LMFDB - Embedded newform 117.2.r.b.43.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(43,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	117.43
Dual form			117.2.r.b.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21740 + 0.702869i) q^{2} +(0.712485 + 1.57872i) q^{3} +(-0.0119503 + 0.0206986i) q^{4} +(2.61504 - 1.50979i) q^{5} +(-1.97702 - 1.42116i) q^{6} +3.19463i q^{7} -2.84507i q^{8} +(-1.98473 + 2.24963i) q^{9} +(-2.12237 + 3.67605i) q^{10} +(-0.687300 + 0.396813i) q^{11} +(-0.0411917 - 0.00411882i) q^{12} +(-3.60510 - 0.0569665i) q^{13} +(-2.24541 - 3.88916i) q^{14} +(4.24672 + 3.05271i) q^{15} +(1.97581 + 3.42221i) q^{16} +(-0.0957495 - 0.165843i) q^{17} +(0.835023 - 4.13372i) q^{18} +(6.28411 - 3.62813i) q^{19} +0.0721699i q^{20} +(-5.04343 + 2.27612i) q^{21} +(0.557815 - 0.966164i) q^{22} +2.54500 q^{23} +(4.49158 - 2.02707i) q^{24} +(2.05894 - 3.56619i) q^{25} +(4.42891 - 2.46456i) q^{26} +(-4.96564 - 1.53051i) q^{27} +(-0.0661242 - 0.0381768i) q^{28} +(-4.22442 - 7.31690i) q^{29} +(-7.31563 - 0.731501i) q^{30} +(6.22662 - 3.59494i) q^{31} +(0.117082 + 0.0675976i) q^{32} +(-1.11615 - 0.802333i) q^{33} +(0.233132 + 0.134599i) q^{34} +(4.82322 + 8.35407i) q^{35} +(-0.0228460 - 0.0679649i) q^{36} +(2.25703 + 1.30310i) q^{37} +(-5.10020 + 8.83381i) q^{38} +(-2.47865 - 5.73204i) q^{39} +(-4.29547 - 7.43997i) q^{40} -0.905916i q^{41} +(4.54008 - 6.31584i) q^{42} -3.97309 q^{43} -0.0189682i q^{44} +(-1.79366 + 8.87940i) q^{45} +(-3.09830 + 1.78880i) q^{46} +(6.60765 + 3.81493i) q^{47} +(-3.99498 + 5.55754i) q^{48} -3.20565 q^{49} +5.78866i q^{50} +(0.193600 - 0.269322i) q^{51} +(0.0442612 - 0.0739396i) q^{52} +0.0692625 q^{53} +(7.12094 - 1.62694i) q^{54} +(-1.19821 + 2.07536i) q^{55} +9.08895 q^{56} +(10.2051 + 7.33587i) q^{57} +(10.2856 + 5.93842i) q^{58} +(-11.7491 - 6.78334i) q^{59} +(-0.113936 + 0.0514200i) q^{60} +0.178857 q^{61} +(-5.05354 + 8.75299i) q^{62} +(-7.18674 - 6.34047i) q^{63} -8.09330 q^{64} +(-9.51347 + 5.29398i) q^{65} +(1.92274 + 0.192258i) q^{66} +10.5897i q^{67} +0.00457694 q^{68} +(1.81328 + 4.01786i) q^{69} +(-11.7436 - 6.78019i) q^{70} +(0.271545 - 0.156777i) q^{71} +(6.40037 + 5.64670i) q^{72} -6.55741i q^{73} -3.66363 q^{74} +(7.09699 + 0.709639i) q^{75} +0.173429i q^{76} +(-1.26767 - 2.19567i) q^{77} +(7.04639 + 5.23605i) q^{78} +(-2.13465 + 3.69732i) q^{79} +(10.3336 + 5.96613i) q^{80} +(-1.12169 - 8.92983i) q^{81} +(0.636740 + 1.10287i) q^{82} +(-7.01438 - 4.04975i) q^{83} +(0.0131581 - 0.131592i) q^{84} +(-0.500776 - 0.289123i) q^{85} +(4.83686 - 2.79256i) q^{86} +(8.54153 - 11.8824i) q^{87} +(1.12896 + 1.95542i) q^{88} +(-4.56933 - 2.63810i) q^{89} +(-4.05744 - 12.0705i) q^{90} +(0.181987 - 11.5170i) q^{91} +(-0.0304136 + 0.0526779i) q^{92} +(10.1118 + 7.26876i) q^{93} -10.7256 q^{94} +(10.9554 - 18.9754i) q^{95} +(-0.0232983 + 0.233003i) q^{96} -17.5710i q^{97} +(3.90257 - 2.25315i) q^{98} +(0.471422 - 2.33374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.21740	+	0.702869i	−0.860835	+	0.497003i	−0.864292	−	0.502991i	$-0.832233\pi$
$2$	−1.21740	+	0.702869i	−0.860835	+	0.497003i	0.00345668	+	0.999994i	$0.498900\pi$
$3$	0.712485	+	1.57872i	0.411353	+	0.911476i
$3$	0.712485	+	1.57872i	0.411353	+	0.911476i
$4$	−0.0119503	+	0.0206986i	−0.00597516	+	0.0103493i
$5$	2.61504	−	1.50979i	1.16948	−	0.675199i	0.215922	−	0.976411i	$-0.430724\pi$
$5$	2.61504	−	1.50979i	1.16948	−	0.675199i	0.953557	+	0.301211i	$0.0973910\pi$
$6$	−1.97702	−	1.42116i	−0.807114	−	0.580186i
$7$			3.19463i			1.20746i	0.797190	+	0.603728i	$0.206319\pi$
$7$			3.19463i			1.20746i	−0.797190	+	0.603728i	$0.793681\pi$
$8$		−	2.84507i		−	1.00589i
$9$	−1.98473	+	2.24963i	−0.661577	+	0.749878i
$10$	−2.12237	+	3.67605i	−0.671153	+	1.16247i
$11$	−0.687300	+	0.396813i	−0.207229	+	0.119644i	−0.600023	−	0.799983i	$-0.704842\pi$
$11$	−0.687300	+	0.396813i	−0.207229	+	0.119644i	0.392794	+	0.919626i	$0.371509\pi$
$12$	−0.0411917	−	0.00411882i	−0.0118910	−	0.00118900i
$13$	−3.60510	−	0.0569665i	−0.999875	−	0.0157997i
$13$	−3.60510	−	0.0569665i	−0.999875	−	0.0157997i
$14$	−2.24541	−	3.88916i	−0.600110	−	1.03942i
$15$	4.24672	+	3.05271i	1.09650	+	0.788207i
$16$	1.97581	+	3.42221i	0.493953	+	0.855552i
$17$	−0.0957495	−	0.165843i	−0.0232227	−	0.0402228i	0.854181	−	0.519977i	$-0.174059\pi$
$17$	−0.0957495	−	0.165843i	−0.0232227	−	0.0402228i	−0.877403	+	0.479754i	$0.840726\pi$
$18$	0.835023	−	4.13372i	0.196817	−	0.974327i
$19$	6.28411	−	3.62813i	1.44167	−	0.832350i	0.443711	−	0.896170i	$-0.353662\pi$
$19$	6.28411	−	3.62813i	1.44167	−	0.832350i	0.997961	+	0.0638195i	$0.0203282\pi$
$20$			0.0721699i			0.0161377i
$21$	−5.04343	+	2.27612i	−1.10057	+	0.496691i
$22$	0.557815	−	0.966164i	0.118927	−	0.205987i
$23$	2.54500			0.530670			0.265335	−	0.964156i	$-0.414517\pi$
$23$	2.54500			0.530670			0.265335	+	0.964156i	$0.414517\pi$
$24$	4.49158	−	2.02707i	0.916840	−	0.413775i
$25$	2.05894	−	3.56619i	0.411788	−	0.713238i
$26$	4.42891	−	2.46456i	0.868580	−	0.483340i
$27$	−4.96564	−	1.53051i	−0.955637	−	0.294546i
$28$	−0.0661242	−	0.0381768i	−0.0124963	−	0.00721474i
$29$	−4.22442	−	7.31690i	−0.784454	−	1.35871i	−0.929325	−	0.369264i	$-0.879610\pi$
$29$	−4.22442	−	7.31690i	−0.784454	−	1.35871i	0.144870	−	0.989451i	$-0.453723\pi$
$30$	−7.31563	−	0.731501i	−1.33564	−	0.133553i
$31$	6.22662	−	3.59494i	1.11833	−	0.645670i	0.177358	−	0.984146i	$-0.443245\pi$
$31$	6.22662	−	3.59494i	1.11833	−	0.645670i	0.940975	+	0.338476i	$0.109911\pi$
$32$	0.117082	+	0.0675976i	0.0206974	+	0.0119497i
$33$	−1.11615	−	0.802333i	−0.194297	−	0.139668i
$34$	0.233132	+	0.134599i	0.0399818	+	0.0230835i
$35$	4.82322	+	8.35407i	0.815273	+	1.41209i
$36$	−0.0228460	−	0.0679649i	−0.00380766	−	0.0113275i
$37$	2.25703	+	1.30310i	0.371054	+	0.214228i	0.673919	−	0.738806i	$-0.264610\pi$
$37$	2.25703	+	1.30310i	0.371054	+	0.214228i	−0.302865	+	0.953033i	$0.597943\pi$
$38$	−5.10020	+	8.83381i	−0.827362	+	1.43303i
$39$	−2.47865	−	5.73204i	−0.396901	−	0.917861i
$40$	−4.29547	−	7.43997i	−0.679173	−	1.17636i
$41$		−	0.905916i		−	0.141480i	−0.997495	−	0.0707402i	$-0.977464\pi$
$41$		−	0.905916i		−	0.141480i	0.997495	−	0.0707402i	$-0.0225361\pi$
$42$	4.54008	−	6.31584i	0.700550	−	0.974555i
$43$	−3.97309			−0.605890			−0.302945	−	0.953008i	$-0.597970\pi$
$43$	−3.97309			−0.605890			−0.302945	+	0.953008i	$0.597970\pi$
$44$		−	0.0189682i		−	0.00285956i
$45$	−1.79366	+	8.87940i	−0.267384	+	1.32366i
$46$	−3.09830	+	1.78880i	−0.456820	+	0.263745i
$47$	6.60765	+	3.81493i	0.963825	+	0.556465i	0.897348	−	0.441323i	$-0.145491\pi$
$47$	6.60765	+	3.81493i	0.963825	+	0.556465i	0.0664769	+	0.997788i	$0.478824\pi$
$48$	−3.99498	+	5.55754i	−0.576626	+	0.802161i
$49$	−3.20565			−0.457950
$50$			5.78866i			0.818640i
$51$	0.193600	−	0.269322i	0.0271094	−	0.0377127i
$52$	0.0442612	−	0.0739396i	0.00613793	−	0.0102536i
$53$	0.0692625			0.00951393			0.00475697	−	0.999989i	$-0.498486\pi$
$53$	0.0692625			0.00951393			0.00475697	+	0.999989i	$0.498486\pi$
$54$	7.12094	−	1.62694i	0.969037	−	0.221399i
$55$	−1.19821	+	2.07536i	−0.161567	+	0.279841i
$56$	9.08895			1.21456
$57$	10.2051	+	7.33587i	1.35170	+	0.971660i
$58$	10.2856	+	5.93842i	1.35057	+	0.779753i
$59$	−11.7491	−	6.78334i	−1.52960	−	0.883116i	−0.999378	−	0.0352582i	$-0.988775\pi$
$59$	−11.7491	−	6.78334i	−1.52960	−	0.883116i	−0.530224	−	0.847858i	$-0.677892\pi$
$60$	−0.113936	+	0.0514200i	−0.0147091	+	0.00663829i
$61$	0.178857			0.0229003			0.0114501	−	0.999934i	$-0.496355\pi$
$61$	0.178857			0.0229003			0.0114501	+	0.999934i	$0.496355\pi$
$62$	−5.05354	+	8.75299i	−0.641800	+	1.11163i
$63$	−7.18674	−	6.34047i	−0.905444	−	0.798825i
$64$	−8.09330			−1.01166
$65$	−9.51347	+	5.29398i	−1.18000	+	0.656638i
$66$	1.92274	+	0.192258i	0.236673	+	0.0236653i
$67$			10.5897i			1.29374i	0.762602	+	0.646868i	$0.223922\pi$
$67$			10.5897i			1.29374i	−0.762602	+	0.646868i	$0.776078\pi$
$68$	0.00457694			0.000555036
$69$	1.81328	+	4.01786i	0.218293	+	0.483693i
$70$	−11.7436	−	6.78019i	−1.40363	−	0.810387i
$71$	0.271545	−	0.156777i	0.0322265	−	0.0186060i	−0.483800	−	0.875178i	$-0.660744\pi$
$71$	0.271545	−	0.156777i	0.0322265	−	0.0186060i	0.516027	+	0.856572i	$0.327411\pi$
$72$	6.40037	+	5.64670i	0.754291	+	0.665470i
$73$		−	6.55741i		−	0.767487i	−0.923440	−	0.383743i	$-0.874635\pi$
$73$		−	6.55741i		−	0.767487i	0.923440	−	0.383743i	$-0.125365\pi$
$74$	−3.66363			−0.425888
$75$	7.09699	+	0.709639i	0.819489	+	0.0819420i
$76$			0.173429i			0.0198937i
$77$	−1.26767	−	2.19567i	−0.144464	−	0.250220i
$78$	7.04639	+	5.23605i	0.797847	+	0.592866i
$79$	−2.13465	+	3.69732i	−0.240167	+	0.415981i	−0.960762	−	0.277376i	$-0.910535\pi$
$79$	−2.13465	+	3.69732i	−0.240167	+	0.415981i	0.720595	+	0.693356i	$0.243869\pi$
$80$	10.3336	+	5.96613i	1.15534	+	0.667034i
$81$	−1.12169	−	8.92983i	−0.124633	−	0.992203i
$82$	0.636740	+	1.10287i	0.0703162	+	0.121791i
$83$	−7.01438	−	4.04975i	−0.769928	−	0.444518i	0.0629208	−	0.998019i	$-0.479958\pi$
$83$	−7.01438	−	4.04975i	−0.769928	−	0.444518i	−0.832849	+	0.553500i	$0.813292\pi$
$84$	0.0131581	−	0.131592i	0.00143567	−	0.0143579i
$85$	−0.500776	−	0.289123i	−0.0543168	−	0.0313598i
$86$	4.83686	−	2.79256i	0.521572	−	0.301130i
$87$	8.54153	−	11.8824i	0.915748	−	1.27392i
$88$	1.12896	+	1.95542i	0.120348	+	0.208448i
$89$	−4.56933	−	2.63810i	−0.484348	−	0.279638i	0.237879	−	0.971295i	$-0.423548\pi$
$89$	−4.56933	−	2.63810i	−0.484348	−	0.279638i	−0.722226	+	0.691657i	$0.756881\pi$
$90$	−4.05744	−	12.0705i	−0.427692	−	1.27235i
$91$	0.181987	−	11.5170i	0.0190774	−	1.20731i
$92$	−0.0304136	+	0.0526779i	−0.00317084	+	0.00549205i
$93$	10.1118	+	7.26876i	1.04854	+	0.753735i
$94$	−10.7256			−1.10626
$95$	10.9554	−	18.9754i	1.12400	−	1.94683i
$96$	−0.0232983	+	0.233003i	−0.00237788	+	0.0237808i
$97$		−	17.5710i		−	1.78406i	−0.451975	−	0.892030i	$-0.649281\pi$
$97$		−	17.5710i		−	1.78406i	0.451975	−	0.892030i	$-0.350719\pi$
$98$	3.90257	−	2.25315i	0.394219	−	0.227603i
$99$	0.471422	−	2.33374i	0.0473797	−	0.234550i
$100$	0.0492100	+	0.0852342i	0.00492100	+	0.00852342i
$101$	−0.748943	−	1.29721i	−0.0745227	−	0.129077i	0.826356	−	0.563148i	$-0.190410\pi$
$101$	−0.748943	−	1.29721i	−0.0745227	−	0.129077i	−0.900879	+	0.434071i	$0.857077\pi$
$102$	−0.0463911	+	0.463950i	−0.00459340	+	0.0459379i
$103$	1.62024	+	2.80634i	0.159647	+	0.276517i	0.934741	−	0.355329i	$-0.115631\pi$
$103$	1.62024	+	2.80634i	0.159647	+	0.276517i	−0.775094	+	0.631846i	$0.782298\pi$
$104$	−0.162074	+	10.2568i	−0.0158927	+	1.00576i
$105$	−9.75228	+	13.5667i	−0.951725	+	1.32397i
$106$	−0.0843205	+	0.0486825i	−0.00818993	+	0.00472846i
$107$	−2.74177	+	4.74888i	−0.265057	+	0.459091i	−0.967578	−	0.252571i	$-0.918724\pi$
$107$	−2.74177	+	4.74888i	−0.265057	+	0.459091i	0.702522	+	0.711662i	$0.252057\pi$
$108$	0.0910202	−	0.0844914i	0.00875843	−	0.00813019i
$109$		−	2.75058i		−	0.263458i	−0.991286	−	0.131729i	$-0.957947\pi$
$109$		−	2.75058i		−	0.263458i	0.991286	−	0.131729i	$-0.0420529\pi$
$110$		−	3.36874i		−	0.321197i
$111$	−0.449128	+	4.49166i	−0.0426294	+	0.426330i
$112$	−10.9327	+	6.31199i	−1.03304	+	0.596427i
$113$	−8.25023	+	14.2898i	−0.776117	+	1.34427i	0.158048	+	0.987431i	$0.449480\pi$
$113$	−8.25023	+	14.2898i	−0.776117	+	1.34427i	−0.934165	+	0.356842i	$0.883853\pi$
$114$	−17.5799	−	1.75785i	−1.64651	−	0.164637i
$115$	6.65528	−	3.84243i	0.620608	−	0.358308i
$116$	0.201932			0.0187490
$117$	7.28331	−	7.99709i	0.673342	−	0.739331i
$118$	19.0712			1.75565
$119$	0.529806	−	0.305884i	0.0485673	−	0.0280403i
$120$	8.68519	−	12.0822i	0.792846	−	1.10295i
$121$	−5.18508	+	8.98082i	−0.471371	+	0.816438i
$122$	−0.217741	+	0.125713i	−0.0197134	+	0.0113815i
$123$	1.43019	−	0.645452i	0.128956	−	0.0581984i
$124$			0.171843i			0.0154319i
$125$			2.66363i			0.238243i
$126$	13.2057	+	2.66759i	1.17646	+	0.237648i
$127$	−7.71406	+	13.3611i	−0.684512	+	1.18561i	0.289078	+	0.957305i	$0.406651\pi$
$127$	−7.71406	+	13.3611i	−0.684512	+	1.18561i	−0.973590	+	0.228304i	$0.926682\pi$
$128$	9.61866	−	5.55334i	0.850178	−	0.490850i
$129$	−2.83077	−	6.27240i	−0.249235	−	0.552254i
$130$	7.86077	−	13.1316i	0.689436	−	1.15172i
$131$	3.53140	+	6.11657i	0.308540	+	0.534407i	0.978043	−	0.208402i	$-0.0668263\pi$
$131$	3.53140	+	6.11657i	0.308540	+	0.534407i	−0.669503	+	0.742809i	$0.733493\pi$
$132$	0.0299455	−	0.0135145i	0.00260642	−	0.00117629i
$133$	11.5905	+	20.0754i	1.00503	+	1.74076i
$134$	−7.44316	−	12.8919i	−0.642992	−	1.11369i
$135$	−15.2961	+	3.49474i	−1.31648	+	0.300779i
$136$	−0.471835	+	0.272414i	−0.0404596	+	0.0233593i
$137$			6.97198i			0.595657i	0.954619	+	0.297828i	$0.0962623\pi$
$137$			6.97198i			0.595657i	−0.954619	+	0.297828i	$0.903738\pi$
$138$	−5.03152	−	3.61686i	−0.428311	−	0.307888i
$139$	5.45262	−	9.44421i	0.462485	−	0.801048i	−0.536599	−	0.843837i	$-0.680291\pi$
$139$	5.45262	−	9.44421i	0.462485	−	0.801048i	0.999084	+	0.0427897i	$0.0136245\pi$
$140$	−0.230556			−0.0194855
$141$	−1.31486	+	13.1497i	−0.110731	+	1.10741i
$142$	−0.220387	+	0.381722i	−0.0184945	+	0.0320334i
$143$	2.50039	−	1.39140i	0.209093	−	0.116355i
$144$	−11.6202	−	2.34731i	−0.968348	−	0.195609i
$145$	−22.0940	−	12.7560i	−1.83481	−	1.05933i
$146$	4.60900	+	7.98302i	0.381444	+	0.660680i
$147$	−2.28398	−	5.06083i	−0.188379	−	0.417410i
$148$	−0.0539445	+	0.0311448i	−0.00443421	+	0.00256009i
$149$	−12.6627	−	7.31084i	−1.03737	−	0.598927i	−0.118284	−	0.992980i	$-0.537739\pi$
$149$	−12.6627	−	7.31084i	−1.03737	−	0.598927i	−0.919088	+	0.394053i	$0.871073\pi$
$150$	−9.13869	+	4.12433i	−0.746171	+	0.336750i
$151$	−0.912654	−	0.526921i	−0.0742707	−	0.0428802i	0.462405	−	0.886669i	$-0.346987\pi$
$151$	−0.912654	−	0.526921i	−0.0742707	−	0.0428802i	−0.536675	+	0.843789i	$0.680320\pi$
$152$	−10.3223	−	17.8787i	−0.837249	−	1.45016i
$153$	0.563122	+	0.113752i	0.0455258	+	0.00919633i
$154$	3.08653	+	1.78201i	0.248720	+	0.143599i
$155$	10.8552	−	18.8018i	0.871912	−	1.51020i
$156$	0.148266	+	0.0171953i	0.0118707	+	0.00137673i
$157$	5.59684	+	9.69401i	0.446677	+	0.773667i	0.998167	−	0.0605145i	$-0.0192741\pi$
$157$	5.59684	+	9.69401i	0.446677	+	0.773667i	−0.551491	+	0.834181i	$0.685941\pi$
$158$		−	6.00151i		−	0.477454i
$159$	0.0493485	+	0.109346i	0.00391359	+	0.00867172i
$160$	0.408233			0.0322736
$161$			8.13034i			0.640761i
$162$	7.64205	+	10.0828i	0.600416	+	0.792180i
$163$	−1.69044	+	0.975977i	−0.132406	+	0.0764444i	−0.564740	−	0.825269i	$-0.691023\pi$
$163$	−1.69044	+	0.975977i	−0.132406	+	0.0764444i	0.432334	+	0.901713i	$0.357690\pi$
$164$	0.0187512	+	0.0108260i	0.00146422	+	0.000845367i
$165$	−4.13012	−	0.412978i	−0.321530	−	0.0321503i
$166$	11.3858			0.883708
$167$			19.8679i			1.53742i	0.639595	+	0.768712i	$0.279102\pi$
$167$			19.8679i			1.53742i	−0.639595	+	0.768712i	$0.720898\pi$
$168$	6.47574	+	14.3489i	0.499614	+	1.10704i
$169$	12.9935	+	0.410740i	0.999501	+	0.0315954i
$170$	0.812864			0.0623438
$171$	−4.31029	+	21.3378i	−0.329616	+	1.63174i
$172$	0.0474797	−	0.0822372i	0.00362029	−	0.00627053i
$173$	−3.37210			−0.256376			−0.128188	−	0.991750i	$-0.540916\pi$
$173$	−3.37210			−0.256376			−0.128188	+	0.991750i	$0.540916\pi$
$174$	−2.04675	+	20.4692i	−0.155164	+	1.55177i
$175$	11.3926	+	6.57755i	0.861203	+	0.497216i
$176$	−2.71595	−	1.56806i	−0.204723	−	0.118197i
$177$	2.33796	−	23.3816i	0.175732	−	1.75747i
$178$	7.41696			0.555925
$179$	6.46527	−	11.1982i	0.483237	−	0.836990i	−0.516578	−	0.856240i	$-0.672794\pi$
$179$	6.46527	−	11.1982i	0.483237	−	0.836990i	0.999815	+	0.0192497i	$0.00612775\pi$
$180$	−0.162356	−	0.143238i	−0.0121013	−	0.0106763i
$181$	−11.3925			−0.846798			−0.423399	−	0.905943i	$-0.639163\pi$
$181$	−11.3925			−0.846798			−0.423399	+	0.905943i	$0.639163\pi$
$182$	7.87336	+	14.1487i	0.583612	+	1.04877i
$183$	0.127433	+	0.282365i	0.00942010	+	0.0208730i
$184$		−	7.24073i		−	0.533793i
$185$	7.86962			0.578586
$186$	−17.4191	−	1.74177i	−1.27723	−	0.127712i
$187$	0.131617	+	0.0759893i	0.00962481	+	0.00555688i
$188$	−0.157927	+	0.0911792i	−0.0115180	+	0.00664993i
$189$	4.88941	−	15.8634i	0.355652	−	1.15389i
$190$			30.8010i			2.23454i
$191$	3.26866			0.236512			0.118256	−	0.992983i	$-0.462270\pi$
$191$	3.26866			0.236512			0.118256	+	0.992983i	$0.462270\pi$
$192$	−5.76636	−	12.7771i	−0.416151	−	0.922106i
$193$		−	19.0634i		−	1.37221i	−0.727501	−	0.686107i	$-0.759318\pi$
$193$		−	19.0634i		−	1.37221i	0.727501	−	0.686107i	$-0.240682\pi$
$194$	12.3501	+	21.3910i	0.886684	+	1.53578i
$195$	−15.1359	−	11.2473i	−1.08391	−	0.805433i
$196$	0.0383085	−	0.0663523i	0.00273632	−	0.00473945i
$197$	−2.13371	−	1.23190i	−0.152020	−	0.0877690i	0.422060	−	0.906568i	$-0.361307\pi$
$197$	−2.13371	−	1.23190i	−0.152020	−	0.0877690i	−0.574081	+	0.818799i	$0.694640\pi$
$198$	1.06640	+	3.17245i	0.0757859	+	0.225456i
$199$	11.7617	+	20.3718i	0.833764	+	1.44412i	0.895033	+	0.446000i	$0.147152\pi$
$199$	11.7617	+	20.3718i	0.833764	+	1.44412i	−0.0612690	+	0.998121i	$0.519515\pi$
$200$	−10.1461	−	5.85784i	−0.717436	−	0.414212i
$201$	−16.7182	+	7.54500i	−1.17921	+	0.532183i
$202$	1.82353	+	1.05282i	0.128303	+	0.0740760i
$203$	23.3748	−	13.4954i	1.64059	−	0.947194i
$204$	0.00326100	+	0.00722573i	0.000228316	+	0.000505902i
$205$	−1.36774	−	2.36900i	−0.0955274	−	0.165458i
$206$	−3.94498	−	2.27763i	−0.274860	−	0.158690i
$207$	−5.05115	+	5.72532i	−0.351079	+	0.397938i
$208$	−6.92806	−	12.4500i	−0.480374	−	0.863250i
$209$	−2.87938	+	4.98723i	−0.199171	+	0.344974i
$210$	2.33687	−	23.3707i	0.161260	−	1.61273i
$211$	−1.44535			−0.0995020			−0.0497510	−	0.998762i	$-0.515843\pi$
$211$	−1.44535			−0.0995020			−0.0497510	+	0.998762i	$0.515843\pi$
$212$	−0.000827709		0.00143363i	−5.68473e−5		9.84623e-5i
$213$	0.440979	+	0.316994i	0.0302154	+	0.0217201i
$214$		−	7.70841i		−	0.526936i
$215$	−10.3898	+	5.99854i	−0.708576	+	0.409097i
$216$	−4.35441	+	14.1276i	−0.296280	+	0.961262i
$217$	11.4845	+	19.8917i	0.779618	+	1.35034i
$218$	1.93330	+	3.34857i	0.130940	+	0.226794i
$219$	10.3523	−	4.67206i	0.699546	−	0.315708i
$220$	−0.0286380	−	0.0496024i	−0.00193077	−	0.00334419i
$221$	0.335739	+	0.603335i	0.0225842	+	0.0405847i
$222$	−2.61028	−	5.78385i	−0.175190	−	0.388187i
$223$	−0.525138	+	0.303188i	−0.0351658	+	0.0203030i	−0.517480	−	0.855695i	$-0.673130\pi$
$223$	−0.525138	+	0.303188i	−0.0351658	+	0.0203030i	0.482314	+	0.875998i	$0.339796\pi$
$224$	−0.215949	+	0.374035i	−0.0144287	+	0.0249912i
$225$	3.93617	+	11.7098i	0.262412	+	0.780652i
$226$		−	23.1953i		−	1.54293i
$227$		−	23.0561i		−	1.53029i	−0.643861	−	0.765143i	$-0.722668\pi$
$227$		−	23.0561i		−	1.53029i	0.643861	−	0.765143i	$-0.277332\pi$
$228$	−0.273797	+	0.123566i	−0.0181326	+	0.00818334i
$229$	3.97688	−	2.29605i	0.262799	−	0.151727i	−0.362812	−	0.931863i	$-0.618183\pi$
$229$	3.97688	−	2.29605i	0.262799	−	0.151727i	0.625611	+	0.780135i	$0.284850\pi$
$230$	−5.40144	+	9.35558i	−0.356161	+	0.616888i
$231$	2.56316	−	3.56568i	0.168643	−	0.234605i
$232$	−20.8171	+	12.0188i	−1.36671	+	0.789071i
$233$	−7.84289			−0.513804			−0.256902	−	0.966437i	$-0.582702\pi$
$233$	−7.84289			−0.513804			−0.256902	+	0.966437i	$0.582702\pi$
$234$	−3.24583	+	14.8549i	−0.212186	+	0.971096i
$235$	23.0390			1.50290
$236$	0.280811	−	0.162126i	0.0182792	−	0.0105535i
$237$	−7.35794	−	0.735732i	−0.477950	−	0.0477909i
$238$	−0.429993	+	0.744769i	−0.0278723	+	0.0482762i
$239$	−1.19864	+	0.692034i	−0.0775334	+	0.0447639i	−0.538266	−	0.842775i	$-0.680920\pi$
$239$	−1.19864	+	0.692034i	−0.0775334	+	0.0447639i	0.460732	+	0.887539i	$0.347587\pi$
$240$	−2.05630	+	20.5647i	−0.132734	+	1.32745i
$241$		−	4.04654i		−	0.260661i	−0.991471	−	0.130330i	$-0.958396\pi$
$241$		−	4.04654i		−	0.260661i	0.991471	−	0.130330i	$-0.0416038\pi$
$242$		−	14.5777i		−	0.937092i
$243$	13.2985	−	8.13321i	0.853101	−	0.521746i
$244$	−0.00213739	+	0.00370208i	−0.000136833	+	0.000237001i
$245$	−8.38288	+	4.83986i	−0.535563	+	0.309207i
$246$	−1.28745	+	1.79101i	−0.0820850	+	0.114191i
$247$	−22.8615	+	12.7218i	−1.45464	+	0.809468i
$248$	−10.2279	−	17.7152i	−0.649470	−	1.12492i
$249$	1.39580	−	13.9591i	0.0884551	−	0.884625i
$250$	−1.87219	−	3.24272i	−0.118407	−	0.205088i
$251$	3.43920	+	5.95686i	0.217080	+	0.375994i	0.953914	−	0.300080i	$-0.0970134\pi$
$251$	3.43920	+	5.95686i	0.217080	+	0.375994i	−0.736834	+	0.676074i	$0.763680\pi$
$252$	0.217122	−	0.0729844i	0.0136774	−	0.00459759i
$253$	−1.74918	+	1.00989i	−0.109970	+	0.0634913i
$254$		−	21.6879i		−	1.36082i
$255$	0.0996499	−	0.996583i	0.00624032	−	0.0624085i
$256$	0.286766	−	0.496694i	0.0179229	−	0.0310434i
$257$	7.53544			0.470048			0.235024	−	0.971990i	$-0.424483\pi$
$257$	7.53544			0.470048			0.235024	+	0.971990i	$0.424483\pi$
$258$	7.85487	+	5.64640i	0.489023	+	0.351529i
$259$	−4.16291	+	7.21037i	−0.258671	+	0.448031i
$260$	0.00411127	−	0.260180i	0.000254970	−	0.0161357i
$261$	24.8447	+	5.01869i	1.53785	+	0.310649i
$262$	−8.59829	−	4.96422i	−0.531204	−	0.306691i
$263$	−2.25667	−	3.90867i	−0.139152	−	0.241019i	0.788024	−	0.615645i	$-0.211104\pi$
$263$	−2.25667	−	3.90867i	−0.139152	−	0.241019i	−0.927176	+	0.374626i	$0.877771\pi$
$264$	−2.28270	+	3.17553i	−0.140490	+	0.195440i
$265$	0.181124	−	0.104572i	0.0111263	−	0.00642380i
$266$	−28.2207	−	16.2932i	−1.73032	−	0.999003i
$267$	0.909254	−	9.09331i	0.0556454	−	0.556501i
$268$	−0.219191	−	0.126550i	−0.0133892	−	0.00773028i
$269$	−7.59726	−	13.1588i	−0.463213	−	0.802309i	0.535906	−	0.844278i	$-0.319970\pi$
$269$	−7.59726	−	13.1588i	−0.463213	−	0.802309i	−0.999119	+	0.0419692i	$0.986637\pi$
$270$	16.1652	−	15.0056i	0.983780	−	0.913214i
$271$	−19.0083	−	10.9744i	−1.15467	−	0.666650i	−0.204650	−	0.978835i	$-0.565606\pi$
$271$	−19.0083	−	10.9744i	−1.15467	−	0.666650i	−0.950021	+	0.312185i	$0.898939\pi$
$272$	0.378366	−	0.655349i	0.0229418	−	0.0397364i
$273$	18.3117	−	7.91835i	1.10828	−	0.479241i
$274$	−4.90039	−	8.48773i	−0.296043	−	0.512762i
$275$			3.26806i			0.197071i
$276$	−0.104833	−	0.0104824i	−0.00631021	−	0.000630968i
$277$	6.04087			0.362961			0.181480	−	0.983395i	$-0.441911\pi$
$277$	6.04087			0.362961			0.181480	+	0.983395i	$0.441911\pi$
$278$			15.3299i			0.919427i
$279$	−4.27086	+	21.1426i	−0.255690	+	1.26577i
$280$	23.7679	−	13.7224i	1.42041	−	0.820072i
$281$	6.56065	+	3.78780i	0.391376	+	0.225961i	0.682756	−	0.730646i	$-0.260781\pi$
$281$	6.56065	+	3.78780i	0.391376	+	0.225961i	−0.291380	+	0.956607i	$0.594114\pi$
$282$	−7.64182	−	16.9327i	−0.455064	−	1.00833i
$283$	−28.0741			−1.66883			−0.834416	−	0.551135i	$-0.814195\pi$
$283$	−28.0741			−1.66883			−0.834416	+	0.551135i	$0.814195\pi$
$284$			0.00749413i			0.000444695i
$285$	37.7624	+	3.77593i	2.23685	+	0.223667i
$286$	−2.06602	+	3.45134i	−0.122166	+	0.204082i
$287$	2.89406			0.170831
$288$	−0.384447	+	0.129229i	−0.0226537	+	0.00761492i
$289$	8.48166	−	14.6907i	0.498921	−	0.864157i
$290$	35.8631			2.10595
$291$	27.7397	−	12.5190i	1.62613	−	0.733880i
$292$	0.135729	+	0.0783631i	0.00794293	+	0.00458586i
$293$	19.8636	+	11.4682i	1.16044	+	0.669982i	0.951410	−	0.307926i	$-0.0996350\pi$
$293$	19.8636	+	11.4682i	1.16044	+	0.669982i	0.209033	+	0.977909i	$0.432968\pi$
$294$	6.33762	+	4.55574i	0.369618	+	0.265696i
$295$	−40.9657			−2.38512
$296$	3.70741	−	6.42142i	0.215489	−	0.373237i
$297$	4.02021	−	0.918510i	0.233276	−	0.0532974i
$298$	20.5542			1.19068
$299$	−9.17500	−	0.144980i	−0.530604	−	0.00838441i
$300$	−0.0994997	+	0.138417i	−0.00574462	+	0.00799151i
$301$		−	12.6925i		−	0.731586i
$302$	1.48143			0.0852465
$303$	1.51432	−	2.10662i	0.0869954	−	0.121022i
$304$	24.8324	+	14.3370i	1.42424	+	0.822285i
$305$	0.467717	−	0.270036i	0.0267814	−	0.0154622i
$306$	−0.765501	+	0.257319i	−0.0437608	+	0.0147099i
$307$			3.31351i			0.189112i	0.995520	+	0.0945560i	$0.0301431\pi$
$307$			3.31351i			0.189112i	−0.995520	+	0.0945560i	$0.969857\pi$
$308$	0.0605962			0.00345279
$309$	−3.27604	+	4.55739i	−0.186367	+	0.259261i
$310$			30.5192i			1.73337i
$311$	12.6695	+	21.9442i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884682\pi$
$311$	12.6695	+	21.9442i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$312$	−16.3081	+	7.05193i	−0.923264	+	0.399237i
$313$	−8.71624	+	15.0970i	−0.492671	+	0.853331i	−0.999964	−	0.00844245i	$-0.997313\pi$
$313$	−8.71624	+	15.0970i	−0.492671	+	0.853331i	0.507294	+	0.861773i	$0.330646\pi$
$314$	−13.6272	−	7.86769i	−0.769030	−	0.444000i
$315$	−28.3664	−	5.73009i	−1.59826	−	0.322854i
$316$	−0.0510194	−	0.0883682i	−0.00287007	−	0.00497110i
$317$	11.2999	+	6.52400i	0.634666	+	0.366425i	0.782557	−	0.622579i	$-0.213915\pi$
$317$	11.2999	+	6.52400i	0.634666	+	0.366425i	−0.147891	+	0.989004i	$0.547248\pi$
$318$	−0.136933	−	0.0984331i	−0.00767883	−	0.00551986i
$319$	5.80688	+	3.35261i	0.325123	+	0.187710i
$320$	−21.1643	+	12.2192i	−1.18312	+	0.683074i
$321$	−9.45063	−	0.944983i	−0.527483	−	0.0527438i
$322$	−5.71457	−	9.89792i	−0.318460	−	0.551589i
$323$	−1.20340	−	0.694783i	−0.0669589	−	0.0386588i
$324$	0.198239	+	0.0834968i	0.0110133	+	0.00463871i
$325$	−7.62584	+	12.7392i	−0.423006	+	0.706643i
$326$	1.37197	−	2.37632i	0.0759862	−	0.131612i
$327$	4.34241	−	1.95975i	0.240136	−	0.108374i
$328$	−2.57740			−0.142313
$329$	−12.1873	+	21.1090i	−0.671907	+	1.16378i
$330$	5.31830	−	2.40018i	0.292763	−	0.132125i
$331$			4.75617i			0.261423i	0.991420	+	0.130711i	$0.0417261\pi$
$331$			4.75617i			0.261423i	−0.991420	+	0.130711i	$0.958274\pi$
$332$	0.167648	−	0.0967917i	0.00920088	−	0.00531213i
$333$	−7.41109	+	2.49119i	−0.406125	+	0.136517i
$334$	−13.9645	−	24.1873i	−0.764105	−	1.32347i
$335$	15.9882	+	27.6924i	0.873530	+	1.51300i
$336$	−17.7543	−	12.7625i	−0.968574	−	0.696250i
$337$	−12.7677	−	22.1143i	−0.695500	−	1.20464i	−0.970012	−	0.243057i	$-0.921850\pi$
$337$	−12.7677	−	22.1143i	−0.695500	−	1.20464i	0.274512	−	0.961584i	$-0.411484\pi$
$338$	−16.1071	+	8.63270i	−0.876108	+	0.469557i
$339$	−28.4378	−	2.84354i	−1.54453	−	0.154440i
$340$	0.0119689	−	0.00691023i	0.000649103	−	0.000374760i
$341$	−2.85304	+	4.94160i	−0.154501	+	0.267603i
$342$	−9.75030	−	29.0063i	−0.527236	−	1.56848i
$343$			12.1215i			0.654502i
$344$			11.3037i			0.609456i
$345$	10.8079	+	7.76916i	0.581878	+	0.418278i
$346$	4.10521	−	2.37014i	0.220697	−	0.127420i
$347$	−2.71373	+	4.70031i	−0.145680	+	0.252326i	−0.929627	−	0.368503i	$-0.879870\pi$
$347$	−2.71373	+	4.70031i	−0.145680	+	0.252326i	0.783946	+	0.620829i	$0.213204\pi$
$348$	0.143874	+	0.318795i	0.00771245	+	0.0170892i
$349$	22.8603	−	13.1984i	1.22368	−	0.706493i	0.257981	−	0.966150i	$-0.416943\pi$
$349$	22.8603	−	13.1984i	1.22368	−	0.706493i	0.965701	+	0.259657i	$0.0836096\pi$
$350$	−18.4926			−0.988472
$351$	17.8144	+	5.80051i	0.950864	+	0.309608i
$352$	−0.107294			−0.00571881
$353$	−25.8786	+	14.9410i	−1.37738	+	0.795230i	−0.991843	−	0.127463i	$-0.959316\pi$
$353$	−25.8786	+	14.9410i	−1.37738	+	0.795230i	−0.385535	+	0.922693i	$0.625983\pi$
$354$	13.5880	+	30.1081i	0.722191	+	1.60023i
$355$	0.473401	−	0.819954i	0.0251255	−	0.0435186i
$356$	0.109210	−	0.0630523i	0.00578811	−	0.00334176i
$357$	0.860385	+	0.618480i	0.0455364	+	0.0327334i
$358$			18.1769i			0.960681i
$359$			27.5815i			1.45570i	0.685738	+	0.727849i	$0.259480\pi$
$359$			27.5815i			1.45570i	−0.685738	+	0.727849i	$0.740520\pi$
$360$	25.2625	+	5.10311i	1.33145	+	0.268957i
$361$	16.8267	−	29.1446i	0.885614	−	1.53393i
$362$	13.8693	−	8.00743i	0.728953	−	0.420861i
$363$	−17.8725	−	1.78710i	−0.938064	−	0.0937985i
$364$	0.236210	+	0.141398i	0.0123807	+	0.00741128i
$365$	−9.90032	−	17.1479i	−0.518207	−	0.897560i
$366$	−0.353603	−	0.254184i	−0.0184831	−	0.0132864i
$367$	−10.7197	−	18.5671i	−0.559565	−	0.969196i	−0.997533	−	0.0702047i	$-0.977635\pi$
$367$	−10.7197	−	18.5671i	−0.559565	−	0.969196i	0.437967	−	0.898991i	$-0.355699\pi$
$368$	5.02845	+	8.70954i	0.262126	+	0.454016i
$369$	2.03798	+	1.79800i	0.106093	+	0.0936001i
$370$	−9.58051	+	5.53131i	−0.498067	+	0.287559i
$371$			0.221268i			0.0114877i
$372$	−0.271292	+	0.122435i	−0.0140658	+	0.00634797i
$373$	12.4225	−	21.5164i	0.643211	−	1.11407i	−0.341500	−	0.939882i	$-0.610935\pi$
$373$	12.4225	−	21.5164i	0.643211	−	1.11407i	0.984712	−	0.174193i	$-0.0557317\pi$
$374$	−0.213642			−0.0110472
$375$	−4.20514	+	1.89780i	−0.217152	+	0.0980019i
$376$	10.8538	−	18.7993i	0.559740	−	0.969498i
$377$	14.8126	+	26.6188i	0.762889	+	1.37094i
$378$	5.19748	+	22.7487i	0.267329	+	1.17007i
$379$	−0.763882	−	0.441027i	−0.0392380	−	0.0226540i	0.480253	−	0.877130i	$-0.340545\pi$
$379$	−0.763882	−	0.441027i	−0.0392380	−	0.0226540i	−0.519491	+	0.854476i	$0.673878\pi$
$380$	0.261842	+	0.453524i	0.0134322	+	0.0232653i
$381$	−26.5897	−	2.65874i	−1.36223	−	0.136212i
$382$	−3.97928	+	2.29744i	−0.203598	+	0.117547i
$383$	2.48536	+	1.43492i	0.126996	+	0.0733210i	0.562152	−	0.827034i	$-0.309974\pi$
$383$	2.48536	+	1.43492i	0.126996	+	0.0733210i	−0.435156	+	0.900355i	$0.643307\pi$
$384$	15.6203	+	11.2285i	0.797122	+	0.573004i
$385$	−6.63000	−	3.82783i	−0.337896	−	0.195084i
$386$	13.3991	+	23.2079i	0.681995	+	1.18125i
$387$	7.88551	−	8.93799i	0.400843	−	0.454344i
$388$	0.363693	+	0.209979i	0.0184637	+	0.0106600i
$389$	6.00741	−	10.4051i	0.304588	−	0.527561i	−0.672582	−	0.740023i	$-0.734815\pi$
$389$	6.00741	−	10.4051i	0.304588	−	0.527561i	0.977169	+	0.212462i	$0.0681481\pi$
$390$	26.3319	+	3.05388i	1.33337	+	0.154639i
$391$	−0.243683	−	0.422071i	−0.0123236	−	0.0213450i
$392$			9.12031i			0.460645i
$393$	−7.14029	+	9.93306i	−0.360180	+	0.501057i
$394$	3.46345			0.174486
$395$			12.8915i			0.648641i
$396$	0.0426714	+	0.0376467i	0.00214432	+	0.00189182i
$397$	7.80521	−	4.50634i	0.391732	−	0.226167i	−0.291178	−	0.956669i	$-0.594047\pi$
$397$	7.80521	−	4.50634i	0.391732	−	0.226167i	0.682910	+	0.730502i	$0.260714\pi$
$398$	−28.6375	−	16.5339i	−1.43547	−	0.828767i
$399$	−23.4354	+	32.6016i	−1.17324	+	1.63212i
$400$	16.2723			0.813616
$401$		−	33.2406i		−	1.65996i	−0.557795	−	0.829979i	$-0.688353\pi$
$401$		−	33.2406i		−	1.65996i	0.557795	−	0.829979i	$-0.311647\pi$
$402$	15.0497	−	20.9360i	0.750608	−	1.04419i
$403$	−22.6524	+	12.6054i	−1.12840	+	0.627920i
$404$	0.0358004			0.00178114
$405$	−16.4154	−	21.6583i	−0.815690	−	1.07621i
$406$	−18.9710	+	32.8588i	−0.941517	+	1.63076i
$407$	−2.06834			−0.102524
$408$	−0.766242	−	0.550806i	−0.0379346	−	0.0272690i
$409$	29.3655	+	16.9542i	1.45203	+	0.838332i	0.998597	−	0.0529572i	$-0.0168647\pi$
$409$	29.3655	+	16.9542i	1.45203	+	0.838332i	0.453436	+	0.891289i	$0.350198\pi$
$410$	3.33020	+	1.92269i	0.164467	+	0.0949549i
$411$	−11.0068	+	4.96743i	−0.542927	+	0.245025i
$412$	−0.0774496			−0.00381567
$413$	21.6703	−	37.5340i	1.06632	−	1.84693i
$414$	2.12514	−	10.5203i	0.104445	−	0.517046i
$415$	−24.4571			−1.20055
$416$	−0.418243	−	0.250366i	−0.0205061	−	0.0122752i
$417$	18.7947	+	1.87931i	0.920381	+	0.0920303i
$418$		−	8.09530i		−	0.395954i
$419$	25.3790			1.23984			0.619921	−	0.784664i	$-0.287164\pi$
$419$	25.3790			1.23984			0.619921	+	0.784664i	$0.287164\pi$
$420$	−0.164268	−	0.363984i	−0.00801545	−	0.0177606i
$421$	−10.2213	−	5.90124i	−0.498153	−	0.287609i	0.229797	−	0.973239i	$-0.426194\pi$
$421$	−10.2213	−	5.90124i	−0.498153	−	0.287609i	−0.727951	+	0.685630i	$0.759527\pi$
$422$	1.75958	−	1.01589i	0.0856549	−	0.0494529i
$423$	−21.6966	+	7.29318i	−1.05492	+	0.354607i
$424$		−	0.197057i		−	0.00956993i
$425$	−0.788570			−0.0382512
$426$	−0.759655	−	0.0759591i	−0.0368054	−	0.00368023i
$427$			0.571381i			0.0276511i
$428$	−0.0655299	−	0.113501i	−0.00316751	−	0.00548629i
$429$	3.97812	+	2.95608i	0.192066	+	0.142721i
$430$	8.43237	−	14.6053i	0.406645	−	0.704330i
$431$	9.96641	+	5.75411i	0.480065	+	0.277166i	0.720444	−	0.693514i	$-0.243938\pi$
$431$	9.96641	+	5.75411i	0.480065	+	0.277166i	−0.240379	+	0.970679i	$0.577272\pi$
$432$	−4.57345	−	20.0174i	−0.220040	−	0.963090i
$433$	7.00567	+	12.1342i	0.336671	+	0.583131i	0.983804	−	0.179246i	$-0.0573657\pi$
$433$	7.00567	+	12.1342i	0.336671	+	0.583131i	−0.647133	+	0.762377i	$0.724032\pi$
$434$	−27.9626	−	16.1442i	−1.34225	−	0.774946i
$435$	4.39650	−	43.9687i	0.210796	−	2.10814i
$436$	0.0569331	+	0.0328703i	0.00272660	+	0.00157420i
$437$	15.9931	−	9.23361i	0.765053	−	0.441703i
$438$	−9.31914	+	12.9641i	−0.445286	+	0.619450i
$439$	17.0399	+	29.5140i	0.813271	+	1.40863i	0.910563	+	0.413371i	$0.135649\pi$
$439$	17.0399	+	29.5140i	0.813271	+	1.40863i	−0.0972920	+	0.995256i	$0.531018\pi$
$440$	5.90455	+	3.40900i	0.281489	+	0.162517i
$441$	6.36235	−	7.21153i	0.302969	−	0.343406i
$442$	−0.832796	−	0.498522i	−0.0396121	−	0.0237123i
$443$	16.3341	−	28.2916i	0.776058	−	1.34417i	−0.158139	−	0.987417i	$-0.550549\pi$
$443$	16.3341	−	28.2916i	0.776058	−	1.34417i	0.934198	−	0.356756i	$-0.116117\pi$
$444$	−0.0876037	−	0.0629731i	−0.00415749	−	0.00298857i
$445$	−15.9319			−0.755246
$446$	0.426204	−	0.738206i	0.0201813	−	0.0349551i
$447$	2.51977	−	25.1998i	0.119181	−	1.19191i
$448$		−	25.8551i		−	1.22154i
$449$	7.66848	−	4.42740i	0.361898	−	0.208942i	−0.308015	−	0.951381i	$-0.599665\pi$
$449$	7.66848	−	4.42740i	0.361898	−	0.208942i	0.669913	+	0.742440i	$0.266331\pi$
$450$	−13.0224	−	11.4889i	−0.613880	−	0.541593i
$451$	0.359479	+	0.622636i	0.0169272	+	0.0293188i
$452$	−0.197186	−	0.341536i	−0.00927484	−	0.0160645i
$453$	0.181610	−	1.81625i	0.00853277	−	0.0853349i
$454$	16.2054	+	28.0686i	0.760557	+	1.31732i
$455$	−16.9123	−	30.3920i	−0.792861	−	1.42480i
$456$	20.8711	−	29.0344i	0.977379	−	1.35966i
$457$	13.1806	−	7.60982i	0.616563	−	0.355973i	−0.158967	−	0.987284i	$-0.550816\pi$
$457$	13.1806	−	7.60982i	0.616563	−	0.355973i	0.775530	+	0.631311i	$0.217483\pi$
$458$	−3.22764	+	5.59044i	−0.150818	+	0.261224i
$459$	0.221633	+	0.970061i	0.0103449	+	0.0452786i
$460$			0.183673i			0.00856379i
$461$			34.8112i			1.62132i	0.585519	+	0.810658i	$0.300891\pi$
$461$			34.8112i			1.62132i	−0.585519	+	0.810658i	$0.699109\pi$
$462$	−0.614192	+	6.14244i	−0.0285748	+	0.285772i
$463$	23.7329	−	13.7022i	1.10296	−	0.636795i	0.165963	−	0.986132i	$-0.446927\pi$
$463$	23.7329	−	13.7022i	1.10296	−	0.636795i	0.936997	+	0.349337i	$0.113593\pi$
$464$	16.6933	−	28.9137i	0.774968	−	1.34228i
$465$	37.4170	+	3.74138i	1.73517	+	0.173502i
$466$	9.54797	−	5.51252i	0.442301	−	0.255363i
$467$	−9.34092			−0.432246			−0.216123	−	0.976366i	$-0.569341\pi$
$467$	−9.34092			−0.432246			−0.216123	+	0.976366i	$0.569341\pi$
$468$	0.0784904	+	0.246322i	0.00362822	+	0.0113862i
$469$	−33.8301			−1.56213
$470$	−28.0478	+	16.1934i	−1.29375	+	0.746946i
$471$	−11.3165	+	15.7427i	−0.521436	+	0.725385i
$472$	−19.2991	+	33.4270i	−0.888314	+	1.53860i
$473$	2.73070	−	1.57657i	0.125558	−	0.0724909i
$474$	9.47472	−	4.27598i	0.435188	−	0.196402i
$475$		−	29.8804i		−	1.37101i
$476$			0.0146216i			0.000670182i
$477$	−0.137467	+	0.155815i	−0.00629420	+	0.00713429i
$478$	0.972818	−	1.68497i	0.0444957	−	0.0770687i
$479$	−9.55816	+	5.51841i	−0.436723	+	0.252142i	−0.702207	−	0.711973i	$-0.747802\pi$
$479$	−9.55816	+	5.51841i	−0.436723	+	0.252142i	0.265483	+	0.964115i	$0.414468\pi$
$480$	0.290860	+	0.644486i	0.0132759	+	0.0294166i
$481$	−8.06259	−	4.82637i	−0.367622	−	0.220064i
$482$	2.84419	+	4.92628i	0.129549	+	0.224386i
$483$	−12.8356	+	5.79275i	−0.584038	+	0.263579i
$484$	−0.123927	−	0.214647i	−0.00563303	−	0.00975669i
$485$	−26.5285	−	45.9487i	−1.20460	−	2.08642i
$486$	−10.4731	+	19.2485i	−0.475070	+	0.873131i
$487$	9.99524	−	5.77075i	0.452928	−	0.261498i	−0.256138	−	0.966640i	$-0.582450\pi$
$487$	9.99524	−	5.77075i	0.452928	−	0.261498i	0.709066	+	0.705142i	$0.249117\pi$
$488$		−	0.508861i		−	0.0230350i
$489$	−2.74521	−	1.97337i	−0.124143	−	0.0892388i
$490$	6.80357	−	11.7841i	0.307354	−	0.532353i
$491$	−21.2444			−0.958747			−0.479373	−	0.877611i	$-0.659136\pi$
$491$	−21.2444			−0.958747			−0.479373	+	0.877611i	$0.659136\pi$
$492$	−0.00373131	+	0.0373162i	−0.000168220	+	0.00168235i
$493$	−0.808971	+	1.40118i	−0.0364342	+	0.0631059i
$494$	18.8900	−	31.5562i	0.849900	−	1.41978i
$495$	−2.29067	−	6.81456i	−0.102958	−	0.306292i
$496$	24.6053	+	14.2059i	1.10481	+	0.637862i
$497$	0.500844	+	0.867487i	0.0224659	+	0.0389121i
$498$	8.11220	+	17.9750i	0.363517	+	0.805479i
$499$	−11.3888	+	6.57531i	−0.509832	+	0.294351i	−0.732764	−	0.680482i	$-0.761770\pi$
$499$	−11.3888	+	6.57531i	−0.509832	+	0.294351i	0.222933	+	0.974834i	$0.428437\pi$
$500$	−0.0551334	−	0.0318313i	−0.00246564	−	0.00142354i
$501$	−31.3659	+	14.1556i	−1.40133	+	0.632425i
$502$	−8.37379	−	4.83461i	−0.373740	−	0.215779i
$503$	−3.54282	−	6.13635i	−0.157967	−	0.273606i	0.776169	−	0.630525i	$-0.217161\pi$
$503$	−3.54282	−	6.13635i	−0.157967	−	0.273606i	−0.934135	+	0.356919i	$0.883827\pi$
$504$	−18.0391	+	20.4468i	−0.803526	+	0.910773i
$505$	−3.91703	−	2.26150i	−0.174305	−	0.100635i
$506$	1.41964	−	2.45889i	0.0631108	−	0.109311i
$507$	8.60924	+	20.8058i	0.382350	+	0.924018i
$508$	−0.184371	−	0.319340i	−0.00818013	−	0.0141684i
$509$			8.66992i			0.384288i	0.981367	+	0.192144i	$0.0615440\pi$
$509$			8.66992i			0.384288i	−0.981367	+	0.192144i	$0.938456\pi$
$510$	0.579153	+	1.28329i	0.0256453	+	0.0568249i
$511$	20.9485			0.926707
$512$			23.0196i			1.01733i
$513$	−36.7575	+	8.39810i	−1.62288	+	0.370785i
$514$	−9.17368	+	5.29643i	−0.404634	+	0.233615i
$515$	8.47398	+	4.89245i	0.373408	+	0.215587i
$516$	0.163658	+	0.0163644i	0.00720465	+	0.000720405i
$517$	−6.05525			−0.266310
$518$		−	11.7039i		−	0.514241i
$519$	−2.40257	−	5.32361i	−0.105461	−	0.233680i
$520$	15.0618	+	27.0665i	0.660502	+	1.18695i
$521$	27.2897			1.19558			0.597792	−	0.801651i	$-0.296045\pi$
$521$	27.2897			1.19558			0.597792	+	0.801651i	$0.296045\pi$
$522$	−33.7735	+	11.3528i	−1.47823	+	0.496897i
$523$	2.33445	−	4.04338i	0.102078	−	0.176805i	−0.810463	−	0.585790i	$-0.800784\pi$
$523$	2.33445	−	4.04338i	0.102078	−	0.176805i	0.912541	+	0.408986i	$0.134117\pi$
$524$	−0.168805			−0.00737430
$525$	−2.26703	+	22.6722i	−0.0989414	+	0.989497i
$526$	5.49456	+	3.17229i	0.239574	+	0.138318i
$527$	−1.19239	−	0.688427i	−0.0519413	−	0.0299883i
$528$	0.540450	−	5.40496i	0.0235201	−	0.235221i
$529$	−16.5230			−0.718389
$530$	−0.147001	+	0.254613i	−0.00638530	+	0.0110597i
$531$	38.5788	−	12.9680i	1.67418	−	0.562765i
$532$	−0.554042			−0.0240208
$533$	−0.0516069	+	3.26592i	−0.00223534	+	0.141463i
$534$	5.28447	+	11.7093i	0.228681	+	0.506712i
$535$			16.5580i			0.715864i
$536$	30.1285			1.30135
$537$	22.2852	+	2.22833i	0.961678	+	0.0961597i
$538$	18.4979	+	10.6798i	0.797500	+	0.460437i
$539$	2.20324	−	1.27204i	0.0949004	−	0.0547908i
$540$	0.110457	−	0.358370i	0.00475330	−	0.0154218i
$541$			39.9796i			1.71886i	0.511255	+	0.859429i	$0.329181\pi$
$541$			39.9796i			1.71886i	−0.511255	+	0.859429i	$0.670819\pi$
$542$	30.8544			1.32531
$543$	−8.11698	−	17.9856i	−0.348333	−	0.771836i
$544$		−	0.0258897i		−	0.00111001i
$545$	−4.15281	−	7.19287i	−0.177887	−	0.308109i
$546$	−16.7272	+	22.5106i	−0.715860	+	0.963365i
$547$	5.31092	−	9.19878i	0.227078	−	0.393311i	−0.729863	−	0.683594i	$-0.760416\pi$
$547$	5.31092	−	9.19878i	0.227078	−	0.393311i	0.956941	+	0.290283i	$0.0937493\pi$
$548$	−0.144310	−	0.0833174i	−0.00616462	−	0.00355914i
$549$	−0.354982	+	0.402362i	−0.0151503	+	0.0171724i
$550$	−2.29702	−	3.97855i	−0.0979451	−	0.169646i
$551$	−53.0934	−	30.6535i	−2.26185	−	1.30588i
$552$	11.4311	−	5.15891i	0.486540	−	0.219578i
$553$	−11.8116	−	6.81940i	−0.502278	−	0.289990i
$554$	−7.35418	+	4.24594i	−0.312449	+	0.180393i
$555$	5.60699	+	12.4239i	0.238003	+	0.527367i
$556$	0.130321	+	0.225723i	0.00552684	+	0.00957277i
$557$	−27.4337	−	15.8389i	−1.16240	−	0.671114i	−0.210525	−	0.977588i	$-0.567517\pi$
$557$	−27.4337	−	15.8389i	−1.16240	−	0.671114i	−0.951879	+	0.306474i	$0.900851\pi$
$558$	−9.66110	−	28.7409i	−0.408987	−	1.21670i
$559$	14.3234	+	0.226333i	0.605815	+	0.00957287i
$560$	−19.0596	+	33.0122i	−0.805414	+	1.39502i
$561$	−0.0261906	+	0.261928i	−0.00110577	+	0.0110586i
$562$	−10.6493			−0.449213
$563$	−10.6403	+	18.4295i	−0.448435	+	0.776713i	−0.998284	−	0.0585513i	$-0.981352\pi$
$563$	−10.6403	+	18.4295i	−0.448435	+	0.776713i	0.549849	+	0.835264i	$0.314685\pi$
$564$	−0.256467	−	0.184359i	−0.0107992	−	0.00776292i
$565$			49.8245i			2.09613i
$566$	34.1776	−	19.7324i	1.43659	−	0.829415i
$567$	28.5275	−	3.58339i	1.19804	−	0.150488i
$568$	−0.446042	−	0.772567i	−0.0187155	−	0.0324162i
$569$	1.90257	+	3.29536i	0.0797601	+	0.138148i	0.903146	−	0.429333i	$-0.141251\pi$
$569$	1.90257	+	3.29536i	0.0797601	+	0.138148i	−0.823386	+	0.567481i	$0.807918\pi$
$570$	−48.6262	+	21.9452i	−2.03673	+	0.919184i
$571$	16.1472	+	27.9678i	0.675740	+	1.17042i	0.976252	+	0.216638i	$0.0695092\pi$
$571$	16.1472	+	27.9678i	0.675740	+	1.17042i	−0.300512	+	0.953778i	$0.597157\pi$
$572$	−0.00108055	+	0.0683821i	−4.51801e−5	+	0.00285920i
$573$	2.32887	+	5.16030i	0.0972899	+	0.215575i
$574$	−3.52325	+	2.03415i	−0.147058	+	0.0849037i
$575$	5.24001	−	9.07597i	0.218524	−	0.378494i
$576$	16.0630	−	18.2070i	0.669293	−	0.758623i
$577$			5.48831i			0.228481i	0.993453	+	0.114241i	$0.0364435\pi$
$577$			5.48831i			0.228481i	−0.993453	+	0.114241i	$0.963557\pi$
$578$			23.8460i			0.991863i
$579$	30.0958	−	13.5824i	1.25074	−	0.564465i
$580$	0.528060	−	0.304876i	0.0219265	−	0.0126593i
$581$	12.9375	−	22.4083i	0.536736	−	0.929654i
$582$	−24.9712	+	34.7381i	−1.03509	+	1.43994i
$583$	−0.0476041	+	0.0274843i	−0.00197156	+	0.00113828i
$584$	−18.6563			−0.772004
$585$	6.97217	−	31.9089i	0.288264	−	1.31927i
$586$	−32.2427			−1.33193
$587$	16.6886	−	9.63518i	0.688813	−	0.397687i	−0.114354	−	0.993440i	$-0.536480\pi$
$587$	16.6886	−	9.63518i	0.688813	−	0.397687i	0.803167	+	0.595753i	$0.203146\pi$
$588$	0.132046	+	0.0132035i	0.00544549	+	0.000544503i
$589$	26.0858	−	45.1820i	1.07485	−	1.86169i
$590$	49.8719	−	28.7935i	2.05319	−	1.18541i
$591$	0.424588	−	4.24624i	0.0174652	−	0.174667i
$592$			10.2987i			0.423274i
$593$			17.9934i			0.738902i	0.929250	+	0.369451i	$0.120454\pi$
$593$			17.9934i			0.738902i	−0.929250	+	0.369451i	$0.879546\pi$
$594$	−4.24863	+	3.94388i	−0.174323	+	0.161819i
$595$	0.923642	−	1.59979i	0.0378656	−	0.0655852i
$596$	0.302647	−	0.174734i	0.0123969	−	0.00715737i
$597$	−23.7815	+	33.0831i	−0.973310	+	1.35400i
$598$	11.2716	−	6.27232i	0.460930	−	0.256494i
$599$	−1.96620	−	3.40556i	−0.0803367	−	0.139147i	0.823058	−	0.567958i	$-0.192266\pi$
$599$	−1.96620	−	3.40556i	−0.0803367	−	0.139147i	−0.903395	+	0.428810i	$0.858933\pi$
$600$	2.01898	−	20.1915i	0.0824243	−	0.824313i
$601$	−12.2462	−	21.2110i	−0.499533	−	0.865216i	0.500467	−	0.865756i	$-0.333162\pi$
$601$	−12.2462	−	21.2110i	−0.499533	−	0.865216i	−1.00000		0.000539252i	$0.999828\pi$
$602$	8.92119	+	15.4520i	0.363601	+	0.629775i
$603$	−23.8229	−	21.0177i	−0.970144	−	0.855906i
$604$	0.0218130	−	0.0125937i	0.000887559	−	0.000512432i
$605$			31.3135i			1.27308i
$606$	−0.362867	+	3.62897i	−0.0147405	+	0.147417i
$607$	−6.72493	+	11.6479i	−0.272956	+	0.472774i	−0.969617	−	0.244626i	$-0.921335\pi$
$607$	−6.72493	+	11.6479i	−0.272956	+	0.472774i	0.696661	+	0.717400i	$0.254668\pi$
$608$	0.981011			0.0397853
$609$	37.9597	+	27.2870i	1.53821	+	1.10572i
$610$	−0.379600	+	0.657487i	−0.0153696	+	0.0266209i
$611$	−23.6039	−	14.1296i	−0.954913	−	0.571623i
$612$	−0.00908400	+	0.0102964i	−0.000367199	+	0.000416209i
$613$	20.2969	+	11.7184i	0.819784	+	0.473303i	0.850342	−	0.526230i	$-0.176395\pi$
$613$	20.2969	+	11.7184i	0.819784	+	0.473303i	−0.0305579	+	0.999533i	$0.509728\pi$
$614$	−2.32896	−	4.03388i	−0.0939893	−	0.162794i
$615$	2.76550	−	3.84717i	0.111516	−	0.155133i
$616$	−6.24684	+	3.60661i	−0.251692	+	0.145315i
$617$	−20.1193	−	11.6159i	−0.809974	−	0.467639i	0.0369726	−	0.999316i	$-0.488229\pi$
$617$	−20.1193	−	11.6159i	−0.809974	−	0.467639i	−0.846947	+	0.531677i	$0.821562\pi$
$618$	0.785015	−	7.85081i	0.0315779	−	0.315806i
$619$	1.01355	+	0.585173i	0.0407380	+	0.0235201i	0.520231	−	0.854026i	$-0.325846\pi$
$619$	1.01355	+	0.585173i	0.0407380	+	0.0235201i	−0.479493	+	0.877546i	$0.659179\pi$
$620$	0.259446	+	0.449374i	0.0104196	+	0.0180473i
$621$	−12.6376	−	3.89515i	−0.507128	−	0.156307i
$622$	−30.8478	−	17.8100i	−1.23688	−	0.714116i
$623$	8.42775	−	14.5973i	0.337651	−	0.584828i
$624$	14.7189	−	19.8079i	0.589228	−	0.792950i
$625$	14.3162	+	24.7964i	0.572649	+	0.991858i
$626$		−	24.5055i		−	0.979436i
$627$	−9.92497	−	0.992413i	−0.396365	−	0.0396332i
$628$	−0.267536			−0.0106759
$629$		−	0.499083i		−	0.0198998i
$630$	38.5609	−	12.9620i	1.53630	−	0.516419i
$631$	−4.36496	+	2.52011i	−0.173766	+	0.100324i	−0.584361	−	0.811494i	$-0.698655\pi$
$631$	−4.36496	+	2.52011i	−0.173766	+	0.100324i	0.410594	+	0.911818i	$0.365321\pi$
$632$	10.5191	+	6.07323i	0.418429	+	0.241580i
$633$	−1.02979	−	2.28181i	−0.0409305	−	0.0906937i
$634$	−18.3421			−0.728457
$635$			46.5865i			1.84873i
$636$	−0.00285304		0.000285280i	−0.000113130		1.13121e-5i
$637$	11.5567	+	0.182615i	0.457893	+	0.00723546i
$638$	−9.42577			−0.373170
$639$	−0.186254	+	0.922037i	−0.00736810	+	0.0364752i
$640$	16.7688	−	29.0443i	0.662844	−	1.14808i
$641$	−34.6823			−1.36987			−0.684934	−	0.728605i	$-0.740169\pi$
$641$	−34.6823			−1.36987			−0.684934	+	0.728605i	$0.740169\pi$
$642$	12.1694	−	5.49213i	0.480290	−	0.216757i
$643$	−33.4281	−	19.2997i	−1.31827	−	0.761106i	−0.334824	−	0.942281i	$-0.608677\pi$
$643$	−33.4281	−	19.2997i	−1.31827	−	0.761106i	−0.983451	+	0.181174i	$0.942010\pi$
$644$	−0.168286	−	0.0971602i	−0.00663141	−	0.00382865i
$645$	−16.8726	−	12.1287i	−0.664357	−	0.477567i
$646$	1.95337			0.0768542
$647$	−18.4314	+	31.9241i	−0.724612	+	1.25507i	0.234521	+	0.972111i	$0.424648\pi$
$647$	−18.4314	+	31.9241i	−0.724612	+	1.25507i	−0.959133	+	0.282954i	$0.908685\pi$
$648$	−25.4060	+	3.19130i	−0.998043	+	0.125366i
$649$	10.7669			0.422637
$650$	0.329760	−	20.8687i	0.0129342	−	0.818538i
$651$	−23.2210	+	32.3034i	−0.910102	+	1.26607i
$652$		−	0.0466529i		−	0.00182707i
$653$	−32.6420			−1.27738			−0.638690	−	0.769464i	$-0.720523\pi$
$653$	−32.6420			−1.27738			−0.638690	+	0.769464i	$0.720523\pi$
$654$	−3.90902	+	5.43795i	−0.152855	+	0.212641i
$655$	18.4695	+	10.6634i	0.721662	+	0.416652i
$656$	3.10024	−	1.78992i	0.121044	−	0.0698847i
$657$	14.7518	+	13.0147i	0.575521	+	0.507751i
$658$		−	34.2642i		−	1.33576i
$659$	8.86611			0.345375			0.172687	−	0.984977i	$-0.444755\pi$
$659$	8.86611			0.345375			0.172687	+	0.984977i	$0.444755\pi$
$660$	0.0579043	−	0.0805524i	0.00225392	−	0.00313550i
$661$			19.1922i			0.746491i	0.927733	+	0.373245i	$0.121755\pi$
$661$			19.1922i			0.746491i	−0.927733	+	0.373245i	$0.878245\pi$
$662$	−3.34296	−	5.79018i	−0.129928	−	0.225042i
$663$	−0.713290	+	0.959906i	−0.0277019	+	0.0372797i
$664$	−11.5219	+	19.9564i	−0.447135	+	0.774460i
$665$	60.6193	+	34.9986i	2.35071	+	1.35719i
$666$	7.27131	−	8.24181i	0.281758	−	0.319364i
$667$	−10.7512	−	18.6215i	−0.416286	−	0.721029i
$668$	−0.411237	−	0.237428i	−0.0159112	−	0.00918635i
$669$	−0.852803	−	0.613030i	−0.0329713	−	0.0237011i
$670$	−38.9283	−	22.4753i	−1.50393	−	0.868295i
$671$	−0.122928	+	0.0709727i	−0.00474559	+	0.00273987i
$672$	−0.744358	−	0.0744295i	−0.0287142	−	0.00287118i
$673$	−2.67791	−	4.63828i	−0.103226	−	0.178792i	0.809786	−	0.586725i	$-0.199583\pi$
$673$	−2.67791	−	4.63828i	−0.103226	−	0.178792i	−0.913012	+	0.407933i	$0.866250\pi$
$674$	31.0869	+	17.9480i	1.19742	+	0.691331i
$675$	−15.6820	+	14.5572i	−0.603602	+	0.560306i
$676$	−0.163778	+	0.264038i	−0.00629916	+	0.0101553i
$677$	1.63177	−	2.82630i	0.0627139	−	0.108624i	−0.832964	−	0.553328i	$-0.813358\pi$
$677$	1.63177	−	2.82630i	0.0627139	−	0.108624i	0.895678	+	0.444704i	$0.146691\pi$
$678$	36.6190	−	16.5263i	1.40634	−	0.634690i
$679$	56.1327			2.15417
$680$	−0.822578	+	1.42475i	−0.0315444	+	0.0546365i
$681$	36.3992	−	16.4271i	1.39482	−	0.629488i
$682$		−	8.02124i		−	0.307149i
$683$	−22.0781	+	12.7468i	−0.844794	+	0.487742i	−0.858891	−	0.512159i	$-0.828846\pi$
$683$	−22.0781	+	12.7468i	−0.844794	+	0.487742i	0.0140968	+	0.999901i	$0.495513\pi$
$684$	−0.390152	−	0.344210i	−0.0149178	−	0.0131612i
$685$	10.5262	+	18.2320i	0.402187	+	0.696608i
$686$	−8.51986	−	14.7568i	−0.325290	−	0.563418i
$687$	6.45829	+	4.64248i	0.246399	+	0.177122i
$688$	−7.85008	−	13.5967i	−0.299282	−	0.518371i
$689$	−0.249698	−	0.00394564i	−0.00951275	−	0.000150317i
$690$	−18.6183	−	1.86167i	−0.708787	−	0.0708727i
$691$	19.2220	−	11.0978i	0.731240	−	0.422182i	−0.0876354	−	0.996153i	$-0.527931\pi$
$691$	19.2220	−	11.0978i	0.731240	−	0.422182i	0.818876	+	0.573971i	$0.194598\pi$
$692$	0.0402976	−	0.0697975i	0.00153189	−	0.00265330i
$693$	7.45543	+	1.50602i	0.283208	+	0.0572089i
$694$		−	7.62958i		−	0.289615i
$695$		−	32.9293i		−	1.24908i
$696$	−33.8062	−	24.3013i	−1.28142	−	0.921137i
$697$	−0.150240	+	0.0867410i	−0.00569074	+	0.00328555i
$698$	−18.5535	+	32.1355i	−0.702259	+	1.21635i
$699$	−5.58794	−	12.3817i	−0.211355	−	0.468320i
$700$	−0.272291	+	0.157208i	−0.0102916	+	0.00594189i
$701$	35.2587			1.33170			0.665851	−	0.746085i	$-0.268069\pi$
$701$	35.2587			1.33170			0.665851	+	0.746085i	$0.268069\pi$
$702$	−25.7644	+	5.45964i	−0.972414	+	0.206061i
$703$	18.9112			0.713250
$704$	5.56253	−	3.21153i	0.209646	−	0.121039i
$705$	16.4149	+	36.3722i	0.618222	+	1.36986i
$706$	21.0031	−	36.3785i	0.790464	−	1.36912i
$707$	4.14410	−	2.39260i	0.155855	−	0.0899828i
$708$	0.456026	+	0.327810i	0.0171385	+	0.0123198i
$709$		−	19.8184i		−	0.744297i	−0.928173	−	0.372149i	$-0.878621\pi$
$709$		−	19.8184i		−	0.744297i	0.928173	−	0.372149i	$-0.121379\pi$
$710$			1.33095i			0.0499498i
$711$	−4.08091	−	12.1403i	−0.153046	−	0.455299i
$712$	−7.50559	+	13.0001i	−0.281284	+	0.487198i
$713$	15.8468	−	9.14913i	0.593466	−	0.342638i
$714$	−1.48215	−	0.148202i	−0.0554680	−	0.00554633i
$715$	4.43789	−	7.41363i	0.165968	−	0.277254i
$716$	0.154524	+	0.267643i	0.00577483	+	0.0100023i
$717$	−1.94654	−	1.39925i	−0.0726949	−	0.0522560i
$718$	−19.3862	−	33.5779i	−0.723487	−	1.25312i
$719$	12.5408	+	21.7214i	0.467695	+	0.810071i	0.999319	−	0.0369095i	$-0.0117513\pi$
$719$	12.5408	+	21.7214i	0.467695	+	0.810071i	−0.531624	+	0.846981i	$0.678418\pi$
$720$	−33.9311	+	11.4057i	−1.26454	+	0.425067i
$721$	−8.96521	+	5.17607i	−0.333882	+	0.192767i
$722$			47.3078i			1.76061i
$723$	6.38837	−	2.88310i	0.237586	−	0.107224i
$724$	0.136144	−	0.235808i	0.00505975	−	0.00876374i
$725$	−34.7913			−1.29212
$726$	23.0142	−	10.3864i	0.854136	−	0.385476i
$727$	−5.05060	+	8.74790i	−0.187317	+	0.324442i	−0.944355	−	0.328929i	$-0.893312\pi$
$727$	−5.05060	+	8.74790i	−0.187317	+	0.324442i	0.757038	+	0.653371i	$0.226646\pi$
$728$	−32.7666	−	0.517766i	−1.21441	−	0.0191897i
$729$	22.3151	+	15.1999i	0.826485	+	0.562959i
$730$	24.1054	+	13.9173i	0.892181	+	0.515101i
$731$	0.380421	+	0.658909i	0.0140704	+	0.0243706i
$732$	−0.00736741		0.000736679i	−0.000272307		2.72284e-5i
$733$	−10.3089	+	5.95182i	−0.380766	+	0.219836i	−0.678152	−	0.734922i	$-0.737219\pi$
$733$	−10.3089	+	5.95182i	−0.380766	+	0.219836i	0.297385	+	0.954758i	$0.403885\pi$
$734$	26.1005	+	15.0691i	0.963387	+	0.556212i
$735$	−13.6135	−	9.78592i	−0.502141	−	0.360959i
$736$	0.297975	+	0.172036i	0.0109835	+	0.00634133i
$737$	−4.20213	−	7.27830i	−0.154787	−	0.268100i
$738$	−3.74480	−	0.756461i	−0.137848	−	0.0278457i
$739$	22.7597	+	13.1403i	0.837231	+	0.483375i	0.856322	−	0.516442i	$-0.172744\pi$
$739$	22.7597	+	13.1403i	0.837231	+	0.483375i	−0.0190912	+	0.999818i	$0.506077\pi$
$740$	−0.0940444	+	0.162890i	−0.00345714	+	0.00598795i
$741$	−36.3727	−	27.0279i	−1.33618	−	0.992895i
$742$	−0.155522	−	0.269373i	−0.00570940	−	0.00988898i
$743$		−	7.21139i		−	0.264560i	−0.991212	−	0.132280i	$-0.957770\pi$
$743$		−	7.21139i		−	0.264560i	0.991212	−	0.132280i	$-0.0422299\pi$
$744$	20.6802	−	28.7688i	0.758171	−	1.05471i
$745$	−44.1513			−1.61758
$746$			34.9255i			1.27871i
$747$	23.0321	−	7.74211i	0.842701	−	0.283269i
$748$	−0.00314574	+	0.00181619i	−0.000115019	+	6.64065e-5i
$749$	−15.1709	−	8.75892i	−0.554333	−	0.320044i
$750$	3.78545	−	5.26605i	0.138225	−	0.192289i
$751$	−0.499000			−0.0182088			−0.00910439	−	0.999959i	$-0.502898\pi$
$751$	−0.499000			−0.0182088			−0.00910439	+	0.999959i	$0.502898\pi$
$752$			30.1504i			1.09947i
$753$	−6.95386	+	9.67371i	−0.253413	+	0.352530i
$754$	−36.7425	−	21.9945i	−1.33808	−	0.800994i
$755$	−3.18216			−0.115811
$756$	0.269919	+	0.290776i	0.00981685	+	0.0105754i
$757$	24.1489	−	41.8272i	0.877708	−	1.52024i	0.0238592	−	0.999715i	$-0.492405\pi$
$757$	24.1489	−	41.8272i	0.877708	−	1.52024i	0.853849	−	0.520520i	$-0.174262\pi$
$758$	1.23994			0.0450366
$759$	−2.84060	−	2.04194i	−0.103107	−	0.0741178i
$760$	−53.9864	−	31.1690i	−1.95829	−	1.13062i
$761$	−27.4526	−	15.8498i	−0.995157	−	0.574554i	−0.0883449	−	0.996090i	$-0.528158\pi$
$761$	−27.4526	−	15.8498i	−0.995157	−	0.574554i	−0.906812	+	0.421536i	$0.861491\pi$
$762$	34.2391	−	15.4523i	1.24035	−	0.559777i
$763$	8.78709			0.318114
$764$	−0.0390615	+	0.0676565i	−0.00141320	+	0.00244773i
$765$	1.64433	−	0.552731i	0.0594508	−	0.0199840i
$766$	−4.03424			−0.145763
$767$	41.9703	+	25.1239i	1.51546	+	0.907173i
$768$	0.988459	+	0.0988376i	0.0356679	+	0.00356649i
$769$		−	8.88528i		−	0.320411i	−0.987084	−	0.160206i	$-0.948784\pi$
$769$		−	8.88528i		−	0.320411i	0.987084	−	0.160206i	$-0.0512158\pi$
$770$	10.7619			0.387831
$771$	5.36889	+	11.8964i	0.193356	+	0.428437i
$772$	0.394585	+	0.227814i	0.0142014	+	0.00819919i
$773$	39.3502	−	22.7188i	1.41533	−	0.817140i	0.419444	−	0.907781i	$-0.362225\pi$
$773$	39.3502	−	22.7188i	1.41533	−	0.817140i	0.995884	+	0.0906413i	$0.0288917\pi$
$774$	−3.31762	+	16.4236i	−0.119249	+	0.590335i
$775$		−	29.6071i		−	1.06352i
$776$	−49.9907			−1.79456
$777$	−14.3492	−	1.43480i	−0.514774	−	0.0514731i
$778$			16.8897i			0.605524i
$779$	−3.28678	−	5.69287i	−0.117761	−	0.203968i
$780$	0.413681	−	0.178884i	0.0148122	−	0.00640507i
$781$	−0.124422	+	0.215506i	−0.00445218	+	0.00771139i
$782$	0.593321	+	0.342554i	0.0212171	+	0.0122497i
$783$	9.77833	+	42.7986i	0.349449	+	1.52950i
$784$	−6.33376	−	10.9704i	−0.226206	−	0.391800i
$785$	29.2719	+	16.9001i	1.04476	+	0.603191i
$786$	1.71098	−	17.1112i	0.0610287	−	0.610338i
$787$	−4.22481	−	2.43919i	−0.150598	−	0.0869478i	0.422807	−	0.906220i	$-0.361045\pi$
$787$	−4.22481	−	2.43919i	−0.150598	−	0.0869478i	−0.573405	+	0.819272i	$0.694378\pi$
$788$	0.0509969	−	0.0294431i	0.00181669	−	0.00104887i
$789$	4.56286	−	6.34752i	0.162442	−	0.225978i
$790$	−9.06102	−	15.6942i	−0.322377	−	0.558373i
$791$	−45.6507	−	26.3564i	−1.62315	−	0.937127i
$792$	−6.63966	−	1.34123i	−0.235930	−	0.0476586i
$793$	−0.644797	−	0.0101889i	−0.0228974	−	0.000361817i
$794$	−6.33473	+	10.9721i	−0.224811	+	0.389385i
$795$	0.294138	+	0.211438i	0.0104320	+	0.00749895i
$796$	−0.562223			−0.0199275
$797$	−17.9543	+	31.0978i	−0.635974	+	1.10154i	0.350333	+	0.936625i	$0.386068\pi$
$797$	−17.9543	+	31.0978i	−0.635974	+	1.10154i	−0.986308	+	0.164915i	$0.947265\pi$
$798$	5.61567	−	56.1614i	0.198792	−	1.98809i
$799$		−	1.46111i		−	0.0516903i
$800$	0.482131	−	0.278359i	0.0170459	−	0.00984146i
$801$	15.0036	−	5.04338i	0.530127	−	0.178199i
$802$	23.3638	+	40.4673i	0.825004	+	1.42895i
$803$	2.60207	+	4.50691i	0.0918249	+	0.159045i
$804$	0.0436171	−	0.436207i	0.00153825	−	0.0153838i
$805$	12.2751	+	21.2611i	0.432641	+	0.749356i
$806$	18.7172	−	31.2675i	0.659284	−	1.10135i
$807$	15.3612	−	21.3694i	0.540741	−	0.752240i
$808$	−3.69065	+	2.13080i	−0.129837	+	0.0749613i
$809$	−12.1005	+	20.9587i	−0.425430	+	0.736867i	−0.996461	−	0.0840620i	$-0.973211\pi$
$809$	−12.1005	+	20.9587i	−0.425430	+	0.736867i	0.571030	+	0.820929i	$0.306544\pi$
$810$	35.2072	+	14.8290i	1.23705	+	0.521038i
$811$		−	14.3469i		−	0.503789i	−0.967755	−	0.251894i	$-0.918946\pi$
$811$		−	14.3469i		−	0.503789i	0.967755	−	0.251894i	$-0.0810536\pi$
$812$			0.645099i			0.0226385i
$813$	3.78248	−	37.8280i	0.132657	−	1.32668i
$814$	2.51801	−	1.45377i	0.0882563	−	0.0509548i
$815$	−2.94704	+	5.10443i	−0.103230	+	0.178800i
$816$	1.30420	+	0.130409i	0.0456560	+	0.00456521i
$817$	−24.9673	+	14.4149i	−0.873496	+	0.504313i
$818$	−47.6663			−1.66661
$819$	25.5477	+	23.2675i	0.892710	+	0.813031i
$820$	0.0653799			0.00228317
$821$	−4.33057	+	2.50026i	−0.151138	+	0.0872596i	−0.573662	−	0.819092i	$-0.694478\pi$
$821$	−4.33057	+	2.50026i	−0.151138	+	0.0872596i	0.422524	+	0.906352i	$0.361144\pi$
$822$	9.90831	−	13.7837i	0.345592	−	0.480763i
$823$	−2.26172	+	3.91741i	−0.0788385	+	0.136552i	−0.902749	−	0.430168i	$-0.858454\pi$
$823$	−2.26172	+	3.91741i	−0.0788385	+	0.136552i	0.823911	+	0.566720i	$0.191788\pi$
$824$	7.98425	−	4.60971i	0.278144	−	0.160587i
$825$	−5.15935	+	2.32844i	−0.179626	+	0.0810659i
$826$			60.9254i			2.11987i
$827$		−	7.63184i		−	0.265385i	−0.991157	−	0.132693i	$-0.957638\pi$
$827$		−	7.63184i		−	0.265385i	0.991157	−	0.132693i	$-0.0423623\pi$
$828$	−0.0581431	−	0.172971i	−0.00202061	−	0.00601115i
$829$	8.47700	−	14.6826i	0.294418	−	0.509948i	−0.680431	−	0.732812i	$-0.738207\pi$
$829$	8.47700	−	14.6826i	0.294418	−	0.509948i	0.974849	+	0.222864i	$0.0715407\pi$
$830$	29.7742	−	17.1902i	1.03348	−	0.596679i
$831$	4.30403	+	9.53685i	0.149305	+	0.330830i
$832$	29.1772	+	0.461047i	1.01154	+	0.0159839i
$833$	0.306939	+	0.531634i	0.0106348	+	0.0184200i
$834$	−24.2017	+	10.9223i	−0.838035	+	0.378209i
$835$	29.9964	+	51.9553i	1.03807	+	1.79799i
$836$	−0.0688190	−	0.119198i	−0.00238015	−	0.00412255i
$837$	−36.4212	+	8.32127i	−1.25890	+	0.287625i
$838$	−30.8965	+	17.8381i	−1.06730	+	0.616206i
$839$		−	22.9697i		−	0.793003i	−0.918034	−	0.396501i	$-0.870224\pi$
$839$		−	22.9697i		−	0.793003i	0.918034	−	0.396501i	$-0.129776\pi$
$840$	38.5982	+	27.7460i	1.33176	+	0.957326i
$841$	−21.1914	+	36.7045i	−0.730737	+	1.26567i
$842$	16.5912			0.571771
$843$	−1.30551	+	13.0562i	−0.0449642	+	0.449679i
$844$	0.0172724	−	0.0299167i	0.000594540	−	0.00102977i
$845$	34.5986	−	18.5434i	1.19023	−	0.637912i
$846$	21.2874	−	24.1286i	0.731875	−	0.829559i
$847$	−28.6904	−	16.5644i	−0.985813	−	0.569159i
$848$	0.136850	+	0.237031i	0.00469944	+	0.00813967i
$849$	−20.0024	−	44.3212i	−0.686480	−	1.52110i
$850$	0.960008	−	0.554261i	0.0329280	−	0.0190110i
$851$	5.74415	+	3.31639i	0.196907	+	0.113684i
$852$	−0.0118312	+	0.00533946i	−0.000405329	+	0.000182927i
$853$	−16.0483	−	9.26548i	−0.549483	−	0.317244i	0.199430	−	0.979912i	$-0.436091\pi$
$853$	−16.0483	−	9.26548i	−0.549483	−	0.317244i	−0.748913	+	0.662668i	$0.769424\pi$
$854$	−0.401606	−	0.695602i	−0.0137427	−	0.0238030i
$855$	20.9440	+	62.3067i	0.716271	+	2.13084i
$856$	13.5109	+	7.80053i	0.461793	+	0.266617i
$857$	20.7985	−	36.0241i	0.710464	−	1.23056i	−0.254219	−	0.967147i	$-0.581819\pi$
$857$	20.7985	−	36.0241i	0.710464	−	1.23056i	0.964683	−	0.263413i	$-0.0848481\pi$
$858$	−6.92072	−	0.802641i	−0.236269	−	0.0274017i
$859$	−7.48523	−	12.9648i	−0.255393	−	0.442353i	0.709609	−	0.704595i	$-0.248871\pi$
$859$	−7.48523	−	12.9648i	−0.255393	−	0.442353i	−0.965002	+	0.262242i	$0.915538\pi$
$860$		−	0.286738i		−	0.00977767i
$861$	2.06198	+	4.56893i	0.0702720	+	0.155709i
$862$	−16.1775			−0.551009
$863$		−	30.1011i		−	1.02465i	−0.858791	−	0.512327i	$-0.828784\pi$
$863$		−	30.1011i		−	1.02465i	0.858791	−	0.512327i	$-0.171216\pi$
$864$	−0.477930	−	0.514860i	−0.0162595	−	0.0175159i
$865$	−8.81815	+	5.09116i	−0.299826	+	0.173105i
$866$	−17.0575	−	9.84813i	−0.579636	−	0.334653i
$867$	29.2356	+	2.92331i	0.992892	+	0.0992808i
$868$	−0.548973			−0.0186334
$869$		−	3.38822i		−	0.114938i
$870$	25.5519	+	56.6179i	0.866292	+	1.91953i
$871$	0.603258	−	38.1769i	0.0204406	−	1.29358i
$872$	−7.82562			−0.265009
$873$	39.5282	+	34.8736i	1.33783	+	1.18029i
$874$	−12.9800	+	22.4821i	−0.439056	+	0.760468i
$875$	−8.50932			−0.287667
$876$	−0.0270088	+	0.270111i	−0.000912543	+	0.00912620i
$877$	3.98782	+	2.30237i	0.134659	+	0.0777454i	0.565816	−	0.824531i	$-0.308561\pi$
$877$	3.98782	+	2.30237i	0.134659	+	0.0777454i	−0.431157	+	0.902277i	$0.641895\pi$
$878$	−41.4890	−	23.9537i	−1.40018	−	0.808397i
$879$	−3.95267	+	39.5301i	−0.133320	+	1.33332i
$880$	−9.46976			−0.319225
$881$	−23.1838	+	40.1555i	−0.781082	+	1.35287i	0.150229	+	0.988651i	$0.451999\pi$
$881$	−23.1838	+	40.1555i	−0.781082	+	1.35287i	−0.931312	+	0.364223i	$0.881334\pi$
$882$	−2.67679	+	13.2512i	−0.0901322	+	0.446193i
$883$	−20.7632			−0.698737			−0.349368	−	0.936985i	$-0.613604\pi$
$883$	−20.7632			−0.698737			−0.349368	+	0.936985i	$0.613604\pi$
$884$	−0.0165003		0.000260733i	−0.000554967		8.76939e-6i
$885$	−29.1875	−	64.6735i	−0.981126	−	2.17398i
$886$			45.9230i			1.54281i
$887$	38.6528			1.29783			0.648916	−	0.760860i	$-0.275222\pi$
$887$	38.6528			1.29783			0.648916	+	0.760860i	$0.275222\pi$
$888$	12.7791	+	1.27780i	0.428839	+	0.0428803i
$889$	−42.6839	−	24.6435i	−1.43157	−	0.826518i
$890$	19.3956	−	11.1981i	0.650142	−	0.375360i
$891$	4.31441	+	5.69237i	0.144538	+	0.190702i
$892$		−	0.0144928i		−	0.000485255i
$893$	55.3643			1.85269
$894$	14.6446	+	32.4494i	0.489788	+	1.08527i
$895$		−	39.0448i		−	1.30512i
$896$	17.7408	+	30.7280i	0.592680	+	1.02655i
$897$	−6.30817	−	14.5881i	−0.210624	−	0.487082i
$898$	−6.22376	+	10.7799i	−0.207690	+	0.359729i
$899$	−52.6076	−	30.3730i	−1.75456	−	1.01300i
$900$	−0.289414	−	0.0584625i	−0.00964713	−	0.00194875i
$901$	−0.00663185	−	0.0114867i	−0.000220939	−	0.000382677i
$902$	−0.875264	−	0.505334i	−0.0291431	−	0.0168258i
$903$	20.0380	−	9.04325i	0.666823	−	0.300940i
$904$	40.6556	+	23.4725i	1.35219	+	0.780685i
$905$	−29.7918	+	17.2003i	−0.990312	+	0.571757i
$906$	1.05549	+	2.33876i	0.0350664	+	0.0777001i
$907$	11.6137	+	20.1154i	0.385625	+	0.667922i	0.991856	−	0.127367i	$-0.0406524\pi$
$907$	11.6137	+	20.1154i	0.385625	+	0.667922i	−0.606230	+	0.795289i	$0.707319\pi$
$908$	0.477227	+	0.275527i	0.0158373	+	0.00914370i
$909$	4.40469	+	0.889760i	0.146094	+	0.0295115i
$910$	41.9507	+	25.1123i	1.39065	+	0.832463i
$911$	−28.3835	+	49.1616i	−0.940386	+	1.62880i	−0.175649	+	0.984453i	$0.556202\pi$
$911$	−28.3835	+	49.1616i	−0.940386	+	1.62880i	−0.764737	+	0.644343i	$0.777131\pi$
$912$	−4.94143	+	49.4185i	−0.163627	+	1.63641i
$913$	6.42798			0.212735
$914$	−10.6974	+	18.5285i	−0.353839	+	0.612867i
$915$	0.759554	+	0.545998i	0.0251101	+	0.0180501i
$916$			0.109754i			0.00362638i
$917$	−19.5401	+	11.2815i	−0.645273	+	0.372548i
$918$	−0.951643	−	1.02518i	−0.0314089	−	0.0338359i
$919$	10.2662	+	17.7815i	0.338649	+	0.586557i	0.984179	−	0.177178i	$-0.0566967\pi$
$919$	10.2662	+	17.7815i	0.338649	+	0.586557i	−0.645530	+	0.763735i	$0.723363\pi$
$920$	−10.9320	−	18.9348i	−0.360417	−	0.624260i
$921$	−5.23111	+	2.36083i	−0.172371	+	0.0777918i
$922$	−24.4677	−	42.3793i	−0.805800	−	1.39569i
$923$	−0.987880	+	0.549727i	−0.0325165	+	0.0180945i
$924$	0.0431739	+	0.0956646i	0.00142032	+	0.00314713i
$925$	9.29418	−	5.36600i	0.305591	−	0.176433i
$926$	−19.2617	+	33.3622i	−0.632978	+	1.09635i
$927$	−9.52898	−	1.92488i	−0.312973	−	0.0632214i
$928$		−	1.14224i		−	0.0374959i
$929$			43.6220i			1.43119i	0.698515	+	0.715595i	$0.253845\pi$
$929$			43.6220i			1.43119i	−0.698515	+	0.715595i	$0.746155\pi$
$930$	−48.1813	+	21.7445i	−1.57993	+	0.713029i
$931$	−20.1446	+	11.6305i	−0.660214	+	0.381175i
$932$	0.0937250	−	0.162336i	0.00307006	−	0.00531750i
$933$	−25.6170	+	35.6365i	−0.838663	+	1.16669i
$934$	11.3717	−	6.56545i	0.372093	−	0.214828i
$935$	0.458912			0.0150080
$936$	−22.7523	−	20.7215i	−0.743683	−	0.677305i
$937$	−50.6045			−1.65318			−0.826588	−	0.562807i	$-0.809721\pi$
$937$	−50.6045			−1.65318			−0.826588	+	0.562807i	$0.809721\pi$
$938$	41.1850	−	23.7781i	1.34474	−	0.776384i
$939$	−30.0441	−	3.00416i	−0.980452	−	0.0980370i
$940$	−0.275323	+	0.476874i	−0.00898005	+	0.0155539i
$941$	6.38079	−	3.68395i	0.208008	−	0.120093i	−0.392377	−	0.919804i	$-0.628347\pi$
$941$	6.38079	−	3.68395i	0.208008	−	0.120093i	0.600385	+	0.799711i	$0.295014\pi$
$942$	2.71170	−	27.1193i	0.0883518	−	0.883593i
$943$		−	2.30556i		−	0.0750794i
$944$		−	53.6105i		−	1.74487i
$945$	−11.1644	−	48.8652i	−0.363178	−	1.58959i
$946$	−2.21625	+	3.83866i	−0.0720565	+	0.124805i
$947$	13.4404	−	7.75979i	0.436753	−	0.252159i	−0.265466	−	0.964120i	$-0.585526\pi$
$947$	13.4404	−	7.75979i	0.436753	−	0.252159i	0.702219	+	0.711961i	$0.252193\pi$
$948$	0.103158	−	0.143506i	0.00335043	−	0.00466087i
$949$	−0.373553	+	23.6401i	−0.0121260	+	0.767391i
$950$	21.0020	+	36.3766i	0.681395	+	1.18021i
$951$	−2.24858	+	22.4877i	−0.0729151	+	0.729213i
$952$	−0.870262	−	1.50734i	−0.0282054	−	0.0488531i
$953$	−11.8288	−	20.4880i	−0.383171	−	0.663672i	0.608343	−	0.793675i	$-0.291835\pi$
$953$	−11.8288	−	20.4880i	−0.383171	−	0.663672i	−0.991514	+	0.130003i	$0.958501\pi$
$954$	0.0578358	−	0.286312i	0.00187250	−	0.00926968i
$955$	8.54766	−	4.93499i	0.276596	−	0.159693i
$956$		−	0.0330801i		−	0.00106989i
$957$	−1.15552	+	11.5561i	−0.0373525	+	0.373557i
$958$	7.75743	−	13.4363i	0.250631	−	0.434106i
$959$	−22.2729			−0.719229
$960$	−34.3700	−	24.7065i	−1.10929	−	0.797400i
$961$	10.3472	−	17.9218i	0.333780	−	0.578123i
$962$	13.2077	+	0.208704i	0.425835	+	0.00672889i
$963$	−5.24157	−	15.5932i	−0.168907	−	0.502484i
$964$	0.0837575	+	0.0483574i	0.00269765	+	0.00155749i
$965$	−28.7818	−	49.8515i	−0.926518	−	1.60478i
$966$	11.5545	−	16.0738i	0.371761	−	0.517167i
$967$	12.2838	−	7.09208i	0.395022	−	0.228066i	−0.289312	−	0.957235i	$-0.593426\pi$
$967$	12.2838	−	7.09208i	0.395022	−	0.228066i	0.684334	+	0.729169i	$0.260093\pi$
$968$	25.5511	+	14.7519i	0.821243	+	0.474145i
$969$	0.239465	−	2.39486i	0.00769274	−	0.0769339i
$970$	64.5918	+	37.2921i	2.07392	+	1.19738i
$971$	−16.0778	−	27.8476i	−0.515963	−	0.893674i	−0.999828	−	0.0185312i	$-0.994101\pi$
$971$	−16.0778	−	27.8476i	−0.515963	−	0.893674i	0.483866	−	0.875142i	$-0.339232\pi$
$972$	0.00942408	+	0.372455i	0.000302278	+	0.0119465i
$973$	30.1707	+	17.4191i	0.967230	+	0.558430i
$974$	−8.11217	+	14.0507i	−0.259931	+	0.450213i
$975$	−25.5449	−	2.96261i	−0.818093	−	0.0948795i
$976$	0.353388	+	0.612085i	0.0113117	+	0.0195924i
$977$		−	52.0954i		−	1.66668i	−0.552760	−	0.833340i	$-0.686425\pi$
$977$		−	52.0954i		−	1.66668i	0.552760	−	0.833340i	$-0.313575\pi$
$978$	4.72905	+	0.472865i	0.151218	+	0.0151206i
$979$	4.18733			0.133828
$980$		−	0.231351i		−	0.00739025i
$981$	6.18780	+	5.45917i	0.197561	+	0.174298i
$982$	25.8630	−	14.9320i	0.825323	−	0.476500i
$983$	−22.2548	−	12.8488i	−0.709819	−	0.409814i	0.101175	−	0.994869i	$-0.467740\pi$
$983$	−22.2548	−	12.8488i	−0.709819	−	0.409814i	−0.810994	+	0.585055i	$0.801073\pi$
$984$	−1.83636	−	4.06900i	−0.0585410	−	0.129715i
$985$	−7.43962			−0.237046
$986$		−	2.27440i		−	0.0724317i
$987$	−42.0085	−	4.20050i	−1.33715	−	0.133703i
$988$	0.00987966	−	0.625230i	0.000314314	−	0.0198912i
$989$	−10.1115			−0.321528
$990$	7.57842	+	6.68604i	0.240858	+	0.212496i
$991$	−6.04305	+	10.4669i	−0.191964	+	0.332491i	−0.945901	−	0.324455i	$-0.894819\pi$
$991$	−6.04305	+	10.4669i	−0.191964	+	0.332491i	0.753937	+	0.656947i	$0.228152\pi$
$992$	0.972036			0.0308622
$993$	−7.50867	+	3.38870i	−0.238280	+	0.107537i
$994$	−1.21946	−	0.704055i	−0.0386789	−	0.0223313i
$995$	61.5145	+	35.5154i	1.95014	+	1.12591i
$996$	0.272254	+	0.195707i	0.00862670	+	0.00620122i
$997$	55.5937			1.76067			0.880335	−	0.474353i	$-0.157318\pi$
$997$	55.5937			1.76067			0.880335	+	0.474353i	$0.157318\pi$
$998$	9.24317	−	16.0096i	0.292587	−	0.506776i
$999$	−9.21319	−	9.92511i	−0.291492	−	0.314017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.r.b.43.3	yes	22
3.2	odd	2		351.2.r.b.316.9		22
9.4	even	3		117.2.l.b.4.3	✓	22
9.5	odd	6		351.2.l.b.199.9		22
13.10	even	6		117.2.l.b.88.9	yes	22
39.23	odd	6		351.2.l.b.127.3		22
117.23	odd	6		351.2.r.b.10.9		22
117.49	even	6	inner	117.2.r.b.49.3	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.3	✓	22	9.4	even	3
117.2.l.b.88.9	yes	22	13.10	even	6
117.2.r.b.43.3	yes	22	1.1	even	1	trivial
117.2.r.b.49.3	yes	22	117.49	even	6	inner
351.2.l.b.127.3		22	39.23	odd	6
351.2.l.b.199.9		22	9.5	odd	6
351.2.r.b.10.9		22	117.23	odd	6
351.2.r.b.316.9		22	3.2	odd	2

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21740 + 0.702869i) q^{2} +(0.712485 + 1.57872i) q^{3} +(-0.0119503 + 0.0206986i) q^{4} +(2.61504 - 1.50979i) q^{5} +(-1.97702 - 1.42116i) q^{6} +3.19463i q^{7} -2.84507i q^{8} +(-1.98473 + 2.24963i) q^{9} +(-2.12237 + 3.67605i) q^{10} +(-0.687300 + 0.396813i) q^{11} +(-0.0411917 - 0.00411882i) q^{12} +(-3.60510 - 0.0569665i) q^{13} +(-2.24541 - 3.88916i) q^{14} +(4.24672 + 3.05271i) q^{15} +(1.97581 + 3.42221i) q^{16} +(-0.0957495 - 0.165843i) q^{17} +(0.835023 - 4.13372i) q^{18} +(6.28411 - 3.62813i) q^{19} +0.0721699i q^{20} +(-5.04343 + 2.27612i) q^{21} +(0.557815 - 0.966164i) q^{22} +2.54500 q^{23} +(4.49158 - 2.02707i) q^{24} +(2.05894 - 3.56619i) q^{25} +(4.42891 - 2.46456i) q^{26} +(-4.96564 - 1.53051i) q^{27} +(-0.0661242 - 0.0381768i) q^{28} +(-4.22442 - 7.31690i) q^{29} +(-7.31563 - 0.731501i) q^{30} +(6.22662 - 3.59494i) q^{31} +(0.117082 + 0.0675976i) q^{32} +(-1.11615 - 0.802333i) q^{33} +(0.233132 + 0.134599i) q^{34} +(4.82322 + 8.35407i) q^{35} +(-0.0228460 - 0.0679649i) q^{36} +(2.25703 + 1.30310i) q^{37} +(-5.10020 + 8.83381i) q^{38} +(-2.47865 - 5.73204i) q^{39} +(-4.29547 - 7.43997i) q^{40} -0.905916i q^{41} +(4.54008 - 6.31584i) q^{42} -3.97309 q^{43} -0.0189682i q^{44} +(-1.79366 + 8.87940i) q^{45} +(-3.09830 + 1.78880i) q^{46} +(6.60765 + 3.81493i) q^{47} +(-3.99498 + 5.55754i) q^{48} -3.20565 q^{49} +5.78866i q^{50} +(0.193600 - 0.269322i) q^{51} +(0.0442612 - 0.0739396i) q^{52} +0.0692625 q^{53} +(7.12094 - 1.62694i) q^{54} +(-1.19821 + 2.07536i) q^{55} +9.08895 q^{56} +(10.2051 + 7.33587i) q^{57} +(10.2856 + 5.93842i) q^{58} +(-11.7491 - 6.78334i) q^{59} +(-0.113936 + 0.0514200i) q^{60} +0.178857 q^{61} +(-5.05354 + 8.75299i) q^{62} +(-7.18674 - 6.34047i) q^{63} -8.09330 q^{64} +(-9.51347 + 5.29398i) q^{65} +(1.92274 + 0.192258i) q^{66} +10.5897i q^{67} +0.00457694 q^{68} +(1.81328 + 4.01786i) q^{69} +(-11.7436 - 6.78019i) q^{70} +(0.271545 - 0.156777i) q^{71} +(6.40037 + 5.64670i) q^{72} -6.55741i q^{73} -3.66363 q^{74} +(7.09699 + 0.709639i) q^{75} +0.173429i q^{76} +(-1.26767 - 2.19567i) q^{77} +(7.04639 + 5.23605i) q^{78} +(-2.13465 + 3.69732i) q^{79} +(10.3336 + 5.96613i) q^{80} +(-1.12169 - 8.92983i) q^{81} +(0.636740 + 1.10287i) q^{82} +(-7.01438 - 4.04975i) q^{83} +(0.0131581 - 0.131592i) q^{84} +(-0.500776 - 0.289123i) q^{85} +(4.83686 - 2.79256i) q^{86} +(8.54153 - 11.8824i) q^{87} +(1.12896 + 1.95542i) q^{88} +(-4.56933 - 2.63810i) q^{89} +(-4.05744 - 12.0705i) q^{90} +(0.181987 - 11.5170i) q^{91} +(-0.0304136 + 0.0526779i) q^{92} +(10.1118 + 7.26876i) q^{93} -10.7256 q^{94} +(10.9554 - 18.9754i) q^{95} +(-0.0232983 + 0.233003i) q^{96} -17.5710i q^{97} +(3.90257 - 2.25315i) q^{98} +(0.471422 - 2.33374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

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