LMFDB - Embedded newform 841.2.e.j.196.4

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			196.4
Character	$\chi$	$=$	841.196
Dual form			841.2.e.j.236.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(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	0.375205	−	0.926942i	$-0.377572\pi$
$2$	1.57747	−	0.360046i	1.11544	−	0.254591i	0.740233	+	0.672351i	$0.234715\pi$
$3$	−0.702039	+	1.45780i	−0.405322	+	0.841660i	0.593986	+	0.804475i	$0.297553\pi$
$3$	−0.702039	+	1.45780i	−0.405322	+	0.841660i	−0.999308	+	0.0371850i	$0.988161\pi$
$4$	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	0.949020	−	0.315217i	$-0.102077\pi$
$11$	2.82869	+	2.25581i	0.852883	+	0.680151i	−0.0961367	+	0.995368i	$0.530649\pi$
$12$			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	$0.296526\pi$
$17$			6.61803i			1.60511i	−0.596579	+	0.802555i	$0.703474\pi$
$18$	0.483198	+	0.385338i	0.113891	+	0.0908250i
$19$	0.804465	+	1.67049i	0.184557	+	0.383236i	0.972635	−	0.232339i	$-0.0746379\pi$
$19$	0.804465	+	1.67049i	0.184557	+	0.383236i	−0.788078	+	0.615575i	$0.788924\pi$
$20$	−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	−0.316898	−	0.948460i	$-0.602641\pi$
$31$	−1.06284	+	0.242586i	−0.190891	+	0.0435697i	0.126006	+	0.992029i	$0.459784\pi$
$32$	−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	0.124263	−	0.992249i	$-0.460343\pi$
$37$	6.80835	−	5.42948i	1.11929	−	0.892600i	0.995023	+	0.0996489i	$0.0317720\pi$
$38$	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	$-0.928458\pi$
$41$		−	2.85410i		−	0.445736i	0.974849	−	0.222868i	$-0.0715419\pi$
$42$	3.64997	−	4.57692i	0.563203	−	0.706234i
$43$	−2.69463	−	0.615033i	−0.410928	−	0.0937916i	0.0120593	−	0.999927i	$-0.496161\pi$
$43$	−2.69463	−	0.615033i	−0.410928	−	0.0937916i	−0.422987	+	0.906136i	$0.639018\pi$
$44$	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	0.136968	−	0.990575i	$-0.456264\pi$
$47$	−5.47282	−	4.36443i	−0.798293	−	0.636617i	−0.935261	+	0.353958i	$0.884836\pi$
$48$	−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	−0.941066	−	0.338224i	$-0.890174\pi$
$61$	−0.702039	+	1.45780i	−0.0898868	+	0.186652i	0.851179	+	0.524876i	$0.175888\pi$
$62$	−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	0.239136	−	0.970986i	$-0.423136\pi$
$73$	0.284480	+	0.0649307i	0.0332959	+	0.00759957i	−0.205841	+	0.978586i	$0.565993\pi$
$74$	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	−0.373509	−	0.927626i	$-0.621846\pi$
$79$	3.97966	−	3.17367i	0.447746	−	0.357066i	0.821255	+	0.570561i	$0.193274\pi$
$80$	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	0.252559	−	0.967582i	$-0.418728\pi$
$89$	8.48987	−	1.93776i	0.899925	−	0.205402i	0.647366	+	0.762180i	$0.275871\pi$
$90$	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	$0.175072\pi$
$97$	7.18612	+	14.9221i	0.729639	+	1.51511i	−0.122883	+	0.992421i	$0.539214\pi$
$98$	−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	0.300281	−	0.953851i	$-0.402920\pi$
$101$	1.57747	+	0.360046i	0.156964	+	0.0358260i	−0.143317	+	0.989677i	$0.545777\pi$
$102$	−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	$0.297788\pi$
$113$	−4.31466	+	8.95948i	−0.405889	+	0.842837i	−0.999281	+	0.0379231i	$0.987926\pi$
$114$	−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	0.688609	−	0.725133i	$-0.258222\pi$
$127$	1.52009	+	1.21223i	0.134886	+	0.107568i	−0.553722	+	0.832701i	$0.686793\pi$
$128$		−	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	0.278632	−	0.960398i	$-0.410119\pi$
$131$	1.29299	+	0.295116i	0.112969	+	0.0257844i	−0.165663	+	0.986182i	$0.552976\pi$
$132$	−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	−0.0398756	−	0.999205i	$-0.512696\pi$
$137$	10.8316	−	8.63789i	0.925404	−	0.737985i	0.965279	+	0.261220i	$0.0841247\pi$
$138$	−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	$-0.928755\pi$
$157$		−	5.56231i		−	0.443920i	0.975056	−	0.221960i	$-0.0712455\pi$
$158$	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	$0.0722595\pi$
$163$	18.0091	+	14.3617i	1.41058	+	1.12490i	0.436234	+	0.899833i	$0.356312\pi$
$164$	−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	$0.143390\pi$
$191$			12.0344i			0.870782i	−0.900242	+	0.435391i	$0.856610\pi$
$192$	5.35875	+	4.27346i	0.386735	+	0.308411i
$193$	1.53068	+	3.17850i	0.110181	+	0.228793i	0.948767	−	0.315976i	$-0.102332\pi$
$193$	1.53068	+	3.17850i	0.110181	+	0.228793i	−0.838586	+	0.544769i	$0.816617\pi$
$194$	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	−0.988066	−	0.154029i	$-0.950775\pi$
$211$	−15.3649	+	12.2531i	−1.05777	+	0.843539i	−0.0696986	+	0.997568i	$0.522204\pi$
$212$	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	$-0.683442\pi$
$229$	6.81553	−	14.1526i	0.450383	−	0.935230i	0.995309	−	0.0967461i	$-0.0308435\pi$
$230$	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	0.997394	−	0.0721491i	$-0.0229857\pi$
$251$	5.05582	+	10.4985i	0.319121	+	0.662661i	−0.678273	+	0.734810i	$0.737271\pi$
$252$	−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	−0.122426	−	0.992478i	$-0.539067\pi$
$263$	3.20926	−	0.732494i	0.197892	−	0.0451675i	0.320318	+	0.947310i	$0.396210\pi$
$264$	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	−0.469964	−	0.882686i	$-0.655733\pi$
$269$	4.69099	−	3.74094i	0.286015	−	0.228089i	0.755978	+	0.654597i	$0.227162\pi$
$270$	15.7559	+	19.7573i	0.958874	+	1.20239i
$271$	5.28485	+	10.9741i	0.321032	+	0.666630i	0.997562	−	0.0697854i	$-0.0222314\pi$
$271$	5.28485	+	10.9741i	0.321032	+	0.666630i	−0.676530	+	0.736415i	$0.736517\pi$
$272$	−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	$0.313347\pi$
$293$	−7.58088	+	15.7419i	−0.442879	+	0.919649i	−0.996234	+	0.0867030i	$0.972367\pi$
$294$	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	$-0.971072\pi$
$307$		−	3.18034i		−	0.181512i	0.995873	−	0.0907558i	$-0.0289283\pi$
$308$	−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	−0.803927	−	0.594728i	$-0.797260\pi$
$311$	−7.10698	+	5.66763i	−0.403000	+	0.321382i	0.400927	+	0.916110i	$0.368688\pi$
$312$	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	0.187479	−	0.982269i	$-0.439968\pi$
$317$	13.9335	−	3.18022i	0.782582	−	0.178619i	0.595103	+	0.803649i	$0.297111\pi$
$318$	−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	$-0.989673\pi$
$331$		−	1.18034i		−	0.0648773i	0.999474	−	0.0324387i	$-0.0103274\pi$
$332$	−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	0.983361	−	0.181663i	$-0.0581478\pi$
$337$	18.8178	+	15.0067i	1.02507	+	0.817467i	0.0417105	+	0.999130i	$0.486719\pi$
$338$	−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	0.998383	−	0.0568505i	$-0.0181058\pi$
$359$	22.0758	+	17.6049i	1.16512	+	0.929151i	0.166736	+	0.986002i	$0.446677\pi$
$360$			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	0.817812	−	0.575485i	$-0.195187\pi$
$367$	−2.72067	−	5.64953i	−0.142018	−	0.294903i	−0.959830	+	0.280582i	$0.909473\pi$
$368$	−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	0.888752	−	0.458388i	$-0.151573\pi$
$379$	36.7628	−	8.39086i	1.88838	−	0.431010i	0.999625	+	0.0273785i	$0.00871593\pi$
$380$	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	$0.179888\pi$
$389$			21.1246i			1.07106i	−0.844516	+	0.535530i	$0.820112\pi$
$390$	−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	−0.907135	−	0.420839i	$-0.861736\pi$
$409$	−0.253211	+	0.525798i	−0.0125205	+	0.0259991i	0.894615	+	0.446838i	$0.147450\pi$
$410$	−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	0.268962	−	0.963151i	$-0.413319\pi$
$421$	1.91628	+	0.437378i	0.0933937	+	0.0213165i	−0.175569	+	0.984467i	$0.556176\pi$
$422$	−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	0.0835436	−	0.996504i	$-0.473376\pi$
$433$	12.3017	−	2.80778i	0.591181	−	0.134933i	0.507637	+	0.861571i	$0.330519\pi$
$434$	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	−0.349454	−	0.936953i	$-0.613633\pi$
$443$	10.2343	−	8.16159i	0.486247	−	0.387769i	0.835701	+	0.549185i	$0.185062\pi$
$444$	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	0.534733	−	0.845021i	$-0.320412\pi$
$449$	13.7705	+	3.14302i	0.649869	+	0.148328i	0.115136	+	0.993350i	$0.463269\pi$
$450$	−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	−0.804663	−	0.593731i	$-0.797654\pi$
$461$	3.46183	−	7.18857i	0.161234	−	0.334805i	0.965897	+	0.258926i	$0.0833686\pi$
$462$	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	−0.900409	−	0.435045i	$-0.856732\pi$
$467$	0.0241795	−	0.0502093i	0.00111889	−	0.00232341i	0.901528	+	0.432722i	$0.142447\pi$
$468$	−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	−0.0338776	−	0.999426i	$-0.510786\pi$
$479$	−10.9000	−	2.48786i	−0.498035	−	0.113673i	−0.464157	+	0.885753i	$0.653643\pi$
$480$	−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	0.369409	−	0.929267i	$-0.379560\pi$
$491$	24.4947	−	5.59075i	1.10543	−	0.252307i	0.736020	+	0.676960i	$0.236703\pi$
$492$	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	0.999989	−	0.00473279i	$-0.00150650\pi$
$503$	8.36116	+	17.3621i	0.372806	+	0.774139i	−0.627183	+	0.778872i	$0.715792\pi$
$504$	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	$0.124081\pi$
$541$	15.0110	+	31.1706i	0.645372	+	1.34013i	−0.279609	+	0.960114i	$0.590205\pi$
$542$	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	$-0.594135\pi$
$563$		−	45.3951i		−	1.91318i	0.291443	−	0.956588i	$-0.405865\pi$
$564$	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	0.848934	−	0.528499i	$-0.177245\pi$
$569$	12.4657	+	9.94109i	0.522591	+	0.416752i	−0.326343	+	0.945251i	$0.605816\pi$
$570$	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	−0.956042	−	0.293229i	$-0.905270\pi$
$577$	−3.13961	+	6.51947i	−0.130704	+	0.271409i	0.825338	+	0.564638i	$0.190984\pi$
$578$	−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	$-0.770449\pi$
$599$	−19.5547	−	40.6057i	−0.798982	−	1.65910i	−0.0479374	−	0.998850i	$-0.515265\pi$
$600$	7.09654	+	8.89878i	0.289715	+	0.363291i
$601$	−31.3976	+	25.0388i	−1.28074	+	1.02135i	−0.282668	+	0.959218i	$0.591219\pi$
$601$	−31.3976	+	25.0388i	−1.28074	+	1.02135i	−0.998068	+	0.0621344i	$0.980209\pi$
$602$	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	−0.863901	−	0.503662i	$-0.831986\pi$
$607$	−35.0767	+	8.00602i	−1.42372	+	0.324954i	−0.559817	+	0.828616i	$0.689128\pi$
$608$	−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	−0.743719	−	0.668493i	$-0.766940\pi$
$617$	−6.39565	+	5.10036i	−0.257479	+	0.205333i	0.486239	+	0.873826i	$0.338368\pi$
$618$	−21.5145	−	26.9783i	−0.865440	−	1.08523i
$619$	−10.8229	−	22.4740i	−0.435010	−	0.903307i	−0.997091	−	0.0762247i	$-0.975713\pi$
$619$	−10.8229	−	22.4740i	−0.435010	−	0.903307i	0.562081	−	0.827082i	$-0.310001\pi$
$620$	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	$0.336540\pi$
$641$	−12.5584	+	26.0779i	−0.496029	+	1.03001i	−0.987279	+	0.158996i	$0.949174\pi$
$642$	−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	0.720494	−	0.693461i	$-0.243915\pi$
$653$	27.3108	+	6.23351i	1.06875	+	0.243936i	0.348261	+	0.937398i	$0.386772\pi$
$654$	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	−0.924807	−	0.380436i	$-0.875774\pi$
$659$	−19.5022	+	15.5525i	−0.759699	+	0.605839i	0.165109	+	0.986275i	$0.447202\pi$
$660$	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	0.766147	−	0.642665i	$-0.222171\pi$
$677$	−5.56795	−	11.5620i	−0.213994	−	0.444363i	−0.980141	+	0.198303i	$0.936457\pi$
$678$	−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	−0.947131	−	0.320847i	$-0.896033\pi$
$727$	−44.7924	+	10.2236i	−1.66126	+	0.379171i	−0.714125	+	0.700018i	$0.753175\pi$
$728$	−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	−0.990113	−	0.140272i	$-0.955202\pi$
$733$	−29.0688	+	23.1816i	−1.07368	+	0.856231i	−0.0835661	+	0.996502i	$0.526631\pi$
$734$	−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	0.364745	−	0.931107i	$-0.381156\pi$
$739$	7.86658	+	1.79550i	0.289377	+	0.0660484i	−0.0753683	+	0.997156i	$0.524013\pi$
$740$	−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	0.955925	−	0.293610i	$-0.0948567\pi$
$743$	24.0522	+	19.1810i	0.882390	+	0.703683i	−0.0735353	+	0.997293i	$0.523428\pi$
$744$	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	$0.309978\pi$
$751$	−11.9197	+	24.7515i	−0.434957	+	0.903196i	−0.997096	+	0.0761541i	$0.975736\pi$
$752$	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	$-0.531475\pi$
$757$	20.3833	−	42.3264i	0.740844	−	1.53838i	0.839563	−	0.543262i	$-0.182811\pi$
$758$	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	−0.247905	−	0.968784i	$-0.579742\pi$
$769$	−24.7248	−	5.64328i	−0.891600	−	0.203502i	−0.643695	+	0.765282i	$0.722599\pi$
$770$	−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	0.762705	−	0.646746i	$-0.223871\pi$
$773$	−6.07437	−	12.6136i	−0.218480	−	0.453678i	−0.981185	+	0.193068i	$0.938156\pi$
$774$	−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	0.566331	−	0.824178i	$-0.308362\pi$
$797$	20.2977	+	4.63281i	0.718980	+	0.164103i	0.152649	+	0.988280i	$0.451220\pi$
$798$	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	−0.753849	−	0.657048i	$-0.771805\pi$
$809$	6.53814	−	13.5766i	0.229869	−	0.477328i	0.983718	+	0.179720i	$0.0575192\pi$
$810$	−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	0.575034	−	0.818129i	$-0.304989\pi$
$823$	−2.71463	−	2.16484i	−0.0946259	−	0.0754616i	−0.669660	+	0.742668i	$0.733560\pi$
$824$		−	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	−0.899660	−	0.436592i	$-0.856185\pi$
$827$	−54.6295	−	12.4688i	−1.89966	−	0.433584i	−0.999995	+	0.00300768i	$0.999043\pi$
$828$	−0.476304	+	0.597266i	−0.0165527	+	0.0207564i
$829$		−	8.20163i		−	0.284854i	−0.989805	−	0.142427i	$-0.954509\pi$
$829$		−	8.20163i		−	0.284854i	0.989805	−	0.142427i	$-0.0454907\pi$
$830$	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	−0.168076	−	0.985774i	$-0.553755\pi$
$839$	3.13418	−	0.715356i	0.108204	−	0.0246968i	0.276280	+	0.961077i	$0.410898\pi$
$840$	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	$-0.720064\pi$
$853$		−	45.0000i		−	1.54077i	0.637579	−	0.770385i	$-0.279936\pi$
$854$	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	0.846067	−	0.533077i	$-0.178964\pi$
$859$	15.0829	+	12.0282i	0.514623	+	0.410398i	−0.331444	+	0.943475i	$0.607536\pi$
$860$	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	0.927929	−	0.372757i	$-0.121587\pi$
$881$	22.8846	+	18.2499i	0.771002	+	0.614854i	−0.156927	+	0.987610i	$0.550159\pi$
$882$		−	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	$-0.890614\pi$
$887$		−	20.0689i		−	0.673847i	0.941532	−	0.336924i	$-0.109386\pi$
$888$	−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	−0.790611	−	0.612318i	$-0.790237\pi$
$907$	−11.1302	+	8.87604i	−0.369572	+	0.294724i	0.421039	+	0.907043i	$0.361666\pi$
$908$	−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	$0.0366987\pi$
$911$			6.94427i			0.230074i	−0.993361	+	0.115037i	$0.963301\pi$
$912$	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	0.975920	−	0.218128i	$-0.0699949\pi$
$947$	6.05943	+	12.5825i	0.196905	+	0.408877i	−0.779015	+	0.627005i	$0.784281\pi$
$948$	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	0.983979	−	0.178284i	$-0.0570547\pi$
$967$	7.18612	+	14.9221i	0.231090	+	0.479863i	−0.752889	+	0.658147i	$0.771340\pi$
$968$	−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	0.501990	−	0.864873i	$-0.332601\pi$
$971$	18.0426	+	4.11810i	0.579014	+	0.132156i	0.0770234	+	0.997029i	$0.475458\pi$
$972$	−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	−0.847377	−	0.530992i	$-0.821820\pi$
$983$	3.01301	−	6.25657i	0.0961000	−	0.199554i	0.943477	+	0.331438i	$0.107534\pi$
$984$	−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	0.210644	−	0.977563i	$-0.432444\pi$
$997$	−21.9618	−	17.5139i	−0.695537	−	0.554672i	−0.906181	+	0.422891i	$0.861015\pi$
$998$			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.196.4		24
29.2	odd	28		841.2.a.c.1.2	yes	2
29.3	odd	28		841.2.d.g.778.2		12
29.4	even	14	inner	841.2.e.j.236.4		24
29.5	even	14		841.2.b.b.840.1		4
29.6	even	14	inner	841.2.e.j.270.4		24
29.7	even	7	inner	841.2.e.j.63.1		24
29.8	odd	28		841.2.d.i.190.2		12
29.9	even	14	inner	841.2.e.j.651.1		24
29.10	odd	28		841.2.d.i.605.2		12
29.11	odd	28		841.2.d.g.574.2		12
29.12	odd	4		841.2.d.i.645.2		12
29.13	even	14	inner	841.2.e.j.267.1		24
29.14	odd	28		841.2.d.g.571.1		12
29.15	odd	28		841.2.d.i.571.2		12
29.16	even	7	inner	841.2.e.j.267.4		24
29.17	odd	4		841.2.d.g.645.1		12
29.18	odd	28		841.2.d.i.574.1		12
29.19	odd	28		841.2.d.g.605.1		12
29.20	even	7	inner	841.2.e.j.651.4		24
29.21	odd	28		841.2.d.g.190.1		12
29.22	even	14	inner	841.2.e.j.63.4		24
29.23	even	7	inner	841.2.e.j.270.1		24
29.24	even	7		841.2.b.b.840.4		4
29.25	even	7	inner	841.2.e.j.236.1		24
29.26	odd	28		841.2.d.i.778.1		12
29.27	odd	28		841.2.a.a.1.1	✓	2
29.28	even	2	inner	841.2.e.j.196.1		24
87.2	even	28		7569.2.a.d.1.1		2
87.56	even	28		7569.2.a.l.1.2		2

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