LMFDB - Embedded newform 572.2.y.a.79.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(79,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 0]))

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

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

chi := DirichletCharacter("572.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.y (of order $10$, degree $4$, 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:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			79.17
Character	$\chi$	$=$	572.79
Dual form			572.2.y.a.391.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08817 + 0.903263i) q^{2} +(1.08813 + 1.49768i) q^{3} +(0.368233 - 1.96581i) q^{4} +(-0.149634 - 0.460526i) q^{5} +(-2.53687 - 0.646867i) q^{6} +(-3.21984 - 2.33935i) q^{7} +(1.37494 + 2.47175i) q^{8} +(-0.131974 + 0.406174i) q^{9} +O(q^{10})$	\(q+(-1.08817 + 0.903263i) q^{2} +(1.08813 + 1.49768i) q^{3} +(0.368233 - 1.96581i) q^{4} +(-0.149634 - 0.460526i) q^{5} +(-2.53687 - 0.646867i) q^{6} +(-3.21984 - 2.33935i) q^{7} +(1.37494 + 2.47175i) q^{8} +(-0.131974 + 0.406174i) q^{9} +(0.578804 + 0.365972i) q^{10} +(-2.47193 - 2.21124i) q^{11} +(3.34484 - 1.58756i) q^{12} +(0.951057 + 0.309017i) q^{13} +(5.61678 - 0.362748i) q^{14} +(0.526901 - 0.725216i) q^{15} +(-3.72881 - 1.44775i) q^{16} +(3.37491 - 1.09657i) q^{17} +(-0.223271 - 0.561194i) q^{18} +(-1.28755 + 0.935463i) q^{19} +(-0.960407 + 0.124571i) q^{20} -7.36781i q^{21} +(4.68721 + 0.173401i) q^{22} -8.89290i q^{23} +(-2.20578 + 4.74881i) q^{24} +(3.85539 - 2.80111i) q^{25} +(-1.31404 + 0.522791i) q^{26} +(4.52997 - 1.47188i) q^{27} +(-5.78437 + 5.46816i) q^{28} +(-0.821613 + 1.13085i) q^{29} +(0.0817030 + 1.26509i) q^{30} +(0.970583 + 0.315361i) q^{31} +(5.36528 - 1.79269i) q^{32} +(0.621948 - 6.10827i) q^{33} +(-2.68198 + 4.24169i) q^{34} +(-0.595535 + 1.83287i) q^{35} +(0.749863 + 0.409002i) q^{36} +(-9.20077 - 6.68475i) q^{37} +(0.556111 - 2.18094i) q^{38} +(0.572064 + 1.76063i) q^{39} +(0.932566 - 1.00305i) q^{40} +(2.48243 + 3.41678i) q^{41} +(6.65507 + 8.01744i) q^{42} -11.3910 q^{43} +(-5.25711 + 4.04509i) q^{44} +0.206801 q^{45} +(8.03262 + 9.67699i) q^{46} +(3.52103 + 4.84628i) q^{47} +(-1.88916 - 7.15991i) q^{48} +(2.73169 + 8.40727i) q^{49} +(-1.66519 + 6.53051i) q^{50} +(5.31466 + 3.86132i) q^{51} +(0.957679 - 1.75581i) q^{52} +(2.10822 - 6.48844i) q^{53} +(-3.59989 + 5.69340i) q^{54} +(-0.648447 + 1.46926i) q^{55} +(1.35519 - 11.1751i) q^{56} +(-2.80205 - 0.910442i) q^{57} +(-0.127402 - 1.97269i) q^{58} +(7.12721 - 9.80976i) q^{59} +(-1.23161 - 1.30283i) q^{60} +(5.92213 - 1.92422i) q^{61} +(-1.34101 + 0.533524i) q^{62} +(1.37512 - 0.999081i) q^{63} +(-4.21907 + 6.79702i) q^{64} -0.484226i q^{65} +(4.84059 + 7.20863i) q^{66} +13.6928i q^{67} +(-0.912903 - 7.03822i) q^{68} +(13.3187 - 9.67662i) q^{69} +(-1.00752 - 2.53240i) q^{70} +(-3.88523 + 1.26239i) q^{71} +(-1.18542 + 0.232259i) q^{72} +(-0.552349 + 0.760243i) q^{73} +(16.0501 - 1.03656i) q^{74} +(8.39033 + 2.72618i) q^{75} +(1.36482 + 2.87555i) q^{76} +(2.78636 + 12.9025i) q^{77} +(-2.21281 - 1.39914i) q^{78} +(-2.49192 + 7.66933i) q^{79} +(-0.108770 + 1.93385i) q^{80} +(8.17013 + 5.93595i) q^{81} +(-5.78756 - 1.47575i) q^{82} +(-4.25610 - 13.0989i) q^{83} +(-14.4837 - 2.71307i) q^{84} +(-1.01000 - 1.39015i) q^{85} +(12.3953 - 10.2890i) q^{86} -2.58768 q^{87} +(2.06686 - 9.15031i) q^{88} +9.69500 q^{89} +(-0.225035 + 0.186796i) q^{90} +(-2.33935 - 3.21984i) q^{91} +(-17.4817 - 3.27466i) q^{92} +(0.583809 + 1.79678i) q^{93} +(-8.20894 - 2.09317i) q^{94} +(0.623467 + 0.452975i) q^{95} +(8.52301 + 6.08480i) q^{96} +(-1.49948 + 4.61492i) q^{97} +(-10.5665 - 6.68112i) q^{98} +(1.22438 - 0.712208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) $ 288 * q - 4 * q^4 + 80 * q^9	$ 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) $ 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.08817	+	0.903263i	−0.769453	+	0.638703i
$2$	−1.08817	+	0.903263i	−0.769453	+	0.638703i
$3$	1.08813	+	1.49768i	0.628232	+	0.864687i	0.997920	−	0.0644691i	$-0.0205354\pi$
$3$	1.08813	+	1.49768i	0.628232	+	0.864687i	−0.369688	+	0.929156i	$0.620535\pi$
$4$	0.368233	−	1.96581i	0.184116	−	0.982904i
$5$	−0.149634	−	0.460526i	−0.0669184	−	0.205954i	0.912006	−	0.410177i	$-0.134533\pi$
$5$	−0.149634	−	0.460526i	−0.0669184	−	0.205954i	−0.978924	+	0.204223i	$0.934533\pi$
$6$	−2.53687	−	0.646867i	−1.03567	−	0.264082i
$7$	−3.21984	−	2.33935i	−1.21698	−	0.884191i	−0.221139	−	0.975242i	$-0.570977\pi$
$7$	−3.21984	−	2.33935i	−1.21698	−	0.884191i	−0.995846	+	0.0910511i	$0.970977\pi$
$8$	1.37494	+	2.47175i	0.486115	+	0.873895i
$9$	−0.131974	+	0.406174i	−0.0439913	+	0.135391i
$10$	0.578804	+	0.365972i	0.183034	+	0.115731i
$11$	−2.47193	−	2.21124i	−0.745315	−	0.666713i
$11$	−2.47193	−	2.21124i	−0.745315	−	0.666713i
$12$	3.34484	−	1.58756i	0.965572	−	0.458289i
$13$	0.951057	+	0.309017i	0.263776	+	0.0857059i
$13$	0.951057	+	0.309017i	0.263776	+	0.0857059i
$14$	5.61678	−	0.362748i	1.50115	−	0.0969484i
$15$	0.526901	−	0.725216i	0.136045	−	0.187250i
$16$	−3.72881	−	1.44775i	−0.932202	−	0.361938i
$17$	3.37491	−	1.09657i	0.818536	−	0.265958i	0.130327	−	0.991471i	$-0.458397\pi$
$17$	3.37491	−	1.09657i	0.818536	−	0.265958i	0.688209	+	0.725513i	$0.258397\pi$
$18$	−0.223271	−	0.561194i	−0.0526256	−	0.132275i
$19$	−1.28755	+	0.935463i	−0.295385	+	0.214610i	−0.725600	−	0.688117i	$-0.758438\pi$
$19$	−1.28755	+	0.935463i	−0.295385	+	0.214610i	0.430215	+	0.902726i	$0.358438\pi$
$20$	−0.960407	+	0.124571i	−0.214753	+	0.0278549i
$21$		−	7.36781i		−	1.60779i
$22$	4.68721	+	0.173401i	0.999316	+	0.0369692i
$23$		−	8.89290i		−	1.85430i	−0.374694	−	0.927149i	$-0.622252\pi$
$23$		−	8.89290i		−	1.85430i	0.374694	−	0.927149i	$-0.377748\pi$
$24$	−2.20578	+	4.74881i	−0.450252	+	0.969346i
$25$	3.85539	−	2.80111i	0.771078	−	0.560221i
$26$	−1.31404	+	0.522791i	−0.257704	+	0.102528i
$27$	4.52997	−	1.47188i	0.871793	−	0.283263i
$28$	−5.78437	+	5.46816i	−1.09314	+	1.03339i
$29$	−0.821613	+	1.13085i	−0.152570	+	0.209994i	−0.878459	−	0.477817i	$-0.841428\pi$
$29$	−0.821613	+	1.13085i	−0.152570	+	0.209994i	0.725890	+	0.687811i	$0.241428\pi$
$30$	0.0817030	+	1.26509i	0.0149169	+	0.230973i
$31$	0.970583	+	0.315361i	0.174322	+	0.0566406i	0.394877	−	0.918734i	$-0.370787\pi$
$31$	0.970583	+	0.315361i	0.174322	+	0.0566406i	−0.220556	+	0.975374i	$0.570787\pi$
$32$	5.36528	−	1.79269i	0.948457	−	0.316906i
$33$	0.621948	−	6.10827i	0.108267	−	1.06331i
$34$	−2.68198	+	4.24169i	−0.459956	+	0.727444i
$35$	−0.595535	+	1.83287i	−0.100664	+	0.309811i
$36$	0.749863	+	0.409002i	0.124977	+	0.0681670i
$37$	−9.20077	−	6.68475i	−1.51260	−	1.09897i	−0.965008	−	0.262219i	$-0.915546\pi$
$37$	−9.20077	−	6.68475i	−1.51260	−	1.09897i	−0.547589	−	0.836748i	$-0.684454\pi$
$38$	0.556111	−	2.18094i	0.0902130	−	0.353796i
$39$	0.572064	+	1.76063i	0.0916035	+	0.281927i
$40$	0.932566	−	1.00305i	0.147452	−	0.158597i
$41$	2.48243	+	3.41678i	0.387691	+	0.533611i	0.957602	−	0.288096i	$-0.0930222\pi$
$41$	2.48243	+	3.41678i	0.387691	+	0.533611i	−0.569911	+	0.821707i	$0.693022\pi$
$42$	6.65507	+	8.01744i	1.02690	+	1.23712i
$43$	−11.3910			−1.73711			−0.868553	−	0.495596i	$-0.834950\pi$
$43$	−11.3910			−1.73711			−0.868553	+	0.495596i	$0.834950\pi$
$44$	−5.25711	+	4.04509i	−0.792540	+	0.609821i
$45$	0.206801			0.0308281
$46$	8.03262	+	9.67699i	1.18435	+	1.42679i
$47$	3.52103	+	4.84628i	0.513595	+	0.706903i	0.984520	−	0.175270i	$-0.0560800\pi$
$47$	3.52103	+	4.84628i	0.513595	+	0.706903i	−0.470926	+	0.882173i	$0.656080\pi$
$48$	−1.88916	−	7.15991i	−0.272676	−	1.03344i
$49$	2.73169	+	8.40727i	0.390241	+	1.20104i
$50$	−1.66519	+	6.53051i	−0.235494	+	0.923554i
$51$	5.31466	+	3.86132i	0.744201	+	0.540694i
$52$	0.957679	−	1.75581i	0.132806	−	0.243486i
$53$	2.10822	−	6.48844i	0.289586	−	0.891255i	−0.695400	−	0.718623i	$-0.744773\pi$
$53$	2.10822	−	6.48844i	0.289586	−	0.891255i	0.984986	−	0.172632i	$-0.0552272\pi$
$54$	−3.59989	+	5.69340i	−0.489883	+	0.774774i
$55$	−0.648447	+	1.46926i	−0.0874366	+	0.198116i
$56$	1.35519	−	11.1751i	0.181095	−	1.49334i
$57$	−2.80205	−	0.910442i	−0.371141	−	0.120591i
$58$	−0.127402	−	1.97269i	−0.0167287	−	0.259027i
$59$	7.12721	−	9.80976i	0.927884	−	1.27712i	−0.0327955	−	0.999462i	$-0.510441\pi$
$59$	7.12721	−	9.80976i	0.927884	−	1.27712i	0.960679	−	0.277660i	$-0.0895590\pi$
$60$	−1.23161	−	1.30283i	−0.159001	−	0.168195i
$61$	5.92213	−	1.92422i	0.758251	−	0.246371i	0.0957229	−	0.995408i	$-0.469484\pi$
$61$	5.92213	−	1.92422i	0.758251	−	0.246371i	0.662528	+	0.749037i	$0.269484\pi$
$62$	−1.34101	+	0.533524i	−0.170309	+	0.0677576i
$63$	1.37512	−	0.999081i	0.173248	−	0.125872i
$64$	−4.21907	+	6.79702i	−0.527384	+	0.849627i
$65$		−	0.484226i		−	0.0600608i
$66$	4.84059	+	7.20863i	0.595836	+	0.887321i
$67$			13.6928i			1.67284i	0.548091	+	0.836419i	$0.315355\pi$
$67$			13.6928i			1.67284i	−0.548091	+	0.836419i	$0.684645\pi$
$68$	−0.912903	−	7.03822i	−0.110706	−	0.853510i
$69$	13.3187	−	9.67662i	1.60339	−	1.16493i
$70$	−1.00752	−	2.53240i	−0.120421	−	0.302679i
$71$	−3.88523	+	1.26239i	−0.461092	+	0.149818i	−0.530346	−	0.847781i	$-0.677938\pi$
$71$	−3.88523	+	1.26239i	−0.461092	+	0.149818i	0.0692540	+	0.997599i	$0.477938\pi$
$72$	−1.18542	+	0.232259i	−0.139703	+	0.0273720i
$73$	−0.552349	+	0.760243i	−0.0646476	+	0.0889798i	−0.840117	−	0.542406i	$-0.817513\pi$
$73$	−0.552349	+	0.760243i	−0.0646476	+	0.0889798i	0.775469	+	0.631386i	$0.217513\pi$
$74$	16.0501	−	1.03656i	1.86579	−	0.120498i
$75$	8.39033	+	2.72618i	0.968832	+	0.314793i
$76$	1.36482	+	2.87555i	0.156556	+	0.329849i
$77$	2.78636	+	12.9025i	0.317535	+	1.47038i
$78$	−2.21281	−	1.39914i	−0.250552	−	0.158422i
$79$	−2.49192	+	7.66933i	−0.280363	+	0.862867i	0.707388	+	0.706826i	$0.249873\pi$
$79$	−2.49192	+	7.66933i	−0.280363	+	0.862867i	−0.987750	+	0.156042i	$0.950127\pi$
$80$	−0.108770	+	1.93385i	−0.0121609	+	0.216211i
$81$	8.17013	+	5.93595i	0.907792	+	0.659550i
$82$	−5.78756	−	1.47575i	−0.639129	−	0.162969i
$83$	−4.25610	−	13.0989i	−0.467168	−	1.43779i	−0.856236	−	0.516585i	$-0.827203\pi$
$83$	−4.25610	−	13.0989i	−0.467168	−	1.43779i	0.389068	−	0.921209i	$-0.372797\pi$
$84$	−14.4837	−	2.71307i	−1.58030	−	0.296020i
$85$	−1.01000	−	1.39015i	−0.109550	−	0.150783i
$86$	12.3953	−	10.2890i	1.33662	−	1.10950i
$87$	−2.58768			−0.277428
$88$	2.06686	−	9.15031i	0.220328	−	0.975426i
$89$	9.69500			1.02767			0.513834	−	0.857890i	$-0.328225\pi$
$89$	9.69500			1.02767			0.513834	+	0.857890i	$0.328225\pi$
$90$	−0.225035	+	0.186796i	−0.0237208	+	0.0196900i
$91$	−2.33935	−	3.21984i	−0.245231	−	0.337531i
$92$	−17.4817	−	3.27466i	−1.82260	−	0.341407i
$93$	0.583809	+	1.79678i	0.0605381	+	0.186317i
$94$	−8.20894	−	2.09317i	−0.846688	−	0.215894i
$95$	0.623467	+	0.452975i	0.0639664	+	0.0464743i
$96$	8.52301	+	6.08480i	0.869876	+	0.621027i
$97$	−1.49948	+	4.61492i	−0.152249	+	0.468574i	−0.997872	−	0.0652067i	$-0.979229\pi$
$97$	−1.49948	+	4.61492i	−0.152249	+	0.468574i	0.845623	+	0.533781i	$0.179229\pi$
$98$	−10.5665	−	6.68112i	−1.06738	−	0.674895i
$99$	1.22438	−	0.712208i	0.123054	−	0.0715796i
$100$	−4.08676	−	8.61042i	−0.408676	−	0.861042i
$101$	−15.0728	−	4.89744i	−1.49980	−	0.487314i	−0.559838	−	0.828602i	$-0.689137\pi$
$101$	−15.0728	−	4.89744i	−1.49980	−	0.487314i	−0.939959	+	0.341288i	$0.889137\pi$
$102$	−9.27105	+	0.598750i	−0.917970	+	0.0592851i
$103$	1.84194	−	2.53521i	0.181491	−	0.249802i	−0.708572	−	0.705639i	$-0.750660\pi$
$103$	1.84194	−	2.53521i	0.181491	−	0.249802i	0.890063	+	0.455837i	$0.150660\pi$
$104$	0.543835	+	2.77565i	0.0533274	+	0.272175i
$105$	−3.39307	+	1.10248i	−0.331130	+	0.107591i
$106$	3.56666	+	8.96481i	0.346424	+	0.870739i
$107$	−10.6583	+	7.74367i	−1.03037	+	0.748609i	−0.968383	−	0.249468i	$-0.919744\pi$
$107$	−10.6583	+	7.74367i	−1.03037	+	0.748609i	−0.0619891	+	0.998077i	$0.519744\pi$
$108$	−1.22534	−	9.44704i	−0.117909	−	0.909042i
$109$		−	5.95819i		−	0.570692i	−0.958425	−	0.285346i	$-0.907892\pi$
$109$		−	5.95819i		−	0.570692i	0.958425	−	0.285346i	$-0.0921084\pi$
$110$	−0.621510	−	2.18453i	−0.0592587	−	0.208287i
$111$		−	21.0537i		−	1.99833i
$112$	8.61937	+	13.3845i	0.814454	+	1.26472i
$113$	3.28622	−	2.38758i	0.309141	−	0.224604i	−0.422387	−	0.906416i	$-0.638808\pi$
$113$	3.28622	−	2.38758i	0.309141	−	0.224604i	0.731528	+	0.681812i	$0.238808\pi$
$114$	3.87148	−	1.54027i	0.362597	−	0.144260i
$115$	−4.09541	+	1.33068i	−0.381899	+	0.124087i
$116$	1.92050	+	2.03155i	0.178314	+	0.188625i
$117$	−0.251029	+	0.345512i	−0.0232077	+	0.0319426i
$118$	1.10517	+	17.1124i	0.101739	+	1.57533i
$119$	−13.4319	−	4.36430i	−1.23130	−	0.400075i
$120$	2.51701	+	0.305235i	0.229770	+	0.0278640i
$121$	1.22087	+	10.9320i	0.110988	+	0.993822i
$122$	−4.70621	+	7.44311i	−0.426081	+	0.673868i
$123$	−2.41603	+	7.43579i	−0.217846	+	0.670462i
$124$	0.977341	−	1.79185i	0.0877678	−	0.160913i
$125$	−3.82562	−	2.77947i	−0.342173	−	0.248604i
$126$	−0.593930	+	2.32926i	−0.0529115	+	0.207507i
$127$	1.36961	+	4.21521i	0.121533	+	0.374040i	0.993253	−	0.115964i	$-0.0369956\pi$
$127$	1.36961	+	4.21521i	0.121533	+	0.374040i	−0.871721	+	0.490003i	$0.836996\pi$
$128$	−1.54842	−	11.2072i	−0.136862	−	0.990590i
$129$	−12.3948	−	17.0600i	−1.09131	−	1.50205i
$130$	0.437383	+	0.526921i	0.0383610	+	0.0462140i
$131$	−0.663901			−0.0580053			−0.0290026	−	0.999579i	$-0.509233\pi$
$131$	−0.663901			−0.0580053			−0.0290026	+	0.999579i	$0.509233\pi$
$132$	−11.7787	−	3.47190i	−1.02520	−	0.302190i
$133$	6.33409			0.549236
$134$	−12.3682	−	14.9001i	−1.06845	−	1.28717i
$135$	−1.35567	−	1.86593i	−0.116678	−	0.160593i
$136$	7.35076	+	6.83420i	0.630322	+	0.586028i
$137$	2.92268	+	8.99510i	0.249702	+	0.768503i	0.994827	+	0.101579i	$0.0323894\pi$
$137$	2.92268	+	8.99510i	0.249702	+	0.768503i	−0.745126	+	0.666924i	$0.767611\pi$
$138$	−5.75252	+	22.5601i	−0.489687	+	1.92045i
$139$	13.8895	+	10.0913i	1.17809	+	0.855932i	0.991955	−	0.126593i	$-0.0404041\pi$
$139$	13.8895	+	10.0913i	1.17809	+	0.855932i	0.186134	+	0.982524i	$0.440404\pi$
$140$	3.38377	+	1.84563i	0.285981	+	0.155984i
$141$	−3.42685	+	10.5468i	−0.288593	+	0.888197i
$142$	3.08753	−	4.88308i	0.259100	−	0.409779i
$143$	−1.66764	−	2.86688i	−0.139455	−	0.239740i
$144$	1.08014	−	1.32348i	0.0900120	−	0.110290i
$145$	0.643729	+	0.209160i	0.0534587	+	0.0173698i
$146$	−0.0856491	−	1.32619i	−0.00708837	−	0.109756i
$147$	−9.61898	+	13.2394i	−0.793360	+	1.09197i
$148$	−16.5290	+	15.6254i	−1.35867	+	1.28440i
$149$	−11.7181	+	3.80744i	−0.959985	+	0.311918i	−0.746766	−	0.665087i	$-0.768395\pi$
$149$	−11.7181	+	3.80744i	−0.959985	+	0.311918i	−0.213219	+	0.977005i	$0.568395\pi$
$150$	−11.5926	+	4.61212i	−0.946530	+	0.376578i
$151$	9.02262	−	6.55531i	0.734250	−	0.533464i	−0.156655	−	0.987653i	$-0.550071\pi$
$151$	9.02262	−	6.55531i	0.734250	−	0.533464i	0.890905	+	0.454189i	$0.150071\pi$
$152$	−4.08254	−	1.89630i	−0.331138	−	0.153810i
$153$			1.51552i			0.122522i
$154$	−14.6864	−	11.5233i	−1.18347	−	0.928578i
$155$		−	0.494168i		−	0.0396925i
$156$	3.67172	−	0.476246i	0.293973	−	0.0381302i
$157$	−8.74542	+	6.35392i	−0.697961	+	0.507098i	−0.879267	−	0.476328i	$-0.841967\pi$
$157$	−8.74542	+	6.35392i	−0.697961	+	0.507098i	0.181307	+	0.983427i	$0.441967\pi$
$158$	−4.21579	−	10.5964i	−0.335390	−	0.843004i
$159$	12.0116	−	3.90281i	0.952584	−	0.309513i
$160$	−1.62841	−	2.20261i	−0.128737	−	0.174131i
$161$	−20.8036	+	28.6337i	−1.63955	+	2.25665i
$162$	−14.2522	+	0.920448i	−1.11976	+	0.0723172i
$163$	−20.4382	−	6.64078i	−1.60084	−	0.520146i	−0.633529	−	0.773719i	$-0.718394\pi$
$163$	−20.4382	−	6.64078i	−1.60084	−	0.520146i	−0.967316	+	0.253573i	$0.918394\pi$
$164$	7.63084	−	3.62182i	0.595869	−	0.282817i
$165$	−2.90609	+	0.627583i	−0.226238	+	0.0488572i
$166$	16.4631	+	10.4095i	1.27779	+	0.807934i
$167$	5.88988	−	18.1272i	0.455773	−	1.40272i	−0.414453	−	0.910071i	$-0.636027\pi$
$167$	5.88988	−	18.1272i	0.455773	−	1.40272i	0.870226	−	0.492653i	$-0.163973\pi$
$168$	18.2114	−	10.1303i	1.40504	−	0.781570i
$169$	0.809017	+	0.587785i	0.0622321	+	0.0452143i
$170$	2.35473	+	0.600423i	0.180599	+	0.0460503i
$171$	−0.210037	−	0.646427i	−0.0160619	−	0.0494335i
$172$	−4.19453	+	22.3925i	−0.319830	+	1.70741i
$173$	−1.74766	−	2.40544i	−0.132872	−	0.182882i	0.737397	−	0.675460i	$-0.236055\pi$
$173$	−1.74766	−	2.40544i	−0.132872	−	0.182882i	−0.870269	+	0.492578i	$0.836055\pi$
$174$	2.81584	−	2.33735i	0.213468	−	0.177194i
$175$	−18.9665			−1.43373
$176$	6.01604	+	11.8240i	0.453476	+	0.891269i
$177$	22.4472			1.68724
$178$	−10.5498	+	8.75713i	−0.790742	+	0.656375i
$179$	5.57710	+	7.67622i	0.416852	+	0.573748i	0.964873	−	0.262717i	$-0.0846185\pi$
$179$	5.57710	+	7.67622i	0.416852	+	0.573748i	−0.548021	+	0.836465i	$0.684619\pi$
$180$	0.0761511	−	0.406532i	0.00567597	−	0.0303011i
$181$	0.552931	+	1.70175i	0.0410990	+	0.126490i	0.969501	−	0.245088i	$-0.0788169\pi$
$181$	0.552931	+	1.70175i	0.0410990	+	0.126490i	−0.928402	+	0.371578i	$0.878817\pi$
$182$	5.45397	+	1.39069i	0.404275	+	0.103085i
$183$	9.32590	+	6.77566i	0.689391	+	0.500872i
$184$	21.9810	−	12.2272i	1.62046	−	0.901402i
$185$	−1.70175	+	5.23746i	−0.125115	+	0.385066i
$186$	−2.25825	−	1.42787i	−0.165583	−	0.104696i
$187$	−10.7673	−	4.75206i	−0.787385	−	0.347505i
$188$	10.8234	−	5.13711i	0.789379	−	0.374662i
$189$	−18.0290	−	5.85798i	−1.31142	−	0.426105i
$190$	−1.08759	+	0.0702399i	−0.0789024	+	0.00509574i
$191$	4.92668	−	6.78100i	0.356482	−	0.490656i	−0.592682	−	0.805436i	$-0.701931\pi$
$191$	4.92668	−	6.78100i	0.356482	−	0.490656i	0.949164	+	0.314781i	$0.101931\pi$
$192$	−14.7707	+	1.07721i	−1.06598	+	0.0777408i
$193$	6.67023	−	2.16729i	0.480134	−	0.156005i	−0.0589435	−	0.998261i	$-0.518773\pi$
$193$	6.67023	−	2.16729i	0.480134	−	0.156005i	0.539077	+	0.842256i	$0.318773\pi$
$194$	−2.53680	−	6.37625i	−0.182131	−	0.457788i
$195$	0.725216	−	0.526901i	0.0519338	−	0.0377321i
$196$	17.5330	−	2.27414i	1.25236	−	0.162439i
$197$		−	16.9459i		−	1.20734i	−0.797233	−	0.603671i	$-0.793704\pi$
$197$		−	16.9459i		−	1.20734i	0.797233	−	0.603671i	$-0.206296\pi$
$198$	−0.689020	+	1.88094i	−0.0489665	+	0.133672i
$199$			3.29004i			0.233224i	0.993178	+	0.116612i	$0.0372035\pi$
$199$			3.29004i			0.233224i	−0.993178	+	0.116612i	$0.962797\pi$
$200$	12.2246	+	5.67820i	0.864407	+	0.401509i
$201$	−20.5074	+	14.8995i	−1.44648	+	1.05093i
$202$	20.8254	−	8.28542i	1.46527	−	0.582960i
$203$	5.29092	−	1.71912i	0.371350	−	0.120659i
$204$	9.54766	−	9.02573i	0.668470	−	0.631928i
$205$	1.20206	−	1.65449i	0.0839554	−	0.115555i
$206$	0.285617	+	4.42250i	0.0198999	+	0.308130i
$207$	3.61206	+	1.17363i	0.251056	+	0.0815729i
$208$	−3.09893	−	2.52916i	−0.214872	−	0.175366i
$209$	5.25127	+	0.534687i	0.363238	+	0.0369851i
$210$	2.69642	−	4.26452i	0.186070	−	0.294280i
$211$	6.40322	−	19.7071i	0.440816	−	1.35669i	−0.446193	−	0.894937i	$-0.647220\pi$
$211$	6.40322	−	19.7071i	0.440816	−	1.35669i	0.887008	−	0.461754i	$-0.152780\pi$
$212$	−11.9787	−	6.53361i	−0.822701	−	0.448730i
$213$	−6.11829	−	4.44520i	−0.419219	−	0.304580i
$214$	4.60343	−	18.0536i	0.314684	−	1.23412i
$215$	1.70448	+	5.24584i	0.116244	+	0.357763i
$216$	9.86655	+	9.17319i	0.671333	+	0.624157i
$217$	−2.38738	−	3.28595i	−0.162066	−	0.223065i
$218$	5.38181	+	6.48353i	0.364502	+	0.439120i
$219$	−1.73963			−0.117553
$220$	2.64951	+	1.81575i	0.178630	+	0.122418i
$221$	3.54859			0.238704
$222$	19.0170	+	22.9100i	1.27634	+	1.53762i
$223$	5.72310	+	7.87717i	0.383247	+	0.527494i	0.956441	−	0.291925i	$-0.0942959\pi$
$223$	5.72310	+	7.87717i	0.383247	+	0.527494i	−0.573194	+	0.819420i	$0.694296\pi$
$224$	−21.4691	−	6.77909i	−1.43446	−	0.452947i
$225$	0.628925	+	1.93563i	0.0419283	+	0.129042i
$226$	−1.41936	+	5.56641i	−0.0944142	+	0.370272i
$227$	22.8705	+	16.6164i	1.51797	+	1.10287i	0.962482	+	0.271346i	$0.0874687\pi$
$227$	22.8705	+	16.6164i	1.51797	+	1.10287i	0.555488	+	0.831524i	$0.312531\pi$
$228$	−2.82156	+	5.17304i	−0.186862	+	0.342593i
$229$	3.46073	−	10.6510i	0.228691	−	0.703840i	−0.769204	−	0.639003i	$-0.779347\pi$
$229$	3.46073	−	10.6510i	0.228691	−	0.703840i	0.997896	−	0.0648372i	$-0.0206528\pi$
$230$	3.25456	−	5.14724i	0.214599	−	0.339399i
$231$	−16.2920	+	18.2127i	−1.07193	+	1.19831i
$232$	−3.92485	−	0.475962i	−0.257679	−	0.0312485i
$233$	1.19872	+	0.389487i	0.0785307	+	0.0255162i	0.348019	−	0.937488i	$-0.386855\pi$
$233$	1.19872	+	0.389487i	0.0785307	+	0.0255162i	−0.269488	+	0.963004i	$0.586855\pi$
$234$	−0.0389254	−	0.602721i	−0.00254463	−	0.0394011i
$235$	1.70497	−	2.34669i	0.111220	−	0.153081i
$236$	−16.6596	−	17.6230i	−1.08445	−	1.14716i
$237$	−14.1977	+	4.61313i	−0.922243	+	0.299655i
$238$	18.5584	−	7.38346i	1.20296	−	0.478599i
$239$	23.0989	−	16.7823i	1.49414	−	1.08556i	0.521498	−	0.853252i	$-0.325373\pi$
$239$	23.0989	−	16.7823i	1.49414	−	1.08556i	0.972643	−	0.232305i	$-0.0746268\pi$
$240$	−3.01464	+	1.94137i	−0.194594	+	0.125315i
$241$			4.43522i			0.285697i	0.989745	+	0.142849i	$0.0456262\pi$
$241$			4.43522i			0.285697i	−0.989745	+	0.142849i	$0.954374\pi$
$242$	−11.2030	−	10.7932i	−0.720158	−	0.693811i
$243$			4.40606i			0.282649i
$244$	−1.60192	−	12.3503i	−0.102552	−	0.790649i
$245$	3.46301	−	2.51603i	0.221244	−	0.160743i
$246$	−4.08741	−	10.2737i	−0.260604	−	0.655029i
$247$	−1.51361	+	0.491802i	−0.0963087	+	0.0312926i
$248$	0.555001	+	2.83264i	0.0352426	+	0.179873i
$249$	14.9868	−	20.6276i	0.949752	−	1.30722i
$250$	6.67352	−	0.430994i	0.422070	−	0.0272585i
$251$	17.1394	+	5.56893i	1.08183	+	0.351508i	0.795084	−	0.606499i	$-0.207427\pi$
$251$	17.1394	+	5.56893i	1.08183	+	0.351508i	0.286745	+	0.958007i	$0.407427\pi$
$252$	−1.45764	−	3.07111i	−0.0918226	−	0.193462i
$253$	−19.6643	+	21.9826i	−1.23628	+	1.38204i
$254$	−5.29781	−	3.34976i	−0.332414	−	0.210183i
$255$	0.982988	−	3.02532i	0.0615571	−	0.189453i
$256$	11.8080	+	10.7968i	0.738002	+	0.674798i
$257$	2.61643	+	1.90095i	0.163209	+	0.118578i	0.666392	−	0.745602i	$-0.267838\pi$
$257$	2.61643	+	1.90095i	0.163209	+	0.118578i	−0.503183	+	0.864180i	$0.667838\pi$
$258$	28.8974	+	7.36844i	1.79907	+	0.458739i
$259$	13.9870	+	43.0476i	0.869112	+	2.67485i
$260$	−0.951896	−	0.178308i	−0.0590341	−	0.0110582i
$261$	−0.350891	−	0.482960i	−0.0217196	−	0.0298945i
$262$	0.722438	−	0.599677i	0.0446323	−	0.0370482i
$263$	−5.58976			−0.344680			−0.172340	−	0.985038i	$-0.555133\pi$
$263$	−5.58976			−0.344680			−0.172340	+	0.985038i	$0.555133\pi$
$264$	15.9533	−	6.86122i	0.981855	−	0.422279i
$265$	−3.30356			−0.202936
$266$	−6.89258	+	5.72135i	−0.422611	+	0.350798i
$267$	10.5494	+	14.5200i	0.645614	+	0.888611i
$268$	26.9174	+	5.04212i	1.64424	+	0.307997i
$269$	4.77658	+	14.7008i	0.291233	+	0.896323i	0.984461	+	0.175605i	$0.0561880\pi$
$269$	4.77658	+	14.7008i	0.291233	+	0.896323i	−0.693228	+	0.720719i	$0.743812\pi$
$270$	3.16063	+	0.805917i	0.192350	+	0.0490465i
$271$	0.776862	+	0.564423i	0.0471910	+	0.0342863i	0.611131	−	0.791530i	$-0.290715\pi$
$271$	0.776862	+	0.564423i	0.0471910	+	0.0342863i	−0.563940	+	0.825816i	$0.690715\pi$
$272$	−14.1720	−	0.797110i	−0.859301	−	0.0483319i
$273$	2.27678	−	7.00720i	0.137797	−	0.424095i
$274$	−11.3053	−	7.14825i	−0.682979	−	0.431842i
$275$	−15.7242	−	1.60104i	−0.948203	−	0.0965465i
$276$	−14.1180	−	29.7453i	−0.849804	−	1.79046i
$277$	9.20983	+	2.99246i	0.553365	+	0.179799i	0.572334	−	0.820021i	$-0.306038\pi$
$277$	9.20983	+	2.99246i	0.553365	+	0.179799i	−0.0189685	+	0.999820i	$0.506038\pi$
$278$	−24.2292	+	1.56479i	−1.45317	+	0.0938498i
$279$	−0.256183	+	0.352606i	−0.0153373	+	0.0211100i
$280$	−5.34921	+	1.04807i	−0.319676	+	0.0626344i
$281$	11.6925	−	3.79913i	0.697518	−	0.226637i	0.0612690	−	0.998121i	$-0.480485\pi$
$281$	11.6925	−	3.79913i	0.697518	−	0.226637i	0.636249	+	0.771484i	$0.280485\pi$
$282$	−5.79750	−	14.5720i	−0.345236	−	0.867751i
$283$	−4.30079	+	3.12470i	−0.255655	+	0.185744i	−0.708229	−	0.705982i	$-0.750506\pi$
$283$	−4.30079	+	3.12470i	−0.255655	+	0.185744i	0.452574	+	0.891727i	$0.350506\pi$
$284$	1.05094	+	8.10248i	0.0623621	+	0.480794i
$285$			1.42665i			0.0845075i
$286$	4.40422	+	1.61334i	0.260427	+	0.0953989i
$287$		−	16.8087i		−	0.992189i
$288$	0.0200683	+	2.41582i	0.00118253	+	0.142354i
$289$	−3.56575	+	2.59067i	−0.209750	+	0.152392i
$290$	−0.889413	+	0.353854i	−0.0522281	+	0.0207790i
$291$	−8.54331	+	2.77589i	−0.500818	+	0.162726i
$292$	1.29110	+	1.36576i	0.0755559	+	0.0799250i
$293$	−8.62664	+	11.8735i	−0.503973	+	0.693660i	−0.982889	−	0.184201i	$-0.941030\pi$
$293$	−8.62664	+	11.8735i	−0.503973	+	0.693660i	0.478915	+	0.877861i	$0.341030\pi$
$294$	−1.49155	−	23.0952i	−0.0869891	−	1.34694i
$295$	−5.58413	−	1.81439i	−0.325120	−	0.105638i
$296$	3.87249	−	31.9331i	0.225084	−	1.85608i
$297$	−14.4524	−	6.37845i	−0.838615	−	0.370115i
$298$	9.31219	−	14.7277i	0.539440	−	0.853152i
$299$	2.74806	−	8.45765i	0.158924	−	0.489118i
$300$	8.44875	−	15.4899i	0.487789	−	0.894311i
$301$	36.6771	+	26.6475i	2.11403	+	1.53593i
$302$	−3.89698	+	15.2831i	−0.224246	+	0.879443i
$303$	−9.06632	−	27.9033i	−0.520846	−	1.60300i
$304$	6.15536	−	1.62410i	0.353034	−	0.0931488i
$305$	−1.77230	−	2.43937i	−0.101482	−	0.139678i
$306$	−1.36891	−	1.64914i	−0.0782554	−	0.0942752i
$307$	0.718574			0.0410112			0.0205056	−	0.999790i	$-0.493472\pi$
$307$	0.718574			0.0410112			0.0205056	+	0.999790i	$0.493472\pi$
$308$	26.3899	−	0.726319i	1.50371	−	0.0413859i
$309$	5.80120			0.330019
$310$	0.446363	+	0.537739i	0.0253517	+	0.0305415i
$311$	8.84641	+	12.1760i	0.501634	+	0.690440i	0.982481	−	0.186365i	$-0.0596706\pi$
$311$	8.84641	+	12.1760i	0.501634	+	0.690440i	−0.480847	+	0.876805i	$0.659671\pi$
$312$	−3.56528	+	3.83476i	−0.201844	+	0.217101i
$313$	−10.1119	−	31.1213i	−0.571560	−	1.75908i	−0.647605	−	0.761976i	$-0.724229\pi$
$313$	−10.1119	−	31.1213i	−0.571560	−	1.75908i	0.0760453	−	0.997104i	$-0.475771\pi$
$314$	3.77726	−	14.8136i	0.213163	−	0.835978i
$315$	−0.665867	−	0.483781i	−0.0375174	−	0.0272580i
$316$	14.1588	+	7.72273i	0.796497	+	0.434438i
$317$	5.67525	−	17.4666i	0.318754	−	0.981023i	−0.655428	−	0.755258i	$-0.727512\pi$
$317$	5.67525	−	17.4666i	0.318754	−	0.981023i	0.974182	−	0.225765i	$-0.0724882\pi$
$318$	−9.54544	+	15.0966i	−0.535282	+	0.846575i
$319$	4.53155	−	0.978609i	0.253718	−	0.0547916i
$320$	3.76152	+	0.925928i	0.210275	+	0.0517609i
$321$	−23.1951	−	7.53655i	−1.29463	−	0.420649i
$322$	−3.22588	−	49.9495i	−0.179771	−	2.78358i
$323$	−3.31957	+	4.56900i	−0.184706	+	0.254226i
$324$	14.6774	−	13.8751i	0.815414	−	0.770839i
$325$	4.53228	−	1.47263i	0.251406	−	0.0816867i
$326$	28.2386	−	11.2348i	1.56399	−	0.622237i
$327$	8.92348	−	6.48329i	0.493469	−	0.358527i
$328$	−5.03221	+	10.8338i	−0.277857	+	0.598197i
$329$		−	23.8412i		−	1.31441i
$330$	2.59545	−	3.30788i	0.142875	−	0.182093i
$331$		−	7.59149i		−	0.417266i	−0.977994	−	0.208633i	$-0.933099\pi$
$331$		−	7.59149i		−	0.417266i	0.977994	−	0.208633i	$-0.0669014\pi$
$332$	−27.3172	+	3.54322i	−1.49923	+	0.194460i
$333$	3.92943	−	2.85490i	0.215331	−	0.156447i
$334$	9.96442	+	25.0456i	0.545229	+	1.37043i
$335$	6.30588	−	2.04890i	0.344527	−	0.111944i
$336$	−10.6668	+	27.4732i	−0.581919	+	1.49878i
$337$	4.12338	−	5.67535i	0.224615	−	0.309156i	−0.681805	−	0.731534i	$-0.738805\pi$
$337$	4.12338	−	5.67535i	0.224615	−	0.309156i	0.906420	+	0.422378i	$0.138805\pi$
$338$	−1.41127	+	0.0911440i	−0.0767632	+	0.00495758i
$339$	7.15166	+	2.32371i	0.388425	+	0.126207i
$340$	−3.10468	+	1.47357i	−0.168375	+	0.0799157i
$341$	−1.70187	−	2.92574i	−0.0921616	−	0.158438i
$342$	0.812450	+	0.513705i	0.0439323	+	0.0277780i
$343$	2.26287	−	6.96439i	0.122183	−	0.376042i
$344$	−15.6619	−	28.1556i	−0.844434	−	1.51805i
$345$	−6.44927	−	4.68567i	−0.347217	−	0.252268i
$346$	4.07449	+	1.03894i	0.219046	+	0.0558537i
$347$	5.79646	+	17.8397i	0.311170	+	0.957684i	0.977302	+	0.211850i	$0.0679489\pi$
$347$	5.79646	+	17.8397i	0.311170	+	0.957684i	−0.666132	+	0.745834i	$0.732051\pi$
$348$	−0.952868	+	5.08688i	−0.0510791	+	0.272685i
$349$	17.5702	+	24.1832i	0.940509	+	1.29450i	0.955616	+	0.294614i	$0.0951910\pi$
$349$	17.5702	+	24.1832i	0.940509	+	1.29450i	−0.0151075	+	0.999886i	$0.504809\pi$
$350$	20.6388	−	17.1317i	1.10319	−	0.915730i
$351$	4.76309			0.254235
$352$	−17.2267	−	7.43249i	−0.918185	−	0.396153i
$353$	21.1948			1.12809			0.564043	−	0.825746i	$-0.309245\pi$
$353$	21.1948			1.12809			0.564043	+	0.825746i	$0.309245\pi$
$354$	−24.4264	+	20.2757i	−1.29825	+	1.07764i
$355$	1.16273	+	1.60036i	0.0617111	+	0.0849381i
$356$	3.57002	−	19.0585i	0.189211	−	1.01010i
$357$	−8.07935	−	24.8657i	−0.427605	−	1.31603i
$358$	−13.0025	−	3.31545i	−0.687203	−	0.175227i
$359$	19.8020	+	14.3870i	1.04511	+	0.759316i	0.971276	−	0.237955i	$-0.0764771\pi$
$359$	19.8020	+	14.3870i	1.04511	+	0.759316i	0.0738321	+	0.997271i	$0.476477\pi$
$360$	0.284340	+	0.511161i	0.0149860	+	0.0269405i
$361$	−5.08862	+	15.6612i	−0.267822	+	0.824271i
$362$	−2.13881	−	1.35235i	−0.112413	−	0.0710779i
$363$	−15.0442	+	13.7240i	−0.789618	+	0.720321i
$364$	−7.19101	+	3.41307i	−0.376912	+	0.178893i
$365$	0.432762	+	0.140613i	0.0226518	+	0.00736002i
$366$	−16.2684	+	1.05066i	−0.850362	+	0.0549187i
$367$	−8.84499	+	12.1741i	−0.461705	+	0.635482i	−0.974861	−	0.222813i	$-0.928476\pi$
$367$	−8.84499	+	12.1741i	−0.461705	+	0.635482i	0.513157	+	0.858295i	$0.328476\pi$
$368$	−12.8747	+	33.1599i	−0.671140	+	1.72858i
$369$	−1.71542	+	0.557374i	−0.0893012	+	0.0290157i
$370$	−2.87900	−	7.23639i	−0.149672	−	0.376202i
$371$	−21.9669	+	15.9599i	−1.14046	+	0.828594i
$372$	3.74710	−	0.486023i	0.194278	−	0.0251991i
$373$			1.25286i			0.0648706i	0.999474	+	0.0324353i	$0.0103263\pi$
$373$			1.25286i			0.0648706i	−0.999474	+	0.0324353i	$0.989674\pi$
$374$	16.0091	−	4.55466i	0.827808	−	0.235516i
$375$		−	8.75398i		−	0.452054i
$376$	−7.13757	+	15.3664i	−0.368092	+	0.792464i
$377$	−1.13085	+	0.821613i	−0.0582419	+	0.0423152i
$378$	24.9099	−	9.91044i	1.28123	−	0.509738i
$379$	7.07815	−	2.29983i	0.363580	−	0.118134i	−0.121529	−	0.992588i	$-0.538780\pi$
$379$	7.07815	−	2.29983i	0.363580	−	0.118134i	0.485109	+	0.874454i	$0.338780\pi$
$380$	1.12004	−	1.05882i	0.0574570	−	0.0543162i
$381$	−4.82274	+	6.63793i	−0.247076	+	0.340071i
$382$	0.763948	+	11.8290i	0.0390870	+	0.605223i
$383$	12.3361	+	4.00823i	0.630343	+	0.204811i	0.606727	−	0.794910i	$-0.292482\pi$
$383$	12.3361	+	4.00823i	0.630343	+	0.204811i	0.0236160	+	0.999721i	$0.492482\pi$
$384$	15.1000	−	14.5140i	0.770569	−	0.740663i
$385$	5.52502	−	3.21385i	0.281581	−	0.163793i
$386$	−5.30072	+	8.38335i	−0.269799	+	0.426701i
$387$	1.50331	−	4.62671i	0.0764175	−	0.235189i
$388$	8.51990	+	4.64706i	0.432532	+	0.235918i
$389$	19.2549	+	13.9895i	0.976263	+	0.709297i	0.956870	−	0.290515i	$-0.0938267\pi$
$389$	19.2549	+	13.9895i	0.976263	+	0.709297i	0.0193927	+	0.999812i	$0.493827\pi$
$390$	−0.313230	+	1.22842i	−0.0158610	+	0.0622034i
$391$	−9.75172	−	30.0127i	−0.493166	−	1.51781i
$392$	−17.0247	+	18.3115i	−0.859879	+	0.924873i
$393$	−0.722410	−	0.994312i	−0.0364408	−	0.0501564i
$394$	15.3066	+	18.4400i	0.771133	+	0.928993i
$395$	3.90480			0.196472
$396$	−0.949209	−	2.66915i	−0.0476995	−	0.134130i
$397$	7.85751			0.394357			0.197179	−	0.980368i	$-0.436822\pi$
$397$	7.85751			0.394357			0.197179	+	0.980368i	$0.436822\pi$
$398$	−2.97177	−	3.58012i	−0.148961	−	0.179455i
$399$	6.89231	+	9.48646i	0.345047	+	0.474917i
$400$	−18.4313	+	4.86314i	−0.921566	+	0.243157i
$401$	−3.40005	−	10.4643i	−0.169791	−	0.522562i	0.829567	−	0.558407i	$-0.188587\pi$
$401$	−3.40005	−	10.4643i	−0.169791	−	0.522562i	−0.999357	+	0.0358460i	$0.988587\pi$
$402$	8.85740	−	34.7368i	0.441767	−	1.73251i
$403$	0.825627	+	0.599853i	0.0411274	+	0.0298808i
$404$	−15.1777	+	27.8268i	−0.755120	+	1.38443i
$405$	1.51113	−	4.65078i	0.0750886	−	0.231099i
$406$	−4.20461	+	6.64979i	−0.208671	+	0.330024i
$407$	7.96210	+	36.8693i	0.394667	+	1.82754i
$408$	−2.23688	+	18.4456i	−0.110742	+	0.913193i
$409$	−21.3986	−	6.95284i	−1.05809	−	0.343796i	−0.272254	−	0.962225i	$-0.587769\pi$
$409$	−21.3986	−	6.95284i	−1.05809	−	0.343796i	−0.785840	+	0.618430i	$0.787769\pi$
$410$	0.186395	+	2.88614i	0.00920540	+	0.142537i
$411$	−10.2915	+	14.1651i	−0.507644	+	0.698712i
$412$	−4.30548	−	4.55444i	−0.212116	−	0.224381i
$413$	−45.8969	+	14.9128i	−2.25844	+	0.733812i
$414$	−4.99064	+	1.98553i	−0.245276	+	0.0975835i
$415$	−5.39554	+	3.92009i	−0.264857	+	0.192430i
$416$	5.65666	−	0.0469899i	0.277341	−	0.00230387i
$417$			31.7826i			1.55640i
$418$	−6.19725	+	4.16145i	−0.303117	+	0.203543i
$419$		−	23.1025i		−	1.12863i	−0.825559	−	0.564316i	$-0.809140\pi$
$419$		−	23.1025i		−	1.12863i	0.825559	−	0.564316i	$-0.190860\pi$
$420$	0.917816	+	7.07610i	0.0447848	+	0.345278i
$421$	−11.4469	+	8.31665i	−0.557887	+	0.405329i	−0.830685	−	0.556743i	$-0.812051\pi$
$421$	−11.4469	+	8.31665i	−0.557887	+	0.405329i	0.272798	+	0.962071i	$0.412051\pi$
$422$	10.8329	+	27.2284i	0.527336	+	1.32546i
$423$	−2.43311	+	0.790567i	−0.118302	+	0.0384387i
$424$	18.9365	−	3.71023i	0.919636	−	0.180185i
$425$	9.93997	−	13.6812i	0.482159	−	0.663636i
$426$	10.6729	−	0.689288i	0.517105	−	0.0333961i
$427$	−23.5697	−	7.65826i	−1.14062	−	0.370609i
$428$	11.2979	+	23.8036i	0.546103	+	1.15059i
$429$	2.47907	−	5.61712i	0.119691	−	0.271197i
$430$	−6.59313	−	4.16878i	−0.317949	−	0.201036i
$431$	2.71127	−	8.34442i	0.130597	−	0.401937i	−0.864282	−	0.503007i	$-0.832227\pi$
$431$	2.71127	−	8.34442i	0.130597	−	0.401937i	0.994879	+	0.101071i	$0.0322269\pi$
$432$	−19.0223	−	1.06992i	−0.915211	−	0.0514766i
$433$	−3.89189	−	2.82762i	−0.187032	−	0.135887i	0.490329	−	0.871537i	$-0.336877\pi$
$433$	−3.89189	−	2.82762i	−0.187032	−	0.135887i	−0.677361	+	0.735650i	$0.736877\pi$
$434$	5.56595	+	1.41924i	0.267174	+	0.0681257i
$435$	0.387205	+	1.19169i	0.0185650	+	0.0571373i
$436$	−11.7127	−	2.19400i	−0.560935	−	0.105074i
$437$	8.31897	+	11.4501i	0.397951	+	0.547732i
$438$	1.89302	−	1.57134i	0.0904518	−	0.0750817i
$439$	8.39100			0.400480			0.200240	−	0.979747i	$-0.435828\pi$
$439$	8.39100			0.400480			0.200240	+	0.979747i	$0.435828\pi$
$440$	−4.52323	+	0.417355i	−0.215636	+	0.0198966i
$441$	−3.77532			−0.179777
$442$	−3.86147	+	3.20531i	−0.183672	+	0.152461i
$443$	7.56543	+	10.4129i	0.359445	+	0.494733i	0.949994	−	0.312269i	$-0.101089\pi$
$443$	7.56543	+	10.4129i	0.359445	+	0.494733i	−0.590549	+	0.807002i	$0.701089\pi$
$444$	−41.3876	−	7.75266i	−1.96417	−	0.367925i
$445$	−1.45070	−	4.46480i	−0.0687699	−	0.211652i
$446$	−13.3429	−	3.40225i	−0.631803	−	0.161101i
$447$	−18.4532	−	13.4070i	−0.872805	−	0.634130i
$448$	29.4853	−	12.0154i	1.39305	−	0.567675i
$449$	−6.52141	+	20.0708i	−0.307764	+	0.947201i	0.670867	+	0.741578i	$0.265922\pi$
$449$	−6.52141	+	20.0708i	−0.307764	+	0.947201i	−0.978631	+	0.205623i	$0.934078\pi$
$450$	−2.43276	−	1.53821i	−0.114681	−	0.0725121i
$451$	1.41890	−	13.9353i	0.0668132	−	0.656186i
$452$	−3.48342	−	7.33926i	−0.163847	−	0.345210i
$453$	19.6355	+	6.37998i	0.922559	+	0.299757i
$454$	−39.8960	+	2.57660i	−1.87241	+	0.120926i
$455$	−1.13277	+	1.55913i	−0.0531053	+	0.0730931i
$456$	−1.60227	−	8.17777i	−0.0750334	−	0.382959i
$457$	−10.2703	+	3.33701i	−0.480422	+	0.156099i	−0.539209	−	0.842172i	$-0.681277\pi$
$457$	−10.2703	+	3.33701i	−0.480422	+	0.156099i	0.0587869	+	0.998271i	$0.481277\pi$
$458$	5.85481	+	14.7161i	0.273577	+	0.687638i
$459$	13.6742	−	9.93489i	0.638257	−	0.463721i
$460$	1.10780	+	8.54080i	0.0516513	+	0.398217i
$461$			38.4401i			1.79033i	0.445732	+	0.895167i	$0.352944\pi$
$461$			38.4401i			1.79033i	−0.445732	+	0.895167i	$0.647056\pi$
$462$	1.27758	−	34.5345i	0.0594386	−	1.60669i
$463$		−	11.9295i		−	0.554410i	−0.960811	−	0.277205i	$-0.910592\pi$
$463$		−	11.9295i		−	0.554410i	0.960811	−	0.277205i	$-0.0894082\pi$
$464$	4.70083	−	3.02724i	0.218231	−	0.140536i
$465$	0.740106	−	0.537718i	0.0343216	−	0.0249361i
$466$	−1.65622	+	0.658929i	−0.0767230	+	0.0305243i
$467$	−12.8270	+	4.16775i	−0.593563	+	0.192860i	−0.590368	−	0.807135i	$-0.701017\pi$
$467$	−12.8270	+	4.16775i	−0.593563	+	0.192860i	−0.00319564	+	0.999995i	$0.501017\pi$
$468$	0.586773	+	0.620704i	0.0271236	+	0.0286921i
$469$	32.0322	−	44.0885i	1.47911	−	2.03582i
$470$	0.264379	+	4.09364i	0.0121949	+	0.188826i
$471$	−19.0323	−	6.18397i	−0.876962	−	0.284942i
$472$	34.0468	+	4.12881i	1.56713	+	0.190044i
$473$	28.1577	+	25.1881i	1.29469	+	1.15815i
$474$	11.2827	−	17.8442i	0.518232	−	0.819610i
$475$	−2.34369	+	7.21315i	−0.107536	+	0.330962i
$476$	−13.5255	+	24.7975i	−0.619938	+	1.13659i
$477$	2.35720	+	1.71261i	0.107929	+	0.0784149i
$478$	−9.97669	+	39.1264i	−0.456323	+	1.78960i
$479$	7.24111	+	22.2859i	0.330855	+	1.01827i	0.968728	+	0.248125i	$0.0798145\pi$
$479$	7.24111	+	22.2859i	0.330855	+	1.01827i	−0.637873	+	0.770142i	$0.720186\pi$
$480$	1.52688	−	4.83556i	0.0696922	−	0.220712i
$481$	−6.68475	−	9.20077i	−0.304798	−	0.419519i
$482$	−4.00617	−	4.82627i	−0.182476	−	0.219831i
$483$	−65.5212			−2.98132
$484$	21.9399	+	1.62553i	0.997267	+	0.0738878i
$485$	2.34967			0.106693
$486$	−3.97983	−	4.79455i	−0.180529	−	0.217485i
$487$	−17.0225	−	23.4295i	−0.771363	−	1.06169i	−0.996183	−	0.0872896i	$-0.972179\pi$
$487$	−17.0225	−	23.4295i	−0.771363	−	1.06169i	0.224820	−	0.974400i	$-0.427821\pi$
$488$	12.8988	+	11.9923i	0.583899	+	0.542867i
$489$	−12.2937	−	37.8360i	−0.555938	−	1.71100i
$490$	−1.49572	+	5.86588i	−0.0675697	+	0.264993i
$491$	10.5655	+	7.67629i	0.476815	+	0.346426i	0.800091	−	0.599878i	$-0.204784\pi$
$491$	10.5655	+	7.67629i	0.476815	+	0.346426i	−0.323276	+	0.946305i	$0.604784\pi$
$492$	13.7277	+	7.48756i	0.618891	+	0.337565i
$493$	−1.53280	+	4.71748i	−0.0690340	+	0.212465i
$494$	1.20284	−	1.90235i	0.0541184	−	0.0855909i
$495$	−0.511199	−	0.457287i	−0.0229767	−	0.0205535i
$496$	−3.16255	−	2.58108i	−0.142003	−	0.115894i
$497$	15.4630	+	5.02423i	0.693610	+	0.225368i
$498$	2.32391	+	35.9834i	0.104137	+	1.61246i
$499$	−10.6915	+	14.7156i	−0.478616	+	0.658759i	−0.978238	−	0.207485i	$-0.933472\pi$
$499$	−10.6915	+	14.7156i	−0.478616	+	0.658759i	0.499622	+	0.866244i	$0.333472\pi$
$500$	−6.87263	+	6.49694i	−0.307353	+	0.290552i
$501$	33.5577	−	10.9036i	1.49925	−	0.487135i
$502$	−23.6808	+	9.42144i	−1.05693	+	0.420499i
$503$	15.2433	−	11.0749i	0.679667	−	0.493807i	−0.193580	−	0.981084i	$-0.562010\pi$
$503$	15.2433	−	11.0749i	0.679667	−	0.493807i	0.873247	+	0.487278i	$0.162010\pi$
$504$	4.36018	+	2.02526i	0.194218	+	0.0902124i
$505$			7.67423i			0.341499i
$506$	1.54204	−	41.6829i	0.0685518	−	1.85303i
$507$			1.85124i			0.0822163i
$508$	8.79064	−	1.14020i	0.390021	−	0.0505883i
$509$	5.32015	−	3.86531i	0.235811	−	0.171327i	−0.463604	−	0.886043i	$-0.653444\pi$
$509$	5.32015	−	3.86531i	0.235811	−	0.171327i	0.699415	+	0.714716i	$0.253444\pi$
$510$	1.66300	+	4.17997i	0.0736391	+	0.185092i
$511$	3.55695	−	1.15572i	0.157350	−	0.0511262i
$512$	−22.6015	−	1.08298i	−0.998854	−	0.0478613i
$513$	−4.45569	+	6.13274i	−0.196724	+	0.270767i
$514$	−4.56418	+	0.294768i	−0.201318	+	0.0130016i
$515$	−1.44315	−	0.468907i	−0.0635927	−	0.0206625i
$516$	−38.1010	+	18.0838i	−1.67730	+	0.796096i
$517$	2.01253	−	19.7655i	0.0885111	−	0.869285i
$518$	−54.1036	−	34.2092i	−2.37718	−	1.50307i
$519$	1.70091	−	5.23486i	0.0746617	−	0.229785i
$520$	1.19688	−	0.665782i	0.0524868	−	0.0291965i
$521$	5.23208	+	3.80133i	0.229222	+	0.166539i	0.696468	−	0.717588i	$-0.254754\pi$
$521$	5.23208	+	3.80133i	0.229222	+	0.166539i	−0.467246	+	0.884127i	$0.654754\pi$
$522$	0.818070	+	0.208597i	0.0358059	+	0.00913002i
$523$	−2.66677	−	8.20749i	−0.116610	−	0.358888i	0.875670	−	0.482911i	$-0.160420\pi$
$523$	−2.66677	−	8.20749i	−0.116610	−	0.358888i	−0.992279	+	0.124023i	$0.960420\pi$
$524$	−0.244470	+	1.30510i	−0.0106797	+	0.0570136i
$525$	−20.6380	−	28.4058i	−0.900717	−	1.23973i
$526$	6.08262	−	5.04903i	0.265215	−	0.220148i
$527$	3.62145			0.157753
$528$	−11.1624	+	21.8762i	−0.485780	+	0.952038i
$529$	−56.0836			−2.43842
$530$	3.59483	−	2.98398i	0.156150	−	0.129616i
$531$	3.04386	+	4.18952i	0.132092	+	0.181810i
$532$	2.33242	−	12.4516i	0.101123	−	0.539846i
$533$	1.30509	+	4.01666i	0.0565298	+	0.173981i
$534$	−24.5950	−	6.27138i	−1.06433	−	0.271389i
$535$	5.16100	+	3.74969i	0.223130	+	0.162113i
$536$	−33.8451	+	18.8267i	−1.46188	+	0.813192i
$537$	−5.42793	+	16.7054i	−0.234232	+	0.720893i
$538$	−18.4764	−	11.6825i	−0.796575	−	0.503667i
$539$	11.8379	−	26.8226i	0.509895	−	1.15533i
$540$	−4.16726	+	1.97790i	−0.179330	+	0.0851154i
$541$	3.29304	+	1.06997i	0.141579	+	0.0460018i	0.378949	−	0.925417i	$-0.376285\pi$
$541$	3.29304	+	1.06997i	0.141579	+	0.0460018i	−0.237370	+	0.971419i	$0.576285\pi$
$542$	−1.35518	+	0.0875214i	−0.0582100	+	0.00375937i
$543$	−1.94701	+	2.67984i	−0.0835544	+	0.115003i
$544$	16.1415	−	11.9336i	0.692062	−	0.511649i
$545$	−2.74390	+	0.891549i	−0.117536	+	0.0381898i
$546$	3.85182	+	9.68157i	0.164843	+	0.414333i
$547$	−6.56940	+	4.77295i	−0.280887	+	0.204077i	−0.719304	−	0.694695i	$-0.755539\pi$
$547$	−6.56940	+	4.77295i	−0.280887	+	0.204077i	0.438417	+	0.898772i	$0.355539\pi$
$548$	18.7589	−	2.43315i	0.801339	−	0.103939i
$549$			2.65936i			0.113499i
$550$	18.5567	−	12.4608i	0.791262	−	0.531332i
$551$		−	2.22462i		−	0.0947721i
$552$	42.2306	+	19.6157i	1.79746	+	0.834901i
$553$	25.9648	−	18.8646i	1.10414	−	0.802202i
$554$	−12.7248	+	5.06259i	−0.540627	+	0.215089i
$555$	−9.69578	+	3.15035i	−0.411563	+	0.133725i
$556$	24.9521	−	23.5881i	1.05820	−	1.00036i
$557$	9.01000	−	12.4012i	0.381766	−	0.525456i	−0.574285	−	0.818655i	$-0.694720\pi$
$557$	9.01000	−	12.4012i	0.381766	−	0.525456i	0.956051	+	0.293199i	$0.0947199\pi$
$558$	−0.0397246	−	0.615096i	−0.00168168	−	0.0260391i
$559$	−10.8335	−	3.52000i	−0.458206	−	0.148880i
$560$	4.87417	−	5.97223i	0.205971	−	0.252373i
$561$	−4.59916	−	21.2969i	−0.194177	−	0.899155i
$562$	−9.29185	+	14.6955i	−0.391953	+	0.619893i
$563$	4.76482	−	14.6646i	0.200813	−	0.618039i	−0.799046	−	0.601270i	$-0.794662\pi$
$563$	4.76482	−	14.6646i	0.200813	−	0.618039i	0.999859	−	0.0167696i	$-0.00533819\pi$
$564$	19.4710	+	10.6202i	0.819878	+	0.447191i
$565$	−1.59127	−	1.15613i	−0.0669453	−	0.0486386i
$566$	1.85756	−	7.28495i	0.0780792	−	0.306209i
$567$	−12.4202	−	38.2256i	−0.521601	−	1.60532i
$568$	−8.46228	−	7.86761i	−0.355069	−	0.330117i
$569$	−0.0417104	−	0.0574094i	−0.00174859	−	0.00240673i	0.808142	−	0.588988i	$-0.200473\pi$
$569$	−0.0417104	−	0.0574094i	−0.00174859	−	0.00240673i	−0.809890	+	0.586581i	$0.800473\pi$
$570$	−1.28864	−	1.55244i	−0.0539752	−	0.0650246i
$571$	15.5231			0.649622			0.324811	−	0.945779i	$-0.394699\pi$
$571$	15.5231			0.649622			0.324811	+	0.945779i	$0.394699\pi$
$572$	−6.24981	+	2.22257i	−0.261318	+	0.0929305i
$573$	15.5166			0.648217
$574$	15.1827	+	18.2908i	0.633714	+	0.763443i
$575$	−24.9099	−	34.2856i	−1.03882	−	1.42981i
$576$	−2.20396	−	2.61070i	−0.0918318	−	0.108779i
$577$	10.2447	+	31.5300i	0.426494	+	1.31261i	0.901557	+	0.432661i	$0.142425\pi$
$577$	10.2447	+	31.5300i	0.426494	+	1.31261i	−0.475063	+	0.879952i	$0.657575\pi$
$578$	1.54009	−	6.03991i	0.0640594	−	0.251227i
$579$	10.5040	+	7.63159i	0.436531	+	0.317158i
$580$	0.648211	−	1.18843i	0.0269155	−	0.0493468i
$581$	−16.9390	+	52.1329i	−0.702749	+	2.16284i
$582$	6.78923	−	10.7375i	0.281423	−	0.445084i
$583$	−19.5588	+	11.3772i	−0.810044	+	0.471195i
$584$	−2.63858	−	0.319977i	−0.109185	−	0.0132408i
$585$	0.196680	+	0.0639052i	0.00813171	+	0.00264215i
$586$	−1.33768	−	20.7126i	−0.0552589	−	0.855628i
$587$	17.6100	−	24.2381i	0.726844	−	1.00041i	−0.272425	−	0.962177i	$-0.587826\pi$
$587$	17.6100	−	24.2381i	0.726844	−	1.00041i	0.999269	−	0.0382376i	$-0.0121744\pi$
$588$	22.4841	+	23.7843i	0.927228	+	0.980847i
$589$	−1.54469	+	0.501899i	−0.0636477	+	0.0206804i
$590$	7.71536	−	3.06956i	0.317636	−	0.126372i
$591$	25.3795	−	18.4393i	1.04397	−	0.758491i
$592$	24.6301	+	38.2466i	1.01229	+	1.57192i
$593$		−	3.95279i		−	0.162322i	−0.996701	−	0.0811608i	$-0.974137\pi$
$593$		−	3.95279i		−	0.162322i	0.996701	−	0.0811608i	$-0.0258627\pi$
$594$	21.4881	−	6.11349i	0.881669	−	0.250840i
$595$			6.83881i			0.280364i
$596$	3.16972	+	24.4376i	0.129837	+	1.00100i
$597$	−4.92743	+	3.57999i	−0.201666	+	0.146519i
$598$	4.64912	+	11.6856i	0.190117	+	0.477859i
$599$	−5.44181	+	1.76815i	−0.222346	+	0.0722448i	−0.418072	−	0.908414i	$-0.637294\pi$
$599$	−5.44181	+	1.76815i	−0.222346	+	0.0722448i	0.195725	+	0.980659i	$0.437294\pi$
$600$	4.79778	+	24.4871i	0.195868	+	0.999682i
$601$	12.2772	−	16.8981i	0.500797	−	0.689288i	−0.481537	−	0.876426i	$-0.659921\pi$
$601$	12.2772	−	16.8981i	0.500797	−	0.689288i	0.982334	+	0.187138i	$0.0599211\pi$
$602$	−63.9806	+	4.13205i	−2.60765	+	0.168410i
$603$	−5.56164	−	1.80709i	−0.226487	−	0.0735902i
$604$	−9.56407	−	20.1506i	−0.389157	−	0.819917i
$605$	4.85181	−	2.19805i	0.197254	−	0.0893634i
$606$	35.0697	+	22.1743i	1.42461	+	0.900768i
$607$	−1.38321	+	4.25710i	−0.0561429	+	0.172790i	−0.975196	−	0.221344i	$-0.928956\pi$
$607$	−1.38321	+	4.25710i	−0.0561429	+	0.172790i	0.919053	+	0.394134i	$0.128956\pi$
$608$	−5.23109	+	7.32721i	−0.212149	+	0.297158i
$609$	8.33191	+	6.05349i	0.337626	+	0.245300i
$610$	4.13196	+	1.05359i	0.167298	+	0.0426587i
$611$	1.85111	+	5.69714i	0.0748881	+	0.230482i
$612$	2.97922	+	0.558064i	0.120428	+	0.0225584i
$613$	−4.42609	−	6.09199i	−0.178768	−	0.246053i	0.710224	−	0.703976i	$-0.248594\pi$
$613$	−4.42609	−	6.09199i	−0.178768	−	0.246053i	−0.888992	+	0.457923i	$0.848594\pi$
$614$	−0.781931	+	0.649061i	−0.0315562	+	0.0261940i
$615$	3.78590			0.152662
$616$	−28.0607	+	24.6274i	−1.13060	+	0.992267i
$617$	6.63332			0.267047			0.133524	−	0.991046i	$-0.457371\pi$
$617$	6.63332			0.267047			0.133524	+	0.991046i	$0.457371\pi$
$618$	−6.31270	+	5.24001i	−0.253934	+	0.210784i
$619$	−13.8904	−	19.1185i	−0.558302	−	0.768436i	0.432808	−	0.901486i	$-0.357523\pi$
$619$	−13.8904	−	19.1185i	−0.558302	−	0.768436i	−0.991109	+	0.133050i	$0.957523\pi$
$620$	−0.971439	−	0.181969i	−0.0390139	−	0.00730804i
$621$	−13.0892	−	40.2845i	−0.525253	−	1.61656i
$622$	−20.6246	−	5.25898i	−0.826970	−	0.210866i
$623$	−31.2163	−	22.6800i	−1.25066	−	0.908655i
$624$	0.415838	−	7.39326i	0.0166469	−	0.295967i
$625$	6.65556	−	20.4837i	0.266223	−	0.819349i
$626$	39.1142	+	24.7316i	1.56332	+	0.988473i
$627$	4.91327	+	8.44654i	0.196217	+	0.337322i
$628$	9.27024	+	19.5316i	0.369923	+	0.779394i
$629$	−38.3821	−	12.4711i	−1.53039	−	0.497255i
$630$	1.16156	−	0.0750167i	0.0462776	−	0.00298874i
$631$	10.4343	−	14.3616i	0.415383	−	0.571726i	−0.549138	−	0.835732i	$-0.685044\pi$
$631$	10.4343	−	14.3616i	0.415383	−	0.571726i	0.964521	+	0.264006i	$0.0850439\pi$
$632$	−22.3829	+	4.38549i	−0.890344	+	0.174446i
$633$	36.4824	−	11.8539i	1.45005	−	0.471149i
$634$	9.60130	+	24.1329i	0.381316	+	0.958440i
$635$	1.73628	−	1.26148i	0.0689020	−	0.0500603i
$636$	−3.24911	−	25.0497i	−0.128836	−	0.993286i
$637$			8.83993i			0.350251i
$638$	−4.04716	+	5.15807i	−0.160229	+	0.204210i
$639$		−	1.74468i		−	0.0690185i
$640$	−4.92954	+	2.39007i	−0.194857	+	0.0944760i
$641$	22.1529	−	16.0951i	0.874989	−	0.635717i	−0.0569322	−	0.998378i	$-0.518132\pi$
$641$	22.1529	−	16.0951i	0.874989	−	0.635717i	0.931921	+	0.362661i	$0.118132\pi$
$642$	32.0477	−	12.7502i	1.26482	−	0.503211i
$643$	13.2701	−	4.31172i	0.523322	−	0.170038i	−0.0354302	−	0.999372i	$-0.511280\pi$
$643$	13.2701	−	4.31172i	0.523322	−	0.170038i	0.558753	+	0.829334i	$0.311280\pi$
$644$	48.6278	+	51.4398i	1.91620	+	2.02701i
$645$	−6.00191	+	8.26092i	−0.236325	+	0.325273i
$646$	−0.514744	−	7.97030i	−0.0202523	−	0.313587i
$647$	−14.6113	−	4.74750i	−0.574429	−	0.186643i	0.00737419	−	0.999973i	$-0.497653\pi$
$647$	−14.6113	−	4.74750i	−0.574429	−	0.186643i	−0.581803	+	0.813329i	$0.697653\pi$
$648$	−3.43871	+	28.3561i	−0.135085	+	1.11393i
$649$	−39.3097	+	8.48910i	−1.54304	+	0.333227i
$650$	−3.60173	+	5.69631i	−0.141271	+	0.223428i
$651$	2.32352	−	7.15107i	0.0910661	−	0.280273i
$652$	−20.5805	+	37.7323i	−0.805996	+	1.47771i
$653$	−2.42694	−	1.76328i	−0.0949736	−	0.0690024i	0.539285	−	0.842123i	$-0.318695\pi$
$653$	−2.42694	−	1.76328i	−0.0949736	−	0.0690024i	−0.634259	+	0.773121i	$0.718695\pi$
$654$	−3.85416	+	15.1152i	−0.150710	+	0.591050i
$655$	0.0993422	+	0.305744i	0.00388162	+	0.0119464i
$656$	−4.30988	−	16.3344i	−0.168272	−	0.637753i
$657$	−0.235895	−	0.324682i	−0.00920315	−	0.0126670i
$658$	21.5348	+	25.9433i	0.839515	+	1.01137i
$659$	−19.7132			−0.767918			−0.383959	−	0.923350i	$-0.625440\pi$
$659$	−19.7132			−0.767918			−0.383959	+	0.923350i	$0.625440\pi$
$660$	0.163591	+	5.94390i	0.00636779	+	0.231366i
$661$	−28.2574			−1.09908			−0.549542	−	0.835466i	$-0.685198\pi$
$661$	−28.2574			−1.09908			−0.549542	+	0.835466i	$0.685198\pi$
$662$	6.85711	+	8.26084i	0.266509	+	0.321067i
$663$	3.86132	+	5.31466i	0.149961	+	0.206404i
$664$	26.5254	−	28.5303i	1.02938	−	1.10719i
$665$	−0.947796	−	2.91702i	−0.0367540	−	0.113117i
$666$	−1.69717	+	6.65593i	−0.0657640	+	0.257912i
$667$	10.0566	+	7.30652i	0.389391	+	0.282909i
$668$	−33.4657	−	18.2534i	−1.29483	−	0.706246i
$669$	−5.57002	+	17.1428i	−0.215350	+	0.662778i
$670$	−5.01117	+	7.92542i	−0.193599	+	0.306186i
$671$	−18.8940	−	8.33869i	−0.729394	−	0.321912i
$672$	−13.2082	−	39.5304i	−0.509518	−	1.52492i
$673$	−6.60656	−	2.14660i	−0.254664	−	0.0827453i	0.178903	−	0.983867i	$-0.442745\pi$
$673$	−6.60656	−	2.14660i	−0.254664	−	0.0827453i	−0.433567	+	0.901121i	$0.642745\pi$
$674$	0.639385	+	9.90025i	0.0246282	+	0.381343i
$675$	13.3419	−	18.3636i	0.513531	−	0.706814i
$676$	1.45338	−	1.37393i	0.0558992	−	0.0528435i
$677$	−17.0477	+	5.53915i	−0.655198	+	0.212887i	−0.617705	−	0.786410i	$-0.711937\pi$
$677$	−17.0477	+	5.53915i	−0.655198	+	0.212887i	−0.0374933	+	0.999297i	$0.511937\pi$
$678$	−9.88115	+	3.93123i	−0.379483	+	0.150978i
$679$	15.6240	−	11.3515i	0.599594	−	0.435631i
$680$	2.04740	−	4.40785i	0.0785143	−	0.169033i
$681$			52.3336i			2.00543i
$682$	4.49464	+	1.64647i	0.172109	+	0.0630464i
$683$			18.8182i			0.720057i	0.932941	+	0.360028i	$0.117233\pi$
$683$			18.8182i			0.720057i	−0.932941	+	0.360028i	$0.882767\pi$
$684$	−1.34809	+	0.174857i	−0.0515457	+	0.00668581i
$685$	3.70514	−	2.69195i	0.141566	−	0.102854i
$686$	3.82829	+	9.62242i	0.146165	+	0.367386i
$687$	19.7176	−	6.40663i	0.752273	−	0.244428i
$688$	42.4747	+	16.4913i	1.61933	+	0.628724i
$689$	4.01007	−	5.51939i	0.152772	−	0.210272i
$690$	11.2503	−	0.726576i	0.428292	−	0.0276603i
$691$	38.5752	+	12.5338i	1.46747	+	0.476810i	0.930343	−	0.366691i	$-0.119509\pi$
$691$	38.5752	+	12.5338i	1.46747	+	0.476810i	0.537128	+	0.843501i	$0.319509\pi$
$692$	−5.37218	+	2.54979i	−0.204220	+	0.0969286i
$693$	−5.60840	−	0.571050i	−0.213045	−	0.0216924i
$694$	−22.4215	−	14.1769i	−0.851107	−	0.538148i
$695$	2.56897	−	7.90646i	0.0974464	−	0.299909i
$696$	−3.55791	−	6.39609i	−0.134862	−	0.242443i
$697$	12.1247	+	8.80913i	0.459257	+	0.333670i
$698$	−40.9632	−	10.4450i	−1.55048	−	0.395351i
$699$	0.721033	+	2.21911i	0.0272720	+	0.0839345i
$700$	−6.98409	+	37.2845i	−0.263974	+	1.40922i
$701$	−3.40742	−	4.68991i	−0.128697	−	0.177136i	0.739806	−	0.672820i	$-0.234917\pi$
$701$	−3.40742	−	4.68991i	−0.128697	−	0.177136i	−0.868503	+	0.495685i	$0.834917\pi$
$702$	−5.18306	+	4.30232i	−0.195622	+	0.162381i
$703$	18.0998			0.682648
$704$	25.4591	−	7.47239i	0.959524	−	0.281626i
$705$	5.36983			0.202240
$706$	−23.0636	+	19.1445i	−0.868009	+	0.720512i
$707$	37.0751	+	51.0295i	1.39435	+	1.91916i
$708$	8.26581	−	44.1270i	0.310648	−	1.65839i
$709$	−1.08470	−	3.33835i	−0.0407366	−	0.125374i	0.928620	−	0.371032i	$-0.120996\pi$
$709$	−1.08470	−	3.33835i	−0.0407366	−	0.125374i	−0.969357	+	0.245658i	$0.920996\pi$
$710$	−2.71079	−	0.691213i	−0.101734	−	0.0259408i
$711$	−2.78621	−	2.02430i	−0.104491	−	0.0759173i
$712$	13.3301	+	23.9636i	0.499565	+	0.898073i
$713$	2.80448	−	8.63129i	0.105028	−	0.323244i
$714$	31.2520	+	19.7603i	1.16958	+	0.739512i
$715$	−1.07074	+	1.19697i	−0.0400433	+	0.0447642i
$716$	17.1437	−	8.13688i	0.640689	−	0.304089i
$717$	50.2691	+	16.3334i	1.87733	+	0.609983i
$718$	−34.5432	+	2.23089i	−1.28914	+	0.0832562i
$719$	5.47709	−	7.53857i	0.204261	−	0.281141i	−0.694580	−	0.719415i	$-0.744410\pi$
$719$	5.47709	−	7.53857i	0.204261	−	0.281141i	0.898842	+	0.438274i	$0.144410\pi$
$720$	−0.771123	−	0.299397i	−0.0287381	−	0.0111579i
$721$	−11.8615	+	3.85403i	−0.441745	+	0.143532i
$722$	−8.60885	−	21.6384i	−0.320388	−	0.805297i
$723$	−6.64254	+	4.82609i	−0.247039	+	0.179484i
$724$	3.54892	−	0.460318i	0.131894	−	0.0171076i
$725$			6.66130i			0.247395i
$726$	3.97438	−	28.5229i	0.147503	−	1.05858i
$727$			43.6030i			1.61715i	0.588396	+	0.808573i	$0.299759\pi$
$727$			43.6030i			1.61715i	−0.588396	+	0.808573i	$0.700241\pi$
$728$	4.74216	−	10.2094i	0.175756	−	0.378385i
$729$	17.9115	−	13.0135i	0.663389	−	0.481981i
$730$	−0.597930	+	0.237887i	−0.0221304	+	0.00880459i
$731$	−38.4435	+	12.4910i	−1.42188	+	0.461998i
$732$	16.7538	−	15.8379i	0.619237	−	0.585386i
$733$	28.7873	−	39.6223i	1.06328	−	1.46348i	0.186587	−	0.982438i	$-0.440257\pi$
$733$	28.7873	−	39.6223i	1.06328	−	1.46348i	0.876696	−	0.481045i	$-0.159743\pi$
$734$	−1.37153	−	21.2368i	−0.0506242	−	0.783866i
$735$	7.53642	+	2.44873i	0.277985	+	0.0903228i
$736$	−15.9422	−	47.7129i	−0.587639	−	1.75872i
$737$	30.2779	−	33.8475i	1.11530	−	1.24679i
$738$	1.36322	−	2.15599i	0.0501807	−	0.0793632i
$739$	8.90772	−	27.4151i	0.327676	−	1.00848i	−0.642542	−	0.766250i	$-0.722120\pi$
$739$	8.90772	−	27.4151i	0.327676	−	1.00848i	0.970218	−	0.242232i	$-0.0778796\pi$
$740$	9.66921	+	5.27393i	0.355447	+	0.193874i
$741$	−2.38357	−	1.73176i	−0.0875625	−	0.0636179i
$742$	9.48776	−	37.2089i	0.348306	−	1.36598i
$743$	−7.93497	−	24.4213i	−0.291106	−	0.895931i	−0.984502	−	0.175374i	$-0.943886\pi$
$743$	−7.93497	−	24.4213i	−0.291106	−	0.895931i	0.693396	−	0.720557i	$-0.256114\pi$
$744$	−3.63848	+	3.91349i	−0.133393	+	0.143476i
$745$	3.50686	+	4.82677i	0.128481	+	0.176839i
$746$	−1.13166	−	1.36333i	−0.0414331	−	0.0499149i
$747$	5.88213			0.215216
$748$	−13.3065	+	19.4166i	−0.486535	+	0.709942i
$749$	52.4330			1.91586
$750$	7.90714	+	9.52583i	0.288728	+	0.347834i
$751$	26.0941	+	35.9154i	0.952187	+	1.31057i	0.950549	+	0.310574i	$0.100521\pi$
$751$	26.0941	+	35.9154i	0.952187	+	1.31057i	0.00163746	+	0.999999i	$0.499479\pi$
$752$	−6.11304	−	23.1684i	−0.222920	−	0.844865i
$753$	10.3094	+	31.7291i	0.375696	+	1.15627i
$754$	0.488429	−	1.91551i	0.0177875	−	0.0697588i
$755$	−4.36898	−	3.17425i	−0.159004	−	0.115523i
$756$	−18.1545	+	33.2845i	−0.660274	+	1.21054i
$757$	10.1404	−	31.2091i	0.368560	−	1.13431i	−0.579161	−	0.815213i	$-0.696620\pi$
$757$	10.1404	−	31.2091i	0.368560	−	1.13431i	0.947721	−	0.319099i	$-0.103380\pi$
$758$	−5.62489	+	8.89604i	−0.204305	+	0.323119i
$759$	−54.3203	−	5.53092i	−1.97170	−	0.200760i
$760$	−0.262410	+	2.16387i	−0.00951861	+	0.0784917i
$761$	−38.1560	−	12.3976i	−1.38315	−	0.449414i	−0.479448	−	0.877570i	$-0.659163\pi$
$761$	−38.1560	−	12.3976i	−1.38315	−	0.449414i	−0.903705	+	0.428157i	$0.859163\pi$
$762$	−0.747830	−	11.5794i	−0.0270910	−	0.419478i
$763$	−13.9383	+	19.1844i	−0.504600	+	0.694523i
$764$	−11.5160	−	12.1819i	−0.416633	−	0.440726i
$765$	0.697936	−	0.226773i	0.0252339	−	0.00819900i
$766$	−17.0442	+	6.78106i	−0.615833	+	0.245010i
$767$	9.80976	−	7.12721i	0.354210	−	0.257349i
$768$	−3.32146	+	29.4330i	−0.119853	+	1.06207i
$769$		−	49.1101i		−	1.77096i	−0.464680	−	0.885479i	$-0.653831\pi$
$769$		−	49.1101i		−	1.77096i	0.464680	−	0.885479i	$-0.346169\pi$
$770$	−3.10922	+	8.48777i	−0.112048	+	0.305878i
$771$			5.98706i			0.215619i
$772$	−1.80428	−	13.9105i	−0.0649374	−	0.500648i
$773$	−22.2089	+	16.1357i	−0.798800	+	0.580362i	−0.910562	−	0.413373i	$-0.864351\pi$
$773$	−22.2089	+	16.1357i	−0.798800	+	0.580362i	0.111762	+	0.993735i	$0.464351\pi$
$774$	2.54328	+	6.39254i	0.0914162	+	0.229775i
$775$	4.62534	−	1.50286i	0.166147	−	0.0539844i
$776$	−13.4686	+	2.63891i	−0.483495	+	0.0947315i
$777$	−49.2520	+	67.7895i	−1.76690	+	2.43194i
$778$	−33.5889	+	2.16926i	−1.20422	+	0.0777718i
$779$	−6.39253	−	2.07706i	−0.229036	−	0.0744184i
$780$	−0.768737	−	1.61966i	−0.0275252	−	0.0579931i
$781$	12.3955	+	5.47063i	0.443545	+	0.195755i
$782$	37.7209	+	23.8506i	1.34890	+	0.852896i
$783$	−2.05740	+	6.33204i	−0.0735256	+	0.226289i
$784$	1.98569	−	35.3039i	0.0709175	−	1.26085i
$785$	4.23476	+	3.07673i	0.151145	+	0.109813i
$786$	1.68423	+	0.429456i	0.0600745	+	0.0153182i
$787$	11.1048	+	34.1772i	0.395845	+	1.21829i	0.928302	+	0.371828i	$0.121269\pi$
$787$	11.1048	+	34.1772i	0.395845	+	1.21829i	−0.532457	+	0.846457i	$0.678731\pi$
$788$	−33.3123	−	6.24002i	−1.18670	−	0.222292i
$789$	−6.08239	−	8.37169i	−0.216539	−	0.298040i
$790$	−4.24910	+	3.52706i	−0.151176	+	0.125487i
$791$	−16.1665			−0.574813
$792$	3.44384	+	2.04710i	0.122372	+	0.0727407i
$793$	6.22689			0.221123
$794$	−8.55032	+	7.09740i	−0.303440	+	0.251877i
$795$	−3.59470	−	4.94768i	−0.127491	−	0.175476i
$796$	6.46758	+	1.21150i	0.229237	+	0.0429405i
$797$	−0.694051	−	2.13607i	−0.0245846	−	0.0756635i	0.938011	−	0.346604i	$-0.112665\pi$
$797$	−0.694051	−	2.13607i	−0.0245846	−	0.0756635i	−0.962596	+	0.270941i	$0.912665\pi$
$798$	−16.0688	−	4.09732i	−0.568829	−	0.145043i
$799$	17.1975	+	12.4947i	0.608402	+	0.442030i
$800$	15.6637	−	21.9403i	0.553797	−	0.775705i
$801$	−1.27949	+	3.93785i	−0.0452084	+	0.139137i
$802$	13.1518	+	8.31579i	0.464408	+	0.293641i
$803$	3.04645	−	0.657894i	0.107507	−	0.0232166i
$804$	21.7381	+	45.8001i	0.766643	+	1.61525i
$805$	16.2995	+	5.29603i	0.574482	+	0.186660i
$806$	−1.44025	+	0.0930153i	−0.0507306	+	0.00327632i
$807$	−16.8196	+	23.1502i	−0.592077	+	0.814924i
$808$	−8.61894	−	43.9898i	−0.303213	−	1.54756i
$809$	18.0848	−	5.87610i	0.635827	−	0.206593i	0.0266723	−	0.999644i	$-0.491509\pi$
$809$	18.0848	−	5.87610i	0.635827	−	0.206593i	0.609154	+	0.793052i	$0.291509\pi$
$810$	2.55651	+	6.42579i	0.0898265	+	0.225779i
$811$	−8.53880	+	6.20380i	−0.299838	+	0.217845i	−0.727524	−	0.686082i	$-0.759329\pi$
$811$	−8.53880	+	6.20380i	−0.299838	+	0.217845i	0.427686	+	0.903927i	$0.359329\pi$
$812$	−1.43118	−	11.0340i	−0.0502245	−	0.387217i
$813$			1.77766i			0.0623452i
$814$	−41.9668	−	32.9282i	−1.47094	−	1.15413i
$815$			10.4060i			0.364507i
$816$	−14.2271	−	22.0924i	−0.498048	−	0.773390i
$817$	14.6665	−	10.6558i	0.513115	−	0.372800i
$818$	29.5656	−	11.7627i	1.03374	−	0.411274i
$819$	1.61655	−	0.525248i	0.0564867	−	0.0183536i
$820$	−2.80978	−	2.97225i	−0.0981216	−	0.103796i
$821$	−10.9835	+	15.1175i	−0.383327	+	0.527604i	−0.956462	−	0.291857i	$-0.905727\pi$
$821$	−10.9835	+	15.1175i	−0.383327	+	0.527604i	0.573135	+	0.819461i	$0.305727\pi$
$822$	−1.59584	−	24.7100i	−0.0556613	−	0.861860i
$823$	10.1680	+	3.30377i	0.354433	+	0.115162i	0.480821	−	0.876819i	$-0.340339\pi$
$823$	10.1680	+	3.30377i	0.354433	+	0.115162i	−0.126389	+	0.991981i	$0.540339\pi$
$824$	8.79895	+	1.06704i	0.306526	+	0.0371721i
$825$	−14.7121	−	25.2919i	−0.512209	−	0.880552i
$826$	36.4735	−	57.6847i	1.26908	−	2.00711i
$827$	5.75524	−	17.7128i	0.200129	−	0.615934i	−0.799749	−	0.600334i	$-0.795034\pi$
$827$	5.75524	−	17.7128i	0.200129	−	0.615934i	0.999878	−	0.0156000i	$-0.00496584\pi$
$828$	3.63721	−	6.66845i	0.126402	−	0.231745i
$829$	−0.539984	−	0.392322i	−0.0187544	−	0.0136259i	0.578369	−	0.815776i	$-0.303690\pi$
$829$	−0.539984	−	0.392322i	−0.0187544	−	0.0136259i	−0.597123	+	0.802150i	$0.703690\pi$
$830$	2.33040	−	9.13932i	0.0808894	−	0.317230i
$831$	5.53974	+	17.0496i	0.192172	+	0.591443i
$832$	−6.11297	+	5.16058i	−0.211929	+	0.178911i
$833$	18.4384	+	25.3783i	0.638852	+	0.879305i
$834$	−28.7081	−	34.5849i	−0.994079	−	1.19758i
$835$	−9.22937			−0.319396
$836$	2.98478	−	10.1261i	0.103231	−	0.350219i
$837$	4.86088			0.168017
$838$	20.8676	+	25.1395i	0.720860	+	0.868429i
$839$	8.60919	+	11.8495i	0.297222	+	0.409092i	0.931343	−	0.364142i	$-0.118638\pi$
$839$	8.60919	+	11.8495i	0.297222	+	0.409092i	−0.634121	+	0.773234i	$0.718638\pi$
$840$	−7.39031	−	6.87097i	−0.254990	−	0.237071i
$841$	8.35771	+	25.7224i	0.288197	+	0.886979i
$842$	4.94405	−	19.3895i	0.170383	−	0.668205i
$843$	18.4129	+	13.3777i	0.634173	+	0.460754i
$844$	−36.3825	−	19.8443i	−1.25234	−	0.683069i
$845$	0.149634	−	0.460526i	0.00514757	−	0.0158426i
$846$	1.93356	−	3.05801i	0.0664770	−	0.105137i
$847$	21.6429	−	38.0555i	0.743657	−	1.30760i
$848$	−17.2548	+	21.1420i	−0.592532	+	0.726018i
$849$	−9.35962	−	3.04113i	−0.321221	−	0.104371i
$850$	1.54133	+	23.8659i	0.0528670	+	0.818593i
$851$	−59.4468	+	81.8215i	−2.03781	+	2.80480i
$852$	−10.9914	+	10.3905i	−0.376558	+	0.355974i
$853$	23.9681	−	7.78770i	0.820651	−	0.266646i	0.131549	−	0.991310i	$-0.458005\pi$
$853$	23.9681	−	7.78770i	0.820651	−	0.266646i	0.689103	+	0.724664i	$0.258005\pi$
$854$	32.5653	−	12.9561i	1.11436	−	0.443350i
$855$	−0.266268	+	0.193455i	−0.00910617	+	0.00661602i
$856$	−33.7949	−	15.6974i	−1.15509	−	0.536526i
$857$		−	55.4807i		−	1.89518i	−0.319482	−	0.947592i	$-0.603509\pi$
$857$		−	55.4807i		−	1.89518i	0.319482	−	0.947592i	$-0.396491\pi$
$858$	2.37609	+	8.35164i	0.0811183	+	0.285120i
$859$			47.4975i			1.62060i	0.586019	+	0.810298i	$0.300695\pi$
$859$			47.4975i			1.62060i	−0.586019	+	0.810298i	$0.699305\pi$
$860$	10.9400	−	1.41898i	0.373050	−	0.0483870i
$861$	25.1742	−	18.2901i	0.857933	−	0.623325i
$862$	4.58688	+	11.5291i	0.156230	+	0.392684i
$863$	22.9800	−	7.46667i	0.782250	−	0.254168i	0.109449	−	0.993992i	$-0.465091\pi$
$863$	22.9800	−	7.46667i	0.782250	−	0.254168i	0.672800	+	0.739824i	$0.265091\pi$
$864$	21.6659	−	16.0179i	0.737090	−	0.544939i
$865$	−0.846260	+	1.16478i	−0.0287737	+	0.0396036i
$866$	6.78913	−	0.438461i	0.230704	−	0.0148995i
$867$	−7.76000	−	2.52138i	−0.263544	−	0.0856305i
$868$	−7.33865	+	3.48314i	−0.249090	+	0.118225i
$869$	23.1185	−	13.4478i	0.784243	−	0.456187i
$870$	−1.49776	−	0.947019i	−0.0507787	−	0.0321070i
$871$	−4.23130	+	13.0226i	−0.143372	+	0.441254i
$872$	14.7272	−	8.19217i	0.498724	−	0.277422i
$873$	−1.67657	−	1.21810i	−0.0567432	−	0.0412264i
$874$	−19.3949	−	4.94543i	−0.656042	−	0.167282i
$875$	5.81571	+	17.8989i	0.196607	+	0.605094i
$876$	−0.640589	+	3.41978i	−0.0216435	+	0.115544i
$877$	−14.3028	−	19.6861i	−0.482971	−	0.664753i	0.496101	−	0.868265i	$-0.334764\pi$
$877$	−14.3028	−	19.6861i	−0.482971	−	0.664753i	−0.979072	+	0.203512i	$0.934764\pi$
$878$	−9.13084	+	7.57927i	−0.308151	+	0.255788i
$879$	−27.1697			−0.916411
$880$	4.54506	−	4.53982i	0.153214	−	0.153037i
$881$	−10.5601			−0.355778			−0.177889	−	0.984051i	$-0.556927\pi$
$881$	−10.5601			−0.355778			−0.177889	+	0.984051i	$0.556927\pi$
$882$	4.10820	−	3.41011i	0.138330	−	0.114824i
$883$	−22.0242	−	30.3137i	−0.741172	−	1.02014i	−0.998550	−	0.0538253i	$-0.982859\pi$
$883$	−22.0242	−	30.3137i	−0.741172	−	1.02014i	0.257378	−	0.966311i	$-0.417141\pi$
$884$	1.30671	−	6.97585i	0.0439493	−	0.234623i
$885$	−3.35887	−	10.3375i	−0.112907	−	0.347493i
$886$	−17.6381	−	4.49747i	−0.592563	−	0.151096i
$887$	−14.6460	−	10.6410i	−0.491766	−	0.357289i	0.314097	−	0.949391i	$-0.398298\pi$
$887$	−14.6460	−	10.6410i	−0.491766	−	0.357289i	−0.805863	+	0.592102i	$0.798298\pi$
$888$	52.0394	−	28.9476i	1.74633	−	0.971418i
$889$	5.45095	−	16.7763i	0.182819	−	0.562659i
$890$	5.61150	+	3.54810i	0.188098	+	0.118933i
$891$	−7.07021	−	32.7393i	−0.236861	−	1.09681i
$892$	17.5924	−	8.34989i	0.589039	−	0.279575i
$893$	−9.06703	−	2.94606i	−0.303417	−	0.0985860i
$894$	32.1902	−	2.07894i	1.07660	−	0.0695300i
$895$	2.70058	−	3.71703i	0.0902703	−	0.124246i
$896$	−21.2320	+	39.7078i	−0.709312	+	1.32655i
$897$	15.6571	−	5.08730i	0.522776	−	0.169860i
$898$	−11.0328	−	27.7311i	−0.368170	−	0.925397i
$899$	−1.15407	+	0.838481i	−0.0384904	+	0.0279649i
$900$	4.03667	−	0.523583i	0.134556	−	0.0174528i
$901$		−	24.2097i		−	0.806542i
$902$	11.0432	+	16.4456i	0.367699	+	0.547579i
$903$			83.9265i			2.79290i
$904$	10.4198	+	4.83992i	0.346559	+	0.160973i
$905$	0.700962	−	0.509279i	0.0233008	−	0.0169290i
$906$	−27.1296	+	10.7936i	−0.901322	+	0.358592i
$907$	−18.1079	+	5.88360i	−0.601262	+	0.195362i	−0.593803	−	0.804610i	$-0.702374\pi$
$907$	−18.1079	+	5.88360i	−0.601262	+	0.195362i	−0.00745867	+	0.999972i	$0.502374\pi$
$908$	41.0864	−	38.8404i	1.36350	−	1.28896i
$909$	3.97842	−	5.47583i	0.131956	−	0.181622i
$910$	−0.175652	−	2.71979i	−0.00582280	−	0.0901602i
$911$	−1.69776	−	0.551635i	−0.0562492	−	0.0182765i	0.280757	−	0.959779i	$-0.409414\pi$
$911$	−1.69776	−	0.551635i	−0.0562492	−	0.0182765i	−0.337006	+	0.941502i	$0.609414\pi$
$912$	9.13022	+	7.45153i	0.302332	+	0.246745i
$913$	−18.4440	+	41.7909i	−0.610408	+	1.38308i
$914$	8.16160	−	12.9080i	0.269962	−	0.426958i
$915$	1.72490	−	5.30869i	0.0570234	−	0.175500i
$916$	−19.6635	−	10.7252i	−0.649702	−	0.354370i
$917$	2.13765	+	1.55310i	0.0705915	+	0.0512878i
$918$	−5.90606	+	23.1623i	−0.194929	+	0.764469i
$919$	−8.67564	−	26.7009i	−0.286183	−	0.880781i	−0.986042	−	0.166499i	$-0.946754\pi$
$919$	−8.67564	−	26.7009i	−0.286183	−	0.880781i	0.699859	−	0.714281i	$-0.253246\pi$
$920$	−8.92006	−	8.29322i	−0.294086	−	0.273419i
$921$	0.781901	+	1.07619i	0.0257645	+	0.0354618i
$922$	−34.7215	−	41.8294i	−1.14349	−	1.37758i
$923$	−4.08518			−0.134465
$924$	29.8035	+	38.7334i	0.980462	+	1.27424i
$925$	−54.1973			−1.78199
$926$	10.7755	+	12.9813i	0.354104	+	0.426593i
$927$	0.786648	+	1.08273i	0.0258369	+	0.0355614i
$928$	−2.38091	+	7.54024i	−0.0781572	+	0.247521i
$929$	6.48791	+	19.9677i	0.212861	+	0.655120i	0.999299	+	0.0374498i	$0.0119234\pi$
$929$	6.48791	+	19.9677i	0.212861	+	0.655120i	−0.786437	+	0.617670i	$0.788077\pi$
$930$	−0.319661	+	1.25364i	−0.0104821	+	0.0411085i
$931$	−11.3819	−	8.26942i	−0.373026	−	0.271019i
$932$	1.20707	−	2.21303i	0.0395387	−	0.0724902i
$933$	−8.60979	+	26.4982i	−0.281872	+	0.867513i
$934$	10.1934	−	16.1214i	0.333539	−	0.527508i
$935$	−0.577292	+	5.66970i	−0.0188795	+	0.185419i
$936$	−1.19917	−	0.145422i	−0.0391961	−	0.00475326i
$937$	−26.5748	−	8.63466i	−0.868159	−	0.282082i	−0.159127	−	0.987258i	$-0.550868\pi$
$937$	−26.5748	−	8.63466i	−0.868159	−	0.282082i	−0.709032	+	0.705176i	$0.750868\pi$
$938$	4.96702	+	76.9093i	0.162179	+	2.51118i
$939$	35.6067	−	49.0085i	1.16198	−	1.59933i
$940$	−3.98533	−	4.21578i	−0.129987	−	0.137504i
$941$	46.0659	−	14.9677i	1.50171	−	0.487934i	0.561192	−	0.827686i	$-0.310343\pi$
$941$	46.0659	−	14.9677i	1.50171	−	0.487934i	0.940515	+	0.339752i	$0.110343\pi$
$942$	26.2962	−	10.4620i	0.856775	−	0.340869i
$943$	30.3850	−	22.0760i	0.989473	−	0.718894i
$944$	−40.7781	+	26.2603i	−1.32721	+	0.854700i
$945$			9.17938i			0.298605i
$946$	−53.3918	−	1.97520i	−1.73592	−	0.0642194i
$947$		−	42.0545i		−	1.36659i	−0.730143	−	0.683295i	$-0.760546\pi$
$947$		−	42.0545i		−	1.36659i	0.730143	−	0.683295i	$-0.239454\pi$
$948$	3.84045	+	29.6088i	0.124732	+	0.961648i
$949$	−0.760243	+	0.552349i	−0.0246785	+	0.0179300i
$950$	−3.96503	−	9.96611i	−0.128643	−	0.323343i
$951$	32.3348	−	10.5062i	1.04853	−	0.340688i
$952$	−7.68068	−	39.2010i	−0.248932	−	1.27051i
$953$	20.8764	−	28.7339i	0.676253	−	0.930782i	−0.323629	−	0.946184i	$-0.604903\pi$
$953$	20.8764	−	28.7339i	0.676253	−	0.930782i	0.999881	+	0.0154022i	$0.00490288\pi$
$954$	−4.11197	+	0.265563i	−0.133130	+	0.00859791i
$955$	−3.86003	−	1.25420i	−0.124908	−	0.0405849i
$956$	−24.4851	−	51.5878i	−0.791903	−	1.66847i
$957$	6.39656	+	5.72197i	0.206771	+	0.184965i
$958$	−28.0096	−	17.7102i	−0.904948	−	0.572191i
$959$	11.6321	−	35.7999i	0.375620	−	1.15604i
$960$	2.70628	+	6.64109i	0.0873447	+	0.214340i
$961$	−24.2369	−	17.6092i	−0.781837	−	0.568038i
$962$	15.5849	+	3.97393i	0.502476	+	0.128125i
$963$	−1.73867	−	5.35106i	−0.0560277	−	0.172436i
$964$	8.71879	+	1.63319i	0.280813	+	0.0526016i
$965$	−1.99619	−	2.74751i	−0.0642595	−	0.0884456i
$966$	71.2983	−	59.1828i	2.29398	−	1.90418i
$967$	28.9595			0.931275			0.465638	−	0.884976i	$-0.345825\pi$
$967$	28.9595			0.931275			0.465638	+	0.884976i	$0.345825\pi$
$968$	−25.3426	+	18.0486i	−0.814542	+	0.580104i
$969$	−10.4550			−0.335864
$970$	−2.55684	+	2.12237i	−0.0820951	+	0.0681451i
$971$	1.64266	+	2.26093i	0.0527155	+	0.0725567i	0.834561	−	0.550916i	$-0.185721\pi$
$971$	1.64266	+	2.26093i	0.0527155	+	0.0725567i	−0.781845	+	0.623472i	$0.785721\pi$
$972$	8.66147	+	1.62246i	0.277817	+	0.0520403i
$973$	−21.1148	−	64.9846i	−0.676909	−	2.08331i
$974$	39.6863	+	10.1195i	1.27163	+	0.324249i
$975$	7.13724	+	5.18551i	0.228575	+	0.166069i
$976$	−24.8683	−	1.39873i	−0.796014	−	0.0447723i
$977$	−13.6241	+	41.9305i	−0.435872	+	1.34148i	0.456318	+	0.889817i	$0.349168\pi$
$977$	−13.6241	+	41.9305i	−0.435872	+	1.34148i	−0.892190	+	0.451660i	$0.850832\pi$
$978$	47.5534	+	30.0676i	1.52059	+	0.961456i
$979$	−23.9654	−	21.4379i	−0.765936	−	0.685159i
$980$	−3.67083	−	7.73411i	−0.117260	−	0.247057i
$981$	2.42006	+	0.786326i	0.0772666	+	0.0251054i
$982$	−18.4308	+	1.19031i	−0.588150	+	0.0379844i
$983$	−13.7713	+	18.9545i	−0.439235	+	0.604555i	−0.970042	−	0.242938i	$-0.921889\pi$
$983$	−13.7713	+	18.9545i	−0.439235	+	0.604555i	0.530807	+	0.847493i	$0.321889\pi$
$984$	−21.7013	+	4.25195i	−0.691812	+	0.135547i
$985$	−7.80401	+	2.53568i	−0.248657	+	0.0807934i
$986$	−2.59318	−	6.51795i	−0.0825835	−	0.207574i
$987$	35.7065	−	25.9423i	1.13655	−	0.825752i
$988$	0.409427	+	3.15657i	0.0130256	+	0.100424i
$989$			101.299i			3.22111i
$990$	0.969322	+	0.0358595i	0.0308071	+	0.00113969i
$991$		−	4.79750i		−	0.152397i	−0.997093	−	0.0761987i	$-0.975722\pi$
$991$		−	4.79750i		−	0.152397i	0.997093	−	0.0761987i	$-0.0242783\pi$
$992$	5.77280	−	0.0479547i	0.183286	−	0.00152256i
$993$	11.3696	−	8.26052i	0.360804	−	0.262140i
$994$	−21.3646	+	8.49993i	−0.677644	+	0.269601i
$995$	1.51515	−	0.492301i	0.0480334	−	0.0156070i
$996$	−35.0313	−	37.0570i	−1.11001	−	1.17420i
$997$	−24.0857	+	33.1511i	−0.762800	+	1.04990i	0.234176	+	0.972194i	$0.424761\pi$
$997$	−24.0857	+	33.1511i	−0.762800	+	1.04990i	−0.996976	+	0.0777103i	$0.975239\pi$
$998$	−1.65786	−	25.6703i	−0.0524786	−	0.812578i
$999$	−51.5183	−	16.7393i	−1.62997	−	0.529609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.y.a.79.17	✓	288
4.3	odd	2	inner	572.2.y.a.79.31	yes	288
11.6	odd	10	inner	572.2.y.a.391.31	yes	288
44.39	even	10	inner	572.2.y.a.391.17	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.y.a.79.17	✓	288	1.1	even	1	trivial
572.2.y.a.79.31	yes	288	4.3	odd	2	inner
572.2.y.a.391.17	yes	288	44.39	even	10	inner
572.2.y.a.391.31	yes	288	11.6	odd	10	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.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08817 + 0.903263i) q^{2} +(1.08813 + 1.49768i) q^{3} +(0.368233 - 1.96581i) q^{4} +(-0.149634 - 0.460526i) q^{5} +(-2.53687 - 0.646867i) q^{6} +(-3.21984 - 2.33935i) q^{7} +(1.37494 + 2.47175i) q^{8} +(-0.131974 + 0.406174i) q^{9} +O(q^{10})\)	\(q+(-1.08817 + 0.903263i) q^{2} +(1.08813 + 1.49768i) q^{3} +(0.368233 - 1.96581i) q^{4} +(-0.149634 - 0.460526i) q^{5} +(-2.53687 - 0.646867i) q^{6} +(-3.21984 - 2.33935i) q^{7} +(1.37494 + 2.47175i) q^{8} +(-0.131974 + 0.406174i) q^{9} +(0.578804 + 0.365972i) q^{10} +(-2.47193 - 2.21124i) q^{11} +(3.34484 - 1.58756i) q^{12} +(0.951057 + 0.309017i) q^{13} +(5.61678 - 0.362748i) q^{14} +(0.526901 - 0.725216i) q^{15} +(-3.72881 - 1.44775i) q^{16} +(3.37491 - 1.09657i) q^{17} +(-0.223271 - 0.561194i) q^{18} +(-1.28755 + 0.935463i) q^{19} +(-0.960407 + 0.124571i) q^{20} -7.36781i q^{21} +(4.68721 + 0.173401i) q^{22} -8.89290i q^{23} +(-2.20578 + 4.74881i) q^{24} +(3.85539 - 2.80111i) q^{25} +(-1.31404 + 0.522791i) q^{26} +(4.52997 - 1.47188i) q^{27} +(-5.78437 + 5.46816i) q^{28} +(-0.821613 + 1.13085i) q^{29} +(0.0817030 + 1.26509i) q^{30} +(0.970583 + 0.315361i) q^{31} +(5.36528 - 1.79269i) q^{32} +(0.621948 - 6.10827i) q^{33} +(-2.68198 + 4.24169i) q^{34} +(-0.595535 + 1.83287i) q^{35} +(0.749863 + 0.409002i) q^{36} +(-9.20077 - 6.68475i) q^{37} +(0.556111 - 2.18094i) q^{38} +(0.572064 + 1.76063i) q^{39} +(0.932566 - 1.00305i) q^{40} +(2.48243 + 3.41678i) q^{41} +(6.65507 + 8.01744i) q^{42} -11.3910 q^{43} +(-5.25711 + 4.04509i) q^{44} +0.206801 q^{45} +(8.03262 + 9.67699i) q^{46} +(3.52103 + 4.84628i) q^{47} +(-1.88916 - 7.15991i) q^{48} +(2.73169 + 8.40727i) q^{49} +(-1.66519 + 6.53051i) q^{50} +(5.31466 + 3.86132i) q^{51} +(0.957679 - 1.75581i) q^{52} +(2.10822 - 6.48844i) q^{53} +(-3.59989 + 5.69340i) q^{54} +(-0.648447 + 1.46926i) q^{55} +(1.35519 - 11.1751i) q^{56} +(-2.80205 - 0.910442i) q^{57} +(-0.127402 - 1.97269i) q^{58} +(7.12721 - 9.80976i) q^{59} +(-1.23161 - 1.30283i) q^{60} +(5.92213 - 1.92422i) q^{61} +(-1.34101 + 0.533524i) q^{62} +(1.37512 - 0.999081i) q^{63} +(-4.21907 + 6.79702i) q^{64} -0.484226i q^{65} +(4.84059 + 7.20863i) q^{66} +13.6928i q^{67} +(-0.912903 - 7.03822i) q^{68} +(13.3187 - 9.67662i) q^{69} +(-1.00752 - 2.53240i) q^{70} +(-3.88523 + 1.26239i) q^{71} +(-1.18542 + 0.232259i) q^{72} +(-0.552349 + 0.760243i) q^{73} +(16.0501 - 1.03656i) q^{74} +(8.39033 + 2.72618i) q^{75} +(1.36482 + 2.87555i) q^{76} +(2.78636 + 12.9025i) q^{77} +(-2.21281 - 1.39914i) q^{78} +(-2.49192 + 7.66933i) q^{79} +(-0.108770 + 1.93385i) q^{80} +(8.17013 + 5.93595i) q^{81} +(-5.78756 - 1.47575i) q^{82} +(-4.25610 - 13.0989i) q^{83} +(-14.4837 - 2.71307i) q^{84} +(-1.01000 - 1.39015i) q^{85} +(12.3953 - 10.2890i) q^{86} -2.58768 q^{87} +(2.06686 - 9.15031i) q^{88} +9.69500 q^{89} +(-0.225035 + 0.186796i) q^{90} +(-2.33935 - 3.21984i) q^{91} +(-17.4817 - 3.27466i) q^{92} +(0.583809 + 1.79678i) q^{93} +(-8.20894 - 2.09317i) q^{94} +(0.623467 + 0.452975i) q^{95} +(8.52301 + 6.08480i) q^{96} +(-1.49948 + 4.61492i) q^{97} +(-10.5665 - 6.68112i) q^{98} +(1.22438 - 0.712208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) \) 288 * q - 4 * q^4 + 80 * q^9	\( 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) \) 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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