LMFDB - Embedded newform 80.2.q.c.29.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,2,Mod(29,80)] 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("80.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.5
Root			$1.40501 + 0.161069i$ of defining polynomial
Character	$\chi$	$=$	80.29
Dual form			80.2.q.c.69.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.161069 + 1.40501i) q^{2} +(-0.734294 + 0.734294i) q^{3} +(-1.94811 + 0.452606i) q^{4} +(1.90421 + 1.17216i) q^{5} +(-1.14996 - 0.913419i) q^{6} -1.71452 q^{7} +(-0.949697 - 2.66422i) q^{8} +1.92163i q^{9} +(-1.34019 + 2.86424i) q^{10} +(2.82684 - 2.82684i) q^{11} +(1.09814 - 1.76283i) q^{12} +(2.59462 - 2.59462i) q^{13} +(-0.276156 - 2.40893i) q^{14} +(-2.25896 + 0.537540i) q^{15} +(3.59030 - 1.76346i) q^{16} -1.89939i q^{17} +(-2.69991 + 0.309513i) q^{18} +(2.89623 + 2.89623i) q^{19} +(-4.24015 - 1.42165i) q^{20} +(1.25896 - 1.25896i) q^{21} +(4.42705 + 3.51643i) q^{22} -2.00613 q^{23} +(2.65368 + 1.25896i) q^{24} +(2.25207 + 4.46410i) q^{25} +(4.06338 + 3.22756i) q^{26} +(-3.61392 - 3.61392i) q^{27} +(3.34009 - 0.776005i) q^{28} +(-6.72307 - 6.72307i) q^{29} +(-1.11910 - 3.08729i) q^{30} -7.11778 q^{31} +(3.05596 + 4.76037i) q^{32} +4.15146i q^{33} +(2.66867 - 0.305932i) q^{34} +(-3.26482 - 2.00970i) q^{35} +(-0.869740 - 3.74355i) q^{36} +(-2.25207 - 2.25207i) q^{37} +(-3.60274 + 4.53572i) q^{38} +3.81042i q^{39} +(1.31448 - 6.18645i) q^{40} +1.59630i q^{41} +(1.97164 + 1.56608i) q^{42} +(8.06886 + 8.06886i) q^{43} +(-4.22756 + 6.78645i) q^{44} +(-2.25246 + 3.65919i) q^{45} +(-0.323124 - 2.81863i) q^{46} -4.43823i q^{47} +(-1.34144 + 3.93123i) q^{48} -4.06040 q^{49} +(-5.90938 + 3.88320i) q^{50} +(1.39471 + 1.39471i) q^{51} +(-3.88027 + 6.22896i) q^{52} +(-0.481758 - 0.481758i) q^{53} +(4.49551 - 5.65968i) q^{54} +(8.69642 - 2.06939i) q^{55} +(1.62828 + 4.56787i) q^{56} -4.25336 q^{57} +(8.36311 - 10.5289i) q^{58} +(3.08580 - 3.08580i) q^{59} +(4.15743 - 2.06961i) q^{60} +(3.46410 + 3.46410i) q^{61} +(-1.14645 - 10.0006i) q^{62} -3.29468i q^{63} +(-6.19615 + 5.06040i) q^{64} +(7.98203 - 1.89939i) q^{65} +(-5.83285 + 0.668669i) q^{66} +(-1.80454 + 1.80454i) q^{67} +(0.859677 + 3.70023i) q^{68} +(1.47309 - 1.47309i) q^{69} +(2.29780 - 4.91081i) q^{70} +0.379150i q^{71} +(5.11964 - 1.82496i) q^{72} -8.37718 q^{73} +(2.80144 - 3.52691i) q^{74} +(-4.93164 - 1.62428i) q^{75} +(-6.95303 - 4.33133i) q^{76} +(-4.84668 + 4.84668i) q^{77} +(-5.35369 + 0.613739i) q^{78} +11.2566 q^{79} +(8.90375 + 0.850413i) q^{80} -0.457524 q^{81} +(-2.24282 + 0.257114i) q^{82} +(8.24890 - 8.24890i) q^{83} +(-1.88279 + 3.02242i) q^{84} +(2.22640 - 3.61685i) q^{85} +(-10.0372 + 12.6365i) q^{86} +9.87341 q^{87} +(-10.2160 - 4.84668i) q^{88} -11.9820i q^{89} +(-5.50400 - 2.57535i) q^{90} +(-4.44854 + 4.44854i) q^{91} +(3.90816 - 0.907986i) q^{92} +(5.22654 - 5.22654i) q^{93} +(6.23577 - 0.714859i) q^{94} +(2.12019 + 8.90989i) q^{95} +(-5.73948 - 1.25154i) q^{96} -6.50543i q^{97} +(-0.654003 - 5.70491i) q^{98} +(5.43213 + 5.43213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36}+ \cdots + 88 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.161069	+	1.40501i	0.113893	+	0.993493i
$2$	0.161069	+	1.40501i	0.113893	+	0.993493i
$3$	−0.734294	+	0.734294i	−0.423945	+	0.423945i	−0.886559	−	0.462615i	$-0.846911\pi$
$3$	−0.734294	+	0.734294i	−0.423945	+	0.423945i	0.462615	+	0.886559i	$0.346911\pi$
$4$	−1.94811	+	0.452606i	−0.974057	+	0.226303i
$5$	1.90421	+	1.17216i	0.851591	+	0.524207i
$5$	1.90421	+	1.17216i	0.851591	+	0.524207i
$6$	−1.14996	−	0.913419i	−0.469470	−	0.372902i
$7$	−1.71452			−0.648029			−0.324015	−	0.946052i	$-0.605033\pi$
$7$	−1.71452			−0.648029			−0.324015	+	0.946052i	$0.605033\pi$
$8$	−0.949697	−	2.66422i	−0.335768	−	0.941945i
$9$			1.92163i			0.640542i
$10$	−1.34019	+	2.86424i	−0.423807	+	0.905753i
$11$	2.82684	−	2.82684i	0.852324	−	0.852324i	−0.138095	−	0.990419i	$-0.544098\pi$
$11$	2.82684	−	2.82684i	0.852324	−	0.852324i	0.990419	+	0.138095i	$0.0440980\pi$
$12$	1.09814	−	1.76283i	0.317006	−	0.508886i
$13$	2.59462	−	2.59462i	0.719618	−	0.719618i	−0.248909	−	0.968527i	$-0.580072\pi$
$13$	2.59462	−	2.59462i	0.719618	−	0.719618i	0.968527	+	0.248909i	$0.0800720\pi$
$14$	−0.276156	−	2.40893i	−0.0738058	−	0.643813i
$15$	−2.25896	+	0.537540i	−0.583262	+	0.138792i
$16$	3.59030	−	1.76346i	0.897574	−	0.440864i
$17$		−	1.89939i		−	0.460671i	−0.973111	−	0.230335i	$-0.926018\pi$
$17$		−	1.89939i		−	0.460671i	0.973111	−	0.230335i	$-0.0739823\pi$
$18$	−2.69991	+	0.309513i	−0.636374	+	0.0729530i
$19$	2.89623	+	2.89623i	0.664440	+	0.664440i	0.956423	−	0.291983i	$-0.0943151\pi$
$19$	2.89623	+	2.89623i	0.664440	+	0.664440i	−0.291983	+	0.956423i	$0.594315\pi$
$20$	−4.24015	−	1.42165i	−0.948127	−	0.317890i
$21$	1.25896	−	1.25896i	0.274729	−	0.274729i
$22$	4.42705	+	3.51643i	0.943851	+	0.749704i
$23$	−2.00613			−0.418306			−0.209153	−	0.977883i	$-0.567071\pi$
$23$	−2.00613			−0.418306			−0.209153	+	0.977883i	$0.567071\pi$
$24$	2.65368	+	1.25896i	0.541680	+	0.256985i
$25$	2.25207	+	4.46410i	0.450413	+	0.892820i
$26$	4.06338	+	3.22756i	0.796895	+	0.632976i
$27$	−3.61392	−	3.61392i	−0.695499	−	0.695499i
$28$	3.34009	−	0.776005i	0.631218	−	0.146651i
$29$	−6.72307	−	6.72307i	−1.24844	−	1.24844i	−0.956408	−	0.292034i	$-0.905668\pi$
$29$	−6.72307	−	6.72307i	−1.24844	−	1.24844i	−0.292034	−	0.956408i	$-0.594332\pi$
$30$	−1.11910	−	3.08729i	−0.204318	−	0.563659i
$31$	−7.11778			−1.27839			−0.639195	−	0.769044i	$-0.720732\pi$
$31$	−7.11778			−1.27839			−0.639195	+	0.769044i	$0.720732\pi$
$32$	3.05596	+	4.76037i	0.540223	+	0.841522i
$33$			4.15146i			0.722676i
$34$	2.66867	−	0.305932i	0.457673	−	0.0524670i
$35$	−3.26482	−	2.00970i	−0.551856	−	0.339702i
$36$	−0.869740	−	3.74355i	−0.144957	−	0.623924i
$37$	−2.25207	−	2.25207i	−0.370237	−	0.370237i	0.497326	−	0.867564i	$-0.334315\pi$
$37$	−2.25207	−	2.25207i	−0.370237	−	0.370237i	−0.867564	+	0.497326i	$0.834315\pi$
$38$	−3.60274	+	4.53572i	−0.584442	+	0.735792i
$39$			3.81042i			0.610156i
$40$	1.31448	−	6.18645i	0.207837	−	0.978163i
$41$			1.59630i			0.249301i	0.992201	+	0.124650i	$0.0397809\pi$
$41$			1.59630i			0.249301i	−0.992201	+	0.124650i	$0.960219\pi$
$42$	1.97164	+	1.56608i	0.304231	+	0.241651i
$43$	8.06886	+	8.06886i	1.23049	+	1.23049i	0.963776	+	0.266715i	$0.0859381\pi$
$43$	8.06886	+	8.06886i	1.23049	+	1.23049i	0.266715	+	0.963776i	$0.414062\pi$
$44$	−4.22756	+	6.78645i	−0.637328	+	1.02310i
$45$	−2.25246	+	3.65919i	−0.335777	+	0.545480i
$46$	−0.323124	−	2.81863i	−0.0476420	−	0.415585i
$47$		−	4.43823i		−	0.647383i	−0.946163	−	0.323691i	$-0.895076\pi$
$47$		−	4.43823i		−	0.647383i	0.946163	−	0.323691i	$-0.104924\pi$
$48$	−1.34144	+	3.93123i	−0.193620	+	0.567424i
$49$	−4.06040			−0.580058
$50$	−5.90938	+	3.88320i	−0.835712	+	0.549168i
$51$	1.39471	+	1.39471i	0.195299	+	0.195299i
$52$	−3.88027	+	6.22896i	−0.538097	+	0.863801i
$53$	−0.481758	−	0.481758i	−0.0661746	−	0.0661746i	0.673245	−	0.739420i	$-0.264900\pi$
$53$	−0.481758	−	0.481758i	−0.0661746	−	0.0661746i	−0.739420	+	0.673245i	$0.764900\pi$
$54$	4.49551	−	5.65968i	0.611761	−	0.770186i
$55$	8.69642	−	2.06939i	1.17263	−	0.279036i
$56$	1.62828	+	4.56787i	0.217588	+	0.610408i
$57$	−4.25336			−0.563372
$58$	8.36311	−	10.5289i	1.09813	−	1.38251i
$59$	3.08580	−	3.08580i	0.401737	−	0.401737i	−0.477108	−	0.878845i	$-0.658315\pi$
$59$	3.08580	−	3.08580i	0.401737	−	0.401737i	0.878845	+	0.477108i	$0.158315\pi$
$60$	4.15743	−	2.06961i	0.536721	−	0.267186i
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	0.893197	−	0.449665i	$-0.148457\pi$
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	−0.449665	+	0.893197i	$0.648457\pi$
$62$	−1.14645	−	10.0006i	−0.145599	−	1.27007i
$63$		−	3.29468i		−	0.415090i
$64$	−6.19615	+	5.06040i	−0.774519	+	0.632551i
$65$	7.98203	−	1.89939i	0.990049	−	0.235591i
$66$	−5.83285	+	0.668669i	−0.717974	+	0.0823075i
$67$	−1.80454	+	1.80454i	−0.220460	+	0.220460i	−0.808692	−	0.588232i	$-0.799824\pi$
$67$	−1.80454	+	1.80454i	−0.220460	+	0.220460i	0.588232	+	0.808692i	$0.299824\pi$
$68$	0.859677	+	3.70023i	0.104251	+	0.448719i
$69$	1.47309	−	1.47309i	0.177339	−	0.177339i
$70$	2.29780	−	4.91081i	0.274639	−	0.586954i
$71$			0.379150i			0.0449969i	0.999747	+	0.0224984i	$0.00716208\pi$
$71$			0.379150i			0.0449969i	−0.999747	+	0.0224984i	$0.992838\pi$
$72$	5.11964	−	1.82496i	0.603355	−	0.215074i
$73$	−8.37718			−0.980475			−0.490237	−	0.871589i	$-0.663090\pi$
$73$	−8.37718			−0.980475			−0.490237	+	0.871589i	$0.663090\pi$
$74$	2.80144	−	3.52691i	0.325661	−	0.409995i
$75$	−4.93164	−	1.62428i	−0.569456	−	0.187556i
$76$	−6.95303	−	4.33133i	−0.797567	−	0.496838i
$77$	−4.84668	+	4.84668i	−0.552331	+	0.552331i
$78$	−5.35369	+	0.613739i	−0.606186	+	0.0694923i
$79$	11.2566			1.26646			0.633231	−	0.773963i	$-0.281728\pi$
$79$	11.2566			1.26646			0.633231	+	0.773963i	$0.281728\pi$
$80$	8.90375	+	0.850413i	0.995470	+	0.0950791i
$81$	−0.457524			−0.0508360
$82$	−2.24282	+	0.257114i	−0.247678	+	0.0283935i
$83$	8.24890	−	8.24890i	0.905435	−	0.905435i	−0.0904649	−	0.995900i	$-0.528835\pi$
$83$	8.24890	−	8.24890i	0.905435	−	0.905435i	0.995900	+	0.0904649i	$0.0288353\pi$
$84$	−1.88279	+	3.02242i	−0.205429	+	0.329773i
$85$	2.22640	−	3.61685i	0.241487	−	0.392303i
$86$	−10.0372	+	12.6365i	−1.08234	+	1.36263i
$87$	9.87341			1.05854
$88$	−10.2160	−	4.84668i	−1.08903	−	0.516658i
$89$		−	11.9820i		−	1.27009i	−0.772474	−	0.635046i	$-0.780981\pi$
$89$		−	11.9820i		−	1.27009i	0.772474	−	0.635046i	$-0.219019\pi$
$90$	−5.50400	−	2.57535i	−0.580173	−	0.271466i
$91$	−4.44854	+	4.44854i	−0.466334	+	0.466334i
$92$	3.90816	−	0.907986i	0.407454	−	0.0946640i
$93$	5.22654	−	5.22654i	0.541967	−	0.541967i
$94$	6.23577	−	0.714859i	0.643170	−	0.0737321i
$95$	2.12019	+	8.90989i	0.217526	+	0.914136i
$96$	−5.73948	−	1.25154i	−0.585783	−	0.127734i
$97$		−	6.50543i		−	0.660526i	−0.943889	−	0.330263i	$-0.892863\pi$
$97$		−	6.50543i		−	0.660526i	0.943889	−	0.330263i	$-0.107137\pi$
$98$	−0.654003	−	5.70491i	−0.0660643	−	0.576283i
$99$	5.43213	+	5.43213i	0.545949	+	0.545949i
$100$	−6.40776	−	7.67728i	−0.640776	−	0.767728i
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	−0.957478	−	0.288508i	$-0.906841\pi$
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	0.288508	+	0.957478i	$0.406841\pi$
$102$	−1.73494	+	2.18423i	−0.171785	+	0.216271i
$103$	−15.1733			−1.49506			−0.747532	−	0.664225i	$-0.768762\pi$
$103$	−15.1733			−1.49506			−0.747532	+	0.664225i	$0.768762\pi$
$104$	−9.37674	−	4.44854i	−0.919465	−	0.436215i
$105$	3.87305	−	0.921626i	0.377971	−	0.0899415i
$106$	0.599280	−	0.754472i	0.0582072	−	0.0732808i
$107$	1.69781	+	1.69781i	0.164134	+	0.164134i	0.784395	−	0.620262i	$-0.212974\pi$
$107$	1.69781	+	1.69781i	0.164134	+	0.164134i	−0.620262	+	0.784395i	$0.712974\pi$
$108$	8.67601	+	5.40464i	0.834849	+	0.520062i
$109$	3.11120	+	3.11120i	0.297999	+	0.297999i	0.840230	−	0.542231i	$-0.182420\pi$
$109$	3.11120	+	3.11120i	0.297999	+	0.297999i	−0.542231	+	0.840230i	$0.682420\pi$
$110$	4.30824	+	11.8853i	0.410774	+	1.13322i
$111$	3.30735			0.313920
$112$	−6.15565	+	3.02349i	−0.581654	+	0.285693i
$113$			15.8259i			1.48877i	0.667748	+	0.744387i	$0.267258\pi$
$113$			15.8259i			1.48877i	−0.667748	+	0.744387i	$0.732742\pi$
$114$	−0.685083	−	5.97602i	−0.0641639	−	0.559706i
$115$	−3.82010	−	2.35151i	−0.356226	−	0.219279i
$116$	16.1402	+	10.0544i	1.49858	+	0.933527i
$117$	4.98589	+	4.98589i	0.460946	+	0.460946i
$118$	4.83261	+	3.83856i	0.444878	+	0.353368i
$119$			3.25656i			0.298528i
$120$	3.57746	+	5.50788i	0.326576	+	0.502799i
$121$		−	4.98203i		−	0.452912i
$122$	−4.30914	+	5.42506i	−0.390132	+	0.491162i
$123$	−1.17216	−	1.17216i	−0.105690	−	0.105690i
$124$	13.8662	−	3.22155i	1.24523	−	0.289304i
$125$	−0.944243	+	11.1404i	−0.0844556	+	0.996427i
$126$	4.62906	−	0.530669i	0.412389	−	0.0472757i
$127$			18.3239i			1.62598i	0.582276	+	0.812991i	$0.302162\pi$
$127$			18.3239i			1.62598i	−0.582276	+	0.812991i	$0.697838\pi$
$128$	−8.10793	−	7.89059i	−0.716647	−	0.697436i
$129$	−11.8498			−1.04332
$130$	3.95432	+	10.9089i	0.346817	+	0.956775i
$131$	−10.2036	−	10.2036i	−0.891491	−	0.891491i	0.103172	−	0.994663i	$-0.467101\pi$
$131$	−10.2036	−	10.2036i	−0.891491	−	0.891491i	−0.994663	+	0.103172i	$0.967101\pi$
$132$	−1.87898	−	8.08751i	−0.163544	−	0.703928i
$133$	−4.96565	−	4.96565i	−0.430577	−	0.430577i
$134$	−2.82606	−	2.24475i	−0.244134	−	0.193917i
$135$	−2.64557	−	11.1178i	−0.227695	−	0.956866i
$136$	−5.06040	+	1.80385i	−0.433926	+	0.154679i
$137$	14.9845			1.28021			0.640107	−	0.768286i	$-0.278890\pi$
$137$	14.9845			1.28021			0.640107	+	0.768286i	$0.278890\pi$
$138$	2.30697	+	1.83244i	0.196382	+	0.155987i
$139$	−8.29094	+	8.29094i	−0.703228	+	0.703228i	−0.965102	−	0.261874i	$-0.915660\pi$
$139$	−8.29094	+	8.29094i	−0.703228	+	0.703228i	0.261874	+	0.965102i	$0.415660\pi$
$140$	7.26985	+	2.43745i	0.614415	+	0.206002i
$141$	3.25896	+	3.25896i	0.274454	+	0.274454i
$142$	−0.532711	+	0.0610692i	−0.0447041	+	0.00512481i
$143$		−	14.6691i		−	1.22670i
$144$	3.38870	+	6.89920i	0.282392	+	0.574934i
$145$	−4.92163	−	20.6827i	−0.408719	−	1.71760i
$146$	−1.34930	−	11.7700i	−0.111669	−	0.974095i
$147$	2.98153	−	2.98153i	0.245912	−	0.245912i
$148$	5.40658	+	3.36798i	0.444418	+	0.276846i
$149$	−7.30735	+	7.30735i	−0.598642	+	0.598642i	−0.939951	−	0.341309i	$-0.889130\pi$
$149$	−7.30735	+	7.30735i	−0.598642	+	0.598642i	0.341309	+	0.939951i	$0.389130\pi$
$150$	1.48781	−	7.19063i	0.121479	−	0.587112i
$151$		−	4.56873i		−	0.371798i	−0.982569	−	0.185899i	$-0.940480\pi$
$151$		−	4.56873i		−	0.371798i	0.982569	−	0.185899i	$-0.0595197\pi$
$152$	4.96565	−	10.4667i	0.402768	−	0.848964i
$153$	3.64992			0.295079
$154$	−7.59030	−	6.02900i	−0.611643	−	0.485831i
$155$	−13.5538	−	8.34320i	−1.08867	−	0.670142i
$156$	−1.72462	−	7.42314i	−0.138080	−	0.594327i
$157$	1.52966	−	1.52966i	0.122080	−	0.122080i	−0.643427	−	0.765507i	$-0.722488\pi$
$157$	1.52966	−	1.52966i	0.122080	−	0.122080i	0.765507	+	0.643427i	$0.222488\pi$
$158$	1.81308	+	15.8156i	0.144241	+	1.25822i
$159$	0.707504			0.0561087
$160$	0.239274	+	12.6468i	0.0189162	+	0.999821i
$161$	3.43955			0.271075
$162$	−0.0736928	−	0.642827i	−0.00578985	−	0.0505053i
$163$	−10.1361	+	10.1361i	−0.793918	+	0.793918i	−0.982129	−	0.188211i	$-0.939731\pi$
$163$	−10.1361	+	10.1361i	−0.793918	+	0.793918i	0.188211	+	0.982129i	$0.439731\pi$
$164$	−0.722497	−	3.10978i	−0.0564175	−	0.242833i
$165$	−4.86619	+	7.90527i	−0.378832	+	0.615424i
$166$	12.9184	+	10.2612i	1.00267	+	0.796421i
$167$	−2.57967			−0.199621			−0.0998105	−	0.995006i	$-0.531824\pi$
$167$	−2.57967			−0.199621			−0.0998105	+	0.995006i	$0.531824\pi$
$168$	−4.54979	−	2.15853i	−0.351024	−	0.166534i
$169$		−	0.464102i		−	0.0357001i
$170$	5.44032	+	2.54556i	0.417254	+	0.195235i
$171$	−5.56547	+	5.56547i	−0.425602	+	0.425602i
$172$	−19.3711	−	12.0670i	−1.47703	−	0.920104i
$173$	14.1773	−	14.1773i	1.07788	−	1.07788i	0.0811779	−	0.996700i	$-0.474132\pi$
$173$	14.1773	−	14.1773i	1.07788	−	1.07788i	0.996700	−	0.0811779i	$-0.0258682\pi$
$174$	1.59030	+	13.8723i	0.120560	+	1.05165i
$175$	−3.86122	−	7.65381i	−0.291881	−	0.578574i
$176$	5.16418	−	15.1342i	0.389264	−	1.14078i
$177$			4.53177i			0.340629i
$178$	16.8349	−	1.92993i	1.26183	−	0.144654i
$179$	−9.88067	−	9.88067i	−0.738516	−	0.738516i	0.233775	−	0.972291i	$-0.424892\pi$
$179$	−9.88067	−	9.88067i	−0.738516	−	0.738516i	−0.972291	+	0.233775i	$0.924892\pi$
$180$	2.73188	−	8.14799i	0.203622	−	0.607315i
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	−0.437832	−	0.899057i	$-0.644254\pi$
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	0.899057	+	0.437832i	$0.144254\pi$
$182$	−6.96677	−	5.53373i	−0.516411	−	0.410187i
$183$	−5.08733			−0.376067
$184$	1.90521	+	5.34477i	0.140454	+	0.394021i
$185$	−1.64863	−	6.92820i	−0.121209	−	0.509372i
$186$	8.18518	+	6.50152i	0.600166	+	0.476714i
$187$	−5.36928	−	5.36928i	−0.392641	−	0.392641i
$188$	2.00877	+	8.64618i	0.146505	+	0.630587i
$189$	6.19615	+	6.19615i	0.450704	+	0.450704i
$190$	−12.1770	+	4.41399i	−0.883413	+	0.320224i
$191$	18.9282			1.36960			0.684798	−	0.728733i	$-0.259890\pi$
$191$	18.9282			1.36960			0.684798	+	0.728733i	$0.259890\pi$
$192$	0.833972	−	8.26562i	0.0601868	−	0.596520i
$193$			4.42987i			0.318869i	0.987209	+	0.159434i	$0.0509670\pi$
$193$			4.42987i			0.318869i	−0.987209	+	0.159434i	$0.949033\pi$
$194$	9.14020	−	1.04782i	0.656228	−	0.0752291i
$195$	−4.46644	+	7.25587i	−0.319849	+	0.519603i
$196$	7.91013	−	1.83776i	0.565009	−	0.131269i
$197$	6.39341	+	6.39341i	0.455511	+	0.455511i	0.897179	−	0.441667i	$-0.145613\pi$
$197$	6.39341	+	6.39341i	0.455511	+	0.455511i	−0.441667	+	0.897179i	$0.645613\pi$
$198$	−6.75725	+	8.50714i	−0.480217	+	0.604576i
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$	9.75458	−	10.2395i	0.689753	−	0.724045i
$201$		−	2.65013i		−	0.186926i
$202$	−10.5289	−	8.36311i	−0.740808	−	0.588426i
$203$	11.5269	+	11.5269i	0.809027	+	0.809027i
$204$	−3.34831	−	2.08580i	−0.234429	−	0.146035i
$205$	−1.87113	+	3.03970i	−0.130685	+	0.212302i
$206$	−2.44393	−	21.3186i	−0.170277	−	1.48534i
$207$		−	3.85503i		−	0.267943i
$208$	4.73995	−	13.8910i	0.328656	−	0.963164i
$209$	16.3743			1.13264
$210$	1.91872	+	5.29324i	0.132404	+	0.365268i
$211$	7.60373	+	7.60373i	0.523462	+	0.523462i	0.918615	−	0.395153i	$-0.129308\pi$
$211$	7.60373	+	7.60373i	0.523462	+	0.523462i	−0.395153	+	0.918615i	$0.629308\pi$
$212$	1.15657	+	0.720473i	0.0794334	+	0.0494823i
$213$	−0.278408	−	0.278408i	−0.0190762	−	0.0190762i
$214$	−2.11198	+	2.65891i	−0.144372	+	0.181759i
$215$	5.90682	+	24.8229i	0.402842	+	1.69291i
$216$	−6.19615	+	13.0604i	−0.421595	+	0.888648i
$217$	12.2036			0.828435
$218$	−3.87016	+	4.87239i	−0.262120	+	0.330000i
$219$	6.15131	−	6.15131i	0.415667	−	0.415667i
$220$	−16.0050	+	7.96746i	−1.07906	+	0.537166i
$221$	−4.92820	−	4.92820i	−0.331507	−	0.331507i
$222$	0.532711	+	4.64687i	0.0357532	+	0.311877i
$223$			9.22430i			0.617705i	0.951110	+	0.308853i	$0.0999450\pi$
$223$			9.22430i			0.617705i	−0.951110	+	0.308853i	$0.900055\pi$
$224$	−5.23952	−	8.16177i	−0.350080	−	0.545331i
$225$	−8.57833	+	4.32763i	−0.571889	+	0.288508i
$226$	−22.2356	+	2.54905i	−1.47909	+	0.169560i
$227$	−9.21725	+	9.21725i	−0.611770	+	0.611770i	−0.943407	−	0.331637i	$-0.892399\pi$
$227$	−9.21725	+	9.21725i	−0.611770	+	0.611770i	0.331637	+	0.943407i	$0.392399\pi$
$228$	8.28603	−	1.92510i	0.548756	−	0.127493i
$229$	1.63811	−	1.63811i	0.108250	−	0.108250i	−0.650907	−	0.759157i	$-0.725611\pi$
$229$	1.63811	−	1.63811i	0.108250	−	0.108250i	0.759157	+	0.650907i	$0.225611\pi$
$230$	2.68860	−	5.74603i	0.177281	−	0.378882i
$231$		−	7.11778i		−	0.468315i
$232$	−11.5269	+	24.2966i	−0.756776	+	1.59515i
$233$	−12.3798			−0.811026			−0.405513	−	0.914089i	$-0.632907\pi$
$233$	−12.3798			−0.811026			−0.405513	+	0.914089i	$0.632907\pi$
$234$	−6.20216	+	7.80830i	−0.405448	+	0.510445i
$235$	5.20233	−	8.45134i	0.339363	−	0.551305i
$236$	−4.61484	+	7.40815i	−0.300401	+	0.482229i
$237$	−8.26562	+	8.26562i	−0.536910	+	0.536910i
$238$	−4.57550	+	0.524529i	−0.296586	+	0.0340002i
$239$	−7.77449			−0.502890			−0.251445	−	0.967872i	$-0.580906\pi$
$239$	−7.77449			−0.502890			−0.251445	+	0.967872i	$0.580906\pi$
$240$	−7.16242	+	5.91351i	−0.462332	+	0.381716i
$241$	−3.47068			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$241$	−3.47068			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$242$	6.99981	−	0.802448i	0.449965	−	0.0515833i
$243$	11.1777	−	11.1777i	0.717051	−	0.717051i
$244$	−8.31634	−	5.18059i	−0.532399	−	0.331653i
$245$	−7.73188	−	4.75946i	−0.493972	−	0.304071i
$246$	1.45809	−	1.83569i	0.0929647	−	0.117039i
$247$	15.0292			0.956286
$248$	6.75973	+	18.9633i	0.429243	+	1.20417i
$249$			12.1142i			0.767708i
$250$	−15.8045	+	0.467695i	−0.999562	+	0.0295796i
$251$	8.94765	−	8.94765i	0.564771	−	0.564771i	−0.365888	−	0.930659i	$-0.619235\pi$
$251$	8.94765	−	8.94765i	0.564771	−	0.564771i	0.930659	+	0.365888i	$0.119235\pi$
$252$	1.49119	+	6.41840i	0.0939362	+	0.404321i
$253$	−5.67100	+	5.67100i	−0.356533	+	0.356533i
$254$	−25.7453	+	2.95140i	−1.61540	+	0.185187i
$255$	1.02100	+	4.29066i	0.0639375	+	0.268692i
$256$	9.78044	−	12.6627i	0.611277	−	0.791416i
$257$			3.62228i			0.225952i	0.993598	+	0.112976i	$0.0360383\pi$
$257$			3.62228i			0.225952i	−0.993598	+	0.112976i	$0.963962\pi$
$258$	−1.90863	−	16.6491i	−0.118826	−	1.03653i
$259$	3.86122	+	3.86122i	0.239925	+	0.239925i
$260$	−14.6902	+	7.31295i	−0.911049	+	0.453530i
$261$	12.9192	−	12.9192i	0.799680	−	0.799680i
$262$	12.6927	−	15.9796i	0.784156	−	0.987224i
$263$	−13.7416			−0.847345			−0.423673	−	0.905815i	$-0.639259\pi$
$263$	−13.7416			−0.847345			−0.423673	+	0.905815i	$0.639259\pi$
$264$	11.0604	−	3.94263i	0.680721	−	0.242652i
$265$	−0.352672	−	1.48207i	−0.0216644	−	0.0910429i
$266$	6.17699	−	7.77661i	0.378736	−	0.476815i
$267$	8.79833	+	8.79833i	0.538449	+	0.538449i
$268$	2.69871	−	4.33221i	0.164850	−	0.264632i
$269$	−4.22240	−	4.22240i	−0.257444	−	0.257444i	0.566570	−	0.824014i	$-0.308270\pi$
$269$	−4.22240	−	4.22240i	−0.257444	−	0.257444i	−0.824014	+	0.566570i	$0.808270\pi$
$270$	15.1945	−	5.50778i	0.924707	−	0.335193i
$271$	−5.40015			−0.328036			−0.164018	−	0.986457i	$-0.552445\pi$
$271$	−5.40015			−0.328036			−0.164018	+	0.986457i	$0.552445\pi$
$272$	−3.34950	−	6.81938i	−0.203093	−	0.413486i
$273$		−	6.53307i		−	0.395399i
$274$	2.41353	+	21.0534i	0.145807	+	1.27188i
$275$	18.9855	+	6.25307i	1.14487	+	0.377074i
$276$	−2.20301	+	3.53647i	−0.132606	+	0.212870i
$277$	−5.08733	−	5.08733i	−0.305668	−	0.305668i	0.537558	−	0.843227i	$-0.319347\pi$
$277$	−5.08733	−	5.08733i	−0.305668	−	0.305668i	−0.843227	+	0.537558i	$0.819347\pi$
$278$	−12.9843	−	10.3135i	−0.778745	−	0.618560i
$279$		−	13.6777i		−	0.818863i
$280$	−2.25370	+	10.6068i	−0.134685	+	0.633879i
$281$			21.2780i			1.26934i	0.772784	+	0.634669i	$0.218864\pi$
$281$			21.2780i			1.26934i	−0.772784	+	0.634669i	$0.781136\pi$
$282$	−4.05397	+	5.10380i	−0.241410	+	0.303927i
$283$	4.08521	+	4.08521i	0.242840	+	0.242840i	0.818024	−	0.575184i	$-0.195069\pi$
$283$	4.08521	+	4.08521i	0.242840	+	0.242840i	−0.575184	+	0.818024i	$0.695069\pi$
$284$	−0.171606	−	0.738628i	−0.0101829	−	0.0438295i
$285$	−8.09931	−	4.98564i	−0.479762	−	0.295324i
$286$	20.6103	−	2.36274i	1.21871	−	0.139712i
$287$		−	2.73690i		−	0.161554i
$288$	−9.14765	+	5.87241i	−0.539030	+	0.346035i
$289$	13.3923			0.787783
$290$	28.2667	−	10.2463i	1.65988	−	0.601682i
$291$	4.77689	+	4.77689i	0.280026	+	0.280026i
$292$	16.3197	−	3.79156i	0.955038	−	0.221884i
$293$	−7.40400	−	7.40400i	−0.432547	−	0.432547i	0.456947	−	0.889494i	$-0.348943\pi$
$293$	−7.40400	−	7.40400i	−0.432547	−	0.432547i	−0.889494	+	0.456947i	$0.848943\pi$
$294$	4.66931	+	3.70885i	0.272320	+	0.216305i
$295$	9.49310	−	2.25896i	0.552709	−	0.131522i
$296$	−3.86122	+	8.13878i	−0.224429	+	0.473057i
$297$	−20.4319			−1.18558
$298$	−11.4439	−	9.08993i	−0.662927	−	0.526566i
$299$	−5.20514	+	5.20514i	−0.301021	+	0.301021i
$300$	10.3426	+	0.932201i	0.597128	+	0.0538206i
$301$	−13.8343	−	13.8343i	−0.797394	−	0.797394i
$302$	6.41911	−	0.735878i	0.369378	−	0.0423450i
$303$		−	9.87341i		−	0.567212i
$304$	15.5057	+	5.29094i	0.889312	+	0.303456i
$305$	2.53590	+	10.6569i	0.145205	+	0.610212i
$306$	0.587888	+	5.12818i	0.0336073	+	0.293159i
$307$	16.6634	−	16.6634i	0.951030	−	0.951030i	−0.0478262	−	0.998856i	$-0.515229\pi$
$307$	16.6634	−	16.6634i	0.951030	−	0.951030i	0.998856	+	0.0478262i	$0.0152294\pi$
$308$	7.24825	−	11.6355i	0.413008	−	0.662996i
$309$	11.1416	−	11.1416i	0.633825	−	0.633825i
$310$	9.53921	−	20.3870i	0.541790	−	1.15791i
$311$			21.9072i			1.24224i	0.783714	+	0.621122i	$0.213323\pi$
$311$			21.9072i			1.24224i	−0.783714	+	0.621122i	$0.786677\pi$
$312$	10.1518	−	3.61875i	0.574733	−	0.204871i
$313$	−12.4820			−0.705525			−0.352763	−	0.935713i	$-0.614758\pi$
$313$	−12.4820			−0.705525			−0.352763	+	0.935713i	$0.614758\pi$
$314$	2.39556	+	1.90280i	0.135189	+	0.107381i
$315$	3.86190	−	6.27377i	0.217593	−	0.353487i
$316$	−21.9291	+	5.09479i	−1.23361	+	0.286604i
$317$	4.24325	−	4.24325i	0.238324	−	0.238324i	−0.577832	−	0.816156i	$-0.696101\pi$
$317$	4.24325	−	4.24325i	0.238324	−	0.238324i	0.816156	+	0.577832i	$0.196101\pi$
$318$	0.113957	+	0.994051i	0.00639037	+	0.0557436i
$319$	−38.0100			−2.12815
$320$	−17.7304	+	2.37319i	−0.991161	+	0.132665i
$321$	−2.49338			−0.139167
$322$	0.554004	+	4.83261i	0.0308734	+	0.269311i
$323$	5.50108	−	5.50108i	0.306088	−	0.306088i
$324$	0.891310	−	0.207078i	0.0495172	−	0.0115044i
$325$	17.4259	+	5.73939i	0.966615	+	0.318364i
$326$	−15.8739	−	12.6087i	−0.879173	−	0.698330i
$327$	−4.56907			−0.252670
$328$	4.25290	−	1.51600i	0.234827	−	0.0837073i
$329$			7.60946i			0.419523i
$330$	−11.8908	−	5.56376i	−0.654566	−	0.306275i
$331$	1.10377	−	1.10377i	0.0606688	−	0.0606688i	−0.676121	−	0.736790i	$-0.736341\pi$
$331$	1.10377	−	1.10377i	0.0606688	−	0.0606688i	0.736790	+	0.676121i	$0.236341\pi$
$332$	−12.3363	+	19.8033i	−0.677042	+	1.08685i
$333$	4.32763	−	4.32763i	0.237152	−	0.237152i
$334$	−0.415504	−	3.62447i	−0.0227354	−	0.198322i
$335$	−5.55146	+	1.32102i	−0.303309	+	0.0721749i
$336$	2.29992	−	6.74018i	0.125471	−	0.367707i
$337$		−	7.47635i		−	0.407263i	−0.979048	−	0.203631i	$-0.934726\pi$
$337$		−	7.47635i		−	0.407263i	0.979048	−	0.203631i	$-0.0652744\pi$
$338$	0.652068	−	0.0747522i	0.0354678	−	0.00406598i
$339$	−11.6208	−	11.6208i	−0.631158	−	0.631158i
$340$	−2.70027	+	8.05372i	−0.146443	+	0.436774i
$341$	−20.1208	+	20.1208i	−1.08960	+	1.08960i
$342$	−8.71597	−	6.92312i	−0.471305	−	0.374360i
$343$	18.9633			1.02392
$344$	13.8343	−	29.1602i	0.745894	−	1.57221i
$345$	4.53177	−	1.07837i	0.243982	−	0.0580577i
$346$	22.2027	+	17.6357i	1.19363	+	0.948102i
$347$	−8.56074	−	8.56074i	−0.459565	−	0.459565i	0.438948	−	0.898512i	$-0.355351\pi$
$347$	−8.56074	−	8.56074i	−0.459565	−	0.459565i	−0.898512	+	0.438948i	$0.855351\pi$
$348$	−19.2345	+	4.46877i	−1.03108	+	0.239551i
$349$	7.91567	+	7.91567i	0.423716	+	0.423716i	0.886481	−	0.462765i	$-0.153143\pi$
$349$	7.91567	+	7.91567i	0.423716	+	0.423716i	−0.462765	+	0.886481i	$0.653143\pi$
$350$	10.1318	−	6.65785i	0.541566	−	0.355877i
$351$	−18.7535			−1.00099
$352$	22.0955	+	4.81809i	1.17769	+	0.256805i
$353$		−	9.67314i		−	0.514849i	−0.966298	−	0.257425i	$-0.917126\pi$
$353$		−	9.67314i		−	0.514849i	0.966298	−	0.257425i	$-0.0828739\pi$
$354$	−6.36719	+	0.729926i	−0.338412	+	0.0387951i
$355$	−0.444426	+	0.721984i	−0.0235877	+	0.0383189i
$356$	5.42314	+	23.3424i	0.287426	+	1.23714i
$357$	−2.39127	−	2.39127i	−0.126559	−	0.126559i
$358$	12.2910	−	15.4739i	0.649599	−	0.817822i
$359$			17.0867i			0.901799i	0.892575	+	0.450900i	$0.148897\pi$
$359$			17.0867i			0.901799i	−0.892575	+	0.450900i	$0.851103\pi$
$360$	11.8880	+	2.52593i	0.626555	+	0.133128i
$361$		−	2.22373i		−	0.117038i
$362$	9.71774	+	7.71884i	0.510753	+	0.405693i
$363$	3.65827	+	3.65827i	0.192010	+	0.192010i
$364$	6.65283	−	10.6797i	0.348703	−	0.559768i
$365$	−15.9519	−	9.81943i	−0.834963	−	0.513972i
$366$	−0.819410	−	7.14776i	−0.0428312	−	0.373620i
$367$		−	13.4500i		−	0.702086i	−0.936359	−	0.351043i	$-0.885827\pi$
$367$		−	13.4500i		−	0.702086i	0.936359	−	0.351043i	$-0.114173\pi$
$368$	−7.20259	+	3.53772i	−0.375461	+	0.184416i
$369$	−3.06750			−0.159688
$370$	9.46866	−	3.43225i	0.492252	−	0.178434i
$371$	0.825987	+	0.825987i	0.0428831	+	0.0428831i
$372$	−7.81633	+	12.5475i	−0.405258	+	0.650555i
$373$	12.0271	+	12.0271i	0.622740	+	0.622740i	0.946231	−	0.323491i	$-0.104857\pi$
$373$	12.0271	+	12.0271i	0.622740	+	0.622740i	−0.323491	+	0.946231i	$0.604857\pi$
$374$	6.67908	−	8.40872i	0.345367	−	0.434804i
$375$	−7.48697	−	8.87367i	−0.386625	−	0.458234i
$376$	−11.8244	+	4.21497i	−0.609798	+	0.217371i
$377$	−34.8876			−1.79680
$378$	−7.70766	+	9.70367i	−0.396439	+	0.499103i
$379$	19.1552	−	19.1552i	0.983936	−	0.983936i	−0.0159369	−	0.999873i	$-0.505073\pi$
$379$	19.1552	−	19.1552i	0.983936	−	0.983936i	0.999873	+	0.0159369i	$0.00507308\pi$
$380$	−8.16304	−	16.3979i	−0.418755	−	0.841193i
$381$	−13.4551	−	13.4551i	−0.689327	−	0.689327i
$382$	3.04874	+	26.5943i	0.155987	+	1.36068i
$383$			17.7503i			0.907000i	0.891256	+	0.453500i	$0.149825\pi$
$383$			17.7503i			0.907000i	−0.891256	+	0.453500i	$0.850175\pi$
$384$	11.7476	−	0.159590i	0.599493	−	0.00814406i
$385$	−14.9102	+	3.54802i	−0.759896	+	0.180824i
$386$	−6.22401	+	0.713512i	−0.316794	+	0.0363168i
$387$	−15.5053	+	15.5053i	−0.788181	+	0.788181i
$388$	2.94440	+	12.6733i	0.149479	+	0.643390i
$389$	−1.18654	+	1.18654i	−0.0601602	+	0.0601602i	−0.736547	−	0.676387i	$-0.763545\pi$
$389$	−1.18654	+	1.18654i	−0.0601602	+	0.0601602i	0.676387	+	0.736547i	$0.263545\pi$
$390$	−10.9140	−	5.10671i	−0.552651	−	0.258588i
$391$			3.81042i			0.192701i
$392$	3.85615	+	10.8178i	0.194765	+	0.546382i
$393$	14.9848			0.755886
$394$	−7.95303	+	10.0126i	−0.400668	+	0.504427i
$395$	21.4349	+	13.1945i	1.07851	+	0.663889i
$396$	−13.0410	−	8.12379i	−0.655336	−	0.408236i
$397$	4.74478	−	4.74478i	0.238134	−	0.238134i	−0.577943	−	0.816077i	$-0.696145\pi$
$397$	4.74478	−	4.74478i	0.238134	−	0.238134i	0.816077	+	0.577943i	$0.196145\pi$
$398$	8.22832	−	0.943283i	0.412448	−	0.0472825i
$399$	7.29250			0.365081
$400$	15.9578	+	12.0560i	0.797891	+	0.602801i
$401$	0.632677			0.0315944			0.0157972	−	0.999875i	$-0.494971\pi$
$401$	0.632677			0.0315944			0.0157972	+	0.999875i	$0.494971\pi$
$402$	3.72346	−	0.426853i	0.185709	−	0.0212895i
$403$	−18.4679	+	18.4679i	−0.919953	+	0.919953i
$404$	10.0544	−	16.1402i	0.500225	−	0.803005i
$405$	−0.871224	−	0.536293i	−0.0432915	−	0.0266486i
$406$	−14.3388	+	18.0520i	−0.711621	+	0.895905i
$407$	−12.7324			−0.631124
$408$	2.39127	−	5.04038i	0.118385	−	0.249536i
$409$			26.3809i			1.30445i	0.758024	+	0.652226i	$0.226165\pi$
$409$			26.3809i			1.30445i	−0.758024	+	0.652226i	$0.773835\pi$
$410$	−4.57220	−	2.13936i	−0.225805	−	0.105655i
$411$	−11.0030	+	11.0030i	−0.542739	+	0.542739i
$412$	29.5592	−	6.86751i	1.45628	−	0.338338i
$413$	−5.29069	+	5.29069i	−0.260338	+	0.260338i
$414$	5.41636	−	0.620923i	0.266199	−	0.0305167i
$415$	25.3767	−	6.03862i	1.24570	−	0.296424i
$416$	20.2804	+	4.42229i	0.994328	+	0.216821i
$417$		−	12.1760i		−	0.596260i
$418$	2.63739	+	23.0061i	0.128999	+	1.12527i
$419$	−1.37589	−	1.37589i	−0.0672167	−	0.0672167i	0.672699	−	0.739916i	$-0.265135\pi$
$419$	−1.37589	−	1.37589i	−0.0672167	−	0.0672167i	−0.739916	+	0.672699i	$0.765135\pi$
$420$	−7.12801	+	3.54840i	−0.347811	+	0.173144i
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	−0.526035	−	0.850463i	$-0.676322\pi$
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	0.850463	+	0.526035i	$0.176322\pi$
$422$	−9.45861	+	11.9081i	−0.460438	+	0.579675i
$423$	8.52862			0.414676
$424$	−0.825987	+	1.74104i	−0.0401135	+	0.0845522i
$425$	8.47908	−	4.27756i	0.411296	−	0.207492i
$426$	0.346323	−	0.436009i	0.0167794	−	0.0211247i
$427$	−5.93929	−	5.93929i	−0.287422	−	0.287422i
$428$	−4.07597	−	2.53909i	−0.197019	−	0.122731i
$429$	10.7715	+	10.7715i	0.520051	+	0.520051i
$430$	−33.9250	+	12.2973i	−1.63601	+	0.593030i
$431$	4.08798			0.196911			0.0984556	−	0.995141i	$-0.468610\pi$
$431$	4.08798			0.196911			0.0984556	+	0.995141i	$0.468610\pi$
$432$	−19.3480	−	6.60204i	−0.930882	−	0.317641i
$433$			29.2913i			1.40765i	0.710373	+	0.703826i	$0.248526\pi$
$433$			29.2913i			1.40765i	−0.710373	+	0.703826i	$0.751474\pi$
$434$	1.96562	+	17.1462i	0.0943526	+	0.823044i
$435$	18.8011	+	11.5732i	0.901443	+	0.554895i
$436$	−7.46912	−	4.65283i	−0.357706	−	0.222830i
$437$	−5.81020	−	5.81020i	−0.277940	−	0.277940i
$438$	9.63344	+	7.65188i	0.460304	+	0.365621i
$439$		−	26.9790i		−	1.28764i	−0.765178	−	0.643819i	$-0.777349\pi$
$439$		−	26.9790i		−	1.28764i	0.765178	−	0.643819i	$-0.222651\pi$
$440$	−13.7723	−	21.2039i	−0.656567	−	1.01086i
$441$		−	7.80258i		−	0.371551i
$442$	6.13040	−	7.71796i	0.291594	−	0.367106i
$443$	−14.5286	−	14.5286i	−0.690276	−	0.690276i	0.272017	−	0.962293i	$-0.412309\pi$
$443$	−14.5286	−	14.5286i	−0.690276	−	0.690276i	−0.962293	+	0.272017i	$0.912309\pi$
$444$	−6.44310	+	1.49693i	−0.305776	+	0.0710411i
$445$	14.0449	−	22.8164i	0.665792	−	1.08160i
$446$	−12.9603	+	1.48575i	−0.613686	+	0.0703521i
$447$		−	10.7315i		−	0.507582i
$448$	10.6235	−	8.67619i	0.501911	−	0.409911i
$449$	23.1572			1.09286			0.546428	−	0.837506i	$-0.315987\pi$
$449$	23.1572			1.09286			0.546428	+	0.837506i	$0.315987\pi$
$450$	−7.46206	−	11.3556i	−0.351765	−	0.535309i
$451$	4.51249	+	4.51249i	0.212485	+	0.212485i
$452$	−7.16290	−	30.8306i	−0.336914	−	1.45015i
$453$	3.35479	+	3.35479i	0.157622	+	0.157622i
$454$	−14.4349	−	11.4657i	−0.677466	−	0.538113i
$455$	−13.6854	+	3.25656i	−0.641581	+	0.152670i
$456$	4.03940	+	11.3319i	0.189162	+	0.530665i
$457$	37.7026			1.76365			0.881827	−	0.471572i	$-0.156313\pi$
$457$	37.7026			1.76365			0.881827	+	0.471572i	$0.156313\pi$
$458$	2.56542	+	2.03772i	0.119874	+	0.0952165i
$459$	−6.86425	+	6.86425i	−0.320396	+	0.320396i
$460$	8.50629	+	2.85201i	0.396608	+	0.132976i
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	0.920491	−	0.390764i	$-0.127789\pi$
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	−0.390764	+	0.920491i	$0.627789\pi$
$462$	10.0006	−	1.14645i	0.465268	−	0.0533377i
$463$		−	7.94895i		−	0.369419i	−0.982793	−	0.184710i	$-0.940866\pi$
$463$		−	7.94895i		−	0.369419i	0.982793	−	0.184710i	$-0.0591344\pi$
$464$	−35.9936	−	12.2820i	−1.67096	−	0.570175i
$465$	16.0788	−	3.82609i	0.745637	−	0.177431i
$466$	−1.99399	−	17.3937i	−0.0923699	−	0.805749i
$467$	−5.34999	+	5.34999i	−0.247568	+	0.247568i	−0.819972	−	0.572404i	$-0.806011\pi$
$467$	−5.34999	+	5.34999i	−0.247568	+	0.247568i	0.572404	+	0.819972i	$0.306011\pi$
$468$	−11.9697	−	7.45643i	−0.553301	−	0.344674i
$469$	3.09394	−	3.09394i	0.142865	−	0.142865i
$470$	12.7122	+	5.94809i	0.586368	+	0.274365i
$471$			2.24643i			0.103510i
$472$	−11.1518	−	5.29069i	−0.513305	−	0.243524i
$473$	45.6187			2.09755
$474$	−12.9446	−	10.2820i	−0.594566	−	0.472266i
$475$	−6.40656	+	19.4515i	−0.293953	+	0.892498i
$476$	−1.47394	−	6.34414i	−0.0675578	−	0.290783i
$477$	0.925759	−	0.925759i	0.0423876	−	0.0423876i
$478$	−1.25222	−	10.9232i	−0.0572754	−	0.499617i
$479$	−9.58973			−0.438166			−0.219083	−	0.975706i	$-0.570307\pi$
$479$	−9.58973			−0.438166			−0.219083	+	0.975706i	$0.570307\pi$
$480$	−9.46220	−	9.11080i	−0.431888	−	0.415849i
$481$	−11.6865			−0.532859
$482$	−0.559017	−	4.87634i	−0.0254625	−	0.222111i
$483$	−2.52564	+	2.52564i	−0.114921	+	0.114921i
$484$	2.25490	+	9.70556i	0.102495	+	0.441162i
$485$	7.62543	−	12.3877i	0.346253	−	0.562498i
$486$	17.5052	+	13.9044i	0.794052	+	0.630718i
$487$	−36.6487			−1.66071			−0.830357	−	0.557232i	$-0.811863\pi$
$487$	−36.6487			−1.66071			−0.830357	+	0.557232i	$0.811863\pi$
$488$	5.93929	−	12.5190i	0.268859	−	0.566708i
$489$		−	14.8857i		−	0.673154i
$490$	5.44173	−	11.6300i	0.245832	−	0.525389i
$491$	23.4273	−	23.4273i	1.05726	−	1.05726i	0.0590019	−	0.998258i	$-0.481208\pi$
$491$	23.4273	−	23.4273i	1.05726	−	1.05726i	0.998258	−	0.0590019i	$-0.0187918\pi$
$492$	2.81402	+	1.75297i	0.126866	+	0.0790298i
$493$	−12.7697	+	12.7697i	−0.575120	+	0.575120i
$494$	2.42073	+	21.1162i	0.108914	+	0.950064i
$495$	3.97659	+	16.7113i	0.178735	+	0.751116i
$496$	−25.5549	+	12.5519i	−1.14745	+	0.563597i
$497$		−	0.650063i		−	0.0291593i
$498$	−17.0206	+	1.95122i	−0.762713	+	0.0874363i
$499$	−9.50152	−	9.50152i	−0.425346	−	0.425346i	0.461693	−	0.887040i	$-0.347242\pi$
$499$	−9.50152	−	9.50152i	−0.425346	−	0.425346i	−0.887040	+	0.461693i	$0.847242\pi$
$500$	−3.20272	−	22.1301i	−0.143230	−	0.989689i
$501$	1.89424	−	1.89424i	0.0846283	−	0.0846283i
$502$	14.0127	+	11.1304i	0.625419	+	0.496772i
$503$	20.6875			0.922411			0.461206	−	0.887293i	$-0.347417\pi$
$503$	20.6875			0.922411			0.461206	+	0.887293i	$0.347417\pi$
$504$	−8.77775	+	3.12894i	−0.390992	+	0.139374i
$505$	−20.6827	+	4.92163i	−0.920368	+	0.219009i
$506$	−8.88124	−	7.05440i	−0.394819	−	0.313606i
$507$	0.340787	+	0.340787i	0.0151349	+	0.0151349i
$508$	−8.29351	−	35.6970i	−0.367965	−	1.58380i
$509$	11.6381	+	11.6381i	0.515850	+	0.515850i	0.916313	−	0.400463i	$-0.131151\pi$
$509$	11.6381	+	11.6381i	0.515850	+	0.515850i	−0.400463	+	0.916313i	$0.631151\pi$
$510$	−5.86398	+	2.12561i	−0.259661	+	0.0941235i
$511$	14.3629			0.635377
$512$	19.3665	+	11.7021i	0.855887	+	0.517163i
$513$		−	20.9335i		−	0.924235i
$514$	−5.08935	+	0.583436i	−0.224482	+	0.0257343i
$515$	−28.8931	−	17.7855i	−1.27318	−	0.783724i
$516$	23.0848	−	5.36331i	1.01625	−	0.236106i
$517$	−12.5462	−	12.5462i	−0.551780	−	0.551780i
$518$	−4.80314	+	6.04698i	−0.211038	+	0.265689i
$519$			20.8205i			0.913921i
$520$	−12.6409	−	19.4621i	−0.554341	−	0.853467i
$521$		−	5.18654i		−	0.227227i	−0.993525	−	0.113613i	$-0.963758\pi$
$521$		−	5.18654i		−	0.227227i	0.993525	−	0.113613i	$-0.0362425\pi$
$522$	20.2325	+	16.0708i	0.885554	+	0.703398i
$523$	−26.9589	−	26.9589i	−1.17883	−	1.17883i	−0.980043	−	0.198788i	$-0.936300\pi$
$523$	−26.9589	−	26.9589i	−1.17883	−	1.17883i	−0.198788	−	0.980043i	$-0.563700\pi$
$524$	24.4959	+	15.2595i	1.07011	+	0.666616i
$525$	8.45542	+	2.78488i	0.369025	+	0.121542i
$526$	−2.21334	−	19.3071i	−0.0965064	−	0.841832i
$527$			13.5195i			0.588917i
$528$	7.32092	+	14.9050i	0.318602	+	0.648655i
$529$	−18.9755			−0.825020
$530$	2.02552	−	0.734223i	0.0879831	−	0.0318926i
$531$	5.92976	+	5.92976i	0.257330	+	0.257330i
$532$	11.9211	+	7.42617i	0.516847	+	0.321965i
$533$	4.14180	+	4.14180i	0.179401	+	0.179401i
$534$	−10.9446	+	13.7789i	−0.473620	+	0.596271i
$535$	1.24288	+	5.22311i	0.0537345	+	0.225815i
$536$	6.52148	+	3.09394i	0.281685	+	0.133638i
$537$	14.5106			0.626179
$538$	5.25243	−	6.61262i	0.226448	−	0.285090i
$539$	−11.4781	+	11.4781i	−0.494397	+	0.494397i
$540$	10.1859	+	20.4613i	0.438329	+	0.880514i
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.979204	+	0.202878i	$0.0650294\pi$
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.202878	+	0.979204i	$0.434971\pi$
$542$	−0.869794	−	7.58727i	−0.0373609	−	0.325901i
$543$			9.11278i			0.391067i
$544$	9.04181	−	5.80447i	0.387664	−	0.248865i
$545$	2.27756	+	9.57123i	0.0975598	+	0.409986i
$546$	9.17903	−	1.05227i	0.392826	−	0.0450331i
$547$	22.5197	−	22.5197i	0.962873	−	0.962873i	−0.0364619	−	0.999335i	$-0.511609\pi$
$547$	22.5197	−	22.5197i	0.962873	−	0.962873i	0.999335	+	0.0364619i	$0.0116088\pi$
$548$	−29.1915	+	6.78208i	−1.24700	+	0.289716i
$549$	−6.65671	+	6.65671i	−0.284101	+	0.284101i
$550$	−5.72767	+	27.6820i	−0.244228	+	1.18037i
$551$		−	38.9431i		−	1.65903i
$552$	−5.32361	−	2.52564i	−0.226588	−	0.107499i
$553$	−19.2996			−0.820704
$554$	6.32835	−	7.96717i	0.268866	−	0.338493i
$555$	6.29791	+	3.87676i	0.267331	+	0.164559i
$556$	12.3992	−	19.9042i	0.525842	−	0.844127i
$557$	13.7333	−	13.7333i	0.581897	−	0.581897i	−0.353527	−	0.935424i	$-0.615018\pi$
$557$	13.7333	−	13.7333i	0.581897	−	0.581897i	0.935424	+	0.353527i	$0.115018\pi$
$558$	19.2173	−	2.20305i	0.813535	−	0.0932625i
$559$	41.8713			1.77097
$560$	−15.2657	−	1.45805i	−0.645094	−	0.0616141i
$561$	7.88525			0.332916
$562$	−29.8958	+	3.42721i	−1.26108	+	0.144568i
$563$	−0.229223	+	0.229223i	−0.00966061	+	0.00966061i	−0.711921	−	0.702260i	$-0.752174\pi$
$563$	−0.229223	+	0.229223i	−0.00966061	+	0.00966061i	0.702260	+	0.711921i	$0.252174\pi$
$564$	−7.82386	−	4.87381i	−0.329444	−	0.205224i
$565$	−18.5505	+	30.1359i	−0.780427	+	1.26783i
$566$	−5.08177	+	6.39776i	−0.213603	+	0.268918i
$567$	0.784437			0.0329433
$568$	1.01014	−	0.360078i	0.0423846	−	0.0151085i
$569$		−	23.0376i		−	0.965787i	−0.875679	−	0.482894i	$-0.839586\pi$
$569$		−	23.0376i		−	0.965787i	0.875679	−	0.482894i	$-0.160414\pi$
$570$	5.70033	−	12.1827i	0.238761	−	0.510275i
$571$	−11.8610	+	11.8610i	−0.496367	+	0.496367i	−0.910305	−	0.413938i	$-0.864153\pi$
$571$	−11.8610	+	11.8610i	−0.496367	+	0.496367i	0.413938	+	0.910305i	$0.364153\pi$
$572$	6.63934	+	28.5772i	0.277605	+	1.19487i
$573$	−13.8989	+	13.8989i	−0.580633	+	0.580633i
$574$	3.84538	−	0.440829i	0.160503	−	0.0183998i
$575$	−4.51793	−	8.95556i	−0.188411	−	0.373473i
$576$	−9.72421	−	11.9067i	−0.405175	−	0.496112i
$577$			39.7168i			1.65343i	0.562621	+	0.826715i	$0.309793\pi$
$577$			39.7168i			1.65343i	−0.562621	+	0.826715i	$0.690207\pi$
$578$	2.15708	+	18.8163i	0.0897226	+	0.782657i
$579$	−3.25282	−	3.25282i	−0.135183	−	0.135183i
$580$	18.9490	+	38.0647i	0.786815	+	1.58055i
$581$	−14.1429	+	14.1429i	−0.586748	+	0.586748i
$582$	−5.94218	+	7.48100i	−0.246311	+	0.310097i
$583$	−2.72371			−0.112804
$584$	7.95578	+	22.3187i	0.329213	+	0.923553i
$585$	3.64992	+	15.3385i	0.150906	+	0.634168i
$586$	9.21016	−	11.5953i	0.380468	−	0.478996i
$587$	8.63887	+	8.63887i	0.356564	+	0.356564i	0.862545	−	0.505980i	$-0.168869\pi$
$587$	8.63887	+	8.63887i	0.356564	+	0.356564i	−0.505980	+	0.862545i	$0.668869\pi$
$588$	−4.45890	+	7.15782i	−0.183882	+	0.295183i
$589$	−20.6147	−	20.6147i	−0.849414	−	0.849414i
$590$	4.70291	+	12.9741i	0.193616	+	0.534134i
$591$	−9.38927			−0.386223
$592$	−12.0570	−	4.11416i	−0.495540	−	0.169091i
$593$		−	45.8229i		−	1.88172i	−0.338795	−	0.940860i	$-0.610019\pi$
$593$		−	45.8229i		−	1.88172i	0.338795	−	0.940860i	$-0.389981\pi$
$594$	−3.29094	−	28.7071i	−0.135029	−	1.17787i
$595$	−3.81722	+	6.20118i	−0.156491	+	0.254224i
$596$	10.9282	−	17.5429i	0.447637	−	0.718586i
$597$	4.30032	+	4.30032i	0.176000	+	0.176000i
$598$	−8.15166	−	6.47489i	−0.333346	−	0.264778i
$599$		−	17.0609i		−	0.697090i	−0.937292	−	0.348545i	$-0.886676\pi$
$599$		−	17.0609i		−	0.697090i	0.937292	−	0.348545i	$-0.113324\pi$
$600$	0.356107	+	14.6816i	0.0145380	+	0.599372i
$601$		−	38.0363i		−	1.55153i	−0.631020	−	0.775766i	$-0.717364\pi$
$601$		−	38.0363i		−	1.55153i	0.631020	−	0.775766i	$-0.282636\pi$
$602$	17.2090	−	21.6656i	0.701388	−	0.883023i
$603$	−3.46766	−	3.46766i	−0.141214	−	0.141214i
$604$	2.06783	+	8.90040i	0.0841390	+	0.362152i
$605$	5.83975	−	9.48685i	0.237420	−	0.385695i
$606$	13.8723	−	1.59030i	0.563522	−	0.0646013i
$607$			8.67169i			0.351973i	0.984393	+	0.175987i	$0.0563115\pi$
$607$			8.67169i			0.351973i	−0.984393	+	0.175987i	$0.943688\pi$
$608$	−4.93635	+	22.6379i	−0.200196	+	0.918087i
$609$	−16.9282			−0.685965
$610$	−14.5646	+	5.27945i	−0.589703	+	0.213759i
$611$	−11.5155	−	11.5155i	−0.465868	−	0.465868i
$612$	−7.11047	+	1.65198i	−0.287424	+	0.0667773i
$613$	13.9739	+	13.9739i	0.564401	+	0.564401i	0.930554	−	0.366153i	$-0.119325\pi$
$613$	13.9739	+	13.9739i	0.564401	+	0.564401i	−0.366153	+	0.930554i	$0.619325\pi$
$614$	26.0962	+	20.7283i	1.05316	+	0.836526i
$615$	−0.858077	−	3.60599i	−0.0346010	−	0.145408i
$616$	17.5155	+	8.30976i	0.705720	+	0.334810i
$617$	−37.3904			−1.50528			−0.752641	−	0.658431i	$-0.771220\pi$
$617$	−37.3904			−1.50528			−0.752641	+	0.658431i	$0.771220\pi$
$618$	17.4487	+	13.8595i	0.701888	+	0.557512i
$619$	−23.2754	+	23.2754i	−0.935516	+	0.935516i	−0.998043	−	0.0625269i	$-0.980084\pi$
$619$	−23.2754	+	23.2754i	−0.935516	+	0.935516i	0.0625269	+	0.998043i	$0.480084\pi$
$620$	30.1805	+	10.1190i	1.21208	+	0.406388i
$621$	7.24998	+	7.24998i	0.290932	+	0.290932i
$622$	−30.7799	+	3.52856i	−1.23416	+	0.141482i
$623$			20.5435i			0.823058i
$624$	6.71952	+	13.6806i	0.268996	+	0.547660i
$625$	−14.8564	+	20.1069i	−0.594256	+	0.804276i
$626$	−2.01046	−	17.5374i	−0.0803541	−	0.700934i
$627$	−12.0236	+	12.0236i	−0.480175	+	0.480175i
$628$	−2.28761	+	3.67228i	−0.0912857	+	0.146540i
$629$	−4.27756	+	4.27756i	−0.170557	+	0.170557i
$630$	9.43675	+	4.41550i	0.375969	+	0.175918i
$631$			19.1834i			0.763680i	0.924228	+	0.381840i	$0.124710\pi$
$631$			19.1834i			0.763680i	−0.924228	+	0.381840i	$0.875290\pi$
$632$	−10.6903	−	29.9900i	−0.425238	−	1.19294i
$633$	−11.1667			−0.443838
$634$	6.64526	+	5.27835i	0.263917	+	0.209630i
$635$	−21.4786	+	34.8926i	−0.852352	+	1.38467i
$636$	−1.37830	+	0.320221i	−0.0546531	+	0.0126976i
$637$	−10.5352	+	10.5352i	−0.417420	+	0.417420i
$638$	−6.12222	−	53.4045i	−0.242381	−	2.11431i
$639$	−0.728585			−0.0288224
$640$	−6.19017	−	24.5292i	−0.244688	−	0.969602i
$641$	−16.1765			−0.638933			−0.319466	−	0.947598i	$-0.603504\pi$
$641$	−16.1765			−0.638933			−0.319466	+	0.947598i	$0.603504\pi$
$642$	−0.401605	−	3.50323i	−0.0158501	−	0.138261i
$643$	15.0289	−	15.0289i	0.592681	−	0.592681i	−0.345674	−	0.938355i	$-0.612350\pi$
$643$	15.0289	−	15.0289i	0.592681	−	0.592681i	0.938355	+	0.345674i	$0.112350\pi$
$644$	−6.70064	+	1.55676i	−0.264042	+	0.0613451i
$645$	−22.5646	−	13.8899i	−0.888481	−	0.546916i
$646$	8.61512	+	6.84302i	0.338958	+	0.269235i
$647$	49.3812			1.94138			0.970688	−	0.240345i	$-0.0772606\pi$
$647$	49.3812			1.94138			0.970688	+	0.240345i	$0.0772606\pi$
$648$	0.434509	+	1.21895i	0.0170691	+	0.0478847i
$649$		−	17.4461i		−	0.684821i
$650$	−5.25715	+	25.4080i	−0.206202	+	0.996585i
$651$	−8.96103	+	8.96103i	−0.351210	+	0.351210i
$652$	15.1586	−	24.3338i	0.593655	−	0.952987i
$653$	−19.8685	+	19.8685i	−0.777514	+	0.777514i	−0.979408	−	0.201893i	$-0.935291\pi$
$653$	−19.8685	+	19.8685i	−0.777514	+	0.777514i	0.201893	+	0.979408i	$0.435291\pi$
$654$	−0.735933	−	6.41960i	−0.0287773	−	0.251026i
$655$	−7.46954	−	31.3901i	−0.291859	−	1.22651i
$656$	2.81501	+	5.73120i	0.109908	+	0.223766i
$657$		−	16.0978i		−	0.628035i
$658$	−10.6914	+	1.22564i	−0.416793	+	0.0477806i
$659$	4.94765	+	4.94765i	0.192733	+	0.192733i	0.796876	−	0.604143i	$-0.206484\pi$
$659$	4.94765	+	4.94765i	0.192733	+	0.192733i	−0.604143	+	0.796876i	$0.706484\pi$
$660$	5.90192	−	17.6028i	0.229732	−	0.685189i
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	−0.429899	−	0.902877i	$-0.641451\pi$
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	0.902877	+	0.429899i	$0.141451\pi$
$662$	1.72860	+	1.37303i	0.0671838	+	0.0533643i
$663$	7.23750			0.281081
$664$	−29.8109	−	14.1429i	−1.15689	−	0.548853i
$665$	−3.63511	−	15.2762i	−0.140964	−	0.592387i
$666$	6.77741	+	5.38332i	0.262619	+	0.208599i
$667$	13.4873	+	13.4873i	0.522231	+	0.522231i
$668$	5.02550	−	1.16758i	0.194442	−	0.0451749i
$669$	−6.77335	−	6.77335i	−0.261873	−	0.261873i
$670$	−2.75021	−	7.58709i	−0.106250	−	0.293115i
$671$	19.5849			0.756067
$672$	9.84048	+	2.14579i	0.379605	+	0.0827756i
$673$		−	32.9882i		−	1.27160i	−0.771853	−	0.635801i	$-0.780670\pi$
$673$		−	32.9882i		−	1.27160i	0.771853	−	0.635801i	$-0.219330\pi$
$674$	10.5044	−	1.20420i	0.404613	−	0.0463842i
$675$	7.99412	−	24.2717i	0.307694	−	0.934217i
$676$	0.210055	+	0.904123i	0.00807905	+	0.0347740i
$677$	18.4610	+	18.4610i	0.709513	+	0.709513i	0.966433	−	0.256920i	$-0.0827076\pi$
$677$	18.4610	+	18.4610i	0.709513	+	0.709513i	−0.256920	+	0.966433i	$0.582708\pi$
$678$	14.4557	−	18.1992i	0.555167	−	0.698935i
$679$			11.1537i			0.428040i
$680$	−11.7505	−	2.49671i	−0.450611	−	0.0957444i
$681$		−	13.5363i		−	0.518713i
$682$	−31.5108	−	25.0291i	−1.20661	−	0.958415i
$683$	−12.2374	−	12.2374i	−0.468251	−	0.468251i	0.433097	−	0.901347i	$-0.357421\pi$
$683$	−12.2374	−	12.2374i	−0.468251	−	0.468251i	−0.901347	+	0.433097i	$0.857421\pi$
$684$	8.32320	−	13.3611i	0.318245	−	0.510875i
$685$	28.5337	+	17.5643i	1.09022	+	0.671097i
$686$	3.05440	+	26.6437i	0.116617	+	1.01726i
$687$			2.40571i			0.0917837i
$688$	43.1987	+	14.7405i	1.64693	+	0.561977i
$689$	−2.49996			−0.0952409
$690$	2.24505	+	6.19350i	0.0854677	+	0.235782i
$691$	−9.46014	−	9.46014i	−0.359881	−	0.359881i	0.503888	−	0.863769i	$-0.331902\pi$
$691$	−9.46014	−	9.46014i	−0.359881	−	0.359881i	−0.863769	+	0.503888i	$0.831902\pi$
$692$	−21.2022	+	34.0356i	−0.805987	+	1.29384i
$693$	−9.31352	−	9.31352i	−0.353791	−	0.353791i
$694$	10.6491	−	13.4068i	0.404233	−	0.508915i
$695$	−25.5061	+	6.06939i	−0.967500	+	0.230225i
$696$	−9.37674	−	26.3049i	−0.355425	−	0.997086i
$697$	3.03201			0.114845
$698$	−9.84664	+	12.3966i	−0.372701	+	0.469217i
$699$	9.09039	−	9.09039i	0.343830	−	0.343830i
$700$	10.9863	+	13.1629i	0.415242	+	0.497510i
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	0.603192	−	0.797596i	$-0.293895\pi$
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	−0.797596	+	0.603192i	$0.793895\pi$
$702$	−3.02060	−	26.3489i	−0.114005	−	0.994474i
$703$		−	13.0450i		−	0.492001i
$704$	−3.21058	+	31.8205i	−0.121003	+	1.19928i
$705$	2.38573	+	10.0258i	0.0898517	+	0.377594i
$706$	13.5909	−	1.55804i	0.511499	−	0.0586375i
$707$	11.5269	−	11.5269i	0.433512	−	0.433512i
$708$	−2.05111	−	8.82840i	−0.0770853	−	0.331792i
$709$	−18.0125	+	18.0125i	−0.676472	+	0.676472i	−0.959200	−	0.282728i	$-0.908761\pi$
$709$	−18.0125	+	18.0125i	−0.676472	+	0.676472i	0.282728	+	0.959200i	$0.408761\pi$
$710$	−1.08598	−	0.508135i	−0.0407560	−	0.0190700i
$711$			21.6309i			0.811222i
$712$	−31.9228	+	11.3793i	−1.19636	+	0.426457i
$713$	14.2792			0.534759
$714$	2.97460	−	3.74492i	0.111322	−	0.140150i
$715$	17.1946	−	27.9332i	0.643043	−	1.04464i
$716$	23.7207	+	14.7766i	0.886485	+	0.552228i
$717$	5.70875	−	5.70875i	0.213197	−	0.213197i
$718$	−24.0069	+	2.75212i	−0.895931	+	0.102708i
$719$	34.5017			1.28669			0.643347	−	0.765574i	$-0.277545\pi$
$719$	34.5017			1.28669			0.643347	+	0.765574i	$0.277545\pi$
$720$	−1.63418	+	17.1097i	−0.0609022	+	0.637640i
$721$	26.0149			0.968846
$722$	3.12437	−	0.358173i	0.116277	−	0.0133298i
$723$	2.54850	−	2.54850i	0.0947796	−	0.0947796i
$724$	−9.27983	+	14.8968i	−0.344882	+	0.553635i
$725$	14.8717	−	45.1532i	0.552320	−	1.67695i
$726$	−4.55068	+	5.72915i	−0.168892	+	0.212629i
$727$	−12.8421			−0.476288			−0.238144	−	0.971230i	$-0.576539\pi$
$727$	−12.8421			−0.476288			−0.238144	+	0.971230i	$0.576539\pi$
$728$	16.0767	+	7.62713i	0.595841	+	0.282680i
$729$			15.0429i			0.557143i
$730$	11.2270	−	23.9943i	0.415532	−	0.888068i
$731$	15.3259	−	15.3259i	0.566851	−	0.566851i
$732$	9.91071	−	2.30256i	0.366310	−	0.0851050i
$733$	−24.1490	+	24.1490i	−0.891965	+	0.891965i	−0.994708	−	0.102743i	$-0.967238\pi$
$733$	−24.1490	+	24.1490i	−0.891965	+	0.891965i	0.102743	+	0.994708i	$0.467238\pi$
$734$	18.8974	−	2.16638i	0.697517	−	0.0799624i
$735$	9.17231	−	2.18263i	0.338326	−	0.0805075i
$736$	−6.13065	−	9.54990i	−0.225979	−	0.352014i
$737$			10.2023i			0.375807i
$738$	−0.494077	−	4.30987i	−0.0181872	−	0.158648i
$739$	35.9398	+	35.9398i	1.32207	+	1.32207i	0.912101	+	0.409966i	$0.134460\pi$
$739$	35.9398	+	35.9398i	1.32207	+	1.32207i	0.409966	+	0.912101i	$0.365540\pi$
$740$	6.34746	+	12.7508i	0.233337	+	0.468727i
$741$	−11.0359	+	11.0359i	−0.405412	+	0.405412i
$742$	−1.02748	+	1.29356i	−0.0377200	+	0.0474881i
$743$	45.9502			1.68575			0.842875	−	0.538109i	$-0.180861\pi$
$743$	45.9502			1.68575			0.842875	+	0.538109i	$0.180861\pi$
$744$	−18.8883	−	8.96103i	−0.692478	−	0.328527i
$745$	−22.4802	+	5.34935i	−0.823610	+	0.195985i
$746$	−14.9610	+	18.8354i	−0.547762	+	0.689613i
$747$	15.8513	+	15.8513i	0.579969	+	0.579969i
$748$	12.8901	+	8.02980i	0.471310	+	0.293598i
$749$	−2.91094	−	2.91094i	−0.106363	−	0.106363i
$750$	11.2617	−	11.9485i	0.411219	−	0.436299i
$751$	−24.4820			−0.893361			−0.446680	−	0.894694i	$-0.647394\pi$
$751$	−24.4820			−0.893361			−0.446680	+	0.894694i	$0.647394\pi$
$752$	−7.82663	−	15.9346i	−0.285408	−	0.581074i
$753$			13.1404i			0.478863i
$754$	−5.61929	−	49.0175i	−0.204643	−	1.78511i
$755$	5.35529	−	8.69983i	0.194899	−	0.316619i
$756$	−14.8752	−	9.26639i	−0.541007	−	0.337015i
$757$	−17.0328	−	17.0328i	−0.619067	−	0.619067i	0.326225	−	0.945292i	$-0.394223\pi$
$757$	−17.0328	−	17.0328i	−0.619067	−	0.619067i	−0.945292	+	0.326225i	$0.894223\pi$
$758$	29.9986	+	23.8280i	1.08960	+	0.865471i
$759$		−	8.32835i		−	0.302300i
$760$	21.7244	−	14.1103i	0.788026	−	0.511836i
$761$			8.53590i			0.309426i	0.987959	+	0.154713i	$0.0494453\pi$
$761$			8.53590i			0.309426i	−0.987959	+	0.154713i	$0.950555\pi$
$762$	16.7374	−	21.0718i	0.606332	−	0.763350i
$763$	−5.33423	−	5.33423i	−0.193112	−	0.193112i
$764$	−36.8743	+	8.56702i	−1.33407	+	0.309944i
$765$	6.95024	+	4.27831i	0.251286	+	0.154683i
$766$	−24.9394	+	2.85902i	−0.901099	+	0.103301i
$767$		−	16.0130i		−	0.578195i
$768$	2.11640	+	16.4798i	0.0763689	+	0.594664i
$769$	−1.87438			−0.0675917			−0.0337959	−	0.999429i	$-0.510760\pi$
$769$	−1.87438			−0.0675917			−0.0337959	+	0.999429i	$0.510760\pi$
$770$	−7.38658	−	20.3776i	−0.266194	−	0.734357i
$771$	−2.65982	−	2.65982i	−0.0957911	−	0.0957911i
$772$	−2.00498	−	8.62988i	−0.0721610	−	0.310596i
$773$	−21.5374	−	21.5374i	−0.774645	−	0.774645i	0.204270	−	0.978915i	$-0.434518\pi$
$773$	−21.5374	−	21.5374i	−0.774645	−	0.774645i	−0.978915	+	0.204270i	$0.934518\pi$
$774$	−24.2826	−	19.2878i	−0.872820	−	0.693284i
$775$	−16.0297	−	31.7745i	−0.575804	−	1.14137i
$776$	−17.3319	+	6.17818i	−0.622179	+	0.221784i
$777$	−5.67054			−0.203429
$778$	−1.85822	−	1.47599i	−0.0666205	−	0.0529169i
$779$	−4.62326	+	4.62326i	−0.165645	+	0.165645i
$780$	5.41709	−	16.1568i	0.193963	−	0.578506i
$781$	1.07180	+	1.07180i	0.0383519	+	0.0383519i
$782$	−5.35369	+	0.613739i	−0.191448	+	0.0219473i
$783$			48.5932i			1.73658i
$784$	−14.5781	+	7.16035i	−0.520645	+	0.255727i
$785$	4.70580	−	1.11979i	0.167957	−	0.0399669i
$786$	2.41359	+	21.0539i	0.0860898	+	0.750967i
$787$	7.03687	−	7.03687i	0.250837	−	0.250837i	−0.570477	−	0.821314i	$-0.693241\pi$
$787$	7.03687	−	7.03687i	0.250837	−	0.250837i	0.821314	+	0.570477i	$0.193241\pi$
$788$	−15.3488	−	9.56139i	−0.546778	−	0.340610i
$789$	10.0904	−	10.0904i	0.359227	−	0.359227i
$790$	−15.0860	+	32.2415i	−0.536735	+	1.14710i
$791$		−	27.1339i		−	0.964770i
$792$	9.31352	−	19.6313i	0.330941	−	0.697566i
$793$	17.9761			0.638348
$794$	7.43071	+	5.90224i	0.263706	+	0.209463i
$795$	1.34724	+	0.829311i	0.0477817	+	0.0294126i
$796$	2.65065	+	11.4089i	0.0939497	+	0.404379i
$797$	8.07933	−	8.07933i	0.286185	−	0.286185i	−0.549385	−	0.835569i	$-0.685138\pi$
$797$	8.07933	−	8.07933i	0.286185	−	0.286185i	0.835569	+	0.549385i	$0.185138\pi$
$798$	1.17459	+	10.2460i	0.0415801	+	0.362706i
$799$	−8.42995			−0.298230
$800$	−14.3685	+	24.3628i	−0.508005	+	0.861354i
$801$	23.0250			0.813548
$802$	0.101904	+	0.888918i	0.00359837	+	0.0313888i
$803$	−23.6809	+	23.6809i	−0.835682	+	0.835682i
$804$	1.19947	+	5.16276i	0.0423019	+	0.182076i
$805$	6.54965	+	4.03172i	0.230845	+	0.142099i
$806$	−28.9222	−	22.9730i	−1.01874	−	0.809191i
$807$	6.20097			0.218284
$808$	24.2966	+	11.5269i	0.854752	+	0.405514i
$809$			5.40185i			0.189919i	0.995481	+	0.0949595i	$0.0302722\pi$
$809$			5.40185i			0.189919i	−0.995481	+	0.0949595i	$0.969728\pi$
$810$	0.613171	−	1.31046i	0.0215447	−	0.0460449i
$811$	−10.3478	+	10.3478i	−0.363360	+	0.363360i	−0.865049	−	0.501688i	$-0.832712\pi$
$811$	−10.3478	+	10.3478i	−0.363360	+	0.363360i	0.501688	+	0.865049i	$0.332712\pi$
$812$	−27.6728	−	17.2385i	−0.971124	−	0.604953i
$813$	3.96530	−	3.96530i	0.139069	−	0.139069i
$814$	−2.05080	−	17.8892i	−0.0718804	−	0.627017i
$815$	−31.1824	+	7.42011i	−1.09227	+	0.259915i
$816$	7.46694	+	2.54791i	0.261395	+	0.0891948i
$817$			46.7385i			1.63517i
$818$	−37.0655	+	4.24913i	−1.29596	+	0.148568i
$819$	−8.54843	−	8.54843i	−0.298706	−	0.298706i
$820$	2.26938	−	6.76857i	0.0792503	−	0.236369i
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	−0.494581	−	0.869132i	$-0.664678\pi$
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	0.869132	+	0.494581i	$0.164678\pi$
$822$	−17.2316	−	13.6871i	−0.601022	−	0.477394i
$823$	3.51588			0.122556			0.0612780	−	0.998121i	$-0.480482\pi$
$823$	3.51588			0.122556			0.0612780	+	0.998121i	$0.480482\pi$
$824$	14.4100	+	40.4249i	0.501996	+	1.40827i
$825$	−18.5325	+	9.34935i	−0.645220	+	0.325503i
$826$	−8.28564	−	6.58131i	−0.288294	−	0.228993i
$827$	27.7375	+	27.7375i	0.964529	+	0.964529i	0.999392	−	0.0348631i	$-0.0110995\pi$
$827$	27.7375	+	27.7375i	0.964529	+	0.964529i	−0.0348631	+	0.999392i	$0.511100\pi$
$828$	1.74481	+	7.51003i	0.0606363	+	0.260992i
$829$	−19.5849	−	19.5849i	−0.680212	−	0.680212i	0.279836	−	0.960048i	$-0.409720\pi$
$829$	−19.5849	−	19.5849i	−0.680212	−	0.680212i	−0.960048	+	0.279836i	$0.909720\pi$
$830$	12.5717	+	34.6820i	0.436371	+	1.20383i
$831$	7.47119			0.259173
$832$	−2.94683	+	29.2065i	−0.102163	+	1.01255i
$833$			7.71231i			0.267216i
$834$	17.1074	−	1.96117i	0.592380	−	0.0679096i
$835$	−4.91225	−	3.02380i	−0.169995	−	0.104643i
$836$	−31.8991	+	7.41113i	−1.10325	+	0.256319i
$837$	25.7231	+	25.7231i	0.889119	+	0.889119i
$838$	1.71153	−	2.15476i	0.0591238	−	0.0744348i
$839$			40.0520i			1.38275i	0.722496	+	0.691375i	$0.242995\pi$
$839$			40.0520i			1.38275i	−0.722496	+	0.691375i	$0.757005\pi$
$840$	−6.13364	−	9.44340i	−0.211631	−	0.325828i
$841$			61.3992i			2.11722i
$842$	10.4249	+	8.28056i	0.359267	+	0.285367i
$843$	−15.6243	−	15.6243i	−0.538129	−	0.538129i
$844$	−18.2544	−	11.3714i	−0.628343	−	0.391421i
$845$	0.544003	−	0.883749i	0.0187143	−	0.0304019i
$846$	1.37369	+	11.9828i	0.0472285	+	0.411977i
$847$			8.54182i			0.293500i
$848$	−2.57922	−	0.880095i	−0.0885706	−	0.0302226i
$849$	−5.99948			−0.205902
$850$	7.37573	+	11.2242i	0.252985	+	0.384988i
$851$	4.51793	+	4.51793i	0.154873	+	0.154873i
$852$	0.668379	+	0.416361i	0.0228983	+	0.0142643i
$853$	13.7328	+	13.7328i	0.470202	+	0.470202i	0.901980	−	0.431778i	$-0.142114\pi$
$853$	13.7328	+	13.7328i	0.470202	+	0.470202i	−0.431778	+	0.901980i	$0.642114\pi$
$854$	7.38814	−	9.30140i	0.252817	−	0.318287i
$855$	−17.1215	+	4.07420i	−0.585542	+	0.139335i
$856$	2.91094	−	6.13575i	0.0994938	−	0.209716i
$857$	39.9485			1.36462			0.682308	−	0.731065i	$-0.260976\pi$
$857$	39.9485			1.36462			0.682308	+	0.731065i	$0.260976\pi$
$858$	−13.3991	+	16.8690i	−0.457437	+	0.575897i
$859$	33.6366	−	33.6366i	1.14766	−	1.14766i	0.160654	−	0.987011i	$-0.448640\pi$
$859$	33.6366	−	33.6366i	1.14766	−	1.14766i	0.987011	−	0.160654i	$-0.0513602\pi$
$860$	−22.7421	−	45.6843i	−0.775501	−	1.55782i
$861$	2.00969	+	2.00969i	0.0684900	+	0.0684900i
$862$	0.658445	+	5.74366i	0.0224267	+	0.195630i
$863$		−	16.5303i		−	0.562697i	−0.959606	−	0.281349i	$-0.909218\pi$
$863$		−	16.5303i		−	0.562697i	0.959606	−	0.281349i	$-0.0907817\pi$
$864$	6.15959	−	28.2476i	0.209554	−	0.961002i
$865$	43.6146	−	10.3785i	1.48294	−	0.352879i
$866$	−41.1546	+	4.71791i	−1.39849	+	0.160321i
$867$	−9.83388	+	9.83388i	−0.333976	+	0.333976i
$868$	−23.7740	+	5.52343i	−0.806943	+	0.187477i
$869$	31.8205	−	31.8205i	1.07944	−	1.07944i
$870$	−13.2323	+	28.2798i	−0.448616	+	0.958776i
$871$			9.36421i			0.317294i
$872$	5.33423	−	11.2436i	0.180640	−	0.380757i
$873$	12.5010			0.423095
$874$	7.22756	−	9.09924i	0.244476	−	0.307786i
$875$	1.61893	−	19.1005i	0.0547297	−	0.645714i
$876$	−9.19933	+	14.7676i	−0.310817	+	0.498950i
$877$	−9.66381	+	9.66381i	−0.326324	+	0.326324i	−0.851187	−	0.524863i	$-0.824117\pi$
$877$	−9.66381	+	9.66381i	−0.326324	+	0.326324i	0.524863	+	0.851187i	$0.324117\pi$
$878$	37.9058	−	4.34547i	1.27926	−	0.146652i
$879$	10.8734			0.366752
$880$	27.5734	−	22.7655i	0.929501	−	0.767424i
$881$	−43.4299			−1.46319			−0.731596	−	0.681739i	$-0.761224\pi$
$881$	−43.4299			−1.46319			−0.731596	+	0.681739i	$0.761224\pi$
$882$	10.9627	−	1.25675i	0.369134	−	0.0423170i
$883$	−22.3879	+	22.3879i	−0.753413	+	0.753413i	−0.975115	−	0.221701i	$-0.928839\pi$
$883$	−22.3879	+	22.3879i	−0.753413	+	0.753413i	0.221701	+	0.975115i	$0.428839\pi$
$884$	11.8312	+	7.37017i	0.397928	+	0.247885i
$885$	−5.31198	+	8.62946i	−0.178560	+	0.290076i
$886$	18.0728	−	22.7530i	0.607167	−	0.764402i
$887$	−31.6913			−1.06409			−0.532045	−	0.846716i	$-0.678576\pi$
$887$	−31.6913			−1.06409			−0.532045	+	0.846716i	$0.678576\pi$
$888$	−3.14098	−	8.81152i	−0.105404	−	0.295695i
$889$		−	31.4168i		−	1.05368i
$890$	34.3194	+	16.0582i	1.15039	+	0.538274i
$891$	−1.29335	+	1.29335i	−0.0433288	+	0.0433288i
$892$	−4.17498	−	17.9700i	−0.139789	−	0.601680i
$893$	12.8541	−	12.8541i	0.430147	−	0.430147i
$894$	15.0779	−	1.72850i	0.504279	−	0.0578098i
$895$	−7.23315	−	30.3967i	−0.241778	−	1.01605i
$896$	13.9012	+	13.5286i	0.464408	+	0.451959i
$897$		−	7.64420i		−	0.255232i
$898$	3.72989	+	32.5361i	0.124468	+	1.08574i
$899$	47.8533	+	47.8533i	1.59600	+	1.59600i
$900$	14.7529	−	12.3133i	0.491762	−	0.410444i
$901$	−0.915049	+	0.915049i	−0.0304847	+	0.0304847i
$902$	−5.61328	+	7.06692i	−0.186902	+	0.235303i
$903$	20.3168			0.676102
$904$	42.1637	−	15.0298i	1.40234	−	0.499884i
$905$	19.0893	−	4.54248i	0.634551	−	0.150997i
$906$	−4.17316	+	5.25386i	−0.138644	+	0.174548i
$907$	−24.9184	−	24.9184i	−0.827401	−	0.827401i	0.159755	−	0.987157i	$-0.448929\pi$
$907$	−24.9184	−	24.9184i	−0.827401	−	0.827401i	−0.987157	+	0.159755i	$0.948929\pi$
$908$	13.7845	−	22.1280i	0.457454	−	0.734345i
$909$	−12.9192	−	12.9192i	−0.428503	−	0.428503i
$910$	−6.77979	−	18.7036i	−0.224748	−	0.620018i
$911$	−47.0459			−1.55870			−0.779350	−	0.626589i	$-0.784451\pi$
$911$	−47.0459			−1.55870			−0.779350	+	0.626589i	$0.784451\pi$
$912$	−15.2708	+	7.50062i	−0.505668	+	0.248370i
$913$		−	46.6366i		−	1.54345i
$914$	6.07271	+	52.9726i	0.200867	+	1.75218i
$915$	−9.68738	−	5.96319i	−0.320255	−	0.197137i
$916$	−2.44981	+	3.93266i	−0.0809441	+	0.129939i
$917$	17.4943	+	17.4943i	0.577712	+	0.577712i
$918$	−10.7500	−	8.53874i	−0.354802	−	0.281820i
$919$			12.5442i			0.413796i	0.978362	+	0.206898i	$0.0663369\pi$
$919$			12.5442i			0.413796i	−0.978362	+	0.206898i	$0.933663\pi$
$920$	−2.63701	+	12.4108i	−0.0869396	+	0.409172i
$921$			24.4716i			0.806368i
$922$	−14.1482	+	17.8121i	−0.465948	+	0.586612i
$923$	0.983751	+	0.983751i	0.0323806	+	0.0323806i
$924$	3.22155	+	13.8662i	0.105981	+	0.456166i
$925$	4.98165	−	15.1252i	0.163796	−	0.497315i
$926$	11.1684	−	1.28033i	0.367015	−	0.0420741i
$927$		−	29.1573i		−	0.957652i
$928$	11.4588	−	52.5497i	0.376155	−	1.72503i
$929$	−26.7421			−0.877380			−0.438690	−	0.898639i	$-0.644557\pi$
$929$	−26.7421			−0.877380			−0.438690	+	0.898639i	$0.644557\pi$
$930$	7.96549	+	21.9746i	0.261199	+	0.720577i
$931$	−11.7599	−	11.7599i	−0.385414	−	0.385414i
$932$	24.1172	−	5.60316i	0.789986	−	0.183538i
$933$	−16.0863	−	16.0863i	−0.526642	−	0.526642i
$934$	−8.37851	−	6.65508i	−0.274153	−	0.217761i
$935$	−3.93058	−	16.5179i	−0.128544	−	0.540194i
$936$	8.54843	−	18.0186i	0.279414	−	0.588956i
$937$	3.06580			0.100155			0.0500777	−	0.998745i	$-0.484053\pi$
$937$	3.06580			0.100155			0.0500777	+	0.998745i	$0.484053\pi$
$938$	4.84535	+	3.84868i	0.158206	+	0.125664i
$939$	9.16546	−	9.16546i	0.299104	−	0.299104i
$940$	−6.30961	+	18.8188i	−0.205797	+	0.613801i
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	0.427836	−	0.903856i	$-0.359276\pi$
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	−0.903856	+	0.427836i	$0.859276\pi$
$942$	−3.15626	+	0.361830i	−0.102837	+	0.0117890i
$943$		−	3.20239i		−	0.104284i
$944$	5.63726	−	16.5206i	0.183477	−	0.537701i
$945$	4.53590	+	19.0617i	0.147553	+	0.620077i
$946$	7.34774	+	64.0949i	0.238896	+	2.08390i
$947$	−29.4872	+	29.4872i	−0.958204	+	0.958204i	−0.999161	−	0.0409570i	$-0.986959\pi$
$947$	−29.4872	+	29.4872i	−0.958204	+	0.958204i	0.0409570	+	0.999161i	$0.486959\pi$
$948$	12.3613	−	19.8434i	0.401476	−	0.644485i
$949$	−21.7356	+	21.7356i	−0.705567	+	0.705567i
$950$	−28.3615	−	5.86826i	−0.920170	−	0.190391i
$951$			6.23158i			0.202073i
$952$	8.67619	−	3.09274i	0.281197	−	0.100236i
$953$	−33.6807			−1.09103			−0.545513	−	0.838103i	$-0.683665\pi$
$953$	−33.6807			−1.09103			−0.545513	+	0.838103i	$0.683665\pi$
$954$	1.44981	+	1.15159i	0.0469394	+	0.0372842i
$955$	36.0434	+	22.1870i	1.16634	+	0.717953i
$956$	15.1456	−	3.51878i	0.489843	−	0.113805i
$957$	27.9105	−	27.9105i	0.902219	−	0.902219i
$958$	−1.54460	−	13.4737i	−0.0499039	−	0.435315i
$959$	−25.6913			−0.829616
$960$	11.2767	−	14.7620i	0.363954	−	0.476440i
$961$	19.6628			0.634283
$962$	−1.88233	−	16.4197i	−0.0606887	−	0.529391i
$963$	−3.26256	+	3.26256i	−0.105134	+	0.105134i
$964$	6.76128	−	1.57085i	0.217766	−	0.0505937i
$965$	−5.19253	+	8.43541i	−0.167153	+	0.271546i
$966$	−3.95536	−	3.14176i	−0.127262	−	0.101084i
$967$	−8.70089			−0.279802			−0.139901	−	0.990166i	$-0.544678\pi$
$967$	−8.70089			−0.279802			−0.139901	+	0.990166i	$0.544678\pi$
$968$	−13.2732	+	4.73142i	−0.426618	+	0.152074i
$969$			8.07881i			0.259529i
$970$	18.6331	+	8.71854i	0.598273	+	0.279935i
$971$	−5.87523	+	5.87523i	−0.188545	+	0.188545i	−0.795067	−	0.606522i	$-0.792564\pi$
$971$	−5.87523	+	5.87523i	−0.188545	+	0.188545i	0.606522	+	0.795067i	$0.292564\pi$
$972$	−16.7164	+	26.8346i	−0.536177	+	0.860719i
$973$	14.2150	−	14.2150i	0.455713	−	0.455713i
$974$	−5.90296	−	51.4919i	−0.189143	−	1.64991i
$975$	−17.0101	+	8.58132i	−0.544760	+	0.274822i
$976$	18.5459	+	6.32835i	0.593641	+	0.202566i
$977$		−	41.8541i		−	1.33903i	−0.742798	−	0.669516i	$-0.766502\pi$
$977$		−	41.8541i		−	1.33903i	0.742798	−	0.669516i	$-0.233498\pi$
$978$	20.9146	−	2.39762i	0.668774	−	0.0766673i
$979$	−33.8713	−	33.8713i	−1.08253	−	1.08253i
$980$	17.2167	+	5.77247i	0.549969	+	0.184395i
$981$	−5.97856	+	5.97856i	−0.190881	+	0.190881i
$982$	36.6890	+	29.1422i	1.17079	+	0.929966i
$983$	−57.4539			−1.83250			−0.916248	−	0.400612i	$-0.868797\pi$
$983$	−57.4539			−1.83250			−0.916248	+	0.400612i	$0.868797\pi$
$984$	−2.00969	+	4.23607i	−0.0640665	+	0.135041i
$985$	4.68030	+	19.6685i	0.149127	+	0.626692i
$986$	−19.9984	−	15.8848i	−0.636880	−	0.505876i
$987$	−5.58758	−	5.58758i	−0.177854	−	0.177854i
$988$	−29.2786	+	6.80232i	−0.931477	+	0.216411i
$989$	−16.1872	−	16.1872i	−0.514722	−	0.514722i
$990$	−22.8390	+	8.27882i	−0.725872	+	0.263118i
$991$	12.8205			0.407258			0.203629	−	0.979048i	$-0.434726\pi$
$991$	12.8205			0.407258			0.203629	+	0.979048i	$0.434726\pi$
$992$	−21.7516	−	33.8832i	−0.690616	−	1.07579i
$993$			1.62099i			0.0514404i
$994$	0.913345	−	0.104705i	0.0289696	−	0.00332103i
$995$	6.86467	−	11.1519i	0.217625	−	0.353538i
$996$	−5.48298	−	23.5999i	−0.173735	−	0.747792i
$997$	−15.0860	−	15.0860i	−0.477777	−	0.477777i	0.426643	−	0.904420i	$-0.359696\pi$
$997$	−15.0860	−	15.0860i	−0.477777	−	0.477777i	−0.904420	+	0.426643i	$0.859696\pi$
$998$	11.8193	−	14.8801i	0.374135	−	0.471022i
$999$			16.2776i			0.514999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.q.c.29.5	yes	16
3.2	odd	2		720.2.bm.f.109.4		16
4.3	odd	2		320.2.q.c.209.6		16
5.2	odd	4		400.2.l.i.301.1		16
5.3	odd	4		400.2.l.i.301.8		16
5.4	even	2	inner	80.2.q.c.29.4	✓	16
8.3	odd	2		640.2.q.f.289.3		16
8.5	even	2		640.2.q.e.289.6		16
15.14	odd	2		720.2.bm.f.109.5		16
16.3	odd	4		640.2.q.f.609.6		16
16.5	even	4	inner	80.2.q.c.69.4	yes	16
16.11	odd	4		320.2.q.c.49.3		16
16.13	even	4		640.2.q.e.609.3		16
20.3	even	4		1600.2.l.h.401.6		16
20.7	even	4		1600.2.l.h.401.3		16
20.19	odd	2		320.2.q.c.209.3		16
40.19	odd	2		640.2.q.f.289.6		16
40.29	even	2		640.2.q.e.289.3		16
48.5	odd	4		720.2.bm.f.469.5		16
80.19	odd	4		640.2.q.f.609.3		16
80.27	even	4		1600.2.l.h.1201.3		16
80.29	even	4		640.2.q.e.609.6		16
80.37	odd	4		400.2.l.i.101.1		16
80.43	even	4		1600.2.l.h.1201.6		16
80.53	odd	4		400.2.l.i.101.8		16
80.59	odd	4		320.2.q.c.49.6		16
80.69	even	4	inner	80.2.q.c.69.5	yes	16
240.149	odd	4		720.2.bm.f.469.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	5.4	even	2	inner
80.2.q.c.29.5	yes	16	1.1	even	1	trivial
80.2.q.c.69.4	yes	16	16.5	even	4	inner
80.2.q.c.69.5	yes	16	80.69	even	4	inner
320.2.q.c.49.3		16	16.11	odd	4
320.2.q.c.49.6		16	80.59	odd	4
320.2.q.c.209.3		16	20.19	odd	2
320.2.q.c.209.6		16	4.3	odd	2
400.2.l.i.101.1		16	80.37	odd	4
400.2.l.i.101.8		16	80.53	odd	4
400.2.l.i.301.1		16	5.2	odd	4
400.2.l.i.301.8		16	5.3	odd	4
640.2.q.e.289.3		16	40.29	even	2
640.2.q.e.289.6		16	8.5	even	2
640.2.q.e.609.3		16	16.13	even	4
640.2.q.e.609.6		16	80.29	even	4
640.2.q.f.289.3		16	8.3	odd	2
640.2.q.f.289.6		16	40.19	odd	2
640.2.q.f.609.3		16	80.19	odd	4
640.2.q.f.609.6		16	16.3	odd	4
720.2.bm.f.109.4		16	3.2	odd	2
720.2.bm.f.109.5		16	15.14	odd	2
720.2.bm.f.469.4		16	240.149	odd	4
720.2.bm.f.469.5		16	48.5	odd	4
1600.2.l.h.401.3		16	20.7	even	4
1600.2.l.h.401.6		16	20.3	even	4
1600.2.l.h.1201.3		16	80.27	even	4
1600.2.l.h.1201.6		16	80.43	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.161069 + 1.40501i) q^{2} +(-0.734294 + 0.734294i) q^{3} +(-1.94811 + 0.452606i) q^{4} +(1.90421 + 1.17216i) q^{5} +(-1.14996 - 0.913419i) q^{6} -1.71452 q^{7} +(-0.949697 - 2.66422i) q^{8} +1.92163i q^{9} +(-1.34019 + 2.86424i) q^{10} +(2.82684 - 2.82684i) q^{11} +(1.09814 - 1.76283i) q^{12} +(2.59462 - 2.59462i) q^{13} +(-0.276156 - 2.40893i) q^{14} +(-2.25896 + 0.537540i) q^{15} +(3.59030 - 1.76346i) q^{16} -1.89939i q^{17} +(-2.69991 + 0.309513i) q^{18} +(2.89623 + 2.89623i) q^{19} +(-4.24015 - 1.42165i) q^{20} +(1.25896 - 1.25896i) q^{21} +(4.42705 + 3.51643i) q^{22} -2.00613 q^{23} +(2.65368 + 1.25896i) q^{24} +(2.25207 + 4.46410i) q^{25} +(4.06338 + 3.22756i) q^{26} +(-3.61392 - 3.61392i) q^{27} +(3.34009 - 0.776005i) q^{28} +(-6.72307 - 6.72307i) q^{29} +(-1.11910 - 3.08729i) q^{30} -7.11778 q^{31} +(3.05596 + 4.76037i) q^{32} +4.15146i q^{33} +(2.66867 - 0.305932i) q^{34} +(-3.26482 - 2.00970i) q^{35} +(-0.869740 - 3.74355i) q^{36} +(-2.25207 - 2.25207i) q^{37} +(-3.60274 + 4.53572i) q^{38} +3.81042i q^{39} +(1.31448 - 6.18645i) q^{40} +1.59630i q^{41} +(1.97164 + 1.56608i) q^{42} +(8.06886 + 8.06886i) q^{43} +(-4.22756 + 6.78645i) q^{44} +(-2.25246 + 3.65919i) q^{45} +(-0.323124 - 2.81863i) q^{46} -4.43823i q^{47} +(-1.34144 + 3.93123i) q^{48} -4.06040 q^{49} +(-5.90938 + 3.88320i) q^{50} +(1.39471 + 1.39471i) q^{51} +(-3.88027 + 6.22896i) q^{52} +(-0.481758 - 0.481758i) q^{53} +(4.49551 - 5.65968i) q^{54} +(8.69642 - 2.06939i) q^{55} +(1.62828 + 4.56787i) q^{56} -4.25336 q^{57} +(8.36311 - 10.5289i) q^{58} +(3.08580 - 3.08580i) q^{59} +(4.15743 - 2.06961i) q^{60} +(3.46410 + 3.46410i) q^{61} +(-1.14645 - 10.0006i) q^{62} -3.29468i q^{63} +(-6.19615 + 5.06040i) q^{64} +(7.98203 - 1.89939i) q^{65} +(-5.83285 + 0.668669i) q^{66} +(-1.80454 + 1.80454i) q^{67} +(0.859677 + 3.70023i) q^{68} +(1.47309 - 1.47309i) q^{69} +(2.29780 - 4.91081i) q^{70} +0.379150i q^{71} +(5.11964 - 1.82496i) q^{72} -8.37718 q^{73} +(2.80144 - 3.52691i) q^{74} +(-4.93164 - 1.62428i) q^{75} +(-6.95303 - 4.33133i) q^{76} +(-4.84668 + 4.84668i) q^{77} +(-5.35369 + 0.613739i) q^{78} +11.2566 q^{79} +(8.90375 + 0.850413i) q^{80} -0.457524 q^{81} +(-2.24282 + 0.257114i) q^{82} +(8.24890 - 8.24890i) q^{83} +(-1.88279 + 3.02242i) q^{84} +(2.22640 - 3.61685i) q^{85} +(-10.0372 + 12.6365i) q^{86} +9.87341 q^{87} +(-10.2160 - 4.84668i) q^{88} -11.9820i q^{89} +(-5.50400 - 2.57535i) q^{90} +(-4.44854 + 4.44854i) q^{91} +(3.90816 - 0.907986i) q^{92} +(5.22654 - 5.22654i) q^{93} +(6.23577 - 0.714859i) q^{94} +(2.12019 + 8.90989i) q^{95} +(-5.73948 - 1.25154i) q^{96} -6.50543i q^{97} +(-0.654003 - 5.70491i) q^{98} +(5.43213 + 5.43213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36}+ \cdots + 88 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

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