LMFDB - Embedded newform 585.2.bt.b.376.42

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			376.42
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.42

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	0.905050	−	0.425304i	$-0.139833\pi$
$2$	1.39901	+	0.807720i	0.989251	+	0.571145i	0.0842010	+	0.996449i	$0.473166\pi$
$3$	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	0.149255	−	0.988799i	$-0.452312\pi$
$7$	−1.67328	−	0.966071i	−0.632442	−	0.365141i	−0.781697	+	0.623658i	$0.785646\pi$
$8$		−	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	−0.972084	−	0.234632i	$-0.924611\pi$
$11$	−5.50999	−	3.18119i	−1.66132	−	0.959166i	−0.689240	−	0.724534i	$-0.742055\pi$
$12$	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	$0.0344519\pi$
$19$			0.941719i			0.216045i	−0.994148	+	0.108023i	$0.965548\pi$
$20$	−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	0.964664	−	0.263485i	$-0.0848718\pi$
$23$	1.21885	+	2.11111i	0.254147	+	0.440196i	−0.710516	+	0.703681i	$0.751539\pi$
$24$	−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	−0.945017	−	0.327021i	$-0.893955\pi$
$29$	−1.01941	+	1.76567i	−0.189300	+	0.327878i	0.755717	+	0.654898i	$0.227289\pi$
$30$	−0.0835184	+	2.79678i	−0.0152483	+	0.510620i
$31$	8.79499	−	5.07779i	1.57963	−	0.911998i	0.584716	−	0.811238i	$-0.301206\pi$
$31$	8.79499	−	5.07779i	1.57963	−	0.911998i	0.994911	−	0.100760i	$-0.0321275\pi$
$32$	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	$-0.915548\pi$
$37$		−	3.18996i		−	0.524427i	0.965010	−	0.262213i	$-0.0844524\pi$
$38$	−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	−0.241272	−	0.970458i	$-0.577565\pi$
$41$	3.06411	−	1.76906i	0.478533	−	0.276281i	0.719805	+	0.694176i	$0.244231\pi$
$42$	−4.76049	+	2.56214i	−0.734560	+	0.395346i
$43$	4.69451	−	8.13113i	0.715906	−	1.23999i	−0.246703	−	0.969091i	$-0.579347\pi$
$43$	4.69451	−	8.13113i	0.715906	−	1.23999i	0.962609	−	0.270894i	$-0.0873194\pi$
$44$		−	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	−0.0947013	−	0.995506i	$-0.530190\pi$
$47$	−6.88435	−	3.97468i	−1.00419	−	0.579767i	−0.909484	+	0.415739i	$0.863523\pi$
$48$	−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	0.102452	−	0.994738i	$-0.467331\pi$
$59$	7.79748	−	4.50188i	1.01515	−	0.586095i	0.912694	+	0.408643i	$0.133998\pi$
$60$	−0.555033	+	0.898307i	−0.0716544	+	0.115971i
$61$	0.789296	−	1.36710i	0.101059	−	0.175039i	−0.811062	−	0.584960i	$-0.801110\pi$
$61$	0.789296	−	1.36710i	0.101059	−	0.175039i	0.912121	+	0.409921i	$0.134444\pi$
$62$	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	−0.533314	−	0.845917i	$-0.679054\pi$
$67$	−0.551568	+	0.318448i	−0.0673848	+	0.0389046i	0.465929	+	0.884822i	$0.345720\pi$
$68$	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	$0.210024\pi$
$71$			10.3299i			1.22593i	−0.790109	+	0.612967i	$0.789976\pi$
$72$	−0.402072	+	6.72608i	−0.0473846	+	0.792676i
$73$		−	0.468938i		−	0.0548850i	−0.999623	−	0.0274425i	$-0.991264\pi$
$73$		−	0.468938i		−	0.0548850i	0.999623	−	0.0274425i	$-0.00873632\pi$
$74$	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	−0.764480	−	0.644648i	$-0.777004\pi$
$79$	1.56469	−	2.71012i	0.176041	−	0.304912i	0.940521	+	0.339735i	$0.110337\pi$
$80$			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	0.318297	−	0.947991i	$-0.396889\pi$
$83$	−3.12979	−	1.80699i	−0.343539	−	0.198342i	−0.661836	+	0.749649i	$0.730222\pi$
$84$	−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	$0.250842\pi$
$89$			13.3769i			1.41795i	−0.705234	+	0.708975i	$0.749158\pi$
$90$	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	0.789790	−	0.613377i	$-0.210189\pi$
$97$	6.43608	+	3.71587i	0.653485	+	0.377290i	−0.136305	+	0.990667i	$0.543523\pi$
$98$		−	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	0.458803	+	0.888538i	$0.348278\pi$
$101$	−5.42789	+	9.40138i	−0.540095	+	0.935472i	−0.998898	+	0.0469340i	$0.985055\pi$
$102$	10.8529	−	17.5652i	1.07460	−	1.73921i
$103$	−6.78223	−	11.7472i	−0.668273	−	1.15748i	−0.978387	−	0.206784i	$-0.933700\pi$
$103$	−6.78223	−	11.7472i	−0.668273	−	1.15748i	0.310113	−	0.950700i	$-0.399633\pi$
$104$	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	$-0.970365\pi$
$109$		−	1.94120i		−	0.185934i	0.995669	−	0.0929668i	$-0.0296350\pi$
$110$	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	0.977387	−	0.211458i	$-0.0678212\pi$
$113$	3.24821	+	5.62606i	0.305566	+	0.529255i	−0.671822	+	0.740713i	$0.734488\pi$
$114$	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	0.594204	−	0.804315i	$-0.297467\pi$
$131$	−4.57197	−	7.91889i	−0.399455	−	0.691877i	−0.993659	+	0.112438i	$0.964134\pi$
$132$	−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	0.680893	−	0.732382i	$-0.261592\pi$
$137$	4.53064	+	2.61576i	0.387078	+	0.223480i	−0.293815	+	0.955862i	$0.594925\pi$
$138$	6.81770	+	0.203592i	0.580361	+	0.0173309i
$139$	−4.74600	−	8.22031i	−0.402550	−	0.697238i	0.591483	−	0.806318i	$-0.298543\pi$
$139$	−4.74600	−	8.22031i	−0.402550	−	0.697238i	−0.994033	+	0.109080i	$0.965210\pi$
$140$	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	−0.0307413	−	0.999527i	$-0.509787\pi$
$149$	10.0033	−	5.77542i	0.819504	−	0.473141i	0.850245	+	0.526386i	$0.176453\pi$
$150$	−1.32606	−	2.46384i	−0.108272	−	0.201172i
$151$	−0.140481	−	0.0811070i	−0.0114322	−	0.00660039i	0.494273	−	0.869307i	$-0.335434\pi$
$151$	−0.140481	−	0.0811070i	−0.0114322	−	0.00660039i	−0.505705	+	0.862706i	$0.668768\pi$
$152$	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	−0.982256	−	0.187544i	$-0.939947\pi$
$157$	−8.18891	−	14.1836i	−0.653546	−	1.13198i	0.328710	−	0.944431i	$-0.393386\pi$
$158$	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	$-0.740385\pi$
$163$		−	18.5925i		−	1.45628i	0.685429	−	0.728140i	$-0.259615\pi$
$164$	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	−0.733648	−	0.679529i	$-0.762184\pi$
$167$	−6.61628	+	3.81991i	−0.511983	+	0.295593i	0.221665	+	0.975123i	$0.428851\pi$
$168$	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	−0.894215	−	0.447637i	$-0.852266\pi$
$173$	−0.781849	+	1.35420i	−0.0594429	+	0.102958i	0.834773	+	0.550595i	$0.185599\pi$
$174$	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	0.315426	+	0.948950i	$0.397853\pi$
$191$	−9.17807	+	15.8969i	−0.664102	+	1.15026i	−0.979528	+	0.201308i	$0.935481\pi$
$192$	−0.222378	+	7.44676i	−0.0160487	+	0.537423i
$193$	3.13840	−	1.81196i	0.225907	−	0.130427i	−0.382775	−	0.923841i	$-0.625032\pi$
$193$	3.13840	−	1.81196i	0.225907	−	0.130427i	0.608682	+	0.793414i	$0.291698\pi$
$194$	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	$0.127488\pi$
$197$			10.9448i			0.779786i	−0.920860	+	0.389893i	$0.872512\pi$
$198$	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	0.987427	+	0.158073i	$0.0505281\pi$
$211$	9.16012	+	15.8658i	0.630609	+	1.09225i	−0.356819	+	0.934174i	$0.616139\pi$
$212$	−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	0.347131	−	0.937817i	$-0.387156\pi$
$223$	−4.35267	−	2.51301i	−0.291476	−	0.168284i	−0.638607	+	0.769533i	$0.720489\pi$
$224$	−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	0.824642	−	0.565655i	$-0.191377\pi$
$227$	11.2561	+	6.49869i	0.747091	+	0.431333i	−0.0775508	+	0.996988i	$0.524710\pi$
$228$	0.471274	+	0.875634i	0.0312109	+	0.0579903i
$229$	3.06469	−	1.76940i	0.202520	−	0.116925i	−0.395310	−	0.918548i	$-0.629363\pi$
$229$	3.06469	−	1.76940i	0.202520	−	0.116925i	0.597830	+	0.801623i	$0.296030\pi$
$230$	−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	−0.0843479	−	0.996436i	$-0.526881\pi$
$239$	11.3847	−	6.57298i	0.736417	−	0.425171i	0.820765	+	0.571266i	$0.193547\pi$
$240$	8.39259	+	0.250623i	0.541740	+	0.0161776i
$241$	−8.14646	−	4.70336i	−0.524759	−	0.302970i	0.214120	−	0.976807i	$-0.431312\pi$
$241$	−8.14646	−	4.70336i	−0.524759	−	0.302970i	−0.738880	+	0.673837i	$0.764645\pi$
$242$			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	−0.928534	−	0.371248i	$-0.878930\pi$
$257$	−12.5970	−	21.8186i	−0.785777	−	1.36101i	0.142757	−	0.989758i	$-0.454403\pi$
$258$	−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	0.116079	−	0.993240i	$-0.462967\pi$
$263$	14.8909	−	25.7917i	0.918210	−	1.59039i	0.802132	−	0.597147i	$-0.203699\pi$
$264$	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	$0.0121405\pi$
$271$			1.25544i			0.0762627i	−0.999273	+	0.0381313i	$0.987859\pi$
$272$	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	0.438896	+	0.898538i	$0.355370\pi$
$277$	−9.29877	+	16.1059i	−0.558709	+	0.967712i	−0.997605	+	0.0691744i	$0.977964\pi$
$278$		−	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	0.935803	−	0.352522i	$-0.114676\pi$
$281$	18.4127	+	10.6306i	1.09841	+	0.634168i	0.162608	+	0.986691i	$0.448009\pi$
$282$	−19.5860	+	10.5413i	−1.16633	+	0.627727i
$283$	−2.45119	−	4.24559i	−0.145708	−	0.252374i	0.783929	−	0.620851i	$-0.213213\pi$
$283$	−2.45119	−	4.24559i	−0.145708	−	0.252374i	−0.929637	+	0.368477i	$0.879879\pi$
$284$	−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	−0.418202	−	0.908354i	$-0.637340\pi$
$293$	2.72771	−	1.57484i	0.159355	−	0.0920034i	0.577557	+	0.816351i	$0.304006\pi$
$294$	−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	$0.0218469\pi$
$307$			2.40325i			0.137161i	−0.997646	+	0.0685803i	$0.978153\pi$
$308$	−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	0.995404	−	0.0957610i	$-0.0305285\pi$
$311$	7.31456	+	12.6692i	0.414771	+	0.718404i	−0.580634	+	0.814165i	$0.697195\pi$
$312$	13.5769	−	3.52261i	0.768641	−	0.199428i
$313$	2.39788	−	4.15325i	0.135536	−	0.234755i	−0.790266	−	0.612764i	$-0.790058\pi$
$313$	2.39788	−	4.15325i	0.135536	−	0.234755i	0.925802	+	0.378009i	$0.123391\pi$
$314$		−	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	0.0125365	−	0.999921i	$-0.496009\pi$
$317$	−15.0831	−	8.70825i	−0.847153	−	0.489104i	−0.859689	+	0.510818i	$0.829343\pi$
$318$	−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	0.889137	−	0.457642i	$-0.151306\pi$
$331$	17.0540	+	9.84616i	0.937375	+	0.541194i	0.0482387	+	0.998836i	$0.484639\pi$
$332$		−	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	0.702130	−	0.712049i	$-0.252233\pi$
$337$	−4.87555	−	8.44469i	−0.265588	−	0.460012i	−0.967717	+	0.252037i	$0.918899\pi$
$338$	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	0.978792	−	0.204858i	$-0.0656732\pi$
$347$	5.81162	+	10.0660i	0.311984	+	0.540372i	−0.666808	+	0.745230i	$0.732340\pi$
$348$	−0.0642616	+	2.15193i	−0.00344478	+	0.115355i
$349$	22.7822	+	13.1533i	1.21950	+	0.704080i	0.964812	−	0.262942i	$-0.0846929\pi$
$349$	22.7822	+	13.1533i	1.21950	+	0.704080i	0.254691	+	0.967023i	$0.418026\pi$
$350$	−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	−0.00150982	−	0.999999i	$-0.500481\pi$
$353$	−16.3137	−	9.41870i	−0.868289	−	0.501307i	−0.866779	+	0.498692i	$0.833814\pi$
$354$	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	$-0.943354\pi$
$359$		−	6.70817i		−	0.354044i	0.984207	−	0.177022i	$-0.0566463\pi$
$360$	−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	−0.682675	−	0.730722i	$-0.739184\pi$
$367$	5.58407	−	9.67189i	0.291486	−	0.504868i	0.974161	+	0.225853i	$0.0725170\pi$
$368$	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	0.972156	−	0.234334i	$-0.0752909\pi$
$373$	5.46832	+	9.47141i	0.283139	+	0.490411i	−0.689017	+	0.724745i	$0.741958\pi$
$374$	−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	$-0.866793\pi$
$379$		−	15.8225i		−	0.812746i	0.913707	−	0.406373i	$-0.133207\pi$
$380$	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	−0.251039	−	0.967977i	$-0.580772\pi$
$383$	9.03633	−	5.21713i	0.461735	−	0.266583i	0.712774	+	0.701394i	$0.247439\pi$
$384$	−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	0.250932	+	0.968005i	$0.419263\pi$
$389$	−14.0596	+	24.3520i	−0.712851	+	1.23469i	−0.963783	+	0.266689i	$0.914070\pi$
$390$	−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	$-0.947620\pi$
$397$		−	6.52799i		−	0.327630i	0.986491	−	0.163815i	$-0.0523801\pi$
$398$	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	−0.250683	−	0.968069i	$-0.580655\pi$
$401$	9.25851	−	5.34540i	0.462348	−	0.266937i	0.713031	+	0.701133i	$0.247322\pi$
$402$	−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	0.331505	−	0.943454i	$-0.392444\pi$
$409$	26.5803	−	15.3461i	1.31431	−	0.758818i	0.982807	+	0.184635i	$0.0591104\pi$
$410$	−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	0.584113	−	0.811673i	$-0.301443\pi$
$419$	−8.41035	−	14.5672i	−0.410873	−	0.711652i	−0.994985	+	0.100020i	$0.968109\pi$
$420$	1.79656	−	0.966922i	0.0876630	−	0.0471810i
$421$	20.0450	+	11.5730i	0.976933	+	0.564033i	0.901343	−	0.433106i	$-0.142583\pi$
$421$	20.0450	+	11.5730i	0.976933	+	0.564033i	0.0755903	+	0.997139i	$0.475916\pi$
$422$			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	$-0.733961\pi$
$431$		−	30.8013i		−	1.48365i	0.670595	−	0.741824i	$-0.266039\pi$
$432$	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	−0.707657	−	0.706556i	$-0.750248\pi$
$439$	5.40709	−	9.36536i	0.258067	−	0.446984i	0.965724	+	0.259571i	$0.0835813\pi$
$440$		−	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	−0.0152125	+	0.999884i	$0.504842\pi$
$443$	−18.3857	+	31.8450i	−0.873531	+	1.51300i	−0.858319	+	0.513117i	$0.828491\pi$
$444$	−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	$-0.819313\pi$
$449$		−	22.7851i		−	1.07530i	0.843169	−	0.537648i	$-0.180687\pi$
$450$	−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	0.399327	−	0.916808i	$-0.369244\pi$
$457$	−4.16837	−	2.40661i	−0.194988	−	0.112576i	−0.594316	+	0.804232i	$0.702577\pi$
$458$	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	0.865712	−	0.500542i	$-0.166866\pi$
$461$	18.5742	+	10.7238i	0.865087	+	0.499458i	−0.000625808		1.00000i	$0.500199\pi$
$462$	34.3809	+	1.02669i	1.59954	+	0.0477662i
$463$	20.1544	−	11.6361i	0.936653	−	0.540777i	0.0477435	−	0.998860i	$-0.484797\pi$
$463$	20.1544	−	11.6361i	0.936653	−	0.540777i	0.888910	+	0.458083i	$0.151464\pi$
$464$	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	−0.322813	−	0.946463i	$-0.604628\pi$
$479$	−28.5368	−	16.4757i	−1.30388	−	0.752795i	−0.981067	+	0.193668i	$0.937962\pi$
$480$	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	$0.0972734\pi$
$487$			13.2788i			0.601718i	−0.953669	+	0.300859i	$0.902727\pi$
$488$	−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	0.866745	−	0.498752i	$-0.166208\pi$
$491$	0.0319103	+	0.0552703i	0.00144009	+	0.00249431i	−0.865304	+	0.501247i	$0.832875\pi$
$492$	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	−0.953636	−	0.300963i	$-0.902692\pi$
$499$	−26.1316	+	15.0871i	−1.16981	+	0.675391i	−0.216176	+	0.976354i	$0.569358\pi$
$500$	−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	−0.155412	−	0.987850i	$-0.549671\pi$
$509$	14.0416	−	8.10694i	0.622384	−	0.359334i	0.777797	+	0.628516i	$0.216337\pi$
$510$	−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	$0.115452\pi$
$541$			16.5050i			0.709604i	−0.934941	+	0.354802i	$0.884548\pi$
$542$	−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	−0.597366	−	0.801969i	$-0.703786\pi$
$547$	9.25797	−	16.0353i	0.395842	−	0.685619i	0.993208	+	0.116350i	$0.0371194\pi$
$548$			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	$0.0525552\pi$
$557$			7.75798i			0.328716i	−0.986401	+	0.164358i	$0.947445\pi$
$558$	−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	0.905132	−	0.425131i	$-0.139772\pi$
$563$	2.00243	+	3.46830i	0.0843922	+	0.146172i	−0.820740	+	0.571302i	$0.806438\pi$
$564$	−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	0.289988	+	0.957030i	$0.406349\pi$
$569$	−16.3116	+	28.2525i	−0.683818	+	1.18441i	−0.973807	+	0.227378i	$0.926985\pi$
$570$	−2.63378	−	0.0786509i	−0.110317	−	0.00329432i
$571$	−14.8576	−	25.7341i	−0.621771	−	1.07694i	−0.989156	−	0.146869i	$-0.953080\pi$
$571$	−14.8576	−	25.7341i	−0.621771	−	1.07694i	0.367385	−	0.930069i	$-0.380253\pi$
$572$	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	$0.0699788\pi$
$577$			10.4768i			0.436157i	−0.975931	+	0.218078i	$0.930021\pi$
$578$	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	0.989936	+	0.141516i	$0.0451977\pi$
$587$	38.9457	+	22.4853i	1.60746	+	0.928068i	0.617525	+	0.786552i	$0.288136\pi$
$588$	−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	$-0.730893\pi$
$593$		−	36.4423i		−	1.49651i	0.663414	−	0.748253i	$-0.269107\pi$
$594$	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	0.710186	+	0.704014i	$0.248611\pi$
$599$	23.6127	+	40.8983i	0.964787	+	1.67106i	0.254601	+	0.967046i	$0.418056\pi$
$600$	−2.04481	+	3.30948i	−0.0834792	+	0.135109i
$601$	10.1585	−	17.5950i	0.414374	−	0.717716i	−0.580989	−	0.813912i	$-0.697334\pi$
$601$	10.1585	−	17.5950i	0.414374	−	0.717716i	0.995362	+	0.0961952i	$0.0306673\pi$
$602$	−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	0.883287	+	0.468832i	$0.155325\pi$
$607$	20.8842	+	36.1725i	0.847664	+	1.46820i	−0.0356232	+	0.999365i	$0.511342\pi$
$608$	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	$-0.926049\pi$
$613$		−	11.4010i		−	0.460480i	0.973134	−	0.230240i	$-0.0739512\pi$
$614$	−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	−0.975777	−	0.218767i	$-0.929797\pi$
$617$	−31.6507	+	18.2735i	−1.27421	+	0.735665i	−0.298431	+	0.954431i	$0.596463\pi$
$618$	−37.9368	−	1.13288i	−1.52604	−	0.0455712i
$619$	2.95784	+	1.70771i	0.118886	+	0.0686387i	0.558264	−	0.829664i	$-0.311468\pi$
$619$	2.95784	+	1.70771i	0.118886	+	0.0686387i	−0.439378	+	0.898302i	$0.644801\pi$
$620$	−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	$0.295816\pi$
$631$			40.2529i			1.60244i	−0.598367	+	0.801222i	$0.704184\pi$
$632$	−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	−0.961747	−	0.273940i	$-0.911673\pi$
$641$	−6.16833	+	10.6839i	−0.243634	+	0.421987i	0.718112	+	0.695927i	$0.245006\pi$
$642$	−2.03234	+	3.28929i	−0.0802100	+	0.129818i
$643$	−35.6794	+	20.5995i	−1.40706	+	0.812365i	−0.995103	−	0.0988389i	$-0.968487\pi$
$643$	−35.6794	+	20.5995i	−1.40706	+	0.812365i	−0.411955	+	0.911204i	$0.635154\pi$
$644$	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	−0.949175	−	0.314749i	$-0.898079\pi$
$653$	−19.0930	−	33.0701i	−0.747168	−	1.29413i	0.202006	−	0.979384i	$-0.435254\pi$
$654$	−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	−0.265881	−	0.964006i	$-0.585663\pi$
$659$	18.0188	−	31.2095i	0.701913	−	1.21575i	0.967794	−	0.251743i	$-0.0810037\pi$
$660$	5.91591	−	3.18399i	0.230276	−	0.123937i
$661$	−33.2598	+	19.2026i	−1.29366	+	0.746894i	−0.979301	−	0.202411i	$-0.935122\pi$
$661$	−33.2598	+	19.2026i	−1.29366	+	0.746894i	−0.314357	+	0.949305i	$0.601789\pi$
$662$	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	−0.877146	−	0.480224i	$-0.840556\pi$
$673$	−0.588557	+	1.01941i	−0.0226872	+	0.0392954i	0.854459	+	0.519519i	$0.173889\pi$
$674$		−	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	−0.790934	−	0.611901i	$-0.790405\pi$
$677$	3.49842	−	6.05943i	0.134455	−	0.232883i	0.925389	+	0.379018i	$0.123738\pi$
$678$	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	$0.110284\pi$
$683$			17.7492i			0.679155i	−0.940578	+	0.339577i	$0.889716\pi$
$684$	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	0.261592	−	0.965179i	$-0.415753\pi$
$691$	−11.6578	−	6.73061i	−0.443482	−	0.256044i	−0.705074	+	0.709134i	$0.749086\pi$
$692$	−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	0.627221	−	0.778841i	$-0.284192\pi$
$709$	7.09173	+	4.09441i	0.266335	+	0.153769i	−0.360886	+	0.932610i	$0.617526\pi$
$710$		−	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	−0.888152	−	0.459550i	$-0.848011\pi$
$727$	−1.24281	+	2.15262i	−0.0460934	+	0.0798362i	0.842058	+	0.539387i	$0.181344\pi$
$728$	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	0.204006	−	0.978970i	$-0.434604\pi$
$733$	31.2386	−	18.0356i	1.15382	−	0.666160i	0.949816	+	0.312810i	$0.101270\pi$
$734$	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	$-0.742746\pi$
$739$		−	39.3108i		−	1.44607i	0.690810	−	0.723036i	$-0.257254\pi$
$740$	−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	−0.583775	−	0.811915i	$-0.698425\pi$
$743$	−4.70265	+	2.71508i	−0.172524	+	0.0996066i	0.411252	+	0.911522i	$0.365092\pi$
$744$	−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	0.776670	−	0.629907i	$-0.216907\pi$
$751$	−4.30744	−	7.46071i	−0.157181	−	0.272245i	−0.933851	+	0.357662i	$0.883574\pi$
$752$	−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	−0.817593	−	0.575797i	$-0.804692\pi$
$761$	−20.0754	+	11.5906i	−0.727734	+	0.420158i	0.0898584	+	0.995955i	$0.471359\pi$
$762$	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	−0.754251	−	0.656586i	$-0.772000\pi$
$769$	−15.6057	+	9.00997i	−0.562757	+	0.324908i	0.191494	+	0.981494i	$0.438667\pi$
$770$	−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	$0.0442178\pi$
$773$			7.69962i			0.276936i	−0.990367	+	0.138468i	$0.955782\pi$
$774$	−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	−0.185297	−	0.982683i	$-0.559325\pi$
$787$	16.0770	−	9.28206i	0.573083	−	0.330870i	0.758380	+	0.651813i	$0.225991\pi$
$788$	−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	−0.974838	−	0.222914i	$-0.928443\pi$
$797$	−19.2104	−	33.2734i	−0.680468	−	1.17860i	0.294370	−	0.955691i	$-0.404890\pi$
$798$	−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	$0.115920\pi$
$811$			20.2864i			0.712352i	−0.934419	+	0.356176i	$0.884080\pi$
$812$	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	0.798376	−	0.602160i	$-0.205693\pi$
$821$	19.3717	+	11.1843i	0.676078	+	0.390334i	−0.122298	+	0.992493i	$0.539026\pi$
$822$	12.8897	−	6.93732i	0.449578	−	0.241967i
$823$	6.33834	+	10.9783i	0.220941	+	0.382681i	0.955094	−	0.296303i	$-0.0957539\pi$
$823$	6.33834	+	10.9783i	0.220941	+	0.382681i	−0.734153	+	0.678984i	$0.762421\pi$
$824$	−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	$0.137277\pi$
$827$			24.0427i			0.836045i	−0.908437	+	0.418023i	$0.862723\pi$
$828$	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	−0.224213	−	0.974540i	$-0.571981\pi$
$839$	−34.1879	−	19.7384i	−1.18030	−	0.681444i	−0.956083	+	0.293096i	$0.905314\pi$
$840$	−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	−0.387699	−	0.921786i	$-0.626730\pi$
$853$	−40.2998	−	23.2671i	−1.37984	−	0.796650i	−0.992140	+	0.125135i	$0.960063\pi$
$854$	−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	0.0476095	+	0.998866i	$0.484840\pi$
$857$	−24.6269	+	42.6550i	−0.841239	+	1.45707i	−0.888848	+	0.458202i	$0.848494\pi$
$858$	45.7457	−	45.0248i	1.56173	−	1.53712i
$859$	3.05400	+	5.28968i	0.104201	+	0.180481i	0.913411	−	0.407037i	$-0.133438\pi$
$859$	3.05400	+	5.28968i	0.104201	+	0.180481i	−0.809210	+	0.587519i	$0.800105\pi$
$860$	−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	$-0.999120\pi$
$863$		−	0.162460i		−	0.00553022i	0.999996	−	0.00276511i	$-0.000880163\pi$
$864$	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	−0.675732	−	0.737148i	$-0.736172\pi$
$877$	−11.1115	+	6.41523i	−0.375209	+	0.216627i	0.300523	+	0.953775i	$0.402839\pi$
$878$	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	0.988592	+	0.150620i	$0.0481270\pi$
$887$	18.6062	+	32.2270i	0.624737	+	1.08208i	−0.363855	+	0.931456i	$0.618540\pi$
$888$	−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	−0.274504	−	0.961586i	$-0.588514\pi$
$907$	20.9462	−	36.2798i	0.695506	−	1.20465i	0.970010	−	0.243065i	$-0.0781530\pi$
$908$			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	−0.927993	−	0.372598i	$-0.878467\pi$
$911$	−4.26536	+	7.38781i	−0.141318	+	0.244769i	0.786675	+	0.617367i	$0.211801\pi$
$912$	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	0.986210	−	0.165498i	$-0.0529231\pi$
$929$	40.7203	+	23.5099i	1.33599	+	0.771334i	0.349780	+	0.936832i	$0.386256\pi$
$930$	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	0.236942	−	0.971524i	$-0.423855\pi$
$941$	36.7120	−	21.1957i	1.19678	−	0.690959i	0.959835	+	0.280564i	$0.0905216\pi$
$942$	−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	−0.0928973	−	0.995676i	$-0.529613\pi$
$947$	−30.8234	−	17.7959i	−1.00163	−	0.578289i	−0.908729	+	0.417386i	$0.862946\pi$
$948$	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	−0.806947	−	0.590623i	$-0.798882\pi$
$967$	−21.7343	+	12.5483i	−0.698926	+	0.403525i	0.108021	+	0.994149i	$0.465549\pi$
$968$	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	0.291613	−	0.956536i	$-0.405808\pi$
$977$	39.5652	−	22.8430i	1.26580	−	0.730812i	0.974191	+	0.225724i	$0.0724748\pi$
$978$	−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	0.218492	−	0.975839i	$-0.429886\pi$
$983$	−16.2208	−	9.36508i	−0.517363	−	0.298700i	−0.735855	+	0.677139i	$0.763219\pi$
$984$	−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	−0.974747	−	0.223313i	$-0.928313\pi$
$997$	−9.28246	+	16.0777i	−0.293978	+	0.509185i	0.680768	+	0.732499i	$0.261646\pi$
$998$	−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.376.42	yes	108
9.4	even	3	inner	585.2.bt.b.571.13	yes	108
13.12	even	2	inner	585.2.bt.b.376.13	✓	108
117.103	even	6	inner	585.2.bt.b.571.42	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.13	✓	108	13.12	even	2	inner
585.2.bt.b.376.42	yes	108	1.1	even	1	trivial
585.2.bt.b.571.13	yes	108	9.4	even	3	inner
585.2.bt.b.571.42	yes	108	117.103	even	6	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
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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