LMFDB - Embedded newform 666.2.k.a.175.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); 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, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.20
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-1.72572 + 0.147954i) q^{3} -1.00000 q^{4} -1.23967i q^{5} +(-0.147954 - 1.72572i) q^{6} +(-1.37235 + 2.37697i) q^{7} -1.00000i q^{8} +(2.95622 - 0.510656i) q^{9} +1.23967 q^{10} +(-1.41594 - 2.45249i) q^{11} +(1.72572 - 0.147954i) q^{12} -1.92556i q^{13} +(-2.37697 - 1.37235i) q^{14} +(0.183414 + 2.13932i) q^{15} +1.00000 q^{16} +(1.21619 + 0.702166i) q^{17} +(0.510656 + 2.95622i) q^{18} +(1.19640 - 0.690743i) q^{19} +1.23967i q^{20} +(2.01660 - 4.30504i) q^{21} +(2.45249 - 1.41594i) q^{22} +(2.66127 + 1.53649i) q^{23} +(0.147954 + 1.72572i) q^{24} +3.46322 q^{25} +1.92556 q^{26} +(-5.02605 + 1.31863i) q^{27} +(1.37235 - 2.37697i) q^{28} +(4.11863 - 2.37789i) q^{29} +(-2.13932 + 0.183414i) q^{30} +(0.786366 + 0.454008i) q^{31} +1.00000i q^{32} +(2.80638 + 4.02281i) q^{33} +(-0.702166 + 1.21619i) q^{34} +(2.94666 + 1.70126i) q^{35} +(-2.95622 + 0.510656i) q^{36} +(-0.296493 + 6.07553i) q^{37} +(0.690743 + 1.19640i) q^{38} +(0.284894 + 3.32297i) q^{39} -1.23967 q^{40} +11.5645 q^{41} +(4.30504 + 2.01660i) q^{42} +(3.06264 - 1.76822i) q^{43} +(1.41594 + 2.45249i) q^{44} +(-0.633043 - 3.66473i) q^{45} +(-1.53649 + 2.66127i) q^{46} +(2.53796 + 4.39587i) q^{47} +(-1.72572 + 0.147954i) q^{48} +(-0.266673 - 0.461891i) q^{49} +3.46322i q^{50} +(-2.20269 - 1.03180i) q^{51} +1.92556i q^{52} +(5.02762 - 8.70809i) q^{53} +(-1.31863 - 5.02605i) q^{54} +(-3.04027 + 1.75530i) q^{55} +(2.37697 + 1.37235i) q^{56} +(-1.96246 + 1.36904i) q^{57} +(2.37789 + 4.11863i) q^{58} +(8.82945 - 5.09768i) q^{59} +(-0.183414 - 2.13932i) q^{60} +(-1.91052 - 1.10304i) q^{61} +(-0.454008 + 0.786366i) q^{62} +(-2.84314 + 7.72766i) q^{63} -1.00000 q^{64} -2.38705 q^{65} +(-4.02281 + 2.80638i) q^{66} -12.6497 q^{67} +(-1.21619 - 0.702166i) q^{68} +(-4.81994 - 2.25780i) q^{69} +(-1.70126 + 2.94666i) q^{70} +(0.513569 + 0.889528i) q^{71} +(-0.510656 - 2.95622i) q^{72} -2.71210 q^{73} +(-6.07553 - 0.296493i) q^{74} +(-5.97655 + 0.512399i) q^{75} +(-1.19640 + 0.690743i) q^{76} +7.77266 q^{77} +(-3.32297 + 0.284894i) q^{78} +(1.95960 + 1.13138i) q^{79} -1.23967i q^{80} +(8.47846 - 3.01922i) q^{81} +11.5645i q^{82} +3.44726 q^{83} +(-2.01660 + 4.30504i) q^{84} +(0.870453 - 1.50767i) q^{85} +(1.76822 + 3.06264i) q^{86} +(-6.75579 + 4.71295i) q^{87} +(-2.45249 + 1.41594i) q^{88} +(-6.58592 - 3.80239i) q^{89} +(3.66473 - 0.633043i) q^{90} +(4.57700 + 2.64253i) q^{91} +(-2.66127 - 1.53649i) q^{92} +(-1.42422 - 0.667145i) q^{93} +(-4.39587 + 2.53796i) q^{94} +(-0.856293 - 1.48314i) q^{95} +(-0.147954 - 1.72572i) q^{96} +(-3.60285 + 2.08011i) q^{97} +(0.461891 - 0.266673i) q^{98} +(-5.43821 - 6.52703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

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

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.72572	+	0.147954i	−0.996345	+	0.0854215i
$3$	−1.72572	+	0.147954i	−0.996345	+	0.0854215i
$4$	−1.00000			−0.500000
$5$		−	1.23967i		−	0.554397i	−0.960813	−	0.277198i	$-0.910594\pi$
$5$		−	1.23967i		−	0.554397i	0.960813	−	0.277198i	$-0.0894059\pi$
$6$	−0.147954	−	1.72572i	−0.0604021	−	0.704522i
$7$	−1.37235	+	2.37697i	−0.518698	+	0.898412i	0.481065	+	0.876685i	$0.340250\pi$
$7$	−1.37235	+	2.37697i	−0.518698	+	0.898412i	−0.999764	+	0.0217274i	$0.993083\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.95622	−	0.510656i	0.985406	−	0.170219i
$10$	1.23967			0.392018
$11$	−1.41594	−	2.45249i	−0.426923	−	0.739452i	0.569675	−	0.821870i	$-0.307069\pi$
$11$	−1.41594	−	2.45249i	−0.426923	−	0.739452i	−0.996598	+	0.0824179i	$0.973736\pi$
$12$	1.72572	−	0.147954i	0.498172	−	0.0427107i
$13$		−	1.92556i		−	0.534053i	−0.963689	−	0.267027i	$-0.913959\pi$
$13$		−	1.92556i		−	0.534053i	0.963689	−	0.267027i	$-0.0860412\pi$
$14$	−2.37697	−	1.37235i	−0.635273	−	0.366775i
$15$	0.183414	+	2.13932i	0.0473574	+	0.552370i
$16$	1.00000			0.250000
$17$	1.21619	+	0.702166i	0.294969	+	0.170300i	0.640180	−	0.768225i	$-0.278860\pi$
$17$	1.21619	+	0.702166i	0.294969	+	0.170300i	−0.345212	+	0.938525i	$0.612193\pi$
$18$	0.510656	+	2.95622i	0.120363	+	0.696788i
$19$	1.19640	−	0.690743i	0.274474	−	0.158467i	−0.356445	−	0.934316i	$-0.616011\pi$
$19$	1.19640	−	0.690743i	0.274474	−	0.158467i	0.630919	+	0.775849i	$0.282678\pi$
$20$			1.23967i			0.277198i
$21$	2.01660	−	4.30504i	0.440059	−	0.939436i
$22$	2.45249	−	1.41594i	0.522872	−	0.301880i
$23$	2.66127	+	1.53649i	0.554914	+	0.320380i	0.751102	−	0.660187i	$-0.229523\pi$
$23$	2.66127	+	1.53649i	0.554914	+	0.320380i	−0.196188	+	0.980566i	$0.562856\pi$
$24$	0.147954	+	1.72572i	0.0302011	+	0.352261i
$25$	3.46322			0.692645
$26$	1.92556			0.377633
$27$	−5.02605	+	1.31863i	−0.967264	+	0.253771i
$28$	1.37235	−	2.37697i	0.259349	−	0.449206i
$29$	4.11863	−	2.37789i	0.764811	−	0.441564i	−0.0662092	−	0.997806i	$-0.521090\pi$
$29$	4.11863	−	2.37789i	0.764811	−	0.441564i	0.831021	+	0.556242i	$0.187757\pi$
$30$	−2.13932	+	0.183414i	−0.390585	+	0.0334867i
$31$	0.786366	+	0.454008i	0.141235	+	0.0815423i	0.568953	−	0.822370i	$-0.307349\pi$
$31$	0.786366	+	0.454008i	0.141235	+	0.0815423i	−0.427717	+	0.903913i	$0.640682\pi$
$32$			1.00000i			0.176777i
$33$	2.80638	+	4.02281i	0.488528	+	0.700281i
$34$	−0.702166	+	1.21619i	−0.120420	+	0.208574i
$35$	2.94666	+	1.70126i	0.498077	+	0.287565i
$36$	−2.95622	+	0.510656i	−0.492703	+	0.0851093i
$37$	−0.296493	+	6.07553i	−0.0487431	+	0.998811i
$37$	−0.296493	+	6.07553i	−0.0487431	+	0.998811i
$38$	0.690743	+	1.19640i	0.112053	+	0.194082i
$39$	0.284894	+	3.32297i	0.0456196	+	0.532101i
$40$	−1.23967			−0.196009
$41$	11.5645			1.80607			0.903035	−	0.429566i	$-0.141333\pi$
$41$	11.5645			1.80607			0.903035	+	0.429566i	$0.141333\pi$
$42$	4.30504	+	2.01660i	0.664282	+	0.311169i
$43$	3.06264	−	1.76822i	0.467049	−	0.269651i	−0.247955	−	0.968772i	$-0.579758\pi$
$43$	3.06264	−	1.76822i	0.467049	−	0.269651i	0.715003	+	0.699121i	$0.246425\pi$
$44$	1.41594	+	2.45249i	0.213461	+	0.369726i
$45$	−0.633043	−	3.66473i	−0.0943685	−	0.546306i
$46$	−1.53649	+	2.66127i	−0.226543	+	0.392384i
$47$	2.53796	+	4.39587i	0.370199	+	0.641204i	0.989596	−	0.143874i	$-0.0459561\pi$
$47$	2.53796	+	4.39587i	0.370199	+	0.641204i	−0.619397	+	0.785078i	$0.712623\pi$
$48$	−1.72572	+	0.147954i	−0.249086	+	0.0213554i
$49$	−0.266673	−	0.461891i	−0.0380962	−	0.0659845i
$50$			3.46322i			0.489774i
$51$	−2.20269	−	1.03180i	−0.308438	−	0.144481i
$52$			1.92556i			0.267027i
$53$	5.02762	−	8.70809i	0.690596	−	1.19615i	−0.281046	−	0.959694i	$-0.590681\pi$
$53$	5.02762	−	8.70809i	0.690596	−	1.19615i	0.971643	−	0.236454i	$-0.0759852\pi$
$54$	−1.31863	−	5.02605i	−0.179443	−	0.683959i
$55$	−3.04027	+	1.75530i	−0.409950	+	0.236685i
$56$	2.37697	+	1.37235i	0.317637	+	0.183388i
$57$	−1.96246	+	1.36904i	−0.259934	+	0.181334i
$58$	2.37789	+	4.11863i	0.312233	+	0.540803i
$59$	8.82945	−	5.09768i	1.14950	−	0.663662i	0.200732	−	0.979646i	$-0.435668\pi$
$59$	8.82945	−	5.09768i	1.14950	−	0.663662i	0.948764	+	0.315984i	$0.102335\pi$
$60$	−0.183414	−	2.13932i	−0.0236787	−	0.276185i
$61$	−1.91052	−	1.10304i	−0.244618	−	0.141230i	0.372680	−	0.927960i	$-0.378439\pi$
$61$	−1.91052	−	1.10304i	−0.244618	−	0.141230i	−0.617297	+	0.786730i	$0.711772\pi$
$62$	−0.454008	+	0.786366i	−0.0576591	+	0.0998685i
$63$	−2.84314	+	7.72766i	−0.358202	+	0.973593i
$64$	−1.00000			−0.125000
$65$	−2.38705			−0.296077
$66$	−4.02281	+	2.80638i	−0.495173	+	0.345441i
$67$	−12.6497			−1.54541			−0.772705	−	0.634765i	$-0.781097\pi$
$67$	−12.6497			−1.54541			−0.772705	+	0.634765i	$0.781097\pi$
$68$	−1.21619	−	0.702166i	−0.147484	−	0.0851501i
$69$	−4.81994	−	2.25780i	−0.580253	−	0.271807i
$70$	−1.70126	+	2.94666i	−0.203339	+	0.352193i
$71$	0.513569	+	0.889528i	0.0609494	+	0.105568i	0.894890	−	0.446287i	$-0.147254\pi$
$71$	0.513569	+	0.889528i	0.0609494	+	0.105568i	−0.833941	+	0.551854i	$0.813920\pi$
$72$	−0.510656	−	2.95622i	−0.0601813	−	0.348394i
$73$	−2.71210			−0.317427			−0.158714	−	0.987325i	$-0.550735\pi$
$73$	−2.71210			−0.317427			−0.158714	+	0.987325i	$0.550735\pi$
$74$	−6.07553	−	0.296493i	−0.706266	−	0.0344666i
$75$	−5.97655	+	0.512399i	−0.690113	+	0.0591667i
$76$	−1.19640	+	0.690743i	−0.137237	+	0.0792337i
$77$	7.77266			0.885777
$78$	−3.32297	+	0.284894i	−0.376252	+	0.0322579i
$79$	1.95960	+	1.13138i	0.220473	+	0.127290i	0.606169	−	0.795336i	$-0.292705\pi$
$79$	1.95960	+	1.13138i	0.220473	+	0.127290i	−0.385696	+	0.922626i	$0.626039\pi$
$80$		−	1.23967i		−	0.138599i
$81$	8.47846	−	3.01922i	0.942051	−	0.335469i
$82$			11.5645i			1.27708i
$83$	3.44726			0.378386			0.189193	−	0.981940i	$-0.439413\pi$
$83$	3.44726			0.378386			0.189193	+	0.981940i	$0.439413\pi$
$84$	−2.01660	+	4.30504i	−0.220029	+	0.469718i
$85$	0.870453	−	1.50767i	0.0944139	−	0.163530i
$86$	1.76822	+	3.06264i	0.190672	+	0.330253i
$87$	−6.75579	+	4.71295i	−0.724297	+	0.505281i
$88$	−2.45249	+	1.41594i	−0.261436	+	0.150940i
$89$	−6.58592	−	3.80239i	−0.698107	−	0.403052i	0.108535	−	0.994093i	$-0.465384\pi$
$89$	−6.58592	−	3.80239i	−0.698107	−	0.403052i	−0.806642	+	0.591041i	$0.798717\pi$
$90$	3.66473	−	0.633043i	0.386297	−	0.0667286i
$91$	4.57700	+	2.64253i	0.479800	+	0.277013i
$92$	−2.66127	−	1.53649i	−0.277457	−	0.160190i
$93$	−1.42422	−	0.667145i	−0.147685	−	0.0691797i
$94$	−4.39587	+	2.53796i	−0.453399	+	0.261770i
$95$	−0.856293	−	1.48314i	−0.0878538	−	0.152167i
$96$	−0.147954	−	1.72572i	−0.0151005	−	0.176131i
$97$	−3.60285	+	2.08011i	−0.365814	+	0.211203i	−0.671628	−	0.740888i	$-0.734405\pi$
$97$	−3.60285	+	2.08011i	−0.365814	+	0.211203i	0.305814	+	0.952091i	$0.401071\pi$
$98$	0.461891	−	0.266673i	0.0466581	−	0.0269380i
$99$	−5.43821	−	6.52703i	−0.546561	−	0.655991i
$100$	−3.46322			−0.346322
$101$	−7.80416	−	13.5172i	−0.776543	−	1.34501i	−0.933923	−	0.357474i	$-0.883638\pi$
$101$	−7.80416	−	13.5172i	−0.776543	−	1.34501i	0.157380	−	0.987538i	$-0.449695\pi$
$102$	1.03180	−	2.20269i	0.102164	−	0.218098i
$103$	−5.43389	−	3.13726i	−0.535417	−	0.309123i	0.207802	−	0.978171i	$-0.433369\pi$
$103$	−5.43389	−	3.13726i	−0.535417	−	0.309123i	−0.743220	+	0.669048i	$0.766702\pi$
$104$	−1.92556			−0.188816
$105$	−5.33682	−	2.49992i	−0.520820	−	0.243967i
$106$	8.70809	+	5.02762i	0.845804	+	0.488325i
$107$	5.52174	+	9.56393i	0.533806	+	0.924580i	0.999220	+	0.0394865i	$0.0125722\pi$
$107$	5.52174	+	9.56393i	0.533806	+	0.924580i	−0.465414	+	0.885093i	$0.654094\pi$
$108$	5.02605	−	1.31863i	0.483632	−	0.126886i
$109$	2.86780	+	1.65572i	0.274685	+	0.158590i	0.631015	−	0.775771i	$-0.282639\pi$
$109$	2.86780	+	1.65572i	0.274685	+	0.158590i	−0.356330	+	0.934360i	$0.615972\pi$
$110$	−1.75530	−	3.04027i	−0.167361	−	0.289878i
$111$	−0.387238	−	10.5285i	−0.0367550	−	0.999324i
$112$	−1.37235	+	2.37697i	−0.129675	+	0.224603i
$113$	13.5571	−	7.82717i	1.27534	−	0.736318i	0.299353	−	0.954142i	$-0.403229\pi$
$113$	13.5571	−	7.82717i	1.27534	−	0.736318i	0.975988	+	0.217824i	$0.0698959\pi$
$114$	−1.36904	−	1.96246i	−0.128223	−	0.183801i
$115$	1.90473	−	3.29910i	0.177617	−	0.307642i
$116$	−4.11863	+	2.37789i	−0.382406	+	0.220782i
$117$	−0.983296	−	5.69237i	−0.0909057	−	0.526259i
$118$	5.09768	+	8.82945i	0.469280	+	0.812817i
$119$	−3.33806	+	1.92723i	−0.306000	+	0.176669i
$120$	2.13932	−	0.183414i	0.195292	−	0.0167434i
$121$	1.49021	−	2.58112i	0.135474	−	0.234647i
$122$	1.10304	−	1.91052i	0.0998647	−	0.172971i
$123$	−19.9571	+	1.71102i	−1.79947	+	0.154277i
$124$	−0.786366	−	0.454008i	−0.0706177	−	0.0407712i
$125$		−	10.4916i		−	0.938396i
$126$	−7.72766	−	2.84314i	−0.688434	−	0.253287i
$127$	4.12507	−	7.14483i	0.366040	−	0.634001i	−0.622902	−	0.782300i	$-0.714046\pi$
$127$	4.12507	−	7.14483i	0.366040	−	0.634001i	0.988943	+	0.148299i	$0.0473798\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.02365	+	3.50458i	−0.442308	+	0.308561i
$130$		−	2.38705i		−	0.209358i
$131$	8.47605	−	4.89365i	0.740556	−	0.427560i	−0.0817152	−	0.996656i	$-0.526040\pi$
$131$	8.47605	−	4.89365i	0.740556	−	0.427560i	0.822272	+	0.569095i	$0.192706\pi$
$132$	−2.80638	−	4.02281i	−0.244264	−	0.350141i
$133$			3.79176i			0.328787i
$134$		−	12.6497i		−	1.09277i
$135$	1.63467	+	6.23064i	0.140690	+	0.536248i
$136$	0.702166	−	1.21619i	0.0602102	−	0.104287i
$137$	−0.345628	−	0.598646i	−0.0295290	−	0.0511458i	0.850883	−	0.525355i	$-0.176067\pi$
$137$	−0.345628	−	0.598646i	−0.0295290	−	0.0511458i	−0.880412	+	0.474209i	$0.842734\pi$
$138$	2.25780	−	4.81994i	0.192197	−	0.410301i
$139$	−10.3452	−	17.9184i	−0.877466	−	1.51982i	−0.854112	−	0.520089i	$-0.825899\pi$
$139$	−10.3452	−	17.9184i	−0.877466	−	1.51982i	−0.0233543	−	0.999727i	$-0.507435\pi$
$140$	−2.94666	−	1.70126i	−0.249038	−	0.143782i
$141$	−5.03019	−	7.21054i	−0.423619	−	0.607237i
$142$	−0.889528	+	0.513569i	−0.0746475	+	0.0430978i
$143$	−4.72240	+	2.72648i	−0.394907	+	0.228000i
$144$	2.95622	−	0.510656i	0.246352	−	0.0425546i
$145$	−2.94780	−	5.10574i	−0.244802	−	0.424009i
$146$		−	2.71210i		−	0.224455i
$147$	0.528542	+	0.757640i	0.0435934	+	0.0624891i
$148$	0.296493	−	6.07553i	0.0243716	−	0.499406i
$149$	−6.26380	+	10.8492i	−0.513150	+	0.888802i	0.486733	+	0.873551i	$0.338188\pi$
$149$	−6.26380	+	10.8492i	−0.513150	+	0.888802i	−0.999884	+	0.0152518i	$0.995145\pi$
$150$	−0.512399	−	5.97655i	−0.0418372	−	0.487983i
$151$	0.915058	−	1.58493i	0.0744663	−	0.128979i	−0.826388	−	0.563102i	$-0.809608\pi$
$151$	0.915058	−	1.58493i	0.0744663	−	0.128979i	0.900854	+	0.434122i	$0.142941\pi$
$152$	−0.690743	−	1.19640i	−0.0560267	−	0.0970411i
$153$	3.95388	+	1.45470i	0.319652	+	0.117606i
$154$			7.77266i			0.626339i
$155$	0.562820	−	0.974832i	0.0452068	−	0.0783004i
$156$	−0.284894	−	3.32297i	−0.0228098	−	0.266051i
$157$	2.26112	+	3.91637i	0.180457	+	0.312560i	0.942036	−	0.335511i	$-0.108909\pi$
$157$	2.26112	+	3.91637i	0.180457	+	0.312560i	−0.761579	+	0.648072i	$0.775576\pi$
$158$	−1.13138	+	1.95960i	−0.0900076	+	0.155898i
$159$	−7.38786	+	15.7716i	−0.585895	+	1.25077i
$160$	1.23967			0.0980044
$161$	−7.30438	+	4.21719i	−0.575666	+	0.332361i
$162$	3.01922	+	8.47846i	0.237212	+	0.666131i
$163$	12.1660	+	7.02404i	0.952914	+	0.550165i	0.893985	−	0.448097i	$-0.147898\pi$
$163$	12.1660	+	7.02404i	0.952914	+	0.550165i	0.0589293	+	0.998262i	$0.481231\pi$
$164$	−11.5645			−0.903035
$165$	4.98695	−	3.47898i	0.388233	−	0.270838i
$166$			3.44726i			0.267559i
$167$		−	11.0755i		−	0.857047i	−0.903531	−	0.428523i	$-0.859034\pi$
$167$		−	11.0755i		−	0.857047i	0.903531	−	0.428523i	$-0.140966\pi$
$168$	−4.30504	−	2.01660i	−0.332141	−	0.155584i
$169$	9.29223			0.714787
$170$	1.50767	+	0.870453i	0.115633	+	0.0667607i
$171$	3.18410	−	2.65294i	0.243494	−	0.202875i
$172$	−3.06264	+	1.76822i	−0.233524	+	0.134825i
$173$	−6.56979			−0.499492			−0.249746	−	0.968311i	$-0.580347\pi$
$173$	−6.56979			−0.499492			−0.249746	+	0.968311i	$0.580347\pi$
$174$	−4.71295	−	6.75579i	−0.357288	−	0.512155i
$175$	−4.75274	+	8.23199i	−0.359274	+	0.622280i
$176$	−1.41594	−	2.45249i	−0.106731	−	0.184863i
$177$	−14.4829	+	10.1035i	−1.08860	+	0.759428i
$178$	3.80239	−	6.58592i	0.285001	−	0.493636i
$179$		−	0.338286i		−	0.0252847i	−0.999920	−	0.0126424i	$-0.995976\pi$
$179$		−	0.338286i		−	0.0252847i	0.999920	−	0.0126424i	$-0.00402429\pi$
$180$	0.633043	+	3.66473i	0.0471843	+	0.273153i
$181$	−1.25459	−	2.17301i	−0.0932529	−	0.161519i	0.815625	−	0.578581i	$-0.196393\pi$
$181$	−1.25459	−	2.17301i	−0.0932529	−	0.161519i	−0.908878	+	0.417062i	$0.863060\pi$
$182$	−2.64253	+	4.57700i	−0.195877	+	0.339270i
$183$	3.46023	+	1.62087i	0.255788	+	0.119818i
$184$	1.53649	−	2.66127i	0.113271	−	0.196192i
$185$	7.53164	+	0.367553i	0.553738	+	0.0270230i
$186$	0.667145	−	1.42422i	0.0489175	−	0.104429i
$187$		−	3.97691i		−	0.290820i
$188$	−2.53796	−	4.39587i	−0.185100	−	0.320602i
$189$	3.76313	−	13.7564i	0.273727	−	1.00063i
$190$	1.48314	−	0.856293i	0.107598	−	0.0621220i
$191$	9.28198	−	5.35895i	0.671621	−	0.387760i	−0.125070	−	0.992148i	$-0.539915\pi$
$191$	9.28198	−	5.35895i	0.671621	−	0.387760i	0.796690	+	0.604388i	$0.206582\pi$
$192$	1.72572	−	0.147954i	0.124543	−	0.0106777i
$193$	0.763709	+	0.440928i	0.0549730	+	0.0317387i	0.527235	−	0.849720i	$-0.323229\pi$
$193$	0.763709	+	0.440928i	0.0549730	+	0.0317387i	−0.472262	+	0.881458i	$0.656562\pi$
$194$	−2.08011	−	3.60285i	−0.149343	−	0.258670i
$195$	4.11938	−	0.353175i	0.294995	−	0.0252914i
$196$	0.266673	+	0.461891i	0.0190481	+	0.0329922i
$197$	−10.0925	+	17.4808i	−0.719062	+	1.24545i	0.242309	+	0.970199i	$0.422095\pi$
$197$	−10.0925	+	17.4808i	−0.719062	+	1.24545i	−0.961372	+	0.275253i	$0.911238\pi$
$198$	6.52703	−	5.43821i	0.463855	−	0.386477i
$199$			20.7170i			1.46859i	0.678831	+	0.734295i	$0.262487\pi$
$199$			20.7170i			1.46859i	−0.678831	+	0.734295i	$0.737513\pi$
$200$		−	3.46322i		−	0.244887i
$201$	21.8299	−	1.87158i	1.53976	−	0.132011i
$202$	13.5172	−	7.80416i	0.951067	−	0.549099i
$203$			13.0532i			0.916154i
$204$	2.20269	+	1.03180i	0.154219	+	0.0722406i
$205$		−	14.3361i		−	1.00128i
$206$	3.13726	−	5.43389i	0.218583	−	0.378597i
$207$	8.65193	+	3.18320i	0.601350	+	0.221248i
$208$		−	1.92556i		−	0.133513i
$209$	−3.38808	−	1.95611i	−0.234358	−	0.135307i
$210$	2.49992	−	5.33682i	0.172511	−	0.368275i
$211$	−8.79114	+	15.2267i	−0.605207	+	1.04825i	0.386812	+	0.922159i	$0.373576\pi$
$211$	−8.79114	+	15.2267i	−0.605207	+	1.04825i	−0.992019	+	0.126090i	$0.959757\pi$
$212$	−5.02762	+	8.70809i	−0.345298	+	0.598074i
$213$	−1.01789	−	1.45909i	−0.0697444	−	0.0999753i
$214$	−9.56393	+	5.52174i	−0.653777	+	0.377458i
$215$	−2.19200	−	3.79666i	−0.149493	−	0.258930i
$216$	1.31863	+	5.02605i	0.0897217	+	0.341980i
$217$	−2.15833	+	1.24611i	−0.146517	+	0.0845917i
$218$	−1.65572	+	2.86780i	−0.112140	+	0.194232i
$219$	4.68032	−	0.401267i	0.316267	−	0.0271151i
$220$	3.04027	−	1.75530i	0.204975	−	0.118342i
$221$	1.35206	−	2.34184i	0.0909494	−	0.157529i
$222$	10.5285	−	0.387238i	0.706629	−	0.0259897i
$223$	6.17989	+	10.7039i	0.413836	+	0.716786i	0.995306	−	0.0967829i	$-0.0308552\pi$
$223$	6.17989	+	10.7039i	0.413836	+	0.716786i	−0.581469	+	0.813568i	$0.697522\pi$
$224$	−2.37697	−	1.37235i	−0.158818	−	0.0916938i
$225$	10.2380	−	1.76851i	0.682536	−	0.117901i
$226$	7.82717	+	13.5571i	0.520656	+	0.901802i
$227$	22.3018	+	12.8759i	1.48022	+	0.854607i	0.999749	−	0.0224027i	$-0.00713159\pi$
$227$	22.3018	+	12.8759i	1.48022	+	0.854607i	0.480473	+	0.877009i	$0.340465\pi$
$228$	1.96246	−	1.36904i	0.129967	−	0.0906671i
$229$	−18.5077			−1.22302			−0.611511	−	0.791236i	$-0.709438\pi$
$229$	−18.5077			−1.22302			−0.611511	+	0.791236i	$0.709438\pi$
$230$	3.29910	+	1.90473i	0.217536	+	0.125594i
$231$	−13.4134	+	1.15000i	−0.882539	+	0.0756644i
$232$	−2.37789	−	4.11863i	−0.156116	−	0.270402i
$233$	−4.45679			−0.291974			−0.145987	−	0.989287i	$-0.546636\pi$
$233$	−4.45679			−0.291974			−0.145987	+	0.989287i	$0.546636\pi$
$234$	5.69237	−	0.983296i	0.372122	−	0.0642801i
$235$	5.44942	−	3.14623i	0.355481	−	0.205237i
$236$	−8.82945	+	5.09768i	−0.574748	+	0.331831i
$237$	−3.54912	−	1.66251i	−0.230540	−	0.107992i
$238$	−1.92723	−	3.33806i	−0.124924	−	0.216374i
$239$	−9.30764	+	5.37377i	−0.602061	+	0.347600i	−0.769852	−	0.638222i	$-0.779670\pi$
$239$	−9.30764	+	5.37377i	−0.602061	+	0.347600i	0.167791	+	0.985823i	$0.446337\pi$
$240$	0.183414	+	2.13932i	0.0118393	+	0.138093i
$241$	3.29747	+	1.90380i	0.212409	+	0.122634i	0.602430	−	0.798171i	$-0.294199\pi$
$241$	3.29747	+	1.90380i	0.212409	+	0.122634i	−0.390021	+	0.920806i	$0.627532\pi$
$242$	2.58112	+	1.49021i	0.165921	+	0.0957943i
$243$	−14.1847	+	6.46475i	−0.909952	+	0.414714i
$244$	1.91052	+	1.10304i	0.122309	+	0.0706150i
$245$	−0.572592	+	0.330586i	−0.0365816	+	0.0211204i
$246$	−1.71102	−	19.9571i	−0.109090	−	1.27242i
$247$	−1.33007	−	2.30374i	−0.0846300	−	0.146583i
$248$	0.454008	−	0.786366i	0.0288296	−	0.0499343i
$249$	−5.94901	+	0.510037i	−0.377003	+	0.0323223i
$250$	10.4916			0.663546
$251$		−	10.4606i		−	0.660265i	−0.943935	−	0.330133i	$-0.892907\pi$
$251$		−	10.4606i		−	0.660265i	0.943935	−	0.330133i	$-0.107093\pi$
$252$	2.84314	−	7.72766i	0.179101	−	0.486797i
$253$		−	8.70232i		−	0.547110i
$254$	7.14483	+	4.12507i	0.448306	+	0.258830i
$255$	−1.27909	+	2.73060i	−0.0800998	+	0.170997i
$256$	1.00000			0.0625000
$257$	−20.8579	+	12.0423i	−1.30108	+	0.751179i	−0.980589	−	0.196073i	$-0.937181\pi$
$257$	−20.8579	+	12.0423i	−1.30108	+	0.751179i	−0.320490	+	0.947252i	$0.603848\pi$
$258$	−3.50458	−	5.02365i	−0.218186	−	0.312759i
$259$	−14.0345	−	9.04249i	−0.872061	−	0.561873i
$260$	2.38705			0.148039
$261$	10.9613	−	9.13278i	0.678488	−	0.565305i
$262$	4.89365	+	8.47605i	0.302331	+	0.523652i
$263$	0.255569	−	0.442658i	0.0157591	−	0.0272955i	−0.858038	−	0.513586i	$-0.828317\pi$
$263$	0.255569	−	0.442658i	0.0157591	−	0.0272955i	0.873797	+	0.486290i	$0.161650\pi$
$264$	4.02281	−	2.80638i	0.247587	−	0.172721i
$265$	−10.7951	−	6.23258i	−0.663140	−	0.382864i
$266$	−3.79176			−0.232488
$267$	11.9280	+	5.58744i	0.729984	+	0.341946i
$268$	12.6497			0.772705
$269$	−5.35280			−0.326366			−0.163183	−	0.986596i	$-0.552176\pi$
$269$	−5.35280			−0.326366			−0.163183	+	0.986596i	$0.552176\pi$
$270$	−6.23064	+	1.63467i	−0.379185	+	0.0994828i
$271$	−10.0119	+	17.3411i	−0.608180	+	1.05340i	0.383361	+	0.923599i	$0.374767\pi$
$271$	−10.0119	+	17.3411i	−0.608180	+	1.05340i	−0.991540	+	0.129799i	$0.958567\pi$
$272$	1.21619	+	0.702166i	0.0737422	+	0.0425751i
$273$	−8.28959	−	3.88308i	−0.501709	−	0.235015i
$274$	0.598646	−	0.345628i	0.0361655	−	0.0208802i
$275$	−4.90373	−	8.49350i	−0.295706	−	0.512178i
$276$	4.81994	+	2.25780i	0.290127	+	0.135904i
$277$	25.2127	+	14.5566i	1.51488	+	0.874618i	0.999848	+	0.0174499i	$0.00555474\pi$
$277$	25.2127	+	14.5566i	1.51488	+	0.874618i	0.515036	+	0.857169i	$0.327779\pi$
$278$	17.9184	−	10.3452i	1.07467	−	0.620462i
$279$	2.55651	+	0.940586i	0.153054	+	0.0563114i
$280$	1.70126	−	2.94666i	0.101669	−	0.176097i
$281$		−	14.5855i		−	0.870098i	−0.900407	−	0.435049i	$-0.856731\pi$
$281$		−	14.5855i		−	0.870098i	0.900407	−	0.435049i	$-0.143269\pi$
$282$	7.21054	−	5.03019i	0.429381	−	0.299544i
$283$		−	10.7407i		−	0.638470i	−0.947676	−	0.319235i	$-0.896574\pi$
$283$		−	10.7407i		−	0.638470i	0.947676	−	0.319235i	$-0.103426\pi$
$284$	−0.513569	−	0.889528i	−0.0304747	−	0.0527838i
$285$	1.69716	+	2.43280i	0.100531	+	0.144106i
$286$	−2.72648	−	4.72240i	−0.161220	−	0.279241i
$287$	−15.8705	+	27.4885i	−0.936806	+	1.62260i
$288$	0.510656	+	2.95622i	0.0300907	+	0.174197i
$289$	−7.51393	−	13.0145i	−0.441996	−	0.765559i
$290$	5.10574	−	2.94780i	0.299819	−	0.173101i
$291$	5.90975	−	4.12274i	0.346436	−	0.241679i
$292$	2.71210			0.158714
$293$	−12.1222			−0.708186			−0.354093	−	0.935210i	$-0.615210\pi$
$293$	−12.1222			−0.708186			−0.354093	+	0.935210i	$0.615210\pi$
$294$	−0.757640	+	0.528542i	−0.0441864	+	0.0308252i
$295$	−6.31944	−	10.9456i	−0.367932	−	0.637277i
$296$	6.07553	+	0.296493i	0.353133	+	0.0172333i
$297$	10.3505	+	10.4592i	0.600599	+	0.606905i
$298$	−10.8492	−	6.26380i	−0.628478	−	0.362852i
$299$	2.95859	−	5.12443i	0.171100	−	0.296354i
$300$	5.97655	−	0.512399i	0.345056	−	0.0295834i
$301$			9.70643i			0.559469i
$302$	1.58493	+	0.915058i	0.0912023	+	0.0526557i
$303$	15.4677	+	22.1722i	0.888598	+	1.27376i
$304$	1.19640	−	0.690743i	0.0686184	−	0.0396169i
$305$	−1.36741	+	2.36842i	−0.0782975	+	0.135615i
$306$	−1.45470	+	3.95388i	−0.0831599	+	0.226028i
$307$	−11.1732			−0.637687			−0.318844	−	0.947807i	$-0.603294\pi$
$307$	−11.1732			−0.637687			−0.318844	+	0.947807i	$0.603294\pi$
$308$	−7.77266			−0.442889
$309$	9.84154	+	4.61006i	0.559866	+	0.262257i
$310$	0.974832	+	0.562820i	0.0553668	+	0.0319660i
$311$	0.317602	−	0.183368i	0.0180096	−	0.0103978i	−0.490968	−	0.871178i	$-0.663357\pi$
$311$	0.317602	−	0.183368i	0.0180096	−	0.0103978i	0.508978	+	0.860780i	$0.330024\pi$
$312$	3.32297	−	0.284894i	0.188126	−	0.0161290i
$313$			4.96407i			0.280586i	0.990110	+	0.140293i	$0.0448044\pi$
$313$			4.96407i			0.280586i	−0.990110	+	0.140293i	$0.955196\pi$
$314$	−3.91637	+	2.26112i	−0.221013	+	0.127602i
$315$	9.57973	+	3.52455i	0.539757	+	0.198586i
$316$	−1.95960	−	1.13138i	−0.110236	−	0.0636450i
$317$	29.3389			1.64784			0.823918	−	0.566709i	$-0.191783\pi$
$317$	29.3389			1.64784			0.823918	+	0.566709i	$0.191783\pi$
$318$	−15.7716	−	7.38786i	−0.884426	−	0.414291i
$319$	−11.6635	−	6.73393i	−0.653031	−	0.377028i
$320$			1.23967i			0.0692996i
$321$	−10.9440	−	15.6877i	−0.610834	−	0.875602i
$322$	−4.21719	−	7.30438i	−0.235015	−	0.407057i
$323$	1.94007			0.107948
$324$	−8.47846	+	3.01922i	−0.471026	+	0.167734i
$325$		−	6.66863i		−	0.369909i
$326$	−7.02404	+	12.1660i	−0.389026	+	0.673812i
$327$	−5.19399	−	2.43301i	−0.287228	−	0.134546i
$328$		−	11.5645i		−	0.638542i
$329$	−13.9318			−0.768087
$330$	3.47898	+	4.98695i	0.191511	+	0.274522i
$331$			24.8511i			1.36594i	0.730447	+	0.682970i	$0.239312\pi$
$331$			24.8511i			1.36594i	−0.730447	+	0.682970i	$0.760688\pi$
$332$	−3.44726			−0.189193
$333$	2.22601	+	18.1120i	0.121984	+	0.992532i
$334$	11.0755			0.606024
$335$			15.6815i			0.856770i
$336$	2.01660	−	4.30504i	0.110015	−	0.234859i
$337$	17.3542			0.945342			0.472671	−	0.881239i	$-0.343290\pi$
$337$	17.3542			0.945342			0.472671	+	0.881239i	$0.343290\pi$
$338$			9.29223i			0.505431i
$339$	−22.2376	+	15.5133i	−1.20778	+	0.842569i
$340$	−0.870453	+	1.50767i	−0.0472069	+	0.0817648i
$341$		−	2.57140i		−	0.139249i
$342$	2.65294	+	3.18410i	0.143454	+	0.172176i
$343$	−17.7490			−0.958355
$344$	−1.76822	−	3.06264i	−0.0953359	−	0.165127i
$345$	−2.79892	+	5.97513i	−0.150689	+	0.321690i
$346$		−	6.56979i		−	0.353194i
$347$	2.29310	+	1.32392i	0.123100	+	0.0710717i	0.560286	−	0.828300i	$-0.310691\pi$
$347$	2.29310	+	1.32392i	0.123100	+	0.0710717i	−0.437186	+	0.899371i	$0.644025\pi$
$348$	6.75579	−	4.71295i	0.362148	−	0.252641i
$349$	29.5645			1.58255			0.791274	−	0.611461i	$-0.209418\pi$
$349$	29.5645			1.58255			0.791274	+	0.611461i	$0.209418\pi$
$350$	−8.23199	−	4.75274i	−0.440019	−	0.254045i
$351$	2.53910	+	9.67795i	0.135527	+	0.516571i
$352$	2.45249	−	1.41594i	0.130718	−	0.0754700i
$353$			31.4380i			1.67327i	0.547757	+	0.836637i	$0.315482\pi$
$353$			31.4380i			1.67327i	−0.547757	+	0.836637i	$0.684518\pi$
$354$	−10.1035	−	14.4829i	−0.536997	−	0.769759i
$355$	1.10272	−	0.636655i	0.0585263	−	0.0337902i
$356$	6.58592	+	3.80239i	0.349053	+	0.201526i
$357$	5.47542	−	3.81974i	0.289790	−	0.202162i
$358$	0.338286			0.0178790
$359$	−1.58279			−0.0835365			−0.0417683	−	0.999127i	$-0.513299\pi$
$359$	−1.58279			−0.0835365			−0.0417683	+	0.999127i	$0.513299\pi$
$360$	−3.66473	+	0.633043i	−0.193148	+	0.0333643i
$361$	−8.54575	+	14.8017i	−0.449776	+	0.779035i
$362$	2.17301	−	1.25459i	0.114211	−	0.0659398i
$363$	−2.18980	+	4.67477i	−0.114935	+	0.245362i
$364$	−4.57700	−	2.64253i	−0.239900	−	0.138506i
$365$			3.36210i			0.175981i
$366$	−1.62087	+	3.46023i	−0.0847243	+	0.180869i
$367$	7.29522	−	12.6357i	0.380808	−	0.659578i	−0.610370	−	0.792116i	$-0.708979\pi$
$367$	7.29522	−	12.6357i	0.380808	−	0.659578i	0.991178	+	0.132538i	$0.0423127\pi$
$368$	2.66127	+	1.53649i	0.138729	+	0.0800949i
$369$	34.1872	−	5.90547i	1.77971	−	0.307427i
$370$	−0.367553	+	7.53164i	−0.0191082	+	0.391552i
$371$	13.7993	+	23.9010i	0.716422	+	1.24088i
$372$	1.42422	+	0.667145i	0.0738423	+	0.0345899i
$373$	14.4684			0.749144			0.374572	−	0.927198i	$-0.377790\pi$
$373$	14.4684			0.749144			0.374572	+	0.927198i	$0.377790\pi$
$374$	3.97691			0.205641
$375$	1.55228	+	18.1055i	0.0801592	+	0.934966i
$376$	4.39587	−	2.53796i	0.226700	−	0.130885i
$377$	−4.57877	−	7.93066i	−0.235819	−	0.408450i
$378$	13.7564	+	3.76313i	0.707554	+	0.193554i
$379$	13.6059	−	23.5661i	0.698889	−	1.21051i	−0.269963	−	0.962871i	$-0.587012\pi$
$379$	13.6059	−	23.5661i	0.698889	−	1.21051i	0.968852	−	0.247640i	$-0.0796551\pi$
$380$	0.856293	+	1.48314i	0.0439269	+	0.0760836i
$381$	−6.06160	+	12.9403i	−0.310545	+	0.662951i
$382$	5.35895	+	9.28198i	0.274188	+	0.474908i
$383$		−	14.7601i		−	0.754205i	−0.926172	−	0.377103i	$-0.876920\pi$
$383$		−	14.7601i		−	0.754205i	0.926172	−	0.377103i	$-0.123080\pi$
$384$	0.147954	+	1.72572i	0.00755026	+	0.0880653i
$385$		−	9.63552i		−	0.491072i
$386$	−0.440928	+	0.763709i	−0.0224426	+	0.0388718i
$387$	8.15089	−	6.79119i	0.414333	−	0.345216i
$388$	3.60285	−	2.08011i	0.182907	−	0.105601i
$389$	−15.9183	−	9.19046i	−0.807092	−	0.465975i	0.0388531	−	0.999245i	$-0.487630\pi$
$389$	−15.9183	−	9.19046i	−0.807092	−	0.465975i	−0.845945	+	0.533270i	$0.820963\pi$
$390$	0.353175	+	4.11938i	0.0178837	+	0.208593i
$391$	2.15774	+	3.73731i	0.109122	+	0.189004i
$392$	−0.461891	+	0.266673i	−0.0233290	+	0.0134690i
$393$	−13.9033	+	9.69914i	−0.701327	+	0.489257i
$394$	−17.4808	−	10.0925i	−0.880668	−	0.508454i
$395$	1.40253	−	2.42926i	0.0705691	−	0.122229i
$396$	5.43821	+	6.52703i	0.273281	+	0.327995i
$397$	−5.51580			−0.276830			−0.138415	−	0.990374i	$-0.544201\pi$
$397$	−5.51580			−0.276830			−0.138415	+	0.990374i	$0.544201\pi$
$398$	−20.7170			−1.03845
$399$	−0.561007	−	6.54351i	−0.0280855	−	0.327585i
$400$	3.46322			0.173161
$401$	−9.38853	−	5.42047i	−0.468841	−	0.270686i	0.246913	−	0.969038i	$-0.420584\pi$
$401$	−9.38853	−	5.42047i	−0.468841	−	0.270686i	−0.715754	+	0.698352i	$0.753917\pi$
$402$	1.87158	+	21.8299i	0.0933461	+	1.08878i
$403$	0.874219	−	1.51419i	0.0435479	−	0.0754272i
$404$	7.80416	+	13.5172i	0.388272	+	0.672506i
$405$	−3.74283	−	10.5105i	−0.185983	−	0.522270i
$406$	−13.0532			−0.647819
$407$	15.3200	−	7.87546i	0.759383	−	0.390372i
$408$	−1.03180	+	2.20269i	−0.0510818	+	0.109049i
$409$	−4.80418	+	2.77369i	−0.237551	+	0.137150i	−0.614051	−	0.789266i	$-0.710461\pi$
$409$	−4.80418	+	2.77369i	−0.237551	+	0.137150i	0.376499	+	0.926417i	$0.377128\pi$
$410$	14.3361			0.708011
$411$	0.685030	+	0.981958i	0.0337900	+	0.0484364i
$412$	5.43389	+	3.13726i	0.267709	+	0.154562i
$413$			27.9832i			1.37696i
$414$	−3.18320	+	8.65193i	−0.156446	+	0.425219i
$415$		−	4.27346i		−	0.209776i
$416$	1.92556			0.0944082
$417$	20.5040	+	29.3915i	1.00408	+	1.43931i
$418$	1.95611	−	3.38808i	0.0956763	−	0.165716i
$419$	−3.14900	−	5.45422i	−0.153839	−	0.266456i	0.778797	−	0.627276i	$-0.215830\pi$
$419$	−3.14900	−	5.45422i	−0.153839	−	0.266456i	−0.932636	+	0.360820i	$0.882497\pi$
$420$	5.33682	+	2.49992i	0.260410	+	0.121984i
$421$	29.7804	−	17.1937i	1.45141	−	0.837972i	0.452848	−	0.891588i	$-0.350408\pi$
$421$	29.7804	−	17.1937i	1.45141	−	0.837972i	0.998562	+	0.0536160i	$0.0170747\pi$
$422$	−15.2267	−	8.79114i	−0.741224	−	0.427946i
$423$	9.74753	+	11.6991i	0.473941	+	0.568831i
$424$	−8.70809	−	5.02762i	−0.422902	−	0.244163i
$425$	4.21193	+	2.43176i	0.204308	+	0.117958i
$426$	1.45909	−	1.01789i	0.0706932	−	0.0493167i
$427$	5.24381	−	3.02751i	0.253766	−	0.146512i
$428$	−5.52174	−	9.56393i	−0.266903	−	0.462290i
$429$	7.74614	−	5.40384i	0.373987	−	0.260900i
$430$	3.79666	−	2.19200i	0.183091	−	0.105708i
$431$	20.9067	−	12.0705i	1.00704	−	0.581416i	0.0967181	−	0.995312i	$-0.469165\pi$
$431$	20.9067	−	12.0705i	1.00704	−	0.581416i	0.910324	+	0.413896i	$0.135832\pi$
$432$	−5.02605	+	1.31863i	−0.241816	+	0.0634428i
$433$	−17.3086			−0.831800			−0.415900	−	0.909410i	$-0.636533\pi$
$433$	−17.3086			−0.831800			−0.415900	+	0.909410i	$0.636533\pi$
$434$	−1.24611	−	2.15833i	−0.0598154	−	0.103603i
$435$	5.84250	+	8.37494i	0.280126	+	0.401548i
$436$	−2.86780	−	1.65572i	−0.137343	−	0.0792948i
$437$	4.24527			0.203079
$438$	0.401267	+	4.68032i	0.0191733	+	0.223635i
$439$	−7.50670	−	4.33400i	−0.358275	−	0.206850i	0.310049	−	0.950721i	$-0.399655\pi$
$439$	−7.50670	−	4.33400i	−0.358275	−	0.206850i	−0.668324	+	0.743870i	$0.732988\pi$
$440$	1.75530	+	3.04027i	0.0836806	+	0.144939i
$441$	−1.02421	−	1.22927i	−0.0487720	−	0.0585368i
$442$	2.34184	+	1.35206i	0.111390	+	0.0643109i
$443$	5.95484	+	10.3141i	0.282923	+	0.490037i	0.972103	−	0.234553i	$-0.0753626\pi$
$443$	5.95484	+	10.3141i	0.282923	+	0.490037i	−0.689180	+	0.724590i	$0.742029\pi$
$444$	0.387238	+	10.5285i	0.0183775	+	0.499662i
$445$	−4.71370	+	8.16436i	−0.223451	+	0.387028i
$446$	−10.7039	+	6.17989i	−0.506844	+	0.292626i
$447$	9.20437	−	19.6495i	0.435352	−	0.929388i
$448$	1.37235	−	2.37697i	0.0648373	−	0.112302i
$449$	8.54656	−	4.93436i	0.403337	−	0.232867i	−0.284586	−	0.958651i	$-0.591856\pi$
$449$	8.54656	−	4.93436i	0.403337	−	0.232867i	0.687923	+	0.725784i	$0.258523\pi$
$450$	1.76851	+	10.2380i	0.0833685	+	0.482626i
$451$	−16.3747	−	28.3618i	−0.771053	−	1.33550i
$452$	−13.5571	+	7.82717i	−0.637670	+	0.368159i
$453$	−1.34464	+	2.87053i	−0.0631765	+	0.134869i
$454$	−12.8759	+	22.3018i	−0.604298	+	1.04668i
$455$	3.27586	−	5.67396i	0.153575	−	0.265999i
$456$	1.36904	+	1.96246i	0.0641113	+	0.0919005i
$457$	−4.59817	−	2.65476i	−0.215093	−	0.124184i	0.388583	−	0.921414i	$-0.372965\pi$
$457$	−4.59817	−	2.65476i	−0.215093	−	0.124184i	−0.603676	+	0.797230i	$0.706298\pi$
$458$		−	18.5077i		−	0.864807i
$459$	−7.03852	−	1.92542i	−0.328530	−	0.0898708i
$460$	−1.90473	+	3.29910i	−0.0888087	+	0.153821i
$461$		−	12.6167i		−	0.587620i	−0.955864	−	0.293810i	$-0.905077\pi$
$461$		−	12.6167i		−	0.587620i	0.955864	−	0.293810i	$-0.0949233\pi$
$462$	−1.15000	−	13.4134i	−0.0535028	−	0.624050i
$463$		−	37.8028i		−	1.75684i	−0.477885	−	0.878422i	$-0.658596\pi$
$463$		−	37.8028i		−	1.75684i	0.477885	−	0.878422i	$-0.341404\pi$
$464$	4.11863	−	2.37789i	0.191203	−	0.110391i
$465$	−0.827039	+	1.76556i	−0.0383530	+	0.0818759i
$466$		−	4.45679i		−	0.206457i
$467$		−	22.3889i		−	1.03603i	−0.855370	−	0.518017i	$-0.826670\pi$
$467$		−	22.3889i		−	1.03603i	0.855370	−	0.518017i	$-0.173330\pi$
$468$	0.983296	+	5.69237i	0.0454529	+	0.263130i
$469$	17.3598	−	30.0681i	0.801602	−	1.38842i
$470$	3.14623	+	5.44942i	0.145125	+	0.251363i
$471$	−4.48150	−	6.42401i	−0.206496	−	0.296003i
$472$	−5.09768	−	8.82945i	−0.234640	−	0.406408i
$473$	−8.67305	−	5.00739i	−0.398787	−	0.230240i
$474$	1.66251	−	3.54912i	0.0763616	−	0.163017i
$475$	4.14341	−	2.39220i	0.190113	−	0.109762i
$476$	3.33806	−	1.92723i	0.153000	−	0.0883345i
$477$	10.4159	−	28.3104i	0.476911	−	1.29624i
$478$	−5.37377	−	9.30764i	−0.245791	−	0.425722i
$479$			13.3122i			0.608249i	0.952632	+	0.304124i	$0.0983639\pi$
$479$			13.3122i			0.608249i	−0.952632	+	0.304124i	$0.901636\pi$
$480$	−2.13932	+	0.183414i	−0.0976462	+	0.00837168i
$481$	11.6988	+	0.570914i	0.533418	+	0.0260314i
$482$	−1.90380	+	3.29747i	−0.0867156	+	0.150196i
$483$	11.9814	−	8.35840i	0.545171	−	0.380320i
$484$	−1.49021	+	2.58112i	−0.0677368	+	0.117324i
$485$	2.57864	+	4.46634i	0.117090	+	0.202806i
$486$	−6.46475	−	14.1847i	−0.293247	−	0.643433i
$487$			40.6102i			1.84022i	0.391656	+	0.920112i	$0.371902\pi$
$487$			40.6102i			1.84022i	−0.391656	+	0.920112i	$0.628098\pi$
$488$	−1.10304	+	1.91052i	−0.0499324	+	0.0864854i
$489$	−22.0343	−	10.3215i	−0.996427	−	0.466755i
$490$	−0.330586	−	0.572592i	−0.0149344	−	0.0258671i
$491$	−2.21150	+	3.83043i	−0.0998037	+	0.172865i	−0.911603	−	0.411071i	$-0.865155\pi$
$491$	−2.21150	+	3.83043i	−0.0998037	+	0.172865i	0.811800	+	0.583936i	$0.198488\pi$
$492$	19.9571	−	1.71102i	0.899735	−	0.0771386i
$493$	6.67871			0.300794
$494$	2.30374	−	1.33007i	0.103650	−	0.0598425i
$495$	−8.09135	+	6.74158i	−0.363679	+	0.303012i
$496$	0.786366	+	0.454008i	0.0353089	+	0.0203856i
$497$	−2.81918			−0.126457
$498$	−0.510037	−	5.94901i	−0.0228553	−	0.266581i
$499$		−	18.9262i		−	0.847254i	−0.905837	−	0.423627i	$-0.860757\pi$
$499$		−	18.9262i		−	0.847254i	0.905837	−	0.423627i	$-0.139243\pi$
$500$			10.4916i			0.469198i
$501$	1.63867	+	19.1132i	0.0732102	+	0.853914i
$502$	10.4606			0.466878
$503$	−19.8574	−	11.4647i	−0.885397	−	0.511184i	−0.0129626	−	0.999916i	$-0.504126\pi$
$503$	−19.8574	−	11.4647i	−0.885397	−	0.511184i	−0.872434	+	0.488732i	$0.837460\pi$
$504$	7.72766	+	2.84314i	0.344217	+	0.126644i
$505$	−16.7568	+	9.67457i	−0.745670	+	0.430513i
$506$	8.70232			0.386865
$507$	−16.0358	+	1.37483i	−0.712175	+	0.0610582i
$508$	−4.12507	+	7.14483i	−0.183020	+	0.317000i
$509$	1.33663	+	2.31511i	0.0592450	+	0.102615i	0.894127	−	0.447814i	$-0.147797\pi$
$509$	1.33663	+	2.31511i	0.0592450	+	0.102615i	−0.834882	+	0.550429i	$0.814464\pi$
$510$	−2.73060	−	1.27909i	−0.120913	−	0.0566391i
$511$	3.72194	−	6.44659i	0.164649	−	0.285180i
$512$			1.00000i			0.0441942i
$513$	−5.10234	+	5.04933i	−0.225274	+	0.222933i
$514$	−12.0423	−	20.8579i	−0.531164	−	0.920002i
$515$	−3.88916	+	6.73622i	−0.171377	+	0.296833i
$516$	5.02365	−	3.50458i	0.221154	−	0.154280i
$517$	7.18721	−	12.4486i	0.316093	−	0.547489i
$518$	9.04249	−	14.0345i	0.397304	−	0.616640i
$519$	11.3376	−	0.972029i	0.497666	−	0.0426674i
$520$			2.38705i			0.104679i
$521$	18.0698	+	31.2978i	0.791653	+	1.37118i	0.924943	+	0.380106i	$0.124112\pi$
$521$	18.0698	+	31.2978i	0.791653	+	1.37118i	−0.133290	+	0.991077i	$0.542554\pi$
$522$	9.13278	+	10.9613i	0.399731	+	0.479763i
$523$	5.60689	−	3.23714i	0.245172	−	0.141550i	−0.372379	−	0.928081i	$-0.621458\pi$
$523$	5.60689	−	3.23714i	0.245172	−	0.141550i	0.617552	+	0.786530i	$0.288125\pi$
$524$	−8.47605	+	4.89365i	−0.370278	+	0.213780i
$525$	6.98395	−	14.9093i	0.304804	−	0.650695i
$526$	0.442658	+	0.255569i	0.0193008	+	0.0111433i
$527$	0.637578	+	1.10432i	0.0277734	+	0.0481049i
$528$	2.80638	+	4.02281i	0.122132	+	0.175070i
$529$	−6.77841	−	11.7406i	−0.294714	−	0.510459i
$530$	6.23258	−	10.7951i	0.270726	−	0.468911i
$531$	23.4986	−	19.5787i	1.01975	−	0.849642i
$532$		−	3.79176i		−	0.164394i
$533$		−	22.2681i		−	0.964538i
$534$	−5.58744	+	11.9280i	−0.241792	+	0.516177i
$535$	11.8561	−	6.84512i	0.512584	−	0.295940i
$536$			12.6497i			0.546385i
$537$	0.0500509	+	0.583787i	0.00215986	+	0.0251923i
$538$		−	5.35280i		−	0.230776i
$539$	−0.755188	+	1.30802i	−0.0325282	+	0.0563406i
$540$	−1.63467	−	6.23064i	−0.0703449	−	0.268124i
$541$			43.5596i			1.87277i	0.350972	+	0.936386i	$0.385851\pi$
$541$			43.5596i			1.87277i	−0.350972	+	0.936386i	$0.614149\pi$
$542$	−17.3411	−	10.0119i	−0.744865	−	0.430048i
$543$	2.48658	+	3.56439i	0.106709	+	0.152963i
$544$	−0.702166	+	1.21619i	−0.0301051	+	0.0521436i
$545$	2.05255	−	3.55512i	0.0879215	−	0.152285i
$546$	3.88308	−	8.28959i	0.166181	−	0.354762i
$547$	−14.6318	+	8.44768i	−0.625611	+	0.361197i	−0.779050	−	0.626961i	$-0.784298\pi$
$547$	−14.6318	+	8.44768i	−0.625611	+	0.361197i	0.153439	+	0.988158i	$0.450965\pi$
$548$	0.345628	+	0.598646i	0.0147645	+	0.0255729i
$549$	−6.21120	−	2.28521i	−0.265088	−	0.0975305i
$550$	8.49350	−	4.90373i	0.362164	−	0.209096i
$551$	3.28503	−	5.68984i	0.139947	−	0.242395i
$552$	−2.25780	+	4.81994i	−0.0960984	+	0.205150i
$553$	−5.37852	+	3.10529i	−0.228718	+	0.132050i
$554$	−14.5566	+	25.2127i	−0.618449	+	1.07118i
$555$	−13.0519	+	0.480046i	−0.554022	+	0.0203768i
$556$	10.3452	+	17.9184i	0.438733	+	0.759908i
$557$	13.6854	+	7.90127i	0.579869	+	0.334787i	0.761081	−	0.648657i	$-0.224669\pi$
$557$	13.6854	+	7.90127i	0.579869	+	0.334787i	−0.181212	+	0.983444i	$0.558002\pi$
$558$	−0.940586	+	2.55651i	−0.0398182	+	0.108226i
$559$	−3.40480	−	5.89729i	−0.144008	−	0.249429i
$560$	2.94666	+	1.70126i	0.124519	+	0.0718912i
$561$	0.588401	+	6.86303i	0.0248423	+	0.289757i
$562$	14.5855			0.615252
$563$	−37.4367	−	21.6141i	−1.57777	−	0.910924i	−0.995170	−	0.0981628i	$-0.968703\pi$
$563$	−37.4367	−	21.6141i	−1.57777	−	0.910924i	−0.582597	−	0.812761i	$-0.697963\pi$
$564$	5.03019	+	7.21054i	0.211809	+	0.303619i
$565$	−9.70310	−	16.8063i	−0.408212	−	0.707045i
$566$	10.7407			0.451467
$567$	−4.45878	+	24.2965i	−0.187251	+	1.02036i
$568$	0.889528	−	0.513569i	0.0373237	−	0.0215489i
$569$	−20.0195	+	11.5582i	−0.839260	+	0.484547i	−0.857013	−	0.515295i	$-0.827682\pi$
$569$	−20.0195	+	11.5582i	−0.839260	+	0.484547i	0.0177527	+	0.999842i	$0.494349\pi$
$570$	−2.43280	+	1.69716i	−0.101899	+	0.0710862i
$571$	6.94137	+	12.0228i	0.290487	+	0.503139i	0.973925	−	0.226870i	$-0.0728493\pi$
$571$	6.94137	+	12.0228i	0.290487	+	0.503139i	−0.683438	+	0.730009i	$0.739516\pi$
$572$	4.72240	−	2.72648i	0.197453	−	0.114000i
$573$	−15.2252	+	10.6214i	−0.636043	+	0.443714i
$574$	−27.4885	−	15.8705i	−1.14735	−	0.662422i
$575$	9.21659	+	5.32120i	0.384358	+	0.221909i
$576$	−2.95622	+	0.510656i	−0.123176	+	0.0212773i
$577$	−6.48754	−	3.74558i	−0.270080	−	0.155931i	0.358844	−	0.933398i	$-0.383171\pi$
$577$	−6.48754	−	3.74558i	−0.270080	−	0.155931i	−0.628924	+	0.777467i	$0.716504\pi$
$578$	13.0145	−	7.51393i	0.541332	−	0.312538i
$579$	−1.38319	−	0.647924i	−0.0574832	−	0.0269268i
$580$	2.94780	+	5.10574i	0.122401	+	0.212004i
$581$	−4.73084	+	8.19405i	−0.196268	+	0.339947i
$582$	4.12274	+	5.90975i	0.170893	+	0.244967i
$583$	−28.4753			−1.17933
$584$			2.71210i			0.112227i
$585$	−7.05665	+	1.21896i	−0.291756	+	0.0503978i
$586$		−	12.1222i		−	0.500763i
$587$	12.8066	+	7.39387i	0.528583	+	0.305177i	0.740439	−	0.672123i	$-0.234618\pi$
$587$	12.8066	+	7.39387i	0.528583	+	0.305177i	−0.211856	+	0.977301i	$0.567951\pi$
$588$	−0.528542	−	0.757640i	−0.0217967	−	0.0312445i
$589$	1.25441			0.0516872
$590$	10.9456	−	6.31944i	0.450623	−	0.260167i
$591$	14.8305	−	31.6601i	0.610046	−	1.30232i
$592$	−0.296493	+	6.07553i	−0.0121858	+	0.249703i
$593$	26.6675			1.09510			0.547552	−	0.836772i	$-0.315560\pi$
$593$	26.6675			1.09510			0.547552	+	0.836772i	$0.315560\pi$
$594$	−10.4592	+	10.3505i	−0.429147	+	0.424688i
$595$	2.38913	+	4.13809i	0.0979446	+	0.169645i
$596$	6.26380	−	10.8492i	0.256575	−	0.444401i
$597$	−3.06517	−	35.7517i	−0.125449	−	1.46322i
$598$	5.12443	+	2.95859i	0.209554	+	0.120986i
$599$	−36.4885			−1.49088			−0.745440	−	0.666573i	$-0.767761\pi$
$599$	−36.4885			−1.49088			−0.745440	+	0.666573i	$0.767761\pi$
$600$	0.512399	+	5.97655i	0.0209186	+	0.243992i
$601$	12.6955			0.517860			0.258930	−	0.965896i	$-0.416630\pi$
$601$	12.6955			0.517860			0.258930	+	0.965896i	$0.416630\pi$
$602$	−9.70643			−0.395605
$603$	−37.3954	+	6.45966i	−1.52286	+	0.263058i
$604$	−0.915058	+	1.58493i	−0.0372332	+	0.0644897i
$605$	−3.19973	−	1.84737i	−0.130088	−	0.0751061i
$606$	−22.1722	+	15.4677i	−0.900686	+	0.628333i
$607$	12.2688	−	7.08342i	0.497977	−	0.287507i	−0.229901	−	0.973214i	$-0.573840\pi$
$607$	12.2688	−	7.08342i	0.497977	−	0.287507i	0.727878	+	0.685707i	$0.240507\pi$
$608$	0.690743	+	1.19640i	0.0280133	+	0.0485205i
$609$	−1.93128	−	22.5261i	−0.0782592	−	0.912806i
$610$	−2.36842	−	1.36741i	−0.0958944	−	0.0553647i
$611$	8.46450	−	4.88698i	0.342437	−	0.197706i
$612$	−3.95388	−	1.45470i	−0.159826	−	0.0588029i
$613$	−23.9113	+	41.4155i	−0.965767	+	1.67276i	−0.258225	+	0.966085i	$0.583138\pi$
$613$	−23.9113	+	41.4155i	−0.965767	+	1.67276i	−0.707541	+	0.706672i	$0.750196\pi$
$614$		−	11.1732i		−	0.450913i
$615$	2.12109	+	24.7402i	0.0855308	+	0.997620i
$616$		−	7.77266i		−	0.313169i
$617$	0.519888	+	0.900472i	0.0209299	+	0.0362516i	0.876301	−	0.481765i	$-0.160004\pi$
$617$	0.519888	+	0.900472i	0.0209299	+	0.0362516i	−0.855371	+	0.518016i	$0.826671\pi$
$618$	−4.61006	+	9.84154i	−0.185444	+	0.395885i
$619$	−17.8366	−	30.8940i	−0.716915	−	1.24173i	−0.962216	−	0.272287i	$-0.912220\pi$
$619$	−17.8366	−	30.8940i	−0.716915	−	1.24173i	0.245301	−	0.969447i	$-0.421113\pi$
$620$	−0.562820	+	0.974832i	−0.0226034	+	0.0391502i
$621$	−15.4018	−	4.21322i	−0.618052	−	0.169071i
$622$	0.183368	+	0.317602i	0.00735238	+	0.0127347i
$623$	18.0763	−	10.4364i	0.724214	−	0.418125i
$624$	0.284894	+	3.32297i	0.0114049	+	0.133025i
$625$	4.31002			0.172401
$626$	−4.96407			−0.198404
$627$	6.13629	+	2.87441i	0.245060	+	0.114793i
$628$	−2.26112	−	3.91637i	−0.0902283	−	0.156280i
$629$	−4.62662	+	7.18080i	−0.184476	+	0.286317i
$630$	−3.52455	+	9.57973i	−0.140422	+	0.381666i
$631$	1.39099	+	0.803091i	0.0553746	+	0.0319705i	0.527432	−	0.849597i	$-0.323155\pi$
$631$	1.39099	+	0.803091i	0.0553746	+	0.0319705i	−0.472057	+	0.881568i	$0.656488\pi$
$632$	1.13138	−	1.95960i	0.0450038	−	0.0779489i
$633$	12.9182	−	27.5777i	0.513452	−	1.09612i
$634$			29.3389i			1.16520i
$635$	−8.85721	−	5.11371i	−0.351488	−	0.202932i
$636$	7.38786	−	15.7716i	0.292948	−	0.625384i
$637$	−0.889398	+	0.513494i	−0.0352392	+	0.0203454i
$638$	6.73393	−	11.6635i	0.266599	−	0.461763i
$639$	1.97246	+	2.36738i	0.0780295	+	0.0936522i
$640$	−1.23967			−0.0490022
$641$	−30.0036			−1.18507			−0.592535	−	0.805544i	$-0.701873\pi$
$641$	−30.0036			−1.18507			−0.592535	+	0.805544i	$0.701873\pi$
$642$	15.6877	−	10.9440i	0.619144	−	0.431925i
$643$	−22.8805	−	13.2100i	−0.902317	−	0.520953i	−0.0243658	−	0.999703i	$-0.507757\pi$
$643$	−22.8805	−	13.2100i	−0.902317	−	0.520953i	−0.877951	+	0.478750i	$0.841090\pi$
$644$	7.30438	−	4.21719i	0.287833	−	0.166180i
$645$	4.34452	+	6.22766i	0.171065	+	0.245214i
$646$			1.94007i			0.0763309i
$647$	−33.6835	+	19.4472i	−1.32424	+	0.764548i	−0.984401	−	0.175937i	$-0.943704\pi$
$647$	−33.6835	+	19.4472i	−1.32424	+	0.764548i	−0.339835	+	0.940485i	$0.610371\pi$
$648$	−3.01922	−	8.47846i	−0.118606	−	0.333065i
$649$	−25.0040	−	14.4361i	−0.981493	−	0.566665i
$650$	6.66863			0.261565
$651$	3.54031	−	2.46978i	0.138756	−	0.0967983i
$652$	−12.1660	−	7.02404i	−0.476457	−	0.275083i
$653$			21.4028i			0.837556i	0.908089	+	0.418778i	$0.137542\pi$
$653$			21.4028i			0.837556i	−0.908089	+	0.418778i	$0.862458\pi$
$654$	2.43301	−	5.19399i	0.0951383	−	0.203101i
$655$	−6.06651	−	10.5075i	−0.237038	−	0.410562i
$656$	11.5645			0.451518
$657$	−8.01756	+	1.38495i	−0.312795	+	0.0540320i
$658$		−	13.9318i		−	0.543119i
$659$	5.26654	−	9.12191i	0.205155	−	0.355339i	−0.745027	−	0.667034i	$-0.767563\pi$
$659$	5.26654	−	9.12191i	0.205155	−	0.355339i	0.950182	+	0.311695i	$0.100897\pi$
$660$	−4.98695	+	3.47898i	−0.194117	+	0.135419i
$661$			26.5433i			1.03241i	0.856464	+	0.516207i	$0.172656\pi$
$661$			26.5433i			1.03241i	−0.856464	+	0.516207i	$0.827344\pi$
$662$	−24.8511			−0.965865
$663$	−1.98679	+	4.24140i	−0.0771606	+	0.164722i
$664$		−	3.44726i		−	0.133780i
$665$	4.70052			0.182278
$666$	−18.1120	+	2.22601i	−0.701826	+	0.0862560i
$667$	14.6144			0.565873
$668$			11.0755i			0.428523i
$669$	−12.2485	−	17.5576i	−0.473553	−	0.678815i
$670$	−15.6815			−0.605828
$671$			6.24738i			0.241177i
$672$	4.30504	+	2.01660i	0.166070	+	0.0777922i
$673$	6.95004	−	12.0378i	0.267905	−	0.464024i	−0.700416	−	0.713735i	$-0.747002\pi$
$673$	6.95004	−	12.0378i	0.267905	−	0.464024i	0.968321	+	0.249711i	$0.0803355\pi$
$674$			17.3542i			0.668458i
$675$	−17.4063	+	4.56672i	−0.669970	+	0.175773i
$676$	−9.29223			−0.357394
$677$	−12.7769	−	22.1302i	−0.491055	−	0.850533i	0.508892	−	0.860831i	$-0.330055\pi$
$677$	−12.7769	−	22.1302i	−0.491055	−	0.850533i	−0.999947	+	0.0102977i	$0.996722\pi$
$678$	−15.5133	−	22.2376i	−0.595786	−	0.854031i
$679$		−	11.4185i		−	0.438202i
$680$	−1.50767	−	0.870453i	−0.0578164	−	0.0333803i
$681$	−40.3917	−	18.9206i	−1.54781	−	0.725040i
$682$	2.57140			0.0984640
$683$	−24.3837	−	14.0780i	−0.933018	−	0.538678i	−0.0452530	−	0.998976i	$-0.514409\pi$
$683$	−24.3837	−	14.0780i	−0.933018	−	0.538678i	−0.887765	+	0.460298i	$0.847743\pi$
$684$	−3.18410	+	2.65294i	−0.121747	+	0.101438i
$685$	−0.742122	+	0.428464i	−0.0283550	+	0.0163708i
$686$		−	17.7490i		−	0.677659i
$687$	31.9391	−	2.73829i	1.21855	−	0.104472i
$688$	3.06264	−	1.76822i	0.116762	−	0.0674127i
$689$	−16.7679	−	9.68096i	−0.638807	−	0.368815i
$690$	−5.97513	−	2.79892i	−0.227469	−	0.106553i
$691$	31.7192			1.20665			0.603327	−	0.797494i	$-0.293841\pi$
$691$	31.7192			1.20665			0.603327	+	0.797494i	$0.293841\pi$
$692$	6.56979			0.249746
$693$	22.9777	−	3.96915i	0.872850	−	0.150776i
$694$	−1.32392	+	2.29310i	−0.0502553	+	0.0870447i
$695$	−22.2128	+	12.8246i	−0.842581	+	0.486464i
$696$	4.71295	+	6.75579i	0.178644	+	0.256078i
$697$	14.0646	+	8.12019i	0.532734	+	0.307574i
$698$			29.5645i			1.11903i
$699$	7.69117	−	0.659401i	0.290907	−	0.0249409i
$700$	4.75274	−	8.23199i	0.179637	−	0.311140i
$701$	−9.75364	−	5.63127i	−0.368390	−	0.212690i	0.304365	−	0.952556i	$-0.401556\pi$
$701$	−9.75364	−	5.63127i	−0.368390	−	0.212690i	−0.672755	+	0.739865i	$0.734889\pi$
$702$	−9.67795	+	2.53910i	−0.365271	+	0.0958323i
$703$	3.84191	+	7.47358i	0.144900	+	0.281872i
$704$	1.41594	+	2.45249i	0.0533654	+	0.0924315i
$705$	−8.93868	+	6.23577i	−0.336650	+	0.234853i
$706$	−31.4380			−1.18318
$707$	42.8401			1.61117
$708$	14.4829	−	10.1035i	0.544302	−	0.379714i
$709$	−26.4971	+	15.2981i	−0.995118	+	0.574532i	−0.906800	−	0.421560i	$-0.861483\pi$
$709$	−26.4971	+	15.2981i	−0.995118	+	0.574532i	−0.0883182	+	0.996092i	$0.528149\pi$
$710$	0.636655	+	1.10272i	0.0238932	+	0.0413843i
$711$	6.37077	+	2.34392i	0.238922	+	0.0879038i
$712$	−3.80239	+	6.58592i	−0.142500	+	0.246818i
$713$	1.39516	+	2.41648i	0.0522490	+	0.0904980i
$714$	3.81974	+	5.47542i	0.142950	+	0.204912i
$715$	3.37993	+	5.85421i	0.126402	+	0.218935i
$716$			0.338286i			0.0126424i
$717$	15.2673	−	10.6507i	0.570168	−	0.397759i
$718$		−	1.58279i		−	0.0590692i
$719$	8.23394	−	14.2616i	0.307074	−	0.531868i	−0.670647	−	0.741777i	$-0.733983\pi$
$719$	8.23394	−	14.2616i	0.307074	−	0.531868i	0.977721	+	0.209909i	$0.0673167\pi$
$720$	−0.633043	−	3.66473i	−0.0235921	−	0.136576i
$721$	14.9144	−	8.61081i	0.555440	−	0.320683i
$722$	−14.8017	−	8.54575i	−0.550861	−	0.318040i
$723$	−5.97219	−	2.79755i	−0.222108	−	0.104042i
$724$	1.25459	+	2.17301i	0.0466265	+	0.0807594i
$725$	14.2637	−	8.23518i	0.529742	−	0.305847i
$726$	−4.67477	−	2.18980i	−0.173497	−	0.0812710i
$727$	−44.3939	−	25.6308i	−1.64648	−	0.950595i	−0.978456	−	0.206454i	$-0.933807\pi$
$727$	−44.3939	−	25.6308i	−1.64648	−	0.950595i	−0.668023	−	0.744141i	$-0.732859\pi$
$728$	2.64253	−	4.57700i	0.0979387	−	0.169635i
$729$	23.5224	−	13.2550i	0.871200	−	0.490928i
$730$	−3.36210			−0.124437
$731$	4.96633			0.183686
$732$	−3.46023	−	1.62087i	−0.127894	−	0.0599091i
$733$	−8.34714			−0.308309			−0.154154	−	0.988047i	$-0.549265\pi$
$733$	−8.34714			−0.308309			−0.154154	+	0.988047i	$0.549265\pi$
$734$	12.6357	+	7.29522i	0.466392	+	0.269272i
$735$	0.939222	−	0.655217i	0.0346437	−	0.0241680i
$736$	−1.53649	+	2.66127i	−0.0566357	+	0.0980959i
$737$	17.9113	+	31.0233i	0.659771	+	1.14276i
$738$	5.90547	+	34.1872i	0.217384	+	1.25845i
$739$	50.5573			1.85978			0.929891	−	0.367836i	$-0.119901\pi$
$739$	50.5573			1.85978			0.929891	+	0.367836i	$0.119901\pi$
$740$	−7.53164	−	0.367553i	−0.276869	−	0.0135115i
$741$	2.63617	+	3.77882i	0.0968421	+	0.138819i
$742$	−23.9010	+	13.7993i	−0.877435	+	0.506587i
$743$	15.3506			0.563160			0.281580	−	0.959538i	$-0.409142\pi$
$743$	15.3506			0.563160			0.281580	+	0.959538i	$0.409142\pi$
$744$	−0.667145	+	1.42422i	−0.0244587	+	0.0522144i
$745$	13.4494	+	7.76503i	0.492749	+	0.284489i
$746$			14.4684i			0.529725i
$747$	10.1909	−	1.76036i	0.372864	−	0.0644083i
$748$			3.97691i			0.145410i
$749$	−30.3110			−1.10754
$750$	−18.1055	+	1.55228i	−0.661121	+	0.0566811i
$751$	−15.8638	+	27.4769i	−0.578877	+	1.00264i	0.416731	+	0.909030i	$0.363176\pi$
$751$	−15.8638	+	27.4769i	−0.578877	+	1.00264i	−0.995608	+	0.0936151i	$0.970158\pi$
$752$	2.53796	+	4.39587i	0.0925498	+	0.160301i
$753$	1.54769	+	18.0520i	0.0564008	+	0.657852i
$754$	7.93066	−	4.57877i	0.288818	−	0.166749i
$755$	−1.96478	−	1.13437i	−0.0715058	−	0.0412839i
$756$	−3.76313	+	13.7564i	−0.136864	+	0.500316i
$757$	−7.64086	−	4.41145i	−0.277712	−	0.160337i	0.354675	−	0.934990i	$-0.384591\pi$
$757$	−7.64086	−	4.41145i	−0.277712	−	0.160337i	−0.632387	+	0.774653i	$0.717925\pi$
$758$	23.5661	+	13.6059i	0.855961	+	0.494189i
$759$	1.28755	+	15.0178i	0.0467349	+	0.545110i
$760$	−1.48314	+	0.856293i	−0.0537992	+	0.0310610i
$761$	−26.6049	−	46.0811i	−0.964428	−	1.67044i	−0.711145	−	0.703046i	$-0.751823\pi$
$761$	−26.6049	−	46.0811i	−0.964428	−	1.67044i	−0.253283	−	0.967392i	$-0.581510\pi$
$762$	−12.9403	−	6.06160i	−0.468777	−	0.219589i
$763$	−7.87123	+	4.54446i	−0.284958	+	0.164520i
$764$	−9.28198	+	5.35895i	−0.335810	+	0.193880i
$765$	1.80335	−	4.90150i	0.0652003	−	0.177214i
$766$	14.7601			0.533303
$767$	−9.81588	−	17.0016i	−0.354431	−	0.613892i
$768$	−1.72572	+	0.147954i	−0.0622716	+	0.00533884i
$769$	28.4605	+	16.4317i	1.02631	+	0.592542i	0.915926	−	0.401347i	$-0.131458\pi$
$769$	28.4605	+	16.4317i	1.02631	+	0.592542i	0.110386	+	0.993889i	$0.464791\pi$
$770$	9.63552			0.347240
$771$	34.2132	−	23.8677i	1.23216	−	0.859573i
$772$	−0.763709	−	0.440928i	−0.0274865	−	0.0158693i
$773$	−14.5634	−	25.2246i	−0.523811	−	0.907267i	−0.999616	−	0.0277160i	$-0.991177\pi$
$773$	−14.5634	−	25.2246i	−0.523811	−	0.907267i	0.475805	−	0.879551i	$-0.342157\pi$
$774$	6.79119	+	8.15089i	0.244104	+	0.292978i
$775$	2.72336	+	1.57233i	0.0978259	+	0.0564798i
$776$	2.08011	+	3.60285i	0.0746715	+	0.129335i
$777$	25.5575	+	13.5283i	0.916870	+	0.485327i
$778$	9.19046	−	15.9183i	0.329494	−	0.570700i
$779$	13.8358	−	7.98810i	0.495719	−	0.286203i
$780$	−4.11938	+	0.353175i	−0.147498	+	0.0126457i
$781$	1.45437	−	2.51904i	0.0520414	−	0.0901384i
$782$	−3.73731	+	2.15774i	−0.133646	+	0.0771606i
$783$	−17.5649	+	17.3824i	−0.627718	+	0.621196i
$784$	−0.266673	−	0.461891i	−0.00952404	−	0.0164961i
$785$	4.85500	−	2.80303i	0.173282	−	0.100045i
$786$	−9.69914	−	13.9033i	−0.345957	−	0.495913i
$787$	23.9599	−	41.4998i	0.854078	−	1.47931i	−0.0234194	−	0.999726i	$-0.507455\pi$
$787$	23.9599	−	41.4998i	0.854078	−	1.47931i	0.877498	−	0.479581i	$-0.159211\pi$
$788$	10.0925	−	17.4808i	0.359531	−	0.622726i
$789$	−0.375547	+	0.801717i	−0.0133698	+	0.0285419i
$790$	2.42926	+	1.40253i	0.0864292	+	0.0498999i
$791$			42.9664i			1.52771i
$792$	−6.52703	+	5.43821i	−0.231928	+	0.193238i
$793$	−2.12397	+	3.67882i	−0.0754244	+	0.130639i
$794$		−	5.51580i		−	0.195748i
$795$	19.5515	+	9.15850i	0.693421	+	0.324818i
$796$		−	20.7170i		−	0.734295i
$797$	−17.5265	+	10.1189i	−0.620821	+	0.358431i	−0.777188	−	0.629268i	$-0.783355\pi$
$797$	−17.5265	+	10.1189i	−0.620821	+	0.358431i	0.156368	+	0.987699i	$0.450021\pi$
$798$	6.54351	−	0.561007i	0.231638	−	0.0198594i
$799$			7.12827i			0.252180i
$800$			3.46322i			0.122443i
$801$	−21.4111	−	7.87754i	−0.756526	−	0.278339i
$802$	5.42047	−	9.38853i	0.191404	−	0.331521i
$803$	3.84018	+	6.65139i	0.135517	+	0.234722i
$804$	−21.8299	+	1.87158i	−0.769881	+	0.0660056i
$805$	5.22791	+	9.05501i	0.184260	+	0.319147i
$806$	1.51419	+	0.874219i	0.0533351	+	0.0307930i
$807$	9.23743	−	0.791970i	0.325173	−	0.0278787i
$808$	−13.5172	+	7.80416i	−0.475534	+	0.274549i
$809$	−36.5839	+	21.1217i	−1.28622	+	0.742600i	−0.977978	−	0.208707i	$-0.933074\pi$
$809$	−36.5839	+	21.1217i	−1.28622	+	0.742600i	−0.308244	+	0.951307i	$0.599741\pi$
$810$	10.5105	−	3.74283i	0.369301	−	0.131510i
$811$	−3.98436	−	6.90111i	−0.139910	−	0.242331i	0.787553	−	0.616247i	$-0.211348\pi$
$811$	−3.98436	−	6.90111i	−0.139910	−	0.242331i	−0.927462	+	0.373917i	$0.878015\pi$
$812$		−	13.0532i		−	0.458077i
$813$	14.7120	−	31.4072i	0.515974	−	1.10150i
$814$	7.87546	+	15.3200i	0.276035	+	0.536965i
$815$	8.70748	−	15.0818i	0.305010	−	0.528292i
$816$	−2.20269	−	1.03180i	−0.0771095	−	0.0361203i
$817$	2.44277	−	4.23100i	0.0854617	−	0.148024i
$818$	−2.77369	−	4.80418i	−0.0969800	−	0.167974i
$819$	14.8800	+	5.47463i	0.519950	+	0.191299i
$820$			14.3361i			0.500640i
$821$	6.90666	−	11.9627i	0.241044	−	0.417501i	−0.719968	−	0.694007i	$-0.755843\pi$
$821$	6.90666	−	11.9627i	0.241044	−	0.417501i	0.961012	+	0.276507i	$0.0891768\pi$
$822$	−0.981958	+	0.685030i	−0.0342497	+	0.0238932i
$823$	7.05964	+	12.2276i	0.246083	+	0.426229i	0.962436	−	0.271510i	$-0.0875229\pi$
$823$	7.05964	+	12.2276i	0.246083	+	0.426229i	−0.716352	+	0.697739i	$0.754190\pi$
$824$	−3.13726	+	5.43389i	−0.109292	+	0.189299i
$825$	9.71911	+	13.9319i	0.338376	+	0.485046i
$826$	−27.9832			−0.973659
$827$	−17.4898	+	10.0977i	−0.608179	+	0.351132i	−0.772252	−	0.635316i	$-0.780870\pi$
$827$	−17.4898	+	10.0977i	−0.608179	+	0.351132i	0.164074	+	0.986448i	$0.447537\pi$
$828$	−8.65193	−	3.18320i	−0.300675	−	0.110624i
$829$	41.7968	+	24.1314i	1.45166	+	0.838118i	0.998576	−	0.0533481i	$-0.0169893\pi$
$829$	41.7968	+	24.1314i	1.45166	+	0.838118i	0.453087	+	0.891466i	$0.350323\pi$
$830$	4.27346			0.148334
$831$	−45.6637	−	21.3902i	−1.58406	−	0.742018i
$832$			1.92556i			0.0667567i
$833$		−	0.748995i		−	0.0259511i
$834$	−29.3915	+	20.5040i	−1.01774	+	0.709995i
$835$	−13.7299			−0.475144
$836$	3.38808	+	1.95611i	0.117179	+	0.0676534i
$837$	−4.55099	−	1.24494i	−0.157305	−	0.0430315i
$838$	5.45422	−	3.14900i	0.188413	−	0.108780i
$839$	27.5006			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$839$	27.5006			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$840$	−2.49992	+	5.33682i	−0.0862554	+	0.184138i
$841$	−3.19123	+	5.52738i	−0.110042	+	0.190599i
$842$	17.1937	+	29.7804i	0.592535	+	1.02630i
$843$	2.15799	+	25.1705i	0.0743251	+	0.866918i
$844$	8.79114	−	15.2267i	0.302603	−	0.524124i
$845$		−	11.5193i		−	0.396276i
$846$	−11.6991	+	9.74753i	−0.402225	+	0.335127i
$847$	4.09017	+	7.08438i	0.140540	+	0.243422i
$848$	5.02762	−	8.70809i	0.172649	−	0.299037i
$849$	1.58914	+	18.5355i	0.0545391	+	0.636137i
$850$	−2.43176	+	4.21193i	−0.0834086	+	0.144468i
$851$	−10.1240	+	15.7131i	−0.347047	+	0.538638i
$852$	1.01789	+	1.45909i	0.0348722	+	0.0499876i
$853$			48.2198i			1.65101i	0.564392	+	0.825507i	$0.309111\pi$
$853$			48.2198i			1.65101i	−0.564392	+	0.825507i	$0.690889\pi$
$854$	3.02751	+	5.24381i	0.103599	+	0.179439i
$855$	−3.28876	−	3.94722i	−0.112473	−	0.134992i
$856$	9.56393	−	5.52174i	0.326888	−	0.188729i
$857$	−1.11957	+	0.646384i	−0.0382438	+	0.0220801i	−0.519000	−	0.854774i	$-0.673696\pi$
$857$	−1.11957	+	0.646384i	−0.0382438	+	0.0220801i	0.480756	+	0.876854i	$0.340362\pi$
$858$	5.40384	+	7.74614i	0.184484	+	0.264449i
$859$	−36.3089	−	20.9629i	−1.23884	−	0.715246i	−0.269985	−	0.962865i	$-0.587019\pi$
$859$	−36.3089	−	20.9629i	−1.23884	−	0.715246i	−0.968858	+	0.247619i	$0.920352\pi$
$860$	2.19200	+	3.79666i	0.0747467	+	0.129465i
$861$	23.3210	−	49.7856i	0.794778	−	1.69669i
$862$	12.0705	+	20.9067i	0.411123	+	0.712087i
$863$	−12.6948	+	21.9880i	−0.432136	+	0.748481i	−0.997057	−	0.0766639i	$-0.975573\pi$
$863$	−12.6948	+	21.9880i	−0.432136	+	0.748481i	0.564921	+	0.825145i	$0.308907\pi$
$864$	−1.31863	−	5.02605i	−0.0448608	−	0.170990i
$865$			8.14436i			0.276917i
$866$		−	17.3086i		−	0.588171i
$867$	14.8925	+	21.3477i	0.505775	+	0.725005i
$868$	2.15833	−	1.24611i	0.0732586	−	0.0422959i
$869$		−	6.40787i		−	0.217372i
$870$	−8.37494	+	5.84250i	−0.283937	+	0.198079i
$871$			24.3578i			0.825332i
$872$	1.65572	−	2.86780i	0.0560699	−	0.0971159i
$873$	−9.58859	+	7.98906i	−0.324525	+	0.270389i
$874$			4.24527i			0.143599i
$875$	24.9382	+	14.3981i	0.843066	+	0.486745i
$876$	−4.68032	+	0.401267i	−0.158134	+	0.0135576i
$877$	−5.78085	+	10.0127i	−0.195205	+	0.338106i	−0.946968	−	0.321328i	$-0.895871\pi$
$877$	−5.78085	+	10.0127i	−0.195205	+	0.338106i	0.751762	+	0.659434i	$0.229204\pi$
$878$	4.33400	−	7.50670i	0.146265	−	0.253339i
$879$	20.9195	−	1.79353i	0.705597	−	0.0604943i
$880$	−3.04027	+	1.75530i	−0.102487	+	0.0591711i
$881$	−15.2766	−	26.4598i	−0.514681	−	0.891453i	−0.999855	−	0.0170357i	$-0.994577\pi$
$881$	−15.2766	−	26.4598i	−0.514681	−	0.891453i	0.485174	−	0.874418i	$-0.338756\pi$
$882$	1.22927	−	1.02421i	0.0413918	−	0.0344870i
$883$	34.8864	−	20.1417i	1.17402	−	0.677821i	0.219396	−	0.975636i	$-0.429591\pi$
$883$	34.8864	−	20.1417i	1.17402	−	0.677821i	0.954624	+	0.297815i	$0.0962579\pi$
$884$	−1.35206	+	2.34184i	−0.0454747	+	0.0787645i
$885$	12.5250	+	17.9540i	0.421024	+	0.603518i
$886$	−10.3141	+	5.95484i	−0.346509	+	0.200057i
$887$	−9.33434	+	16.1675i	−0.313416	+	0.542853i	−0.979100	−	0.203381i	$-0.934807\pi$
$887$	−9.33434	+	16.1675i	−0.313416	+	0.542853i	0.665683	+	0.746234i	$0.268140\pi$
$888$	−10.5285	+	0.387238i	−0.353314	+	0.0129948i
$889$	11.3220	+	19.6104i	0.379729	+	0.657710i
$890$	−8.16436	−	4.71370i	−0.273670	−	0.158003i
$891$	−19.4096	−	16.5183i	−0.650246	−	0.553383i
$892$	−6.17989	−	10.7039i	−0.206918	−	0.358393i
$893$	6.07284	+	3.50615i	0.203220	+	0.117329i
$894$	19.6495	+	9.20437i	0.657176	+	0.307840i
$895$	−0.419363			−0.0140178
$896$	2.37697	+	1.37235i	0.0794092	+	0.0458469i
$897$	−4.34752	+	9.28107i	−0.145160	+	0.309886i
$898$	4.93436	+	8.54656i	0.164662	+	0.285202i
$899$	4.31834			0.144025
$900$	−10.2380	+	1.76851i	−0.341268	+	0.0589505i
$901$	12.2290	−	7.06044i	0.407409	−	0.235217i
$902$	28.3618	−	16.3747i	0.944343	−	0.545217i
$903$	−1.43611	−	16.7506i	−0.0477907	−	0.557425i
$904$	−7.82717	−	13.5571i	−0.260328	−	0.450901i
$905$	−2.69381	+	1.55527i	−0.0895454	+	0.0516991i
$906$	−2.87053	−	1.34464i	−0.0953668	−	0.0446726i
$907$	31.7573	+	18.3351i	1.05448	+	0.608807i	0.923901	−	0.382631i	$-0.124982\pi$
$907$	31.7573	+	18.3351i	1.05448	+	0.608807i	0.130583	+	0.991437i	$0.458315\pi$
$908$	−22.3018	−	12.8759i	−0.740111	−	0.427303i
$909$	−29.9734	−	35.9746i	−0.994156	−	1.19320i
$910$	5.67396	+	3.27586i	0.188090	+	0.108594i
$911$	7.08375	−	4.08980i	0.234695	−	0.135501i	−0.378041	−	0.925789i	$-0.623402\pi$
$911$	7.08375	−	4.08980i	0.234695	−	0.135501i	0.612736	+	0.790288i	$0.290069\pi$
$912$	−1.96246	+	1.36904i	−0.0649835	+	0.0453335i
$913$	−4.88112	−	8.45436i	−0.161542	−	0.279798i
$914$	2.65476	−	4.59817i	0.0878115	−	0.152094i
$915$	2.00934	−	4.28954i	0.0664268	−	0.141808i
$916$	18.5077			0.611511
$917$			26.8632i			0.887100i
$918$	1.92542	−	7.03852i	0.0635482	−	0.232306i
$919$			14.9852i			0.494317i	0.968975	+	0.247158i	$0.0794968\pi$
$919$			14.9852i			0.494317i	−0.968975	+	0.247158i	$0.920503\pi$
$920$	−3.29910	−	1.90473i	−0.108768	−	0.0627972i
$921$	19.2818	−	1.65312i	0.635356	−	0.0544722i
$922$	12.6167			0.415510
$923$	1.71284	−	0.988906i	0.0563787	−	0.0325502i
$924$	13.4134	−	1.15000i	0.441270	−	0.0378322i
$925$	−1.02682	+	21.0409i	−0.0337617	+	0.691821i
$926$	37.8028			1.24228
$927$	−17.6658	−	6.49958i	−0.580222	−	0.213474i
$928$	2.37789	+	4.11863i	0.0780582	+	0.135201i
$929$	4.10036	−	7.10203i	0.134528	−	0.233010i	−0.790889	−	0.611960i	$-0.790381\pi$
$929$	4.10036	−	7.10203i	0.134528	−	0.233010i	0.925417	+	0.378950i	$0.123715\pi$
$930$	−1.76556	−	0.827039i	−0.0578950	−	0.0271197i
$931$	−0.638097	−	0.368405i	−0.0209128	−	0.0120740i
$932$	4.45679			0.145987
$933$	−0.520962	+	0.363432i	−0.0170555	+	0.0118982i
$934$	22.3889			0.732587
$935$	−4.93005			−0.161230
$936$	−5.69237	+	0.983296i	−0.186061	+	0.0321400i
$937$	15.5944	−	27.0103i	0.509447	−	0.882389i	−0.490493	−	0.871445i	$-0.663183\pi$
$937$	15.5944	−	27.0103i	0.509447	−	0.882389i	0.999940	−	0.0109436i	$-0.00348352\pi$
$938$	30.0681	+	17.3598i	0.981758	+	0.566818i
$939$	−0.734455	−	8.56659i	−0.0239680	−	0.279560i
$940$	−5.44942	+	3.14623i	−0.177741	+	0.102619i
$941$	−4.83622	−	8.37659i	−0.157656	−	0.273069i	0.776367	−	0.630281i	$-0.217061\pi$
$941$	−4.83622	−	8.37659i	−0.157656	−	0.273069i	−0.934023	+	0.357213i	$0.883727\pi$
$942$	6.42401	−	4.48150i	0.209306	−	0.146015i
$943$	30.7763	+	17.7687i	1.00221	+	0.578629i
$944$	8.82945	−	5.09768i	0.287374	−	0.165915i
$945$	−17.0534	−	4.66503i	−0.554747	−	0.151753i
$946$	5.00739	−	8.67305i	0.162804	−	0.281985i
$947$		−	47.9172i		−	1.55710i	−0.627582	−	0.778550i	$-0.715955\pi$
$947$		−	47.9172i		−	1.55710i	0.627582	−	0.778550i	$-0.284045\pi$
$948$	3.54912	+	1.66251i	0.115270	+	0.0539958i
$949$			5.22230i			0.169523i
$950$	2.39220	+	4.14341i	0.0776132	+	0.134430i
$951$	−50.6307	+	4.34082i	−1.64181	+	0.140761i
$952$	1.92723	+	3.33806i	0.0624619	+	0.108187i
$953$	5.68521	−	9.84707i	0.184162	−	0.318978i	−0.759132	−	0.650937i	$-0.774376\pi$
$953$	5.68521	−	9.84707i	0.184162	−	0.318978i	0.943294	+	0.331959i	$0.107710\pi$
$954$	28.3104	+	10.4159i	0.916583	+	0.337227i
$955$	−6.64333	−	11.5066i	−0.214973	−	0.372344i
$956$	9.30764	−	5.37377i	0.301031	−	0.173800i
$957$	21.1243	+	9.89521i	0.682850	+	0.319867i
$958$	−13.3122			−0.430097
$959$	1.89729			0.0612666
$960$	−0.183414	−	2.13932i	−0.00591967	−	0.0690463i
$961$	−15.0878	−	26.1328i	−0.486702	−	0.842992i
$962$	−0.570914	+	11.6988i	−0.0184070	+	0.377184i
$963$	21.2073	+	25.4534i	0.683397	+	0.820223i
$964$	−3.29747	−	1.90380i	−0.106204	−	0.0613172i
$965$	0.546604	−	0.946746i	0.0175958	−	0.0304768i
$966$	8.35840	+	11.9814i	0.268927	+	0.385494i
$967$			29.2826i			0.941666i	0.882222	+	0.470833i	$0.156047\pi$
$967$			29.2826i			0.941666i	−0.882222	+	0.470833i	$0.843953\pi$
$968$	−2.58112	−	1.49021i	−0.0829603	−	0.0478972i
$969$	−3.34801	+	0.287041i	−0.107554	+	0.00922109i
$970$	−4.46634	+	2.57864i	−0.143405	+	0.0827952i
$971$	26.3852	−	45.7005i	0.846741	−	1.46660i	−0.0373590	−	0.999302i	$-0.511895\pi$
$971$	26.3852	−	45.7005i	0.846741	−	1.46660i	0.884100	−	0.467297i	$-0.154772\pi$
$972$	14.1847	−	6.46475i	0.454976	−	0.207357i
$973$	56.7887			1.82056
$974$	−40.6102			−1.30123
$975$	0.986653	+	11.5082i	0.0315982	+	0.368557i
$976$	−1.91052	−	1.10304i	−0.0611544	−	0.0353075i
$977$	31.8118	−	18.3666i	1.01775	−	0.587598i	0.104299	−	0.994546i	$-0.466740\pi$
$977$	31.8118	−	18.3666i	1.01775	−	0.587598i	0.913451	+	0.406948i	$0.133407\pi$
$978$	10.3215	−	22.0343i	0.330046	−	0.704581i
$979$			21.5358i			0.688289i
$980$	0.572592	−	0.330586i	0.0182908	−	0.0105602i
$981$	9.32334	+	3.43023i	0.297671	+	0.109519i
$982$	−3.83043	−	2.21150i	−0.122234	−	0.0705719i
$983$	11.2900			0.360097			0.180048	−	0.983658i	$-0.442375\pi$
$983$	11.2900			0.360097			0.180048	+	0.983658i	$0.442375\pi$
$984$	1.71102	+	19.9571i	0.0545452	+	0.636209i
$985$	21.6703	+	12.5114i	0.690475	+	0.398646i
$986$			6.67871i			0.212693i
$987$	24.0424	−	2.06128i	0.765279	−	0.0656111i
$988$	1.33007	+	2.30374i	0.0423150	+	0.0732917i
$989$	10.8674			0.345562
$990$	−6.74158	−	8.09135i	−0.214261	−	0.257160i
$991$			23.3231i			0.740882i	0.928856	+	0.370441i	$0.120793\pi$
$991$			23.3231i			0.740882i	−0.928856	+	0.370441i	$0.879207\pi$
$992$	−0.454008	+	0.786366i	−0.0144148	+	0.0249671i
$993$	−3.67683	−	42.8860i	−0.116681	−	1.36095i
$994$		−	2.81918i		−	0.0894190i
$995$	25.6822			0.814181
$996$	5.94901	−	0.510037i	0.188501	−	0.0161611i
$997$			10.1587i			0.321730i	0.986976	+	0.160865i	$0.0514283\pi$
$997$			10.1587i			0.321730i	−0.986976	+	0.160865i	$0.948572\pi$
$998$	18.9262			0.599099
$999$	−6.52121	−	30.9269i	−0.206322	−	0.978484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.20	✓	76
3.2	odd	2		1998.2.k.a.1063.10		76
9.2	odd	6		1998.2.t.a.397.5		76
9.7	even	3		666.2.t.a.619.33	yes	76
37.11	even	6		666.2.t.a.85.33	yes	76
111.11	odd	6		1998.2.t.a.307.5		76
333.11	odd	6		1998.2.k.a.1639.29		76
333.196	even	6	inner	666.2.k.a.529.1	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.20	✓	76	1.1	even	1	trivial
666.2.k.a.529.1	yes	76	333.196	even	6	inner
666.2.t.a.85.33	yes	76	37.11	even	6
666.2.t.a.619.33	yes	76	9.7	even	3
1998.2.k.a.1063.10		76	3.2	odd	2
1998.2.k.a.1639.29		76	333.11	odd	6
1998.2.t.a.307.5		76	111.11	odd	6
1998.2.t.a.397.5		76	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.72572 + 0.147954i) q^{3} -1.00000 q^{4} -1.23967i q^{5} +(-0.147954 - 1.72572i) q^{6} +(-1.37235 + 2.37697i) q^{7} -1.00000i q^{8} +(2.95622 - 0.510656i) q^{9} +1.23967 q^{10} +(-1.41594 - 2.45249i) q^{11} +(1.72572 - 0.147954i) q^{12} -1.92556i q^{13} +(-2.37697 - 1.37235i) q^{14} +(0.183414 + 2.13932i) q^{15} +1.00000 q^{16} +(1.21619 + 0.702166i) q^{17} +(0.510656 + 2.95622i) q^{18} +(1.19640 - 0.690743i) q^{19} +1.23967i q^{20} +(2.01660 - 4.30504i) q^{21} +(2.45249 - 1.41594i) q^{22} +(2.66127 + 1.53649i) q^{23} +(0.147954 + 1.72572i) q^{24} +3.46322 q^{25} +1.92556 q^{26} +(-5.02605 + 1.31863i) q^{27} +(1.37235 - 2.37697i) q^{28} +(4.11863 - 2.37789i) q^{29} +(-2.13932 + 0.183414i) q^{30} +(0.786366 + 0.454008i) q^{31} +1.00000i q^{32} +(2.80638 + 4.02281i) q^{33} +(-0.702166 + 1.21619i) q^{34} +(2.94666 + 1.70126i) q^{35} +(-2.95622 + 0.510656i) q^{36} +(-0.296493 + 6.07553i) q^{37} +(0.690743 + 1.19640i) q^{38} +(0.284894 + 3.32297i) q^{39} -1.23967 q^{40} +11.5645 q^{41} +(4.30504 + 2.01660i) q^{42} +(3.06264 - 1.76822i) q^{43} +(1.41594 + 2.45249i) q^{44} +(-0.633043 - 3.66473i) q^{45} +(-1.53649 + 2.66127i) q^{46} +(2.53796 + 4.39587i) q^{47} +(-1.72572 + 0.147954i) q^{48} +(-0.266673 - 0.461891i) q^{49} +3.46322i q^{50} +(-2.20269 - 1.03180i) q^{51} +1.92556i q^{52} +(5.02762 - 8.70809i) q^{53} +(-1.31863 - 5.02605i) q^{54} +(-3.04027 + 1.75530i) q^{55} +(2.37697 + 1.37235i) q^{56} +(-1.96246 + 1.36904i) q^{57} +(2.37789 + 4.11863i) q^{58} +(8.82945 - 5.09768i) q^{59} +(-0.183414 - 2.13932i) q^{60} +(-1.91052 - 1.10304i) q^{61} +(-0.454008 + 0.786366i) q^{62} +(-2.84314 + 7.72766i) q^{63} -1.00000 q^{64} -2.38705 q^{65} +(-4.02281 + 2.80638i) q^{66} -12.6497 q^{67} +(-1.21619 - 0.702166i) q^{68} +(-4.81994 - 2.25780i) q^{69} +(-1.70126 + 2.94666i) q^{70} +(0.513569 + 0.889528i) q^{71} +(-0.510656 - 2.95622i) q^{72} -2.71210 q^{73} +(-6.07553 - 0.296493i) q^{74} +(-5.97655 + 0.512399i) q^{75} +(-1.19640 + 0.690743i) q^{76} +7.77266 q^{77} +(-3.32297 + 0.284894i) q^{78} +(1.95960 + 1.13138i) q^{79} -1.23967i q^{80} +(8.47846 - 3.01922i) q^{81} +11.5645i q^{82} +3.44726 q^{83} +(-2.01660 + 4.30504i) q^{84} +(0.870453 - 1.50767i) q^{85} +(1.76822 + 3.06264i) q^{86} +(-6.75579 + 4.71295i) q^{87} +(-2.45249 + 1.41594i) q^{88} +(-6.58592 - 3.80239i) q^{89} +(3.66473 - 0.633043i) q^{90} +(4.57700 + 2.64253i) q^{91} +(-2.66127 - 1.53649i) q^{92} +(-1.42422 - 0.667145i) q^{93} +(-4.39587 + 2.53796i) q^{94} +(-0.856293 - 1.48314i) q^{95} +(-0.147954 - 1.72572i) q^{96} +(-3.60285 + 2.08011i) q^{97} +(0.461891 - 0.266673i) q^{98} +(-5.43821 - 6.52703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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