LMFDB - Embedded newform 570.2.x.b.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			487.4
Character	$\chi$	$=$	570.487
Dual form			570.2.x.b.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.392079 - 2.20143i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.01170 - 3.01170i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.392079 - 2.20143i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.01170 - 3.01170i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.948490 + 2.02494i) q^{10} +0.889913 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.48983 + 0.935096i) q^{13} +(2.12960 + 3.68857i) q^{14} +(2.02494 + 0.948490i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.12690 + 7.93771i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-1.13751 + 4.20786i) q^{19} +(1.44026 - 1.71045i) q^{20} +(3.68857 - 2.12960i) q^{21} +(-0.859590 - 0.230326i) q^{22} +(0.772077 + 2.88143i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.69255 - 1.72627i) q^{25} +3.61294 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.10236 - 4.11406i) q^{28} +(-3.84671 + 6.66270i) q^{29} +(-1.71045 - 1.44026i) q^{30} -4.64175i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.230326 + 0.859590i) q^{33} +(4.10886 - 7.11676i) q^{34} +(-7.81087 + 5.44921i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.39772 - 3.39772i) q^{37} +(2.18783 - 3.77007i) q^{38} -3.61294i q^{39} +(-1.83388 + 1.27940i) q^{40} +(4.93258 - 2.84783i) q^{41} +(-4.11406 + 1.10236i) q^{42} +(-11.1463 - 2.98664i) q^{43} +(0.770687 + 0.444956i) q^{44} +(-1.44026 + 1.71045i) q^{45} -2.98307i q^{46} +(-9.22311 + 2.47133i) q^{47} +(-0.965926 + 0.258819i) q^{48} +11.1407i q^{49} +(4.08586 + 2.88197i) q^{50} +(-7.11676 - 4.10886i) q^{51} +(-3.48983 - 0.935096i) q^{52} +(10.6952 - 2.86577i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.348916 - 1.95908i) q^{55} +4.25919i q^{56} +(-3.77007 - 2.18783i) q^{57} +(5.44007 - 5.44007i) q^{58} +(-1.41987 - 2.45929i) q^{59} +(1.27940 + 1.83388i) q^{60} +(-2.57826 + 4.46567i) q^{61} +(-1.20137 + 4.48358i) q^{62} +(1.10236 + 4.11406i) q^{63} +1.00000i q^{64} +(0.690256 + 8.04923i) q^{65} +(0.444956 - 0.770687i) q^{66} +(-1.57298 - 5.87045i) q^{67} +(-5.81081 + 5.81081i) q^{68} -2.98307 q^{69} +(8.95508 - 3.24194i) q^{70} +(-1.67297 + 0.965889i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-3.11813 - 0.835499i) q^{73} +(-4.16134 + 2.40255i) q^{74} +(2.88197 - 4.08586i) q^{75} +(-3.08904 + 3.07535i) q^{76} +(-2.68015 - 2.68015i) q^{77} +(-0.935096 + 3.48983i) q^{78} +(-5.06765 - 8.77743i) q^{79} +(2.10253 - 0.761162i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.50158 + 1.47414i) q^{82} +(-4.14696 + 4.14696i) q^{83} +4.25919 q^{84} +(16.6404 + 7.79443i) q^{85} +(9.99350 + 5.76975i) q^{86} +(-5.44007 - 5.44007i) q^{87} +(-0.629263 - 0.629263i) q^{88} +(-4.50636 + 7.80525i) q^{89} +(1.83388 - 1.27940i) q^{90} +(13.3266 + 7.69409i) q^{91} +(-0.772077 + 2.88143i) q^{92} +(4.48358 + 1.20137i) q^{93} +9.54847 q^{94} +(8.81729 + 4.15396i) q^{95} +1.00000 q^{96} +(1.59348 + 0.426972i) q^{97} +(2.88343 - 10.7611i) q^{98} +(-0.770687 - 0.444956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.392079	−	2.20143i	0.175343	−	0.984507i
$5$	0.392079	−	2.20143i	0.175343	−	0.984507i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−3.01170	−	3.01170i	−1.13832	−	1.13832i	−0.988752	−	0.149565i	$-0.952213\pi$
$7$	−3.01170	−	3.01170i	−1.13832	−	1.13832i	−0.149565	−	0.988752i	$-0.547787\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.948490	+	2.02494i	−0.299939	+	0.640341i
$11$	0.889913			0.268319			0.134159	−	0.990960i	$-0.457167\pi$
$11$	0.889913			0.268319			0.134159	+	0.990960i	$0.457167\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−3.48983	+	0.935096i	−0.967904	+	0.259349i	−0.707943	−	0.706270i	$-0.750376\pi$
$13$	−3.48983	+	0.935096i	−0.967904	+	0.259349i	−0.259961	+	0.965619i	$0.583710\pi$
$14$	2.12960	+	3.68857i	0.569159	+	0.985811i
$15$	2.02494	+	0.948490i	0.522836	+	0.244899i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.12690	+	7.93771i	−0.515850	+	1.92518i	−0.177701	+	0.984084i	$0.556866\pi$
$17$	−2.12690	+	7.93771i	−0.515850	+	1.92518i	−0.338148	+	0.941093i	$0.609801\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−1.13751	+	4.20786i	−0.260963	+	0.965349i
$19$	−1.13751	+	4.20786i	−0.260963	+	0.965349i
$20$	1.44026	−	1.71045i	0.322053	−	0.382468i
$21$	3.68857	−	2.12960i	0.804912	−	0.464716i
$22$	−0.859590	−	0.230326i	−0.183265	−	0.0491057i
$23$	0.772077	+	2.88143i	0.160989	+	0.600820i	0.998518	+	0.0544262i	$0.0173330\pi$
$23$	0.772077	+	2.88143i	0.160989	+	0.600820i	−0.837529	+	0.546393i	$0.816000\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.69255	−	1.72627i	−0.938510	−	0.345253i
$26$	3.61294			0.708555
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.10236	−	4.11406i	−0.208326	−	0.777485i
$29$	−3.84671	+	6.66270i	−0.714316	+	1.23723i	0.248907	+	0.968527i	$0.419929\pi$
$29$	−3.84671	+	6.66270i	−0.714316	+	1.23723i	−0.963223	+	0.268704i	$0.913405\pi$
$30$	−1.71045	−	1.44026i	−0.312284	−	0.262955i
$31$		−	4.64175i		−	0.833683i	−0.908979	−	0.416841i	$-0.863137\pi$
$31$		−	4.64175i		−	0.833683i	0.908979	−	0.416841i	$-0.136863\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.230326	+	0.859590i	−0.0400947	+	0.149635i
$34$	4.10886	−	7.11676i	0.704664	−	1.22051i
$35$	−7.81087	+	5.44921i	−1.32028	+	0.921085i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	3.39772	−	3.39772i	0.558582	−	0.558582i	−0.370322	−	0.928904i	$-0.620752\pi$
$37$	3.39772	−	3.39772i	0.558582	−	0.558582i	0.928904	+	0.370322i	$0.120752\pi$
$38$	2.18783	−	3.77007i	0.354912	−	0.611586i
$39$		−	3.61294i		−	0.578533i
$40$	−1.83388	+	1.27940i	−0.289963	+	0.202291i
$41$	4.93258	−	2.84783i	0.770340	−	0.444756i	−0.0626558	−	0.998035i	$-0.519957\pi$
$41$	4.93258	−	2.84783i	0.770340	−	0.444756i	0.832996	+	0.553279i	$0.186624\pi$
$42$	−4.11406	+	1.10236i	−0.634814	+	0.170098i
$43$	−11.1463	−	2.98664i	−1.69980	−	0.455459i	−0.726907	−	0.686736i	$-0.759043\pi$
$43$	−11.1463	−	2.98664i	−1.69980	−	0.455459i	−0.972888	+	0.231277i	$0.925710\pi$
$44$	0.770687	+	0.444956i	0.116185	+	0.0670797i
$45$	−1.44026	+	1.71045i	−0.214702	+	0.254979i
$46$		−	2.98307i		−	0.439830i
$47$	−9.22311	+	2.47133i	−1.34533	+	0.360480i	−0.858409	−	0.512966i	$-0.828547\pi$
$47$	−9.22311	+	2.47133i	−1.34533	+	0.360480i	−0.486921	+	0.873446i	$0.661880\pi$
$48$	−0.965926	+	0.258819i	−0.139419	+	0.0373573i
$49$			11.1407i			1.59153i
$50$	4.08586	+	2.88197i	0.577828	+	0.407572i
$51$	−7.11676	−	4.10886i	−0.996545	−	0.575356i
$52$	−3.48983	−	0.935096i	−0.483952	−	0.129675i
$53$	10.6952	−	2.86577i	1.46910	−	0.393644i	0.566477	−	0.824077i	$-0.308306\pi$
$53$	10.6952	−	2.86577i	1.46910	−	0.393644i	0.902622	+	0.430433i	$0.141639\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	0.348916	−	1.95908i	0.0470479	−	0.264162i
$56$			4.25919i			0.569159i
$57$	−3.77007	−	2.18783i	−0.499358	−	0.289785i
$58$	5.44007	−	5.44007i	0.714316	−	0.714316i
$59$	−1.41987	−	2.45929i	−0.184852	−	0.320172i	0.758675	−	0.651469i	$-0.225847\pi$
$59$	−1.41987	−	2.45929i	−0.184852	−	0.320172i	−0.943526	+	0.331297i	$0.892514\pi$
$60$	1.27940	+	1.83388i	0.165170	+	0.236753i
$61$	−2.57826	+	4.46567i	−0.330112	+	0.571771i	−0.982534	−	0.186085i	$-0.940420\pi$
$61$	−2.57826	+	4.46567i	−0.330112	+	0.571771i	0.652421	+	0.757856i	$0.273753\pi$
$62$	−1.20137	+	4.48358i	−0.152574	+	0.569416i
$63$	1.10236	+	4.11406i	0.138884	+	0.518323i
$64$			1.00000i			0.125000i
$65$	0.690256	+	8.04923i	0.0856158	+	0.998384i
$66$	0.444956	−	0.770687i	0.0547703	−	0.0948650i
$67$	−1.57298	−	5.87045i	−0.192170	−	0.717190i	−0.992981	−	0.118272i	$-0.962264\pi$
$67$	−1.57298	−	5.87045i	−0.192170	−	0.717190i	0.800811	−	0.598917i	$-0.204402\pi$
$68$	−5.81081	+	5.81081i	−0.704664	+	0.704664i
$69$	−2.98307			−0.359120
$70$	8.95508	−	3.24194i	1.07034	−	0.387485i
$71$	−1.67297	+	0.965889i	−0.198545	+	0.114630i	−0.595977	−	0.803002i	$-0.703235\pi$
$71$	−1.67297	+	0.965889i	−0.198545	+	0.114630i	0.397432	+	0.917632i	$0.369902\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−3.11813	−	0.835499i	−0.364949	−	0.0977878i	0.0716843	−	0.997427i	$-0.477163\pi$
$73$	−3.11813	−	0.835499i	−0.364949	−	0.0977878i	−0.436633	+	0.899640i	$0.643829\pi$
$74$	−4.16134	+	2.40255i	−0.483746	+	0.279291i
$75$	2.88197	−	4.08586i	0.332781	−	0.471795i
$76$	−3.08904	+	3.07535i	−0.354338	+	0.352767i
$77$	−2.68015	−	2.68015i	−0.305432	−	0.305432i
$78$	−0.935096	+	3.48983i	−0.105879	+	0.395145i
$79$	−5.06765	−	8.77743i	−0.570155	−	0.987538i	−0.996549	−	0.0830007i	$-0.973550\pi$
$79$	−5.06765	−	8.77743i	−0.570155	−	0.987538i	0.426394	−	0.904538i	$-0.359784\pi$
$80$	2.10253	−	0.761162i	0.235070	−	0.0851005i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−5.50158	+	1.47414i	−0.607548	+	0.162792i
$83$	−4.14696	+	4.14696i	−0.455188	+	0.455188i	−0.897072	−	0.441884i	$-0.854310\pi$
$83$	−4.14696	+	4.14696i	−0.455188	+	0.455188i	0.441884	+	0.897072i	$0.354310\pi$
$84$	4.25919			0.464716
$85$	16.6404	+	7.79443i	1.80490	+	0.845424i
$86$	9.99350	+	5.76975i	1.07763	+	0.622168i
$87$	−5.44007	−	5.44007i	−0.583236	−	0.583236i
$88$	−0.629263	−	0.629263i	−0.0670797	−	0.0670797i
$89$	−4.50636	+	7.80525i	−0.477673	+	0.827354i	−0.999672	−	0.0255916i	$-0.991853\pi$
$89$	−4.50636	+	7.80525i	−0.477673	+	0.827354i	0.521999	+	0.852946i	$0.325186\pi$
$90$	1.83388	−	1.27940i	0.193308	−	0.134861i
$91$	13.3266	+	7.69409i	1.39700	+	0.806560i
$92$	−0.772077	+	2.88143i	−0.0804946	+	0.300410i
$93$	4.48358	+	1.20137i	0.464926	+	0.124577i
$94$	9.54847			0.984849
$95$	8.81729	+	4.15396i	0.904635	+	0.426188i
$96$	1.00000			0.102062
$97$	1.59348	+	0.426972i	0.161793	+	0.0433524i	0.338806	−	0.940856i	$-0.389977\pi$
$97$	1.59348	+	0.426972i	0.161793	+	0.0433524i	−0.177013	+	0.984209i	$0.556643\pi$
$98$	2.88343	−	10.7611i	0.291270	−	1.08704i
$99$	−0.770687	−	0.444956i	−0.0774569	−	0.0447198i
$100$	−3.20073	−	3.84126i	−0.320073	−	0.384126i
$101$	8.14890	−	14.1143i	0.810846	−	1.40443i	−0.101427	−	0.994843i	$-0.532341\pi$
$101$	8.14890	−	14.1143i	0.810846	−	1.40443i	0.912273	−	0.409583i	$-0.134326\pi$
$102$	5.81081	+	5.81081i	0.575356	+	0.575356i
$103$	−2.00833	−	2.00833i	−0.197886	−	0.197886i	0.601207	−	0.799093i	$-0.294687\pi$
$103$	−2.00833	−	2.00833i	−0.197886	−	0.197886i	−0.799093	+	0.601207i	$0.794687\pi$
$104$	3.12889	+	1.80647i	0.306813	+	0.177139i
$105$	−3.24194	−	8.95508i	−0.316381	−	0.873926i
$106$	−11.0725			−1.07546
$107$	2.23070	−	2.23070i	0.215650	−	0.215650i	−0.591013	−	0.806662i	$-0.701272\pi$
$107$	2.23070	−	2.23070i	0.215650	−	0.215650i	0.806662	+	0.591013i	$0.201272\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	7.92699	+	13.7300i	0.759268	+	1.31509i	0.943224	+	0.332157i	$0.107776\pi$
$109$	7.92699	+	13.7300i	0.759268	+	1.31509i	−0.183956	+	0.982934i	$0.558890\pi$
$110$	−0.844073	+	1.80202i	−0.0804792	+	0.171815i
$111$	2.40255	+	4.16134i	0.228040	+	0.394977i
$112$	1.10236	−	4.11406i	0.104163	−	0.388742i
$113$	−11.9135	−	11.9135i	−1.12073	−	1.12073i	−0.991632	−	0.129097i	$-0.958792\pi$
$113$	−11.9135	−	11.9135i	−1.12073	−	1.12073i	−0.129097	−	0.991632i	$-0.541208\pi$
$114$	3.07535	+	3.08904i	0.288033	+	0.289315i
$115$	6.64597	−	0.569921i	0.619740	−	0.0531454i
$116$	−6.66270	+	3.84671i	−0.618616	+	0.357158i
$117$	3.48983	+	0.935096i	0.322635	+	0.0864497i
$118$	0.734980	+	2.74298i	0.0676604	+	0.252512i
$119$	30.3116	−	17.5004i	2.77866	−	1.60426i
$120$	−0.761162	−	2.10253i	−0.0694843	−	0.191934i
$121$	−10.2081			−0.928005
$122$	3.64621	−	3.64621i	0.330112	−	0.330112i
$123$	1.47414	+	5.50158i	0.132919	+	0.496061i
$124$	2.32087	−	4.01987i	0.208421	−	0.360995i
$125$	−5.64010	+	9.65346i	−0.504466	+	0.863432i
$126$		−	4.25919i		−	0.379439i
$127$	−1.87722	−	7.00588i	−0.166576	−	0.621671i	−0.997834	−	0.0657838i	$-0.979045\pi$
$127$	−1.87722	−	7.00588i	−0.166576	−	0.621671i	0.831258	−	0.555887i	$-0.187621\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	5.76975	−	9.99350i	0.507998	−	0.879879i
$130$	1.41656	−	7.95361i	0.124240	−	0.697578i
$131$	−2.89242	−	5.00982i	−0.252712	−	0.437710i	0.711559	−	0.702626i	$-0.247989\pi$
$131$	−2.89242	−	5.00982i	−0.252712	−	0.437710i	−0.964272	+	0.264916i	$0.914656\pi$
$132$	−0.629263	+	0.629263i	−0.0547703	+	0.0547703i
$133$	16.0987	−	9.24697i	1.39593	−	0.801814i
$134$			6.07754i			0.525019i
$135$	−1.27940	−	1.83388i	−0.110113	−	0.157836i
$136$	7.11676	−	4.10886i	0.610257	−	0.352332i
$137$	7.07023	−	1.89446i	0.604051	−	0.161855i	0.0561838	−	0.998420i	$-0.482107\pi$
$137$	7.07023	−	1.89446i	0.604051	−	0.161855i	0.547867	+	0.836566i	$0.315440\pi$
$138$	2.88143	+	0.772077i	0.245284	+	0.0657235i
$139$	−18.5428	−	10.7057i	−1.57278	−	0.908047i	−0.995826	−	0.0912724i	$-0.970907\pi$
$139$	−18.5428	−	10.7057i	−1.57278	−	0.908047i	−0.576957	−	0.816774i	$-0.695760\pi$
$140$	−9.48902	+	0.813725i	−0.801968	+	0.0687723i
$141$		−	9.54847i		−	0.804126i
$142$	1.86595	−	0.499981i	0.156587	−	0.0419574i
$143$	−3.10564	+	0.832154i	−0.259707	+	0.0695882i
$144$		−	1.00000i		−	0.0833333i
$145$	13.1592	+	11.0805i	1.09281	+	0.920189i
$146$	2.79563	+	1.61406i	0.231368	+	0.133581i
$147$	−10.7611	−	2.88343i	−0.887561	−	0.237821i
$148$	4.64138	−	1.24365i	0.381519	−	0.102228i
$149$	−0.728806	+	0.420776i	−0.0597061	+	0.0344713i	−0.529556	−	0.848275i	$-0.677641\pi$
$149$	−0.728806	+	0.420776i	−0.0597061	+	0.0344713i	0.469850	+	0.882746i	$0.344308\pi$
$150$	−3.84126	+	3.20073i	−0.313638	+	0.261339i
$151$		−	17.3302i		−	1.41031i	−0.709053	−	0.705155i	$-0.750877\pi$
$151$		−	17.3302i		−	1.41031i	0.709053	−	0.705155i	$-0.249123\pi$
$152$	3.77975	−	2.17106i	0.306578	−	0.176096i
$153$	5.81081	−	5.81081i	0.469776	−	0.469776i
$154$	1.89515	+	3.28250i	0.152716	+	0.264512i
$155$	−10.2185	−	1.81993i	−0.820767	−	0.146181i
$156$	1.80647	−	3.12889i	0.144633	−	0.250512i
$157$	−3.11335	+	11.6192i	−0.248472	+	0.927311i	0.723134	+	0.690708i	$0.242701\pi$
$157$	−3.11335	+	11.6192i	−0.248472	+	0.927311i	−0.971606	+	0.236603i	$0.923966\pi$
$158$	2.62321	+	9.78995i	0.208691	+	0.778847i
$159$			11.0725i			0.878106i
$160$	−2.22789	+	0.191051i	−0.176130	+	0.0151039i
$161$	6.35274	−	11.0033i	0.500666	−	0.867180i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	−0.451359	+	0.451359i	−0.0353532	+	0.0353532i	−0.724562	−	0.689209i	$-0.757958\pi$
$163$	−0.451359	+	0.451359i	−0.0353532	+	0.0353532i	0.689209	+	0.724562i	$0.257958\pi$
$164$	5.69566			0.444756
$165$	1.80202	+	0.844073i	0.140287	+	0.0657110i
$166$	5.07897	−	2.93234i	0.394205	−	0.227594i
$167$	5.80976	+	21.6823i	0.449573	+	1.67783i	0.703573	+	0.710623i	$0.251587\pi$
$167$	5.80976	+	21.6823i	0.449573	+	1.67783i	−0.254000	+	0.967204i	$0.581746\pi$
$168$	−4.11406	−	1.10236i	−0.317407	−	0.0850489i
$169$	0.0461604	−	0.0266507i	0.00355080	−	0.00205006i
$170$	−14.0560	−	11.8357i	−1.07805	−	0.907755i
$171$	3.08904	−	3.07535i	0.236225	−	0.235178i
$172$	−8.15966	−	8.15966i	−0.622168	−	0.622168i
$173$	−1.03654	+	3.86843i	−0.0788069	+	0.294112i	−0.994070	−	0.108746i	$-0.965316\pi$
$173$	−1.03654	+	3.86843i	−0.0788069	+	0.294112i	0.915263	+	0.402858i	$0.131983\pi$
$174$	3.84671	+	6.66270i	0.291618	+	0.505098i
$175$	8.93356	+	19.3316i	0.675314	+	1.46133i
$176$	0.444956	+	0.770687i	0.0335398	+	0.0580927i
$177$	2.74298	−	0.734980i	0.206175	−	0.0552444i
$178$	6.37296	−	6.37296i	0.477673	−	0.477673i
$179$	−0.766579			−0.0572968			−0.0286484	−	0.999590i	$-0.509120\pi$
$179$	−0.766579			−0.0572968			−0.0286484	+	0.999590i	$0.509120\pi$
$180$	−2.10253	+	0.761162i	−0.156713	+	0.0567337i
$181$	5.26999	+	3.04263i	0.391715	+	0.226157i	0.682903	−	0.730509i	$-0.260717\pi$
$181$	5.26999	+	3.04263i	0.391715	+	0.226157i	−0.291188	+	0.956666i	$0.594050\pi$
$182$	−10.8811	−	10.8811i	−0.806560	−	0.806560i
$183$	−3.64621	−	3.64621i	−0.269535	−	0.269535i
$184$	1.49154	−	2.58342i	0.109958	−	0.190452i
$185$	−6.14766	−	8.81201i	−0.451985	−	0.647872i
$186$	−4.01987	−	2.32087i	−0.294751	−	0.170175i
$187$	−1.89276	+	7.06387i	−0.138412	+	0.516561i
$188$	−9.22311	−	2.47133i	−0.672665	−	0.180240i
$189$	−4.25919			−0.309811
$190$	−7.44172	−	6.29450i	−0.539879	−	0.456651i
$191$	1.53791			0.111279			0.0556397	−	0.998451i	$-0.482280\pi$
$191$	1.53791			0.111279			0.0556397	+	0.998451i	$0.482280\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−4.64259	+	17.3264i	−0.334181	+	1.24718i	0.570573	+	0.821247i	$0.306721\pi$
$193$	−4.64259	+	17.3264i	−0.334181	+	1.24718i	−0.904754	+	0.425934i	$0.859945\pi$
$194$	−1.42867	−	0.824846i	−0.102573	−	0.0592205i
$195$	−7.95361	−	1.41656i	−0.569570	−	0.101442i
$196$	−5.57036	+	9.64815i	−0.397883	+	0.689153i
$197$	−8.77379	−	8.77379i	−0.625106	−	0.625106i	0.321726	−	0.946833i	$-0.395737\pi$
$197$	−8.77379	−	8.77379i	−0.625106	−	0.625106i	−0.946833	+	0.321726i	$0.895737\pi$
$198$	0.629263	+	0.629263i	0.0447198	+	0.0447198i
$199$	9.63986	+	5.56557i	0.683351	+	0.394533i	0.801116	−	0.598508i	$-0.204240\pi$
$199$	9.63986	+	5.56557i	0.683351	+	0.394533i	−0.117765	+	0.993041i	$0.537573\pi$
$200$	2.09748	+	4.53879i	0.148314	+	0.320941i
$201$	6.07754			0.428676
$202$	−11.5243	+	11.5243i	−0.810846	+	0.810846i
$203$	31.6512	−	8.48092i	2.22148	−	0.595244i
$204$	−4.10886	−	7.11676i	−0.287678	−	0.498273i
$205$	−4.33532	−	11.9753i	−0.302792	−	0.836391i
$206$	1.42010	+	2.45969i	0.0989432	+	0.171375i
$207$	0.772077	−	2.88143i	0.0536630	−	0.200273i
$208$	−2.55473	−	2.55473i	−0.177139	−	0.177139i
$209$	−1.01229	+	3.74463i	−0.0700214	+	0.259021i
$210$	0.813725	+	9.48902i	0.0561523	+	0.654804i
$211$	−6.95628	+	4.01621i	−0.478890	+	0.276487i	−0.719954	−	0.694022i	$-0.755837\pi$
$211$	−6.95628	+	4.01621i	−0.478890	+	0.276487i	0.241064	+	0.970509i	$0.422504\pi$
$212$	10.6952	+	2.86577i	0.734550	+	0.196822i
$213$	−0.499981	−	1.86595i	−0.0342581	−	0.127853i
$214$	−2.73204	+	1.57734i	−0.186758	+	0.107825i
$215$	−10.9451	+	23.3668i	−0.746450	+	1.59360i
$216$	−1.00000			−0.0680414
$217$	−13.9796	+	13.9796i	−0.948995	+	0.948995i
$218$	−4.10331	−	15.3138i	−0.277911	−	1.03718i
$219$	1.61406	−	2.79563i	0.109068	−	0.188911i
$220$	1.28171	−	1.52215i	0.0864128	−	0.102623i
$221$		−	29.6901i		−	1.99717i
$222$	−1.24365	−	4.64138i	−0.0834685	−	0.311509i
$223$	2.70800	−	10.1064i	0.181341	−	0.676775i	−0.814043	−	0.580805i	$-0.802738\pi$
$223$	2.70800	−	10.1064i	0.181341	−	0.676775i	0.995384	−	0.0959704i	$-0.0305954\pi$
$224$	−2.12960	+	3.68857i	−0.142290	+	0.246453i
$225$	3.20073	+	3.84126i	0.213382	+	0.256084i
$226$	8.42413	+	14.5910i	0.560365	+	0.970580i
$227$	7.19042	−	7.19042i	0.477245	−	0.477245i	−0.427005	−	0.904249i	$-0.640431\pi$
$227$	7.19042	−	7.19042i	0.477245	−	0.477245i	0.904249	+	0.427005i	$0.140431\pi$
$228$	−2.17106	−	3.77975i	−0.143782	−	0.250320i
$229$			0.0561666i			0.00371159i	0.999998	+	0.00185580i	$0.000590719\pi$
$229$			0.0561666i			0.00371159i	−0.999998	+	0.00185580i	$0.999409\pi$
$230$	−6.56702	−	1.16960i	−0.433016	−	0.0771212i
$231$	3.28250	−	1.89515i	0.215973	−	0.124692i
$232$	7.43127	−	1.99120i	0.487887	−	0.130729i
$233$	12.2855	+	3.29189i	0.804850	+	0.215659i	0.637712	−	0.770275i	$-0.279881\pi$
$233$	12.2855	+	3.29189i	0.804850	+	0.215659i	0.167138	+	0.985934i	$0.446548\pi$
$234$	−3.12889	−	1.80647i	−0.204542	−	0.118092i
$235$	1.82425	+	21.2729i	0.119001	+	1.38769i
$236$		−	2.83974i		−	0.184852i
$237$	9.78995	−	2.62321i	0.635926	−	0.170396i
$238$	−33.8082	+	9.05889i	−2.19146	+	0.587200i
$239$			3.69602i			0.239076i	0.992830	+	0.119538i	$0.0381413\pi$
$239$			3.69602i			0.239076i	−0.992830	+	0.119538i	$0.961859\pi$
$240$	0.191051	+	2.22789i	0.0123323	+	0.143810i
$241$	2.16652	+	1.25084i	0.139558	+	0.0805737i	0.568153	−	0.822923i	$-0.307658\pi$
$241$	2.16652	+	1.25084i	0.139558	+	0.0805737i	−0.428595	+	0.903496i	$0.640991\pi$
$242$	9.86022	+	2.64204i	0.633839	+	0.169837i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−4.46567	+	2.57826i	−0.285885	+	0.165056i
$245$	24.5255	+	4.36804i	1.56687	+	0.279064i
$246$		−	5.69566i		−	0.363142i
$247$	0.0349713	−	15.7484i	0.00222517	−	1.00205i
$248$	−3.28221	+	3.28221i	−0.208421	+	0.208421i
$249$	−2.93234	−	5.07897i	−0.185830	−	0.321867i
$250$	7.94641	−	7.86476i	0.502575	−	0.497411i
$251$	−6.50797	+	11.2721i	−0.410780	+	0.711491i	−0.994975	−	0.100122i	$-0.968077\pi$
$251$	−6.50797	+	11.2721i	−0.410780	+	0.711491i	0.584196	+	0.811613i	$0.301410\pi$
$252$	−1.10236	+	4.11406i	−0.0694422	+	0.259162i
$253$	0.687081	+	2.56422i	0.0431964	+	0.161211i
$254$			7.25302i			0.455095i
$255$	−11.8357	+	14.0560i	−0.741179	+	0.880221i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.96906	+	22.2768i	0.372340	+	1.38959i	0.857193	+	0.514995i	$0.172206\pi$
$257$	5.96906	+	22.2768i	0.372340	+	1.38959i	−0.484854	+	0.874595i	$0.661127\pi$
$258$	−8.15966	+	8.15966i	−0.507998	+	0.507998i
$259$	−20.4659			−1.27169
$260$	−3.42683	+	7.31596i	−0.212523	+	0.453717i
$261$	6.66270	−	3.84671i	0.412410	−	0.238105i
$262$	1.49723	+	5.58773i	0.0924991	+	0.345211i
$263$	1.96675	+	0.526989i	0.121275	+	0.0324955i	0.318946	−	0.947773i	$-0.396671\pi$
$263$	1.96675	+	0.526989i	0.121275	+	0.0324955i	−0.197671	+	0.980268i	$0.563338\pi$
$264$	0.770687	−	0.444956i	0.0474325	−	0.0273852i
$265$	−2.11542	−	24.6683i	−0.129949	−	1.51536i
$266$	−17.9434	+	4.76524i	−1.10018	+	0.292176i
$267$	−6.37296	−	6.37296i	−0.390019	−	0.390019i
$268$	1.57298	−	5.87045i	0.0960852	−	0.358595i
$269$	−3.47464	−	6.01826i	−0.211853	−	0.366940i	0.740442	−	0.672121i	$-0.234616\pi$
$269$	−3.47464	−	6.01826i	−0.211853	−	0.366940i	−0.952294	+	0.305181i	$0.901283\pi$
$270$	0.761162	+	2.10253i	0.0463229	+	0.127956i
$271$	7.52127	+	13.0272i	0.456885	+	0.791347i	0.998794	−	0.0490893i	$-0.0156319\pi$
$271$	7.52127	+	13.0272i	0.456885	+	0.791347i	−0.541910	+	0.840437i	$0.682299\pi$
$272$	−7.93771	+	2.12690i	−0.481294	+	0.128962i
$273$	−10.8811	+	10.8811i	−0.658554	+	0.658554i
$274$	−7.31964			−0.442196
$275$	−4.17596	−	1.53623i	−0.251820	−	0.0926379i
$276$	−2.58342	−	1.49154i	−0.155504	−	0.0897800i
$277$	10.5441	+	10.5441i	0.633536	+	0.633536i	0.948953	−	0.315417i	$-0.102145\pi$
$277$	10.5441	+	10.5441i	0.633536	+	0.633536i	−0.315417	+	0.948953i	$0.602145\pi$
$278$	15.1402	+	15.1402i	0.908047	+	0.908047i
$279$	−2.32087	+	4.01987i	−0.138947	+	0.240663i
$280$	9.37629	+	1.66994i	0.560341	+	0.0997980i
$281$	11.4404	+	6.60509i	0.682474	+	0.394027i	0.800787	−	0.598950i	$-0.204415\pi$
$281$	11.4404	+	6.60509i	0.682474	+	0.394027i	−0.118312	+	0.992976i	$0.537748\pi$
$282$	−2.47133	+	9.22311i	−0.147165	+	0.549228i
$283$	8.20996	+	2.19985i	0.488032	+	0.130768i	0.494440	−	0.869212i	$-0.335373\pi$
$283$	8.20996	+	2.19985i	0.488032	+	0.130768i	−0.00640826	+	0.999979i	$0.502040\pi$
$284$	−1.93178			−0.114630
$285$	−6.29450	+	7.44172i	−0.372854	+	0.440810i
$286$	3.21520			0.190119
$287$	−23.4323	−	6.27867i	−1.38316	−	0.370618i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	−43.7611	−	25.2655i	−2.57418	−	1.48620i
$290$	−9.84297	−	14.1088i	−0.577999	−	0.828500i
$291$	−0.824846	+	1.42867i	−0.0483533	+	0.0837504i
$292$	−2.28263	−	2.28263i	−0.133581	−	0.133581i
$293$	−16.0567	−	16.0567i	−0.938040	−	0.938040i	0.0601493	−	0.998189i	$-0.480842\pi$
$293$	−16.0567	−	16.0567i	−0.938040	−	0.938040i	−0.998189	+	0.0601493i	$0.980842\pi$
$294$	9.64815	+	5.57036i	0.562691	+	0.324870i
$295$	−5.97064	+	2.16150i	−0.347624	+	0.125848i
$296$	−4.80511			−0.279291
$297$	0.629263	−	0.629263i	0.0365136	−	0.0365136i
$298$	0.812877	−	0.217810i	0.0470887	−	0.0126174i
$299$	−5.38883	−	9.33372i	−0.311644	−	0.539783i
$300$	4.53879	−	2.09748i	0.262047	−	0.121098i
$301$	24.5745	+	42.5642i	1.41645	+	2.45336i
$302$	−4.48538	+	16.7397i	−0.258105	+	0.963260i
$303$	11.5243	+	11.5243i	0.662053	+	0.662053i
$304$	−4.21287	+	1.11881i	−0.241625	+	0.0641684i
$305$	8.81997	+	7.42674i	0.505030	+	0.425254i
$306$	−7.11676	+	4.10886i	−0.406838	+	0.234888i
$307$	−3.95047	−	1.05852i	−0.225465	−	0.0604132i	0.144318	−	0.989531i	$-0.453901\pi$
$307$	−3.95047	−	1.05852i	−0.225465	−	0.0604132i	−0.369783	+	0.929118i	$0.620568\pi$
$308$	−0.981004	−	3.66116i	−0.0558979	−	0.208614i
$309$	2.45969	−	1.42010i	0.139927	−	0.0807868i
$310$	9.39924	+	4.40265i	0.533841	+	0.250054i
$311$	−28.2199			−1.60021			−0.800103	−	0.599862i	$-0.795222\pi$
$311$	−28.2199			−1.60021			−0.800103	+	0.599862i	$0.795222\pi$
$312$	−2.55473	+	2.55473i	−0.144633	+	0.144633i
$313$	3.25587	+	12.1511i	0.184032	+	0.686818i	0.994836	+	0.101499i	$0.0323640\pi$
$313$	3.25587	+	12.1511i	0.184032	+	0.686818i	−0.810803	+	0.585319i	$0.800969\pi$
$314$	6.01452	−	10.4175i	0.339419	−	0.587891i
$315$	9.48902	−	0.813725i	0.534646	−	0.0458482i
$316$		−	10.1353i		−	0.570155i
$317$	−5.43467	−	20.2825i	−0.305242	−	1.13918i	−0.932737	−	0.360557i	$-0.882587\pi$
$317$	−5.43467	−	20.2825i	−0.305242	−	1.13918i	0.627495	−	0.778620i	$-0.284080\pi$
$318$	2.86577	−	10.6952i	0.160705	−	0.599757i
$319$	−3.42323	+	5.92922i	−0.191664	+	0.331972i
$320$	2.20143	+	0.392079i	0.123063	+	0.0219179i
$321$	1.57734	+	2.73204i	0.0880387	+	0.152488i
$322$	−8.98414	+	8.98414i	−0.500666	+	0.500666i
$323$	−30.9814	−	17.9790i	−1.72385	−	1.00038i
$324$			1.00000i			0.0555556i
$325$	17.9904	+	1.63639i	0.997928	+	0.0907704i
$326$	0.552800	−	0.319159i	0.0306167	−	0.0176766i
$327$	−15.3138	+	4.10331i	−0.846854	+	0.226914i
$328$	−5.50158	−	1.47414i	−0.303774	−	0.0813960i
$329$	35.2202	+	20.3344i	1.94175	+	1.12107i
$330$	−1.52215	−	1.28171i	−0.0837917	−	0.0705557i
$331$			2.19604i			0.120705i	0.998177	+	0.0603526i	$0.0192225\pi$
$331$			2.19604i			0.120705i	−0.998177	+	0.0603526i	$0.980777\pi$
$332$	−5.66486	+	1.51789i	−0.310899	+	0.0833052i
$333$	−4.64138	+	1.24365i	−0.254346	+	0.0681518i
$334$		−	22.4472i		−	1.22826i
$335$	−13.5401	+	1.16112i	−0.739774	+	0.0634389i
$336$	3.68857	+	2.12960i	0.201228	+	0.116179i
$337$	17.8655	+	4.78705i	0.973196	+	0.260767i	0.710176	−	0.704024i	$-0.248615\pi$
$337$	17.8655	+	4.78705i	0.973196	+	0.260767i	0.263019	+	0.964791i	$0.415282\pi$
$338$	−0.0514852	+	0.0137954i	−0.00280043	+	0.000750373i
$339$	14.5910	−	8.42413i	0.792475	−	0.457536i
$340$	10.5138	+	15.0704i	0.570189	+	0.817305i
$341$		−	4.13075i		−	0.223693i
$342$	−3.77975	+	2.17106i	−0.204385	+	0.117398i
$343$	12.4706	−	12.4706i	0.673350	−	0.673350i
$344$	5.76975	+	9.99350i	0.311084	+	0.538813i
$345$	−1.16960	+	6.56702i	−0.0629692	+	0.353556i
$346$	2.00245	−	3.46834i	0.107652	−	0.186459i
$347$	1.39422	−	5.20328i	0.0748454	−	0.279327i	−0.918353	−	0.395763i	$-0.870480\pi$
$347$	1.39422	−	5.20328i	0.0748454	−	0.279327i	0.993198	+	0.116436i	$0.0371469\pi$
$348$	−1.99120	−	7.43127i	−0.106740	−	0.398358i
$349$		−	22.4566i		−	1.20208i	−0.799220	−	0.601038i	$-0.794754\pi$
$349$		−	22.4566i		−	1.20208i	0.799220	−	0.601038i	$-0.205246\pi$
$350$	−3.62578	−	20.9850i	−0.193806	−	1.12170i
$351$	−1.80647	+	3.12889i	−0.0964221	+	0.167008i
$352$	−0.230326	−	0.859590i	−0.0122764	−	0.0458163i
$353$	−3.16087	+	3.16087i	−0.168236	+	0.168236i	−0.786204	−	0.617967i	$-0.787956\pi$
$353$	−3.16087	+	3.16087i	−0.168236	+	0.168236i	0.617967	+	0.786204i	$0.287956\pi$
$354$	−2.83974			−0.150931
$355$	1.47040	+	4.06162i	0.0780405	+	0.215568i
$356$	−7.80525	+	4.50636i	−0.413677	+	0.238837i
$357$	9.05889	+	33.8082i	0.479447	+	1.78932i
$358$	0.740458	+	0.198405i	0.0391344	+	0.0104860i
$359$	−9.59054	+	5.53710i	−0.506170	+	0.292237i	−0.731258	−	0.682101i	$-0.761066\pi$
$359$	−9.59054	+	5.53710i	−0.506170	+	0.292237i	0.225088	+	0.974338i	$0.427733\pi$
$360$	2.22789	−	0.191051i	0.117420	−	0.0100693i
$361$	−16.4121	−	9.57298i	−0.863796	−	0.503841i
$362$	−4.30293	−	4.30293i	−0.226157	−	0.226157i
$363$	2.64204	−	9.86022i	0.138671	−	0.517528i
$364$	7.69409	+	13.3266i	0.403280	+	0.698502i
$365$	−3.06184	+	6.53674i	−0.160264	+	0.342149i
$366$	2.57826	+	4.46567i	0.134768	+	0.233424i
$367$	35.1030	−	9.40583i	1.83236	−	0.490980i	0.834194	−	0.551471i	$-0.185933\pi$
$367$	35.1030	−	9.40583i	1.83236	−	0.490980i	0.998169	+	0.0604905i	$0.0192665\pi$
$368$	−2.10935	+	2.10935i	−0.109958	+	0.109958i
$369$	−5.69566			−0.296504
$370$	3.65746	+	10.1029i	0.190143	+	0.525224i
$371$	−40.8417	−	23.5799i	−2.12039	−	1.22421i
$372$	3.28221	+	3.28221i	0.170175	+	0.170175i
$373$	−16.3428	−	16.3428i	−0.846196	−	0.846196i	0.143460	−	0.989656i	$-0.454177\pi$
$373$	−16.3428	−	16.3428i	−0.846196	−	0.846196i	−0.989656	+	0.143460i	$0.954177\pi$
$374$	3.65653	−	6.33329i	0.189075	−	0.327487i
$375$	−7.86476	−	7.94641i	−0.406135	−	0.410351i
$376$	8.26922	+	4.77423i	0.426452	+	0.246212i
$377$	7.19409	−	26.8487i	0.370514	−	1.38278i
$378$	4.11406	+	1.10236i	0.211605	+	0.0566993i
$379$	−26.9783			−1.38578			−0.692890	−	0.721043i	$-0.743663\pi$
$379$	−26.9783			−1.38578			−0.692890	+	0.721043i	$0.743663\pi$
$380$	5.55901	+	8.00608i	0.285171	+	0.410703i
$381$	7.25302			0.371583
$382$	−1.48551	−	0.398041i	−0.0760053	−	0.0203656i
$383$	5.12712	−	19.1347i	0.261984	−	0.977737i	−0.702087	−	0.712091i	$-0.747748\pi$
$383$	5.12712	−	19.1347i	0.261984	−	0.977737i	0.964071	−	0.265646i	$-0.0855851\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	−6.95099	+	4.84932i	−0.354255	+	0.247144i
$386$	8.96880	−	15.5344i	0.456500	−	0.790681i
$387$	8.15966	+	8.15966i	0.414779	+	0.414779i
$388$	1.16651	+	1.16651i	0.0592205	+	0.0592205i
$389$	−21.7505	−	12.5576i	−1.10279	−	0.636697i	−0.165839	−	0.986153i	$-0.553033\pi$
$389$	−21.7505	−	12.5576i	−1.10279	−	0.636697i	−0.936953	+	0.349455i	$0.886367\pi$
$390$	7.31596	+	3.42683i	0.370458	+	0.173524i
$391$	−24.5141			−1.23973
$392$	7.87768	−	7.87768i	0.397883	−	0.397883i
$393$	5.58773	−	1.49723i	0.281864	−	0.0755252i
$394$	6.20400	+	10.7456i	0.312553	+	0.541358i
$395$	−21.3098	+	7.71461i	−1.07221	+	0.388164i
$396$	−0.444956	−	0.770687i	−0.0223599	−	0.0387285i
$397$	8.56614	−	31.9693i	0.429922	−	1.60449i	−0.323011	−	0.946395i	$-0.604695\pi$
$397$	8.56614	−	31.9693i	0.429922	−	1.60449i	0.752933	−	0.658097i	$-0.228638\pi$
$398$	−7.87091	−	7.87091i	−0.394533	−	0.394533i
$399$	4.76524	+	17.9434i	0.238561	+	0.898294i
$400$	−0.851283	−	4.92700i	−0.0425642	−	0.246350i
$401$	−21.8962	+	12.6418i	−1.09344	+	0.631300i	−0.934491	−	0.355986i	$-0.884145\pi$
$401$	−21.8962	+	12.6418i	−1.09344	+	0.631300i	−0.158952	+	0.987286i	$0.550812\pi$
$402$	−5.87045	−	1.57298i	−0.292791	−	0.0784532i
$403$	4.34048	+	16.1989i	0.216215	+	0.806925i
$404$	14.1143	−	8.14890i	0.702213	−	0.405423i
$405$	2.10253	−	0.761162i	0.104476	−	0.0378225i
$406$	−32.7677			−1.62624
$407$	3.02368	−	3.02368i	0.149878	−	0.149878i
$408$	2.12690	+	7.93771i	0.105297	+	0.392975i
$409$	−7.34262	+	12.7178i	−0.363069	+	0.628855i	−0.988464	−	0.151454i	$-0.951605\pi$
$409$	−7.34262	+	12.7178i	−0.363069	+	0.628855i	0.625395	+	0.780308i	$0.284938\pi$
$410$	1.08816	+	12.6893i	0.0537406	+	0.626680i
$411$			7.31964i			0.361051i
$412$	−0.735099	−	2.74343i	−0.0362157	−	0.135159i
$413$	−3.13042	+	11.6829i	−0.154038	+	0.574877i
$414$	−1.49154	+	2.58342i	−0.0733051	+	0.126968i
$415$	7.50329	+	10.7552i	0.368322	+	0.527950i
$416$	1.80647	+	3.12889i	0.0885694	+	0.153407i
$417$	15.1402	−	15.1402i	0.741417	−	0.741417i
$418$	1.94697	−	3.35503i	0.0952296	−	0.164100i
$419$		−	17.0956i		−	0.835175i	−0.908637	−	0.417588i	$-0.862876\pi$
$419$		−	17.0956i		−	0.835175i	0.908637	−	0.417588i	$-0.137124\pi$
$420$	1.66994	−	9.37629i	0.0814848	−	0.457516i
$421$	9.73185	−	5.61868i	0.474301	−	0.273838i	−0.243737	−	0.969841i	$-0.578373\pi$
$421$	9.73185	−	5.61868i	0.474301	−	0.273838i	0.718039	+	0.696003i	$0.245040\pi$
$422$	7.75872	−	2.07894i	0.377689	−	0.101201i
$423$	9.22311	+	2.47133i	0.448443	+	0.120160i
$424$	−9.58906	−	5.53625i	−0.465686	−	0.268864i
$425$	23.6832	−	33.5765i	1.14880	−	1.62870i
$426$			1.93178i			0.0935949i
$427$	21.2142	−	5.68434i	1.02663	−	0.275084i
$428$	3.04719	−	0.816493i	0.147292	−	0.0394667i
$429$		−	3.21520i		−	0.155231i
$430$	16.6199	−	19.7377i	0.801484	−	0.951839i
$431$	26.8447	+	15.4988i	1.29306	+	0.746551i	0.979196	−	0.202916i	$-0.0650418\pi$
$431$	26.8447	+	15.4988i	1.29306	+	0.746551i	0.313868	+	0.949467i	$0.398375\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	17.8385	−	4.77981i	0.857263	−	0.229703i	0.196691	−	0.980466i	$-0.436980\pi$
$433$	17.8385	−	4.77981i	0.857263	−	0.229703i	0.660572	+	0.750763i	$0.270314\pi$
$434$	17.1214	−	9.88505i	0.821854	−	0.474498i
$435$	−14.1088	+	9.84297i	−0.676467	+	0.471934i
$436$			15.8540i			0.759268i
$437$	−13.0029	−	0.0288746i	−0.622013	−	0.00138126i
$438$	−2.28263	+	2.28263i	−0.109068	+	0.109068i
$439$	1.62739	+	2.81873i	0.0776713	+	0.134531i	0.902245	−	0.431224i	$-0.141918\pi$
$439$	1.62739	+	2.81873i	0.0776713	+	0.134531i	−0.824574	+	0.565755i	$0.808585\pi$
$440$	−1.63200	+	1.13856i	−0.0778024	+	0.0542785i
$441$	5.57036	−	9.64815i	0.265255	−	0.459436i
$442$	−7.68436	+	28.6784i	−0.365508	+	1.36409i
$443$	4.79182	+	17.8833i	0.227666	+	0.849661i	0.981319	+	0.192388i	$0.0616233\pi$
$443$	4.79182	+	17.8833i	0.227666	+	0.849661i	−0.753653	+	0.657273i	$0.771710\pi$
$444$			4.80511i			0.228040i
$445$	15.4158	+	12.9807i	0.730780	+	0.615344i
$446$	−5.23146	+	9.06116i	−0.247717	+	0.429058i
$447$	−0.217810	−	0.812877i	−0.0103021	−	0.0384478i
$448$	3.01170	−	3.01170i	0.142290	−	0.142290i
$449$	32.0359			1.51187			0.755933	−	0.654649i	$-0.227184\pi$
$449$	32.0359			1.51187			0.755933	+	0.654649i	$0.227184\pi$
$450$	−2.09748	−	4.53879i	−0.0988761	−	0.213960i
$451$	4.38957	−	2.53432i	0.206697	−	0.119336i
$452$	−4.36065	−	16.2742i	−0.205108	−	0.765472i
$453$	16.7397	+	4.48538i	0.786499	+	0.210742i
$454$	−8.80643	+	5.08439i	−0.413306	+	0.238622i
$455$	22.1630	−	26.3207i	1.03902	−	1.23394i
$456$	1.11881	+	4.21287i	0.0523932	+	0.197286i
$457$	12.2869	+	12.2869i	0.574757	+	0.574757i	0.933454	−	0.358697i	$-0.116779\pi$
$457$	12.2869	+	12.2869i	0.574757	+	0.574757i	−0.358697	+	0.933454i	$0.616779\pi$
$458$	0.0145370	−	0.0542528i	0.000679269	−	0.00253507i
$459$	4.10886	+	7.11676i	0.191785	+	0.332182i
$460$	6.04054	+	2.82942i	0.281641	+	0.131922i
$461$	4.30458	+	7.45574i	0.200484	+	0.347249i	0.948684	−	0.316224i	$-0.102415\pi$
$461$	4.30458	+	7.45574i	0.200484	+	0.347249i	−0.748200	+	0.663473i	$0.769082\pi$
$462$	−3.66116	+	0.981004i	−0.170332	+	0.0456404i
$463$	−14.7616	+	14.7616i	−0.686030	+	0.686030i	−0.961352	−	0.275322i	$-0.911216\pi$
$463$	−14.7616	+	14.7616i	−0.686030	+	0.686030i	0.275322	+	0.961352i	$0.411216\pi$
$464$	−7.69342			−0.357158
$465$	4.40265	−	9.39924i	0.204168	−	0.435879i
$466$	−11.0149	−	6.35944i	−0.510255	−	0.294596i
$467$	15.9023	+	15.9023i	0.735873	+	0.735873i	0.971776	−	0.235904i	$-0.0758050\pi$
$467$	15.9023	+	15.9023i	0.735873	+	0.735873i	−0.235904	+	0.971776i	$0.575805\pi$
$468$	2.55473	+	2.55473i	0.118092	+	0.118092i
$469$	−12.9427	+	22.4174i	−0.597638	+	1.03514i
$470$	3.74376	−	21.0202i	0.172687	−	0.969591i
$471$	−10.4175	−	6.01452i	−0.480011	−	0.277135i
$472$	−0.734980	+	2.74298i	−0.0338302	+	0.126256i
$473$	−9.91923	−	2.65785i	−0.456087	−	0.122208i
$474$	−10.1353			−0.465530
$475$	12.6017	−	17.7819i	0.578206	−	0.815891i
$476$	35.0009			1.60426
$477$	−10.6952	−	2.86577i	−0.489700	−	0.131215i
$478$	0.956600	−	3.57008i	0.0437539	−	0.163292i
$479$	−19.1110	−	11.0337i	−0.873202	−	0.504144i	−0.00479122	−	0.999989i	$-0.501525\pi$
$479$	−19.1110	−	11.0337i	−0.873202	−	0.504144i	−0.868411	+	0.495845i	$0.834858\pi$
$480$	0.392079	−	2.20143i	0.0178959	−	0.100481i
$481$	−8.68027	+	15.0347i	−0.395786	+	0.685522i
$482$	−1.76895	−	1.76895i	−0.0805737	−	0.0805737i
$483$	8.98414	+	8.98414i	0.408792	+	0.408792i
$484$	−8.84044	−	5.10403i	−0.401838	−	0.232001i
$485$	1.56472	−	3.34052i	0.0710501	−	0.151685i
$486$	1.00000			0.0453609
$487$	20.0414	−	20.0414i	0.908162	−	0.908162i	−0.0879618	−	0.996124i	$-0.528035\pi$
$487$	20.0414	−	20.0414i	0.908162	−	0.908162i	0.996124	+	0.0879618i	$0.0280353\pi$
$488$	4.98081	−	1.33460i	0.225471	−	0.0604147i
$489$	−0.319159	−	0.552800i	−0.0144329	−	0.0249985i
$490$	−22.5592	−	10.5669i	−1.01912	−	0.477362i
$491$	−2.06664	−	3.57953i	−0.0932663	−	0.161542i	0.815617	−	0.578592i	$-0.196397\pi$
$491$	−2.06664	−	3.57953i	−0.0932663	−	0.161542i	−0.908884	+	0.417050i	$0.863064\pi$
$492$	−1.47414	+	5.50158i	−0.0664596	+	0.248030i
$493$	−44.7050	−	44.7050i	−2.01341	−	2.01341i
$494$	−4.10976	+	15.2027i	−0.184907	+	0.684003i
$495$	−1.28171	+	1.52215i	−0.0576085	+	0.0684156i
$496$	4.01987	−	2.32087i	0.180498	−	0.104210i
$497$	7.94745	+	2.12951i	0.356492	+	0.0955218i
$498$	1.51789	+	5.66486i	0.0680184	+	0.253848i
$499$	13.7226	−	7.92273i	0.614307	−	0.354670i	−0.160342	−	0.987061i	$-0.551260\pi$
$499$	13.7226	−	7.92273i	0.614307	−	0.354670i	0.774649	+	0.632391i	$0.217926\pi$
$500$	−9.71120	+	5.54009i	−0.434298	+	0.247761i
$501$	−22.4472			−1.00287
$502$	9.20367	−	9.20367i	0.410780	−	0.410780i
$503$	8.00608	+	29.8791i	0.356973	+	1.33224i	0.877983	+	0.478692i	$0.158889\pi$
$503$	8.00608	+	29.8791i	0.356973	+	1.33224i	−0.521010	+	0.853551i	$0.674444\pi$
$504$	2.12960	−	3.68857i	0.0948598	−	0.164302i
$505$	−27.8766	−	23.4731i	−1.24049	−	1.04454i
$506$		−	2.65468i		−	0.118015i
$507$	0.0137954	+	0.0514852i	0.000612677	+	0.00228654i
$508$	1.87722	−	7.00588i	0.0832881	−	0.310836i
$509$	3.56557	−	6.17574i	0.158041	−	0.273735i	−0.776121	−	0.630584i	$-0.782816\pi$
$509$	3.56557	−	6.17574i	0.158041	−	0.273735i	0.934162	+	0.356849i	$0.116149\pi$
$510$	15.0704	−	10.5138i	0.667326	−	0.465557i
$511$	6.87459	+	11.9071i	0.304114	+	0.526741i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	2.17106	+	3.77975i	0.0958547	+	0.166880i
$514$		−	23.0627i		−	1.01725i
$515$	−5.20861	+	3.63376i	−0.229519	+	0.160123i
$516$	9.99350	−	5.76975i	0.439939	−	0.253999i
$517$	−8.20776	+	2.19926i	−0.360977	+	0.0967235i
$518$	19.7685	+	5.29696i	0.868578	+	0.232735i
$519$	−3.46834	−	2.00245i	−0.152243	−	0.0878977i
$520$	5.20358	−	6.17975i	0.228192	−	0.271000i
$521$			17.2097i			0.753969i	0.926220	+	0.376984i	$0.123039\pi$
$521$			17.2097i			0.753969i	−0.926220	+	0.376984i	$0.876961\pi$
$522$	−7.43127	+	1.99120i	−0.325258	+	0.0871526i
$523$	22.2508	−	5.96209i	0.972960	−	0.260704i	0.262883	−	0.964828i	$-0.415327\pi$
$523$	22.2508	−	5.96209i	0.972960	−	0.260704i	0.710077	+	0.704124i	$0.248660\pi$
$524$		−	5.78484i		−	0.252712i
$525$	−20.9850	+	3.62578i	−0.915862	+	0.158242i
$526$	−1.76334	−	1.01806i	−0.0768853	−	0.0443897i
$527$	36.8448	+	9.87255i	1.60499	+	0.430055i
$528$	−0.859590	+	0.230326i	−0.0374088	+	0.0100237i
$529$	12.2121	−	7.05063i	0.530959	−	0.306549i
$530$	−4.34129	+	24.3753i	−0.188574	+	1.05879i
$531$			2.83974i			0.123234i
$532$	18.5653	+	0.0412267i	0.804910	+	0.00178740i
$533$	−14.5509	+	14.5509i	−0.630268	+	0.630268i
$534$	4.50636	+	7.80525i	0.195009	+	0.337766i
$535$	−4.03611	−	5.78533i	−0.174496	−	0.250122i
$536$	−3.03877	+	5.26330i	−0.131255	+	0.227340i
$537$	0.198405	−	0.740458i	0.00856182	−	0.0319531i
$538$	1.79861	+	6.71249i	0.0775435	+	0.289396i
$539$			9.91427i			0.427038i
$540$	−0.191051	−	2.22789i	−0.00822154	−	0.0958732i
$541$	−7.67134	+	13.2872i	−0.329817	+	0.571259i	−0.982475	−	0.186393i	$-0.940320\pi$
$541$	−7.67134	+	13.2872i	−0.329817	+	0.571259i	0.652659	+	0.757652i	$0.273654\pi$
$542$	−3.89330	−	14.5300i	−0.167231	−	0.624116i
$543$	−4.30293	+	4.30293i	−0.184656	+	0.184656i
$544$	8.21772			0.352332
$545$	33.3335	−	12.0675i	1.42785	−	0.516913i
$546$	13.3266	−	7.69409i	0.570324	−	0.329277i
$547$	4.16262	+	15.5351i	0.177981	+	0.664233i	0.996025	+	0.0890775i	$0.0283919\pi$
$547$	4.16262	+	15.5351i	0.177981	+	0.664233i	−0.818044	+	0.575156i	$0.804941\pi$
$548$	7.07023	+	1.89446i	0.302025	+	0.0809274i
$549$	4.46567	−	2.57826i	0.190590	−	0.110037i
$550$	3.63606	+	2.56470i	0.155042	+	0.109359i
$551$	−23.6600	−	23.7653i	−1.00795	−	1.01244i
$552$	2.10935	+	2.10935i	0.0897800	+	0.0897800i
$553$	−11.1728	+	41.6973i	−0.475114	+	1.77315i
$554$	−7.45583	−	12.9139i	−0.316768	−	0.548658i
$555$	10.1029	−	3.65746i	0.428843	−	0.155251i
$556$	−10.7057	−	18.5428i	−0.454023	−	0.786392i
$557$	1.32306	−	0.354514i	0.0560600	−	0.0150212i	−0.230680	−	0.973030i	$-0.574095\pi$
$557$	1.32306	−	0.354514i	0.0560600	−	0.0150212i	0.286740	+	0.958008i	$0.407428\pi$
$558$	3.28221	−	3.28221i	0.138947	−	0.138947i
$559$	41.6915			1.76336
$560$	−8.62459	−	4.03980i	−0.364456	−	0.170713i
$561$	−6.33329	−	3.65653i	−0.267392	−	0.154379i
$562$	−9.34101	−	9.34101i	−0.394027	−	0.394027i
$563$	−8.79410	−	8.79410i	−0.370627	−	0.370627i	0.497078	−	0.867706i	$-0.334406\pi$
$563$	−8.79410	−	8.79410i	−0.370627	−	0.370627i	−0.867706	+	0.497078i	$0.834406\pi$
$564$	4.77423	−	8.26922i	0.201032	−	0.348197i
$565$	−30.8978	+	21.5557i	−1.29988	+	0.906854i
$566$	−7.36085	−	4.24979i	−0.309400	−	0.178632i
$567$	1.10236	−	4.11406i	0.0462948	−	0.172774i
$568$	1.86595	+	0.499981i	0.0782937	+	0.0209787i
$569$	−14.3911			−0.603305			−0.301652	−	0.953418i	$-0.597538\pi$
$569$	−14.3911			−0.603305			−0.301652	+	0.953418i	$0.597538\pi$
$570$	8.00608	−	5.55901i	0.335338	−	0.232842i
$571$	−34.2382			−1.43282			−0.716412	−	0.697678i	$-0.754217\pi$
$571$	−34.2382			−1.43282			−0.716412	+	0.697678i	$0.754217\pi$
$572$	−3.10564	−	0.832154i	−0.129853	−	0.0347941i
$573$	−0.398041	+	1.48551i	−0.0166284	+	0.0620581i
$574$	21.0088	+	12.1295i	0.876891	+	0.506273i
$575$	1.35111	−	14.8541i	0.0563451	−	0.619457i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−24.0197	−	24.0197i	−0.999952	−	0.999952i	4.75497e−5	−	1.00000i	$-0.499985\pi$
$577$	−24.0197	−	24.0197i	−0.999952	−	0.999952i	−1.00000		4.75497e-5i	$0.999985\pi$
$578$	35.7308	+	35.7308i	1.48620	+	1.48620i
$579$	−15.5344	−	8.96880i	−0.645589	−	0.372731i
$580$	5.85594	+	16.1756i	0.243155	+	0.671657i
$581$	24.9788			1.03630
$582$	1.16651	−	1.16651i	0.0483533	−	0.0483533i
$583$	9.51780	−	2.55029i	0.394187	−	0.105622i
$584$	1.61406	+	2.79563i	0.0667903	+	0.115684i
$585$	3.42683	−	7.31596i	0.141682	−	0.302478i
$586$	11.3538	+	19.6653i	0.469020	+	0.812367i
$587$	−1.71013	+	6.38229i	−0.0705846	+	0.263425i	−0.992196	−	0.124689i	$-0.960207\pi$
$587$	−1.71013	+	6.38229i	−0.0705846	+	0.263425i	0.921611	+	0.388114i	$0.126873\pi$
$588$	−7.87768	−	7.87768i	−0.324870	−	0.324870i
$589$	19.5318	+	5.28005i	0.804794	+	0.217561i
$590$	6.32664	−	0.542537i	0.260464	−	0.0223359i
$591$	10.7456	−	6.20400i	0.442017	−	0.255199i
$592$	4.64138	+	1.24365i	0.190759	+	0.0511138i
$593$	5.82353	+	21.7337i	0.239144	+	0.892496i	0.976237	+	0.216705i	$0.0695311\pi$
$593$	5.82353	+	21.7337i	0.239144	+	0.892496i	−0.737093	+	0.675791i	$0.763802\pi$
$594$	−0.770687	+	0.444956i	−0.0316217	+	0.0182568i
$595$	−26.6413	−	73.5903i	−1.09219	−	3.01691i
$596$	−0.841552			−0.0344713
$597$	−7.87091	+	7.87091i	−0.322135	+	0.322135i
$598$	2.78946	+	10.4104i	0.114070	+	0.425714i
$599$	10.3826	−	17.9832i	0.424222	−	0.734774i	−0.572125	−	0.820166i	$-0.693881\pi$
$599$	10.3826	−	17.9832i	0.424222	−	0.734774i	0.996347	+	0.0853919i	$0.0272142\pi$
$600$	−4.92700	+	0.851283i	−0.201144	+	0.0347535i
$601$			29.4494i			1.20127i	0.799525	+	0.600633i	$0.205085\pi$
$601$			29.4494i			1.20127i	−0.799525	+	0.600633i	$0.794915\pi$
$602$	−12.7207	−	47.4742i	−0.518456	−	1.93491i
$603$	−1.57298	+	5.87045i	−0.0640568	+	0.239063i
$604$	8.66509	−	15.0084i	0.352578	−	0.610682i
$605$	−4.00237	+	22.4723i	−0.162719	+	0.913628i
$606$	−8.14890	−	14.1143i	−0.331026	−	0.573355i
$607$	2.91441	−	2.91441i	0.118292	−	0.118292i	−0.645483	−	0.763775i	$-0.723344\pi$
$607$	2.91441	−	2.91441i	0.118292	−	0.118292i	0.763775	+	0.645483i	$0.223344\pi$
$608$	4.35889	+	0.00967947i	0.176776	+	0.000392554i
$609$			32.7677i			1.32782i
$610$	−6.59725	−	9.45645i	−0.267115	−	0.382881i
$611$	29.8761	−	17.2490i	1.20866	−	0.697820i
$612$	7.93771	−	2.12690i	0.320863	−	0.0859749i
$613$	−6.00674	−	1.60950i	−0.242610	−	0.0650071i	0.135465	−	0.990782i	$-0.456747\pi$
$613$	−6.00674	−	1.60950i	−0.242610	−	0.0650071i	−0.378075	+	0.925775i	$0.623414\pi$
$614$	3.54189	+	2.04491i	0.142939	+	0.0825259i
$615$	12.6893	−	1.08816i	0.511682	−	0.0438790i
$616$			3.79031i			0.152716i
$617$	12.3914	−	3.32026i	0.498858	−	0.133669i	−0.000611790	−	1.00000i	$-0.500195\pi$
$617$	12.3914	−	3.32026i	0.498858	−	0.133669i	0.499470	+	0.866331i	$0.333528\pi$
$618$	−2.74343	+	0.735099i	−0.110357	+	0.0295700i
$619$			0.966180i			0.0388341i	0.999811	+	0.0194170i	$0.00618102\pi$
$619$			0.966180i			0.0388341i	−0.999811	+	0.0194170i	$0.993819\pi$
$620$	−7.93948	−	6.68534i	−0.318857	−	0.268490i
$621$	2.58342	+	1.49154i	0.103669	+	0.0598533i
$622$	27.2584	+	7.30386i	1.09296	+	0.292858i
$623$	37.0789	−	9.93526i	1.48554	−	0.398048i
$624$	3.12889	−	1.80647i	0.125256	−	0.0723166i
$625$	19.0400	+	16.2012i	0.761600	+	0.648047i
$626$		−	12.5797i		−	0.502786i
$627$	−3.35503	−	1.94697i	−0.133987	−	0.0777547i
$628$	−8.50582	+	8.50582i	−0.339419	+	0.339419i
$629$	19.7435	+	34.1968i	0.787225	+	1.36351i
$630$	−9.37629	−	1.66994i	−0.373561	−	0.0665320i
$631$	9.50801	−	16.4684i	0.378508	−	0.655595i	−0.612338	−	0.790596i	$-0.709771\pi$
$631$	9.50801	−	16.4684i	0.378508	−	0.655595i	0.990845	+	0.135002i	$0.0431040\pi$
$632$	−2.62321	+	9.78995i	−0.104346	+	0.389423i
$633$	−2.07894	−	7.75872i	−0.0826306	−	0.308382i
$634$			20.9980i			0.833936i
$635$	−16.1589	+	1.38570i	−0.641248	+	0.0549898i
$636$	−5.53625	+	9.58906i	−0.219526	+	0.380231i
$637$	−10.4176	−	38.8792i	−0.412762	−	1.54045i
$638$	4.84118	−	4.84118i	0.191664	−	0.191664i
$639$	1.93178			0.0764199
$640$	−2.02494	−	0.948490i	−0.0800426	−	0.0374924i
$641$	−23.3421	+	13.4766i	−0.921959	+	0.532293i	−0.884259	−	0.466996i	$-0.845336\pi$
$641$	−23.3421	+	13.4766i	−0.921959	+	0.532293i	−0.0376993	+	0.999289i	$0.512003\pi$
$642$	−0.816493	−	3.04719i	−0.0322244	−	0.120263i
$643$	−29.1266	−	7.80445i	−1.14864	−	0.307777i	−0.366221	−	0.930528i	$-0.619348\pi$
$643$	−29.1266	−	7.80445i	−1.14864	−	0.307777i	−0.782420	+	0.622751i	$0.786015\pi$
$644$	11.0033	−	6.35274i	0.433590	−	0.250333i
$645$	−19.7377	−	16.6199i	−0.777173	−	0.654409i
$646$	25.2724	+	25.3849i	0.994330	+	0.998756i
$647$	15.5426	+	15.5426i	0.611042	+	0.611042i	0.943218	−	0.332175i	$-0.107783\pi$
$647$	15.5426	+	15.5426i	0.611042	+	0.611042i	−0.332175	+	0.943218i	$0.607783\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−1.26356	−	2.18855i	−0.0495991	−	0.0859082i
$650$	−16.9539	−	6.23689i	−0.664986	−	0.244631i
$651$	−9.88505	−	17.1214i	−0.387426	−	0.671041i
$652$	−0.616568	+	0.165209i	−0.0241467	+	0.00647008i
$653$	−16.8608	+	16.8608i	−0.659816	+	0.659816i	−0.955336	−	0.295520i	$-0.904507\pi$
$653$	−16.8608	+	16.8608i	−0.659816	+	0.659816i	0.295520	+	0.955336i	$0.404507\pi$
$654$	15.8540			0.619940
$655$	−12.1628	+	4.40320i	−0.475240	+	0.172047i
$656$	4.93258	+	2.84783i	0.192585	+	0.111189i
$657$	2.28263	+	2.28263i	0.0890537	+	0.0890537i
$658$	−28.7572	−	28.7572i	−1.12107	−	1.12107i
$659$	−5.40290	+	9.35810i	−0.210467	+	0.364540i	−0.951861	−	0.306531i	$-0.900832\pi$
$659$	−5.40290	+	9.35810i	−0.210467	+	0.364540i	0.741394	+	0.671070i	$0.234165\pi$
$660$	1.13856	+	1.63200i	0.0443182	+	0.0635254i
$661$	1.33739	+	0.772145i	0.0520186	+	0.0300330i	0.525784	−	0.850618i	$-0.323772\pi$
$661$	1.33739	+	0.772145i	0.0520186	+	0.0300330i	−0.473765	+	0.880651i	$0.657105\pi$
$662$	0.568377	−	2.12121i	0.0220906	−	0.0824432i
$663$	28.6784	+	7.68436i	1.11378	+	0.298436i
$664$	5.86469			0.227594
$665$	−14.0446	−	39.0656i	−0.544625	−	1.51490i
$666$	4.80511			0.186194
$667$	−22.1680	−	5.93991i	−0.858350	−	0.229994i
$668$	−5.80976	+	21.6823i	−0.224786	+	0.838914i
$669$	9.06116	+	5.23146i	0.350325	+	0.202260i
$670$	13.3792	+	2.38288i	0.516885	+	0.0920585i
$671$	−2.29442	+	3.97406i	−0.0885753	+	0.153417i
$672$	−3.01170	−	3.01170i	−0.116179	−	0.116179i
$673$	−1.72576	−	1.72576i	−0.0665231	−	0.0665231i	0.673063	−	0.739586i	$-0.264978\pi$
$673$	−1.72576	−	1.72576i	−0.0665231	−	0.0665231i	−0.739586	+	0.673063i	$0.764978\pi$
$674$	−16.0178	−	9.24786i	−0.616981	−	0.356214i
$675$	−4.53879	+	2.09748i	−0.174698	+	0.0807320i
$676$	0.0533015			0.00205006
$677$	−22.9742	+	22.9742i	−0.882970	+	0.882970i	−0.993835	−	0.110865i	$-0.964638\pi$
$677$	−22.9742	+	22.9742i	−0.882970	+	0.882970i	0.110865	+	0.993835i	$0.464638\pi$
$678$	−16.2742	+	4.36065i	−0.625006	+	0.167470i
$679$	−3.51318	−	6.08500i	−0.134823	−	0.233521i
$680$	−6.25502	−	17.2780i	−0.239869	−	0.662581i
$681$	5.08439	+	8.80643i	0.194834	+	0.337463i
$682$	−1.06912	+	3.99000i	−0.0409386	+	0.152785i
$683$	24.3696	+	24.3696i	0.932477	+	0.932477i	0.997860	−	0.0653830i	$-0.0208269\pi$
$683$	24.3696	+	24.3696i	0.932477	+	0.932477i	−0.0653830	+	0.997860i	$0.520827\pi$
$684$	4.21287	−	1.11881i	0.161083	−	0.0427789i
$685$	−1.39843	−	16.3074i	−0.0534312	−	0.623072i
$686$	−15.2733	+	8.81806i	−0.583138	+	0.336675i
$687$	−0.0542528	−	0.0145370i	−0.00206987	−	0.000554621i
$688$	−2.98664	−	11.1463i	−0.113865	−	0.424949i
$689$	−34.6447	+	20.0021i	−1.31986	+	0.762019i
$690$	2.82942	−	6.04054i	0.107714	−	0.229959i
$691$	33.0103			1.25577			0.627885	−	0.778306i	$-0.283921\pi$
$691$	33.0103			1.25577			0.627885	+	0.778306i	$0.283921\pi$
$692$	−2.83189	+	2.83189i	−0.107652	+	0.107652i
$693$	0.981004	+	3.66116i	0.0372653	+	0.139076i
$694$	−2.69342	+	4.66514i	−0.102241	+	0.177086i
$695$	−30.8381	+	36.6232i	−1.16976	+	1.38920i
$696$			7.69342i			0.291618i
$697$	12.1141	+	45.2105i	0.458855	+	1.71247i
$698$	−5.81221	+	21.6915i	−0.219995	+	0.821034i
$699$	−6.35944	+	11.0149i	−0.240536	+	0.416621i
$700$	−1.92909	+	21.2084i	−0.0729128	+	0.801602i
$701$	−10.7338	−	18.5915i	−0.405411	−	0.702193i	0.588958	−	0.808164i	$-0.299538\pi$
$701$	−10.7338	−	18.5915i	−0.405411	−	0.702193i	−0.994369	+	0.105971i	$0.966205\pi$
$702$	2.55473	−	2.55473i	0.0964221	−	0.0964221i
$703$	10.4322	+	18.1621i	0.393457	+	0.684996i
$704$			0.889913i			0.0335398i
$705$	−21.0202	−	3.74376i	−0.791668	−	0.140998i
$706$	3.87126	−	2.23508i	0.145697	−	0.0841182i
$707$	−67.0502	+	17.9660i	−2.52168	+	0.675683i
$708$	2.74298	+	0.734980i	0.103088	+	0.0276222i
$709$	−20.8763	−	12.0530i	−0.784027	−	0.452658i	0.0538286	−	0.998550i	$-0.482858\pi$
$709$	−20.8763	−	12.0530i	−0.784027	−	0.452658i	−0.837856	+	0.545892i	$0.816191\pi$
$710$	−0.369069	−	4.30379i	−0.0138509	−	0.161518i
$711$			10.1353i			0.380104i
$712$	8.70562	−	2.33266i	0.326257	−	0.0874203i
$713$	13.3749	−	3.58378i	0.500893	−	0.134214i
$714$		−	35.0009i		−	1.30987i
$715$	0.614268	+	7.16311i	0.0229723	+	0.267885i
$716$	−0.663877	−	0.383289i	−0.0248102	−	0.0143242i
$717$	−3.57008	−	0.956600i	−0.133327	−	0.0357249i
$718$	10.6969	−	2.86622i	0.399203	−	0.106966i
$719$	−20.1378	+	11.6265i	−0.751012	+	0.433597i	−0.826059	−	0.563583i	$-0.809422\pi$
$719$	−20.1378	+	11.6265i	−0.751012	+	0.433597i	0.0750478	+	0.997180i	$0.476089\pi$
$720$	−2.20143	−	0.392079i	−0.0820423	−	0.0146119i
$721$			12.0970i			0.450515i
$722$	13.3752	+	13.4946i	0.497774	+	0.502216i
$723$	−1.76895	+	1.76895i	−0.0657881	+	0.0657881i
$724$	3.04263	+	5.26999i	0.113078	+	0.195858i
$725$	29.5525	−	24.6246i	1.09755	−	0.914534i
$726$	−5.10403	+	8.84044i	−0.189428	+	0.328099i
$727$	−10.2400	+	38.2160i	−0.379779	+	1.41735i	0.466456	+	0.884545i	$0.345531\pi$
$727$	−10.2400	+	38.2160i	−0.379779	+	1.41735i	−0.846235	+	0.532810i	$0.821136\pi$
$728$	−3.98276	−	14.8638i	−0.147611	−	0.550891i
$729$		−	1.00000i		−	0.0370370i
$730$	4.64934	−	5.52154i	0.172080	−	0.204361i
$731$	47.4142	−	82.1238i	1.75368	−	3.03746i
$732$	−1.33460	−	4.98081i	−0.0493284	−	0.184096i
$733$	−9.43267	+	9.43267i	−0.348404	+	0.348404i	−0.859515	−	0.511111i	$-0.829234\pi$
$733$	−9.43267	+	9.43267i	−0.348404	+	0.348404i	0.511111	+	0.859515i	$0.329234\pi$
$734$	−36.3413			−1.34138
$735$	−10.5669	+	22.5592i	−0.389765	+	0.832110i
$736$	2.58342	−	1.49154i	0.0952261	−	0.0549788i
$737$	−1.39982	−	5.22419i	−0.0515629	−	0.192435i
$738$	5.50158	+	1.47414i	0.202516	+	0.0542640i
$739$	−13.5881	+	7.84511i	−0.499847	+	0.288587i	−0.728650	−	0.684886i	$-0.759852\pi$
$739$	−13.5881	+	7.84511i	−0.499847	+	0.288587i	0.228803	+	0.973473i	$0.426519\pi$
$740$	−0.918022	−	10.7053i	−0.0337472	−	0.393533i
$741$	15.2027	+	4.10976i	0.558486	+	0.150976i
$742$	33.3471	+	33.3471i	1.22421	+	1.22421i
$743$	−9.15371	+	34.1621i	−0.335817	+	1.25329i	0.567163	+	0.823605i	$0.308041\pi$
$743$	−9.15371	+	34.1621i	−0.335817	+	1.25329i	−0.902981	+	0.429682i	$0.858626\pi$
$744$	−2.32087	−	4.01987i	−0.0850874	−	0.147376i
$745$	0.640558	+	1.76939i	0.0234682	+	0.0648254i
$746$	11.5561	+	20.0157i	0.423098	+	0.732827i
$747$	5.66486	−	1.51789i	0.207266	−	0.0555368i
$748$	−5.17111	+	5.17111i	−0.189075	+	0.189075i
$749$	−13.4364			−0.490956
$750$	5.54009	+	9.71120i	0.202296	+	0.354603i
$751$	9.58595	+	5.53445i	0.349796	+	0.201955i	0.664595	−	0.747203i	$-0.268604\pi$
$751$	9.58595	+	5.53445i	0.349796	+	0.201955i	−0.314799	+	0.949158i	$0.601937\pi$
$752$	−6.75179	−	6.75179i	−0.246212	−	0.246212i
$753$	−9.20367	−	9.20367i	−0.335400	−	0.335400i
$754$	−13.8979	+	24.0719i	−0.506132	+	0.876646i
$755$	−38.1511	−	6.79481i	−1.38846	−	0.247288i
$756$	−3.68857	−	2.12960i	−0.134152	−	0.0774527i
$757$	12.6414	−	47.1785i	0.459461	−	1.71473i	−0.215171	−	0.976576i	$-0.569031\pi$
$757$	12.6414	−	47.1785i	0.459461	−	1.71473i	0.674632	−	0.738154i	$-0.264302\pi$
$758$	26.0590	+	6.98249i	0.946506	+	0.253615i
$759$	−2.65468			−0.0963586
$760$	−3.29747	−	9.17206i	−0.119612	−	0.332706i
$761$	−2.67989			−0.0971460			−0.0485730	−	0.998820i	$-0.515467\pi$
$761$	−2.67989			−0.0971460			−0.0485730	+	0.998820i	$0.515467\pi$
$762$	−7.00588	−	1.87722i	−0.253796	−	0.0680045i
$763$	17.4768	−	65.2243i	0.632703	−	2.36128i
$764$	1.33187	+	0.768956i	0.0481854	+	0.0278199i
$765$	−10.5138	−	15.0704i	−0.380126	−	0.544870i
$766$	−9.90484	+	17.1557i	−0.357877	+	0.619860i
$767$	7.25478	+	7.25478i	0.261955	+	0.261955i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−0.467320	−	0.269807i	−0.0168520	−	0.00972950i	0.491550	−	0.870849i	$-0.336430\pi$
$769$	−0.467320	−	0.269807i	−0.0168520	−	0.00972950i	−0.508402	+	0.861120i	$0.669764\pi$
$770$	7.96924	−	2.88504i	0.287191	−	0.103970i
$771$	−23.0627			−0.830582
$772$	−12.6838	+	12.6838i	−0.456500	+	0.456500i
$773$	−16.7939	+	4.49992i	−0.604036	+	0.161851i	−0.547860	−	0.836570i	$-0.684557\pi$
$773$	−16.7939	+	4.49992i	−0.604036	+	0.161851i	−0.0561756	+	0.998421i	$0.517891\pi$
$774$	−5.76975	−	9.99350i	−0.207389	−	0.359209i
$775$	−8.01289	+	21.7816i	−0.287832	+	0.782419i
$776$	−0.824846	−	1.42867i	−0.0296102	−	0.0512864i
$777$	5.29696	−	19.7685i	0.190027	−	0.709191i
$778$	17.7592	+	17.7592i	0.636697	+	0.636697i
$779$	6.37238	+	23.9951i	0.228314	+	0.859712i
$780$	−6.17975	−	5.20358i	−0.221270	−	0.186318i
$781$	−1.48880	+	0.859556i	−0.0532733	+	0.0307573i
$782$	23.6788	+	6.34471i	0.846751	+	0.226886i
$783$	1.99120	+	7.43127i	0.0711598	+	0.265572i
$784$	−9.64815	+	5.57036i	−0.344577	+	0.198941i
$785$	24.3581	+	11.4094i	0.869376	+	0.407220i
$786$	−5.78484			−0.206339
$787$	14.3168	−	14.3168i	0.510339	−	0.510339i	−0.404291	−	0.914630i	$-0.632482\pi$
$787$	14.3168	−	14.3168i	0.510339	−	0.510339i	0.914630	+	0.404291i	$0.132482\pi$
$788$	−3.21143	−	11.9852i	−0.114402	−	0.426956i
$789$	−1.01806	+	1.76334i	−0.0362441	+	0.0627766i
$790$	22.5804	−	1.93636i	0.803373	−	0.0688927i
$791$			71.7600i			2.55149i
$792$	0.230326	+	0.859590i	0.00818429	+	0.0305442i
$793$	4.82184	−	17.9953i	0.171229	−	0.639034i
$794$	−16.5485	+	28.6629i	−0.587285	+	1.01721i
$795$	24.3753	+	4.34129i	0.864502	+	0.153970i
$796$	5.56557	+	9.63986i	0.197267	+	0.341676i
$797$	−11.7278	+	11.7278i	−0.415420	+	0.415420i	−0.883622	−	0.468201i	$-0.844902\pi$
$797$	−11.7278	+	11.7278i	−0.415420	+	0.415420i	0.468201	+	0.883622i	$0.344902\pi$
$798$	0.0412267	−	18.5653i	0.00145941	−	0.657206i
$799$		−	78.4667i		−	2.77595i
$800$	−0.452924	+	4.97944i	−0.0160133	+	0.176050i
$801$	7.80525	−	4.50636i	0.275785	−	0.159224i
$802$	24.4220	−	6.54386i	0.862372	−	0.231072i
$803$	−2.77486	−	0.743521i	−0.0979226	−	0.0262383i
$804$	5.26330	+	3.03877i	0.185622	+	0.107169i
$805$	−21.7321	−	18.2993i	−0.765956	−	0.644964i
$806$		−	16.7703i		−	0.590710i
$807$	6.71249	−	1.79861i	0.236291	−	0.0633140i
$808$	−15.7425	+	4.21818i	−0.553818	+	0.148395i
$809$		−	26.0180i		−	0.914744i	−0.889276	−	0.457372i	$-0.848791\pi$
$809$		−	26.0180i		−	0.914744i	0.889276	−	0.457372i	$-0.151209\pi$
$810$	−2.22789	+	0.191051i	−0.0782801	+	0.00671286i
$811$	−42.5858	−	24.5869i	−1.49539	−	0.863364i	−0.495405	−	0.868662i	$-0.664980\pi$
$811$	−42.5858	−	24.5869i	−1.49539	−	0.863364i	−0.999986	+	0.00529810i	$0.998314\pi$
$812$	31.6512	+	8.48092i	1.11074	+	0.297622i
$813$	−14.5300	+	3.89330i	−0.509589	+	0.136544i
$814$	−3.70323	+	2.13806i	−0.129798	+	0.0749390i
$815$	0.816665	+	1.17060i	0.0286065	+	0.0410044i
$816$		−	8.21772i		−	0.287678i
$817$	25.2464	−	43.5047i	0.883261	−	1.52204i
$818$	10.3840	−	10.3840i	0.363069	−	0.363069i
$819$	−7.69409	−	13.3266i	−0.268853	−	0.465668i
$820$	2.23315	−	12.5386i	0.0779849	−	0.437866i
$821$	5.72154	−	9.91000i	0.199683	−	0.345862i	−0.748742	−	0.662861i	$-0.769342\pi$
$821$	5.72154	−	9.91000i	0.199683	−	0.345862i	0.948426	+	0.316999i	$0.102675\pi$
$822$	1.89446	−	7.07023i	0.0660770	−	0.246603i
$823$	1.70962	+	6.38041i	0.0595938	+	0.222407i	0.989300	−	0.145895i	$-0.0466061\pi$
$823$	1.70962	+	6.38041i	0.0595938	+	0.222407i	−0.929706	+	0.368302i	$0.879939\pi$
$824$			2.84021i			0.0989432i
$825$	2.56470	−	3.63606i	0.0892913	−	0.126591i
$826$	6.04751	−	10.4746i	0.210420	−	0.364457i
$827$	−0.989077	−	3.69128i	−0.0343936	−	0.128359i	0.946595	−	0.322426i	$-0.104498\pi$
$827$	−0.989077	−	3.69128i	−0.0343936	−	0.128359i	−0.980988	+	0.194068i	$0.937832\pi$
$828$	2.10935	−	2.10935i	0.0733051	−	0.0733051i
$829$	−12.6535			−0.439475			−0.219738	−	0.975559i	$-0.570520\pi$
$829$	−12.6535			−0.439475			−0.219738	+	0.975559i	$0.570520\pi$
$830$	−4.46398	−	12.3307i	−0.154947	−	0.428004i
$831$	−12.9139	+	7.45583i	−0.447977	+	0.258640i
$832$	−0.935096	−	3.48983i	−0.0324186	−	0.120988i
$833$	−88.4318	−	23.6952i	−3.06398	−	0.820991i
$834$	−18.5428	+	10.7057i	−0.642086	+	0.370709i
$835$	50.0099	−	4.28857i	1.73066	−	0.148412i
$836$	−2.74898	+	2.73680i	−0.0950754	+	0.0946541i
$837$	−3.28221	−	3.28221i	−0.113450	−	0.113450i
$838$	−4.42467	+	16.5131i	−0.152848	+	0.570435i
$839$	4.80476	+	8.32209i	0.165879	+	0.287310i	0.936967	−	0.349418i	$-0.113621\pi$
$839$	4.80476	+	8.32209i	0.165879	+	0.287310i	−0.771088	+	0.636728i	$0.780287\pi$
$840$	−4.03980	+	8.62459i	−0.139386	+	0.297577i
$841$	−15.0943	−	26.1442i	−0.520494	−	0.901523i
$842$	−10.8545	+	2.90844i	−0.374070	+	0.100232i
$843$	−9.34101	+	9.34101i	−0.321721	+	0.321721i
$844$	−8.03242			−0.276487
$845$	−0.0405710	−	0.112068i	−0.00139569	−	0.00385525i
$846$	−8.26922	−	4.77423i	−0.284302	−	0.164142i
$847$	30.7436	+	30.7436i	1.05636	+	1.05636i
$848$	7.82944	+	7.82944i	0.268864	+	0.268864i
$849$	−4.24979	+	7.36085i	−0.145852	+	0.252624i
$850$	−31.5664	+	26.3027i	−1.08272	+	0.902176i
$851$	12.4136	+	7.16699i	0.425533	+	0.245681i
$852$	0.499981	−	1.86595i	0.0171291	−	0.0639265i
$853$	20.2409	+	5.42354i	0.693036	+	0.185698i	0.588109	−	0.808782i	$-0.299873\pi$
$853$	20.2409	+	5.42354i	0.693036	+	0.185698i	0.104927	+	0.994480i	$0.466539\pi$
$854$	−21.9626			−0.751544
$855$	−5.55901	−	8.00608i	−0.190114	−	0.273802i
$856$	−3.15469			−0.107825
$857$	21.8388	+	5.85170i	0.746001	+	0.199890i	0.611743	−	0.791056i	$-0.290469\pi$
$857$	21.8388	+	5.85170i	0.746001	+	0.199890i	0.134257	+	0.990947i	$0.457135\pi$
$858$	−0.832154	+	3.10564i	−0.0284093	+	0.106025i
$859$	21.4516	+	12.3851i	0.731918	+	0.422573i	0.819123	−	0.573617i	$-0.194460\pi$
$859$	21.4516	+	12.3851i	0.731918	+	0.422573i	−0.0872056	+	0.996190i	$0.527794\pi$
$860$	−21.1621	+	14.7636i	−0.721622	+	0.503436i
$861$	12.1295	−	21.0088i	0.413371	−	0.715979i
$862$	−21.9186	−	21.9186i	−0.746551	−	0.746551i
$863$	−3.08808	−	3.08808i	−0.105119	−	0.105119i	0.652591	−	0.757710i	$-0.273682\pi$
$863$	−3.08808	−	3.08808i	−0.105119	−	0.105119i	−0.757710	+	0.652591i	$0.773682\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	8.10966	+	3.79861i	0.275737	+	0.129156i
$866$	−18.4678			−0.627560
$867$	35.7308	−	35.7308i	1.21348	−	1.21348i
$868$	−19.0964	+	5.11688i	−0.648176	+	0.173678i
$869$	−4.50977	−	7.81115i	−0.152983	−	0.264975i
$870$	16.1756	−	5.85594i	0.548406	−	0.198535i
$871$	10.9789	+	19.0160i	0.372005	+	0.644331i
$872$	4.10331	−	15.3138i	0.138956	−	0.518590i
$873$	−1.16651	−	1.16651i	−0.0394803	−	0.0394803i
$874$	12.5524	+	3.39329i	0.424590	+	0.114780i
$875$	46.0597	−	12.0871i	1.55710	−	0.408617i
$876$	2.79563	−	1.61406i	0.0944557	−	0.0545340i
$877$	−13.0751	−	3.50347i	−0.441515	−	0.118304i	0.0312113	−	0.999513i	$-0.490064\pi$
$877$	−13.0751	−	3.50347i	−0.441515	−	0.118304i	−0.472727	+	0.881209i	$0.656730\pi$
$878$	−0.842401	−	3.14388i	−0.0284297	−	0.106101i
$879$	19.6653	−	11.3538i	0.663295	−	0.382953i
$880$	1.87107	−	0.677368i	0.0630737	−	0.0228341i
$881$	−3.27016			−0.110175			−0.0550873	−	0.998482i	$-0.517544\pi$
$881$	−3.27016			−0.110175			−0.0550873	+	0.998482i	$0.517544\pi$
$882$	−7.87768	+	7.87768i	−0.265255	+	0.265255i
$883$	−9.78143	−	36.5048i	−0.329171	−	1.22848i	−0.910051	−	0.414495i	$-0.863958\pi$
$883$	−9.78143	−	36.5048i	−0.329171	−	1.22848i	0.580880	−	0.813989i	$-0.302709\pi$
$884$	14.8450	−	25.7124i	0.499293	−	0.864801i
$885$	−0.542537	−	6.32664i	−0.0182372	−	0.212668i
$886$		−	18.5142i		−	0.621995i
$887$	14.4837	+	54.0539i	0.486315	+	1.81495i	0.574065	+	0.818810i	$0.305366\pi$
$887$	14.4837	+	54.0539i	0.486315	+	1.81495i	−0.0877499	+	0.996143i	$0.527968\pi$
$888$	1.24365	−	4.64138i	0.0417343	−	0.155754i
$889$	−15.4460	+	26.7533i	−0.518042	+	0.897275i
$890$	−11.5309	−	16.5283i	−0.386516	−	0.554030i
$891$	0.444956	+	0.770687i	0.0149066	+	0.0258190i
$892$	7.39841	−	7.39841i	0.247717	−	0.247717i
$893$	0.0924241	−	41.6207i	0.00309285	−	1.39278i
$894$			0.841552i			0.0281457i
$895$	−0.300560	+	1.68757i	−0.0100466	+	0.0564091i
$896$	−3.68857	+	2.12960i	−0.123226	+	0.0711448i
$897$	10.4104	−	2.78946i	0.347594	−	0.0931375i
$898$	−30.9443	−	8.29149i	−1.03262	−	0.276691i
$899$	30.9266	+	17.8555i	1.03146	+	0.595513i
$900$	0.851283	+	4.92700i	0.0283761	+	0.164233i
$901$			90.9907i			3.03134i
$902$	−4.89593	+	1.31186i	−0.163017	+	0.0436802i
$903$	−47.4742	+	12.7207i	−1.57984	+	0.423318i
$904$			16.8483i			0.560365i
$905$	8.76438	−	10.4085i	0.291338	−	0.345992i
$906$	−15.0084	−	8.66509i	−0.498620	−	0.287878i
$907$	−25.2237	−	6.75866i	−0.837538	−	0.224418i	−0.185539	−	0.982637i	$-0.559403\pi$
$907$	−25.2237	−	6.75866i	−0.837538	−	0.224418i	−0.652000	+	0.758219i	$0.726070\pi$
$908$	9.82229	−	2.63188i	0.325964	−	0.0873419i
$909$	−14.1143	+	8.14890i	−0.468142	+	0.270282i
$910$	−28.2202	+	19.6877i	−0.935489	+	0.652640i
$911$			5.72973i			0.189835i	0.995485	+	0.0949173i	$0.0302587\pi$
$911$			5.72973i			0.189835i	−0.995485	+	0.0949173i	$0.969741\pi$
$912$	0.00967947	−	4.35889i	0.000320519	−	0.144337i
$913$	−3.69043	+	3.69043i	−0.122136	+	0.122136i
$914$	−8.68815	−	15.0483i	−0.287379	−	0.497754i
$915$	−9.45645	+	6.59725i	−0.312621	+	0.218098i
$916$	−0.0280833	+	0.0486417i	−0.000927898	+	0.00160717i
$917$	−6.37698	+	23.7992i	−0.210586	+	0.785919i
$918$	−2.12690	−	7.93771i	−0.0701983	−	0.261983i
$919$			23.1134i			0.762440i	0.924484	+	0.381220i	$0.124496\pi$
$919$			23.1134i			0.762440i	−0.924484	+	0.381220i	$0.875504\pi$
$920$	−5.10240	−	4.29641i	−0.168221	−	0.141649i
$921$	2.04491	−	3.54189i	0.0673822	−	0.116709i
$922$	−2.22821	−	8.31580i	−0.0733823	−	0.273866i
$923$	4.93517	−	4.93517i	0.162443	−	0.162443i
$924$	3.79031			0.124692
$925$	−21.8093	+	10.0786i	−0.717087	+	0.331382i
$926$	18.0792	−	10.4380i	0.594120	−	0.343015i
$927$	0.735099	+	2.74343i	0.0241438	+	0.0901060i
$928$	7.43127	+	1.99120i	0.243943	+	0.0653644i
$929$	4.52917	−	2.61491i	0.148597	−	0.0857926i	−0.423858	−	0.905729i	$-0.639324\pi$
$929$	4.52917	−	2.61491i	0.148597	−	0.0857926i	0.572455	+	0.819936i	$0.305991\pi$
$930$	−6.68534	+	7.93948i	−0.219221	+	0.260346i
$931$	−46.8786	−	12.6727i	−1.53638	−	0.415331i
$932$	8.99361	+	8.99361i	0.294596	+	0.294596i
$933$	7.30386	−	27.2584i	0.239118	−	0.892399i
$934$	−11.2447	−	19.4763i	−0.367936	−	0.637285i
$935$	14.8085	+	6.93636i	0.484289	+	0.226843i
$936$	−1.80647	−	3.12889i	−0.0590462	−	0.102271i
$937$	22.3133	−	5.97882i	0.728943	−	0.195320i	0.124784	−	0.992184i	$-0.460176\pi$
$937$	22.3133	−	5.97882i	0.728943	−	0.195320i	0.604158	+	0.796864i	$0.293509\pi$
$938$	18.3037	−	18.3037i	0.597638	−	0.597638i
$939$	−12.5797			−0.410523
$940$	−9.05663	+	19.3350i	−0.295395	+	0.630639i
$941$	39.5043	+	22.8078i	1.28780	+	0.743514i	0.978262	−	0.207371i	$-0.0664909\pi$
$941$	39.5043	+	22.8078i	1.28780	+	0.743514i	0.309542	+	0.950886i	$0.399824\pi$
$942$	8.50582	+	8.50582i	0.277135	+	0.277135i
$943$	12.0141	+	12.0141i	0.391235	+	0.391235i
$944$	1.41987	−	2.45929i	0.0462129	−	0.0800431i
$945$	−1.66994	+	9.37629i	−0.0543232	+	0.305011i
$946$	8.89334	+	5.13457i	0.289147	+	0.166939i
$947$	−4.79669	+	17.9015i	−0.155871	+	0.581720i	0.843158	+	0.537666i	$0.180694\pi$
$947$	−4.79669	+	17.9015i	−0.155871	+	0.581720i	−0.999029	+	0.0440537i	$0.985973\pi$
$948$	9.78995	+	2.62321i	0.317963	+	0.0851979i
$949$	11.6630			0.378597
$950$	−16.7746	+	13.9145i	−0.544241	+	0.451444i
$951$	20.9980			0.680906
$952$	−33.8082	−	9.05889i	−1.09573	−	0.293600i
$953$	1.74976	−	6.53019i	0.0566802	−	0.211534i	−0.931778	−	0.363030i	$-0.881742\pi$
$953$	1.74976	−	6.53019i	0.0566802	−	0.211534i	0.988458	+	0.151496i	$0.0484091\pi$
$954$	9.58906	+	5.53625i	0.310457	+	0.179243i
$955$	0.602984	−	3.38560i	0.0195121	−	0.109555i
$956$	−1.84801	+	3.20085i	−0.0597689	+	0.103523i
$957$	−4.84118	−	4.84118i	−0.156493	−	0.156493i
$958$	15.6040	+	15.6040i	0.504144	+	0.504144i
$959$	−26.9990	−	15.5879i	−0.871843	−	0.503359i
$960$	−0.948490	+	2.02494i	−0.0306124	+	0.0653545i
$961$	9.45418			0.304973
$962$	12.2758	−	12.2758i	0.395786	−	0.395786i
$963$	−3.04719	+	0.816493i	−0.0981944	+	0.0263111i
$964$	1.25084	+	2.16652i	0.0402868	+	0.0697788i
$965$	36.3225	+	17.0136i	1.16926	+	0.547689i
$966$	−6.35274	−	11.0033i	−0.204396	−	0.354025i
$967$	6.67297	−	24.9039i	0.214588	−	0.800854i	−0.771723	−	0.635959i	$-0.780605\pi$
$967$	6.67297	−	24.9039i	0.214588	−	0.800854i	0.986311	−	0.164895i	$-0.0527286\pi$
$968$	7.21819	+	7.21819i	0.232001	+	0.232001i
$969$	25.3849	−	25.2724i	0.815481	−	0.811867i
$970$	−2.37599	+	2.82172i	−0.0762884	+	0.0905998i
$971$	−17.0956	+	9.87015i	−0.548624	+	0.316748i	−0.748567	−	0.663059i	$-0.769258\pi$
$971$	−17.0956	+	9.87015i	−0.548624	+	0.316748i	0.199943	+	0.979808i	$0.435924\pi$
$972$	−0.965926	−	0.258819i	−0.0309821	−	0.00830162i
$973$	23.6031	+	88.0880i	0.756681	+	2.82397i
$974$	−24.5456	+	14.1714i	−0.786491	+	0.454081i
$975$	−6.23689	+	16.9539i	−0.199740	+	0.542958i
$976$	−5.15652			−0.165056
$977$	−11.1105	+	11.1105i	−0.355458	+	0.355458i	−0.862135	−	0.506678i	$-0.830873\pi$
$977$	−11.1105	+	11.1105i	−0.355458	+	0.355458i	0.506678	+	0.862135i	$0.330873\pi$
$978$	0.165209	+	0.616568i	0.00528280	+	0.0197157i
$979$	−4.01027	+	6.94599i	−0.128169	+	0.221995i
$980$	19.0557	+	16.0456i	0.608710	+	0.512557i
$981$		−	15.8540i		−	0.506179i
$982$	1.06977	+	3.99245i	0.0341378	+	0.127404i
$983$	−4.45165	+	16.6138i	−0.141986	+	0.529897i	0.857886	+	0.513841i	$0.171778\pi$
$983$	−4.45165	+	16.6138i	−0.141986	+	0.529897i	−0.999871	+	0.0160564i	$0.994889\pi$
$984$	2.84783	−	4.93258i	0.0907855	−	0.157245i
$985$	−22.7549	+	15.8748i	−0.725030	+	0.505814i
$986$	31.6112	+	54.7522i	1.00671	+	1.74366i
$987$	−28.7572	+	28.7572i	−0.915350	+	0.915350i
$988$	7.90448	−	13.6210i	0.251475	−	0.433342i
$989$		−	34.4232i		−	1.09459i
$990$	1.63200	−	1.13856i	0.0518683	−	0.0361857i
$991$	4.69224	−	2.70907i	0.149054	−	0.0860563i	−0.423618	−	0.905841i	$-0.639240\pi$
$991$	4.69224	−	2.70907i	0.149054	−	0.0860563i	0.572672	+	0.819785i	$0.305907\pi$
$992$	−4.48358	+	1.20137i	−0.142354	+	0.0381436i
$993$	−2.12121	−	0.568377i	−0.0673146	−	0.0180369i
$994$	−7.12549	−	4.11391i	−0.226007	−	0.130485i
$995$	16.0318	−	19.0393i	0.508242	−	0.603586i
$996$		−	5.86469i		−	0.185830i
$997$	−50.4883	+	13.5283i	−1.59898	+	0.428445i	−0.944734	−	0.327837i	$-0.893680\pi$
$997$	−50.4883	+	13.5283i	−1.59898	+	0.428445i	−0.654245	+	0.756282i	$0.727014\pi$
$998$	−15.3055	+	4.10111i	−0.484489	+	0.129818i
$999$		−	4.80511i		−	0.152027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.487.4	yes	40
5.3	odd	4	inner	570.2.x.b.373.1	yes	40
19.8	odd	6	inner	570.2.x.b.217.1	yes	40
95.8	even	12	inner	570.2.x.b.103.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.4	✓	40	95.8	even	12	inner
570.2.x.b.217.1	yes	40	19.8	odd	6	inner
570.2.x.b.373.1	yes	40	5.3	odd	4	inner
570.2.x.b.487.4	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.392079 - 2.20143i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.01170 - 3.01170i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.392079 - 2.20143i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.01170 - 3.01170i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.948490 + 2.02494i) q^{10} +0.889913 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.48983 + 0.935096i) q^{13} +(2.12960 + 3.68857i) q^{14} +(2.02494 + 0.948490i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.12690 + 7.93771i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-1.13751 + 4.20786i) q^{19} +(1.44026 - 1.71045i) q^{20} +(3.68857 - 2.12960i) q^{21} +(-0.859590 - 0.230326i) q^{22} +(0.772077 + 2.88143i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.69255 - 1.72627i) q^{25} +3.61294 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.10236 - 4.11406i) q^{28} +(-3.84671 + 6.66270i) q^{29} +(-1.71045 - 1.44026i) q^{30} -4.64175i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.230326 + 0.859590i) q^{33} +(4.10886 - 7.11676i) q^{34} +(-7.81087 + 5.44921i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.39772 - 3.39772i) q^{37} +(2.18783 - 3.77007i) q^{38} -3.61294i q^{39} +(-1.83388 + 1.27940i) q^{40} +(4.93258 - 2.84783i) q^{41} +(-4.11406 + 1.10236i) q^{42} +(-11.1463 - 2.98664i) q^{43} +(0.770687 + 0.444956i) q^{44} +(-1.44026 + 1.71045i) q^{45} -2.98307i q^{46} +(-9.22311 + 2.47133i) q^{47} +(-0.965926 + 0.258819i) q^{48} +11.1407i q^{49} +(4.08586 + 2.88197i) q^{50} +(-7.11676 - 4.10886i) q^{51} +(-3.48983 - 0.935096i) q^{52} +(10.6952 - 2.86577i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.348916 - 1.95908i) q^{55} +4.25919i q^{56} +(-3.77007 - 2.18783i) q^{57} +(5.44007 - 5.44007i) q^{58} +(-1.41987 - 2.45929i) q^{59} +(1.27940 + 1.83388i) q^{60} +(-2.57826 + 4.46567i) q^{61} +(-1.20137 + 4.48358i) q^{62} +(1.10236 + 4.11406i) q^{63} +1.00000i q^{64} +(0.690256 + 8.04923i) q^{65} +(0.444956 - 0.770687i) q^{66} +(-1.57298 - 5.87045i) q^{67} +(-5.81081 + 5.81081i) q^{68} -2.98307 q^{69} +(8.95508 - 3.24194i) q^{70} +(-1.67297 + 0.965889i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-3.11813 - 0.835499i) q^{73} +(-4.16134 + 2.40255i) q^{74} +(2.88197 - 4.08586i) q^{75} +(-3.08904 + 3.07535i) q^{76} +(-2.68015 - 2.68015i) q^{77} +(-0.935096 + 3.48983i) q^{78} +(-5.06765 - 8.77743i) q^{79} +(2.10253 - 0.761162i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.50158 + 1.47414i) q^{82} +(-4.14696 + 4.14696i) q^{83} +4.25919 q^{84} +(16.6404 + 7.79443i) q^{85} +(9.99350 + 5.76975i) q^{86} +(-5.44007 - 5.44007i) q^{87} +(-0.629263 - 0.629263i) q^{88} +(-4.50636 + 7.80525i) q^{89} +(1.83388 - 1.27940i) q^{90} +(13.3266 + 7.69409i) q^{91} +(-0.772077 + 2.88143i) q^{92} +(4.48358 + 1.20137i) q^{93} +9.54847 q^{94} +(8.81729 + 4.15396i) q^{95} +1.00000 q^{96} +(1.59348 + 0.426972i) q^{97} +(2.88343 - 10.7611i) q^{98} +(-0.770687 - 0.444956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

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