LMFDB - Embedded newform 572.2.s.a.43.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(43,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("572.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.s (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.14
Character	$\chi$	$=$	572.43
Dual form			572.2.s.a.439.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20341 + 0.742836i) q^{2} +(-0.371524 - 0.214500i) q^{3} +(0.896390 - 1.78787i) q^{4} -0.666498i q^{5} +(0.606434 - 0.0178505i) q^{6} +(-1.08520 + 0.626541i) q^{7} +(0.249370 + 2.81741i) q^{8} +(-1.40798 - 2.43869i) q^{9} +O(q^{10})$	\(q+(-1.20341 + 0.742836i) q^{2} +(-0.371524 - 0.214500i) q^{3} +(0.896390 - 1.78787i) q^{4} -0.666498i q^{5} +(0.606434 - 0.0178505i) q^{6} +(-1.08520 + 0.626541i) q^{7} +(0.249370 + 2.81741i) q^{8} +(-1.40798 - 2.43869i) q^{9} +(0.495098 + 0.802070i) q^{10} +(-1.15735 + 3.10814i) q^{11} +(-0.716528 + 0.471962i) q^{12} +(0.456423 + 3.57655i) q^{13} +(0.840524 - 1.56011i) q^{14} +(-0.142963 + 0.247620i) q^{15} +(-2.39297 - 3.20526i) q^{16} +(3.16061 - 1.82478i) q^{17} +(3.50592 + 1.88885i) q^{18} +(-4.42491 + 2.55472i) q^{19} +(-1.19161 - 0.597442i) q^{20} +0.537571 q^{21} +(-0.916078 - 4.60009i) q^{22} +(6.23829 + 3.60168i) q^{23} +(0.511687 - 1.10023i) q^{24} +4.55578 q^{25} +(-3.20605 - 3.96500i) q^{26} +2.49504i q^{27} +(0.147411 + 2.50182i) q^{28} +(5.46790 + 3.15689i) q^{29} +(-0.0118973 - 0.404187i) q^{30} +3.36773 q^{31} +(5.26070 + 2.07966i) q^{32} +(1.09668 - 0.906500i) q^{33} +(-2.44799 + 4.54376i) q^{34} +(0.417588 + 0.723284i) q^{35} +(-5.62217 + 0.331266i) q^{36} +(-2.30894 - 1.33307i) q^{37} +(3.42724 - 6.36136i) q^{38} +(0.597595 - 1.42668i) q^{39} +(1.87780 - 0.166204i) q^{40} +(-1.00414 + 1.73922i) q^{41} +(-0.646918 + 0.399327i) q^{42} +(1.39414 + 2.41471i) q^{43} +(4.51953 + 4.85529i) q^{44} +(-1.62538 + 0.938416i) q^{45} +(-10.1827 + 0.299729i) q^{46} -7.02399 q^{47} +(0.201518 + 1.70412i) q^{48} +(-2.71489 + 4.70233i) q^{49} +(-5.48247 + 3.38420i) q^{50} -1.56565 q^{51} +(6.80354 + 2.38995i) q^{52} +12.4876 q^{53} +(-1.85341 - 3.00256i) q^{54} +(2.07157 + 0.771368i) q^{55} +(-2.03584 - 2.90122i) q^{56} +2.19195 q^{57} +(-8.92517 + 0.262714i) q^{58} +(5.41516 + 9.37933i) q^{59} +(0.314562 + 0.477565i) q^{60} +(-7.08084 + 4.08812i) q^{61} +(-4.05276 + 2.50167i) q^{62} +(3.05588 + 1.76431i) q^{63} +(-7.87563 + 1.40516i) q^{64} +(2.38376 - 0.304205i) q^{65} +(-0.646371 + 1.90554i) q^{66} +(-1.30558 + 2.26133i) q^{67} +(-0.429329 - 7.28647i) q^{68} +(-1.54512 - 2.67622i) q^{69} +(-1.03981 - 0.560208i) q^{70} +(0.954941 + 1.65401i) q^{71} +(6.51970 - 4.57500i) q^{72} -6.31191 q^{73} +(3.76885 - 0.110937i) q^{74} +(-1.69258 - 0.977213i) q^{75} +(0.601070 + 10.2012i) q^{76} +(-0.691426 - 4.09808i) q^{77} +(0.340634 + 2.16079i) q^{78} -6.65406 q^{79} +(-2.13630 + 1.59491i) q^{80} +(-3.68875 + 6.38911i) q^{81} +(-0.0835636 - 2.83890i) q^{82} -7.67436i q^{83} +(0.481873 - 0.961108i) q^{84} +(-1.21621 - 2.10654i) q^{85} +(-3.47145 - 1.87028i) q^{86} +(-1.35430 - 2.34572i) q^{87} +(-9.04553 - 2.48564i) q^{88} +(11.8060 + 6.81619i) q^{89} +(1.25891 - 2.33669i) q^{90} +(-2.73616 - 3.59530i) q^{91} +(12.0313 - 7.92475i) q^{92} +(-1.25119 - 0.722377i) q^{93} +(8.45274 - 5.21767i) q^{94} +(1.70272 + 2.94920i) q^{95} +(-1.50839 - 1.90106i) q^{96} +(-0.573354 + 0.331026i) q^{97} +(-0.225932 - 7.67555i) q^{98} +(9.20932 - 1.55379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{4} + 68 q^{9}+O(q^{10}) $ 160 * q - 2 * q^4 + 68 * q^9	$ 160 q - 2 q^{4} + 68 q^{9} - 36 q^{12} - 8 q^{14} - 6 q^{16} + 30 q^{20} - 20 q^{22} - 144 q^{25} - 40 q^{26} - 6 q^{33} + 46 q^{36} - 12 q^{37} - 56 q^{38} - 2 q^{42} + 48 q^{45} - 40 q^{48} + 44 q^{49} - 32 q^{53} + 30 q^{56} + 78 q^{58} + 64 q^{64} - 4 q^{66} - 44 q^{69} - 44 q^{77} + 16 q^{78} + 24 q^{80} - 40 q^{81} - 6 q^{82} - 10 q^{88} + 24 q^{89} - 24 q^{92} - 96 q^{93}+O(q^{100}) $ 160 * q - 2 * q^4 + 68 * q^9 - 36 * q^12 - 8 * q^14 - 6 * q^16 + 30 * q^20 - 20 * q^22 - 144 * q^25 - 40 * q^26 - 6 * q^33 + 46 * q^36 - 12 * q^37 - 56 * q^38 - 2 * q^42 + 48 * q^45 - 40 * q^48 + 44 * q^49 - 32 * q^53 + 30 * q^56 + 78 * q^58 + 64 * q^64 - 4 * q^66 - 44 * q^69 - 44 * q^77 + 16 * q^78 + 24 * q^80 - 40 * q^81 - 6 * q^82 - 10 * q^88 + 24 * q^89 - 24 * q^92 - 96 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.20341	+	0.742836i	−0.850939	+	0.525264i
$2$	−1.20341	+	0.742836i	−0.850939	+	0.525264i
$3$	−0.371524	−	0.214500i	−0.214500	−	0.123841i	0.388901	−	0.921279i	$-0.372855\pi$
$3$	−0.371524	−	0.214500i	−0.214500	−	0.123841i	−0.603401	+	0.797438i	$0.706188\pi$
$4$	0.896390	−	1.78787i	0.448195	−	0.893936i
$5$		−	0.666498i		−	0.298067i	−0.988832	−	0.149033i	$-0.952384\pi$
$5$		−	0.666498i		−	0.298067i	0.988832	−	0.149033i	$-0.0476162\pi$
$6$	0.606434	−	0.0178505i	0.247576	−	0.00728744i
$7$	−1.08520	+	0.626541i	−0.410167	+	0.236810i	−0.690862	−	0.722987i	$-0.742769\pi$
$7$	−1.08520	+	0.626541i	−0.410167	+	0.236810i	0.280694	+	0.959797i	$0.409435\pi$
$8$	0.249370	+	2.81741i	0.0881655	+	0.996106i
$9$	−1.40798	−	2.43869i	−0.469327	−	0.812898i
$10$	0.495098	+	0.802070i	0.156564	+	0.253637i
$11$	−1.15735	+	3.10814i	−0.348953	+	0.937140i
$11$	−1.15735	+	3.10814i	−0.348953	+	0.937140i
$12$	−0.716528	+	0.471962i	−0.206844	+	0.136244i
$13$	0.456423	+	3.57655i	0.126589	+	0.991955i
$13$	0.456423	+	3.57655i	0.126589	+	0.991955i
$14$	0.840524	−	1.56011i	0.224640	−	0.416957i
$15$	−0.142963	+	0.247620i	−0.0369130	+	0.0639352i
$16$	−2.39297	−	3.20526i	−0.598242	−	0.801315i
$17$	3.16061	−	1.82478i	0.766559	−	0.442573i	−0.0650865	−	0.997880i	$-0.520732\pi$
$17$	3.16061	−	1.82478i	0.766559	−	0.442573i	0.831646	+	0.555306i	$0.187399\pi$
$18$	3.50592	+	1.88885i	0.826354	+	0.445206i
$19$	−4.42491	+	2.55472i	−1.01514	+	0.586094i	−0.912694	−	0.408644i	$-0.866002\pi$
$19$	−4.42491	+	2.55472i	−1.01514	+	0.586094i	−0.102451	+	0.994738i	$0.532668\pi$
$20$	−1.19161	−	0.597442i	−0.266453	−	0.133592i
$21$	0.537571			0.117308
$22$	−0.916078	−	4.60009i	−0.195309	−	0.980742i
$23$	6.23829	+	3.60168i	1.30077	+	0.751001i	0.980537	−	0.196336i	$-0.0629044\pi$
$23$	6.23829	+	3.60168i	1.30077	+	0.751001i	0.320236	+	0.947338i	$0.396238\pi$
$24$	0.511687	−	1.10023i	0.104448	−	0.224583i
$25$	4.55578			0.911156
$26$	−3.20605	−	3.96500i	−0.628758	−	0.777601i
$27$			2.49504i			0.480171i
$28$	0.147411	+	2.50182i	0.0278581	+	0.472800i
$29$	5.46790	+	3.15689i	1.01536	+	0.586220i	0.912757	−	0.408502i	$-0.133949\pi$
$29$	5.46790	+	3.15689i	1.01536	+	0.586220i	0.102605	+	0.994722i	$0.467282\pi$
$30$	−0.0118973	−	0.404187i	−0.00217214	−	0.0737941i
$31$	3.36773			0.604862			0.302431	−	0.953171i	$-0.402202\pi$
$31$	3.36773			0.604862			0.302431	+	0.953171i	$0.402202\pi$
$32$	5.26070	+	2.07966i	0.929970	+	0.367636i
$33$	1.09668	−	0.906500i	0.190907	−	0.157801i
$34$	−2.44799	+	4.54376i	−0.419828	+	0.779249i
$35$	0.417588	+	0.723284i	0.0705853	+	0.122257i
$36$	−5.62217	+	0.331266i	−0.937028	+	0.0552111i
$37$	−2.30894	−	1.33307i	−0.379587	−	0.219155i	0.298051	−	0.954550i	$-0.403663\pi$
$37$	−2.30894	−	1.33307i	−0.379587	−	0.219155i	−0.677639	+	0.735395i	$0.736997\pi$
$38$	3.42724	−	6.36136i	0.555972	−	1.03195i
$39$	0.597595	−	1.42668i	0.0956918	−	0.228451i
$40$	1.87780	−	0.166204i	0.296906	−	0.0262792i
$41$	−1.00414	+	1.73922i	−0.156820	+	0.271620i	−0.933720	−	0.358004i	$-0.883458\pi$
$41$	−1.00414	+	1.73922i	−0.156820	+	0.271620i	0.776900	+	0.629624i	$0.216791\pi$
$42$	−0.646918	+	0.399327i	−0.0998216	+	0.0616175i
$43$	1.39414	+	2.41471i	0.212604	+	0.368241i	0.952529	−	0.304449i	$-0.0984723\pi$
$43$	1.39414	+	2.41471i	0.212604	+	0.368241i	−0.739925	+	0.672690i	$0.765139\pi$
$44$	4.51953	+	4.85529i	0.681344	+	0.731963i
$45$	−1.62538	+	0.938416i	−0.242298	+	0.139891i
$46$	−10.1827	+	0.299729i	−1.50135	+	0.0441926i
$47$	−7.02399			−1.02455			−0.512277	−	0.858820i	$-0.671198\pi$
$47$	−7.02399			−1.02455			−0.512277	+	0.858820i	$0.671198\pi$
$48$	0.201518	+	1.70412i	0.0290867	+	0.245969i
$49$	−2.71489	+	4.70233i	−0.387842	+	0.671762i
$50$	−5.48247	+	3.38420i	−0.775338	+	0.478598i
$51$	−1.56565			−0.219236
$52$	6.80354	+	2.38995i	0.943481	+	0.331427i
$53$	12.4876			1.71530			0.857652	−	0.514230i	$-0.171922\pi$
$53$	12.4876			1.71530			0.857652	+	0.514230i	$0.171922\pi$
$54$	−1.85341	−	3.00256i	−0.252217	−	0.408596i
$55$	2.07157	+	0.771368i	0.279331	+	0.104011i
$56$	−2.03584	−	2.90122i	−0.272051	−	0.387692i
$57$	2.19195			0.290331
$58$	−8.92517	+	0.262714i	−1.17193	+	0.0344961i
$59$	5.41516	+	9.37933i	0.704994	+	1.22109i	0.966694	+	0.255936i	$0.0823837\pi$
$59$	5.41516	+	9.37933i	0.704994	+	1.22109i	−0.261700	+	0.965149i	$0.584283\pi$
$60$	0.314562	+	0.477565i	0.0406097	+	0.0616533i
$61$	−7.08084	+	4.08812i	−0.906608	+	0.523431i	−0.879338	−	0.476198i	$-0.842015\pi$
$61$	−7.08084	+	4.08812i	−0.906608	+	0.523431i	−0.0272700	+	0.999628i	$0.508681\pi$
$62$	−4.05276	+	2.50167i	−0.514701	+	0.317713i
$63$	3.05588	+	1.76431i	0.385005	+	0.222283i
$64$	−7.87563	+	1.40516i	−0.984454	+	0.175644i
$65$	2.38376	−	0.304205i	0.295669	−	0.0377320i
$66$	−0.646371	+	1.90554i	−0.0795628	+	0.234556i
$67$	−1.30558	+	2.26133i	−0.159502	+	0.276265i	−0.934689	−	0.355466i	$-0.884322\pi$
$67$	−1.30558	+	2.26133i	−0.159502	+	0.276265i	0.775187	+	0.631732i	$0.217655\pi$
$68$	−0.429329	−	7.28647i	−0.0520638	−	0.883614i
$69$	−1.54512	−	2.67622i	−0.186010	−	0.322179i
$70$	−1.03981	−	0.560208i	−0.124281	−	0.0669576i
$71$	0.954941	+	1.65401i	0.113331	+	0.196294i	0.917111	−	0.398631i	$-0.130515\pi$
$71$	0.954941	+	1.65401i	0.113331	+	0.196294i	−0.803781	+	0.594926i	$0.797181\pi$
$72$	6.51970	−	4.57500i	0.768354	−	0.539169i
$73$	−6.31191			−0.738753			−0.369376	−	0.929280i	$-0.620429\pi$
$73$	−6.31191			−0.738753			−0.369376	+	0.929280i	$0.620429\pi$
$74$	3.76885	−	0.110937i	0.438120	−	0.0128961i
$75$	−1.69258	−	0.977213i	−0.195443	−	0.112839i
$76$	0.601070	+	10.2012i	0.0689475	+	1.17016i
$77$	−0.691426	−	4.09808i	−0.0787953	−	0.467020i
$78$	0.340634	+	2.16079i	0.0385692	+	0.244661i
$79$	−6.65406			−0.748640			−0.374320	−	0.927300i	$-0.622124\pi$
$79$	−6.65406			−0.748640			−0.374320	+	0.927300i	$0.622124\pi$
$80$	−2.13630	+	1.59491i	−0.238846	+	0.178316i
$81$	−3.68875	+	6.38911i	−0.409862	+	0.709901i
$82$	−0.0835636	−	2.83890i	−0.00922806	−	0.313504i
$83$		−	7.67436i		−	0.842370i	−0.906975	−	0.421185i	$-0.861614\pi$
$83$		−	7.67436i		−	0.842370i	0.906975	−	0.421185i	$-0.138386\pi$
$84$	0.481873	−	0.961108i	0.0525767	−	0.104865i
$85$	−1.21621	−	2.10654i	−0.131916	−	0.228486i
$86$	−3.47145	−	1.87028i	−0.374336	−	0.201677i
$87$	−1.35430	−	2.34572i	−0.145197	−	0.251488i
$88$	−9.04553	−	2.48564i	−0.964257	−	0.264970i
$89$	11.8060	+	6.81619i	1.25143	+	0.722515i	0.971394	−	0.237474i	$-0.0763194\pi$
$89$	11.8060	+	6.81619i	1.25143	+	0.722515i	0.280039	+	0.959989i	$0.409653\pi$
$90$	1.25891	−	2.33669i	0.132701	−	0.246309i
$91$	−2.73616	−	3.59530i	−0.286828	−	0.376890i
$92$	12.0313	−	7.92475i	1.25435	−	0.826212i
$93$	−1.25119	−	0.722377i	−0.129743	−	0.0749070i
$94$	8.45274	−	5.21767i	0.871834	−	0.538162i
$95$	1.70272	+	2.94920i	0.174695	+	0.302581i
$96$	−1.50839	−	1.90106i	−0.153950	−	0.194026i
$97$	−0.573354	+	0.331026i	−0.0582153	+	0.0336106i	−0.528825	−	0.848731i	$-0.677367\pi$
$97$	−0.573354	+	0.331026i	−0.0582153	+	0.0336106i	0.470610	+	0.882341i	$0.344034\pi$
$98$	−0.225932	−	7.67555i	−0.0228225	−	0.775348i
$99$	9.20932	−	1.55379i	0.925572	−	0.156162i
$100$	4.08376	−	8.14515i	0.408376	−	0.814515i
$101$	−16.0826	−	9.28527i	−1.60027	−	0.923919i	−0.991431	−	0.130628i	$-0.958301\pi$
$101$	−16.0826	−	9.28527i	−1.60027	−	0.923919i	−0.608843	−	0.793291i	$-0.708366\pi$
$102$	1.88412	−	1.16302i	0.186556	−	0.115157i
$103$			2.81067i			0.276943i	0.990366	+	0.138472i	$0.0442190\pi$
$103$			2.81067i			0.276943i	−0.990366	+	0.138472i	$0.955781\pi$
$104$	−9.96279	+	2.17782i	−0.976932	+	0.213552i
$105$		−	0.358290i		−	0.0349655i
$106$	−15.0277	+	9.27624i	−1.45962	+	0.900988i
$107$	−5.33353	+	9.23794i	−0.515612	+	0.893066i	0.484224	+	0.874944i	$0.339102\pi$
$107$	−5.33353	+	9.23794i	−0.515612	+	0.893066i	−0.999836	+	0.0181217i	$0.994231\pi$
$108$	4.46081	+	2.23653i	0.429242	+	0.215210i
$109$	7.03447			0.673780			0.336890	−	0.941544i	$-0.390625\pi$
$109$	7.03447			0.673780			0.336890	+	0.941544i	$0.390625\pi$
$110$	−3.06595	+	0.610564i	−0.292327	+	0.0582150i
$111$	0.571884	+	0.990532i	0.0542808	+	0.0940172i
$112$	4.60508	+	1.97906i	0.435139	+	0.187003i
$113$	−2.13418	−	3.69650i	−0.200766	−	0.347738i	0.748009	−	0.663688i	$-0.231010\pi$
$113$	−2.13418	−	3.69650i	−0.200766	−	0.347738i	−0.948776	+	0.315951i	$0.897677\pi$
$114$	−2.63781	+	1.62826i	−0.247054	+	0.152500i
$115$	2.40051	−	4.15780i	0.223849	−	0.387717i
$116$	10.5455	−	6.94609i	0.979124	−	0.644928i
$117$	8.07946	−	6.14878i	0.746946	−	0.568455i
$118$	−13.4840	−	7.26461i	−1.24130	−	0.668761i
$119$	−2.28659	+	3.96050i	−0.209612	+	0.363058i
$120$	−0.733299	−	0.341038i	−0.0669407	−	0.0311324i
$121$	−8.32110	−	7.19439i	−0.756464	−	0.654036i
$122$	5.48435	−	10.1796i	0.496529	−	0.921616i
$123$	0.746122	−	0.430774i	0.0672756	−	0.0388416i
$124$	3.01880	−	6.02107i	0.271096	−	0.540708i
$125$		−	6.36891i		−	0.569652i
$126$	−4.98807	+	0.146825i	−0.444373	+	0.0130802i
$127$	8.18046	−	14.1690i	0.725899	−	1.25729i	−0.232704	−	0.972548i	$-0.574757\pi$
$127$	8.18046	−	14.1690i	0.725899	−	1.25729i	0.958603	−	0.284746i	$-0.0919093\pi$
$128$	8.43381	−	7.54128i	0.745451	−	0.666561i
$129$		−	1.19617i		−	0.105317i
$130$	−2.64267	+	2.13683i	−0.231777	+	0.187412i
$131$	22.0261			1.92443			0.962214	−	0.272295i	$-0.0877827\pi$
$131$	22.0261			1.92443			0.962214	+	0.272295i	$0.0877827\pi$
$132$	−0.637655	−	2.77330i	−0.0555007	−	0.241384i
$133$	3.20128	−	5.54478i	0.277586	−	0.480793i
$134$	−0.108649	−	3.69114i	−0.00938588	−	0.318866i
$135$	1.66294			0.143123
$136$	5.92931	+	8.44969i	0.508434	+	0.724555i
$137$	8.59902	−	4.96464i	0.734663	−	0.424158i	−0.0854623	−	0.996341i	$-0.527237\pi$
$137$	8.59902	−	4.96464i	0.734663	−	0.424158i	0.820126	+	0.572183i	$0.193903\pi$
$138$	3.84740	+	2.07282i	0.327512	+	0.176450i
$139$	4.68691	+	8.11797i	0.397539	+	0.688557i	0.993422	−	0.114514i	$-0.0365311\pi$
$139$	4.68691	+	8.11797i	0.397539	+	0.688557i	−0.595883	+	0.803071i	$0.703198\pi$
$140$	1.66746	−	0.0982492i	0.140926	−	0.00830358i
$141$	2.60958	+	1.50664i	0.219766	+	0.126882i
$142$	−2.37784	−	1.28108i	−0.199544	−	0.107506i
$143$	−11.6447	−	2.72067i	−0.973775	−	0.227514i
$144$	−4.44740	+	10.3487i	−0.370616	+	0.862388i
$145$	2.10406	−	3.64434i	0.174733	−	0.302646i
$146$	7.59581	−	4.68871i	0.628634	−	0.388040i
$147$	2.01730	−	1.16469i	0.166384	−	0.0960617i
$148$	−4.45306	+	2.93314i	−0.366039	+	0.241102i
$149$	6.64704	+	11.5130i	0.544547	+	0.943182i	0.998635	+	0.0522259i	$0.0166316\pi$
$149$	6.64704	+	11.5130i	0.544547	+	0.943182i	−0.454089	+	0.890956i	$0.650035\pi$
$150$	2.76278	−	0.0813230i	0.225580	−	0.00663999i
$151$		−	17.9419i		−	1.46009i	−0.683400	−	0.730044i	$-0.739500\pi$
$151$		−	17.9419i		−	1.46009i	0.683400	−	0.730044i	$-0.260500\pi$
$152$	−8.30115	−	11.8297i	−0.673312	−	0.959518i
$153$	−8.90014	−	5.13850i	−0.719533	−	0.415423i
$154$	3.87627	+	4.41806i	0.312359	+	0.356017i
$155$		−	2.24459i		−	0.180289i
$156$	−2.01503	−	2.34728i	−0.161332	−	0.187933i
$157$	4.12169			0.328947			0.164473	−	0.986382i	$-0.447408\pi$
$157$	4.12169			0.328947			0.164473	+	0.986382i	$0.447408\pi$
$158$	8.00756	−	4.94287i	0.637047	−	0.393234i
$159$	−4.63945	−	2.67859i	−0.367932	−	0.212426i
$160$	1.38609	−	3.50625i	0.109580	−	0.277193i
$161$	−9.02639			−0.711379
$162$	−0.306976	−	10.4289i	−0.0241183	−	0.819368i
$163$	−3.37673	−	5.84866i	−0.264486	−	0.458103i	0.702943	−	0.711246i	$-0.251869\pi$
$163$	−3.37673	−	5.84866i	−0.264486	−	0.458103i	−0.967429	+	0.253144i	$0.918536\pi$
$164$	2.20940	+	3.35429i	0.172525	+	0.261926i
$165$	−0.604180	−	0.730933i	−0.0470354	−	0.0569030i
$166$	5.70079	+	9.23540i	0.442467	+	0.716806i
$167$	−15.3959	−	8.88882i	−1.19137	−	0.687838i	−0.232753	−	0.972536i	$-0.574773\pi$
$167$	−15.3959	−	8.88882i	−1.19137	−	0.687838i	−0.958617	+	0.284698i	$0.908107\pi$
$168$	0.134054	+	1.51456i	0.0103425	+	0.116851i
$169$	−12.5834	+	3.26484i	−0.967950	+	0.251141i
$170$	3.02841	+	1.63158i	0.232268	+	0.125137i
$171$	12.4604	+	7.19400i	0.952869	+	0.550139i
$172$	5.56689	−	0.328009i	0.424471	−	0.0250105i
$173$	10.0779	−	5.81846i	0.766206	−	0.442369i	−0.0653135	−	0.997865i	$-0.520805\pi$
$173$	10.0779	−	5.81846i	0.766206	−	0.442369i	0.831519	+	0.555496i	$0.187471\pi$
$174$	3.37227	+	1.81684i	0.255651	+	0.137734i
$175$	−4.94394	+	2.85438i	−0.373726	+	0.215771i
$176$	12.7319	−	3.72809i	0.959703	−	0.281016i
$177$		−	4.64620i		−	0.349230i
$178$	−19.2708	+	0.567239i	−1.44440	+	0.0425164i
$179$	−15.4247	−	8.90545i	−1.15290	−	0.665625i	−0.203304	−	0.979116i	$-0.565168\pi$
$179$	−15.4247	−	8.90545i	−1.15290	−	0.665625i	−0.949591	+	0.313491i	$0.898501\pi$
$180$	0.220788	+	3.74716i	0.0164566	+	0.279297i
$181$	−23.1427			−1.72019			−0.860093	−	0.510138i	$-0.829594\pi$
$181$	−23.1427			−1.72019			−0.860093	+	0.510138i	$0.829594\pi$
$182$	5.96344	+	2.29410i	0.442040	+	0.170050i
$183$	3.50760			0.259289
$184$	−8.59177	+	18.4740i	−0.633394	+	1.36192i
$185$	−0.888486	+	1.53890i	−0.0653228	+	0.113142i
$186$	2.04231	−	0.0601157i	0.149749	−	0.00440790i
$187$	2.01375	+	11.9355i	0.147260	+	0.872811i
$188$	−6.29624	+	12.5580i	−0.459200	+	0.915886i
$189$	−1.56325	−	2.70762i	−0.113709	−	0.196950i
$190$	−4.23984	−	2.28425i	−0.307590	−	0.165717i
$191$	−8.91896	+	5.14936i	−0.645353	+	0.372595i	−0.786674	−	0.617369i	$-0.788199\pi$
$191$	−8.91896	+	5.14936i	−0.645353	+	0.372595i	0.141320	+	0.989964i	$0.454865\pi$
$192$	3.22739	+	1.16727i	0.232917	+	0.0842405i
$193$	−4.31263	+	7.46970i	−0.310430	+	0.537681i	−0.978455	−	0.206458i	$-0.933806\pi$
$193$	−4.31263	+	7.46970i	−0.310430	+	0.537681i	0.668025	+	0.744138i	$0.267140\pi$
$194$	0.444082	−	0.824268i	0.0318832	−	0.0591790i
$195$	−0.950876	−	0.398296i	−0.0680937	−	0.0285226i
$196$	5.97356	+	9.06901i	0.426683	+	0.647786i
$197$	−9.18129	+	15.9025i	−0.654140	+	1.13300i	0.327969	+	0.944688i	$0.393636\pi$
$197$	−9.18129	+	15.9025i	−0.654140	+	1.13300i	−0.982109	+	0.188315i	$0.939698\pi$
$198$	−9.92838	+	8.71086i	−0.705579	+	0.619054i
$199$	11.4220	−	6.59452i	0.809688	−	0.467473i	−0.0371598	−	0.999309i	$-0.511831\pi$
$199$	11.4220	−	6.59452i	0.809688	−	0.467473i	0.846847	+	0.531836i	$0.178498\pi$
$200$	1.13607	+	12.8355i	0.0803326	+	0.907608i
$201$	0.970109	−	0.560092i	0.0684262	−	0.0395059i
$202$	26.2513	−	0.772714i	1.84704	−	0.0543679i
$203$	−7.91168			−0.555291
$204$	−1.40344	+	2.79919i	−0.0982603	+	0.195982i
$205$	1.15918	+	0.669255i	0.0809609	+	0.0467428i
$206$	−2.08787	−	3.38239i	−0.145468	−	0.235662i
$207$		−	20.2844i		−	1.40986i
$208$	10.3716	−	10.0215i	0.719138	−	0.694867i
$209$	−2.81930	−	16.7100i	−0.195015	−	1.15585i
$210$	0.266150	+	0.431170i	0.0183661	+	0.0297535i
$211$	−8.59603	+	14.8888i	−0.591775	+	1.02498i	0.402218	+	0.915544i	$0.368239\pi$
$211$	−8.59603	+	14.8888i	−0.591775	+	1.02498i	−0.993993	+	0.109441i	$0.965094\pi$
$212$	11.1938	−	22.3262i	0.768791	−	1.53337i
$213$		−	0.819338i		−	0.0561401i
$214$	−0.443853	−	15.0790i	−0.0303411	−	1.03078i
$215$	1.60940	−	0.929189i	0.109760	−	0.0633702i
$216$	−7.02956	+	0.622188i	−0.478301	+	0.0423345i
$217$	−3.65466	+	2.11002i	−0.248095	+	0.143238i
$218$	−8.46535	+	5.22545i	−0.573346	+	0.353912i
$219$	2.34503	+	1.35390i	0.158462	+	0.0914881i
$220$	3.23604	−	3.01225i	0.218174	−	0.203086i
$221$	7.96897	+	10.4712i	0.536051	+	0.704368i
$222$	−1.42401	−	0.767201i	−0.0955736	−	0.0514911i
$223$	2.45646	−	4.25471i	0.164496	−	0.284916i	−0.771980	−	0.635647i	$-0.780733\pi$
$223$	2.45646	−	4.25471i	0.164496	−	0.284916i	0.936476	+	0.350731i	$0.114067\pi$
$224$	−7.01191	+	1.03920i	−0.468503	+	0.0694343i
$225$	−6.41445	−	11.1101i	−0.427630	−	0.740677i
$226$	5.31418	+	2.86306i	0.353494	+	0.190448i
$227$	9.22605	−	5.32666i	0.612355	−	0.353543i	−0.161532	−	0.986867i	$-0.551643\pi$
$227$	9.22605	−	5.32666i	0.612355	−	0.353543i	0.773886	+	0.633324i	$0.218310\pi$
$228$	1.96484	−	3.91892i	0.130125	−	0.259537i
$229$			22.5009i			1.48690i	0.668792	+	0.743449i	$0.266811\pi$
$229$			22.5009i			1.48690i	−0.668792	+	0.743449i	$0.733189\pi$
$230$	0.199769	+	6.78673i	0.0131724	+	0.447504i
$231$	−0.622155	+	1.67085i	−0.0409348	+	0.109934i
$232$	−7.53074	+	16.1926i	−0.494417	+	1.06309i
$233$		−	6.06294i		−	0.397197i	−0.980081	−	0.198598i	$-0.936361\pi$
$233$		−	6.06294i		−	0.397197i	0.980081	−	0.198598i	$-0.0636389\pi$
$234$	−5.15537	+	13.4012i	−0.337017	+	0.876065i
$235$			4.68148i			0.305386i
$236$	21.6231	−	1.27407i	1.40755	−	0.0829347i
$237$	2.47214	+	1.42729i	0.160583	+	0.0927126i
$238$	−0.190289	−	6.46466i	−0.0123346	−	0.419042i
$239$			3.73108i			0.241343i	0.992692	+	0.120672i	$0.0385048\pi$
$239$			3.73108i			0.241343i	−0.992692	+	0.120672i	$0.961495\pi$
$240$	1.13579	−	0.134312i	0.0733152	−	0.00866978i
$241$	10.9040	+	18.8862i	0.702386	+	1.21657i	0.967627	+	0.252386i	$0.0812152\pi$
$241$	10.9040	+	18.8862i	0.702386	+	1.21657i	−0.265241	+	0.964182i	$0.585451\pi$
$242$	15.3579	+	2.47659i	0.987246	+	0.159201i
$243$	9.22323	−	5.32503i	0.591671	−	0.341601i
$244$	0.961845	+	16.3242i	0.0615758	+	1.04505i
$245$	3.13409	+	1.80947i	0.200230	+	0.115603i
$246$	−0.577897	+	1.07264i	−0.0368454	+	0.0683893i
$247$	−11.1567	−	14.6599i	−0.709885	−	0.932785i
$248$	0.839810	+	9.48829i	0.0533280	+	0.602507i
$249$	−1.64615	+	2.85121i	−0.104320	+	0.180688i
$250$	4.73105	+	7.66441i	0.299218	+	0.484740i
$251$	4.52825	−	2.61438i	0.285820	−	0.165018i	−0.350235	−	0.936662i	$-0.613898\pi$
$251$	4.52825	−	2.61438i	0.285820	−	0.165018i	0.636055	+	0.771643i	$0.280565\pi$
$252$	5.89363	−	3.88201i	0.371264	−	0.244544i
$253$	−18.4144	+	15.2211i	−1.15770	+	0.956942i
$254$	0.680773	+	23.1278i	0.0427155	+	1.45117i
$255$			1.04351i			0.0653469i
$256$	−4.54740	+	15.3402i	−0.284213	+	0.958761i
$257$	−7.11864	+	12.3298i	−0.444048	+	0.769114i	−0.997985	−	0.0634442i	$-0.979791\pi$
$257$	−7.11864	+	12.3298i	−0.444048	+	0.769114i	0.553937	+	0.832559i	$0.313125\pi$
$258$	0.888555	+	1.43948i	0.0553190	+	0.0896180i
$259$	3.34088			0.207592
$260$	1.59290	−	4.53454i	0.0987874	−	0.281220i
$261$		−	17.7794i		−	1.10051i
$262$	−26.5064	+	16.3618i	−1.63757	+	1.01083i
$263$	7.18027	−	12.4366i	0.442754	−	0.766873i	−0.555139	−	0.831758i	$-0.687335\pi$
$263$	7.18027	−	12.4366i	0.442754	−	0.766873i	0.997893	+	0.0648851i	$0.0206681\pi$
$264$	2.82746	+	2.86374i	0.174018	+	0.176251i
$265$		−	8.32296i		−	0.511275i
$266$	0.266408	+	9.05066i	0.0163345	+	0.554932i
$267$	−2.92414	−	5.06476i	−0.178955	−	0.309958i
$268$	2.87266	+	4.36124i	0.175476	+	0.266405i
$269$	4.28217	+	7.41693i	0.261088	+	0.452218i	0.966531	−	0.256548i	$-0.0825852\pi$
$269$	4.28217	+	7.41693i	0.261088	+	0.452218i	−0.705443	+	0.708767i	$0.749252\pi$
$270$	−2.00120	+	1.23529i	−0.121789	+	0.0751774i
$271$	−16.0309	−	9.25542i	−0.973806	−	0.562227i	−0.0734113	−	0.997302i	$-0.523389\pi$
$271$	−16.0309	−	9.25542i	−0.973806	−	0.562227i	−0.900394	+	0.435075i	$0.856722\pi$
$272$	−13.4121	−	5.76393i	−0.813229	−	0.349490i
$273$	0.245360	+	1.92265i	0.0148499	+	0.116364i
$274$	−6.66023	+	12.3622i	−0.402359	+	0.746825i
$275$	−5.27261	+	14.1600i	−0.317951	+	0.853881i
$276$	−6.16976	+	0.363532i	−0.371376	+	0.0218820i
$277$	14.7297	−	8.50420i	0.885022	−	0.510968i	0.0127111	−	0.999919i	$-0.495954\pi$
$277$	14.7297	−	8.50420i	0.885022	−	0.510968i	0.872311	+	0.488951i	$0.162620\pi$
$278$	−11.6706	−	6.28764i	−0.699956	−	0.377108i
$279$	−4.74170	−	8.21286i	−0.283878	−	0.491691i
$280$	−1.93366	+	1.35688i	−0.115558	+	0.0810893i
$281$	14.2851			0.852177			0.426089	−	0.904681i	$-0.359891\pi$
$281$	14.2851			0.852177			0.426089	+	0.904681i	$0.359891\pi$
$282$	−4.25959	+	0.125382i	−0.253655	+	0.00746638i
$283$	−2.06180	+	3.57113i	−0.122561	+	0.212282i	−0.920777	−	0.390090i	$-0.872444\pi$
$283$	−2.06180	+	3.57113i	−0.122561	+	0.212282i	0.798216	+	0.602371i	$0.205777\pi$
$284$	3.81315	−	0.224676i	0.226269	−	0.0133321i
$285$		−	1.46093i		−	0.0865380i
$286$	16.0343	−	5.37598i	0.948128	−	0.317888i
$287$		−	2.51653i		−	0.148546i
$288$	−2.33531	−	15.7574i	−0.137610	−	0.928511i
$289$	−1.84038	+	3.18764i	−0.108258	+	0.187508i
$290$	0.175099	+	5.94861i	0.0102821	+	0.349314i
$291$	0.284020			0.0166495
$292$	−5.65793	+	11.2849i	−0.331105	+	0.660397i
$293$	−2.09795	−	3.63376i	−0.122564	−	0.212286i	0.798214	−	0.602373i	$-0.205778\pi$
$293$	−2.09795	−	3.63376i	−0.122564	−	0.212286i	−0.920778	+	0.390087i	$0.872445\pi$
$294$	−1.56246	+	2.90012i	−0.0911247	+	0.169138i
$295$	6.25131	−	3.60919i	0.363965	−	0.210135i
$296$	3.18002	−	6.83766i	0.184835	−	0.397431i
$297$	−7.75495	−	2.88763i	−0.449988	−	0.167557i
$298$	−16.5514	−	8.91721i	−0.958796	−	0.516560i
$299$	−10.0343	+	23.9554i	−0.580296	+	1.38538i
$300$	−3.26435	+	2.15016i	−0.188467	+	0.124139i
$301$	−3.02583	−	1.74697i	−0.174406	−	0.100693i
$302$	13.3278	+	21.5914i	0.766932	+	1.24245i
$303$	3.98337	+	6.89940i	0.228839	+	0.396360i
$304$	18.7772	+	8.06963i	1.07695	+	0.462825i
$305$	2.72473	+	4.71936i	0.156017	+	0.270230i
$306$	14.5276	−	0.427622i	0.830486	−	0.0244455i
$307$		−	12.8959i		−	0.736007i	−0.929824	−	0.368003i	$-0.880042\pi$
$307$		−	12.8959i		−	0.736007i	0.929824	−	0.368003i	$-0.119958\pi$
$308$	−7.94663	−	2.43730i	−0.452801	−	0.138878i
$309$	0.602887	−	1.04423i	0.0342971	−	0.0594043i
$310$	1.66736	+	2.70116i	0.0946996	+	0.153415i
$311$		−	13.4972i		−	0.765359i	−0.923881	−	0.382679i	$-0.875001\pi$
$311$		−	13.4972i		−	0.765359i	0.923881	−	0.382679i	$-0.124999\pi$
$312$	4.16856	+	1.32790i	0.235998	+	0.0751777i
$313$	6.68383			0.377792			0.188896	−	0.981997i	$-0.439509\pi$
$313$	6.68383			0.377792			0.188896	+	0.981997i	$0.439509\pi$
$314$	−4.96008	+	3.06174i	−0.279914	+	0.172784i
$315$	1.17591	−	2.03674i	0.0662551	−	0.114757i
$316$	−5.96463	+	11.8966i	−0.335537	+	0.669236i
$317$		−	14.6245i		−	0.821395i	−0.911772	−	0.410697i	$-0.865285\pi$
$317$		−	14.6245i		−	0.821395i	0.911772	−	0.410697i	$-0.134715\pi$
$318$	7.57290	−	0.222910i	0.424667	−	0.0125002i
$319$	−16.1403	+	13.3414i	−0.903684	+	0.746974i
$320$	0.936533	+	5.24909i	0.0523538	+	0.293433i
$321$	3.96307	−	2.28808i	0.221197	−	0.127708i
$322$	10.8624	−	6.70512i	0.605340	−	0.373662i
$323$	−9.32360	+	16.1490i	−0.518779	+	0.898552i
$324$	8.11634	+	12.3222i	0.450908	+	0.684564i
$325$	2.07936	+	16.2940i	0.115342	+	0.903826i
$326$	8.40818	+	4.52998i	0.465686	+	0.250893i
$327$	−2.61347	−	1.50889i	−0.144525	−	0.0834418i
$328$	−5.15049	−	2.39536i	−0.284388	−	0.132262i
$329$	7.62244	−	4.40082i	0.420239	−	0.242625i
$330$	1.27004	+	0.430805i	0.0699134	+	0.0237150i
$331$	−16.1185	−	27.9181i	−0.885955	−	1.53452i	−0.844615	−	0.535374i	$-0.820171\pi$
$331$	−16.1185	−	27.9181i	−0.885955	−	1.53452i	−0.0413398	−	0.999145i	$-0.513163\pi$
$332$	−13.7208	−	6.87922i	−0.753025	−	0.377546i
$333$			7.50772i			0.411421i
$334$	25.1305	−	0.739722i	1.37508	−	0.0404758i
$335$	1.50717	+	0.870166i	0.0823456	+	0.0475422i
$336$	−1.28639	−	1.72306i	−0.0701783	−	0.0940004i
$337$			24.8629i			1.35437i	0.735812	+	0.677185i	$0.236801\pi$
$337$			24.8629i			1.35437i	−0.735812	+	0.677185i	$0.763199\pi$
$338$	12.7177	−	13.2763i	0.691751	−	0.722136i
$339$			1.83112i			0.0994528i
$340$	−4.85642	+	0.286147i	−0.263376	+	0.0155185i
$341$	−3.89763	+	10.4674i	−0.211068	+	0.566841i
$342$	−20.3389	+	0.598680i	−1.09980	+	0.0323729i
$343$		−	15.5755i		−	0.841000i
$344$	−6.45559	+	4.53001i	−0.348062	+	0.244242i
$345$	−1.78369	+	1.02982i	−0.0960309	+	0.0554435i
$346$	−7.80564	+	14.4882i	−0.419634	+	0.778890i
$347$	16.1205	+	27.9216i	0.865396	+	1.49891i	0.866654	+	0.498910i	$0.166266\pi$
$347$	16.1205	+	27.9216i	0.865396	+	1.49891i	−0.00125798	+	0.999999i	$0.500400\pi$
$348$	−5.40783	+	0.318638i	−0.289890	+	0.0170808i
$349$	−7.59388	+	13.1530i	−0.406491	+	0.704063i	−0.994494	−	0.104796i	$-0.966581\pi$
$349$	−7.59388	+	13.1530i	−0.406491	+	0.704063i	0.588003	+	0.808859i	$0.299914\pi$
$350$	3.82924	−	7.10752i	0.204682	−	0.379913i
$351$	−8.92363	+	1.13879i	−0.476308	+	0.0607844i
$352$	−12.5523	+	13.9441i	−0.669042	+	0.743225i
$353$	24.6199	+	14.2143i	1.31038	+	0.756550i	0.982160	−	0.188050i	$-0.0602165\pi$
$353$	24.6199	+	14.2143i	1.31038	+	0.756550i	0.328224	+	0.944600i	$0.393550\pi$
$354$	3.45136	+	5.59128i	0.183438	+	0.297173i
$355$	1.10239	−	0.636466i	0.0585089	−	0.0337801i
$356$	22.7693	−	14.9976i	1.20677	−	0.794873i
$357$	1.69905	−	0.980947i	0.0899232	−	0.0519172i
$358$	25.1775	−	0.741105i	1.33067	−	0.0391686i
$359$		−	28.0415i		−	1.47997i	−0.672622	−	0.739986i	$-0.734832\pi$
$359$		−	28.0415i		−	1.47997i	0.672622	−	0.739986i	$-0.265168\pi$
$360$	−3.04923	−	4.34536i	−0.160708	−	0.229021i
$361$	3.55324	−	6.15439i	0.187012	−	0.323915i
$362$	27.8502	−	17.1912i	1.46377	−	0.903552i
$363$	1.54830	+	4.45776i	0.0812645	+	0.233972i
$364$	−8.88061	+	1.66911i	−0.465470	+	0.0874853i
$365$			4.20687i			0.220198i
$366$	−4.22108	+	2.60557i	−0.220640	+	0.136195i
$367$	1.00490	+	0.580180i	0.0524554	+	0.0302852i	0.525998	−	0.850486i	$-0.323692\pi$
$367$	1.00490	+	0.580180i	0.0524554	+	0.0302852i	−0.473543	+	0.880771i	$0.657025\pi$
$368$	−3.38371	−	28.6140i	−0.176388	−	1.49161i
$369$	5.65522			0.294399
$370$	−0.0739392	−	2.51193i	−0.00384391	−	0.130589i
$371$	−13.5516	+	7.82399i	−0.703562	+	0.406202i
$372$	−2.41307	+	1.58944i	−0.125112	+	0.0824087i
$373$	9.40123	−	5.42781i	0.486777	−	0.281041i	−0.236459	−	0.971641i	$-0.575987\pi$
$373$	9.40123	−	5.42781i	0.486777	−	0.281041i	0.723237	+	0.690600i	$0.242654\pi$
$374$	−11.2895	−	12.8674i	−0.583766	−	0.665359i
$375$	−1.36613	+	2.36620i	−0.0705465	+	0.122190i
$376$	−1.75157	−	19.7895i	−0.0903304	−	1.02056i
$377$	−8.79509	+	20.9971i	−0.452970	+	1.08140i
$378$	3.89254	+	2.09714i	0.200211	+	0.107865i
$379$	6.08917	−	10.5468i	0.312780	−	0.541751i	−0.666183	−	0.745788i	$-0.732073\pi$
$379$	6.08917	−	10.5468i	0.312780	−	0.541751i	0.978963	+	0.204038i	$0.0654065\pi$
$380$	6.79908	−	0.400612i	0.348786	−	0.0205510i
$381$	−6.07848	+	3.50941i	−0.311410	+	0.179793i
$382$	6.90803	−	12.8221i	0.353446	−	0.656036i
$383$	3.78031	+	6.54769i	0.193165	+	0.334571i	0.946297	−	0.323298i	$-0.104791\pi$
$383$	3.78031	+	6.54769i	0.193165	+	0.334571i	−0.753133	+	0.657869i	$0.771458\pi$
$384$	−4.75096	+	0.992717i	−0.242447	+	0.0506594i
$385$	−2.73136	+	0.460834i	−0.139203	+	0.0234863i
$386$	−0.358894	−	12.1927i	−0.0182672	−	0.620591i
$387$	3.92583	−	6.79974i	0.199561	−	0.345650i
$388$	0.0778831	+	1.32181i	0.00395392	+	0.0671049i
$389$	−21.8766			−1.10919			−0.554595	−	0.832120i	$-0.687127\pi$
$389$	−21.8766			−1.10919			−0.554595	+	0.832120i	$0.687127\pi$
$390$	1.44016	−	0.227032i	0.0729254	−	0.0114962i
$391$	26.2890			1.32949
$392$	−13.9254	−	6.47636i	−0.703340	−	0.327105i
$393$	−8.18322	−	4.72458i	−0.412789	−	0.238324i
$394$	−0.764060	−	25.9574i	−0.0384928	−	1.30771i
$395$			4.43492i			0.223145i
$396$	5.47717	−	17.8579i	0.275238	−	0.897393i
$397$	23.3533	−	13.4830i	1.17207	−	0.676694i	0.217902	−	0.975971i	$-0.430079\pi$
$397$	23.3533	−	13.4830i	1.17207	−	0.676694i	0.954166	+	0.299276i	$0.0967453\pi$
$398$	−8.84676	+	16.4206i	−0.443448	+	0.823091i
$399$	−2.37870	+	1.37335i	−0.119084	+	0.0687533i
$400$	−10.9018	−	14.6025i	−0.545092	−	0.730123i
$401$	−16.6145	−	9.59237i	−0.829688	−	0.479020i	0.0240581	−	0.999711i	$-0.492341\pi$
$401$	−16.6145	−	9.59237i	−0.829688	−	0.479020i	−0.853746	+	0.520690i	$0.825675\pi$
$402$	−0.751382	+	1.39465i	−0.0374755	+	0.0695589i
$403$	1.53711	+	12.0448i	0.0765690	+	0.599996i
$404$	−31.0171	+	20.4303i	−1.54316	+	1.01645i
$405$	4.25833	+	2.45855i	0.211598	+	0.122166i
$406$	9.52100	−	5.87708i	0.472519	−	0.291675i
$407$	6.81560	−	5.63369i	0.337837	−	0.279252i
$408$	−0.390427	−	4.41110i	−0.0193290	−	0.218382i
$409$	−2.27179	−	3.93486i	−0.112333	−	0.194566i	0.804378	−	0.594118i	$-0.202499\pi$
$409$	−2.27179	−	3.93486i	−0.112333	−	0.194566i	−0.916710	+	0.399552i	$0.869166\pi$
$410$	−1.89212	+	0.0556950i	−0.0934452	+	0.00275058i
$411$	−4.25966			−0.210113
$412$	5.02512	+	2.51946i	0.247570	+	0.124125i
$413$	−11.7531	−	6.78564i	−0.578331	−	0.333900i
$414$	15.0679	+	24.4104i	0.740549	+	1.19971i
$415$	−5.11494			−0.251083
$416$	−5.03689	+	19.7644i	−0.246954	+	0.969027i
$417$		−	4.02136i		−	0.196927i
$418$	15.8055	+	18.0147i	0.773073	+	0.881126i
$419$	−23.5181	−	13.5782i	−1.14893	−	0.663337i	−0.200307	−	0.979733i	$-0.564194\pi$
$419$	−23.5181	−	13.5782i	−1.14893	−	0.663337i	−0.948627	+	0.316396i	$0.897527\pi$
$420$	−0.640576	−	0.321168i	−0.0312569	−	0.0156714i
$421$		−	15.9574i		−	0.777715i	−0.921298	−	0.388858i	$-0.872870\pi$
$421$		−	15.9574i		−	0.777715i	0.921298	−	0.388858i	$-0.127130\pi$
$422$	−0.715356	−	24.3027i	−0.0348230	−	1.18304i
$423$	9.88964	+	17.1294i	0.480851	+	0.832858i
$424$	3.11403	+	35.1827i	0.151231	+	1.70862i
$425$	14.3990	−	8.31328i	0.698455	−	0.403253i
$426$	0.608633	+	0.985999i	0.0294884	+	0.0477718i
$427$	5.12275	−	8.87287i	0.247907	−	0.429388i
$428$	11.7353	+	17.8165i	0.567249	+	0.861192i
$429$	3.74269	+	3.50857i	0.180699	+	0.169395i
$430$	−1.24654	+	2.31372i	−0.0601133	+	0.111577i
$431$	21.4828	+	12.4031i	1.03479	+	0.597435i	0.918353	−	0.395763i	$-0.129520\pi$
$431$	21.4828	+	12.4031i	1.03479	+	0.597435i	0.116436	+	0.993198i	$0.462853\pi$
$432$	7.99726	−	5.97056i	0.384768	−	0.287259i
$433$	−12.0327	−	20.8412i	−0.578254	−	1.00156i	−0.995680	−	0.0928538i	$-0.970401\pi$
$433$	−12.0327	−	20.8412i	−0.578254	−	1.00156i	0.417426	−	0.908711i	$-0.362932\pi$
$434$	2.83066	−	5.25404i	0.135876	−	0.252202i
$435$	−1.56342	+	0.902640i	−0.0749602	+	0.0432783i
$436$	6.30563	−	12.5767i	0.301985	−	0.602316i
$437$	−36.8052			−1.76063
$438$	−3.82775	+	0.112671i	−0.182897	+	0.00538361i
$439$	9.96735	−	17.2640i	0.475716	−	0.823964i	−0.523897	−	0.851781i	$-0.675522\pi$
$439$	9.96735	−	17.2640i	0.475716	−	0.823964i	0.999613	+	0.0278177i	$0.00885579\pi$
$440$	−1.65668	+	6.02883i	−0.0789789	+	0.287413i
$441$	15.2901			0.728098
$442$	−17.3683	−	6.68148i	−0.826126	−	0.317806i
$443$			36.7456i			1.74584i	0.487867	+	0.872918i	$0.337775\pi$
$443$			36.7456i			1.74584i	−0.487867	+	0.872918i	$0.662225\pi$
$444$	2.28358	−	0.134552i	0.108374	−	0.00638554i
$445$	4.54298	−	7.86867i	0.215358	−	0.373011i
$446$	0.204425	+	6.94490i	0.00967978	+	0.328850i
$447$		−	5.70315i		−	0.269750i
$448$	7.66625	−	6.45928i	0.362196	−	0.305172i
$449$	21.8239	−	12.6000i	1.02993	−	0.594633i	0.112968	−	0.993599i	$-0.463964\pi$
$449$	21.8239	−	12.6000i	1.02993	−	0.594633i	0.916966	+	0.398966i	$0.130631\pi$
$450$	15.9722	+	8.60518i	0.752938	+	0.405652i
$451$	−4.24360	−	5.13388i	−0.199823	−	0.241745i
$452$	−8.52193	+	0.502125i	−0.400838	+	0.0236180i
$453$	−3.84852	+	6.66583i	−0.180819	+	0.313188i
$454$	−7.14589	+	13.2636i	−0.335373	+	0.622492i
$455$	−2.39626	+	1.82365i	−0.112338	+	0.0854939i
$456$	0.546606	+	6.17563i	0.0255972	+	0.289200i
$457$	10.6802	−	18.4986i	0.499598	−	0.865329i	−0.500402	−	0.865793i	$-0.666815\pi$
$457$	10.6802	−	18.4986i	0.499598	−	0.865329i	1.00000		0.000464500i	$0.000147855\pi$
$458$	−16.7144	−	27.0777i	−0.781014	−	1.26526i
$459$	4.55289	+	7.88584i	0.212511	+	0.368080i
$460$	−5.28183	−	8.01882i	−0.246266	−	0.373879i
$461$	−4.35019	−	7.53475i	−0.202609	−	0.350928i	0.746760	−	0.665094i	$-0.231609\pi$
$461$	−4.35019	−	7.53475i	−0.202609	−	0.350928i	−0.949368	+	0.314166i	$0.898275\pi$
$462$	−0.492457	−	2.47287i	−0.0229112	−	0.115048i
$463$	23.7175			1.10225			0.551123	−	0.834424i	$-0.314199\pi$
$463$	23.7175			1.10225			0.551123	+	0.834424i	$0.314199\pi$
$464$	−2.96584	−	25.0804i	−0.137686	−	1.16433i
$465$	−0.481463	+	0.833918i	−0.0223273	+	0.0386720i
$466$	4.50377	+	7.29620i	0.208633	+	0.337990i
$467$			35.9786i			1.66489i	0.554107	+	0.832445i	$0.313060\pi$
$467$			35.9786i			1.66489i	−0.554107	+	0.832445i	$0.686940\pi$
$468$	−3.75088	−	19.9567i	−0.173384	−	0.922501i
$469$		−	3.27200i		−	0.151087i
$470$	−3.47757	−	5.63373i	−0.160408	−	0.259865i
$471$	−1.53131	−	0.884100i	−0.0705589	−	0.0407372i
$472$	−25.0751	+	17.5957i	−1.15417	+	0.809906i
$473$	−9.11878	+	1.53851i	−0.419282	+	0.0707410i
$474$	−4.03525	+	0.118778i	−0.185345	+	0.00545567i
$475$	−20.1589	+	11.6388i	−0.924955	+	0.534023i
$476$	5.03118	+	7.63829i	0.230604	+	0.350100i
$477$	−17.5823	−	30.4534i	−0.805038	−	1.39437i
$478$	−2.77158	−	4.49002i	−0.126769	−	0.205369i
$479$	−25.0080	−	14.4384i	−1.14265	−	0.659707i	−0.195561	−	0.980691i	$-0.562653\pi$
$479$	−25.0080	−	14.4384i	−1.14265	−	0.659707i	−0.947084	+	0.320985i	$0.895986\pi$
$480$	−1.26705	+	1.00534i	−0.0578329	+	0.0458873i
$481$	3.71392	−	8.86647i	0.169340	−	0.404276i
$482$	−27.1513	−	14.6280i	−1.23671	−	0.666287i
$483$	3.35352	+	1.93616i	0.152591	+	0.0880982i
$484$	−20.3216	+	8.42808i	−0.923709	+	0.383094i
$485$	0.220628	+	0.382139i	0.0100182	+	0.0173521i
$486$	−7.14370	+	13.2595i	−0.324045	+	0.601465i
$487$	16.3116	+	28.2525i	0.739149	+	1.28024i	0.952879	+	0.303351i	$0.0981053\pi$
$487$	16.3116	+	28.2525i	0.739149	+	1.28024i	−0.213730	+	0.976893i	$0.568561\pi$
$488$	−13.2837	−	18.9302i	−0.601324	−	0.856929i
$489$			2.89723i			0.131017i
$490$	−5.11574	+	0.150583i	−0.231106	+	0.00680264i
$491$	3.06907	−	5.31579i	0.138505	−	0.239898i	−0.788426	−	0.615130i	$-0.789104\pi$
$491$	3.06907	−	5.31579i	0.138505	−	0.239898i	0.926931	+	0.375232i	$0.122437\pi$
$492$	−0.101352	−	1.72011i	−0.00456928	−	0.0775487i
$493$	23.0425			1.03778
$494$	24.3160	+	9.35422i	1.09403	+	0.420866i
$495$	−1.03560	−	6.13799i	−0.0465467	−	0.275882i
$496$	−8.05888	−	10.7945i	−0.361854	−	0.484686i
$497$	−2.07260	−	1.19662i	−0.0929690	−	0.0536757i
$498$	−0.136991	−	4.65399i	−0.00613872	−	0.208550i
$499$	26.2899			1.17690			0.588450	−	0.808534i	$-0.299739\pi$
$499$	26.2899			1.17690			0.588450	+	0.808534i	$0.299739\pi$
$500$	−11.3868	−	5.70903i	−0.509233	−	0.255315i
$501$	3.81330	+	6.60483i	0.170366	+	0.295082i
$502$	−3.50728	+	6.50992i	−0.156537	+	0.290552i
$503$	−5.59921	−	9.69811i	−0.249656	−	0.432417i	0.713774	−	0.700376i	$-0.246984\pi$
$503$	−5.59921	−	9.69811i	−0.249656	−	0.432417i	−0.963430	+	0.267959i	$0.913651\pi$
$504$	−4.20876	+	9.04965i	−0.187473	+	0.403103i
$505$	−6.18861	+	10.7190i	−0.275390	+	0.476989i
$506$	10.8533	−	31.9961i	0.482487	−	1.42240i
$507$	5.37533	+	1.48616i	0.238727	+	0.0660026i
$508$	−17.9994	−	27.3266i	−0.798595	−	1.21242i
$509$	13.7814	+	7.95668i	0.610848	+	0.352673i	0.773297	−	0.634043i	$-0.218606\pi$
$509$	13.7814	+	7.95668i	0.610848	+	0.352673i	−0.162449	+	0.986717i	$0.551939\pi$
$510$	−0.775153	−	1.25576i	−0.0343244	−	0.0556062i
$511$	6.84968	−	3.95467i	0.303012	−	0.174944i
$512$	−5.92285	−	21.8385i	−0.261755	−	0.965134i
$513$	−6.37414	−	11.0403i	−0.281425	−	0.487443i
$514$	−0.592408	−	20.1258i	−0.0261300	−	0.887712i
$515$	1.87331			0.0825477
$516$	−2.13859	−	1.07223i	−0.0941463	−	0.0472024i
$517$	8.12919	−	21.8316i	0.357521	−	0.960151i
$518$	−4.02045	+	2.48173i	−0.176648	+	0.109041i
$519$	−4.99223			−0.219134
$520$	1.45151	+	6.64018i	0.0636529	+	0.291191i
$521$	−16.7490			−0.733788			−0.366894	−	0.930263i	$-0.619579\pi$
$521$	−16.7490			−0.733788			−0.366894	+	0.930263i	$0.619579\pi$
$522$	13.2071	+	21.3959i	0.578061	+	0.936471i
$523$	−0.483358	+	0.837201i	−0.0211358	+	0.0366083i	−0.876400	−	0.481584i	$-0.840062\pi$
$523$	−0.483358	+	0.837201i	−0.0211358	+	0.0366083i	0.855264	+	0.518192i	$0.173395\pi$
$524$	19.7440	−	39.3798i	0.862519	−	1.72031i
$525$	2.44906			0.106886
$526$	0.597537	+	20.3001i	0.0260538	+	0.885125i
$527$	10.6441	−	6.14536i	0.463663	−	0.267696i
$528$	−5.52988	−	1.34591i	−0.240657	−	0.0585732i
$529$	14.4441	+	25.0180i	0.628006	+	1.08774i
$530$	6.18259	+	10.0159i	0.268555	+	0.435064i
$531$	15.2489	−	26.4118i	0.661745	−	1.14618i
$532$	−7.04375	−	10.6938i	−0.305385	−	0.463633i
$533$	−6.67870	−	2.79752i	−0.289287	−	0.121174i
$534$	7.28122	+	3.92283i	0.315089	+	0.169757i
$535$	6.15707	+	3.55479i	0.266193	+	0.153687i
$536$	−6.69667	−	3.11445i	−0.289252	−	0.134524i
$537$	3.82043	+	6.61718i	0.164864	+	0.285552i
$538$	−10.6628	−	5.74466i	−0.459705	−	0.247670i
$539$	−11.4735	−	13.8805i	−0.494197	−	0.597875i
$540$	1.49064	−	2.97312i	0.0641471	−	0.127943i
$541$	−2.98791			−0.128460			−0.0642302	−	0.997935i	$-0.520459\pi$
$541$	−2.98791			−0.128460			−0.0642302	+	0.997935i	$0.520459\pi$
$542$	26.1670	−	0.770230i	1.12397	−	0.0330842i
$543$	8.59808	+	4.96410i	0.368979	+	0.213030i
$544$	20.4219	−	3.02662i	0.875583	−	0.129765i
$545$		−	4.68846i		−	0.200831i
$546$	−1.72348	−	2.13147i	−0.0737581	−	0.0912185i
$547$	33.4166			1.42879			0.714395	−	0.699743i	$-0.246702\pi$
$547$	33.4166			1.42879			0.714395	+	0.699743i	$0.246702\pi$
$548$	−1.16807	−	19.8242i	−0.0498975	−	0.846848i
$549$	19.9394	+	11.5120i	0.850991	+	0.491320i
$550$	−4.17345	−	20.9570i	−0.177957	−	0.893609i
$551$	−32.2600			−1.37432
$552$	7.15471	−	5.02060i	0.304525	−	0.213691i
$553$	7.22099	−	4.16904i	0.307068	−	0.177286i
$554$	−11.4086	+	21.1758i	−0.484707	+	0.899673i
$555$	0.660188	−	0.381160i	0.0280234	−	0.0161793i
$556$	18.7152	−	1.10273i	0.793701	−	0.0467660i
$557$	11.7956	−	20.4306i	0.499796	−	0.865673i	−0.500204	−	0.865908i	$-0.666742\pi$
$557$	11.7956	−	20.4306i	0.499796	−	0.865673i	1.00000		0.000235187i	$7.48624e-5\pi$
$558$	11.8070	+	6.36114i	0.499831	+	0.269288i
$559$	−8.00002	+	6.08832i	−0.338365	+	0.257509i
$560$	1.31904	−	3.06927i	0.0557396	−	0.129701i
$561$	1.81200	−	4.86628i	0.0765029	−	0.205454i
$562$	−17.1908	+	10.6115i	−0.725151	+	0.447618i
$563$	0.957957	+	1.65923i	0.0403731	+	0.0699282i	0.885506	−	0.464628i	$-0.153812\pi$
$563$	0.957957	+	1.65923i	0.0403731	+	0.0699282i	−0.845133	+	0.534556i	$0.820479\pi$
$564$	5.03289	−	3.31506i	0.211923	−	0.139589i
$565$	−2.46371	+	1.42242i	−0.103649	+	0.0598418i
$566$	−0.171581	−	5.82911i	−0.00721209	−	0.245016i
$567$		−	9.24462i		−	0.388238i
$568$	−4.42188	+	3.10292i	−0.185538	+	0.130196i
$569$	27.8855	+	16.0997i	1.16902	+	0.674934i	0.953449	−	0.301554i	$-0.0975053\pi$
$569$	27.8855	+	16.0997i	1.16902	+	0.674934i	0.215571	+	0.976488i	$0.430839\pi$
$570$	1.08523	+	1.75810i	0.0454553	+	0.0736386i
$571$	−34.9958			−1.46453			−0.732265	−	0.681019i	$-0.761537\pi$
$571$	−34.9958			−1.46453			−0.732265	+	0.681019i	$0.761537\pi$
$572$	−15.3024	+	18.3804i	−0.639824	+	0.768521i
$573$	4.41814			0.184571
$574$	1.86937	+	3.02842i	0.0780260	+	0.126404i
$575$	28.4203	+	16.4084i	1.18521	+	0.684280i
$576$	14.5155	+	17.2278i	0.604811	+	0.717825i
$577$			2.42416i			0.100919i	0.998726	+	0.0504595i	$0.0160686\pi$
$577$			2.42416i			0.100919i	−0.998726	+	0.0504595i	$0.983931\pi$
$578$	−0.153155	−	5.20313i	−0.00637042	−	0.216422i
$579$	3.20449	−	1.85012i	0.133174	−	0.0768882i
$580$	−4.62955	−	7.02854i	−0.192232	−	0.291844i
$581$	4.80830	+	8.32822i	0.199482	+	0.345513i
$582$	−0.341792	+	0.210980i	−0.0141677	+	0.00874541i
$583$	−14.4525	+	38.8133i	−0.598560	+	1.60748i
$584$	−1.57400	−	17.7832i	−0.0651325	−	0.735876i
$585$	−4.09815	−	5.38494i	−0.169438	−	0.222640i
$586$	5.22398	+	2.81446i	0.215800	+	0.116264i
$587$	−8.26078	+	14.3081i	−0.340959	+	0.590558i	−0.984611	−	0.174760i	$-0.944085\pi$
$587$	−8.26078	+	14.3081i	−0.340959	+	0.590558i	0.643652	+	0.765318i	$0.277418\pi$
$588$	−0.274025	−	4.65068i	−0.0113006	−	0.191791i
$589$	−14.9019	+	8.60363i	−0.614023	+	0.354506i
$590$	−4.84185	+	8.98703i	−0.199336	+	0.369990i
$591$	6.82214	−	3.93876i	0.280625	−	0.162019i
$592$	1.25239	+	10.5907i	0.0514730	+	0.435277i
$593$	−43.3582			−1.78051			−0.890253	−	0.455466i	$-0.849473\pi$
$593$	−43.3582			−1.78051			−0.890253	+	0.455466i	$0.849473\pi$
$594$	11.4774	−	2.28565i	0.470924	−	0.0937815i
$595$	2.63966	+	1.52401i	0.108216	+	0.0624783i
$596$	26.5421	−	1.56390i	1.08721	−	0.0640599i
$597$	−5.65809			−0.231570
$598$	−5.71960	−	36.2820i	−0.233892	−	1.48368i
$599$			31.5150i			1.28767i	0.765165	+	0.643834i	$0.222657\pi$
$599$			31.5150i			1.28767i	−0.765165	+	0.643834i	$0.777343\pi$
$600$	2.33113	−	5.01239i	0.0951681	−	0.204630i
$601$	−21.4213	−	12.3676i	−0.873792	−	0.504484i	−0.00518582	−	0.999987i	$-0.501651\pi$
$601$	−21.4213	−	12.3676i	−0.873792	−	0.504484i	−0.868607	+	0.495502i	$0.834984\pi$
$602$	4.93903	−	0.145381i	0.201300	−	0.00592530i
$603$	7.35292			0.299434
$604$	−32.0777	−	16.0829i	−1.30522	−	0.654404i
$605$	−4.79505	+	5.54600i	−0.194946	+	0.225477i
$606$	−9.91875	−	5.34382i	−0.402922	−	0.217078i
$607$	−8.53958	−	14.7910i	−0.346611	−	0.600348i	0.639034	−	0.769178i	$-0.279334\pi$
$607$	−8.53958	−	14.7910i	−0.346611	−	0.600348i	−0.985645	+	0.168831i	$0.946001\pi$
$608$	−28.5911	+	4.23734i	−1.15952	+	0.171847i
$609$	2.93938	+	1.69705i	0.119110	+	0.0687681i
$610$	−6.78467	−	3.65530i	−0.274703	−	0.147999i
$611$	−3.20591	−	25.1216i	−0.129697	−	1.01631i
$612$	−17.1650	+	11.3062i	−0.693853	+	0.457026i
$613$	14.4087	−	24.9566i	0.581963	−	1.00799i	−0.413284	−	0.910602i	$-0.635618\pi$
$613$	14.4087	−	24.9566i	0.581963	−	1.00799i	0.995247	−	0.0973867i	$-0.0310483\pi$
$614$	9.57952	+	15.5190i	0.386598	+	0.626297i
$615$	−0.287110	−	0.497289i	−0.0115774	−	0.0200526i
$616$	11.3736	−	2.96997i	0.458254	−	0.119664i
$617$	9.40240	−	5.42848i	0.378526	−	0.218542i	−0.298651	−	0.954363i	$-0.596536\pi$
$617$	9.40240	−	5.42848i	0.378526	−	0.218542i	0.677177	+	0.735820i	$0.263203\pi$
$618$	0.0501719	+	1.70448i	0.00201821	+	0.0685644i
$619$	−8.81976			−0.354496			−0.177248	−	0.984166i	$-0.556719\pi$
$619$	−8.81976			−0.354496			−0.177248	+	0.984166i	$0.556719\pi$
$620$	−4.01303	−	2.01203i	−0.161167	−	0.0808049i
$621$	−8.98633	+	15.5648i	−0.360609	+	0.624593i
$622$	10.0262	+	16.2427i	0.402015	+	0.651274i
$623$	−17.0825			−0.684396
$624$	−6.00289	+	1.49854i	−0.240308	+	0.0599897i
$625$	18.5340			0.741362
$626$	−8.04339	+	4.96499i	−0.321478	+	0.198441i
$627$	−2.53684	+	6.81289i	−0.101312	+	0.272081i
$628$	3.69464	−	7.36905i	0.147432	−	0.294057i
$629$	−9.73019			−0.387968
$630$	0.0978585	+	3.32454i	0.00389878	+	0.132453i
$631$	−1.36100	−	2.35731i	−0.0541804	−	0.0938432i	0.837663	−	0.546187i	$-0.183921\pi$
$631$	−1.36100	−	2.35731i	−0.0541804	−	0.0938432i	−0.891844	+	0.452344i	$0.850588\pi$
$632$	−1.65932	−	18.7472i	−0.0660042	−	0.745725i
$633$	6.38727	−	3.68769i	0.253871	−	0.146573i
$634$	10.8636	+	17.5993i	0.431449	+	0.698957i
$635$	−9.44360	−	5.45226i	−0.374758	−	0.216366i
$636$	−8.94772	+	5.89368i	−0.354800	+	0.233699i
$637$	−18.0572	−	7.56368i	−0.715454	−	0.299684i
$638$	9.51295	−	28.0448i	0.376621	−	1.11030i
$639$	2.68907	−	4.65761i	0.106378	−	0.184252i
$640$	−5.02624	−	5.62112i	−0.198680	−	0.222194i
$641$	−1.29738	−	2.24713i	−0.0512436	−	0.0887564i	0.839266	−	0.543721i	$-0.182985\pi$
$641$	−1.29738	−	2.24713i	−0.0512436	−	0.0887564i	−0.890509	+	0.454965i	$0.849652\pi$
$642$	−3.06953	+	5.69741i	−0.121145	+	0.224859i
$643$	10.8764	+	18.8385i	0.428924	+	0.742919i	0.996778	−	0.0802108i	$-0.0255594\pi$
$643$	10.8764	+	18.8385i	0.428924	+	0.742919i	−0.567854	+	0.823130i	$0.692226\pi$
$644$	−8.09117	+	16.1380i	−0.318837	+	0.635927i
$645$	−0.797242			−0.0313914
$646$	−0.775904	−	26.3597i	−0.0305275	−	1.03711i
$647$	−16.0931	−	9.29138i	−0.632686	−	0.365282i	0.149105	−	0.988821i	$-0.452361\pi$
$647$	−16.0931	−	9.29138i	−0.632686	−	0.365282i	−0.781792	+	0.623540i	$0.785694\pi$
$648$	−18.9206	−	8.79949i	−0.743272	−	0.345677i
$649$	−35.4195	+	5.97596i	−1.39034	+	0.234577i
$650$	−14.6061	−	18.0637i	−0.572897	−	0.708516i
$651$	1.81039			0.0709550
$652$	−13.4835	+	0.794469i	−0.528055	+	0.0311138i
$653$	−6.14117	+	10.6368i	−0.240323	+	0.416251i	−0.960806	−	0.277221i	$-0.910587\pi$
$653$	−6.14117	+	10.6368i	−0.240323	+	0.416251i	0.720484	+	0.693472i	$0.243920\pi$
$654$	4.26594	−	0.125569i	0.166811	−	0.00491013i
$655$		−	14.6803i		−	0.573608i
$656$	7.97751	−	0.943369i	0.311470	−	0.0368324i
$657$	8.88704	+	15.3928i	0.346716	+	0.600530i
$658$	−5.90383	+	10.9582i	−0.230155	+	0.427195i
$659$	21.9440	+	38.0082i	0.854819	+	1.48059i	0.876813	+	0.480831i	$0.159665\pi$
$659$	21.9440	+	38.0082i	0.854819	+	1.48059i	−0.0219945	+	0.999758i	$0.507002\pi$
$660$	−1.84840	+	0.424995i	−0.0719487	+	0.0165429i
$661$	34.6682	+	20.0157i	1.34844	+	0.778520i	0.988028	−	0.154274i	$-0.0493039\pi$
$661$	34.6682	+	20.0157i	1.34844	+	0.778520i	0.360409	+	0.932794i	$0.382637\pi$
$662$	40.1358	+	21.6235i	1.55992	+	0.840422i
$663$	−0.714601	−	5.59964i	−0.0277528	−	0.217472i
$664$	21.6218	−	1.91375i	0.839090	−	0.0742680i
$665$	−3.69558	−	2.13365i	−0.143309	−	0.0827392i
$666$	−5.57700	−	9.03487i	−0.216104	−	0.350094i
$667$	22.7402	+	39.3872i	0.880504	+	1.52508i
$668$	−29.6928	+	19.5580i	−1.14885	+	0.756723i
$669$	−1.82526	+	1.05382i	−0.0705688	+	0.0407429i
$670$	−2.46014	+	0.0724146i	−0.0950433	+	0.00279762i
$671$	−4.51149	−	26.7396i	−0.174164	−	1.03227i
$672$	2.82800	+	1.11796i	0.109093	+	0.0431264i
$673$	−19.6727	−	11.3580i	−0.758326	−	0.437820i	0.0703684	−	0.997521i	$-0.477583\pi$
$673$	−19.6727	−	11.3580i	−0.758326	−	0.437820i	−0.828694	+	0.559701i	$0.810916\pi$
$674$	−18.4691	−	29.9203i	−0.711403	−	1.15249i
$675$			11.3669i			0.437511i
$676$	−5.44249	+	25.4240i	−0.209327	+	0.977846i
$677$		−	5.20886i		−	0.200193i	−0.994978	−	0.100096i	$-0.968085\pi$
$677$		−	5.20886i		−	0.200193i	0.994978	−	0.100096i	$-0.0319151\pi$
$678$	−1.36022	−	2.20359i	−0.0522390	−	0.0846283i
$679$	0.414803	−	0.718460i	0.0159187	−	0.0275720i
$680$	5.63170	−	3.95187i	0.215966	−	0.151547i
$681$	−4.57027			−0.175133
$682$	−3.08511	−	15.4919i	−0.118135	−	0.593214i
$683$	13.5287	+	23.4324i	0.517662	+	0.896617i	0.999790	+	0.0205161i	$0.00653095\pi$
$683$	13.5287	+	23.4324i	0.517662	+	0.896617i	−0.482127	+	0.876101i	$0.660136\pi$
$684$	24.0313	−	15.8289i	0.918860	−	0.605234i
$685$	−3.30892	−	5.73123i	−0.126428	−	0.218979i
$686$	11.5701	+	18.7438i	0.441747	+	0.715640i
$687$	4.82642	−	8.35961i	0.184140	−	0.318939i
$688$	4.40367	−	10.2469i	0.167888	−	0.390660i
$689$	5.69963	+	44.6625i	0.217139	+	1.70151i
$690$	1.38153	−	2.56428i	0.0525940	−	0.0976206i
$691$	−8.37019	+	14.4976i	−0.318417	+	0.551515i	−0.980158	−	0.198218i	$-0.936485\pi$
$691$	−8.37019	+	14.4976i	−0.318417	+	0.551515i	0.661741	+	0.749733i	$0.269818\pi$
$692$	−1.36895	−	23.2335i	−0.0520398	−	0.883207i
$693$	−9.02045	+	7.45619i	−0.342659	+	0.283237i
$694$	−40.1408	−	21.6262i	−1.52372	−	0.820919i
$695$	5.41061	−	3.12382i	0.205236	−	0.118493i
$696$	6.27115	−	4.40058i	0.237707	−	0.166804i
$697$			7.32930i			0.277617i
$698$	−0.631957	−	21.4694i	−0.0239199	−	0.812630i
$699$	−1.30050	+	2.25253i	−0.0491894	+	0.0851985i
$700$	0.671573	+	11.3978i	0.0253831	+	0.430795i
$701$			0.733835i			0.0277165i	0.999904	+	0.0138583i	$0.00441137\pi$
$701$			0.733835i			0.0277165i	−0.999904	+	0.0138583i	$0.995589\pi$
$702$	9.89285	−	7.99923i	0.373381	−	0.301911i
$703$	13.6225			0.513781
$704$	4.74740	−	26.1048i	0.178924	−	0.983863i
$705$	1.00417	−	1.73928i	0.0378194	−	0.0655051i
$706$	−40.1867	+	1.18290i	−1.51245	+	0.0445192i
$707$	23.2704			0.875174
$708$	−8.30681	−	4.16481i	−0.312189	−	0.156523i
$709$	−20.4698	+	11.8182i	−0.768759	+	0.443843i	−0.832432	−	0.554128i	$-0.813052\pi$
$709$	−20.4698	+	11.8182i	−0.768759	+	0.443843i	0.0636730	+	0.997971i	$0.479719\pi$
$710$	−0.853839	+	1.58483i	−0.0320440	+	0.0594774i
$711$	9.36878	+	16.2272i	0.351357	+	0.608568i
$712$	−16.2600	+	34.9621i	−0.609368	+	1.31026i
$713$	21.0089	+	12.1295i	0.786789	+	0.454253i
$714$	−1.31597	+	2.44260i	−0.0492490	+	0.0914118i
$715$	−1.81332	+	7.76114i	−0.0678144	+	0.290250i
$716$	−29.7483	+	19.5946i	−1.11175	+	0.732285i
$717$	0.800315	−	1.38619i	0.0298883	−	0.0517680i
$718$	20.8302	+	33.7454i	0.777377	+	1.25937i
$719$	−33.0536	+	19.0835i	−1.23269	+	0.711694i	−0.967590	−	0.252527i	$-0.918738\pi$
$719$	−33.0536	+	19.0835i	−1.23269	+	0.711694i	−0.265100	+	0.964221i	$0.585405\pi$
$720$	6.89736	+	2.96418i	0.257049	+	0.110468i
$721$	−1.76100	−	3.05014i	−0.0655830	−	0.113593i
$722$	0.295698	+	10.0457i	0.0110047	+	0.373863i
$723$		−	9.35558i		−	0.347938i
$724$	−20.7449	+	41.3762i	−0.770979	+	1.53773i
$725$	24.9105	+	14.3821i	0.925154	+	0.534138i
$726$	−5.17462	−	4.21439i	−0.192048	−	0.156410i
$727$		−	50.4080i		−	1.86953i	−0.355269	−	0.934764i	$-0.615611\pi$
$727$		−	50.4080i		−	1.86953i	0.355269	−	0.934764i	$-0.384389\pi$
$728$	9.44713	−	8.60546i	0.350134	−	0.318940i
$729$	17.5637			0.650506
$730$	−3.12501	−	5.06259i	−0.115662	−	0.187375i
$731$	8.81263	+	5.08797i	0.325947	+	0.188186i
$732$	3.14418	−	6.27114i	0.116212	−	0.231788i
$733$	13.8379			0.511114			0.255557	−	0.966794i	$-0.417741\pi$
$733$	13.8379			0.511114			0.255557	+	0.966794i	$0.417741\pi$
$734$	−1.64029	+	0.0482822i	−0.0605441	+	0.00178213i
$735$	−0.776261	−	1.34452i	−0.0286328	−	0.0495935i
$736$	25.3275	+	31.9209i	0.933585	+	1.17662i
$737$	−5.51753	−	6.67507i	−0.203241	−	0.245879i
$738$	−6.80555	+	4.20090i	−0.250516	+	0.154637i
$739$	17.4620	+	10.0817i	0.642351	+	0.370861i	0.785520	−	0.618837i	$-0.212396\pi$
$739$	17.4620	+	10.0817i	0.642351	+	0.370861i	−0.143169	+	0.989698i	$0.545729\pi$
$740$	1.95493	+	2.96796i	0.0718646	+	0.109104i
$741$	1.00046	+	7.83961i	0.0367527	+	0.287995i
$742$	10.4961	−	19.4820i	0.385325	−	0.715209i
$743$	−13.0436	−	7.53075i	−0.478525	−	0.276277i	0.241277	−	0.970456i	$-0.422434\pi$
$743$	−13.0436	−	7.53075i	−0.478525	−	0.276277i	−0.719802	+	0.694180i	$0.755767\pi$
$744$	1.72322	−	3.70527i	0.0631765	−	0.135842i
$745$	7.67340	−	4.43024i	0.281131	−	0.162311i
$746$	−7.28157	+	13.5154i	−0.266597	+	0.494836i
$747$	−18.7154	+	10.8053i	−0.684761	+	0.395347i
$748$	23.1443	+	7.09854i	0.846238	+	0.259549i
$749$		−	13.3667i		−	0.488408i
$750$	−0.113688	−	3.86232i	−0.00415131	−	0.141032i
$751$	11.8807	+	6.85934i	0.433534	+	0.250301i	0.700851	−	0.713308i	$-0.252804\pi$
$751$	11.8807	+	6.85934i	0.433534	+	0.250301i	−0.267317	+	0.963609i	$0.586137\pi$
$752$	16.8082	+	22.5137i	0.612932	+	0.820991i
$753$	−2.24314			−0.0817444
$754$	−5.01327	−	31.8014i	−0.182572	−	1.15814i
$755$	−11.9582			−0.435204
$756$	−6.24216	+	0.367797i	−0.227025	+	0.0133766i
$757$	13.8139	−	23.9264i	0.502075	−	0.869619i	−0.497923	−	0.867222i	$-0.665904\pi$
$757$	13.8139	−	23.9264i	0.502075	−	0.869619i	0.999997	−	0.00239720i	$-0.000763054\pi$
$758$	0.506737	+	17.2153i	0.0184055	+	0.625289i
$759$	10.1063	−	1.70513i	0.366836	−	0.0618923i
$760$	−7.88449	+	5.53270i	−0.286001	+	0.200692i
$761$	20.2036	+	34.9936i	0.732379	+	1.26852i	0.955864	+	0.293811i	$0.0949236\pi$
$761$	20.2036	+	34.9936i	0.732379	+	1.26852i	−0.223484	+	0.974708i	$0.571743\pi$
$762$	4.70799	−	8.73857i	0.170552	−	0.316565i
$763$	−7.63381	+	4.40738i	−0.276362	+	0.159558i
$764$	1.21153	+	20.5618i	0.0438317	+	0.743899i
$765$	−3.42480	+	5.93192i	−0.123824	+	0.214469i
$766$	−9.41311	−	5.07140i	−0.340110	−	0.183237i
$767$	−31.0740	+	23.6485i	−1.12202	+	0.853899i
$768$	4.97993	−	4.72383i	0.179698	−	0.170457i
$769$	11.6327	−	20.1484i	0.419486	−	0.726571i	−0.576402	−	0.817166i	$-0.695544\pi$
$769$	11.6327	−	20.1484i	0.419486	−	0.726571i	0.995888	+	0.0905953i	$0.0288770\pi$
$770$	2.94463	−	2.58353i	0.106117	−	0.0931038i
$771$	5.28949	−	3.05389i	0.190496	−	0.109983i
$772$	9.48906	+	14.4062i	0.341519	+	0.518490i
$773$	29.8307	−	17.2228i	1.07294	−	0.619460i	0.143954	−	0.989584i	$-0.454018\pi$
$773$	29.8307	−	17.2228i	1.07294	−	0.619460i	0.928982	+	0.370124i	$0.120685\pi$
$774$	0.326705	+	11.0991i	0.0117432	+	0.398950i
$775$	15.3426			0.551124
$776$	−1.07561	−	1.53283i	−0.0386123	−	0.0550253i
$777$	−1.24122	−	0.716618i	−0.0445285	−	0.0257085i
$778$	26.3266	−	16.2508i	0.943853	−	0.582618i
$779$		−	10.2612i		−	0.367645i
$780$	−1.56446	+	1.34302i	−0.0560166	+	0.0480877i
$781$	−6.24608	+	1.05384i	−0.223502	+	0.0377092i
$782$	−31.6365	+	19.5284i	−1.13132	+	0.698335i
$783$	−7.87657	+	13.6426i	−0.281486	+	0.487548i
$784$	21.5689	−	2.55059i	0.770316	−	0.0910926i
$785$		−	2.74710i		−	0.0980481i
$786$	13.3574	−	0.393177i	0.476441	−	0.0140241i
$787$	−4.56510	+	2.63566i	−0.162728	+	0.0939513i	−0.579153	−	0.815219i	$-0.696616\pi$
$787$	−4.56510	+	2.63566i	−0.162728	+	0.0939513i	0.416424	+	0.909170i	$0.363283\pi$
$788$	20.2015	+	30.6698i	0.719650	+	1.09257i
$789$	−5.33528	+	3.08033i	−0.189941	+	0.109663i
$790$	−3.29441	−	5.33702i	−0.117210	−	0.189883i
$791$	4.63202	+	2.67430i	0.164696	+	0.0950871i
$792$	6.67420	+	25.5590i	0.237157	+	0.908199i
$793$	−17.8532	−	23.4590i	−0.633986	−	0.833054i
$794$	−18.0879	+	33.5733i	−0.641916	+	1.19147i
$795$	−1.78527	+	3.09218i	−0.0633171	+	0.109668i
$796$	−1.55155	−	26.3324i	−0.0549931	−	0.933328i
$797$	−0.738050	−	1.27834i	−0.0261431	−	0.0452811i	0.852658	−	0.522470i	$-0.174989\pi$
$797$	−0.738050	−	1.27834i	−0.0261431	−	0.0452811i	−0.878801	+	0.477189i	$0.841656\pi$
$798$	1.84239	−	3.41968i	0.0652198	−	0.121056i
$799$	−22.2001	+	12.8172i	−0.785382	+	0.453440i
$800$	23.9666	+	9.47448i	0.847348	+	0.334973i
$801$		−	38.3883i		−	1.35638i
$802$	27.1196	−	0.798271i	0.957626	−	0.0281879i
$803$	7.30506	−	19.6183i	0.257790	−	0.692315i
$804$	−0.131777	−	2.23649i	−0.00464743	−	0.0788750i
$805$			6.01607i			0.212039i
$806$	−10.7971	−	13.3531i	−0.380312	−	0.470342i
$807$		−	3.67409i		−	0.129334i
$808$	22.1499	−	47.6267i	0.779232	−	1.67550i
$809$	26.4218	+	15.2547i	0.928943	+	0.536325i	0.886477	−	0.462773i	$-0.153145\pi$
$809$	26.4218	+	15.2547i	0.928943	+	0.536325i	0.0424657	+	0.999098i	$0.486479\pi$
$810$	−6.95081	+	0.204599i	−0.244227	+	0.00718886i
$811$			5.08850i			0.178681i	0.996001	+	0.0893407i	$0.0284760\pi$
$811$			5.08850i			0.178681i	−0.996001	+	0.0893407i	$0.971524\pi$
$812$	−7.09196	+	14.1451i	−0.248879	+	0.496395i
$813$	3.97057	+	6.87723i	0.139254	+	0.241195i
$814$	−4.01705	+	11.8425i	−0.140798	+	0.415080i
$815$	−3.89812	+	2.25058i	−0.136545	+	0.0788344i
$816$	3.74656	+	5.01833i	0.131156	+	0.175677i
$817$	−12.3379	−	7.12327i	−0.431647	−	0.249212i
$818$	5.65685	+	3.04768i	0.197787	+	0.106560i
$819$	−4.91537	+	11.7348i	−0.171757	+	0.410046i
$820$	2.23562	−	1.47256i	0.0780714	−	0.0514240i
$821$	21.7228	−	37.6249i	0.758130	−	1.31312i	−0.185673	−	0.982612i	$-0.559447\pi$
$821$	21.7228	−	37.6249i	0.758130	−	1.31312i	0.943803	−	0.330508i	$-0.107220\pi$
$822$	5.12611	−	3.16422i	0.178794	−	0.110365i
$823$	16.7617	−	9.67736i	0.584276	−	0.337332i	−0.178555	−	0.983930i	$-0.557142\pi$
$823$	16.7617	−	9.67736i	0.584276	−	0.337332i	0.762831	+	0.646598i	$0.223809\pi$
$824$	−7.91882	+	0.700896i	−0.275865	+	0.0244169i
$825$	4.99622	−	4.12981i	0.173946	−	0.143782i
$826$	19.1844	−	0.564696i	0.667510	−	0.0196483i
$827$		−	51.7637i		−	1.80000i	−0.435890	−	0.900000i	$-0.643566\pi$
$827$		−	51.7637i		−	1.80000i	0.435890	−	0.900000i	$-0.356434\pi$
$828$	−36.2658	−	18.1827i	−1.26032	−	0.631892i
$829$	6.26890	−	10.8580i	0.217728	−	0.377116i	−0.736385	−	0.676563i	$-0.763469\pi$
$829$	6.26890	−	10.8580i	0.217728	−	0.377116i	0.954113	+	0.299447i	$0.0968022\pi$
$830$	6.15537	−	3.79956i	0.213656	−	0.131885i
$831$	−7.29659			−0.253116
$832$	−8.62022	−	27.5262i	−0.298852	−	0.954299i
$833$			19.8163i			0.686594i
$834$	2.98721	+	4.83935i	0.103439	+	0.167573i
$835$	−5.92438	+	10.2613i	−0.205022	+	0.355108i
$836$	−32.4025	−	9.93811i	−1.12066	−	0.343717i
$837$			8.40263i			0.290437i
$838$	38.3883	−	1.12997i	1.32610	−	0.0390341i
$839$	−7.11093	−	12.3165i	−0.245497	−	0.425213i	0.716775	−	0.697305i	$-0.245618\pi$
$839$	−7.11093	−	12.3165i	−0.245497	−	0.425213i	−0.962271	+	0.272092i	$0.912284\pi$
$840$	1.00945	−	0.0893467i	0.0348293	−	0.00308275i
$841$	5.43192	+	9.40837i	0.187308	+	0.324426i
$842$	11.8537	+	19.2033i	0.408506	+	0.661788i
$843$	−5.30726	−	3.06415i	−0.182792	−	0.105535i
$844$	18.9138	+	28.7147i	0.651040	+	0.988402i
$845$	2.17601	+	8.38678i	0.0748569	+	0.288514i
$846$	−24.6256	−	13.2673i	−0.846645	−	0.456138i
$847$	13.5376	+	2.59385i	0.465159	+	0.0891256i
$848$	−29.8824	−	40.0260i	−1.02617	−	1.37450i
$849$	1.53201	−	0.884508i	0.0525786	−	0.0303562i
$850$	−11.1525	+	20.7004i	−0.382528	+	0.710018i
$851$	−9.60255	−	16.6321i	−0.329171	−	0.570141i
$852$	−1.46487	−	0.734446i	−0.0501856	−	0.0251617i
$853$	−32.5742			−1.11532			−0.557660	−	0.830070i	$-0.688301\pi$
$853$	−32.5742			−1.11532			−0.557660	+	0.830070i	$0.688301\pi$
$854$	0.426312	+	14.4831i	0.0145881	+	0.495600i
$855$	4.79479	−	8.30481i	0.163978	−	0.284019i
$856$	−27.3571	−	12.7231i	−0.935047	−	0.434866i
$857$		−	1.67954i		−	0.0573719i	−0.999588	−	0.0286859i	$-0.990868\pi$
$857$		−	1.67954i		−	0.0573719i	0.999588	−	0.0286859i	$-0.00913227\pi$
$858$	−7.11028	−	1.44204i	−0.242741	−	0.0492306i
$859$		−	23.4154i		−	0.798922i	−0.916750	−	0.399461i	$-0.869197\pi$
$859$		−	23.4154i		−	0.798922i	0.916750	−	0.399461i	$-0.130803\pi$
$860$	−0.218618	−	3.71032i	−0.00745480	−	0.126521i
$861$	−0.539795	+	0.934952i	−0.0183962	+	0.0318631i
$862$	−35.0660	+	1.03218i	−1.19435	+	0.0351561i
$863$	−1.69795			−0.0577988			−0.0288994	−	0.999582i	$-0.509200\pi$
$863$	−1.69795			−0.0577988			−0.0288994	+	0.999582i	$0.509200\pi$
$864$	−5.18884	+	13.1257i	−0.176528	+	0.446545i
$865$	−3.87799	−	6.71688i	−0.131856	−	0.228381i
$866$	29.9618	+	16.1422i	1.01814	+	0.548535i
$867$	1.36749	−	0.789522i	0.0464425	−	0.0268136i
$868$	0.496441	+	8.42547i	0.0168503	+	0.285979i
$869$	7.70105	−	20.6818i	0.261240	−	0.701581i
$870$	1.21092	−	2.24761i	0.0410540	−	0.0762011i
$871$	−8.68365	−	3.63734i	−0.294234	−	0.123247i
$872$	1.75418	+	19.8190i	0.0594041	+	0.671156i
$873$	1.61454	+	0.932157i	0.0546440	+	0.0315487i
$874$	44.2917	−	27.3402i	1.49819	−	0.924796i
$875$	3.99038	+	6.91154i	0.134899	+	0.233653i
$876$	4.52266	−	2.97898i	0.152806	−	0.100650i
$877$	1.57820	+	2.73352i	0.0532920	+	0.0923045i	0.891441	−	0.453137i	$-0.149695\pi$
$877$	1.57820	+	2.73352i	0.0532920	+	0.0923045i	−0.838149	+	0.545442i	$0.816362\pi$
$878$	0.829476	+	28.1797i	0.0279935	+	0.951019i
$879$			1.80004i			0.0607137i
$880$	−2.48477	−	8.48579i	−0.0837614	−	0.286056i
$881$	−9.06234	+	15.6964i	−0.305318	+	0.528826i	−0.977332	−	0.211712i	$-0.932096\pi$
$881$	−9.06234	+	15.6964i	−0.305318	+	0.528826i	0.672014	+	0.740538i	$0.265429\pi$
$882$	−18.4002	+	11.3580i	−0.619567	+	0.382444i
$883$			13.6711i			0.460070i	0.973182	+	0.230035i	$0.0738841\pi$
$883$			13.6711i			0.460070i	−0.973182	+	0.230035i	$0.926116\pi$
$884$	25.8644	−	4.86123i	0.869915	−	0.163501i
$885$	−3.09668			−0.104094
$886$	−27.2959	−	44.2200i	−0.917025	−	1.48560i
$887$	−8.22265	+	14.2420i	−0.276090	+	0.478201i	−0.970409	−	0.241465i	$-0.922372\pi$
$887$	−8.22265	+	14.2420i	−0.276090	+	0.478201i	0.694320	+	0.719667i	$0.255705\pi$
$888$	−2.64813	+	1.85824i	−0.0888654	+	0.0623585i
$889$			20.5016i			0.687601i
$890$	0.378064	+	12.8439i	0.0126727	+	0.430529i
$891$	−15.5891	−	18.8596i	−0.522255	−	0.631820i
$892$	−5.40492	−	8.20570i	−0.180970	−	0.274747i
$893$	31.0806	−	17.9444i	1.04007	−	0.600485i
$894$	4.23650	+	6.86322i	0.141690	+	0.229541i
$895$	−5.93546	+	10.2805i	−0.198401	+	0.343640i
$896$	−4.42746	+	13.4679i	−0.147911	+	0.449932i
$897$	8.86639	−	6.74767i	0.296040	−	0.225298i
$898$	−16.9034	+	31.3746i	−0.564072	+	1.04698i
$899$	18.4144	+	10.6316i	0.614155	+	0.354582i
$900$	−25.6134	+	1.50918i	−0.853779	+	0.0503059i
$901$	39.4684	−	22.7871i	1.31488	−	0.759148i
$902$	8.92042	+	3.02586i	0.297017	+	0.100750i
$903$	0.749447	+	1.29808i	0.0249400	+	0.0431974i
$904$	9.88237	−	6.93465i	0.328683	−	0.230643i
$905$			15.4246i			0.512730i
$906$	−0.320271	−	10.8805i	−0.0106403	−	0.361482i
$907$	−18.0894	−	10.4439i	−0.600649	−	0.346785i	0.168648	−	0.985676i	$-0.446060\pi$
$907$	−18.0894	−	10.4439i	−0.600649	−	0.346785i	−0.769297	+	0.638891i	$0.779393\pi$
$908$	−1.25325	−	21.2698i	−0.0415904	−	0.705862i
$909$			52.2939i			1.73448i
$910$	1.52901	−	3.97462i	0.0506863	−	0.131757i
$911$		−	28.3948i		−	0.940761i	−0.882464	−	0.470380i	$-0.844117\pi$
$911$		−	28.3948i		−	0.940761i	0.882464	−	0.470380i	$-0.155883\pi$
$912$	−5.24527	−	7.02577i	−0.173688	−	0.232646i
$913$	23.8530	+	8.88189i	0.789419	+	0.293948i
$914$	0.888797	+	30.1950i	0.0293988	+	0.998763i
$915$		−	2.33781i		−	0.0772856i
$916$	40.2286	+	20.1695i	1.32919	+	0.666421i
$917$	−23.9027	+	13.8002i	−0.789337	+	0.455724i
$918$	−11.3369	−	6.10785i	−0.374173	−	0.201589i
$919$	10.5930	+	18.3476i	0.349431	+	0.605233i	0.986149	−	0.165865i	$-0.0530415\pi$
$919$	10.5930	+	18.3476i	0.349431	+	0.605233i	−0.636717	+	0.771097i	$0.719708\pi$
$920$	12.3129	+	5.72640i	0.405943	+	0.188794i
$921$	−2.76616	+	4.79113i	−0.0911481	+	0.157873i
$922$	10.8321	+	5.83592i	0.356738	+	0.192196i
$923$	−5.47977	+	4.17032i	−0.180369	+	0.137268i
$924$	2.42957	+	2.61006i	0.0799268	+	0.0858648i
$925$	−10.5190	−	6.07316i	−0.345863	−	0.199684i
$926$	−28.5419	+	17.6182i	−0.937945	+	0.578971i
$927$	6.85436	−	3.95737i	0.225127	−	0.129977i
$928$	22.1997	+	27.9788i	0.728742	+	0.918450i
$929$	−25.7164	+	14.8474i	−0.843728	+	0.487127i	−0.858530	−	0.512764i	$-0.828622\pi$
$929$	−25.7164	+	14.8474i	−0.843728	+	0.487127i	0.0148014	+	0.999890i	$0.495288\pi$
$930$	−0.0400670	−	1.36119i	−0.00131385	−	0.0446353i
$931$		−	27.7432i		−	0.909247i
$932$	−10.8398	−	5.43476i	−0.355068	−	0.178022i
$933$	−2.89515	+	5.01455i	−0.0947831	+	0.164169i
$934$	−26.7262	−	43.2970i	−0.874507	−	1.41672i
$935$	7.95499	−	1.34216i	0.260156	−	0.0438934i
$936$	19.3384	+	21.2299i	0.632096	+	0.693920i
$937$			1.62042i			0.0529369i	0.999650	+	0.0264685i	$0.00842616\pi$
$937$			1.62042i			0.0529369i	−0.999650	+	0.0264685i	$0.991574\pi$
$938$	2.43055	+	3.93755i	0.0793604	+	0.128566i
$939$	−2.48320	−	1.43368i	−0.0810363	−	0.0467863i
$940$	8.36988	+	4.19643i	0.272995	+	0.136872i
$941$	−46.4178			−1.51318			−0.756589	−	0.653891i	$-0.773135\pi$
$941$	−46.4178			−1.51318			−0.756589	+	0.653891i	$0.773135\pi$
$942$	2.49953	−	0.0735742i	0.0814391	−	0.00239718i
$943$	−12.5282	+	7.23316i	−0.407974	+	0.235544i
$944$	17.1049	−	39.8015i	0.556717	−	1.29543i
$945$	−1.80462	+	1.04190i	−0.0587044	+	0.0338930i
$946$	9.83076	−	8.62522i	0.319626	−	0.280430i
$947$	12.1014	−	20.9603i	0.393244	−	0.681118i	−0.599631	−	0.800276i	$-0.704686\pi$
$947$	12.1014	−	20.9603i	0.393244	−	0.681118i	0.992875	+	0.119158i	$0.0380195\pi$
$948$	4.76782	−	3.14046i	0.154852	−	0.101998i
$949$	−2.88090	−	22.5748i	−0.0935180	−	0.732810i
$950$	15.6138	−	28.9810i	0.506578	−	0.940267i
$951$	−3.13695	+	5.43336i	−0.101723	+	0.176189i
$952$	−11.7286	−	5.45465i	−0.380125	−	0.176786i
$953$	−15.2205	+	8.78758i	−0.493041	+	0.284658i	−0.725835	−	0.687869i	$-0.758547\pi$
$953$	−15.2205	+	8.78758i	−0.493041	+	0.284658i	0.232794	+	0.972526i	$0.425213\pi$
$954$	43.7806	+	23.5872i	1.41745	+	0.763664i
$955$	3.43204	+	5.94447i	0.111058	+	0.192358i
$956$	6.67069	+	3.34450i	0.215745	+	0.108169i
$957$	8.85824	−	1.49456i	0.286346	−	0.0483122i
$958$	40.8203	−	1.20155i	1.31884	−	0.0388204i
$959$	−6.22110	+	10.7753i	−0.200890	+	0.347952i
$960$	0.777983	−	2.15105i	0.0251093	−	0.0694248i
$961$	−19.6584			−0.634141
$962$	2.11696	+	13.4288i	0.0682535	+	0.432963i
$963$	30.0380			0.967961
$964$	43.5403	−	2.56546i	1.40234	−	0.0826279i
$965$	4.97854	+	2.87436i	0.160265	+	0.0925289i
$966$	−5.47391	+	0.161126i	−0.176120	+	0.00518413i
$967$		−	30.9052i		−	0.993845i	−0.867795	−	0.496922i	$-0.834463\pi$
$967$		−	30.9052i		−	0.993845i	0.867795	−	0.496922i	$-0.165537\pi$
$968$	18.1945	−	25.2380i	0.584795	−	0.811181i
$969$	6.92789	−	3.99982i	0.222556	−	0.128493i
$970$	−0.549373	−	0.295980i	−0.0176393	−	0.00950334i
$971$	4.81657	−	2.78085i	0.154571	−	0.0892416i	−0.420719	−	0.907191i	$-0.638222\pi$
$971$	4.81657	−	2.78085i	0.154571	−	0.0892416i	0.575291	+	0.817949i	$0.304889\pi$
$972$	−1.25286	−	21.2633i	−0.0401856	−	0.682019i
$973$	−10.1725	−	5.87308i	−0.326115	−	0.188282i
$974$	−40.6165	−	21.8825i	−1.30144	−	0.701161i
$975$	2.72251	−	6.49962i	0.0871902	−	0.208154i
$976$	30.0477	+	12.9132i	0.961804	+	0.413341i
$977$	1.00607	+	0.580856i	0.0321871	+	0.0185832i	0.516007	−	0.856584i	$-0.327418\pi$
$977$	1.00607	+	0.580856i	0.0321871	+	0.0185832i	−0.483820	+	0.875167i	$0.660751\pi$
$978$	−2.15216	−	3.48655i	−0.0688186	−	0.111488i
$979$	−34.8493	+	28.8060i	−1.11379	+	0.920644i
$980$	6.04447	−	3.98137i	0.193084	−	0.127180i
$981$	−9.90439	−	17.1549i	−0.316223	−	0.547714i
$982$	0.255406	+	8.67690i	0.00815034	+	0.276891i
$983$	34.5105			1.10071			0.550357	−	0.834929i	$-0.314492\pi$
$983$	34.5105			1.10071			0.550357	+	0.834929i	$0.314492\pi$
$984$	1.39973	+	1.99471i	0.0446217	+	0.0635891i
$985$	10.5990	+	6.11931i	0.337711	+	0.194977i
$986$	−27.7295	+	17.1168i	−0.883089	+	0.545109i
$987$	−3.77589			−0.120188
$988$	−36.2107	+	6.80582i	−1.15202	+	0.216522i
$989$			20.0849i			0.638663i
$990$	5.80577	+	6.61724i	0.184520	+	0.210310i
$991$	−39.2870	−	22.6824i	−1.24799	−	0.720529i	−0.277284	−	0.960788i	$-0.589434\pi$
$991$	−39.2870	−	22.6824i	−1.24799	−	0.720529i	−0.970709	+	0.240259i	$0.922768\pi$
$992$	17.7166	+	7.00374i	0.562504	+	0.222369i
$993$			13.8297i			0.438872i
$994$	3.38308	−	0.0995818i	0.107305	−	0.00315854i
$995$	−4.39524	−	7.61277i	−0.139338	−	0.241341i
$996$	3.62201	+	5.49890i	0.114768	+	0.174239i
$997$	4.90304	−	2.83077i	0.155281	−	0.0896514i	−0.420346	−	0.907364i	$-0.638091\pi$
$997$	4.90304	−	2.83077i	0.155281	−	0.0896514i	0.575627	+	0.817712i	$0.304758\pi$
$998$	−31.6376	+	19.5291i	−1.00147	+	0.618183i
$999$	3.32606	−	5.76090i	0.105232	−	0.182267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.s.a.43.14	✓	160
4.3	odd	2	inner	572.2.s.a.43.39	yes	160
11.10	odd	2	inner	572.2.s.a.43.67	yes	160
13.10	even	6	inner	572.2.s.a.439.42	yes	160
44.43	even	2	inner	572.2.s.a.43.42	yes	160
52.23	odd	6	inner	572.2.s.a.439.67	yes	160
143.10	odd	6	inner	572.2.s.a.439.39	yes	160
572.439	even	6	inner	572.2.s.a.439.14	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.s.a.43.14	✓	160	1.1	even	1	trivial
572.2.s.a.43.39	yes	160	4.3	odd	2	inner
572.2.s.a.43.42	yes	160	44.43	even	2	inner
572.2.s.a.43.67	yes	160	11.10	odd	2	inner
572.2.s.a.439.14	yes	160	572.439	even	6	inner
572.2.s.a.439.39	yes	160	143.10	odd	6	inner
572.2.s.a.439.42	yes	160	13.10	even	6	inner
572.2.s.a.439.67	yes	160	52.23	odd	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20341 + 0.742836i) q^{2} +(-0.371524 - 0.214500i) q^{3} +(0.896390 - 1.78787i) q^{4} -0.666498i q^{5} +(0.606434 - 0.0178505i) q^{6} +(-1.08520 + 0.626541i) q^{7} +(0.249370 + 2.81741i) q^{8} +(-1.40798 - 2.43869i) q^{9} +O(q^{10})\)	\(q+(-1.20341 + 0.742836i) q^{2} +(-0.371524 - 0.214500i) q^{3} +(0.896390 - 1.78787i) q^{4} -0.666498i q^{5} +(0.606434 - 0.0178505i) q^{6} +(-1.08520 + 0.626541i) q^{7} +(0.249370 + 2.81741i) q^{8} +(-1.40798 - 2.43869i) q^{9} +(0.495098 + 0.802070i) q^{10} +(-1.15735 + 3.10814i) q^{11} +(-0.716528 + 0.471962i) q^{12} +(0.456423 + 3.57655i) q^{13} +(0.840524 - 1.56011i) q^{14} +(-0.142963 + 0.247620i) q^{15} +(-2.39297 - 3.20526i) q^{16} +(3.16061 - 1.82478i) q^{17} +(3.50592 + 1.88885i) q^{18} +(-4.42491 + 2.55472i) q^{19} +(-1.19161 - 0.597442i) q^{20} +0.537571 q^{21} +(-0.916078 - 4.60009i) q^{22} +(6.23829 + 3.60168i) q^{23} +(0.511687 - 1.10023i) q^{24} +4.55578 q^{25} +(-3.20605 - 3.96500i) q^{26} +2.49504i q^{27} +(0.147411 + 2.50182i) q^{28} +(5.46790 + 3.15689i) q^{29} +(-0.0118973 - 0.404187i) q^{30} +3.36773 q^{31} +(5.26070 + 2.07966i) q^{32} +(1.09668 - 0.906500i) q^{33} +(-2.44799 + 4.54376i) q^{34} +(0.417588 + 0.723284i) q^{35} +(-5.62217 + 0.331266i) q^{36} +(-2.30894 - 1.33307i) q^{37} +(3.42724 - 6.36136i) q^{38} +(0.597595 - 1.42668i) q^{39} +(1.87780 - 0.166204i) q^{40} +(-1.00414 + 1.73922i) q^{41} +(-0.646918 + 0.399327i) q^{42} +(1.39414 + 2.41471i) q^{43} +(4.51953 + 4.85529i) q^{44} +(-1.62538 + 0.938416i) q^{45} +(-10.1827 + 0.299729i) q^{46} -7.02399 q^{47} +(0.201518 + 1.70412i) q^{48} +(-2.71489 + 4.70233i) q^{49} +(-5.48247 + 3.38420i) q^{50} -1.56565 q^{51} +(6.80354 + 2.38995i) q^{52} +12.4876 q^{53} +(-1.85341 - 3.00256i) q^{54} +(2.07157 + 0.771368i) q^{55} +(-2.03584 - 2.90122i) q^{56} +2.19195 q^{57} +(-8.92517 + 0.262714i) q^{58} +(5.41516 + 9.37933i) q^{59} +(0.314562 + 0.477565i) q^{60} +(-7.08084 + 4.08812i) q^{61} +(-4.05276 + 2.50167i) q^{62} +(3.05588 + 1.76431i) q^{63} +(-7.87563 + 1.40516i) q^{64} +(2.38376 - 0.304205i) q^{65} +(-0.646371 + 1.90554i) q^{66} +(-1.30558 + 2.26133i) q^{67} +(-0.429329 - 7.28647i) q^{68} +(-1.54512 - 2.67622i) q^{69} +(-1.03981 - 0.560208i) q^{70} +(0.954941 + 1.65401i) q^{71} +(6.51970 - 4.57500i) q^{72} -6.31191 q^{73} +(3.76885 - 0.110937i) q^{74} +(-1.69258 - 0.977213i) q^{75} +(0.601070 + 10.2012i) q^{76} +(-0.691426 - 4.09808i) q^{77} +(0.340634 + 2.16079i) q^{78} -6.65406 q^{79} +(-2.13630 + 1.59491i) q^{80} +(-3.68875 + 6.38911i) q^{81} +(-0.0835636 - 2.83890i) q^{82} -7.67436i q^{83} +(0.481873 - 0.961108i) q^{84} +(-1.21621 - 2.10654i) q^{85} +(-3.47145 - 1.87028i) q^{86} +(-1.35430 - 2.34572i) q^{87} +(-9.04553 - 2.48564i) q^{88} +(11.8060 + 6.81619i) q^{89} +(1.25891 - 2.33669i) q^{90} +(-2.73616 - 3.59530i) q^{91} +(12.0313 - 7.92475i) q^{92} +(-1.25119 - 0.722377i) q^{93} +(8.45274 - 5.21767i) q^{94} +(1.70272 + 2.94920i) q^{95} +(-1.50839 - 1.90106i) q^{96} +(-0.573354 + 0.331026i) q^{97} +(-0.225932 - 7.67555i) q^{98} +(9.20932 - 1.55379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{4} + 68 q^{9}+O(q^{10}) \) 160 * q - 2 * q^4 + 68 * q^9	\( 160 q - 2 q^{4} + 68 q^{9} - 36 q^{12} - 8 q^{14} - 6 q^{16} + 30 q^{20} - 20 q^{22} - 144 q^{25} - 40 q^{26} - 6 q^{33} + 46 q^{36} - 12 q^{37} - 56 q^{38} - 2 q^{42} + 48 q^{45} - 40 q^{48} + 44 q^{49} - 32 q^{53} + 30 q^{56} + 78 q^{58} + 64 q^{64} - 4 q^{66} - 44 q^{69} - 44 q^{77} + 16 q^{78} + 24 q^{80} - 40 q^{81} - 6 q^{82} - 10 q^{88} + 24 q^{89} - 24 q^{92} - 96 q^{93}+O(q^{100}) \) 160 * q - 2 * q^4 + 68 * q^9 - 36 * q^12 - 8 * q^14 - 6 * q^16 + 30 * q^20 - 20 * q^22 - 144 * q^25 - 40 * q^26 - 6 * q^33 + 46 * q^36 - 12 * q^37 - 56 * q^38 - 2 * q^42 + 48 * q^45 - 40 * q^48 + 44 * q^49 - 32 * q^53 + 30 * q^56 + 78 * q^58 + 64 * q^64 - 4 * q^66 - 44 * q^69 - 44 * q^77 + 16 * q^78 + 24 * q^80 - 40 * q^81 - 6 * q^82 - 10 * q^88 + 24 * q^89 - 24 * q^92 - 96 * q^93

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