LMFDB - Embedded newform 731.2.m.b.87.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.13
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.482959 - 0.482959i) q^{2} +(-1.45483 + 0.602612i) q^{3} -1.53350i q^{4} +(1.15531 + 2.78915i) q^{5} +(0.993661 + 0.411588i) q^{6} +(-1.39214 + 3.36091i) q^{7} +(-1.70653 + 1.70653i) q^{8} +(-0.367918 + 0.367918i) q^{9} +O(q^{10})$	\(q+(-0.482959 - 0.482959i) q^{2} +(-1.45483 + 0.602612i) q^{3} -1.53350i q^{4} +(1.15531 + 2.78915i) q^{5} +(0.993661 + 0.411588i) q^{6} +(-1.39214 + 3.36091i) q^{7} +(-1.70653 + 1.70653i) q^{8} +(-0.367918 + 0.367918i) q^{9} +(0.789081 - 1.90501i) q^{10} +(5.19523 + 2.15194i) q^{11} +(0.924107 + 2.23099i) q^{12} -3.13516i q^{13} +(2.29553 - 0.950838i) q^{14} +(-3.36156 - 3.36156i) q^{15} -1.41863 q^{16} +(-3.98423 - 1.06109i) q^{17} +0.355379 q^{18} +(-4.86495 - 4.86495i) q^{19} +(4.27717 - 1.77166i) q^{20} -5.72849i q^{21} +(-1.46979 - 3.54838i) q^{22} +(-4.78949 - 1.98387i) q^{23} +(1.45435 - 3.51110i) q^{24} +(-2.90911 + 2.90911i) q^{25} +(-1.51415 + 1.51415i) q^{26} +(2.12138 - 5.12148i) q^{27} +(5.15397 + 2.13484i) q^{28} +(2.19203 + 5.29203i) q^{29} +3.24698i q^{30} +(-4.06594 + 1.68417i) q^{31} +(4.09821 + 4.09821i) q^{32} -8.85499 q^{33} +(1.41175 + 2.43668i) q^{34} -10.9825 q^{35} +(0.564204 + 0.564204i) q^{36} +(-1.62600 + 0.673513i) q^{37} +4.69914i q^{38} +(1.88929 + 4.56114i) q^{39} +(-6.73136 - 2.78822i) q^{40} +(-0.976273 + 2.35693i) q^{41} +(-2.76662 + 2.76662i) q^{42} +(0.707107 - 0.707107i) q^{43} +(3.30000 - 7.96690i) q^{44} +(-1.45124 - 0.601123i) q^{45} +(1.35500 + 3.27126i) q^{46} +7.89088i q^{47} +(2.06388 - 0.854886i) q^{48} +(-4.40796 - 4.40796i) q^{49} +2.80996 q^{50} +(6.43582 - 0.857230i) q^{51} -4.80778 q^{52} +(-4.09877 - 4.09877i) q^{53} +(-3.49800 + 1.44892i) q^{54} +16.9764i q^{55} +(-3.35979 - 8.11125i) q^{56} +(10.0094 + 4.14602i) q^{57} +(1.49717 - 3.61449i) q^{58} +(2.68897 - 2.68897i) q^{59} +(-5.15495 + 5.15495i) q^{60} +(4.03241 - 9.73509i) q^{61} +(2.77706 + 1.15030i) q^{62} +(-0.724350 - 1.74874i) q^{63} -1.12127i q^{64} +(8.74444 - 3.62207i) q^{65} +(4.27659 + 4.27659i) q^{66} -11.5615 q^{67} +(-1.62719 + 6.10982i) q^{68} +8.16343 q^{69} +(5.30407 + 5.30407i) q^{70} +(-7.55494 + 3.12936i) q^{71} -1.25573i q^{72} +(5.22739 + 12.6200i) q^{73} +(1.11057 + 0.460013i) q^{74} +(2.47921 - 5.98535i) q^{75} +(-7.46041 + 7.46041i) q^{76} +(-14.4649 + 14.4649i) q^{77} +(1.29039 - 3.11529i) q^{78} +(-9.53375 - 3.94901i) q^{79} +(-1.63895 - 3.95679i) q^{80} +7.16833i q^{81} +(1.60980 - 0.666801i) q^{82} +(-1.13256 - 1.13256i) q^{83} -8.78466 q^{84} +(-1.64345 - 12.3385i) q^{85} -0.683006 q^{86} +(-6.37808 - 6.37808i) q^{87} +(-12.5382 + 5.19349i) q^{88} -15.1885i q^{89} +(0.410571 + 0.991206i) q^{90} +(10.5370 + 4.36457i) q^{91} +(-3.04227 + 7.34470i) q^{92} +(4.90037 - 4.90037i) q^{93} +(3.81097 - 3.81097i) q^{94} +(7.94859 - 19.1896i) q^{95} +(-8.43185 - 3.49259i) q^{96} +(4.35676 + 10.5181i) q^{97} +4.25772i q^{98} +(-2.70316 + 1.11969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.482959	−	0.482959i	−0.341503	−	0.341503i	0.515429	−	0.856932i	$-0.327633\pi$
$2$	−0.482959	−	0.482959i	−0.341503	−	0.341503i	−0.856932	+	0.515429i	$0.827633\pi$
$3$	−1.45483	+	0.602612i	−0.839949	+	0.347918i	−0.760833	−	0.648947i	$-0.775210\pi$
$3$	−1.45483	+	0.602612i	−0.839949	+	0.347918i	−0.0791156	+	0.996865i	$0.525210\pi$
$4$		−	1.53350i		−	0.766751i
$5$	1.15531	+	2.78915i	0.516668	+	1.24735i	0.939938	+	0.341344i	$0.110882\pi$
$5$	1.15531	+	2.78915i	0.516668	+	1.24735i	−0.423270	+	0.906003i	$0.639118\pi$
$6$	0.993661	+	0.411588i	0.405661	+	0.168030i
$7$	−1.39214	+	3.36091i	−0.526178	+	1.27031i	0.407831	+	0.913057i	$0.366285\pi$
$7$	−1.39214	+	3.36091i	−0.526178	+	1.27031i	−0.934009	+	0.357249i	$0.883715\pi$
$8$	−1.70653	+	1.70653i	−0.603351	+	0.603351i
$9$	−0.367918	+	0.367918i	−0.122639	+	0.122639i
$10$	0.789081	−	1.90501i	0.249529	−	0.602417i
$11$	5.19523	+	2.15194i	1.56642	+	0.648833i	0.986190	−	0.165618i	$-0.0529620\pi$
$11$	5.19523	+	2.15194i	1.56642	+	0.648833i	0.580232	+	0.814451i	$0.302962\pi$
$12$	0.924107	+	2.23099i	0.266767	+	0.644032i
$13$		−	3.13516i		−	0.869537i	−0.900542	−	0.434769i	$-0.856830\pi$
$13$		−	3.13516i		−	0.869537i	0.900542	−	0.434769i	$-0.143170\pi$
$14$	2.29553	−	0.950838i	0.613505	−	0.254122i
$15$	−3.36156	−	3.36156i	−0.867950	−	0.867950i
$16$	−1.41863			−0.354658
$17$	−3.98423	−	1.06109i	−0.966317	−	0.257353i
$17$	−3.98423	−	1.06109i	−0.966317	−	0.257353i
$18$	0.355379			0.0837636
$19$	−4.86495	−	4.86495i	−1.11610	−	1.11610i	−0.992309	−	0.123787i	$-0.960496\pi$
$19$	−4.86495	−	4.86495i	−1.11610	−	1.11610i	−0.123787	−	0.992309i	$-0.539504\pi$
$20$	4.27717	−	1.77166i	0.956405	−	0.396156i
$21$		−	5.72849i		−	1.25006i
$22$	−1.46979	−	3.54838i	−0.313359	−	0.756517i
$23$	−4.78949	−	1.98387i	−0.998679	−	0.413666i	−0.177366	−	0.984145i	$-0.556758\pi$
$23$	−4.78949	−	1.98387i	−0.998679	−	0.413666i	−0.821312	+	0.570479i	$0.806758\pi$
$24$	1.45435	−	3.51110i	0.296867	−	0.716701i
$25$	−2.90911	+	2.90911i	−0.581823	+	0.581823i
$26$	−1.51415	+	1.51415i	−0.296950	+	0.296950i
$27$	2.12138	−	5.12148i	0.408261	−	0.985629i
$28$	5.15397	+	2.13484i	0.974009	+	0.403448i
$29$	2.19203	+	5.29203i	0.407050	+	0.982705i	0.985910	+	0.167278i	$0.0534978\pi$
$29$	2.19203	+	5.29203i	0.407050	+	0.982705i	−0.578860	+	0.815427i	$0.696502\pi$
$30$			3.24698i			0.592815i
$31$	−4.06594	+	1.68417i	−0.730264	+	0.302485i	−0.716661	−	0.697422i	$-0.754330\pi$
$31$	−4.06594	+	1.68417i	−0.730264	+	0.302485i	−0.0136037	+	0.999907i	$0.504330\pi$
$32$	4.09821	+	4.09821i	0.724468	+	0.724468i
$33$	−8.85499			−1.54146
$34$	1.41175	+	2.43668i	0.242114	+	0.417887i
$35$	−10.9825			−1.85637
$36$	0.564204	+	0.564204i	0.0940340	+	0.0940340i
$37$	−1.62600	+	0.673513i	−0.267313	+	0.110725i	−0.512314	−	0.858798i	$-0.671212\pi$
$37$	−1.62600	+	0.673513i	−0.267313	+	0.110725i	0.245001	+	0.969523i	$0.421212\pi$
$38$			4.69914i			0.762301i
$39$	1.88929	+	4.56114i	0.302528	+	0.730367i
$40$	−6.73136	−	2.78822i	−1.06432	−	0.440856i
$41$	−0.976273	+	2.35693i	−0.152468	+	0.368091i	−0.981596	−	0.190968i	$-0.938837\pi$
$41$	−0.976273	+	2.35693i	−0.152468	+	0.368091i	0.829128	+	0.559059i	$0.188837\pi$
$42$	−2.76662	+	2.76662i	−0.426899	+	0.426899i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	3.30000	−	7.96690i	0.497493	−	1.20106i
$45$	−1.45124	−	0.601123i	−0.216338	−	0.0896101i
$46$	1.35500	+	3.27126i	0.199784	+	0.482320i
$47$			7.89088i			1.15100i	0.817801	+	0.575502i	$0.195193\pi$
$47$			7.89088i			1.15100i	−0.817801	+	0.575502i	$0.804807\pi$
$48$	2.06388	−	0.854886i	0.297895	−	0.123392i
$49$	−4.40796	−	4.40796i	−0.629708	−	0.629708i
$50$	2.80996			0.397389
$51$	6.43582	−	0.857230i	0.901195	−	0.120036i
$52$	−4.80778			−0.666718
$53$	−4.09877	−	4.09877i	−0.563010	−	0.563010i	0.367151	−	0.930161i	$-0.380333\pi$
$53$	−4.09877	−	4.09877i	−0.563010	−	0.563010i	−0.930161	+	0.367151i	$0.880333\pi$
$54$	−3.49800	+	1.44892i	−0.476018	+	0.197173i
$55$			16.9764i			2.28910i
$56$	−3.35979	−	8.11125i	−0.448971	−	1.08391i
$57$	10.0094	+	4.14602i	1.32577	+	0.549153i
$58$	1.49717	−	3.61449i	0.196588	−	0.474606i
$59$	2.68897	−	2.68897i	0.350074	−	0.350074i	−0.510063	−	0.860137i	$-0.670378\pi$
$59$	2.68897	−	2.68897i	0.350074	−	0.350074i	0.860137	+	0.510063i	$0.170378\pi$
$60$	−5.15495	+	5.15495i	−0.665502	+	0.665502i
$61$	4.03241	−	9.73509i	0.516297	−	1.24645i	−0.423866	−	0.905725i	$-0.639327\pi$
$61$	4.03241	−	9.73509i	0.516297	−	1.24645i	0.940163	−	0.340726i	$-0.110673\pi$
$62$	2.77706	+	1.15030i	0.352687	+	0.146088i
$63$	−0.724350	−	1.74874i	−0.0912595	−	0.220320i
$64$		−	1.12127i		−	0.140158i
$65$	8.74444	−	3.62207i	1.08461	−	0.449262i
$66$	4.27659	+	4.27659i	0.526412	+	0.526412i
$67$	−11.5615			−1.41246			−0.706228	−	0.707984i	$-0.749605\pi$
$67$	−11.5615			−1.41246			−0.706228	+	0.707984i	$0.749605\pi$
$68$	−1.62719	+	6.10982i	−0.197326	+	0.740925i
$69$	8.16343			0.982761
$70$	5.30407	+	5.30407i	0.633957	+	0.633957i
$71$	−7.55494	+	3.12936i	−0.896606	+	0.371386i	−0.782914	−	0.622130i	$-0.786268\pi$
$71$	−7.55494	+	3.12936i	−0.896606	+	0.371386i	−0.113692	+	0.993516i	$0.536268\pi$
$72$		−	1.25573i		−	0.147989i
$73$	5.22739	+	12.6200i	0.611819	+	1.47706i	0.861000	+	0.508606i	$0.169839\pi$
$73$	5.22739	+	12.6200i	0.611819	+	1.47706i	−0.249180	+	0.968457i	$0.580161\pi$
$74$	1.11057	+	0.460013i	0.129101	+	0.0534755i
$75$	2.47921	−	5.98535i	0.286275	−	0.691128i
$76$	−7.46041	+	7.46041i	−0.855768	+	0.855768i
$77$	−14.4649	+	14.4649i	−1.64843	+	1.64843i
$78$	1.29039	−	3.11529i	0.146108	−	0.352737i
$79$	−9.53375	−	3.94901i	−1.07263	−	0.444298i	−0.224712	−	0.974425i	$-0.572144\pi$
$79$	−9.53375	−	3.94901i	−1.07263	−	0.444298i	−0.847918	+	0.530127i	$0.822144\pi$
$80$	−1.63895	−	3.95679i	−0.183241	−	0.442382i
$81$			7.16833i			0.796481i
$82$	1.60980	−	0.666801i	0.177773	−	0.0736358i
$83$	−1.13256	−	1.13256i	−0.124314	−	0.124314i	0.642212	−	0.766527i	$-0.278017\pi$
$83$	−1.13256	−	1.13256i	−0.124314	−	0.124314i	−0.766527	+	0.642212i	$0.778017\pi$
$84$	−8.78466			−0.958485
$85$	−1.64345	−	12.3385i	−0.178257	−	1.33830i
$86$	−0.683006			−0.0736505
$87$	−6.37808	−	6.37808i	−0.683802	−	0.683802i
$88$	−12.5382	+	5.19349i	−1.33658	+	0.553628i
$89$		−	15.1885i		−	1.60997i	−0.593293	−	0.804986i	$-0.702173\pi$
$89$		−	15.1885i		−	1.60997i	0.593293	−	0.804986i	$-0.297827\pi$
$90$	0.410571	+	0.991206i	0.0432780	+	0.104482i
$91$	10.5370	+	4.36457i	1.10458	+	0.457531i
$92$	−3.04227	+	7.34470i	−0.317179	+	0.765738i
$93$	4.90037	−	4.90037i	0.508145	−	0.508145i
$94$	3.81097	−	3.81097i	0.393071	−	0.393071i
$95$	7.94859	−	19.1896i	0.815508	−	1.96881i
$96$	−8.43185	−	3.49259i	−0.860572	−	0.356461i
$97$	4.35676	+	10.5181i	0.442362	+	1.06796i	0.975118	+	0.221687i	$0.0711563\pi$
$97$	4.35676	+	10.5181i	0.442362	+	1.06796i	−0.532756	+	0.846269i	$0.678844\pi$
$98$			4.25772i			0.430095i
$99$	−2.70316	+	1.11969i	−0.271678	+	0.112533i
$100$	4.46113	+	4.46113i	0.446113	+	0.446113i
$101$	8.46662			0.842460			0.421230	−	0.906954i	$-0.361598\pi$
$101$	8.46662			0.842460			0.421230	+	0.906954i	$0.361598\pi$
$102$	−3.52224	−	2.69423i	−0.348754	−	0.266768i
$103$	−16.9535			−1.67048			−0.835239	−	0.549887i	$-0.814671\pi$
$103$	−16.9535			−1.67048			−0.835239	+	0.549887i	$0.814671\pi$
$104$	5.35026	+	5.35026i	0.524636	+	0.524636i
$105$	15.9776	−	6.61816i	1.55926	−	0.645866i
$106$			3.95907i			0.384539i
$107$	3.61449	+	8.72616i	0.349426	+	0.843590i	0.996688	+	0.0813219i	$0.0259142\pi$
$107$	3.61449	+	8.72616i	0.349426	+	0.843590i	−0.647261	+	0.762268i	$0.724086\pi$
$108$	−7.85379	−	3.25315i	−0.755732	−	0.313034i
$109$	−2.86994	+	6.92866i	−0.274891	+	0.663645i	−0.999679	−	0.0253263i	$-0.991938\pi$
$109$	−2.86994	+	6.92866i	−0.274891	+	0.663645i	0.724788	+	0.688972i	$0.241938\pi$
$110$	8.19892	−	8.19892i	0.781736	−	0.781736i
$111$	1.95970	−	1.95970i	0.186006	−	0.186006i
$112$	1.97493	−	4.76791i	0.186613	−	0.450525i
$113$	−13.3357	−	5.52381i	−1.25451	−	0.519637i	−0.346293	−	0.938127i	$-0.612560\pi$
$113$	−13.3357	−	5.52381i	−1.25451	−	0.519637i	−0.908222	+	0.418490i	$0.862560\pi$
$114$	−2.83176	−	6.83647i	−0.265218	−	0.640294i
$115$		−	15.6506i		−	1.45943i
$116$	8.11534	−	3.36148i	0.753490	−	0.312106i
$117$	1.15348	+	1.15348i	0.106640	+	0.106640i
$118$	−2.59732			−0.239103
$119$	9.11283	−	11.9135i	0.835372	−	1.09211i
$120$	11.4732			1.04736
$121$	14.5814	+	14.5814i	1.32559	+	1.32559i
$122$	−6.64913	+	2.75416i	−0.601984	+	0.249350i
$123$		−	4.01726i		−	0.362224i
$124$	2.58267	+	6.23513i	0.231931	+	0.559931i
$125$	2.47089	+	1.02347i	0.221003	+	0.0915423i
$126$	−0.494736	+	1.19440i	−0.0440746	+	0.106405i
$127$	−8.76571	+	8.76571i	−0.777831	+	0.777831i	−0.979462	−	0.201631i	$-0.935376\pi$
$127$	−8.76571	+	8.76571i	−0.777831	+	0.777831i	0.201631	+	0.979462i	$0.435376\pi$
$128$	7.65490	−	7.65490i	0.676604	−	0.676604i
$129$	−0.602612	+	1.45483i	−0.0530570	+	0.128091i
$130$	−5.97251	−	2.47390i	−0.523824	−	0.216975i
$131$	−0.933385	−	2.25339i	−0.0815502	−	0.196880i	0.877845	−	0.478945i	$-0.158981\pi$
$131$	−0.933385	−	2.25339i	−0.0815502	−	0.196880i	−0.959395	+	0.282065i	$0.908981\pi$
$132$			13.5791i			1.18191i
$133$	23.1233	−	9.57800i	2.00505	−	0.830518i
$134$	5.58370	+	5.58370i	0.482358	+	0.482358i
$135$	16.7354			1.44036
$136$	8.61002	−	4.98843i	0.738303	−	0.427755i
$137$	12.7773			1.09164			0.545821	−	0.837902i	$-0.316218\pi$
$137$	12.7773			1.09164			0.545821	+	0.837902i	$0.316218\pi$
$138$	−3.94260	−	3.94260i	−0.335616	−	0.335616i
$139$	8.89141	−	3.68294i	0.754159	−	0.312383i	0.0277219	−	0.999616i	$-0.491175\pi$
$139$	8.89141	−	3.68294i	0.754159	−	0.312383i	0.726437	+	0.687233i	$0.241175\pi$
$140$			16.8416i			1.42338i
$141$	−4.75514	−	11.4799i	−0.400455	−	0.966784i
$142$	5.16007	+	2.13737i	0.433024	+	0.179364i
$143$	6.74666	−	16.2879i	0.564184	−	1.36206i
$144$	0.521941	−	0.521941i	0.0434951	−	0.0434951i
$145$	−12.2278	+	12.2278i	−1.01547	+	1.01547i
$146$	3.57034	−	8.61956i	0.295483	−	0.713360i
$147$	9.06913	+	3.75656i	0.748010	+	0.309836i
$148$	1.03283	+	2.49348i	0.0848983	+	0.204963i
$149$		−	17.0958i		−	1.40054i	−0.713876	−	0.700272i	$-0.753062\pi$
$149$		−	17.0958i		−	1.40054i	0.713876	−	0.700272i	$-0.246938\pi$
$150$	−4.08803	+	1.69332i	−0.333786	+	0.138259i
$151$	4.86002	+	4.86002i	0.395503	+	0.395503i	0.876643	−	0.481141i	$-0.159777\pi$
$151$	4.86002	+	4.86002i	0.395503	+	0.395503i	−0.481141	+	0.876643i	$0.659777\pi$
$152$	16.6044			1.34680
$153$	1.85627	−	1.07548i	0.150070	−	0.0869471i
$154$	13.9719			1.12589
$155$	−9.39480	−	9.39480i	−0.754609	−	0.754609i
$156$	6.99452	−	2.89722i	0.560010	−	0.231964i
$157$		−	4.51146i		−	0.360054i	−0.983662	−	0.180027i	$-0.942382\pi$
$157$		−	4.51146i		−	0.360054i	0.983662	−	0.180027i	$-0.0576185\pi$
$158$	2.69720	+	6.51161i	0.214578	+	0.518036i
$159$	8.43301	+	3.49307i	0.668781	+	0.277018i
$160$	−6.69586	+	16.1652i	−0.529354	+	1.27797i
$161$	13.3353	−	13.3353i	1.05097	−	1.05097i
$162$	3.46200	−	3.46200i	0.272001	−	0.272001i
$163$	1.81531	−	4.38255i	0.142186	−	0.343268i	−0.836704	−	0.547656i	$-0.815520\pi$
$163$	1.81531	−	4.38255i	0.142186	−	0.343268i	0.978890	+	0.204388i	$0.0655203\pi$
$164$	3.61436	+	1.49712i	0.282234	+	0.116905i
$165$	−10.2302	−	24.6979i	−0.796421	−	1.92273i
$166$			1.09396i			0.0849074i
$167$	−21.4997	+	8.90545i	−1.66369	+	0.689125i	−0.998351	−	0.0574125i	$-0.981715\pi$
$167$	−21.4997	+	8.90545i	−1.66369	+	0.689125i	−0.665344	+	0.746537i	$0.731715\pi$
$168$	9.77587	+	9.77587i	0.754225	+	0.754225i
$169$	3.17077			0.243905
$170$	−5.16527	+	6.75271i	−0.396158	+	0.517909i
$171$	3.57981			0.273755
$172$	−1.08435	−	1.08435i	−0.0826809	−	0.0826809i
$173$	−11.5721	+	4.79331i	−0.879809	+	0.364429i	−0.776423	−	0.630212i	$-0.782968\pi$
$173$	−11.5721	+	4.79331i	−0.879809	+	0.364429i	−0.103386	+	0.994641i	$0.532968\pi$
$174$			6.16070i			0.467041i
$175$	−5.72740	−	13.8272i	−0.432951	−	1.04524i
$176$	−7.37013	−	3.05281i	−0.555544	−	0.230114i
$177$	−2.29160	+	5.53241i	−0.172247	+	0.415841i
$178$	−7.33539	+	7.33539i	−0.549811	+	0.549811i
$179$	−10.5112	+	10.5112i	−0.785647	+	0.785647i	−0.980777	−	0.195130i	$-0.937487\pi$
$179$	−10.5112	+	10.5112i	−0.785647	+	0.785647i	0.195130	+	0.980777i	$0.437487\pi$
$180$	−0.921823	+	2.22548i	−0.0687087	+	0.165877i
$181$	8.68804	+	3.59870i	0.645777	+	0.267489i	0.681440	−	0.731874i	$-0.261354\pi$
$181$	8.68804	+	3.59870i	0.645777	+	0.267489i	−0.0356628	+	0.999364i	$0.511354\pi$
$182$	−2.98103	−	7.19684i	−0.220969	−	0.533466i
$183$			16.5929i			1.22658i
$184$	11.5590	−	4.78789i	0.852140	−	0.352968i
$185$	−3.75706	−	3.75706i	−0.276225	−	0.276225i
$186$	−4.73335			−0.347066
$187$	−18.4156	−	14.0864i	−1.34668	−	1.03010i
$188$	12.1007			0.882533
$189$	14.2596	+	14.2596i	1.03723	+	1.03723i
$190$	−13.1066	+	5.42894i	−0.950854	+	0.393857i
$191$			18.4073i			1.33190i	0.745995	+	0.665951i	$0.231974\pi$
$191$			18.4073i			1.33190i	−0.745995	+	0.665951i	$0.768026\pi$
$192$	0.675688	+	1.63126i	0.0487636	+	0.117726i
$193$	0.916446	+	0.379604i	0.0659672	+	0.0273245i	0.415423	−	0.909628i	$-0.363634\pi$
$193$	0.916446	+	0.379604i	0.0659672	+	0.0273245i	−0.349456	+	0.936953i	$0.613634\pi$
$194$	2.97569	−	7.18396i	0.213642	−	0.515778i
$195$	−10.5390	+	10.5390i	−0.754715	+	0.754715i
$196$	−6.75961	+	6.75961i	−0.482829	+	0.482829i
$197$	−2.60139	+	6.28031i	−0.185341	+	0.447454i	−0.989052	−	0.147567i	$-0.952856\pi$
$197$	−2.60139	+	6.28031i	−0.185341	+	0.447454i	0.803711	+	0.595020i	$0.202856\pi$
$198$	1.84628	+	0.764752i	0.131209	+	0.0543486i
$199$	6.31628	+	15.2488i	0.447749	+	1.08096i	0.973163	+	0.230115i	$0.0739103\pi$
$199$	6.31628	+	15.2488i	0.447749	+	1.08096i	−0.525414	+	0.850846i	$0.676090\pi$
$200$		−	9.92901i		−	0.702087i
$201$	16.8200	−	6.96707i	1.18639	−	0.491419i
$202$	−4.08903	−	4.08903i	−0.287703	−	0.287703i
$203$	−20.8377			−1.46252
$204$	−1.31456	−	9.86935i	−0.0920379	−	0.690992i
$205$	−7.70174			−0.537913
$206$	8.18784	+	8.18784i	0.570474	+	0.570474i
$207$	2.49205	−	1.03224i	0.173209	−	0.0717456i
$208$			4.44764i			0.308389i
$209$	−14.8055	−	35.7436i	−1.02412	−	2.47244i
$210$	−10.9128	−	4.52024i	−0.753057	−	0.311927i
$211$	−7.67434	+	18.5275i	−0.528324	+	1.27549i	0.404297	+	0.914628i	$0.367516\pi$
$211$	−7.67434	+	18.5275i	−0.528324	+	1.27549i	−0.932621	+	0.360858i	$0.882484\pi$
$212$	−6.28548	+	6.28548i	−0.431688	+	0.431688i
$213$	9.10540	−	9.10540i	0.623891	−	0.623891i
$214$	2.46872	−	5.96003i	0.168758	−	0.407419i
$215$	2.78915	+	1.15531i	0.190219	+	0.0787912i
$216$	5.11976	+	12.3602i	0.348356	+	0.841005i
$217$		−	16.0099i		−	1.08682i
$218$	4.73232	−	1.96019i	0.320513	−	0.132761i
$219$	−15.2100	−	15.2100i	−1.02779	−	1.02779i
$220$	26.0334			1.75517
$221$	−3.32670	+	12.4912i	−0.223778	+	0.840249i
$222$	−1.89291			−0.127044
$223$	19.4997	+	19.4997i	1.30580	+	1.30580i	0.924418	+	0.381380i	$0.124551\pi$
$223$	19.4997	+	19.4997i	1.30580	+	1.30580i	0.381380	+	0.924418i	$0.375449\pi$
$224$	−19.4790	+	8.06847i	−1.30150	+	0.539097i
$225$		−	2.14063i		−	0.142709i
$226$	3.77280	+	9.10835i	0.250963	+	0.605878i
$227$	14.2298	+	5.89418i	0.944466	+	0.391210i	0.801148	−	0.598466i	$-0.204223\pi$
$227$	14.2298	+	5.89418i	0.944466	+	0.391210i	0.143318	+	0.989677i	$0.454223\pi$
$228$	6.35793	−	15.3494i	0.421064	−	1.01654i
$229$	14.4313	−	14.4313i	0.953645	−	0.953645i	−0.0453270	−	0.998972i	$-0.514433\pi$
$229$	14.4313	−	14.4313i	0.953645	−	0.953645i	0.998972	+	0.0453270i	$0.0144330\pi$
$230$	−7.55860	+	7.55860i	−0.498399	+	0.498399i
$231$	12.3273	−	29.7609i	0.811080	−	1.95812i
$232$	−12.7718	−	5.29026i	−0.838510	−	0.347322i
$233$	−0.686156	−	1.65653i	−0.0449516	−	0.108523i	0.899809	−	0.436284i	$-0.143706\pi$
$233$	−0.686156	−	1.65653i	−0.0449516	−	0.108523i	−0.944761	+	0.327761i	$0.893706\pi$
$234$		−	1.11417i		−	0.0728355i
$235$	−22.0089	+	9.11638i	−1.43570	+	0.594687i
$236$	−4.12354	−	4.12354i	−0.268419	−	0.268419i
$237$	16.2497			1.05553
$238$	−10.1548	+	1.35259i	−0.658240	+	0.0876754i
$239$	16.7282			1.08206			0.541030	−	0.841003i	$-0.318035\pi$
$239$	16.7282			1.08206			0.541030	+	0.841003i	$0.318035\pi$
$240$	4.76881	+	4.76881i	0.307826	+	0.307826i
$241$	−5.66582	+	2.34686i	−0.364968	+	0.151175i	−0.557628	−	0.830091i	$-0.688288\pi$
$241$	−5.66582	+	2.34686i	−0.364968	+	0.151175i	0.192660	+	0.981265i	$0.438288\pi$
$242$		−	14.0845i		−	0.905384i
$243$	2.04443	+	4.93570i	0.131150	+	0.316625i
$244$	−14.9288	−	6.18370i	−0.955717	−	0.395871i
$245$	7.20193	−	17.3870i	0.460115	−	1.11081i
$246$	−1.94017	+	1.94017i	−0.123701	+	0.123701i
$247$	−15.2524	+	15.2524i	−0.970487	+	0.970487i
$248$	4.06458	−	9.81276i	0.258101	−	0.623111i
$249$	2.33018	+	0.965190i	0.147669	+	0.0611664i
$250$	−0.699040	−	1.68763i	−0.0442112	−	0.106735i
$251$		−	16.2939i		−	1.02846i	−0.857652	−	0.514230i	$-0.828078\pi$
$251$		−	16.2939i		−	1.02846i	0.857652	−	0.514230i	$-0.171922\pi$
$252$	−2.68169	+	1.11079i	−0.168931	+	0.0699733i
$253$	−20.6134	−	20.6134i	−1.29595	−	1.29595i
$254$	8.46695			0.531263
$255$	9.82629	+	16.9601i	0.615346	+	1.06208i
$256$	−9.63653			−0.602283
$257$	16.9509	+	16.9509i	1.05737	+	1.05737i	0.998251	+	0.0591143i	$0.0188276\pi$
$257$	16.9509	+	16.9509i	1.05737	+	1.05737i	0.0591143	+	0.998251i	$0.481172\pi$
$258$	0.993661	−	0.411588i	0.0618627	−	0.0256244i
$259$		−	6.40248i		−	0.397831i
$260$	−5.55445	−	13.4096i	−0.344472	−	0.831630i
$261$	−2.75352	−	1.14055i	−0.170439	−	0.0705981i
$262$	−0.637508	+	1.53908i	−0.0393854	+	0.0950847i
$263$	−8.53051	+	8.53051i	−0.526014	+	0.526014i	−0.919381	−	0.393368i	$-0.871310\pi$
$263$	−8.53051	+	8.53051i	−0.526014	+	0.526014i	0.393368	+	0.919381i	$0.371310\pi$
$264$	15.1113	−	15.1113i	0.930039	−	0.930039i
$265$	6.69677	−	16.1674i	0.411379	−	0.993158i
$266$	−15.7934	−	6.54184i	−0.968355	−	0.401106i
$267$	9.15275	+	22.0967i	0.560139	+	1.35230i
$268$			17.7295i			1.08300i
$269$	−3.78806	+	1.56907i	−0.230962	+	0.0956676i	−0.495163	−	0.868800i	$-0.664892\pi$
$269$	−3.78806	+	1.56907i	−0.230962	+	0.0956676i	0.264201	+	0.964468i	$0.414892\pi$
$270$	−8.08252	−	8.08252i	−0.491886	−	0.491886i
$271$	−19.5319			−1.18648			−0.593240	−	0.805026i	$-0.702152\pi$
$271$	−19.5319			−1.18648			−0.593240	+	0.805026i	$0.702152\pi$
$272$	5.65216	+	1.50530i	0.342713	+	0.0912723i
$273$	−17.9597			−1.08697
$274$	−6.17093	−	6.17093i	−0.372799	−	0.372799i
$275$	−21.3738	+	8.85330i	−1.28889	+	0.533874i
$276$		−	12.5186i		−	0.753533i
$277$	10.6124	+	25.6206i	0.637638	+	1.53939i	0.829818	+	0.558034i	$0.188444\pi$
$277$	10.6124	+	25.6206i	0.637638	+	1.53939i	−0.192181	+	0.981360i	$0.561556\pi$
$278$	−6.07289	−	2.51547i	−0.364228	−	0.150868i
$279$	0.876298	−	2.11557i	0.0524626	−	0.126656i
$280$	18.7419	−	18.7419i	1.12004	−	1.12004i
$281$	3.65400	−	3.65400i	0.217980	−	0.217980i	−0.589667	−	0.807647i	$-0.700741\pi$
$281$	3.65400	−	3.65400i	0.217980	−	0.217980i	0.807647	+	0.589667i	$0.200741\pi$
$282$	−3.24779	+	7.84086i	−0.193403	+	0.466917i
$283$	−16.7714	−	6.94695i	−0.996957	−	0.412953i	−0.176277	−	0.984341i	$-0.556405\pi$
$283$	−16.7714	−	6.94695i	−0.996957	−	0.412953i	−0.820680	+	0.571388i	$0.806405\pi$
$284$	4.79888	+	11.5855i	0.284761	+	0.687474i
$285$			32.7076i			1.93743i
$286$	−11.1247	+	4.60802i	−0.657819	+	0.272478i
$287$	−6.56234	−	6.56234i	−0.387363	−	0.387363i
$288$	−3.01561			−0.177697
$289$	14.7482	+	8.45528i	0.867539	+	0.497369i
$290$	11.8111			0.693569
$291$	−12.6767	−	12.6767i	−0.743123	−	0.743123i
$292$	19.3528	−	8.01621i	1.13254	−	0.469113i
$293$		−	7.72847i		−	0.451502i	−0.974185	−	0.225751i	$-0.927516\pi$
$293$		−	7.72847i		−	0.451502i	0.974185	−	0.225751i	$-0.0724836\pi$
$294$	−2.56575	−	6.19428i	−0.149638	−	0.361258i
$295$	10.6065	+	4.39337i	0.617536	+	0.255792i
$296$	1.62546	−	3.92420i	0.0944779	−	0.228090i
$297$	22.0422	−	22.0422i	1.27902	−	1.27902i
$298$	−8.25657	+	8.25657i	−0.478291	+	0.478291i
$299$	−6.21976	+	15.0158i	−0.359698	+	0.868388i
$300$	−9.17854	−	3.80188i	−0.529923	−	0.219501i
$301$	1.39214	+	3.36091i	0.0802414	+	0.193720i
$302$		−	4.69438i		−	0.270131i
$303$	−12.3175	+	5.10209i	−0.707624	+	0.293107i
$304$	6.90158	+	6.90158i	0.395833	+	0.395833i
$305$	31.8113			1.82151
$306$	−1.41591	−	0.377090i	−0.0809422	−	0.0215568i
$307$	−8.48545			−0.484290			−0.242145	−	0.970240i	$-0.577851\pi$
$307$	−8.48545			−0.484290			−0.242145	+	0.970240i	$0.577851\pi$
$308$	22.1820	+	22.1820i	1.26394	+	1.26394i
$309$	24.6645	−	10.2164i	1.40312	−	0.581190i
$310$			9.07460i			0.515403i
$311$	−1.63060	−	3.93661i	−0.0924626	−	0.223225i	0.870882	−	0.491493i	$-0.163549\pi$
$311$	−1.63060	−	3.93661i	−0.0924626	−	0.223225i	−0.963344	+	0.268268i	$0.913549\pi$
$312$	−11.0079	−	4.55961i	−0.623198	−	0.258137i
$313$	−1.60357	+	3.87135i	−0.0906389	+	0.218822i	−0.962698	−	0.270580i	$-0.912785\pi$
$313$	−1.60357	+	3.87135i	−0.0906389	+	0.218822i	0.872059	+	0.489401i	$0.162785\pi$
$314$	−2.17885	+	2.17885i	−0.122960	+	0.122960i
$315$	4.04065	−	4.04065i	0.227665	−	0.227665i
$316$	−6.05581	+	14.6200i	−0.340666	+	0.822441i
$317$	−14.0573	−	5.82271i	−0.789535	−	0.327036i	−0.0487781	−	0.998810i	$-0.515533\pi$
$317$	−14.0573	−	5.82271i	−0.789535	−	0.327036i	−0.740756	+	0.671774i	$0.765533\pi$
$318$	−2.38579	−	5.75980i	−0.133788	−	0.322993i
$319$			32.2104i			1.80344i
$320$	3.12738	−	1.29540i	0.174826	−	0.0724153i
$321$	−10.5170	−	10.5170i	−0.587001	−	0.587001i
$322$	−12.8808			−0.717816
$323$	14.2209	+	24.5452i	0.791272	+	1.36573i
$324$	10.9926			0.610702
$325$	9.12054	+	9.12054i	0.505917	+	0.505917i
$326$	−2.99331	+	1.23987i	−0.165784	+	0.0686701i
$327$		−	11.8095i		−	0.653068i
$328$	−2.35614	−	5.68823i	−0.130096	−	0.314080i
$329$	−26.5206	−	10.9852i	−1.46213	−	0.605633i
$330$	−6.98730	+	16.8688i	−0.384638	+	0.928599i
$331$	9.40717	−	9.40717i	0.517065	−	0.517065i	−0.399617	−	0.916682i	$-0.630857\pi$
$331$	9.40717	−	9.40717i	0.517065	−	0.517065i	0.916682	+	0.399617i	$0.130857\pi$
$332$	−1.73678	+	1.73678i	−0.0953181	+	0.0953181i
$333$	0.350439	−	0.846034i	0.0192039	−	0.0463624i
$334$	14.6844	+	6.08248i	0.803495	+	0.332819i
$335$	−13.3570	−	32.2467i	−0.729771	−	1.76182i
$336$			8.12663i			0.443344i
$337$	7.33619	−	3.03875i	0.399628	−	0.165531i	−0.173812	−	0.984779i	$-0.555609\pi$
$337$	7.33619	−	3.03875i	0.399628	−	0.165531i	0.573440	+	0.819248i	$0.305609\pi$
$338$	−1.53135	−	1.53135i	−0.0832944	−	0.0832944i
$339$	22.7299			1.23452
$340$	−18.9211	+	2.52023i	−1.02614	+	0.136679i
$341$	−24.7477			−1.34016
$342$	−1.72890	−	1.72890i	−0.0934882	−	0.0934882i
$343$	−2.57516	+	1.06667i	−0.139046	+	0.0575946i
$344$			2.41340i			0.130122i
$345$	9.43125	+	22.7691i	0.507762	+	1.22584i
$346$	7.90381	+	3.27386i	0.424911	+	0.176004i
$347$	1.11283	−	2.68662i	0.0597401	−	0.144225i	−0.891191	−	0.453629i	$-0.850129\pi$
$347$	1.11283	−	2.68662i	0.0597401	−	0.144225i	0.950931	+	0.309403i	$0.100129\pi$
$348$	−9.78080	+	9.78080i	−0.524306	+	0.524306i
$349$	−13.5947	+	13.5947i	−0.727706	+	0.727706i	−0.970162	−	0.242456i	$-0.922047\pi$
$349$	−13.5947	+	13.5947i	−0.727706	+	0.727706i	0.242456	+	0.970162i	$0.422047\pi$
$350$	−3.91185	+	9.44405i	−0.209097	+	0.504805i
$351$	−16.0566	−	6.65088i	−0.857041	−	0.354998i
$352$	12.4721	+	30.1102i	0.664764	+	1.60488i
$353$		−	13.2634i		−	0.705942i	−0.935634	−	0.352971i	$-0.885171\pi$
$353$		−	13.2634i		−	0.705942i	0.935634	−	0.352971i	$-0.114829\pi$
$354$	3.77867	−	1.56518i	0.200834	−	0.0831882i
$355$	−17.4565	−	17.4565i	−0.926496	−	0.926496i
$356$	−23.2915			−1.23445
$357$	−6.07846	+	22.8236i	−0.321706	+	1.20795i
$358$	10.1530			0.536602
$359$	−8.67894	−	8.67894i	−0.458057	−	0.458057i	0.439960	−	0.898017i	$-0.354992\pi$
$359$	−8.67894	−	8.67894i	−0.458057	−	0.458057i	−0.898017	+	0.439960i	$0.854992\pi$
$360$	3.50243	−	1.45075i	0.184594	−	0.0764614i
$361$			28.3355i			1.49134i
$362$	−2.45794	−	5.93399i	−0.129186	−	0.311883i
$363$	−30.0005	−	12.4266i	−1.57462	−	0.652229i
$364$	6.69308	−	16.1585i	0.350813	−	0.846937i
$365$	−29.1600	+	29.1600i	−1.52630	+	1.52630i
$366$	8.01369	−	8.01369i	0.418882	−	0.418882i
$367$	10.3747	−	25.0467i	0.541554	−	1.30743i	−0.382073	−	0.924132i	$-0.624790\pi$
$367$	10.3747	−	25.0467i	0.541554	−	1.30743i	0.923626	−	0.383294i	$-0.125210\pi$
$368$	6.79454	+	2.81439i	0.354190	+	0.146710i
$369$	−0.507970	−	1.22635i	−0.0264439	−	0.0638411i
$370$			3.62901i			0.188663i
$371$	19.4817	−	8.06957i	1.01144	−	0.418951i
$372$	−7.51473	−	7.51473i	−0.389620	−	0.389620i
$373$	−8.17782			−0.423432			−0.211716	−	0.977331i	$-0.567905\pi$
$373$	−8.17782			−0.423432			−0.211716	+	0.977331i	$0.567905\pi$
$374$	2.09081	+	15.6971i	0.108113	+	0.811679i
$375$	−4.21149			−0.217480
$376$	−13.4661	−	13.4661i	−0.694459	−	0.694459i
$377$	16.5914	−	6.87237i	0.854499	−	0.353945i
$378$		−	13.7736i		−	0.708436i
$379$	2.85578	+	6.89446i	0.146692	+	0.354145i	0.980098	−	0.198517i	$-0.0636123\pi$
$379$	2.85578	+	6.89446i	0.146692	+	0.354145i	−0.833406	+	0.552661i	$0.813612\pi$
$380$	−29.4273	−	12.1892i	−1.50959	−	0.625292i
$381$	7.47033	−	18.0350i	0.382717	−	0.923960i
$382$	8.88994	−	8.88994i	0.454849	−	0.454849i
$383$	10.5115	−	10.5115i	0.537115	−	0.537115i	−0.385566	−	0.922680i	$-0.625994\pi$
$383$	10.5115	−	10.5115i	0.537115	−	0.537115i	0.922680	+	0.385566i	$0.125994\pi$
$384$	−6.52367	+	15.7495i	−0.332910	+	0.803715i
$385$	−57.0564	−	23.6335i	−2.90786	−	1.20448i
$386$	−0.259272	−	0.625939i	−0.0131966	−	0.0318594i
$387$			0.520315i			0.0264491i
$388$	16.1296	−	6.68110i	0.818856	−	0.339181i
$389$	20.6500	+	20.6500i	1.04699	+	1.04699i	0.998840	+	0.0481543i	$0.0153339\pi$
$389$	20.6500	+	20.6500i	1.04699	+	1.04699i	0.0481543	+	0.998840i	$0.484666\pi$
$390$	10.1798			0.515475
$391$	16.9774	+	12.9863i	0.858583	+	0.656746i
$392$	15.0447			0.759870
$393$	2.71584	+	2.71584i	0.136996	+	0.136996i
$394$	4.28949	−	1.77677i	0.216102	−	0.0895122i
$395$		−	31.1534i		−	1.56750i
$396$	1.71704	+	4.14530i	0.0862845	+	0.208309i
$397$	−3.62071	−	1.49975i	−0.181718	−	0.0752702i	0.289969	−	0.957036i	$-0.406355\pi$
$397$	−3.62071	−	1.49975i	−0.181718	−	0.0752702i	−0.471688	+	0.881766i	$0.656355\pi$
$398$	4.31406	−	10.4151i	0.216244	−	0.522060i
$399$	−27.8688	+	27.8688i	−1.39519	+	1.39519i
$400$	4.12697	−	4.12697i	0.206348	−	0.206348i
$401$	1.31146	−	3.16614i	0.0654910	−	0.158109i	−0.887746	−	0.460335i	$-0.847729\pi$
$401$	1.31146	−	3.16614i	0.0654910	−	0.158109i	0.953237	+	0.302225i	$0.0977295\pi$
$402$	−11.4882	−	4.75856i	−0.572978	−	0.237335i
$403$	5.28013	+	12.7474i	0.263022	+	0.634992i
$404$		−	12.9836i		−	0.645957i
$405$	−19.9936	+	8.28161i	−0.993488	+	0.411516i
$406$	10.0637	+	10.0637i	0.499454	+	0.499454i
$407$	−9.89682			−0.490567
$408$	−9.52006	+	12.4458i	−0.471313	+	0.616161i
$409$	−11.8171			−0.584319			−0.292159	−	0.956370i	$-0.594374\pi$
$409$	−11.8171			−0.584319			−0.292159	+	0.956370i	$0.594374\pi$
$410$	3.71962	+	3.71962i	0.183699	+	0.183699i
$411$	−18.5889	+	7.69978i	−0.916924	+	0.379802i
$412$			25.9982i			1.28084i
$413$	5.29398	+	12.7808i	0.260500	+	0.628902i
$414$	−1.70208	−	0.705026i	−0.0836529	−	0.0346502i
$415$	1.85043	−	4.46732i	0.0908338	−	0.219292i
$416$	12.8485	−	12.8485i	0.629952	−	0.629952i
$417$	−10.7161	+	10.7161i	−0.524772	+	0.524772i
$418$	−10.1122	+	24.4131i	−0.494606	+	1.19408i
$419$	23.2133	+	9.61526i	1.13404	+	0.469736i	0.869153	−	0.494543i	$-0.164664\pi$
$419$	23.2133	+	9.61526i	1.13404	+	0.469736i	0.264890	+	0.964279i	$0.414664\pi$
$420$	−10.1490	−	24.5018i	−0.495219	−	1.19556i
$421$			29.7838i			1.45158i	0.687919	+	0.725788i	$0.258525\pi$
$421$			29.7838i			1.45158i	−0.687919	+	0.725788i	$0.741475\pi$
$422$	12.6544	−	5.24163i	0.616007	−	0.255158i
$423$	−2.90320	−	2.90320i	−0.141158	−	0.141158i
$424$	13.9894			0.679385
$425$	14.6774	−	8.50374i	0.711959	−	0.412492i
$426$	−8.79506			−0.426122
$427$	27.1052	+	27.1052i	1.31171	+	1.31171i
$428$	13.3816	−	5.54284i	0.646824	−	0.267923i
$429$			27.7618i			1.34035i
$430$	−0.789081	−	1.90501i	−0.0380529	−	0.0918677i
$431$	−15.1891	−	6.29153i	−0.731634	−	0.303053i	−0.0144105	−	0.999896i	$-0.504587\pi$
$431$	−15.1891	−	6.29153i	−0.731634	−	0.303053i	−0.717223	+	0.696844i	$0.754587\pi$
$432$	−3.00947	+	7.26550i	−0.144793	+	0.349561i
$433$	15.3658	−	15.3658i	0.738433	−	0.738433i	−0.233842	−	0.972275i	$-0.575130\pi$
$433$	15.3658	−	15.3658i	0.738433	−	0.738433i	0.972275	+	0.233842i	$0.0751298\pi$
$434$	−7.73210	+	7.73210i	−0.371153	+	0.371153i
$435$	10.4208	−	25.1581i	0.499640	−	1.20624i
$436$	10.6251	+	4.40107i	0.508851	+	0.210773i
$437$	13.6492	+	32.9521i	0.652930	+	1.57631i
$438$			14.6916i			0.701990i
$439$	−4.57734	+	1.89600i	−0.218464	+	0.0904910i	−0.489232	−	0.872154i	$-0.662723\pi$
$439$	−4.57734	+	1.89600i	−0.218464	+	0.0904910i	0.270767	+	0.962645i	$0.412723\pi$
$440$	−28.9709	−	28.9709i	−1.38113	−	1.38113i
$441$	3.24354			0.154454
$442$	7.63939	−	4.42607i	0.363369	−	0.210527i
$443$	28.3272			1.34586			0.672932	−	0.739704i	$-0.265035\pi$
$443$	28.3272			1.34586			0.672932	+	0.739704i	$0.265035\pi$
$444$	−3.00520	−	3.00520i	−0.142621	−	0.142621i
$445$	42.3629	−	17.5473i	2.00820	−	0.831822i
$446$		−	18.8351i		−	0.891869i
$447$	10.3022	+	24.8716i	0.487275	+	1.17639i
$448$	3.76848	+	1.56095i	0.178044	+	0.0737481i
$449$	−6.70048	+	16.1764i	−0.316215	+	0.763411i	0.683233	+	0.730200i	$0.260573\pi$
$449$	−6.70048	+	16.1764i	−0.316215	+	0.763411i	−0.999448	+	0.0332108i	$0.989427\pi$
$450$	−1.03384	+	1.03384i	−0.0487356	+	0.0487356i
$451$	−10.1439	+	10.1439i	−0.477659	+	0.477659i
$452$	−8.47078	+	20.4503i	−0.398432	+	0.961900i
$453$	−9.99923	−	4.14182i	−0.469805	−	0.194600i
$454$	−4.02576	−	9.71905i	−0.188938	−	0.456138i
$455$			34.4317i			1.61419i
$456$	−24.1567	+	10.0060i	−1.13124	+	0.468575i
$457$	−16.9554	−	16.9554i	−0.793142	−	0.793142i	0.188861	−	0.982004i	$-0.439520\pi$
$457$	−16.9554	−	16.9554i	−0.793142	−	0.793142i	−0.982004	+	0.188861i	$0.939520\pi$
$458$	−13.9394			−0.651346
$459$	−13.8864	+	18.1541i	−0.648164	+	0.847363i
$460$	−24.0003			−1.11902
$461$	−19.4093	−	19.4093i	−0.903983	−	0.903983i	0.0917951	−	0.995778i	$-0.470740\pi$
$461$	−19.4093	−	19.4093i	−0.903983	−	0.903983i	−0.995778	+	0.0917951i	$0.970740\pi$
$462$	−20.3269	+	8.41966i	−0.945691	+	0.391718i
$463$		−	11.2491i		−	0.522792i	−0.965232	−	0.261396i	$-0.915817\pi$
$463$		−	11.2491i		−	0.522792i	0.965232	−	0.261396i	$-0.0841828\pi$
$464$	−3.10969	−	7.50745i	−0.144364	−	0.348525i
$465$	19.3293	+	8.00646i	0.896375	+	0.371291i
$466$	−0.468649	+	1.13142i	−0.0217097	+	0.0524120i
$467$	−1.40473	+	1.40473i	−0.0650033	+	0.0650033i	−0.738861	−	0.673858i	$-0.764636\pi$
$467$	−1.40473	+	1.40473i	−0.0650033	+	0.0650033i	0.673858	+	0.738861i	$0.264636\pi$
$468$	1.76887	−	1.76887i	0.0817660	−	0.0817660i
$469$	16.0951	−	38.8571i	0.743204	−	1.79425i
$470$	15.0322	+	6.22654i	0.693384	+	0.287209i
$471$	2.71866	+	6.56343i	0.125269	+	0.302427i
$472$			9.17763i			0.422435i
$473$	5.19523	−	2.15194i	0.238877	−	0.0989461i
$474$	−7.84795	−	7.84795i	−0.360468	−	0.360468i
$475$	28.3054			1.29874
$476$	−18.2693	−	13.9746i	−0.837373	−	0.640522i
$477$	3.01603			0.138094
$478$	−8.07904	−	8.07904i	−0.369527	−	0.369527i
$479$	5.67591	−	2.35104i	0.259339	−	0.107422i	−0.249226	−	0.968445i	$-0.580176\pi$
$479$	5.67591	−	2.35104i	0.259339	−	0.107422i	0.508565	+	0.861024i	$0.330176\pi$
$480$		−	27.5527i		−	1.25760i
$481$	2.11157	+	5.09778i	0.0962793	+	0.232439i
$482$	3.86979	+	1.60292i	0.176264	+	0.0730110i
$483$	−11.3646	+	27.4366i	−0.517107	+	1.24841i
$484$	22.3607	−	22.3607i	1.01639	−	1.01639i
$485$	−24.3033	+	24.3033i	−1.10356	+	1.10356i
$486$	1.39636	−	3.37111i	0.0633402	−	0.152917i
$487$	−22.5750	−	9.35087i	−1.02297	−	0.423728i	−0.192800	−	0.981238i	$-0.561757\pi$
$487$	−22.5750	−	9.35087i	−1.02297	−	0.423728i	−0.830171	+	0.557510i	$0.811757\pi$
$488$	9.73183	+	23.4947i	0.440539	+	1.06356i
$489$			7.46982i			0.337797i
$490$	−11.8754	+	4.91897i	−0.536477	+	0.222216i
$491$	23.8026	+	23.8026i	1.07419	+	1.07419i	0.997017	+	0.0771771i	$0.0245907\pi$
$491$	23.8026	+	23.8026i	1.07419	+	1.07419i	0.0771771	+	0.997017i	$0.475409\pi$
$492$	−6.16048			−0.277736
$493$	−3.11822	−	23.4106i	−0.140437	−	1.05436i
$494$	14.7325			0.662849
$495$	−6.24595	−	6.24595i	−0.280734	−	0.280734i
$496$	5.76808	−	2.38922i	0.258994	−	0.107279i
$497$		−	29.7480i		−	1.33438i
$498$	−0.659231	−	1.59152i	−0.0295409	−	0.0713179i
$499$	15.0932	+	6.25181i	0.675665	+	0.279869i	0.694013	−	0.719962i	$-0.255841\pi$
$499$	15.0932	+	6.25181i	0.675665	+	0.279869i	−0.0183486	+	0.999832i	$0.505841\pi$
$500$	1.56950	−	3.78911i	0.0701902	−	0.169454i
$501$	25.9119	−	25.9119i	1.15766	−	1.15766i
$502$	−7.86927	+	7.86927i	−0.351223	+	0.351223i
$503$	−0.999145	+	2.41215i	−0.0445497	+	0.107552i	−0.944588	−	0.328258i	$-0.893538\pi$
$503$	−0.999145	+	2.41215i	−0.0445497	+	0.107552i	0.900038	+	0.435811i	$0.143538\pi$
$504$	4.22041	+	1.74815i	0.187992	+	0.0778688i
$505$	9.78153	+	23.6147i	0.435273	+	1.05084i
$506$			19.9108i			0.885143i
$507$	−4.61294	+	1.91074i	−0.204868	+	0.0848591i
$508$	13.4422	+	13.4422i	0.596403	+	0.596403i
$509$	13.3426			0.591402			0.295701	−	0.955281i	$-0.404447\pi$
$509$	13.3426			0.591402			0.295701	+	0.955281i	$0.404447\pi$
$510$	3.44535	−	12.9367i	0.152563	−	0.572848i
$511$	−49.6921			−2.19825
$512$	−10.6558	−	10.6558i	−0.470922	−	0.470922i
$513$	−35.2361	+	14.5953i	−1.55571	+	0.644398i
$514$		−	16.3731i		−	0.722187i
$515$	−19.5865	−	47.2859i	−0.863083	−	2.08367i
$516$	2.23099	+	0.924107i	0.0982139	+	0.0406815i
$517$	−16.9807	+	40.9950i	−0.746809	+	1.80296i
$518$	−3.09213	+	3.09213i	−0.135860	+	0.135860i
$519$	13.9470	−	13.9470i	0.612203	−	0.612203i
$520$	−8.74152	+	21.1039i	−0.383341	+	0.925467i
$521$	−12.9714	−	5.37291i	−0.568285	−	0.235391i	0.0799924	−	0.996795i	$-0.474510\pi$
$521$	−12.9714	−	5.37291i	−0.568285	−	0.235391i	−0.648278	+	0.761404i	$0.724510\pi$
$522$	0.779001	+	1.88067i	0.0340959	+	0.0823149i
$523$			1.78146i			0.0778980i	0.999241	+	0.0389490i	$0.0124010\pi$
$523$			1.78146i			0.0778980i	−0.999241	+	0.0389490i	$0.987599\pi$
$524$	−3.45558	+	1.43135i	−0.150958	+	0.0625287i
$525$	16.6648	+	16.6648i	0.727313	+	0.727313i
$526$	8.23976			0.359271
$527$	17.9867	−	2.39577i	0.783513	−	0.104361i
$528$	12.5620			0.546690
$529$	2.74005	+	2.74005i	0.119133	+	0.119133i
$530$	−11.0425	+	4.57394i	−0.479654	+	0.198679i
$531$			1.97864i			0.0858657i
$532$	−14.6879	−	35.4597i	−0.636801	−	1.53737i
$533$	7.38936	+	3.06077i	0.320069	+	0.132577i
$534$	6.25139	−	15.0922i	0.270524	−	0.653102i
$535$	−20.1628	+	20.1628i	−0.871712	+	0.871712i
$536$	19.7300	−	19.7300i	0.852207	−	0.852207i
$537$	8.95792	−	21.6263i	0.386563	−	0.933245i
$538$	2.58727	+	1.07168i	0.111545	+	0.0462035i
$539$	−13.4147	−	32.3860i	−0.577813	−	1.39496i
$540$		−	25.6638i		−	1.10439i
$541$	−22.0213	+	9.12154i	−0.946772	+	0.392166i	−0.802017	−	0.597302i	$-0.796239\pi$
$541$	−22.0213	+	9.12154i	−0.946772	+	0.392166i	−0.144755	+	0.989468i	$0.546239\pi$
$542$	9.43311	+	9.43311i	0.405187	+	0.405187i
$543$	−14.8083			−0.635484
$544$	−11.9796	−	20.6768i	−0.513622	−	0.886510i
$545$	−22.6408			−0.969824
$546$	8.67381	+	8.67381i	0.371205	+	0.371205i
$547$	−5.16744	+	2.14042i	−0.220944	+	0.0915179i	−0.490410	−	0.871492i	$-0.663153\pi$
$547$	−5.16744	+	2.14042i	−0.220944	+	0.0915179i	0.269466	+	0.963010i	$0.413153\pi$
$548$		−	19.5941i		−	0.837018i
$549$	2.09812	+	5.06532i	0.0895457	+	0.216182i
$550$	14.5984	+	6.04686i	0.622478	+	0.257839i
$551$	15.0813	−	36.4096i	0.642487	−	1.55110i
$552$	−13.9312	+	13.9312i	−0.592950	+	0.592950i
$553$	26.5446	−	26.5446i	1.12879	−	1.12879i
$554$	7.24834	−	17.4990i	0.307952	−	0.743463i
$555$	7.72995	+	3.20185i	0.328118	+	0.135911i
$556$	−5.64780	−	13.6350i	−0.239520	−	0.578252i
$557$			15.8546i			0.671782i	0.941901	+	0.335891i	$0.109037\pi$
$557$			15.8546i			0.671782i	−0.941901	+	0.335891i	$0.890963\pi$
$558$	−1.44495	+	0.598517i	−0.0611695	+	0.0253373i
$559$	−2.21689	−	2.21689i	−0.0937646	−	0.0937646i
$560$	15.5801			0.658378
$561$	35.2803	+	9.39597i	1.48954	+	0.396698i
$562$	−3.52946			−0.148881
$563$	5.68267	+	5.68267i	0.239496	+	0.239496i	0.816641	−	0.577145i	$-0.195833\pi$
$563$	5.68267	+	5.68267i	0.239496	+	0.239496i	−0.577145	+	0.816641i	$0.695833\pi$
$564$	−17.6045	+	7.29202i	−0.741283	+	0.307049i
$565$		−	43.5769i		−	1.83329i
$566$	4.74481	+	11.4550i	0.199439	+	0.481489i
$567$	−24.0921	−	9.97929i	−1.01177	−	0.419091i
$568$	7.55241	−	18.2331i	0.316892	−	0.765045i
$569$	−15.3387	+	15.3387i	−0.643031	+	0.643031i	−0.951300	−	0.308268i	$-0.900251\pi$
$569$	−15.3387	+	15.3387i	−0.643031	+	0.643031i	0.308268	+	0.951300i	$0.400251\pi$
$570$	15.7964	−	15.7964i	0.661639	−	0.661639i
$571$	−5.79887	+	13.9997i	−0.242675	+	0.585869i	−0.997547	−	0.0700032i	$-0.977699\pi$
$571$	−5.79887	+	13.9997i	−0.242675	+	0.585869i	0.754872	+	0.655872i	$0.227699\pi$
$572$	−24.9775	−	10.3460i	−1.04436	−	0.432589i
$573$	−11.0924	−	26.7795i	−0.463393	−	1.11873i
$574$			6.33868i			0.264571i
$575$	19.7045	−	8.16187i	0.821735	−	0.340374i
$576$	0.412534	+	0.412534i	0.0171889	+	0.0171889i
$577$	27.8078			1.15766			0.578828	−	0.815450i	$-0.303510\pi$
$577$	27.8078			1.15766			0.578828	+	0.815450i	$0.303510\pi$
$578$	−3.03920	−	11.2063i	−0.126414	−	0.466121i
$579$	−1.56203			−0.0649158
$580$	18.7514	+	18.7514i	0.778609	+	0.778609i
$581$	5.38310	−	2.22975i	0.223329	−	0.0925057i
$582$			12.2447i			0.507558i
$583$	−12.4738	−	30.1144i	−0.516611	−	1.24721i
$584$	−30.4572	−	12.6158i	−1.26033	−	0.522046i
$585$	−1.88462	+	4.54987i	−0.0779193	+	0.188114i
$586$	−3.73253	+	3.73253i	−0.154189	+	0.154189i
$587$	0.762323	−	0.762323i	0.0314644	−	0.0314644i	−0.691200	−	0.722664i	$-0.742917\pi$
$587$	0.762323	−	0.762323i	0.0314644	−	0.0314644i	0.722664	+	0.691200i	$0.242917\pi$
$588$	5.76069	−	13.9075i	0.237567	−	0.573537i
$589$	27.9740	+	11.5872i	1.15265	+	0.477442i
$590$	−3.00070	−	7.24432i	−0.123537	−	0.298244i
$591$		−	10.7044i		−	0.440322i
$592$	2.30670	−	0.955467i	0.0948049	−	0.0392695i
$593$	−3.72790	−	3.72790i	−0.153086	−	0.153086i	0.626408	−	0.779495i	$-0.284524\pi$
$593$	−3.72790	−	3.72790i	−0.153086	−	0.153086i	−0.779495	+	0.626408i	$0.784524\pi$
$594$	−21.2909			−0.873577
$595$	43.7566	+	11.6534i	1.79385	+	0.477743i
$596$	−26.2165			−1.07387
$597$	−18.3783	−	18.3783i	−0.752173	−	0.752173i
$598$	10.2559	−	4.24814i	0.419395	−	0.173719i
$599$		−	12.5324i		−	0.512059i	−0.966669	−	0.256030i	$-0.917586\pi$
$599$		−	12.5324i		−	0.512059i	0.966669	−	0.256030i	$-0.0824145\pi$
$600$	5.98334	+	14.4451i	0.244269	+	0.589717i
$601$	17.6415	+	7.30734i	0.719611	+	0.298073i	0.712275	−	0.701900i	$-0.247665\pi$
$601$	17.6415	+	7.30734i	0.719611	+	0.298073i	0.00733615	+	0.999973i	$0.497665\pi$
$602$	0.950838	−	2.29553i	0.0387533	−	0.0935587i
$603$	4.25367	−	4.25367i	0.173223	−	0.173223i
$604$	7.45285	−	7.45285i	0.303252	−	0.303252i
$605$	−23.8239	+	57.5159i	−0.968578	+	2.33835i
$606$	8.41296	+	3.48476i	0.341753	+	0.141559i
$607$	−4.81783	−	11.6313i	−0.195550	−	0.472099i	0.795441	−	0.606031i	$-0.207239\pi$
$607$	−4.81783	−	11.6313i	−0.195550	−	0.472099i	−0.990990	+	0.133933i	$0.957239\pi$
$608$		−	39.8752i		−	1.61715i
$609$	30.3154	−	12.5570i	1.22844	−	0.508837i
$610$	−15.3636	−	15.3636i	−0.622052	−	0.622052i
$611$	24.7392			1.00084
$612$	−1.64924	−	2.84659i	−0.0666667	−	0.115067i
$613$	−11.1077			−0.448635			−0.224317	−	0.974516i	$-0.572015\pi$
$613$	−11.1077			−0.448635			−0.224317	+	0.974516i	$0.572015\pi$
$614$	4.09812	+	4.09812i	0.165387	+	0.165387i
$615$	11.2048	−	4.64116i	0.451819	−	0.187150i
$616$		−	49.3699i		−	1.98917i
$617$	18.2015	+	43.9424i	0.732766	+	1.76905i	0.633152	+	0.774027i	$0.281761\pi$
$617$	18.2015	+	43.9424i	0.732766	+	1.76905i	0.0996137	+	0.995026i	$0.468239\pi$
$618$	−16.8460	−	6.97786i	−0.677647	−	0.280691i
$619$	−6.54067	+	15.7906i	−0.262892	+	0.634677i	−0.999115	−	0.0420621i	$-0.986607\pi$
$619$	−6.54067	+	15.7906i	−0.262892	+	0.634677i	0.736223	+	0.676739i	$0.236607\pi$
$620$	−14.4070	+	14.4070i	−0.578597	+	0.578597i
$621$	−20.3207	+	20.3207i	−0.815443	+	0.815443i
$622$	−1.11371	+	2.68873i	−0.0446556	+	0.107808i
$623$	51.0471	+	21.1444i	2.04516	+	0.847132i
$624$	−2.68020	−	6.47058i	−0.107294	−	0.259031i
$625$			28.6447i			1.14579i
$626$	2.64416	−	1.09525i	0.105682	−	0.0437748i
$627$	43.0791	+	43.0791i	1.72041	+	1.72041i
$628$	−6.91833			−0.276072
$629$	7.19303	−	0.958088i	0.286805	−	0.0382015i
$630$	−3.90293			−0.155496
$631$	−20.7079	−	20.7079i	−0.824368	−	0.824368i	0.162363	−	0.986731i	$-0.448088\pi$
$631$	−20.7079	−	20.7079i	−0.824368	−	0.824368i	−0.986731	+	0.162363i	$0.948088\pi$
$632$	23.0088	−	9.53056i	0.915241	−	0.379105i
$633$		−	31.5791i		−	1.25516i
$634$	3.97695	+	9.60120i	0.157945	+	0.381312i
$635$	−34.5760	−	14.3218i	−1.37211	−	0.568345i
$636$	5.35662	−	12.9320i	0.212404	−	0.512788i
$637$	−13.8196	+	13.8196i	−0.547554	+	0.547554i
$638$	15.5563	−	15.5563i	0.615880	−	0.615880i
$639$	1.62825	−	3.93095i	0.0644127	−	0.155506i
$640$	30.1944	+	12.5069i	1.19354	+	0.494380i
$641$	8.06076	+	19.4604i	0.318381	+	0.768640i	0.999340	+	0.0363183i	$0.0115630\pi$
$641$	8.06076	+	19.4604i	0.318381	+	0.768640i	−0.680959	+	0.732321i	$0.738437\pi$
$642$			10.1585i			0.400925i
$643$	−11.7704	+	4.87546i	−0.464180	+	0.192270i	−0.602501	−	0.798118i	$-0.705829\pi$
$643$	−11.7704	+	4.87546i	−0.464180	+	0.192270i	0.138322	+	0.990387i	$0.455829\pi$
$644$	−20.4497	−	20.4497i	−0.805829	−	0.805829i
$645$	−4.75396			−0.187187
$646$	4.98622	−	18.7224i	0.196180	−	0.736624i
$647$	24.1677			0.950130			0.475065	−	0.879951i	$-0.342425\pi$
$647$	24.1677			0.950130			0.475065	+	0.879951i	$0.342425\pi$
$648$	−12.2330	−	12.2330i	−0.480558	−	0.480558i
$649$	19.7563	−	8.18333i	0.775503	−	0.321224i
$650$		−	8.80969i		−	0.345544i
$651$	9.64774	+	23.2917i	0.378125	+	0.912874i
$652$	−6.72066	−	2.78379i	−0.263201	−	0.109022i
$653$	−0.596455	+	1.43997i	−0.0233411	+	0.0563504i	−0.935120	−	0.354330i	$-0.884709\pi$
$653$	−0.596455	+	1.43997i	−0.0233411	+	0.0563504i	0.911779	+	0.410681i	$0.134709\pi$
$654$	−5.70351	+	5.70351i	−0.223025	+	0.223025i
$655$	5.20671	−	5.20671i	0.203443	−	0.203443i
$656$	1.38497	−	3.34362i	0.0540741	−	0.130547i
$657$	−6.56639	−	2.71989i	−0.256179	−	0.106113i
$658$	7.50295	+	18.1137i	0.292496	+	0.706147i
$659$			12.3885i			0.482589i	0.970452	+	0.241294i	$0.0775719\pi$
$659$			12.3885i			0.482589i	−0.970452	+	0.241294i	$0.922428\pi$
$660$	−37.8743	+	15.6881i	−1.47426	+	0.610657i
$661$	8.89516	+	8.89516i	0.345982	+	0.345982i	0.858610	−	0.512629i	$-0.171328\pi$
$661$	8.89516	+	8.89516i	0.345982	+	0.345982i	−0.512629	+	0.858610i	$0.671328\pi$
$662$	−9.08654			−0.353159
$663$	−2.68755	−	20.1773i	−0.104376	−	0.783623i
$664$	3.86550			0.150010
$665$	53.4291	+	53.4291i	2.07189	+	2.07189i
$666$	−0.577847	+	0.239352i	−0.0223911	+	0.00927470i
$667$		−	29.6949i		−	1.14979i
$668$	13.6565	+	32.9698i	0.528387	+	1.27564i
$669$	−40.1196	−	16.6181i	−1.55112	−	0.642493i
$670$	−9.12292	+	22.0247i	−0.352449	+	0.850888i
$671$	41.8986	−	41.8986i	1.61748	−	1.61748i
$672$	23.4766	−	23.4766i	0.905628	−	0.905628i
$673$	−9.29794	+	22.4472i	−0.358409	+	0.865276i	0.637115	+	0.770769i	$0.280128\pi$
$673$	−9.29794	+	22.4472i	−0.358409	+	0.865276i	−0.995524	+	0.0945074i	$0.969872\pi$
$674$	−5.01067	−	2.07549i	−0.193004	−	0.0799447i
$675$	8.72761	+	21.0703i	0.335926	+	0.810997i
$676$		−	4.86238i		−	0.187015i
$677$	3.57685	−	1.48158i	0.137469	−	0.0569417i	−0.312888	−	0.949790i	$-0.601297\pi$
$677$	3.57685	−	1.48158i	0.137469	−	0.0569417i	0.450358	+	0.892848i	$0.351297\pi$
$678$	−10.9776	−	10.9776i	−0.421592	−	0.421592i
$679$	−41.4158			−1.58939
$680$	23.8607	+	18.2515i	0.915016	+	0.699913i
$681$	−24.2539			−0.929412
$682$	11.9521	+	11.9521i	0.457670	+	0.457670i
$683$	7.43856	−	3.08115i	0.284629	−	0.117897i	−0.235802	−	0.971801i	$-0.575772\pi$
$683$	7.43856	−	3.08115i	0.284629	−	0.117897i	0.520430	+	0.853904i	$0.325772\pi$
$684$		−	5.48964i		−	0.209902i
$685$	14.7617	+	35.6380i	0.564017	+	1.36166i
$686$	1.75885	+	0.728541i	0.0671533	+	0.0278158i
$687$	−12.2987	+	29.6916i	−0.469223	+	1.13280i
$688$	−1.00313	+	1.00313i	−0.0382438	+	0.0382438i
$689$	−12.8503	+	12.8503i	−0.489558	+	0.489558i
$690$	6.44161	−	15.5514i	0.245228	−	0.592032i
$691$	−3.94740	−	1.63507i	−0.150166	−	0.0622009i	0.306334	−	0.951924i	$-0.400897\pi$
$691$	−3.94740	−	1.63507i	−0.150166	−	0.0622009i	−0.456501	+	0.889723i	$0.650897\pi$
$692$	7.35056	+	17.7458i	0.279426	+	0.674595i
$693$		−	10.6438i		−	0.404326i
$694$	−1.83498	+	0.760073i	−0.0696549	+	0.0288520i
$695$	20.5446	+	20.5446i	0.779300	+	0.779300i
$696$	21.7688			0.825146
$697$	6.39062	−	8.35464i	0.242062	−	0.316455i
$698$	13.1313			0.497028
$699$	1.99649	+	1.99649i	0.0755141	+	0.0755141i
$700$	−21.2040	+	8.78298i	−0.801436	+	0.331966i
$701$			30.6784i			1.15871i	0.815076	+	0.579354i	$0.196695\pi$
$701$			30.6784i			1.15871i	−0.815076	+	0.579354i	$0.803305\pi$
$702$	4.54260	+	10.9668i	0.171449	+	0.413915i
$703$	11.1870	+	4.63382i	0.421927	+	0.174768i
$704$	2.41289	−	5.82523i	0.0909392	−	0.219547i
$705$	26.5256	−	26.5256i	0.999013	−	0.999013i
$706$	−6.40569	+	6.40569i	−0.241082	+	0.241082i
$707$	−11.7867	+	28.4556i	−0.443284	+	1.07018i
$708$	8.48396	+	3.51417i	0.318847	+	0.132071i
$709$	0.354232	+	0.855192i	0.0133035	+	0.0321174i	0.930392	−	0.366567i	$-0.119467\pi$
$709$	0.354232	+	0.855192i	0.0133035	+	0.0321174i	−0.917088	+	0.398684i	$0.869467\pi$
$710$			16.8616i			0.632803i
$711$	4.96056	−	2.05473i	0.186035	−	0.0770584i
$712$	25.9196	+	25.9196i	0.971379	+	0.971379i
$713$	22.8150			0.854427
$714$	13.9585	−	8.08722i	0.522384	−	0.302657i
$715$	53.2239			1.99046
$716$	16.1190	+	16.1190i	0.602396	+	0.602396i
$717$	−24.3368	+	10.0806i	−0.908875	+	0.376468i
$718$			8.38313i			0.312856i
$719$	−3.62083	−	8.74146i	−0.135034	−	0.326002i	0.841870	−	0.539681i	$-0.181455\pi$
$719$	−3.62083	−	8.74146i	−0.135034	−	0.326002i	−0.976904	+	0.213680i	$0.931455\pi$
$720$	2.05878	+	0.852773i	0.0767261	+	0.0317810i
$721$	23.6016	−	56.9793i	0.878969	−	2.12202i
$722$	13.6848	−	13.6848i	0.509297	−	0.509297i
$723$	6.82858	−	6.82858i	0.253958	−	0.253958i
$724$	5.51862	−	13.3231i	0.205098	−	0.495150i
$725$	−21.7720	−	9.01825i	−0.808591	−	0.334929i
$726$	8.48747	+	20.4906i	0.314999	+	0.760476i
$727$		−	23.7132i		−	0.879473i	−0.898127	−	0.439736i	$-0.855072\pi$
$727$		−	23.7132i		−	0.879473i	0.898127	−	0.439736i	$-0.144928\pi$
$728$	−25.4301	+	10.5335i	−0.942501	+	0.390397i
$729$	−21.1549	−	21.1549i	−0.783516	−	0.783516i
$730$	28.1661			1.04247
$731$	−3.56758	+	2.06697i	−0.131952	+	0.0764496i
$732$	25.4453			0.940485
$733$	−12.6201	−	12.6201i	−0.466134	−	0.466134i	0.434525	−	0.900660i	$-0.356916\pi$
$733$	−12.6201	−	12.6201i	−0.466134	−	0.466134i	−0.900660	+	0.434525i	$0.856916\pi$
$734$	−17.1070	+	7.08597i	−0.631433	+	0.261548i
$735$			29.6352i			1.09311i
$736$	−11.4980	−	27.7587i	−0.423823	−	1.02320i
$737$	−60.0644	−	24.8795i	−2.21250	−	0.916448i
$738$	−0.346947	+	0.837603i	−0.0127713	+	0.0308326i
$739$	−5.22259	+	5.22259i	−0.192116	+	0.192116i	−0.796610	−	0.604494i	$-0.793375\pi$
$739$	−5.22259	+	5.22259i	−0.192116	+	0.192116i	0.604494	+	0.796610i	$0.293375\pi$
$740$	−5.76146	+	5.76146i	−0.211795	+	0.211795i
$741$	12.9984	−	31.3810i	0.477509	−	1.15281i
$742$	−13.3061	−	5.51157i	−0.488483	−	0.202336i
$743$	8.57597	+	20.7042i	0.314622	+	0.759564i	0.999522	+	0.0309268i	$0.00984587\pi$
$743$	8.57597	+	20.7042i	0.314622	+	0.759564i	−0.684900	+	0.728637i	$0.740154\pi$
$744$			16.7253i			0.613179i
$745$	47.6829	−	19.7509i	1.74697	−	0.723617i
$746$	3.94955	+	3.94955i	0.144603	+	0.144603i
$747$	0.833377			0.0304917
$748$	−21.6016	+	28.2404i	−0.789832	+	1.03257i
$749$	−34.3598			−1.25548
$750$	2.03397	+	2.03397i	0.0742702	+	0.0742702i
$751$	−38.5858	+	15.9828i	−1.40801	+	0.583219i	−0.951819	−	0.306660i	$-0.900788\pi$
$751$	−38.5858	+	15.9828i	−1.40801	+	0.583219i	−0.456196	+	0.889879i	$0.650788\pi$
$752$		−	11.1943i		−	0.408213i
$753$	9.81889	+	23.7049i	0.357820	+	0.863855i
$754$	−11.3320	−	4.69387i	−0.412687	−	0.170941i
$755$	−7.94054	+	19.1702i	−0.288986	+	0.697673i
$756$	21.8671	−	21.8671i	0.795299	−	0.795299i
$757$	−12.4530	+	12.4530i	−0.452613	+	0.452613i	−0.896221	−	0.443608i	$-0.853698\pi$
$757$	−12.4530	+	12.4530i	−0.452613	+	0.452613i	0.443608	+	0.896221i	$0.353698\pi$
$758$	1.95052	−	4.70896i	0.0708459	−	0.171037i
$759$	42.4109	+	17.5672i	1.53942	+	0.637648i
$760$	19.1832	+	46.3123i	0.695846	+	1.67992i
$761$			5.27868i			0.191352i	0.995413	+	0.0956760i	$0.0305013\pi$
$761$			5.27868i			0.191352i	−0.995413	+	0.0956760i	$0.969499\pi$
$762$	−12.3180	+	5.10228i	−0.446234	+	0.184836i
$763$	−19.2913	−	19.2913i	−0.698391	−	0.698391i
$764$	28.2276			1.02124
$765$	5.14422	+	3.93491i	0.185990	+	0.142267i
$766$	−10.1533			−0.366853
$767$	−8.43034	−	8.43034i	−0.304402	−	0.304402i
$768$	14.0195	−	5.80709i	0.505887	−	0.209545i
$769$			5.26069i			0.189705i	0.995491	+	0.0948527i	$0.0302380\pi$
$769$			5.26069i			0.189705i	−0.995491	+	0.0948527i	$0.969762\pi$
$770$	16.1419	+	38.9699i	0.581712	+	1.40438i
$771$	−34.8755	−	14.4459i	−1.25601	−	0.520256i
$772$	0.582124	−	1.40537i	0.0209511	−	0.0505804i
$773$	2.49968	−	2.49968i	0.0899073	−	0.0899073i	−0.660723	−	0.750630i	$-0.729750\pi$
$773$	2.49968	−	2.49968i	0.0899073	−	0.0899073i	0.750630	+	0.660723i	$0.229750\pi$
$774$	0.251291	−	0.251291i	0.00903246	−	0.00903246i
$775$	6.92885	−	16.7277i	0.248892	−	0.600877i
$776$	−25.3845	−	10.5146i	−0.911252	−	0.377453i
$777$	3.85821	+	9.31455i	0.138413	+	0.334158i
$778$		−	19.9461i		−	0.715104i
$779$	16.2159	−	6.71683i	0.580994	−	0.240656i
$780$	16.1616	+	16.1616i	0.578678	+	0.578678i
$781$	−45.9838			−1.64543
$782$	−1.92752	−	14.4712i	−0.0689279	−	0.517490i
$783$	31.7531			1.13476
$784$	6.25327	+	6.25327i	0.223331	+	0.223331i
$785$	12.5832	−	5.21211i	0.449112	−	0.186028i
$786$		−	2.62328i		−	0.0935692i
$787$	−8.39871	−	20.2763i	−0.299382	−	0.722771i	−0.999958	−	0.00919364i	$-0.997074\pi$
$787$	−8.39871	−	20.2763i	−0.299382	−	0.722771i	0.700576	−	0.713578i	$-0.252926\pi$
$788$	9.63087	+	3.98924i	0.343086	+	0.142111i
$789$	7.26989	−	17.5511i	0.258815	−	0.624835i
$790$	−15.0458	+	15.0458i	−0.535306	+	0.535306i
$791$	37.1301	−	37.1301i	1.32020	−	1.32020i
$792$	2.70225	−	6.52382i	0.0960204	−	0.231814i
$793$	−30.5211	−	12.6422i	−1.08384	−	0.448939i
$794$	1.02434	+	2.47297i	0.0363524	+	0.0877625i
$795$			27.5565i			0.977329i
$796$	23.3841	−	9.68602i	0.828829	−	0.343312i
$797$	37.8247	+	37.8247i	1.33982	+	1.33982i	0.896232	+	0.443586i	$0.146294\pi$
$797$	37.8247	+	37.8247i	1.33982	+	1.33982i	0.443586	+	0.896232i	$0.353706\pi$
$798$	26.9190			0.952921
$799$	8.37296	−	31.4391i	0.296214	−	1.11223i
$800$	−23.8443			−0.843024
$801$	5.58811	+	5.58811i	0.197446	+	0.197446i
$802$	−2.16249	+	0.895733i	−0.0763602	+	0.0316294i
$803$			76.8130i			2.71067i
$804$	−10.6840	−	25.7935i	−0.376796	−	0.909667i
$805$	52.6004	+	21.7878i	1.85392	+	0.767919i
$806$	3.60637	−	8.70654i	0.127029	−	0.306675i
$807$	4.56546	−	4.56546i	0.160712	−	0.160712i
$808$	−14.4486	+	14.4486i	−0.508300	+	0.508300i
$809$	−4.71642	+	11.3864i	−0.165820	+	0.400326i	−0.984846	−	0.173431i	$-0.944515\pi$
$809$	−4.71642	+	11.3864i	−0.165820	+	0.400326i	0.819026	+	0.573757i	$0.194515\pi$
$810$	13.6557	+	5.65639i	0.479814	+	0.198745i
$811$	−17.8122	−	43.0024i	−0.625470	−	1.51002i	−0.845196	−	0.534456i	$-0.820517\pi$
$811$	−17.8122	−	43.0024i	−0.625470	−	1.51002i	0.219727	−	0.975561i	$-0.429483\pi$
$812$			31.9546i			1.12139i
$813$	28.4157	−	11.7702i	0.996583	−	0.412798i
$814$	4.77975	+	4.77975i	0.167530	+	0.167530i
$815$	14.3209			0.501638
$816$	−9.13007	+	1.21610i	−0.319616	+	0.0425718i
$817$	−6.88008			−0.240703
$818$	5.70717	+	5.70717i	0.199547	+	0.199547i
$819$	−5.48257	+	2.27095i	−0.191576	+	0.0793535i
$820$			11.8106i			0.412445i
$821$	−8.63879	−	20.8559i	−0.301496	−	0.727875i	−0.999926	−	0.0121966i	$-0.996118\pi$
$821$	−8.63879	−	20.8559i	−0.301496	−	0.727875i	0.698430	−	0.715678i	$-0.253882\pi$
$822$	12.6964	+	5.25900i	0.442836	+	0.183429i
$823$	6.35629	−	15.3454i	0.221566	−	0.534908i	−0.773537	−	0.633751i	$-0.781514\pi$
$823$	6.35629	−	15.3454i	0.221566	−	0.534908i	0.995103	+	0.0988431i	$0.0315142\pi$
$824$	28.9317	−	28.9317i	1.00788	−	1.00788i
$825$	25.7602	−	25.7602i	0.896854	−	0.896854i
$826$	3.61582	−	8.72937i	0.125811	−	0.303734i
$827$	23.5118	+	9.73893i	0.817587	+	0.338656i	0.751977	−	0.659190i	$-0.229101\pi$
$827$	23.5118	+	9.73893i	0.817587	+	0.338656i	0.0656104	+	0.997845i	$0.479101\pi$
$828$	−1.58294	−	3.82156i	−0.0550110	−	0.132808i
$829$			16.7997i			0.583477i	0.956498	+	0.291739i	$0.0942338\pi$
$829$			16.7997i			0.583477i	−0.956498	+	0.291739i	$0.905766\pi$
$830$	−3.05121	+	1.26385i	−0.105909	+	0.0438690i
$831$	−30.8786	−	30.8786i	−1.07117	−	1.07117i
$832$	−3.51535			−0.121873
$833$	12.8851	+	22.2396i	0.446441	+	0.770555i
$834$	10.3509			0.358422
$835$	−49.6774	−	49.6774i	−1.71916	−	1.71916i
$836$	−54.8129	+	22.7042i	−1.89574	+	0.785243i
$837$			24.3964i			0.843262i
$838$	−6.56728	−	15.8548i	−0.226863	−	0.547696i
$839$	−26.0644	−	10.7962i	−0.899843	−	0.372727i	−0.115683	−	0.993286i	$-0.536906\pi$
$839$	−26.0644	−	10.7962i	−0.899843	−	0.372727i	−0.784160	+	0.620559i	$0.786906\pi$
$840$	−15.9723	+	38.5605i	−0.551097	+	1.33046i
$841$	−2.69448	+	2.69448i	−0.0929133	+	0.0929133i
$842$	14.3844	−	14.3844i	0.495718	−	0.495718i
$843$	−3.11402	+	7.51792i	−0.107253	+	0.258931i
$844$	28.4120	+	11.7686i	0.977980	+	0.405093i
$845$	3.66321	+	8.84376i	0.126018	+	0.304235i
$846$			2.80425i			0.0964121i
$847$	−69.3063	+	28.7076i	−2.38139	+	0.986406i
$848$	5.81465	+	5.81465i	0.199676	+	0.199676i
$849$	28.5859			0.981067
$850$	−11.1955	−	2.98163i	−0.384004	−	0.102269i
$851$	9.12390			0.312763
$852$	−13.9631	−	13.9631i	−0.478369	−	0.478369i
$853$	−15.0469	+	6.23265i	−0.515197	+	0.213402i	−0.625106	−	0.780540i	$-0.714944\pi$
$853$	−15.0469	+	6.23265i	−0.515197	+	0.213402i	0.109909	+	0.993942i	$0.464944\pi$
$854$		−	26.1813i		−	0.895907i
$855$	4.13577	+	9.98464i	0.141440	+	0.341467i
$856$	−21.0598	−	8.72324i	−0.719808	−	0.298154i
$857$	12.7524	−	30.7870i	0.435614	−	1.05167i	−0.541833	−	0.840486i	$-0.682270\pi$
$857$	12.7524	−	30.7870i	0.435614	−	1.05167i	0.977447	−	0.211179i	$-0.0677304\pi$
$858$	13.4078	−	13.4078i	0.457735	−	0.457735i
$859$	−5.43586	+	5.43586i	−0.185469	+	0.185469i	−0.793734	−	0.608265i	$-0.791866\pi$
$859$	−5.43586	+	5.43586i	−0.185469	+	0.185469i	0.608265	+	0.793734i	$0.291866\pi$
$860$	1.77166	−	4.27717i	0.0604132	−	0.145850i
$861$	13.5017	+	5.59257i	0.460136	+	0.190594i
$862$	4.29716	+	10.3743i	0.146362	+	0.353349i
$863$			18.1780i			0.618787i	0.950934	+	0.309393i	$0.100126\pi$
$863$			18.1780i			0.618787i	−0.950934	+	0.309393i	$0.899874\pi$
$864$	29.6828	−	12.2950i	1.00983	−	0.418285i
$865$	−26.7386	−	26.7386i	−0.909139	−	0.909139i
$866$	−14.8421			−0.504354
$867$	−26.5514	−	3.41360i	−0.901732	−	0.115932i
$868$	−24.5512			−0.833321
$869$	−41.0320	−	41.0320i	−1.39192	−	1.39192i
$870$	−17.1831	+	7.11749i	−0.582563	+	0.241305i
$871$			36.2470i			1.22818i
$872$	−6.92634	−	16.7217i	−0.234555	−	0.566267i
$873$	−5.47275	−	2.26689i	−0.185225	−	0.0767225i
$874$	9.32249	−	22.5065i	0.315338	−	0.761293i
$875$	−6.87962	+	6.87962i	−0.232574	+	0.232574i
$876$	−23.3245	+	23.3245i	−0.788062	+	0.788062i
$877$	13.3021	−	32.1142i	0.449181	−	1.08442i	−0.523448	−	0.852058i	$-0.675355\pi$
$877$	13.3021	−	32.1142i	0.449181	−	1.08442i	0.972629	−	0.232362i	$-0.0746455\pi$
$878$	3.12635	+	1.29498i	0.105509	+	0.0437034i
$879$	4.65727	+	11.2436i	0.157086	+	0.379239i
$880$		−	24.0834i		−	0.811850i
$881$	−2.15228	+	0.891503i	−0.0725121	+	0.0300355i	−0.418645	−	0.908150i	$-0.637495\pi$
$881$	−2.15228	+	0.891503i	−0.0725121	+	0.0300355i	0.346133	+	0.938186i	$0.387495\pi$
$882$	−1.56649	−	1.56649i	−0.0527466	−	0.0527466i
$883$	37.7201			1.26938			0.634691	−	0.772766i	$-0.281127\pi$
$883$	37.7201			1.26938			0.634691	+	0.772766i	$0.281127\pi$
$884$	19.1553	+	5.10150i	0.644262	+	0.171582i
$885$	−18.0782			−0.607693
$886$	−13.6808	−	13.6808i	−0.459617	−	0.459617i
$887$	−49.6637	+	20.5714i	−1.66754	+	0.690719i	−0.998615	−	0.0526084i	$-0.983246\pi$
$887$	−49.6637	+	20.5714i	−1.66754	+	0.690719i	−0.668928	+	0.743327i	$0.733246\pi$
$888$			6.68859i			0.224454i
$889$	−17.2577	−	41.6639i	−0.578806	−	1.39736i
$890$	−28.9342	−	11.9849i	−0.969875	−	0.401735i
$891$	−15.4258	+	37.2411i	−0.516783	+	1.24762i
$892$	29.9029	−	29.9029i	1.00122	−	1.00122i
$893$	38.3887	−	38.3887i	1.28463	−	1.28463i
$894$	7.03644	−	16.9875i	0.235334	−	0.568146i
$895$	−41.4612	−	17.1738i	−1.38589	−	0.574056i
$896$	15.0708	+	36.3841i	0.503480	+	1.21551i
$897$		−	25.5937i		−	0.854547i
$898$	11.0486	−	4.57647i	0.368696	−	0.152719i
$899$	−17.8253	−	17.8253i	−0.594508	−	0.594508i
$900$	−3.28267			−0.109422
$901$	11.9813	+	20.6796i	0.399154	+	0.688938i
$902$	9.79820			0.326244
$903$	−4.05066	−	4.05066i	−0.134797	−	0.134797i
$904$	32.1844	−	13.3312i	1.07044	−	0.443389i
$905$			28.3899i			0.943711i
$906$	2.82889	+	6.82954i	0.0939835	+	0.226896i
$907$	21.8674	+	9.05778i	0.726095	+	0.300759i	0.714946	−	0.699179i	$-0.246451\pi$
$907$	21.8674	+	9.05778i	0.726095	+	0.300759i	0.0111490	+	0.999938i	$0.496451\pi$
$908$	9.03874	−	21.8214i	0.299961	−	0.724170i
$909$	−3.11503	+	3.11503i	−0.103319	+	0.103319i
$910$	16.6291	−	16.6291i	0.551249	−	0.551249i
$911$	−14.9550	+	36.1046i	−0.495482	+	1.19620i	0.456411	+	0.889769i	$0.349135\pi$
$911$	−14.9550	+	36.1046i	−0.495482	+	1.19620i	−0.951893	+	0.306430i	$0.900865\pi$
$912$	−14.1996	−	5.88168i	−0.470197	−	0.194762i
$913$	−3.44671	−	8.32109i	−0.114069	−	0.275388i
$914$			16.3776i			0.541721i
$915$	−46.2802	+	19.1699i	−1.52998	+	0.633737i
$916$	−22.1304	−	22.1304i	−0.731209	−	0.731209i
$917$	8.87285			0.293007
$918$	15.4743	−	2.06112i	0.510727	−	0.0680272i
$919$	−37.9745			−1.25266			−0.626332	−	0.779556i	$-0.715445\pi$
$919$	−37.9745			−1.25266			−0.626332	+	0.779556i	$0.715445\pi$
$920$	26.7083	+	26.7083i	0.880547	+	0.880547i
$921$	12.3449	−	5.11344i	0.406779	−	0.168493i
$922$			18.7478i			0.617426i
$923$	9.81104	+	23.6859i	0.322934	+	0.779632i
$924$	−45.6383	−	18.9040i	−1.50139	−	0.621896i
$925$	2.77090	−	6.68955i	0.0911068	−	0.219951i
$926$	−5.43287	+	5.43287i	−0.178535	+	0.178535i
$927$	6.23750	−	6.23750i	0.204867	−	0.204867i
$928$	−12.7045	+	30.6713i	−0.417044	+	1.00683i
$929$	0.536326	+	0.222153i	0.0175963	+	0.00728862i	0.391464	−	0.920193i	$-0.371969\pi$
$929$	0.536326	+	0.222153i	0.0175963	+	0.00728862i	−0.373868	+	0.927482i	$0.621969\pi$
$930$	−5.46846	−	13.2020i	−0.179318	−	0.432912i
$931$			42.8890i			1.40563i
$932$	−2.54029	+	1.05222i	−0.0832099	+	0.0344667i
$933$	4.74450	+	4.74450i	0.155328	+	0.155328i
$934$	1.35686			0.0443977
$935$	18.0136	−	67.6380i	0.589107	−	2.21200i
$936$	−3.93692			−0.128682
$937$	−15.4305	−	15.4305i	−0.504094	−	0.504094i	0.408614	−	0.912707i	$-0.366012\pi$
$937$	−15.4305	−	15.4305i	−0.504094	−	0.504094i	−0.912707	+	0.408614i	$0.866012\pi$
$938$	−26.5396	+	10.9931i	−0.866549	+	0.358936i
$939$		−	6.59850i		−	0.215334i
$940$	13.9800	+	33.7507i	0.455977	+	1.10083i
$941$	54.4275	+	22.5446i	1.77429	+	0.734933i	0.993984	+	0.109530i	$0.0349345\pi$
$941$	54.4275	+	22.5446i	1.77429	+	0.734933i	0.780302	+	0.625403i	$0.215066\pi$
$942$	1.85686	−	4.48286i	0.0604999	−	0.146060i
$943$	9.35171	−	9.35171i	0.304534	−	0.304534i
$944$	−3.81466	+	3.81466i	−0.124157	+	0.124157i
$945$	−23.2980	+	56.2464i	−0.757884	+	1.82969i
$946$	−3.54838	−	1.46979i	−0.115368	−	0.0477869i
$947$	−20.7061	−	49.9890i	−0.672858	−	1.62442i	−0.776730	−	0.629833i	$-0.783123\pi$
$947$	−20.7061	−	49.9890i	−0.672858	−	1.62442i	0.103872	−	0.994591i	$-0.466877\pi$
$948$		−	24.9190i		−	0.809332i
$949$	39.5658	−	16.3887i	1.28436	−	0.532000i
$950$	−13.6703	−	13.6703i	−0.443524	−	0.443524i
$951$	23.9598			0.776951
$952$	4.77938	+	35.8821i	0.154901	+	1.16295i
$953$	−23.7012			−0.767756			−0.383878	−	0.923384i	$-0.625412\pi$
$953$	−23.7012			−0.767756			−0.383878	+	0.923384i	$0.625412\pi$
$954$	−1.45662	−	1.45662i	−0.0471597	−	0.0471597i
$955$	−51.3407	+	21.2660i	−1.66135	+	0.688152i
$956$		−	25.6528i		−	0.829670i
$957$	−19.4104	−	46.8609i	−0.627449	−	1.51480i
$958$	−3.87669	−	1.60578i	−0.125250	−	0.0518803i
$959$	−17.7878	+	42.9436i	−0.574398	+	1.38672i
$960$	−3.76920	+	3.76920i	−0.121650	+	0.121650i
$961$	−8.22486	+	8.22486i	−0.265318	+	0.265318i
$962$	1.44222	−	3.48182i	0.0464989	−	0.112258i
$963$	−4.54036	−	1.88068i	−0.146311	−	0.0606040i
$964$	3.59891	+	8.68855i	0.115913	+	0.279839i
$965$			2.99467i			0.0964018i
$966$	18.7394	−	7.76210i	0.602929	−	0.249741i
$967$	−33.4222	−	33.4222i	−1.07479	−	1.07479i	−0.996968	−	0.0778177i	$-0.975205\pi$
$967$	−33.4222	−	33.4222i	−1.07479	−	1.07479i	−0.0778177	−	0.996968i	$-0.524795\pi$
$968$	−49.7675			−1.59959
$969$	−35.4803	−	27.1396i	−1.13979	−	0.871848i
$970$	23.4750			0.753737
$971$	−36.6061	−	36.6061i	−1.17475	−	1.17475i	−0.981064	−	0.193683i	$-0.937957\pi$
$971$	−36.6061	−	36.6061i	−1.17475	−	1.17475i	−0.193683	−	0.981064i	$-0.562043\pi$
$972$	7.56891	−	3.13514i	0.242773	−	0.100560i
$973$			35.0104i			1.12238i
$974$	6.38671	+	15.4189i	0.204643	+	0.494053i
$975$	−18.7650	−	7.77273i	−0.600962	−	0.248927i
$976$	−5.72051	+	13.8105i	−0.183109	+	0.442064i
$977$	−27.8601	+	27.8601i	−0.891325	+	0.891325i	−0.994648	−	0.103323i	$-0.967052\pi$
$977$	−27.8601	+	27.8601i	−0.891325	+	0.891325i	0.103323	+	0.994648i	$0.467052\pi$
$978$	3.60761	−	3.60761i	0.115359	−	0.115359i
$979$	32.6846	−	78.9075i	1.04460	−	2.52190i
$980$	−26.6630	−	11.0442i	−0.851718	−	0.352793i
$981$	−1.49328	−	3.60509i	−0.0476766	−	0.115102i
$982$		−	22.9913i		−	0.733682i
$983$	44.6090	−	18.4777i	1.42281	−	0.589346i	0.467243	−	0.884129i	$-0.345247\pi$
$983$	44.6090	−	18.4777i	1.42281	−	0.589346i	0.955564	+	0.294783i	$0.0952475\pi$
$984$	6.85560	+	6.85560i	0.218548	+	0.218548i
$985$	−20.5222			−0.653890
$986$	−9.80038	+	12.8123i	−0.312108	+	0.408027i
$987$	45.2029			1.43882
$988$	23.3896	+	23.3896i	0.744122	+	0.744122i
$989$	−4.78949	+	1.98387i	−0.152297	+	0.0630835i
$990$			6.03307i			0.191743i
$991$	−14.7366	−	35.5772i	−0.468122	−	1.13015i	−0.964982	−	0.262317i	$-0.915514\pi$
$991$	−14.7366	−	35.5772i	−0.468122	−	1.13015i	0.496859	−	0.867831i	$-0.334486\pi$
$992$	−23.5652	−	9.76101i	−0.748194	−	0.309912i
$993$	−8.01700	+	19.3547i	−0.254412	+	0.614204i
$994$	−14.3670	+	14.3670i	−0.455695	+	0.455695i
$995$	−35.2341	+	35.2341i	−1.11700	+	1.11700i
$996$	1.48012	−	3.57333i	0.0468994	−	0.113225i
$997$	−10.9213	−	4.52377i	−0.345882	−	0.143269i	0.202978	−	0.979183i	$-0.434938\pi$
$997$	−10.9213	−	4.52377i	−0.345882	−	0.143269i	−0.548860	+	0.835914i	$0.684938\pi$
$998$	−4.27003	−	10.3088i	−0.135165	−	0.326318i
$999$			9.75632i			0.308676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.13	✓	116
17.9	even	8	inner	731.2.m.b.689.13	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.13	✓	116	1.1	even	1	trivial
731.2.m.b.689.13	yes	116	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.482959 - 0.482959i) q^{2} +(-1.45483 + 0.602612i) q^{3} -1.53350i q^{4} +(1.15531 + 2.78915i) q^{5} +(0.993661 + 0.411588i) q^{6} +(-1.39214 + 3.36091i) q^{7} +(-1.70653 + 1.70653i) q^{8} +(-0.367918 + 0.367918i) q^{9} +O(q^{10})\)	\(q+(-0.482959 - 0.482959i) q^{2} +(-1.45483 + 0.602612i) q^{3} -1.53350i q^{4} +(1.15531 + 2.78915i) q^{5} +(0.993661 + 0.411588i) q^{6} +(-1.39214 + 3.36091i) q^{7} +(-1.70653 + 1.70653i) q^{8} +(-0.367918 + 0.367918i) q^{9} +(0.789081 - 1.90501i) q^{10} +(5.19523 + 2.15194i) q^{11} +(0.924107 + 2.23099i) q^{12} -3.13516i q^{13} +(2.29553 - 0.950838i) q^{14} +(-3.36156 - 3.36156i) q^{15} -1.41863 q^{16} +(-3.98423 - 1.06109i) q^{17} +0.355379 q^{18} +(-4.86495 - 4.86495i) q^{19} +(4.27717 - 1.77166i) q^{20} -5.72849i q^{21} +(-1.46979 - 3.54838i) q^{22} +(-4.78949 - 1.98387i) q^{23} +(1.45435 - 3.51110i) q^{24} +(-2.90911 + 2.90911i) q^{25} +(-1.51415 + 1.51415i) q^{26} +(2.12138 - 5.12148i) q^{27} +(5.15397 + 2.13484i) q^{28} +(2.19203 + 5.29203i) q^{29} +3.24698i q^{30} +(-4.06594 + 1.68417i) q^{31} +(4.09821 + 4.09821i) q^{32} -8.85499 q^{33} +(1.41175 + 2.43668i) q^{34} -10.9825 q^{35} +(0.564204 + 0.564204i) q^{36} +(-1.62600 + 0.673513i) q^{37} +4.69914i q^{38} +(1.88929 + 4.56114i) q^{39} +(-6.73136 - 2.78822i) q^{40} +(-0.976273 + 2.35693i) q^{41} +(-2.76662 + 2.76662i) q^{42} +(0.707107 - 0.707107i) q^{43} +(3.30000 - 7.96690i) q^{44} +(-1.45124 - 0.601123i) q^{45} +(1.35500 + 3.27126i) q^{46} +7.89088i q^{47} +(2.06388 - 0.854886i) q^{48} +(-4.40796 - 4.40796i) q^{49} +2.80996 q^{50} +(6.43582 - 0.857230i) q^{51} -4.80778 q^{52} +(-4.09877 - 4.09877i) q^{53} +(-3.49800 + 1.44892i) q^{54} +16.9764i q^{55} +(-3.35979 - 8.11125i) q^{56} +(10.0094 + 4.14602i) q^{57} +(1.49717 - 3.61449i) q^{58} +(2.68897 - 2.68897i) q^{59} +(-5.15495 + 5.15495i) q^{60} +(4.03241 - 9.73509i) q^{61} +(2.77706 + 1.15030i) q^{62} +(-0.724350 - 1.74874i) q^{63} -1.12127i q^{64} +(8.74444 - 3.62207i) q^{65} +(4.27659 + 4.27659i) q^{66} -11.5615 q^{67} +(-1.62719 + 6.10982i) q^{68} +8.16343 q^{69} +(5.30407 + 5.30407i) q^{70} +(-7.55494 + 3.12936i) q^{71} -1.25573i q^{72} +(5.22739 + 12.6200i) q^{73} +(1.11057 + 0.460013i) q^{74} +(2.47921 - 5.98535i) q^{75} +(-7.46041 + 7.46041i) q^{76} +(-14.4649 + 14.4649i) q^{77} +(1.29039 - 3.11529i) q^{78} +(-9.53375 - 3.94901i) q^{79} +(-1.63895 - 3.95679i) q^{80} +7.16833i q^{81} +(1.60980 - 0.666801i) q^{82} +(-1.13256 - 1.13256i) q^{83} -8.78466 q^{84} +(-1.64345 - 12.3385i) q^{85} -0.683006 q^{86} +(-6.37808 - 6.37808i) q^{87} +(-12.5382 + 5.19349i) q^{88} -15.1885i q^{89} +(0.410571 + 0.991206i) q^{90} +(10.5370 + 4.36457i) q^{91} +(-3.04227 + 7.34470i) q^{92} +(4.90037 - 4.90037i) q^{93} +(3.81097 - 3.81097i) q^{94} +(7.94859 - 19.1896i) q^{95} +(-8.43185 - 3.49259i) q^{96} +(4.35676 + 10.5181i) q^{97} +4.25772i q^{98} +(-2.70316 + 1.11969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more