LMFDB - Embedded newform 600.2.bm.a.61.16

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			61.16
Character	$\chi$	$=$	600.61
Dual form			600.2.bm.a.541.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.950206 + 1.04743i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.194215 - 1.99055i) q^{4} +(1.11784 - 1.93660i) q^{5} +(1.22737 - 0.702534i) q^{6} +4.51209 q^{7} +(2.26950 + 1.68800i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.966272 + 3.01103i) q^{10} +(-1.61190 - 2.21859i) q^{11} +(-0.430403 + 1.95314i) q^{12} +(-0.411556 + 0.566458i) q^{13} +(-4.28742 + 4.72610i) q^{14} +(-1.66157 + 1.49639i) q^{15} +(-3.92456 + 0.773190i) q^{16} +(-1.08530 - 3.34021i) q^{17} +(-1.38440 + 0.288871i) q^{18} +(0.564031 - 0.183265i) q^{19} +(-4.07200 - 1.84900i) q^{20} +(-4.29125 - 1.39431i) q^{21} +(3.85545 + 0.419767i) q^{22} +(0.897976 - 0.652418i) q^{23} +(-1.63680 - 2.30670i) q^{24} +(-2.50085 - 4.32963i) q^{25} +(-0.202262 - 0.969328i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.876318 - 8.98153i) q^{28} +(-1.62221 - 0.527088i) q^{29} +(0.0114812 - 3.16226i) q^{30} +(2.95086 + 9.08180i) q^{31} +(2.91928 - 4.84539i) q^{32} +(0.847425 + 2.60811i) q^{33} +(4.52989 + 2.03712i) q^{34} +(5.04381 - 8.73812i) q^{35} +(1.01289 - 1.72454i) q^{36} +(5.41338 - 7.45088i) q^{37} +(-0.343989 + 0.764922i) q^{38} +(0.566458 - 0.411556i) q^{39} +(5.80594 - 2.50820i) q^{40} +(-1.74197 - 1.26562i) q^{41} +(5.53802 - 3.16990i) q^{42} +5.56243i q^{43} +(-4.10315 + 3.63944i) q^{44} +(2.04266 - 0.909692i) q^{45} +(-0.169901 + 1.56050i) q^{46} +(2.78094 - 8.55887i) q^{47} +(3.97141 + 0.477408i) q^{48} +13.3590 q^{49} +(6.91131 + 1.49458i) q^{50} +3.51211i q^{51} +(1.20749 + 0.709207i) q^{52} +(-5.23428 - 1.70072i) q^{53} +(1.40591 + 0.153070i) q^{54} +(-6.09837 + 0.641573i) q^{55} +(10.2402 + 7.61643i) q^{56} -0.593058 q^{57} +(2.09352 - 1.19831i) q^{58} +(-1.93999 + 2.67016i) q^{59} +(3.30133 + 3.01682i) q^{60} +(-7.38519 - 10.1648i) q^{61} +(-12.3165 - 5.53877i) q^{62} +(3.65036 + 2.65214i) q^{63} +(2.30128 + 7.66186i) q^{64} +(0.636949 + 1.43023i) q^{65} +(-3.53703 - 1.59062i) q^{66} +(13.1016 - 4.25697i) q^{67} +(-6.43807 + 2.80906i) q^{68} +(-1.05563 + 0.342996i) q^{69} +(4.35991 + 13.5861i) q^{70} +(-4.53468 + 13.9563i) q^{71} +(0.843882 + 2.69960i) q^{72} +(-4.32915 + 3.14531i) q^{73} +(2.66044 + 12.7500i) q^{74} +(1.04052 + 4.89053i) q^{75} +(-0.474341 - 1.08714i) q^{76} +(-7.27303 - 10.0105i) q^{77} +(-0.107177 + 0.984388i) q^{78} +(2.44930 - 7.53816i) q^{79} +(-2.88968 + 8.46462i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.98088 - 0.621996i) q^{82} +(11.4357 - 3.71570i) q^{83} +(-1.94202 + 8.81274i) q^{84} +(-7.68186 - 1.63204i) q^{85} +(-5.82625 - 5.28545i) q^{86} +(1.37994 + 1.00258i) q^{87} +(0.0867785 - 7.75598i) q^{88} +(4.61400 - 3.35227i) q^{89} +(-0.988110 + 3.00394i) q^{90} +(-1.85698 + 2.55591i) q^{91} +(-1.47307 - 1.66076i) q^{92} -9.54917i q^{93} +(6.32233 + 11.0455i) q^{94} +(0.275587 - 1.29717i) q^{95} +(-4.27371 + 3.70613i) q^{96} +(-0.672191 + 2.06879i) q^{97} +(-12.6938 + 13.9926i) q^{98} -2.74232i 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 $

$2$	−0.950206	+	1.04743i	−0.671897	+	0.740644i
$2$	−0.950206	+	1.04743i	−0.671897	+	0.740644i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.194215	−	1.99055i	−0.0971077	−	0.995274i
$5$	1.11784	−	1.93660i	0.499915	−	0.866075i
$5$	1.11784	−	1.93660i	0.499915	−	0.866075i
$6$	1.22737	−	0.702534i	0.501073	−	0.286808i
$7$	4.51209			1.70541			0.852705	−	0.522393i	$-0.174960\pi$
$7$	4.51209			1.70541			0.852705	+	0.522393i	$0.174960\pi$
$8$	2.26950	+	1.68800i	0.802390	+	0.596800i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.966272	+	3.01103i	0.305562	+	0.952172i
$11$	−1.61190	−	2.21859i	−0.486006	−	0.668929i	0.493640	−	0.869667i	$-0.335666\pi$
$11$	−1.61190	−	2.21859i	−0.486006	−	0.668929i	−0.979645	+	0.200737i	$0.935666\pi$
$12$	−0.430403	+	1.95314i	−0.124247	+	0.563823i
$13$	−0.411556	+	0.566458i	−0.114145	+	0.157107i	−0.862267	−	0.506454i	$-0.830956\pi$
$13$	−0.411556	+	0.566458i	−0.114145	+	0.157107i	0.748122	+	0.663562i	$0.230956\pi$
$14$	−4.28742	+	4.72610i	−1.14586	+	1.26310i
$15$	−1.66157	+	1.49639i	−0.429017	+	0.386365i
$16$	−3.92456	+	0.773190i	−0.981140	+	0.193298i
$17$	−1.08530	−	3.34021i	−0.263224	−	0.810120i	−0.992097	−	0.125472i	$-0.959956\pi$
$17$	−1.08530	−	3.34021i	−0.263224	−	0.810120i	0.728873	−	0.684649i	$-0.240044\pi$
$18$	−1.38440	+	0.288871i	−0.326305	+	0.0680875i
$19$	0.564031	−	0.183265i	0.129398	−	0.0420439i	−0.243602	−	0.969875i	$-0.578329\pi$
$19$	0.564031	−	0.183265i	0.129398	−	0.0420439i	0.373000	+	0.927831i	$0.378329\pi$
$20$	−4.07200	−	1.84900i	−0.910527	−	0.413449i
$21$	−4.29125	−	1.39431i	−0.936428	−	0.304264i
$22$	3.85545	+	0.419767i	0.821985	+	0.0894946i
$23$	0.897976	−	0.652418i	0.187241	−	0.136039i	−0.490216	−	0.871601i	$-0.663082\pi$
$23$	0.897976	−	0.652418i	0.187241	−	0.136039i	0.677457	+	0.735563i	$0.263082\pi$
$24$	−1.63680	−	2.30670i	−0.334111	−	0.470854i
$25$	−2.50085	−	4.32963i	−0.500171	−	0.865927i
$26$	−0.202262	−	0.969328i	−0.0396668	−	0.190101i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−0.876318	−	8.98153i	−0.165609	−	1.69735i
$29$	−1.62221	−	0.527088i	−0.301237	−	0.0978779i	0.154499	−	0.987993i	$-0.450624\pi$
$29$	−1.62221	−	0.527088i	−0.301237	−	0.0978779i	−0.455736	+	0.890115i	$0.650624\pi$
$30$	0.0114812	−	3.16226i	0.00209617	−	0.577346i
$31$	2.95086	+	9.08180i	0.529989	+	1.63114i	0.754234	+	0.656606i	$0.228009\pi$
$31$	2.95086	+	9.08180i	0.529989	+	1.63114i	−0.224244	+	0.974533i	$0.571991\pi$
$32$	2.91928	−	4.84539i	0.516061	−	0.856552i
$33$	0.847425	+	2.60811i	0.147518	+	0.454013i
$34$	4.52989	+	2.03712i	0.776870	+	0.349362i
$35$	5.04381	−	8.73812i	0.852559	−	1.47701i
$36$	1.01289	−	1.72454i	0.168815	−	0.287424i
$37$	5.41338	−	7.45088i	0.889954	−	1.22492i	−0.0836088	−	0.996499i	$-0.526645\pi$
$37$	5.41338	−	7.45088i	0.889954	−	1.22492i	0.973563	−	0.228418i	$-0.0733554\pi$
$38$	−0.343989	+	0.764922i	−0.0558024	+	0.124087i
$39$	0.566458	−	0.411556i	0.0907059	−	0.0659017i
$40$	5.80594	−	2.50820i	0.918000	−	0.396581i
$41$	−1.74197	−	1.26562i	−0.272051	−	0.197656i	0.443392	−	0.896328i	$-0.353775\pi$
$41$	−1.74197	−	1.26562i	−0.272051	−	0.197656i	−0.715443	+	0.698671i	$0.753775\pi$
$42$	5.53802	−	3.16990i	0.854535	−	0.489126i
$43$			5.56243i			0.848262i	0.905601	+	0.424131i	$0.139420\pi$
$43$			5.56243i			0.848262i	−0.905601	+	0.424131i	$0.860580\pi$
$44$	−4.10315	+	3.63944i	−0.618573	+	0.548667i
$45$	2.04266	−	0.909692i	0.304502	−	0.135609i
$46$	−0.169901	+	1.56050i	−0.0250506	+	0.230083i
$47$	2.78094	−	8.55887i	0.405642	−	1.24844i	−0.514715	−	0.857361i	$-0.672102\pi$
$47$	2.78094	−	8.55887i	0.405642	−	1.24844i	0.920358	−	0.391078i	$-0.127898\pi$
$48$	3.97141	+	0.477408i	0.573223	+	0.0689079i
$49$	13.3590			1.90842
$50$	6.91131	+	1.49458i	0.977407	+	0.211365i
$51$			3.51211i			0.491793i
$52$	1.20749	+	0.709207i	0.167449	+	0.0983493i
$53$	−5.23428	−	1.70072i	−0.718984	−	0.233612i	−0.0734014	−	0.997302i	$-0.523385\pi$
$53$	−5.23428	−	1.70072i	−0.718984	−	0.233612i	−0.645583	+	0.763690i	$0.723385\pi$
$54$	1.40591	+	0.153070i	0.191319	+	0.0208302i
$55$	−6.09837	+	0.641573i	−0.822304	+	0.0865097i
$56$	10.2402	+	7.61643i	1.36840	+	1.01779i
$57$	−0.593058			−0.0785524
$58$	2.09352	−	1.19831i	0.274893	−	0.157346i
$59$	−1.93999	+	2.67016i	−0.252565	+	0.347626i	−0.916407	−	0.400247i	$-0.868924\pi$
$59$	−1.93999	+	2.67016i	−0.252565	+	0.347626i	0.663843	+	0.747872i	$0.268924\pi$
$60$	3.30133	+	3.01682i	0.426200	+	0.389470i
$61$	−7.38519	−	10.1648i	−0.945576	−	1.30147i	−0.953464	−	0.301505i	$-0.902511\pi$
$61$	−7.38519	−	10.1648i	−0.945576	−	1.30147i	0.00788814	−	0.999969i	$-0.497489\pi$
$62$	−12.3165	−	5.53877i	−1.56419	−	0.703425i
$63$	3.65036	+	2.65214i	0.459902	+	0.334138i
$64$	2.30128	+	7.66186i	0.287660	+	0.957732i
$65$	0.636949	+	1.43023i	0.0790038	+	0.177398i
$66$	−3.53703	−	1.59062i	−0.435379	−	0.195792i
$67$	13.1016	−	4.25697i	1.60062	−	0.520072i	0.633356	−	0.773861i	$-0.281677\pi$
$67$	13.1016	−	4.25697i	1.60062	−	0.520072i	0.967260	+	0.253789i	$0.0816769\pi$
$68$	−6.43807	+	2.80906i	−0.780730	+	0.340649i
$69$	−1.05563	+	0.342996i	−0.127083	+	0.0412919i
$70$	4.35991	+	13.5861i	0.521108	+	1.62384i
$71$	−4.53468	+	13.9563i	−0.538167	+	1.65631i	0.198537	+	0.980093i	$0.436381\pi$
$71$	−4.53468	+	13.9563i	−0.538167	+	1.65631i	−0.736705	+	0.676215i	$0.763619\pi$
$72$	0.843882	+	2.69960i	0.0994524	+	0.318151i
$73$	−4.32915	+	3.14531i	−0.506689	+	0.368131i	−0.811566	−	0.584261i	$-0.801385\pi$
$73$	−4.32915	+	3.14531i	−0.506689	+	0.368131i	0.304877	+	0.952392i	$0.401385\pi$
$74$	2.66044	+	12.7500i	0.309270	+	1.48216i
$75$	1.04052	+	4.89053i	0.120149	+	0.564710i
$76$	−0.474341	−	1.08714i	−0.0544107	−	0.124703i
$77$	−7.27303	−	10.0105i	−0.828839	−	1.14080i
$78$	−0.107177	+	0.984388i	−0.0121354	+	0.111460i
$79$	2.44930	−	7.53816i	0.275567	−	0.848109i	−0.713501	−	0.700654i	$-0.752892\pi$
$79$	2.44930	−	7.53816i	0.275567	−	0.848109i	0.989069	−	0.147455i	$-0.0471083\pi$
$80$	−2.88968	+	8.46462i	−0.323076	+	0.946373i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.98088	−	0.621996i	0.329183	−	0.0686880i
$83$	11.4357	−	3.71570i	1.25524	−	0.407851i	0.395441	−	0.918491i	$-0.370592\pi$
$83$	11.4357	−	3.71570i	1.25524	−	0.407851i	0.859794	+	0.510641i	$0.170592\pi$
$84$	−1.94202	+	8.81274i	−0.211892	+	0.961549i
$85$	−7.68186	−	1.63204i	−0.833214	−	0.177019i
$86$	−5.82625	−	5.28545i	−0.628260	−	0.569945i
$87$	1.37994	+	1.00258i	0.147945	+	0.107488i
$88$	0.0867785	−	7.75598i	0.00925061	−	0.826790i
$89$	4.61400	−	3.35227i	0.489083	−	0.355339i	−0.315749	−	0.948843i	$-0.602256\pi$
$89$	4.61400	−	3.35227i	0.489083	−	0.355339i	0.804831	+	0.593503i	$0.202256\pi$
$90$	−0.988110	+	3.00394i	−0.104156	+	0.316643i
$91$	−1.85698	+	2.55591i	−0.194664	+	0.267932i
$92$	−1.47307	−	1.66076i	−0.153578	−	0.173146i
$93$		−	9.54917i		−	0.990203i
$94$	6.32233	+	11.0455i	0.652099	+	1.13926i
$95$	0.275587	−	1.29717i	0.0282747	−	0.133086i
$96$	−4.27371	+	3.70613i	−0.436184	+	0.378256i
$97$	−0.672191	+	2.06879i	−0.0682507	+	0.210054i	−0.979365	−	0.202100i	$-0.935223\pi$
$97$	−0.672191	+	2.06879i	−0.0682507	+	0.210054i	0.911114	+	0.412154i	$0.135223\pi$
$98$	−12.6938	+	13.9926i	−1.28226	+	1.41346i
$99$		−	2.74232i		−	0.275614i
$100$	−8.13264	+	5.81895i	−0.813264	+	0.581895i
$101$		−	2.97352i		−	0.295876i	−0.988997	−	0.147938i	$-0.952736\pi$
$101$		−	2.97352i		−	0.295876i	0.988997	−	0.147938i	$-0.0472637\pi$
$102$	−3.67868	−	3.33723i	−0.364244	−	0.330435i
$103$	5.21566	−	16.0521i	0.513914	−	1.58166i	−0.271335	−	0.962485i	$-0.587465\pi$
$103$	5.21566	−	16.0521i	0.513914	−	1.58166i	0.785249	−	0.619180i	$-0.212535\pi$
$104$	−1.89021	+	0.590870i	−0.185350	+	0.0579396i
$105$	−7.49718	+	6.75183i	−0.731649	+	0.658911i
$106$	6.75503	−	3.86650i	0.656107	−	0.375548i
$107$			14.1577i			1.36868i	0.729163	+	0.684340i	$0.239910\pi$
$107$			14.1577i			1.36868i	−0.729163	+	0.684340i	$0.760090\pi$
$108$	−1.49623	+	1.32714i	−0.143975	+	0.127704i
$109$	−3.66170	+	5.03990i	−0.350727	+	0.482735i	−0.947536	−	0.319649i	$-0.896435\pi$
$109$	−3.66170	+	5.03990i	−0.350727	+	0.482735i	0.596809	+	0.802384i	$0.296435\pi$
$110$	5.12271	−	6.99724i	0.488431	−	0.667160i
$111$	−7.45088	+	5.41338i	−0.707206	+	0.513815i
$112$	−17.7080	+	3.48871i	−1.67325	+	0.329652i
$113$	−8.45052	−	6.13966i	−0.794958	−	0.577571i	0.114473	−	0.993426i	$-0.463482\pi$
$113$	−8.45052	−	6.13966i	−0.794958	−	0.577571i	−0.909431	+	0.415856i	$0.863482\pi$
$114$	0.563527	−	0.621186i	0.0527792	−	0.0581794i
$115$	−0.259678	−	2.46832i	−0.0242151	−	0.230172i
$116$	−0.734136	+	3.33146i	−0.0681628	+	0.309318i
$117$	−0.665912	+	0.216368i	−0.0615636	+	0.0200032i
$118$	−0.953419	−	4.56921i	−0.0877693	−	0.420630i
$119$	−4.89697	−	15.0713i	−0.448905	−	1.38159i
$120$	−6.29685	+	0.591305i	−0.574821	+	0.0539785i
$121$	1.07527	−	3.30935i	0.0977520	−	0.300850i
$122$	17.6644	+	1.92323i	1.59926	+	0.174121i
$123$	1.26562	+	1.74197i	0.114117	+	0.157069i
$124$	17.5047	−	7.63764i	1.57196	−	0.685881i
$125$	−11.1803	+	0.00331017i	−1.00000	+	0.000296070i
$126$	−6.24652	+	1.30341i	−0.556485	+	0.116117i
$127$	3.26915	−	2.37518i	0.290091	−	0.210763i	−0.433216	−	0.901290i	$-0.642621\pi$
$127$	3.26915	−	2.37518i	0.290091	−	0.210763i	0.723307	+	0.690527i	$0.242621\pi$
$128$	−10.2119	−	4.86992i	−0.902617	−	0.430444i
$129$	1.71888	−	5.29018i	0.151339	−	0.465774i
$130$	−2.10330	−	0.691856i	−0.184472	−	0.0606798i
$131$	−1.71246	+	0.556413i	−0.149619	+	0.0486141i	−0.382869	−	0.923803i	$-0.625064\pi$
$131$	−1.71246	+	0.556413i	−0.149619	+	0.0486141i	0.233250	+	0.972417i	$0.425064\pi$
$132$	5.02698	−	2.19337i	0.437542	−	0.190909i
$133$	2.54496	−	0.826908i	0.220676	−	0.0717020i
$134$	−7.99035	+	17.7680i	−0.690262	+	1.53492i
$135$	−2.22380	+	0.233952i	−0.191394	+	0.0201354i
$136$	3.17520	−	9.41261i	0.272271	−	0.807125i
$137$	3.43939	+	2.49886i	0.293847	+	0.213492i	0.724934	−	0.688818i	$-0.241870\pi$
$137$	3.43939	+	2.49886i	0.293847	+	0.213492i	−0.431088	+	0.902310i	$0.641870\pi$
$138$	0.643806	−	1.43162i	0.0548044	−	0.121868i
$139$	8.16151	+	11.2333i	0.692250	+	0.952800i	0.999999	+	0.00133273i	$0.000424221\pi$
$139$	8.16151	+	11.2333i	0.692250	+	0.952800i	−0.307749	+	0.951468i	$0.599576\pi$
$140$	−18.3732	−	8.34286i	−1.55282	−	0.705101i
$141$	−5.28967	+	7.28061i	−0.445471	+	0.613138i
$142$	−10.3094	−	18.0111i	−0.865142	−	1.51146i
$143$	1.92012			0.160569
$144$	−3.62951	−	1.68127i	−0.302459	−	0.140106i
$145$	−2.83414	+	2.55238i	−0.235362	+	0.211963i
$146$	0.819095	−	7.52317i	0.0677888	−	0.622622i
$147$	−12.7051	−	4.12815i	−1.04790	−	0.340484i
$148$	−15.8827	−	9.32852i	−1.30555	−	0.766799i
$149$			10.7286i			0.878925i	0.898261	+	0.439462i	$0.144831\pi$
$149$			10.7286i			0.878925i	−0.898261	+	0.439462i	$0.855169\pi$
$150$	−6.11120	−	3.55714i	−0.498977	−	0.290439i
$151$	−14.7375			−1.19932			−0.599659	−	0.800256i	$-0.704697\pi$
$151$	−14.7375			−1.19932			−0.599659	+	0.800256i	$0.704697\pi$
$152$	1.58942	+	0.536167i	0.128919	+	0.0434889i
$153$	1.08530	−	3.34021i	0.0877413	−	0.270040i
$154$	17.3961	+	1.89403i	1.40182	+	0.152625i
$155$	20.8864	+	4.43739i	1.67764	+	0.356420i
$156$	−0.929237	−	1.04763i	−0.0743985	−	0.0838777i
$157$			20.5516i			1.64019i	0.572225	+	0.820096i	$0.306080\pi$
$157$			20.5516i			1.64019i	−0.572225	+	0.820096i	$0.693920\pi$
$158$	5.56835	+	9.72827i	0.442994	+	0.773940i
$159$	4.45255	+	3.23496i	0.353110	+	0.256549i
$160$	−6.12029	−	11.0699i	−0.483852	−	0.875150i
$161$	4.05175	−	2.94377i	0.319323	−	0.232002i
$162$	−1.28979	−	0.580027i	−0.101336	−	0.0455712i
$163$	−8.04964	+	11.0794i	−0.630497	+	0.867804i	−0.998064	−	0.0621925i	$-0.980191\pi$
$163$	−8.04964	+	11.0794i	−0.630497	+	0.867804i	0.367567	+	0.929997i	$0.380191\pi$
$164$	−2.18096	+	3.71329i	−0.170304	+	0.289959i
$165$	5.99815	+	1.27433i	0.466955	+	0.0992063i
$166$	−6.97438	+	15.5088i	−0.541317	+	1.20372i
$167$	4.29389	+	13.2152i	0.332271	+	1.02262i	0.968051	+	0.250754i	$0.0806786\pi$
$167$	4.29389	+	13.2152i	0.332271	+	1.02262i	−0.635780	+	0.771870i	$0.719321\pi$
$168$	−7.38540	−	10.4081i	−0.569796	−	0.802999i
$169$	3.86572	+	11.8975i	0.297363	+	0.915190i
$170$	9.00879	−	6.49543i	0.690943	−	0.498177i
$171$	0.564031	+	0.183265i	0.0431326	+	0.0140146i
$172$	11.0723	−	1.08031i	0.844253	−	0.0823728i
$173$	13.7845	+	18.9728i	1.04802	+	1.44248i	0.890513	+	0.454957i	$0.150346\pi$
$173$	13.7845	+	18.9728i	1.04802	+	1.44248i	0.157507	+	0.987518i	$0.449654\pi$
$174$	−2.36136	+	0.492725i	−0.179014	+	0.0373534i
$175$	−11.2841	−	19.5357i	−0.852997	−	1.47676i
$176$	8.04138	+	7.46068i	0.606142	+	0.562370i
$177$	2.67016	−	1.93999i	0.200702	−	0.145818i
$178$	−0.872990	+	8.01818i	−0.0654333	+	0.600988i
$179$	−11.8123	−	3.83806i	−0.882896	−	0.286870i	−0.167737	−	0.985832i	$-0.553646\pi$
$179$	−11.8123	−	3.83806i	−0.882896	−	0.286870i	−0.715159	+	0.698961i	$0.753646\pi$
$180$	−2.20750	−	3.88934i	−0.164538	−	0.289894i
$181$	−7.05779	+	2.29322i	−0.524602	+	0.170453i	−0.559333	−	0.828943i	$-0.688943\pi$
$181$	−7.05779	+	2.29322i	−0.524602	+	0.170453i	0.0347310	+	0.999397i	$0.488943\pi$
$182$	−0.912623	−	4.37370i	−0.0676481	−	0.324200i
$183$	3.88262	+	11.9495i	0.287012	+	0.883331i
$184$	3.13924	+	0.0351237i	0.231428	+	0.00258935i
$185$	−8.37808	−	18.8125i	−0.615969	−	1.38312i
$186$	10.0021	+	9.07368i	0.733388	+	0.665315i
$187$	−5.66116	+	7.79191i	−0.413985	+	0.569801i
$188$	−17.5769	−	3.87334i	−1.28193	−	0.282492i
$189$	−2.65214	−	3.65036i	−0.192915	−	0.265524i
$190$	1.09682	+	1.52123i	0.0795720	+	0.110362i
$191$	−5.16238	−	3.75069i	−0.373537	−	0.271390i	0.385139	−	0.922859i	$-0.374153\pi$
$191$	−5.16238	−	3.75069i	−0.373537	−	0.271390i	−0.758676	+	0.651468i	$0.774153\pi$
$192$	0.178995	−	7.99800i	0.0129178	−	0.577206i
$193$	13.4470			0.967933			0.483966	−	0.875087i	$-0.339196\pi$
$193$	13.4470			0.967933			0.483966	+	0.875087i	$0.339196\pi$
$194$	−1.52819	−	2.66985i	−0.109718	−	0.191684i
$195$	−0.163809	−	1.55706i	−0.0117306	−	0.111503i
$196$	−2.59452	−	26.5917i	−0.185323	−	1.89940i
$197$	2.29537	+	0.745810i	0.163538	+	0.0531367i	0.389642	−	0.920966i	$-0.372599\pi$
$197$	2.29537	+	0.745810i	0.163538	+	0.0531367i	−0.226104	+	0.974103i	$0.572599\pi$
$198$	2.87239	+	2.60577i	0.204132	+	0.185184i
$199$	−23.4983			−1.66575			−0.832874	−	0.553463i	$-0.813306\pi$
$199$	−23.4983			−1.66575			−0.832874	+	0.553463i	$0.813306\pi$
$200$	1.63274	−	14.0476i	0.115452	−	0.993313i
$201$	−13.7758			−0.971673
$202$	3.11455	+	2.82546i	0.219139	+	0.198799i
$203$	−7.31957	−	2.37827i	−0.513733	−	0.166922i
$204$	6.99101	−	0.682105i	0.489469	−	0.0477569i
$205$	−4.39825	+	1.95875i	−0.307187	+	0.136805i
$206$	11.8575	+	20.7159i	0.826153	+	1.44334i
$207$	1.10996			0.0771475
$208$	1.17720	−	2.54131i	0.0816239	−	0.176208i
$209$	−1.31575	−	0.955949i	−0.0910124	−	0.0661244i
$210$	0.0518042	−	14.2684i	0.00357483	−	0.984612i
$211$	1.09216	+	1.50323i	0.0751876	+	0.103487i	0.844954	−	0.534838i	$-0.179628\pi$
$211$	1.09216	+	1.50323i	0.0751876	+	0.103487i	−0.769767	+	0.638325i	$0.779628\pi$
$212$	−2.36879	+	10.7494i	−0.162689	+	0.738272i
$213$	8.62547	−	11.8719i	0.591007	−	0.813452i
$214$	−14.8292	−	13.4528i	−1.01371	−	0.919613i
$215$	10.7722	+	6.21792i	0.734658	+	0.424058i
$216$	0.0316441	−	2.82825i	0.00215311	−	0.192438i
$217$	13.3145	+	40.9779i	0.903849	+	2.78176i
$218$	−1.79957	−	8.62432i	−0.121882	−	0.584113i
$219$	5.08922	−	1.65359i	0.343898	−	0.111739i
$220$	2.46148	+	12.0145i	0.165953	+	0.810017i
$221$	2.33875	+	0.759907i	0.157322	+	0.0511169i
$222$	1.40974	−	12.9481i	0.0946156	−	0.869019i
$223$	−16.0752	+	11.6793i	−1.07647	+	0.782103i	−0.977064	−	0.212944i	$-0.931695\pi$
$223$	−16.0752	+	11.6793i	−1.07647	+	0.782103i	−0.0994075	+	0.995047i	$0.531695\pi$
$224$	13.1721	−	21.8628i	0.880095	−	1.46077i
$225$	0.521661	−	4.97271i	0.0347774	−	0.331514i
$226$	14.4606	−	3.01737i	0.961905	−	0.200713i
$227$	16.4486	+	22.6396i	1.09173	+	1.50264i	0.845907	+	0.533330i	$0.179060\pi$
$227$	16.4486	+	22.6396i	1.09173	+	1.50264i	0.245827	+	0.969314i	$0.420940\pi$
$228$	0.115181	+	1.18051i	0.00762805	+	0.0781812i
$229$	1.63673	+	0.531806i	0.108158	+	0.0351427i	0.362596	−	0.931946i	$-0.381890\pi$
$229$	1.63673	+	0.531806i	0.108158	+	0.0351427i	−0.254438	+	0.967089i	$0.581890\pi$
$230$	2.83214	+	2.07342i	0.186746	+	0.136717i
$231$	3.82366	+	11.7680i	0.251578	+	0.774278i
$232$	−2.79189	−	3.93453i	−0.183296	−	0.258314i
$233$	−8.18709	−	25.1973i	−0.536354	−	1.65073i	−0.740704	−	0.671831i	$-0.765508\pi$
$233$	−8.18709	−	25.1973i	−0.536354	−	1.65073i	0.204350	−	0.978898i	$-0.434492\pi$
$234$	0.406124	−	0.903089i	0.0265491	−	0.0590368i
$235$	−13.4665	−	14.9530i	−0.878455	−	0.975429i
$236$	5.69187	+	3.34305i	0.370509	+	0.217614i
$237$	−4.65884	+	6.41234i	−0.302624	+	0.416526i
$238$	20.4393	+	9.19165i	1.32488	+	0.595806i
$239$	4.28234	−	3.11130i	0.277001	−	0.201253i	−0.440607	−	0.897700i	$-0.645237\pi$
$239$	4.28234	−	3.11130i	0.277001	−	0.201253i	0.717608	+	0.696447i	$0.245237\pi$
$240$	5.36396	−	7.15737i	0.346242	−	0.462006i
$241$	9.65865	+	7.01742i	0.622169	+	0.452032i	0.853678	−	0.520801i	$-0.174367\pi$
$241$	9.65865	+	7.01742i	0.622169	+	0.452032i	−0.231510	+	0.972833i	$0.574367\pi$
$242$	2.44458	+	4.27083i	0.157143	+	0.274540i
$243$		−	1.00000i		−	0.0641500i
$244$	−18.7993	+	16.6747i	−1.20350	+	1.06749i
$245$	14.9332	−	25.8710i	0.954049	−	1.65284i
$246$	−3.02719	−	0.329590i	−0.193007	−	0.0210139i
$247$	−0.128319	+	0.394924i	−0.00816472	+	0.0251284i
$248$	−8.63314	+	25.5922i	−0.548205	+	1.62511i
$249$	−12.0242			−0.762006
$250$	10.6202	−	11.7138i	0.671678	−	0.740843i
$251$			2.93108i			0.185008i	0.995712	+	0.0925042i	$0.0294872\pi$
$251$			2.93108i			0.185008i	−0.995712	+	0.0925042i	$0.970513\pi$
$252$	4.57026	−	7.78130i	0.287899	−	0.490176i
$253$	−2.89489	−	0.940608i	−0.182000	−	0.0591355i
$254$	−0.618539	+	5.68112i	−0.0388106	+	0.356465i
$255$	6.80155	+	3.92598i	0.425930	+	0.245855i
$256$	14.8044	−	6.06886i	0.925272	−	0.379304i
$257$	15.9650			0.995870			0.497935	−	0.867214i	$-0.334092\pi$
$257$	15.9650			0.995870			0.497935	+	0.867214i	$0.334092\pi$
$258$	3.90779	+	6.82717i	0.243289	+	0.425041i
$259$	24.4257	−	33.6190i	1.51774	−	2.08899i
$260$	2.72324	−	1.54565i	0.168888	−	0.0958572i
$261$	−1.00258	−	1.37994i	−0.0620583	−	0.0854159i
$262$	1.04439	−	2.32239i	0.0645227	−	0.143478i
$263$	17.4351	+	12.6673i	1.07509	+	0.781100i	0.976820	−	0.214060i	$-0.0686688\pi$
$263$	17.4351	+	12.6673i	1.07509	+	0.781100i	0.0982709	+	0.995160i	$0.468669\pi$
$264$	−2.47926	+	7.34956i	−0.152588	+	0.452334i
$265$	−9.14473	+	8.23558i	−0.561756	+	0.505908i
$266$	−1.55211	+	3.45140i	−0.0951660	+	0.211619i
$267$	−5.42408	+	1.76239i	−0.331948	+	0.107857i
$268$	−11.0182	−	25.2526i	−0.673046	−	1.54255i
$269$	24.2612	−	7.88293i	1.47923	−	0.480631i	0.545347	−	0.838211i	$-0.316398\pi$
$269$	24.2612	−	7.88293i	1.47923	−	0.480631i	0.933883	+	0.357580i	$0.116398\pi$
$270$	1.86802	−	2.55157i	0.113684	−	0.155284i
$271$	−3.10591	+	9.55901i	−0.188671	+	0.580669i	−0.999992	−	0.00393152i	$-0.998749\pi$
$271$	−3.10591	+	9.55901i	−0.188671	+	0.580669i	0.811322	+	0.584600i	$0.198749\pi$
$272$	6.84195	+	12.2697i	0.414854	+	0.743961i
$273$	2.55591	−	1.85698i	0.154691	−	0.112389i
$274$	−5.88551	+	1.22808i	−0.355557	+	0.0741911i
$275$	−5.57455	+	12.5273i	−0.336158	+	0.755424i
$276$	0.887771	+	2.03468i	0.0534376	+	0.122473i
$277$	−17.8119	−	24.5160i	−1.07021	−	1.47302i	−0.869861	−	0.493297i	$-0.835792\pi$
$277$	−17.8119	−	24.5160i	−1.07021	−	1.47302i	−0.200352	−	0.979724i	$-0.564208\pi$
$278$	−19.5213	−	2.12540i	−1.17081	−	0.127473i
$279$	−2.95086	+	9.08180i	−0.176663	+	0.543713i
$280$	26.1969	−	11.3172i	1.56557	−	0.676333i
$281$	2.47409	+	7.61446i	0.147592	+	0.454241i	0.997335	−	0.0729558i	$-0.0232432\pi$
$281$	2.47409	+	7.61446i	0.147592	+	0.454241i	−0.849743	+	0.527196i	$0.823243\pi$
$282$	−2.59964	−	12.4586i	−0.154806	−	0.741901i
$283$	−12.4483	+	4.04470i	−0.739976	+	0.240433i	−0.654662	−	0.755922i	$-0.727189\pi$
$283$	−12.4483	+	4.04470i	−0.739976	+	0.240433i	−0.0853133	+	0.996354i	$0.527189\pi$
$284$	28.6614	+	6.31596i	1.70074	+	0.374783i
$285$	−0.662945	+	1.14852i	−0.0392695	+	0.0680323i
$286$	−1.82451	+	2.01119i	−0.107886	+	0.118924i
$287$	−7.85995	−	5.71059i	−0.463958	−	0.337085i
$288$	5.20980	−	2.20409i	0.306990	−	0.129877i
$289$	3.77415	−	2.74208i	0.222009	−	0.161299i
$290$	0.0195834	−	5.39384i	0.00114998	−	0.316737i
$291$	1.27858	−	1.75982i	0.0749519	−	0.103162i
$292$	7.10168	+	8.00651i	0.415594	+	0.468546i
$293$			10.0764i			0.588670i	0.955702	+	0.294335i	$0.0950981\pi$
$293$			10.0764i			0.588670i	−0.955702	+	0.294335i	$0.904902\pi$
$294$	16.3964	−	9.38513i	0.956260	−	0.547352i
$295$	3.00244	+	6.74181i	0.174809	+	0.392523i
$296$	24.8628	−	7.77198i	1.44512	−	0.451737i
$297$	−0.847425	+	2.60811i	−0.0491726	+	0.151338i
$298$	−11.2375	−	10.1944i	−0.650970	−	0.590547i
$299$			0.777173i			0.0449451i
$300$	9.53275	−	3.02103i	0.550374	−	0.174419i
$301$			25.0982i			1.44663i
$302$	14.0036	−	15.4364i	0.805818	−	0.888268i
$303$	−0.918869	+	2.82799i	−0.0527876	+	0.162464i
$304$	−2.07188	+	1.15534i	−0.118830	+	0.0662632i
$305$	−27.9407	+	2.93948i	−1.59988	+	0.168314i
$306$	2.46738	+	4.31067i	0.141050	+	0.246424i
$307$			1.44022i			0.0821974i	0.999155	+	0.0410987i	$0.0130858\pi$
$307$			1.44022i			0.0821974i	−0.999155	+	0.0410987i	$0.986914\pi$
$308$	−18.5138	+	16.4215i	−1.05492	+	0.935702i
$309$	−9.92077	+	13.6548i	−0.564373	+	0.776793i
$310$	−24.4943	+	17.6606i	−1.39118	+	1.00306i
$311$	4.20491	−	3.05505i	0.238439	−	0.173236i	−0.462149	−	0.886802i	$-0.652921\pi$
$311$	4.20491	−	3.05505i	0.238439	−	0.173236i	0.700587	+	0.713567i	$0.252921\pi$
$312$	1.98029	+	0.0221566i	0.112112	+	0.00125437i
$313$	1.03608	+	0.752755i	0.0585626	+	0.0425482i	0.616681	−	0.787213i	$-0.288477\pi$
$313$	1.03608	+	0.752755i	0.0585626	+	0.0425482i	−0.558119	+	0.829761i	$0.688477\pi$
$314$	−21.5263	−	19.5282i	−1.21480	−	1.10204i
$315$	9.21667	−	4.10461i	0.519300	−	0.231269i
$316$	−15.4808	−	3.41142i	−0.870861	−	0.191907i
$317$	−9.71888	+	3.15786i	−0.545867	+	0.177363i	−0.568952	−	0.822371i	$-0.692651\pi$
$317$	−9.71888	+	3.15786i	−0.545867	+	0.177363i	0.0230854	+	0.999733i	$0.492651\pi$
$318$	−7.61923	+	1.58984i	−0.427265	+	0.0891540i
$319$	1.44545	+	4.44863i	0.0809295	+	0.249076i
$320$	17.4104	+	4.10809i	0.973274	+	0.229649i
$321$	4.37498	−	13.4648i	0.244188	−	0.751533i
$322$	−0.766610	+	7.04111i	−0.0427215	+	0.392386i
$323$	−1.22429	−	1.68509i	−0.0681212	−	0.0937607i
$324$	1.83311	−	0.799823i	0.101839	−	0.0444346i
$325$	3.48180	+	0.365257i	0.193135	+	0.0202608i
$326$	−3.95605	−	18.9591i	−0.219105	−	1.05005i
$327$	5.03990	−	3.66170i	0.278707	−	0.202493i
$328$	−1.81705	−	5.81278i	−0.100330	−	0.320957i
$329$	12.5479	−	38.6184i	0.691787	−	2.12910i
$330$	−7.03425	+	5.07176i	−0.387223	+	0.279191i
$331$	13.0812	−	4.25034i	0.719007	−	0.233620i	0.0734146	−	0.997302i	$-0.476610\pi$
$331$	13.0812	−	4.25034i	0.719007	−	0.233620i	0.645593	+	0.763682i	$0.276610\pi$
$332$	−9.61727	−	22.0417i	−0.527816	−	1.20970i
$333$	8.75903	−	2.84598i	0.479992	−	0.155959i
$334$	−17.9221	−	8.05965i	−0.980653	−	0.441004i
$335$	6.40148	−	30.1312i	0.349750	−	1.64624i
$336$	17.9194	+	2.15411i	0.977581	+	0.117516i
$337$	17.5041	+	12.7174i	0.953507	+	0.692763i	0.951634	−	0.307235i	$-0.0994038\pi$
$337$	17.5041	+	12.7174i	0.953507	+	0.692763i	0.00187305	+	0.999998i	$0.499404\pi$
$338$	−16.1350	−	7.25599i	−0.877628	−	0.394674i
$339$	6.13966	+	8.45052i	0.333461	+	0.458969i
$340$	−1.75671	+	15.6081i	−0.0952710	+	0.846466i
$341$	15.3923	−	21.1857i	0.833539	−	1.14727i
$342$	−0.727903	+	0.416643i	−0.0393605	+	0.0225295i
$343$	28.6922			1.54923
$344$	−9.38940	+	12.6239i	−0.506242	+	0.680637i
$345$	−0.515786	+	2.42776i	−0.0277690	+	0.130706i
$346$	−32.9708	−	3.58974i	−1.77252	−	0.192986i
$347$	19.9928	+	6.49607i	1.07327	+	0.348727i	0.791761	−	0.610831i	$-0.209164\pi$
$347$	19.9928	+	6.49607i	1.07327	+	0.348727i	0.281511	+	0.959558i	$0.409164\pi$
$348$	1.72768	−	2.94154i	0.0926135	−	0.157683i
$349$			11.4483i			0.612815i	0.951901	+	0.306407i	$0.0991269\pi$
$349$			11.4483i			0.612815i	−0.951901	+	0.306407i	$0.900873\pi$
$350$	31.1845	+	6.74367i	1.66688	+	0.360464i
$351$	0.700181			0.0373729
$352$	−15.4555	+	1.33359i	−0.823781	+	0.0710808i
$353$	−2.82197	+	8.68512i	−0.150198	+	0.462262i	−0.997643	−	0.0686215i	$-0.978140\pi$
$353$	−2.82197	+	8.68512i	−0.150198	+	0.462262i	0.847445	+	0.530884i	$0.178140\pi$
$354$	−0.505207	+	4.64020i	−0.0268515	+	0.246624i
$355$	21.9587	+	24.3828i	1.16545	+	1.29411i
$356$	−7.56895	−	8.53332i	−0.401154	−	0.452265i
$357$			15.8469i			0.838709i
$358$	15.2443	−	8.72564i	0.805685	−	0.461165i
$359$	−12.1769	−	8.84703i	−0.642672	−	0.466928i	0.218095	−	0.975927i	$-0.430016\pi$
$359$	−12.1769	−	8.84703i	−0.642672	−	0.466928i	−0.860767	+	0.508999i	$0.830016\pi$
$360$	6.17139	+	1.38347i	0.325261	+	0.0729153i
$361$	−15.0868	+	10.9612i	−0.794041	+	0.576904i
$362$	4.30438	−	9.57157i	0.226233	−	0.503070i
$363$	−2.04529	+	2.81510i	−0.107350	+	0.147754i
$364$	5.44832	+	3.20001i	0.285569	+	0.167726i
$365$	1.25191	+	11.8998i	0.0655278	+	0.622864i
$366$	−16.2055	−	7.28770i	−0.847077	−	0.380934i
$367$	−7.75779	−	23.8760i	−0.404953	−	1.24632i	−0.920934	−	0.389718i	$-0.872573\pi$
$367$	−7.75779	−	23.8760i	−0.404953	−	1.24632i	0.515981	−	0.856600i	$-0.327427\pi$
$368$	−3.01972	+	3.25476i	−0.157414	+	0.169666i
$369$	−0.665375	−	2.04781i	−0.0346380	−	0.106605i
$370$	27.6656	+	9.10029i	1.43827	+	0.473102i
$371$	−23.6176	−	7.67381i	−1.22616	−	0.398404i
$372$	−19.0081	+	1.85460i	−0.985523	+	0.0961563i
$373$	−8.15207	−	11.2204i	−0.422098	−	0.580968i	0.544019	−	0.839073i	$-0.316902\pi$
$373$	−8.15207	−	11.2204i	−0.422098	−	0.580968i	−0.966117	+	0.258105i	$0.916902\pi$
$374$	−2.78221	−	13.3336i	−0.143865	−	0.689463i
$375$	10.6342	+	3.45177i	0.549146	+	0.178248i
$376$	20.7588	−	14.7301i	1.07055	−	0.759648i
$377$	0.966205	−	0.701989i	0.0497621	−	0.0361543i
$378$	6.34357	+	0.690665i	0.326278	+	0.0355240i
$379$	11.2698	+	3.66177i	0.578889	+	0.188092i	0.583803	−	0.811896i	$-0.301564\pi$
$379$	11.2698	+	3.66177i	0.578889	+	0.188092i	−0.00491392	+	0.999988i	$0.501564\pi$
$380$	−2.63559	−	0.296640i	−0.135203	−	0.0152173i
$381$	−3.84312	+	1.24871i	−0.196889	+	0.0639731i
$382$	8.83391	−	1.84330i	0.451982	−	0.0943114i
$383$	4.62551	+	14.2359i	0.236352	+	0.727418i	0.996939	+	0.0781817i	$0.0249114\pi$
$383$	4.62551	+	14.2359i	0.236352	+	0.727418i	−0.760587	+	0.649236i	$0.775089\pi$
$384$	8.20725	+	7.78723i	0.418825	+	0.397391i
$385$	−27.5164	+	2.89484i	−1.40237	+	0.147534i
$386$	−12.7774	+	14.0847i	−0.650352	+	0.716894i
$387$	−3.26951	+	4.50010i	−0.166199	+	0.228753i
$388$	4.24858	+	0.936238i	0.215689	+	0.0475303i
$389$	−3.30414	−	4.54775i	−0.167526	−	0.230580i	0.716997	−	0.697076i	$-0.245516\pi$
$389$	−3.30414	−	4.54775i	−0.167526	−	0.230580i	−0.884523	+	0.466496i	$0.845516\pi$
$390$	1.78656	+	1.30795i	0.0904661	+	0.0662306i
$391$	−3.15379	−	2.29136i	−0.159494	−	0.115879i
$392$	30.3182	+	22.5500i	1.53130	+	1.13895i
$393$	1.80059			0.0908278
$394$	−2.96225	+	1.69556i	−0.149236	+	0.0854211i
$395$	−11.8605	−	13.1698i	−0.596766	−	0.662644i
$396$	−5.45873	+	0.532602i	−0.274311	+	0.0267643i
$397$	33.1333	+	10.7656i	1.66291	+	0.540312i	0.981479	−	0.191569i	$-0.0613577\pi$
$397$	33.1333	+	10.7656i	1.66291	+	0.540312i	0.681432	+	0.731882i	$0.261358\pi$
$398$	22.3282	−	24.6128i	1.11921	−	1.23373i
$399$	−2.67593			−0.133964
$400$	13.1624	+	15.0583i	0.658119	+	0.752914i
$401$	12.2527			0.611870			0.305935	−	0.952052i	$-0.401031\pi$
$401$	12.2527			0.611870			0.305935	+	0.952052i	$0.401031\pi$
$402$	13.0899	−	14.4292i	0.652865	−	0.719664i
$403$	−6.35890	−	2.06613i	−0.316760	−	0.102921i
$404$	−5.91894	+	0.577504i	−0.294478	+	0.0287319i
$405$	2.18725	+	0.464689i	0.108685	+	0.0230906i
$406$	9.44617	−	5.40688i	0.468806	−	0.268339i
$407$	−25.2562			−1.25191
$408$	−5.92845	+	7.97073i	−0.293502	+	0.394610i
$409$	7.90492	+	5.74326i	0.390873	+	0.283986i	0.765813	−	0.643063i	$-0.222337\pi$
$409$	7.90492	+	5.74326i	0.390873	+	0.283986i	−0.374940	+	0.927049i	$0.622337\pi$
$410$	2.12760	−	6.46807i	0.105075	−	0.319435i
$411$	−2.49886	−	3.43939i	−0.123260	−	0.169653i
$412$	−32.9655	−	7.26444i	−1.62409	−	0.357893i
$413$	−8.75340	+	12.0480i	−0.430727	+	0.592845i
$414$	−1.05469	+	1.16260i	−0.0518352	+	0.0571389i
$415$	5.58753	−	26.3000i	0.274281	−	1.29102i
$416$	1.54326	+	3.64780i	0.0756647	+	0.178848i
$417$	−4.29076	−	13.2056i	−0.210119	−	0.646681i
$418$	2.25152	−	0.469807i	0.110126	−	0.0229790i
$419$	−34.2393	+	11.1250i	−1.67270	+	0.543494i	−0.983474	−	0.181051i	$-0.942050\pi$
$419$	−34.2393	+	11.1250i	−1.67270	+	0.543494i	−0.689228	+	0.724545i	$0.742050\pi$
$420$	14.8959	+	13.6122i	0.726846	+	0.664206i
$421$	−2.24619	−	0.729830i	−0.109472	−	0.0355697i	0.253769	−	0.967265i	$-0.418330\pi$
$421$	−2.24619	−	0.729830i	−0.109472	−	0.0355697i	−0.363241	+	0.931695i	$0.618330\pi$
$422$	−2.61231	−	0.284419i	−0.127165	−	0.0138453i
$423$	7.28061	−	5.28967i	0.353995	−	0.257193i
$424$	−9.00839	−	12.6953i	−0.437486	−	0.616537i
$425$	−11.7477	+	13.0523i	−0.569848	+	0.633131i
$426$	4.23904	+	20.3154i	0.205382	+	0.984282i
$427$	−33.3226	−	45.8647i	−1.61260	−	2.21955i
$428$	28.1817	−	2.74965i	1.36221	−	0.132910i
$429$	−1.82615	−	0.593351i	−0.0881672	−	0.0286473i
$430$	−16.7486	+	5.37481i	−0.807691	+	0.259197i
$431$	11.1268	+	34.2447i	0.535959	+	1.64951i	0.741569	+	0.670877i	$0.234082\pi$
$431$	11.1268	+	34.2447i	0.535959	+	1.64951i	−0.205610	+	0.978634i	$0.565918\pi$
$432$	2.93232	+	2.72057i	0.141081	+	0.130893i
$433$	−6.93916	−	21.3565i	−0.333475	−	1.02633i	−0.967469	−	0.252991i	$-0.918586\pi$
$433$	−6.93916	−	21.3565i	−0.333475	−	1.02633i	0.633994	−	0.773338i	$-0.281414\pi$
$434$	−55.5730	−	24.9914i	−2.66759	−	1.19963i
$435$	3.48415	−	1.55166i	0.167052	−	0.0743963i
$436$	10.7433	+	6.30997i	0.514512	+	0.302193i
$437$	0.386922	−	0.532552i	0.0185090	−	0.0254754i
$438$	−3.10379	+	6.90185i	−0.148305	+	0.329783i
$439$	−2.98418	+	2.16813i	−0.142427	+	0.103479i	−0.656717	−	0.754137i	$-0.728055\pi$
$439$	−2.98418	+	2.16813i	−0.142427	+	0.103479i	0.514290	+	0.857616i	$0.328055\pi$
$440$	−14.9232	−	8.83802i	−0.711438	−	0.421336i
$441$	10.8076	+	7.85220i	0.514649	+	0.373914i
$442$	−3.01825	+	1.72761i	−0.143563	+	0.0821740i
$443$		−	2.38343i		−	0.113240i	−0.998396	−	0.0566200i	$-0.981968\pi$
$443$		−	2.38343i		−	0.113240i	0.998396	−	0.0566200i	$-0.0180323\pi$
$444$	12.2227	+	13.7800i	0.580062	+	0.653968i
$445$	−1.33428	−	12.6828i	−0.0632509	−	0.601222i
$446$	3.04149	−	27.9353i	0.144019	−	1.32278i
$447$	3.31533	−	10.2035i	0.156810	−	0.482611i
$448$	10.3836	+	34.5710i	0.490579	+	1.63333i
$449$	−12.3245			−0.581631			−0.290816	−	0.956779i	$-0.593927\pi$
$449$	−12.3245			−0.581631			−0.290816	+	0.956779i	$0.593927\pi$
$450$	4.71288	+	5.27151i	0.222167	+	0.248501i
$451$			5.90477i			0.278045i
$452$	−10.5801	+	18.0136i	−0.497645	+	0.847288i
$453$	14.0162	+	4.55413i	0.658537	+	0.213971i
$454$	−39.3430	−	4.28352i	−1.84646	−	0.201036i
$455$	2.87397	+	6.45334i	0.134734	+	0.302537i
$456$	−1.34595	−	1.00108i	−0.0630297	−	0.0468801i
$457$	−16.6515			−0.778923			−0.389461	−	0.921043i	$-0.627339\pi$
$457$	−16.6515			−0.778923			−0.389461	+	0.921043i	$0.627339\pi$
$458$	−2.11226	+	1.20903i	−0.0986994	+	0.0564944i
$459$	−2.06436	+	2.84135i	−0.0963563	+	0.132623i
$460$	−4.86288	+	0.996287i	−0.226733	+	0.0464521i
$461$	2.84472	+	3.91542i	0.132492	+	0.182359i	0.870108	−	0.492861i	$-0.164049\pi$
$461$	2.84472	+	3.91542i	0.132492	+	0.182359i	−0.737617	+	0.675220i	$0.764049\pi$
$462$	−15.9594	−	7.17703i	−0.742500	−	0.333906i
$463$	−5.86100	−	4.25827i	−0.272384	−	0.197898i	0.443205	−	0.896420i	$-0.353841\pi$
$463$	−5.86100	−	4.25827i	−0.272384	−	0.197898i	−0.715589	+	0.698522i	$0.753841\pi$
$464$	6.77401	+	0.814312i	0.314475	+	0.0378035i
$465$	−18.4929	−	10.6745i	−0.857590	−	0.495017i
$466$	34.1718	+	15.3672i	1.58298	+	0.711873i
$467$	6.70577	−	2.17884i	0.310306	−	0.100825i	−0.149724	−	0.988728i	$-0.547839\pi$
$467$	6.70577	−	2.17884i	0.310306	−	0.100825i	0.460030	+	0.887903i	$0.347839\pi$
$468$	0.560021	+	1.28351i	0.0258870	+	0.0593301i
$469$	59.1156	−	19.2078i	2.72971	−	0.886935i
$470$	28.4582	+	0.103323i	1.31268	+	0.00476594i
$471$	6.35078	−	19.5457i	0.292629	−	0.900618i
$472$	−8.91006	+	2.78524i	−0.410119	+	0.128201i
$473$	12.3407	−	8.96606i	0.567427	−	0.412260i
$474$	−2.28961	−	10.9729i	−0.105165	−	0.504000i
$475$	−2.20403	−	1.98373i	−0.101128	−	0.0910198i
$476$	−29.0491	+	12.6747i	−1.33147	+	0.580946i
$477$	−3.23496	−	4.45255i	−0.148119	−	0.203868i
$478$	−0.810238	+	7.44182i	−0.0370594	+	0.340381i
$479$	5.92273	−	18.2283i	0.270617	−	0.832872i	−0.719729	−	0.694255i	$-0.755734\pi$
$479$	5.92273	−	18.2283i	0.270617	−	0.832872i	0.990346	−	0.138617i	$-0.0442658\pi$
$480$	2.39997	+	12.4193i	0.109543	+	0.566863i
$481$	1.99270	+	6.13291i	0.0908594	+	0.279637i
$482$	−16.5280	+	3.44875i	−0.752828	+	0.157086i
$483$	−4.76312	+	1.54763i	−0.216729	+	0.0704197i
$484$	−6.79625	−	1.49765i	−0.308920	−	0.0680752i
$485$	3.25502	+	3.61435i	0.147803	+	0.164119i
$486$	1.04743	+	0.950206i	0.0475123	+	0.0431022i
$487$	−15.4420	−	11.2193i	−0.699745	−	0.508395i	0.180104	−	0.983648i	$-0.442357\pi$
$487$	−15.4420	−	11.2193i	−0.699745	−	0.508395i	−0.879849	+	0.475253i	$0.842357\pi$
$488$	0.397590	−	35.5354i	0.0179981	−	1.60861i
$489$	11.0794	−	8.04964i	0.501027	−	0.364018i
$490$	12.9084	+	40.2243i	0.583142	+	1.81715i
$491$	4.70358	−	6.47392i	0.212269	−	0.292164i	−0.689584	−	0.724206i	$-0.742207\pi$
$491$	4.70358	−	6.47392i	0.212269	−	0.292164i	0.901854	+	0.432042i	$0.142207\pi$
$492$	3.22168	−	2.85759i	0.145245	−	0.128830i
$493$			5.99058i			0.269802i
$494$	−0.291726	−	0.509664i	−0.0131254	−	0.0229309i
$495$	−5.31079	−	3.06549i	−0.238702	−	0.137783i
$496$	−18.6028	−	33.3605i	−0.835289	−	1.49793i
$497$	−20.4609	+	62.9721i	−0.917796	+	2.82468i
$498$	11.4255	−	12.5945i	0.511990	−	0.564375i
$499$			0.335155i			0.0150036i	0.999972	+	0.00750180i	$0.00238792\pi$
$499$			0.335155i			0.0150036i	−0.999972	+	0.00750180i	$0.997612\pi$
$500$	2.17798	+	22.2544i	0.0974024	+	0.995245i
$501$		−	13.8953i		−	0.620797i
$502$	−3.07010	−	2.78514i	−0.137025	−	0.124307i
$503$	−7.87715	+	24.2434i	−0.351225	+	1.08096i	0.606942	+	0.794746i	$0.292396\pi$
$503$	−7.87715	+	24.2434i	−0.351225	+	1.08096i	−0.958166	+	0.286212i	$0.907604\pi$
$504$	3.80767	+	12.1809i	0.169607	+	0.542579i
$505$	−5.75853	−	3.32393i	−0.256251	−	0.147913i
$506$	3.73597	−	2.13842i	0.166084	−	0.0950645i
$507$		−	12.5097i		−	0.555577i
$508$	−5.36283	−	6.04611i	−0.237937	−	0.268253i
$509$	−15.1923	+	20.9104i	−0.673387	+	0.926838i	−0.999831	−	0.0183784i	$-0.994150\pi$
$509$	−15.1923	+	20.9104i	−0.673387	+	0.926838i	0.326444	+	0.945217i	$0.394150\pi$
$510$	−10.5751	+	3.39365i	−0.468272	+	0.150273i
$511$	−19.5335	+	14.1919i	−0.864112	+	0.627814i
$512$	−7.71049	+	21.2732i	−0.340759	+	0.940151i
$513$	−0.479794	−	0.348591i	−0.0211834	−	0.0153907i
$514$	−15.1701	+	16.7222i	−0.669122	+	0.737585i
$515$	−25.2563	−	28.0444i	−1.11293	−	1.23579i
$516$	−10.8642	−	2.39409i	−0.478269	−	0.105394i
$517$	−23.4712	+	7.62625i	−1.03226	+	0.335402i
$518$	12.0041	+	57.5292i	0.527432	+	2.52769i
$519$	−7.24697	−	22.3039i	−0.318106	−	0.979031i
$520$	−0.968679	+	4.32109i	−0.0424794	+	0.189492i
$521$	−0.360318	+	1.10895i	−0.0157858	+	0.0485838i	−0.958639	−	0.284624i	$-0.908131\pi$
$521$	−0.360318	+	1.10895i	−0.0157858	+	0.0485838i	0.942853	+	0.333208i	$0.108131\pi$
$522$	2.39804	+	0.261090i	0.104960	+	0.0114276i
$523$	−16.3338	−	22.4816i	−0.714228	−	0.983051i	−0.999696	−	0.0246623i	$-0.992149\pi$
$523$	−16.3338	−	22.4816i	−0.714228	−	0.983051i	0.285468	−	0.958388i	$-0.407851\pi$
$524$	1.44015	+	3.30068i	0.0629134	+	0.144191i
$525$	4.69494	+	22.0665i	0.204904	+	0.963062i
$526$	−29.8350	+	6.22542i	−1.30087	+	0.271441i
$527$	27.1326	−	19.7130i	1.18191	−	0.858710i
$528$	−5.34233	−	9.58045i	−0.232495	−	0.416936i
$529$	−6.72668	+	20.7026i	−0.292464	+	0.900113i
$530$	0.0631885	−	17.4040i	0.00274473	−	0.755980i
$531$	−3.13897	+	1.01991i	−0.136220	+	0.0442604i
$532$	−2.14027	−	4.90527i	−0.0927925	−	0.212670i
$533$	1.43384	−	0.465883i	0.0621065	−	0.0201796i
$534$	3.30802	−	7.35597i	0.143152	−	0.318324i
$535$	27.4179	+	15.8261i	1.18538	+	0.684223i
$536$	36.9199	+	12.4544i	1.59470	+	0.537947i
$537$	10.0482	+	7.30043i	0.433611	+	0.315037i
$538$	−14.7963	+	32.9023i	−0.637914	+	1.41852i
$539$	−21.5333	−	29.6380i	−0.927504	−	1.27660i
$540$	0.897589	+	4.38113i	0.0386261	+	0.188534i
$541$	−17.6431	+	24.2836i	−0.758535	+	1.04403i	0.238800	+	0.971069i	$0.423246\pi$
$541$	−17.6431	+	24.2836i	−0.758535	+	1.04403i	−0.997335	+	0.0729645i	$0.976754\pi$
$542$	−7.06113	−	12.3363i	−0.303301	−	0.529887i
$543$	7.42100			0.318466
$544$	−19.3529	−	4.49231i	−0.829750	−	0.192606i
$545$	5.66707	+	12.7251i	0.242751	+	0.545082i
$546$	−0.483590	+	4.44165i	−0.0206958	+	0.190085i
$547$	−20.3611	−	6.61572i	−0.870577	−	0.282868i	−0.160538	−	0.987030i	$-0.551323\pi$
$547$	−20.3611	−	6.61572i	−0.870577	−	0.282868i	−0.710039	+	0.704162i	$0.751323\pi$
$548$	4.30612	−	7.33159i	0.183948	−	0.313190i
$549$		−	12.5644i		−	0.536237i
$550$	−7.82448	−	17.7425i	−0.333637	−	0.756541i
$551$	−1.01158			−0.0430946
$552$	−2.97474	−	1.00348i	−0.126614	−	0.0427111i
$553$	11.0515	−	34.0129i	0.469955	−	1.44637i
$554$	42.6037	+	4.63853i	1.81006	+	0.197072i
$555$	2.15465	+	20.4807i	0.0914599	+	0.869357i
$556$	20.7754	−	18.4276i	0.881074	−	0.781503i
$557$			15.5039i			0.656921i	0.944518	+	0.328460i	$0.106530\pi$
$557$			15.5039i			0.656921i	−0.944518	+	0.328460i	$0.893470\pi$
$558$	−6.70862	−	11.7204i	−0.283998	−	0.496164i
$559$	−3.15088	−	2.28925i	−0.133268	−	0.0968250i
$560$	−13.0385	+	38.1931i	−0.550977	+	1.61395i
$561$	7.79191	−	5.66116i	0.328975	−	0.239014i
$562$	−10.3265	−	4.64388i	−0.435597	−	0.195890i
$563$	0.886476	−	1.22013i	0.0373605	−	0.0514223i	−0.789928	−	0.613199i	$-0.789882\pi$
$563$	0.886476	−	1.22013i	0.0373605	−	0.0514223i	0.827289	+	0.561777i	$0.189882\pi$
$564$	15.5197	+	9.11533i	0.653498	+	0.383825i
$565$	−21.3364	+	9.50212i	−0.897631	+	0.399757i
$566$	7.59193	−	16.8820i	0.319113	−	0.709605i
$567$	1.39431	+	4.29125i	0.0585556	+	0.180216i
$568$	−33.8498	+	24.0193i	−1.42030	+	1.00783i
$569$	0.157311	+	0.484153i	0.00659481	+	0.0202967i	0.954300	−	0.298851i	$-0.0966034\pi$
$569$	0.157311	+	0.484153i	0.00659481	+	0.0202967i	−0.947705	+	0.319148i	$0.896603\pi$
$570$	−0.573055	−	1.78572i	−0.0240026	−	0.0747954i
$571$	−8.86317	−	2.87982i	−0.370912	−	0.120517i	0.117629	−	0.993058i	$-0.462471\pi$
$571$	−8.86317	−	2.87982i	−0.370912	−	0.120517i	−0.488541	+	0.872541i	$0.662471\pi$
$572$	−0.372918	−	3.82210i	−0.0155925	−	0.159810i
$573$	3.75069	+	5.16238i	0.156687	+	0.215662i
$574$	13.4500	−	2.80650i	0.561392	−	0.117141i
$575$	−5.07044	−	2.25631i	−0.211452	−	0.0940945i
$576$	−2.64175	+	7.55123i	−0.110073	+	0.314635i
$577$	27.6438	−	20.0844i	1.15083	−	0.836126i	0.162238	−	0.986752i	$-0.448129\pi$
$577$	27.6438	−	20.0844i	1.15083	−	0.836126i	0.988591	+	0.150626i	$0.0481289\pi$
$578$	−0.714087	+	6.55870i	−0.0297021	+	0.272806i
$579$	−12.7888	−	4.15534i	−0.531485	−	0.172690i
$580$	5.63106	+	5.14578i	0.233817	+	0.213667i
$581$	51.5991	−	16.7656i	2.14069	−	0.695553i
$582$	0.628368	+	3.01142i	0.0260467	+	0.124827i
$583$	4.66393	+	14.3541i	0.193160	+	0.594486i
$584$	−15.1343	−	0.169332i	−0.626262	−	0.00700699i
$585$	−0.325366	+	1.53147i	−0.0134522	+	0.0633185i
$586$	−10.5543	−	9.57466i	−0.435995	−	0.395526i
$587$	−12.9931	+	17.8835i	−0.536284	+	0.738131i	−0.988072	−	0.153994i	$-0.950786\pi$
$587$	−12.9931	+	17.8835i	−0.536284	+	0.738131i	0.451788	+	0.892125i	$0.350786\pi$
$588$	−5.74974	+	26.0919i	−0.237115	+	1.07601i
$589$	3.32875	+	4.58163i	0.137159	+	0.188783i
$590$	−9.91451	−	3.26126i	−0.408174	−	0.134264i
$591$	−1.95256	−	1.41861i	−0.0803174	−	0.0583540i
$592$	−15.4842	+	33.4270i	−0.636396	+	1.37384i
$593$	−8.99081			−0.369208			−0.184604	−	0.982813i	$-0.559100\pi$
$593$	−8.99081			−0.369208			−0.184604	+	0.982813i	$0.559100\pi$
$594$	−1.92658	−	3.36586i	−0.0790484	−	0.138103i
$595$	−34.6612	−	7.36390i	−1.42097	−	0.301890i
$596$	21.3559	−	2.08367i	0.874771	−	0.0853504i
$597$	22.3482	+	7.26136i	0.914650	+	0.297188i
$598$	−0.814033	−	0.738475i	−0.0332883	−	0.0301985i
$599$	−21.6466			−0.884456			−0.442228	−	0.896903i	$-0.645812\pi$
$599$	−21.6466			−0.884456			−0.442228	+	0.896903i	$0.645812\pi$
$600$	−5.89377	+	12.8555i	−0.240612	+	0.524823i
$601$	5.10372			0.208185			0.104093	−	0.994568i	$-0.466806\pi$
$601$	5.10372			0.208185			0.104093	+	0.994568i	$0.466806\pi$
$602$	−26.2886	−	23.8484i	−1.07144	−	0.971990i
$603$	13.1016	+	4.25697i	0.533539	+	0.173357i
$604$	2.86224	+	29.3356i	0.116463	+	1.19365i
$605$	−5.20690	−	5.78171i	−0.211691	−	0.235060i
$606$	−2.08900	−	3.64962i	−0.0848599	−	0.148256i
$607$	34.0945			1.38385			0.691927	−	0.721967i	$-0.256762\pi$
$607$	34.0945			1.38385			0.691927	+	0.721967i	$0.256762\pi$
$608$	0.758576	−	3.26795i	0.0307643	−	0.132533i
$609$	6.22639	+	4.52374i	0.252306	+	0.183311i
$610$	23.4706	−	32.0590i	0.950295	−	1.29803i
$611$	3.70373	+	5.09774i	0.149837	+	0.206233i
$612$	−6.85963	−	1.51162i	−0.277284	−	0.0611037i
$613$	8.79877	−	12.1105i	0.355379	−	0.489137i	−0.593475	−	0.804852i	$-0.702244\pi$
$613$	8.79877	−	12.1105i	0.355379	−	0.489137i	0.948854	+	0.315715i	$0.102244\pi$
$614$	−1.50852	−	1.36850i	−0.0608790	−	0.0552282i
$615$	4.78827	−	0.503746i	0.193082	−	0.0203130i
$616$	0.391552	−	34.9957i	0.0157761	−	1.41002i
$617$	4.55073	+	14.0057i	0.183205	+	0.563848i	0.999913	−	0.0132037i	$-0.00420298\pi$
$617$	4.55073	+	14.0057i	0.183205	+	0.563848i	−0.816707	+	0.577052i	$0.804203\pi$
$618$	−4.87562	−	23.3662i	−0.196126	−	0.939925i
$619$	7.91859	−	2.57291i	0.318275	−	0.103414i	−0.145523	−	0.989355i	$-0.546486\pi$
$619$	7.91859	−	2.57291i	0.318275	−	0.103414i	0.463798	+	0.885941i	$0.346486\pi$
$620$	4.77637	−	42.4372i	0.191824	−	1.70432i
$621$	−1.05563	−	0.342996i	−0.0423612	−	0.0137640i
$622$	−0.795589	+	7.30728i	−0.0319002	+	0.292995i
$623$	20.8188	−	15.1257i	0.834087	−	0.605999i
$624$	−1.90489	+	2.05316i	−0.0762566	+	0.0821921i
$625$	−12.4915	+	21.6556i	−0.499658	+	0.866223i
$626$	−1.77295	+	0.369946i	−0.0708612	+	0.0147860i
$627$	0.955949	+	1.31575i	0.0381769	+	0.0525460i
$628$	40.9089	−	3.99143i	1.63244	−	0.159275i
$629$	−30.7627	−	9.99539i	−1.22659	−	0.398542i
$630$	−4.45844	+	13.5540i	−0.177629	+	0.540006i
$631$	−9.75081	−	30.0099i	−0.388174	−	1.19468i	−0.934152	−	0.356876i	$-0.883842\pi$
$631$	−9.75081	−	30.0099i	−0.388174	−	1.19468i	0.545978	−	0.837799i	$-0.316158\pi$
$632$	18.2831	−	12.9735i	0.727264	−	0.516056i
$633$	−0.574184	−	1.76716i	−0.0228218	−	0.0702382i
$634$	5.92731	−	13.1805i	0.235404	−	0.523463i
$635$	−0.945377	−	8.98613i	−0.0375161	−	0.356604i
$636$	5.57460	−	9.49129i	0.221047	−	0.376354i
$637$	−5.49796	+	7.56730i	−0.217837	+	0.299827i
$638$	−6.03310	−	2.71311i	−0.238853	−	0.107413i
$639$	−11.8719	+	8.62547i	−0.469647	+	0.341218i
$640$	−20.8464	+	14.3327i	−0.824028	+	0.566549i
$641$	−4.05109	−	2.94329i	−0.160009	−	0.116253i	0.504900	−	0.863178i	$-0.331529\pi$
$641$	−4.05109	−	2.94329i	−0.160009	−	0.116253i	−0.664908	+	0.746925i	$0.731529\pi$
$642$	9.94630	+	17.3768i	0.392549	+	0.685809i
$643$			27.0882i			1.06826i	0.845404	+	0.534128i	$0.179360\pi$
$643$			27.0882i			1.06826i	−0.845404	+	0.534128i	$0.820640\pi$
$644$	−6.64663	−	7.49348i	−0.261914	−	0.295284i
$645$	−8.32353	−	9.24238i	−0.327739	−	0.363919i
$646$	2.92833	+	0.318826i	0.115214	+	0.0125441i
$647$	−13.4466	+	41.3842i	−0.528639	+	1.62698i	0.228367	+	0.973575i	$0.426661\pi$
$647$	−13.4466	+	41.3842i	−0.528639	+	1.62698i	−0.757006	+	0.653408i	$0.773339\pi$
$648$	−0.904073	+	2.68005i	−0.0355153	+	0.105282i
$649$	9.05106			0.355285
$650$	−3.69101	+	3.29987i	−0.144773	+	0.129431i
$651$		−	43.0867i		−	1.68870i
$652$	23.6174	+	13.8714i	0.924929	+	0.543247i
$653$	−19.6947	−	6.39918i	−0.770712	−	0.250419i	−0.102842	−	0.994698i	$-0.532794\pi$
$653$	−19.6947	−	6.39918i	−0.770712	−	0.250419i	−0.667870	+	0.744278i	$0.732794\pi$
$654$	−0.953573	+	8.75831i	−0.0372876	+	0.342477i
$655$	−0.836715	+	3.93834i	−0.0326931	+	0.153884i
$656$	7.81505	+	3.62012i	0.305126	+	0.141342i
$657$	−5.35112			−0.208767
$658$	28.5269	+	49.8384i	1.11210	+	1.94290i
$659$	15.3421	−	21.1166i	0.597643	−	0.822585i	−0.397847	−	0.917452i	$-0.630242\pi$
$659$	15.3421	−	21.1166i	0.597643	−	0.822585i	0.995490	+	0.0948666i	$0.0302425\pi$
$660$	1.37168	−	12.1871i	0.0533924	−	0.474382i
$661$	26.1971	+	36.0572i	1.01895	+	1.40246i	0.912938	+	0.408099i	$0.133808\pi$
$661$	26.1971	+	36.0572i	1.01895	+	1.40246i	0.106012	+	0.994365i	$0.466192\pi$
$662$	−7.97791	+	17.7403i	−0.310070	+	0.689497i
$663$	−1.98946	−	1.44543i	−0.0772643	−	0.0561358i
$664$	32.2255	+	10.8708i	1.25059	+	0.421869i
$665$	1.24348	−	5.85293i	0.0482199	−	0.226967i
$666$	−5.34193	+	11.8787i	−0.206995	+	0.460292i
$667$	−1.80059	+	0.585047i	−0.0697191	+	0.0226531i
$668$	25.4716	−	11.1138i	0.985526	−	0.430005i
$669$	18.8975	−	6.14016i	0.730619	−	0.237392i
$670$	25.4776	+	35.3360i	0.984285	+	1.36515i
$671$	−10.6474	+	32.7694i	−0.411039	+	1.26505i
$672$	−19.2834	+	16.7224i	−0.743872	+	0.645081i
$673$	−16.4022	+	11.9169i	−0.632259	+	0.459363i	−0.857182	−	0.515013i	$-0.827787\pi$
$673$	−16.4022	+	11.9169i	−0.632259	+	0.459363i	0.224923	+	0.974377i	$0.427787\pi$
$674$	−29.9531	+	6.25006i	−1.15375	+	0.240743i
$675$	−2.03278	+	4.56813i	−0.0782418	+	0.175827i
$676$	22.9317	−	10.0056i	0.881989	−	0.384830i
$677$	−1.72530	−	2.37467i	−0.0663087	−	0.0912661i	0.774575	−	0.632483i	$-0.217964\pi$
$677$	−1.72530	−	2.37467i	−0.0663087	−	0.0912661i	−0.840883	+	0.541216i	$0.817964\pi$
$678$	−14.6853	−	1.59888i	−0.563984	−	0.0614045i
$679$	−3.03299	+	9.33458i	−0.116395	+	0.358228i
$680$	−14.6791	−	16.6709i	−0.562918	−	0.639300i
$681$	−8.64756	−	26.6145i	−0.331375	−	1.01987i
$682$	7.56463	+	36.2531i	0.289665	+	1.38820i
$683$	45.0484	−	14.6371i	1.72373	−	0.560074i	0.731210	−	0.682152i	$-0.238956\pi$
$683$	45.0484	−	14.6371i	1.72373	−	0.560074i	0.992521	+	0.122078i	$0.0389558\pi$
$684$	0.255254	−	1.15832i	0.00975988	−	0.0442896i
$685$	8.68400	−	3.86739i	0.331799	−	0.147765i
$686$	−27.2635	+	30.0531i	−1.04093	+	1.14743i
$687$	−1.39229	−	1.01155i	−0.0531190	−	0.0385932i
$688$	−4.30081	−	21.8301i	−0.163967	−	0.832264i
$689$	3.11759	−	2.26506i	0.118771	−	0.0862919i
$690$	−2.05280	−	2.84712i	−0.0781489	−	0.108388i
$691$	−9.72525	+	13.3857i	−0.369966	+	0.509214i	−0.952892	−	0.303311i	$-0.901908\pi$
$691$	−9.72525	+	13.3857i	−0.369966	+	0.509214i	0.582926	+	0.812525i	$0.301908\pi$
$692$	35.0891	−	31.1236i	1.33389	−	1.18314i
$693$		−	12.3736i		−	0.470035i
$694$	−25.8015	+	14.7685i	−0.979411	+	0.560604i
$695$	30.8778	−	3.24847i	1.17126	−	0.123221i
$696$	1.43940	+	4.60470i	0.0545605	+	0.174541i
$697$	−2.33687	+	7.19214i	−0.0885152	+	0.272422i
$698$	−11.9913	−	10.8783i	−0.453878	−	0.411749i
$699$			26.4940i			1.00209i
$700$	−36.6952	+	26.2556i	−1.38695	+	0.992370i
$701$		−	35.4426i		−	1.33865i	−0.742970	−	0.669325i	$-0.766584\pi$
$701$		−	35.4426i		−	1.33865i	0.742970	−	0.669325i	$-0.233416\pi$
$702$	−0.665316	+	0.733390i	−0.0251108	+	0.0276800i
$703$	1.68783	−	5.19461i	0.0636578	−	0.195919i
$704$	13.2891	−	17.4557i	0.500851	−	0.657888i
$705$	8.18662	+	18.3826i	0.308326	+	0.692327i
$706$	−6.41560	−	11.2085i	−0.241454	−	0.421836i
$707$		−	13.4168i		−	0.504591i
$708$	−4.38023	−	4.93831i	−0.164619	−	0.185593i
$709$	22.7987	−	31.3798i	0.856225	−	1.17849i	−0.126232	−	0.992001i	$-0.540288\pi$
$709$	22.7987	−	31.3798i	0.856225	−	1.17849i	0.982457	−	0.186491i	$-0.0597117\pi$
$710$	−46.4046	−	0.168481i	−1.74153	−	0.00632299i
$711$	6.41234	−	4.65884i	0.240482	−	0.174720i
$712$	16.1301	+	0.180473i	0.604502	+	0.00676352i
$713$	8.57493	+	6.23005i	0.321134	+	0.233317i
$714$	−16.5985	−	15.0579i	−0.621185	−	0.563526i
$715$	2.14640	−	3.71852i	0.0802707	−	0.139065i
$716$	−5.34571	+	24.2585i	−0.199779	+	0.906581i
$717$	−5.03419	+	1.63571i	−0.188005	+	0.0610866i
$718$	20.8372	−	4.34793i	0.777637	−	0.162263i
$719$	−1.50067	−	4.61857i	−0.0559654	−	0.172244i	0.919166	−	0.393869i	$-0.128864\pi$
$719$	−1.50067	−	4.61857i	−0.0559654	−	0.172244i	−0.975132	+	0.221626i	$0.928864\pi$
$720$	−7.31318	+	5.14951i	−0.272546	+	0.191911i
$721$	23.5335	−	72.4287i	0.876434	−	2.69739i
$722$	2.85449	−	26.2177i	0.106233	−	0.975722i
$723$	−7.01742	−	9.65865i	−0.260981	−	0.359209i
$724$	5.93549	+	13.6035i	0.220591	+	0.505570i
$725$	1.77482	+	8.34175i	0.0659150	+	0.309805i
$726$	−1.00517	−	4.81722i	−0.0373054	−	0.178784i
$727$	−2.82261	+	2.05075i	−0.104685	+	0.0760581i	−0.638896	−	0.769293i	$-0.720609\pi$
$727$	−2.82261	+	2.05075i	−0.104685	+	0.0760581i	0.534211	+	0.845351i	$0.320609\pi$
$728$	−8.52881	+	2.66606i	−0.316099	+	0.0988108i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−13.6538	−	9.99599i	−0.505349	−	0.369968i
$731$	18.5797	−	6.03690i	0.687194	−	0.223283i
$732$	23.0320	−	10.0493i	0.851286	−	0.371434i
$733$	−35.4255	+	11.5104i	−1.30847	+	0.425148i	−0.878520	−	0.477705i	$-0.841469\pi$
$733$	−35.4255	+	11.5104i	−1.30847	+	0.425148i	−0.429950	+	0.902853i	$0.641469\pi$
$734$	32.3799	+	14.5614i	1.19516	+	0.537471i
$735$	−22.1969	+	19.9902i	−0.818746	+	0.737348i
$736$	−0.539774	−	6.25564i	−0.0198963	−	0.230586i
$737$	−30.5629	−	22.2053i	−1.12580	−	0.817941i
$738$	2.77718	+	1.24891i	0.102230	+	0.0459731i
$739$	18.7143	+	25.7580i	0.688415	+	0.947522i	0.999996	−	0.00269743i	$-0.000858619\pi$
$739$	18.7143	+	25.7580i	0.688415	+	0.947522i	−0.311581	+	0.950220i	$0.600859\pi$
$740$	−35.8200	+	20.3306i	−1.31677	+	0.747369i
$741$	0.244077	−	0.335943i	0.00896638	−	0.0123412i
$742$	30.4793	−	17.4460i	1.11893	−	0.640463i
$743$	40.0527			1.46939			0.734695	−	0.678398i	$-0.237325\pi$
$743$	40.0527			1.46939			0.734695	+	0.678398i	$0.237325\pi$
$744$	16.1190	−	21.6719i	0.590953	−	0.794529i
$745$	20.7771	+	11.9929i	0.761214	+	0.439387i
$746$	19.4987	+	2.12294i	0.713897	+	0.0777265i
$747$	11.4357	+	3.71570i	0.418412	+	0.135950i
$748$	16.6097	+	9.75549i	0.607309	+	0.356696i
$749$			63.8810i			2.33416i
$750$	−13.7201	+	7.85864i	−0.500988	+	0.286957i
$751$	−21.5831			−0.787579			−0.393789	−	0.919201i	$-0.628836\pi$
$751$	−21.5831			−0.787579			−0.393789	+	0.919201i	$0.628836\pi$
$752$	−4.29635	+	35.7400i	−0.156672	+	1.30330i
$753$	0.905755	−	2.78763i	0.0330075	−	0.101587i
$754$	−0.182810	+	1.67907i	−0.00665756	+	0.0611479i
$755$	−16.4742	+	28.5406i	−0.599556	+	1.03870i
$756$	−6.75113	+	5.98817i	−0.245536	+	0.217788i
$757$		−	44.5213i		−	1.61815i	−0.587702	−	0.809077i	$-0.699967\pi$
$757$		−	44.5213i		−	1.61815i	0.587702	−	0.809077i	$-0.300033\pi$
$758$	−14.5440	+	8.32484i	−0.528263	+	0.302372i
$759$	2.46254	+	1.78914i	0.0893846	+	0.0649417i
$760$	2.81507	−	2.47873i	0.102113	−	0.0899129i
$761$	28.3700	−	20.6120i	1.02841	−	0.747184i	0.0604209	−	0.998173i	$-0.480756\pi$
$761$	28.3700	−	20.6120i	1.02841	−	0.747184i	0.967990	+	0.250989i	$0.0807557\pi$
$762$	2.34383	−	5.21193i	0.0849079	−	0.188808i
$763$	−16.5219	+	22.7405i	−0.598134	+	0.823261i
$764$	−6.46332	+	11.0044i	−0.233835	+	0.398126i
$765$	−5.25546	−	5.83563i	−0.190012	−	0.210988i
$766$	−19.3062	−	8.68211i	−0.697563	−	0.313697i
$767$	−0.714123	−	2.19784i	−0.0257855	−	0.0793596i
$768$	−15.9552	+	1.19704i	−0.575732	+	0.0431943i
$769$	1.00195	+	3.08369i	0.0361313	+	0.111201i	0.967496	−	0.252888i	$-0.0813805\pi$
$769$	1.00195	+	3.08369i	0.0361313	+	0.111201i	−0.931364	+	0.364089i	$0.881380\pi$
$770$	23.1141	−	31.5722i	0.832975	−	1.13778i
$771$	−15.1836	−	4.93346i	−0.546825	−	0.177674i
$772$	−2.61161	−	26.7668i	−0.0939938	−	0.963358i
$773$	10.9399	+	15.0575i	0.393480	+	0.541579i	0.959093	−	0.283092i	$-0.0913602\pi$
$773$	10.9399	+	15.0575i	0.393480	+	0.541579i	−0.565612	+	0.824671i	$0.691360\pi$
$774$	−1.60682	−	7.70060i	−0.0577560	−	0.276792i
$775$	31.9412	−	35.4884i	1.14736	−	1.27478i
$776$	−5.01767	+	3.56047i	−0.180124	+	0.127813i
$777$	−33.6190	+	24.4257i	−1.20608	+	0.876266i
$778$	7.90306	+	0.860456i	0.283339	+	0.0308488i
$779$	−1.21447	−	0.394606i	−0.0435130	−	0.0141382i
$780$	−3.06759	+	0.628474i	−0.109837	+	0.0225030i
$781$	38.2727	−	12.4356i	1.36951	−	0.444979i
$782$	5.39679	−	1.12610i	0.192989	−	0.0402694i
$783$	0.527088	+	1.62221i	0.0188366	+	0.0579731i
$784$	−52.4281	+	10.3290i	−1.87243	+	0.368894i
$785$	39.8002	+	22.9734i	1.42053	+	0.819956i
$786$	−1.71093	+	1.88599i	−0.0610270	+	0.0672711i
$787$	20.1499	−	27.7339i	0.718266	−	0.988608i	−0.281314	−	0.959616i	$-0.590770\pi$
$787$	20.1499	−	27.7339i	0.718266	−	0.988608i	0.999580	−	0.0289922i	$-0.00922981\pi$
$788$	1.03877	−	4.71388i	0.0370048	−	0.167925i
$789$	−12.6673	−	17.4351i	−0.450968	−	0.620704i
$790$	25.0643	+	0.0910011i	0.891749	+	0.00323767i
$791$	−38.1295	−	27.7027i	−1.35573	−	0.984995i
$792$	4.62906	−	6.22371i	0.164486	−	0.221150i
$793$	8.79738			0.312404
$794$	−42.7597	+	24.4752i	−1.51748	+	0.868591i
$795$	11.2421	−	5.00663i	0.398716	−	0.177567i
$796$	4.56373	+	46.7744i	0.161757	+	1.65788i
$797$	−14.3775	−	4.67155i	−0.509279	−	0.165475i	0.0430955	−	0.999071i	$-0.486278\pi$
$797$	−14.3775	−	4.67155i	−0.509279	−	0.165475i	−0.552374	+	0.833596i	$0.686278\pi$
$798$	2.54269	−	2.80285i	0.0900101	−	0.0992197i
$799$	−31.6066			−1.11816
$800$	−28.2795	−	0.521801i	−0.999830	−	0.0184484i
$801$	5.70321			0.201513
$802$	−11.6426	+	12.8338i	−0.411114	+	0.453178i
$803$	13.9563	+	4.53468i	0.492507	+	0.160025i
$804$	2.67548	+	27.4215i	0.0943570	+	0.967081i
$805$	−1.17169	−	11.1373i	−0.0412966	−	0.392538i
$806$	8.20640	−	4.69725i	0.289058	−	0.165453i
$807$	−25.5097			−0.897984
$808$	5.01932	−	6.74841i	0.176579	−	0.237408i
$809$	30.2673	+	21.9905i	1.06414	+	0.773144i	0.974850	−	0.222862i	$-0.0715398\pi$
$809$	30.2673	+	21.9905i	1.06414	+	0.773144i	0.0892914	+	0.996006i	$0.471540\pi$
$810$	−2.56507	+	1.84944i	−0.0901273	+	0.0649827i
$811$	3.25493	+	4.48003i	0.114296	+	0.157315i	0.862332	−	0.506343i	$-0.169003\pi$
$811$	3.25493	+	4.48003i	0.114296	+	0.157315i	−0.748036	+	0.663658i	$0.769003\pi$
$812$	−3.31249	+	15.0318i	−0.116246	+	0.527514i
$813$	5.90779	−	8.13138i	0.207195	−	0.285180i
$814$	23.9986	−	26.4541i	0.841152	−	0.927217i
$815$	12.4581	+	27.9740i	0.436389	+	0.979885i
$816$	−2.71553	−	13.7835i	−0.0950624	−	0.482518i
$817$	1.01940	+	3.13738i	0.0356642	+	0.109763i
$818$	−13.5270	+	2.82256i	−0.472959	+	0.0986885i
$819$	−3.00465	+	0.976271i	−0.104991	+	0.0341137i
$820$	4.75319	+	8.37451i	0.165989	+	0.292451i
$821$	−45.4175	−	14.7570i	−1.58508	−	0.515024i	−0.621722	−	0.783238i	$-0.713567\pi$
$821$	−45.4175	−	14.7570i	−1.58508	−	0.515024i	−0.963359	+	0.268214i	$0.913567\pi$
$822$	5.97695	+	0.650748i	0.208470	+	0.0226975i
$823$	22.3296	−	16.2234i	0.778362	−	0.565513i	−0.126125	−	0.992014i	$-0.540254\pi$
$823$	22.3296	−	16.2234i	0.778362	−	0.565513i	0.904487	+	0.426501i	$0.140254\pi$
$824$	38.9330	−	27.6263i	1.35630	−	0.962409i
$825$	9.17286	−	10.1915i	0.319358	−	0.354824i
$826$	−4.30191	−	20.6167i	−0.149683	−	0.717346i
$827$	−14.6189	−	20.1211i	−0.508347	−	0.699680i	0.475292	−	0.879828i	$-0.342342\pi$
$827$	−14.6189	−	20.1211i	−0.508347	−	0.699680i	−0.983640	+	0.180148i	$0.942342\pi$
$828$	−0.215571	−	2.20943i	−0.00749162	−	0.0767829i
$829$	−48.6171	−	15.7967i	−1.68854	−	0.548640i	−0.702004	−	0.712173i	$-0.747711\pi$
$829$	−48.6171	−	15.7967i	−1.68854	−	0.548640i	−0.986538	+	0.163533i	$0.947711\pi$
$830$	22.2381	+	30.8430i	0.771896	+	1.07058i
$831$	9.36426	+	28.8202i	0.324843	+	0.999763i
$832$	−5.28723	−	1.84970i	−0.183302	−	0.0641270i
$833$	−14.4985	−	44.6218i	−0.502343	−	1.54605i
$834$	17.9090	+	8.05378i	0.620139	+	0.278879i
$835$	30.3925	+	6.45699i	1.05178	+	0.223454i
$836$	−1.64732	+	2.80472i	−0.0569738	+	0.0970034i
$837$	5.61286	−	7.72544i	0.194009	−	0.267030i
$838$	20.8818	−	46.4344i	0.721348	−	1.60405i
$839$	−37.3145	+	27.1106i	−1.28824	+	0.935962i	−0.999768	−	0.0215265i	$-0.993147\pi$
$839$	−37.3145	+	27.1106i	−1.28824	+	0.935962i	−0.288472	+	0.957488i	$0.593147\pi$
$840$	−28.4120	+	2.66802i	−0.980306	+	0.0920556i
$841$	−21.1077	−	15.3357i	−0.727853	−	0.528816i
$842$	2.89879	−	1.65923i	0.0998987	−	0.0571809i
$843$		−	8.00632i		−	0.275752i
$844$	2.78014	−	2.46595i	0.0956965	−	0.0848816i
$845$	27.3619	+	5.81314i	0.941280	+	0.199978i
$846$	−1.37752	+	12.6522i	−0.0473603	+	0.434991i
$847$	4.85173	−	14.9321i	0.166707	−	0.513072i
$848$	21.8572	+	2.62749i	0.750581	+	0.0902283i
$849$	13.0889			0.449211
$850$	−2.50865	−	24.7073i	−0.0860458	−	0.847454i
$851$		−	10.2225i		−	0.350423i
$852$	−25.3069	−	14.8637i	−0.866999	−	0.509222i
$853$	31.4203	+	10.2091i	1.07581	+	0.349552i	0.792748	−	0.609549i	$-0.208650\pi$
$853$	31.4203	+	10.2091i	1.07581	+	0.349552i	0.283062	+	0.959101i	$0.408650\pi$
$854$	79.7034	+	8.67781i	2.72739	+	0.296949i
$855$	0.985410	−	0.887443i	0.0337003	−	0.0303499i
$856$	−23.8983	+	32.1310i	−0.816828	+	1.09822i
$857$	−0.208662			−0.00712775			−0.00356387	−	0.999994i	$-0.501134\pi$
$857$	−0.208662			−0.00712775			−0.00356387	+	0.999994i	$0.501134\pi$
$858$	2.35671	−	1.34895i	0.0804567	−	0.0460525i
$859$	13.5335	−	18.6272i	0.461756	−	0.635552i	−0.513116	−	0.858319i	$-0.671509\pi$
$859$	13.5335	−	18.6272i	0.461756	−	0.635552i	0.974872	+	0.222767i	$0.0715089\pi$
$860$	10.2849	−	22.6502i	0.350713	−	0.772365i
$861$	5.71059	+	7.85995i	0.194616	+	0.267866i
$862$	−46.4417	−	20.8850i	−1.58181	−	0.711348i
$863$	−16.7125	−	12.1423i	−0.568899	−	0.413330i	0.265806	−	0.964027i	$-0.414362\pi$
$863$	−16.7125	−	12.1423i	−0.568899	−	0.413330i	−0.834705	+	0.550697i	$0.814362\pi$
$864$	−5.63591	+	0.486301i	−0.191738	+	0.0165443i
$865$	52.1517	−	5.48657i	1.77321	−	0.186549i
$866$	28.9631	+	13.0248i	0.984206	+	0.442602i
$867$	−4.43678	+	1.44160i	−0.150681	+	0.0489593i
$868$	78.9826	−	34.4617i	2.68084	−	1.16971i
$869$	−20.6721	+	6.71677i	−0.701253	+	0.227851i
$870$	−1.68541	+	5.12380i	−0.0571409	+	0.173713i
$871$	−2.98065	+	9.17349i	−0.100995	+	0.310832i
$872$	−16.8176	+	5.25710i	−0.569516	+	0.178028i
$873$	−1.75982	+	1.27858i	−0.0595609	+	0.0432735i
$874$	0.190155	+	0.911307i	0.00643209	+	0.0308254i
$875$	−50.4467	+	0.0149358i	−1.70541	+	0.000504921i
$876$	−4.27995	−	9.80918i	−0.144606	−	0.331422i
$877$	−17.5774	−	24.1932i	−0.593547	−	0.816948i	0.401551	−	0.915837i	$-0.368471\pi$
$877$	−17.5774	−	24.1932i	−0.593547	−	0.816948i	−0.995098	+	0.0988889i	$0.968471\pi$
$878$	0.564621	−	5.18589i	0.0190550	−	0.175015i
$879$	3.11378	−	9.58323i	0.105025	−	0.323234i
$880$	23.4374	−	7.23309i	0.790073	−	0.243828i
$881$	−11.7563	−	36.1820i	−0.396078	−	1.21900i	−0.928119	−	0.372285i	$-0.878574\pi$
$881$	−11.7563	−	36.1820i	−0.396078	−	1.21900i	0.532040	−	0.846719i	$-0.321426\pi$
$882$	−18.4941	+	3.85901i	−0.622729	+	0.129940i
$883$	22.8903	−	7.43752i	0.770321	−	0.250293i	0.102619	−	0.994721i	$-0.467278\pi$
$883$	22.8903	−	7.43752i	0.770321	−	0.250293i	0.667702	+	0.744428i	$0.267278\pi$
$884$	1.05841	−	4.80298i	0.0355981	−	0.161542i
$885$	−0.772160	−	7.33965i	−0.0259559	−	0.246720i
$886$	2.49647	+	2.26475i	0.0838705	+	0.0760856i
$887$	−1.79173	−	1.30177i	−0.0601606	−	0.0437092i	0.557299	−	0.830312i	$-0.311838\pi$
$887$	−1.79173	−	1.30177i	−0.0601606	−	0.0437092i	−0.617459	+	0.786603i	$0.711838\pi$
$888$	−26.0476	−	0.291436i	−0.874100	−	0.00977994i
$889$	14.7507	−	10.7170i	0.494723	−	0.359438i
$890$	14.5522	+	10.6537i	0.487789	+	0.357113i
$891$	1.61190	−	2.21859i	0.0540006	−	0.0743255i
$892$	26.3702	+	29.7301i	0.882940	+	0.995436i
$893$		−	5.33712i		−	0.178600i
$894$	7.53724	+	13.1681i	0.252083	+	0.440406i
$895$	−20.6372	+	18.5855i	−0.689824	+	0.621244i
$896$	−46.0772	−	21.9735i	−1.53933	−	0.734084i
$897$	0.240160	−	0.739135i	0.00801870	−	0.0246790i
$898$	11.7109	−	12.9091i	0.390796	−	0.430782i
$899$		−	16.2880i		−	0.543234i
$900$	−9.99974	−	0.0726130i	−0.333325	−	0.00242043i
$901$			19.3294i			0.643956i
$902$	−6.18483	−	5.61075i	−0.205932	−	0.186818i
$903$	7.75576	−	23.8698i	0.258096	−	0.794336i
$904$	−8.81470	−	28.1985i	−0.293173	−	0.937868i
$905$	−3.44846	+	16.2316i	−0.114631	+	0.539556i
$906$	−18.0884	+	10.3536i	−0.600946	+	0.343974i
$907$		−	24.4794i		−	0.812825i	−0.913690	−	0.406413i	$-0.866780\pi$
$907$		−	24.4794i		−	0.812825i	0.913690	−	0.406413i	$-0.133220\pi$
$908$	41.8706	−	37.1388i	1.38953	−	1.23249i
$909$	1.74779	−	2.40563i	0.0579706	−	0.0797897i
$910$	−9.49028	−	3.12172i	−0.314600	−	0.103484i
$911$	18.3568	−	13.3370i	0.608187	−	0.441874i	−0.240589	−	0.970627i	$-0.577340\pi$
$911$	18.3568	−	13.3370i	0.608187	−	0.441874i	0.848775	+	0.528754i	$0.177340\pi$
$912$	2.32749	−	0.458547i	0.0770709	−	0.0151840i
$913$	−26.6768	−	19.3819i	−0.882875	−	0.641446i
$914$	15.8223	−	17.4412i	0.523356	−	0.576905i
$915$	27.4816	+	5.83855i	0.908512	+	0.193017i
$916$	0.740706	−	3.36127i	0.0244736	−	0.111060i
$917$	−7.72679	+	2.51059i	−0.255161	+	0.0829069i
$918$	−1.01454	−	4.86215i	−0.0334850	−	0.160475i
$919$	−6.85071	−	21.0843i	−0.225984	−	0.695507i	−0.998190	−	0.0601352i	$-0.980847\pi$
$919$	−6.85071	−	21.0843i	−0.225984	−	0.695507i	0.772206	−	0.635372i	$-0.219153\pi$
$920$	3.57720	−	6.04020i	0.117937	−	0.199140i
$921$	0.445051	−	1.36973i	0.0146649	−	0.0451340i
$922$	−6.80419	−	0.740815i	−0.224084	−	0.0243974i
$923$	−6.03939	−	8.31251i	−0.198789	−	0.273609i
$924$	22.6822	−	9.89671i	0.746189	−	0.325578i
$925$	−45.7977	−	4.80439i	−1.50582	−	0.157967i
$926$	10.0294	−	2.09275i	0.329586	−	0.0687720i
$927$	13.6548	−	9.92077i	0.448482	−	0.325841i
$928$	−7.28964	+	6.32153i	−0.239294	+	0.207514i
$929$	−13.8788	+	42.7146i	−0.455349	+	1.40142i	0.415376	+	0.909650i	$0.363650\pi$
$929$	−13.8788	+	42.7146i	−0.455349	+	1.40142i	−0.870725	+	0.491771i	$0.836350\pi$
$930$	28.7529	−	9.22709i	0.942843	−	0.302568i
$931$	7.53488	−	2.44823i	0.246946	−	0.0802375i
$932$	−48.5663	+	21.1905i	−1.59084	+	0.694118i
$933$	−4.94317	+	1.60613i	−0.161832	+	0.0525825i
$934$	−4.08969	+	9.09417i	−0.133819	+	0.297570i
$935$	8.76155	+	19.6735i	0.286533	+	0.643394i
$936$	−1.87652	−	0.633015i	−0.0613359	−	0.0206907i
$937$	4.65047	+	3.37876i	0.151924	+	0.110379i	0.661151	−	0.750253i	$-0.270068\pi$
$937$	4.65047	+	3.37876i	0.151924	+	0.110379i	−0.509226	+	0.860633i	$0.670068\pi$
$938$	−36.0532	+	80.1708i	−1.17718	+	2.61767i
$939$	−0.752755	−	1.03608i	−0.0245652	−	0.0338111i
$940$	−27.1494	+	29.7097i	−0.885515	+	0.969025i
$941$	−3.82356	+	5.26268i	−0.124645	+	0.171558i	−0.866779	−	0.498693i	$-0.833814\pi$
$941$	−3.82356	+	5.26268i	−0.124645	+	0.171558i	0.742134	+	0.670251i	$0.233814\pi$
$942$	14.4382	+	25.2244i	0.470421	+	0.821856i
$943$	−2.38996			−0.0778279
$944$	5.54905	−	11.9792i	0.180606	−	0.389890i
$945$	−10.0340	+	1.05561i	−0.326405	+	0.0343391i
$946$	−2.33492	+	21.4456i	−0.0759149	+	0.697258i
$947$	47.9991	+	15.5959i	1.55976	+	0.506797i	0.956744	−	0.290931i	$-0.0939651\pi$
$947$	47.9991	+	15.5959i	1.55976	+	0.506797i	0.603017	+	0.797728i	$0.293965\pi$
$948$	13.6689	+	8.02827i	0.443945	+	0.260746i
$949$		−	3.74675i		−	0.121625i
$950$	4.17210	−	0.423612i	0.135361	−	0.0137438i
$951$	10.2190			0.331375
$952$	14.3268	−	42.4706i	0.464334	−	1.37648i
$953$	−18.4077	+	56.6530i	−0.596283	+	1.83517i	−0.0480475	+	0.998845i	$0.515300\pi$
$953$	−18.4077	+	56.6530i	−0.596283	+	1.83517i	−0.548235	+	0.836324i	$0.684700\pi$
$954$	7.73761	+	0.842443i	0.250514	+	0.0272751i
$955$	−13.0343	+	5.80480i	−0.421781	+	0.187839i
$956$	−7.02489	−	7.91993i	−0.227201	−	0.256149i
$957$		−	4.67757i		−	0.151204i
$958$	13.4650	+	23.5243i	0.435035	+	0.760035i
$959$	15.5188	+	11.2751i	0.501129	+	0.364092i
$960$	−15.2888	−	9.28715i	−0.493445	−	0.299741i
$961$	−48.6920	+	35.3768i	−1.57071	+	1.14119i
$962$	−8.31727	−	3.74031i	−0.268159	−	0.120593i
$963$	−8.32171	+	11.4539i	−0.268163	+	0.369095i
$964$	12.0927	−	20.5889i	0.389478	−	0.663124i
$965$	15.0316	−	26.0414i	0.483884	−	0.838302i
$966$	2.90491	−	6.45960i	0.0934640	−	0.207834i
$967$	−10.4356	−	32.1174i	−0.335585	−	1.03283i	−0.966433	−	0.256919i	$-0.917293\pi$
$967$	−10.4356	−	32.1174i	−0.335585	−	1.03283i	0.630848	−	0.775907i	$-0.282707\pi$
$968$	8.02653	−	5.69551i	0.257982	−	0.183061i
$969$	0.643646	+	1.98094i	0.0206769	+	0.0636369i
$970$	−6.87872	−	0.0249746i	−0.220862	−	0.000801885i
$971$	−26.2957	−	8.54400i	−0.843870	−	0.274190i	−0.144994	−	0.989433i	$-0.546316\pi$
$971$	−26.2957	−	8.54400i	−0.843870	−	0.274190i	−0.698876	+	0.715242i	$0.746316\pi$
$972$	−1.99055	+	0.194215i	−0.0638468	+	0.00622946i
$973$	36.8255	+	50.6859i	1.18057	+	1.62492i
$974$	26.4245	−	5.51379i	0.846697	−	0.176673i
$975$	−3.19852	−	1.42332i	−0.102435	−	0.0455826i
$976$	36.8430	+	34.1824i	1.17931	+	1.09415i
$977$	−2.72149	+	1.97728i	−0.0870683	+	0.0632588i	−0.630468	−	0.776215i	$-0.717137\pi$
$977$	−2.72149	+	1.97728i	−0.0870683	+	0.0632588i	0.543399	+	0.839474i	$0.317137\pi$
$978$	−2.09627	+	19.2537i	−0.0670314	+	0.615665i
$979$	−14.8746	−	4.83305i	−0.475394	−	0.154465i
$980$	−54.3977	−	24.7007i	−1.73767	−	0.789036i
$981$	−5.92476	+	1.92507i	−0.189163	+	0.0614628i
$982$	2.31160	+	11.0782i	0.0737661	+	0.353520i
$983$	−7.77165	−	23.9187i	−0.247877	−	0.762887i	−0.995150	−	0.0983697i	$-0.968637\pi$
$983$	−7.77165	−	23.9187i	−0.247877	−	0.762887i	0.747273	−	0.664517i	$-0.231363\pi$
$984$	−0.0681361	+	6.08978i	−0.00217210	+	0.194135i
$985$	4.01020	−	3.61151i	0.127775	−	0.115072i
$986$	−6.27471	−	5.69229i	−0.199827	−	0.181279i
$987$	−23.8675	+	32.8508i	−0.759710	+	1.04565i
$988$	0.811037	+	0.178724i	0.0258025	+	0.00568597i
$989$	3.62903	+	4.99493i	0.115396	+	0.158829i
$990$	8.25723	−	2.64983i	0.262432	−	0.0842172i
$991$	15.8948	+	11.5482i	0.504914	+	0.366841i	0.810891	−	0.585197i	$-0.198983\pi$
$991$	15.8948	+	11.5482i	0.504914	+	0.366841i	−0.305977	+	0.952039i	$0.598983\pi$
$992$	52.6192	+	12.2143i	1.67066	+	0.387804i
$993$	−13.7544			−0.436482
$994$	−46.5168	−	81.2678i	−1.47542	−	2.57766i
$995$	−26.2674	+	45.5068i	−0.832732	+	1.44266i
$996$	2.33529	+	23.9348i	0.0739966	+	0.758404i
$997$	26.9080	+	8.74295i	0.852186	+	0.276892i	0.702361	−	0.711821i	$-0.252129\pi$
$997$	26.9080	+	8.74295i	0.852186	+	0.276892i	0.149824	+	0.988713i	$0.452129\pi$
$998$	−0.351051	−	0.318467i	−0.0111123	−	0.0100809i
$999$	−9.20979			−0.291385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bm.a.61.16	yes	240
8.5	even	2	inner	600.2.bm.a.61.9	✓	240
25.16	even	5	inner	600.2.bm.a.541.9	yes	240
200.141	even	10	inner	600.2.bm.a.541.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bm.a.61.9	✓	240	8.5	even	2	inner
600.2.bm.a.61.16	yes	240	1.1	even	1	trivial
600.2.bm.a.541.9	yes	240	25.16	even	5	inner
600.2.bm.a.541.16	yes	240	200.141	even	10	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+(-0.950206 + 1.04743i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.194215 - 1.99055i) q^{4} +(1.11784 - 1.93660i) q^{5} +(1.22737 - 0.702534i) q^{6} +4.51209 q^{7} +(2.26950 + 1.68800i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.966272 + 3.01103i) q^{10} +(-1.61190 - 2.21859i) q^{11} +(-0.430403 + 1.95314i) q^{12} +(-0.411556 + 0.566458i) q^{13} +(-4.28742 + 4.72610i) q^{14} +(-1.66157 + 1.49639i) q^{15} +(-3.92456 + 0.773190i) q^{16} +(-1.08530 - 3.34021i) q^{17} +(-1.38440 + 0.288871i) q^{18} +(0.564031 - 0.183265i) q^{19} +(-4.07200 - 1.84900i) q^{20} +(-4.29125 - 1.39431i) q^{21} +(3.85545 + 0.419767i) q^{22} +(0.897976 - 0.652418i) q^{23} +(-1.63680 - 2.30670i) q^{24} +(-2.50085 - 4.32963i) q^{25} +(-0.202262 - 0.969328i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.876318 - 8.98153i) q^{28} +(-1.62221 - 0.527088i) q^{29} +(0.0114812 - 3.16226i) q^{30} +(2.95086 + 9.08180i) q^{31} +(2.91928 - 4.84539i) q^{32} +(0.847425 + 2.60811i) q^{33} +(4.52989 + 2.03712i) q^{34} +(5.04381 - 8.73812i) q^{35} +(1.01289 - 1.72454i) q^{36} +(5.41338 - 7.45088i) q^{37} +(-0.343989 + 0.764922i) q^{38} +(0.566458 - 0.411556i) q^{39} +(5.80594 - 2.50820i) q^{40} +(-1.74197 - 1.26562i) q^{41} +(5.53802 - 3.16990i) q^{42} +5.56243i q^{43} +(-4.10315 + 3.63944i) q^{44} +(2.04266 - 0.909692i) q^{45} +(-0.169901 + 1.56050i) q^{46} +(2.78094 - 8.55887i) q^{47} +(3.97141 + 0.477408i) q^{48} +13.3590 q^{49} +(6.91131 + 1.49458i) q^{50} +3.51211i q^{51} +(1.20749 + 0.709207i) q^{52} +(-5.23428 - 1.70072i) q^{53} +(1.40591 + 0.153070i) q^{54} +(-6.09837 + 0.641573i) q^{55} +(10.2402 + 7.61643i) q^{56} -0.593058 q^{57} +(2.09352 - 1.19831i) q^{58} +(-1.93999 + 2.67016i) q^{59} +(3.30133 + 3.01682i) q^{60} +(-7.38519 - 10.1648i) q^{61} +(-12.3165 - 5.53877i) q^{62} +(3.65036 + 2.65214i) q^{63} +(2.30128 + 7.66186i) q^{64} +(0.636949 + 1.43023i) q^{65} +(-3.53703 - 1.59062i) q^{66} +(13.1016 - 4.25697i) q^{67} +(-6.43807 + 2.80906i) q^{68} +(-1.05563 + 0.342996i) q^{69} +(4.35991 + 13.5861i) q^{70} +(-4.53468 + 13.9563i) q^{71} +(0.843882 + 2.69960i) q^{72} +(-4.32915 + 3.14531i) q^{73} +(2.66044 + 12.7500i) q^{74} +(1.04052 + 4.89053i) q^{75} +(-0.474341 - 1.08714i) q^{76} +(-7.27303 - 10.0105i) q^{77} +(-0.107177 + 0.984388i) q^{78} +(2.44930 - 7.53816i) q^{79} +(-2.88968 + 8.46462i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.98088 - 0.621996i) q^{82} +(11.4357 - 3.71570i) q^{83} +(-1.94202 + 8.81274i) q^{84} +(-7.68186 - 1.63204i) q^{85} +(-5.82625 - 5.28545i) q^{86} +(1.37994 + 1.00258i) q^{87} +(0.0867785 - 7.75598i) q^{88} +(4.61400 - 3.35227i) q^{89} +(-0.988110 + 3.00394i) q^{90} +(-1.85698 + 2.55591i) q^{91} +(-1.47307 - 1.66076i) q^{92} -9.54917i q^{93} +(6.32233 + 11.0455i) q^{94} +(0.275587 - 1.29717i) q^{95} +(-4.27371 + 3.70613i) q^{96} +(-0.672191 + 2.06879i) q^{97} +(-12.6938 + 13.9926i) q^{98} -2.74232i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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