LMFDB - Embedded newform 117.2.l.b.4.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(4,117)] 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("117.4"); 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([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (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			4.3
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.40574i q^{2} +(-1.72346 + 0.172331i) q^{3} +0.0239006 q^{4} +(-2.61504 - 1.50979i) q^{5} +(0.242252 + 2.42273i) q^{6} +(-2.76663 - 1.59731i) q^{7} -2.84507i q^{8} +(2.94060 - 0.594010i) q^{9} +(-2.12237 + 3.67605i) q^{10} -0.793626i q^{11} +(-0.0411917 + 0.00411882i) q^{12} +(1.75322 + 3.15059i) q^{13} +(-2.24541 + 3.88916i) q^{14} +(4.76708 + 2.15141i) q^{15} -3.95163 q^{16} +(-0.0957495 - 0.165843i) q^{17} +(-0.835023 - 4.13372i) q^{18} +(6.28411 - 3.62813i) q^{19} +(-0.0625010 - 0.0360850i) q^{20} +(5.04343 + 2.27612i) q^{21} -1.11563 q^{22} +(-1.27250 - 2.20404i) q^{23} +(0.490295 + 4.90336i) 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} +8.44883 q^{29} +(3.02432 - 6.70127i) q^{30} +(-6.22662 - 3.59494i) q^{31} -0.135195i q^{32} +(0.136766 + 1.36778i) q^{33} +(-0.233132 + 0.134599i) q^{34} +(4.82322 + 8.35407i) q^{35} +(0.0702823 - 0.0141972i) q^{36} +(2.25703 + 1.30310i) q^{37} +(-5.10020 - 8.83381i) q^{38} +(-3.56454 - 5.12778i) q^{39} +(-4.29547 + 7.43997i) q^{40} +(-0.784546 + 0.452958i) q^{41} +(3.19964 - 7.08974i) q^{42} +(1.98654 - 3.44080i) q^{43} -0.0189682i q^{44} +(-8.58662 - 2.88634i) q^{45} +(-3.09830 + 1.78880i) q^{46} +(-6.60765 + 3.81493i) q^{47} +(6.81046 - 0.680988i) q^{48} +(1.60282 + 2.77617i) q^{49} +(5.01313 - 2.89433i) q^{50} +(0.193600 + 0.269322i) q^{51} +(0.0419030 + 0.0753011i) q^{52} +0.0692625 q^{53} +(2.15149 + 6.98038i) q^{54} +(-1.19821 + 2.07536i) q^{55} +(-4.54448 + 7.87126i) q^{56} +(-10.2051 + 7.33587i) q^{57} -11.8768i q^{58} +13.5667i q^{59} +(0.113936 + 0.0514200i) q^{60} +(-0.0894284 + 0.154895i) q^{61} +(-5.05354 + 8.75299i) q^{62} +(-9.08438 - 3.05366i) q^{63} -8.09330 q^{64} +(0.172015 - 10.8859i) q^{65} +(1.92274 - 0.192258i) q^{66} +(9.17094 - 5.29484i) q^{67} +(-0.00228847 - 0.00396375i) q^{68} +(2.57293 + 3.57927i) q^{69} +(11.7436 - 6.78019i) q^{70} +(0.271545 - 0.156777i) q^{71} +(-1.69000 - 8.36624i) q^{72} -6.55741i q^{73} +(1.83181 - 3.17279i) q^{74} +(-4.16306 - 5.79135i) q^{75} +(0.150194 - 0.0867146i) q^{76} +(-1.26767 + 2.19567i) q^{77} +(-7.20831 + 5.01080i) q^{78} +(-2.13465 - 3.69732i) q^{79} +(10.3336 + 5.96613i) q^{80} +(8.29430 - 3.49350i) q^{81} +(0.636740 + 1.10287i) q^{82} +(7.01438 - 4.04975i) q^{83} +(0.120541 + 0.0544008i) q^{84} +0.578247i q^{85} +(-4.83686 - 2.79256i) q^{86} +(-14.5612 + 1.45600i) q^{87} -2.25792 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} +(11.3508 + 5.12268i) q^{93} +(5.36279 + 9.28863i) q^{94} -21.9109 q^{95} +(0.0232983 + 0.233003i) q^{96} +(15.2169 + 8.78548i) q^{97} +(3.90257 - 2.25315i) q^{98} +(-0.471422 - 2.33374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

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

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

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 $

$2$		−	1.40574i		−	0.994007i	−0.867749	−	0.497003i	$-0.834434\pi$
$2$		−	1.40574i		−	0.994007i	0.867749	−	0.497003i	$-0.165566\pi$
$3$	−1.72346	+	0.172331i	−0.995038	+	0.0994954i
$3$	−1.72346	+	0.172331i	−0.995038	+	0.0994954i
$4$	0.0239006			0.0119503
$5$	−2.61504	−	1.50979i	−1.16948	−	0.675199i	−0.215922	−	0.976411i	$-0.569276\pi$
$5$	−2.61504	−	1.50979i	−1.16948	−	0.675199i	−0.953557	+	0.301211i	$0.902609\pi$
$6$	0.242252	+	2.42273i	0.0988991	+	0.989075i
$7$	−2.76663	−	1.59731i	−1.04569	−	0.603728i	−0.124249	−	0.992251i	$-0.539652\pi$
$7$	−2.76663	−	1.59731i	−1.04569	−	0.603728i	−0.921439	+	0.388523i	$0.872985\pi$
$8$		−	2.84507i		−	1.00589i
$9$	2.94060	−	0.594010i	0.980201	−	0.198003i
$10$	−2.12237	+	3.67605i	−0.671153	+	1.16247i
$11$		−	0.793626i		−	0.239287i	−0.992817	−	0.119644i	$-0.961825\pi$
$11$		−	0.793626i		−	0.239287i	0.992817	−	0.119644i	$-0.0381752\pi$
$12$	−0.0411917	+	0.00411882i	−0.0118910	+	0.00118900i
$13$	1.75322	+	3.15059i	0.486255	+	0.873817i
$13$	1.75322	+	3.15059i	0.486255	+	0.873817i
$14$	−2.24541	+	3.88916i	−0.600110	+	1.03942i
$15$	4.76708	+	2.15141i	1.23086	+	0.555491i
$16$	−3.95163			−0.987907
$17$	−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	$0.0203282\pi$
$20$	−0.0625010	−	0.0360850i	−0.0139756	−	0.00806884i
$21$	5.04343	+	2.27612i	1.10057	+	0.496691i
$22$	−1.11563			−0.237853
$23$	−1.27250	−	2.20404i	−0.265335	−	0.459574i	0.702316	−	0.711865i	$-0.252149\pi$
$23$	−1.27250	−	2.20404i	−0.265335	−	0.459574i	−0.967651	+	0.252291i	$0.918816\pi$
$24$	0.490295	+	4.90336i	0.100081	+	1.00089i
$25$	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
$29$	8.44883			1.56891			0.784454	−	0.620187i	$-0.212943\pi$
$29$	8.44883			1.56891			0.784454	+	0.620187i	$0.212943\pi$
$30$	3.02432	−	6.70127i	0.552162	−	1.22348i
$31$	−6.22662	−	3.59494i	−1.11833	−	0.645670i	−0.177358	−	0.984146i	$-0.556755\pi$
$31$	−6.22662	−	3.59494i	−1.11833	−	0.645670i	−0.940975	+	0.338476i	$0.890089\pi$
$32$		−	0.135195i		−	0.0238993i
$33$	0.136766	+	1.36778i	0.0238080	+	0.238100i
$34$	−0.233132	+	0.134599i	−0.0399818	+	0.0230835i
$35$	4.82322	+	8.35407i	0.815273	+	1.41209i
$36$	0.0702823	−	0.0141972i	0.0117137	−	0.00236620i
$37$	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
$39$	−3.56454	−	5.12778i	−0.570783	−	0.821101i
$40$	−4.29547	+	7.43997i	−0.679173	+	1.17636i
$41$	−0.784546	+	0.452958i	−0.122526	+	0.0707402i	−0.560010	−	0.828486i	$-0.689203\pi$
$41$	−0.784546	+	0.452958i	−0.122526	+	0.0707402i	0.437485	+	0.899226i	$0.355869\pi$
$42$	3.19964	−	7.08974i	0.493714	−	1.09397i
$43$	1.98654	−	3.44080i	0.302945	−	0.524716i	−0.673857	−	0.738862i	$-0.735363\pi$
$43$	1.98654	−	3.44080i	0.302945	−	0.524716i	0.976802	+	0.214146i	$0.0686968\pi$
$44$		−	0.0189682i		−	0.00285956i
$45$	−8.58662	−	2.88634i	−1.28002	−	0.430270i
$46$	−3.09830	+	1.78880i	−0.456820	+	0.263745i
$47$	−6.60765	+	3.81493i	−0.963825	+	0.556465i	−0.897348	−	0.441323i	$-0.854509\pi$
$47$	−6.60765	+	3.81493i	−0.963825	+	0.556465i	−0.0664769	+	0.997788i	$0.521176\pi$
$48$	6.81046	−	0.680988i	0.983005	−	0.0982922i
$49$	1.60282	+	2.77617i	0.228975	+	0.396596i
$50$	5.01313	−	2.89433i	0.708963	−	0.409320i
$51$	0.193600	+	0.269322i	0.0271094	+	0.0377127i
$52$	0.0419030	+	0.0753011i	0.00581090	+	0.0104424i
$53$	0.0692625			0.00951393			0.00475697	−	0.999989i	$-0.498486\pi$
$53$	0.0692625			0.00951393			0.00475697	+	0.999989i	$0.498486\pi$
$54$	2.15149	+	6.98038i	0.292781	+	0.949910i
$55$	−1.19821	+	2.07536i	−0.161567	+	0.279841i
$56$	−4.54448	+	7.87126i	−0.607281	+	1.05184i
$57$	−10.2051	+	7.33587i	−1.35170	+	0.971660i
$58$		−	11.8768i		−	1.55951i
$59$			13.5667i			1.76623i	0.469155	+	0.883116i	$0.344559\pi$
$59$			13.5667i			1.76623i	−0.469155	+	0.883116i	$0.655441\pi$
$60$	0.113936	+	0.0514200i	0.0147091	+	0.00663829i
$61$	−0.0894284	+	0.154895i	−0.0114501	+	0.0198322i	−0.871694	−	0.490051i	$-0.836978\pi$
$61$	−0.0894284	+	0.154895i	−0.0114501	+	0.0198322i	0.860244	+	0.509883i	$0.170311\pi$
$62$	−5.05354	+	8.75299i	−0.641800	+	1.11163i
$63$	−9.08438	−	3.05366i	−1.14452	−	0.384725i
$64$	−8.09330			−1.01166
$65$	0.172015	−	10.8859i	0.0213359	−	1.35023i
$66$	1.92274	−	0.192258i	0.236673	−	0.0236653i
$67$	9.17094	−	5.29484i	1.12041	−	0.646868i	0.178903	−	0.983867i	$-0.442745\pi$
$67$	9.17094	−	5.29484i	1.12041	−	0.646868i	0.941505	+	0.336998i	$0.109412\pi$
$68$	−0.00228847	−	0.00396375i	−0.000277518	−	0.000480675i
$69$	2.57293	+	3.57927i	0.309744	+	0.430894i
$70$	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	$0.327411\pi$
$72$	−1.69000	−	8.36624i	−0.199169	−	0.985970i
$73$		−	6.55741i		−	0.767487i	−0.923440	−	0.383743i	$-0.874635\pi$
$73$		−	6.55741i		−	0.767487i	0.923440	−	0.383743i	$-0.125365\pi$
$74$	1.83181	−	3.17279i	0.212944	−	0.368830i
$75$	−4.16306	−	5.79135i	−0.480709	−	0.668728i
$76$	0.150194	−	0.0867146i	0.0172284	−	0.00994685i
$77$	−1.26767	+	2.19567i	−0.144464	+	0.250220i
$78$	−7.20831	+	5.01080i	−0.816180	+	0.567362i
$79$	−2.13465	−	3.69732i	−0.240167	−	0.415981i	0.720595	−	0.693356i	$-0.243869\pi$
$79$	−2.13465	−	3.69732i	−0.240167	−	0.415981i	−0.960762	+	0.277376i	$0.910535\pi$
$80$	10.3336	+	5.96613i	1.15534	+	0.667034i
$81$	8.29430	−	3.49350i	0.921589	−	0.388166i
$82$	0.636740	+	1.10287i	0.0703162	+	0.121791i
$83$	7.01438	−	4.04975i	0.769928	−	0.444518i	−0.0629208	−	0.998019i	$-0.520042\pi$
$83$	7.01438	−	4.04975i	0.769928	−	0.444518i	0.832849	+	0.553500i	$0.186708\pi$
$84$	0.120541	+	0.0544008i	0.0131521	+	0.00593562i
$85$			0.578247i			0.0627197i
$86$	−4.83686	−	2.79256i	−0.521572	−	0.301130i
$87$	−14.5612	+	1.45600i	−1.56112	+	0.156099i
$88$	−2.25792			−0.240696
$89$	−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
$93$	11.3508	+	5.12268i	1.17703	+	0.531197i
$94$	5.36279	+	9.28863i	0.553130	+	0.958049i
$95$	−21.9109			−2.24801
$96$	0.0232983	+	0.233003i	0.00237788	+	0.0237808i
$97$	15.2169	+	8.78548i	1.54504	+	0.892030i	0.998509	+	0.0545930i	$0.0173861\pi$
$97$	15.2169	+	8.78548i	1.54504	+	0.892030i	0.546533	+	0.837437i	$0.315947\pi$
$98$	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
$101$	1.49789			0.149045			0.0745227	−	0.997219i	$-0.476257\pi$
$101$	1.49789			0.149045			0.0745227	+	0.997219i	$0.476257\pi$
$102$	0.378597	−	0.272151i	0.0374867	−	0.0269469i
$103$	1.62024	−	2.80634i	0.159647	−	0.276517i	−0.775094	−	0.631846i	$-0.782298\pi$
$103$	1.62024	−	2.80634i	0.159647	−	0.276517i	0.934741	+	0.355329i	$0.115631\pi$
$104$	8.96367	−	4.98803i	0.878960	−	0.489117i
$105$	−9.75228	−	13.5667i	−0.951725	−	1.32397i
$106$		−	0.0973649i		−	0.00945692i
$107$	−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	$0.252057\pi$
$108$	−0.118682	+	0.0365801i	−0.0114202	+	0.00351992i
$109$		−	2.75058i		−	0.263458i	−0.991286	−	0.131729i	$-0.957947\pi$
$109$		−	2.75058i		−	0.263458i	0.991286	−	0.131729i	$-0.0420529\pi$
$110$	2.91741	+	1.68437i	0.278164	+	0.160598i
$111$	−4.11446	−	1.85687i	−0.390527	−	0.176247i
$112$	10.9327	+	6.31199i	1.03304	+	0.596427i
$113$	16.5005			1.55223			0.776117	−	0.630589i	$-0.217187\pi$
$113$	16.5005			1.55223			0.776117	+	0.630589i	$0.217187\pi$
$114$	10.3123	+	14.3458i	0.965837	+	1.34360i
$115$			7.68485i			0.716616i
$116$	0.201932			0.0187490
$117$	7.02700	+	8.22322i	0.649646	+	0.760237i
$118$	19.0712			1.75565
$119$			0.611768i			0.0560807i
$120$	6.12091	−	13.5627i	0.558760	−	1.23810i
$121$	10.3702			0.942742
$122$	0.217741	+	0.125713i	0.0197134	+	0.0113815i
$123$	1.27407	−	0.915855i	0.114879	−	0.0825799i
$124$	−0.148820	−	0.0859213i	−0.0133644	−	0.00771596i
$125$			2.66363i			0.238243i
$126$	−4.29265	+	12.7703i	−0.382420	+	1.13767i
$127$	−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	$0.926682\pi$
$128$			11.1067i			0.981701i
$129$	−2.83077	+	6.27240i	−0.249235	+	0.552254i
$130$	−15.3027	−	0.241808i	−1.34214	−	0.0212080i
$131$	3.53140	−	6.11657i	0.308540	−	0.534407i	−0.669503	−	0.742809i	$-0.733493\pi$
$131$	3.53140	−	6.11657i	0.308540	−	0.534407i	0.978043	+	0.208402i	$0.0668263\pi$
$132$	0.00326880	+	0.0326908i	0.000284513	+	0.00284537i
$133$	−23.1811			−2.01005
$134$	−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
$137$	−6.03791	−	3.48599i	−0.515854	−	0.297828i	0.219383	−	0.975639i	$-0.429596\pi$
$137$	−6.03791	−	3.48599i	−0.515854	−	0.297828i	−0.735237	+	0.677811i	$0.762929\pi$
$138$	5.03152	−	3.61686i	0.428311	−	0.307888i
$139$	−10.9052			−0.924970			−0.462485	−	0.886627i	$-0.653042\pi$
$139$	−10.9052			−0.924970			−0.462485	+	0.886627i	$0.653042\pi$
$140$	0.115278	+	0.199667i	0.00974277	+	0.0168750i
$141$	10.7306	−	7.71357i	0.903677	−	0.649600i
$142$	−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
$146$	−9.21800			−0.762887
$147$	−3.24082	−	4.50840i	−0.267298	−	0.371846i
$148$	0.0539445	+	0.0311448i	0.00443421	+	0.00256009i
$149$			14.6217i			1.19785i	0.800804	+	0.598927i	$0.204406\pi$
$149$			14.6217i			1.19785i	−0.800804	+	0.598927i	$0.795594\pi$
$150$	−8.14112	+	5.85217i	−0.664720	+	0.477828i
$151$	0.912654	−	0.526921i	0.0742707	−	0.0428802i	−0.462405	−	0.886669i	$-0.653013\pi$
$151$	0.912654	−	0.526921i	0.0742707	−	0.0428802i	0.536675	+	0.843789i	$0.319680\pi$
$152$	−10.3223	−	17.8787i	−0.837249	−	1.45016i
$153$	−0.380074	−	0.430802i	−0.0307271	−	0.0348283i
$154$	3.08653	+	1.78201i	0.248720	+	0.143599i
$155$	10.8552	+	18.8018i	0.871912	+	1.51020i
$156$	−0.0851947	−	0.122557i	−0.00682103	−	0.00981242i
$157$	5.59684	−	9.69401i	0.446677	−	0.773667i	−0.551491	−	0.834181i	$-0.685941\pi$
$157$	5.59684	−	9.69401i	0.446677	−	0.773667i	0.998167	+	0.0605145i	$0.0192741\pi$
$158$	−5.19746	+	3.00075i	−0.413488	+	0.238727i
$159$	−0.119371	+	0.0119361i	−0.00946673	+	0.000946593i
$160$	−0.204116	+	0.353540i	−0.0161368	+	0.0279498i
$161$			8.13034i			0.640761i
$162$	−4.91094	−	11.6596i	−0.385840	−	0.916066i
$163$	−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
$165$	1.70741	−	3.78328i	0.132922	−	0.294528i
$166$	−5.69289	−	9.86038i	−0.441854	−	0.765314i
$167$	17.2061	−	9.93395i	1.33145	−	0.768712i	0.345927	−	0.938261i	$-0.387565\pi$
$167$	17.2061	−	9.93395i	1.33145	−	0.768712i	0.985522	+	0.169549i	$0.0542312\pi$
$168$	6.47574	−	14.3489i	0.499614	−	1.10704i
$169$	−6.85247	+	11.0473i	−0.527113	+	0.849795i
$170$	0.812864			0.0623438
$171$	16.3239	−	14.4017i	1.24832	−	1.10133i
$172$	0.0474797	−	0.0822372i	0.00362029	−	0.00627053i
$173$	1.68605	−	2.92032i	0.128188	−	0.222028i	−0.794787	−	0.606889i	$-0.792417\pi$
$173$	1.68605	−	2.92032i	0.128188	−	0.222028i	0.922975	+	0.384861i	$0.125751\pi$
$174$	2.04675	+	20.4692i	0.155164	+	1.55177i
$175$		−	13.1551i		−	0.994432i
$176$			3.13611i			0.236394i
$177$	−2.33796	−	23.3816i	−0.175732	−	1.75747i
$178$	−3.70848	+	6.42327i	−0.277962	+	0.481445i
$179$	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	$0.00612775\pi$
$180$	−0.205226	−	0.0689854i	−0.0152966	−	0.00514186i
$181$	−11.3925			−0.846798			−0.423399	−	0.905943i	$-0.639163\pi$
$181$	−11.3925			−0.846798			−0.423399	+	0.905943i	$0.639163\pi$
$182$	−16.1898	−	0.255826i	−1.20007	−	0.0189631i
$183$	0.127433	−	0.282365i	0.00942010	−	0.0208730i
$184$	−6.27065	+	3.62036i	−0.462279	+	0.266897i
$185$	−3.93481	−	6.81529i	−0.289293	−	0.501070i
$186$	7.20115	−	15.9563i	0.528014	−	1.16997i
$187$	−0.131617	+	0.0759893i	−0.00962481	+	0.00555688i
$188$	−0.157927	+	0.0911792i	−0.0115180	+	0.00664993i
$189$	16.1828	+	3.69733i	1.17712	+	0.268941i
$190$			30.8010i			2.23454i
$191$	−1.63433	+	2.83074i	−0.118256	+	0.204825i	−0.919077	−	0.394079i	$-0.871064\pi$
$191$	−1.63433	+	2.83074i	−0.118256	+	0.204825i	0.800821	+	0.598904i	$0.204397\pi$
$192$	13.9485	−	1.39473i	1.00664	−	0.100656i
$193$	−16.5094	+	9.53170i	−1.18837	+	0.686107i	−0.957936	−	0.286981i	$-0.907348\pi$
$193$	−16.5094	+	9.53170i	−1.18837	+	0.686107i	−0.230436	+	0.973088i	$0.574015\pi$
$194$	12.3501	−	21.3910i	0.886684	−	1.53578i
$195$	1.57952	+	18.7910i	0.113112	+	1.34565i
$196$	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	$0.694640\pi$
$198$	−3.28063	+	0.662696i	−0.233144	+	0.0470957i
$199$	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
$201$	−14.8932	+	10.7059i	−1.05049	+	0.755134i
$202$		−	2.10564i		−	0.148152i
$203$	−23.3748	−	13.4954i	−1.64059	−	0.947194i
$204$	0.00462716	+	0.00643698i	0.000323966	+	0.000450678i
$205$	2.73549			0.191055
$206$	−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
$210$	−19.0712	+	13.7091i	−1.31604	+	0.946021i
$211$	0.722675	+	1.25171i	0.0497510	+	0.0861713i	0.889828	−	0.456295i	$-0.150824\pi$
$211$	0.722675	+	1.25171i	0.0497510	+	0.0861713i	−0.840077	+	0.542466i	$0.817491\pi$
$212$	0.00165542			0.000113695
$213$	−0.440979	+	0.316994i	−0.0302154	+	0.0217201i
$214$	6.67568	+	3.85421i	0.456340	+	0.263468i
$215$	−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
$218$	−3.86660			−0.261879
$219$	1.13005	+	11.3014i	0.0763614	+	0.763679i
$220$	−0.0286380	+	0.0496024i	−0.00193077	+	0.00334419i
$221$	0.354634	−	0.592426i	0.0238553	−	0.0398509i
$222$	−2.61028	+	5.78385i	−0.175190	+	0.388187i
$223$		−	0.606377i		−	0.0406060i	−0.999794	−	0.0203030i	$-0.993537\pi$
$223$		−	0.606377i		−	0.0406060i	0.999794	−	0.0203030i	$-0.00646309\pi$
$224$	−0.215949	+	0.374035i	−0.0144287	+	0.0249912i
$225$	8.17288	+	9.26372i	0.544859	+	0.617581i
$226$		−	23.1953i		−	1.54293i
$227$	19.9671	+	11.5280i	1.32527	+	0.765143i	0.984563	−	0.175028i	$-0.0560017\pi$
$227$	19.9671	+	11.5280i	1.32527	+	0.765143i	0.340703	+	0.940171i	$0.389335\pi$
$228$	−0.243909	+	0.175332i	−0.0161533	+	0.0116116i
$229$	−3.97688	−	2.29605i	−0.262799	−	0.151727i	0.362812	−	0.931863i	$-0.381817\pi$
$229$	−3.97688	−	2.29605i	−0.262799	−	0.151727i	−0.625611	+	0.780135i	$0.715150\pi$
$230$	10.8029			0.712321
$231$	1.80639	−	4.00260i	0.118852	−	0.263352i
$232$		−	24.0375i		−	1.57814i
$233$	−7.84289			−0.513804			−0.256902	−	0.966437i	$-0.582702\pi$
$233$	−7.84289			−0.513804			−0.256902	+	0.966437i	$0.582702\pi$
$234$	11.5597	−	9.87812i	0.755680	−	0.645753i
$235$	23.0390			1.50290
$236$			0.324252i			0.0211070i
$237$	4.31613	+	6.00430i	0.280363	+	0.390021i
$238$	0.859985			0.0557446
$239$	1.19864	+	0.692034i	0.0775334	+	0.0447639i	0.538266	−	0.842775i	$-0.319080\pi$
$239$	1.19864	+	0.692034i	0.0775334	+	0.0447639i	−0.460732	+	0.887539i	$0.652413\pi$
$240$	−18.8377	−	8.50156i	−1.21597	−	0.548773i
$241$	3.50441	+	2.02327i	0.225739	+	0.130330i	0.608605	−	0.793474i	$-0.291730\pi$
$241$	3.50441	+	2.02327i	0.225739	+	0.130330i	−0.382866	+	0.923804i	$0.625063\pi$
$242$		−	14.5777i		−	0.937092i
$243$	−13.6928	+	7.45026i	−0.878396	+	0.477934i
$244$	−0.00213739	+	0.00370208i	−0.000136833	+	0.000237001i
$245$		−	9.67972i		−	0.618415i
$246$	−1.28745	−	1.79101i	−0.0820850	−	0.114191i
$247$	22.4482	+	13.4378i	1.42834	+	0.855024i
$248$	−10.2279	+	17.7152i	−0.649470	+	1.12492i
$249$	−11.3911	+	8.18837i	−0.721880	+	0.518917i
$250$	3.74437			0.236815
$251$	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
$254$	18.7823	+	10.8439i	1.17850	+	0.680409i
$255$	−0.0996499	−	0.996583i	−0.00624032	−	0.0624085i
$256$	−0.573533			−0.0358458
$257$	−3.76772	−	6.52588i	−0.235024	−	0.407073i	0.724256	−	0.689531i	$-0.242183\pi$
$257$	−3.76772	−	6.52588i	−0.235024	−	0.407073i	−0.959280	+	0.282458i	$0.908850\pi$
$258$	8.81736	+	3.97932i	0.548945	+	0.247741i
$259$	−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
$263$	4.51334			0.278304			0.139152	−	0.990271i	$-0.455562\pi$
$263$	4.51334			0.278304			0.139152	+	0.990271i	$0.455562\pi$
$264$	3.89143	−	0.389111i	0.239501	−	0.0239481i
$265$	−0.181124	−	0.104572i	−0.0111263	−	0.00642380i
$266$			32.5865i			1.99801i
$267$	8.32966	+	3.75922i	0.509767	+	0.230060i
$268$	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	$0.986637\pi$
$270$	4.91269	−	21.5023i	0.298977	−	1.30859i
$271$	−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
$273$	1.67108	+	19.8803i	0.101139	+	1.20321i
$274$	−4.90039	+	8.48773i	−0.296043	+	0.512762i
$275$	2.83022	−	1.63403i	0.170669	−	0.0985356i
$276$	0.0614946	+	0.0855469i	0.00370154	+	0.00514932i
$277$	−3.02043	+	5.23154i	−0.181480	+	0.314333i	−0.942385	−	0.334531i	$-0.891422\pi$
$277$	−3.02043	+	5.23154i	−0.181480	+	0.314333i	0.760905	+	0.648864i	$0.224756\pi$
$278$			15.3299i			0.919427i
$279$	−20.4454	−	6.87262i	−1.22404	−	0.411453i
$280$	23.7679	−	13.7224i	1.42041	−	0.820072i
$281$	−6.56065	+	3.78780i	−0.391376	+	0.225961i	−0.682756	−	0.730646i	$-0.739219\pi$
$281$	−6.56065	+	3.78780i	−0.391376	+	0.225961i	0.291380	+	0.956607i	$0.405886\pi$
$282$	−10.8433	−	15.0844i	−0.645707	−	0.898261i
$283$	14.0371	+	24.3129i	0.834416	+	1.44525i	0.894505	+	0.447058i	$0.147528\pi$
$283$	14.0371	+	24.3129i	0.834416	+	1.44525i	−0.0600886	+	0.998193i	$0.519138\pi$
$284$	0.00649011	−	0.00374707i	0.000385117	−	0.000222347i
$285$	37.7624	−	3.77593i	2.23685	−	0.223667i
$286$	−1.95594	−	3.51490i	−0.115657	−	0.207840i
$287$	2.89406			0.170831
$288$	−0.0803073	−	0.397555i	−0.00473215	−	0.0234262i
$289$	8.48166	−	14.6907i	0.498921	−	0.864157i
$290$	−17.9316	+	31.0584i	−1.05298	+	1.82381i
$291$	−27.7397	−	12.5190i	−1.62613	−	0.733880i
$292$		−	0.156726i		−	0.00917171i
$293$		−	22.9365i		−	1.33996i	−0.742377	−	0.669982i	$-0.766302\pi$
$293$		−	22.9365i		−	1.33996i	0.742377	−	0.669982i	$-0.233698\pi$
$294$	−6.33762	+	4.55574i	−0.369618	+	0.265696i
$295$	20.4829	−	35.4774i	1.19256	−	2.06557i
$296$	3.70741	−	6.42142i	0.215489	−	0.373237i
$297$	1.21465	+	3.94086i	0.0704812	+	0.228672i
$298$	20.5542			1.19068
$299$	4.71306	−	7.87329i	0.272563	−	0.455324i
$300$	−0.0994997	−	0.138417i	−0.00574462	−	0.00799151i
$301$	−10.9921	+	6.34627i	−0.633572	+	0.365793i
$302$	−0.740713	−	1.28295i	−0.0426232	−	0.0738256i
$303$	−2.58154	+	0.258133i	−0.148306	+	0.0148293i
$304$	−24.8324	+	14.3370i	−1.42424	+	0.822285i
$305$	0.467717	−	0.270036i	0.0267814	−	0.0154622i
$306$	−0.605595	+	0.534284i	−0.0346196	+	0.0305430i
$307$			3.31351i			0.189112i	0.995520	+	0.0945560i	$0.0301431\pi$
$307$			3.31351i			0.189112i	−0.995520	+	0.0945560i	$0.969857\pi$
$308$	−0.0302981	+	0.0524779i	−0.00172640	+	0.00299020i
$309$	−2.30880	+	5.11582i	−0.131343	+	0.291029i
$310$	26.4304	−	15.2596i	1.50114	−	0.866686i
$311$	12.6695	−	21.9442i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$311$	12.6695	−	21.9442i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884682\pi$
$312$	−14.5889	+	10.1414i	−0.825934	+	0.574142i
$313$	−8.71624	−	15.0970i	−0.492671	−	0.853331i	0.507294	−	0.861773i	$-0.330646\pi$
$313$	−8.71624	−	15.0970i	−0.492671	−	0.853331i	−0.999964	+	0.00844245i	$0.997313\pi$
$314$	−13.6272	−	7.86769i	−0.769030	−	0.444000i
$315$	19.1456	+	21.7010i	1.07873	+	1.22271i
$316$	−0.0510194	−	0.0883682i	−0.00287007	−	0.00497110i
$317$	−11.2999	+	6.52400i	−0.634666	+	0.366425i	−0.782557	−	0.622579i	$-0.786085\pi$
$317$	−11.2999	+	6.52400i	−0.634666	+	0.366425i	0.147891	+	0.989004i	$0.452752\pi$
$318$	0.0167790	+	0.167804i	0.000940920	+	0.00940999i
$319$		−	6.70521i		−	0.375420i
$320$	21.1643	+	12.2192i	1.18312	+	0.683074i
$321$	3.90694	−	8.65698i	0.218064	−	0.483185i
$322$	11.4291			0.636921
$323$	−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
$327$	0.474011	+	4.74051i	0.0262129	+	0.262151i
$328$	1.28870	+	2.23209i	0.0711565	+	0.123247i
$329$	24.3746			1.34381
$330$	−5.31830	−	2.40018i	−0.292763	−	0.132125i
$331$	−4.11896	−	2.37808i	−0.226399	−	0.130711i	0.382511	−	0.923951i	$-0.375059\pi$
$331$	−4.11896	−	2.37808i	−0.226399	−	0.130711i	−0.608910	+	0.793240i	$0.708393\pi$
$332$	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
$335$	−31.9764			−1.74706
$336$	−19.9298	−	8.99440i	−1.08726	−	0.490685i
$337$	−12.7677	+	22.1143i	−0.695500	+	1.20464i	0.274512	+	0.961584i	$0.411484\pi$
$337$	−12.7677	+	22.1143i	−0.695500	+	1.20464i	−0.970012	+	0.243057i	$0.921850\pi$
$338$	15.5297	+	9.63277i	0.844702	+	0.523954i
$339$	−28.4378	+	2.84354i	−1.54453	+	0.154440i
$340$			0.0138205i			0.000749520i
$341$	−2.85304	+	4.94160i	−0.154501	+	0.267603i
$342$	−20.2450	−	22.9472i	−1.09473	−	1.24084i
$343$			12.1215i			0.654502i
$344$	−9.78932	−	5.65187i	−0.527805	−	0.304728i
$345$	−1.32434	−	13.2445i	−0.0713000	−	0.713060i
$346$	−4.10521	−	2.37014i	−0.220697	−	0.127420i
$347$	5.42745			0.291361			0.145680	−	0.989332i	$-0.453463\pi$
$347$	5.42745			0.291361			0.145680	+	0.989332i	$0.453463\pi$
$348$	−0.348022	+	0.0347992i	−0.0186559	+	0.00186543i
$349$			26.3967i			1.41299i	0.707720	+	0.706493i	$0.249724\pi$
$349$			26.3967i			1.41299i	−0.707720	+	0.706493i	$0.750276\pi$
$350$	−18.4926			−0.988472
$351$	−13.5278	−	12.9614i	−0.722063	−	0.691828i
$352$	−0.107294			−0.00571881
$353$		−	29.8820i		−	1.59046i	−0.606308	−	0.795230i	$-0.707350\pi$
$353$		−	29.8820i		−	1.59046i	0.606308	−	0.795230i	$-0.292650\pi$
$354$	−32.8684	+	3.28656i	−1.74694	+	0.174679i
$355$	−0.946801			−0.0502510
$356$	−0.109210	−	0.0630523i	−0.00578811	−	0.00334176i
$357$	−0.105427	−	1.05436i	−0.00557977	−	0.0558024i
$358$	−15.7417	−	9.08847i	−0.831974	−	0.480341i
$359$			27.5815i			1.45570i	0.685738	+	0.727849i	$0.259480\pi$
$359$			27.5815i			1.45570i	−0.685738	+	0.727849i	$0.740520\pi$
$360$	−8.21185	+	24.4296i	−0.432803	+	1.28755i
$361$	16.8267	−	29.1446i	0.885614	−	1.53393i
$362$			16.0149i			0.841723i
$363$	−17.8725	+	1.78710i	−0.938064	+	0.0937985i
$364$	0.00434960	−	0.275263i	0.000227981	−	0.0144277i
$365$	−9.90032	+	17.1479i	−0.518207	+	0.897560i
$366$	−0.396932	−	0.179137i	−0.0207479	−	0.00936365i
$367$	21.4395			1.11913			0.559565	−	0.828786i	$-0.310968\pi$
$367$	21.4395			1.11913			0.559565	+	0.828786i	$0.310968\pi$
$368$	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
$371$	−0.191624	−	0.110634i	−0.00994860	−	0.00574383i
$372$	0.271292	+	0.122435i	0.0140658	+	0.00634797i
$373$	−24.8449			−1.28642			−0.643211	−	0.765689i	$-0.722398\pi$
$373$	−24.8449			−1.28642			−0.643211	+	0.765689i	$0.722398\pi$
$374$	0.106821	+	0.185019i	0.00552358	+	0.00956712i
$375$	−0.459027	−	4.59066i	−0.0237041	−	0.237060i
$376$	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	$0.673878\pi$
$380$	−0.523684			−0.0268644
$381$	10.9923	−	24.3567i	0.563153	−	1.24783i
$382$	3.97928	+	2.29744i	0.203598	+	0.117547i
$383$		−	2.86984i		−	0.146642i	−0.997308	−	0.0733210i	$-0.976640\pi$
$383$		−	2.86984i		−	0.146642i	0.997308	−	0.0733210i	$-0.0233598\pi$
$384$	−1.91403	−	19.1419i	−0.0976747	−	0.976829i
$385$	6.63000	−	3.82783i	0.337896	−	0.195084i
$386$	13.3991	+	23.2079i	0.681995	+	1.18125i
$387$	3.79777	−	11.2980i	0.193052	−	0.574312i
$388$	0.363693	+	0.209979i	0.0184637	+	0.0106600i
$389$	6.00741	+	10.4051i	0.304588	+	0.527561i	0.977169	−	0.212462i	$-0.0681481\pi$
$389$	6.00741	+	10.4051i	0.304588	+	0.527561i	−0.672582	+	0.740023i	$0.734815\pi$
$390$	26.4153	−	2.22039i	1.33759	−	0.112434i
$391$	−0.243683	+	0.422071i	−0.0123236	+	0.0213450i
$392$	7.89842	−	4.56015i	0.398930	−	0.230323i
$393$	−5.03214	+	11.1502i	−0.253838	+	0.562453i
$394$	−1.73172	+	2.99943i	−0.0872430	+	0.151109i
$395$			12.8915i			0.648641i
$396$	−0.0112673	−	0.0557779i	−0.000566202	−	0.00280294i
$397$	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
$399$	39.9515	−	3.99482i	2.00008	−	0.199991i
$400$	−8.13616	−	14.0922i	−0.406808	−	0.704612i
$401$	−28.7872	+	16.6203i	−1.43757	+	0.829979i	−0.997680	−	0.0680755i	$-0.978314\pi$
$401$	−28.7872	+	16.6203i	−1.43757	+	0.829979i	−0.439885	+	0.898054i	$0.644981\pi$
$402$	15.0497	+	20.9360i	0.750608	+	1.04419i
$403$	0.409582	−	25.9202i	0.0204028	−	1.29118i
$404$	0.0358004			0.00178114
$405$	−26.9644	−	3.38705i	−1.33987	−	0.168304i
$406$	−18.9710	+	32.8588i	−0.941517	+	1.63076i
$407$	1.03417	−	1.79124i	0.0512620	−	0.0887884i
$408$	0.766242	−	0.550806i	0.0379346	−	0.0272690i
$409$		−	33.9084i		−	1.67666i	−0.545161	−	0.838332i	$-0.683531\pi$
$409$		−	33.9084i		−	1.67666i	0.545161	−	0.838332i	$-0.316469\pi$
$410$		−	3.84538i		−	0.189910i
$411$	11.0068	+	4.96743i	0.542927	+	0.245025i
$412$	0.0387248	−	0.0670733i	0.00190783	−	0.00330446i
$413$	21.6703	−	37.5340i	1.06632	−	1.84693i
$414$	−8.04831	+	7.10059i	−0.395553	+	0.348975i
$415$	−24.4571			−1.20055
$416$	0.425945	−	0.237026i	0.0208837	−	0.0116212i
$417$	18.7947	−	1.87931i	0.920381	−	0.0920303i
$418$	−7.01074	+	4.04765i	−0.342906	+	0.197977i
$419$	−12.6895	−	21.9788i	−0.619921	−	1.07374i	−0.989500	−	0.144536i	$-0.953831\pi$
$419$	−12.6895	−	21.9788i	−0.619921	−	1.07374i	0.369578	−	0.929200i	$-0.379502\pi$
$420$	−0.233086	−	0.324252i	−0.0113734	−	0.0158219i
$421$	10.2213	−	5.90124i	0.498153	−	0.287609i	−0.229797	−	0.973239i	$-0.573806\pi$
$421$	10.2213	−	5.90124i	0.498153	−	0.287609i	0.727951	+	0.685630i	$0.240473\pi$
$422$	1.75958	−	1.01589i	0.0856549	−	0.0494529i
$423$	−17.1644	+	15.1432i	−0.834561	+	0.736288i
$424$		−	0.197057i		−	0.00956993i
$425$	0.394285	−	0.682921i	0.0191256	−	0.0331265i
$426$	0.445610	+	0.619901i	0.0215899	+	0.0300343i
$427$	0.494830	−	0.285690i	0.0239465	−	0.0138255i
$428$	−0.0655299	+	0.113501i	−0.00316751	+	0.00548629i
$429$	−4.06954	+	2.82891i	−0.196479	+	0.136581i
$430$	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	$0.577272\pi$
$432$	19.6223	−	6.04800i	0.944081	−	0.290985i
$433$	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
$435$	40.2763	+	18.1769i	1.93110	+	0.871515i
$436$		−	0.0657407i		−	0.00314841i
$437$	−15.9931	−	9.23361i	−0.765053	−	0.441703i
$438$	15.8868	−	1.58855i	0.759102	−	0.0759038i
$439$	−34.0798			−1.62654			−0.813271	−	0.581885i	$-0.802315\pi$
$439$	−34.0798			−1.62654			−0.813271	+	0.581885i	$0.802315\pi$
$440$	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	0.934198	+	0.356756i	$0.116117\pi$
$443$	16.3341	+	28.2916i	0.776058	+	1.34417i	−0.158139	+	0.987417i	$0.550549\pi$
$444$	−0.0983381	−	0.0443805i	−0.00466692	−	0.00210620i
$445$	7.96597	+	13.7975i	0.377623	+	0.654062i
$446$	−0.852407			−0.0403626
$447$	−2.51977	−	25.1998i	−0.119181	−	1.19191i
$448$	22.3912	+	12.9275i	1.05788	+	0.610769i
$449$	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
$452$	0.394372			0.0185497
$453$	−1.48211	+	1.06540i	−0.0696358	+	0.0500571i
$454$	16.2054	−	28.0686i	0.760557	−	1.31732i
$455$	−17.8641	+	29.8425i	−0.837482	+	1.39904i
$456$	20.8711	+	29.0344i	0.977379	+	1.35966i
$457$			15.2196i			0.711945i	0.934496	+	0.355973i	$0.115850\pi$
$457$			15.2196i			0.711945i	−0.934496	+	0.355973i	$0.884150\pi$
$458$	−3.22764	+	5.59044i	−0.150818	+	0.261224i
$459$	0.729281	+	0.676970i	0.0340399	+	0.0315983i
$460$			0.183673i			0.00856379i
$461$	−30.1473	−	17.4056i	−1.40410	−	0.810658i	−0.409291	−	0.912404i	$-0.634224\pi$
$461$	−30.1473	−	17.4056i	−1.40410	−	0.810658i	−0.994810	+	0.101745i	$0.967557\pi$
$462$	−5.62660	−	2.53931i	−0.261773	−	0.118140i
$463$	−23.7329	−	13.7022i	−1.10296	−	0.636795i	−0.165963	−	0.986132i	$-0.553073\pi$
$463$	−23.7329	−	13.7022i	−1.10296	−	0.636795i	−0.936997	+	0.349337i	$0.886407\pi$
$464$	−33.3866			−1.54994
$465$	−21.9486	−	30.5334i	−1.01784	−	1.41595i
$466$			11.0250i			0.510725i
$467$	−9.34092			−0.432246			−0.216123	−	0.976366i	$-0.569341\pi$
$467$	−9.34092			−0.432246			−0.216123	+	0.976366i	$0.569341\pi$
$468$	0.167950	+	0.196540i	0.00776348	+	0.00908507i
$469$	−33.8301			−1.56213
$470$		−	32.3868i		−	1.49389i
$471$	−7.97533	+	17.6717i	−0.367484	+	0.814270i
$472$	38.5982			1.77663
$473$	−2.73070	−	1.57657i	−0.125558	−	0.0724909i
$474$	8.44047	−	6.06735i	0.387684	−	0.278683i
$475$	25.8772	+	14.9402i	1.18733	+	0.685504i
$476$			0.0146216i			0.000670182i
$477$	0.203674	−	0.0411426i	0.00932557	−	0.00188379i
$478$	0.972818	−	1.68497i	0.0444957	−	0.0770687i
$479$		−	11.0368i		−	0.504285i	−0.967690	−	0.252142i	$-0.918865\pi$
$479$		−	11.0368i		−	0.504285i	0.967690	−	0.252142i	$-0.0811351\pi$
$480$	0.290860	−	0.644486i	0.0132759	−	0.0294166i
$481$	−0.148466	+	9.39559i	−0.00676946	+	0.428402i
$482$	2.84419	−	4.92628i	0.129549	−	0.224386i
$483$	−1.40111	−	14.0123i	−0.0637528	−	0.637581i
$484$	0.247853			0.0112661
$485$	−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	$0.249117\pi$
$488$	0.440686	+	0.254430i	0.0199489	+	0.0115175i
$489$	2.74521	−	1.97337i	0.124143	−	0.0892388i
$490$	−13.6071			−0.614708
$491$	10.6222	+	18.3982i	0.479373	+	0.830299i	0.999720	−	0.0236560i	$-0.00753066\pi$
$491$	10.6222	+	18.3982i	0.479373	+	0.830299i	−0.520347	+	0.853955i	$0.674197\pi$
$492$	0.0304511	−	0.0218895i	0.00137284	−	0.000986856i
$493$	−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
$497$	−1.00169			−0.0449318
$498$	11.5107	+	16.0129i	0.515807	+	0.717554i
$499$	11.3888	+	6.57531i	0.509832	+	0.294351i	0.732764	−	0.680482i	$-0.238230\pi$
$499$	11.3888	+	6.57531i	0.509832	+	0.294351i	−0.222933	+	0.974834i	$0.571563\pi$
$500$			0.0636625i			0.00284707i
$501$	−27.9420	+	20.0859i	−1.24836	+	0.897371i
$502$	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	$0.883827\pi$
$504$	−8.68789	+	25.8457i	−0.386990	+	1.15126i
$505$	−3.91703	−	2.26150i	−0.174305	−	0.100635i
$506$	1.41964	+	2.45889i	0.0631108	+	0.109311i
$507$	9.90613	−	20.2205i	0.439947	−	0.898024i
$508$	−0.184371	+	0.319340i	−0.00818013	+	0.0141684i
$509$	7.50837	−	4.33496i	0.332803	−	0.192144i	−0.324282	−	0.945960i	$-0.605123\pi$
$509$	7.50837	−	4.33496i	0.332803	−	0.192144i	0.657085	+	0.753817i	$0.271789\pi$
$510$	−1.40093	+	0.140082i	−0.0620344	+	0.00620292i
$511$	−10.4742	+	18.1419i	−0.463353	+	0.802551i
$512$			23.0196i			1.01733i
$513$	−25.6517	+	27.6339i	−1.13255	+	1.22006i
$514$	−9.17368	+	5.29643i	−0.404634	+	0.233615i
$515$	−8.47398	+	4.89245i	−0.373408	+	0.215587i
$516$	−0.0676571	+	0.149914i	−0.00297844	+	0.00659961i
$517$	3.02763	+	5.24400i	0.133155	+	0.230631i
$518$	−10.1359	+	5.85196i	−0.445346	+	0.257120i
$519$	−2.40257	+	5.32361i	−0.105461	+	0.233680i
$520$	−30.9712	−	0.489396i	−1.35818	−	0.0214614i
$521$	27.2897			1.19558			0.597792	−	0.801651i	$-0.296045\pi$
$521$	27.2897			1.19558			0.597792	+	0.801651i	$0.296045\pi$
$522$	−7.05497	−	34.9251i	−0.308788	−	1.52863i
$523$	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	$0.134117\pi$
$524$	0.0844027	−	0.146190i	0.00368715	−	0.00638633i
$525$	2.26703	+	22.6722i	0.0989414	+	0.989497i
$526$		−	6.34457i		−	0.276636i
$527$			1.37685i			0.0599767i
$528$	−0.540450	−	5.40496i	−0.0235201	−	0.235221i
$529$	8.26148	−	14.3093i	0.359195	−	0.622143i
$530$	−0.147001	+	0.254613i	−0.00638530	+	0.0110597i
$531$	8.05875	+	39.8943i	0.349720	+	1.73126i
$532$	−0.554042			−0.0240208
$533$	−2.80257	−	1.67765i	−0.121393	−	0.0726672i
$534$	5.28447	−	11.7093i	0.228681	−	0.506712i
$535$	14.3396	−	8.27899i	0.619956	−	0.357932i
$536$	−15.0642	−	26.0920i	−0.650675	−	1.12700i
$537$	−9.21281	+	20.4137i	−0.397562	+	0.880917i
$538$	−18.4979	+	10.6798i	−0.797500	+	0.460437i
$539$	2.20324	−	1.27204i	0.0949004	−	0.0547908i
$540$	0.365586	+	0.0835265i	0.0157323	+	0.00359441i
$541$			39.9796i			1.71886i	0.511255	+	0.859429i	$0.329181\pi$
$541$			39.9796i			1.71886i	−0.511255	+	0.859429i	$0.670819\pi$
$542$	−15.4272	+	26.7207i	−0.662655	+	1.14775i
$543$	19.6345	−	1.96328i	0.842596	−	0.0842525i
$544$	−0.0224212	+	0.0129449i	−0.000961299	+	0.000555006i
$545$	−4.15281	+	7.19287i	−0.177887	+	0.308109i
$546$	27.9465	−	2.34911i	1.19600	−	0.100532i
$547$	5.31092	+	9.19878i	0.227078	+	0.393311i	0.956941	−	0.290283i	$-0.0937493\pi$
$547$	5.31092	+	9.19878i	0.227078	+	0.393311i	−0.729863	+	0.683594i	$0.760416\pi$
$548$	−0.144310	−	0.0833174i	−0.00616462	−	0.00355914i
$549$	−0.170965	+	0.508605i	−0.00729659	+	0.0217067i
$550$	−2.29702	−	3.97855i	−0.0979451	−	0.169646i
$551$	53.0934	−	30.6535i	2.26185	−	1.30588i
$552$	10.1833	−	7.32017i	0.433430	−	0.311567i
$553$			13.6388i			0.579981i
$554$	7.35418	+	4.24594i	0.312449	+	0.180393i
$555$	7.95596	+	11.0678i	0.337712	+	0.469800i
$556$	−0.260642			−0.0110537
$557$	−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
$561$	0.213741	−	0.153646i	0.00902416	−	0.00648694i
$562$	5.32465	+	9.22256i	0.224607	+	0.389030i
$563$	21.2806			0.896871			0.448435	−	0.893815i	$-0.351981\pi$
$563$	21.2806			0.896871			0.448435	+	0.893815i	$0.351981\pi$
$564$	0.256467	−	0.184359i	0.0107992	−	0.00776292i
$565$	−43.1493	−	24.9123i	−1.81530	−	1.04807i
$566$	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
$569$	−3.80515			−0.159520			−0.0797601	−	0.996814i	$-0.525415\pi$
$569$	−3.80515			−0.159520			−0.0797601	+	0.996814i	$0.525415\pi$
$570$	−5.30796	−	53.0841i	−0.222326	−	2.22345i
$571$	16.1472	−	27.9678i	0.675740	−	1.17042i	−0.300512	−	0.953778i	$-0.597157\pi$
$571$	16.1472	−	27.9678i	0.675740	−	1.17042i	0.976252	−	0.216638i	$-0.0695092\pi$
$572$	0.0597609	−	0.0332553i	0.00249873	−	0.00139047i
$573$	2.32887	−	5.16030i	0.0972899	−	0.215575i
$574$		−	4.06830i		−	0.169807i
$575$	5.24001	−	9.07597i	0.218524	−	0.378494i
$576$	−23.7992	+	4.80751i	−0.991633	+	0.200313i
$577$			5.48831i			0.228481i	0.993453	+	0.114241i	$0.0364435\pi$
$577$			5.48831i			0.228481i	−0.993453	+	0.114241i	$0.963557\pi$
$578$	−20.6512	−	11.9230i	−0.858978	−	0.495931i
$579$	26.8106	−	19.2726i	1.11421	−	0.800940i
$580$	−0.528060	−	0.304876i	−0.0219265	−	0.0126593i
$581$	−25.8749			−1.07347
$582$	−17.5985	+	38.9947i	−0.729481	+	1.61638i
$583$		−	0.0549685i		−	0.00227656i
$584$	−18.6563			−0.772004
$585$	−5.96051	−	32.1133i	−0.246437	−	1.32772i
$586$	−32.2427			−1.33193
$587$			19.2704i			0.795373i	0.917521	+	0.397687i	$0.130187\pi$
$587$			19.2704i			0.795373i	−0.917521	+	0.397687i	$0.869813\pi$
$588$	−0.0774576	−	0.107754i	−0.00319430	−	0.00444368i
$589$	−52.1716			−2.14969
$590$	−49.8719	−	28.7935i	−2.05319	−	1.18541i
$591$	3.88964	+	1.75542i	0.159999	+	0.0722081i
$592$	−8.91894	−	5.14935i	−0.366566	−	0.211637i
$593$			17.9934i			0.738902i	0.929250	+	0.369451i	$0.120454\pi$
$593$			17.9934i			0.738902i	−0.929250	+	0.369451i	$0.879546\pi$
$594$	5.53981	−	1.70748i	0.227301	−	0.0700588i
$595$	0.923642	−	1.59979i	0.0378656	−	0.0655852i
$596$			0.349467i			0.0143147i
$597$	−23.7815	−	33.0831i	−0.973310	−	1.35400i
$598$	−11.0678	−	6.62532i	−0.452595	−	0.270930i
$599$	−1.96620	+	3.40556i	−0.0803367	+	0.139147i	−0.903395	−	0.428810i	$-0.858933\pi$
$599$	−1.96620	+	3.40556i	−0.0803367	+	0.139147i	0.823058	+	0.567958i	$0.192266\pi$
$600$	−16.4768	+	11.8442i	−0.672664	+	0.483538i
$601$	24.4924			0.999066			0.499533	−	0.866295i	$-0.333505\pi$
$601$	24.4924			0.999066			0.499533	+	0.866295i	$0.333505\pi$
$602$	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
$605$	−27.1183	−	15.6568i	−1.10252	−	0.636538i
$606$	0.362867	+	3.62897i	0.0147405	+	0.147417i
$607$	13.4499			0.545913			0.272956	−	0.962026i	$-0.411999\pi$
$607$	13.4499			0.545913			0.272956	+	0.962026i	$0.411999\pi$
$608$	−0.490506	−	0.849580i	−0.0198926	−	0.0344550i
$609$	42.6111	+	19.2306i	1.72669	+	0.779263i
$610$	−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	$0.509728\pi$
$614$	4.65792			0.187979
$615$	−4.71450	+	0.471410i	−0.190107	+	0.0190091i
$616$	6.24684	+	3.60661i	0.251692	+	0.145315i
$617$			23.2318i			0.935278i	0.883920	+	0.467639i	$0.154895\pi$
$617$			23.2318i			0.935278i	−0.883920	+	0.467639i	$0.845105\pi$
$618$	7.19151	+	3.24556i	0.289285	+	0.130556i
$619$	−1.01355	+	0.585173i	−0.0407380	+	0.0235201i	−0.520231	−	0.854026i	$-0.674154\pi$
$619$	−1.01355	+	0.585173i	−0.0407380	+	0.0235201i	0.479493	+	0.877546i	$0.340821\pi$
$620$	0.259446	+	0.449374i	0.0104196	+	0.0180473i
$621$	9.69208	+	8.99688i	0.388930	+	0.361032i
$622$	−30.8478	−	17.8100i	−1.23688	−	0.714116i
$623$	8.42775	+	14.5973i	0.337651	+	0.584828i
$624$	14.0857	+	20.2631i	0.563880	+	0.811171i
$625$	14.3162	−	24.7964i	0.572649	−	0.991858i
$626$	−21.2224	+	12.2527i	−0.848217	+	0.489718i
$627$	5.82194	+	8.09907i	0.232506	+	0.323446i
$628$	0.133768	−	0.231693i	0.00533793	−	0.00924556i
$629$		−	0.499083i		−	0.0198998i
$630$	30.5059	−	26.9137i	1.21538	−	1.07227i
$631$	−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
$633$	−1.46121	−	2.03273i	−0.0580778	−	0.0807937i
$634$	9.17104	+	15.8847i	0.364229	+	0.630862i
$635$	40.3451	−	23.2932i	1.60104	−	0.924364i
$636$	−0.00285304		0.000285280i	−0.000113130		1.13121e-5i
$637$	−5.93649	+	9.91708i	−0.235212	+	0.392929i
$638$	−9.42577			−0.373170
$639$	0.705381	−	0.622319i	0.0279044	−	0.0246186i
$640$	16.7688	−	29.0443i	0.662844	−	1.14808i
$641$	17.3411	−	30.0357i	0.684934	−	1.18634i	−0.288524	−	0.957473i	$-0.593164\pi$
$641$	17.3411	−	30.0357i	0.684934	−	1.18634i	0.973458	−	0.228868i	$-0.0735023\pi$
$642$	−12.1694	−	5.49213i	−0.480290	−	0.216757i
$643$			38.5994i			1.52221i	0.648627	+	0.761106i	$0.275343\pi$
$643$			38.5994i			1.52221i	−0.648627	+	0.761106i	$0.724657\pi$
$644$			0.194320i			0.00765729i
$645$	16.8726	−	12.1287i	0.664357	−	0.477567i
$646$	−0.976683	+	1.69166i	−0.0384271	+	0.0665577i
$647$	−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	$0.908685\pi$
$648$	−9.93926	−	23.5979i	−0.390451	−	0.927013i
$649$	10.7669			0.422637
$650$	17.9080	+	10.7199i	0.702408	+	0.420470i
$651$	−23.2210	−	32.3034i	−0.910102	−	1.26607i
$652$	−0.0404026	+	0.0233265i	−0.00158229	+	0.000913534i
$653$	16.3210	+	28.2688i	0.638690	+	1.10624i	0.985721	+	0.168389i	$0.0538566\pi$
$653$	16.3210	+	28.2688i	0.638690	+	1.10624i	−0.347031	+	0.937854i	$0.612810\pi$
$654$	6.66392	−	0.666336i	0.260580	−	0.0260558i
$655$	−18.4695	+	10.6634i	−0.721662	+	0.416652i
$656$	3.10024	−	1.78992i	0.121044	−	0.0698847i
$657$	−3.89517	−	19.2827i	−0.151965	−	0.752292i
$658$		−	34.2642i		−	1.33576i
$659$	−4.43305	+	7.67828i	−0.172687	+	0.299103i	−0.939358	−	0.342937i	$-0.888578\pi$
$659$	−4.43305	+	7.67828i	−0.172687	+	0.299103i	0.766671	+	0.642040i	$0.221912\pi$
$660$	0.0408082	−	0.0904228i	0.00158846	−	0.00351970i
$661$	16.6210	−	9.59611i	0.646480	−	0.373245i	−0.140626	−	0.990063i	$-0.544912\pi$
$661$	16.6210	−	9.59611i	0.646480	−	0.373245i	0.787106	+	0.616817i	$0.211578\pi$
$662$	−3.34296	+	5.79018i	−0.129928	+	0.225042i
$663$	−0.509103	+	1.08213i	−0.0197719	+	0.0420266i
$664$	−11.5219	−	19.9564i	−0.447135	−	0.774460i
$665$	60.6193	+	34.9986i	2.35071	+	1.35719i
$666$	3.50196	−	10.4180i	0.135698	−	0.403691i
$667$	−10.7512	−	18.6215i	−0.416286	−	0.721029i
$668$	0.411237	−	0.237428i	0.0159112	−	0.00918635i
$669$	0.104498	+	1.04506i	0.00404011	+	0.0404045i
$670$			44.9505i			1.73659i
$671$	0.122928	+	0.0709727i	0.00474559	+	0.00273987i
$672$	0.307721	−	0.681847i	0.0118706	−	0.0263028i
$673$	5.35582			0.206452			0.103226	−	0.994658i	$-0.467084\pi$
$673$	5.35582			0.206452			0.103226	+	0.994658i	$0.467084\pi$
$674$	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	0.895678	−	0.444704i	$-0.146691\pi$
$677$	1.63177	+	2.82630i	0.0627139	+	0.108624i	−0.832964	+	0.553328i	$0.813358\pi$
$678$	3.99728	+	39.9761i	0.153515	+	1.53527i
$679$	−28.0663	−	48.6123i	−1.07709	−	1.86557i
$680$	1.64516			0.0630888
$681$	−36.3992	−	16.4271i	−1.39482	−	0.629488i
$682$	6.94660	+	4.01062i	0.265999	+	0.153575i
$683$	−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
$686$	17.0397			0.650579
$687$	7.24965	+	3.27180i	0.276591	+	0.124827i
$688$	−7.85008	+	13.5967i	−0.299282	+	0.518371i
$689$	0.121432	+	0.218218i	0.00462619	+	0.00831344i
$690$	−18.6183	+	1.86167i	−0.708787	+	0.0708727i
$691$			22.1957i			0.844364i	0.906511	+	0.422182i	$0.138736\pi$
$691$			22.1957i			0.844364i	−0.906511	+	0.422182i	$0.861264\pi$
$692$	0.0402976	−	0.0697975i	0.00153189	−	0.00265330i
$693$	−2.42347	+	7.20960i	−0.0920598	+	0.273870i
$694$		−	7.62958i		−	0.289615i
$695$	28.5176	+	16.4646i	1.08173	+	0.624539i
$696$	4.14242	+	41.4277i	0.157018	+	1.57031i
$697$	0.150240	+	0.0867410i	0.00569074	+	0.00328555i
$698$	37.1069			1.40452
$699$	13.5169	−	1.35157i	0.511255	−	0.0511212i
$700$		−	0.314415i		−	0.0118838i
$701$	35.2587			1.33170			0.665851	−	0.746085i	$-0.268069\pi$
$701$	35.2587			1.33170			0.665851	+	0.746085i	$0.268069\pi$
$702$	−18.2203	+	19.0166i	−0.687681	+	0.717735i
$703$	18.9112			0.713250
$704$			6.42306i			0.242078i
$705$	−39.7067	+	3.97034i	−1.49544	+	0.149531i
$706$	−42.0063			−1.58093
$707$	−4.14410	−	2.39260i	−0.155855	−	0.0899828i
$708$	−0.0558788	−	0.558835i	−0.00210005	−	0.0210023i
$709$	17.1633	+	9.90922i	0.644580	+	0.372149i	0.786377	−	0.617747i	$-0.211954\pi$
$709$	17.1633	+	9.90922i	0.644580	+	0.372149i	−0.141796	+	0.989896i	$0.545288\pi$
$710$			1.33095i			0.0499498i
$711$	−8.47339	−	9.60434i	−0.317777	−	0.360191i
$712$	−7.50559	+	13.0001i	−0.281284	+	0.487198i
$713$			18.2983i			0.685276i
$714$	−1.48215	+	0.148202i	−0.0554680	+	0.00554633i
$715$	−8.63933	−	0.136516i	−0.323093	−	0.00510540i
$716$	0.154524	−	0.267643i	0.00577483	−	0.0100023i
$717$	−2.18506	−	0.986127i	−0.0816025	−	0.0368276i
$718$	38.7724			1.44697
$719$	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
$722$	−40.9697	−	23.6539i	−1.52474	−	0.880306i
$723$	−6.38837	−	2.88310i	−0.237586	−	0.107224i
$724$	−0.272288			−0.0101195
$725$	17.3956	+	30.1301i	0.646058	+	1.11900i
$726$	2.51220	+	25.1241i	0.0932363	+	0.932442i
$727$	−5.05060	−	8.74790i	−0.187317	−	0.324442i	0.757038	−	0.653371i	$-0.226646\pi$
$727$	−5.05060	−	8.74790i	−0.187317	−	0.324442i	−0.944355	+	0.328929i	$0.893312\pi$
$728$	−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
$731$	−0.760842			−0.0281408
$732$	0.00304572	−	0.00674871i	0.000112573	−	0.000249439i
$733$	10.3089	+	5.95182i	0.380766	+	0.219836i	0.678152	−	0.734922i	$-0.262781\pi$
$733$	10.3089	+	5.95182i	0.380766	+	0.219836i	−0.297385	+	0.954758i	$0.596115\pi$
$734$		−	30.1383i		−	1.11242i
$735$	1.66812	+	16.6826i	0.0615294	+	0.615346i
$736$	−0.297975	+	0.172036i	−0.0109835	+	0.00634133i
$737$	−4.20213	−	7.27830i	−0.154787	−	0.268100i
$738$	2.52752	+	2.86486i	0.0930391	+	0.105457i
$739$	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
$741$	−41.0042	−	19.2909i	−1.50633	−	0.708668i
$742$	−0.155522	+	0.269373i	−0.00570940	+	0.00988898i
$743$	−6.24525	+	3.60570i	−0.229116	+	0.132280i	−0.610164	−	0.792275i	$-0.708897\pi$
$743$	−6.24525	+	3.60570i	−0.229116	+	0.132280i	0.381048	+	0.924555i	$0.375563\pi$
$744$	14.5744	−	32.2939i	0.534324	−	1.18395i
$745$	22.0757	−	38.2362i	0.808790	−	1.40087i
$746$			34.9255i			1.27871i
$747$	18.2209	−	16.0753i	0.666669	−	0.588166i
$748$	−0.00314574	+	0.00181619i	−0.000115019	+	6.64065e-5i
$749$	15.1709	−	8.75892i	0.554333	−	0.320044i
$750$	−6.45326	+	0.645272i	−0.235640	+	0.0235620i
$751$	0.249500	+	0.432147i	0.00910439	+	0.0157693i	0.870542	−	0.492095i	$-0.163769\pi$
$751$	0.249500	+	0.432147i	0.00910439	+	0.0157693i	−0.861437	+	0.507864i	$0.830435\pi$
$752$	26.1110	−	15.0752i	0.952169	−	0.549735i
$753$	−6.95386	−	9.67371i	−0.253413	−	0.352530i
$754$	37.4191	−	20.8227i	1.36272	−	0.758317i
$755$	−3.18216			−0.115811
$756$	0.386779	+	0.0883685i	0.0140670	+	0.00321393i
$757$	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	$-0.174262\pi$
$758$	−0.619969	+	1.07382i	−0.0225183	+	0.0390028i
$759$	2.84060	−	2.04194i	0.103107	−	0.0741178i
$760$			62.3381i			2.26124i
$761$			31.6996i			1.14911i	0.818467	+	0.574554i	$0.194824\pi$
$761$			31.6996i			1.14911i	−0.818467	+	0.574554i	$0.805176\pi$
$762$	−34.2391	−	15.4523i	−1.24035	−	0.559777i
$763$	−4.39355	+	7.60985i	−0.159057	+	0.275495i
$764$	−0.0390615	+	0.0676565i	−0.00141320	+	0.00244773i
$765$	0.343485	+	1.70039i	0.0124187	+	0.0614779i
$766$	−4.03424			−0.145763
$767$	−42.7431	+	23.7853i	−1.54336	+	0.858839i
$768$	0.988459	−	0.0988376i	0.0356679	−	0.00356649i
$769$	−7.69488	+	4.44264i	−0.277484	+	0.160206i	−0.632284	−	0.774737i	$-0.717882\pi$
$769$	−7.69488	+	4.44264i	−0.277484	+	0.160206i	0.354800	+	0.934942i	$0.384549\pi$
$770$	−5.38093	−	9.32005i	−0.193915	−	0.335871i
$771$	7.61811	+	10.5978i	0.274360	+	0.381670i
$772$	−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	$0.0288917\pi$
$774$	−15.8821	−	5.33867i	−0.570870	−	0.191895i
$775$		−	29.6071i		−	1.06352i
$776$	24.9953	−	43.2932i	0.897280	−	1.55414i
$777$	8.41717	+	11.7094i	0.301964	+	0.420071i
$778$	14.6269	−	8.44484i	0.524399	−	0.302762i
$779$	−3.28678	+	5.69287i	−0.117761	+	0.203968i
$780$	0.0377515	+	0.449117i	0.00135172	+	0.0160810i
$781$	−0.124422	−	0.215506i	−0.00445218	−	0.00771139i
$782$	0.593321	+	0.342554i	0.0212171	+	0.0122497i
$783$	−41.9538	+	12.9310i	−1.49931	+	0.462116i
$784$	−6.33376	−	10.9704i	−0.226206	−	0.391800i
$785$	−29.2719	+	16.9001i	−1.04476	+	0.603191i
$786$	15.6743	+	7.07387i	0.559083	+	0.252317i
$787$			4.87839i			0.173896i	0.996213	+	0.0869478i	$0.0277113\pi$
$787$			4.87839i			0.173896i	−0.996213	+	0.0869478i	$0.972289\pi$
$788$	−0.0509969	−	0.0294431i	−0.00181669	−	0.00104887i
$789$	−7.77854	+	0.777789i	−0.276923	+	0.0276900i
$790$	18.1220			0.644754
$791$	−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
$795$	0.330180	+	0.149012i	0.0117103	+	0.00528491i
$796$	0.281112	+	0.486900i	0.00996374	+	0.0172577i
$797$	35.9086			1.27195			0.635974	−	0.771710i	$-0.280598\pi$
$797$	35.9086			1.27195			0.635974	+	0.771710i	$0.280598\pi$
$798$	−5.61567	−	56.1614i	−0.198792	−	1.98809i
$799$	1.26536	+	0.730555i	0.0447652	+	0.0258452i
$800$	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
$803$	−5.20413			−0.183650
$804$	−0.355958	+	0.255877i	−0.0125537	+	0.00902409i
$805$	12.2751	−	21.2611i	0.432641	−	0.749356i
$806$	−36.4371	−	0.575766i	−1.28344	−	0.0202805i
$807$	15.3612	+	21.3694i	0.540741	+	0.752240i
$808$		−	4.26160i		−	0.149923i
$809$	−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	$0.306544\pi$
$810$	−4.76130	+	37.9048i	−0.167295	+	1.33184i
$811$		−	14.3469i		−	0.503789i	−0.967755	−	0.251894i	$-0.918946\pi$
$811$		−	14.3469i		−	0.503789i	0.967755	−	0.251894i	$-0.0810536\pi$
$812$	−0.558672	−	0.322549i	−0.0196055	−	0.0113193i
$813$	34.6512	+	15.6383i	1.21527	+	0.548458i
$814$	−2.51801	−	1.45377i	−0.0882563	−	0.0509548i
$815$	5.89408			0.206461
$816$	−0.765035	−	1.06426i	−0.0267816	−	0.0372566i
$817$		−	28.8298i		−	1.00863i
$818$	−47.6663			−1.66661
$819$	−6.30604	−	33.9749i	−0.220351	−	1.18718i
$820$	0.0653799			0.00228317
$821$		−	5.00052i		−	0.174519i	−0.996186	−	0.0872596i	$-0.972189\pi$
$821$		−	5.00052i		−	0.174519i	0.996186	−	0.0872596i	$-0.0278110\pi$
$822$	6.98291	−	15.4727i	0.243557	−	0.539673i
$823$	4.52344			0.157677			0.0788385	−	0.996887i	$-0.474879\pi$
$823$	4.52344			0.157677			0.0788385	+	0.996887i	$0.474879\pi$
$824$	−7.98425	−	4.60971i	−0.278144	−	0.160587i
$825$	−4.59617	+	3.30391i	−0.160018	+	0.115027i
$826$	−52.7630	−	30.4627i	−1.83586	−	1.05993i
$827$		−	7.63184i		−	0.265385i	−0.991157	−	0.132693i	$-0.957638\pi$
$827$		−	7.63184i		−	0.265385i	0.991157	−	0.132693i	$-0.0423623\pi$
$828$	−0.120726	−	0.136839i	−0.00419550	−	0.00475548i
$829$	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	$0.0715407\pi$
$830$			34.3803i			1.19336i
$831$	4.30403	−	9.53685i	0.149305	−	0.330830i
$832$	−14.1893	−	25.4987i	−0.491926	−	0.884008i
$833$	0.306939	−	0.531634i	0.0106348	−	0.0184200i
$834$	−2.64182	−	26.4204i	−0.0914787	−	0.914865i
$835$	−59.9928			−2.07614
$836$	−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
$839$	19.8924	+	11.4849i	0.686760	+	0.396501i	0.802397	−	0.596790i	$-0.203558\pi$
$839$	19.8924	+	11.4849i	0.686760	+	0.396501i	−0.115637	+	0.993292i	$0.536891\pi$
$840$	−38.5982	+	27.7460i	−1.33176	+	0.957326i
$841$	42.3827			1.46147
$842$	−8.29560	−	14.3684i	−0.285885	−	0.495168i
$843$	10.6542	−	7.65871i	0.366952	−	0.263780i
$844$	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
$848$	−0.273700			−0.00939888
$849$	−28.3821	−	39.4832i	−0.974072	−	1.35506i
$850$	−0.960008	−	0.554261i	−0.0329280	−	0.0190110i
$851$		−	6.63278i		−	0.227369i
$852$	−0.0105397	+	0.00757635i	−0.000361084	+	0.000259561i
$853$	16.0483	−	9.26548i	0.549483	−	0.317244i	−0.199430	−	0.979912i	$-0.563909\pi$
$853$	16.0483	−	9.26548i	0.549483	−	0.317244i	0.748913	+	0.662668i	$0.230576\pi$
$854$	−0.401606	−	0.695602i	−0.0137427	−	0.0238030i
$855$	−64.4312	+	13.0153i	−2.20350	+	0.445114i
$856$	13.5109	+	7.80053i	0.461793	+	0.266617i
$857$	20.7985	+	36.0241i	0.710464	+	1.23056i	0.964683	+	0.263413i	$0.0848481\pi$
$857$	20.7985	+	36.0241i	0.710464	+	1.23056i	−0.254219	+	0.967147i	$0.581819\pi$
$858$	3.97670	+	5.72070i	0.135762	+	0.195302i
$859$	−7.48523	+	12.9648i	−0.255393	+	0.442353i	−0.965002	−	0.262242i	$-0.915538\pi$
$859$	−7.48523	+	12.9648i	−0.255393	+	0.442353i	0.709609	+	0.704595i	$0.248871\pi$
$860$	−0.248322	+	0.143369i	−0.00846771	+	0.00488883i
$861$	−4.98779	+	0.498737i	−0.169984	+	0.0169969i
$862$	8.08877	−	14.0102i	0.275505	−	0.477188i
$863$		−	30.1011i		−	1.02465i	−0.858791	−	0.512327i	$-0.828784\pi$
$863$		−	30.1011i		−	1.02465i	0.858791	−	0.512327i	$-0.171216\pi$
$864$	0.206917	+	0.671330i	0.00703947	+	0.0228391i
$865$	−8.81815	+	5.09116i	−0.299826	+	0.173105i
$866$	17.0575	−	9.84813i	0.579636	−	0.334653i
$867$	−12.0861	+	26.7804i	−0.410466	+	0.909510i
$868$	0.274487	+	0.475425i	0.00931668	+	0.0161370i
$869$	−2.93429	+	1.69411i	−0.0995388	+	0.0574688i
$870$	25.5519	−	56.6179i	0.866292	−	1.91953i
$871$	32.7605	+	19.6109i	1.11005	+	0.664490i
$872$	−7.82562			−0.265009
$873$	49.9655	+	16.7956i	1.69108	+	0.568446i
$874$	−12.9800	+	22.4821i	−0.439056	+	0.760468i
$875$	4.25466	−	7.36929i	0.143834	−	0.249127i
$876$	0.0270088	+	0.270111i	0.000912543	+	0.00912620i
$877$		−	4.60474i		−	0.155491i	−0.996973	−	0.0777454i	$-0.975228\pi$
$877$		−	4.60474i		−	0.155491i	0.996973	−	0.0777454i	$-0.0247721\pi$
$878$			47.9073i			1.61679i
$879$	3.95267	+	39.5301i	0.133320	+	1.33332i
$880$	4.73488	−	8.20105i	0.159613	−	0.276457i
$881$	−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	$0.881334\pi$
$882$	10.1375	−	8.94379i	0.341348	−	0.301153i
$883$	−20.7632			−0.698737			−0.349368	−	0.936985i	$-0.613604\pi$
$883$	−20.7632			−0.698737			−0.349368	+	0.936985i	$0.613604\pi$
$884$	0.00847598	−	0.0141594i	0.000285078	−	0.000476231i
$885$	−29.1875	+	64.6735i	−0.981126	+	2.17398i
$886$	39.7705	−	22.9615i	1.33612	−	0.771407i
$887$	−19.3264	−	33.4743i	−0.648916	−	1.12396i	−0.983382	−	0.181548i	$-0.941889\pi$
$887$	−19.3264	−	33.4743i	−0.648916	−	1.12396i	0.334466	−	0.942408i	$-0.391444\pi$
$888$	−5.28295	+	11.7059i	−0.177284	+	0.392826i
$889$	42.6839	−	24.6435i	1.43157	−	0.826518i
$890$	19.3956	−	11.1981i	0.650142	−	0.375360i
$891$	−2.77253	−	6.58257i	−0.0928833	−	0.220525i
$892$		−	0.0144928i		−	0.000485255i
$893$	−27.6821	+	47.9468i	−0.926347	+	1.60448i
$894$	−35.4243	+	3.54213i	−1.18477	+	0.118467i
$895$	−33.8138	+	19.5224i	−1.13027	+	0.652562i
$896$	17.7408	−	30.7280i	0.592680	−	1.02655i
$897$	−6.76593	+	14.3815i	−0.225908	+	0.480184i
$898$	−6.22376	−	10.7799i	−0.207690	−	0.359729i
$899$	−52.6076	−	30.3730i	−1.75456	−	1.01300i
$900$	0.195337	+	0.221409i	0.00651123	+	0.00738029i
$901$	−0.00663185	−	0.0114867i	−0.000220939	−	0.000382677i
$902$	0.875264	−	0.505334i	0.0291431	−	0.0168258i
$903$	17.8507	−	12.8318i	0.594033	−	0.427015i
$904$		−	46.9450i		−	1.56137i
$905$	29.7918	+	17.2003i	0.990312	+	0.571757i
$906$	1.49768	+	2.08347i	0.0497571	+	0.0692185i
$907$	−23.2273			−0.771250			−0.385625	−	0.922656i	$-0.626014\pi$
$907$	−23.2273			−0.771250			−0.385625	+	0.922656i	$0.626014\pi$
$908$	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	−0.764737	−	0.644343i	$-0.777131\pi$
$911$	−28.3835	−	49.1616i	−0.940386	−	1.62880i	−0.175649	−	0.984453i	$-0.556202\pi$
$912$	40.3269	−	28.9886i	1.33536	−	0.959910i
$913$	−3.21399	−	5.56679i	−0.106368	−	0.184234i
$914$	21.3948			0.707678
$915$	−0.759554	+	0.545998i	−0.0251101	+	0.0180501i
$916$	−0.0950498	−	0.0548770i	−0.00314053	−	0.00181319i
$917$	−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	$0.723363\pi$
$920$	21.8640			0.720834
$921$	−0.571021	−	5.71069i	−0.0188158	−	0.188174i
$922$	−24.4677	+	42.3793i	−0.805800	+	1.39569i
$923$	0.970018	+	0.580665i	0.0319285	+	0.0191128i
$924$	0.0431739	−	0.0956646i	0.00142032	−	0.00314713i
$925$			10.7320i			0.352866i
$926$	−19.2617	+	33.3622i	−0.632978	+	1.09635i
$927$	3.09749	−	9.21478i	0.101735	−	0.302653i
$928$		−	1.14224i		−	0.0374959i
$929$	−37.7777	−	21.8110i	−1.23945	−	0.715595i	−0.270466	−	0.962729i	$-0.587178\pi$
$929$	−37.7777	−	21.8110i	−1.23945	−	0.715595i	−0.968981	+	0.247134i	$0.920511\pi$
$930$	−42.9219	+	30.8540i	−1.40746	+	1.01174i
$931$	20.1446	+	11.6305i	0.660214	+	0.381175i
$932$	−0.187450			−0.00614013
$933$	−18.0537	+	40.0032i	−0.591050	+	1.30965i
$934$			13.1309i			0.429656i
$935$	0.458912			0.0150080
$936$	23.3957	−	19.9923i	0.764711	−	0.653470i
$937$	−50.6045			−1.65318			−0.826588	−	0.562807i	$-0.809721\pi$
$937$	−50.6045			−1.65318			−0.826588	+	0.562807i	$0.809721\pi$
$938$			47.5563i			1.55277i
$939$	17.6237	+	24.5169i	0.575129	+	0.800078i
$940$	0.550646			0.0179601
$941$	−6.38079	−	3.68395i	−0.208008	−	0.120093i	0.392377	−	0.919804i	$-0.371653\pi$
$941$	−6.38079	−	3.68395i	−0.208008	−	0.120093i	−0.600385	+	0.799711i	$0.704986\pi$
$942$	24.8418	+	11.2112i	0.809390	+	0.365282i
$943$	1.99667	+	1.15278i	0.0650207	+	0.0375397i
$944$		−	53.6105i		−	1.74487i
$945$	−36.7363	−	34.1013i	−1.19503	−	1.10931i
$946$	−2.21625	+	3.83866i	−0.0720565	+	0.124805i
$947$			15.5196i			0.504319i	0.967686	+	0.252159i	$0.0811407\pi$
$947$			15.5196i			0.504319i	−0.967686	+	0.252159i	$0.918859\pi$
$948$	0.103158	+	0.143506i	0.00335043	+	0.00466087i
$949$	20.6597	−	11.4966i	0.670643	−	0.373194i
$950$	21.0020	−	36.3766i	0.681395	−	1.18021i
$951$	18.3506	−	13.1912i	0.595059	−	0.427753i
$952$	1.74052			0.0564107
$953$	−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
$956$	0.0286482	+	0.0165400i	0.000926549	+	0.000534943i
$957$	1.15552	+	11.5561i	0.0373525	+	0.373557i
$958$	−15.5149			−0.501263
$959$	11.1364	+	19.2889i	0.359615	+	0.622871i
$960$	−38.5815	−	17.4120i	−1.24521	−	0.561970i
$961$	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
$965$	57.5635			1.85304
$966$	−19.6976	+	1.96959i	−0.633760	+	0.0633707i
$967$	−12.2838	−	7.09208i	−0.395022	−	0.228066i	0.289312	−	0.957235i	$-0.406574\pi$
$967$	−12.2838	−	7.09208i	−0.395022	−	0.228066i	−0.684334	+	0.729169i	$0.739907\pi$
$968$		−	29.5039i		−	0.948290i
$969$	2.19374	+	0.990045i	0.0704731	+	0.0318048i
$970$	−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	$-0.339232\pi$
$972$	−0.327267	+	0.178066i	−0.0104971	+	0.00571147i
$973$	30.1707	+	17.4191i	0.967230	+	0.558430i
$974$	−8.11217	−	14.0507i	−0.259931	−	0.450213i
$975$	10.9474	−	23.2696i	0.350599	−	0.745223i
$976$	0.353388	−	0.612085i	0.0113117	−	0.0195924i
$977$	−45.1160	+	26.0477i	−1.44339	+	0.833340i	−0.998074	−	0.0620342i	$-0.980241\pi$
$977$	−45.1160	+	26.0477i	−1.44339	+	0.833340i	−0.445314	+	0.895375i	$0.646908\pi$
$978$	−2.77404	−	3.85905i	−0.0887040	−	0.123399i
$979$	−2.09367	+	3.62634i	−0.0669138	+	0.115898i
$980$		−	0.231351i		−	0.00739025i
$981$	−1.63388	−	8.08838i	−0.0521656	−	0.258242i
$982$	25.8630	−	14.9320i	0.825323	−	0.476500i
$983$	22.2548	−	12.8488i	0.709819	−	0.409814i	−0.101175	−	0.994869i	$-0.532260\pi$
$983$	22.2548	−	12.8488i	0.709819	−	0.409814i	0.810994	+	0.585055i	$0.198927\pi$
$984$	−2.60568	−	3.62483i	−0.0830659	−	0.115555i
$985$	3.71981	+	6.44290i	0.118523	+	0.205288i
$986$	−1.96969	+	1.13720i	−0.0627277	+	0.0362159i
$987$	−42.0085	+	4.20050i	−1.33715	+	0.133703i
$988$	0.536525	+	0.321171i	0.0170691	+	0.0102178i
$989$	−10.1115			−0.321528
$990$	9.57949	+	3.22009i	0.304456	+	0.102341i
$991$	−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	$0.228152\pi$
$992$	−0.486018	+	0.841808i	−0.0154311	+	0.0267274i
$993$	7.50867	+	3.38870i	0.238280	+	0.107537i
$994$			1.40811i			0.0446625i
$995$		−	71.0308i		−	2.25183i
$996$	−0.272254	+	0.195707i	−0.00862670	+	0.00620122i
$997$	−27.7968	+	48.1455i	−0.880335	+	1.52478i	−0.0293652	+	0.999569i	$0.509349\pi$
$997$	−27.7968	+	48.1455i	−0.880335	+	1.52478i	−0.850969	+	0.525215i	$0.823985\pi$
$998$	9.24317	−	16.0096i	0.292587	−	0.506776i
$999$	−13.2020	−	3.01630i	−0.417693	−	0.0954316i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.3	✓	22	1.1	even	1	trivial
117.2.l.b.88.9	yes	22	117.88	even	6	inner
117.2.r.b.43.3	yes	22	9.7	even	3
117.2.r.b.49.3	yes	22	13.10	even	6
351.2.l.b.127.3		22	117.101	odd	6
351.2.l.b.199.9		22	3.2	odd	2
351.2.r.b.10.9		22	39.23	odd	6
351.2.r.b.316.9		22	9.2	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.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.40574i q^{2} +(-1.72346 + 0.172331i) q^{3} +0.0239006 q^{4} +(-2.61504 - 1.50979i) q^{5} +(0.242252 + 2.42273i) q^{6} +(-2.76663 - 1.59731i) q^{7} -2.84507i q^{8} +(2.94060 - 0.594010i) q^{9} +(-2.12237 + 3.67605i) q^{10} -0.793626i q^{11} +(-0.0411917 + 0.00411882i) q^{12} +(1.75322 + 3.15059i) q^{13} +(-2.24541 + 3.88916i) q^{14} +(4.76708 + 2.15141i) q^{15} -3.95163 q^{16} +(-0.0957495 - 0.165843i) q^{17} +(-0.835023 - 4.13372i) q^{18} +(6.28411 - 3.62813i) q^{19} +(-0.0625010 - 0.0360850i) q^{20} +(5.04343 + 2.27612i) q^{21} -1.11563 q^{22} +(-1.27250 - 2.20404i) q^{23} +(0.490295 + 4.90336i) 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} +8.44883 q^{29} +(3.02432 - 6.70127i) q^{30} +(-6.22662 - 3.59494i) q^{31} -0.135195i q^{32} +(0.136766 + 1.36778i) q^{33} +(-0.233132 + 0.134599i) q^{34} +(4.82322 + 8.35407i) q^{35} +(0.0702823 - 0.0141972i) q^{36} +(2.25703 + 1.30310i) q^{37} +(-5.10020 - 8.83381i) q^{38} +(-3.56454 - 5.12778i) q^{39} +(-4.29547 + 7.43997i) q^{40} +(-0.784546 + 0.452958i) q^{41} +(3.19964 - 7.08974i) q^{42} +(1.98654 - 3.44080i) q^{43} -0.0189682i q^{44} +(-8.58662 - 2.88634i) q^{45} +(-3.09830 + 1.78880i) q^{46} +(-6.60765 + 3.81493i) q^{47} +(6.81046 - 0.680988i) q^{48} +(1.60282 + 2.77617i) q^{49} +(5.01313 - 2.89433i) q^{50} +(0.193600 + 0.269322i) q^{51} +(0.0419030 + 0.0753011i) q^{52} +0.0692625 q^{53} +(2.15149 + 6.98038i) q^{54} +(-1.19821 + 2.07536i) q^{55} +(-4.54448 + 7.87126i) q^{56} +(-10.2051 + 7.33587i) q^{57} -11.8768i q^{58} +13.5667i q^{59} +(0.113936 + 0.0514200i) q^{60} +(-0.0894284 + 0.154895i) q^{61} +(-5.05354 + 8.75299i) q^{62} +(-9.08438 - 3.05366i) q^{63} -8.09330 q^{64} +(0.172015 - 10.8859i) q^{65} +(1.92274 - 0.192258i) q^{66} +(9.17094 - 5.29484i) q^{67} +(-0.00228847 - 0.00396375i) q^{68} +(2.57293 + 3.57927i) q^{69} +(11.7436 - 6.78019i) q^{70} +(0.271545 - 0.156777i) q^{71} +(-1.69000 - 8.36624i) q^{72} -6.55741i q^{73} +(1.83181 - 3.17279i) q^{74} +(-4.16306 - 5.79135i) q^{75} +(0.150194 - 0.0867146i) q^{76} +(-1.26767 + 2.19567i) q^{77} +(-7.20831 + 5.01080i) q^{78} +(-2.13465 - 3.69732i) q^{79} +(10.3336 + 5.96613i) q^{80} +(8.29430 - 3.49350i) q^{81} +(0.636740 + 1.10287i) q^{82} +(7.01438 - 4.04975i) q^{83} +(0.120541 + 0.0544008i) q^{84} +0.578247i q^{85} +(-4.83686 - 2.79256i) q^{86} +(-14.5612 + 1.45600i) q^{87} -2.25792 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} +(11.3508 + 5.12268i) q^{93} +(5.36279 + 9.28863i) q^{94} -21.9109 q^{95} +(0.0232983 + 0.233003i) q^{96} +(15.2169 + 8.78548i) q^{97} +(3.90257 - 2.25315i) q^{98} +(-0.471422 - 2.33374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Introduction

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