LMFDB - Embedded newform 117.2.f.a.94.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(61,117)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.61"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.f (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			94.7
Character	$\chi$	$=$	117.94
Dual form			117.2.f.a.61.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0816825 - 0.141478i) q^{2} +(-1.72478 - 0.158582i) q^{3} +(0.986656 + 1.70894i) q^{4} +(-1.55806 + 2.69863i) q^{5} +(-0.163320 + 0.231065i) q^{6} -0.136429 q^{7} +0.649100 q^{8} +(2.94970 + 0.547036i) q^{9} +(0.254532 + 0.440862i) q^{10} +(-2.08885 + 3.61800i) q^{11} +(-1.43075 - 3.10400i) q^{12} +(2.96116 - 2.05707i) q^{13} +(-0.0111438 + 0.0193017i) q^{14} +(3.11525 - 4.40745i) q^{15} +(-1.92029 + 3.32604i) q^{16} +(2.67892 - 4.64002i) q^{17} +(0.318333 - 0.372636i) q^{18} +(-0.154748 + 0.268032i) q^{19} -6.14906 q^{20} +(0.235309 + 0.0216351i) q^{21} +(0.341246 + 0.591055i) q^{22} -1.92347 q^{23} +(-1.11955 - 0.102936i) 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} +(1.37935 - 2.38910i) q^{29} +(-0.369098 - 0.800752i) q^{30} +(2.28432 - 3.95657i) q^{31} +(0.962809 + 1.66763i) q^{32} +(4.17655 - 5.90899i) q^{33} +(-0.437642 - 0.758018i) q^{34} +(0.212564 - 0.368171i) q^{35} +(1.97549 + 5.58060i) q^{36} +(4.48902 + 7.77522i) q^{37} +(0.0252804 + 0.0437870i) q^{38} +(-5.43355 + 3.07839i) q^{39} +(-1.01133 + 1.75168i) q^{40} +7.13754 q^{41} +(0.0222815 - 0.0315239i) q^{42} +10.6442 q^{43} -8.24392 q^{44} +(-6.07205 + 7.10785i) q^{45} +(-0.157114 + 0.272129i) q^{46} +(-0.663436 - 1.14910i) q^{47} +(3.83952 - 5.43215i) q^{48} -6.98139 q^{49} -0.769473 q^{50} +(-5.35636 + 7.57817i) q^{51} +(6.43705 + 3.03083i) q^{52} +7.10873 q^{53} +(-0.608146 + 0.592231i) q^{54} +(-6.50910 - 11.2741i) q^{55} -0.0885560 q^{56} +(0.309411 - 0.437754i) q^{57} +(-0.225338 - 0.390296i) q^{58} +(2.40470 + 4.16507i) q^{59} +(10.6057 + 0.975129i) q^{60} -7.23295 q^{61} +(-0.373179 - 0.646365i) q^{62} +(-0.402424 - 0.0746315i) q^{63} -7.36659 q^{64} +(0.937606 + 11.1961i) q^{65} +(-0.494842 - 1.07355i) q^{66} -13.0674 q^{67} +10.5727 q^{68} +(3.31755 + 0.305027i) q^{69} +(-0.0347255 - 0.0601463i) q^{70} +(2.24787 - 3.89343i) q^{71} +(1.91465 + 0.355081i) q^{72} +1.18478 q^{73} +1.46670 q^{74} +(3.41510 + 7.40901i) q^{75} -0.610733 q^{76} +(0.284980 - 0.493599i) q^{77} +(-0.00830107 + 1.02018i) q^{78} +(-1.41978 - 2.45913i) q^{79} +(-5.98384 - 10.3643i) q^{80} +(8.40150 + 3.22719i) q^{81} +(0.583013 - 1.00981i) q^{82} +(-5.19008 - 8.98948i) q^{83} +(0.195196 + 0.423475i) q^{84} +(8.34781 + 14.4588i) q^{85} +(0.869443 - 1.50592i) q^{86} +(-2.75794 + 3.90193i) q^{87} +(-1.35588 + 2.34845i) 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} +(-4.56739 + 6.46194i) q^{93} -0.216764 q^{94} +(-0.482212 - 0.835216i) q^{95} +(-1.39617 - 3.02898i) q^{96} -16.1151 q^{97} +(-0.570257 + 0.987715i) q^{98} +(-8.14068 + 9.52935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Character values

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

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

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 $

$2$	0.0816825	−	0.141478i	0.0577583	−	0.100040i	−0.835701	−	0.549185i	$-0.814938\pi$
$2$	0.0816825	−	0.141478i	0.0577583	−	0.100040i	0.893459	+	0.449145i	$0.148271\pi$
$3$	−1.72478	−	0.158582i	−0.995800	−	0.0915573i
$3$	−1.72478	−	0.158582i	−0.995800	−	0.0915573i
$4$	0.986656	+	1.70894i	0.493328	+	0.854469i
$5$	−1.55806	+	2.69863i	−0.696783	+	1.20686i	0.272792	+	0.962073i	$0.412053\pi$
$5$	−1.55806	+	2.69863i	−0.696783	+	1.20686i	−0.969576	+	0.244791i	$0.921281\pi$
$6$	−0.163320	+	0.231065i	−0.0666751	+	0.0943319i
$7$	−0.136429			−0.0515652			−0.0257826	−	0.999668i	$-0.508208\pi$
$7$	−0.136429			−0.0515652			−0.0257826	+	0.999668i	$0.508208\pi$
$8$	0.649100			0.229492
$9$	2.94970	+	0.547036i	0.983235	+	0.182345i
$10$	0.254532	+	0.440862i	0.0804900	+	0.139413i
$11$	−2.08885	+	3.61800i	−0.629813	+	1.09087i	0.357776	+	0.933807i	$0.383535\pi$
$11$	−2.08885	+	3.61800i	−0.629813	+	1.09087i	−0.987589	+	0.157061i	$0.949798\pi$
$12$	−1.43075	−	3.10400i	−0.413023	−	0.896048i
$13$	2.96116	−	2.05707i	0.821279	−	0.570527i
$13$	2.96116	−	2.05707i	0.821279	−	0.570527i
$14$	−0.0111438	+	0.0193017i	−0.00297832	+	0.00515860i
$15$	3.11525	−	4.40745i	0.804354	−	1.13800i
$16$	−1.92029	+	3.32604i	−0.480073	+	0.831511i
$17$	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	$0.177970\pi$
$20$	−6.14906			−1.37497
$21$	0.235309	+	0.0216351i	0.0513486	+	0.00472117i
$22$	0.341246	+	0.591055i	0.0727538	+	0.126013i
$23$	−1.92347			−0.401071			−0.200536	−	0.979686i	$-0.564268\pi$
$23$	−1.92347			−0.401071			−0.200536	+	0.979686i	$0.564268\pi$
$24$	−1.11955	−	0.102936i	−0.228528	−	0.0210116i
$25$	−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
$29$	1.37935	−	2.38910i	0.256139	−	0.443645i	−0.709065	−	0.705143i	$-0.750883\pi$
$29$	1.37935	−	2.38910i	0.256139	−	0.443645i	0.965204	+	0.261497i	$0.0842162\pi$
$30$	−0.369098	−	0.800752i	−0.0673877	−	0.146197i
$31$	2.28432	−	3.95657i	0.410277	−	0.710620i	−0.584643	−	0.811291i	$-0.698765\pi$
$31$	2.28432	−	3.95657i	0.410277	−	0.710620i	0.994920	+	0.100670i	$0.0320988\pi$
$32$	0.962809	+	1.66763i	0.170202	+	0.294799i
$33$	4.17655	−	5.90899i	0.727045	−	1.02862i
$34$	−0.437642	−	0.758018i	−0.0750550	−	0.129999i
$35$	0.212564	−	0.368171i	0.0359298	−	0.0622322i
$36$	1.97549	+	5.58060i	0.329249	+	0.930100i
$37$	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
$39$	−5.43355	+	3.07839i	−0.870065	+	0.492937i
$40$	−1.01133	+	1.75168i	−0.159906	+	0.276965i
$41$	7.13754			1.11470			0.557349	−	0.830279i	$-0.311819\pi$
$41$	7.13754			1.11470			0.557349	+	0.830279i	$0.311819\pi$
$42$	0.0222815	−	0.0315239i	0.00343812	−	0.00486425i
$43$	10.6442			1.62322			0.811610	−	0.584199i	$-0.198591\pi$
$43$	10.6442			1.62322			0.811610	+	0.584199i	$0.198591\pi$
$44$	−8.24392			−1.24282
$45$	−6.07205	+	7.10785i	−0.905168	+	1.05958i
$46$	−0.157114	+	0.272129i	−0.0231652	+	0.0401233i
$47$	−0.663436	−	1.14910i	−0.0967720	−	0.167614i	0.813575	−	0.581460i	$-0.197518\pi$
$47$	−0.663436	−	1.14910i	−0.0967720	−	0.167614i	−0.910347	+	0.413846i	$0.864185\pi$
$48$	3.83952	−	5.43215i	0.554187	−	0.784064i
$49$	−6.98139			−0.997341
$50$	−0.769473			−0.108820
$51$	−5.35636	+	7.57817i	−0.750040	+	1.06116i
$52$	6.43705	+	3.03083i	0.892658	+	0.420300i
$53$	7.10873			0.976459			0.488230	−	0.872715i	$-0.337643\pi$
$53$	7.10873			0.976459			0.488230	+	0.872715i	$0.337643\pi$
$54$	−0.608146	+	0.592231i	−0.0827582	+	0.0805925i
$55$	−6.50910	−	11.2741i	−0.877687	−	1.52020i
$56$	−0.0885560			−0.0118338
$57$	0.309411	−	0.437754i	0.0409825	−	0.0579820i
$58$	−0.225338	−	0.390296i	−0.0295883	−	0.0512484i
$59$	2.40470	+	4.16507i	0.313066	+	0.542246i	0.979024	−	0.203743i	$-0.0653107\pi$
$59$	2.40470	+	4.16507i	0.313066	+	0.542246i	−0.665959	+	0.745989i	$0.731977\pi$
$60$	10.6057	+	0.975129i	1.36920	+	0.125889i
$61$	−7.23295			−0.926084			−0.463042	−	0.886336i	$-0.653242\pi$
$61$	−7.23295			−0.926084			−0.463042	+	0.886336i	$0.653242\pi$
$62$	−0.373179	−	0.646365i	−0.0473938	−	0.0820884i
$63$	−0.402424	−	0.0746315i	−0.0507007	−	0.00940268i
$64$	−7.36659			−0.920823
$65$	0.937606	+	11.1961i	0.116296	+	1.38871i
$66$	−0.494842	−	1.07355i	−0.0609108	−	0.132145i
$67$	−13.0674			−1.59644			−0.798218	−	0.602369i	$-0.794224\pi$
$67$	−13.0674			−1.59644			−0.798218	+	0.602369i	$0.794224\pi$
$68$	10.5727			1.28213
$69$	3.31755	+	0.305027i	0.399386	+	0.0367210i
$70$	−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	$0.0807092\pi$
$72$	1.91465	+	0.355081i	0.225644	+	0.0418467i
$73$	1.18478			0.138668			0.0693340	−	0.997594i	$-0.477913\pi$
$73$	1.18478			0.138668			0.0693340	+	0.997594i	$0.477913\pi$
$74$	1.46670			0.170500
$75$	3.41510	+	7.40901i	0.394342	+	0.855519i
$76$	−0.610733			−0.0700559
$77$	0.284980	−	0.493599i	0.0324764	−	0.0562509i
$78$	−0.00830107	+	1.02018i	−0.000939911	+	0.115513i
$79$	−1.41978	−	2.45913i	−0.159737	−	0.276673i	0.775037	−	0.631916i	$-0.217731\pi$
$79$	−1.41978	−	2.45913i	−0.159737	−	0.276673i	−0.934774	+	0.355243i	$0.884398\pi$
$80$	−5.98384	−	10.3643i	−0.669014	−	1.15877i
$81$	8.40150	+	3.22719i	0.933500	+	0.358577i
$82$	0.583013	−	1.00981i	0.0643830	−	0.111515i
$83$	−5.19008	−	8.98948i	−0.569685	−	0.986724i	−0.996597	−	0.0824302i	$-0.973732\pi$
$83$	−5.19008	−	8.98948i	−0.569685	−	0.986724i	0.426912	−	0.904293i	$-0.359601\pi$
$84$	0.195196	+	0.423475i	0.0212976	+	0.0462049i
$85$	8.34781	+	14.4588i	0.905447	+	1.56828i
$86$	0.869443	−	1.50592i	0.0937545	−	0.162387i
$87$	−2.75794	+	3.90193i	−0.295682	+	0.418331i
$88$	−1.35588	+	2.34845i	−0.144537	+	0.250345i
$89$	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
$93$	−4.56739	+	6.46194i	−0.473616	+	0.670072i
$94$	−0.216764			−0.0223575
$95$	−0.482212	−	0.835216i	−0.0494740	−	0.0856914i
$96$	−1.39617	−	3.02898i	−0.142496	−	0.309144i
$97$	−16.1151			−1.63624			−0.818121	−	0.575046i	$-0.804984\pi$
$97$	−16.1151			−1.63624			−0.818121	+	0.575046i	$0.804984\pi$
$98$	−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
$101$	8.72439	−	15.1111i	0.868110	−	1.50361i	0.00418351	−	0.999991i	$-0.498668\pi$
$101$	8.72439	−	15.1111i	0.868110	−	1.50361i	0.863926	−	0.503619i	$-0.167998\pi$
$102$	0.634626	+	1.37681i	0.0628374	+	0.136325i
$103$	7.28512	−	12.6182i	0.717824	−	1.24331i	−0.244036	−	0.969766i	$-0.578471\pi$
$103$	7.28512	−	12.6182i	0.717824	−	1.24331i	0.961860	−	0.273542i	$-0.0881953\pi$
$104$	1.92209	−	1.33524i	0.188477	−	0.130931i
$105$	−0.425010	+	0.601303i	−0.0414767	+	0.0586812i
$106$	0.580659	−	1.00573i	0.0563986	−	0.0976852i
$107$	−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	$0.917912\pi$
$108$	−2.52230	−	9.93856i	−0.242708	−	0.956338i
$109$	−3.10914			−0.297802			−0.148901	−	0.988852i	$-0.547574\pi$
$109$	−3.10914			−0.297802			−0.148901	+	0.988852i	$0.547574\pi$
$110$	−2.12672			−0.202775
$111$	−6.50955	−	14.1224i	−0.617859	−	1.34044i
$112$	0.261983	−	0.453768i	0.0247551	−	0.0428770i
$113$	−3.51432	−	6.08698i	−0.330599	−	0.572615i	0.652030	−	0.758193i	$-0.273918\pi$
$113$	−3.51432	−	6.08698i	−0.330599	−	0.572615i	−0.982629	+	0.185578i	$0.940584\pi$
$114$	−0.0366593	−	0.0795318i	−0.00343346	−	0.00744884i
$115$	2.99687	−	5.19073i	0.279460	−	0.484038i
$116$	5.44377			0.505442
$117$	9.85984	−	4.44787i	0.911543	−	0.411206i
$118$	0.785689			0.0723285
$119$	−0.365482	+	0.633033i	−0.0335036	+	0.0580300i
$120$	2.02211	−	2.86088i	0.184593	−	0.261161i
$121$	−3.22662	−	5.58866i	−0.293329	−	0.508060i
$122$	−0.590805	+	1.02331i	−0.0534890	+	0.0926457i
$123$	−12.3107	−	1.13188i	−1.11002	−	0.102059i
$124$	9.01537			0.809604
$125$	−0.903222			−0.0807866
$126$	−0.0434298	+	0.0508382i	−0.00386903	+	0.00452903i
$127$	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	$0.814413\pi$
$128$	−2.52734	+	4.37748i	−0.223387	+	0.386918i
$129$	−18.3588	−	1.68797i	−1.61640	−	0.148618i
$130$	1.66059	+	0.781875i	0.145644	+	0.0685750i
$131$	−6.59535	+	11.4235i	−0.576238	+	0.998074i	0.419668	+	0.907678i	$0.362147\pi$
$131$	−6.59535	+	11.4235i	−0.576238	+	0.998074i	−0.995906	+	0.0903959i	$0.971187\pi$
$132$	14.2189	+	1.30734i	1.23760	+	0.113789i
$133$	0.0211121	−	0.0365672i	0.00183065	−	0.00317078i
$134$	−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
$137$	−8.28878			−0.708158			−0.354079	−	0.935216i	$-0.615206\pi$
$137$	−8.28878			−0.708158			−0.354079	+	0.935216i	$0.615206\pi$
$138$	0.314141	−	0.444446i	0.0267415	−	0.0378338i
$139$	3.07899	+	5.33296i	0.261156	+	0.452336i	0.966549	−	0.256480i	$-0.0825629\pi$
$139$	3.07899	+	5.33296i	0.261156	+	0.452336i	−0.705393	+	0.708816i	$0.749230\pi$
$140$	0.838908			0.0709007
$141$	0.962051	+	2.08716i	0.0810193	+	0.175770i
$142$	−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
$146$	0.0967758	−	0.167621i	0.00800923	−	0.0138724i
$147$	12.0413	+	1.10712i	0.993152	+	0.0913138i
$148$	−8.85824	+	15.3429i	−0.728143	+	1.26118i
$149$	1.98580	+	3.43950i	0.162683	+	0.281775i	0.935830	−	0.352452i	$-0.114652\pi$
$149$	1.98580	+	3.43950i	0.162683	+	0.281775i	−0.773147	+	0.634227i	$0.781319\pi$
$150$	1.32717	+	0.122024i	0.108363	+	0.00996325i
$151$	4.38546	+	7.59584i	0.356884	+	0.618141i	0.987438	−	0.158004i	$-0.0505059\pi$
$151$	4.38546	+	7.59584i	0.356884	+	0.618141i	−0.630555	+	0.776145i	$0.717173\pi$
$152$	−0.100447	+	0.173979i	−0.00814734	+	0.0141116i
$153$	10.4403	−	12.2212i	0.844046	−	0.988028i
$154$	−0.0465557	−	0.0806369i	−0.00375157	−	0.00649791i
$155$	7.11821	+	12.3291i	0.571748	+	0.990297i
$156$	−10.6218	−	6.24830i	−0.850427	−	0.500264i
$157$	6.29755	−	10.9077i	0.502599	−	0.870527i	−0.497397	−	0.867523i	$-0.665711\pi$
$157$	6.29755	−	10.9077i	0.502599	−	0.870527i	0.999995	−	0.00300365i	$-0.000956092\pi$
$158$	−0.463884			−0.0369046
$159$	−12.2610	−	1.12732i	−0.972358	−	0.0894019i
$160$	−6.00044			−0.474376
$161$	0.262417			0.0206813
$162$	1.14283	−	0.925025i	0.0897895	−	0.0726769i
$163$	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
$165$	9.43887	+	20.4775i	0.734815	+	1.59417i
$166$	−1.69576			−0.131616
$167$	−9.32561			−0.721637			−0.360819	−	0.932636i	$-0.617503\pi$
$167$	−9.32561			−0.721637			−0.360819	+	0.932636i	$0.617503\pi$
$168$	0.152739	+	0.0140434i	0.0117841	+	0.00108347i
$169$	4.53696	−	12.1826i	0.348997	−	0.937124i
$170$	2.72748			0.209188
$171$	−0.603084	+	0.705961i	−0.0461190	+	0.0539862i
$172$	10.5021	+	18.1902i	0.800780	+	1.38699i
$173$	−8.54806			−0.649897			−0.324948	−	0.945732i	$-0.605347\pi$
$173$	−8.54806			−0.649897			−0.324948	+	0.945732i	$0.605347\pi$
$174$	0.326763	+	0.708908i	0.0247718	+	0.0537422i
$175$	0.321300	+	0.556507i	0.0242880	+	0.0420680i
$176$	−8.02242	−	13.8952i	−0.604712	−	1.04739i
$177$	−3.48707	−	7.56515i	−0.262104	−	0.568631i
$178$	2.01722			0.151197
$179$	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	$0.795286\pi$
$180$	−18.1379	−	3.36376i	−1.35192	−	0.250720i
$181$	−1.50392			−0.111786			−0.0558928	−	0.998437i	$-0.517801\pi$
$181$	−1.50392			−0.111786			−0.0558928	+	0.998437i	$0.517801\pi$
$182$	0.00670614	+	0.0800791i	0.000497092	+	0.00593586i
$183$	12.4752	+	1.14701i	0.922194	+	0.0847897i
$184$	−1.24852			−0.0920425
$185$	−27.9766			−2.05688
$186$	0.541148	+	1.17401i	0.0396789	+	0.0860828i
$187$	11.1917	+	19.3847i	0.818421	+	1.41755i
$188$	1.30917	−	2.26754i	0.0954807	−	0.165377i
$189$	0.682257	+	0.192540i	0.0496269	+	0.0140052i
$190$	−0.157553			−0.0114301
$191$	20.1119			1.45524			0.727621	−	0.685979i	$-0.240626\pi$
$191$	20.1119			1.45524			0.727621	+	0.685979i	$0.240626\pi$
$192$	12.7057	+	1.16821i	0.916956	+	0.0843081i
$193$	7.89708			0.568445			0.284222	−	0.958758i	$-0.408265\pi$
$193$	7.89708			0.568445			0.284222	+	0.958758i	$0.408265\pi$
$194$	−1.31632	+	2.27994i	−0.0945065	+	0.163690i
$195$	0.158339	−	19.4595i	0.0113389	−	1.39352i
$196$	−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	$-0.477634\pi$
$198$	0.683245	+	1.93011i	0.0485561	+	0.137167i
$199$	−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
$201$	22.5383	+	2.07225i	1.58973	+	0.146165i
$202$	−1.42526	−	2.46862i	−0.100281	−	0.173692i
$203$	−0.188183	+	0.325942i	−0.0132079	+	0.0228767i
$204$	−18.2355	−	1.67664i	−1.27674	−	0.117388i
$205$	−11.1207	+	19.2616i	−0.776702	+	1.34529i
$206$	−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
$210$	0.0503555	+	0.109246i	0.00347486	+	0.00753867i
$211$	12.4831			0.859375			0.429687	−	0.902978i	$-0.358624\pi$
$211$	12.4831			0.859375			0.429687	+	0.902978i	$0.358624\pi$
$212$	7.01387	+	12.1484i	0.481715	+	0.834354i
$213$	−4.49450	+	6.35882i	−0.307958	+	0.435699i
$214$	−0.887505			−0.0606686
$215$	−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
$218$	−0.253963	+	0.439876i	−0.0172005	+	0.0297922i
$219$	−2.04348	−	0.187885i	−0.138086	−	0.0126961i
$220$	12.8445	−	22.2473i	0.865975	−	1.49991i
$221$	−1.61212	−	19.2506i	−0.108443	−	1.29493i
$222$	−2.52973	−	0.232592i	−0.169784	−	0.0156105i
$223$	4.94399	−	8.56324i	0.331074	−	0.573437i	−0.651649	−	0.758521i	$-0.725922\pi$
$223$	4.94399	−	8.56324i	0.331074	−	0.573437i	0.982723	+	0.185084i	$0.0592557\pi$
$224$	−0.131355	−	0.227513i	−0.00877651	−	0.0152014i
$225$	−4.71535	−	13.3205i	−0.314356	−	0.888031i
$226$	−1.14823			−0.0763794
$227$	10.0378			0.666235			0.333118	−	0.942885i	$-0.391899\pi$
$227$	10.0378			0.666235			0.333118	+	0.942885i	$0.391899\pi$
$228$	1.05338	+	0.0968511i	0.0697616	+	0.00641412i
$229$	−2.85730	+	4.94899i	−0.188816	+	0.327039i	−0.944856	−	0.327487i	$-0.893798\pi$
$229$	−2.85730	+	4.94899i	−0.188816	+	0.327039i	0.756040	+	0.654526i	$0.227132\pi$
$230$	−0.489584	−	0.847985i	−0.0322822	−	0.0559144i
$231$	−0.569802	+	0.806156i	−0.0374902	+	0.0530411i
$232$	0.895336	−	1.55077i	0.0587817	−	0.101813i
$233$	20.4987			1.34292			0.671458	−	0.741043i	$-0.265669\pi$
$233$	20.4987			1.34292			0.671458	+	0.741043i	$0.265669\pi$
$234$	0.176100	−	1.75827i	0.0115120	−	0.114942i
$235$	4.13468			0.269717
$236$	−4.74523	+	8.21898i	−0.308888	+	0.535010i
$237$	2.05882	+	4.46659i	0.133735	+	0.290136i
$238$	0.0597069	+	0.103415i	0.00387023	+	0.00670343i
$239$	14.9837	−	25.9525i	0.969212	−	1.67872i	0.271368	−	0.962476i	$-0.412524\pi$
$239$	14.9837	−	25.9525i	0.969212	−	1.67872i	0.697845	−	0.716249i	$-0.254143\pi$
$240$	8.67719	+	18.8251i	0.560110	+	1.21515i
$241$	15.3294			0.987455			0.493727	−	0.869617i	$-0.335634\pi$
$241$	15.3294			0.987455			0.493727	+	0.869617i	$0.335634\pi$
$242$	−1.05423			−0.0677687
$243$	−13.9789	−	6.89850i	−0.896749	−	0.442539i
$244$	−7.13643	−	12.3607i	−0.456863	−	0.791310i
$245$	10.8774	−	18.8402i	0.694931	−	1.20366i
$246$	−1.16570	+	1.64924i	−0.0743225	+	0.105151i
$247$	0.0931243	+	1.11201i	0.00592536	+	0.0707557i
$248$	1.48276	−	2.56821i	0.0941551	−	0.163081i
$249$	7.52615	+	16.3279i	0.476951	+	1.03474i
$250$	−0.0737775	+	0.127786i	−0.00466610	+	0.00808192i
$251$	−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
$254$	0.218738			0.0137249
$255$	−12.1052	−	26.2620i	−0.758056	−	1.64459i
$256$	−6.95371	−	12.0442i	−0.434607	−	0.752761i
$257$	−27.9950			−1.74628			−0.873140	−	0.487470i	$-0.837920\pi$
$257$	−27.9950			−1.74628			−0.873140	+	0.487470i	$0.837920\pi$
$258$	−1.73841	+	2.45950i	−0.108228	+	0.153122i
$259$	−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
$263$	1.31922	−	2.28495i	0.0813464	−	0.140896i	−0.822482	−	0.568791i	$-0.807411\pi$
$263$	1.31922	−	2.28495i	0.0813464	−	0.140896i	0.903828	+	0.427895i	$0.140745\pi$
$264$	2.71100	−	3.83552i	0.166851	−	0.236060i
$265$	−11.0758	+	19.1838i	−0.680381	+	1.17845i
$266$	−0.00344898	−	0.00597381i	−0.000211471	−	0.000366278i
$267$	−8.95289	−	19.4232i	−0.547908	−	1.18868i
$268$	−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	$0.204767\pi$
$270$	−0.650688	−	2.56389i	−0.0395996	−	0.156033i
$271$	−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
$273$	0.741293	−	0.419981i	0.0448651	−	0.0254184i
$274$	−0.677048	+	1.17268i	−0.0409020	+	0.0708443i
$275$	19.6776			1.18660
$276$	2.75201	+	5.97045i	0.165652	+	0.359379i
$277$	−2.96139			−0.177933			−0.0889664	−	0.996035i	$-0.528356\pi$
$277$	−2.96139			−0.177933			−0.0889664	+	0.996035i	$0.528356\pi$
$278$	1.00600			0.0603358
$279$	8.90246	−	10.4211i	0.532977	−	0.623894i
$280$	0.137975	−	0.238980i	0.00824559	−	0.0142818i
$281$	−2.16169	−	3.74415i	−0.128955	−	0.223357i	0.794317	−	0.607504i	$-0.207829\pi$
$281$	−2.16169	−	3.74415i	−0.128955	−	0.223357i	−0.923272	+	0.384147i	$0.874496\pi$
$282$	0.373870	+	0.0343749i	0.0222636	+	0.00204700i
$283$	−21.7993			−1.29583			−0.647916	−	0.761712i	$-0.724359\pi$
$283$	−21.7993			−1.29583			−0.647916	+	0.761712i	$0.724359\pi$
$284$	8.87150			0.526427
$285$	0.699258	+	1.51703i	0.0414205	+	0.0898612i
$286$	2.22632	+	1.04824i	0.131645	+	0.0619840i
$287$	−0.973766			−0.0574796
$288$	1.92775	+	5.44572i	0.113593	+	0.320892i
$289$	−5.85322	−	10.1381i	−0.344307	−	0.596357i
$290$	1.40435			0.0824665
$291$	27.7950	+	2.55556i	1.62937	+	0.149810i
$292$	1.16897	+	2.02472i	0.0684088	+	0.118488i
$293$	5.32071	+	9.21574i	0.310839	+	0.538390i	0.978544	−	0.206036i	$-0.0660565\pi$
$293$	5.32071	+	9.21574i	0.310839	+	0.538390i	−0.667705	+	0.744426i	$0.732723\pi$
$294$	1.14020	−	1.61315i	0.0664978	−	0.0940811i
$295$	−14.9866			−0.872556
$296$	2.91383	+	5.04690i	0.169363	+	0.293345i
$297$	15.5520	−	15.1450i	0.902420	−	0.878804i
$298$	0.648819			0.0375851
$299$	−5.69570	+	3.95670i	−0.329391	+	0.228822i
$300$	−9.29202	+	13.1463i	−0.536475	+	0.759004i
$301$	−1.45217			−0.0837018
$302$	1.43286			0.0824519
$303$	−17.4440	+	24.6797i	−1.00213	+	1.41781i
$304$	−0.594323	−	1.02940i	−0.0340868	−	0.0590400i
$305$	11.2693	−	19.5191i	0.645280	−	1.11766i
$306$	−0.876251	−	2.47533i	−0.0500919	−	0.141505i
$307$	10.9099			0.622662			0.311331	−	0.950302i	$-0.399225\pi$
$307$	10.9099			0.622662			0.311331	+	0.950302i	$0.399225\pi$
$308$	1.12471			0.0640862
$309$	−14.5662	+	20.6083i	−0.828643	+	1.17236i
$310$	2.32573			0.132093
$311$	−0.145889	+	0.252687i	−0.00827259	+	0.0143285i	−0.870132	−	0.492819i	$-0.835967\pi$
$311$	−0.145889	+	0.252687i	−0.00827259	+	0.0143285i	0.861859	+	0.507147i	$0.169300\pi$
$312$	−3.52692	+	1.99818i	−0.199673	+	0.113125i
$313$	4.12641	+	7.14715i	0.233239	+	0.403981i	0.958759	−	0.284219i	$-0.0917344\pi$
$313$	4.12641	+	7.14715i	0.233239	+	0.403981i	−0.725521	+	0.688200i	$0.758401\pi$
$314$	−1.02880	−	1.78193i	−0.0580585	−	0.100560i
$315$	0.828402	−	0.969715i	0.0466752	−	0.0546372i
$316$	2.80166	−	4.85262i	0.157606	−	0.272981i
$317$	−7.08881	−	12.2782i	−0.398147	−	0.689611i	0.595350	−	0.803466i	$-0.297013\pi$
$317$	−7.08881	−	12.2782i	−0.398147	−	0.689611i	−0.993497	+	0.113855i	$0.963680\pi$
$318$	−1.16100	+	1.64258i	−0.0651055	+	0.0921112i
$319$	5.76252	+	9.98098i	0.322639	+	0.558827i
$320$	11.4776	−	19.8797i	0.641615	−	1.11131i
$321$	3.93895	+	8.54550i	0.219851	+	0.476963i
$322$	0.0214348	−	0.0371262i	0.00119452	−	0.00206896i
$323$	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
$327$	5.36257	+	0.493053i	0.296551	+	0.0272659i
$328$	4.63298			0.255814
$329$	0.0905117	+	0.156771i	0.00499007	+	0.00864306i
$330$	3.66811	+	0.337259i	0.201923	+	0.0185655i
$331$	11.5096			0.632628			0.316314	−	0.948655i	$-0.397555\pi$
$331$	11.5096			0.632628			0.316314	+	0.948655i	$0.397555\pi$
$332$	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
$335$	20.3597	−	35.2641i	1.11237	−	1.92668i
$336$	−0.523821	+	0.741102i	−0.0285768	+	0.0404304i
$337$	−6.72098	+	11.6411i	−0.366115	+	0.634130i	−0.988954	−	0.148220i	$-0.952646\pi$
$337$	−6.72098	+	11.6411i	−0.366115	+	0.634130i	0.622839	+	0.782350i	$0.285979\pi$
$338$	−1.35298	−	1.63699i	−0.0735926	−	0.0890404i
$339$	5.09613	+	11.0560i	0.276784	+	0.600478i
$340$	−16.4728	+	28.5318i	−0.893365	+	1.54735i
$341$	9.54324	+	16.5294i	0.516795	+	0.895116i
$342$	0.0506167	+	0.142988i	0.00273704	+	0.00773191i
$343$	1.90746			0.102993
$344$	6.90914			0.372516
$345$	−5.99209	+	8.47760i	−0.322603	+	0.456419i
$346$	−0.698227	+	1.20937i	−0.0375369	+	0.0650159i
$347$	4.25719	+	7.37367i	0.228538	+	0.395839i	0.957375	−	0.288848i	$-0.0932722\pi$
$347$	4.25719	+	7.37367i	0.228538	+	0.395839i	−0.728837	+	0.684687i	$0.759939\pi$
$348$	−9.38929	−	0.863284i	−0.503319	−	0.0462769i
$349$	5.29682	−	9.17436i	0.283532	−	0.491092i	−0.688720	−	0.725027i	$-0.741827\pi$
$349$	5.29682	−	9.17436i	0.283532	−	0.491092i	0.972252	+	0.233935i	$0.0751604\pi$
$350$	0.104978			0.00561132
$351$	−17.7114	+	6.10799i	−0.945363	+	0.326020i
$352$	−8.04467			−0.428782
$353$	0.845276	−	1.46406i	0.0449895	−	0.0779241i	−0.842654	−	0.538456i	$-0.819008\pi$
$353$	0.845276	−	1.46406i	0.0449895	−	0.0779241i	0.887643	+	0.460532i	$0.152341\pi$
$354$	−1.35514	−	0.124596i	−0.0720247	−	0.00662220i
$355$	7.00462	+	12.1324i	0.371766	+	0.643918i
$356$	−12.1832	+	21.1018i	−0.645706	+	1.11840i
$357$	0.730761	−	1.03388i	0.0386760	−	0.0547188i
$358$	0.521256			0.0275493
$359$	−31.9604			−1.68680			−0.843402	−	0.537282i	$-0.819451\pi$
$359$	−31.9604			−1.68680			−0.843402	+	0.537282i	$0.819451\pi$
$360$	−3.94137	+	4.61371i	−0.207728	+	0.243164i
$361$	9.45211	+	16.3715i	0.497479	+	0.861659i
$362$	−0.122844	+	0.212772i	−0.00645655	+	0.0111831i
$363$	4.67893	+	10.1509i	0.245580	+	0.532783i
$364$	−0.878198	−	0.413492i	−0.0460301	−	0.0216729i
$365$	−1.84595	+	3.19728i	−0.0966216	+	0.167353i
$366$	1.18128	−	1.67128i	0.0617467	−	0.0873593i
$367$	−9.41066	+	16.2997i	−0.491232	+	0.850840i	−0.999949	−	0.0100944i	$-0.996787\pi$
$367$	−9.41066	+	16.2997i	−0.491232	+	0.850840i	0.508717	+	0.860934i	$0.330120\pi$
$368$	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
$371$	−0.969835			−0.0503513
$372$	−15.5495	−	1.42967i	−0.806203	−	0.0741251i
$373$	−7.29721	−	12.6391i	−0.377835	−	0.654430i	0.612912	−	0.790151i	$-0.289998\pi$
$373$	−7.29721	−	12.6391i	−0.377835	−	0.654430i	−0.990747	+	0.135721i	$0.956665\pi$
$374$	3.65668			0.189082
$375$	1.55786	+	0.143235i	0.0804473	+	0.00739660i
$376$	−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	$0.999605\pi$
$380$	0.951555	−	1.64814i	0.0488138	−	0.0845479i
$381$	−0.970811	−	2.10616i	−0.0497362	−	0.107902i
$382$	1.64279	−	2.84539i	0.0840523	−	0.145583i
$383$	4.12978	+	7.15299i	0.211022	+	0.365501i	0.952035	−	0.305990i	$-0.0989875\pi$
$383$	4.12978	+	7.15299i	0.211022	+	0.365501i	−0.741013	+	0.671491i	$0.765654\pi$
$384$	5.05328	−	7.14938i	0.257874	−	0.364840i
$385$	0.888028	+	1.53811i	0.0452581	+	0.0783893i
$386$	0.645054	−	1.11727i	0.0328324	−	0.0568674i
$387$	31.3972	+	5.82275i	1.59601	+	0.295987i
$388$	−15.9001	−	27.5397i	−0.807204	−	1.39812i
$389$	3.64491	+	6.31318i	0.184805	+	0.320091i	0.943511	−	0.331342i	$-0.107501\pi$
$389$	3.64491	+	6.31318i	0.184805	+	0.320091i	−0.758706	+	0.651433i	$0.774168\pi$
$390$	−2.74016	−	1.61190i	−0.138753	−	0.0816217i
$391$	−5.15282	+	8.92494i	−0.260589	+	0.451354i
$392$	−4.53162			−0.228881
$393$	13.1870	−	18.6570i	0.665199	−	0.941123i
$394$	−3.80070			−0.191477
$395$	8.84837			0.445210
$396$	−24.3171	−	4.50972i	−1.22198	−	0.226622i
$397$	−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
$399$	−0.0422125	+	0.0597223i	−0.00211327	+	0.00298985i
$400$	18.0897			0.904485
$401$	−0.112843			−0.00563509			−0.00281755	−	0.999996i	$-0.500897\pi$
$401$	−0.112843			−0.00563509			−0.00281755	+	0.999996i	$0.500897\pi$
$402$	2.13417	−	3.01942i	0.106442	−	0.150595i
$403$	−1.37466	−	16.4150i	−0.0684767	−	0.817691i
$404$	34.4319			1.71305
$405$	−21.7990	+	17.6444i	−1.08320	+	0.876758i
$406$	0.0307425	+	0.0532476i	0.00152573	+	0.00264263i
$407$	−37.5076			−1.85918
$408$	−3.47681	+	4.91900i	−0.172128	+	0.243527i
$409$	−12.7606	−	22.1019i	−0.630969	−	1.09287i	−0.987354	−	0.158532i	$-0.949324\pi$
$409$	−12.7606	−	22.1019i	−0.630969	−	1.09287i	0.356385	−	0.934339i	$-0.384009\pi$
$410$	1.81673	+	3.14667i	0.0897220	+	0.155403i
$411$	14.2963	+	1.31445i	0.705183	+	0.0648370i
$412$	28.7516			1.41649
$413$	−0.328071	−	0.568235i	−0.0161433	−	0.0279610i
$414$	−0.612304	+	0.716753i	−0.0300931	+	0.0352265i
$415$	32.3457			1.58779
$416$	6.28147	+	2.95757i	0.307974	+	0.145007i
$417$	−4.46485	−	9.68644i	−0.218645	−	0.474347i
$418$	−0.211229			−0.0103315
$419$	15.6048			0.762343			0.381171	−	0.924504i	$-0.375521\pi$
$419$	15.6048			0.762343			0.381171	+	0.924504i	$0.375521\pi$
$420$	−1.44693	−	0.133036i	−0.0706029	−	0.00649147i
$421$	−4.15567	−	7.19784i	−0.202535	−	0.350801i	0.746809	−	0.665038i	$-0.231585\pi$
$421$	−4.15567	−	7.19784i	−0.202535	−	0.350801i	−0.949345	+	0.314237i	$0.898251\pi$
$422$	1.01965	−	1.76609i	0.0496360	−	0.0859721i
$423$	−1.32834	−	3.75244i	−0.0645859	−	0.182450i
$424$	4.61428			0.224089
$425$	−25.2362			−1.22414
$426$	0.532513	+	1.15528i	0.0258003	+	0.0559734i
$427$	0.986782			0.0477537
$428$	5.36015	−	9.28406i	0.259093	−	0.448762i
$429$	0.212282	−	26.0889i	0.0102491	−	1.25958i
$430$	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	$0.683181\pi$
$432$	14.2970	−	13.9229i	0.687867	−	0.669865i
$433$	−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
$435$	−6.23285	−	13.5221i	−0.298842	−	0.648334i
$436$	−3.06765	−	5.31333i	−0.146914	−	0.254462i
$437$	0.297653	−	0.515551i	0.0142387	−	0.0246621i
$438$	−0.193498	+	0.273761i	−0.00924570	+	0.0130808i
$439$	17.6688	−	30.6032i	0.843285	−	1.46061i	−0.0438164	−	0.999040i	$-0.513952\pi$
$439$	17.6688	−	30.6032i	0.843285	−	1.46061i	0.887102	−	0.461574i	$-0.152715\pi$
$440$	−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	0.955957	−	0.293508i	$-0.0948228\pi$
$443$	4.71029	+	8.15846i	0.223793	+	0.387620i	−0.732164	+	0.681129i	$0.761489\pi$
$444$	17.7116	−	25.0583i	0.840555	−	1.18922i
$445$	−38.4775			−1.82401
$446$	−0.807675	−	1.39893i	−0.0382445	−	0.0662415i
$447$	−2.87961	−	6.24728i	−0.136201	−	0.295486i
$448$	1.00501			0.0474825
$449$	−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
$452$	6.93485	−	12.0115i	0.326188	−	0.564974i
$453$	−6.35937	−	13.7966i	−0.298789	−	0.648220i
$454$	0.819917	−	1.42014i	0.0384806	−	0.0666503i
$455$	−0.127916	−	1.52747i	−0.00599681	−	0.0716089i
$456$	0.200839	−	0.284147i	0.00940514	−	0.0133064i
$457$	−10.9573	+	18.9786i	−0.512562	+	0.887784i	0.487332	+	0.873217i	$0.337970\pi$
$457$	−10.9573	+	18.9786i	−0.512562	+	0.887784i	−0.999894	+	0.0145668i	$0.995363\pi$
$458$	0.466784	+	0.808493i	0.0218114	+	0.0377784i
$459$	−19.9452	+	19.4232i	−0.930962	+	0.906599i
$460$	11.8275			0.551461
$461$	−32.5148			−1.51436			−0.757182	−	0.653204i	$-0.773424\pi$
$461$	−32.5148			−1.51436			−0.757182	+	0.653204i	$0.773424\pi$
$462$	0.0675107	+	0.146463i	0.00314088	+	0.00681410i
$463$	5.55585	−	9.62301i	0.258202	−	0.447219i	−0.707558	−	0.706655i	$-0.750203\pi$
$463$	5.55585	−	9.62301i	0.258202	−	0.447219i	0.965760	+	0.259436i	$0.0835366\pi$
$464$	5.29751	+	9.17555i	0.245931	+	0.425964i
$465$	−10.3221	−	22.3937i	−0.478678	−	1.03848i
$466$	1.67439	−	2.90012i	0.0775645	−	0.134346i
$467$	−22.2399			−1.02914			−0.514571	−	0.857448i	$-0.672049\pi$
$467$	−22.2399			−1.02914			−0.514571	+	0.857448i	$0.672049\pi$
$468$	17.3294	+	12.4613i	0.801052	+	0.576026i
$469$	1.78277			0.0823206
$470$	0.337731	−	0.584967i	0.0155784	−	0.0269825i
$471$	−12.5916	+	17.8146i	−0.580191	+	0.820854i
$472$	1.56089	+	2.70355i	0.0718459	+	0.124441i
$473$	−22.2341	+	38.5106i	−1.02233	+	1.77072i
$474$	0.800096	+	0.0735636i	0.0367496	+	0.00337889i
$475$	1.45777			0.0668872
$476$	−1.44242			−0.0661131
$477$	20.9686	+	3.88873i	0.960088	+	0.178053i
$478$	−2.44781	−	4.23973i	−0.111960	−	0.193921i
$479$	−10.0218	+	17.3582i	−0.457907	+	0.793118i	−0.998850	−	0.0479409i	$-0.984734\pi$
$479$	−10.0218	+	17.3582i	−0.457907	+	0.793118i	0.540943	+	0.841059i	$0.318067\pi$
$480$	10.3494	+	0.951560i	0.472384	+	0.0434326i
$481$	29.2869	+	13.7895i	1.33537	+	0.628745i
$482$	1.25215	−	2.16878i	0.0570337	−	0.0987852i
$483$	−0.452610	−	0.0416145i	−0.0205945	−	0.00189352i
$484$	6.36712	−	11.0282i	0.289415	−	0.501281i
$485$	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	$0.171808\pi$
$488$	−4.69491			−0.212529
$489$	−2.11669	+	2.99469i	−0.0957199	+	0.135424i
$490$	−1.77699	−	3.07783i	−0.0802760	−	0.139042i
$491$	−10.1877			−0.459765			−0.229882	−	0.973218i	$-0.573834\pi$
$491$	−10.1877			−0.459765			−0.229882	+	0.973218i	$0.573834\pi$
$492$	−10.2121	−	22.1549i	−0.460396	−	0.998822i
$493$	−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
$497$	−0.306674	+	0.531175i	−0.0137562	+	0.0238265i
$498$	2.92480	+	0.268916i	0.131063	+	0.0120504i
$499$	19.9631	−	34.5772i	0.893673	−	1.54789i	0.0582348	−	0.998303i	$-0.481453\pi$
$499$	19.9631	−	34.5772i	0.893673	−	1.54789i	0.835438	−	0.549584i	$-0.185214\pi$
$500$	−0.891169	−	1.54355i	−0.0398543	−	0.0690297i
$501$	16.0846	+	1.47887i	0.718606	+	0.0660711i
$502$	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	$-0.0126922\pi$
$504$	−0.261214	−	0.0484433i	−0.0116354	−	0.00215784i
$505$	27.1862	+	47.0878i	1.20977	+	2.09538i
$506$	−0.656376	−	1.13688i	−0.0291795	−	0.0505403i
$507$	−9.75719	+	20.2928i	−0.433332	+	0.901234i
$508$	−1.32109	+	2.28819i	−0.0586137	+	0.101522i
$509$	15.1138			0.669907			0.334954	−	0.942235i	$-0.391279\pi$
$509$	15.1138			0.669907			0.334954	+	0.942235i	$0.391279\pi$
$510$	−4.70429	−	0.432529i	−0.208310	−	0.0191527i
$511$	−0.161638			−0.00715045
$512$	−12.3813			−0.547183
$513$	1.15214	−	1.12199i	0.0508681	−	0.0495369i
$514$	−2.28670	+	3.96068i	−0.100862	+	0.174698i
$515$	22.7012	+	39.3197i	1.00034	+	1.73263i
$516$	−15.2292	−	33.0395i	−0.670428	−	1.45448i
$517$	5.54328			0.243793
$518$	−0.200100			−0.00879189
$519$	14.7435	+	1.35557i	0.647167	+	0.0595028i
$520$	0.608600	+	7.26740i	0.0266889	+	0.318696i
$521$	−19.9265			−0.872994			−0.436497	−	0.899706i	$-0.643781\pi$
$521$	−19.9265			−0.872994			−0.436497	+	0.899706i	$0.643781\pi$
$522$	−0.451173	−	1.27453i	−0.0197473	−	0.0557845i
$523$	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	$0.726614\pi$
$524$	−26.0293			−1.13710
$525$	−0.465918	−	1.01080i	−0.0203343	−	0.0441150i
$526$	−0.215514	−	0.373281i	−0.00939686	−	0.0162758i
$527$	−12.2390	−	21.1986i	−0.533141	−	0.923427i
$528$	11.6333	+	25.2384i	0.506276	+	1.09836i
$529$	−19.3003			−0.839142
$530$	1.80940	+	3.13397i	0.0785952	+	0.136131i
$531$	4.81472	+	13.6012i	0.208941	+	0.590241i
$532$	0.0833215			0.00361245
$533$	21.1354	−	14.6824i	0.915477	−	0.635965i
$534$	−3.47925	−	0.319894i	−0.150562	−	0.0138432i
$535$	16.9287			0.731893
$536$	−8.48205			−0.366369
$537$	−2.31346	−	5.01901i	−0.0998330	−	0.216586i
$538$	0.319948	+	0.554166i	0.0137939	+	0.0238918i
$539$	14.5831	−	25.2587i	0.628138	−	1.08797i
$540$	30.7504	+	8.67807i	1.32329	+	0.373445i
$541$	−34.9072			−1.50078			−0.750389	−	0.660997i	$-0.770134\pi$
$541$	−34.9072			−1.50078			−0.750389	+	0.660997i	$0.770134\pi$
$542$	−3.11970			−0.134003
$543$	2.59393	+	0.238495i	0.111316	+	0.0102348i
$544$	10.3172			0.442344
$545$	4.84421	−	8.39042i	0.207503	−	0.359406i
$546$	0.00113250	−	0.139182i	4.84667e−5	−	0.00595644i
$547$	6.34298	+	10.9864i	0.271206	+	0.469743i	0.969171	−	0.246389i	$-0.0792441\pi$
$547$	6.34298	+	10.9864i	0.271206	+	0.469743i	−0.697965	+	0.716132i	$0.745911\pi$
$548$	−8.17817	−	14.1650i	−0.349354	−	0.605099i
$549$	−21.3350	−	3.95668i	−0.910558	−	0.168867i
$550$	1.60732	−	2.78395i	0.0685362	−	0.118708i
$551$	0.426904	+	0.739419i	0.0181867	+	0.0315003i
$552$	2.15343	+	0.197993i	0.0916559	+	0.00842716i
$553$	0.193698	+	0.335496i	0.00823690	+	0.0142667i
$554$	−0.241894	+	0.418973i	−0.0102771	+	0.0178005i
$555$	48.2533	+	4.43658i	2.04824	+	0.188322i
$556$	−6.07580	+	10.5236i	−0.257671	+	0.446300i
$557$	−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
$561$	−16.2292	−	35.2090i	−0.685197	−	1.48653i
$562$	−0.706288			−0.0297930
$563$	9.28939	+	16.0897i	0.391501	+	0.678100i	0.992648	−	0.121039i	$-0.0386225\pi$
$563$	9.28939	+	16.0897i	0.391501	+	0.678100i	−0.601146	+	0.799139i	$0.705289\pi$
$564$	−2.61761	+	3.70339i	−0.110221	+	0.155941i
$565$	21.9020			0.921424
$566$	−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
$569$	−13.0734	+	22.6438i	−0.548066	+	0.949278i	0.450341	+	0.892857i	$0.351302\pi$
$569$	−13.0734	+	22.6438i	−0.548066	+	0.949278i	−0.998407	+	0.0564215i	$0.982031\pi$
$570$	0.271744	+	0.0249851i	0.0113821	+	0.00104651i
$571$	−13.5880	+	23.5351i	−0.568640	+	0.984913i	0.428061	+	0.903750i	$0.359197\pi$
$571$	−13.5880	+	23.5351i	−0.568640	+	0.984913i	−0.996701	+	0.0811634i	$0.974136\pi$
$572$	−24.4116	+	16.9583i	−1.02070	+	0.709061i
$573$	−34.6884	−	3.18937i	−1.44913	−	0.133238i
$574$	−0.0795397	+	0.137767i	−0.00331992	+	0.00575028i
$575$	4.52991	+	7.84603i	0.188910	+	0.327202i
$576$	−21.7293	−	4.02979i	−0.905385	−	0.167908i
$577$	6.97981			0.290573			0.145287	−	0.989390i	$-0.453590\pi$
$577$	6.97981			0.290573			0.145287	+	0.989390i	$0.453590\pi$
$578$	−1.91242			−0.0795463
$579$	−13.6207	−	1.25233i	−0.566057	−	0.0520452i
$580$	−8.48170	+	14.6907i	−0.352183	+	0.610000i
$581$	0.708076	+	1.22642i	0.0293759	+	0.0508806i
$582$	2.63192	−	3.72364i	0.109097	−	0.154350i
$583$	−14.8491	+	25.7194i	−0.614987	+	1.06519i
$584$	0.769041			0.0318232
$585$	−3.35902	+	33.5381i	−0.138878	+	1.38663i
$586$	1.73844			0.0718142
$587$	−22.8508	+	39.5788i	−0.943155	+	1.63359i	−0.183751	+	0.982973i	$0.558824\pi$
$587$	−22.8508	+	39.5788i	−0.943155	+	1.63359i	−0.759404	+	0.650620i	$0.774509\pi$
$588$	9.98865	+	21.6702i	0.411925	+	0.893665i
$589$	0.706990	+	1.22454i	0.0291310	+	0.0504564i
$590$	−1.22415	+	2.12028i	−0.0503973	+	0.0872907i
$591$	16.8684	+	36.5958i	0.693874	+	1.50535i
$592$	−34.4809			−1.41716
$593$	−18.9869			−0.779700			−0.389850	−	0.920878i	$-0.627473\pi$
$593$	−18.9869			−0.779700			−0.389850	+	0.920878i	$0.627473\pi$
$594$	−0.872365	−	3.43736i	−0.0357936	−	0.141037i
$595$	−1.13888	−	1.97260i	−0.0466896	−	0.0808687i
$596$	−3.91859	+	6.78720i	−0.160512	+	0.278015i
$597$	9.18392	−	12.9934i	0.375873	−	0.531785i
$598$	0.0945479	+	1.12901i	0.00386635	+	0.0461687i
$599$	6.44845	−	11.1690i	0.263477	−	0.456355i	−0.703687	−	0.710510i	$-0.748464\pi$
$599$	6.44845	−	11.1690i	0.263477	−	0.456355i	0.967163	+	0.254155i	$0.0817975\pi$
$600$	2.21674	+	4.80919i	0.0904981	+	0.196335i
$601$	11.9177	−	20.6421i	0.486135	−	0.842010i	−0.513738	−	0.857947i	$-0.671740\pi$
$601$	11.9177	−	20.6421i	0.486135	−	0.842010i	0.999873	+	0.0159372i	$0.00507317\pi$
$602$	−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
$605$	20.1090			0.817547
$606$	2.06678	+	4.48385i	0.0839571	+	0.182144i
$607$	17.3898	+	30.1201i	0.705831	+	1.22254i	0.966391	+	0.257078i	$0.0827596\pi$
$607$	17.3898	+	30.1201i	0.705831	+	1.22254i	−0.260560	+	0.965458i	$0.583907\pi$
$608$	−0.595972			−0.0241698
$609$	0.376262	−	0.532335i	0.0152469	−	0.0215713i
$610$	−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	$-0.484519\pi$
$614$	0.891149	−	1.54352i	0.0359639	−	0.0622912i
$615$	22.2352	−	31.4584i	0.896611	−	1.26852i
$616$	0.184980	−	0.320396i	0.00745307	−	0.0129091i
$617$	19.6199	+	33.9827i	0.789868	+	1.36809i	0.926047	+	0.377407i	$0.123184\pi$
$617$	19.6199	+	33.9827i	0.789868	+	1.36809i	−0.136179	+	0.990684i	$0.543482\pi$
$618$	1.72582	+	3.74414i	0.0694226	+	0.150611i
$619$	15.9718	+	27.6639i	0.641959	+	1.11191i	0.984995	+	0.172584i	$0.0552116\pi$
$619$	15.9718	+	27.6639i	0.641959	+	1.11191i	−0.343035	+	0.939322i	$0.611455\pi$
$620$	−14.0464	+	24.3291i	−0.564119	+	0.977082i
$621$	9.61894	+	2.71456i	0.385995	+	0.108932i
$622$	0.0238331	+	0.0412802i	0.000955621	+	0.00165518i
$623$	−0.842306	−	1.45892i	−0.0337463	−	0.0584503i
$624$	0.195151	−	23.9836i	0.00781231	−	0.960114i
$625$	13.1826	−	22.8330i	0.527305	−	0.913319i
$626$	1.34822			0.0538858
$627$	0.937481	+	2.03385i	0.0374394	+	0.0812243i
$628$	24.8540			0.991785
$629$	48.1029			1.91799
$630$	−0.0695276	−	0.196410i	−0.00277005	−	0.00782515i
$631$	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
$633$	−21.5306	−	1.97960i	−0.855765	−	0.0786820i
$634$	−2.31613			−0.0919852
$635$	−4.17233			−0.165574
$636$	−10.1708	−	22.0655i	−0.403300	−	0.874954i
$637$	−20.6730	+	14.3612i	−0.819095	+	0.569010i
$638$	1.88279			0.0745403
$639$	8.76040	−	10.2548i	0.346556	−	0.405673i
$640$	−7.87547	−	13.6407i	−0.311305	−	0.539197i
$641$	36.1754			1.42884			0.714421	−	0.699716i	$-0.246690\pi$
$641$	36.1754			1.42884			0.714421	+	0.699716i	$0.246690\pi$
$642$	1.53075	+	0.140742i	0.0604138	+	0.00555465i
$643$	4.13822	+	7.16760i	0.163195	+	0.282663i	0.936013	−	0.351966i	$-0.114487\pi$
$643$	4.13822	+	7.16760i	0.163195	+	0.282663i	−0.772818	+	0.634628i	$0.781153\pi$
$644$	0.258915	+	0.448454i	0.0102027	+	0.0176715i
$645$	33.1593	−	46.9137i	1.30564	−	1.84723i
$646$	0.270897			0.0106583
$647$	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	$0.748833\pi$
$648$	5.45342	+	2.09477i	0.214231	+	0.0822903i
$649$	−20.0923			−0.788691
$650$	−2.27853	+	1.58286i	−0.0893715	+	0.0620847i
$651$	0.623123	−	0.881594i	0.0244221	−	0.0345524i
$652$	4.17804			0.163625
$653$	9.71764			0.380281			0.190140	−	0.981757i	$-0.439106\pi$
$653$	9.71764			0.380281			0.190140	+	0.981757i	$0.439106\pi$
$654$	0.507785	−	0.718414i	0.0198560	−	0.0280922i
$655$	−20.5518	−	35.5968i	−0.803026	−	1.39088i
$656$	−13.7062	+	23.7398i	−0.535136	+	0.926883i
$657$	3.49475	+	0.648118i	0.136343	+	0.0252855i
$658$	0.0295729			0.00115287
$659$	−23.7040			−0.923378			−0.461689	−	0.887042i	$-0.652756\pi$
$659$	−23.7040			−0.923378			−0.461689	+	0.887042i	$0.652756\pi$
$660$	−25.6819	+	36.3347i	−0.999665	+	1.41433i
$661$	−19.7363			−0.767652			−0.383826	−	0.923405i	$-0.625394\pi$
$661$	−19.7363			−0.767652			−0.383826	+	0.923405i	$0.625394\pi$
$662$	0.940137	−	1.62837i	0.0365395	−	0.0632882i
$663$	−0.272248	+	33.4586i	−0.0105732	+	1.29942i
$664$	−3.36888	−	5.83507i	−0.130738	−	0.226445i
$665$	0.0657876	+	0.113948i	0.00255114	+	0.00441870i
$666$	4.32633	+	0.802338i	0.167642	+	0.0310899i
$667$	−2.65314	+	4.59537i	−0.102730	+	0.177933i
$668$	−9.20117	−	15.9369i	−0.356004	−	0.616617i
$669$	−9.88525	+	13.9856i	−0.382186	+	0.540716i
$670$	−3.32607	−	5.76092i	−0.128497	−	0.222564i
$671$	15.1086	−	26.1688i	0.583260	−	1.01024i
$672$	0.190478	+	0.413240i	0.00734786	+	0.0159411i
$673$	−3.54264	+	6.13603i	−0.136559	+	0.236527i	−0.926192	−	0.377053i	$-0.876938\pi$
$673$	−3.54264	+	6.13603i	−0.136559	+	0.236527i	0.789633	+	0.613579i	$0.210271\pi$
$674$	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	−0.986416	−	0.164266i	$-0.947474\pi$
$677$	−16.5344	−	28.6383i	−0.635467	−	1.10066i	0.350949	−	0.936394i	$-0.385859\pi$
$678$	1.98045	+	0.182089i	0.0760586	+	0.00699309i
$679$	2.19856			0.0843732
$680$	5.41857	+	9.38523i	0.207793	+	0.359907i
$681$	−17.3130	−	1.59182i	−0.663437	−	0.0609987i
$682$	3.11806			0.119397
$683$	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
$686$	0.155806	−	0.269865i	0.00594872	−	0.0103035i
$687$	5.71303	−	8.08279i	0.217966	−	0.308378i
$688$	−20.4399	+	35.4030i	−0.779264	+	1.34973i
$689$	21.0501	−	14.6231i	0.801945	−	0.557097i
$690$	0.709948	+	1.54022i	0.0270273	+	0.0586353i
$691$	15.9044	−	27.5471i	0.605030	−	1.04794i	−0.387017	−	0.922073i	$-0.626494\pi$
$691$	15.9044	−	27.5471i	0.605030	−	1.04794i	0.992047	−	0.125870i	$-0.0401723\pi$
$692$	−8.43399	−	14.6081i	−0.320612	−	0.555317i
$693$	1.11062	−	1.30008i	0.0421890	−	0.0493859i
$694$	1.39095			0.0527998
$695$	−19.1889			−0.727878
$696$	−1.79018	+	2.53274i	−0.0678565	+	0.0960034i
$697$	19.1209	−	33.1184i	0.724256	−	1.25445i
$698$	−0.865315	−	1.49877i	−0.0327527	−	0.0567293i
$699$	−35.3557	−	3.25072i	−1.33727	−	0.122954i
$700$	−0.634024	+	1.09816i	−0.0239639	+	0.0415066i
$701$	−21.3043			−0.804652			−0.402326	−	0.915496i	$-0.631798\pi$
$701$	−21.3043			−0.804652			−0.402326	+	0.915496i	$0.631798\pi$
$702$	−0.582562	+	3.00469i	−0.0219874	+	0.113405i
$703$	−2.77867			−0.104800
$704$	15.3877	−	26.6523i	0.579947	−	1.00450i
$705$	−7.13139	−	0.655685i	−0.268584	−	0.0246945i
$706$	−0.138089	−	0.239177i	−0.00519704	−	0.00900153i
$707$	−1.19026	+	2.06159i	−0.0447643	+	0.0775340i
$708$	9.48783	−	13.4234i	0.356575	−	0.504482i
$709$	7.40658			0.278160			0.139080	−	0.990281i	$-0.455585\pi$
$709$	7.40658			0.278160			0.139080	+	0.990281i	$0.455585\pi$
$710$	2.28862			0.0858904
$711$	−2.84269	−	8.03036i	−0.106609	−	0.301162i
$712$	4.00752	+	6.94123i	0.150188	+	0.260134i
$713$	−4.39383	+	7.61033i	−0.164550	+	0.285009i
$714$	−0.0865813	−	0.187837i	−0.00324022	−	0.00702962i
$715$	−42.4660	−	19.9948i	−1.58814	−	0.747762i
$716$	−3.14817	+	5.45279i	−0.117653	+	0.203780i
$717$	−29.9590	+	42.3860i	−1.11884	+	1.58294i
$718$	−2.61061	+	4.52170i	−0.0974269	+	0.168748i
$719$	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
$722$	3.08829			0.114934
$723$	−26.4398	−	2.43097i	−0.983307	−	0.0904086i
$724$	−1.48385	−	2.57011i	−0.0551470	−	0.0955174i
$725$	−12.9939			−0.482580
$726$	1.81832	+	0.167182i	0.0674840	+	0.00620471i
$727$	−7.16724	−	12.4140i	−0.265818	−	0.460411i	0.701959	−	0.712217i	$-0.252309\pi$
$727$	−7.16724	−	12.4140i	−0.265818	−	0.460411i	−0.967778	+	0.251806i	$0.918975\pi$
$728$	−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
$731$	28.5149	−	49.3892i	1.05466	−	1.82673i
$732$	10.3486	+	22.4511i	0.382494	+	0.829816i
$733$	−3.57055	+	6.18437i	−0.131881	+	0.228425i	−0.924402	−	0.381420i	$-0.875435\pi$
$733$	−3.57055	+	6.18437i	−0.131881	+	0.228425i	0.792521	+	0.609845i	$0.208768\pi$
$734$	1.53737	+	2.66281i	0.0567455	+	0.0982861i
$735$	−21.7488	+	30.7701i	−0.802215	+	1.13497i
$736$	−1.85193	−	3.20764i	−0.0682632	−	0.118235i
$737$	27.2959	−	47.2778i	1.00546	−	1.74150i
$738$	2.27212	−	2.65970i	0.0836377	−	0.0979051i
$739$	−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
$741$	0.0157264	−	1.93274i	0.000577725	−	0.0710010i
$742$	−0.0792186	+	0.137211i	−0.00290821	+	0.00503716i
$743$	24.0668			0.882924			0.441462	−	0.897280i	$-0.354460\pi$
$743$	24.0668			0.882924			0.441462	+	0.897280i	$0.354460\pi$
$744$	−2.96469	+	4.19445i	−0.108691	+	0.153776i
$745$	−12.3759			−0.453418
$746$	−2.38422			−0.0872925
$747$	−10.3916	−	29.3555i	−0.380210	−	1.07406i
$748$	−22.0848	+	38.2520i	−0.807500	+	1.39863i
$749$	0.370585	+	0.641871i	0.0135409	+	0.0234535i
$750$	0.147514	−	0.208703i	0.00538646	−	0.00762076i
$751$	−1.99884			−0.0729388			−0.0364694	−	0.999335i	$-0.511611\pi$
$751$	−1.99884			−0.0729388			−0.0364694	+	0.999335i	$0.511611\pi$
$752$	5.09596			0.185831
$753$	20.2961	−	28.7150i	0.739633	−	1.04643i
$754$	−1.47013	−	0.692196i	−0.0535388	−	0.0252083i
$755$	−27.3312			−0.994683
$756$	0.344114	+	1.35590i	0.0125153	+	0.0493138i
$757$	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	$0.791370\pi$
$758$	−3.17354			−0.115268
$759$	−8.03347	+	11.3658i	−0.291597	+	0.412551i
$760$	−0.313004	−	0.542139i	−0.0113539	−	0.0196655i
$761$	−9.23009	−	15.9870i	−0.334591	−	0.579528i	0.648816	−	0.760946i	$-0.275265\pi$
$761$	−9.23009	−	15.9870i	−0.334591	−	0.579528i	−0.983406	+	0.181418i	$0.941931\pi$
$762$	−0.377275	−	0.0346879i	−0.0136672	−	0.00125661i
$763$	0.424176			0.0153562
$764$	19.8435	+	34.3699i	0.717912	+	1.24346i
$765$	16.7141	+	47.2158i	0.604298	+	1.70709i
$766$	1.34932			0.0487531
$767$	15.6885	+	7.38681i	0.566480	+	0.266722i
$768$	10.0836	+	21.8762i	0.363861	+	0.789391i
$769$	28.8885			1.04174			0.520872	−	0.853635i	$-0.325607\pi$
$769$	28.8885			1.04174			0.520872	+	0.853635i	$0.325607\pi$
$770$	0.290146			0.0104561
$771$	48.2851	+	4.43950i	1.73895	+	0.159885i
$772$	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	$0.293516\pi$
$774$	3.38839	−	3.96640i	0.121793	−	0.142569i
$775$	−21.5190			−0.772985
$776$	−10.4603			−0.375504
$777$	0.888090	+	1.92670i	0.0318600	+	0.0691199i
$778$	1.19090			0.0426960
$779$	−1.10452	+	1.91309i	−0.0395736	+	0.0685435i
$780$	33.4112	−	18.9292i	1.19631	−	0.677774i
$781$	9.39095	+	16.2656i	0.336035	+	0.582029i
$782$	0.841791	+	1.45802i	0.0301024	+	0.0521388i
$783$	−10.2696	+	10.0008i	−0.367005	+	0.357401i
$784$	13.4063	−	23.2204i	0.478796	−	0.829300i
$785$	19.6239	+	33.9895i	0.700405	+	1.21314i
$786$	−1.56241	−	3.38964i	−0.0557294	−	0.120904i
$787$	−13.9138	−	24.0994i	−0.495973	−	0.859051i	0.504016	−	0.863694i	$-0.331855\pi$
$787$	−13.9138	−	24.0994i	−0.495973	−	0.859051i	−0.999989	+	0.00464363i	$0.998522\pi$
$788$	22.9546	−	39.7586i	0.817725	−	1.41634i
$789$	−2.63770	+	3.73182i	−0.0939048	+	0.132856i
$790$	0.722757	−	1.25185i	0.0257145	−	0.0445389i
$791$	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
$795$	22.1455	−	31.3314i	0.785419	−	1.11121i
$796$	−18.1277			−0.642521
$797$	19.4505	+	33.6892i	0.688970	+	1.19333i	0.972171	+	0.234271i	$0.0752703\pi$
$797$	19.4505	+	33.6892i	0.688970	+	1.19333i	−0.283201	+	0.959061i	$0.591396\pi$
$798$	0.00500138	+	0.0108504i	0.000177047	+	0.000384101i
$799$	−7.10916			−0.251504
$800$	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
$803$	−2.47483	+	4.28653i	−0.0873349	+	0.151269i
$804$	18.6962	+	40.5612i	0.659365	+	1.43048i
$805$	−0.408859	+	0.708165i	−0.0144104	+	0.0249595i
$806$	−2.43466	−	1.14634i	−0.0857571	−	0.0403780i
$807$	3.91588	−	5.54019i	0.137846	−	0.195024i
$808$	5.66301	−	9.80862i	0.199224	−	0.345066i
$809$	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	$0.703678\pi$
$810$	0.715705	+	4.52533i	0.0251473	+	0.159004i
$811$	−26.2480			−0.921692			−0.460846	−	0.887480i	$-0.652454\pi$
$811$	−26.2480			−0.921692			−0.460846	+	0.887480i	$0.652454\pi$
$812$	−0.742687			−0.0260632
$813$	13.8459	+	30.0386i	0.485599	+	1.05350i
$814$	−3.06372	+	5.30652i	−0.107383	+	0.185993i
$815$	3.29883	+	5.71373i	0.115553	+	0.200143i
$816$	−14.9196	−	32.3678i	−0.522289	−	1.13310i
$817$	−1.64717	+	2.85298i	−0.0576270	+	0.0998130i
$818$	−4.16926			−0.145775
$819$	−1.34517	+	0.606817i	−0.0470039	+	0.0212039i
$820$	−43.8892			−1.53268
$821$	1.69185	−	2.93037i	0.0590460	−	0.102271i	−0.834991	−	0.550263i	$-0.814527\pi$
$821$	1.69185	−	2.93037i	0.0590460	−	0.102271i	0.894037	+	0.447992i	$0.147861\pi$
$822$	1.35372	−	1.91525i	0.0472165	−	0.0668019i
$823$	−19.3119	−	33.4493i	−0.673172	−	1.16597i	−0.977000	−	0.213241i	$-0.931598\pi$
$823$	−19.3119	−	33.4493i	−0.673172	−	1.16597i	0.303828	−	0.952727i	$-0.401735\pi$
$824$	4.72878	−	8.19048i	0.164735	−	0.285329i
$825$	−33.9395	−	3.12051i	−1.18162	−	0.108642i
$826$	−0.107191			−0.00372964
$827$	−11.8393			−0.411694			−0.205847	−	0.978584i	$-0.565995\pi$
$827$	−11.8393			−0.411694			−0.205847	+	0.978584i	$0.565995\pi$
$828$	−3.79980	−	10.7341i	−0.132052	−	0.373036i
$829$	−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	$0.916636\pi$
$830$	2.64208	−	4.57622i	0.0917079	−	0.158843i
$831$	5.10774	+	0.469623i	0.177185	+	0.0162910i
$832$	−21.8137	+	15.1536i	−0.756253	+	0.525355i
$833$	−18.7026	+	32.3938i	−0.648006	+	1.12238i
$834$	−1.73512	−	0.159533i	−0.0600823	−	0.00552418i
$835$	14.5298	−	25.1664i	0.502825	−	0.870918i
$836$	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
$839$	52.8136			1.82333			0.911665	−	0.410935i	$-0.134798\pi$
$839$	52.8136			1.82333			0.911665	+	0.410935i	$0.134798\pi$
$840$	−0.275874	+	0.390306i	−0.00951856	+	0.0134668i
$841$	10.6948	+	18.5239i	0.368786	+	0.638756i
$842$	−1.35778			−0.0467923
$843$	3.13467	+	6.80063i	0.107964	+	0.234226i
$844$	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
$848$	−13.6508	+	23.6439i	−0.468772	+	0.811936i
$849$	37.5989	+	3.45697i	1.29039	+	0.118643i
$850$	−2.06136	+	3.57037i	−0.0707039	+	0.122463i
$851$	−8.63450	−	14.9554i	−0.295987	−	0.512664i
$852$	−15.3014	−	1.40686i	−0.524216	−	0.0481982i
$853$	11.5316	+	19.9733i	0.394834	+	0.683873i	0.993080	−	0.117440i	$-0.0374686\pi$
$853$	11.5316	+	19.9733i	0.394834	+	0.683873i	−0.598246	+	0.801313i	$0.704135\pi$
$854$	0.0806029	−	0.139608i	0.00275817	−	0.00477730i
$855$	−0.965490	−	2.72743i	−0.0330191	−	0.0932761i
$856$	−1.76317	−	3.05389i	−0.0602638	−	0.104380i
$857$	−13.4357	−	23.2713i	−0.458955	−	0.794933i	0.539951	−	0.841696i	$-0.318443\pi$
$857$	−13.4357	−	23.2713i	−0.458955	−	0.794933i	−0.998906	+	0.0467630i	$0.985109\pi$
$858$	−3.67367	−	2.16104i	−0.125417	−	0.0737767i
$859$	−15.1421	+	26.2269i	−0.516642	+	0.894850i	0.483172	+	0.875526i	$0.339485\pi$
$859$	−15.1421	+	26.2269i	−0.516642	+	0.894850i	−0.999813	+	0.0193240i	$0.993849\pi$
$860$	−65.4516			−2.23188
$861$	1.67953	+	0.154422i	0.0572382	+	0.00526267i
$862$	3.08236			0.104985
$863$	−4.43659			−0.151023			−0.0755116	−	0.997145i	$-0.524059\pi$
$863$	−4.43659			−0.151023			−0.0755116	+	0.997145i	$0.524059\pi$
$864$	−2.46134	−	9.69835i	−0.0837364	−	0.329945i
$865$	13.3183	−	23.0681i	0.452837	−	0.784337i
$866$	0.889348	+	1.54040i	0.0302213	+	0.0523448i
$867$	8.48777	+	18.4141i	0.288260	+	0.625376i
$868$	−1.22996			−0.0417474
$869$	11.8628			0.402419
$870$	−2.42220	−	0.222705i	−0.0821201	−	0.00755040i
$871$	−38.6947	+	26.8805i	−1.31112	+	0.910810i
$872$	−2.01814			−0.0683430
$873$	−47.5348	−	8.81555i	−1.60881	−	0.298361i
$874$	−0.0486262	−	0.0842230i	−0.00164480	−	0.00284889i
$875$	0.123225			0.00416578
$876$	−1.69513	−	3.67756i	−0.0572731	−	0.124253i
$877$	−4.31465	−	7.47319i	−0.145695	−	0.252352i	0.783937	−	0.620841i	$-0.213209\pi$
$877$	−4.31465	−	7.47319i	−0.145695	−	0.252352i	−0.929632	+	0.368489i	$0.879875\pi$
$878$	−2.88646	−	4.99950i	−0.0974134	−	0.168725i
$879$	−7.71559	−	16.7389i	−0.260240	−	0.564588i
$880$	49.9975			1.68541
$881$	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	$0.640495\pi$
$882$	−2.22241	+	2.60151i	−0.0748323	+	0.0875976i
$883$	17.4612			0.587615			0.293807	−	0.955865i	$-0.405078\pi$
$883$	17.4612			0.587615			0.293807	+	0.955865i	$0.405078\pi$
$884$	31.3074	−	21.7487i	1.05298	−	0.731488i
$885$	25.8486	+	2.37661i	0.868891	+	0.0798888i
$886$	1.53899			0.0517035
$887$	−34.1918			−1.14805			−0.574024	−	0.818839i	$-0.694618\pi$
$887$	−34.1918			−1.14805			−0.574024	+	0.818839i	$0.694618\pi$
$888$	−4.22535	−	9.16684i	−0.141794	−	0.307619i
$889$	−0.0913359	−	0.158198i	−0.00306331	−	0.00530580i
$890$	−3.14294	+	5.44373i	−0.105352	+	0.182474i
$891$	−29.2255	+	23.6555i	−0.979090	+	0.792490i
$892$	19.5121			0.653312
$893$	0.410662			0.0137423
$894$	−1.11907	−	0.102891i	−0.0374272	−	0.00344119i
$895$	−9.94271			−0.332348
$896$	0.344802	−	0.597214i	0.0115190	−	0.0199515i
$897$	10.4513	−	5.92119i	0.348958	−	0.197703i
$898$	1.76634	+	3.05938i	0.0589434	+	0.102093i
$899$	−6.30176	−	10.9150i	−0.210176	−	0.364035i
$900$	18.1114	−	21.2009i	0.603714	−	0.706698i
$901$	19.0437	−	32.9847i	0.634438	−	1.09888i
$902$	2.43566	+	4.21868i	0.0810985	+	0.140467i
$903$	2.50467	+	0.230288i	0.0833502	+	0.00766350i
$904$	−2.28115	−	3.95106i	−0.0758698	−	0.131410i
$905$	2.34319	−	4.05853i	0.0778904	−	0.134910i
$906$	−2.47137	−	0.227226i	−0.0821056	−	0.00754907i
$907$	7.68673	−	13.3138i	0.255234	−	0.442078i	−0.709725	−	0.704479i	$-0.751181\pi$
$907$	7.68673	−	13.3138i	0.255234	−	0.442078i	0.964959	+	0.262401i	$0.0845143\pi$
$908$	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	0.907384	+	0.420302i	$0.138076\pi$
$911$	24.6800	+	42.7470i	0.817685	+	1.41627i	−0.0896996	+	0.995969i	$0.528591\pi$
$912$	0.861831	+	1.86973i	0.0285381	+	0.0619129i
$913$	43.3652			1.43518
$914$	1.79004	+	3.10045i	0.0592094	+	0.102554i
$915$	−22.5324	+	31.8789i	−0.744899	+	1.05388i
$916$	−11.2767			−0.372593
$917$	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	$0.244911\pi$
$920$	1.94527	−	3.36931i	0.0641337	−	0.111083i
$921$	−18.8172	−	1.73011i	−0.620046	−	0.0570092i
$922$	−2.65589	+	4.60013i	−0.0874670	+	0.151497i
$923$	−1.35272	−	16.1531i	−0.0445254	−	0.531685i
$924$	−1.93987	−	0.178358i	−0.0638170	−	0.00586755i
$925$	21.1439	−	36.6224i	0.695209	−	1.20414i
$926$	−0.907632	−	1.57206i	−0.0298266	−	0.0516612i
$927$	28.3916	−	33.2347i	0.932501	−	1.09157i
$928$	5.31220			0.174382
$929$	−48.3584			−1.58659			−0.793294	−	0.608838i	$-0.791636\pi$
$929$	−48.3584			−1.58659			−0.793294	+	0.608838i	$0.791636\pi$
$930$	−4.01137	−	0.368819i	−0.131538	−	0.0120940i
$931$	1.08036	−	1.87123i	0.0354073	−	0.0613272i
$932$	20.2252	+	35.0310i	0.662498	+	1.14748i
$933$	0.291697	−	0.412692i	0.00954972	−	0.0135109i
$934$	−1.81662	+	3.14647i	−0.0594415	+	0.102956i
$935$	−69.7494			−2.28105
$936$	6.40003	−	2.88711i	0.209191	−	0.0943683i
$937$	26.8065			0.875730			0.437865	−	0.899041i	$-0.355735\pi$
$937$	26.8065			0.875730			0.437865	+	0.899041i	$0.355735\pi$
$938$	0.145621	−	0.252223i	0.00475469	−	0.00823537i
$939$	−5.98373	−	12.9816i	−0.195272	−	0.423639i
$940$	4.07950	+	7.06591i	0.133059	+	0.230464i
$941$	13.4825	−	23.3523i	0.439516	−	0.761264i	−0.558136	−	0.829749i	$-0.688483\pi$
$941$	13.4825	−	23.3523i	0.439516	−	0.761264i	0.997652	+	0.0684856i	$0.0218167\pi$
$942$	1.49187	+	3.23658i	0.0486076	+	0.105454i
$943$	−13.7288			−0.447073
$944$	−18.4709			−0.601177
$945$	−1.58259	+	1.54117i	−0.0514816	+	0.0501343i
$946$	3.63228	+	6.29129i	0.118096	+	0.204547i
$947$	7.03373	−	12.1828i	0.228566	−	0.395887i	−0.728818	−	0.684708i	$-0.759930\pi$
$947$	7.03373	−	12.1828i	0.228566	−	0.395887i	0.957383	+	0.288821i	$0.0932631\pi$
$948$	−5.60178	+	7.92539i	−0.181937	+	0.257405i
$949$	3.50833	−	2.43717i	0.113885	−	0.0791139i
$950$	0.119075	−	0.206243i	0.00386329	−	0.00669141i
$951$	10.2795	+	22.3013i	0.333336	+	0.723168i
$952$	−0.237234	+	0.410902i	−0.00768881	+	0.0133174i
$953$	−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
$956$	59.1349			1.91256
$957$	−8.35625	−	18.1288i	−0.270119	−	0.586020i
$958$	1.63721	+	2.83573i	0.0528958	+	0.0916183i
$959$	1.13083			0.0365163
$960$	−22.9488	+	32.4679i	−0.740668	+	1.04790i
$961$	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
$965$	−12.3041	+	21.3113i	−0.396083	+	0.686036i
$966$	−0.0428579	+	0.0606353i	−0.00137893	+	0.00195091i
$967$	−10.2769	+	17.8001i	−0.330483	+	0.572413i	−0.982607	−	0.185699i	$-0.940545\pi$
$967$	−10.2769	+	17.8001i	−0.330483	+	0.572413i	0.652124	+	0.758113i	$0.273878\pi$
$968$	−2.09440	−	3.62760i	−0.0673165	−	0.116596i
$969$	−1.20230	−	2.60838i	−0.0386236	−	0.0837933i
$970$	−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	$0.139179\pi$
$972$	−2.00328	−	30.6956i	−0.0642553	−	0.984561i
$973$	−0.420062	−	0.727569i	−0.0134666	−	0.0233248i
$974$	0.0582299	+	0.100857i	0.00186581	+	0.00323167i
$975$	25.3535	+	14.9142i	0.811961	+	0.477637i
$976$	13.8894	−	24.0571i	0.444588	−	0.770049i
$977$	10.2887			0.329166			0.164583	−	0.986363i	$-0.447372\pi$
$977$	10.2887			0.329166			0.164583	+	0.986363i	$0.447372\pi$
$978$	0.250787	+	0.544079i	0.00801928	+	0.0173977i
$979$	−51.5860			−1.64870
$980$	42.9290			1.37132
$981$	−9.17104	−	1.70081i	−0.292809	−	0.0543028i
$982$	−0.832158	+	1.44134i	−0.0265552	+	0.0459950i
$983$	21.7938	+	37.7480i	0.695115	+	1.20397i	0.970142	+	0.242538i	$0.0779799\pi$
$983$	21.7938	+	37.7480i	0.695115	+	1.20397i	−0.275027	+	0.961437i	$0.588687\pi$
$984$	−7.99086	−	0.734707i	−0.254739	−	0.0234216i
$985$	72.4966			2.30993
$986$	−2.41464			−0.0768980
$987$	−0.131251	−	0.284748i	−0.00417778	−	0.00906363i
$988$	−1.80848	+	1.25632i	−0.0575354	+	0.0399688i
$989$	−20.4737			−0.651027
$990$	−6.27319	−	1.16339i	−0.199375	−	0.0369750i
$991$	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	$0.818753\pi$
$992$	8.79747			0.279320
$993$	−19.8516	−	1.82522i	−0.629970	−	0.0579216i
$994$	0.0500999	+	0.0867755i	0.00158907	+	0.00275235i
$995$	−14.3130	−	24.7909i	−0.453753	−	0.785923i
$996$	−20.4776	+	28.9717i	−0.648858	+	0.918005i
$997$	−5.29626			−0.167734			−0.0838671	−	0.996477i	$-0.526727\pi$
$997$	−5.29626			−0.167734			−0.0838671	+	0.996477i	$0.526727\pi$
$998$	−3.26128	−	5.64870i	−0.103234	−	0.178807i
$999$	−11.4758	−	45.2178i	−0.363078	−	1.43063i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.7	✓	24	117.61	even	3	inner
117.2.f.a.94.7	yes	24	1.1	even	1	trivial
117.2.h.a.16.6	yes	24	9.7	even	3
117.2.h.a.22.6	yes	24	13.9	even	3
351.2.f.a.100.6		24	117.74	odd	6
351.2.f.a.172.6		24	3.2	odd	2
351.2.h.a.289.7		24	9.2	odd	6
351.2.h.a.334.7		24	39.35	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0816825 - 0.141478i) q^{2} +(-1.72478 - 0.158582i) q^{3} +(0.986656 + 1.70894i) q^{4} +(-1.55806 + 2.69863i) q^{5} +(-0.163320 + 0.231065i) q^{6} -0.136429 q^{7} +0.649100 q^{8} +(2.94970 + 0.547036i) q^{9} +(0.254532 + 0.440862i) q^{10} +(-2.08885 + 3.61800i) q^{11} +(-1.43075 - 3.10400i) q^{12} +(2.96116 - 2.05707i) q^{13} +(-0.0111438 + 0.0193017i) q^{14} +(3.11525 - 4.40745i) q^{15} +(-1.92029 + 3.32604i) q^{16} +(2.67892 - 4.64002i) q^{17} +(0.318333 - 0.372636i) q^{18} +(-0.154748 + 0.268032i) q^{19} -6.14906 q^{20} +(0.235309 + 0.0216351i) q^{21} +(0.341246 + 0.591055i) q^{22} -1.92347 q^{23} +(-1.11955 - 0.102936i) 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} +(1.37935 - 2.38910i) q^{29} +(-0.369098 - 0.800752i) q^{30} +(2.28432 - 3.95657i) q^{31} +(0.962809 + 1.66763i) q^{32} +(4.17655 - 5.90899i) q^{33} +(-0.437642 - 0.758018i) q^{34} +(0.212564 - 0.368171i) q^{35} +(1.97549 + 5.58060i) q^{36} +(4.48902 + 7.77522i) q^{37} +(0.0252804 + 0.0437870i) q^{38} +(-5.43355 + 3.07839i) q^{39} +(-1.01133 + 1.75168i) q^{40} +7.13754 q^{41} +(0.0222815 - 0.0315239i) q^{42} +10.6442 q^{43} -8.24392 q^{44} +(-6.07205 + 7.10785i) q^{45} +(-0.157114 + 0.272129i) q^{46} +(-0.663436 - 1.14910i) q^{47} +(3.83952 - 5.43215i) q^{48} -6.98139 q^{49} -0.769473 q^{50} +(-5.35636 + 7.57817i) q^{51} +(6.43705 + 3.03083i) q^{52} +7.10873 q^{53} +(-0.608146 + 0.592231i) q^{54} +(-6.50910 - 11.2741i) q^{55} -0.0885560 q^{56} +(0.309411 - 0.437754i) q^{57} +(-0.225338 - 0.390296i) q^{58} +(2.40470 + 4.16507i) q^{59} +(10.6057 + 0.975129i) q^{60} -7.23295 q^{61} +(-0.373179 - 0.646365i) q^{62} +(-0.402424 - 0.0746315i) q^{63} -7.36659 q^{64} +(0.937606 + 11.1961i) q^{65} +(-0.494842 - 1.07355i) q^{66} -13.0674 q^{67} +10.5727 q^{68} +(3.31755 + 0.305027i) q^{69} +(-0.0347255 - 0.0601463i) q^{70} +(2.24787 - 3.89343i) q^{71} +(1.91465 + 0.355081i) q^{72} +1.18478 q^{73} +1.46670 q^{74} +(3.41510 + 7.40901i) q^{75} -0.610733 q^{76} +(0.284980 - 0.493599i) q^{77} +(-0.00830107 + 1.02018i) q^{78} +(-1.41978 - 2.45913i) q^{79} +(-5.98384 - 10.3643i) q^{80} +(8.40150 + 3.22719i) q^{81} +(0.583013 - 1.00981i) q^{82} +(-5.19008 - 8.98948i) q^{83} +(0.195196 + 0.423475i) q^{84} +(8.34781 + 14.4588i) q^{85} +(0.869443 - 1.50592i) q^{86} +(-2.75794 + 3.90193i) q^{87} +(-1.35588 + 2.34845i) 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} +(-4.56739 + 6.46194i) q^{93} -0.216764 q^{94} +(-0.482212 - 0.835216i) q^{95} +(-1.39617 - 3.02898i) q^{96} -16.1151 q^{97} +(-0.570257 + 0.987715i) q^{98} +(-8.14068 + 9.52935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Introduction

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