LMFDB - Embedded newform 200.2.o.a.109.5

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			109.5
Character	$\chi$	$=$	200.109
Dual form			200.2.o.a.189.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23493 - 0.689173i) q^{2} +(-0.0756938 - 0.232961i) q^{3} +(1.05008 + 1.70215i) q^{4} +(-2.03665 + 0.923061i) q^{5} +(-0.0670745 + 0.339856i) q^{6} -1.59435i q^{7} +(-0.123695 - 2.82572i) q^{8} +(2.37851 - 1.72809i) q^{9} +(3.15126 + 0.263695i) q^{10} +(2.84212 - 3.91185i) q^{11} +(0.317052 - 0.373471i) q^{12} +(1.50262 - 1.09172i) q^{13} +(-1.09878 + 1.96890i) q^{14} +(0.369200 + 0.404592i) q^{15} +(-1.79466 + 3.57480i) q^{16} +(-4.17890 - 1.35781i) q^{17} +(-4.12823 + 0.494857i) q^{18} +(2.84592 + 0.924695i) q^{19} +(-3.70984 - 2.49741i) q^{20} +(-0.371422 + 0.120682i) q^{21} +(-6.20575 + 2.87212i) q^{22} +(3.38091 - 4.65342i) q^{23} +(-0.648921 + 0.242706i) q^{24} +(3.29592 - 3.75991i) q^{25} +(-2.60801 + 0.312625i) q^{26} +(-1.17712 - 0.855230i) q^{27} +(2.71383 - 1.67420i) q^{28} +(-3.24693 + 1.05499i) q^{29} +(-0.177100 - 0.754083i) q^{30} +(-0.378200 + 1.16398i) q^{31} +(4.67992 - 3.17779i) q^{32} +(-1.12644 - 0.366003i) q^{33} +(4.22487 + 4.55678i) q^{34} +(1.47168 + 3.24714i) q^{35} +(5.43910 + 2.23395i) q^{36} +(-6.39864 + 4.64888i) q^{37} +(-2.87722 - 3.10326i) q^{38} +(-0.368067 - 0.267416i) q^{39} +(2.86024 + 5.64084i) q^{40} +(-6.95275 + 5.05147i) q^{41} +(0.541850 + 0.106940i) q^{42} +10.9570 q^{43} +(9.64302 + 0.729970i) q^{44} +(-3.24907 + 5.71503i) q^{45} +(-7.38218 + 3.41660i) q^{46} +(0.890923 - 0.289478i) q^{47} +(0.968635 + 0.147495i) q^{48} +4.45804 q^{49} +(-6.66144 + 2.37175i) q^{50} +1.07630i q^{51} +(3.43614 + 1.41130i) q^{52} +(1.66447 + 5.12271i) q^{53} +(0.864258 + 1.86739i) q^{54} +(-2.17755 + 10.5905i) q^{55} +(-4.50519 + 0.197214i) q^{56} -0.732983i q^{57} +(4.73679 + 0.934861i) q^{58} +(-5.45825 - 7.51263i) q^{59} +(-0.300988 + 1.05329i) q^{60} +(3.06376 - 4.21690i) q^{61} +(1.26923 - 1.17678i) q^{62} +(-2.75518 - 3.79218i) q^{63} +(-7.96940 + 0.699057i) q^{64} +(-2.05260 + 3.61046i) q^{65} +(1.13883 + 1.22830i) q^{66} +(-0.757501 + 2.33135i) q^{67} +(-2.07699 - 8.53894i) q^{68} +(-1.33998 - 0.435386i) q^{69} +(0.420422 - 5.02422i) q^{70} +(4.47330 + 13.7674i) q^{71} +(-5.17731 - 6.50725i) q^{72} +(-1.89010 + 2.60150i) q^{73} +(11.1057 - 1.33126i) q^{74} +(-1.12539 - 0.483220i) q^{75} +(1.41448 + 5.81520i) q^{76} +(-6.23686 - 4.53134i) q^{77} +(0.270239 + 0.583901i) q^{78} +(-3.26966 - 10.0630i) q^{79} +(0.355332 - 8.93721i) q^{80} +(2.61539 - 8.04936i) q^{81} +(12.0675 - 1.44654i) q^{82} +(-0.539736 + 1.66114i) q^{83} +(-0.595444 - 0.505491i) q^{84} +(9.76431 - 1.09200i) q^{85} +(-13.5310 - 7.55125i) q^{86} +(0.491545 + 0.676554i) q^{87} +(-11.4053 - 7.54717i) q^{88} +(9.19471 + 6.68035i) q^{89} +(7.95100 - 4.81846i) q^{90} +(-1.74058 - 2.39570i) q^{91} +(11.4711 + 0.868351i) q^{92} +0.299790 q^{93} +(-1.29972 - 0.256515i) q^{94} +(-6.64970 + 0.743672i) q^{95} +(-1.09454 - 0.849703i) q^{96} +(-13.6106 + 4.42235i) q^{97} +(-5.50535 - 3.07236i) q^{98} -14.2158i 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 $

$2$	−1.23493	−	0.689173i	−0.873224	−	0.487319i
$2$	−1.23493	−	0.689173i	−0.873224	−	0.487319i
$3$	−0.0756938	−	0.232961i	−0.0437018	−	0.134500i	0.926825	−	0.375494i	$-0.122527\pi$
$3$	−0.0756938	−	0.232961i	−0.0437018	−	0.134500i	−0.970527	+	0.240993i	$0.922527\pi$
$4$	1.05008	+	1.70215i	0.525041	+	0.851077i
$5$	−2.03665	+	0.923061i	−0.910819	+	0.412805i
$5$	−2.03665	+	0.923061i	−0.910819	+	0.412805i
$6$	−0.0670745	+	0.339856i	−0.0273830	+	0.138746i
$7$		−	1.59435i		−	0.602608i	−0.953528	−	0.301304i	$-0.902578\pi$
$7$		−	1.59435i		−	0.602608i	0.953528	−	0.301304i	$-0.0974219\pi$
$8$	−0.123695	−	2.82572i	−0.0437329	−	0.999043i
$9$	2.37851	−	1.72809i	0.792836	−	0.576029i
$10$	3.15126	+	0.263695i	0.996517	+	0.0833877i
$11$	2.84212	−	3.91185i	0.856932	−	1.17947i	−0.125360	−	0.992111i	$-0.540009\pi$
$11$	2.84212	−	3.91185i	0.856932	−	1.17947i	0.982292	−	0.187355i	$-0.0599913\pi$
$12$	0.317052	−	0.373471i	0.0915249	−	0.107812i
$13$	1.50262	−	1.09172i	0.416752	−	0.302788i	−0.359578	−	0.933115i	$-0.617079\pi$
$13$	1.50262	−	1.09172i	0.416752	−	0.302788i	0.776330	+	0.630327i	$0.217079\pi$
$14$	−1.09878	+	1.96890i	−0.293662	+	0.526212i
$15$	0.369200	+	0.404592i	0.0953269	+	0.104465i
$16$	−1.79466	+	3.57480i	−0.448664	+	0.893701i
$17$	−4.17890	−	1.35781i	−1.01353	−	0.329317i	−0.245272	−	0.969454i	$-0.578877\pi$
$17$	−4.17890	−	1.35781i	−1.01353	−	0.329317i	−0.768260	+	0.640138i	$0.778877\pi$
$18$	−4.12823	+	0.494857i	−0.973034	+	0.116639i
$19$	2.84592	+	0.924695i	0.652899	+	0.212140i	0.616692	−	0.787205i	$-0.288472\pi$
$19$	2.84592	+	0.924695i	0.652899	+	0.212140i	0.0362069	+	0.999344i	$0.488472\pi$
$20$	−3.70984	−	2.49741i	−0.829547	−	0.558438i
$21$	−0.371422	+	0.120682i	−0.0810510	+	0.0263351i
$22$	−6.20575	+	2.87212i	−1.32307	+	0.612339i
$23$	3.38091	−	4.65342i	0.704968	−	0.970305i	−0.294923	−	0.955521i	$-0.595294\pi$
$23$	3.38091	−	4.65342i	0.704968	−	0.970305i	0.999891	−	0.0147838i	$-0.00470601\pi$
$24$	−0.648921	+	0.242706i	−0.132460	+	0.0495421i
$25$	3.29592	−	3.75991i	0.659184	−	0.751982i
$26$	−2.60801	+	0.312625i	−0.511472	+	0.0613108i
$27$	−1.17712	−	0.855230i	−0.226537	−	0.164589i
$28$	2.71383	−	1.67420i	0.512866	−	0.316394i
$29$	−3.24693	+	1.05499i	−0.602941	+	0.195907i	−0.594551	−	0.804058i	$-0.702670\pi$
$29$	−3.24693	+	1.05499i	−0.602941	+	0.195907i	−0.00838909	+	0.999965i	$0.502670\pi$
$30$	−0.177100	−	0.754083i	−0.0323339	−	0.137676i
$31$	−0.378200	+	1.16398i	−0.0679268	+	0.209057i	−0.979258	−	0.202616i	$-0.935056\pi$
$31$	−0.378200	+	1.16398i	−0.0679268	+	0.209057i	0.911331	+	0.411673i	$0.135056\pi$
$32$	4.67992	−	3.17779i	0.827301	−	0.561759i
$33$	−1.12644	−	0.366003i	−0.196088	−	0.0637129i
$34$	4.22487	+	4.55678i	0.724559	+	0.781481i
$35$	1.47168	+	3.24714i	0.248760	+	0.548867i
$36$	5.43910	+	2.23395i	0.906517	+	0.372326i
$37$	−6.39864	+	4.64888i	−1.05193	+	0.764271i	−0.972578	−	0.232575i	$-0.925285\pi$
$37$	−6.39864	+	4.64888i	−1.05193	+	0.764271i	−0.0793510	+	0.996847i	$0.525285\pi$
$38$	−2.87722	−	3.10326i	−0.466747	−	0.503415i
$39$	−0.368067	−	0.267416i	−0.0589379	−	0.0428209i
$40$	2.86024	+	5.64084i	0.452243	+	0.891895i
$41$	−6.95275	+	5.05147i	−1.08584	+	0.788907i	−0.978691	−	0.205336i	$-0.934171\pi$
$41$	−6.95275	+	5.05147i	−1.08584	+	0.788907i	−0.107146	+	0.994243i	$0.534171\pi$
$42$	0.541850	+	0.106940i	0.0836093	+	0.0165012i
$43$	10.9570			1.67092			0.835461	−	0.549549i	$-0.185201\pi$
$43$	10.9570			1.67092			0.835461	+	0.549549i	$0.185201\pi$
$44$	9.64302	+	0.729970i	1.45374	+	0.110047i
$45$	−3.24907	+	5.71503i	−0.484343	+	0.851946i
$46$	−7.38218	+	3.41660i	−1.08844	+	0.503750i
$47$	0.890923	−	0.289478i	0.129954	−	0.0422248i	−0.243318	−	0.969947i	$-0.578236\pi$
$47$	0.890923	−	0.289478i	0.129954	−	0.0422248i	0.373272	+	0.927722i	$0.378236\pi$
$48$	0.968635	+	0.147495i	0.139810	+	0.0212891i
$49$	4.45804			0.636864
$50$	−6.66144	+	2.37175i	−0.942070	+	0.335416i
$51$			1.07630i			0.150712i
$52$	3.43614	+	1.41130i	0.476508	+	0.195712i
$53$	1.66447	+	5.12271i	0.228633	+	0.703659i	0.997903	+	0.0647347i	$0.0206201\pi$
$53$	1.66447	+	5.12271i	0.228633	+	0.703659i	−0.769270	+	0.638924i	$0.779380\pi$
$54$	0.864258	+	1.86739i	0.117611	+	0.254119i
$55$	−2.17755	+	10.5905i	−0.293621	+	1.42803i
$56$	−4.50519	+	0.197214i	−0.602032	+	0.0263538i
$57$		−	0.732983i		−	0.0970860i
$58$	4.73679	+	0.934861i	0.621972	+	0.122753i
$59$	−5.45825	−	7.51263i	−0.710603	−	0.978061i	−0.999784	−	0.0207867i	$-0.993383\pi$
$59$	−5.45825	−	7.51263i	−0.710603	−	0.978061i	0.289181	−	0.957274i	$-0.406617\pi$
$60$	−0.300988	+	1.05329i	−0.0388574	+	0.135979i
$61$	3.06376	−	4.21690i	0.392274	−	0.539919i	−0.566510	−	0.824055i	$-0.691707\pi$
$61$	3.06376	−	4.21690i	0.392274	−	0.539919i	0.958784	+	0.284136i	$0.0917066\pi$
$62$	1.26923	−	1.17678i	0.161193	−	0.149452i
$63$	−2.75518	−	3.79218i	−0.347120	−	0.477770i
$64$	−7.96940	+	0.699057i	−0.996175	+	0.0873821i
$65$	−2.05260	+	3.61046i	−0.254593	+	0.447822i
$66$	1.13883	+	1.22830i	0.140180	+	0.151193i
$67$	−0.757501	+	2.33135i	−0.0925434	+	0.284819i	−0.986606	−	0.163123i	$-0.947843\pi$
$67$	−0.757501	+	2.33135i	−0.0925434	+	0.284819i	0.894062	+	0.447943i	$0.147843\pi$
$68$	−2.07699	−	8.53894i	−0.251872	−	1.03550i
$69$	−1.33998	−	0.435386i	−0.161315	−	0.0524143i
$70$	0.420422	−	5.02422i	0.0502501	−	0.600509i
$71$	4.47330	+	13.7674i	0.530883	+	1.63389i	0.752381	+	0.658728i	$0.228905\pi$
$71$	4.47330	+	13.7674i	0.530883	+	1.63389i	−0.221499	+	0.975161i	$0.571095\pi$
$72$	−5.17731	−	6.50725i	−0.610151	−	0.766887i
$73$	−1.89010	+	2.60150i	−0.221219	+	0.304482i	−0.905173	−	0.425043i	$-0.860259\pi$
$73$	−1.89010	+	2.60150i	−0.221219	+	0.304482i	0.683954	+	0.729525i	$0.260259\pi$
$74$	11.1057	−	1.33126i	1.29101	−	0.154756i
$75$	−1.12539	−	0.483220i	−0.129949	−	0.0557974i
$76$	1.41448	+	5.81520i	0.162251	+	0.667049i
$77$	−6.23686	−	4.53134i	−0.710756	−	0.516394i
$78$	0.270239	+	0.583901i	0.0305986	+	0.0661138i
$79$	−3.26966	−	10.0630i	−0.367865	−	1.13217i	−0.948167	−	0.317772i	$-0.897065\pi$
$79$	−3.26966	−	10.0630i	−0.367865	−	1.13217i	0.580302	−	0.814402i	$-0.302935\pi$
$80$	0.355332	−	8.93721i	0.0397273	−	0.999211i
$81$	2.61539	−	8.04936i	0.290599	−	0.894373i
$82$	12.0675	−	1.44654i	1.33263	−	0.159744i
$83$	−0.539736	+	1.66114i	−0.0592437	+	0.182333i	−0.976299	−	0.216427i	$-0.930560\pi$
$83$	−0.539736	+	1.66114i	−0.0592437	+	0.182333i	0.917055	+	0.398761i	$0.130560\pi$
$84$	−0.595444	−	0.505491i	−0.0649683	−	0.0551536i
$85$	9.76431	−	1.09200i	1.05909	−	0.118444i
$86$	−13.5310	−	7.55125i	−1.45909	−	0.814272i
$87$	0.491545	+	0.676554i	0.0526992	+	0.0725342i
$88$	−11.4053	−	7.54717i	−1.21581	−	0.804531i
$89$	9.19471	+	6.68035i	0.974637	+	0.708116i	0.956504	−	0.291720i	$-0.0942276\pi$
$89$	9.19471	+	6.68035i	0.974637	+	0.708116i	0.0181337	+	0.999836i	$0.494228\pi$
$90$	7.95100	−	4.81846i	0.838109	−	0.507910i
$91$	−1.74058	−	2.39570i	−0.182462	−	0.251138i
$92$	11.4711	+	0.868351i	1.19594	+	0.0905319i
$93$	0.299790			0.0310868
$94$	−1.29972	−	0.256515i	−0.134056	−	0.0264575i
$95$	−6.64970	+	0.743672i	−0.682245	+	0.0762992i
$96$	−1.09454	−	0.849703i	−0.111711	−	0.0867224i
$97$	−13.6106	+	4.42235i	−1.38195	+	0.449022i	−0.903309	−	0.428990i	$-0.858869\pi$
$97$	−13.6106	+	4.42235i	−1.38195	+	0.449022i	−0.478638	+	0.878012i	$0.658869\pi$
$98$	−5.50535	−	3.07236i	−0.556125	−	0.310355i
$99$		−	14.2158i		−	1.42874i
$100$	9.86093	+	1.66195i	0.986093	+	0.166195i
$101$		−	9.35559i		−	0.930916i	−0.885070	−	0.465458i	$-0.845890\pi$
$101$		−	9.35559i		−	0.930916i	0.885070	−	0.465458i	$-0.154110\pi$
$102$	0.741757	−	1.32915i	0.0734449	−	0.131606i
$103$	−8.54607	+	2.77679i	−0.842069	+	0.273605i	−0.698121	−	0.715980i	$-0.745980\pi$
$103$	−8.54607	+	2.77679i	−0.842069	+	0.273605i	−0.143949	+	0.989585i	$0.545980\pi$
$104$	−3.27076	−	4.11094i	−0.320724	−	0.403111i
$105$	0.645062	−	0.588634i	0.0629516	−	0.0574448i
$106$	1.47494	−	7.47328i	0.143259	−	0.725869i
$107$	−1.58107			−0.152847			−0.0764237	−	0.997075i	$-0.524350\pi$
$107$	−1.58107			−0.152847			−0.0764237	+	0.997075i	$0.524350\pi$
$108$	0.219657	−	2.90171i	0.0211365	−	0.279217i
$109$	−2.12791	−	2.92882i	−0.203817	−	0.280530i	0.694856	−	0.719149i	$-0.255468\pi$
$109$	−2.12791	−	2.92882i	−0.203817	−	0.280530i	−0.898673	+	0.438618i	$0.855468\pi$
$110$	9.98781	−	11.5778i	0.952300	−	1.10390i
$111$	1.56735	+	1.13874i	0.148766	+	0.108085i
$112$	5.69949	+	2.86131i	0.538551	+	0.270368i
$113$	11.8710	+	16.3390i	1.11673	+	1.53705i	0.811111	+	0.584892i	$0.198863\pi$
$113$	11.8710	+	16.3390i	1.11673	+	1.53705i	0.305618	+	0.952154i	$0.401137\pi$
$114$	−0.505152	+	0.905180i	−0.0473118	+	0.0847778i
$115$	−2.59035	+	12.5982i	−0.241551	+	1.17479i
$116$	−5.20531	−	4.41895i	−0.483301	−	0.410289i
$117$	1.68741	−	5.19332i	0.156001	−	0.480123i
$118$	1.56303	+	13.0392i	0.143888	+	1.20036i
$119$	−2.16482	+	6.66264i	−0.198449	+	0.610763i
$120$	1.09760	−	1.09330i	0.100196	−	0.0998043i
$121$	−3.82569	−	11.7743i	−0.347790	−	1.07039i
$122$	−6.68969	+	3.09610i	−0.605656	+	0.280308i
$123$	1.70308	+	1.23736i	0.153561	+	0.111569i
$124$	−2.37842	+	0.578520i	−0.213588	+	0.0519527i
$125$	−3.24202	+	10.7000i	−0.289975	+	0.957034i
$126$	0.788975	+	6.58185i	0.0702875	+	0.586358i
$127$	5.95921	−	8.20214i	0.528794	−	0.727822i	−0.458152	−	0.888874i	$-0.651488\pi$
$127$	5.95921	−	8.20214i	0.528794	−	0.727822i	0.986946	+	0.161051i	$0.0514885\pi$
$128$	10.3234	+	4.62901i	0.912467	+	0.409150i
$129$	−0.829374	−	2.55255i	−0.0730223	−	0.224740i
$130$	5.02303	−	3.04406i	0.440549	−	0.266981i
$131$	−5.82215	−	1.89173i	−0.508683	−	0.165281i	0.0434199	−	0.999057i	$-0.486175\pi$
$131$	−5.82215	−	1.89173i	−0.508683	−	0.165281i	−0.552103	+	0.833776i	$0.686175\pi$
$132$	−0.559862	−	2.30171i	−0.0487297	−	0.200338i
$133$	1.47429	−	4.53740i	0.127837	−	0.393442i
$134$	2.54216	−	2.35699i	0.219609	−	0.203613i
$135$	3.18682	+	0.655251i	0.274278	+	0.0563950i
$136$	−3.31987	+	11.9764i	−0.284677	+	1.02696i
$137$	1.38590	+	1.90752i	0.118405	+	0.162971i	0.864105	−	0.503311i	$-0.167885\pi$
$137$	1.38590	+	1.90752i	0.118405	+	0.162971i	−0.745700	+	0.666282i	$0.767885\pi$
$138$	1.35472	+	1.46115i	0.115321	+	0.124381i
$139$	−11.6027	+	15.9697i	−0.984127	+	1.35453i	−0.0495502	+	0.998772i	$0.515779\pi$
$139$	−11.6027	+	15.9697i	−0.984127	+	1.35453i	−0.934576	+	0.355762i	$0.884221\pi$
$140$	−3.98175	+	5.91480i	−0.336519	+	0.499891i
$141$	−0.134875	−	0.185639i	−0.0113585	−	0.0156336i
$142$	3.96392	−	20.0846i	0.332645	−	1.68546i
$143$		−	8.98081i		−	0.751013i
$144$	1.90897	+	11.6040i	0.159081	+	0.967002i
$145$	5.63906	−	5.14577i	0.468298	−	0.427333i
$146$	4.12701	−	1.91005i	0.341554	−	0.158077i
$147$	−0.337446	−	1.03855i	−0.0278321	−	0.0856584i
$148$	−14.6322	−	6.00976i	−1.20276	−	0.493999i
$149$		−	12.5490i		−	1.02806i	−0.857774	−	0.514028i	$-0.828153\pi$
$149$		−	12.5490i		−	1.02806i	0.857774	−	0.514028i	$-0.171847\pi$
$150$	1.05676	+	1.37233i	0.0862838	+	0.112050i
$151$	10.1466			0.825718			0.412859	−	0.910795i	$-0.364530\pi$
$151$	10.1466			0.825718			0.412859	+	0.910795i	$0.364530\pi$
$152$	2.26090	−	8.15616i	0.183384	−	0.661552i
$153$	−12.2860	+	3.99195i	−0.993262	+	0.322730i
$154$	4.57918	+	9.89414i	0.369000	+	0.797292i
$155$	−0.304162	−	2.71973i	−0.0244309	−	0.218454i
$156$	0.0686831	−	0.907316i	0.00549905	−	0.0726434i
$157$	7.71018			0.615340			0.307670	−	0.951493i	$-0.400451\pi$
$157$	7.71018			0.615340			0.307670	+	0.951493i	$0.400451\pi$
$158$	−2.89734	+	14.6804i	−0.230500	+	1.16791i
$159$	1.06740	−	0.775515i	0.0846507	−	0.0615023i
$160$	−6.59809	+	10.7919i	−0.521625	+	0.853175i
$161$	−7.41918	−	5.39035i	−0.584714	−	0.424819i
$162$	−8.77721	+	8.13790i	−0.689603	+	0.639374i
$163$	−7.65059	+	5.55848i	−0.599240	+	0.435374i	−0.845609	−	0.533803i	$-0.820763\pi$
$163$	−7.65059	+	5.55848i	−0.599240	+	0.435374i	0.246369	+	0.969176i	$0.420763\pi$
$164$	−15.8993	−	6.53019i	−1.24153	−	0.509923i
$165$	2.63201	−	0.294352i	0.204902	−	0.0229153i
$166$	1.81134	−	1.67941i	0.140587	−	0.130347i
$167$	20.1937	+	6.56132i	1.56263	+	0.507730i	0.957509	−	0.288402i	$-0.0931239\pi$
$167$	20.1937	+	6.56132i	1.56263	+	0.507730i	0.605123	+	0.796132i	$0.293124\pi$
$168$	0.386958	+	1.03461i	0.0298545	+	0.0798217i
$169$	−2.95120	+	9.08286i	−0.227015	+	0.698682i
$170$	−12.8108	−	5.38077i	−0.982542	−	0.412686i
$171$	8.36700	−	2.71860i	0.639841	−	0.207897i
$172$	11.5057	+	18.6505i	0.877303	+	1.42208i
$173$	14.5968	+	10.6052i	1.10977	+	0.806296i	0.982628	−	0.185588i	$-0.0594191\pi$
$173$	14.5968	+	10.6052i	1.10977	+	0.806296i	0.127144	+	0.991884i	$0.459419\pi$
$174$	−0.140759	−	1.17425i	−0.0106709	−	0.0890199i
$175$	−5.99462	−	5.25485i	−0.453150	−	0.397229i
$176$	8.88345	+	17.1804i	0.669615	+	1.29502i
$177$	−1.33700	+	1.84022i	−0.100495	+	0.138319i
$178$	−6.75087	−	14.5865i	−0.505999	−	1.09330i
$179$	4.37062	−	1.42010i	0.326675	−	0.106143i	−0.141088	−	0.989997i	$-0.545060\pi$
$179$	4.37062	−	1.42010i	0.326675	−	0.106143i	0.467763	+	0.883854i	$0.345060\pi$
$180$	−13.1396	+	0.470829i	−0.979371	+	0.0350936i
$181$	20.8534	+	6.77570i	1.55002	+	0.503633i	0.954121	−	0.299422i	$-0.0967940\pi$
$181$	20.8534	+	6.77570i	1.55002	+	0.503633i	0.595904	+	0.803056i	$0.296794\pi$
$182$	0.498434	+	4.15808i	0.0369464	+	0.308217i
$183$	−1.21428	−	0.394545i	−0.0897624	−	0.0291656i
$184$	−13.5675	−	8.97789i	−1.00021	−	0.661859i
$185$	8.74061	−	15.3745i	0.642622	−	1.13036i
$186$	−0.370218	−	0.206607i	−0.0271457	−	0.0151492i
$187$	−17.1885	+	12.4882i	−1.25695	+	0.913225i
$188$	1.42828	+	1.21251i	0.104168	+	0.0884315i
$189$	−1.36354	+	1.87675i	−0.0991827	+	0.136513i
$190$	8.72441	+	3.66441i	0.632935	+	0.265845i
$191$	5.50448	−	3.99924i	0.398290	−	0.289375i	−0.370554	−	0.928811i	$-0.620832\pi$
$191$	5.50448	−	3.99924i	0.398290	−	0.289375i	0.768844	+	0.639436i	$0.220832\pi$
$192$	0.766087	+	1.80365i	0.0552876	+	0.130167i
$193$			5.92258i			0.426317i	0.977018	+	0.213158i	$0.0683751\pi$
$193$			5.92258i			0.426317i	−0.977018	+	0.213158i	$0.931625\pi$
$194$	19.8558	+	3.91878i	1.42557	+	0.281352i
$195$	0.996466	+	0.204886i	0.0713584	+	0.0146722i
$196$	4.68131	+	7.58828i	0.334379	+	0.542020i
$197$	2.88473	+	8.87830i	0.205529	+	0.632552i	0.999691	+	0.0248470i	$0.00790987\pi$
$197$	2.88473	+	8.87830i	0.205529	+	0.632552i	−0.794163	+	0.607705i	$0.792090\pi$
$198$	−9.79714	+	17.5555i	−0.696252	+	1.24761i
$199$	−21.5328			−1.52642			−0.763211	−	0.646149i	$-0.776378\pi$
$199$	−21.5328			−1.52642			−0.763211	+	0.646149i	$0.776378\pi$
$200$	−11.0321	−	8.84826i	−0.780091	−	0.625667i
$201$	0.600452			0.0423526
$202$	−6.44762	+	11.5535i	−0.453653	+	0.812899i
$203$	1.68203	+	5.17675i	0.118055	+	0.363337i
$204$	−1.83203	+	1.13020i	−0.128268	+	0.0791301i
$205$	9.49753	−	16.7059i	0.663337	−	1.16679i
$206$	12.4674	+	2.46059i	0.868648	+	0.171438i
$207$		−	16.9107i		−	1.17538i
$208$	1.20599	+	7.33082i	0.0836203	+	0.508301i
$209$	11.7057	−	8.50470i	0.809701	−	0.588283i
$210$	−1.20227	+	0.282360i	−0.0829647	+	0.0194847i
$211$	−0.604508	+	0.832033i	−0.0416160	+	0.0572795i	−0.829318	−	0.558777i	$-0.811271\pi$
$211$	−0.604508	+	0.832033i	−0.0416160	+	0.0572795i	0.787702	+	0.616057i	$0.211271\pi$
$212$	−6.97181	+	8.21245i	−0.478826	+	0.564034i
$213$	2.86867	−	2.08421i	0.196558	−	0.142808i
$214$	1.95250	+	1.08963i	0.133470	+	0.0744854i
$215$	−22.3156	+	10.1139i	−1.52191	+	0.689766i
$216$	−2.27104	+	3.43201i	−0.154524	+	0.233519i
$217$	1.85579	+	0.602984i	0.125980	+	0.0409332i
$218$	0.609351	+	5.08338i	0.0412704	+	0.344290i
$219$	0.749118	+	0.243403i	0.0506207	+	0.0164477i
$220$	−20.3133	+	7.41440i	−1.36952	+	0.499879i
$221$	−7.76164	+	2.52191i	−0.522105	+	0.169642i
$222$	−1.15077	−	2.48644i	−0.0772343	−	0.166879i
$223$	11.9690	−	16.4740i	0.801506	−	1.10318i	−0.191073	−	0.981576i	$-0.561197\pi$
$223$	11.9690	−	16.4740i	0.801506	−	1.10318i	0.992579	−	0.121602i	$-0.0388032\pi$
$224$	−5.06651	−	7.46144i	−0.338520	−	0.498538i
$225$	1.34192	−	14.6386i	0.0894610	−	0.975908i
$226$	−3.39939	−	28.3586i	−0.226124	−	1.88639i
$227$	−0.991152	−	0.720114i	−0.0657850	−	0.0477956i	0.554407	−	0.832246i	$-0.312945\pi$
$227$	−0.991152	−	0.720114i	−0.0657850	−	0.0477956i	−0.620192	+	0.784450i	$0.712945\pi$
$228$	1.24765	−	0.769693i	0.0826277	−	0.0509741i
$229$	−0.927598	+	0.301395i	−0.0612974	+	0.0199167i	−0.339505	−	0.940604i	$-0.610260\pi$
$229$	−0.927598	+	0.301395i	−0.0612974	+	0.0199167i	0.278208	+	0.960521i	$0.410260\pi$
$230$	11.8812	−	13.7726i	0.783424	−	0.908140i
$231$	−0.583537	+	1.79594i	−0.0383939	+	0.118164i
$232$	3.38275	+	9.04443i	0.222088	+	0.593796i
$233$	2.40539	+	0.781559i	0.157583	+	0.0512017i	0.386746	−	0.922186i	$-0.373599\pi$
$233$	2.40539	+	0.781559i	0.157583	+	0.0512017i	−0.229163	+	0.973388i	$0.573599\pi$
$234$	−5.66292	+	5.25044i	−0.370197	+	0.343232i
$235$	−1.54729	+	1.41194i	−0.100934	+	0.0921050i
$236$	7.05605	−	17.1797i	0.459310	−	1.11830i
$237$	−2.09679	+	1.52341i	−0.136201	+	0.0989560i
$238$	7.26510	−	6.73592i	0.470927	−	0.436625i
$239$	−15.9729	−	11.6050i	−1.03320	−	0.750665i	−0.0642544	−	0.997934i	$-0.520467\pi$
$239$	−15.9729	−	11.6050i	−1.03320	−	0.750665i	−0.968947	+	0.247269i	$0.920467\pi$
$240$	−2.10892	+	0.593712i	−0.136130	+	0.0383240i
$241$	12.9006	−	9.37282i	0.830999	−	0.603756i	−0.0888425	−	0.996046i	$-0.528317\pi$
$241$	12.9006	−	9.37282i	0.830999	−	0.603756i	0.919842	+	0.392289i	$0.128317\pi$
$242$	−3.39006	+	17.1769i	−0.217921	+	1.10417i
$243$	−6.43817			−0.413009
$244$	10.3950	+	0.786896i	0.665473	+	0.0503758i
$245$	−9.07949	+	4.11505i	−0.580068	+	0.262901i
$246$	−1.25042	−	2.70176i	−0.0797239	−	0.172258i
$247$	5.28584	−	1.71747i	0.336330	−	0.109280i
$248$	3.33587	+	0.924710i	0.211828	+	0.0587191i
$249$	0.427835			0.0271129
$250$	11.3778	−	10.9794i	0.719594	−	0.694395i
$251$			15.4738i			0.976698i	0.872648	+	0.488349i	$0.162401\pi$
$251$			15.4738i			0.976698i	−0.872648	+	0.488349i	$0.837599\pi$
$252$	3.56171	−	8.67184i	0.224366	−	0.546274i
$253$	−8.59451	−	26.4512i	−0.540332	−	1.66297i
$254$	−13.0119	+	6.02211i	−0.816437	+	0.377861i
$255$	−0.993491	−	2.19205i	−0.0622148	−	0.137272i
$256$	−9.55843	−	12.8311i	−0.597402	−	0.801942i
$257$			6.14189i			0.383120i	0.981481	+	0.191560i	$0.0613547\pi$
$257$			6.14189i			0.383120i	−0.981481	+	0.191560i	$0.938645\pi$
$258$	−0.734933	+	3.72379i	−0.0457550	+	0.231833i
$259$	7.41195	+	10.2017i	0.460556	+	0.633901i
$260$	−8.30095	+	0.297446i	−0.514803	+	0.0184468i
$261$	−5.89974	+	8.12030i	−0.365185	+	0.502634i
$262$	5.88619	+	6.34861i	0.363650	+	0.392219i
$263$	13.2738	+	18.2699i	0.818500	+	1.12657i	0.989956	+	0.141377i	$0.0451530\pi$
$263$	13.2738	+	18.2699i	0.818500	+	1.12657i	−0.171456	+	0.985192i	$0.554847\pi$
$264$	−0.894886	+	3.22828i	−0.0550764	+	0.198687i
$265$	−8.11852	−	8.89678i	−0.498717	−	0.546525i
$266$	−4.94769	+	4.58731i	−0.303362	+	0.281266i
$267$	0.860281	−	2.64767i	0.0526484	−	0.162035i
$268$	−4.76375	+	1.15872i	−0.290992	+	0.0707803i
$269$	20.0823	+	6.52512i	1.22444	+	0.397844i	0.848696	−	0.528881i	$-0.177388\pi$
$269$	20.0823	+	6.52512i	1.22444	+	0.397844i	0.375741	+	0.926725i	$0.377388\pi$
$270$	−3.48390	−	3.00546i	−0.212024	−	0.182906i
$271$	−1.68049	−	5.17201i	−0.102082	−	0.314177i	0.886952	−	0.461861i	$-0.152818\pi$
$271$	−1.68049	−	5.17201i	−0.102082	−	0.314177i	−0.989035	+	0.147684i	$0.952818\pi$
$272$	12.3536	−	12.5020i	0.749046	−	0.758042i
$273$	−0.426355	+	0.586828i	−0.0258042	+	0.0355164i
$274$	−0.396866	−	3.31077i	−0.0239756	−	0.200011i
$275$	−5.34079	−	23.5792i	−0.322062	−	1.42188i
$276$	−0.665996	−	2.73804i	−0.0400882	−	0.164811i
$277$	−2.18015	−	1.58397i	−0.130992	−	0.0951714i	0.520360	−	0.853947i	$-0.325798\pi$
$277$	−2.18015	−	1.58397i	−0.130992	−	0.0951714i	−0.651352	+	0.758776i	$0.725798\pi$
$278$	25.3343	−	11.7252i	1.51945	−	0.703229i
$279$	1.11191	+	3.42210i	0.0665682	+	0.204876i
$280$	8.99348	−	4.56022i	0.537463	−	0.272525i
$281$	−2.50433	+	7.70752i	−0.149396	+	0.459792i	−0.997550	−	0.0699568i	$-0.977714\pi$
$281$	−2.50433	+	7.70752i	−0.149396	+	0.459792i	0.848154	+	0.529749i	$0.177714\pi$
$282$	0.0386228	+	0.322202i	0.00229995	+	0.0191869i
$283$	6.50726	−	20.0273i	0.386816	−	1.19050i	−0.548338	−	0.836257i	$-0.684739\pi$
$283$	6.50726	−	20.0273i	0.386816	−	1.19050i	0.935154	−	0.354241i	$-0.115261\pi$
$284$	−18.7369	+	22.0711i	−1.11183	+	1.30968i
$285$	0.676588	+	1.49283i	0.0400776	+	0.0884278i
$286$	−6.18933	+	11.0906i	−0.365983	+	0.655803i
$287$	8.05382	+	11.0851i	0.475402	+	0.654334i
$288$	5.63974	−	15.6457i	0.332325	−	0.921933i
$289$	1.86629	+	1.35594i	0.109782	+	0.0797610i
$290$	−10.5101	+	2.46836i	−0.617177	+	0.144947i
$291$	2.06047	+	2.83600i	0.120787	+	0.166249i
$292$	−6.41291	−	0.485453i	−0.375287	−	0.0284090i
$293$	−26.3688			−1.54048			−0.770242	−	0.637751i	$-0.779865\pi$
$293$	−26.3688			−1.54048			−0.770242	+	0.637751i	$0.779865\pi$
$294$	−0.299021	+	1.51509i	−0.0174393	+	0.0883621i
$295$	18.0512	+	10.2623i	1.05098	+	0.597496i
$296$	13.9279	+	17.5057i	0.809544	+	1.01750i
$297$	−6.69105	+	2.17405i	−0.388254	+	0.126151i
$298$	−8.64844	+	15.4971i	−0.500990	+	0.897723i
$299$		−	10.6833i		−	0.617832i
$300$	−0.359242	−	2.42302i	−0.0207408	−	0.139893i
$301$		−	17.4693i		−	1.00691i
$302$	−12.5303	−	6.99275i	−0.721037	−	0.402388i
$303$	−2.17949	+	0.708160i	−0.125209	+	0.0406827i
$304$	−8.41305	+	8.51409i	−0.482521	+	0.488317i
$305$	−2.34736	+	11.4164i	−0.134410	+	0.653702i
$306$	17.9234	+	3.53739i	1.02461	+	0.202219i
$307$	18.9501			1.08154			0.540770	−	0.841171i	$-0.318133\pi$
$307$	18.9501			1.08154			0.540770	+	0.841171i	$0.318133\pi$
$308$	1.16383	−	15.3744i	0.0663153	−	0.876036i
$309$	1.29377	+	1.78072i	0.0735999	+	0.101302i
$310$	−1.49874	+	3.56828i	−0.0851230	+	0.202665i
$311$	10.7210	+	7.78926i	0.607932	+	0.441689i	0.848686	−	0.528898i	$-0.177395\pi$
$311$	10.7210	+	7.78926i	0.607932	+	0.441689i	−0.240753	+	0.970586i	$0.577395\pi$
$312$	−0.710116	+	1.07313i	−0.0402024	+	0.0607542i
$313$	10.1086	+	13.9133i	0.571372	+	0.786426i	0.992716	−	0.120475i	$-0.0384417\pi$
$313$	10.1086	+	13.9133i	0.571372	+	0.786426i	−0.421345	+	0.906901i	$0.638442\pi$
$314$	−9.52150	−	5.31365i	−0.537330	−	0.299867i
$315$	9.11176	+	5.18016i	0.513389	+	0.291869i
$316$	13.6953	−	16.1324i	0.770422	−	0.907519i
$317$	0.717389	−	2.20790i	0.0402926	−	0.124008i	−0.928887	−	0.370364i	$-0.879233\pi$
$317$	0.717389	−	2.20790i	0.0402926	−	0.124008i	0.969180	+	0.246356i	$0.0792331\pi$
$318$	−1.85263	+	0.222077i	−0.103890	+	0.0124535i
$319$	−5.10121	+	15.6999i	−0.285613	+	0.879027i
$320$	15.5856	−	8.77998i	0.871264	−	0.490816i
$321$	0.119677	+	0.368327i	0.00667971	+	0.0205580i
$322$	5.44726	+	11.7698i	0.303564	+	0.655904i
$323$	−10.6373	−	7.72842i	−0.591873	−	0.430021i
$324$	16.4476	−	4.00068i	0.913757	−	0.222260i
$325$	0.847753	−	9.24793i	0.0470249	−	0.512983i
$326$	13.2787	−	1.59173i	0.735437	−	0.0881578i
$327$	−0.521233	+	0.717415i	−0.0288242	+	0.0396731i
$328$	15.1341	+	19.0217i	0.835639	+	1.05030i
$329$	−0.461530	−	1.42044i	−0.0254450	−	0.0783116i
$330$	−3.45320	−	1.45041i	−0.190092	−	0.0798423i
$331$	−10.8707	−	3.53209i	−0.597505	−	0.194141i	−0.00537779	−	0.999986i	$-0.501712\pi$
$331$	−10.8707	−	3.53209i	−0.597505	−	0.194141i	−0.592127	+	0.805844i	$0.701712\pi$
$332$	−3.39427	+	0.825615i	−0.186285	+	0.0453115i
$333$	−7.18554	+	22.1148i	−0.393765	+	1.21188i
$334$	−20.4158	−	22.0197i	−1.11710	−	1.20486i
$335$	−0.609208	−	5.44737i	−0.0332846	−	0.297621i
$336$	0.235159	−	1.54434i	0.0128290	−	0.0842509i
$337$	−8.15904	−	11.2300i	−0.444451	−	0.611735i	0.526743	−	0.850025i	$-0.323413\pi$
$337$	−8.15904	−	11.2300i	−0.444451	−	0.611735i	−0.971194	+	0.238290i	$0.923413\pi$
$338$	9.90417	−	9.18277i	0.538716	−	0.499477i
$339$	2.90780	−	4.00225i	0.157930	−	0.217372i
$340$	12.1121	+	15.4737i	0.656870	+	0.839178i
$341$	3.47842	+	4.78764i	0.188367	+	0.259265i
$342$	−12.2062	−	2.40904i	−0.660036	−	0.130266i
$343$		−	18.2681i		−	0.986387i
$344$	−1.35533	−	30.9613i	−0.0730743	−	1.66932i
$345$	3.13096	−	0.350153i	0.168565	−	0.0188516i
$346$	−10.7171	−	23.1563i	−0.576156	−	1.24489i
$347$	5.01875	+	15.4461i	0.269421	+	0.829191i	0.990642	+	0.136486i	$0.0435810\pi$
$347$	5.01875	+	15.4461i	0.269421	+	0.829191i	−0.721221	+	0.692705i	$0.756419\pi$
$348$	−0.635436	+	1.54712i	−0.0340630	+	0.0829345i
$349$			10.1963i			0.545797i	0.962043	+	0.272899i	$0.0879824\pi$
$349$			10.1963i			0.545797i	−0.962043	+	0.272899i	$0.912018\pi$
$350$	3.78141	+	10.6207i	0.202125	+	0.567699i
$351$	−2.70244			−0.144245
$352$	0.869895	−	27.3388i	0.0463656	−	1.45716i
$353$	−12.7644	+	4.14740i	−0.679379	+	0.220744i	−0.628324	−	0.777952i	$-0.716259\pi$
$353$	−12.7644	+	4.14740i	−0.679379	+	0.220744i	−0.0510557	+	0.998696i	$0.516259\pi$
$354$	2.91932	−	1.35111i	0.155160	−	0.0718108i
$355$	−21.8187	−	23.9103i	−1.15802	−	1.26903i
$356$	−1.71578	+	22.6657i	−0.0909361	+	1.20128i
$357$	1.71600			0.0908204
$358$	−6.37608	−	1.25839i	−0.336986	−	0.0665081i
$359$	6.13662	−	4.45851i	0.323878	−	0.235311i	−0.413950	−	0.910299i	$-0.635851\pi$
$359$	6.13662	−	4.45851i	0.323878	−	0.235311i	0.737829	+	0.674988i	$0.235851\pi$
$360$	16.5510	+	8.47404i	0.872312	+	0.446621i
$361$	−8.12712	−	5.90470i	−0.427743	−	0.310774i
$362$	−21.0828	−	22.7391i	−1.10809	−	1.19514i
$363$	−2.45337	+	1.78248i	−0.128768	+	0.0935558i
$364$	2.25010	−	5.47842i	0.117937	−	0.287147i
$365$	1.44814	−	7.04303i	0.0757990	−	0.368649i
$366$	1.22764	+	1.32408i	0.0641698	+	0.0692110i
$367$	−8.32507	−	2.70498i	−0.434565	−	0.141199i	0.0835618	−	0.996503i	$-0.473370\pi$
$367$	−8.32507	−	2.70498i	−0.434565	−	0.141199i	−0.518127	+	0.855304i	$0.673370\pi$
$368$	10.5675	+	20.4374i	0.550869	+	1.06537i
$369$	−7.80780	+	24.0299i	−0.406458	+	1.25095i
$370$	−21.3897	+	12.9626i	−1.11200	+	0.673892i
$371$	8.16740	−	2.65375i	0.424030	−	0.137776i
$372$	0.314804	+	0.510289i	0.0163218	+	0.0264572i
$373$	−4.80051	−	3.48778i	−0.248561	−	0.180590i	0.456528	−	0.889709i	$-0.349093\pi$
$373$	−4.80051	−	3.48778i	−0.248561	−	0.180590i	−0.705089	+	0.709119i	$0.749093\pi$
$374$	29.8330	−	3.57612i	1.54263	−	0.184917i
$375$	2.73808	−	0.0546554i	0.141394	−	0.00282239i
$376$	−0.928188	−	2.48169i	−0.0478676	−	0.127983i
$377$	−3.72715	+	5.12999i	−0.191958	+	0.264208i
$378$	2.97727	−	1.37793i	0.153134	−	0.0708731i
$379$	−5.13756	+	1.66929i	−0.263899	+	0.0857458i	−0.437978	−	0.898986i	$-0.644305\pi$
$379$	−5.13756	+	1.66929i	−0.263899	+	0.0857458i	0.174079	+	0.984732i	$0.444305\pi$
$380$	−8.24858	−	10.5379i	−0.423143	−	0.540583i
$381$	−2.36186	−	0.767414i	−0.121002	−	0.0393158i
$382$	−9.55378	+	1.14522i	−0.488814	+	0.0585948i
$383$	−25.9411	−	8.42878i	−1.32553	−	0.430690i	−0.441139	−	0.897439i	$-0.645425\pi$
$383$	−25.9411	−	8.42878i	−1.32553	−	0.430690i	−0.884390	+	0.466749i	$0.845425\pi$
$384$	0.296965	−	2.75534i	0.0151544	−	0.140608i
$385$	16.8850	+	3.47178i	0.860540	+	0.176938i
$386$	4.08168	−	7.31395i	0.207752	−	0.372270i
$387$	26.0613	−	18.9346i	1.32477	−	0.962501i
$388$	−21.8198	−	18.5235i	−1.10773	−	0.940388i
$389$	−17.0621	+	23.4839i	−0.865081	+	1.19068i	0.115253	+	0.993336i	$0.463232\pi$
$389$	−17.0621	+	23.4839i	−0.865081	+	1.19068i	−0.980334	+	0.197346i	$0.936768\pi$
$390$	−1.08936	−	0.939757i	−0.0551619	−	0.0475864i
$391$	−20.4469	+	14.8556i	−1.03405	+	0.751278i
$392$	−0.551439	−	12.5972i	−0.0278519	−	0.636254i
$393$			1.49953i			0.0756412i
$394$	2.55625	−	12.9521i	0.128782	−	0.652518i
$395$	15.9479	+	17.4767i	0.802426	+	0.879349i
$396$	24.1975	−	14.9278i	1.21597	−	0.750148i
$397$	−3.36051	−	10.3426i	−0.168659	−	0.519080i	0.830628	−	0.556828i	$-0.187982\pi$
$397$	−3.36051	−	10.3426i	−0.168659	−	0.519080i	−0.999287	+	0.0377479i	$0.987982\pi$
$398$	26.5915	+	14.8398i	1.33291	+	0.743854i
$399$	−1.16863			−0.0585048
$400$	7.52590	+	18.5300i	0.376295	+	0.926500i
$401$	−27.9140			−1.39396			−0.696980	−	0.717090i	$-0.745474\pi$
$401$	−27.9140			−1.39396			−0.696980	+	0.717090i	$0.745474\pi$
$402$	−0.741514	−	0.413815i	−0.0369833	−	0.0206392i
$403$	0.702447	+	2.16191i	0.0349914	+	0.107692i
$404$	15.9247	−	9.82414i	0.792281	−	0.488769i
$405$	2.10339	+	18.8079i	0.104518	+	0.934573i
$406$	1.49050	−	7.55211i	0.0739721	−	0.374805i
$407$			38.2432i			1.89564i
$408$	3.04132	−	0.133133i	0.150568	−	0.00659108i
$409$	8.51534	−	6.18676i	0.421057	−	0.305916i	−0.357006	−	0.934102i	$-0.616203\pi$
$409$	8.51534	−	6.18676i	0.421057	−	0.305916i	0.778063	+	0.628186i	$0.216203\pi$
$410$	−23.2420	+	14.0851i	−1.14784	+	0.695614i
$411$	0.339476	−	0.467248i	0.0167451	−	0.0230476i
$412$	−13.7006	−	11.6309i	−0.674980	−	0.573012i
$413$	−11.9778	+	8.70236i	−0.589388	+	0.428215i
$414$	−11.6544	+	20.8835i	−0.572782	+	1.02637i
$415$	−0.434074	−	3.88137i	−0.0213079	−	0.190529i
$416$	3.56290	−	9.88416i	0.174685	−	0.484611i
$417$	4.59858	+	1.49417i	0.225193	+	0.0731698i
$418$	−20.3169	+	2.43541i	−0.993732	+	0.119120i
$419$	22.7262	+	7.38420i	1.11025	+	0.360742i	0.806039	−	0.591863i	$-0.201607\pi$
$419$	22.7262	+	7.38420i	1.11025	+	0.360742i	0.304211	+	0.952605i	$0.401607\pi$
$420$	1.67931	+	0.479880i	0.0819421	+	0.0234158i
$421$	−30.5748	+	9.93434i	−1.49012	+	0.484170i	−0.937119	−	0.349009i	$-0.886518\pi$
$421$	−30.5748	+	9.93434i	−1.49012	+	0.484170i	−0.553003	+	0.833179i	$0.686518\pi$
$422$	1.31994	−	0.610889i	0.0642535	−	0.0297376i
$423$	1.61882	−	2.22812i	0.0787099	−	0.108335i
$424$	14.2695	−	5.33698i	0.692987	−	0.259187i
$425$	−18.8786	+	11.2371i	−0.915744	+	0.545078i
$426$	−4.97898	+	0.596836i	−0.241232	+	0.0289168i
$427$	−6.72323	−	4.88471i	−0.325360	−	0.236388i
$428$	−1.66025	−	2.69122i	−0.0802511	−	0.130085i
$429$	−2.09218	+	0.679791i	−0.101012	+	0.0328206i
$430$	34.5283	+	2.88930i	1.66510	+	0.139334i
$431$	1.14163	−	3.51358i	0.0549904	−	0.169243i	−0.919789	−	0.392413i	$-0.871640\pi$
$431$	1.14163	−	3.51358i	0.0549904	−	0.169243i	0.974780	+	0.223170i	$0.0716404\pi$
$432$	5.16981	−	2.67314i	0.248732	−	0.128611i
$433$	−9.52464	−	3.09474i	−0.457725	−	0.148724i	0.0710739	−	0.997471i	$-0.477357\pi$
$433$	−9.52464	−	3.09474i	−0.457725	−	0.148724i	−0.528799	+	0.848747i	$0.677357\pi$
$434$	−1.87621	−	2.02360i	−0.0900608	−	0.0971361i
$435$	−1.62561	−	0.924180i	−0.0779419	−	0.0443111i
$436$	2.75082	−	6.69754i	0.131740	−	0.320754i
$437$	13.9248	−	10.1169i	0.666113	−	0.483959i
$438$	−0.757358	−	0.816856i	−0.0361880	−	0.0390309i
$439$	23.2982	+	16.9271i	1.11196	+	0.807887i	0.982971	−	0.183759i	$-0.0588268\pi$
$439$	23.2982	+	16.9271i	1.11196	+	0.807887i	0.128989	+	0.991646i	$0.458827\pi$
$440$	30.1952	+	4.84315i	1.43950	+	0.230888i
$441$	10.6035	−	7.70389i	0.504929	−	0.366852i
$442$	11.3231	+	2.23474i	0.538584	+	0.106296i
$443$	21.7711			1.03438			0.517188	−	0.855872i	$-0.326979\pi$
$443$	21.7711			1.03438			0.517188	+	0.855872i	$0.326979\pi$
$444$	−0.292475	+	3.86364i	−0.0138802	+	0.183360i
$445$	−24.8928	−	5.11828i	−1.18003	−	0.242630i
$446$	−26.1343	+	12.0954i	−1.23749	+	0.572733i
$447$	−2.92344	+	0.949882i	−0.138274	+	0.0449279i
$448$	1.11454	+	12.7060i	0.0526572	+	0.600303i
$449$	−2.36468			−0.111596			−0.0557981	−	0.998442i	$-0.517770\pi$
$449$	−2.36468			−0.111596			−0.0557981	+	0.998442i	$0.517770\pi$
$450$	−11.7457	+	17.1528i	−0.553698	+	0.808590i
$451$			41.5550i			1.95675i
$452$	−15.3460	+	37.3636i	−0.721816	+	1.75743i
$453$	−0.768034	−	2.36376i	−0.0360854	−	0.111059i
$454$	0.727716	+	1.57236i	0.0341534	+	0.0737946i
$455$	5.75634	+	3.27256i	0.269861	+	0.153420i
$456$	−2.07121	+	0.0906666i	−0.0969931	+	0.00424585i
$457$			11.3909i			0.532843i	0.963857	+	0.266422i	$0.0858414\pi$
$457$			11.3909i			0.532843i	−0.963857	+	0.266422i	$0.914159\pi$
$458$	1.35323	+	0.267075i	0.0632322	+	0.0124796i
$459$	3.75784	+	5.17223i	0.175401	+	0.241419i
$460$	−24.1641	+	8.81996i	−1.12666	+	0.411233i
$461$	−21.5814	+	29.7043i	−1.00515	+	1.38347i	−0.0830335	+	0.996547i	$0.526461\pi$
$461$	−21.5814	+	29.7043i	−1.00515	+	1.38347i	−0.922114	+	0.386919i	$0.873539\pi$
$462$	1.95834	−	1.81570i	0.0911101	−	0.0844738i
$463$	9.00559	+	12.3951i	0.418525	+	0.576051i	0.965272	−	0.261247i	$-0.0841339\pi$
$463$	9.00559	+	12.3951i	0.418525	+	0.576051i	−0.546747	+	0.837298i	$0.684134\pi$
$464$	2.05574	−	13.5005i	0.0954352	−	0.626745i
$465$	−0.610569	+	0.276724i	−0.0283144	+	0.0128328i
$466$	−2.43185	−	2.62290i	−0.112653	−	0.121503i
$467$	9.33412	−	28.7275i	0.431931	−	1.32935i	−0.464267	−	0.885695i	$-0.653682\pi$
$467$	9.33412	−	28.7275i	0.431931	−	1.32935i	0.896199	−	0.443653i	$-0.146318\pi$
$468$	10.6117	−	2.58118i	0.490528	−	0.119315i
$469$	3.71699	+	1.20772i	0.171634	+	0.0557674i
$470$	2.88387	−	0.677291i	0.133023	−	0.0312411i
$471$	−0.583613	−	1.79618i	−0.0268915	−	0.0827634i
$472$	−20.5534	+	16.3528i	−0.946049	+	0.752697i
$473$	31.1411	−	42.8620i	1.43187	−	1.97080i
$474$	3.63927	−	0.436245i	0.167157	−	0.0200374i
$475$	12.8567	−	7.65268i	0.589905	−	0.351129i
$476$	−13.6141	+	3.31146i	−0.624000	+	0.151780i
$477$	12.8115	+	9.30807i	0.586596	+	0.426187i
$478$	11.7275	+	25.3394i	0.536403	+	1.15900i
$479$	−10.3930	−	31.9863i	−0.474868	−	1.46149i	−0.846136	−	0.532967i	$-0.821077\pi$
$479$	−10.3930	−	31.9863i	−0.474868	−	1.46149i	0.371268	−	0.928526i	$-0.378923\pi$
$480$	3.01353	+	0.720221i	0.137548	+	0.0328734i
$481$	−4.53945	+	13.9710i	−0.206981	+	0.637023i
$482$	−22.3907	+	2.68401i	−1.01987	+	0.122253i
$483$	−0.694158	+	2.13640i	−0.0315853	+	0.0972095i
$484$	16.0243	−	18.8759i	0.728378	−	0.857993i
$485$	23.6380	−	21.5702i	1.07335	−	0.979453i
$486$	7.95066	+	4.43701i	0.360649	+	0.201267i
$487$	−20.9661	−	28.8574i	−0.950065	−	1.30765i	−0.951498	−	0.307654i	$-0.900456\pi$
$487$	−20.9661	−	28.8574i	−0.950065	−	1.30765i	0.00143291	−	0.999999i	$-0.499544\pi$
$488$	−12.2948	−	8.13572i	−0.556558	−	0.368287i
$489$	1.87401	+	1.36155i	0.0847458	+	0.0615714i
$490$	14.0485	+	1.17556i	0.634645	+	0.0531066i
$491$	−19.3917	−	26.6904i	−0.875135	−	1.20452i	−0.977745	−	0.209798i	$-0.932719\pi$
$491$	−19.3917	−	26.6904i	−0.875135	−	1.20452i	0.102610	−	0.994722i	$-0.467281\pi$
$492$	−0.317803	+	4.19823i	−0.0143277	+	0.189271i
$493$	15.0011			0.675615
$494$	−7.71126	−	1.52190i	−0.346946	−	0.0684737i
$495$	13.1220	+	28.9527i	0.589792	+	1.30133i
$496$	−3.48226	−	3.44094i	−0.156358	−	0.154503i
$497$	21.9501	−	7.13200i	0.984594	−	0.319914i
$498$	−0.528344	−	0.294852i	−0.0236757	−	0.0132126i
$499$			34.7937i			1.55758i	0.627285	+	0.778790i	$0.284166\pi$
$499$			34.7937i			1.55758i	−0.627285	+	0.778790i	$0.715834\pi$
$500$	−21.6174	+	5.71743i	−0.966759	+	0.255691i
$501$		−	5.20100i		−	0.232363i
$502$	10.6641	−	19.1090i	0.475963	−	0.852876i
$503$	−16.3408	+	5.30944i	−0.728600	+	0.236736i	−0.649748	−	0.760150i	$-0.725125\pi$
$503$	−16.3408	+	5.30944i	−0.728600	+	0.236736i	−0.0788520	+	0.996886i	$0.525125\pi$
$504$	−10.3748	+	8.25444i	−0.462132	+	0.367682i
$505$	8.63578	+	19.0541i	0.384287	+	0.847896i
$506$	−7.61585	+	38.5883i	−0.338566	+	1.71546i
$507$	2.33934			0.103894
$508$	20.2190	+	1.53056i	0.897071	+	0.0679077i
$509$	−3.41389	−	4.69882i	−0.151318	−	0.208271i	0.726628	−	0.687031i	$-0.241086\pi$
$509$	−3.41389	−	4.69882i	−0.151318	−	0.208271i	−0.877946	+	0.478760i	$0.841086\pi$
$510$	−0.283815	+	3.39171i	−0.0125675	+	0.150187i
$511$	4.14770	+	3.01348i	0.183484	+	0.133309i
$512$	2.96112	+	22.4328i	0.130864	+	0.991400i
$513$	−2.55917	−	3.52240i	−0.112990	−	0.155518i
$514$	4.23282	−	7.58477i	0.186702	−	0.334550i
$515$	14.8422	−	13.5439i	0.654027	−	0.596815i
$516$	3.47392	−	4.09211i	0.152931	−	0.180145i
$517$	1.39972	−	4.30788i	0.0615595	−	0.189461i
$518$	−2.12249	−	17.7064i	−0.0932569	−	0.777975i
$519$	1.36571	−	4.20323i	0.0599481	−	0.184501i
$520$	10.4560	+	5.35346i	0.458528	+	0.234765i
$521$	1.56244	+	4.80869i	0.0684517	+	0.210673i	0.979431	−	0.201779i	$-0.0646724\pi$
$521$	1.56244	+	4.80869i	0.0684517	+	0.210673i	−0.910979	+	0.412452i	$0.864672\pi$
$522$	12.8820	−	5.96202i	0.563831	−	0.260951i
$523$	−15.9638	−	11.5984i	−0.698047	−	0.507161i	0.181249	−	0.983437i	$-0.441986\pi$
$523$	−15.9638	−	11.5984i	−0.698047	−	0.507161i	−0.879296	+	0.476277i	$0.841986\pi$
$524$	−2.89372	−	11.8967i	−0.126413	−	0.519708i
$525$	−0.770422	+	1.79427i	−0.0336240	+	0.0783085i
$526$	−3.80111	−	31.7099i	−0.165736	−	1.38262i
$527$	3.16092	−	4.35064i	0.137692	−	0.189517i
$528$	3.32996	−	3.36995i	0.144918	−	0.146658i
$529$	−3.11638	−	9.59125i	−0.135495	−	0.417011i
$530$	3.89435	+	16.5819i	0.169160	+	0.720273i
$531$	−25.9650	−	8.43653i	−1.12678	−	0.366114i
$532$	9.27147	−	2.25517i	0.401969	−	0.0977741i
$533$	−4.93257	+	15.1809i	−0.213653	+	0.657557i
$534$	−2.88709	+	2.67680i	−0.124937	+	0.115836i
$535$	3.22008	−	1.45942i	0.139216	−	0.0630962i
$536$	6.68144	+	1.85211i	0.288594	+	0.0799989i
$537$	−0.661657	−	0.910692i	−0.0285526	−	0.0392993i
$538$	−20.3032	−	21.8982i	−0.875331	−	0.944097i
$539$	12.6703	−	17.4392i	0.545749	−	0.751159i
$540$	2.23108	+	6.11253i	0.0960106	+	0.263041i
$541$	12.7304	+	17.5219i	0.547322	+	0.753324i	0.989646	−	0.143532i	$-0.0458459\pi$
$541$	12.7304	+	17.5219i	0.547322	+	0.753324i	−0.442324	+	0.896855i	$0.645846\pi$
$542$	−1.48913	+	7.54520i	−0.0639637	+	0.324094i
$543$		−	5.37093i		−	0.230489i
$544$	−23.8718	+	6.92523i	−1.02349	+	0.296917i
$545$	7.03730	+	4.00080i	0.301445	+	0.171376i
$546$	0.930943	−	0.430856i	0.0398407	−	0.0184389i
$547$	0.523296	+	1.61054i	0.0223745	+	0.0688618i	0.961620	−	0.274384i	$-0.0884738\pi$
$547$	0.523296	+	1.61054i	0.0223745	+	0.0688618i	−0.939246	+	0.343245i	$0.888474\pi$
$548$	−1.79159	+	4.36207i	−0.0765330	+	0.186338i
$549$		−	15.3244i		−	0.654029i
$550$	−9.65470	+	32.7993i	−0.411678	+	1.39857i
$551$	−10.2161			−0.435219
$552$	−1.06453	+	3.84027i	−0.0453094	+	0.163453i
$553$	−16.0439	+	5.21298i	−0.682257	+	0.221679i
$554$	1.60069	+	3.45858i	0.0680068	+	0.146941i
$555$	−4.24327	−	0.872472i	−0.180117	−	0.0370344i
$556$	−39.3667	−	2.98003i	−1.66952	−	0.126381i
$557$	1.82388			0.0772805			0.0386402	−	0.999253i	$-0.487697\pi$
$557$	1.82388			0.0772805			0.0386402	+	0.999253i	$0.487697\pi$
$558$	0.985295	−	4.99234i	0.0417109	−	0.211343i
$559$	16.4642	−	11.9619i	0.696360	−	0.505935i
$560$	−14.2491	−	0.566524i	−0.602132	−	0.0239400i
$561$	4.21032	+	3.05898i	0.177760	+	0.129150i
$562$	8.40447	−	7.79230i	0.354521	−	0.328698i
$563$	−34.1809	+	24.8339i	−1.44055	+	1.04662i	−0.452627	+	0.891700i	$0.649513\pi$
$563$	−34.1809	+	24.8339i	−1.44055	+	1.04662i	−0.987926	+	0.154924i	$0.950487\pi$
$564$	0.174357	−	0.424513i	0.00734174	−	0.0178752i
$565$	−39.2590	−	22.3193i	−1.65164	−	0.938980i
$566$	−21.8382	+	20.2476i	−0.917930	+	0.851069i
$567$	−12.8335	−	4.16986i	−0.538956	−	0.175118i
$568$	38.3495	−	14.3432i	1.60911	−	0.601829i
$569$	8.58452	−	26.4204i	0.359882	−	1.10760i	−0.593243	−	0.805024i	$-0.702153\pi$
$569$	8.58452	−	26.4204i	0.359882	−	1.10760i	0.953125	−	0.302578i	$-0.0978474\pi$
$570$	0.193284	−	2.30982i	0.00809578	−	0.0967479i
$571$	26.0253	−	8.45612i	1.08912	−	0.353878i	0.291216	−	0.956657i	$-0.405940\pi$
$571$	26.0253	−	8.45612i	1.08912	−	0.353878i	0.797908	+	0.602780i	$0.205940\pi$
$572$	15.2867	−	9.43059i	0.639170	−	0.394313i
$573$	−1.34832	−	0.979614i	−0.0563270	−	0.0409239i
$574$	−2.30630	−	19.2398i	−0.0962630	−	0.803053i
$575$	−6.35325	−	28.0492i	−0.264949	−	1.16973i
$576$	−17.7473	+	15.4345i	−0.739469	+	0.643106i
$577$	5.08591	−	7.00015i	0.211729	−	0.291420i	−0.689923	−	0.723883i	$-0.742355\pi$
$577$	5.08591	−	7.00015i	0.211729	−	0.291420i	0.901652	+	0.432463i	$0.142355\pi$
$578$	−1.37025	−	2.96068i	−0.0569950	−	0.123148i
$579$	1.37973	−	0.448303i	0.0573398	−	0.0186308i
$580$	14.6804	+	4.19506i	0.609569	+	0.174190i
$581$	2.64843	+	0.860528i	0.109875	+	0.0357007i
$582$	−0.590039	−	4.92227i	−0.0244579	−	0.204035i
$583$	24.7699	+	8.04822i	1.02586	+	0.333323i
$584$	7.58491	+	5.01910i	0.313866	+	0.207692i
$585$	1.35708	+	12.1346i	0.0561081	+	0.501703i
$586$	32.5636	+	18.1727i	1.34519	+	0.750707i
$587$	1.70175	−	1.23640i	0.0702388	−	0.0510315i	−0.552112	−	0.833770i	$-0.686178\pi$
$587$	1.70175	−	1.23640i	0.0702388	−	0.0510315i	0.622351	+	0.782739i	$0.286178\pi$
$588$	1.41343	−	1.66495i	0.0582889	−	0.0686614i
$589$	−2.15266	+	2.96288i	−0.0886986	+	0.122083i
$590$	−15.2193	−	25.1136i	−0.626570	−	1.03391i
$591$	1.84994	−	1.34406i	0.0760965	−	0.0552874i
$592$	−5.13549	−	31.2170i	−0.211067	−	1.28301i
$593$		−	39.8777i		−	1.63758i	−0.574091	−	0.818791i	$-0.694645\pi$
$593$		−	39.8777i		−	1.63758i	0.574091	−	0.818791i	$-0.305355\pi$
$594$	9.76125	+	1.92649i	0.400509	+	0.0790450i
$595$	−1.74102	−	15.5677i	−0.0713751	−	0.638215i
$596$	21.3603	−	13.1775i	0.874954	−	0.539771i
$597$	1.62990	+	5.01632i	0.0667074	+	0.205304i
$598$	−7.36265	+	13.1931i	−0.301081	+	0.539506i
$599$	13.7239			0.560745			0.280373	−	0.959891i	$-0.409542\pi$
$599$	13.7239			0.560745			0.280373	+	0.959891i	$0.409542\pi$
$600$	−1.22624	+	3.23982i	−0.0500610	+	0.132265i
$601$	25.6448			1.04607			0.523036	−	0.852310i	$-0.324799\pi$
$601$	25.6448			1.04607			0.523036	+	0.852310i	$0.324799\pi$
$602$	−12.0393	+	21.5732i	−0.490687	+	0.879259i
$603$	2.22705	+	6.85416i	0.0906926	+	0.279123i
$604$	10.6548	+	17.2711i	0.433536	+	0.702749i
$605$	18.6600	+	20.4488i	0.758635	+	0.831360i
$606$	3.17955	+	0.627522i	0.129161	+	0.0254913i
$607$		−	9.08062i		−	0.368571i	−0.982873	−	0.184286i	$-0.941003\pi$
$607$		−	9.08062i		−	0.368571i	0.982873	−	0.184286i	$-0.0589971\pi$
$608$	16.2572	−	4.71623i	0.659315	−	0.191268i
$609$	1.07866	−	0.783696i	0.0437097	−	0.0317570i
$610$	10.7667	−	12.4807i	0.435931	−	0.505328i
$611$	1.02269	−	1.40761i	0.0413736	−	0.0569459i
$612$	−19.6962	−	16.7207i	−0.796171	−	0.675895i
$613$	33.2712	−	24.1729i	1.34381	−	0.976335i	0.344516	−	0.938780i	$-0.388043\pi$
$613$	33.2712	−	24.1729i	1.34381	−	0.976335i	0.999295	−	0.0375550i	$-0.0119569\pi$
$614$	−23.4020	−	13.0599i	−0.944426	−	0.527054i
$615$	−4.61074	−	0.948027i	−0.185923	−	0.0382281i
$616$	−12.0328	+	18.1841i	−0.484817	+	0.732659i
$617$	−35.7710	−	11.6227i	−1.44009	−	0.467912i	−0.518162	−	0.855283i	$-0.673384\pi$
$617$	−35.7710	−	11.6227i	−1.44009	−	0.467912i	−0.921924	+	0.387370i	$0.873384\pi$
$618$	−0.370484	−	3.09069i	−0.0149031	−	0.124326i
$619$	−23.5409	−	7.64891i	−0.946190	−	0.307436i	−0.205024	−	0.978757i	$-0.565727\pi$
$619$	−23.5409	−	7.64891i	−0.946190	−	0.307436i	−0.741167	+	0.671321i	$0.765727\pi$
$620$	4.31000	−	3.37367i	0.173094	−	0.135490i
$621$	−7.95948	+	2.58619i	−0.319403	+	0.103780i
$622$	−7.87149	−	17.0078i	−0.315618	−	0.681950i
$623$	10.6508	−	14.6596i	0.426716	−	0.587324i
$624$	1.61651	−	0.835847i	0.0647123	−	0.0334606i
$625$	−3.27385	−	24.7847i	−0.130954	−	0.991388i
$626$	−2.89471	−	24.1485i	−0.115696	−	0.965166i
$627$	−2.86732	−	2.08323i	−0.114510	−	0.0831961i
$628$	8.09633	+	13.1239i	0.323079	+	0.523701i
$629$	33.0516	−	10.7391i	1.31785	−	0.428196i
$630$	−7.68232	−	12.6767i	−0.306071	−	0.505051i
$631$	2.94258	−	9.05633i	0.117142	−	0.360527i	−0.875246	−	0.483679i	$-0.839300\pi$
$631$	2.94258	−	9.05633i	0.117142	−	0.360527i	0.992388	+	0.123152i	$0.0393003\pi$
$632$	−28.0307	+	10.4839i	−1.11500	+	0.417027i
$633$	0.239589	+	0.0778472i	0.00952281	+	0.00309415i
$634$	−2.40755	+	2.23218i	−0.0956158	+	0.0886514i
$635$	−4.56576	+	22.2056i	−0.181187	+	0.881204i
$636$	2.44091	+	1.00253i	0.0967883	+	0.0397530i
$637$	6.69875	−	4.86692i	0.265414	−	0.192835i
$638$	17.1196	−	15.8726i	0.677771	−	0.628403i
$639$	34.4310	+	25.0156i	1.36207	+	0.989602i
$640$	−25.2980	+	0.101422i	−0.999992	+	0.00400906i
$641$	−16.5944	+	12.0565i	−0.655440	+	0.476205i	−0.865120	−	0.501565i	$-0.832758\pi$
$641$	−16.5944	+	12.0565i	−0.655440	+	0.476205i	0.209680	+	0.977770i	$0.432758\pi$
$642$	0.106049	−	0.537335i	0.00418543	−	0.0212069i
$643$	3.19936			0.126170			0.0630852	−	0.998008i	$-0.479906\pi$
$643$	3.19936			0.126170			0.0630852	+	0.998008i	$0.479906\pi$
$644$	1.38446	−	18.2889i	0.0545552	−	0.720684i
$645$	4.04531	+	4.43310i	0.159284	+	0.174553i
$646$	7.81001	+	16.8749i	0.307281	+	0.663935i
$647$	6.93701	−	2.25397i	0.272722	−	0.0886128i	−0.169463	−	0.985537i	$-0.554203\pi$
$647$	6.93701	−	2.25397i	0.272722	−	0.0886128i	0.442185	+	0.896924i	$0.354203\pi$
$648$	−23.0687	−	6.39471i	−0.906226	−	0.251208i
$649$	−44.9013			−1.76253
$650$	−7.42033	+	10.8363i	−0.291049	+	0.425033i
$651$		−	0.477971i		−	0.0187331i
$652$	−17.4951	−	7.18562i	−0.685162	−	0.281411i
$653$	−11.3622	−	34.9692i	−0.444637	−	1.36845i	−0.882881	−	0.469596i	$-0.844399\pi$
$653$	−11.3622	−	34.9692i	−0.444637	−	1.36845i	0.438244	−	0.898856i	$-0.355601\pi$
$654$	1.13811	−	0.526735i	0.0445035	−	0.0205970i
$655$	13.6039	−	1.52140i	0.531548	−	0.0594458i
$656$	−5.58021	−	33.9204i	−0.217871	−	1.32437i
$657$			9.45395i			0.368834i
$658$	−0.408976	+	2.07222i	−0.0159435	+	0.0807834i
$659$	6.86949	+	9.45505i	0.267598	+	0.368316i	0.921577	−	0.388196i	$-0.126902\pi$
$659$	6.86949	+	9.45505i	0.267598	+	0.368316i	−0.653979	+	0.756512i	$0.726902\pi$
$660$	3.26486	+	4.17099i	0.127085	+	0.162356i
$661$	11.7497	−	16.1721i	0.457012	−	0.629023i	−0.516874	−	0.856062i	$-0.672904\pi$
$661$	11.7497	−	16.1721i	0.457012	−	0.629023i	0.973886	+	0.227039i	$0.0729044\pi$
$662$	10.9902	+	11.8536i	0.427147	+	0.460704i
$663$	1.17502	+	1.61727i	0.0456338	+	0.0628096i
$664$	4.76067	+	1.31967i	0.184750	+	0.0512130i
$665$	1.18567	+	10.6020i	0.0459785	+	0.411126i
$666$	24.1145	−	22.3581i	0.934419	−	0.866358i
$667$	−6.06826	+	18.6762i	−0.234964	+	0.723144i
$668$	10.0366	+	41.2626i	0.388329	+	1.59650i
$669$	−4.74378	−	1.54135i	−0.183405	−	0.0595919i
$670$	−3.00185	+	7.14694i	−0.115972	+	0.276110i
$671$	−7.78830	−	23.9699i	−0.300664	−	0.925348i
$672$	−1.35472	+	1.74509i	−0.0522596	+	0.0673181i
$673$	3.65125	−	5.02552i	0.140746	−	0.193720i	−0.732825	−	0.680417i	$-0.761799\pi$
$673$	3.65125	−	5.02552i	0.140746	−	0.193720i	0.873571	+	0.486698i	$0.161799\pi$
$674$	2.33643	+	19.4911i	0.0899959	+	0.750771i
$675$	−7.09529	+	1.60711i	−0.273098	+	0.0618576i
$676$	−18.5594	+	4.51435i	−0.713824	+	0.173629i
$677$	6.22446	+	4.52233i	0.239225	+	0.173807i	0.700938	−	0.713222i	$-0.252765\pi$
$677$	6.22446	+	4.52233i	0.239225	+	0.173807i	−0.461713	+	0.887030i	$0.652765\pi$
$678$	−6.34916	+	2.93850i	−0.243838	+	0.112852i
$679$	7.05078	+	21.7001i	0.270584	+	0.832772i
$680$	−4.29348	−	27.4562i	−0.164647	−	1.05290i
$681$	−0.0927347	+	0.285408i	−0.00355360	+	0.0109369i
$682$	−0.996083	−	8.30961i	−0.0381420	−	0.318191i
$683$	8.24813	−	25.3851i	0.315606	−	0.971336i	−0.659898	−	0.751355i	$-0.729401\pi$
$683$	8.24813	−	25.3851i	0.315606	−	0.971336i	0.975504	−	0.219981i	$-0.0705994\pi$
$684$	13.4135	+	11.3872i	0.512879	+	0.435399i
$685$	−4.58335	−	2.60570i	−0.175121	−	0.0995586i
$686$	−12.5899	+	22.5598i	−0.480685	+	0.861337i
$687$	0.140427	+	0.193281i	0.00535762	+	0.00737413i
$688$	−19.6640	+	39.1690i	−0.749682	+	1.49330i
$689$	8.09362	+	5.88036i	0.308342	+	0.224024i
$690$	−4.10782	−	1.72536i	−0.156382	−	0.0656834i
$691$	29.7127	+	40.8960i	1.13033	+	1.55576i	0.787451	+	0.616378i	$0.211400\pi$
$691$	29.7127	+	40.8960i	1.13033	+	1.55576i	0.342874	+	0.939381i	$0.388600\pi$
$692$	−2.72383	+	35.9822i	−0.103544	+	1.36784i
$693$	−22.6650			−0.860971
$694$	4.44726	−	22.5336i	0.168816	−	0.855363i
$695$	8.88962	−	43.2348i	0.337203	−	1.63999i
$696$	1.85095	−	1.47266i	0.0701601	−	0.0558209i
$697$	35.9138	−	11.6691i	1.36033	−	0.441999i
$698$	7.02704	−	12.5917i	0.265977	−	0.476603i
$699$		−	0.619523i		−	0.0234325i
$700$	2.64972	−	15.7218i	0.100150	−	0.594228i
$701$		−	45.0199i		−	1.70038i	−0.526477	−	0.850190i	$-0.676487\pi$
$701$		−	45.0199i		−	1.70038i	0.526477	−	0.850190i	$-0.323513\pi$
$702$	3.33731	+	1.86245i	0.125959	+	0.0702935i
$703$	−22.5088	+	7.31355i	−0.848936	+	0.275836i
$704$	−19.9154	+	33.1619i	−0.750590	+	1.24983i
$705$	0.446049	+	0.253585i	0.0167992	+	0.00955056i
$706$	18.6213	+	3.67513i	0.700823	+	0.138315i
$707$	−14.9161			−0.560978
$708$	−4.53630	−	0.343394i	−0.170484	−	0.0129055i
$709$	23.2922	+	32.0589i	0.874756	+	1.20400i	0.977846	+	0.209326i	$0.0671271\pi$
$709$	23.2922	+	32.0589i	0.874756	+	1.20400i	−0.103090	+	0.994672i	$0.532873\pi$
$710$	10.4661	+	44.5643i	0.392787	+	1.67247i
$711$	−25.1666	−	18.2846i	−0.943822	−	0.685727i
$712$	17.7395	−	26.8080i	0.664814	−	1.00467i
$713$	4.13783	+	5.69523i	0.154963	+	0.213288i
$714$	−2.11913	−	1.18262i	−0.0793066	−	0.0442585i
$715$	8.28983	+	18.2908i	0.310022	+	0.684037i
$716$	7.00673	+	5.94824i	0.261854	+	0.222296i
$717$	−1.49447	+	4.59950i	−0.0558119	+	0.171771i
$718$	−10.6509	+	1.27674i	−0.397490	+	0.0476476i
$719$	−6.66328	+	20.5075i	−0.248499	+	0.764800i	0.746543	+	0.665337i	$0.231712\pi$
$719$	−6.66328	+	20.5075i	−0.248499	+	0.764800i	−0.995041	+	0.0994625i	$0.968288\pi$
$720$	−14.5991	−	21.8713i	−0.544077	−	0.815095i
$721$	4.42717	+	13.6254i	0.164877	+	0.507438i
$722$	5.96703	+	12.8929i	0.222070	+	0.479823i
$723$	−3.16000	−	2.29587i	−0.117522	−	0.0853845i
$724$	10.3646	+	42.6108i	0.385196	+	1.58362i
$725$	−6.73495	+	15.6854i	−0.250130	+	0.582539i
$726$	4.25816	−	0.510431i	0.158035	−	0.0189439i
$727$	−23.9026	+	32.8992i	−0.886500	+	1.22016i	0.0880780	+	0.996114i	$0.471928\pi$
$727$	−23.9026	+	32.8992i	−0.886500	+	1.22016i	−0.974578	+	0.224049i	$0.928072\pi$
$728$	−6.55429	+	5.21473i	−0.242918	+	0.193271i
$729$	−7.35885	−	22.6482i	−0.272550	−	0.838823i
$730$	−6.64221	+	7.69960i	−0.245839	+	0.284975i
$731$	−45.7881	−	14.8775i	−1.69353	−	0.550263i
$732$	−0.603522	−	2.48120i	−0.0223068	−	0.0917079i
$733$	0.328621	−	1.01139i	0.0121379	−	0.0373566i	−0.944804	−	0.327636i	$-0.893748\pi$
$733$	0.328621	−	1.01139i	0.0121379	−	0.0373566i	0.956942	+	0.290279i	$0.0937481\pi$
$734$	8.41664	+	9.07785i	0.310664	+	0.335070i
$735$	1.64591	+	1.80369i	0.0607102	+	0.0665301i
$736$	1.03480	−	32.5214i	0.0381433	−	1.19876i
$737$	6.96696	+	9.58920i	0.256631	+	0.353223i
$738$	26.2028	−	24.2943i	0.964539	−	0.894284i
$739$	−4.06593	+	5.59628i	−0.149568	+	0.205862i	−0.877226	−	0.480077i	$-0.840609\pi$
$739$	−4.06593	+	5.59628i	−0.149568	+	0.205862i	0.727658	+	0.685940i	$0.240609\pi$
$740$	35.3481	−	1.26662i	1.29942	−	0.0465619i
$741$	−0.800210	−	1.10140i	−0.0293965	−	0.0404608i
$742$	−11.9150	−	2.35157i	−0.437414	−	0.0863287i
$743$			31.5085i			1.15594i	0.816059	+	0.577968i	$0.196154\pi$
$743$			31.5085i			1.15594i	−0.816059	+	0.577968i	$0.803846\pi$
$744$	−0.0370826	−	0.847123i	−0.00135951	−	0.0310570i
$745$	11.5835	+	25.5580i	0.424387	+	0.936372i
$746$	3.52460	+	7.61553i	0.129045	+	0.278824i
$747$	1.58682	+	4.88374i	0.0580588	+	0.178687i
$748$	−39.3061	−	16.1438i	−1.43717	−	0.590277i
$749$			2.52077i			0.0921071i
$750$	−3.41899	−	1.81951i	−0.124844	−	0.0664393i
$751$	−31.8120			−1.16084			−0.580418	−	0.814319i	$-0.697111\pi$
$751$	−31.8120			−1.16084			−0.580418	+	0.814319i	$0.697111\pi$
$752$	−0.564071	+	3.70439i	−0.0205696	+	0.135085i
$753$	3.60480	−	1.17127i	0.131366	−	0.0426835i
$754$	8.13820	−	3.76650i	0.296376	−	0.137168i
$755$	−20.6651	+	9.36592i	−0.752080	+	0.340861i
$756$	−4.62634	−	0.350210i	−0.168258	−	0.0127370i
$757$	−32.4034			−1.17772			−0.588860	−	0.808235i	$-0.700423\pi$
$757$	−32.4034			−1.17772			−0.588860	+	0.808235i	$0.700423\pi$
$758$	7.49493	+	1.47921i	0.272228	+	0.0537273i
$759$	−5.51155	+	4.00438i	−0.200057	+	0.145350i
$760$	2.92395	+	18.6982i	0.106063	+	0.678256i
$761$	32.4295	+	23.5614i	1.17557	+	0.854099i	0.991665	−	0.128845i	$-0.0411271\pi$
$761$	32.4295	+	23.5614i	1.17557	+	0.854099i	0.183902	+	0.982945i	$0.441127\pi$
$762$	2.38784	+	2.57543i	0.0865022	+	0.0932979i
$763$	−4.66957	+	3.39264i	−0.169050	+	0.122822i
$764$	12.5875	+	5.16994i	0.455399	+	0.187042i
$765$	21.3374	−	19.4709i	0.771457	−	0.703973i
$766$	26.2265	+	28.2868i	0.947600	+	1.02204i
$767$	−16.4033	−	5.32977i	−0.592290	−	0.192447i
$768$	−2.26563	+	3.19798i	−0.0817540	+	0.115397i
$769$	−7.33782	+	22.5835i	−0.264609	+	0.814382i	0.727175	+	0.686453i	$0.240833\pi$
$769$	−7.33782	+	22.5835i	−0.264609	+	0.814382i	−0.991783	+	0.127929i	$0.959167\pi$
$770$	−18.4591	−	15.9241i	−0.665219	−	0.573864i
$771$	1.43082	−	0.464902i	0.0515298	−	0.0167430i
$772$	−10.0811	+	6.21920i	−0.362829	+	0.223834i
$773$	34.2854	+	24.9098i	1.23316	+	0.895943i	0.997123	−	0.0758016i	$-0.0241516\pi$
$773$	34.2854	+	24.9098i	1.23316	+	0.895943i	0.236036	+	0.971744i	$0.424152\pi$
$774$	−45.2329	+	5.42213i	−1.62586	+	0.194894i
$775$	3.12995	+	5.25838i	0.112431	+	0.188887i
$776$	14.1799	+	37.9127i	0.509029	+	1.36099i
$777$	1.81556	−	2.49890i	0.0651328	−	0.0896476i
$778$	37.2549	−	17.2422i	1.33565	−	0.618162i
$779$	−24.4580	+	7.94690i	−0.876300	+	0.284727i
$780$	0.697623	+	1.91129i	0.0249789	+	0.0684350i
$781$	66.5696	+	21.6298i	2.38205	+	0.773974i
$782$	35.4885	−	4.25405i	1.26907	−	0.152124i
$783$	4.72430	+	1.53502i	0.168833	+	0.0548571i
$784$	−8.00065	+	15.9366i	−0.285738	+	0.569165i
$785$	−15.7030	+	7.11697i	−0.560463	+	0.254015i
$786$	1.03343	−	1.85181i	0.0368614	−	0.0660517i
$787$	−23.8094	+	17.2985i	−0.848714	+	0.616627i	−0.924791	−	0.380475i	$-0.875760\pi$
$787$	−23.8094	+	17.2985i	−0.848714	+	0.616627i	0.0760773	+	0.997102i	$0.475760\pi$
$788$	−12.0830	+	14.2332i	−0.430440	+	0.507037i
$789$	3.25143	−	4.47521i	0.115754	−	0.159322i
$790$	−7.65000	−	32.5733i	−0.272175	−	1.15891i
$791$	26.0501	−	18.9265i	0.926236	−	0.672950i
$792$	−40.1699	+	1.75843i	−1.42737	+	0.0624830i
$793$		−	9.68116i		−	0.343788i
$794$	−2.97785	+	15.0883i	−0.105680	+	0.535464i
$795$	−1.45809	+	2.56473i	−0.0517130	+	0.0909617i
$796$	−22.6113	−	36.6522i	−0.801435	−	1.29910i
$797$	2.93039	+	9.01881i	0.103800	+	0.319462i	0.989447	−	0.144896i	$-0.0462848\pi$
$797$	2.93039	+	9.01881i	0.103800	+	0.319462i	−0.885647	+	0.464359i	$0.846285\pi$
$798$	1.44317	+	0.805390i	0.0510878	+	0.0285105i
$799$	−4.11613			−0.145618
$800$	3.47644	−	28.0698i	0.122911	−	0.992418i
$801$	33.4139			1.18062
$802$	34.4718	+	19.2376i	1.21724	+	0.679303i
$803$	4.80477	+	14.7876i	0.169557	+	0.521842i
$804$	0.630524	+	1.02206i	0.0222369	+	0.0360453i
$805$	20.0859	+	4.12993i	0.707936	+	0.145561i
$806$	0.622459	−	3.15390i	0.0219252	−	0.111091i
$807$		−	5.17230i		−	0.182074i
$808$	−26.4363	+	1.15724i	−0.930026	+	0.0407117i
$809$	−18.6979	+	13.5848i	−0.657383	+	0.477617i	−0.865778	−	0.500428i	$-0.833176\pi$
$809$	−18.6979	+	13.5848i	−0.657383	+	0.477617i	0.208395	+	0.978045i	$0.433176\pi$
$810$	10.3644	−	24.6760i	0.364167	−	0.867026i
$811$	22.3488	−	30.7604i	0.784771	−	1.08014i	−0.209968	−	0.977708i	$-0.567336\pi$
$811$	22.3488	−	30.7604i	0.784771	−	1.08014i	0.994740	−	0.102437i	$-0.0326639\pi$
$812$	−7.04536	+	8.29909i	−0.247244	+	0.291241i
$813$	−1.07768	+	0.782978i	−0.0377958	+	0.0274602i
$814$	26.3561	−	47.2275i	0.923782	−	1.65532i
$815$	10.4508	−	18.3827i	0.366075	−	0.643916i
$816$	−3.84756	−	1.93159i	−0.134692	−	0.0676191i
$817$	31.1827	+	10.1319i	1.09094	+	0.354469i
$818$	−14.7796	+	1.77164i	−0.516755	+	0.0619441i
$819$	−8.27997	−	2.69033i	−0.289326	−	0.0940076i
$820$	38.4092	−	1.37631i	1.34131	−	0.0480627i
$821$	−7.25976	+	2.35884i	−0.253367	+	0.0823240i	−0.432947	−	0.901419i	$-0.642526\pi$
$821$	−7.25976	+	2.35884i	−0.253367	+	0.0823240i	0.179580	+	0.983743i	$0.442526\pi$
$822$	−0.741242	+	0.343059i	−0.0258538	+	0.0119656i
$823$	−13.1698	+	18.1266i	−0.459069	+	0.631855i	−0.974315	−	0.225188i	$-0.927700\pi$
$823$	−13.1698	+	18.1266i	−0.459069	+	0.631855i	0.515246	+	0.857042i	$0.327700\pi$
$824$	8.90353	+	23.8053i	0.310169	+	0.829298i
$825$	−5.08879	+	3.02900i	−0.177169	+	0.105456i
$826$	20.7891	−	2.49201i	0.723345	−	0.0867083i
$827$	25.6961	+	18.6693i	0.893542	+	0.649196i	0.936799	−	0.349868i	$-0.113773\pi$
$827$	25.6961	+	18.6693i	0.893542	+	0.649196i	−0.0432571	+	0.999064i	$0.513773\pi$
$828$	28.7846	−	17.7576i	1.00033	−	0.617120i
$829$	−1.36860	+	0.444686i	−0.0475335	+	0.0154446i	−0.332687	−	0.943037i	$-0.607955\pi$
$829$	−1.36860	+	0.444686i	−0.0475335	+	0.0154446i	0.285154	+	0.958482i	$0.407955\pi$
$830$	−2.13888	+	5.09235i	−0.0742417	+	0.176758i
$831$	−0.203980	+	0.627786i	−0.00707599	+	0.0217777i
$832$	−11.2118	+	9.75075i	−0.388699	+	0.338046i
$833$	−18.6297	−	6.05317i	−0.645482	−	0.209730i
$834$	−4.64916	−	5.01440i	−0.160987	−	0.173635i
$835$	−47.1840	+	5.27684i	−1.63287	+	0.182613i
$836$	26.7683	+	10.9943i	0.925800	+	0.380246i
$837$	1.44066	−	1.04670i	0.0497965	−	0.0361793i
$838$	−22.9762	−	24.7812i	−0.793700	−	0.856054i
$839$	−24.7233	−	17.9626i	−0.853544	−	0.620136i	0.0725766	−	0.997363i	$-0.476878\pi$
$839$	−24.7233	−	17.9626i	−0.853544	−	0.620136i	−0.926121	+	0.377227i	$0.876878\pi$
$840$	−1.74311	−	1.74995i	−0.0601429	−	0.0603791i
$841$	−14.0319	+	10.1948i	−0.483859	+	0.351544i
$842$	44.6040	+	8.80312i	1.53716	+	0.303375i
$843$	1.98512			0.0683711
$844$	−2.05103	−	0.155262i	−0.0705994	−	0.00534433i
$845$	−2.37346	−	21.2228i	−0.0816495	−	0.730086i
$846$	−3.53469	+	1.63591i	−0.121525	+	0.0562438i
$847$	−18.7723	+	6.09949i	−0.645024	+	0.209581i
$848$	−21.2998	−	3.24335i	−0.731439	−	0.111377i
$849$	−5.15814			−0.177027
$850$	31.0579	−	0.866366i	1.06528	−	0.0297161i
$851$			45.4930i			1.55948i
$852$	6.55999	+	2.69433i	0.224741	+	0.0923061i
$853$	3.92833	+	12.0902i	0.134504	+	0.413960i	0.995512	−	0.0946304i	$-0.0301669\pi$
$853$	3.92833	+	12.0902i	0.134504	+	0.413960i	−0.861009	+	0.508590i	$0.830167\pi$
$854$	4.93628	+	10.6657i	0.168916	+	0.364973i
$855$	−14.5313	+	13.2601i	−0.496958	+	0.453486i
$856$	0.195570	+	4.46765i	0.00668446	+	0.152701i
$857$		−	36.9869i		−	1.26345i	−0.775194	−	0.631724i	$-0.782348\pi$
$857$		−	36.9869i		−	1.26345i	0.775194	−	0.631724i	$-0.217652\pi$
$858$	3.05218	+	0.602383i	0.104200	+	0.0205650i
$859$	−16.1605	−	22.2430i	−0.551388	−	0.758921i	0.438811	−	0.898579i	$-0.355400\pi$
$859$	−16.1605	−	22.2430i	−0.551388	−	0.758921i	−0.990200	+	0.139658i	$0.955400\pi$
$860$	−40.6487	−	27.3640i	−1.38611	−	0.933106i
$861$	1.97278	−	2.71530i	0.0672323	−	0.0925373i
$862$	−3.83129	+	3.55223i	−0.130494	+	0.120989i
$863$	27.0253	+	37.1971i	0.919951	+	1.26620i	0.963652	+	0.267159i	$0.0860850\pi$
$863$	27.0253	+	37.1971i	0.919951	+	1.26620i	−0.0437013	+	0.999045i	$0.513915\pi$
$864$	−8.22658	−	0.261762i	−0.279874	−	0.00890533i
$865$	−39.5178	−	8.12536i	−1.34364	−	0.276271i
$866$	9.62940	+	10.3859i	0.327220	+	0.352927i
$867$	0.174615	−	0.537409i	0.00593023	−	0.0182514i
$868$	0.922365	+	3.79203i	0.0313071	+	0.128710i
$869$	−48.6576	−	15.8098i	−1.65060	−	0.536311i
$870$	1.37059	+	2.26162i	0.0464672	+	0.0766761i
$871$	1.40694	+	4.33011i	0.0476722	+	0.146720i
$872$	−8.01282	+	6.37517i	−0.271348	+	0.215890i
$873$	−24.7307	+	34.0389i	−0.837008	+	1.15204i
$874$	−24.1684	+	2.89710i	−0.817508	+	0.0979958i
$875$	17.0595	+	5.16892i	0.576717	+	0.174741i
$876$	0.372326	+	1.53071i	0.0125797	+	0.0517178i
$877$	−14.3723	−	10.4421i	−0.485317	−	0.352604i	0.318063	−	0.948069i	$-0.396968\pi$
$877$	−14.3723	−	10.4421i	−0.485317	−	0.352604i	−0.803381	+	0.595466i	$0.796968\pi$
$878$	−17.1058	−	36.9602i	−0.577293	−	1.24735i
$879$	1.99596	+	6.14292i	0.0673220	+	0.207196i
$880$	−33.9511	−	26.7906i	−1.14449	−	0.903113i
$881$	−1.85556	+	5.71084i	−0.0625155	+	0.192403i	−0.977436	−	0.211231i	$-0.932253\pi$
$881$	−1.85556	+	5.71084i	−0.0625155	+	0.192403i	0.914921	+	0.403634i	$0.132253\pi$
$882$	−18.4038	+	2.20609i	−0.619690	+	0.0742830i
$883$	7.67204	−	23.6121i	0.258185	−	0.794611i	−0.735001	−	0.678066i	$-0.762818\pi$
$883$	7.67204	−	23.6121i	0.258185	−	0.794611i	0.993185	−	0.116545i	$-0.0371818\pi$
$884$	−12.4430	−	10.5633i	−0.418505	−	0.355282i
$885$	1.02437	−	4.98202i	0.0344337	−	0.167469i
$886$	−26.8857	−	15.0041i	−0.903243	−	0.504071i
$887$	4.59197	+	6.32030i	0.154183	+	0.212215i	0.879120	−	0.476600i	$-0.158131\pi$
$887$	4.59197	+	6.32030i	0.154183	+	0.212215i	−0.724937	+	0.688815i	$0.758131\pi$
$888$	3.02390	−	4.56974i	0.101475	−	0.153351i
$889$	−13.0771	−	9.50107i	−0.438592	−	0.318655i
$890$	27.2134	+	23.4761i	0.912195	+	0.786922i
$891$	−24.0546	−	33.1083i	−0.805858	−	1.10917i
$892$	40.6097	+	3.07412i	1.35971	+	0.102929i
$893$	2.80317			0.0938046
$894$	4.26486	+	0.841719i	0.142638	+	0.0281513i
$895$	−7.59060	+	6.92660i	−0.253726	+	0.231531i
$896$	7.38027	−	16.4591i	0.246557	−	0.549860i
$897$	−2.48880	+	0.808660i	−0.0830986	+	0.0270004i
$898$	2.92020	+	1.62967i	0.0974484	+	0.0543829i
$899$		−	4.17837i		−	0.139356i
$900$	26.3263	−	13.0876i	0.877543	−	0.436254i
$901$		−	23.6673i		−	0.788473i
$902$	28.6386	−	51.3173i	0.953560	−	1.70868i
$903$	−4.06966	+	1.32231i	−0.135430	+	0.0440039i
$904$	44.7011	−	35.5652i	1.48674	−	1.18288i
$905$	−48.7256	+	5.44925i	−1.61969	+	0.181139i
$906$	−0.680577	+	3.44838i	−0.0226107	+	0.114565i
$907$	−33.1767			−1.10162			−0.550808	−	0.834632i	$-0.685680\pi$
$907$	−33.1767			−1.10162			−0.550808	+	0.834632i	$0.685680\pi$
$908$	0.184954	−	2.44327i	0.00613791	−	0.0810828i
$909$	−16.1673	−	22.2524i	−0.536235	−	0.738064i
$910$	−4.85329	−	8.00848i	−0.160885	−	0.265478i
$911$	3.00382	+	2.18240i	0.0995209	+	0.0723062i	0.636433	−	0.771332i	$-0.280409\pi$
$911$	3.00382	+	2.18240i	0.0995209	+	0.0723062i	−0.536912	+	0.843638i	$0.680409\pi$
$912$	2.62027	+	1.31545i	0.0867658	+	0.0435590i
$913$	4.96411	+	6.83251i	0.164288	+	0.226123i
$914$	7.85029	−	14.0669i	0.259665	−	0.465292i
$915$	2.83726	−	0.317307i	0.0937971	−	0.0104898i
$916$	−1.48707	−	1.26243i	−0.0491343	−	0.0417117i
$917$	−3.01608	+	9.28255i	−0.0995998	+	0.306537i
$918$	−1.07610	−	8.97712i	−0.0355165	−	0.296289i
$919$	10.6715	−	32.8435i	0.352020	−	1.08341i	−0.605697	−	0.795695i	$-0.707106\pi$
$919$	10.6715	−	32.8435i	0.352020	−	1.08341i	0.957717	−	0.287711i	$-0.0928944\pi$
$920$	35.9194	+	5.76127i	1.18423	+	0.189943i
$921$	−1.43440	−	4.41464i	−0.0472652	−	0.145467i
$922$	47.1228	−	21.8092i	1.55191	−	0.718249i
$923$	21.7518	+	15.8036i	0.715968	+	0.520181i
$924$	−3.66973	+	0.892616i	−0.120725	+	0.0293649i
$925$	−3.61000	+	39.3806i	−0.118696	+	1.29483i
$926$	−2.57885	−	21.5135i	−0.0847462	−	0.706977i
$927$	−15.5284	+	21.3730i	−0.510019	+	0.701981i
$928$	−11.8429	+	15.2554i	−0.388761	+	0.500781i
$929$	0.229893	+	0.707539i	0.00754256	+	0.0232136i	0.954757	−	0.297387i	$-0.0961152\pi$
$929$	0.229893	+	0.707539i	0.00754256	+	0.0232136i	−0.947214	+	0.320601i	$0.896115\pi$
$930$	0.944718	+	0.0790531i	0.0309785	+	0.00259225i
$931$	12.6872	+	4.12233i	0.415807	+	0.135104i
$932$	1.19553	+	4.91505i	0.0391607	+	0.160998i
$933$	1.00309	−	3.08718i	0.0328395	−	0.101070i
$934$	−31.3251	+	29.0435i	−1.02499	+	0.950331i
$935$	23.4797	−	41.3001i	0.767867	−	1.35066i
$936$	−14.8836	−	4.12577i	−0.486486	−	0.134855i
$937$	14.4220	+	19.8502i	0.471148	+	0.648479i	0.976774	−	0.214274i	$-0.0687384\pi$
$937$	14.4220	+	19.8502i	0.471148	+	0.648479i	−0.505626	+	0.862753i	$0.668738\pi$
$938$	−3.75787	−	4.05309i	−0.122699	−	0.132338i
$939$	2.47610	−	3.40806i	0.0808046	−	0.111218i
$940$	−4.02813	−	1.15108i	−0.131383	−	0.0375440i
$941$	−6.85654	−	9.43722i	−0.223517	−	0.307645i	0.682500	−	0.730885i	$-0.260892\pi$
$941$	−6.85654	−	9.43722i	−0.223517	−	0.307645i	−0.906017	+	0.423241i	$0.860892\pi$
$942$	−0.517157	+	2.62035i	−0.0168499	+	0.0853757i
$943$			49.4326i			1.60975i
$944$	36.6518	−	6.02957i	1.19292	−	0.196246i
$945$	1.04470	−	5.08091i	0.0339841	−	0.165282i
$946$	−67.9962	+	31.4698i	−2.21075	+	1.02317i
$947$	−15.2784	−	47.0221i	−0.496481	−	1.52801i	−0.814635	−	0.579973i	$-0.803063\pi$
$947$	−15.2784	−	47.0221i	−0.496481	−	1.52801i	0.318154	−	0.948039i	$-0.396937\pi$
$948$	−4.79488	−	1.96936i	−0.155730	−	0.0639618i
$949$			5.97252i			0.193876i
$950$	−21.1511	+	0.590014i	−0.686231	+	0.0191426i
$951$	−0.568657			−0.0184400
$952$	19.0945	+	5.29305i	0.618857	+	0.171549i
$953$	35.8144	−	11.6368i	1.16014	−	0.376953i	0.335187	−	0.942151i	$-0.391200\pi$
$953$	35.8144	−	11.6368i	1.16014	−	0.376953i	0.824955	+	0.565198i	$0.191200\pi$
$954$	−9.40633	−	20.3241i	−0.304541	−	0.658016i
$955$	−7.51918	+	13.2260i	−0.243315	+	0.427984i
$956$	2.98062	−	39.3745i	0.0964003	−	1.27346i
$957$	4.04361			0.130711
$958$	−9.20954	+	46.6633i	−0.297547	+	1.50762i
$959$	3.04126	−	2.20961i	0.0982075	−	0.0713519i
$960$	−3.22513	−	2.96626i	−0.104091	−	0.0957357i
$961$	23.8677	+	17.3409i	0.769926	+	0.559384i
$962$	15.2343	−	14.1247i	0.491174	−	0.455398i
$963$	−3.76058	+	2.73222i	−0.121183	+	0.0880446i
$964$	29.5007	+	12.1165i	0.950152	+	0.390248i
$965$	−5.46690	−	12.0623i	−0.175986	−	0.388298i
$966$	2.32958	−	2.15990i	0.0749531	−	0.0694936i
$967$	−3.60438	−	1.17113i	−0.115909	−	0.0376611i	0.250488	−	0.968120i	$-0.419409\pi$
$967$	−3.60438	−	1.17113i	−0.115909	−	0.0376611i	−0.366397	+	0.930459i	$0.619409\pi$
$968$	−32.7976	+	12.2668i	−1.05415	+	0.394268i
$969$	−0.995250	+	3.06306i	−0.0319720	+	0.0983998i
$970$	−44.0567	+	10.3470i	−1.41458	+	0.332221i
$971$	50.3226	−	16.3508i	1.61493	−	0.524722i	0.644191	−	0.764865i	$-0.277194\pi$
$971$	50.3226	−	16.3508i	1.61493	−	0.524722i	0.970738	+	0.240143i	$0.0771943\pi$
$972$	−6.76061	−	10.9588i	−0.216847	−	0.351502i
$973$	25.4613	+	18.4987i	0.816253	+	0.593043i
$974$	6.00387	+	50.0860i	0.192376	+	1.60486i
$975$	−2.21858	+	0.502516i	−0.0710514	+	0.0160934i
$976$	9.57621	+	18.5202i	0.306527	+	0.592818i
$977$	23.6179	−	32.5072i	0.755603	−	1.04000i	−0.241964	−	0.970285i	$-0.577792\pi$
$977$	23.6179	−	32.5072i	0.755603	−	1.04000i	0.997567	−	0.0697129i	$-0.0222083\pi$
$978$	−1.37592	−	2.97293i	−0.0439972	−	0.0950639i
$979$	52.2650	−	16.9819i	1.67040	−	0.542745i
$980$	−16.5387	−	11.1336i	−0.528308	−	0.355649i
$981$	−10.1225	−	3.28901i	−0.323187	−	0.105010i
$982$	5.55302	+	46.3249i	0.177204	+	1.47829i
$983$	8.03684	+	2.61133i	0.256336	+	0.0832885i	0.434366	−	0.900737i	$-0.356973\pi$
$983$	8.03684	+	2.61133i	0.256336	+	0.0832885i	−0.178030	+	0.984025i	$0.556973\pi$
$984$	3.28577	−	4.96548i	0.104746	−	0.158294i
$985$	−14.0704	−	15.4192i	−0.448321	−	0.491298i
$986$	−18.5252	−	10.3383i	−0.589964	−	0.329240i
$987$	−0.295974	+	0.215037i	−0.00942094	+	0.00684472i
$988$	8.47397	+	7.19383i	0.269593	+	0.228866i
$989$	37.0445	−	50.9874i	1.17795	−	1.62130i
$990$	3.74864	−	44.7977i	0.119139	−	1.42377i
$991$	19.3979	−	14.0934i	0.616193	−	0.447691i	−0.235397	−	0.971899i	$-0.575639\pi$
$991$	19.3979	−	14.0934i	0.616193	−	0.447691i	0.851590	+	0.524209i	$0.175639\pi$
$992$	1.92894	+	6.64918i	0.0612438	+	0.211112i
$993$			2.79980i			0.0888490i
$994$	−32.0219	−	6.31988i	−1.01567	−	0.200454i
$995$	43.8549	−	19.8761i	1.39030	−	0.630115i
$996$	0.449262	+	0.728241i	0.0142354	+	0.0230752i
$997$	−2.81825	−	8.67368i	−0.0892548	−	0.274698i	0.896459	−	0.443127i	$-0.146131\pi$
$997$	−2.81825	−	8.67368i	−0.0892548	−	0.274698i	−0.985714	+	0.168428i	$0.946131\pi$
$998$	23.9789	−	42.9676i	0.759038	−	1.36012i
$999$	11.5078			0.364092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.109.5	✓	112
4.3	odd	2		800.2.be.a.209.15		112
5.2	odd	4		1000.2.t.b.701.37		224
5.3	odd	4		1000.2.t.b.701.20		224
5.4	even	2		1000.2.o.a.549.24		112
8.3	odd	2		800.2.be.a.209.14		112
8.5	even	2	inner	200.2.o.a.109.22	yes	112
25.2	odd	20		1000.2.t.b.301.16		224
25.11	even	5		1000.2.o.a.949.7		112
25.14	even	10	inner	200.2.o.a.189.22	yes	112
25.23	odd	20		1000.2.t.b.301.41		224
40.13	odd	4		1000.2.t.b.701.41		224
40.29	even	2		1000.2.o.a.549.7		112
40.37	odd	4		1000.2.t.b.701.16		224
100.39	odd	10		800.2.be.a.689.14		112
200.61	even	10		1000.2.o.a.949.24		112
200.77	odd	20		1000.2.t.b.301.37		224
200.139	odd	10		800.2.be.a.689.15		112
200.173	odd	20		1000.2.t.b.301.20		224
200.189	even	10	inner	200.2.o.a.189.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.5	✓	112	1.1	even	1	trivial
200.2.o.a.109.22	yes	112	8.5	even	2	inner
200.2.o.a.189.5	yes	112	200.189	even	10	inner
200.2.o.a.189.22	yes	112	25.14	even	10	inner
800.2.be.a.209.14		112	8.3	odd	2
800.2.be.a.209.15		112	4.3	odd	2
800.2.be.a.689.14		112	100.39	odd	10
800.2.be.a.689.15		112	200.139	odd	10
1000.2.o.a.549.7		112	40.29	even	2
1000.2.o.a.549.24		112	5.4	even	2
1000.2.o.a.949.7		112	25.11	even	5
1000.2.o.a.949.24		112	200.61	even	10
1000.2.t.b.301.16		224	25.2	odd	20
1000.2.t.b.301.20		224	200.173	odd	20
1000.2.t.b.301.37		224	200.77	odd	20
1000.2.t.b.301.41		224	25.23	odd	20
1000.2.t.b.701.16		224	40.37	odd	4
1000.2.t.b.701.20		224	5.3	odd	4
1000.2.t.b.701.37		224	5.2	odd	4
1000.2.t.b.701.41		224	40.13	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+(-1.23493 - 0.689173i) q^{2} +(-0.0756938 - 0.232961i) q^{3} +(1.05008 + 1.70215i) q^{4} +(-2.03665 + 0.923061i) q^{5} +(-0.0670745 + 0.339856i) q^{6} -1.59435i q^{7} +(-0.123695 - 2.82572i) q^{8} +(2.37851 - 1.72809i) q^{9} +(3.15126 + 0.263695i) q^{10} +(2.84212 - 3.91185i) q^{11} +(0.317052 - 0.373471i) q^{12} +(1.50262 - 1.09172i) q^{13} +(-1.09878 + 1.96890i) q^{14} +(0.369200 + 0.404592i) q^{15} +(-1.79466 + 3.57480i) q^{16} +(-4.17890 - 1.35781i) q^{17} +(-4.12823 + 0.494857i) q^{18} +(2.84592 + 0.924695i) q^{19} +(-3.70984 - 2.49741i) q^{20} +(-0.371422 + 0.120682i) q^{21} +(-6.20575 + 2.87212i) q^{22} +(3.38091 - 4.65342i) q^{23} +(-0.648921 + 0.242706i) q^{24} +(3.29592 - 3.75991i) q^{25} +(-2.60801 + 0.312625i) q^{26} +(-1.17712 - 0.855230i) q^{27} +(2.71383 - 1.67420i) q^{28} +(-3.24693 + 1.05499i) q^{29} +(-0.177100 - 0.754083i) q^{30} +(-0.378200 + 1.16398i) q^{31} +(4.67992 - 3.17779i) q^{32} +(-1.12644 - 0.366003i) q^{33} +(4.22487 + 4.55678i) q^{34} +(1.47168 + 3.24714i) q^{35} +(5.43910 + 2.23395i) q^{36} +(-6.39864 + 4.64888i) q^{37} +(-2.87722 - 3.10326i) q^{38} +(-0.368067 - 0.267416i) q^{39} +(2.86024 + 5.64084i) q^{40} +(-6.95275 + 5.05147i) q^{41} +(0.541850 + 0.106940i) q^{42} +10.9570 q^{43} +(9.64302 + 0.729970i) q^{44} +(-3.24907 + 5.71503i) q^{45} +(-7.38218 + 3.41660i) q^{46} +(0.890923 - 0.289478i) q^{47} +(0.968635 + 0.147495i) q^{48} +4.45804 q^{49} +(-6.66144 + 2.37175i) q^{50} +1.07630i q^{51} +(3.43614 + 1.41130i) q^{52} +(1.66447 + 5.12271i) q^{53} +(0.864258 + 1.86739i) q^{54} +(-2.17755 + 10.5905i) q^{55} +(-4.50519 + 0.197214i) q^{56} -0.732983i q^{57} +(4.73679 + 0.934861i) q^{58} +(-5.45825 - 7.51263i) q^{59} +(-0.300988 + 1.05329i) q^{60} +(3.06376 - 4.21690i) q^{61} +(1.26923 - 1.17678i) q^{62} +(-2.75518 - 3.79218i) q^{63} +(-7.96940 + 0.699057i) q^{64} +(-2.05260 + 3.61046i) q^{65} +(1.13883 + 1.22830i) q^{66} +(-0.757501 + 2.33135i) q^{67} +(-2.07699 - 8.53894i) q^{68} +(-1.33998 - 0.435386i) q^{69} +(0.420422 - 5.02422i) q^{70} +(4.47330 + 13.7674i) q^{71} +(-5.17731 - 6.50725i) q^{72} +(-1.89010 + 2.60150i) q^{73} +(11.1057 - 1.33126i) q^{74} +(-1.12539 - 0.483220i) q^{75} +(1.41448 + 5.81520i) q^{76} +(-6.23686 - 4.53134i) q^{77} +(0.270239 + 0.583901i) q^{78} +(-3.26966 - 10.0630i) q^{79} +(0.355332 - 8.93721i) q^{80} +(2.61539 - 8.04936i) q^{81} +(12.0675 - 1.44654i) q^{82} +(-0.539736 + 1.66114i) q^{83} +(-0.595444 - 0.505491i) q^{84} +(9.76431 - 1.09200i) q^{85} +(-13.5310 - 7.55125i) q^{86} +(0.491545 + 0.676554i) q^{87} +(-11.4053 - 7.54717i) q^{88} +(9.19471 + 6.68035i) q^{89} +(7.95100 - 4.81846i) q^{90} +(-1.74058 - 2.39570i) q^{91} +(11.4711 + 0.868351i) q^{92} +0.299790 q^{93} +(-1.29972 - 0.256515i) q^{94} +(-6.64970 + 0.743672i) q^{95} +(-1.09454 - 0.849703i) q^{96} +(-13.6106 + 4.42235i) q^{97} +(-5.50535 - 3.07236i) q^{98} -14.2158i 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

L-functions

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