LMFDB - Embedded newform 841.2.e.j.196.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] 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("841.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-2,2,-6,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			196.1
Character	$\chi$	$=$	841.196
Dual form			841.2.e.j.236.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57747 + 0.360046i) q^{2} +(0.702039 - 1.45780i) q^{3} +(0.556829 - 0.268155i) q^{4} +(-0.635097 - 2.78254i) q^{5} +(-0.582567 + 2.55239i) q^{6} +(-2.01463 - 0.970194i) q^{7} +(1.74823 - 1.39417i) q^{8} +(0.238152 + 0.298633i) q^{9} +(2.00369 + 4.16070i) q^{10} +(-2.82869 - 2.25581i) q^{11} -1.00000i q^{12} +(-2.64115 + 3.31189i) q^{13} +(3.52732 + 0.805088i) q^{14} +(-4.50225 - 1.02761i) q^{15} +(-3.02648 + 3.79509i) q^{16} -6.61803i q^{17} +(-0.483198 - 0.385338i) q^{18} +(-0.804465 - 1.67049i) q^{19} +(-1.09979 - 1.37910i) q^{20} +(-2.82869 + 2.25581i) q^{21} +(5.27436 + 2.54000i) q^{22} +(-0.720093 + 3.15493i) q^{23} +(-0.805088 - 3.52732i) q^{24} +(-2.83436 + 1.36495i) q^{25} +(2.97388 - 6.17533i) q^{26} +(5.33494 - 1.21766i) q^{27} -1.38197 q^{28} +7.47214 q^{30} +(1.06284 - 0.242586i) q^{31} +(1.46738 - 3.04705i) q^{32} +(-5.27436 + 2.54000i) q^{33} +(2.38280 + 10.4397i) q^{34} +(-1.42012 + 6.22196i) q^{35} +(0.212690 + 0.102426i) q^{36} +(-6.80835 + 5.42948i) q^{37} +(1.87047 + 2.34549i) q^{38} +(2.97388 + 6.17533i) q^{39} +(-4.98962 - 3.97909i) q^{40} +2.85410i q^{41} +(3.64997 - 4.57692i) q^{42} +(2.69463 + 0.615033i) q^{43} +(-2.18001 - 0.497572i) q^{44} +(0.679710 - 0.852329i) q^{45} -5.23607i q^{46} +(5.47282 + 4.36443i) q^{47} +(3.40777 + 7.07630i) q^{48} +(-1.24698 - 1.56366i) q^{49} +(3.97966 - 3.17367i) q^{50} +(-9.64776 - 4.64612i) q^{51} +(-0.582567 + 2.55239i) q^{52} +(0.445042 + 1.94986i) q^{53} +(-7.97727 + 3.84165i) q^{54} +(-4.48039 + 9.30362i) q^{55} +(-4.87464 + 1.11260i) q^{56} -3.00000 q^{57} -5.09017 q^{59} +(-2.78254 + 0.635097i) q^{60} +(0.702039 - 1.45780i) q^{61} +(-1.58925 + 0.765341i) q^{62} +(-0.190056 - 0.832688i) q^{63} +(0.942614 - 4.12986i) q^{64} +(10.8929 + 5.24573i) q^{65} +(7.40561 - 5.90578i) q^{66} +(6.52927 + 8.18745i) q^{67} +(-1.77466 - 3.68512i) q^{68} +(4.09372 + 3.26463i) q^{69} -10.3262i q^{70} +(-0.952608 + 1.19453i) q^{71} +(0.832688 + 0.190056i) q^{72} +(-0.284480 - 0.0649307i) q^{73} +(8.78508 - 11.0161i) q^{74} +5.09017i q^{75} +(-0.895899 - 0.714456i) q^{76} +(3.51019 + 7.28899i) q^{77} +(-6.91461 - 8.67064i) q^{78} +(-3.97966 + 3.17367i) q^{79} +(12.4821 + 6.01107i) q^{80} +(1.71524 - 7.51494i) q^{81} +(-1.02761 - 4.50225i) q^{82} +(-7.15754 + 3.44689i) q^{83} +(-0.970194 + 2.01463i) q^{84} +(-18.4150 + 4.20310i) q^{85} -4.47214 q^{86} -8.09017 q^{88} +(-8.48987 + 1.93776i) q^{89} +(-0.765341 + 1.58925i) q^{90} +(8.53410 - 4.10981i) q^{91} +(0.445042 + 1.94986i) q^{92} +(0.392512 - 1.71971i) q^{93} +(-10.2046 - 4.91427i) q^{94} +(-4.13729 + 3.29938i) q^{95} +(-3.41182 - 4.27829i) q^{96} +(-7.18612 - 14.9221i) q^{97} +(2.53006 + 2.01766i) q^{98} -1.38197i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38}+ \cdots + 4 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

Coefficient data

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

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

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

$2$	−1.57747	+	0.360046i	−1.11544	+	0.254591i	−0.740233	−	0.672351i	$-0.765285\pi$
$2$	−1.57747	+	0.360046i	−1.11544	+	0.254591i	−0.375205	+	0.926942i	$0.622428\pi$
$3$	0.702039	−	1.45780i	0.405322	−	0.841660i	−0.593986	−	0.804475i	$-0.702447\pi$
$3$	0.702039	−	1.45780i	0.405322	−	0.841660i	0.999308	−	0.0371850i	$-0.0118391\pi$
$4$	0.556829	−	0.268155i	0.278415	−	0.134077i
$5$	−0.635097	−	2.78254i	−0.284024	−	1.24439i	−0.892583	−	0.450883i	$-0.851109\pi$
$5$	−0.635097	−	2.78254i	−0.284024	−	1.24439i	0.608559	−	0.793509i	$-0.291748\pi$
$6$	−0.582567	+	2.55239i	−0.237832	+	1.04201i
$7$	−2.01463	−	0.970194i	−0.761458	−	0.366699i	0.0125117	−	0.999922i	$-0.496017\pi$
$7$	−2.01463	−	0.970194i	−0.761458	−	0.366699i	−0.773969	+	0.633223i	$0.781732\pi$
$8$	1.74823	−	1.39417i	0.618092	−	0.492912i
$9$	0.238152	+	0.298633i	0.0793840	+	0.0995444i
$10$	2.00369	+	4.16070i	0.633622	+	1.31573i
$11$	−2.82869	−	2.25581i	−0.852883	−	0.680151i	0.0961367	−	0.995368i	$-0.469351\pi$
$11$	−2.82869	−	2.25581i	−0.852883	−	0.680151i	−0.949020	+	0.315217i	$0.897923\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.64115	+	3.31189i	−0.732522	+	0.918553i	−0.998974	−	0.0452949i	$-0.985577\pi$
$13$	−2.64115	+	3.31189i	−0.732522	+	0.918553i	0.266452	+	0.963848i	$0.414149\pi$
$14$	3.52732	+	0.805088i	0.942717	+	0.215169i
$15$	−4.50225	−	1.02761i	−1.16248	−	0.265328i
$16$	−3.02648	+	3.79509i	−0.756621	+	0.948772i
$17$		−	6.61803i		−	1.60511i	−0.596579	−	0.802555i	$-0.703474\pi$
$17$		−	6.61803i		−	1.60511i	0.596579	−	0.802555i	$-0.296526\pi$
$18$	−0.483198	−	0.385338i	−0.113891	−	0.0908250i
$19$	−0.804465	−	1.67049i	−0.184557	−	0.383236i	0.788078	−	0.615575i	$-0.211076\pi$
$19$	−0.804465	−	1.67049i	−0.184557	−	0.383236i	−0.972635	+	0.232339i	$0.925362\pi$
$20$	−1.09979	−	1.37910i	−0.245921	−	0.308376i
$21$	−2.82869	+	2.25581i	−0.617271	+	0.492258i
$22$	5.27436	+	2.54000i	1.12450	+	0.541530i
$23$	−0.720093	+	3.15493i	−0.150150	+	0.657849i	0.842690	+	0.538398i	$0.180970\pi$
$23$	−0.720093	+	3.15493i	−0.150150	+	0.657849i	−0.992840	+	0.119451i	$0.961887\pi$
$24$	−0.805088	−	3.52732i	−0.164338	−	0.720012i
$25$	−2.83436	+	1.36495i	−0.566871	+	0.272991i
$26$	2.97388	−	6.17533i	0.583227	−	1.21108i
$27$	5.33494	−	1.21766i	1.02671	−	0.234340i
$28$	−1.38197			−0.261167
$29$		0			0
$29$		0			0
$30$	7.47214			1.36422
$31$	1.06284	−	0.242586i	0.190891	−	0.0435697i	−0.126006	−	0.992029i	$-0.540216\pi$
$31$	1.06284	−	0.242586i	0.190891	−	0.0435697i	0.316898	+	0.948460i	$0.397359\pi$
$32$	1.46738	−	3.04705i	0.259399	−	0.538647i
$33$	−5.27436	+	2.54000i	−0.918149	+	0.442157i
$34$	2.38280	+	10.4397i	0.408647	+	1.79040i
$35$	−1.42012	+	6.22196i	−0.240044	+	1.05170i
$36$	0.212690	+	0.102426i	0.0354483	+	0.0170710i
$37$	−6.80835	+	5.42948i	−1.11929	+	0.892600i	−0.995023	−	0.0996489i	$-0.968228\pi$
$37$	−6.80835	+	5.42948i	−1.11929	+	0.892600i	−0.124263	+	0.992249i	$0.539657\pi$
$38$	1.87047	+	2.34549i	0.303430	+	0.380489i
$39$	2.97388	+	6.17533i	0.476202	+	0.988845i
$40$	−4.98962	−	3.97909i	−0.788929	−	0.629149i
$41$			2.85410i			0.445736i	0.974849	+	0.222868i	$0.0715419\pi$
$41$			2.85410i			0.445736i	−0.974849	+	0.222868i	$0.928458\pi$
$42$	3.64997	−	4.57692i	0.563203	−	0.706234i
$43$	2.69463	+	0.615033i	0.410928	+	0.0937916i	0.422987	−	0.906136i	$-0.360982\pi$
$43$	2.69463	+	0.615033i	0.410928	+	0.0937916i	−0.0120593	+	0.999927i	$0.503839\pi$
$44$	−2.18001	−	0.497572i	−0.328648	−	0.0750118i
$45$	0.679710	−	0.852329i	0.101325	−	0.127058i
$46$		−	5.23607i		−	0.772016i
$47$	5.47282	+	4.36443i	0.798293	+	0.636617i	0.935261	−	0.353958i	$-0.115164\pi$
$47$	5.47282	+	4.36443i	0.798293	+	0.636617i	−0.136968	+	0.990575i	$0.543736\pi$
$48$	3.40777	+	7.07630i	0.491869	+	1.02138i
$49$	−1.24698	−	1.56366i	−0.178140	−	0.223380i
$50$	3.97966	−	3.17367i	0.562808	−	0.448825i
$51$	−9.64776	−	4.64612i	−1.35096	−	0.650586i
$52$	−0.582567	+	2.55239i	−0.0807876	+	0.353953i
$53$	0.445042	+	1.94986i	0.0611312	+	0.267833i	0.996252	−	0.0864950i	$-0.0275667\pi$
$53$	0.445042	+	1.94986i	0.0611312	+	0.267833i	−0.935121	+	0.354328i	$0.884710\pi$
$54$	−7.97727	+	3.84165i	−1.08557	+	0.522782i
$55$	−4.48039	+	9.30362i	−0.604135	+	1.25450i
$56$	−4.87464	+	1.11260i	−0.651401	+	0.148678i
$57$	−3.00000			−0.397360
$58$		0			0
$59$	−5.09017			−0.662684			−0.331342	−	0.943511i	$-0.607501\pi$
$59$	−5.09017			−0.662684			−0.331342	+	0.943511i	$0.607501\pi$
$60$	−2.78254	+	0.635097i	−0.359225	+	0.0819907i
$61$	0.702039	−	1.45780i	0.0898868	−	0.186652i	−0.851179	−	0.524876i	$-0.824112\pi$
$61$	0.702039	−	1.45780i	0.0898868	−	0.186652i	0.941066	+	0.338224i	$0.109826\pi$
$62$	−1.58925	+	0.765341i	−0.201835	+	0.0971985i
$63$	−0.190056	−	0.832688i	−0.0239448	−	0.104909i
$64$	0.942614	−	4.12986i	0.117827	−	0.516233i
$65$	10.8929	+	5.24573i	1.35109	+	0.650652i
$66$	7.40561	−	5.90578i	0.911568	−	0.726951i
$67$	6.52927	+	8.18745i	0.797677	+	1.00026i	0.999782	+	0.0208917i	$0.00665052\pi$
$67$	6.52927	+	8.18745i	0.797677	+	1.00026i	−0.202104	+	0.979364i	$0.564778\pi$
$68$	−1.77466	−	3.68512i	−0.215209	−	0.446886i
$69$	4.09372	+	3.26463i	0.492826	+	0.393016i
$70$		−	10.3262i		−	1.23422i
$71$	−0.952608	+	1.19453i	−0.113054	+	0.141765i	−0.835139	−	0.550040i	$-0.814613\pi$
$71$	−0.952608	+	1.19453i	−0.113054	+	0.141765i	0.722085	+	0.691805i	$0.243184\pi$
$72$	0.832688	+	0.190056i	0.0981332	+	0.0223983i
$73$	−0.284480	−	0.0649307i	−0.0332959	−	0.00759957i	0.205841	−	0.978586i	$-0.434007\pi$
$73$	−0.284480	−	0.0649307i	−0.0332959	−	0.00759957i	−0.239136	+	0.970986i	$0.576864\pi$
$74$	8.78508	−	11.0161i	1.02124	−	1.28060i
$75$			5.09017i			0.587762i
$76$	−0.895899	−	0.714456i	−0.102767	−	0.0819537i
$77$	3.51019	+	7.28899i	0.400024	+	0.830658i
$78$	−6.91461	−	8.67064i	−0.782925	−	0.981757i
$79$	−3.97966	+	3.17367i	−0.447746	+	0.357066i	−0.821255	−	0.570561i	$-0.806726\pi$
$79$	−3.97966	+	3.17367i	−0.447746	+	0.357066i	0.373509	+	0.927626i	$0.378154\pi$
$80$	12.4821	+	6.01107i	1.39554	+	0.672058i
$81$	1.71524	−	7.51494i	0.190582	−	0.834994i
$82$	−1.02761	−	4.50225i	−0.113480	−	0.497190i
$83$	−7.15754	+	3.44689i	−0.785642	+	0.378345i	−0.783294	−	0.621652i	$-0.786462\pi$
$83$	−7.15754	+	3.44689i	−0.785642	+	0.378345i	−0.00234861	+	0.999997i	$0.500748\pi$
$84$	−0.970194	+	2.01463i	−0.105857	+	0.219814i
$85$	−18.4150	+	4.20310i	−1.99738	+	0.455890i
$86$	−4.47214			−0.482243
$87$		0			0
$88$	−8.09017			−0.862415
$89$	−8.48987	+	1.93776i	−0.899925	+	0.205402i	−0.647366	−	0.762180i	$-0.724129\pi$
$89$	−8.48987	+	1.93776i	−0.899925	+	0.205402i	−0.252559	+	0.967582i	$0.581272\pi$
$90$	−0.765341	+	1.58925i	−0.0806741	+	0.167521i
$91$	8.53410	−	4.10981i	0.894617	−	0.430825i
$92$	0.445042	+	1.94986i	0.0463988	+	0.203287i
$93$	0.392512	−	1.71971i	0.0407016	−	0.178325i
$94$	−10.2046	−	4.91427i	−1.05252	−	0.506868i
$95$	−4.13729	+	3.29938i	−0.424477	+	0.338509i
$96$	−3.41182	−	4.27829i	−0.348218	−	0.436651i
$97$	−7.18612	−	14.9221i	−0.729639	−	1.51511i	−0.852522	−	0.522691i	$-0.824928\pi$
$97$	−7.18612	−	14.9221i	−0.729639	−	1.51511i	0.122883	−	0.992421i	$-0.460786\pi$
$98$	2.53006	+	2.01766i	0.255575	+	0.203814i
$99$		−	1.38197i		−	0.138893i
$100$	−1.21223	+	1.52009i	−0.121223	+	0.152009i
$101$	−1.57747	−	0.360046i	−0.156964	−	0.0358260i	0.143317	−	0.989677i	$-0.454223\pi$
$101$	−1.57747	−	0.360046i	−0.156964	−	0.0358260i	−0.300281	+	0.953851i	$0.597080\pi$
$102$	16.8918	+	3.85545i	1.67254	+	0.381746i
$103$	−8.21781	+	10.3048i	−0.809725	+	1.01536i	0.189713	+	0.981840i	$0.439244\pi$
$103$	−8.21781	+	10.3048i	−0.809725	+	1.01536i	−0.999438	+	0.0335230i	$0.989327\pi$
$104$			9.47214i			0.928819i
$105$	8.07338	+	6.43830i	0.787881	+	0.628314i
$106$	−1.40408	−	2.91560i	−0.136376	−	0.283188i
$107$	7.00557	+	8.78471i	0.677254	+	0.849250i	0.995098	−	0.0988930i	$-0.0315302\pi$
$107$	7.00557	+	8.78471i	0.677254	+	0.849250i	−0.317844	+	0.948143i	$0.602959\pi$
$108$	2.64413	−	2.10862i	0.254431	−	0.202902i
$109$	−14.9723	−	7.21029i	−1.43409	−	0.690621i	−0.454336	−	0.890830i	$-0.650123\pi$
$109$	−14.9723	−	7.21029i	−1.43409	−	0.690621i	−0.979753	+	0.200209i	$0.935838\pi$
$110$	3.71793	−	16.2893i	0.354490	−	1.55312i
$111$	3.13536	+	13.7369i	0.297595	+	1.30385i
$112$	9.77921	−	4.70942i	0.924048	−	0.444998i
$113$	4.31466	−	8.95948i	0.405889	−	0.842837i	−0.593392	−	0.804914i	$-0.702212\pi$
$113$	4.31466	−	8.95948i	0.405889	−	0.842837i	0.999281	−	0.0379231i	$-0.0120742\pi$
$114$	4.73240	−	1.08014i	0.443230	−	0.101164i
$115$	9.23607			0.861268
$116$		0			0
$117$	−1.61803			−0.149587
$118$	8.02957	−	1.83270i	0.739182	−	0.168713i
$119$	−6.42077	+	13.3329i	−0.588591	+	1.22222i
$120$	−9.30362	+	4.48039i	−0.849300	+	0.409001i
$121$	0.465107	+	2.03777i	0.0422824	+	0.185251i
$122$	−0.582567	+	2.55239i	−0.0527432	+	0.231083i
$123$	4.16070	+	2.00369i	0.375158	+	0.180667i
$124$	0.526768	−	0.420084i	0.0473052	−	0.0377246i
$125$	−3.29938	−	4.13729i	−0.295106	−	0.370051i
$126$	0.599613	+	1.24511i	0.0534177	+	0.110923i
$127$	−1.52009	−	1.21223i	−0.134886	−	0.107568i	0.553722	−	0.832701i	$-0.313207\pi$
$127$	−1.52009	−	1.21223i	−0.134886	−	0.107568i	−0.688609	+	0.725133i	$0.741778\pi$
$128$			13.6180i			1.20368i
$129$	2.78833	−	3.49646i	0.245499	−	0.307846i
$130$	−19.0718	−	4.35302i	−1.67271	−	0.381785i
$131$	−1.29299	−	0.295116i	−0.112969	−	0.0257844i	0.165663	−	0.986182i	$-0.447024\pi$
$131$	−1.29299	−	0.295116i	−0.112969	−	0.0257844i	−0.278632	+	0.960398i	$0.589881\pi$
$132$	−2.25581	+	2.82869i	−0.196343	+	0.246206i
$133$			4.14590i			0.359495i
$134$	−13.2476	−	10.5646i	−1.14442	−	0.912641i
$135$	−6.77641	−	14.0714i	−0.583221	−	1.21107i
$136$	−9.22664	−	11.5698i	−0.791177	−	0.992105i
$137$	−10.8316	+	8.63789i	−0.925404	+	0.737985i	−0.965279	−	0.261220i	$-0.915875\pi$
$137$	−10.8316	+	8.63789i	−0.925404	+	0.737985i	0.0398756	+	0.999205i	$0.487304\pi$
$138$	−7.63313	−	3.67592i	−0.649775	−	0.312915i
$139$	−3.27288	+	14.3394i	−0.277602	+	1.21626i	0.623213	+	0.782052i	$0.285827\pi$
$139$	−3.27288	+	14.3394i	−0.277602	+	1.21626i	−0.900815	+	0.434203i	$0.857030\pi$
$140$	0.877683	+	3.84538i	0.0741778	+	0.324994i
$141$	10.2046	−	4.91427i	0.859381	−	0.413856i
$142$	1.07262	−	2.22732i	0.0900122	−	0.186912i
$143$	14.9420	−	3.41041i	1.24951	−	0.285193i
$144$	−1.85410			−0.154508
$145$		0			0
$146$	0.472136			0.0390742
$147$	−3.15493	+	0.720093i	−0.260214	+	0.0593923i
$148$	−2.33515	+	4.84898i	−0.191948	+	0.398584i
$149$	6.65092	−	3.20292i	0.544865	−	0.262393i	−0.141141	−	0.989990i	$-0.545077\pi$
$149$	6.65092	−	3.20292i	0.544865	−	0.262393i	0.686005	+	0.727597i	$0.259363\pi$
$150$	−1.83270	−	8.02957i	−0.149639	−	0.655612i
$151$	4.07797	−	17.8668i	0.331861	−	1.45398i	−0.483664	−	0.875254i	$-0.660694\pi$
$151$	4.07797	−	17.8668i	0.331861	−	1.45398i	0.815524	−	0.578723i	$-0.196449\pi$
$152$	−3.73533	−	1.79884i	−0.302975	−	0.145905i
$153$	1.97636	−	1.57610i	0.159780	−	0.127420i
$154$	−8.16159	−	10.2343i	−0.657679	−	0.824704i
$155$	−1.35001	−	2.80333i	−0.108435	−	0.225168i
$156$	3.31189	+	2.64115i	0.265164	+	0.211461i
$157$			5.56231i			0.443920i	0.975056	+	0.221960i	$0.0712455\pi$
$157$			5.56231i			0.443920i	−0.975056	+	0.221960i	$0.928755\pi$
$158$	5.13510	−	6.43922i	0.408527	−	0.512277i
$159$	3.15493	+	0.720093i	0.250202	+	0.0571071i
$160$	−9.41047	−	2.14788i	−0.743963	−	0.169805i
$161$	4.51161	−	5.65739i	0.355565	−	0.445864i
$162$			12.4721i			0.979904i
$163$	−18.0091	−	14.3617i	−1.41058	−	1.12490i	−0.974344	−	0.225065i	$-0.927741\pi$
$163$	−18.0091	−	14.3617i	−1.41058	−	1.12490i	−0.436234	−	0.899833i	$-0.643688\pi$
$164$	0.765341	+	1.58925i	0.0597631	+	0.124099i
$165$	10.4174	+	13.0630i	0.810993	+	1.01695i
$166$	10.0497	−	8.01440i	0.780011	−	0.622038i
$167$	17.5438	+	8.44864i	1.35758	+	0.653776i	0.964095	−	0.265556i	$-0.0855555\pi$
$167$	17.5438	+	8.44864i	1.35758	+	0.653776i	0.393484	+	0.919332i	$0.371270\pi$
$168$	−1.80023	+	7.88733i	−0.138891	+	0.608521i
$169$	−1.10020	−	4.82031i	−0.0846311	−	0.370793i
$170$	27.5357	−	13.2605i	2.11189	−	1.01703i
$171$	0.307278	−	0.638070i	0.0234981	−	0.0487944i
$172$	1.66538	−	0.380111i	0.126984	−	0.0289832i
$173$	7.09017			0.539056			0.269528	−	0.962993i	$-0.413132\pi$
$173$	7.09017			0.539056			0.269528	+	0.962993i	$0.413132\pi$
$174$		0			0
$175$	7.03444			0.531754
$176$	17.1220	−	3.90798i	1.29062	−	0.294575i
$177$	−3.57350	+	7.42044i	−0.268600	+	0.557754i
$178$	12.6948	−	6.11350i	0.951516	−	0.458226i
$179$	−3.56033	−	15.5988i	−0.266112	−	1.16591i	−0.914495	−	0.404598i	$-0.867411\pi$
$179$	−3.56033	−	15.5988i	−0.266112	−	1.16591i	0.648383	−	0.761315i	$-0.275446\pi$
$180$	0.149926	−	0.656869i	0.0111748	−	0.0489602i
$181$	10.7614	+	5.18243i	0.799890	+	0.385207i	0.788737	−	0.614731i	$-0.210735\pi$
$181$	10.7614	+	5.18243i	0.799890	+	0.385207i	0.0111531	+	0.999938i	$0.496450\pi$
$182$	−11.9825	+	9.55575i	−0.888205	+	0.708320i
$183$	−1.63232	−	2.04686i	−0.120664	−	0.151308i
$184$	3.13961	+	6.51947i	0.231455	+	0.480622i
$185$	19.4317	+	15.4963i	1.42865	+	1.13931i
$186$			2.85410i			0.209273i
$187$	−14.9290	+	18.7204i	−1.09172	+	1.36897i
$188$	4.21777	+	0.962679i	0.307613	+	0.0702105i
$189$	−11.9293	−	2.72278i	−0.867728	−	0.198053i
$190$	5.33851	−	6.69428i	0.387296	−	0.485654i
$191$		−	12.0344i		−	0.870782i	−0.900242	−	0.435391i	$-0.856610\pi$
$191$		−	12.0344i		−	0.870782i	0.900242	−	0.435391i	$-0.143390\pi$
$192$	−5.35875	−	4.27346i	−0.386735	−	0.308411i
$193$	−1.53068	−	3.17850i	−0.110181	−	0.228793i	0.838586	−	0.544769i	$-0.183383\pi$
$193$	−1.53068	−	3.17850i	−0.110181	−	0.228793i	−0.948767	+	0.315976i	$0.897668\pi$
$194$	16.7085	+	20.9518i	1.19960	+	1.50425i
$195$	15.2944	−	12.1969i	1.09526	−	0.873438i
$196$	−1.11366	−	0.536310i	−0.0795471	−	0.0383078i
$197$	4.38549	−	19.2141i	0.312453	−	1.36895i	−0.538022	−	0.842931i	$-0.680828\pi$
$197$	4.38549	−	19.2141i	0.312453	−	1.36895i	0.850475	−	0.526016i	$-0.176315\pi$
$198$	0.497572	+	2.18001i	0.0353609	+	0.154926i
$199$	−0.769519	+	0.370581i	−0.0545498	+	0.0262698i	−0.460960	−	0.887421i	$-0.652495\pi$
$199$	−0.769519	+	0.370581i	−0.0545498	+	0.0262698i	0.406410	+	0.913691i	$0.366780\pi$
$200$	−3.05213	+	6.33781i	−0.215818	+	0.448151i
$201$	16.5194	−	3.77046i	1.16519	−	0.265947i
$202$	2.61803			0.184204
$203$		0			0
$204$	−6.61803			−0.463355
$205$	7.94166	−	1.81263i	0.554670	−	0.126600i
$206$	9.25311	−	19.2143i	0.644695	−	1.33872i
$207$	−1.11366	+	0.536310i	−0.0774046	+	0.0372761i
$208$	−4.57554	−	20.0468i	−0.317257	−	1.38999i
$209$	−1.49272	+	6.54002i	−0.103253	+	0.452382i
$210$	−15.0536	−	7.24942i	−1.03880	−	0.500257i
$211$	15.3649	−	12.2531i	1.05777	−	0.843539i	0.0696986	−	0.997568i	$-0.477796\pi$
$211$	15.3649	−	12.2531i	1.05777	−	0.843539i	0.988066	+	0.154029i	$0.0492248\pi$
$212$	0.770676	+	0.966397i	0.0529302	+	0.0663724i
$213$	1.07262	+	2.22732i	0.0734947	+	0.152613i
$214$	−14.2140	−	11.3353i	−0.971646	−	0.774862i
$215$		−	7.88854i		−	0.537994i
$216$	7.62906	−	9.56654i	0.519092	−	0.650921i
$217$	−2.37658	−	0.542438i	−0.161332	−	0.0368231i
$218$	26.2144	+	5.98326i	1.77546	+	0.405238i
$219$	−0.294372	+	0.369131i	−0.0198918	+	0.0249435i
$220$			6.38197i			0.430272i
$221$	21.9182	+	17.4792i	1.47438	+	1.17578i
$222$	−9.89184	−	20.5406i	−0.663897	−	1.37860i
$223$	11.4262	+	14.3280i	0.765156	+	0.959476i	0.999921	−	0.0125764i	$-0.00400331\pi$
$223$	11.4262	+	14.3280i	0.765156	+	0.959476i	−0.234764	+	0.972052i	$0.575432\pi$
$224$	−5.91245	+	4.71502i	−0.395042	+	0.315036i
$225$	−1.08263	−	0.521366i	−0.0721752	−	0.0347577i
$226$	−3.58040	+	15.6868i	−0.238165	+	1.04347i
$227$	−3.31301	−	14.5153i	−0.219892	−	0.963411i	−0.957557	−	0.288244i	$-0.906929\pi$
$227$	−3.31301	−	14.5153i	−0.219892	−	0.963411i	0.737665	−	0.675167i	$-0.235929\pi$
$228$	−1.67049	+	0.804465i	−0.110631	+	0.0532770i
$229$	−6.81553	+	14.1526i	−0.450383	+	0.935230i	0.544926	+	0.838484i	$0.316558\pi$
$229$	−6.81553	+	14.1526i	−0.450383	+	0.935230i	−0.995309	+	0.0967461i	$0.969157\pi$
$230$	−14.5696	+	3.32541i	−0.960690	+	0.219271i
$231$	13.0902			0.861270
$232$		0			0
$233$	10.7639			0.705169			0.352584	−	0.935780i	$-0.385303\pi$
$233$	10.7639			0.705169			0.352584	+	0.935780i	$0.385303\pi$
$234$	2.55239	−	0.582567i	0.166855	−	0.0380836i
$235$	8.66844	−	18.0002i	0.565467	−	1.17420i
$236$	−2.83436	+	1.36495i	−0.184501	+	0.0888509i
$237$	1.83270	+	8.02957i	0.119046	+	0.521577i
$238$	5.32810	−	23.3439i	0.345370	−	1.51316i
$239$	−13.2827	−	6.39659i	−0.859184	−	0.413761i	−0.0482058	−	0.998837i	$-0.515350\pi$
$239$	−13.2827	−	6.39659i	−0.859184	−	0.413761i	−0.810978	+	0.585076i	$0.801065\pi$
$240$	17.5259	−	13.9764i	1.13129	−	0.902173i
$241$	−16.6175	−	20.8377i	−1.07043	−	1.34228i	−0.936256	−	0.351319i	$-0.885733\pi$
$241$	−16.6175	−	20.8377i	−1.07043	−	1.34228i	−0.134175	−	0.990958i	$-0.542838\pi$
$242$	−1.46738	−	3.04705i	−0.0943268	−	0.195872i
$243$	3.08376	+	2.45921i	0.197823	+	0.157759i
$244$		−	1.00000i		−	0.0640184i
$245$	−3.55901	+	4.46285i	−0.227377	+	0.285121i
$246$	−7.28479	−	1.66271i	−0.464461	−	0.106010i
$247$	7.65718	+	1.74770i	0.487215	+	0.111204i
$248$	1.51988	−	1.90587i	0.0965123	−	0.121023i
$249$			12.8541i			0.814596i
$250$	6.69428	+	5.33851i	0.423383	+	0.337637i
$251$	−5.05582	−	10.4985i	−0.319121	−	0.662661i	0.678273	−	0.734810i	$-0.262729\pi$
$251$	−5.05582	−	10.4985i	−0.319121	−	0.662661i	−0.997394	+	0.0721491i	$0.977014\pi$
$252$	−0.329118	−	0.412701i	−0.0207325	−	0.0259977i
$253$	9.15384	−	7.29995i	0.575497	−	0.458944i
$254$	2.83436	+	1.36495i	0.177843	+	0.0856448i
$255$	−6.80075	+	29.7960i	−0.425880	+	1.86590i
$256$	−3.01790	−	13.2223i	−0.188619	−	0.826392i
$257$	0.738488	−	0.355637i	0.0460656	−	0.0221840i	−0.410709	−	0.911766i	$-0.634719\pi$
$257$	0.738488	−	0.355637i	0.0460656	−	0.0221840i	0.456775	+	0.889582i	$0.349005\pi$
$258$	−3.13961	+	6.51947i	−0.195464	+	0.405885i
$259$	18.9839	−	4.33296i	1.17960	−	0.269237i
$260$	7.47214			0.463402
$261$		0			0
$262$	2.14590			0.132574
$263$	−3.20926	+	0.732494i	−0.197892	+	0.0451675i	−0.320318	−	0.947310i	$-0.603790\pi$
$263$	−3.20926	+	0.732494i	−0.197892	+	0.0451675i	0.122426	+	0.992478i	$0.460933\pi$
$264$	−5.67961	+	11.7938i	−0.349556	+	0.725860i
$265$	5.14291	−	2.47670i	0.315927	−	0.152142i
$266$	−1.49272	−	6.54002i	−0.0915243	−	0.400994i
$267$	−3.13536	+	13.7369i	−0.191881	+	0.840685i
$268$	5.83119	+	2.80815i	0.356197	+	0.171535i
$269$	−4.69099	+	3.74094i	−0.286015	+	0.228089i	−0.755978	−	0.654597i	$-0.772838\pi$
$269$	−4.69099	+	3.74094i	−0.286015	+	0.228089i	0.469964	+	0.882686i	$0.344267\pi$
$270$	15.7559	+	19.7573i	0.958874	+	1.20239i
$271$	−5.28485	−	10.9741i	−0.321032	−	0.666630i	0.676530	−	0.736415i	$-0.263483\pi$
$271$	−5.28485	−	10.9741i	−0.321032	−	0.666630i	−0.997562	+	0.0697854i	$0.977769\pi$
$272$	25.1160	+	20.0294i	1.52288	+	1.21446i
$273$		−	15.3262i		−	0.927586i
$274$	13.9764	−	17.5259i	0.844345	−	1.05878i
$275$	11.0966	+	2.53273i	0.669150	+	0.152729i
$276$	3.15493	+	0.720093i	0.189905	+	0.0433445i
$277$	−14.7256	+	18.4653i	−0.884776	+	1.10947i	0.108545	+	0.994091i	$0.465381\pi$
$277$	−14.7256	+	18.4653i	−0.884776	+	1.10947i	−0.993321	+	0.115382i	$0.963191\pi$
$278$		−	23.7984i		−	1.42733i
$279$	0.325561	+	0.259626i	0.0194908	+	0.0155434i
$280$	6.19174	+	12.8573i	0.370027	+	0.768370i
$281$	−10.6770	−	13.3886i	−0.636938	−	0.798695i	0.353679	−	0.935367i	$-0.384931\pi$
$281$	−10.6770	−	13.3886i	−0.636938	−	0.798695i	−0.990616	+	0.136672i	$0.956359\pi$
$282$	−14.3280	+	11.4262i	−0.853222	+	0.680422i
$283$	−0.688279	−	0.331458i	−0.0409139	−	0.0197031i	0.413315	−	0.910588i	$-0.364371\pi$
$283$	−0.688279	−	0.331458i	−0.0409139	−	0.0197031i	−0.454229	+	0.890885i	$0.650085\pi$
$284$	−0.210120	+	0.920597i	−0.0124683	+	0.0546274i
$285$	1.90529	+	8.34763i	0.112860	+	0.494471i
$286$	−22.3426	+	10.7596i	−1.32114	+	0.636229i
$287$	2.76903	−	5.74995i	0.163451	−	0.339409i
$288$	1.25941	−	0.287452i	0.0742113	−	0.0169383i
$289$	−26.7984			−1.57637
$290$		0			0
$291$	−26.7984			−1.57095
$292$	−0.175818	+	0.0401294i	−0.0102890	+	0.00234840i
$293$	7.58088	−	15.7419i	0.442879	−	0.919649i	−0.553355	−	0.832946i	$-0.686653\pi$
$293$	7.58088	−	15.7419i	0.442879	−	0.919649i	0.996234	−	0.0867030i	$-0.0276331\pi$
$294$	4.71753	−	2.27184i	0.275132	−	0.132497i
$295$	3.23275	+	14.1636i	0.188218	+	0.824638i
$296$	−4.33296	+	18.9839i	−0.251848	+	1.10342i
$297$	−17.8377	−	8.59019i	−1.03505	−	0.498454i
$298$	−9.33841	+	7.44713i	−0.540959	+	0.431401i
$299$	−8.54693	−	10.7175i	−0.494281	−	0.619809i
$300$	1.36495	+	2.83436i	0.0788057	+	0.163642i
$301$	−4.83198	−	3.85338i	−0.278511	−	0.222105i
$302$			29.6525i			1.70631i
$303$	−1.63232	+	2.04686i	−0.0937742	+	0.117589i
$304$	8.77435	+	2.00269i	0.503244	+	0.114862i
$305$	−4.50225	−	1.02761i	−0.257798	−	0.0588407i
$306$	−2.55018	+	3.19782i	−0.145784	+	0.182807i
$307$			3.18034i			0.181512i	0.995873	+	0.0907558i	$0.0289283\pi$
$307$			3.18034i			0.181512i	−0.995873	+	0.0907558i	$0.971072\pi$
$308$	3.90916	+	3.11745i	0.222745	+	0.177633i
$309$	9.25311	+	19.2143i	0.526391	+	1.09306i
$310$	3.13892	+	3.93609i	0.178279	+	0.223555i
$311$	7.10698	−	5.66763i	0.403000	−	0.321382i	−0.400927	−	0.916110i	$-0.631312\pi$
$311$	7.10698	−	5.66763i	0.403000	−	0.321382i	0.803927	+	0.594728i	$0.202740\pi$
$312$	13.8085	+	6.64981i	0.781750	+	0.376471i
$313$	5.36057	−	23.4862i	0.302997	−	1.32752i	−0.562580	−	0.826743i	$-0.690191\pi$
$313$	5.36057	−	23.4862i	0.302997	−	1.32752i	0.865578	−	0.500775i	$-0.166952\pi$
$314$	−2.00269	−	8.77435i	−0.113018	−	0.495165i
$315$	−2.19629	+	1.05768i	−0.123747	+	0.0595933i
$316$	−1.36495	+	2.83436i	−0.0767847	+	0.159445i
$317$	−13.9335	+	3.18022i	−0.782582	+	0.178619i	−0.595103	−	0.803649i	$-0.702889\pi$
$317$	−13.9335	+	3.18022i	−0.782582	+	0.178619i	−0.187479	+	0.982269i	$0.560032\pi$
$318$	−5.23607			−0.293624
$319$		0			0
$320$	−12.0902			−0.675861
$321$	17.7245	−	4.04551i	0.989286	−	0.225798i
$322$	−5.08000	+	10.5487i	−0.283097	+	0.587858i
$323$	−11.0553	+	5.32397i	−0.615136	+	0.296234i
$324$	−1.06007	−	4.64449i	−0.0588930	−	0.258027i
$325$	2.96537	−	12.9921i	0.164489	−	0.720673i
$326$	33.5796	+	16.1711i	1.85980	+	0.895633i
$327$	−21.0223	+	16.7647i	−1.16254	+	0.927092i
$328$	3.97909	+	4.98962i	0.219709	+	0.275506i
$329$	−6.79135	−	14.1024i	−0.374420	−	0.777490i
$330$	−21.1364	−	16.8557i	−1.16352	−	0.927876i
$331$			1.18034i			0.0648773i	0.999474	+	0.0324387i	$0.0103274\pi$
$331$			1.18034i			0.0648773i	−0.999474	+	0.0324387i	$0.989673\pi$
$332$	−3.06123	+	3.83866i	−0.168007	+	0.210674i
$333$	−3.24284	−	0.740158i	−0.177707	−	0.0405604i
$334$	−30.7166	−	7.01087i	−1.68074	−	0.383618i
$335$	18.6352	−	23.3678i	1.01815	−	1.27672i
$336$		−	17.5623i		−	0.958102i
$337$	−18.8178	−	15.0067i	−1.02507	−	0.817467i	−0.0417105	−	0.999130i	$-0.513281\pi$
$337$	−18.8178	−	15.0067i	−1.02507	−	0.817467i	−0.983361	+	0.181663i	$0.941852\pi$
$338$	3.47107	+	7.20775i	0.188801	+	0.392050i
$339$	−10.0321	−	12.5798i	−0.544867	−	0.683241i
$340$	−9.12691	+	7.27847i	−0.494976	+	0.394731i
$341$	−3.55367	−	1.71136i	−0.192442	−	0.0926751i
$342$	−0.254986	+	1.11717i	−0.0137881	+	0.0604095i
$343$	4.47815	+	19.6200i	0.241797	+	1.05938i
$344$	5.56829	−	2.68155i	0.300222	−	0.144579i
$345$	6.48408	−	13.4643i	0.349091	−	0.724895i
$346$	−11.1845	+	2.55279i	−0.601283	+	0.137239i
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$		0			0
$349$	13.4721			0.721147			0.360573	−	0.932731i	$-0.382581\pi$
$349$	13.4721			0.721147			0.360573	+	0.932731i	$0.382581\pi$
$350$	−11.0966	+	2.53273i	−0.593138	+	0.135380i
$351$	−10.0576	+	20.8848i	−0.536834	+	1.11475i
$352$	−11.0243	+	5.30903i	−0.587598	+	0.282972i
$353$	4.70067	+	20.5950i	0.250191	+	1.09616i	0.931379	+	0.364051i	$0.118607\pi$
$353$	4.70067	+	20.5950i	0.250191	+	1.09616i	−0.681188	+	0.732109i	$0.738536\pi$
$354$	2.96537	−	12.9921i	0.157607	−	0.690523i
$355$	3.92884	+	1.89203i	0.208521	+	0.100418i
$356$	−4.20779	+	3.35560i	−0.223012	+	0.177846i
$357$	14.9290	+	18.7204i	0.790127	+	0.990788i
$358$	11.2326	+	23.3248i	0.593662	+	1.23275i
$359$	−22.0758	−	17.6049i	−1.16512	−	0.929151i	−0.166736	−	0.986002i	$-0.553323\pi$
$359$	−22.0758	−	17.6049i	−1.16512	−	0.929151i	−0.998383	+	0.0568505i	$0.981894\pi$
$360$		−	2.43769i		−	0.128478i
$361$	9.70294	−	12.1671i	0.510681	−	0.640374i
$362$	−18.8417	−	4.30049i	−0.990297	−	0.226029i
$363$	3.29717	+	0.752558i	0.173057	+	0.0394991i
$364$	3.64997	−	4.57692i	0.191311	−	0.239896i
$365$			0.832816i			0.0435916i
$366$	3.31189	+	2.64115i	0.173115	+	0.138055i
$367$	2.72067	+	5.64953i	0.142018	+	0.294903i	0.959830	−	0.280582i	$-0.0905275\pi$
$367$	2.72067	+	5.64953i	0.142018	+	0.294903i	−0.817812	+	0.575485i	$0.804813\pi$
$368$	−9.79390	−	12.2812i	−0.510543	−	0.640200i
$369$	−0.852329	+	0.679710i	−0.0443705	+	0.0353843i
$370$	−36.2323	−	17.4485i	−1.88363	−	0.907106i
$371$	0.995144	−	4.36001i	0.0516653	−	0.226360i
$372$	−0.242586	−	1.06284i	−0.0125775	−	0.0551055i
$373$	−16.5616	+	7.97564i	−0.857526	+	0.412963i	−0.810366	−	0.585925i	$-0.800731\pi$
$373$	−16.5616	+	7.97564i	−0.857526	+	0.412963i	−0.0471604	+	0.998887i	$0.515017\pi$
$374$	16.8098	−	34.9059i	0.869214	−	1.80494i
$375$	−8.34763	+	1.90529i	−0.431070	+	0.0983889i
$376$	15.6525			0.807215
$377$		0			0
$378$	19.7984			1.01832
$379$	−36.7628	+	8.39086i	−1.88838	+	0.431010i	−0.999625	−	0.0273785i	$-0.991284\pi$
$379$	−36.7628	+	8.39086i	−1.88838	+	0.431010i	−0.888752	+	0.458388i	$0.848427\pi$
$380$	−1.41902	+	2.94663i	−0.0727942	+	0.151159i
$381$	−2.83436	+	1.36495i	−0.145208	+	0.0699287i
$382$	4.33296	+	18.9839i	0.221693	+	0.971302i
$383$	−4.92793	+	21.5907i	−0.251805	+	1.10323i	0.677966	+	0.735093i	$0.262862\pi$
$383$	−4.92793	+	21.5907i	−0.251805	+	1.10323i	−0.929771	+	0.368138i	$0.879996\pi$
$384$	19.8523	+	9.56039i	1.01309	+	0.487876i
$385$	18.0526	−	14.3965i	0.920047	−	0.733713i
$386$	3.55901	+	4.46285i	0.181149	+	0.227153i
$387$	0.458063	+	0.951178i	0.0232847	+	0.0483511i
$388$	−8.00288	−	6.38208i	−0.406285	−	0.324001i
$389$		−	21.1246i		−	1.07106i	−0.844516	−	0.535530i	$-0.820112\pi$
$389$		−	21.1246i		−	1.07106i	0.844516	−	0.535530i	$-0.179888\pi$
$390$	−19.7350	+	24.7469i	−0.999320	+	1.25311i
$391$	20.8795	+	4.76560i	1.05592	+	0.241007i
$392$	−4.36001	−	0.995144i	−0.220214	−	0.0502624i
$393$	−1.33795	+	1.67773i	−0.0674904	+	0.0846303i
$394$			31.8885i			1.60652i
$395$	11.3583	+	9.05798i	0.571500	+	0.455756i
$396$	−0.370581	−	0.769519i	−0.0186224	−	0.0386698i
$397$	−19.9169	−	24.9750i	−0.999602	−	1.25346i	−0.967208	−	0.253986i	$-0.918258\pi$
$397$	−19.9169	−	24.9750i	−0.999602	−	1.25346i	−0.0323941	−	0.999475i	$-0.510313\pi$
$398$	1.08046	−	0.861642i	0.0541588	−	0.0431902i
$399$	6.04388	+	2.91058i	0.302573	+	0.145711i
$400$	3.39801	−	14.8876i	0.169900	−	0.744382i
$401$	7.35852	+	32.2398i	0.367467	+	1.60998i	0.733713	+	0.679460i	$0.237786\pi$
$401$	7.35852	+	32.2398i	0.367467	+	1.60998i	−0.366246	+	0.930518i	$0.619357\pi$
$402$	−24.7013	+	11.8955i	−1.23199	+	0.593295i
$403$	−2.00369	+	4.16070i	−0.0998109	+	0.207259i
$404$	−0.974928	+	0.222521i	−0.0485045	+	0.0110708i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	31.5066			1.56172
$408$	−23.3439	+	5.32810i	−1.15570	+	0.263780i
$409$	0.253211	−	0.525798i	0.0125205	−	0.0259991i	−0.894615	−	0.446838i	$-0.852550\pi$
$409$	0.253211	−	0.525798i	0.0125205	−	0.0259991i	0.907135	+	0.420839i	$0.138264\pi$
$410$	−11.8751	+	5.71874i	−0.586468	+	0.282428i
$411$	4.98812	+	21.8544i	0.246046	+	1.07800i
$412$	−1.81263	+	7.94166i	−0.0893020	+	0.391258i
$413$	10.2548	+	4.93845i	0.504606	+	0.243005i
$414$	1.56366	−	1.24698i	0.0768498	−	0.0612857i
$415$	14.1369	+	17.7271i	0.693951	+	0.870187i
$416$	6.21592	+	12.9075i	0.304761	+	0.632842i
$417$	18.6063	+	14.8380i	0.911155	+	0.726622i
$418$		−	10.8541i		−	0.530891i
$419$	−1.59757	+	2.00329i	−0.0780465	+	0.0978672i	−0.819322	−	0.573334i	$-0.805650\pi$
$419$	−1.59757	+	2.00329i	−0.0780465	+	0.0978672i	0.741275	+	0.671201i	$0.234221\pi$
$420$	6.22196	+	1.42012i	0.303600	+	0.0692948i
$421$	−1.91628	−	0.437378i	−0.0933937	−	0.0213165i	0.175569	−	0.984467i	$-0.443824\pi$
$421$	−1.91628	−	0.437378i	−0.0933937	−	0.0213165i	−0.268962	+	0.963151i	$0.586681\pi$
$422$	−19.8260	+	24.8610i	−0.965113	+	1.21021i
$423$			2.67376i			0.130003i
$424$	3.49646	+	2.78833i	0.169803	+	0.135413i
$425$	9.03331	+	18.7579i	0.438180	+	0.909890i
$426$	−2.49396	−	3.12733i	−0.120833	−	0.151519i
$427$	−2.82869	+	2.25581i	−0.136890	+	0.109166i
$428$	6.25657	+	3.01301i	0.302423	+	0.145639i
$429$	5.51816	−	24.1766i	0.266419	−	1.16726i
$430$	2.84024	+	12.4439i	0.136969	+	0.600099i
$431$	31.1706	−	15.0110i	1.50143	−	0.723053i	0.510814	−	0.859691i	$-0.329344\pi$
$431$	31.1706	−	15.0110i	1.50143	−	0.723053i	0.990621	+	0.136639i	$0.0436299\pi$
$432$	−11.5250	+	23.9318i	−0.554495	+	1.15142i
$433$	−12.3017	+	2.80778i	−0.591181	+	0.134933i	−0.507637	−	0.861571i	$-0.669481\pi$
$433$	−12.3017	+	2.80778i	−0.591181	+	0.134933i	−0.0835436	+	0.996504i	$0.526624\pi$
$434$	3.94427			0.189331
$435$		0			0
$436$	−10.2705			−0.491868
$437$	5.84957	−	1.33513i	0.279823	−	0.0638677i
$438$	0.331458	−	0.688279i	0.0158377	−	0.0328872i
$439$	−2.75312	+	1.32583i	−0.131399	+	0.0632784i	−0.498428	−	0.866931i	$-0.666089\pi$
$439$	−2.75312	+	1.32583i	−0.131399	+	0.0632784i	0.367029	+	0.930209i	$0.380375\pi$
$440$	5.13805	+	22.5113i	0.244947	+	1.07318i
$441$	0.169991	−	0.744779i	0.00809480	−	0.0354657i
$442$	−40.8686	−	19.6813i	−1.94392	−	0.936142i
$443$	−10.2343	+	8.16159i	−0.486247	+	0.387769i	−0.835701	−	0.549185i	$-0.814938\pi$
$443$	−10.2343	+	8.16159i	−0.486247	+	0.387769i	0.349454	+	0.936953i	$0.386367\pi$
$444$	5.42948	+	6.80835i	0.257672	+	0.323110i
$445$	10.7838	+	22.3928i	0.511201	+	1.06152i
$446$	−23.1832	−	18.4880i	−1.09776	−	0.875433i
$447$		−	11.9443i		−	0.564945i
$448$	−5.90578	+	7.40561i	−0.279022	+	0.349882i
$449$	−13.7705	−	3.14302i	−0.649869	−	0.148328i	−0.115136	−	0.993350i	$-0.536731\pi$
$449$	−13.7705	−	3.14302i	−0.649869	−	0.148328i	−0.534733	+	0.845021i	$0.679588\pi$
$450$	1.89552	+	0.432641i	0.0893559	+	0.0203949i
$451$	6.43830	−	8.07338i	0.303168	−	0.380161i
$452$		−	6.14590i		−	0.289079i
$453$	−23.1832	−	18.4880i	−1.08924	−	0.868643i
$454$	10.4523	+	21.7045i	0.490552	+	1.01864i
$455$	−16.8557	−	21.1364i	−0.790207	−	0.990889i
$456$	−5.24469	+	4.18250i	−0.245605	+	0.195863i
$457$	4.76774	+	2.29602i	0.223026	+	0.107403i	0.542060	−	0.840340i	$-0.317644\pi$
$457$	4.76774	+	2.29602i	0.223026	+	0.107403i	−0.319035	+	0.947743i	$0.603359\pi$
$458$	5.65568	−	24.7792i	0.264273	−	1.15785i
$459$	−8.05855	−	35.3068i	−0.376141	−	1.64798i
$460$	5.14291	−	2.47670i	0.239790	−	0.115477i
$461$	−3.46183	+	7.18857i	−0.161234	+	0.334805i	−0.965897	−	0.258926i	$-0.916631\pi$
$461$	−3.46183	+	7.18857i	−0.161234	+	0.334805i	0.804663	+	0.593731i	$0.202346\pi$
$462$	−20.6493	+	4.71307i	−0.960693	+	0.219272i
$463$	2.70820			0.125861			0.0629305	−	0.998018i	$-0.479955\pi$
$463$	2.70820			0.125861			0.0629305	+	0.998018i	$0.479955\pi$
$464$		0			0
$465$	−5.03444			−0.233467
$466$	−16.9797	+	3.87552i	−0.786571	+	0.179530i
$467$	−0.0241795	+	0.0502093i	−0.00111889	+	0.00232341i	−0.901528	−	0.432722i	$-0.857553\pi$
$467$	−0.0241795	+	0.0502093i	−0.00111889	+	0.00232341i	0.900409	+	0.435045i	$0.143268\pi$
$468$	−0.900969	+	0.433884i	−0.0416473	+	0.0200563i
$469$	−5.21064	−	22.8293i	−0.240605	−	1.05416i
$470$	−7.19326	+	31.5158i	−0.331801	+	1.45371i
$471$	8.10872	+	3.90495i	0.373630	+	0.179931i
$472$	−8.89878	+	7.09654i	−0.409600	+	0.326645i
$473$	−6.23490	−	7.81831i	−0.286681	−	0.359486i
$474$	−5.78204	−	12.0065i	−0.265578	−	0.551478i
$475$	4.56028	+	3.63670i	0.209240	+	0.166863i
$476$			9.14590i			0.419202i
$477$	−0.476304	+	0.597266i	−0.0218085	+	0.0273469i
$478$	23.2560	+	5.30804i	1.06371	+	0.242784i
$479$	10.9000	+	2.48786i	0.498035	+	0.113673i	0.464157	−	0.885753i	$-0.346357\pi$
$479$	10.9000	+	2.48786i	0.498035	+	0.113673i	0.0338776	+	0.999426i	$0.489214\pi$
$480$	−9.73768	+	12.2107i	−0.444462	+	0.557338i
$481$		−	36.8885i		−	1.68197i
$482$	33.7162	+	26.8878i	1.53573	+	1.22470i
$483$	−5.08000	−	10.5487i	−0.231148	−	0.479984i
$484$	0.805422	+	1.00997i	0.0366101	+	0.0459076i
$485$	−36.9576	+	29.4727i	−1.67816	+	1.33829i
$486$	−5.74995	−	2.76903i	−0.260823	−	0.125606i
$487$	−4.99286	+	21.8751i	−0.226248	+	0.991257i	0.726422	+	0.687249i	$0.241182\pi$
$487$	−4.99286	+	21.8751i	−0.226248	+	0.991257i	−0.952670	+	0.304008i	$0.901675\pi$
$488$	−0.805088	−	3.52732i	−0.0364446	−	0.159674i
$489$	−33.5796	+	16.1711i	−1.51852	+	0.731281i
$490$	4.00738	−	8.32141i	0.181035	−	0.375923i
$491$	−24.4947	+	5.59075i	−1.10543	+	0.252307i	−0.736020	−	0.676960i	$-0.763297\pi$
$491$	−24.4947	+	5.59075i	−1.10543	+	0.252307i	−0.369409	+	0.929267i	$0.620440\pi$
$492$	2.85410			0.128673
$493$		0			0
$494$	−12.7082			−0.571769
$495$	−3.84538	+	0.877683i	−0.172837	+	0.0394489i
$496$	−2.29602	+	4.76774i	−0.103095	+	0.214078i
$497$	3.07808	−	1.48232i	0.138071	−	0.0664913i
$498$	−4.62807	−	20.2769i	−0.207389	−	0.908630i
$499$	−7.94109	+	34.7922i	−0.355492	+	1.55751i	0.408790	+	0.912629i	$0.365951\pi$
$499$	−7.94109	+	34.7922i	−0.355492	+	1.55751i	−0.764281	+	0.644883i	$0.776906\pi$
$500$	−2.94663	−	1.41902i	−0.131777	−	0.0634605i
$501$	24.6328	−	19.6440i	1.10051	−	0.877631i
$502$	11.7553	+	14.7407i	0.524667	+	0.657911i
$503$	−8.36116	−	17.3621i	−0.372806	−	0.774139i	0.627183	−	0.778872i	$-0.284208\pi$
$503$	−8.36116	−	17.3621i	−0.372806	−	0.774139i	−0.999989	+	0.00473279i	$0.998494\pi$
$504$	−1.49317	−	1.19076i	−0.0665109	−	0.0530406i
$505$			4.61803i			0.205500i
$506$	−11.8116	+	14.8112i	−0.525088	+	0.658439i
$507$	−7.79942	−	1.78017i	−0.346385	−	0.0790600i
$508$	−1.17150	−	0.267387i	−0.0519769	−	0.0118634i
$509$	7.13129	−	8.94235i	0.316089	−	0.396363i	−0.598252	−	0.801308i	$-0.704138\pi$
$509$	7.13129	−	8.94235i	0.316089	−	0.396363i	0.914341	+	0.404945i	$0.132709\pi$
$510$		−	49.4508i		−	2.18972i
$511$	0.510126	+	0.406812i	0.0225667	+	0.0179963i
$512$	−2.29602	−	4.76774i	−0.101471	−	0.210706i
$513$	−6.32586	−	7.93238i	−0.279294	−	0.350223i
$514$	−1.03689	+	0.826896i	−0.0457355	+	0.0364728i
$515$	33.8927	+	16.3219i	1.49349	+	0.719227i
$516$	0.615033	−	2.69463i	0.0270753	−	0.118625i
$517$	−5.63562	−	24.6913i	−0.247854	−	1.08592i
$518$	−28.3864	+	13.6702i	−1.24723	+	0.600634i
$519$	4.97757	−	10.3360i	0.218491	−	0.453702i
$520$	26.3566	−	6.01573i	1.15581	−	0.263807i
$521$	7.09017			0.310626			0.155313	−	0.987865i	$-0.450361\pi$
$521$	7.09017			0.310626			0.155313	+	0.987865i	$0.450361\pi$
$522$		0			0
$523$	−22.6180			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$523$	−22.6180			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$524$	−0.799110	+	0.182392i	−0.0349093	+	0.00796781i
$525$	4.93845	−	10.2548i	0.215532	−	0.447556i
$526$	4.79877	−	2.31097i	0.209237	−	0.100763i
$527$	−1.60544	−	7.03389i	−0.0699341	−	0.306401i
$528$	6.32325	−	27.7039i	0.275184	−	1.20566i
$529$	11.2872	+	5.43564i	0.490748	+	0.236332i
$530$	−7.22105	+	5.75859i	−0.313662	+	0.250137i
$531$	−1.21223	−	1.52009i	−0.0526065	−	0.0659664i
$532$	1.11174	+	2.30856i	0.0482002	+	0.100089i
$533$	−9.45248	−	7.53810i	−0.409432	−	0.326511i
$534$		−	22.7984i		−	0.986582i
$535$	19.9946	−	25.0725i	0.864443	−	1.08398i
$536$	22.8293	+	5.21064i	0.986076	+	0.225065i
$537$	−25.2395	−	5.76074i	−1.08916	−	0.248594i
$538$	6.05297	−	7.59018i	0.260962	−	0.327236i
$539$			7.23607i			0.311680i
$540$	−7.54661	−	6.01822i	−0.324754	−	0.258983i
$541$	−15.0110	−	31.1706i	−0.645372	−	1.34013i	−0.924981	−	0.380014i	$-0.875919\pi$
$541$	−15.0110	−	31.1706i	−0.645372	−	1.34013i	0.279609	−	0.960114i	$-0.409795\pi$
$542$	12.2879	+	15.4085i	0.527809	+	0.661852i
$543$	15.1099	−	12.0497i	0.648426	−	0.517103i
$544$	−20.1655	−	9.71117i	−0.864587	−	0.416363i
$545$	−10.5541	+	46.2404i	−0.452087	+	1.98072i
$546$	5.51816	+	24.1766i	0.236155	+	1.03466i
$547$	−8.66555	+	4.17311i	−0.370512	+	0.178429i	−0.609869	−	0.792503i	$-0.708778\pi$
$547$	−8.66555	+	4.17311i	−0.370512	+	0.178429i	0.239357	+	0.970932i	$0.423064\pi$
$548$	−3.71505	+	7.71437i	−0.158699	+	0.329542i
$549$	0.602539	−	0.137526i	0.0257157	−	0.00586945i
$550$	−18.4164			−0.785278
$551$		0			0
$552$	11.7082			0.498334
$553$	11.0966	−	2.53273i	0.471875	−	0.107702i
$554$	16.5808	−	34.4303i	0.704450	−	1.46280i
$555$	36.2323	−	17.4485i	1.53797	−	0.740649i
$556$	2.02275	+	8.86226i	0.0857838	+	0.375844i
$557$	7.23339	−	31.6916i	0.306489	−	1.34281i	−0.553648	−	0.832751i	$-0.686765\pi$
$557$	7.23339	−	31.6916i	0.306489	−	1.34281i	0.860136	−	0.510064i	$-0.170378\pi$
$558$	−0.607039	−	0.292334i	−0.0256980	−	0.0123755i
$559$	−9.15384	+	7.29995i	−0.387166	+	0.308755i
$560$	−19.3149	−	24.2201i	−0.816204	−	1.02349i
$561$	16.8098	+	34.9059i	0.709710	+	1.47373i
$562$	21.6631	+	17.2758i	0.913805	+	0.728735i
$563$			45.3951i			1.91318i	0.291443	+	0.956588i	$0.405865\pi$
$563$			45.3951i			1.91318i	−0.291443	+	0.956588i	$0.594135\pi$
$564$	4.36443	−	5.47282i	0.183776	−	0.230447i
$565$	−27.6704	−	6.31558i	−1.16410	−	0.265699i
$566$	1.20508	+	0.275051i	0.0506532	+	0.0115613i
$567$	−10.7465	+	13.4757i	−0.451311	+	0.565926i
$568$			3.41641i			0.143349i
$569$	−12.4657	−	9.94109i	−0.522591	−	0.416752i	0.326343	−	0.945251i	$-0.394184\pi$
$569$	−12.4657	−	9.94109i	−0.522591	−	0.416752i	−0.848934	+	0.528499i	$0.822755\pi$
$570$	−6.01107	−	12.4821i	−0.251776	−	0.522818i
$571$	2.18632	+	2.74155i	0.0914945	+	0.114730i	0.825471	−	0.564444i	$-0.190909\pi$
$571$	2.18632	+	2.74155i	0.0914945	+	0.114730i	−0.733977	+	0.679174i	$0.762338\pi$
$572$	7.40561	−	5.90578i	0.309644	−	0.246933i
$573$	−17.5438	−	8.44864i	−0.732902	−	0.352947i
$574$	−2.29780	+	10.0673i	−0.0959085	+	0.420203i
$575$	−2.26534	−	9.92510i	−0.0944712	−	0.413905i
$576$	1.45780	−	0.702039i	0.0607416	−	0.0292516i
$577$	3.13961	−	6.51947i	0.130704	−	0.271409i	−0.825338	−	0.564638i	$-0.809016\pi$
$577$	3.13961	−	6.51947i	0.130704	−	0.271409i	0.956042	+	0.293229i	$0.0947299\pi$
$578$	42.2735	−	9.64866i	1.75835	−	0.401331i
$579$	−5.70820			−0.237225
$580$		0			0
$581$	17.7639			0.736972
$582$	42.2735	−	9.64866i	1.75229	−	0.399950i
$583$	3.13961	−	6.51947i	0.130029	−	0.270009i
$584$	−0.587860	+	0.283099i	−0.0243258	+	0.0117147i
$585$	1.02761	+	4.50225i	0.0424864	+	0.186145i
$586$	−6.29078	+	27.5617i	−0.259870	+	1.13856i
$587$	−39.9868	−	19.2566i	−1.65043	−	0.794805i	−0.999359	−	0.0357889i	$-0.988606\pi$
$587$	−39.9868	−	19.2566i	−1.65043	−	0.794805i	−0.651071	−	0.759017i	$-0.725680\pi$
$588$	−1.56366	+	1.24698i	−0.0644844	+	0.0514246i
$589$	−1.26025	−	1.58031i	−0.0519278	−	0.0651153i
$590$	−10.1991	−	21.1787i	−0.419891	−	0.871913i
$591$	−24.9315	−	19.8822i	−1.02554	−	0.817844i
$592$		−	42.2705i		−	1.73731i
$593$	21.5492	−	27.0219i	0.884921	−	1.10966i	−0.108381	−	0.994109i	$-0.534567\pi$
$593$	21.5492	−	27.0219i	0.884921	−	1.10966i	0.993302	−	0.115547i	$-0.0368621\pi$
$594$	31.2313	+	7.12833i	1.28143	+	0.292479i
$595$	41.1771	+	9.39841i	1.68810	+	0.385297i
$596$	2.84455	−	3.56695i	0.116517	−	0.146108i
$597$			1.38197i			0.0565601i
$598$	17.3413	+	13.8292i	0.709138	+	0.565519i
$599$	19.5547	+	40.6057i	0.798982	+	1.65910i	0.751044	+	0.660252i	$0.229551\pi$
$599$	19.5547	+	40.6057i	0.798982	+	1.65910i	0.0479374	+	0.998850i	$0.484735\pi$
$600$	7.09654	+	8.89878i	0.289715	+	0.363291i
$601$	31.3976	−	25.0388i	1.28074	−	1.02135i	0.282668	−	0.959218i	$-0.408781\pi$
$601$	31.3976	−	25.0388i	1.28074	−	1.02135i	0.998068	−	0.0621344i	$-0.0197907\pi$
$602$	9.00969	+	4.33884i	0.367207	+	0.176838i
$603$	−0.890084	+	3.89971i	−0.0362470	+	0.158809i
$604$	−2.52033	−	11.0423i	−0.102551	−	0.449303i
$605$	5.37478	−	2.58836i	0.218516	−	0.105232i
$606$	1.83796	−	3.81657i	0.0746621	−	0.155037i
$607$	35.0767	−	8.00602i	1.42372	−	0.324954i	0.559817	−	0.828616i	$-0.310872\pi$
$607$	35.0767	−	8.00602i	1.42372	−	0.324954i	0.863901	+	0.503662i	$0.168014\pi$
$608$	−6.27051			−0.254303
$609$		0			0
$610$	7.47214			0.302538
$611$	−28.9090	+	6.59830i	−1.16953	+	0.266939i
$612$	0.677859	−	1.40759i	0.0274008	−	0.0568984i
$613$	−35.6252	+	17.1562i	−1.43889	+	0.692933i	−0.980627	−	0.195884i	$-0.937242\pi$
$613$	−35.6252	+	17.1562i	−1.43889	+	0.692933i	−0.458262	+	0.888817i	$0.651528\pi$
$614$	−1.14507	−	5.01688i	−0.0462113	−	0.202465i
$615$	2.93290	−	12.8499i	0.118266	−	0.518157i
$616$	16.2987	+	7.84903i	0.656693	+	0.316246i
$617$	6.39565	−	5.10036i	0.257479	−	0.205333i	−0.486239	−	0.873826i	$-0.661632\pi$
$617$	6.39565	−	5.10036i	0.257479	−	0.205333i	0.743719	+	0.668493i	$0.233060\pi$
$618$	−21.5145	−	26.9783i	−0.865440	−	1.08523i
$619$	10.8229	+	22.4740i	0.435010	+	0.903307i	0.997091	+	0.0762247i	$0.0242866\pi$
$619$	10.8229	+	22.4740i	0.435010	+	0.903307i	−0.562081	+	0.827082i	$0.689999\pi$
$620$	−1.50345	−	1.19896i	−0.0603800	−	0.0481515i
$621$			17.7082i			0.710606i
$622$	−9.17042	+	11.4993i	−0.367700	+	0.461081i
$623$	18.9839	+	4.33296i	0.760575	+	0.173596i
$624$	−32.4363	−	7.40338i	−1.29849	−	0.296373i
$625$	−19.2239	+	24.1061i	−0.768958	+	0.964243i
$626$			38.9787i			1.55790i
$627$	8.48608	+	6.76742i	0.338901	+	0.270265i
$628$	1.49156	+	3.09726i	0.0595197	+	0.123594i
$629$	35.9325	+	45.0579i	1.43272	+	1.79658i
$630$	3.08376	−	2.45921i	0.122860	−	0.0979774i
$631$	20.9158	+	10.0725i	0.832645	+	0.400981i	0.801106	−	0.598522i	$-0.204245\pi$
$631$	20.9158	+	10.0725i	0.832645	+	0.400981i	0.0315383	+	0.999503i	$0.489959\pi$
$632$	−2.53273	+	11.0966i	−0.100746	+	0.441399i
$633$	−7.07580	−	31.0011i	−0.281238	−	1.23218i
$634$	20.8346	−	10.0334i	0.827446	−	0.398477i
$635$	−2.40769	+	4.99961i	−0.0955461	+	0.198404i
$636$	1.94986	−	0.445042i	0.0773168	−	0.0176471i
$637$	8.47214			0.335678
$638$		0			0
$639$	−0.583592			−0.0230865
$640$	37.8928	−	8.64878i	1.49784	−	0.341873i
$641$	12.5584	−	26.0779i	0.496029	−	1.03001i	−0.491250	−	0.871018i	$-0.663460\pi$
$641$	12.5584	−	26.0779i	0.496029	−	1.03001i	0.987279	−	0.158996i	$-0.0508258\pi$
$642$	−26.5033	+	12.7633i	−1.04600	+	0.503727i
$643$	−2.35507	−	10.3182i	−0.0928749	−	0.406912i	0.907025	−	0.421077i	$-0.138348\pi$
$643$	−2.35507	−	10.3182i	−0.0928749	−	0.406912i	−0.999900	+	0.0141657i	$0.995491\pi$
$644$	0.995144	−	4.36001i	0.0392142	−	0.171808i
$645$	−11.4999	−	5.53806i	−0.452808	−	0.218061i
$646$	15.5226	−	12.3788i	0.610727	−	0.487039i
$647$	24.6105	+	30.8606i	0.967538	+	1.21325i	0.976987	+	0.213298i	$0.0684207\pi$
$647$	24.6105	+	30.8606i	0.967538	+	1.21325i	−0.00944952	+	0.999955i	$0.503008\pi$
$648$	−7.47845	−	15.5292i	−0.293781	−	0.610043i
$649$	14.3985	+	11.4824i	0.565192	+	0.450725i
$650$			21.5623i			0.845743i
$651$	−2.45921	+	3.08376i	−0.0963842	+	0.120862i
$652$	−13.8791	−	3.16782i	−0.543549	−	0.124062i
$653$	−27.3108	−	6.23351i	−1.06875	−	0.243936i	−0.348261	−	0.937398i	$-0.613228\pi$
$653$	−27.3108	−	6.23351i	−1.06875	−	0.243936i	−0.720494	+	0.693461i	$0.756085\pi$
$654$	27.1259	−	34.0148i	1.06071	−	1.33008i
$655$			3.78522i			0.147901i
$656$	−10.8316	−	8.63789i	−0.422902	−	0.337253i
$657$	−0.0483590	−	0.100419i	−0.00188667	−	0.00391770i
$658$	15.7907	+	19.8009i	0.615584	+	0.771918i
$659$	19.5022	−	15.5525i	0.759699	−	0.605839i	−0.165109	−	0.986275i	$-0.552798\pi$
$659$	19.5022	−	15.5525i	0.759699	−	0.605839i	0.924807	+	0.380436i	$0.124226\pi$
$660$	9.30362	+	4.48039i	0.362143	+	0.174399i
$661$	−4.10570	+	17.9882i	−0.159693	+	0.699662i	0.830155	+	0.557533i	$0.188252\pi$
$661$	−4.10570	+	17.9882i	−0.159693	+	0.699662i	−0.989848	+	0.142129i	$0.954605\pi$
$662$	−0.424977	−	1.86195i	−0.0165172	−	0.0723666i
$663$	40.8686	−	19.6813i	1.58720	−	0.764357i
$664$	−7.70748	+	16.0047i	−0.299108	+	0.621105i
$665$	11.5361	−	2.63305i	0.447352	−	0.102105i
$666$	5.38197			0.208547
$667$		0			0
$668$	12.0344			0.465627
$669$	28.9090	−	6.59830i	1.11769	−	0.255105i
$670$	−20.9829	+	43.5715i	−0.810641	+	1.68331i
$671$	−5.27436	+	2.54000i	−0.203615	+	0.0980556i
$672$	2.72278	+	11.9293i	0.105034	+	0.460182i
$673$	0.550102	−	2.41015i	0.0212049	−	0.0929046i	−0.963218	−	0.268721i	$-0.913399\pi$
$673$	0.550102	−	2.41015i	0.0212049	−	0.0929046i	0.984423	+	0.175816i	$0.0562563\pi$
$674$	35.0876	+	16.8973i	1.35152	+	0.650859i
$675$	−13.4591	+	10.7332i	−0.518039	+	0.413123i
$676$	−1.90522	−	2.38906i	−0.0732775	−	0.0918871i
$677$	5.56795	+	11.5620i	0.213994	+	0.444363i	0.980141	−	0.198303i	$-0.0635429\pi$
$677$	5.56795	+	11.5620i	0.213994	+	0.444363i	−0.766147	+	0.642665i	$0.777829\pi$
$678$	20.3545	+	16.2322i	0.781712	+	0.623394i
$679$			37.0344i			1.42125i
$680$	−26.3338	+	33.0215i	−1.00985	+	1.26632i
$681$	−23.4862	−	5.36057i	−0.899992	−	0.205417i
$682$	6.22196	+	1.42012i	0.238251	+	0.0543792i
$683$	8.81982	−	11.0597i	0.337481	−	0.423188i	−0.583914	−	0.811816i	$-0.698479\pi$
$683$	8.81982	−	11.0597i	0.337481	−	0.423188i	0.921395	+	0.388628i	$0.127051\pi$
$684$		−	0.437694i		−	0.0167357i
$685$	30.9144	+	24.6534i	1.18118	+	0.941959i
$686$	−14.1283	−	29.3376i	−0.539419	−	1.12012i
$687$	15.8469	+	19.8713i	0.604596	+	0.758139i
$688$	−10.4894	+	8.36499i	−0.399903	+	0.318912i
$689$	−7.63313	−	3.67592i	−0.290799	−	0.140041i
$690$	−5.38063	+	23.5741i	−0.204837	+	0.897450i
$691$	9.30868	+	40.7840i	0.354119	+	1.55150i	0.767567	+	0.640968i	$0.221467\pi$
$691$	9.30868	+	40.7840i	0.354119	+	1.55150i	−0.413449	+	0.910527i	$0.635676\pi$
$692$	3.94801	−	1.90126i	0.150081	−	0.0722752i
$693$	−1.34077	+	2.78415i	−0.0509318	+	0.105761i
$694$	12.8163	−	2.92524i	0.486500	−	0.111040i
$695$	41.9787			1.59234
$696$		0			0
$697$	18.8885			0.715455
$698$	−21.2518	+	4.85059i	−0.804394	+	0.183598i
$699$	7.55670	−	15.6916i	0.285820	−	0.593512i
$700$	3.91698	−	1.88632i	0.148048	−	0.0712962i
$701$	−8.66592	−	37.9679i	−0.327307	−	1.43403i	−0.824242	−	0.566238i	$-0.808398\pi$
$701$	−8.66592	−	37.9679i	−0.327307	−	1.43403i	0.496935	−	0.867788i	$-0.334459\pi$
$702$	8.34600	−	36.5662i	0.314999	−	1.38010i
$703$	14.5470	+	7.00544i	0.548649	+	0.264215i
$704$	−11.9825	+	9.55575i	−0.451609	+	0.360146i
$705$	−20.1551	−	25.2737i	−0.759084	−	0.951861i
$706$	−14.8303	−	30.7954i	−0.558145	−	1.15900i
$707$	2.82869	+	2.25581i	0.106384	+	0.0848384i
$708$			5.09017i			0.191300i
$709$	2.17811	−	2.73127i	0.0818008	−	0.102575i	−0.739247	−	0.673434i	$-0.764818\pi$
$709$	2.17811	−	2.73127i	0.0818008	−	0.102575i	0.821048	+	0.570859i	$0.193390\pi$
$710$	−6.87883	−	1.57005i	−0.258158	−	0.0589228i
$711$	−1.89552	−	0.432641i	−0.0710877	−	0.0162253i
$712$	−12.1407	+	15.2239i	−0.454991	+	0.570541i
$713$			3.52786i			0.132120i
$714$	−30.2902	−	24.1556i	−1.13358	−	0.904002i
$715$	−18.9792	−	39.4108i	−0.709783	−	1.47388i
$716$	−6.16541	−	7.73117i	−0.230412	−	0.288928i
$717$	−18.6499	+	14.8728i	−0.696493	+	0.555434i
$718$	41.1625	+	19.8228i	1.53617	+	0.739781i
$719$	6.56583	−	28.7668i	0.244864	−	1.07282i	−0.691662	−	0.722222i	$-0.743121\pi$
$719$	6.56583	−	28.7668i	0.244864	−	1.07282i	0.936526	−	0.350598i	$-0.114022\pi$
$720$	1.17754	+	5.15912i	0.0438842	+	0.192269i
$721$	26.5535	−	12.7875i	0.988903	−	0.476231i
$722$	−10.9253	+	22.6867i	−0.406599	+	0.844312i
$723$	−42.0434	+	9.59613i	−1.56361	+	0.356884i
$724$	7.38197			0.274349
$725$		0			0
$726$	−5.47214			−0.203090
$727$	44.7924	−	10.2236i	1.66126	−	0.379171i	0.714125	−	0.700018i	$-0.246825\pi$
$727$	44.7924	−	10.2236i	1.66126	−	0.379171i	0.947131	+	0.320847i	$0.103967\pi$
$728$	9.18981	−	19.0828i	0.340597	−	0.707257i
$729$	26.5845	−	12.8024i	0.984611	−	0.474164i
$730$	−0.299852	−	1.31374i	−0.0110980	−	0.0486237i
$731$	4.07031	−	17.8332i	0.150546	−	0.659584i
$732$	−1.45780	−	0.702039i	−0.0538818	−	0.0259481i
$733$	29.0688	−	23.1816i	1.07368	−	0.856231i	0.0835661	−	0.996502i	$-0.473369\pi$
$733$	29.0688	−	23.1816i	1.07368	−	0.856231i	0.990113	+	0.140272i	$0.0447976\pi$
$734$	−6.32586	−	7.93238i	−0.233492	−	0.292790i
$735$	4.00738	+	8.32141i	0.147814	+	0.306940i
$736$	8.55658	+	6.82364i	0.315400	+	0.251523i
$737$		−	37.8885i		−	1.39564i
$738$	1.09979	−	1.37910i	0.0404840	−	0.0507653i
$739$	−7.86658	−	1.79550i	−0.289377	−	0.0660484i	0.0753683	−	0.997156i	$-0.475987\pi$
$739$	−7.86658	−	1.79550i	−0.289377	−	0.0660484i	−0.364745	+	0.931107i	$0.618844\pi$
$740$	14.9756	+	3.41807i	0.550512	+	0.125651i
$741$	7.92344	−	9.93567i	0.291075	−	0.364996i
$742$			7.23607i			0.265644i
$743$	−24.0522	−	19.1810i	−0.882390	−	0.703683i	0.0735353	−	0.997293i	$-0.476572\pi$
$743$	−24.0522	−	19.1810i	−0.882390	−	0.703683i	−0.955925	+	0.293610i	$0.905143\pi$
$744$	−1.71136	−	3.55367i	−0.0627413	−	0.130284i
$745$	−13.1362	−	16.4723i	−0.481274	−	0.603499i
$746$	23.2537	−	18.5442i	0.851380	−	0.678953i
$747$	−2.73394	−	1.31659i	−0.100030	−	0.0481717i
$748$	−3.29295	+	14.4273i	−0.120402	+	0.527516i
$749$	−5.59075	−	24.4947i	−0.204282	−	0.895016i
$750$	12.4821	−	6.01107i	0.455782	−	0.219493i
$751$	11.9197	−	24.7515i	0.434957	−	0.903196i	−0.562140	−	0.827042i	$-0.690022\pi$
$751$	11.9197	−	24.7515i	0.434957	−	0.903196i	0.997096	−	0.0761541i	$-0.0242641\pi$
$752$	−33.1268	+	7.56098i	−1.20801	+	0.275720i
$753$	−18.8541			−0.687082
$754$		0			0
$755$	−52.3050			−1.90357
$756$	−7.37270	+	1.68277i	−0.268143	+	0.0612018i
$757$	−20.3833	+	42.3264i	−0.740844	+	1.53838i	0.0987194	+	0.995115i	$0.468525\pi$
$757$	−20.3833	+	42.3264i	−0.740844	+	1.53838i	−0.839563	+	0.543262i	$0.817189\pi$
$758$	54.9710	−	26.4726i	1.99663	−	0.961529i
$759$	−4.21550	−	18.4693i	−0.153013	−	0.670393i
$760$	−2.63305	+	11.5361i	−0.0955107	+	0.418460i
$761$	−44.8668	−	21.6067i	−1.62642	−	0.783242i	−0.999993	−	0.00376214i	$-0.998802\pi$
$761$	−44.8668	−	21.6067i	−1.62642	−	0.783242i	−0.626427	−	0.779480i	$-0.715483\pi$
$762$	3.97966	−	3.17367i	0.144168	−	0.114970i
$763$	23.1683	+	29.0521i	0.838748	+	1.05176i
$764$	−3.22709	−	6.70113i	−0.116752	−	0.242438i
$765$	−5.64074	−	4.49834i	−0.203942	−	0.162638i
$766$		−	35.8328i		−	1.29469i
$767$	13.4439	−	16.8581i	0.485430	−	0.608710i
$768$	−21.3941	−	4.88306i	−0.771992	−	0.176202i
$769$	24.7248	+	5.64328i	0.891600	+	0.203502i	0.643695	−	0.765282i	$-0.277401\pi$
$769$	24.7248	+	5.64328i	0.891600	+	0.203502i	0.247905	+	0.968784i	$0.420258\pi$
$770$	−23.2940	+	29.2098i	−0.839458	+	1.05265i
$771$		−	1.32624i		−	0.0477633i
$772$	−1.70466	−	1.35942i	−0.0613520	−	0.0489266i
$773$	6.07437	+	12.6136i	0.218480	+	0.453678i	0.981185	−	0.193068i	$-0.0618437\pi$
$773$	6.07437	+	12.6136i	0.218480	+	0.453678i	−0.762705	+	0.646746i	$0.776129\pi$
$774$	−1.06505	−	1.33553i	−0.0382824	−	0.0480045i
$775$	−2.68134	+	2.13830i	−0.0963166	+	0.0768099i
$776$	−33.3669	−	16.0686i	−1.19780	−	0.576831i
$777$	7.01087	−	30.7166i	0.251514	−	1.10195i
$778$	7.60584	+	33.3234i	0.272683	+	1.19470i
$779$	4.76774	−	2.29602i	0.170822	−	0.0822636i
$780$	5.24573	−	10.8929i	0.187827	−	0.390027i
$781$	5.38927	−	1.23007i	0.192843	−	0.0440152i
$782$	−34.6525			−1.23917
$783$		0			0
$784$	9.70820			0.346722
$785$	15.4774	−	3.53261i	0.552411	−	0.126084i
$786$	1.50650	−	3.12829i	0.0537352	−	0.111582i
$787$	−22.8492	+	11.0036i	−0.814485	+	0.392236i	−0.794274	−	0.607560i	$-0.792148\pi$
$787$	−22.8492	+	11.0036i	−0.814485	+	0.392236i	−0.0202118	+	0.999796i	$0.506434\pi$
$788$	−2.71038	−	11.8750i	−0.0965533	−	0.423028i
$789$	−1.18520	+	5.19270i	−0.0421942	+	0.184865i
$790$	−21.1787	−	10.1991i	−0.753504	−	0.362868i
$791$	−17.3849	+	13.8640i	−0.618134	+	0.492946i
$792$	−1.92669	−	2.41599i	−0.0684619	−	0.0858485i
$793$	2.97388	+	6.17533i	0.105606	+	0.219292i
$794$	40.4105	+	32.2263i	1.43411	+	1.14367i
$795$		−	9.23607i		−	0.327570i
$796$	−0.329118	+	0.412701i	−0.0116653	+	0.0146278i
$797$	−20.2977	−	4.63281i	−0.718980	−	0.164103i	−0.152649	−	0.988280i	$-0.548780\pi$
$797$	−20.2977	−	4.63281i	−0.718980	−	0.164103i	−0.566331	+	0.824178i	$0.691638\pi$
$798$	−10.5820	−	2.41526i	−0.374598	−	0.0854995i
$799$	28.8839	−	36.2193i	1.02184	−	1.28135i
$800$			10.6393i			0.376157i
$801$	−2.60056	−	2.07388i	−0.0918862	−	0.0732768i
$802$	−23.2156	−	48.2078i	−0.819773	−	1.70228i
$803$	0.658236	+	0.825401i	0.0232286	+	0.0291278i
$804$	8.18745	−	6.52927i	0.288749	−	0.230270i
$805$	−18.6072	−	8.96077i	−0.655819	−	0.315826i
$806$	1.66271	−	7.28479i	0.0585663	−	0.256596i
$807$	2.16028	+	9.46480i	0.0760454	+	0.333177i
$808$	−3.25974	+	1.56981i	−0.114677	+	0.0552256i
$809$	−6.53814	+	13.5766i	−0.229869	+	0.477328i	−0.983718	−	0.179720i	$-0.942481\pi$
$809$	−6.53814	+	13.5766i	−0.229869	+	0.477328i	0.753849	+	0.657048i	$0.228195\pi$
$810$	34.7043	−	7.92102i	1.21938	−	0.278316i
$811$	25.6525			0.900780			0.450390	−	0.892832i	$-0.351285\pi$
$811$	25.6525			0.900780			0.450390	+	0.892832i	$0.351285\pi$
$812$		0			0
$813$	−19.7082			−0.691197
$814$	−49.7006	+	11.3438i	−1.74200	+	0.397601i
$815$	−28.5247	+	59.2321i	−0.999175	+	2.07481i
$816$	46.8312	−	22.5527i	1.63942	−	0.789503i
$817$	−1.14033	−	4.99613i	−0.0398952	−	0.174792i
$818$	−0.210120	+	0.920597i	−0.00734668	+	0.0321879i
$819$	3.25974	+	1.56981i	0.113904	+	0.0548535i
$820$	3.93609	−	3.13892i	0.137454	−	0.109616i
$821$	−22.0818	−	27.6897i	−0.770659	−	0.966376i	0.229317	−	0.973352i	$-0.426351\pi$
$821$	−22.0818	−	27.6897i	−0.770659	−	0.966376i	−0.999976	+	0.00697599i	$0.997779\pi$
$822$	−15.7372	−	32.6786i	−0.548897	−	1.13980i
$823$	2.71463	+	2.16484i	0.0946259	+	0.0754616i	0.669660	−	0.742668i	$-0.266440\pi$
$823$	2.71463	+	2.16484i	0.0946259	+	0.0754616i	−0.575034	+	0.818129i	$0.695011\pi$
$824$			29.4721i			1.02671i
$825$	11.4824	−	14.3985i	0.399767	−	0.501292i
$826$	−17.9547	−	4.09804i	−0.624723	−	0.142589i
$827$	54.6295	+	12.4688i	1.89966	+	0.433584i	0.999995	−	0.00300768i	$-0.000957377\pi$
$827$	54.6295	+	12.4688i	1.89966	+	0.433584i	0.899660	+	0.436592i	$0.143815\pi$
$828$	−0.476304	+	0.597266i	−0.0165527	+	0.0207564i
$829$			8.20163i			0.284854i	0.989805	+	0.142427i	$0.0454907\pi$
$829$			8.20163i			0.284854i	−0.989805	+	0.142427i	$0.954509\pi$
$830$	−28.6830	−	22.8739i	−0.995601	−	0.793965i
$831$	16.5808	+	34.4303i	0.575181	+	1.19437i
$832$	11.1881	+	14.0294i	0.387877	+	0.486382i
$833$	−10.3484	+	8.25255i	−0.358550	+	0.285934i
$834$	−34.6932	−	16.7074i	−1.20133	−	0.578529i
$835$	12.3667	−	54.1821i	0.427967	−	1.87505i
$836$	0.922549	+	4.04195i	0.0319070	+	0.139794i
$837$	5.37478	−	2.58836i	0.185780	−	0.0894668i
$838$	1.79884	−	3.73533i	0.0621398	−	0.129035i
$839$	−3.13418	+	0.715356i	−0.108204	+	0.0246968i	−0.276280	−	0.961077i	$-0.589102\pi$
$839$	−3.13418	+	0.715356i	−0.108204	+	0.0246968i	0.168076	+	0.985774i	$0.446245\pi$
$840$	23.0902			0.796687
$841$		0			0
$842$	3.18034			0.109602
$843$	−27.0135	+	6.16566i	−0.930394	+	0.212356i
$844$	5.26991	−	10.9431i	0.181398	−	0.376676i
$845$	−12.7140	+	6.12273i	−0.437374	+	0.210628i
$846$	−0.962679	−	4.21777i	−0.0330976	−	0.145010i
$847$	1.04001	−	4.55658i	0.0357352	−	0.156566i
$848$	−8.74679	−	4.21223i	−0.300366	−	0.144649i
$849$	−0.966397	+	0.770676i	−0.0331667	+	0.0264495i
$850$	−21.0034	−	26.3375i	−0.720412	−	0.903369i
$851$	−12.2270	−	25.3896i	−0.419136	−	0.870345i
$852$	1.19453	+	0.952608i	0.0409240	+	0.0326358i
$853$			45.0000i			1.54077i	0.637579	+	0.770385i	$0.279936\pi$
$853$			45.0000i			1.54077i	−0.637579	+	0.770385i	$0.720064\pi$
$854$	3.64997	−	4.57692i	0.124900	−	0.156619i
$855$	−1.97061	−	0.449779i	−0.0673934	−	0.0153821i
$856$	24.4947	+	5.59075i	0.837211	+	0.191088i
$857$	−18.5013	+	23.1999i	−0.631992	+	0.792493i	−0.989976	−	0.141235i	$-0.954893\pi$
$857$	−18.5013	+	23.1999i	−0.631992	+	0.792493i	0.357984	+	0.933728i	$0.383464\pi$
$858$			40.1246i			1.36983i
$859$	−15.0829	−	12.0282i	−0.514623	−	0.410398i	0.331444	−	0.943475i	$-0.392464\pi$
$859$	−15.0829	−	12.0282i	−0.514623	−	0.410398i	−0.846067	+	0.533077i	$0.821036\pi$
$860$	−2.11535	−	4.39257i	−0.0721329	−	0.149785i
$861$	−6.43830	−	8.07338i	−0.219417	−	0.275140i
$862$	−43.7659	+	34.9022i	−1.49067	+	1.18877i
$863$	−22.2924	−	10.7354i	−0.758841	−	0.365438i	0.0141135	−	0.999900i	$-0.495507\pi$
$863$	−22.2924	−	10.7354i	−0.758841	−	0.365438i	−0.772954	+	0.634462i	$0.781222\pi$
$864$	4.11810	−	18.0426i	0.140101	−	0.613821i
$865$	−4.50295	−	19.7287i	−0.153105	−	0.670796i
$866$	18.3945	−	8.85835i	0.625072	−	0.301019i
$867$	−18.8135	+	39.0666i	−0.638940	+	1.32677i
$868$	−1.46880	+	0.335245i	−0.0498545	+	0.0113790i
$869$	18.4164			0.624734
$870$		0			0
$871$	−44.3607			−1.50310
$872$	−36.2274	+	8.26867i	−1.22681	+	0.280012i
$873$	2.74485	−	5.69974i	0.0928992	−	0.192907i
$874$	−8.74679	+	4.21223i	−0.295865	+	0.142481i
$875$	2.63305	+	11.5361i	0.0890133	+	0.389993i
$876$	−0.0649307	+	0.284480i	−0.00219381	+	0.00961169i
$877$	−5.96264	−	2.87146i	−0.201344	−	0.0969622i	0.330495	−	0.943808i	$-0.392784\pi$
$877$	−5.96264	−	2.87146i	−0.201344	−	0.0969622i	−0.531839	+	0.846846i	$0.678499\pi$
$878$	3.86559	−	3.08270i	0.130457	−	0.104036i
$879$	−17.6264	−	22.1028i	−0.594523	−	0.745508i
$880$	−21.7483	−	45.1607i	−0.733133	−	1.52237i
$881$	−22.8846	−	18.2499i	−0.771002	−	0.614854i	0.156927	−	0.987610i	$-0.449841\pi$
$881$	−22.8846	−	18.2499i	−0.771002	−	0.614854i	−0.927929	+	0.372757i	$0.878413\pi$
$882$			1.23607i			0.0416206i
$883$	−24.7444	+	31.0285i	−0.832715	+	1.04419i	0.165602	+	0.986193i	$0.447043\pi$
$883$	−24.7444	+	31.0285i	−0.832715	+	1.04419i	−0.998317	+	0.0579988i	$0.981528\pi$
$884$	16.8918	+	3.85545i	0.568134	+	0.129673i
$885$	22.9172	+	5.23071i	0.770354	+	0.175828i
$886$	13.2057	−	16.5595i	0.443655	−	0.556326i
$887$			20.0689i			0.673847i	0.941532	+	0.336924i	$0.109386\pi$
$887$			20.0689i			0.673847i	−0.941532	+	0.336924i	$0.890614\pi$
$888$	24.6328	+	19.6440i	0.826624	+	0.659210i
$889$	1.88632	+	3.91698i	0.0632651	+	0.131371i
$890$	−25.0735	−	31.4412i	−0.840466	−	1.05391i
$891$	−21.8041	+	17.3882i	−0.730466	+	0.582527i
$892$	10.2046	+	4.91427i	0.341675	+	0.164542i
$893$	2.88804	−	12.6533i	0.0966444	−	0.423427i
$894$	4.30049	+	18.8417i	0.143830	+	0.630160i
$895$	−41.1433	+	19.8136i	−1.37527	+	0.662295i
$896$	13.2121	−	27.4353i	0.441386	−	0.916548i
$897$	−21.6242	+	4.93559i	−0.722012	+	0.164795i
$898$	22.8541			0.762651
$899$		0			0
$900$	−0.742646			−0.0247549
$901$	12.9042	−	2.94530i	0.429902	−	0.0981222i
$902$	−7.24942	+	15.0536i	−0.241379	+	0.501229i
$903$	−9.00969	+	4.33884i	−0.299824	+	0.144387i
$904$	−4.94799	−	21.6786i	−0.164568	−	0.721018i
$905$	7.58578	−	33.2355i	0.252160	−	1.10478i
$906$	43.2273	+	20.8172i	1.43613	+	0.691605i
$907$	11.1302	−	8.87604i	0.369572	−	0.294724i	−0.421039	−	0.907043i	$-0.638334\pi$
$907$	11.1302	−	8.87604i	0.369572	−	0.294724i	0.790611	+	0.612318i	$0.209763\pi$
$908$	−5.73712	−	7.19412i	−0.190393	−	0.238745i
$909$	−0.268155	−	0.556829i	−0.00889414	−	0.0184689i
$910$	34.1994	+	27.2731i	1.13370	+	0.904094i
$911$		−	6.94427i		−	0.230074i	−0.993361	−	0.115037i	$-0.963301\pi$
$911$		−	6.94427i		−	0.230074i	0.993361	−	0.115037i	$-0.0366987\pi$
$912$	9.07945	−	11.3853i	0.300651	−	0.377004i
$913$	28.0220	+	6.39584i	0.927393	+	0.211671i
$914$	−8.34763	−	1.90529i	−0.276115	−	0.0630215i
$915$	−4.65880	+	5.84195i	−0.154015	+	0.193129i
$916$			9.70820i			0.320768i
$917$	2.31857	+	1.84900i	0.0765658	+	0.0610592i
$918$	25.4242	+	52.7938i	0.839123	+	1.74246i
$919$	−19.5183	−	24.4752i	−0.643850	−	0.807362i	0.347629	−	0.937632i	$-0.386987\pi$
$919$	−19.5183	−	24.4752i	−0.643850	−	0.807362i	−0.991479	+	0.130270i	$0.958416\pi$
$920$	16.1468	−	12.8766i	0.532343	−	0.424529i
$921$	4.63629	+	2.23272i	0.152771	+	0.0735707i
$922$	2.87271	−	12.5862i	0.0946076	−	0.414503i
$923$	−1.44019	−	6.30987i	−0.0474043	−	0.207692i
$924$	7.28899	−	3.51019i	0.239790	−	0.115477i
$925$	11.8863	−	24.6822i	0.390819	−	0.811544i
$926$	−4.27210	+	0.975079i	−0.140390	+	0.0320431i
$927$	−5.03444			−0.165353
$928$		0			0
$929$	27.6525			0.907248			0.453624	−	0.891193i	$-0.350131\pi$
$929$	27.6525			0.907248			0.453624	+	0.891193i	$0.350131\pi$
$930$	7.94166	−	1.81263i	0.260417	−	0.0594386i
$931$	−1.60893	+	3.34098i	−0.0527305	+	0.109496i
$932$	5.99367	−	2.88640i	0.196329	−	0.0945472i
$933$	−3.27288	−	14.3394i	−0.107149	−	0.469452i
$934$	0.0200647	−	0.0879092i	0.000656537	−	0.00287648i
$935$	61.5717	+	29.6514i	2.01361	+	0.969703i
$936$	−2.82869	+	2.25581i	−0.0924587	+	0.0737334i
$937$	15.3706	+	19.2741i	0.502135	+	0.629657i	0.966709	−	0.255877i	$-0.0823642\pi$
$937$	15.3706	+	19.2741i	0.502135	+	0.629657i	−0.464575	+	0.885534i	$0.653793\pi$
$938$	16.4392	+	34.1364i	0.536760	+	1.11459i
$939$	−30.4748	−	24.3028i	−0.994507	−	0.793093i
$940$		−	12.3475i		−	0.402732i
$941$	−0.553998	+	0.694692i	−0.0180598	+	0.0226463i	−0.790779	−	0.612101i	$-0.790324\pi$
$941$	−0.553998	+	0.694692i	−0.0180598	+	0.0226463i	0.772720	+	0.634748i	$0.218896\pi$
$942$	−14.1972	−	3.24042i	−0.462570	−	0.105579i
$943$	−9.00450	−	2.05522i	−0.293227	−	0.0669271i
$944$	15.4053	−	19.3177i	0.501400	−	0.628736i
$945$			34.9230i			1.13604i
$946$	12.6503	+	10.0883i	0.411297	+	0.327998i
$947$	−6.05943	−	12.5825i	−0.196905	−	0.408877i	0.779015	−	0.627005i	$-0.215719\pi$
$947$	−6.05943	−	12.5825i	−0.196905	−	0.408877i	−0.975920	+	0.218128i	$0.930005\pi$
$948$	3.17367	+	3.97966i	0.103076	+	0.129253i
$949$	0.966397	−	0.770676i	0.0313706	−	0.0250172i
$950$	−8.50307	−	4.09486i	−0.275876	−	0.132855i
$951$	−5.14571	+	22.5448i	−0.166861	+	0.731066i
$952$	7.36326	+	32.2605i	0.238644	+	1.04557i
$953$	32.1026	−	15.4598i	1.03990	−	0.500792i	0.165612	−	0.986191i	$-0.447040\pi$
$953$	32.1026	−	15.4598i	1.03990	−	0.500792i	0.874293	+	0.485399i	$0.161326\pi$
$954$	0.536310	−	1.11366i	0.0173637	−	0.0360560i
$955$	−33.4864	+	7.64304i	−1.08359	+	0.247323i
$956$	−9.11146			−0.294686
$957$		0			0
$958$	−18.0902			−0.584467
$959$	30.2020	−	6.89341i	0.975274	−	0.222600i
$960$	−8.48777	+	17.6250i	−0.273941	+	0.568845i
$961$	−26.8593	+	12.9347i	−0.866428	+	0.417250i
$962$	13.2816	+	58.1904i	0.428216	+	1.87614i
$963$	−0.955014	+	4.18419i	−0.0307749	+	0.134834i
$964$	−14.8409	−	7.14699i	−0.477993	−	0.230189i
$965$	−7.87217	+	6.27785i	−0.253414	+	0.202091i
$966$	11.8116	+	14.8112i	0.380031	+	0.476543i
$967$	−7.18612	−	14.9221i	−0.231090	−	0.479863i	0.752889	−	0.658147i	$-0.228660\pi$
$967$	−7.18612	−	14.9221i	−0.231090	−	0.479863i	−0.983979	+	0.178284i	$0.942945\pi$
$968$	3.65409	+	2.91404i	0.117447	+	0.0936609i
$969$			19.8541i			0.637806i
$970$	47.6878	−	59.7986i	1.53116	−	1.92002i
$971$	−18.0426	−	4.11810i	−0.579014	−	0.132156i	−0.0770234	−	0.997029i	$-0.524542\pi$
$971$	−18.0426	−	4.11810i	−0.579014	−	0.132156i	−0.501990	+	0.864873i	$0.667399\pi$
$972$	2.37658	+	0.542438i	0.0762287	+	0.0173987i
$973$	20.5057	−	25.7133i	0.657382	−	0.824331i
$974$		−	36.3050i		−	1.16329i
$975$	−16.8581	−	13.4439i	−0.539891	−	0.430549i
$976$	3.40777	+	7.07630i	0.109080	+	0.226507i
$977$	3.87485	+	4.85891i	0.123968	+	0.155450i	0.839942	−	0.542676i	$-0.182589\pi$
$977$	3.87485	+	4.85891i	0.123968	+	0.155450i	−0.715975	+	0.698126i	$0.754017\pi$
$978$	47.1483	−	37.5995i	1.50764	−	1.20230i
$979$	28.3864	+	13.6702i	0.907235	+	0.436901i
$980$	−0.785024	+	3.43941i	−0.0250767	+	0.109868i
$981$	−1.41246	−	6.18838i	−0.0450963	−	0.197580i
$982$	36.6266	−	17.6384i	1.16880	−	0.562866i
$983$	−3.01301	+	6.25657i	−0.0961000	+	0.199554i	−0.943477	−	0.331438i	$-0.892466\pi$
$983$	−3.01301	+	6.25657i	−0.0961000	+	0.199554i	0.847377	+	0.530992i	$0.178180\pi$
$984$	10.0673	−	2.29780i	0.320935	−	0.0732513i
$985$	−56.2492			−1.79225
$986$		0			0
$987$	−25.3262			−0.806143
$988$	4.73240	−	1.08014i	0.150558	−	0.0343638i
$989$	−3.88077	+	8.05851i	−0.123401	+	0.256246i
$990$	5.74995	−	2.76903i	0.182745	−	0.0880056i
$991$	8.60099	+	37.6834i	0.273219	+	1.19705i	0.906188	+	0.422875i	$0.138979\pi$
$991$	8.60099	+	37.6834i	0.273219	+	1.19705i	−0.632969	+	0.774177i	$0.718164\pi$
$992$	0.820416	−	3.59448i	0.0260482	−	0.114125i
$993$	1.72070	+	0.828644i	0.0546047	+	0.0262962i
$994$	−4.32186	+	3.44657i	−0.137081	+	0.109318i
$995$	1.51988	+	1.90587i	0.0481834	+	0.0604200i
$996$	3.44689	+	7.15754i	0.109219	+	0.226795i
$997$	21.9618	+	17.5139i	0.695537	+	0.554672i	0.906181	−	0.422891i	$-0.138985\pi$
$997$	21.9618	+	17.5139i	0.695537	+	0.554672i	−0.210644	+	0.977563i	$0.567556\pi$
$998$		−	57.7426i		−	1.82781i
$999$	−29.7108	+	37.2562i	−0.940009	+	1.17873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.j.196.1		24
29.2	odd	28		841.2.a.a.1.1	✓	2
29.3	odd	28		841.2.d.i.778.1		12
29.4	even	14	inner	841.2.e.j.236.1		24
29.5	even	14		841.2.b.b.840.4		4
29.6	even	14	inner	841.2.e.j.270.1		24
29.7	even	7	inner	841.2.e.j.63.4		24
29.8	odd	28		841.2.d.g.190.1		12
29.9	even	14	inner	841.2.e.j.651.4		24
29.10	odd	28		841.2.d.g.605.1		12
29.11	odd	28		841.2.d.i.574.1		12
29.12	odd	4		841.2.d.g.645.1		12
29.13	even	14	inner	841.2.e.j.267.4		24
29.14	odd	28		841.2.d.i.571.2		12
29.15	odd	28		841.2.d.g.571.1		12
29.16	even	7	inner	841.2.e.j.267.1		24
29.17	odd	4		841.2.d.i.645.2		12
29.18	odd	28		841.2.d.g.574.2		12
29.19	odd	28		841.2.d.i.605.2		12
29.20	even	7	inner	841.2.e.j.651.1		24
29.21	odd	28		841.2.d.i.190.2		12
29.22	even	14	inner	841.2.e.j.63.1		24
29.23	even	7	inner	841.2.e.j.270.4		24
29.24	even	7		841.2.b.b.840.1		4
29.25	even	7	inner	841.2.e.j.236.4		24
29.26	odd	28		841.2.d.g.778.2		12
29.27	odd	28		841.2.a.c.1.2	yes	2
29.28	even	2	inner	841.2.e.j.196.4		24
87.2	even	28		7569.2.a.l.1.2		2
87.56	even	28		7569.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.a.1.1	✓	2	29.2	odd	28
841.2.a.c.1.2	yes	2	29.27	odd	28
841.2.b.b.840.1		4	29.24	even	7
841.2.b.b.840.4		4	29.5	even	14
841.2.d.g.190.1		12	29.8	odd	28
841.2.d.g.571.1		12	29.15	odd	28
841.2.d.g.574.2		12	29.18	odd	28
841.2.d.g.605.1		12	29.10	odd	28
841.2.d.g.645.1		12	29.12	odd	4
841.2.d.g.778.2		12	29.26	odd	28
841.2.d.i.190.2		12	29.21	odd	28
841.2.d.i.571.2		12	29.14	odd	28
841.2.d.i.574.1		12	29.11	odd	28
841.2.d.i.605.2		12	29.19	odd	28
841.2.d.i.645.2		12	29.17	odd	4
841.2.d.i.778.1		12	29.3	odd	28
841.2.e.j.63.1		24	29.22	even	14	inner
841.2.e.j.63.4		24	29.7	even	7	inner
841.2.e.j.196.1		24	1.1	even	1	trivial
841.2.e.j.196.4		24	29.28	even	2	inner
841.2.e.j.236.1		24	29.4	even	14	inner
841.2.e.j.236.4		24	29.25	even	7	inner
841.2.e.j.267.1		24	29.16	even	7	inner
841.2.e.j.267.4		24	29.13	even	14	inner
841.2.e.j.270.1		24	29.6	even	14	inner
841.2.e.j.270.4		24	29.23	even	7	inner
841.2.e.j.651.1		24	29.20	even	7	inner
841.2.e.j.651.4		24	29.9	even	14	inner
7569.2.a.d.1.1		2	87.56	even	28
7569.2.a.l.1.2		2	87.2	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.57747 + 0.360046i) q^{2} +(0.702039 - 1.45780i) q^{3} +(0.556829 - 0.268155i) q^{4} +(-0.635097 - 2.78254i) q^{5} +(-0.582567 + 2.55239i) q^{6} +(-2.01463 - 0.970194i) q^{7} +(1.74823 - 1.39417i) q^{8} +(0.238152 + 0.298633i) q^{9} +(2.00369 + 4.16070i) q^{10} +(-2.82869 - 2.25581i) q^{11} -1.00000i q^{12} +(-2.64115 + 3.31189i) q^{13} +(3.52732 + 0.805088i) q^{14} +(-4.50225 - 1.02761i) q^{15} +(-3.02648 + 3.79509i) q^{16} -6.61803i q^{17} +(-0.483198 - 0.385338i) q^{18} +(-0.804465 - 1.67049i) q^{19} +(-1.09979 - 1.37910i) q^{20} +(-2.82869 + 2.25581i) q^{21} +(5.27436 + 2.54000i) q^{22} +(-0.720093 + 3.15493i) q^{23} +(-0.805088 - 3.52732i) q^{24} +(-2.83436 + 1.36495i) q^{25} +(2.97388 - 6.17533i) q^{26} +(5.33494 - 1.21766i) q^{27} -1.38197 q^{28} +7.47214 q^{30} +(1.06284 - 0.242586i) q^{31} +(1.46738 - 3.04705i) q^{32} +(-5.27436 + 2.54000i) q^{33} +(2.38280 + 10.4397i) q^{34} +(-1.42012 + 6.22196i) q^{35} +(0.212690 + 0.102426i) q^{36} +(-6.80835 + 5.42948i) q^{37} +(1.87047 + 2.34549i) q^{38} +(2.97388 + 6.17533i) q^{39} +(-4.98962 - 3.97909i) q^{40} +2.85410i q^{41} +(3.64997 - 4.57692i) q^{42} +(2.69463 + 0.615033i) q^{43} +(-2.18001 - 0.497572i) q^{44} +(0.679710 - 0.852329i) q^{45} -5.23607i q^{46} +(5.47282 + 4.36443i) q^{47} +(3.40777 + 7.07630i) q^{48} +(-1.24698 - 1.56366i) q^{49} +(3.97966 - 3.17367i) q^{50} +(-9.64776 - 4.64612i) q^{51} +(-0.582567 + 2.55239i) q^{52} +(0.445042 + 1.94986i) q^{53} +(-7.97727 + 3.84165i) q^{54} +(-4.48039 + 9.30362i) q^{55} +(-4.87464 + 1.11260i) q^{56} -3.00000 q^{57} -5.09017 q^{59} +(-2.78254 + 0.635097i) q^{60} +(0.702039 - 1.45780i) q^{61} +(-1.58925 + 0.765341i) q^{62} +(-0.190056 - 0.832688i) q^{63} +(0.942614 - 4.12986i) q^{64} +(10.8929 + 5.24573i) q^{65} +(7.40561 - 5.90578i) q^{66} +(6.52927 + 8.18745i) q^{67} +(-1.77466 - 3.68512i) q^{68} +(4.09372 + 3.26463i) q^{69} -10.3262i q^{70} +(-0.952608 + 1.19453i) q^{71} +(0.832688 + 0.190056i) q^{72} +(-0.284480 - 0.0649307i) q^{73} +(8.78508 - 11.0161i) q^{74} +5.09017i q^{75} +(-0.895899 - 0.714456i) q^{76} +(3.51019 + 7.28899i) q^{77} +(-6.91461 - 8.67064i) q^{78} +(-3.97966 + 3.17367i) q^{79} +(12.4821 + 6.01107i) q^{80} +(1.71524 - 7.51494i) q^{81} +(-1.02761 - 4.50225i) q^{82} +(-7.15754 + 3.44689i) q^{83} +(-0.970194 + 2.01463i) q^{84} +(-18.4150 + 4.20310i) q^{85} -4.47214 q^{86} -8.09017 q^{88} +(-8.48987 + 1.93776i) q^{89} +(-0.765341 + 1.58925i) q^{90} +(8.53410 - 4.10981i) q^{91} +(0.445042 + 1.94986i) q^{92} +(0.392512 - 1.71971i) q^{93} +(-10.2046 - 4.91427i) q^{94} +(-4.13729 + 3.29938i) q^{95} +(-3.41182 - 4.27829i) q^{96} +(-7.18612 - 14.9221i) q^{97} +(2.53006 + 2.01766i) q^{98} -1.38197i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38}+ \cdots + 4 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

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