0.0210079i
$883$	17.4612			0.587615			0.293807	−	0.955865i	$-0.405078\pi$
$883$	17.4612			0.587615			0.293807	+	0.955865i	$0.405078\pi$
$884$	−34.4887	−	16.2387i	−1.15998	−	0.546166i
$885$	25.8486	−	2.37661i	0.868891	−	0.0798888i
$886$	−0.769497	+	1.33281i	−0.0258518	+	0.0447766i
$887$	17.0959	−	29.6110i	0.574024	−	0.994238i	−0.422123	−	0.906539i	$-0.638715\pi$
$887$	17.0959	−	29.6110i	0.574024	−	0.994238i	0.996147	−	0.0876999i	$-0.0279517\pi$
$888$	10.0514	−	0.924160i	0.337303	−	0.0310128i
$889$	−0.0913359	+	0.158198i	−0.00306331	+	0.00530580i
$890$	−3.14294	+	5.44373i	−0.105352	+	0.182474i
$891$	−5.87354	+	37.1378i	−0.196771	+	1.24416i
$892$	19.5121			0.653312
$893$	−0.205331	−	0.355644i	−0.00687114	−	0.0119012i
$894$	0.470428	−	1.02059i	0.0157335	−	0.0341335i
$895$	4.97136	−	8.61064i	0.166174	−	0.287822i
$896$	0.344802	+	0.597214i	0.0115190	+	0.0199515i
$897$	9.19635	−	7.72766i	0.307057	−	0.258019i
$898$	1.76634	−	3.05938i	0.0589434	−	0.102093i
$899$	−6.30176	−	10.9150i	−0.210176	−	0.364035i
$900$	−27.4163	+	5.08447i	−0.913876	+	0.169482i
$901$	19.0437	−	32.9847i	0.634438	−	1.09888i
$902$	2.43566	−	4.21868i	0.0810985	−	0.140467i
$903$	−1.45177	−	2.05396i	−0.0483119	−	0.0683516i
$904$	4.56229			0.151740
$905$	2.34319	+	4.05853i	0.0778904	+	0.134910i
$906$	1.43247	+	2.02665i	0.0475905	+	0.0673310i
$907$	−15.3735			−0.510467			−0.255234	−	0.966879i	$-0.582152\pi$
$907$	−15.3735			−0.510467			−0.255234	+	0.966879i	$0.582152\pi$
$908$	9.90390	+	17.1541i	0.328672	+	0.569277i
$909$	34.0007	+	39.8007i	1.12773	+	1.32011i
$910$	−0.226553	−	0.106670i	−0.00751014	−	0.00353609i
$911$	24.6800	−	42.7470i	0.817685	−	1.41627i	−0.0896996	−	0.995969i	$-0.528591\pi$
$911$	24.6800	−	42.7470i	0.817685	−	1.41627i	0.907384	−	0.420302i	$-0.138076\pi$
$912$	1.18832	+	1.68123i	0.0393491	+	0.0556712i
$913$	−21.6826	+	37.5554i	−0.717590	+	1.24290i
$914$	−3.58009			−0.118419
$915$	−22.5324	−	31.8789i	−0.744899	−	1.05388i
$916$	5.63835	+	9.76591i	0.186296	+	0.322675i
$917$	0.899795	−	1.55849i	0.0297138	−	0.0514659i
$918$	1.11879	−	4.40835i	0.0369257	−	0.145497i
$919$	−7.37698	+	12.7773i	−0.243344	+	0.421485i	−0.961665	−	0.274228i	$-0.911578\pi$
$919$	−7.37698	+	12.7773i	−0.243344	+	0.421485i	0.718321	+	0.695712i	$0.244911\pi$
$920$	−3.89054			−0.128267
$921$	7.91025	−	17.1612i	0.260652	−	0.565480i
$922$	−2.65589	−	4.60013i	−0.0874670	−	0.151497i
$923$	14.6653	+	6.90505i	0.482716	+	0.227283i
$924$	−1.93987	+	0.178358i	−0.0638170	+	0.00586755i
$925$	−42.2879			−1.39042
$926$	−0.907632	−	1.57206i	−0.0298266	−	0.0516612i
$927$	14.5863	−	41.2052i	0.479078	−	1.35336i
$928$	5.31220			0.174382
$929$	24.1792	+	41.8796i	0.793294	+	1.37403i	0.923917	+	0.382594i	$0.124969\pi$
$929$	24.1792	+	41.8796i	0.793294	+	1.37403i	−0.130622	+	0.991432i	$0.541698\pi$
$930$	2.32509	+	3.28954i	0.0762427	+	0.107868i
$931$	1.08036	+	1.87123i	0.0354073	+	0.0613272i
$932$	−40.4503			−1.32500
$933$	−0.503250	+	0.0462706i	−0.0164757	+	0.00151483i
$934$	3.63323			0.118883
$935$	−69.7494			−2.28105
$936$	4.93918	−	4.99002i	0.161442	−	0.163104i
$937$	26.8065			0.875730			0.437865	−	0.899041i	$-0.355735\pi$
$937$	26.8065			0.875730			0.437865	+	0.899041i	$0.355735\pi$
$938$	−0.291242			−0.00950939
$939$	−8.25054	−	11.6729i	−0.269246	−	0.380930i
$940$	−8.15901			−0.266117
$941$	13.4825	+	23.3523i	0.439516	+	0.761264i	0.997652	−	0.0684856i	$-0.0218167\pi$
$941$	13.4825	+	23.3523i	0.439516	+	0.761264i	−0.558136	+	0.829749i	$0.688483\pi$
$942$	−3.54890	+	0.326298i	−0.115629	+	0.0106314i
$943$	6.86442	+	11.8895i	0.223536	+	0.387176i
$944$	−18.4709			−0.601177
$945$	−0.543400	+	2.14115i	−0.0176768	+	0.0696515i
$946$	3.63228	+	6.29129i	0.118096	+	0.204547i
$947$	−14.0675			−0.457131			−0.228566	−	0.973529i	$-0.573404\pi$
$947$	−14.0675			−0.457131			−0.228566	+	0.973529i	$0.573404\pi$
$948$	−5.60178	−	7.92539i	−0.181937	−	0.257405i
$949$	0.356488	+	4.25688i	0.0115721	+	0.138184i
$950$	0.119075	+	0.206243i	0.00386329	+	0.00669141i
$951$	14.1737	+	20.0529i	0.459614	+	0.650261i
$952$	0.474469			0.0153776
$953$	−20.9114	+	36.2196i	−0.677386	+	1.17327i	0.298380	+	0.954447i	$0.403554\pi$
$953$	−20.9114	+	36.2196i	−0.677386	+	1.17327i	−0.975765	+	0.218819i	$0.929779\pi$
$954$	2.26294	+	2.64897i	0.0732655	+	0.0857635i
$955$	−31.3354	+	54.2745i	−1.01399	+	1.75628i
$956$	−29.5674	−	51.2123i	−0.956279	−	1.65632i
$957$	−8.35625	+	18.1288i	−0.270119	+	0.586020i
$958$	−3.27442			−0.105792
$959$	−0.565414	+	0.979325i	−0.0182582	+	0.0316241i
$960$	39.5924	−	3.64026i	1.27784	−	0.117489i
$961$	5.06373	−	8.77063i	0.163346	−	0.282924i
$962$	4.34313	−	3.01710i	0.140028	−	0.0972751i
$963$	−5.43865	+	15.3637i	−0.175258	+	0.495089i
$964$	15.1249	+	26.1970i	0.487139	+	0.843750i
$965$	24.6082			0.792166
$966$	−0.0310828	+	0.0674336i	−0.00100007	+	0.00216964i
$967$	−10.2769	−	17.8001i	−0.330483	−	0.572413i	0.652124	−	0.758113i	$-0.273878\pi$
$967$	−10.2769	−	17.8001i	−0.330483	−	0.572413i	−0.982607	+	0.185699i	$0.940545\pi$
$968$	4.18880			0.134633
$969$	2.86008	−	0.262965i	0.0918789	−	0.00844766i
$970$	−4.10181	+	7.10454i	−0.131701	+	0.228113i
$971$	2.68759	−	4.65505i	0.0862489	−	0.149388i	−0.819674	−	0.572831i	$-0.805845\pi$
$971$	2.68759	−	4.65505i	0.0862489	−	0.149388i	0.905923	+	0.423443i	$0.139179\pi$
$972$	−25.5815	−	17.0827i	−0.820528	−	0.547927i
$973$	−0.420062	−	0.727569i	−0.0134666	−	0.0233248i
$974$	0.0582299	−	0.100857i	0.00186581	−	0.00323167i
$975$	−22.5198	+	18.9233i	−0.721211	+	0.606031i
$976$	13.8894	+	24.0571i	0.444588	+	0.770049i
$977$	−5.14437	+	8.91031i	−0.164583	+	0.285066i	−0.936507	−	0.350649i	$-0.885961\pi$
$977$	−5.14437	+	8.91031i	−0.164583	+	0.285066i	0.771924	+	0.635715i	$0.219294\pi$
$978$	0.345793	+	0.489227i	0.0110572	+	0.0156438i
$979$	25.7930	+	44.6748i	0.824348	+	1.42781i
$980$	42.9290			1.37132
$981$	6.05847	+	7.09195i	0.193432	+	0.226429i
$982$	−0.832158	+	1.44134i	−0.0265552	+	0.0459950i
$983$	21.7938	−	37.7480i	0.695115	−	1.20397i	−0.275027	−	0.961437i	$-0.588687\pi$
$983$	21.7938	−	37.7480i	0.695115	−	1.20397i	0.970142	−	0.242538i	$-0.0779799\pi$
$984$	4.63170	+	6.55293i	0.147653	+	0.208900i
$985$	−36.2483	+	62.7839i	−1.15497	+	2.00046i
$986$	1.20732	−	2.09114i	0.0384490	−	0.0665956i
$987$	−0.131251	+	0.284748i	−0.00417778	+	0.00906363i
$988$	1.99224	+	0.938030i	0.0633817	+	0.0298427i
$989$	−20.4737			−0.651027
$990$	2.12907	−	6.01444i	0.0676662	−	0.191151i
$991$	1.44149	+	2.49674i	0.0457905	+	0.0793115i	0.888012	−	0.459820i	$-0.152086\pi$
$991$	1.44149	+	2.49674i	0.0457905	+	0.0793115i	−0.842222	+	0.539131i	$0.818753\pi$
$992$	−4.39874	−	7.61883i	−0.139660	−	0.241898i
$993$	−19.8516	+	1.82522i	−0.629970	+	0.0579216i
$994$	−0.100200			−0.00317814
$995$	28.6260			0.907506
$996$	−20.4776	−	28.9717i	−0.648858	−	0.918005i
$997$	2.64813	+	4.58669i	0.0838671	+	0.145262i	0.904908	−	0.425607i	$-0.139940\pi$
$997$	2.64813	+	4.58669i	0.0838671	+	0.145262i	−0.821041	+	0.570870i	$0.806606\pi$
$998$	−3.26128	−	5.64870i	−0.103234	−	0.178807i
$999$	−33.4219	−	32.5472i	−1.05742	−	1.02975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.h.a.16.6	yes	24
3.2	odd	2		351.2.h.a.289.7		24
9.4	even	3		117.2.f.a.94.7	yes	24
9.5	odd	6		351.2.f.a.172.6		24
13.9	even	3		117.2.f.a.61.7	✓	24
39.35	odd	6		351.2.f.a.100.6		24
117.22	even	3	inner	117.2.h.a.22.6	yes	24
117.113	odd	6		351.2.h.a.334.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.7	✓	24	13.9	even	3
117.2.f.a.94.7	yes	24	9.4	even	3
117.2.h.a.16.6	yes	24	1.1	even	1	trivial
117.2.h.a.22.6	yes	24	117.22	even	3	inner
351.2.f.a.100.6		24	39.35	odd	6
351.2.f.a.172.6		24	9.5	odd	6
351.2.h.a.289.7		24	3.2	odd	2
351.2.h.a.334.7		24	117.113	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.163365 q^{2} +(0.725052 - 1.57299i) q^{3} -1.97331 q^{4} +(-1.55806 - 2.69863i) q^{5} +(-0.118448 + 0.256972i) q^{6} +(0.0682144 + 0.118151i) q^{7} +0.649100 q^{8} +(-1.94860 - 2.28100i) q^{9} +(0.254532 + 0.440862i) q^{10} +4.17771 q^{11} +(-1.43075 + 3.10400i) q^{12} +(0.300890 + 3.59297i) q^{13} +(-0.0111438 - 0.0193017i) q^{14} +(-5.37459 + 0.494158i) q^{15} +3.84058 q^{16} +(2.67892 - 4.64002i) q^{17} +(0.318333 + 0.372636i) q^{18} +(-0.154748 + 0.268032i) q^{19} +(3.07453 + 5.32524i) q^{20} +(0.235309 - 0.0216351i) q^{21} -0.682491 q^{22} +(0.961735 - 1.66577i) q^{23} +(0.470632 - 1.02103i) q^{24} +(-2.35507 + 4.07910i) q^{25} +(-0.0491549 - 0.586967i) q^{26} +(-5.00083 + 1.41128i) q^{27} +(-0.134608 - 0.233148i) q^{28} -2.75870 q^{29} +(0.878021 - 0.0807282i) q^{30} +(2.28432 + 3.95657i) q^{31} -1.92562 q^{32} +(3.02905 - 6.57149i) q^{33} +(-0.437642 + 0.758018i) q^{34} +(0.212564 - 0.368171i) q^{35} +(3.84519 + 4.50112i) q^{36} +(4.48902 + 7.77522i) q^{37} +(0.0252804 - 0.0437870i) q^{38} +(5.86988 + 2.13180i) q^{39} +(-1.01133 - 1.75168i) q^{40} +(-3.56877 + 6.18129i) q^{41} +(-0.0384413 + 0.00353442i) q^{42} +(-5.32209 - 9.21812i) q^{43} -8.24392 q^{44} +(-3.11955 + 8.81247i) q^{45} +(-0.157114 + 0.272129i) q^{46} +(-0.663436 + 1.14910i) q^{47} +(2.78462 - 6.04120i) q^{48} +(3.49069 - 6.04606i) q^{49} +(0.384737 - 0.666383i) q^{50} +(-5.35636 - 7.57817i) q^{51} +(-0.593749 - 7.09006i) q^{52} +7.10873 q^{53} +(0.816961 - 0.230555i) q^{54} +(-6.50910 - 11.2741i) q^{55} +(0.0442780 + 0.0766917i) q^{56} +(0.309411 + 0.437754i) q^{57} +0.450675 q^{58} -4.80940 q^{59} +(10.6057 - 0.975129i) q^{60} +(3.61647 + 6.26392i) q^{61} +(-0.373179 - 0.646365i) q^{62} +(0.136579 - 0.385825i) q^{63} -7.36659 q^{64} +(9.22731 - 6.41004i) q^{65} +(-0.494842 + 1.07355i) q^{66} +(6.53369 - 11.3167i) q^{67} +(-5.28634 + 9.15621i) q^{68} +(-1.92294 - 2.72057i) q^{69} +(-0.0347255 + 0.0601463i) q^{70} +(2.24787 - 3.89343i) q^{71} +(-1.26484 - 1.48060i) q^{72} +1.18478 q^{73} +(-0.733350 - 1.27020i) q^{74} +(4.70884 + 6.66207i) q^{75} +(0.305366 - 0.528910i) q^{76} +(0.284980 + 0.493599i) q^{77} +(-0.958933 - 0.348261i) q^{78} +(-1.41978 + 2.45913i) q^{79} +(-5.98384 - 10.3643i) q^{80} +(-1.40592 + 8.88951i) q^{81} +(0.583013 - 1.00981i) q^{82} +(-5.19008 + 8.98948i) q^{83} +(-0.464338 + 0.0426928i) q^{84} -16.6956 q^{85} +(0.869443 + 1.50592i) q^{86} +(-2.00020 + 4.33941i) q^{87} +2.71175 q^{88} +(6.17396 + 10.6936i) q^{89} +(0.509626 - 1.43965i) q^{90} +(-0.403988 + 0.280643i) q^{91} +(-1.89780 + 3.28709i) q^{92} +(7.87989 - 0.724505i) q^{93} +(0.108382 - 0.187723i) q^{94} +0.964425 q^{95} +(-1.39617 + 3.02898i) q^{96} +(8.05756 + 13.9561i) q^{97} +(-0.570257 + 0.987715i) q^{98} +(-8.14068 - 9.52935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

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