LMFDB - Embedded newform 735.2.y.g.263.3

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			263.3
Character	$\chi$	$=$	735.263
Dual form			735.2.y.g.422.3

$q$-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} +(1.24391 - 1.20528i) 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} +(0.0946229 - 2.99851i) q^{9} +(-3.52156 - 1.75429i) q^{10} +(1.34425 + 0.776103i) q^{11} +(-1.84080 + 0.462248i) q^{12} +(4.50889 + 4.50889i) q^{13} +(2.08755 + 3.26223i) q^{15} +(-2.49541 - 4.32218i) q^{16} +(-2.91469 + 0.780989i) q^{17} +(5.05296 + 1.52630i) 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} +(-0.0434629 + 2.75528i) q^{24} +(-4.60386 - 1.95052i) q^{25} +(-9.71628 + 5.60970i) q^{26} +(-3.49632 - 3.84392i) q^{27} +2.97115 q^{29} +(-6.49490 + 2.06228i) q^{30} +(-2.89885 + 5.02095i) q^{31} +(5.40856 - 1.44922i) q^{32} +(2.60754 - 0.654789i) q^{33} -5.30926i q^{34} +(-1.73265 + 2.79366i) q^{36} +(1.68190 + 0.450663i) q^{37} +(-1.91715 - 7.15489i) q^{38} +(11.0431 + 0.174198i) q^{39} +(-1.96452 - 2.96587i) q^{40} +2.68458i q^{41} +(-2.09578 - 2.09578i) q^{43} +(-0.850438 - 1.47300i) q^{44} +(6.52861 + 1.54184i) q^{45} +(-4.67860 + 8.10358i) q^{46} +(0.0131194 - 0.0489622i) q^{47} +(-8.31349 - 2.36874i) q^{48} +(5.41150 - 6.93615i) q^{50} +(-2.68431 + 4.48449i) q^{51} +(-1.80844 - 6.74919i) q^{52} +(1.57696 + 5.88528i) q^{53} +(8.12504 - 4.19163i) q^{54} +(-2.29896 + 2.60029i) q^{55} +(-1.99811 + 7.01270i) q^{57} +(-1.35302 + 5.04955i) q^{58} +(-2.46880 + 4.27609i) q^{59} +(-0.193688 - 4.23952i) q^{60} +(1.65843 + 2.87249i) q^{61} +(-7.21316 - 7.21316i) q^{62} -0.129684i q^{64} +(-11.8872 + 7.87377i) q^{65} +(-0.0746095 + 4.72978i) q^{66} +(0.625932 + 2.33601i) q^{67} +(3.19386 + 0.855793i) q^{68} +(8.04889 - 4.47927i) q^{69} -5.73577i q^{71} +(3.26681 + 3.47970i) q^{72} +(9.92795 - 2.66019i) q^{73} +(-1.53183 + 2.65321i) q^{74} +(-8.07769 + 3.12265i) q^{75} +4.61315 q^{76} +(-5.32495 + 18.6887i) q^{78} +(3.11231 - 1.79689i) q^{79} +(10.5819 - 3.54467i) q^{80} +(-8.98209 - 0.567455i) 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} +(3.69584 - 3.58105i) q^{87} +(-2.38535 + 0.639153i) q^{88} +(-0.678216 - 1.17470i) q^{89} +(-5.59346 + 10.3934i) q^{90} +(-4.12069 - 4.12069i) q^{92} +(2.44573 + 9.73953i) q^{93} +(0.0772383 + 0.0445936i) q^{94} +(-2.99005 - 8.92620i) q^{95} +(4.98105 - 8.32150i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.455388	+	1.69953i	−0.322008	+	1.20175i	0.595278	+	0.803520i	$0.297042\pi$
$2$	−0.455388	+	1.69953i	−0.322008	+	1.20175i	−0.917286	+	0.398229i	$0.869625\pi$
$3$	1.24391	−	1.20528i	0.718172	−	0.695866i
$3$	1.24391	−	1.20528i	0.718172	−	0.695866i
$4$	−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
$9$	0.0946229	−	2.99851i	0.0315410	−	0.999502i
$10$	−3.52156	−	1.75429i	−1.11361	−	0.554754i
$11$	1.34425	+	0.776103i	0.405307	+	0.234004i	0.688771	−	0.724979i	$-0.258150\pi$
$11$	1.34425	+	0.776103i	0.405307	+	0.234004i	−0.283465	+	0.958983i	$0.591484\pi$
$12$	−1.84080	+	0.462248i	−0.531392	+	0.133440i
$13$	4.50889	+	4.50889i	1.25054	+	1.25054i	0.955478	+	0.295062i	$0.0953402\pi$
$13$	4.50889	+	4.50889i	1.25054	+	1.25054i	0.295062	+	0.955478i	$0.404660\pi$
$14$		0			0
$15$	2.08755	+	3.26223i	0.539003	+	0.842304i
$16$	−2.49541	−	4.32218i	−0.623853	−	1.08055i
$17$	−2.91469	+	0.780989i	−0.706917	+	0.189418i	−0.594327	−	0.804224i	$-0.702581\pi$
$17$	−2.91469	+	0.780989i	−0.706917	+	0.189418i	−0.112590	+	0.993642i	$0.535915\pi$
$18$	5.05296	+	1.52630i	1.19099	+	0.359752i
$19$	−3.64590	+	2.10496i	−0.836427	+	0.482912i	−0.856048	−	0.516896i	$-0.827087\pi$
$19$	−3.64590	+	2.10496i	−0.836427	+	0.482912i	0.0196209	+	0.999807i	$0.493754\pi$
$20$	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	$-0.229593\pi$
$23$	5.13695	+	1.37644i	1.07113	+	0.287008i	0.320171	+	0.947360i	$0.396260\pi$
$24$	−0.0434629	+	2.75528i	−0.00887183	+	0.562419i
$25$	−4.60386	−	1.95052i	−0.920771	−	0.390103i
$26$	−9.71628	+	5.60970i	−1.90552	+	1.10015i
$27$	−3.49632	−	3.84392i	−0.672868	−	0.739763i
$28$		0			0
$29$	2.97115			0.551728			0.275864	−	0.961197i	$-0.411036\pi$
$29$	2.97115			0.551728			0.275864	+	0.961197i	$0.411036\pi$
$30$	−6.49490	+	2.06228i	−1.18580	+	0.376518i
$31$	−2.89885	+	5.02095i	−0.520649	+	0.901790i	0.479063	+	0.877781i	$0.340977\pi$
$31$	−2.89885	+	5.02095i	−0.520649	+	0.901790i	−0.999712	+	0.0240096i	$0.992357\pi$
$32$	5.40856	−	1.44922i	0.956108	−	0.256188i
$33$	2.60754	−	0.654789i	0.453915	−	0.113984i
$34$		−	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	0.394405	−	0.918937i	$-0.370951\pi$
$37$	1.68190	+	0.450663i	0.276502	+	0.0740885i	−0.117903	+	0.993025i	$0.537617\pi$
$38$	−1.91715	−	7.15489i	−0.311003	−	1.16068i
$39$	11.0431	+	0.174198i	1.76831	+	0.0278940i
$40$	−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	0.529011	−	0.848615i	$-0.322563\pi$
$43$	−2.09578	−	2.09578i	−0.319603	−	0.319603i	−0.848615	+	0.529011i	$0.822563\pi$
$44$	−0.850438	−	1.47300i	−0.128208	−	0.222063i
$45$	6.52861	+	1.54184i	0.973227	+	0.229845i
$46$	−4.67860	+	8.10358i	−0.689822	+	1.19481i
$47$	0.0131194	−	0.0489622i	0.00191366	−	0.00714187i	−0.964962	−	0.262388i	$-0.915490\pi$
$47$	0.0131194	−	0.0489622i	0.00191366	−	0.00714187i	0.966876	+	0.255246i	$0.0821566\pi$
$48$	−8.31349	−	2.36874i	−1.19995	−	0.341899i
$49$		0			0
$50$	5.41150	−	6.93615i	0.765302	−	0.980920i
$51$	−2.68431	+	4.48449i	−0.375878	+	0.627954i
$52$	−1.80844	−	6.74919i	−0.250785	−	0.935944i
$53$	1.57696	+	5.88528i	0.216612	+	0.808406i	0.985593	+	0.169134i	$0.0540972\pi$
$53$	1.57696	+	5.88528i	0.216612	+	0.808406i	−0.768981	+	0.639271i	$0.779236\pi$
$54$	8.12504	−	4.19163i	1.10568	−	0.570409i
$55$	−2.29896	+	2.60029i	−0.309992	+	0.350623i
$56$		0			0
$57$	−1.99811	+	7.01270i	−0.264657	+	0.928855i
$58$	−1.35302	+	5.04955i	−0.177661	+	0.663038i
$59$	−2.46880	+	4.27609i	−0.321410	+	0.556699i	−0.980779	−	0.195120i	$-0.937490\pi$
$59$	−2.46880	+	4.27609i	−0.321410	+	0.556699i	0.659369	+	0.751820i	$0.270824\pi$
$60$	−0.193688	−	4.23952i	−0.0250050	−	0.547319i
$61$	1.65843	+	2.87249i	0.212341	+	0.367785i	0.952447	−	0.304705i	$-0.0985580\pi$
$61$	1.65843	+	2.87249i	0.212341	+	0.367785i	−0.740106	+	0.672490i	$0.765225\pi$
$62$	−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
$66$	−0.0746095	+	4.72978i	−0.00918379	+	0.582196i
$67$	0.625932	+	2.33601i	0.0764698	+	0.285389i	0.993563	−	0.113285i	$-0.0361372\pi$
$67$	0.625932	+	2.33601i	0.0764698	+	0.285389i	−0.917093	+	0.398674i	$0.869471\pi$
$68$	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	$-0.110547\pi$
$72$	3.26681	+	3.47970i	0.384997	+	0.410087i
$73$	9.92795	−	2.66019i	1.16198	−	0.311351i	0.374223	−	0.927339i	$-0.377910\pi$
$73$	9.92795	−	2.66019i	1.16198	−	0.311351i	0.787756	+	0.615988i	$0.211243\pi$
$74$	−1.53183	+	2.65321i	−0.178072	+	0.308429i
$75$	−8.07769	+	3.12265i	−0.932731	+	0.360572i
$76$	4.61315			0.529165
$77$		0			0
$78$	−5.32495	+	18.6887i	−0.602931	+	2.11608i
$79$	3.11231	−	1.79689i	0.350163	−	0.202166i	−0.314594	−	0.949226i	$-0.601868\pi$
$79$	3.11231	−	1.79689i	0.350163	−	0.202166i	0.664757	+	0.747060i	$0.268535\pi$
$80$	10.5819	−	3.54467i	1.18309	−	0.396307i
$81$	−8.98209	−	0.567455i	−0.998010	−	0.0630505i
$82$	−4.56252	−	1.22252i	−0.503847	−	0.135005i
$83$	12.2139	−	12.2139i	1.34065	−	1.34065i	0.445228	−	0.895417i	$-0.353123\pi$
$83$	12.2139	−	12.2139i	1.34065	−	1.34065i	0.895417	−	0.445228i	$-0.146877\pi$
$84$		0			0
$85$	−0.414214	−	6.73463i	−0.0449278	−	0.730474i
$86$	4.51623	−	2.60745i	0.486998	−	0.281168i
$87$	3.69584	−	3.58105i	0.396235	−	0.383929i
$88$	−2.38535	+	0.639153i	−0.254279	+	0.0681339i
$89$	−0.678216	−	1.17470i	−0.0718908	−	0.124518i	0.827839	−	0.560965i	$-0.189570\pi$
$89$	−0.678216	−	1.17470i	−0.0718908	−	0.124518i	−0.899730	+	0.436447i	$0.856237\pi$
$90$	−5.59346	+	10.3934i	−0.589602	+	1.09556i
$91$		0			0
$92$	−4.12069	−	4.12069i	−0.429611	−	0.429611i
$93$	2.44573	+	9.73953i	0.253610	+	1.00994i
$94$	0.0772383	+	0.0445936i	0.00796652	+	0.00459948i
$95$	−2.99005	−	8.92620i	−0.306773	−	0.915808i
$96$	4.98105	−	8.32150i	0.508377	−	0.849310i
$97$	−10.9812	+	10.9812i	−1.11497	+	1.11497i	−0.122503	+	0.992468i	$0.539092\pi$
$97$	−10.9812	+	10.9812i	−1.11497	+	1.11497i	−0.992468	+	0.122503i	$0.960908\pi$
$98$		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	$-0.551104\pi$
$101$	−11.0014	−	6.35165i	−1.09468	−	0.632012i	−0.934818	+	0.355127i	$0.884437\pi$
$102$	−6.39912	−	6.60424i	−0.633607	−	0.653917i
$103$	0.537318	−	2.00530i	0.0529435	−	0.197588i	−0.934388	−	0.356256i	$-0.884053\pi$
$103$	0.537318	−	2.00530i	0.0529435	−	0.197588i	0.987332	+	0.158668i	$0.0507199\pi$
$104$	−10.1448			−0.994779
$105$		0			0
$106$	−10.7203			−1.04125
$107$	4.96049	−	18.5128i	0.479548	−	1.78970i	−0.123898	−	0.992295i	$-0.539540\pi$
$107$	4.96049	−	18.5128i	0.479548	−	1.78970i	0.603446	−	0.797404i	$-0.293794\pi$
$108$	1.21187	+	5.56338i	0.116613	+	0.535336i
$109$	4.19293	+	2.42079i	0.401610	+	0.231869i	0.687178	−	0.726489i	$-0.258849\pi$
$109$	4.19293	+	2.42079i	0.401610	+	0.231869i	−0.285569	+	0.958358i	$0.592182\pi$
$110$	−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	$-0.500238\pi$
$113$	10.6222	−	10.6222i	0.999254	−	0.999254i	1.00000		0.000746132i	$0.000237501\pi$
$114$	−11.0084	−	6.58935i	−1.03103	−	0.617149i
$115$	−5.30245	+	10.6442i	−0.494456	+	0.992573i
$116$	−2.81954	−	1.62786i	−0.261788	−	0.151143i
$117$	13.9466	−	13.0933i	1.28936	−	1.21047i
$118$	−6.14308	−	6.14308i	−0.565516	−	0.565516i
$119$		0			0
$120$	−6.01838	−	1.32149i	−0.549401	−	0.120635i
$121$	−4.29533	−	7.43973i	−0.390484	−	0.676339i
$122$	−5.63711	+	1.51046i	−0.510360	+	0.136751i
$123$	3.23566	+	3.33938i	0.291749	+	0.301101i
$124$	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	−0.0940560	−	0.995567i	$-0.529983\pi$
$127$	10.1595	−	10.1595i	0.901511	−	0.901511i	0.995567	+	0.0940560i	$0.0299833\pi$
$128$	11.0375	+	2.95750i	0.975588	+	0.261408i
$129$	−5.13295	−	0.0809693i	−0.451931	−	0.00712895i
$130$	−7.96844	−	23.7882i	−0.698878	−	2.08636i
$131$	−0.441131	+	0.254687i	−0.0385418	+	0.0222521i	−0.519147	−	0.854685i	$-0.673750\pi$
$131$	−0.441131	+	0.254687i	−0.0385418	+	0.0222521i	0.480605	+	0.876937i	$0.340417\pi$
$132$	−2.83324	−	0.807270i	−0.246602	−	0.0702638i
$133$		0			0
$134$	−4.25516			−0.367590
$135$	9.97935	−	5.95085i	0.858885	−	0.512168i
$136$	2.40037	−	4.15756i	0.205830	−	0.356508i
$137$	−3.57827	+	0.958794i	−0.305712	+	0.0819153i	−0.408414	−	0.912797i	$-0.633918\pi$
$137$	−3.57827	+	0.958794i	−0.305712	+	0.0819153i	0.102702	+	0.994712i	$0.467251\pi$
$138$	3.94728	+	15.7191i	0.336015	+	1.33810i
$139$		−	6.35379i		−	0.538921i	−0.963011	−	0.269461i	$-0.913155\pi$
$139$		−	6.35379i		−	0.538921i	0.963011	−	0.269461i	$-0.0868454\pi$
$140$		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
$144$	−13.1962	+	7.07354i	−1.09968	+	0.589461i
$145$	−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	$-0.222757\pi$
$149$	−2.13982	−	3.70628i	−0.175301	−	0.303631i	−0.940265	+	0.340442i	$0.889423\pi$
$150$	−1.62855	−	15.1503i	−0.132971	−	1.23702i
$151$	2.60616	−	4.51400i	0.212086	−	0.367344i	−0.740281	−	0.672297i	$-0.765308\pi$
$151$	2.60616	−	4.51400i	0.212086	−	0.367344i	0.952367	+	0.304954i	$0.0986409\pi$
$152$	1.73352	−	6.46960i	0.140607	−	0.524754i
$153$	2.06601	+	8.81363i	0.167027	+	0.712539i
$154$		0			0
$155$	−9.71243	−	8.58693i	−0.780121	−	0.689719i
$156$	−10.3842	−	6.21571i	−0.831398	−	0.497655i
$157$	1.59587	+	5.95585i	0.127364	+	0.475329i	0.999913	−	0.0131979i	$-0.00420114\pi$
$157$	1.59587	+	5.95585i	0.127364	+	0.475329i	−0.872549	+	0.488527i	$0.837534\pi$
$158$	1.63657	+	6.10775i	0.130198	+	0.485907i
$159$	9.05498	+	5.42009i	0.718106	+	0.429841i
$160$	0.768623	+	12.4969i	0.0607650	+	0.987968i
$161$		0			0
$162$	5.05474	−	15.0069i	0.397138	−	1.17906i
$163$	1.95582	−	7.29921i	0.153191	−	0.571718i	−0.846062	−	0.533084i	$-0.821033\pi$
$163$	1.95582	−	7.29921i	0.153191	−	0.571718i	0.999253	−	0.0386337i	$-0.0123005\pi$
$164$	1.47085	−	2.54760i	0.114854	−	0.198934i
$165$	0.274364	+	6.00540i	0.0213592	+	0.467520i
$166$	15.1958	+	26.3199i	1.17942	+	2.04282i
$167$	13.8232	+	13.8232i	1.06967	+	1.06967i	0.997384	+	0.0722908i	$0.0230310\pi$
$167$	13.8232	+	13.8232i	1.06967	+	1.06967i	0.0722908	+	0.997384i	$0.476969\pi$
$168$		0			0
$169$			27.6601i			2.12770i
$170$	11.6343	+	2.36290i	0.892313	+	0.181226i
$171$	5.96676	+	11.1314i	0.456290	+	0.851243i
$172$	0.840583	+	3.13710i	0.0640938	+	0.239201i
$173$	2.82269	+	0.756337i	0.214605	+	0.0575032i	0.364520	−	0.931196i	$-0.381233\pi$
$173$	2.82269	+	0.756337i	0.214605	+	0.0575032i	−0.149915	+	0.988699i	$0.547900\pi$
$174$	4.40306	+	7.91195i	0.333795	+	0.599803i
$175$		0			0
$176$		−	7.74679i		−	0.583936i
$177$	2.08290	+	8.29465i	0.156560	+	0.623464i
$178$	2.30530	−	0.617702i	0.172789	−	0.0462988i
$179$	−5.95932	+	10.3218i	−0.445420	+	0.771491i	−0.998081	−	0.0619153i	$-0.980279\pi$
$179$	−5.95932	+	10.3218i	−0.445420	+	0.771491i	0.552661	+	0.833406i	$0.313612\pi$
$180$	−5.35071	−	5.04013i	−0.398819	−	0.375669i
$181$	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
$183$	5.52508	+	1.57425i	0.408426	+	0.116372i
$184$	−7.32742	+	4.23049i	−0.540184	+	0.311876i
$185$	−1.73608	+	3.48502i	−0.127639	+	0.256224i
$186$	−17.6664	−	0.278677i	−1.29536	−	0.0204336i
$187$	−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	$-0.602430\pi$
$191$	4.79798	−	2.77011i	0.347169	−	0.200438i	0.663438	+	0.748231i	$0.269097\pi$
$192$	−0.156305	−	0.161315i	−0.0112803	−	0.0116419i
$193$	18.9915	−	5.08875i	1.36704	−	0.366296i	0.500641	−	0.865655i	$-0.333098\pi$
$193$	18.9915	−	5.08875i	1.36704	−	0.366296i	0.866395	+	0.499359i	$0.166431\pi$
$194$	−13.6622	−	23.6636i	−0.980886	−	1.69895i
$195$	−5.29649	+	24.1215i	−0.379289	+	1.72738i
$196$		0			0
$197$	12.7155	+	12.7155i	0.905939	+	0.905939i	0.995942	−	0.0900024i	$-0.0286875\pi$
$197$	12.7155	+	12.7155i	0.905939	+	0.905939i	−0.0900024	+	0.995942i	$0.528687\pi$
$198$	5.60788	+	5.97335i	0.398535	+	0.424507i
$199$	−5.29564	−	3.05744i	−0.375398	−	0.216736i	0.300416	−	0.953808i	$-0.402874\pi$
$199$	−5.29564	−	3.05744i	−0.375398	−	0.216736i	−0.675814	+	0.737072i	$0.736208\pi$
$200$	7.37352	−	2.98495i	0.521387	−	0.211068i
$201$	3.59414	+	2.15137i	0.253511	+	0.151746i
$202$	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
$207$	4.61334	−	15.2729i	0.320649	−	1.06154i
$208$	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
$213$	−6.91319	−	7.13479i	−0.473684	−	0.488867i
$214$	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
$219$	9.14321	−	15.2749i	0.617841	−	1.03218i
$220$	3.60632	−	1.20803i	0.243138	−	0.0814452i
$221$	−16.6634	−	9.62062i	−1.12090	−	0.647153i
$222$	1.29239	+	5.14663i	0.0867393	+	0.345419i
$223$	−8.80424	−	8.80424i	−0.589576	−	0.589576i	0.347941	−	0.937516i	$-0.386881\pi$
$223$	−8.80424	−	8.80424i	−0.589576	−	0.589576i	−0.937516	+	0.347941i	$0.886881\pi$
$224$		0			0
$225$	−6.28427	+	13.6201i	−0.418951	+	0.908009i
$226$	13.2155	+	22.8900i	0.879085	+	1.52262i
$227$	21.5045	−	5.76211i	1.42730	−	0.382445i	0.539234	−	0.842156i	$-0.318714\pi$
$227$	21.5045	−	5.76211i	1.42730	−	0.382445i	0.888068	+	0.459711i	$0.152047\pi$
$228$	5.73835	−	5.56012i	0.380031	−	0.368228i
$229$	7.16589	−	4.13723i	0.473535	−	0.273396i	−0.244183	−	0.969729i	$-0.578520\pi$
$229$	7.16589	−	4.13723i	0.473535	−	0.273396i	0.717718	+	0.696333i	$0.245186\pi$
$230$	−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	$-0.615829\pi$
$233$	−17.2700	−	4.62748i	−1.13140	−	0.303156i	−0.775486	+	0.631364i	$0.782495\pi$
$234$	15.9013	+	29.6651i	1.03950	+	1.93927i
$235$	0.101454	+	0.0505397i	0.00661810	+	0.00329684i
$236$	4.68565	−	2.70526i	0.305010	−	0.176098i
$237$	1.70568	−	5.98637i	0.110796	−	0.388856i
$238$		0			0
$239$	−25.8260			−1.67054			−0.835271	−	0.549838i	$-0.814689\pi$
$239$	−25.8260			−1.67054			−0.835271	+	0.549838i	$0.814689\pi$
$240$	8.89064	−	17.1634i	0.573889	−	1.10789i
$241$	−5.25983	+	9.11029i	−0.338815	+	0.586846i	−0.984210	−	0.177004i	$-0.943360\pi$
$241$	−5.25983	+	9.11029i	−0.338815	+	0.586846i	0.645395	+	0.763849i	$0.276693\pi$
$242$	14.6001	−	3.91208i	0.938529	−	0.251478i
$243$	−11.8569	+	10.1200i	−0.760617	+	0.649200i
$244$		−	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
$249$	0.471876	−	29.9140i	0.0299039	−	1.89572i
$250$	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
$255$	−8.63233	−	7.87804i	−0.540578	−	0.493342i
$256$	−9.92302	+	17.1872i	−0.620189	+	1.07420i
$257$	−2.99064	+	11.1612i	−0.186551	+	0.696217i	0.807742	+	0.589536i	$0.200689\pi$
$257$	−2.99064	+	11.1612i	−0.186551	+	0.696217i	−0.994293	+	0.106681i	$0.965977\pi$
$258$	2.47509	−	8.68674i	0.154093	−	0.540813i
$259$		0			0
$260$	15.5945	−	0.959142i	0.967133	−	0.0594835i
$261$	0.281138	−	8.90900i	0.0174020	−	0.551453i
$262$	−0.231963	−	0.865696i	−0.0143307	−	0.0534829i
$263$	0.0435058	+	0.162366i	0.00268268	+	0.0100119i	0.967254	−	0.253810i	$-0.0816837\pi$
$263$	0.0435058	+	0.162366i	0.00268268	+	0.0100119i	−0.964572	+	0.263822i	$0.915017\pi$
$264$	−2.19681	+	3.67005i	−0.135204	+	0.225876i
$265$	−13.5984	+	0.836371i	−0.835345	+	0.0513779i
$266$		0			0
$267$	−2.25948	−	0.643790i	−0.138278	−	0.0393993i
$268$	0.685884	−	2.55975i	0.0418970	−	0.156362i
$269$	3.30165	−	5.71862i	0.201305	−	0.348671i	−0.747644	−	0.664100i	$-0.768815\pi$
$269$	3.30165	−	5.71862i	0.201305	−	0.348671i	0.948949	+	0.315429i	$0.102148\pi$
$270$	5.56918	+	19.6701i	0.338930	+	1.19709i
$271$	−11.9146	−	20.6367i	−0.723759	−	1.25359i	−0.959483	−	0.281768i	$-0.909079\pi$
$271$	−11.9146	−	20.6367i	−0.723759	−	1.25359i	0.235723	−	0.971820i	$-0.424254\pi$
$272$	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
$276$	−10.0923	−	0.159200i	−0.607487	−	0.00958274i
$277$	−5.26787	−	19.6600i	−0.316516	−	1.18125i	−0.922570	−	0.385829i	$-0.873915\pi$
$277$	−5.26787	−	19.6600i	−0.316516	−	1.18125i	0.606055	−	0.795423i	$-0.292751\pi$
$278$	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	$-0.0143127\pi$
$282$	0.149825	−	0.0376231i	0.00892195	−	0.00224042i
$283$	11.5991	−	3.10797i	0.689496	−	0.184750i	0.102975	−	0.994684i	$-0.467164\pi$
$283$	11.5991	−	3.10797i	0.689496	−	0.184750i	0.586521	+	0.809934i	$0.300497\pi$
$284$	−3.14257	+	5.44310i	−0.186477	+	0.322988i
$285$	−14.4779	−	7.49955i	−0.857595	−	0.444235i
$286$	−17.4148			−1.02976
$287$		0			0
$288$	−3.83372	−	16.3547i	−0.225904	−	0.963712i
$289$	−6.83695	+	3.94731i	−0.402173	+	0.232195i
$290$	−10.4631	−	5.21224i	−0.614412	−	0.306073i
$291$	−0.424252	+	26.8950i	−0.0248701	+	1.57661i
$292$	−10.8788	−	2.91498i	−0.636636	−	0.170586i
$293$	2.35851	−	2.35851i	0.137786	−	0.137786i	−0.634850	−	0.772635i	$-0.718938\pi$
$293$	2.35851	−	2.35851i	0.137786	−	0.137786i	0.772635	+	0.634850i	$0.218938\pi$
$294$		0			0
$295$	−8.27157	−	7.31304i	−0.481590	−	0.425782i
$296$	−2.39908	+	1.38511i	−0.139444	+	0.0805079i
$297$	−1.71666	−	7.88070i	−0.0996105	−	0.457284i
$298$	7.27339	−	1.94890i	0.421336	−	0.112897i
$299$	16.9557	+	29.3681i	0.980573	+	1.69840i
$300$	9.37638	+	1.46238i	0.541346	+	0.0844303i
$301$		0			0
$302$	6.48486	+	6.48486i	0.373162	+	0.373162i
$303$	−21.3402	+	5.35881i	−1.22596	+	0.307856i
$304$	18.1961	+	10.5055i	1.04362	+	0.602532i
$305$	−7.03267	+	2.35576i	−0.402689	+	0.134891i
$306$	−15.9199	−	0.502378i	−0.910077	−	0.0287190i
$307$	0.793602	−	0.793602i	0.0452933	−	0.0452933i	−0.684097	−	0.729391i	$-0.739804\pi$
$307$	0.793602	−	0.793602i	0.0452933	−	0.0452933i	0.729391	+	0.684097i	$0.239804\pi$
$308$		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	$-0.424039\pi$
$311$	−8.58683	−	4.95761i	−0.486914	−	0.281120i	−0.723293	+	0.690541i	$0.757373\pi$
$312$	−12.6192	+	12.2273i	−0.714422	+	0.692233i
$313$	3.64245	−	13.5938i	0.205884	−	0.768368i	−0.783295	−	0.621650i	$-0.786462\pi$
$313$	3.64245	−	13.5938i	0.205884	−	0.768368i	0.989178	−	0.146718i	$-0.0468709\pi$
$314$	−10.8489			−0.612238
$315$		0			0
$316$	−3.93800			−0.221530
$317$	−5.48264	+	20.4615i	−0.307936	+	1.14923i	0.622453	+	0.782657i	$0.286136\pi$
$317$	−5.48264	+	20.4615i	−0.307936	+	1.14923i	−0.930389	+	0.366574i	$0.880531\pi$
$318$	−13.3351	+	12.9210i	−0.747797	+	0.724571i
$319$	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
$324$	8.21286	+	5.45970i	0.456270	+	0.303317i
$325$	−11.9636	−	29.5529i	−0.663622	−	1.63930i
$326$	11.5146	+	6.64794i	0.637733	+	0.368195i
$327$	8.13334	−	2.04239i	0.449775	−	0.112944i
$328$	−3.02009	−	3.02009i	−0.166757	−	0.166757i
$329$		0			0
$330$	−10.3313	−	2.26850i	−0.568720	−	0.124877i
$331$	1.55123	+	2.68682i	0.0852635	+	0.147681i	0.905503	−	0.424339i	$-0.139493\pi$
$331$	1.55123	+	2.68682i	0.0852635	+	0.147681i	−0.820240	+	0.572020i	$0.806160\pi$
$332$	−18.2825	+	4.89878i	−1.00338	+	0.268855i
$333$	1.51046	−	5.00054i	0.0827728	−	0.274028i
$334$	−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	−0.314784	+	0.949163i	$0.601932\pi$
$337$	−23.2030	+	23.2030i	−1.26395	+	1.26395i	−0.949163	+	0.314784i	$0.898068\pi$
$338$	−47.0092	−	12.5961i	−2.55696	−	0.685136i
$339$	0.410383	−	26.0158i	0.0222890	−	1.41298i
$340$	−3.29676	+	6.61793i	−0.178792	+	0.358908i
$341$	−7.79356	+	4.49961i	−0.422045	+	0.243668i
$342$	−21.6354	+	5.07157i	−1.16991	+	0.274239i
$343$		0			0
$344$	4.71541			0.254238
$345$	6.23337	+	19.6313i	0.335593	+	1.05691i
$346$	−2.57083	+	4.45282i	−0.138209	+	0.239385i
$347$	19.3753	−	5.19161i	1.04012	−	0.278700i	0.301959	−	0.953321i	$-0.402360\pi$
$347$	19.3753	−	5.19161i	1.04012	−	0.278700i	0.738164	+	0.674621i	$0.235693\pi$
$348$	−5.46927	+	1.37341i	−0.293184	+	0.0736224i
$349$		−	9.27152i		−	0.496293i	−0.968723	−	0.248146i	$-0.920179\pi$
$349$		−	9.27152i		−	0.496293i	0.968723	−	0.248146i	$-0.0798214\pi$
$350$		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	0.822887	+	0.568205i	$0.192362\pi$
$353$	7.40914	+	27.6513i	0.394349	+	1.47173i	−0.428538	+	0.903524i	$0.640971\pi$
$354$	−15.0455	−	0.237334i	−0.799661	−	0.0126142i
$355$	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	$-0.00114720\pi$
$359$	9.41445	+	16.3063i	0.496876	+	0.860614i	−0.503118	+	0.864218i	$0.667814\pi$
$360$	−9.07908	+	5.61000i	−0.478510	+	0.295673i
$361$	−0.638264	+	1.10551i	−0.0335928	+	0.0581845i
$362$	−8.01230	+	29.9023i	−0.421117	+	1.57163i
$363$	−14.3099	−	4.07730i	−0.751076	−	0.214003i
$364$		0			0
$365$	1.41088	+	22.9393i	0.0738490	+	1.20070i
$366$	−5.19154	+	8.67315i	−0.271366	+	0.453353i
$367$	−0.344800	−	1.28681i	−0.0179984	−	0.0671711i	0.956343	−	0.292248i	$-0.0944033\pi$
$367$	−0.344800	−	1.28681i	−0.0179984	−	0.0671711i	−0.974341	+	0.225077i	$0.927737\pi$
$368$	−6.86957	−	25.6376i	−0.358101	−	1.33645i
$369$	8.04973	+	0.254023i	0.419052	+	0.0132239i
$370$	−5.13231	−	4.53756i	−0.266816	−	0.235897i
$371$		0			0
$372$	3.01526	−	10.5825i	0.156334	−	0.548679i
$373$	2.70837	−	10.1078i	0.140234	−	0.523361i	−0.859687	−	0.510821i	$-0.829342\pi$
$373$	2.70837	−	10.1078i	0.140234	−	0.523361i	0.999921	−	0.0125400i	$-0.00399170\pi$
$374$	4.12053	−	7.13697i	0.213068	−	0.369044i
$375$	−3.24776	−	19.0906i	−0.167713	−	0.985836i
$376$	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	$-0.809373\pi$
$379$		−	21.9486i		−	1.12743i	0.825971	−	0.563713i	$-0.190627\pi$
$380$	−2.05310	+	10.1089i	−0.105322	+	0.518578i
$381$	0.392507	−	24.8825i	0.0201087	−	1.27477i
$382$	2.52295	+	9.41578i	0.129085	+	0.481753i
$383$	−26.4066	−	7.07564i	−1.34932	−	0.361548i	−0.489434	−	0.872040i	$-0.662797\pi$
$383$	−26.4066	−	7.07564i	−1.34932	−	0.361548i	−0.859882	+	0.510492i	$0.829463\pi$
$384$	17.2943	−	9.62440i	0.882545	−	0.491143i
$385$		0			0
$386$			34.5939i			1.76079i
$387$	−6.48252	+	6.08590i	−0.329525	+	0.309364i
$388$	16.4373	−	4.40437i	0.834480	−	0.223598i
$389$	−15.3981	+	26.6702i	−0.780712	+	1.35223i	0.150815	+	0.988562i	$0.451810\pi$
$389$	−15.3981	+	26.6702i	−0.780712	+	1.35223i	−0.931527	+	0.363671i	$0.881523\pi$
$390$	−38.5833	−	19.9862i	−1.95374	−	1.01204i
$391$	−16.0476			−0.811562
$392$		0			0
$393$	−0.241759	+	0.848491i	−0.0121951	+	0.0428007i
$394$	−27.4008	+	15.8198i	−1.38043	+	0.796992i
$395$	2.55245	+	7.61982i	0.128427	+	0.383395i
$396$	−4.49728	+	2.41067i	−0.225997	+	0.121141i
$397$	−28.4481	−	7.62264i	−1.42777	−	0.382569i	−0.539536	−	0.841963i	$-0.681400\pi$
$397$	−28.4481	−	7.62264i	−1.42777	−	0.382569i	−0.888233	+	0.459393i	$0.848067\pi$
$398$	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	$-0.491831\pi$
$401$	18.1072	−	10.4542i	0.904231	−	0.522058i	0.878570	+	0.477613i	$0.158498\pi$
$402$	−5.29304	+	5.12864i	−0.263993	+	0.255793i
$403$	−35.7095	+	9.56833i	−1.77882	+	0.476632i
$404$	6.96001	+	12.0551i	0.346273	+	0.599763i
$405$	5.24099	−	19.4302i	0.260427	−	0.965494i
$406$		0			0
$407$	1.91113	+	1.91113i	0.0947311	+	0.0947311i
$408$	−2.02516	−	8.06474i	−0.100261	−	0.399264i
$409$	−10.0262	−	5.78865i	−0.495765	−	0.286230i	0.231198	−	0.972907i	$-0.425736\pi$
$409$	−10.0262	−	5.78865i	−0.495765	−	0.286230i	−0.726963	+	0.686677i	$0.759069\pi$
$410$	4.70952	−	9.45391i	0.232587	−	0.466895i
$411$	−3.29543	+	5.50545i	−0.162552	+	0.271564i
$412$	−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
$417$	−7.65806	−	7.90354i	−0.375017	−	0.387038i
$418$	2.97581	−	11.1059i	0.145552	−	0.543206i
$419$	0.525515			0.0256731			0.0128365	−	0.999918i	$-0.495914\pi$
$419$	0.525515			0.0256731			0.0128365	+	0.999918i	$0.495914\pi$
$420$		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
$423$	−0.145572	−	0.0439715i	−0.00707796	−	0.00213797i
$424$	−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
$429$	14.7095	+	8.80475i	0.710181	+	0.425097i
$430$	3.70382	+	11.0570i	0.178614	+	0.533216i
$431$	19.9310	+	11.5072i	0.960044	+	0.554282i	0.896187	−	0.443677i	$-0.146326\pi$
$431$	19.9310	+	11.5072i	0.960044	+	0.554282i	0.0638575	+	0.997959i	$0.479660\pi$
$432$	−7.88935	+	24.7039i	−0.379576	+	1.18857i
$433$	15.4001	+	15.4001i	0.740081	+	0.740081i	0.972593	−	0.232513i	$-0.0746947\pi$
$433$	15.4001	+	15.4001i	0.740081	+	0.740081i	−0.232513	+	0.972593i	$0.574695\pi$
$434$		0			0
$435$	6.20242	+	9.69255i	0.297383	+	0.464722i
$436$	−2.65265	−	4.59453i	−0.127039	−	0.220038i
$437$	−21.6262	+	5.79471i	−1.03452	+	0.277199i
$438$	21.7965	+	22.4952i	1.04148	+	1.07486i
$439$	−5.23329	+	3.02144i	−0.249771	+	0.144205i	−0.619659	−	0.784871i	$-0.712729\pi$
$439$	−5.23329	+	3.02144i	−0.249771	+	0.144205i	0.369888	+	0.929076i	$0.379396\pi$
$440$	−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	$-0.322842\pi$
$443$	11.8124	+	3.16511i	0.561222	+	0.150379i	0.0329544	+	0.999457i	$0.489508\pi$
$444$	−3.30435	−	0.0521241i	−0.156817	−	0.00247370i
$445$	2.87601	−	0.963390i	0.136336	−	0.0456690i
$446$	18.9724	−	10.9537i	0.898370	−	0.518674i
$447$	−7.12884	−	2.03121i	−0.337183	−	0.0960727i
$448$		0			0
$449$	−20.7599			−0.979723			−0.489861	−	0.871800i	$-0.662953\pi$
$449$	−20.7599			−0.979723			−0.489861	+	0.871800i	$0.662953\pi$
$450$	−20.2860	−	16.8827i	−0.956293	−	0.795860i
$451$	−2.08351	+	3.60875i	−0.0981087	+	0.169929i
$452$	−15.9000	+	4.26039i	−0.747873	+	0.200392i
$453$	−2.19878	−	8.75614i	−0.103308	−	0.411399i
$454$			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	−0.340765	−	0.940148i	$-0.610686\pi$
$457$	−23.6425	−	6.33500i	−1.10595	−	0.296339i	−0.765186	+	0.643810i	$0.777353\pi$
$458$	3.76809	+	14.0627i	0.176071	+	0.657106i
$459$	13.1928	+	8.47325i	0.615786	+	0.395497i
$460$	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	0.752951	−	0.658076i	$-0.228630\pi$
$463$	2.04147	+	2.04147i	0.0948752	+	0.0948752i	−0.658076	+	0.752951i	$0.728630\pi$
$464$	−7.41424	−	12.8418i	−0.344197	−	0.596167i
$465$	−22.4310	+	1.02479i	−1.04021	+	0.0475234i
$466$	15.7291	−	27.2436i	0.728636	−	1.26203i
$467$	5.11079	−	19.0737i	0.236499	−	0.882628i	−0.740968	−	0.671540i	$-0.765633\pi$
$467$	5.11079	−	19.0737i	0.236499	−	0.882628i	0.977467	−	0.211087i	$-0.0677004\pi$
$468$	−20.4086	+	4.78399i	−0.943388	+	0.221140i
$469$		0			0
$470$	−0.132094	+	0.149408i	−0.00609306	+	0.00689169i
$471$	9.16356	+	5.48509i	0.422234	+	0.252739i
$472$	−2.03316	−	7.58785i	−0.0935837	−	0.349259i
$473$	−1.19071	−	4.44379i	−0.0547489	−	0.204326i
$474$	9.39727	+	5.62498i	0.431631	+	0.258364i
$475$	20.8910	−	2.57956i	0.958544	−	0.118358i
$476$		0			0
$477$	17.7963	−	4.17163i	0.814836	−	0.191006i
$478$	11.7608	−	43.8920i	0.537928	−	2.00757i
$479$	8.00337	−	13.8622i	0.365683	−	0.633382i	−0.623202	−	0.782061i	$-0.714169\pi$
$479$	8.00337	−	13.8622i	0.365683	−	0.633382i	0.988886	+	0.148679i	$0.0475020\pi$
$480$	16.0183	+	14.6186i	0.731133	+	0.667247i
$481$	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
$486$	−11.7998	−	24.7596i	−0.535251	−	1.12312i
$487$	7.54362	+	28.1532i	0.341834	+	1.27574i	0.896267	+	0.443514i	$0.146268\pi$
$487$	7.54362	+	28.1532i	0.341834	+	1.27574i	−0.554433	+	0.832228i	$0.687065\pi$
$488$	−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	$0.764429\pi$
$492$	−1.24094	−	4.94176i	−0.0559460	−	0.222792i
$493$	−8.65997	+	2.32043i	−0.390026	+	0.104507i
$494$	23.6164	−	40.9048i	1.06255	−	1.84039i
$495$	7.57945	+	7.13950i	0.340671	+	0.320897i
$496$	28.9353			1.29923
$497$		0			0
$498$	50.6249	+	14.4244i	2.26855	+	0.646374i
$499$	0.814586	−	0.470302i	0.0364659	−	0.0210536i	−0.481656	−	0.876360i	$-0.659965\pi$
$499$	0.814586	−	0.470302i	0.0364659	−	0.0210536i	0.518122	+	0.855307i	$0.326631\pi$
$500$	−11.0523	+	5.28559i	−0.494276	+	0.236379i
$501$	33.8557	+	0.534053i	1.51256	+	0.0238597i
$502$	11.8043	+	3.16296i	0.526852	+	0.141170i
$503$	−23.0051	+	23.0051i	−1.02575	+	1.02575i	−0.0260875	+	0.999660i	$0.508305\pi$
$503$	−23.0051	+	23.0051i	−1.02575	+	1.02575i	−0.999660	+	0.0260875i	$0.991695\pi$
$504$		0			0
$505$	18.8147	−	21.2808i	0.837245	−	0.946984i
$506$	−12.5784	+	7.26216i	−0.559179	+	0.322842i
$507$	33.3380	+	34.4067i	1.48059	+	1.52805i
$508$	−15.2074	+	4.07481i	−0.674719	+	0.180791i
$509$	−12.9064	−	22.3545i	−0.572066	−	0.990847i	−0.996354	−	0.0853198i	$-0.972809\pi$
$509$	−12.9064	−	22.3545i	−0.572066	−	0.990847i	0.424288	−	0.905527i	$-0.360525\pi$
$510$	17.3200	−	11.0833i	0.766943	−	0.490779i
$511$		0			0
$512$	−8.53124	−	8.53124i	−0.377031	−	0.377031i
$513$	20.8386	+	6.65492i	0.920045	+	0.293822i
$514$	−17.6069	−	10.1654i	−0.776607	−	0.448374i
$515$	4.15514	+	2.06991i	0.183097	+	0.0912110i
$516$	4.82667	+	2.88913i	0.212482	+	0.127187i
$517$	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	−0.963959	−	0.266051i	$-0.914281\pi$
$521$	−38.2633	−	22.0913i	−1.67635	−	0.967838i	−0.712386	−	0.701787i	$-0.752386\pi$
$522$	15.0131	+	4.53485i	0.657105	+	0.198485i
$523$	−4.78341	+	17.8519i	−0.209164	+	0.780611i	0.778976	+	0.627054i	$0.215740\pi$
$523$	−4.78341	+	17.8519i	−0.209164	+	0.780611i	−0.988140	+	0.153557i	$0.950927\pi$
$524$	0.558162			0.0243834
$525$		0			0
$526$	−0.295757			−0.0128956
$527$	4.52794	−	16.8985i	0.197240	−	0.736111i
$528$	−9.33702	−	9.63631i	−0.406341	−	0.419367i
$529$	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
$534$	2.12308	−	3.54688i	0.0918747	−	0.153489i
$535$	38.3599	+	19.1092i	1.65845	+	0.826164i
$536$	−3.33212	−	1.92380i	−0.143926	−	0.0830956i
$537$	5.02781	+	20.0221i	0.216966	+	0.864016i
$538$	8.21544	+	8.21544i	0.354193	+	0.354193i
$539$		0			0
$540$	−12.7305	+	0.179618i	−0.547836	+	0.00772954i
$541$	−10.7795	−	18.6706i	−0.463446	−	0.802713i	0.535683	−	0.844419i	$-0.320054\pi$
$541$	−10.7795	−	18.6706i	−0.463446	−	0.802713i	−0.999130	+	0.0417061i	$0.986721\pi$
$542$	40.4984	−	10.8515i	1.73955	−	0.466112i
$543$	21.8859	−	21.2062i	0.939215	−	0.910044i
$544$	−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	−0.321555	+	0.946891i	$0.604205\pi$
$547$	−29.6665	+	29.6665i	−1.26845	+	1.26845i	−0.946891	+	0.321555i	$0.895795\pi$
$548$	3.92099	+	1.05063i	0.167497	+	0.0448806i
$549$	8.77011	−	4.70102i	0.374299	−	0.200635i
$550$	12.6576	−	5.12404i	0.539721	−	0.218490i
$551$	−10.8325	+	6.25415i	−0.461480	+	0.266436i
$552$	−4.01574	+	14.0939i	−0.170921	+	0.599876i
$553$		0			0
$554$	35.8116			1.52149
$555$	2.04088	+	6.42751i	0.0866305	+	0.272833i
$556$	−3.48118	+	6.02957i	−0.147635	+	0.255711i
$557$	−26.2818	+	7.04218i	−1.11359	+	0.298387i	−0.768289	−	0.640103i	$-0.778892\pi$
$557$	−26.2818	+	7.04218i	−1.11359	+	0.298387i	−0.345306	+	0.938490i	$0.612225\pi$
$558$	−22.3113	+	20.9462i	−0.944511	+	0.886723i
$559$		−	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	$-0.0640105\pi$
$563$	0.745132	+	2.78087i	0.0314036	+	0.117200i	−0.948445	+	0.316942i	$0.897344\pi$
$564$	−0.00151740	+	0.0961938i	−6.38941e−5	+	0.00405049i
$565$	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	0.938948	+	0.344058i	$0.111802\pi$
$569$	18.3062	+	31.7073i	0.767437	+	1.32924i	−0.171511	+	0.985182i	$0.554865\pi$
$570$	19.3388	−	21.1904i	0.810011	−	0.887567i
$571$	4.94431	−	8.56380i	0.206913	−	0.358384i	−0.743827	−	0.668372i	$-0.766992\pi$
$571$	4.94431	−	8.56380i	0.206913	−	0.358384i	0.950741	+	0.309988i	$0.100325\pi$
$572$	2.80707	−	10.4761i	0.117370	−	0.438029i
$573$	2.62950	−	9.22865i	0.109849	−	0.385533i
$574$		0			0
$575$	−20.9650	−	16.3566i	−0.874300	−	0.682118i
$576$	−0.388858	−	0.0122711i	−0.0162024	−	0.000511294i
$577$	−1.26261	−	4.71214i	−0.0525633	−	0.196169i	0.934651	−	0.355566i	$-0.115712\pi$
$577$	−1.26261	−	4.71214i	−0.0525633	−	0.196169i	−0.987215	+	0.159397i	$0.949045\pi$
$578$	−3.59512	−	13.4172i	−0.149537	−	0.558080i
$579$	17.4903	−	29.2199i	0.726874	−	1.21434i
$580$	4.82202	−	5.45405i	0.200224	−	0.226467i
$581$		0			0
$582$	−45.5156	−	12.9687i	−1.88668	−	0.537569i
$583$	−2.44776	+	9.13517i	−0.101376	+	0.378340i
$584$	−8.17607	+	14.1614i	−0.338328	+	0.586002i
$585$	22.4847	+	36.3887i	0.929630	+	1.50449i
$586$	2.93432	+	5.08239i	0.121216	+	0.209952i
$587$	4.70846	+	4.70846i	0.194339	+	0.194339i	0.797568	−	0.603229i	$-0.206120\pi$
$587$	4.70846	+	4.70846i	0.194339	+	0.194339i	−0.603229	+	0.797568i	$0.706120\pi$
$588$		0			0
$589$		−	24.4079i		−	1.00571i
$590$	16.1955	−	10.7275i	0.666758	−	0.441645i
$591$	31.1425	+	0.491255i	1.28103	+	0.0202075i
$592$	−2.24918	−	8.39405i	−0.0924407	−	0.344993i
$593$	20.8865	+	5.59652i	0.857705	+	0.229821i	0.660764	−	0.750594i	$-0.270232\pi$
$593$	20.8865	+	5.59652i	0.857705	+	0.229821i	0.196941	+	0.980415i	$0.436899\pi$
$594$	14.1752	+	0.671263i	0.581617	+	0.0275422i
$595$		0			0
$596$			4.68955i			0.192092i
$597$	−10.2723	+	2.57952i	−0.420419	+	0.105573i
$598$	−57.6334	+	15.4428i	−2.35680	+	0.631504i
$599$	−4.69422	+	8.13063i	−0.191801	+	0.332208i	−0.945847	−	0.324613i	$-0.894766\pi$
$599$	−4.69422	+	8.13063i	−0.191801	+	0.332208i	0.754046	+	0.656821i	$0.228099\pi$
$600$	5.57431	−	12.6001i	0.227570	−	0.514398i
$601$	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
$603$	7.06377	−	1.65582i	0.287659	−	0.0674303i
$604$	−4.94635	+	2.85578i	−0.201264	+	0.116200i
$605$	18.2145	−	6.10141i	0.740527	−	0.248058i
$606$	0.610606	−	38.7086i	0.0248042	−	1.57243i
$607$	−3.50094	−	0.938074i	−0.142099	−	0.0380753i	0.187069	−	0.982347i	$-0.440101\pi$
$607$	−3.50094	−	0.938074i	−0.142099	−	0.0380753i	−0.329167	+	0.944272i	$0.606768\pi$
$608$	−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
$612$	2.86831	−	9.49584i	0.115945	−	0.383847i
$613$	−45.7845	+	12.2679i	−1.84922	+	0.495496i	−0.999496	−	0.0317359i	$-0.989896\pi$
$613$	−45.7845	+	12.2679i	−1.84922	+	0.495496i	−0.849721	+	0.527232i	$0.823230\pi$
$614$	0.987354	+	1.71015i	0.0398464	+	0.0690159i
$615$	−8.75771	+	5.60420i	−0.353145	+	0.225983i
$616$		0			0
$617$	2.15297	+	2.15297i	0.0866754	+	0.0866754i	0.749115	−	0.662440i	$-0.230479\pi$
$617$	2.15297	+	2.15297i	0.0866754	+	0.0866754i	−0.662440	+	0.749115i	$0.730479\pi$
$618$	6.13624	−	1.54089i	0.246836	−	0.0619838i
$619$	−8.82839	−	5.09707i	−0.354843	−	0.204869i	0.311973	−	0.950091i	$-0.399010\pi$
$619$	−8.82839	−	5.09707i	−0.354843	−	0.204869i	−0.666816	+	0.745222i	$0.732343\pi$
$620$	4.51214	+	13.4701i	0.181212	+	0.540973i
$621$	−12.6695	−	24.5585i	−0.508410	−	0.985498i
$622$	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
$627$	−8.12854	+	7.87608i	−0.324623	+	0.314540i
$628$	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
$633$	15.5365	−	15.0539i	0.617519	−	0.598339i
$634$	−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
$639$	−17.1988	−	0.542736i	−0.680373	−	0.0214703i
$640$	−11.3931	+	22.8706i	−0.450353	+	0.904041i
$641$	−13.6251	−	7.86647i	−0.538160	−	0.310707i	0.206173	−	0.978516i	$-0.433899\pi$
$641$	−13.6251	−	7.86647i	−0.538160	−	0.310707i	−0.744333	+	0.667809i	$0.767232\pi$
$642$	56.6494	−	14.2254i	2.23577	−	0.561433i
$643$	11.7811	+	11.7811i	0.464600	+	0.464600i	0.900160	−	0.435560i	$-0.143449\pi$
$643$	11.7811	+	11.7811i	0.464600	+	0.464600i	−0.435560	+	0.900160i	$0.643449\pi$
$644$		0			0
$645$	2.46187	−	11.2120i	0.0969359	−	0.441470i
$646$	11.1758	+	19.3570i	0.439706	+	0.761593i
$647$	14.7533	−	3.95315i	0.580014	−	0.155414i	0.0431286	−	0.999070i	$-0.486267\pi$
$647$	14.7533	−	3.95315i	0.580014	−	0.155414i	0.536885	+	0.843655i	$0.319601\pi$
$648$	10.7430	−	9.46628i	0.422026	−	0.371871i
$649$	−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	$-0.486666\pi$
$653$	−10.7688	−	2.88548i	−0.421414	−	0.112918i	−0.463293	+	0.886205i	$0.653332\pi$
$654$	−0.232719	+	14.7529i	−0.00910002	+	0.576885i
$655$	−0.361777	−	1.08001i	−0.0141358	−	0.0421996i
$656$	11.6032	−	6.69914i	0.453031	−	0.261557i
$657$	−7.03717	−	30.0207i	−0.274546	−	1.17122i
$658$		0			0
$659$	6.73141			0.262219			0.131109	−	0.991368i	$-0.458146\pi$
$659$	6.73141			0.262219			0.131109	+	0.991368i	$0.458146\pi$
$660$	3.02994	−	5.84929i	0.117940	−	0.227683i
$661$	2.21595	−	3.83814i	0.0861906	−	0.149286i	−0.819707	−	0.572783i	$-0.805864\pi$
$661$	2.21595	−	3.83814i	0.0861906	−	0.149286i	0.905898	+	0.423496i	$0.139197\pi$
$662$	−5.27274	+	1.41283i	−0.204931	+	0.0549110i
$663$	−32.3233	+	8.11681i	−1.25533	+	0.315231i
$664$			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
$669$	−21.5632	−	0.340147i	−0.833682	−	0.0131508i
$670$	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	0.639451	−	0.768832i	$-0.279162\pi$
$673$	−3.35642	−	3.35642i	−0.129381	−	0.129381i	−0.768832	+	0.639451i	$0.779162\pi$
$674$	−28.8678	−	50.0005i	−1.11195	−	1.92595i
$675$	8.59895	+	24.5165i	0.330974	+	0.943640i
$676$	15.1547	−	26.2487i	0.582873	−	1.00957i
$677$	2.31012	−	8.62148i	0.0887850	−	0.331350i	−0.907219	−	0.420659i	$-0.861799\pi$
$677$	2.31012	−	8.62148i	0.0887850	−	0.331350i	0.996004	+	0.0893084i	$0.0284657\pi$
$678$	44.0277	+	12.5447i	1.69087	+	0.481777i
$679$		0			0
$680$	8.04230	+	7.11034i	0.308408	+	0.272669i
$681$	19.8047	−	33.0864i	0.758918	−	1.26787i
$682$	−4.09814	−	15.2945i	−0.156926	−	0.585655i
$683$	7.85053	+	29.2986i	0.300392	+	1.12108i	0.936840	+	0.349759i	$0.113736\pi$
$683$	7.85053	+	29.2986i	0.300392	+	1.12108i	−0.636448	+	0.771320i	$0.719597\pi$
$684$	0.436510	−	13.8326i	0.0166904	−	0.528902i
$685$	−0.508516	−	8.26788i	−0.0194294	−	0.315899i
$686$		0			0
$687$	3.92722	−	13.7832i	0.149833	−	0.525862i
$688$	−3.82851	+	14.2882i	−0.145960	+	0.544732i
$689$	−19.4257	+	33.6464i	−0.740062	+	1.28183i
$690$	−36.2025	+	1.65396i	−1.37821	+	0.0629651i
$691$	9.39714	+	16.2763i	0.357484	+	0.619180i	0.987540	−	0.157369i	$-0.0503013\pi$
$691$	9.39714	+	16.2763i	0.357484	+	0.619180i	−0.630056	+	0.776550i	$0.716968\pi$
$692$	−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
$696$	−0.129135	+	8.18634i	−0.00489483	+	0.310302i
$697$	−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	$-0.0606652\pi$
$702$	55.5345	+	17.7353i	2.09601	+	0.669375i
$703$	−7.08066	+	1.89726i	−0.267052	+	0.0715564i
$704$	0.100648	−	0.174327i	0.00379331	−	0.00657021i
$705$	0.187113	−	0.0594127i	0.00704709	−	0.00223761i
$706$	−50.3682			−1.89563
$707$		0			0
$708$	2.56794	−	9.01260i	0.0965092	−	0.338714i
$709$	41.9323	−	24.2096i	1.57480	−	0.909211i	0.579232	−	0.815163i	$-0.303352\pi$
$709$	41.9323	−	24.2096i	1.57480	−	0.909211i	0.995568	−	0.0940486i	$-0.0299809\pi$
$710$	−10.0622	+	20.1989i	−0.377627	+	0.758050i
$711$	−5.09351	−	9.50232i	−0.191021	−	0.356365i
$712$	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
$717$	−32.1252	+	31.1274i	−1.19974	+	1.16247i
$718$	−32.0003	+	8.57445i	−1.19424	+	0.319996i
$719$	−5.34656	−	9.26052i	−0.199393	−	0.345359i	0.748939	−	0.662639i	$-0.230564\pi$
$719$	−5.34656	−	9.26052i	−0.199393	−	0.345359i	−0.948332	+	0.317280i	$0.897230\pi$
$720$	−9.62744	−	32.0654i	−0.358794	−	1.19501i
$721$		0			0
$722$	−1.58818	−	1.58818i	−0.0591060	−	0.0591060i
$723$	4.43766	+	17.6719i	0.165038	+	0.657226i
$724$	−16.6967	−	9.63983i	−0.620527	−	0.358261i
$725$	−13.6787	−	5.79527i	−0.508015	−	0.215231i
$726$	13.4460	−	22.4634i	0.499030	−	0.833694i
$727$	−30.9245	+	30.9245i	−1.14693	+	1.14693i	−0.159773	+	0.987154i	$0.551076\pi$
$727$	−30.9245	+	30.9245i	−1.14693	+	1.14693i	−0.987154	+	0.159773i	$0.948924\pi$
$728$		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
$732$	−4.38064	−	4.52106i	−0.161913	−	0.167103i
$733$	8.42207	−	31.4316i	0.311076	−	1.16095i	−0.616511	−	0.787346i	$-0.711455\pi$
$733$	8.42207	−	31.4316i	0.311076	−	1.16095i	0.927587	−	0.373606i	$-0.121879\pi$
$734$	2.34399			0.0865184
$735$		0			0
$736$	29.7782			1.09764
$737$	−0.971576	+	3.62597i	−0.0357885	+	0.133564i
$738$	−4.09747	+	13.5651i	−0.150830	+	0.499338i
$739$	−26.9299	−	15.5480i	−0.990631	−	0.571941i	−0.0851681	−	0.996367i	$-0.527143\pi$
$739$	−26.9299	−	15.5480i	−0.990631	−	0.571941i	−0.905463	+	0.424426i	$0.860476\pi$
$740$	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	$-0.713451\pi$
$743$	4.41646	−	4.41646i	0.162024	−	0.162024i	0.783463	+	0.621439i	$0.213451\pi$
$744$	−13.7081	−	8.20537i	−0.502565	−	0.300823i
$745$	9.07403	−	3.03957i	0.332447	−	0.111361i
$746$	15.9451	+	9.20591i	0.583792	+	0.337052i
$747$	−35.4676	−	37.7791i	−1.29769	−	1.38226i
$748$	3.62917	+	3.62917i	0.132695	+	0.132695i
$749$		0			0
$750$	33.9241	+	3.17398i	1.23873	+	0.115897i
$751$	10.3817	+	17.9816i	0.378834	+	0.656160i	0.990893	−	0.134653i	$-0.0429918\pi$
$751$	10.3817	+	17.9816i	0.378834	+	0.656160i	−0.612059	+	0.790812i	$0.709658\pi$
$752$	−0.244362	+	0.0654766i	−0.00891096	+	0.00238768i
$753$	−8.37140	−	8.63974i	−0.305071	−	0.314850i
$754$	−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	0.00868333	−	0.999962i	$-0.497236\pi$
$757$	27.7515	−	27.7515i	1.00865	−	1.00865i	0.999962	−	0.00868333i	$-0.00276403\pi$
$758$	37.3024	+	9.99514i	1.35488	+	0.363040i
$759$	14.2961	+	0.225512i	0.518915	+	0.00818558i
$760$	13.4055	+	6.67804i	0.486269	+	0.242238i
$761$	44.7004	−	25.8078i	1.62039	−	0.935531i	0.633570	−	0.773685i	$-0.281589\pi$
$761$	44.7004	−	25.8078i	1.62039	−	0.935531i	0.986816	−	0.161846i	$-0.0517447\pi$
$762$	42.1099	+	11.9983i	1.52548	+	0.434652i
$763$		0			0
$764$	−6.07087			−0.219636
$765$	−20.2330	+	0.604772i	−0.731527	+	0.0218656i
$766$	24.0505	−	41.6567i	0.868980	−	1.50512i
$767$	−30.4119	+	8.14885i	−1.09811	+	0.294238i
$768$	8.37194	+	33.3393i	0.302096	+	1.20303i
$769$		−	15.3442i		−	0.553327i	−0.960967	−	0.276663i	$-0.910771\pi$
$769$		−	15.3442i		−	0.553327i	0.960967	−	0.276663i	$-0.0892287\pi$
$770$		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	−0.987114	−	0.160020i	$-0.948844\pi$
$773$	−5.90138	−	22.0243i	−0.212258	−	0.792158i	0.774856	−	0.632138i	$-0.217822\pi$
$774$	−7.39112	−	13.7887i	−0.265668	−	0.495624i
$775$	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
$780$	18.2422	−	19.9888i	0.653175	−	0.715714i
$781$	4.45155	−	7.71032i	0.159289	−	0.275897i
$782$	7.30788	−	27.2734i	0.261329	−	0.975294i
$783$	−10.3881	−	11.4208i	−0.371240	−	0.408148i
$784$		0			0
$785$	−13.7615	+	0.846400i	−0.491168	+	0.0302093i
$786$	−1.33194	−	0.797269i	−0.0475088	−	0.0284376i
$787$	2.26808	+	8.46457i	0.0808482	+	0.301729i	0.994496	−	0.104778i	$-0.0334132\pi$
$787$	2.26808	+	8.46457i	0.0808482	+	0.301729i	−0.913647	+	0.406507i	$0.866747\pi$
$788$	−5.09996	−	19.0333i	−0.181679	−	0.678034i
$789$	0.249813	+	0.149532i	0.00889356	+	0.00532348i
$790$	−14.1125	+	0.867987i	−0.502099	+	0.0308816i
$791$		0			0
$792$	1.69080	+	7.21297i	0.0600798	+	0.256302i
$793$	−5.47405	+	20.4294i	−0.194389	+	0.725470i
$794$	25.9098	−	44.8771i	0.919505	−	1.59263i
$795$	−15.9072	+	17.4302i	−0.564169	+	0.618186i
$796$	3.35028	+	5.80285i	0.118747	+	0.205677i
$797$	−24.6954	−	24.6954i	−0.874755	−	0.874755i	0.118231	−	0.992986i	$-0.462278\pi$
$797$	−24.6954	−	24.6954i	−0.874755	−	0.874755i	−0.992986	+	0.118231i	$0.962278\pi$
$798$		0			0
$799$			0.152956i			0.00541119i
$800$	−27.7270	−	3.87748i	−0.980296	−	0.137090i
$801$	−3.58654	+	1.92248i	−0.126724	+	0.0679276i
$802$	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
$807$	−2.78556	−	11.0928i	−0.0980564	−	0.390487i
$808$	19.5218	−	5.23084i	0.686773	−	0.184020i
$809$	10.2032	−	17.6724i	0.358725	−	0.621329i	−0.629023	−	0.777386i	$-0.716545\pi$
$809$	10.2032	−	17.6724i	0.358725	−	0.621329i	0.987748	+	0.156057i	$0.0498784\pi$
$810$	30.6355	+	17.7555i	1.07642	+	0.623864i
$811$	−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
$813$	−39.6935	−	11.3098i	−1.39211	−	0.396652i
$814$	−4.11832	+	2.37772i	−0.144347	+	0.0833389i
$815$	15.1245	+	7.53437i	0.529789	+	0.263918i
$816$	26.0812	+	0.411416i	0.913025	+	0.0144024i
$817$	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	−0.734969	+	0.678100i	$0.762803\pi$
$821$	−48.4153	+	27.9526i	−1.68971	+	0.975552i	−0.954737	+	0.297452i	$0.903863\pi$
$822$	−7.85598	−	8.10780i	−0.274009	−	0.282792i
$823$	35.2310	−	9.44013i	1.22808	−	0.329062i	0.414246	−	0.910165i	$-0.364045\pi$
$823$	35.2310	−	9.44013i	1.22808	−	0.329062i	0.813830	+	0.581103i	$0.197378\pi$
$824$	1.65145	+	2.86039i	0.0575309	+	0.0996464i
$825$	−13.2819	−	2.07150i	−0.462417	−	0.0721204i
$826$		0			0
$827$	−25.9659	−	25.9659i	−0.902922	−	0.902922i	0.0927663	−	0.995688i	$-0.470429\pi$
$827$	−25.9659	−	25.9659i	−0.902922	−	0.902922i	−0.995688	+	0.0927663i	$0.970429\pi$
$828$	−12.7458	+	11.9660i	−0.442948	+	0.415847i
$829$	10.9810	+	6.33987i	0.381385	+	0.220193i	0.678421	−	0.734674i	$-0.262665\pi$
$829$	10.9810	+	6.33987i	0.381385	+	0.220193i	−0.297036	+	0.954866i	$0.595998\pi$
$830$	−64.4384	+	21.5852i	−2.23669	+	0.749235i
$831$	−30.2484	−	18.1060i	−1.04931	−	0.628089i
$832$	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
$837$	29.4355	−	6.41194i	1.01744	−	0.221629i
$838$	−0.239313	+	0.893128i	−0.00826693	+	0.0308526i
$839$	27.2730			0.941569			0.470785	−	0.882248i	$-0.343971\pi$
$839$	27.2730			0.941569			0.470785	+	0.882248i	$0.343971\pi$
$840$		0			0
$841$	−20.1723			−0.695596
$842$	7.07203	−	26.3932i	0.243718	−	0.909569i
$843$	−1.81633	−	1.87455i	−0.0625577	−	0.0645630i
$844$	−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
$849$	10.6823	−	17.8462i	0.366615	−	0.612479i
$850$	−10.3558	+	24.4431i	−0.355201	+	0.838390i
$851$	8.01950	+	4.63006i	0.274905	+	0.158716i
$852$	2.65135	+	10.5584i	0.0908339	+	0.361724i
$853$	−8.57549	−	8.57549i	−0.293619	−	0.293619i	0.544889	−	0.838508i	$-0.316572\pi$
$853$	−8.57549	−	8.57549i	−0.293619	−	0.293619i	−0.838508	+	0.544889i	$0.816572\pi$
$854$		0			0
$855$	−27.0482	+	8.12106i	−0.925029	+	0.277734i
$856$	15.2460	+	26.4069i	0.521099	+	0.902570i
$857$	−28.4758	+	7.63008i	−0.972716	+	0.260638i	−0.709974	−	0.704228i	$-0.751293\pi$
$857$	−28.4758	+	7.63008i	−0.972716	+	0.260638i	−0.262742	+	0.964866i	$0.584627\pi$
$858$	−21.6624	+	20.9896i	−0.739544	+	0.716574i
$859$	8.25133	−	4.76391i	0.281532	−	0.162543i	−0.352585	−	0.935780i	$-0.614697\pi$
$859$	8.25133	−	4.76391i	0.281532	−	0.162543i	0.634117	+	0.773237i	$0.281364\pi$
$860$	−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	$-0.132228\pi$
$863$	44.2282	+	11.8509i	1.50554	+	0.403409i	0.590592	+	0.806971i	$0.298894\pi$
$864$	−24.4808	−	15.7231i	−0.832853	−	0.534912i
$865$	−2.91363	+	5.84883i	−0.0990663	+	0.198866i
$866$	−33.1859	+	19.1599i	−1.12770	+	0.651080i
$867$	−3.74695	+	13.1505i	−0.127253	+	0.446615i
$868$		0			0
$869$	5.57830			0.189231
$870$	−19.2973	+	6.12732i	−0.654239	+	0.207736i
$871$	−7.71055	+	13.3551i	−0.261262	+	0.452519i
$872$	−7.44029	+	1.99362i	−0.251960	+	0.0675124i
$873$	31.8881	+	33.9663i	1.07925	+	1.14958i
$874$		−	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	0.733446	−	0.679747i	$-0.237911\pi$
$877$	30.4658	+	8.16328i	1.02876	+	0.275654i	0.295310	+	0.955402i	$0.404577\pi$
$878$	−2.75185	−	10.2701i	−0.0928705	−	0.346598i
$879$	0.0911197	−	5.77642i	0.00307339	−	0.194834i
$880$	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	0.304816	−	0.952411i	$-0.401405\pi$
$883$	−19.2435	−	19.2435i	−0.647595	−	0.647595i	−0.952411	+	0.304816i	$0.901405\pi$
$884$	10.5421	+	18.2594i	0.354569	+	0.614131i
$885$	−19.1033	+	0.872759i	−0.642151	+	0.0293375i
$886$	−10.7584	+	18.6341i	−0.361436	+	0.626025i
$887$	2.66050	−	9.92913i	0.0893309	−	0.333388i	−0.906768	−	0.421630i	$-0.861458\pi$
$887$	2.66050	−	9.92913i	0.0893309	−	0.333388i	0.996099	+	0.0882421i	$0.0281249\pi$
$888$	−1.31480	+	4.61451i	−0.0441219	+	0.154853i
$889$		0			0
$890$	0.327611	+	5.32658i	0.0109815	+	0.178547i
$891$	−11.6338	−	7.73383i	−0.389746	−	0.259093i
$892$	3.53123	+	13.1787i	0.118234	+	0.441257i
$893$	0.0552316	+	0.206127i	0.00184826	+	0.00689778i
$894$	6.69848	−	11.1907i	0.224031	−	0.374273i
$895$	−19.9664	−	17.6526i	−0.667402	−	0.590061i
$896$		0			0
$897$	56.4880	+	16.0950i	1.88608	+	0.537397i
$898$	9.45382	−	35.2822i	0.315478	−	1.17738i
$899$	−8.61290	+	14.9180i	−0.287256	+	0.497543i
$900$	13.4259	−	9.48206i	0.447531	−	0.316069i
$901$	−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
$906$	15.8826	+	0.250539i	0.527665	+	0.00832360i
$907$	7.33317	+	27.3678i	0.243494	+	0.908732i	0.974134	+	0.225969i	$0.0725550\pi$
$907$	7.33317	+	27.3678i	0.243494	+	0.908732i	−0.730640	+	0.682763i	$0.760778\pi$
$908$	−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	$0.807989\pi$
$912$	35.2963	−	8.86337i	1.16878	−	0.293496i
$913$	25.8977	−	6.93927i	0.857089	−	0.229656i
$914$	21.5330	−	37.2963i	0.712250	−	1.23365i
$915$	−5.90866	+	11.4067i	−0.195334	+	0.377092i
$916$	−9.06698			−0.299582
$917$		0			0
$918$	−20.4084	+	18.5629i	−0.673576	+	0.612667i
$919$	38.4001	−	22.1703i	1.26670	−	0.731331i	0.292340	−	0.956315i	$-0.405566\pi$
$919$	38.4001	−	22.1703i	1.26670	−	0.731331i	0.974363	+	0.224984i	$0.0722329\pi$
$920$	−6.00930	−	17.9396i	−0.198121	−	0.591450i
$921$	0.0306604	−	1.94368i	0.00101029	−	0.0640464i
$922$	−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
$927$	−5.96206	−	1.80090i	−0.195820	−	0.0591493i
$928$	16.0696	−	4.30584i	0.527511	−	0.141346i
$929$	4.94121	+	8.55843i	0.162116	+	0.280793i	0.935627	−	0.352989i	$-0.114835\pi$
$929$	4.94121	+	8.55843i	0.162116	+	0.280793i	−0.773511	+	0.633782i	$0.781501\pi$
$930$	8.47314	−	38.5888i	0.277845	−	1.26538i
$931$		0			0
$932$	13.8534	+	13.8534i	0.453784	+	0.453784i
$933$	−16.6565	+	4.18267i	−0.545310	+	0.136935i
$934$	30.0890	+	17.3719i	0.984542	+	0.568426i
$935$	4.66996	−	9.37450i	0.152724	−	0.306579i
$936$	−0.959930	+	30.4192i	−0.0313763	+	0.994284i
$937$	22.4981	−	22.4981i	0.734980	−	0.734980i	−0.236622	−	0.971602i	$-0.576040\pi$
$937$	22.4981	−	22.4981i	0.734980	−	0.734980i	0.971602	+	0.236622i	$0.0760403\pi$
$938$		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	0.992844	+	0.119415i	$0.0381020\pi$
$941$	48.8567	+	28.2074i	1.59268	+	0.919536i	0.599839	+	0.800121i	$0.295231\pi$
$942$	−13.4950	+	13.0759i	−0.439692	+	0.426036i
$943$	−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	$-0.855951\pi$
$947$	3.02006	−	11.2710i	0.0981386	−	0.366258i	0.997477	+	0.0709958i	$0.0226177\pi$
$948$	−4.89852	+	4.74638i	−0.159097	+	0.154155i
$949$	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	$-0.612185\pi$
$953$	18.3169	−	18.3169i	0.593344	−	0.593344i	0.938533	+	0.345189i	$0.112185\pi$
$954$	−1.01439	+	32.1450i	−0.0328421	+	1.04073i
$955$	3.93488	+	11.7468i	0.127330	+	0.380117i
$956$	24.5081	+	14.1498i	0.792650	+	0.457637i
$957$	7.74739	−	1.94547i	0.250438	−	0.0628882i
$958$	19.9147	+	19.9147i	0.643414	+	0.643414i
$959$		0			0
$960$	0.423058	−	0.270721i	0.0136541	−	0.00873749i
$961$	−1.30666	−	2.26320i	−0.0421503	−	0.0730064i
$962$	−18.8699	+	5.05616i	−0.608389	+	0.163017i
$963$	−55.0414	−	16.6258i	−1.77368	−	0.535759i
$964$	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	−0.804645	−	0.593756i	$-0.797644\pi$
$967$	−6.55794	+	6.55794i	−0.210889	+	0.210889i	0.593756	+	0.804645i	$0.297644\pi$
$968$	13.2017	+	3.53738i	0.424318	+	0.113696i
$969$	0.347043	−	22.0004i	0.0111486	−	0.706754i
$970$	57.9351	−	19.4068i	1.86018	−	0.623114i
$971$	−12.0561	+	6.96061i	−0.386899	+	0.223377i	−0.680816	−	0.732455i	$-0.738375\pi$
$971$	−12.0561	+	6.96061i	−0.386899	+	0.223377i	0.293916	+	0.955831i	$0.405041\pi$
$972$	16.7965	−	3.10739i	0.538748	−	0.0996696i
$973$		0			0
$974$	−51.2825			−1.64320
$975$	−50.5010	−	22.3417i	−1.61733	−	0.715507i
$976$	8.27695	−	14.3361i	0.264939	−	0.458887i
$977$	37.1577	−	9.95638i	1.18878	−	0.318533i	0.390377	−	0.920655i	$-0.372345\pi$
$977$	37.1577	−	9.95638i	1.18878	−	0.318533i	0.798404	+	0.602122i	$0.205678\pi$
$978$	22.3357	−	5.60879i	0.714216	−	0.179349i
$979$		−	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	−0.752251	−	0.658877i	$-0.771032\pi$
$983$	−13.4886	−	50.3403i	−0.430221	−	1.60561i	0.322030	−	0.946730i	$-0.395635\pi$
$984$	−7.39677	−	0.116680i	−0.235800	−	0.00371961i
$985$	−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
$990$	−15.5854	+	9.63026i	−0.495336	+	0.306070i
$991$	20.9326	−	36.2563i	0.664945	−	1.15172i	−0.314356	−	0.949305i	$-0.601788\pi$
$991$	20.9326	−	36.2563i	0.664945	−	1.15172i	0.979300	−	0.202413i	$-0.0648782\pi$
$992$	−8.40214	+	31.3572i	−0.266768	+	0.995592i
$993$	5.16795	+	1.47249i	0.164000	+	0.0467281i
$994$		0			0
$995$	9.05669	−	10.2438i	0.287116	−	0.324749i
$996$	−16.8374	+	28.1291i	−0.533513	+	0.891303i
$997$	−4.18963	−	15.6359i	−0.132687	−	0.495194i	0.867310	−	0.497769i	$-0.165847\pi$
$997$	−4.18963	−	15.6359i	−0.132687	−	0.495194i	−0.999997	+	0.00257448i	$0.999181\pi$
$998$	0.428339	+	1.59858i	0.0135588	+	0.0506023i
$999$	−4.14814	−	8.04074i	−0.131241	−	0.254398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.g.263.3		48
3.2	odd	2	inner	735.2.y.g.263.10		48
5.2	odd	4	inner	735.2.y.g.557.3		48
7.2	even	3	inner	735.2.y.g.128.10		48
7.3	odd	6		105.2.j.a.8.3	✓	24
7.4	even	3		735.2.j.h.638.3		24
7.5	odd	6		735.2.y.j.128.10		48
7.6	odd	2		735.2.y.j.263.3		48
15.2	even	4	inner	735.2.y.g.557.10		48
21.2	odd	6	inner	735.2.y.g.128.3		48
21.5	even	6		735.2.y.j.128.3		48
21.11	odd	6		735.2.j.h.638.10		24
21.17	even	6		105.2.j.a.8.10	yes	24
21.20	even	2		735.2.y.j.263.10		48
35.2	odd	12	inner	735.2.y.g.422.10		48
35.3	even	12		525.2.j.b.407.3		24
35.12	even	12		735.2.y.j.422.10		48
35.17	even	12		105.2.j.a.92.10	yes	24
35.24	odd	6		525.2.j.b.218.10		24
35.27	even	4		735.2.y.j.557.3		48
35.32	odd	12		735.2.j.h.197.10		24
105.2	even	12	inner	735.2.y.g.422.3		48
105.17	odd	12		105.2.j.a.92.3	yes	24
105.32	even	12		735.2.j.h.197.3		24
105.38	odd	12		525.2.j.b.407.10		24
105.47	odd	12		735.2.y.j.422.3		48
105.59	even	6		525.2.j.b.218.3		24
105.62	odd	4		735.2.y.j.557.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.3	✓	24	7.3	odd	6
105.2.j.a.8.10	yes	24	21.17	even	6
105.2.j.a.92.3	yes	24	105.17	odd	12
105.2.j.a.92.10	yes	24	35.17	even	12
525.2.j.b.218.3		24	105.59	even	6
525.2.j.b.218.10		24	35.24	odd	6
525.2.j.b.407.3		24	35.3	even	12
525.2.j.b.407.10		24	105.38	odd	12
735.2.j.h.197.3		24	105.32	even	12
735.2.j.h.197.10		24	35.32	odd	12
735.2.j.h.638.3		24	7.4	even	3
735.2.j.h.638.10		24	21.11	odd	6
735.2.y.g.128.3		48	21.2	odd	6	inner
735.2.y.g.128.10		48	7.2	even	3	inner
735.2.y.g.263.3		48	1.1	even	1	trivial
735.2.y.g.263.10		48	3.2	odd	2	inner
735.2.y.g.422.3		48	105.2	even	12	inner
735.2.y.g.422.10		48	35.2	odd	12	inner
735.2.y.g.557.3		48	5.2	odd	4	inner
735.2.y.g.557.10		48	15.2	even	4	inner
735.2.y.j.128.3		48	21.5	even	6
735.2.y.j.128.10		48	7.5	odd	6
735.2.y.j.263.3		48	7.6	odd	2
735.2.y.j.263.10		48	21.20	even	2
735.2.y.j.422.3		48	105.47	odd	12
735.2.y.j.422.10		48	35.12	even	12
735.2.y.j.557.3		48	35.27	even	4
735.2.y.j.557.10		48	105.62	odd	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.455388 + 1.69953i) q^{2} +(1.24391 - 1.20528i) 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} +(0.0946229 - 2.99851i) q^{9} +(-3.52156 - 1.75429i) q^{10} +(1.34425 + 0.776103i) q^{11} +(-1.84080 + 0.462248i) q^{12} +(4.50889 + 4.50889i) q^{13} +(2.08755 + 3.26223i) q^{15} +(-2.49541 - 4.32218i) q^{16} +(-2.91469 + 0.780989i) q^{17} +(5.05296 + 1.52630i) 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} +(-0.0434629 + 2.75528i) q^{24} +(-4.60386 - 1.95052i) q^{25} +(-9.71628 + 5.60970i) q^{26} +(-3.49632 - 3.84392i) q^{27} +2.97115 q^{29} +(-6.49490 + 2.06228i) q^{30} +(-2.89885 + 5.02095i) q^{31} +(5.40856 - 1.44922i) q^{32} +(2.60754 - 0.654789i) q^{33} -5.30926i q^{34} +(-1.73265 + 2.79366i) q^{36} +(1.68190 + 0.450663i) q^{37} +(-1.91715 - 7.15489i) q^{38} +(11.0431 + 0.174198i) q^{39} +(-1.96452 - 2.96587i) q^{40} +2.68458i q^{41} +(-2.09578 - 2.09578i) q^{43} +(-0.850438 - 1.47300i) q^{44} +(6.52861 + 1.54184i) q^{45} +(-4.67860 + 8.10358i) q^{46} +(0.0131194 - 0.0489622i) q^{47} +(-8.31349 - 2.36874i) q^{48} +(5.41150 - 6.93615i) q^{50} +(-2.68431 + 4.48449i) q^{51} +(-1.80844 - 6.74919i) q^{52} +(1.57696 + 5.88528i) q^{53} +(8.12504 - 4.19163i) q^{54} +(-2.29896 + 2.60029i) q^{55} +(-1.99811 + 7.01270i) q^{57} +(-1.35302 + 5.04955i) q^{58} +(-2.46880 + 4.27609i) q^{59} +(-0.193688 - 4.23952i) q^{60} +(1.65843 + 2.87249i) q^{61} +(-7.21316 - 7.21316i) q^{62} -0.129684i q^{64} +(-11.8872 + 7.87377i) q^{65} +(-0.0746095 + 4.72978i) q^{66} +(0.625932 + 2.33601i) q^{67} +(3.19386 + 0.855793i) q^{68} +(8.04889 - 4.47927i) q^{69} -5.73577i q^{71} +(3.26681 + 3.47970i) q^{72} +(9.92795 - 2.66019i) q^{73} +(-1.53183 + 2.65321i) q^{74} +(-8.07769 + 3.12265i) q^{75} +4.61315 q^{76} +(-5.32495 + 18.6887i) q^{78} +(3.11231 - 1.79689i) q^{79} +(10.5819 - 3.54467i) q^{80} +(-8.98209 - 0.567455i) 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} +(3.69584 - 3.58105i) q^{87} +(-2.38535 + 0.639153i) q^{88} +(-0.678216 - 1.17470i) q^{89} +(-5.59346 + 10.3934i) q^{90} +(-4.12069 - 4.12069i) q^{92} +(2.44573 + 9.73953i) q^{93} +(0.0772383 + 0.0445936i) q^{94} +(-2.99005 - 8.92620i) q^{95} +(4.98105 - 8.32150i) 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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