LMFDB - Embedded newform 666.2.g.b.565.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(211,666)] 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("666.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36] 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			565.11
Character	$\chi$	$=$	666.565
Dual form			666.2.g.b.211.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.211906 - 1.71904i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.03934 - 3.53223i) q^{5} +(1.59468 - 0.676003i) q^{6} +4.94838 q^{7} -1.00000 q^{8} +(-2.91019 - 0.728551i) q^{9} +4.07867 q^{10} +(-1.34686 + 2.33282i) q^{11} +(1.38278 + 1.04304i) q^{12} +(1.43689 - 2.48876i) q^{13} +(2.47419 + 4.28542i) q^{14} +(-5.63990 - 4.25420i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.71933 + 4.71002i) q^{17} +(-0.824152 - 2.88458i) q^{18} +(0.179633 + 0.311133i) q^{19} +(2.03934 + 3.53223i) q^{20} +(1.04859 - 8.50645i) q^{21} -2.69371 q^{22} +(0.147957 + 0.256269i) q^{23} +(-0.211906 + 1.71904i) q^{24} +(-5.81779 - 10.0767i) q^{25} +2.87378 q^{26} +(-1.86910 + 4.84835i) q^{27} +(-2.47419 + 4.28542i) q^{28} +(-1.72918 + 2.99502i) q^{29} +(0.864297 - 7.01140i) q^{30} +(0.980010 + 1.69743i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.72481 + 2.80964i) q^{33} -5.43866 q^{34} +(10.0914 - 17.4788i) q^{35} +(2.08604 - 2.15602i) q^{36} +(-6.08268 + 0.0307620i) q^{37} +(-0.179633 + 0.311133i) q^{38} +(-3.97380 - 2.99745i) q^{39} +(-2.03934 + 3.53223i) q^{40} +(-1.23247 + 2.13471i) q^{41} +(7.89110 - 3.34512i) q^{42} +(3.92593 - 6.79991i) q^{43} +(-1.34686 - 2.33282i) q^{44} +(-8.50827 + 8.79372i) q^{45} +(-0.147957 + 0.256269i) q^{46} +(-3.83844 + 6.64837i) q^{47} +(-1.59468 + 0.676003i) q^{48} +17.4864 q^{49} +(5.81779 - 10.0767i) q^{50} +(7.52046 + 5.67272i) q^{51} +(1.43689 + 2.48876i) q^{52} +(2.45992 - 4.26070i) q^{53} +(-5.13334 + 0.805490i) q^{54} +(5.49339 + 9.51483i) q^{55} -4.94838 q^{56} +(0.572915 - 0.242864i) q^{57} -3.45835 q^{58} +6.55947 q^{59} +(6.50420 - 2.75720i) q^{60} +4.14777 q^{61} +(-0.980010 + 1.69743i) q^{62} +(-14.4007 - 3.60514i) q^{63} +1.00000 q^{64} +(-5.86060 - 10.1509i) q^{65} +(-0.570815 + 4.63060i) q^{66} +(0.283030 - 0.490223i) q^{67} +(-2.71933 - 4.71002i) q^{68} +(0.471889 - 0.200039i) q^{69} +20.1828 q^{70} +(5.34228 + 9.25310i) q^{71} +(2.91019 + 0.728551i) q^{72} +8.59878 q^{73} +(-3.06798 - 5.25238i) q^{74} +(-18.5551 + 7.86568i) q^{75} -0.359265 q^{76} +(-6.66475 + 11.5437i) q^{77} +(0.608972 - 4.94014i) q^{78} -14.1855 q^{79} -4.07867 q^{80} +(7.93843 + 4.24044i) q^{81} -2.46495 q^{82} +(-6.24400 - 10.8149i) q^{83} +(6.84251 + 5.16133i) q^{84} +(11.0913 + 19.2106i) q^{85} +7.85186 q^{86} +(4.78213 + 3.60719i) q^{87} +(1.34686 - 2.33282i) q^{88} +(-9.19327 + 15.9232i) q^{89} +(-11.8697 - 2.97152i) q^{90} +(7.11027 - 12.3153i) q^{91} -0.295914 q^{92} +(3.12562 - 1.32498i) q^{93} -7.67687 q^{94} +1.46533 q^{95} +(-1.38278 - 1.04304i) q^{96} +(0.696052 - 1.20560i) q^{97} +(8.74321 + 15.1437i) q^{98} +(5.61919 - 5.80771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 2 q^{3} - 18 q^{4} + 4 q^{5} + 2 q^{6} - 8 q^{7} - 36 q^{8} - 2 q^{9} + 8 q^{10} + 3 q^{11} + 4 q^{12} + q^{13} - 4 q^{14} - 7 q^{15} - 18 q^{16} + 3 q^{17} + 2 q^{18} + 9 q^{19} + 4 q^{20}+ \cdots - 23 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 2 * q^3 - 18 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^7 - 36 * q^8 - 2 * q^9 + 8 * q^10 + 3 * q^11 + 4 * q^12 + q^13 - 4 * q^14 - 7 * q^15 - 18 * q^16 + 3 * q^17 + 2 * q^18 + 9 * q^19 + 4 * q^20 - 13 * q^21 + 6 * q^22 + 11 * q^23 + 2 * q^24 - 22 * q^25 + 2 * q^26 - 2 * q^27 + 4 * q^28 - 12 * q^29 + q^30 + 16 * q^31 + 18 * q^32 + 13 * q^33 + 6 * q^34 + 3 * q^35 + 4 * q^36 + 8 * q^37 - 9 * q^38 - 47 * q^39 - 4 * q^40 - 6 * q^41 - 2 * q^42 + 4 * q^43 + 3 * q^44 - 40 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 + 24 * q^49 + 22 * q^50 + 6 * q^51 + q^52 + 8 * q^53 + 8 * q^54 + 9 * q^55 + 8 * q^56 - 12 * q^57 - 24 * q^58 + 24 * q^59 + 8 * q^60 + 30 * q^61 - 16 * q^62 + 23 * q^63 + 36 * q^64 - 26 * q^65 - q^66 - 14 * q^67 + 3 * q^68 - 5 * q^69 + 6 * q^70 + 2 * q^72 + 22 * q^73 + 16 * q^74 + 3 * q^75 - 18 * q^76 + 25 * q^77 - 46 * q^78 - 32 * q^79 - 8 * q^80 + 34 * q^81 - 12 * q^82 + 11 * q^84 + 15 * q^85 + 8 * q^86 - 7 * q^87 - 3 * q^88 + 3 * q^89 - 50 * q^90 + 37 * q^91 - 22 * q^92 - q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 11 * q^97 + 12 * q^98 - 23 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.211906	−	1.71904i	0.122344	−	0.992488i
$3$	0.211906	−	1.71904i	0.122344	−	0.992488i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.03934	−	3.53223i	0.912019	−	1.57966i	0.100811	−	0.994906i	$-0.467856\pi$
$5$	2.03934	−	3.53223i	0.912019	−	1.57966i	0.811208	−	0.584758i	$-0.198810\pi$
$6$	1.59468	−	0.676003i	0.651027	−	0.275977i
$7$	4.94838			1.87031			0.935155	−	0.354238i	$-0.115260\pi$
$7$	4.94838			1.87031			0.935155	+	0.354238i	$0.115260\pi$
$8$	−1.00000			−0.353553
$9$	−2.91019	−	0.728551i	−0.970064	−	0.242850i
$10$	4.07867			1.28979
$11$	−1.34686	+	2.33282i	−0.406093	+	0.703373i	−0.994448	−	0.105229i	$-0.966442\pi$
$11$	−1.34686	+	2.33282i	−0.406093	+	0.703373i	0.588355	+	0.808603i	$0.299776\pi$
$12$	1.38278	+	1.04304i	0.399174	+	0.301099i
$13$	1.43689	−	2.48876i	0.398521	−	0.690259i	−0.595022	−	0.803709i	$-0.702857\pi$
$13$	1.43689	−	2.48876i	0.398521	−	0.690259i	0.993544	+	0.113450i	$0.0361902\pi$
$14$	2.47419	+	4.28542i	0.661255	+	1.14533i
$15$	−5.63990	−	4.25420i	−1.45622	−	1.09843i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.71933	+	4.71002i	−0.659535	+	1.14235i	0.321202	+	0.947011i	$0.395913\pi$
$17$	−2.71933	+	4.71002i	−0.659535	+	1.14235i	−0.980736	+	0.195337i	$0.937420\pi$
$18$	−0.824152	−	2.88458i	−0.194255	−	0.679901i
$19$	0.179633	+	0.311133i	0.0412105	+	0.0713788i	0.885895	−	0.463886i	$-0.153545\pi$
$19$	0.179633	+	0.311133i	0.0412105	+	0.0713788i	−0.844684	+	0.535265i	$0.820212\pi$
$20$	2.03934	+	3.53223i	0.456009	+	0.789832i
$21$	1.04859	−	8.50645i	0.228822	−	1.85626i
$22$	−2.69371			−0.574302
$23$	0.147957	+	0.256269i	0.0308511	+	0.0534357i	0.881039	−	0.473044i	$-0.156845\pi$
$23$	0.147957	+	0.256269i	0.0308511	+	0.0534357i	−0.850188	+	0.526480i	$0.823512\pi$
$24$	−0.211906	+	1.71904i	−0.0432552	+	0.350897i
$25$	−5.81779	−	10.0767i	−1.16356	−	2.01534i
$26$	2.87378			0.563594
$27$	−1.86910	+	4.84835i	−0.359708	+	0.933065i
$28$	−2.47419	+	4.28542i	−0.467578	+	0.809868i
$29$	−1.72918	+	2.99502i	−0.321100	+	0.556161i	−0.980715	−	0.195442i	$-0.937386\pi$
$29$	−1.72918	+	2.99502i	−0.321100	+	0.556161i	0.659615	+	0.751603i	$0.270719\pi$
$30$	0.864297	−	7.01140i	0.157798	−	1.28010i
$31$	0.980010	+	1.69743i	0.176015	+	0.304867i	0.940512	−	0.339760i	$-0.110346\pi$
$31$	0.980010	+	1.69743i	0.176015	+	0.304867i	−0.764497	+	0.644627i	$0.777013\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.72481	+	2.80964i	0.648406	+	0.489096i
$34$	−5.43866			−0.932723
$35$	10.0914	−	17.4788i	1.70576	−	2.95446i
$36$	2.08604	−	2.15602i	0.347673	−	0.359337i
$37$	−6.08268	+	0.0307620i	−0.999987	+	0.00505725i
$37$	−6.08268	+	0.0307620i	−0.999987	+	0.00505725i
$38$	−0.179633	+	0.311133i	−0.0291403	+	0.0504724i
$39$	−3.97380	−	2.99745i	−0.636317	−	0.479977i
$40$	−2.03934	+	3.53223i	−0.322447	+	0.558495i
$41$	−1.23247	+	2.13471i	−0.192480	+	0.333386i	−0.946072	−	0.323958i	$-0.894986\pi$
$41$	−1.23247	+	2.13471i	−0.192480	+	0.333386i	0.753591	+	0.657343i	$0.228320\pi$
$42$	7.89110	−	3.34512i	1.21762	−	0.516163i
$43$	3.92593	−	6.79991i	0.598699	−	1.03698i	−0.394314	−	0.918976i	$-0.629018\pi$
$43$	3.92593	−	6.79991i	0.598699	−	1.03698i	0.993013	−	0.118001i	$-0.0376487\pi$
$44$	−1.34686	−	2.33282i	−0.203046	−	0.351687i
$45$	−8.50827	+	8.79372i	−1.26834	+	1.31089i
$46$	−0.147957	+	0.256269i	−0.0218150	+	0.0377848i
$47$	−3.83844	+	6.64837i	−0.559893	+	0.969764i	0.437611	+	0.899164i	$0.355825\pi$
$47$	−3.83844	+	6.64837i	−0.559893	+	0.969764i	−0.997505	+	0.0705996i	$0.977509\pi$
$48$	−1.59468	+	0.676003i	−0.230173	+	0.0975727i
$49$	17.4864			2.49806
$50$	5.81779	−	10.0767i	0.822759	−	1.42506i
$51$	7.52046	+	5.67272i	1.05308	+	0.794340i
$52$	1.43689	+	2.48876i	0.199261	+	0.345130i
$53$	2.45992	−	4.26070i	0.337896	−	0.585252i	−0.646141	−	0.763218i	$-0.723618\pi$
$53$	2.45992	−	4.26070i	0.337896	−	0.585252i	0.984037	+	0.177966i	$0.0569516\pi$
$54$	−5.13334	+	0.805490i	−0.698559	+	0.109613i
$55$	5.49339	+	9.51483i	0.740728	+	1.28298i
$56$	−4.94838			−0.661255
$57$	0.572915	−	0.242864i	0.0758844	−	0.0321682i
$58$	−3.45835			−0.454104
$59$	6.55947			0.853971			0.426985	−	0.904259i	$-0.359576\pi$
$59$	6.55947			0.853971			0.426985	+	0.904259i	$0.359576\pi$
$60$	6.50420	−	2.75720i	0.839688	−	0.355952i
$61$	4.14777			0.531067			0.265534	−	0.964102i	$-0.414452\pi$
$61$	4.14777			0.531067			0.265534	+	0.964102i	$0.414452\pi$
$62$	−0.980010	+	1.69743i	−0.124461	+	0.215574i
$63$	−14.4007	−	3.60514i	−1.81432	−	0.454205i
$64$	1.00000			0.125000
$65$	−5.86060	−	10.1509i	−0.726918	−	1.25906i
$66$	−0.570815	+	4.63060i	−0.0702625	+	0.569987i
$67$	0.283030	−	0.490223i	0.0345777	−	0.0598903i	−0.848219	−	0.529646i	$-0.822325\pi$
$67$	0.283030	−	0.490223i	0.0345777	−	0.0598903i	0.882796	+	0.469756i	$0.155658\pi$
$68$	−2.71933	−	4.71002i	−0.329767	−	0.571174i
$69$	0.471889	−	0.200039i	0.0568088	−	0.0240818i
$70$	20.1828			2.41231
$71$	5.34228	+	9.25310i	0.634012	+	1.09814i	0.986724	+	0.162409i	$0.0519263\pi$
$71$	5.34228	+	9.25310i	0.634012	+	1.09814i	−0.352712	+	0.935732i	$0.614740\pi$
$72$	2.91019	+	0.728551i	0.342969	+	0.0858605i
$73$	8.59878			1.00641			0.503206	−	0.864167i	$-0.332154\pi$
$73$	8.59878			1.00641			0.503206	+	0.864167i	$0.332154\pi$
$74$	−3.06798	−	5.25238i	−0.356646	−	0.610577i
$75$	−18.5551	+	7.86568i	−2.14256	+	0.908251i
$76$	−0.359265			−0.0412105
$77$	−6.66475	+	11.5437i	−0.759519	+	1.31553i
$78$	0.608972	−	4.94014i	0.0689525	−	0.559360i
$79$	−14.1855			−1.59599			−0.797995	−	0.602664i	$-0.794106\pi$
$79$	−14.1855			−1.59599			−0.797995	+	0.602664i	$0.794106\pi$
$80$	−4.07867			−0.456009
$81$	7.93843	+	4.24044i	0.882047	+	0.471161i
$82$	−2.46495			−0.272208
$83$	−6.24400	−	10.8149i	−0.685368	−	1.18709i	−0.973321	−	0.229448i	$-0.926308\pi$
$83$	−6.24400	−	10.8149i	−0.685368	−	1.18709i	0.287953	−	0.957644i	$-0.407025\pi$
$84$	6.84251	+	5.16133i	0.746579	+	0.563148i
$85$	11.0913	+	19.2106i	1.20302	+	2.08368i
$86$	7.85186			0.846688
$87$	4.78213	+	3.60719i	0.512699	+	0.386731i
$88$	1.34686	−	2.33282i	0.143575	−	0.248680i
$89$	−9.19327	+	15.9232i	−0.974485	+	1.68786i	−0.292859	+	0.956156i	$0.594607\pi$
$89$	−9.19327	+	15.9232i	−0.974485	+	1.68786i	−0.681626	+	0.731701i	$0.738727\pi$
$90$	−11.8697	−	2.97152i	−1.25118	−	0.313226i
$91$	7.11027	−	12.3153i	0.745358	−	1.29100i
$92$	−0.295914			−0.0308511
$93$	3.12562	−	1.32498i	0.324111	−	0.137394i
$94$	−7.67687			−0.791809
$95$	1.46533			0.150339
$96$	−1.38278	−	1.04304i	−0.141129	−	0.106454i
$97$	0.696052	−	1.20560i	0.0706734	−	0.122410i	−0.828523	−	0.559955i	$-0.810819\pi$
$97$	0.696052	−	1.20560i	0.0706734	−	0.122410i	0.899197	+	0.437545i	$0.144152\pi$
$98$	8.74321	+	15.1437i	0.883198	+	1.52974i
$99$	5.61919	−	5.80771i	0.564750	−	0.583697i
$100$	11.6356			1.16356
$101$	1.38693	−	2.40224i	0.138005	−	0.239032i	−0.788736	−	0.614732i	$-0.789264\pi$
$101$	1.38693	−	2.40224i	0.138005	−	0.239032i	0.926741	+	0.375700i	$0.122598\pi$
$102$	−1.15249	+	9.34927i	−0.114113	+	0.925716i
$103$	−0.774343	−	1.34120i	−0.0762983	−	0.132152i	0.825352	−	0.564619i	$-0.190977\pi$
$103$	−0.774343	−	1.34120i	−0.0762983	−	0.132152i	−0.901650	+	0.432466i	$0.857643\pi$
$104$	−1.43689	+	2.48876i	−0.140899	+	0.244043i
$105$	−27.9083	−	21.0514i	−2.72358	−	2.05441i
$106$	4.91984			0.477857
$107$	−5.19514	−	8.99825i	−0.502234	−	0.869894i	−0.999997	−	0.00258098i	$-0.999178\pi$
$107$	−5.19514	−	8.99825i	−0.502234	−	0.869894i	0.497763	−	0.867313i	$-0.334155\pi$
$108$	−3.26424	−	4.04286i	−0.314102	−	0.389024i
$109$	−9.23262	+	15.9914i	−0.884325	+	1.53170i	−0.0378394	+	0.999284i	$0.512048\pi$
$109$	−9.23262	+	15.9914i	−0.884325	+	1.53170i	−0.846485	+	0.532412i	$0.821286\pi$
$110$	−5.49339	+	9.51483i	−0.523774	+	0.907203i
$111$	−1.23608	+	10.4629i	−0.117323	+	0.993094i
$112$	−2.47419	−	4.28542i	−0.233789	−	0.404934i
$113$	−15.9980			−1.50497			−0.752483	−	0.658611i	$-0.771144\pi$
$113$	−15.9980			−1.50497			−0.752483	+	0.658611i	$0.771144\pi$
$114$	0.496784	+	0.374727i	0.0465281	+	0.0350964i
$115$	1.20694			0.112547
$116$	−1.72918	−	2.99502i	−0.160550	−	0.278081i
$117$	−5.99481	+	6.19593i	−0.554221	+	0.572814i
$118$	3.27974	+	5.68067i	0.301924	+	0.522948i
$119$	−13.4563	+	23.3069i	−1.23353	+	2.13654i
$120$	5.63990	+	4.25420i	0.514850	+	0.388354i
$121$	1.87195	+	3.24232i	0.170177	+	0.294756i
$122$	2.07388	+	3.59207i	0.187761	+	0.325211i
$123$	3.40848	+	2.57103i	0.307332	+	0.231822i
$124$	−1.96002			−0.176015
$125$	−27.0643			−2.42071
$126$	−4.07821	−	14.2740i	−0.363316	−	1.27163i
$127$	7.60717	−	13.1760i	0.675027	−	1.16918i	−0.301434	−	0.953487i	$-0.597465\pi$
$127$	7.60717	−	13.1760i	0.675027	−	1.16918i	0.976461	−	0.215694i	$-0.0692014\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−10.8574	−	8.18978i	−0.955940	−	0.721069i
$130$	5.86060	−	10.1509i	0.514009	−	0.890289i
$131$	0.895375			0.0782293			0.0391146	−	0.999235i	$-0.487546\pi$
$131$	0.895375			0.0782293			0.0391146	+	0.999235i	$0.487546\pi$
$132$	−4.29562	+	1.82096i	−0.373886	+	0.158494i
$133$	0.888890	+	1.53960i	0.0770765	+	0.133500i
$134$	0.566061			0.0489002
$135$	13.3138	+	16.4895i	1.14587	+	1.41919i
$136$	2.71933	−	4.71002i	0.233181	−	0.403881i
$137$	3.53417	−	6.12135i	0.301944	−	0.522983i	−0.674632	−	0.738154i	$-0.735698\pi$
$137$	3.53417	−	6.12135i	0.301944	−	0.522983i	0.976576	+	0.215172i	$0.0690311\pi$
$138$	0.409183	+	0.308649i	0.0348320	+	0.0262739i
$139$	7.66523			0.650156			0.325078	−	0.945687i	$-0.394609\pi$
$139$	7.66523			0.650156			0.325078	+	0.945687i	$0.394609\pi$
$140$	10.0914	+	17.4788i	0.852879	+	1.47723i
$141$	10.6154	+	8.00725i	0.893979	+	0.674332i
$142$	−5.34228	+	9.25310i	−0.448314	+	0.776503i
$143$	3.87057	+	6.70402i	0.323673	+	0.560618i
$144$	0.824152	+	2.88458i	0.0686793	+	0.240381i
$145$	7.05274	+	12.2157i	0.585698	+	1.01446i
$146$	4.29939	+	7.44676i	0.355820	+	0.616299i
$147$	3.70549	−	30.0598i	0.305623	−	2.47929i
$148$	3.01470	−	5.28314i	0.247807	−	0.434271i
$149$	−1.76498	−	3.05704i	−0.144593	−	0.250442i	0.784628	−	0.619967i	$-0.212854\pi$
$149$	−1.76498	−	3.05704i	−0.144593	−	0.250442i	−0.929221	+	0.369525i	$0.879521\pi$
$150$	−16.0894	−	12.1363i	−1.31370	−	0.990926i
$151$	2.27585			0.185206			0.0926032	−	0.995703i	$-0.470481\pi$
$151$	2.27585			0.185206			0.0926032	+	0.995703i	$0.470481\pi$
$152$	−0.179633	−	0.311133i	−0.0145701	−	0.0252362i
$153$	11.3453	−	11.7259i	0.917210	−	0.947982i
$154$	−13.3295			−1.07412
$155$	7.99428			0.642116
$156$	4.58277	−	1.94268i	0.366915	−	0.155539i
$157$	−10.3560			−0.826502			−0.413251	−	0.910617i	$-0.635607\pi$
$157$	−10.3560			−0.826502			−0.413251	+	0.910617i	$0.635607\pi$
$158$	−7.09273	−	12.2850i	−0.564267	−	0.977340i
$159$	−6.80304	−	5.13156i	−0.539516	−	0.406960i
$160$	−2.03934	−	3.53223i	−0.161224	−	0.279248i
$161$	0.732146	+	1.26811i	0.0577012	+	0.0999414i
$162$	0.296881	+	8.99510i	0.0233252	+	0.706722i
$163$	0.937663	−	1.62408i	0.0734434	−	0.127208i	−0.826965	−	0.562254i	$-0.809935\pi$
$163$	0.937663	−	1.62408i	0.0734434	−	0.127208i	0.900408	+	0.435046i	$0.143268\pi$
$164$	−1.23247	−	2.13471i	−0.0962401	−	0.166693i
$165$	17.5204	−	7.42710i	1.36397	−	0.578199i
$166$	6.24400	−	10.8149i	0.484628	−	0.839401i
$167$	10.0209	−	17.3567i	0.775438	−	1.34310i	−0.159110	−	0.987261i	$-0.550862\pi$
$167$	10.0209	−	17.3567i	0.775438	−	1.34310i	0.934548	−	0.355837i	$-0.115804\pi$
$168$	−1.04859	+	8.50645i	−0.0809007	+	0.656287i
$169$	2.37070	+	4.10617i	0.182362	+	0.315860i
$170$	−11.0913	+	19.2106i	−0.850661	+	1.47339i
$171$	−0.296089	−	1.03633i	−0.0226425	−	0.0792499i
$172$	3.92593	+	6.79991i	0.299349	+	0.518488i
$173$	6.96095	+	12.0567i	0.529231	+	0.916655i	0.999419	+	0.0340885i	$0.0108528\pi$
$173$	6.96095	+	12.0567i	0.529231	+	0.916655i	−0.470188	+	0.882566i	$0.655814\pi$
$174$	−0.732847	+	5.94504i	−0.0555570	+	0.450693i
$175$	−28.7886	−	49.8633i	−2.17621	−	3.76931i
$176$	2.69371			0.203046
$177$	1.38999	−	11.2760i	0.104478	−	0.847555i
$178$	−18.3865			−1.37813
$179$	24.6042			1.83900			0.919502	−	0.393086i	$-0.128593\pi$
$179$	24.6042			1.83900			0.919502	+	0.393086i	$0.128593\pi$
$180$	−3.36145	−	11.7652i	−0.250547	−	0.876929i
$181$	0.918274	+	1.59050i	0.0682547	+	0.118221i	0.898133	−	0.439724i	$-0.144924\pi$
$181$	0.918274	+	1.59050i	0.0682547	+	0.118221i	−0.829878	+	0.557944i	$0.811590\pi$
$182$	14.2205			1.05410
$183$	0.878938	−	7.13017i	0.0649730	−	0.527077i
$184$	−0.147957	−	0.256269i	−0.0109075	−	0.0188924i
$185$	−12.2960	+	21.5482i	−0.904019	+	1.58426i
$186$	2.71027	+	2.04437i	0.198727	+	0.149901i
$187$	−7.32510	−	12.6874i	−0.535664	−	0.927798i
$188$	−3.83844	−	6.64837i	−0.279947	−	0.484882i
$189$	−9.24899	+	23.9915i	−0.672765	+	1.74512i
$190$	0.732663	+	1.26901i	0.0531529	+	0.0920636i
$191$	8.45520	−	14.6448i	0.611797	−	1.05966i	−0.379140	−	0.925339i	$-0.623780\pi$
$191$	8.45520	−	14.6448i	0.611797	−	1.05966i	0.990937	−	0.134324i	$-0.0428864\pi$
$192$	0.211906	−	1.71904i	0.0152930	−	0.124061i
$193$	10.3364	+	17.9031i	0.744029	+	1.28870i	0.950647	+	0.310274i	$0.100421\pi$
$193$	10.3364	+	17.9031i	0.744029	+	1.28870i	−0.206618	+	0.978422i	$0.566246\pi$
$194$	1.39210			0.0999473
$195$	−18.6916	+	7.92357i	−1.33853	+	0.567419i
$196$	−8.74321	+	15.1437i	−0.624515	+	1.08169i
$197$	−7.80217	+	13.5138i	−0.555882	+	0.962816i	0.441952	+	0.897039i	$0.354286\pi$
$197$	−7.80217	+	13.5138i	−0.555882	+	0.962816i	−0.997834	+	0.0657773i	$0.979047\pi$
$198$	7.83922	+	1.96251i	0.557109	+	0.139469i
$199$	−10.2576			−0.727144			−0.363572	−	0.931566i	$-0.618443\pi$
$199$	−10.2576			−0.727144			−0.363572	+	0.931566i	$0.618443\pi$
$200$	5.81779	+	10.0767i	0.411380	+	0.712530i
$201$	−0.782737	−	0.590422i	−0.0552100	−	0.0416451i
$202$	2.77387			0.195169
$203$	−8.55661	+	14.8205i	−0.600557	+	1.04019i
$204$	−8.67295	+	3.67655i	−0.607228	+	0.257410i
$205$	5.02686	+	8.70678i	0.351091	+	0.608108i
$206$	0.774343	−	1.34120i	0.0539510	−	0.0934459i
$207$	−0.243878	−	0.853585i	−0.0169507	−	0.0593283i
$208$	−2.87378			−0.199261
$209$	−0.967758			−0.0669412
$210$	4.27687	−	34.6950i	0.295132	−	2.39418i
$211$	10.6091	+	18.3755i	0.730359	+	1.26502i	0.956730	+	0.290978i	$0.0939805\pi$
$211$	10.6091	+	18.3755i	0.730359	+	1.26502i	−0.226371	+	0.974041i	$0.572686\pi$
$212$	2.45992	+	4.26070i	0.168948	+	0.292626i
$213$	17.0385	−	7.22280i	1.16746	−	0.494898i
$214$	5.19514	−	8.99825i	0.355133	−	0.615108i
$215$	−16.0126	−	27.7346i	−1.09205	−	1.89149i
$216$	1.86910	−	4.84835i	0.127176	−	0.329888i
$217$	4.84946	+	8.39951i	0.329203	+	0.570196i
$218$	−18.4652			−1.25062
$219$	1.82214	−	14.7816i	0.123129	−	0.998851i
$220$	−10.9868			−0.740728
$221$	7.81475	+	13.5355i	0.525677	+	0.910499i
$222$	−9.67917	+	4.16097i	−0.649623	+	0.279266i
$223$	−8.98920	+	15.5698i	−0.601962	+	1.04263i	0.390562	+	0.920577i	$0.372281\pi$
$223$	−8.98920	+	15.5698i	−0.601962	+	1.04263i	−0.992524	+	0.122052i	$0.961053\pi$
$224$	2.47419	−	4.28542i	0.165314	−	0.286332i
$225$	9.58948	+	33.5637i	0.639299	+	2.23758i
$226$	−7.99901	−	13.8547i	−0.532086	−	0.921600i
$227$	−6.08457			−0.403847			−0.201923	−	0.979401i	$-0.564719\pi$
$227$	−6.08457			−0.403847			−0.201923	+	0.979401i	$0.564719\pi$
$228$	−0.0761306	+	0.617591i	−0.00504187	+	0.0409010i
$229$	7.47380	−	12.9450i	0.493883	−	0.855430i	−0.506092	−	0.862479i	$-0.668911\pi$
$229$	7.47380	−	12.9450i	0.493883	−	0.855430i	0.999975	+	0.00704923i	$0.00224386\pi$
$230$	0.603468	+	1.04524i	0.0397915	+	0.0689209i
$231$	18.4318	+	13.9032i	1.21272	+	0.914761i
$232$	1.72918	−	2.99502i	0.113526	−	0.196633i
$233$	−13.7687			−0.902021			−0.451010	−	0.892519i	$-0.648936\pi$
$233$	−13.7687			−0.902021			−0.451010	+	0.892519i	$0.648936\pi$
$234$	−8.36324	−	2.09369i	−0.546722	−	0.136869i
$235$	15.6557	+	27.1165i	1.02127	+	1.76889i
$236$	−3.27974	+	5.68067i	−0.213493	+	0.369780i
$237$	−3.00599	+	24.3854i	−0.195260	+	1.58400i
$238$	−26.9125			−1.74448
$239$	5.24382			0.339195			0.169597	−	0.985513i	$-0.445753\pi$
$239$	5.24382			0.339195			0.169597	+	0.985513i	$0.445753\pi$
$240$	−0.864297	+	7.01140i	−0.0557901	+	0.452584i
$241$	−30.8073			−1.98447			−0.992237	−	0.124359i	$-0.960313\pi$
$241$	−30.8073			−1.98447			−0.992237	+	0.124359i	$0.960313\pi$
$242$	−1.87195	+	3.24232i	−0.120334	+	0.208424i
$243$	8.97169	−	12.7479i	0.575534	−	0.817778i
$244$	−2.07388	+	3.59207i	−0.132767	+	0.229959i
$245$	35.6607	−	61.7662i	2.27828	−	3.94609i
$246$	−0.522339	+	4.23734i	−0.0333031	+	0.270163i
$247$	1.03245			0.0656931
$248$	−0.980010	−	1.69743i	−0.0622307	−	0.107787i
$249$	−19.9144	+	8.44193i	−1.26203	+	0.534985i
$250$	−13.5322	−	23.4384i	−0.855849	−	1.48237i
$251$	−15.4213			−0.973381			−0.486691	−	0.873574i	$-0.661796\pi$
$251$	−15.4213			−0.973381			−0.486691	+	0.873574i	$0.661796\pi$
$252$	10.3225	−	10.6688i	0.650257	−	0.672072i
$253$	−0.797107			−0.0501137
$254$	15.2143			0.954632
$255$	35.3741	−	14.9955i	2.21521	−	0.939052i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.9244			0.743825			0.371912	−	0.928268i	$-0.378702\pi$
$257$	11.9244			0.743825			0.371912	+	0.928268i	$0.378702\pi$
$258$	1.66386	−	13.4977i	0.103587	−	0.840328i
$259$	−30.0994	+	0.152222i	−1.87029	+	0.00945862i
$260$	11.7212			0.726918
$261$	7.21426	−	7.45629i	0.446551	−	0.461533i
$262$	0.447688	+	0.775418i	0.0276582	+	0.0479055i
$263$	−30.8388			−1.90160			−0.950800	−	0.309805i	$-0.899736\pi$
$263$	−30.8388			−1.90160			−0.950800	+	0.309805i	$0.899736\pi$
$264$	−3.72481	−	2.80964i	−0.229246	−	0.172921i
$265$	−10.0332	−	17.3780i	−0.616335	−	1.06752i
$266$	−0.888890	+	1.53960i	−0.0545013	+	0.0943991i
$267$	25.4245	+	19.1778i	1.55595	+	1.17366i
$268$	0.283030	+	0.490223i	0.0172888	+	0.0299451i
$269$	18.7661			1.14419			0.572093	−	0.820189i	$-0.306132\pi$
$269$	18.7661			1.14419			0.572093	+	0.820189i	$0.306132\pi$
$270$	−7.62343	+	19.7748i	−0.463947	+	1.20346i
$271$	−1.55135	+	2.68702i	−0.0942379	+	0.163225i	−0.909290	−	0.416162i	$-0.863375\pi$
$271$	−1.55135	+	2.68702i	−0.0942379	+	0.163225i	0.815052	+	0.579387i	$0.196708\pi$
$272$	5.43866			0.329767
$273$	−19.6638	−	14.8325i	−1.19011	−	0.897705i
$274$	7.06833			0.427013
$275$	31.3429			1.89005
$276$	−0.0627060	+	0.508687i	−0.00377446	+	0.0306194i
$277$	−5.14649			−0.309223			−0.154611	−	0.987975i	$-0.549413\pi$
$277$	−5.14649			−0.309223			−0.154611	+	0.987975i	$0.549413\pi$
$278$	3.83262	+	6.63828i	0.229865	+	0.398138i
$279$	−1.61536	−	5.65383i	−0.0967088	−	0.338486i
$280$	−10.0914	+	17.4788i	−0.603077	+	1.04456i
$281$	−4.00722	−	6.94072i	−0.239051	−	0.414048i	0.721391	−	0.692528i	$-0.243503\pi$
$281$	−4.00722	−	6.94072i	−0.239051	−	0.414048i	−0.960442	+	0.278479i	$0.910170\pi$
$282$	−1.62678	+	13.1968i	−0.0968732	+	0.785861i
$283$	3.04698	−	5.27752i	0.181124	−	0.313716i	−0.761140	−	0.648588i	$-0.775360\pi$
$283$	3.04698	−	5.27752i	0.181124	−	0.313716i	0.942264	+	0.334872i	$0.108693\pi$
$284$	−10.6846			−0.634012
$285$	0.310512	−	2.51895i	0.0183931	−	0.149210i
$286$	−3.87057	+	6.70402i	−0.228871	+	0.396417i
$287$	−6.09875	+	10.5633i	−0.359998	+	0.623534i
$288$	−2.08604	+	2.15602i	−0.122921	+	0.127045i
$289$	−6.28952	−	10.8938i	−0.369972	−	0.640810i
$290$	−7.05274	+	12.2157i	−0.414151	+	0.717331i
$291$	−1.92497	−	1.45202i	−0.112844	−	0.0851186i
$292$	−4.29939	+	7.44676i	−0.251603	+	0.435789i
$293$	2.58056	−	4.46967i	0.150758	−	0.261121i	−0.780748	−	0.624846i	$-0.785162\pi$
$293$	2.58056	−	4.46967i	0.150758	−	0.261121i	0.931506	+	0.363725i	$0.118495\pi$
$294$	27.8853	−	11.8209i	1.62631	−	0.689408i
$295$	13.3770	−	23.1696i	0.778837	−	1.34899i
$296$	6.08268	−	0.0307620i	0.353549	−	0.00178801i
$297$	−8.79294	−	10.8903i	−0.510218	−	0.631920i
$298$	1.76498	−	3.05704i	0.102243	−	0.177089i
$299$	0.850390			0.0491793
$300$	2.46565	−	20.0020i	0.142355	−	1.15482i
$301$	19.4270	−	33.6485i	1.11975	−	1.93947i
$302$	1.13793	+	1.97095i	0.0654803	+	0.113415i
$303$	−3.83564	−	2.89324i	−0.220352	−	0.166212i
$304$	0.179633	−	0.311133i	0.0103026	−	0.0178447i
$305$	8.45869	−	14.6509i	0.484343	−	0.838907i
$306$	15.8275	+	3.96234i	0.904801	+	0.226512i
$307$	29.9546			1.70960			0.854799	−	0.518959i	$-0.173680\pi$
$307$	29.9546			1.70960			0.854799	+	0.518959i	$0.173680\pi$
$308$	−6.66475	−	11.5437i	−0.379760	−	0.657763i
$309$	−2.46967	+	1.04692i	−0.140494	+	0.0595570i
$310$	3.99714	+	6.92325i	0.227022	+	0.393214i
$311$	7.32117			0.415145			0.207573	−	0.978220i	$-0.433444\pi$
$311$	7.32117			0.415145			0.207573	+	0.978220i	$0.433444\pi$
$312$	3.97380	+	2.99745i	0.224972	+	0.169697i
$313$	8.87251	+	15.3676i	0.501504	+	0.868630i	0.999998	+	0.00173736i	$0.000553019\pi$
$313$	8.87251	+	15.3676i	0.501504	+	0.868630i	−0.498495	+	0.866893i	$0.666114\pi$
$314$	−5.17802	−	8.96859i	−0.292213	−	0.506127i
$315$	−42.1021	+	43.5146i	−2.37219	+	2.45177i
$316$	7.09273	−	12.2850i	0.398997	−	0.691084i
$317$	3.22560	+	5.58691i	0.181168	+	0.313792i	0.942279	−	0.334830i	$-0.108679\pi$
$317$	3.22560	+	5.58691i	0.181168	+	0.313792i	−0.761111	+	0.648622i	$0.775346\pi$
$318$	1.04254	−	8.45739i	0.0584630	−	0.474267i
$319$	−4.65791	−	8.06773i	−0.260793	−	0.451706i
$320$	2.03934	−	3.53223i	0.114002	−	0.197458i
$321$	−16.5692	+	7.02387i	−0.924804	+	0.392034i
$322$	−0.732146	+	1.26811i	−0.0408009	+	0.0706693i
$323$	−1.95392			−0.108719
$324$	−7.64155	+	4.75466i	−0.424530	+	0.264148i
$325$	−33.4380			−1.85481
$326$	1.87533			0.103865
$327$	25.5333	+	19.2599i	1.41200	+	1.06508i
$328$	1.23247	−	2.13471i	0.0680520	−	0.117870i
$329$	−18.9940	+	32.8986i	−1.04717	+	1.81376i
$330$	15.1923	+	11.4596i	0.836307	+	0.630830i
$331$	3.05243	+	5.28697i	0.167777	+	0.290598i	0.937638	−	0.347613i	$-0.113008\pi$
$331$	3.05243	+	5.28697i	0.167777	+	0.290598i	−0.769861	+	0.638212i	$0.779674\pi$
$332$	12.4880			0.685368
$333$	17.7242	+	4.34202i	0.971280	+	0.237941i
$334$	20.0417			1.09664
$335$	−1.15439	−	1.99946i	−0.0630710	−	0.109242i
$336$	−7.89110	+	3.34512i	−0.430495	+	0.182491i
$337$	13.2353	−	22.9242i	0.720973	−	1.24876i	−0.239637	−	0.970863i	$-0.577028\pi$
$337$	13.2353	−	22.9242i	0.720973	−	1.24876i	0.960610	−	0.277899i	$-0.0896382\pi$
$338$	−2.37070	+	4.10617i	−0.128949	+	0.223346i
$339$	−3.39008	+	27.5012i	−0.184124	+	1.49366i
$340$	−22.1825			−1.20302
$341$	−5.27974			−0.285914
$342$	0.749441	−	0.774585i	0.0405251	−	0.0418847i
$343$	51.8908			2.80184
$344$	−3.92593	+	6.79991i	−0.211672	+	0.366627i
$345$	0.255757	−	2.07477i	0.0137695	−	0.111702i
$346$	−6.96095	+	12.0567i	−0.374223	+	0.648173i
$347$	1.05120	+	1.82073i	0.0564313	+	0.0977419i	0.892861	−	0.450332i	$-0.148694\pi$
$347$	1.05120	+	1.82073i	0.0564313	+	0.0977419i	−0.836430	+	0.548074i	$0.815361\pi$
$348$	−5.51498	+	2.33786i	−0.295634	+	0.125322i
$349$	−7.47844	−	12.9530i	−0.400312	−	0.693361i	0.593451	−	0.804870i	$-0.297765\pi$
$349$	−7.47844	−	12.9530i	−0.400312	−	0.693361i	−0.993763	+	0.111509i	$0.964432\pi$
$350$	28.7886	−	49.8633i	1.53882	−	2.66531i
$351$	9.38071	+	11.6183i	0.500705	+	0.620138i
$352$	1.34686	+	2.33282i	0.0717877	+	0.124340i
$353$	−10.1499	−	17.5801i	−0.540225	−	0.935696i	−0.998891	−	0.0470878i	$-0.985006\pi$
$353$	−10.1499	−	17.5801i	−0.540225	−	0.935696i	0.458666	−	0.888609i	$-0.348327\pi$
$354$	10.4603	−	4.43422i	0.555958	−	0.235676i
$355$	43.5788			2.31292
$356$	−9.19327	−	15.9232i	−0.487242	−	0.843928i
$357$	37.2141	+	28.0707i	1.96958	+	1.48566i
$358$	12.3021	+	21.3079i	0.650186	+	1.12615i
$359$	0.967788			0.0510779			0.0255390	−	0.999674i	$-0.491870\pi$
$359$	0.967788			0.0510779			0.0255390	+	0.999674i	$0.491870\pi$
$360$	8.50827	−	8.79372i	0.448425	−	0.463470i
$361$	9.43546	−	16.3427i	0.496603	−	0.860142i
$362$	−0.918274	+	1.59050i	−0.0482634	+	0.0835947i
$363$	5.97035	−	2.53089i	0.313362	−	0.132837i
$364$	7.11027	+	12.3153i	0.372679	+	0.645499i
$365$	17.5358	−	30.3729i	0.917866	−	1.58979i
$366$	6.61438	−	2.80390i	0.345739	−	0.146562i
$367$	−4.89677			−0.255609			−0.127805	−	0.991799i	$-0.540793\pi$
$367$	−4.89677			−0.255609			−0.127805	+	0.991799i	$0.540793\pi$
$368$	0.147957	−	0.256269i	0.00771278	−	0.0133589i
$369$	5.14198	−	5.31449i	0.267681	−	0.276661i
$370$	−24.8093	+	0.125468i	−1.28977	+	0.00652278i
$371$	12.1726	−	21.0836i	0.631970	−	1.09460i
$372$	−0.415341	+	3.36935i	−0.0215344	+	0.174693i
$373$	−9.82976	+	17.0256i	−0.508965	+	0.881554i	0.490981	+	0.871170i	$0.336639\pi$
$373$	−9.82976	+	17.0256i	−0.508965	+	0.881554i	−0.999946	+	0.0103836i	$0.996695\pi$
$374$	7.32510	−	12.6874i	0.378772	−	0.656052i
$375$	−5.73510	+	46.5246i	−0.296160	+	2.40252i
$376$	3.83844	−	6.64837i	0.197952	−	0.342863i
$377$	4.96927	+	8.60702i	0.255930	+	0.443284i
$378$	−25.4017	+	3.98587i	−1.30652	+	0.205011i
$379$	5.06580	−	8.77422i	0.260213	−	0.450701i	−0.706086	−	0.708126i	$-0.749541\pi$
$379$	5.06580	−	8.77422i	0.260213	−	0.450701i	0.966298	+	0.257425i	$0.0828740\pi$
$380$	−0.732663	+	1.26901i	−0.0375848	+	0.0650988i
$381$	−21.0381	−	15.8691i	−1.07781	−	0.812999i
$382$	16.9104			0.865212
$383$	2.21846	−	3.84248i	0.113358	−	0.196342i	−0.803764	−	0.594948i	$-0.797173\pi$
$383$	2.21846	−	3.84248i	0.113358	−	0.196342i	0.917122	+	0.398606i	$0.130506\pi$
$384$	1.59468	−	0.676003i	0.0813784	−	0.0344971i
$385$	27.1834	+	47.0830i	1.38539	+	2.39957i
$386$	−10.3364	+	17.9031i	−0.526108	+	0.911246i
$387$	−16.3793	+	16.9288i	−0.832606	+	0.860540i
$388$	0.696052	+	1.20560i	0.0353367	+	0.0612050i
$389$	0.900596			0.0456620			0.0228310	−	0.999739i	$-0.492732\pi$
$389$	0.900596			0.0456620			0.0228310	+	0.999739i	$0.492732\pi$
$390$	−16.2078	−	12.2256i	−0.820715	−	0.619069i
$391$	−1.60937			−0.0813896
$392$	−17.4864			−0.883198
$393$	0.189736	−	1.53919i	0.00957090	−	0.0776416i
$394$	−15.6043			−0.786136
$395$	−28.9289	+	50.1064i	−1.45557	+	2.52113i
$396$	2.22003	+	7.77022i	0.111561	+	0.390468i
$397$	−10.9614			−0.550138			−0.275069	−	0.961424i	$-0.588701\pi$
$397$	−10.9614			−0.550138			−0.275069	+	0.961424i	$0.588701\pi$
$398$	−5.12882	−	8.88337i	−0.257084	−	0.445283i
$399$	2.83500	−	1.20178i	0.141927	−	0.0601645i
$400$	−5.81779	+	10.0767i	−0.290889	+	0.503835i
$401$	−8.41549	−	14.5761i	−0.420250	−	0.727894i	0.575714	−	0.817651i	$-0.304724\pi$
$401$	−8.41549	−	14.5761i	−0.420250	−	0.727894i	−0.995964	+	0.0897573i	$0.971391\pi$
$402$	0.119952	−	0.973081i	0.00598266	−	0.0485329i
$403$	5.63266			0.280583
$404$	1.38693	+	2.40224i	0.0690025	+	0.119516i
$405$	31.1674	−	19.3927i	1.54872	−	0.963631i
$406$	−17.1132			−0.849315
$407$	8.12074	−	14.2313i	0.402530	−	0.705418i
$408$	−7.52046	−	5.67272i	−0.372318	−	0.280841i
$409$	−5.94053			−0.293740			−0.146870	−	0.989156i	$-0.546920\pi$
$409$	−5.94053			−0.293740			−0.146870	+	0.989156i	$0.546920\pi$
$410$	−5.02686	+	8.70678i	−0.248259	+	0.429997i
$411$	−9.77394	−	7.37252i	−0.482113	−	0.363660i
$412$	1.54869			0.0762983
$413$	32.4587			1.59719
$414$	0.617288	−	0.637997i	0.0303380	−	0.0313559i
$415$	−50.9345			−2.50027
$416$	−1.43689	−	2.48876i	−0.0704493	−	0.122022i
$417$	1.62431	−	13.1768i	0.0795429	−	0.645272i
$418$	−0.483879	−	0.838103i	−0.0236673	−	0.0409929i
$419$	−24.0390			−1.17438			−0.587191	−	0.809449i	$-0.699766\pi$
$419$	−24.0390			−1.17438			−0.587191	+	0.809449i	$0.699766\pi$
$420$	32.1852	−	13.6436i	1.57048	−	0.665742i
$421$	−4.13010	+	7.15355i	−0.201289	+	0.348642i	−0.948944	−	0.315445i	$-0.897846\pi$
$421$	−4.13010	+	7.15355i	−0.201289	+	0.348642i	0.747655	+	0.664087i	$0.231180\pi$
$422$	−10.6091	+	18.3755i	−0.516442	+	0.894503i
$423$	16.0143	−	16.5515i	0.778640	−	0.804762i
$424$	−2.45992	+	4.26070i	−0.119464	+	0.206918i
$425$	63.2819			3.06962
$426$	14.7744	+	11.1444i	0.715821	+	0.539947i
$427$	20.5247			0.993260
$428$	10.3903			0.502234
$429$	12.3447	−	5.23303i	0.596006	−	0.252653i
$430$	16.0126	−	27.7346i	0.772196	−	1.33748i
$431$	0.940710	+	1.62936i	0.0453124	+	0.0784834i	0.887792	−	0.460245i	$-0.152238\pi$
$431$	0.940710	+	1.62936i	0.0453124	+	0.0784834i	−0.842480	+	0.538728i	$0.818905\pi$
$432$	5.13334	−	0.805490i	0.246978	−	0.0387541i
$433$	−4.97802			−0.239229			−0.119614	−	0.992820i	$-0.538166\pi$
$433$	−4.97802			−0.239229			−0.119614	+	0.992820i	$0.538166\pi$
$434$	−4.84946	+	8.39951i	−0.232782	+	0.403189i
$435$	22.4938	−	9.53535i	1.07850	−	0.457185i
$436$	−9.23262	−	15.9914i	−0.442162	−	0.765848i
$437$	−0.0531558	+	0.0920685i	−0.00254278	+	0.00440423i
$438$	13.7123	−	5.81281i	0.655201	−	0.277747i
$439$	−7.99787			−0.381718			−0.190859	−	0.981617i	$-0.561127\pi$
$439$	−7.99787			−0.381718			−0.190859	+	0.981617i	$0.561127\pi$
$440$	−5.49339	−	9.51483i	−0.261887	−	0.453602i
$441$	−50.8888	−	12.7397i	−2.42328	−	0.606655i
$442$	−7.81475	+	13.5355i	−0.371710	+	0.643820i
$443$	10.2402	−	17.7365i	0.486525	−	0.842685i	−0.513355	−	0.858176i	$-0.671598\pi$
$443$	10.2402	−	17.7365i	0.486525	−	0.842685i	0.999880	+	0.0154907i	$0.00493103\pi$
$444$	−8.44309	−	6.30192i	−0.400691	−	0.299076i
$445$	37.4963	+	64.9456i	1.77750	+	3.07871i
$446$	−17.9784			−0.851302
$447$	−5.62917	+	2.38627i	−0.266251	+	0.112866i
$448$	4.94838			0.233789
$449$	−16.2173	−	28.0891i	−0.765340	−	1.32561i	−0.940066	−	0.340991i	$-0.889237\pi$
$449$	−16.2173	−	28.0891i	−0.765340	−	1.32561i	0.174726	−	0.984617i	$-0.444096\pi$
$450$	−24.2723	+	25.0866i	−1.14421	+	1.18259i
$451$	−3.31993	−	5.75029i	−0.156330	−	0.270771i
$452$	7.99901	−	13.8547i	0.376242	−	0.651670i
$453$	0.482268	−	3.91228i	0.0226589	−	0.183815i
$454$	−3.04228	−	5.26939i	−0.142781	−	0.247305i
$455$	−29.0004	−	50.2303i	−1.35956	−	2.35483i
$456$	−0.572915	+	0.242864i	−0.0268292	+	0.0113732i
$457$	−24.8484			−1.16236			−0.581180	−	0.813775i	$-0.697409\pi$
$457$	−24.8484			−1.16236			−0.581180	+	0.813775i	$0.697409\pi$
$458$	14.9476			0.698456
$459$	−17.7531	−	21.9877i	−0.828645	−	1.02630i
$460$	−0.603468	+	1.04524i	−0.0281368	+	0.0487344i
$461$	−16.6402	−	28.8216i	−0.775010	−	1.34236i	−0.934789	−	0.355204i	$-0.884412\pi$
$461$	−16.6402	−	28.8216i	−0.775010	−	1.34236i	0.159779	−	0.987153i	$-0.448922\pi$
$462$	−2.82461	+	22.9139i	−0.131413	+	1.06605i
$463$	15.1489	−	26.2386i	0.704028	−	1.21941i	−0.263014	−	0.964792i	$-0.584716\pi$
$463$	15.1489	−	26.2386i	0.704028	−	1.21941i	0.967041	−	0.254620i	$-0.0819503\pi$
$464$	3.45835			0.160550
$465$	1.69404	−	13.7425i	0.0785592	−	0.637293i
$466$	−6.88437	−	11.9241i	−0.318912	−	0.552373i
$467$	0.866573			0.0401002			0.0200501	−	0.999799i	$-0.493617\pi$
$467$	0.866573			0.0401002			0.0200501	+	0.999799i	$0.493617\pi$
$468$	−2.36843	−	8.28963i	−0.109481	−	0.383188i
$469$	1.40054	−	2.42581i	0.0646710	−	0.112013i
$470$	−15.6557	+	27.1165i	−0.722145	+	1.25079i
$471$	−2.19451	+	17.8024i	−0.101118	+	0.820293i
$472$	−6.55947			−0.301924
$473$	10.5753	+	18.3170i	0.486254	+	0.842217i
$474$	−22.6213	+	9.58942i	−1.03903	+	0.440457i
$475$	2.09013	−	3.62021i	0.0959017	−	0.166107i
$476$	−13.4563	−	23.3069i	−0.616767	−	1.06827i
$477$	−10.2630	+	10.6073i	−0.469909	+	0.485674i
$478$	2.62191	+	4.54128i	0.119923	+	0.207714i
$479$	6.10719	+	10.5780i	0.279045	+	0.483320i	0.971148	−	0.238479i	$-0.0766489\pi$
$479$	6.10719	+	10.5780i	0.279045	+	0.483320i	−0.692103	+	0.721799i	$0.743316\pi$
$480$	−6.50420	+	2.75720i	−0.296875	+	0.125848i
$481$	−8.66358	+	15.1826i	−0.395025	+	0.692266i
$482$	−15.4037	−	26.6799i	−0.701618	−	1.21524i
$483$	2.33508	−	0.989866i	0.106250	−	0.0450405i
$484$	−3.74390			−0.170177
$485$	−2.83897	−	4.91724i	−0.128911	−	0.223280i
$486$	15.5258	+	1.39577i	0.704267	+	0.0633134i
$487$	−32.8770			−1.48980			−0.744899	−	0.667177i	$-0.767503\pi$
$487$	−32.8770			−1.48980			−0.744899	+	0.667177i	$0.767503\pi$
$488$	−4.14777			−0.187761
$489$	−2.59316	−	1.95603i	−0.117267	−	0.0884548i
$490$	71.3214			3.22197
$491$	−1.47498	−	2.55474i	−0.0665650	−	0.115294i	0.830822	−	0.556538i	$-0.187871\pi$
$491$	−1.47498	−	2.55474i	−0.0665650	−	0.115294i	−0.897387	+	0.441244i	$0.854537\pi$
$492$	−3.93082	+	1.66631i	−0.177215	+	0.0751232i
$493$	−9.40440	−	16.2889i	−0.423553	−	0.733615i
$494$	0.516224	+	0.894126i	0.0232260	+	0.0402287i
$495$	−9.05478	−	31.6922i	−0.406982	−	1.42446i
$496$	0.980010	−	1.69743i	0.0440038	−	0.0762168i
$497$	26.4356	+	45.7878i	1.18580	+	2.05386i
$498$	−17.2681	−	13.0254i	−0.773804	−	0.583683i
$499$	0.184995	−	0.320420i	0.00828150	−	0.0143440i	−0.861855	−	0.507155i	$-0.830697\pi$
$499$	0.184995	−	0.320420i	0.00828150	−	0.0143440i	0.870136	+	0.492811i	$0.164031\pi$
$500$	13.5322	−	23.4384i	0.605177	−	1.04820i
$501$	−27.7133	−	20.9043i	−1.23814	−	0.933933i
$502$	−7.71063	−	13.3552i	−0.344142	−	0.596072i
$503$	10.7459	−	18.6124i	0.479136	−	0.829888i	−0.520578	−	0.853814i	$-0.674283\pi$
$503$	10.7459	−	18.6124i	0.479136	−	0.829888i	0.999714	+	0.0239263i	$0.00761671\pi$
$504$	14.4007	+	3.60514i	0.641459	+	0.160586i
$505$	−5.65685	−	9.79795i	−0.251726	−	0.436003i
$506$	−0.398553	−	0.690315i	−0.0177179	−	0.0306882i
$507$	7.56104	−	3.20520i	0.335798	−	0.142348i
$508$	7.60717	+	13.1760i	0.337514	+	0.584591i
$509$	6.25991			0.277465			0.138733	−	0.990330i	$-0.455697\pi$
$509$	6.25991			0.277465			0.138733	+	0.990330i	$0.455697\pi$
$510$	30.6735	+	23.1372i	1.35825	+	1.02453i
$511$	42.5500			1.88230
$512$	−1.00000			−0.0441942
$513$	−1.84423	+	0.289384i	−0.0814248	+	0.0127766i
$514$	5.96221	+	10.3268i	0.262982	+	0.455498i
$515$	−6.31658			−0.278342
$516$	12.5212	−	5.30788i	0.551217	−	0.233667i
$517$	−10.3396	−	17.9088i	−0.454737	−	0.787628i
$518$	−15.1815	−	25.9907i	−0.667038	−	1.14197i
$519$	22.2010	−	9.41124i	0.974517	−	0.413108i
$520$	5.86060	+	10.1509i	0.257004	+	0.445144i
$521$	−7.69612	−	13.3301i	−0.337173	−	0.584001i	0.646727	−	0.762722i	$-0.276137\pi$
$521$	−7.69612	−	13.3301i	−0.337173	−	0.584001i	−0.983900	+	0.178721i	$0.942804\pi$
$522$	10.0645	+	2.51959i	0.440510	+	0.110279i
$523$	−14.3709	−	24.8912i	−0.628397	−	1.08842i	−0.987873	−	0.155261i	$-0.950378\pi$
$523$	−14.3709	−	24.8912i	−0.628397	−	1.08842i	0.359477	−	0.933154i	$-0.382955\pi$
$524$	−0.447688	+	0.775418i	−0.0195573	+	0.0338743i
$525$	−91.8175	+	38.9224i	−4.00724	+	1.69871i
$526$	−15.4194	−	26.7072i	−0.672317	−	1.16449i
$527$	−10.6599			−0.464352
$528$	0.570815	−	4.63060i	0.0248415	−	0.201521i
$529$	11.4562	−	19.8428i	0.498096	−	0.862728i
$530$	10.0332	−	17.3780i	0.435814	−	0.754853i
$531$	−19.0893	−	4.77891i	−0.828406	−	0.207387i
$532$	−1.77778			−0.0770765
$533$	3.54186	+	6.13468i	0.153415	+	0.265722i
$534$	−3.89623	+	31.6072i	−0.168606	+	1.36778i
$535$	−42.3786			−1.83219
$536$	−0.283030	+	0.490223i	−0.0122251	+	0.0211744i
$537$	5.21378	−	42.2956i	0.224991	−	1.82519i
$538$	9.38303	+	16.2519i	0.404531	+	0.700668i
$539$	−23.5517	+	40.7928i	−1.01444	+	1.75707i
$540$	−20.9372	+	3.28533i	−0.900994	+	0.141378i
$541$	−26.9707			−1.15956			−0.579781	−	0.814772i	$-0.696862\pi$
$541$	−26.9707			−1.15956			−0.579781	+	0.814772i	$0.696862\pi$
$542$	−3.10270			−0.133272
$543$	2.92871	−	1.24151i	0.125683	−	0.0532784i
$544$	2.71933	+	4.71002i	0.116590	+	0.201940i
$545$	37.6568	+	65.2236i	1.61304	+	2.79387i
$546$	3.01342	−	24.4457i	0.128963	−	1.04618i
$547$	4.30857	−	7.46266i	0.184221	−	0.319080i	−0.759093	−	0.650983i	$-0.774357\pi$
$547$	4.30857	−	7.46266i	0.184221	−	0.319080i	0.943314	+	0.331902i	$0.107690\pi$
$548$	3.53417	+	6.12135i	0.150972	+	0.261491i
$549$	−12.0708	−	3.02186i	−0.515169	−	0.128970i
$550$	15.6715	+	27.1438i	0.668233	+	1.15741i
$551$	−1.24247			−0.0529308
$552$	−0.471889	+	0.200039i	−0.0200849	+	0.00851421i
$553$	−70.1950			−2.98500
$554$	−2.57324	−	4.45699i	−0.109327	−	0.189359i
$555$	34.4366	+	25.7035i	1.46175	+	1.09105i
$556$	−3.83262	+	6.63828i	−0.162539	+	0.281526i
$557$	16.0140	−	27.7370i	0.678533	−	1.17525i	−0.296890	−	0.954912i	$-0.595949\pi$
$557$	16.0140	−	27.7370i	0.678533	−	1.17525i	0.975423	−	0.220342i	$-0.0707173\pi$
$558$	4.08868	−	4.22585i	0.173088	−	0.178895i
$559$	−11.2823	−	19.5414i	−0.477188	−	0.826515i
$560$	−20.1828			−0.852879
$561$	−23.3624	+	9.90358i	−0.986363	+	0.418130i
$562$	4.00722	−	6.94072i	0.169035	−	0.292776i
$563$	1.61380	+	2.79518i	0.0680134	+	0.117803i	0.898027	−	0.439941i	$-0.145001\pi$
$563$	1.61380	+	2.79518i	0.0680134	+	0.117803i	−0.830013	+	0.557744i	$0.811667\pi$
$564$	−12.2422	+	5.18959i	−0.515489	+	0.218521i
$565$	−32.6253	+	56.5087i	−1.37256	+	2.37734i
$566$	6.09395			0.256148
$567$	39.2823	+	20.9833i	1.64970	+	0.881216i
$568$	−5.34228	−	9.25310i	−0.224157	−	0.388251i
$569$	−10.5932	+	18.3479i	−0.444089	+	0.769185i	−0.997988	−	0.0633988i	$-0.979806\pi$
$569$	−10.5932	+	18.3479i	−0.444089	+	0.769185i	0.553899	+	0.832584i	$0.313139\pi$
$570$	2.33673	−	0.990565i	0.0978749	−	0.0414902i
$571$	−32.6931			−1.36816			−0.684081	−	0.729406i	$-0.739797\pi$
$571$	−32.6931			−1.36816			−0.684081	+	0.729406i	$0.739797\pi$
$572$	−7.74113			−0.323673
$573$	−23.3833	−	17.6382i	−0.976853	−	0.736845i
$574$	−12.1975			−0.509114
$575$	1.72156	−	2.98183i	0.0717941	−	0.124351i
$576$	−2.91019	−	0.728551i	−0.121258	−	0.0303563i
$577$	−20.3587	+	35.2622i	−0.847542	+	1.46799i	0.0358537	+	0.999357i	$0.488585\pi$
$577$	−20.3587	+	35.2622i	−0.847542	+	1.46799i	−0.883395	+	0.468628i	$0.844748\pi$
$578$	6.28952	−	10.8938i	0.261609	−	0.453121i
$579$	32.9665	−	13.9749i	1.37004	−	0.580775i
$580$	−14.1055			−0.585698
$581$	−30.8977	−	53.5163i	−1.28185	−	2.22023i
$582$	0.294996	−	2.39308i	0.0122280	−	0.0991965i
$583$	6.62631	+	11.4771i	0.274434	+	0.475333i
$584$	−8.59878			−0.355820
$585$	9.66005	+	33.8107i	0.399394	+	1.39790i
$586$	5.16113			0.213204
$587$	−11.2883			−0.465919			−0.232960	−	0.972486i	$-0.574841\pi$
$587$	−11.2883			−0.465919			−0.232960	+	0.972486i	$0.574841\pi$
$588$	24.1799	+	18.2390i	0.997160	+	0.752162i
$589$	−0.352084	+	0.609827i	−0.0145074	+	0.0251275i
$590$	26.7539			1.10144
$591$	21.5774	+	16.2759i	0.887574	+	0.669501i
$592$	3.06798	+	5.25238i	0.126093	+	0.215871i
$593$	−6.64250			−0.272775			−0.136387	−	0.990656i	$-0.543549\pi$
$593$	−6.64250			−0.272775			−0.136387	+	0.990656i	$0.543549\pi$
$594$	5.03481	−	13.0601i	0.206581	−	0.535861i
$595$	54.8837	+	95.0614i	2.25001	+	3.89714i
$596$	3.52996			0.144593
$597$	−2.17366	+	17.6333i	−0.0889619	+	0.721682i
$598$	0.425195	+	0.736460i	0.0173875	+	0.0301161i
$599$	−16.7403	+	28.9950i	−0.683988	+	1.18470i	0.289765	+	0.957098i	$0.406423\pi$
$599$	−16.7403	+	28.9950i	−0.683988	+	1.18470i	−0.973754	+	0.227605i	$0.926911\pi$
$600$	18.5551	−	7.86568i	0.757508	−	0.321115i
$601$	−7.94617	−	13.7632i	−0.324131	−	0.561411i	0.657205	−	0.753712i	$-0.271739\pi$
$601$	−7.94617	−	13.7632i	−0.324131	−	0.561411i	−0.981336	+	0.192300i	$0.938405\pi$
$602$	38.8540			1.58357
$603$	−1.18083	+	1.22044i	−0.0480869	+	0.0497002i
$604$	−1.13793	+	1.97095i	−0.0463016	+	0.0801967i
$605$	15.2702			0.620820
$606$	0.587800	−	4.76839i	0.0238777	−	0.193702i
$607$	−36.0658			−1.46387			−0.731933	−	0.681377i	$-0.761381\pi$
$607$	−36.0658			−1.46387			−0.731933	+	0.681377i	$0.761381\pi$
$608$	0.359265			0.0145701
$609$	23.6638	+	17.8497i	0.958906	+	0.723307i
$610$	16.9174			0.684965
$611$	11.0308	+	19.1059i	0.446259	+	0.772943i
$612$	4.48228	+	15.6882i	0.181186	+	0.634159i
$613$	−10.5010	+	18.1882i	−0.424130	+	0.734615i	−0.996339	−	0.0854929i	$-0.972754\pi$
$613$	−10.5010	+	18.1882i	−0.424130	+	0.734615i	0.572208	+	0.820108i	$0.306087\pi$
$614$	14.9773	+	25.9414i	0.604434	+	1.04691i
$615$	16.0325	−	6.79635i	0.646494	−	0.274055i
$616$	6.66475	−	11.5437i	0.268531	−	0.465109i
$617$	34.1661			1.37548			0.687738	−	0.725959i	$-0.258604\pi$
$617$	34.1661			1.37548			0.687738	+	0.725959i	$0.258604\pi$
$618$	−2.14149	−	1.61533i	−0.0861433	−	0.0649783i
$619$	−3.48390	+	6.03430i	−0.140030	+	0.242539i	−0.927508	−	0.373804i	$-0.878053\pi$
$619$	−3.48390	+	6.03430i	−0.140030	+	0.242539i	0.787478	+	0.616343i	$0.211387\pi$
$620$	−3.99714	+	6.92325i	−0.160529	+	0.278045i
$621$	−1.51903	+	0.238356i	−0.0609564	+	0.00956488i
$622$	3.66058	+	6.34032i	0.146776	+	0.254224i
$623$	−45.4918	+	78.7940i	−1.82259	+	3.15682i
$624$	−0.608972	+	4.94014i	−0.0243784	+	0.197764i
$625$	−26.1043	+	45.2140i	−1.04417	+	1.80856i
$626$	−8.87251	+	15.3676i	−0.354617	+	0.614214i
$627$	−0.205074	+	1.66361i	−0.00818987	+	0.0664383i
$628$	5.17802	−	8.96859i	0.206625	−	0.357886i
$629$	16.3959	−	28.7332i	0.653749	−	1.14567i
$630$	−58.7358	−	14.7042i	−2.34009	−	0.585829i
$631$	21.2519	−	36.8094i	0.846025	−	1.46536i	−0.0387024	−	0.999251i	$-0.512322\pi$
$631$	21.2519	−	36.8094i	0.846025	−	1.46536i	0.884728	−	0.466108i	$-0.154344\pi$
$632$	14.1855			0.564267
$633$	33.8363	−	14.3435i	1.34487	−	0.570104i
$634$	−3.22560	+	5.58691i	−0.128105	+	0.221884i
$635$	−31.0272	−	53.7406i	−1.23127	−	2.13263i
$636$	7.84559	−	3.32582i	0.311098	−	0.131878i
$637$	25.1260	−	43.5196i	0.995530	−	1.72431i
$638$	4.65791	−	8.06773i	0.184408	−	0.319404i
$639$	−8.80570	−	30.8204i	−0.348348	−	1.21924i
$640$	4.07867			0.161224
$641$	12.0383	+	20.8509i	0.475484	+	0.823562i	0.999606	−	0.0280815i	$-0.00893980\pi$
$641$	12.0383	+	20.8509i	0.475484	+	0.823562i	−0.524122	+	0.851643i	$0.675606\pi$
$642$	−14.3675	−	10.8374i	−0.567039	−	0.427720i
$643$	−18.6736	−	32.3437i	−0.736416	−	1.27551i	−0.954099	−	0.299491i	$-0.903183\pi$
$643$	−18.6736	−	32.3437i	−0.736416	−	1.27551i	0.217683	−	0.976019i	$-0.430150\pi$
$644$	−1.46429			−0.0577012
$645$	−51.0701	+	21.6491i	−2.01088	+	0.852434i
$646$	−0.976961	−	1.69215i	−0.0384380	−	0.0665766i
$647$	8.21733	+	14.2328i	0.323057	+	0.559551i	0.981117	−	0.193415i	$-0.0619562\pi$
$647$	8.21733	+	14.2328i	0.323057	+	0.559551i	−0.658060	+	0.752965i	$0.728623\pi$
$648$	−7.93843	−	4.24044i	−0.311851	−	0.166580i
$649$	−8.83467	+	15.3021i	−0.346791	+	0.600660i
$650$	−16.7190	−	28.9582i	−0.655774	−	1.13583i
$651$	15.4667	−	6.55650i	0.606189	−	0.256970i
$652$	0.937663	+	1.62408i	0.0367217	+	0.0636039i
$653$	−0.637439	+	1.10408i	−0.0249449	+	0.0432058i	−0.878228	−	0.478241i	$-0.841274\pi$
$653$	−0.637439	+	1.10408i	−0.0249449	+	0.0432058i	0.853283	+	0.521447i	$0.174608\pi$
$654$	−3.91290	+	31.7425i	−0.153007	+	1.24123i
$655$	1.82597	−	3.16268i	0.0713466	−	0.123576i
$656$	2.46495			0.0962401
$657$	−25.0241	−	6.26465i	−0.976283	−	0.244407i
$658$	−37.9880			−1.48093
$659$	15.9693			0.622075			0.311037	−	0.950398i	$-0.399324\pi$
$659$	15.9693			0.622075			0.311037	+	0.950398i	$0.399324\pi$
$660$	−2.32817	+	18.8867i	−0.0906238	+	0.735164i
$661$	−8.76973	+	15.1896i	−0.341103	+	0.590807i	−0.984638	−	0.174609i	$-0.944134\pi$
$661$	−8.76973	+	15.1896i	−0.341103	+	0.590807i	0.643535	+	0.765417i	$0.277467\pi$
$662$	−3.05243	+	5.28697i	−0.118636	+	0.205484i
$663$	24.9241	−	10.5656i	0.967973	−	0.410334i
$664$	6.24400	+	10.8149i	0.242314	+	0.419700i
$665$	7.25098			0.281181
$666$	5.10179	+	17.5206i	0.197690	+	0.678910i
$667$	−1.02337			−0.0396252
$668$	10.0209	+	17.3567i	0.387719	+	0.671549i
$669$	24.8602	+	18.7521i	0.961149	+	0.724999i
$670$	1.15439	−	1.99946i	0.0445979	−	0.0772459i
$671$	−5.58645	+	9.67601i	−0.215662	+	0.373538i
$672$	−6.84251	−	5.16133i	−0.263955	−	0.199103i
$673$	−6.59789			−0.254330			−0.127165	−	0.991882i	$-0.540588\pi$
$673$	−6.59789			−0.254330			−0.127165	+	0.991882i	$0.540588\pi$
$674$	26.4706			1.01961
$675$	59.7294	−	9.37234i	2.29898	−	0.360741i
$676$	−4.74140			−0.182362
$677$	3.41586	−	5.91644i	0.131282	−	0.227387i	−0.792889	−	0.609366i	$-0.791424\pi$
$677$	3.41586	−	5.91644i	0.131282	−	0.227387i	0.924171	+	0.381979i	$0.124757\pi$
$678$	−25.5118	+	10.8147i	−0.979774	+	0.415336i
$679$	3.44433	−	5.96575i	0.132181	−	0.228945i
$680$	−11.0913	−	19.2106i	−0.425330	−	0.736694i
$681$	−1.28936	+	10.4596i	−0.0494083	+	0.400813i
$682$	−2.63987	−	4.57239i	−0.101086	−	0.175086i
$683$	18.4475	−	31.9520i	0.705873	−	1.22261i	−0.260502	−	0.965473i	$-0.583888\pi$
$683$	18.4475	−	31.9520i	0.705873	−	1.22261i	0.966376	−	0.257135i	$-0.0827785\pi$
$684$	1.04553	+	0.261743i	0.0399769	+	0.0100080i
$685$	−14.4147	−	24.9670i	−0.550758	−	0.953940i
$686$	25.9454	+	44.9387i	0.990599	+	1.71577i
$687$	−20.6692	−	15.5909i	−0.788580	−	0.594830i
$688$	−7.85186			−0.299349
$689$	−7.06926	−	12.2443i	−0.269317	−	0.466471i
$690$	1.92468	−	0.815892i	0.0732714	−	0.0310605i
$691$	23.3727	+	40.4827i	0.889138	+	1.54003i	0.840896	+	0.541197i	$0.182029\pi$
$691$	23.3727	+	40.4827i	0.889138	+	1.54003i	0.0482425	+	0.998836i	$0.484638\pi$
$692$	−13.9219			−0.529231
$693$	27.8059	−	28.7387i	1.05626	−	1.09169i
$694$	−1.05120	+	1.82073i	−0.0399030	+	0.0691139i
$695$	15.6320	−	27.0754i	0.592955	−	1.02703i
$696$	−4.78213	−	3.60719i	−0.181266	−	0.136730i
$697$	−6.70301	−	11.6100i	−0.253895	−	0.439759i
$698$	7.47844	−	12.9530i	0.283063	−	0.490280i
$699$	−2.91769	+	23.6690i	−0.110357	+	0.895245i
$700$	57.5772			2.17621
$701$	5.64416	−	9.77597i	0.213177	−	0.369233i	−0.739530	−	0.673123i	$-0.764952\pi$
$701$	5.64416	−	9.77597i	0.213177	−	0.369233i	0.952707	+	0.303890i	$0.0982856\pi$
$702$	−5.37137	+	13.9331i	−0.202729	+	0.525870i
$703$	−1.10222	−	1.88700i	−0.0415710	−	0.0711694i
$704$	−1.34686	+	2.33282i	−0.0507616	+	0.0879216i
$705$	49.9319	−	21.1666i	1.88054	−	0.797182i
$706$	10.1499	−	17.5801i	0.381996	−	0.661637i
$707$	6.86307	−	11.8872i	0.258112	−	0.447063i
$708$	9.07030	+	6.84177i	0.340883	+	0.257129i
$709$	5.62324	−	9.73975i	0.211185	−	0.365784i	−0.740900	−	0.671615i	$-0.765601\pi$
$709$	5.62324	−	9.73975i	0.211185	−	0.365784i	0.952086	+	0.305831i	$0.0989343\pi$
$710$	21.7894	+	37.7404i	0.817742	+	1.41637i
$711$	41.2824	+	10.3348i	1.54821	+	0.387586i
$712$	9.19327	−	15.9232i	0.344532	−	0.596747i
$713$	−0.289999	+	0.502292i	−0.0108605	+	0.0188110i
$714$	−5.70294	+	46.2637i	−0.213427	+	1.73138i
$715$	31.5736			1.18078
$716$	−12.3021	+	21.3079i	−0.459751	+	0.796312i
$717$	1.11120	−	9.01434i	0.0414985	−	0.336647i
$718$	0.483894	+	0.838129i	0.0180588	+	0.0312787i
$719$	−7.44352	+	12.8926i	−0.277597	+	0.480811i	−0.970787	−	0.239943i	$-0.922871\pi$
$719$	−7.44352	+	12.8926i	−0.277597	+	0.480811i	0.693190	+	0.720755i	$0.256205\pi$
$720$	11.8697	+	2.97152i	0.442358	+	0.110742i
$721$	−3.83174	−	6.63677i	−0.142701	−	0.247166i
$722$	18.8709			0.702303
$723$	−6.52827	+	52.9590i	−0.242789	+	1.96957i
$724$	−1.83655			−0.0682547
$725$	40.2399			1.49447
$726$	5.17699	+	3.90503i	0.192136	+	0.144929i
$727$	25.4314			0.943199			0.471600	−	0.881813i	$-0.343677\pi$
$727$	25.4314			0.943199			0.471600	+	0.881813i	$0.343677\pi$
$728$	−7.11027	+	12.3153i	−0.263524	+	0.456437i
$729$	−20.0130	−	18.1241i	−0.741221	−	0.671261i
$730$	35.0716			1.29806
$731$	21.3518	+	36.9824i	0.789725	+	1.36784i
$732$	5.73544	+	4.32627i	0.211988	+	0.159904i
$733$	−9.32685	+	16.1546i	−0.344495	+	0.596683i	−0.985262	−	0.171052i	$-0.945283\pi$
$733$	−9.32685	+	16.1546i	−0.344495	+	0.596683i	0.640767	+	0.767736i	$0.278617\pi$
$734$	−2.44838	−	4.24073i	−0.0903715	−	0.156528i
$735$	−98.6217	−	74.3908i	−3.63772	−	2.74395i
$736$	0.295914			0.0109075
$737$	0.762403	+	1.32052i	0.0280835	+	0.0486420i
$738$	7.17347	+	1.79584i	0.264059	+	0.0661058i
$739$	5.66251			0.208299			0.104149	−	0.994562i	$-0.466788\pi$
$739$	5.66251			0.208299			0.104149	+	0.994562i	$0.466788\pi$
$740$	−12.5133	−	21.4227i	−0.459998	−	0.787515i
$741$	0.218782	−	1.77482i	0.00803717	−	0.0651996i
$742$	24.3452			0.893740
$743$	−2.38154	+	4.12495i	−0.0873702	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$743$	−2.38154	+	4.12495i	−0.0873702	+	0.151330i	0.819029	+	0.573753i	$0.194513\pi$
$744$	−3.12562	+	1.32498i	−0.114591	+	0.0485761i
$745$	−14.3976			−0.527486
$746$	−19.6595			−0.719786
$747$	10.2920	+	36.0226i	0.376565	+	1.31800i
$748$	14.6502			0.535664
$749$	−25.7075	−	44.5267i	−0.939333	−	1.62697i
$750$	−43.1591	+	18.2956i	−1.57595	+	0.668060i
$751$	8.90826	+	15.4296i	0.325067	+	0.563033i	0.981526	−	0.191329i	$-0.0612797\pi$
$751$	8.90826	+	15.4296i	0.325067	+	0.563033i	−0.656459	+	0.754362i	$0.727946\pi$
$752$	7.67687			0.279947
$753$	−3.26786	+	26.5097i	−0.119088	+	0.966069i
$754$	−4.96927	+	8.60702i	−0.180970	+	0.313449i
$755$	4.64123	−	8.03885i	0.168912	−	0.292564i
$756$	−16.1527	−	20.0056i	−0.587468	−	0.727596i
$757$	1.08317	−	1.87611i	0.0393685	−	0.0681882i	−0.845670	−	0.533706i	$-0.820799\pi$
$757$	1.08317	−	1.87611i	0.0393685	−	0.0681882i	0.885038	+	0.465518i	$0.154132\pi$
$758$	10.1316			0.367996
$759$	−0.168912	+	1.37026i	−0.00613112	+	0.0497372i
$760$	−1.46533			−0.0531529
$761$	−8.50026			−0.308134			−0.154067	−	0.988060i	$-0.549237\pi$
$761$	−8.50026			−0.308134			−0.154067	+	0.988060i	$0.549237\pi$
$762$	3.22402	−	26.1540i	0.116794	−	0.947461i
$763$	−45.6865	+	79.1313i	−1.65396	+	2.86475i
$764$	8.45520	+	14.6448i	0.305899	+	0.529832i
$765$	−18.2818	−	63.9871i	−0.660979	−	2.31346i
$766$	4.43692			0.160312
$767$	9.42523	−	16.3250i	0.340325	−	0.589461i
$768$	1.38278	+	1.04304i	0.0498967	+	0.0376373i
$769$	−7.78195	−	13.4787i	−0.280624	−	0.486055i	0.690914	−	0.722937i	$-0.257208\pi$
$769$	−7.78195	−	13.4787i	−0.280624	−	0.486055i	−0.971539	+	0.236881i	$0.923875\pi$
$770$	−27.1834	+	47.0830i	−0.979620	+	1.69675i
$771$	2.52686	−	20.4985i	0.0910026	−	0.738237i
$772$	−20.6728			−0.744029
$773$	12.3527	+	21.3954i	0.444294	+	0.769540i	0.998003	−	0.0631705i	$-0.0201212\pi$
$773$	12.3527	+	21.3954i	0.444294	+	0.769540i	−0.553709	+	0.832710i	$0.686788\pi$
$774$	−22.8504	−	5.72048i	−0.821342	−	0.205618i
$775$	11.4030	−	19.7505i	0.409607	−	0.709461i
$776$	−0.696052	+	1.20560i	−0.0249868	+	0.0432784i
$777$	−6.11658	+	51.7743i	−0.219431	+	1.85739i
$778$	0.450298	+	0.779939i	0.0161440	+	0.0279622i
$779$	−0.885571			−0.0317289
$780$	2.48380	−	20.1492i	0.0889342	−	0.721457i
$781$	−28.7811			−1.02987
$782$	−0.804687	−	1.39376i	−0.0287756	−	0.0498407i
$783$	−11.2889	−	13.9816i	−0.403433	−	0.499663i
$784$	−8.74321	−	15.1437i	−0.312258	−	0.540846i
$785$	−21.1194	+	36.5800i	−0.753785	+	1.30559i
$786$	1.42784	−	0.605277i	0.0509294	−	0.0215895i
$787$	4.71774	+	8.17137i	0.168169	+	0.291278i	0.937776	−	0.347240i	$-0.112881\pi$
$787$	4.71774	+	8.17137i	0.168169	+	0.291278i	−0.769607	+	0.638518i	$0.779548\pi$
$788$	−7.80217	−	13.5138i	−0.277941	−	0.481408i
$789$	−6.53493	+	53.0131i	−0.232650	+	1.88731i
$790$	−57.8579			−2.05849
$791$	−79.1642			−2.81475
$792$	−5.61919	+	5.80771i	−0.199669	+	0.206368i
$793$	5.95988	−	10.3228i	0.211641	−	0.366574i
$794$	−5.48071	−	9.49287i	−0.194503	−	0.336889i
$795$	−31.9996	+	13.5650i	−1.13491	+	0.481099i
$796$	5.12882	−	8.88337i	0.181786	−	0.314863i
$797$	19.3134			0.684116			0.342058	−	0.939679i	$-0.388876\pi$
$797$	19.3134			0.684116			0.342058	+	0.939679i	$0.388876\pi$
$798$	2.45827	+	1.85429i	0.0870220	+	0.0656411i
$799$	−20.8760	−	36.1582i	−0.738538	−	1.27919i
$800$	−11.6356			−0.411380
$801$	38.3550	−	39.6418i	1.35521	−	1.40067i
$802$	8.41549	−	14.5761i	0.297161	−	0.514699i
$803$	−11.5813	+	20.0595i	−0.408696	+	0.707883i
$804$	0.902689	−	0.382659i	0.0318354	−	0.0134953i
$805$	5.97237			0.210498
$806$	2.81633	+	4.87803i	0.0992011	+	0.171821i
$807$	3.97665	−	32.2596i	0.139985	−	1.13559i
$808$	−1.38693	+	2.40224i	−0.0487921	+	0.0845105i
$809$	4.56673	+	7.90981i	0.160558	+	0.278094i	0.935069	−	0.354466i	$-0.115337\pi$
$809$	4.56673	+	7.90981i	0.160558	+	0.278094i	−0.774511	+	0.632560i	$0.782004\pi$
$810$	32.3782	+	17.2954i	1.13766	+	0.607698i
$811$	8.80739	+	15.2548i	0.309269	+	0.535670i	0.978203	−	0.207652i	$-0.0665822\pi$
$811$	8.80739	+	15.2548i	0.309269	+	0.535670i	−0.668933	+	0.743322i	$0.733249\pi$
$812$	−8.55661	−	14.8205i	−0.300278	−	0.520097i
$813$	4.29035	+	3.23623i	0.150469	+	0.113500i
$814$	16.3850	−	0.0828641i	0.574294	−	0.00290439i
$815$	−3.82442	−	6.62409i	−0.133964	−	0.232032i
$816$	1.15249	−	9.34927i	0.0403451	−	0.327290i
$817$	2.82090			0.0986908
$818$	−2.97026	−	5.14465i	−0.103853	−	0.179878i
$819$	−29.6646	+	30.6598i	−1.03656	+	1.07134i
$820$	−10.0537			−0.351091
$821$	−47.2036			−1.64742			−0.823709	−	0.567013i	$-0.808099\pi$
$821$	−47.2036			−1.64742			−0.823709	+	0.567013i	$0.808099\pi$
$822$	1.49782	−	12.1507i	0.0522426	−	0.423806i
$823$	−5.13864			−0.179122			−0.0895609	−	0.995981i	$-0.528546\pi$
$823$	−5.13864			−0.179122			−0.0895609	+	0.995981i	$0.528546\pi$
$824$	0.774343	+	1.34120i	0.0269755	+	0.0467230i
$825$	6.64176	−	53.8797i	0.231236	−	1.87585i
$826$	16.2294	+	28.1101i	0.564692	+	0.978075i
$827$	−12.8003	−	22.1707i	−0.445110	−	0.770952i	0.552950	−	0.833214i	$-0.313502\pi$
$827$	−12.8003	−	22.1707i	−0.445110	−	0.770952i	−0.998060	+	0.0622618i	$0.980169\pi$
$828$	0.861166	+	0.215588i	0.0299276	+	0.00749221i
$829$	15.7572	−	27.2923i	0.547271	−	0.947900i	−0.451190	−	0.892428i	$-0.649000\pi$
$829$	15.7572	−	27.2923i	0.547271	−	0.947900i	0.998460	−	0.0554724i	$-0.0176665\pi$
$830$	−25.4672	−	44.1105i	−0.883980	−	1.53110i
$831$	−1.09057	+	8.84702i	−0.0378316	+	0.306900i
$832$	1.43689	−	2.48876i	0.0498152	−	0.0862824i
$833$	−47.5514	+	82.3614i	−1.64756	+	2.85365i
$834$	12.2236	−	5.18172i	0.423270	−	0.179428i
$835$	−40.8718	−	70.7921i	−1.41443	−	2.44986i
$836$	0.483879	−	0.838103i	0.0167353	−	0.0289864i
$837$	−10.0615	+	1.57878i	−0.347775	+	0.0545705i
$838$	−12.0195	−	20.8184i	−0.415206	−	0.719159i
$839$	−13.2397	−	22.9319i	−0.457087	−	0.791697i	0.541719	−	0.840560i	$-0.317774\pi$
$839$	−13.2397	−	22.9319i	−0.457087	−	0.791697i	−0.998806	+	0.0488625i	$0.984440\pi$
$840$	27.9083	+	21.0514i	0.962930	+	0.726342i
$841$	8.51990	+	14.7569i	0.293790	+	0.508859i
$842$	−8.26020			−0.284665
$843$	−12.7805	+	5.41779i	−0.440184	+	0.186599i
$844$	−21.2182			−0.730359
$845$	19.3386			0.665269
$846$	22.3412	+	5.59299i	0.768105	+	0.192291i
$847$	9.26312	+	16.0442i	0.318285	+	0.551285i
$848$	−4.91984			−0.168948
$849$	−8.42658	−	6.35621i	−0.289200	−	0.218145i
$850$	31.6410	+	54.8038i	1.08528	+	1.87975i
$851$	−0.907858	−	1.55425i	−0.0311210	−	0.0532790i
$852$	−2.26413	+	18.3672i	−0.0775677	+	0.629249i
$853$	2.42038	+	4.19223i	0.0828724	+	0.143539i	0.904483	−	0.426511i	$-0.140257\pi$
$853$	2.42038	+	4.19223i	0.0828724	+	0.143539i	−0.821610	+	0.570050i	$0.806924\pi$
$854$	10.2624	+	17.7749i	0.351170	+	0.608245i
$855$	−4.26438	−	1.06756i	−0.145839	−	0.0365099i
$856$	5.19514	+	8.99825i	0.177566	+	0.307554i
$857$	−5.98835	+	10.3721i	−0.204558	+	0.354305i	−0.949992	−	0.312275i	$-0.898909\pi$
$857$	−5.98835	+	10.3721i	−0.204558	+	0.354305i	0.745434	+	0.666580i	$0.232242\pi$
$858$	10.7043	+	8.07428i	0.365438	+	0.275651i
$859$	−4.83688	−	8.37773i	−0.165032	−	0.285844i	0.771634	−	0.636066i	$-0.219440\pi$
$859$	−4.83688	−	8.37773i	−0.165032	−	0.285844i	−0.936667	+	0.350222i	$0.886106\pi$
$860$	32.0252			1.09205
$861$	16.8664	+	12.7224i	0.574807	+	0.433579i
$862$	−0.940710	+	1.62936i	−0.0320407	+	0.0554961i
$863$	10.6682	−	18.4778i	0.363148	−	0.628991i	−0.625329	−	0.780361i	$-0.715035\pi$
$863$	10.6682	−	18.4778i	0.363148	−	0.628991i	0.988477	+	0.151370i	$0.0483685\pi$
$864$	3.26424	+	4.04286i	0.111052	+	0.137541i
$865$	56.7828			1.93067
$866$	−2.48901	−	4.31109i	−0.0845801	−	0.146497i
$867$	−20.0596	+	8.50347i	−0.681260	+	0.288793i
$868$	−9.69892			−0.329203
$869$	19.1058	−	33.0922i	0.648120	−	1.12258i
$870$	19.5048	+	14.7125i	0.661273	+	0.498801i
$871$	−0.813366	−	1.40879i	−0.0275599	−	0.0477351i
$872$	9.23262	−	15.9914i	0.312656	−	0.541536i
$873$	−2.90398	+	3.00141i	−0.0982850	+	0.101582i
$874$	−0.106312			−0.00359604
$875$	−133.924			−4.52747
$876$	11.8902	+	8.96884i	0.401733	+	0.303029i
$877$	−0.927137	−	1.60585i	−0.0313072	−	0.0542257i	0.849947	−	0.526868i	$-0.176634\pi$
$877$	−0.927137	−	1.60585i	−0.0313072	−	0.0542257i	−0.881254	+	0.472642i	$0.843300\pi$
$878$	−3.99894	−	6.92636i	−0.134958	−	0.233753i
$879$	−7.13670	−	5.38324i	−0.240715	−	0.181572i
$880$	5.49339	−	9.51483i	0.185182	−	0.320745i
$881$	2.98102	+	5.16327i	0.100433	+	0.173955i	0.911863	−	0.410494i	$-0.134644\pi$
$881$	2.98102	+	5.16327i	0.100433	+	0.173955i	−0.811430	+	0.584449i	$0.801311\pi$
$882$	−14.4115	−	50.4409i	−0.485260	−	1.69843i
$883$	9.62006	+	16.6624i	0.323741	+	0.560736i	0.981257	−	0.192705i	$-0.0617261\pi$
$883$	9.62006	+	16.6624i	0.323741	+	0.560736i	−0.657516	+	0.753441i	$0.728393\pi$
$884$	−15.6295			−0.525677
$885$	−36.9948	−	27.9053i	−1.24357	−	0.938027i
$886$	20.4803			0.688050
$887$	21.7165	+	37.6140i	0.729167	+	1.26295i	0.957236	+	0.289309i	$0.0934257\pi$
$887$	21.7165	+	37.6140i	0.729167	+	1.26295i	−0.228068	+	0.973645i	$0.573241\pi$
$888$	1.23608	−	10.4629i	0.0414801	−	0.351112i
$889$	37.6431	−	65.1998i	1.26251	−	2.18673i
$890$	−37.4963	+	64.9456i	−1.25688	+	2.17698i
$891$	−20.5841	+	12.8077i	−0.689595	+	0.429074i
$892$	−8.98920	−	15.5698i	−0.300981	−	0.521314i
$893$	−2.75803			−0.0922941
$894$	−4.88115	−	3.68188i	−0.163250	−	0.123140i
$895$	50.1762	−	86.9078i	1.67721	−	2.90501i
$896$	2.47419	+	4.28542i	0.0826568	+	0.143166i
$897$	0.180203	−	1.46185i	0.00601681	−	0.0488099i
$898$	16.2173	−	28.0891i	0.541177	−	0.937347i
$899$	−6.77844			−0.226074
$900$	−33.8617	−	8.47711i	−1.12872	−	0.282570i
$901$	13.3787	+	23.1725i	0.445708	+	0.771988i
$902$	3.31993	−	5.75029i	0.110542	−	0.191464i
$903$	−53.7264	−	40.5261i	−1.78790	−	1.34862i
$904$	15.9980			0.532086
$905$	7.49068			0.248998
$906$	3.62927	−	1.53848i	0.120574	−	0.0511127i
$907$	30.5998			1.01605			0.508024	−	0.861343i	$-0.330376\pi$
$907$	30.5998			1.01605			0.508024	+	0.861343i	$0.330376\pi$
$908$	3.04228	−	5.26939i	0.100962	−	0.174871i
$909$	−5.78639	+	5.98052i	−0.191923	+	0.198361i
$910$	29.0004	−	50.2303i	0.961356	−	1.66512i
$911$	1.87114	−	3.24090i	0.0619935	−	0.107376i	−0.833363	−	0.552726i	$-0.813588\pi$
$911$	1.87114	−	3.24090i	0.0619935	−	0.107376i	0.895356	+	0.445350i	$0.146921\pi$
$912$	−0.496784	−	0.374727i	−0.0164502	−	0.0124084i
$913$	33.6391			1.11329
$914$	−12.4242	−	21.5194i	−0.410956	−	0.711798i
$915$	−23.3930	−	17.6454i	−0.773348	−	0.583340i
$916$	7.47380	+	12.9450i	0.246941	+	0.427715i
$917$	4.43065			0.146313
$918$	10.1654	−	26.3685i	0.335507	−	0.870291i
$919$	−22.1894			−0.731961			−0.365980	−	0.930623i	$-0.619266\pi$
$919$	−22.1894			−0.731961			−0.365980	+	0.930623i	$0.619266\pi$
$920$	−1.20694			−0.0397915
$921$	6.34757	−	51.4931i	0.209159	−	1.69676i
$922$	16.6402	−	28.8216i	0.548015	−	0.949189i
$923$	30.7050			1.01067
$924$	−21.2564	+	9.01079i	−0.699283	+	0.296433i
$925$	35.6977	+	61.1144i	1.17373	+	2.00943i
$926$	30.2977			0.995646
$927$	1.27635	+	4.46730i	0.0419209	+	0.146725i
$928$	1.72918	+	2.99502i	0.0567630	+	0.0983164i
$929$	27.4629			0.901028			0.450514	−	0.892769i	$-0.351241\pi$
$929$	27.4629			0.901028			0.450514	+	0.892769i	$0.351241\pi$
$930$	12.7484	−	5.40416i	0.418035	−	0.177209i
$931$	3.14113	+	5.44060i	0.102946	+	0.178308i
$932$	6.88437	−	11.9241i	0.225505	−	0.390586i
$933$	1.55140	−	12.5854i	0.0507906	−	0.412027i
$934$	0.433287	+	0.750474i	0.0141776	+	0.0245563i
$935$	−59.7534			−1.95414
$936$	5.99481	−	6.19593i	0.195947	−	0.202520i
$937$	19.8980	−	34.4643i	0.650039	−	1.12590i	−0.333074	−	0.942901i	$-0.608086\pi$
$937$	19.8980	−	34.4643i	0.650039	−	1.12590i	0.983113	−	0.183000i	$-0.0585808\pi$
$938$	2.80108			0.0914586
$939$	28.2977	−	11.9957i	0.923461	−	0.391465i
$940$	−31.3114			−1.02127
$941$	−27.4120			−0.893607			−0.446803	−	0.894632i	$-0.647438\pi$
$941$	−27.4120			−0.893607			−0.446803	+	0.894632i	$0.647438\pi$
$942$	−16.5146	+	7.00072i	−0.538075	+	0.228096i
$943$	−0.729412			−0.0237529
$944$	−3.27974	−	5.68067i	−0.106746	−	0.184890i
$945$	65.8816	+	81.5962i	2.14313	+	2.65433i
$946$	−10.5753	+	18.3170i	−0.343834	+	0.595538i
$947$	20.5322	+	35.5628i	0.667206	+	1.15563i	0.978682	+	0.205381i	$0.0658433\pi$
$947$	20.5322	+	35.5628i	0.667206	+	1.15563i	−0.311476	+	0.950254i	$0.600823\pi$
$948$	−19.6154	−	14.7959i	−0.637077	−	0.480550i
$949$	12.3555	−	21.4003i	0.401076	−	0.694685i
$950$	4.18026			0.135625
$951$	10.2876	−	4.36103i	0.333599	−	0.141416i
$952$	13.4563	−	23.3069i	0.436120	−	0.755382i
$953$	25.2544	−	43.7419i	0.818070	−	1.41694i	−0.0890318	−	0.996029i	$-0.528377\pi$
$953$	25.2544	−	43.7419i	0.818070	−	1.41694i	0.907102	−	0.420911i	$-0.138289\pi$
$954$	−14.3177	−	3.58435i	−0.463551	−	0.116048i
$955$	−34.4860	−	59.7315i	−1.11594	−	1.93287i
$956$	−2.62191	+	4.54128i	−0.0847987	+	0.146876i
$957$	−14.8558	+	6.29752i	−0.480219	+	0.203570i
$958$	−6.10719	+	10.5780i	−0.197314	+	0.341759i
$959$	17.4884	−	30.2908i	0.564729	−	0.978140i
$960$	−5.63990	−	4.25420i	−0.182027	−	0.137304i
$961$	13.5792	−	23.5198i	0.438037	−	0.758703i
$962$	−17.4803	+	0.0884032i	−0.563587	+	0.00285023i
$963$	8.56318	+	29.9716i	0.275945	+	0.965820i
$964$	15.4037	−	26.6799i	0.496119	−	0.859303i
$965$	84.3174			2.71427
$966$	2.02479	+	1.52731i	0.0651466	+	0.0491404i
$967$	0.959371	−	1.66168i	0.0308513	−	0.0534360i	−0.850188	−	0.526480i	$-0.823512\pi$
$967$	0.959371	−	1.66168i	0.0308513	−	0.0534360i	0.881039	+	0.473044i	$0.156845\pi$
$968$	−1.87195	−	3.24232i	−0.0601668	−	0.104212i
$969$	−0.414049	+	3.35887i	−0.0133012	+	0.107902i
$970$	2.83897	−	4.91724i	0.0911538	−	0.157883i
$971$	15.2072	−	26.3397i	0.488024	−	0.845282i	−0.511881	−	0.859056i	$-0.671051\pi$
$971$	15.2072	−	26.3397i	0.488024	−	0.845282i	0.999905	+	0.0137742i	$0.00438460\pi$
$972$	6.55415	+	14.1437i	0.210224	+	0.453658i
$973$	37.9304			1.21599
$974$	−16.4385	−	28.4723i	−0.526723	−	0.912312i
$975$	−7.08574	+	57.4813i	−0.226925	+	1.84088i
$976$	−2.07388	−	3.59207i	−0.0663834	−	0.114979i
$977$	−38.4283			−1.22943			−0.614715	−	0.788749i	$-0.710729\pi$
$977$	−38.4283			−1.22943			−0.614715	+	0.788749i	$0.710729\pi$
$978$	0.397393	−	3.22376i	0.0127072	−	0.103084i
$979$	−24.7640	−	42.8926i	−0.791462	−	1.37085i
$980$	35.6607	+	61.7662i	1.13914	+	1.97305i
$981$	38.5192	−	39.8115i	1.22982	−	1.27108i
$982$	1.47498	−	2.55474i	0.0470686	−	0.0815252i
$983$	13.2253	+	22.9068i	0.421820	+	0.730614i	0.996118	−	0.0880325i	$-0.0280579\pi$
$983$	13.2253	+	22.9068i	0.421820	+	0.730614i	−0.574297	+	0.818647i	$0.694725\pi$
$984$	−3.40848	−	2.57103i	−0.108658	−	0.0819615i
$985$	31.8225	+	55.1182i	1.01395	+	1.75621i
$986$	9.40440	−	16.2889i	0.299497	−	0.518744i
$987$	52.5291	+	39.6229i	1.67202	+	1.26121i
$988$	−0.516224	+	0.894126i	−0.0164233	+	0.0284460i
$989$	2.32347			0.0738822
$990$	22.9189	−	23.6878i	0.728409	−	0.752846i
$991$	15.7162			0.499243			0.249621	−	0.968344i	$-0.419694\pi$
$991$	15.7162			0.499243			0.249621	+	0.968344i	$0.419694\pi$
$992$	1.96002			0.0622307
$993$	9.73534	−	4.12691i	0.308942	−	0.130964i
$994$	−26.4356	+	45.7878i	−0.838487	+	1.45230i
$995$	−20.9188	+	36.2324i	−0.663170	+	1.14864i
$996$	2.64629	−	21.4674i	0.0838508	−	0.680219i
$997$	−9.30360	−	16.1143i	−0.294648	−	0.510345i	0.680255	−	0.732976i	$-0.261869\pi$
$997$	−9.30360	−	16.1143i	−0.294648	−	0.510345i	−0.974903	+	0.222630i	$0.928536\pi$
$998$	0.369989			0.0117118
$999$	11.2200	−	29.5485i	0.354984	−	0.934872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.g.b.565.11	yes	36
3.2	odd	2		1998.2.g.b.343.2		36
9.4	even	3		666.2.h.b.121.3	yes	36
9.5	odd	6		1998.2.h.b.1009.17		36
37.26	even	3		666.2.h.b.655.3	yes	36
111.26	odd	6		1998.2.h.b.1099.17		36
333.211	even	3	inner	666.2.g.b.211.11	✓	36
333.248	odd	6		1998.2.g.b.1765.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.g.b.211.11	✓	36	333.211	even	3	inner
666.2.g.b.565.11	yes	36	1.1	even	1	trivial
666.2.h.b.121.3	yes	36	9.4	even	3
666.2.h.b.655.3	yes	36	37.26	even	3
1998.2.g.b.343.2		36	3.2	odd	2
1998.2.g.b.1765.2		36	333.248	odd	6
1998.2.h.b.1009.17		36	9.5	odd	6
1998.2.h.b.1099.17		36	111.26	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.211906 - 1.71904i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.03934 - 3.53223i) q^{5} +(1.59468 - 0.676003i) q^{6} +4.94838 q^{7} -1.00000 q^{8} +(-2.91019 - 0.728551i) q^{9} +4.07867 q^{10} +(-1.34686 + 2.33282i) q^{11} +(1.38278 + 1.04304i) q^{12} +(1.43689 - 2.48876i) q^{13} +(2.47419 + 4.28542i) q^{14} +(-5.63990 - 4.25420i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.71933 + 4.71002i) q^{17} +(-0.824152 - 2.88458i) q^{18} +(0.179633 + 0.311133i) q^{19} +(2.03934 + 3.53223i) q^{20} +(1.04859 - 8.50645i) q^{21} -2.69371 q^{22} +(0.147957 + 0.256269i) q^{23} +(-0.211906 + 1.71904i) q^{24} +(-5.81779 - 10.0767i) q^{25} +2.87378 q^{26} +(-1.86910 + 4.84835i) q^{27} +(-2.47419 + 4.28542i) q^{28} +(-1.72918 + 2.99502i) q^{29} +(0.864297 - 7.01140i) q^{30} +(0.980010 + 1.69743i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.72481 + 2.80964i) q^{33} -5.43866 q^{34} +(10.0914 - 17.4788i) q^{35} +(2.08604 - 2.15602i) q^{36} +(-6.08268 + 0.0307620i) q^{37} +(-0.179633 + 0.311133i) q^{38} +(-3.97380 - 2.99745i) q^{39} +(-2.03934 + 3.53223i) q^{40} +(-1.23247 + 2.13471i) q^{41} +(7.89110 - 3.34512i) q^{42} +(3.92593 - 6.79991i) q^{43} +(-1.34686 - 2.33282i) q^{44} +(-8.50827 + 8.79372i) q^{45} +(-0.147957 + 0.256269i) q^{46} +(-3.83844 + 6.64837i) q^{47} +(-1.59468 + 0.676003i) q^{48} +17.4864 q^{49} +(5.81779 - 10.0767i) q^{50} +(7.52046 + 5.67272i) q^{51} +(1.43689 + 2.48876i) q^{52} +(2.45992 - 4.26070i) q^{53} +(-5.13334 + 0.805490i) q^{54} +(5.49339 + 9.51483i) q^{55} -4.94838 q^{56} +(0.572915 - 0.242864i) q^{57} -3.45835 q^{58} +6.55947 q^{59} +(6.50420 - 2.75720i) q^{60} +4.14777 q^{61} +(-0.980010 + 1.69743i) q^{62} +(-14.4007 - 3.60514i) q^{63} +1.00000 q^{64} +(-5.86060 - 10.1509i) q^{65} +(-0.570815 + 4.63060i) q^{66} +(0.283030 - 0.490223i) q^{67} +(-2.71933 - 4.71002i) q^{68} +(0.471889 - 0.200039i) q^{69} +20.1828 q^{70} +(5.34228 + 9.25310i) q^{71} +(2.91019 + 0.728551i) q^{72} +8.59878 q^{73} +(-3.06798 - 5.25238i) q^{74} +(-18.5551 + 7.86568i) q^{75} -0.359265 q^{76} +(-6.66475 + 11.5437i) q^{77} +(0.608972 - 4.94014i) q^{78} -14.1855 q^{79} -4.07867 q^{80} +(7.93843 + 4.24044i) q^{81} -2.46495 q^{82} +(-6.24400 - 10.8149i) q^{83} +(6.84251 + 5.16133i) q^{84} +(11.0913 + 19.2106i) q^{85} +7.85186 q^{86} +(4.78213 + 3.60719i) q^{87} +(1.34686 - 2.33282i) q^{88} +(-9.19327 + 15.9232i) q^{89} +(-11.8697 - 2.97152i) q^{90} +(7.11027 - 12.3153i) q^{91} -0.295914 q^{92} +(3.12562 - 1.32498i) q^{93} -7.67687 q^{94} +1.46533 q^{95} +(-1.38278 - 1.04304i) q^{96} +(0.696052 - 1.20560i) q^{97} +(8.74321 + 15.1437i) q^{98} +(5.61919 - 5.80771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 2 q^{3} - 18 q^{4} + 4 q^{5} + 2 q^{6} - 8 q^{7} - 36 q^{8} - 2 q^{9} + 8 q^{10} + 3 q^{11} + 4 q^{12} + q^{13} - 4 q^{14} - 7 q^{15} - 18 q^{16} + 3 q^{17} + 2 q^{18} + 9 q^{19} + 4 q^{20}+ \cdots - 23 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 2 * q^3 - 18 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^7 - 36 * q^8 - 2 * q^9 + 8 * q^10 + 3 * q^11 + 4 * q^12 + q^13 - 4 * q^14 - 7 * q^15 - 18 * q^16 + 3 * q^17 + 2 * q^18 + 9 * q^19 + 4 * q^20 - 13 * q^21 + 6 * q^22 + 11 * q^23 + 2 * q^24 - 22 * q^25 + 2 * q^26 - 2 * q^27 + 4 * q^28 - 12 * q^29 + q^30 + 16 * q^31 + 18 * q^32 + 13 * q^33 + 6 * q^34 + 3 * q^35 + 4 * q^36 + 8 * q^37 - 9 * q^38 - 47 * q^39 - 4 * q^40 - 6 * q^41 - 2 * q^42 + 4 * q^43 + 3 * q^44 - 40 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 + 24 * q^49 + 22 * q^50 + 6 * q^51 + q^52 + 8 * q^53 + 8 * q^54 + 9 * q^55 + 8 * q^56 - 12 * q^57 - 24 * q^58 + 24 * q^59 + 8 * q^60 + 30 * q^61 - 16 * q^62 + 23 * q^63 + 36 * q^64 - 26 * q^65 - q^66 - 14 * q^67 + 3 * q^68 - 5 * q^69 + 6 * q^70 + 2 * q^72 + 22 * q^73 + 16 * q^74 + 3 * q^75 - 18 * q^76 + 25 * q^77 - 46 * q^78 - 32 * q^79 - 8 * q^80 + 34 * q^81 - 12 * q^82 + 11 * q^84 + 15 * q^85 + 8 * q^86 - 7 * q^87 - 3 * q^88 + 3 * q^89 - 50 * q^90 + 37 * q^91 - 22 * q^92 - q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 11 * q^97 + 12 * q^98 - 23 * q^99

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