LMFDB - Embedded newform 171.2.k.a.50.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(50,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 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("171.50"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			50.8
Character	$\chi$	$=$	171.50
Dual form			171.2.k.a.65.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.345701 + 0.598772i) q^{2} +(0.763607 - 1.55464i) q^{3} +(0.760981 + 1.31806i) q^{4} -0.106947i q^{5} +(0.666895 + 0.994667i) q^{6} +(1.77987 + 3.08283i) q^{7} -2.43509 q^{8} +(-1.83381 - 2.37427i) q^{9} +(0.0640371 + 0.0369718i) q^{10} +(3.79750 - 2.19249i) q^{11} +(2.63020 - 0.176573i) q^{12} +(-0.360891 + 0.208361i) q^{13} -2.46122 q^{14} +(-0.166265 - 0.0816658i) q^{15} +(-0.680148 + 1.17805i) q^{16} +(3.21900 - 1.85849i) q^{17} +(2.05559 - 0.277246i) q^{18} +(-4.10727 - 1.45956i) q^{19} +(0.140963 - 0.0813850i) q^{20} +(6.15181 - 0.412990i) q^{21} +3.03178i q^{22} +(-4.68779 + 2.70650i) q^{23} +(-1.85945 + 3.78569i) q^{24} +4.98856 q^{25} -0.288122i q^{26} +(-5.09144 + 1.03790i) q^{27} +(-2.70890 + 4.69195i) q^{28} -5.50797 q^{29} +(0.106377 - 0.0713227i) q^{30} +(-3.01840 - 1.74267i) q^{31} +(-2.90535 - 5.03221i) q^{32} +(-0.508730 - 7.57794i) q^{33} +2.56993i q^{34} +(0.329701 - 0.190353i) q^{35} +(1.73393 - 4.22384i) q^{36} +1.84627i q^{37} +(2.29383 - 1.95475i) q^{38} +(0.0483466 + 0.720161i) q^{39} +0.260427i q^{40} -9.97283 q^{41} +(-1.87940 + 3.82631i) q^{42} +(5.40204 - 9.35660i) q^{43} +(5.77965 + 3.33688i) q^{44} +(-0.253922 + 0.196121i) q^{45} -3.74256i q^{46} -0.251097i q^{47} +(1.31208 + 1.95695i) q^{48} +(-2.83590 + 4.91192i) q^{49} +(-1.72455 + 2.98701i) q^{50} +(-0.431231 - 6.42353i) q^{51} +(-0.549263 - 0.317117i) q^{52} +(-1.44192 + 2.49748i) q^{53} +(1.13865 - 3.40742i) q^{54} +(-0.234481 - 0.406133i) q^{55} +(-4.33416 - 7.50698i) q^{56} +(-5.40543 + 5.27080i) q^{57} +(1.90411 - 3.29802i) q^{58} -2.37489 q^{59} +(-0.0188840 - 0.281293i) q^{60} -12.8567 q^{61} +(2.08693 - 1.20489i) q^{62} +(4.05552 - 9.87922i) q^{63} +1.29694 q^{64} +(0.0222836 + 0.0385964i) q^{65} +(4.71333 + 2.31509i) q^{66} +(9.17875 - 5.29935i) q^{67} +(4.89919 + 2.82855i) q^{68} +(0.627998 + 9.35453i) q^{69} +0.263221i q^{70} +(5.43426 + 9.41241i) q^{71} +(4.46550 + 5.78156i) q^{72} +(2.47284 + 4.28309i) q^{73} +(-1.10550 - 0.638258i) q^{74} +(3.80930 - 7.75542i) q^{75} +(-1.20177 - 6.52432i) q^{76} +(13.5181 + 7.80470i) q^{77} +(-0.447926 - 0.220012i) q^{78} +(0.947726 + 0.547170i) q^{79} +(0.125990 + 0.0727401i) q^{80} +(-2.27429 + 8.70790i) q^{81} +(3.44762 - 5.97145i) q^{82} +(7.21082 - 4.16317i) q^{83} +(5.22576 + 7.79417i) q^{84} +(-0.198760 - 0.344263i) q^{85} +(3.73498 + 6.46918i) q^{86} +(-4.20592 + 8.56290i) q^{87} +(-9.24726 + 5.33891i) q^{88} +(-2.61637 + 4.53168i) q^{89} +(-0.0296508 - 0.219841i) q^{90} +(-1.28468 - 0.741711i) q^{91} +(-7.13465 - 4.11919i) q^{92} +(-5.01410 + 3.36180i) q^{93} +(0.150350 + 0.0868045i) q^{94} +(-0.156096 + 0.439262i) q^{95} +(-10.0418 + 0.674138i) q^{96} +(11.3602 + 6.55883i) q^{97} +(-1.96075 - 3.39611i) q^{98} +(-12.1694 - 4.99568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 6 q^{3} - 15 q^{4} + 4 q^{6} - q^{7} + 12 q^{8} - 4 q^{9} - 6 q^{10} - 9 q^{11} + 15 q^{12} - 6 q^{13} - 6 q^{14} + 9 q^{15} - 9 q^{16} - 27 q^{17} + 6 q^{18} + q^{19} + 9 q^{20} - 3 q^{21}+ \cdots + 28 q^{99}+O(q^{100}) $ 36 * q - 3 * q^2 - 6 * q^3 - 15 * q^4 + 4 * q^6 - q^7 + 12 * q^8 - 4 * q^9 - 6 * q^10 - 9 * q^11 + 15 * q^12 - 6 * q^13 - 6 * q^14 + 9 * q^15 - 9 * q^16 - 27 * q^17 + 6 * q^18 + q^19 + 9 * q^20 - 3 * q^21 + 9 * q^23 - 11 * q^24 - 22 * q^25 + 9 * q^27 + 2 * q^28 - 24 * q^29 - 35 * q^30 + 12 * q^31 - 15 * q^32 - 12 * q^33 + 15 * q^35 + 30 * q^36 - 18 * q^38 - 14 * q^39 + 36 * q^41 - 5 * q^42 + 3 * q^43 + 66 * q^44 + 29 * q^45 + 33 * q^48 - 9 * q^49 + 3 * q^50 - 24 * q^51 + 15 * q^52 - 12 * q^53 - 37 * q^54 - 7 * q^55 + 6 * q^56 + 2 * q^57 - 6 * q^58 - 18 * q^59 + 48 * q^60 - 16 * q^61 - 12 * q^62 - 34 * q^63 + 12 * q^64 - 18 * q^65 + 14 * q^66 + 27 * q^67 + 60 * q^68 - 51 * q^69 + 9 * q^71 - 102 * q^72 - 18 * q^73 + 90 * q^74 - 23 * q^76 - 6 * q^77 + 36 * q^78 - 6 * q^79 - 12 * q^80 + 40 * q^81 - 9 * q^82 - 9 * q^83 - 96 * q^84 + 11 * q^85 + 51 * q^86 - 19 * q^87 + 3 * q^88 - 18 * q^89 + 36 * q^90 + 27 * q^91 - 93 * q^92 - 28 * q^93 + 12 * q^94 - 9 * q^96 + 24 * q^97 - 84 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.345701	+	0.598772i	−0.244448	+	0.423396i	−0.961976	−	0.273133i	$-0.911940\pi$
$2$	−0.345701	+	0.598772i	−0.244448	+	0.423396i	0.717529	+	0.696529i	$0.245273\pi$
$3$	0.763607	−	1.55464i	0.440869	−	0.897572i
$3$	0.763607	−	1.55464i	0.440869	−	0.897572i
$4$	0.760981	+	1.31806i	0.380491	+	0.659029i
$5$		−	0.106947i		−	0.0478283i	−0.999714	−	0.0239142i	$-0.992387\pi$
$5$		−	0.106947i		−	0.0478283i	0.999714	−	0.0239142i	$-0.00761284\pi$
$6$	0.666895	+	0.994667i	0.272259	+	0.406071i
$7$	1.77987	+	3.08283i	0.672729	+	1.16520i	0.977127	+	0.212656i	$0.0682113\pi$
$7$	1.77987	+	3.08283i	0.672729	+	1.16520i	−0.304398	+	0.952545i	$0.598455\pi$
$8$	−2.43509			−0.860936
$9$	−1.83381	−	2.37427i	−0.611270	−	0.791422i
$10$	0.0640371	+	0.0369718i	0.0202503	+	0.0116915i
$11$	3.79750	−	2.19249i	1.14499	−	0.661060i	0.197328	−	0.980338i	$-0.436774\pi$
$11$	3.79750	−	2.19249i	1.14499	−	0.661060i	0.947661	+	0.319278i	$0.103440\pi$
$12$	2.63020	−	0.176573i	0.759272	−	0.0509723i
$13$	−0.360891	+	0.208361i	−0.100093	+	0.0577888i	−0.549211	−	0.835684i	$-0.685072\pi$
$13$	−0.360891	+	0.208361i	−0.100093	+	0.0577888i	0.449118	+	0.893473i	$0.351738\pi$
$14$	−2.46122			−0.657788
$15$	−0.166265	−	0.0816658i	−0.0429294	−	0.0210860i
$16$	−0.680148	+	1.17805i	−0.170037	+	0.294513i
$17$	3.21900	−	1.85849i	0.780721	−	0.450749i	−0.0559647	−	0.998433i	$-0.517823\pi$
$17$	3.21900	−	1.85849i	0.780721	−	0.450749i	0.836686	+	0.547683i	$0.184490\pi$
$18$	2.05559	−	0.277246i	0.484508	−	0.0653475i
$19$	−4.10727	−	1.45956i	−0.942273	−	0.334846i
$19$	−4.10727	−	1.45956i	−0.942273	−	0.334846i
$20$	0.140963	−	0.0813850i	0.0315203	−	0.0181982i
$21$	6.15181	−	0.412990i	1.34244	−	0.0901218i
$22$			3.03178i			0.646378i
$23$	−4.68779	+	2.70650i	−0.977472	+	0.564344i	−0.901506	−	0.432767i	$-0.857537\pi$
$23$	−4.68779	+	2.70650i	−0.977472	+	0.564344i	−0.0759662	+	0.997110i	$0.524204\pi$
$24$	−1.85945	+	3.78569i	−0.379560	+	0.772751i
$25$	4.98856			0.997712
$26$		−	0.288122i		−	0.0565054i
$27$	−5.09144	+	1.03790i	−0.979848	+	0.199745i
$28$	−2.70890	+	4.69195i	−0.511934	+	0.886696i
$29$	−5.50797			−1.02280			−0.511402	−	0.859342i	$-0.670874\pi$
$29$	−5.50797			−1.02280			−0.511402	+	0.859342i	$0.670874\pi$
$30$	0.106377	−	0.0713227i	0.0194217	−	0.0130217i
$31$	−3.01840	−	1.74267i	−0.542120	−	0.312993i	0.203817	−	0.979009i	$-0.434665\pi$
$31$	−3.01840	−	1.74267i	−0.542120	−	0.312993i	−0.745938	+	0.666016i	$0.767998\pi$
$32$	−2.90535	−	5.03221i	−0.513598	−	0.889578i
$33$	−0.508730	−	7.57794i	−0.0885585	−	1.31915i
$34$			2.56993i			0.440739i
$35$	0.329701	−	0.190353i	0.0557296	−	0.0321755i
$36$	1.73393	−	4.22384i	0.288988	−	0.703973i
$37$			1.84627i			0.303525i	0.988417	+	0.151763i	$0.0484949\pi$
$37$			1.84627i			0.303525i	−0.988417	+	0.151763i	$0.951505\pi$
$38$	2.29383	−	1.95475i	0.372109	−	0.317102i
$39$	0.0483466	+	0.720161i	0.00774165	+	0.115318i
$40$			0.260427i			0.0411771i
$41$	−9.97283			−1.55749			−0.778747	−	0.627338i	$-0.784145\pi$
$41$	−9.97283			−1.55749			−0.778747	+	0.627338i	$0.784145\pi$
$42$	−1.87940	+	3.82631i	−0.289998	+	0.590412i
$43$	5.40204	−	9.35660i	0.823803	−	1.42687i	−0.0790282	−	0.996872i	$-0.525182\pi$
$43$	5.40204	−	9.35660i	0.823803	−	1.42687i	0.902831	−	0.429996i	$-0.141485\pi$
$44$	5.77965	+	3.33688i	0.871315	+	0.503054i
$45$	−0.253922	+	0.196121i	−0.0378524	+	0.0292360i
$46$		−	3.74256i		−	0.551810i
$47$		−	0.251097i		−	0.0366263i	−0.999832	−	0.0183131i	$-0.994170\pi$
$47$		−	0.251097i		−	0.0366263i	0.999832	−	0.0183131i	$-0.00582958\pi$
$48$	1.31208	+	1.95695i	0.189382	+	0.282462i
$49$	−2.83590	+	4.91192i	−0.405128	+	0.701703i
$50$	−1.72455	+	2.98701i	−0.243888	+	0.422427i
$51$	−0.431231	−	6.42353i	−0.0603845	−	0.899474i
$52$	−0.549263	−	0.317117i	−0.0761690	−	0.0439762i
$53$	−1.44192	+	2.49748i	−0.198063	+	0.343055i	−0.947900	−	0.318567i	$-0.896798\pi$
$53$	−1.44192	+	2.49748i	−0.198063	+	0.343055i	0.749837	+	0.661622i	$0.230132\pi$
$54$	1.13865	−	3.40742i	0.154950	−	0.463691i
$55$	−0.234481	−	0.406133i	−0.0316174	−	0.0547629i
$56$	−4.33416	−	7.50698i	−0.579176	−	1.00316i
$57$	−5.40543	+	5.27080i	−0.715967	+	0.698134i
$58$	1.90411	−	3.29802i	0.250022	−	0.433051i
$59$	−2.37489			−0.309184			−0.154592	−	0.987978i	$-0.549406\pi$
$59$	−2.37489			−0.309184			−0.154592	+	0.987978i	$0.549406\pi$
$60$	−0.0188840	−	0.281293i	−0.00243792	−	0.0363147i
$61$	−12.8567			−1.64613			−0.823064	−	0.567948i	$-0.807737\pi$
$61$	−12.8567			−1.64613			−0.823064	+	0.567948i	$0.807737\pi$
$62$	2.08693	−	1.20489i	0.265040	−	0.153021i
$63$	4.05552	−	9.87922i	0.510947	−	1.24466i
$64$	1.29694			0.162117
$65$	0.0222836	+	0.0385964i	0.00276394	+	0.00478729i
$66$	4.71333	+	2.31509i	0.580170	+	0.284968i
$67$	9.17875	−	5.29935i	1.12136	−	0.647419i	0.179614	−	0.983737i	$-0.442515\pi$
$67$	9.17875	−	5.29935i	1.12136	−	0.647419i	0.941748	+	0.336318i	$0.109182\pi$
$68$	4.89919	+	2.82855i	0.594114	+	0.343012i
$69$	0.627998	+	9.35453i	0.0756021	+	1.12615i
$70$			0.263221i			0.0314609i
$71$	5.43426	+	9.41241i	0.644928	+	1.11705i	0.984318	+	0.176402i	$0.0564459\pi$
$71$	5.43426	+	9.41241i	0.644928	+	1.11705i	−0.339390	+	0.940646i	$0.610221\pi$
$72$	4.46550	+	5.78156i	0.526264	+	0.681364i
$73$	2.47284	+	4.28309i	0.289424	+	0.501297i	0.973672	−	0.227952i	$-0.0732029\pi$
$73$	2.47284	+	4.28309i	0.289424	+	0.501297i	−0.684248	+	0.729249i	$0.739870\pi$
$74$	−1.10550	−	0.638258i	−0.128511	−	0.0741960i
$75$	3.80930	−	7.75542i	0.439860	−	0.895518i
$76$	−1.20177	−	6.52432i	−0.137852	−	0.748391i
$77$	13.5181	+	7.80470i	1.54053	+	0.889428i
$78$	−0.447926	−	0.220012i	−0.0507176	−	0.0249114i
$79$	0.947726	+	0.547170i	0.106627	+	0.0615614i	0.552365	−	0.833602i	$-0.313725\pi$
$79$	0.947726	+	0.547170i	0.106627	+	0.0615614i	−0.445738	+	0.895164i	$0.647059\pi$
$80$	0.125990	+	0.0727401i	0.0140861	+	0.00813259i
$81$	−2.27429	+	8.70790i	−0.252699	+	0.967545i
$82$	3.44762	−	5.97145i	0.380726	−	0.659437i
$83$	7.21082	−	4.16317i	0.791490	−	0.456967i	−0.0489969	−	0.998799i	$-0.515602\pi$
$83$	7.21082	−	4.16317i	0.791490	−	0.456967i	0.840487	+	0.541832i	$0.182269\pi$
$84$	5.22576	+	7.79417i	0.570177	+	0.850414i
$85$	−0.198760	−	0.344263i	−0.0215586	−	0.0373406i
$86$	3.73498	+	6.46918i	0.402753	+	0.697589i
$87$	−4.20592	+	8.56290i	−0.450922	+	0.918039i
$88$	−9.24726	+	5.33891i	−0.985761	+	0.569130i
$89$	−2.61637	+	4.53168i	−0.277335	+	0.480358i	−0.970721	−	0.240208i	$-0.922784\pi$
$89$	−2.61637	+	4.53168i	−0.277335	+	0.480358i	0.693387	+	0.720565i	$0.256118\pi$
$90$	−0.0296508	−	0.219841i	−0.00312546	−	0.0231732i
$91$	−1.28468	−	0.741711i	−0.134671	−	0.0777524i
$92$	−7.13465	−	4.11919i	−0.743838	−	0.429455i
$93$	−5.01410	+	3.36180i	−0.519938	+	0.348603i
$94$	0.150350	+	0.0868045i	0.0155074	+	0.00895320i
$95$	−0.156096	+	0.439262i	−0.0160151	+	0.0450673i
$96$	−10.0418	+	0.674138i	−1.02489	+	0.0688039i
$97$	11.3602	+	6.55883i	1.15346	+	0.665948i	0.949727	−	0.313079i	$-0.101361\pi$
$97$	11.3602	+	6.55883i	1.15346	+	0.665948i	0.203729	+	0.979027i	$0.434694\pi$
$98$	−1.96075	−	3.39611i	−0.198065	−	0.343059i
$99$	−12.1694	−	4.99568i	−1.22307	−	0.502084i
$100$	3.79620	+	6.57522i	0.379620	+	0.657522i
$101$			1.76933i			0.176055i	0.996118	+	0.0880276i	$0.0280564\pi$
$101$			1.76933i			0.176055i	−0.996118	+	0.0880276i	$0.971944\pi$
$102$	3.99531	+	1.96241i	0.395594	+	0.194308i
$103$	1.56658	+	0.904463i	0.154359	+	0.0891194i	0.575190	−	0.818020i	$-0.304928\pi$
$103$	1.56658	+	0.904463i	0.154359	+	0.0891194i	−0.420831	+	0.907139i	$0.638261\pi$
$104$	0.878803	−	0.507377i	0.0861738	−	0.0497524i
$105$	−0.0441682	−	0.657921i	−0.00431038	−	0.0642065i
$106$	−0.996947	−	1.72676i	−0.0968320	−	0.167718i
$107$	13.6046			1.31520			0.657601	−	0.753366i	$-0.271571\pi$
$107$	13.6046			1.31520			0.657601	+	0.753366i	$0.271571\pi$
$108$	−5.24251	−	5.92099i	−0.504461	−	0.569747i
$109$	10.9897	−	6.34490i	1.05262	−	0.607731i	0.129239	−	0.991613i	$-0.458747\pi$
$109$	10.9897	−	6.34490i	1.05262	−	0.607731i	0.923382	+	0.383883i	$0.125413\pi$
$110$	0.324241			0.0309152
$111$	2.87029	+	1.40983i	0.272436	+	0.133815i
$112$	−4.84231			−0.457555
$113$	2.83696	−	4.91376i	0.266879	−	0.462247i	−0.701175	−	0.712989i	$-0.747341\pi$
$113$	2.83696	−	4.91376i	0.266879	−	0.462247i	0.968054	+	0.250741i	$0.0806744\pi$
$114$	−1.28734	−	5.05874i	−0.120570	−	0.473795i
$115$	0.289453	+	0.501347i	0.0269916	+	0.0467509i
$116$	−4.19146	−	7.25982i	−0.389167	−	0.674057i
$117$	1.15651	+	0.474759i	0.106919	+	0.0438914i
$118$	0.821001	−	1.42202i	0.0755793	−	0.130907i
$119$	11.4588	+	6.61574i	1.05043	+	0.606464i
$120$	0.404870	+	0.198864i	0.0369594	+	0.0181537i
$121$	4.11399	−	7.12565i	0.374000	−	0.647786i
$122$	4.44457	−	7.69822i	0.402392	−	0.696964i
$123$	−7.61532	+	15.5042i	−0.686651	+	1.39796i
$124$		−	5.30457i		−	0.476364i
$125$		−	1.06825i		−	0.0955473i
$126$	4.51340	+	5.84359i	0.402086	+	0.520588i
$127$	−14.2508	−	8.22768i	−1.26455	−	0.730089i	−0.290599	−	0.956845i	$-0.593855\pi$
$127$	−14.2508	−	8.22768i	−1.26455	−	0.730089i	−0.973951	+	0.226756i	$0.927188\pi$
$128$	5.36235	−	9.28786i	0.473969	−	0.820938i
$129$	−10.4211	−	15.5430i	−0.917527	−	1.36848i
$130$	−0.0308139			−0.00270256
$131$		−	9.66429i		−	0.844373i	−0.906509	−	0.422187i	$-0.861263\pi$
$131$		−	9.66429i		−	0.844373i	0.906509	−	0.422187i	$-0.138737\pi$
$132$	9.60103	−	6.43721i	0.835663	−	0.560287i
$133$	−2.81084	−	15.2599i	−0.243731	−	1.32320i
$134$			7.32797i			0.633040i
$135$	0.111001	+	0.544516i	0.00955346	+	0.0468645i
$136$	−7.83855	+	4.52559i	−0.672150	+	0.388066i
$137$			12.5958i			1.07613i	0.842904	+	0.538064i	$0.180844\pi$
$137$			12.5958i			1.07613i	−0.842904	+	0.538064i	$0.819156\pi$
$138$	−5.81833	−	2.85784i	−0.495289	−	0.243276i
$139$	−5.07945	−	8.79786i	−0.430833	−	0.746225i	0.566112	−	0.824328i	$-0.308447\pi$
$139$	−5.07945	−	8.79786i	−0.430833	−	0.746225i	−0.996945	+	0.0781032i	$0.975114\pi$
$140$	0.501792	+	0.289710i	0.0424092	+	0.0244850i
$141$	−0.390365	−	0.191739i	−0.0328747	−	0.0161474i
$142$	−7.51452			−0.630604
$143$	−0.913655	+	1.58250i	−0.0764037	+	0.132335i
$144$	4.04427	−	0.545467i	0.337023	−	0.0454556i
$145$			0.589063i			0.0489190i
$146$	−3.41946			−0.282996
$147$	5.47075	+	8.15957i	0.451220	+	0.672990i
$148$	−2.43349	+	1.40498i	−0.200032	+	0.115489i
$149$			17.1225i			1.40273i	0.712802	+	0.701365i	$0.247426\pi$
$149$			17.1225i			1.40273i	−0.712802	+	0.701365i	$0.752574\pi$
$150$	3.32685	+	4.96196i	0.271636	+	0.405142i
$151$	0.724901	−	0.418522i	0.0589916	−	0.0340588i	−0.470214	−	0.882552i	$-0.655823\pi$
$151$	0.724901	−	0.418522i	0.0589916	−	0.0340588i	0.529206	+	0.848494i	$0.322490\pi$
$152$	10.0016	+	3.55417i	0.811236	+	0.288281i
$153$	−10.3156	−	4.23464i	−0.833964	−	0.342351i
$154$	−9.34647	+	5.39619i	−0.753160	+	0.434837i
$155$	−0.186374	+	0.322810i	−0.0149699	+	0.0259287i
$156$	−0.912424	+	0.611753i	−0.0730523	+	0.0489794i
$157$	−14.9279			−1.19138			−0.595688	−	0.803216i	$-0.703121\pi$
$157$	−14.9279			−1.19138			−0.595688	+	0.803216i	$0.703121\pi$
$158$	−0.655260	+	0.378314i	−0.0521297	+	0.0300971i
$159$	2.78162	+	4.14876i	0.220597	+	0.329018i
$160$	−0.538182	+	0.310720i	−0.0425470	+	0.0245645i
$161$	−16.6874	−	9.63445i	−1.31515	−	0.759301i
$162$	−4.42782	−	4.37212i	−0.347883	−	0.343506i
$163$	3.88920			0.304626			0.152313	−	0.988332i	$-0.451328\pi$
$163$	3.88920			0.304626			0.152313	+	0.988332i	$0.451328\pi$
$164$	−7.58914	−	13.1448i	−0.592612	−	1.02643i
$165$	−0.810441	+	0.0544074i	−0.0630927	+	0.00423561i
$166$			5.75685i			0.446818i
$167$	−4.78677	−	8.29094i	−0.370412	−	0.641572i	0.619217	−	0.785220i	$-0.287450\pi$
$167$	−4.78677	−	8.29094i	−0.370412	−	0.641572i	−0.989629	+	0.143648i	$0.954117\pi$
$168$	−14.9802	+	1.00567i	−1.15575	+	0.0775891i
$169$	−6.41317	+	11.1079i	−0.493321	+	0.854457i
$170$	0.274847			0.0210798
$171$	4.06656	+	12.4283i	0.310978	+	0.950417i
$172$	16.4434			1.25380
$173$	2.24276	−	3.88458i	0.170514	−	0.295339i	−0.768086	−	0.640347i	$-0.778790\pi$
$173$	2.24276	−	3.88458i	0.170514	−	0.295339i	0.938600	+	0.345008i	$0.112124\pi$
$174$	−3.67323	−	5.47859i	−0.278467	−	0.415331i
$175$	8.87901	+	15.3789i	0.671190	+	1.16254i
$176$			5.96486i			0.449618i
$177$	−1.81348	+	3.69209i	−0.136310	+	0.277515i
$178$	−1.80896	−	3.13322i	−0.135588	−	0.234845i
$179$	5.02157			0.375330			0.187665	−	0.982233i	$-0.439908\pi$
$179$	5.02157			0.375330			0.187665	+	0.982233i	$0.439908\pi$
$180$	−0.451729	−	0.185439i	−0.0336699	−	0.0138218i
$181$	10.9563	+	6.32561i	0.814374	+	0.470179i	0.848473	−	0.529239i	$-0.177523\pi$
$181$	10.9563	+	6.32561i	0.814374	+	0.470179i	−0.0340985	+	0.999418i	$0.510856\pi$
$182$	0.888231	−	0.512821i	0.0658401	−	0.0380128i
$183$	−9.81745	+	19.9875i	−0.725727	+	1.47752i
$184$	11.4152	−	6.59058i	0.841541	−	0.485864i
$185$	0.197454			0.0145171
$186$	−0.279574	−	4.16448i	−0.0204994	−	0.305355i
$187$	8.14942	−	14.1152i	0.595945	−	1.03221i
$188$	0.330961	−	0.191080i	0.0241378	−	0.0139360i
$189$	−12.2618	−	13.8487i	−0.891915	−	1.00735i
$190$	−0.209055	−	0.245320i	−0.0151665	−	0.0177973i
$191$	12.8859	−	7.43970i	0.932394	−	0.538318i	0.0448259	−	0.998995i	$-0.485727\pi$
$191$	12.8859	−	7.43970i	0.932394	−	0.538318i	0.887568	+	0.460677i	$0.152393\pi$
$192$	0.990351	−	2.01627i	0.0714724	−	0.145512i
$193$			13.3486i			0.960853i	0.877035	+	0.480426i	$0.159518\pi$
$193$			13.3486i			0.960853i	−0.877035	+	0.480426i	$0.840482\pi$
$194$	−7.85449	+	4.53479i	−0.563919	+	0.325579i
$195$	0.0770194	−	0.00517054i	0.00551547	−	0.000370270i
$196$	−8.63226			−0.616590
$197$			21.4163i			1.52585i	0.646488	+	0.762925i	$0.276237\pi$
$197$			21.4163i			1.52585i	−0.646488	+	0.762925i	$0.723763\pi$
$198$	7.19826	−	5.55971i	0.511558	−	0.395111i
$199$	2.50917	−	4.34600i	0.177870	−	0.308080i	−0.763281	−	0.646067i	$-0.776413\pi$
$199$	2.50917	−	4.34600i	0.177870	−	0.308080i	0.941151	+	0.337987i	$0.109746\pi$
$200$	−12.1476			−0.858966
$201$	−1.22963	−	18.3163i	−0.0867312	−	1.29193i
$202$	−1.05943	−	0.611661i	−0.0745411	−	0.0430363i
$203$	−9.80348	−	16.9801i	−0.688069	−	1.19177i
$204$	8.13843	−	5.45658i	0.569804	−	0.382037i
$205$			1.06657i			0.0744924i
$206$	−1.08313	+	0.625348i	−0.0754655	+	0.0435700i
$207$	15.0225	+	6.16687i	1.04413	+	0.428627i
$208$		−	0.566864i		−	0.0393050i
$209$	−18.7974	+	3.46246i	−1.30025	+	0.239503i
$210$	0.409213	+	0.200997i	0.0282384	+	0.0138701i
$211$			16.0094i			1.10213i	0.834462	+	0.551066i	$0.185779\pi$
$211$			16.0094i			1.10213i	−0.834462	+	0.551066i	$0.814221\pi$
$212$	−4.38910			−0.301444
$213$	18.7825	−	1.26093i	1.28696	−	0.0863975i
$214$	−4.70311	+	8.14603i	−0.321498	+	0.556851i
$215$	−1.00066	−	0.577734i	−0.0682447	−	0.0394011i
$216$	12.3981	−	2.52739i	0.843586	−	0.171967i
$217$		−	12.4069i		−	0.842239i
$218$			8.77375i			0.594233i
$219$	8.54693	−	0.573782i	0.577548	−	0.0387726i
$220$	0.356871	−	0.618119i	0.0240602	−	0.0416736i
$221$	−0.774471	+	1.34142i	−0.0520966	+	0.0902339i
$222$	−1.83643	+	1.23127i	−0.123253	+	0.0826374i
$223$	7.10493	+	4.10203i	0.475781	+	0.274693i	0.718657	−	0.695365i	$-0.244757\pi$
$223$	7.10493	+	4.10203i	0.475781	+	0.274693i	−0.242875	+	0.970058i	$0.578091\pi$
$224$	10.3423	−	17.9134i	0.691024	−	1.19689i
$225$	−9.14807	−	11.8442i	−0.609871	−	0.789612i
$226$	1.96148	+	3.39738i	0.130476	+	0.225991i
$227$	14.4019	+	24.9448i	0.955888	+	1.65565i	0.732322	+	0.680958i	$0.238437\pi$
$227$	14.4019	+	24.9448i	0.955888	+	1.65565i	0.223566	+	0.974689i	$0.428230\pi$
$228$	−11.0607	−	3.11370i	−0.732510	−	0.206210i
$229$	9.25025	−	16.0219i	0.611274	−	1.05876i	−0.379753	−	0.925088i	$-0.623991\pi$
$229$	9.25025	−	16.0219i	0.611274	−	1.05876i	0.991026	−	0.133669i	$-0.0426758\pi$
$230$	−0.400257			−0.0263922
$231$	22.4560	−	15.0561i	1.47750	−	0.990619i
$232$	13.4124			0.880568
$233$	−17.8445	+	10.3025i	−1.16903	+	0.674941i	−0.953452	−	0.301545i	$-0.902498\pi$
$233$	−17.8445	+	10.3025i	−1.16903	+	0.674941i	−0.215580	+	0.976486i	$0.569164\pi$
$234$	−0.684079	+	0.528360i	−0.0447196	+	0.0345400i
$235$	−0.0268542			−0.00175177
$236$	−1.80725	−	3.13024i	−0.117642	−	0.203761i
$237$	1.57434	−	1.05555i	0.102265	−	0.0685653i
$238$	−7.92265	+	4.57414i	−0.513549	+	0.296498i
$239$	−25.5747	−	14.7655i	−1.65429	−	0.955104i	−0.975280	−	0.220972i	$-0.929077\pi$
$239$	−25.5747	−	14.7655i	−1.65429	−	0.955104i	−0.679008	−	0.734131i	$-0.737590\pi$
$240$	0.209291	−	0.140323i	0.0135097	−	0.00905784i
$241$		−	4.30851i		−	0.277536i	−0.990325	−	0.138768i	$-0.955686\pi$
$241$		−	4.30851i		−	0.277536i	0.990325	−	0.138768i	$-0.0443142\pi$
$242$	2.84443	+	4.92669i	0.182847	+	0.316700i
$243$	11.8010	+	10.1851i	0.757034	+	0.653376i
$244$	−9.78369	−	16.9459i	−0.626337	−	1.08485i
$245$	0.525317	+	0.303292i	0.0335613	+	0.0193766i
$246$	−6.65083	−	9.91965i	−0.424041	−	0.632454i
$247$	1.78639	−	0.329051i	0.113665	−	0.0209370i
$248$	7.35008	+	4.24357i	0.466731	+	0.269467i
$249$	−0.965994	−	14.3892i	−0.0612174	−	0.911881i
$250$	0.639639	+	0.369296i	0.0404543	+	0.0233563i
$251$	−10.3715	−	5.98796i	−0.654640	−	0.377957i	0.135592	−	0.990765i	$-0.456707\pi$
$251$	−10.3715	−	5.98796i	−0.654640	−	0.377957i	−0.790232	+	0.612808i	$0.790040\pi$
$252$	16.1076	−	2.17249i	1.01468	−	0.136854i
$253$	−11.8679	+	20.5558i	−0.746130	+	1.29233i
$254$	9.85301	−	5.68864i	0.618233	−	0.356937i
$255$	−0.686980	+	0.0461191i	−0.0430204	+	0.00288809i
$256$	5.00448	+	8.66801i	0.312780	+	0.541750i
$257$	9.98699	+	17.2980i	0.622972	+	1.07902i	0.988929	+	0.148387i	$0.0474081\pi$
$257$	9.98699	+	17.2980i	0.622972	+	1.07902i	−0.365958	+	0.930631i	$0.619259\pi$
$258$	12.9093	−	0.866640i	0.803697	−	0.0539547i
$259$	−5.69174	+	3.28613i	−0.353668	+	0.204190i
$260$	−0.0339148	+	0.0587422i	−0.00210331	+	0.00364304i
$261$	10.1006	+	13.0774i	0.625209	+	0.809470i
$262$	5.78671	+	3.34096i	0.357504	+	0.206405i
$263$	7.30226	+	4.21596i	0.450277	+	0.259967i	0.707947	−	0.706266i	$-0.249622\pi$
$263$	7.30226	+	4.21596i	0.450277	+	0.259967i	−0.257670	+	0.966233i	$0.582955\pi$
$264$	1.23881	+	18.4530i	0.0762432	+	1.13570i
$265$	0.267099	+	0.154210i	0.0164078	+	0.00947302i
$266$	10.1089	+	3.59230i	0.619816	+	0.220258i
$267$	5.04726	+	7.52794i	0.308887	+	0.460702i
$268$	13.9697	+	8.06542i	0.853336	+	0.492674i
$269$	−10.9044	−	18.8870i	−0.664856	−	1.15156i	−0.979324	−	0.202296i	$-0.935160\pi$
$269$	−10.9044	−	18.8870i	−0.664856	−	1.15156i	0.314469	−	0.949268i	$-0.398174\pi$
$270$	−0.364414	−	0.121776i	−0.0221775	−	0.00741102i
$271$	2.11392	+	3.66142i	0.128412	+	0.222416i	0.923061	−	0.384653i	$-0.125679\pi$
$271$	2.11392	+	3.66142i	0.128412	+	0.222416i	−0.794650	+	0.607068i	$0.792345\pi$
$272$			5.05619i			0.306576i
$273$	−2.13408	+	1.43084i	−0.129161	+	0.0865984i
$274$	−7.54199	−	4.35437i	−0.455628	−	0.263057i
$275$	18.9441	−	10.9374i	1.14237	−	0.659547i
$276$	−11.8519	+	7.94636i	−0.713402	+	0.478315i
$277$	8.28717	+	14.3538i	0.497928	+	0.862436i	0.999997	−	0.00239145i	$-0.000761224\pi$
$277$	8.28717	+	14.3538i	0.497928	+	0.862436i	−0.502070	+	0.864827i	$0.667428\pi$
$278$	7.02389			0.421265
$279$	1.39759	+	10.3622i	0.0836717	+	0.620370i
$280$	−0.802852	+	0.463527i	−0.0479796	+	0.0277010i
$281$	−17.6086			−1.05044			−0.525220	−	0.850966i	$-0.676017\pi$
$281$	−17.6086			−1.05044			−0.525220	+	0.850966i	$0.676017\pi$
$282$	0.249758	−	0.167455i	0.0148729	−	0.00997182i
$283$	−31.9287			−1.89797			−0.948983	−	0.315329i	$-0.897885\pi$
$283$	−31.9287			−1.89797			−0.948983	+	0.315329i	$0.897885\pi$
$284$	−8.27074	+	14.3253i	−0.490778	+	0.850053i
$285$	0.563698	+	0.578097i	0.0333906	+	0.0342435i
$286$	−0.631703	−	1.09414i	−0.0373534	−	0.0646980i
$287$	−17.7504	−	30.7446i	−1.04777	−	1.81479i
$288$	−6.61996	+	16.1262i	−0.390085	+	0.950245i
$289$	−1.59205	+	2.75751i	−0.0936498	+	0.162206i
$290$	−0.352714	−	0.203640i	−0.0207121	−	0.0119581i
$291$	18.8714	−	12.6527i	1.10626	−	0.741714i
$292$	−3.76357	+	6.51870i	−0.220246	+	0.381478i
$293$	14.0550	−	24.3440i	0.821101	−	1.42219i	−0.0837616	−	0.996486i	$-0.526693\pi$
$293$	14.0550	−	24.3440i	0.821101	−	1.42219i	0.904863	−	0.425703i	$-0.139973\pi$
$294$	−6.77697	+	0.454959i	−0.395241	+	0.0265337i
$295$			0.253988i			0.0147878i
$296$		−	4.49584i		−	0.261316i
$297$	−17.0591	+	15.1044i	−0.989872	+	0.876443i
$298$	−10.2525	−	5.91927i	−0.593910	−	0.342894i
$299$	1.12785	−	1.95350i	0.0652255	−	0.112974i
$300$	13.1209	−	0.880846i	0.757535	−	0.0508557i
$301$	38.4598			2.21678
$302$			0.578734i			0.0333024i
$303$	2.75068	+	1.35108i	0.158022	+	0.0776173i
$304$	4.51299	−	3.84586i	0.258838	−	0.220575i
$305$			1.37499i			0.0787316i
$306$	6.10169	−	4.71275i	0.348810	−	0.269410i
$307$	−8.38574	+	4.84151i	−0.478599	+	0.276319i	−0.719833	−	0.694148i	$-0.755781\pi$
$307$	−8.38574	+	4.84151i	−0.478599	+	0.276319i	0.241233	+	0.970467i	$0.422448\pi$
$308$			23.7569i			1.35368i
$309$	2.60236	−	1.74481i	0.148043	−	0.0992586i
$310$	−0.128860	−	0.223192i	−0.00731874	−	0.0126764i
$311$	0.0989162	+	0.0571093i	0.00560902	+	0.00323837i	0.502802	−	0.864402i	$-0.332303\pi$
$311$	0.0989162	+	0.0571093i	0.00560902	+	0.00323837i	−0.497193	+	0.867640i	$0.665636\pi$
$312$	−0.117728	−	1.75366i	−0.00666506	−	0.0992814i
$313$	−2.26753			−0.128168			−0.0640841	−	0.997944i	$-0.520413\pi$
$313$	−2.26753			−0.128168			−0.0640841	+	0.997944i	$0.520413\pi$
$314$	5.16059	−	8.93841i	0.291229	−	0.504424i
$315$	−1.05656	−	0.433727i	−0.0595302	−	0.0244378i
$316$			1.66554i			0.0936942i
$317$	9.86385			0.554009			0.277004	−	0.960869i	$-0.410658\pi$
$317$	9.86385			0.554009			0.277004	+	0.960869i	$0.410658\pi$
$318$	−3.44577	+	0.231325i	−0.193229	+	0.0129721i
$319$	−20.9165	+	12.0761i	−1.17110	+	0.676134i
$320$		−	0.138704i		−	0.00775380i
$321$	10.3885	−	21.1502i	0.579832	−	1.18049i
$322$	11.5377	−	6.66128i	0.642969	−	0.371219i
$323$	−15.9339	+	2.93499i	−0.886584	+	0.163307i
$324$	−13.2082	+	3.62890i	−0.733790	+	0.201606i
$325$	−1.80033	+	1.03942i	−0.0998642	+	0.0576566i
$326$	−1.34450	+	2.32874i	−0.0744650	+	0.128977i
$327$	−1.47223	−	21.9300i	−0.0814144	−	1.21273i
$328$	24.2848			1.34090
$329$	0.774090	−	0.446921i	0.0426769	−	0.0246395i
$330$	0.247593	−	0.504078i	0.0136295	−	0.0277486i
$331$	−6.56652	+	3.79118i	−0.360929	+	0.208382i	−0.669488	−	0.742823i	$-0.733486\pi$
$331$	−6.56652	+	3.79118i	−0.360929	+	0.208382i	0.308559	+	0.951205i	$0.400153\pi$
$332$	10.9746	+	6.33618i	0.602309	+	0.347743i
$333$	4.38354	−	3.38571i	0.240217	−	0.185536i
$334$	6.61917			0.362185
$335$	−0.566752	−	0.981643i	−0.0309650	−	0.0536329i
$336$	−3.69762	+	7.52805i	−0.201722	+	0.410689i
$337$		−	14.1127i		−	0.768768i	−0.923173	−	0.384384i	$-0.874414\pi$
$337$		−	14.1127i		−	0.768768i	0.923173	−	0.384384i	$-0.125586\pi$
$338$	−4.43408	−	7.68006i	−0.241182	−	0.417740i
$339$	−5.47280	−	8.16263i	−0.297242	−	0.443333i
$340$	0.302506	−	0.523956i	0.0164057	−	0.0284155i
$341$	−15.2831			−0.827629
$342$	−8.84754	−	1.86154i	−0.478420	−	0.100661i
$343$	4.72808			0.255292
$344$	−13.1545	+	22.7842i	−0.709241	+	1.22844i
$345$	1.00044	−	0.0671628i	0.0538620	−	0.00361592i
$346$	1.55065	+	2.68581i	0.0833636	+	0.144390i
$347$		−	6.86219i		−	0.368381i	−0.982891	−	0.184191i	$-0.941034\pi$
$347$		−	6.86219i		−	0.368381i	0.982891	−	0.184191i	$-0.0589664\pi$
$348$	−14.4870	+	0.972559i	−0.776586	+	0.0521346i
$349$	3.10669	+	5.38094i	0.166297	+	0.288035i	0.937115	−	0.349020i	$-0.113486\pi$
$349$	3.10669	+	5.38094i	0.166297	+	0.288035i	−0.770818	+	0.637056i	$0.780152\pi$
$350$	−12.2779			−0.656283
$351$	1.62120	−	1.43543i	0.0865331	−	0.0766173i
$352$	−22.0661	−	12.7399i	−1.17613	−	0.679038i
$353$	−11.0335	+	6.37017i	−0.587252	+	0.339050i	−0.764010	−	0.645204i	$-0.776772\pi$
$353$	−11.0335	+	6.37017i	−0.587252	+	0.339050i	0.176758	+	0.984254i	$0.443439\pi$
$354$	−1.58380	−	2.36222i	−0.0841780	−	0.125551i
$355$	1.00663	−	0.581180i	0.0534265	−	0.0308458i
$356$	−7.96403			−0.422093
$357$	19.0351	−	12.7625i	1.00745	−	0.675462i
$358$	−1.73596	+	3.00678i	−0.0917485	+	0.158913i
$359$	13.1829	−	7.61116i	0.695767	−	0.401701i	−0.110002	−	0.993931i	$-0.535086\pi$
$359$	13.1829	−	7.61116i	0.695767	−	0.401701i	0.805769	+	0.592230i	$0.201752\pi$
$360$	0.618323	−	0.477573i	0.0325885	−	0.0251703i
$361$	14.7394	+	11.9896i	0.775756	+	0.631033i
$362$	−7.57520	+	4.37354i	−0.398144	+	0.229868i
$363$	−7.93634	−	11.8370i	−0.416550	−	0.621280i
$364$		−	2.25771i		−	0.118336i
$365$	0.458065	−	0.264464i	0.0239762	−	0.0138427i
$366$	−8.57405	−	12.7881i	−0.448173	−	0.668445i
$367$	−7.66563			−0.400143			−0.200071	−	0.979781i	$-0.564117\pi$
$367$	−7.66563			−0.400143			−0.200071	+	0.979781i	$0.564117\pi$
$368$		−	7.36328i		−	0.383837i
$369$	18.2883	+	23.6782i	0.952049	+	1.23264i
$370$	−0.0682601	+	0.118230i	−0.00354867	+	0.00614648i
$371$	−10.2657			−0.532971
$372$	−8.24669	−	4.05060i	−0.427571	−	0.210014i
$373$	−16.3704	−	9.45148i	−0.847629	−	0.489379i	0.0122211	−	0.999925i	$-0.496110\pi$
$373$	−16.3704	−	9.45148i	−0.847629	−	0.489379i	−0.859850	+	0.510546i	$0.829443\pi$
$374$	5.63453	+	9.75929i	0.291354	+	0.504641i
$375$	−1.66075	−	0.815724i	−0.0857605	−	0.0421238i
$376$			0.611445i			0.0315329i
$377$	1.98778	−	1.14764i	0.102376	−	0.0591066i
$378$	12.5311	−	2.55451i	0.644532	−	0.131390i
$379$		−	24.7158i		−	1.26957i	−0.772690	−	0.634784i	$-0.781089\pi$
$379$		−	24.7158i		−	1.26957i	0.772690	−	0.634784i	$-0.218911\pi$
$380$	−0.697759	+	0.128526i	−0.0357943	+	0.00659325i
$381$	−23.6731	+	15.8721i	−1.21281	+	0.813151i
$382$			10.2877i			0.526362i
$383$	22.8913			1.16969			0.584845	−	0.811145i	$-0.301155\pi$
$383$	22.8913			1.16969			0.584845	+	0.811145i	$0.301155\pi$
$384$	−10.3445	−	15.4288i	−0.527893	−	0.787347i
$385$	0.834692	−	1.44573i	0.0425398	−	0.0736812i
$386$	−7.99276	−	4.61462i	−0.406821	−	0.234878i
$387$	−32.1214	+	4.33234i	−1.63282	+	0.220225i
$388$			19.9646i			1.01355i
$389$		−	3.79097i		−	0.192210i	−0.995371	−	0.0961049i	$-0.969362\pi$
$389$		−	3.79097i		−	0.192210i	0.995371	−	0.0961049i	$-0.0306384\pi$
$390$	−0.0235297	+	0.0479045i	−0.00119147	+	0.00242574i
$391$	−10.0600	+	17.4244i	−0.508755	+	0.881190i
$392$	6.90567	−	11.9610i	0.348789	−	0.604121i
$393$	−15.0245	−	7.37972i	−0.757885	−	0.372258i
$394$	−12.8235	−	7.40364i	−0.646038	−	0.372990i
$395$	0.0585184	−	0.101357i	0.00294438	−	0.00509982i
$396$	−2.67612	−	19.8416i	−0.134480	−	0.997080i
$397$	3.53802	+	6.12804i	0.177568	+	0.307557i	0.941047	−	0.338276i	$-0.109844\pi$
$397$	3.53802	+	6.12804i	0.177568	+	0.307557i	−0.763479	+	0.645833i	$0.776510\pi$
$398$	1.73484	+	3.00484i	0.0869598	+	0.150619i
$399$	−25.8700	−	7.28269i	−1.29512	−	0.364590i
$400$	−3.39296	+	5.87678i	−0.169648	+	0.293839i
$401$	−12.6565			−0.632036			−0.316018	−	0.948753i	$-0.602346\pi$
$401$	−12.6565			−0.632036			−0.316018	+	0.948753i	$0.602346\pi$
$402$	11.3924	+	5.59569i	0.568199	+	0.279088i
$403$	1.45242			0.0723501
$404$	−2.33209	+	1.34643i	−0.116026	+	0.0669874i
$405$	0.931288	+	0.243230i	0.0462761	+	0.0120862i
$406$	13.5563			0.672788
$407$	4.04793	+	7.01121i	0.200648	+	0.347533i
$408$	1.05009	+	15.6419i	0.0519871	+	0.774389i
$409$	20.9336	−	12.0860i	1.03510	−	0.597615i	0.116658	−	0.993172i	$-0.462782\pi$
$409$	20.9336	−	12.0860i	1.03510	−	0.597615i	0.918441	+	0.395557i	$0.129448\pi$
$410$	−0.638631	−	0.368714i	−0.0315398	−	0.0182095i
$411$	19.5819	+	9.61821i	0.965902	+	0.474431i
$412$			2.75312i			0.135636i
$413$	−4.22700	−	7.32138i	−0.207997	−	0.360261i
$414$	−8.88583	+	6.86314i	−0.436715	+	0.337305i
$415$	−0.445240	−	0.771178i	−0.0218560	−	0.0378556i
$416$	2.09703	+	1.21072i	0.102815	+	0.0593604i
$417$	−17.5562	+	1.17860i	−0.859731	+	0.0577164i
$418$	4.42507	−	12.4523i	0.216437	−	0.609064i
$419$	23.3582	+	13.4859i	1.14112	+	0.658828i	0.946709	−	0.322091i	$-0.104386\pi$
$419$	23.3582	+	13.4859i	1.14112	+	0.658828i	0.194415	+	0.980919i	$0.437719\pi$
$420$	0.833567	−	0.558882i	0.0406739	−	0.0272706i
$421$	22.9894	+	13.2730i	1.12044	+	0.646885i	0.941512	−	0.336978i	$-0.109405\pi$
$421$	22.9894	+	13.2730i	1.12044	+	0.646885i	0.178925	+	0.983863i	$0.442738\pi$
$422$	−9.58598	−	5.53447i	−0.466638	−	0.269414i
$423$	−0.596172	+	0.460464i	−0.0289869	+	0.0223885i
$424$	3.51121	−	6.08159i	0.170519	−	0.295348i
$425$	16.0582	−	9.27118i	0.778935	−	0.449718i
$426$	−5.73814	+	11.6824i	−0.278014	+	0.566013i
$427$	−22.8833	−	39.6350i	−1.10740	−	1.91807i
$428$	10.3528	+	17.9316i	0.500422	+	0.866757i
$429$	1.76254	+	2.62881i	0.0850962	+	0.126920i
$430$	0.691862	−	0.399446i	0.0333645	−	0.0192630i
$431$	−8.45285	+	14.6408i	−0.407159	+	0.705221i	−0.994570	−	0.104068i	$-0.966814\pi$
$431$	−8.45285	+	14.6408i	−0.407159	+	0.705221i	0.587411	+	0.809289i	$0.300147\pi$
$432$	2.24023	−	6.70390i	0.107783	−	0.322542i
$433$	−13.0398	−	7.52854i	−0.626653	−	0.361799i	0.152801	−	0.988257i	$-0.451171\pi$
$433$	−13.0398	−	7.52854i	−0.626653	−	0.361799i	−0.779455	+	0.626458i	$0.784504\pi$
$434$	7.42893	+	4.28910i	0.356600	+	0.205883i
$435$	0.915780	+	0.449812i	0.0439083	+	0.0215669i
$436$	16.7259	+	9.65670i	0.801025	+	0.462472i
$437$	23.2043	−	4.27420i	1.11001	−	0.204463i
$438$	−2.61112	+	5.31602i	−0.124764	+	0.254009i
$439$	−12.9671	−	7.48654i	−0.618884	−	0.357313i	0.157550	−	0.987511i	$-0.449640\pi$
$439$	−12.9671	−	7.48654i	−0.618884	−	0.357313i	−0.776434	+	0.630198i	$0.782974\pi$
$440$	0.570983	+	0.988971i	0.0272205	+	0.0471473i
$441$	16.8627	−	2.27434i	0.802986	−	0.108302i
$442$	−0.535471	−	0.927463i	−0.0254698	−	0.0441149i
$443$		−	13.9092i		−	0.660844i	−0.943833	−	0.330422i	$-0.892809\pi$
$443$		−	13.9092i		−	0.660844i	0.943833	−	0.330422i	$-0.107191\pi$
$444$	0.326002	+	4.85606i	0.0154714	+	0.230458i
$445$	0.484652	+	0.279814i	0.0229747	+	0.0132644i
$446$	−4.91237	+	2.83616i	−0.232607	+	0.134296i
$447$	26.6193	+	13.0749i	1.25905	+	0.618420i
$448$	2.30839	+	3.99824i	0.109061	+	0.188899i
$449$	33.9028			1.59997			0.799986	−	0.600018i	$-0.204840\pi$
$449$	33.9028			1.59997			0.799986	+	0.600018i	$0.204840\pi$
$450$	10.2545	−	1.38306i	0.483400	−	0.0651981i
$451$	−37.8718	+	21.8653i	−1.78331	+	1.02960i
$452$	8.63549			0.406179
$453$	−0.0971110	−	1.44655i	−0.00456267	−	0.0679646i
$454$	−19.9150			−0.934659
$455$	−0.0793240	+	0.137393i	−0.00371877	+	0.00644110i
$456$	13.1627	−	12.8349i	0.616402	−	0.601048i
$457$	−17.4349	−	30.1981i	−0.815569	−	1.41261i	−0.908919	−	0.416973i	$-0.863091\pi$
$457$	−17.4349	−	30.1981i	−0.815569	−	1.41261i	0.0933501	−	0.995633i	$-0.470242\pi$
$458$	6.39564	+	11.0776i	0.298849	+	0.517621i
$459$	−14.4604	+	12.8034i	−0.674953	+	0.597611i
$460$	−0.440537	+	0.763032i	−0.0205401	+	0.0355765i
$461$	−10.5657	−	6.10014i	−0.492096	−	0.284112i	0.233348	−	0.972393i	$-0.425032\pi$
$461$	−10.5657	−	6.10014i	−0.492096	−	0.284112i	−0.725443	+	0.688282i	$0.758365\pi$
$462$	1.25210	+	18.6510i	0.0582527	+	0.867721i
$463$	7.89622	−	13.6766i	0.366968	−	0.635608i	−0.622122	−	0.782921i	$-0.713729\pi$
$463$	7.89622	−	13.6766i	0.366968	−	0.635608i	0.989090	+	0.147313i	$0.0470624\pi$
$464$	3.74623	−	6.48867i	0.173914	−	0.301229i
$465$	0.359536	+	0.536245i	0.0166731	+	0.0248678i
$466$		−	14.2464i		−	0.659951i
$467$		−	1.00890i		−	0.0466861i	−0.999728	−	0.0233430i	$-0.992569\pi$
$467$		−	1.00890i		−	0.0466861i	0.999728	−	0.0233430i	$-0.00743100\pi$
$468$	0.254322	+	1.88563i	0.0117560	+	0.0871632i
$469$	32.6740	+	18.8644i	1.50875	+	0.871075i
$470$	0.00928352	−	0.0160795i	0.000428217	−	0.000741693i
$471$	−11.3990	+	23.2075i	−0.525240	+	1.06935i
$472$	5.78307			0.266188
$473$		−	47.3756i		−	2.17833i
$474$	0.0877816	+	1.30758i	0.00403194	+	0.0600590i
$475$	−20.4894	−	7.28111i	−0.940117	−	0.334080i
$476$			20.1378i			0.923016i
$477$	8.57389	−	1.15639i	0.392571	−	0.0529477i
$478$	17.6824	−	10.2089i	0.808774	−	0.466946i
$479$		−	43.5986i		−	1.99207i	−0.0889514	−	0.996036i	$-0.528352\pi$
$479$		−	43.5986i		−	1.99207i	0.0889514	−	0.996036i	$-0.471648\pi$
$480$	0.0720973	+	1.07395i	0.00329078	+	0.0490187i
$481$	−0.384690	−	0.666303i	−0.0175404	−	0.0303808i
$482$	2.57982	+	1.48946i	0.117507	+	0.0678429i
$483$	−27.7207	+	18.5859i	−1.26133	+	0.845687i
$484$	12.5227			0.569213
$485$	0.701450	−	1.21495i	0.0318512	−	0.0551679i
$486$	−10.1782	+	3.54509i	−0.461692	+	0.160809i
$487$		−	18.8798i		−	0.855523i	−0.903892	−	0.427762i	$-0.859302\pi$
$487$		−	18.8798i		−	0.855523i	0.903892	−	0.427762i	$-0.140698\pi$
$488$	31.3072			1.41721
$489$	2.96982	−	6.04630i	0.134300	−	0.273423i
$490$	−0.363205	+	0.209697i	−0.0164079	+	0.00947313i
$491$			27.7179i			1.25089i	0.780269	+	0.625445i	$0.215082\pi$
$491$			27.7179i			1.25089i	−0.780269	+	0.625445i	$0.784918\pi$
$492$	−26.2305	+	1.76093i	−1.18256	+	0.0793890i
$493$	−17.7301	+	10.2365i	−0.798524	+	0.461028i
$494$	−0.420532	+	1.18340i	−0.0189206	+	0.0532435i
$495$	−0.534275	+	1.30149i	−0.0240139	+	0.0584976i
$496$	4.10592	−	2.37055i	0.184361	−	0.106441i
$497$	−19.3446	+	33.5058i	−0.867723	+	1.50294i
$498$	8.94982	+	4.39597i	0.401051	+	0.196988i
$499$	17.1864			0.769368			0.384684	−	0.923048i	$-0.374310\pi$
$499$	17.1864			0.769368			0.384684	+	0.923048i	$0.374310\pi$
$500$	1.40802	−	0.812919i	0.0629684	−	0.0363548i
$501$	−16.5446	+	1.11069i	−0.739160	+	0.0496220i
$502$	7.17085	−	4.14009i	0.320050	−	0.184781i
$503$	30.9064	+	17.8438i	1.37805	+	0.795617i	0.991924	−	0.126830i	$-0.0404804\pi$
$503$	30.9064	+	17.8438i	1.37805	+	0.795617i	0.386124	+	0.922447i	$0.373814\pi$
$504$	−9.87557	+	24.0568i	−0.439893	+	1.07158i
$505$	0.189226			0.00842043
$506$	−8.20551	−	14.2124i	−0.364779	−	0.631816i
$507$	12.3717	+	18.4523i	0.549446	+	0.819494i
$508$		−	25.0444i		−	1.11117i
$509$	14.3449	+	24.8461i	0.635826	+	1.10128i	0.986339	+	0.164726i	$0.0526739\pi$
$509$	14.3449	+	24.8461i	0.635826	+	1.10128i	−0.350513	+	0.936558i	$0.613993\pi$
$510$	0.209875	−	0.427288i	0.00929342	−	0.0189206i
$511$	−8.80269	+	15.2467i	−0.389408	+	0.674474i
$512$	14.5292			0.642105
$513$	22.4268	+	3.16832i	0.990168	+	0.139885i
$514$	−13.8101			−0.609136
$515$	0.0967299	−	0.167541i	0.00426243	−	0.00738275i
$516$	12.5563	−	25.5636i	0.552760	−	1.12537i
$517$	−0.550527	−	0.953540i	−0.0242121	−	0.0419367i
$518$		−	4.54408i		−	0.199655i
$519$	−4.32653	−	6.45298i	−0.189914	−	0.283255i
$520$	−0.0542627	−	0.0939857i	−0.00237958	−	0.00412155i
$521$	−19.0866			−0.836198			−0.418099	−	0.908402i	$-0.637303\pi$
$521$	−19.0866			−0.836198			−0.418099	+	0.908402i	$0.637303\pi$
$522$	−11.3221	+	1.52706i	−0.495557	+	0.0668377i
$523$	6.44315	+	3.71996i	0.281739	+	0.162662i	0.634211	−	0.773160i	$-0.281325\pi$
$523$	6.44315	+	3.71996i	0.281739	+	0.162662i	−0.352471	+	0.935823i	$0.614659\pi$
$524$	12.7381	−	7.35435i	0.556467	−	0.321276i
$525$	30.6887	−	2.06023i	1.33937	−	0.0899157i
$526$	−5.04880	+	2.91493i	−0.220138	+	0.127097i
$527$	−12.9549			−0.564326
$528$	9.27321	+	4.55481i	0.403565	+	0.198223i
$529$	3.15026	−	5.45642i	0.136968	−	0.237236i
$530$	−0.184673	+	0.106621i	−0.00802167	+	0.00463132i
$531$	4.35509	+	5.63862i	0.188995	+	0.244695i
$532$	17.9744	−	15.3173i	0.779288	−	0.664090i
$533$	3.59911	−	2.07794i	0.155895	−	0.0900058i
$534$	−6.25236	+	0.419740i	−0.270566	+	0.0181639i
$535$		−	1.45497i		−	0.0629039i
$536$	−22.3511	+	12.9044i	−0.965421	+	0.557386i
$537$	3.83451	−	7.80673i	0.165471	−	0.336885i
$538$	15.0787			0.650089
$539$			24.8707i			1.07126i
$540$	−0.633234	+	0.560673i	−0.0272501	+	0.0241275i
$541$	5.10236	−	8.83755i	0.219368	−	0.379956i	−0.735247	−	0.677799i	$-0.762934\pi$
$541$	5.10236	−	8.83755i	0.219368	−	0.379956i	0.954615	+	0.297843i	$0.0962672\pi$
$542$	−2.92314			−0.125560
$543$	18.2003	−	12.2028i	0.781051	−	0.523672i
$544$	−18.7046	−	10.7991i	−0.801954	−	0.463008i
$545$	−0.678570	−	1.17532i	−0.0290668	−	0.0503451i
$546$	−0.118991	−	1.77247i	−0.00509237	−	0.0758548i
$547$			33.2332i			1.42095i	0.703724	+	0.710474i	$0.251519\pi$
$547$			33.2332i			1.42095i	−0.703724	+	0.710474i	$0.748481\pi$
$548$	−16.6019	+	9.58514i	−0.709200	+	0.409457i
$549$	23.5767	+	30.5252i	1.00623	+	1.30278i
$550$			15.1242i			0.644899i
$551$	22.6227	+	8.03921i	0.963760	+	0.342482i
$552$	−1.52923	−	22.7792i	−0.0650885	−	0.969545i
$553$			3.89557i			0.165657i
$554$	−11.4595			−0.486869
$555$	0.150777	−	0.306970i	0.00640014	−	0.0130301i
$556$	7.73073	−	13.3900i	0.327856	−	0.567863i
$557$	22.7991	+	13.1631i	0.966030	+	0.557738i	0.898024	−	0.439947i	$-0.145003\pi$
$557$	22.7991	+	13.1631i	0.966030	+	0.557738i	0.0680066	+	0.997685i	$0.478336\pi$
$558$	−6.68775	−	2.74539i	−0.283115	−	0.116222i
$559$			4.50228i			0.190426i
$560$			0.517873i			0.0218841i
$561$	−15.7211	−	23.4479i	−0.663746	−	0.989970i
$562$	6.08731	−	10.5435i	0.256778	−	0.444752i
$563$	5.84768	−	10.1285i	0.246450	−	0.426864i	−0.716088	−	0.698010i	$-0.754069\pi$
$563$	5.84768	−	10.1285i	0.246450	−	0.426864i	0.962538	+	0.271146i	$0.0874025\pi$
$564$	−0.0443370	−	0.660435i	−0.00186692	−	0.0278093i
$565$	−0.525514	−	0.303405i	−0.0221085	−	0.0127644i
$566$	11.0378	−	19.1180i	0.463953	−	0.803590i
$567$	−30.8929	+	8.48771i	−1.29738	+	0.356450i
$568$	−13.2329	−	22.9201i	−0.555241	−	0.961706i
$569$	−9.05101	−	15.6768i	−0.379438	−	0.657206i	0.611543	−	0.791211i	$-0.290549\pi$
$569$	−9.05101	−	15.6768i	−0.379438	−	0.657206i	−0.990981	+	0.134006i	$0.957216\pi$
$570$	−0.541019	+	0.137678i	−0.0226608	+	0.00576668i
$571$	4.87651	−	8.44636i	0.204076	−	0.353469i	−0.745762	−	0.666212i	$-0.767914\pi$
$571$	4.87651	−	8.44636i	0.204076	−	0.353469i	0.949838	+	0.312743i	$0.101248\pi$
$572$	−2.78110			−0.116284
$573$	−1.72626	−	25.7140i	−0.0721155	−	1.07422i
$574$	24.5453			1.02450
$575$	−23.3853	+	13.5015i	−0.975236	+	0.563053i
$576$	−2.37834	−	3.07928i	−0.0990973	−	0.128303i
$577$	−25.3878			−1.05691			−0.528454	−	0.848962i	$-0.677228\pi$
$577$	−25.3878			−1.05691			−0.528454	+	0.848962i	$0.677228\pi$
$578$	−1.10074	−	1.90655i	−0.0457850	−	0.0793019i
$579$	20.7523	+	10.1931i	0.862434	+	0.423610i
$580$	−0.776419	+	0.448266i	−0.0322390	+	0.0186132i
$581$	25.6687	+	14.8198i	1.06492	+	0.614830i
$582$	1.05222	+	15.6737i	0.0436160	+	0.649695i
$583$			12.6456i			0.523726i
$584$	−6.02160	−	10.4297i	−0.249176	−	0.431585i
$585$	0.0507742	−	0.123686i	0.00209925	−	0.00511377i
$586$	9.71765	+	16.8315i	0.401433	+	0.695302i
$587$	16.6038	+	9.58622i	0.685313	+	0.395666i	0.801854	−	0.597520i	$-0.203847\pi$
$587$	16.6038	+	9.58622i	0.685313	+	0.395666i	−0.116541	+	0.993186i	$0.537181\pi$
$588$	−6.59165	+	13.4201i	−0.271835	+	0.553434i
$589$	9.85384	+	11.5632i	0.406021	+	0.476452i
$590$	−0.152081	−	0.0878040i	−0.00626107	−	0.00361483i
$591$	33.2946	+	16.3536i	1.36956	+	0.672699i
$592$	−2.17500	−	1.25574i	−0.0893921	−	0.0516105i
$593$	2.09357	+	1.20873i	0.0859728	+	0.0496364i	0.542370	−	0.840140i	$-0.317527\pi$
$593$	2.09357	+	1.20873i	0.0859728	+	0.0496364i	−0.456397	+	0.889776i	$0.650860\pi$
$594$	−3.14670	−	15.4361i	−0.129111	−	0.633352i
$595$	0.707537	−	1.22549i	0.0290062	−	0.0502402i
$596$	−22.5685	+	13.0299i	−0.924440	+	0.533726i
$597$	−4.84045	−	7.21949i	−0.198106	−	0.295474i
$598$	0.779801	+	1.35066i	0.0318885	+	0.0552324i
$599$	−16.0932	−	27.8742i	−0.657550	−	1.13891i	−0.981248	−	0.192749i	$-0.938260\pi$
$599$	−16.0932	−	27.8742i	−0.657550	−	1.13891i	0.323698	−	0.946160i	$-0.395074\pi$
$600$	−9.27600	+	18.8852i	−0.378691	+	0.770984i
$601$	−23.2325	+	13.4133i	−0.947675	+	0.547140i	−0.892358	−	0.451329i	$-0.850950\pi$
$601$	−23.2325	+	13.4133i	−0.947675	+	0.547140i	−0.0553168	+	0.998469i	$0.517617\pi$
$602$	−13.2956	+	23.0286i	−0.541887	+	0.938577i
$603$	−29.4141	−	12.0748i	−1.19784	−	0.491724i
$604$	1.10327	+	0.636974i	0.0448915	+	0.0259181i
$605$	−0.762070	−	0.439981i	−0.0309825	−	0.0178878i
$606$	−1.75990	+	1.17996i	−0.0714910	+	0.0479326i
$607$	21.3827	+	12.3453i	0.867897	+	0.501081i	0.866649	−	0.498919i	$-0.166269\pi$
$607$	21.3827	+	12.3453i	0.867897	+	0.501081i	0.00124816	+	0.999999i	$0.499603\pi$
$608$	4.58824	+	24.9092i	0.186078	+	1.01020i
$609$	−33.8840	+	2.27474i	−1.37305	+	0.0921769i
$610$	−0.823304	−	0.475335i	−0.0333346	−	0.0192458i
$611$	0.0523187	+	0.0906187i	0.00211659	+	0.00366604i
$612$	−2.26845	−	16.8190i	−0.0916965	−	0.679868i
$613$	−1.93026	−	3.34330i	−0.0779624	−	0.135035i	0.824408	−	0.565996i	$-0.191508\pi$
$613$	−1.93026	−	3.34330i	−0.0779624	−	0.135035i	−0.902371	+	0.430961i	$0.858175\pi$
$614$		−	6.69486i		−	0.270183i
$615$	1.65813	+	0.814439i	0.0668622	+	0.0328414i
$616$	−32.9179	−	19.0052i	−1.32630	−	0.765740i
$617$	18.6070	−	10.7427i	0.749088	−	0.432486i	−0.0762764	−	0.997087i	$-0.524303\pi$
$617$	18.6070	−	10.7427i	0.749088	−	0.432486i	0.825364	+	0.564601i	$0.190970\pi$
$618$	0.145102	+	2.16140i	0.00583684	+	0.0869444i
$619$	−16.6647	−	28.8640i	−0.669809	−	1.16014i	−0.977957	−	0.208805i	$-0.933042\pi$
$619$	−16.6647	−	28.8640i	−0.669809	−	1.16014i	0.308148	−	0.951339i	$-0.400291\pi$
$620$	−0.567310			−0.0227837
$621$	21.0585	−	18.6454i	0.845050	−	0.748216i
$622$	−0.0683909	+	0.0394855i	−0.00274223	+	0.00158322i
$623$	−18.6272			−0.746284
$624$	−0.881269	−	0.432861i	−0.0352790	−	0.0173283i
$625$	24.8286			0.993143
$626$	0.783887	−	1.35773i	0.0313304	−	0.0542659i
$627$	−8.97098	+	31.8672i	−0.358266	+	1.27265i
$628$	−11.3599	−	19.6758i	−0.453308	−	0.785152i
$629$	3.43127	+	5.94314i	0.136814	+	0.236969i
$630$	0.624957	−	0.482697i	0.0248989	−	0.0192311i
$631$	−10.5833	+	18.3308i	−0.421313	+	0.729736i	−0.996068	−	0.0885897i	$-0.971764\pi$
$631$	−10.5833	+	18.3308i	−0.421313	+	0.729736i	0.574755	+	0.818325i	$0.305097\pi$
$632$	−2.30780	−	1.33241i	−0.0917994	−	0.0530004i
$633$	24.8888	+	12.2249i	0.989242	+	0.485896i
$634$	−3.40994	+	5.90620i	−0.135426	+	0.234565i
$635$	−0.879929	+	1.52408i	−0.0349189	+	0.0604813i
$636$	−3.35155	+	6.82346i	−0.132897	+	0.270568i
$637$		−	2.36356i		−	0.0936475i
$638$		−	16.6989i		−	0.661118i
$639$	12.3822	−	30.1629i	0.489832	−	1.19323i
$640$	−0.993312	−	0.573489i	−0.0392641	−	0.0226691i
$641$	−15.1501	+	26.2408i	−0.598393	+	1.03645i	0.394665	+	0.918825i	$0.370861\pi$
$641$	−15.1501	+	26.2408i	−0.598393	+	1.03645i	−0.993058	+	0.117623i	$0.962473\pi$
$642$	9.07281	+	13.5320i	0.358075	+	0.534066i
$643$	8.52483			0.336186			0.168093	−	0.985771i	$-0.446239\pi$
$643$	8.52483			0.336186			0.168093	+	0.985771i	$0.446239\pi$
$644$		−	29.3265i		−	1.15563i
$645$	−1.66228	+	1.11451i	−0.0654523	+	0.0438838i
$646$	3.75096	−	10.5554i	0.147580	−	0.415296i
$647$		−	30.0725i		−	1.18227i	−0.806572	−	0.591135i	$-0.798680\pi$
$647$		−	30.0725i		−	1.18227i	0.806572	−	0.591135i	$-0.201320\pi$
$648$	5.53811	−	21.2046i	0.217558	−	0.832994i
$649$	−9.01863	+	5.20691i	−0.354012	+	0.204389i
$650$		−	1.43731i		−	0.0563761i
$651$	−19.2883	−	9.47403i	−0.755969	−	0.371317i
$652$	2.95961	+	5.12619i	0.115907	+	0.200757i
$653$	−38.8242	−	22.4151i	−1.51931	−	0.877173i	−0.999741	−	0.0227422i	$-0.992760\pi$
$653$	−38.8242	−	22.4151i	−1.51931	−	0.877173i	−0.519566	−	0.854430i	$-0.673906\pi$
$654$	13.6400	+	6.69970i	0.533367	+	0.261979i
$655$	−1.03357			−0.0403850
$656$	6.78300	−	11.7485i	0.264832	−	0.458702i
$657$	5.63447	−	13.7255i	0.219822	−	0.535485i
$658$			0.618004i			0.0240923i
$659$	7.71805			0.300653			0.150326	−	0.988636i	$-0.451968\pi$
$659$	7.71805			0.300653			0.150326	+	0.988636i	$0.451968\pi$
$660$	−0.688443	−	1.02681i	−0.0267976	−	0.0399684i
$661$	4.72895	−	2.73026i	0.183935	−	0.106195i	−0.405205	−	0.914226i	$-0.632800\pi$
$661$	4.72895	−	2.73026i	0.183935	−	0.106195i	0.589140	+	0.808031i	$0.299467\pi$
$662$		−	5.24247i		−	0.203754i
$663$	1.49404	+	2.22834i	0.0580236	+	0.0865417i
$664$	−17.5590	+	10.1377i	−0.681422	+	0.393419i
$665$	−1.63200	+	0.300612i	−0.0632863	+	0.0116572i
$666$	0.511872	+	3.79519i	0.0198346	+	0.147060i
$667$	25.8202	−	14.9073i	0.999762	−	0.577213i
$668$	7.28529	−	12.6185i	0.281876	−	0.488224i
$669$	11.8026	−	7.91327i	0.456313	−	0.305945i
$670$	0.783707			0.0302773
$671$	−48.8232	+	28.1881i	−1.88480	+	1.08819i
$672$	−19.9514	−	29.7574i	−0.769643	−	1.14792i
$673$	7.25030	−	4.18596i	0.279478	−	0.161357i	−0.353709	−	0.935356i	$-0.615080\pi$
$673$	7.25030	−	4.18596i	0.279478	−	0.161357i	0.633187	+	0.773999i	$0.281746\pi$
$674$	8.45029	+	4.87878i	0.325493	+	0.187924i
$675$	−25.3990	+	5.17765i	−0.977607	+	0.199288i
$676$	−19.5212			−0.750816
$677$	−18.8962	−	32.7292i	−0.726241	−	1.25789i	−0.958461	−	0.285223i	$-0.907932\pi$
$677$	−18.8962	−	32.7292i	−0.726241	−	1.25789i	0.232220	−	0.972663i	$-0.425401\pi$
$678$	6.77951	−	0.455129i	0.260365	−	0.0174791i
$679$			46.6955i			1.79201i
$680$	0.484000	+	0.838313i	0.0185606	+	0.0321478i
$681$	49.7776	−	3.34172i	1.90748	−	0.128055i
$682$	5.28340	−	9.15112i	0.202312	−	0.350415i
$683$	−6.09850			−0.233352			−0.116676	−	0.993170i	$-0.537224\pi$
$683$	−6.09850			−0.233352			−0.116676	+	0.993170i	$0.537224\pi$
$684$	−13.2867	+	14.8177i	−0.508029	+	0.566568i
$685$	1.34708			0.0514694
$686$	−1.63450	+	2.83104i	−0.0624056	+	0.108090i
$687$	−17.8447	−	26.6152i	−0.680819	−	1.01543i
$688$	7.34837	+	12.7277i	0.280154	+	0.485241i
$689$		−	1.20176i		−	0.0457833i
$690$	−0.305639	+	0.622255i	−0.0116355	+	0.0236889i
$691$	−16.5151	−	28.6050i	−0.628265	−	1.08819i	−0.987900	−	0.155094i	$-0.950432\pi$
$691$	−16.5151	−	28.6050i	−0.628265	−	1.08819i	0.359635	−	0.933093i	$-0.382901\pi$
$692$	6.82681			0.259516
$693$	−6.25923	−	46.4080i	−0.237768	−	1.76289i
$694$	4.10889	+	2.37227i	0.155971	+	0.0900500i
$695$	−0.940909	+	0.543234i	−0.0356907	+	0.0206060i
$696$	10.2418	−	20.8515i	0.388215	−	0.790373i
$697$	−32.1025	+	18.5344i	−1.21597	+	0.702040i
$698$	−4.29595			−0.162604
$699$	2.39053	+	35.6089i	0.0904182	+	1.34685i
$700$	−13.5135	+	23.4061i	−0.510763	+	0.884668i
$701$	−5.80129	+	3.34938i	−0.219112	+	0.126504i	−0.605539	−	0.795816i	$-0.707042\pi$
$701$	−5.80129	+	3.34938i	−0.219112	+	0.126504i	0.386427	+	0.922320i	$0.373709\pi$
$702$	0.299043	+	1.46696i	0.0112866	+	0.0553667i
$703$	2.69475	−	7.58314i	0.101634	−	0.286004i
$704$	4.92512	−	2.84352i	0.185622	−	0.107169i
$705$	−0.0205060	+	0.0417486i	−0.000772302	+	0.00157234i
$706$		−	8.80870i		−	0.331520i
$707$	−5.45456	+	3.14919i	−0.205140	+	0.118437i
$708$	−6.24642	+	0.419341i	−0.234755	+	0.0157598i
$709$	21.8491			0.820561			0.410280	−	0.911959i	$-0.365431\pi$
$709$	21.8491			0.820561			0.410280	+	0.911959i	$0.365431\pi$
$710$			0.803658i			0.0301608i
$711$	−0.438820	−	3.25356i	−0.0164571	−	0.122018i
$712$	6.37110	−	11.0351i	0.238767	−	0.413557i
$713$	18.8662			0.706543
$714$	1.06135	+	15.8097i	0.0397202	+	0.591663i
$715$	0.169244	+	0.0977131i	0.00632937	+	0.00365426i
$716$	3.82132	+	6.61872i	0.142809	+	0.247353i
$717$	−42.4841	+	28.4843i	−1.58660	+	1.06377i
$718$			10.5247i			0.392780i
$719$	−20.5211	+	11.8479i	−0.765309	+	0.441851i	−0.831199	−	0.555975i	$-0.812345\pi$
$719$	−20.5211	+	11.8479i	−0.765309	+	0.441851i	0.0658895	+	0.997827i	$0.479012\pi$
$720$	−0.0583362	−	0.432524i	−0.00217406	−	0.0161192i
$721$			6.43932i			0.239813i
$722$	−12.2745	+	4.68069i	−0.456808	+	0.174197i
$723$	−6.69818	−	3.29001i	−0.249108	−	0.122357i
$724$			19.2547i			0.715595i
$725$	−27.4768			−1.02046
$726$	9.83125	−	0.660002i	0.364872	−	0.0244950i
$727$	9.23595	−	15.9971i	0.342542	−	0.593301i	−0.642362	−	0.766402i	$-0.722045\pi$
$727$	9.23595	−	15.9971i	0.342542	−	0.593301i	0.984904	+	0.173101i	$0.0553786\pi$
$728$	3.12832	+	1.80613i	0.115943	+	0.0669398i
$729$	24.8455	−	10.5689i	0.920204	−	0.391439i
$730$			0.365702i			0.0135352i
$731$		−	40.1585i		−	1.48531i
$732$	−33.8156	+	2.27014i	−1.24986	+	0.0839069i
$733$	−20.4287	+	35.3835i	−0.754550	+	1.30692i	0.191048	+	0.981581i	$0.438811\pi$
$733$	−20.4287	+	35.3835i	−0.754550	+	1.30692i	−0.945598	+	0.325338i	$0.894522\pi$
$734$	2.65002	−	4.58997i	0.0978140	−	0.169419i
$735$	0.872645	−	0.585083i	0.0321880	−	0.0215811i
$736$	27.2393	+	15.7266i	1.00406	+	0.579692i
$737$	23.2375	−	40.2486i	0.855965	−	1.48257i
$738$	−20.5001	+	2.76493i	−0.754619	+	0.101778i
$739$	1.64367	+	2.84692i	0.0604633	+	0.104726i	0.894673	−	0.446722i	$-0.147409\pi$
$739$	1.64367	+	2.84692i	0.0604633	+	0.104726i	−0.834209	+	0.551448i	$0.814076\pi$
$740$	0.150259	+	0.260256i	0.00552362	+	0.00956720i
$741$	0.852547	−	3.02846i	0.0313191	−	0.111253i
$742$	3.54888	−	6.14684i	0.130283	−	0.225658i
$743$	−33.7360			−1.23765			−0.618826	−	0.785528i	$-0.712392\pi$
$743$	−33.7360			−1.23765			−0.618826	+	0.785528i	$0.712392\pi$
$744$	12.2098	−	8.18631i	0.447633	−	0.300125i
$745$	1.83121			0.0670902
$746$	11.3186	−	6.53477i	0.414402	−	0.239255i
$747$	−23.1077	−	9.48596i	−0.845468	−	0.347073i
$748$	24.8062			0.907005
$749$	24.2144	+	41.9405i	0.884774	+	1.53247i
$750$	1.06255	−	0.712411i	0.0387990	−	0.0260136i
$751$	−34.3050	+	19.8060i	−1.25181	+	0.722731i	−0.971468	−	0.237170i	$-0.923780\pi$
$751$	−34.3050	+	19.8060i	−1.25181	+	0.722731i	−0.280339	+	0.959901i	$0.590447\pi$
$752$	0.295805	+	0.170783i	0.0107869	+	0.00622782i
$753$	−17.2288	+	11.5514i	−0.627854	+	0.420957i
$754$			1.58697i			0.0577939i
$755$	−0.0447598	−	0.0775263i	−0.00162898	−	0.00282147i
$756$	8.92241	−	26.7004i	0.324505	−	0.971083i
$757$	2.10833	+	3.65174i	0.0766287	+	0.132725i	0.901793	−	0.432167i	$-0.142251\pi$
$757$	2.10833	+	3.65174i	0.0766287	+	0.132725i	−0.825165	+	0.564892i	$0.808918\pi$
$758$	14.7992	+	8.54429i	0.537529	+	0.310343i
$759$	22.8945	+	34.1469i	0.831018	+	1.23945i
$760$	0.380109	−	1.06964i	0.0137880	−	0.0388001i
$761$	−6.65646	−	3.84311i	−0.241297	−	0.139313i	0.374476	−	0.927237i	$-0.377823\pi$
$761$	−6.65646	−	3.84311i	−0.241297	−	0.139313i	−0.615773	+	0.787924i	$0.711156\pi$
$762$	−1.31995	−	19.6618i	−0.0478169	−	0.712270i
$763$	39.1205	+	22.5862i	1.41626	+	0.817676i
$764$	19.6119	+	11.3229i	0.709534	+	0.409650i
$765$	−0.452884	+	1.10322i	−0.0163741	+	0.0398871i
$766$	−7.91354	+	13.7067i	−0.285928	+	0.495242i
$767$	0.857076	−	0.494833i	0.0309472	−	0.0178674i
$768$	17.2971	−	1.16121i	0.624155	−	0.0419014i
$769$	8.84877	+	15.3265i	0.319095	+	0.552689i	0.980299	−	0.197517i	$-0.0632878\pi$
$769$	8.84877	+	15.3265i	0.319095	+	0.552689i	−0.661204	+	0.750206i	$0.729954\pi$
$770$	0.577108	+	0.999580i	0.0207975	+	0.0360224i
$771$	34.5183	−	2.31732i	1.24314	−	0.0834561i
$772$	−17.5942	+	10.1580i	−0.633230	+	0.365596i
$773$	0.137641	−	0.238402i	0.00495061	−	0.00857471i	−0.863539	−	0.504281i	$-0.831757\pi$
$773$	0.137641	−	0.238402i	0.00495061	−	0.00857471i	0.868490	+	0.495707i	$0.165091\pi$
$774$	8.51031	−	20.7311i	0.305897	−	0.745163i
$775$	−15.0575	−	8.69343i	−0.540880	−	0.312277i
$776$	−27.6632	−	15.9714i	−0.993051	−	0.573338i
$777$	0.762492	+	11.3579i	0.0273542	+	0.407463i
$778$	2.26993	+	1.31054i	0.0813808	+	0.0469852i
$779$	40.9611	+	14.5560i	1.46758	+	0.521521i
$780$	0.0654254	+	0.0975813i	0.00234260	+	0.00349397i
$781$	41.2732	+	23.8291i	1.47687	+	0.852671i
$782$	−6.95550	−	12.0473i	−0.248728	−	0.430810i
$783$	28.0435	−	5.71674i	1.00219	−	0.204300i
$784$	−3.85766	−	6.68166i	−0.137774	−	0.238631i
$785$			1.59650i			0.0569815i
$786$	9.61276	−	6.44507i	0.342876	−	0.229888i
$787$	−11.1612	−	6.44390i	−0.397853	−	0.229700i	0.287704	−	0.957719i	$-0.407108\pi$
$787$	−11.1612	−	6.44390i	−0.397853	−	0.229700i	−0.685557	+	0.728019i	$0.740441\pi$
$788$	−28.2280	+	16.2974i	−1.00558	+	0.580571i
$789$	12.1304	−	8.13304i	0.431852	−	0.289544i
$790$	0.0404598	+	0.0700783i	0.00143949	+	0.00249328i
$791$	20.1977			0.718148
$792$	29.6337	+	12.1649i	1.05299	+	0.432262i
$793$	4.63986	−	2.67882i	0.164766	−	0.0951278i
$794$	−4.89240			−0.173625
$795$	0.443699	−	0.297487i	0.0157364	−	0.0105508i
$796$	7.63771			0.270712
$797$	−24.8067	+	42.9665i	−0.878699	+	1.52195i	−0.0259298	+	0.999664i	$0.508255\pi$
$797$	−24.8067	+	42.9665i	−0.878699	+	1.52195i	−0.852769	+	0.522288i	$0.825079\pi$
$798$	13.3039	−	12.9726i	0.470955	−	0.459224i
$799$	−0.466661	−	0.808280i	−0.0165093	−	0.0285949i
$800$	−14.4935	−	25.1035i	−0.512423	−	0.887543i
$801$	15.5573	−	2.09828i	0.549692	−	0.0741391i
$802$	4.37537	−	7.57837i	0.154500	−	0.267602i
$803$	18.7812	+	10.8433i	0.662775	+	0.382653i
$804$	23.2062	−	15.5591i	0.818419	−	0.548726i
$805$	−1.03038	+	1.78467i	−0.0363161	+	0.0629013i
$806$	−0.502102	+	0.869667i	−0.0176858	+	0.0306327i
$807$	−37.6893	+	2.53019i	−1.32672	+	0.0890671i
$808$		−	4.30849i		−	0.151572i
$809$			23.6970i			0.833142i	0.909103	+	0.416571i	$0.136768\pi$
$809$			23.6970i			0.833142i	−0.909103	+	0.416571i	$0.863232\pi$
$810$	−0.467586	+	0.473544i	−0.0164293	+	0.0166386i
$811$	35.4486	+	20.4662i	1.24477	+	0.718667i	0.970061	−	0.242861i	$-0.0780860\pi$
$811$	35.4486	+	20.4662i	1.24477	+	0.718667i	0.274707	+	0.961528i	$0.411419\pi$
$812$	14.9205	−	25.8431i	0.523608	−	0.906916i
$813$	7.30640	−	0.490501i	0.256247	−	0.0172026i
$814$	−5.59749			−0.196192
$815$		−	0.415940i		−	0.0145697i
$816$	7.86055	+	3.86094i	0.275174	+	0.135160i
$817$	−35.8442	+	30.5455i	−1.25403	+	1.06865i
$818$			16.7126i			0.584342i
$819$	0.594839	+	4.41033i	0.0207853	+	0.154109i
$820$	−1.40580	+	0.811639i	−0.0490927	+	0.0283437i
$821$		−	52.2099i		−	1.82214i	−0.412255	−	0.911068i	$-0.635259\pi$
$821$		−	52.2099i		−	1.82214i	0.412255	−	0.911068i	$-0.364741\pi$
$822$	−12.5286	+	8.40004i	−0.436985	+	0.292985i
$823$	6.85347	+	11.8706i	0.238897	+	0.413782i	0.960398	−	0.278632i	$-0.0898808\pi$
$823$	6.85347	+	11.8706i	0.238897	+	0.413782i	−0.721501	+	0.692413i	$0.756548\pi$
$824$	−3.81476	−	2.20245i	−0.132893	−	0.0767260i
$825$	−2.53783	−	37.8030i	−0.0883560	−	1.31613i
$826$	5.84511			0.203378
$827$	5.42239	−	9.39185i	0.188555	−	0.326587i	−0.756214	−	0.654325i	$-0.772953\pi$
$827$	5.42239	−	9.39185i	0.188555	−	0.326587i	0.944769	+	0.327738i	$0.106286\pi$
$828$	3.30352	+	24.4934i	0.114805	+	0.851203i
$829$		−	44.0349i		−	1.52939i	−0.644390	−	0.764697i	$-0.722889\pi$
$829$		−	44.0349i		−	1.52939i	0.644390	−	0.764697i	$-0.277111\pi$
$830$	0.615680			0.0213706
$831$	28.6431	−	1.92290i	0.993618	−	0.0667046i
$832$	−0.468053	+	0.270231i	−0.0162268	+	0.00936856i
$833$			21.0819i			0.730445i
$834$	5.36349	−	10.9196i	0.185722	−	0.378115i
$835$	−0.886694	+	0.511933i	−0.0306853	+	0.0177162i
$836$	−18.8682	−	22.1412i	−0.652571	−	0.765771i
$837$	17.1767	+	5.73991i	0.593714	+	0.198400i
$838$	−16.1499	+	9.32416i	−0.557890	+	0.322098i
$839$	−20.5691	+	35.6267i	−0.710124	+	1.22997i	0.254686	+	0.967024i	$0.418028\pi$
$839$	−20.5691	+	35.6267i	−0.710124	+	1.22997i	−0.964810	+	0.262947i	$0.915306\pi$
$840$	0.107554	+	1.60210i	0.00371096	+	0.0552776i
$841$	1.33769			0.0461272
$842$	−15.8950	+	9.17696i	−0.547776	+	0.316259i
$843$	−13.4460	+	27.3750i	−0.463106	+	0.942846i
$844$	−21.1013	+	12.1829i	−0.726337	+	0.419351i
$845$	1.18797	+	0.685872i	0.0408672	+	0.0235947i
$846$	−0.0696157	−	0.516154i	−0.00239344	−	0.0177457i
$847$	29.2896			1.00640
$848$	−1.96144	−	3.39731i	−0.0673561	−	0.116664i
$849$	−24.3810	+	49.6376i	−0.836753	+	1.70356i
$850$			12.8202i			0.439730i
$851$	−4.99693	−	8.65494i	−0.171293	−	0.296688i
$852$	15.9551	+	23.7969i	0.546614	+	0.815270i
$853$	6.24927	−	10.8240i	0.213971	−	0.370608i	−0.738983	−	0.673724i	$-0.764694\pi$
$853$	6.24927	−	10.8240i	0.213971	−	0.370608i	0.952954	+	0.303116i	$0.0980269\pi$
$854$	31.6431			1.08280
$855$	1.32918	−	0.434908i	0.0454569	−	0.0148735i
$856$	−33.1284			−1.13230
$857$	2.42104	−	4.19336i	0.0827012	−	0.143243i	−0.821708	−	0.569908i	$-0.806979\pi$
$857$	2.42104	−	4.19336i	0.0827012	−	0.143243i	0.904409	+	0.426666i	$0.140312\pi$
$858$	−2.18337	+	0.146576i	−0.0745390	+	0.00500403i
$859$	−7.05200	−	12.2144i	−0.240611	−	0.416751i	0.720277	−	0.693686i	$-0.244014\pi$
$859$	−7.05200	−	12.2144i	−0.240611	−	0.416751i	−0.960889	+	0.276936i	$0.910681\pi$
$860$		−	1.75858i		−	0.0599670i
$861$	−61.3510	+	4.11868i	−2.09084	+	0.140364i
$862$	−5.84432	−	10.1227i	−0.199058	−	0.344779i
$863$	37.3291			1.27070			0.635348	−	0.772226i	$-0.280857\pi$
$863$	37.3291			1.27070			0.635348	+	0.772226i	$0.280857\pi$
$864$	20.0154	+	22.6057i	0.680937	+	0.769063i
$865$	−0.415446	−	0.239858i	−0.0141256	−	0.00815541i
$866$	9.01576	−	5.20525i	0.306368	−	0.176882i
$867$	3.07123	+	4.58071i	0.104304	+	0.155569i
$868$	16.3531	−	9.44146i	0.555060	−	0.320464i
$869$	4.79865			0.162783
$870$	−0.585921	+	0.392843i	−0.0198646	+	0.0133186i
$871$	−2.20835	+	3.82498i	−0.0748272	+	0.129604i
$872$	−26.7609	+	15.4504i	−0.906239	+	0.523217i
$873$	−5.26006	−	38.9998i	−0.178026	−	1.31994i
$874$	−5.46249	+	15.3717i	−0.184772	+	0.519956i
$875$	3.29324	−	1.90135i	0.111332	−	0.0642774i
$876$	7.26034	+	10.8287i	0.245304	+	0.365869i
$877$		−	16.9261i		−	0.571552i	−0.958296	−	0.285776i	$-0.907749\pi$
$877$		−	16.9261i		−	0.571552i	0.958296	−	0.285776i	$-0.0922514\pi$
$878$	8.96546	−	5.17621i	0.302570	−	0.174689i
$879$	−27.1136	−	40.4397i	−0.914519	−	1.36400i
$880$	0.637927			0.0215045
$881$		−	11.2468i		−	0.378913i	−0.981889	−	0.189457i	$-0.939327\pi$
$881$		−	11.2468i		−	0.378913i	0.981889	−	0.189457i	$-0.0606727\pi$
$882$	−4.46764	+	10.8832i	−0.150433	+	0.366455i
$883$	−2.49791	+	4.32650i	−0.0840613	+	0.145598i	−0.904991	−	0.425431i	$-0.860122\pi$
$883$	−2.49791	+	4.32650i	−0.0840613	+	0.145598i	0.820930	+	0.571030i	$0.193456\pi$
$884$	−2.35743			−0.0792890
$885$	0.394860	+	0.193947i	0.0132731	+	0.00651946i
$886$	8.32842	+	4.80841i	0.279799	+	0.161542i
$887$	−14.3062	−	24.7790i	−0.480354	−	0.831998i	0.519392	−	0.854536i	$-0.326159\pi$
$887$	−14.3062	−	24.7790i	−0.480354	−	0.831998i	−0.999746	+	0.0225383i	$0.992825\pi$
$888$	−6.98942	−	3.43306i	−0.234550	−	0.115206i
$889$		−	58.5769i		−	1.96461i
$890$	−0.335089	+	0.193464i	−0.0112322	+	0.00648493i
$891$	10.4553	+	38.0546i	0.350267	+	1.27488i
$892$			12.4863i			0.418072i
$893$	−0.366492	+	1.03132i	−0.0122642	+	0.0345119i
$894$	−17.0312	+	11.4189i	−0.569608	+	0.381905i
$895$		−	0.537044i		−	0.0179514i
$896$	38.1772			1.27541
$897$	−2.17575	−	3.24512i	−0.0726463	−	0.108351i
$898$	−11.7202	+	20.3001i	−0.391110	+	0.677422i
$899$	16.6252	+	9.59858i	0.554483	+	0.320131i
$900$	8.64981	−	21.0709i	0.288327	−	0.702363i
$901$			10.7192i			0.357107i
$902$		−	30.2354i		−	1.00673i
$903$	29.3681	−	59.7911i	0.977310	−	1.98972i
$904$	−6.90826	+	11.9655i	−0.229765	+	0.397965i
$905$	0.676508	−	1.17175i	0.0224879	−	0.0389502i
$906$	0.899722	+	0.441925i	0.0298913	+	0.0146820i
$907$	20.6325	+	11.9122i	0.685090	+	0.395537i	0.801770	−	0.597633i	$-0.203892\pi$
$907$	20.6325	+	11.9122i	0.685090	+	0.395537i	−0.116680	+	0.993170i	$0.537225\pi$
$908$	−21.9192	+	37.9651i	−0.727413	+	1.25992i
$909$	4.20087	−	3.24462i	0.139334	−	0.107617i
$910$	−0.0548448	−	0.0949940i	−0.00181809	−	0.00314902i
$911$	−20.4314	−	35.3881i	−0.676921	−	1.17246i	−0.975903	−	0.218203i	$-0.929981\pi$
$911$	−20.4314	−	35.3881i	−0.676921	−	1.17246i	0.298982	−	0.954259i	$-0.403353\pi$
$912$	−2.53277	−	9.95280i	−0.0838684	−	0.329570i
$913$	18.2554	−	31.6192i	0.604165	−	1.04644i
$914$	24.1090			0.797455
$915$	2.13761	+	1.04995i	0.0706672	+	0.0347103i
$916$	28.1571			0.930336
$917$	29.7934	−	17.2012i	0.983864	−	0.568034i
$918$	−2.66734	−	13.0846i	−0.0880352	−	0.431857i
$919$	−48.0310			−1.58440			−0.792198	−	0.610264i	$-0.791063\pi$
$919$	−48.0310			−1.58440			−0.792198	+	0.610264i	$0.791063\pi$
$920$	−0.704845	−	1.22083i	−0.0232381	−	0.0402495i
$921$	1.12339	+	16.7338i	0.0370170	+	0.551398i
$922$	7.30518	−	4.21765i	0.240583	−	0.138901i
$923$	−3.92235	−	2.26457i	−0.129106	−	0.0745392i
$924$	36.9334	+	18.1409i	1.21502	+	0.596793i
$925$			9.21024i			0.302831i
$926$	5.45946	+	9.45606i	0.179409	+	0.310746i
$927$	−0.725363	−	5.37808i	−0.0238240	−	0.176639i
$928$	16.0026	+	27.7173i	0.525310	+	0.909864i
$929$	−11.6585	−	6.73102i	−0.382502	−	0.220838i	0.296404	−	0.955063i	$-0.404212\pi$
$929$	−11.6585	−	6.73102i	−0.382502	−	0.220838i	−0.678906	+	0.734225i	$0.737546\pi$
$930$	−0.445381	+	0.0298997i	−0.0146046	+	0.000980451i
$931$	18.8170	−	16.0354i	0.616704	−	0.525539i
$932$	−27.1587	−	15.6801i	−0.889612	−	0.513618i
$933$	0.164318	−	0.110170i	0.00537951	−	0.00360680i
$934$	0.604098	+	0.348776i	0.0197667	+	0.0114123i
$935$	−1.50958	−	0.871559i	−0.0493687	−	0.0285030i
$936$	−2.81621	−	1.15608i	−0.0920506	−	0.0377877i
$937$	7.39153	−	12.8025i	0.241471	−	0.418240i	−0.719663	−	0.694324i	$-0.755704\pi$
$937$	7.39153	−	12.8025i	0.241471	−	0.418240i	0.961133	+	0.276084i	$0.0890369\pi$
$938$	−22.5909	+	13.0429i	−0.737619	+	0.425864i
$939$	−1.73150	+	3.52519i	−0.0565054	+	0.115040i
$940$	−0.0204355	−	0.0353954i	−0.000666533	−	0.00115447i
$941$	9.89021	+	17.1303i	0.322412	+	0.558433i	0.980985	−	0.194083i	$-0.0621731\pi$
$941$	9.89021	+	17.1303i	0.322412	+	0.558433i	−0.658573	+	0.752516i	$0.728840\pi$
$942$	−9.95534	−	14.8483i	−0.324362	−	0.483784i
$943$	46.7506	−	26.9915i	1.52241	−	0.878963i
$944$	1.61528	−	2.79774i	0.0525727	−	0.0910587i
$945$	−1.48108	+	1.31137i	−0.0481796	+	0.0426588i
$946$	28.3672	+	16.3778i	0.922296	+	0.532488i
$947$	26.5620	+	15.3356i	0.863150	+	0.498340i	0.865066	−	0.501658i	$-0.167276\pi$
$947$	26.5620	+	15.3356i	0.863150	+	0.498340i	−0.00191559	+	0.999998i	$0.500610\pi$
$948$	2.58932	+	1.27182i	0.0840972	+	0.0413068i
$949$	−1.78485	−	1.03048i	−0.0579388	−	0.0334510i
$950$	11.4429	−	9.75138i	0.371258	−	0.316376i
$951$	7.53210	−	15.3347i	0.244245	−	0.497263i
$952$	−27.9033	−	16.1100i	−0.904350	−	0.522127i
$953$	−20.9938	−	36.3623i	−0.680055	−	1.17789i	−0.974964	−	0.222365i	$-0.928622\pi$
$953$	−20.9938	−	36.3623i	−0.680055	−	1.17789i	0.294908	−	0.955526i	$-0.404711\pi$
$954$	−2.27159	+	5.53357i	−0.0735453	+	0.179156i
$955$	−0.795657	−	1.37812i	−0.0257468	−	0.0445948i
$956$		−	44.9452i		−	1.45363i
$957$	2.80207	+	41.7390i	0.0905780	+	1.34923i
$958$	26.1056	+	15.0721i	0.843435	+	0.486957i
$959$	−38.8306	+	22.4188i	−1.25391	+	0.723942i
$960$	−0.215635	−	0.105915i	−0.00695959	−	0.00341841i
$961$	−9.42618	−	16.3266i	−0.304070	−	0.526665i
$962$	0.531951			0.0171508
$963$	−24.9482	−	32.3009i	−0.803943	−	1.04088i
$964$	5.67887	−	3.27870i	0.182904	−	0.105600i
$965$	1.42760			0.0459560
$966$	−1.54564	−	23.0235i	−0.0497301	−	0.740770i
$967$	−33.5211			−1.07796			−0.538982	−	0.842317i	$-0.681191\pi$
$967$	−33.5211			−1.07796			−0.538982	+	0.842317i	$0.681191\pi$
$968$	−10.0180	+	17.3516i	−0.321989	+	0.557702i
$969$	−7.60436	+	27.0126i	−0.244287	+	0.867770i
$970$	0.484984	+	0.840017i	0.0155719	+	0.0269713i
$971$	15.4529	+	26.7652i	0.495907	+	0.858936i	0.999989	−	0.00471955i	$-0.00150229\pi$
$971$	15.4529	+	26.7652i	0.495907	+	0.858936i	−0.504082	+	0.863656i	$0.668169\pi$
$972$	−4.44425	+	23.3051i	−0.142550	+	0.747511i
$973$	18.0816	−	31.3182i	0.579668	−	1.00401i
$974$	11.3047	+	6.52675i	0.362225	+	0.209131i
$975$	0.241180	+	3.59257i	0.00772394	+	0.115054i
$976$	8.74444	−	15.1458i	0.279903	−	0.484806i
$977$	−18.1095	+	31.3666i	−0.579375	+	1.00351i	0.416176	+	0.909284i	$0.363370\pi$
$977$	−18.1095	+	31.3666i	−0.579375	+	1.00351i	−0.995551	+	0.0942233i	$0.969963\pi$
$978$	2.59369	+	3.86846i	0.0829370	+	0.123700i
$979$			22.9454i			0.733339i
$980$			0.923198i			0.0294905i
$981$	−35.2175	−	14.4571i	−1.12441	−	0.461580i
$982$	−16.5967	−	9.58210i	−0.529621	−	0.305777i
$983$	−7.75751	+	13.4364i	−0.247426	+	0.428554i	−0.962811	−	0.270176i	$-0.912918\pi$
$983$	−7.75751	+	13.4364i	−0.247426	+	0.428554i	0.715385	+	0.698731i	$0.246251\pi$
$984$	18.5440	−	37.7541i	0.591162	−	1.20356i
$985$	2.29042			0.0729788
$986$		−	14.1551i		−	0.450789i
$987$	−0.103701	−	1.54470i	−0.00330083	−	0.0491684i
$988$	1.79312	+	2.10417i	0.0570467	+	0.0669425i
$989$			58.4824i			1.85963i
$990$	−0.594596	−	0.769835i	−0.0188975	−	0.0244670i
$991$	−3.23093	+	1.86538i	−0.102634	+	0.0592558i	−0.550438	−	0.834876i	$-0.685539\pi$
$991$	−3.23093	+	1.86538i	−0.102634	+	0.0592558i	0.447804	+	0.894132i	$0.352206\pi$
$992$			20.2523i			0.643011i
$993$	0.879681	+	13.1036i	0.0279158	+	0.415829i
$994$	−13.3749	−	23.1660i	−0.424226	−	0.734781i
$995$	−0.464794	−	0.268349i	−0.0147350	−	0.00850723i
$996$	18.2308	−	12.2232i	0.577664	−	0.387306i
$997$	−40.7013			−1.28902			−0.644512	−	0.764595i	$-0.722939\pi$
$997$	−40.7013			−1.28902			−0.644512	+	0.764595i	$0.722939\pi$
$998$	−5.94135	+	10.2907i	−0.188070	+	0.325747i
$999$	−1.91625	−	9.40018i	−0.0606276	−	0.297409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.k.a.50.8	✓	36
3.2	odd	2		513.2.k.a.449.11		36
9.2	odd	6		171.2.t.a.164.8	yes	36
9.7	even	3		513.2.t.a.278.11		36
19.8	odd	6		171.2.t.a.122.8	yes	36
57.8	even	6		513.2.t.a.179.11		36
171.65	even	6	inner	171.2.k.a.65.8	yes	36
171.160	odd	6		513.2.k.a.8.11		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.8	✓	36	1.1	even	1	trivial
171.2.k.a.65.8	yes	36	171.65	even	6	inner
171.2.t.a.122.8	yes	36	19.8	odd	6
171.2.t.a.164.8	yes	36	9.2	odd	6
513.2.k.a.8.11		36	171.160	odd	6
513.2.k.a.449.11		36	3.2	odd	2
513.2.t.a.179.11		36	57.8	even	6
513.2.t.a.278.11		36	9.7	even	3

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.345701 + 0.598772i) q^{2} +(0.763607 - 1.55464i) q^{3} +(0.760981 + 1.31806i) q^{4} -0.106947i q^{5} +(0.666895 + 0.994667i) q^{6} +(1.77987 + 3.08283i) q^{7} -2.43509 q^{8} +(-1.83381 - 2.37427i) q^{9} +(0.0640371 + 0.0369718i) q^{10} +(3.79750 - 2.19249i) q^{11} +(2.63020 - 0.176573i) q^{12} +(-0.360891 + 0.208361i) q^{13} -2.46122 q^{14} +(-0.166265 - 0.0816658i) q^{15} +(-0.680148 + 1.17805i) q^{16} +(3.21900 - 1.85849i) q^{17} +(2.05559 - 0.277246i) q^{18} +(-4.10727 - 1.45956i) q^{19} +(0.140963 - 0.0813850i) q^{20} +(6.15181 - 0.412990i) q^{21} +3.03178i q^{22} +(-4.68779 + 2.70650i) q^{23} +(-1.85945 + 3.78569i) q^{24} +4.98856 q^{25} -0.288122i q^{26} +(-5.09144 + 1.03790i) q^{27} +(-2.70890 + 4.69195i) q^{28} -5.50797 q^{29} +(0.106377 - 0.0713227i) q^{30} +(-3.01840 - 1.74267i) q^{31} +(-2.90535 - 5.03221i) q^{32} +(-0.508730 - 7.57794i) q^{33} +2.56993i q^{34} +(0.329701 - 0.190353i) q^{35} +(1.73393 - 4.22384i) q^{36} +1.84627i q^{37} +(2.29383 - 1.95475i) q^{38} +(0.0483466 + 0.720161i) q^{39} +0.260427i q^{40} -9.97283 q^{41} +(-1.87940 + 3.82631i) q^{42} +(5.40204 - 9.35660i) q^{43} +(5.77965 + 3.33688i) q^{44} +(-0.253922 + 0.196121i) q^{45} -3.74256i q^{46} -0.251097i q^{47} +(1.31208 + 1.95695i) q^{48} +(-2.83590 + 4.91192i) q^{49} +(-1.72455 + 2.98701i) q^{50} +(-0.431231 - 6.42353i) q^{51} +(-0.549263 - 0.317117i) q^{52} +(-1.44192 + 2.49748i) q^{53} +(1.13865 - 3.40742i) q^{54} +(-0.234481 - 0.406133i) q^{55} +(-4.33416 - 7.50698i) q^{56} +(-5.40543 + 5.27080i) q^{57} +(1.90411 - 3.29802i) q^{58} -2.37489 q^{59} +(-0.0188840 - 0.281293i) q^{60} -12.8567 q^{61} +(2.08693 - 1.20489i) q^{62} +(4.05552 - 9.87922i) q^{63} +1.29694 q^{64} +(0.0222836 + 0.0385964i) q^{65} +(4.71333 + 2.31509i) q^{66} +(9.17875 - 5.29935i) q^{67} +(4.89919 + 2.82855i) q^{68} +(0.627998 + 9.35453i) q^{69} +0.263221i q^{70} +(5.43426 + 9.41241i) q^{71} +(4.46550 + 5.78156i) q^{72} +(2.47284 + 4.28309i) q^{73} +(-1.10550 - 0.638258i) q^{74} +(3.80930 - 7.75542i) q^{75} +(-1.20177 - 6.52432i) q^{76} +(13.5181 + 7.80470i) q^{77} +(-0.447926 - 0.220012i) q^{78} +(0.947726 + 0.547170i) q^{79} +(0.125990 + 0.0727401i) q^{80} +(-2.27429 + 8.70790i) q^{81} +(3.44762 - 5.97145i) q^{82} +(7.21082 - 4.16317i) q^{83} +(5.22576 + 7.79417i) q^{84} +(-0.198760 - 0.344263i) q^{85} +(3.73498 + 6.46918i) q^{86} +(-4.20592 + 8.56290i) q^{87} +(-9.24726 + 5.33891i) q^{88} +(-2.61637 + 4.53168i) q^{89} +(-0.0296508 - 0.219841i) q^{90} +(-1.28468 - 0.741711i) q^{91} +(-7.13465 - 4.11919i) q^{92} +(-5.01410 + 3.36180i) q^{93} +(0.150350 + 0.0868045i) q^{94} +(-0.156096 + 0.439262i) q^{95} +(-10.0418 + 0.674138i) q^{96} +(11.3602 + 6.55883i) q^{97} +(-1.96075 - 3.39611i) q^{98} +(-12.1694 - 4.99568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 6 q^{3} - 15 q^{4} + 4 q^{6} - q^{7} + 12 q^{8} - 4 q^{9} - 6 q^{10} - 9 q^{11} + 15 q^{12} - 6 q^{13} - 6 q^{14} + 9 q^{15} - 9 q^{16} - 27 q^{17} + 6 q^{18} + q^{19} + 9 q^{20} - 3 q^{21}+ \cdots + 28 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 6 * q^3 - 15 * q^4 + 4 * q^6 - q^7 + 12 * q^8 - 4 * q^9 - 6 * q^10 - 9 * q^11 + 15 * q^12 - 6 * q^13 - 6 * q^14 + 9 * q^15 - 9 * q^16 - 27 * q^17 + 6 * q^18 + q^19 + 9 * q^20 - 3 * q^21 + 9 * q^23 - 11 * q^24 - 22 * q^25 + 9 * q^27 + 2 * q^28 - 24 * q^29 - 35 * q^30 + 12 * q^31 - 15 * q^32 - 12 * q^33 + 15 * q^35 + 30 * q^36 - 18 * q^38 - 14 * q^39 + 36 * q^41 - 5 * q^42 + 3 * q^43 + 66 * q^44 + 29 * q^45 + 33 * q^48 - 9 * q^49 + 3 * q^50 - 24 * q^51 + 15 * q^52 - 12 * q^53 - 37 * q^54 - 7 * q^55 + 6 * q^56 + 2 * q^57 - 6 * q^58 - 18 * q^59 + 48 * q^60 - 16 * q^61 - 12 * q^62 - 34 * q^63 + 12 * q^64 - 18 * q^65 + 14 * q^66 + 27 * q^67 + 60 * q^68 - 51 * q^69 + 9 * q^71 - 102 * q^72 - 18 * q^73 + 90 * q^74 - 23 * q^76 - 6 * q^77 + 36 * q^78 - 6 * q^79 - 12 * q^80 + 40 * q^81 - 9 * q^82 - 9 * q^83 - 96 * q^84 + 11 * q^85 + 51 * q^86 - 19 * q^87 + 3 * q^88 - 18 * q^89 + 36 * q^90 + 27 * q^91 - 93 * q^92 - 28 * q^93 + 12 * q^94 - 9 * q^96 + 24 * q^97 - 84 * q^98 + 28 * q^99

Introduction

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