LMFDB - Embedded newform 220.2.l.d.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09671 + 0.892874i) q^{2} +(-1.63523 + 1.63523i) q^{3} +(0.405551 - 1.95845i) q^{4} +(2.22762 + 0.194242i) q^{5} +(0.333320 - 3.25343i) q^{6} +(2.27323 + 2.27323i) q^{7} +(1.30388 + 2.50996i) q^{8} -2.34794i q^{9} +(-2.61648 + 1.77595i) q^{10} +1.00000i q^{11} +(2.53934 + 3.86568i) q^{12} +(-0.723993 - 0.723993i) q^{13} +(-4.52278 - 0.463369i) q^{14} +(-3.96029 + 3.32503i) q^{15} +(-3.67106 - 1.58850i) q^{16} +(-0.922419 + 0.922419i) q^{17} +(2.09641 + 2.57501i) q^{18} -1.41633 q^{19} +(1.28383 - 4.28390i) q^{20} -7.43450 q^{21} +(-0.892874 - 1.09671i) q^{22} +(-3.57116 + 3.57116i) q^{23} +(-6.23649 - 1.97222i) q^{24} +(4.92454 + 0.865394i) q^{25} +(1.44045 + 0.147577i) q^{26} +(-1.06627 - 1.06627i) q^{27} +(5.37392 - 3.53010i) q^{28} +9.64395i q^{29} +(1.37446 - 7.18264i) q^{30} -7.64876i q^{31} +(5.44442 - 1.53566i) q^{32} +(-1.63523 - 1.63523i) q^{33} +(0.188023 - 1.83523i) q^{34} +(4.62232 + 5.50544i) q^{35} +(-4.59832 - 0.952210i) q^{36} +(-1.95305 + 1.95305i) q^{37} +(1.55330 - 1.26460i) q^{38} +2.36779 q^{39} +(2.41700 + 5.84450i) q^{40} +8.11796 q^{41} +(8.15350 - 6.63807i) q^{42} +(3.57789 - 3.57789i) q^{43} +(1.95845 + 0.405551i) q^{44} +(0.456069 - 5.23031i) q^{45} +(0.727934 - 7.10512i) q^{46} +(8.61919 + 8.61919i) q^{47} +(8.60058 - 3.40545i) q^{48} +3.33515i q^{49} +(-6.17349 + 3.44791i) q^{50} -3.01673i q^{51} +(-1.71152 + 1.12429i) q^{52} +(-7.92764 - 7.92764i) q^{53} +(2.12143 + 0.217345i) q^{54} +(-0.194242 + 2.22762i) q^{55} +(-2.74171 + 8.66973i) q^{56} +(2.31601 - 2.31601i) q^{57} +(-8.61084 - 10.5766i) q^{58} +2.51199 q^{59} +(4.90580 + 9.10450i) q^{60} -3.54775 q^{61} +(6.82938 + 8.38848i) q^{62} +(5.33741 - 5.33741i) q^{63} +(-4.59981 + 6.54536i) q^{64} +(-1.47215 - 1.75341i) q^{65} +(3.25343 + 0.333320i) q^{66} +(-7.01754 - 7.01754i) q^{67} +(1.43242 + 2.18060i) q^{68} -11.6793i q^{69} +(-9.98502 - 1.91072i) q^{70} -14.9871i q^{71} +(5.89324 - 3.06143i) q^{72} +(1.98983 + 1.98983i) q^{73} +(0.398104 - 3.88576i) q^{74} +(-9.46786 + 6.63763i) q^{75} +(-0.574393 + 2.77380i) q^{76} +(-2.27323 + 2.27323i) q^{77} +(-2.59678 + 2.11414i) q^{78} +14.1444 q^{79} +(-7.86915 - 4.25165i) q^{80} +10.5310 q^{81} +(-8.90305 + 7.24831i) q^{82} +(-3.37507 + 3.37507i) q^{83} +(-3.01507 + 14.5601i) q^{84} +(-2.23397 + 1.87562i) q^{85} +(-0.729306 + 7.11851i) q^{86} +(-15.7701 - 15.7701i) q^{87} +(-2.50996 + 1.30388i) q^{88} +4.70719i q^{89} +(4.16983 + 6.14335i) q^{90} -3.29161i q^{91} +(5.54565 + 8.44222i) q^{92} +(12.5075 + 12.5075i) q^{93} +(-17.1486 - 1.75691i) q^{94} +(-3.15503 - 0.275110i) q^{95} +(-6.39172 + 11.4140i) q^{96} +(0.309689 - 0.309689i) q^{97} +(-2.97787 - 3.65769i) q^{98} +2.34794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100}) $ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * q^18 - 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 + 8 * q^23 - 28 * q^24 - 4 * q^25 + 4 * q^26 - 44 * q^27 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.09671	+	0.892874i	−0.775492	+	0.631357i
$2$	−1.09671	+	0.892874i	−0.775492	+	0.631357i
$3$	−1.63523	+	1.63523i	−0.944099	+	0.944099i	−0.998518	−	0.0544190i	$-0.982669\pi$
$3$	−1.63523	+	1.63523i	−0.944099	+	0.944099i	0.0544190	+	0.998518i	$0.482669\pi$
$4$	0.405551	−	1.95845i	0.202776	−	0.979225i
$5$	2.22762	+	0.194242i	0.996220	+	0.0868678i
$5$	2.22762	+	0.194242i	0.996220	+	0.0868678i
$6$	0.333320	−	3.25343i	0.136077	−	1.32821i
$7$	2.27323	+	2.27323i	0.859200	+	0.859200i	0.991244	−	0.132044i	$-0.0421540\pi$
$7$	2.27323	+	2.27323i	0.859200	+	0.859200i	−0.132044	+	0.991244i	$0.542154\pi$
$8$	1.30388	+	2.50996i	0.460990	+	0.887405i
$9$		−	2.34794i		−	0.782647i
$10$	−2.61648	+	1.77595i	−0.827405	+	0.561606i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	2.53934	+	3.86568i	0.733045	+	1.11593i
$13$	−0.723993	−	0.723993i	−0.200800	−	0.200800i	0.599543	−	0.800343i	$-0.295349\pi$
$13$	−0.723993	−	0.723993i	−0.200800	−	0.200800i	−0.800343	+	0.599543i	$0.795349\pi$
$14$	−4.52278	−	0.463369i	−1.20877	−	0.123840i
$15$	−3.96029	+	3.32503i	−1.02254	+	0.858519i
$16$	−3.67106	−	1.58850i	−0.917764	−	0.397126i
$17$	−0.922419	+	0.922419i	−0.223720	+	0.223720i	−0.810063	−	0.586343i	$-0.800567\pi$
$17$	−0.922419	+	0.922419i	−0.223720	+	0.223720i	0.586343	+	0.810063i	$0.300567\pi$
$18$	2.09641	+	2.57501i	0.494130	+	0.606936i
$19$	−1.41633			−0.324927			−0.162464	−	0.986715i	$-0.551944\pi$
$19$	−1.41633			−0.324927			−0.162464	+	0.986715i	$0.551944\pi$
$20$	1.28383	−	4.28390i	0.287072	−	0.957909i
$21$	−7.43450			−1.62234
$22$	−0.892874	−	1.09671i	−0.190361	−	0.233820i
$23$	−3.57116	+	3.57116i	−0.744638	+	0.744638i	−0.973467	−	0.228829i	$-0.926510\pi$
$23$	−3.57116	+	3.57116i	−0.744638	+	0.744638i	0.228829	+	0.973467i	$0.426510\pi$
$24$	−6.23649	−	1.97222i	−1.27302	−	0.402578i
$25$	4.92454	+	0.865394i	0.984908	+	0.173079i
$26$	1.44045	+	0.147577i	0.282495	+	0.0289422i
$27$	−1.06627	−	1.06627i	−0.205203	−	0.205203i
$28$	5.37392	−	3.53010i	1.01558	−	0.667126i
$29$			9.64395i			1.79084i	0.445225	+	0.895419i	$0.353124\pi$
$29$			9.64395i			1.79084i	−0.445225	+	0.895419i	$0.646876\pi$
$30$	1.37446	−	7.18264i	0.250941	−	1.31136i
$31$		−	7.64876i		−	1.37376i	−0.726772	−	0.686879i	$-0.758980\pi$
$31$		−	7.64876i		−	1.37376i	0.726772	−	0.686879i	$-0.241020\pi$
$32$	5.44442	−	1.53566i	0.962447	−	0.271469i
$33$	−1.63523	−	1.63523i	−0.284657	−	0.284657i
$34$	0.188023	−	1.83523i	0.0322457	−	0.314740i
$35$	4.62232	+	5.50544i	0.781315	+	0.930589i
$36$	−4.59832	−	0.952210i	−0.766387	−	0.158702i
$37$	−1.95305	+	1.95305i	−0.321080	+	0.321080i	−0.849181	−	0.528102i	$-0.822904\pi$
$37$	−1.95305	+	1.95305i	−0.321080	+	0.321080i	0.528102	+	0.849181i	$0.322904\pi$
$38$	1.55330	−	1.26460i	0.251979	−	0.205145i
$39$	2.36779			0.379149
$40$	2.41700	+	5.84450i	0.382161	+	0.924096i
$41$	8.11796			1.26781			0.633906	−	0.773410i	$-0.281451\pi$
$41$	8.11796			1.26781			0.633906	+	0.773410i	$0.281451\pi$
$42$	8.15350	−	6.63807i	1.25811	−	1.02428i
$43$	3.57789	−	3.57789i	0.545623	−	0.545623i	−0.379549	−	0.925172i	$-0.623921\pi$
$43$	3.57789	−	3.57789i	0.545623	−	0.545623i	0.925172	+	0.379549i	$0.123921\pi$
$44$	1.95845	+	0.405551i	0.295248	+	0.0611392i
$45$	0.456069	−	5.23031i	0.0679868	−	0.779688i
$46$	0.727934	−	7.10512i	0.107328	−	1.04759i
$47$	8.61919	+	8.61919i	1.25724	+	1.25724i	0.952406	+	0.304833i	$0.0986006\pi$
$47$	8.61919	+	8.61919i	1.25724	+	1.25724i	0.304833	+	0.952406i	$0.401399\pi$
$48$	8.60058	−	3.40545i	1.24139	−	0.491534i
$49$			3.33515i			0.476450i
$50$	−6.17349	+	3.44791i	−0.873063	+	0.487608i
$51$		−	3.01673i		−	0.422427i
$52$	−1.71152	+	1.12429i	−0.237345	+	0.155911i
$53$	−7.92764	−	7.92764i	−1.08894	−	1.08894i	−0.995637	−	0.0933073i	$-0.970256\pi$
$53$	−7.92764	−	7.92764i	−1.08894	−	1.08894i	−0.0933073	−	0.995637i	$-0.529744\pi$
$54$	2.12143	+	0.217345i	0.288690	+	0.0295769i
$55$	−0.194242	+	2.22762i	−0.0261916	+	0.300372i
$56$	−2.74171	+	8.66973i	−0.366376	+	1.15854i
$57$	2.31601	−	2.31601i	0.306764	−	0.306764i
$58$	−8.61084	−	10.5766i	−1.13066	−	1.38878i
$59$	2.51199			0.327034			0.163517	−	0.986541i	$-0.447716\pi$
$59$	2.51199			0.327034			0.163517	+	0.986541i	$0.447716\pi$
$60$	4.90580	+	9.10450i	0.633336	+	1.17539i
$61$	−3.54775			−0.454243			−0.227122	−	0.973866i	$-0.572931\pi$
$61$	−3.54775			−0.454243			−0.227122	+	0.973866i	$0.572931\pi$
$62$	6.82938	+	8.38848i	0.867332	+	1.06534i
$63$	5.33741	−	5.33741i	0.672450	−	0.672450i
$64$	−4.59981	+	6.54536i	−0.574976	+	0.818170i
$65$	−1.47215	−	1.75341i	−0.182598	−	0.217484i
$66$	3.25343	+	0.333320i	0.400469	+	0.0410289i
$67$	−7.01754	−	7.01754i	−0.857329	−	0.857329i	0.133693	−	0.991023i	$-0.457316\pi$
$67$	−7.01754	−	7.01754i	−0.857329	−	0.857329i	−0.991023	+	0.133693i	$0.957316\pi$
$68$	1.43242	+	2.18060i	0.173707	+	0.264437i
$69$		−	11.6793i		−	1.40602i
$70$	−9.98502	−	1.91072i	−1.19344	−	0.228375i
$71$		−	14.9871i		−	1.77864i	−0.457284	−	0.889321i	$-0.651178\pi$
$71$		−	14.9871i		−	1.77864i	0.457284	−	0.889321i	$-0.348822\pi$
$72$	5.89324	−	3.06143i	0.694525	−	0.360792i
$73$	1.98983	+	1.98983i	0.232891	+	0.232891i	0.813899	−	0.581007i	$-0.197341\pi$
$73$	1.98983	+	1.98983i	0.232891	+	0.232891i	−0.581007	+	0.813899i	$0.697341\pi$
$74$	0.398104	−	3.88576i	0.0462787	−	0.451711i
$75$	−9.46786	+	6.63763i	−1.09325	+	0.766447i
$76$	−0.574393	+	2.77380i	−0.0658873	+	0.318177i
$77$	−2.27323	+	2.27323i	−0.259059	+	0.259059i
$78$	−2.59678	+	2.11414i	−0.294027	+	0.239379i
$79$	14.1444			1.59136			0.795682	−	0.605714i	$-0.207112\pi$
$79$	14.1444			1.59136			0.795682	+	0.605714i	$0.207112\pi$
$80$	−7.86915	−	4.25165i	−0.879797	−	0.475349i
$81$	10.5310			1.17011
$82$	−8.90305	+	7.24831i	−0.983178	+	0.800442i
$83$	−3.37507	+	3.37507i	−0.370462	+	0.370462i	−0.867645	−	0.497183i	$-0.834368\pi$
$83$	−3.37507	+	3.37507i	−0.370462	+	0.370462i	0.497183	+	0.867645i	$0.334368\pi$
$84$	−3.01507	+	14.5601i	−0.328971	+	1.58864i
$85$	−2.23397	+	1.87562i	−0.242308	+	0.203440i
$86$	−0.729306	+	7.11851i	−0.0786431	+	0.767609i
$87$	−15.7701	−	15.7701i	−1.69073	−	1.69073i
$88$	−2.50996	+	1.30388i	−0.267563	+	0.138994i
$89$			4.70719i			0.498961i	0.968380	+	0.249481i	$0.0802599\pi$
$89$			4.70719i			0.498961i	−0.968380	+	0.249481i	$0.919740\pi$
$90$	4.16983	+	6.14335i	0.439539	+	0.647566i
$91$		−	3.29161i		−	0.345054i
$92$	5.54565	+	8.44222i	0.578174	+	0.880162i
$93$	12.5075	+	12.5075i	1.29696	+	1.29696i
$94$	−17.1486	−	1.75691i	−1.76875	−	0.181212i
$95$	−3.15503	−	0.275110i	−0.323699	−	0.0282257i
$96$	−6.39172	+	11.4140i	−0.652352	+	1.16494i
$97$	0.309689	−	0.309689i	0.0314442	−	0.0314442i	−0.691210	−	0.722654i	$-0.742922\pi$
$97$	0.309689	−	0.309689i	0.0314442	−	0.0314442i	0.722654	+	0.691210i	$0.242922\pi$
$98$	−2.97787	−	3.65769i	−0.300810	−	0.369483i
$99$	2.34794			0.235977
$100$	3.69198	−	9.29351i	0.369198	−	0.929351i
$101$	8.34044			0.829905			0.414952	−	0.909843i	$-0.363798\pi$
$101$	8.34044			0.829905			0.414952	+	0.909843i	$0.363798\pi$
$102$	2.69356	+	3.30848i	0.266702	+	0.327589i
$103$	9.04433	−	9.04433i	0.891164	−	0.891164i	−0.103469	−	0.994633i	$-0.532994\pi$
$103$	9.04433	−	9.04433i	0.891164	−	0.891164i	0.994633	+	0.103469i	$0.0329941\pi$
$104$	0.873196	−	2.76119i	0.0856240	−	0.270757i
$105$	−16.5612	−	1.44409i	−1.61621	−	0.140929i
$106$	15.7727	+	1.61595i	1.53198	+	0.156955i
$107$	0.464738	+	0.464738i	0.0449280	+	0.0449280i	0.729214	−	0.684286i	$-0.239886\pi$
$107$	0.464738	+	0.464738i	0.0449280	+	0.0449280i	−0.684286	+	0.729214i	$0.739886\pi$
$108$	−2.52066	+	1.65580i	−0.242550	+	0.159330i
$109$		−	6.78445i		−	0.649832i	−0.945743	−	0.324916i	$-0.894664\pi$
$109$		−	6.78445i		−	0.649832i	0.945743	−	0.324916i	$-0.105336\pi$
$110$	−1.77595	−	2.61648i	−0.169330	−	0.249472i
$111$		−	6.38737i		−	0.606262i
$112$	−4.73412	−	11.9562i	−0.447332	−	1.12975i
$113$	−3.36794	−	3.36794i	−0.316829	−	0.316829i	0.530719	−	0.847548i	$-0.321922\pi$
$113$	−3.36794	−	3.36794i	−0.316829	−	0.316829i	−0.847548	+	0.530719i	$0.821922\pi$
$114$	−0.472090	+	4.60791i	−0.0442152	+	0.431570i
$115$	−8.64883	+	7.26149i	−0.806508	+	0.677138i
$116$	18.8872	+	3.91112i	1.75363	+	0.363138i
$117$	−1.69989	+	1.69989i	−0.157155	+	0.157155i
$118$	−2.75493	+	2.24290i	−0.253612	+	0.206475i
$119$	−4.19374			−0.384440
$120$	−13.5094	−	5.60474i	−1.23324	−	0.511641i
$121$	−1.00000			−0.0909091
$122$	3.89086	−	3.16770i	0.352262	−	0.286790i
$123$	−13.2747	+	13.2747i	−1.19694	+	1.19694i
$124$	−14.9797	−	3.10197i	−1.34522	−	0.278565i
$125$	10.8019	+	2.88432i	0.966150	+	0.257981i
$126$	−1.08796	+	10.6192i	−0.0969233	+	0.946036i
$127$	5.74732	+	5.74732i	0.509992	+	0.509992i	0.914524	−	0.404532i	$-0.132566\pi$
$127$	5.74732	+	5.74732i	0.509992	+	0.509992i	−0.404532	+	0.914524i	$0.632566\pi$
$128$	−0.799523	−	11.2854i	−0.0706685	−	0.997500i
$129$			11.7013i			1.03024i
$130$	3.18009	+	0.608539i	0.278913	+	0.0533724i
$131$			18.0937i			1.58085i	0.612556	+	0.790427i	$0.290141\pi$
$131$			18.0937i			1.58085i	−0.612556	+	0.790427i	$0.709859\pi$
$132$	−3.86568	+	2.53934i	−0.336464	+	0.221022i
$133$	−3.21963	−	3.21963i	−0.279178	−	0.279178i
$134$	13.9620	+	1.43044i	1.20613	+	0.123571i
$135$	−2.16812	−	2.58235i	−0.186602	−	0.222253i
$136$	−3.51796	−	1.11252i	−0.301662	−	0.0953974i
$137$	6.35346	−	6.35346i	0.542812	−	0.542812i	−0.381540	−	0.924352i	$-0.624606\pi$
$137$	6.35346	−	6.35346i	0.542812	−	0.542812i	0.924352	+	0.381540i	$0.124606\pi$
$138$	10.4282	+	12.8088i	0.887704	+	1.09036i
$139$	0.935850			0.0793778			0.0396889	−	0.999212i	$-0.487363\pi$
$139$	0.935850			0.0793778			0.0396889	+	0.999212i	$0.487363\pi$
$140$	12.6567	−	6.81986i	1.06969	−	0.576383i
$141$	−28.1887			−2.37392
$142$	13.3816	+	16.4365i	1.12296	+	1.37932i
$143$	0.723993	−	0.723993i	0.0605433	−	0.0605433i
$144$	−3.72971	+	8.61942i	−0.310809	+	0.718285i
$145$	−1.87326	+	21.4830i	−0.155566	+	1.78407i
$146$	−3.95893	−	0.405600i	−0.327643	−	0.0335677i
$147$	−5.45373	−	5.45373i	−0.449816	−	0.449816i
$148$	3.03289	+	4.61702i	0.249302	+	0.379516i
$149$		−	12.5283i		−	1.02636i	−0.858281	−	0.513180i	$-0.828467\pi$
$149$		−	12.5283i		−	1.02636i	0.858281	−	0.513180i	$-0.171533\pi$
$150$	4.45694	−	15.7332i	0.363908	−	1.28461i
$151$			11.6081i			0.944655i	0.881423	+	0.472328i	$0.156586\pi$
$151$			11.6081i			0.944655i	−0.881423	+	0.472328i	$0.843414\pi$
$152$	−1.84671	−	3.55492i	−0.149788	−	0.288342i
$153$	2.16579	+	2.16579i	0.175093	+	0.175093i
$154$	0.463369	−	4.52278i	0.0373393	−	0.364456i
$155$	1.48571	−	17.0385i	0.119335	−	1.36857i
$156$	0.960259	−	4.63719i	0.0768823	−	0.371273i
$157$	2.67425	−	2.67425i	0.213428	−	0.213428i	−0.592294	−	0.805722i	$-0.701778\pi$
$157$	2.67425	−	2.67425i	0.213428	−	0.213428i	0.805722	+	0.592294i	$0.201778\pi$
$158$	−15.5123	+	12.6291i	−1.23409	+	1.00472i
$159$	25.9270			2.05614
$160$	12.4264	−	2.36333i	0.982391	−	0.186837i
$161$	−16.2361			−1.27959
$162$	−11.5495	+	9.40286i	−0.907412	+	0.738758i
$163$	5.14228	−	5.14228i	0.402775	−	0.402775i	−0.476435	−	0.879210i	$-0.658071\pi$
$163$	5.14228	−	5.14228i	0.402775	−	0.402775i	0.879210	+	0.476435i	$0.158071\pi$
$164$	3.29225	−	15.8986i	0.257081	−	1.24147i
$165$	−3.32503	−	3.96029i	−0.258853	−	0.308308i
$166$	0.687964	−	6.71499i	0.0533964	−	0.521184i
$167$	−10.2219	−	10.2219i	−0.790991	−	0.790991i	0.190665	−	0.981655i	$-0.438936\pi$
$167$	−10.2219	−	10.2219i	−0.790991	−	0.790991i	−0.981655	+	0.190665i	$0.938936\pi$
$168$	−9.69367	−	18.6603i	−0.747883	−	1.43967i
$169$		−	11.9517i		−	0.919359i
$170$	0.775323	−	4.05167i	0.0594646	−	0.310749i
$171$			3.32545i			0.254303i
$172$	−5.55610	−	8.45813i	−0.423649	−	0.644927i
$173$	13.4480	+	13.4480i	1.02244	+	1.02244i	0.999742	+	0.0226936i	$0.00722423\pi$
$173$	13.4480	+	13.4480i	1.02244	+	1.02244i	0.0226936	+	0.999742i	$0.492776\pi$
$174$	31.3759	+	3.21452i	2.37860	+	0.243692i
$175$	9.22737	+	13.1618i	0.697524	+	0.994942i
$176$	1.58850	−	3.67106i	0.119738	−	0.276716i
$177$	−4.10768	+	4.10768i	−0.308752	+	0.308752i
$178$	−4.20293	−	5.16243i	−0.315023	−	0.386941i
$179$	−5.08038			−0.379725			−0.189863	−	0.981811i	$-0.560804\pi$
$179$	−5.08038			−0.379725			−0.189863	+	0.981811i	$0.560804\pi$
$180$	−10.0583	−	3.01435i	−0.749704	−	0.224676i
$181$	−9.69715			−0.720783			−0.360392	−	0.932801i	$-0.617357\pi$
$181$	−9.69715			−0.720783			−0.360392	+	0.932801i	$0.617357\pi$
$182$	2.93899	+	3.60994i	0.217852	+	0.267587i
$183$	5.80138	−	5.80138i	0.428851	−	0.428851i
$184$	−13.6198	−	4.30711i	−1.00407	−	0.317525i
$185$	−4.73001	+	3.97128i	−0.347757	+	0.291974i
$186$	−24.8847	−	2.54949i	−1.82463	−	0.186937i
$187$	−0.922419	−	0.922419i	−0.0674540	−	0.0674540i
$188$	20.3758	−	13.3847i	1.48606	−	0.976183i
$189$		−	4.84774i		−	0.352621i
$190$	3.70579	−	2.51533i	0.268847	−	0.182481i
$191$		−	6.59943i		−	0.477518i	−0.971079	−	0.238759i	$-0.923259\pi$
$191$		−	6.59943i		−	0.477518i	0.971079	−	0.238759i	$-0.0767405\pi$
$192$	−3.18142	−	18.2249i	−0.229599	−	1.31527i
$193$	−7.19452	−	7.19452i	−0.517873	−	0.517873i	0.399054	−	0.916927i	$-0.369338\pi$
$193$	−7.19452	−	7.19452i	−0.517873	−	0.517873i	−0.916927	+	0.399054i	$0.869338\pi$
$194$	−0.0631262	+	0.616153i	−0.00453219	+	0.0442372i
$195$	5.27452	+	0.459924i	0.377716	+	0.0329359i
$196$	6.53172	+	1.35257i	0.466551	+	0.0966124i
$197$	14.8919	−	14.8919i	1.06100	−	1.06100i	0.0629865	−	0.998014i	$-0.479937\pi$
$197$	14.8919	−	14.8919i	1.06100	−	1.06100i	0.998014	−	0.0629865i	$-0.0200625\pi$
$198$	−2.57501	+	2.09641i	−0.182998	+	0.148986i
$199$	20.8386			1.47721			0.738605	−	0.674139i	$-0.235485\pi$
$199$	20.8386			1.47721			0.738605	+	0.674139i	$0.235485\pi$
$200$	4.24889	+	13.4888i	0.300442	+	0.953800i
$201$	22.9506			1.61881
$202$	−9.14705	+	7.44696i	−0.643584	+	0.523966i
$203$	−21.9229	+	21.9229i	−1.53869	+	1.53869i
$204$	−5.90812	−	1.22344i	−0.413651	−	0.0856579i
$205$	18.0837	+	1.57685i	1.26302	+	0.110132i
$206$	−1.84357	+	17.9945i	−0.128448	+	1.25373i
$207$	8.38486	+	8.38486i	0.582788	+	0.582788i
$208$	1.50775	+	3.80789i	0.104544	+	0.264029i
$209$		−	1.41633i		−	0.0979693i
$210$	19.4522	−	13.2033i	1.34233	−	0.911115i
$211$		−	1.74833i		−	0.120360i	−0.998188	−	0.0601799i	$-0.980833\pi$
$211$		−	1.74833i		−	0.120360i	0.998188	−	0.0601799i	$-0.0191674\pi$
$212$	−18.7409	+	12.3108i	−1.28713	+	0.845511i
$213$	24.5073	+	24.5073i	1.67921	+	1.67921i
$214$	−0.924637	−	0.0947309i	−0.0632069	−	0.00647567i
$215$	8.66514	−	7.27518i	0.590957	−	0.496163i
$216$	1.28601	−	4.06657i	0.0875017	−	0.276695i
$217$	17.3874	−	17.3874i	1.18033	−	1.18033i
$218$	6.05766	+	7.44058i	0.410276	+	0.503940i
$219$	−6.50764			−0.439745
$220$	4.28390	+	1.28383i	0.288820	+	0.0865555i
$221$	1.33565			0.0898456
$222$	5.70312	+	7.00510i	0.382768	+	0.470151i
$223$	−4.01382	+	4.01382i	−0.268785	+	0.268785i	−0.828611	−	0.559825i	$-0.810868\pi$
$223$	−4.01382	+	4.01382i	−0.268785	+	0.268785i	0.559825	+	0.828611i	$0.310868\pi$
$224$	15.8673	+	8.88551i	1.06018	+	0.593688i
$225$	2.03189	−	11.5625i	0.135460	−	0.770835i
$226$	6.70080	+	0.686511i	0.445731	+	0.0456660i
$227$	−7.34061	−	7.34061i	−0.487213	−	0.487213i	0.420213	−	0.907426i	$-0.361956\pi$
$227$	−7.34061	−	7.34061i	−0.487213	−	0.487213i	−0.907426	+	0.420213i	$0.861956\pi$
$228$	−3.59654	−	5.47506i	−0.238186	−	0.362595i
$229$		−	1.92059i		−	0.126916i	−0.997985	−	0.0634581i	$-0.979787\pi$
$229$		−	1.92059i		−	0.126916i	0.997985	−	0.0634581i	$-0.0202129\pi$
$230$	3.00167	−	15.6861i	0.197924	−	1.03431i
$231$		−	7.43450i		−	0.489154i
$232$	−24.2059	+	12.5745i	−1.58920	+	0.825558i
$233$	−15.6936	−	15.6936i	−1.02812	−	1.02812i	−0.999593	−	0.0285271i	$-0.990918\pi$
$233$	−15.6936	−	15.6936i	−1.02812	−	1.02812i	−0.0285271	−	0.999593i	$-0.509082\pi$
$234$	0.346501	−	3.38208i	0.0226515	−	0.221094i
$235$	17.5260	+	20.8745i	1.14327	+	1.36170i
$236$	1.01874	−	4.91962i	0.0663145	−	0.320240i
$237$	−23.1293	+	23.1293i	−1.50241	+	1.50241i
$238$	4.59932	−	3.74448i	0.298130	−	0.242719i
$239$	−24.5204			−1.58609			−0.793047	−	0.609161i	$-0.791506\pi$
$239$	−24.5204			−1.58609			−0.793047	+	0.609161i	$0.791506\pi$
$240$	19.8203	−	5.91543i	1.27939	−	0.381839i
$241$	5.52210			0.355710			0.177855	−	0.984057i	$-0.443084\pi$
$241$	5.52210			0.355710			0.177855	+	0.984057i	$0.443084\pi$
$242$	1.09671	−	0.892874i	0.0704993	−	0.0573961i
$243$	−14.0218	+	14.0218i	−0.899498	+	0.899498i
$244$	−1.43880	+	6.94810i	−0.0921095	+	0.444806i
$245$	−0.647826	+	7.42942i	−0.0413881	+	0.474649i
$246$	2.70588	−	26.4112i	0.172520	−	1.68391i
$247$	1.02541	+	1.02541i	0.0652453	+	0.0652453i
$248$	19.1981	−	9.97305i	1.21908	−	0.633289i
$249$		−	11.0380i		−	0.699506i
$250$	−14.4219	+	6.48146i	−0.912120	+	0.409924i
$251$			13.1078i			0.827357i	0.910423	+	0.413678i	$0.135756\pi$
$251$			13.1078i			0.827357i	−0.910423	+	0.413678i	$0.864244\pi$
$252$	−8.28845	−	12.6176i	−0.522124	−	0.794837i
$253$	−3.57116	−	3.57116i	−0.224517	−	0.224517i
$254$	−11.4348	−	1.17152i	−0.717482	−	0.0735075i
$255$	0.585977	−	6.72012i	0.0366953	−	0.420830i
$256$	10.9533	+	11.6630i	0.684582	+	0.728936i
$257$	−20.6594	+	20.6594i	−1.28870	+	1.28870i	−0.353121	+	0.935578i	$0.614880\pi$
$257$	−20.6594	+	20.6594i	−1.28870	+	1.28870i	−0.935578	+	0.353121i	$0.885120\pi$
$258$	−10.4478	−	12.8330i	−0.650452	−	0.798946i
$259$	−8.87947			−0.551743
$260$	−4.03099	+	2.17203i	−0.249992	+	0.134704i
$261$	22.6434			1.40159
$262$	−16.1554	−	19.8436i	−0.998084	−	1.22594i
$263$	5.86258	−	5.86258i	0.361502	−	0.361502i	−0.502864	−	0.864366i	$-0.667720\pi$
$263$	5.86258	−	5.86258i	0.361502	−	0.361502i	0.864366	+	0.502864i	$0.167720\pi$
$264$	1.97222	−	6.23649i	0.121382	−	0.383830i
$265$	−16.1198	−	19.1996i	−0.990234	−	1.17942i
$266$	6.40574	+	0.656281i	0.392761	+	0.0402391i
$267$	−7.69733	−	7.69733i	−0.471069	−	0.471069i
$268$	−16.5895	+	10.8975i	−1.01336	+	0.665673i
$269$		−	12.8329i		−	0.782437i	−0.920298	−	0.391219i	$-0.872054\pi$
$269$		−	12.8329i		−	0.782437i	0.920298	−	0.391219i	$-0.127946\pi$
$270$	4.68351	+	0.896231i	0.285029	+	0.0545429i
$271$			18.6929i			1.13551i	0.823196	+	0.567757i	$0.192189\pi$
$271$			18.6929i			1.13551i	−0.823196	+	0.567757i	$0.807811\pi$
$272$	4.85152	−	1.92099i	0.294167	−	0.116477i
$273$	5.38252	+	5.38252i	0.325765	+	0.325765i
$274$	−1.29507	+	12.6407i	−0.0782380	+	0.763655i
$275$	−0.865394	+	4.92454i	−0.0521852	+	0.296961i
$276$	−22.8734	−	4.73656i	−1.37681	−	0.285107i
$277$	−6.37661	+	6.37661i	−0.383133	+	0.383133i	−0.872230	−	0.489097i	$-0.837327\pi$
$277$	−6.37661	+	6.37661i	−0.383133	+	0.383133i	0.489097	+	0.872230i	$0.337327\pi$
$278$	−1.02636	+	0.835597i	−0.0615568	+	0.0501158i
$279$	−17.9588			−1.07517
$280$	−7.79149	+	18.7803i	−0.465631	+	1.12234i
$281$	−16.5985			−0.990183			−0.495092	−	0.868841i	$-0.664866\pi$
$281$	−16.5985			−0.990183			−0.495092	+	0.868841i	$0.664866\pi$
$282$	30.9149	−	25.1690i	1.84095	−	1.49879i
$283$	10.6084	−	10.6084i	0.630606	−	0.630606i	−0.317614	−	0.948220i	$-0.602882\pi$
$283$	10.6084	−	10.6084i	0.630606	−	0.630606i	0.948220	+	0.317614i	$0.102882\pi$
$284$	−29.3515	−	6.07804i	−1.74169	−	0.360665i
$285$	5.60906	−	4.70932i	0.332252	−	0.278956i
$286$	−0.147577	+	1.44045i	−0.00872639	+	0.0851754i
$287$	18.4540	+	18.4540i	1.08930	+	1.08930i
$288$	−3.60564	−	12.7832i	−0.212464	−	0.753256i
$289$			15.2983i			0.899899i
$290$	−17.1272	−	25.2333i	−1.00574	−	1.48175i
$291$			1.01283i			0.0593729i
$292$	4.70395	−	3.09000i	0.275278	−	0.180828i
$293$	−15.3588	−	15.3588i	−0.897270	−	0.897270i	0.0979236	−	0.995194i	$-0.468780\pi$
$293$	−15.3588	−	15.3588i	−0.897270	−	0.897270i	−0.995194	+	0.0979236i	$0.968780\pi$
$294$	10.8507	+	1.11167i	0.632823	+	0.0648340i
$295$	5.59576	+	0.487935i	0.325798	+	0.0284087i
$296$	−7.44862	−	2.35554i	−0.432942	−	0.136913i
$297$	1.06627	−	1.06627i	0.0618711	−	0.0618711i
$298$	11.1862	+	13.7399i	0.647999	+	0.795933i
$299$	5.17099			0.299046
$300$	9.15976	+	21.2342i	0.528839	+	1.22596i
$301$	16.2667			0.937598
$302$	−10.3646	−	12.7308i	−0.596415	−	0.732573i
$303$	−13.6385	+	13.6385i	−0.783512	+	0.783512i
$304$	5.19941	+	2.24984i	0.298207	+	0.129037i
$305$	−7.90303	−	0.689123i	−0.452526	−	0.0394591i
$306$	−4.30902	−	0.441467i	−0.246330	−	0.0252370i
$307$	−0.975912	−	0.975912i	−0.0556982	−	0.0556982i	0.678709	−	0.734407i	$-0.262540\pi$
$307$	−0.975912	−	0.975912i	−0.0556982	−	0.0556982i	−0.734407	+	0.678709i	$0.762540\pi$
$308$	3.53010	+	5.37392i	0.201146	+	0.306207i
$309$			29.5791i			1.68269i
$310$	13.5838	+	20.0129i	0.771510	+	1.13665i
$311$		−	5.31250i		−	0.301244i	−0.988591	−	0.150622i	$-0.951872\pi$
$311$		−	5.31250i		−	0.301244i	0.988591	−	0.150622i	$-0.0481277\pi$
$312$	3.08730	+	5.94305i	0.174784	+	0.336459i
$313$	4.06321	+	4.06321i	0.229666	+	0.229666i	0.812553	−	0.582887i	$-0.198077\pi$
$313$	4.06321	+	4.06321i	0.229666	+	0.229666i	−0.582887	+	0.812553i	$0.698077\pi$
$314$	−0.545110	+	5.32064i	−0.0307624	+	0.300261i
$315$	12.9264	−	10.8529i	0.728322	−	0.611494i
$316$	5.73626	−	27.7010i	0.322690	−	1.55830i
$317$	−7.01485	+	7.01485i	−0.393993	+	0.393993i	−0.876108	−	0.482115i	$-0.839869\pi$
$317$	−7.01485	+	7.01485i	−0.393993	+	0.393993i	0.482115	+	0.876108i	$0.339869\pi$
$318$	−28.4344	+	23.1495i	−1.59452	+	1.29816i
$319$	−9.64395			−0.539958
$320$	−11.5180	+	13.6871i	−0.643875	+	0.765131i
$321$	−1.51991			−0.0848329
$322$	17.8063	−	14.4968i	0.992308	−	0.807876i
$323$	1.30645	−	1.30645i	0.0726926	−	0.0726926i
$324$	4.27086	−	20.6244i	0.237270	−	1.14580i
$325$	−2.93879	−	4.19187i	−0.163015	−	0.232523i
$326$	−1.04819	+	10.2310i	−0.0580537	+	0.566643i
$327$	11.0941	+	11.0941i	0.613506	+	0.613506i
$328$	10.5848	+	20.3758i	0.584449	+	1.12506i
$329$			39.1868i			2.16044i
$330$	7.18264	+	1.37446i	0.395391	+	0.0756616i
$331$			25.0017i			1.37422i	0.726556	+	0.687108i	$0.241120\pi$
$331$			25.0017i			1.37422i	−0.726556	+	0.687108i	$0.758880\pi$
$332$	5.24114	+	7.97867i	0.287645	+	0.437886i
$333$	4.58565	+	4.58565i	0.251292	+	0.251292i
$334$	20.3372	+	2.08359i	1.11280	+	0.114009i
$335$	−14.2693	−	16.9955i	−0.779614	−	0.928563i
$336$	27.2925	+	11.8097i	1.48893	+	0.644274i
$337$	2.87545	−	2.87545i	0.156636	−	0.156636i	−0.624438	−	0.781074i	$-0.714672\pi$
$337$	2.87545	−	2.87545i	0.156636	−	0.156636i	0.781074	+	0.624438i	$0.214672\pi$
$338$	10.6713	+	13.1075i	0.580444	+	0.712956i
$339$	11.0147			0.598236
$340$	2.76733	+	5.13578i	0.150079	+	0.278527i
$341$	7.64876			0.414204
$342$	−2.96921	−	3.64706i	−0.160556	−	0.197210i
$343$	8.33105	−	8.33105i	0.449835	−	0.449835i
$344$	13.6455	+	4.31523i	0.735715	+	0.232662i
$345$	2.26862	−	26.0170i	0.122138	−	1.40071i
$346$	−26.7560	−	2.74121i	−1.43841	−	0.147368i
$347$	−0.444682	−	0.444682i	−0.0238718	−	0.0238718i	0.695070	−	0.718942i	$-0.255373\pi$
$347$	−0.444682	−	0.444682i	−0.0238718	−	0.0238718i	−0.718942	+	0.695070i	$0.755373\pi$
$348$	−37.2805	+	24.4893i	−1.99844	+	1.31277i
$349$			11.1765i			0.598262i	0.954212	+	0.299131i	$0.0966968\pi$
$349$			11.1765i			0.598262i	−0.954212	+	0.299131i	$0.903303\pi$
$350$	−21.8716	−	6.19587i	−1.16909	−	0.331183i
$351$			1.54394i			0.0824094i
$352$	1.53566	+	5.44442i	0.0818510	+	0.290189i
$353$	9.52218	+	9.52218i	0.506814	+	0.506814i	0.913547	−	0.406733i	$-0.133332\pi$
$353$	9.52218	+	9.52218i	0.506814	+	0.506814i	−0.406733	+	0.913547i	$0.633332\pi$
$354$	0.837298	−	8.17259i	0.0445019	−	0.434368i
$355$	2.91113	−	33.3855i	0.154507	−	1.77192i
$356$	9.21880	+	1.90901i	0.488596	+	0.101177i
$357$	6.85772	−	6.85772i	0.362949	−	0.362949i
$358$	5.57171	−	4.53614i	0.294474	−	0.239742i
$359$	−23.9996			−1.26665			−0.633326	−	0.773885i	$-0.718311\pi$
$359$	−23.9996			−1.26665			−0.633326	+	0.773885i	$0.718311\pi$
$360$	13.7225	−	5.67496i	0.723241	−	0.299097i
$361$	−16.9940			−0.894422
$362$	10.6350	−	8.65833i	0.558962	−	0.455072i
$363$	1.63523	−	1.63523i	0.0858272	−	0.0858272i
$364$	−6.44645	−	1.33491i	−0.337886	−	0.0699686i
$365$	4.04606	+	4.81907i	0.211780	+	0.252242i
$366$	−1.18254	+	11.5424i	−0.0618122	+	0.603328i
$367$	−10.7096	−	10.7096i	−0.559038	−	0.559038i	0.369996	−	0.929033i	$-0.379359\pi$
$367$	−10.7096	−	10.7096i	−0.559038	−	0.559038i	−0.929033	+	0.369996i	$0.879359\pi$
$368$	18.7827	−	7.43712i	0.979117	−	0.387687i
$369$		−	19.0605i		−	0.992249i
$370$	1.64160	−	8.57865i	0.0853428	−	0.445983i
$371$		−	36.0427i		−	1.87124i
$372$	29.5677	−	19.4228i	1.53301	−	1.00703i
$373$	−12.7491	−	12.7491i	−0.660125	−	0.660125i	0.295284	−	0.955409i	$-0.404586\pi$
$373$	−12.7491	−	12.7491i	−0.660125	−	0.660125i	−0.955409	+	0.295284i	$0.904586\pi$
$374$	1.83523	+	0.188023i	0.0948976	+	0.00972245i
$375$	−22.3801	+	12.9470i	−1.15570	+	0.668581i
$376$	−10.3955	+	32.8722i	−0.536105	+	1.69526i
$377$	6.98216	−	6.98216i	0.359599	−	0.359599i
$378$	4.32842	+	5.31657i	0.222630	+	0.273455i
$379$	11.9690			0.614804			0.307402	−	0.951580i	$-0.400540\pi$
$379$	11.9690			0.614804			0.307402	+	0.951580i	$0.400540\pi$
$380$	−1.81832	+	6.06739i	−0.0932776	+	0.311251i
$381$	−18.7963			−0.962966
$382$	5.89246	+	7.23766i	0.301484	+	0.370311i
$383$	0.0817471	−	0.0817471i	0.00417708	−	0.00417708i	−0.705015	−	0.709192i	$-0.749060\pi$
$383$	0.0817471	−	0.0817471i	0.00417708	−	0.00417708i	0.709192	+	0.705015i	$0.249060\pi$
$384$	19.7616	+	17.1468i	1.00846	+	0.875021i
$385$	−5.50544	+	4.62232i	−0.280583	+	0.235575i
$386$	14.3141	+	1.46651i	0.728569	+	0.0746434i
$387$	−8.40067	−	8.40067i	−0.427030	−	0.427030i
$388$	−0.480916	−	0.732106i	−0.0244148	−	0.0371671i
$389$		−	13.0833i		−	0.663347i	−0.943394	−	0.331674i	$-0.892387\pi$
$389$		−	13.0833i		−	0.663347i	0.943394	−	0.331674i	$-0.107613\pi$
$390$	−6.19528	+	4.20508i	−0.313710	+	0.212932i
$391$		−	6.58821i		−	0.333180i
$392$	−8.37109	+	4.34862i	−0.422804	+	0.219639i
$393$	−29.5873	−	29.5873i	−1.49248	−	1.49248i
$394$	−3.03551	+	29.6286i	−0.152927	+	1.49267i
$395$	31.5082	+	2.74743i	1.58535	+	0.138238i
$396$	0.952210	−	4.59832i	0.0478504	−	0.231074i
$397$	13.8205	−	13.8205i	0.693631	−	0.693631i	−0.269398	−	0.963029i	$-0.586825\pi$
$397$	13.8205	−	13.8205i	0.693631	−	0.693631i	0.963029	+	0.269398i	$0.0868248\pi$
$398$	−22.8539	+	18.6063i	−1.14556	+	0.932647i
$399$	10.5297			0.527143
$400$	−16.7036	−	10.9996i	−0.835179	−	0.549978i
$401$	29.9011			1.49319			0.746595	−	0.665279i	$-0.231687\pi$
$401$	29.9011			1.49319			0.746595	+	0.665279i	$0.231687\pi$
$402$	−25.1701	+	20.4920i	−1.25537	+	1.02205i
$403$	−5.53765	+	5.53765i	−0.275850	+	0.275850i
$404$	3.38248	−	16.3343i	0.168284	−	0.812664i
$405$	23.4590	+	2.04556i	1.16569	+	0.101645i
$406$	4.46870	−	43.6175i	0.221778	−	2.16470i
$407$	−1.95305	−	1.95305i	−0.0968091	−	0.0968091i
$408$	7.57188	−	3.93345i	0.374864	−	0.194735i
$409$			25.5845i			1.26507i	0.774531	+	0.632536i	$0.217986\pi$
$409$			25.5845i			1.26507i	−0.774531	+	0.632536i	$0.782014\pi$
$410$	−21.2405	+	14.4171i	−1.04899	+	0.712010i
$411$			20.7787i			1.02494i
$412$	−14.0449	−	21.3808i	−0.691944	−	1.05336i
$413$	5.71034	+	5.71034i	0.280988	+	0.280988i
$414$	−16.6824	−	1.70915i	−0.819895	−	0.0839999i
$415$	−8.17394	+	6.86277i	−0.401243	+	0.336880i
$416$	−5.05353	−	2.82992i	−0.247770	−	0.138748i
$417$	−1.53033	+	1.53033i	−0.0749405	+	0.0749405i
$418$	1.26460	+	1.55330i	0.0618536	+	0.0759744i
$419$	5.31123			0.259470			0.129735	−	0.991549i	$-0.458587\pi$
$419$	5.31123			0.259470			0.129735	+	0.991549i	$0.458587\pi$
$420$	−9.54460	+	31.8486i	−0.465729	+	1.55405i
$421$	14.3707			0.700385			0.350192	−	0.936678i	$-0.386116\pi$
$421$	14.3707			0.700385			0.350192	+	0.936678i	$0.386116\pi$
$422$	1.56104	+	1.91741i	0.0759900	+	0.0933381i
$423$	20.2374	−	20.2374i	0.983974	−	0.983974i
$424$	9.56139	−	30.2347i	0.464342	−	1.46833i
$425$	−5.34075	+	3.74424i	−0.259064	+	0.181622i
$426$	−48.7594	−	4.99550i	−2.36240	−	0.242033i
$427$	−8.06486	−	8.06486i	−0.390286	−	0.390286i
$428$	1.09864	−	0.721692i	0.0531049	−	0.0348843i
$429$			2.36779i			0.114318i
$430$	−3.00733	+	15.7156i	−0.145026	+	0.757876i
$431$		−	38.3768i		−	1.84854i	−0.381734	−	0.924272i	$-0.624673\pi$
$431$		−	38.3768i		−	1.84854i	0.381734	−	0.924272i	$-0.375327\pi$
$432$	2.22056	+	5.60809i	0.106837	+	0.269820i
$433$	−6.38327	−	6.38327i	−0.306760	−	0.306760i	0.536891	−	0.843651i	$-0.319599\pi$
$433$	−6.38327	−	6.38327i	−0.306760	−	0.306760i	−0.843651	+	0.536891i	$0.819599\pi$
$434$	−3.54420	+	34.5937i	−0.170127	+	1.66055i
$435$	−32.0664	−	38.1928i	−1.53747	−	1.83121i
$436$	−13.2870	−	2.75144i	−0.636332	−	0.131770i
$437$	5.05792	−	5.05792i	0.241953	−	0.241953i
$438$	7.13700	−	5.81050i	0.341019	−	0.277636i
$439$	−16.3392			−0.779827			−0.389913	−	0.920852i	$-0.627495\pi$
$439$	−16.3392			−0.779827			−0.389913	+	0.920852i	$0.627495\pi$
$440$	−5.84450	+	2.41700i	−0.278625	+	0.115226i
$441$	7.83073			0.372892
$442$	−1.46482	+	1.19257i	−0.0696745	+	0.0567247i
$443$	−6.87247	+	6.87247i	−0.326521	+	0.326521i	−0.851262	−	0.524741i	$-0.824162\pi$
$443$	−6.87247	+	6.87247i	−0.326521	+	0.326521i	0.524741	+	0.851262i	$0.324162\pi$
$444$	−12.5093	−	2.59040i	−0.593667	−	0.122935i
$445$	−0.914335	+	10.4858i	−0.0433437	+	0.497075i
$446$	0.818166	−	7.98584i	0.0387413	−	0.378141i
$447$	20.4866	+	20.4866i	0.968985	+	0.968985i
$448$	−25.3355	+	4.42269i	−1.19699	+	0.208952i
$449$			4.44137i			0.209601i	0.994493	+	0.104801i	$0.0334204\pi$
$449$			4.44137i			0.209601i	−0.994493	+	0.104801i	$0.966580\pi$
$450$	8.09548	+	14.4950i	0.381625	+	0.683300i
$451$			8.11796i			0.382260i
$452$	−7.96181	+	5.23007i	−0.374492	+	0.246002i
$453$	−18.9819	−	18.9819i	−0.891848	−	0.891848i
$454$	14.6048	+	1.49629i	0.685436	+	0.0702243i
$455$	0.639369	−	7.33243i	0.0299741	−	0.343750i
$456$	8.83291	+	2.79331i	0.413639	+	0.130809i
$457$	−11.8533	+	11.8533i	−0.554476	+	0.554476i	−0.927729	−	0.373254i	$-0.878242\pi$
$457$	−11.8533	+	11.8533i	−0.554476	+	0.554476i	0.373254	+	0.927729i	$0.378242\pi$
$458$	1.71485	+	2.10633i	0.0801295	+	0.0984225i
$459$	1.96709			0.0918159
$460$	10.7137	+	19.8832i	0.499530	+	0.927060i
$461$	−25.5894			−1.19182			−0.595909	−	0.803052i	$-0.703208\pi$
$461$	−25.5894			−1.19182			−0.595909	+	0.803052i	$0.703208\pi$
$462$	6.63807	+	8.15350i	0.308831	+	0.379335i
$463$	16.4285	−	16.4285i	0.763499	−	0.763499i	−0.213454	−	0.976953i	$-0.568471\pi$
$463$	16.4285	−	16.4285i	0.763499	−	0.763499i	0.976953	+	0.213454i	$0.0684714\pi$
$464$	15.3195	−	35.4035i	0.711188	−	1.64357i
$465$	25.4324	+	30.2913i	1.17940	+	1.40473i
$466$	31.2237	+	3.19893i	1.44641	+	0.148188i
$467$	19.5335	+	19.5335i	0.903901	+	0.903901i	0.995771	−	0.0918697i	$-0.0292843\pi$
$467$	19.5335	+	19.5335i	0.903901	+	0.903901i	−0.0918697	+	0.995771i	$0.529284\pi$
$468$	2.63976	+	4.01855i	0.122023	+	0.185757i
$469$		−	31.9050i		−	1.47323i
$470$	−37.8593	−	7.24471i	−1.74632	−	0.334174i
$471$			8.74600i			0.402995i
$472$	3.27533	+	6.30501i	0.150759	+	0.290212i
$473$	3.57789	+	3.57789i	0.164511	+	0.164511i
$474$	4.71460	−	46.0176i	0.216549	−	2.11366i
$475$	−6.97475	−	1.22568i	−0.320024	−	0.0562380i
$476$	−1.70078	+	8.21324i	−0.0779550	+	0.376453i
$477$	−18.6136	+	18.6136i	−0.852259	+	0.852259i
$478$	26.8918	−	21.8936i	1.23000	−	1.00139i
$479$	1.19428			0.0545681			0.0272840	−	0.999628i	$-0.491314\pi$
$479$	1.19428			0.0545681			0.0272840	+	0.999628i	$0.491314\pi$
$480$	−16.4554	+	24.1845i	−0.751082	+	1.10387i
$481$	2.82799			0.128945
$482$	−6.05615	+	4.93054i	−0.275850	+	0.224580i
$483$	26.5498	−	26.5498i	1.20806	−	1.20806i
$484$	−0.405551	+	1.95845i	−0.0184341	+	0.0890205i
$485$	0.750023	−	0.629714i	0.0340568	−	0.0285938i
$486$	2.85816	−	27.8975i	0.129649	−	1.26546i
$487$	3.24221	+	3.24221i	0.146919	+	0.146919i	0.776740	−	0.629821i	$-0.216872\pi$
$487$	3.24221	+	3.24221i	0.146919	+	0.146919i	−0.629821	+	0.776740i	$0.716872\pi$
$488$	−4.62583	−	8.90472i	−0.209402	−	0.403098i
$489$			16.8176i			0.760518i
$490$	−5.92306	−	8.72636i	−0.267577	−	0.394217i
$491$			11.6132i			0.524095i	0.965055	+	0.262047i	$0.0843977\pi$
$491$			11.6132i			0.524095i	−0.965055	+	0.262047i	$0.915602\pi$
$492$	20.6143	+	31.3814i	0.929364	+	1.41478i
$493$	−8.89577	−	8.89577i	−0.400645	−	0.400645i
$494$	−2.04014	−	0.209017i	−0.0917903	−	0.00940410i
$495$	5.23031	+	0.456069i	0.235085	+	0.0204988i
$496$	−12.1501	+	28.0790i	−0.545555	+	1.26079i
$497$	34.0691	−	34.0691i	1.52821	−	1.52821i
$498$	9.85556	+	12.1055i	0.441638	+	0.542461i
$499$	−16.5509			−0.740919			−0.370459	−	0.928849i	$-0.620800\pi$
$499$	−16.5509			−0.740919			−0.370459	+	0.928849i	$0.620800\pi$
$500$	10.0295	−	19.9852i	0.448533	−	0.893766i
$501$	33.4301			1.49355
$502$	−11.7036	−	14.3755i	−0.522358	−	0.641608i
$503$	2.09623	−	2.09623i	0.0934662	−	0.0934662i	−0.658828	−	0.752294i	$-0.728947\pi$
$503$	2.09623	−	2.09623i	0.0934662	−	0.0934662i	0.752294	+	0.658828i	$0.228947\pi$
$504$	20.3560	+	6.43736i	0.906729	+	0.286743i
$505$	18.5793	+	1.62007i	0.826767	+	0.0720920i
$506$	7.10512	+	0.727934i	0.315861	+	0.0323606i
$507$	19.5437	+	19.5437i	0.867966	+	0.867966i
$508$	13.5867	−	8.92500i	0.602811	−	0.395983i
$509$		−	34.7631i		−	1.54085i	−0.637533	−	0.770423i	$-0.720045\pi$
$509$		−	34.7631i		−	1.54085i	0.637533	−	0.770423i	$-0.279955\pi$
$510$	5.35757	+	7.89323i	0.237237	+	0.349518i
$511$			9.04666i			0.400201i
$512$	−22.4262	−	3.01099i	−0.991107	−	0.133068i
$513$	1.51018	+	1.51018i	0.0666761	+	0.0666761i
$514$	4.21115	−	41.1037i	0.185746	−	1.81301i
$515$	21.9041	−	18.3905i	0.965209	−	0.810382i
$516$	22.9165	+	4.74549i	1.00884	+	0.208908i
$517$	−8.61919	+	8.61919i	−0.379072	+	0.379072i
$518$	9.73821	−	7.92825i	0.427872	−	0.348347i
$519$	−43.9812			−1.93056
$520$	2.48149	−	5.98126i	0.108820	−	0.262296i
$521$	−28.2376			−1.23711			−0.618555	−	0.785741i	$-0.712282\pi$
$521$	−28.2376			−1.23711			−0.618555	+	0.785741i	$0.712282\pi$
$522$	−24.8333	+	20.2177i	−1.08692	+	0.884906i
$523$	23.3918	−	23.3918i	1.02285	−	1.02285i	0.0231215	−	0.999733i	$-0.492640\pi$
$523$	23.3918	−	23.3918i	1.02285	−	1.02285i	0.999733	−	0.0231215i	$-0.00736045\pi$
$524$	35.4356	+	7.33793i	1.54801	+	0.320559i
$525$	−36.6115	−	6.43377i	−1.59786	−	0.280793i
$526$	−1.19501	+	11.6641i	−0.0521049	+	0.508579i
$527$	7.05537	+	7.05537i	0.307337	+	0.307337i
$528$	3.40545	+	8.60058i	0.148203	+	0.374292i
$529$		−	2.50633i		−	0.108971i
$530$	34.8216	+	6.66343i	1.51256	+	0.289441i
$531$		−	5.89801i		−	0.255952i
$532$	−7.61122	+	4.99977i	−0.329988	+	0.216767i
$533$	−5.87734	−	5.87734i	−0.254576	−	0.254576i
$534$	15.3145	+	1.56900i	0.662723	+	0.0678973i
$535$	0.944987	+	1.12553i	0.0408553	+	0.0486609i
$536$	8.46374	−	26.7638i	0.365578	−	1.15602i
$537$	8.30757	−	8.30757i	0.358498	−	0.358498i
$538$	11.4582	+	14.0740i	0.493997	+	0.606774i
$539$	−3.33515			−0.143655
$540$	−5.93668	+	3.19888i	−0.255474	+	0.137658i
$541$	−21.3400			−0.917478			−0.458739	−	0.888571i	$-0.651699\pi$
$541$	−21.3400			−0.917478			−0.458739	+	0.888571i	$0.651699\pi$
$542$	−16.6904	−	20.5008i	−0.716916	−	0.880583i
$543$	15.8570	−	15.8570i	0.680491	−	0.680491i
$544$	−3.60552	+	6.43857i	−0.154585	+	0.276051i
$545$	1.31783	−	15.1131i	0.0564495	−	0.647376i
$546$	−10.7090	−	1.09716i	−0.458303	−	0.0469540i
$547$	−17.5485	−	17.5485i	−0.750320	−	0.750320i	0.224219	−	0.974539i	$-0.428017\pi$
$547$	−17.5485	−	17.5485i	−0.750320	−	0.750320i	−0.974539	+	0.224219i	$0.928017\pi$
$548$	−9.86628	−	15.0196i	−0.421466	−	0.641605i
$549$			8.32991i			0.355512i
$550$	−3.44791	−	6.17349i	−0.147019	−	0.263238i
$551$		−	13.6590i		−	0.581892i
$552$	29.3146	−	15.2284i	1.24771	−	0.648163i
$553$	32.1534	+	32.1534i	1.36730	+	1.36730i
$554$	1.29979	−	12.6868i	0.0552227	−	0.539011i
$555$	1.24070	−	14.2286i	0.0526646	−	0.603970i
$556$	0.379535	−	1.83282i	0.0160959	−	0.0777287i
$557$	−5.97438	+	5.97438i	−0.253143	+	0.253143i	−0.822258	−	0.569115i	$-0.807286\pi$
$557$	−5.97438	+	5.97438i	−0.253143	+	0.253143i	0.569115	+	0.822258i	$0.307286\pi$
$558$	19.6957	−	16.0350i	0.833784	−	0.678815i
$559$	−5.18073			−0.219122
$560$	−8.22340	−	27.5534i	−0.347502	−	1.16434i
$561$	3.01673			0.127367
$562$	18.2038	−	14.8204i	0.767879	−	0.625160i
$563$	−5.46575	+	5.46575i	−0.230354	+	0.230354i	−0.812840	−	0.582486i	$-0.802080\pi$
$563$	−5.46575	+	5.46575i	−0.230354	+	0.230354i	0.582486	+	0.812840i	$0.302080\pi$
$564$	−11.4320	+	55.2062i	−0.481372	+	2.32460i
$565$	−6.84828	−	8.15667i	−0.288109	−	0.343154i
$566$	−2.16239	+	21.1064i	−0.0908921	+	0.887168i
$567$	23.9394	+	23.9394i	1.00536	+	1.00536i
$568$	37.6170	−	19.5413i	1.57838	−	0.819936i
$569$			35.6456i			1.49434i	0.664632	+	0.747171i	$0.268588\pi$
$569$			35.6456i			1.49434i	−0.664632	+	0.747171i	$0.731412\pi$
$570$	−1.94668	+	10.1729i	−0.0815376	+	0.426098i
$571$		−	0.929679i		−	0.0389059i	−0.999811	−	0.0194529i	$-0.993808\pi$
$571$		−	0.929679i		−	0.0389059i	0.999811	−	0.0194529i	$-0.00619245\pi$
$572$	−1.12429	−	1.71152i	−0.0470089	−	0.0715623i
$573$	10.7916	+	10.7916i	0.450824	+	0.450824i
$574$	−36.7158	−	3.76161i	−1.53249	−	0.157006i
$575$	−20.6768	+	14.4958i	−0.862281	+	0.604519i
$576$	15.3681	+	10.8001i	0.640338	+	0.450003i
$577$	−21.1801	+	21.1801i	−0.881740	+	0.881740i	−0.993711	−	0.111972i	$-0.964283\pi$
$577$	−21.1801	+	21.1801i	−0.881740	+	0.881740i	0.111972	+	0.993711i	$0.464283\pi$
$578$	−13.6594	−	16.7778i	−0.568158	−	0.697865i
$579$	23.5294			0.977847
$580$	41.3137	+	12.3812i	1.71546	+	0.514100i
$581$	−15.3446			−0.636602
$582$	−0.904325	−	1.11078i	−0.0374855	−	0.0460432i
$583$	7.92764	−	7.92764i	0.328329	−	0.328329i
$584$	−2.39990	+	7.58887i	−0.0993084	+	0.314030i
$585$	−4.11690	+	3.45652i	−0.170213	+	0.142909i
$586$	30.5576	+	3.13069i	1.26232	+	0.129328i
$587$	9.39519	+	9.39519i	0.387781	+	0.387781i	0.873895	−	0.486114i	$-0.161586\pi$
$587$	9.39519	+	9.39519i	0.387781	+	0.387781i	−0.486114	+	0.873895i	$0.661586\pi$
$588$	−12.8926	+	8.46909i	−0.531683	+	0.349259i
$589$			10.8331i			0.446372i
$590$	−6.57260	+	4.46118i	−0.270590	+	0.183664i
$591$			48.7032i			2.00338i
$592$	10.2722	−	4.06733i	0.422184	−	0.167166i
$593$	22.6726	+	22.6726i	0.931054	+	0.931054i	0.997772	−	0.0667183i	$-0.0212529\pi$
$593$	22.6726	+	22.6726i	0.931054	+	0.931054i	−0.0667183	+	0.997772i	$0.521253\pi$
$594$	−0.217345	+	2.12143i	−0.00891776	+	0.0870433i
$595$	−9.34205	−	0.814602i	−0.382987	−	0.0333954i
$596$	−24.5361	−	5.08087i	−1.00504	−	0.208121i
$597$	−34.0759	+	34.0759i	−1.39463	+	1.39463i
$598$	−5.67108	+	4.61704i	−0.231908	+	0.188805i
$599$	−17.6219			−0.720011			−0.360006	−	0.932950i	$-0.617225\pi$
$599$	−17.6219			−0.720011			−0.360006	+	0.932950i	$0.617225\pi$
$600$	−29.0051	−	15.1093i	−1.18413	−	0.616835i
$601$	−9.95444			−0.406050			−0.203025	−	0.979174i	$-0.565077\pi$
$601$	−9.95444			−0.406050			−0.203025	+	0.979174i	$0.565077\pi$
$602$	−17.8399	+	14.5241i	−0.727100	+	0.591960i
$603$	−16.4768	+	16.4768i	−0.670986	+	0.670986i
$604$	22.7339	+	4.70769i	0.925030	+	0.191553i
$605$	−2.22762	−	0.194242i	−0.0905654	−	0.00789707i
$606$	2.78004	−	27.1350i	0.112931	−	1.10228i
$607$	30.5524	+	30.5524i	1.24008	+	1.24008i	0.959966	+	0.280116i	$0.0903728\pi$
$607$	30.5524	+	30.5524i	1.24008	+	1.24008i	0.280116	+	0.959966i	$0.409627\pi$
$608$	−7.71107	+	2.17500i	−0.312725	+	0.0882077i
$609$		−	71.6979i		−	2.90535i
$610$	9.28264	−	6.30064i	0.375843	−	0.255106i
$611$		−	12.4805i		−	0.504906i
$612$	5.11992	−	3.36325i	0.206961	−	0.135951i
$613$	−15.5026	−	15.5026i	−0.626145	−	0.626145i	0.320951	−	0.947096i	$-0.395998\pi$
$613$	−15.5026	−	15.5026i	−0.626145	−	0.626145i	−0.947096	+	0.320951i	$0.895998\pi$
$614$	1.94166	+	0.198927i	0.0783590	+	0.00802804i
$615$	−32.1495	+	26.9924i	−1.29639	+	1.08844i
$616$	−8.66973	−	2.74171i	−0.349313	−	0.110466i
$617$	25.9842	−	25.9842i	1.04608	−	1.04608i	0.0471977	−	0.998886i	$-0.484971\pi$
$617$	25.9842	−	25.9842i	1.04608	−	1.04608i	0.998886	−	0.0471977i	$-0.0150291\pi$
$618$	−26.4104	−	32.4397i	−1.06238	−	1.30492i
$619$	−8.25617			−0.331843			−0.165922	−	0.986139i	$-0.553060\pi$
$619$	−8.25617			−0.331843			−0.165922	+	0.986139i	$0.553060\pi$
$620$	−32.7665	−	9.81968i	−1.31594	−	0.394368i
$621$	7.61561			0.305604
$622$	4.74339	+	5.82628i	0.190193	+	0.233613i
$623$	−10.7005	+	10.7005i	−0.428708	+	0.428708i
$624$	−8.69228	−	3.76124i	−0.347970	−	0.150570i
$625$	23.5022	+	8.52333i	0.940087	+	0.340933i
$626$	−8.08410	−	0.828233i	−0.323106	−	0.0331028i
$627$	2.31601	+	2.31601i	0.0924927	+	0.0924927i
$628$	−4.15283	−	6.32192i	−0.165716	−	0.252272i
$629$		−	3.60306i		−	0.143664i
$630$	−4.48626	+	23.4442i	−0.178737	+	0.934040i
$631$			10.1166i			0.402735i	0.979516	+	0.201367i	$0.0645385\pi$
$631$			10.1166i			0.402735i	−0.979516	+	0.201367i	$0.935462\pi$
$632$	18.4425	+	35.5018i	0.733604	+	1.41219i
$633$	2.85891	+	2.85891i	0.113632	+	0.113632i
$634$	1.42989	−	13.9566i	0.0567880	−	0.554289i
$635$	11.6864	+	13.9192i	0.463762	+	0.552366i
$636$	10.5147	−	50.7767i	0.416936	−	2.01343i
$637$	2.41462	−	2.41462i	0.0956709	−	0.0956709i
$638$	10.5766	−	8.61084i	0.418733	−	0.340906i
$639$	−35.1888			−1.39205
$640$	0.411076	−	25.2949i	0.0162492	−	0.999868i
$641$	−33.6135			−1.32765			−0.663827	−	0.747886i	$-0.731069\pi$
$641$	−33.6135			−1.32765			−0.663827	+	0.747886i	$0.731069\pi$
$642$	1.66690	−	1.35709i	0.0657872	−	0.0535599i
$643$	−29.4474	+	29.4474i	−1.16129	+	1.16129i	−0.177097	+	0.984193i	$0.556671\pi$
$643$	−29.4474	+	29.4474i	−1.16129	+	1.16129i	−0.984193	+	0.177097i	$0.943329\pi$
$644$	−6.58458	+	31.7976i	−0.259469	+	1.25300i
$645$	−2.27289	+	26.0660i	−0.0894950	+	1.02635i
$646$	−0.266302	+	2.59929i	−0.0104775	+	0.102268i
$647$	−5.15400	−	5.15400i	−0.202625	−	0.202625i	0.598499	−	0.801124i	$-0.295764\pi$
$647$	−5.15400	−	5.15400i	−0.202625	−	0.202625i	−0.801124	+	0.598499i	$0.795764\pi$
$648$	13.7311	+	26.4324i	0.539410	+	1.03836i
$649$			2.51199i			0.0986044i
$650$	6.96582	+	1.97330i	0.273222	+	0.0773992i
$651$			56.8647i			2.22870i
$652$	−7.98545	−	12.1564i	−0.312734	−	0.476080i
$653$	16.9805	+	16.9805i	0.664498	+	0.664498i	0.956437	−	0.291939i	$-0.0943004\pi$
$653$	16.9805	+	16.9805i	0.664498	+	0.664498i	−0.291939	+	0.956437i	$0.594300\pi$
$654$	−22.0727	−	2.26139i	−0.863111	−	0.0884275i
$655$	−3.51456	+	40.3058i	−0.137325	+	1.57488i
$656$	−29.8015	−	12.8954i	−1.16355	−	0.503481i
$657$	4.67199	−	4.67199i	0.182272	−	0.182272i
$658$	−34.9889	−	42.9766i	−1.36401	−	1.67540i
$659$	−38.6928			−1.50726			−0.753629	−	0.657300i	$-0.771699\pi$
$659$	−38.6928			−1.50726			−0.753629	+	0.657300i	$0.771699\pi$
$660$	−9.10450	+	4.90580i	−0.354392	+	0.190958i
$661$	3.52220			0.136998			0.0684988	−	0.997651i	$-0.478179\pi$
$661$	3.52220			0.136998			0.0684988	+	0.997651i	$0.478179\pi$
$662$	−22.3233	−	27.4196i	−0.867621	−	1.06569i
$663$	−2.18409	+	2.18409i	−0.0848231	+	0.0848231i
$664$	−12.8720	−	4.07062i	−0.499529	−	0.157971i
$665$	−6.54672	−	7.79749i	−0.253871	−	0.302374i
$666$	−9.12354	−	0.934725i	−0.353530	−	0.0362198i
$667$	−34.4401	−	34.4401i	−1.33352	−	1.33352i
$668$	−24.1645	+	15.8735i	−0.934952	+	0.614164i
$669$		−	13.1270i		−	0.507520i
$670$	30.8241	+	5.89847i	1.19084	+	0.227878i
$671$		−	3.54775i		−	0.136960i
$672$	−40.4765	+	11.4169i	−1.56142	+	0.440415i
$673$	−2.73473	−	2.73473i	−0.105416	−	0.105416i	0.652432	−	0.757848i	$-0.273749\pi$
$673$	−2.73473	−	2.73473i	−0.105416	−	0.105416i	−0.757848	+	0.652432i	$0.773749\pi$
$674$	−0.586124	+	5.72096i	−0.0225766	+	0.220363i
$675$	−4.32813	−	6.17361i	−0.166590	−	0.237623i
$676$	−23.4067	−	4.84701i	−0.900260	−	0.186424i
$677$	3.78865	−	3.78865i	0.145610	−	0.145610i	−0.630544	−	0.776154i	$-0.717168\pi$
$677$	3.78865	−	3.78865i	0.145610	−	0.145610i	0.776154	+	0.630544i	$0.217168\pi$
$678$	−12.0799	+	9.83474i	−0.463927	+	0.377701i
$679$	1.40799			0.0540337
$680$	−7.62056	−	3.16159i	−0.292235	−	0.121242i
$681$	24.0071			0.919955
$682$	−8.38848	+	6.82938i	−0.321212	+	0.261511i
$683$	13.7937	−	13.7937i	0.527802	−	0.527802i	−0.392115	−	0.919916i	$-0.628256\pi$
$683$	13.7937	−	13.7937i	0.527802	−	0.527802i	0.919916	+	0.392115i	$0.128256\pi$
$684$	6.51272	+	1.34864i	0.249020	+	0.0515665i
$685$	15.3872	−	12.9189i	0.587913	−	0.493608i
$686$	−1.69818	+	16.5753i	−0.0648367	+	0.632849i
$687$	3.14060	+	3.14060i	0.119822	+	0.119822i
$688$	−18.8181	+	7.45114i	−0.717434	+	0.284072i
$689$			11.4791i			0.437319i
$690$	20.7419	+	30.5587i	0.789631	+	1.16335i
$691$			22.1562i			0.842861i	0.906861	+	0.421431i	$0.138472\pi$
$691$			22.1562i			0.842861i	−0.906861	+	0.421431i	$0.861528\pi$
$692$	31.7912	−	20.8835i	1.20852	−	0.793870i
$693$	5.33741	+	5.33741i	0.202751	+	0.202751i
$694$	0.884733	+	0.0906427i	0.0335840	+	0.00344075i
$695$	2.08471	+	0.181782i	0.0790777	+	0.00689537i
$696$	19.0200	−	60.1445i	0.720952	−	2.27977i
$697$	−7.48816	+	7.48816i	−0.283634	+	0.283634i
$698$	−9.97917	−	12.2573i	−0.377717	−	0.463948i
$699$	51.3251			1.94129
$700$	29.5190	−	12.7335i	1.11571	−	0.481283i
$701$	3.91585			0.147899			0.0739497	−	0.997262i	$-0.476440\pi$
$701$	3.91585			0.147899			0.0739497	+	0.997262i	$0.476440\pi$
$702$	−1.37854	−	1.69326i	−0.0520298	−	0.0639078i
$703$	2.76616	−	2.76616i	0.104328	−	0.104328i
$704$	−6.54536	−	4.59981i	−0.246688	−	0.173362i
$705$	−62.7936	−	5.47543i	−2.36494	−	0.206217i
$706$	−18.9452	−	1.94097i	−0.713011	−	0.0730495i
$707$	18.9597	+	18.9597i	0.713054	+	0.713054i
$708$	6.37882	+	9.71057i	0.239731	+	0.364946i
$709$			14.8137i			0.556341i	0.960532	+	0.278170i	$0.0897280\pi$
$709$			14.8137i			0.556341i	−0.960532	+	0.278170i	$0.910272\pi$
$710$	26.6164	+	39.2135i	0.998895	+	1.47166i
$711$		−	33.2101i		−	1.24548i
$712$	−11.8149	+	6.13760i	−0.442781	+	0.230016i
$713$	27.3149	+	27.3149i	1.02295	+	1.02295i
$714$	−1.39786	+	13.6440i	−0.0523135	+	0.510615i
$715$	1.75341	−	1.47215i	0.0655738	−	0.0550552i
$716$	−2.06035	+	9.94966i	−0.0769990	+	0.371836i
$717$	40.0965	−	40.0965i	1.49743	−	1.49743i
$718$	26.3206	−	21.4286i	0.982278	−	0.799710i
$719$	−10.4233			−0.388724			−0.194362	−	0.980930i	$-0.562264\pi$
$719$	−10.4233			−0.388724			−0.194362	+	0.980930i	$0.562264\pi$
$720$	−9.98262	+	18.4763i	−0.372030	+	0.688570i
$721$	41.1197			1.53138
$722$	18.6375	−	15.1735i	0.693617	−	0.564700i
$723$	−9.02990	+	9.02990i	−0.335825	+	0.335825i
$724$	−3.93269	+	18.9914i	−0.146157	+	0.705809i
$725$	−8.34582	+	47.4920i	−0.309956	+	1.76381i
$726$	−0.333320	+	3.25343i	−0.0123707	+	0.120746i
$727$	−21.3788	−	21.3788i	−0.792897	−	0.792897i	0.189067	−	0.981964i	$-0.439454\pi$
$727$	−21.3788	−	21.3788i	−0.792897	−	0.792897i	−0.981964	+	0.189067i	$0.939454\pi$
$728$	8.26180	−	4.29185i	0.306203	−	0.159067i
$729$		−	14.2646i		−	0.528319i
$730$	−8.74018	−	1.67251i	−0.323489	−	0.0619025i
$731$			6.60063i			0.244133i
$732$	−9.00897	−	13.7145i	−0.332981	−	0.506902i
$733$	1.02633	+	1.02633i	0.0379083	+	0.0379083i	0.725807	−	0.687899i	$-0.241467\pi$
$733$	1.02633	+	1.02633i	0.0379083	+	0.0379083i	−0.687899	+	0.725807i	$0.741467\pi$
$734$	21.3077	+	2.18302i	0.786482	+	0.0805766i
$735$	−11.0895	−	13.2081i	−0.409041	−	0.487190i
$736$	−13.9588	+	24.9270i	−0.514528	+	0.918821i
$737$	7.01754	−	7.01754i	0.258495	−	0.258495i
$738$	17.0186	+	20.9038i	0.626464	+	0.769481i
$739$	5.29534			0.194792			0.0973961	−	0.995246i	$-0.468949\pi$
$739$	5.29534			0.194792			0.0973961	+	0.995246i	$0.468949\pi$
$740$	5.85930	+	10.8741i	0.215392	+	0.399738i
$741$	−3.35356			−0.123196
$742$	32.1816	+	39.5284i	1.18142	+	1.45113i
$743$	−32.9662	+	32.9662i	−1.20941	+	1.20941i	−0.238196	+	0.971217i	$0.576556\pi$
$743$	−32.9662	+	32.9662i	−1.20941	+	1.20941i	−0.971217	+	0.238196i	$0.923444\pi$
$744$	−15.0851	+	47.7015i	−0.553045	+	1.74882i
$745$	2.43353	−	27.9083i	0.0891575	−	1.02248i
$746$	25.3655	+	2.59875i	0.928697	+	0.0951469i
$747$	7.92446	+	7.92446i	0.289941	+	0.289941i
$748$	−2.18060	+	1.43242i	−0.0797307	+	0.0523746i
$749$			2.11291i			0.0772042i
$750$	12.9844	−	34.1817i	0.474123	−	1.24814i
$751$			21.6289i			0.789249i	0.918842	+	0.394625i	$0.129125\pi$
$751$			21.6289i			0.789249i	−0.918842	+	0.394625i	$0.870875\pi$
$752$	−17.9499	−	45.3332i	−0.654566	−	1.65313i
$753$	−21.4342	−	21.4342i	−0.781107	−	0.781107i
$754$	−1.42322	+	13.8916i	−0.0518307	+	0.505902i
$755$	−2.25479	+	25.8584i	−0.0820601	+	0.941084i
$756$	−9.49406	−	1.96601i	−0.345295	−	0.0715030i
$757$	18.2612	−	18.2612i	0.663714	−	0.663714i	−0.292539	−	0.956254i	$-0.594500\pi$
$757$	18.2612	−	18.2612i	0.663714	−	0.663714i	0.956254	+	0.292539i	$0.0945002\pi$
$758$	−13.1265	+	10.6868i	−0.476776	+	0.388161i
$759$	11.6793			0.423932
$760$	−3.42325	−	8.27771i	−0.124174	−	0.300264i
$761$	10.6344			0.385497			0.192749	−	0.981248i	$-0.438260\pi$
$761$	10.6344			0.385497			0.192749	+	0.981248i	$0.438260\pi$
$762$	20.6142	−	16.7828i	0.746772	−	0.607976i
$763$	15.4226	−	15.4226i	0.558336	−	0.558336i
$764$	−12.9246	−	2.67641i	−0.467597	−	0.0968290i
$765$	4.40385	+	5.24522i	0.159222	+	0.189641i
$766$	−0.0166631	+	0.162643i	−0.000602062	+	0.00587653i
$767$	−1.81867	−	1.81867i	−0.0656683	−	0.0656683i
$768$	−36.9828	−	1.16047i	−1.33450	−	0.0418748i
$769$		−	23.9199i		−	0.862572i	−0.902215	−	0.431286i	$-0.858060\pi$
$769$		−	23.9199i		−	0.862572i	0.902215	−	0.431286i	$-0.141940\pi$
$770$	1.91072	−	9.98502i	0.0688577	−	0.359835i
$771$		−	67.5657i		−	2.43332i
$772$	−17.0079	+	11.1724i	−0.612126	+	0.402102i
$773$	0.715023	+	0.715023i	0.0257176	+	0.0257176i	0.719849	−	0.694131i	$-0.244211\pi$
$773$	0.715023	+	0.715023i	0.0257176	+	0.0257176i	−0.694131	+	0.719849i	$0.744211\pi$
$774$	16.7138	+	1.71237i	0.600767	+	0.0615498i
$775$	6.61919	−	37.6666i	0.237768	−	1.35303i
$776$	1.18110	+	0.373511i	0.0423992	+	0.0134083i
$777$	14.5200	−	14.5200i	0.520900	−	0.520900i
$778$	11.6817	+	14.3486i	0.418809	+	0.514421i
$779$	−11.4977			−0.411947
$780$	3.03983	−	10.1434i	0.108843	−	0.363191i
$781$	14.9871			0.536280
$782$	5.88244	+	7.22536i	0.210356	+	0.258378i
$783$	10.2830	−	10.2830i	0.367485	−	0.367485i
$784$	5.29790	−	12.2435i	0.189211	−	0.437268i
$785$	6.47664	−	5.43774i	0.231161	−	0.194081i
$786$	58.8665	+	6.03100i	2.09970	+	0.215119i
$787$	−6.63240	−	6.63240i	−0.236420	−	0.236420i	0.578946	−	0.815366i	$-0.303464\pi$
$787$	−6.63240	−	6.63240i	−0.236420	−	0.236420i	−0.815366	+	0.578946i	$0.803464\pi$
$788$	−23.1256	−	35.2044i	−0.823814	−	1.25410i
$789$			19.1733i			0.682587i
$790$	−37.0085	+	25.1197i	−1.31670	+	0.893719i
$791$		−	15.3122i		−	0.544439i
$792$	3.06143	+	5.89324i	0.108783	+	0.209407i
$793$	2.56855	+	2.56855i	0.0912119	+	0.0912119i
$794$	−2.81713	+	27.4971i	−0.0999762	+	0.975834i
$795$	57.7553	+	5.03611i	2.04837	+	0.178613i
$796$	8.45112	−	40.8114i	0.299542	−	1.44652i
$797$	2.54383	−	2.54383i	0.0901071	−	0.0901071i	−0.660616	−	0.750724i	$-0.729705\pi$
$797$	2.54383	−	2.54383i	0.0901071	−	0.0901071i	0.750724	+	0.660616i	$0.229705\pi$
$798$	−11.5480	+	9.40167i	−0.408795	+	0.332815i
$799$	−15.9010			−0.562538
$800$	28.1402	−	2.85085i	0.994907	−	0.100793i
$801$	11.0522			0.390510
$802$	−32.7929	+	26.6979i	−1.15796	+	0.942736i
$803$	−1.98983	+	1.98983i	−0.0702194	+	0.0702194i
$804$	9.30763	−	44.9475i	0.328255	−	1.58518i
$805$	−36.1678	−	3.15374i	−1.27475	−	0.111155i
$806$	1.12878	−	11.0176i	0.0397595	−	0.388080i
$807$	20.9848	+	20.9848i	0.738698	+	0.738698i
$808$	10.8749	+	20.9342i	0.382578	+	0.736462i
$809$		−	6.12905i		−	0.215486i	−0.994179	−	0.107743i	$-0.965638\pi$
$809$		−	6.12905i		−	0.215486i	0.994179	−	0.107743i	$-0.0343624\pi$
$810$	−27.5542	+	18.7026i	−0.968156	+	0.657141i
$811$		−	16.4078i		−	0.576156i	−0.957607	−	0.288078i	$-0.906984\pi$
$811$		−	16.4078i		−	0.576156i	0.957607	−	0.288078i	$-0.0930163\pi$
$812$	34.0441	+	51.8258i	1.19471	+	1.81873i
$813$	−30.5672	−	30.5672i	−1.07204	−	1.07204i
$814$	3.88576	+	0.398104i	0.136196	+	0.0139535i
$815$	12.4539	−	10.4562i	0.436240	−	0.366264i
$816$	−4.79209	+	11.0746i	−0.167757	+	0.387688i
$817$	−5.06745	+	5.06745i	−0.177288	+	0.177288i
$818$	−22.8437	−	28.0588i	−0.798712	−	0.981053i
$819$	−7.72849			−0.270055
$820$	10.4220	−	34.7765i	0.363954	−	1.21445i
$821$	1.10741			0.0386488			0.0193244	−	0.999813i	$-0.493848\pi$
$821$	1.10741			0.0386488			0.0193244	+	0.999813i	$0.493848\pi$
$822$	−18.5528	−	22.7882i	−0.647102	−	0.794831i
$823$	−2.63390	+	2.63390i	−0.0918121	+	0.0918121i	−0.751521	−	0.659709i	$-0.770680\pi$
$823$	−2.63390	+	2.63390i	−0.0918121	+	0.0918121i	0.659709	+	0.751521i	$0.270680\pi$
$824$	34.4936	+	10.9082i	1.20164	+	0.380006i
$825$	−6.63763	−	9.46786i	−0.231093	−	0.329629i
$826$	−11.3612	−	1.16398i	−0.395307	−	0.0405000i
$827$	23.9250	+	23.9250i	0.831955	+	0.831955i	0.987784	−	0.155829i	$-0.0498049\pi$
$827$	23.9250	+	23.9250i	0.831955	+	0.831955i	−0.155829	+	0.987784i	$0.549805\pi$
$828$	19.8218	−	13.0208i	0.688856	−	0.452506i
$829$			7.35056i			0.255296i	0.991820	+	0.127648i	$0.0407427\pi$
$829$			7.35056i			0.255296i	−0.991820	+	0.127648i	$0.959257\pi$
$830$	2.83685	−	14.8248i	0.0984686	−	0.514576i
$831$		−	20.8544i		−	0.723431i
$832$	8.06903	−	1.40857i	0.279743	−	0.0488333i
$833$	−3.07640	−	3.07640i	−0.106591	−	0.106591i
$834$	0.311938	−	3.04472i	0.0108015	−	0.105430i
$835$	−20.7848	−	24.7559i	−0.719289	−	0.856712i
$836$	−2.77380	−	0.574393i	−0.0959340	−	0.0198658i
$837$	−8.15562	+	8.15562i	−0.281900	+	0.281900i
$838$	−5.82488	+	4.74226i	−0.201217	+	0.163819i
$839$	43.5458			1.50337			0.751684	−	0.659523i	$-0.229242\pi$
$839$	43.5458			1.50337			0.751684	+	0.659523i	$0.229242\pi$
$840$	−17.9692	−	43.4509i	−0.619995	−	1.49920i
$841$	−64.0058			−2.20710
$842$	−15.7605	+	12.8312i	−0.543143	+	0.442193i
$843$	27.1423	−	27.1423i	0.934831	−	0.934831i
$844$	−3.42401	−	0.709036i	−0.117859	−	0.0244060i
$845$	2.32152	−	26.6237i	0.0798627	−	0.915884i
$846$	−4.12512	+	40.2639i	−0.141825	+	1.38430i
$847$	−2.27323	−	2.27323i	−0.0781091	−	0.0781091i
$848$	16.5097	+	41.6959i	0.566946	+	1.43184i
$849$			34.6944i			1.19071i
$850$	2.51413	−	8.87496i	0.0862338	−	0.304409i
$851$		−	13.9493i		−	0.478176i
$852$	57.9353	−	38.0574i	1.98483	−	1.30382i
$853$	37.1733	+	37.1733i	1.27279	+	1.27279i	0.944617	+	0.328174i	$0.106433\pi$
$853$	37.1733	+	37.1733i	1.27279	+	1.27279i	0.328174	+	0.944617i	$0.393567\pi$
$854$	16.0457	+	1.64392i	0.549073	+	0.0562537i
$855$	−0.645942	+	7.40782i	−0.0220908	+	0.253342i
$856$	−0.560513	+	1.77244i	−0.0191580	+	0.0605807i
$857$	−12.1732	+	12.1732i	−0.415830	+	0.415830i	−0.883763	−	0.467934i	$-0.844999\pi$
$857$	−12.1732	+	12.1732i	−0.415830	+	0.415830i	0.467934	+	0.883763i	$0.344999\pi$
$858$	−2.11414	−	2.59678i	−0.0721754	−	0.0886526i
$859$	9.73794			0.332254			0.166127	−	0.986104i	$-0.446874\pi$
$859$	9.73794			0.332254			0.166127	+	0.986104i	$0.446874\pi$
$860$	−10.7339	−	19.9207i	−0.366024	−	0.679290i
$861$	−60.3529			−2.05682
$862$	34.2656	+	42.0882i	1.16709	+	1.43353i
$863$	−9.20125	+	9.20125i	−0.313214	+	0.313214i	−0.846154	−	0.532939i	$-0.821087\pi$
$863$	−9.20125	+	9.20125i	−0.313214	+	0.313214i	0.532939	+	0.846154i	$0.321087\pi$
$864$	−7.44263	−	4.16778i	−0.253203	−	0.141791i
$865$	27.3449	+	32.5693i	0.929754	+	1.10739i
$866$	12.7001	+	1.30115i	0.431565	+	0.0442148i
$867$	−25.0162	−	25.0162i	−0.849594	−	0.849594i
$868$	−27.0009	−	41.1038i	−0.916469	−	1.39515i
$869$			14.1444i			0.479815i
$870$	69.2690	+	13.2552i	2.34844	+	0.449395i
$871$			10.1613i			0.344303i
$872$	17.0287	−	8.84609i	0.576665	−	0.299566i
$873$	−0.727132	−	0.727132i	−0.0246097	−	0.0246097i
$874$	−1.03099	+	10.0632i	−0.0348738	+	0.340392i
$875$	17.9984	+	31.1119i	0.608459	+	1.05177i
$876$	−2.63918	+	12.7449i	−0.0891696	+	0.430610i
$877$	17.7574	−	17.7574i	0.599624	−	0.599624i	−0.340588	−	0.940213i	$-0.610626\pi$
$877$	17.7574	−	17.7574i	0.599624	−	0.599624i	0.940213	+	0.340588i	$0.110626\pi$
$878$	17.9194	−	14.5888i	0.604749	−	0.492349i
$879$	50.2303			1.69422
$880$	4.25165	−	7.86915i	0.143323	−	0.265269i
$881$	27.2559			0.918274			0.459137	−	0.888365i	$-0.348159\pi$
$881$	27.2559			0.918274			0.459137	+	0.888365i	$0.348159\pi$
$882$	−8.58804	+	6.99185i	−0.289175	+	0.235428i
$883$	8.06986	−	8.06986i	0.271573	−	0.271573i	−0.558160	−	0.829733i	$-0.688493\pi$
$883$	8.06986	−	8.06986i	0.271573	−	0.271573i	0.829733	+	0.558160i	$0.188493\pi$
$884$	0.541675	−	2.61581i	0.0182185	−	0.0879791i
$885$	−9.94823	+	8.35245i	−0.334406	+	0.280765i
$886$	1.40086	−	13.6734i	0.0470629	−	0.459366i
$887$	−0.528230	−	0.528230i	−0.0177362	−	0.0177362i	0.698183	−	0.715919i	$-0.253992\pi$
$887$	−0.528230	−	0.528230i	−0.0177362	−	0.0177362i	−0.715919	+	0.698183i	$0.753992\pi$
$888$	16.0320	−	8.32834i	0.538000	−	0.279481i
$889$			26.1299i			0.876370i
$890$	−8.35975	−	12.3163i	−0.280219	−	0.412843i
$891$			10.5310i			0.352802i
$892$	6.23306	+	9.48868i	0.208698	+	0.317705i
$893$	−12.2076	−	12.2076i	−0.408511	−	0.408511i
$894$	−40.7599	−	4.17594i	−1.36322	−	0.139664i
$895$	−11.3171	−	0.986823i	−0.378290	−	0.0329859i
$896$	23.8369	−	27.4719i	0.796334	−	0.917770i
$897$	−8.45574	+	8.45574i	−0.282329	+	0.282329i
$898$	−3.96558	−	4.87090i	−0.132333	−	0.162544i
$899$	73.7643			2.46018
$900$	−21.8206	−	8.66856i	−0.727353	−	0.288952i
$901$	14.6252			0.487236
$902$	−7.24831	−	8.90305i	−0.241342	−	0.296439i
$903$	−26.5998	+	26.5998i	−0.885186	+	0.885186i
$904$	4.06202	−	12.8448i	0.135101	−	0.427211i
$905$	−21.6015	−	1.88359i	−0.718058	−	0.0626128i
$906$	37.7661	+	3.86922i	1.25470	+	0.128546i
$907$	−1.27942	−	1.27942i	−0.0424825	−	0.0424825i	0.685546	−	0.728029i	$-0.259563\pi$
$907$	−1.27942	−	1.27942i	−0.0424825	−	0.0424825i	−0.728029	+	0.685546i	$0.759563\pi$
$908$	−17.3532	+	11.3992i	−0.575886	+	0.378296i
$909$		−	19.5828i		−	0.649522i
$910$	5.84574	+	8.61244i	0.193784	+	0.285499i
$911$		−	39.0054i		−	1.29231i	−0.763208	−	0.646153i	$-0.776377\pi$
$911$		−	39.0054i		−	1.29231i	0.763208	−	0.646153i	$-0.223623\pi$
$912$	−12.1812	+	4.82322i	−0.403360	+	0.159713i
$913$	−3.37507	−	3.37507i	−0.111698	−	0.111698i
$914$	2.41615	−	23.5832i	0.0799191	−	0.780064i
$915$	14.0501	−	11.7964i	0.464483	−	0.389976i
$916$	−3.76138	−	0.778898i	−0.124280	−	0.0257355i
$917$	−41.1312	+	41.1312i	−1.35827	+	1.35827i
$918$	−2.15733	+	1.75636i	−0.0712025	+	0.0579687i
$919$	−44.5397			−1.46923			−0.734615	−	0.678484i	$-0.762637\pi$
$919$	−44.5397			−1.46923			−0.734615	+	0.678484i	$0.762637\pi$
$920$	−29.5031	−	12.2401i	−0.972688	−	0.403545i
$921$	3.19168			0.105169
$922$	28.0642	−	22.8481i	0.924245	−	0.752463i
$923$	−10.8506	+	10.8506i	−0.357150	+	0.357150i
$924$	−14.5601	−	3.01507i	−0.478992	−	0.0991885i
$925$	−11.3080	+	7.92772i	−0.371806	+	0.260662i
$926$	−3.34875	+	32.6860i	−0.110047	+	1.07413i
$927$	−21.2355	−	21.2355i	−0.697467	−	0.697467i
$928$	14.8098	+	52.5058i	0.486157	+	1.72359i
$929$		−	38.4798i		−	1.26248i	−0.775587	−	0.631241i	$-0.782546\pi$
$929$		−	38.4798i		−	1.26248i	0.775587	−	0.631241i	$-0.217454\pi$
$930$	−54.9383	−	10.5129i	−1.80150	−	0.344733i
$931$		−	4.72365i		−	0.154811i
$932$	−37.0996	+	24.3705i	−1.21524	+	0.798283i
$933$	8.68715	+	8.68715i	0.284404	+	0.284404i
$934$	−38.8635	−	3.98165i	−1.27165	−	0.130283i
$935$	−1.87562	−	2.23397i	−0.0613394	−	0.0730586i
$936$	−6.48311	−	2.05021i	−0.211907	−	0.0670133i
$937$	−12.6310	+	12.6310i	−0.412637	+	0.412637i	−0.882656	−	0.470019i	$-0.844247\pi$
$937$	−12.6310	+	12.6310i	−0.412637	+	0.412637i	0.470019	+	0.882656i	$0.344247\pi$
$938$	28.4871	+	34.9905i	0.930138	+	1.14248i
$939$	−13.2885			−0.433655
$940$	47.9893	−	25.8582i	1.56524	−	0.843402i
$941$	−0.184281			−0.00600739			−0.00300370	−	0.999995i	$-0.500956\pi$
$941$	−0.184281			−0.00600739			−0.00300370	+	0.999995i	$0.500956\pi$
$942$	−7.80908	−	9.59184i	−0.254434	−	0.312519i
$943$	−28.9905	+	28.9905i	−0.944060	+	0.944060i
$944$	−9.22167	−	3.99031i	−0.300140	−	0.129874i
$945$	0.941636	−	10.7989i	0.0306314	−	0.351288i
$946$	−7.11851	−	0.729306i	−0.231443	−	0.0237118i
$947$	−29.9611	−	29.9611i	−0.973605	−	0.973605i	0.0260556	−	0.999660i	$-0.491705\pi$
$947$	−29.9611	−	29.9611i	−0.973605	−	0.973605i	−0.999660	+	0.0260556i	$0.991705\pi$
$948$	35.9174	+	54.6776i	1.16654	+	1.77585i
$949$		−	2.88124i		−	0.0935290i
$950$	8.74367	−	4.88336i	0.283682	−	0.158437i
$951$		−	22.9417i		−	0.743937i
$952$	−5.46813	−	10.5261i	−0.177223	−	0.341154i
$953$	25.4062	+	25.4062i	0.822988	+	0.822988i	0.986535	−	0.163548i	$-0.0522938\pi$
$953$	25.4062	+	25.4062i	0.822988	+	0.822988i	−0.163548	+	0.986535i	$0.552294\pi$
$954$	3.79414	−	37.0334i	0.122840	−	1.19900i
$955$	1.28189	−	14.7010i	0.0414809	−	0.475713i
$956$	−9.94429	+	48.0220i	−0.321621	+	1.55314i
$957$	15.7701	−	15.7701i	0.509774	−	0.509774i
$958$	−1.30978	+	1.06634i	−0.0423171	+	0.0344520i
$959$	28.8857			0.932769
$960$	−3.54694	−	41.2160i	−0.114477	−	1.33024i
$961$	−27.5036			−0.887212
$962$	−3.10149	+	2.52504i	−0.0999960	+	0.0814106i
$963$	1.09118	−	1.09118i	0.0351627	−	0.0351627i
$964$	2.23950	−	10.8148i	0.0721293	−	0.348320i
$965$	−14.6291	−	17.4241i	−0.470929	−	0.560902i
$966$	−5.41182	+	52.8230i	−0.174123	+	1.69955i
$967$	−14.3306	−	14.3306i	−0.460842	−	0.460842i	0.438089	−	0.898931i	$-0.355655\pi$
$967$	−14.3306	−	14.3306i	−0.460842	−	0.460842i	−0.898931	+	0.438089i	$0.855655\pi$
$968$	−1.30388	−	2.50996i	−0.0419082	−	0.0806732i
$969$			4.27267i			0.137258i
$970$	−0.260304	+	1.36029i	−0.00835785	+	0.0436763i
$971$		−	27.6798i		−	0.888287i	−0.895956	−	0.444143i	$-0.853508\pi$
$971$		−	27.6798i		−	0.888287i	0.895956	−	0.444143i	$-0.146492\pi$
$972$	21.7744	+	33.1475i	0.698415	+	1.06321i
$973$	2.12740	+	2.12740i	0.0682014	+	0.0682014i
$974$	−6.45065	−	0.660882i	−0.206692	−	0.0211760i
$975$	11.6603	+	2.04907i	0.373427	+	0.0656227i
$976$	13.0240	+	5.63562i	0.416888	+	0.180392i
$977$	−10.8893	+	10.8893i	−0.348381	+	0.348381i	−0.859506	−	0.511125i	$-0.829229\pi$
$977$	−10.8893	+	10.8893i	−0.348381	+	0.348381i	0.511125	+	0.859506i	$0.329229\pi$
$978$	−15.0160	−	18.4441i	−0.480159	−	0.589776i
$979$	−4.70719			−0.150443
$980$	14.2874	+	4.28175i	0.456395	+	0.136775i
$981$	−15.9295			−0.508589
$982$	−10.3691	−	12.7363i	−0.330891	−	0.406431i
$983$	1.95471	−	1.95471i	0.0623455	−	0.0623455i	−0.675247	−	0.737592i	$-0.735963\pi$
$983$	1.95471	−	1.95471i	0.0623455	−	0.0623455i	0.737592	+	0.675247i	$0.235963\pi$
$984$	−50.6276	−	16.0104i	−1.61395	−	0.510393i
$985$	36.0660	−	30.2807i	1.14916	−	0.964823i
$986$	17.6989	+	1.81329i	0.563648	+	0.0577468i
$987$	−64.0794	−	64.0794i	−2.03967	−	2.03967i
$988$	2.42407	−	1.59236i	0.0771200	−	0.0506597i
$989$			25.5544i			0.812583i
$990$	−6.14335	+	4.16983i	−0.195248	+	0.132526i
$991$			0.700492i			0.0222519i	0.999938	+	0.0111259i	$0.00354157\pi$
$991$			0.700492i			0.0222519i	−0.999938	+	0.0111259i	$0.996458\pi$
$992$	−11.7459	−	41.6431i	−0.372933	−	1.32217i
$993$	−40.8834	−	40.8834i	−1.29740	−	1.29740i
$994$	−6.94455	+	67.7834i	−0.220268	+	2.14996i
$995$	46.4204	+	4.04774i	1.47163	+	0.128322i
$996$	−21.6174	−	4.47648i	−0.684974	−	0.141843i
$997$	4.80082	−	4.80082i	0.152044	−	0.152044i	−0.626987	−	0.779030i	$-0.715712\pi$
$997$	4.80082	−	4.80082i	0.152044	−	0.152044i	0.779030	+	0.626987i	$0.215712\pi$
$998$	18.1515	−	14.7778i	0.574577	−	0.467785i
$999$	4.16495			0.131773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.d.23.3	yes	28
4.3	odd	2		220.2.l.c.23.5	✓	28
5.2	odd	4		220.2.l.c.67.5	yes	28
20.7	even	4	inner	220.2.l.d.67.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.5	✓	28	4.3	odd	2
220.2.l.c.67.5	yes	28	5.2	odd	4
220.2.l.d.23.3	yes	28	1.1	even	1	trivial
220.2.l.d.67.3	yes	28	20.7	even	4	inner

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09671 + 0.892874i) q^{2} +(-1.63523 + 1.63523i) q^{3} +(0.405551 - 1.95845i) q^{4} +(2.22762 + 0.194242i) q^{5} +(0.333320 - 3.25343i) q^{6} +(2.27323 + 2.27323i) q^{7} +(1.30388 + 2.50996i) q^{8} -2.34794i q^{9} +(-2.61648 + 1.77595i) q^{10} +1.00000i q^{11} +(2.53934 + 3.86568i) q^{12} +(-0.723993 - 0.723993i) q^{13} +(-4.52278 - 0.463369i) q^{14} +(-3.96029 + 3.32503i) q^{15} +(-3.67106 - 1.58850i) q^{16} +(-0.922419 + 0.922419i) q^{17} +(2.09641 + 2.57501i) q^{18} -1.41633 q^{19} +(1.28383 - 4.28390i) q^{20} -7.43450 q^{21} +(-0.892874 - 1.09671i) q^{22} +(-3.57116 + 3.57116i) q^{23} +(-6.23649 - 1.97222i) q^{24} +(4.92454 + 0.865394i) q^{25} +(1.44045 + 0.147577i) q^{26} +(-1.06627 - 1.06627i) q^{27} +(5.37392 - 3.53010i) q^{28} +9.64395i q^{29} +(1.37446 - 7.18264i) q^{30} -7.64876i q^{31} +(5.44442 - 1.53566i) q^{32} +(-1.63523 - 1.63523i) q^{33} +(0.188023 - 1.83523i) q^{34} +(4.62232 + 5.50544i) q^{35} +(-4.59832 - 0.952210i) q^{36} +(-1.95305 + 1.95305i) q^{37} +(1.55330 - 1.26460i) q^{38} +2.36779 q^{39} +(2.41700 + 5.84450i) q^{40} +8.11796 q^{41} +(8.15350 - 6.63807i) q^{42} +(3.57789 - 3.57789i) q^{43} +(1.95845 + 0.405551i) q^{44} +(0.456069 - 5.23031i) q^{45} +(0.727934 - 7.10512i) q^{46} +(8.61919 + 8.61919i) q^{47} +(8.60058 - 3.40545i) q^{48} +3.33515i q^{49} +(-6.17349 + 3.44791i) q^{50} -3.01673i q^{51} +(-1.71152 + 1.12429i) q^{52} +(-7.92764 - 7.92764i) q^{53} +(2.12143 + 0.217345i) q^{54} +(-0.194242 + 2.22762i) q^{55} +(-2.74171 + 8.66973i) q^{56} +(2.31601 - 2.31601i) q^{57} +(-8.61084 - 10.5766i) q^{58} +2.51199 q^{59} +(4.90580 + 9.10450i) q^{60} -3.54775 q^{61} +(6.82938 + 8.38848i) q^{62} +(5.33741 - 5.33741i) q^{63} +(-4.59981 + 6.54536i) q^{64} +(-1.47215 - 1.75341i) q^{65} +(3.25343 + 0.333320i) q^{66} +(-7.01754 - 7.01754i) q^{67} +(1.43242 + 2.18060i) q^{68} -11.6793i q^{69} +(-9.98502 - 1.91072i) q^{70} -14.9871i q^{71} +(5.89324 - 3.06143i) q^{72} +(1.98983 + 1.98983i) q^{73} +(0.398104 - 3.88576i) q^{74} +(-9.46786 + 6.63763i) q^{75} +(-0.574393 + 2.77380i) q^{76} +(-2.27323 + 2.27323i) q^{77} +(-2.59678 + 2.11414i) q^{78} +14.1444 q^{79} +(-7.86915 - 4.25165i) q^{80} +10.5310 q^{81} +(-8.90305 + 7.24831i) q^{82} +(-3.37507 + 3.37507i) q^{83} +(-3.01507 + 14.5601i) q^{84} +(-2.23397 + 1.87562i) q^{85} +(-0.729306 + 7.11851i) q^{86} +(-15.7701 - 15.7701i) q^{87} +(-2.50996 + 1.30388i) q^{88} +4.70719i q^{89} +(4.16983 + 6.14335i) q^{90} -3.29161i q^{91} +(5.54565 + 8.44222i) q^{92} +(12.5075 + 12.5075i) q^{93} +(-17.1486 - 1.75691i) q^{94} +(-3.15503 - 0.275110i) q^{95} +(-6.39172 + 11.4140i) q^{96} +(0.309689 - 0.309689i) q^{97} +(-2.97787 - 3.65769i) q^{98} +2.34794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * q^18 - 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 + 8 * q^23 - 28 * q^24 - 4 * q^25 + 4 * q^26 - 44 * q^27 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * q^98 + 20 * q^99

Introduction

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