LMFDB - Embedded newform 572.2.bs.a.15.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.4
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40184 + 0.186682i) q^{2} +(0.154145 + 0.725193i) q^{3} +(1.93030 - 0.523395i) q^{4} +(0.469822 - 2.96634i) q^{5} +(-0.351466 - 0.987827i) q^{6} +(-2.19466 + 1.42523i) q^{7} +(-2.60826 + 1.09407i) q^{8} +(2.23849 - 0.996641i) q^{9} +O(q^{10})$	\(q+(-1.40184 + 0.186682i) q^{2} +(0.154145 + 0.725193i) q^{3} +(1.93030 - 0.523395i) q^{4} +(0.469822 - 2.96634i) q^{5} +(-0.351466 - 0.987827i) q^{6} +(-2.19466 + 1.42523i) q^{7} +(-2.60826 + 1.09407i) q^{8} +(2.23849 - 0.996641i) q^{9} +(-0.104853 + 4.24603i) q^{10} +(-2.99570 - 1.42329i) q^{11} +(0.677108 + 1.31916i) q^{12} +(2.73260 - 2.35222i) q^{13} +(2.81049 - 2.40764i) q^{14} +(2.22359 - 0.116533i) q^{15} +(3.45212 - 2.02062i) q^{16} +(-6.00252 + 0.630890i) q^{17} +(-2.95195 + 1.81501i) q^{18} +(0.0779342 - 1.48707i) q^{19} +(-0.645669 - 5.97183i) q^{20} +(-1.37186 - 1.37186i) q^{21} +(4.46519 + 1.43598i) q^{22} +(-2.26551 - 3.92398i) q^{23} +(-1.19546 - 1.72285i) q^{24} +(-3.82315 - 1.24222i) q^{25} +(-3.39154 + 3.80755i) q^{26} +(2.37515 + 3.26911i) q^{27} +(-3.49039 + 3.89979i) q^{28} +(-5.11266 + 5.67819i) q^{29} +(-3.09536 + 0.578464i) q^{30} +(-0.677349 - 4.27661i) q^{31} +(-4.46209 + 3.47703i) q^{32} +(0.570391 - 2.39186i) q^{33} +(8.29678 - 2.00497i) q^{34} +(3.19661 + 7.17971i) q^{35} +(3.79932 - 3.09543i) q^{36} +(-5.12523 + 0.268602i) q^{37} +(0.168358 + 2.09918i) q^{38} +(2.12703 + 1.61908i) q^{39} +(2.01995 + 8.25100i) q^{40} +(4.64040 - 7.14560i) q^{41} +(2.17923 + 1.66703i) q^{42} +(1.96816 - 3.40896i) q^{43} +(-6.52755 - 1.17945i) q^{44} +(-1.90468 - 7.10837i) q^{45} +(3.90841 + 5.07785i) q^{46} +(-5.57572 - 10.9430i) q^{47} +(1.99746 + 2.19198i) q^{48} +(-0.0619014 + 0.139033i) q^{49} +(5.59133 + 1.02767i) q^{50} +(-1.38277 - 4.25574i) q^{51} +(4.04359 - 5.97071i) q^{52} +(5.44474 + 3.95583i) q^{53} +(-3.93986 - 4.13937i) q^{54} +(-5.62941 + 8.21758i) q^{55} +(4.16495 - 6.11847i) q^{56} +(1.09043 - 0.172707i) q^{57} +(6.10711 - 8.91434i) q^{58} +(2.07266 - 1.34600i) q^{59} +(4.23120 - 1.38876i) q^{60} +(-1.19927 - 11.4103i) q^{61} +(1.74790 + 5.86867i) q^{62} +(-3.49229 + 5.37765i) q^{63} +(5.60604 - 5.70722i) q^{64} +(-5.69364 - 9.21093i) q^{65} +(-0.353080 + 3.45948i) q^{66} +(-3.60263 + 13.4452i) q^{67} +(-11.2565 + 4.35949i) q^{68} +(2.49642 - 2.24779i) q^{69} +(-5.82145 - 9.46804i) q^{70} +(8.58491 - 10.6015i) q^{71} +(-4.74818 + 5.04856i) q^{72} +(6.18073 - 12.1304i) q^{73} +(7.13460 - 1.33332i) q^{74} +(0.311529 - 2.96400i) q^{75} +(-0.627890 - 2.91129i) q^{76} +(8.60307 - 1.14592i) q^{77} +(-3.28400 - 1.87261i) q^{78} +(5.16600 - 7.11039i) q^{79} +(-4.37196 - 11.1895i) q^{80} +(2.91416 - 3.23650i) q^{81} +(-5.17114 + 10.8832i) q^{82} +(-10.3436 - 1.63827i) q^{83} +(-3.36613 - 1.93008i) q^{84} +(-0.948681 + 18.1019i) q^{85} +(-2.12266 + 5.14623i) q^{86} +(-4.90587 - 2.83241i) q^{87} +(9.37075 + 0.434818i) q^{88} +(-2.74795 + 10.2555i) q^{89} +(3.99706 + 9.60921i) q^{90} +(-2.64467 + 9.05689i) q^{91} +(-6.42690 - 6.38869i) q^{92} +(2.99696 - 1.15043i) q^{93} +(9.85910 + 14.2994i) q^{94} +(-4.37455 - 0.929838i) q^{95} +(-3.20932 - 2.69992i) q^{96} +(-4.95274 + 12.9023i) q^{97} +(0.0608208 - 0.206457i) q^{98} +(-8.12437 - 0.200389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−1.40184	+	0.186682i	−0.991249	+	0.132004i
$2$	−1.40184	+	0.186682i	−0.991249	+	0.132004i
$3$	0.154145	+	0.725193i	0.0889954	+	0.418690i	0.999980	+	0.00625111i	$0.00198980\pi$
$3$	0.154145	+	0.725193i	0.0889954	+	0.418690i	−0.910985	+	0.412439i	$0.864677\pi$
$4$	1.93030	−	0.523395i	0.965150	−	0.261697i
$5$	0.469822	−	2.96634i	0.210111	−	1.32659i	−0.626771	−	0.779203i	$-0.715624\pi$
$5$	0.469822	−	2.96634i	0.210111	−	1.32659i	0.836882	−	0.547384i	$-0.184376\pi$
$6$	−0.351466	−	0.987827i	−0.143485	−	0.403279i
$7$	−2.19466	+	1.42523i	−0.829504	+	0.538686i	−0.888129	−	0.459594i	$-0.847995\pi$
$7$	−2.19466	+	1.42523i	−0.829504	+	0.538686i	0.0586255	+	0.998280i	$0.481328\pi$
$8$	−2.60826	+	1.09407i	−0.922159	+	0.386811i
$9$	2.23849	−	0.996641i	0.746164	−	0.332214i
$10$	−0.104853	+	4.24603i	−0.0331575	+	1.34271i
$11$	−2.99570	−	1.42329i	−0.903239	−	0.429139i
$11$	−2.99570	−	1.42329i	−0.903239	−	0.429139i
$12$	0.677108	+	1.31916i	0.195464	+	0.380809i
$13$	2.73260	−	2.35222i	0.757886	−	0.652388i
$13$	2.73260	−	2.35222i	0.757886	−	0.652388i
$14$	2.81049	−	2.40764i	0.751136	−	0.643470i
$15$	2.22359	−	0.116533i	0.574128	−	0.0300888i
$16$	3.45212	−	2.02062i	0.863029	−	0.505155i
$17$	−6.00252	+	0.630890i	−1.45582	+	0.153013i	−0.799137	−	0.601149i	$-0.794710\pi$
$17$	−6.00252	+	0.630890i	−1.45582	+	0.153013i	−0.656688	+	0.754163i	$0.728043\pi$
$18$	−2.95195	+	1.81501i	−0.695781	+	0.427803i
$19$	0.0779342	−	1.48707i	0.0178793	−	0.341158i	−0.975013	−	0.222146i	$-0.928694\pi$
$19$	0.0779342	−	1.48707i	0.0178793	−	0.341158i	0.992893	−	0.119012i	$-0.0379727\pi$
$20$	−0.645669	−	5.97183i	−0.144376	−	1.33534i
$21$	−1.37186	−	1.37186i	−0.299365	−	0.299365i
$22$	4.46519	+	1.43598i	0.951982	+	0.306153i
$23$	−2.26551	−	3.92398i	−0.472391	−	0.818205i	0.527110	−	0.849797i	$-0.323276\pi$
$23$	−2.26551	−	3.92398i	−0.472391	−	0.818205i	−0.999501	+	0.0315918i	$0.989942\pi$
$24$	−1.19546	−	1.72285i	−0.244022	−	0.351675i
$25$	−3.82315	−	1.24222i	−0.764630	−	0.248443i
$26$	−3.39154	+	3.80755i	−0.665136	+	0.746722i
$27$	2.37515	+	3.26911i	0.457098	+	0.629141i
$28$	−3.49039	+	3.89979i	−0.659623	+	0.736992i
$29$	−5.11266	+	5.67819i	−0.949397	+	1.05441i	0.0490548	+	0.998796i	$0.484379\pi$
$29$	−5.11266	+	5.67819i	−0.949397	+	1.05441i	−0.998452	+	0.0556166i	$0.982288\pi$
$30$	−3.09536	+	0.578464i	−0.565132	+	0.105613i
$31$	−0.677349	−	4.27661i	−0.121655	−	0.768102i	−0.970791	−	0.239927i	$-0.922876\pi$
$31$	−0.677349	−	4.27661i	−0.121655	−	0.768102i	0.849135	−	0.528175i	$-0.177124\pi$
$32$	−4.46209	+	3.47703i	−0.788794	+	0.614657i
$33$	0.570391	−	2.39186i	0.0992923	−	0.416369i
$34$	8.29678	−	2.00497i	1.42289	−	0.343849i
$35$	3.19661	+	7.17971i	0.540326	+	1.21359i
$36$	3.79932	−	3.09543i	0.633221	−	0.515905i
$37$	−5.12523	+	0.268602i	−0.842583	+	0.0441579i	−0.468742	−	0.883335i	$-0.655293\pi$
$37$	−5.12523	+	0.268602i	−0.842583	+	0.0441579i	−0.373841	+	0.927493i	$0.621959\pi$
$38$	0.168358	+	2.09918i	0.0273113	+	0.340533i
$39$	2.12703	+	1.61908i	0.340597	+	0.259260i
$40$	2.01995	+	8.25100i	0.319383	+	1.30460i
$41$	4.64040	−	7.14560i	0.724709	−	1.11595i	−0.263768	−	0.964586i	$-0.584965\pi$
$41$	4.64040	−	7.14560i	0.724709	−	1.11595i	0.988477	−	0.151369i	$-0.0483680\pi$
$42$	2.17923	+	1.66703i	0.336262	+	0.257228i
$43$	1.96816	−	3.40896i	0.300142	−	0.519861i	−0.676026	−	0.736878i	$-0.736299\pi$
$43$	1.96816	−	3.40896i	0.300142	−	0.519861i	0.976168	+	0.217017i	$0.0696326\pi$
$44$	−6.52755	−	1.17945i	−0.984065	−	0.177808i
$45$	−1.90468	−	7.10837i	−0.283933	−	1.05965i
$46$	3.90841	+	5.07785i	0.576264	+	0.748688i
$47$	−5.57572	−	10.9430i	−0.813302	−	1.59619i	−0.802799	−	0.596250i	$-0.796657\pi$
$47$	−5.57572	−	10.9430i	−0.813302	−	1.59619i	−0.0105029	−	0.999945i	$-0.503343\pi$
$48$	1.99746	+	2.19198i	0.288309	+	0.316386i
$49$	−0.0619014	+	0.139033i	−0.00884305	+	0.0198618i
$50$	5.59133	+	1.02767i	0.790734	+	0.145335i
$51$	−1.38277	−	4.25574i	−0.193627	−	0.595922i
$52$	4.04359	−	5.97071i	0.560745	−	0.827989i
$53$	5.44474	+	3.95583i	0.747892	+	0.543376i	0.895173	−	0.445719i	$-0.147052\pi$
$53$	5.44474	+	3.95583i	0.747892	+	0.543376i	−0.147281	+	0.989095i	$0.547052\pi$
$54$	−3.93986	−	4.13937i	−0.536147	−	0.563297i
$55$	−5.62941	+	8.21758i	−0.759070	+	1.10806i
$56$	4.16495	−	6.11847i	0.556565	−	0.817615i
$57$	1.09043	−	0.172707i	0.144431	−	0.0228756i
$58$	6.10711	−	8.91434i	0.801903	−	1.17051i
$59$	2.07266	−	1.34600i	0.269837	−	0.175234i	−0.402627	−	0.915364i	$-0.631903\pi$
$59$	2.07266	−	1.34600i	0.269837	−	0.175234i	0.672464	+	0.740130i	$0.265236\pi$
$60$	4.23120	−	1.38876i	0.546246	−	0.179288i
$61$	−1.19927	−	11.4103i	−0.153551	−	1.46094i	−0.751673	−	0.659536i	$-0.770753\pi$
$61$	−1.19927	−	11.4103i	−0.153551	−	1.46094i	0.598122	−	0.801405i	$-0.295914\pi$
$62$	1.74790	+	5.86867i	0.221983	+	0.745322i
$63$	−3.49229	+	5.37765i	−0.439987	+	0.677520i
$64$	5.60604	−	5.70722i	0.700755	−	0.713402i
$65$	−5.69364	−	9.21093i	−0.706209	−	1.14247i
$66$	−0.353080	+	3.45948i	−0.0434611	+	0.425832i
$67$	−3.60263	+	13.4452i	−0.440132	+	1.64259i	0.288347	+	0.957526i	$0.406894\pi$
$67$	−3.60263	+	13.4452i	−0.440132	+	1.64259i	−0.728479	+	0.685068i	$0.759772\pi$
$68$	−11.2565	+	4.35949i	−1.36505	+	0.528666i
$69$	2.49642	−	2.24779i	0.300534	−	0.270602i
$70$	−5.82145	−	9.46804i	−0.695797	−	1.13165i
$71$	8.58491	−	10.6015i	1.01884	−	1.25816i	0.0531183	−	0.998588i	$-0.483084\pi$
$71$	8.58491	−	10.6015i	1.01884	−	1.25816i	0.965723	−	0.259576i	$-0.0835827\pi$
$72$	−4.74818	+	5.04856i	−0.559578	+	0.594978i
$73$	6.18073	−	12.1304i	0.723399	−	1.41975i	−0.176789	−	0.984249i	$-0.556571\pi$
$73$	6.18073	−	12.1304i	0.723399	−	1.41975i	0.900188	−	0.435502i	$-0.143429\pi$
$74$	7.13460	−	1.33332i	0.829381	−	0.154996i
$75$	0.311529	−	2.96400i	0.0359723	−	0.342254i
$76$	−0.627890	−	2.91129i	−0.0720239	−	0.333947i
$77$	8.60307	−	1.14592i	0.980411	−	0.130590i
$78$	−3.28400	−	1.87261i	−0.371840	−	0.212031i
$79$	5.16600	−	7.11039i	0.581220	−	0.799981i	−0.412608	−	0.910909i	$-0.635382\pi$
$79$	5.16600	−	7.11039i	0.581220	−	0.799981i	0.993828	+	0.110928i	$0.0353821\pi$
$80$	−4.37196	−	11.1895i	−0.488800	−	1.25102i
$81$	2.91416	−	3.23650i	0.323795	−	0.359611i
$82$	−5.17114	+	10.8832i	−0.571057	+	1.20185i
$83$	−10.3436	−	1.63827i	−1.13536	−	0.179824i	−0.439667	−	0.898161i	$-0.644904\pi$
$83$	−10.3436	−	1.63827i	−1.13536	−	0.179824i	−0.695695	+	0.718337i	$0.744904\pi$
$84$	−3.36613	−	1.93008i	−0.367275	−	0.210589i
$85$	−0.948681	+	18.1019i	−0.102899	+	1.96343i
$86$	−2.12266	+	5.14623i	−0.228892	+	0.554932i
$87$	−4.90587	−	2.83241i	−0.525965	−	0.303666i
$88$	9.37075	+	0.434818i	0.998925	+	0.0463518i
$89$	−2.74795	+	10.2555i	−0.291282	+	1.08708i	0.652843	+	0.757493i	$0.273576\pi$
$89$	−2.74795	+	10.2555i	−0.291282	+	1.08708i	−0.944125	+	0.329587i	$0.893091\pi$
$90$	3.99706	+	9.60921i	0.421327	+	1.01290i
$91$	−2.64467	+	9.05689i	−0.277237	+	0.949420i
$92$	−6.42690	−	6.38869i	−0.670051	−	0.666067i
$93$	2.99696	−	1.15043i	0.310770	−	0.119294i
$94$	9.85910	+	14.2994i	1.01689	+	1.47487i
$95$	−4.37455	−	0.929838i	−0.448819	−	0.0953994i
$96$	−3.20932	−	2.69992i	−0.327550	−	0.275559i
$97$	−4.95274	+	12.9023i	−0.502875	+	1.31003i	0.413788	+	0.910373i	$0.364205\pi$
$97$	−4.95274	+	12.9023i	−0.502875	+	1.31003i	−0.916663	+	0.399661i	$0.869128\pi$
$98$	0.0608208	−	0.206457i	0.00614383	−	0.0208553i
$99$	−8.12437	−	0.200389i	−0.816530	−	0.0201398i
$100$	−8.02999	−	0.396834i	−0.802999	−	0.0396834i
$101$	6.48455	+	0.681553i	0.645237	+	0.0678171i	0.421494	−	0.906831i	$-0.361506\pi$
$101$	6.48455	+	0.681553i	0.645237	+	0.0678171i	0.223743	+	0.974648i	$0.428173\pi$
$102$	2.73289	+	5.70771i	0.270597	+	0.565148i
$103$	1.77272	+	5.45589i	0.174672	+	0.537584i	0.999618	−	0.0276264i	$-0.00879486\pi$
$103$	1.77272	+	5.45589i	0.174672	+	0.537584i	−0.824947	+	0.565211i	$0.808795\pi$
$104$	−4.55384	+	9.12483i	−0.446540	+	0.894763i
$105$	−4.71393	+	3.42487i	−0.460033	+	0.334233i
$106$	−8.37112	−	4.52901i	−0.813075	−	0.439896i
$107$	0.685673	+	3.22584i	0.0662865	+	0.311853i	0.998783	−	0.0493264i	$-0.0157074\pi$
$107$	0.685673	+	3.22584i	0.0662865	+	0.311853i	−0.932496	+	0.361180i	$0.882374\pi$
$108$	6.29579	+	5.06723i	0.605813	+	0.487594i
$109$	−2.71719	+	2.71719i	−0.260260	+	0.260260i	−0.825160	−	0.564900i	$-0.808915\pi$
$109$	−2.71719	+	2.71719i	−0.260260	+	0.260260i	0.564900	+	0.825160i	$0.308915\pi$
$110$	6.35746	−	12.5706i	0.606160	−	1.19856i
$111$	−0.984815	−	3.67538i	−0.0934745	−	0.348852i
$112$	−4.69638	+	9.35462i	−0.443766	+	0.883929i
$113$	−3.20157	−	3.55570i	−0.301178	−	0.334492i	0.573492	−	0.819211i	$-0.305588\pi$
$113$	−3.20157	−	3.55570i	−0.301178	−	0.334492i	−0.874670	+	0.484719i	$0.838922\pi$
$114$	−1.49636	+	0.445670i	−0.140147	+	0.0417408i
$115$	−12.7042	+	4.87670i	−1.18468	+	0.454754i
$116$	−6.89704	+	13.6365i	−0.640374	+	1.26612i
$117$	3.77258	−	7.98883i	0.348775	−	0.738568i
$118$	−2.65426	+	2.27380i	−0.244344	+	0.209320i
$119$	12.2743	−	9.93955i	1.12519	−	0.911157i
$120$	−5.67220	+	2.73670i	−0.517799	+	0.249826i
$121$	6.94848	+	8.52752i	0.631680	+	0.775229i
$122$	3.81128	+	15.7715i	0.345057	+	1.42789i
$123$	5.89723	+	2.26374i	0.531735	+	0.204114i
$124$	−3.54584	−	7.90062i	−0.318426	−	0.709497i
$125$	1.33635	−	2.62273i	0.119527	−	0.234584i
$126$	3.89171	−	8.19054i	0.346701	−	0.729671i
$127$	16.0828	+	7.16051i	1.42712	+	0.635393i	0.967533	−	0.252743i	$-0.0813327\pi$
$127$	16.0828	+	7.16051i	1.42712	+	0.635393i	0.459582	+	0.888135i	$0.347999\pi$
$128$	−6.79332	+	9.04714i	−0.600451	+	0.799662i
$129$	2.77553	+	0.901826i	0.244372	+	0.0794013i
$130$	9.70107	+	11.8493i	0.850840	+	1.03925i
$131$		−	4.11874i		−	0.359856i	−0.983680	−	0.179928i	$-0.942414\pi$
$131$		−	4.11874i		−	0.359856i	0.983680	−	0.179928i	$-0.0575865\pi$
$132$	−0.150860	−	4.91554i	−0.0131307	−	0.427843i
$133$	1.94838	+	3.37469i	0.168946	+	0.292623i
$134$	2.54034	−	19.5206i	0.219452	−	1.68632i
$135$	10.8132	−	5.50960i	0.930652	−	0.474191i
$136$	14.9659	−	8.21268i	1.28331	−	0.704231i
$137$	−1.51568	+	1.87171i	−0.129493	+	0.159911i	−0.837769	−	0.546025i	$-0.816140\pi$
$137$	−1.51568	+	1.87171i	−0.129493	+	0.159911i	0.708275	+	0.705936i	$0.249474\pi$
$138$	−3.07996	+	3.61708i	−0.262184	+	0.307906i
$139$	−1.89306	+	8.90615i	−0.160567	+	0.755410i	0.821998	+	0.569491i	$0.192860\pi$
$139$	−1.89306	+	8.90615i	−0.160567	+	0.755410i	−0.982565	+	0.185919i	$0.940474\pi$
$140$	9.92824	+	12.1859i	0.839090	+	1.02990i
$141$	7.07629	−	5.73027i	0.595931	−	0.482576i
$142$	−10.0555	+	16.4642i	−0.843843	+	1.38164i
$143$	−11.5339	+	3.15726i	−0.964516	+	0.264023i
$144$	5.71370	−	7.96366i	0.476142	−	0.663638i
$145$	14.4414	+	17.8336i	1.19929	+	1.48100i
$146$	−6.39986	+	18.1586i	−0.529656	+	1.50282i
$147$	−0.110367	−	0.0234593i	−0.00910295	−	0.00193489i
$148$	−9.75265	+	3.20100i	−0.801663	+	0.263121i
$149$	1.63206	+	1.32162i	0.133704	+	0.108271i	0.693840	−	0.720130i	$-0.255918\pi$
$149$	1.63206	+	1.32162i	0.133704	+	0.108271i	−0.560136	+	0.828401i	$0.689251\pi$
$150$	0.116611	+	4.21321i	0.00952128	+	0.344007i
$151$	4.15162	+	8.14801i	0.337854	+	0.663075i	0.995955	−	0.0898542i	$-0.0286401\pi$
$151$	4.15162	+	8.14801i	0.337854	+	0.663075i	−0.658101	+	0.752929i	$0.728640\pi$
$152$	1.42368	+	3.96394i	0.115476	+	0.321518i
$153$	−12.8078	+	7.39459i	−1.03545	+	0.597818i
$154$	−11.8462	+	3.21243i	−0.954593	+	0.258865i
$155$	−13.0041			−1.04452
$156$	4.95322	+	2.01203i	0.396575	+	0.161091i
$157$	3.68087	−	11.3286i	0.293766	−	0.904118i	−0.689868	−	0.723936i	$-0.742331\pi$
$157$	3.68087	−	11.3286i	0.293766	−	0.904118i	0.983633	−	0.180182i	$-0.0576687\pi$
$158$	−5.91451	+	10.9320i	−0.470534	+	0.869704i
$159$	−2.02947	+	4.55826i	−0.160947	+	0.361493i
$160$	8.21765	+	14.8697i	0.649662	+	1.17555i
$161$	10.5646	+	5.38292i	0.832606	+	0.424234i
$162$	−3.48098	+	5.08107i	−0.273492	+	0.399207i
$163$	0.466056	−	1.21412i	0.0365043	−	0.0950971i	−0.914117	−	0.405451i	$-0.867114\pi$
$163$	0.466056	−	1.21412i	0.0365043	−	0.0950971i	0.950621	+	0.310354i	$0.100448\pi$
$164$	5.21740	−	16.2219i	0.407411	−	1.26672i
$165$	−6.82707	−	2.81572i	−0.531487	−	0.219203i
$166$	14.8059	+	0.365624i	1.14916	+	0.0283779i
$167$	11.7620	+	14.5249i	0.910171	+	1.12397i	0.991863	+	0.127311i	$0.0406345\pi$
$167$	11.7620	+	14.5249i	0.910171	+	1.12397i	−0.0816914	+	0.996658i	$0.526032\pi$
$168$	5.07908	+	2.07726i	0.391859	+	0.160264i
$169$	1.93415	−	12.8553i	0.148781	−	0.988870i
$170$	−2.04940	−	25.5530i	−0.157182	−	1.95983i
$171$	−1.30762	−	3.40647i	−0.0999964	−	0.260499i
$172$	2.01491	−	7.61044i	0.153636	−	0.580290i
$173$	−0.345967	+	0.311510i	−0.0263034	+	0.0236837i	−0.682177	−	0.731187i	$-0.738967\pi$
$173$	−0.345967	+	0.311510i	−0.0263034	+	0.0236837i	0.655874	+	0.754870i	$0.272300\pi$
$174$	7.40599	+	3.05474i	0.561447	+	0.231579i
$175$	10.1610	−	2.72262i	0.768096	−	0.205811i
$176$	−13.2174	+	1.13980i	−0.996302	+	0.0859158i
$177$	1.29560	+	1.29560i	0.0973832	+	0.0973832i
$178$	1.93767	−	14.8895i	0.145234	−	1.11602i
$179$	−11.8429	+	2.51728i	−0.885177	+	0.188150i	−0.627999	−	0.778214i	$-0.716126\pi$
$179$	−11.8429	+	2.51728i	−0.885177	+	0.188150i	−0.257178	+	0.966364i	$0.582793\pi$
$180$	−7.39709	−	12.7244i	−0.551347	−	0.948419i
$181$	3.56502	+	4.90682i	0.264986	+	0.364721i	0.920689	−	0.390297i	$-0.127628\pi$
$181$	3.56502	+	4.90682i	0.264986	+	0.364721i	−0.655703	+	0.755019i	$0.727628\pi$
$182$	2.01664	−	13.1900i	0.149484	−	0.977708i
$183$	8.08982	−	2.62854i	0.598016	−	0.194307i
$184$	10.2021	+	7.75613i	0.752111	+	0.571790i
$185$	−1.61118	+	15.3294i	−0.118456	+	1.12704i
$186$	−3.98649	+	2.17219i	−0.292304	+	0.159272i
$187$	18.8797	+	6.65338i	1.38062	+	0.486543i
$188$	−16.4903	−	18.2049i	−1.20268	−	1.32773i
$189$	−9.87188	−	3.78946i	−0.718074	−	0.275643i
$190$	6.30599	+	0.486835i	0.457484	+	0.0353188i
$191$	1.53475	−	7.22042i	0.111050	−	0.522451i	−0.887096	−	0.461586i	$-0.847281\pi$
$191$	1.53475	−	7.22042i	0.111050	−	0.522451i	0.998146	−	0.0608652i	$-0.0193860\pi$
$192$	5.00298	+	3.18572i	0.361059	+	0.229910i
$193$	1.82624	+	4.75752i	0.131456	+	0.342454i	0.983472	−	0.181062i	$-0.0579534\pi$
$193$	1.82624	+	4.75752i	0.131456	+	0.342454i	−0.852016	+	0.523516i	$0.824620\pi$
$194$	4.53432	−	19.0116i	0.325545	−	1.36495i
$195$	5.80206	−	5.54880i	0.415494	−	0.397358i
$196$	−0.0467192	+	0.300774i	−0.00333708	+	0.0214838i
$197$	−2.10232	−	0.563316i	−0.149784	−	0.0401346i	0.183148	−	0.983085i	$-0.441371\pi$
$197$	−2.10232	−	0.563316i	−0.149784	−	0.0401346i	−0.332932	+	0.942951i	$0.608038\pi$
$198$	11.4265	−	1.23576i	0.812043	−	0.0878215i
$199$	−5.83785	+	10.1115i	−0.413834	+	0.716782i	−0.995305	−	0.0967852i	$-0.969144\pi$
$199$	−5.83785	+	10.1115i	−0.413834	+	0.716782i	0.581471	+	0.813567i	$0.302477\pi$
$200$	11.3308	−	0.942756i	0.801211	−	0.0666629i
$201$	−10.3057	−	0.540099i	−0.726908	−	0.0380957i
$202$	−9.21752	+	0.255118i	−0.648542	+	0.0179501i
$203$	3.12784	−	19.7484i	0.219531	−	1.38607i
$204$	−4.89660	−	7.49111i	−0.342830	−	0.524483i
$205$	−19.0161	−	17.1222i	−1.32814	−	1.19586i
$206$	−3.50359	−	7.31733i	−0.244106	−	0.509823i
$207$	−8.98212	−	6.52589i	−0.624300	−	0.453581i
$208$	4.68030	−	13.6417i	0.324521	−	0.945879i
$209$	−2.35001	+	4.34391i	−0.162553	+	0.300474i
$210$	5.96881	−	5.68112i	0.411887	−	0.392035i
$211$	−15.1636	−	1.59375i	−1.04390	−	0.109719i	−0.432975	−	0.901406i	$-0.642536\pi$
$211$	−15.1636	−	1.59375i	−1.04390	−	0.109719i	−0.610927	+	0.791687i	$0.709203\pi$
$212$	12.5804	+	4.78620i	0.864028	+	0.328717i
$213$	9.01144	+	4.59156i	0.617453	+	0.314608i
$214$	−1.56341	−	4.39410i	−0.106872	−	0.300374i
$215$	−9.18743	−	7.43984i	−0.626578	−	0.507393i
$216$	−9.77164	−	5.92813i	−0.664876	−	0.403358i
$217$	7.58170	+	8.42033i	0.514679	+	0.571609i
$218$	3.30182	−	4.31632i	0.223627	−	0.292338i
$219$	9.74958	+	2.61239i	0.658815	+	0.176529i
$220$	−6.56542	+	18.8088i	−0.442641	+	1.26809i
$221$	−14.9185	+	15.8432i	−1.00352	+	1.06573i
$222$	2.06668	+	4.96844i	0.138706	+	0.333460i
$223$	−4.11162	−	2.67012i	−0.275334	−	0.178804i	0.399584	−	0.916697i	$-0.369155\pi$
$223$	−4.11162	−	2.67012i	−0.275334	−	0.178804i	−0.674918	+	0.737892i	$0.735821\pi$
$224$	4.83722	−	13.9904i	0.323201	−	0.934773i
$225$	−9.79613	+	1.02961i	−0.653075	+	0.0686410i
$226$	5.15186	+	4.38684i	0.342697	+	0.291808i
$227$	6.95149	+	10.7044i	0.461387	+	0.710473i	0.990414	−	0.138132i	$-0.0441097\pi$
$227$	6.95149	+	10.7044i	0.461387	+	0.710473i	−0.529027	+	0.848605i	$0.677443\pi$
$228$	2.01446	−	0.904100i	0.133411	−	0.0598755i
$229$	1.32750	+	8.38150i	0.0877237	+	0.553865i	0.991932	+	0.126773i	$0.0404620\pi$
$229$	1.32750	+	8.38150i	0.0877237	+	0.553865i	−0.904208	+	0.427092i	$0.859538\pi$
$230$	16.8989	−	9.20798i	1.11428	−	0.607156i
$231$	2.15713	+	6.06225i	0.141929	+	0.398867i
$232$	7.12284	−	20.4038i	0.467637	−	1.33957i
$233$	−2.71509	+	3.73700i	−0.177871	+	0.244819i	−0.888638	−	0.458609i	$-0.848348\pi$
$233$	−2.71509	+	3.73700i	−0.177871	+	0.244819i	0.710767	+	0.703427i	$0.248348\pi$
$234$	−3.79717	+	11.9033i	−0.248229	+	0.778144i
$235$	−35.0801	+	11.3982i	−2.28837	+	0.743538i
$236$	3.29636	−	3.68300i	0.214575	−	0.239743i
$237$	5.95271	+	2.65032i	0.386670	+	0.172157i
$238$	−15.3511	+	16.2250i	−0.995063	+	1.05171i
$239$	9.48580	−	4.83326i	0.613585	−	0.312637i	−0.119437	−	0.992842i	$-0.538109\pi$
$239$	9.48580	−	4.83326i	0.613585	−	0.312637i	0.733023	+	0.680204i	$0.238109\pi$
$240$	7.44062	−	4.89531i	0.480290	−	0.315991i
$241$	−23.9739	+	6.42378i	−1.54429	+	0.413792i	−0.927650	−	0.373451i	$-0.878174\pi$
$241$	−23.9739	+	6.42378i	−1.54429	+	0.413792i	−0.616643	+	0.787243i	$0.711508\pi$
$242$	−11.3326	−	10.6571i	−0.728485	−	0.685061i
$243$	13.2947	+	7.67571i	0.852857	+	0.492397i
$244$	−8.28705	−	21.3976i	−0.530524	−	1.36984i
$245$	0.383336	+	0.248941i	0.0244904	+	0.0159043i
$246$	−8.68956	−	2.07249i	−0.554026	−	0.132137i
$247$	−3.28495	−	4.24689i	−0.209017	−	0.270223i
$248$	6.44560	+	10.4134i	0.409296	+	0.661255i
$249$	−0.406353	−	7.75367i	−0.0257515	−	0.491369i
$250$	−1.38373	+	3.92611i	−0.0875146	+	0.248309i
$251$	27.5946	−	12.2859i	1.74176	−	0.775480i	0.748027	−	0.663669i	$-0.231001\pi$
$251$	27.5946	−	12.2859i	1.74176	−	0.775480i	0.993729	−	0.111811i	$-0.0356652\pi$
$252$	−3.92653	+	12.2083i	−0.247348	+	0.769052i
$253$	1.20183	+	14.9795i	0.0755581	+	0.941756i
$254$	−23.8822	−	7.03552i	−1.49850	−	0.441448i
$255$	−13.2736	+	2.10233i	−0.831226	+	0.131653i
$256$	7.83420	−	13.9508i	0.489638	−	0.871926i
$257$	2.63036	+	2.36839i	0.164078	+	0.147736i	0.747080	−	0.664735i	$-0.231455\pi$
$257$	2.63036	+	2.36839i	0.164078	+	0.147736i	−0.583002	+	0.812471i	$0.698122\pi$
$258$	−4.05920	−	0.746072i	−0.252715	−	0.0464484i
$259$	10.8653	−	7.89412i	0.675138	−	0.490517i
$260$	−15.8114	−	14.7998i	−0.980580	−	0.917846i
$261$	−5.78554	+	17.8061i	−0.358116	+	1.10217i
$262$	0.768893	+	5.77381i	0.0475024	+	0.356707i
$263$	11.4709	−	6.62274i	0.707327	−	0.408376i	−0.102743	−	0.994708i	$-0.532762\pi$
$263$	11.4709	−	6.62274i	0.707327	−	0.408376i	0.810071	+	0.586332i	$0.199429\pi$
$264$	1.12912	+	6.86263i	0.0694927	+	0.422366i
$265$	14.2924	−	14.2924i	0.877975	−	0.877975i
$266$	−3.36131	−	4.36705i	−0.206095	−	0.267761i
$267$	−7.86079	−	0.411967i	−0.481073	−	0.0252119i
$268$	0.0829914	+	27.8389i	0.00506951	+	1.70053i
$269$	−0.341512	−	3.24927i	−0.0208224	−	0.198112i	0.979165	−	0.203065i	$-0.0650901\pi$
$269$	−0.341512	−	3.24927i	−0.0208224	−	0.198112i	−0.999988	+	0.00495286i	$0.998423\pi$
$270$	−14.1298	+	9.74219i	−0.859913	+	0.592891i
$271$	−0.640288	−	12.2174i	−0.0388947	−	0.742156i	−0.946573	−	0.322489i	$-0.895480\pi$
$271$	−0.640288	−	12.2174i	−0.0388947	−	0.742156i	0.907678	−	0.419667i	$-0.137853\pi$
$272$	−19.4466	+	14.3067i	−1.17912	+	0.867471i
$273$	−6.97566	−	0.521826i	−0.422186	−	0.0315824i
$274$	1.77532	−	2.90678i	0.107251	−	0.175605i
$275$	9.68498	+	9.16277i	0.584026	+	0.552536i
$276$	3.64237	−	5.64553i	0.219245	−	0.339821i
$277$	−5.43815	−	12.2143i	−0.326747	−	0.733885i	0.673238	−	0.739426i	$-0.264903\pi$
$277$	−5.43815	−	12.2143i	−0.326747	−	0.733885i	−0.999985	+	0.00554077i	$0.998236\pi$
$278$	0.991149	−	12.8384i	0.0594452	−	0.769995i
$279$	−5.77849	−	8.89809i	−0.345949	−	0.532715i
$280$	−16.1927	−	15.2292i	−0.967697	−	0.910121i
$281$	3.36925	+	0.533637i	0.200993	+	0.0318341i	0.256119	−	0.966645i	$-0.417556\pi$
$281$	3.36925	+	0.533637i	0.200993	+	0.0318341i	−0.0551262	+	0.998479i	$0.517556\pi$
$282$	−8.85008	+	9.35392i	−0.527015	+	0.557018i
$283$	0.0365723	−	0.00777368i	0.00217400	−	0.000462098i	−0.206825	−	0.978378i	$-0.566313\pi$
$283$	0.0365723	−	0.00777368i	0.00217400	−	0.000462098i	0.208999	+	0.977916i	$0.432980\pi$
$284$	11.0227	−	24.9573i	0.654076	−	1.48094i
$285$		−	3.31572i		−	0.196406i
$286$	15.5793	−	6.57914i	0.921224	−	0.389033i
$287$			22.2958i			1.31608i
$288$	−6.52302	+	12.2304i	−0.384372	+	0.720683i
$289$	19.0037	−	4.03936i	1.11786	−	0.237609i
$290$	−23.5737	−	22.3039i	−1.38429	−	1.30973i
$291$	−10.1201	−	1.60287i	−0.593252	−	0.0939619i
$292$	5.58169	−	26.6502i	0.326644	−	1.55958i
$293$	−4.89379	−	7.53578i	−0.285898	−	0.440245i	0.666319	−	0.745667i	$-0.267869\pi$
$293$	−4.89379	−	7.53578i	−0.285898	−	0.440245i	−0.952217	+	0.305422i	$0.901202\pi$
$294$	0.159097	+	0.0122826i	0.00927870	+	0.000716335i
$295$	−3.01891	−	6.78059i	−0.175768	−	0.394781i
$296$	13.0741	−	6.30793i	0.759915	−	0.366641i
$297$	−2.46234	−	13.1738i	−0.142879	−	0.764423i
$298$	−2.53461	−	1.54802i	−0.146826	−	0.0896743i
$299$	−15.4208	−	5.39367i	−0.891805	−	0.311924i
$300$	−0.949999	−	5.88447i	−0.0548482	−	0.339740i
$301$	0.539097	+	10.2866i	0.0310730	+	0.592909i
$302$	−7.34098	−	10.6472i	−0.422426	−	0.612675i
$303$	0.505300	+	4.80761i	0.0290287	+	0.276190i
$304$	−2.73577	−	5.29102i	−0.156907	−	0.303461i
$305$	−34.4103	−	1.80337i	−1.97033	−	0.103260i
$306$	16.5740	−	12.7570i	0.947475	−	0.729270i
$307$	14.8583	−	14.8583i	0.848008	−	0.848008i	−0.141876	−	0.989884i	$-0.545314\pi$
$307$	14.8583	−	14.8583i	0.848008	−	0.848008i	0.989884	+	0.141876i	$0.0453135\pi$
$308$	16.0067	−	6.71477i	0.912068	−	0.382610i
$309$	−3.68331	+	2.12656i	−0.209536	+	0.120976i
$310$	18.2297	−	2.42763i	1.03537	−	0.137880i
$311$	2.66984	−	8.21691i	0.151393	−	0.465938i	−0.846385	−	0.532572i	$-0.821226\pi$
$311$	2.66984	−	8.21691i	0.151393	−	0.465938i	0.997778	+	0.0666331i	$0.0212257\pi$
$312$	−7.31922	−	1.89587i	−0.414369	−	0.107332i
$313$	9.44545	−	6.86252i	0.533888	−	0.387893i	−0.287922	−	0.957654i	$-0.592964\pi$
$313$	9.44545	−	6.86252i	0.533888	−	0.387893i	0.821810	+	0.569761i	$0.192964\pi$
$314$	−3.04515	+	16.5680i	−0.171848	+	0.934984i
$315$	14.3112	+	12.8858i	0.806344	+	0.726035i
$316$	6.25039	−	16.4290i	0.351612	−	0.924206i
$317$	23.5733	−	3.73364i	1.32401	−	0.209702i	0.545910	−	0.837844i	$-0.316184\pi$
$317$	23.5733	−	3.73364i	1.32401	−	0.209702i	0.778099	+	0.628142i	$0.216184\pi$
$318$	1.99404	−	6.76880i	0.111820	−	0.379576i
$319$	23.3977	−	9.73335i	1.31002	−	0.544963i
$320$	−14.2957	−	19.3108i	−0.799154	−	1.07951i
$321$	−2.23366	+	0.994490i	−0.124671	+	0.0555070i
$322$	−15.8147	−	5.57377i	−0.881320	−	0.310614i
$323$	0.470378	+	8.97535i	0.0261725	+	0.499402i
$324$	3.93123	−	7.77267i	0.218402	−	0.431815i
$325$	−13.3691	+	5.59840i	−0.741583	+	0.310543i
$326$	−0.426682	+	1.78900i	−0.0236317	+	0.0990836i
$327$	−2.38933	−	1.55165i	−0.132130	−	0.0858064i
$328$	−4.28562	+	23.7145i	−0.236634	+	1.30941i
$329$	27.8330	+	16.0694i	1.53448	+	0.885935i
$330$	10.0961	+	2.67269i	0.555772	+	0.147127i
$331$	8.42316	−	2.25698i	0.462979	−	0.124055i	−0.0197872	−	0.999804i	$-0.506299\pi$
$331$	8.42316	−	2.25698i	0.462979	−	0.124055i	0.482766	+	0.875749i	$0.339632\pi$
$332$	−20.8238	+	2.25145i	−1.14285	+	0.123565i
$333$	−11.2051	+	5.70928i	−0.614035	+	0.312867i
$334$	−19.2000	−	18.1658i	−1.05057	−	0.993986i
$335$	38.1905	+	17.0035i	2.08657	+	0.929000i
$336$	−7.50783	−	1.96382i	−0.409586	−	0.107135i
$337$	1.28000	−	0.415897i	0.0697261	−	0.0226554i	−0.273946	−	0.961745i	$-0.588329\pi$
$337$	1.28000	−	0.415897i	0.0697261	−	0.0226554i	0.343672	+	0.939090i	$0.388329\pi$
$338$	−0.311518	+	18.3821i	−0.0169443	+	0.999856i
$339$	2.08506	−	2.86985i	0.113245	−	0.155869i
$340$	7.64321	+	35.4386i	0.414511	+	1.92193i
$341$	−4.05773	+	13.7755i	−0.219739	+	0.745987i
$342$	2.46900	+	4.53121i	0.133508	+	0.245020i
$343$	−2.92784	−	18.4857i	−0.158089	−	0.998132i
$344$	−1.40385	+	11.0447i	−0.0756907	+	0.595493i
$345$	−5.49483	−	8.46130i	−0.295832	−	0.455541i
$346$	0.426836	−	0.501272i	0.0229469	−	0.0269486i
$347$	−1.16296	+	0.122232i	−0.0624311	+	0.00656177i	−0.135693	−	0.990751i	$-0.543326\pi$
$347$	−1.16296	+	0.122232i	−0.0624311	+	0.00656177i	0.0732614	+	0.997313i	$0.476659\pi$
$348$	−10.9523	−	2.89969i	−0.587103	−	0.155439i
$349$	−10.6529	−	6.91805i	−0.570234	−	0.370315i	0.227082	−	0.973876i	$-0.427081\pi$
$349$	−10.6529	−	6.91805i	−0.570234	−	0.370315i	−0.797317	+	0.603561i	$0.793748\pi$
$350$	−13.7357	+	5.71354i	−0.734207	+	0.305401i
$351$	14.1800	+	3.34630i	0.756872	+	0.178612i
$352$	18.3159	−	4.06527i	0.976243	−	0.216680i
$353$	25.4896	+	6.82992i	1.35667	+	0.363520i	0.862594	−	0.505897i	$-0.168838\pi$
$353$	25.4896	+	6.82992i	1.35667	+	0.363520i	0.494080	+	0.869416i	$0.335505\pi$
$354$	−2.05809	−	1.57436i	−0.109386	−	0.0836761i
$355$	−27.4142	−	30.4465i	−1.45499	−	1.61593i
$356$	0.0633026	+	21.2344i	0.00335503	+	1.12542i
$357$	9.10011	+	7.36913i	0.481629	+	0.390016i
$358$	16.1318	−	5.73966i	0.852595	−	0.303351i
$359$	31.7613	+	16.1832i	1.67630	+	0.854116i	0.992190	+	0.124734i	$0.0398078\pi$
$359$	31.7613	+	16.1832i	1.67630	+	0.854116i	0.684107	+	0.729382i	$0.260192\pi$
$360$	12.7449	+	16.4566i	0.671717	+	0.867340i
$361$	16.6906	+	1.75425i	0.878453	+	0.0923291i
$362$	−5.91359	−	6.21305i	−0.310811	−	0.326551i
$363$	−5.11303	+	6.35346i	−0.268365	+	0.333470i
$364$	−0.364677	+	18.8667i	−0.0191143	+	0.988885i
$365$	−33.0789	−	24.0332i	−1.73143	−	1.25796i
$366$	−10.8499	+	5.19501i	−0.567134	+	0.271547i
$367$	−18.0683	−	16.2687i	−0.943156	−	0.849221i	0.0455699	−	0.998961i	$-0.485490\pi$
$367$	−18.0683	−	16.2687i	−0.943156	−	0.849221i	−0.988725	+	0.149740i	$0.952156\pi$
$368$	−15.7497	−	8.96829i	−0.821007	−	0.467504i
$369$	3.26592	−	20.6202i	0.170017	−	1.07344i
$370$	−0.603096	−	21.7901i	−0.0313535	−	1.13281i
$371$	−17.5873	−	0.921712i	−0.913088	−	0.0478529i
$372$	5.18290	−	3.78926i	0.268721	−	0.196464i
$373$	13.6775	−	23.6901i	0.708192	−	1.22663i	−0.257335	−	0.966322i	$-0.582844\pi$
$373$	13.6775	−	23.6901i	0.708192	−	1.22663i	0.965527	−	0.260303i	$-0.0838224\pi$
$374$	−27.7083	−	5.80247i	−1.43276	−	0.300038i
$375$	2.10798	+	0.564831i	0.108855	+	0.0291677i
$376$	26.5152	+	22.4419i	1.36742	+	1.15735i
$377$	−0.614510	+	27.5423i	−0.0316489	+	1.41850i
$378$	14.5462	+	3.46931i	0.748176	+	0.178442i
$379$	2.80210	+	7.29972i	0.143934	+	0.374962i	0.986529	−	0.163587i	$-0.0523063\pi$
$379$	2.80210	+	7.29972i	0.143934	+	0.374962i	−0.842595	+	0.538548i	$0.818973\pi$
$380$	−8.93086	+	0.494748i	−0.458143	+	0.0253800i
$381$	−2.71368	+	12.7669i	−0.139026	+	0.654067i
$382$	−0.803547	+	10.4084i	−0.0411131	+	0.532538i
$383$	10.2199	+	3.92306i	0.522214	+	0.200459i	0.605173	−	0.796094i	$-0.293104\pi$
$383$	10.2199	+	3.92306i	0.522214	+	0.200459i	−0.0829592	+	0.996553i	$0.526437\pi$
$384$	−7.60808	−	3.53190i	−0.388248	−	0.180237i
$385$	0.642724	−	26.0580i	0.0327562	−	1.32804i
$386$	−3.44824	−	6.32835i	−0.175511	−	0.322105i
$387$	1.00821	−	9.59247i	0.0512502	−	0.487613i
$388$	−2.80726	+	27.4976i	−0.142517	+	1.39598i
$389$	−7.46491	+	2.42550i	−0.378486	+	0.122978i	−0.492081	−	0.870550i	$-0.663763\pi$
$389$	−7.46491	+	2.42550i	−0.378486	+	0.122978i	0.113595	+	0.993527i	$0.463763\pi$
$390$	−7.09768	+	8.86166i	−0.359405	+	0.448728i
$391$	16.0743	+	22.1244i	0.812915	+	1.11888i
$392$	0.00934378	−	0.430358i	0.000471932	−	0.0217363i
$393$	2.98688	−	0.634881i	0.150668	−	0.0320255i
$394$	3.05228	+	0.397212i	0.153771	+	0.0200113i
$395$	−18.6647	−	18.6647i	−0.939124	−	0.939124i
$396$	−15.7874	+	3.86544i	−0.793344	+	0.194246i
$397$	1.10033	−	0.294832i	0.0552239	−	0.0147972i	−0.231101	−	0.972930i	$-0.574233\pi$
$397$	1.10033	−	0.294832i	0.0552239	−	0.0147972i	0.286325	+	0.958132i	$0.407566\pi$
$398$	6.29610	−	15.2644i	0.315595	−	0.765137i
$399$	−2.14697	+	1.93314i	−0.107483	+	0.0967782i
$400$	−15.7080	+	3.43685i	−0.785400	+	0.171842i
$401$	3.80084	+	9.90153i	0.189805	+	0.494459i	0.995152	−	0.0983443i	$-0.0313546\pi$
$401$	3.80084	+	9.90153i	0.189805	+	0.494459i	−0.805348	+	0.592803i	$0.798021\pi$
$402$	14.5478	−	1.16675i	0.725576	−	0.0581924i
$403$	−11.9104	−	10.0930i	−0.593301	−	0.502767i
$404$	12.8738	−	2.07838i	0.640498	−	0.103403i
$405$	−8.23142	−	10.1650i	−0.409023	−	0.505101i
$406$	−0.698060	+	28.2680i	−0.0346442	+	1.40292i
$407$	15.7360	+	6.49005i	0.780003	+	0.321700i
$408$	8.26269	+	9.58722i	0.409064	+	0.474638i
$409$	7.52046	−	19.5915i	0.371863	−	0.968736i	−0.612166	−	0.790729i	$-0.709702\pi$
$409$	7.52046	−	19.5915i	0.371863	−	0.968736i	0.984029	−	0.178007i	$-0.0569649\pi$
$410$	29.8539	+	20.4526i	1.47438	+	1.01008i
$411$	−1.59098	−	0.810647i	−0.0784775	−	0.0399863i
$412$	6.27747	+	9.60366i	0.309269	+	0.473138i
$413$	−2.63042	+	5.90803i	−0.129435	+	0.290715i
$414$	13.8097	+	7.47144i	0.678711	+	0.367201i
$415$	−9.71934	+	29.9130i	−0.477104	+	1.46837i
$416$	−4.01438	+	19.9971i	−0.196821	+	0.980439i
$417$	−6.75048			−0.330573
$418$	2.48340	−	6.52815i	0.121467	−	0.319302i
$419$	−4.66752	+	2.69480i	−0.228023	+	0.131649i	−0.609660	−	0.792663i	$-0.708694\pi$
$419$	−4.66752	+	2.69480i	−0.228023	+	0.131649i	0.381636	+	0.924313i	$0.375361\pi$
$420$	−7.30675	+	9.07828i	−0.356533	+	0.442975i
$421$	0.322040	+	0.632039i	0.0156953	+	0.0308037i	0.898721	−	0.438521i	$-0.144497\pi$
$421$	0.322040	+	0.632039i	0.0156953	+	0.0308037i	−0.883026	+	0.469325i	$0.844497\pi$
$422$	21.5544	−	0.596572i	1.04925	−	0.0290407i
$423$	−23.3874	−	18.9387i	−1.13713	−	0.920833i
$424$	−18.5292	−	4.36094i	−0.899859	−	0.211786i
$425$	23.7322	+	5.04444i	1.15118	+	0.244691i
$426$	−13.4897	−	4.75435i	−0.653580	−	0.230349i
$427$	18.8943	+	23.3325i	0.914359	+	1.12914i
$428$	3.01194	+	5.86795i	0.145588	+	0.283638i
$429$	−4.06752	−	7.87766i	−0.196382	−	0.380337i
$430$	14.2682	+	8.71432i	0.688073	+	0.420242i
$431$	5.59979	−	4.53462i	0.269732	−	0.218425i	−0.484905	−	0.874567i	$-0.661146\pi$
$431$	5.59979	−	4.53462i	0.269732	−	0.218425i	0.754638	+	0.656142i	$0.227813\pi$
$432$	14.8049	+	6.48609i	0.712302	+	0.312062i
$433$	1.53726	−	7.23223i	0.0738759	−	0.347559i	−0.925649	−	0.378384i	$-0.876480\pi$
$433$	1.53726	−	7.23223i	0.0738759	−	0.347559i	0.999525	+	0.0308246i	$0.00981334\pi$
$434$	−12.2002	−	10.3886i	−0.585630	−	0.498668i
$435$	−10.7068	+	13.2217i	−0.513350	+	0.633934i
$436$	−3.82283	+	6.66716i	−0.183081	+	0.319299i
$437$	−6.01180	+	3.06316i	−0.287583	+	0.146531i
$438$	−14.1550	−	1.84208i	−0.676353	−	0.0880181i
$439$	−14.5357	−	25.1766i	−0.693753	−	1.20161i	−0.970599	−	0.240701i	$-0.922623\pi$
$439$	−14.5357	−	25.1766i	−0.693753	−	1.20161i	0.276847	−	0.960914i	$-0.410711\pi$
$440$	5.69240	−	27.5925i	0.271375	−	1.31542i
$441$			0.372917i			0.0177580i
$442$	17.9556	−	24.9946i	0.854062	−	1.18887i
$443$	−9.75326	−	3.16903i	−0.463391	−	0.150565i	0.0680109	−	0.997685i	$-0.478335\pi$
$443$	−9.75326	−	3.16903i	−0.463391	−	0.150565i	−0.531402	+	0.847120i	$0.678335\pi$
$444$	−3.82466	−	6.57914i	−0.181510	−	0.312232i
$445$	29.1302	+	12.9696i	1.38090	+	0.614818i
$446$	6.26229	+	2.97551i	0.296528	+	0.140894i
$447$	−0.706855	+	1.38728i	−0.0334331	+	0.0656161i
$448$	−4.16925	+	20.5153i	−0.196979	+	0.969256i
$449$	−38.1436	−	14.6419i	−1.80011	−	0.690996i	−0.995230	−	0.0975520i	$-0.968899\pi$
$449$	−38.1436	−	14.6419i	−1.80011	−	0.690996i	−0.804875	−	0.593444i	$-0.797768\pi$
$450$	13.5404	−	3.27211i	0.638300	−	0.154249i
$451$	−24.0716	+	14.8014i	−1.13349	+	0.696972i
$452$	−8.04102	−	5.18788i	−0.378218	−	0.244017i
$453$	−5.26893	+	4.26669i	−0.247556	+	0.200467i
$454$	−11.7432	−	13.7081i	−0.551135	−	0.643351i
$455$	25.6233	+	12.1001i	1.20124	+	0.567262i
$456$	−2.65517	+	1.64346i	−0.124340	+	0.0769623i
$457$	−4.25758	+	1.63433i	−0.199161	+	0.0764508i	−0.455904	−	0.890029i	$-0.650684\pi$
$457$	−4.25758	+	1.63433i	−0.199161	+	0.0764508i	0.256743	+	0.966480i	$0.417351\pi$
$458$	−3.42561	−	11.5017i	−0.160068	−	0.537439i
$459$	−16.3193	−	18.1245i	−0.761721	−	0.845977i
$460$	−21.9705	+	16.0628i	−1.02438	+	0.748932i
$461$	6.18034	+	23.0653i	0.287847	+	1.07426i	0.946734	+	0.322017i	$0.104361\pi$
$461$	6.18034	+	23.0653i	0.287847	+	1.07426i	−0.658887	+	0.752242i	$0.728972\pi$
$462$	−4.15566	−	8.09559i	−0.193339	−	0.376641i
$463$	−24.6549	+	24.6549i	−1.14581	+	1.14581i	−0.158443	+	0.987368i	$0.550647\pi$
$463$	−24.6549	+	24.6549i	−1.14581	+	1.14581i	−0.987368	+	0.158443i	$0.949353\pi$
$464$	−6.17605	+	29.9325i	−0.286716	+	1.38958i
$465$	−2.00451	−	9.43049i	−0.0929571	−	0.437329i
$466$	3.10848	−	5.74552i	0.143998	−	0.266156i
$467$	−27.1187	+	19.7029i	−1.25490	+	0.911739i	−0.998496	−	0.0548299i	$-0.982538\pi$
$467$	−27.1187	+	19.7029i	−1.25490	+	0.911739i	−0.256406	+	0.966569i	$0.582538\pi$
$468$	3.10089	−	17.3954i	0.143339	−	0.804102i
$469$	−11.2560	−	34.6423i	−0.519751	−	1.59963i
$470$	47.0488	−	22.5273i	2.17020	−	1.03911i
$471$	8.78278	+	0.923108i	0.404689	+	0.0425346i
$472$	−3.93342	+	5.77835i	−0.181050	+	0.265970i
$473$	−10.7480	+	7.41095i	−0.494192	+	0.340756i
$474$	−8.83951	−	2.60406i	−0.406012	−	0.119608i
$475$	−2.14522	+	5.58849i	−0.0984294	+	0.256417i
$476$	18.4908	−	25.6106i	0.847525	−	1.17386i
$477$	16.1305	+	3.42865i	0.738567	+	0.156987i
$478$	−12.3953	+	8.54627i	−0.566947	+	0.390897i
$479$	9.19076	−	3.52800i	0.419937	−	0.161199i	−0.139218	−	0.990262i	$-0.544459\pi$
$479$	9.19076	−	3.52800i	0.419937	−	0.161199i	0.559155	+	0.829063i	$0.311126\pi$
$480$	−9.51667	+	8.25146i	−0.434375	+	0.376626i
$481$	−13.3734	+	12.7896i	−0.609773	+	0.583157i
$482$	32.4083	−	13.4806i	1.47616	−	0.614024i
$483$	−2.27519	+	8.49111i	−0.103525	+	0.386359i
$484$	17.8759	+	12.8239i	0.812541	+	0.582904i
$485$	35.9458	+	20.7533i	1.63221	+	0.942360i
$486$	−20.0700	−	8.27822i	−0.910392	−	0.375508i
$487$	1.32595	−	25.3006i	0.0600845	−	1.14648i	−0.787672	−	0.616095i	$-0.788714\pi$
$487$	1.32595	−	25.3006i	0.0600845	−	1.14648i	0.847756	−	0.530386i	$-0.177953\pi$
$488$	15.6116	+	28.4490i	0.706706	+	1.28782i
$489$	0.952310	+	0.150831i	0.0430650	+	0.00682082i
$490$	−0.583847	−	0.277413i	−0.0263755	−	0.0125323i
$491$	−8.35445	+	9.27855i	−0.377031	+	0.418735i	−0.901558	−	0.432659i	$-0.857576\pi$
$491$	−8.35445	+	9.27855i	−0.377031	+	0.418735i	0.524527	+	0.851394i	$0.324242\pi$
$492$	12.5683	+	1.28311i	0.566621	+	0.0578469i
$493$	27.1065	−	37.3089i	1.22082	−	1.68031i
$494$	5.39779	+	5.34021i	0.242858	+	0.240267i
$495$	−4.41143	+	24.0055i	−0.198279	+	1.07897i
$496$	−10.9797	−	13.3947i	−0.493002	−	0.601440i
$497$	−3.73142	+	35.5021i	−0.167377	+	1.59249i
$498$	2.01711	+	10.7935i	0.0903888	+	0.483670i
$499$	4.57197	−	8.97300i	0.204669	−	0.401686i	−0.765740	−	0.643150i	$-0.777627\pi$
$499$	4.57197	−	8.97300i	0.204669	−	0.401686i	0.970410	+	0.241463i	$0.0776273\pi$
$500$	1.20683	−	5.76209i	0.0539710	−	0.257689i
$501$	−8.72029	+	10.7687i	−0.389594	+	0.481108i
$502$	−36.3896	+	22.3743i	−1.62415	+	0.998612i
$503$	24.3731	−	21.9456i	1.08674	−	0.978508i	0.0868996	−	0.996217i	$-0.472304\pi$
$503$	24.3731	−	21.9456i	1.08674	−	0.978508i	0.999843	+	0.0177095i	$0.00563739\pi$
$504$	3.22528	−	17.8471i	0.143666	−	0.794973i
$505$	5.06830	−	18.9152i	0.225536	−	0.841713i
$506$	−4.48117	−	20.7745i	−0.199212	−	0.923541i
$507$	9.62072	−	0.578942i	0.427271	−	0.0257117i
$508$	34.7923	+	5.40429i	1.54366	+	0.239777i
$509$	−5.89910	+	9.08382i	−0.261473	+	0.402633i	−0.944886	−	0.327399i	$-0.893828\pi$
$509$	−5.89910	+	9.08382i	−0.261473	+	0.402633i	0.683413	+	0.730032i	$0.260495\pi$
$510$	18.2150	−	5.42507i	0.806573	−	0.240226i
$511$	3.72394	+	35.4310i	0.164738	+	1.56737i
$512$	−8.37793	+	21.0193i	−0.370255	+	0.928930i
$513$	5.04652	−	3.27725i	0.222809	−	0.144694i
$514$	−4.12948	−	2.82906i	−0.182143	−	0.124784i
$515$	17.0169	−	2.69521i	0.749853	−	0.118765i
$516$	5.82962	+	0.288094i	0.256635	+	0.0126826i
$517$	1.12816	+	40.7177i	0.0496164	+	1.79076i
$518$	−13.7577	+	13.0946i	−0.604480	+	0.575345i
$519$	−0.279234	−	0.202875i	−0.0122570	−	0.00890523i
$520$	24.9279	+	17.7953i	1.09316	+	0.780374i
$521$	−2.59716	−	7.99324i	−0.113784	−	0.350190i	0.877908	−	0.478830i	$-0.158939\pi$
$521$	−2.59716	−	7.99324i	−0.113784	−	0.350190i	−0.991691	+	0.128640i	$0.958939\pi$
$522$	4.78633	−	26.0413i	0.209492	−	1.13980i
$523$	−3.09014	+	6.94057i	−0.135122	+	0.303490i	−0.968416	−	0.249341i	$-0.919786\pi$
$523$	−3.09014	+	6.94057i	−0.135122	+	0.303490i	0.833293	+	0.552831i	$0.186453\pi$
$524$	−2.15573	−	7.95040i	−0.0941734	−	0.347315i
$525$	3.54068	+	6.94898i	0.154528	+	0.303278i
$526$	−14.8440	+	11.4254i	−0.647231	+	0.498172i
$527$	6.76387	+	25.2431i	0.294639	+	1.09961i
$528$	−2.86397	−	9.40951i	−0.124638	−	0.409496i
$529$	1.23494	−	2.13898i	0.0536932	−	0.0929993i
$530$	−17.3675	+	22.7038i	−0.754396	+	0.986188i
$531$	3.29815	−	5.07871i	0.143128	−	0.220397i
$532$	5.52725	+	5.49440i	0.239637	+	0.238212i
$533$	−4.12765	−	30.4413i	−0.178788	−	1.31856i
$534$	11.0965	−	0.889955i	0.480191	−	0.0385121i
$535$	9.89106	−	0.518369i	0.427628	−	0.0224110i
$536$	−5.31335	−	39.0101i	−0.229502	−	1.68498i
$537$	−3.65103	−	8.20034i	−0.157553	−	0.353871i
$538$	1.08532	+	4.49120i	0.0467917	+	0.193629i
$539$	0.383322	−	0.328397i	0.0165109	−	0.0141451i
$540$	17.9890	−	16.2948i	0.774124	−	0.701214i
$541$	4.97292	+	31.3978i	0.213803	+	1.34990i	0.827993	+	0.560739i	$0.189483\pi$
$541$	4.97292	+	31.3978i	0.213803	+	1.34990i	−0.614190	+	0.789158i	$0.710517\pi$
$542$	3.17835	+	17.0073i	0.136522	+	0.730527i
$543$	−3.00887	+	3.34169i	−0.129123	+	0.143405i
$544$	24.5902	−	23.6860i	1.05430	−	1.01553i
$545$	6.78352	+	9.33671i	0.290574	+	0.399941i
$546$	9.87616	−	0.570711i	0.422660	−	0.0244242i
$547$	−24.3885	−	7.92430i	−1.04278	−	0.338819i	−0.262947	−	0.964810i	$-0.584694\pi$
$547$	−24.3885	−	7.92430i	−1.04278	−	0.338819i	−0.779830	+	0.625991i	$0.784694\pi$
$548$	−1.94607	+	4.40626i	−0.0831322	+	0.188226i
$549$	−14.0565	−	24.3466i	−0.599918	−	1.03909i
$550$	−15.2873	−	11.0367i	−0.651853	−	0.470607i
$551$	8.04542	+	8.04542i	0.342747	+	0.342747i
$552$	−4.05209	+	8.59408i	−0.172468	+	0.365788i
$553$	−1.20368	+	22.9676i	−0.0511857	+	0.976682i
$554$	9.90359	+	16.1072i	0.420763	+	0.684331i
$555$	−11.3651	+	1.19452i	−0.482422	+	0.0507046i
$556$	1.00726	+	18.1824i	0.0427173	+	0.771104i
$557$	−32.3490	+	1.69534i	−1.37067	+	0.0718339i	−0.723403	−	0.690426i	$-0.757423\pi$
$557$	−32.3490	+	1.69534i	−1.37067	+	0.0718339i	−0.647271	+	0.762260i	$0.724090\pi$
$558$	9.76161	+	11.3949i	0.413242	+	0.482386i
$559$	−2.64042	−	13.9448i	−0.111678	−	0.589804i
$560$	25.5425	+	18.3261i	1.07937	+	0.774417i
$561$	−1.91478	+	14.7170i	−0.0808421	+	0.621353i
$562$	−4.82277	−	0.119095i	−0.203436	−	0.00502373i
$563$	−29.2420	+	13.0194i	−1.23240	+	0.548701i	−0.916479	−	0.400083i	$-0.868981\pi$
$563$	−29.2420	+	13.0194i	−1.23240	+	0.548701i	−0.315924	+	0.948784i	$0.602315\pi$
$564$	10.6602	−	14.7648i	0.448874	−	0.621712i
$565$	−12.0516	+	7.82638i	−0.507013	+	0.329258i
$566$	−0.0498172	+	0.0177248i	−0.00209397	+	0.000745030i
$567$	−1.78283	+	11.2564i	−0.0748719	+	0.472723i
$568$	−10.7929	+	37.0439i	−0.452862	+	1.55433i
$569$	−2.01808	−	9.49432i	−0.0846023	−	0.398023i	0.915387	−	0.402574i	$-0.131884\pi$
$569$	−2.01808	−	9.49432i	−0.0846023	−	0.398023i	−0.999990	+	0.00455170i	$0.998551\pi$
$570$	0.618984	+	4.64810i	0.0259264	+	0.194688i
$571$	−20.3157			−0.850185			−0.425093	−	0.905150i	$-0.639758\pi$
$571$	−20.3157			−0.850185			−0.425093	+	0.905150i	$0.639758\pi$
$572$	−20.6115	+	12.1313i	−0.861809	+	0.507234i
$573$	5.47277			0.228628
$574$	−4.16222	−	31.2551i	−0.173728	−	1.30456i
$575$	3.78695	+	17.8162i	0.157927	+	0.742987i
$576$	6.86102	−	18.3628i	0.285876	−	0.765115i
$577$	4.02562	−	25.4168i	0.167589	−	1.05811i	−0.750248	−	0.661156i	$-0.770066\pi$
$577$	4.02562	−	25.4168i	0.167589	−	1.05811i	0.917837	−	0.396958i	$-0.129934\pi$
$578$	−25.8860	+	9.21016i	−1.07672	+	0.383092i
$579$	−3.16862	+	2.05772i	−0.131683	+	0.0855161i
$580$	37.2102	+	26.8657i	1.54507	+	1.11554i
$581$	25.0357	−	11.1466i	1.03866	−	0.462439i
$582$	14.4860	+	0.357723i	0.600464	+	0.0148281i
$583$	−10.6805	−	19.6000i	−0.442342	−	0.811747i
$584$	−2.84952	+	38.4012i	−0.117914	+	1.58905i
$585$	−21.9251	−	14.9441i	−0.906493	−	0.617861i
$586$	8.26709	+	9.65036i	0.341511	+	0.398653i
$587$	−27.6652	+	1.44987i	−1.14187	+	0.0598427i	−0.613873	−	0.789405i	$-0.710389\pi$
$587$	−27.6652	+	1.44987i	−1.14187	+	0.0598427i	−0.527994	+	0.849248i	$0.677056\pi$
$588$	−0.225321	+	0.0124822i	−0.00929207	+	0.000514758i
$589$	−6.41242	+	0.673973i	−0.264219	+	0.0277706i
$590$	5.49784	+	8.94171i	0.226342	+	0.368124i
$591$	0.0844511	−	1.61142i	0.00347385	−	0.0662851i
$592$	−17.1502	+	11.2834i	−0.704867	+	0.463744i
$593$	6.34235	+	6.34235i	0.260449	+	0.260449i	0.825236	−	0.564787i	$-0.191042\pi$
$593$	6.34235	+	6.34235i	0.260449	+	0.260449i	−0.564787	+	0.825236i	$0.691042\pi$
$594$	5.91112	+	18.0079i	0.242536	+	0.738873i
$595$	−23.7173	−	41.0796i	−0.972315	−	1.68410i
$596$	3.84210	+	1.69691i	0.157378	+	0.0695080i
$597$	−8.23263	−	2.67494i	−0.336939	−	0.109478i
$598$	22.6243	+	4.68228i	0.925177	+	0.191473i
$599$	−4.51037	−	6.20798i	−0.184289	−	0.253651i	0.706870	−	0.707344i	$-0.250107\pi$
$599$	−4.51037	−	6.20798i	−0.184289	−	0.253651i	−0.891158	+	0.453692i	$0.850107\pi$
$600$	2.43027	+	8.07172i	0.0992152	+	0.329527i
$601$	25.9476	−	28.8177i	1.05842	−	1.17550i	0.0744433	−	0.997225i	$-0.476282\pi$
$601$	25.9476	−	28.8177i	1.05842	−	1.17550i	0.983981	−	0.178274i	$-0.0570513\pi$
$602$	−2.67604	−	14.3195i	−0.109067	−	0.583619i
$603$	5.33558	+	33.6875i	0.217282	+	1.37186i
$604$	12.2785	+	13.5552i	0.499605	+	0.551552i
$605$	28.5601	−	16.6051i	1.16113	−	0.675094i
$606$	−1.60584	−	6.64516i	−0.0652328	−	0.269941i
$607$	−2.11334	−	4.74665i	−0.0857780	−	0.192660i	0.865563	−	0.500799i	$-0.166961\pi$
$607$	−2.11334	−	4.74665i	−0.0857780	−	0.192660i	−0.951341	+	0.308139i	$0.900294\pi$
$608$	4.82284	+	6.90644i	0.195592	+	0.280093i
$609$	14.8035	−	0.775821i	0.599870	−	0.0314378i
$610$	48.5743	−	3.89574i	1.96672	−	0.157734i
$611$	−40.9764	−	16.7874i	−1.65773	−	0.679145i
$612$	−20.8526	+	20.9773i	−0.842918	+	0.847958i
$613$	9.60991	−	14.7980i	0.388141	−	0.597684i	−0.589551	−	0.807731i	$-0.700695\pi$
$613$	9.60991	−	14.7980i	0.388141	−	0.597684i	0.977691	+	0.210047i	$0.0673618\pi$
$614$	−18.0552	+	23.6027i	−0.728647	+	0.952528i
$615$	9.48565	−	16.4296i	0.382498	−	0.662507i
$616$	−21.1853	+	12.4012i	−0.853581	+	0.499658i
$617$	−1.00569	−	3.75328i	−0.0404874	−	0.151101i	0.942723	−	0.333577i	$-0.108256\pi$
$617$	−1.00569	−	3.75328i	−0.0404874	−	0.151101i	−0.983210	+	0.182476i	$0.941589\pi$
$618$	4.76642	−	3.66870i	0.191734	−	0.147577i
$619$	5.94862	+	11.6748i	0.239095	+	0.469251i	0.979108	−	0.203342i	$-0.0651805\pi$
$619$	5.94862	+	11.6748i	0.239095	+	0.469251i	−0.740013	+	0.672593i	$0.765180\pi$
$620$	−25.1018	+	6.80629i	−1.00811	+	0.273347i
$621$	7.44700	−	16.7262i	0.298838	−	0.671201i
$622$	−2.20873	+	12.0172i	−0.0885621	+	0.481846i
$623$	−8.58560	−	26.4238i	−0.343975	−	1.05865i
$624$	10.6143	+	1.29134i	0.424911	+	0.0516948i
$625$	−23.4129	−	17.0105i	−0.936515	−	0.680418i
$626$	−11.9599	+	11.3834i	−0.478013	+	0.454974i
$627$	−3.51241	−	1.03462i	−0.140272	−	0.0413187i
$628$	1.17588	−	23.7941i	0.0469226	−	0.949487i
$629$	30.5948	−	4.84575i	1.21990	−	0.193213i
$630$	−22.4675	−	15.3922i	−0.895127	−	0.613241i
$631$	13.1699	−	8.55263i	0.524285	−	0.340475i	−0.255207	−	0.966886i	$-0.582144\pi$
$631$	13.1699	−	8.55263i	0.524285	−	0.340475i	0.779493	+	0.626411i	$0.215477\pi$
$632$	−5.69503	+	24.1977i	−0.226536	+	0.962532i
$633$	−1.18160	−	11.2422i	−0.0469644	−	0.446836i
$634$	−32.3489	+	9.63467i	−1.28474	+	0.382642i
$635$	28.7965	−	44.3428i	1.14276	−	1.75969i
$636$	−1.53171	+	9.86102i	−0.0607363	+	0.391015i
$637$	0.157884	+	0.525526i	0.00625558	+	0.0208221i
$638$	−30.9828	+	18.0125i	−1.22662	+	0.713122i
$639$	8.65138	−	32.2874i	0.342243	−	1.27727i
$640$	23.6452	+	24.4018i	0.934660	+	0.964567i
$641$	−29.1714	+	26.2661i	−1.15220	+	1.03745i	−0.153416	+	0.988162i	$0.549028\pi$
$641$	−29.1714	+	26.2661i	−1.15220	+	1.03745i	−0.998785	+	0.0492850i	$0.984306\pi$
$642$	2.94558	−	1.81110i	0.116253	−	0.0714783i
$643$	15.3092	−	18.9053i	0.603736	−	0.745552i	−0.380036	−	0.924972i	$-0.624088\pi$
$643$	15.3092	−	18.9053i	0.603736	−	0.745552i	0.983773	+	0.179419i	$0.0574218\pi$
$644$	23.2102	+	4.86121i	0.914610	+	0.191558i
$645$	3.97913	−	7.80948i	0.156678	−	0.307498i
$646$	−2.33493	−	12.4942i	−0.0918664	−	0.491577i
$647$	2.46453	−	23.4484i	0.0968905	−	0.921851i	−0.832816	−	0.553550i	$-0.813273\pi$
$647$	2.46453	−	23.4484i	0.0968905	−	0.921851i	0.929706	−	0.368301i	$-0.120061\pi$
$648$	−4.05993	+	11.6299i	−0.159489	+	0.456866i
$649$	−8.12483	+	1.08222i	−0.318927	+	0.0424808i
$650$	17.6962	−	10.3438i	0.694101	−	0.405718i
$651$	−4.93769	+	6.79615i	−0.193523	+	0.266362i
$652$	0.264165	−	2.58754i	0.0103455	−	0.101336i
$653$	−1.12592	+	1.25046i	−0.0440607	+	0.0489344i	−0.764772	−	0.644301i	$-0.777149\pi$
$653$	−1.12592	+	1.25046i	−0.0440607	+	0.0489344i	0.720712	+	0.693235i	$0.243815\pi$
$654$	3.63912	+	1.72912i	0.142301	+	0.0676138i
$655$	−12.2176	−	1.93507i	−0.477380	−	0.0756096i
$656$	1.58069	−	34.0439i	0.0617156	−	1.32919i
$657$	1.74590	−	33.3137i	0.0681139	−	1.29969i
$658$	−42.0173	−	17.3308i	−1.63800	−	0.675624i
$659$	−12.2476	−	7.07113i	−0.477097	−	0.275452i	0.242109	−	0.970249i	$-0.422161\pi$
$659$	−12.2476	−	7.07113i	−0.477097	−	0.275452i	−0.719206	+	0.694797i	$0.755494\pi$
$660$	−14.6520	−	1.86192i	−0.570330	−	0.0724753i
$661$	−0.388771	+	1.45091i	−0.0151214	+	0.0564339i	−0.973074	−	0.230492i	$-0.925967\pi$
$661$	−0.388771	+	1.45091i	−0.0151214	+	0.0564339i	0.957953	+	0.286926i	$0.0926332\pi$
$662$	−11.3866	+	4.73637i	−0.442551	+	0.184084i
$663$	−13.7890	−	8.37662i	−0.535519	−	0.325321i
$664$	28.7713	−	7.04359i	1.11654	−	0.273344i
$665$	10.9259	−	4.19405i	0.423687	−	0.162638i
$666$	14.6419	−	10.0953i	0.567362	−	0.391184i
$667$	33.8638	+	7.19798i	1.31121	+	0.278707i
$668$	30.3064	+	21.8812i	1.17259	+	0.846608i
$669$	1.30257	−	3.39330i	0.0503601	−	0.131193i
$670$	−56.7111	−	16.7067i	−2.19094	−	0.645435i
$671$	−12.6475	+	35.8888i	−0.488253	+	1.38547i
$672$	10.8914	+	1.35138i	0.420144	+	0.0521305i
$673$	21.7801	+	2.28918i	0.839561	+	0.0882414i	0.514541	−	0.857466i	$-0.327962\pi$
$673$	21.7801	+	2.28918i	0.839561	+	0.0882414i	0.325020	+	0.945707i	$0.394629\pi$
$674$	−1.71671	+	0.821973i	−0.0661253	+	0.0316612i
$675$	−5.01961	−	15.4488i	−0.193205	−	0.594623i
$676$	−2.99491	−	25.8269i	−0.115189	−	0.993344i
$677$	9.11610	−	6.62323i	0.350360	−	0.254551i	−0.398660	−	0.917099i	$-0.630525\pi$
$677$	9.11610	−	6.62323i	0.350360	−	0.254551i	0.749020	+	0.662547i	$0.230525\pi$
$678$	−2.38718	+	4.41230i	−0.0916789	+	0.169453i
$679$	−7.51920	−	35.3750i	−0.288560	−	1.35757i
$680$	−17.3303	−	48.2524i	−0.664586	−	1.85039i
$681$	−6.69119	+	6.69119i	−0.256407	+	0.256407i
$682$	3.11665	−	20.0686i	0.119343	−	0.768465i
$683$	8.77044	+	32.7317i	0.335592	+	1.25245i	0.903226	+	0.429165i	$0.141192\pi$
$683$	8.77044	+	32.7317i	0.335592	+	1.25245i	−0.567635	+	0.823281i	$0.692141\pi$
$684$	−4.30703	−	5.89111i	−0.164684	−	0.225252i
$685$	4.84002	+	5.37539i	0.184928	+	0.205383i
$686$	7.55529	+	25.3673i	0.288462	+	0.968529i
$687$	−5.87358	+	2.25466i	−0.224091	+	0.0860205i
$688$	−0.0938768	−	15.7450i	−0.00357902	−	0.600273i
$689$	24.1832	−	1.99751i	0.921308	−	0.0760991i
$690$	9.28244	+	10.8356i	0.353376	+	0.412504i
$691$	14.6803	−	11.8878i	0.558463	−	0.452235i	−0.308063	−	0.951366i	$-0.599681\pi$
$691$	14.6803	−	11.8878i	0.558463	−	0.452235i	0.866526	+	0.499131i	$0.166347\pi$
$692$	−0.504777	+	0.782385i	−0.0191887	+	0.0297418i
$693$	18.1158	−	11.1393i	0.688163	−	0.423147i
$694$	1.60747	−	0.388454i	0.0610186	−	0.0147455i
$695$	25.5292	+	9.79976i	0.968379	+	0.371726i
$696$	15.8946	+	2.02030i	0.602484	+	0.0765793i
$697$	−23.3460	+	45.8192i	−0.884294	+	1.73552i
$698$	16.2251	+	7.70929i	0.614127	+	0.291801i
$699$	−3.12856	−	1.39292i	−0.118333	−	0.0526853i
$700$	18.1887	−	10.5737i	0.687468	−	0.399647i
$701$	−7.62447	−	2.47734i	−0.287972	−	0.0935679i	0.161469	−	0.986878i	$-0.448377\pi$
$701$	−7.62447	−	2.47734i	−0.287972	−	0.0935679i	−0.449441	+	0.893310i	$0.648377\pi$
$702$	−20.5027	−	2.04382i	−0.773826	−	0.0771391i
$703$			7.64253i			0.288243i
$704$	−24.9171	+	9.11810i	−0.939097	+	0.343651i
$705$	−13.6733	−	23.6829i	−0.514967	−	0.891949i
$706$	−37.0073	−	4.81600i	−1.39279	−	0.181252i
$707$	−15.2027	+	7.74619i	−0.571758	+	0.291325i
$708$	3.17901	+	1.82279i	0.119474	+	0.0685045i
$709$	−27.9690	+	34.5388i	−1.05040	+	1.29713i	−0.0970418	+	0.995280i	$0.530938\pi$
$709$	−27.9690	+	34.5388i	−1.05040	+	1.29713i	−0.953355	+	0.301852i	$0.902395\pi$
$710$	44.1141	+	37.5634i	1.65557	+	1.40973i
$711$	4.47754	−	21.0652i	0.167921	−	0.790006i
$712$	−4.05282	−	29.7554i	−0.151886	−	1.11513i
$713$	−15.2468	+	12.3466i	−0.570996	+	0.462384i
$714$	−14.1326	−	8.63150i	−0.528898	−	0.323026i
$715$	3.94661	+	35.6969i	0.147595	+	1.33499i
$716$	−21.5427	+	11.0576i	−0.805090	+	0.413242i
$717$	4.96723	+	6.13402i	0.185505	+	0.229079i
$718$	−47.5453	−	16.7570i	−1.77437	−	0.625364i
$719$	21.5526	+	4.58116i	0.803778	+	0.170848i	0.591441	−	0.806348i	$-0.298559\pi$
$719$	21.5526	+	4.58116i	0.803778	+	0.170848i	0.212337	+	0.977197i	$0.431893\pi$
$720$	−20.9385	−	20.6903i	−0.780331	−	0.771081i
$721$	−11.6664	−	9.44727i	−0.434480	−	0.351835i
$722$	−23.7250	+	0.656651i	−0.882954	+	0.0244380i
$723$	−8.35392	−	16.3955i	−0.310686	−	0.609755i
$724$	9.44976	+	7.60573i	0.351197	+	0.282665i
$725$	26.6000	−	15.3575i	0.987899	−	0.570364i
$726$	5.98157	−	9.86103i	0.221997	−	0.365977i
$727$	−1.00902			−0.0374223			−0.0187112	−	0.999825i	$-0.505956\pi$
$727$	−1.00902			−0.0374223			−0.0187112	+	0.999825i	$0.505956\pi$
$728$	−3.01085	−	26.5162i	−0.111590	−	0.982754i
$729$	0.520374	−	1.60155i	0.0192731	−	0.0593166i
$730$	50.8578	+	27.5155i	1.88233	+	1.01839i
$731$	−9.66325	+	21.7040i	−0.357408	+	0.802752i
$732$	14.2400	−	9.30804i	0.526326	−	0.344035i
$733$	−0.476970	−	0.243029i	−0.0176173	−	0.00897647i	0.445160	−	0.895451i	$-0.353147\pi$
$733$	−0.476970	−	0.243029i	−0.0176173	−	0.00897647i	−0.462777	+	0.886475i	$0.653147\pi$
$734$	28.3658	+	19.4331i	1.04700	+	0.717290i
$735$	−0.121441	+	0.316365i	−0.00447943	+	0.0116693i
$736$	23.7527	+	9.63192i	0.875535	+	0.355037i
$737$	29.9289	−	35.1503i	1.10245	−	1.29478i
$738$	−0.728876	+	29.5158i	−0.0268303	+	1.08649i
$739$	−4.10002	−	5.06310i	−0.150822	−	0.186249i	0.696135	−	0.717910i	$-0.254901\pi$
$739$	−4.10002	−	5.06310i	−0.150822	−	0.186249i	−0.846957	+	0.531661i	$0.821568\pi$
$740$	4.91325	+	30.4336i	0.180615	+	1.11876i
$741$	2.57345	−	3.03686i	0.0945382	−	0.111562i
$742$	24.8266	−	1.99114i	0.911414	−	0.0730970i
$743$	−16.0443	−	41.7969i	−0.588610	−	1.53338i	−0.826994	−	0.562210i	$-0.809951\pi$
$743$	−16.0443	−	41.7969i	−0.588610	−	1.53338i	0.238384	−	0.971171i	$-0.423382\pi$
$744$	−6.55821	+	6.27948i	−0.240436	+	0.230217i
$745$	4.68714	−	4.22032i	0.171724	−	0.154621i
$746$	−14.7511	+	35.7630i	−0.540076	+	1.30938i
$747$	−24.7869	+	6.64164i	−0.906906	+	0.243005i
$748$	39.9258	+	2.96148i	1.45983	+	0.108282i
$749$	−6.10237	−	6.10237i	−0.222976	−	0.222976i
$750$	−3.06048	−	0.398280i	−0.111753	−	0.0145431i
$751$	−5.38192	+	1.14396i	−0.196389	+	0.0417438i	−0.305056	−	0.952334i	$-0.598675\pi$
$751$	−5.38192	+	1.14396i	−0.196389	+	0.0417438i	0.108667	+	0.994078i	$0.465342\pi$
$752$	−41.3596	−	26.5100i	−1.50823	−	0.966719i
$753$	13.1632	+	18.1176i	0.479694	+	0.660243i
$754$	−4.28019	−	38.7245i	−0.155875	−	1.41026i
$755$	26.1203	−	8.48699i	0.950614	−	0.308873i
$756$	−21.0391	−	2.14790i	−0.765184	−	0.0781185i
$757$	−1.87119	+	17.8032i	−0.0680095	+	0.647067i	0.906421	+	0.422376i	$0.138804\pi$
$757$	−1.87119	+	17.8032i	−0.0680095	+	0.647067i	−0.974430	+	0.224691i	$0.927863\pi$
$758$	−5.29082	−	9.70993i	−0.192171	−	0.352681i
$759$	−10.6778	+	3.18057i	−0.387580	+	0.115447i
$760$	12.4273	−	2.36078i	0.450784	−	0.0856346i
$761$	−3.89210	−	1.49404i	−0.141088	−	0.0541587i	0.286799	−	0.957991i	$-0.407409\pi$
$761$	−3.89210	−	1.49404i	−0.141088	−	0.0541587i	−0.427888	+	0.903832i	$0.640742\pi$
$762$	1.42080	−	18.4037i	0.0514702	−	0.666695i
$763$	2.09069	−	9.83594i	0.0756882	−	0.356085i
$764$	−0.816607	−	14.7408i	−0.0295438	−	0.533305i
$765$	15.9175	+	41.4665i	0.575498	+	1.49922i
$766$	−15.0591	−	3.59163i	−0.544106	−	0.129771i
$767$	2.49765	−	8.55342i	0.0901850	−	0.308846i
$768$	11.3246	+	3.53087i	0.408643	+	0.127409i
$769$	18.6033	+	4.98474i	0.670852	+	0.179754i	0.578139	−	0.815939i	$-0.303779\pi$
$769$	18.6033	+	4.98474i	0.670852	+	0.179754i	0.0927135	+	0.995693i	$0.470446\pi$
$770$	3.96355	+	36.6491i	0.142837	+	1.32074i
$771$	−1.31208	+	2.27260i	−0.0472535	+	0.0818455i
$772$	6.01526	+	8.22760i	0.216494	+	0.296118i
$773$	22.8971	+	1.19999i	0.823553	+	0.0431606i	0.459456	−	0.888201i	$-0.348044\pi$
$773$	22.8971	+	1.19999i	0.823553	+	0.0431606i	0.364097	+	0.931361i	$0.381378\pi$
$774$	0.377392	+	13.6353i	0.0135651	+	0.490111i
$775$	−2.72287	+	17.1915i	−0.0978084	+	0.617538i
$776$	−1.19797	−	39.0713i	−0.0430047	−	1.40258i
$777$	7.39959	+	6.66262i	0.265459	+	0.239020i
$778$	10.0118	−	4.79371i	0.358940	−	0.171863i
$779$	−10.2644	−	7.45751i	−0.367759	−	0.267193i
$780$	8.29550	−	13.7476i	0.297026	−	0.492244i
$781$	−40.8068	+	19.5400i	−1.46018	+	0.699198i
$782$	−26.6639	−	28.0141i	−0.953498	−	1.00178i
$783$	−30.7060	−	3.22733i	−1.09734	−	0.115335i
$784$	0.0672414	+	0.605036i	0.00240148	+	0.0216084i
$785$	−31.8750	−	16.2411i	−1.13767	−	0.579670i
$786$	−4.06860	+	1.44760i	−0.145122	+	0.0516341i
$787$	31.1879	+	25.2555i	1.11173	+	0.900260i	0.995668	−	0.0929822i	$-0.0296400\pi$
$787$	31.1879	+	25.2555i	1.11173	+	0.900260i	0.116061	+	0.993242i	$0.462973\pi$
$788$	−4.35295	+	0.0129767i	−0.155067	+	0.000462276i
$789$	6.57095	+	7.29778i	0.233932	+	0.259808i
$790$	29.6493	+	22.6805i	1.05487	+	0.806938i
$791$	12.0940	+	3.24059i	0.430014	+	0.115222i
$792$	21.4097	−	8.36593i	0.760761	−	0.297271i
$793$	−30.1166	−	28.3588i	−1.06947	−	1.00705i
$794$	−1.48744	+	0.618719i	−0.0527874	+	0.0219575i
$795$	12.5678	+	8.16165i	0.445736	+	0.289464i
$796$	−5.97652	+	22.5736i	−0.211832	+	0.800101i
$797$	21.6412	−	2.27458i	0.766570	−	0.0805697i	0.286831	−	0.957981i	$-0.407398\pi$
$797$	21.6412	−	2.27458i	0.766570	−	0.0805697i	0.479739	+	0.877411i	$0.340731\pi$
$798$	2.64882	−	3.11075i	0.0937674	−	0.110119i
$799$	40.3721	+	62.1676i	1.42826	+	2.19933i
$800$	21.3785	−	7.75030i	0.755843	−	0.274015i
$801$	4.06977	+	25.6955i	0.143798	+	0.907907i
$802$	−7.17660	−	13.1708i	−0.253414	−	0.465077i
$803$	−35.7807	+	27.5420i	−1.26267	+	0.971935i
$804$	−20.1758	+	4.35140i	−0.711545	+	0.153462i
$805$	20.9310	−	28.8091i	0.737723	−	1.01539i
$806$	18.5807	+	11.9253i	0.654476	+	0.420049i
$807$	2.30371	−	0.748520i	0.0810944	−	0.0263492i
$808$	−17.6590	+	5.31686i	−0.621243	+	0.187046i
$809$	−49.9979	−	22.2605i	−1.75783	−	0.782638i	−0.989841	−	0.142180i	$-0.954589\pi$
$809$	−49.9979	−	22.2605i	−1.75783	−	0.782638i	−0.767993	−	0.640458i	$-0.778744\pi$
$810$	13.4367	+	12.7130i	0.472119	+	0.446688i
$811$	6.11399	−	3.11523i	0.214691	−	0.109391i	−0.343338	−	0.939212i	$-0.611558\pi$
$811$	6.11399	−	3.11523i	0.214691	−	0.109391i	0.558029	+	0.829821i	$0.311558\pi$
$812$	−4.29854	−	39.7574i	−0.150849	−	1.39521i
$813$	8.76130	−	2.34758i	0.307272	−	0.0823333i
$814$	−23.2709	−	6.16039i	−0.815643	−	0.215921i
$815$	−3.38252	−	1.95290i	−0.118485	−	0.0684071i
$816$	−13.3727	−	11.8972i	−0.468138	−	0.416487i
$817$	−4.91598	−	3.19247i	−0.171988	−	0.111691i
$818$	−6.88510	+	28.8680i	−0.240732	+	1.00935i
$819$	3.10639	+	22.9096i	0.108546	+	0.800525i
$820$	−45.6684	−	23.0980i	−1.59481	−	0.806617i
$821$	−0.0542609	−	1.03536i	−0.00189372	−	0.0361343i	0.997519	−	0.0703946i	$-0.0224258\pi$
$821$	−0.0542609	−	1.03536i	−0.00189372	−	0.0361343i	−0.999413	+	0.0342602i	$0.989092\pi$
$822$	2.38164	+	0.839388i	0.0830691	+	0.0292770i
$823$	13.3413	−	5.93994i	0.465049	−	0.207053i	−0.160816	−	0.986984i	$-0.551413\pi$
$823$	13.3413	−	5.93994i	0.465049	−	0.207053i	0.625865	+	0.779931i	$0.284746\pi$
$824$	−10.5928	−	12.2909i	−0.369019	−	0.428173i
$825$	−5.15189	+	8.43587i	−0.179366	+	0.293699i
$826$	2.58451	−	8.77315i	0.0899265	−	0.305257i
$827$	47.0612	−	7.45377i	1.63648	−	0.259193i	0.730624	−	0.682780i	$-0.239229\pi$
$827$	47.0612	−	7.45377i	1.63648	−	0.259193i	0.905855	+	0.423587i	$0.139229\pi$
$828$	−20.7538	−	7.89573i	−0.721244	−	0.274396i
$829$	−24.8839	−	22.4055i	−0.864253	−	0.778177i	0.112251	−	0.993680i	$-0.464194\pi$
$829$	−24.8839	−	22.4055i	−0.864253	−	0.778177i	−0.976503	+	0.215503i	$0.930861\pi$
$830$	8.04072	−	43.7477i	0.279098	−	1.51850i
$831$	8.01945	−	5.82647i	0.278192	−	0.202118i
$832$	1.89441	−	28.7821i	0.0656770	−	0.997841i
$833$	0.283850	−	0.873599i	0.00983481	−	0.0302684i
$834$	9.46308	−	1.26019i	0.327680	−	0.0436368i
$835$	48.6117	−	28.0660i	1.68228	−	0.971264i
$836$	−2.26264	+	9.61502i	−0.0782551	+	0.332542i
$837$	12.3719	−	12.3719i	0.427636	−	0.427636i
$838$	6.04004	−	4.64901i	0.208650	−	0.160597i
$839$	−1.51702	−	0.0795036i	−0.0523733	−	0.00274477i	0.0261313	−	0.999659i	$-0.491681\pi$
$839$	−1.51702	−	0.0795036i	−0.0523733	−	0.00274477i	−0.0785046	+	0.996914i	$0.525015\pi$
$840$	8.54813	−	14.0903i	0.294938	−	0.486162i
$841$	−3.07116	−	29.2202i	−0.105902	−	1.00759i
$842$	−0.569438	−	0.825897i	−0.0196241	−	0.0284623i
$843$	0.132362	+	2.52562i	0.00455879	+	0.0869868i
$844$	−30.1044	+	4.86010i	−1.03623	+	0.167292i
$845$	−37.2245	−	11.7771i	−1.28056	−	0.405143i
$846$	36.3209	+	22.1830i	1.24874	+	0.762669i
$847$	−27.4032	−	8.81185i	−0.941586	−	0.302779i
$848$	26.7891	+	2.65426i	0.919941	+	0.0911476i
$849$	0.0112748	+	0.0253237i	0.000386952	+	0.000869108i
$850$	−34.2104	−	2.64112i	−1.17341	−	0.0905896i
$851$	12.6652	+	19.5028i	0.434159	+	0.668546i
$852$	19.7980	+	4.14654i	0.678267	+	0.142058i
$853$	1.03953	+	0.164646i	0.0355929	+	0.00563737i	0.174206	−	0.984709i	$-0.444264\pi$
$853$	1.03953	+	0.164646i	0.0355929	+	0.00563737i	−0.138613	+	0.990347i	$0.544264\pi$
$854$	−30.8425	−	29.1812i	−1.05541	−	0.998560i
$855$	−10.7191	+	2.27841i	−0.366585	+	0.0779201i
$856$	−5.31769	−	7.66365i	−0.181755	−	0.261938i
$857$		−	38.9865i		−	1.33176i	−0.746061	−	0.665878i	$-0.768057\pi$
$857$		−	38.9865i		−	1.33176i	0.746061	−	0.665878i	$-0.231943\pi$
$858$	7.17262	+	10.2839i	0.244869	+	0.351086i
$859$			46.3691i			1.58209i	0.611756	+	0.791047i	$0.290464\pi$
$859$			46.3691i			1.58209i	−0.611756	+	0.791047i	$0.709536\pi$
$860$	−21.6285	−	9.55246i	−0.737525	−	0.325736i
$861$	−16.1688	+	3.43678i	−0.551030	+	0.117125i
$862$	−7.00347	+	7.40218i	−0.238539	+	0.252119i
$863$	−20.0511	−	3.17578i	−0.682547	−	0.108105i	−0.194474	−	0.980908i	$-0.562300\pi$
$863$	−20.0511	−	3.17578i	−0.682547	−	0.108105i	−0.488073	+	0.872803i	$0.662300\pi$
$864$	−21.9649	−	6.32864i	−0.747263	−	0.215305i
$865$	0.761501	+	1.17261i	0.0258918	+	0.0398699i
$866$	−0.804863	+	10.4254i	−0.0273503	+	0.354270i
$867$	5.85863	+	13.1587i	0.198969	+	0.446893i
$868$	19.0421	+	12.2855i	0.646331	+	0.416998i
$869$	−25.5960	+	13.9479i	−0.868283	+	0.473150i
$870$	12.5409	−	20.5335i	0.425176	−	0.696151i
$871$	21.7815	+	45.2145i	0.738039	+	1.53204i
$872$	4.11436	−	10.0599i	0.139330	−	0.340672i
$873$	1.77232	+	33.8179i	0.0599840	+	1.14456i
$874$	7.85573	−	5.41635i	0.265724	−	0.183211i
$875$	0.805162	+	7.66060i	0.0272194	+	0.258976i
$876$	20.1869	−	0.0601799i	0.682053	−	0.00203329i
$877$	−25.2872	−	1.32525i	−0.853889	−	0.0447504i	−0.379633	−	0.925137i	$-0.623950\pi$
$877$	−25.2872	−	1.32525i	−0.853889	−	0.0447504i	−0.474256	+	0.880387i	$0.657283\pi$
$878$	25.0768	+	32.5800i	0.846300	+	1.09952i
$879$	4.71054	−	4.71054i	0.158883	−	0.158883i
$880$	−2.82881	+	39.7429i	−0.0953590	+	1.33973i
$881$	−11.4405	+	6.60519i	−0.385441	+	0.222535i	−0.680183	−	0.733042i	$-0.738100\pi$
$881$	−11.4405	+	6.60519i	−0.385441	+	0.222535i	0.294742	+	0.955577i	$0.404766\pi$
$882$	−0.0696168	−	0.522769i	−0.00234412	−	0.0176026i
$883$	3.54569	−	10.9125i	0.119322	−	0.367235i	−0.873502	−	0.486821i	$-0.838157\pi$
$883$	3.54569	−	10.9125i	0.119322	−	0.367235i	0.992824	+	0.119585i	$0.0381565\pi$
$884$	−20.5049	+	38.3903i	−0.689653	+	1.29121i
$885$	4.45189	−	3.23449i	0.149649	−	0.108726i
$886$	14.2641	+	2.62171i	0.479211	+	0.0880780i
$887$	−14.7127	−	13.2474i	−0.494005	−	0.444805i	0.384086	−	0.923297i	$-0.374517\pi$
$887$	−14.7127	−	13.2474i	−0.494005	−	0.444805i	−0.878091	+	0.478493i	$0.841183\pi$
$888$	6.58976	+	8.50889i	0.221138	+	0.285540i
$889$	−45.5016	+	7.20674i	−1.52607	+	0.241706i
$890$	−43.2570	−	12.7432i	−1.44998	−	0.427153i
$891$	−13.3364	+	5.54790i	−0.446788	+	0.185862i
$892$	−9.33418	−	3.00213i	−0.312532	−	0.100519i
$893$	−16.7075	+	7.43866i	−0.559096	+	0.248925i
$894$	0.731916	−	2.07670i	0.0244789	−	0.0694552i
$895$	1.90306	+	36.3126i	0.0636124	+	1.21380i
$896$	2.01479	−	29.5374i	0.0673094	−	0.986777i
$897$	1.53443	−	12.0144i	0.0512330	−	0.401150i
$898$	56.2045	+	13.4049i	1.87557	+	0.447328i
$899$	27.7465	+	18.0188i	0.925396	+	0.600959i
$900$	−18.3706	+	7.11471i	−0.612353	+	0.237157i
$901$	−35.1778	−	20.3099i	−1.17194	−	0.676622i
$902$	30.9813	−	25.2429i	1.03156	−	0.840498i
$903$	−7.37666	+	1.97657i	−0.245480	+	0.0657761i
$904$	12.2407	+	5.77146i	0.407119	+	0.191956i
$905$	16.2302	−	8.26971i	0.539511	−	0.274894i
$906$	6.58967	−	6.96483i	0.218927	−	0.231391i
$907$	24.4197	+	10.8724i	0.810843	+	0.361011i	0.769911	−	0.638151i	$-0.220301\pi$
$907$	24.4197	+	10.8724i	0.810843	+	0.361011i	0.0409321	+	0.999162i	$0.486967\pi$
$908$	19.0211	+	17.0243i	0.631237	+	0.564970i
$909$	15.1949	−	4.93711i	0.503982	−	0.163754i
$910$	−38.1786	−	12.1790i	−1.26561	−	0.403730i
$911$	−15.6666	+	21.5632i	−0.519056	+	0.714420i	−0.985414	−	0.170177i	$-0.945566\pi$
$911$	−15.6666	+	21.5632i	−0.519056	+	0.714420i	0.466357	+	0.884596i	$0.345566\pi$
$912$	3.41531	−	2.79954i	0.113092	−	0.0927021i
$913$	28.6547	+	19.6298i	0.948334	+	0.649652i
$914$	5.66334	−	3.08588i	0.187327	−	0.102072i
$915$	−3.99637	−	25.2321i	−0.132116	−	0.834147i
$916$	6.94931	+	15.4840i	0.229612	+	0.511606i
$917$	5.87015	+	9.03923i	0.193849	+	0.298502i
$918$	26.2606	+	22.3610i	0.866728	+	0.738024i
$919$	26.5193	−	2.78729i	0.874791	−	0.0919442i	0.343519	−	0.939146i	$-0.388381\pi$
$919$	26.5193	−	2.78729i	0.874791	−	0.0919442i	0.531272	+	0.847201i	$0.321714\pi$
$920$	27.8005	−	26.6190i	0.916555	−	0.877601i
$921$	13.0655	+	8.48481i	0.430522	+	0.279584i
$922$	−12.9697	−	31.1801i	−0.427134	−	1.02686i
$923$	−1.47790	−	49.1631i	−0.0486456	−	1.61822i
$924$	7.33686	+	10.5729i	0.241365	+	0.347824i
$925$	19.9282	+	5.33974i	0.655235	+	0.175570i
$926$	29.9596	−	39.1648i	0.984533	−	1.28704i
$927$	9.40579	+	10.4462i	0.308927	+	0.343098i
$928$	3.06998	−	43.1135i	0.100777	−	1.41527i
$929$	44.2646	+	35.8448i	1.45227	+	1.17603i	0.950376	+	0.311103i	$0.100698\pi$
$929$	44.2646	+	35.8448i	1.45227	+	1.17603i	0.501899	+	0.864926i	$0.332635\pi$
$930$	4.57050	+	12.8458i	0.149873	+	0.421231i
$931$	0.201928	+	0.102887i	0.00661791	+	0.00337199i
$932$	−3.28501	+	8.63459i	−0.107604	+	0.282835i
$933$	6.37039	+	0.669555i	0.208557	+	0.0219202i
$934$	34.3378	−	32.6828i	1.12357	−	1.06941i
$935$	28.6063	−	52.8777i	0.935525	−	1.72929i
$936$	−1.09955	+	24.9644i	−0.0359398	+	0.815987i
$937$	−14.8924	−	10.8200i	−0.486514	−	0.353473i	0.317328	−	0.948316i	$-0.397214\pi$
$937$	−14.8924	−	10.8200i	−0.486514	−	0.353473i	−0.803842	+	0.594843i	$0.797214\pi$
$938$	22.2461	+	46.4615i	0.726361	+	1.51702i
$939$	6.43262	+	5.79196i	0.209921	+	0.189013i
$940$	−61.7494	+	40.3627i	−2.01404	+	1.31649i
$941$	−2.87639	+	18.1608i	−0.0937675	+	0.592025i	0.895403	+	0.445256i	$0.146887\pi$
$941$	−2.87639	+	18.1608i	−0.0937675	+	0.592025i	−0.989171	+	0.146769i	$0.953113\pi$
$942$	−12.4844	+	0.345537i	−0.406763	+	0.0112582i
$943$	−38.5520	−	2.02043i	−1.25543	−	0.0657941i
$944$	4.43531	−	8.83460i	0.144357	−	0.287542i
$945$	−15.8789	+	27.5030i	−0.516539	+	0.894672i
$946$	13.6834	−	12.3954i	0.444887	−	0.403009i
$947$	10.8292	+	2.90168i	0.351902	+	0.0942920i	0.430440	−	0.902619i	$-0.358358\pi$
$947$	10.8292	+	2.90168i	0.351902	+	0.0942920i	−0.0785376	+	0.996911i	$0.525025\pi$
$948$	12.8777	+	2.00029i	0.418248	+	0.0649664i
$949$	−11.6438	−	47.6858i	−0.377974	−	1.54795i
$950$	1.96398	−	8.23463i	0.0637200	−	0.267167i
$951$	6.34131	+	16.5197i	0.205631	+	0.535687i
$952$	−21.1401	+	39.3538i	−0.685154	+	1.27547i
$953$	−7.77476	+	36.5774i	−0.251849	+	1.18486i	0.652407	+	0.757868i	$0.273759\pi$
$953$	−7.77476	+	36.5774i	−0.251849	+	1.18486i	−0.904257	+	0.426989i	$0.859574\pi$
$954$	−23.2525	−	1.79514i	−0.752827	−	0.0581198i
$955$	−20.6971	−	7.94489i	−0.669744	−	0.257091i
$956$	15.7807	−	14.2945i	0.510386	−	0.462316i
$957$	10.6652	+	15.4675i	0.344757	+	0.499994i
$958$	−12.2253	+	6.66144i	−0.394983	+	0.215221i
$959$	0.658789	−	6.26796i	0.0212734	−	0.202403i
$960$	11.8004	−	13.3438i	0.380858	−	0.430669i
$961$	11.6521	−	3.78601i	0.375876	−	0.122129i
$962$	16.3597	−	20.4256i	0.527458	−	0.658547i
$963$	4.74987	+	6.53764i	0.153062	+	0.210672i
$964$	−42.9146	+	24.9476i	−1.38219	+	0.803509i
$965$	14.9704	−	3.18206i	0.481915	−	0.102434i
$966$	1.60431	−	12.3279i	0.0516178	−	0.396644i
$967$	−33.7614	−	33.7614i	−1.08569	−	1.08569i	−0.995966	−	0.0897284i	$-0.971400\pi$
$967$	−33.7614	−	33.7614i	−1.08569	−	1.08569i	−0.0897284	−	0.995966i	$-0.528600\pi$
$968$	−27.4531	−	14.6399i	−0.882376	−	0.470544i
$969$	−6.43635	+	1.72462i	−0.206765	+	0.0554026i
$970$	−54.2645	−	22.3824i	−1.74233	−	0.718655i
$971$	40.6644	−	36.6144i	1.30498	−	1.17501i	0.332221	−	0.943202i	$-0.392202\pi$
$971$	40.6644	−	36.6144i	1.30498	−	1.17501i	0.972761	−	0.231810i	$-0.0744647\pi$
$972$	29.6802	+	7.85803i	0.951994	+	0.252047i
$973$	−8.53867	−	22.2440i	−0.273737	−	0.713110i
$974$	2.86439	+	35.7149i	0.0917811	+	1.14438i
$975$	−6.12069	−	8.83220i	−0.196019	−	0.282857i
$976$	−27.1959	−	36.9664i	−0.870520	−	1.18327i
$977$	−18.0673	−	22.3112i	−0.578024	−	0.713800i	0.401334	−	0.915932i	$-0.368547\pi$
$977$	−18.0673	−	22.3112i	−0.578024	−	0.713800i	−0.979358	+	0.202131i	$0.935213\pi$
$978$	−1.36314	−	0.0336620i	−0.0435885	−	0.00107639i
$979$	22.8286	−	26.8113i	0.729605	−	0.856892i
$980$	0.870247	+	0.279895i	0.0277990	+	0.00894092i
$981$	−3.37435	+	8.79048i	−0.107735	+	0.280658i
$982$	9.97944	−	14.5666i	0.318457	−	0.464840i
$983$	−8.89120	−	4.53029i	−0.283585	−	0.144494i	0.306412	−	0.951899i	$-0.400871\pi$
$983$	−8.89120	−	4.53029i	−0.283585	−	0.144494i	−0.589998	+	0.807405i	$0.700871\pi$
$984$	−17.8582	+	0.547554i	−0.569298	+	0.0174554i
$985$	−2.65870	+	5.97154i	−0.0847133	+	0.190269i
$986$	−31.0341	+	57.3614i	−0.988326	+	1.82676i
$987$	−7.36311	+	22.6613i	−0.234370	+	0.721318i
$988$	−8.56375	−	6.47843i	−0.272449	−	0.206106i
$989$	−17.8356			−0.567138
$990$	1.70272	−	34.4753i	0.0541161	−	1.09570i
$991$	19.1610	−	11.0626i	0.608669	−	0.351415i	−0.163775	−	0.986498i	$-0.552367\pi$
$991$	19.1610	−	11.0626i	0.608669	−	0.351415i	0.772444	+	0.635082i	$0.219034\pi$
$992$	17.8923	+	16.7275i	0.568081	+	0.531098i
$993$	2.93513	+	5.76052i	0.0931435	+	0.182804i
$994$	−1.39674	−	50.4648i	−0.0443020	−	1.60065i
$995$	27.2512	+	22.0676i	0.863922	+	0.699591i
$996$	−4.84261	−	14.7542i	−0.153444	−	0.467505i
$997$	−51.9925	−	11.0513i	−1.64662	−	0.350000i	−0.711049	−	0.703142i	$-0.751780\pi$
$997$	−51.9925	−	11.0513i	−1.64662	−	0.350000i	−0.935570	+	0.353142i	$0.885113\pi$
$998$	−4.73407	+	13.4322i	−0.149854	+	0.425189i
$999$	−13.0513	−	16.1170i	−0.412925	−	0.509919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.4	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.49	yes	1280
11.3	even	5	inner	572.2.bs.a.223.37	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.18	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.18	yes	1280
52.7	even	12	inner	572.2.bs.a.59.37	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.49	yes	1280
572.267	even	60	inner	572.2.bs.a.267.4	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.4	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.49	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.18	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.37	yes	1280	52.7	even	12	inner
572.2.bs.a.223.18	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.37	yes	1280	11.3	even	5	inner
572.2.bs.a.267.4	yes	1280	572.267	even	60	inner
572.2.bs.a.267.49	yes	1280	143.124	odd	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40184 + 0.186682i) q^{2} +(0.154145 + 0.725193i) q^{3} +(1.93030 - 0.523395i) q^{4} +(0.469822 - 2.96634i) q^{5} +(-0.351466 - 0.987827i) q^{6} +(-2.19466 + 1.42523i) q^{7} +(-2.60826 + 1.09407i) q^{8} +(2.23849 - 0.996641i) q^{9} +O(q^{10})\)	\(q+(-1.40184 + 0.186682i) q^{2} +(0.154145 + 0.725193i) q^{3} +(1.93030 - 0.523395i) q^{4} +(0.469822 - 2.96634i) q^{5} +(-0.351466 - 0.987827i) q^{6} +(-2.19466 + 1.42523i) q^{7} +(-2.60826 + 1.09407i) q^{8} +(2.23849 - 0.996641i) q^{9} +(-0.104853 + 4.24603i) q^{10} +(-2.99570 - 1.42329i) q^{11} +(0.677108 + 1.31916i) q^{12} +(2.73260 - 2.35222i) q^{13} +(2.81049 - 2.40764i) q^{14} +(2.22359 - 0.116533i) q^{15} +(3.45212 - 2.02062i) q^{16} +(-6.00252 + 0.630890i) q^{17} +(-2.95195 + 1.81501i) q^{18} +(0.0779342 - 1.48707i) q^{19} +(-0.645669 - 5.97183i) q^{20} +(-1.37186 - 1.37186i) q^{21} +(4.46519 + 1.43598i) q^{22} +(-2.26551 - 3.92398i) q^{23} +(-1.19546 - 1.72285i) q^{24} +(-3.82315 - 1.24222i) q^{25} +(-3.39154 + 3.80755i) q^{26} +(2.37515 + 3.26911i) q^{27} +(-3.49039 + 3.89979i) q^{28} +(-5.11266 + 5.67819i) q^{29} +(-3.09536 + 0.578464i) q^{30} +(-0.677349 - 4.27661i) q^{31} +(-4.46209 + 3.47703i) q^{32} +(0.570391 - 2.39186i) q^{33} +(8.29678 - 2.00497i) q^{34} +(3.19661 + 7.17971i) q^{35} +(3.79932 - 3.09543i) q^{36} +(-5.12523 + 0.268602i) q^{37} +(0.168358 + 2.09918i) q^{38} +(2.12703 + 1.61908i) q^{39} +(2.01995 + 8.25100i) q^{40} +(4.64040 - 7.14560i) q^{41} +(2.17923 + 1.66703i) q^{42} +(1.96816 - 3.40896i) q^{43} +(-6.52755 - 1.17945i) q^{44} +(-1.90468 - 7.10837i) q^{45} +(3.90841 + 5.07785i) q^{46} +(-5.57572 - 10.9430i) q^{47} +(1.99746 + 2.19198i) q^{48} +(-0.0619014 + 0.139033i) q^{49} +(5.59133 + 1.02767i) q^{50} +(-1.38277 - 4.25574i) q^{51} +(4.04359 - 5.97071i) q^{52} +(5.44474 + 3.95583i) q^{53} +(-3.93986 - 4.13937i) q^{54} +(-5.62941 + 8.21758i) q^{55} +(4.16495 - 6.11847i) q^{56} +(1.09043 - 0.172707i) q^{57} +(6.10711 - 8.91434i) q^{58} +(2.07266 - 1.34600i) q^{59} +(4.23120 - 1.38876i) q^{60} +(-1.19927 - 11.4103i) q^{61} +(1.74790 + 5.86867i) q^{62} +(-3.49229 + 5.37765i) q^{63} +(5.60604 - 5.70722i) q^{64} +(-5.69364 - 9.21093i) q^{65} +(-0.353080 + 3.45948i) q^{66} +(-3.60263 + 13.4452i) q^{67} +(-11.2565 + 4.35949i) q^{68} +(2.49642 - 2.24779i) q^{69} +(-5.82145 - 9.46804i) q^{70} +(8.58491 - 10.6015i) q^{71} +(-4.74818 + 5.04856i) q^{72} +(6.18073 - 12.1304i) q^{73} +(7.13460 - 1.33332i) q^{74} +(0.311529 - 2.96400i) q^{75} +(-0.627890 - 2.91129i) q^{76} +(8.60307 - 1.14592i) q^{77} +(-3.28400 - 1.87261i) q^{78} +(5.16600 - 7.11039i) q^{79} +(-4.37196 - 11.1895i) q^{80} +(2.91416 - 3.23650i) q^{81} +(-5.17114 + 10.8832i) q^{82} +(-10.3436 - 1.63827i) q^{83} +(-3.36613 - 1.93008i) q^{84} +(-0.948681 + 18.1019i) q^{85} +(-2.12266 + 5.14623i) q^{86} +(-4.90587 - 2.83241i) q^{87} +(9.37075 + 0.434818i) q^{88} +(-2.74795 + 10.2555i) q^{89} +(3.99706 + 9.60921i) q^{90} +(-2.64467 + 9.05689i) q^{91} +(-6.42690 - 6.38869i) q^{92} +(2.99696 - 1.15043i) q^{93} +(9.85910 + 14.2994i) q^{94} +(-4.37455 - 0.929838i) q^{95} +(-3.20932 - 2.69992i) q^{96} +(-4.95274 + 12.9023i) q^{97} +(0.0608208 - 0.206457i) q^{98} +(-8.12437 - 0.200389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

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