LMFDB - Embedded newform 735.2.y.g.422.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(128,735)] 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("735.128"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			422.10
Character	$\chi$	$=$	735.422
Dual form			735.2.y.g.263.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.455388 + 1.69953i) q^{2} +(1.67990 - 0.421844i) q^{3} +(-0.948973 + 0.547890i) q^{4} +(0.445053 + 2.19133i) q^{5} +(1.48194 + 2.66293i) q^{6} +(1.12498 + 1.12498i) q^{8} +(2.64410 - 1.41731i) q^{9} +(-3.52156 + 1.75429i) q^{10} +(-1.34425 + 0.776103i) q^{11} +(-1.36305 + 1.32072i) q^{12} +(4.50889 - 4.50889i) q^{13} +(1.67204 + 3.49346i) q^{15} +(-2.49541 + 4.32218i) q^{16} +(2.91469 + 0.780989i) q^{17} +(3.61285 + 3.84829i) q^{18} +(-3.64590 - 2.10496i) q^{19} +(-1.62295 - 1.83567i) q^{20} +(-1.93117 - 1.93117i) q^{22} +(-5.13695 + 1.37644i) q^{23} +(2.36441 + 1.41528i) q^{24} +(-4.60386 + 1.95052i) q^{25} +(9.71628 + 5.60970i) q^{26} +(3.84392 - 3.49632i) q^{27} -2.97115 q^{29} +(-5.17582 + 4.43256i) q^{30} +(-2.89885 - 5.02095i) q^{31} +(-5.40856 - 1.44922i) q^{32} +(-1.93080 + 1.87084i) q^{33} +5.30926i q^{34} +(-1.73265 + 2.79366i) q^{36} +(1.68190 - 0.450663i) q^{37} +(1.91715 - 7.15489i) q^{38} +(5.67241 - 9.47650i) q^{39} +(-1.96452 + 2.96587i) q^{40} +2.68458i q^{41} +(-2.09578 + 2.09578i) q^{43} +(0.850438 - 1.47300i) q^{44} +(4.28255 + 5.16331i) q^{45} +(-4.67860 - 8.10358i) q^{46} +(-0.0131194 - 0.0489622i) q^{47} +(-2.36874 + 8.31349i) q^{48} +(-5.41150 - 6.93615i) q^{50} +(5.22583 + 0.0824344i) q^{51} +(-1.80844 + 6.74919i) q^{52} +(-1.57696 + 5.88528i) q^{53} +(7.69258 + 4.94067i) q^{54} +(-2.29896 - 2.60029i) q^{55} +(-7.01270 - 1.99811i) q^{57} +(-1.35302 - 5.04955i) q^{58} +(2.46880 + 4.27609i) q^{59} +(-3.50076 - 2.39911i) q^{60} +(1.65843 - 2.87249i) q^{61} +(7.21316 - 7.21316i) q^{62} +0.129684i q^{64} +(11.8872 + 7.87377i) q^{65} +(-4.05881 - 2.42950i) q^{66} +(0.625932 - 2.33601i) q^{67} +(-3.19386 + 0.855793i) q^{68} +(-8.04889 + 4.47927i) q^{69} -5.73577i q^{71} +(4.56899 + 1.38011i) q^{72} +(9.92795 + 2.66019i) q^{73} +(1.53183 + 2.65321i) q^{74} +(-6.91118 + 5.21877i) q^{75} +4.61315 q^{76} +(18.6887 + 5.32495i) q^{78} +(3.11231 + 1.79689i) q^{79} +(-10.5819 - 3.54467i) q^{80} +(4.98248 - 7.49499i) q^{81} +(-4.56252 + 1.22252i) q^{82} +(-12.2139 - 12.2139i) q^{83} +(-0.414214 + 6.73463i) q^{85} +(-4.51623 - 2.60745i) q^{86} +(-4.99121 + 1.25336i) q^{87} +(-2.38535 - 0.639153i) q^{88} +(0.678216 - 1.17470i) q^{89} +(-6.82498 + 9.62963i) q^{90} +(4.12069 - 4.12069i) q^{92} +(-6.98782 - 7.21181i) q^{93} +(0.0772383 - 0.0445936i) q^{94} +(2.99005 - 8.92620i) q^{95} +(-9.69716 - 0.152967i) q^{96} +(-10.9812 - 10.9812i) q^{97} +(-2.45435 + 3.95731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 16 q^{10} + 16 q^{12} + 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} + 32 q^{27} - 20 q^{30} + 28 q^{33} + 32 q^{36} + 16 q^{37} + 64 q^{40} - 80 q^{43} + 20 q^{45}+ \cdots - 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 + 16 * q^13 - 32 * q^15 + 16 * q^16 + 20 * q^18 + 16 * q^22 + 16 * q^25 + 32 * q^27 - 20 * q^30 + 28 * q^33 + 32 * q^36 + 16 * q^37 + 64 * q^40 - 80 * q^43 + 20 * q^45 + 64 * q^46 - 32 * q^48 + 20 * q^51 - 80 * q^55 + 8 * q^57 - 40 * q^58 - 32 * q^60 + 32 * q^61 - 16 * q^66 - 24 * q^67 + 8 * q^72 + 32 * q^73 - 60 * q^75 - 64 * q^76 + 120 * q^78 - 52 * q^81 - 80 * q^82 + 48 * q^85 + 4 * q^87 - 96 * q^88 + 48 * q^90 + 76 * q^93 - 96 * q^96 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.455388	+	1.69953i	0.322008	+	1.20175i	0.917286	+	0.398229i	$0.130375\pi$
$2$	0.455388	+	1.69953i	0.322008	+	1.20175i	−0.595278	+	0.803520i	$0.702958\pi$
$3$	1.67990	−	0.421844i	0.969888	−	0.243552i
$3$	1.67990	−	0.421844i	0.969888	−	0.243552i
$4$	−0.948973	+	0.547890i	−0.474487	+	0.273945i
$5$	0.445053	+	2.19133i	0.199034	+	0.979993i
$5$	0.445053	+	2.19133i	0.199034	+	0.979993i
$6$	1.48194	+	2.66293i	0.605000	+	1.08714i
$7$		0			0
$7$		0			0
$8$	1.12498	+	1.12498i	0.397740	+	0.397740i
$9$	2.64410	−	1.41731i	0.881365	−	0.472436i
$10$	−3.52156	+	1.75429i	−1.11361	+	0.554754i
$11$	−1.34425	+	0.776103i	−0.405307	+	0.234004i	−0.688771	−	0.724979i	$-0.741850\pi$
$11$	−1.34425	+	0.776103i	−0.405307	+	0.234004i	0.283465	+	0.958983i	$0.408516\pi$
$12$	−1.36305	+	1.32072i	−0.393479	+	0.381258i
$13$	4.50889	−	4.50889i	1.25054	−	1.25054i	0.295062	−	0.955478i	$-0.404660\pi$
$13$	4.50889	−	4.50889i	1.25054	−	1.25054i	0.955478	−	0.295062i	$-0.0953402\pi$
$14$		0			0
$15$	1.67204	+	3.49346i	0.431719	+	0.902008i
$16$	−2.49541	+	4.32218i	−0.623853	+	1.08055i
$17$	2.91469	+	0.780989i	0.706917	+	0.189418i	0.594327	−	0.804224i	$-0.297419\pi$
$17$	2.91469	+	0.780989i	0.706917	+	0.189418i	0.112590	+	0.993642i	$0.464085\pi$
$18$	3.61285	+	3.84829i	0.851556	+	0.907052i
$19$	−3.64590	−	2.10496i	−0.836427	−	0.482912i	0.0196209	−	0.999807i	$-0.493754\pi$
$19$	−3.64590	−	2.10496i	−0.836427	−	0.482912i	−0.856048	+	0.516896i	$0.827087\pi$
$20$	−1.62295	−	1.83567i	−0.362903	−	0.410469i
$21$		0			0
$22$	−1.93117	−	1.93117i	−0.411726	−	0.411726i
$23$	−5.13695	+	1.37644i	−1.07113	+	0.287008i	−0.750956	−	0.660352i	$-0.770407\pi$
$23$	−5.13695	+	1.37644i	−1.07113	+	0.287008i	−0.320171	+	0.947360i	$0.603740\pi$
$24$	2.36441	+	1.41528i	0.482633	+	0.288893i
$25$	−4.60386	+	1.95052i	−0.920771	+	0.390103i
$26$	9.71628	+	5.60970i	1.90552	+	1.10015i
$27$	3.84392	−	3.49632i	0.739763	−	0.672868i
$28$		0			0
$29$	−2.97115			−0.551728			−0.275864	−	0.961197i	$-0.588964\pi$
$29$	−2.97115			−0.551728			−0.275864	+	0.961197i	$0.588964\pi$
$30$	−5.17582	+	4.43256i	−0.944970	+	0.809272i
$31$	−2.89885	−	5.02095i	−0.520649	−	0.901790i	−0.999712	−	0.0240096i	$-0.992357\pi$
$31$	−2.89885	−	5.02095i	−0.520649	−	0.901790i	0.479063	−	0.877781i	$-0.340977\pi$
$32$	−5.40856	−	1.44922i	−0.956108	−	0.256188i
$33$	−1.93080	+	1.87084i	−0.336110	+	0.325671i
$34$			5.30926i			0.910531i
$35$		0			0
$36$	−1.73265	+	2.79366i	−0.288775	+	0.465610i
$37$	1.68190	−	0.450663i	0.276502	−	0.0740885i	−0.117903	−	0.993025i	$-0.537617\pi$
$37$	1.68190	−	0.450663i	0.276502	−	0.0740885i	0.394405	+	0.918937i	$0.370951\pi$
$38$	1.91715	−	7.15489i	0.311003	−	1.16068i
$39$	5.67241	−	9.47650i	0.908312	−	1.51745i
$40$	−1.96452	+	2.96587i	−0.310619	+	0.468946i
$41$			2.68458i			0.419261i	0.977781	+	0.209631i	$0.0672261\pi$
$41$			2.68458i			0.419261i	−0.977781	+	0.209631i	$0.932774\pi$
$42$		0			0
$43$	−2.09578	+	2.09578i	−0.319603	+	0.319603i	−0.848615	−	0.529011i	$-0.822563\pi$
$43$	−2.09578	+	2.09578i	−0.319603	+	0.319603i	0.529011	+	0.848615i	$0.322563\pi$
$44$	0.850438	−	1.47300i	0.128208	−	0.222063i
$45$	4.28255	+	5.16331i	0.638405	+	0.769701i
$46$	−4.67860	−	8.10358i	−0.689822	−	1.19481i
$47$	−0.0131194	−	0.0489622i	−0.00191366	−	0.00714187i	0.964962	−	0.262388i	$-0.0845101\pi$
$47$	−0.0131194	−	0.0489622i	−0.00191366	−	0.00714187i	−0.966876	+	0.255246i	$0.917843\pi$
$48$	−2.36874	+	8.31349i	−0.341899	+	1.19995i
$49$		0			0
$50$	−5.41150	−	6.93615i	−0.765302	−	0.980920i
$51$	5.22583	+	0.0824344i	0.731763	+	0.0115431i
$52$	−1.80844	+	6.74919i	−0.250785	+	0.935944i
$53$	−1.57696	+	5.88528i	−0.216612	+	0.808406i	0.768981	+	0.639271i	$0.220764\pi$
$53$	−1.57696	+	5.88528i	−0.216612	+	0.808406i	−0.985593	+	0.169134i	$0.945903\pi$
$54$	7.69258	+	4.94067i	1.04683	+	0.672340i
$55$	−2.29896	−	2.60029i	−0.309992	−	0.350623i
$56$		0			0
$57$	−7.01270	−	1.99811i	−0.928855	−	0.264657i
$58$	−1.35302	−	5.04955i	−0.177661	−	0.663038i
$59$	2.46880	+	4.27609i	0.321410	+	0.556699i	0.980779	−	0.195120i	$-0.0625098\pi$
$59$	2.46880	+	4.27609i	0.321410	+	0.556699i	−0.659369	+	0.751820i	$0.729176\pi$
$60$	−3.50076	−	2.39911i	−0.451946	−	0.309723i
$61$	1.65843	−	2.87249i	0.212341	−	0.367785i	−0.740106	−	0.672490i	$-0.765225\pi$
$61$	1.65843	−	2.87249i	0.212341	−	0.367785i	0.952447	+	0.304705i	$0.0985580\pi$
$62$	7.21316	−	7.21316i	0.916073	−	0.916073i
$63$		0			0
$64$			0.129684i			0.0162105i
$65$	11.8872	+	7.87377i	1.47442	+	0.976620i
$66$	−4.05881	−	2.42950i	−0.499604	−	0.299051i
$67$	0.625932	−	2.33601i	0.0764698	−	0.285389i	−0.917093	−	0.398674i	$-0.869471\pi$
$67$	0.625932	−	2.33601i	0.0764698	−	0.285389i	0.993563	+	0.113285i	$0.0361372\pi$
$68$	−3.19386	+	0.855793i	−0.387313	+	0.103780i
$69$	−8.04889	+	4.47927i	−0.968972	+	0.539240i
$70$		0			0
$71$		−	5.73577i		−	0.680711i	−0.940297	−	0.340356i	$-0.889453\pi$
$71$		−	5.73577i		−	0.680711i	0.940297	−	0.340356i	$-0.110547\pi$
$72$	4.56899	+	1.38011i	0.538461	+	0.162647i
$73$	9.92795	+	2.66019i	1.16198	+	0.311351i	0.787756	−	0.615988i	$-0.211243\pi$
$73$	9.92795	+	2.66019i	1.16198	+	0.311351i	0.374223	+	0.927339i	$0.377910\pi$
$74$	1.53183	+	2.65321i	0.178072	+	0.308429i
$75$	−6.91118	+	5.21877i	−0.798034	+	0.602612i
$76$	4.61315			0.529165
$77$		0			0
$78$	18.6887	+	5.32495i	2.11608	+	0.602931i
$79$	3.11231	+	1.79689i	0.350163	+	0.202166i	0.664757	−	0.747060i	$-0.268535\pi$
$79$	3.11231	+	1.79689i	0.350163	+	0.202166i	−0.314594	+	0.949226i	$0.601868\pi$
$80$	−10.5819	−	3.54467i	−1.18309	−	0.396307i
$81$	4.98248	−	7.49499i	0.553609	−	0.832777i
$82$	−4.56252	+	1.22252i	−0.503847	+	0.135005i
$83$	−12.2139	−	12.2139i	−1.34065	−	1.34065i	−0.895417	−	0.445228i	$-0.853123\pi$
$83$	−12.2139	−	12.2139i	−1.34065	−	1.34065i	−0.445228	−	0.895417i	$-0.646877\pi$
$84$		0			0
$85$	−0.414214	+	6.73463i	−0.0449278	+	0.730474i
$86$	−4.51623	−	2.60745i	−0.486998	−	0.281168i
$87$	−4.99121	+	1.25336i	−0.535114	+	0.134374i
$88$	−2.38535	−	0.639153i	−0.254279	−	0.0681339i
$89$	0.678216	−	1.17470i	0.0718908	−	0.124518i	−0.827839	−	0.560965i	$-0.810430\pi$
$89$	0.678216	−	1.17470i	0.0718908	−	0.124518i	0.899730	+	0.436447i	$0.143763\pi$
$90$	−6.82498	+	9.62963i	−0.719416	+	1.01505i
$91$		0			0
$92$	4.12069	−	4.12069i	0.429611	−	0.429611i
$93$	−6.98782	−	7.21181i	−0.724604	−	0.747830i
$94$	0.0772383	−	0.0445936i	0.00796652	−	0.00459948i
$95$	2.99005	−	8.92620i	0.306773	−	0.915808i
$96$	−9.69716	−	0.152967i	−0.989712	−	0.0156121i
$97$	−10.9812	−	10.9812i	−1.11497	−	1.11497i	−0.992468	−	0.122503i	$-0.960908\pi$
$97$	−10.9812	−	10.9812i	−1.11497	−	1.11497i	−0.122503	−	0.992468i	$-0.539092\pi$
$98$		0			0
$99$	−2.45435	+	3.95731i	−0.246671	+	0.397724i
$100$	3.30027	−	4.37339i	0.330027	−	0.437339i
$101$	11.0014	−	6.35165i	1.09468	−	0.632012i	0.159860	−	0.987140i	$-0.448896\pi$
$101$	11.0014	−	6.35165i	1.09468	−	0.632012i	0.934818	+	0.355127i	$0.115563\pi$
$102$	2.23968	+	8.91900i	0.221761	+	0.883113i
$103$	0.537318	+	2.00530i	0.0529435	+	0.197588i	0.987332	−	0.158668i	$-0.0507199\pi$
$103$	0.537318	+	2.00530i	0.0529435	+	0.197588i	−0.934388	+	0.356256i	$0.884053\pi$
$104$	10.1448			0.994779
$105$		0			0
$106$	−10.7203			−1.04125
$107$	−4.96049	−	18.5128i	−0.479548	−	1.78970i	−0.603446	−	0.797404i	$-0.706206\pi$
$107$	−4.96049	−	18.5128i	−0.479548	−	1.78970i	0.123898	−	0.992295i	$-0.460460\pi$
$108$	−1.73218	+	5.42396i	−0.166679	+	0.521921i
$109$	4.19293	−	2.42079i	0.401610	−	0.231869i	−0.285569	−	0.958358i	$-0.592182\pi$
$109$	4.19293	−	2.42079i	0.401610	−	0.231869i	0.687178	+	0.726489i	$0.258849\pi$
$110$	3.37235	−	5.09129i	0.321541	−	0.485436i
$111$	2.63530	−	1.46656i	0.250132	−	0.139200i
$112$		0			0
$113$	−10.6222	−	10.6222i	−0.999254	−	0.999254i	0.000746132	−	1.00000i	$-0.499762\pi$
$113$	−10.6222	−	10.6222i	−0.999254	−	0.999254i	−1.00000		0.000746132i	$0.999762\pi$
$114$	0.202357	−	12.8282i	0.0189525	−	1.20147i
$115$	−5.30245	−	10.6442i	−0.494456	−	0.992573i
$116$	2.81954	−	1.62786i	0.261788	−	0.151143i
$117$	5.53144	−	18.3124i	0.511382	−	1.69298i
$118$	−6.14308	+	6.14308i	−0.565516	+	0.565516i
$119$		0			0
$120$	−2.04906	+	5.81108i	−0.187053	+	0.530477i
$121$	−4.29533	+	7.43973i	−0.390484	+	0.676339i
$122$	5.63711	+	1.51046i	0.510360	+	0.136751i
$123$	1.13247	+	4.50981i	0.102112	+	0.406636i
$124$	5.50186	+	3.17650i	0.494082	+	0.285258i
$125$	−6.32318	−	9.22049i	−0.565563	−	0.824705i
$126$		0			0
$127$	10.1595	+	10.1595i	0.901511	+	0.901511i	0.995567	−	0.0940560i	$-0.0299833\pi$
$127$	10.1595	+	10.1595i	0.901511	+	0.901511i	−0.0940560	+	0.995567i	$0.529983\pi$
$128$	−11.0375	+	2.95750i	−0.975588	+	0.261408i
$129$	−2.63660	+	4.40478i	−0.232140	+	0.387820i
$130$	−7.96844	+	23.7882i	−0.698878	+	2.08636i
$131$	0.441131	+	0.254687i	0.0385418	+	0.0222521i	0.519147	−	0.854685i	$-0.326250\pi$
$131$	0.441131	+	0.254687i	0.0385418	+	0.0222521i	−0.480605	+	0.876937i	$0.659583\pi$
$132$	0.807270	−	2.83324i	0.0702638	−	0.246602i
$133$		0			0
$134$	4.25516			0.367590
$135$	9.37235	+	6.86725i	0.806643	+	0.591039i
$136$	2.40037	+	4.15756i	0.205830	+	0.356508i
$137$	3.57827	+	0.958794i	0.305712	+	0.0819153i	0.408414	−	0.912797i	$-0.366082\pi$
$137$	3.57827	+	0.958794i	0.305712	+	0.0819153i	−0.102702	+	0.994712i	$0.532749\pi$
$138$	−11.2780	−	11.6395i	−0.960048	−	0.990822i
$139$			6.35379i			0.538921i	0.963011	+	0.269461i	$0.0868454\pi$
$139$			6.35379i			0.538921i	−0.963011	+	0.269461i	$0.913155\pi$
$140$		0			0
$141$	−0.0426936	−	0.0767170i	−0.00359545	−	0.00646074i
$142$	9.74812	−	2.61200i	0.818044	−	0.219194i
$143$	−2.56171	+	9.56043i	−0.214221	+	0.799483i
$144$	−0.472246	+	14.9650i	−0.0393539	+	1.24709i
$145$	−1.32232	−	6.51076i	−0.109812	−	0.540689i
$146$			18.0843i			1.49666i
$147$		0			0
$148$	−1.34916	+	1.34916i	−0.110900	+	0.110900i
$149$	2.13982	−	3.70628i	0.175301	−	0.303631i	−0.764964	−	0.644073i	$-0.777243\pi$
$149$	2.13982	−	3.70628i	0.175301	−	0.303631i	0.940265	+	0.340442i	$0.110577\pi$
$150$	−12.0167	−	9.36920i	−0.981161	−	0.764992i
$151$	2.60616	+	4.51400i	0.212086	+	0.367344i	0.952367	−	0.304954i	$-0.0986409\pi$
$151$	2.60616	+	4.51400i	0.212086	+	0.367344i	−0.740281	+	0.672297i	$0.765308\pi$
$152$	−1.73352	−	6.46960i	−0.140607	−	0.524754i
$153$	8.81363	−	2.06601i	0.712539	−	0.167027i
$154$		0			0
$155$	9.71243	−	8.58693i	0.780121	−	0.689719i
$156$	−0.190883	+	12.1008i	−0.0152829	+	0.968840i
$157$	1.59587	−	5.95585i	0.127364	−	0.475329i	−0.872549	−	0.488527i	$-0.837534\pi$
$157$	1.59587	−	5.95585i	0.127364	−	0.475329i	0.999913	+	0.0131979i	$0.00420114\pi$
$158$	−1.63657	+	6.10775i	−0.130198	+	0.485907i
$159$	−0.166450	+	10.5519i	−0.0132003	+	0.836819i
$160$	0.768623	−	12.4969i	0.0607650	−	0.987968i
$161$		0			0
$162$	15.0069	+	5.05474i	1.17906	+	0.397138i
$163$	1.95582	+	7.29921i	0.153191	+	0.571718i	0.999253	+	0.0386337i	$0.0123005\pi$
$163$	1.95582	+	7.29921i	0.153191	+	0.571718i	−0.846062	+	0.533084i	$0.821033\pi$
$164$	−1.47085	−	2.54760i	−0.114854	−	0.198934i
$165$	−4.95893	−	3.39841i	−0.386052	−	0.264566i
$166$	15.1958	−	26.3199i	1.17942	−	2.04282i
$167$	−13.8232	+	13.8232i	−1.06967	+	1.06967i	−0.0722908	+	0.997384i	$0.523031\pi$
$167$	−13.8232	+	13.8232i	−1.06967	+	1.06967i	−0.997384	+	0.0722908i	$0.976969\pi$
$168$		0			0
$169$		−	27.6601i		−	2.12770i
$170$	−11.6343	+	2.36290i	−0.892313	+	0.181226i
$171$	−12.6235	−	0.398355i	−0.965343	−	0.0304630i
$172$	0.840583	−	3.13710i	0.0640938	−	0.239201i
$173$	−2.82269	+	0.756337i	−0.214605	+	0.0575032i	−0.364520	−	0.931196i	$-0.618767\pi$
$173$	−2.82269	+	0.756337i	−0.214605	+	0.0575032i	0.149915	+	0.988699i	$0.452100\pi$
$174$	−4.40306	−	7.91195i	−0.333795	−	0.599803i
$175$		0			0
$176$		−	7.74679i		−	0.583936i
$177$	5.95117	+	6.14193i	0.447317	+	0.461656i
$178$	2.30530	+	0.617702i	0.172789	+	0.0462988i
$179$	5.95932	+	10.3218i	0.445420	+	0.771491i	0.998081	−	0.0619153i	$-0.0197209\pi$
$179$	5.95932	+	10.3218i	0.445420	+	0.771491i	−0.552661	+	0.833406i	$0.686388\pi$
$180$	−6.89295	−	2.55347i	−0.513770	−	0.190325i
$181$	17.5945			1.30779			0.653893	−	0.756587i	$-0.273135\pi$
$181$	17.5945			1.30779			0.653893	+	0.756587i	$0.273135\pi$
$182$		0			0
$183$	1.57425	−	5.52508i	0.116372	−	0.408426i
$184$	−7.32742	−	4.23049i	−0.540184	−	0.311876i
$185$	1.73608	+	3.48502i	0.127639	+	0.256224i
$186$	9.07453	−	15.1602i	0.665377	−	1.11160i
$187$	−4.52420	+	1.21226i	−0.330842	+	0.0886490i
$188$	0.0392758	+	0.0392758i	0.00286449	+	0.00286449i
$189$		0			0
$190$	16.5320	+	1.01680i	1.19936	+	0.0737663i
$191$	−4.79798	−	2.77011i	−0.347169	−	0.200438i	0.316268	−	0.948670i	$-0.397570\pi$
$191$	−4.79798	−	2.77011i	−0.347169	−	0.200438i	−0.663438	+	0.748231i	$0.730903\pi$
$192$	0.0547063	+	0.217855i	0.00394809	+	0.0157223i
$193$	18.9915	+	5.08875i	1.36704	+	0.366296i	0.866395	−	0.499359i	$-0.166431\pi$
$193$	18.9915	+	5.08875i	1.36704	+	0.366296i	0.500641	+	0.865655i	$0.333098\pi$
$194$	13.6622	−	23.6636i	0.980886	−	1.69895i
$195$	23.2907	+	8.21257i	1.66788	+	0.588115i
$196$		0			0
$197$	−12.7155	+	12.7155i	−0.905939	+	0.905939i	−0.995942	−	0.0900024i	$-0.971313\pi$
$197$	−12.7155	+	12.7155i	−0.905939	+	0.905939i	0.0900024	+	0.995942i	$0.471313\pi$
$198$	−7.84324	−	2.36913i	−0.557395	−	0.168367i
$199$	−5.29564	+	3.05744i	−0.375398	+	0.216736i	−0.675814	−	0.737072i	$-0.736208\pi$
$199$	−5.29564	+	3.05744i	−0.375398	+	0.216736i	0.300416	+	0.953808i	$0.402874\pi$
$200$	−7.37352	−	2.98495i	−0.521387	−	0.211068i
$201$	0.0660679	−	4.18830i	0.00466007	−	0.295420i
$202$	15.8047	+	15.8047i	1.11201	+	1.11201i
$203$		0			0
$204$	−5.00434	+	2.78495i	−0.350374	+	0.194986i
$205$	−5.88280	+	1.19478i	−0.410873	+	0.0834471i
$206$	−3.16338	+	1.82638i	−0.220403	+	0.127250i
$207$	−11.6317	+	10.9201i	−0.808461	+	0.758997i
$208$	8.23669	+	30.7398i	0.571112	+	2.13142i
$209$	6.53467			0.452013
$210$		0			0
$211$	12.4900			0.859849			0.429924	−	0.902865i	$-0.358540\pi$
$211$	12.4900			0.859849			0.429924	+	0.902865i	$0.358540\pi$
$212$	−1.72800	−	6.44897i	−0.118679	−	0.442917i
$213$	−2.41960	−	9.63550i	−0.165788	−	0.660214i
$214$	29.2041	−	16.8610i	1.99635	−	1.15259i
$215$	−5.52528	−	3.65981i	−0.376821	−	0.249597i
$216$	8.25761	+	0.391036i	0.561859	+	0.0266067i
$217$		0			0
$218$	6.02361	+	6.02361i	0.407970	+	0.407970i
$219$	17.8001	+	0.280786i	1.20282	+	0.0189738i
$220$	3.60632	+	1.20803i	0.243138	+	0.0814452i
$221$	16.6634	−	9.62062i	1.12090	−	0.647153i
$222$	3.69255	+	3.81092i	0.247828	+	0.255772i
$223$	−8.80424	+	8.80424i	−0.589576	+	0.589576i	−0.937516	−	0.347941i	$-0.886881\pi$
$223$	−8.80424	+	8.80424i	−0.589576	+	0.589576i	0.347941	+	0.937516i	$0.386881\pi$
$224$		0			0
$225$	−9.40855	+	11.6824i	−0.627237	+	0.778829i
$226$	13.2155	−	22.8900i	0.879085	−	1.52262i
$227$	−21.5045	−	5.76211i	−1.42730	−	0.382445i	−0.539234	−	0.842156i	$-0.681286\pi$
$227$	−21.5045	−	5.76211i	−1.42730	−	0.382445i	−0.888068	+	0.459711i	$0.847953\pi$
$228$	7.74961	−	1.94603i	0.513231	−	0.128879i
$229$	7.16589	+	4.13723i	0.473535	+	0.273396i	0.717718	−	0.696333i	$-0.245186\pi$
$229$	7.16589	+	4.13723i	0.473535	+	0.273396i	−0.244183	+	0.969729i	$0.578520\pi$
$230$	15.6754	−	13.8589i	1.03360	−	0.913828i
$231$		0			0
$232$	−3.34247	−	3.34247i	−0.219444	−	0.219444i
$233$	17.2700	−	4.62748i	1.13140	−	0.303156i	0.355909	−	0.934521i	$-0.384171\pi$
$233$	17.2700	−	4.62748i	1.13140	−	0.303156i	0.775486	+	0.631364i	$0.217505\pi$
$234$	33.6414	+	1.06161i	2.19921	+	0.0693997i
$235$	0.101454	−	0.0505397i	0.00661810	−	0.00329684i
$236$	−4.68565	−	2.70526i	−0.305010	−	0.176098i
$237$	5.98637	+	1.70568i	0.388856	+	0.110796i
$238$		0			0
$239$	25.8260			1.67054			0.835271	−	0.549838i	$-0.185311\pi$
$239$	25.8260			1.67054			0.835271	+	0.549838i	$0.185311\pi$
$240$	−19.2718	−	1.49076i	−1.24399	−	0.0962282i
$241$	−5.25983	−	9.11029i	−0.338815	−	0.586846i	0.645395	−	0.763849i	$-0.276693\pi$
$241$	−5.25983	−	9.11029i	−0.338815	−	0.586846i	−0.984210	+	0.177004i	$0.943360\pi$
$242$	−14.6001	−	3.91208i	−0.938529	−	0.251478i
$243$	5.20832	−	14.6926i	0.334114	−	0.942533i
$244$			3.63456i			0.232679i
$245$		0			0
$246$	−7.14885	+	3.97839i	−0.455794	+	0.253653i
$247$	−25.9300	+	6.94792i	−1.64989	+	0.442086i
$248$	2.38732	−	8.90961i	0.151595	−	0.565761i
$249$	−25.6704	−	15.3657i	−1.62679	−	0.973759i
$250$	12.7910	−	14.9453i	0.808973	−	0.945226i
$251$		−	6.94563i		−	0.438405i	−0.975679	−	0.219202i	$-0.929655\pi$
$251$		−	6.94563i		−	0.438405i	0.975679	−	0.219202i	$-0.0703455\pi$
$252$		0			0
$253$	5.83708	−	5.83708i	0.366974	−	0.366974i
$254$	−12.6399	+	21.8929i	−0.793096	+	1.37368i
$255$	2.14513	+	11.4882i	0.134333	+	0.719420i
$256$	−9.92302	−	17.1872i	−0.620189	−	1.07420i
$257$	2.99064	+	11.1612i	0.186551	+	0.696217i	0.994293	+	0.106681i	$0.0340225\pi$
$257$	2.99064	+	11.1612i	0.186551	+	0.696217i	−0.807742	+	0.589536i	$0.799311\pi$
$258$	−8.68674	−	2.47509i	−0.540813	−	0.154093i
$259$		0			0
$260$	−15.5945	−	0.959142i	−0.967133	−	0.0594835i
$261$	−7.85599	+	4.21103i	−0.486274	+	0.260656i
$262$	−0.231963	+	0.865696i	−0.0143307	+	0.0534829i
$263$	−0.0435058	+	0.162366i	−0.00268268	+	0.0100119i	−0.967254	−	0.253810i	$-0.918316\pi$
$263$	−0.0435058	+	0.162366i	−0.00268268	+	0.0100119i	0.964572	+	0.263822i	$0.0849830\pi$
$264$	−4.27676	−	0.0674634i	−0.263217	−	0.00415208i
$265$	−13.5984	−	0.836371i	−0.835345	−	0.0513779i
$266$		0			0
$267$	0.643790	−	2.25948i	0.0393993	−	0.138278i
$268$	0.685884	+	2.55975i	0.0418970	+	0.156362i
$269$	−3.30165	−	5.71862i	−0.201305	−	0.348671i	0.747644	−	0.664100i	$-0.231185\pi$
$269$	−3.30165	−	5.71862i	−0.201305	−	0.348671i	−0.948949	+	0.315429i	$0.897852\pi$
$270$	−7.40304	+	19.0558i	−0.450535	+	1.15970i
$271$	−11.9146	+	20.6367i	−0.723759	+	1.25359i	0.235723	+	0.971820i	$0.424254\pi$
$271$	−11.9146	+	20.6367i	−0.723759	+	1.25359i	−0.959483	+	0.281768i	$0.909079\pi$
$272$	−10.6489	+	10.6489i	−0.645687	+	0.645687i
$273$		0			0
$274$			6.51800i			0.393767i
$275$	4.67493	−	6.19505i	0.281909	−	0.373575i
$276$	5.18403	−	8.66061i	0.312042	−	0.521307i
$277$	−5.26787	+	19.6600i	−0.316516	+	1.18125i	0.606055	+	0.795423i	$0.292751\pi$
$277$	−5.26787	+	19.6600i	−0.316516	+	1.18125i	−0.922570	+	0.385829i	$0.873915\pi$
$278$	−10.7984	+	2.89344i	−0.647648	+	0.173537i
$279$	−14.7811	−	9.16732i	−0.884920	−	0.548833i
$280$		0			0
$281$		−	1.50698i		−	0.0898991i	−0.998989	−	0.0449495i	$-0.985687\pi$
$281$		−	1.50698i		−	0.0898991i	0.998989	−	0.0449495i	$-0.0143127\pi$
$282$	0.110941	−	0.107495i	0.00660643	−	0.00640124i
$283$	11.5991	+	3.10797i	0.689496	+	0.184750i	0.586521	−	0.809934i	$-0.300497\pi$
$283$	11.5991	+	3.10797i	0.689496	+	0.184750i	0.102975	+	0.994684i	$0.467164\pi$
$284$	3.14257	+	5.44310i	0.186477	+	0.322988i
$285$	1.25751	−	16.2564i	0.0744882	−	0.962946i
$286$	−17.4148			−1.02976
$287$		0			0
$288$	−16.3547	+	3.83372i	−0.963712	+	0.225904i
$289$	−6.83695	−	3.94731i	−0.402173	−	0.232195i
$290$	10.4631	−	5.21224i	0.614412	−	0.306073i
$291$	−23.0796	−	13.8149i	−1.35295	−	0.809844i
$292$	−10.8788	+	2.91498i	−0.636636	+	0.170586i
$293$	−2.35851	−	2.35851i	−0.137786	−	0.137786i	0.634850	−	0.772635i	$-0.281062\pi$
$293$	−2.35851	−	2.35851i	−0.137786	−	0.137786i	−0.772635	+	0.634850i	$0.781062\pi$
$294$		0			0
$295$	−8.27157	+	7.31304i	−0.481590	+	0.425782i
$296$	2.39908	+	1.38511i	0.139444	+	0.0805079i
$297$	−2.45368	+	7.68321i	−0.142377	+	0.445825i
$298$	7.27339	+	1.94890i	0.421336	+	0.112897i
$299$	−16.9557	+	29.3681i	−0.980573	+	1.69840i
$300$	3.69921	−	8.73904i	0.213574	−	0.504549i
$301$		0			0
$302$	−6.48486	+	6.48486i	−0.373162	+	0.373162i
$303$	15.8017	−	15.3110i	0.907787	−	0.879592i
$304$	18.1961	−	10.5055i	1.04362	−	0.602532i
$305$	7.03267	+	2.35576i	0.402689	+	0.134891i
$306$	7.52486	+	14.0382i	0.430167	+	0.802510i
$307$	0.793602	+	0.793602i	0.0452933	+	0.0452933i	0.729391	−	0.684097i	$-0.239804\pi$
$307$	0.793602	+	0.793602i	0.0452933	+	0.0452933i	−0.684097	+	0.729391i	$0.739804\pi$
$308$		0			0
$309$	1.74856	+	3.14203i	0.0994722	+	0.178744i
$310$	19.0167	+	12.5962i	1.08007	+	0.715415i
$311$	8.58683	−	4.95761i	0.486914	−	0.281120i	−0.236379	−	0.971661i	$-0.575961\pi$
$311$	8.58683	−	4.95761i	0.486914	−	0.281120i	0.723293	+	0.690541i	$0.242627\pi$
$312$	17.0422	−	4.27952i	0.964824	−	0.242280i
$313$	3.64245	+	13.5938i	0.205884	+	0.768368i	0.989178	+	0.146718i	$0.0468709\pi$
$313$	3.64245	+	13.5938i	0.205884	+	0.768368i	−0.783295	+	0.621650i	$0.786462\pi$
$314$	10.8489			0.612238
$315$		0			0
$316$	−3.93800			−0.221530
$317$	5.48264	+	20.4615i	0.307936	+	1.14923i	0.930389	+	0.366574i	$0.119469\pi$
$317$	5.48264	+	20.4615i	0.307936	+	1.14923i	−0.622453	+	0.782657i	$0.713864\pi$
$318$	−18.0090	+	4.52231i	−1.00990	+	0.253599i
$319$	3.99396	−	2.30592i	0.223619	−	0.129106i
$320$	−0.284180	+	0.0577161i	−0.0158861	+	0.00322643i
$321$	−16.1426	−	29.0070i	−0.900992	−	1.61901i
$322$		0			0
$323$	−8.98273	−	8.98273i	−0.499812	−	0.499812i
$324$	−0.621806	+	9.84240i	−0.0345448	+	0.546800i
$325$	−11.9636	+	29.5529i	−0.663622	+	1.63930i
$326$	−11.5146	+	6.64794i	−0.637733	+	0.368195i
$327$	6.02248	−	5.83543i	0.333044	−	0.322700i
$328$	−3.02009	+	3.02009i	−0.166757	+	0.166757i
$329$		0			0
$330$	3.51746	−	9.97544i	0.193630	−	0.549130i
$331$	1.55123	−	2.68682i	0.0852635	−	0.147681i	−0.820240	−	0.572020i	$-0.806160\pi$
$331$	1.55123	−	2.68682i	0.0852635	−	0.147681i	0.905503	+	0.424339i	$0.139493\pi$
$332$	18.2825	+	4.89878i	1.00338	+	0.268855i
$333$	3.80837	−	3.57536i	0.208697	−	0.195929i
$334$	−29.7879	−	17.1981i	−1.62992	−	0.941037i
$335$	5.39754	+	0.331976i	0.294899	+	0.0181378i
$336$		0			0
$337$	−23.2030	−	23.2030i	−1.26395	−	1.26395i	−0.949163	−	0.314784i	$-0.898068\pi$
$337$	−23.2030	−	23.2030i	−1.26395	−	1.26395i	−0.314784	−	0.949163i	$-0.601932\pi$
$338$	47.0092	−	12.5961i	2.55696	−	0.685136i
$339$	−22.3251	−	13.3633i	−1.21253	−	0.725794i
$340$	−3.29676	−	6.61793i	−0.178792	−	0.358908i
$341$	7.79356	+	4.49961i	0.422045	+	0.243668i
$342$	−5.07157	−	21.6354i	−0.274239	−	1.16991i
$343$		0			0
$344$	−4.71541			−0.254238
$345$	−13.3977	−	15.6443i	−0.721310	−	0.842258i
$346$	−2.57083	−	4.45282i	−0.138209	−	0.239385i
$347$	−19.3753	−	5.19161i	−1.04012	−	0.278700i	−0.301959	−	0.953321i	$-0.597640\pi$
$347$	−19.3753	−	5.19161i	−1.04012	−	0.278700i	−0.738164	+	0.674621i	$0.764307\pi$
$348$	4.04982	−	3.92404i	0.217093	−	0.210351i
$349$			9.27152i			0.496293i	0.968723	+	0.248146i	$0.0798214\pi$
$349$			9.27152i			0.496293i	−0.968723	+	0.248146i	$0.920179\pi$
$350$		0			0
$351$	1.56726	−	33.0963i	0.0836544	−	1.76655i
$352$	8.39520	−	2.24949i	0.447466	−	0.119898i
$353$	−7.40914	+	27.6513i	−0.394349	+	1.47173i	0.428538	+	0.903524i	$0.359029\pi$
$353$	−7.40914	+	27.6513i	−0.394349	+	1.47173i	−0.822887	+	0.568205i	$0.807638\pi$
$354$	−7.72831	+	12.9111i	−0.410755	+	0.686220i
$355$	12.5690	−	2.55272i	0.667092	−	0.135484i
$356$			1.48635i			0.0787765i
$357$		0			0
$358$	−14.8285	+	14.8285i	−0.783710	+	0.783710i
$359$	−9.41445	+	16.3063i	−0.496876	+	0.860614i	−0.999994	−	0.00360404i	$-0.998853\pi$
$359$	−9.41445	+	16.3063i	−0.496876	+	0.860614i	0.503118	+	0.864218i	$0.332186\pi$
$360$	−0.990832	+	10.6264i	−0.0522214	+	0.560060i
$361$	−0.638264	−	1.10551i	−0.0335928	−	0.0581845i
$362$	8.01230	+	29.9023i	0.421117	+	1.57163i
$363$	−4.07730	+	14.3099i	−0.214003	+	0.751076i
$364$		0			0
$365$	−1.41088	+	22.9393i	−0.0738490	+	1.20070i
$366$	10.1069	+	0.159431i	0.528298	+	0.00833359i
$367$	−0.344800	+	1.28681i	−0.0179984	+	0.0671711i	−0.974341	−	0.225077i	$-0.927737\pi$
$367$	−0.344800	+	1.28681i	−0.0179984	+	0.0671711i	0.956343	+	0.292248i	$0.0944033\pi$
$368$	6.86957	−	25.6376i	0.358101	−	1.33645i
$369$	3.80488	+	7.09829i	0.198074	+	0.369522i
$370$	−5.13231	+	4.53756i	−0.266816	+	0.235897i
$371$		0			0
$372$	10.5825	+	3.01526i	0.548679	+	0.156334i
$373$	2.70837	+	10.1078i	0.140234	+	0.523361i	0.999921	+	0.0125400i	$0.00399170\pi$
$373$	2.70837	+	10.1078i	0.140234	+	0.523361i	−0.859687	+	0.510821i	$0.829342\pi$
$374$	−4.12053	−	7.13697i	−0.213068	−	0.369044i
$375$	−14.5119	−	12.8221i	−0.749391	−	0.662128i
$376$	0.0403224	−	0.0698404i	0.00207947	−	0.00360174i
$377$	−13.3966	+	13.3966i	−0.689958	+	0.689958i
$378$		0			0
$379$			21.9486i			1.12743i	0.825971	+	0.563713i	$0.190627\pi$
$379$			21.9486i			1.12743i	−0.825971	+	0.563713i	$0.809373\pi$
$380$	2.05310	+	10.1089i	0.105322	+	0.518578i
$381$	21.3526	+	12.7812i	1.09393	+	0.654800i
$382$	2.52295	−	9.41578i	0.129085	−	0.481753i
$383$	26.4066	−	7.07564i	1.34932	−	0.361548i	0.489434	−	0.872040i	$-0.337203\pi$
$383$	26.4066	−	7.07564i	1.34932	−	0.361548i	0.859882	+	0.510492i	$0.170537\pi$
$384$	−17.2943	+	9.62440i	−0.882545	+	0.491143i
$385$		0			0
$386$			34.5939i			1.76079i
$387$	−2.57108	+	8.51181i	−0.130695	+	0.432679i
$388$	16.4373	+	4.40437i	0.834480	+	0.223598i
$389$	15.3981	+	26.6702i	0.780712	+	1.35223i	0.931527	+	0.363671i	$0.118477\pi$
$389$	15.3981	+	26.6702i	0.780712	+	1.35223i	−0.150815	+	0.988562i	$0.548190\pi$
$390$	−3.35123	+	43.3231i	−0.169696	+	2.19375i
$391$	−16.0476			−0.811562
$392$		0			0
$393$	0.848491	+	0.241759i	0.0428007	+	0.0121951i
$394$	−27.4008	−	15.8198i	−1.38043	−	0.796992i
$395$	−2.55245	+	7.61982i	−0.128427	+	0.383395i
$396$	0.160942	−	5.10009i	0.00808763	−	0.256289i
$397$	−28.4481	+	7.62264i	−1.42777	+	0.382569i	−0.888233	−	0.459393i	$-0.848067\pi$
$397$	−28.4481	+	7.62264i	−1.42777	+	0.382569i	−0.539536	+	0.841963i	$0.681400\pi$
$398$	−7.60777	−	7.60777i	−0.381343	−	0.381343i
$399$		0			0
$400$	3.05804	−	24.7660i	0.152902	−	1.23830i
$401$	−18.1072	−	10.4542i	−0.904231	−	0.522058i	−0.0256602	−	0.999671i	$-0.508169\pi$
$401$	−18.1072	−	10.4542i	−0.904231	−	0.522058i	−0.878570	+	0.477613i	$0.841502\pi$
$402$	7.14823	−	1.79502i	0.356521	−	0.0895272i
$403$	−35.7095	−	9.56833i	−1.77882	−	0.476632i
$404$	−6.96001	+	12.0551i	−0.346273	+	0.599763i
$405$	18.6415	+	7.58258i	0.926302	+	0.376782i
$406$		0			0
$407$	−1.91113	+	1.91113i	−0.0947311	+	0.0947311i
$408$	5.78621	+	5.97168i	0.286460	+	0.295642i
$409$	−10.0262	+	5.78865i	−0.495765	+	0.286230i	−0.726963	−	0.686677i	$-0.759069\pi$
$409$	−10.0262	+	5.78865i	−0.495765	+	0.286230i	0.231198	+	0.972907i	$0.425736\pi$
$410$	−4.70952	−	9.45391i	−0.232587	−	0.466895i
$411$	6.41558	+	0.101202i	0.316457	+	0.00499192i
$412$	−1.60858	−	1.60858i	−0.0792493	−	0.0792493i
$413$		0			0
$414$	−23.8559	−	14.7956i	−1.17246	−	0.727165i
$415$	21.3288	−	32.2004i	1.04699	−	1.58066i
$416$	−30.9210	+	17.8522i	−1.51602	+	0.875277i
$417$	2.68031	+	10.6737i	0.131255	+	0.522693i
$418$	2.97581	+	11.1059i	0.145552	+	0.543206i
$419$	−0.525515			−0.0256731			−0.0128365	−	0.999918i	$-0.504086\pi$
$419$	−0.525515			−0.0256731			−0.0128365	+	0.999918i	$0.504086\pi$
$420$		0			0
$421$	−15.5297			−0.756871			−0.378435	−	0.925628i	$-0.623538\pi$
$421$	−15.5297			−0.756871			−0.378435	+	0.925628i	$0.623538\pi$
$422$	5.68780	+	21.2272i	0.276878	+	1.03332i
$423$	−0.104083	−	0.110867i	−0.00506071	−	0.00539051i
$424$	−8.39486	+	4.84677i	−0.407690	+	0.235380i
$425$	−14.9422	+	2.08959i	−0.724801	+	0.101360i
$426$	15.2740	−	8.50008i	0.740026	−	0.411830i
$427$		0			0
$428$	14.8503	+	14.8503i	0.717818	+	0.717818i
$429$	−0.270392	+	17.1412i	−0.0130546	+	0.827583i
$430$	3.70382	−	11.0570i	0.178614	−	0.533216i
$431$	−19.9310	+	11.5072i	−0.960044	+	0.554282i	−0.896187	−	0.443677i	$-0.853674\pi$
$431$	−19.9310	+	11.5072i	−0.960044	+	0.554282i	−0.0638575	+	0.997959i	$0.520340\pi$
$432$	5.51959	+	25.3389i	0.265561	+	1.21912i
$433$	15.4001	−	15.4001i	0.740081	−	0.740081i	−0.232513	−	0.972593i	$-0.574695\pi$
$433$	15.4001	−	15.4001i	0.740081	−	0.740081i	0.972593	+	0.232513i	$0.0746947\pi$
$434$		0			0
$435$	−4.96788	−	10.3796i	−0.238192	−	0.497663i
$436$	−2.65265	+	4.59453i	−0.127039	+	0.220038i
$437$	21.6262	+	5.79471i	1.03452	+	0.277199i
$438$	7.62874	+	30.3797i	0.364515	+	1.45160i
$439$	−5.23329	−	3.02144i	−0.249771	−	0.144205i	0.369888	−	0.929076i	$-0.379396\pi$
$439$	−5.23329	−	3.02144i	−0.249771	−	0.144205i	−0.619659	+	0.784871i	$0.712729\pi$
$440$	0.338988	−	5.51155i	0.0161606	−	0.262753i
$441$		0			0
$442$	23.9388	+	23.9388i	1.13865	+	1.13865i
$443$	−11.8124	+	3.16511i	−0.561222	+	0.150379i	−0.528268	−	0.849078i	$-0.677158\pi$
$443$	−11.8124	+	3.16511i	−0.561222	+	0.150379i	−0.0329544	+	0.999457i	$0.510492\pi$
$444$	−1.69731	+	2.83559i	−0.0805509	+	0.134571i
$445$	2.87601	+	0.963390i	0.136336	+	0.0456690i
$446$	−18.9724	−	10.9537i	−0.898370	−	0.518674i
$447$	2.03121	−	7.12884i	0.0960727	−	0.337183i
$448$		0			0
$449$	20.7599			0.979723			0.489861	−	0.871800i	$-0.337047\pi$
$449$	20.7599			0.979723			0.489861	+	0.871800i	$0.337047\pi$
$450$	−24.1392	−	10.6701i	−1.13793	−	0.502992i
$451$	−2.08351	−	3.60875i	−0.0981087	−	0.169929i
$452$	15.9000	+	4.26039i	0.747873	+	0.200392i
$453$	6.28227	+	6.48365i	0.295167	+	0.304628i
$454$		−	39.1715i		−	1.83841i
$455$		0			0
$456$	−5.64130	−	10.1370i	−0.264178	−	0.474707i
$457$	−23.6425	+	6.33500i	−1.10595	+	0.296339i	−0.765186	−	0.643810i	$-0.777353\pi$
$457$	−23.6425	+	6.33500i	−1.10595	+	0.296339i	−0.340765	+	0.940148i	$0.610686\pi$
$458$	−3.76809	+	14.0627i	−0.176071	+	0.657106i
$459$	13.9344	−	7.18865i	0.650404	−	0.335537i
$460$	10.8637	+	7.19586i	0.506523	+	0.335509i
$461$			4.36421i			0.203262i	0.994822	+	0.101631i	$0.0324061\pi$
$461$			4.36421i			0.203262i	−0.994822	+	0.101631i	$0.967594\pi$
$462$		0			0
$463$	2.04147	−	2.04147i	0.0948752	−	0.0948752i	−0.658076	−	0.752951i	$-0.728630\pi$
$463$	2.04147	−	2.04147i	0.0948752	−	0.0948752i	0.752951	+	0.658076i	$0.228630\pi$
$464$	7.41424	−	12.8418i	0.344197	−	0.596167i
$465$	12.6935	−	18.5223i	0.588648	−	0.858950i
$466$	15.7291	+	27.2436i	0.728636	+	1.26203i
$467$	−5.11079	−	19.0737i	−0.236499	−	0.882628i	−0.977467	−	0.211087i	$-0.932300\pi$
$467$	−5.11079	−	19.0737i	−0.236499	−	0.882628i	0.740968	−	0.671540i	$-0.234367\pi$
$468$	4.78399	+	20.4086i	0.221140	+	0.943388i
$469$		0			0
$470$	0.132094	+	0.149408i	0.00609306	+	0.00689169i
$471$	0.168446	−	10.6784i	0.00776157	−	0.492035i
$472$	−2.03316	+	7.58785i	−0.0935837	+	0.349259i
$473$	1.19071	−	4.44379i	0.0547489	−	0.204326i
$474$	−0.172742	+	10.9508i	−0.00793429	+	0.502985i
$475$	20.8910	+	2.57956i	0.958544	+	0.118358i
$476$		0			0
$477$	4.17163	+	17.7963i	0.191006	+	0.814836i
$478$	11.7608	+	43.8920i	0.537928	+	2.00757i
$479$	−8.00337	−	13.8622i	−0.365683	−	0.633382i	0.623202	−	0.782061i	$-0.285831\pi$
$479$	−8.00337	−	13.8622i	−0.365683	−	0.633382i	−0.988886	+	0.148679i	$0.952498\pi$
$480$	−3.98055	−	21.3178i	−0.181686	−	0.973018i
$481$	5.55149	−	9.61547i	0.253126	−	0.438428i
$482$	13.0880	−	13.0880i	0.596140	−	0.596140i
$483$		0			0
$484$		−	9.41347i		−	0.427885i
$485$	19.1762	−	28.9506i	0.870747	−	1.31458i
$486$	27.3424	+	2.16085i	1.24028	+	0.0980182i
$487$	7.54362	−	28.1532i	0.341834	−	1.27574i	−0.554433	−	0.832228i	$-0.687065\pi$
$487$	7.54362	−	28.1532i	0.341834	−	1.27574i	0.896267	−	0.443514i	$-0.146268\pi$
$488$	5.09719	−	1.36579i	0.230739	−	0.0618263i
$489$	6.36470	+	11.4369i	0.287822	+	0.517192i
$490$		0			0
$491$			29.8846i			1.34867i	0.738423	+	0.674337i	$0.235571\pi$
$491$			29.8846i			1.34867i	−0.738423	+	0.674337i	$0.764429\pi$
$492$	−3.54557	−	3.65922i	−0.159847	−	0.164970i
$493$	−8.65997	−	2.32043i	−0.390026	−	0.104507i
$494$	−23.6164	−	40.9048i	−1.06255	−	1.84039i
$495$	−9.76408	−	3.61708i	−0.438863	−	0.162575i
$496$	28.9353			1.29923
$497$		0			0
$498$	14.4244	−	50.6249i	0.646374	−	2.26855i
$499$	0.814586	+	0.470302i	0.0364659	+	0.0210536i	0.518122	−	0.855307i	$-0.326631\pi$
$499$	0.814586	+	0.470302i	0.0364659	+	0.0210536i	−0.481656	+	0.876360i	$0.659965\pi$
$500$	11.0523	+	5.28559i	0.494276	+	0.236379i
$501$	−17.3903	+	29.0528i	−0.776943	+	1.29799i
$502$	11.8043	−	3.16296i	0.526852	−	0.141170i
$503$	23.0051	+	23.0051i	1.02575	+	1.02575i	0.999660	+	0.0260875i	$0.00830487\pi$
$503$	23.0051	+	23.0051i	1.02575	+	1.02575i	0.0260875	+	0.999660i	$0.491695\pi$
$504$		0			0
$505$	18.8147	+	21.2808i	0.837245	+	0.946984i
$506$	12.5784	+	7.26216i	0.559179	+	0.322842i
$507$	−11.6683	−	46.4661i	−0.518205	−	2.06363i
$508$	−15.2074	−	4.07481i	−0.674719	−	0.180791i
$509$	12.9064	−	22.3545i	0.572066	−	0.990847i	−0.424288	−	0.905527i	$-0.639475\pi$
$509$	12.9064	−	22.3545i	0.572066	−	0.990847i	0.996354	−	0.0853198i	$-0.0271912\pi$
$510$	−18.5477	+	8.87730i	−0.821306	+	0.393094i
$511$		0			0
$512$	8.53124	−	8.53124i	0.377031	−	0.377031i
$513$	−21.3742	+	4.65595i	−0.943693	+	0.205565i
$514$	−17.6069	+	10.1654i	−0.776607	+	0.448374i
$515$	−4.15514	+	2.06991i	−0.183097	+	0.0912110i
$516$	0.0887245	−	5.62459i	0.00390588	−	0.247609i
$517$	0.0556354	+	0.0556354i	0.00244684	+	0.00244684i
$518$		0			0
$519$	−4.42276	+	2.46130i	−0.194138	+	0.108039i
$520$	4.51497	+	22.2306i	0.197995	+	0.974876i
$521$	38.2633	−	22.0913i	1.67635	−	0.967838i	0.712386	−	0.701787i	$-0.247614\pi$
$521$	38.2633	−	22.0913i	1.67635	−	0.967838i	0.963959	−	0.266051i	$-0.0857190\pi$
$522$	−10.7343	−	11.4338i	−0.469827	−	0.500446i
$523$	−4.78341	−	17.8519i	−0.209164	−	0.780611i	−0.988140	−	0.153557i	$-0.950927\pi$
$523$	−4.78341	−	17.8519i	−0.209164	−	0.780611i	0.778976	−	0.627054i	$-0.215740\pi$
$524$	−0.558162			−0.0243834
$525$		0			0
$526$	−0.295757			−0.0128956
$527$	−4.52794	−	16.8985i	−0.197240	−	0.736111i
$528$	−3.26794	−	13.0138i	−0.142219	−	0.566353i
$529$	4.57503	−	2.64140i	0.198915	−	0.114843i
$530$	−4.77112	−	23.4918i	−0.207244	−	1.02042i
$531$	12.5883	+	7.80733i	0.546285	+	0.338809i
$532$		0			0
$533$	12.1045	+	12.1045i	0.524303	+	0.524303i
$534$	4.13323	+	0.0651993i	0.178862	+	0.00282145i
$535$	38.3599	−	19.1092i	1.65845	−	0.826164i
$536$	3.33212	−	1.92380i	0.143926	−	0.0830956i
$537$	14.3652	+	14.8257i	0.619906	+	0.639777i
$538$	8.21544	−	8.21544i	0.354193	−	0.354193i
$539$		0			0
$540$	−12.6566	−	1.38182i	−0.544654	−	0.0594640i
$541$	−10.7795	+	18.6706i	−0.463446	+	0.802713i	−0.999130	−	0.0417061i	$-0.986721\pi$
$541$	−10.7795	+	18.6706i	−0.463446	+	0.802713i	0.535683	+	0.844419i	$0.320054\pi$
$542$	−40.4984	−	10.8515i	−1.73955	−	0.466112i
$543$	29.5568	−	7.42212i	1.26841	−	0.318514i
$544$	−14.6325	−	8.44806i	−0.627362	−	0.362207i
$545$	7.17082	+	8.11071i	0.307164	+	0.347425i
$546$		0			0
$547$	−29.6665	−	29.6665i	−1.26845	−	1.26845i	−0.946891	−	0.321555i	$-0.895795\pi$
$547$	−29.6665	−	29.6665i	−1.26845	−	1.26845i	−0.321555	−	0.946891i	$-0.604205\pi$
$548$	−3.92099	+	1.05063i	−0.167497	+	0.0448806i
$549$	0.313852	−	9.94565i	0.0133949	−	0.424470i
$550$	12.6576	+	5.12404i	0.539721	+	0.218490i
$551$	10.8325	+	6.25415i	0.461480	+	0.266436i
$552$	−14.0939	−	4.01574i	−0.599876	−	0.170921i
$553$		0			0
$554$	−35.8116			−1.52149
$555$	4.38657	+	5.12211i	0.186200	+	0.217422i
$556$	−3.48118	−	6.02957i	−0.147635	−	0.255711i
$557$	26.2818	+	7.04218i	1.11359	+	0.298387i	0.768289	−	0.640103i	$-0.221108\pi$
$557$	26.2818	+	7.04218i	1.11359	+	0.298387i	0.345306	+	0.938490i	$0.387775\pi$
$558$	8.84902	−	29.2956i	0.374609	−	1.24018i
$559$			18.8993i			0.799354i
$560$		0			0
$561$	−7.08880	+	3.94497i	−0.299290	+	0.166557i
$562$	2.56116	−	0.686262i	0.108036	−	0.0289482i
$563$	−0.745132	+	2.78087i	−0.0314036	+	0.117200i	−0.979848	−	0.199742i	$-0.935989\pi$
$563$	−0.745132	+	2.78087i	−0.0314036	+	0.117200i	0.948445	+	0.316942i	$0.102656\pi$
$564$	0.0825476	+	0.0494110i	0.00347588	+	0.00208058i
$565$	18.5493	−	28.0042i	0.780376	−	1.17815i
$566$			21.1284i			0.888092i
$567$		0			0
$568$	6.45262	−	6.45262i	0.270746	−	0.270746i
$569$	−18.3062	+	31.7073i	−0.767437	+	1.32924i	0.171511	+	0.985182i	$0.445135\pi$
$569$	−18.3062	+	31.7073i	−0.767437	+	1.32924i	−0.938948	+	0.344058i	$0.888198\pi$
$570$	28.2009	−	5.26580i	1.18121	−	0.220560i
$571$	4.94431	+	8.56380i	0.206913	+	0.358384i	0.950741	−	0.309988i	$-0.100325\pi$
$571$	4.94431	+	8.56380i	0.206913	+	0.358384i	−0.743827	+	0.668372i	$0.766992\pi$
$572$	−2.80707	−	10.4761i	−0.117370	−	0.438029i
$573$	−9.22865	−	2.62950i	−0.385533	−	0.109849i
$574$		0			0
$575$	20.9650	−	16.3566i	0.874300	−	0.682118i
$576$	0.183802	+	0.342896i	0.00765841	+	0.0142873i
$577$	−1.26261	+	4.71214i	−0.0525633	+	0.196169i	−0.987215	−	0.159397i	$-0.949045\pi$
$577$	−1.26261	+	4.71214i	−0.0525633	+	0.196169i	0.934651	+	0.355566i	$0.115712\pi$
$578$	3.59512	−	13.4172i	0.149537	−	0.558080i
$579$	34.0503	+	0.537124i	1.41508	+	0.0223221i
$580$	4.82202	+	5.45405i	0.200224	+	0.226467i
$581$		0			0
$582$	12.9687	−	45.5156i	0.537569	−	1.88668i
$583$	−2.44776	−	9.13517i	−0.101376	−	0.378340i
$584$	8.17607	+	14.1614i	0.338328	+	0.586002i
$585$	42.5903	+	3.97123i	1.76089	+	0.164190i
$586$	2.93432	−	5.08239i	0.121216	−	0.209952i
$587$	−4.70846	+	4.70846i	−0.194339	+	0.194339i	−0.797568	−	0.603229i	$-0.793880\pi$
$587$	−4.70846	+	4.70846i	−0.194339	+	0.194339i	0.603229	+	0.797568i	$0.293880\pi$
$588$		0			0
$589$			24.4079i			1.00571i
$590$	−16.1955	−	10.7275i	−0.666758	−	0.441645i
$591$	−15.9967	+	26.7246i	−0.658016	+	1.09930i
$592$	−2.24918	+	8.39405i	−0.0924407	+	0.344993i
$593$	−20.8865	+	5.59652i	−0.857705	+	0.229821i	−0.660764	−	0.750594i	$-0.729768\pi$
$593$	−20.8865	+	5.59652i	−0.857705	+	0.229821i	−0.196941	+	0.980415i	$0.563101\pi$
$594$	−14.1752	−	0.671263i	−0.581617	−	0.0275422i
$595$		0			0
$596$			4.68955i			0.192092i
$597$	−7.60635	+	7.37011i	−0.311307	+	0.301638i
$598$	−57.6334	−	15.4428i	−2.35680	−	0.631504i
$599$	4.69422	+	8.13063i	0.191801	+	0.332208i	0.945847	−	0.324613i	$-0.105234\pi$
$599$	4.69422	+	8.13063i	0.191801	+	0.332208i	−0.754046	+	0.656821i	$0.771901\pi$
$600$	−13.6459	−	1.90392i	−0.557093	−	0.0777274i
$601$	4.87361			0.198799			0.0993993	−	0.995048i	$-0.468308\pi$
$601$	4.87361			0.198799			0.0993993	+	0.995048i	$0.468308\pi$
$602$		0			0
$603$	−1.65582	−	7.06377i	−0.0674303	−	0.287659i
$604$	−4.94635	−	2.85578i	−0.201264	−	0.116200i
$605$	−18.2145	−	6.10141i	−0.740527	−	0.248058i
$606$	33.2174	+	19.8831i	1.34936	+	0.807696i
$607$	−3.50094	+	0.938074i	−0.142099	+	0.0380753i	−0.329167	−	0.944272i	$-0.606768\pi$
$607$	−3.50094	+	0.938074i	−0.142099	+	0.0380753i	0.187069	+	0.982347i	$0.440101\pi$
$608$	16.6685	+	16.6685i	0.675998	+	0.675998i
$609$		0			0
$610$	−0.801103	+	13.0250i	−0.0324357	+	0.527367i
$611$	−0.279919	−	0.161611i	−0.0113243	−	0.00653809i
$612$	−7.23195	+	6.78948i	−0.292334	+	0.274449i
$613$	−45.7845	−	12.2679i	−1.84922	−	0.495496i	−0.849721	−	0.527232i	$-0.823230\pi$
$613$	−45.7845	−	12.2679i	−1.84922	−	0.495496i	−0.999496	+	0.0317359i	$0.989896\pi$
$614$	−0.987354	+	1.71015i	−0.0398464	+	0.0690159i
$615$	−9.37848	+	4.48873i	−0.378177	+	0.181003i
$616$		0			0
$617$	−2.15297	+	2.15297i	−0.0866754	+	0.0866754i	−0.749115	−	0.662440i	$-0.769521\pi$
$617$	−2.15297	+	2.15297i	−0.0866754	+	0.0866754i	0.662440	+	0.749115i	$0.269521\pi$
$618$	−4.54370	+	4.40257i	−0.182774	+	0.177098i
$619$	−8.82839	+	5.09707i	−0.354843	+	0.204869i	−0.666816	−	0.745222i	$-0.732343\pi$
$619$	−8.82839	+	5.09707i	−0.354843	+	0.204869i	0.311973	+	0.950091i	$0.399010\pi$
$620$	−4.51214	+	13.4701i	−0.181212	+	0.540973i
$621$	−14.9335	+	23.2514i	−0.599262	+	0.933045i
$622$	12.3359	+	12.3359i	0.494626	+	0.494626i
$623$		0			0
$624$	26.8042	+	48.1650i	1.07303	+	1.92814i
$625$	17.3910	−	17.9598i	0.695639	−	0.718391i
$626$	−21.4444	+	12.3809i	−0.857090	+	0.494841i
$627$	10.9776	−	2.75661i	0.438402	−	0.110089i
$628$	1.74872	+	6.52631i	0.0697815	+	0.260428i
$629$	5.25417			0.209498
$630$		0			0
$631$	44.6402			1.77710			0.888550	−	0.458781i	$-0.151714\pi$
$631$	44.6402			1.77710			0.888550	+	0.458781i	$0.151714\pi$
$632$	1.47982	+	5.52275i	0.0588640	+	0.219683i
$633$	20.9819	−	5.26884i	0.833957	−	0.209418i
$634$	−32.2782	+	18.6358i	−1.28193	+	0.740123i
$635$	−17.7413	+	26.7844i	−0.704043	+	1.06291i
$636$	−5.62332	−	10.1047i	−0.222979	−	0.400676i
$637$		0			0
$638$	5.73777	+	5.73777i	0.227161	+	0.227161i
$639$	−8.12936	−	15.1659i	−0.321592	−	0.599955i
$640$	−11.3931	−	22.8706i	−0.450353	−	0.904041i
$641$	13.6251	−	7.86647i	0.538160	−	0.310707i	−0.206173	−	0.978516i	$-0.566101\pi$
$641$	13.6251	−	7.86647i	0.538160	−	0.310707i	0.744333	+	0.667809i	$0.232768\pi$
$642$	41.9471	−	40.6443i	1.65552	−	1.60410i
$643$	11.7811	−	11.7811i	0.464600	−	0.464600i	−0.435560	−	0.900160i	$-0.643449\pi$
$643$	11.7811	−	11.7811i	0.464600	−	0.464600i	0.900160	+	0.435560i	$0.143449\pi$
$644$		0			0
$645$	−10.8258	−	3.81730i	−0.426264	−	0.150306i
$646$	11.1758	−	19.3570i	0.439706	−	0.761593i
$647$	−14.7533	−	3.95315i	−0.580014	−	0.155414i	−0.0431286	−	0.999070i	$-0.513733\pi$
$647$	−14.7533	−	3.95315i	−0.580014	−	0.155414i	−0.536885	+	0.843655i	$0.680399\pi$
$648$	14.0369	−	2.82653i	0.551421	−	0.111036i
$649$	−6.63737	−	3.83209i	−0.260540	−	0.150423i
$650$	−55.6741	−	6.87448i	−2.18372	−	0.269639i
$651$		0			0
$652$	−5.85518	−	5.85518i	−0.229307	−	0.229307i
$653$	10.7688	−	2.88548i	0.421414	−	0.112918i	−0.0418789	−	0.999123i	$-0.513334\pi$
$653$	10.7688	−	2.88548i	0.421414	−	0.112918i	0.463293	+	0.886205i	$0.346668\pi$
$654$	12.6601	+	7.57801i	0.495047	+	0.296324i
$655$	−0.361777	+	1.08001i	−0.0141358	+	0.0421996i
$656$	−11.6032	−	6.69914i	−0.453031	−	0.261557i
$657$	30.0207	−	7.03717i	1.17122	−	0.274546i
$658$		0			0
$659$	−6.73141			−0.262219			−0.131109	−	0.991368i	$-0.541854\pi$
$659$	−6.73141			−0.262219			−0.131109	+	0.991368i	$0.541854\pi$
$660$	6.56785	+	0.508052i	0.255653	+	0.0197759i
$661$	2.21595	+	3.83814i	0.0861906	+	0.149286i	0.905898	−	0.423496i	$-0.139197\pi$
$661$	2.21595	+	3.83814i	0.0861906	+	0.149286i	−0.819707	+	0.572783i	$0.805864\pi$
$662$	5.27274	+	1.41283i	0.204931	+	0.0549110i
$663$	23.9344	−	23.1910i	0.929534	−	0.900664i
$664$		−	27.4807i		−	1.06646i
$665$		0			0
$666$	7.81072	+	4.84426i	0.302659	+	0.187711i
$667$	15.2626	−	4.08960i	0.590971	−	0.158350i
$668$	5.54427	−	20.6915i	0.214514	−	0.800578i
$669$	−11.0762	+	18.5042i	−0.428230	+	0.715414i
$670$	1.89377	+	9.32447i	0.0731628	+	0.360236i
$671$			5.14846i			0.198754i
$672$		0			0
$673$	−3.35642	+	3.35642i	−0.129381	+	0.129381i	−0.768832	−	0.639451i	$-0.779162\pi$
$673$	−3.35642	+	3.35642i	−0.129381	+	0.129381i	0.639451	+	0.768832i	$0.279162\pi$
$674$	28.8678	−	50.0005i	1.11195	−	1.92595i
$675$	−10.8772	+	23.5942i	−0.418664	+	0.908141i
$676$	15.1547	+	26.2487i	0.582873	+	1.00957i
$677$	−2.31012	−	8.62148i	−0.0887850	−	0.331350i	0.907219	−	0.420659i	$-0.138201\pi$
$677$	−2.31012	−	8.62148i	−0.0887850	−	0.331350i	−0.996004	+	0.0893084i	$0.971534\pi$
$678$	12.5447	−	44.0277i	0.481777	−	1.69087i
$679$		0			0
$680$	−8.04230	+	7.11034i	−0.308408	+	0.272669i
$681$	−38.5560	−	0.608198i	−1.47747	−	0.0233062i
$682$	−4.09814	+	15.2945i	−0.156926	+	0.585655i
$683$	−7.85053	+	29.2986i	−0.300392	+	1.12108i	0.636448	+	0.771320i	$0.280403\pi$
$683$	−7.85053	+	29.2986i	−0.300392	+	1.12108i	−0.936840	+	0.349759i	$0.886264\pi$
$684$	12.1976	−	6.53826i	0.466387	−	0.249997i
$685$	−0.508516	+	8.26788i	−0.0194294	+	0.315899i
$686$		0			0
$687$	13.7832	+	3.92722i	0.525862	+	0.149833i
$688$	−3.82851	−	14.2882i	−0.145960	−	0.544732i
$689$	19.4257	+	33.6464i	0.740062	+	1.28183i
$690$	20.4867	−	29.8940i	0.779916	−	1.13805i
$691$	9.39714	−	16.2763i	0.357484	−	0.619180i	−0.630056	−	0.776550i	$-0.716968\pi$
$691$	9.39714	−	16.2763i	0.357484	−	0.619180i	0.987540	+	0.157369i	$0.0503013\pi$
$692$	2.26427	−	2.26427i	0.0860745	−	0.0860745i
$693$		0			0
$694$		−	35.2932i		−	1.33971i
$695$	−13.9232	+	2.82777i	−0.528139	+	0.107263i
$696$	−7.02501	−	4.20500i	−0.266282	−	0.159390i
$697$	−2.09663	+	7.82473i	−0.0794155	+	0.296383i
$698$	−15.7572	+	4.22214i	−0.596420	+	0.159810i
$699$	27.0597	−	15.0589i	1.02349	−	0.569581i
$700$		0			0
$701$		−	10.0310i		−	0.378867i	−0.981894	−	0.189434i	$-0.939335\pi$
$701$		−	10.0310i		−	0.378867i	0.981894	−	0.189434i	$-0.0606652\pi$
$702$	56.9619	−	12.4080i	2.14989	−	0.468311i
$703$	−7.08066	−	1.89726i	−0.267052	−	0.0715564i
$704$	−0.100648	−	0.174327i	−0.00379331	−	0.00657021i
$705$	0.149111	−	0.127699i	0.00561586	−	0.00480942i
$706$	−50.3682			−1.89563
$707$		0			0
$708$	−9.01260	−	2.56794i	−0.338714	−	0.0965092i
$709$	41.9323	+	24.2096i	1.57480	+	0.909211i	0.995568	+	0.0940486i	$0.0299809\pi$
$709$	41.9323	+	24.2096i	1.57480	+	0.909211i	0.579232	+	0.815163i	$0.303352\pi$
$710$	10.0622	+	20.1989i	0.377627	+	0.758050i
$711$	10.7760	+	0.340055i	0.404132	+	0.0127530i
$712$	2.08450	−	0.558539i	0.0781198	−	0.0209321i
$713$	21.8023	+	21.8023i	0.816502	+	0.816502i
$714$		0			0
$715$	−22.0902	−	1.35865i	−0.826125	−	0.0508108i
$716$	−11.3105	−	6.53010i	−0.422692	−	0.244041i
$717$	43.3849	−	10.8945i	1.62024	−	0.406864i
$718$	−32.0003	−	8.57445i	−1.19424	−	0.319996i
$719$	5.34656	−	9.26052i	0.199393	−	0.345359i	−0.748939	−	0.662639i	$-0.769436\pi$
$719$	5.34656	−	9.26052i	0.199393	−	0.345359i	0.948332	+	0.317280i	$0.102770\pi$
$720$	−33.0035	+	5.62538i	−1.22997	+	0.209646i
$721$		0			0
$722$	1.58818	−	1.58818i	0.0591060	−	0.0591060i
$723$	−12.6791	−	13.0855i	−0.471540	−	0.486655i
$724$	−16.6967	+	9.63983i	−0.620527	+	0.358261i
$725$	13.6787	−	5.79527i	0.508015	−	0.215231i
$726$	−26.1769	−	0.412925i	−0.971515	−	0.0153251i
$727$	−30.9245	−	30.9245i	−1.14693	−	1.14693i	−0.987154	−	0.159773i	$-0.948924\pi$
$727$	−30.9245	−	30.9245i	−1.14693	−	1.14693i	−0.159773	−	0.987154i	$-0.551076\pi$
$728$		0			0
$729$	2.55143	−	26.8792i	0.0944974	−	0.995525i
$730$	−39.6286	+	8.04845i	−1.46672	+	0.297887i
$731$	−7.74534	+	4.47177i	−0.286472	+	0.165394i
$732$	1.53322	+	6.10567i	0.0566693	+	0.225672i
$733$	8.42207	+	31.4316i	0.311076	+	1.16095i	0.927587	+	0.373606i	$0.121879\pi$
$733$	8.42207	+	31.4316i	0.311076	+	1.16095i	−0.616511	+	0.787346i	$0.711455\pi$
$734$	−2.34399			−0.0865184
$735$		0			0
$736$	29.7782			1.09764
$737$	0.971576	+	3.62597i	0.0357885	+	0.133564i
$738$	−10.3311	+	9.69897i	−0.380291	+	0.357024i
$739$	−26.9299	+	15.5480i	−0.990631	+	0.571941i	−0.905463	−	0.424426i	$-0.860476\pi$
$739$	−26.9299	+	15.5480i	−0.990631	+	0.571941i	−0.0851681	+	0.996367i	$0.527143\pi$
$740$	−3.55691	−	2.35601i	−0.130754	−	0.0866086i
$741$	−40.6287	+	22.6102i	−1.49253	+	0.830606i
$742$		0			0
$743$	−4.41646	−	4.41646i	−0.162024	−	0.162024i	0.621439	−	0.783463i	$-0.286549\pi$
$743$	−4.41646	−	4.41646i	−0.162024	−	0.162024i	−0.783463	+	0.621439i	$0.786549\pi$
$744$	0.251985	−	15.9743i	0.00923821	−	0.585646i
$745$	9.07403	+	3.03957i	0.332447	+	0.111361i
$746$	−15.9451	+	9.20591i	−0.583792	+	0.337052i
$747$	−49.6054	−	14.9838i	−1.81497	−	0.548229i
$748$	3.62917	−	3.62917i	0.132695	−	0.132695i
$749$		0			0
$750$	15.1829	−	30.5024i	0.554402	−	1.11379i
$751$	10.3817	−	17.9816i	0.378834	−	0.656160i	−0.612059	−	0.790812i	$-0.709658\pi$
$751$	10.3817	−	17.9816i	0.378834	−	0.656160i	0.990893	+	0.134653i	$0.0429918\pi$
$752$	0.244362	+	0.0654766i	0.00891096	+	0.00238768i
$753$	−2.92998	−	11.6679i	−0.106774	−	0.425203i
$754$	−28.8685	−	16.6672i	−1.05133	−	0.606984i
$755$	−8.73178	+	7.71992i	−0.317782	+	0.280957i
$756$		0			0
$757$	27.7515	+	27.7515i	1.00865	+	1.00865i	0.999962	+	0.00868333i	$0.00276403\pi$
$757$	27.7515	+	27.7515i	1.00865	+	1.00865i	0.00868333	+	0.999962i	$0.497236\pi$
$758$	−37.3024	+	9.99514i	−1.35488	+	0.363040i
$759$	7.34334	−	12.2680i	0.266546	−	0.445301i
$760$	13.4055	−	6.67804i	0.486269	−	0.242238i
$761$	−44.7004	−	25.8078i	−1.62039	−	0.935531i	−0.986816	−	0.161846i	$-0.948255\pi$
$761$	−44.7004	−	25.8078i	−1.62039	−	0.935531i	−0.633570	−	0.773685i	$-0.718411\pi$
$762$	−11.9983	+	42.1099i	−0.434652	+	1.52548i
$763$		0			0
$764$	6.07087			0.219636
$765$	8.44983	+	18.3941i	0.305504	+	0.665039i
$766$	24.0505	+	41.6567i	0.868980	+	1.50512i
$767$	30.4119	+	8.14885i	1.09811	+	0.294238i
$768$	−23.9199	−	24.6867i	−0.863137	−	0.890804i
$769$			15.3442i			0.553327i	0.960967	+	0.276663i	$0.0892287\pi$
$769$			15.3442i			0.553327i	−0.960967	+	0.276663i	$0.910771\pi$
$770$		0			0
$771$	9.73225	+	17.4881i	0.350498	+	0.629818i
$772$	−20.8105	+	5.57615i	−0.748986	+	0.200690i
$773$	5.90138	−	22.0243i	0.212258	−	0.792158i	−0.774856	−	0.632138i	$-0.782178\pi$
$773$	5.90138	−	22.0243i	0.212258	−	0.792158i	0.987114	−	0.160020i	$-0.0511558\pi$
$774$	−15.6369	−	0.493449i	−0.562057	−	0.0177366i
$775$	23.1393	+	17.4615i	0.831189	+	0.627236i
$776$		−	24.7072i		−	0.886937i
$777$		0			0
$778$	−38.3147	+	38.3147i	−1.37365	+	1.37365i
$779$	5.65094	−	9.78772i	0.202466	−	0.350681i
$780$	−26.6018	+	4.96721i	−0.952498	+	0.177855i
$781$	4.45155	+	7.71032i	0.159289	+	0.275897i
$782$	−7.30788	−	27.2734i	−0.261329	−	0.975294i
$783$	−11.4208	+	10.3881i	−0.408148	+	0.371240i
$784$		0			0
$785$	13.7615	+	0.846400i	0.491168	+	0.0302093i
$786$	−0.0244839	+	1.55213i	−0.000873313	+	0.0553627i
$787$	2.26808	−	8.46457i	0.0808482	−	0.301729i	−0.913647	−	0.406507i	$-0.866747\pi$
$787$	2.26808	−	8.46457i	0.0808482	−	0.301729i	0.994496	+	0.104778i	$0.0334132\pi$
$788$	5.09996	−	19.0333i	0.181679	−	0.678034i
$789$	−0.00459209	+	0.291110i	−0.000163483	+	0.0103638i
$790$	−14.1125	−	0.867987i	−0.502099	−	0.0308816i
$791$		0			0
$792$	−7.21297	+	1.69080i	−0.256302	+	0.0600798i
$793$	−5.47405	−	20.4294i	−0.194389	−	0.725470i
$794$	−25.9098	−	44.8771i	−0.919505	−	1.59263i
$795$	−23.1967	+	4.33140i	−0.822704	+	0.153619i
$796$	3.35028	−	5.80285i	0.118747	−	0.205677i
$797$	24.6954	−	24.6954i	0.874755	−	0.874755i	−0.118231	−	0.992986i	$-0.537722\pi$
$797$	24.6954	−	24.6954i	0.874755	−	0.874755i	0.992986	+	0.118231i	$0.0377223\pi$
$798$		0			0
$799$		−	0.152956i		−	0.00541119i
$800$	27.7270	−	3.87748i	0.980296	−	0.137090i
$801$	0.128350	−	4.06727i	0.00453501	−	0.143710i
$802$	9.52143	−	35.5344i	0.336213	−	1.25477i
$803$	−15.4102	+	4.12916i	−0.543815	+	0.145715i
$804$	2.23203	+	4.01078i	0.0787177	+	0.141449i
$805$		0			0
$806$		−	65.0467i		−	2.29117i
$807$	−7.95879	−	8.21391i	−0.280163	−	0.289143i
$808$	19.5218	+	5.23084i	0.686773	+	0.184020i
$809$	−10.2032	−	17.6724i	−0.358725	−	0.621329i	0.629023	−	0.777386i	$-0.283455\pi$
$809$	−10.2032	−	17.6724i	−0.358725	−	0.621329i	−0.987748	+	0.156057i	$0.950122\pi$
$810$	−4.39773	+	35.1348i	−0.154521	+	1.23451i
$811$	−10.0632			−0.353368			−0.176684	−	0.984268i	$-0.556537\pi$
$811$	−10.0632			−0.353368			−0.176684	+	0.984268i	$0.556537\pi$
$812$		0			0
$813$	−11.3098	+	39.6935i	−0.396652	+	1.39211i
$814$	−4.11832	−	2.37772i	−0.144347	−	0.0833389i
$815$	−15.1245	+	7.53437i	−0.529789	+	0.263918i
$816$	−13.3969	+	22.3813i	−0.468986	+	0.783502i
$817$	12.0525	−	3.22947i	0.421665	−	0.112985i
$818$	−14.4038	−	14.4038i	−0.503617	−	0.503617i
$819$		0			0
$820$	4.92801	−	4.35694i	0.172094	−	0.152151i
$821$	48.4153	+	27.9526i	1.68971	+	0.975552i	0.954737	+	0.297452i	$0.0961368\pi$
$821$	48.4153	+	27.9526i	1.68971	+	0.975552i	0.734969	+	0.678100i	$0.237197\pi$
$822$	2.74958	+	10.9496i	0.0959026	+	0.381909i
$823$	35.2310	+	9.44013i	1.22808	+	0.329062i	0.813830	−	0.581103i	$-0.197378\pi$
$823$	35.2310	+	9.44013i	1.22808	+	0.329062i	0.414246	+	0.910165i	$0.364045\pi$
$824$	−1.65145	+	2.86039i	−0.0575309	+	0.0996464i
$825$	5.24005	−	12.3791i	0.182435	−	0.430986i
$826$		0			0
$827$	25.9659	−	25.9659i	0.902922	−	0.902922i	−0.0927663	−	0.995688i	$-0.529571\pi$
$827$	25.9659	−	25.9659i	0.902922	−	0.902922i	0.995688	+	0.0927663i	$0.0295710\pi$
$828$	5.05521	−	16.7358i	0.175681	−	0.581608i
$829$	10.9810	−	6.33987i	0.381385	−	0.220193i	−0.297036	−	0.954866i	$-0.595998\pi$
$829$	10.9810	−	6.33987i	0.381385	−	0.220193i	0.678421	+	0.734674i	$0.262665\pi$
$830$	64.4384	+	21.5852i	2.23669	+	0.749235i
$831$	−0.556030	+	35.2489i	−0.0192885	+	1.22277i
$832$	0.584729	+	0.584729i	0.0202718	+	0.0202718i
$833$		0			0
$834$	−16.9197	+	9.41593i	−0.585881	+	0.326047i
$835$	−36.4434	−	24.1392i	−1.26117	−	0.835372i
$836$	−6.20123	+	3.58028i	−0.214474	+	0.123827i
$837$	−28.6978	−	9.16483i	−0.991942	−	0.316783i
$838$	−0.239313	−	0.893128i	−0.00826693	−	0.0308526i
$839$	−27.2730			−0.941569			−0.470785	−	0.882248i	$-0.656029\pi$
$839$	−27.2730			−0.941569			−0.470785	+	0.882248i	$0.656029\pi$
$840$		0			0
$841$	−20.1723			−0.695596
$842$	−7.07203	−	26.3932i	−0.243718	−	0.909569i
$843$	−0.635712	−	2.53157i	−0.0218951	−	0.0871920i
$844$	−11.8527	+	6.84316i	−0.407987	+	0.235551i
$845$	60.6124	−	12.3102i	2.08513	−	0.423484i
$846$	0.141023	−	0.227380i	0.00484846	−	0.00781749i
$847$		0			0
$848$	−21.5021	−	21.5021i	−0.738385	−	0.738385i
$849$	20.7964	+	0.328051i	0.713730	+	0.0112587i
$850$	−10.3558	−	24.4431i	−0.355201	−	0.838390i
$851$	−8.01950	+	4.63006i	−0.274905	+	0.158716i
$852$	7.57533	+	7.81816i	0.259527	+	0.267846i
$853$	−8.57549	+	8.57549i	−0.293619	+	0.293619i	−0.838508	−	0.544889i	$-0.816572\pi$
$853$	−8.57549	+	8.57549i	−0.293619	+	0.293619i	0.544889	+	0.838508i	$0.316572\pi$
$854$		0			0
$855$	−4.74519	−	27.8395i	−0.162282	−	0.952092i
$856$	15.2460	−	26.4069i	0.521099	−	0.902570i
$857$	28.4758	+	7.63008i	0.972716	+	0.260638i	0.709974	−	0.704228i	$-0.248707\pi$
$857$	28.4758	+	7.63008i	0.972716	+	0.260638i	0.262742	+	0.964866i	$0.415373\pi$
$858$	−29.2551	+	7.34634i	−0.998751	+	0.250800i
$859$	8.25133	+	4.76391i	0.281532	+	0.162543i	0.634117	−	0.773237i	$-0.281364\pi$
$859$	8.25133	+	4.76391i	0.281532	+	0.162543i	−0.352585	+	0.935780i	$0.614697\pi$
$860$	7.24852	+	0.445820i	0.247172	+	0.0152023i
$861$		0			0
$862$	−28.6332	−	28.6332i	−0.975249	−	0.975249i
$863$	−44.2282	+	11.8509i	−1.50554	+	0.403409i	−0.914953	−	0.403561i	$-0.867772\pi$
$863$	−44.2282	+	11.8509i	−1.50554	+	0.403409i	−0.590592	+	0.806971i	$0.701106\pi$
$864$	−25.8570	+	13.3394i	−0.879673	+	0.453816i
$865$	−2.91363	−	5.84883i	−0.0990663	−	0.198866i
$866$	33.1859	+	19.1599i	1.12770	+	0.651080i
$867$	−13.1505	−	3.74695i	−0.446615	−	0.127253i
$868$		0			0
$869$	−5.57830			−0.189231
$870$	15.3781	−	13.1698i	0.521366	−	0.446498i
$871$	−7.71055	−	13.3551i	−0.261262	−	0.452519i
$872$	7.44029	+	1.99362i	0.251960	+	0.0675124i
$873$	−44.5991	−	13.4716i	−1.50945	−	0.455944i
$874$			39.3931i			1.33249i
$875$		0			0
$876$	−17.0457	+	9.48604i	−0.575919	+	0.320503i
$877$	30.4658	−	8.16328i	1.02876	−	0.275654i	0.295310	−	0.955402i	$-0.404577\pi$
$877$	30.4658	−	8.16328i	1.02876	−	0.275654i	0.733446	+	0.679747i	$0.237911\pi$
$878$	2.75185	−	10.2701i	0.0928705	−	0.346598i
$879$	−4.95697	−	2.96712i	−0.167194	−	0.100079i
$880$	16.9758	−	3.44773i	0.572253	−	0.116223i
$881$		−	31.6927i		−	1.06775i	−0.845562	−	0.533877i	$-0.820734\pi$
$881$		−	31.6927i		−	1.06775i	0.845562	−	0.533877i	$-0.179266\pi$
$882$		0			0
$883$	−19.2435	+	19.2435i	−0.647595	+	0.647595i	−0.952411	−	0.304816i	$-0.901405\pi$
$883$	−19.2435	+	19.2435i	−0.647595	+	0.647595i	0.304816	+	0.952411i	$0.401405\pi$
$884$	−10.5421	+	18.2594i	−0.354569	+	0.614131i
$885$	−10.8104	+	15.7745i	−0.363388	+	0.530253i
$886$	−10.7584	−	18.6341i	−0.361436	−	0.626025i
$887$	−2.66050	−	9.92913i	−0.0893309	−	0.333388i	0.906768	−	0.421630i	$-0.138542\pi$
$887$	−2.66050	−	9.92913i	−0.0893309	−	0.333388i	−0.996099	+	0.0882421i	$0.971875\pi$
$888$	4.61451	+	1.31480i	0.154853	+	0.0441219i
$889$		0			0
$890$	−0.327611	+	5.32658i	−0.0109815	+	0.178547i
$891$	−0.880807	+	13.9421i	−0.0295081	+	0.467077i
$892$	3.53123	−	13.1787i	0.118234	−	0.441257i
$893$	−0.0552316	+	0.206127i	−0.00184826	+	0.00689778i
$894$	13.0407	+	0.205709i	0.436145	+	0.00687993i
$895$	−19.9664	+	17.6526i	−0.667402	+	0.590061i
$896$		0			0
$897$	−16.0950	+	56.4880i	−0.537397	+	1.88608i
$898$	9.45382	+	35.2822i	0.315478	+	1.17738i
$899$	8.61290	+	14.9180i	0.287256	+	0.497543i
$900$	2.52778	−	16.2412i	0.0842593	−	0.541372i
$901$	−9.19269	+	15.9222i	−0.306253	+	0.530445i
$902$	5.18437	−	5.18437i	0.172621	−	0.172621i
$903$		0			0
$904$		−	23.8995i		−	0.794886i
$905$	7.83046	+	38.5553i	0.260293	+	1.28162i
$906$	−8.15829	+	13.6295i	−0.271041	+	0.452809i
$907$	7.33317	−	27.3678i	0.243494	−	0.908732i	−0.730640	−	0.682763i	$-0.760778\pi$
$907$	7.33317	−	27.3678i	0.243494	−	0.908732i	0.974134	−	0.225969i	$-0.0725550\pi$
$908$	23.5642	−	6.31400i	0.782005	−	0.209538i
$909$	20.0864	−	32.3867i	0.666225	−	1.07420i
$910$		0			0
$911$			34.2452i			1.13459i	0.823514	+	0.567296i	$0.192011\pi$
$911$			34.2452i			1.13459i	−0.823514	+	0.567296i	$0.807989\pi$
$912$	26.1358	−	25.3240i	0.865443	−	0.838563i
$913$	25.8977	+	6.93927i	0.857089	+	0.229656i
$914$	−21.5330	−	37.2963i	−0.712250	−	1.23365i
$915$	12.8079	+	0.990748i	0.423416	+	0.0327531i
$916$	−9.06698			−0.299582
$917$		0			0
$918$	18.5629	+	20.4084i	0.612667	+	0.673576i
$919$	38.4001	+	22.1703i	1.26670	+	0.731331i	0.974363	−	0.224984i	$-0.0722329\pi$
$919$	38.4001	+	22.1703i	1.26670	+	0.731331i	0.292340	+	0.956315i	$0.405566\pi$
$920$	6.00930	−	17.9396i	0.198121	−	0.591450i
$921$	1.66794	+	0.998392i	0.0549607	+	0.0328981i
$922$	−7.41711	+	1.98741i	−0.244270	+	0.0654518i
$923$	−25.8620	−	25.8620i	−0.851257	−	0.851257i
$924$		0			0
$925$	−6.86418	+	5.35535i	−0.225693	+	0.176083i
$926$	4.39920	+	2.53988i	0.144567	+	0.0834656i
$927$	4.26285	+	4.54066i	0.140010	+	0.149135i
$928$	16.0696	+	4.30584i	0.527511	+	0.141346i
$929$	−4.94121	+	8.55843i	−0.162116	+	0.280793i	−0.935627	−	0.352989i	$-0.885165\pi$
$929$	−4.94121	+	8.55843i	−0.162116	+	0.280793i	0.773511	+	0.633782i	$0.218499\pi$
$930$	37.2596	+	13.1382i	1.22179	+	0.430818i
$931$		0			0
$932$	−13.8534	+	13.8534i	−0.453784	+	0.453784i
$933$	12.3336	−	11.9506i	0.403785	−	0.391244i
$934$	30.0890	−	17.3719i	0.984542	−	0.568426i
$935$	−4.66996	−	9.37450i	−0.152724	−	0.306579i
$936$	26.8238	−	14.3783i	0.876764	−	0.469969i
$937$	22.4981	+	22.4981i	0.734980	+	0.734980i	0.971602	−	0.236622i	$-0.0760403\pi$
$937$	22.4981	+	22.4981i	0.734980	+	0.734980i	−0.236622	+	0.971602i	$0.576040\pi$
$938$		0			0
$939$	11.8534	+	21.2996i	0.386821	+	0.695088i
$940$	−0.0685865	+	0.103546i	−0.00223705	+	0.00337730i
$941$	−48.8567	+	28.2074i	−1.59268	+	0.919536i	−0.599839	+	0.800121i	$0.704769\pi$
$941$	−48.8567	+	28.2074i	−1.59268	+	0.919536i	−0.992844	+	0.119415i	$0.961898\pi$
$942$	18.2250	−	4.57654i	0.593802	−	0.149112i
$943$	−3.69516	−	13.7905i	−0.120331	−	0.449082i
$944$	−24.6427			−0.802052
$945$		0			0
$946$	8.09460			0.263178
$947$	−3.02006	−	11.2710i	−0.0981386	−	0.366258i	0.899338	−	0.437254i	$-0.144049\pi$
$947$	−3.02006	−	11.2710i	−0.0981386	−	0.366258i	−0.997477	+	0.0709958i	$0.977382\pi$
$948$	−6.61543	+	1.66122i	−0.214859	+	0.0539540i
$949$	56.7584	−	32.7695i	1.84246	−	1.06374i
$950$	5.12946	+	36.6795i	0.166422	+	1.19004i
$951$	17.8418	+	32.0603i	0.578560	+	1.03963i
$952$		0			0
$953$	−18.3169	−	18.3169i	−0.593344	−	0.593344i	0.345189	−	0.938533i	$-0.387815\pi$
$953$	−18.3169	−	18.3169i	−0.593344	−	0.593344i	−0.938533	+	0.345189i	$0.887815\pi$
$954$	−28.3456	+	15.1940i	−0.917723	+	0.491925i
$955$	3.93488	−	11.7468i	0.127330	−	0.380117i
$956$	−24.5081	+	14.1498i	−0.792650	+	0.457637i
$957$	5.73670	−	5.55853i	0.185441	−	0.179682i
$958$	19.9147	−	19.9147i	0.643414	−	0.643414i
$959$		0			0
$960$	−0.453045	+	0.216837i	−0.0146220	+	0.00699837i
$961$	−1.30666	+	2.26320i	−0.0421503	+	0.0730064i
$962$	18.8699	+	5.05616i	0.608389	+	0.163017i
$963$	−39.3543	−	41.9190i	−1.26818	−	1.35082i
$964$	9.98288	+	5.76362i	0.321527	+	0.185634i
$965$	−2.69892	+	43.8814i	−0.0868814	+	1.41259i
$966$		0			0
$967$	−6.55794	−	6.55794i	−0.210889	−	0.210889i	0.593756	−	0.804645i	$-0.297644\pi$
$967$	−6.55794	−	6.55794i	−0.210889	−	0.210889i	−0.804645	+	0.593756i	$0.797644\pi$
$968$	−13.2017	+	3.53738i	−0.424318	+	0.113696i
$969$	−18.8794	−	11.3007i	−0.606492	−	0.363032i
$970$	57.9351	+	19.4068i	1.86018	+	0.623114i
$971$	12.0561	+	6.96061i	0.386899	+	0.223377i	0.680816	−	0.732455i	$-0.261625\pi$
$971$	12.0561	+	6.96061i	0.386899	+	0.223377i	−0.293916	+	0.955831i	$0.594959\pi$
$972$	3.10739	+	16.7965i	0.0996696	+	0.538748i
$973$		0			0
$974$	51.2825			1.64320
$975$	−7.63088	+	54.6926i	−0.244384	+	1.75156i
$976$	8.27695	+	14.3361i	0.264939	+	0.458887i
$977$	−37.1577	−	9.95638i	−1.18878	−	0.318533i	−0.390377	−	0.920655i	$-0.627655\pi$
$977$	−37.1577	−	9.95638i	−1.18878	−	0.318533i	−0.798404	+	0.602122i	$0.794322\pi$
$978$	−16.5389	+	16.0252i	−0.528855	+	0.512429i
$979$			2.10546i			0.0672909i
$980$		0			0
$981$	7.65550	−	12.3435i	0.244421	−	0.394096i
$982$	−50.7898	+	13.6091i	−1.62077	+	0.434284i
$983$	13.4886	−	50.3403i	0.430221	−	1.60561i	−0.322030	−	0.946730i	$-0.604365\pi$
$983$	13.4886	−	50.3403i	0.430221	−	1.60561i	0.752251	−	0.658877i	$-0.228968\pi$
$984$	−3.79943	+	6.34745i	−0.121121	+	0.202349i
$985$	−33.5228	−	22.2047i	−1.06813	−	0.707501i
$986$		−	15.7746i		−	0.502365i
$987$		0			0
$988$	20.8002	−	20.8002i	0.661742	−	0.661742i
$989$	7.88119	−	13.6506i	0.250607	−	0.434065i
$990$	1.70089	−	18.2415i	0.0540577	−	0.579753i
$991$	20.9326	+	36.2563i	0.664945	+	1.15172i	0.979300	+	0.202413i	$0.0648782\pi$
$991$	20.9326	+	36.2563i	0.664945	+	1.15172i	−0.314356	+	0.949305i	$0.601788\pi$
$992$	8.40214	+	31.3572i	0.266768	+	0.995592i
$993$	1.47249	−	5.16795i	0.0467281	−	0.164000i
$994$		0			0
$995$	−9.05669	−	10.2438i	−0.287116	−	0.324749i
$996$	32.7792	+	0.517072i	1.03865	+	0.0163841i
$997$	−4.18963	+	15.6359i	−0.132687	+	0.495194i	−0.999997	−	0.00257448i	$-0.999181\pi$
$997$	−4.18963	+	15.6359i	−0.132687	+	0.495194i	0.867310	+	0.497769i	$0.165847\pi$
$998$	−0.428339	+	1.59858i	−0.0135588	+	0.0506023i
$999$	4.88941	−	7.61277i	0.154694	−	0.240857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.g.422.10		48
3.2	odd	2	inner	735.2.y.g.422.3		48
5.3	odd	4	inner	735.2.y.g.128.10		48
7.2	even	3		735.2.j.h.197.10		24
7.3	odd	6		735.2.y.j.557.3		48
7.4	even	3	inner	735.2.y.g.557.3		48
7.5	odd	6		105.2.j.a.92.10	yes	24
7.6	odd	2		735.2.y.j.422.10		48
15.8	even	4	inner	735.2.y.g.128.3		48
21.2	odd	6		735.2.j.h.197.3		24
21.5	even	6		105.2.j.a.92.3	yes	24
21.11	odd	6	inner	735.2.y.g.557.10		48
21.17	even	6		735.2.y.j.557.10		48
21.20	even	2		735.2.y.j.422.3		48
35.3	even	12		735.2.y.j.263.3		48
35.12	even	12		525.2.j.b.218.10		24
35.13	even	4		735.2.y.j.128.10		48
35.18	odd	12	inner	735.2.y.g.263.3		48
35.19	odd	6		525.2.j.b.407.3		24
35.23	odd	12		735.2.j.h.638.3		24
35.33	even	12		105.2.j.a.8.3	✓	24
105.23	even	12		735.2.j.h.638.10		24
105.38	odd	12		735.2.y.j.263.10		48
105.47	odd	12		525.2.j.b.218.3		24
105.53	even	12	inner	735.2.y.g.263.10		48
105.68	odd	12		105.2.j.a.8.10	yes	24
105.83	odd	4		735.2.y.j.128.3		48
105.89	even	6		525.2.j.b.407.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.3	✓	24	35.33	even	12
105.2.j.a.8.10	yes	24	105.68	odd	12
105.2.j.a.92.3	yes	24	21.5	even	6
105.2.j.a.92.10	yes	24	7.5	odd	6
525.2.j.b.218.3		24	105.47	odd	12
525.2.j.b.218.10		24	35.12	even	12
525.2.j.b.407.3		24	35.19	odd	6
525.2.j.b.407.10		24	105.89	even	6
735.2.j.h.197.3		24	21.2	odd	6
735.2.j.h.197.10		24	7.2	even	3
735.2.j.h.638.3		24	35.23	odd	12
735.2.j.h.638.10		24	105.23	even	12
735.2.y.g.128.3		48	15.8	even	4	inner
735.2.y.g.128.10		48	5.3	odd	4	inner
735.2.y.g.263.3		48	35.18	odd	12	inner
735.2.y.g.263.10		48	105.53	even	12	inner
735.2.y.g.422.3		48	3.2	odd	2	inner
735.2.y.g.422.10		48	1.1	even	1	trivial
735.2.y.g.557.3		48	7.4	even	3	inner
735.2.y.g.557.10		48	21.11	odd	6	inner
735.2.y.j.128.3		48	105.83	odd	4
735.2.y.j.128.10		48	35.13	even	4
735.2.y.j.263.3		48	35.3	even	12
735.2.y.j.263.10		48	105.38	odd	12
735.2.y.j.422.3		48	21.20	even	2
735.2.y.j.422.10		48	7.6	odd	2
735.2.y.j.557.3		48	7.3	odd	6
735.2.y.j.557.10		48	21.17	even	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.455388 + 1.69953i) q^{2} +(1.67990 - 0.421844i) q^{3} +(-0.948973 + 0.547890i) q^{4} +(0.445053 + 2.19133i) q^{5} +(1.48194 + 2.66293i) q^{6} +(1.12498 + 1.12498i) q^{8} +(2.64410 - 1.41731i) q^{9} +(-3.52156 + 1.75429i) q^{10} +(-1.34425 + 0.776103i) q^{11} +(-1.36305 + 1.32072i) q^{12} +(4.50889 - 4.50889i) q^{13} +(1.67204 + 3.49346i) q^{15} +(-2.49541 + 4.32218i) q^{16} +(2.91469 + 0.780989i) q^{17} +(3.61285 + 3.84829i) q^{18} +(-3.64590 - 2.10496i) q^{19} +(-1.62295 - 1.83567i) q^{20} +(-1.93117 - 1.93117i) q^{22} +(-5.13695 + 1.37644i) q^{23} +(2.36441 + 1.41528i) q^{24} +(-4.60386 + 1.95052i) q^{25} +(9.71628 + 5.60970i) q^{26} +(3.84392 - 3.49632i) q^{27} -2.97115 q^{29} +(-5.17582 + 4.43256i) q^{30} +(-2.89885 - 5.02095i) q^{31} +(-5.40856 - 1.44922i) q^{32} +(-1.93080 + 1.87084i) q^{33} +5.30926i q^{34} +(-1.73265 + 2.79366i) q^{36} +(1.68190 - 0.450663i) q^{37} +(1.91715 - 7.15489i) q^{38} +(5.67241 - 9.47650i) q^{39} +(-1.96452 + 2.96587i) q^{40} +2.68458i q^{41} +(-2.09578 + 2.09578i) q^{43} +(0.850438 - 1.47300i) q^{44} +(4.28255 + 5.16331i) q^{45} +(-4.67860 - 8.10358i) q^{46} +(-0.0131194 - 0.0489622i) q^{47} +(-2.36874 + 8.31349i) q^{48} +(-5.41150 - 6.93615i) q^{50} +(5.22583 + 0.0824344i) q^{51} +(-1.80844 + 6.74919i) q^{52} +(-1.57696 + 5.88528i) q^{53} +(7.69258 + 4.94067i) q^{54} +(-2.29896 - 2.60029i) q^{55} +(-7.01270 - 1.99811i) q^{57} +(-1.35302 - 5.04955i) q^{58} +(2.46880 + 4.27609i) q^{59} +(-3.50076 - 2.39911i) q^{60} +(1.65843 - 2.87249i) q^{61} +(7.21316 - 7.21316i) q^{62} +0.129684i q^{64} +(11.8872 + 7.87377i) q^{65} +(-4.05881 - 2.42950i) q^{66} +(0.625932 - 2.33601i) q^{67} +(-3.19386 + 0.855793i) q^{68} +(-8.04889 + 4.47927i) q^{69} -5.73577i q^{71} +(4.56899 + 1.38011i) q^{72} +(9.92795 + 2.66019i) q^{73} +(1.53183 + 2.65321i) q^{74} +(-6.91118 + 5.21877i) q^{75} +4.61315 q^{76} +(18.6887 + 5.32495i) q^{78} +(3.11231 + 1.79689i) q^{79} +(-10.5819 - 3.54467i) q^{80} +(4.98248 - 7.49499i) q^{81} +(-4.56252 + 1.22252i) q^{82} +(-12.2139 - 12.2139i) q^{83} +(-0.414214 + 6.73463i) q^{85} +(-4.51623 - 2.60745i) q^{86} +(-4.99121 + 1.25336i) q^{87} +(-2.38535 - 0.639153i) q^{88} +(0.678216 - 1.17470i) q^{89} +(-6.82498 + 9.62963i) q^{90} +(4.12069 - 4.12069i) q^{92} +(-6.98782 - 7.21181i) q^{93} +(0.0772383 - 0.0445936i) q^{94} +(2.99005 - 8.92620i) q^{95} +(-9.69716 - 0.152967i) q^{96} +(-10.9812 - 10.9812i) q^{97} +(-2.45435 + 3.95731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 16 q^{10} + 16 q^{12} + 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} + 32 q^{27} - 20 q^{30} + 28 q^{33} + 32 q^{36} + 16 q^{37} + 64 q^{40} - 80 q^{43} + 20 q^{45}+ \cdots - 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 + 16 * q^13 - 32 * q^15 + 16 * q^16 + 20 * q^18 + 16 * q^22 + 16 * q^25 + 32 * q^27 - 20 * q^30 + 28 * q^33 + 32 * q^36 + 16 * q^37 + 64 * q^40 - 80 * q^43 + 20 * q^45 + 64 * q^46 - 32 * q^48 + 20 * q^51 - 80 * q^55 + 8 * q^57 - 40 * q^58 - 32 * q^60 + 32 * q^61 - 16 * q^66 - 24 * q^67 + 8 * q^72 + 32 * q^73 - 60 * q^75 - 64 * q^76 + 120 * q^78 - 52 * q^81 - 80 * q^82 + 48 * q^85 + 4 * q^87 - 96 * q^88 + 48 * q^90 + 76 * q^93 - 96 * q^96 - 48 * q^97

Introduction

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