LMFDB - Embedded newform 585.2.bt.b.571.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.42
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39901 - 0.807720i) q^{2} +(0.0517001 + 1.73128i) q^{3} +(0.304825 - 0.527972i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.47072 + 2.38032i) q^{6} +(-1.67328 + 0.966071i) q^{7} +2.24603i q^{8} +(-2.99465 + 0.179015i) q^{9} +O(q^{10})$	\(q+(1.39901 - 0.807720i) q^{2} +(0.0517001 + 1.73128i) q^{3} +(0.304825 - 0.527972i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.47072 + 2.38032i) q^{6} +(-1.67328 + 0.966071i) q^{7} +2.24603i q^{8} +(-2.99465 + 0.179015i) q^{9} -1.61544 q^{10} +(-5.50999 + 3.18119i) q^{11} +(0.929826 + 0.500440i) q^{12} +(-3.46141 - 1.00927i) q^{13} +(-1.56063 + 2.70309i) q^{14} +(0.820866 - 1.52518i) q^{15} +(2.42381 + 4.19817i) q^{16} +7.37934 q^{17} +(-4.04497 + 2.66929i) q^{18} -0.941719i q^{19} +(-0.527972 + 0.304825i) q^{20} +(-1.75905 - 2.84698i) q^{21} +(-5.13903 + 8.90106i) q^{22} +(1.21885 - 2.11111i) q^{23} +(-3.88850 + 0.116120i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.65777 + 1.38387i) q^{26} +(-0.464748 - 5.17533i) q^{27} +1.17793i q^{28} +(-1.01941 - 1.76567i) q^{29} +(-0.0835184 - 2.79678i) q^{30} +(8.79499 + 5.07779i) q^{31} +(2.89165 + 1.66950i) q^{32} +(-5.79240 - 9.37486i) q^{33} +(10.3238 - 5.96044i) q^{34} +1.93214 q^{35} +(-0.818330 + 1.63566i) q^{36} +3.18996i q^{37} +(-0.760646 - 1.31748i) q^{38} +(1.56837 - 6.04485i) q^{39} +(1.12301 - 1.94512i) q^{40} +(3.06411 + 1.76906i) q^{41} +(-4.76049 - 2.56214i) q^{42} +(4.69451 + 8.13113i) q^{43} +3.87882i q^{44} +(2.68295 + 1.34230i) q^{45} -3.93795i q^{46} +(-6.88435 + 3.97468i) q^{47} +(-7.14289 + 4.41334i) q^{48} +(-1.63341 + 2.82915i) q^{49} +(1.39901 + 0.807720i) q^{50} +(0.381512 + 12.7757i) q^{51} +(-1.58799 + 1.51988i) q^{52} -9.73349 q^{53} +(-4.83041 - 6.86496i) q^{54} +6.36239 q^{55} +(-2.16982 - 3.75825i) q^{56} +(1.63038 - 0.0486869i) q^{57} +(-2.85234 - 1.64680i) q^{58} +(7.79748 + 4.50188i) q^{59} +(-0.555033 - 0.898307i) q^{60} +(0.789296 + 1.36710i) q^{61} +16.4057 q^{62} +(4.83797 - 3.19259i) q^{63} -4.30130 q^{64} +(2.49304 + 2.60476i) q^{65} +(-15.6759 - 8.43691i) q^{66} +(-0.551568 - 0.318448i) q^{67} +(2.24940 - 3.89608i) q^{68} +(3.71793 + 2.00102i) q^{69} +(2.70309 - 1.56063i) q^{70} -10.3299i q^{71} +(-0.402072 - 6.72608i) q^{72} +0.468938i q^{73} +(2.57660 + 4.46280i) q^{74} +(-1.47348 + 0.910413i) q^{75} +(-0.497201 - 0.287059i) q^{76} +(6.14652 - 10.6461i) q^{77} +(-2.68838 - 9.72363i) q^{78} +(1.56469 + 2.71012i) q^{79} -4.84763i q^{80} +(8.93591 - 1.07217i) q^{81} +5.71563 q^{82} +(-3.12979 + 1.80699i) q^{83} +(-2.03932 + 0.0608990i) q^{84} +(-6.39069 - 3.68967i) q^{85} +(13.1354 + 7.58370i) q^{86} +(3.00417 - 1.85617i) q^{87} +(-7.14505 - 12.3756i) q^{88} -13.3769i q^{89} +(4.83769 - 0.289187i) q^{90} +(6.76695 - 1.65518i) q^{91} +(-0.743070 - 1.28703i) q^{92} +(-8.33637 + 15.4891i) q^{93} +(-6.42086 + 11.1213i) q^{94} +(-0.470859 + 0.815552i) q^{95} +(-2.74087 + 5.09257i) q^{96} +(6.43608 - 3.71587i) q^{97} +5.27736i q^{98} +(15.9310 - 10.5129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	1.39901	−	0.807720i	0.989251	−	0.571145i	0.0842010	−	0.996449i	$-0.473166\pi$
$2$	1.39901	−	0.807720i	0.989251	−	0.571145i	0.905050	+	0.425304i	$0.139833\pi$
$3$	0.0517001	+	1.73128i	0.0298491	+	0.999554i
$3$	0.0517001	+	1.73128i	0.0298491	+	0.999554i
$4$	0.304825	−	0.527972i	0.152412	−	0.263986i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.47072	+	2.38032i	0.600418	+	0.971763i
$7$	−1.67328	+	0.966071i	−0.632442	+	0.365141i	−0.781697	−	0.623658i	$-0.785646\pi$
$7$	−1.67328	+	0.966071i	−0.632442	+	0.365141i	0.149255	+	0.988799i	$0.452312\pi$
$8$			2.24603i			0.794091i
$9$	−2.99465	+	0.179015i	−0.998218	+	0.0596715i
$10$	−1.61544			−0.510847
$11$	−5.50999	+	3.18119i	−1.66132	+	0.959166i	−0.689240	+	0.724534i	$0.742055\pi$
$11$	−5.50999	+	3.18119i	−1.66132	+	0.959166i	−0.972084	+	0.234632i	$0.924611\pi$
$12$	0.929826	+	0.500440i	0.268418	+	0.144465i
$13$	−3.46141	−	1.00927i	−0.960023	−	0.279921i
$13$	−3.46141	−	1.00927i	−0.960023	−	0.279921i
$14$	−1.56063	+	2.70309i	−0.417096	+	0.722432i
$15$	0.820866	−	1.52518i	0.211947	−	0.393800i
$16$	2.42381	+	4.19817i	0.605953	+	1.04954i
$17$	7.37934			1.78975			0.894876	−	0.446315i	$-0.147264\pi$
$17$	7.37934			1.78975			0.894876	+	0.446315i	$0.147264\pi$
$18$	−4.04497	+	2.66929i	−0.953408	+	0.629157i
$19$		−	0.941719i		−	0.216045i	−0.994148	−	0.108023i	$-0.965548\pi$
$19$		−	0.941719i		−	0.216045i	0.994148	−	0.108023i	$-0.0344519\pi$
$20$	−0.527972	+	0.304825i	−0.118058	+	0.0681609i
$21$	−1.75905	−	2.84698i	−0.383856	−	0.621261i
$22$	−5.13903	+	8.90106i	−1.09564	+	1.89771i
$23$	1.21885	−	2.11111i	0.254147	−	0.440196i	−0.710516	−	0.703681i	$-0.751539\pi$
$23$	1.21885	−	2.11111i	0.254147	−	0.440196i	0.964664	+	0.263485i	$0.0848718\pi$
$24$	−3.88850	+	0.116120i	−0.793738	+	0.0237029i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.65777	+	1.38387i	−1.10958	+	0.271400i
$27$	−0.464748	−	5.17533i	−0.0894408	−	0.995992i
$28$			1.17793i			0.222608i
$29$	−1.01941	−	1.76567i	−0.189300	−	0.327878i	0.755717	−	0.654898i	$-0.227289\pi$
$29$	−1.01941	−	1.76567i	−0.189300	−	0.327878i	−0.945017	+	0.327021i	$0.893955\pi$
$30$	−0.0835184	−	2.79678i	−0.0152483	−	0.510620i
$31$	8.79499	+	5.07779i	1.57963	+	0.911998i	0.994911	+	0.100760i	$0.0321275\pi$
$31$	8.79499	+	5.07779i	1.57963	+	0.911998i	0.584716	+	0.811238i	$0.301206\pi$
$32$	2.89165	+	1.66950i	0.511177	+	0.295128i
$33$	−5.79240	−	9.37486i	−1.00833	−	1.63195i
$34$	10.3238	−	5.96044i	1.77051	−	1.02221i
$35$	1.93214			0.326592
$36$	−0.818330	+	1.63566i	−0.136388	+	0.272610i
$37$			3.18996i			0.524427i	0.965010	+	0.262213i	$0.0844524\pi$
$37$			3.18996i			0.524427i	−0.965010	+	0.262213i	$0.915548\pi$
$38$	−0.760646	−	1.31748i	−0.123393	−	0.213723i
$39$	1.56837	−	6.04485i	0.251140	−	0.967951i
$40$	1.12301	−	1.94512i	0.177564	−	0.307550i
$41$	3.06411	+	1.76906i	0.478533	+	0.276281i	0.719805	−	0.694176i	$-0.244231\pi$
$41$	3.06411	+	1.76906i	0.478533	+	0.276281i	−0.241272	+	0.970458i	$0.577565\pi$
$42$	−4.76049	−	2.56214i	−0.734560	−	0.395346i
$43$	4.69451	+	8.13113i	0.715906	+	1.23999i	0.962609	+	0.270894i	$0.0873194\pi$
$43$	4.69451	+	8.13113i	0.715906	+	1.23999i	−0.246703	+	0.969091i	$0.579347\pi$
$44$			3.87882i			0.584755i
$45$	2.68295	+	1.34230i	0.399951	+	0.200098i
$46$		−	3.93795i		−	0.580620i
$47$	−6.88435	+	3.97468i	−1.00419	+	0.579767i	−0.909484	−	0.415739i	$-0.863523\pi$
$47$	−6.88435	+	3.97468i	−1.00419	+	0.579767i	−0.0947013	+	0.995506i	$0.530190\pi$
$48$	−7.14289	+	4.41334i	−1.03099	+	0.637011i
$49$	−1.63341	+	2.82915i	−0.233345	+	0.404165i
$50$	1.39901	+	0.807720i	0.197850	+	0.114229i
$51$	0.381512	+	12.7757i	0.0534224	+	1.78895i
$52$	−1.58799	+	1.51988i	−0.220214	+	0.210769i
$53$	−9.73349			−1.33700			−0.668499	−	0.743713i	$-0.733063\pi$
$53$	−9.73349			−1.33700			−0.668499	+	0.743713i	$0.733063\pi$
$54$	−4.83041	−	6.86496i	−0.657335	−	0.934203i
$55$	6.36239			0.857904
$56$	−2.16982	−	3.75825i	−0.289955	−	0.502217i
$57$	1.63038	−	0.0486869i	0.215949	−	0.00644874i
$58$	−2.85234	−	1.64680i	−0.374531	−	0.216236i
$59$	7.79748	+	4.50188i	1.01515	+	0.586095i	0.912694	−	0.408643i	$-0.133998\pi$
$59$	7.79748	+	4.50188i	1.01515	+	0.586095i	0.102452	+	0.994738i	$0.467331\pi$
$60$	−0.555033	−	0.898307i	−0.0716544	−	0.115971i
$61$	0.789296	+	1.36710i	0.101059	+	0.175039i	0.912121	−	0.409921i	$-0.134444\pi$
$61$	0.789296	+	1.36710i	0.101059	+	0.175039i	−0.811062	+	0.584960i	$0.801110\pi$
$62$	16.4057			2.08353
$63$	4.83797	−	3.19259i	0.609527	−	0.402229i
$64$	−4.30130			−0.537663
$65$	2.49304	+	2.60476i	0.309223	+	0.323081i
$66$	−15.6759	−	8.43691i	−1.92957	−	1.03851i
$67$	−0.551568	−	0.318448i	−0.0673848	−	0.0389046i	0.465929	−	0.884822i	$-0.345720\pi$
$67$	−0.551568	−	0.318448i	−0.0673848	−	0.0389046i	−0.533314	+	0.845917i	$0.679054\pi$
$68$	2.24940	−	3.89608i	0.272780	−	0.472469i
$69$	3.71793	+	2.00102i	0.447586	+	0.240895i
$70$	2.70309	−	1.56063i	0.323081	−	0.186531i
$71$		−	10.3299i		−	1.22593i	−0.790109	−	0.612967i	$-0.789976\pi$
$71$		−	10.3299i		−	1.22593i	0.790109	−	0.612967i	$-0.210024\pi$
$72$	−0.402072	−	6.72608i	−0.0473846	−	0.792676i
$73$			0.468938i			0.0548850i	0.999623	+	0.0274425i	$0.00873632\pi$
$73$			0.468938i			0.0548850i	−0.999623	+	0.0274425i	$0.991264\pi$
$74$	2.57660	+	4.46280i	0.299524	+	0.518790i
$75$	−1.47348	+	0.910413i	−0.170143	+	0.105125i
$76$	−0.497201	−	0.287059i	−0.0570329	−	0.0329279i
$77$	6.14652	−	10.6461i	0.700461	−	1.21323i
$78$	−2.68838	−	9.72363i	−0.304399	−	1.10098i
$79$	1.56469	+	2.71012i	0.176041	+	0.304912i	0.940521	−	0.339735i	$-0.110337\pi$
$79$	1.56469	+	2.71012i	0.176041	+	0.304912i	−0.764480	+	0.644648i	$0.777004\pi$
$80$		−	4.84763i		−	0.541981i
$81$	8.93591	−	1.07217i	0.992879	−	0.119130i
$82$	5.71563			0.631186
$83$	−3.12979	+	1.80699i	−0.343539	+	0.198342i	−0.661836	−	0.749649i	$-0.730222\pi$
$83$	−3.12979	+	1.80699i	−0.343539	+	0.198342i	0.318297	+	0.947991i	$0.396889\pi$
$84$	−2.03932	+	0.0608990i	−0.222509	+	0.00664463i
$85$	−6.39069	−	3.68967i	−0.693168	−	0.400201i
$86$	13.1354	+	7.58370i	1.41642	+	0.817772i
$87$	3.00417	−	1.85617i	0.322081	−	0.199003i
$88$	−7.14505	−	12.3756i	−0.761665	−	1.31924i
$89$		−	13.3769i		−	1.41795i	−0.705234	−	0.708975i	$-0.749158\pi$
$89$		−	13.3769i		−	1.41795i	0.705234	−	0.708975i	$-0.250842\pi$
$90$	4.83769	−	0.289187i	0.509937	−	0.0304830i
$91$	6.76695	−	1.65518i	0.709370	−	0.173510i
$92$	−0.743070	−	1.28703i	−0.0774704	−	0.134183i
$93$	−8.33637	+	15.4891i	−0.864441	+	1.60615i
$94$	−6.42086	+	11.1213i	−0.662261	+	1.14707i
$95$	−0.470859	+	0.815552i	−0.0483092	+	0.0836739i
$96$	−2.74087	+	5.09257i	−0.279739	+	0.519759i
$97$	6.43608	−	3.71587i	0.653485	−	0.377290i	−0.136305	−	0.990667i	$-0.543523\pi$
$97$	6.43608	−	3.71587i	0.653485	−	0.377290i	0.789790	+	0.613377i	$0.210189\pi$
$98$			5.27736i			0.533094i
$99$	15.9310	−	10.5129i	1.60113	−	1.05659i
$100$	0.609649			0.0609649
$101$	−5.42789	−	9.40138i	−0.540095	−	0.935472i	−0.998898	−	0.0469340i	$-0.985055\pi$
$101$	−5.42789	−	9.40138i	−0.540095	−	0.935472i	0.458803	−	0.888538i	$-0.348278\pi$
$102$	10.8529	+	17.5652i	1.07460	+	1.73921i
$103$	−6.78223	+	11.7472i	−0.668273	+	1.15748i	0.310113	+	0.950700i	$0.399633\pi$
$103$	−6.78223	+	11.7472i	−0.668273	+	1.15748i	−0.978387	+	0.206784i	$0.933700\pi$
$104$	2.26685	−	7.77443i	0.222283	−	0.762346i
$105$	0.0998919	+	3.34508i	0.00974845	+	0.326446i
$106$	−13.6173	+	7.86194i	−1.32263	+	0.763619i
$107$	−1.38187			−0.133590			−0.0667951	−	0.997767i	$-0.521277\pi$
$107$	−1.38187			−0.133590			−0.0667951	+	0.997767i	$0.521277\pi$
$108$	−2.87409	−	1.33219i	−0.276560	−	0.128190i
$109$			1.94120i			0.185934i	0.995669	+	0.0929668i	$0.0296350\pi$
$109$			1.94120i			0.185934i	−0.995669	+	0.0929668i	$0.970365\pi$
$110$	8.90106	−	5.13903i	0.848683	−	0.489987i
$111$	−5.52272	+	0.164921i	−0.524193	+	0.0156536i
$112$	−8.11146	−	4.68315i	−0.766461	−	0.442516i
$113$	3.24821	−	5.62606i	0.305566	−	0.529255i	−0.671822	−	0.740713i	$-0.734488\pi$
$113$	3.24821	−	5.62606i	0.305566	−	0.529255i	0.977387	+	0.211458i	$0.0678212\pi$
$114$	2.24159	−	1.38500i	0.209945	−	0.129717i
$115$	−2.11111	+	1.21885i	−0.196862	+	0.113658i
$116$	−1.24297			−0.115407
$117$	10.5464	+	2.40277i	0.975016	+	0.222136i
$118$	14.5450			1.33898
$119$	−12.3477	+	7.12896i	−1.13191	+	0.653511i
$120$	3.42560	+	1.84369i	0.312713	+	0.168305i
$121$	14.7400	−	25.5304i	1.34000	−	2.32094i
$122$	2.20847	+	1.27506i	0.199946	+	0.115439i
$123$	−2.90433	+	5.39628i	−0.261874	+	0.486567i
$124$	5.36186	−	3.09567i	0.481509	−	0.277999i
$125$		−	1.00000i		−	0.0894427i
$126$	4.18966	−	8.37420i	0.373244	−	0.746033i
$127$	12.1445			1.07765			0.538823	−	0.842419i	$-0.318869\pi$
$127$	12.1445			1.07765			0.538823	+	0.842419i	$0.318869\pi$
$128$	−11.8009	+	6.81325i	−1.04306	+	0.602212i
$129$	−13.8345	+	8.54789i	−1.21806	+	0.752599i
$130$	5.59171	+	1.63041i	0.490425	+	0.142997i
$131$	−4.57197	+	7.91889i	−0.399455	+	0.691877i	−0.993659	−	0.112438i	$-0.964134\pi$
$131$	−4.57197	+	7.91889i	−0.399455	+	0.691877i	0.594204	+	0.804315i	$0.297467\pi$
$132$	−6.71533	+	0.200535i	−0.584494	+	0.0174544i
$133$	0.909768	+	1.57576i	0.0788869	+	0.136636i
$134$	−1.02887			−0.0888806
$135$	−2.18518	+	4.71434i	−0.188070	+	0.405746i
$136$			16.5742i			1.42123i
$137$	4.53064	−	2.61576i	0.387078	−	0.223480i	−0.293815	−	0.955862i	$-0.594925\pi$
$137$	4.53064	−	2.61576i	0.387078	−	0.223480i	0.680893	+	0.732382i	$0.261592\pi$
$138$	6.81770	−	0.203592i	0.580361	−	0.0173309i
$139$	−4.74600	+	8.22031i	−0.402550	+	0.697238i	−0.994033	−	0.109080i	$-0.965210\pi$
$139$	−4.74600	+	8.22031i	−0.402550	+	0.697238i	0.591483	+	0.806318i	$0.298543\pi$
$140$	0.588965	−	1.02012i	0.0497766	−	0.0862156i
$141$	−7.23720	−	11.7132i	−0.609482	−	0.986432i
$142$	−8.34367	−	14.4517i	−0.700185	−	1.21276i
$143$	22.2830	−	5.45036i	1.86340	−	0.455782i
$144$	−8.01002	−	12.1382i	−0.667501	−	1.01151i
$145$			2.03883i			0.169315i
$146$	0.378771	+	0.656050i	0.0313473	+	0.0542951i
$147$	−4.98250	−	2.68162i	−0.410950	−	0.221177i
$148$	1.68421	+	0.972380i	0.138441	+	0.0799291i
$149$	10.0033	+	5.77542i	0.819504	+	0.473141i	0.850245	−	0.526386i	$-0.176453\pi$
$149$	10.0033	+	5.77542i	0.819504	+	0.473141i	−0.0307413	+	0.999527i	$0.509787\pi$
$150$	−1.32606	+	2.46384i	−0.108272	+	0.201172i
$151$	−0.140481	+	0.0811070i	−0.0114322	+	0.00660039i	−0.505705	−	0.862706i	$-0.668768\pi$
$151$	−0.140481	+	0.0811070i	−0.0114322	+	0.00660039i	0.494273	+	0.869307i	$0.335434\pi$
$152$	2.11513			0.171560
$153$	−22.0986	+	1.32101i	−1.78656	+	0.106797i
$154$		−	19.8587i		−	1.60026i
$155$	−5.07779	−	8.79499i	−0.407858	−	0.706431i
$156$	−2.71343	−	2.67067i	−0.217248	−	0.213825i
$157$	−8.18891	+	14.1836i	−0.653546	+	1.13198i	0.328710	+	0.944431i	$0.393386\pi$
$157$	−8.18891	+	14.1836i	−0.653546	+	1.13198i	−0.982256	+	0.187544i	$0.939947\pi$
$158$	4.37804	+	2.52766i	0.348298	+	0.201090i
$159$	−0.503222	−	16.8514i	−0.0399081	−	1.33640i
$160$	−1.66950	−	2.89165i	−0.131985	−	0.228605i
$161$			4.70998i			0.371198i
$162$	11.6354	−	8.71770i	0.914166	−	0.684927i
$163$			18.5925i			1.45628i	0.685429	+	0.728140i	$0.259615\pi$
$163$			18.5925i			1.45628i	−0.685429	+	0.728140i	$0.740385\pi$
$164$	1.86803	−	1.07851i	0.145869	−	0.0842173i
$165$	0.328936	+	11.0151i	0.0256076	+	0.857522i
$166$	−2.91908	+	5.05599i	−0.226564	+	0.392421i
$167$	−6.61628	−	3.81991i	−0.511983	−	0.295593i	0.221665	−	0.975123i	$-0.428851\pi$
$167$	−6.61628	−	3.81991i	−0.511983	−	0.295593i	−0.733648	+	0.679529i	$0.762184\pi$
$168$	6.39439	−	3.95087i	0.493338	−	0.304817i
$169$	10.9628	+	6.98699i	0.843289	+	0.537461i
$170$	−11.9209			−0.914290
$171$	0.168581	+	2.82012i	0.0128917	+	0.215660i
$172$	5.72401			0.436452
$173$	−0.781849	−	1.35420i	−0.0594429	−	0.102958i	0.834773	−	0.550595i	$-0.185599\pi$
$173$	−0.781849	−	1.35420i	−0.0594429	−	0.102958i	−0.894215	+	0.447637i	$0.852266\pi$
$174$	2.70361	−	5.02334i	0.204960	−	0.380819i
$175$	−1.67328	−	0.966071i	−0.126488	−	0.0730281i
$176$	−26.7104	−	15.4212i	−2.01337	−	1.16242i
$177$	−7.39088	+	13.7324i	−0.555532	+	1.03219i
$178$	−10.8048	−	18.7145i	−0.809854	−	1.40271i
$179$	18.4354			1.37792			0.688962	−	0.724798i	$-0.258067\pi$
$179$	18.4354			1.37792			0.688962	+	0.724798i	$0.258067\pi$
$180$	1.52652	−	1.00736i	0.113780	−	0.0750841i
$181$	−13.1750			−0.979287			−0.489644	−	0.871923i	$-0.662873\pi$
$181$	−13.1750			−0.979287			−0.489644	+	0.871923i	$0.662873\pi$
$182$	8.13014	−	7.78142i	0.602646	−	0.576797i
$183$	−2.32603	+	1.43717i	−0.171945	+	0.106239i
$184$	4.74161	+	2.73757i	0.349556	+	0.201816i
$185$	1.59498	−	2.76259i	0.117265	−	0.203110i
$186$	0.848178	+	28.4029i	0.0621914	+	2.08260i
$187$	−40.6600	+	23.4751i	−2.97336	+	1.71667i
$188$			4.84632i			0.353454i
$189$	5.77739	+	8.21082i	0.420243	+	0.597249i
$190$			1.52129i			0.110366i
$191$	−9.17807	−	15.8969i	−0.664102	−	1.15026i	−0.979528	−	0.201308i	$-0.935481\pi$
$191$	−9.17807	−	15.8969i	−0.664102	−	1.15026i	0.315426	−	0.948950i	$-0.397853\pi$
$192$	−0.222378	−	7.44676i	−0.0160487	−	0.537423i
$193$	3.13840	+	1.81196i	0.225907	+	0.130427i	0.608682	−	0.793414i	$-0.291698\pi$
$193$	3.13840	+	1.81196i	0.225907	+	0.130427i	−0.382775	+	0.923841i	$0.625032\pi$
$194$	6.00277	−	10.3971i	0.430974	−	0.746469i
$195$	−4.38067	+	4.45081i	−0.313707	+	0.318729i
$196$	0.995808	+	1.72479i	0.0711292	+	0.123199i
$197$		−	10.9448i		−	0.779786i	−0.920860	−	0.389893i	$-0.872512\pi$
$197$		−	10.9448i		−	0.779786i	0.920860	−	0.389893i	$-0.127488\pi$
$198$	13.7962	−	27.5756i	0.980453	−	1.95971i
$199$	0.431232			0.0305693			0.0152846	−	0.999883i	$-0.495135\pi$
$199$	0.431232			0.0305693			0.0152846	+	0.999883i	$0.495135\pi$
$200$	−1.94512	+	1.12301i	−0.137541	+	0.0794091i
$201$	0.522806	−	0.971382i	0.0368759	−	0.0685160i
$202$	−15.1874	−	8.76843i	−1.06858	−	0.616945i
$203$	3.41154	+	1.96965i	0.239443	+	0.138242i
$204$	6.86150	+	3.69292i	0.480401	+	0.258556i
$205$	−1.76906	−	3.06411i	−0.123557	−	0.214006i
$206$			21.9126i			1.52672i
$207$	−3.27211	+	6.54023i	−0.227427	+	0.454577i
$208$	−4.15274	−	16.9779i	−0.287941	−	1.17720i
$209$	2.99579	+	5.18886i	0.207223	+	0.358921i
$210$	2.84164	+	4.59912i	0.196092	+	0.317370i
$211$	9.16012	−	15.8658i	0.630609	−	1.09225i	−0.356819	−	0.934174i	$-0.616139\pi$
$211$	9.16012	−	15.8658i	0.630609	−	1.09225i	0.987427	−	0.158073i	$-0.0505281\pi$
$212$	−2.96701	+	5.13901i	−0.203775	+	0.352948i
$213$	17.8839	−	0.534057i	1.22539	−	0.0365930i
$214$	−1.93325	+	1.11616i	−0.132154	+	0.0762993i
$215$		−	9.38902i		−	0.640326i
$216$	11.6239	−	1.04384i	0.790909	−	0.0710241i
$217$	−19.6220			−1.33203
$218$	1.56795	+	2.71577i	0.106195	+	0.183935i
$219$	−0.811862	+	0.0242441i	−0.0548606	+	0.00163827i
$220$	1.93941	−	3.35916i	0.130755	−	0.226474i
$221$	−25.5429	−	7.44773i	−1.71820	−	0.500989i
$222$	−7.59314	+	4.69154i	−0.509618	+	0.314875i
$223$	−4.35267	+	2.51301i	−0.291476	+	0.168284i	−0.638607	−	0.769533i	$-0.720489\pi$
$223$	−4.35267	+	2.51301i	−0.291476	+	0.168284i	0.347131	+	0.937817i	$0.387156\pi$
$224$	−6.45141			−0.431053
$225$	−1.65236	−	2.50394i	−0.110157	−	0.166929i
$226$		−	10.4946i		−	0.698088i
$227$	11.2561	−	6.49869i	0.747091	−	0.431333i	−0.0775508	−	0.996988i	$-0.524710\pi$
$227$	11.2561	−	6.49869i	0.747091	−	0.431333i	0.824642	+	0.565655i	$0.191377\pi$
$228$	0.471274	−	0.875634i	0.0312109	−	0.0579903i
$229$	3.06469	+	1.76940i	0.202520	+	0.116925i	0.597830	−	0.801623i	$-0.296030\pi$
$229$	3.06469	+	1.76940i	0.202520	+	0.116925i	−0.395310	+	0.918548i	$0.629363\pi$
$230$	−1.96898	+	3.41037i	−0.129830	+	0.224873i
$231$	18.7491	+	10.0909i	1.23360	+	0.663935i
$232$	3.96576	−	2.28963i	0.260365	−	0.150322i
$233$	−23.3569			−1.53016			−0.765080	−	0.643936i	$-0.777300\pi$
$233$	−23.3569			−1.53016			−0.765080	+	0.643936i	$0.777300\pi$
$234$	16.6953	−	5.15705i	1.09141	−	0.337127i
$235$	7.94936			0.518559
$236$	4.75373	−	2.74457i	0.309441	−	0.178656i
$237$	−4.61108	+	2.84903i	−0.299522	+	0.185064i
$238$	−11.5164	+	19.9470i	−0.746499	+	1.29297i
$239$	11.3847	+	6.57298i	0.736417	+	0.425171i	0.820765	−	0.571266i	$-0.193547\pi$
$239$	11.3847	+	6.57298i	0.736417	+	0.425171i	−0.0843479	+	0.996436i	$0.526881\pi$
$240$	8.39259	−	0.250623i	0.541740	−	0.0161776i
$241$	−8.14646	+	4.70336i	−0.524759	+	0.302970i	−0.738880	−	0.673837i	$-0.764645\pi$
$241$	−8.14646	+	4.70336i	−0.524759	+	0.302970i	0.214120	+	0.976807i	$0.431312\pi$
$242$		−	47.6231i		−	3.06133i
$243$	2.31822	+	15.4151i	0.148714	+	0.988880i
$244$	0.962388			0.0616106
$245$	2.82915	−	1.63341i	0.180748	−	0.104355i
$246$	0.295499	+	9.89535i	0.0188403	+	0.630905i
$247$	−0.950447	+	3.25968i	−0.0604755	+	0.207408i
$248$	−11.4049	+	19.7538i	−0.724210	+	1.25437i
$249$	−3.29021	−	5.32512i	−0.208508	−	0.337466i
$250$	−0.807720	−	1.39901i	−0.0510847	−	0.0884813i
$251$	15.2020			0.959539			0.479770	−	0.877394i	$-0.340720\pi$
$251$	15.2020			0.959539			0.479770	+	0.877394i	$0.340720\pi$
$252$	−0.210866	−	3.52749i	−0.0132833	−	0.222211i
$253$			15.5096i			0.975078i
$254$	16.9903	−	9.80933i	1.06606	−	0.615492i
$255$	6.05745	−	11.2548i	0.379332	−	0.704805i
$256$	−6.70509	+	11.6136i	−0.419068	+	0.725847i
$257$	−12.5970	+	21.8186i	−0.785777	+	1.36101i	0.142757	+	0.989758i	$0.454403\pi$
$257$	−12.5970	+	21.8186i	−0.785777	+	1.36101i	−0.928534	+	0.371248i	$0.878930\pi$
$258$	−12.4504	+	23.1330i	−0.775128	+	1.44020i
$259$	−3.08173	−	5.33772i	−0.191490	−	0.331670i
$260$	2.13518	−	0.522258i	0.132418	−	0.0323891i
$261$	3.36887	+	5.10510i	0.208528	+	0.315998i
$262$			14.7715i			0.912587i
$263$	14.8909	+	25.7917i	0.918210	+	1.59039i	0.802132	+	0.597147i	$0.203699\pi$
$263$	14.8909	+	25.7917i	0.918210	+	1.59039i	0.116079	+	0.993240i	$0.462967\pi$
$264$	21.0562	−	13.0099i	1.29592	−	0.800704i
$265$	8.42945	+	4.86674i	0.517817	+	0.298962i
$266$	2.54555	+	1.46968i	0.156078	+	0.0901116i
$267$	23.1592	−	0.691587i	1.41732	−	0.0423245i
$268$	−0.336263	+	0.194142i	−0.0205405	+	0.0118591i
$269$	2.22833			0.135864			0.0679318	−	0.997690i	$-0.478360\pi$
$269$	2.22833			0.135864			0.0679318	+	0.997690i	$0.478360\pi$
$270$	0.750773	+	8.36043i	0.0456906	+	0.508800i
$271$		−	1.25544i		−	0.0762627i	−0.999273	−	0.0381313i	$-0.987859\pi$
$271$		−	1.25544i		−	0.0762627i	0.999273	−	0.0381313i	$-0.0121405\pi$
$272$	17.8861	+	30.9797i	1.08451	+	1.87842i
$273$	3.21543	+	11.6299i	0.194606	+	0.703874i
$274$	4.22561	−	7.31898i	0.255279	−	0.442155i
$275$	−5.50999	−	3.18119i	−0.332265	−	0.191833i
$276$	2.18980	−	1.35300i	0.131810	−	0.0814411i
$277$	−9.29877	−	16.1059i	−0.558709	−	0.967712i	−0.997605	−	0.0691744i	$-0.977964\pi$
$277$	−9.29877	−	16.1059i	−0.558709	−	0.967712i	0.438896	−	0.898538i	$-0.355370\pi$
$278$			15.3338i			0.919658i
$279$	−27.2470	−	13.6318i	−1.63123	−	0.816114i
$280$			4.33965i			0.259344i
$281$	18.4127	−	10.6306i	1.09841	−	0.634168i	0.162608	−	0.986691i	$-0.448009\pi$
$281$	18.4127	−	10.6306i	1.09841	−	0.634168i	0.935803	+	0.352522i	$0.114676\pi$
$282$	−19.5860	−	10.5413i	−1.16633	−	0.627727i
$283$	−2.45119	+	4.24559i	−0.145708	+	0.252374i	−0.929637	−	0.368477i	$-0.879879\pi$
$283$	−2.45119	+	4.24559i	−0.145708	+	0.252374i	0.783929	+	0.620851i	$0.213213\pi$
$284$	−5.45390	−	3.14881i	−0.323629	−	0.186847i
$285$	−1.43629	−	0.773025i	−0.0850786	−	0.0457900i
$286$	26.7719	−	25.6236i	1.58305	−	1.51515i
$287$	−6.83616			−0.403526
$288$	−8.95837	−	4.48192i	−0.527877	−	0.264100i
$289$	37.4546			2.20321
$290$	1.64680	+	2.85234i	0.0967035	+	0.167495i
$291$	6.76596	+	10.9505i	0.396627	+	0.641932i
$292$	0.247586	+	0.142944i	0.0144889	+	0.00836516i
$293$	2.72771	+	1.57484i	0.159355	+	0.0920034i	0.577557	−	0.816351i	$-0.304006\pi$
$293$	2.72771	+	1.57484i	0.159355	+	0.0920034i	−0.418202	+	0.908354i	$0.637340\pi$
$294$	−9.13659	+	0.272840i	−0.532857	+	0.0159124i
$295$	−4.50188	−	7.79748i	−0.262110	−	0.453987i
$296$	−7.16475			−0.416443
$297$	19.0245	+	27.0375i	1.10391	+	1.56888i
$298$	18.6597			1.08093
$299$	−6.34961	+	6.07727i	−0.367207	+	0.351457i
$300$	0.0315189	+	1.05547i	0.00181975	+	0.0609378i
$301$	−15.7105	−	9.07046i	−0.905538	−	0.522813i
$302$	−0.131024	+	0.226939i	−0.00753956	+	0.0130589i
$303$	15.9958	−	9.88324i	0.918934	−	0.567777i
$304$	3.95349	−	2.28255i	0.226748	−	0.130913i
$305$		−	1.57859i		−	0.0903899i
$306$	−29.8492	+	19.6976i	−1.70636	+	1.12603i
$307$		−	2.40325i		−	0.137161i	−0.997646	−	0.0685803i	$-0.978153\pi$
$307$		−	2.40325i		−	0.137161i	0.997646	−	0.0685803i	$-0.0218469\pi$
$308$	−3.74722	−	6.49038i	−0.213518	−	0.369823i
$309$	−20.6883	−	11.1346i	−1.17692	−	0.633426i
$310$	−14.2078	−	8.20287i	−0.806948	−	0.465892i
$311$	7.31456	−	12.6692i	0.414771	−	0.718404i	−0.580634	−	0.814165i	$-0.697195\pi$
$311$	7.31456	−	12.6692i	0.414771	−	0.718404i	0.995404	+	0.0957610i	$0.0305285\pi$
$312$	13.5769	+	3.52261i	0.768641	+	0.199428i
$313$	2.39788	+	4.15325i	0.135536	+	0.234755i	0.925802	−	0.378009i	$-0.123391\pi$
$313$	2.39788	+	4.15325i	0.135536	+	0.234755i	−0.790266	+	0.612764i	$0.790058\pi$
$314$			26.4574i			1.49308i
$315$	−5.78610	+	0.345882i	−0.326010	+	0.0194882i
$316$	1.90782			0.107323
$317$	−15.0831	+	8.70825i	−0.847153	+	0.489104i	−0.859689	−	0.510818i	$-0.829343\pi$
$317$	−15.0831	+	8.70825i	−0.847153	+	0.489104i	0.0125365	+	0.999921i	$0.496009\pi$
$318$	−14.3152	−	23.1688i	−0.802758	−	1.29924i
$319$	11.2339	+	6.48590i	0.628978	+	0.363141i
$320$	3.72504	+	2.15065i	0.208236	+	0.120225i
$321$	−0.0714427	−	2.39240i	−0.00398754	−	0.133531i
$322$	3.80434	+	6.58932i	0.212008	+	0.367208i
$323$		−	6.94926i		−	0.386667i
$324$	2.15781	−	5.04473i	0.119878	−	0.280263i
$325$	−0.856654	−	3.50231i	−0.0475186	−	0.194273i
$326$	15.0176	+	26.0112i	0.831746	+	1.44063i
$327$	−3.36076	+	0.100360i	−0.185851	+	0.00554994i
$328$	−3.97337	+	6.88207i	−0.219392	+	0.379999i
$329$	7.67965	−	13.3015i	0.423393	−	0.733338i
$330$	9.35728	+	15.1445i	0.515101	+	0.833679i
$331$	17.0540	−	9.84616i	0.937375	−	0.541194i	0.0482387	−	0.998836i	$-0.484639\pi$
$331$	17.0540	−	9.84616i	0.937375	−	0.541194i	0.889137	+	0.457642i	$0.151306\pi$
$332$			2.20326i			0.120919i
$333$	−0.571050	−	9.55284i	−0.0312933	−	0.523492i
$334$	−12.3417			−0.675306
$335$	0.318448	+	0.551568i	0.0173987	+	0.0301354i
$336$	7.68848	−	14.2853i	0.419441	−	0.779328i
$337$	−4.87555	+	8.44469i	−0.265588	+	0.460012i	−0.967717	−	0.252037i	$-0.918899\pi$
$337$	−4.87555	+	8.44469i	−0.265588	+	0.460012i	0.702130	+	0.712049i	$0.252233\pi$
$338$	20.9806	+	0.920050i	1.14119	+	0.0500441i
$339$	9.90821	+	5.33268i	0.538140	+	0.289632i
$340$	−3.89608	+	2.24940i	−0.211295	+	0.121991i
$341$	−64.6137			−3.49903
$342$	2.51372	+	3.80922i	0.135926	+	0.205979i
$343$		−	19.8370i		−	1.07110i
$344$	−18.2628	+	10.5440i	−0.984662	+	0.568495i
$345$	−2.21931	−	3.59190i	−0.119484	−	0.193381i
$346$	−2.18763	−	1.26303i	−0.117608	−	0.0679010i
$347$	5.81162	−	10.0660i	0.311984	−	0.540372i	−0.666808	−	0.745230i	$-0.732340\pi$
$347$	5.81162	−	10.0660i	0.311984	−	0.540372i	0.978792	+	0.204858i	$0.0656732\pi$
$348$	−0.0642616	−	2.15193i	−0.00344478	−	0.115355i
$349$	22.7822	−	13.1533i	1.21950	−	0.704080i	0.254691	−	0.967023i	$-0.418026\pi$
$349$	22.7822	−	13.1533i	1.21950	−	0.704080i	0.964812	+	0.262942i	$0.0846929\pi$
$350$	−3.12126			−0.166838
$351$	−3.61461	+	18.3830i	−0.192934	+	0.981212i
$352$	−21.2440			−1.13231
$353$	−16.3137	+	9.41870i	−0.868289	+	0.501307i	−0.866779	−	0.498692i	$-0.833814\pi$
$353$	−16.3137	+	9.41870i	−0.868289	+	0.501307i	−0.00150982	+	0.999999i	$0.500481\pi$
$354$	0.751980	+	25.1815i	0.0399673	+	1.33838i
$355$	−5.16495	+	8.94596i	−0.274127	+	0.474802i
$356$	−7.06263	−	4.07761i	−0.374319	−	0.216113i
$357$	−12.9806	−	21.0088i	−0.687007	−	1.11190i
$358$	25.7913	−	14.8906i	1.36311	−	0.786994i
$359$			6.70817i			0.354044i	0.984207	+	0.177022i	$0.0566463\pi$
$359$			6.70817i			0.354044i	−0.984207	+	0.177022i	$0.943354\pi$
$360$	−3.01484	+	6.02599i	−0.158896	+	0.317598i
$361$	18.1132			0.953325
$362$	−18.4319	+	10.6417i	−0.968761	+	0.559315i
$363$	44.9623	+	24.1991i	2.35991	+	1.27012i
$364$	1.18885	−	4.07730i	0.0623125	−	0.213709i
$365$	0.234469	−	0.406112i	0.0122727	−	0.0212569i
$366$	−2.09331	+	3.88940i	−0.109419	+	0.203302i
$367$	5.58407	+	9.67189i	0.291486	+	0.504868i	0.974161	−	0.225853i	$-0.0725170\pi$
$367$	5.58407	+	9.67189i	0.291486	+	0.504868i	−0.682675	+	0.730722i	$0.739184\pi$
$368$	11.8170			0.616006
$369$	−9.49263	−	4.74921i	−0.494166	−	0.247234i
$370$		−	5.15320i		−	0.267902i
$371$	16.2869	−	9.40324i	0.845573	−	0.488192i
$372$	5.63668	+	9.12283i	0.292248	+	0.472997i
$373$	5.46832	−	9.47141i	0.283139	−	0.490411i	−0.689017	−	0.724745i	$-0.741958\pi$
$373$	5.46832	−	9.47141i	0.283139	−	0.490411i	0.972156	+	0.234334i	$0.0752909\pi$
$374$	−37.9226	+	65.6839i	−1.96093	+	3.39643i
$375$	1.73128	−	0.0517001i	0.0894029	−	0.00266978i
$376$	−8.92725	−	15.4624i	−0.460388	−	0.797415i
$377$	1.74657	+	7.14059i	0.0899528	+	0.367759i
$378$	14.7147	+	6.82052i	0.756842	+	0.350810i
$379$			15.8225i			0.812746i	0.913707	+	0.406373i	$0.133207\pi$
$379$			15.8225i			0.812746i	−0.913707	+	0.406373i	$0.866793\pi$
$380$	0.287059	+	0.497201i	0.0147258	+	0.0255059i
$381$	0.627870	+	21.0255i	0.0321667	+	1.07717i
$382$	−25.6805	−	14.8266i	−1.31393	−	0.758596i
$383$	9.03633	+	5.21713i	0.461735	+	0.266583i	0.712774	−	0.701394i	$-0.247439\pi$
$383$	9.03633	+	5.21713i	0.461735	+	0.266583i	−0.251039	+	0.967977i	$0.580772\pi$
$384$	−12.4057	−	20.0784i	−0.633078	−	1.02462i
$385$	−10.6461	+	6.14652i	−0.542575	+	0.313256i
$386$	5.85422			0.297972
$387$	−15.5140	−	23.5095i	−0.788622	−	1.19506i
$388$		−	4.53076i		−	0.230014i
$389$	−14.0596	−	24.3520i	−0.712851	−	1.23469i	−0.963783	−	0.266689i	$-0.914070\pi$
$389$	−14.0596	−	24.3520i	−0.712851	−	1.23469i	0.250932	−	0.968005i	$-0.419263\pi$
$390$	−2.53361	+	9.76510i	−0.128294	+	0.494475i
$391$	8.99429	−	15.5786i	0.454861	−	0.787842i
$392$	−6.35436	−	3.66869i	−0.320944	−	0.185297i
$393$	−13.9462	−	7.50595i	−0.703492	−	0.378625i
$394$	−8.84036	−	15.3119i	−0.445371	−	0.771405i
$395$		−	3.12938i		−	0.157456i
$396$	−0.694366	−	11.6157i	−0.0348932	−	0.583713i
$397$			6.52799i			0.327630i	0.986491	+	0.163815i	$0.0523801\pi$
$397$			6.52799i			0.327630i	−0.986491	+	0.163815i	$0.947620\pi$
$398$	0.603300	−	0.348315i	0.0302407	−	0.0174595i
$399$	−2.68105	+	1.65653i	−0.134220	+	0.0829302i
$400$	−2.42381	+	4.19817i	−0.121191	+	0.209908i
$401$	9.25851	+	5.34540i	0.462348	+	0.266937i	0.713031	−	0.701133i	$-0.247322\pi$
$401$	9.25851	+	5.34540i	0.462348	+	0.266937i	−0.250683	+	0.968069i	$0.580655\pi$
$402$	−0.0531925	−	1.78126i	−0.00265300	−	0.0888410i
$403$	−25.3182	−	26.4528i	−1.26119	−	1.31771i
$404$	−6.61822			−0.329269
$405$	−8.27481	−	3.53942i	−0.411179	−	0.175875i
$406$	6.36371			0.315826
$407$	−10.1479	−	17.5767i	−0.503012	−	0.871243i
$408$	−28.6946	+	0.856888i	−1.42059	+	0.0424223i
$409$	26.5803	+	15.3461i	1.31431	+	0.758818i	0.982807	−	0.184635i	$-0.0591104\pi$
$409$	26.5803	+	15.3461i	1.31431	+	0.758818i	0.331505	+	0.943454i	$0.392444\pi$
$410$	−4.94988	−	2.85782i	−0.244457	−	0.141137i
$411$	4.76285	+	7.70856i	0.234934	+	0.380235i
$412$	4.13478	+	7.16166i	0.203706	+	0.352829i
$413$	−17.3965			−0.856028
$414$	0.704951	+	11.7928i	0.0346464	+	0.579585i
$415$	3.61397			0.177403
$416$	−8.32424	−	8.69728i	−0.408129	−	0.426419i
$417$	−14.4770	−	7.79166i	−0.708943	−	0.381559i
$418$	8.38229	+	4.83952i	0.409991	+	0.236709i
$419$	−8.41035	+	14.5672i	−0.410873	+	0.711652i	−0.994985	−	0.100020i	$-0.968109\pi$
$419$	−8.41035	+	14.5672i	−0.410873	+	0.711652i	0.584113	+	0.811673i	$0.301443\pi$
$420$	1.79656	+	0.966922i	0.0876630	+	0.0471810i
$421$	20.0450	−	11.5730i	0.976933	−	0.564033i	0.0755903	−	0.997139i	$-0.475916\pi$
$421$	20.0450	−	11.5730i	0.976933	−	0.564033i	0.901343	+	0.433106i	$0.142583\pi$
$422$		−	29.5953i		−	1.44068i
$423$	19.9047	−	13.1352i	0.967800	−	0.638655i
$424$		−	21.8617i		−	1.06170i
$425$	3.68967	+	6.39069i	0.178975	+	0.309994i
$426$	24.5885	−	15.1924i	1.19132	−	0.736073i
$427$	−2.64143	−	1.52503i	−0.127828	−	0.0738015i
$428$	−0.421227	+	0.729587i	−0.0203608	+	0.0352659i
$429$	10.5881	+	38.2963i	0.511200	+	1.84896i
$430$	−7.58370	−	13.1354i	−0.365719	−	0.633443i
$431$			30.8013i			1.48365i	0.670595	+	0.741824i	$0.266039\pi$
$431$			30.8013i			1.48365i	−0.670595	+	0.741824i	$0.733961\pi$
$432$	20.6004	−	14.4951i	0.991139	−	0.697397i
$433$	7.60315			0.365384			0.182692	−	0.983170i	$-0.441519\pi$
$433$	7.60315			0.365384			0.182692	+	0.983170i	$0.441519\pi$
$434$	−27.4515	+	15.8491i	−1.31771	+	0.760782i
$435$	−3.52978	+	0.105407i	−0.169240	+	0.00505390i
$436$	1.02490	+	0.591727i	0.0490838	+	0.0283386i
$437$	−1.98807	−	1.14781i	−0.0951022	−	0.0549073i
$438$	−1.11622	+	0.689676i	−0.0533352	+	0.0329540i
$439$	5.40709	+	9.36536i	0.258067	+	0.446984i	0.965724	−	0.259571i	$-0.0835813\pi$
$439$	5.40709	+	9.36536i	0.258067	+	0.446984i	−0.707657	+	0.706556i	$0.750248\pi$
$440$			14.2901i			0.681254i
$441$	4.38505	−	8.76474i	0.208812	−	0.417369i
$442$	−41.7506	+	10.2121i	−1.98587	+	0.485739i
$443$	−18.3857	−	31.8450i	−0.873531	−	1.51300i	−0.858319	−	0.513117i	$-0.828491\pi$
$443$	−18.3857	−	31.8450i	−0.873531	−	1.51300i	−0.0152125	−	0.999884i	$-0.504842\pi$
$444$	−1.59639	+	2.96611i	−0.0757611	+	0.140765i
$445$	−6.68846	+	11.5847i	−0.317063	+	0.549170i
$446$	−4.05962	+	7.03148i	−0.192229	+	0.332950i
$447$	−9.48169	+	17.6171i	−0.448469	+	0.833262i
$448$	7.19731	−	4.15537i	0.340041	−	0.196323i
$449$			22.7851i			1.07530i	0.843169	+	0.537648i	$0.180687\pi$
$449$			22.7851i			1.07530i	−0.843169	+	0.537648i	$0.819313\pi$
$450$	−4.33415	−	2.16840i	−0.204314	−	0.102219i
$451$	−22.5109			−1.06000
$452$	−1.98027	−	3.42992i	−0.0931439	−	0.161330i
$453$	−0.147682	−	0.239019i	−0.00693869	−	0.0112301i
$454$	10.4982	−	18.1835i	0.492707	−	0.853394i
$455$	−6.68794	−	1.95005i	−0.313536	−	0.0914198i
$456$	0.109352	+	3.66188i	0.00512089	+	0.171483i
$457$	−4.16837	+	2.40661i	−0.194988	+	0.112576i	−0.594316	−	0.804232i	$-0.702577\pi$
$457$	−4.16837	+	2.40661i	−0.194988	+	0.112576i	0.399327	+	0.916808i	$0.369244\pi$
$458$	5.71672			0.267125
$459$	−3.42953	−	38.1905i	−0.160077	−	1.78258i
$460$			1.48614i			0.0692916i
$461$	18.5742	−	10.7238i	0.865087	−	0.499458i	−0.000625808	−	1.00000i	$-0.500199\pi$
$461$	18.5742	−	10.7238i	0.865087	−	0.499458i	0.865712	+	0.500542i	$0.166866\pi$
$462$	34.3809	−	1.02669i	1.59954	−	0.0477662i
$463$	20.1544	+	11.6361i	0.936653	+	0.540777i	0.888910	−	0.458083i	$-0.151464\pi$
$463$	20.1544	+	11.6361i	0.936653	+	0.540777i	0.0477435	+	0.998860i	$0.484797\pi$
$464$	4.94173	−	8.55933i	0.229414	−	0.397357i
$465$	14.9641	−	9.24577i	0.693942	−	0.428762i
$466$	−32.6766	+	18.8658i	−1.51371	+	0.873942i
$467$	28.0592			1.29842			0.649212	−	0.760608i	$-0.275099\pi$
$467$	28.0592			1.29842			0.649212	+	0.760608i	$0.275099\pi$
$468$	4.48340	−	4.83578i	0.207245	−	0.223534i
$469$	1.23057			0.0568226
$470$	11.1213	−	6.42086i	0.512985	−	0.296172i
$471$	−24.9792	−	13.4440i	−1.15098	−	0.619467i
$472$	−10.1114	+	17.5134i	−0.465413	+	0.806118i
$473$	−51.7334	−	29.8683i	−2.37870	−	1.37334i
$474$	−4.14974	+	7.71029i	−0.190604	+	0.354145i
$475$	0.815552	−	0.470859i	0.0374201	−	0.0216045i
$476$			8.69234i			0.398413i
$477$	29.1484	−	1.74244i	1.33461	−	0.0797806i
$478$	21.2365			0.971336
$479$	−28.5368	+	16.4757i	−1.30388	+	0.752795i	−0.981067	−	0.193668i	$-0.937962\pi$
$479$	−28.5368	+	16.4757i	−1.30388	+	0.752795i	−0.322813	+	0.946463i	$0.604628\pi$
$480$	4.91995	−	3.03986i	0.224564	−	0.138750i
$481$	3.21953	−	11.0418i	0.146798	−	0.503462i
$482$	−7.59800	+	13.1601i	−0.346079	+	0.599427i
$483$	−8.15428	+	0.243506i	−0.371033	+	0.0110799i
$484$	−8.98621	−	15.5646i	−0.408464	−	0.707481i
$485$	−7.43175			−0.337458
$486$	15.6943	+	19.6935i	0.711909	+	0.893314i
$487$		−	13.2788i		−	0.601718i	−0.953669	−	0.300859i	$-0.902727\pi$
$487$		−	13.2788i		−	0.601718i	0.953669	−	0.300859i	$-0.0972734\pi$
$488$	−3.07055	+	1.77278i	−0.138997	+	0.0802501i
$489$	−32.1889	+	0.961235i	−1.45563	+	0.0434686i
$490$	2.63868	−	4.57033i	0.119203	−	0.206466i
$491$	0.0319103	−	0.0552703i	0.00144009	−	0.00249431i	−0.865304	−	0.501247i	$-0.832875\pi$
$491$	0.0319103	−	0.0552703i	0.00144009	−	0.00249431i	0.866745	+	0.498752i	$0.166208\pi$
$492$	1.96378	+	3.17832i	0.0885338	+	0.143290i
$493$	−7.52259	−	13.0295i	−0.338800	−	0.586820i
$494$	1.30322	+	5.32803i	0.0586346	+	0.239719i
$495$	−19.0531	+	1.13896i	−0.856375	+	0.0511924i
$496$			49.2305i			2.21051i
$497$	9.97942	+	17.2849i	0.447638	+	0.775332i
$498$	−8.90425	−	4.79235i	−0.399009	−	0.214750i
$499$	−26.1316	−	15.0871i	−1.16981	−	0.675391i	−0.216176	−	0.976354i	$-0.569358\pi$
$499$	−26.1316	−	15.0871i	−1.16981	−	0.675391i	−0.953636	+	0.300963i	$0.902692\pi$
$500$	−0.527972	−	0.304825i	−0.0236116	−	0.0136322i
$501$	6.27127	−	11.6521i	0.280180	−	0.520578i
$502$	21.2677	−	12.2789i	0.949226	−	0.548036i
$503$	−18.8547			−0.840690			−0.420345	−	0.907364i	$-0.638091\pi$
$503$	−18.8547			−0.840690			−0.420345	+	0.907364i	$0.638091\pi$
$504$	7.17066	+	10.8662i	0.319406	+	0.484020i
$505$			10.8558i			0.483076i
$506$	12.5274	+	21.6981i	0.556910	+	0.964597i
$507$	−11.5297	+	19.3408i	−0.512050	+	0.858956i
$508$	3.70193	−	6.41193i	0.164247	−	0.284484i
$509$	14.0416	+	8.10694i	0.622384	+	0.359334i	0.777797	−	0.628516i	$-0.216337\pi$
$509$	14.0416	+	8.10694i	0.622384	+	0.359334i	−0.155412	+	0.987850i	$0.549671\pi$
$510$	−0.616310	−	20.6384i	−0.0272907	−	0.913882i
$511$	−0.453028	−	0.784667i	−0.0200408	−	0.0347116i
$512$		−	5.58962i		−	0.247029i
$513$	−4.87370	+	0.437662i	−0.215179	+	0.0193232i
$514$			40.6993i			1.79517i
$515$	11.7472	−	6.78223i	0.517642	−	0.298861i
$516$	0.295932	+	9.90986i	0.0130277	+	0.436257i
$517$	25.2884	−	43.8009i	1.11218	−	1.92636i
$518$	−8.62277	−	4.97836i	−0.378863	−	0.218736i
$519$	2.30408	−	1.42361i	0.101138	−	0.0624896i
$520$	−5.85036	+	5.59943i	−0.256555	+	0.245551i
$521$	5.86377			0.256897			0.128448	−	0.991716i	$-0.459000\pi$
$521$	5.86377			0.256897			0.128448	+	0.991716i	$0.459000\pi$
$522$	8.83658	+	4.42099i	0.386767	+	0.193501i
$523$	0.906536			0.0396401			0.0198200	−	0.999804i	$-0.493691\pi$
$523$	0.906536			0.0396401			0.0198200	+	0.999804i	$0.493691\pi$
$524$	2.78730	+	4.82774i	0.121764	+	0.210901i
$525$	1.58603	−	2.94687i	0.0692200	−	0.128612i
$526$	41.6650	+	24.0553i	1.81668	+	1.04886i
$527$	64.9012	+	37.4707i	2.82714	+	1.63225i
$528$	25.3175	−	47.0404i	1.10180	−	2.04717i
$529$	8.52882	+	14.7723i	0.370818	+	0.642276i
$530$	15.7239			0.683001
$531$	−24.1567	−	12.0857i	−1.04831	−	0.524475i
$532$	1.10928			0.0480933
$533$	−8.82068	−	9.21596i	−0.382066	−	0.399188i
$534$	31.8414	−	19.6737i	1.37791	−	0.851363i
$535$	1.19673	+	0.690934i	0.0517393	+	0.0298717i
$536$	0.715244	−	1.23884i	0.0308938	−	0.0535097i
$537$	0.953109	+	31.9168i	0.0411297	+	1.37731i
$538$	3.11746	−	1.79987i	0.134403	−	0.0775978i
$539$		−	20.7848i		−	0.895265i
$540$	1.82294	+	2.59076i	0.0784469	+	0.111489i
$541$		−	16.5050i		−	0.709604i	−0.934941	−	0.354802i	$-0.884548\pi$
$541$		−	16.5050i		−	0.709604i	0.934941	−	0.354802i	$-0.115452\pi$
$542$	−1.01405	−	1.75638i	−0.0435570	−	0.0754430i
$543$	−0.681147	−	22.8095i	−0.0292308	−	0.978851i
$544$	21.3385	+	12.3198i	0.914880	+	0.528206i
$545$	0.970602	−	1.68113i	0.0415760	−	0.0720118i
$546$	13.8921	+	13.6732i	0.594529	+	0.585160i
$547$	9.25797	+	16.0353i	0.395842	+	0.685619i	0.993208	−	0.116350i	$-0.0371194\pi$
$547$	9.25797	+	16.0353i	0.395842	+	0.685619i	−0.597366	+	0.801969i	$0.703786\pi$
$548$		−	3.18940i		−	0.136244i
$549$	−2.60840	−	3.95270i	−0.111324	−	0.168697i
$550$	−10.2781			−0.438258
$551$	−1.66277	+	0.960000i	−0.0708364	+	0.0408974i
$552$	−4.49435	+	8.35058i	−0.191292	+	0.355424i
$553$	−5.23634	−	3.02320i	−0.222672	−	0.128560i
$554$	−26.0182	−	15.0216i	−1.10541	−	0.638207i
$555$	4.86527	+	2.61853i	0.206519	+	0.111151i
$556$	2.89339	+	5.01151i	0.122707	+	0.212535i
$557$		−	7.75798i		−	0.328716i	−0.986401	−	0.164358i	$-0.947445\pi$
$557$		−	7.75798i		−	0.328716i	0.986401	−	0.164358i	$-0.0525552\pi$
$558$	−49.1295	+	2.93687i	−2.07982	+	0.124327i
$559$	−8.04314	−	32.8832i	−0.340189	−	1.39081i
$560$	4.68315	+	8.11146i	0.197899	+	0.342772i
$561$	−42.7441	−	69.1802i	−1.80466	−	2.92079i
$562$	17.1731	−	29.7447i	0.724404	−	1.25470i
$563$	2.00243	−	3.46830i	0.0843922	−	0.146172i	−0.820740	−	0.571302i	$-0.806438\pi$
$563$	2.00243	−	3.46830i	0.0843922	−	0.146172i	0.905132	+	0.425131i	$0.139772\pi$
$564$	−8.39033	+	0.250555i	−0.353297	+	0.0105503i
$565$	−5.62606	+	3.24821i	−0.236690	+	0.136653i
$566$			7.91951i			0.332882i
$567$	−13.9165	+	10.4268i	−0.584439	+	0.437883i
$568$	23.2013			0.973503
$569$	−16.3116	−	28.2525i	−0.683818	−	1.18441i	−0.973807	−	0.227378i	$-0.926985\pi$
$569$	−16.3116	−	28.2525i	−0.683818	−	1.18441i	0.289988	−	0.957030i	$-0.406349\pi$
$570$	−2.63378	+	0.0786509i	−0.110317	+	0.00329432i
$571$	−14.8576	+	25.7341i	−0.621771	+	1.07694i	0.367385	+	0.930069i	$0.380253\pi$
$571$	−14.8576	+	25.7341i	−0.621771	+	1.07694i	−0.989156	+	0.146869i	$0.953080\pi$
$572$	3.91478	−	13.4262i	0.163685	−	0.561378i
$573$	27.0474	−	16.7117i	1.12992	−	0.698140i
$574$	−9.56388	+	5.52171i	−0.399189	+	0.230472i
$575$	2.43770			0.101659
$576$	12.8809	−	0.769996i	0.536705	−	0.0320832i
$577$		−	10.4768i		−	0.436157i	−0.975931	−	0.218078i	$-0.930021\pi$
$577$		−	10.4768i		−	0.436157i	0.975931	−	0.218078i	$-0.0699788\pi$
$578$	52.3995	−	30.2528i	2.17953	−	1.25835i
$579$	−2.97475	+	5.52713i	−0.123626	+	0.229700i
$580$	1.07644	+	0.621484i	0.0446968	+	0.0258057i
$581$	3.49135	−	6.04720i	0.144846	−	0.250880i
$582$	18.3106	+	9.85494i	0.759000	+	0.408501i
$583$	53.6314	−	30.9641i	2.22119	−	1.28240i
$584$	−1.05325			−0.0435837
$585$	−7.93207	−	7.35406i	−0.327951	−	0.304053i
$586$	5.08814			0.210189
$587$	38.9457	−	22.4853i	1.60746	−	0.928068i	0.617525	−	0.786552i	$-0.288136\pi$
$587$	38.9457	−	22.4853i	1.60746	−	0.928068i	0.989936	−	0.141516i	$-0.0451977\pi$
$588$	−2.93461	+	1.81319i	−0.121021	+	0.0747749i
$589$	4.78185	−	8.28241i	0.197033	−	0.341271i
$590$	−12.5964	−	7.27252i	−0.518584	−	0.299405i
$591$	18.9485	−	0.565848i	0.779439	−	0.0232759i
$592$	−13.3920	+	7.73188i	−0.550408	+	0.317778i
$593$			36.4423i			1.49651i	0.663414	+	0.748253i	$0.269107\pi$
$593$			36.4423i			1.49651i	−0.663414	+	0.748253i	$0.730893\pi$
$594$	48.4542	+	22.4594i	1.98810	+	0.921521i
$595$	14.2579			0.584518
$596$	6.09852	−	3.52098i	0.249805	−	0.144225i
$597$	0.0222947	+	0.746584i	0.000912463	+	0.0305556i
$598$	−3.97445	+	13.6309i	−0.162527	+	0.557408i
$599$	23.6127	−	40.8983i	0.964787	−	1.67106i	0.254601	−	0.967046i	$-0.418056\pi$
$599$	23.6127	−	40.8983i	0.964787	−	1.67106i	0.710186	−	0.704014i	$-0.248611\pi$
$600$	−2.04481	−	3.30948i	−0.0834792	−	0.135109i
$601$	10.1585	+	17.5950i	0.414374	+	0.717716i	0.995362	−	0.0961952i	$-0.0306673\pi$
$601$	10.1585	+	17.5950i	0.414374	+	0.717716i	−0.580989	+	0.813912i	$0.697334\pi$
$602$	−29.3056			−1.19441
$603$	1.70876	+	0.854903i	0.0695862	+	0.0348143i
$604$			0.0988936i			0.00402392i
$605$	−25.5304	+	14.7400i	−1.03796	+	0.599265i
$606$	14.3954	−	26.7469i	0.584774	−	1.08652i
$607$	20.8842	−	36.1725i	0.847664	−	1.46820i	−0.0356232	−	0.999365i	$-0.511342\pi$
$607$	20.8842	−	36.1725i	0.847664	−	1.46820i	0.883287	−	0.468832i	$-0.155325\pi$
$608$	1.57220	−	2.72313i	0.0637610	−	0.110437i
$609$	−3.23364	+	6.00815i	−0.131034	+	0.243463i
$610$	−1.27506	−	2.20847i	−0.0516257	−	0.0894184i
$611$	27.8411	−	6.80985i	1.12633	−	0.275497i
$612$	−6.03873	+	12.0701i	−0.244101	+	0.487904i
$613$			11.4010i			0.460480i	0.973134	+	0.230240i	$0.0739512\pi$
$613$			11.4010i			0.460480i	−0.973134	+	0.230240i	$0.926049\pi$
$614$	−1.94115	−	3.36217i	−0.0783385	−	0.135686i
$615$	5.21336	−	3.22116i	0.210223	−	0.129890i
$616$	23.9114	+	13.8053i	0.963418	+	0.556230i
$617$	−31.6507	−	18.2735i	−1.27421	−	0.735665i	−0.298431	−	0.954431i	$-0.596463\pi$
$617$	−31.6507	−	18.2735i	−1.27421	−	0.735665i	−0.975777	+	0.218767i	$0.929797\pi$
$618$	−37.9368	+	1.13288i	−1.52604	+	0.0455712i
$619$	2.95784	−	1.70771i	0.118886	−	0.0686387i	−0.439378	−	0.898302i	$-0.644801\pi$
$619$	2.95784	−	1.70771i	0.118886	−	0.0686387i	0.558264	+	0.829664i	$0.311468\pi$
$620$	−6.19134			−0.248650
$621$	−11.4921	−	5.32680i	−0.461163	−	0.213757i
$622$		−	23.6325i		−	0.947576i
$623$	12.9231	+	22.3834i	0.517751	+	0.896771i
$624$	29.1787	−	8.06731i	1.16808	−	0.322951i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.70932	+	3.87363i	0.268158	+	0.154821i
$627$	−8.82848	+	5.45481i	−0.352576	+	0.217844i
$628$	4.99236	+	8.64703i	0.199217	+	0.345054i
$629$			23.5398i			0.938594i
$630$	−7.81545	+	5.15744i	−0.311375	+	0.205477i
$631$		−	40.2529i		−	1.60244i	−0.598367	−	0.801222i	$-0.704184\pi$
$631$		−	40.2529i		−	1.60244i	0.598367	−	0.801222i	$-0.295816\pi$
$632$	−6.08701	+	3.51434i	−0.242128	+	0.139793i
$633$	27.9417	+	15.0385i	1.11058	+	0.597725i
$634$	−14.0677	+	24.3659i	−0.558698	+	0.967693i
$635$	−10.5174	−	6.07223i	−0.417371	−	0.240969i
$636$	−9.05045	−	4.87103i	−0.358874	−	0.193149i
$637$	8.50929	−	8.14431i	0.337150	−	0.322689i
$638$	20.9552			0.829623
$639$	1.84920	+	30.9345i	0.0731533	+	1.22375i
$640$	13.6265			0.538634
$641$	−6.16833	−	10.6839i	−0.243634	−	0.421987i	0.718112	−	0.695927i	$-0.245006\pi$
$641$	−6.16833	−	10.6839i	−0.243634	−	0.421987i	−0.961747	+	0.273940i	$0.911673\pi$
$642$	−2.03234	−	3.28929i	−0.0802100	−	0.129818i
$643$	−35.6794	−	20.5995i	−1.40706	−	0.812365i	−0.411955	−	0.911204i	$-0.635154\pi$
$643$	−35.6794	−	20.5995i	−1.40706	−	0.812365i	−0.995103	+	0.0988389i	$0.968487\pi$
$644$	2.48673	+	1.43572i	0.0979911	+	0.0565752i
$645$	16.2550	−	0.485413i	0.640040	−	0.0191131i
$646$	−5.61306	−	9.72210i	−0.220843	−	0.382511i
$647$	−4.93239			−0.193912			−0.0969561	−	0.995289i	$-0.530911\pi$
$647$	−4.93239			−0.193912			−0.0969561	+	0.995289i	$0.530911\pi$
$648$	2.40813	+	20.0703i	0.0946004	+	0.788436i
$649$	−57.2854			−2.24865
$650$	−4.02735	−	4.20783i	−0.157966	−	0.165045i
$651$	−1.01446	−	33.9712i	−0.0397598	−	1.33144i
$652$	9.81633	+	5.66746i	0.384437	+	0.221955i
$653$	−19.0930	+	33.0701i	−0.747168	+	1.29413i	0.202006	+	0.979384i	$0.435254\pi$
$653$	−19.0930	+	33.0701i	−0.747168	+	1.29413i	−0.949175	+	0.314749i	$0.898079\pi$
$654$	−4.62069	+	2.85496i	−0.180683	+	0.111638i
$655$	7.91889	−	4.57197i	0.309417	−	0.178642i
$656$			17.1515i			0.669654i
$657$	−0.0839467	−	1.40431i	−0.00327507	−	0.0547872i
$658$		−	24.8120i		−	0.967274i
$659$	18.0188	+	31.2095i	0.701913	+	1.21575i	0.967794	+	0.251743i	$0.0810037\pi$
$659$	18.0188	+	31.2095i	0.701913	+	1.21575i	−0.265881	+	0.964006i	$0.585663\pi$
$660$	5.91591	+	3.18399i	0.230276	+	0.123937i
$661$	−33.2598	−	19.2026i	−1.29366	−	0.746894i	−0.314357	−	0.949305i	$-0.601789\pi$
$661$	−33.2598	−	19.2026i	−1.29366	−	0.746894i	−0.979301	+	0.202411i	$0.935122\pi$
$662$	15.9059	−	27.5498i	0.618200	−	1.07075i
$663$	11.5735	−	44.6070i	0.449479	−	1.73239i
$664$	−4.05854	−	7.02960i	−0.157502	−	0.272802i
$665$		−	1.81954i		−	0.0705585i
$666$	−8.51493	−	12.9033i	−0.329947	−	0.499993i
$667$	−4.97004			−0.192441
$668$	−4.03361	+	2.32880i	−0.156065	+	0.0901042i
$669$	−4.57576	−	7.40576i	−0.176909	−	0.286323i
$670$	0.891026	+	0.514434i	0.0344233	+	0.0198743i
$671$	−8.69802	−	5.02181i	−0.335784	−	0.193865i
$672$	−0.333539	−	11.1692i	−0.0128665	−	0.430861i
$673$	−0.588557	−	1.01941i	−0.0226872	−	0.0392954i	0.854459	−	0.519519i	$-0.173889\pi$
$673$	−0.588557	−	1.01941i	−0.0226872	−	0.0392954i	−0.877146	+	0.480224i	$0.840556\pi$
$674$			15.7523i			0.606756i
$675$	4.24959	−	2.99015i	0.163567	−	0.115091i
$676$	7.03065	−	3.65822i	0.270410	−	0.140701i
$677$	3.49842	+	6.05943i	0.134455	+	0.232883i	0.925389	−	0.379018i	$-0.123738\pi$
$677$	3.49842	+	6.05943i	0.134455	+	0.232883i	−0.790934	+	0.611901i	$0.790405\pi$
$678$	18.1690	−	0.542570i	0.697777	−	0.0208373i
$679$	−7.17960	+	12.4354i	−0.275528	+	0.477228i
$680$	8.28710	−	14.3537i	0.317796	−	0.550439i
$681$	11.8330	+	19.1514i	0.453441	+	0.733883i
$682$	−90.3954	+	52.1898i	−3.46142	+	1.99845i
$683$		−	17.7492i		−	0.679155i	−0.940578	−	0.339577i	$-0.889716\pi$
$683$		−	17.7492i		−	0.679155i	0.940578	−	0.339577i	$-0.110284\pi$
$684$	1.54033	+	0.770636i	0.0588961	+	0.0294660i
$685$	−5.23153			−0.199886
$686$	−16.0227	−	27.7522i	−0.611751	−	1.05958i
$687$	−2.90488	+	5.39731i	−0.110828	+	0.205920i
$688$	−22.7572	+	39.4167i	−0.867611	+	1.50275i
$689$	33.6916	+	9.82370i	1.28355	+	0.374253i
$690$	−6.00609	−	3.23253i	−0.228648	−	0.123060i
$691$	−11.6578	+	6.73061i	−0.443482	+	0.256044i	−0.705074	−	0.709134i	$-0.749086\pi$
$691$	−11.6578	+	6.73061i	−0.443482	+	0.256044i	0.261592	+	0.965179i	$0.415753\pi$
$692$	−0.953307			−0.0362393
$693$	−16.5009	+	32.9817i	−0.626817	+	1.25287i
$694$		−	18.7766i		−	0.712752i
$695$	8.22031	−	4.74600i	0.311814	−	0.180026i
$696$	4.16902	+	6.74746i	0.158026	+	0.255762i
$697$	22.6111	+	13.0545i	0.856455	+	0.494475i
$698$	21.2484	−	36.8033i	0.804263	−	1.39302i
$699$	−1.20755	−	40.4373i	−0.0456738	−	1.52948i
$700$	−1.02012	+	0.588965i	−0.0385568	+	0.0222608i
$701$	−5.70172			−0.215351			−0.107676	−	0.994186i	$-0.534341\pi$
$701$	−5.70172			−0.215351			−0.107676	+	0.994186i	$0.534341\pi$
$702$	9.79143	+	28.6376i	0.369554	+	1.08086i
$703$	3.00405			0.113300
$704$	23.7001	−	13.6833i	0.893232	−	0.515708i
$705$	0.410982	+	13.7626i	0.0154785	+	0.518328i
$706$	−15.2154	+	26.3538i	−0.572638	+	0.991837i
$707$	18.1648	+	10.4875i	0.683158	+	0.394421i
$708$	4.99738	+	8.08814i	0.187813	+	0.303971i
$709$	7.09173	−	4.09441i	0.266335	−	0.153769i	−0.360886	−	0.932610i	$-0.617526\pi$
$709$	7.09173	−	4.09441i	0.266335	−	0.153769i	0.627221	+	0.778841i	$0.284192\pi$
$710$			16.6873i			0.626265i
$711$	−5.17085	−	7.83577i	−0.193922	−	0.293864i
$712$	30.0449			1.12598
$713$	21.4395	−	12.3781i	0.802916	−	0.463564i
$714$	−35.1293	−	18.9069i	−1.31468	−	0.707572i
$715$	−22.0228	−	6.42136i	−0.823608	−	0.240145i
$716$	5.61955	−	9.73335i	0.210012	−	0.363752i
$717$	−10.7911	+	20.0500i	−0.403000	+	0.748780i
$718$	5.41832	+	9.38481i	0.202210	+	0.350238i
$719$	−18.0584			−0.673464			−0.336732	−	0.941601i	$-0.609322\pi$
$719$	−18.0584			−0.673464			−0.336732	+	0.941601i	$0.609322\pi$
$720$	0.867795	+	14.5170i	0.0323408	+	0.541015i
$721$		−	26.2085i		−	0.976055i
$722$	25.3406	−	14.6304i	0.943078	−	0.544486i
$723$	−8.56400	−	13.8606i	−0.318498	−	0.515482i
$724$	−4.01605	+	6.95601i	−0.149255	+	0.258518i
$725$	1.01941	−	1.76567i	0.0378600	−	0.0655755i
$726$	82.4489	−	2.46212i	3.05997	−	0.0913778i
$727$	−1.24281	−	2.15262i	−0.0460934	−	0.0798362i	0.842058	−	0.539387i	$-0.181344\pi$
$727$	−1.24281	−	2.15262i	−0.0460934	−	0.0798362i	−0.888152	+	0.459550i	$0.848011\pi$
$728$	3.71758	+	15.1988i	0.137783	+	0.563304i
$729$	−26.5680	+	4.81044i	−0.984001	+	0.178165i
$730$		−	0.757542i		−	0.0280379i
$731$	34.6424	+	60.0023i	1.28129	+	2.21927i
$732$	0.0497555	+	1.66616i	0.00183902	+	0.0615831i
$733$	31.2386	+	18.0356i	1.15382	+	0.666160i	0.949816	−	0.312810i	$-0.101270\pi$
$733$	31.2386	+	18.0356i	1.15382	+	0.666160i	0.204006	+	0.978970i	$0.434604\pi$
$734$	15.6244	+	9.02073i	0.576706	+	0.332961i
$735$	2.97416	+	4.81361i	0.109704	+	0.177553i
$736$	7.04897	−	4.06973i	0.259829	−	0.150012i
$737$	4.05218			0.149264
$738$	−17.1163	+	1.02318i	−0.630061	+	0.0376638i
$739$			39.3108i			1.44607i	0.690810	+	0.723036i	$0.257254\pi$
$739$			39.3108i			1.44607i	−0.690810	+	0.723036i	$0.742746\pi$
$740$	−0.972380	−	1.68421i	−0.0357454	−	0.0619128i
$741$	−5.69255	−	1.47696i	−0.209121	−	0.0542576i
$742$	15.1904	−	26.3105i	0.557657	−	0.965889i
$743$	−4.70265	−	2.71508i	−0.172524	−	0.0996066i	0.411252	−	0.911522i	$-0.365092\pi$
$743$	−4.70265	−	2.71508i	−0.172524	−	0.0996066i	−0.583775	+	0.811915i	$0.698425\pi$
$744$	−34.7890	−	18.7237i	−1.27543	−	0.686445i
$745$	−5.77542	−	10.0033i	−0.211595	−	0.366493i
$746$		−	17.6675i		−	0.646853i
$747$	9.04917	−	5.97158i	0.331092	−	0.218489i
$748$			28.6231i			1.04657i
$749$	2.31226	−	1.33498i	0.0844881	−	0.0487792i
$750$	2.38032	−	1.47072i	0.0869171	−	0.0537030i
$751$	−4.30744	+	7.46071i	−0.157181	+	0.272245i	−0.933851	−	0.357662i	$-0.883574\pi$
$751$	−4.30744	+	7.46071i	−0.157181	+	0.272245i	0.776670	+	0.629907i	$0.216907\pi$
$752$	−33.3727	−	19.2678i	−1.21698	−	0.702623i
$753$	0.785943	+	26.3188i	0.0286413	+	0.959112i
$754$	8.21107	+	8.57904i	0.299030	+	0.312430i
$755$	0.162214			0.00590357
$756$	6.09617	−	0.547440i	0.221716	−	0.0199102i
$757$	−4.32671			−0.157257			−0.0786285	−	0.996904i	$-0.525054\pi$
$757$	−4.32671			−0.157257			−0.0786285	+	0.996904i	$0.525054\pi$
$758$	12.7801	+	22.1358i	0.464195	+	0.804010i
$759$	−26.8514	+	0.801845i	−0.974643	+	0.0291051i
$760$	−1.83175	−	1.05756i	−0.0664447	−	0.0383619i
$761$	−20.0754	−	11.5906i	−0.727734	−	0.420158i	0.0898584	−	0.995955i	$-0.471359\pi$
$761$	−20.0754	−	11.5906i	−0.727734	−	0.420158i	−0.817593	+	0.575797i	$0.804692\pi$
$762$	17.8611	+	28.9077i	0.647039	+	1.04722i
$763$	−1.87534	−	3.24819i	−0.0678919	−	0.117592i
$764$	−11.1908			−0.404869
$765$	19.7984	+	9.90525i	0.715813	+	0.358125i
$766$	16.8559			0.609029
$767$	−22.4467	−	23.4526i	−0.810503	−	0.846825i
$768$	−20.4530	−	11.0080i	−0.738033	−	0.397216i
$769$	−15.6057	−	9.00997i	−0.562757	−	0.324908i	0.191494	−	0.981494i	$-0.438667\pi$
$769$	−15.6057	−	9.00997i	−0.562757	−	0.324908i	−0.754251	+	0.656586i	$0.772000\pi$
$770$	−9.92934	+	17.1981i	−0.357828	+	0.619777i
$771$	−38.4253	−	20.6808i	−1.38385	−	0.744802i
$772$	1.91332	−	1.10466i	0.0688620	−	0.0397575i
$773$		−	7.69962i		−	0.276936i	−0.990367	−	0.138468i	$-0.955782\pi$
$773$		−	7.69962i		−	0.276936i	0.990367	−	0.138468i	$-0.0442178\pi$
$774$	−40.6934	−	20.3591i	−1.46270	−	0.731794i
$775$			10.1556i			0.364799i
$776$	8.34596	+	14.4556i	0.299602	+	0.518927i
$777$	9.08175	−	5.61130i	0.325806	−	0.201304i
$778$	−39.3392	−	22.7125i	−1.41038	−	0.814282i
$779$	1.66596	−	2.88553i	0.0596892	−	0.103385i
$780$	1.01456	+	3.66959i	0.0363272	+	0.131392i
$781$	32.8614	+	56.9176i	1.17587	+	2.03667i
$782$		−	29.0595i		−	1.03916i
$783$	−8.66417	+	6.09639i	−0.309632	+	0.217867i
$784$	−15.8363			−0.565584
$785$	14.1836	−	8.18891i	0.506235	−	0.292275i
$786$	−25.5736	+	0.763688i	−0.912180	+	0.0272398i
$787$	16.0770	+	9.28206i	0.573083	+	0.330870i	0.758380	−	0.651813i	$-0.225991\pi$
$787$	16.0770	+	9.28206i	0.573083	+	0.330870i	−0.185297	+	0.982683i	$0.559325\pi$
$788$	−5.77856	−	3.33625i	−0.205853	−	0.118849i
$789$	−43.8828	+	27.1137i	−1.56227	+	0.965273i
$790$	−2.52766	−	4.37804i	−0.0899302	−	0.155764i
$791$			12.5520i			0.446298i
$792$	23.6124	+	35.7816i	0.839029	+	1.27144i
$793$	−1.35231	−	5.52871i	−0.0480218	−	0.196330i
$794$	5.27279	+	9.13274i	0.187124	+	0.324109i
$795$	−7.98989	+	14.8453i	−0.283372	+	0.526510i
$796$	0.131450	−	0.227679i	0.00465913	−	0.00806985i
$797$	−19.2104	+	33.2734i	−0.680468	+	1.17860i	0.294370	+	0.955691i	$0.404890\pi$
$797$	−19.2104	+	33.2734i	−0.680468	+	1.17860i	−0.974838	+	0.222914i	$0.928443\pi$
$798$	−2.41281	+	4.48304i	−0.0854127	+	0.158698i
$799$	−50.8019	+	29.3305i	−1.79724	+	1.03764i
$800$			3.33899i			0.118051i
$801$	2.39466	+	40.0592i	0.0846112	+	1.41542i
$802$	17.2704			0.609838
$803$	−1.49178	−	2.58384i	−0.0526438	−	0.0911818i
$804$	−0.353498	−	0.572128i	−0.0124669	−	0.0201774i
$805$	2.35499	−	4.07896i	0.0830024	−	0.143764i
$806$	−56.7870	−	16.5578i	−2.00024	−	0.583224i
$807$	0.115205	+	3.85786i	0.00405540	+	0.135803i
$808$	21.1158	−	12.1912i	0.742850	−	0.428885i
$809$	−32.7943			−1.15299			−0.576494	−	0.817102i	$-0.695580\pi$
$809$	−32.7943			−1.15299			−0.576494	+	0.817102i	$0.695580\pi$
$810$	−14.4354	+	1.73203i	−0.507209	+	0.0608574i
$811$		−	20.2864i		−	0.712352i	−0.934419	−	0.356176i	$-0.884080\pi$
$811$		−	20.2864i		−	0.712352i	0.934419	−	0.356176i	$-0.115920\pi$
$812$	2.07984	−	1.20080i	0.0729881	−	0.0421397i
$813$	2.17352	−	0.0649064i	0.0762287	−	0.00227637i
$814$	−28.3941	−	16.3933i	−0.995211	−	0.574585i
$815$	9.29627	−	16.1016i	0.325634	−	0.564015i
$816$	−52.7098	+	32.5675i	−1.84521	+	1.14009i
$817$	7.65724	−	4.42091i	0.267893	−	0.154668i
$818$	49.5816			1.73358
$819$	−19.9684	+	6.16807i	−0.697752	+	0.215530i
$820$	−2.15702			−0.0753262
$821$	19.3717	−	11.1843i	0.676078	−	0.390334i	−0.122298	−	0.992493i	$-0.539026\pi$
$821$	19.3717	−	11.1843i	0.676078	−	0.390334i	0.798376	+	0.602160i	$0.205693\pi$
$822$	12.8897	+	6.93732i	0.449578	+	0.241967i
$823$	6.33834	−	10.9783i	0.220941	−	0.382681i	−0.734153	−	0.678984i	$-0.762421\pi$
$823$	6.33834	−	10.9783i	0.220941	−	0.382681i	0.955094	+	0.296303i	$0.0957539\pi$
$824$	−26.3845	−	15.2331i	−0.919148	−	0.530670i
$825$	5.22267	−	9.70379i	0.181830	−	0.337843i
$826$	−24.3380	+	14.0515i	−0.846827	+	0.488916i
$827$		−	24.0427i		−	0.836045i	−0.908437	−	0.418023i	$-0.862723\pi$
$827$		−	24.0427i		−	0.836045i	0.908437	−	0.418023i	$-0.137277\pi$
$828$	2.45563	+	3.72120i	0.0853392	+	0.129321i
$829$	−6.18974			−0.214979			−0.107489	−	0.994206i	$-0.534281\pi$
$829$	−6.18974			−0.214979			−0.107489	+	0.994206i	$0.534281\pi$
$830$	5.05599	−	2.91908i	0.175496	−	0.101323i
$831$	27.4031	−	16.9314i	0.950604	−	0.587345i
$832$	14.8886	+	4.34117i	0.516169	+	0.150503i
$833$	−12.0535	+	20.8773i	−0.417629	+	0.723354i
$834$	−26.5470	+	0.792757i	−0.919248	+	0.0274509i
$835$	3.81991	+	6.61628i	0.132193	+	0.228966i
$836$	3.65276			0.126333
$837$	22.1918	−	47.8768i	0.767060	−	1.65487i
$838$			27.1729i			0.938671i
$839$	−34.1879	+	19.7384i	−1.18030	+	0.681444i	−0.956083	−	0.293096i	$-0.905314\pi$
$839$	−34.1879	+	19.7384i	−1.18030	+	0.681444i	−0.224213	+	0.974540i	$0.571981\pi$
$840$	−7.51314	+	0.224360i	−0.259228	+	0.00774116i
$841$	12.4216	−	21.5148i	0.428331	−	0.741891i
$842$	18.6955	−	32.3815i	0.644288	−	1.11594i
$843$	19.3565	+	31.3280i	0.666672	+	1.07899i
$844$	−5.58446	−	9.67257i	−0.192225	−	0.332944i
$845$	−6.00053	−	11.5323i	−0.206424	−	0.396723i
$846$	17.2374	−	34.4537i	0.592634	−	1.18454i
$847$			56.9595i			1.95715i
$848$	−23.5922	−	40.8628i	−0.810158	−	1.40323i
$849$	−7.47702	−	4.02420i	−0.256611	−	0.138110i
$850$	10.3238	+	5.96044i	0.354103	+	0.204441i
$851$	6.73435	+	3.88808i	0.230851	+	0.133282i
$852$	5.16950	−	9.60501i	0.177104	−	0.329062i
$853$	−40.2998	+	23.2671i	−1.37984	+	0.796650i	−0.992140	−	0.125135i	$-0.960063\pi$
$853$	−40.2998	+	23.2671i	−1.37984	+	0.796650i	−0.387699	+	0.921786i	$0.626730\pi$
$854$	−4.92720			−0.168605
$855$	1.26407	−	2.52659i	0.0432301	−	0.0864075i
$856$		−	3.10372i		−	0.106083i
$857$	−24.6269	−	42.6550i	−0.841239	−	1.45707i	−0.888848	−	0.458202i	$-0.848494\pi$
$857$	−24.6269	−	42.6550i	−0.841239	−	1.45707i	0.0476095	−	0.998866i	$-0.484840\pi$
$858$	45.7457	+	45.0248i	1.56173	+	1.53712i
$859$	3.05400	−	5.28968i	0.104201	−	0.180481i	−0.809210	−	0.587519i	$-0.800105\pi$
$859$	3.05400	−	5.28968i	0.104201	−	0.180481i	0.913411	+	0.407037i	$0.133438\pi$
$860$	−4.95714	−	2.86200i	−0.169037	−	0.0975935i
$861$	−0.353430	−	11.8353i	−0.0120449	−	0.403346i
$862$	24.8789	+	43.0915i	0.847377	+	1.46770i
$863$			0.162460i			0.00553022i	0.999996	+	0.00276511i	$0.000880163\pi$
$863$			0.162460i			0.00553022i	−0.999996	+	0.00276511i	$0.999120\pi$
$864$	7.29630	−	15.7412i	0.248225	−	0.535525i
$865$			1.56370i			0.0531673i
$866$	10.6369	−	6.14122i	0.361457	−	0.208687i
$867$	1.93641	+	64.8444i	0.0657638	+	2.20223i
$868$	−5.98128	+	10.3599i	−0.203018	+	0.351637i
$869$	−17.2428	−	9.95515i	−0.584923	−	0.337705i
$870$	−4.85306	+	2.99854i	−0.164534	+	0.101660i
$871$	1.58781	+	1.65896i	0.0538007	+	0.0562117i
$872$	−4.36000			−0.147648
$873$	−18.6086	+	12.2799i	−0.629807	+	0.415612i
$874$	−3.70845			−0.125440
$875$	0.966071	+	1.67328i	0.0326592	+	0.0565673i
$876$	−0.234675	+	0.436031i	−0.00792895	+	0.0147321i
$877$	−11.1115	−	6.41523i	−0.375209	−	0.216627i	0.300523	−	0.953775i	$-0.402839\pi$
$877$	−11.1115	−	6.41523i	−0.375209	−	0.216627i	−0.675732	+	0.737148i	$0.736172\pi$
$878$	15.1292	+	8.73484i	0.510585	+	0.294787i
$879$	−2.58547	+	4.80385i	−0.0872058	+	0.162030i
$880$	15.4212	+	26.7104i	0.519850	+	0.900406i
$881$	40.4434			1.36257			0.681286	−	0.732018i	$-0.261421\pi$
$881$	40.4434			1.36257			0.681286	+	0.732018i	$0.261421\pi$
$882$	−0.944724	−	15.8039i	−0.0318105	−	0.532144i
$883$	−35.7957			−1.20462			−0.602311	−	0.798262i	$-0.705753\pi$
$883$	−35.7957			−1.20462			−0.602311	+	0.798262i	$0.705753\pi$
$884$	−11.7183	+	11.2157i	−0.394129	+	0.377224i
$885$	13.2669	−	8.19714i	0.445961	−	0.275544i
$886$	−51.4437	−	29.7010i	−1.72828	−	0.997826i
$887$	18.6062	−	32.2270i	0.624737	−	1.08208i	−0.363855	−	0.931456i	$-0.618540\pi$
$887$	18.6062	−	32.2270i	0.624737	−	1.08208i	0.988592	−	0.150620i	$-0.0481270\pi$
$888$	−0.370418	−	12.4042i	−0.0124304	−	0.416257i
$889$	−20.3211	+	11.7324i	−0.681549	+	0.393493i
$890$			21.6096i			0.724356i
$891$	−45.8260	+	34.3345i	−1.53523	+	1.15025i
$892$			3.06411i			0.102594i
$893$	3.74303	+	6.48312i	0.125256	+	0.216949i
$894$	0.964708	+	32.3052i	0.0322647	+	1.08045i
$895$	−15.9655	−	9.21768i	−0.533667	−	0.308113i
$896$	13.1642	−	22.8010i	0.439784	−	0.761728i
$897$	−10.8497	−	10.6788i	−0.362262	−	0.356553i
$898$	18.4040	+	31.8767i	0.614150	+	1.06374i
$899$		−	20.7055i		−	0.690566i
$900$	−1.82569	+	0.109136i	−0.0608563	+	0.00363787i
$901$	−71.8267			−2.39289
$902$	−31.4931	+	18.1825i	−1.04860	+	0.605412i
$903$	14.8913	−	27.6682i	0.495550	−	0.920740i
$904$	12.6363	+	7.29557i	0.420277	+	0.242647i
$905$	11.4099	+	6.58748i	0.379276	+	0.218975i
$906$	−0.399669	−	0.215105i	−0.0132781	−	0.00714640i
$907$	20.9462	+	36.2798i	0.695506	+	1.20465i	0.970010	+	0.243065i	$0.0781530\pi$
$907$	20.9462	+	36.2798i	0.695506	+	1.20465i	−0.274504	+	0.961586i	$0.588514\pi$
$908$		−	7.92384i		−	0.262962i
$909$	17.9376	+	27.1822i	0.594954	+	0.901577i
$910$	−10.9316	+	2.67384i	−0.362379	+	0.0886370i
$911$	−4.26536	−	7.38781i	−0.141318	−	0.244769i	0.786675	−	0.617367i	$-0.211801\pi$
$911$	−4.26536	−	7.38781i	−0.141318	−	0.244769i	−0.927993	+	0.372598i	$0.878467\pi$
$912$	4.15613	+	6.72659i	0.137623	+	0.222740i
$913$	11.4967	−	19.9129i	0.380487	−	0.659022i
$914$	−3.88773	+	6.73375i	−0.128595	+	0.222733i
$915$	2.73298	−	0.0816133i	0.0903497	−	0.00269805i
$916$	1.86838	−	1.07871i	0.0617331	−	0.0356416i
$917$		−	17.6674i		−	0.583429i
$918$	−35.6452	−	50.6589i	−1.17647	−	1.67199i
$919$	24.6432			0.812906			0.406453	−	0.913672i	$-0.366766\pi$
$919$	24.6432			0.812906			0.406453	+	0.913672i	$0.366766\pi$
$920$	−2.73757	−	4.74161i	−0.0902550	−	0.156326i
$921$	4.16069	−	0.124248i	0.137099	−	0.00409411i
$922$	17.3237	−	30.0055i	0.570525	−	0.988179i
$923$	−10.4256	+	35.7560i	−0.343164	+	1.17692i
$924$	11.0429	−	6.82304i	0.363285	−	0.224461i
$925$	−2.76259	+	1.59498i	−0.0908334	+	0.0524427i
$926$	37.5950			1.23545
$927$	18.2075	−	36.3928i	0.598014	−	1.19530i
$928$		−	6.80763i		−	0.223471i
$929$	40.7203	−	23.5099i	1.33599	−	0.771334i	0.349780	−	0.936832i	$-0.386256\pi$
$929$	40.7203	−	23.5099i	1.33599	−	0.771334i	0.986210	+	0.165498i	$0.0529231\pi$
$930$	13.4669	−	25.0217i	0.441597	−	0.820495i
$931$	2.66427	+	1.53822i	0.0873178	+	0.0504130i
$932$	−7.11975	+	12.3318i	−0.233215	+	0.403940i
$933$	22.3121	+	12.0085i	0.730464	+	0.393142i
$934$	39.2551	−	22.6640i	1.28447	−	0.741588i
$935$	46.9502			1.53544
$936$	−5.39669	+	23.6875i	−0.176396	+	0.774252i
$937$	1.15002			0.0375694			0.0187847	−	0.999824i	$-0.494020\pi$
$937$	1.15002			0.0375694			0.0187847	+	0.999824i	$0.494020\pi$
$938$	1.72159	−	0.993960i	0.0562119	−	0.0324539i
$939$	−7.06646	+	4.36612i	−0.230605	+	0.142483i
$940$	2.42316	−	4.19704i	0.0790348	−	0.136892i
$941$	36.7120	+	21.1957i	1.19678	+	0.690959i	0.959835	−	0.280564i	$-0.0905216\pi$
$941$	36.7120	+	21.1957i	1.19678	+	0.690959i	0.236942	+	0.971524i	$0.423855\pi$
$942$	−45.8051	+	1.36785i	−1.49241	+	0.0445669i
$943$	7.46936	−	4.31244i	0.243236	−	0.140432i
$944$			43.6469i			1.42058i
$945$	−0.897959	−	9.99947i	−0.0292106	−	0.325283i
$946$	−96.5009			−3.13751
$947$	−30.8234	+	17.7959i	−1.00163	+	0.578289i	−0.908729	−	0.417386i	$-0.862946\pi$
$947$	−30.8234	+	17.7959i	−1.00163	+	0.578289i	−0.0928973	+	0.995676i	$0.529613\pi$
$948$	0.0986346	+	3.30297i	0.00320350	+	0.107276i
$949$	0.473284	−	1.62319i	0.0153635	−	0.0526909i
$950$	0.760646	−	1.31748i	0.0246786	−	0.0427446i
$951$	−15.8562	−	25.6629i	−0.514173	−	0.832176i
$952$	−16.0119	−	27.7334i	−0.518948	−	0.898843i
$953$	20.3876			0.660421			0.330210	−	0.943907i	$-0.392880\pi$
$953$	20.3876			0.660421			0.330210	+	0.943907i	$0.392880\pi$
$954$	39.3716	−	25.9815i	1.27470	−	0.841181i
$955$			18.3561i			0.593991i
$956$	6.94070	−	4.00721i	0.224478	−	0.129603i
$957$	−10.6481	+	19.7843i	−0.344204	+	0.639537i
$958$	−26.6156	+	46.0995i	−0.859910	+	1.48941i
$959$	−5.05403	+	8.75384i	−0.163203	+	0.282676i
$960$	−3.53079	+	6.56027i	−0.113956	+	0.211732i
$961$	36.0679	+	62.4715i	1.16348	+	2.01521i
$962$	−4.41451	−	18.0481i	−0.142329	−	0.581893i
$963$	4.13822	−	0.247374i	0.133352	−	0.00797153i
$964$			5.73480i			0.184705i
$965$	−1.81196	−	3.13840i	−0.0583289	−	0.101029i
$966$	−11.2113	+	6.92705i	−0.360716	+	0.222874i
$967$	−21.7343	−	12.5483i	−0.698926	−	0.403525i	0.108021	−	0.994149i	$-0.465549\pi$
$967$	−21.7343	−	12.5483i	−0.698926	−	0.403525i	−0.806947	+	0.590623i	$0.798882\pi$
$968$	57.3420	+	33.1064i	1.84304	+	1.06408i
$969$	12.0311	−	0.359277i	0.386495	−	0.0115416i
$970$	−10.3971	+	6.00277i	−0.333831	+	0.192737i
$971$	7.07326			0.226992			0.113496	−	0.993538i	$-0.463795\pi$
$971$	7.07326			0.226992			0.113496	+	0.993538i	$0.463795\pi$
$972$	8.84540	+	3.47495i	0.283716	+	0.111459i
$973$		−	18.3399i		−	0.587950i
$974$	−10.7255	−	18.5772i	−0.343668	−	0.595251i
$975$	6.01918	−	1.66418i	0.192768	−	0.0532963i
$976$	−3.82621	+	6.62720i	−0.122474	+	0.212131i
$977$	39.5652	+	22.8430i	1.26580	+	0.730812i	0.974191	−	0.225724i	$-0.0724748\pi$
$977$	39.5652	+	22.8430i	1.26580	+	0.730812i	0.291613	+	0.956536i	$0.405808\pi$
$978$	−44.2562	+	27.3444i	−1.41516	+	0.874377i
$979$	42.5545	+	73.7066i	1.36005	+	2.35567i
$980$		−	1.99162i		−	0.0636199i
$981$	−0.347504	−	5.81323i	−0.0110949	−	0.185602i
$982$		−	0.103099i		−	0.00329001i
$983$	−16.2208	+	9.36508i	−0.517363	+	0.298700i	−0.735855	−	0.677139i	$-0.763219\pi$
$983$	−16.2208	+	9.36508i	−0.517363	+	0.298700i	0.218492	+	0.975839i	$0.429886\pi$
$984$	−12.1202	−	6.52320i	−0.386378	−	0.207952i
$985$	−5.47241	+	9.47849i	−0.174365	+	0.302010i
$986$	−21.0484	−	12.1523i	−0.670318	−	0.387008i
$987$	23.4257	+	12.6079i	0.745649	+	0.401315i
$988$	1.43130	+	1.49544i	0.0455356	+	0.0475763i
$989$	22.8876			0.727783
$990$	−25.7356	+	16.9830i	−0.817932	+	0.539756i
$991$	−2.22644			−0.0707251			−0.0353626	−	0.999375i	$-0.511259\pi$
$991$	−2.22644			−0.0707251			−0.0353626	+	0.999375i	$0.511259\pi$
$992$	16.9547	+	29.3664i	0.538313	+	0.932385i
$993$	17.9281	+	29.0163i	0.568932	+	0.920803i
$994$	27.9227	+	16.1212i	0.885654	+	0.511332i
$995$	−0.373458	−	0.215616i	−0.0118394	−	0.00683549i
$996$	−3.81445	+	0.113908i	−0.120865	+	0.00360933i
$997$	−9.28246	−	16.0777i	−0.293978	−	0.509185i	0.680768	−	0.732499i	$-0.261646\pi$
$997$	−9.28246	−	16.0777i	−0.293978	−	0.509185i	−0.974747	+	0.223313i	$0.928313\pi$
$998$	−48.7446			−1.54298
$999$	16.5091	−	1.48253i	0.522325	−	0.0469051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.42	yes	108
9.7	even	3	inner	585.2.bt.b.376.13	✓	108
13.12	even	2	inner	585.2.bt.b.571.13	yes	108
117.25	even	6	inner	585.2.bt.b.376.42	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.13	✓	108	9.7	even	3	inner
585.2.bt.b.376.42	yes	108	117.25	even	6	inner
585.2.bt.b.571.13	yes	108	13.12	even	2	inner
585.2.bt.b.571.42	yes	108	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39901 - 0.807720i) q^{2} +(0.0517001 + 1.73128i) q^{3} +(0.304825 - 0.527972i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.47072 + 2.38032i) q^{6} +(-1.67328 + 0.966071i) q^{7} +2.24603i q^{8} +(-2.99465 + 0.179015i) q^{9} +O(q^{10})\)	\(q+(1.39901 - 0.807720i) q^{2} +(0.0517001 + 1.73128i) q^{3} +(0.304825 - 0.527972i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.47072 + 2.38032i) q^{6} +(-1.67328 + 0.966071i) q^{7} +2.24603i q^{8} +(-2.99465 + 0.179015i) q^{9} -1.61544 q^{10} +(-5.50999 + 3.18119i) q^{11} +(0.929826 + 0.500440i) q^{12} +(-3.46141 - 1.00927i) q^{13} +(-1.56063 + 2.70309i) q^{14} +(0.820866 - 1.52518i) q^{15} +(2.42381 + 4.19817i) q^{16} +7.37934 q^{17} +(-4.04497 + 2.66929i) q^{18} -0.941719i q^{19} +(-0.527972 + 0.304825i) q^{20} +(-1.75905 - 2.84698i) q^{21} +(-5.13903 + 8.90106i) q^{22} +(1.21885 - 2.11111i) q^{23} +(-3.88850 + 0.116120i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.65777 + 1.38387i) q^{26} +(-0.464748 - 5.17533i) q^{27} +1.17793i q^{28} +(-1.01941 - 1.76567i) q^{29} +(-0.0835184 - 2.79678i) q^{30} +(8.79499 + 5.07779i) q^{31} +(2.89165 + 1.66950i) q^{32} +(-5.79240 - 9.37486i) q^{33} +(10.3238 - 5.96044i) q^{34} +1.93214 q^{35} +(-0.818330 + 1.63566i) q^{36} +3.18996i q^{37} +(-0.760646 - 1.31748i) q^{38} +(1.56837 - 6.04485i) q^{39} +(1.12301 - 1.94512i) q^{40} +(3.06411 + 1.76906i) q^{41} +(-4.76049 - 2.56214i) q^{42} +(4.69451 + 8.13113i) q^{43} +3.87882i q^{44} +(2.68295 + 1.34230i) q^{45} -3.93795i q^{46} +(-6.88435 + 3.97468i) q^{47} +(-7.14289 + 4.41334i) q^{48} +(-1.63341 + 2.82915i) q^{49} +(1.39901 + 0.807720i) q^{50} +(0.381512 + 12.7757i) q^{51} +(-1.58799 + 1.51988i) q^{52} -9.73349 q^{53} +(-4.83041 - 6.86496i) q^{54} +6.36239 q^{55} +(-2.16982 - 3.75825i) q^{56} +(1.63038 - 0.0486869i) q^{57} +(-2.85234 - 1.64680i) q^{58} +(7.79748 + 4.50188i) q^{59} +(-0.555033 - 0.898307i) q^{60} +(0.789296 + 1.36710i) q^{61} +16.4057 q^{62} +(4.83797 - 3.19259i) q^{63} -4.30130 q^{64} +(2.49304 + 2.60476i) q^{65} +(-15.6759 - 8.43691i) q^{66} +(-0.551568 - 0.318448i) q^{67} +(2.24940 - 3.89608i) q^{68} +(3.71793 + 2.00102i) q^{69} +(2.70309 - 1.56063i) q^{70} -10.3299i q^{71} +(-0.402072 - 6.72608i) q^{72} +0.468938i q^{73} +(2.57660 + 4.46280i) q^{74} +(-1.47348 + 0.910413i) q^{75} +(-0.497201 - 0.287059i) q^{76} +(6.14652 - 10.6461i) q^{77} +(-2.68838 - 9.72363i) q^{78} +(1.56469 + 2.71012i) q^{79} -4.84763i q^{80} +(8.93591 - 1.07217i) q^{81} +5.71563 q^{82} +(-3.12979 + 1.80699i) q^{83} +(-2.03932 + 0.0608990i) q^{84} +(-6.39069 - 3.68967i) q^{85} +(13.1354 + 7.58370i) q^{86} +(3.00417 - 1.85617i) q^{87} +(-7.14505 - 12.3756i) q^{88} -13.3769i q^{89} +(4.83769 - 0.289187i) q^{90} +(6.76695 - 1.65518i) q^{91} +(-0.743070 - 1.28703i) q^{92} +(-8.33637 + 15.4891i) q^{93} +(-6.42086 + 11.1213i) q^{94} +(-0.470859 + 0.815552i) q^{95} +(-2.74087 + 5.09257i) q^{96} +(6.43608 - 3.71587i) q^{97} +5.27736i q^{98} +(15.9310 - 10.5129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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