LMFDB - Embedded newform 117.2.z.b.5.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(5,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	117.5
Dual form			117.2.z.b.47.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.267684 + 0.999012i) q^{2} +(-1.73168 - 0.0358377i) q^{3} +(0.805681 + 0.465160i) q^{4} +(1.80337 - 0.483213i) q^{5} +(0.499346 - 1.72038i) q^{6} +(-1.07064 + 3.99567i) q^{7} +(-2.14302 + 2.14302i) q^{8} +(2.99743 + 0.124119i) q^{9} +1.93094i q^{10} +(-3.71604 - 0.995710i) q^{11} +(-1.37851 - 0.834382i) q^{12} +(3.39856 + 1.20407i) q^{13} +(-3.70513 - 2.13916i) q^{14} +(-3.14018 + 0.772141i) q^{15} +(-0.636932 - 1.10320i) q^{16} +0.582460 q^{17} +(-0.926362 + 2.96125i) q^{18} +(4.41048 - 4.41048i) q^{19} +(1.67772 + 0.449542i) q^{20} +(1.99720 - 6.88085i) q^{21} +(1.98945 - 3.44583i) q^{22} +(2.65310 - 4.59531i) q^{23} +(3.78783 - 3.63423i) q^{24} +(-1.31146 + 0.757174i) q^{25} +(-2.11262 + 3.07289i) q^{26} +(-5.18614 - 0.322355i) q^{27} +(-2.72122 + 2.72122i) q^{28} +(5.19577 - 2.99978i) q^{29} +(0.0692004 - 3.34377i) q^{30} +(-0.574604 - 2.14445i) q^{31} +(-4.58224 + 1.22781i) q^{32} +(6.39931 + 1.85742i) q^{33} +(-0.155916 + 0.581885i) q^{34} +7.72303i q^{35} +(2.35724 + 1.49429i) q^{36} +(-4.32606 - 4.32606i) q^{37} +(3.22551 + 5.58674i) q^{38} +(-5.84207 - 2.20685i) q^{39} +(-2.82914 + 4.90021i) q^{40} +(-6.13140 + 1.64290i) q^{41} +(6.33944 + 3.83712i) q^{42} +(5.20669 - 3.00608i) q^{43} +(-2.53078 - 2.53078i) q^{44} +(5.46547 - 1.22456i) q^{45} +(3.88057 + 3.88057i) q^{46} +(6.15742 + 1.64988i) q^{47} +(1.06343 + 1.93321i) q^{48} +(-8.75694 - 5.05582i) q^{49} +(-0.405367 - 1.51285i) q^{50} +(-1.00863 - 0.0208740i) q^{51} +(2.17807 + 2.55097i) q^{52} -1.69062i q^{53} +(1.71029 - 5.09473i) q^{54} -7.18255 q^{55} +(-6.26842 - 10.8572i) q^{56} +(-7.79561 + 7.47948i) q^{57} +(1.60599 + 5.99363i) q^{58} +(1.72888 + 6.45229i) q^{59} +(-2.88916 - 0.838589i) q^{60} +(-1.12715 - 1.95228i) q^{61} +2.29614 q^{62} +(-3.70510 + 11.8439i) q^{63} -7.45411i q^{64} +(6.71070 + 0.529152i) q^{65} +(-3.56858 + 5.89578i) q^{66} +(0.594213 + 2.21763i) q^{67} +(0.469277 + 0.270937i) q^{68} +(-4.75901 + 7.86252i) q^{69} +(-7.71540 - 2.06734i) q^{70} +(1.87415 + 1.87415i) q^{71} +(-6.68956 + 6.15758i) q^{72} +(5.42937 + 5.42937i) q^{73} +(5.47981 - 3.16377i) q^{74} +(2.29817 - 1.26418i) q^{75} +(5.60502 - 1.50186i) q^{76} +(7.95706 - 13.7820i) q^{77} +(3.76850 - 5.24556i) q^{78} +(-1.10654 - 1.91658i) q^{79} +(-1.68171 - 1.68171i) q^{80} +(8.96919 + 0.744075i) q^{81} -6.56512i q^{82} +(-2.95269 + 11.0196i) q^{83} +(4.80980 - 4.61476i) q^{84} +(1.05039 - 0.281452i) q^{85} +(1.60936 + 6.00623i) q^{86} +(-9.10492 + 5.00845i) q^{87} +(10.0974 - 5.82973i) q^{88} +(0.110864 - 0.110864i) q^{89} +(-0.239666 + 5.78786i) q^{90} +(-8.44967 + 12.2904i) q^{91} +(4.27511 - 2.46823i) q^{92} +(0.918178 + 3.73409i) q^{93} +(-3.29649 + 5.70969i) q^{94} +(5.82255 - 10.0850i) q^{95} +(7.97898 - 1.96195i) q^{96} +(-10.8682 - 2.91212i) q^{97} +(7.39493 - 7.39493i) q^{98} +(-11.0150 - 3.44580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.267684	+	0.999012i	−0.189281	+	0.706408i	0.804392	+	0.594099i	$0.202491\pi$
$2$	−0.267684	+	0.999012i	−0.189281	+	0.706408i	−0.993673	+	0.112309i	$0.964175\pi$
$3$	−1.73168	−	0.0358377i	−0.999786	−	0.0206909i
$3$	−1.73168	−	0.0358377i	−0.999786	−	0.0206909i
$4$	0.805681	+	0.465160i	0.402840	+	0.232580i
$5$	1.80337	−	0.483213i	0.806493	−	0.216099i	0.168060	−	0.985777i	$-0.446250\pi$
$5$	1.80337	−	0.483213i	0.806493	−	0.216099i	0.638433	+	0.769677i	$0.279583\pi$
$6$	0.499346	−	1.72038i	0.203857	−	0.702340i
$7$	−1.07064	+	3.99567i	−0.404663	+	1.51022i	0.400014	+	0.916509i	$0.369005\pi$
$7$	−1.07064	+	3.99567i	−0.404663	+	1.51022i	−0.804677	+	0.593713i	$0.797662\pi$
$8$	−2.14302	+	2.14302i	−0.757673	+	0.757673i
$9$	2.99743	+	0.124119i	0.999144	+	0.0413729i
$10$			1.93094i			0.610617i
$11$	−3.71604	−	0.995710i	−1.12043	−	0.300218i	−0.349371	−	0.936984i	$-0.613605\pi$
$11$	−3.71604	−	0.995710i	−1.12043	−	0.300218i	−0.771057	+	0.636767i	$0.780271\pi$
$12$	−1.37851	−	0.834382i	−0.397942	−	0.240865i
$13$	3.39856	+	1.20407i	0.942592	+	0.333948i
$13$	3.39856	+	1.20407i	0.942592	+	0.333948i
$14$	−3.70513	−	2.13916i	−0.990238	−	0.571714i
$15$	−3.14018	+	0.772141i	−0.810792	+	0.199366i
$16$	−0.636932	−	1.10320i	−0.159233	−	0.275800i
$17$	0.582460			0.141267			0.0706337	−	0.997502i	$-0.477498\pi$
$17$	0.582460			0.141267			0.0706337	+	0.997502i	$0.477498\pi$
$18$	−0.926362	+	2.96125i	−0.218346	+	0.697972i
$19$	4.41048	−	4.41048i	1.01183	−	1.01183i	0.0119052	−	0.999929i	$-0.496210\pi$
$19$	4.41048	−	4.41048i	1.01183	−	1.01183i	0.999929	−	0.0119052i	$-0.00378963\pi$
$20$	1.67772	+	0.449542i	0.375149	+	0.100521i
$21$	1.99720	−	6.88085i	0.435824	−	1.50153i
$22$	1.98945	−	3.44583i	0.424153	−	0.734654i
$23$	2.65310	−	4.59531i	0.553210	−	0.958187i	−0.444831	−	0.895615i	$-0.646736\pi$
$23$	2.65310	−	4.59531i	0.553210	−	0.958187i	0.998040	−	0.0625727i	$-0.0199305\pi$
$24$	3.78783	−	3.63423i	0.773188	−	0.741834i
$25$	−1.31146	+	0.757174i	−0.262293	+	0.151435i
$26$	−2.11262	+	3.07289i	−0.414318	+	0.602644i
$27$	−5.18614	−	0.322355i	−0.998074	−	0.0620372i
$28$	−2.72122	+	2.72122i	−0.514262	+	0.514262i
$29$	5.19577	−	2.99978i	0.964830	−	0.557045i	0.0671740	−	0.997741i	$-0.478602\pi$
$29$	5.19577	−	2.99978i	0.964830	−	0.557045i	0.897656	+	0.440696i	$0.145268\pi$
$30$	0.0692004	−	3.34377i	0.0126342	−	0.610486i
$31$	−0.574604	−	2.14445i	−0.103202	−	0.385155i	0.894933	−	0.446200i	$-0.147223\pi$
$31$	−0.574604	−	2.14445i	−0.103202	−	0.385155i	−0.998135	+	0.0610457i	$0.980556\pi$
$32$	−4.58224	+	1.22781i	−0.810034	+	0.217048i
$33$	6.39931	+	1.85742i	1.11398	+	0.323336i
$34$	−0.155916	+	0.581885i	−0.0267393	+	0.0997924i
$35$			7.72303i			1.30543i
$36$	2.35724	+	1.49429i	0.392873	+	0.249048i
$37$	−4.32606	−	4.32606i	−0.711200	−	0.711200i	0.255586	−	0.966786i	$-0.417732\pi$
$37$	−4.32606	−	4.32606i	−0.711200	−	0.711200i	−0.966786	+	0.255586i	$0.917732\pi$
$38$	3.22551	+	5.58674i	0.523246	+	0.906289i
$39$	−5.84207	−	2.20685i	−0.935480	−	0.353379i
$40$	−2.82914	+	4.90021i	−0.447326	+	0.774791i
$41$	−6.13140	+	1.64290i	−0.957564	+	0.256578i	−0.703569	−	0.710627i	$-0.748411\pi$
$41$	−6.13140	+	1.64290i	−0.957564	+	0.256578i	−0.253995	+	0.967206i	$0.581745\pi$
$42$	6.33944	+	3.83712i	0.978196	+	0.592080i
$43$	5.20669	−	3.00608i	0.794013	−	0.458424i	−0.0473604	−	0.998878i	$-0.515081\pi$
$43$	5.20669	−	3.00608i	0.794013	−	0.458424i	0.841373	+	0.540454i	$0.181748\pi$
$44$	−2.53078	−	2.53078i	−0.381529	−	0.381529i
$45$	5.46547	−	1.22456i	0.814744	−	0.182547i
$46$	3.88057	+	3.88057i	0.572159	+	0.572159i
$47$	6.15742	+	1.64988i	0.898152	+	0.240659i	0.678223	−	0.734856i	$-0.262751\pi$
$47$	6.15742	+	1.64988i	0.898152	+	0.240659i	0.219930	+	0.975516i	$0.429417\pi$
$48$	1.06343	+	1.93321i	0.153492	+	0.279035i
$49$	−8.75694	−	5.05582i	−1.25099	−	0.722261i
$50$	−0.405367	−	1.51285i	−0.0573276	−	0.213949i
$51$	−1.00863	−	0.0208740i	−0.141237	−	0.00292295i
$52$	2.17807	+	2.55097i	0.302044	+	0.353756i
$53$		−	1.69062i		−	0.232225i	−0.993236	−	0.116112i	$-0.962957\pi$
$53$		−	1.69062i		−	0.232225i	0.993236	−	0.116112i	$-0.0370433\pi$
$54$	1.71029	−	5.09473i	0.232740	−	0.693305i
$55$	−7.18255			−0.968495
$56$	−6.26842	−	10.8572i	−0.837653	−	1.45086i
$57$	−7.79561	+	7.47948i	−1.03255	+	0.990682i
$58$	1.60599	+	5.99363i	0.210877	+	0.787002i
$59$	1.72888	+	6.45229i	0.225082	+	0.840016i	0.982372	+	0.186938i	$0.0598562\pi$
$59$	1.72888	+	6.45229i	0.225082	+	0.840016i	−0.757290	+	0.653079i	$0.773477\pi$
$60$	−2.88916	−	0.838589i	−0.372988	−	0.108261i
$61$	−1.12715	−	1.95228i	−0.144316	−	0.249963i	0.784801	−	0.619747i	$-0.212765\pi$
$61$	−1.12715	−	1.95228i	−0.144316	−	0.249963i	−0.929118	+	0.369784i	$0.879432\pi$
$62$	2.29614			0.291611
$63$	−3.70510	+	11.8439i	−0.466798	+	1.49219i
$64$		−	7.45411i		−	0.931764i
$65$	6.71070	+	0.529152i	0.832360	+	0.0656332i
$66$	−3.56858	+	5.89578i	−0.439262	+	0.725720i
$67$	0.594213	+	2.21763i	0.0725947	+	0.270927i	0.992677	−	0.120798i	$-0.0385452\pi$
$67$	0.594213	+	2.21763i	0.0725947	+	0.270927i	−0.920082	+	0.391725i	$0.871879\pi$
$68$	0.469277	+	0.270937i	0.0569082	+	0.0328560i
$69$	−4.75901	+	7.86252i	−0.572917	+	0.946536i
$70$	−7.71540	−	2.06734i	−0.922167	−	0.247094i
$71$	1.87415	+	1.87415i	0.222420	+	0.222420i	0.809517	−	0.587097i	$-0.199729\pi$
$71$	1.87415	+	1.87415i	0.222420	+	0.222420i	−0.587097	+	0.809517i	$0.699729\pi$
$72$	−6.68956	+	6.15758i	−0.788372	+	0.725677i
$73$	5.42937	+	5.42937i	0.635460	+	0.635460i	0.949432	−	0.313972i	$-0.101660\pi$
$73$	5.42937	+	5.42937i	0.635460	+	0.635460i	−0.313972	+	0.949432i	$0.601660\pi$
$74$	5.47981	−	3.16377i	0.637015	−	0.367781i
$75$	2.29817	−	1.26418i	0.265370	−	0.145975i
$76$	5.60502	−	1.50186i	0.642940	−	0.172275i
$77$	7.95706	−	13.7820i	0.906791	−	1.57061i
$78$	3.76850	−	5.24556i	0.426699	−	0.593943i
$79$	−1.10654	−	1.91658i	−0.124495	−	0.215632i	0.797040	−	0.603926i	$-0.206398\pi$
$79$	−1.10654	−	1.91658i	−0.124495	−	0.215632i	−0.921535	+	0.388294i	$0.873064\pi$
$80$	−1.68171	−	1.68171i	−0.188020	−	0.188020i
$81$	8.96919	+	0.744075i	0.996577	+	0.0826750i
$82$		−	6.56512i		−	0.724996i
$83$	−2.95269	+	11.0196i	−0.324100	+	1.20956i	0.591113	+	0.806588i	$0.298689\pi$
$83$	−2.95269	+	11.0196i	−0.324100	+	1.20956i	−0.915213	+	0.402969i	$0.867978\pi$
$84$	4.80980	−	4.61476i	0.524792	−	0.503511i
$85$	1.05039	−	0.281452i	0.113931	−	0.0305278i
$86$	1.60936	+	6.00623i	0.173542	+	0.647668i
$87$	−9.10492	+	5.00845i	−0.976150	+	0.536963i
$88$	10.0974	−	5.82973i	1.07639	−	0.621451i
$89$	0.110864	−	0.110864i	0.0117515	−	0.0117515i	−0.701207	−	0.712958i	$-0.747355\pi$
$89$	0.110864	−	0.110864i	0.0117515	−	0.0117515i	0.712958	+	0.701207i	$0.247355\pi$
$90$	−0.239666	+	5.78786i	−0.0252630	+	0.610094i
$91$	−8.44967	+	12.2904i	−0.885767	+	1.28839i
$92$	4.27511	−	2.46823i	0.445711	−	0.257331i
$93$	0.918178	+	3.73409i	0.0952106	+	0.387207i
$94$	−3.29649	+	5.70969i	−0.340007	+	0.588910i
$95$	5.82255	−	10.0850i	0.597381	−	1.03469i
$96$	7.97898	−	1.96195i	0.814352	−	0.200241i
$97$	−10.8682	−	2.91212i	−1.10350	−	0.295681i	−0.339308	−	0.940675i	$-0.610193\pi$
$97$	−10.8682	−	2.91212i	−1.10350	−	0.295681i	−0.764187	+	0.644994i	$0.776860\pi$
$98$	7.39493	−	7.39493i	0.747000	−	0.747000i
$99$	−11.0150	−	3.44580i	−1.10705	−	0.346316i
$100$	−1.40883			−0.140883
$101$	3.68805	+	6.38789i	0.366975	+	0.635619i	0.989091	−	0.147306i	$-0.0470602\pi$
$101$	3.68805	+	6.38789i	0.366975	+	0.635619i	−0.622116	+	0.782925i	$0.713727\pi$
$102$	0.290849	−	1.00205i	0.0287984	−	0.0992178i
$103$	−10.0414	−	5.79738i	−0.989404	−	0.571233i	−0.0843082	−	0.996440i	$-0.526868\pi$
$103$	−10.0414	−	5.79738i	−0.989404	−	0.571233i	−0.905096	+	0.425207i	$0.860201\pi$
$104$	−9.86354	+	4.70286i	−0.967200	+	0.461153i
$105$	0.276776	−	13.3738i	0.0270105	−	1.30515i
$106$	1.68895	+	0.452553i	0.164045	+	0.0439559i
$107$		−	13.0948i		−	1.26592i	−0.774184	−	0.632960i	$-0.781840\pi$
$107$		−	13.0948i		−	1.26592i	0.774184	−	0.632960i	$-0.218160\pi$
$108$	−4.02843	−	2.67210i	−0.387636	−	0.257123i
$109$	4.03976	−	4.03976i	0.386939	−	0.386939i	−0.486655	−	0.873594i	$-0.661783\pi$
$109$	4.03976	−	4.03976i	0.386939	−	0.386939i	0.873594	+	0.486655i	$0.161783\pi$
$110$	1.92266	−	7.17545i	0.183318	−	0.684152i
$111$	7.33632	+	7.64639i	0.696333	+	0.725763i
$112$	5.08994	−	1.36385i	0.480954	−	0.128871i
$113$	−11.5455	−	6.66581i	−1.08611	−	0.627066i	−0.153572	−	0.988137i	$-0.549078\pi$
$113$	−11.5455	−	6.66581i	−1.08611	−	0.627066i	−0.932538	+	0.361071i	$0.882411\pi$
$114$	−5.38533	−	9.79005i	−0.504383	−	0.916922i
$115$	2.56402	−	9.56907i	0.239096	−	0.892320i
$116$	5.58151			0.518230
$117$	10.0375	+	4.03093i	0.927968	+	0.372659i
$118$	−6.90871			−0.635998
$119$	−0.623603	+	2.32732i	−0.0571656	+	0.213345i
$120$	5.07477	−	8.38421i	0.463261	−	0.765370i
$121$	3.29123	+	1.90019i	0.299203	+	0.172745i
$122$	2.25207	−	0.603439i	0.203892	−	0.0546328i
$123$	10.6765	−	2.62525i	0.962668	−	0.236711i
$124$	0.534565	−	1.99503i	0.0480054	−	0.179159i
$125$	−8.59999	+	8.59999i	−0.769207	+	0.769207i
$126$	−10.8404	−	6.87185i	−0.965736	−	0.612193i
$127$			3.14850i			0.279384i	0.990195	+	0.139692i	$0.0446112\pi$
$127$			3.14850i			0.279384i	−0.990195	+	0.139692i	$0.955389\pi$
$128$	−1.71774	−	0.460268i	−0.151829	−	0.0406823i
$129$	−9.12405	+	5.01898i	−0.803328	+	0.441897i
$130$	−2.32498	+	6.56242i	−0.203914	+	0.575563i
$131$	11.0320	+	6.36931i	0.963868	+	0.556489i	0.897361	−	0.441297i	$-0.145481\pi$
$131$	11.0320	+	6.36931i	0.963868	+	0.556489i	0.0665064	+	0.997786i	$0.478815\pi$
$132$	4.29180	+	4.47319i	0.373553	+	0.389342i
$133$	12.9008	+	22.3449i	1.11864	+	1.93755i
$134$	−2.37451			−0.205126
$135$	−9.50832	+	1.92468i	−0.818346	+	0.165650i
$136$	−1.24823	+	1.24823i	−0.107035	+	0.107035i
$137$	−9.98866	−	2.67645i	−0.853389	−	0.228665i	−0.194498	−	0.980903i	$-0.562308\pi$
$137$	−9.98866	−	2.67645i	−0.853389	−	0.228665i	−0.658891	+	0.752238i	$0.728974\pi$
$138$	−6.58084	−	6.85898i	−0.560198	−	0.583875i
$139$	8.51145	−	14.7423i	0.721932	−	1.25042i	−0.238292	−	0.971193i	$-0.576588\pi$
$139$	8.51145	−	14.7423i	0.721932	−	1.25042i	0.960224	−	0.279229i	$-0.0900790\pi$
$140$	−3.59245	+	6.22230i	−0.303617	+	0.525880i
$141$	−10.6036	−	3.07773i	−0.892981	−	0.259191i
$142$	−2.37398	+	1.37062i	−0.199220	+	0.115020i
$143$	−11.4303	−	7.85834i	−0.955849	−	0.657147i
$144$	−1.77223	−	3.38582i	−0.147686	−	0.282151i
$145$	7.92039	−	7.92039i	0.657752	−	0.657752i
$146$	−6.87737	+	3.97065i	−0.569175	+	0.328613i
$147$	14.9830	+	9.06890i	1.23578	+	0.747990i
$148$	−1.47311	−	5.49774i	−0.121089	−	0.451911i
$149$	−2.42278	+	0.649181i	−0.198482	+	0.0531830i	−0.356690	−	0.934223i	$-0.616095\pi$
$149$	−2.42278	+	0.649181i	−0.198482	+	0.0531830i	0.158209	+	0.987406i	$0.449428\pi$
$150$	0.647749	+	2.63430i	0.0528885	+	0.215090i
$151$	1.76494	−	6.58685i	0.143629	−	0.536030i	−0.856184	−	0.516672i	$-0.827171\pi$
$151$	1.76494	−	6.58685i	0.143629	−	0.536030i	0.999813	−	0.0193588i	$-0.00616249\pi$
$152$			18.9035i			1.53328i
$153$	1.74588	+	0.0722942i	0.141146	+	0.00584464i
$154$	11.6384	+	11.6384i	0.937851	+	0.937851i
$155$	−2.07245	−	3.58959i	−0.166463	−	0.288323i
$156$	−3.68031	−	4.49552i	−0.294660	−	0.359929i
$157$	−2.09675	+	3.63167i	−0.167339	+	0.289839i	−0.937483	−	0.348030i	$-0.886851\pi$
$157$	−2.09675	+	3.63167i	−0.167339	+	0.289839i	0.770145	+	0.637869i	$0.220184\pi$
$158$	2.21088	−	0.592405i	0.175889	−	0.0471292i
$159$	−0.0605879	+	2.92762i	−0.00480494	+	0.232175i
$160$	−7.67021	+	4.42840i	−0.606383	+	0.350096i
$161$	15.5208	+	15.5208i	1.22321	+	1.22321i
$162$	−3.14425	+	8.76115i	−0.247036	+	0.688341i
$163$	−5.06027	−	5.06027i	−0.396351	−	0.396351i	0.480593	−	0.876944i	$-0.340421\pi$
$163$	−5.06027	−	5.06027i	−0.396351	−	0.396351i	−0.876944	+	0.480593i	$0.840421\pi$
$164$	−5.70417	−	1.52843i	−0.445420	−	0.119350i
$165$	12.4379	+	0.257406i	0.968287	+	0.0200390i
$166$	−10.2183	−	5.89955i	−0.793095	−	0.457894i
$167$	3.87797	+	14.4728i	0.300086	+	1.11994i	0.937093	+	0.349079i	$0.113506\pi$
$167$	3.87797	+	14.4728i	0.300086	+	1.11994i	−0.637007	+	0.770858i	$0.719828\pi$
$168$	10.4658	+	19.0259i	0.807454	+	1.46788i
$169$	10.1005	+	8.18418i	0.776958	+	0.629552i
$170$			1.12470i			0.0862603i
$171$	13.7675	−	12.6727i	1.05283	−	0.969105i
$172$	5.59324			0.426481
$173$	4.14686	+	7.18257i	0.315280	+	0.546081i	0.979497	−	0.201459i	$-0.0645683\pi$
$173$	4.14686	+	7.18257i	0.315280	+	0.546081i	−0.664217	+	0.747540i	$0.731235\pi$
$174$	−2.56626	−	10.4366i	−0.194548	−	0.791197i
$175$	−1.62132	−	6.05083i	−0.122560	−	0.457400i
$176$	1.26840	+	4.73373i	0.0956092	+	0.356818i
$177$	−2.76264	−	11.2353i	−0.207653	−	0.844493i
$178$	0.0810777	+	0.140431i	0.00607703	+	0.0105257i
$179$	−11.3122			−0.845516			−0.422758	−	0.906243i	$-0.638938\pi$
$179$	−11.3122			−0.845516			−0.422758	+	0.906243i	$0.638938\pi$
$180$	4.97304	+	1.55571i	0.370669	+	0.115956i
$181$			5.84729i			0.434625i	0.976102	+	0.217313i	$0.0697291\pi$
$181$			5.84729i			0.434625i	−0.976102	+	0.217313i	$0.930271\pi$
$182$	−10.0164	−	11.7313i	−0.742467	−	0.869580i
$183$	1.88189	+	3.42111i	0.139113	+	0.252896i
$184$	4.16219	+	15.5335i	0.306841	+	1.14515i
$185$	−9.89192	−	5.71110i	−0.727268	−	0.419889i
$186$	−3.97619	−	0.0822884i	−0.291548	−	0.00603368i
$187$	−2.16445	−	0.579961i	−0.158280	−	0.0424110i
$188$	4.19346	+	4.19346i	0.305840	+	0.305840i
$189$	6.84050	−	20.3770i	0.497573	−	1.48221i
$190$	8.51638	+	8.51638i	0.617843	+	0.617843i
$191$	−9.02346	+	5.20970i	−0.652915	+	0.376961i	−0.789572	−	0.613658i	$-0.789697\pi$
$191$	−9.02346	+	5.20970i	−0.652915	+	0.376961i	0.136657	+	0.990618i	$0.456364\pi$
$192$	−0.267138	+	12.9081i	−0.0192790	+	0.931564i
$193$	4.17338	−	1.11825i	0.300407	−	0.0804937i	−0.105467	−	0.994423i	$-0.533634\pi$
$193$	4.17338	−	1.11825i	0.300407	−	0.0804937i	0.405874	+	0.913929i	$0.366967\pi$
$194$	5.81848	−	10.0779i	0.417743	−	0.723551i
$195$	−11.6018	−	1.15682i	−0.830824	−	0.0828414i
$196$	−4.70354	−	8.14676i	−0.335967	−	0.581912i
$197$	−13.2865	−	13.2865i	−0.946621	−	0.946621i	0.0520252	−	0.998646i	$-0.483432\pi$
$197$	−13.2865	−	13.2865i	−0.946621	−	0.946621i	−0.998646	+	0.0520252i	$0.983432\pi$
$198$	6.39094	−	10.0817i	0.454184	−	0.716476i
$199$			1.03922i			0.0736684i	0.999321	+	0.0368342i	$0.0117273\pi$
$199$			1.03922i			0.0736684i	−0.999321	+	0.0368342i	$0.988273\pi$
$200$	1.18786	−	4.43314i	0.0839941	−	0.313470i
$201$	−0.949513	−	3.86153i	−0.0669735	−	0.272371i
$202$	−7.36881	+	1.97447i	−0.518468	+	0.138923i
$203$	6.42335	+	23.9723i	0.450831	+	1.68252i
$204$	−0.802928	−	0.485994i	−0.0562162	−	0.0340264i
$205$	−10.2633	+	5.92554i	−0.716823	+	0.413858i
$206$	8.47957	−	8.47957i	0.590799	−	0.590799i
$207$	8.52285	−	13.4448i	0.592379	−	0.934479i
$208$	−0.836330	−	4.51620i	−0.0579891	−	0.313142i
$209$	−20.7811	+	11.9980i	−1.43746	+	0.829917i
$210$	13.2865	+	3.85647i	0.916857	+	0.266121i
$211$	−12.1856	+	21.1061i	−0.838893	+	1.45300i	0.0519286	+	0.998651i	$0.483463\pi$
$211$	−12.1856	+	21.1061i	−0.838893	+	1.45300i	−0.890821	+	0.454354i	$0.849870\pi$
$212$	0.786410	−	1.36210i	0.0540109	−	0.0935495i
$213$	−3.17826	−	3.31259i	−0.217771	−	0.226975i
$214$	13.0818	+	3.50527i	0.894257	+	0.239615i
$215$	7.93703	−	7.93703i	0.541301	−	0.541301i
$216$	11.8048	−	10.4232i	0.803218	−	0.709210i
$217$	9.18371			0.623431
$218$	2.95439	+	5.11715i	0.200096	+	0.346577i
$219$	−9.20736	−	9.59651i	−0.622176	−	0.648472i
$220$	−5.78684	−	3.34103i	−0.390149	−	0.225253i
$221$	1.97953	+	0.701320i	0.133157	+	0.0471759i
$222$	−9.60266	+	5.28225i	−0.644488	+	0.354521i
$223$	−16.9108	−	4.53123i	−1.13243	−	0.303433i	−0.356526	−	0.934285i	$-0.616039\pi$
$223$	−16.9108	−	4.53123i	−1.13243	−	0.303433i	−0.775903	+	0.630852i	$0.782706\pi$
$224$		−	19.6237i		−	1.31116i
$225$	−4.02500	+	2.10680i	−0.268333	+	0.140453i
$226$	9.74977	−	9.74977i	0.648545	−	0.648545i
$227$	1.29090	−	4.81770i	0.0856800	−	0.319762i	−0.909762	−	0.415130i	$-0.863736\pi$
$227$	1.29090	−	4.81770i	0.0856800	−	0.319762i	0.995442	+	0.0953678i	$0.0304027\pi$
$228$	−9.75993	+	2.39987i	−0.646367	+	0.158935i
$229$	15.4164	−	4.13081i	1.01875	−	0.272972i	0.289466	−	0.957188i	$-0.406522\pi$
$229$	15.4164	−	4.13081i	1.01875	−	0.272972i	0.729279	+	0.684216i	$0.239856\pi$
$230$	8.87326	+	5.12298i	0.585086	+	0.337799i
$231$	−14.2730	+	23.5809i	−0.939094	+	1.55151i
$232$	−4.70606	+	17.5633i	−0.308968	+	1.15308i
$233$	−5.29023			−0.346575			−0.173287	−	0.984871i	$-0.555439\pi$
$233$	−5.29023			−0.346575			−0.173287	+	0.984871i	$0.555439\pi$
$234$	−6.71383	+	8.94858i	−0.438897	+	0.584987i
$235$	11.9014			0.776360
$236$	−1.60842	+	6.00269i	−0.104699	+	0.390742i
$237$	1.84748	+	3.35855i	0.120007	+	0.218161i
$238$	−2.15809	−	1.24597i	−0.139888	−	0.0807645i
$239$	7.85038	−	2.10350i	0.507799	−	0.136064i	0.00418163	−	0.999991i	$-0.498669\pi$
$239$	7.85038	−	2.10350i	0.507799	−	0.136064i	0.503617	+	0.863927i	$0.332002\pi$
$240$	2.85191	+	2.97245i	0.184090	+	0.191871i
$241$	1.58687	−	5.92226i	0.102219	−	0.381486i	−0.895796	−	0.444466i	$-0.853394\pi$
$241$	1.58687	−	5.92226i	0.102219	−	0.381486i	0.998015	+	0.0629793i	$0.0200602\pi$
$242$	−2.77933	+	2.77933i	−0.178662	+	0.178662i
$243$	−15.5051	−	1.60993i	−0.994653	−	0.103277i
$244$		−	2.09721i		−	0.134260i
$245$	−18.2351	−	4.88608i	−1.16500	−	0.312160i
$246$	−0.235279	+	11.3687i	−0.0150008	+	0.724841i
$247$	20.2998	−	9.67879i	1.29165	−	0.615847i
$248$	5.82700	+	3.36422i	0.370015	+	0.213628i
$249$	5.50803	−	18.9766i	0.349057	−	1.20259i
$250$	−6.28941	−	10.8936i	−0.397777	−	0.688970i
$251$	13.2914			0.838945			0.419472	−	0.907768i	$-0.362215\pi$
$251$	13.2914			0.838945			0.419472	+	0.907768i	$0.362215\pi$
$252$	−8.49442	+	7.81891i	−0.535098	+	0.492545i
$253$	−14.4346	+	14.4346i	−0.907497	+	0.907497i
$254$	−3.14539	−	0.842804i	−0.197359	−	0.0528822i
$255$	−1.82903	+	0.449741i	−0.114538	+	0.0281639i
$256$	8.37374	−	14.5037i	0.523359	−	0.906484i
$257$	10.9925	−	19.0396i	0.685694	−	1.18766i	−0.287525	−	0.957773i	$-0.592832\pi$
$257$	10.9925	−	19.0396i	0.685694	−	1.18766i	0.973218	−	0.229883i	$-0.0738343\pi$
$258$	−2.57165	−	10.4585i	−0.160104	−	0.651120i
$259$	21.9172	−	12.6539i	1.36187	−	0.786274i
$260$	5.16054	+	3.54788i	0.320043	+	0.220030i
$261$	15.9463	−	8.34674i	0.987051	−	0.516650i
$262$	−9.31610	+	9.31610i	−0.575551	+	0.575551i
$263$	−2.98325	+	1.72238i	−0.183955	+	0.106206i	−0.589149	−	0.808024i	$-0.700537\pi$
$263$	−2.98325	+	1.72238i	−0.183955	+	0.106206i	0.405195	+	0.914230i	$0.367204\pi$
$264$	−17.6944	+	9.73336i	−1.08901	+	0.599047i
$265$	−0.816930	−	3.04882i	−0.0501836	−	0.187288i
$266$	−25.7761	+	6.90669i	−1.58044	+	0.423477i
$267$	−0.195954	+	0.188007i	−0.0119922	+	0.0115059i
$268$	−0.552809	+	2.06311i	−0.0337682	+	0.126025i
$269$		−	11.4792i		−	0.699897i	−0.936769	−	0.349949i	$-0.886199\pi$
$269$		−	11.4792i		−	0.699897i	0.936769	−	0.349949i	$-0.113801\pi$
$270$	0.622448	−	10.0141i	0.0378810	−	0.609441i
$271$	−12.6571	−	12.6571i	−0.768862	−	0.768862i	0.209044	−	0.977906i	$-0.432965\pi$
$271$	−12.6571	−	12.6571i	−0.768862	−	0.768862i	−0.977906	+	0.209044i	$0.932965\pi$
$272$	−0.370988	−	0.642569i	−0.0224944	−	0.0389615i
$273$	15.0726	−	20.9803i	0.912235	−	1.26978i
$274$	5.34762	−	9.26235i	0.323061	−	0.559559i
$275$	5.62737	−	1.50785i	0.339343	−	0.0909268i
$276$	−7.49157	+	4.12098i	−0.450940	+	0.248054i
$277$	−8.64049	+	4.98859i	−0.519157	+	0.299735i	−0.736590	−	0.676340i	$-0.763565\pi$
$277$	−8.64049	+	4.98859i	−0.519157	+	0.299735i	0.217433	+	0.976075i	$0.430232\pi$
$278$	12.4493	+	12.4493i	0.746660	+	0.746660i
$279$	−1.45617	−	6.49916i	−0.0871785	−	0.389095i
$280$	−16.5506	−	16.5506i	−0.989090	−	0.989090i
$281$	8.53106	+	2.28589i	0.508920	+	0.136365i	0.504137	−	0.863624i	$-0.331811\pi$
$281$	8.53106	+	2.28589i	0.508920	+	0.136365i	0.00478344	+	0.999989i	$0.498477\pi$
$282$	5.91309	−	9.76922i	0.352120	−	0.581749i
$283$	21.0010	+	12.1249i	1.24838	+	0.720751i	0.970786	−	0.239947i	$-0.0771302\pi$
$283$	21.0010	+	12.1249i	1.24838	+	0.720751i	0.277592	+	0.960699i	$0.410464\pi$
$284$	0.638186	+	2.38174i	0.0378694	+	0.141330i
$285$	−10.4442	+	17.2552i	−0.618662	+	1.02211i
$286$	10.9103	−	9.31544i	0.645138	−	0.550834i
$287$		−	26.2580i		−	1.54996i
$288$	−13.8874	+	3.11153i	−0.818320	+	0.183349i
$289$	−16.6607			−0.980044
$290$	5.79240	+	10.0327i	0.340141	+	0.589142i
$291$	18.7158	+	5.43235i	1.09714	+	0.318450i
$292$	1.84881	+	6.89987i	0.108194	+	0.403784i
$293$	−6.53292	−	24.3812i	−0.381657	−	1.42436i	−0.843369	−	0.537334i	$-0.819431\pi$
$293$	−6.53292	−	24.3812i	−0.381657	−	1.42436i	0.461712	−	0.887030i	$-0.347235\pi$
$294$	−13.0707	+	12.5406i	−0.762297	+	0.731384i
$295$	6.23565	+	10.8005i	0.363054	+	0.628828i
$296$	18.5417			1.07771
$297$	18.9509	+	6.36178i	1.09965	+	0.369148i
$298$		−	2.59416i		−	0.150276i
$299$	14.5498	−	12.4229i	0.841435	−	0.718436i
$300$	2.43964	+	0.0504891i	0.140853	+	0.00291499i
$301$	6.43685	+	24.0227i	0.371014	+	1.38464i
$302$	6.10790	+	3.52640i	0.351470	+	0.202921i
$303$	−6.15760	−	11.1940i	−0.353745	−	0.643076i
$304$	−7.67482	−	2.05646i	−0.440181	−	0.117946i
$305$	−2.97603	−	2.97603i	−0.170407	−	0.170407i
$306$	−0.539569	+	1.72481i	−0.0308451	+	0.0986007i
$307$	−3.40491	−	3.40491i	−0.194329	−	0.194329i	0.603235	−	0.797564i	$-0.293878\pi$
$307$	−3.40491	−	3.40491i	−0.194329	−	0.194329i	−0.797564	+	0.603235i	$0.793878\pi$
$308$	12.8217	−	7.40261i	0.730584	−	0.421803i
$309$	17.1807	+	10.3991i	0.977373	+	0.591582i
$310$	4.14081	−	1.10953i	0.235182	−	0.0630168i
$311$	−12.5475	+	21.7329i	−0.711502	+	1.23236i	0.252791	+	0.967521i	$0.418652\pi$
$311$	−12.5475	+	21.7329i	−0.711502	+	1.23236i	−0.964293	+	0.264837i	$0.914682\pi$
$312$	17.2490	−	7.79036i	0.976534	−	0.441042i
$313$	7.79376	+	13.4992i	0.440529	+	0.763019i	0.997729	−	0.0673596i	$-0.0214575\pi$
$313$	7.79376	+	13.4992i	0.440529	+	0.763019i	−0.557199	+	0.830379i	$0.688124\pi$
$314$	−3.06682	−	3.06682i	−0.173071	−	0.173071i
$315$	−0.958573	+	23.1493i	−0.0540095	+	1.30431i
$316$		−	2.05886i		−	0.115820i
$317$	8.47660	−	31.6351i	0.476093	−	1.77680i	−0.141104	−	0.989995i	$-0.545065\pi$
$317$	8.47660	−	31.6351i	0.476093	−	1.77680i	0.617197	−	0.786809i	$-0.288268\pi$
$318$	−2.90851	−	0.844205i	−0.163101	−	0.0473407i
$319$	−22.2946	+	5.97382i	−1.24826	+	0.334470i
$320$	−3.60192	−	13.4425i	−0.201353	−	0.751461i
$321$	−0.469287	+	22.6760i	−0.0261930	+	1.26565i
$322$	−19.6602	+	11.3508i	−1.09562	+	0.632556i
$323$	2.56893	−	2.56893i	0.142939	−	0.142939i
$324$	6.88019	+	4.77160i	0.382233	+	0.265089i
$325$	−5.36878	+	0.994215i	−0.297806	+	0.0551491i
$326$	6.40982	−	3.70071i	0.355007	−	0.204963i
$327$	−7.14035	+	6.85080i	−0.394862	+	0.378850i
$328$	9.61895	−	16.6605i	0.531118	−	0.919923i
$329$	−13.1847	+	22.8366i	−0.726897	+	1.25902i
$330$	−3.58658	+	12.3567i	−0.197435	+	0.680213i
$331$	−5.57612	−	1.49412i	−0.306491	−	0.0821241i	0.102295	−	0.994754i	$-0.467381\pi$
$331$	−5.57612	−	1.49412i	−0.306491	−	0.0821241i	−0.408787	+	0.912630i	$0.634048\pi$
$332$	−7.50480	+	7.50480i	−0.411880	+	0.411880i
$333$	−12.4301	−	13.5040i	−0.681167	−	0.740016i
$334$	−15.4965			−0.847933
$335$	2.14318	+	3.71209i	0.117094	+	0.202813i
$336$	−8.86303	+	2.17933i	−0.483518	+	0.118892i
$337$	−28.5632	−	16.4910i	−1.55594	−	0.898321i	−0.997639	−	0.0686811i	$-0.978121\pi$
$337$	−28.5632	−	16.4910i	−1.55594	−	0.898321i	−0.558299	−	0.829640i	$-0.688546\pi$
$338$	−10.8798	+	7.89970i	−0.591785	+	0.429687i
$339$	19.7542	+	11.9568i	1.07290	+	0.649405i
$340$	0.977203	+	0.261841i	0.0529962	+	0.0142003i
$341$			8.54100i			0.462521i
$342$	8.97482	+	17.1462i	0.485303	+	0.927162i
$343$	9.10168	−	9.10168i	0.491444	−	0.491444i
$344$	−4.71595	+	17.6002i	−0.254267	+	0.948938i
$345$	−4.78300	+	16.4787i	−0.257508	+	0.887182i
$346$	−8.28553	+	2.22010i	−0.445433	+	0.119353i
$347$	21.4908	+	12.4077i	1.15369	+	0.666082i	0.949783	−	0.312909i	$-0.101303\pi$
$347$	21.4908	+	12.4077i	1.15369	+	0.666082i	0.203905	+	0.978991i	$0.434637\pi$
$348$	−9.66539	−	0.200028i	−0.518119	−	0.0107226i
$349$	−5.26839	+	19.6619i	−0.282011	+	1.05248i	0.668986	+	0.743275i	$0.266729\pi$
$349$	−5.26839	+	19.6619i	−0.282011	+	1.05248i	−0.950996	+	0.309203i	$0.899938\pi$
$350$	6.47886			0.346309
$351$	−17.2373	−	7.34000i	−0.920059	−	0.391780i
$352$	18.2503			0.972746
$353$	−0.140094	+	0.522838i	−0.00745645	+	0.0278279i	−0.969554	−	0.244878i	$-0.921252\pi$
$353$	−0.140094	+	0.522838i	−0.00745645	+	0.0278279i	0.962097	+	0.272706i	$0.0879187\pi$
$354$	11.9637	+	0.247592i	0.635862	+	0.0131594i
$355$	4.28540	+	2.47418i	0.227445	+	0.131316i
$356$	0.140890	−	0.0377514i	0.00746716	−	0.00200082i
$357$	1.16329	−	4.00782i	0.0615677	−	0.212117i
$358$	3.02811	−	11.3010i	0.160040	−	0.597279i
$359$	−19.0909	+	19.0909i	−1.00758	+	1.00758i	−0.00760632	+	0.999971i	$0.502421\pi$
$359$	−19.0909	+	19.0909i	−1.00758	+	1.00758i	−0.999971	+	0.00760632i	$0.997579\pi$
$360$	−9.08835	+	14.3369i	−0.478998	+	0.755621i
$361$		−	19.9047i		−	1.04762i
$362$	−5.84151	−	1.56523i	−0.307023	−	0.0822665i
$363$	−5.63126	−	3.40847i	−0.295564	−	0.178898i
$364$	−12.5248	+	5.97171i	−0.656475	+	0.313002i
$365$	12.4147	+	7.16765i	0.649817	+	0.375172i
$366$	−3.92148	+	0.964255i	−0.204979	+	0.0504024i
$367$	−12.2840	−	21.2764i	−0.641217	−	1.11062i	−0.985161	−	0.171631i	$-0.945096\pi$
$367$	−12.2840	−	21.2764i	−0.641217	−	1.11062i	0.343944	−	0.938990i	$-0.388237\pi$
$368$	−6.75938			−0.352357
$369$	−18.5824	+	4.16347i	−0.967359	+	0.216742i
$370$	8.35337	−	8.35337i	0.434271	−	0.434271i
$371$	6.75517	+	1.81004i	0.350711	+	0.0939727i
$372$	−0.997193	+	3.43559i	−0.0517021	+	0.178127i
$373$	−17.9289	+	31.0537i	−0.928322	+	1.60790i	−0.142193	+	0.989839i	$0.545415\pi$
$373$	−17.9289	+	31.0537i	−0.928322	+	1.60790i	−0.786129	+	0.618062i	$0.787918\pi$
$374$	1.15878	−	2.00706i	0.0599189	−	0.103783i
$375$	15.2006	−	14.5842i	0.784957	−	0.753126i
$376$	−16.7312	+	9.65978i	−0.862847	+	0.498165i
$377$	21.2701	−	3.93889i	1.09546	−	0.202863i
$378$	18.5258	+	12.2883i	0.952863	+	0.632044i
$379$	4.51433	−	4.51433i	0.231886	−	0.231886i	−0.581594	−	0.813479i	$-0.697571\pi$
$379$	4.51433	−	4.51433i	0.231886	−	0.231886i	0.813479	+	0.581594i	$0.197571\pi$
$380$	9.38224	−	5.41684i	0.481299	−	0.277878i
$381$	0.112835	−	5.45219i	0.00578070	−	0.279324i
$382$	−2.78911	−	10.4091i	−0.142703	−	0.532576i
$383$	−0.405052	+	0.108533i	−0.0206972	+	0.00554580i	−0.269153	−	0.963097i	$-0.586744\pi$
$383$	−0.405052	+	0.108533i	−0.0206972	+	0.00554580i	0.248456	+	0.968643i	$0.420077\pi$
$384$	2.95809	+	0.858597i	0.150954	+	0.0438151i
$385$	7.68990	−	28.6991i	0.391914	−	1.46264i
$386$			4.46860i			0.227446i
$387$	15.9798	−	8.36428i	0.812299	−	0.425180i
$388$	−7.40168	−	7.40168i	−0.375763	−	0.375763i
$389$	13.7379	+	23.7947i	0.696539	+	1.20644i	0.969659	+	0.244460i	$0.0786108\pi$
$389$	13.7379	+	23.7947i	0.696539	+	1.20644i	−0.273121	+	0.961980i	$0.588056\pi$
$390$	4.26130	−	11.2807i	0.215779	−	0.571220i
$391$	1.54533	−	2.67658i	0.0781505	−	0.135361i
$392$	29.6011	−	7.93159i	1.49508	−	0.400606i
$393$	−18.8756	−	11.4250i	−0.952147	−	0.576313i
$394$	16.8299	−	9.71675i	0.847878	−	0.489523i
$395$	−2.92161	−	2.92161i	−0.147002	−	0.147002i
$396$	−7.27171	−	7.89995i	−0.365417	−	0.396987i
$397$	14.8082	+	14.8082i	0.743200	+	0.743200i	0.973192	−	0.229992i	$-0.0738701\pi$
$397$	14.8082	+	14.8082i	0.743200	+	0.743200i	−0.229992	+	0.973192i	$0.573870\pi$
$398$	−1.03819	−	0.278183i	−0.0520399	−	0.0139441i
$399$	−21.5393	−	39.1565i	−1.07831	−	1.96028i
$400$	1.67063	+	0.964536i	0.0835313	+	0.0482268i
$401$	3.84739	+	14.3586i	0.192129	+	0.717036i	0.992991	+	0.118187i	$0.0377084\pi$
$401$	3.84739	+	14.3586i	0.192129	+	0.717036i	−0.800862	+	0.598849i	$0.795625\pi$
$402$	4.11188	+	0.0850967i	0.205082	+	0.00424424i
$403$	0.629232	−	7.97991i	0.0313443	−	0.397508i
$404$			6.86214i			0.341404i
$405$	16.5343	−	2.99218i	0.821598	−	0.148683i
$406$	−25.6680			−1.27388
$407$	11.7683	+	20.3833i	0.583334	+	1.01036i
$408$	2.20626	−	2.11679i	0.109226	−	0.104797i
$409$	6.67267	+	24.9027i	0.329942	+	1.23136i	0.909249	+	0.416252i	$0.136657\pi$
$409$	6.67267	+	24.9027i	0.329942	+	1.23136i	−0.579307	+	0.815110i	$0.696677\pi$
$410$	−3.17235	−	11.8394i	−0.156671	−	0.584705i
$411$	17.2012	+	4.99273i	0.848475	+	0.246273i
$412$	−5.39342	−	9.34168i	−0.265715	−	0.460231i
$413$	−27.6322			−1.35969
$414$	11.1501	+	12.1134i	0.547997	+	0.595341i
$415$			21.2992i			1.04554i
$416$	−17.0514	−	1.34454i	−0.836014	−	0.0659214i
$417$	−15.2674	+	25.2239i	−0.747650	+	1.23522i
$418$	−6.42334	−	23.9722i	−0.314176	−	1.17252i
$419$	−30.4159	−	17.5606i	−1.48592	−	0.857894i	−0.486044	−	0.873934i	$-0.661561\pi$
$419$	−30.4159	−	17.5606i	−1.48592	−	0.857894i	−0.999871	+	0.0160405i	$0.994894\pi$
$420$	6.44396	−	10.6463i	0.314433	−	0.519486i
$421$	−12.3529	−	3.30996i	−0.602045	−	0.161318i	−0.0550929	−	0.998481i	$-0.517545\pi$
$421$	−12.3529	−	3.30996i	−0.602045	−	0.161318i	−0.546952	+	0.837164i	$0.684212\pi$
$422$	−17.8234	−	17.8234i	−0.867627	−	0.867627i
$423$	18.2517	+	5.70964i	0.887427	+	0.277612i
$424$	3.62304	+	3.62304i	0.175951	+	0.175951i
$425$	−0.763875	+	0.441024i	−0.0370534	+	0.0213928i
$426$	4.16009	−	2.28839i	0.201557	−	0.110873i
$427$	9.00741	−	2.41353i	0.435899	−	0.116799i
$428$	6.09117	−	10.5502i	0.294428	−	0.509964i
$429$	19.5120	+	14.0178i	0.942047	+	0.676784i
$430$	5.80457	+	10.0538i	0.279921	+	0.484838i
$431$	−23.5930	−	23.5930i	−1.13643	−	1.13643i	−0.989084	−	0.147349i	$-0.952926\pi$
$431$	−23.5930	−	23.5930i	−1.13643	−	1.13643i	−0.147349	−	0.989084i	$-0.547074\pi$
$432$	2.94760	+	5.92666i	0.141816	+	0.285147i
$433$			10.2411i			0.492156i	0.969250	+	0.246078i	$0.0791419\pi$
$433$			10.2411i			0.492156i	−0.969250	+	0.246078i	$0.920858\pi$
$434$	−2.45834	+	9.17463i	−0.118004	+	0.440397i
$435$	−13.9994	+	13.4317i	−0.671221	+	0.644002i
$436$	5.13390	−	1.37562i	0.245869	−	0.0658804i
$437$	−8.56606	−	31.9690i	−0.409770	−	1.52928i
$438$	12.0517	−	6.62943i	0.575852	−	0.316766i
$439$	15.7968	−	9.12026i	0.753938	−	0.435286i	−0.0731771	−	0.997319i	$-0.523314\pi$
$439$	15.7968	−	9.12026i	0.753938	−	0.435286i	0.827115	+	0.562033i	$0.189980\pi$
$440$	15.3924	−	15.3924i	0.733802	−	0.733802i
$441$	−25.6208	−	16.2414i	−1.22004	−	0.773399i
$442$	−1.23052	+	1.78984i	−0.0585297	+	0.0851340i
$443$	−8.26190	+	4.77001i	−0.392535	+	0.226630i	−0.683258	−	0.730177i	$-0.739437\pi$
$443$	−8.26190	+	4.77001i	−0.392535	+	0.226630i	0.290723	+	0.956807i	$0.406104\pi$
$444$	2.35394	+	9.57312i	0.111713	+	0.454320i
$445$	0.146358	−	0.253500i	0.00693803	−	0.0120170i
$446$	9.05350	−	15.6811i	0.428696	−	0.742523i
$447$	4.21874	−	1.03735i	0.199539	−	0.0490648i
$448$	29.7842	+	7.98064i	1.40717	+	0.377050i
$449$	−3.01171	+	3.01171i	−0.142132	+	0.142132i	−0.774592	−	0.632461i	$-0.782045\pi$
$449$	−3.01171	+	3.01171i	−0.142132	+	0.142132i	0.632461	+	0.774592i	$0.282045\pi$
$450$	−1.02729	−	4.58498i	−0.0484268	−	0.216138i
$451$	24.4204			1.14991
$452$	−6.20133	−	10.7410i	−0.291686	−	0.505215i
$453$	−3.29237	+	11.3431i	−0.154689	+	0.532944i
$454$	4.46739	+	2.57925i	0.209665	+	0.121050i
$455$	−9.29904	+	26.2472i	−0.435946	+	1.23049i
$456$	0.677459	−	32.7349i	0.0317249	−	1.53295i
$457$	26.3464	+	7.05949i	1.23243	+	0.330229i	0.815526	−	0.578721i	$-0.196448\pi$
$457$	26.3464	+	7.05949i	1.23243	+	0.330229i	0.416906	+	0.908950i	$0.363115\pi$
$458$			16.5069i			0.771318i
$459$	−3.02072	−	0.187759i	−0.140995	−	0.00876384i
$460$	6.51693	−	6.51693i	0.303854	−	0.303854i
$461$	7.17460	−	26.7760i	0.334154	−	1.24708i	−0.570629	−	0.821208i	$-0.693301\pi$
$461$	7.17460	−	26.7760i	0.334154	−	1.24708i	0.904783	−	0.425873i	$-0.140033\pi$
$462$	−19.7369	−	20.5711i	−0.918245	−	0.957055i
$463$	23.1664	−	6.20741i	1.07663	−	0.288483i	0.323416	−	0.946257i	$-0.395169\pi$
$463$	23.1664	−	6.20741i	1.07663	−	0.288483i	0.753215	+	0.657774i	$0.228502\pi$
$464$	−6.61870	−	3.82131i	−0.307266	−	0.177400i
$465$	3.46018	+	6.29029i	0.160462	+	0.291705i
$466$	1.41611	−	5.28501i	0.0656002	−	0.244823i
$467$	36.2129			1.67573			0.837866	−	0.545875i	$-0.183803\pi$
$467$	36.2129			1.67573			0.837866	+	0.545875i	$0.183803\pi$
$468$	6.21200	+	7.91669i	0.287150	+	0.365949i
$469$	−9.49713			−0.438536
$470$	−3.18581	+	11.8896i	−0.146951	+	0.548427i
$471$	3.76105	−	6.21376i	0.173300	−	0.286315i
$472$	−17.5324	−	10.1224i	−0.806996	−	0.465919i
$473$	−22.3415	+	5.98638i	−1.02726	+	0.275254i
$474$	−3.84977	+	0.946622i	−0.176826	+	0.0434798i
$475$	−2.44469	+	9.12369i	−0.112170	+	0.418624i
$476$	−1.58500	+	1.58500i	−0.0726484	+	0.0726484i
$477$	0.209838	−	5.06752i	0.00960782	−	0.232026i
$478$			8.40569i			0.384468i
$479$	11.2114	+	3.00409i	0.512263	+	0.137260i	0.505685	−	0.862718i	$-0.331240\pi$
$479$	11.2114	+	3.00409i	0.512263	+	0.137260i	0.00657751	+	0.999978i	$0.497906\pi$
$480$	13.4410	−	7.39368i	0.613497	−	0.337474i
$481$	−9.49353	−	19.9113i	−0.432868	−	0.907875i
$482$	5.49163	+	3.17059i	0.250137	+	0.144417i
$483$	−26.3209	−	27.4333i	−1.19764	−	1.24826i
$484$	1.76779	+	3.06190i	0.0803539	+	0.139177i
$485$	−21.0066			−0.953858
$486$	5.75882	−	15.0588i	0.261225	−	0.683082i
$487$	−19.9178	+	19.9178i	−0.902563	+	0.902563i	−0.995657	−	0.0930945i	$-0.970324\pi$
$487$	−19.9178	+	19.9178i	−0.902563	+	0.902563i	0.0930945	+	0.995657i	$0.470324\pi$
$488$	6.59927	+	1.76827i	0.298735	+	0.0800458i
$489$	8.58141	+	8.94411i	0.388065	+	0.404467i
$490$	9.76250	−	16.9091i	0.441025	−	0.763877i
$491$	18.2158	−	31.5507i	0.822069	−	1.42386i	−0.0820707	−	0.996627i	$-0.526153\pi$
$491$	18.2158	−	31.5507i	0.822069	−	1.42386i	0.904139	−	0.427238i	$-0.140513\pi$
$492$	9.82301	+	2.85117i	0.442856	+	0.128541i
$493$	3.02633	−	1.74725i	0.136299	−	0.0786923i
$494$	4.23529	+	22.8706i	0.190555	+	1.02900i
$495$	−21.5292	−	0.891489i	−0.967665	−	0.0400694i
$496$	−1.99977	+	1.99977i	−0.0897924	+	0.0897924i
$497$	−9.49501	+	5.48195i	−0.425909	+	0.245899i
$498$	17.4834	+	10.5823i	0.783451	+	0.474206i
$499$	7.32032	+	27.3198i	0.327702	+	1.22300i	0.911567	+	0.411151i	$0.134873\pi$
$499$	7.32032	+	27.3198i	0.327702	+	1.22300i	−0.583865	+	0.811851i	$0.698460\pi$
$500$	−10.9292	+	2.92848i	−0.488770	+	0.130965i
$501$	−6.19673	−	25.2012i	−0.276849	−	1.12591i
$502$	−3.55790	+	13.2783i	−0.158797	+	0.592637i
$503$			25.6015i			1.14151i	0.821119	+	0.570757i	$0.193350\pi$
$503$			25.6015i			1.14151i	−0.821119	+	0.570757i	$0.806650\pi$
$504$	−17.4416	−	33.3218i	−0.776909	−	1.48427i
$505$	9.73764	+	9.73764i	0.433319	+	0.433319i
$506$	−10.5564	−	18.2843i	−0.469291	−	0.812835i
$507$	−17.1975	−	14.5344i	−0.763766	−	0.645494i
$508$	−1.46456	+	2.53668i	−0.0649791	+	0.112547i
$509$	−2.53192	+	0.678425i	−0.112225	+	0.0300707i	−0.314495	−	0.949259i	$-0.601835\pi$
$509$	−2.53192	+	0.678425i	−0.112225	+	0.0300707i	0.202269	+	0.979330i	$0.435168\pi$
$510$	0.0403065	−	1.94761i	0.00178480	−	0.0862418i
$511$	−27.5069	+	15.8811i	−1.21683	+	0.702538i
$512$	9.73294	+	9.73294i	0.430139	+	0.430139i
$513$	−24.2951	+	21.4517i	−1.07266	+	0.947114i
$514$	16.0782	+	16.0782i	0.709181	+	0.709181i
$515$	−20.9097	−	5.60274i	−0.921391	−	0.246886i
$516$	−9.68571	−	0.200449i	−0.426389	−	0.00882426i
$517$	−21.2384	−	12.2620i	−0.934065	−	0.539283i
$518$	6.77449	+	25.2828i	0.297654	+	1.11086i
$519$	−6.92363	−	12.5865i	−0.303914	−	0.552487i
$520$	−15.5152	+	13.2472i	−0.680385	+	0.580928i
$521$			17.0961i			0.748995i	0.927228	+	0.374497i	$0.122185\pi$
$521$			17.0961i			0.748995i	−0.927228	+	0.374497i	$0.877815\pi$
$522$	4.06992	+	18.1648i	0.178135	+	0.795053i
$523$	27.8541			1.21797			0.608987	−	0.793180i	$-0.291576\pi$
$523$	27.8541			1.21797			0.608987	+	0.793180i	$0.291576\pi$
$524$	5.92550	+	10.2633i	0.258857	+	0.448353i
$525$	2.59075	+	10.5362i	0.113070	+	0.459838i
$526$	−0.922108	−	3.44135i	−0.0402058	−	0.150050i
$527$	−0.334684	−	1.24906i	−0.0145791	−	0.0544098i
$528$	−2.02681	−	8.24276i	−0.0882058	−	0.358720i
$529$	−2.57789	−	4.46504i	−0.112082	−	0.194132i
$530$	3.26449			0.141800
$531$	4.38136	+	19.5549i	0.190135	+	0.848609i
$532$			24.0038i			1.04070i
$533$	−22.8161	−	1.79910i	−0.988275	−	0.0779275i
$534$	−0.135368	−	0.246087i	−0.00585794	−	0.0106492i
$535$	−6.32757	−	23.6148i	−0.273565	−	1.02096i
$536$	−6.02586	−	3.47903i	−0.260277	−	0.150271i
$537$	19.5892	+	0.405404i	0.845334	+	0.0174945i
$538$	11.4678	+	3.07279i	0.494413	+	0.132478i
$539$	27.5070	+	27.5070i	1.18481	+	1.18481i
$540$	−8.55596	−	2.87221i	−0.368190	−	0.123600i
$541$	−1.32533	−	1.32533i	−0.0569802	−	0.0569802i	0.678043	−	0.735023i	$-0.262829\pi$
$541$	−1.32533	−	1.32533i	−0.0569802	−	0.0569802i	−0.735023	+	0.678043i	$0.762829\pi$
$542$	16.0327	−	9.25646i	0.688662	−	0.397599i
$543$	0.209553	−	10.1256i	0.00899278	−	0.434532i
$544$	−2.66898	+	0.715150i	−0.114431	+	0.0306618i
$545$	5.33314	−	9.23727i	0.228447	−	0.395681i
$546$	16.9248	+	20.6738i	0.724316	+	0.884756i
$547$	−13.9248	−	24.1185i	−0.595383	−	1.03123i	−0.993493	−	0.113895i	$-0.963667\pi$
$547$	−13.9248	−	24.1185i	−0.595383	−	1.03123i	0.398110	−	0.917338i	$-0.369666\pi$
$548$	−6.80269	−	6.80269i	−0.290597	−	0.290597i
$549$	−3.13623	−	5.99171i	−0.133851	−	0.255720i
$550$			6.02544i			0.256926i
$551$	9.68538	−	36.1463i	0.412611	−	1.53989i
$552$	−6.65090	−	27.0482i	−0.283081	−	1.15125i
$553$	8.84270	−	2.36940i	0.376030	−	0.100757i
$554$	−2.67074	−	9.96732i	−0.113469	−	0.423471i
$555$	16.9250	+	10.2443i	0.718425	+	0.434846i
$556$	13.7150	−	7.91838i	0.581647	−	0.335814i
$557$	−19.8794	+	19.8794i	−0.842316	+	0.842316i	−0.989160	−	0.146844i	$-0.953089\pi$
$557$	−19.8794	+	19.8794i	−0.842316	+	0.842316i	0.146844	+	0.989160i	$0.453089\pi$
$558$	6.88253	+	0.284994i	0.291361	+	0.0120648i
$559$	21.3148	−	3.94717i	0.901520	−	0.166948i
$560$	8.52004	−	4.91905i	0.360037	−	0.207868i
$561$	3.72734	+	1.08188i	0.157368	+	0.0456768i
$562$	−4.56726	+	7.91073i	−0.192658	+	0.333694i
$563$	11.1038	−	19.2324i	0.467971	−	0.810550i	−0.531359	−	0.847147i	$-0.678318\pi$
$563$	11.1038	−	19.2324i	0.467971	−	0.810550i	0.999330	+	0.0365971i	$0.0116518\pi$
$564$	−7.11145	−	7.41202i	−0.299446	−	0.312102i
$565$	−24.0419	−	6.44200i	−1.01145	−	0.271017i
$566$	−17.7346	+	17.7346i	−0.745440	+	0.745440i
$567$	−12.5758	+	35.0413i	−0.528135	+	1.47160i
$568$	−8.03269			−0.337044
$569$	18.3923	+	31.8565i	0.771047	+	1.33549i	0.936990	+	0.349357i	$0.113600\pi$
$569$	18.3923	+	31.8565i	0.771047	+	1.33549i	−0.165943	+	0.986135i	$0.553067\pi$
$570$	−14.4424	−	15.0529i	−0.604927	−	0.630495i
$571$	9.94938	+	5.74427i	0.416368	+	0.240390i	0.693522	−	0.720435i	$-0.256058\pi$
$571$	9.94938	+	5.74427i	0.416368	+	0.240390i	−0.277154	+	0.960826i	$0.589391\pi$
$572$	−5.55378	−	11.6482i	−0.232215	−	0.487037i
$573$	15.8125	−	8.69815i	0.660575	−	0.363370i
$574$	26.2321	+	7.02886i	1.09491	+	0.293379i
$575$			8.03543i			0.335101i
$576$	0.925195	−	22.3432i	0.0385498	−	0.930966i
$577$	−0.440859	+	0.440859i	−0.0183532	+	0.0183532i	−0.716224	−	0.697871i	$-0.754131\pi$
$577$	−0.440859	+	0.440859i	−0.0183532	+	0.0183532i	0.697871	+	0.716224i	$0.254131\pi$
$578$	4.45982	−	16.6443i	0.185504	−	0.692311i
$579$	−7.26704	+	1.78690i	−0.302008	+	0.0742608i
$580$	10.0656	−	2.69706i	0.417949	−	0.111989i
$581$	−40.8694	−	23.5960i	−1.69555	−	0.978926i
$582$	−10.4369	+	17.2432i	−0.432624	+	0.714753i
$583$	−1.68337	+	6.28242i	−0.0697180	+	0.260191i
$584$	−23.2705			−0.962942
$585$	20.0492	+	2.41902i	0.828932	+	0.100014i
$586$	26.1059			1.07842
$587$	−3.63747	+	13.5752i	−0.150134	+	0.560309i	0.849339	+	0.527848i	$0.177001\pi$
$587$	−3.63747	+	13.5752i	−0.150134	+	0.560309i	−0.999473	+	0.0324605i	$0.989666\pi$
$588$	7.85306	+	14.2761i	0.323855	+	0.588738i
$589$	−11.9923	−	6.92378i	−0.494136	−	0.285289i
$590$	−12.4590	+	3.33837i	−0.512928	+	0.137439i
$591$	22.5317	+	23.4840i	0.926831	+	0.966004i
$592$	−2.01710	+	7.52791i	−0.0829022	+	0.309395i
$593$	8.84434	−	8.84434i	0.363194	−	0.363194i	−0.501794	−	0.864987i	$-0.667326\pi$
$593$	8.84434	−	8.84434i	0.363194	−	0.363194i	0.864987	+	0.501794i	$0.167326\pi$
$594$	−11.4284	+	17.2293i	−0.468911	+	0.706925i
$595$			4.49836i			0.184415i
$596$	−2.25396	−	0.603946i	−0.0923257	−	0.0247386i
$597$	0.0372432	−	1.79960i	0.00152426	−	0.0736526i
$598$	8.51590	+	17.8608i	0.348241	+	0.730383i
$599$	−12.8510	−	7.41956i	−0.525080	−	0.303155i	0.213931	−	0.976849i	$-0.431373\pi$
$599$	−12.8510	−	7.41956i	−0.525080	−	0.303155i	−0.739010	+	0.673694i	$0.764707\pi$
$600$	−2.21586	+	7.63421i	−0.0904621	+	0.311665i
$601$	22.5672	+	39.0875i	0.920535	+	1.59441i	0.798588	+	0.601878i	$0.205580\pi$
$601$	22.5672	+	39.0875i	0.920535	+	1.59441i	0.121947	+	0.992537i	$0.461086\pi$
$602$	−25.7220			−1.04835
$603$	1.50586	+	6.72096i	0.0613235	+	0.273699i
$604$	4.48592	−	4.48592i	0.182529	−	0.182529i
$605$	6.85351	+	1.83639i	0.278635	+	0.0746600i
$606$	12.8312	−	3.15506i	0.521231	−	0.128166i
$607$	−16.1981	+	28.0560i	−0.657462	+	1.13876i	0.323809	+	0.946123i	$0.395037\pi$
$607$	−16.1981	+	28.0560i	−0.657462	+	1.13876i	−0.981271	+	0.192635i	$0.938297\pi$
$608$	−14.7947	+	25.6251i	−0.600004	+	1.03924i
$609$	−10.2641	−	41.7425i	−0.415921	−	1.69149i
$610$	3.76973	−	2.17645i	0.152632	−	0.0881220i
$611$	18.9398	+	13.0211i	0.766223	+	0.526779i
$612$	1.37300	+	0.870362i	0.0555001	+	0.0351823i
$613$	6.23484	−	6.23484i	0.251823	−	0.251823i	−0.569895	−	0.821718i	$-0.693016\pi$
$613$	6.23484	−	6.23484i	0.251823	−	0.251823i	0.821718	+	0.569895i	$0.193016\pi$
$614$	4.31299	−	2.49011i	0.174058	−	0.100492i
$615$	17.9852	−	9.89333i	0.725232	−	0.398937i
$616$	12.4830	+	46.5874i	0.502956	+	1.87706i
$617$	38.9743	−	10.4431i	1.56905	−	0.420425i	0.633533	−	0.773715i	$-0.281604\pi$
$617$	38.9743	−	10.4431i	1.56905	−	0.420425i	0.935514	+	0.353290i	$0.114937\pi$
$618$	−14.9878	+	14.3800i	−0.602897	+	0.578449i
$619$	−4.13024	+	15.4143i	−0.166008	+	0.619552i	0.831901	+	0.554924i	$0.187253\pi$
$619$	−4.13024	+	15.4143i	−0.166008	+	0.619552i	−0.997909	+	0.0646279i	$0.979414\pi$
$620$		−	3.85609i		−	0.154864i
$621$	−15.2407	+	22.9767i	−0.611588	+	0.922022i
$622$	−18.3526	−	18.3526i	−0.735874	−	0.735874i
$623$	0.324280	+	0.561670i	0.0129920	+	0.0225028i
$624$	1.28641	+	7.85058i	0.0514975	+	0.314275i
$625$	−7.56751	+	13.1073i	−0.302700	+	0.524292i
$626$	−15.5721	+	4.17254i	−0.622387	+	0.166768i
$627$	36.4162	−	20.0319i	1.45432	−	0.799997i
$628$	−3.37862	+	1.95065i	−0.134822	+	0.0778393i
$629$	−2.51976	−	2.51976i	−0.100469	−	0.100469i
$630$	−22.8698	−	7.15432i	−0.911155	−	0.285035i
$631$	−0.416393	−	0.416393i	−0.0165763	−	0.0165763i	0.698770	−	0.715346i	$-0.253731\pi$
$631$	−0.416393	−	0.416393i	−0.0165763	−	0.0165763i	−0.715346	+	0.698770i	$0.753731\pi$
$632$	6.47860	+	1.73594i	0.257705	+	0.0690518i
$633$	21.8580	−	36.1123i	0.868777	−	1.43534i
$634$	29.3348	+	16.9364i	1.16503	+	0.672632i
$635$	1.52139	+	5.67792i	0.0603747	+	0.225321i
$636$	−1.41062	+	2.33054i	−0.0559349	+	0.0924120i
$637$	−23.6735	−	27.7265i	−0.937977	−	1.09856i
$638$		−	23.8717i		−	0.945088i
$639$	5.38501	+	5.85025i	0.213028	+	0.231432i
$640$	−3.32014			−0.131240
$641$	1.11318	+	1.92808i	0.0439678	+	0.0761545i	0.887172	−	0.461439i	$-0.152667\pi$
$641$	1.11318	+	1.92808i	0.0439678	+	0.0761545i	−0.843204	+	0.537594i	$0.819333\pi$
$642$	−22.5280	−	6.53883i	−0.889107	−	0.258067i
$643$	−10.9485	−	40.8604i	−0.431767	−	1.61138i	−0.748687	−	0.662923i	$-0.769316\pi$
$643$	−10.9485	−	40.8604i	−0.431767	−	1.61138i	0.316921	−	0.948452i	$-0.397351\pi$
$644$	5.28516	+	19.7245i	0.208265	+	0.777254i
$645$	−14.0288	+	13.4600i	−0.552385	+	0.529985i
$646$	1.87873	+	3.25406i	0.0739177	+	0.128029i
$647$	−39.4845			−1.55230			−0.776148	−	0.630551i	$-0.782829\pi$
$647$	−39.4845			−1.55230			−0.776148	+	0.630551i	$0.782829\pi$
$648$	−20.8158	+	17.6266i	−0.817720	+	0.692439i
$649$		−	25.6984i		−	1.00875i
$650$	0.443906	−	5.62961i	0.0174114	−	0.220811i
$651$	−15.9032	−	0.329123i	−0.623297	−	0.0128993i
$652$	−1.72313	−	6.43079i	−0.0674828	−	0.251849i
$653$	24.0076	+	13.8608i	0.939489	+	0.542414i	0.889800	−	0.456350i	$-0.150844\pi$
$653$	24.0076	+	13.8608i	0.939489	+	0.542414i	0.0496892	+	0.998765i	$0.484177\pi$
$654$	−4.93267	−	8.96715i	−0.192883	−	0.350643i
$655$	22.9725	+	6.15546i	0.897610	+	0.240514i
$656$	5.71773	+	5.71773i	0.223240	+	0.223240i
$657$	15.6003	+	16.9481i	0.608625	+	0.661207i
$658$	−19.2847	−	19.2847i	−0.751796	−	0.751796i
$659$	15.0701	−	8.70074i	0.587048	−	0.338933i	−0.176881	−	0.984232i	$-0.556601\pi$
$659$	15.0701	−	8.70074i	0.587048	−	0.338933i	0.763930	+	0.645300i	$0.223267\pi$
$660$	9.90122	+	5.99299i	0.385405	+	0.233277i
$661$	10.9492	−	2.93383i	0.425875	−	0.114113i	−0.0395143	−	0.999219i	$-0.512581\pi$
$661$	10.9492	−	2.93383i	0.425875	−	0.114113i	0.465389	+	0.885106i	$0.345914\pi$
$662$	2.98528	−	5.17066i	0.116026	−	0.200963i
$663$	−3.40277	−	1.28540i	−0.132153	−	0.0499209i
$664$	−17.2876	−	29.9429i	−0.670888	−	1.16201i
$665$	34.0623	+	34.0623i	1.32088	+	1.32088i
$666$	16.8180	−	8.80303i	0.651685	−	0.341111i
$667$		−	31.8349i		−	1.23265i
$668$	−3.60775	+	13.4643i	−0.139588	+	0.520950i
$669$	29.1217	+	8.45268i	1.12591	+	0.326800i
$670$	−4.28212	+	1.14739i	−0.165433	+	0.0443276i
$671$	2.24462	+	8.37704i	0.0866526	+	0.323392i
$672$	−0.703267	+	33.9819i	−0.0271291	+	1.31088i
$673$	0.0645645	−	0.0372764i	0.00248878	−	0.00143690i	−0.498755	−	0.866743i	$-0.666209\pi$
$673$	0.0645645	−	0.0372764i	0.00248878	−	0.00143690i	0.501244	+	0.865306i	$0.332876\pi$
$674$	24.1206	−	24.1206i	0.929091	−	0.929091i
$675$	7.04552	−	3.50405i	0.271182	−	0.134871i
$676$	4.33079	+	11.2922i	0.166569	+	0.434314i
$677$	−11.3297	+	6.54119i	−0.435435	+	0.251398i	−0.701659	−	0.712513i	$-0.747557\pi$
$677$	−11.3297	+	6.54119i	−0.435435	+	0.251398i	0.266224	+	0.963911i	$0.414224\pi$
$678$	−17.2329	+	16.5341i	−0.661825	+	0.634987i
$679$	23.2717	−	40.3078i	0.893087	−	1.54687i
$680$	−1.64786	+	2.85418i	−0.0631926	+	0.109453i
$681$	−2.40808	+	8.29646i	−0.0922779	+	0.317921i
$682$	−8.53256	−	2.28629i	−0.326729	−	0.0875467i
$683$	18.4883	−	18.4883i	0.707435	−	0.707435i	−0.258560	−	0.965995i	$-0.583248\pi$
$683$	18.4883	−	18.4883i	0.707435	−	0.707435i	0.965995	+	0.258560i	$0.0832480\pi$
$684$	16.9871	−	3.80604i	0.649517	−	0.145528i
$685$	−19.3066			−0.737667
$686$	6.65631	+	11.5291i	0.254139	+	0.440182i
$687$	−26.8443	+	6.60076i	−1.02418	+	0.251835i
$688$	−6.63262	−	3.82934i	−0.252866	−	0.145992i
$689$	2.03562	−	5.74568i	0.0775509	−	0.218893i
$690$	−15.1821	−	9.18936i	−0.577971	−	0.349833i
$691$	−24.2455	−	6.49655i	−0.922341	−	0.247140i	−0.233755	−	0.972295i	$-0.575101\pi$
$691$	−24.2455	−	6.49655i	−0.922341	−	0.247140i	−0.688586	+	0.725155i	$0.741768\pi$
$692$			7.71582i			0.293311i
$693$	25.5613	−	40.3231i	0.970995	−	1.53175i
$694$	−18.1482	+	18.1482i	−0.688898	+	0.688898i
$695$	8.22568	−	30.6987i	0.312018	−	1.16447i
$696$	8.77882	−	30.2453i	0.332760	−	1.14644i
$697$	−3.57130	+	0.956926i	−0.135273	+	0.0362462i
$698$	−18.2322	−	10.5264i	−0.690100	−	0.398429i
$699$	9.16099	+	0.189590i	0.346500	+	0.00717094i
$700$	1.50834	−	5.62921i	0.0570100	−	0.212764i
$701$	−29.8002			−1.12554			−0.562770	−	0.826614i	$-0.690264\pi$
$701$	−29.8002			−1.12554			−0.562770	+	0.826614i	$0.690264\pi$
$702$	11.9469	−	15.2555i	0.450907	−	0.575780i
$703$	−38.1601			−1.43923
$704$	−7.42213	+	27.6998i	−0.279732	+	1.04397i
$705$	−20.6094	−	0.426518i	−0.776194	−	0.0160636i
$706$	−0.484821	−	0.279911i	−0.0182465	−	0.0105346i
$707$	−29.4725	+	7.89712i	−1.10843	+	0.297002i
$708$	3.00039	−	10.3371i	0.112761	−	0.388492i
$709$	4.61268	−	17.2147i	0.173233	−	0.646513i	−0.823613	−	0.567152i	$-0.808045\pi$
$709$	4.61268	−	17.2147i	0.173233	−	0.646513i	0.996846	−	0.0793614i	$-0.0252881\pi$
$710$	−3.61887	+	3.61887i	−0.135814	+	0.135814i
$711$	−3.07888	−	5.88215i	−0.115467	−	0.220598i
$712$			0.475167i			0.0178076i
$713$	−11.3789	−	3.04896i	−0.426143	−	0.114185i
$714$	3.69247	+	2.23497i	0.138187	+	0.0836417i
$715$	−24.4103	−	8.64826i	−0.912895	−	0.323426i
$716$	−9.11404	−	5.26200i	−0.340608	−	0.196650i
$717$	−13.6697	+	3.36125i	−0.510505	+	0.125528i
$718$	−13.9617	−	24.1823i	−0.521045	−	0.902477i
$719$	21.4168			0.798713			0.399356	−	0.916796i	$-0.369234\pi$
$719$	21.4168			0.798713			0.399356	+	0.916796i	$0.369234\pi$
$720$	−4.83207	−	5.24953i	−0.180081	−	0.195638i
$721$	33.9151	−	33.9151i	1.26306	−	1.26306i
$722$	19.8851	+	5.32819i	0.740045	+	0.198295i
$723$	−2.96018	+	10.1986i	−0.110090	+	0.379290i
$724$	−2.71992	+	4.71105i	−0.101085	+	0.175085i
$725$	−4.54271	+	7.86820i	−0.168712	+	0.292218i
$726$	4.91251	−	4.71330i	0.182320	−	0.174927i
$727$	24.4305	−	14.1050i	0.906079	−	0.523125i	0.0269114	−	0.999638i	$-0.491433\pi$
$727$	24.4305	−	14.1050i	0.906079	−	0.523125i	0.879167	+	0.476513i	$0.158099\pi$
$728$	−8.23081	−	44.4465i	−0.305054	−	1.64730i
$729$	26.7922	+	3.34356i	0.992303	+	0.123835i
$730$	−10.4838	+	10.4838i	−0.388023	+	0.388023i
$731$	3.03269	−	1.75093i	0.112168	−	0.0647603i
$732$	−0.0751593	+	3.63170i	−0.00277797	+	0.134232i
$733$	−10.9998	−	41.0517i	−0.406286	−	1.51628i	−0.801672	−	0.597764i	$-0.796056\pi$
$733$	−10.9998	−	41.0517i	−0.406286	−	1.51628i	0.395386	−	0.918515i	$-0.370611\pi$
$734$	24.5436	−	6.57645i	0.905922	−	0.242741i
$735$	31.4022	+	9.11462i	1.15829	+	0.336198i
$736$	−6.51500	+	24.3143i	−0.240146	+	0.896237i
$737$		−	8.83248i		−	0.325349i
$738$	0.814855	−	19.6785i	0.0299952	−	0.724376i
$739$	−30.0670	−	30.0670i	−1.10603	−	1.10603i	−0.993667	−	0.112367i	$-0.964157\pi$
$739$	−30.0670	−	30.0670i	−1.10603	−	1.10603i	−0.112367	−	0.993667i	$-0.535843\pi$
$740$	−5.31315	−	9.20265i	−0.195315	−	0.338296i
$741$	−35.4996	+	16.0331i	−1.30411	+	0.588990i
$742$	−3.61651	+	6.26397i	−0.132766	+	0.229958i
$743$	35.5907	−	9.53650i	1.30570	−	0.349860i	0.462095	−	0.886831i	$-0.347098\pi$
$743$	35.5907	−	9.53650i	1.30570	−	0.349860i	0.843601	+	0.536970i	$0.180431\pi$
$744$	−9.96993	−	6.03458i	−0.365515	−	0.221238i
$745$	−4.05548	+	2.34143i	−0.148581	+	0.0857834i
$746$	−26.2238	−	26.2238i	−0.960120	−	0.960120i
$747$	−10.2182	+	32.6640i	−0.373865	+	1.19511i
$748$	−1.47408	−	1.47408i	−0.0538976	−	0.0538976i
$749$	52.3224	+	14.0198i	1.91182	+	0.512271i
$750$	10.5008	+	19.0896i	0.383437	+	0.697053i
$751$	4.86388	+	2.80816i	0.177486	+	0.102471i	0.586111	−	0.810231i	$-0.300658\pi$
$751$	4.86388	+	2.80816i	0.177486	+	0.102471i	−0.408625	+	0.912702i	$0.633992\pi$
$752$	−2.10172	−	7.84372i	−0.0766418	−	0.286031i
$753$	−23.0164	−	0.476332i	−0.838765	−	0.0173585i
$754$	−1.75867	+	22.3034i	−0.0640470	+	0.812244i
$755$		−	12.7314i		−	0.463343i
$756$	14.9898	−	13.2354i	0.545175	−	0.481368i
$757$	−1.31552			−0.0478135			−0.0239067	−	0.999714i	$-0.507610\pi$
$757$	−1.31552			−0.0478135			−0.0239067	+	0.999714i	$0.507610\pi$
$758$	3.30146	+	5.71829i	0.119914	+	0.207698i
$759$	25.5134	−	24.4788i	0.926079	−	0.888525i
$760$	9.13443	+	34.0902i	0.331341	+	1.23658i
$761$	5.27446	+	19.6846i	0.191199	+	0.713565i	0.993218	+	0.116266i	$0.0370926\pi$
$761$	5.27446	+	19.6846i	0.191199	+	0.713565i	−0.802019	+	0.597299i	$0.796241\pi$
$762$	5.41660	+	1.57219i	0.196223	+	0.0569544i
$763$	11.8164	+	20.4667i	0.427784	+	0.740944i
$764$	−9.69338			−0.350694
$765$	3.18342	−	0.713260i	0.115097	−	0.0257880i
$766$		−	0.433704i		−	0.0156704i
$767$	−1.89325	+	24.0102i	−0.0683613	+	0.866958i
$768$	−15.0204	+	24.8157i	−0.542002	+	0.895461i
$769$	3.16193	+	11.8005i	0.114022	+	0.425536i	0.999212	−	0.0396941i	$-0.0126383\pi$
$769$	3.16193	+	11.8005i	0.114022	+	0.425536i	−0.885190	+	0.465230i	$0.845972\pi$
$770$	26.6123	+	15.3646i	0.959040	+	0.553702i
$771$	−19.7178	+	32.5765i	−0.710120	+	1.17321i
$772$	3.88258	+	1.04033i	0.139737	+	0.0374425i
$773$	13.6325	+	13.6325i	0.490328	+	0.490328i	0.908409	−	0.418082i	$-0.137297\pi$
$773$	13.6325	+	13.6325i	0.490328	+	0.490328i	−0.418082	+	0.908409i	$0.637297\pi$
$774$	4.07847	+	18.2030i	0.146598	+	0.654294i
$775$	2.37729	+	2.37729i	0.0853949	+	0.0853949i
$776$	29.5315	−	17.0500i	1.06012	−	0.612060i
$777$	−38.4070	+	21.1270i	−1.37784	+	0.757927i
$778$	−27.4486	+	7.35484i	−0.984081	+	0.263684i
$779$	−19.7964	+	34.2884i	−0.709281	+	1.22851i
$780$	−8.80926	−	6.32873i	−0.315422	−	0.226605i
$781$	−5.09830	−	8.83051i	−0.182431	−	0.315981i
$782$	2.26028	+	2.26028i	0.0808274	+	0.0808274i
$783$	−27.9130	+	13.8824i	−0.997529	+	0.496117i
$784$			12.8809i			0.460031i
$785$	−2.02635	+	7.56244i	−0.0723236	+	0.269915i
$786$	16.4664	−	15.7986i	0.587336	−	0.563519i
$787$	−8.57064	+	2.29650i	−0.305510	+	0.0818612i	−0.408317	−	0.912840i	$-0.633884\pi$
$787$	−8.57064	+	2.29650i	−0.305510	+	0.0818612i	0.102807	+	0.994701i	$0.467218\pi$
$788$	−4.52431	−	16.8850i	−0.161172	−	0.601502i
$789$	5.22775	−	2.87569i	0.186113	−	0.102377i
$790$	3.70079	−	2.13665i	0.131668	−	0.0760188i
$791$	38.9954	−	38.9954i	1.38652	−	1.38652i
$792$	30.9898	−	16.2209i	1.10117	−	0.576386i
$793$	−1.48001	−	7.99209i	−0.0525567	−	0.283807i
$794$	−18.7574	+	10.8296i	−0.665677	+	0.384329i
$795$	1.30540	+	5.30886i	0.0462977	+	0.188286i
$796$	−0.483404	+	0.837280i	−0.0171338	+	0.0296766i
$797$	15.0420	−	26.0535i	0.532815	−	0.922862i	−0.466451	−	0.884547i	$-0.654468\pi$
$797$	15.0420	−	26.0535i	0.532815	−	0.922862i	0.999266	−	0.0383151i	$-0.0121991\pi$
$798$	44.8835	−	11.0364i	1.58886	−	0.390685i
$799$	3.58645	+	0.960988i	0.126880	+	0.0339973i
$800$	5.07978	−	5.07978i	0.179597	−	0.179597i
$801$	0.346067	−	0.318546i	0.0122277	−	0.0112553i
$802$	−15.3743			−0.542887
$803$	−14.7697	−	25.5818i	−0.521211	−	0.902764i
$804$	1.03122	−	3.55284i	0.0363685	−	0.125299i
$805$	35.4897	+	20.4900i	1.25085	+	0.722177i
$806$	7.80359	+	2.76471i	0.274870	+	0.0973826i
$807$	−0.411386	+	19.8782i	−0.0144815	+	0.699747i
$808$	−21.5930	−	5.78582i	−0.759638	−	0.203544i
$809$		−	6.00821i		−	0.211237i	−0.994407	−	0.105619i	$-0.966318\pi$
$809$		−	6.00821i		−	0.211237i	0.994407	−	0.105619i	$-0.0336823\pi$
$810$	−1.43676	+	17.3190i	−0.0504828	+	0.608527i
$811$	−23.4539	+	23.4539i	−0.823577	+	0.823577i	−0.986619	−	0.163042i	$-0.947869\pi$
$811$	−23.4539	+	23.4539i	−0.823577	+	0.823577i	0.163042	+	0.986619i	$0.447869\pi$
$812$	−5.97577	+	22.3019i	−0.209708	+	0.782642i
$813$	21.4644	+	22.3716i	0.752789	+	0.784606i
$814$	−23.5134	+	6.30039i	−0.824143	+	0.220829i
$815$	−11.5707	−	6.68037i	−0.405305	−	0.234003i
$816$	0.619404	+	1.12602i	0.0216835	+	0.0394186i
$817$	9.70574	−	36.2223i	0.339561	−	1.26726i
$818$	−26.6643			−0.932296
$819$	−26.8528	+	35.7909i	−0.938312	+	1.25064i
$820$	−11.0253			−0.385020
$821$	6.68517	−	24.9494i	0.233314	−	0.870740i	−0.745588	−	0.666408i	$-0.767831\pi$
$821$	6.68517	−	24.9494i	0.233314	−	0.870740i	0.978902	−	0.204332i	$-0.0655023\pi$
$822$	−9.59231	+	15.8478i	−0.334570	+	0.552755i
$823$	30.3848	+	17.5427i	1.05915	+	0.611500i	0.925197	−	0.379488i	$-0.123900\pi$
$823$	30.3848	+	17.5427i	1.05915	+	0.611500i	0.133952	+	0.990988i	$0.457233\pi$
$824$	33.9428	−	9.09494i	1.18245	−	0.316837i
$825$	−9.79885	+	2.40944i	−0.341152	+	0.0838860i
$826$	7.39672	−	27.6049i	0.257365	−	0.960498i
$827$	24.5496	−	24.5496i	0.853673	−	0.853673i	−0.136910	−	0.990583i	$-0.543717\pi$
$827$	24.5496	−	24.5496i	0.853673	−	0.853673i	0.990583	+	0.136910i	$0.0437172\pi$
$828$	13.1207	−	6.86774i	0.455975	−	0.238670i
$829$			17.7371i			0.616036i	0.951380	+	0.308018i	$0.0996658\pi$
$829$			17.7371i			0.616036i	−0.951380	+	0.308018i	$0.900334\pi$
$830$	−21.2782	−	5.70147i	−0.738577	−	0.197901i
$831$	15.1413	−	8.32898i	0.525247	−	0.288929i
$832$	8.97524	−	25.3333i	0.311160	−	0.878273i
$833$	−5.10057	−	2.94482i	−0.176724	−	0.102032i
$834$	−21.1121	−	22.0044i	−0.731052	−	0.761950i
$835$	13.9869	+	24.2259i	0.484035	+	0.838373i
$836$	−22.3239			−0.772088
$837$	2.28870	+	11.3067i	0.0791092	+	0.390815i
$838$	25.6852	−	25.6852i	0.887279	−	0.887279i
$839$	−34.6089	−	9.27344i	−1.19483	−	0.320155i	−0.394039	−	0.919094i	$-0.628922\pi$
$839$	−34.6089	−	9.27344i	−1.19483	−	0.320155i	−0.800795	+	0.598939i	$0.795589\pi$
$840$	28.0673	+	29.2536i	0.968413	+	1.00934i
$841$	3.49735	−	6.05759i	0.120598	−	0.208882i
$842$	6.61338	−	11.4547i	0.227912	−	0.394755i
$843$	−14.6911	−	4.26416i	−0.505990	−	0.146866i
$844$	−19.6354	+	11.3365i	−0.675880	+	0.390219i
$845$	22.1696	+	9.87848i	0.762657	+	0.339830i
$846$	−10.5897	+	16.7053i	−0.364081	+	0.574338i
$847$	−11.1163	+	11.1163i	−0.381959	+	0.381959i
$848$	−1.86509	+	1.07681i	−0.0640475	+	0.0369779i
$849$	−35.9324	−	21.7491i	−1.23320	−	0.746427i
$850$	−0.236110	−	0.881176i	−0.00809852	−	0.0302241i
$851$	−31.3571	+	8.40210i	−1.07491	+	0.288020i
$852$	−1.01978	−	4.14729i	−0.0349370	−	0.142084i
$853$	−2.51473	+	9.38509i	−0.0861026	+	0.321339i	−0.995521	−	0.0945437i	$-0.969861\pi$
$853$	−2.51473	+	9.38509i	−0.0861026	+	0.321339i	0.909418	+	0.415883i	$0.136527\pi$
$854$			9.64458i			0.330031i
$855$	18.7044	−	29.5063i	0.639678	−	1.00909i
$856$	28.0624	+	28.0624i	0.959154	+	0.959154i
$857$	13.1258	+	22.7345i	0.448367	+	0.776595i	0.998280	−	0.0586274i	$-0.0186724\pi$
$857$	13.1258	+	22.7345i	0.448367	+	0.776595i	−0.549913	+	0.835222i	$0.685339\pi$
$858$	−19.2270	+	15.7404i	−0.656398	+	0.537367i
$859$	−7.14845	+	12.3815i	−0.243902	+	0.422450i	−0.961822	−	0.273675i	$-0.911761\pi$
$859$	−7.14845	+	12.3815i	−0.243902	+	0.422450i	0.717920	+	0.696125i	$0.245094\pi$
$860$	10.0867	−	2.70273i	0.343954	−	0.0921622i
$861$	−0.941026	+	45.4705i	−0.0320701	+	1.54963i
$862$	29.8851	−	17.2542i	1.01789	−	0.587680i
$863$	5.14669	+	5.14669i	0.175195	+	0.175195i	0.789258	−	0.614062i	$-0.210466\pi$
$863$	5.14669	+	5.14669i	0.175195	+	0.175195i	−0.614062	+	0.789258i	$0.710466\pi$
$864$	24.1600	−	4.89048i	0.821939	−	0.166378i
$865$	10.9490	+	10.9490i	0.372279	+	0.372279i
$866$	−10.2310	−	2.74138i	−0.347663	−	0.0931560i
$867$	28.8511	+	0.597082i	0.979834	+	0.0202780i
$868$	7.39914	+	4.27189i	0.251143	+	0.144998i
$869$	2.20358	+	8.22386i	0.0747512	+	0.278975i
$870$	−9.67103	−	17.5811i	−0.327879	−	0.596054i
$871$	−0.650706	+	8.25224i	−0.0220483	+	0.279617i
$872$			17.3146i			0.586347i
$873$	−32.2151	−	10.0778i	−1.09032	−	0.341082i
$874$	34.2304			1.15786
$875$	−25.1553	−	43.5702i	−0.850403	−	1.47294i
$876$	−2.95428	−	12.0146i	−0.0998159	−	0.405936i
$877$	−5.19207	−	19.3771i	−0.175324	−	0.654318i	−0.996496	−	0.0836374i	$-0.973346\pi$
$877$	−5.19207	−	19.3771i	−0.175324	−	0.654318i	0.821172	−	0.570680i	$-0.193320\pi$
$878$	4.88270	+	18.2225i	0.164783	+	0.614980i
$879$	10.4392	+	42.4545i	0.352104	+	1.43196i
$880$	4.57479	+	7.92378i	0.154216	+	0.267110i
$881$	26.1641			0.881491			0.440746	−	0.897632i	$-0.354714\pi$
$881$	26.1641			0.881491			0.440746	+	0.897632i	$0.354714\pi$
$882$	23.0836	−	21.2479i	0.777266	−	0.715455i
$883$		−	18.8889i		−	0.635661i	−0.948148	−	0.317830i	$-0.897046\pi$
$883$		−	18.8889i		−	0.635661i	0.948148	−	0.317830i	$-0.102954\pi$
$884$	1.26864	+	1.48584i	0.0426690	+	0.0499741i
$885$	−10.4111	−	18.9264i	−0.349965	−	0.636205i
$886$	−2.55372	−	9.53059i	−0.0857937	−	0.320187i
$887$	24.3843	+	14.0783i	0.818745	+	0.472702i	0.849983	−	0.526810i	$-0.176612\pi$
$887$	24.3843	+	14.0783i	0.818745	+	0.472702i	−0.0312387	+	0.999512i	$0.509945\pi$
$888$	−32.1083	−	0.664492i	−1.07748	−	0.0222989i
$889$	−12.5804	−	3.37090i	−0.421932	−	0.113056i
$890$	0.214071	+	0.214071i	0.00717569	+	0.00717569i
$891$	−32.5890	−	11.6957i	−1.09177	−	0.391821i
$892$	−11.5169	−	11.5169i	−0.385616	−	0.385616i
$893$	34.4340	−	19.8805i	1.15229	−	0.665274i
$894$	−0.0929686	+	4.49225i	−0.00310933	+	0.150243i
$895$	−20.4002	+	5.46621i	−0.681903	+	0.182715i
$896$	3.67816	−	6.37076i	0.122879	−	0.212832i
$897$	−25.6408	+	20.9911i	−0.856120	+	0.700873i
$898$	−2.20255	−	3.81493i	−0.0735000	−	0.127306i
$899$	−9.41839	−	9.41839i	−0.314121	−	0.314121i
$900$	−4.22286	−	0.174862i	−0.140762	−	0.00582873i
$901$		−	0.984720i		−	0.0328058i
$902$	−6.53696	+	24.3962i	−0.217657	+	0.812306i
$903$	−10.2856	−	41.8302i	−0.342285	−	1.39202i
$904$	39.0273	−	10.4573i	1.29803	−	0.347806i
$905$	2.82548	+	10.5448i	0.0939222	+	0.350523i
$906$	−10.4505	−	6.32548i	−0.347196	−	0.210150i
$907$	−47.3000	+	27.3087i	−1.57057	+	0.906770i	−0.574473	+	0.818524i	$0.694793\pi$
$907$	−47.3000	+	27.3087i	−1.57057	+	0.906770i	−0.996099	+	0.0882463i	$0.971874\pi$
$908$	3.28106	−	3.28106i	0.108886	−	0.108886i
$909$	10.2618	+	19.6050i	0.340363	+	0.650257i
$910$	−23.7321	−	16.3158i	−0.786711	−	0.540864i
$911$	−40.4995	+	23.3824i	−1.34181	+	0.774694i	−0.987073	−	0.160272i	$-0.948763\pi$
$911$	−40.4995	+	23.3824i	−1.34181	+	0.774694i	−0.354736	+	0.934966i	$0.615429\pi$
$912$	13.2166	+	3.83618i	0.437646	+	0.127029i
$913$	21.9446	−	38.0092i	0.726261	−	1.25792i
$914$	−14.1050	+	24.4306i	−0.466553	+	0.808093i
$915$	5.04688	+	5.26019i	0.166845	+	0.173896i
$916$	14.3422	+	3.84298i	0.473880	+	0.126976i
$917$	−37.2609	+	37.2609i	−1.23046	+	1.23046i
$918$	0.996174	−	2.96748i	0.0328786	−	0.0979414i
$919$	12.6186			0.416249			0.208125	−	0.978102i	$-0.433264\pi$
$919$	12.6186			0.416249			0.208125	+	0.978102i	$0.433264\pi$
$920$	15.0120	+	26.0015i	0.494930	+	0.857244i
$921$	5.77419	+	6.01824i	0.190266	+	0.198308i
$922$	24.8290	+	14.3350i	0.817699	+	0.472099i
$923$	4.11281	+	8.62600i	0.135375	+	0.283928i
$924$	−22.4684	+	12.3595i	−0.739155	+	0.406596i
$925$	8.94905	+	2.39789i	0.294243	+	0.0788422i
$926$			24.8051i			0.815146i
$927$	−29.3787	−	18.6236i	−0.964924	−	0.611678i
$928$	−20.1251	+	20.1251i	−0.660640	+	0.660640i
$929$	−0.122766	+	0.458170i	−0.00402783	+	0.0150321i	−0.967911	−	0.251295i	$-0.919144\pi$
$929$	−0.122766	+	0.458170i	−0.00402783	+	0.0150321i	0.963883	+	0.266327i	$0.0858102\pi$
$930$	−7.21031	+	1.77295i	−0.236436	+	0.0581372i
$931$	−60.9210	+	16.3237i	−1.99660	+	0.534989i
$932$	−4.26224	−	2.46081i	−0.139614	−	0.0806064i
$933$	22.5071	−	37.1847i	0.736849	−	1.21737i
$934$	−9.69363	+	36.1771i	−0.317185	+	1.18375i
$935$	−4.18355			−0.136817
$936$	−30.1490	+	12.8722i	−0.985451	+	0.420743i
$937$	17.5439			0.573135			0.286567	−	0.958060i	$-0.407486\pi$
$937$	17.5439			0.573135			0.286567	+	0.958060i	$0.407486\pi$
$938$	2.54223	−	9.48774i	0.0830068	−	0.309786i
$939$	−13.0125	−	23.6556i	−0.424647	−	0.771971i
$940$	9.58871	+	5.53605i	0.312749	+	0.180566i
$941$	−22.6468	+	6.06819i	−0.738264	+	0.197817i	−0.608306	−	0.793702i	$-0.708151\pi$
$941$	−22.6468	+	6.06819i	−0.738264	+	0.197817i	−0.129958	+	0.991520i	$0.541484\pi$
$942$	5.20084	+	5.42066i	0.169453	+	0.176615i
$943$	−8.71758	+	32.5344i	−0.283883	+	1.05947i
$944$	6.01697	−	6.01697i	0.195836	−	0.195836i
$945$	2.48956	−	40.0528i	0.0809853	−	1.30292i
$946$		−	23.9218i		−	0.777766i
$947$	−31.3363	−	8.39653i	−1.01829	−	0.272851i	−0.289202	−	0.957268i	$-0.593390\pi$
$947$	−31.3363	−	8.39653i	−1.01829	−	0.272851i	−0.729090	+	0.684418i	$0.760057\pi$
$948$	−0.0737849	+	3.56529i	−0.00239642	+	0.115795i
$949$	11.9147	+	24.9894i	0.386769	+	0.811190i
$950$	−8.46027	−	4.88454i	−0.274487	−	0.158475i
$951$	−15.8125	+	54.4781i	−0.512755	+	1.76657i
$952$	−3.65110	−	6.32390i	−0.118333	−	0.204959i
$953$	34.3236			1.11185			0.555925	−	0.831232i	$-0.312364\pi$
$953$	34.3236			1.11185			0.555925	+	0.831232i	$0.312364\pi$
$954$	5.00635	+	1.56613i	0.162086	+	0.0507053i
$955$	−13.7553	+	13.7553i	−0.445111	+	0.445111i
$956$	7.30336	+	1.95693i	0.236208	+	0.0632917i
$957$	38.8212	−	9.54576i	1.25491	−	0.308570i
$958$	−6.00225	+	10.3962i	−0.193924	+	0.335886i
$959$	21.3885	−	37.0459i	0.690669	−	1.19627i
$960$	5.75562	+	23.4073i	0.185762	+	0.755467i
$961$	22.5783	−	13.0356i	0.728332	−	0.420503i
$962$	22.4329	−	4.15422i	0.723264	−	0.133937i
$963$	1.62531	−	39.2507i	0.0523748	−	1.26484i
$964$	4.03331	−	4.03331i	0.129904	−	0.129904i
$965$	6.98582	−	4.03326i	0.224881	−	0.129835i
$966$	34.4519	−	18.9514i	1.10847	−	0.609751i
$967$	0.684445	+	2.55438i	0.0220103	+	0.0821434i	0.976057	−	0.217513i	$-0.0697945\pi$
$967$	0.684445	+	2.55438i	0.0220103	+	0.0821434i	−0.954047	+	0.299657i	$0.903128\pi$
$968$	−11.1253	+	2.98103i	−0.357582	+	0.0958138i
$969$	−4.54063	+	4.35650i	−0.145866	+	0.139951i
$970$	5.62313	−	20.9858i	0.180548	−	0.673813i
$971$			29.5656i			0.948806i	0.880308	+	0.474403i	$0.157336\pi$
$971$			29.5656i			0.948806i	−0.880308	+	0.474403i	$0.842664\pi$
$972$	−11.7433	−	8.50945i	−0.376666	−	0.272941i
$973$	49.7926	+	49.7926i	1.59628	+	1.59628i
$974$	−14.5665	−	25.2298i	−0.466739	−	0.808416i
$975$	9.33263	−	1.52926i	0.298883	−	0.0489754i
$976$	−1.43583	+	2.48693i	−0.0459598	+	0.0796048i
$977$	−4.28200	+	1.14736i	−0.136993	+	0.0367072i	−0.326664	−	0.945141i	$-0.605925\pi$
$977$	−4.28200	+	1.14736i	−0.136993	+	0.0367072i	0.189671	+	0.981848i	$0.439258\pi$
$978$	−11.2324	+	6.17874i	−0.359172	+	0.197574i
$979$	−0.522362	+	0.301586i	−0.0166948	+	0.00963872i
$980$	−12.4189	−	12.4189i	−0.396706	−	0.396706i
$981$	12.6103	−	11.6075i	0.402617	−	0.370599i
$982$	26.6435	+	26.6435i	0.850227	+	0.850227i
$983$	−44.0183	−	11.7947i	−1.40396	−	0.376191i	−0.524198	−	0.851597i	$-0.675635\pi$
$983$	−44.0183	−	11.7947i	−1.40396	−	0.376191i	−0.879767	+	0.475406i	$0.842301\pi$
$984$	−17.2540	+	28.5060i	−0.550038	+	0.908737i
$985$	−30.3806	−	17.5403i	−0.968007	−	0.558879i
$986$	0.935425	+	3.49105i	0.0297900	+	0.111178i
$987$	23.6501	−	39.0732i	0.752792	−	1.24371i
$988$	20.8574	+	1.64464i	0.663561	+	0.0523231i
$989$		−	31.9018i		−	1.01442i
$990$	6.65364	−	21.2693i	0.211467	−	0.675982i
$991$	18.3655			0.583399			0.291700	−	0.956510i	$-0.405779\pi$
$991$	18.3655			0.583399			0.291700	+	0.956510i	$0.405779\pi$
$992$	5.26595	+	9.12089i	0.167194	+	0.289589i
$993$	9.60251	+	2.78717i	0.304727	+	0.0884481i
$994$	−2.93486	−	10.9531i	−0.0930882	−	0.347410i
$995$	0.502164	+	1.87410i	0.0159197	+	0.0594130i
$996$	13.2649	−	12.7270i	0.420314	−	0.403269i
$997$	−7.61410	−	13.1880i	−0.241141	−	0.417668i	0.719899	−	0.694079i	$-0.244188\pi$
$997$	−7.61410	−	13.1880i	−0.241141	−	0.417668i	−0.961040	+	0.276411i	$0.910855\pi$
$998$	−29.2523			−0.925966
$999$	21.0411	+	23.8301i	0.665710	+	0.753951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.5.4	✓	44
3.2	odd	2		351.2.bc.b.44.8		44
9.2	odd	6	inner	117.2.z.b.83.4	yes	44
9.7	even	3		351.2.bc.b.278.8		44
13.8	odd	4	inner	117.2.z.b.86.4	yes	44
39.8	even	4		351.2.bc.b.125.8		44
117.34	odd	12		351.2.bc.b.8.8		44
117.47	even	12	inner	117.2.z.b.47.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.4	✓	44	1.1	even	1	trivial
117.2.z.b.47.4	yes	44	117.47	even	12	inner
117.2.z.b.83.4	yes	44	9.2	odd	6	inner
117.2.z.b.86.4	yes	44	13.8	odd	4	inner
351.2.bc.b.8.8		44	117.34	odd	12
351.2.bc.b.44.8		44	3.2	odd	2
351.2.bc.b.125.8		44	39.8	even	4
351.2.bc.b.278.8		44	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.267684 + 0.999012i) q^{2} +(-1.73168 - 0.0358377i) q^{3} +(0.805681 + 0.465160i) q^{4} +(1.80337 - 0.483213i) q^{5} +(0.499346 - 1.72038i) q^{6} +(-1.07064 + 3.99567i) q^{7} +(-2.14302 + 2.14302i) q^{8} +(2.99743 + 0.124119i) q^{9} +1.93094i q^{10} +(-3.71604 - 0.995710i) q^{11} +(-1.37851 - 0.834382i) q^{12} +(3.39856 + 1.20407i) q^{13} +(-3.70513 - 2.13916i) q^{14} +(-3.14018 + 0.772141i) q^{15} +(-0.636932 - 1.10320i) q^{16} +0.582460 q^{17} +(-0.926362 + 2.96125i) q^{18} +(4.41048 - 4.41048i) q^{19} +(1.67772 + 0.449542i) q^{20} +(1.99720 - 6.88085i) q^{21} +(1.98945 - 3.44583i) q^{22} +(2.65310 - 4.59531i) q^{23} +(3.78783 - 3.63423i) q^{24} +(-1.31146 + 0.757174i) q^{25} +(-2.11262 + 3.07289i) q^{26} +(-5.18614 - 0.322355i) q^{27} +(-2.72122 + 2.72122i) q^{28} +(5.19577 - 2.99978i) q^{29} +(0.0692004 - 3.34377i) q^{30} +(-0.574604 - 2.14445i) q^{31} +(-4.58224 + 1.22781i) q^{32} +(6.39931 + 1.85742i) q^{33} +(-0.155916 + 0.581885i) q^{34} +7.72303i q^{35} +(2.35724 + 1.49429i) q^{36} +(-4.32606 - 4.32606i) q^{37} +(3.22551 + 5.58674i) q^{38} +(-5.84207 - 2.20685i) q^{39} +(-2.82914 + 4.90021i) q^{40} +(-6.13140 + 1.64290i) q^{41} +(6.33944 + 3.83712i) q^{42} +(5.20669 - 3.00608i) q^{43} +(-2.53078 - 2.53078i) q^{44} +(5.46547 - 1.22456i) q^{45} +(3.88057 + 3.88057i) q^{46} +(6.15742 + 1.64988i) q^{47} +(1.06343 + 1.93321i) q^{48} +(-8.75694 - 5.05582i) q^{49} +(-0.405367 - 1.51285i) q^{50} +(-1.00863 - 0.0208740i) q^{51} +(2.17807 + 2.55097i) q^{52} -1.69062i q^{53} +(1.71029 - 5.09473i) q^{54} -7.18255 q^{55} +(-6.26842 - 10.8572i) q^{56} +(-7.79561 + 7.47948i) q^{57} +(1.60599 + 5.99363i) q^{58} +(1.72888 + 6.45229i) q^{59} +(-2.88916 - 0.838589i) q^{60} +(-1.12715 - 1.95228i) q^{61} +2.29614 q^{62} +(-3.70510 + 11.8439i) q^{63} -7.45411i q^{64} +(6.71070 + 0.529152i) q^{65} +(-3.56858 + 5.89578i) q^{66} +(0.594213 + 2.21763i) q^{67} +(0.469277 + 0.270937i) q^{68} +(-4.75901 + 7.86252i) q^{69} +(-7.71540 - 2.06734i) q^{70} +(1.87415 + 1.87415i) q^{71} +(-6.68956 + 6.15758i) q^{72} +(5.42937 + 5.42937i) q^{73} +(5.47981 - 3.16377i) q^{74} +(2.29817 - 1.26418i) q^{75} +(5.60502 - 1.50186i) q^{76} +(7.95706 - 13.7820i) q^{77} +(3.76850 - 5.24556i) q^{78} +(-1.10654 - 1.91658i) q^{79} +(-1.68171 - 1.68171i) q^{80} +(8.96919 + 0.744075i) q^{81} -6.56512i q^{82} +(-2.95269 + 11.0196i) q^{83} +(4.80980 - 4.61476i) q^{84} +(1.05039 - 0.281452i) q^{85} +(1.60936 + 6.00623i) q^{86} +(-9.10492 + 5.00845i) q^{87} +(10.0974 - 5.82973i) q^{88} +(0.110864 - 0.110864i) q^{89} +(-0.239666 + 5.78786i) q^{90} +(-8.44967 + 12.2904i) q^{91} +(4.27511 - 2.46823i) q^{92} +(0.918178 + 3.73409i) q^{93} +(-3.29649 + 5.70969i) q^{94} +(5.82255 - 10.0850i) q^{95} +(7.97898 - 1.96195i) q^{96} +(-10.8682 - 2.91212i) q^{97} +(7.39493 - 7.39493i) q^{98} +(-11.0150 - 3.44580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Introduction

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