LMFDB - Embedded newform 168.2.t.a.115.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.4
Character	$\chi$	$=$	168.115
Dual form			168.2.t.a.19.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03162 - 0.967346i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.128485 + 1.99587i) q^{4} +(-1.25150 - 2.16767i) q^{5} +(-0.409738 - 1.35356i) q^{6} +(-1.36321 - 2.26752i) q^{7} +(1.79815 - 2.18327i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.805806 + 3.44685i) q^{10} +(2.83809 - 4.91572i) q^{11} +(-0.886663 + 1.79272i) q^{12} +5.31228 q^{13} +(-0.787162 + 3.65792i) q^{14} -2.50301i q^{15} +(-3.96698 + 0.512879i) q^{16} +(-0.393919 - 0.227429i) q^{17} +(0.321935 - 1.37708i) q^{18} +(-3.19938 + 1.84716i) q^{19} +(4.16558 - 2.77635i) q^{20} +(-0.0468128 - 2.64534i) q^{21} +(-7.68304 + 2.32575i) q^{22} +(-4.43443 + 2.56022i) q^{23} +(2.64888 - 0.991694i) q^{24} +(-0.632521 + 1.09556i) q^{25} +(-5.48026 - 5.13881i) q^{26} +1.00000i q^{27} +(4.35053 - 3.01213i) q^{28} +2.57962i q^{29} +(-2.42127 + 2.58215i) q^{30} +(-3.00333 + 5.20192i) q^{31} +(4.58856 + 3.30835i) q^{32} +(4.91572 - 2.83809i) q^{33} +(0.186372 + 0.615676i) q^{34} +(-3.20917 + 5.79280i) q^{35} +(-1.66423 + 1.10921i) q^{36} +(7.80778 - 4.50782i) q^{37} +(5.08739 + 1.18933i) q^{38} +(4.60057 + 2.65614i) q^{39} +(-6.98299 - 1.16541i) q^{40} +4.65692i q^{41} +(-2.51066 + 2.77427i) q^{42} +3.66703 q^{43} +(10.1758 + 5.03286i) q^{44} +(1.25150 - 2.16767i) q^{45} +(7.05126 + 1.64845i) q^{46} +(0.478841 + 0.829377i) q^{47} +(-3.69195 - 1.53933i) q^{48} +(-3.28332 + 6.18222i) q^{49} +(1.71230 - 0.518335i) q^{50} +(-0.227429 - 0.393919i) q^{51} +(0.682549 + 10.6026i) q^{52} +(5.41124 + 3.12418i) q^{53} +(0.967346 - 1.03162i) q^{54} -14.2075 q^{55} +(-7.40187 - 1.10108i) q^{56} -3.69433 q^{57} +(2.49539 - 2.66119i) q^{58} +(-8.76604 - 5.06108i) q^{59} +(4.99567 - 0.321599i) q^{60} +(2.50184 + 4.33331i) q^{61} +(8.13036 - 2.46115i) q^{62} +(1.28213 - 2.31434i) q^{63} +(-1.53334 - 7.85168i) q^{64} +(-6.64834 - 11.5153i) q^{65} +(-7.81658 - 1.82736i) q^{66} +(4.65133 - 8.05634i) q^{67} +(0.403306 - 0.815431i) q^{68} -5.12043 q^{69} +(8.91429 - 2.87159i) q^{70} +7.35240i q^{71} +(2.78984 + 0.465606i) q^{72} +(5.93541 + 3.42681i) q^{73} +(-12.4153 - 2.90245i) q^{74} +(-1.09556 + 0.632521i) q^{75} +(-4.09777 - 6.14821i) q^{76} +(-15.0154 + 0.265718i) q^{77} +(-2.17664 - 7.19047i) q^{78} +(7.71882 - 4.45646i) q^{79} +(6.07644 + 7.95723i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50485 - 4.80418i) q^{82} +1.96259i q^{83} +(5.27373 - 0.433319i) q^{84} +1.13851i q^{85} +(-3.78299 - 3.54728i) q^{86} +(-1.28981 + 2.23402i) q^{87} +(-5.62904 - 15.0355i) q^{88} +(5.91361 - 3.41423i) q^{89} +(-3.38796 + 1.02558i) q^{90} +(-7.24175 - 12.0457i) q^{91} +(-5.67961 - 8.52158i) q^{92} +(-5.20192 + 3.00333i) q^{93} +(0.308312 - 1.31881i) q^{94} +(8.00807 + 4.62346i) q^{95} +(2.31963 + 5.15939i) q^{96} +3.71270i q^{97} +(9.36748 - 3.20160i) q^{98} +5.67619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$

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 $

$2$	−1.03162	−	0.967346i	−0.729466	−	0.684017i
$2$	−1.03162	−	0.967346i	−0.729466	−	0.684017i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.128485	+	1.99587i	0.0642426	+	0.997934i
$5$	−1.25150	−	2.16767i	−0.559689	−	0.969410i	−0.997522	−	0.0703538i	$-0.977587\pi$
$5$	−1.25150	−	2.16767i	−0.559689	−	0.969410i	0.437833	−	0.899056i	$-0.355746\pi$
$6$	−0.409738	−	1.35356i	−0.167275	−	0.552587i
$7$	−1.36321	−	2.26752i	−0.515245	−	0.857043i
$7$	−1.36321	−	2.26752i	−0.515245	−	0.857043i
$8$	1.79815	−	2.18327i	0.635741	−	0.771903i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.805806	+	3.44685i	−0.254818	+	1.08999i
$11$	2.83809	−	4.91572i	0.855717	−	1.48215i	−0.0202603	−	0.999795i	$-0.506450\pi$
$11$	2.83809	−	4.91572i	0.855717	−	1.48215i	0.875978	−	0.482351i	$-0.160217\pi$
$12$	−0.886663	+	1.79272i	−0.255958	+	0.517512i
$13$	5.31228			1.47336			0.736681	−	0.676241i	$-0.236392\pi$
$13$	5.31228			1.47336			0.736681	+	0.676241i	$0.236392\pi$
$14$	−0.787162	+	3.65792i	−0.210378	+	0.977620i
$15$		−	2.50301i		−	0.646273i
$16$	−3.96698	+	0.512879i	−0.991746	+	0.128220i
$17$	−0.393919	−	0.227429i	−0.0955393	−	0.0551596i	0.451469	−	0.892287i	$-0.350900\pi$
$17$	−0.393919	−	0.227429i	−0.0955393	−	0.0551596i	−0.547008	+	0.837127i	$0.684233\pi$
$18$	0.321935	−	1.37708i	0.0758808	−	0.324582i
$19$	−3.19938	+	1.84716i	−0.733988	+	0.423768i	−0.819879	−	0.572536i	$-0.805960\pi$
$19$	−3.19938	+	1.84716i	−0.733988	+	0.423768i	0.0858912	+	0.996305i	$0.472626\pi$
$20$	4.16558	−	2.77635i	0.931452	−	0.620811i
$21$	−0.0468128	−	2.64534i	−0.0102154	−	0.577260i
$22$	−7.68304	+	2.32575i	−1.63803	+	0.495851i
$23$	−4.43443	+	2.56022i	−0.924642	+	0.533842i	−0.885113	−	0.465376i	$-0.845919\pi$
$23$	−4.43443	+	2.56022i	−0.924642	+	0.533842i	−0.0395287	+	0.999218i	$0.512586\pi$
$24$	2.64888	−	0.991694i	0.540699	−	0.202429i
$25$	−0.632521	+	1.09556i	−0.126504	+	0.219112i
$26$	−5.48026	−	5.13881i	−1.07477	−	1.00780i
$27$			1.00000i			0.192450i
$28$	4.35053	−	3.01213i	0.822172	−	0.569239i
$29$			2.57962i			0.479024i	0.970893	+	0.239512i	$0.0769874\pi$
$29$			2.57962i			0.479024i	−0.970893	+	0.239512i	$0.923013\pi$
$30$	−2.42127	+	2.58215i	−0.442062	+	0.471435i
$31$	−3.00333	+	5.20192i	−0.539414	+	0.934293i	0.459521	+	0.888167i	$0.348021\pi$
$31$	−3.00333	+	5.20192i	−0.539414	+	0.934293i	−0.998936	+	0.0461260i	$0.985312\pi$
$32$	4.58856	+	3.30835i	0.811150	+	0.584839i
$33$	4.91572	−	2.83809i	0.855717	−	0.494049i
$34$	0.186372	+	0.615676i	0.0319626	+	0.105588i
$35$	−3.20917	+	5.79280i	−0.542449	+	0.979161i
$36$	−1.66423	+	1.10921i	−0.277372	+	0.184868i
$37$	7.80778	−	4.50782i	1.28359	−	0.741082i	0.306088	−	0.952003i	$-0.400980\pi$
$37$	7.80778	−	4.50782i	1.28359	−	0.741082i	0.977503	+	0.210922i	$0.0676465\pi$
$38$	5.08739	+	1.18933i	0.825284	+	0.192935i
$39$	4.60057	+	2.65614i	0.736681	+	0.425323i
$40$	−6.98299	−	1.16541i	−1.10411	−	0.184268i
$41$			4.65692i			0.727289i	0.931538	+	0.363644i	$0.118468\pi$
$41$			4.65692i			0.727289i	−0.931538	+	0.363644i	$0.881532\pi$
$42$	−2.51066	+	2.77427i	−0.387404	+	0.428079i
$43$	3.66703			0.559217			0.279608	−	0.960114i	$-0.409795\pi$
$43$	3.66703			0.559217			0.279608	+	0.960114i	$0.409795\pi$
$44$	10.1758	+	5.03286i	1.53406	+	0.758733i
$45$	1.25150	−	2.16767i	0.186563	−	0.323137i
$46$	7.05126	+	1.64845i	1.03965	+	0.243050i
$47$	0.478841	+	0.829377i	0.0698461	+	0.120977i	0.898833	−	0.438290i	$-0.144416\pi$
$47$	0.478841	+	0.829377i	0.0698461	+	0.120977i	−0.828987	+	0.559267i	$0.811082\pi$
$48$	−3.69195	−	1.53933i	−0.532887	−	0.222182i
$49$	−3.28332	+	6.18222i	−0.469046	+	0.883174i
$50$	1.71230	−	0.518335i	0.242156	−	0.0733036i
$51$	−0.227429	−	0.393919i	−0.0318464	−	0.0551596i
$52$	0.682549	+	10.6026i	0.0946526	+	1.47032i
$53$	5.41124	+	3.12418i	0.743290	+	0.429139i	0.823264	−	0.567658i	$-0.192150\pi$
$53$	5.41124	+	3.12418i	0.743290	+	0.429139i	−0.0799741	+	0.996797i	$0.525484\pi$
$54$	0.967346	−	1.03162i	0.131639	−	0.140386i
$55$	−14.2075			−1.91574
$56$	−7.40187	−	1.10108i	−0.989116	−	0.147138i
$57$	−3.69433			−0.489326
$58$	2.49539	−	2.66119i	0.327660	−	0.349432i
$59$	−8.76604	−	5.06108i	−1.14124	−	0.658896i	−0.194503	−	0.980902i	$-0.562310\pi$
$59$	−8.76604	−	5.06108i	−1.14124	−	0.658896i	−0.946738	+	0.322006i	$0.895643\pi$
$60$	4.99567	−	0.321599i	0.644938	−	0.0415183i
$61$	2.50184	+	4.33331i	0.320327	+	0.554823i	0.980555	−	0.196242i	$-0.0628738\pi$
$61$	2.50184	+	4.33331i	0.320327	+	0.554823i	−0.660228	+	0.751065i	$0.729540\pi$
$62$	8.13036	−	2.46115i	1.03256	−	0.312567i
$63$	1.28213	−	2.31434i	0.161533	−	0.291579i
$64$	−1.53334	−	7.85168i	−0.191667	−	0.981460i
$65$	−6.64834	−	11.5153i	−0.824625	−	1.42829i
$66$	−7.81658	−	1.82736i	−0.962155	−	0.224933i
$67$	4.65133	−	8.05634i	0.568251	−	0.984239i	−0.428489	−	0.903547i	$-0.640954\pi$
$67$	4.65133	−	8.05634i	0.568251	−	0.984239i	0.996739	−	0.0806916i	$-0.0257129\pi$
$68$	0.403306	−	0.815431i	0.0489080	−	0.0988856i
$69$	−5.12043			−0.616428
$70$	8.91429	−	2.87159i	1.06546	−	0.343221i
$71$			7.35240i			0.872569i	0.899809	+	0.436285i	$0.143706\pi$
$71$			7.35240i			0.872569i	−0.899809	+	0.436285i	$0.856294\pi$
$72$	2.78984	+	0.465606i	0.328786	+	0.0548721i
$73$	5.93541	+	3.42681i	0.694687	+	0.401078i	0.805366	−	0.592779i	$-0.201969\pi$
$73$	5.93541	+	3.42681i	0.694687	+	0.401078i	−0.110678	+	0.993856i	$0.535302\pi$
$74$	−12.4153	−	2.90245i	−1.44325	−	0.337403i
$75$	−1.09556	+	0.632521i	−0.126504	+	0.0730372i
$76$	−4.09777	−	6.14821i	−0.470046	−	0.705248i
$77$	−15.0154	+	0.265718i	−1.71117	+	0.0302814i
$78$	−2.17664	−	7.19047i	−0.246456	−	0.814161i
$79$	7.71882	−	4.45646i	0.868435	−	0.501391i	0.00160740	−	0.999999i	$-0.499488\pi$
$79$	7.71882	−	4.45646i	0.868435	−	0.501391i	0.866828	+	0.498607i	$0.166155\pi$
$80$	6.07644	+	7.95723i	0.679367	+	0.889645i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.50485	−	4.80418i	0.497478	−	0.530533i
$83$			1.96259i			0.215423i	0.994182	+	0.107711i	$0.0343522\pi$
$83$			1.96259i			0.215423i	−0.994182	+	0.107711i	$0.965648\pi$
$84$	5.27373	−	0.433319i	0.575411	−	0.0472790i
$85$			1.13851i			0.123489i
$86$	−3.78299	−	3.54728i	−0.407930	−	0.382514i
$87$	−1.28981	+	2.23402i	−0.138282	+	0.239512i
$88$	−5.62904	−	15.0355i	−0.600058	−	1.60279i
$89$	5.91361	−	3.41423i	0.626842	−	0.361907i	−0.152686	−	0.988275i	$-0.548792\pi$
$89$	5.91361	−	3.41423i	0.626842	−	0.361907i	0.779528	+	0.626367i	$0.215459\pi$
$90$	−3.38796	+	1.02558i	−0.357122	+	0.108105i
$91$	−7.24175	−	12.0457i	−0.759142	−	1.26273i
$92$	−5.67961	−	8.52158i	−0.592141	−	0.888436i
$93$	−5.20192	+	3.00333i	−0.539414	+	0.311431i
$94$	0.308312	−	1.31881i	0.0317999	−	0.136025i
$95$	8.00807	+	4.62346i	0.821611	+	0.474357i
$96$	2.31963	+	5.15939i	0.236747	+	0.526578i
$97$			3.71270i			0.376967i	0.982076	+	0.188484i	$0.0603573\pi$
$97$			3.71270i			0.376967i	−0.982076	+	0.188484i	$0.939643\pi$
$98$	9.36748	−	3.20160i	0.946259	−	0.323411i
$99$	5.67619			0.570478
$100$	−2.26786	−	1.12167i	−0.226786	−	0.112167i
$101$	−2.84077	+	4.92036i	−0.282667	+	0.489594i	−0.972041	−	0.234812i	$-0.924553\pi$
$101$	−2.84077	+	4.92036i	−0.282667	+	0.489594i	0.689373	+	0.724406i	$0.257886\pi$
$102$	−0.146435	+	0.626377i	−0.0144992	+	0.0620206i
$103$	−2.95345	−	5.11553i	−0.291013	−	0.504049i	0.683037	−	0.730384i	$-0.260659\pi$
$103$	−2.95345	−	5.11553i	−0.291013	−	0.504049i	−0.974049	+	0.226335i	$0.927325\pi$
$104$	9.55226	−	11.5981i	0.936676	−	1.13729i
$105$	−5.67562	+	3.41212i	−0.553884	+	0.332989i
$106$	−2.56019	−	8.45750i	−0.248667	−	0.821465i
$107$	5.33045	+	9.23261i	0.515314	+	0.892550i	0.999842	+	0.0177741i	$0.00565795\pi$
$107$	5.33045	+	9.23261i	0.515314	+	0.892550i	−0.484528	+	0.874776i	$0.661009\pi$
$108$	−1.99587	+	0.128485i	−0.192053	+	0.0123635i
$109$	−2.75319	−	1.58956i	−0.263708	−	0.152252i	0.362317	−	0.932055i	$-0.381986\pi$
$109$	−2.75319	−	1.58956i	−0.263708	−	0.152252i	−0.626025	+	0.779803i	$0.715319\pi$
$110$	14.6568	+	13.7436i	1.39747	+	1.31040i
$111$	9.01565			0.855727
$112$	6.57079	+	8.29606i	0.620882	+	0.783904i
$113$	−0.302446			−0.0284518			−0.0142259	−	0.999899i	$-0.504528\pi$
$113$	−0.302446			−0.0284518			−0.0142259	+	0.999899i	$0.504528\pi$
$114$	3.81115	+	3.57369i	0.356947	+	0.334707i
$115$	11.0994	+	6.40824i	1.03502	+	0.597571i
$116$	−5.14859	+	0.331443i	−0.478034	+	0.0307737i
$117$	2.65614	+	4.60057i	0.245560	+	0.425323i
$118$	4.14742	+	13.7009i	0.381801	+	1.26127i
$119$	0.0212932	+	1.20325i	0.00195194	+	0.110302i
$120$	−5.46474	−	4.50077i	−0.498860	−	0.410862i
$121$	−10.6096	−	18.3763i	−0.964505	−	1.67057i
$122$	1.61086	−	6.89047i	0.145840	−	0.623834i
$123$	−2.32846	+	4.03301i	−0.209950	+	0.363644i
$124$	−10.7682	−	5.32588i	−0.967016	−	0.478278i
$125$	−9.34863			−0.836167
$126$	−3.56143	+	1.14726i	−0.317278	+	0.102206i
$127$		−	6.39751i		−	0.567687i	−0.958871	−	0.283843i	$-0.908390\pi$
$127$		−	6.39751i		−	0.567687i	0.958871	−	0.283843i	$-0.0916096\pi$
$128$	−6.01346	+	9.58323i	−0.531520	+	0.847046i
$129$	3.17574	+	1.83351i	0.279608	+	0.161432i
$130$	−4.28067	+	18.3106i	−0.375439	+	1.60595i
$131$	−12.5596	+	7.25130i	−1.09734	+	0.633549i	−0.935521	−	0.353272i	$-0.885069\pi$
$131$	−12.5596	+	7.25130i	−1.09734	+	0.633549i	−0.161818	+	0.986821i	$0.551736\pi$
$132$	6.29606	+	9.44648i	0.548002	+	0.822211i
$133$	8.54991	+	4.73660i	0.741371	+	0.410715i
$134$	−12.5917	+	3.81165i	−1.08776	+	0.329276i
$135$	2.16767	−	1.25150i	0.186563	−	0.107712i
$136$	−1.20486	+	0.451080i	−0.103316	+	0.0386798i
$137$	−0.615559	+	1.06618i	−0.0525908	+	0.0910899i	−0.891122	−	0.453763i	$-0.850081\pi$
$137$	−0.615559	+	1.06618i	−0.0525908	+	0.0910899i	0.838532	+	0.544853i	$0.183415\pi$
$138$	5.28235	+	4.95323i	0.449663	+	0.421647i
$139$			15.7788i			1.33834i	0.743108	+	0.669172i	$0.233351\pi$
$139$			15.7788i			1.33834i	−0.743108	+	0.669172i	$0.766649\pi$
$140$	−11.9740	−	5.66080i	−1.01199	−	0.478425i
$141$			0.957682i			0.0806514i
$142$	7.11231	−	7.58489i	0.596852	−	0.636510i
$143$	15.0768	−	26.1137i	1.26078	−	2.18374i
$144$	−2.42766	−	3.17907i	−0.202305	−	0.264922i
$145$	5.59176	−	3.22841i	0.464371	−	0.268104i
$146$	−2.80819	−	9.27676i	−0.232407	−	0.767750i
$147$	−5.93455	+	3.71230i	−0.489473	+	0.306185i
$148$	10.0002	+	15.0041i	0.822012	+	1.23333i
$149$	5.15767	−	2.97778i	0.422532	−	0.243949i	−0.273628	−	0.961836i	$-0.588224\pi$
$149$	5.15767	−	2.97778i	0.422532	−	0.243949i	0.696160	+	0.717886i	$0.254890\pi$
$150$	1.74207	+	0.407261i	0.142239	+	0.0332527i
$151$	−3.11126	−	1.79629i	−0.253191	−	0.146180i	0.368034	−	0.929812i	$-0.380031\pi$
$151$	−3.11126	−	1.79629i	−0.253191	−	0.146180i	−0.621224	+	0.783633i	$0.713364\pi$
$152$	−1.72010	+	10.3066i	−0.139518	+	0.835974i
$153$		−	0.454858i		−	0.0367731i
$154$	15.7473	+	14.2510i	1.26895	+	1.14838i
$155$	15.0347			1.20762
$156$	−4.71020	+	9.52341i	−0.377118	+	0.762483i
$157$	0.491762	−	0.851757i	0.0392469	−	0.0679776i	−0.845735	−	0.533604i	$-0.820837\pi$
$157$	0.491762	−	0.851757i	0.0392469	−	0.0679776i	0.884982	+	0.465626i	$0.154171\pi$
$158$	−12.2738	−	2.86939i	−0.976455	−	0.228276i
$159$	3.12418	+	5.41124i	0.247763	+	0.429139i
$160$	1.42880	−	14.0869i	0.112957	−	1.11366i
$161$	11.8504	+	6.56505i	0.933942	+	0.517398i
$162$	1.35356	−	0.409738i	0.106345	−	0.0321920i
$163$	−1.26083	−	2.18383i	−0.0987562	−	0.171051i	0.812414	−	0.583081i	$-0.198153\pi$
$163$	−1.26083	−	2.18383i	−0.0987562	−	0.171051i	−0.911170	+	0.412030i	$0.864820\pi$
$164$	−9.29460	+	0.598345i	−0.725787	+	0.0467229i
$165$	−12.3041	−	7.10377i	−0.957872	−	0.553028i
$166$	1.89851	−	2.02465i	0.147353	−	0.157144i
$167$	5.26232			0.407211			0.203605	−	0.979053i	$-0.434734\pi$
$167$	5.26232			0.407211			0.203605	+	0.979053i	$0.434734\pi$
$168$	−5.85966	−	4.65450i	−0.452083	−	0.359102i
$169$	15.2203			1.17079
$170$	1.10134	−	1.17451i	0.0844686	−	0.0900811i
$171$	−3.19938	−	1.84716i	−0.244663	−	0.141256i
$172$	0.471159	+	7.31891i	0.0359255	+	0.558062i
$173$	0.0718117	+	0.124381i	0.00545974	+	0.00945654i	0.868742	−	0.495264i	$-0.164929\pi$
$173$	0.0718117	+	0.124381i	0.00545974	+	0.00945654i	−0.863283	+	0.504721i	$0.831595\pi$
$174$	3.49166	−	1.05697i	0.264702	−	0.0801285i
$175$	3.34646	−	0.0592202i	0.252969	−	0.00447662i
$176$	−8.73750	+	20.9562i	−0.658614	+	1.57963i
$177$	−5.06108	−	8.76604i	−0.380414	−	0.658896i
$178$	−9.40335	−	2.19832i	−0.704811	−	0.164771i
$179$	9.46239	−	16.3893i	0.707252	−	1.22500i	−0.258621	−	0.965979i	$-0.583268\pi$
$179$	9.46239	−	16.3893i	0.707252	−	1.22500i	0.965873	−	0.259018i	$-0.0833987\pi$
$180$	4.48718	+	2.21932i	0.334455	+	0.165419i
$181$	−22.2260			−1.65204			−0.826022	−	0.563637i	$-0.809402\pi$
$181$	−22.2260			−1.65204			−0.826022	+	0.563637i	$0.809402\pi$
$182$	−4.18163	+	19.4319i	−0.309963	+	1.44039i
$183$			5.00367i			0.369882i
$184$	−2.38410	+	14.2852i	−0.175758	+	1.05312i
$185$	−19.5429	−	11.2831i	−1.43682	−	0.829551i
$186$	8.27167	+	1.93376i	0.606508	+	0.141790i
$187$	−2.23596	+	1.29093i	−0.163509	+	0.0944021i
$188$	−1.59380	+	1.06227i	−0.116240	+	0.0774737i
$189$	2.26752	−	1.36321i	0.164938	−	0.0991589i
$190$	−3.78881	−	12.5162i	−0.274869	−	0.908023i
$191$	10.2112	−	5.89547i	0.738860	−	0.426581i	−0.0827947	−	0.996567i	$-0.526385\pi$
$191$	10.2112	−	5.89547i	0.738860	−	0.426581i	0.821655	+	0.569986i	$0.193051\pi$
$192$	2.59793	−	7.56642i	0.187489	−	0.546060i
$193$	−13.4112	+	23.2289i	−0.965361	+	1.67205i	−0.256719	+	0.966486i	$0.582641\pi$
$193$	−13.4112	+	23.2289i	−0.965361	+	1.67205i	−0.708642	+	0.705568i	$0.750692\pi$
$194$	3.59146	−	3.83010i	0.257852	−	0.274985i
$195$		−	13.2967i		−	0.952195i
$196$	−12.7608	−	5.75875i	−0.911482	−	0.411339i
$197$		−	16.5842i		−	1.18157i	−0.806828	−	0.590786i	$-0.798818\pi$
$197$		−	16.5842i		−	1.18157i	0.806828	−	0.590786i	$-0.201182\pi$
$198$	−5.85568	−	5.49083i	−0.416145	−	0.390217i
$199$	−5.70420	+	9.87996i	−0.404360	+	0.700372i	−0.994247	−	0.107114i	$-0.965839\pi$
$199$	−5.70420	+	9.87996i	−0.404360	+	0.700372i	0.589887	+	0.807486i	$0.299172\pi$
$200$	1.25453	+	3.35094i	0.0887090	+	0.236947i
$201$	8.05634	−	4.65133i	0.568251	−	0.328080i
$202$	7.69029	−	2.32794i	0.541087	−	0.163793i
$203$	5.84935	−	3.51657i	0.410544	−	0.246815i
$204$	0.756989	−	0.504531i	0.0529998	−	0.0353242i
$205$	10.0947	−	5.82815i	0.705041	−	0.407056i
$206$	−1.90164	+	8.13430i	−0.132494	+	0.566744i
$207$	−4.43443	−	2.56022i	−0.308214	−	0.177947i
$208$	−21.0737	+	2.72456i	−1.46120	+	0.188914i
$209$			20.9697i			1.45050i
$210$	9.15580	+	1.97027i	0.631810	+	0.135962i
$211$	−4.13300			−0.284527			−0.142264	−	0.989829i	$-0.545438\pi$
$211$	−4.13300			−0.284527			−0.142264	+	0.989829i	$0.545438\pi$
$212$	−5.54019	+	11.2015i	−0.380502	+	0.769324i
$213$	−3.67620	+	6.36736i	−0.251889	+	0.436285i
$214$	3.43212	−	14.6809i	0.234615	−	1.00357i
$215$	−4.58930	−	7.94890i	−0.312988	−	0.542110i
$216$	2.18327	+	1.79815i	0.148553	+	0.122348i
$217$	15.8896	−	0.281189i	1.07866	−	0.0190883i
$218$	1.30260	+	4.30311i	0.0882233	+	0.291443i
$219$	3.42681	+	5.93541i	0.231562	+	0.401078i
$220$	−1.82546	−	28.3564i	−0.123072	−	1.91179i
$221$	−2.09261	−	1.20817i	−0.140764	−	0.0812701i
$222$	−9.30073	−	8.72125i	−0.624224	−	0.585332i
$223$	18.1063			1.21249			0.606245	−	0.795278i	$-0.292675\pi$
$223$	18.1063			1.21249			0.606245	+	0.795278i	$0.292675\pi$
$224$	1.24659	−	14.9146i	0.0832911	−	0.996525i
$225$	−1.26504			−0.0843361
$226$	0.312010	+	0.292570i	0.0207546	+	0.0194615i
$227$	6.86343	+	3.96260i	0.455542	+	0.263007i	0.710168	−	0.704032i	$-0.248619\pi$
$227$	6.86343	+	3.96260i	0.455542	+	0.263007i	−0.254626	+	0.967040i	$0.581952\pi$
$228$	−0.474666	−	7.37339i	−0.0314355	−	0.488315i
$229$	−1.07787	−	1.86692i	−0.0712274	−	0.123370i	0.828212	−	0.560415i	$-0.189358\pi$
$229$	−1.07787	−	1.86692i	−0.0712274	−	0.123370i	−0.899440	+	0.437045i	$0.856025\pi$
$230$	−5.25139	−	17.3478i	−0.346266	−	1.14388i
$231$	−13.1366	−	7.27760i	−0.864325	−	0.478831i
$232$	5.63201	+	4.63854i	0.369760	+	0.304535i
$233$	10.0072	+	17.3330i	0.655594	+	1.13552i	0.981745	+	0.190204i	$0.0609149\pi$
$233$	10.0072	+	17.3330i	0.655594	+	1.13552i	−0.326151	+	0.945318i	$0.605752\pi$
$234$	1.71021	−	7.31545i	0.111800	−	0.478226i
$235$	1.19854	−	2.07594i	0.0781843	−	0.135419i
$236$	8.97493	−	18.1461i	0.584219	−	1.18121i
$237$	8.91293			0.578957
$238$	1.14199	−	1.26190i	0.0740245	−	0.0817968i
$239$			18.8923i			1.22204i	0.791614	+	0.611021i	$0.209241\pi$
$239$			18.8923i			1.22204i	−0.791614	+	0.611021i	$0.790759\pi$
$240$	1.28374	+	9.92938i	0.0828650	+	0.640939i
$241$	−15.8555	−	9.15417i	−1.02134	−	0.589672i	−0.106849	−	0.994275i	$-0.534076\pi$
$241$	−15.8555	−	9.15417i	−1.02134	−	0.589672i	−0.914492	+	0.404603i	$0.867410\pi$
$242$	−6.83118	+	29.2205i	−0.439125	+	1.87836i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−8.32726	+	5.55010i	−0.533098	+	0.355309i
$245$	17.5101	−	0.619923i	1.11868	−	0.0396054i
$246$	6.30341	−	1.90812i	0.401890	−	0.121657i
$247$	−16.9960	+	9.81265i	−1.08143	+	0.624364i
$248$	5.95677	+	15.9109i	0.378255	+	1.01034i
$249$	−0.981297	+	1.69966i	−0.0621872	+	0.107711i
$250$	9.64424	+	9.04335i	0.609955	+	0.571952i
$251$			3.43251i			0.216658i	0.994115	+	0.108329i	$0.0345500\pi$
$251$			3.43251i			0.216658i	−0.994115	+	0.108329i	$0.965450\pi$
$252$	4.78384	+	2.26160i	0.301354	+	0.142467i
$253$			29.0645i			1.82727i
$254$	−6.18860	+	6.59981i	−0.388307	+	0.414109i
$255$	−0.569256	+	0.985981i	−0.0356482	+	0.0617445i
$256$	15.4739	−	4.06917i	0.967119	−	0.254323i
$257$	21.7104	−	12.5345i	1.35426	−	0.781882i	0.365417	−	0.930844i	$-0.380927\pi$
$257$	21.7104	−	12.5345i	1.35426	−	0.781882i	0.988843	+	0.148962i	$0.0475932\pi$
$258$	−1.50252	−	4.96353i	−0.0935428	−	0.309016i
$259$	−20.8652	−	11.5592i	−1.29650	−	0.718254i
$260$	22.1287	−	14.7487i	1.37237	−	0.914678i
$261$	−2.23402	+	1.28981i	−0.138282	+	0.0798373i
$262$	19.9713	+	4.66890i	1.23383	+	0.288445i
$263$	−13.4314	−	7.75460i	−0.828214	−	0.478169i	0.0250270	−	0.999687i	$-0.492033\pi$
$263$	−13.4314	−	7.75460i	−0.828214	−	0.478169i	−0.853241	+	0.521517i	$0.825366\pi$
$264$	2.64286	−	15.8357i	0.162657	−	0.974617i
$265$		−	15.6397i		−	0.960738i
$266$	−4.23834	−	13.1571i	−0.259870	−	0.806713i
$267$	6.82845			0.417894
$268$	16.6770	+	8.24832i	1.01871	+	0.503847i
$269$	11.8667	−	20.5537i	0.723523	−	1.25318i	−0.236055	−	0.971740i	$-0.575855\pi$
$269$	11.8667	−	20.5537i	0.723523	−	1.25318i	0.959579	−	0.281440i	$-0.0908120\pi$
$270$	−3.44685	−	0.805806i	−0.209768	−	0.0490398i
$271$	−7.35684	−	12.7424i	−0.446896	−	0.774047i	0.551286	−	0.834316i	$-0.314137\pi$
$271$	−7.35684	−	12.7424i	−0.446896	−	0.774047i	−0.998182	+	0.0602693i	$0.980804\pi$
$272$	1.67931	+	0.700175i	0.101823	+	0.0424543i
$273$	−0.248683	−	14.0528i	−0.0150510	−	0.850513i
$274$	1.66639	−	0.504436i	0.100670	−	0.0304741i
$275$	3.59031	+	6.21859i	0.216504	+	0.374995i
$276$	−0.657900	−	10.2197i	−0.0396009	−	0.615154i
$277$	−6.16822	−	3.56123i	−0.370613	−	0.213973i	0.303113	−	0.952954i	$-0.401974\pi$
$277$	−6.16822	−	3.56123i	−0.370613	−	0.213973i	−0.673726	+	0.738981i	$0.735307\pi$
$278$	15.2636	−	16.2778i	0.915449	−	0.976277i
$279$	−6.00666			−0.359609
$280$	6.87668	+	17.4228i	0.410960	+	1.04121i
$281$	−13.0561			−0.778861			−0.389430	−	0.921056i	$-0.627328\pi$
$281$	−13.0561			−0.778861			−0.389430	+	0.921056i	$0.627328\pi$
$282$	0.926409	−	0.987965i	0.0551669	−	0.0588325i
$283$	−1.83051	−	1.05685i	−0.108813	−	0.0628230i	0.444606	−	0.895726i	$-0.353344\pi$
$283$	−1.83051	−	1.05685i	−0.108813	−	0.0628230i	−0.553419	+	0.832903i	$0.686677\pi$
$284$	−14.6744	+	0.944674i	−0.870767	+	0.0560561i
$285$	4.62346	+	8.00807i	0.273870	+	0.474357i
$286$	−40.8145	+	12.3550i	−2.41341	+	0.730568i
$287$	10.5597	−	6.34836i	0.623318	−	0.374732i
$288$	−0.570834	+	5.62798i	−0.0336367	+	0.331632i
$289$	−8.39655	−	14.5433i	−0.493915	−	0.855486i
$290$	−8.89156	−	2.07867i	−0.522131	−	0.122064i
$291$	−1.85635	+	3.21529i	−0.108821	+	0.188484i
$292$	−6.07685	+	12.2866i	−0.355621	+	0.719018i
$293$	−0.334002			−0.0195126			−0.00975630	−	0.999952i	$-0.503106\pi$
$293$	−0.334002			−0.0195126			−0.00975630	+	0.999952i	$0.503106\pi$
$294$	9.71328	+	1.91107i	0.566490	+	0.111456i
$295$			25.3358i			1.47511i
$296$	4.19774	−	25.1522i	0.243988	−	1.46194i
$297$	4.91572	+	2.83809i	0.285239	+	0.164683i
$298$	−8.20130	−	1.91730i	−0.475089	−	0.111066i
$299$	−23.5569	+	13.6006i	−1.36233	+	0.786542i
$300$	−1.40319	−	2.10532i	−0.0810133	−	0.121551i
$301$	−4.99893	−	8.31507i	−0.288134	−	0.479273i
$302$	1.47201	+	4.86275i	0.0847047	+	0.279820i
$303$	−4.92036	+	2.84077i	−0.282667	+	0.163198i
$304$	11.7445	−	8.96856i	0.673594	−	0.514382i
$305$	6.26211	−	10.8463i	0.358567	−	0.621057i
$306$	−0.440005	+	0.469241i	−0.0251534	+	0.0268247i
$307$		−	9.39141i		−	0.535996i	−0.963419	−	0.267998i	$-0.913638\pi$
$307$		−	9.39141i		−	0.535996i	0.963419	−	0.267998i	$-0.0863621\pi$
$308$	−2.45960	−	29.9347i	−0.140149	−	1.70569i
$309$		−	5.90691i		−	0.336032i
$310$	−15.5101	−	14.5438i	−0.880916	−	0.826030i
$311$	−7.93750	+	13.7482i	−0.450095	+	0.779587i	−0.998391	−	0.0566971i	$-0.981943\pi$
$311$	−7.93750	+	13.7482i	−0.450095	+	0.779587i	0.548297	+	0.836284i	$0.315276\pi$
$312$	14.0716	−	5.26816i	0.796646	−	0.298251i
$313$	−27.8562	+	16.0828i	−1.57453	+	0.909054i	−0.578924	+	0.815381i	$0.696527\pi$
$313$	−27.8562	+	16.0828i	−1.57453	+	0.909054i	−0.995603	+	0.0936727i	$0.970139\pi$
$314$	−1.33125	+	0.402987i	−0.0751271	+	0.0227418i
$315$	−6.62130	+	0.117173i	−0.373068	+	0.00660194i
$316$	9.88627	+	14.8332i	0.556146	+	0.834431i
$317$	−13.2252	+	7.63558i	−0.742802	+	0.428857i	−0.823087	−	0.567915i	$-0.807750\pi$
$317$	−13.2252	+	7.63558i	−0.742802	+	0.428857i	0.0802854	+	0.996772i	$0.474417\pi$
$318$	2.01157	−	8.60451i	0.112803	−	0.482517i
$319$	12.6807	+	7.32121i	0.709983	+	0.409909i
$320$	−15.1009	+	13.1502i	−0.844163	+	0.735117i
$321$			10.6609i			0.595033i
$322$	−5.87446	−	18.2361i	−0.327371	−	1.01626i
$323$	1.68039			0.0934996
$324$	−1.79272	−	0.886663i	−0.0995953	−	0.0492590i
$325$	−3.36013	+	5.81991i	−0.186386	+	0.322831i
$326$	−0.811814	+	3.47255i	−0.0449622	+	0.192327i
$327$	−1.58956	−	2.75319i	−0.0879027	−	0.152252i
$328$	10.1673	+	8.37383i	0.561396	+	0.462367i
$329$	1.22787	−	2.21640i	0.0676947	−	0.122194i
$330$	5.82136	+	19.2307i	0.320455	+	1.05862i
$331$	10.5189	+	18.2193i	0.578174	+	1.00143i	0.995689	+	0.0927561i	$0.0295677\pi$
$331$	10.5189	+	18.2193i	0.578174	+	1.00143i	−0.417515	+	0.908670i	$0.637099\pi$
$332$	−3.91708	+	0.252164i	−0.214978	+	0.0138393i
$333$	7.80778	+	4.50782i	0.427864	+	0.247027i
$334$	−5.42872	−	5.09048i	−0.297046	−	0.278539i
$335$	−23.2846			−1.27217
$336$	1.54244	+	10.4700i	0.0841472	+	0.571185i
$337$	1.18351			0.0644697			0.0322348	−	0.999480i	$-0.489738\pi$
$337$	1.18351			0.0644697			0.0322348	+	0.999480i	$0.489738\pi$
$338$	−15.7016	−	14.7233i	−0.854056	−	0.800843i
$339$	−0.261926	−	0.151223i	−0.0142259	−	0.00821332i
$340$	−2.27232	+	0.146282i	−0.123234	+	0.00793326i
$341$	17.0475	+	29.5271i	0.923172	+	1.59898i
$342$	1.51370	+	5.00048i	0.0818517	+	0.270395i
$343$	18.4942	−	0.982659i	0.998591	−	0.0530586i
$344$	6.59386	−	8.00612i	0.355517	−	0.431661i
$345$	6.40824	+	11.0994i	0.345008	+	0.597571i
$346$	0.0462374	−	0.197781i	0.00248574	−	0.0106328i
$347$	2.40670	−	4.16854i	0.129199	−	0.223779i	−0.794168	−	0.607699i	$-0.792093\pi$
$347$	2.40670	−	4.16854i	0.129199	−	0.223779i	0.923366	+	0.383920i	$0.125426\pi$
$348$	−4.62453	−	2.28726i	−0.247901	−	0.122610i
$349$	35.4792			1.89916			0.949578	−	0.313530i	$-0.101512\pi$
$349$	35.4792			1.89916			0.949578	+	0.313530i	$0.101512\pi$
$350$	−3.50957	−	3.17609i	−0.187594	−	0.169769i
$351$			5.31228i			0.283549i
$352$	29.2857	−	13.1667i	1.56093	−	0.701786i
$353$	−4.13712	−	2.38857i	−0.220197	−	0.127131i	0.385845	−	0.922564i	$-0.373910\pi$
$353$	−4.13712	−	2.38857i	−0.220197	−	0.127131i	−0.606041	+	0.795433i	$0.707243\pi$
$354$	−3.25868	+	13.9390i	−0.173197	+	0.740852i
$355$	15.9375	−	9.20155i	0.845877	−	0.488367i
$356$	7.57416	+	11.3641i	0.401430	+	0.602297i
$357$	−0.583186	+	1.05269i	−0.0308655	+	0.0557145i
$358$	−25.6158	+	7.75419i	−1.35383	+	0.409822i
$359$	−31.9690	+	18.4573i	−1.68726	+	0.974140i	−0.730656	+	0.682745i	$0.760786\pi$
$359$	−31.9690	+	18.4573i	−1.68726	+	0.974140i	−0.956603	+	0.291394i	$0.905881\pi$
$360$	−2.48222	−	6.63015i	−0.130824	−	0.349440i
$361$	−2.67598	+	4.63493i	−0.140841	+	0.243943i
$362$	22.9288	+	21.5002i	1.20511	+	1.13003i
$363$		−	21.2191i		−	1.11371i
$364$	23.1112	−	16.0013i	1.21136	−	0.838695i
$365$		−	17.1547i		−	0.897916i
$366$	4.84028	−	5.16189i	0.253005	−	0.269816i
$367$	−0.284416	+	0.492623i	−0.0148464	+	0.0257147i	−0.873353	−	0.487088i	$-0.838059\pi$
$367$	−0.284416	+	0.492623i	−0.0148464	+	0.0257147i	0.858507	+	0.512802i	$0.171393\pi$
$368$	16.2782	−	12.4307i	0.848560	−	0.647993i
$369$	−4.03301	+	2.32846i	−0.209950	+	0.121215i
$370$	9.24623	+	30.5447i	0.480689	+	1.58794i
$371$	−0.292503	−	16.5290i	−0.0151860	−	0.858143i
$372$	−6.66262	−	9.99647i	−0.345441	−	0.518293i
$373$	−20.2929	+	11.7161i	−1.05073	+	0.606638i	−0.922853	−	0.385153i	$-0.874149\pi$
$373$	−20.2929	+	11.7161i	−1.05073	+	0.606638i	−0.127874	+	0.991790i	$0.540815\pi$
$374$	3.55544	+	0.831191i	0.183847	+	0.0429799i
$375$	−8.09615	−	4.67431i	−0.418083	−	0.241380i
$376$	2.67178	+	0.445902i	0.137787	+	0.0229956i
$377$			13.7037i			0.705775i
$378$	−3.65792	−	0.787162i	−0.188143	−	0.0404872i
$379$	−14.7240			−0.756320			−0.378160	−	0.925740i	$-0.623443\pi$
$379$	−14.7240			−0.756320			−0.378160	+	0.925740i	$0.623443\pi$
$380$	−8.19890	+	16.5771i	−0.420595	+	0.850387i
$381$	3.19875	−	5.54040i	0.163877	−	0.283843i
$382$	−16.2371	−	3.79592i	−0.830762	−	0.194216i
$383$	2.49754	+	4.32587i	0.127618	+	0.221042i	0.922753	−	0.385391i	$-0.125933\pi$
$383$	2.49754	+	4.32587i	0.127618	+	0.221042i	−0.795135	+	0.606432i	$0.792600\pi$
$384$	−9.99943	+	5.29259i	−0.510281	+	0.270086i
$385$	19.3678	+	32.2159i	0.987077	+	1.64187i
$386$	36.3057	−	10.9902i	1.84791	−	0.559385i
$387$	1.83351	+	3.17574i	0.0932028	+	0.161432i
$388$	−7.41006	+	0.477027i	−0.376189	+	0.0242174i
$389$	27.6098	+	15.9405i	1.39987	+	0.808216i	0.994379	−	0.105883i	$-0.0337668\pi$
$389$	27.6098	+	15.9405i	1.39987	+	0.808216i	0.405492	+	0.914099i	$0.367100\pi$
$390$	−12.8625	+	13.7171i	−0.651317	+	0.694594i
$391$	2.32907			0.117786
$392$	7.59356	+	18.2849i	0.383533	+	0.923527i
$393$	−14.5026			−0.731559
$394$	−16.0426	+	17.1086i	−0.808215	+	0.861917i
$395$	−19.3203	−	11.1546i	−0.972108	−	0.561247i
$396$	0.729306	+	11.3289i	0.0366490	+	0.569300i
$397$	−16.4530	−	28.4975i	−0.825753	−	1.43025i	−0.901343	−	0.433107i	$-0.857417\pi$
$397$	−16.4530	−	28.4975i	−0.825753	−	1.43025i	0.0755896	−	0.997139i	$-0.475916\pi$
$398$	15.4419	−	4.67445i	0.774033	−	0.234309i
$399$	5.03614	+	8.37697i	0.252122	+	0.419373i
$400$	1.94731	−	4.67047i	0.0973655	−	0.233523i
$401$	−0.106236	−	0.184006i	−0.00530517	−	0.00918883i	0.863361	−	0.504587i	$-0.168355\pi$
$401$	−0.106236	−	0.184006i	−0.00530517	−	0.00918883i	−0.868666	+	0.495399i	$0.835022\pi$
$402$	−12.8105	−	2.99485i	−0.638932	−	0.149370i
$403$	−15.9545	+	27.6341i	−0.794752	+	1.37655i
$404$	−10.1854	−	5.03762i	−0.506742	−	0.250631i
$405$	2.50301			0.124375
$406$	−9.43605	−	2.03058i	−0.468303	−	0.100776i
$407$		−	51.1745i		−	2.53663i
$408$	−1.26898	−	0.211784i	−0.0628240	−	0.0104849i
$409$	17.7288	+	10.2357i	0.876633	+	0.506124i	0.869547	−	0.493851i	$-0.164411\pi$
$409$	17.7288	+	10.2357i	0.876633	+	0.506124i	0.00708628	+	0.999975i	$0.497744\pi$
$410$	−16.0517	−	3.75257i	−0.792737	−	0.185326i
$411$	−1.06618	+	0.615559i	−0.0525908	+	0.0303633i
$412$	9.83046	−	6.55198i	0.484312	−	0.322793i
$413$	0.473847	+	26.7765i	0.0233165	+	1.31759i
$414$	2.09803	+	6.93080i	0.103113	+	0.340630i
$415$	4.25425	−	2.45619i	0.208833	−	0.120570i
$416$	24.3757	+	17.5749i	1.19512	+	0.861679i
$417$	−7.88942	+	13.6649i	−0.386347	+	0.669172i
$418$	20.2849	−	21.6328i	0.992169	−	1.05809i
$419$		−	11.8439i		−	0.578614i	−0.957236	−	0.289307i	$-0.906575\pi$
$419$		−	11.8439i		−	0.578614i	0.957236	−	0.289307i	$-0.0934248\pi$
$420$	−7.53938	−	10.8894i	−0.367884	−	0.531348i
$421$		−	21.7928i		−	1.06211i	−0.847336	−	0.531057i	$-0.821795\pi$
$421$		−	21.7928i		−	1.06211i	0.847336	−	0.531057i	$-0.178205\pi$
$422$	4.26369	+	3.99804i	0.207553	+	0.194621i
$423$	−0.478841	+	0.829377i	−0.0232820	+	0.0403257i
$424$	16.5511	−	6.19646i	0.803793	−	0.300927i
$425$	0.498323	−	0.287707i	0.0241722	−	0.0139558i
$426$	9.95188	−	3.01255i	0.482170	−	0.145959i
$427$	6.41534	−	11.5802i	0.310460	−	0.560404i
$428$	−17.7422	+	11.8251i	−0.857601	+	0.571589i
$429$	26.1137	−	15.0768i	1.26078	−	0.727912i
$430$	−2.95491	+	12.6397i	−0.142499	+	0.609540i
$431$	14.3234	+	8.26964i	0.689936	+	0.398335i	0.803588	−	0.595186i	$-0.202922\pi$
$431$	14.3234	+	8.26964i	0.689936	+	0.398335i	−0.113652	+	0.993521i	$0.536255\pi$
$432$	−0.512879	−	3.96698i	−0.0246759	−	0.190862i
$433$		−	39.2724i		−	1.88731i	−0.330929	−	0.943656i	$-0.607362\pi$
$433$		−	39.2724i		−	1.88731i	0.330929	−	0.943656i	$-0.392638\pi$
$434$	−16.6641	−	15.0807i	−0.799903	−	0.723897i
$435$	6.45681			0.309580
$436$	2.81880	−	5.69924i	0.134996	−	0.272944i
$437$	9.45828	−	16.3822i	0.452451	−	0.783668i
$438$	2.20642	−	9.43800i	0.105427	−	0.450965i
$439$	15.5165	+	26.8754i	0.740564	+	1.28269i	0.952239	+	0.305355i	$0.0987750\pi$
$439$	15.5165	+	26.8754i	0.740564	+	1.28269i	−0.211674	+	0.977340i	$0.567892\pi$
$440$	−25.5472	+	31.0189i	−1.21792	+	1.47877i
$441$	−6.99562	+	0.247671i	−0.333125	+	0.0117939i
$442$	0.990063	+	3.27064i	0.0470925	+	0.155569i
$443$	0.422464	+	0.731729i	0.0200719	+	0.0347655i	0.875887	−	0.482517i	$-0.160277\pi$
$443$	0.422464	+	0.731729i	0.0200719	+	0.0347655i	−0.855815	+	0.517282i	$0.826944\pi$
$444$	1.15838	+	17.9940i	0.0549741	+	0.853960i
$445$	−14.8018	−	8.54583i	−0.701673	−	0.405111i
$446$	−18.6789	−	17.5151i	−0.884470	−	0.829363i
$447$	5.95556			0.281688
$448$	−15.7136	+	14.1804i	−0.742398	+	0.669959i
$449$	−41.7433			−1.96999			−0.984995	−	0.172585i	$-0.944788\pi$
$449$	−41.7433			−1.96999			−0.984995	+	0.172585i	$0.944788\pi$
$450$	1.30504	+	1.22373i	0.0615203	+	0.0576873i
$451$	22.8921	+	13.2168i	1.07795	+	0.622354i
$452$	−0.0388599	−	0.603643i	−0.00182782	−	0.0283930i
$453$	−1.79629	−	3.11126i	−0.0843968	−	0.146180i
$454$	−3.24726	−	10.7272i	−0.152401	−	0.503453i
$455$	−17.0480	+	30.7730i	−0.799224	+	1.44266i
$456$	−6.64294	+	8.06571i	−0.311084	+	0.377712i
$457$	3.74286	+	6.48282i	0.175083	+	0.303254i	0.940190	−	0.340650i	$-0.110647\pi$
$457$	3.74286	+	6.48282i	0.175083	+	0.303254i	−0.765107	+	0.643904i	$0.777314\pi$
$458$	−0.694006	+	2.96862i	−0.0324288	+	0.138715i
$459$	0.227429	−	0.393919i	0.0106155	−	0.0183865i
$460$	−11.3639	+	22.9763i	−0.529844	+	1.07128i
$461$	−4.33499			−0.201901			−0.100950	−	0.994891i	$-0.532188\pi$
$461$	−4.33499			−0.201901			−0.100950	+	0.994891i	$0.532188\pi$
$462$	6.51205	+	20.2154i	0.302968	+	0.940504i
$463$		−	35.3200i		−	1.64146i	−0.571316	−	0.820730i	$-0.693567\pi$
$463$		−	35.3200i		−	1.64146i	0.571316	−	0.820730i	$-0.306433\pi$
$464$	−1.32303	−	10.2333i	−0.0614203	−	0.475070i
$465$	13.0204	+	7.51736i	0.603809	+	0.348609i
$466$	6.44334	−	27.5615i	0.298482	−	1.27676i
$467$	9.09213	−	5.24934i	0.420733	−	0.242911i	−0.274658	−	0.961542i	$-0.588565\pi$
$467$	9.09213	−	5.24934i	0.420733	−	0.242911i	0.695391	+	0.718632i	$0.255231\pi$
$468$	−8.84086	+	5.89241i	−0.408669	+	0.272377i
$469$	−24.6087	+	0.435484i	−1.13632	+	0.0201088i
$470$	−3.24459	+	0.982175i	−0.149662	+	0.0453044i
$471$	0.851757	−	0.491762i	0.0392469	−	0.0226592i
$472$	−26.8123	+	10.0381i	−1.23414	+	0.462040i
$473$	10.4074	−	18.0261i	0.478532	−	0.828841i
$474$	−9.19477	−	8.62188i	−0.422330	−	0.396016i
$475$		−	4.67348i		−	0.214434i
$476$	−2.39880	+	0.197099i	−0.109949	+	0.00903400i
$477$			6.24836i			0.286093i
$478$	18.2754	−	19.4897i	0.835897	−	0.891439i
$479$	−8.46375	+	14.6596i	−0.386719	+	0.669816i	−0.992006	−	0.126191i	$-0.959725\pi$
$479$	−8.46375	+	14.6596i	−0.386719	+	0.669816i	0.605287	+	0.796007i	$0.293058\pi$
$480$	8.28081	−	11.4852i	0.377966	−	0.524225i
$481$	41.4771	−	23.9468i	1.89119	−	1.09188i
$482$	7.50161	+	24.7814i	0.341689	+	1.12876i
$483$	6.98022	+	11.6107i	0.317611	+	0.528305i
$484$	35.3135	−	23.5364i	1.60516	−	1.06983i
$485$	8.04790	−	4.64645i	0.365436	−	0.210985i
$486$	1.37708	+	0.321935i	0.0624658	+	0.0146033i
$487$	−20.5482	−	11.8635i	−0.931127	−	0.537586i	−0.0439591	−	0.999033i	$-0.513997\pi$
$487$	−20.5482	−	11.8635i	−0.931127	−	0.537586i	−0.887168	+	0.461447i	$0.847330\pi$
$488$	13.9594	+	2.32974i	0.631914	+	0.105462i
$489$		−	2.52167i		−	0.114034i
$490$	−18.6634	−	16.2988i	−0.843129	−	0.736303i
$491$	−3.41198			−0.153980			−0.0769901	−	0.997032i	$-0.524531\pi$
$491$	−3.41198			−0.153980			−0.0769901	+	0.997032i	$0.524531\pi$
$492$	−8.34854	−	4.12912i	−0.376381	−	0.186155i
$493$	0.586681	−	1.01616i	0.0264228	−	0.0457656i
$494$	27.0257	+	6.31807i	1.21594	+	0.284264i
$495$	−7.10377	−	12.3041i	−0.319291	−	0.553028i
$496$	9.24621	−	22.1763i	0.415167	−	0.995744i
$497$	16.6717	−	10.0229i	0.747829	−	0.449587i
$498$	2.65648	−	0.804149i	0.119040	−	0.0360348i
$499$	8.72998	+	15.1208i	0.390808	+	0.676899i	0.992556	−	0.121787i	$-0.0388624\pi$
$499$	8.72998	+	15.1208i	0.390808	+	0.676899i	−0.601749	+	0.798686i	$0.705529\pi$
$500$	−1.20116	−	18.6586i	−0.0537175	−	0.834439i
$501$	4.55730	+	2.63116i	0.203605	+	0.117552i
$502$	3.32043	−	3.54105i	0.148198	−	0.158045i
$503$	−7.08646			−0.315970			−0.157985	−	0.987442i	$-0.550500\pi$
$503$	−7.08646			−0.315970			−0.157985	+	0.987442i	$0.550500\pi$
$504$	−2.74737	−	6.96075i	−0.122377	−	0.310056i
$505$	14.2209			0.632824
$506$	28.1155	−	29.9836i	1.24988	−	1.33293i
$507$	13.1812	+	7.61017i	0.585397	+	0.337979i
$508$	12.7686	−	0.821985i	0.566514	−	0.0364697i
$509$	−18.9653	−	32.8488i	−0.840622	−	1.45600i	−0.889370	−	0.457188i	$-0.848857\pi$
$509$	−18.9653	−	32.8488i	−0.840622	−	1.45600i	0.0487485	−	0.998811i	$-0.484477\pi$
$510$	1.54104	−	0.466491i	0.0682385	−	0.0206566i
$511$	−0.320837	−	18.1301i	−0.0141930	−	0.802030i
$512$	−19.8995	−	10.7708i	−0.879442	−	0.476006i
$513$	−1.84716	−	3.19938i	−0.0815543	−	0.141256i
$514$	−34.5222	−	8.07061i	−1.52271	−	0.355979i
$515$	−7.39252	+	12.8042i	−0.325753	+	0.564221i
$516$	−3.25142	+	6.57394i	−0.143136	+	0.289402i
$517$	5.43598			0.239074
$518$	10.3433	+	32.1086i	0.454457	+	1.41077i
$519$			0.143623i			0.00630436i
$520$	−37.0956	−	6.19100i	−1.62675	−	0.271494i
$521$	6.91166	+	3.99045i	0.302805	+	0.174825i	0.643702	−	0.765276i	$-0.277397\pi$
$521$	6.91166	+	3.99045i	0.302805	+	0.174825i	−0.340897	+	0.940101i	$0.610731\pi$
$522$	3.55235	+	0.830471i	0.155482	+	0.0363487i
$523$	12.3267	−	7.11681i	0.539008	−	0.311196i	−0.205669	−	0.978622i	$-0.565937\pi$
$523$	12.3267	−	7.11681i	0.539008	−	0.311196i	0.744677	+	0.667425i	$0.232604\pi$
$524$	−16.0864	−	24.1357i	−0.702736	−	1.05437i
$525$	2.92773	+	1.62194i	0.127777	+	0.0707874i
$526$	6.35470	+	20.9926i	0.277078	+	0.915320i
$527$	2.36614	−	1.36609i	0.103071	−	0.0595078i
$528$	−18.0450	+	13.7798i	−0.785307	+	0.599691i
$529$	1.60942	−	2.78759i	0.0699747	−	0.121200i
$530$	−15.1290	+	16.1342i	−0.657161	+	0.700826i
$531$		−	10.1222i		−	0.439264i
$532$	−8.35509	+	17.6731i	−0.362239	+	0.766225i
$533$			24.7389i			1.07156i
$534$	−7.04438	−	6.60547i	−0.304840	−	0.285847i
$535$	13.3421	−	23.1093i	0.576831	−	0.999101i
$536$	−9.22540	−	24.6416i	−0.398476	−	1.06435i
$537$	16.3893	−	9.46239i	0.707252	−	0.408332i
$538$	−32.1244	+	9.72444i	−1.38498	+	0.419250i
$539$	21.0717	+	33.6856i	0.907622	+	1.45094i
$540$	2.77635	+	4.16558i	0.119475	+	0.179258i
$541$	6.43282	−	3.71399i	0.276569	−	0.159677i	−0.355300	−	0.934752i	$-0.615621\pi$
$541$	6.43282	−	3.71399i	0.276569	−	0.159677i	0.631869	+	0.775075i	$0.282288\pi$
$542$	−4.73685	+	20.2620i	−0.203465	+	0.870326i
$543$	−19.2483	−	11.1130i	−0.826022	−	0.476904i
$544$	−1.05510	−	2.34679i	−0.0452372	−	0.100618i
$545$			7.95734i			0.340855i
$546$	−13.3373	+	14.7377i	−0.570786	+	0.630716i
$547$	−28.2287			−1.20697			−0.603485	−	0.797374i	$-0.706222\pi$
$547$	−28.2287			−1.20697			−0.603485	+	0.797374i	$0.706222\pi$
$548$	−2.20705	−	1.09159i	−0.0942803	−	0.0466303i
$549$	−2.50184	+	4.33331i	−0.106776	+	0.184941i
$550$	2.31169	−	9.88830i	0.0985708	−	0.421638i
$551$	−4.76498	−	8.25319i	−0.202995	−	0.351598i
$552$	−9.20729	+	11.1793i	−0.391888	+	0.475822i
$553$	−20.6275	−	11.4275i	−0.877171	−	0.485947i
$554$	2.91834	+	9.64064i	0.123988	+	0.409592i
$555$	−11.2831	−	19.5429i	−0.478941	−	0.829551i
$556$	−31.4925	+	2.02735i	−1.33558	+	0.0859787i
$557$	−29.9378	−	17.2846i	−1.26850	−	0.732371i	−0.293799	−	0.955867i	$-0.594920\pi$
$557$	−29.9378	−	17.2846i	−1.26850	−	0.732371i	−0.974705	+	0.223496i	$0.928253\pi$
$558$	6.19660	+	5.81052i	0.262323	+	0.245979i
$559$	19.4803			0.823929
$560$	9.75973	−	24.6258i	0.412424	−	1.04063i
$561$	−2.58186			−0.109006
$562$	13.4689	+	12.6297i	0.568153	+	0.532754i
$563$	−10.1504	−	5.86033i	−0.427788	−	0.246983i	0.270616	−	0.962687i	$-0.412773\pi$
$563$	−10.1504	−	5.86033i	−0.427788	−	0.246983i	−0.698404	+	0.715704i	$0.746106\pi$
$564$	−1.91141	+	0.123048i	−0.0804848	+	0.00518125i
$565$	0.378513	+	0.655603i	0.0159242	+	0.0275814i
$566$	0.866059	+	2.86100i	0.0364032	+	0.120257i
$567$	2.64534	−	0.0468128i	0.111094	−	0.00196595i
$568$	16.0523	+	13.2207i	0.673538	+	0.554728i
$569$	5.55324	+	9.61849i	0.232804	+	0.403228i	0.958632	−	0.284648i	$-0.0918766\pi$
$569$	5.55324	+	9.61849i	0.232804	+	0.403228i	−0.725828	+	0.687876i	$0.758543\pi$
$570$	2.97691	−	12.7338i	0.124689	−	0.533359i
$571$	17.7557	−	30.7537i	0.743052	−	1.28700i	−0.208047	−	0.978119i	$-0.566711\pi$
$571$	17.7557	−	30.7537i	0.743052	−	1.28700i	0.951099	−	0.308885i	$-0.0999558\pi$
$572$	54.0567	+	26.7360i	2.26022	+	1.11789i
$573$	11.7909			0.492573
$574$	−17.0346	−	3.66575i	−0.711012	−	0.153005i
$575$		−	6.47756i		−	0.270133i
$576$	6.03309	−	5.25375i	0.251379	−	0.218906i
$577$	−23.4304	−	13.5276i	−0.975421	−	0.563159i	−0.0745363	−	0.997218i	$-0.523748\pi$
$577$	−23.4304	−	13.5276i	−0.975421	−	0.563159i	−0.900885	+	0.434059i	$0.857081\pi$
$578$	−5.40629	+	23.1255i	−0.224872	+	0.961894i
$579$	−23.2289	+	13.4112i	−0.965361	+	0.557351i
$580$	7.16193	+	10.7456i	0.297383	+	0.446188i
$581$	4.45023	−	2.67543i	0.184627	−	0.110995i
$582$	5.02535	−	1.52123i	0.208307	−	0.0630571i
$583$	30.7152	−	17.7334i	1.27209	−	0.734443i
$584$	18.1544	−	6.79669i	0.751234	−	0.281249i
$585$	6.64834	−	11.5153i	0.274875	−	0.476097i
$586$	0.344563	+	0.323095i	0.0142338	+	0.0133469i
$587$		−	35.3797i		−	1.46027i	−0.683300	−	0.730137i	$-0.739456\pi$
$587$		−	35.3797i		−	1.46027i	0.683300	−	0.730137i	$-0.260544\pi$
$588$	−8.17176	−	11.3676i	−0.336998	−	0.468792i
$589$		−	22.1906i		−	0.914347i
$590$	24.5085	−	26.1370i	1.00900	−	1.07604i
$591$	8.29208	−	14.3623i	0.341091	−	0.590786i
$592$	−28.6614	+	21.8869i	−1.17797	+	0.899546i
$593$	−33.9659	+	19.6102i	−1.39481	+	0.805294i	−0.993843	−	0.110798i	$-0.964659\pi$
$593$	−33.9659	+	19.6102i	−1.39481	+	0.805294i	−0.400968	+	0.916092i	$0.631326\pi$
$594$	−2.32575	−	7.68304i	−0.0954266	−	0.315239i
$595$	2.58160	−	1.55203i	0.105835	−	0.0636271i
$596$	6.60594	+	9.91142i	0.270590	+	0.405988i
$597$	−9.87996	+	5.70420i	−0.404360	+	0.233457i
$598$	37.4583	+	8.75702i	1.53178	+	0.358101i
$599$	41.2853	+	23.8361i	1.68687	+	0.973916i	0.956890	+	0.290450i	$0.0938051\pi$
$599$	41.2853	+	23.8361i	1.68687	+	0.973916i	0.729982	+	0.683466i	$0.239528\pi$
$600$	−0.589010	+	3.52926i	−0.0240462	+	0.144082i
$601$		−	13.4207i		−	0.547442i	−0.961809	−	0.273721i	$-0.911746\pi$
$601$		−	13.4207i		−	0.547442i	0.961809	−	0.273721i	$-0.0882544\pi$
$602$	−2.88655	+	13.4137i	−0.117647	+	0.546702i
$603$	9.30266			0.378834
$604$	3.18540	−	6.44046i	0.129612	−	0.262058i
$605$	−26.5558	+	45.9960i	−1.07965	+	1.87000i
$606$	7.82396	+	1.82909i	0.317827	+	0.0743017i
$607$	19.1391	+	33.1498i	0.776831	+	1.34551i	0.933760	+	0.357901i	$0.116507\pi$
$607$	19.1391	+	33.1498i	0.776831	+	1.34551i	−0.156929	+	0.987610i	$0.550159\pi$
$608$	−20.7916	−	2.10885i	−0.843210	−	0.0855251i
$609$	6.82397	−	0.120759i	0.276521	−	0.00489342i
$610$	−16.9522	+	5.13164i	−0.686376	+	0.207774i
$611$	2.54374	+	4.40588i	0.102909	+	0.178243i
$612$	0.907837	−	0.0584425i	0.0366971	−	0.00236240i
$613$	−16.9225	−	9.77021i	−0.683493	−	0.394615i	0.117677	−	0.993052i	$-0.462455\pi$
$613$	−16.9225	−	9.77021i	−0.683493	−	0.394615i	−0.801170	+	0.598437i	$0.795789\pi$
$614$	−9.08474	+	9.68838i	−0.366630	+	0.390991i
$615$	11.6563			0.470028
$616$	−26.4198	+	33.2605i	−1.06448	+	1.34011i
$617$	−1.16195			−0.0467785			−0.0233892	−	0.999726i	$-0.507446\pi$
$617$	−1.16195			−0.0467785			−0.0233892	+	0.999726i	$0.507446\pi$
$618$	−5.71402	+	6.09369i	−0.229852	+	0.245124i
$619$	31.0842	+	17.9465i	1.24938	+	0.721330i	0.970986	−	0.239137i	$-0.0768645\pi$
$619$	31.0842	+	17.9465i	1.24938	+	0.721330i	0.278394	+	0.960467i	$0.410198\pi$
$620$	1.93174	+	30.0073i	0.0775805	+	1.20512i
$621$	−2.56022	−	4.43443i	−0.102738	−	0.177947i
$622$	21.4877	−	6.50459i	0.861579	−	0.260810i
$623$	−15.8033	−	8.75495i	−0.633147	−	0.350759i
$624$	−19.6127	−	8.17733i	−0.785135	−	0.327355i
$625$	14.8624	+	25.7425i	0.594498	+	1.02970i
$626$	44.2947	+	10.3552i	1.77037	+	0.413879i
$627$	−10.4848	+	18.1603i	−0.418724	+	0.725252i
$628$	1.76318	+	0.872054i	0.0703585	+	0.0347987i
$629$	−4.10084			−0.163511
$630$	6.94402	+	6.28420i	0.276656	+	0.250369i
$631$		−	8.26460i		−	0.329008i	−0.986376	−	0.164504i	$-0.947398\pi$
$631$		−	8.26460i		−	0.329008i	0.986376	−	0.164504i	$-0.0526024\pi$
$632$	4.14991	−	24.8657i	0.165075	−	0.989103i
$633$	−3.57928	−	2.06650i	−0.142264	−	0.0821360i
$634$	21.0296	+	4.91632i	0.835194	+	0.195252i
$635$	−13.8677	+	8.00650i	−0.550322	+	0.317728i
$636$	−10.3987	+	6.93071i	−0.412335	+	0.274821i
$637$	−17.4419	+	32.8417i	−0.691074	+	1.30123i
$638$	−5.99955	−	19.8193i	−0.237524	−	0.784655i
$639$	−6.36736	+	3.67620i	−0.251889	+	0.145428i
$640$	28.2991	+	1.04175i	1.11862	+	0.0411787i
$641$	−14.4955	+	25.1070i	−0.572539	+	0.991666i	0.423766	+	0.905772i	$0.360708\pi$
$641$	−14.4955	+	25.1070i	−0.572539	+	0.991666i	−0.996304	+	0.0858940i	$0.972625\pi$
$642$	10.3128	−	10.9980i	0.407013	−	0.434057i
$643$			39.1239i			1.54289i	0.636293	+	0.771447i	$0.280467\pi$
$643$			39.1239i			1.54289i	−0.636293	+	0.771447i	$0.719533\pi$
$644$	−11.5804	+	24.4954i	−0.456331	+	0.965252i
$645$		−	9.17860i		−	0.361407i
$646$	−1.73353	−	1.62552i	−0.0682049	−	0.0639553i
$647$	−6.09491	+	10.5567i	−0.239616	+	0.415027i	−0.960604	−	0.277921i	$-0.910355\pi$
$647$	−6.09491	+	10.5567i	−0.239616	+	0.415027i	0.720988	+	0.692947i	$0.243688\pi$
$648$	0.991694	+	2.64888i	0.0389574	+	0.104058i
$649$	−49.7577	+	28.7276i	−1.95316	+	1.12766i
$650$	9.09624	−	2.75354i	0.356784	−	0.108003i
$651$	13.9014	+	7.70131i	0.544840	+	0.301838i
$652$	4.19664	−	2.79705i	0.164353	−	0.109541i
$653$	−8.80194	+	5.08180i	−0.344446	+	0.198866i	−0.662237	−	0.749295i	$-0.730393\pi$
$653$	−8.80194	+	5.08180i	−0.344446	+	0.198866i	0.317790	+	0.948161i	$0.397059\pi$
$654$	−1.02347	+	4.37790i	−0.0400208	+	0.171190i
$655$	31.4368	+	18.1500i	1.22834	+	0.709181i
$656$	−2.38844	−	18.4739i	−0.0932528	−	0.721286i
$657$			6.85362i			0.267385i
$658$	−3.41072	+	1.09871i	−0.132964	+	0.0428321i
$659$	−8.28558			−0.322760			−0.161380	−	0.986892i	$-0.551595\pi$
$659$	−8.28558			−0.322760			−0.161380	+	0.986892i	$0.551595\pi$
$660$	12.5973	−	25.4701i	0.490349	−	0.991421i
$661$	−8.30890	+	14.3914i	−0.323179	+	0.559762i	−0.981142	−	0.193288i	$-0.938085\pi$
$661$	−8.30890	+	14.3914i	−0.323179	+	0.559762i	0.657963	+	0.753050i	$0.271418\pi$
$662$	6.77284	−	28.9709i	0.263234	−	1.12599i
$663$	−1.20817	−	2.09261i	−0.0469213	−	0.0812701i
$664$	4.28487	+	3.52903i	0.166285	+	0.136953i
$665$	−0.432875	−	24.4612i	−0.0167862	−	0.948566i
$666$	−3.69405	−	12.2032i	−0.143141	−	0.472864i
$667$	−6.60439	−	11.4391i	−0.255723	−	0.442925i
$668$	0.676130	+	10.5029i	0.0261603	+	0.406369i
$669$	15.6805	+	9.05316i	0.606245	+	0.350016i
$670$	24.0209	+	22.5243i	0.928009	+	0.870189i
$671$	28.4018			1.09644
$672$	8.53689	−	12.2931i	0.329318	−	0.474219i
$673$	13.1599			0.507278			0.253639	−	0.967299i	$-0.418372\pi$
$673$	13.1599			0.507278			0.253639	+	0.967299i	$0.418372\pi$
$674$	−1.22093	−	1.14486i	−0.0470285	−	0.0440983i
$675$	−1.09556	−	0.632521i	−0.0421680	−	0.0243457i
$676$	1.95559	+	30.3778i	0.0752149	+	1.16838i
$677$	10.2201	+	17.7017i	0.392790	+	0.680332i	0.992816	−	0.119648i	$-0.0381766\pi$
$677$	10.2201	+	17.7017i	0.392790	+	0.680332i	−0.600026	+	0.799980i	$0.704843\pi$
$678$	0.123924	+	0.409378i	0.00475926	+	0.0157221i
$679$	8.41863	−	5.06119i	0.323077	−	0.194231i
$680$	2.48568	+	2.04721i	0.0953215	+	0.0785070i
$681$	3.96260	+	6.86343i	0.151847	+	0.263007i
$682$	10.9764	−	46.9516i	0.420307	−	1.79787i
$683$	7.87273	−	13.6360i	0.301242	−	0.521766i	−0.675176	−	0.737657i	$-0.735932\pi$
$683$	7.87273	−	13.6360i	0.301242	−	0.521766i	0.976418	+	0.215891i	$0.0692655\pi$
$684$	3.27562	−	6.62288i	0.125247	−	0.253232i
$685$	3.08150			0.117738
$686$	−20.0296	−	16.8765i	−0.764732	−	0.644349i
$687$		−	2.15573i		−	0.0822464i
$688$	−14.5470	+	1.88074i	−0.554601	+	0.0717026i
$689$	28.7460	+	16.5965i	1.09514	+	0.632277i
$690$	4.12607	−	17.6494i	0.157077	−	0.671899i
$691$	2.76346	−	1.59549i	0.105127	−	0.0606952i	−0.446515	−	0.894776i	$-0.647335\pi$
$691$	2.76346	−	1.59549i	0.105127	−	0.0606952i	0.551642	+	0.834081i	$0.314002\pi$
$692$	−0.239022	+	0.159308i	−0.00908626	+	0.00605597i
$693$	−7.73783	−	12.8709i	−0.293936	−	0.488924i
$694$	−6.51522	+	1.97223i	−0.247314	+	0.0748650i
$695$	34.2033	−	19.7473i	1.29740	−	0.749057i
$696$	2.55820	+	6.83310i	0.0969682	+	0.259008i
$697$	1.05912	−	1.83445i	0.0401170	−	0.0694847i
$698$	−36.6011	−	34.3206i	−1.38537	−	1.29905i
$699$			20.0144i			0.757015i
$700$	0.548166	+	6.67149i	0.0207187	+	0.252158i
$701$			39.2121i			1.48102i	0.672045	+	0.740511i	$0.265416\pi$
$701$			39.2121i			1.48102i	−0.672045	+	0.740511i	$0.734584\pi$
$702$	5.13881	−	5.48026i	0.193952	−	0.206839i
$703$	−16.6534	+	28.8445i	−0.628094	+	1.08789i
$704$	−42.9484	−	14.7463i	−1.61868	−	0.555774i
$705$	2.07594	−	1.19854i	0.0781843	−	0.0451397i
$706$	1.95737	+	6.46612i	0.0736666	+	0.243356i
$707$	15.0296	−	0.265969i	0.565246	−	0.0100028i
$708$	16.8456	−	11.2275i	0.633096	−	0.421957i
$709$	−33.3653	+	19.2635i	−1.25306	+	0.723454i	−0.971716	−	0.236153i	$-0.924113\pi$
$709$	−33.3653	+	19.2635i	−1.25306	+	0.723454i	−0.281343	+	0.959607i	$0.590780\pi$
$710$	−25.3426	−	5.92460i	−0.951091	−	0.222346i
$711$	7.71882	+	4.45646i	0.289478	+	0.167130i
$712$	3.17936	−	19.0503i	0.119152	−	0.713940i
$713$		−	30.7567i		−	1.15185i
$714$	1.61995	−	0.521839i	0.0606250	−	0.0195293i
$715$	−75.4744			−2.82258
$716$	33.9267	+	16.7799i	1.26790	+	0.627094i
$717$	−9.44616	+	16.3612i	−0.352773	+	0.611021i
$718$	50.8345	+	11.8841i	1.89713	+	0.443511i
$719$	−11.5009	−	19.9202i	−0.428912	−	0.742897i	0.567865	−	0.823122i	$-0.307770\pi$
$719$	−11.5009	−	19.9202i	−0.428912	−	0.742897i	−0.996777	+	0.0802246i	$0.974436\pi$
$720$	−3.85294	+	9.24097i	−0.143591	+	0.344391i
$721$	−7.57341	+	13.6706i	−0.282049	+	0.509119i
$722$	7.24417	−	2.19289i	0.269600	−	0.0816111i
$723$	−9.15417	−	15.8555i	−0.340447	−	0.589672i
$724$	−2.85571	−	44.3602i	−0.106132	−	1.64863i
$725$	−2.82613	−	1.63166i	−0.104960	−	0.0605985i
$726$	−20.5262	+	21.8901i	−0.761799	+	0.812417i
$727$	−21.8433			−0.810125			−0.405062	−	0.914289i	$-0.632750\pi$
$727$	−21.8433			−0.810125			−0.405062	+	0.914289i	$0.632750\pi$
$728$	−39.3208	−	5.84926i	−1.45733	−	0.216788i
$729$	−1.00000			−0.0370370
$730$	−16.5945	+	17.6971i	−0.614189	+	0.654999i
$731$	−1.44451	−	0.833989i	−0.0534272	−	0.0308462i
$732$	−9.98667	+	0.642898i	−0.369118	+	0.0237622i
$733$	24.0681	+	41.6871i	0.888974	+	1.53975i	0.841089	+	0.540896i	$0.181915\pi$
$733$	24.0681	+	41.6871i	0.888974	+	1.53975i	0.0478850	+	0.998853i	$0.484752\pi$
$734$	0.769946	−	0.233072i	0.0284192	−	0.00860283i
$735$	15.4741	+	8.21817i	0.570772	+	0.303132i
$736$	−28.8177	−	2.92292i	−1.06223	−	0.107740i
$737$	−26.4018	−	45.7293i	−0.972524	−	1.68446i
$738$	6.41297	+	1.49923i	0.236065	+	0.0551873i
$739$	3.23455	−	5.60241i	0.118985	−	0.206088i	−0.800381	−	0.599492i	$-0.795369\pi$
$739$	3.23455	−	5.60241i	0.118985	−	0.206088i	0.919366	+	0.393404i	$0.128703\pi$
$740$	20.0086	−	40.4548i	0.735532	−	1.48715i
$741$	−19.6253			−0.720953
$742$	−15.6875	+	17.3346i	−0.575907	+	0.636374i
$743$			16.6709i			0.611597i	0.952096	+	0.305798i	$0.0989234\pi$
$743$			16.6709i			0.611597i	−0.952096	+	0.305798i	$0.901077\pi$
$744$	−2.79673	+	16.7576i	−0.102533	+	0.614364i
$745$	−12.9097	−	7.45340i	−0.472974	−	0.273072i
$746$	32.2681	+	7.54366i	1.18142	+	0.276193i
$747$	−1.69966	+	0.981297i	−0.0621872	+	0.0359038i
$748$	−2.86381	−	4.29681i	−0.104711	−	0.157107i
$749$	13.6686	−	24.6729i	0.499441	−	0.901528i
$750$	3.83048	+	12.6539i	0.139869	+	0.462055i
$751$	−21.2698	+	12.2801i	−0.776145	+	0.448108i	−0.835062	−	0.550155i	$-0.814569\pi$
$751$	−21.2698	+	12.2801i	−0.776145	+	0.448108i	0.0589171	+	0.998263i	$0.481235\pi$
$752$	−2.32492	−	3.04454i	−0.0847813	−	0.111023i
$753$	−1.71626	+	2.97264i	−0.0625439	+	0.108329i
$754$	13.2562	−	14.1370i	0.482762	−	0.514839i
$755$			8.99223i			0.327261i
$756$	3.01213	+	4.35053i	0.109550	+	0.158227i
$757$		−	2.80888i		−	0.102091i	−0.998696	−	0.0510453i	$-0.983745\pi$
$757$		−	2.80888i		−	0.102091i	0.998696	−	0.0510453i	$-0.0162553\pi$
$758$	15.1896	+	14.2432i	0.551710	+	0.517335i
$759$	−14.5323	+	25.1706i	−0.527488	+	0.913636i
$760$	24.4940	−	9.17012i	0.888489	−	0.332635i
$761$	−17.4708	+	10.0868i	−0.633317	+	0.365646i	−0.782036	−	0.623234i	$-0.785819\pi$
$761$	−17.4708	+	10.0868i	−0.633317	+	0.365646i	0.148718	+	0.988880i	$0.452485\pi$
$762$	−8.65939	+	2.62130i	−0.313697	+	0.0949596i
$763$	0.148823	+	8.40982i	0.00538776	+	0.304456i
$764$	13.0786	+	19.6228i	0.473166	+	0.709929i
$765$	−0.985981	+	0.569256i	−0.0356482	+	0.0205815i
$766$	1.60809	−	6.87864i	0.0581028	−	0.248536i
$767$	−46.5677	−	26.8859i	−1.68146	−	0.970792i
$768$	15.4354	+	4.21295i	0.556976	+	0.152022i
$769$		−	32.1388i		−	1.15895i	−0.814988	−	0.579477i	$-0.803257\pi$
$769$		−	32.1388i		−	1.15895i	0.814988	−	0.579477i	$-0.196743\pi$
$770$	11.1836	−	51.9700i	0.403030	−	1.87287i
$771$	25.0690			0.902840
$772$	−48.0850	−	23.7825i	−1.73062	−	0.855950i
$773$	11.2931	−	19.5603i	0.406186	−	0.703534i	−0.588273	−	0.808662i	$-0.700192\pi$
$773$	11.2931	−	19.5603i	0.406186	−	0.703534i	0.994459	+	0.105128i	$0.0335253\pi$
$774$	1.18055	−	5.04980i	0.0424338	−	0.181511i
$775$	−3.79934	−	6.58065i	−0.136476	−	0.236384i
$776$	8.10583	+	6.67598i	0.290982	+	0.239654i
$777$	−12.2902	−	20.4432i	−0.440909	−	0.733395i
$778$	−13.0628	−	43.1528i	−0.468326	−	1.54710i
$779$	−8.60209	−	14.8993i	−0.308202	−	0.533822i
$780$	26.5384	−	1.70843i	0.950228	−	0.0611714i
$781$	36.1423	+	20.8668i	1.29327	+	0.746673i
$782$	−2.40272	−	2.25302i	−0.0859210	−	0.0805677i
$783$	−2.57962			−0.0921882
$784$	9.85414	−	26.2087i	0.351934	−	0.936025i
$785$	−2.46177			−0.0878642
$786$	14.9612	+	14.0290i	0.533648	+	0.500399i
$787$	−29.2593	−	16.8929i	−1.04298	−	0.602166i	−0.122306	−	0.992492i	$-0.539029\pi$
$787$	−29.2593	−	16.8929i	−1.04298	−	0.602166i	−0.920677	+	0.390326i	$0.872362\pi$
$788$	33.0998	−	2.13082i	1.17913	−	0.0759073i
$789$	−7.75460	−	13.4314i	−0.276071	−	0.478169i
$790$	9.14088	+	30.1967i	0.325218	+	1.07435i
$791$	0.412298	+	0.685804i	0.0146596	+	0.0243844i
$792$	10.2066	−	12.3927i	0.362676	−	0.440354i
$793$	13.2905	+	23.0197i	0.471958	+	0.817455i
$794$	−10.5936	+	45.3143i	−0.375953	+	1.60815i
$795$	7.81984	−	13.5444i	0.277341	−	0.480369i
$796$	−20.4520	−	10.1154i	−0.724902	−	0.358531i
$797$	−27.0472			−0.958061			−0.479030	−	0.877798i	$-0.659012\pi$
$797$	−27.0472			−0.958061			−0.479030	+	0.877798i	$0.659012\pi$
$798$	2.90803	−	13.5136i	0.102943	−	0.478374i
$799$		−	0.435609i		−	0.0154108i
$800$	−6.52684	+	2.93443i	−0.230759	+	0.103748i
$801$	5.91361	+	3.41423i	0.208947	+	0.120636i
$802$	−0.0684022	+	0.292591i	−0.00241536	+	0.0103318i
$803$	33.6905	−	19.4512i	1.18891	−	0.686418i
$804$	10.3186	+	15.4818i	0.363908	+	0.546000i
$805$	−0.599976	−	33.9039i	−0.0211464	−	1.19496i
$806$	43.1907	−	13.0743i	1.52133	−	0.460524i
$807$	20.5537	−	11.8667i	0.723523	−	0.417726i
$808$	5.63436	+	15.0497i	0.198216	+	0.529447i
$809$	24.9224	−	43.1669i	0.876226	−	1.51767i	0.0207751	−	0.999784i	$-0.493387\pi$
$809$	24.9224	−	43.1669i	0.876226	−	1.51767i	0.855451	−	0.517884i	$-0.173280\pi$
$810$	−2.58215	−	2.42127i	−0.0907277	−	0.0850748i
$811$			36.5330i			1.28285i	0.767188	+	0.641423i	$0.221655\pi$
$811$			36.5330i			1.28285i	−0.767188	+	0.641423i	$0.778345\pi$
$812$	7.77016	+	11.2227i	0.272679	+	0.393840i
$813$		−	14.7137i		−	0.516031i
$814$	−49.5034	+	52.7927i	−1.73509	+	1.85038i
$815$	−3.15588	+	5.46614i	−0.110546	+	0.191470i
$816$	1.10424	+	1.44603i	0.0386561	+	0.0506210i
$817$	−11.7322	+	6.77360i	−0.410459	+	0.236978i
$818$	−8.38793	−	27.7093i	−0.293277	−	0.968832i
$819$	6.81102	−	12.2944i	0.237996	−	0.429601i
$820$	12.9292	+	19.3988i	0.451509	+	0.677435i
$821$	2.59911	−	1.50060i	0.0907095	−	0.0523711i	−0.453959	−	0.891023i	$-0.649989\pi$
$821$	2.59911	−	1.50060i	0.0907095	−	0.0523711i	0.544669	+	0.838651i	$0.316655\pi$
$822$	1.69535	+	0.396340i	0.0591322	+	0.0138240i
$823$	−13.8543	−	7.99877i	−0.482930	−	0.278820i	0.238707	−	0.971092i	$-0.423277\pi$
$823$	−13.8543	−	7.99877i	−0.482930	−	0.278820i	−0.721637	+	0.692272i	$0.756610\pi$
$824$	−16.4793	−	2.75029i	−0.574085	−	0.0958109i
$825$			7.18061i			0.249997i
$826$	25.4133	−	28.0816i	0.884242	−	0.977083i
$827$	4.57856			0.159212			0.0796060	−	0.996826i	$-0.474634\pi$
$827$	4.57856			0.159212			0.0796060	+	0.996826i	$0.474634\pi$
$828$	4.54010	−	9.17948i	0.157779	−	0.319009i
$829$	1.53077	−	2.65136i	0.0531657	−	0.0920857i	−0.838218	−	0.545336i	$-0.816402\pi$
$829$	1.53077	−	2.65136i	0.0531657	−	0.0920857i	0.891383	+	0.453250i	$0.149736\pi$
$830$	−6.76477	−	1.58147i	−0.234808	−	0.0548936i
$831$	−3.56123	−	6.16822i	−0.123538	−	0.213973i
$832$	−8.14552	−	41.7103i	−0.282395	−	1.44605i
$833$	2.69938	−	1.68857i	0.0935279	−	0.0585054i
$834$	21.3575	−	6.46518i	0.739551	−	0.223871i
$835$	−6.58581	−	11.4070i	−0.227911	−	0.394754i
$836$	−41.8527	+	2.69429i	−1.44751	+	0.0931841i
$837$	−5.20192	−	3.00333i	−0.179805	−	0.103810i
$838$	−11.4572	+	12.2184i	−0.395781	+	0.422079i
$839$	39.0864			1.34941			0.674706	−	0.738087i	$-0.264270\pi$
$839$	39.0864			1.34941			0.674706	+	0.738087i	$0.264270\pi$
$840$	−2.75602	+	18.5269i	−0.0950917	+	0.639239i
$841$	22.3456			0.770536
$842$	−21.0811	+	22.4819i	−0.726504	+	0.774777i
$843$	−11.3069	−	6.52804i	−0.389430	−	0.224838i
$844$	−0.531029	−	8.24892i	−0.0182788	−	0.283940i
$845$	−19.0483	−	32.9926i	−0.655281	−	1.13498i
$846$	1.29628	−	0.392398i	0.0445669	−	0.0134909i
$847$	−27.2056	+	49.1081i	−0.934795	+	1.68738i
$848$	−23.0686	−	9.61825i	−0.792179	−	0.330292i
$849$	−1.05685	−	1.83051i	−0.0362709	−	0.0628230i
$850$	−0.792393	−	0.185246i	−0.0271789	−	0.00635389i
$851$	−23.0820	+	39.9792i	−0.791241	+	1.37047i
$852$	−13.1808	−	6.51910i	−0.451565	−	0.223341i
$853$	26.4897			0.906989			0.453495	−	0.891259i	$-0.350177\pi$
$853$	26.4897			0.906989			0.453495	+	0.891259i	$0.350177\pi$
$854$	−17.8202	+	5.74050i	−0.609796	+	0.196436i
$855$			9.24692i			0.316238i
$856$	29.7422	+	4.96377i	1.01657	+	0.169658i
$857$	38.9066	+	22.4627i	1.32902	+	0.767312i	0.985149	−	0.171703i	$-0.0549269\pi$
$857$	38.9066	+	22.4627i	1.32902	+	0.767312i	0.343875	+	0.939015i	$0.388260\pi$
$858$	−41.5239	−	9.70747i	−1.41760	−	0.331408i
$859$	30.6621	−	17.7028i	1.04618	−	0.604011i	0.124601	−	0.992207i	$-0.460235\pi$
$859$	30.6621	−	17.7028i	1.04618	−	0.604011i	0.921577	+	0.388196i	$0.126902\pi$
$860$	15.2753	−	10.1810i	0.520883	−	0.347168i
$861$	12.3191	−	0.218004i	0.419835	−	0.00742955i
$862$	−6.77677	−	22.3869i	−0.230818	−	0.762499i
$863$	−2.40437	+	1.38816i	−0.0818456	+	0.0472536i	−0.540364	−	0.841431i	$-0.681714\pi$
$863$	−2.40437	+	1.38816i	−0.0818456	+	0.0472536i	0.458519	+	0.888685i	$0.348380\pi$
$864$	−3.30835	+	4.58856i	−0.112552	+	0.156106i
$865$	0.179745	−	0.311328i	0.00611151	−	0.0105855i
$866$	−37.9900	+	40.5143i	−1.29095	+	1.37673i
$867$		−	16.7931i		−	0.570324i
$868$	2.60280	+	31.6775i	0.0883448	+	1.07520i
$869$		−	50.5915i		−	1.71620i
$870$	−6.66098	−	6.24597i	−0.225828	−	0.211758i
$871$	24.7092	−	42.7976i	0.837239	−	1.45014i
$872$	−8.42107	+	3.15271i	−0.285174	+	0.106764i
$873$	−3.21529	+	1.85635i	−0.108821	+	0.0628279i
$874$	−25.6046	+	7.75082i	−0.866089	+	0.262175i
$875$	12.7441	+	21.1982i	0.430830	+	0.716631i
$876$	−11.4060	+	7.60207i	−0.385373	+	0.256850i
$877$	14.3264	−	8.27135i	0.483768	−	0.279304i	−0.238217	−	0.971212i	$-0.576563\pi$
$877$	14.3264	−	8.27135i	0.483768	−	0.279304i	0.721986	+	0.691908i	$0.243230\pi$
$878$	9.99064	−	42.7351i	0.337168	−	1.44224i
$879$	−0.289254	−	0.167001i	−0.00975630	−	0.00563280i
$880$	56.3610	−	7.28675i	1.89993	−	0.245636i
$881$			24.6158i			0.829327i	0.909975	+	0.414664i	$0.136101\pi$
$881$			24.6158i			0.829327i	−0.909975	+	0.414664i	$0.863899\pi$
$882$	7.45641	+	6.51168i	0.251070	+	0.219260i
$883$	40.4623			1.36167			0.680833	−	0.732439i	$-0.261618\pi$
$883$	40.4623			1.36167			0.680833	+	0.732439i	$0.261618\pi$
$884$	2.14247	−	4.33180i	0.0720592	−	0.145694i
$885$	−12.6679	+	21.9415i	−0.425827	+	0.737554i
$886$	0.272012	−	1.16354i	0.00913843	−	0.0390898i
$887$	−4.64231	−	8.04072i	−0.155873	−	0.269981i	0.777503	−	0.628879i	$-0.216486\pi$
$887$	−4.64231	−	8.04072i	−0.155873	−	0.269981i	−0.933377	+	0.358898i	$0.883153\pi$
$888$	16.2115	−	19.6836i	0.544021	−	0.660538i
$889$	−14.5065	+	8.72114i	−0.486532	+	0.292498i
$890$	7.00309	+	23.1345i	0.234744	+	0.775471i
$891$	2.83809	+	4.91572i	0.0950797	+	0.164683i
$892$	2.32639	+	36.1379i	0.0778935	+	1.20998i
$893$	−3.06399	−	1.76900i	−0.102533	−	0.0591972i
$894$	−6.14388	−	5.76108i	−0.205482	−	0.192679i
$895$	−47.3688			−1.58337
$896$	29.9278	+	0.571717i	0.999818	+	0.0190997i
$897$	−27.2012			−0.908221
$898$	43.0633	+	40.3802i	1.43704	+	1.34751i
$899$	−13.4190	−	7.74746i	−0.447548	−	0.258392i
$900$	−0.162539	−	2.52486i	−0.00541797	−	0.0841619i
$901$	−1.42106	−	2.46134i	−0.0473423	−	0.0819993i
$902$	−10.8308	−	35.7793i	−0.360627	−	1.19132i
$903$	−0.171664	−	9.70053i	−0.00571262	−	0.322813i
$904$	−0.543843	+	0.660322i	−0.0180880	+	0.0219620i
$905$	27.8159	+	48.1786i	0.924632	+	1.60151i
$906$	−1.15657	+	4.94727i	−0.0384246	+	0.164362i
$907$	−2.55327	+	4.42240i	−0.0847800	+	0.146843i	−0.905297	−	0.424778i	$-0.860352\pi$
$907$	−2.55327	+	4.42240i	−0.0847800	+	0.146843i	0.820517	+	0.571621i	$0.193685\pi$
$908$	−7.02699	+	14.2076i	−0.233199	+	0.471497i
$909$	−5.68155			−0.188445
$910$	47.3552	−	15.2547i	1.56981	−	0.505689i
$911$			36.3702i			1.20500i	0.798119	+	0.602500i	$0.205829\pi$
$911$			36.3702i			1.20500i	−0.798119	+	0.602500i	$0.794171\pi$
$912$	14.6553	−	1.89474i	0.485287	−	0.0627412i
$913$	9.64757	+	5.57003i	0.319288	+	0.184341i
$914$	2.40991	−	10.3085i	0.0797129	−	0.340973i
$915$	10.8463	−	6.26211i	0.358567	−	0.207019i
$916$	3.58764	−	2.39115i	0.118539	−	0.0790059i
$917$	33.5639	+	18.5942i	1.10838	+	0.614034i
$918$	−0.615676	+	0.186372i	−0.0203203	+	0.00615121i
$919$	−40.4248	+	23.3393i	−1.33349	+	0.769892i	−0.985833	−	0.167729i	$-0.946357\pi$
$919$	−40.4248	+	23.3393i	−1.33349	+	0.769892i	−0.347659	+	0.937621i	$0.613023\pi$
$920$	33.9493	−	12.7100i	1.11927	−	0.419037i
$921$	4.69571	−	8.13320i	0.154729	−	0.267998i
$922$	4.47207	+	4.19343i	0.147280	+	0.138103i
$923$			39.0580i			1.28561i
$924$	12.8373	−	27.1540i	0.422315	−	0.893301i
$925$			11.4052i			0.375000i
$926$	−34.1666	+	36.4369i	−1.12279	+	1.19739i
$927$	2.95345	−	5.11553i	0.0970042	−	0.168016i
$928$	−8.53428	+	11.8367i	−0.280152	+	0.388560i
$929$	33.8671	−	19.5532i	1.11114	−	0.641518i	0.172017	−	0.985094i	$-0.444972\pi$
$929$	33.8671	−	19.5532i	1.11114	−	0.641518i	0.939125	+	0.343576i	$0.111638\pi$
$930$	−6.16029	−	20.3503i	−0.202004	−	0.667314i
$931$	−0.914979	−	25.8441i	−0.0299872	−	0.847006i
$932$	−33.3086	+	22.2001i	−1.09106	+	0.727188i
$933$	−13.7482	+	7.93750i	−0.450095	+	0.259862i
$934$	−14.4576	−	3.37990i	−0.473066	−	0.110594i
$935$	5.59661	+	3.23121i	0.183029	+	0.105672i
$936$	14.8204	+	2.47343i	0.484421	+	0.0808465i
$937$		−	14.4038i		−	0.470551i	−0.971929	−	0.235275i	$-0.924401\pi$
$937$		−	14.4038i		−	0.470551i	0.971929	−	0.235275i	$-0.0755992\pi$
$938$	25.8081	+	23.3558i	0.842664	+	0.762595i
$939$	−32.1656			−1.04969
$940$	4.29729	+	2.12541i	0.140162	+	0.0693231i
$941$	13.1269	−	22.7364i	0.427924	−	0.741186i	−0.568765	−	0.822500i	$-0.692579\pi$
$941$	13.1269	−	22.7364i	0.427924	−	0.741186i	0.996688	+	0.0813146i	$0.0259118\pi$
$942$	−1.35439	−	0.316631i	−0.0441285	−	0.0103164i
$943$	−11.9227	−	20.6508i	−0.388257	−	0.672482i
$944$	37.3704	+	15.5813i	1.21630	+	0.507128i
$945$	−5.79280	−	3.20917i	−0.188440	−	0.104394i
$946$	−28.1739	+	8.52858i	−0.916014	+	0.277288i
$947$	−7.85354	−	13.6027i	−0.255206	−	0.442030i	0.709746	−	0.704458i	$-0.248810\pi$
$947$	−7.85354	−	13.6027i	−0.255206	−	0.442030i	−0.964951	+	0.262429i	$0.915477\pi$
$948$	1.14518	+	17.7890i	0.0371937	+	0.577761i
$949$	31.5306	+	18.2042i	1.02353	+	0.590933i
$950$	−4.52087	+	4.82126i	−0.146676	+	0.156422i
$951$	−15.2712			−0.495201
$952$	2.66531	+	2.11714i	0.0863833	+	0.0686168i
$953$	42.8466			1.38794			0.693968	−	0.720006i	$-0.255861\pi$
$953$	42.8466			1.38794			0.693968	+	0.720006i	$0.255861\pi$
$954$	6.04432	−	6.44594i	0.195692	−	0.208695i
$955$	−25.5588	−	14.7564i	−0.827064	−	0.477506i
$956$	−37.7066	+	2.42738i	−1.21952	+	0.0785072i
$957$	7.32121	+	12.6807i	0.236661	+	0.409909i
$958$	22.9123	−	6.93583i	0.740264	−	0.224087i
$959$	3.25672	−	0.0576322i	0.105165	−	0.00186104i
$960$	−19.6528	+	3.83795i	−0.634292	+	0.123869i
$961$	−2.53999	−	4.39939i	−0.0819352	−	0.141916i
$962$	−65.9535	−	15.4187i	−2.12643	−	0.497117i
$963$	−5.33045	+	9.23261i	−0.171771	+	0.297517i
$964$	16.2333	−	32.8216i	0.522840	−	1.05711i
$965$	67.1368			2.16121
$966$	4.03061	−	18.7301i	0.129683	−	0.602632i
$967$			0.672082i			0.0216127i	0.999942	+	0.0108063i	$0.00343983\pi$
$967$			0.672082i			0.0216127i	−0.999942	+	0.0108063i	$0.996560\pi$
$968$	−59.1979	−	9.87973i	−1.90269	−	0.317547i
$969$	1.45526	+	0.840197i	0.0467498	+	0.0269910i
$970$	−12.7971	−	2.99171i	−0.410890	−	0.0960582i
$971$	−6.45838	+	3.72875i	−0.207259	+	0.119661i	−0.600037	−	0.799972i	$-0.704847\pi$
$971$	−6.45838	+	3.72875i	−0.207259	+	0.119661i	0.392778	+	0.919633i	$0.371514\pi$
$972$	−1.10921	−	1.66423i	−0.0355778	−	0.0533802i
$973$	35.7789	−	21.5099i	1.14702	−	0.689575i
$974$	9.72184	+	32.1158i	0.311508	+	1.02906i
$975$	−5.81991	+	3.36013i	−0.186386	+	0.107610i
$976$	−12.1472	−	15.9070i	−0.388822	−	0.509171i
$977$	−8.78701	+	15.2195i	−0.281121	+	0.486916i	−0.971661	−	0.236378i	$-0.924040\pi$
$977$	−8.78701	+	15.2195i	−0.281121	+	0.486916i	0.690540	+	0.723294i	$0.257373\pi$
$978$	−2.43933	+	2.60141i	−0.0780010	+	0.0831838i
$979$		−	38.7596i		−	1.23876i
$980$	3.48707	+	34.8682i	0.111390	+	1.11382i
$981$		−	3.17911i		−	0.101501i
$982$	3.51987	+	3.30056i	0.112323	+	0.105325i
$983$	21.3661	−	37.0072i	0.681472	−	1.18034i	−0.293059	−	0.956094i	$-0.594673\pi$
$983$	21.3661	−	37.0072i	0.681472	−	1.18034i	0.974532	−	0.224250i	$-0.0719934\pi$
$984$	4.61824	+	12.3356i	0.147224	+	0.393245i
$985$	−35.9489	+	20.7551i	−1.14543	+	0.661313i
$986$	−1.58821	+	0.480770i	−0.0505790	+	0.0153108i
$987$	2.17157	−	1.30552i	0.0691217	−	0.0415552i
$988$	−21.7685	−	32.6610i	−0.692548	−	1.03909i
$989$	−16.2612	+	9.38839i	−0.517075	+	0.298533i
$990$	−4.57390	+	19.5650i	−0.145368	+	0.621815i
$991$	−39.3373	−	22.7114i	−1.24959	−	0.721451i	−0.278563	−	0.960418i	$-0.589858\pi$
$991$	−39.3373	−	22.7114i	−1.24959	−	0.721451i	−0.971028	+	0.238967i	$0.923191\pi$
$992$	−30.9907	+	13.9332i	−0.983956	+	0.442381i
$993$			21.0379i			0.667617i
$994$	−26.8945	−	5.78753i	−0.853041	−	0.183569i
$995$	28.5553			0.905264
$996$	−3.51837	−	1.74016i	−0.111484	−	0.0551391i
$997$	21.8718	−	37.8831i	0.692687	−	1.19977i	−0.278268	−	0.960504i	$-0.589760\pi$
$997$	21.8718	−	37.8831i	0.692687	−	1.19977i	0.970954	−	0.239265i	$-0.0769065\pi$
$998$	5.62098	−	24.0438i	0.177929	−	0.761094i
$999$	4.50782	+	7.80778i	0.142621	+	0.247027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.t.a.115.4	yes	32
3.2	odd	2		504.2.bk.c.451.13		32
4.3	odd	2		672.2.bb.a.367.2		32
7.3	odd	6		1176.2.p.a.979.26		32
7.4	even	3		1176.2.p.a.979.25		32
7.5	odd	6	inner	168.2.t.a.19.8	yes	32
8.3	odd	2	inner	168.2.t.a.115.8	yes	32
8.5	even	2		672.2.bb.a.367.7		32
12.11	even	2		2016.2.bs.c.1711.13		32
21.5	even	6		504.2.bk.c.19.9		32
24.5	odd	2		2016.2.bs.c.1711.4		32
24.11	even	2		504.2.bk.c.451.9		32
28.3	even	6		4704.2.p.a.3919.15		32
28.11	odd	6		4704.2.p.a.3919.2		32
28.19	even	6		672.2.bb.a.271.7		32
56.3	even	6		1176.2.p.a.979.27		32
56.5	odd	6		672.2.bb.a.271.2		32
56.11	odd	6		1176.2.p.a.979.28		32
56.19	even	6	inner	168.2.t.a.19.4	✓	32
56.45	odd	6		4704.2.p.a.3919.1		32
56.53	even	6		4704.2.p.a.3919.16		32
84.47	odd	6		2016.2.bs.c.271.4		32
168.5	even	6		2016.2.bs.c.271.13		32
168.131	odd	6		504.2.bk.c.19.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.4	✓	32	56.19	even	6	inner
168.2.t.a.19.8	yes	32	7.5	odd	6	inner
168.2.t.a.115.4	yes	32	1.1	even	1	trivial
168.2.t.a.115.8	yes	32	8.3	odd	2	inner
504.2.bk.c.19.9		32	21.5	even	6
504.2.bk.c.19.13		32	168.131	odd	6
504.2.bk.c.451.9		32	24.11	even	2
504.2.bk.c.451.13		32	3.2	odd	2
672.2.bb.a.271.2		32	56.5	odd	6
672.2.bb.a.271.7		32	28.19	even	6
672.2.bb.a.367.2		32	4.3	odd	2
672.2.bb.a.367.7		32	8.5	even	2
1176.2.p.a.979.25		32	7.4	even	3
1176.2.p.a.979.26		32	7.3	odd	6
1176.2.p.a.979.27		32	56.3	even	6
1176.2.p.a.979.28		32	56.11	odd	6
2016.2.bs.c.271.4		32	84.47	odd	6
2016.2.bs.c.271.13		32	168.5	even	6
2016.2.bs.c.1711.4		32	24.5	odd	2
2016.2.bs.c.1711.13		32	12.11	even	2
4704.2.p.a.3919.1		32	56.45	odd	6
4704.2.p.a.3919.2		32	28.11	odd	6
4704.2.p.a.3919.15		32	28.3	even	6
4704.2.p.a.3919.16		32	56.53	even	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03162 - 0.967346i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.128485 + 1.99587i) q^{4} +(-1.25150 - 2.16767i) q^{5} +(-0.409738 - 1.35356i) q^{6} +(-1.36321 - 2.26752i) q^{7} +(1.79815 - 2.18327i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.805806 + 3.44685i) q^{10} +(2.83809 - 4.91572i) q^{11} +(-0.886663 + 1.79272i) q^{12} +5.31228 q^{13} +(-0.787162 + 3.65792i) q^{14} -2.50301i q^{15} +(-3.96698 + 0.512879i) q^{16} +(-0.393919 - 0.227429i) q^{17} +(0.321935 - 1.37708i) q^{18} +(-3.19938 + 1.84716i) q^{19} +(4.16558 - 2.77635i) q^{20} +(-0.0468128 - 2.64534i) q^{21} +(-7.68304 + 2.32575i) q^{22} +(-4.43443 + 2.56022i) q^{23} +(2.64888 - 0.991694i) q^{24} +(-0.632521 + 1.09556i) q^{25} +(-5.48026 - 5.13881i) q^{26} +1.00000i q^{27} +(4.35053 - 3.01213i) q^{28} +2.57962i q^{29} +(-2.42127 + 2.58215i) q^{30} +(-3.00333 + 5.20192i) q^{31} +(4.58856 + 3.30835i) q^{32} +(4.91572 - 2.83809i) q^{33} +(0.186372 + 0.615676i) q^{34} +(-3.20917 + 5.79280i) q^{35} +(-1.66423 + 1.10921i) q^{36} +(7.80778 - 4.50782i) q^{37} +(5.08739 + 1.18933i) q^{38} +(4.60057 + 2.65614i) q^{39} +(-6.98299 - 1.16541i) q^{40} +4.65692i q^{41} +(-2.51066 + 2.77427i) q^{42} +3.66703 q^{43} +(10.1758 + 5.03286i) q^{44} +(1.25150 - 2.16767i) q^{45} +(7.05126 + 1.64845i) q^{46} +(0.478841 + 0.829377i) q^{47} +(-3.69195 - 1.53933i) q^{48} +(-3.28332 + 6.18222i) q^{49} +(1.71230 - 0.518335i) q^{50} +(-0.227429 - 0.393919i) q^{51} +(0.682549 + 10.6026i) q^{52} +(5.41124 + 3.12418i) q^{53} +(0.967346 - 1.03162i) q^{54} -14.2075 q^{55} +(-7.40187 - 1.10108i) q^{56} -3.69433 q^{57} +(2.49539 - 2.66119i) q^{58} +(-8.76604 - 5.06108i) q^{59} +(4.99567 - 0.321599i) q^{60} +(2.50184 + 4.33331i) q^{61} +(8.13036 - 2.46115i) q^{62} +(1.28213 - 2.31434i) q^{63} +(-1.53334 - 7.85168i) q^{64} +(-6.64834 - 11.5153i) q^{65} +(-7.81658 - 1.82736i) q^{66} +(4.65133 - 8.05634i) q^{67} +(0.403306 - 0.815431i) q^{68} -5.12043 q^{69} +(8.91429 - 2.87159i) q^{70} +7.35240i q^{71} +(2.78984 + 0.465606i) q^{72} +(5.93541 + 3.42681i) q^{73} +(-12.4153 - 2.90245i) q^{74} +(-1.09556 + 0.632521i) q^{75} +(-4.09777 - 6.14821i) q^{76} +(-15.0154 + 0.265718i) q^{77} +(-2.17664 - 7.19047i) q^{78} +(7.71882 - 4.45646i) q^{79} +(6.07644 + 7.95723i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50485 - 4.80418i) q^{82} +1.96259i q^{83} +(5.27373 - 0.433319i) q^{84} +1.13851i q^{85} +(-3.78299 - 3.54728i) q^{86} +(-1.28981 + 2.23402i) q^{87} +(-5.62904 - 15.0355i) q^{88} +(5.91361 - 3.41423i) q^{89} +(-3.38796 + 1.02558i) q^{90} +(-7.24175 - 12.0457i) q^{91} +(-5.67961 - 8.52158i) q^{92} +(-5.20192 + 3.00333i) q^{93} +(0.308312 - 1.31881i) q^{94} +(8.00807 + 4.62346i) q^{95} +(2.31963 + 5.15939i) q^{96} +3.71270i q^{97} +(9.36748 - 3.20160i) q^{98} +5.67619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Introduction

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