LMFDB - Embedded newform 666.2.t.a.85.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(85,666)] 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("666.85"); 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, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.t (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			85.33
Character	$\chi$	$=$	666.85
Dual form			666.2.t.a.619.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.990992 + 1.42054i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.07358 - 0.619834i) q^{5} +(0.147954 + 1.72572i) q^{6} +2.74469 q^{7} +1.00000i q^{8} +(-1.03587 + 2.81549i) q^{9} +1.23967 q^{10} +(-1.41594 - 2.45249i) q^{11} +(-0.734728 + 1.56849i) q^{12} +(1.66758 - 0.962778i) q^{13} +(2.37697 + 1.37235i) q^{14} +(1.94441 + 0.910819i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.21619 - 0.702166i) q^{17} +(-2.30483 + 1.92035i) q^{18} +(1.19640 + 0.690743i) q^{19} +(1.07358 + 0.619834i) q^{20} +(2.71997 + 3.89895i) q^{21} -2.83189i q^{22} +(-2.66127 - 1.53649i) q^{23} +(-1.42054 + 0.990992i) q^{24} +(-1.73161 + 2.99924i) q^{25} +1.92556 q^{26} +(-5.02605 + 1.31863i) q^{27} +(1.37235 + 2.37697i) q^{28} +(-4.11863 + 2.37789i) q^{29} +(1.22850 + 1.76100i) q^{30} +(-0.786366 - 0.454008i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.08067 - 4.44180i) q^{33} +1.40433 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} +(3.02022 + 1.41476i) q^{39} +(0.619834 + 1.07358i) q^{40} +(-5.78225 - 10.0151i) q^{41} +(0.406089 + 4.73657i) 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} +0.533346 q^{49} +(-2.99924 + 1.73161i) q^{50} +(2.20269 + 1.03180i) q^{51} +(1.66758 + 0.962778i) q^{52} +(5.02762 + 8.70809i) q^{53} +(-5.01201 - 1.37106i) q^{54} +(-3.04027 - 1.75530i) q^{55} +2.74469i q^{56} +(0.204397 + 2.38406i) q^{57} -4.75579 q^{58} -10.1954i q^{59} +(0.183414 + 2.13932i) q^{60} -2.20608i q^{61} +(-0.454008 - 0.786366i) q^{62} +(-2.84314 + 7.72766i) q^{63} -1.00000 q^{64} +(1.19353 - 2.06725i) q^{65} +(4.02281 - 2.80638i) q^{66} +(6.32487 + 10.9550i) q^{67} +(1.21619 + 0.702166i) q^{68} +(-0.454660 - 5.30309i) q^{69} +3.40251 q^{70} +(0.513569 - 0.889528i) q^{71} +(-2.81549 - 1.03587i) q^{72} -2.71210 q^{73} +(2.78100 - 5.40981i) q^{74} +(-5.97655 + 0.512399i) q^{75} +1.38149i q^{76} +(-3.88633 - 6.73132i) q^{77} +(1.90821 + 2.73533i) q^{78} +2.26276i q^{79} +1.23967i q^{80} +(-6.85395 - 5.83295i) q^{81} -11.5645i q^{82} +(-1.72363 + 2.98542i) q^{83} +(-2.01660 + 4.30504i) q^{84} +(0.870453 - 1.50767i) q^{85} -3.53643 q^{86} +(-7.45943 - 3.49421i) q^{87} +(2.45249 - 1.41594i) q^{88} +(-6.58592 + 3.80239i) q^{89} +(-1.28413 + 3.49027i) q^{90} +(4.57700 - 2.64253i) q^{91} -3.07298i q^{92} +(-0.134345 - 1.56698i) q^{93} +5.07591i q^{94} +1.71259 q^{95} +(-1.56849 - 0.734728i) q^{96} +(3.60285 - 2.08011i) q^{97} +(0.461891 + 0.266673i) q^{98} +(8.37168 - 1.44612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} + 38 q^{4} + 4 q^{7} + 2 q^{9} - 4 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{15} - 38 q^{16} - 12 q^{21} - 12 q^{23} + 50 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} - 18 q^{29} - 12 q^{30} - 6 q^{31}+ \cdots - 10 q^{99}+O(q^{100}) $ 76 * q - 2 * q^3 + 38 * q^4 + 4 * q^7 + 2 * q^9 - 4 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^15 - 38 * q^16 - 12 * q^21 - 12 * q^23 + 50 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 - 18 * q^29 - 12 * q^30 - 6 * q^31 + 4 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 18 * q^39 - 36 * q^41 + 42 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^47 + 4 * q^48 + 72 * q^49 + 18 * q^51 + 6 * q^52 + 14 * q^53 + 18 * q^54 + 36 * q^57 + 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 - 16 * q^65 - 20 * q^67 - 66 * q^69 + 2 * q^71 + 28 * q^73 - 20 * q^74 - 78 * q^75 + 12 * q^77 + 22 * q^78 + 26 * q^81 + 32 * q^83 - 6 * q^84 - 12 * q^85 - 8 * q^86 - 72 * q^87 + 60 * q^89 - 10 * q^90 + 42 * q^91 - 6 * q^93 + 28 * q^95 + 12 * q^97 - 24 * q^98 - 10 * q^99

Character values

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

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.990992	+	1.42054i	0.572150	+	0.820149i
$3$	0.990992	+	1.42054i	0.572150	+	0.820149i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.07358	−	0.619834i	0.480121	−	0.277198i	−0.240346	−	0.970687i	$-0.577261\pi$
$5$	1.07358	−	0.619834i	0.480121	−	0.277198i	0.720467	+	0.693489i	$0.243927\pi$
$6$	0.147954	+	1.72572i	0.0604021	+	0.704522i
$7$	2.74469			1.03740			0.518698	−	0.854957i	$-0.326417\pi$
$7$	2.74469			1.03740			0.518698	+	0.854957i	$0.326417\pi$
$8$			1.00000i			0.353553i
$9$	−1.03587	+	2.81549i	−0.345290	+	0.938496i
$10$	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	$0.973736\pi$
$12$	−0.734728	+	1.56849i	−0.212098	+	0.452785i
$13$	1.66758	−	0.962778i	0.462504	−	0.267027i	−0.250593	−	0.968093i	$-0.580626\pi$
$13$	1.66758	−	0.962778i	0.462504	−	0.267027i	0.713096	+	0.701066i	$0.247292\pi$
$14$	2.37697	+	1.37235i	0.635273	+	0.366775i
$15$	1.94441	+	0.910819i	0.502045	+	0.235172i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.21619	−	0.702166i	0.294969	−	0.170300i	−0.345212	−	0.938525i	$-0.612193\pi$
$17$	1.21619	−	0.702166i	0.294969	−	0.170300i	0.640180	+	0.768225i	$0.278860\pi$
$18$	−2.30483	+	1.92035i	−0.543254	+	0.452631i
$19$	1.19640	+	0.690743i	0.274474	+	0.158467i	0.630919	−	0.775849i	$-0.282678\pi$
$19$	1.19640	+	0.690743i	0.274474	+	0.158467i	−0.356445	+	0.934316i	$0.616011\pi$
$20$	1.07358	+	0.619834i	0.240061	+	0.138599i
$21$	2.71997	+	3.89895i	0.593546	+	0.850820i
$22$		−	2.83189i		−	0.603760i
$23$	−2.66127	−	1.53649i	−0.554914	−	0.320380i	0.196188	−	0.980566i	$-0.437144\pi$
$23$	−2.66127	−	1.53649i	−0.554914	−	0.320380i	−0.751102	+	0.660187i	$0.770477\pi$
$24$	−1.42054	+	0.990992i	−0.289967	+	0.202285i
$25$	−1.73161	+	2.99924i	−0.346322	+	0.599848i
$26$	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	−0.831021	−	0.556242i	$-0.812243\pi$
$29$	−4.11863	+	2.37789i	−0.764811	+	0.441564i	0.0662092	+	0.997806i	$0.478910\pi$
$30$	1.22850	+	1.76100i	0.224293	+	0.321513i
$31$	−0.786366	−	0.454008i	−0.141235	−	0.0815423i	0.427717	−	0.903913i	$-0.359318\pi$
$31$	−0.786366	−	0.454008i	−0.141235	−	0.0815423i	−0.568953	+	0.822370i	$0.692651\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.08067	−	4.44180i	0.362197	−	0.773218i
$34$	1.40433			0.240841
$35$	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
$39$	3.02022	+	1.41476i	0.483623	+	0.226543i
$40$	0.619834	+	1.07358i	0.0980044	+	0.169749i
$41$	−5.78225	−	10.0151i	−0.903035	−	1.56410i	−0.823533	−	0.567269i	$-0.808000\pi$
$41$	−5.78225	−	10.0151i	−0.903035	−	1.56410i	−0.0795026	−	0.996835i	$-0.525333\pi$
$42$	0.406089	+	4.73657i	0.0626610	+	0.730869i
$43$	−3.06264	+	1.76822i	−0.467049	+	0.269651i	−0.715003	−	0.699121i	$-0.753575\pi$
$43$	−3.06264	+	1.76822i	−0.467049	+	0.269651i	0.247955	+	0.968772i	$0.420242\pi$
$44$	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
$49$	0.533346			0.0761923
$50$	−2.99924	+	1.73161i	−0.424156	+	0.244887i
$51$	2.20269	+	1.03180i	0.308438	+	0.144481i
$52$	1.66758	+	0.962778i	0.231252	+	0.133513i
$53$	5.02762	+	8.70809i	0.690596	+	1.19615i	0.971643	+	0.236454i	$0.0759852\pi$
$53$	5.02762	+	8.70809i	0.690596	+	1.19615i	−0.281046	+	0.959694i	$0.590681\pi$
$54$	−5.01201	−	1.37106i	−0.682048	−	0.186577i
$55$	−3.04027	−	1.75530i	−0.409950	−	0.236685i
$56$			2.74469i			0.366775i
$57$	0.204397	+	2.38406i	0.0270730	+	0.315776i
$58$	−4.75579			−0.624466
$59$		−	10.1954i		−	1.32732i	−0.748033	−	0.663662i	$-0.769001\pi$
$59$		−	10.1954i		−	1.32732i	0.748033	−	0.663662i	$-0.230999\pi$
$60$	0.183414	+	2.13932i	0.0236787	+	0.276185i
$61$		−	2.20608i		−	0.282460i	−0.989977	−	0.141230i	$-0.954894\pi$
$61$		−	2.20608i		−	0.282460i	0.989977	−	0.141230i	$-0.0451057\pi$
$62$	−0.454008	−	0.786366i	−0.0576591	−	0.0998685i
$63$	−2.84314	+	7.72766i	−0.358202	+	0.973593i
$64$	−1.00000			−0.125000
$65$	1.19353	−	2.06725i	0.148039	−	0.256410i
$66$	4.02281	−	2.80638i	0.495173	−	0.345441i
$67$	6.32487	+	10.9550i	0.772705	+	1.33836i	0.936075	+	0.351800i	$0.114430\pi$
$67$	6.32487	+	10.9550i	0.772705	+	1.33836i	−0.163370	+	0.986565i	$0.552236\pi$
$68$	1.21619	+	0.702166i	0.147484	+	0.0851501i
$69$	−0.454660	−	5.30309i	−0.0547346	−	0.638418i
$70$	3.40251			0.406678
$71$	0.513569	−	0.889528i	0.0609494	−	0.105568i	−0.833941	−	0.551854i	$-0.813920\pi$
$71$	0.513569	−	0.889528i	0.0609494	−	0.105568i	0.894890	+	0.446287i	$0.147254\pi$
$72$	−2.81549	−	1.03587i	−0.331809	−	0.122078i
$73$	−2.71210			−0.317427			−0.158714	−	0.987325i	$-0.550735\pi$
$73$	−2.71210			−0.317427			−0.158714	+	0.987325i	$0.550735\pi$
$74$	2.78100	−	5.40981i	0.323284	−	0.628878i
$75$	−5.97655	+	0.512399i	−0.690113	+	0.0591667i
$76$			1.38149i			0.158467i
$77$	−3.88633	−	6.73132i	−0.442889	−	0.767105i
$78$	1.90821	+	2.73533i	0.216062	+	0.309715i
$79$			2.26276i			0.254580i	0.991866	+	0.127290i	$0.0406279\pi$
$79$			2.26276i			0.254580i	−0.991866	+	0.127290i	$0.959372\pi$
$80$			1.23967i			0.138599i
$81$	−6.85395	−	5.83295i	−0.761550	−	0.648106i
$82$		−	11.5645i		−	1.27708i
$83$	−1.72363	+	2.98542i	−0.189193	+	0.327692i	−0.944981	−	0.327124i	$-0.893921\pi$
$83$	−1.72363	+	2.98542i	−0.189193	+	0.327692i	0.755788	+	0.654816i	$0.227254\pi$
$84$	−2.01660	+	4.30504i	−0.220029	+	0.469718i
$85$	0.870453	−	1.50767i	0.0944139	−	0.163530i
$86$	−3.53643			−0.381344
$87$	−7.45943	−	3.49421i	−0.799735	−	0.374619i
$88$	2.45249	−	1.41594i	0.261436	−	0.150940i
$89$	−6.58592	+	3.80239i	−0.698107	+	0.403052i	−0.806642	−	0.591041i	$-0.798717\pi$
$89$	−6.58592	+	3.80239i	−0.698107	+	0.403052i	0.108535	+	0.994093i	$0.465384\pi$
$90$	−1.28413	+	3.49027i	−0.135360	+	0.367907i
$91$	4.57700	−	2.64253i	0.479800	−	0.277013i
$92$		−	3.07298i		−	0.320380i
$93$	−0.134345	−	1.56698i	−0.0139309	−	0.162489i
$94$			5.07591i			0.523541i
$95$	1.71259			0.175708
$96$	−1.56849	−	0.734728i	−0.160084	−	0.0749878i
$97$	3.60285	−	2.08011i	0.365814	−	0.211203i	−0.305814	−	0.952091i	$-0.598929\pi$
$97$	3.60285	−	2.08011i	0.365814	−	0.211203i	0.671628	+	0.740888i	$0.265595\pi$
$98$	0.461891	+	0.266673i	0.0466581	+	0.0269380i
$99$	8.37168	−	1.44612i	0.841385	−	0.145340i
$100$	−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	$-0.449695\pi$
$102$	1.39168	+	1.99491i	0.137797	+	0.197525i
$103$	5.43389	+	3.13726i	0.535417	+	0.309123i	0.743220	−	0.669048i	$-0.233298\pi$
$103$	5.43389	+	3.13726i	0.535417	+	0.309123i	−0.207802	+	0.978171i	$0.566631\pi$
$104$	0.962778	+	1.66758i	0.0944082	+	0.163520i
$105$	5.33682	+	2.49992i	0.520820	+	0.243967i
$106$			10.0552i			0.976651i
$107$	5.52174	−	9.56393i	0.533806	−	0.924580i	−0.465414	−	0.885093i	$-0.654094\pi$
$107$	5.52174	−	9.56393i	0.533806	−	0.924580i	0.999220	−	0.0394865i	$-0.0125722\pi$
$108$	−3.65500	−	3.69337i	−0.351702	−	0.355395i
$109$	2.86780	−	1.65572i	0.274685	−	0.158590i	−0.356330	−	0.934360i	$-0.615972\pi$
$109$	2.86780	−	1.65572i	0.274685	−	0.158590i	0.631015	+	0.775771i	$0.282639\pi$
$110$	−1.75530	−	3.04027i	−0.167361	−	0.289878i
$111$	8.33672	−	6.44199i	0.791286	−	0.611446i
$112$	−1.37235	+	2.37697i	−0.129675	+	0.224603i
$113$		−	15.6543i		−	1.47264i	−0.676635	−	0.736318i	$-0.736563\pi$
$113$		−	15.6543i		−	1.47264i	0.676635	−	0.736318i	$-0.263437\pi$
$114$	−1.01502	+	2.16685i	−0.0950650	+	0.202945i
$115$	−3.80947			−0.355235
$116$	−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
$120$	−0.910819	+	1.94441i	−0.0831460	+	0.177500i
$121$	1.49021	−	2.58112i	0.135474	−	0.234647i
$122$	1.10304	−	1.91052i	0.0998647	−	0.172971i
$123$	8.49676	−	18.1388i	0.766127	−	1.63552i
$124$		−	0.908017i		−	0.0815423i
$125$			10.4916i			0.938396i
$126$	−6.32606	+	5.27077i	−0.563570	+	0.469558i
$127$	4.12507	+	7.14483i	0.366040	+	0.634001i	0.988943	−	0.148299i	$-0.0473798\pi$
$127$	4.12507	+	7.14483i	0.366040	+	0.634001i	−0.622902	+	0.782300i	$0.714046\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−5.54688	−	2.59832i	−0.488375	−	0.228769i
$130$	2.06725	−	1.19353i	0.181310	−	0.104679i
$131$		−	9.78730i		−	0.855121i	−0.903987	−	0.427560i	$-0.859373\pi$
$131$		−	9.78730i		−	0.855121i	0.903987	−	0.427560i	$-0.140627\pi$
$132$	4.88704	−	0.418990i	0.425362	−	0.0364684i
$133$	3.28376	+	1.89588i	0.284738	+	0.164394i
$134$			12.6497i			1.09277i
$135$	−4.57856	+	4.53098i	−0.394059	+	0.389965i
$136$	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
$139$	20.6904			1.75493			0.877466	−	0.479638i	$-0.159232\pi$
$139$	20.6904			1.75493			0.877466	+	0.479638i	$0.159232\pi$
$140$	2.94666	+	1.70126i	0.249038	+	0.143782i
$141$	−3.72942	+	7.96154i	−0.314073	+	0.670483i
$142$	0.889528	−	0.513569i	0.0746475	−	0.0430978i
$143$	−4.72240	−	2.72648i	−0.394907	−	0.228000i
$144$	−1.92035	−	2.30483i	−0.160029	−	0.192069i
$145$	−2.94780	+	5.10574i	−0.244802	+	0.424009i
$146$	−2.34875	−	1.35605i	−0.194384	−	0.112227i
$147$	0.528542	+	0.757640i	0.0435934	+	0.0624891i
$148$	5.11332	−	3.29454i	0.420312	−	0.270809i
$149$	−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	$0.995145\pi$
$150$	−5.43205	−	2.54453i	−0.443525	−	0.207760i
$151$	−1.83012			−0.148933			−0.0744663	−	0.997224i	$-0.523725\pi$
$151$	−1.83012			−0.148933			−0.0744663	+	0.997224i	$0.523725\pi$
$152$	−0.690743	+	1.19640i	−0.0560267	+	0.0970411i
$153$	0.717130	+	4.15151i	0.0579765	+	0.335630i
$154$		−	7.77266i		−	0.626339i
$155$	−1.12564			−0.0904135
$156$	0.284894	+	3.32297i	0.0228098	+	0.266051i
$157$	−4.52223			−0.360913			−0.180457	−	0.983583i	$-0.557758\pi$
$157$	−4.52223			−0.360913			−0.180457	+	0.983583i	$0.557758\pi$
$158$	−1.13138	+	1.95960i	−0.0900076	+	0.155898i
$159$	−7.38786	+	15.7716i	−0.585895	+	1.25077i
$160$	−0.619834	+	1.07358i	−0.0490022	+	0.0848743i
$161$	−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	0.0589293	−	0.998262i	$-0.481231\pi$
$163$	12.1660	−	7.02404i	0.952914	−	0.550165i	0.893985	+	0.448097i	$0.147898\pi$
$164$	5.78225	−	10.0151i	0.451518	−	0.782052i
$165$	−0.519408	−	6.05831i	−0.0404359	−	0.471639i
$166$	−2.98542	+	1.72363i	−0.231713	+	0.133780i
$167$	9.59165	−	5.53774i	0.742224	−	0.428523i	−0.0806532	−	0.996742i	$-0.525701\pi$
$167$	9.59165	−	5.53774i	0.742224	−	0.428523i	0.822878	+	0.568219i	$0.192367\pi$
$168$	−3.89895	+	2.71997i	−0.300810	+	0.209850i
$169$	−4.64612	+	8.04731i	−0.357394	+	0.619024i
$170$	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
$173$	3.28490	−	5.68961i	0.249746	−	0.432573i	−0.713709	−	0.700442i	$-0.752986\pi$
$173$	3.28490	−	5.68961i	0.249746	−	0.432573i	0.963455	+	0.267869i	$0.0863195\pi$
$174$	−4.71295	−	6.75579i	−0.357288	−	0.512155i
$175$	−4.75274	+	8.23199i	−0.359274	+	0.622280i
$176$	2.83189			0.213461
$177$	14.4829	−	10.1035i	1.08860	−	0.759428i
$178$	−7.60477			−0.570002
$179$			0.338286i			0.0252847i	0.999920	+	0.0126424i	$0.00402429\pi$
$179$			0.338286i			0.0252847i	−0.999920	+	0.0126424i	$0.995976\pi$
$180$	−2.85723	+	2.38060i	−0.212965	+	0.177439i
$181$	−1.25459	+	2.17301i	−0.0932529	+	0.161519i	−0.908878	−	0.417062i	$-0.863060\pi$
$181$	−1.25459	+	2.17301i	−0.0932529	+	0.161519i	0.815625	+	0.578581i	$0.196393\pi$
$182$	5.28506			0.391755
$183$	3.13383	−	2.18621i	0.231659	−	0.161609i
$184$	1.53649	−	2.66127i	0.113271	−	0.196192i
$185$	−4.08413	−	6.33882i	−0.300271	−	0.466039i
$186$	0.667145	−	1.42422i	0.0489175	−	0.104429i
$187$	−3.44410	−	1.98845i	−0.251858	−	0.145410i
$188$	−2.53796	+	4.39587i	−0.185100	+	0.320602i
$189$	−13.7950	+	3.61925i	−1.00344	+	0.263261i
$190$	1.48314	+	0.856293i	0.107598	+	0.0621220i
$191$	−9.28198	+	5.35895i	−0.671621	+	0.387760i	−0.796690	−	0.604388i	$-0.793418\pi$
$191$	−9.28198	+	5.35895i	−0.671621	+	0.387760i	0.125070	+	0.992148i	$0.460085\pi$
$192$	−0.990992	−	1.42054i	−0.0715187	−	0.102519i
$193$	−0.763709	−	0.440928i	−0.0549730	−	0.0317387i	0.472262	−	0.881458i	$-0.343438\pi$
$193$	−0.763709	−	0.440928i	−0.0549730	−	0.0317387i	−0.527235	+	0.849720i	$0.676771\pi$
$194$	4.16021			0.298686
$195$	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	−0.961372	−	0.275253i	$-0.911238\pi$
$197$	−10.0925	−	17.4808i	−0.719062	−	1.24545i	0.242309	−	0.970199i	$-0.422095\pi$
$198$	7.97314	+	2.93346i	0.566627	+	0.208472i
$199$		−	20.7170i		−	1.46859i	−0.678831	−	0.734295i	$-0.737513\pi$
$199$		−	20.7170i		−	1.46859i	0.678831	−	0.734295i	$-0.262487\pi$
$200$	−2.99924	−	1.73161i	−0.212078	−	0.122443i
$201$	−9.29411	+	19.8410i	−0.655556	+	1.39948i
$202$		−	15.6083i		−	1.09820i
$203$	−11.3044	+	6.52659i	−0.793413	+	0.458077i
$204$	0.207777	+	2.42348i	0.0145473	+	0.169678i
$205$	−12.4155	−	7.16807i	−0.867133	−	0.500640i
$206$	3.13726	+	5.43389i	0.218583	+	0.378597i
$207$	7.08269	−	5.90119i	0.492281	−	0.410161i
$208$			1.92556i			0.133513i
$209$		−	3.91221i		−	0.270613i
$210$	3.37186	+	4.83340i	0.232681	+	0.333536i
$211$	−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
$213$	1.77255	−	0.151970i	0.121453	−	0.0104128i
$214$	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
$218$	3.31145			0.224280
$219$	−2.68767	−	3.85265i	−0.181616	−	0.260338i
$220$		−	3.51060i		−	0.236685i
$221$	1.35206	−	2.34184i	0.0909494	−	0.157529i
$222$	10.4408	−	1.41056i	0.700741	−	0.0946709i
$223$	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
$225$	−6.65060	−	7.98215i	−0.443373	−	0.532143i
$226$	7.82717	−	13.5571i	0.520656	−	0.901802i
$227$			25.7519i			1.70921i	0.519276	+	0.854607i	$0.326202\pi$
$227$			25.7519i			1.70921i	−0.519276	+	0.854607i	$0.673798\pi$
$228$	−1.96246	+	1.36904i	−0.129967	+	0.0906671i
$229$	9.25384	+	16.0281i	0.611511	+	1.05917i	0.990986	+	0.133966i	$0.0427714\pi$
$229$	9.25384	+	16.0281i	0.611511	+	1.05917i	−0.379475	+	0.925202i	$0.623895\pi$
$230$	−3.29910	−	1.90473i	−0.217536	−	0.125594i
$231$	5.71079	−	12.1914i	0.375742	−	0.802134i
$232$	−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	$0.546636\pi$
$234$	−1.99462	+	5.42138i	−0.130393	+	0.354407i
$235$	5.44942	+	3.14623i	0.355481	+	0.205237i
$236$	8.82945	−	5.09768i	0.574748	−	0.331831i
$237$	−3.21434	+	2.24237i	−0.208794	+	0.145658i
$238$	3.85446			0.249848
$239$			10.7475i			0.695201i	0.937643	+	0.347600i	$0.113003\pi$
$239$			10.7475i			0.695201i	−0.937643	+	0.347600i	$0.886997\pi$
$240$	−1.76100	+	1.22850i	−0.113672	+	0.0792994i
$241$			3.80759i			0.245269i	0.992452	+	0.122634i	$0.0391342\pi$
$241$			3.80759i			0.245269i	−0.992452	+	0.122634i	$0.960866\pi$
$242$	2.58112	−	1.49021i	0.165921	−	0.0957943i
$243$	1.49373	−	15.5167i	0.0958230	−	0.995398i
$244$	1.91052	−	1.10304i	0.122309	−	0.0706150i
$245$	0.572592	−	0.330586i	0.0365816	−	0.0211204i
$246$	16.4278	−	11.4603i	1.04740	−	0.730684i
$247$	2.66013			0.169260
$248$	0.454008	−	0.786366i	0.0288296	−	0.0499343i
$249$	−5.94901	+	0.510037i	−0.377003	+	0.0323223i
$250$	−5.24579	+	9.08598i	−0.331773	+	0.574648i
$251$			10.4606i			0.660265i	0.943935	+	0.330133i	$0.107093\pi$
$251$			10.4606i			0.660265i	−0.943935	+	0.330133i	$0.892907\pi$
$252$	−8.11392	+	1.40159i	−0.511129	+	0.0882921i
$253$			8.70232i			0.547110i
$254$			8.25013i			0.517659i
$255$	3.00432	−	0.257575i	0.188138	−	0.0161299i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$			24.0846i			1.50236i	0.660099	+	0.751179i	$0.270514\pi$
$257$			24.0846i			1.50236i	−0.660099	+	0.751179i	$0.729486\pi$
$258$	−3.50458	−	5.02365i	−0.218186	−	0.312759i
$259$	−0.813782	−	16.6755i	−0.0505660	−	1.03616i
$260$	2.38705			0.148039
$261$	−2.42857	−	14.0592i	−0.150325	−	0.870240i
$262$	4.89365	−	8.47605i	0.302331	−	0.523652i
$263$	−0.511138			−0.0315181			−0.0157591	−	0.999876i	$-0.505016\pi$
$263$	−0.511138			−0.0315181			−0.0157591	+	0.999876i	$0.505016\pi$
$264$	4.44180	+	2.08067i	0.273374	+	0.128056i
$265$	10.7951	+	6.23258i	0.663140	+	0.382864i
$266$	1.89588	+	3.28376i	0.116244	+	0.201340i
$267$	−11.9280	−	5.58744i	−0.729984	−	0.341946i
$268$	−6.32487	+	10.9550i	−0.386353	+	0.669182i
$269$	−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	−0.991540	−	0.129799i	$-0.958567\pi$
$271$	−10.0119	−	17.3411i	−0.608180	−	1.05340i	0.383361	−	0.923599i	$-0.374767\pi$
$272$			1.40433i			0.0851501i
$273$	8.28959	+	3.88308i	0.501709	+	0.235015i
$274$		−	0.691256i		−	0.0417603i
$275$	9.80745			0.591412
$276$	4.36528	−	3.04529i	0.262759	−	0.183305i
$277$			29.1131i			1.74924i	0.484812	+	0.874618i	$0.338888\pi$
$277$			29.1131i			1.74924i	−0.484812	+	0.874618i	$0.661112\pi$
$278$	17.9184	+	10.3452i	1.07467	+	0.620462i
$279$	2.09283	−	1.74371i	0.125294	−	0.104393i
$280$	1.70126	+	2.94666i	0.101669	+	0.176097i
$281$	−12.6314	−	7.29275i	−0.753527	−	0.435049i	0.0734397	−	0.997300i	$-0.476602\pi$
$281$	−12.6314	−	7.29275i	−0.753527	−	0.435049i	−0.826967	+	0.562250i	$0.809936\pi$
$282$	−7.21054	+	5.03019i	−0.429381	+	0.299544i
$283$	9.30175	−	5.37037i	0.552931	−	0.319235i	−0.197372	−	0.980329i	$-0.563241\pi$
$283$	9.30175	−	5.37037i	0.552931	−	0.319235i	0.750304	+	0.661094i	$0.229907\pi$
$284$	1.02714			0.0609494
$285$	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
$291$	6.52527	+	3.05662i	0.382518	+	0.179182i
$292$	−1.35605	−	2.34875i	−0.0793568	−	0.137450i
$293$	6.06109	+	10.4981i	0.354093	+	0.613307i	0.986962	−	0.160952i	$-0.0514563\pi$
$293$	6.06109	+	10.4981i	0.354093	+	0.613307i	−0.632869	+	0.774259i	$0.718123\pi$
$294$	0.0789109	+	0.920406i	0.00460218	+	0.0536792i
$295$	−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
$299$	−5.91719			−0.342200
$300$	−3.43203	−	4.91965i	−0.198148	−	0.284036i
$301$	−8.40602	+	4.85322i	−0.484515	+	0.279735i
$302$	−1.58493	−	0.915058i	−0.0912023	−	0.0526557i
$303$	11.4679	−	24.4816i	0.658812	−	1.40643i
$304$	−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	$0.603294\pi$
$308$	3.88633	−	6.73132i	0.221444	−	0.383553i
$309$	0.928342	+	10.8281i	0.0528115	+	0.615987i
$310$	−0.974832	−	0.562820i	−0.0553668	−	0.0319660i
$311$		−	0.366735i		−	0.0207957i	−0.999946	−	0.0103978i	$-0.996690\pi$
$311$		−	0.366735i		−	0.0207957i	0.999946	−	0.0103978i	$-0.00330979\pi$
$312$	−1.41476	+	3.02022i	−0.0800950	+	0.170987i
$313$	4.29901	+	2.48203i	0.242994	+	0.140293i	0.616552	−	0.787314i	$-0.288529\pi$
$313$	4.29901	+	2.48203i	0.242994	+	0.140293i	−0.373558	+	0.927607i	$0.621862\pi$
$314$	−3.91637	−	2.26112i	−0.221013	−	0.127602i
$315$	1.73751	+	10.0586i	0.0978976	+	0.566736i
$316$	−1.95960	+	1.13138i	−0.110236	+	0.0636450i
$317$	−14.6694	+	25.4082i	−0.823918	+	1.42707i	0.0788249	+	0.996888i	$0.474883\pi$
$317$	−14.6694	+	25.4082i	−0.823918	+	1.42707i	−0.902743	+	0.430180i	$0.858450\pi$
$318$	−14.2839	+	9.96466i	−0.800999	+	0.558790i
$319$	11.6635	+	6.73393i	0.653031	+	0.377028i
$320$	−1.07358	+	0.619834i	−0.0600152	+	0.0346498i
$321$	19.0579	−	1.63393i	1.06371	−	0.0911971i
$322$	−4.21719	−	7.30438i	−0.235015	−	0.407057i
$323$	1.94007			0.107948
$324$	1.62451	−	8.85217i	0.0902506	−	0.491787i
$325$			6.66863i			0.369909i
$326$	14.0481			0.778051
$327$	5.19399	+	2.43301i	0.287228	+	0.134546i
$328$	10.0151	−	5.78225i	0.552994	−	0.319271i
$329$	6.96592	+	12.0653i	0.384043	+	0.665183i
$330$	2.57934	−	5.50636i	0.141988	−	0.303115i
$331$	21.5217	+	12.4255i	1.18294	+	0.682970i	0.956692	−	0.291101i	$-0.0940214\pi$
$331$	21.5217	+	12.4255i	1.18294	+	0.682970i	0.226246	+	0.974070i	$0.427355\pi$
$332$	−3.44726			−0.189193
$333$	17.4127	+	5.45868i	0.954211	+	0.299134i
$334$	11.0755			0.606024
$335$	13.5806	+	7.84074i	0.741985	+	0.428385i
$336$	−4.73657	+	0.406089i	−0.258401	+	0.0221540i
$337$	−8.67709	−	15.0292i	−0.472671	−	0.818690i	0.526840	−	0.849965i	$-0.323377\pi$
$337$	−8.67709	−	15.0292i	−0.472671	−	0.818690i	−0.999511	+	0.0312742i	$0.990043\pi$
$338$	−8.04731	+	4.64612i	−0.437716	+	0.252715i
$339$	22.2376	−	15.5133i	1.20778	−	0.842569i
$340$	1.74091			0.0944139
$341$			2.57140i			0.139249i
$342$	−4.08398	+	0.705464i	−0.220836	+	0.0381471i
$343$	−17.7490			−0.958355
$344$	−1.76822	−	3.06264i	−0.0953359	−	0.165127i
$345$	−3.77515	−	5.41150i	−0.203248	−	0.291346i
$346$	5.68961	−	3.28490i	0.305875	−	0.176597i
$347$	−2.29310	−	1.32392i	−0.123100	−	0.0710717i	0.437186	−	0.899371i	$-0.355975\pi$
$347$	−2.29310	−	1.32392i	−0.123100	−	0.0710717i	−0.560286	+	0.828300i	$0.689309\pi$
$348$	−0.703640	−	8.20716i	−0.0377190	−	0.439950i
$349$	−14.7822	+	25.6036i	−0.791274	+	1.37053i	0.133904	+	0.990994i	$0.457249\pi$
$349$	−14.7822	+	25.6036i	−0.791274	+	1.37053i	−0.925178	+	0.379533i	$0.876085\pi$
$350$	−8.23199	+	4.75274i	−0.440019	+	0.254045i
$351$	−7.11180	+	7.03790i	−0.379600	+	0.375655i
$352$	2.45249	+	1.41594i	0.130718	+	0.0754700i
$353$	27.2261	+	15.7190i	1.44910	+	0.836637i	0.998428	−	0.0560529i	$-0.0178516\pi$
$353$	27.2261	+	15.7190i	1.44910	+	0.836637i	0.450671	+	0.892690i	$0.351185\pi$
$354$	17.5944	−	1.50845i	0.935129	−	0.0801732i
$355$		−	1.27331i		−	0.0675803i
$356$	−6.58592	−	3.80239i	−0.349053	−	0.201526i
$357$	6.04570	+	2.83198i	0.319972	+	0.149884i
$358$	−0.169143	+	0.292965i	−0.00893949	+	0.0154837i
$359$	−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
$363$	5.14337	−	0.440966i	0.269957	−	0.0231447i
$364$	4.57700	+	2.64253i	0.239900	+	0.138506i
$365$	−2.91167	+	1.68105i	−0.152404	+	0.0879903i
$366$	3.80708	−	0.326400i	0.198999	−	0.0170612i
$367$	−14.5904			−0.761615			−0.380808	−	0.924654i	$-0.624354\pi$
$367$	−14.5904			−0.761615			−0.380808	+	0.924654i	$0.624354\pi$
$368$	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
$372$	1.28987	−	0.899838i	0.0668769	−	0.0466544i
$373$	−7.23418	−	12.5300i	−0.374572	−	0.648777i	0.615691	−	0.787988i	$-0.288877\pi$
$373$	−7.23418	−	12.5300i	−0.374572	−	0.648777i	−0.990263	+	0.139210i	$0.955544\pi$
$374$	−1.98845	−	3.44410i	−0.102821	−	0.178090i
$375$	−14.9037	+	10.3971i	−0.769625	+	0.536903i
$376$	−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	0.968852	+	0.247640i	$0.0796551\pi$
$379$	13.6059	+	23.5661i	0.698889	+	1.21051i	−0.269963	+	0.962871i	$0.587012\pi$
$380$	0.856293	+	1.48314i	0.0439269	+	0.0760836i
$381$	−6.06160	+	12.9403i	−0.310545	+	0.662951i
$382$	−10.7179			−0.548376
$383$	12.7826	−	7.38004i	0.653161	−	0.377103i	−0.136505	−	0.990639i	$-0.543587\pi$
$383$	12.7826	−	7.38004i	0.653161	−	0.377103i	0.789666	+	0.613537i	$0.210254\pi$
$384$	−0.147954	−	1.72572i	−0.00755026	−	0.0880653i
$385$	−8.34461	−	4.81776i	−0.425281	−	0.245536i
$386$	−0.440928	−	0.763709i	−0.0224426	−	0.0388718i
$387$	−1.80590	−	10.4545i	−0.0917991	−	0.531431i
$388$	3.60285	+	2.08011i	0.182907	+	0.105601i
$389$		−	18.3809i		−	0.931949i	−0.884798	−	0.465975i	$-0.845704\pi$
$389$		−	18.3809i		−	0.931949i	0.884798	−	0.465975i	$-0.154296\pi$
$390$	3.74408	+	1.75383i	0.189589	+	0.0888088i
$391$	−4.31548			−0.218243
$392$			0.533346i			0.0269380i
$393$	13.9033	−	9.69914i	0.701327	−	0.489257i
$394$		−	20.1850i		−	1.01691i
$395$	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	$0.544201\pi$
$398$	10.3585	−	17.9415i	0.519225	−	0.899324i
$399$	0.561007	+	6.54351i	0.0280855	+	0.327585i
$400$	−1.73161	−	2.99924i	−0.0865806	−	0.149962i
$401$	9.38853	+	5.42047i	0.468841	+	0.270686i	0.715754	−	0.698352i	$-0.246083\pi$
$401$	9.38853	+	5.42047i	0.468841	+	0.270686i	−0.246913	+	0.969038i	$0.579416\pi$
$402$	−17.9695	+	12.5358i	−0.896235	+	0.625228i
$403$	−1.74844			−0.0870959
$404$	7.80416	−	13.5172i	0.388272	−	0.672506i
$405$	−10.9738	−	2.01385i	−0.545290	−	0.100069i
$406$	−13.0532			−0.647819
$407$	−14.4803	+	9.32975i	−0.717764	+	0.462459i
$408$	−1.03180	+	2.20269i	−0.0510818	+	0.109049i
$409$			5.54739i			0.274301i	0.990550	+	0.137150i	$0.0437944\pi$
$409$			5.54739i			0.274301i	−0.990550	+	0.137150i	$0.956206\pi$
$410$	−7.16807	−	12.4155i	−0.354006	−	0.613156i
$411$	0.507885	−	1.08423i	0.0250521	−	0.0534812i
$412$			6.27452i			0.309123i
$413$		−	27.9832i		−	1.37696i
$414$	9.08439	−	1.56923i	0.446473	−	0.0771235i
$415$			4.27346i			0.209776i
$416$	−0.962778	+	1.66758i	−0.0472041	+	0.0817599i
$417$	20.5040	+	29.3915i	1.00408	+	1.43931i
$418$	1.95611	−	3.38808i	0.0956763	−	0.165716i
$419$	6.29800			0.307677			0.153839	−	0.988096i	$-0.450836\pi$
$419$	6.29800			0.307677			0.153839	+	0.988096i	$0.450836\pi$
$420$	0.503416	+	5.87178i	0.0245642	+	0.286514i
$421$	−29.7804	+	17.1937i	−1.45141	+	0.837972i	−0.998562	−	0.0536160i	$-0.982925\pi$
$421$	−29.7804	+	17.1937i	−1.45141	+	0.837972i	−0.452848	+	0.891588i	$0.649592\pi$
$422$	−15.2267	+	8.79114i	−0.741224	+	0.427946i
$423$	−15.0055	+	2.59204i	−0.729593	+	0.126029i
$424$	−8.70809	+	5.02762i	−0.422902	+	0.244163i
$425$			4.86351i			0.235915i
$426$	1.61106	+	0.754667i	0.0780561	+	0.0365637i
$427$		−	6.05503i		−	0.293023i
$428$	11.0435			0.533806
$429$	−0.806789	−	9.41028i	−0.0389521	−	0.454332i
$430$	−3.79666	+	2.19200i	−0.183091	+	0.105708i
$431$	20.9067	+	12.0705i	1.00704	+	0.581416i	0.910324	−	0.413896i	$-0.135832\pi$
$431$	20.9067	+	12.0705i	1.00704	+	0.581416i	0.0967181	+	0.995312i	$0.469165\pi$
$432$	1.37106	−	5.01201i	0.0659650	−	0.241140i
$433$	−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
$435$	−10.1742	+	0.872280i	−0.487814	+	0.0418226i
$436$	2.86780	+	1.65572i	0.137343	+	0.0792948i
$437$	−2.12264	−	3.67652i	−0.101540	−	0.175872i
$438$	−0.401267	−	4.68032i	−0.0191733	−	0.223635i
$439$		−	8.66800i		−	0.413701i	−0.978373	−	0.206850i	$-0.933679\pi$
$439$		−	8.66800i		−	0.413701i	0.978373	−	0.206850i	$-0.0663214\pi$
$440$	1.75530	−	3.04027i	0.0836806	−	0.144939i
$441$	−0.552477	+	1.50163i	−0.0263084	+	0.0715062i
$442$	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	$0.742029\pi$
$444$	9.74728	+	3.99881i	0.462585	+	0.189775i
$445$	−4.71370	+	8.16436i	−0.223451	+	0.387028i
$446$			12.3598i			0.585253i
$447$	−21.6191	+	1.85351i	−1.02255	+	0.0876681i
$448$	−2.74469			−0.129675
$449$	8.54656	+	4.93436i	0.403337	+	0.232867i	0.687923	−	0.725784i	$-0.258523\pi$
$449$	8.54656	+	4.93436i	0.403337	+	0.232867i	−0.284586	+	0.958651i	$0.591856\pi$
$450$	−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
$453$	−1.81363	−	2.59975i	−0.0852118	−	0.122147i
$454$	−12.8759	+	22.3018i	−0.604298	+	1.04668i
$455$	3.27586	−	5.67396i	0.153575	−	0.265999i
$456$	−2.38406	+	0.204397i	−0.111644	+	0.00957176i
$457$		−	5.30951i		−	0.248368i	−0.992259	−	0.124184i	$-0.960369\pi$
$457$		−	5.30951i		−	0.248368i	0.992259	−	0.124184i	$-0.0396314\pi$
$458$			18.5077i			0.864807i
$459$	−5.18672	+	5.13283i	−0.242095	+	0.239580i
$460$	−1.90473	−	3.29910i	−0.0888087	−	0.153821i
$461$	−10.9264	−	6.30837i	−0.508894	−	0.293810i	0.223485	−	0.974707i	$-0.428257\pi$
$461$	−10.9264	−	6.30837i	−0.508894	−	0.293810i	−0.732379	+	0.680897i	$0.761590\pi$
$462$	11.0414	−	7.70265i	0.513691	−	0.358360i
$463$	32.7382	−	18.9014i	1.52147	−	0.878422i	0.521794	−	0.853072i	$-0.325263\pi$
$463$	32.7382	−	18.9014i	1.52147	−	0.878422i	0.999679	−	0.0253507i	$-0.00807023\pi$
$464$		−	4.75579i		−	0.220782i
$465$	−1.11550	−	1.59902i	−0.0517301	−	0.0741526i
$466$	−3.85969	−	2.22839i	−0.178797	−	0.103228i
$467$			22.3889i			1.03603i	0.855370	+	0.518017i	$0.173330\pi$
$467$			22.3889i			1.03603i	−0.855370	+	0.518017i	$0.826670\pi$
$468$	−4.43809	+	3.69774i	−0.205151	+	0.170928i
$469$	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
$472$	10.1954			0.469280
$473$	8.67305	+	5.00739i	0.398787	+	0.230240i
$474$	−3.90488	+	0.334785i	−0.179357	+	0.0153772i
$475$	−4.14341	+	2.39220i	−0.190113	+	0.109762i
$476$	3.33806	+	1.92723i	0.153000	+	0.0883345i
$477$	−29.7255	+	5.13476i	−1.36104	+	0.235105i
$478$	−5.37377	+	9.30764i	−0.245791	+	0.425722i
$479$	11.5287	+	6.65609i	0.526759	+	0.304124i	0.739696	−	0.672942i	$-0.234969\pi$
$479$	11.5287	+	6.65609i	0.526759	+	0.304124i	−0.212937	+	0.977066i	$0.568303\pi$
$480$	−2.13932	+	0.183414i	−0.0976462	+	0.00837168i
$481$	−6.34382	−	9.84598i	−0.289253	−	0.448938i
$482$	−1.90380	+	3.29747i	−0.0867156	+	0.150196i
$483$	−1.24790	−	14.5554i	−0.0567815	−	0.662292i
$484$	2.98042			0.135474
$485$	2.57864	−	4.46634i	0.117090	−	0.202806i
$486$	9.05197	−	12.6910i	0.410606	−	0.575676i
$487$		−	40.6102i		−	1.84022i	−0.391656	−	0.920112i	$-0.628098\pi$
$487$		−	40.6102i		−	1.84022i	0.391656	−	0.920112i	$-0.371902\pi$
$488$	2.20608			0.0998647
$489$	22.0343	+	10.3215i	0.996427	+	0.466755i
$490$	0.661172			0.0298687
$491$	−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
$493$	−3.33935	+	5.78393i	−0.150397	+	0.260495i
$494$	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
$497$	1.40959	−	2.44148i	0.0632287	−	0.109515i
$498$	−5.40701	−	2.53280i	−0.242294	−	0.113497i
$499$	16.3906	−	9.46311i	0.733743	−	0.423627i	−0.0860468	−	0.996291i	$-0.527423\pi$
$499$	16.3906	−	9.46311i	0.733743	−	0.423627i	0.819790	+	0.572664i	$0.194090\pi$
$500$	−9.08598	+	5.24579i	−0.406337	+	0.234599i
$501$	17.3718	+	8.13747i	0.776117	+	0.363555i
$502$	−5.23028	+	9.05912i	−0.233439	+	0.404328i
$503$	−19.8574	+	11.4647i	−0.885397	+	0.511184i	−0.872434	−	0.488732i	$-0.837460\pi$
$503$	−19.8574	+	11.4647i	−0.885397	+	0.511184i	−0.0129626	+	0.999916i	$0.504126\pi$
$504$	−7.72766	−	2.84314i	−0.344217	−	0.126644i
$505$	−16.7568	−	9.67457i	−0.745670	−	0.430513i
$506$	−4.35116	+	7.53643i	−0.193433	+	0.335035i
$507$	−16.0358	+	1.37483i	−0.712175	+	0.0610582i
$508$	−4.12507	+	7.14483i	−0.183020	+	0.317000i
$509$	−2.67326			−0.118490			−0.0592450	−	0.998243i	$-0.518869\pi$
$509$	−2.67326			−0.118490			−0.0592450	+	0.998243i	$0.518869\pi$
$510$	2.73060	+	1.27909i	0.120913	+	0.0566391i
$511$	−7.44388			−0.329298
$512$		−	1.00000i		−	0.0441942i
$513$	−6.92402	−	1.89410i	−0.305703	−	0.0836264i
$514$	−12.0423	+	20.8579i	−0.531164	+	0.920002i
$515$	7.77832			0.342754
$516$	−0.523231	−	6.10290i	−0.0230340	−	0.268665i
$517$	7.18721	−	12.4486i	0.316093	−	0.547489i
$518$	7.63298	−	14.8483i	0.335374	−	0.652396i
$519$	11.3376	−	0.972029i	0.497666	−	0.0426674i
$520$	2.06725	+	1.19353i	0.0906548	+	0.0523396i
$521$	18.0698	−	31.2978i	0.791653	−	1.37118i	−0.133290	−	0.991077i	$-0.542554\pi$
$521$	18.0698	−	31.2978i	0.791653	−	1.37118i	0.924943	−	0.380106i	$-0.124112\pi$
$522$	4.92637	−	13.3899i	0.215622	−	0.586059i
$523$	5.60689	+	3.23714i	0.245172	+	0.141550i	0.617552	−	0.786530i	$-0.288125\pi$
$523$	5.60689	+	3.23714i	0.245172	+	0.141550i	−0.372379	+	0.928081i	$0.621458\pi$
$524$	8.47605	−	4.89365i	0.370278	−	0.213780i
$525$	−16.4038	+	1.40638i	−0.715921	+	0.0613794i
$526$	−0.442658	−	0.255569i	−0.0193008	−	0.0111433i
$527$	−1.27516			−0.0555467
$528$	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
$531$	28.7049	+	10.5611i	1.24569	+	0.458311i
$532$			3.79176i			0.164394i
$533$	−19.2847	−	11.1340i	−0.835314	−	0.482269i
$534$	−7.53627	−	10.8029i	−0.326126	−	0.467486i
$535$		−	13.6902i		−	0.591881i
$536$	−10.9550	+	6.32487i	−0.473183	+	0.273193i
$537$	−0.480549	+	0.335239i	−0.0207372	+	0.0144666i
$538$	−4.63566	−	2.67640i	−0.199857	−	0.115388i
$539$	−0.755188	−	1.30802i	−0.0325282	−	0.0563406i
$540$	−6.21323	−	1.69965i	−0.267375	−	0.0731415i
$541$		−	43.5596i		−	1.87277i	−0.350972	−	0.936386i	$-0.614149\pi$
$541$		−	43.5596i		−	1.87277i	0.350972	−	0.936386i	$-0.385851\pi$
$542$		−	20.0238i		−	0.860096i
$543$	−4.33014	+	0.371244i	−0.185824	+	0.0159316i
$544$	−0.702166	+	1.21619i	−0.0301051	+	0.0521436i
$545$	2.05255	−	3.55512i	0.0879215	−	0.152285i
$546$	5.23746	+	7.50764i	0.224142	+	0.321298i
$547$	14.6318	−	8.44768i	0.625611	−	0.361197i	−0.153439	−	0.988158i	$-0.549035\pi$
$547$	14.6318	−	8.44768i	0.625611	−	0.361197i	0.779050	+	0.626961i	$0.215702\pi$
$548$	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
$551$	−6.57006			−0.279894
$552$	5.30309	−	0.454660i	0.225715	−	0.0193516i
$553$			6.21058i			0.264101i
$554$	−14.5566	+	25.2127i	−0.618449	+	1.07118i
$555$	4.95720	−	12.0834i	0.210422	−	0.512912i
$556$	10.3452	+	17.9184i	0.438733	+	0.759908i
$557$	13.6854	−	7.90127i	0.579869	−	0.334787i	−0.181212	−	0.983444i	$-0.558002\pi$
$557$	13.6854	−	7.90127i	0.579869	−	0.334787i	0.761081	+	0.648657i	$0.224669\pi$
$558$	2.68430	−	0.463684i	0.113635	−	0.0196293i
$559$	−3.40480	+	5.89729i	−0.144008	+	0.249429i
$560$			3.40251i			0.143782i
$561$	−0.588401	−	6.86303i	−0.0248423	−	0.289757i
$562$	−7.29275	−	12.6314i	−0.307626	−	0.532824i
$563$	37.4367	+	21.6141i	1.57777	+	0.910924i	0.995170	+	0.0981628i	$0.0312966\pi$
$563$	37.4367	+	21.6141i	1.57777	+	0.910924i	0.582597	+	0.812761i	$0.302037\pi$
$564$	−8.75961	+	0.751004i	−0.368846	+	0.0316230i
$565$	−9.70310	−	16.8063i	−0.408212	−	0.707045i
$566$	10.7407			0.451467
$567$	−18.8120	−	16.0097i	−0.790030	−	0.672343i
$568$	0.889528	+	0.513569i	0.0373237	+	0.0215489i
$569$	20.0195	−	11.5582i	0.839260	−	0.484547i	−0.0177527	−	0.999842i	$-0.505651\pi$
$569$	20.0195	−	11.5582i	0.839260	−	0.484547i	0.857013	+	0.515295i	$0.172318\pi$
$570$	0.253384	+	2.95544i	0.0106131	+	0.123790i
$571$	−13.8827			−0.580974			−0.290487	−	0.956879i	$-0.593817\pi$
$571$	−13.8827			−0.580974			−0.290487	+	0.956879i	$0.593817\pi$
$572$		−	5.45296i		−	0.228000i
$573$	−16.8110	−	7.87475i	−0.702289	−	0.328972i
$574$		−	31.7410i		−	1.32484i
$575$	9.21659	−	5.32120i	0.384358	−	0.221909i
$576$	1.03587	−	2.81549i	0.0431612	−	0.117312i
$577$	−6.48754	+	3.74558i	−0.270080	+	0.155931i	−0.628924	−	0.777467i	$-0.716504\pi$
$577$	−6.48754	+	3.74558i	−0.270080	+	0.155931i	0.358844	+	0.933398i	$0.383171\pi$
$578$	−13.0145	+	7.51393i	−0.541332	+	0.312538i
$579$	−0.130474	−	1.52184i	−0.00542233	−	0.0632453i
$580$	−5.89560			−0.244802
$581$	−4.73084	+	8.19405i	−0.196268	+	0.339947i
$582$	4.12274	+	5.90975i	0.170893	+	0.244967i
$583$	14.2376	−	24.6603i	0.589663	−	1.02133i
$584$		−	2.71210i		−	0.112227i
$585$	4.58397	+	5.50175i	0.189524	+	0.227470i
$586$			12.1222i			0.500763i
$587$			14.7877i			0.610355i	0.952295	+	0.305177i	$0.0987158\pi$
$587$			14.7877i			0.610355i	−0.952295	+	0.305177i	$0.901284\pi$
$588$	−0.391864	+	0.836550i	−0.0161602	+	0.0344988i
$589$	−0.627207	−	1.08635i	−0.0258436	−	0.0447624i
$590$		−	12.6389i		−	0.520334i
$591$	14.8305	−	31.6601i	0.610046	−	1.30232i
$592$	5.40981	+	2.78100i	0.222342	+	0.114298i
$593$	26.6675			1.09510			0.547552	−	0.836772i	$-0.315560\pi$
$593$	26.6675			1.09510			0.547552	+	0.836772i	$0.315560\pi$
$594$	3.73422	+	14.2332i	0.153217	+	0.583996i
$595$	2.38913	−	4.13809i	0.0979446	−	0.169645i
$596$	−12.5276			−0.513150
$597$	29.4293	−	20.5304i	1.20446	−	0.840253i
$598$	−5.12443	−	2.95859i	−0.209554	−	0.120986i
$599$	18.2443	+	31.6000i	0.745440	+	1.29114i	0.949989	+	0.312284i	$0.101094\pi$
$599$	18.2443	+	31.6000i	0.745440	+	1.29114i	−0.204549	+	0.978856i	$0.565573\pi$
$600$	−0.512399	−	5.97655i	−0.0209186	−	0.243992i
$601$	−6.34775	+	10.9946i	−0.258930	+	0.448480i	−0.965956	−	0.258708i	$-0.916703\pi$
$601$	−6.34775	+	10.9946i	−0.258930	+	0.448480i	0.707025	+	0.707188i	$0.250037\pi$
$602$	−9.70643			−0.395605
$603$	−37.3954	+	6.45966i	−1.52286	+	0.263058i
$604$	−0.915058	−	1.58493i	−0.0372332	−	0.0644897i
$605$		−	3.69473i		−	0.150212i
$606$	22.1722	−	15.4677i	0.900686	−	0.628333i
$607$		−	14.1668i		−	0.575014i	−0.957778	−	0.287507i	$-0.907173\pi$
$607$		−	14.1668i		−	0.575014i	0.957778	−	0.287507i	$-0.0928265\pi$
$608$	−1.38149			−0.0560267
$609$	−20.4739	−	9.59054i	−0.829642	−	0.388628i
$610$		−	2.73481i		−	0.110729i
$611$	8.46450	+	4.88698i	0.342437	+	0.197706i
$612$	−3.23675	+	2.69681i	−0.130838	+	0.109012i
$613$	−23.9113	−	41.4155i	−0.965767	−	1.67276i	−0.707541	−	0.706672i	$-0.750196\pi$
$613$	−23.9113	−	41.4155i	−0.965767	−	1.67276i	−0.258225	−	0.966085i	$-0.583138\pi$
$614$	−9.67626	−	5.58659i	−0.390502	−	0.225456i
$615$	−2.12109	−	24.7402i	−0.0855308	−	0.997620i
$616$	6.73132	−	3.88633i	0.271213	−	0.156585i
$617$	−1.03978			−0.0418598			−0.0209299	−	0.999781i	$-0.506663\pi$
$617$	−1.03978			−0.0418598			−0.0209299	+	0.999781i	$0.506663\pi$
$618$	−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
$624$	−2.73533	+	1.90821i	−0.109501	+	0.0763896i
$625$	−2.15501	−	3.73259i	−0.0862005	−	0.149304i
$626$	2.48203	+	4.29901i	0.0992020	+	0.171823i
$627$	5.55746	−	3.87697i	0.221943	−	0.154831i
$628$	−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	−0.472057	−	0.881568i	$-0.656488\pi$
$631$	1.39099	−	0.803091i	0.0553746	−	0.0319705i	0.527432	+	0.849597i	$0.323155\pi$
$632$	−2.26276			−0.0900076
$633$	−30.3421	+	2.60137i	−1.20599	+	0.103395i
$634$	−25.4082	+	14.6694i	−1.00909	+	0.582598i
$635$	8.85721	+	5.11371i	0.351488	+	0.202932i
$636$	−17.3525	+	1.48772i	−0.688072	+	0.0589918i
$637$	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
$641$	15.0018	−	25.9839i	0.592535	−	1.02630i	−0.401354	−	0.915923i	$-0.631460\pi$
$641$	15.0018	−	25.9839i	0.592535	−	1.02630i	0.993890	−	0.110378i	$-0.0352063\pi$
$642$	17.3216	+	8.11395i	0.683630	+	0.320232i
$643$	22.8805	+	13.2100i	0.902317	+	0.520953i	0.877951	−	0.478750i	$-0.158910\pi$
$643$	22.8805	+	13.2100i	0.902317	+	0.520953i	0.0243658	+	0.999703i	$0.492243\pi$
$644$		−	8.43438i		−	0.332361i
$645$	−7.56557	+	0.648633i	−0.297894	+	0.0255399i
$646$	1.68015	+	0.970033i	0.0661045	+	0.0381654i
$647$	−33.6835	−	19.4472i	−1.32424	−	0.764548i	−0.339835	−	0.940485i	$-0.610371\pi$
$647$	−33.6835	−	19.4472i	−1.32424	−	0.764548i	−0.984401	+	0.175937i	$0.943704\pi$
$648$	5.83295	−	6.85395i	0.229140	−	0.269249i
$649$	−25.0040	+	14.4361i	−0.981493	+	0.566665i
$650$	−3.33431	+	5.77520i	−0.130783	+	0.226522i
$651$	−0.368736	−	4.30089i	−0.0144519	−	0.168565i
$652$	12.1660	+	7.02404i	0.476457	+	0.275083i
$653$	−18.5354	+	10.7014i	−0.725345	+	0.418778i	−0.816717	−	0.577039i	$-0.804208\pi$
$653$	−18.5354	+	10.7014i	−0.725345	+	0.418778i	0.0913717	+	0.995817i	$0.470875\pi$
$654$	3.28162	+	4.70404i	0.128321	+	0.183943i
$655$	−6.06651	−	10.5075i	−0.237038	−	0.410562i
$656$	11.5645			0.451518
$657$	2.80938	−	7.63589i	0.109604	−	0.297904i
$658$			13.9318i			0.543119i
$659$	−10.5331			−0.410310			−0.205155	−	0.978729i	$-0.565770\pi$
$659$	−10.5331			−0.410310			−0.205155	+	0.978729i	$0.565770\pi$
$660$	4.98695	−	3.47898i	0.194117	−	0.135419i
$661$	−22.9872	+	13.2716i	−0.894097	+	0.516207i	−0.875280	−	0.483616i	$-0.839323\pi$
$661$	−22.9872	+	13.2716i	−0.894097	+	0.516207i	−0.0188163	+	0.999823i	$0.505990\pi$
$662$	12.4255	+	21.5217i	0.482932	+	0.836464i
$663$	4.66655	−	0.400086i	0.181234	−	0.0155381i
$664$	−2.98542	−	1.72363i	−0.115857	−	0.0668898i
$665$	4.70052			0.182278
$666$	12.3505	+	13.4337i	0.478573	+	0.520546i
$667$	14.6144			0.565873
$668$	9.59165	+	5.53774i	0.371112	+	0.214262i
$669$	−9.08108	+	19.3863i	−0.351095	+	0.749516i
$670$	7.84074	+	13.5806i	0.302914	+	0.524663i
$671$	−5.41039	+	3.12369i	−0.208866	+	0.120589i
$672$	−4.30504	−	2.01660i	−0.166070	−	0.0777922i
$673$	−13.9001			−0.535809			−0.267905	−	0.963445i	$-0.586331\pi$
$673$	−13.9001			−0.535809			−0.267905	+	0.963445i	$0.586331\pi$
$674$		−	17.3542i		−	0.668458i
$675$	4.74827	−	17.3577i	0.182761	−	0.668098i
$676$	−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	$0.996722\pi$
$678$	27.0150	−	2.31613i	1.03751	−	0.0889504i
$679$	9.88872	−	5.70925i	0.379494	−	0.219101i
$680$	1.50767	+	0.870453i	0.0578164	+	0.0333803i
$681$	−36.5816	+	25.5199i	−1.40181	+	0.977926i
$682$	−1.28570	+	2.22690i	−0.0492320	+	0.0852723i
$683$	−24.3837	+	14.0780i	−0.933018	+	0.538678i	−0.887765	−	0.460298i	$-0.847743\pi$
$683$	−24.3837	+	14.0780i	−0.933018	+	0.538678i	−0.0452530	+	0.998976i	$0.514409\pi$
$684$	−3.88956	−	1.43104i	−0.148721	−	0.0547171i
$685$	−0.742122	−	0.428464i	−0.0283550	−	0.0163708i
$686$	−15.3711	−	8.87449i	−0.586870	−	0.338830i
$687$	−13.5981	+	29.0292i	−0.518800	+	1.10753i
$688$		−	3.53643i		−	0.134825i
$689$	16.7679	+	9.68096i	0.638807	+	0.368815i
$690$	−0.563628	−	6.57408i	−0.0214569	−	0.250271i
$691$	−15.8596	+	27.4696i	−0.603327	+	1.04499i	0.388986	+	0.921244i	$0.372825\pi$
$691$	−15.8596	+	27.4696i	−0.603327	+	1.04499i	−0.992313	+	0.123750i	$0.960508\pi$
$692$	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
$696$	3.49421	−	7.45943i	0.132448	−	0.282749i
$697$	−14.0646	−	8.12019i	−0.532734	−	0.307574i
$698$	−25.6036	+	14.7822i	−0.969109	+	0.559515i
$699$	−4.41664	−	6.33105i	−0.167053	−	0.239462i
$700$	−9.50549			−0.359274
$701$	−9.75364	+	5.63127i	−0.368390	+	0.212690i	−0.672755	−	0.739865i	$-0.734889\pi$
$701$	−9.75364	+	5.63127i	−0.368390	+	0.212690i	0.304365	+	0.952556i	$0.401556\pi$
$702$	−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
$705$	0.930995	+	10.8590i	0.0350633	+	0.408974i
$706$	15.7190	+	27.2261i	0.591592	+	1.02467i
$707$	−21.4200	−	37.1006i	−0.805583	−	1.39531i
$708$	15.9914	+	7.49082i	0.600993	+	0.281522i
$709$	26.4971	−	15.2981i	0.995118	−	0.574532i	0.0883182	−	0.996092i	$-0.471851\pi$
$709$	26.4971	−	15.2981i	0.995118	−	0.574532i	0.906800	+	0.421560i	$0.138517\pi$
$710$	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
$715$	−6.75986			−0.252804
$716$	−0.292965	+	0.169143i	−0.0109486	+	0.00632118i
$717$	−15.2673	+	10.6507i	−0.570168	+	0.397759i
$718$	−1.37074	−	0.791396i	−0.0511555	−	0.0295346i
$719$	8.23394	+	14.2616i	0.307074	+	0.531868i	0.977721	−	0.209909i	$-0.0673167\pi$
$719$	8.23394	+	14.2616i	0.307074	+	0.531868i	−0.670647	+	0.741777i	$0.733983\pi$
$720$	−3.49027	−	1.28413i	−0.130075	−	0.0478568i
$721$	14.9144	+	8.61081i	0.555440	+	0.320683i
$722$		−	17.0915i		−	0.636080i
$723$	−5.40884	+	3.77330i	−0.201157	+	0.140330i
$724$	−2.50918			−0.0932529
$725$		−	16.4704i		−	0.611694i
$726$	4.67477	+	2.18980i	0.173497	+	0.0812710i
$727$		−	51.2617i		−	1.90119i	−0.310433	−	0.950595i	$-0.600474\pi$
$727$		−	51.2617i		−	1.90119i	0.310433	−	0.950595i	$-0.399526\pi$
$728$	2.64253	+	4.57700i	0.0979387	+	0.169635i
$729$	23.5224	−	13.2550i	0.871200	−	0.490928i
$730$	−3.36210			−0.124437
$731$	−2.48316	+	4.30097i	−0.0918431	+	0.159077i
$732$	3.46023	+	1.62087i	0.127894	+	0.0599091i
$733$	4.17357	+	7.22884i	0.154154	+	0.267003i	0.932751	−	0.360522i	$-0.117401\pi$
$733$	4.17357	+	7.22884i	0.154154	+	0.267003i	−0.778596	+	0.627525i	$0.784068\pi$
$734$	−12.6357	−	7.29522i	−0.466392	−	0.269272i
$735$	1.03705	+	0.485782i	0.0382520	+	0.0179183i
$736$	3.07298			0.113271
$737$	17.9113	−	31.0233i	0.659771	−	1.14276i
$738$	32.5597	+	11.9793i	1.19854	+	0.440964i
$739$	50.5573			1.85978			0.929891	−	0.367836i	$-0.119901\pi$
$739$	50.5573			1.85978			0.929891	+	0.367836i	$0.119901\pi$
$740$	3.44751	−	6.70637i	0.126733	−	0.246531i
$741$	2.63617	+	3.77882i	0.0968421	+	0.138819i
$742$			27.5985i			1.01317i
$743$	−7.67532	−	13.2940i	−0.281580	−	0.487711i	0.690194	−	0.723624i	$-0.257525\pi$
$743$	−7.67532	−	13.2940i	−0.281580	−	0.487711i	−0.971774	+	0.235913i	$0.924192\pi$
$744$	1.56698	−	0.134345i	0.0574484	−	0.00492533i
$745$			15.5301i			0.568977i
$746$		−	14.4684i		−	0.529725i
$747$	−6.61995	−	7.94536i	−0.242211	−	0.290706i
$748$		−	3.97691i		−	0.145410i
$749$	15.1555	−	26.2501i	0.553769	−	0.959156i
$750$	−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	$0.970158\pi$
$752$	−5.07591			−0.185100
$753$	−14.8597	+	10.3663i	−0.541516	+	0.377770i
$754$	−7.93066	+	4.57877i	−0.288818	+	0.166749i
$755$	−1.96478	+	1.13437i	−0.0715058	+	0.0412839i
$756$	−10.0318	−	10.1372i	−0.364855	−	0.368686i
$757$	−7.64086	+	4.41145i	−0.277712	+	0.160337i	−0.632387	−	0.774653i	$-0.717925\pi$
$757$	−7.64086	+	4.41145i	−0.277712	+	0.160337i	0.354675	+	0.934990i	$0.384591\pi$
$758$			27.2118i			0.988378i
$759$	−12.3620	+	8.62393i	−0.448712	+	0.313029i
$760$			1.71259i			0.0621220i
$761$	53.2098			1.92886			0.964428	−	0.264347i	$-0.0851563\pi$
$761$	53.2098			1.92886			0.964428	+	0.264347i	$0.0851563\pi$
$762$	−11.7196	+	8.17582i	−0.424558	+	0.296179i
$763$	7.87123	−	4.54446i	0.284958	−	0.164520i
$764$	−9.28198	−	5.35895i	−0.335810	−	0.193880i
$765$	3.34315	+	4.01250i	0.120872	+	0.145072i
$766$	14.7601			0.533303
$767$	−9.81588	−	17.0016i	−0.354431	−	0.613892i
$768$	0.734728	−	1.56849i	0.0265122	−	0.0565982i
$769$	−28.4605	−	16.4317i	−1.02631	−	0.592542i	−0.110386	−	0.993889i	$-0.535209\pi$
$769$	−28.4605	−	16.4317i	−1.02631	−	0.592542i	−0.915926	+	0.401347i	$0.868542\pi$
$770$	−4.81776	−	8.34461i	−0.173620	−	0.300719i
$771$	−34.2132	+	23.8677i	−1.23216	+	0.859573i
$772$		−	0.881856i		−	0.0317387i
$773$	−14.5634	+	25.2246i	−0.523811	+	0.907267i	0.475805	+	0.879551i	$0.342157\pi$
$773$	−14.5634	+	25.2246i	−0.523811	+	0.907267i	−0.999616	+	0.0277160i	$0.991177\pi$
$774$	3.66328	−	9.95679i	0.131674	−	0.357889i
$775$	2.72336	−	1.57233i	0.0978259	−	0.0564798i
$776$	2.08011	+	3.60285i	0.0746715	+	0.129335i
$777$	22.8817	−	17.6813i	0.820878	−	0.634312i
$778$	9.19046	−	15.9183i	0.329494	−	0.570700i
$779$		−	15.9762i		−	0.572407i
$780$	2.36555	+	3.39090i	0.0847002	+	0.121414i
$781$	−2.90874			−0.104083
$782$	−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
$786$	16.8901	−	1.44807i	0.602452	−	0.0516511i
$787$	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
$789$	−0.506534	−	0.726092i	−0.0180331	−	0.0258496i
$790$			2.80507i			0.0997998i
$791$		−	42.9664i		−	1.52771i
$792$	1.44612	+	8.37168i	0.0513856	+	0.297475i
$793$	−2.12397	−	3.67882i	−0.0754244	−	0.130639i
$794$	−4.77682	−	2.75790i	−0.169523	−	0.0978742i
$795$	1.84427	+	21.5114i	0.0654097	+	0.762930i
$796$	17.9415	−	10.3585i	0.635918	−	0.367147i
$797$			20.2379i			0.716862i	0.933556	+	0.358431i	$0.116688\pi$
$797$			20.2379i			0.716862i	−0.933556	+	0.358431i	$0.883312\pi$
$798$	−2.78591	+	5.94735i	−0.0986202	+	0.210534i
$799$	6.17326	+	3.56413i	0.218394	+	0.126090i
$800$		−	3.46322i		−	0.122443i
$801$	−3.88342	−	22.4814i	−0.137214	−	0.794340i
$802$	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
$805$	−10.4558			−0.368520
$806$	−1.51419	−	0.874219i	−0.0533351	−	0.0307930i
$807$	−5.30458	−	7.60386i	−0.186730	−	0.267669i
$808$	13.5172	−	7.80416i	0.475534	−	0.274549i
$809$	−36.5839	−	21.1217i	−1.28622	−	0.742600i	−0.308244	−	0.951307i	$-0.599741\pi$
$809$	−36.5839	−	21.1217i	−1.28622	−	0.742600i	−0.977978	+	0.208707i	$0.933074\pi$
$810$	−8.49663	−	7.23093i	−0.298541	−	0.254069i
$811$	−3.98436	+	6.90111i	−0.139910	+	0.242331i	−0.927462	−	0.373917i	$-0.878015\pi$
$811$	−3.98436	+	6.90111i	−0.139910	+	0.242331i	0.787553	+	0.616247i	$0.211348\pi$
$812$	−11.3044	−	6.52659i	−0.396706	−	0.229039i
$813$	14.7120	−	31.4072i	0.515974	−	1.10150i
$814$	−17.2052	+	0.839634i	−0.603043	+	0.0294292i
$815$	8.70748	−	15.0818i	0.305010	−	0.528292i
$816$	−1.99491	+	1.39168i	−0.0698358	+	0.0487186i
$817$	−4.88554			−0.170923
$818$	−2.77369	+	4.80418i	−0.0969800	+	0.167974i
$819$	2.69885	+	15.6238i	0.0943053	+	0.545940i
$820$		−	14.3361i		−	0.500640i
$821$	−13.8133			−0.482088			−0.241044	−	0.970514i	$-0.577490\pi$
$821$	−13.8133			−0.482088			−0.241044	+	0.970514i	$0.577490\pi$
$822$	0.981958	−	0.685030i	0.0342497	−	0.0238932i
$823$	−14.1193			−0.492167			−0.246083	−	0.969249i	$-0.579144\pi$
$823$	−14.1193			−0.492167			−0.246083	+	0.969249i	$0.579144\pi$
$824$	−3.13726	+	5.43389i	−0.109292	+	0.189299i
$825$	9.71911	+	13.9319i	0.338376	+	0.485046i
$826$	13.9916	−	24.2341i	0.486829	−	0.843213i
$827$	−17.4898	−	10.0977i	−0.608179	−	0.351132i	0.164074	−	0.986448i	$-0.447537\pi$
$827$	−17.4898	−	10.0977i	−0.608179	−	0.351132i	−0.772252	+	0.635316i	$0.780870\pi$
$828$	8.65193	+	3.18320i	0.300675	+	0.110624i
$829$	41.7968	−	24.1314i	1.45166	−	0.838118i	0.453087	−	0.891466i	$-0.350323\pi$
$829$	41.7968	−	24.1314i	1.45166	−	0.838118i	0.998576	+	0.0533481i	$0.0169893\pi$
$830$	−2.13673	+	3.70092i	−0.0741670	+	0.128461i
$831$	−41.3563	+	28.8509i	−1.43464	+	1.00083i
$832$	−1.66758	+	0.962778i	−0.0578130	+	0.0333783i
$833$	0.648649	−	0.374497i	0.0224743	−	0.0129756i
$834$	3.06123	+	35.7058i	0.106002	+	1.23639i
$835$	6.86496	−	11.8905i	0.237572	−	0.411487i
$836$	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
$839$	−13.7503	+	23.8162i	−0.474713	+	0.822226i	−0.999581	−	0.0289573i	$-0.990781\pi$
$839$	−13.7503	+	23.8162i	−0.474713	+	0.822226i	0.524868	+	0.851184i	$0.324115\pi$
$840$	−2.49992	+	5.33682i	−0.0862554	+	0.184138i
$841$	−3.19123	+	5.52738i	−0.110042	+	0.190599i
$842$	−34.3875			−1.18507
$843$	−2.15799	−	25.1705i	−0.0743251	−	0.866918i
$844$	−17.5823			−0.605207
$845$			11.5193i			0.396276i
$846$	−14.2912	−	5.25798i	−0.491341	−	0.180773i
$847$	4.09017	−	7.08438i	0.140540	−	0.243422i
$848$	−10.0552			−0.345298
$849$	16.8468	+	7.89151i	0.578180	+	0.270836i
$850$	−2.43176	+	4.21193i	−0.0834086	+	0.144468i
$851$	−8.54593	+	16.6242i	−0.292951	+	0.569871i
$852$	1.01789	+	1.45909i	0.0348722	+	0.0499876i
$853$	41.7596	+	24.1099i	1.42982	+	0.825507i	0.997106	−	0.0760245i	$-0.0242227\pi$
$853$	41.7596	+	24.1099i	1.42982	+	0.825507i	0.432714	+	0.901531i	$0.357556\pi$
$854$	3.02751	−	5.24381i	0.103599	−	0.179439i
$855$	−1.77401	+	4.82176i	−0.0606700	+	0.164901i
$856$	9.56393	+	5.52174i	0.326888	+	0.188729i
$857$	1.11957	−	0.646384i	0.0382438	−	0.0220801i	−0.480756	−	0.876854i	$-0.659638\pi$
$857$	1.11957	−	0.646384i	0.0382438	−	0.0220801i	0.519000	+	0.854774i	$0.326304\pi$
$858$	4.00644	−	8.55293i	0.136778	−	0.291992i
$859$	36.3089	+	20.9629i	1.23884	+	0.715246i	0.968858	−	0.247619i	$-0.0796480\pi$
$859$	36.3089	+	20.9629i	1.23884	+	0.715246i	0.269985	+	0.962865i	$0.412981\pi$
$860$	−4.38401			−0.149493
$861$	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	0.564921	−	0.825145i	$-0.308907\pi$
$863$	−12.6948	−	21.9880i	−0.432136	−	0.748481i	−0.997057	+	0.0766639i	$0.975573\pi$
$864$	3.69337	−	3.65500i	0.125651	−	0.124346i
$865$		−	8.14436i		−	0.276917i
$866$	−14.9897	−	8.65431i	−0.509371	−	0.294086i
$867$	−25.9339	+	2.22344i	−0.880760	+	0.0755118i
$868$		−	2.49223i		−	0.0845917i
$869$	5.54938	−	3.20394i	0.188250	−	0.108686i
$870$	−9.24722	−	4.33166i	−0.313510	−	0.146857i
$871$	21.0944	+	12.1789i	0.714758	+	0.412666i
$872$	1.65572	+	2.86780i	0.0560699	+	0.0971159i
$873$	2.12444	+	12.2985i	0.0719012	+	0.416241i
$874$		−	4.24527i		−	0.143599i
$875$			28.7962i			0.973489i
$876$	1.99266	−	4.25391i	0.0673256	−	0.143726i
$877$	−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
$879$	−8.90651	+	19.0136i	−0.300409	+	0.641312i
$880$	3.04027	−	1.75530i	0.102487	−	0.0591711i
$881$	−15.2766	+	26.4598i	−0.514681	+	0.891453i	0.485174	+	0.874418i	$0.338756\pi$
$881$	−15.2766	+	26.4598i	−0.514681	+	0.891453i	−0.999855	+	0.0170357i	$0.994577\pi$
$882$	−1.22927	+	1.02421i	−0.0413918	+	0.0344870i
$883$	34.8864	+	20.1417i	1.17402	+	0.677821i	0.954624	−	0.297815i	$-0.0962579\pi$
$883$	34.8864	+	20.1417i	1.17402	+	0.677821i	0.219396	+	0.975636i	$0.429591\pi$
$884$	2.70412			0.0909494
$885$	9.28613	−	19.8240i	0.312150	−	0.666377i
$886$			11.9097i			0.400114i
$887$	−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	$0.268140\pi$
$888$	6.44199	+	8.33672i	0.216179	+	0.279762i
$889$	11.3220	+	19.6104i	0.379729	+	0.657710i
$890$	−8.16436	+	4.71370i	−0.273670	+	0.158003i
$891$	−4.60043	+	25.0683i	−0.154120	+	0.839821i
$892$	−6.17989	+	10.7039i	−0.206918	+	0.358393i
$893$			7.01231i			0.234658i
$894$	−19.6495	−	9.20437i	−0.657176	−	0.307840i
$895$	0.209681	+	0.363179i	0.00700888	+	0.0121397i
$896$	−2.37697	−	1.37235i	−0.0794092	−	0.0458469i
$897$	−5.86389	−	8.40560i	−0.195789	−	0.280655i
$898$	4.93436	+	8.54656i	0.164662	+	0.285202i
$899$	4.31834			0.144025
$900$	3.58744	−	9.75066i	0.119581	−	0.325022i
$901$	12.2290	+	7.06044i	0.407409	+	0.235217i
$902$	−28.3618	+	16.3747i	−0.944343	+	0.545217i
$903$	−15.2245	−	7.13159i	−0.506639	−	0.237324i
$904$	15.6543			0.520656
$905$			3.11055i			0.103398i
$906$	−0.270774	−	3.15827i	−0.00899585	−	0.104926i
$907$			36.6702i			1.21761i	0.793319	+	0.608807i	$0.208352\pi$
$907$			36.6702i			1.21761i	−0.793319	+	0.608807i	$0.791648\pi$
$908$	−22.3018	+	12.8759i	−0.740111	+	0.427303i
$909$	46.1416	−	7.97048i	1.53042	−	0.264364i
$910$	5.67396	−	3.27586i	0.188090	−	0.108594i
$911$	−7.08375	+	4.08980i	−0.234695	+	0.135501i	−0.612736	−	0.790288i	$-0.709931\pi$
$911$	−7.08375	+	4.08980i	−0.234695	+	0.135501i	0.378041	+	0.925789i	$0.376598\pi$
$912$	−2.16685	−	1.01502i	−0.0717517	−	0.0336106i
$913$	9.76225			0.323083
$914$	2.65476	−	4.59817i	0.0878115	−	0.152094i
$915$	2.00934	−	4.28954i	0.0664268	−	0.141808i
$916$	−9.25384	+	16.0281i	−0.305756	+	0.529584i
$917$		−	26.8632i		−	0.887100i
$918$	−7.05825	+	1.85180i	−0.232957	+	0.0611185i
$919$		−	14.9852i		−	0.494317i	−0.968975	−	0.247158i	$-0.920503\pi$
$919$		−	14.9852i		−	0.494317i	0.968975	−	0.247158i	$-0.0794968\pi$
$920$		−	3.80947i		−	0.125594i
$921$	−11.0725	−	15.8720i	−0.364853	−	0.522999i
$922$	−6.30837	−	10.9264i	−0.207755	−	0.359842i
$923$		−	1.97781i		−	0.0651005i
$924$	13.4134	−	1.15000i	0.441270	−	0.0378322i
$925$	18.7354	+	9.63121i	0.616016	+	0.316672i
$926$	37.8028			1.24228
$927$	−14.4617	+	12.0493i	−0.474985	+	0.395750i
$928$	2.37789	−	4.11863i	0.0780582	−	0.135201i
$929$	−8.20071			−0.269057			−0.134528	−	0.990910i	$-0.542952\pi$
$929$	−8.20071			−0.269057			−0.134528	+	0.990910i	$0.542952\pi$
$930$	−0.166543	−	1.94254i	−0.00546117	−	0.0636984i
$931$	0.638097	+	0.368405i	0.0209128	+	0.0120740i
$932$	−2.22839	−	3.85969i	−0.0729935	−	0.126428i
$933$	0.520962	−	0.363432i	0.0170555	−	0.0118982i
$934$	−11.1944	+	19.3893i	−0.366293	+	0.634439i
$935$	−4.93005			−0.161230
$936$	−5.69237	+	0.983296i	−0.186061	+	0.0321400i
$937$	15.5944	+	27.0103i	0.509447	+	0.882389i	0.999940	+	0.0109436i	$0.00348352\pi$
$937$	15.5944	+	27.0103i	0.509447	+	0.882389i	−0.490493	+	0.871445i	$0.663183\pi$
$938$			34.7196i			1.13364i
$939$	0.734455	+	8.56659i	0.0239680	+	0.279560i
$940$			6.29245i			0.205237i
$941$	9.67245			0.315313			0.157656	−	0.987494i	$-0.449606\pi$
$941$	9.67245			0.315313			0.157656	+	0.987494i	$0.449606\pi$
$942$	−0.669084	−	7.80411i	−0.0217999	−	0.254272i
$943$			35.5374i			1.15726i
$944$	8.82945	+	5.09768i	0.287374	+	0.165915i
$945$	−12.5667	+	12.4362i	−0.408796	+	0.404548i
$946$	5.00739	+	8.67305i	0.162804	+	0.281985i
$947$	−41.4975	−	23.9586i	−1.34849	−	0.778550i	−0.360453	−	0.932777i	$-0.617378\pi$
$947$	−41.4975	−	23.9586i	−1.34849	−	0.778550i	−0.988035	+	0.154227i	$0.950711\pi$
$948$	−3.54912	−	1.66251i	−0.115270	−	0.0539958i
$949$	−4.52265	+	2.61115i	−0.146811	+	0.0847615i
$950$	−4.78440			−0.155226
$951$	−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	0.943294	−	0.331959i	$-0.107710\pi$
$953$	5.68521	+	9.84707i	0.184162	+	0.318978i	−0.759132	+	0.650937i	$0.774376\pi$
$954$	−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
$957$	1.99263	+	23.2417i	0.0644125	+	0.751299i
$958$	6.65609	+	11.5287i	0.215048	+	0.372475i
$959$	−0.948644	−	1.64310i	−0.0306333	−	0.0530584i
$960$	−1.94441	−	0.910819i	−0.0627557	−	0.0293965i
$961$	−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
$965$	−1.09321			−0.0351916
$966$	6.19697	−	13.2293i	0.199384	−	0.425645i
$967$	−25.3595	+	14.6413i	−0.815506	+	0.470833i	−0.848864	−	0.528611i	$-0.822713\pi$
$967$	−25.3595	+	14.6413i	−0.815506	+	0.470833i	0.0333580	+	0.999443i	$0.489380\pi$
$968$	2.58112	+	1.49021i	0.0829603	+	0.0478972i
$969$	1.92259	+	2.75594i	0.0617625	+	0.0885336i
$970$	4.46634	−	2.57864i	0.143405	−	0.0827952i
$971$	26.3852	+	45.7005i	0.846741	+	1.46660i	0.884100	+	0.467297i	$0.154772\pi$
$971$	26.3852	+	45.7005i	0.846741	+	1.46660i	−0.0373590	+	0.999302i	$0.511895\pi$
$972$	14.1847	−	6.46475i	0.454976	−	0.207357i
$973$	56.7887			1.82056
$974$	20.3051	−	35.1695i	0.650617	−	1.12690i
$975$	−9.47306	+	6.60856i	−0.303381	+	0.211643i
$976$	1.91052	+	1.10304i	0.0611544	+	0.0353075i
$977$		−	36.7331i		−	1.17520i	−0.809153	−	0.587598i	$-0.800074\pi$
$977$		−	36.7331i		−	1.17520i	0.809153	−	0.587598i	$-0.199926\pi$
$978$	13.9215	+	19.9559i	0.445162	+	0.638118i
$979$	18.6506	+	10.7679i	0.596075	+	0.344144i
$980$	0.572592	+	0.330586i	0.0182908	+	0.0105602i
$981$	1.69101	+	9.78936i	0.0539898	+	0.312550i
$982$	−3.83043	+	2.21150i	−0.122234	+	0.0705719i
$983$	−5.64502	+	9.77747i	−0.180048	+	0.311853i	−0.941897	−	0.335903i	$-0.890959\pi$
$983$	−5.64502	+	9.77747i	−0.180048	+	0.311853i	0.761848	+	0.647755i	$0.224292\pi$
$984$	18.1388	+	8.49676i	0.578245	+	0.270867i
$985$	−21.6703	−	12.5114i	−0.690475	−	0.398646i
$986$	−5.78393	+	3.33935i	−0.184198	+	0.106347i
$987$	−10.2361	+	21.8520i	−0.325819	+	0.695557i
$988$	1.33007	+	2.30374i	0.0423150	+	0.0732917i
$989$	10.8674			0.345562
$990$	10.3781	−	1.79271i	0.329838	−	0.0569760i
$991$		−	23.3231i		−	0.740882i	−0.928856	−	0.370441i	$-0.879207\pi$
$991$		−	23.3231i		−	0.740882i	0.928856	−	0.370441i	$-0.120793\pi$
$992$	0.908017			0.0288296
$993$	3.67683	+	42.8860i	0.116681	+	1.36095i
$994$	2.44148	−	1.40959i	0.0774391	−	0.0447095i
$995$	−12.8411	−	22.2414i	−0.407090	−	0.705101i
$996$	−3.41621	−	4.89697i	−0.108247	−	0.155166i
$997$	8.79770	+	5.07935i	0.278626	+	0.160865i	0.632801	−	0.774314i	$-0.281905\pi$
$997$	8.79770	+	5.07935i	0.278626	+	0.160865i	−0.354175	+	0.935179i	$0.615238\pi$
$998$	18.9262			0.599099
$999$	9.50159	+	30.1450i	0.300617	+	0.953745i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.20	✓	76	37.27	even	6
666.2.k.a.529.1	yes	76	9.7	even	3
666.2.t.a.85.33	yes	76	1.1	even	1	trivial
666.2.t.a.619.33	yes	76	333.286	even	6	inner
1998.2.k.a.1063.10		76	111.101	odd	6
1998.2.k.a.1639.29		76	9.2	odd	6
1998.2.t.a.307.5		76	3.2	odd	2
1998.2.t.a.397.5		76	333.101	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.990992 + 1.42054i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.07358 - 0.619834i) q^{5} +(0.147954 + 1.72572i) q^{6} +2.74469 q^{7} +1.00000i q^{8} +(-1.03587 + 2.81549i) q^{9} +1.23967 q^{10} +(-1.41594 - 2.45249i) q^{11} +(-0.734728 + 1.56849i) q^{12} +(1.66758 - 0.962778i) q^{13} +(2.37697 + 1.37235i) q^{14} +(1.94441 + 0.910819i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.21619 - 0.702166i) q^{17} +(-2.30483 + 1.92035i) q^{18} +(1.19640 + 0.690743i) q^{19} +(1.07358 + 0.619834i) q^{20} +(2.71997 + 3.89895i) q^{21} -2.83189i q^{22} +(-2.66127 - 1.53649i) q^{23} +(-1.42054 + 0.990992i) q^{24} +(-1.73161 + 2.99924i) q^{25} +1.92556 q^{26} +(-5.02605 + 1.31863i) q^{27} +(1.37235 + 2.37697i) q^{28} +(-4.11863 + 2.37789i) q^{29} +(1.22850 + 1.76100i) q^{30} +(-0.786366 - 0.454008i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.08067 - 4.44180i) q^{33} +1.40433 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} +(3.02022 + 1.41476i) q^{39} +(0.619834 + 1.07358i) q^{40} +(-5.78225 - 10.0151i) q^{41} +(0.406089 + 4.73657i) 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} +0.533346 q^{49} +(-2.99924 + 1.73161i) q^{50} +(2.20269 + 1.03180i) q^{51} +(1.66758 + 0.962778i) q^{52} +(5.02762 + 8.70809i) q^{53} +(-5.01201 - 1.37106i) q^{54} +(-3.04027 - 1.75530i) q^{55} +2.74469i q^{56} +(0.204397 + 2.38406i) q^{57} -4.75579 q^{58} -10.1954i q^{59} +(0.183414 + 2.13932i) q^{60} -2.20608i q^{61} +(-0.454008 - 0.786366i) q^{62} +(-2.84314 + 7.72766i) q^{63} -1.00000 q^{64} +(1.19353 - 2.06725i) q^{65} +(4.02281 - 2.80638i) q^{66} +(6.32487 + 10.9550i) q^{67} +(1.21619 + 0.702166i) q^{68} +(-0.454660 - 5.30309i) q^{69} +3.40251 q^{70} +(0.513569 - 0.889528i) q^{71} +(-2.81549 - 1.03587i) q^{72} -2.71210 q^{73} +(2.78100 - 5.40981i) q^{74} +(-5.97655 + 0.512399i) q^{75} +1.38149i q^{76} +(-3.88633 - 6.73132i) q^{77} +(1.90821 + 2.73533i) q^{78} +2.26276i q^{79} +1.23967i q^{80} +(-6.85395 - 5.83295i) q^{81} -11.5645i q^{82} +(-1.72363 + 2.98542i) q^{83} +(-2.01660 + 4.30504i) q^{84} +(0.870453 - 1.50767i) q^{85} -3.53643 q^{86} +(-7.45943 - 3.49421i) q^{87} +(2.45249 - 1.41594i) q^{88} +(-6.58592 + 3.80239i) q^{89} +(-1.28413 + 3.49027i) q^{90} +(4.57700 - 2.64253i) q^{91} -3.07298i q^{92} +(-0.134345 - 1.56698i) q^{93} +5.07591i q^{94} +1.71259 q^{95} +(-1.56849 - 0.734728i) q^{96} +(3.60285 - 2.08011i) q^{97} +(0.461891 + 0.266673i) q^{98} +(8.37168 - 1.44612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} + 38 q^{4} + 4 q^{7} + 2 q^{9} - 4 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{15} - 38 q^{16} - 12 q^{21} - 12 q^{23} + 50 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} - 18 q^{29} - 12 q^{30} - 6 q^{31}+ \cdots - 10 q^{99}+O(q^{100}) \) 76 * q - 2 * q^3 + 38 * q^4 + 4 * q^7 + 2 * q^9 - 4 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^15 - 38 * q^16 - 12 * q^21 - 12 * q^23 + 50 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 - 18 * q^29 - 12 * q^30 - 6 * q^31 + 4 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 18 * q^39 - 36 * q^41 + 42 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^47 + 4 * q^48 + 72 * q^49 + 18 * q^51 + 6 * q^52 + 14 * q^53 + 18 * q^54 + 36 * q^57 + 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 - 16 * q^65 - 20 * q^67 - 66 * q^69 + 2 * q^71 + 28 * q^73 - 20 * q^74 - 78 * q^75 + 12 * q^77 + 22 * q^78 + 26 * q^81 + 32 * q^83 - 6 * q^84 - 12 * q^85 - 8 * q^86 - 72 * q^87 + 60 * q^89 - 10 * q^90 + 42 * q^91 - 6 * q^93 + 28 * q^95 + 12 * q^97 - 24 * q^98 - 10 * q^99

Introduction

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