LMFDB - Embedded newform 200.2.o.a.109.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(29,200)] 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("200.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.17
Character	$\chi$	$=$	200.109
Dual form			200.2.o.a.189.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.287182 - 1.38475i) q^{2} +(-0.970606 - 2.98722i) q^{3} +(-1.83505 - 0.795350i) q^{4} +(-0.762120 + 2.10218i) q^{5} +(-4.41529 + 0.486168i) q^{6} -1.71800i q^{7} +(-1.62835 + 2.31267i) q^{8} +(-5.55435 + 4.03547i) q^{9} +(2.69213 + 1.65905i) q^{10} +(1.35234 - 1.86134i) q^{11} +(-0.594772 + 6.25368i) q^{12} +(4.80828 - 3.49342i) q^{13} +(-2.37899 - 0.493379i) q^{14} +(7.01940 + 0.236226i) q^{15} +(2.73484 + 2.91902i) q^{16} +(-2.53693 - 0.824300i) q^{17} +(3.99300 + 8.85029i) q^{18} +(-5.48112 - 1.78092i) q^{19} +(3.07050 - 3.25146i) q^{20} +(-5.13203 + 1.66750i) q^{21} +(-2.18912 - 2.40720i) q^{22} +(-0.393834 + 0.542066i) q^{23} +(8.48896 + 2.61955i) q^{24} +(-3.83835 - 3.20423i) q^{25} +(-3.45665 - 7.66150i) q^{26} +(9.82268 + 7.13660i) q^{27} +(-1.36641 + 3.15262i) q^{28} +(-1.22579 + 0.398283i) q^{29} +(2.34296 - 9.65226i) q^{30} +(0.362926 - 1.11697i) q^{31} +(4.82750 - 2.94877i) q^{32} +(-6.87282 - 2.23312i) q^{33} +(-1.87001 + 3.27629i) q^{34} +(3.61155 + 1.30932i) q^{35} +(13.4021 - 2.98765i) q^{36} +(2.95345 - 2.14581i) q^{37} +(-4.04021 + 7.07852i) q^{38} +(-15.1026 - 10.9726i) q^{39} +(-3.62066 - 5.18563i) q^{40} +(6.21636 - 4.51645i) q^{41} +(0.835236 + 7.58545i) q^{42} -3.75396 q^{43} +(-3.96204 + 2.34007i) q^{44} +(-4.25022 - 14.7518i) q^{45} +(0.637522 + 0.701032i) q^{46} +(8.51974 - 2.76823i) q^{47} +(6.06530 - 11.0028i) q^{48} +4.04848 q^{49} +(-5.53936 + 4.39494i) q^{50} +8.37845i q^{51} +(-11.6019 + 2.58634i) q^{52} +(1.09116 + 3.35825i) q^{53} +(12.7033 - 11.5524i) q^{54} +(2.88223 + 4.26144i) q^{55} +(3.97317 + 2.79751i) q^{56} +18.1019i q^{57} +(0.199497 + 1.81179i) q^{58} +(3.58141 + 4.92938i) q^{59} +(-12.6931 - 6.01637i) q^{60} +(0.542140 - 0.746192i) q^{61} +(-1.44250 - 0.823336i) q^{62} +(6.93293 + 9.54236i) q^{63} +(-2.69692 - 7.53171i) q^{64} +(3.67932 + 12.7703i) q^{65} +(-5.06605 + 8.87581i) q^{66} +(4.74089 - 14.5910i) q^{67} +(3.99980 + 3.53039i) q^{68} +(2.00153 + 0.650336i) q^{69} +(2.85025 - 4.62507i) q^{70} +(1.92683 + 5.93017i) q^{71} +(-0.288281 - 19.4166i) q^{72} +(3.14398 - 4.32732i) q^{73} +(-2.12322 - 4.70603i) q^{74} +(-5.84621 + 14.5760i) q^{75} +(8.64169 + 7.62750i) q^{76} +(-3.19778 - 2.32332i) q^{77} +(-19.5315 + 17.7621i) q^{78} +(-0.125628 - 0.386644i) q^{79} +(-8.22058 + 3.52448i) q^{80} +(5.41990 - 16.6807i) q^{81} +(-4.46891 - 9.90513i) q^{82} +(-0.356893 + 1.09840i) q^{83} +(10.7438 + 1.02182i) q^{84} +(3.66628 - 4.70489i) q^{85} +(-1.07807 + 5.19828i) q^{86} +(2.37952 + 3.27513i) q^{87} +(2.10258 + 6.15845i) q^{88} +(3.34918 + 2.43332i) q^{89} +(-21.6481 + 1.64903i) q^{90} +(-6.00168 - 8.26061i) q^{91} +(1.15384 - 0.681483i) q^{92} -3.68890 q^{93} +(-1.38658 - 12.5927i) q^{94} +(7.92110 - 10.1650i) q^{95} +(-13.4942 - 11.5587i) q^{96} +(-14.4383 + 4.69127i) q^{97} +(1.16265 - 5.60613i) q^{98} +15.7959i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.287182	−	1.38475i	0.203069	−	0.979165i
$2$	0.287182	−	1.38475i	0.203069	−	0.979165i
$3$	−0.970606	−	2.98722i	−0.560380	−	1.72467i	−0.681295	−	0.732009i	$-0.738583\pi$
$3$	−0.970606	−	2.98722i	−0.560380	−	1.72467i	0.120915	−	0.992663i	$-0.461417\pi$
$4$	−1.83505	−	0.795350i	−0.917526	−	0.397675i
$5$	−0.762120	+	2.10218i	−0.340830	+	0.940125i
$5$	−0.762120	+	2.10218i	−0.340830	+	0.940125i
$6$	−4.41529	+	0.486168i	−1.80253	+	0.198477i
$7$		−	1.71800i		−	0.649342i	−0.945827	−	0.324671i	$-0.894746\pi$
$7$		−	1.71800i		−	0.649342i	0.945827	−	0.324671i	$-0.105254\pi$
$8$	−1.62835	+	2.31267i	−0.575710	+	0.817654i
$9$	−5.55435	+	4.03547i	−1.85145	+	1.34516i
$10$	2.69213	+	1.65905i	0.851325	+	0.524639i
$11$	1.35234	−	1.86134i	0.407747	−	0.561215i	−0.554920	−	0.831903i	$-0.687251\pi$
$11$	1.35234	−	1.86134i	0.407747	−	0.561215i	0.962667	+	0.270688i	$0.0872513\pi$
$12$	−0.594772	+	6.25368i	−0.171696	+	1.80528i
$13$	4.80828	−	3.49342i	1.33358	−	0.968900i	0.333922	−	0.942601i	$-0.391628\pi$
$13$	4.80828	−	3.49342i	1.33358	−	0.968900i	0.999654	−	0.0262994i	$-0.00837233\pi$
$14$	−2.37899	−	0.493379i	−0.635813	−	0.131861i
$15$	7.01940	+	0.236226i	1.81240	+	0.0609934i
$16$	2.73484	+	2.91902i	0.683709	+	0.729755i
$17$	−2.53693	−	0.824300i	−0.615297	−	0.199922i	−0.0152459	−	0.999884i	$-0.504853\pi$
$17$	−2.53693	−	0.824300i	−0.615297	−	0.199922i	−0.600051	+	0.799962i	$0.704853\pi$
$18$	3.99300	+	8.85029i	0.941159	+	2.08603i
$19$	−5.48112	−	1.78092i	−1.25746	−	0.408572i	−0.396868	−	0.917876i	$-0.629903\pi$
$19$	−5.48112	−	1.78092i	−1.25746	−	0.408572i	−0.860587	+	0.509304i	$0.829903\pi$
$20$	3.07050	−	3.25146i	0.686585	−	0.727050i
$21$	−5.13203	+	1.66750i	−1.11990	+	0.363878i
$22$	−2.18912	−	2.40720i	−0.466721	−	0.513216i
$23$	−0.393834	+	0.542066i	−0.0821200	+	0.113029i	−0.848101	−	0.529835i	$-0.822254\pi$
$23$	−0.393834	+	0.542066i	−0.0821200	+	0.113029i	0.765981	+	0.642864i	$0.222254\pi$
$24$	8.48896	+	2.61955i	1.73280	+	0.534714i
$25$	−3.83835	−	3.20423i	−0.767669	−	0.640846i
$26$	−3.45665	−	7.66150i	−0.677905	−	1.50254i
$27$	9.82268	+	7.13660i	1.89038	+	1.37344i
$28$	−1.36641	+	3.15262i	−0.258227	+	0.595788i
$29$	−1.22579	+	0.398283i	−0.227624	+	0.0739594i	−0.420608	−	0.907242i	$-0.638183\pi$
$29$	−1.22579	+	0.398283i	−0.227624	+	0.0739594i	0.192985	+	0.981202i	$0.438183\pi$
$30$	2.34296	−	9.65226i	0.427764	−	1.76225i
$31$	0.362926	−	1.11697i	0.0651834	−	0.200614i	−0.913160	−	0.407600i	$-0.866366\pi$
$31$	0.362926	−	1.11697i	0.0651834	−	0.200614i	0.978344	+	0.206986i	$0.0663656\pi$
$32$	4.82750	−	2.94877i	0.853390	−	0.521273i
$33$	−6.87282	−	2.23312i	−1.19640	−	0.388735i
$34$	−1.87001	+	3.27629i	−0.320704	+	0.561879i
$35$	3.61155	+	1.30932i	0.610463	+	0.221315i
$36$	13.4021	−	2.98765i	2.23369	−	0.497941i
$37$	2.95345	−	2.14581i	0.485545	−	0.352769i	−0.317924	−	0.948116i	$-0.602986\pi$
$37$	2.95345	−	2.14581i	0.485545	−	0.352769i	0.803468	+	0.595347i	$0.202986\pi$
$38$	−4.04021	+	7.07852i	−0.655409	+	1.14829i
$39$	−15.1026	−	10.9726i	−2.41834	−	1.75703i
$40$	−3.62066	−	5.18563i	−0.572477	−	0.819921i
$41$	6.21636	−	4.51645i	0.970832	−	0.705351i	0.0151912	−	0.999885i	$-0.495164\pi$
$41$	6.21636	−	4.51645i	0.970832	−	0.705351i	0.955641	+	0.294534i	$0.0951643\pi$
$42$	0.835236	+	7.58545i	0.128880	+	1.17046i
$43$	−3.75396			−0.572473			−0.286236	−	0.958159i	$-0.592404\pi$
$43$	−3.75396			−0.572473			−0.286236	+	0.958159i	$0.592404\pi$
$44$	−3.96204	+	2.34007i	−0.597300	+	0.352779i
$45$	−4.25022	−	14.7518i	−0.633585	−	2.19906i
$46$	0.637522	+	0.701032i	0.0939975	+	0.103362i
$47$	8.51974	−	2.76823i	1.24273	−	0.403788i	0.387421	−	0.921903i	$-0.373366\pi$
$47$	8.51974	−	2.76823i	1.24273	−	0.403788i	0.855311	+	0.518115i	$0.173366\pi$
$48$	6.06530	−	11.0028i	0.875451	−	1.58811i
$49$	4.04848			0.578355
$50$	−5.53936	+	4.39494i	−0.783383	+	0.621539i
$51$			8.37845i			1.17322i
$52$	−11.6019	+	2.58634i	−1.60890	+	0.358661i
$53$	1.09116	+	3.35825i	0.149882	+	0.461291i	0.997607	−	0.0691467i	$-0.0220277\pi$
$53$	1.09116	+	3.35825i	0.149882	+	0.461291i	−0.847724	+	0.530438i	$0.822028\pi$
$54$	12.7033	−	11.5524i	1.72870	−	1.57209i
$55$	2.88223	+	4.26144i	0.388640	+	0.574612i
$56$	3.97317	+	2.79751i	0.530937	+	0.373833i
$57$			18.1019i			2.39765i
$58$	0.199497	+	1.81179i	0.0261952	+	0.237900i
$59$	3.58141	+	4.92938i	0.466259	+	0.641751i	0.975792	−	0.218700i	$-0.0701818\pi$
$59$	3.58141	+	4.92938i	0.466259	+	0.641751i	−0.509533	+	0.860451i	$0.670182\pi$
$60$	−12.6931	−	6.01637i	−1.63867	−	0.776710i
$61$	0.542140	−	0.746192i	0.0694139	−	0.0955401i	−0.772898	−	0.634530i	$-0.781194\pi$
$61$	0.542140	−	0.746192i	0.0694139	−	0.0955401i	0.842312	+	0.538990i	$0.181194\pi$
$62$	−1.44250	−	0.823336i	−0.183197	−	0.104564i
$63$	6.93293	+	9.54236i	0.873467	+	1.20222i
$64$	−2.69692	−	7.53171i	−0.337116	−	0.941463i
$65$	3.67932	+	12.7703i	0.456364	+	1.58396i
$66$	−5.06605	+	8.87581i	−0.623588	+	1.09254i
$67$	4.74089	−	14.5910i	0.579192	−	1.78257i	−0.0422481	−	0.999107i	$-0.513452\pi$
$67$	4.74089	−	14.5910i	0.579192	−	1.78257i	0.621440	−	0.783462i	$-0.286548\pi$
$68$	3.99980	+	3.53039i	0.485047	+	0.428122i
$69$	2.00153	+	0.650336i	0.240956	+	0.0782912i
$70$	2.85025	−	4.62507i	0.340670	−	0.552801i
$71$	1.92683	+	5.93017i	0.228673	+	0.703782i	0.997898	+	0.0648044i	$0.0206424\pi$
$71$	1.92683	+	5.93017i	0.228673	+	0.703782i	−0.769225	+	0.638978i	$0.779358\pi$
$72$	−0.288281	−	19.4166i	−0.0339743	−	2.28827i
$73$	3.14398	−	4.32732i	0.367975	−	0.506475i	−0.584374	−	0.811485i	$-0.698660\pi$
$73$	3.14398	−	4.32732i	0.367975	−	0.506475i	0.952349	+	0.305010i	$0.0986598\pi$
$74$	−2.12322	−	4.70603i	−0.246820	−	0.547064i
$75$	−5.84621	+	14.5760i	−0.675063	+	1.68309i
$76$	8.64169	+	7.62750i	0.991269	+	0.874934i
$77$	−3.19778	−	2.32332i	−0.364421	−	0.264767i
$78$	−19.5315	+	17.7621i	−2.21151	+	2.01116i
$79$	−0.125628	−	0.386644i	−0.0141343	−	0.0435008i	0.943741	−	0.330687i	$-0.107280\pi$
$79$	−0.125628	−	0.386644i	−0.0141343	−	0.0435008i	−0.957875	+	0.287186i	$0.907280\pi$
$80$	−8.22058	+	3.52448i	−0.919089	+	0.394049i
$81$	5.41990	−	16.6807i	0.602211	−	1.85342i
$82$	−4.46891	−	9.90513i	−0.493509	−	1.09384i
$83$	−0.356893	+	1.09840i	−0.0391741	+	0.120565i	−0.968731	−	0.248113i	$-0.920190\pi$
$83$	−0.356893	+	1.09840i	−0.0391741	+	0.120565i	0.929557	+	0.368678i	$0.120190\pi$
$84$	10.7438	+	1.02182i	1.17224	+	0.111489i
$85$	3.66628	−	4.70489i	0.397664	−	0.510317i
$86$	−1.07807	+	5.19828i	−0.116251	+	0.560545i
$87$	2.37952	+	3.27513i	0.255111	+	0.351131i
$88$	2.10258	+	6.15845i	0.224136	+	0.656493i
$89$	3.34918	+	2.43332i	0.355013	+	0.257932i	0.750969	−	0.660338i	$-0.229587\pi$
$89$	3.34918	+	2.43332i	0.355013	+	0.257932i	−0.395956	+	0.918269i	$0.629587\pi$
$90$	−21.6481	+	1.64903i	−2.28191	+	0.173823i
$91$	−6.00168	−	8.26061i	−0.629148	−	0.865947i
$92$	1.15384	−	0.681483i	0.120296	−	0.0710496i
$93$	−3.68890			−0.382521
$94$	−1.38658	−	12.5927i	−0.143015	−	1.29884i
$95$	7.92110	−	10.1650i	0.812688	−	1.04291i
$96$	−13.4942	−	11.5587i	−1.37725	−	1.17971i
$97$	−14.4383	+	4.69127i	−1.46598	+	0.476327i	−0.929892	−	0.367833i	$-0.880100\pi$
$97$	−14.4383	+	4.69127i	−1.46598	+	0.476327i	−0.536091	+	0.844160i	$0.680100\pi$
$98$	1.16265	−	5.60613i	0.117446	−	0.566305i
$99$			15.7959i			1.58754i
$100$	4.49508	+	8.93276i	0.449508	+	0.893276i
$101$			13.7524i			1.36842i	0.729286	+	0.684209i	$0.239852\pi$
$101$			13.7524i			1.36842i	−0.729286	+	0.684209i	$0.760148\pi$
$102$	11.6020	+	2.40614i	1.14877	+	0.238244i
$103$	8.32817	−	2.70599i	0.820599	−	0.266629i	0.131519	−	0.991314i	$-0.458015\pi$
$103$	8.32817	−	2.70599i	0.820599	−	0.266629i	0.689081	+	0.724685i	$0.258015\pi$
$104$	0.249559	+	16.8085i	0.0244713	+	1.64821i
$105$	0.405836	−	12.0593i	0.0396056	−	1.17687i
$106$	4.96369	−	0.546553i	0.482116	−	0.0530859i
$107$	−3.49350			−0.337729			−0.168865	−	0.985639i	$-0.554010\pi$
$107$	−3.49350			−0.337729			−0.168865	+	0.985639i	$0.554010\pi$
$108$	−12.3490	−	20.9085i	−1.18829	−	2.01192i
$109$	2.56568	+	3.53135i	0.245747	+	0.338242i	0.914016	−	0.405678i	$-0.132964\pi$
$109$	2.56568	+	3.53135i	0.245747	+	0.338242i	−0.668269	+	0.743920i	$0.732964\pi$
$110$	6.72874	−	2.76735i	0.641560	−	0.263857i
$111$	−9.27664	−	6.73988i	−0.880500	−	0.639721i
$112$	5.01487	−	4.69844i	0.473860	−	0.443961i
$113$	−0.895884	−	1.23308i	−0.0842776	−	0.115998i	0.764796	−	0.644272i	$-0.222839\pi$
$113$	−0.895884	−	1.23308i	−0.0842776	−	0.115998i	−0.849074	+	0.528274i	$0.822839\pi$
$114$	25.0665	+	5.19854i	2.34770	+	0.486888i
$115$	−0.839373	−	1.24103i	−0.0782719	−	0.115727i
$116$	2.56616	+	0.244062i	0.238262	+	0.0226606i
$117$	−12.6093	+	38.8073i	−1.16573	+	3.58774i
$118$	7.85447	−	3.54371i	0.723062	−	0.326225i
$119$	−1.41615	+	4.35845i	−0.129818	+	0.399538i
$120$	−11.9764	+	15.8489i	−1.09329	+	1.44680i
$121$	1.76343	+	5.42728i	0.160312	+	0.493389i
$122$	−0.877594	−	0.965021i	−0.0794537	−	0.0873689i
$123$	−19.5253	−	14.1859i	−1.76053	−	1.27910i
$124$	−1.55437	+	1.76105i	−0.139587	+	0.158147i
$125$	9.66116	−	5.62690i	0.864120	−	0.503285i
$126$	15.2048	−	6.85996i	1.35455	−	0.611134i
$127$	−9.99210	+	13.7529i	−0.886655	+	1.22038i	0.0878777	+	0.996131i	$0.471992\pi$
$127$	−9.99210	+	13.7529i	−0.886655	+	1.22038i	−0.974533	+	0.224245i	$0.928008\pi$
$128$	−11.2040	+	1.57159i	−0.990305	+	0.138910i
$129$	3.64361	+	11.2139i	0.320802	+	0.987328i
$130$	18.7403	−	1.42753i	1.64363	−	0.125203i
$131$	−5.71604	−	1.85725i	−0.499413	−	0.162269i	0.0484693	−	0.998825i	$-0.484566\pi$
$131$	−5.71604	−	1.85725i	−0.499413	−	0.162269i	−0.547882	+	0.836556i	$0.684566\pi$
$132$	10.8359	+	9.56419i	0.943142	+	0.832455i
$133$	−3.05962	+	9.41655i	−0.265303	+	0.816519i
$134$	−18.8433	−	10.7552i	−1.62781	−	0.929108i
$135$	−22.4885	+	15.2101i	−1.93550	+	1.30908i
$136$	6.03737	−	4.52485i	0.517700	−	0.388003i
$137$	−2.43382	−	3.34986i	−0.207935	−	0.286198i	0.692293	−	0.721616i	$-0.256600\pi$
$137$	−2.43382	−	3.34986i	−0.207935	−	0.286198i	−0.900228	+	0.435418i	$0.856600\pi$
$138$	1.47535	−	2.58485i	0.125590	−	0.220037i
$139$	5.91784	−	8.14520i	0.501944	−	0.690867i	−0.480591	−	0.876945i	$-0.659578\pi$
$139$	5.91784	−	8.14520i	0.501944	−	0.690867i	0.982535	+	0.186078i	$0.0595777\pi$
$140$	−5.58601	−	5.27511i	−0.472104	−	0.445829i
$141$	−16.5386	−	22.7635i	−1.39280	−	1.91703i
$142$	8.76514	−	0.965132i	0.735555	−	0.0809921i
$143$		−	13.6741i		−	1.14349i
$144$	−26.9699	−	5.17690i	−2.24749	−	0.431409i
$145$	0.0969343	−	2.88038i	0.00804996	−	0.239202i
$146$	−5.08935	−	5.59635i	−0.421198	−	0.463157i
$147$	−3.92948	−	12.0937i	−0.324098	−	0.997472i
$148$	−7.12641	+	1.58864i	−0.585787	+	0.130586i
$149$			13.6951i			1.12195i	0.827834	+	0.560973i	$0.189573\pi$
$149$			13.6951i			1.12195i	−0.827834	+	0.560973i	$0.810427\pi$
$150$	18.5052	+	12.2815i	1.51094	+	1.00278i
$151$	−12.0927			−0.984088			−0.492044	−	0.870570i	$-0.663750\pi$
$151$	−12.0927			−0.984088			−0.492044	+	0.870570i	$0.663750\pi$
$152$	13.0439	−	9.77607i	1.05800	−	0.792944i
$153$	17.4175	−	5.65928i	1.40812	−	0.457525i
$154$	−4.13556	+	3.76090i	−0.333253	+	0.303062i
$155$	2.07149	+	1.61420i	0.166386	+	0.129656i
$156$	18.9869	+	32.1472i	1.52017	+	2.57384i
$157$	12.6051			1.00599			0.502997	−	0.864288i	$-0.332231\pi$
$157$	12.6051			1.00599			0.502997	+	0.864288i	$0.332231\pi$
$158$	−0.571482	+	0.0629261i	−0.0454647	+	0.00500613i
$159$	8.97273	−	6.51907i	0.711584	−	0.516996i
$160$	2.51971	+	12.3956i	0.199201	+	0.979959i
$161$	0.931268	+	0.676606i	0.0733942	+	0.0533240i
$162$	−21.5421	−	12.2956i	−1.69251	−	0.966034i
$163$	9.55541	−	6.94241i	0.748438	−	0.543772i	−0.146904	−	0.989151i	$-0.546931\pi$
$163$	9.55541	−	6.94241i	0.748438	−	0.543772i	0.895342	+	0.445379i	$0.146931\pi$
$164$	−14.9995	+	3.34374i	−1.17126	+	0.261102i
$165$	9.93233	−	12.7460i	0.773231	−	0.992277i
$166$	1.41852	+	0.809649i	0.110098	+	0.0628409i
$167$	10.4420	+	3.39280i	0.808023	+	0.262543i	0.683760	−	0.729707i	$-0.260343\pi$
$167$	10.4420	+	3.39280i	0.808023	+	0.262543i	0.124263	+	0.992249i	$0.460343\pi$
$168$	4.50039	−	14.5840i	0.347213	−	1.12518i
$169$	6.89835	−	21.2309i	0.530642	−	1.63315i
$170$	−5.46219	−	6.42803i	−0.418931	−	0.493007i
$171$	37.6309	−	12.2270i	2.87771	−	0.935024i
$172$	6.88871	+	2.98571i	0.525259	+	0.227658i
$173$	12.2681	+	8.91328i	0.932725	+	0.677664i	0.946659	−	0.322238i	$-0.104435\pi$
$173$	12.2681	+	8.91328i	0.932725	+	0.677664i	−0.0139334	+	0.999903i	$0.504435\pi$
$174$	5.21858	−	2.35448i	0.395620	−	0.178492i
$175$	−5.50486	+	6.59427i	−0.416128	+	0.498480i
$176$	9.13172	−	1.14294i	0.688329	−	0.0861527i
$177$	11.2490	−	15.4829i	0.845527	−	1.16377i
$178$	4.33136	−	3.93896i	0.324649	−	0.295238i
$179$	−20.5530	+	6.67808i	−1.53620	+	0.499143i	−0.950326	−	0.311256i	$-0.899250\pi$
$179$	−20.5530	+	6.67808i	−1.53620	+	0.499143i	−0.585878	+	0.810399i	$0.699250\pi$
$180$	−3.93345	+	30.4507i	−0.293182	+	2.26966i
$181$	−8.26366	−	2.68502i	−0.614233	−	0.199576i	−0.0146547	−	0.999893i	$-0.504665\pi$
$181$	−8.26366	−	2.68502i	−0.614233	−	0.199576i	−0.599578	+	0.800316i	$0.704665\pi$
$182$	−13.1624	+	5.93852i	−0.975665	+	0.440192i
$183$	−2.75524	−	0.895233i	−0.203673	−	0.0661775i
$184$	−0.612321	−	1.79348i	−0.0451409	−	0.132217i
$185$	2.26000	+	7.84406i	0.166158	+	0.576707i
$186$	−1.05939	+	5.10819i	−0.0776780	+	0.374551i
$187$	−4.96511	+	3.60736i	−0.363085	+	0.263796i
$188$	−17.8359	−	1.69633i	−1.30082	−	0.123717i
$189$	12.2607	−	16.8753i	0.891831	−	1.22750i
$190$	−11.8012	−	13.8879i	−0.856150	−	1.00754i
$191$	0.689197	−	0.500731i	0.0498686	−	0.0362316i	−0.562572	−	0.826748i	$-0.690188\pi$
$191$	0.689197	−	0.500731i	0.0498686	−	0.0362316i	0.612440	+	0.790517i	$0.290188\pi$
$192$	−19.8812	+	15.3666i	−1.43480	+	1.10899i
$193$			10.7404i			0.773113i	0.922266	+	0.386557i	$0.126336\pi$
$193$			10.7404i			0.773113i	−0.922266	+	0.386557i	$0.873664\pi$
$194$	2.34982	+	21.3406i	0.168707	+	1.53217i
$195$	34.5765	−	23.3859i	2.47607	−	1.67470i
$196$	−7.42918	−	3.21996i	−0.530656	−	0.229997i
$197$	−6.98882	−	21.5094i	−0.497933	−	1.53248i	−0.812336	−	0.583190i	$-0.801804\pi$
$197$	−6.98882	−	21.5094i	−0.497933	−	1.53248i	0.314403	−	0.949290i	$-0.398196\pi$
$198$	21.8733	+	4.53630i	1.55447	+	0.322381i
$199$	0.706769			0.0501015			0.0250508	−	0.999686i	$-0.492025\pi$
$199$	0.706769			0.0501015			0.0250508	+	0.999686i	$0.492025\pi$
$200$	13.6605	−	3.65922i	0.965945	−	0.258746i
$201$	−48.1879			−3.39891
$202$	19.0436	+	3.94945i	1.33991	+	0.277883i
$203$	0.684250	+	2.10590i	0.0480249	+	0.147806i
$204$	6.66380	−	15.3749i	0.466560	−	1.07646i
$205$	4.75679	+	16.5100i	0.332229	+	1.15311i
$206$	−1.35541	−	12.3095i	−0.0944356	−	0.857646i
$207$		−	4.60013i		−	0.319731i
$208$	23.3472	+	4.48153i	1.61884	+	0.310738i
$209$	−10.7273	+	7.79381i	−0.742020	+	0.539109i
$210$	−16.5826	−	4.02520i	−1.14430	−	0.277765i
$211$	−10.7903	+	14.8516i	−0.742834	+	1.02242i	0.255616	+	0.966778i	$0.417722\pi$
$211$	−10.7903	+	14.8516i	−0.742834	+	1.02242i	−0.998451	+	0.0556452i	$0.982278\pi$
$212$	0.668646	−	7.03042i	0.0459228	−	0.482851i
$213$	15.8445	−	11.5117i	1.08565	−	0.788770i
$214$	−1.00327	+	4.83762i	−0.0685822	+	0.330693i
$215$	2.86096	−	7.89150i	0.195116	−	0.538196i
$216$	−32.4994	+	11.0958i	−2.21131	+	0.754971i
$217$	−1.91895	−	0.623506i	−0.130267	−	0.0423263i
$218$	5.62685	−	2.53868i	0.381098	−	0.171941i
$219$	−15.9782	−	5.19164i	−1.07971	−	0.350818i
$220$	−1.89971	−	10.1123i	−0.128078	−	0.681774i
$221$	−15.0779	+	4.89911i	−1.01425	+	0.329550i
$222$	−11.9971	+	10.9102i	−0.805194	+	0.732247i
$223$	−4.51123	+	6.20918i	−0.302094	+	0.415797i	−0.932895	−	0.360147i	$-0.882726\pi$
$223$	−4.51123	+	6.20918i	−0.302094	+	0.415797i	0.630801	+	0.775945i	$0.282726\pi$
$224$	−5.06597	−	8.29364i	−0.338485	−	0.554142i
$225$	34.2501	+	2.30788i	2.28334	+	0.153858i
$226$	−1.96478	+	0.886455i	−0.130695	+	0.0589661i
$227$	9.47829	+	6.88638i	0.629096	+	0.457065i	0.856087	−	0.516832i	$-0.172889\pi$
$227$	9.47829	+	6.88638i	0.629096	+	0.457065i	−0.226991	+	0.973897i	$0.572889\pi$
$228$	14.3973	−	33.2179i	0.953487	−	2.19991i
$229$	25.6372	−	8.33003i	1.69415	−	0.550464i	0.706582	−	0.707631i	$-0.250236\pi$
$229$	25.6372	−	8.33003i	1.69415	−	0.550464i	0.987572	+	0.157167i	$0.0502361\pi$
$230$	−1.95957	+	0.805918i	−0.129210	+	0.0531407i
$231$	−3.83649	+	11.8075i	−0.252422	+	0.776876i
$232$	1.07492	−	3.48340i	0.0705720	−	0.228696i
$233$	13.2560	+	4.30712i	0.868426	+	0.282169i	0.709144	−	0.705064i	$-0.249082\pi$
$233$	13.2560	+	4.30712i	0.868426	+	0.282169i	0.159283	+	0.987233i	$0.449082\pi$
$234$	50.1172	+	28.6054i	3.27626	+	1.87000i
$235$	−0.673733	+	20.0198i	−0.0439495	+	1.30595i
$236$	−2.65148	−	11.8941i	−0.172597	−	0.774243i
$237$	−1.03305	+	0.750558i	−0.0671041	+	0.0487540i
$238$	5.62866	+	3.21267i	0.364852	+	0.208247i
$239$	7.73830	+	5.62220i	0.500549	+	0.363670i	0.809227	−	0.587497i	$-0.199886\pi$
$239$	7.73830	+	5.62220i	0.500549	+	0.363670i	−0.308678	+	0.951167i	$0.599886\pi$
$240$	18.5074	+	21.1358i	1.19464	+	1.36431i
$241$	20.3460	−	14.7823i	1.31060	−	0.952210i	0.310606	−	0.950539i	$-0.399468\pi$
$241$	20.3460	−	14.7823i	1.31060	−	0.952210i	0.999999	−	0.00167085i	$-0.000531849\pi$
$242$	8.02184	−	0.883287i	0.515664	−	0.0567799i
$243$	−18.6651			−1.19737
$244$	−1.58834	+	0.938110i	−0.101683	+	0.0600563i
$245$	−3.08543	+	8.51066i	−0.197121	+	0.543726i
$246$	−25.2513	+	22.9636i	−1.60996	+	1.46411i
$247$	−32.5763	+	10.5847i	−2.07278	+	0.673486i
$248$	1.99222	+	2.65816i	0.126506	+	0.168793i
$249$	3.62757			0.229888
$250$	−5.01732	−	14.9942i	−0.317323	−	0.948317i
$251$		−	6.91776i		−	0.436645i	−0.975877	−	0.218323i	$-0.929941\pi$
$251$		−	6.91776i		−	0.436645i	0.975877	−	0.218323i	$-0.0700585\pi$
$252$	−5.13277	−	23.0248i	−0.323334	−	1.45043i
$253$	0.476370	+	1.46612i	0.0299492	+	0.0921740i
$254$	16.1748	+	17.7861i	1.01490	+	1.11600i
$255$	−17.6130	−	6.38538i	−1.10297	−	0.399868i
$256$	−1.04135	+	15.9661i	−0.0650841	+	0.997880i
$257$		−	29.8090i		−	1.85943i	−0.368277	−	0.929716i	$-0.620052\pi$
$257$		−	29.8090i		−	1.85943i	0.368277	−	0.929716i	$-0.379948\pi$
$258$	16.5748	−	1.82505i	1.03190	−	0.113623i
$259$	−3.68650	−	5.07403i	−0.229068	−	0.315285i
$260$	3.40510	−	26.3605i	0.211175	−	1.63481i
$261$	5.20121	−	7.15885i	0.321947	−	0.443122i
$262$	−4.21337	+	7.38190i	−0.260303	+	0.456055i
$263$	−15.5573	−	21.4128i	−0.959304	−	1.32037i	−0.947269	−	0.320441i	$-0.896169\pi$
$263$	−15.5573	−	21.4128i	−0.959304	−	1.32037i	−0.0120353	−	0.999928i	$-0.503831\pi$
$264$	16.3559	−	12.2583i	1.00663	−	0.754446i
$265$	−7.89125	−	0.265567i	−0.484755	−	0.0163137i
$266$	12.1609	+	6.94107i	0.745631	+	0.425585i
$267$	4.01813	−	12.3665i	0.245906	−	0.756820i
$268$	−20.3047	+	23.0045i	−1.24031	+	1.40522i
$269$	7.64014	+	2.48243i	0.465827	+	0.151357i	0.532521	−	0.846417i	$-0.321245\pi$
$269$	7.64014	+	2.48243i	0.465827	+	0.151357i	−0.0666932	+	0.997774i	$0.521245\pi$
$270$	14.6039	+	35.5090i	0.888765	+	2.16101i
$271$	2.87827	+	8.85842i	0.174843	+	0.538111i	0.999626	−	0.0273381i	$-0.00870306\pi$
$271$	2.87827	+	8.85842i	0.174843	+	0.538111i	−0.824784	+	0.565449i	$0.808703\pi$
$272$	−4.53195	−	9.65969i	−0.274790	−	0.585705i
$273$	−18.8510	+	25.9461i	−1.14091	+	1.57033i
$274$	−5.33766	+	2.40820i	−0.322460	+	0.145485i
$275$	−11.1549	+	2.81125i	−0.672667	+	0.169525i
$276$	−3.15566	−	2.78531i	−0.189949	−	0.167656i
$277$	−3.05174	−	2.21722i	−0.183361	−	0.133220i	0.492318	−	0.870415i	$-0.336150\pi$
$277$	−3.05174	−	2.21722i	−0.183361	−	0.133220i	−0.675679	+	0.737196i	$0.736150\pi$
$278$	−9.57955	−	10.5339i	−0.574543	−	0.631780i
$279$	2.49169	+	7.66863i	0.149173	+	0.459109i
$280$	−8.90891	+	6.22029i	−0.532409	+	0.371734i
$281$	−6.62409	+	20.3869i	−0.395160	+	1.21618i	0.533676	+	0.845689i	$0.320810\pi$
$281$	−6.62409	+	20.3869i	−0.395160	+	1.21618i	−0.928837	+	0.370489i	$0.879190\pi$
$282$	−36.2713	+	16.3646i	−2.15992	+	0.974495i
$283$	0.286114	−	0.880568i	0.0170077	−	0.0523443i	−0.942192	−	0.335072i	$-0.891239\pi$
$283$	0.286114	−	0.880568i	0.0170077	−	0.0523443i	0.959200	+	0.282728i	$0.0912393\pi$
$284$	1.18073	−	12.4147i	0.0700635	−	0.736676i
$285$	−38.0535	−	13.7958i	−2.25409	−	0.817193i
$286$	−18.9352	−	3.92697i	−1.11966	−	0.232207i
$287$	−7.75925	−	10.6797i	−0.458014	−	0.630402i
$288$	−14.9140	+	35.8597i	−0.878814	+	2.11305i
$289$	−7.99672	−	5.80996i	−0.470395	−	0.341762i
$290$	−3.96076	−	0.961423i	−0.232584	−	0.0564567i
$291$	28.0277	+	38.5769i	1.64301	+	2.26142i
$292$	−9.21111	+	5.44029i	−0.539039	+	0.318369i
$293$	−13.3571			−0.780332			−0.390166	−	0.920744i	$-0.627582\pi$
$293$	−13.3571			−0.780332			−0.390166	+	0.920744i	$0.627582\pi$
$294$	−17.8752	+	1.96824i	−1.04250	+	0.114790i
$295$	−13.0919	+	3.77199i	−0.762241	+	0.219614i
$296$	0.153290	+	10.3245i	0.00890980	+	0.600100i
$297$	26.5673	−	8.63223i	1.54159	−	0.500893i
$298$	18.9642	+	3.93299i	1.09857	+	0.227832i
$299$			3.98223i			0.230298i
$300$	22.3212	−	22.0980i	1.28871	−	1.27583i
$301$			6.44929i			0.371731i
$302$	−3.47280	+	16.7453i	−0.199837	+	0.963584i
$303$	41.0815	−	13.3482i	2.36007	−	0.766833i
$304$	−9.79141	−	20.8700i	−0.561576	−	1.19698i
$305$	1.15546	+	1.70837i	0.0661612	+	0.0978207i
$306$	−2.83468	−	25.7440i	−0.162048	−	1.47169i
$307$	−14.1781			−0.809186			−0.404593	−	0.914497i	$-0.632587\pi$
$307$	−14.1781			−0.809186			−0.404593	+	0.914497i	$0.632587\pi$
$308$	4.02024	+	6.80677i	0.229074	+	0.387852i
$309$	−16.1668	−	22.2516i	−0.919695	−	1.26585i
$310$	2.83016	−	2.40491i	0.160742	−	0.136590i
$311$	0.386936	+	0.281125i	0.0219411	+	0.0159412i	0.598702	−	0.800972i	$-0.295683\pi$
$311$	0.386936	+	0.281125i	0.0219411	+	0.0159412i	−0.576761	+	0.816913i	$0.695683\pi$
$312$	49.9685	−	17.0599i	2.82891	−	0.965828i
$313$	−6.67701	−	9.19012i	−0.377407	−	0.519456i	0.577488	−	0.816399i	$-0.304033\pi$
$313$	−6.67701	−	9.19012i	−0.377407	−	0.519456i	−0.954895	+	0.296943i	$0.904033\pi$
$314$	3.61995	−	17.4548i	0.204286	−	0.985033i
$315$	−25.3435	+	7.30187i	−1.42794	+	0.411414i
$316$	−0.0769829	+	0.809430i	−0.00433063	+	0.0455340i
$317$	−4.27173	+	13.1470i	−0.239924	+	0.738411i	0.756505	+	0.653987i	$0.226905\pi$
$317$	−4.27173	+	13.1470i	−0.239924	+	0.738411i	−0.996430	+	0.0844241i	$0.973095\pi$
$318$	−6.45046	−	14.2971i	−0.361724	−	0.801744i
$319$	−0.916348	+	2.82023i	−0.0513056	+	0.157902i
$320$	17.8884	+	0.0706325i	0.999992	+	0.00394848i
$321$	3.39081	+	10.4358i	0.189257	+	0.582472i
$322$	1.20437	−	1.09526i	0.0671170	−	0.0610365i
$323$	12.4372	+	9.03618i	0.692026	+	0.502786i
$324$	−23.2128	+	26.2993i	−1.28960	+	1.46107i
$325$	−29.6496	−	1.99788i	−1.64466	−	0.110822i
$326$	−6.86935	−	15.2256i	−0.380458	−	0.843267i
$327$	8.05866	−	11.0918i	0.445645	−	0.613378i
$328$	0.322641	+	21.7308i	0.0178149	+	1.19988i
$329$	−4.75581	−	14.6369i	−0.262197	−	0.806958i
$330$	−14.7976	−	17.4142i	−0.814584	−	0.958621i
$331$	−6.42804	−	2.08860i	−0.353317	−	0.114800i	0.126981	−	0.991905i	$-0.459471\pi$
$331$	−6.42804	−	2.08860i	−0.353317	−	0.114800i	−0.480298	+	0.877105i	$0.659471\pi$
$332$	1.52853	−	1.73177i	0.0838891	−	0.0950434i
$333$	−7.74516	+	23.8372i	−0.424432	+	1.30627i
$334$	7.69692	−	13.4851i	0.421157	−	0.737874i
$335$	27.0597	+	21.0863i	1.47843	+	1.15207i
$336$	−18.9027	−	10.4202i	−1.03123	−	0.568467i
$337$	−9.77379	−	13.4525i	−0.532412	−	0.732803i	0.455083	−	0.890449i	$-0.349609\pi$
$337$	−9.77379	−	13.4525i	−0.532412	−	0.732803i	−0.987496	+	0.157646i	$0.949609\pi$
$338$	−27.4184	−	15.6496i	−1.49136	−	0.851227i
$339$	−2.81392	+	3.87303i	−0.152831	+	0.210354i
$340$	−10.4698	+	5.71774i	−0.567807	+	0.310088i
$341$	−1.58826	−	2.18606i	−0.0860093	−	0.118382i
$342$	−6.12441	−	55.6207i	−0.331170	−	3.00762i
$343$		−	18.9813i		−	1.02489i
$344$	6.11277	−	8.68168i	0.329578	−	0.468085i
$345$	−2.89253	+	3.71194i	−0.155728	+	0.199844i
$346$	15.8658	−	14.4285i	0.852952	−	0.775679i
$347$	0.155098	+	0.477342i	0.00832608	+	0.0256250i	0.955133	−	0.296176i	$-0.0957116\pi$
$347$	0.155098	+	0.477342i	0.00832608	+	0.0256250i	−0.946807	+	0.321801i	$0.895712\pi$
$348$	−1.76167	−	7.90258i	−0.0944354	−	0.423623i
$349$			1.38740i			0.0742660i	0.999310	+	0.0371330i	$0.0118225\pi$
$349$			1.38740i			0.0742660i	−0.999310	+	0.0371330i	$0.988177\pi$
$350$	7.55050	+	9.51660i	0.403591	+	0.508684i
$351$	72.1613			3.85169
$352$	1.03978	−	12.9734i	0.0554204	−	0.691483i
$353$	−27.1323	+	8.81582i	−1.44411	+	0.469218i	−0.923175	−	0.384380i	$-0.874415\pi$
$353$	−27.1323	+	8.81582i	−1.44411	+	0.469218i	−0.520931	+	0.853599i	$0.674415\pi$
$354$	−18.2094	−	20.0235i	−0.967821	−	1.06423i
$355$	−13.9348	−	0.468952i	−0.739582	−	0.0248894i
$356$	−4.21058	−	7.12905i	−0.223160	−	0.377839i
$357$	14.3942			0.761820
$358$	3.34499	+	30.3786i	0.176788	+	1.60556i
$359$	−18.7073	+	13.5917i	−0.987336	+	0.717342i	−0.959336	−	0.282266i	$-0.908914\pi$
$359$	−18.7073	+	13.5917i	−0.987336	+	0.717342i	−0.0279998	+	0.999608i	$0.508914\pi$
$360$	41.0369	+	14.1917i	2.16283	+	0.747970i
$361$	11.4997	+	8.35500i	0.605246	+	0.439737i
$362$	−6.09126	+	10.6720i	−0.320149	+	0.560907i
$363$	14.5009	−	10.5355i	0.761099	−	0.552971i
$364$	4.44333	+	19.9321i	0.232894	+	1.04473i
$365$	6.70073	+	9.90716i	0.350732	+	0.518565i
$366$	−2.03093	+	3.55822i	−0.106158	+	0.185991i
$367$	26.8195	+	8.71417i	1.39996	+	0.454876i	0.909179	−	0.416405i	$-0.136710\pi$
$367$	26.8195	+	8.71417i	1.39996	+	0.454876i	0.490785	+	0.871281i	$0.336710\pi$
$368$	−2.65937	+	0.332852i	−0.138629	+	0.0173511i
$369$	−16.3018	+	50.1719i	−0.848640	+	2.61184i
$370$	11.5111	−	0.876852i	0.598433	−	0.0455854i
$371$	5.76946	−	1.87461i	0.299535	−	0.0973250i
$372$	6.76932	+	2.93397i	0.350973	+	0.152119i
$373$	−14.5528	−	10.5732i	−0.753515	−	0.547461i	0.143399	−	0.989665i	$-0.454197\pi$
$373$	−14.5528	−	10.5732i	−0.753515	−	0.547461i	−0.896914	+	0.442204i	$0.854197\pi$
$374$	3.56939	+	7.91139i	0.184569	+	0.409088i
$375$	−26.1860	−	23.3985i	−1.35224	−	1.20829i
$376$	−7.47114	+	24.2110i	−0.385295	+	1.24859i
$377$	−4.50257	+	6.19726i	−0.231894	+	0.319175i
$378$	−19.8471	−	21.8242i	−1.02082	−	1.12252i
$379$	5.18753	−	1.68553i	0.266466	−	0.0865799i	−0.172737	−	0.984968i	$-0.555261\pi$
$379$	5.18753	−	1.68553i	0.266466	−	0.0865799i	0.439203	+	0.898388i	$0.355261\pi$
$380$	−22.6204	+	12.3533i	−1.16040	+	0.633713i
$381$	50.7814	+	16.4999i	2.60161	+	0.845315i
$382$	−0.495461	−	1.09817i	−0.0253500	−	0.0561870i
$383$	−13.2382	−	4.30135i	−0.676440	−	0.219789i	−0.0494042	−	0.998779i	$-0.515732\pi$
$383$	−13.2382	−	4.30135i	−0.676440	−	0.219789i	−0.627036	+	0.778990i	$0.715732\pi$
$384$	15.5694	+	31.9435i	0.794521	+	1.63011i
$385$	7.32114	−	4.95166i	0.373120	−	0.252360i
$386$	14.8728	+	3.08446i	0.757005	+	0.156995i
$387$	20.8508	−	15.1490i	1.05990	−	0.770066i
$388$	30.2262	+	2.87474i	1.53450	+	0.145943i
$389$	21.7230	−	29.8991i	1.10140	−	1.51594i	0.267880	−	0.963452i	$-0.413677\pi$
$389$	21.7230	−	29.8991i	1.10140	−	1.51594i	0.833518	−	0.552492i	$-0.186323\pi$
$390$	−22.4538	−	54.5957i	−1.13699	−	2.76456i
$391$	1.44596	−	1.05055i	0.0731251	−	0.0531285i
$392$	−6.59237	+	9.36283i	−0.332965	+	0.472894i
$393$			18.8777i			0.952255i
$394$	−31.7921	+	3.50064i	−1.60166	+	0.176360i
$395$	0.908540	+	0.0305754i	0.0457136	+	0.00153842i
$396$	12.5633	−	28.9863i	0.631327	−	1.45661i
$397$	7.32490	+	22.5437i	0.367626	+	1.13144i	0.948320	+	0.317315i	$0.102781\pi$
$397$	7.32490	+	22.5437i	0.367626	+	1.13144i	−0.580694	+	0.814122i	$0.697219\pi$
$398$	0.202972	−	0.978697i	0.0101740	−	0.0490576i
$399$	31.0990			1.55690
$400$	−1.14404	−	19.9673i	−0.0572020	−	0.998363i
$401$	−0.881338			−0.0440119			−0.0220060	−	0.999758i	$-0.507005\pi$
$401$	−0.881338			−0.0440119			−0.0220060	+	0.999758i	$0.507005\pi$
$402$	−13.8387	+	66.7281i	−0.690213	+	3.32810i
$403$	−2.15700	−	6.63856i	−0.107448	−	0.330690i
$404$	10.9380	−	25.2364i	0.544186	−	1.25556i
$405$	30.9354	+	24.1063i	1.53719	+	1.19785i
$406$	3.11265	−	0.342735i	0.154478	−	0.0170096i
$407$		−	8.39925i		−	0.416335i
$408$	−19.3766	−	13.6431i	−0.959286	−	0.675433i
$409$	28.9714	−	21.0489i	1.43254	−	1.04080i	0.443005	−	0.896519i	$-0.353912\pi$
$409$	28.9714	−	21.0489i	1.43254	−	1.04080i	0.989536	−	0.144283i	$-0.0460876\pi$
$410$	24.2283	−	1.84558i	1.19655	−	0.0911466i
$411$	−7.64449	+	10.5217i	−0.377075	+	0.518999i
$412$	−17.4348	−	1.65819i	−0.858953	−	0.0816930i
$413$	8.46866	−	6.15285i	0.416716	−	0.302762i
$414$	−6.37002	−	1.32108i	−0.313069	−	0.0649273i
$415$	−2.03705	−	1.58737i	−0.0999949	−	0.0779209i
$416$	12.9107	−	31.0430i	0.632999	−	1.52201i
$417$	−30.0754	−	9.77209i	−1.47280	−	0.478541i
$418$	7.71178	+	17.0928i	0.377196	+	0.836036i
$419$	18.1069	+	5.88329i	0.884581	+	0.287418i	0.715858	−	0.698246i	$-0.246036\pi$
$419$	18.1069	+	5.88329i	0.884581	+	0.287418i	0.168723	+	0.985664i	$0.446036\pi$
$420$	−10.3361	+	21.8067i	−0.504350	+	1.06406i
$421$	−8.42477	+	2.73737i	−0.410598	+	0.133411i	−0.507031	−	0.861928i	$-0.669257\pi$
$421$	−8.42477	+	2.73737i	−0.410598	+	0.133411i	0.0964323	+	0.995340i	$0.469257\pi$
$422$	17.4669	+	19.2069i	0.850275	+	0.934979i
$423$	−36.1505	+	49.7569i	−1.75770	+	2.41926i
$424$	−9.54333	−	2.94492i	−0.463465	−	0.143018i
$425$	7.09639	+	11.2929i	0.344225	+	0.547785i
$426$	−11.3906	−	25.2466i	−0.551875	−	1.22320i
$427$	−1.28196	−	0.931395i	−0.0620382	−	0.0450734i
$428$	6.41075	+	2.77856i	0.309876	+	0.134307i
$429$	−40.8476	+	13.2722i	−1.97214	+	0.640788i
$430$	−10.1061	−	6.22801i	−0.487360	−	0.300341i
$431$	0.956566	−	2.94401i	0.0460762	−	0.141808i	−0.925372	−	0.379061i	$-0.876247\pi$
$431$	0.956566	−	2.94401i	0.0460762	−	0.141808i	0.971448	+	0.237253i	$0.0762471\pi$
$432$	6.03156	+	48.1900i	0.290194	+	2.31854i
$433$	8.67407	+	2.81837i	0.416849	+	0.135442i	0.509930	−	0.860216i	$-0.329671\pi$
$433$	8.67407	+	2.81837i	0.416849	+	0.135442i	−0.0930806	+	0.995659i	$0.529671\pi$
$434$	−1.41449	+	2.47821i	−0.0678976	+	0.118958i
$435$	−8.69840	+	2.50615i	−0.417056	+	0.120161i
$436$	−1.89949	−	8.52083i	−0.0909692	−	0.408074i
$437$	3.12403	−	2.26974i	0.149443	−	0.108576i
$438$	−11.7778	+	20.6349i	−0.562764	+	0.985972i
$439$	31.0958	+	22.5924i	1.48412	+	1.07828i	0.976200	+	0.216872i	$0.0695854\pi$
$439$	31.0958	+	22.5924i	1.48412	+	1.07828i	0.507920	+	0.861404i	$0.330415\pi$
$440$	−14.5486	−	0.273467i	−0.693577	−	0.0130370i
$441$	−22.4867	+	16.3375i	−1.07080	+	0.777978i
$442$	2.45392	+	22.2860i	0.116721	+	1.06004i
$443$	33.8214			1.60690			0.803451	−	0.595371i	$-0.202995\pi$
$443$	33.8214			1.60690			0.803451	+	0.595371i	$0.202995\pi$
$444$	11.6626	+	19.7462i	0.553481	+	0.937113i
$445$	−7.66777	+	5.18611i	−0.363487	+	0.245845i
$446$	7.30260	+	8.03008i	0.345788	+	0.380236i
$447$	40.9102	−	13.2925i	1.93499	−	0.628715i
$448$	−12.9395	+	4.63331i	−0.611332	+	0.218903i
$449$	11.7494			0.554489			0.277245	−	0.960799i	$-0.410579\pi$
$449$	11.7494			0.554489			0.277245	+	0.960799i	$0.410579\pi$
$450$	13.0319	−	46.7650i	0.614327	−	2.20452i
$451$		−	17.6785i		−	0.832450i
$452$	0.663265	+	2.97530i	0.0311973	+	0.139947i
$453$	11.7372	+	36.1235i	0.551463	+	1.69723i
$454$	12.2579	−	11.1474i	0.575292	−	0.523173i
$455$	21.9393	−	6.32107i	1.02853	−	0.296336i
$456$	−41.8638	−	29.4763i	−1.96045	−	1.38035i
$457$			12.5132i			0.585342i	0.956213	+	0.292671i	$0.0945441\pi$
$457$			12.5132i			0.585342i	−0.956213	+	0.292671i	$0.905456\pi$
$458$	−4.17244	−	37.8933i	−0.194965	−	1.77064i
$459$	−19.0368	−	26.2019i	−0.888562	−	1.22300i
$460$	0.553240	+	2.94495i	0.0257950	+	0.137309i
$461$	−7.24736	+	9.97513i	−0.337543	+	0.464588i	−0.943722	−	0.330740i	$-0.892702\pi$
$461$	−7.24736	+	9.97513i	−0.337543	+	0.464588i	0.606179	+	0.795328i	$0.292702\pi$
$462$	15.2486	+	8.70347i	0.709430	+	0.404922i
$463$	−9.71829	−	13.3761i	−0.451647	−	0.621639i	0.521103	−	0.853494i	$-0.325521\pi$
$463$	−9.71829	−	13.3761i	−0.451647	−	0.621639i	−0.972751	+	0.231854i	$0.925521\pi$
$464$	−4.51493	−	2.48887i	−0.209600	−	0.115543i
$465$	2.81138	−	7.75474i	0.130375	−	0.359617i
$466$	9.77115	−	17.1192i	0.452640	−	0.793033i
$467$	4.96826	−	15.2907i	0.229904	−	0.707571i	−0.767853	−	0.640626i	$-0.778675\pi$
$467$	4.96826	−	15.2907i	0.229904	−	0.707571i	0.997757	−	0.0669450i	$-0.0213252\pi$
$468$	54.0041	−	61.1847i	2.49634	−	2.82826i
$469$	−25.0672	−	8.14484i	−1.15750	−	0.376094i
$470$	27.5289	+	6.68228i	1.26981	+	0.308230i
$471$	−12.2346	−	37.6541i	−0.563739	−	1.73501i
$472$	−17.2318	+	0.255844i	−0.793160	+	0.0117762i
$473$	−5.07663	+	6.98739i	−0.233424	+	0.321280i
$474$	0.742658	+	1.64607i	0.0341114	+	0.0756063i
$475$	15.3320	+	24.3986i	0.703478	+	1.11948i
$476$	6.06519	−	6.87165i	0.277998	−	0.314962i
$477$	−19.6128	−	14.2495i	−0.898008	−	0.652441i
$478$	10.0076	−	9.10099i	0.457739	−	0.416270i
$479$	−6.65413	−	20.4793i	−0.304035	−	0.935723i	−0.980036	−	0.198822i	$-0.936288\pi$
$479$	−6.65413	−	20.4793i	−0.304035	−	0.935723i	0.676001	−	0.736901i	$-0.263712\pi$
$480$	34.5827	−	19.5582i	1.57848	−	0.892705i
$481$	6.70481	−	20.6353i	0.305713	−	0.940889i
$482$	−14.6267	−	32.4194i	−0.666227	−	1.47666i
$483$	1.11727	−	3.43862i	0.0508378	−	0.156463i
$484$	1.08060	−	11.3619i	0.0491183	−	0.516450i
$485$	1.14176	−	33.9272i	0.0518448	−	1.54055i
$486$	−5.36029	+	25.8465i	−0.243148	+	1.17242i
$487$	15.7256	+	21.6444i	0.712593	+	0.980800i	0.999737	+	0.0229129i	$0.00729405\pi$
$487$	15.7256	+	21.6444i	0.712593	+	0.980800i	−0.287144	+	0.957887i	$0.592706\pi$
$488$	0.842903	+	2.46886i	0.0381564	+	0.111760i
$489$	−30.0131	−	21.8058i	−1.35724	−	0.986091i
$490$	10.8990	+	6.71665i	0.492368	+	0.303427i
$491$	0.191575	+	0.263680i	0.00864564	+	0.0118997i	0.813318	−	0.581820i	$-0.197659\pi$
$491$	0.191575	+	0.263680i	0.00864564	+	0.0118997i	−0.804672	+	0.593719i	$0.797659\pi$
$492$	24.5471	+	41.5614i	1.10667	+	1.87373i
$493$	3.43806			0.154842
$494$	5.30177	+	48.1496i	0.238538	+	2.16635i
$495$	−33.2058	−	12.0383i	−1.49249	−	0.541083i
$496$	4.25300	−	1.99535i	0.190966	−	0.0895937i
$497$	10.1880	−	3.31029i	0.456995	−	0.148487i
$498$	1.04178	−	5.02328i	0.0466831	−	0.225098i
$499$			23.2206i			1.03950i	0.854320	+	0.519748i	$0.173974\pi$
$499$			23.2206i			1.03950i	−0.854320	+	0.519748i	$0.826026\pi$
$500$	−22.2041	+	2.64165i	−0.992997	+	0.118138i
$501$		−	34.4855i		−	1.54070i
$502$	−9.57936	−	1.98666i	−0.427548	−	0.0886689i
$503$	−8.85545	+	2.87731i	−0.394845	+	0.128293i	−0.499708	−	0.866194i	$-0.666559\pi$
$503$	−8.85545	+	2.87731i	−0.394845	+	0.128293i	0.104863	+	0.994487i	$0.466559\pi$
$504$	−33.3576	+	0.495267i	−1.48587	+	0.0220609i
$505$	−28.9101	−	10.4810i	−1.28648	−	0.466398i
$506$	2.16701	−	0.238610i	0.0963353	−	0.0106075i
$507$	−70.1170			−3.11401
$508$	29.2744	−	17.2902i	1.29884	−	0.767126i
$509$	11.8276	+	16.2793i	0.524249	+	0.721567i	0.986240	−	0.165318i	$-0.0528650\pi$
$509$	11.8276	+	16.2793i	0.524249	+	0.721567i	−0.461992	+	0.886884i	$0.652865\pi$
$510$	−13.9003	+	22.5558i	−0.615516	+	0.998790i
$511$	−7.43433	−	5.40135i	−0.328875	−	0.238942i
$512$	21.8099	+	6.02718i	0.963872	+	0.266366i
$513$	−41.1296	−	56.6100i	−1.81592	−	2.49939i
$514$	−41.2779	−	8.56061i	−1.82069	−	0.377592i
$515$	−0.658584	+	19.5696i	−0.0290207	+	0.862341i
$516$	2.23275	−	23.4760i	0.0982912	−	1.03347i
$517$	6.36899	−	19.6017i	0.280108	−	0.862083i
$518$	−8.08494	+	3.64770i	−0.355232	+	0.160271i
$519$	14.7185	−	45.2987i	0.646068	−	1.98839i
$520$	−35.5247	−	12.2855i	−1.55786	−	0.538754i
$521$	5.18227	+	15.9494i	0.227039	+	0.698755i	0.998078	+	0.0619670i	$0.0197373\pi$
$521$	5.18227	+	15.9494i	0.227039	+	0.698755i	−0.771039	+	0.636788i	$0.780263\pi$
$522$	−8.41950	−	9.25825i	−0.368512	−	0.405223i
$523$	0.0366350	+	0.0266169i	0.00160194	+	0.00116388i	0.588586	−	0.808435i	$-0.299685\pi$
$523$	0.0366350	+	0.0266169i	0.00160194	+	0.00116388i	−0.586984	+	0.809599i	$0.699685\pi$
$524$	9.01207	+	7.95441i	0.393694	+	0.347490i
$525$	25.0416	+	10.0438i	1.09290	+	0.438347i
$526$	−34.1191	+	15.3936i	−1.48766	+	0.671191i
$527$	−1.84144	+	2.53452i	−0.0802144	+	0.110406i
$528$	−12.2775	−	26.1691i	−0.534311	−	1.13886i
$529$	6.96866	+	21.4473i	0.302985	+	0.932493i
$530$	−2.63397	+	10.8511i	−0.114412	+	0.471343i
$531$	−39.7848	−	12.9268i	−1.72651	−	0.560978i
$532$	13.1040	−	14.8464i	0.568132	−	0.643673i
$533$	14.1121	−	43.4327i	0.611265	−	1.88128i
$534$	−15.9706	−	9.11555i	−0.691115	−	0.394468i
$535$	2.66246	−	7.34397i	0.115108	−	0.317508i
$536$	26.0243	+	34.7234i	1.12408	+	1.49982i
$537$	39.8978	+	54.9146i	1.72172	+	2.36974i
$538$	5.63165	−	9.86675i	0.242798	−	0.425386i
$539$	5.47494	−	7.53561i	0.235822	−	0.324582i
$540$	53.3650	−	10.0252i	2.29646	−	0.431415i
$541$	−10.3777	−	14.2837i	−0.446173	−	0.614104i	0.525397	−	0.850857i	$-0.323917\pi$
$541$	−10.3777	−	14.2837i	−0.446173	−	0.614104i	−0.971570	+	0.236753i	$0.923917\pi$
$542$	13.0933	−	1.44170i	0.562404	−	0.0619264i
$543$			27.2915i			1.17119i
$544$	−14.6777	+	3.50152i	−0.629302	+	0.150126i
$545$	−9.37891	+	2.70221i	−0.401748	+	0.115750i
$546$	30.5152	+	33.5551i	1.30593	+	1.43603i
$547$	10.9369	+	33.6604i	0.467630	+	1.43922i	0.855645	+	0.517563i	$0.173161\pi$
$547$	10.9369	+	33.6604i	0.467630	+	1.43922i	−0.388015	+	0.921653i	$0.626839\pi$
$548$	1.80187	+	8.08291i	0.0769720	+	0.345285i
$549$			6.33240i			0.270260i
$550$	0.689377	+	16.2541i	0.0293951	+	0.693077i
$551$	7.42802			0.316444
$552$	−4.76321	+	3.56990i	−0.202736	+	0.151945i
$553$	−0.664253	+	0.215829i	−0.0282469	+	0.00917798i
$554$	−3.94669	+	3.58914i	−0.167679	+	0.152488i
$555$	21.2384	−	14.3646i	0.901518	−	0.609744i
$556$	−17.3378	+	10.2401i	−0.735288	+	0.434278i
$557$	−27.7529			−1.17593			−0.587964	−	0.808887i	$-0.700070\pi$
$557$	−27.7529			−1.17593			−0.587964	+	0.808887i	$0.700070\pi$
$558$	11.3347	−	1.24806i	0.479835	−	0.0528348i
$559$	−18.0501	+	13.1141i	−0.763436	+	0.554669i
$560$	6.05505	+	14.1229i	0.255873	+	0.596803i
$561$	15.5951	+	11.3305i	0.658428	+	0.478376i
$562$	26.3283	+	15.0274i	1.11059	+	0.633894i
$563$	−23.5565	+	17.1148i	−0.992788	+	0.721303i	−0.960530	−	0.278177i	$-0.910270\pi$
$563$	−23.5565	+	17.1148i	−0.992788	+	0.721303i	−0.0322580	+	0.999480i	$0.510270\pi$
$564$	12.2443	+	54.9262i	0.515579	+	2.31281i
$565$	3.27493	−	0.943558i	0.137777	−	0.0396958i
$566$	−1.13720	−	0.649079i	−0.0478000	−	0.0272828i
$567$	−28.6575	−	9.31138i	−1.20350	−	0.391041i
$568$	−16.8521	−	5.20029i	−0.707099	−	0.218199i
$569$	5.68191	−	17.4871i	0.238198	−	0.733098i	−0.758483	−	0.651693i	$-0.774059\pi$
$569$	5.68191	−	17.4871i	0.238198	−	0.733098i	0.996681	−	0.0814052i	$-0.0259408\pi$
$570$	−30.0320	+	48.7326i	−1.25790	+	2.04118i
$571$	20.4740	−	6.65241i	0.856811	−	0.278395i	0.152515	−	0.988301i	$-0.451263\pi$
$571$	20.4740	−	6.65241i	0.856811	−	0.278395i	0.704296	+	0.709906i	$0.251263\pi$
$572$	−10.8757	+	25.0928i	−0.454737	+	1.04918i
$573$	−2.16473	−	1.57277i	−0.0904330	−	0.0657034i
$574$	−17.0170	+	7.67758i	−0.710276	+	0.320456i
$575$	3.24857	−	0.818702i	0.135475	−	0.0341422i
$576$	45.3736	+	30.9504i	1.89057	+	1.28960i
$577$	1.65018	−	2.27128i	0.0686978	−	0.0945545i	−0.773285	−	0.634058i	$-0.781388\pi$
$577$	1.65018	−	2.27128i	0.0686978	−	0.0945545i	0.841983	+	0.539504i	$0.181388\pi$
$578$	−10.3418	+	9.40492i	−0.430164	+	0.391193i
$579$	32.0840	−	10.4247i	1.33337	−	0.433237i
$580$	−2.46879	+	5.20854i	−0.102511	+	0.216273i
$581$	1.88705	+	0.613141i	0.0782882	+	0.0254374i
$582$	61.4683	−	27.7327i	2.54794	−	1.14956i
$583$	7.72646	+	2.51048i	0.319997	+	0.103973i
$584$	4.88817	+	14.3174i	0.202274	+	0.592459i
$585$	−71.9704	−	56.0828i	−2.97561	−	2.31874i
$586$	−3.83593	+	18.4963i	−0.158461	+	0.764074i
$587$	−9.41724	+	6.84202i	−0.388691	+	0.282401i	−0.764919	−	0.644127i	$-0.777221\pi$
$587$	−9.41724	+	6.84202i	−0.388691	+	0.282401i	0.376228	+	0.926527i	$0.377221\pi$
$588$	−2.40793	+	25.3179i	−0.0993012	+	1.04409i
$589$	−3.97848	+	5.47591i	−0.163931	+	0.225631i
$590$	1.46349	+	19.2123i	0.0602508	+	0.790956i
$591$	−57.4698	+	41.7543i	−2.36399	+	1.71754i
$592$	14.3409	+	2.75275i	0.589406	+	0.113137i
$593$			12.6560i			0.519720i	0.965646	+	0.259860i	$0.0836765\pi$
$593$			12.6560i			0.519720i	−0.965646	+	0.259860i	$0.916324\pi$
$594$	−4.32381	−	39.2680i	−0.177408	−	1.61118i
$595$	−8.08298	−	6.29866i	−0.331370	−	0.258220i
$596$	10.8924	−	25.1312i	0.446170	−	1.02941i
$597$	−0.685994	−	2.11127i	−0.0280759	−	0.0864087i
$598$	5.51438	+	1.14363i	0.225500	+	0.0467664i
$599$	−20.9771			−0.857101			−0.428550	−	0.903518i	$-0.640976\pi$
$599$	−20.9771			−0.857101			−0.428550	+	0.903518i	$0.640976\pi$
$600$	−24.1899	−	37.2553i	−0.987549	−	1.52094i
$601$	23.0207			0.939032			0.469516	−	0.882924i	$-0.344428\pi$
$601$	23.0207			0.939032			0.469516	+	0.882924i	$0.344428\pi$
$602$	8.93064	+	1.85212i	0.363986	+	0.0754868i
$603$	32.5488	+	100.175i	1.32549	+	4.07944i
$604$	22.1907	+	9.61792i	0.902927	+	0.391347i
$605$	−12.7531	−	0.429184i	−0.518487	−	0.0174488i
$606$	−6.68599	−	60.7209i	−0.271600	−	2.46662i
$607$			26.0419i			1.05701i	0.848931	+	0.528504i	$0.177247\pi$
$607$			26.0419i			1.05701i	−0.848931	+	0.528504i	$0.822753\pi$
$608$	−31.7117	+	7.56513i	−1.28608	+	0.306807i
$609$	5.62666	−	4.08801i	0.228004	−	0.165654i
$610$	2.69748	−	1.10940i	0.109218	−	0.0449184i
$611$	31.2947	−	43.0734i	1.26605	−	1.74257i
$612$	−36.4631	−	3.46791i	−1.47393	−	0.140182i
$613$	−13.6825	+	9.94089i	−0.552629	+	0.401509i	−0.828754	−	0.559613i	$-0.810950\pi$
$613$	−13.6825	+	9.94089i	−0.552629	+	0.401509i	0.276125	+	0.961122i	$0.410950\pi$
$614$	−4.07170	+	19.6331i	−0.164320	+	0.792327i
$615$	44.7020	−	30.2343i	1.80256	−	1.21916i
$616$	10.5802	−	3.61223i	0.426288	−	0.145541i
$617$	5.20768	+	1.69208i	0.209653	+	0.0681205i	0.411961	−	0.911202i	$-0.364844\pi$
$617$	5.20768	+	1.69208i	0.209653	+	0.0681205i	−0.202308	+	0.979322i	$0.564844\pi$
$618$	−35.4557	+	15.9966i	−1.42624	+	0.643478i
$619$	15.1429	+	4.92021i	0.608643	+	0.197760i	0.597091	−	0.802173i	$-0.296323\pi$
$619$	15.1429	+	4.92021i	0.608643	+	0.197760i	0.0115514	+	0.999933i	$0.496323\pi$
$620$	−2.51743	−	4.60970i	−0.101102	−	0.185130i
$621$	−7.73701	+	2.51391i	−0.310476	+	0.100880i
$622$	0.500409	−	0.455074i	0.0200646	−	0.0182468i
$623$	4.18044	−	5.75389i	0.167486	−	0.230525i
$624$	−9.27363	−	74.0930i	−0.371242	−	2.96609i
$625$	4.46582	+	24.5979i	0.178633	+	0.983916i
$626$	−14.6435	+	6.60673i	−0.585272	+	0.264058i
$627$	33.6938	+	24.4799i	1.34560	+	0.977635i
$628$	−23.1310	−	10.0254i	−0.923026	−	0.400059i
$629$	−9.26151	+	3.00925i	−0.369281	+	0.119987i
$630$	2.83304	+	37.1913i	0.112871	+	1.48174i
$631$	−15.0147	+	46.2106i	−0.597727	+	1.83961i	−0.0570726	+	0.998370i	$0.518177\pi$
$631$	−15.0147	+	46.2106i	−0.597727	+	1.83961i	−0.540654	+	0.841245i	$0.681823\pi$
$632$	1.09875	+	0.339056i	0.0437059	+	0.0134869i
$633$	54.8380	+	17.8179i	2.17961	+	0.708200i
$634$	16.9786	+	9.69087i	0.674305	+	0.384874i
$635$	−21.2960	−	31.4866i	−0.845107	−	1.24951i
$636$	−21.6504	+	4.82637i	−0.858494	+	0.191378i
$637$	19.4662	−	14.1431i	0.771280	−	0.560368i
$638$	3.64215	+	2.07883i	0.144194	+	0.0823017i
$639$	−34.6333	−	25.1626i	−1.37007	−	0.995417i
$640$	5.23504	−	24.7506i	0.206933	−	0.978355i
$641$	15.1755	−	11.0256i	0.599396	−	0.435486i	−0.246269	−	0.969202i	$-0.579205\pi$
$641$	15.1755	−	11.0256i	0.599396	−	0.435486i	0.845664	+	0.533715i	$0.179205\pi$
$642$	15.4248	−	1.69843i	0.608768	−	0.0670316i
$643$	−37.8673			−1.49334			−0.746669	−	0.665195i	$-0.768348\pi$
$643$	−37.8673			−1.49334			−0.746669	+	0.665195i	$0.768348\pi$
$644$	−1.17079	−	1.98229i	−0.0461355	−	0.0781132i
$645$	−26.3505	−	0.886783i	−1.03755	−	0.0349171i
$646$	16.0846	−	14.6274i	0.632839	−	0.575507i
$647$	−37.5073	+	12.1869i	−1.47456	+	0.479115i	−0.932484	−	0.361212i	$-0.882363\pi$
$647$	−37.5073	+	12.1869i	−1.47456	+	0.479115i	−0.542080	+	0.840327i	$0.682363\pi$
$648$	29.7516	+	39.6966i	1.16875	+	1.55943i
$649$	14.0185			0.550276
$650$	−11.2814	+	40.4834i	−0.442492	+	1.58789i
$651$			6.33752i			0.248387i
$652$	−23.0563	+	5.13979i	−0.902956	+	0.201290i
$653$	−6.71891	−	20.6787i	−0.262931	−	0.809219i	−0.992163	−	0.124952i	$-0.960122\pi$
$653$	−6.71891	−	20.6787i	−0.262931	−	0.809219i	0.729232	−	0.684267i	$-0.239878\pi$
$654$	−13.0450	−	14.3446i	−0.510101	−	0.560918i
$655$	8.26059	−	10.6007i	0.322768	−	0.414204i
$656$	30.1843	+	5.79393i	1.17850	+	0.226215i
$657$			36.7229i			1.43270i
$658$	−21.6342	+	2.38215i	−0.843389	+	0.0928657i
$659$	3.19947	+	4.40369i	0.124634	+	0.171543i	0.866774	−	0.498701i	$-0.166189\pi$
$659$	3.19947	+	4.40369i	0.124634	+	0.171543i	−0.742141	+	0.670244i	$0.766189\pi$
$660$	−28.3639	+	15.4900i	−1.10406	+	0.602946i
$661$	26.8362	−	36.9368i	1.04381	−	1.43668i	0.149747	−	0.988724i	$-0.452154\pi$
$661$	26.8362	−	36.9368i	1.04381	−	1.43668i	0.894058	−	0.447951i	$-0.147846\pi$
$662$	−4.73820	+	8.30141i	−0.184155	+	0.322643i
$663$	29.2694	+	40.2859i	1.13673	+	1.56458i
$664$	−1.95910	−	2.61397i	−0.0760279	−	0.101442i
$665$	−17.4635	−	13.6084i	−0.677206	−	0.527712i
$666$	30.7842	+	17.5707i	1.19286	+	0.680851i
$667$	0.266862	−	0.821317i	0.0103329	−	0.0318015i
$668$	−16.4631	−	14.5310i	−0.636976	−	0.562221i
$669$	22.9268	+	7.44937i	0.886402	+	0.288009i
$670$	36.9702	−	31.4153i	1.42829	−	1.21368i
$671$	−0.655758	−	2.01821i	−0.0253152	−	0.0779123i
$672$	−19.8578	+	23.1830i	−0.766033	+	0.894305i
$673$	25.2847	−	34.8014i	0.974654	−	1.34150i	0.0349929	−	0.999388i	$-0.488859\pi$
$673$	25.2847	−	34.8014i	0.974654	−	1.34150i	0.939661	−	0.342108i	$-0.111141\pi$
$674$	−21.4351	+	9.67092i	−0.825651	+	0.372510i
$675$	−14.8356	−	58.8669i	−0.571021	−	2.26579i
$676$	−29.5448	+	33.4733i	−1.13634	+	1.28743i
$677$	−37.8808	−	27.5220i	−1.45588	−	1.05776i	−0.984413	−	0.175873i	$-0.943725\pi$
$677$	−37.8808	−	27.5220i	−1.45588	−	1.05776i	−0.471466	−	0.881884i	$-0.656275\pi$
$678$	4.55507	+	5.00884i	0.174936	+	0.192363i
$679$	8.05960	+	24.8049i	0.309299	+	0.951924i
$680$	4.91087	+	16.1401i	0.188323	+	0.618946i
$681$	11.3714	−	34.9977i	0.435755	−	1.34111i
$682$	−3.48326	+	1.57155i	−0.133381	+	0.0601776i
$683$	−0.331130	+	1.01911i	−0.0126703	+	0.0389953i	−0.957192	−	0.289454i	$-0.906526\pi$
$683$	−0.331130	+	1.01911i	−0.0126703	+	0.0389953i	0.944521	+	0.328450i	$0.106526\pi$
$684$	−78.7795	−	7.49253i	−3.01221	−	0.286484i
$685$	8.89688	−	2.56333i	0.339932	−	0.0979399i
$686$	−26.2843	−	5.45109i	−1.00354	−	0.208123i
$687$	−49.7673	−	68.4988i	−1.89874	−	2.61339i
$688$	−10.2665	−	10.9579i	−0.391405	−	0.417765i
$689$	16.9784	+	12.3355i	0.646824	+	0.469945i
$690$	4.30942	+	5.07143i	0.164057	+	0.193066i
$691$	−8.71658	−	11.9973i	−0.331595	−	0.456401i	0.610368	−	0.792118i	$-0.291021\pi$
$691$	−8.71658	−	11.9973i	−0.331595	−	0.456401i	−0.941963	+	0.335717i	$0.891021\pi$
$692$	−15.4234	−	26.1138i	−0.586309	−	0.992697i
$693$	27.1373			1.03086
$694$	0.705539	−	0.0776871i	0.0267819	−	0.00294896i
$695$	12.6126	+	18.6480i	0.478424	+	0.707359i
$696$	−11.4490	+	0.169985i	−0.433973	+	0.00644328i
$697$	−19.4934	+	6.33379i	−0.738366	+	0.239910i
$698$	1.92120	+	0.398438i	0.0727187	+	0.0150811i
$699$		−	43.7790i		−	1.65587i
$700$	15.3465	−	7.72254i	0.580042	−	0.291885i
$701$		−	6.33651i		−	0.239327i	−0.992815	−	0.119663i	$-0.961818\pi$
$701$		−	6.33651i		−	0.239327i	0.992815	−	0.119663i	$-0.0381815\pi$
$702$	20.7235	−	99.9252i	0.782157	−	3.77143i
$703$	−20.0098	+	6.50156i	−0.754682	+	0.245211i
$704$	−17.6662	−	5.16555i	−0.665821	−	0.194684i
$705$	60.4574	−	17.4187i	2.27696	−	0.656027i
$706$	4.41576	+	40.1031i	0.166189	+	1.50930i
$707$	23.6266			0.888571
$708$	−32.9569	+	19.4651i	−1.23860	+	0.731543i
$709$	25.4810	+	35.0716i	0.956960	+	1.31714i	0.948366	+	0.317179i	$0.102736\pi$
$709$	25.4810	+	35.0716i	0.956960	+	1.31714i	0.00859395	+	0.999963i	$0.497264\pi$
$710$	−4.65121	+	19.1615i	−0.174557	+	0.719118i
$711$	2.25807	+	1.64059i	0.0846843	+	0.0615268i
$712$	−11.0811	+	3.78325i	−0.415283	+	0.141783i
$713$	0.462540	+	0.636631i	0.0173222	+	0.0238420i
$714$	4.13375	−	19.9323i	0.154702	−	0.745947i
$715$	28.7455	+	10.4213i	1.07502	+	0.389736i
$716$	43.0273	+	4.09222i	1.60800	+	0.152933i
$717$	9.28391	−	28.5729i	0.346714	−	1.06708i
$718$	13.4486	+	29.8082i	0.501898	+	1.11243i
$719$	2.82195	−	8.68507i	0.105241	−	0.323898i	−0.884546	−	0.466453i	$-0.845532\pi$
$719$	2.82195	−	8.68507i	0.105241	−	0.323898i	0.989787	+	0.142555i	$0.0455316\pi$
$720$	31.4371	−	52.7501i	1.17159	−	1.96588i
$721$	−4.64888	−	14.3078i	−0.173133	−	0.532850i
$722$	14.8721	−	13.5247i	0.553481	−	0.503339i
$723$	−63.9059	−	46.4303i	−2.37669	−	1.72676i
$724$	13.0287	+	11.4997i	0.484208	+	0.427382i
$725$	5.98120	+	2.39896i	0.222136	+	0.0890953i
$726$	−10.4246	−	23.1057i	−0.386894	−	0.857532i
$727$	24.3866	−	33.5653i	0.904449	−	1.24487i	−0.0645777	−	0.997913i	$-0.520570\pi$
$727$	24.3866	−	33.5653i	0.904449	−	1.24487i	0.969027	−	0.246955i	$-0.0794300\pi$
$728$	28.8770	−	0.428742i	1.07025	−	0.0158902i
$729$	1.85677	+	5.71454i	0.0687691	+	0.211649i
$730$	15.6433	−	6.43366i	0.578983	−	0.238120i
$731$	9.52354	+	3.09439i	0.352241	+	0.114450i
$732$	4.34399	+	3.83418i	0.160559	+	0.141715i
$733$	−11.2254	+	34.5481i	−0.414619	+	1.27606i	0.497973	+	0.867193i	$0.334078\pi$
$733$	−11.2254	+	34.5481i	−0.414619	+	1.27606i	−0.912592	+	0.408872i	$0.865922\pi$
$734$	19.7690	−	34.6356i	0.729687	−	1.27842i
$735$	28.4179	+	0.956359i	1.04821	+	0.0352758i
$736$	−0.302808	+	3.77815i	−0.0111617	+	0.139264i
$737$	−20.7474	−	28.5564i	−0.764241	−	1.05189i
$738$	64.7938	+	36.9824i	2.38509	+	1.36134i
$739$	27.2866	−	37.5567i	1.00375	−	1.38155i	0.0807577	−	0.996734i	$-0.474266\pi$
$739$	27.2866	−	37.5567i	1.00375	−	1.38155i	0.922995	−	0.384813i	$-0.125734\pi$
$740$	2.09156	−	16.1918i	0.0768873	−	0.595221i
$741$	63.2375	+	87.0389i	2.32309	+	3.19745i
$742$	−0.938977	−	8.52760i	−0.0344709	−	0.313058i
$743$			43.8156i			1.60744i	0.595008	+	0.803720i	$0.297149\pi$
$743$			43.8156i			1.60744i	−0.595008	+	0.803720i	$0.702851\pi$
$744$	6.00683	−	8.53122i	0.220221	−	0.312770i
$745$	−28.7896	−	10.4373i	−1.05477	−	0.382393i
$746$	−18.8206	+	17.1155i	−0.689070	+	0.626643i
$747$	−2.45027	−	7.54115i	−0.0896506	−	0.275916i
$748$	11.9804	−	2.67070i	0.438045	−	0.0976504i
$749$			6.00182i			0.219302i
$750$	−39.9212	+	29.5413i	−1.45771	+	1.07870i
$751$	0.0692442			0.00252676			0.00126338	−	0.999999i	$-0.499598\pi$
$751$	0.0692442			0.00252676			0.00126338	+	0.999999i	$0.499598\pi$
$752$	31.3806	+	17.2986i	1.14433	+	0.630816i
$753$	−20.6649	+	6.71442i	−0.753070	+	0.244687i
$754$	7.28858	+	8.01467i	0.265434	+	0.291877i
$755$	9.21607	−	25.4210i	0.335407	−	0.925166i
$756$	−35.9208	+	21.2156i	−1.30643	+	0.771605i
$757$	17.1602			0.623700			0.311850	−	0.950131i	$-0.399051\pi$
$757$	17.1602			0.623700			0.311850	+	0.950131i	$0.399051\pi$
$758$	−0.844268	−	7.66748i	−0.0306652	−	0.278495i
$759$	3.91725	−	2.84605i	0.142187	−	0.103305i
$760$	10.6101	+	34.8712i	0.384868	+	1.26491i
$761$	8.77922	+	6.37847i	0.318246	+	0.231220i	0.735427	−	0.677604i	$-0.236982\pi$
$761$	8.77922	+	6.37847i	0.318246	+	0.231220i	−0.417180	+	0.908824i	$0.636982\pi$
$762$	37.4317	−	65.5810i	1.35601	−	2.37575i
$763$	6.06686	−	4.40783i	0.219635	−	0.159574i
$764$	−1.66297	+	0.370715i	−0.0601641	+	0.0134120i
$765$	−1.37736	+	40.9277i	−0.0497984	+	1.47975i
$766$	−9.75807	+	17.0963i	−0.352573	+	0.617714i
$767$	34.4408	+	11.1905i	1.24358	+	0.404065i
$768$	48.7049	−	12.3860i	1.75749	−	0.446943i
$769$	5.30296	−	16.3208i	0.191230	−	0.588545i	−0.808770	−	0.588125i	$-0.799866\pi$
$769$	5.30296	−	16.3208i	0.191230	−	0.588545i	1.00000		0.000419828i	$-0.000133635\pi$
$770$	−4.75430	−	11.5600i	−0.171333	−	0.416592i
$771$	−89.0459	+	28.9328i	−3.20691	+	1.04199i
$772$	8.54241	−	19.7093i	0.307448	−	0.709352i
$773$	−29.9036	−	21.7262i	−1.07556	−	0.781437i	−0.0986535	−	0.995122i	$-0.531454\pi$
$773$	−29.9036	−	21.7262i	−1.07556	−	0.781437i	−0.976903	+	0.213685i	$0.931454\pi$
$774$	−14.9895	−	33.2236i	−0.538788	−	1.19420i
$775$	−4.97207	+	3.12443i	−0.178602	+	0.112233i
$776$	12.6612	−	41.0300i	0.454511	−	1.47289i
$777$	−11.5791	+	15.9372i	−0.415398	+	0.571746i
$778$	−35.1643	−	38.6673i	−1.26070	−	1.38629i
$779$	−42.1161	+	13.6843i	−1.50896	+	0.490292i
$780$	−82.0496	+	15.4139i	−2.93785	+	0.551905i
$781$	13.6438	+	4.43314i	0.488214	+	0.158630i
$782$	−1.03949	−	2.30398i	−0.0371721	−	0.0823903i
$783$	−14.8829	−	4.83576i	−0.531873	−	0.172816i
$784$	11.0719	+	11.8176i	0.395426	+	0.422057i
$785$	−9.60657	+	26.4982i	−0.342873	+	0.945760i
$786$	26.1409	+	5.42135i	0.932414	+	0.193373i
$787$	−19.5842	+	14.2288i	−0.698102	+	0.507201i	−0.879313	−	0.476244i	$-0.841998\pi$
$787$	−19.5842	+	14.2288i	−0.698102	+	0.507201i	0.181212	+	0.983444i	$0.441998\pi$
$788$	−4.28264	+	45.0294i	−0.152563	+	1.60411i
$789$	−48.8646	+	67.2564i	−1.73963	+	2.39439i
$790$	0.303256	−	1.24932i	0.0107894	−	0.0444487i
$791$	−2.11843	+	1.53913i	−0.0753225	+	0.0547250i
$792$	−36.5307	−	25.7213i	−1.29806	−	0.913966i
$793$		−	5.48182i		−	0.194665i
$794$	33.3209	−	3.66898i	1.18252	−	0.130207i
$795$	6.86599	+	23.8306i	0.243511	+	0.845186i
$796$	−1.29696	−	0.562129i	−0.0459695	−	0.0199241i
$797$	−0.311905	−	0.959946i	−0.0110483	−	0.0340030i	0.945380	−	0.325969i	$-0.105691\pi$
$797$	−0.311905	−	0.959946i	−0.0110483	−	0.0340030i	−0.956429	+	0.291966i	$0.905691\pi$
$798$	8.93108	−	43.0643i	0.316157	−	1.52446i
$799$	−23.8959			−0.845375
$800$	−27.9782	−	4.15004i	−0.989177	−	0.146726i
$801$	−28.4221			−1.00425
$802$	−0.253105	+	1.22043i	−0.00893744	+	0.0430949i
$803$	−3.80287	−	11.7040i	−0.134200	−	0.413027i
$804$	88.4274	+	38.3263i	3.11859	+	1.35166i
$805$	−2.13209	+	1.44204i	−0.0751462	+	0.0508253i
$806$	−9.81219	+	1.08042i	−0.345620	+	0.0380563i
$807$		−	25.2322i		−	0.888217i
$808$	−31.8049	−	22.3938i	−1.11889	−	0.787812i
$809$	−14.0834	+	10.2322i	−0.495147	+	0.359745i	−0.807160	−	0.590332i	$-0.798997\pi$
$809$	−14.0834	+	10.2322i	−0.495147	+	0.359745i	0.312013	+	0.950078i	$0.398997\pi$
$810$	42.2653	−	35.9147i	1.48505	−	1.26192i
$811$	−4.13632	+	5.69316i	−0.145246	+	0.199914i	−0.875441	−	0.483325i	$-0.839429\pi$
$811$	−4.13632	+	5.69316i	−0.145246	+	0.199914i	0.730195	+	0.683238i	$0.239429\pi$
$812$	0.419297	−	4.40866i	0.0147145	−	0.154714i
$813$	23.6684	−	17.1961i	0.830086	−	0.603093i
$814$	−11.6308	−	2.41212i	−0.407661	−	0.0845446i
$815$	7.31186	+	25.3782i	0.256123	+	0.888959i
$816$	−24.4569	+	22.9137i	−0.856161	+	0.802140i
$817$	20.5759	+	6.68551i	0.719859	+	0.233896i
$818$	−20.8274	−	46.1629i	−0.728212	−	1.61405i
$819$	66.6709	+	21.6627i	2.32967	+	0.756956i
$820$	4.40227	−	34.0800i	0.153734	−	1.19013i
$821$	−24.4826	+	7.95489i	−0.854450	+	0.277628i	−0.703309	−	0.710884i	$-0.748295\pi$
$821$	−24.4826	+	7.95489i	−0.854450	+	0.277628i	−0.151141	+	0.988512i	$0.548295\pi$
$822$	12.3746	+	13.6073i	0.431613	+	0.474611i
$823$	24.5580	−	33.8012i	0.856038	−	1.17823i	−0.126462	−	0.991971i	$-0.540362\pi$
$823$	24.5580	−	33.8012i	0.856038	−	1.17823i	0.982500	−	0.186264i	$-0.0596378\pi$
$824$	−7.30315	+	23.6667i	−0.254417	+	0.824467i
$825$	19.2249	+	30.5936i	0.669324	+	1.06513i
$826$	−6.08809	−	13.4940i	−0.211832	−	0.469515i
$827$	−21.0719	−	15.3096i	−0.732741	−	0.532368i	0.157688	−	0.987489i	$-0.449596\pi$
$827$	−21.0719	−	15.3096i	−0.732741	−	0.532368i	−0.890429	+	0.455121i	$0.849596\pi$
$828$	−3.65871	+	8.44148i	−0.127149	+	0.293362i
$829$	3.94736	−	1.28257i	0.137097	−	0.0445457i	−0.239665	−	0.970856i	$-0.577037\pi$
$829$	3.94736	−	1.28257i	0.137097	−	0.0445457i	0.376762	+	0.926310i	$0.377037\pi$
$830$	−2.78311	+	2.36494i	−0.0966032	+	0.0820881i
$831$	−3.66128	+	11.2683i	−0.127008	+	0.390892i
$832$	−39.2790	−	26.7931i	−1.36175	−	0.928882i
$833$	−10.2707	−	3.33717i	−0.355860	−	0.115626i
$834$	−22.1690	+	38.8405i	−0.767650	+	1.34494i
$835$	−15.0903	+	19.3652i	−0.522222	+	0.670160i
$836$	25.8839	−	5.77012i	0.895213	−	0.199564i
$837$	11.5363	−	8.38160i	0.398752	−	0.289710i
$838$	13.3469	−	23.3839i	0.461060	−	0.807785i
$839$	−31.5974	−	22.9568i	−1.09086	−	0.792557i	−0.111317	−	0.993785i	$-0.535507\pi$
$839$	−31.5974	−	22.9568i	−1.09086	−	0.792557i	−0.979545	+	0.201227i	$0.935507\pi$
$840$	27.2284	+	20.5754i	0.939469	+	0.709919i
$841$	−22.1176	+	16.0693i	−0.762674	+	0.554115i
$842$	1.37113	+	12.4523i	0.0472522	+	0.429135i
$843$	67.3294			2.31895
$844$	31.6129	−	18.6713i	1.08816	−	0.642694i
$845$	39.3739	+	30.6821i	1.35450	+	1.05550i
$846$	58.5190	+	64.3486i	2.01192	+	2.21235i
$847$	9.32406	−	3.02957i	0.320378	−	0.104097i
$848$	−6.81864	+	12.3694i	−0.234153	+	0.424766i
$849$	−2.90815			−0.0998075
$850$	17.6757	−	6.58359i	0.606273	−	0.225815i
$851$			2.44606i			0.0838498i
$852$	−38.2314	+	8.52267i	−1.30979	+	0.291982i
$853$	3.09392	+	9.52211i	0.105934	+	0.326031i	0.989948	−	0.141428i	$-0.0451695\pi$
$853$	3.09392	+	9.52211i	0.105934	+	0.326031i	−0.884015	+	0.467459i	$0.845169\pi$
$854$	−1.65790	+	1.50771i	−0.0567323	+	0.0515926i
$855$	−2.97582	+	88.4256i	−0.101771	+	3.02409i
$856$	5.68865	−	8.07933i	0.194434	−	0.276146i
$857$		−	31.6591i		−	1.08146i	−0.841198	−	0.540728i	$-0.818149\pi$
$857$		−	31.6591i		−	1.08146i	0.841198	−	0.540728i	$-0.181851\pi$
$858$	6.64793	+	60.3752i	0.226957	+	2.06118i
$859$	−10.6822	−	14.7028i	−0.364473	−	0.501654i	0.586915	−	0.809649i	$-0.300342\pi$
$859$	−10.6822	−	14.7028i	−0.364473	−	0.501654i	−0.951388	+	0.307994i	$0.900342\pi$
$860$	−11.5265	+	12.2059i	−0.393051	+	0.416216i
$861$	−24.3714	+	33.5444i	−0.830575	+	1.14319i
$862$	−3.80200	−	2.17007i	−0.129497	−	0.0739129i
$863$	1.06034	+	1.45943i	0.0360944	+	0.0496797i	0.826683	−	0.562668i	$-0.190225\pi$
$863$	1.06034	+	1.45943i	0.0360944	+	0.0496797i	−0.790588	+	0.612348i	$0.790225\pi$
$864$	68.4632	+	5.48713i	2.32916	+	0.186676i
$865$	−28.0871	+	18.9968i	−0.954990	+	0.645909i
$866$	6.39378	−	11.2020i	0.217269	−	0.380660i
$867$	−9.59395	+	29.5271i	−0.325828	+	1.00279i
$868$	3.02548	+	2.67041i	0.102691	+	0.0906395i
$869$	−0.889568	−	0.289038i	−0.0301765	−	0.00980495i
$870$	0.972354	+	12.7648i	0.0329659	+	0.432767i
$871$	−28.1768	−	86.7193i	−0.954735	−	2.93837i
$872$	−12.3447	+	0.183284i	−0.418044	+	0.00620678i
$873$	61.2636	−	84.3221i	2.07346	−	2.85387i
$874$	−2.24585	−	4.97782i	−0.0759671	−	0.168377i
$875$	−9.66700	−	16.5978i	−0.326804	−	0.561110i
$876$	25.1917	+	22.2352i	0.851149	+	0.751258i
$877$	25.8054	+	18.7487i	0.871387	+	0.633100i	0.930959	−	0.365124i	$-0.118974\pi$
$877$	25.8054	+	18.7487i	0.871387	+	0.633100i	−0.0595719	+	0.998224i	$0.518974\pi$
$878$	40.2149	−	36.5717i	1.35719	−	1.23423i
$879$	12.9645	+	39.9007i	0.437282	+	1.34582i
$880$	−4.55679	+	20.0676i	−0.153609	+	0.676479i
$881$	5.46376	−	16.8157i	0.184079	−	0.566536i	−0.815852	−	0.578260i	$-0.803732\pi$
$881$	5.46376	−	16.8157i	0.184079	−	0.566536i	0.999931	+	0.0117237i	$0.00373186\pi$
$882$	16.1656	+	35.8303i	0.544324	+	1.20647i
$883$	3.19347	−	9.82850i	0.107469	−	0.330755i	−0.882833	−	0.469687i	$-0.844367\pi$
$883$	3.19347	−	9.82850i	0.107469	−	0.330755i	0.990302	+	0.138932i	$0.0443668\pi$
$884$	31.5653	+	3.00210i	1.06166	+	0.100971i
$885$	23.9749	+	35.4473i	0.805906	+	1.19155i
$886$	9.71291	−	46.8341i	0.326311	−	1.57342i
$887$	18.9891	+	26.1362i	0.637591	+	0.877568i	0.998484	−	0.0550388i	$-0.0175282\pi$
$887$	18.9891	+	26.1362i	0.637591	+	0.877568i	−0.360894	+	0.932607i	$0.617528\pi$
$888$	30.6928	−	10.4789i	1.02998	−	0.351650i
$889$	23.6275	+	17.1664i	0.792442	+	0.575742i
$890$	4.97941	+	12.1073i	0.166910	+	0.405837i
$891$	−23.7190	−	32.6464i	−0.794615	−	1.09369i
$892$	13.2168	−	7.80616i	0.442532	−	0.261370i
$893$	−51.6277			−1.72766
$894$	−6.65812	−	60.4677i	−0.222681	−	2.02234i
$895$	1.62531	−	48.2957i	0.0543282	−	1.61435i
$896$	2.69998	+	19.2485i	0.0902001	+	0.643047i
$897$	11.8958	−	3.86518i	0.397189	−	0.129055i
$898$	3.37423	−	16.2700i	0.112599	−	0.542936i
$899$			1.51372i			0.0504854i
$900$	−61.0152	−	31.4759i	−2.03384	−	1.04920i
$901$		−	9.41910i		−	0.313796i
$902$	−24.4803	−	5.07697i	−0.815106	−	0.169045i
$903$	19.2654	−	6.25972i	0.641113	−	0.208310i
$904$	4.31052	−	0.0639991i	0.143366	−	0.00212858i
$905$	11.9423	−	15.3254i	0.396976	−	0.509434i
$906$	53.3926	−	5.87908i	1.77385	−	0.195319i
$907$	38.2694			1.27071			0.635357	−	0.772219i	$-0.280853\pi$
$907$	38.2694			1.27071			0.635357	+	0.772219i	$0.280853\pi$
$908$	−11.9161	−	20.1754i	−0.395449	−	0.669545i
$909$	−55.4975	−	76.3858i	−1.84074	−	2.53356i
$910$	−2.45250	−	32.1957i	−0.0812995	−	1.06728i
$911$	−39.1122	−	28.4167i	−1.29584	−	0.941486i	−0.295938	−	0.955207i	$-0.595632\pi$
$911$	−39.1122	−	28.4167i	−1.29584	−	0.941486i	−0.999906	+	0.0137212i	$0.995632\pi$
$912$	−52.8397	+	49.5057i	−1.74970	+	1.63930i
$913$	1.56186	+	2.14972i	0.0516901	+	0.0711453i
$914$	17.3276	+	3.59357i	0.573146	+	0.118865i
$915$	3.98177	−	5.10975i	0.131633	−	0.168923i
$916$	−53.6709	−	5.10451i	−1.77334	−	0.168658i
$917$	−3.19076	+	9.82014i	−0.105368	+	0.324290i
$918$	−41.7501	+	18.8364i	−1.37796	+	0.621695i
$919$	−2.97260	+	9.14872i	−0.0980570	+	0.301788i	−0.988038	−	0.154209i	$-0.950717\pi$
$919$	−2.97260	+	9.14872i	−0.0980570	+	0.301788i	0.889981	+	0.455997i	$0.150717\pi$
$920$	4.23689	+	0.0796400i	0.139686	+	0.00262565i
$921$	13.7613	+	42.3531i	0.453452	+	1.39558i
$922$	11.7317	+	12.9004i	0.386364	+	0.424853i
$923$	29.9813	+	21.7827i	0.986847	+	0.716986i
$924$	16.4312	−	18.6160i	0.540548	−	0.612422i
$925$	−18.2120	−	1.22718i	−0.598808	−	0.0403495i
$926$	−21.3134	+	9.61601i	−0.700403	+	0.316002i
$927$	−35.3377	+	48.6381i	−1.16064	+	1.59749i
$928$	−4.74306	+	5.53728i	−0.155699	+	0.181770i
$929$	5.02685	+	15.4710i	0.164926	+	0.507589i	0.999031	−	0.0440168i	$-0.0140155\pi$
$929$	5.02685	+	15.4710i	0.164926	+	0.507589i	−0.834105	+	0.551605i	$0.814015\pi$
$930$	−9.93097	−	6.12008i	−0.325649	−	0.200685i
$931$	−22.1902	−	7.21004i	−0.727255	−	0.236300i
$932$	−20.8997	−	18.4469i	−0.684593	−	0.604249i
$933$	0.464221	−	1.42872i	0.0151979	−	0.0467743i
$934$	−19.7470	−	11.2710i	−0.646142	−	0.368799i
$935$	−3.79933	−	13.1868i	−0.124251	−	0.431255i
$936$	−69.2164	−	92.3532i	−2.26241	−	3.01866i
$937$	2.13418	+	2.93745i	0.0697207	+	0.0959623i	0.842453	−	0.538769i	$-0.181111\pi$
$937$	2.13418	+	2.93745i	0.0697207	+	0.0959623i	−0.772733	+	0.634732i	$0.781111\pi$
$938$	−18.4774	+	32.3727i	−0.603309	+	1.05701i
$939$	−20.9721	+	28.8657i	−0.684400	+	0.941996i
$940$	17.1591	−	36.2015i	0.559667	−	1.18076i
$941$	23.9722	+	32.9948i	0.781470	+	1.07560i	0.995118	+	0.0986904i	$0.0314654\pi$
$941$	23.9722	+	32.9948i	0.781470	+	1.07560i	−0.213648	+	0.976911i	$0.568535\pi$
$942$	−55.6550	+	6.12818i	−1.81334	+	0.199667i
$943$			5.14841i			0.167655i
$944$	−4.59440	+	23.9352i	−0.149535	+	0.779026i
$945$	26.1310	+	38.6352i	0.850041	+	1.25680i
$946$	8.21785	+	9.03651i	0.267185	+	0.293802i
$947$	7.79156	+	23.9800i	0.253192	+	0.779244i	0.994181	+	0.107727i	$0.0343572\pi$
$947$	7.79156	+	23.9800i	0.253192	+	0.779244i	−0.740989	+	0.671517i	$0.765643\pi$
$948$	2.49266	−	0.555673i	0.0809580	−	0.0180474i
$949$		−	31.7902i		−	1.03195i
$950$	38.1889	−	14.2240i	1.23901	−	0.461489i
$951$	43.4193			1.40797
$952$	−7.77368	−	10.3722i	−0.251947	−	0.336164i
$953$	22.2071	−	7.21551i	0.719357	−	0.233733i	0.0736128	−	0.997287i	$-0.476547\pi$
$953$	22.2071	−	7.21551i	0.719357	−	0.233733i	0.645745	+	0.763554i	$0.276547\pi$
$954$	−25.3645	+	23.0666i	−0.821205	+	0.746808i
$955$	0.527378	+	1.83044i	0.0170655	+	0.0592315i
$956$	−9.72856	−	16.4717i	−0.314644	−	0.532733i
$957$	9.31405			0.301081
$958$	−30.2696	+	3.33299i	−0.977967	+	0.107684i
$959$	−5.75505	+	4.18129i	−0.185840	+	0.135021i
$960$	−17.1516	−	53.5051i	−0.553566	−	1.72687i
$961$	23.9636	+	17.4106i	0.773020	+	0.561632i
$962$	−26.6492	−	15.2106i	−0.859204	−	0.490408i
$963$	19.4041	−	14.0979i	0.625289	−	0.454299i
$964$	−49.0932	+	10.9440i	−1.58118	+	0.352483i
$965$	−22.5784	−	8.18550i	−0.726823	−	0.263500i
$966$	−4.44076	−	2.53465i	−0.142879	−	0.0815512i
$967$	−23.8786	−	7.75862i	−0.767883	−	0.249500i	−0.101225	−	0.994864i	$-0.532276\pi$
$967$	−23.8786	−	7.75862i	−0.767883	−	0.249500i	−0.666659	+	0.745363i	$0.732276\pi$
$968$	−15.4230	−	4.75930i	−0.495715	−	0.152970i
$969$	14.9214	−	45.9233i	0.479344	−	1.47527i
$970$	−46.6527	−	11.3243i	−1.49793	−	0.363603i
$971$	−9.54087	+	3.10002i	−0.306181	+	0.0994843i	−0.458078	−	0.888912i	$-0.651462\pi$
$971$	−9.54087	+	3.10002i	−0.306181	+	0.0994843i	0.151897	+	0.988396i	$0.451462\pi$
$972$	34.2515	+	14.8453i	1.09862	+	0.476163i
$973$	−13.9934	−	10.1668i	−0.448609	−	0.325934i
$974$	34.4881	−	15.5600i	1.10507	−	0.498576i
$975$	22.8100	+	90.5089i	0.730503	+	2.89860i
$976$	3.66081	−	0.458195i	0.117180	−	0.0146665i
$977$	12.8529	−	17.6906i	0.411202	−	0.565971i	−0.552309	−	0.833640i	$-0.686253\pi$
$977$	12.8529	−	17.6906i	0.411202	−	0.565971i	0.963511	+	0.267668i	$0.0862531\pi$
$978$	−38.8147	+	35.2983i	−1.24116	+	1.12871i
$979$	9.05848	−	2.94328i	0.289510	−	0.0940676i
$980$	12.4309	−	13.1635i	0.397090	−	0.420493i
$981$	−28.5014	−	9.26065i	−0.909978	−	0.295670i
$982$	0.420147	−	0.189558i	0.0134074	−	0.00604905i
$983$	−17.7241	−	5.75890i	−0.565311	−	0.183681i	0.0123987	−	0.999923i	$-0.496053\pi$
$983$	−17.7241	−	5.75890i	−0.565311	−	0.183681i	−0.577709	+	0.816243i	$0.696053\pi$
$984$	64.6015	−	22.0558i	2.05942	−	0.703115i
$985$	50.5430	+	1.70094i	1.61043	+	0.0541965i
$986$	0.987349	−	4.76084i	0.0314436	−	0.151616i
$987$	−39.1076	+	28.4133i	−1.24481	+	0.904406i
$988$	68.1977	+	6.48612i	2.16966	+	0.206351i
$989$	1.47843	−	2.03489i	0.0470115	−	0.0647058i
$990$	−26.2062	+	42.5245i	−0.832888	+	1.35152i
$991$	29.3074	−	21.2931i	0.930981	−	0.676398i	−0.0152515	−	0.999884i	$-0.504855\pi$
$991$	29.3074	−	21.2931i	0.930981	−	0.676398i	0.946233	+	0.323486i	$0.104855\pi$
$992$	−1.54166	−	6.46237i	−0.0489478	−	0.205180i
$993$			21.2292i			0.673688i
$994$	−1.65809	−	15.0585i	−0.0525916	−	0.477627i
$995$	−0.538643	+	1.48576i	−0.0170761	+	0.0471017i
$996$	−6.65679	−	2.88519i	−0.210928	−	0.0914208i
$997$	5.62136	+	17.3008i	0.178030	+	0.547921i	0.999759	−	0.0219581i	$-0.00699003\pi$
$997$	5.62136	+	17.3008i	0.178030	+	0.547921i	−0.821729	+	0.569879i	$0.806990\pi$
$998$	32.1546	+	6.66854i	1.01784	+	0.211089i
$999$	44.3246			1.40237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.109.17	✓	112
4.3	odd	2		800.2.be.a.209.28		112
5.2	odd	4		1000.2.t.b.701.53		224
5.3	odd	4		1000.2.t.b.701.4		224
5.4	even	2		1000.2.o.a.549.12		112
8.3	odd	2		800.2.be.a.209.1		112
8.5	even	2	inner	200.2.o.a.109.24	yes	112
25.2	odd	20		1000.2.t.b.301.38		224
25.11	even	5		1000.2.o.a.949.5		112
25.14	even	10	inner	200.2.o.a.189.24	yes	112
25.23	odd	20		1000.2.t.b.301.19		224
40.13	odd	4		1000.2.t.b.701.19		224
40.29	even	2		1000.2.o.a.549.5		112
40.37	odd	4		1000.2.t.b.701.38		224
100.39	odd	10		800.2.be.a.689.1		112
200.61	even	10		1000.2.o.a.949.12		112
200.77	odd	20		1000.2.t.b.301.53		224
200.139	odd	10		800.2.be.a.689.28		112
200.173	odd	20		1000.2.t.b.301.4		224
200.189	even	10	inner	200.2.o.a.189.17	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.17	✓	112	1.1	even	1	trivial
200.2.o.a.109.24	yes	112	8.5	even	2	inner
200.2.o.a.189.17	yes	112	200.189	even	10	inner
200.2.o.a.189.24	yes	112	25.14	even	10	inner
800.2.be.a.209.1		112	8.3	odd	2
800.2.be.a.209.28		112	4.3	odd	2
800.2.be.a.689.1		112	100.39	odd	10
800.2.be.a.689.28		112	200.139	odd	10
1000.2.o.a.549.5		112	40.29	even	2
1000.2.o.a.549.12		112	5.4	even	2
1000.2.o.a.949.5		112	25.11	even	5
1000.2.o.a.949.12		112	200.61	even	10
1000.2.t.b.301.4		224	200.173	odd	20
1000.2.t.b.301.19		224	25.23	odd	20
1000.2.t.b.301.38		224	25.2	odd	20
1000.2.t.b.301.53		224	200.77	odd	20
1000.2.t.b.701.4		224	5.3	odd	4
1000.2.t.b.701.19		224	40.13	odd	4
1000.2.t.b.701.38		224	40.37	odd	4
1000.2.t.b.701.53		224	5.2	odd	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.287182 - 1.38475i) q^{2} +(-0.970606 - 2.98722i) q^{3} +(-1.83505 - 0.795350i) q^{4} +(-0.762120 + 2.10218i) q^{5} +(-4.41529 + 0.486168i) q^{6} -1.71800i q^{7} +(-1.62835 + 2.31267i) q^{8} +(-5.55435 + 4.03547i) q^{9} +(2.69213 + 1.65905i) q^{10} +(1.35234 - 1.86134i) q^{11} +(-0.594772 + 6.25368i) q^{12} +(4.80828 - 3.49342i) q^{13} +(-2.37899 - 0.493379i) q^{14} +(7.01940 + 0.236226i) q^{15} +(2.73484 + 2.91902i) q^{16} +(-2.53693 - 0.824300i) q^{17} +(3.99300 + 8.85029i) q^{18} +(-5.48112 - 1.78092i) q^{19} +(3.07050 - 3.25146i) q^{20} +(-5.13203 + 1.66750i) q^{21} +(-2.18912 - 2.40720i) q^{22} +(-0.393834 + 0.542066i) q^{23} +(8.48896 + 2.61955i) q^{24} +(-3.83835 - 3.20423i) q^{25} +(-3.45665 - 7.66150i) q^{26} +(9.82268 + 7.13660i) q^{27} +(-1.36641 + 3.15262i) q^{28} +(-1.22579 + 0.398283i) q^{29} +(2.34296 - 9.65226i) q^{30} +(0.362926 - 1.11697i) q^{31} +(4.82750 - 2.94877i) q^{32} +(-6.87282 - 2.23312i) q^{33} +(-1.87001 + 3.27629i) q^{34} +(3.61155 + 1.30932i) q^{35} +(13.4021 - 2.98765i) q^{36} +(2.95345 - 2.14581i) q^{37} +(-4.04021 + 7.07852i) q^{38} +(-15.1026 - 10.9726i) q^{39} +(-3.62066 - 5.18563i) q^{40} +(6.21636 - 4.51645i) q^{41} +(0.835236 + 7.58545i) q^{42} -3.75396 q^{43} +(-3.96204 + 2.34007i) q^{44} +(-4.25022 - 14.7518i) q^{45} +(0.637522 + 0.701032i) q^{46} +(8.51974 - 2.76823i) q^{47} +(6.06530 - 11.0028i) q^{48} +4.04848 q^{49} +(-5.53936 + 4.39494i) q^{50} +8.37845i q^{51} +(-11.6019 + 2.58634i) q^{52} +(1.09116 + 3.35825i) q^{53} +(12.7033 - 11.5524i) q^{54} +(2.88223 + 4.26144i) q^{55} +(3.97317 + 2.79751i) q^{56} +18.1019i q^{57} +(0.199497 + 1.81179i) q^{58} +(3.58141 + 4.92938i) q^{59} +(-12.6931 - 6.01637i) q^{60} +(0.542140 - 0.746192i) q^{61} +(-1.44250 - 0.823336i) q^{62} +(6.93293 + 9.54236i) q^{63} +(-2.69692 - 7.53171i) q^{64} +(3.67932 + 12.7703i) q^{65} +(-5.06605 + 8.87581i) q^{66} +(4.74089 - 14.5910i) q^{67} +(3.99980 + 3.53039i) q^{68} +(2.00153 + 0.650336i) q^{69} +(2.85025 - 4.62507i) q^{70} +(1.92683 + 5.93017i) q^{71} +(-0.288281 - 19.4166i) q^{72} +(3.14398 - 4.32732i) q^{73} +(-2.12322 - 4.70603i) q^{74} +(-5.84621 + 14.5760i) q^{75} +(8.64169 + 7.62750i) q^{76} +(-3.19778 - 2.32332i) q^{77} +(-19.5315 + 17.7621i) q^{78} +(-0.125628 - 0.386644i) q^{79} +(-8.22058 + 3.52448i) q^{80} +(5.41990 - 16.6807i) q^{81} +(-4.46891 - 9.90513i) q^{82} +(-0.356893 + 1.09840i) q^{83} +(10.7438 + 1.02182i) q^{84} +(3.66628 - 4.70489i) q^{85} +(-1.07807 + 5.19828i) q^{86} +(2.37952 + 3.27513i) q^{87} +(2.10258 + 6.15845i) q^{88} +(3.34918 + 2.43332i) q^{89} +(-21.6481 + 1.64903i) q^{90} +(-6.00168 - 8.26061i) q^{91} +(1.15384 - 0.681483i) q^{92} -3.68890 q^{93} +(-1.38658 - 12.5927i) q^{94} +(7.92110 - 10.1650i) q^{95} +(-13.4942 - 11.5587i) q^{96} +(-14.4383 + 4.69127i) q^{97} +(1.16265 - 5.60613i) q^{98} +15.7959i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Introduction

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