LMFDB - Embedded newform 600.2.bm.a.61.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(61,600)] 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("600.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bm (of order $10$, degree $4$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	600.61
Dual form			600.2.bm.a.541.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37700 - 0.322293i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(1.79225 + 0.887595i) q^{4} +(-2.23466 + 0.0794374i) q^{5} +(1.21001 + 0.732035i) q^{6} -4.30924 q^{7} +(-2.18187 - 1.79985i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.10272 + 0.610829i) q^{10} +(-3.04623 - 4.19278i) q^{11} +(-1.43025 - 1.39799i) q^{12} +(1.45885 - 2.00793i) q^{13} +(5.93382 + 1.38884i) q^{14} +(2.14983 + 0.614997i) q^{15} +(2.42435 + 3.18159i) q^{16} +(1.48875 + 4.58190i) q^{17} +(-0.924577 - 1.07012i) q^{18} +(4.61750 - 1.50032i) q^{19} +(-4.07558 - 1.84110i) q^{20} +(4.09833 + 1.33163i) q^{21} +(2.84335 + 6.75523i) q^{22} +(-2.74867 + 1.99703i) q^{23} +(1.51889 + 2.38599i) q^{24} +(4.98738 - 0.355031i) q^{25} +(-2.65598 + 2.29475i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-7.72325 - 3.82486i) q^{28} +(-1.28057 - 0.416081i) q^{29} +(-2.76211 - 1.53973i) q^{30} +(2.77186 + 8.53091i) q^{31} +(-2.31292 - 5.16240i) q^{32} +(1.60150 + 4.92891i) q^{33} +(-0.573292 - 6.78908i) q^{34} +(9.62967 - 0.342315i) q^{35} +(0.928249 + 1.77154i) q^{36} +(-4.91725 + 6.76801i) q^{37} +(-6.84183 + 0.577746i) q^{38} +(-2.00793 + 1.45885i) q^{39} +(5.01870 + 3.84872i) q^{40} +(1.81673 + 1.31993i) q^{41} +(-5.21422 - 3.15451i) q^{42} +3.51118i q^{43} +(-1.73813 - 10.2183i) q^{44} +(-1.85457 - 1.24923i) q^{45} +(4.42854 - 1.86403i) q^{46} +(3.75423 - 11.5543i) q^{47} +(-1.32253 - 3.77504i) q^{48} +11.5695 q^{49} +(-6.98204 - 1.11852i) q^{50} -4.81769i q^{51} +(4.39686 - 2.30386i) q^{52} +(8.65798 + 2.81315i) q^{53} +(0.548639 + 1.30346i) q^{54} +(7.14034 + 9.12743i) q^{55} +(9.40219 + 7.75598i) q^{56} -4.85512 q^{57} +(1.62924 + 0.985662i) q^{58} +(-3.40084 + 4.68086i) q^{59} +(3.30718 + 3.01041i) q^{60} +(-0.798686 - 1.09930i) q^{61} +(-1.06740 - 12.6404i) q^{62} +(-3.48625 - 2.53291i) q^{63} +(1.52109 + 7.85406i) q^{64} +(-3.10052 + 4.60293i) q^{65} +(-0.616710 - 7.30325i) q^{66} +(4.43612 - 1.44138i) q^{67} +(-1.39865 + 9.53333i) q^{68} +(3.23126 - 1.04990i) q^{69} +(-13.3704 - 2.63221i) q^{70} +(-1.10154 + 3.39020i) q^{71} +(-0.707243 - 2.73858i) q^{72} +(0.609838 - 0.443073i) q^{73} +(8.95233 - 7.73475i) q^{74} +(-4.85299 - 1.20353i) q^{75} +(9.60740 + 1.40952i) q^{76} +(13.1269 + 18.0677i) q^{77} +(3.23510 - 1.36169i) q^{78} +(2.03296 - 6.25680i) q^{79} +(-5.67033 - 6.91718i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-2.07623 - 2.40307i) q^{82} +(3.72222 - 1.20942i) q^{83} +(6.16330 + 6.02427i) q^{84} +(-3.69082 - 10.1207i) q^{85} +(1.13163 - 4.83490i) q^{86} +(1.08932 + 0.791434i) q^{87} +(-0.899895 + 14.6308i) q^{88} +(1.48256 - 1.07714i) q^{89} +(2.15112 + 2.31791i) q^{90} +(-6.28653 + 8.65267i) q^{91} +(-6.69887 + 1.13947i) q^{92} -8.96992i q^{93} +(-8.89345 + 14.7003i) q^{94} +(-10.1993 + 3.71949i) q^{95} +(0.604451 + 5.62447i) q^{96} +(4.18100 - 12.8678i) q^{97} +(-15.9312 - 3.72878i) q^{98} -5.18256i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) $ 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.37700	−	0.322293i	−0.973686	−	0.227896i
$2$	−1.37700	−	0.322293i	−0.973686	−	0.227896i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	1.79225	+	0.887595i	0.896127	+	0.443797i
$5$	−2.23466	+	0.0794374i	−0.999369	+	0.0355255i
$5$	−2.23466	+	0.0794374i	−0.999369	+	0.0355255i
$6$	1.21001	+	0.732035i	0.493985	+	0.298852i
$7$	−4.30924			−1.62874			−0.814370	−	0.580347i	$-0.802917\pi$
$7$	−4.30924			−1.62874			−0.814370	+	0.580347i	$0.802917\pi$
$8$	−2.18187	−	1.79985i	−0.771406	−	0.636343i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	3.10272	+	0.610829i	0.981167	+	0.193161i
$11$	−3.04623	−	4.19278i	−0.918473	−	1.26417i	−0.964189	−	0.265216i	$-0.914557\pi$
$11$	−3.04623	−	4.19278i	−0.918473	−	1.26417i	0.0457158	−	0.998954i	$-0.485443\pi$
$12$	−1.43025	−	1.39799i	−0.412879	−	0.403565i
$13$	1.45885	−	2.00793i	0.404612	−	0.556901i	−0.557282	−	0.830323i	$-0.688156\pi$
$13$	1.45885	−	2.00793i	0.404612	−	0.556901i	0.961894	+	0.273423i	$0.0881557\pi$
$14$	5.93382	+	1.38884i	1.58588	+	0.371183i
$15$	2.14983	+	0.614997i	0.555084	+	0.158792i
$16$	2.42435	+	3.18159i	0.606088	+	0.795398i
$17$	1.48875	+	4.58190i	0.361075	+	1.11127i	0.952403	+	0.304842i	$0.0986038\pi$
$17$	1.48875	+	4.58190i	0.361075	+	1.11127i	−0.591328	+	0.806431i	$0.701396\pi$
$18$	−0.924577	−	1.07012i	−0.217925	−	0.252230i
$19$	4.61750	−	1.50032i	1.05933	−	0.344196i	0.273004	−	0.962013i	$-0.411983\pi$
$19$	4.61750	−	1.50032i	1.05933	−	0.344196i	0.786322	+	0.617817i	$0.211983\pi$
$20$	−4.07558	−	1.84110i	−0.911328	−	0.411682i
$21$	4.09833	+	1.33163i	0.894329	+	0.290585i
$22$	2.84335	+	6.75523i	0.606205	+	1.44022i
$23$	−2.74867	+	1.99703i	−0.573137	+	0.416409i	−0.836244	−	0.548358i	$-0.815253\pi$
$23$	−2.74867	+	1.99703i	−0.573137	+	0.416409i	0.263106	+	0.964767i	$0.415253\pi$
$24$	1.51889	+	2.38599i	0.310043	+	0.487039i
$25$	4.98738	−	0.355031i	0.997476	−	0.0710061i
$26$	−2.65598	+	2.29475i	−0.520880	+	0.450037i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−7.72325	−	3.82486i	−1.45956	−	0.722830i
$29$	−1.28057	−	0.416081i	−0.237795	−	0.0772644i	0.187695	−	0.982227i	$-0.439898\pi$
$29$	−1.28057	−	0.416081i	−0.237795	−	0.0772644i	−0.425490	+	0.904963i	$0.639898\pi$
$30$	−2.76211	−	1.53973i	−0.504290	−	0.281114i
$31$	2.77186	+	8.53091i	0.497841	+	1.53220i	0.812483	+	0.582985i	$0.198116\pi$
$31$	2.77186	+	8.53091i	0.497841	+	1.53220i	−0.314642	+	0.949210i	$0.601884\pi$
$32$	−2.31292	−	5.16240i	−0.408871	−	0.912592i
$33$	1.60150	+	4.92891i	0.278785	+	0.858012i
$34$	−0.573292	−	6.78908i	−0.0983187	−	1.16432i
$35$	9.62967	−	0.342315i	1.62771	−	0.0578617i
$36$	0.928249	+	1.77154i	0.154708	+	0.295257i
$37$	−4.91725	+	6.76801i	−0.808390	+	1.11265i	0.183179	+	0.983079i	$0.441361\pi$
$37$	−4.91725	+	6.76801i	−0.808390	+	1.11265i	−0.991570	+	0.129574i	$0.958639\pi$
$38$	−6.84183	+	0.577746i	−1.10989	+	0.0937228i
$39$	−2.00793	+	1.45885i	−0.321527	+	0.233603i
$40$	5.01870	+	3.84872i	0.793526	+	0.608536i
$41$	1.81673	+	1.31993i	0.283726	+	0.206139i	0.720541	−	0.693412i	$-0.243894\pi$
$41$	1.81673	+	1.31993i	0.283726	+	0.206139i	−0.436815	+	0.899551i	$0.643894\pi$
$42$	−5.21422	−	3.15451i	−0.804572	−	0.486752i
$43$			3.51118i			0.535450i	0.963495	+	0.267725i	$0.0862719\pi$
$43$			3.51118i			0.535450i	−0.963495	+	0.267725i	$0.913728\pi$
$44$	−1.73813	−	10.2183i	−0.262033	−	1.54047i
$45$	−1.85457	−	1.24923i	−0.276463	−	0.186225i
$46$	4.42854	−	1.86403i	0.652953	−	0.274836i
$47$	3.75423	−	11.5543i	0.547610	−	1.68537i	−0.167091	−	0.985942i	$-0.553437\pi$
$47$	3.75423	−	11.5543i	0.547610	−	1.68537i	0.714701	−	0.699430i	$-0.246563\pi$
$48$	−1.32253	−	3.77504i	−0.190891	−	0.544880i
$49$	11.5695			1.65279
$50$	−6.98204	−	1.11852i	−0.987410	−	0.158183i
$51$		−	4.81769i		−	0.674612i
$52$	4.39686	−	2.30386i	0.609735	−	0.319488i
$53$	8.65798	+	2.81315i	1.18926	+	0.386416i	0.835801	−	0.549033i	$-0.185004\pi$
$53$	8.65798	+	2.81315i	1.18926	+	0.386416i	0.353464	+	0.935448i	$0.385004\pi$
$54$	0.548639	+	1.30346i	0.0746603	+	0.177378i
$55$	7.14034	+	9.12743i	0.962804	+	1.23074i
$56$	9.40219	+	7.75598i	1.25642	+	1.03644i
$57$	−4.85512			−0.643077
$58$	1.62924	+	0.985662i	0.213930	+	0.129424i
$59$	−3.40084	+	4.68086i	−0.442752	+	0.609396i	−0.970821	−	0.239806i	$-0.922916\pi$
$59$	−3.40084	+	4.68086i	−0.442752	+	0.609396i	0.528069	+	0.849201i	$0.322916\pi$
$60$	3.30718	+	3.01041i	0.426955	+	0.388643i
$61$	−0.798686	−	1.09930i	−0.102261	−	0.140751i	0.754820	−	0.655932i	$-0.227724\pi$
$61$	−0.798686	−	1.09930i	−0.102261	−	0.140751i	−0.857081	+	0.515182i	$0.827724\pi$
$62$	−1.06740	−	12.6404i	−0.135559	−	1.60533i
$63$	−3.48625	−	2.53291i	−0.439226	−	0.319116i
$64$	1.52109	+	7.85406i	0.190136	+	0.981758i
$65$	−3.10052	+	4.60293i	−0.384573	+	0.570923i
$66$	−0.616710	−	7.30325i	−0.0759117	−	0.898968i
$67$	4.43612	−	1.44138i	0.541958	−	0.176093i	−0.0252291	−	0.999682i	$-0.508032\pi$
$67$	4.43612	−	1.44138i	0.541958	−	0.176093i	0.567187	+	0.823589i	$0.308032\pi$
$68$	−1.39865	+	9.53333i	−0.169612	+	1.15609i
$69$	3.23126	−	1.04990i	0.388997	−	0.126393i
$70$	−13.3704	−	2.63221i	−1.59807	−	0.314609i
$71$	−1.10154	+	3.39020i	−0.130729	+	0.402343i	−0.994901	−	0.100853i	$-0.967843\pi$
$71$	−1.10154	+	3.39020i	−0.130729	+	0.402343i	0.864172	+	0.503196i	$0.167843\pi$
$72$	−0.707243	−	2.73858i	−0.0833494	−	0.322744i
$73$	0.609838	−	0.443073i	0.0713761	−	0.0518578i	−0.551525	−	0.834158i	$-0.685954\pi$
$73$	0.609838	−	0.443073i	0.0713761	−	0.0518578i	0.622901	+	0.782301i	$0.285954\pi$
$74$	8.95233	−	7.73475i	1.04069	−	0.899146i
$75$	−4.85299	−	1.20353i	−0.560375	−	0.138972i
$76$	9.60740	+	1.40952i	1.10204	+	0.161683i
$77$	13.1269	+	18.0677i	1.49595	+	2.05900i
$78$	3.23510	−	1.36169i	0.366303	−	0.154181i
$79$	2.03296	−	6.25680i	0.228726	−	0.703945i	−0.769166	−	0.639049i	$-0.779328\pi$
$79$	2.03296	−	6.25680i	0.228726	−	0.703945i	0.997892	−	0.0648965i	$-0.0206717\pi$
$80$	−5.67033	−	6.91718i	−0.633962	−	0.773364i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−2.07623	−	2.40307i	−0.229282	−	0.265374i
$83$	3.72222	−	1.20942i	0.408566	−	0.132751i	−0.0975211	−	0.995233i	$-0.531091\pi$
$83$	3.72222	−	1.20942i	0.408566	−	0.132751i	0.506087	+	0.862482i	$0.331091\pi$
$84$	6.16330	+	6.02427i	0.672471	+	0.657302i
$85$	−3.69082	−	10.1207i	−0.400325	−	1.09774i
$86$	1.13163	−	4.83490i	0.122027	−	0.521360i
$87$	1.08932	+	0.791434i	0.116787	+	0.0848506i
$88$	−0.899895	+	14.6308i	−0.0959292	+	1.55965i
$89$	1.48256	−	1.07714i	0.157151	−	0.114177i	−0.506431	−	0.862281i	$-0.669035\pi$
$89$	1.48256	−	1.07714i	0.157151	−	0.114177i	0.663582	+	0.748104i	$0.269035\pi$
$90$	2.15112	+	2.31791i	0.226748	+	0.244329i
$91$	−6.28653	+	8.65267i	−0.659008	+	0.907046i
$92$	−6.69887	+	1.13947i	−0.698405	+	0.118798i
$93$		−	8.96992i		−	0.930138i
$94$	−8.89345	+	14.7003i	−0.917289	+	1.51622i
$95$	−10.1993	+	3.71949i	−1.04643	+	0.381612i
$96$	0.604451	+	5.62447i	0.0616915	+	0.574045i
$97$	4.18100	−	12.8678i	0.424517	−	1.30653i	−0.478940	−	0.877848i	$-0.658979\pi$
$97$	4.18100	−	12.8678i	0.424517	−	1.30653i	0.903456	−	0.428680i	$-0.141021\pi$
$98$	−15.9312	−	3.72878i	−1.60930	−	0.376664i
$99$		−	5.18256i		−	0.520867i
$100$	9.25378	+	3.79047i	0.925378	+	0.379047i
$101$			8.87332i			0.882928i	0.897279	+	0.441464i	$0.145541\pi$
$101$			8.87332i			0.882928i	−0.897279	+	0.441464i	$0.854459\pi$
$102$	−1.55271	+	6.63396i	−0.153741	+	0.656860i
$103$	1.35332	−	4.16508i	0.133346	−	0.410398i	−0.861983	−	0.506937i	$-0.830778\pi$
$103$	1.35332	−	4.16508i	0.133346	−	0.410398i	0.995329	+	0.0965398i	$0.0307775\pi$
$104$	−6.79700	+	1.75534i	−0.666500	+	0.172125i
$105$	−9.26414	−	2.65017i	−0.904088	−	0.258630i
$106$	−11.0154	−	6.66411i	−1.06991	−	0.647276i
$107$		−	2.05154i		−	0.198329i	−0.995071	−	0.0991647i	$-0.968383\pi$
$107$		−	2.05154i		−	0.198329i	0.995071	−	0.0991647i	$-0.0316171\pi$
$108$	−0.335381	−	1.97168i	−0.0322721	−	0.189725i
$109$	3.48630	−	4.79848i	0.333927	−	0.459611i	−0.608728	−	0.793379i	$-0.708320\pi$
$109$	3.48630	−	4.79848i	0.333927	−	0.459611i	0.942655	+	0.333768i	$0.108320\pi$
$110$	−6.89054	−	14.8698i	−0.656987	−	1.41778i
$111$	6.76801	−	4.91725i	0.642391	−	0.466724i
$112$	−10.4471	−	13.7102i	−0.987159	−	1.29550i
$113$	11.2593	+	8.18038i	1.05919	+	0.769546i	0.973938	−	0.226814i	$-0.0728309\pi$
$113$	11.2593	+	8.18038i	1.05919	+	0.769546i	0.0852505	+	0.996360i	$0.472831\pi$
$114$	6.68550	+	1.56477i	0.626155	+	0.146554i
$115$	5.98370	−	4.68101i	0.557982	−	0.436507i
$116$	−1.92579	−	1.88235i	−0.178805	−	0.174772i
$117$	2.36047	−	0.766963i	0.218225	−	0.0709057i
$118$	6.19157	−	5.34947i	0.569980	−	0.492459i
$119$	−6.41537	−	19.7445i	−0.588096	−	1.80997i
$120$	−3.58375	−	5.21122i	−0.327150	−	0.475717i
$121$	−4.90067	+	15.0827i	−0.445516	+	1.37116i
$122$	0.745494	+	1.77114i	0.0674939	+	0.160352i
$123$	−1.31993	−	1.81673i	−0.119014	−	0.163809i
$124$	−2.60411	+	17.7498i	−0.233856	+	1.59398i
$125$	−11.1169	+	1.18956i	−0.994324	+	0.106397i
$126$	3.98422	+	4.61141i	0.354943	+	0.410817i
$127$	−2.85729	+	2.07594i	−0.253544	+	0.184210i	−0.707296	−	0.706918i	$-0.750085\pi$
$127$	−2.85729	+	2.07594i	−0.253544	+	0.184210i	0.453752	+	0.891128i	$0.350085\pi$
$128$	0.436775	−	11.3053i	0.0386058	−	0.999255i
$129$	1.08502	−	3.33933i	0.0955303	−	0.294012i
$130$	5.75291	−	5.33896i	0.504564	−	0.468257i
$131$	−15.3484	+	4.98699i	−1.34099	+	0.435715i	−0.889653	−	0.456637i	$-0.849054\pi$
$131$	−15.3484	+	4.98699i	−1.34099	+	0.435715i	−0.451340	+	0.892352i	$0.649054\pi$
$132$	−1.50458	+	10.2553i	−0.130957	+	0.892612i
$133$	−19.8979	+	6.46522i	−1.72537	+	0.560606i
$134$	−6.57308	+	0.555052i	−0.567828	+	0.0479492i
$135$	1.37776	+	1.76118i	0.118579	+	0.151578i
$136$	4.99847	−	12.6766i	0.428615	−	1.08701i
$137$	6.86560	+	4.98815i	0.586568	+	0.426166i	0.841086	−	0.540902i	$-0.181917\pi$
$137$	6.86560	+	4.98815i	0.586568	+	0.426166i	−0.254518	+	0.967068i	$0.581917\pi$
$138$	−4.78781	+	0.404298i	−0.407566	+	0.0344161i
$139$	−11.7349	−	16.1516i	−0.995337	−	1.36996i	−0.928143	−	0.372224i	$-0.878595\pi$
$139$	−11.7349	−	16.1516i	−0.995337	−	1.36996i	−0.0671941	−	0.997740i	$-0.521405\pi$
$140$	17.5627	+	7.93373i	1.48431	+	0.670523i
$141$	−7.14097	+	9.82870i	−0.601378	+	0.827725i
$142$	2.60946	−	4.31329i	0.218981	−	0.361963i
$143$	−12.8628			−1.07564
$144$	0.0912479	+	3.99896i	0.00760399	+	0.333247i
$145$	2.89468	+	0.828074i	0.240390	+	0.0687678i
$146$	−0.982546	+	0.413565i	−0.0813161	+	0.0342269i
$147$	−11.0033	−	3.57518i	−0.907536	−	0.294876i
$148$	−14.8202	+	7.76547i	−1.21821	+	0.638318i
$149$			3.67120i			0.300756i	0.988629	+	0.150378i	$0.0480491\pi$
$149$			3.67120i			0.300756i	−0.988629	+	0.150378i	$0.951951\pi$
$150$	6.29467	+	3.22135i	0.513958	+	0.263022i
$151$	−16.3625			−1.33156			−0.665781	−	0.746148i	$-0.731901\pi$
$151$	−16.3625			−1.33156			−0.665781	+	0.746148i	$0.731901\pi$
$152$	−12.7751	−	5.03731i	−1.03620	−	0.408580i
$153$	−1.48875	+	4.58190i	−0.120358	+	0.370424i
$154$	−12.2527	−	29.1099i	−0.987350	−	2.34574i
$155$	−6.87183	−	18.8435i	−0.551958	−	1.51354i
$156$	−4.89360	+	0.832397i	−0.391801	+	0.0666451i
$157$		−	2.50867i		−	0.200214i	−0.994977	−	0.100107i	$-0.968081\pi$
$157$		−	2.50867i		−	0.200214i	0.994977	−	0.100107i	$-0.0319185\pi$
$158$	−4.81591	+	7.96040i	−0.383133	+	0.633296i
$159$	−7.36492	−	5.35093i	−0.584076	−	0.424356i
$160$	5.57868	+	11.3525i	0.441033	+	0.897491i
$161$	11.8447	−	8.60566i	0.933491	−	0.678221i
$162$	−0.118997	−	1.40920i	−0.00934930	−	0.110717i
$163$	−2.71299	+	3.73411i	−0.212498	+	0.292478i	−0.901939	−	0.431863i	$-0.857856\pi$
$163$	−2.71299	+	3.73411i	−0.212498	+	0.292478i	0.689441	+	0.724342i	$0.257856\pi$
$164$	2.08448	+	3.97818i	0.162771	+	0.310644i
$165$	−3.97034	−	10.8872i	−0.309090	−	0.847567i
$166$	−5.51528	+	0.465727i	−0.428068	+	0.0361475i
$167$	6.79063	+	20.8994i	0.525474	+	1.61724i	0.763376	+	0.645955i	$0.223541\pi$
$167$	6.79063	+	20.8994i	0.525474	+	1.61724i	−0.237901	+	0.971289i	$0.576459\pi$
$168$	−6.54528	−	10.2818i	−0.504979	−	0.793259i
$169$	2.11366	+	6.50518i	0.162589	+	0.500399i
$170$	1.82042	+	15.1257i	0.139620	+	1.16009i
$171$	4.61750	+	1.50032i	0.353109	+	0.114732i
$172$	−3.11651	+	6.29293i	−0.237632	+	0.479832i
$173$	8.49647	+	11.6944i	0.645974	+	0.889108i	0.998917	−	0.0465376i	$-0.0148187\pi$
$173$	8.49647	+	11.6944i	0.645974	+	0.889108i	−0.352942	+	0.935645i	$0.614819\pi$
$174$	−1.24491	−	1.44088i	−0.0943766	−	0.109233i
$175$	−21.4918	+	1.52991i	−1.62463	+	0.115650i
$176$	5.95458	−	19.8566i	0.448843	−	1.49675i
$177$	4.68086	−	3.40084i	0.351835	−	0.255623i
$178$	−2.38864	+	1.00541i	−0.179036	+	0.0753583i
$179$	21.0821	+	6.84998i	1.57575	+	0.511992i	0.960957	−	0.276698i	$-0.0892401\pi$
$179$	21.0821	+	6.84998i	1.57575	+	0.511992i	0.614792	+	0.788690i	$0.289240\pi$
$180$	−2.21504	−	3.88505i	−0.165100	−	0.289574i
$181$	−22.4936	+	7.30863i	−1.67194	+	0.543246i	−0.983321	−	0.181879i	$-0.941782\pi$
$181$	−22.4936	+	7.30863i	−1.67194	+	0.543246i	−0.688618	+	0.725125i	$0.741782\pi$
$182$	11.4452	−	9.88861i	0.848378	−	0.732993i
$183$	0.419894	+	1.29230i	0.0310395	+	0.0955296i
$184$	9.59158	+	0.589947i	0.707100	+	0.0434914i
$185$	10.4507	−	15.5148i	0.768352	−	1.14067i
$186$	−2.89095	+	12.3516i	−0.211974	+	0.905662i
$187$	14.6758	−	20.1995i	1.07320	−	1.47713i
$188$	16.9841	−	17.3761i	1.23869	−	1.26728i
$189$	2.53291	+	3.48625i	0.184242	+	0.253587i
$190$	15.2432	−	1.83456i	1.10586	−	0.133093i
$191$	9.87743	+	7.17637i	0.714706	+	0.519264i	0.884688	−	0.466183i	$-0.154371\pi$
$191$	9.87743	+	7.17637i	0.714706	+	0.519264i	−0.169982	+	0.985447i	$0.554371\pi$
$192$	0.980399	−	7.93970i	0.0707542	−	0.572998i
$193$	10.0475			0.723233			0.361617	−	0.932327i	$-0.382225\pi$
$193$	10.0475			0.723233			0.361617	+	0.932327i	$0.382225\pi$
$194$	−9.90445	+	16.3715i	−0.711098	+	1.17540i
$195$	4.37116	−	3.41953i	0.313025	−	0.244878i
$196$	20.7356	+	10.2691i	1.48111	+	0.733505i
$197$	−9.22644	−	2.99785i	−0.657357	−	0.213588i	−0.0387017	−	0.999251i	$-0.512322\pi$
$197$	−9.22644	−	2.99785i	−0.657357	−	0.213588i	−0.618655	+	0.785663i	$0.712322\pi$
$198$	−1.67030	+	7.13638i	−0.118703	+	0.507160i
$199$	19.3383			1.37085			0.685427	−	0.728141i	$-0.259616\pi$
$199$	19.3383			1.37085			0.685427	+	0.728141i	$0.259616\pi$
$200$	−11.5208	−	8.20190i	−0.814644	−	0.579962i
$201$	−4.66441			−0.329002
$202$	2.85981	−	12.2186i	0.201216	−	0.859694i
$203$	5.51827	+	1.79299i	0.387307	+	0.125844i
$204$	4.27616	−	8.63453i	0.299391	−	0.604538i
$205$	−4.16463	−	2.80528i	−0.290870	−	0.195929i
$206$	−3.20589	+	5.29915i	−0.223365	+	0.369209i
$207$	−3.39754			−0.236146
$208$	9.92519	−	0.226472i	0.688188	−	0.0157030i
$209$	−20.3565	−	14.7898i	−1.40809	−	1.02303i
$210$	11.9026	+	6.63505i	0.821356	+	0.457862i
$211$	7.70558	+	10.6058i	0.530474	+	0.730135i	0.987203	−	0.159471i	$-0.0509789\pi$
$211$	7.70558	+	10.6058i	0.530474	+	0.730135i	−0.456729	+	0.889606i	$0.650979\pi$
$212$	13.0204	+	12.7267i	0.894242	+	0.874070i
$213$	2.09526	−	2.88388i	0.143565	−	0.197600i
$214$	−0.661196	+	2.82496i	−0.0451984	+	0.193111i
$215$	−0.278919	−	7.84629i	−0.0190221	−	0.535112i
$216$	−0.173639	+	2.82309i	−0.0118147	+	0.192087i
$217$	−11.9446	−	36.7617i	−0.810853	−	2.49555i
$218$	−6.34715	+	5.48390i	−0.429883	+	0.371416i
$219$	−0.716907	+	0.232937i	−0.0484441	+	0.0157404i
$220$	4.69585	+	22.6964i	0.316594	+	1.53019i
$221$	11.3720	+	3.69499i	0.764964	+	0.248552i
$222$	−10.9043	+	4.58976i	−0.731851	+	0.308045i
$223$	−20.7917	+	15.1061i	−1.39232	+	1.01158i	−0.396712	+	0.917943i	$0.629849\pi$
$223$	−20.7917	+	15.1061i	−1.39232	+	1.01158i	−0.995607	+	0.0936350i	$0.970151\pi$
$224$	9.96694	+	22.2460i	0.665944	+	1.48637i
$225$	4.24356	+	2.64428i	0.282904	+	0.176285i
$226$	−12.8676	−	14.8932i	−0.855941	−	0.990680i
$227$	3.64347	+	5.01480i	0.241825	+	0.332844i	0.912627	−	0.408792i	$-0.134050\pi$
$227$	3.64347	+	5.01480i	0.241825	+	0.332844i	−0.670802	+	0.741636i	$0.734050\pi$
$228$	−8.70162	−	4.30938i	−0.576279	−	0.285396i
$229$	10.1404	+	3.29483i	0.670099	+	0.217728i	0.624256	−	0.781220i	$-0.285402\pi$
$229$	10.1404	+	3.29483i	0.670099	+	0.217728i	0.0458436	+	0.998949i	$0.485402\pi$
$230$	−9.74820	+	4.51725i	−0.642777	+	0.297859i
$231$	−6.90124	−	21.2398i	−0.454068	−	1.39748i
$232$	2.04514	+	3.21266i	0.134270	+	0.210922i
$233$	0.239404	+	0.736809i	0.0156839	+	0.0482700i	0.958592	−	0.284782i	$-0.0919214\pi$
$233$	0.239404	+	0.736809i	0.0156839	+	0.0482700i	−0.942908	+	0.333052i	$0.891921\pi$
$234$	−3.49755	+	0.295344i	−0.228642	+	0.0193073i
$235$	−7.47156	+	26.1182i	−0.487391	+	1.70376i
$236$	−10.2499	+	5.37072i	−0.667210	+	0.349604i
$237$	−3.86692	+	5.32235i	−0.251183	+	0.345724i
$238$	2.47045	+	29.2558i	0.160136	+	1.89637i
$239$	10.8942	−	7.91509i	0.704687	−	0.511985i	−0.176768	−	0.984252i	$-0.556564\pi$
$239$	10.8942	−	7.91509i	0.704687	−	0.511985i	0.881455	+	0.472268i	$0.156564\pi$
$240$	3.25528	+	8.33086i	0.210127	+	0.537755i
$241$	11.8814	+	8.63234i	0.765348	+	0.556058i	0.900546	−	0.434761i	$-0.143167\pi$
$241$	11.8814	+	8.63234i	0.765348	+	0.556058i	−0.135198	+	0.990819i	$0.543167\pi$
$242$	11.6093	−	19.1894i	0.746273	−	1.23354i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.455718	−	2.67913i	−0.0291743	−	0.171514i
$245$	−25.8539	+	0.919054i	−1.65175	+	0.0587162i
$246$	1.23203	+	2.92705i	0.0785512	+	0.186622i
$247$	3.72370	−	11.4604i	0.236933	−	0.729206i
$248$	9.30651	−	23.6022i	0.590964	−	1.49874i
$249$	−3.91377			−0.248025
$250$	15.6913	+	1.94488i	0.992406	+	0.123005i
$251$			20.0085i			1.26293i	0.775405	+	0.631464i	$0.217546\pi$
$251$			20.0085i			1.26293i	−0.775405	+	0.631464i	$0.782454\pi$
$252$	−4.00005	−	7.63399i	−0.251979	−	0.480896i
$253$	16.7462	+	5.44116i	1.05282	+	0.342083i
$254$	4.60355	−	1.93769i	0.288853	−	0.121581i
$255$	0.382705	+	10.7659i	0.0239659	+	0.674186i
$256$	−4.24505	+	15.4266i	−0.265316	+	0.964162i
$257$	−31.5526			−1.96820			−0.984100	−	0.177618i	$-0.943161\pi$
$257$	−31.5526			−1.96820			−0.984100	+	0.177618i	$0.943161\pi$
$258$	−2.57031	+	4.24857i	−0.160020	+	0.264504i
$259$	21.1896	−	29.1650i	1.31666	−	1.81222i
$260$	−9.64246	+	5.49761i	−0.598000	+	0.340948i
$261$	−0.791434	−	1.08932i	−0.0489885	−	0.0674269i
$262$	22.7420	−	1.92040i	1.40500	−	0.118643i
$263$	3.73610	+	2.71443i	0.230378	+	0.167379i	0.696986	−	0.717085i	$-0.254524\pi$
$263$	3.73610	+	2.71443i	0.230378	+	0.167379i	−0.466608	+	0.884464i	$0.654524\pi$
$264$	5.37703	−	13.6367i	0.330933	−	0.839279i
$265$	−19.5711	−	5.59865i	−1.20224	−	0.343922i
$266$	29.4831	−	2.48964i	1.80772	−	0.152650i
$267$	−1.74285	+	0.566287i	−0.106661	+	0.0346562i
$268$	9.23002	+	1.35415i	0.563813	+	0.0827181i
$269$	5.27092	−	1.71262i	0.321374	−	0.104421i	−0.143888	−	0.989594i	$-0.545960\pi$
$269$	5.27092	−	1.71262i	0.321374	−	0.104421i	0.465261	+	0.885173i	$0.345960\pi$
$270$	−1.32956	−	2.86919i	−0.0809146	−	0.174613i
$271$	0.668140	−	2.05632i	0.0405866	−	0.124913i	−0.928710	−	0.370806i	$-0.879081\pi$
$271$	0.668140	−	2.05632i	0.0405866	−	0.124913i	0.969297	+	0.245894i	$0.0790814\pi$
$272$	−10.9685	+	15.8447i	−0.665062	+	0.960727i
$273$	8.65267	−	6.28653i	0.523683	−	0.380478i
$274$	−7.84628	−	9.08141i	−0.474011	−	0.548628i
$275$	−16.6813	−	19.8295i	−1.00592	−	1.19576i
$276$	6.72312	+	0.986361i	0.404684	+	0.0593720i
$277$	7.96255	+	10.9595i	0.478423	+	0.658493i	0.978201	−	0.207661i	$-0.0665850\pi$
$277$	7.96255	+	10.9595i	0.478423	+	0.658493i	−0.499778	+	0.866154i	$0.666585\pi$
$278$	10.9533	+	26.0229i	0.656936	+	1.56075i
$279$	−2.77186	+	8.53091i	−0.165947	+	0.510732i
$280$	−21.6268	−	16.5851i	−1.29245	−	0.991147i
$281$	−2.06599	−	6.35846i	−0.123247	−	0.379314i	0.870331	−	0.492467i	$-0.163905\pi$
$281$	−2.06599	−	6.35846i	−0.123247	−	0.379314i	−0.993578	+	0.113153i	$0.963905\pi$
$282$	13.0008	−	11.2326i	0.774188	−	0.668893i
$283$	20.0026	−	6.49925i	1.18903	−	0.386340i	0.353318	−	0.935503i	$-0.385053\pi$
$283$	20.0026	−	6.49925i	1.18903	−	0.386340i	0.835715	+	0.549163i	$0.185053\pi$
$284$	−4.98337	+	5.09838i	−0.295709	+	0.302533i
$285$	10.8495	−	0.385678i	0.642671	−	0.0228456i
$286$	17.7121	+	4.14560i	1.04734	+	0.245134i
$287$	−7.82874	−	5.68791i	−0.462116	−	0.335747i
$288$	1.16319	−	5.53597i	0.0685416	−	0.326210i
$289$	−5.02412	+	3.65024i	−0.295536	+	0.214720i
$290$	−3.71909	−	2.07319i	−0.218392	−	0.121742i
$291$	−7.95274	+	10.9460i	−0.466198	+	0.641667i
$292$	1.48625	−	0.252811i	0.0869764	−	0.0147946i
$293$		−	11.2612i		−	0.657887i	−0.944350	−	0.328944i	$-0.893307\pi$
$293$		−	11.2612i		−	0.657887i	0.944350	−	0.328944i	$-0.106693\pi$
$294$	13.9993	+	8.46931i	0.816453	+	0.493940i
$295$	7.22788	−	10.7303i	0.420823	−	0.624740i
$296$	22.9102	−	5.91659i	1.33163	−	0.343895i
$297$	−1.60150	+	4.92891i	−0.0929284	+	0.286004i
$298$	1.18320	−	5.05523i	0.0685410	−	0.292842i
$299$			8.43251i			0.487665i
$300$	−7.62954	−	6.46452i	−0.440492	−	0.373229i
$301$		−	15.1305i		−	0.872109i
$302$	22.5311	+	5.27352i	1.29652	+	0.303457i
$303$	2.74201	−	8.43903i	0.157524	−	0.484809i
$304$	15.9678	+	11.0537i	0.915817	+	0.633973i
$305$	1.87211	+	2.39311i	0.107197	+	0.137029i
$306$	3.52672	−	5.82946i	0.201609	−	0.333248i
$307$			28.9717i			1.65350i	0.562567	+	0.826752i	$0.309814\pi$
$307$			28.9717i			1.65350i	−0.562567	+	0.826752i	$0.690186\pi$
$308$	7.49003	+	44.0333i	0.426784	+	2.50903i
$309$	−2.57416	+	3.54303i	−0.146439	+	0.201556i
$310$	3.38938	+	28.1622i	0.192504	+	1.59950i
$311$	13.5943	−	9.87682i	0.770861	−	0.560063i	−0.131362	−	0.991335i	$-0.541935\pi$
$311$	13.5943	−	9.87682i	0.770861	−	0.560063i	0.902222	+	0.431271i	$0.141935\pi$
$312$	7.00676	+	0.430963i	0.396679	+	0.0243985i
$313$	−7.06662	−	5.13420i	−0.399429	−	0.290202i	0.369879	−	0.929080i	$-0.379399\pi$
$313$	−7.06662	−	5.13420i	−0.399429	−	0.290202i	−0.769308	+	0.638878i	$0.779399\pi$
$314$	−0.808529	+	3.45444i	−0.0456279	+	0.194945i
$315$	7.99177	+	5.38324i	0.450285	+	0.303311i
$316$	9.19708	−	9.40933i	0.517376	−	0.529316i
$317$	12.5669	−	4.08325i	0.705829	−	0.229338i	0.0659608	−	0.997822i	$-0.478989\pi$
$317$	12.5669	−	4.08325i	0.705829	−	0.229338i	0.639869	+	0.768484i	$0.278989\pi$
$318$	8.41692	+	9.74188i	0.471997	+	0.546298i
$319$	2.15637	+	6.63661i	0.120733	+	0.371579i
$320$	−4.02301	−	17.4303i	−0.224893	−	0.974383i
$321$	−0.633959	+	1.95113i	−0.0353842	+	0.108901i
$322$	−19.0837	+	8.03253i	−1.06349	+	0.447635i
$323$	13.7486	+	18.9233i	0.764992	+	1.05292i
$324$	−0.290316	+	1.97882i	−0.0161287	+	0.109934i
$325$	6.56296	−	10.5323i	0.364048	−	0.584225i
$326$	4.93927	−	4.26749i	0.273561	−	0.236355i
$327$	−4.79848	+	3.48630i	−0.265357	+	0.192793i
$328$	−1.58819	−	6.14976i	−0.0876930	−	0.339564i
$329$	−16.1779	+	49.7903i	−0.891915	+	2.74503i
$330$	1.95829	+	16.2713i	0.107800	+	0.895704i
$331$	−31.9463	+	10.3800i	−1.75593	+	0.570536i	−0.996766	−	0.0803645i	$-0.974392\pi$
$331$	−31.9463	+	10.3800i	−1.75593	+	0.570536i	−0.759163	+	0.650900i	$0.774392\pi$
$332$	7.74463	+	1.13623i	0.425042	+	0.0623587i
$333$	−7.95627	+	2.58515i	−0.436001	+	0.141665i
$334$	−2.61495	−	30.9670i	−0.143084	−	1.69444i
$335$	−9.79870	+	3.57339i	−0.535360	+	0.195235i
$336$	5.69909	+	16.2675i	0.310911	+	0.887467i
$337$	14.7946	+	10.7489i	0.805915	+	0.585532i	0.912643	−	0.408756i	$-0.134037\pi$
$337$	14.7946	+	10.7489i	0.805915	+	0.585532i	−0.106728	+	0.994288i	$0.534037\pi$
$338$	−0.813935	−	9.63885i	−0.0442722	−	0.524285i
$339$	−8.18038	−	11.2593i	−0.444297	−	0.611523i
$340$	2.36821	−	21.4148i	0.128434	−	1.16138i
$341$	27.3245	−	37.6089i	1.47970	−	2.03664i
$342$	−5.87475	−	3.55412i	−0.317670	−	0.192185i
$343$	−19.6912			−1.06323
$344$	6.31960	−	7.66093i	0.340730	−	0.413050i
$345$	−7.13735	+	2.60285i	−0.384262	+	0.140132i
$346$	−7.93061	−	18.8415i	−0.426352	−	1.01293i
$347$	25.5635	+	8.30608i	1.37232	+	0.445894i	0.900137	−	0.435607i	$-0.143466\pi$
$347$	25.5635	+	8.30608i	1.37232	+	0.445894i	0.472183	+	0.881501i	$0.343466\pi$
$348$	1.24986	+	2.38532i	0.0669994	+	0.127867i
$349$		−	26.6371i		−	1.42585i	−0.701241	−	0.712925i	$-0.747370\pi$
$349$		−	26.6371i		−	1.42585i	0.701241	−	0.712925i	$-0.252630\pi$
$350$	30.0873	+	4.81998i	1.60823	+	0.257639i
$351$	−2.48194			−0.132476
$352$	−14.5991	+	25.4234i	−0.778135	+	1.35507i
$353$	4.02838	−	12.3981i	0.214409	−	0.659883i	−0.784786	−	0.619767i	$-0.787227\pi$
$353$	4.02838	−	12.3981i	0.214409	−	0.659883i	0.999195	−	0.0401163i	$-0.0127729\pi$
$354$	−7.54161	+	3.17435i	−0.400832	+	0.168715i
$355$	2.19226	−	7.66344i	0.116353	−	0.406733i
$356$	3.61319	−	0.614601i	0.191499	−	0.0325738i
$357$			20.7606i			1.09877i
$358$	−26.8223	−	16.2270i	−1.41760	−	0.857625i
$359$	7.89611	+	5.73686i	0.416741	+	0.302780i	0.776325	−	0.630333i	$-0.217082\pi$
$359$	7.89611	+	5.73686i	0.416741	+	0.302780i	−0.359584	+	0.933113i	$0.617082\pi$
$360$	1.79799	+	6.06360i	0.0947624	+	0.319580i
$361$	3.69901	−	2.68749i	0.194685	−	0.141447i
$362$	33.3292	−	2.81443i	1.75175	−	0.147923i
$363$	9.32163	−	12.8301i	0.489259	−	0.673407i
$364$	−18.9471	+	9.92789i	−0.993100	+	0.520363i
$365$	−1.32758	+	1.03856i	−0.0694888	+	0.0543607i
$366$	−0.161694	−	1.91483i	−0.00845188	−	0.100090i
$367$	2.83251	+	8.71758i	0.147856	+	0.455054i	0.997367	−	0.0725167i	$-0.0231031\pi$
$367$	2.83251	+	8.71758i	0.147856	+	0.455054i	−0.849511	+	0.527570i	$0.823103\pi$
$368$	−13.0175	−	3.90366i	−0.678582	−	0.203492i
$369$	0.693930	+	2.13570i	0.0361246	+	0.111180i
$370$	−19.3909	+	17.9957i	−1.00809	+	0.935550i
$371$	−37.3093	−	12.1225i	−1.93700	−	0.629370i
$372$	7.96166	−	16.0764i	0.412793	−	0.833522i
$373$	−16.7245	−	23.0193i	−0.865962	−	1.19189i	−0.980115	−	0.198431i	$-0.936416\pi$
$373$	−16.7245	−	23.0193i	−0.865962	−	1.19189i	0.114153	−	0.993463i	$-0.463584\pi$
$374$	−26.7187	+	23.0848i	−1.38159	+	1.19369i
$375$	10.9404	+	2.30397i	0.564958	+	0.118976i
$376$	−28.9873	+	18.4530i	−1.49490	+	0.951639i
$377$	−2.70362	+	1.96429i	−0.139243	+	0.101166i
$378$	−2.36422	−	5.61690i	−0.121602	−	0.288902i
$379$	−17.9020	−	5.81672i	−0.919566	−	0.298785i	−0.189277	−	0.981924i	$-0.560614\pi$
$379$	−17.9020	−	5.81672i	−0.919566	−	0.298785i	−0.730289	+	0.683139i	$0.760614\pi$
$380$	−21.5812	−	2.38661i	−1.10709	−	0.122430i
$381$	3.35895	−	1.09139i	0.172084	−	0.0559135i
$382$	−11.2883	−	13.0653i	−0.577561	−	0.668479i
$383$	7.14628	+	21.9940i	0.365158	+	1.12384i	0.949882	+	0.312608i	$0.101203\pi$
$383$	7.14628	+	21.9940i	0.365158	+	1.12384i	−0.584725	+	0.811232i	$0.698797\pi$
$384$	−3.90892	+	10.6170i	−0.199476	+	0.541796i
$385$	−30.7694	−	39.3323i	−1.56816	−	2.00456i
$386$	−13.8354	−	3.23823i	−0.704202	−	0.164822i
$387$	−2.06382	+	2.84061i	−0.104910	+	0.144396i
$388$	18.9148	−	19.3513i	0.960255	−	0.982416i
$389$	15.9812	+	21.9962i	0.810277	+	1.11525i	0.991281	+	0.131768i	$0.0420654\pi$
$389$	15.9812	+	21.9962i	0.810277	+	1.11525i	−0.181004	+	0.983482i	$0.557935\pi$
$390$	−7.12117	+	3.29990i	−0.360595	+	0.167097i
$391$	−13.2422	−	9.62105i	−0.669689	−	0.486558i
$392$	−25.2432	−	20.8234i	−1.27497	−	1.05174i
$393$	16.1382			0.814066
$394$	11.7386	+	7.10166i	0.591383	+	0.357777i
$395$	−4.04594	+	14.1433i	−0.203573	+	0.711626i
$396$	4.60001	−	9.28846i	0.231159	−	0.466763i
$397$	−2.38044	−	0.773450i	−0.119471	−	0.0388184i	0.248672	−	0.968588i	$-0.420006\pi$
$397$	−2.38044	−	0.773450i	−0.119471	−	0.0388184i	−0.368142	+	0.929770i	$0.620006\pi$
$398$	−26.6288	−	6.23259i	−1.33478	−	0.312412i
$399$	20.9219			1.04740
$400$	13.2207	+	15.0071i	0.661036	+	0.750354i
$401$	−3.06672			−0.153145			−0.0765723	−	0.997064i	$-0.524398\pi$
$401$	−3.06672			−0.153145			−0.0765723	+	0.997064i	$0.524398\pi$
$402$	6.42289	+	1.50331i	0.320345	+	0.0749782i
$403$	21.1732	+	6.87960i	1.05471	+	0.342697i
$404$	−7.87591	+	15.9032i	−0.391841	+	0.791216i
$405$	−0.766096	−	2.10074i	−0.0380676	−	0.104386i
$406$	−7.02078	−	4.24745i	−0.348436	−	0.210798i
$407$	43.3558			2.14907
$408$	−8.67112	+	10.5116i	−0.429284	+	0.520400i
$409$	−11.2500	−	8.17357i	−0.556275	−	0.404157i	0.273819	−	0.961781i	$-0.411713\pi$
$409$	−11.2500	−	8.17357i	−0.556275	−	0.404157i	−0.830094	+	0.557624i	$0.811713\pi$
$410$	4.83056	+	5.20510i	0.238565	+	0.257062i
$411$	−4.98815	−	6.86560i	−0.246047	−	0.338655i
$412$	6.12239	−	6.26369i	0.301629	−	0.308590i
$413$	14.6550	−	20.1709i	0.721127	−	0.992547i
$414$	4.67841	+	1.09501i	0.229932	+	0.0538166i
$415$	−8.22180	+	2.99832i	−0.403592	+	0.147182i
$416$	−13.7400	−	2.88697i	−0.673658	−	0.141545i
$417$	6.16938	+	18.9874i	0.302116	+	0.929816i
$418$	23.2642	+	26.9263i	1.13789	+	1.31701i
$419$	−13.4166	+	4.35933i	−0.655446	+	0.212967i	−0.617814	−	0.786324i	$-0.711982\pi$
$419$	−13.4166	+	4.35933i	−0.655446	+	0.212967i	−0.0376321	+	0.999292i	$0.511982\pi$
$420$	−14.2514	−	12.9726i	−0.695398	−	0.632997i
$421$	0.409506	+	0.133057i	0.0199581	+	0.00648479i	0.318979	−	0.947762i	$-0.396660\pi$
$421$	0.409506	+	0.133057i	0.0199581	+	0.00648479i	−0.299021	+	0.954247i	$0.596660\pi$
$422$	−7.19240	−	17.0877i	−0.350120	−	0.831815i
$423$	9.82870	−	7.14097i	0.477888	−	0.347206i
$424$	−13.8273	−	21.7210i	−0.671514	−	1.05486i
$425$	9.05167	+	22.3231i	0.439070	+	1.08283i
$426$	−3.81463	+	3.29581i	−0.184819	+	0.159683i
$427$	3.44173	+	4.73713i	0.166557	+	0.229246i
$428$	1.82093	−	3.67687i	0.0880181	−	0.177728i
$429$	12.2333	+	3.97483i	0.590628	+	0.191907i
$430$	−2.14473	+	10.8942i	−0.103428	+	0.525366i
$431$	−6.24226	−	19.2117i	−0.300679	−	0.925395i	−0.981254	−	0.192717i	$-0.938270\pi$
$431$	−6.24226	−	19.2117i	−0.300679	−	0.925395i	0.680575	−	0.732678i	$-0.261730\pi$
$432$	1.14896	−	3.83143i	0.0552796	−	0.184340i
$433$	−5.05735	−	15.5649i	−0.243041	−	0.748002i	−0.995953	−	0.0898807i	$-0.971351\pi$
$433$	−5.05735	−	15.5649i	−0.243041	−	0.748002i	0.752912	−	0.658121i	$-0.228649\pi$
$434$	4.59966	+	54.4705i	0.220791	+	2.61467i
$435$	−2.49712	−	1.68205i	−0.119728	−	0.0806482i
$436$	10.5074	−	5.50568i	0.503215	−	0.263674i
$437$	−9.69581	+	13.3451i	−0.463813	+	0.638384i
$438$	1.06226	−	0.0897002i	0.0507565	−	0.00428604i
$439$	−19.2599	+	13.9931i	−0.919226	+	0.667857i	−0.943331	−	0.331853i	$-0.892326\pi$
$439$	−19.2599	+	13.9931i	−0.919226	+	0.667857i	0.0241055	+	0.999709i	$0.492326\pi$
$440$	0.848721	−	32.7664i	0.0404612	−	1.56208i
$441$	9.35995	+	6.80041i	0.445712	+	0.323829i
$442$	−14.4684	−	8.75312i	−0.688191	−	0.416343i
$443$			25.3310i			1.20351i	0.798680	+	0.601755i	$0.205532\pi$
$443$			25.3310i			1.20351i	−0.798680	+	0.601755i	$0.794468\pi$
$444$	16.4945	−	2.80570i	0.782795	−	0.133153i
$445$	−3.22745	+	2.52481i	−0.152996	+	0.119688i
$446$	33.4988	−	14.1000i	1.58621	−	0.667656i
$447$	1.13446	−	3.49151i	0.0536582	−	0.165143i
$448$	−6.55473	−	33.8450i	−0.309682	−	1.59903i
$449$	−35.1144			−1.65715			−0.828575	−	0.559878i	$-0.810848\pi$
$449$	−35.1144			−1.65715			−0.828575	+	0.559878i	$0.810848\pi$
$450$	−4.99114	−	5.00884i	−0.235285	−	0.236119i
$451$		−	11.6380i		−	0.548011i
$452$	12.9187	+	24.6550i	0.607645	+	1.15968i
$453$	15.5617	+	5.05629i	0.731151	+	0.237565i
$454$	−3.40081	−	8.07964i	−0.159608	−	0.379196i
$455$	13.3609	−	19.8351i	0.626368	−	0.929885i
$456$	10.5932	+	8.73849i	0.496074	+	0.409217i
$457$	27.6574			1.29376			0.646878	−	0.762593i	$-0.276074\pi$
$457$	27.6574			1.29376			0.646878	+	0.762593i	$0.276074\pi$
$458$	−12.9015	−	7.80517i	−0.602846	−	0.364712i
$459$	2.83177	−	3.89759i	0.132176	−	0.181924i
$460$	14.8791	−	3.07847i	0.693744	−	0.143534i
$461$	7.51682	+	10.3460i	0.350093	+	0.481862i	0.947355	−	0.320184i	$-0.103745\pi$
$461$	7.51682	+	10.3460i	0.350093	+	0.481862i	−0.597262	+	0.802046i	$0.703745\pi$
$462$	2.65755	+	31.4715i	0.123640	+	1.46418i
$463$	9.66665	+	7.02323i	0.449247	+	0.326397i	0.789299	−	0.614010i	$-0.210444\pi$
$463$	9.66665	+	7.02323i	0.449247	+	0.326397i	−0.340051	+	0.940407i	$0.610444\pi$
$464$	−1.78074	−	5.08297i	−0.0826689	−	0.235971i
$465$	0.712547	+	20.0447i	0.0330436	+	0.929551i
$466$	−0.0921903	−	1.09174i	−0.00427063	−	0.0505740i
$467$	−22.3988	+	7.27781i	−1.03649	+	0.336777i	−0.777354	−	0.629063i	$-0.783439\pi$
$467$	−22.3988	+	7.27781i	−1.03649	+	0.336777i	−0.259138	+	0.965840i	$0.583439\pi$
$468$	4.91131	+	0.720548i	0.227025	+	0.0333073i
$469$	−19.1163	+	6.21126i	−0.882709	+	0.286809i
$470$	18.7060	−	33.5567i	0.862846	−	1.54785i
$471$	−0.775223	+	2.38589i	−0.0357204	+	0.109936i
$472$	15.8450	−	4.09201i	0.729326	−	0.188350i
$473$	14.7216	−	10.6959i	0.676900	−	0.491797i
$474$	7.04010	−	6.08259i	0.323362	−	0.279383i
$475$	22.4966	−	9.12200i	1.03221	−	0.418546i
$476$	6.02713	−	41.0814i	0.276253	−	1.88296i
$477$	5.35093	+	7.36492i	0.245002	+	0.337216i
$478$	−17.5523	+	7.38796i	−0.802822	+	0.337917i
$479$	6.36901	−	19.6018i	0.291007	−	0.895629i	−0.693526	−	0.720432i	$-0.743944\pi$
$479$	6.36901	−	19.6018i	0.291007	−	0.895629i	0.984533	−	0.175197i	$-0.0560562\pi$
$480$	−1.79753	−	12.5207i	−0.0820458	−	0.571491i
$481$	6.41619	+	19.7470i	0.292553	+	0.900386i
$482$	−13.5785	−	15.7160i	−0.618485	−	0.715845i
$483$	−13.9243	+	4.52426i	−0.633575	+	0.205861i
$484$	−22.1706	+	22.6823i	−1.00775	+	1.03101i
$485$	−8.32092	+	29.0873i	−0.377834	+	1.32078i
$486$	−0.322293	+	1.37700i	−0.0146195	+	0.0624620i
$487$	23.3782	+	16.9852i	1.05937	+	0.769674i	0.973971	−	0.226673i	$-0.0727850\pi$
$487$	23.3782	+	16.9852i	1.05937	+	0.769674i	0.0853944	+	0.996347i	$0.472785\pi$
$488$	−0.235942	+	3.83603i	−0.0106806	+	0.173649i
$489$	3.73411	−	2.71299i	0.168862	−	0.122686i
$490$	35.8971	+	7.06701i	1.62166	+	0.319255i
$491$	8.64055	−	11.8927i	0.389942	−	0.536710i	−0.568242	−	0.822862i	$-0.692376\pi$
$491$	8.64055	−	11.8927i	0.389942	−	0.536710i	0.958184	+	0.286152i	$0.0923762\pi$
$492$	−0.753134	−	4.42761i	−0.0339539	−	0.199612i
$493$		−	6.48687i		−	0.292154i
$494$	−8.82113	+	14.5808i	−0.396881	+	0.656021i
$495$	0.411689	+	11.5812i	0.0185040	+	0.520538i
$496$	−20.4219	+	29.5008i	−0.916970	+	1.32463i
$497$	4.74682	−	14.6092i	0.212924	−	0.655312i
$498$	5.38926	+	1.26138i	0.241498	+	0.0565238i
$499$			11.7877i			0.527689i	0.964565	+	0.263844i	$0.0849905\pi$
$499$			11.7877i			0.527689i	−0.964565	+	0.263844i	$0.915009\pi$
$500$	−20.9801	−	7.73530i	−0.938259	−	0.345933i
$501$		−	21.9749i		−	0.981767i
$502$	6.44862	−	27.5517i	0.287816	−	1.22969i
$503$	9.21308	−	28.3550i	0.410791	−	1.26429i	−0.505171	−	0.863019i	$-0.668570\pi$
$503$	9.21308	−	28.3550i	0.410791	−	1.26429i	0.915962	−	0.401266i	$-0.131430\pi$
$504$	3.04768	+	11.8012i	0.135754	+	0.525667i
$505$	−0.704873	−	19.8288i	−0.0313664	−	0.882371i
$506$	−21.3058	−	12.8897i	−0.947159	−	0.573015i
$507$		−	6.83996i		−	0.303773i
$508$	−6.96359	+	1.18450i	−0.308959	+	0.0525538i
$509$	6.17438	−	8.49831i	0.273675	−	0.376681i	−0.649951	−	0.759976i	$-0.725211\pi$
$509$	6.17438	−	8.49831i	0.273675	−	0.376681i	0.923626	+	0.383295i	$0.125211\pi$
$510$	2.94279	−	14.9480i	0.130309	−	0.661907i
$511$	−2.62794	+	1.90931i	−0.116253	+	0.0844628i
$512$	10.8173	−	19.8742i	0.478062	−	0.878326i
$513$	−3.92788	−	2.85377i	−0.173420	−	0.125997i
$514$	43.4480	+	10.1692i	1.91641	+	0.448544i
$515$	−2.69333	+	9.41503i	−0.118683	+	0.414876i
$516$	4.90860	−	5.02188i	0.216089	−	0.221076i
$517$	−59.8810	+	19.4565i	−2.63356	+	0.855696i
$518$	−38.5777	+	33.3309i	−1.69501	+	1.46447i
$519$	−4.46686	−	13.7476i	−0.196073	−	0.603451i
$520$	15.0495	−	4.46251i	0.659965	−	0.195694i
$521$	8.41873	−	25.9102i	0.368831	−	1.13515i	−0.578716	−	0.815529i	$-0.696446\pi$
$521$	8.41873	−	25.9102i	0.368831	−	1.13515i	0.947547	−	0.319616i	$-0.103554\pi$
$522$	0.738725	+	1.75506i	0.0323331	+	0.0768169i
$523$	3.56330	+	4.90446i	0.155812	+	0.214457i	0.879786	−	0.475371i	$-0.157686\pi$
$523$	3.56330	+	4.90446i	0.155812	+	0.214457i	−0.723973	+	0.689828i	$0.757686\pi$
$524$	−31.9346	−	4.68519i	−1.39507	−	0.204673i
$525$	20.9127	+	5.18630i	0.912705	+	0.226349i
$526$	−4.26976	−	4.94189i	−0.186170	−	0.215477i
$527$	−34.9611	+	25.4007i	−1.52293	+	1.10647i
$528$	−11.7992	+	17.0447i	−0.513493	+	0.741776i
$529$	−3.54032	+	10.8960i	−0.153927	+	0.473738i
$530$	25.1450	+	14.0170i	1.09223	+	0.608858i
$531$	−5.50268	+	1.78793i	−0.238796	+	0.0775895i
$532$	−41.4006	−	6.07396i	−1.79494	−	0.263340i
$533$	5.30068	−	1.72230i	0.229598	−	0.0746009i
$534$	2.58242	−	0.218068i	0.111752	−	0.00943671i
$535$	0.162969	+	4.58448i	0.00704575	+	0.198204i
$536$	−12.2733	−	4.83944i	−0.530126	−	0.209032i
$537$	−17.9335	−	13.0294i	−0.773887	−	0.562262i
$538$	−7.81002	+	0.659503i	−0.336714	+	0.0284332i
$539$	−35.2435	−	48.5085i	−1.51804	−	2.08941i
$540$	0.906087	+	4.37938i	0.0389918	+	0.188459i
$541$	15.6856	−	21.5894i	0.674378	−	0.928201i	−0.325472	−	0.945552i	$-0.605523\pi$
$541$	15.6856	−	21.5894i	0.674378	−	0.928201i	0.999849	+	0.0173504i	$0.00552309\pi$
$542$	−1.58277	+	2.61622i	−0.0679857	+	0.112376i
$543$	23.6512			1.01497
$544$	20.2102	−	18.2831i	0.866506	−	0.783881i
$545$	−7.40951	+	10.9999i	−0.317388	+	0.471184i
$546$	−13.9408	+	5.86785i	−0.596612	+	0.251121i
$547$	−19.6504	−	6.38480i	−0.840190	−	0.272994i	−0.142859	−	0.989743i	$-0.545629\pi$
$547$	−19.6504	−	6.38480i	−0.840190	−	0.272994i	−0.697332	+	0.716749i	$0.745629\pi$
$548$	7.87744	+	15.0339i	0.336508	+	0.642217i
$549$		−	1.35881i		−	0.0579924i
$550$	16.5792	+	32.6814i	0.706940	+	1.39354i
$551$	−6.53727			−0.278497
$552$	−8.93983	−	3.52503i	−0.380504	−	0.150035i
$553$	−8.76050	+	26.9620i	−0.372534	+	1.14654i
$554$	−7.43225	−	17.6575i	−0.315766	−	0.750196i
$555$	−14.7336	+	11.5260i	−0.625405	+	0.489251i
$556$	−6.69572	−	39.3636i	−0.283962	−	1.66939i
$557$		−	0.300258i		−	0.0127223i	−0.999980	−	0.00636116i	$-0.997975\pi$
$557$		−	0.300258i		−	0.0127223i	0.999980	−	0.00636116i	$-0.00202483\pi$
$558$	6.56630	−	10.8537i	0.277974	−	0.459474i
$559$	7.05023	+	5.12229i	0.298193	+	0.216650i
$560$	24.4348	+	29.8078i	1.03256	+	1.25961i
$561$	−20.1995	+	14.6758i	−0.852824	+	0.619613i
$562$	0.795577	+	9.42145i	0.0335594	+	0.397420i
$563$	−11.7142	+	16.1232i	−0.493695	+	0.679512i	−0.981064	−	0.193684i	$-0.937956\pi$
$563$	−11.7142	+	16.1232i	−0.493695	+	0.679512i	0.487369	+	0.873196i	$0.337956\pi$
$564$	−21.5223	+	11.2772i	−0.906253	+	0.474857i
$565$	−25.8106	−	17.3859i	−1.08586	−	0.731432i
$566$	−29.6383	+	2.50275i	−1.24579	+	0.105198i
$567$	−1.33163	−	4.09833i	−0.0559231	−	0.172114i
$568$	8.50528	−	5.41436i	0.356873	−	0.227181i
$569$	6.14619	+	18.9160i	0.257662	+	0.793001i	0.993294	+	0.115619i	$0.0368853\pi$
$569$	6.14619	+	18.9160i	0.257662	+	0.793001i	−0.735632	+	0.677381i	$0.763115\pi$
$570$	−15.0641	−	2.96565i	−0.630966	−	0.124217i
$571$	29.1683	+	9.47735i	1.22065	+	0.396615i	0.847320	−	0.531082i	$-0.178214\pi$
$571$	29.1683	+	9.47735i	1.22065	+	0.396615i	0.373334	+	0.927697i	$0.378214\pi$
$572$	−23.0534	−	11.4170i	−0.963913	−	0.477368i
$573$	−7.17637	−	9.87743i	−0.299797	−	0.412636i
$574$	8.94699	+	10.3554i	0.373440	+	0.432226i
$575$	−12.9997	+	10.9358i	−0.542123	+	0.456054i
$576$	−3.38592	+	7.24814i	−0.141080	+	0.302006i
$577$	−25.4828	+	18.5144i	−1.06086	+	0.770763i	−0.974248	−	0.225478i	$-0.927606\pi$
$577$	−25.4828	+	18.5144i	−1.06086	+	0.770763i	−0.0866166	+	0.996242i	$0.527606\pi$
$578$	8.09465	−	3.40713i	0.336693	−	0.141718i
$579$	−9.55572	−	3.10484i	−0.397122	−	0.129033i
$580$	4.45301	+	4.05342i	0.184901	+	0.168309i
$581$	−16.0399	+	5.21168i	−0.665448	+	0.216217i
$582$	14.4787	−	12.5095i	0.600163	−	0.518537i
$583$	−14.5793	−	44.8705i	−0.603813	−	1.85835i
$584$	−2.12805	−	0.130889i	−0.0880593	−	0.00541624i
$585$	−5.21391	+	1.90141i	−0.215569	+	0.0786135i
$586$	−3.62941	+	15.5067i	−0.149930	+	0.640575i
$587$	16.1867	−	22.2790i	0.668095	−	0.919554i	−0.331621	−	0.943413i	$-0.607595\pi$
$587$	16.1867	−	22.2790i	0.668095	−	0.919554i	0.999715	+	0.0238593i	$0.00759537\pi$
$588$	−16.5474	−	16.1741i	−0.682402	−	0.667009i
$589$	25.5981	+	35.2328i	1.05475	+	1.45174i
$590$	−13.4111	+	12.4461i	−0.552125	+	0.512396i
$591$	7.84848	+	5.70226i	0.322843	+	0.234559i
$592$	−33.4542	+	0.763354i	−1.37496	+	0.0313737i
$593$	−36.0832			−1.48176			−0.740880	−	0.671637i	$-0.765591\pi$
$593$	−36.0832			−1.48176			−0.740880	+	0.671637i	$0.765591\pi$
$594$	3.79382	−	6.27095i	0.155662	−	0.257300i
$595$	15.9046	+	43.6125i	0.652025	+	1.78794i
$596$	−3.25854	+	6.57972i	−0.133475	+	0.269516i
$597$	−18.3918	−	5.97586i	−0.752726	−	0.244575i
$598$	2.71774	−	11.6116i	0.111137	−	0.474832i
$599$	23.2859			0.951436			0.475718	−	0.879598i	$-0.342188\pi$
$599$	23.2859			0.951436			0.475718	+	0.879598i	$0.342188\pi$
$600$	8.42241	+	11.3606i	0.343843	+	0.463794i
$601$	−10.0941			−0.411747			−0.205874	−	0.978579i	$-0.566004\pi$
$601$	−10.0941			−0.411747			−0.205874	+	0.978579i	$0.566004\pi$
$602$	−4.87647	+	20.8347i	−0.198750	+	0.849160i
$603$	4.43612	+	1.44138i	0.180653	+	0.0586976i
$604$	−29.3258	−	14.5233i	−1.19325	−	0.590943i
$605$	9.75319	−	34.0940i	0.396524	−	1.38612i
$606$	−6.49558	+	10.7368i	−0.263865	+	0.436153i
$607$	34.7473			1.41035			0.705175	−	0.709034i	$-0.250869\pi$
$607$	34.7473			1.41035			0.705175	+	0.709034i	$0.250869\pi$
$608$	−18.4251	−	20.3673i	−0.747238	−	0.826001i
$609$	−4.69412	−	3.41048i	−0.190215	−	0.138200i
$610$	−1.80662	−	3.89867i	−0.0731478	−	0.157853i
$611$	−17.7235	−	24.3943i	−0.717015	−	0.986886i
$612$	−6.73508	+	6.89052i	−0.272250	+	0.278533i
$613$	16.3204	−	22.4632i	0.659176	−	0.907279i	−0.340277	−	0.940325i	$-0.610521\pi$
$613$	16.3204	−	22.4632i	0.659176	−	0.907279i	0.999454	+	0.0330465i	$0.0105210\pi$
$614$	9.33739	−	39.8940i	0.376826	−	1.60999i
$615$	3.09391	+	3.95492i	0.124759	+	0.159478i
$616$	3.87786	−	63.0478i	0.156244	−	2.54027i
$617$	2.08759	+	6.42495i	0.0840434	+	0.258659i	0.984244	−	0.176817i	$-0.0565801\pi$
$617$	2.08759	+	6.42495i	0.0840434	+	0.258659i	−0.900200	+	0.435476i	$0.856580\pi$
$618$	4.68651	−	4.04911i	0.188519	−	0.162879i
$619$	−0.625732	+	0.203313i	−0.0251503	+	0.00817182i	−0.321565	−	0.946887i	$-0.604209\pi$
$619$	−0.625732	+	0.203313i	−0.0251503	+	0.00817182i	0.296415	+	0.955059i	$0.404209\pi$
$620$	4.40930	−	39.8717i	0.177082	−	1.60128i
$621$	3.23126	+	1.04990i	0.129666	+	0.0421310i
$622$	−21.9025	+	9.21903i	−0.878212	+	0.369649i
$623$	−6.38870	+	4.64166i	−0.255958	+	0.185964i
$624$	−9.50940	−	2.85167i	−0.380681	−	0.114158i
$625$	24.7479	−	3.54134i	0.989916	−	0.141654i
$626$	8.07601	+	9.34731i	0.322782	+	0.373594i
$627$	14.7898	+	20.3565i	0.590649	+	0.812958i
$628$	2.22669	−	4.49618i	0.0888545	−	0.179417i
$629$	−38.3309	−	12.4545i	−1.52835	−	0.496592i
$630$	−9.26969	−	9.98841i	−0.369313	−	0.397948i
$631$	9.03449	+	27.8053i	0.359657	+	1.10691i	0.953260	+	0.302153i	$0.0977053\pi$
$631$	9.03449	+	27.8053i	0.359657	+	1.10691i	−0.593602	+	0.804759i	$0.702295\pi$
$632$	−15.6969	+	9.99249i	−0.624391	+	0.397480i
$633$	−4.05106	−	12.4679i	−0.161015	−	0.495554i
$634$	−18.6207	+	1.57239i	−0.739521	+	0.0624475i
$635$	6.22016	−	4.86600i	0.246839	−	0.193101i
$636$	−8.45035	−	16.1273i	−0.335078	−	0.639488i
$637$	16.8782	−	23.2309i	0.668740	−	0.920441i
$638$	−0.830380	−	9.83359i	−0.0328750	−	0.389316i
$639$	−2.88388	+	2.09526i	−0.114084	+	0.0828872i
$640$	−0.0779805	+	25.2981i	−0.00308245	+	0.999995i
$641$	26.8789	+	19.5287i	1.06165	+	0.771335i	0.974393	−	0.224850i	$-0.0721893\pi$
$641$	26.8789	+	19.5287i	1.06165	+	0.771335i	0.0872587	+	0.996186i	$0.472189\pi$
$642$	1.50180	−	2.48238i	0.0592712	−	0.0979717i
$643$			24.5583i			0.968484i	0.874934	+	0.484242i	$0.160905\pi$
$643$			24.5583i			0.968484i	−0.874934	+	0.484242i	$0.839095\pi$
$644$	28.8670	−	4.91026i	1.13752	−	0.193491i
$645$	−2.15937	+	7.54845i	−0.0850250	+	0.297220i
$646$	−12.8329	−	30.4884i	−0.504905	−	1.19955i
$647$	−10.1798	+	31.3302i	−0.400209	+	1.23172i	0.524621	+	0.851336i	$0.324207\pi$
$647$	−10.1798	+	31.3302i	−0.400209	+	1.23172i	−0.924830	+	0.380380i	$0.875793\pi$
$648$	1.03752	−	2.63126i	0.0407578	−	0.103366i
$649$	29.9855			1.17704
$650$	−12.4317	+	12.3877i	−0.487610	+	0.485887i
$651$			38.6535i			1.51495i
$652$	−8.17675	+	4.28444i	−0.320226	+	0.167792i
$653$	−6.99209	−	2.27187i	−0.273621	−	0.0889050i	0.168992	−	0.985617i	$-0.445949\pi$
$653$	−6.99209	−	2.27187i	−0.273621	−	0.0889050i	−0.442614	+	0.896712i	$0.645949\pi$
$654$	7.73112	−	3.25412i	0.302311	−	0.127246i
$655$	33.9022	−	12.3634i	1.32467	−	0.483080i
$656$	0.204907	+	8.98008i	0.00800026	+	0.350613i
$657$	0.753801			0.0294086
$658$	38.3240	−	63.3473i	1.49402	−	2.46953i
$659$	0.516993	−	0.711580i	0.0201392	−	0.0277192i	−0.798829	−	0.601559i	$-0.794547\pi$
$659$	0.516993	−	0.711580i	0.0201392	−	0.0277192i	0.818968	+	0.573839i	$0.194547\pi$
$660$	2.54756	−	23.0367i	0.0991637	−	0.896701i
$661$	8.89376	+	12.2412i	0.345927	+	0.476128i	0.946161	−	0.323697i	$-0.104926\pi$
$661$	8.89376	+	12.2412i	0.345927	+	0.476128i	−0.600234	+	0.799825i	$0.704926\pi$
$662$	47.3355	−	3.99716i	1.83975	−	0.155354i
$663$	−9.67361	−	7.02829i	−0.375692	−	0.272956i
$664$	−10.2982	−	4.06063i	−0.399646	−	0.157583i
$665$	43.9514	−	16.0282i	1.70436	−	0.621546i
$666$	11.7890	−	0.995497i	0.456813	−	0.0385747i
$667$	4.35078	−	1.41365i	0.168463	−	0.0547369i
$668$	−6.37967	+	43.4844i	−0.246837	+	1.68246i
$669$	24.4422	−	7.94174i	0.944989	−	0.307045i
$670$	14.6445	−	1.76250i	0.565766	−	0.0680913i
$671$	−2.17613	+	6.69743i	−0.0840084	+	0.258551i
$672$	−2.60472	−	24.2372i	−0.100479	−	0.934969i
$673$	32.3853	−	23.5293i	1.24836	−	0.906989i	0.250237	−	0.968185i	$-0.419491\pi$
$673$	32.3853	−	23.5293i	1.24836	−	0.906989i	0.998126	+	0.0611956i	$0.0194914\pi$
$674$	−16.9079	−	19.5695i	−0.651268	−	0.753788i
$675$	−3.21873	−	3.82619i	−0.123889	−	0.147270i
$676$	−1.98575	+	13.5350i	−0.0763749	+	0.520578i
$677$	−9.83837	−	13.5414i	−0.378119	−	0.520437i	0.576966	−	0.816768i	$-0.304237\pi$
$677$	−9.83837	−	13.5414i	−0.378119	−	0.520437i	−0.955085	+	0.296332i	$0.904237\pi$
$678$	7.63557	+	18.1406i	0.293242	+	0.696684i
$679$	−18.0169	+	55.4505i	−0.691427	+	2.12799i
$680$	−10.1629	+	28.7249i	−0.389728	+	1.10155i
$681$	−1.91548	−	5.89525i	−0.0734015	−	0.225906i
$682$	−49.7469	+	42.9809i	−1.90491	+	1.64583i
$683$	7.41246	−	2.40845i	0.283630	−	0.0921569i	−0.163747	−	0.986502i	$-0.552358\pi$
$683$	7.41246	−	2.40845i	0.283630	−	0.0921569i	0.447377	+	0.894345i	$0.352358\pi$
$684$	6.94406	+	6.78741i	0.265513	+	0.259523i
$685$	−15.7385	−	10.6014i	−0.601337	−	0.405059i
$686$	27.1148	+	6.34635i	1.03525	+	0.242305i
$687$	−8.62597	−	6.26714i	−0.329101	−	0.239106i
$688$	−11.1712	+	8.51234i	−0.425896	+	0.324530i
$689$	18.2793	−	13.2807i	0.696386	−	0.505954i
$690$	10.6670	−	1.28380i	0.406086	−	0.0488734i
$691$	−13.6634	+	18.8060i	−0.519779	+	0.715415i	−0.985530	−	0.169501i	$-0.945784\pi$
$691$	−13.6634	+	18.8060i	−0.519779	+	0.715415i	0.465751	+	0.884916i	$0.345784\pi$
$692$	4.84795	+	28.5007i	0.184291	+	1.08344i
$693$			22.3329i			0.848356i
$694$	−32.5239	−	19.6764i	−1.23459	−	0.746906i
$695$	27.5064	+	35.1612i	1.04338	+	1.33374i
$696$	−0.952280	−	3.68741i	−0.0360961	−	0.139771i
$697$	−3.34314	+	10.2891i	−0.126631	+	0.389729i
$698$	−8.58494	+	36.6792i	−0.324945	+	1.38833i
$699$		−	0.774727i		−	0.0293029i
$700$	−39.8767	−	16.3340i	−1.50720	−	0.617368i
$701$		−	3.23114i		−	0.122039i	−0.998137	−	0.0610193i	$-0.980565\pi$
$701$		−	3.23114i		−	0.122039i	0.998137	−	0.0610193i	$-0.0194351\pi$
$702$	3.41763	+	0.799914i	0.128990	+	0.0301908i
$703$	−12.5512	+	38.6287i	−0.473378	+	1.45691i
$704$	28.2968	−	30.3029i	1.06647	−	1.14208i
$705$	15.1768	−	22.5310i	0.571593	−	0.848567i
$706$	−9.54289	+	15.7738i	−0.359152	+	0.593656i
$707$		−	38.2372i		−	1.43806i
$708$	11.4079	−	1.94047i	0.428733	−	0.0729272i
$709$	22.9197	−	31.5463i	0.860767	−	1.18474i	−0.120619	−	0.992699i	$-0.538488\pi$
$709$	22.9197	−	31.5463i	0.860767	−	1.18474i	0.981386	−	0.192046i	$-0.0615122\pi$
$710$	−5.48862	+	9.84600i	−0.205984	+	0.369514i
$711$	5.32235	−	3.86692i	0.199604	−	0.145021i
$712$	−5.17344	−	0.318202i	−0.193883	−	0.0119251i
$713$	−24.6554	−	17.9132i	−0.923351	−	0.670854i
$714$	6.69099	−	28.5873i	0.250404	−	1.06985i
$715$	28.7440	−	1.02179i	1.07496	−	0.0382127i
$716$	31.7044	+	30.9893i	1.18485	+	1.15812i
$717$	−12.8069	+	4.16121i	−0.478282	+	0.155403i
$718$	−9.02399	−	10.4445i	−0.336772	−	0.389786i
$719$	−11.5707	−	35.6109i	−0.431514	−	1.32806i	−0.896617	−	0.442807i	$-0.853983\pi$
$719$	−11.5707	−	35.6109i	−0.431514	−	1.32806i	0.465103	−	0.885256i	$-0.346017\pi$
$720$	−0.521575	−	8.92905i	−0.0194379	−	0.332766i
$721$	−5.83177	+	17.9483i	−0.217186	+	0.668431i
$722$	−5.95969	+	2.50850i	−0.221797	+	0.0933567i
$723$	−8.63234	−	11.8814i	−0.321040	−	0.441874i
$724$	−46.8014	−	6.86632i	−1.73936	−	0.255185i
$725$	−6.53440	−	1.62052i	−0.242681	−	0.0601844i
$726$	−16.9709	+	14.6628i	−0.629851	+	0.544187i
$727$	12.6871	−	9.21770i	0.470538	−	0.341866i	−0.327113	−	0.944985i	$-0.606076\pi$
$727$	12.6871	−	9.21770i	0.470538	−	0.341866i	0.797651	+	0.603120i	$0.206076\pi$
$728$	29.2899	−	7.56417i	1.08556	−	0.280347i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	2.16280	−	1.00223i	0.0800488	−	0.0370941i
$731$	−16.0879	+	5.22727i	−0.595032	+	0.193338i
$732$	−0.394483	+	2.68883i	−0.0145805	+	0.0993819i
$733$	−0.616838	+	0.200423i	−0.0227834	+	0.00740279i	−0.320387	−	0.947287i	$-0.603813\pi$
$733$	−0.616838	+	0.200423i	−0.0227834	+	0.00740279i	0.297603	+	0.954690i	$0.403813\pi$
$734$	−1.09075	−	12.9170i	−0.0402604	−	0.476775i
$735$	24.8726	+	7.11524i	0.917439	+	0.262449i
$736$	16.6669	+	9.57077i	0.614351	+	0.352783i
$737$	−19.5568	−	14.2089i	−0.720386	−	0.523391i
$738$	−0.267221	−	3.16450i	−0.00983653	−	0.116487i
$739$	10.1985	+	14.0371i	0.375159	+	0.516362i	0.954294	−	0.298869i	$-0.0966095\pi$
$739$	10.1985	+	14.0371i	0.375159	+	0.516362i	−0.579135	+	0.815232i	$0.696609\pi$
$740$	32.5012	−	18.5304i	1.19477	−	0.681192i
$741$	−7.08290	+	9.74877i	−0.260197	+	0.358130i
$742$	47.4679	+	28.7172i	1.74260	+	1.05424i
$743$	49.1552			1.80333			0.901665	−	0.432436i	$-0.142346\pi$
$743$	49.1552			1.80333			0.901665	+	0.432436i	$0.142346\pi$
$744$	−16.1445	+	19.5712i	−0.591886	+	0.717514i
$745$	−0.291630	−	8.20386i	−0.0106845	−	0.300566i
$746$	15.6107	+	37.0877i	0.571547	+	1.35788i
$747$	3.72222	+	1.20942i	0.136189	+	0.0442504i
$748$	44.2318	−	23.1765i	1.61727	−	0.847416i
$749$			8.84056i			0.323027i
$750$	−14.3223	−	6.69857i	−0.522978	−	0.244597i
$751$	26.0724			0.951394			0.475697	−	0.879609i	$-0.342196\pi$
$751$	26.0724			0.951394			0.475697	+	0.879609i	$0.342196\pi$
$752$	45.8627	−	16.0673i	1.67244	−	0.585915i
$753$	6.18298	−	19.0293i	0.225320	−	0.693465i
$754$	4.35596	−	1.83347i	0.158635	−	0.0667712i
$755$	36.5646	−	1.29979i	1.33072	−	0.0473044i
$756$	1.44524	+	8.49644i	0.0525628	+	0.309012i
$757$			12.3636i			0.449364i	0.974432	+	0.224682i	$0.0721344\pi$
$757$			12.3636i			0.449364i	−0.974432	+	0.224682i	$0.927866\pi$
$758$	22.7764	+	13.7793i	0.827276	+	0.500488i
$759$	−14.2451	−	10.3497i	−0.517066	−	0.375670i
$760$	28.9481	+	10.2418i	1.05006	+	0.371510i
$761$	−22.1641	+	16.1031i	−0.803447	+	0.583738i	−0.911923	−	0.410361i	$-0.865403\pi$
$761$	−22.1641	+	16.1031i	−0.803447	+	0.583738i	0.108477	+	0.994099i	$0.465403\pi$
$762$	−4.97702	+	0.420275i	−0.180298	+	0.0152250i
$763$	−15.0233	+	20.6778i	−0.543880	+	0.748587i
$764$	11.3332	+	21.6290i	0.410019	+	0.782511i
$765$	2.96287	−	10.3572i	0.107123	−	0.374466i
$766$	−2.75191	−	32.5889i	−0.0994305	−	1.17748i
$767$	4.43754	+	13.6573i	0.160230	+	0.493138i
$768$	8.80436	−	13.3598i	0.317700	−	0.482079i
$769$	−5.46390	−	16.8161i	−0.197033	−	0.606406i	−0.999947	−	0.0103105i	$-0.996718\pi$
$769$	−5.46390	−	16.8161i	−0.197033	−	0.606406i	0.802914	−	0.596095i	$-0.203282\pi$
$770$	29.6930	+	64.0773i	1.07006	+	2.30919i
$771$	30.0083	+	9.75030i	1.08072	+	0.351148i
$772$	18.0076	+	8.91809i	0.648109	+	0.320969i
$773$	−6.00032	−	8.25874i	−0.215817	−	0.297046i	0.687359	−	0.726318i	$-0.258770\pi$
$773$	−6.00032	−	8.25874i	−0.215817	−	0.297046i	−0.903175	+	0.429272i	$0.858770\pi$
$774$	3.75739	−	3.24636i	0.135057	−	0.116688i
$775$	16.8530	+	41.5628i	0.605379	+	1.49298i
$776$	−32.2825	+	20.5507i	−1.15887	+	0.737726i
$777$	−29.1650	+	21.1896i	−1.04629	+	0.760172i
$778$	−14.9168	−	35.4393i	−0.534794	−	1.27056i
$779$	10.3691	+	3.36912i	0.371511	+	0.120711i
$780$	10.8694	−	2.24886i	0.389186	−	0.0805220i
$781$	17.5699	−	5.70881i	0.628701	−	0.204277i
$782$	15.1338	+	17.5161i	0.541182	+	0.626373i
$783$	0.416081	+	1.28057i	0.0148695	+	0.0457637i
$784$	28.0486	+	36.8096i	1.00174	+	1.31463i
$785$	0.199283	+	5.60602i	0.00711270	+	0.200088i
$786$	−22.2223	−	5.20124i	−0.792645	−	0.185522i
$787$	4.64676	−	6.39572i	0.165639	−	0.227983i	−0.718126	−	0.695913i	$-0.755000\pi$
$787$	4.64676	−	6.39572i	0.165639	−	0.227983i	0.883766	+	0.467930i	$0.155000\pi$
$788$	−13.8753	−	13.5623i	−0.494285	−	0.483136i
$789$	−2.71443	−	3.73610i	−0.0966364	−	0.133009i
$790$	10.1295	−	18.1713i	0.360393	−	0.646507i
$791$	−48.5191	−	35.2512i	−1.72514	−	1.25339i
$792$	−9.32782	+	11.3077i	−0.331450	+	0.401800i
$793$	−3.37248			−0.119760
$794$	3.02858	+	1.83224i	0.107480	+	0.0650237i
$795$	16.8831	+	11.3724i	0.598783	+	0.403339i
$796$	34.6591	+	17.1646i	1.22846	+	0.608382i
$797$	−1.41398	−	0.459430i	−0.0500857	−	0.0162738i	0.283867	−	0.958864i	$-0.408383\pi$
$797$	−1.41398	−	0.459430i	−0.0500857	−	0.0162738i	−0.333953	+	0.942590i	$0.608383\pi$
$798$	−28.8094	−	6.74298i	−1.01984	−	0.238699i
$799$	58.5298			2.07064
$800$	−13.3682	−	24.9257i	−0.472639	−	0.881256i
$801$	1.83254			0.0647498
$802$	4.22287	+	0.988383i	0.149115	+	0.0349010i
$803$	−3.71541	−	1.20721i	−0.131114	−	0.0426016i
$804$	−8.35981	−	4.14011i	−0.294828	−	0.146010i
$805$	−25.7852	+	20.1716i	−0.908808	+	0.710956i
$806$	−26.9383	−	16.2972i	−0.948860	−	0.574044i
$807$	−5.54217			−0.195094
$808$	15.9706	−	19.3604i	0.561845	−	0.681096i
$809$	−2.96125	−	2.15147i	−0.104112	−	0.0756417i	0.534511	−	0.845161i	$-0.320496\pi$
$809$	−2.96125	−	2.15147i	−0.104112	−	0.0756417i	−0.638623	+	0.769520i	$0.720496\pi$
$810$	0.377861	+	3.13962i	0.0132767	+	0.110315i
$811$	2.33562	+	3.21470i	0.0820146	+	0.112883i	0.848053	−	0.529911i	$-0.177775\pi$
$811$	2.33562	+	3.21470i	0.0820146	+	0.112883i	−0.766038	+	0.642795i	$0.777775\pi$
$812$	8.29869	+	8.11149i	0.291227	+	0.284657i
$813$	−1.27088	+	1.74921i	−0.0445716	+	0.0613476i
$814$	−59.7009	−	13.9733i	−2.09252	−	0.489763i
$815$	5.76598	−	8.55998i	0.201973	−	0.299843i
$816$	15.3279	−	11.6798i	0.536585	−	0.408874i
$817$	5.26788	+	16.2129i	0.184300	+	0.567217i
$818$	12.8569	+	14.8808i	0.449531	+	0.520295i
$819$	−10.1718	+	3.30503i	−0.355432	+	0.115487i
$820$	−4.97411	−	8.72428i	−0.173704	−	0.304665i
$821$	−5.00773	−	1.62711i	−0.174771	−	0.0567865i	0.220324	−	0.975427i	$-0.429288\pi$
$821$	−5.00773	−	1.62711i	−0.174771	−	0.0567865i	−0.395095	+	0.918640i	$0.629288\pi$
$822$	4.65594	+	11.0616i	0.162395	+	0.385817i
$823$	−27.2503	+	19.7985i	−0.949886	+	0.690132i	−0.950780	−	0.309867i	$-0.899715\pi$
$823$	−27.2503	+	19.7985i	−0.949886	+	0.690132i	0.000894000		1.00000i	$0.499715\pi$
$824$	−10.4493	+	6.65189i	−0.364018	+	0.231729i
$825$	9.73719	+	24.0137i	0.339006	+	0.836051i
$826$	−26.6809	+	23.0521i	−0.928348	+	0.802087i
$827$	−3.45961	−	4.76175i	−0.120302	−	0.165582i	0.744618	−	0.667490i	$-0.232631\pi$
$827$	−3.45961	−	4.76175i	−0.120302	−	0.165582i	−0.864921	+	0.501908i	$0.832631\pi$
$828$	−6.08926	−	3.01564i	−0.211616	−	0.104801i
$829$	19.9973	+	6.49752i	0.694535	+	0.225668i	0.634948	−	0.772555i	$-0.281022\pi$
$829$	19.9973	+	6.49752i	0.694535	+	0.225668i	0.0595874	+	0.998223i	$0.481022\pi$
$830$	12.2878	−	1.47886i	0.426514	−	0.0513320i
$831$	−4.18616	−	12.8837i	−0.145216	−	0.446930i
$832$	17.9895	+	8.40365i	0.623673	+	0.291344i
$833$	17.2241	+	53.0104i	0.596781	+	1.83670i
$834$	−2.37572	−	28.1340i	−0.0822645	−	0.974200i
$835$	−16.8349	−	46.1635i	−0.582596	−	1.59756i
$836$	−23.3566	−	44.5754i	−0.807804	−	1.54167i
$837$	5.27239	−	7.25682i	0.182240	−	0.250832i
$838$	19.8797	−	1.67870i	0.686733	−	0.0579899i
$839$	−35.3637	+	25.6932i	−1.22089	+	0.887028i	−0.996174	−	0.0873965i	$-0.972145\pi$
$839$	−35.3637	+	25.6932i	−1.22089	+	0.887028i	−0.224716	+	0.974424i	$0.572145\pi$
$840$	15.4432	+	22.4564i	0.532842	+	0.774819i
$841$	−21.9948	−	15.9801i	−0.758440	−	0.551039i
$842$	−0.521007	−	0.315200i	−0.0179551	−	0.0108625i
$843$			6.68568i			0.230267i
$844$	4.39668	+	25.8478i	0.151340	+	0.889717i
$845$	−5.24006	−	14.3689i	−0.180264	−	0.494307i
$846$	−15.8356	+	6.66538i	−0.544439	+	0.229161i
$847$	21.1182	−	64.9950i	0.725629	−	2.23326i
$848$	12.0397	+	34.3662i	0.413445	+	1.18014i
$849$	−21.0320			−0.721817
$850$	−5.26955	−	33.6562i	−0.180744	−	1.15440i
$851$		−	28.4229i		−	0.974324i
$852$	6.31496	−	3.30890i	0.216347	−	0.113361i
$853$	−14.1859	−	4.60927i	−0.485716	−	0.157819i	0.0559144	−	0.998436i	$-0.482193\pi$
$853$	−14.1859	−	4.60927i	−0.485716	−	0.157819i	−0.541630	+	0.840617i	$0.682193\pi$
$854$	−3.21251	−	7.63228i	−0.109930	−	0.261171i
$855$	−10.4377	−	2.98589i	−0.356962	−	0.102115i
$856$	−3.69245	+	4.47618i	−0.126205	+	0.152993i
$857$	−34.1889			−1.16787			−0.583935	−	0.811801i	$-0.698488\pi$
$857$	−34.1889			−1.16787			−0.583935	+	0.811801i	$0.698488\pi$
$858$	−15.5641	−	9.41604i	−0.531351	−	0.321458i
$859$	−23.3213	+	32.0991i	−0.795714	+	1.09521i	0.197659	+	0.980271i	$0.436666\pi$
$859$	−23.3213	+	32.0991i	−0.795714	+	1.09521i	−0.993373	+	0.114935i	$0.963334\pi$
$860$	6.46443	−	14.3101i	0.220435	−	0.487971i
$861$	5.68791	+	7.82874i	0.193843	+	0.266803i
$862$	2.40379	+	28.4663i	0.0818733	+	0.969567i
$863$	−7.24064	−	5.26064i	−0.246474	−	0.179074i	0.457688	−	0.889113i	$-0.348678\pi$
$863$	−7.24064	−	5.26064i	−0.246474	−	0.179074i	−0.704163	+	0.710039i	$0.748678\pi$
$864$	−2.81697	+	4.90558i	−0.0958352	+	0.166891i
$865$	−19.9157	−	25.4580i	−0.677153	−	0.865598i
$866$	1.94750	+	23.0628i	0.0661787	+	0.783707i
$867$	5.90621	−	1.91904i	0.200585	−	0.0651741i
$868$	11.2217	−	76.4883i	0.380891	−	2.59618i
$869$	−32.4262	+	10.5359i	−1.09998	+	0.357407i
$870$	2.89641	+	3.12099i	0.0981976	+	0.105811i
$871$	3.57743	−	11.0102i	0.121217	−	0.373066i
$872$	−16.2432	+	4.19483i	−0.550064	+	0.142055i
$873$	10.9460	−	7.95274i	0.370466	−	0.269160i
$874$	17.6522	−	15.2513i	0.597093	−	0.515884i
$875$	47.9053	−	5.12608i	1.61949	−	0.173293i
$876$	−1.49163	−	0.218840i	−0.0503976	−	0.00739393i
$877$	24.1742	+	33.2729i	0.816303	+	1.12354i	0.990320	+	0.138802i	$0.0443252\pi$
$877$	24.1742	+	33.2729i	0.816303	+	1.12354i	−0.174017	+	0.984743i	$0.555675\pi$
$878$	31.0308	−	13.0612i	1.04724	−	0.440795i
$879$	−3.47991	+	10.7101i	−0.117374	+	0.361241i
$880$	−11.7291	+	44.8458i	−0.395387	+	1.51175i
$881$	−2.12588	−	6.54278i	−0.0716226	−	0.220432i	0.908837	−	0.417151i	$-0.136971\pi$
$881$	−2.12588	−	6.54278i	−0.0716226	−	0.220432i	−0.980460	+	0.196719i	$0.936971\pi$
$882$	−10.6969	−	12.3808i	−0.360184	−	0.416883i
$883$	−30.4452	+	9.89225i	−1.02456	+	0.332901i	−0.772638	−	0.634846i	$-0.781063\pi$
$883$	−30.4452	+	9.89225i	−1.02456	+	0.332901i	−0.251924	+	0.967747i	$0.581063\pi$
$884$	17.1019	+	16.7161i	0.575198	+	0.562223i
$885$	−10.1900	+	7.97155i	−0.342532	+	0.267961i
$886$	8.16400	−	34.8807i	0.274275	−	1.17184i
$887$	31.8920	+	23.1709i	1.07083	+	0.778002i	0.976061	−	0.217498i	$-0.0697895\pi$
$887$	31.8920	+	23.1709i	1.07083	+	0.778002i	0.0947668	+	0.995500i	$0.469789\pi$
$888$	−23.6172	−	1.45262i	−0.792541	−	0.0487466i
$889$	12.3128	−	8.94574i	0.412957	−	0.300031i
$890$	5.25792	−	2.43648i	0.176246	−	0.0816711i
$891$	3.04623	−	4.19278i	0.102053	−	0.140463i
$892$	−50.6722	+	8.61930i	−1.69663	+	0.288595i
$893$		−	58.9846i		−	1.97384i
$894$	−2.68744	+	4.44218i	−0.0898816	+	0.148569i
$895$	−47.6554	−	13.6327i	−1.59294	−	0.455689i
$896$	−1.88217	+	48.7171i	−0.0628788	+	1.62753i
$897$	2.60579	−	8.01979i	0.0870048	−	0.267773i
$898$	48.3525	+	11.3171i	1.61354	+	0.377657i
$899$		−	12.0777i		−	0.402814i
$900$	5.25848	+	8.50579i	0.175283	+	0.283526i
$901$			43.8580i			1.46112i
$902$	−3.75084	+	16.0255i	−0.124889	+	0.533590i
$903$	−4.67559	+	14.3900i	−0.155594	+	0.478869i
$904$	−9.84291	−	38.1136i	−0.327370	−	1.26764i
$905$	49.6850	−	18.1191i	1.65158	−	0.602299i
$906$	−19.7988	−	11.9779i	−0.657771	−	0.397940i
$907$		−	11.5734i		−	0.384288i	−0.981367	−	0.192144i	$-0.938456\pi$
$907$		−	11.5734i		−	0.384288i	0.981367	−	0.192144i	$-0.0615441\pi$
$908$	2.07890	+	12.2217i	0.0689909	+	0.405592i
$909$	−5.21561	+	7.17866i	−0.172991	+	0.238101i
$910$	−24.7907	+	23.0068i	−0.821803	+	0.762669i
$911$	−21.9988	+	15.9831i	−0.728852	+	0.529542i	−0.889200	−	0.457518i	$-0.848738\pi$
$911$	−21.9988	+	15.9831i	−0.728852	+	0.529542i	0.160348	+	0.987061i	$0.448738\pi$
$912$	−11.7705	−	15.4470i	−0.389761	−	0.511502i
$913$	−16.4096	−	11.9222i	−0.543077	−	0.394569i
$914$	−38.0842	−	8.91378i	−1.25971	−	0.294842i
$915$	−1.04098	−	2.85449i	−0.0344136	−	0.0943667i
$916$	15.2498	+	14.9058i	0.503867	+	0.492501i
$917$	66.1398	−	21.4901i	2.18413	−	0.709667i
$918$	−5.15551	+	4.45433i	−0.170157	+	0.147015i
$919$	−6.04908	−	18.6172i	−0.199541	−	0.614123i	−0.999894	−	0.0145939i	$-0.995354\pi$
$919$	−6.04908	−	18.6172i	−0.199541	−	0.614123i	0.800353	−	0.599529i	$-0.204646\pi$
$920$	−21.4807	−	0.556398i	−0.708199	−	0.0183439i
$921$	8.95275	−	27.5537i	0.295003	−	0.907927i
$922$	−7.01621	−	16.6691i	−0.231066	−	0.548967i
$923$	5.20032	+	7.15762i	0.171171	+	0.235596i
$924$	6.48359	−	44.1927i	0.213295	−	1.45383i
$925$	−22.1213	+	35.5004i	−0.727345	+	1.16725i
$926$	−11.0474	−	12.7865i	−0.363041	−	0.420190i
$927$	3.54303	−	2.57416i	0.116368	−	0.0845466i
$928$	0.813874	+	7.57317i	0.0267167	+	0.248601i
$929$	−10.0704	+	30.9935i	−0.330399	+	1.01686i	0.638545	+	0.769584i	$0.279536\pi$
$929$	−10.0704	+	30.9935i	−0.330399	+	1.01686i	−0.968944	+	0.247279i	$0.920464\pi$
$930$	5.47909	−	27.8312i	0.179667	−	0.912621i
$931$	53.4223	−	17.3580i	1.75085	−	0.568884i
$932$	−0.224916	+	1.53304i	−0.00736735	+	0.0502165i
$933$	−15.9810	+	5.19255i	−0.523195	+	0.169997i
$934$	33.1887	−	2.80256i	1.08597	−	0.0917025i
$935$	−31.1908	+	46.3048i	−1.02005	+	1.51433i
$936$	−6.53065	−	2.57508i	−0.213461	−	0.0841690i
$937$	−22.4330	−	16.2985i	−0.732854	−	0.532449i	0.157611	−	0.987501i	$-0.449621\pi$
$937$	−22.4330	−	16.2985i	−0.732854	−	0.532449i	−0.890465	+	0.455052i	$0.849621\pi$
$938$	28.3250	−	2.39185i	0.924843	−	0.0780967i
$939$	5.13420	+	7.06662i	0.167548	+	0.230610i
$940$	−36.5733	+	40.1787i	−1.19289	+	1.31048i
$941$	2.73448	−	3.76368i	0.0891414	−	0.122693i	−0.762117	−	0.647439i	$-0.775840\pi$
$941$	2.73448	−	3.76368i	0.0891414	−	0.122693i	0.851258	+	0.524747i	$0.175840\pi$
$942$	1.83644	−	3.03552i	0.0598344	−	0.0989026i
$943$	−7.62954			−0.248452
$944$	−23.1374	+	0.527947i	−0.753059	+	0.0171832i
$945$	−5.93712	−	7.58936i	−0.193134	−	0.246882i
$946$	−23.7189	+	9.98354i	−0.771167	+	0.324593i
$947$	16.2281	+	5.27284i	0.527344	+	0.171344i	0.560576	−	0.828103i	$-0.310580\pi$
$947$	16.2281	+	5.27284i	0.527344	+	0.171344i	−0.0332318	+	0.999448i	$0.510580\pi$
$948$	−11.6546	+	6.10675i	−0.378523	+	0.198338i
$949$		−	1.87089i		−	0.0607317i
$950$	−33.9177	+	5.31050i	−1.10044	+	0.172295i
$951$	−13.2137			−0.428482
$952$	−21.5396	+	54.6266i	−0.698103	+	1.77046i
$953$	−0.659884	+	2.03091i	−0.0213757	+	0.0657878i	−0.961175	−	0.275938i	$-0.911011\pi$
$953$	−0.659884	+	2.03091i	−0.0213757	+	0.0657878i	0.939800	+	0.341726i	$0.111011\pi$
$954$	−4.99456	−	11.8661i	−0.161705	−	0.384178i
$955$	−22.6427	−	15.2521i	−0.732702	−	0.493546i
$956$	26.5506	−	4.51623i	0.858707	−	0.146065i
$957$		−	6.97815i		−	0.225571i
$958$	−15.0876	+	24.9390i	−0.487460	+	0.805741i
$959$	−29.5855	−	21.4951i	−0.955366	−	0.694114i
$960$	−1.56015	+	17.8204i	−0.0503535	+	0.575150i
$961$	−40.0136	+	29.0716i	−1.29076	+	0.937793i
$962$	−2.47077	−	29.2595i	−0.0796607	−	0.943365i
$963$	1.20586	−	1.65973i	0.0388584	−	0.0534840i
$964$	13.6325	+	26.0172i	0.439072	+	0.837958i
$965$	−22.4527	+	0.798145i	−0.722777	+	0.0256932i
$966$	20.6318	−	1.74222i	0.663818	−	0.0560549i
$967$	−3.17693	−	9.77757i	−0.102163	−	0.314426i	0.886891	−	0.461979i	$-0.152860\pi$
$967$	−3.17693	−	9.77757i	−0.102163	−	0.314426i	−0.989054	+	0.147553i	$0.952860\pi$
$968$	37.8392	−	24.0880i	1.21620	−	0.774218i
$969$	−7.22806	−	22.2457i	−0.232199	−	0.714634i
$970$	20.8325	−	37.3714i	0.668892	−	1.19992i
$971$	37.7018	+	12.2501i	1.20991	+	0.393123i	0.843397	−	0.537291i	$-0.180552\pi$
$971$	37.7018	+	12.2501i	1.20991	+	0.393123i	0.366511	+	0.930414i	$0.380552\pi$
$972$	0.887595	−	1.79225i	0.0284696	−	0.0574866i
$973$	50.5683	+	69.6013i	1.62114	+	2.23131i
$974$	−26.7175	−	30.9233i	−0.856083	−	0.990845i
$975$	−9.49640	+	7.98872i	−0.304128	+	0.255844i
$976$	1.56122	−	5.20617i	0.0499734	−	0.166646i
$977$	−20.6473	+	15.0012i	−0.660567	+	0.479930i	−0.866854	−	0.498561i	$-0.833862\pi$
$977$	−20.6473	+	15.0012i	−0.660567	+	0.479930i	0.206287	+	0.978491i	$0.433862\pi$
$978$	−6.01625	+	2.53231i	−0.192379	+	0.0809743i
$979$	−9.03244	−	2.93482i	−0.288678	−	0.0937972i
$980$	−47.1526	−	21.3007i	−1.50623	−	0.680425i
$981$	5.64095	−	1.83286i	0.180102	−	0.0585186i
$982$	−15.7310	+	13.5914i	−0.501995	+	0.433720i
$983$	−8.63673	−	26.5811i	−0.275469	−	0.847806i	−0.989095	−	0.147279i	$-0.952948\pi$
$983$	−8.63673	−	26.5811i	−0.275469	−	0.847806i	0.713626	−	0.700527i	$-0.247052\pi$
$984$	−0.389925	+	6.33955i	−0.0124304	+	0.202097i
$985$	20.8561	+	5.96625i	0.664530	+	0.190100i
$986$	−2.09067	+	8.93241i	−0.0665806	+	0.284466i
$987$	30.7721	−	42.3542i	0.979488	−	1.34815i
$988$	16.8460	−	17.2348i	0.535942	−	0.548311i
$989$	−7.01192	−	9.65108i	−0.222966	−	0.306887i
$990$	3.16566	−	16.0800i	0.100611	−	0.511057i
$991$	−8.87381	−	6.44720i	−0.281886	−	0.204802i	0.437854	−	0.899046i	$-0.355739\pi$
$991$	−8.87381	−	6.44720i	−0.281886	−	0.204802i	−0.719740	+	0.694244i	$0.755739\pi$
$992$	37.6289	−	34.0408i	1.19472	−	1.08080i
$993$	33.5904			1.06596
$994$	−11.2448	+	18.5870i	−0.356664	+	0.589543i
$995$	−43.2144	+	1.53618i	−1.36999	+	0.0487002i
$996$	−7.01447	−	3.47384i	−0.222262	−	0.110073i
$997$	−12.6657	−	4.11535i	−0.401128	−	0.130334i	0.101503	−	0.994835i	$-0.467635\pi$
$997$	−12.6657	−	4.11535i	−0.401128	−	0.130334i	−0.502631	+	0.864501i	$0.667635\pi$
$998$	3.79909	−	16.2316i	0.120258	−	0.513803i
$999$	8.36572			0.264680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bm.a.61.4	✓	240
8.5	even	2	inner	600.2.bm.a.61.30	yes	240
25.16	even	5	inner	600.2.bm.a.541.30	yes	240
200.141	even	10	inner	600.2.bm.a.541.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bm.a.61.4	✓	240	1.1	even	1	trivial
600.2.bm.a.61.30	yes	240	8.5	even	2	inner
600.2.bm.a.541.4	yes	240	200.141	even	10	inner
600.2.bm.a.541.30	yes	240	25.16	even	5	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bm (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37700 - 0.322293i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(1.79225 + 0.887595i) q^{4} +(-2.23466 + 0.0794374i) q^{5} +(1.21001 + 0.732035i) q^{6} -4.30924 q^{7} +(-2.18187 - 1.79985i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.10272 + 0.610829i) q^{10} +(-3.04623 - 4.19278i) q^{11} +(-1.43025 - 1.39799i) q^{12} +(1.45885 - 2.00793i) q^{13} +(5.93382 + 1.38884i) q^{14} +(2.14983 + 0.614997i) q^{15} +(2.42435 + 3.18159i) q^{16} +(1.48875 + 4.58190i) q^{17} +(-0.924577 - 1.07012i) q^{18} +(4.61750 - 1.50032i) q^{19} +(-4.07558 - 1.84110i) q^{20} +(4.09833 + 1.33163i) q^{21} +(2.84335 + 6.75523i) q^{22} +(-2.74867 + 1.99703i) q^{23} +(1.51889 + 2.38599i) q^{24} +(4.98738 - 0.355031i) q^{25} +(-2.65598 + 2.29475i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-7.72325 - 3.82486i) q^{28} +(-1.28057 - 0.416081i) q^{29} +(-2.76211 - 1.53973i) q^{30} +(2.77186 + 8.53091i) q^{31} +(-2.31292 - 5.16240i) q^{32} +(1.60150 + 4.92891i) q^{33} +(-0.573292 - 6.78908i) q^{34} +(9.62967 - 0.342315i) q^{35} +(0.928249 + 1.77154i) q^{36} +(-4.91725 + 6.76801i) q^{37} +(-6.84183 + 0.577746i) q^{38} +(-2.00793 + 1.45885i) q^{39} +(5.01870 + 3.84872i) q^{40} +(1.81673 + 1.31993i) q^{41} +(-5.21422 - 3.15451i) q^{42} +3.51118i q^{43} +(-1.73813 - 10.2183i) q^{44} +(-1.85457 - 1.24923i) q^{45} +(4.42854 - 1.86403i) q^{46} +(3.75423 - 11.5543i) q^{47} +(-1.32253 - 3.77504i) q^{48} +11.5695 q^{49} +(-6.98204 - 1.11852i) q^{50} -4.81769i q^{51} +(4.39686 - 2.30386i) q^{52} +(8.65798 + 2.81315i) q^{53} +(0.548639 + 1.30346i) q^{54} +(7.14034 + 9.12743i) q^{55} +(9.40219 + 7.75598i) q^{56} -4.85512 q^{57} +(1.62924 + 0.985662i) q^{58} +(-3.40084 + 4.68086i) q^{59} +(3.30718 + 3.01041i) q^{60} +(-0.798686 - 1.09930i) q^{61} +(-1.06740 - 12.6404i) q^{62} +(-3.48625 - 2.53291i) q^{63} +(1.52109 + 7.85406i) q^{64} +(-3.10052 + 4.60293i) q^{65} +(-0.616710 - 7.30325i) q^{66} +(4.43612 - 1.44138i) q^{67} +(-1.39865 + 9.53333i) q^{68} +(3.23126 - 1.04990i) q^{69} +(-13.3704 - 2.63221i) q^{70} +(-1.10154 + 3.39020i) q^{71} +(-0.707243 - 2.73858i) q^{72} +(0.609838 - 0.443073i) q^{73} +(8.95233 - 7.73475i) q^{74} +(-4.85299 - 1.20353i) q^{75} +(9.60740 + 1.40952i) q^{76} +(13.1269 + 18.0677i) q^{77} +(3.23510 - 1.36169i) q^{78} +(2.03296 - 6.25680i) q^{79} +(-5.67033 - 6.91718i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-2.07623 - 2.40307i) q^{82} +(3.72222 - 1.20942i) q^{83} +(6.16330 + 6.02427i) q^{84} +(-3.69082 - 10.1207i) q^{85} +(1.13163 - 4.83490i) q^{86} +(1.08932 + 0.791434i) q^{87} +(-0.899895 + 14.6308i) q^{88} +(1.48256 - 1.07714i) q^{89} +(2.15112 + 2.31791i) q^{90} +(-6.28653 + 8.65267i) q^{91} +(-6.69887 + 1.13947i) q^{92} -8.96992i q^{93} +(-8.89345 + 14.7003i) q^{94} +(-10.1993 + 3.71949i) q^{95} +(0.604451 + 5.62447i) q^{96} +(4.18100 - 12.8678i) q^{97} +(-15.9312 - 3.72878i) q^{98} -5.18256i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) \) 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

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