LMFDB - Embedded newform 572.2.bb.b.51.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(51,572)]

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, 7, 5]))

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

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

chi := DirichletCharacter("572.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bb (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:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.15
Character	$\chi$	$=$	572.51
Dual form			572.2.bb.b.415.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21395 + 0.725477i) q^{2} +(1.24296 + 0.403861i) q^{3} +(0.947367 - 1.76139i) q^{4} +(-1.74166 - 2.39719i) q^{5} +(-1.80188 + 0.411468i) q^{6} +(-2.61403 + 0.849351i) q^{7} +(0.127789 + 2.82554i) q^{8} +(-1.04521 - 0.759392i) q^{9} +O(q^{10})$	\(q+(-1.21395 + 0.725477i) q^{2} +(1.24296 + 0.403861i) q^{3} +(0.947367 - 1.76139i) q^{4} +(-1.74166 - 2.39719i) q^{5} +(-1.80188 + 0.411468i) q^{6} +(-2.61403 + 0.849351i) q^{7} +(0.127789 + 2.82554i) q^{8} +(-1.04521 - 0.759392i) q^{9} +(3.85340 + 1.64654i) q^{10} +(2.77621 + 1.81456i) q^{11} +(1.88889 - 1.80673i) q^{12} +(-1.27746 + 3.37166i) q^{13} +(2.55713 - 2.92749i) q^{14} +(-1.19668 - 3.68299i) q^{15} +(-2.20499 - 3.33737i) q^{16} +(-0.566486 - 0.779701i) q^{17} +(1.81976 + 0.163589i) q^{18} +(-3.91589 - 1.27235i) q^{19} +(-5.87238 + 0.796726i) q^{20} -3.59215 q^{21} +(-4.68662 - 0.188716i) q^{22} +6.59413i q^{23} +(-0.982289 + 3.56363i) q^{24} +(-1.16805 + 3.59489i) q^{25} +(-0.895279 - 5.01981i) q^{26} +(-3.29703 - 4.53798i) q^{27} +(-0.980410 + 5.40898i) q^{28} +(-8.73240 + 2.83733i) q^{29} +(4.12463 + 3.60282i) q^{30} +(-4.60793 - 3.34786i) q^{31} +(5.09794 + 2.45174i) q^{32} +(2.71788 + 3.37663i) q^{33} +(1.25334 + 0.535549i) q^{34} +(6.58881 + 4.78705i) q^{35} +(-2.32779 + 1.12161i) q^{36} +(0.309368 - 0.100520i) q^{37} +(5.67677 - 1.29631i) q^{38} +(-2.94951 + 3.67491i) q^{39} +(6.55079 - 5.22746i) q^{40} +(-3.19225 + 9.82475i) q^{41} +(4.36070 - 2.60602i) q^{42} +1.32576 q^{43} +(5.82625 - 3.17094i) q^{44} +3.82818i q^{45} +(-4.78389 - 8.00497i) q^{46} +(1.10843 - 3.41140i) q^{47} +(-1.39288 - 5.03871i) q^{48} +(0.448654 - 0.325966i) q^{49} +(-1.19005 - 5.21143i) q^{50} +(-0.389227 - 1.19792i) q^{51} +(4.72858 + 5.44431i) q^{52} +(-0.580121 - 0.421482i) q^{53} +(7.29465 + 3.11697i) q^{54} +(-0.485371 - 9.81546i) q^{55} +(-2.73392 - 7.27752i) q^{56} +(-4.35343 - 3.16295i) q^{57} +(8.54231 - 9.77954i) q^{58} +(1.13283 + 3.48648i) q^{59} +(-7.62088 - 1.38133i) q^{60} +(-7.60736 - 10.4706i) q^{61} +(8.02260 + 0.721196i) q^{62} +(3.37721 + 1.09732i) q^{63} +(-7.96734 + 0.722144i) q^{64} +(10.3074 - 2.80996i) q^{65} +(-5.74905 - 2.12731i) q^{66} +0.0932566 q^{67} +(-1.91003 + 0.259140i) q^{68} +(-2.66311 + 8.19622i) q^{69} +(-11.4714 - 1.03123i) q^{70} +(-4.60571 + 3.34624i) q^{71} +(2.01213 - 3.05033i) q^{72} +(-4.29864 - 13.2299i) q^{73} +(-0.302634 + 0.346466i) q^{74} +(-2.90367 + 3.99656i) q^{75} +(-5.95088 + 5.69203i) q^{76} +(-8.79832 - 2.38535i) q^{77} +(0.914513 - 6.60097i) q^{78} +(10.5103 + 7.63616i) q^{79} +(-4.15995 + 11.0983i) q^{80} +(-1.06765 - 3.28589i) q^{81} +(-3.25238 - 14.2427i) q^{82} +(9.73278 + 13.3960i) q^{83} +(-3.40308 + 6.32718i) q^{84} +(-0.882465 + 2.71595i) q^{85} +(-1.60941 + 0.961805i) q^{86} -11.9999 q^{87} +(-4.77235 + 8.07618i) q^{88} -10.8735i q^{89} +(-2.77725 - 4.64723i) q^{90} +(0.475612 - 9.89864i) q^{91} +(11.6148 + 6.24706i) q^{92} +(-4.37539 - 6.02220i) q^{93} +(1.12931 + 4.94543i) q^{94} +(3.77008 + 11.6031i) q^{95} +(5.34636 + 5.10626i) q^{96} +(7.91003 - 10.8872i) q^{97} +(-0.308164 + 0.721196i) q^{98} +(-1.52377 - 4.00484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) $ 304 * q - 14 * q^4 + 72 * q^9	$ 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) $ 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.21395	+	0.725477i	−0.858395	+	0.512990i
$2$	−1.21395	+	0.725477i	−0.858395	+	0.512990i
$3$	1.24296	+	0.403861i	0.717621	+	0.233169i	0.644992	−	0.764190i	$-0.276861\pi$
$3$	1.24296	+	0.403861i	0.717621	+	0.233169i	0.0726298	+	0.997359i	$0.476861\pi$
$4$	0.947367	−	1.76139i	0.473683	−	0.880695i
$5$	−1.74166	−	2.39719i	−0.778894	−	1.07206i	−0.995403	−	0.0957749i	$-0.969467\pi$
$5$	−1.74166	−	2.39719i	−0.778894	−	1.07206i	0.216509	−	0.976281i	$-0.430533\pi$
$6$	−1.80188	+	0.411468i	−0.735616	+	0.167981i
$7$	−2.61403	+	0.849351i	−0.988012	+	0.321024i	−0.758065	−	0.652179i	$-0.773855\pi$
$7$	−2.61403	+	0.849351i	−0.988012	+	0.321024i	−0.229947	+	0.973203i	$0.573855\pi$
$8$	0.127789	+	2.82554i	0.0451801	+	0.998979i
$9$	−1.04521	−	0.759392i	−0.348404	−	0.253131i
$10$	3.85340	+	1.64654i	1.21855	+	0.520682i
$11$	2.77621	+	1.81456i	0.837060	+	0.547111i
$11$	2.77621	+	1.81456i	0.837060	+	0.547111i
$12$	1.88889	−	1.80673i	0.545276	−	0.521557i
$13$	−1.27746	+	3.37166i	−0.354305	+	0.935130i
$13$	−1.27746	+	3.37166i	−0.354305	+	0.935130i
$14$	2.55713	−	2.92749i	0.683422	−	0.782405i
$15$	−1.19668	−	3.68299i	−0.308980	−	0.950944i
$16$	−2.20499	−	3.33737i	−0.551248	−	0.834341i
$17$	−0.566486	−	0.779701i	−0.137393	−	0.189105i	0.734776	−	0.678310i	$-0.237287\pi$
$17$	−0.566486	−	0.779701i	−0.137393	−	0.189105i	−0.872169	+	0.489204i	$0.837287\pi$
$18$	1.81976	+	0.163589i	0.428922	+	0.0385582i
$19$	−3.91589	−	1.27235i	−0.898366	−	0.291897i	−0.176804	−	0.984246i	$-0.556576\pi$
$19$	−3.91589	−	1.27235i	−0.898366	−	0.291897i	−0.721563	+	0.692349i	$0.756576\pi$
$20$	−5.87238	+	0.796726i	−1.31310	+	0.178153i
$21$	−3.59215			−0.783871
$22$	−4.68662	−	0.188716i	−0.999190	−	0.0402343i
$23$			6.59413i			1.37497i	0.726198	+	0.687486i	$0.241286\pi$
$23$			6.59413i			1.37497i	−0.726198	+	0.687486i	$0.758714\pi$
$24$	−0.982289	+	3.56363i	−0.200509	+	0.727423i
$25$	−1.16805	+	3.59489i	−0.233610	+	0.718978i
$26$	−0.895279	−	5.01981i	−0.175579	−	0.984465i
$27$	−3.29703	−	4.53798i	−0.634515	−	0.873334i
$28$	−0.980410	+	5.40898i	−0.185280	+	1.02220i
$29$	−8.73240	+	2.83733i	−1.62157	+	0.526879i	−0.972311	−	0.233692i	$-0.924919\pi$
$29$	−8.73240	+	2.83733i	−1.62157	+	0.526879i	−0.649256	+	0.760570i	$0.724919\pi$
$30$	4.12463	+	3.60282i	0.753052	+	0.657782i
$31$	−4.60793	−	3.34786i	−0.827608	−	0.601293i	0.0912734	−	0.995826i	$-0.470906\pi$
$31$	−4.60793	−	3.34786i	−0.827608	−	0.601293i	−0.918882	+	0.394533i	$0.870906\pi$
$32$	5.09794	+	2.45174i	0.901197	+	0.433410i
$33$	2.71788	+	3.37663i	0.473123	+	0.587795i
$34$	1.25334	+	0.535549i	0.214947	+	0.0918459i
$35$	6.58881	+	4.78705i	1.11371	+	0.809159i
$36$	−2.32779	+	1.12161i	−0.387964	+	0.186934i
$37$	0.309368	−	0.100520i	0.0508598	−	0.0165254i	−0.283477	−	0.958979i	$-0.591488\pi$
$37$	0.309368	−	0.100520i	0.0508598	−	0.0165254i	0.334336	+	0.942454i	$0.391488\pi$
$38$	5.67677	−	1.29631i	0.920893	−	0.210290i
$39$	−2.94951	+	3.67491i	−0.472300	+	0.588456i
$40$	6.55079	−	5.22746i	1.03577	−	0.826534i
$41$	−3.19225	+	9.82475i	−0.498546	+	1.53437i	0.312810	+	0.949816i	$0.398730\pi$
$41$	−3.19225	+	9.82475i	−0.498546	+	1.53437i	−0.811356	+	0.584552i	$0.801270\pi$
$42$	4.36070	−	2.60602i	0.672871	−	0.402118i
$43$	1.32576			0.202176			0.101088	−	0.994877i	$-0.467768\pi$
$43$	1.32576			0.202176			0.101088	+	0.994877i	$0.467768\pi$
$44$	5.82625	−	3.17094i	0.878340	−	0.478037i
$45$			3.82818i			0.570671i
$46$	−4.78389	−	8.00497i	−0.705346	−	1.18027i
$47$	1.10843	−	3.41140i	0.161681	−	0.497604i	−0.837095	−	0.547058i	$-0.815748\pi$
$47$	1.10843	−	3.41140i	0.161681	−	0.497604i	0.998776	+	0.0494532i	$0.0157479\pi$
$48$	−1.39288	−	5.03871i	−0.201045	−	0.727275i
$49$	0.448654	−	0.325966i	0.0640934	−	0.0465666i
$50$	−1.19005	−	5.21143i	−0.168299	−	0.737007i
$51$	−0.389227	−	1.19792i	−0.0545027	−	0.167742i
$52$	4.72858	+	5.44431i	0.655736	+	0.754990i
$53$	−0.580121	−	0.421482i	−0.0796857	−	0.0578950i	0.547229	−	0.836983i	$-0.315683\pi$
$53$	−0.580121	−	0.421482i	−0.0796857	−	0.0578950i	−0.626915	+	0.779088i	$0.715683\pi$
$54$	7.29465	+	3.11697i	0.992676	+	0.424166i
$55$	−0.485371	−	9.81546i	−0.0654474	−	1.32352i
$56$	−2.73392	−	7.27752i	−0.365335	−	0.972499i
$57$	−4.35343	−	3.16295i	−0.576625	−	0.418943i
$58$	8.54231	−	9.77954i	1.12166	−	1.28412i
$59$	1.13283	+	3.48648i	0.147482	+	0.453901i	0.997322	−	0.0731389i	$-0.0233017\pi$
$59$	1.13283	+	3.48648i	0.147482	+	0.453901i	−0.849840	+	0.527040i	$0.823302\pi$
$60$	−7.62088	−	1.38133i	−0.983851	−	0.178329i
$61$	−7.60736	−	10.4706i	−0.974023	−	1.34063i	−0.939988	−	0.341207i	$-0.889164\pi$
$61$	−7.60736	−	10.4706i	−0.974023	−	1.34063i	−0.0340351	−	0.999421i	$-0.510836\pi$
$62$	8.02260	+	0.721196i	1.01887	+	0.0915920i
$63$	3.37721	+	1.09732i	0.425489	+	0.138250i
$64$	−7.96734	+	0.722144i	−0.995918	+	0.0902680i
$65$	10.3074	−	2.80996i	1.27848	−	0.348533i
$66$	−5.74905	−	2.12731i	−0.707659	−	0.261854i
$67$	0.0932566			0.0113931			0.00569655	−	0.999984i	$-0.498187\pi$
$67$	0.0932566			0.0113931			0.00569655	+	0.999984i	$0.498187\pi$
$68$	−1.91003	+	0.259140i	−0.231625	+	0.0314254i
$69$	−2.66311	+	8.19622i	−0.320601	+	0.986709i
$70$	−11.4714	−	1.03123i	−1.37110	−	0.123255i
$71$	−4.60571	+	3.34624i	−0.546597	+	0.397126i	−0.826529	−	0.562894i	$-0.809688\pi$
$71$	−4.60571	+	3.34624i	−0.546597	+	0.397126i	0.279932	+	0.960020i	$0.409688\pi$
$72$	2.01213	−	3.05033i	0.237131	−	0.359485i
$73$	−4.29864	−	13.2299i	−0.503118	−	1.54844i	−0.803912	−	0.594749i	$-0.797252\pi$
$73$	−4.29864	−	13.2299i	−0.503118	−	1.54844i	0.300794	−	0.953689i	$-0.402748\pi$
$74$	−0.302634	+	0.346466i	−0.0351805	+	0.0402759i
$75$	−2.90367	+	3.99656i	−0.335287	+	0.461483i
$76$	−5.95088	+	5.69203i	−0.682613	+	0.652920i
$77$	−8.79832	−	2.38535i	−1.00266	−	0.271835i
$78$	0.914513	−	6.60097i	0.103548	−	0.747413i
$79$	10.5103	+	7.63616i	1.18250	+	0.859135i	0.992451	−	0.122640i	$-0.0391362\pi$
$79$	10.5103	+	7.63616i	1.18250	+	0.859135i	0.190046	+	0.981775i	$0.439136\pi$
$80$	−4.15995	+	11.0983i	−0.465096	+	1.24083i
$81$	−1.06765	−	3.28589i	−0.118628	−	0.365099i
$82$	−3.25238	−	14.2427i	−0.359165	−	1.57284i
$83$	9.73278	+	13.3960i	1.06831	+	1.47040i	0.871774	+	0.489909i	$0.162970\pi$
$83$	9.73278	+	13.3960i	1.06831	+	1.47040i	0.196538	+	0.980496i	$0.437030\pi$
$84$	−3.40308	+	6.32718i	−0.371307	+	0.690352i
$85$	−0.882465	+	2.71595i	−0.0957168	+	0.294586i
$86$	−1.60941	+	0.961805i	−0.173547	+	0.103714i
$87$	−11.9999			−1.28652
$88$	−4.77235	+	8.07618i	−0.508734	+	0.860924i
$89$		−	10.8735i		−	1.15259i	−0.817241	−	0.576296i	$-0.804497\pi$
$89$		−	10.8735i		−	1.15259i	0.817241	−	0.576296i	$-0.195503\pi$
$90$	−2.77725	−	4.64723i	−0.292748	−	0.489861i
$91$	0.475612	−	9.89864i	0.0498577	−	1.03766i
$92$	11.6148	+	6.24706i	1.21093	+	0.651301i
$93$	−4.37539	−	6.02220i	−0.453706	−	0.624473i
$94$	1.12931	+	4.94543i	0.116479	+	0.510082i
$95$	3.77008	+	11.6031i	0.386802	+	1.19046i
$96$	5.34636	+	5.10626i	0.545660	+	0.521156i
$97$	7.91003	−	10.8872i	0.803142	−	1.10543i	−0.189204	−	0.981938i	$-0.560591\pi$
$97$	7.91003	−	10.8872i	0.803142	−	1.10543i	0.992346	−	0.123492i	$-0.0394093\pi$
$98$	−0.308164	+	0.721196i	−0.0311293	+	0.0728518i
$99$	−1.52377	−	4.00484i	−0.153145	−	0.402502i
$100$	5.22544	+	5.46307i	0.522544	+	0.546307i
$101$	2.16693	−	2.98252i	0.215617	−	0.296772i	−0.687484	−	0.726200i	$-0.741285\pi$
$101$	2.16693	−	2.98252i	0.215617	−	0.296772i	0.903101	+	0.429428i	$0.141285\pi$
$102$	1.34156	+	1.17184i	0.132835	+	0.116030i
$103$	−5.09257	+	1.65468i	−0.501786	+	0.163040i	−0.548963	−	0.835846i	$-0.684977\pi$
$103$	−5.09257	+	1.65468i	−0.501786	+	0.163040i	0.0471776	+	0.998887i	$0.484977\pi$
$104$	−9.69000	−	3.17866i	−0.950183	−	0.311694i
$105$	6.25630	+	8.61106i	0.610553	+	0.840354i
$106$	1.01002	+	0.0907959i	0.0981013	+	0.00881888i
$107$	5.82624	−	17.9313i	0.563244	−	1.73349i	−0.109868	−	0.993946i	$-0.535043\pi$
$107$	5.82624	−	17.9313i	0.563244	−	1.73349i	0.673112	−	0.739540i	$-0.264957\pi$
$108$	−11.1167	+	1.50824i	−1.06970	+	0.145130i
$109$	−5.62126			−0.538419			−0.269209	−	0.963082i	$-0.586762\pi$
$109$	−5.62126			−0.538419			−0.269209	+	0.963082i	$0.586762\pi$
$110$	7.71011	+	11.5634i	0.735130	+	1.10253i
$111$	0.425127			0.0403513
$112$	8.59852	+	6.85117i	0.812484	+	0.647375i
$113$	−2.32700	+	7.16178i	−0.218906	+	0.673724i	0.779947	+	0.625845i	$0.215246\pi$
$113$	−2.32700	+	7.16178i	−0.218906	+	0.673724i	−0.998853	+	0.0478781i	$0.984754\pi$
$114$	7.57950	+	0.681364i	0.709886	+	0.0638156i
$115$	15.8074	−	11.4847i	1.47405	−	1.07096i
$116$	−3.27514	+	18.0692i	−0.304089	+	1.67768i
$117$	3.89563	−	2.55401i	0.360151	−	0.236118i
$118$	−3.90456	−	3.41059i	−0.359444	−	0.313970i
$119$	2.14305	+	1.55702i	0.196453	+	0.142732i
$120$	10.2535	−	3.85190i	0.936013	−	0.351629i
$121$	4.41473	+	10.0752i	0.401339	+	0.915930i
$122$	16.8312	+	7.19190i	1.52382	+	0.651124i
$123$	−7.93566	+	10.9225i	−0.715535	+	0.984849i
$124$	−10.2623	+	4.94471i	−0.921580	+	0.444048i
$125$	−3.43834	+	1.11718i	−0.307535	+	0.0999240i
$126$	−4.89586	+	1.11799i	−0.436158	+	0.0995985i
$127$	5.66675	−	4.11713i	0.502842	−	0.365336i	−0.307259	−	0.951626i	$-0.599412\pi$
$127$	5.66675	−	4.11713i	0.502842	−	0.365336i	0.810102	+	0.586289i	$0.199412\pi$
$128$	9.14808	−	6.65677i	0.808584	−	0.588381i
$129$	1.64786	+	0.535421i	0.145086	+	0.0471412i
$130$	−10.4742	+	10.8889i	−0.918644	+	0.955024i
$131$	13.5992			1.18816			0.594082	−	0.804404i	$-0.297515\pi$
$131$	13.5992			1.18816			0.594082	+	0.804404i	$0.297515\pi$
$132$	8.52239	−	1.58835i	0.741779	−	0.138248i
$133$	11.3169			0.981302
$134$	−0.113209	+	0.0676555i	−0.00977978	+	0.00584454i
$135$	−5.13608	+	15.8072i	−0.442043	+	1.36047i
$136$	2.13069	−	1.70027i	0.182705	−	0.145797i
$137$	7.12513	+	9.80691i	0.608741	+	0.837861i	0.996473	−	0.0839117i	$-0.0267414\pi$
$137$	7.12513	+	9.80691i	0.608741	+	0.837861i	−0.387732	+	0.921772i	$0.626741\pi$
$138$	−2.71327	−	11.8819i	−0.230969	−	1.01145i
$139$	−1.96004	−	6.03240i	−0.166249	−	0.511661i	0.832877	−	0.553458i	$-0.186692\pi$
$139$	−1.96004	−	6.03240i	−0.166249	−	0.511661i	−0.999126	+	0.0417964i	$0.986692\pi$
$140$	14.6739	−	7.07038i	1.24017	−	0.597556i
$141$	2.75547	−	3.79257i	0.232052	−	0.319392i
$142$	3.16349	−	7.40352i	0.265475	−	0.621290i
$143$	−9.66460	+	7.04241i	−0.808194	+	0.588916i
$144$	−0.229681	+	5.16271i	−0.0191401	+	0.430226i
$145$	22.0105	+	15.9916i	1.82787	+	1.32803i
$146$	14.8163	+	12.9419i	1.22621	+	1.07108i
$147$	0.689302	−	0.223968i	0.0568527	−	0.0184726i
$148$	0.116031	−	0.640148i	0.00953765	−	0.0526198i
$149$	6.68531	−	4.85716i	0.547682	−	0.397914i	−0.279248	−	0.960219i	$-0.590085\pi$
$149$	6.68531	−	4.85716i	0.547682	−	0.397914i	0.826930	+	0.562305i	$0.190085\pi$
$150$	0.625511	−	6.95819i	0.0510727	−	0.568134i
$151$	−11.9258	−	3.87492i	−0.970507	−	0.315337i	−0.219486	−	0.975616i	$-0.570438\pi$
$151$	−11.9258	−	3.87492i	−0.970507	−	0.315337i	−0.751021	+	0.660279i	$0.770438\pi$
$152$	3.09467	−	11.2271i	0.251010	−	0.910637i
$153$			1.24514i			0.100664i
$154$	12.4113	−	3.48727i	1.00013	−	0.281013i
$155$			16.8769i			1.35559i
$156$	3.67868	+	8.67673i	0.294530	+	0.694695i
$157$	−3.20530	+	9.86489i	−0.255811	+	0.787304i	0.737858	+	0.674956i	$0.235837\pi$
$157$	−3.20530	+	9.86489i	−0.255811	+	0.787304i	−0.993669	+	0.112349i	$0.964163\pi$
$158$	−18.2988	−	1.64498i	−1.45578	−	0.130868i
$159$	−0.550844	−	0.758172i	−0.0436848	−	0.0601270i
$160$	−3.00160	−	16.4908i	−0.237298	−	1.30371i
$161$	−5.60073	−	17.2373i	−0.441400	−	1.35849i
$162$	3.67991	+	3.21436i	0.289121	+	0.252544i
$163$	7.27984	+	5.28911i	0.570201	+	0.414275i	0.835178	−	0.549979i	$-0.185364\pi$
$163$	7.27984	+	5.28911i	0.570201	+	0.414275i	−0.264977	+	0.964255i	$0.585364\pi$
$164$	14.2810	+	14.9304i	1.11516	+	1.16587i
$165$	3.36079	−	12.3962i	0.261637	−	0.965044i
$166$	−21.5337	−	9.20125i	−1.67134	−	0.714155i
$167$	0.0263793	−	0.0363079i	0.00204129	−	0.00280959i	−0.807995	−	0.589189i	$-0.799447\pi$
$167$	0.0263793	−	0.0363079i	0.00204129	−	0.00280959i	0.810036	+	0.586380i	$0.199447\pi$
$168$	−0.459036	−	10.1498i	−0.0354154	−	0.783071i
$169$	−9.73617	−	8.61435i	−0.748936	−	0.662642i
$170$	−0.899086	−	3.93724i	−0.0689568	−	0.301973i
$171$	3.12673	+	4.30357i	0.239107	+	0.329102i
$172$	1.25598	−	2.33517i	0.0957673	−	0.178055i
$173$	−4.65048	−	1.51103i	−0.353570	−	0.114882i	0.126847	−	0.991922i	$-0.459514\pi$
$173$	−4.65048	−	1.51103i	−0.353570	−	0.114882i	−0.480416	+	0.877041i	$0.659514\pi$
$174$	14.5673	−	8.70564i	1.10434	−	0.659973i
$175$		−	10.3893i		−	0.785354i
$176$	−0.0656738	−	13.2663i	−0.00495035	−	0.999988i
$177$			4.79105i			0.360118i
$178$	7.88850	+	13.2000i	0.591268	+	0.989379i
$179$	−1.81385	−	0.589357i	−0.135574	−	0.0440506i	0.240444	−	0.970663i	$-0.422707\pi$
$179$	−1.81385	−	0.589357i	−0.135574	−	0.0440506i	−0.376018	+	0.926612i	$0.622707\pi$
$180$	6.74291	+	3.62669i	0.502587	+	0.270317i
$181$	6.87435	−	4.99450i	0.510966	−	0.371239i	−0.302224	−	0.953237i	$-0.597729\pi$
$181$	6.87435	−	4.99450i	0.510966	−	0.371239i	0.813190	+	0.581998i	$0.197729\pi$
$182$	6.60387	+	12.3615i	0.489511	+	0.916298i
$183$	−5.22694	−	16.0869i	−0.386387	−	1.18918i
$184$	−18.6320	+	0.842656i	−1.37357	+	0.0621214i
$185$	−0.779779	−	0.566543i	−0.0573305	−	0.0416531i
$186$	9.68048	+	4.13643i	0.709808	+	0.303298i
$187$	−0.157870	−	3.19254i	−0.0115446	−	0.233462i
$188$	−4.95872	−	5.18423i	−0.361652	−	0.378099i
$189$	12.4729	+	9.06209i	0.907270	+	0.659170i
$190$	−12.9945	−	11.3505i	−0.942720	−	0.823455i
$191$	−17.7937	+	5.78154i	−1.28751	+	0.418337i	−0.871219	−	0.490894i	$-0.836670\pi$
$191$	−17.7937	+	5.78154i	−1.28751	+	0.418337i	−0.416291	+	0.909232i	$0.636670\pi$
$192$	−10.1947	−	2.32010i	−0.735739	−	0.167439i
$193$	−9.55446	+	6.94172i	−0.687745	+	0.499676i	−0.875918	−	0.482460i	$-0.839743\pi$
$193$	−9.55446	+	6.94172i	−0.687745	+	0.499676i	0.188173	+	0.982136i	$0.439743\pi$
$194$	−1.70398	+	18.9551i	−0.122339	+	1.36090i
$195$	13.9465	+	0.670104i	0.998730	+	0.0479871i
$196$	−0.149114	−	1.09906i	−0.0106510	−	0.0785046i
$197$	−4.92381			−0.350807			−0.175404	−	0.984497i	$-0.556123\pi$
$197$	−4.92381			−0.350807			−0.175404	+	0.984497i	$0.556123\pi$
$198$	4.75521	+	3.75623i	0.337938	+	0.266944i
$199$			3.23115i			0.229050i	0.993420	+	0.114525i	$0.0365346\pi$
$199$			3.23115i			0.229050i	−0.993420	+	0.114525i	$0.963465\pi$
$200$	−10.3068	−	2.84099i	−0.728799	−	0.200888i
$201$	0.115914	+	0.0376627i	0.00817593	+	0.00265652i
$202$	−0.466801	+	5.19270i	−0.0328440	+	0.365357i
$203$	20.4169	−	14.8337i	1.43299	−	1.04112i
$204$	−2.47874	−	0.449286i	−0.173547	−	0.0314563i
$205$	29.1116	−	9.45893i	2.03324	−	0.660640i
$206$	4.98171	−	5.70324i	0.347092	−	0.397364i
$207$	5.00753	−	6.89228i	0.348048	−	0.479046i
$208$	14.0693	−	3.17112i	0.975527	−	0.219878i
$209$	−8.56258	−	10.6379i	−0.592286	−	0.735841i
$210$	−13.8420	−	5.91463i	−0.955188	−	0.408148i
$211$	3.01883	+	2.19331i	0.207825	+	0.150994i	0.686829	−	0.726819i	$-0.259002\pi$
$211$	3.01883	+	2.19331i	0.207825	+	0.150994i	−0.479004	+	0.877813i	$0.659002\pi$
$212$	−1.29198	+	0.622521i	−0.0887337	+	0.0427549i
$213$	−7.07611	+	2.29917i	−0.484847	+	0.157536i
$214$	5.93597	+	25.9946i	0.405775	+	1.77695i
$215$	−2.30901	−	3.17809i	−0.157474	−	0.216744i
$216$	12.4009	−	9.89580i	0.843775	−	0.673324i
$217$	14.8888	+	4.83766i	1.01072	+	0.328402i
$218$	6.82394	−	4.07809i	0.462176	−	0.276203i
$219$		−	18.1802i		−	1.22850i
$220$	−17.7487	−	8.44391i	−1.19662	−	0.569288i
$221$	3.35255	−	0.913958i	0.225517	−	0.0614795i
$222$	−0.516085	+	0.308420i	−0.0346374	+	0.0206998i
$223$	−3.28765	+	10.1183i	−0.220157	+	0.677575i	0.778590	+	0.627533i	$0.215935\pi$
$223$	−3.28765	+	10.1183i	−0.220157	+	0.677575i	−0.998747	+	0.0500415i	$0.984065\pi$
$224$	−15.4086	−	2.07898i	−1.02953	−	0.138908i
$225$	3.95079	−	2.87042i	0.263386	−	0.191361i
$226$	−2.37083	−	10.3823i	−0.157705	−	0.690617i
$227$	−6.38003	+	2.07300i	−0.423457	+	0.137590i	−0.512991	−	0.858394i	$-0.671462\pi$
$227$	−6.38003	+	2.07300i	−0.423457	+	0.137590i	0.0895333	+	0.995984i	$0.471462\pi$
$228$	−9.69548	+	4.67161i	−0.642099	+	0.309385i
$229$	−3.12180	+	4.29679i	−0.206294	+	0.283940i	−0.899610	−	0.436694i	$-0.856149\pi$
$229$	−3.12180	+	4.29679i	−0.206294	+	0.283940i	0.693316	+	0.720634i	$0.256149\pi$
$230$	−10.8575	+	25.4098i	−0.715924	+	1.67547i
$231$	−9.97258	−	6.51818i	−0.656147	−	0.428865i
$232$	−9.13289	−	24.3112i	−0.599603	−	1.59611i
$233$	−16.5853	+	22.8277i	−1.08654	+	1.49549i	−0.234421	+	0.972135i	$0.575319\pi$
$233$	−16.5853	+	22.8277i	−1.08654	+	1.49549i	−0.852115	+	0.523354i	$0.824681\pi$
$234$	−2.87625	+	5.92664i	−0.188026	+	0.387436i
$235$	−10.1083	+	3.28438i	−0.659392	+	0.214250i
$236$	7.21426	+	1.30763i	0.469608	+	0.0851193i
$237$	9.97986	+	13.7361i	0.648262	+	0.892256i
$238$	−3.73115	−	0.335414i	−0.241855	−	0.0217417i
$239$	−9.75680	−	3.17018i	−0.631115	−	0.205062i	−0.0240460	−	0.999711i	$-0.507655\pi$
$239$	−9.75680	−	3.17018i	−0.631115	−	0.205062i	−0.607069	+	0.794649i	$0.707655\pi$
$240$	−9.65282	+	12.1147i	−0.623087	+	0.782001i
$241$	−24.6980			−1.59094			−0.795470	−	0.605993i	$-0.792776\pi$
$241$	−24.6980			−1.59094			−0.795470	+	0.605993i	$0.792776\pi$
$242$	−12.6686	−	9.02807i	−0.814370	−	0.580347i
$243$			12.3124i			0.789838i
$244$	−25.6498	+	3.48000i	−1.64206	+	0.222784i
$245$	−1.56280	−	0.507786i	−0.0998439	−	0.0324413i
$246$	1.70950	−	19.0166i	0.108994	−	1.21245i
$247$	9.29233	−	11.5777i	0.591257	−	0.736669i
$248$	8.87065	−	13.4477i	0.563287	−	0.853930i
$249$	6.68729	+	20.5814i	0.423790	+	1.30429i
$250$	3.36349	−	3.85065i	0.212726	−	0.243536i
$251$	−10.1032	+	13.9058i	−0.637707	+	0.877728i	−0.998491	−	0.0549211i	$-0.982509\pi$
$251$	−10.1032	+	13.9058i	−0.637707	+	0.877728i	0.360784	+	0.932650i	$0.382509\pi$
$252$	5.13227	−	4.90902i	0.323303	−	0.309239i
$253$	−11.9655	+	18.3067i	−0.752262	+	1.15093i
$254$	−3.89228	+	9.10910i	−0.244224	+	0.571556i
$255$	−2.19373	+	3.01941i	−0.137377	+	0.189083i
$256$	−6.27601	+	14.7177i	−0.392251	+	0.919858i
$257$	−5.18840	−	15.9683i	−0.323644	−	0.996073i	−0.972049	−	0.234778i	$-0.924564\pi$
$257$	−5.18840	−	15.9683i	−0.323644	−	0.996073i	0.648405	−	0.761295i	$-0.275436\pi$
$258$	−2.38886	+	0.545505i	−0.148724	+	0.0339617i
$259$	−0.723322	+	0.525525i	−0.0449451	+	0.0326545i
$260$	4.81546	−	20.8174i	0.298642	−	1.29104i
$261$	11.2819	+	3.66570i	0.698330	+	0.226901i
$262$	−16.5087	+	9.86588i	−1.01991	+	0.609516i
$263$	−0.0380682			−0.00234739			−0.00117369	−	0.999999i	$-0.500374\pi$
$263$	−0.0380682			−0.00234739			−0.00117369	+	0.999999i	$0.500374\pi$
$264$	−9.19348	+	8.11098i	−0.565819	+	0.499196i
$265$			2.12474i			0.130522i
$266$	−13.7382	+	8.21017i	−0.842345	+	0.503398i
$267$	4.39140	−	13.5153i	0.268749	−	0.827125i
$268$	0.0883482	−	0.164261i	0.00539672	−	0.0100339i
$269$	20.5670	−	14.9428i	1.25399	−	0.911077i	0.255543	−	0.966798i	$-0.417746\pi$
$269$	20.5670	−	14.9428i	1.25399	−	0.911077i	0.998446	+	0.0557207i	$0.0177456\pi$
$270$	−5.23282	−	22.9153i	−0.318459	−	1.39458i
$271$	−10.5342	+	3.42278i	−0.639909	+	0.207919i	−0.610959	−	0.791662i	$-0.709216\pi$
$271$	−10.5342	+	3.42278i	−0.639909	+	0.207919i	−0.0289494	+	0.999581i	$0.509216\pi$
$272$	−1.35305	+	3.60981i	−0.0820407	+	0.218877i
$273$	4.58884	−	12.1115i	0.277729	−	0.733022i
$274$	−15.7643	−	6.73601i	−0.952354	−	0.406937i
$275$	−9.76591	+	7.86069i	−0.588907	+	0.474017i
$276$	11.9138	+	12.4556i	0.717127	+	0.749740i
$277$	4.46295	−	6.14273i	0.268153	−	0.369081i	−0.653612	−	0.756830i	$-0.726747\pi$
$277$	4.46295	−	6.14273i	0.268153	−	0.369081i	0.921765	+	0.387749i	$0.126747\pi$
$278$	6.75577	+	5.90108i	0.405184	+	0.353923i
$279$	2.27393	+	6.99845i	0.136137	+	0.418986i
$280$	−12.6840	+	19.2287i	−0.758015	+	1.14913i
$281$	17.5801	−	12.7727i	1.04874	−	0.761954i	0.0767668	−	0.997049i	$-0.475540\pi$
$281$	17.5801	−	12.7727i	1.04874	−	0.761954i	0.971972	+	0.235096i	$0.0755403\pi$
$282$	−0.593584	+	6.60304i	−0.0353474	+	0.393205i
$283$	2.81425	−	8.66139i	0.167290	−	0.514866i	−0.831908	−	0.554914i	$-0.812751\pi$
$283$	2.81425	−	8.66139i	0.167290	−	0.514866i	0.999198	+	0.0400481i	$0.0127511\pi$
$284$	1.53075	+	11.2826i	0.0908331	+	0.669497i
$285$			15.9448i			0.944486i
$286$	6.62327	−	15.5606i	0.391642	−	0.920118i
$287$		−	28.3936i		−	1.67602i
$288$	−3.46661	−	6.43392i	−0.204272	−	0.379122i
$289$	4.96626	−	15.2846i	0.292133	−	0.899093i
$290$	−38.3212	−	3.44491i	−2.25030	−	0.202292i
$291$	14.2287	−	10.3378i	0.834104	−	0.606012i
$292$	−27.3753	−	4.96194i	−1.60202	−	0.290376i
$293$	2.92511	+	9.00256i	0.170887	+	0.525935i	0.999422	−	0.0340021i	$-0.0108253\pi$
$293$	2.92511	+	9.00256i	0.170887	+	0.525935i	−0.828535	+	0.559937i	$0.810825\pi$
$294$	−0.674298	+	0.771960i	−0.0393258	+	0.0450216i
$295$	6.38476	−	8.78787i	0.371735	−	0.511649i
$296$	0.323557	+	0.861287i	0.0188063	+	0.0500613i
$297$	−0.918828	−	18.5811i	−0.0533158	−	1.07818i
$298$	−4.59190	+	10.7464i	−0.266001	+	0.622522i
$299$	−22.2332	−	8.42377i	−1.28578	−	0.487159i
$300$	4.28867	+	8.90072i	0.247606	+	0.513883i
$301$	−3.46557	+	1.12603i	−0.199752	+	0.0649034i
$302$	17.2885	−	3.94791i	0.994843	−	0.227177i
$303$	3.89792	−	2.83201i	0.223930	−	0.162695i
$304$	4.38821	+	15.8743i	0.251681	+	0.910452i
$305$	−11.8507	+	36.4726i	−0.678567	+	2.08841i
$306$	−0.903320	−	1.51154i	−0.0516394	−	0.0864091i
$307$			29.2222i			1.66780i	0.551918	+	0.833898i	$0.313896\pi$
$307$			29.2222i			1.66780i	−0.551918	+	0.833898i	$0.686104\pi$
$308$	−12.5368	+	13.2375i	−0.714348	+	0.754275i
$309$	−6.99810			−0.398108
$310$	−12.2438	−	20.4878i	−0.695401	−	1.16363i
$311$	6.47880	+	2.10509i	0.367379	+	0.119369i	0.486888	−	0.873464i	$-0.338132\pi$
$311$	6.47880	+	2.10509i	0.367379	+	0.119369i	−0.119509	+	0.992833i	$0.538132\pi$
$312$	−10.7605	−	7.86436i	−0.609194	−	0.445231i
$313$	8.15380	−	5.92408i	0.460880	−	0.334849i	−0.332996	−	0.942928i	$-0.608060\pi$
$313$	8.15380	−	5.92408i	0.460880	−	0.334849i	0.793876	+	0.608079i	$0.208060\pi$
$314$	−3.26567	−	14.3009i	−0.184292	−	0.807046i
$315$	−3.25147	−	10.0070i	−0.183199	−	0.563829i
$316$	23.4073	−	11.2784i	1.31677	−	0.634462i
$317$	5.20667	−	7.16637i	0.292436	−	0.402503i	−0.637368	−	0.770560i	$-0.719977\pi$
$317$	5.20667	−	7.16637i	0.292436	−	0.402503i	0.929803	+	0.368057i	$0.119977\pi$
$318$	1.21874	+	0.520761i	0.0683433	+	0.0292028i
$319$	−29.3915	−	7.96845i	−1.64561	−	0.446148i
$320$	15.6075	+	17.8415i	0.872486	+	0.997370i
$321$	14.4835	−	19.9349i	0.808392	−	1.11266i
$322$	19.3043	+	16.8621i	1.07579	+	0.939686i
$323$	1.22624	+	3.77399i	0.0682301	+	0.209991i
$324$	−6.79919	−	1.23239i	−0.377733	−	0.0684663i
$325$	−10.6286	−	8.53062i	−0.589569	−	0.473193i
$326$	−12.6745	−	1.13938i	−0.701977	−	0.0631046i
$327$	−6.98698	−	2.27021i	−0.386381	−	0.125543i
$328$	−28.1681	−	7.76434i	−1.55532	−	0.428714i
$329$			9.85897i			0.543543i
$330$	4.91333	+	17.4866i	0.270470	+	0.962606i
$331$	−18.2027			−1.00051			−0.500256	−	0.865878i	$-0.666761\pi$
$331$	−18.2027			−1.00051			−0.500256	+	0.865878i	$0.666761\pi$
$332$	32.8161	−	4.45228i	1.80102	−	0.244351i
$333$	−0.399690	−	0.129867i	−0.0219029	−	0.00711667i
$334$	−0.00568263	+	0.0632137i	−0.000310940	+	0.00345890i
$335$	−0.162421	−	0.223554i	−0.00887402	−	0.0122140i
$336$	7.92066	+	11.9883i	0.432108	+	0.654016i
$337$	−24.9734	+	8.11435i	−1.36039	+	0.442017i	−0.896173	−	0.443706i	$-0.853664\pi$
$337$	−24.9734	+	8.11435i	−1.36039	+	0.442017i	−0.464215	+	0.885722i	$0.653664\pi$
$338$	18.0688	+	3.39405i	0.982811	+	0.184612i
$339$	−5.78473	+	7.96200i	−0.314183	+	0.432436i
$340$	3.94783	+	4.12737i	0.214101	+	0.223838i
$341$	−6.71770	−	17.6557i	−0.363784	−	0.956112i
$342$	−6.91784	−	2.95597i	−0.374074	−	0.159840i
$343$	10.4130	−	14.3323i	0.562249	−	0.773869i
$344$	0.169417	+	3.74597i	0.00913433	+	0.201969i
$345$	24.2861	−	7.89104i	1.30752	−	0.424839i
$346$	6.74169	−	1.53949i	0.362436	−	0.0827637i
$347$	−6.67923	+	4.85274i	−0.358560	+	0.260509i	−0.752451	−	0.658648i	$-0.771129\pi$
$347$	−6.67923	+	4.85274i	−0.358560	+	0.260509i	0.393891	+	0.919157i	$0.371129\pi$
$348$	−11.3683	+	21.1365i	−0.609404	+	1.13303i
$349$	−3.01846	+	9.28985i	−0.161574	+	0.497275i	−0.998768	−	0.0496327i	$-0.984195\pi$
$349$	−3.01846	+	9.28985i	−0.161574	+	0.497275i	0.837193	+	0.546907i	$0.184195\pi$
$350$	7.53716	+	12.6121i	0.402878	+	0.674143i
$351$	19.5124	−	5.31937i	1.04149	−	0.283927i
$352$	9.70414	+	16.0571i	0.517233	+	0.855845i
$353$		−	21.1262i		−	1.12443i	−0.826990	−	0.562216i	$-0.809949\pi$
$353$		−	21.1262i		−	1.12443i	0.826990	−	0.562216i	$-0.190051\pi$
$354$	−3.47580	−	5.81612i	−0.184737	−	0.309123i
$355$	16.0432	+	5.21274i	0.851482	+	0.276663i
$356$	−19.1525	−	10.3012i	−1.01508	−	0.545964i
$357$	2.03490	+	2.80080i	0.107699	+	0.148234i
$358$	2.62950	−	0.600457i	0.138973	−	0.0317351i
$359$	−16.3572	+	5.31477i	−0.863299	+	0.280503i	−0.707006	−	0.707208i	$-0.749955\pi$
$359$	−16.3572	+	5.31477i	−0.863299	+	0.280503i	−0.156293	+	0.987711i	$0.549955\pi$
$360$	−10.8167	+	0.489198i	−0.570088	+	0.0257830i
$361$	−1.65602	−	1.20317i	−0.0871589	−	0.0633247i
$362$	−4.72174	+	11.0503i	−0.248169	+	0.580790i
$363$	1.41832	+	14.3060i	0.0744426	+	0.750871i
$364$	−16.9848	−	10.2154i	−0.890245	−	0.535432i
$365$	−24.2277	+	33.3466i	−1.26814	+	1.74544i
$366$	18.0159	+	15.7367i	0.941707	+	0.822570i
$367$	24.2036	−	7.86422i	1.26342	−	0.410509i	0.400706	−	0.916207i	$-0.368765\pi$
$367$	24.2036	−	7.86422i	1.26342	−	0.410509i	0.862711	+	0.505697i	$0.168765\pi$
$368$	22.0070	−	14.5400i	1.14720	−	0.757951i
$369$	10.7974	−	7.84478i	0.562091	−	0.408383i
$370$	1.35763	+	0.122045i	0.0705798	+	0.00634481i
$371$	1.87444	+	0.609043i	0.0973161	+	0.0316199i
$372$	−14.7525	+	2.00153i	−0.764884	+	0.103774i
$373$		−	8.42557i		−	0.436260i	−0.975920	−	0.218130i	$-0.930004\pi$
$373$		−	8.42557i		−	0.436260i	0.975920	−	0.218130i	$-0.0699956\pi$
$374$	2.50776	+	3.76107i	0.129673	+	0.194480i
$375$	−4.72490			−0.243993
$376$	9.78070	+	2.69598i	0.504401	+	0.139035i
$377$	1.58882	−	33.0673i	0.0818285	−	1.70305i
$378$	−21.7159	−	1.95216i	−1.11694	−	0.100408i
$379$	7.38723	−	5.36713i	0.379456	−	0.275691i	−0.381665	−	0.924301i	$-0.624649\pi$
$379$	7.38723	−	5.36713i	0.379456	−	0.275691i	0.761121	+	0.648610i	$0.224649\pi$
$380$	24.0093	+	4.35182i	1.23165	+	0.223244i
$381$	8.70627	−	2.82884i	0.446036	−	0.144926i
$382$	17.4064	−	19.9275i	0.890589	−	1.01958i
$383$	−19.2956	−	14.0190i	−0.985957	−	0.716340i	−0.0269249	−	0.999637i	$-0.508571\pi$
$383$	−19.2956	−	14.0190i	−0.985957	−	0.716340i	−0.959032	+	0.283298i	$0.908571\pi$
$384$	14.0591	−	4.57952i	0.717449	−	0.233698i
$385$	9.60555	+	25.2457i	0.489544	+	1.28664i
$386$	6.56261	−	15.3585i	0.334028	−	0.781725i
$387$	−1.38570	−	1.00677i	−0.0704390	−	0.0511769i
$388$	−11.6829	−	24.2468i	−0.593112	−	1.23095i
$389$	7.65021	+	23.5449i	0.387881	+	1.19378i	0.934368	+	0.356308i	$0.115965\pi$
$389$	7.65021	+	23.5449i	0.387881	+	1.19378i	−0.546487	+	0.837467i	$0.684035\pi$
$390$	−17.4165	+	9.30439i	−0.881921	+	0.471146i
$391$	5.14146	−	3.73549i	0.260015	−	0.188912i
$392$	0.978363	+	1.22603i	0.0494148	+	0.0619241i
$393$	16.9032	+	5.49217i	0.852652	+	0.277043i
$394$	5.97728	−	3.57211i	0.301131	−	0.179960i
$395$		−	38.4947i		−	1.93688i
$396$	−8.49766	−	1.11009i	−0.427023	−	0.0557843i
$397$		−	6.13764i		−	0.308039i	−0.988068	−	0.154020i	$-0.950778\pi$
$397$		−	6.13764i		−	0.308039i	0.988068	−	0.154020i	$-0.0492219\pi$
$398$	−2.34413	−	3.92247i	−0.117500	−	0.196616i
$399$	14.0665	+	4.57047i	0.704204	+	0.228810i
$400$	14.5730	−	4.02850i	0.728651	−	0.201425i
$401$	−5.58953	−	7.69333i	−0.279128	−	0.384187i	0.646317	−	0.763069i	$-0.276308\pi$
$401$	−5.58953	−	7.69333i	−0.279128	−	0.384187i	−0.925445	+	0.378883i	$0.876308\pi$
$402$	−0.168037	+	0.0383721i	−0.00838095	+	0.00191382i
$403$	17.1743	−	11.2596i	0.855512	−	0.560880i
$404$	−3.20051	−	6.64235i	−0.159231	−	0.330469i
$405$	−6.01741	+	8.28226i	−0.299008	+	0.411549i
$406$	−14.0236	+	32.8195i	−0.695981	+	1.62880i
$407$	1.04127	+	0.282303i	0.0516139	+	0.0139933i
$408$	3.33502	−	1.25286i	0.165108	−	0.0620256i
$409$	−23.7549	−	17.2590i	−1.17461	−	0.853401i	−0.183053	−	0.983103i	$-0.558598\pi$
$409$	−23.7549	−	17.2590i	−1.17461	−	0.853401i	−0.991553	+	0.129702i	$0.958598\pi$
$410$	−28.4779	+	32.6025i	−1.40642	+	1.61012i
$411$	4.89561	+	15.0671i	0.241482	+	0.743206i
$412$	−1.91000	+	10.5376i	−0.0940989	+	0.519150i
$413$	−5.92249	−	8.15161i	−0.291427	−	0.401115i
$414$	−1.07872	+	11.9998i	−0.0530164	+	0.589756i
$415$	15.1616	−	46.6626i	0.744254	−	2.29058i
$416$	−14.7789	+	14.0565i	−0.724593	+	0.689177i
$417$		−	8.28959i		−	0.405943i
$418$	18.1122	+	6.70200i	0.885895	+	0.327806i
$419$		−	3.56221i		−	0.174025i	−0.996207	−	0.0870127i	$-0.972268\pi$
$419$		−	3.56221i		−	0.174025i	0.996207	−	0.0870127i	$-0.0277321\pi$
$420$	21.0945	−	2.86196i	1.02930	−	0.139649i
$421$	4.26346	+	1.38528i	0.207788	+	0.0675145i	0.411062	−	0.911608i	$-0.365158\pi$
$421$	4.26346	+	1.38528i	0.207788	+	0.0675145i	−0.203274	+	0.979122i	$0.565158\pi$
$422$	−5.25592	−	0.472484i	−0.255854	−	0.0230002i
$423$	−3.74914	+	2.72391i	−0.182289	+	0.132441i
$424$	1.11678	−	1.69301i	0.0542357	−	0.0822200i
$425$	3.46463	−	1.12573i	0.168059	−	0.0546057i
$426$	6.92208	−	7.92464i	0.335376	−	0.383950i
$427$	28.7791	+	20.9093i	1.39272	+	1.01187i
$428$	−26.0645	−	27.2498i	−1.25987	−	1.31717i
$429$	−14.8568	+	4.85025i	−0.717295	+	0.234172i
$430$	5.10866	+	2.18291i	0.246362	+	0.105269i
$431$	−10.3300	+	14.2180i	−0.497577	+	0.684856i	−0.981763	−	0.190109i	$-0.939116\pi$
$431$	−10.3300	+	14.2180i	−0.497577	+	0.684856i	0.484186	+	0.874965i	$0.339116\pi$
$432$	−7.87496	+	21.0096i	−0.378884	+	1.01083i
$433$	12.0493	+	37.0839i	0.579052	+	1.78214i	0.621946	+	0.783060i	$0.286342\pi$
$433$	12.0493	+	37.0839i	0.579052	+	1.78214i	−0.0428936	+	0.999080i	$0.513658\pi$
$434$	−21.5839	+	4.92877i	−1.03606	+	0.236589i
$435$	20.8997	+	28.7660i	1.00206	+	1.37922i
$436$	−5.32539	+	9.90122i	−0.255040	+	0.474183i
$437$	8.39004	−	25.8219i	0.401350	−	1.23523i
$438$	13.1893	+	22.0699i	0.630210	+	1.05454i
$439$	−2.03427			−0.0970903			−0.0485452	−	0.998821i	$-0.515458\pi$
$439$	−2.03427			−0.0970903			−0.0485452	+	0.998821i	$0.515458\pi$
$440$	27.6719	−	2.62574i	1.31921	−	0.125177i
$441$	−0.716475			−0.0341179
$442$	−3.40679	+	3.54170i	−0.162044	+	0.168462i
$443$	31.1121	+	10.1089i	1.47818	+	0.480289i	0.933568	−	0.358400i	$-0.116678\pi$
$443$	31.1121	+	10.1089i	1.47818	+	0.480289i	0.544610	+	0.838689i	$0.316678\pi$
$444$	0.402752	−	0.748815i	0.0191137	−	0.0355372i
$445$	−26.0659	+	18.9380i	−1.23564	+	0.897747i
$446$	−3.34957	−	14.6683i	−0.158607	−	0.694565i
$447$	10.2712	−	3.33730i	0.485809	−	0.157849i
$448$	20.2135	−	8.65478i	0.955000	−	0.408900i
$449$	2.17653	−	2.99573i	0.102717	−	0.141377i	−0.754565	−	0.656226i	$-0.772152\pi$
$449$	2.17653	−	2.99573i	0.102717	−	0.141377i	0.857281	+	0.514849i	$0.172152\pi$
$450$	−2.71366	+	6.35077i	−0.127923	+	0.299378i
$451$	−26.6900	+	21.4831i	−1.25678	+	1.01160i
$452$	10.4102	+	10.8836i	0.489653	+	0.511921i
$453$	−13.2583	−	9.63273i	−0.622930	−	0.452585i
$454$	6.24115	−	7.14508i	0.292911	−	0.335335i
$455$	−24.5573	+	16.0999i	−1.15126	+	0.754777i
$456$	8.38072	−	12.7050i	0.392463	−	0.594964i
$457$	−14.6852	+	10.6694i	−0.686943	+	0.499094i	−0.875654	−	0.482939i	$-0.839569\pi$
$457$	−14.6852	+	10.6694i	−0.686943	+	0.499094i	0.188711	+	0.982033i	$0.439569\pi$
$458$	0.672499	−	7.48089i	0.0314238	−	0.349559i
$459$	−1.67054	+	5.14141i	−0.0779743	+	0.239980i
$460$	−5.25372	−	38.7232i	−0.244956	−	1.80548i
$461$	23.8976			1.11302			0.556510	−	0.830841i	$-0.312140\pi$
$461$	23.8976			1.11302			0.556510	+	0.830841i	$0.312140\pi$
$462$	16.8350	+	0.677895i	0.783237	+	0.0315385i
$463$	5.09543			0.236805			0.118402	−	0.992966i	$-0.462223\pi$
$463$	5.09543			0.236805			0.118402	+	0.992966i	$0.462223\pi$
$464$	28.7241	+	22.8869i	1.33348	+	1.06250i
$465$	−6.81592	+	20.9773i	−0.316081	+	0.972797i
$466$	3.57280	−	39.7439i	0.165507	−	1.84110i
$467$	5.81516	+	8.00388i	0.269094	+	0.370376i	0.922083	−	0.386991i	$-0.126486\pi$
$467$	5.81516	+	8.00388i	0.269094	+	0.370376i	−0.652990	+	0.757367i	$0.726486\pi$
$468$	−0.808011	−	9.28131i	−0.0373503	−	0.429029i
$469$	−0.243776	+	0.0792075i	−0.0112565	+	0.00365746i
$470$	9.88825	−	11.3204i	0.456111	−	0.522172i
$471$	−7.96809	+	10.9671i	−0.367150	+	0.505339i
$472$	−9.70643	+	3.64638i	−0.446775	+	0.167838i
$473$	3.68058	+	2.40567i	0.169233	+	0.110613i
$474$	−22.0803	−	9.43483i	−1.01418	−	0.433356i
$475$	9.14791	−	12.5910i	0.419735	−	0.577716i
$476$	4.77278	−	2.29969i	0.218760	−	0.105406i
$477$	0.286280	+	0.881078i	0.0131078	+	0.0403418i
$478$	14.1442	−	3.22989i	0.646940	−	0.147732i
$479$	10.5507	+	14.5217i	0.482072	+	0.663515i	0.978901	−	0.204333i	$-0.0655027\pi$
$479$	10.5507	+	14.5217i	0.482072	+	0.663515i	−0.496830	+	0.867848i	$0.665503\pi$
$480$	2.92914	−	21.7096i	0.133696	−	0.990903i
$481$	−0.0562882	+	1.17150i	−0.00256652	+	0.0534156i
$482$	29.9823	−	17.9179i	1.36566	−	0.816136i
$483$		−	23.6871i		−	1.07780i
$484$	21.9288	+	1.76888i	0.996762	+	0.0804034i
$485$	−39.8753			−1.81064
$486$	−8.93233	−	14.9466i	−0.405179	−	0.677993i
$487$	2.56023	−	7.87959i	0.116015	−	0.357058i	−0.876142	−	0.482053i	$-0.839891\pi$
$487$	2.56023	−	7.87959i	0.116015	−	0.357058i	0.992157	+	0.124995i	$0.0398913\pi$
$488$	28.6131	−	22.8329i	1.29525	−	1.03360i
$489$	6.91246	+	9.51419i	0.312592	+	0.430246i
$490$	2.26556	−	0.517350i	0.102348	−	0.0233715i
$491$	7.55986	+	23.2669i	0.341172	+	1.05002i	0.963601	+	0.267343i	$0.0861457\pi$
$491$	7.55986	+	23.2669i	0.341172	+	1.05002i	−0.622430	+	0.782676i	$0.713854\pi$
$492$	11.7208	+	24.3254i	0.528415	+	1.09667i
$493$	7.15906	+	5.20136i	0.322428	+	0.234257i
$494$	−2.88114	+	20.7961i	−0.129629	+	0.935661i
$495$	−6.94646	+	10.6278i	−0.312220	+	0.477686i
$496$	−1.01257	+	22.7603i	−0.0454657	+	1.02197i
$497$	9.19734	−	12.6591i	0.412557	−	0.567836i
$498$	−23.0494	−	20.1334i	−1.03287	−	0.902197i
$499$	6.61651	+	20.3635i	0.296196	+	0.911597i	0.982817	+	0.184582i	$0.0590930\pi$
$499$	6.61651	+	20.3635i	0.296196	+	0.911597i	−0.686622	+	0.727015i	$0.740907\pi$
$500$	−1.28957	+	7.11464i	−0.0576714	+	0.318177i
$501$	0.0474516	−	0.0344756i	0.00211998	−	0.00154026i
$502$	2.17643	−	24.2107i	0.0971389	−	1.08057i
$503$	4.13950	−	12.7401i	0.184571	−	0.568051i	−0.815370	−	0.578941i	$-0.803466\pi$
$503$	4.13950	−	12.7401i	0.184571	−	0.568051i	0.999941	+	0.0108893i	$0.00346624\pi$
$504$	−2.66896	+	9.68267i	−0.118885	+	0.431300i
$505$	−10.9237			−0.486099
$506$	1.24442	−	30.9042i	0.0553210	−	1.37386i
$507$	−8.62264	−	14.6393i	−0.382945	−	0.650155i
$508$	−1.88339	−	13.8818i	−0.0835619	−	0.615905i
$509$	37.1041	+	12.0559i	1.64461	+	0.534366i	0.977562	−	0.210648i	$-0.0675573\pi$
$509$	37.1041	+	12.0559i	1.64461	+	0.534366i	0.667049	+	0.745014i	$0.267557\pi$
$510$	0.472575	−	5.25693i	0.0209260	−	0.232781i
$511$	22.4736	+	30.9322i	0.994173	+	1.36836i
$512$	−3.05858	−	22.4197i	−0.135172	−	0.990822i
$513$	7.13692	+	21.9652i	0.315103	+	0.969787i
$514$	17.8831	+	15.6207i	0.788789	+	0.688998i
$515$	12.8361	+	9.32597i	0.565626	+	0.410951i
$516$	2.50421	−	2.39528i	0.110242	−	0.105446i
$517$	9.26745	−	7.45947i	0.407582	−	0.328067i
$518$	0.496824	−	1.16272i	0.0218292	−	0.0510868i
$519$	−5.17010	−	3.75630i	−0.226942	−	0.164883i
$520$	9.25682	+	28.7649i	0.405939	+	1.26142i
$521$	−8.80779	−	27.1076i	−0.385876	−	1.18760i	−0.935843	−	0.352418i	$-0.885360\pi$
$521$	−8.80779	−	27.1076i	−0.385876	−	1.18760i	0.549967	−	0.835187i	$-0.314640\pi$
$522$	−16.3550	+	3.73474i	−0.715841	+	0.163465i
$523$	−32.0022	+	23.2509i	−1.39936	+	1.01669i	−0.404593	+	0.914497i	$0.632587\pi$
$523$	−32.0022	+	23.2509i	−1.39936	+	1.01669i	−0.994764	+	0.102195i	$0.967413\pi$
$524$	12.8834	−	23.9534i	0.562814	−	1.04641i
$525$	4.19581	−	12.9134i	0.183120	−	0.563587i
$526$	0.0462131	−	0.0276176i	0.00201499	−	0.00120419i
$527$			5.48932i			0.239119i
$528$	5.27613	−	16.5160i	0.229614	−	0.718767i
$529$	−20.4826			−0.890548
$530$	−1.54145	−	2.57933i	−0.0669562	−	0.112039i
$531$	1.46356	−	4.50438i	0.0635132	−	0.195473i
$532$	10.7213	−	19.9335i	0.464827	−	0.864228i
$533$	−29.0477	−	23.3139i	−1.25820	−	1.00984i
$534$	4.47411	+	19.5928i	0.193614	+	0.847865i
$535$	−53.1321	+	17.2637i	−2.29710	+	0.746373i
$536$	0.0119171	+	0.263500i	0.000514742	+	0.0113815i
$537$	−2.01652	−	1.46509i	−0.0870194	−	0.0632233i
$538$	−14.1267	+	33.0607i	−0.609045	+	1.42535i
$539$	1.83704	−	0.0908413i	0.0791271	−	0.00391281i
$540$	22.9770	+	24.0219i	0.988771	+	1.03374i
$541$	13.6852	+	9.94286i	0.588372	+	0.427477i	0.841733	−	0.539895i	$-0.181536\pi$
$541$	13.6852	+	9.94286i	0.588372	+	0.427477i	−0.253361	+	0.967372i	$0.581536\pi$
$542$	10.3049	−	11.7974i	0.442634	−	0.506743i
$543$	10.5616	−	3.43167i	0.453242	−	0.147267i
$544$	−0.976291	−	5.36375i	−0.0418581	−	0.229969i
$545$	9.79031	+	13.4752i	0.419371	+	0.577215i
$546$	3.21597	+	18.0319i	0.137631	+	0.771694i
$547$	−13.0910	+	40.2900i	−0.559732	+	1.72268i	0.123376	+	0.992360i	$0.460628\pi$
$547$	−13.0910	+	40.2900i	−0.559732	+	1.72268i	−0.683108	+	0.730317i	$0.739372\pi$
$548$	24.0239	−	3.25941i	1.02625	−	0.139235i
$549$			16.7210i			0.713636i
$550$	6.15262	−	16.6275i	0.262349	−	0.708997i
$551$	37.8052			1.61055
$552$	−23.4991	−	6.47735i	−1.00019	−	0.275694i
$553$	−33.9600	−	11.0343i	−1.44412	−	0.469225i
$554$	−0.961411	+	10.6948i	−0.0408464	+	0.454377i
$555$	−0.740427	−	1.01911i	−0.0314294	−	0.0432588i
$556$	−12.4823	−	2.26249i	−0.529367	−	0.0959509i
$557$	1.43501	+	4.41650i	0.0608033	+	0.187133i	0.976844	−	0.213951i	$-0.0686334\pi$
$557$	1.43501	+	4.41650i	0.0608033	+	0.187133i	−0.916041	+	0.401084i	$0.868633\pi$
$558$	−7.83766	−	6.84610i	−0.331795	−	0.289819i
$559$	−1.69360	+	4.47000i	−0.0716319	+	0.189061i
$560$	1.44786	−	32.5447i	0.0611832	−	1.37526i
$561$	1.09312	−	4.03195i	0.0461515	−	0.170229i
$562$	−12.0751	+	28.2594i	−0.509358	+	1.19205i
$563$	−3.93957	−	2.86226i	−0.166033	−	0.120630i	0.501666	−	0.865061i	$-0.332721\pi$
$563$	−3.93957	−	2.86226i	−0.166033	−	0.120630i	−0.667699	+	0.744431i	$0.732721\pi$
$564$	−4.06977	−	8.44641i	−0.171368	−	0.355658i
$565$	21.2210	−	6.89512i	0.892774	−	0.290080i
$566$	2.86726	+	12.5562i	0.120520	+	0.527776i
$567$	5.58175	+	7.68261i	0.234411	+	0.322639i
$568$	−10.0435	−	12.5860i	−0.421416	−	0.528097i
$569$	−27.3760	−	8.89502i	−1.14766	−	0.372898i	−0.327401	−	0.944886i	$-0.606173\pi$
$569$	−27.3760	−	8.89502i	−1.14766	−	0.372898i	−0.820263	+	0.571987i	$0.806173\pi$
$570$	−11.5676	−	19.3562i	−0.484512	−	0.810742i
$571$	3.22679			0.135037			0.0675185	−	0.997718i	$-0.478492\pi$
$571$	3.22679			0.135037			0.0675185	+	0.997718i	$0.478492\pi$
$572$	3.24851	+	23.6949i	0.135827	+	0.990733i
$573$	−24.4518			−1.02149
$574$	20.5989	+	34.4685i	0.859780	+	1.43869i
$575$	−23.7052	−	7.70229i	−0.988575	−	0.321208i
$576$	8.87596	+	5.29554i	0.369832	+	0.220647i
$577$	7.20652	+	9.91892i	0.300011	+	0.412930i	0.932234	−	0.361857i	$-0.117857\pi$
$577$	7.20652	+	9.91892i	0.300011	+	0.412930i	−0.632222	+	0.774787i	$0.717857\pi$
$578$	5.05980	+	22.1577i	0.210460	+	0.921638i
$579$	−14.6793	+	4.76958i	−0.610050	+	0.198217i
$580$	49.0194	−	23.6192i	2.03542	−	0.980734i
$581$	−36.8197	−	26.7511i	−1.52754	−	1.10982i
$582$	−9.77321	+	22.8722i	−0.405113	+	0.948084i
$583$	−0.845733	−	2.22279i	−0.0350267	−	0.0920586i
$584$	36.8322	−	13.8366i	1.52413	−	0.572563i
$585$	−12.9073	−	4.89036i	−0.533651	−	0.202191i
$586$	−10.0821	−	8.80659i	−0.416487	−	0.363797i
$587$	−6.49094	−	19.9771i	−0.267910	−	0.824542i	−0.991009	−	0.133797i	$-0.957283\pi$
$587$	−6.49094	−	19.9771i	−0.267910	−	0.824542i	0.723099	−	0.690745i	$-0.242717\pi$
$588$	0.258527	−	1.42631i	0.0106615	−	0.0588200i
$589$	13.7845	+	18.9727i	0.567980	+	0.781757i
$590$	−1.37541	+	15.3001i	−0.0566246	+	0.629893i
$591$	−6.12009	−	1.98854i	−0.251747	−	0.0817975i
$592$	−1.01763	−	0.810830i	−0.0418242	−	0.0333249i
$593$	−36.2761			−1.48968			−0.744840	−	0.667243i	$-0.767474\pi$
$593$	−36.2761			−1.48968			−0.744840	+	0.667243i	$0.767474\pi$
$594$	14.5956	+	21.8900i	0.598863	+	0.898157i
$595$		−	7.84910i		−	0.321782i
$596$	−2.22192	−	16.3769i	−0.0910133	−	0.670826i
$597$	−1.30494	+	4.01618i	−0.0534075	+	0.164371i
$598$	33.1013	−	5.90359i	1.35361	−	0.241416i
$599$	−22.7211	−	31.2729i	−0.928358	−	1.27778i	−0.960497	−	0.278292i	$-0.910232\pi$
$599$	−22.7211	−	31.2729i	−0.928358	−	1.27778i	0.0321385	−	0.999483i	$-0.489768\pi$
$600$	−11.6635	−	7.69373i	−0.476161	−	0.314095i
$601$	−22.3537	+	7.26314i	−0.911825	+	0.296270i	−0.727109	−	0.686522i	$-0.759136\pi$
$601$	−22.3537	+	7.26314i	−0.911825	+	0.296270i	−0.184716	+	0.982792i	$0.559136\pi$
$602$	3.39013	−	3.88114i	0.138171	−	0.158183i
$603$	−0.0974730	−	0.0708183i	−0.00396941	−	0.00288394i
$604$	−18.1234	+	17.3350i	−0.737429	+	0.705351i
$605$	16.4633	−	28.1305i	0.669327	−	1.14367i
$606$	−2.67734	+	6.26578i	−0.108760	+	0.254530i
$607$	−26.2801	−	19.0936i	−1.06668	−	0.774986i	−0.0913644	−	0.995818i	$-0.529123\pi$
$607$	−26.2801	−	19.0936i	−1.06668	−	0.774986i	−0.975312	+	0.220832i	$0.929123\pi$
$608$	−16.8435	−	16.0871i	−0.683094	−	0.652417i
$609$	31.3681	−	10.1921i	1.27110	−	0.413005i
$610$	−12.0739	−	52.8734i	−0.488856	−	2.14078i
$611$	10.0861	+	8.09520i	0.408040	+	0.327497i
$612$	2.19318	+	1.17960i	0.0886539	+	0.0476827i
$613$	10.2628	−	31.5856i	0.414510	−	1.27573i	−0.498179	−	0.867074i	$-0.665998\pi$
$613$	10.2628	−	31.5856i	0.414510	−	1.27573i	0.912689	−	0.408656i	$-0.134002\pi$
$614$	−21.2000	−	35.4743i	−0.855562	−	1.43163i
$615$	40.0045			1.61314
$616$	5.61556	−	25.1648i	0.226258	−	1.01392i
$617$			34.0901i			1.37242i	0.727405	+	0.686208i	$0.240726\pi$
$617$			34.0901i			1.37242i	−0.727405	+	0.686208i	$0.759274\pi$
$618$	8.49537	−	5.07696i	0.341734	−	0.204225i
$619$	−1.51042	+	4.64860i	−0.0607090	+	0.186843i	−0.976812	−	0.214101i	$-0.931318\pi$
$619$	−1.51042	+	4.64860i	−0.0607090	+	0.186843i	0.916103	+	0.400944i	$0.131318\pi$
$620$	29.7268	+	15.9886i	1.19386	+	0.642118i
$621$	29.9240	−	21.7411i	1.20081	−	0.872440i
$622$	−9.39215	+	2.14474i	−0.376591	+	0.0859961i
$623$	9.23545	+	28.4238i	0.370010	+	1.13877i
$624$	18.7682	+	1.74046i	0.751328	+	0.0696742i
$625$	23.9565	+	17.4054i	0.958260	+	0.696217i
$626$	−5.60055	+	13.1070i	−0.223843	+	0.523859i
$627$	−6.34667	−	16.6806i	−0.253462	−	0.666158i
$628$	14.3393	+	14.9915i	0.572202	+	0.598224i
$629$	−0.253628	−	0.184272i	−0.0101128	−	0.00734740i
$630$	11.2070	+	9.78915i	0.446496	+	0.390009i
$631$	11.0851	+	34.1165i	0.441292	+	1.35816i	0.886499	+	0.462730i	$0.153130\pi$
$631$	11.0851	+	34.1165i	0.441292	+	1.35816i	−0.445207	+	0.895427i	$0.646870\pi$
$632$	−20.2332	+	30.6730i	−0.804832	+	1.22011i
$633$	2.86649	+	3.94538i	0.113933	+	0.156815i
$634$	−1.12162	+	12.4770i	−0.0445453	+	0.495523i
$635$	−19.7391	−	6.41362i	−0.783322	−	0.254517i
$636$	−1.85729	+	0.251985i	−0.0736463	+	0.00999185i
$637$	0.525907	+	1.92912i	0.0208372	+	0.0764344i
$638$	41.4609	−	11.6495i	1.64145	−	0.461210i
$639$	7.35506			0.290962
$640$	−31.8904	−	10.3359i	−1.26058	−	0.408560i
$641$	−12.2916	+	37.8297i	−0.485490	+	1.49418i	0.345780	+	0.938315i	$0.387614\pi$
$641$	−12.2916	+	37.8297i	−0.485490	+	1.49418i	−0.831270	+	0.555868i	$0.812386\pi$
$642$	−3.12005	+	34.7075i	−0.123138	+	1.36979i
$643$	13.1048	−	9.52117i	0.516802	−	0.375478i	−0.298596	−	0.954380i	$-0.596518\pi$
$643$	13.1048	−	9.52117i	0.516802	−	0.375478i	0.815398	+	0.578901i	$0.196518\pi$
$644$	−35.6675	−	6.46495i	−1.40550	−	0.254755i
$645$	−1.58650	−	4.88274i	−0.0624684	−	0.192258i
$646$	−4.22655	−	3.69184i	−0.166291	−	0.145253i
$647$	−27.6005	+	37.9889i	−1.08509	+	1.49350i	−0.231297	+	0.972883i	$0.574297\pi$
$647$	−27.6005	+	37.9889i	−1.08509	+	1.49350i	−0.853792	+	0.520614i	$0.825703\pi$
$648$	9.14797	−	3.43659i	0.359366	−	0.135002i
$649$	−3.18147	+	11.7348i	−0.124884	+	0.460632i
$650$	19.0914	+	2.64496i	0.748826	+	0.103744i
$651$	16.5524	+	12.0260i	0.648738	+	0.471336i
$652$	16.2129	−	7.81191i	0.634945	−	0.305938i
$653$	−5.04208	−	15.5179i	−0.197312	−	0.607264i	−0.999942	−	0.0107863i	$-0.996567\pi$
$653$	−5.04208	−	15.5179i	−0.197312	−	0.607264i	0.802630	−	0.596477i	$-0.203433\pi$
$654$	10.1288	−	2.31296i	0.396069	−	0.0904441i
$655$	−23.6851	−	32.5998i	−0.925454	−	1.27378i
$656$	39.8277	−	11.0098i	1.55501	−	0.429860i
$657$	−5.55365	+	17.0924i	−0.216669	+	0.666837i
$658$	−7.15245	−	11.9683i	−0.278832	−	0.466574i
$659$	13.6741			0.532666			0.266333	−	0.963881i	$-0.414188\pi$
$659$	13.6741			0.532666			0.266333	+	0.963881i	$0.414188\pi$
$660$	−18.6507	−	17.6634i	−0.725976	−	0.687548i
$661$		−	16.1730i		−	0.629056i	−0.949248	−	0.314528i	$-0.898154\pi$
$661$		−	16.1730i		−	0.629056i	0.949248	−	0.314528i	$-0.101846\pi$
$662$	22.0972	−	13.2056i	0.858834	−	0.513252i
$663$	4.53619	+	0.217956i	0.176171	+	0.00846470i
$664$	−36.6073	+	29.2122i	−1.42064	+	1.13365i
$665$	−19.7102	−	27.1288i	−0.764330	−	1.05201i
$666$	0.579421	−	0.132313i	0.0224521	−	0.00512703i
$667$	−18.7097	−	57.5826i	−0.724444	−	2.22961i
$668$	−0.0389616	−	0.0808611i	−0.00150747	−	0.00312861i
$669$	−8.17282	+	11.2489i	−0.315979	+	0.434908i
$670$	0.359355	+	0.153551i	0.0138831	+	0.00593219i
$671$	−2.12004	−	42.8728i	−0.0818434	−	1.65508i
$672$	−18.3126	−	8.80700i	−0.706423	−	0.339737i
$673$	5.66002	−	7.79035i	0.218178	−	0.300296i	−0.685873	−	0.727721i	$-0.740579\pi$
$673$	5.66002	−	7.79035i	0.218178	−	0.300296i	0.904051	+	0.427426i	$0.140579\pi$
$674$	24.4298	−	27.9681i	0.941000	−	1.07729i
$675$	20.1646	−	6.55189i	0.776138	−	0.252182i
$676$	−24.3970	+	8.98825i	−0.938344	+	0.345702i
$677$	11.2493	+	15.4834i	0.432346	+	0.595074i	0.968490	−	0.249053i	$-0.0801194\pi$
$677$	11.2493	+	15.4834i	0.432346	+	0.595074i	−0.536143	+	0.844127i	$0.680119\pi$
$678$	1.24615	−	13.8622i	0.0478580	−	0.532374i
$679$	−11.4300	+	35.1780i	−0.438643	+	1.35001i
$680$	−7.78679	−	2.14637i	−0.298610	−	0.0823096i
$681$	−8.76730			−0.335964
$682$	20.9638	+	16.5597i	0.802746	+	0.634104i
$683$	13.3766			0.511842			0.255921	−	0.966698i	$-0.417621\pi$
$683$	13.3766			0.511842			0.255921	+	0.966698i	$0.417621\pi$
$684$	10.5424	−	1.43033i	0.403100	−	0.0546899i
$685$	11.0994	−	34.1606i	0.424088	−	1.30521i
$686$	−2.24317	+	24.9531i	−0.0856447	+	0.952713i
$687$	−5.61557	+	4.07995i	−0.214247	+	0.155660i
$688$	−2.92328	−	4.42453i	−0.111449	−	0.168684i
$689$	2.16218	−	1.41754i	0.0823724	−	0.0540040i
$690$	−23.7575	+	27.1984i	−0.904431	+	1.03542i
$691$	−13.3833	−	9.72355i	−0.509125	−	0.369901i	0.303366	−	0.952874i	$-0.401889\pi$
$691$	−13.3833	−	9.72355i	−0.509125	−	0.369901i	−0.812492	+	0.582973i	$0.801889\pi$
$692$	−7.06723	+	6.75981i	−0.268656	+	0.256970i
$693$	7.38470	+	9.17457i	0.280522	+	0.348513i
$694$	4.58772	−	10.7366i	0.174147	−	0.407557i
$695$	−11.0471	+	15.2050i	−0.419039	+	0.576758i
$696$	−1.53345	−	33.9061i	−0.0581253	−	1.28521i
$697$	9.46874	−	3.07658i	0.358654	−	0.116534i
$698$	−3.07531	−	13.4673i	−0.116402	−	0.509744i
$699$	−29.8340	+	21.6756i	−1.12842	+	0.819848i
$700$	−18.2995	−	9.84243i	−0.691657	−	0.372009i
$701$	12.2137	+	3.96849i	0.461307	+	0.149888i	0.530445	−	0.847719i	$-0.322025\pi$
$701$	12.2137	+	3.96849i	0.461307	+	0.149888i	−0.0691380	+	0.997607i	$0.522025\pi$
$702$	−19.8280	+	20.6132i	−0.748360	+	0.777996i
$703$	−1.33935			−0.0505145
$704$	−23.4294	−	12.4524i	−0.883029	−	0.469318i
$705$	−13.8906			−0.523150
$706$	15.3265	+	25.6462i	0.576822	+	0.965207i
$707$	−3.13122	+	9.63689i	−0.117762	+	0.362433i
$708$	8.43891	+	4.53888i	0.317154	+	0.170582i
$709$	−15.7707	−	21.7065i	−0.592281	−	0.815205i	0.402693	−	0.915335i	$-0.368074\pi$
$709$	−15.7707	−	21.7065i	−0.592281	−	0.815205i	−0.994974	+	0.100130i	$0.968074\pi$
$710$	−23.2574	+	5.31092i	−0.872833	+	0.199315i
$711$	−5.18664	−	15.9628i	−0.194514	−	0.598653i
$712$	30.7236	−	1.38952i	1.15142	−	0.0520743i
$713$	22.0762	−	30.3853i	0.826760	−	1.13794i
$714$	−4.50220	−	1.92377i	−0.168491	−	0.0719953i
$715$	33.7144	+	10.9024i	1.26085	+	0.407726i
$716$	−2.75647	+	2.63657i	−0.103014	+	0.0985331i
$717$	−10.8470	−	7.88078i	−0.405087	−	0.294313i
$718$	16.0011	−	18.3186i	0.597156	−	0.683646i
$719$	−39.7788	+	12.9249i	−1.48350	+	0.482018i	−0.935156	−	0.354236i	$-0.884741\pi$
$719$	−39.7788	+	12.9249i	−1.48350	+	0.482018i	−0.548343	+	0.836254i	$0.684741\pi$
$720$	12.7760	−	8.44110i	0.476134	−	0.314581i
$721$	11.9067	−	8.65076i	0.443430	−	0.322171i
$722$	2.88320	+	0.259187i	0.107302	+	0.00964595i
$723$	−30.6986	−	9.97458i	−1.14169	−	0.370958i
$724$	−2.28475	−	16.8400i	−0.0849119	−	0.625855i
$725$		−	34.7062i		−	1.28896i
$726$	−12.1005	−	16.3379i	−0.449090	−	0.606355i
$727$			7.66458i			0.284263i	0.989848	+	0.142132i	$0.0453957\pi$
$727$			7.66458i			0.284263i	−0.989848	+	0.142132i	$0.954604\pi$
$728$	28.0298	+	0.0789240i	1.03885	+	0.00292512i
$729$	−8.17543	+	25.1614i	−0.302794	+	0.931903i
$730$	5.21914	−	58.0578i	0.193169	−	2.14882i
$731$	−0.751022	−	1.03369i	−0.0277776	−	0.0382325i
$732$	−33.2871	−	6.03348i	−1.23033	−	0.223004i
$733$	10.0043	+	30.7900i	0.369516	+	1.13725i	0.947105	+	0.320925i	$0.103994\pi$
$733$	10.0043	+	30.7900i	0.369516	+	1.13725i	−0.577589	+	0.816328i	$0.696006\pi$
$734$	−23.6767	+	27.1060i	−0.873924	+	1.00050i
$735$	−1.73742	−	1.26231i	−0.0640858	−	0.0465611i
$736$	−16.1671	+	33.6165i	−0.595926	+	1.23912i
$737$	0.258900	+	0.169220i	0.00953671	+	0.00623329i
$738$	−7.41636	+	17.3565i	−0.273000	+	0.638901i
$739$	−8.77907	+	12.0834i	−0.322943	+	0.444493i	−0.939363	−	0.342925i	$-0.888582\pi$
$739$	−8.77907	+	12.0834i	−0.322943	+	0.444493i	0.616420	+	0.787418i	$0.288582\pi$
$740$	−1.73664	+	0.836772i	−0.0638402	+	0.0307604i
$741$	16.2257	−	10.6377i	0.596067	−	0.390786i
$742$	−2.71733	+	0.620514i	−0.0997563	+	0.0227798i
$743$	13.3156	+	18.3273i	0.488502	+	0.672365i	0.980111	−	0.198451i	$-0.0635911\pi$
$743$	13.3156	+	18.3273i	0.488502	+	0.672365i	−0.491609	+	0.870816i	$0.663591\pi$
$744$	16.4568	−	13.1324i	0.603337	−	0.481457i
$745$	−23.2871	−	7.56642i	−0.853172	−	0.277212i
$746$	6.11256	+	10.2283i	0.223797	+	0.374483i
$747$		−	21.3927i		−	0.782718i
$748$	−5.77288	−	2.74644i	−0.211077	−	0.100420i
$749$			51.8216i			1.89352i
$750$	5.73580	−	3.42780i	0.209442	−	0.125166i
$751$	−7.08086	−	2.30071i	−0.258384	−	0.0839542i	0.176960	−	0.984218i	$-0.443374\pi$
$751$	−7.08086	−	2.30071i	−0.258384	−	0.0839542i	−0.435345	+	0.900264i	$0.643374\pi$
$752$	−13.8292	+	3.82288i	−0.504298	+	0.139406i
$753$	−18.1738	+	13.2041i	−0.662292	+	0.481183i
$754$	22.0608	+	41.2948i	0.803406	+	1.50387i
$755$	11.4817	+	35.3372i	0.417863	+	1.28605i
$756$	27.7783	−	13.3845i	1.01029	−	0.486790i
$757$	−0.962462	−	0.699269i	−0.0349813	−	0.0254154i	0.570157	−	0.821536i	$-0.306882\pi$
$757$	−0.962462	−	0.699269i	−0.0349813	−	0.0254154i	−0.605139	+	0.796120i	$0.706882\pi$
$758$	−5.07402	+	11.8747i	−0.184297	+	0.431309i
$759$	−22.2659	+	17.9221i	−0.808202	+	0.650530i
$760$	−32.3033	+	12.1353i	−1.17176	+	0.440192i
$761$	−5.96472	−	4.33363i	−0.216221	−	0.157094i	0.474403	−	0.880308i	$-0.342664\pi$
$761$	−5.96472	−	4.33363i	−0.216221	−	0.157094i	−0.690624	+	0.723214i	$0.742664\pi$
$762$	−8.51675	+	9.75028i	−0.308529	+	0.353215i
$763$	14.6941	−	4.77442i	0.531964	−	0.172846i
$764$	−6.67365	+	36.8190i	−0.241444	+	1.33206i
$765$	2.98483	−	2.16861i	0.107917	−	0.0784062i
$766$	33.5944	+	3.01999i	1.21382	+	0.109117i
$767$	−13.2024	−	0.634350i	−0.476710	−	0.0229051i
$768$	−13.7447	+	15.7589i	−0.495970	+	0.568649i
$769$	−15.3497			−0.553525			−0.276763	−	0.960938i	$-0.589262\pi$
$769$	−15.3497			−0.553525			−0.276763	+	0.960938i	$0.589262\pi$
$770$	−29.9758	−	23.6785i	−1.08025	−	0.853314i
$771$		−	21.9433i		−	0.790267i
$772$	3.17550	+	23.4055i	0.114289	+	0.842382i
$773$	−11.0515	−	3.59085i	−0.397494	−	0.129154i	0.103447	−	0.994635i	$-0.467013\pi$
$773$	−11.0515	−	3.59085i	−0.397494	−	0.129154i	−0.500941	+	0.865481i	$0.667013\pi$
$774$	2.41256	+	0.216878i	0.0867177	+	0.00779553i
$775$	17.4175	−	12.6545i	0.625654	−	0.454564i
$776$	31.7731	+	20.9588i	1.14059	+	0.752378i
$777$	−1.11130	+	0.361082i	−0.0398676	+	0.0129538i
$778$	−26.3683	−	23.0324i	−0.945350	−	0.825752i
$779$	25.0010	−	34.4109i	0.895754	−	1.23290i
$780$	14.3928	−	23.9304i	0.515344	−	0.856846i
$781$	−18.8584	+	0.932542i	−0.674807	+	0.0333690i
$782$	−3.53148	+	8.26471i	−0.126285	+	0.295546i
$783$	41.6668	+	30.2727i	1.48905	+	1.08186i
$784$	−2.07715	−	0.778569i	−0.0741838	−	0.0278060i
$785$	29.2306	−	9.49758i	1.04328	−	0.338983i
$786$	−24.5041	+	5.59561i	−0.874032	+	0.199589i
$787$	15.8272	+	21.7843i	0.564178	+	0.776525i	0.991850	−	0.127409i	$-0.0406661\pi$
$787$	15.8272	+	21.7843i	0.564178	+	0.776525i	−0.427672	+	0.903934i	$0.640666\pi$
$788$	−4.66466	+	8.67276i	−0.166171	+	0.308954i
$789$	−0.0473172	−	0.0153743i	−0.00168454	−	0.000547339i
$790$	27.9270	+	46.7308i	0.993598	+	1.66261i
$791$		−	20.6976i		−	0.735921i
$792$	11.1211	−	4.81725i	0.395171	−	0.171174i
$793$	45.0216	−	12.2736i	1.59876	−	0.435847i
$794$	4.45271	+	7.45081i	0.158021	+	0.264419i
$795$	−0.858099	+	2.64096i	−0.0304336	+	0.0936651i
$796$	5.69132	+	3.06109i	0.201723	+	0.108497i
$797$	−37.0423	+	26.9128i	−1.31210	+	0.953299i	−0.312109	+	0.950046i	$0.601036\pi$
$797$	−37.0423	+	26.9128i	−1.31210	+	0.953299i	−0.999995	+	0.00325336i	$0.998964\pi$
$798$	−20.3918	+	4.65655i	−0.721862	+	0.164840i
$799$	−3.28779	+	1.06827i	−0.116314	+	0.0377926i
$800$	−14.7684	+	15.4628i	−0.522141	+	0.546692i
$801$	−8.25728	+	11.3652i	−0.291757	+	0.401568i
$802$	12.3668	+	5.28427i	0.436686	+	0.186594i
$803$	12.0725	−	44.5291i	0.426028	−	1.57140i
$804$	0.176152	−	0.168489i	0.00621239	−	0.00594216i
$805$	−31.5665	+	43.4475i	−1.11257	+	1.53132i
$806$	−12.6802	+	26.1282i	−0.446641	+	0.920326i
$807$	31.5986	−	10.2670i	1.11233	−	0.361416i
$808$	8.70414	+	5.74161i	0.306211	+	0.201989i
$809$	−27.4060	−	37.7211i	−0.963543	−	1.32620i	−0.945242	−	0.326371i	$-0.894174\pi$
$809$	−27.4060	−	37.7211i	−0.963543	−	1.32620i	−0.0183016	−	0.999833i	$-0.505826\pi$
$810$	1.29627	−	14.4198i	0.0455464	−	0.506659i
$811$	22.4585	+	7.29721i	0.788624	+	0.256240i	0.675518	−	0.737343i	$-0.263920\pi$
$811$	22.4585	+	7.29721i	0.788624	+	0.256240i	0.113106	+	0.993583i	$0.463920\pi$
$812$	−6.78573	−	50.0151i	−0.238132	−	1.75519i
$813$	−14.4759			−0.507693
$814$	−1.46886	+	0.412716i	−0.0514835	+	0.0144657i
$815$		−	26.6630i		−	0.933964i
$816$	−3.13964	+	3.94039i	−0.109910	+	0.137941i
$817$	−5.19151	−	1.68682i	−0.181628	−	0.0590145i
$818$	41.3584	+	3.71793i	1.44606	+	0.129995i
$819$	−8.01407	+	9.98502i	−0.280034	+	0.348905i
$820$	10.9185	−	60.2379i	0.381290	−	2.10360i
$821$	5.38200	+	16.5641i	0.187833	+	0.578091i	0.999986	−	0.00535421i	$-0.00170431\pi$
$821$	5.38200	+	16.5641i	0.187833	+	0.578091i	−0.812153	+	0.583445i	$0.801704\pi$
$822$	−16.8739	−	14.7391i	−0.588544	−	0.514087i
$823$	17.1481	−	23.6024i	0.597747	−	0.822728i	−0.397753	−	0.917493i	$-0.630210\pi$
$823$	17.1481	−	23.6024i	0.597747	−	0.822728i	0.995500	+	0.0947648i	$0.0302099\pi$
$824$	−5.32612	−	14.1778i	−0.185544	−	0.493907i
$825$	−15.3132	+	5.82642i	−0.533138	+	0.202850i
$826$	13.1034	+	5.59905i	0.455927	+	0.194816i
$827$	15.8761	−	21.8516i	0.552066	−	0.759854i	−0.438225	−	0.898865i	$-0.644393\pi$
$827$	15.8761	−	21.8516i	0.552066	−	0.759854i	0.990291	+	0.139012i	$0.0443926\pi$
$828$	−7.39602	−	15.3497i	−0.257030	−	0.533440i
$829$	−2.80165	−	8.62259i	−0.0973053	−	0.299475i	0.890542	−	0.454900i	$-0.150325\pi$
$829$	−2.80165	−	8.62259i	−0.0973053	−	0.299475i	−0.987848	+	0.155425i	$0.950325\pi$
$830$	15.4472	+	67.6457i	0.536179	+	2.34802i
$831$	8.02807	−	5.83273i	0.278490	−	0.202335i
$832$	7.74317	−	27.7857i	0.268446	−	0.963295i
$833$	−0.508313	−	0.165161i	−0.0176120	−	0.00572248i
$834$	6.01391	+	10.0632i	0.208245	+	0.348459i
$835$	−0.132981			−0.00460199
$836$	−26.8495	+	5.00403i	−0.928608	+	0.173068i
$837$			31.9487i			1.10431i
$838$	2.58430	+	4.32436i	0.0892732	+	0.149382i
$839$	−8.95118	+	27.5489i	−0.309029	+	0.951093i	0.669114	+	0.743160i	$0.266674\pi$
$839$	−8.95118	+	27.5489i	−0.309029	+	0.951093i	−0.978143	+	0.207933i	$0.933326\pi$
$840$	−23.5314	+	18.7778i	−0.811911	+	0.647896i
$841$	44.7429	−	32.5076i	1.54286	−	1.12095i
$842$	−6.18063	+	1.41137i	−0.212999	+	0.0486391i
$843$	27.0097	−	8.77597i	0.930262	−	0.302260i
$844$	6.72322	−	3.23947i	0.231423	−	0.111507i
$845$	−3.69312	+	38.3427i	−0.127047	+	1.31903i
$846$	2.57515	−	6.02662i	0.0885355	−	0.207199i
$847$	−20.0976	−	22.5873i	−0.690563	−	0.776110i
$848$	−0.127479	+	2.86544i	−0.00437764	+	0.0983996i
$849$	6.99599	−	9.62916i	0.240102	−	0.330472i
$850$	−3.38921	+	3.88009i	−0.116249	+	0.133086i
$851$	0.662841	+	2.04002i	0.0227219	+	0.0699309i
$852$	−2.65394	+	14.6420i	−0.0909225	+	0.501625i
$853$	2.34236	−	1.70182i	0.0802008	−	0.0582693i	−0.546962	−	0.837157i	$-0.684216\pi$
$853$	2.34236	−	1.70182i	0.0802008	−	0.0582693i	0.627163	+	0.778888i	$0.284216\pi$
$854$	−50.1057	−	4.50428i	−1.71458	−	0.154133i
$855$	4.87078	−	14.9907i	0.166577	−	0.512671i
$856$	51.4102	+	14.1708i	1.75716	+	0.484350i
$857$			4.68800i			0.160139i	0.996789	+	0.0800696i	$0.0255142\pi$
$857$			4.68800i			0.160139i	−0.996789	+	0.0800696i	$0.974486\pi$
$858$	14.5168	−	16.6663i	0.495594	−	0.568977i
$859$			7.43682i			0.253741i	0.991919	+	0.126871i	$0.0404933\pi$
$859$			7.43682i			0.253741i	−0.991919	+	0.126871i	$0.959507\pi$
$860$	−7.78533	+	1.05626i	−0.265478	+	0.0360183i
$861$	11.4671	−	35.2920i	0.390796	−	1.20275i
$862$	2.22528	−	24.7541i	0.0757935	−	0.843128i
$863$	20.8181	−	15.1253i	0.708658	−	0.514870i	−0.174083	−	0.984731i	$-0.555696\pi$
$863$	20.8181	−	15.1253i	0.708658	−	0.514870i	0.882740	+	0.469861i	$0.155696\pi$
$864$	−5.68216	−	31.2178i	−0.193311	−	1.06205i
$865$	4.47733	+	13.7798i	0.152234	+	0.468527i
$866$	−41.5308	−	36.2767i	−1.41127	−	1.23273i
$867$	12.3457	−	16.9924i	0.419282	−	0.577092i
$868$	22.6261	−	21.6419i	0.767981	−	0.734575i
$869$	15.3225	+	40.2711i	0.519779	+	1.36610i
$870$	−46.2403	−	19.7583i	−1.56769	−	0.669870i
$871$	−0.119132	+	0.314429i	−0.00403663	+	0.0106540i
$872$	−0.718333	−	15.8831i	−0.0243258	−	0.537869i
$873$	−16.5353	+	5.37266i	−0.559636	+	0.181837i
$874$	8.54806	+	37.4334i	0.289143	+	1.26620i
$875$	8.03906	−	5.84072i	0.271770	−	0.197452i
$876$	−32.0224	−	17.2233i	−1.08194	−	0.581922i
$877$	9.43032	−	29.0235i	0.318439	−	0.980056i	−0.655876	−	0.754868i	$-0.727701\pi$
$877$	9.43032	−	29.0235i	0.318439	−	0.980056i	0.974316	−	0.225187i	$-0.0722993\pi$
$878$	2.46951	−	1.47581i	0.0833418	−	0.0498063i
$879$			12.3711i			0.417268i
$880$	−31.6875	+	23.2629i	−1.06819	+	0.784191i
$881$	13.0891			0.440982			0.220491	−	0.975389i	$-0.429234\pi$
$881$	13.0891			0.440982			0.220491	+	0.975389i	$0.429234\pi$
$882$	0.869768	−	0.519786i	0.0292866	−	0.0175021i
$883$	23.6287	+	7.67743i	0.795169	+	0.258366i	0.678304	−	0.734782i	$-0.262715\pi$
$883$	23.6287	+	7.67743i	0.795169	+	0.258366i	0.116866	+	0.993148i	$0.462715\pi$
$884$	1.56626	−	6.77101i	0.0526790	−	0.227734i
$885$	11.4851	−	8.34438i	0.386066	−	0.280493i
$886$	−45.1024	+	10.2993i	−1.51524	+	0.346012i
$887$	7.67123	+	23.6096i	0.257575	+	0.792734i	0.993311	+	0.115466i	$0.0368361\pi$
$887$	7.67123	+	23.6096i	0.257575	+	0.792734i	−0.735737	+	0.677268i	$0.763164\pi$
$888$	0.0543265	+	1.20121i	0.00182308	+	0.0403101i
$889$	−11.3162	+	15.5754i	−0.379532	+	0.522381i
$890$	17.9037	−	41.9001i	0.600135	−	1.40449i
$891$	2.99843	−	11.0596i	0.100451	−	0.370512i
$892$	14.7078	+	15.3766i	0.492452	+	0.514847i
$893$	−8.68099	+	11.9484i	−0.290498	+	0.399837i
$894$	−10.0476	+	11.5028i	−0.336041	+	0.384712i
$895$	1.74632	+	5.37461i	0.0583729	+	0.179653i
$896$	−18.2595	+	25.1710i	−0.610006	+	0.840902i
$897$	−24.2328	−	19.4495i	−0.809111	−	0.649400i
$898$	−0.468868	+	5.21570i	−0.0156463	+	0.174050i
$899$	49.7372	+	16.1606i	1.65883	+	0.538987i
$900$	−1.31308	−	9.67823i	−0.0437693	−	0.322608i
$901$			0.691085i			0.0230234i
$902$	16.8150	−	45.4424i	0.559877	−	1.51307i
$903$	−4.76231			−0.158480
$904$	−20.5333	−	5.65984i	−0.682926	−	0.188244i
$905$	−23.9455	−	7.78038i	−0.795977	−	0.258629i
$906$	23.0833	+	2.07509i	0.766891	+	0.0689401i
$907$	−3.87514	−	5.33367i	−0.128672	−	0.177102i	0.739820	−	0.672805i	$-0.234911\pi$
$907$	−3.87514	−	5.33367i	−0.128672	−	0.177102i	−0.868492	+	0.495703i	$0.834911\pi$
$908$	−2.39287	+	13.2016i	−0.0794101	+	0.438111i
$909$	−4.52981	+	1.47182i	−0.150244	+	0.0488173i
$910$	18.1313	−	37.3603i	0.601045	−	1.23848i
$911$	−26.1242	+	35.9569i	−0.865533	+	1.19130i	0.114689	+	0.993401i	$0.463413\pi$
$911$	−26.1242	+	35.9569i	−0.865533	+	1.19130i	−0.980222	+	0.197902i	$0.936587\pi$
$912$	−0.956644	+	21.5033i	−0.0316777	+	0.712044i
$913$	2.71236	+	54.8510i	0.0897661	+	1.81530i
$914$	10.0867	−	23.6059i	0.333639	−	0.780814i
$915$	−29.4597	+	40.5478i	−0.973908	+	1.34047i
$916$	4.61083	+	9.56934i	0.152346	+	0.316180i
$917$	−35.5487	+	11.5505i	−1.17392	+	0.381430i
$918$	−1.70201	−	7.45337i	−0.0561746	−	0.245998i
$919$	28.7221	−	20.8679i	0.947456	−	0.688367i	−0.00274785	−	0.999996i	$-0.500875\pi$
$919$	28.7221	−	20.8679i	0.947456	−	0.688367i	0.950204	+	0.311629i	$0.100875\pi$
$920$	34.4706	+	43.1968i	1.13646	+	1.42415i
$921$	−11.8017	+	36.3219i	−0.388879	+	1.19685i
$922$	−29.0105	+	17.3371i	−0.955411	+	0.570968i
$923$	−5.39877	−	19.8036i	−0.177703	−	0.651843i
$924$	−20.9287	+	11.3905i	−0.688505	+	0.374720i
$925$			1.22956i			0.0404276i
$926$	−6.18561	+	3.69661i	−0.203272	+	0.121478i
$927$	6.57937	+	2.13777i	0.216095	+	0.0702135i
$928$	−51.4736	−	6.94501i	−1.68971	−	0.227981i
$929$	28.8368	+	39.6904i	0.946104	+	1.30220i	0.953236	+	0.302226i	$0.0977299\pi$
$929$	28.8368	+	39.6904i	0.946104	+	1.30220i	−0.00713170	+	0.999975i	$0.502270\pi$
$930$	−6.94430	−	30.4102i	−0.227712	−	0.997190i
$931$	−2.17162	+	0.705602i	−0.0711720	+	0.0231252i
$932$	24.4961	+	50.8393i	0.802396	+	1.66530i
$933$	7.20270	+	5.23307i	0.235806	+	0.171323i
$934$	−12.8660	−	5.49758i	−0.420987	−	0.179886i
$935$	−7.37817	+	5.93877i	−0.241292	+	0.194218i
$936$	7.71427	+	10.6809i	0.252149	+	0.349116i
$937$	22.3189	−	30.7193i	0.729127	−	1.00356i	−0.270044	−	0.962848i	$-0.587038\pi$
$937$	22.3189	−	30.7193i	0.729127	−	1.00356i	0.999171	−	0.0407088i	$-0.0129616\pi$
$938$	0.238469	−	0.273008i	0.00778630	−	0.00891403i
$939$	12.5273	−	4.07038i	0.408814	−	0.132832i
$940$	−3.79118	+	20.9162i	−0.123655	+	0.682210i
$941$	16.4056	−	11.9193i	0.534806	−	0.388559i	−0.287346	−	0.957827i	$-0.592773\pi$
$941$	16.4056	−	11.9193i	0.534806	−	0.388559i	0.822152	+	0.569267i	$0.192773\pi$
$942$	1.71649	−	19.0943i	0.0559263	−	0.622125i
$943$	−64.7857	−	21.0501i	−2.10971	−	0.685487i
$944$	9.13779	−	11.4683i	0.297410	−	0.373262i
$945$		−	45.6830i		−	1.48607i
$946$	−6.21331	−	0.250191i	−0.202012	−	0.00813440i
$947$	−29.9964			−0.974753			−0.487376	−	0.873192i	$-0.662046\pi$
$947$	−29.9964			−0.974753			−0.487376	+	0.873192i	$0.662046\pi$
$948$	33.6492	−	4.56531i	1.09288	−	0.148274i
$949$	50.0979	+	2.40711i	1.62625	+	0.0781382i
$950$	−1.97065	+	21.9215i	−0.0639362	+	0.711228i
$951$	9.36588	−	6.80471i	0.303710	−	0.220658i
$952$	−4.12556	+	6.25425i	−0.133710	+	0.202701i
$953$	−21.2862	+	6.91631i	−0.689528	+	0.224041i	−0.632762	−	0.774346i	$-0.718079\pi$
$953$	−21.2862	+	6.91631i	−0.689528	+	0.224041i	−0.0567660	+	0.998388i	$0.518079\pi$
$954$	−0.986732	−	0.861899i	−0.0319466	−	0.0279050i
$955$	44.8501	+	32.5855i	1.45131	+	1.05444i
$956$	−14.8272	+	14.1822i	−0.479545	+	0.458686i
$957$	−33.3142	−	21.7745i	−1.07690	−	0.703871i
$958$	−23.3432	−	9.97445i	−0.754184	−	0.322260i
$959$	−26.9548	−	19.5838i	−0.870417	−	0.632395i
$960$	12.1940	+	28.4795i	0.393559	+	0.919171i
$961$	0.445335	+	1.37060i	0.0143656	+	0.0442129i
$962$	−0.781561	−	1.46298i	−0.0251985	−	0.0471683i
$963$	−19.7066	+	14.3177i	−0.635035	+	0.461380i
$964$	−23.3981	+	43.5029i	−0.753602	+	1.40113i
$965$	33.2812	+	10.8137i	1.07136	+	0.348106i
$966$	17.1845	+	28.7551i	0.552901	+	0.925179i
$967$		−	19.6035i		−	0.630405i	−0.949024	−	0.315202i	$-0.897928\pi$
$967$		−	19.6035i		−	0.630405i	0.949024	−	0.315202i	$-0.102072\pi$
$968$	−27.9038	+	13.7615i	−0.896862	+	0.442311i
$969$			5.18614i			0.166603i
$970$	48.4068	−	28.9286i	1.55425	−	0.928842i
$971$	−20.6807	−	6.71956i	−0.663674	−	0.215641i	−0.0422404	−	0.999107i	$-0.513450\pi$
$971$	−20.6807	−	6.71956i	−0.663674	−	0.215641i	−0.621434	+	0.783467i	$0.713450\pi$
$972$	21.6869	+	11.6643i	0.695606	+	0.374133i
$973$	10.2472	+	14.1041i	0.328512	+	0.452157i
$974$	2.60845	+	11.4228i	0.0835803	+	0.366012i
$975$	−9.76571	−	14.8957i	−0.312753	−	0.477043i
$976$	−18.1702	+	48.4762i	−0.581613	+	1.55169i
$977$	−16.9336	+	23.3071i	−0.541755	+	0.745661i	−0.988865	−	0.148818i	$-0.952453\pi$
$977$	−16.9336	+	23.3071i	−0.541755	+	0.745661i	0.447110	+	0.894479i	$0.352453\pi$
$978$	−15.2937	−	6.53495i	−0.489039	−	0.208965i
$979$	19.7307	−	30.1873i	0.630596	−	0.964789i
$980$	−2.37496	+	2.27165i	−0.0758653	+	0.0725652i
$981$	5.87541	+	4.26874i	0.187587	+	0.136290i
$982$	−26.0569	−	22.7604i	−0.831509	−	0.726313i
$983$	0.000207219	0	0.000637755i	6.60927e−6	0	2.03412e-5i	0.951060	−	0.309007i	$-0.0999966\pi$
$983$	0.000207219	0	0.000637755i	6.60927e−6	0	2.03412e-5i	−0.951053	+	0.309027i	$0.899997\pi$
$984$	−31.8761	−	21.0268i	−1.01617	−	0.670309i
$985$	8.57561	+	11.8033i	0.273242	+	0.376085i
$986$	−12.4642	−	1.12048i	−0.396942	−	0.0356833i
$987$	−3.98165	+	12.2543i	−0.126737	+	0.390058i
$988$	−11.5895	−	27.3357i	−0.368712	−	0.869665i
$989$			8.74221i			0.277986i
$990$	0.722437	−	17.9412i	0.0229605	−	0.570209i
$991$		−	8.21285i		−	0.260890i	−0.991456	−	0.130445i	$-0.958359\pi$
$991$		−	8.21285i		−	0.260890i	0.991456	−	0.130445i	$-0.0416406\pi$
$992$	−15.2829	−	28.3646i	−0.485232	−	0.900577i
$993$	−22.6252	−	7.35136i	−0.717988	−	0.233289i
$994$	−1.98129	+	22.0400i	−0.0628429	+	0.699065i
$995$	7.74568	−	5.62757i	0.245555	−	0.178406i
$996$	42.5872	+	7.71917i	1.34943	+	0.244591i
$997$	−10.1415	+	3.29517i	−0.321184	+	0.104359i	−0.465172	−	0.885220i	$-0.654007\pi$
$997$	−10.1415	+	3.29517i	−0.321184	+	0.104359i	0.143988	+	0.989579i	$0.454007\pi$
$998$	−22.8054	−	19.9202i	−0.721892	−	0.630564i
$999$	−1.47616	−	1.07249i	−0.0467035	−	0.0339321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.b.51.15	✓	304
4.3	odd	2	inner	572.2.bb.b.51.44	yes	304
11.8	odd	10	inner	572.2.bb.b.415.33	yes	304
13.12	even	2	inner	572.2.bb.b.51.62	yes	304
44.19	even	10	inner	572.2.bb.b.415.62	yes	304
52.51	odd	2	inner	572.2.bb.b.51.33	yes	304
143.129	odd	10	inner	572.2.bb.b.415.44	yes	304
572.415	even	10	inner	572.2.bb.b.415.15	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.b.51.15	✓	304	1.1	even	1	trivial
572.2.bb.b.51.33	yes	304	52.51	odd	2	inner
572.2.bb.b.51.44	yes	304	4.3	odd	2	inner
572.2.bb.b.51.62	yes	304	13.12	even	2	inner
572.2.bb.b.415.15	yes	304	572.415	even	10	inner
572.2.bb.b.415.33	yes	304	11.8	odd	10	inner
572.2.bb.b.415.44	yes	304	143.129	odd	10	inner
572.2.bb.b.415.62	yes	304	44.19	even	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.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21395 + 0.725477i) q^{2} +(1.24296 + 0.403861i) q^{3} +(0.947367 - 1.76139i) q^{4} +(-1.74166 - 2.39719i) q^{5} +(-1.80188 + 0.411468i) q^{6} +(-2.61403 + 0.849351i) q^{7} +(0.127789 + 2.82554i) q^{8} +(-1.04521 - 0.759392i) q^{9} +O(q^{10})\)	\(q+(-1.21395 + 0.725477i) q^{2} +(1.24296 + 0.403861i) q^{3} +(0.947367 - 1.76139i) q^{4} +(-1.74166 - 2.39719i) q^{5} +(-1.80188 + 0.411468i) q^{6} +(-2.61403 + 0.849351i) q^{7} +(0.127789 + 2.82554i) q^{8} +(-1.04521 - 0.759392i) q^{9} +(3.85340 + 1.64654i) q^{10} +(2.77621 + 1.81456i) q^{11} +(1.88889 - 1.80673i) q^{12} +(-1.27746 + 3.37166i) q^{13} +(2.55713 - 2.92749i) q^{14} +(-1.19668 - 3.68299i) q^{15} +(-2.20499 - 3.33737i) q^{16} +(-0.566486 - 0.779701i) q^{17} +(1.81976 + 0.163589i) q^{18} +(-3.91589 - 1.27235i) q^{19} +(-5.87238 + 0.796726i) q^{20} -3.59215 q^{21} +(-4.68662 - 0.188716i) q^{22} +6.59413i q^{23} +(-0.982289 + 3.56363i) q^{24} +(-1.16805 + 3.59489i) q^{25} +(-0.895279 - 5.01981i) q^{26} +(-3.29703 - 4.53798i) q^{27} +(-0.980410 + 5.40898i) q^{28} +(-8.73240 + 2.83733i) q^{29} +(4.12463 + 3.60282i) q^{30} +(-4.60793 - 3.34786i) q^{31} +(5.09794 + 2.45174i) q^{32} +(2.71788 + 3.37663i) q^{33} +(1.25334 + 0.535549i) q^{34} +(6.58881 + 4.78705i) q^{35} +(-2.32779 + 1.12161i) q^{36} +(0.309368 - 0.100520i) q^{37} +(5.67677 - 1.29631i) q^{38} +(-2.94951 + 3.67491i) q^{39} +(6.55079 - 5.22746i) q^{40} +(-3.19225 + 9.82475i) q^{41} +(4.36070 - 2.60602i) q^{42} +1.32576 q^{43} +(5.82625 - 3.17094i) q^{44} +3.82818i q^{45} +(-4.78389 - 8.00497i) q^{46} +(1.10843 - 3.41140i) q^{47} +(-1.39288 - 5.03871i) q^{48} +(0.448654 - 0.325966i) q^{49} +(-1.19005 - 5.21143i) q^{50} +(-0.389227 - 1.19792i) q^{51} +(4.72858 + 5.44431i) q^{52} +(-0.580121 - 0.421482i) q^{53} +(7.29465 + 3.11697i) q^{54} +(-0.485371 - 9.81546i) q^{55} +(-2.73392 - 7.27752i) q^{56} +(-4.35343 - 3.16295i) q^{57} +(8.54231 - 9.77954i) q^{58} +(1.13283 + 3.48648i) q^{59} +(-7.62088 - 1.38133i) q^{60} +(-7.60736 - 10.4706i) q^{61} +(8.02260 + 0.721196i) q^{62} +(3.37721 + 1.09732i) q^{63} +(-7.96734 + 0.722144i) q^{64} +(10.3074 - 2.80996i) q^{65} +(-5.74905 - 2.12731i) q^{66} +0.0932566 q^{67} +(-1.91003 + 0.259140i) q^{68} +(-2.66311 + 8.19622i) q^{69} +(-11.4714 - 1.03123i) q^{70} +(-4.60571 + 3.34624i) q^{71} +(2.01213 - 3.05033i) q^{72} +(-4.29864 - 13.2299i) q^{73} +(-0.302634 + 0.346466i) q^{74} +(-2.90367 + 3.99656i) q^{75} +(-5.95088 + 5.69203i) q^{76} +(-8.79832 - 2.38535i) q^{77} +(0.914513 - 6.60097i) q^{78} +(10.5103 + 7.63616i) q^{79} +(-4.15995 + 11.0983i) q^{80} +(-1.06765 - 3.28589i) q^{81} +(-3.25238 - 14.2427i) q^{82} +(9.73278 + 13.3960i) q^{83} +(-3.40308 + 6.32718i) q^{84} +(-0.882465 + 2.71595i) q^{85} +(-1.60941 + 0.961805i) q^{86} -11.9999 q^{87} +(-4.77235 + 8.07618i) q^{88} -10.8735i q^{89} +(-2.77725 - 4.64723i) q^{90} +(0.475612 - 9.89864i) q^{91} +(11.6148 + 6.24706i) q^{92} +(-4.37539 - 6.02220i) q^{93} +(1.12931 + 4.94543i) q^{94} +(3.77008 + 11.6031i) q^{95} +(5.34636 + 5.10626i) q^{96} +(7.91003 - 10.8872i) q^{97} +(-0.308164 + 0.721196i) q^{98} +(-1.52377 - 4.00484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) \) 304 * q - 14 * q^4 + 72 * q^9	\( 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) \) 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more