LMFDB - Embedded newform 289.2.d.f.155.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,2,Mod(110,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.110"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0] 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.3
Character	$\chi$	$=$	289.155
Dual form			289.2.d.f.179.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.245576 + 0.245576i) q^{2} +(-0.812446 + 0.336526i) q^{3} -1.87939i q^{4} +(-0.898271 - 2.16862i) q^{5} +(-0.282160 - 0.116874i) q^{6} +(-0.719210 + 1.73633i) q^{7} +(0.952682 - 0.952682i) q^{8} +(-1.57450 + 1.57450i) q^{9} +(0.311966 - 0.753153i) q^{10} +(-4.67869 - 1.93798i) q^{11} +(0.632462 + 1.52690i) q^{12} -4.71688i q^{13} +(-0.603020 + 0.249779i) q^{14} +(1.45959 + 1.45959i) q^{15} -3.29086 q^{16} -0.773318 q^{18} +(0.245576 + 0.245576i) q^{19} +(-4.07567 + 1.68820i) q^{20} -1.65270i q^{21} +(-0.673052 - 1.62489i) q^{22} +(1.63833 + 0.678620i) q^{23} +(-0.453400 + 1.09461i) q^{24} +(-0.360483 + 0.360483i) q^{25} +(1.15835 - 1.15835i) q^{26} +(1.75892 - 4.24640i) q^{27} +(3.26322 + 1.35167i) q^{28} +(-0.852114 - 2.05719i) q^{29} +0.716881i q^{30} +(1.79562 - 0.743769i) q^{31} +(-2.71352 - 2.71352i) q^{32} +4.45336 q^{33} +4.41147 q^{35} +(2.95910 + 2.95910i) q^{36} +(5.70056 - 2.36125i) q^{37} +0.120615i q^{38} +(1.58735 + 3.83221i) q^{39} +(-2.92177 - 1.21024i) q^{40} +(1.97857 - 4.77668i) q^{41} +(0.405864 - 0.405864i) q^{42} +(-1.04344 + 1.04344i) q^{43} +(-3.64221 + 8.79306i) q^{44} +(4.82882 + 2.00016i) q^{45} +(0.235682 + 0.568987i) q^{46} +8.53209i q^{47} +(2.67365 - 1.10746i) q^{48} +(2.45218 + 2.45218i) q^{49} -0.177052 q^{50} -8.86484 q^{52} +(-7.39164 - 7.39164i) q^{53} +(1.47476 - 0.610865i) q^{54} +11.8871i q^{55} +(0.968988 + 2.33935i) q^{56} +(-0.282160 - 0.116874i) q^{57} +(0.295936 - 0.714453i) q^{58} +(-3.54101 + 3.54101i) q^{59} +(2.74314 - 2.74314i) q^{60} +(0.0707170 - 0.170726i) q^{61} +(0.623612 + 0.258308i) q^{62} +(-1.60145 - 3.86624i) q^{63} +5.24897i q^{64} +(-10.2291 + 4.23704i) q^{65} +(1.09364 + 1.09364i) q^{66} +2.44831 q^{67} -1.55943 q^{69} +(1.08335 + 1.08335i) q^{70} +(9.16606 - 3.79671i) q^{71} +3.00000i q^{72} +(4.17189 + 10.0718i) q^{73} +(1.97978 + 0.820054i) q^{74} +(0.171561 - 0.414185i) q^{75} +(0.461531 - 0.461531i) q^{76} +(6.72992 - 6.72992i) q^{77} +(-0.551282 + 1.33091i) q^{78} +(4.09626 + 1.69673i) q^{79} +(2.95608 + 7.13662i) q^{80} -2.63816i q^{81} +(1.65892 - 0.687149i) q^{82} +(-9.60373 - 9.60373i) q^{83} -3.10607 q^{84} -0.512489 q^{86} +(1.38459 + 1.38459i) q^{87} +(-6.30358 + 2.61103i) q^{88} -6.32770i q^{89} +(0.694650 + 1.67703i) q^{90} +(8.19004 + 3.39243i) q^{91} +(1.27539 - 3.07906i) q^{92} +(-1.20854 + 1.20854i) q^{93} +(-2.09527 + 2.09527i) q^{94} +(0.311966 - 0.753153i) q^{95} +(3.11776 + 1.29142i) q^{96} +(-3.54989 - 8.57019i) q^{97} +1.20439i q^{98} +(10.4180 - 4.31526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{16} - 72 q^{18} + 24 q^{35} - 168 q^{50} - 24 q^{52} + 72 q^{67} + 168 q^{69} + 24 q^{84} + 48 q^{86}+O(q^{100}) $ 24 * q + 48 * q^16 - 72 * q^18 + 24 * q^35 - 168 * q^50 - 24 * q^52 + 72 * q^67 + 168 * q^69 + 24 * q^84 + 48 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	0.245576	+	0.245576i	0.173648	+	0.173648i	0.788580	−	0.614932i	$-0.210817\pi$
$2$	0.245576	+	0.245576i	0.173648	+	0.173648i	−0.614932	+	0.788580i	$0.710817\pi$
$3$	−0.812446	+	0.336526i	−0.469066	+	0.194293i	−0.604680	−	0.796468i	$-0.706699\pi$
$3$	−0.812446	+	0.336526i	−0.469066	+	0.194293i	0.135614	+	0.990762i	$0.456699\pi$
$4$		−	1.87939i		−	0.939693i
$5$	−0.898271	−	2.16862i	−0.401719	−	0.969836i	−0.987249	−	0.159185i	$-0.949113\pi$
$5$	−0.898271	−	2.16862i	−0.401719	−	0.969836i	0.585530	−	0.810651i	$-0.300887\pi$
$6$	−0.282160	−	0.116874i	−0.115191	−	0.0477137i
$7$	−0.719210	+	1.73633i	−0.271836	+	0.656269i	−0.999562	−	0.0295984i	$-0.990577\pi$
$7$	−0.719210	+	1.73633i	−0.271836	+	0.656269i	0.727726	+	0.685868i	$0.240577\pi$
$8$	0.952682	−	0.952682i	0.336824	−	0.336824i
$9$	−1.57450	+	1.57450i	−0.524834	+	0.524834i
$10$	0.311966	−	0.753153i	0.0986524	−	0.238168i
$11$	−4.67869	−	1.93798i	−1.41068	−	0.584322i	−0.458178	−	0.888860i	$-0.651498\pi$
$11$	−4.67869	−	1.93798i	−1.41068	−	0.584322i	−0.952500	+	0.304538i	$0.901498\pi$
$12$	0.632462	+	1.52690i	0.182576	+	0.440778i
$13$		−	4.71688i		−	1.30823i	−0.756396	−	0.654114i	$-0.773042\pi$
$13$		−	4.71688i		−	1.30823i	0.756396	−	0.654114i	$-0.226958\pi$
$14$	−0.603020	+	0.249779i	−0.161164	+	0.0667562i
$15$	1.45959	+	1.45959i	0.376866	+	0.376866i
$16$	−3.29086			−0.822715
$17$		0			0
$17$		0			0
$18$	−0.773318			−0.182273
$19$	0.245576	+	0.245576i	0.0563389	+	0.0563389i	0.734715	−	0.678376i	$-0.237316\pi$
$19$	0.245576	+	0.245576i	0.0563389	+	0.0563389i	−0.678376	+	0.734715i	$0.737316\pi$
$20$	−4.07567	+	1.68820i	−0.911348	+	0.377493i
$21$		−	1.65270i		−	0.360650i
$22$	−0.673052	−	1.62489i	−0.143495	−	0.346428i
$23$	1.63833	+	0.678620i	0.341616	+	0.141502i	0.546894	−	0.837202i	$-0.315810\pi$
$23$	1.63833	+	0.678620i	0.341616	+	0.141502i	−0.205278	+	0.978704i	$0.565810\pi$
$24$	−0.453400	+	1.09461i	−0.0925500	+	0.223435i
$25$	−0.360483	+	0.360483i	−0.0720966	+	0.0720966i
$26$	1.15835	−	1.15835i	0.227171	−	0.227171i
$27$	1.75892	−	4.24640i	0.338503	−	0.817219i
$28$	3.26322	+	1.35167i	0.616691	+	0.255442i
$29$	−0.852114	−	2.05719i	−0.158234	−	0.382010i	0.824803	−	0.565421i	$-0.191286\pi$
$29$	−0.852114	−	2.05719i	−0.158234	−	0.382010i	−0.983036	+	0.183411i	$0.941286\pi$
$30$			0.716881i			0.130884i
$31$	1.79562	−	0.743769i	0.322503	−	0.133585i	−0.215558	−	0.976491i	$-0.569157\pi$
$31$	1.79562	−	0.743769i	0.322503	−	0.133585i	0.538061	+	0.842906i	$0.319157\pi$
$32$	−2.71352	−	2.71352i	−0.479687	−	0.479687i
$33$	4.45336			0.775231
$34$		0			0
$35$	4.41147			0.745675
$36$	2.95910	+	2.95910i	0.493183	+	0.493183i
$37$	5.70056	−	2.36125i	0.937167	−	0.388187i	0.138774	−	0.990324i	$-0.455684\pi$
$37$	5.70056	−	2.36125i	0.937167	−	0.388187i	0.798393	+	0.602137i	$0.205684\pi$
$38$			0.120615i			0.0195663i
$39$	1.58735	+	3.83221i	0.254180	+	0.613645i
$40$	−2.92177	−	1.21024i	−0.461973	−	0.191355i
$41$	1.97857	−	4.77668i	0.309000	−	0.745993i	−0.690738	−	0.723105i	$-0.742714\pi$
$41$	1.97857	−	4.77668i	0.309000	−	0.745993i	0.999738	−	0.0228873i	$-0.00728588\pi$
$42$	0.405864	−	0.405864i	0.0626261	−	0.0626261i
$43$	−1.04344	+	1.04344i	−0.159124	+	0.159124i	−0.782178	−	0.623055i	$-0.785891\pi$
$43$	−1.04344	+	1.04344i	−0.159124	+	0.159124i	0.623055	+	0.782178i	$0.285891\pi$
$44$	−3.64221	+	8.79306i	−0.549083	+	1.32560i
$45$	4.82882	+	2.00016i	0.719839	+	0.298167i
$46$	0.235682	+	0.568987i	0.0347494	+	0.0838925i
$47$			8.53209i			1.24453i	0.782805	+	0.622267i	$0.213788\pi$
$47$			8.53209i			1.24453i	−0.782805	+	0.622267i	$0.786212\pi$
$48$	2.67365	−	1.10746i	0.385908	−	0.159848i
$49$	2.45218	+	2.45218i	0.350312	+	0.350312i
$50$	−0.177052			−0.0250389
$51$		0			0
$52$	−8.86484			−1.22933
$53$	−7.39164	−	7.39164i	−1.01532	−	1.01532i	−0.999881	−	0.0154396i	$-0.995085\pi$
$53$	−7.39164	−	7.39164i	−1.01532	−	1.01532i	−0.0154396	−	0.999881i	$-0.504915\pi$
$54$	1.47476	−	0.610865i	0.200689	−	0.0831282i
$55$			11.8871i			1.60286i
$56$	0.968988	+	2.33935i	0.129487	+	0.312608i
$57$	−0.282160	−	0.116874i	−0.0373729	−	0.0154804i
$58$	0.295936	−	0.714453i	0.0388583	−	0.0938123i
$59$	−3.54101	+	3.54101i	−0.461000	+	0.461000i	−0.898983	−	0.437983i	$-0.855693\pi$
$59$	−3.54101	+	3.54101i	−0.461000	+	0.461000i	0.437983	+	0.898983i	$0.355693\pi$
$60$	2.74314	−	2.74314i	0.354138	−	0.354138i
$61$	0.0707170	−	0.170726i	0.00905439	−	0.0218592i	−0.919288	−	0.393586i	$-0.871234\pi$
$61$	0.0707170	−	0.170726i	0.00905439	−	0.0218592i	0.928342	+	0.371727i	$0.121234\pi$
$62$	0.623612	+	0.258308i	0.0791988	+	0.0328052i
$63$	−1.60145	−	3.86624i	−0.201764	−	0.487101i
$64$			5.24897i			0.656121i
$65$	−10.2291	+	4.23704i	−1.26877	+	0.525540i
$66$	1.09364	+	1.09364i	0.134617	+	0.134617i
$67$	2.44831			0.299109			0.149554	−	0.988754i	$-0.452216\pi$
$67$	2.44831			0.299109			0.149554	+	0.988754i	$0.452216\pi$
$68$		0			0
$69$	−1.55943			−0.187733
$70$	1.08335	+	1.08335i	0.129485	+	0.129485i
$71$	9.16606	−	3.79671i	1.08781	−	0.450586i	0.234568	−	0.972100i	$-0.424632\pi$
$71$	9.16606	−	3.79671i	1.08781	−	0.450586i	0.853243	+	0.521513i	$0.174632\pi$
$72$			3.00000i			0.353553i
$73$	4.17189	+	10.0718i	0.488283	+	1.17882i	0.955584	+	0.294721i	$0.0952265\pi$
$73$	4.17189	+	10.0718i	0.488283	+	1.17882i	−0.467301	+	0.884098i	$0.654773\pi$
$74$	1.97978	+	0.820054i	0.230145	+	0.0953293i
$75$	0.171561	−	0.414185i	0.0198102	−	0.0478260i
$76$	0.461531	−	0.461531i	0.0529413	−	0.0529413i
$77$	6.72992	−	6.72992i	0.766945	−	0.766945i
$78$	−0.551282	+	1.33091i	−0.0624204	+	0.150696i
$79$	4.09626	+	1.69673i	0.460866	+	0.190897i	0.601022	−	0.799233i	$-0.294760\pi$
$79$	4.09626	+	1.69673i	0.460866	+	0.190897i	−0.140156	+	0.990129i	$0.544760\pi$
$80$	2.95608	+	7.13662i	0.330500	+	0.797898i
$81$		−	2.63816i		−	0.293128i
$82$	1.65892	−	0.687149i	0.183198	−	0.0758829i
$83$	−9.60373	−	9.60373i	−1.05415	−	1.05415i	−0.998448	−	0.0556982i	$-0.982262\pi$
$83$	−9.60373	−	9.60373i	−1.05415	−	1.05415i	−0.0556982	−	0.998448i	$-0.517738\pi$
$84$	−3.10607			−0.338900
$85$		0			0
$86$	−0.512489			−0.0552631
$87$	1.38459	+	1.38459i	0.148444	+	0.148444i
$88$	−6.30358	+	2.61103i	−0.671964	+	0.278337i
$89$		−	6.32770i		−	0.670734i	−0.942087	−	0.335367i	$-0.891140\pi$
$89$		−	6.32770i		−	0.670734i	0.942087	−	0.335367i	$-0.108860\pi$
$90$	0.694650	+	1.67703i	0.0732225	+	0.176775i
$91$	8.19004	+	3.39243i	0.858550	+	0.355623i
$92$	1.27539	−	3.07906i	0.132968	−	0.321014i
$93$	−1.20854	+	1.20854i	−0.125320	+	0.125320i
$94$	−2.09527	+	2.09527i	−0.216111	+	0.216111i
$95$	0.311966	−	0.753153i	0.0320071	−	0.0772719i
$96$	3.11776	+	1.29142i	0.318205	+	0.131805i
$97$	−3.54989	−	8.57019i	−0.360437	−	0.870171i	−0.995236	−	0.0974943i	$-0.968917\pi$
$97$	−3.54989	−	8.57019i	−0.360437	−	0.870171i	0.634799	−	0.772677i	$-0.281083\pi$
$98$			1.20439i			0.121662i
$99$	10.4180	−	4.31526i	1.04704	−	0.433700i
$100$	0.677487	+	0.677487i	0.0677487	+	0.0677487i
$101$	7.04963			0.701464			0.350732	−	0.936476i	$-0.385933\pi$
$101$	7.04963			0.701464			0.350732	+	0.936476i	$0.385933\pi$
$102$		0			0
$103$	5.29860			0.522087			0.261043	−	0.965327i	$-0.415933\pi$
$103$	5.29860			0.522087			0.261043	+	0.965327i	$0.415933\pi$
$104$	−4.49369	−	4.49369i	−0.440643	−	0.440643i
$105$	−3.58408	+	1.48458i	−0.349771	+	0.144880i
$106$		−	3.63041i		−	0.352617i
$107$	−5.96843	−	14.4091i	−0.576990	−	1.39298i	−0.895502	−	0.445058i	$-0.853183\pi$
$107$	−5.96843	−	14.4091i	−0.576990	−	1.39298i	0.318511	−	0.947919i	$-0.396817\pi$
$108$	−7.98062	−	3.30568i	−0.767935	−	0.318089i
$109$	0.716247	−	1.72917i	0.0686041	−	0.165625i	−0.885859	−	0.463955i	$-0.846430\pi$
$109$	0.716247	−	1.72917i	0.0686041	−	0.165625i	0.954463	+	0.298331i	$0.0964298\pi$
$110$	−2.91919	+	2.91919i	−0.278334	+	0.278334i
$111$	−3.83678	+	3.83678i	−0.364171	+	0.364171i
$112$	2.36682	−	5.71400i	0.223643	−	0.539923i
$113$	−11.1917	−	4.63575i	−1.05283	−	0.436095i	−0.211927	−	0.977286i	$-0.567974\pi$
$113$	−11.1917	−	4.63575i	−1.05283	−	0.436095i	−0.840900	+	0.541191i	$0.817974\pi$
$114$	−0.0405900	−	0.0979930i	−0.00380160	−	0.00917788i
$115$		−	4.16250i		−	0.388155i
$116$	−3.86624	+	1.60145i	−0.358972	+	0.148691i
$117$	7.42674	+	7.42674i	0.686602	+	0.686602i
$118$	−1.73917			−0.160104
$119$		0			0
$120$	2.78106			0.253875
$121$	10.3562	+	10.3562i	0.941474	+	0.941474i
$122$	0.0592925	−	0.0245598i	0.00536809	−	0.00222354i
$123$			4.54664i			0.409956i
$124$	−1.39783	−	3.37466i	−0.125529	−	0.303053i
$125$	−9.73753	−	4.03342i	−0.870951	−	0.360760i
$126$	0.556178	−	1.34273i	0.0495483	−	0.119620i
$127$	8.15989	−	8.15989i	0.724073	−	0.724073i	−0.245359	−	0.969432i	$-0.578906\pi$
$127$	8.15989	−	8.15989i	0.724073	−	0.724073i	0.969432	+	0.245359i	$0.0789058\pi$
$128$	−6.71606	+	6.71606i	−0.593621	+	0.593621i
$129$	0.496595	−	1.19889i	0.0437228	−	0.105556i
$130$	−3.55254	−	1.47151i	−0.311578	−	0.129060i
$131$	7.41435	+	17.8998i	0.647795	+	1.56392i	0.815929	+	0.578151i	$0.196226\pi$
$131$	7.41435	+	17.8998i	0.647795	+	1.56392i	−0.168134	+	0.985764i	$0.553774\pi$
$132$		−	8.36959i		−	0.728479i
$133$	−0.603020	+	0.249779i	−0.0522884	+	0.0216586i
$134$	0.601245	+	0.601245i	0.0519397	+	0.0519397i
$135$	−10.7888			−0.928552
$136$		0			0
$137$	−0.448311			−0.0383018			−0.0191509	−	0.999817i	$-0.506096\pi$
$137$	−0.448311			−0.0383018			−0.0191509	+	0.999817i	$0.506096\pi$
$138$	−0.382958	−	0.382958i	−0.0325995	−	0.0325995i
$139$	−10.7910	+	4.46976i	−0.915277	+	0.379120i	−0.790074	−	0.613011i	$-0.789958\pi$
$139$	−10.7910	+	4.46976i	−0.915277	+	0.379120i	−0.125203	+	0.992131i	$0.539958\pi$
$140$		−	8.29086i		−	0.700706i
$141$	−2.87127	−	6.93186i	−0.241805	−	0.583768i
$142$	3.18334	+	1.31858i	0.267140	+	0.110653i
$143$	−9.14121	+	22.0688i	−0.764426	+	1.84549i
$144$	5.18146	−	5.18146i	0.431789	−	0.431789i
$145$	−3.69582	+	3.69582i	−0.306921	+	0.306921i
$146$	−1.44888	+	3.49791i	−0.119910	+	0.289489i
$147$	−2.81749	−	1.16704i	−0.232383	−	0.0962561i
$148$	−4.43770	−	10.7136i	−0.364777	−	0.880649i
$149$		−	8.46791i		−	0.693718i	−0.937917	−	0.346859i	$-0.887248\pi$
$149$		−	8.46791i		−	0.693718i	0.937917	−	0.346859i	$-0.112752\pi$
$150$	0.143845	−	0.0595825i	0.0117449	−	0.00486489i
$151$	9.73439	+	9.73439i	0.792174	+	0.792174i	0.981847	−	0.189674i	$-0.0607430\pi$
$151$	9.73439	+	9.73439i	0.792174	+	0.792174i	−0.189674	+	0.981847i	$0.560743\pi$
$152$	0.467911			0.0379526
$153$		0			0
$154$	3.30541			0.266357
$155$	−3.22590	−	3.22590i	−0.259111	−	0.259111i
$156$	7.20220	−	2.98325i	0.576638	−	0.238851i
$157$		−	17.9786i		−	1.43485i	−0.696635	−	0.717426i	$-0.745320\pi$
$157$		−	17.9786i		−	1.43485i	0.696635	−	0.717426i	$-0.254680\pi$
$158$	0.589267	+	1.42262i	0.0468796	+	0.113177i
$159$	8.49279	+	3.51783i	0.673522	+	0.278982i
$160$	−3.44711	+	8.32207i	−0.272518	+	0.657917i
$161$	−2.35661	+	2.35661i	−0.185727	+	0.185727i
$162$	0.647867	−	0.647867i	0.0509012	−	0.0509012i
$163$	2.76849	−	6.68373i	0.216845	−	0.523511i	−0.777601	−	0.628758i	$-0.783564\pi$
$163$	2.76849	−	6.68373i	0.216845	−	0.523511i	0.994446	+	0.105248i	$0.0335635\pi$
$164$	−8.97723	−	3.71849i	−0.701004	−	0.290365i
$165$	−4.00033	−	9.65765i	−0.311425	−	0.751847i
$166$		−	4.71688i		−	0.366101i
$167$	−4.71739	+	1.95401i	−0.365043	+	0.151206i	−0.557662	−	0.830068i	$-0.688302\pi$
$167$	−4.71739	+	1.95401i	−0.365043	+	0.151206i	0.192620	+	0.981273i	$0.438302\pi$
$168$	−1.57450	−	1.57450i	−0.121475	−	0.121475i
$169$	−9.24897			−0.711459
$170$		0			0
$171$	−0.773318			−0.0591371
$172$	1.96103	+	1.96103i	0.149527	+	0.149527i
$173$	−11.8493	+	4.90816i	−0.900889	+	0.373160i	−0.784562	−	0.620051i	$-0.787112\pi$
$173$	−11.8493	+	4.90816i	−0.900889	+	0.373160i	−0.116327	+	0.993211i	$0.537112\pi$
$174$			0.680045i			0.0515541i
$175$	−0.366653	−	0.885179i	−0.0277164	−	0.0669132i
$176$	15.3969	+	6.37761i	1.16059	+	0.480730i
$177$	1.68524	−	4.06852i	0.126670	−	0.305809i
$178$	1.55393	−	1.55393i	0.116472	−	0.116472i
$179$	3.02024	−	3.02024i	0.225743	−	0.225743i	−0.585169	−	0.810912i	$-0.698972\pi$
$179$	3.02024	−	3.02024i	0.225743	−	0.225743i	0.810912	+	0.585169i	$0.198972\pi$
$180$	3.75908	−	9.07522i	0.280185	−	0.676427i
$181$	−0.427626	−	0.177128i	−0.0317852	−	0.0131658i	0.366734	−	0.930326i	$-0.380476\pi$
$181$	−0.427626	−	0.177128i	−0.0317852	−	0.0131658i	−0.398519	+	0.917160i	$0.630476\pi$
$182$	1.17818	+	2.84437i	0.0873323	+	0.210839i
$183$			0.162504i			0.0120126i
$184$	2.20732	−	0.914302i	0.162726	−	0.0674032i
$185$	−10.2413	−	10.2413i	−0.752956	−	0.752956i
$186$	−0.593578			−0.0435233
$187$		0			0
$188$	16.0351			1.16948
$189$	6.10810	+	6.10810i	0.444299	+	0.444299i
$190$	0.261567	−	0.108345i	0.0189761	−	0.00786016i
$191$		−	1.43107i		−	0.103549i	−0.998659	−	0.0517745i	$-0.983512\pi$
$191$		−	1.43107i		−	0.103549i	0.998659	−	0.0517745i	$-0.0164877\pi$
$192$	−1.76642	−	4.26451i	−0.127480	−	0.307764i
$193$	−22.8426	−	9.46170i	−1.64424	−	0.681068i	−0.647528	−	0.762042i	$-0.724197\pi$
$193$	−22.8426	−	9.46170i	−1.64424	−	0.681068i	−0.996716	+	0.0809733i	$0.974197\pi$
$194$	1.23286	−	2.97640i	0.0885145	−	0.213693i
$195$	6.88473	−	6.88473i	0.493026	−	0.493026i
$196$	4.60860	−	4.60860i	0.329186	−	0.329186i
$197$	−4.50092	+	10.8662i	−0.320677	+	0.774183i	0.678538	+	0.734565i	$0.262614\pi$
$197$	−4.50092	+	10.8662i	−0.320677	+	0.774183i	−0.999215	+	0.0396173i	$0.987386\pi$
$198$	3.61812	+	1.49867i	0.257128	+	0.106506i
$199$	7.85275	+	18.9582i	0.556667	+	1.34391i	0.912390	+	0.409321i	$0.134234\pi$
$199$	7.85275	+	18.9582i	0.556667	+	1.34391i	−0.355723	+	0.934591i	$0.615766\pi$
$200$			0.686852i			0.0485678i
$201$	−1.98912	+	0.823921i	−0.140302	+	0.0581149i
$202$	1.73122	+	1.73122i	0.121808	+	0.121808i
$203$	4.18479			0.293715
$204$		0			0
$205$	−12.1361			−0.847622
$206$	1.30121	+	1.30121i	0.0906594	+	0.0906594i
$207$	−3.64804	+	1.51107i	−0.253557	+	0.105027i
$208$			15.5226i			1.07630i
$209$	−0.673052	−	1.62489i	−0.0465560	−	0.112396i
$210$	−1.24474	−	0.515588i	−0.0858952	−	0.0355790i
$211$	8.31105	−	20.0646i	0.572156	−	1.38131i	−0.327559	−	0.944831i	$-0.606226\pi$
$211$	8.31105	−	20.0646i	0.572156	−	1.38131i	0.899716	−	0.436477i	$-0.143774\pi$
$212$	−13.8917	+	13.8917i	−0.954089	+	0.954089i
$213$	−6.16924	+	6.16924i	−0.422709	+	0.422709i
$214$	2.07281	−	5.00422i	0.141695	−	0.342081i
$215$	3.20013	+	1.32554i	0.218247	+	0.0904008i
$216$	−2.36978	−	5.72115i	−0.161243	−	0.389275i
$217$			3.65270i			0.247962i
$218$	0.600536	−	0.248750i	0.0406734	−	0.0168475i
$219$	−6.77887	−	6.77887i	−0.458074	−	0.458074i
$220$	22.3405			1.50620
$221$		0			0
$222$	−1.88444			−0.126475
$223$	−14.1077	−	14.1077i	−0.944722	−	0.944722i	0.0538286	−	0.998550i	$-0.482858\pi$
$223$	−14.1077	−	14.1077i	−0.944722	−	0.944722i	−0.998550	+	0.0538286i	$0.982858\pi$
$224$	6.66314	−	2.75996i	0.445200	−	0.184408i
$225$		−	1.13516i		−	0.0756775i
$226$	−1.60998	−	3.88684i	−0.107094	−	0.258549i
$227$	3.90028	+	1.61555i	0.258870	+	0.107228i	0.508344	−	0.861154i	$-0.330258\pi$
$227$	3.90028	+	1.61555i	0.258870	+	0.107228i	−0.249474	+	0.968382i	$0.580258\pi$
$228$	−0.219652	+	0.530286i	−0.0145468	+	0.0351191i
$229$	−10.2571	+	10.2571i	−0.677806	+	0.677806i	−0.959503	−	0.281697i	$-0.909103\pi$
$229$	−10.2571	+	10.2571i	−0.677806	+	0.677806i	0.281697	+	0.959503i	$0.409103\pi$
$230$	1.02221	−	1.02221i	0.0674025	−	0.0674025i
$231$	−3.20290	+	7.73249i	−0.210735	+	0.508760i
$232$	−2.77164	−	1.14805i	−0.181967	−	0.0753732i
$233$	−1.96218	−	4.73712i	−0.128547	−	0.310339i	0.846482	−	0.532417i	$-0.178716\pi$
$233$	−1.96218	−	4.73712i	−0.128547	−	0.310339i	−0.975029	+	0.222078i	$0.928716\pi$
$234$			3.64765i			0.238454i
$235$	18.5029	−	7.66413i	1.20699	−	0.499953i
$236$	6.65492	+	6.65492i	0.433198	+	0.433198i
$237$	−3.89899			−0.253266
$238$		0			0
$239$	−15.8503			−1.02527			−0.512635	−	0.858607i	$-0.671331\pi$
$239$	−15.8503			−1.02527			−0.512635	+	0.858607i	$0.671331\pi$
$240$	−4.80332	−	4.80332i	−0.310053	−	0.310053i
$241$	16.7375	−	6.93288i	1.07815	−	0.446586i	0.228293	−	0.973592i	$-0.426686\pi$
$241$	16.7375	−	6.93288i	1.07815	−	0.446586i	0.849861	+	0.527006i	$0.176686\pi$
$242$			5.08647i			0.326970i
$243$	6.16455	+	14.8825i	0.395456	+	0.954716i
$244$	−0.320860	−	0.132905i	−0.0205410	−	0.00850834i
$245$	3.11513	−	7.52058i	0.199018	−	0.480472i
$246$	−1.11654	+	1.11654i	−0.0711882	+	0.0711882i
$247$	1.15835	−	1.15835i	0.0737041	−	0.0737041i
$248$	1.00208	−	2.41923i	0.0636320	−	0.153621i
$249$	11.0344	+	4.57060i	0.699278	+	0.289650i
$250$	−1.40079	−	3.38181i	−0.0885938	−	0.213884i
$251$			29.6810i			1.87345i	0.350070	+	0.936723i	$0.386158\pi$
$251$			29.6810i			1.87345i	−0.350070	+	0.936723i	$0.613842\pi$
$252$	−7.26616	+	3.00974i	−0.457725	+	0.189596i
$253$	−6.35010	−	6.35010i	−0.399227	−	0.399227i
$254$	4.00774			0.251468
$255$		0			0
$256$	7.19934			0.449959
$257$	5.23042	+	5.23042i	0.326264	+	0.326264i	0.851164	−	0.524900i	$-0.175897\pi$
$257$	5.23042	+	5.23042i	0.326264	+	0.326264i	−0.524900	+	0.851164i	$0.675897\pi$
$258$	0.416369	−	0.172466i	0.0259220	−	0.0107373i
$259$			11.5963i			0.720557i
$260$	7.96303	+	19.2245i	0.493846	+	1.19225i
$261$	4.58070	+	1.89739i	0.283538	+	0.117445i
$262$	−2.57498	+	6.21655i	−0.159083	+	0.384059i
$263$	16.3984	−	16.3984i	1.01117	−	1.01117i	0.0112290	−	0.999937i	$-0.496426\pi$
$263$	16.3984	−	16.3984i	1.01117	−	1.01117i	0.999937	−	0.0112290i	$-0.00357439\pi$
$264$	4.24264	−	4.24264i	0.261116	−	0.261116i
$265$	−9.38996	+	22.6694i	−0.576821	+	1.39257i
$266$	−0.209426	−	0.0867473i	−0.0128408	−	0.00531882i
$267$	2.12944	+	5.14091i	0.130319	+	0.314619i
$268$		−	4.60132i		−	0.281070i
$269$	−14.6959	+	6.08724i	−0.896025	+	0.371146i	−0.782690	−	0.622411i	$-0.786153\pi$
$269$	−14.6959	+	6.08724i	−0.896025	+	0.371146i	−0.113334	+	0.993557i	$0.536153\pi$
$270$	−2.64947	−	2.64947i	−0.161241	−	0.161241i
$271$	−17.0000			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$271$	−17.0000			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$272$		0			0
$273$	−7.79561			−0.471812
$274$	−0.110094	−	0.110094i	−0.00665103	−	0.00665103i
$275$	2.38520	−	0.987981i	0.143833	−	0.0595775i
$276$			2.93077i			0.176412i
$277$	6.43127	+	15.5265i	0.386417	+	0.932894i	0.990693	+	0.136118i	$0.0434628\pi$
$277$	6.43127	+	15.5265i	0.386417	+	0.932894i	−0.604275	+	0.796776i	$0.706537\pi$
$278$	−3.74766	−	1.55233i	−0.224770	−	0.0931026i
$279$	−1.65614	+	3.99827i	−0.0991504	+	0.239370i
$280$	4.20273	−	4.20273i	0.251161	−	0.251161i
$281$	20.0259	−	20.0259i	1.19464	−	1.19464i	0.218897	−	0.975748i	$-0.429754\pi$
$281$	20.0259	−	20.0259i	1.19464	−	1.19464i	0.975748	−	0.218897i	$-0.0702457\pi$
$282$	0.997182	−	2.40741i	0.0593813	−	0.143359i
$283$	29.7807	+	12.3356i	1.77028	+	0.733274i	0.994794	+	0.101910i	$0.0324954\pi$
$283$	29.7807	+	12.3356i	1.77028	+	0.733274i	0.775487	+	0.631364i	$0.217505\pi$
$284$	−7.13548	−	17.2266i	−0.423413	−	1.02221i
$285$			0.716881i			0.0424644i
$286$	−7.66442	+	3.17471i	−0.453207	+	0.187724i
$287$	6.87087	+	6.87087i	0.405575	+	0.405575i
$288$	8.54488			0.503512
$289$		0			0
$290$	−1.81521			−0.106593
$291$	5.76819	+	5.76819i	0.338137	+	0.338137i
$292$	18.9289	−	7.84059i	1.10773	−	0.458836i
$293$			13.9709i			0.816189i	0.912940	+	0.408094i	$0.133807\pi$
$293$			13.9709i			0.816189i	−0.912940	+	0.408094i	$0.866193\pi$
$294$	−0.405310	−	0.978504i	−0.0236381	−	0.0570675i
$295$	10.8599	+	4.49831i	0.632287	+	0.261902i
$296$	3.18130	−	7.68035i	0.184910	−	0.446411i
$297$	−16.4588	+	16.4588i	−0.955039	+	0.955039i
$298$	2.07951	−	2.07951i	0.120463	−	0.120463i
$299$	3.20097	−	7.72782i	0.185117	−	0.446911i
$300$	−0.778413	−	0.322429i	−0.0449417	−	0.0186155i
$301$	−1.06130	−	2.56221i	−0.0611725	−	0.147683i
$302$			4.78106i			0.275119i
$303$	−5.72744	+	2.37238i	−0.329033	+	0.136290i
$304$	−0.808155	−	0.808155i	−0.0463509	−	0.0463509i
$305$	−0.433763			−0.0248372
$306$		0			0
$307$	9.04963			0.516490			0.258245	−	0.966080i	$-0.416856\pi$
$307$	9.04963			0.516490			0.258245	+	0.966080i	$0.416856\pi$
$308$	−12.6481	−	12.6481i	−0.720693	−	0.720693i
$309$	−4.30483	+	1.78312i	−0.244893	+	0.101438i
$310$		−	1.58441i		−	0.0899883i
$311$	−0.898271	−	2.16862i	−0.0509363	−	0.122971i	0.896363	−	0.443321i	$-0.146200\pi$
$311$	−0.898271	−	2.16862i	−0.0509363	−	0.122971i	−0.947299	+	0.320349i	$0.896200\pi$
$312$	5.16312	+	2.13864i	0.292304	+	0.121076i
$313$	−5.78937	+	13.9768i	−0.327235	+	0.790014i	0.671561	+	0.740949i	$0.265624\pi$
$313$	−5.78937	+	13.9768i	−0.327235	+	0.790014i	−0.998796	+	0.0490649i	$0.984376\pi$
$314$	4.41512	−	4.41512i	0.249159	−	0.249159i
$315$	−6.94587	+	6.94587i	−0.391356	+	0.391356i
$316$	3.18880	−	7.69846i	0.179384	−	0.433072i
$317$	9.55088	+	3.95611i	0.536431	+	0.222197i	0.634417	−	0.772991i	$-0.281240\pi$
$317$	9.55088	+	3.95611i	0.536431	+	0.222197i	−0.0979863	+	0.995188i	$0.531240\pi$
$318$	1.22173	+	2.94952i	0.0685112	+	0.165401i
$319$			11.2763i			0.631352i
$320$	11.3830	−	4.71500i	0.636330	−	0.263577i
$321$	9.69806	+	9.69806i	0.541293	+	0.541293i
$322$	−1.15745			−0.0645022
$323$		0			0
$324$	−4.95811			−0.275451
$325$	1.70036	+	1.70036i	0.0943188	+	0.0943188i
$326$	2.32124	−	0.961488i	0.128561	−	0.0532519i
$327$			1.64590i			0.0910183i
$328$	−2.66572	−	6.43561i	−0.147190	−	0.355347i
$329$	−14.8145	−	6.13636i	−0.816749	−	0.338308i
$330$	1.38930	−	3.35407i	0.0764784	−	0.184635i
$331$	−12.9094	+	12.9094i	−0.709567	+	0.709567i	−0.966444	−	0.256877i	$-0.917307\pi$
$331$	−12.9094	+	12.9094i	−0.709567	+	0.709567i	0.256877	+	0.966444i	$0.417307\pi$
$332$	−18.0491	+	18.0491i	−0.990573	+	0.990573i
$333$	−5.25775	+	12.6933i	−0.288123	+	0.695591i
$334$	−1.63833	−	0.678620i	−0.0896456	−	0.0371324i
$335$	−2.19925	−	5.30945i	−0.120158	−	0.290086i
$336$			5.43882i			0.296712i
$337$	15.2396	−	6.31246i	0.830155	−	0.343862i	0.0731911	−	0.997318i	$-0.476682\pi$
$337$	15.2396	−	6.31246i	0.830155	−	0.343862i	0.756964	+	0.653456i	$0.226682\pi$
$338$	−2.27132	−	2.27132i	−0.123544	−	0.123544i
$339$	10.6527			0.578575
$340$		0			0
$341$	−9.84255			−0.533004
$342$	−0.189908	−	0.189908i	−0.0102691	−	0.0102691i
$343$	−18.1757	+	7.52862i	−0.981396	+	0.406507i
$344$			1.98814i			0.107193i
$345$	1.40079	+	3.38181i	0.0754161	+	0.182071i
$346$	−4.11523	−	1.70459i	−0.221236	−	0.0916391i
$347$	7.87265	−	19.0063i	0.422626	−	1.02031i	−0.558944	−	0.829205i	$-0.688793\pi$
$347$	7.87265	−	19.0063i	0.422626	−	1.02031i	0.981570	−	0.191104i	$-0.0612067\pi$
$348$	2.60218	−	2.60218i	0.139492	−	0.139492i
$349$	4.54264	−	4.54264i	0.243162	−	0.243162i	−0.574995	−	0.818157i	$-0.694996\pi$
$349$	4.54264	−	4.54264i	0.243162	−	0.243162i	0.818157	+	0.574995i	$0.194996\pi$
$350$	0.127337	−	0.307419i	0.00680647	−	0.0164323i
$351$	−20.0297	−	8.29659i	−1.06911	−	0.442839i
$352$	7.43698	+	17.9545i	0.396392	+	0.956976i
$353$		−	27.1685i		−	1.44603i	−0.690831	−	0.723016i	$-0.742755\pi$
$353$		−	27.1685i		−	1.44603i	0.690831	−	0.723016i	$-0.257245\pi$
$354$	1.41298	−	0.585276i	0.0750991	−	0.0311071i
$355$	−16.4672	−	16.4672i	−0.873989	−	0.873989i
$356$	−11.8922			−0.630284
$357$		0			0
$358$	1.48339			0.0783997
$359$	11.9465	+	11.9465i	0.630511	+	0.630511i	0.948196	−	0.317685i	$-0.102906\pi$
$359$	11.9465	+	11.9465i	0.630511	+	0.630511i	−0.317685	+	0.948196i	$0.602906\pi$
$360$	6.50586	−	2.69481i	0.342889	−	0.142029i
$361$		−	18.8794i		−	0.993652i
$362$	−0.0615160	−	0.148513i	−0.00323321	−	0.00780566i
$363$	−11.8990	−	4.92873i	−0.624536	−	0.258691i
$364$	6.37568	−	15.3922i	0.334176	−	0.806773i
$365$	18.0945	−	18.0945i	0.947108	−	0.947108i
$366$	−0.0399070	+	0.0399070i	−0.00208597	+	0.00208597i
$367$	0.569246	−	1.37428i	0.0297144	−	0.0717369i	−0.908326	−	0.418263i	$-0.862639\pi$
$367$	0.569246	−	1.37428i	0.0297144	−	0.0717369i	0.938040	+	0.346526i	$0.112639\pi$
$368$	−5.39152	−	2.23324i	−0.281053	−	0.116416i
$369$	4.40564	+	10.6362i	0.229348	+	0.553696i
$370$		−	5.03003i		−	0.261499i
$371$	18.1504	−	7.51816i	0.942324	−	0.390323i
$372$	2.27132	+	2.27132i	0.117763	+	0.117763i
$373$	24.0496			1.24524			0.622621	−	0.782523i	$-0.286068\pi$
$373$	24.0496			1.24524			0.622621	+	0.782523i	$0.286068\pi$
$374$		0			0
$375$	9.26857			0.478627
$376$	8.12837	+	8.12837i	0.419189	+	0.419189i
$377$	−9.70350	+	4.01932i	−0.499756	+	0.207006i
$378$			3.00000i			0.154303i
$379$	−7.72928	−	18.6601i	−0.397027	−	0.958507i	−0.988367	−	0.152085i	$-0.951401\pi$
$379$	−7.72928	−	18.6601i	−0.397027	−	0.958507i	0.591341	−	0.806422i	$-0.298599\pi$
$380$	−1.41547	−	0.586305i	−0.0726119	−	0.0300768i
$381$	−3.88345	+	9.37549i	−0.198955	+	0.480321i
$382$	0.351437	−	0.351437i	0.0179811	−	0.0179811i
$383$	−6.02828	+	6.02828i	−0.308031	+	0.308031i	−0.844145	−	0.536114i	$-0.819892\pi$
$383$	−6.02828	+	6.02828i	−0.308031	+	0.308031i	0.536114	+	0.844145i	$0.319892\pi$
$384$	3.19631	−	7.71656i	0.163111	−	0.393784i
$385$	−20.6399	−	8.54934i	−1.05191	−	0.435714i
$386$	−3.28602	−	7.93314i	−0.167254	−	0.403786i
$387$		−	3.28581i		−	0.167027i
$388$	−16.1067	+	6.67161i	−0.817694	+	0.338700i
$389$	9.13315	+	9.13315i	0.463069	+	0.463069i	0.899660	−	0.436591i	$-0.143814\pi$
$389$	9.13315	+	9.13315i	0.463069	+	0.463069i	−0.436591	+	0.899660i	$0.643814\pi$
$390$	3.38144			0.171226
$391$		0			0
$392$	4.67230			0.235987
$393$	−12.0475	−	12.0475i	−0.607717	−	0.607717i
$394$	−3.77378	+	1.56315i	−0.190120	+	0.0787504i
$395$		−	10.4074i		−	0.523651i
$396$	−8.11003	−	19.5793i	−0.407544	−	0.983899i
$397$	22.3809	+	9.27048i	1.12327	+	0.465272i	0.865487	−	0.500932i	$-0.167009\pi$
$397$	22.3809	+	9.27048i	1.12327	+	0.465272i	0.257779	+	0.966204i	$0.417009\pi$
$398$	−2.72723	+	6.58412i	−0.136704	+	0.330032i
$399$	0.405864	−	0.405864i	0.0203186	−	0.0203186i
$400$	1.18630	−	1.18630i	0.0593150	−	0.0593150i
$401$	9.77264	−	23.5932i	0.488022	−	1.17819i	−0.467691	−	0.883892i	$-0.654914\pi$
$401$	9.77264	−	23.5932i	0.488022	−	1.17819i	0.955714	−	0.294298i	$-0.0950859\pi$
$402$	−0.690814	−	0.286145i	−0.0344547	−	0.0142716i
$403$	−3.50827	−	8.46972i	−0.174759	−	0.421907i
$404$		−	13.2490i		−	0.659161i
$405$	−5.72115	+	2.36978i	−0.284286	+	0.117755i
$406$	1.02768	+	1.02768i	0.0510030	+	0.0510030i
$407$	−31.2472			−1.54887
$408$		0			0
$409$	10.3523			0.511891			0.255945	−	0.966691i	$-0.417613\pi$
$409$	10.3523			0.511891			0.255945	+	0.966691i	$0.417613\pi$
$410$	−2.98033	−	2.98033i	−0.147188	−	0.147188i
$411$	0.364228	−	0.150868i	0.0179661	−	0.00744178i
$412$		−	9.95811i		−	0.490601i
$413$	−3.60162	−	8.69507i	−0.177224	−	0.427856i
$414$	−1.26695	−	0.524789i	−0.0622673	−	0.0257920i
$415$	−12.2001	+	29.4536i	−0.598878	+	1.44582i
$416$	−12.7994	+	12.7994i	−0.627540	+	0.627540i
$417$	7.26288	−	7.26288i	0.355665	−	0.355665i
$418$	0.233749	−	0.564319i	0.0114330	−	0.0276017i
$419$	−1.21319	−	0.502520i	−0.0592682	−	0.0245497i	0.352852	−	0.935679i	$-0.385212\pi$
$419$	−1.21319	−	0.502520i	−0.0592682	−	0.0245497i	−0.412121	+	0.911129i	$0.635212\pi$
$420$	2.79009	+	6.73588i	0.136143	+	0.328677i
$421$		−	8.01548i		−	0.390651i	−0.980739	−	0.195325i	$-0.937424\pi$
$421$		−	8.01548i		−	0.390651i	0.980739	−	0.195325i	$-0.0625763\pi$
$422$	6.96838	−	2.88640i	0.339215	−	0.140508i
$423$	−13.4338	−	13.4338i	−0.653173	−	0.653173i
$424$	−14.0838			−0.683969
$425$		0			0
$426$	−3.03003			−0.146805
$427$	0.245576	+	0.245576i	0.0118842	+	0.0118842i
$428$	−27.0802	+	11.2170i	−1.30897	+	0.542193i
$429$		−	21.0060i		−	1.01418i
$430$	0.460354	+	1.11139i	0.0222002	+	0.0535961i
$431$	13.6060	+	5.63577i	0.655376	+	0.271466i	0.685491	−	0.728081i	$-0.259587\pi$
$431$	13.6060	+	5.63577i	0.655376	+	0.271466i	−0.0301153	+	0.999546i	$0.509587\pi$
$432$	−5.78834	+	13.9743i	−0.278492	+	0.672339i
$433$	5.82743	−	5.82743i	0.280048	−	0.280048i	−0.553080	−	0.833128i	$-0.686548\pi$
$433$	5.82743	−	5.82743i	0.280048	−	0.280048i	0.833128	+	0.553080i	$0.186548\pi$
$434$	−0.897015	+	0.897015i	−0.0430581	+	0.0430581i
$435$	1.75892	−	4.24640i	0.0843335	−	0.203599i
$436$	−3.24978	−	1.34610i	−0.155636	−	0.0644667i
$437$	0.235682	+	0.568987i	0.0112742	+	0.0272183i
$438$		−	3.32945i		−	0.159087i
$439$	−36.9149	+	15.2906i	−1.76185	+	0.729782i	−0.765595	+	0.643323i	$0.777555\pi$
$439$	−36.9149	+	15.2906i	−1.76185	+	0.729782i	−0.996255	+	0.0864590i	$0.972445\pi$
$440$	11.3247	+	11.3247i	0.539882	+	0.539882i
$441$	−7.72193			−0.367711
$442$		0			0
$443$	13.9463			0.662606			0.331303	−	0.943524i	$-0.392512\pi$
$443$	13.9463			0.662606			0.331303	+	0.943524i	$0.392512\pi$
$444$	7.21078	+	7.21078i	0.342209	+	0.342209i
$445$	−13.7224	+	5.68399i	−0.650502	+	0.269447i
$446$		−	6.92902i		−	0.328098i
$447$	2.84967	+	6.87972i	0.134785	+	0.325400i
$448$	−9.11392	−	3.77511i	−0.430592	−	0.178357i
$449$	−3.91552	+	9.45289i	−0.184785	+	0.446109i	−0.988941	−	0.148308i	$-0.952617\pi$
$449$	−3.91552	+	9.45289i	−0.184785	+	0.446109i	0.804157	+	0.594417i	$0.202617\pi$
$450$	0.278768	−	0.278768i	0.0131413	−	0.0131413i
$451$	−18.5142	+	18.5142i	−0.871800	+	0.871800i
$452$	−8.71237	+	21.0335i	−0.409795	+	0.989333i
$453$	−11.1845	−	4.63279i	−0.525496	−	0.217668i
$454$	0.561074	+	1.35455i	0.0263325	+	0.0635723i
$455$		−	20.8084i		−	0.975513i
$456$	−0.380153	+	0.157464i	−0.0178023	+	0.00737394i
$457$	8.32309	+	8.32309i	0.389338	+	0.389338i	0.874451	−	0.485113i	$-0.161222\pi$
$457$	8.32309	+	8.32309i	0.389338	+	0.389338i	−0.485113	+	0.874451i	$0.661222\pi$
$458$	−5.03777			−0.235400
$459$		0			0
$460$	−7.82295			−0.364747
$461$	13.7888	+	13.7888i	0.642208	+	0.642208i	0.951098	−	0.308890i	$-0.0999574\pi$
$461$	13.7888	+	13.7888i	0.642208	+	0.642208i	−0.308890	+	0.951098i	$0.599957\pi$
$462$	−2.68547	+	1.11236i	−0.124939	+	0.0517515i
$463$		−	1.43107i		−	0.0665077i	−0.999447	−	0.0332538i	$-0.989413\pi$
$463$		−	1.43107i		−	0.0665077i	0.999447	−	0.0332538i	$-0.0105870\pi$
$464$	2.80419	+	6.76991i	0.130181	+	0.314285i
$465$	3.70647	+	1.53527i	0.171884	+	0.0711965i
$466$	0.681458	−	1.64518i	0.0315679	−	0.0762117i
$467$	7.55865	−	7.55865i	0.349772	−	0.349772i	−0.510252	−	0.860025i	$-0.670448\pi$
$467$	7.55865	−	7.55865i	0.349772	−	0.349772i	0.860025	+	0.510252i	$0.170448\pi$
$468$	13.9577	−	13.9577i	0.645195	−	0.645195i
$469$	−1.76085	+	4.25106i	−0.0813084	+	0.196296i
$470$	6.42597	+	2.66172i	0.296408	+	0.122776i
$471$	6.05028	+	14.6067i	0.278782	+	0.673040i
$472$			6.74691i			0.310552i
$473$	6.90412	−	2.85978i	0.317452	−	0.131493i
$474$	−0.957496	−	0.957496i	−0.0439792	−	0.0439792i
$475$	−0.177052			−0.00812369
$476$		0			0
$477$	23.2763			1.06575
$478$	−3.89244	−	3.89244i	−0.178036	−	0.178036i
$479$	35.9089	−	14.8740i	1.64072	−	0.679608i	0.644350	−	0.764731i	$-0.277128\pi$
$479$	35.9089	−	14.8740i	1.64072	−	0.679608i	0.996370	+	0.0851226i	$0.0271282\pi$
$480$		−	7.92127i		−	0.361555i
$481$	−11.1377	−	26.8889i	−0.507837	−	1.22603i
$482$	5.81286	+	2.40776i	0.264768	+	0.109671i
$483$	1.12156	−	2.70768i	0.0510326	−	0.123204i
$484$	19.4633	−	19.4633i	0.884696	−	0.884696i
$485$	−15.3967	+	15.3967i	−0.699129	+	0.699129i
$486$	−2.14093	+	5.16866i	−0.0971144	+	0.234455i
$487$	−34.1962	−	14.1645i	−1.54958	−	0.641857i	−0.566339	−	0.824172i	$-0.691641\pi$
$487$	−34.1962	−	14.1645i	−1.54958	−	0.641857i	−0.983240	+	0.182316i	$0.941641\pi$
$488$	−0.0952768	−	0.230019i	−0.00431298	−	0.0104125i
$489$			6.36184i			0.287693i
$490$	2.61187	−	1.08187i	0.117992	−	0.0488740i
$491$	17.9729	+	17.9729i	0.811104	+	0.811104i	0.984799	−	0.173696i	$-0.0555709\pi$
$491$	17.9729	+	17.9729i	0.811104	+	0.811104i	−0.173696	+	0.984799i	$0.555571\pi$
$492$	8.54488			0.385233
$493$		0			0
$494$	0.568926			0.0255972
$495$	−18.7163	−	18.7163i	−0.841235	−	0.841235i
$496$	−5.90913	+	2.44764i	−0.265328	+	0.109902i
$497$			18.6459i			0.836383i
$498$	1.58735	+	3.83221i	0.0711310	+	0.171726i
$499$	−20.1626	−	8.35164i	−0.902604	−	0.373871i	−0.117383	−	0.993087i	$-0.537451\pi$
$499$	−20.1626	−	8.35164i	−0.902604	−	0.373871i	−0.785221	+	0.619216i	$0.787451\pi$
$500$	−7.58035	+	18.3006i	−0.339003	+	0.818427i
$501$	3.17505	−	3.17505i	0.141851	−	0.141851i
$502$	−7.28892	+	7.28892i	−0.325321	+	0.325321i
$503$	12.7958	−	30.8918i	0.570537	−	1.37740i	−0.330562	−	0.943784i	$-0.607238\pi$
$503$	12.7958	−	30.8918i	0.570537	−	1.37740i	0.901099	−	0.433614i	$-0.142762\pi$
$504$	−5.20898	−	2.15763i	−0.232026	−	0.0961084i
$505$	−6.33248	−	15.2880i	−0.281792	−	0.680305i
$506$		−	3.11886i		−	0.138650i
$507$	7.51429	−	3.11252i	0.333721	−	0.138232i
$508$	−15.3356	−	15.3356i	−0.680406	−	0.680406i
$509$	19.1530			0.848942			0.424471	−	0.905441i	$-0.360460\pi$
$509$	19.1530			0.848942			0.424471	+	0.905441i	$0.360460\pi$
$510$		0			0
$511$	−20.4884			−0.906355
$512$	15.2001	+	15.2001i	0.671756	+	0.671756i
$513$	1.47476	−	0.610865i	0.0651122	−	0.0269703i
$514$			2.56893i			0.113310i
$515$	−4.75958	−	11.4906i	−0.209732	−	0.506338i
$516$	−2.25317	−	0.933294i	−0.0991903	−	0.0410860i
$517$	16.5350	−	39.9190i	0.727208	−	1.75564i
$518$	−2.84776	+	2.84776i	−0.125123	+	0.125123i
$519$	7.97523	−	7.97523i	0.350074	−	0.350074i
$520$	−5.70855	+	13.7817i	−0.250336	+	0.604366i
$521$	32.8282	+	13.5979i	1.43823	+	0.595735i	0.959369	−	0.282155i	$-0.0910493\pi$
$521$	32.8282	+	13.5979i	1.43823	+	0.595735i	0.478862	+	0.877890i	$0.341049\pi$
$522$	0.658956	+	1.59086i	0.0288417	+	0.0696300i
$523$			11.8307i			0.517320i	0.965968	+	0.258660i	$0.0832809\pi$
$523$			11.8307i			0.517320i	−0.965968	+	0.258660i	$0.916719\pi$
$524$	33.6407	−	13.9344i	1.46960	−	0.608728i
$525$	0.595772	+	0.595772i	0.0260016	+	0.0260016i
$526$	8.05407			0.351174
$527$		0			0
$528$	−14.6554			−0.637794
$529$	−14.0398	−	14.0398i	−0.610428	−	0.610428i
$530$	−7.87299	+	3.26110i	−0.341981	+	0.141653i
$531$		−	11.1506i		−	0.483897i
$532$	0.469431	+	1.13331i	0.0203524	+	0.0491350i
$533$	−22.5310	−	9.33267i	−0.975928	−	0.404243i
$534$	−0.739545	+	1.78542i	−0.0320032	+	0.0772627i
$535$	−25.8865	+	25.8865i	−1.11917	+	1.11917i
$536$	2.33246	−	2.33246i	0.100747	−	0.100747i
$537$	−1.43739	+	3.47017i	−0.0620280	+	0.149749i
$538$	−5.10383	−	2.11408i	−0.220042	−	0.0911443i
$539$	−6.72073	−	16.2253i	−0.289482	−	0.698872i
$540$			20.2763i			0.872554i
$541$	−5.13538	+	2.12714i	−0.220787	+	0.0914531i	−0.490335	−	0.871534i	$-0.663126\pi$
$541$	−5.13538	+	2.12714i	−0.220787	+	0.0914531i	0.269548	+	0.962987i	$0.413126\pi$
$542$	−4.17479	−	4.17479i	−0.179322	−	0.179322i
$543$	0.407031			0.0174674
$544$		0			0
$545$	−4.39330			−0.188188
$546$	−1.91441	−	1.91441i	−0.0819292	−	0.0819292i
$547$	4.64217	−	1.92285i	0.198485	−	0.0822152i	−0.281227	−	0.959641i	$-0.590741\pi$
$547$	4.64217	−	1.92285i	0.198485	−	0.0822152i	0.479712	+	0.877426i	$0.340741\pi$
$548$			0.842549i			0.0359919i
$549$	0.157464	+	0.380153i	0.00672041	+	0.0162245i
$550$	0.828370	+	0.343122i	0.0353218	+	0.0146308i
$551$	0.295936	−	0.714453i	0.0126073	−	0.0304367i
$552$	−1.48564	+	1.48564i	−0.0632331	+	0.0632331i
$553$	−5.89214	+	5.89214i	−0.250559	+	0.250559i
$554$	−2.23356	+	5.39228i	−0.0948947	+	0.229096i
$555$	11.7670	+	4.87404i	0.499480	+	0.206891i
$556$	8.40040	+	20.2804i	0.356256	+	0.860079i
$557$		−	3.86659i		−	0.163833i	−0.996639	−	0.0819164i	$-0.973896\pi$
$557$		−	3.86659i		−	0.163833i	0.996639	−	0.0819164i	$-0.0261040\pi$
$558$	−1.38858	+	0.575171i	−0.0587835	+	0.0243489i
$559$	4.92180	+	4.92180i	0.208170	+	0.208170i
$560$	−14.5175			−0.613478
$561$		0			0
$562$	9.83574			0.414896
$563$	20.3938	+	20.3938i	0.859494	+	0.859494i	0.991278	−	0.131784i	$-0.0420706\pi$
$563$	20.3938	+	20.3938i	0.859494	+	0.859494i	−0.131784	+	0.991278i	$0.542071\pi$
$564$	−13.0276	+	5.39622i	−0.548563	+	0.227222i
$565$			28.4347i			1.19626i
$566$	4.28410	+	10.3427i	0.180074	+	0.434738i
$567$	4.58070	+	1.89739i	0.192371	+	0.0796828i
$568$	5.11529	−	12.3494i	0.214633	−	0.518169i
$569$	−1.52846	+	1.52846i	−0.0640764	+	0.0640764i	−0.738419	−	0.674342i	$-0.764427\pi$
$569$	−1.52846	+	1.52846i	−0.0640764	+	0.0640764i	0.674342	+	0.738419i	$0.264427\pi$
$570$	−0.176049	+	0.176049i	−0.00737386	+	0.00737386i
$571$	−2.18866	+	5.28389i	−0.0915926	+	0.221124i	−0.963036	−	0.269371i	$-0.913184\pi$
$571$	−2.18866	+	5.28389i	−0.0915926	+	0.221124i	0.871444	+	0.490495i	$0.163184\pi$
$572$	41.4758	+	17.1799i	1.73419	+	0.718326i
$573$	0.481594	+	1.16267i	0.0201189	+	0.0485713i
$574$			3.37464i			0.140855i
$575$	−0.835222	+	0.345960i	−0.0348312	+	0.0144275i
$576$	−8.26451	−	8.26451i	−0.344355	−	0.344355i
$577$	10.8007			0.449637			0.224819	−	0.974401i	$-0.427821\pi$
$577$	10.8007			0.449637			0.224819	+	0.974401i	$0.427821\pi$
$578$		0			0
$579$	21.7425			0.903586
$580$	6.94587	+	6.94587i	0.288412	+	0.288412i
$581$	23.5823	−	9.76810i	0.978358	−	0.405249i
$582$			2.83305i			0.117434i
$583$	20.2584	+	48.9080i	0.839016	+	2.02556i
$584$	13.5697	+	5.62077i	0.561520	+	0.232589i
$585$	9.43454	−	22.7770i	0.390070	−	0.941713i
$586$	−3.43091	+	3.43091i	−0.141730	+	0.141730i
$587$	14.7211	−	14.7211i	0.607606	−	0.607606i	−0.334714	−	0.942320i	$-0.608640\pi$
$587$	14.7211	−	14.7211i	0.607606	−	0.607606i	0.942320	+	0.334714i	$0.108640\pi$
$588$	−2.19332	+	5.29515i	−0.0904511	+	0.218368i
$589$	0.623612	+	0.258308i	0.0256955	+	0.0106434i
$590$	1.56225	+	3.77160i	0.0643167	+	0.155274i
$591$		−	10.3429i		−	0.425448i
$592$	−18.7598	+	7.77054i	−0.771021	+	0.319367i
$593$	−14.5886	−	14.5886i	−0.599081	−	0.599081i	0.340987	−	0.940068i	$-0.389239\pi$
$593$	−14.5886	−	14.5886i	−0.599081	−	0.599081i	−0.940068	+	0.340987i	$0.889239\pi$
$594$	−8.08378			−0.331681
$595$		0			0
$596$	−15.9145			−0.651882
$597$	−12.7599	−	12.7599i	−0.522227	−	0.522227i
$598$	2.68384	−	1.11168i	0.109751	−	0.0454602i
$599$			31.8212i			1.30018i	0.759858	+	0.650089i	$0.225269\pi$
$599$			31.8212i			1.30018i	−0.759858	+	0.650089i	$0.774731\pi$
$600$	−0.231144	−	0.558030i	−0.00943640	−	0.0227815i
$601$	44.4547	+	18.4137i	1.81335	+	0.751112i	0.980186	+	0.198079i	$0.0634704\pi$
$601$	44.4547	+	18.4137i	1.81335	+	0.751112i	0.833159	+	0.553033i	$0.186530\pi$
$602$	0.368587	−	0.889847i	0.0150225	−	0.0362675i
$603$	−3.85487	+	3.85487i	−0.156982	+	0.156982i
$604$	18.2947	−	18.2947i	0.744400	−	0.744400i
$605$	13.1560	−	31.7614i	0.534867	−	1.29128i
$606$	−1.98912	−	0.823921i	−0.0808025	−	0.0334695i
$607$	−5.92228	−	14.2976i	−0.240378	−	0.580323i	0.756943	−	0.653481i	$-0.226692\pi$
$607$	−5.92228	−	14.2976i	−0.240378	−	0.580323i	−0.997320	+	0.0731581i	$0.976692\pi$
$608$		−	1.33275i		−	0.0540501i
$609$	−3.39992	+	1.40829i	−0.137772	+	0.0570669i
$610$	−0.106522	−	0.106522i	−0.00431293	−	0.00431293i
$611$	40.2449			1.62813
$612$		0			0
$613$	−5.04963			−0.203953			−0.101976	−	0.994787i	$-0.532517\pi$
$613$	−5.04963			−0.203953			−0.101976	+	0.994787i	$0.532517\pi$
$614$	2.22237	+	2.22237i	0.0896875	+	0.0896875i
$615$	9.85992	−	4.08411i	0.397590	−	0.164687i
$616$		−	12.8229i		−	0.516651i
$617$	10.5645	+	25.5050i	0.425311	+	1.02679i	0.980756	+	0.195238i	$0.0625479\pi$
$617$	10.5645	+	25.5050i	0.425311	+	1.02679i	−0.555445	+	0.831553i	$0.687452\pi$
$618$	−1.49505	−	0.619270i	−0.0601398	−	0.0249107i
$619$	−5.67636	+	13.7040i	−0.228152	+	0.550808i	−0.995953	−	0.0898809i	$-0.971351\pi$
$619$	−5.67636	+	13.7040i	−0.228152	+	0.550808i	0.767800	+	0.640689i	$0.221351\pi$
$620$	−6.06272	+	6.06272i	−0.243485	+	0.243485i
$621$	5.76338	−	5.76338i	0.231276	−	0.231276i
$622$	0.311966	−	0.753153i	0.0125087	−	0.0301987i
$623$	10.9869	+	4.55094i	0.440182	+	0.182330i
$624$	−5.22376	−	12.6113i	−0.209118	−	0.504855i
$625$			27.2891i			1.09156i
$626$	−4.85408	+	2.01063i	−0.194008	+	0.0803608i
$627$	1.09364	+	1.09364i	0.0436757	+	0.0436757i
$628$	−33.7888			−1.34832
$629$		0			0
$630$	−3.41147			−0.135916
$631$	−24.0774	−	24.0774i	−0.958506	−	0.958506i	0.0406672	−	0.999173i	$-0.487052\pi$
$631$	−24.0774	−	24.0774i	−0.958506	−	0.958506i	−0.999173	+	0.0406672i	$0.987052\pi$
$632$	5.51888	−	2.28599i	0.219529	−	0.0909320i
$633$			19.0983i			0.759090i
$634$	1.37394	+	3.31699i	0.0545662	+	0.131734i
$635$	−25.0255	−	10.3659i	−0.993106	−	0.411358i
$636$	6.61136	−	15.9612i	0.262157	−	0.632904i
$637$	11.5667	−	11.5667i	0.458288	−	0.458288i
$638$	−2.76919	+	2.76919i	−0.109633	+	0.109633i
$639$	−8.45406	+	20.4099i	−0.334437	+	0.807403i
$640$	20.5974	+	8.53173i	0.814184	+	0.337246i
$641$	−5.74914	−	13.8796i	−0.227077	−	0.548213i	0.768742	−	0.639559i	$-0.220883\pi$
$641$	−5.74914	−	13.8796i	−0.227077	−	0.548213i	−0.995819	+	0.0913460i	$0.970883\pi$
$642$			4.76321i			0.187989i
$643$	16.4432	−	6.81099i	0.648456	−	0.268599i	−0.0341158	−	0.999418i	$-0.510862\pi$
$643$	16.4432	−	6.81099i	0.648456	−	0.268599i	0.682572	+	0.730819i	$0.260862\pi$
$644$	4.42898	+	4.42898i	0.174526	+	0.174526i
$645$	−3.04601			−0.119936
$646$		0			0
$647$	−46.4971			−1.82799			−0.913995	−	0.405725i	$-0.867019\pi$
$647$	−46.4971			−1.82799			−0.913995	+	0.405725i	$0.867019\pi$
$648$	−2.51332	−	2.51332i	−0.0987327	−	0.0987327i
$649$	23.4297	−	9.70489i	0.919695	−	0.380950i
$650$			0.835132i			0.0327566i
$651$	−1.22923	−	2.96762i	−0.0481773	−	0.116310i
$652$	−12.5613	−	5.20307i	−0.491939	−	0.203768i
$653$	−11.6835	+	28.2064i	−0.457209	+	1.10380i	0.512314	+	0.858798i	$0.328788\pi$
$653$	−11.6835	+	28.2064i	−0.457209	+	1.10380i	−0.969523	+	0.245002i	$0.921212\pi$
$654$	−0.404192	+	0.404192i	−0.0158052	+	0.0158052i
$655$	32.1578	−	32.1578i	1.25651	−	1.25651i
$656$	−6.51119	+	15.7194i	−0.254219	+	0.613739i
$657$	−22.4268	−	9.28947i	−0.874951	−	0.362417i
$658$	−2.13114	−	5.14502i	−0.0830803	−	0.200574i
$659$			9.83481i			0.383110i	0.981482	+	0.191555i	$0.0613530\pi$
$659$			9.83481i			0.383110i	−0.981482	+	0.191555i	$0.938647\pi$
$660$	−18.1504	+	7.51816i	−0.706505	+	0.292644i
$661$	−8.79367	−	8.79367i	−0.342034	−	0.342034i	0.515097	−	0.857132i	$-0.327756\pi$
$661$	−8.79367	−	8.79367i	−0.342034	−	0.342034i	−0.857132	+	0.515097i	$0.827756\pi$
$662$	−6.34049			−0.246430
$663$		0			0
$664$	−18.2986			−0.710123
$665$	1.08335	+	1.08335i	0.0420105	+	0.0420105i
$666$	−4.40835	+	1.82600i	−0.170820	+	0.0707560i
$667$		−	3.94862i		−	0.152891i
$668$	3.67233	+	8.86579i	0.142087	+	0.343028i
$669$	16.2094	+	6.71414i	0.626690	+	0.259583i
$670$	0.763791	−	1.84395i	0.0295078	−	0.0712382i
$671$	−0.661726	+	0.661726i	−0.0255457	+	0.0255457i
$672$	−4.48464	+	4.48464i	−0.172999	+	0.172999i
$673$	−4.82631	+	11.6517i	−0.186040	+	0.449141i	−0.989191	−	0.146635i	$-0.953156\pi$
$673$	−4.82631	+	11.6517i	−0.186040	+	0.449141i	0.803150	+	0.595777i	$0.203156\pi$
$674$	5.29267	+	2.19229i	0.203866	+	0.0844440i
$675$	0.896695	+	2.16481i	0.0345138	+	0.0833237i
$676$			17.3824i			0.668553i
$677$	4.20273	−	1.74083i	0.161524	−	0.0669054i	−0.300456	−	0.953796i	$-0.597139\pi$
$677$	4.20273	−	1.74083i	0.161524	−	0.0669054i	0.461980	+	0.886890i	$0.347139\pi$
$678$	2.61604	+	2.61604i	0.100469	+	0.100469i
$679$	17.4338			0.669046
$680$		0			0
$681$	−3.71244			−0.142261
$682$	−2.41709	−	2.41709i	−0.0925552	−	0.0925552i
$683$	4.49701	−	1.86272i	0.172073	−	0.0712751i	−0.294984	−	0.955502i	$-0.595314\pi$
$683$	4.49701	−	1.86272i	0.172073	−	0.0712751i	0.467057	+	0.884227i	$0.345314\pi$
$684$			1.45336i			0.0555707i
$685$	0.402705	+	0.972215i	0.0153866	+	0.0371464i
$686$	−6.31235	−	2.61466i	−0.241007	−	0.0998283i
$687$	4.88154	−	11.7851i	0.186242	−	0.449629i
$688$	3.43383	−	3.43383i	0.130913	−	0.130913i
$689$	−34.8655	+	34.8655i	−1.32827	+	1.32827i
$690$	−0.486490	+	1.17449i	−0.0185203	+	0.0447121i
$691$	−5.09668	−	2.11111i	−0.193887	−	0.0803106i	0.283627	−	0.958935i	$-0.408462\pi$
$691$	−5.09668	−	2.11111i	−0.193887	−	0.0803106i	−0.477514	+	0.878624i	$0.658462\pi$
$692$	9.22432	+	22.2695i	0.350656	+	0.846559i
$693$			21.1925i			0.805038i
$694$	6.60080	−	2.73414i	0.250563	−	0.103787i
$695$	19.3864	+	19.3864i	0.735369	+	0.735369i
$696$	2.63816			0.0999990
$697$		0			0
$698$	2.23112			0.0844493
$699$	3.18833	+	3.18833i	0.120594	+	0.120594i
$700$	−1.66359	+	0.689083i	−0.0628779	+	0.0260449i
$701$			22.3233i			0.843138i	0.906796	+	0.421569i	$0.138520\pi$
$701$			22.3233i			0.843138i	−0.906796	+	0.421569i	$0.861480\pi$
$702$	−2.88138	−	6.95626i	−0.108751	−	0.262547i
$703$	1.97978	+	0.820054i	0.0746690	+	0.0309289i
$704$	10.1724	−	24.5583i	0.383386	−	0.925576i
$705$	−12.4534	+	12.4534i	−0.469022	+	0.469022i
$706$	6.67192	−	6.67192i	0.251101	−	0.251101i
$707$	−5.07016	+	12.2405i	−0.190683	+	0.460350i
$708$	−7.64631	−	3.16721i	−0.287366	−	0.119031i
$709$	13.3084	+	32.1294i	0.499809	+	1.20665i	0.949587	+	0.313505i	$0.101503\pi$
$709$	13.3084	+	32.1294i	0.499809	+	1.20665i	−0.449778	+	0.893140i	$0.648497\pi$
$710$		−	8.08790i		−	0.303533i
$711$	−9.12107	+	3.77807i	−0.342067	+	0.141689i
$712$	−6.02828	−	6.02828i	−0.225920	−	0.225920i
$713$	3.44656			0.129075
$714$		0			0
$715$	56.0702			2.09691
$716$	−5.67619	−	5.67619i	−0.212129	−	0.212129i
$717$	12.8775	−	5.33404i	0.480919	−	0.199203i
$718$			5.86753i			0.218974i
$719$	1.62637	+	3.92640i	0.0606533	+	0.146430i	0.951301	−	0.308265i	$-0.0997483\pi$
$719$	1.62637	+	3.92640i	0.0606533	+	0.146430i	−0.890647	+	0.454695i	$0.849748\pi$
$720$	−15.8910	−	6.58226i	−0.592222	−	0.245306i
$721$	−3.81080	+	9.20009i	−0.141922	+	0.342629i
$722$	4.63632	−	4.63632i	0.172546	−	0.172546i
$723$	−11.2652	+	11.2652i	−0.418957	+	0.418957i
$724$	−0.332892	+	0.803673i	−0.0123718	+	0.0298683i
$725$	1.04875	+	0.434408i	0.0389497	+	0.0161335i
$726$	−1.71173	−	4.13248i	−0.0635282	−	0.153371i
$727$		−	29.1644i		−	1.08165i	−0.841136	−	0.540823i	$-0.818113\pi$
$727$		−	29.1644i		−	1.08165i	0.841136	−	0.540823i	$-0.181887\pi$
$728$	11.0344	−	4.57060i	0.408963	−	0.169398i
$729$	−4.42036	−	4.42036i	−0.163717	−	0.163717i
$730$	8.88713			0.328927
$731$		0			0
$732$	0.305407			0.0112882
$733$	−0.355670	−	0.355670i	−0.0131370	−	0.0131370i	0.700508	−	0.713645i	$-0.252957\pi$
$733$	−0.355670	−	0.355670i	−0.0131370	−	0.0131370i	−0.713645	+	0.700508i	$0.752957\pi$
$734$	0.477283	−	0.197697i	0.0176168	−	0.00729713i
$735$			7.15839i			0.264041i
$736$	−2.60420	−	6.28709i	−0.0959921	−	0.231745i
$737$	−11.4549	−	4.74477i	−0.421946	−	0.174776i
$738$	−1.53006	+	3.69390i	−0.0563224	+	0.135974i
$739$	−10.5770	+	10.5770i	−0.389081	+	0.389081i	−0.874359	−	0.485279i	$-0.838718\pi$
$739$	−10.5770	+	10.5770i	−0.389081	+	0.389081i	0.485279	+	0.874359i	$0.338718\pi$
$740$	−19.2474	+	19.2474i	−0.707547	+	0.707547i
$741$	−0.551282	+	1.33091i	−0.0202519	+	0.0488923i
$742$	6.30358	+	2.61103i	0.231412	+	0.0958539i
$743$	−8.94544	−	21.5962i	−0.328177	−	0.792288i	−0.998728	−	0.0504250i	$-0.983942\pi$
$743$	−8.94544	−	21.5962i	−0.328177	−	0.792288i	0.670551	−	0.741863i	$-0.266058\pi$
$744$			2.30272i			0.0844218i
$745$	−18.3637	+	7.60648i	−0.672793	+	0.278680i
$746$	5.90600	+	5.90600i	0.216234	+	0.216234i
$747$	30.2422			1.10650
$748$		0			0
$749$	29.3114			1.07102
$750$	2.27613	+	2.27613i	0.0831127	+	0.0831127i
$751$	−15.7328	+	6.51675i	−0.574099	+	0.237800i	−0.650793	−	0.759255i	$-0.725564\pi$
$751$	−15.7328	+	6.51675i	−0.574099	+	0.237800i	0.0766940	+	0.997055i	$0.475564\pi$
$752$		−	28.0779i		−	1.02390i
$753$	−9.98843	−	24.1142i	−0.363998	−	0.878770i
$754$	−3.36999	−	1.39590i	−0.122728	−	0.0508355i
$755$	12.3661	−	29.8543i	0.450047	−	1.08651i
$756$	11.4795	−	11.4795i	0.417504	−	0.417504i
$757$	11.5786	−	11.5786i	0.420832	−	0.420832i	−0.464658	−	0.885490i	$-0.653823\pi$
$757$	11.5786	−	11.5786i	0.420832	−	0.420832i	0.885490	+	0.464658i	$0.153823\pi$
$758$	2.68435	−	6.48060i	0.0975000	−	0.235386i
$759$	7.29609	+	3.02214i	0.264831	+	0.109697i
$760$	−0.420311	−	1.01472i	−0.0152463	−	0.0368078i
$761$			18.8803i			0.684411i	0.939625	+	0.342206i	$0.111174\pi$
$761$			18.8803i			0.684411i	−0.939625	+	0.342206i	$0.888826\pi$
$762$	−3.25607	+	1.34871i	−0.117955	+	0.0488586i
$763$	2.48728	+	2.48728i	0.0900455	+	0.0900455i
$764$	−2.68954			−0.0973042
$765$		0			0
$766$	−2.96080			−0.106978
$767$	16.7025	+	16.7025i	0.603093	+	0.603093i
$768$	−5.84908	+	2.42277i	−0.211060	+	0.0874241i
$769$		−	27.4766i		−	0.990831i	−0.868656	−	0.495416i	$-0.835016\pi$
$769$		−	27.4766i		−	0.990831i	0.868656	−	0.495416i	$-0.164984\pi$
$770$	−2.96915	−	7.16817i	−0.107001	−	0.258323i
$771$	−6.00960	−	2.48926i	−0.216431	−	0.0896485i
$772$	−17.7822	+	42.9300i	−0.639995	+	1.54508i
$773$	−7.00344	+	7.00344i	−0.251896	+	0.251896i	−0.821748	−	0.569851i	$-0.807001\pi$
$773$	−7.00344	+	7.00344i	−0.251896	+	0.251896i	0.569851	+	0.821748i	$0.307001\pi$
$774$	0.806914	−	0.806914i	0.0290039	−	0.0290039i
$775$	−0.379174	+	0.915406i	−0.0136203	+	0.0328824i
$776$	−11.5466	−	4.78275i	−0.414498	−	0.171691i
$777$	−3.90245	−	9.42134i	−0.140000	−	0.337989i
$778$			4.48576i			0.160822i
$779$	1.65892	−	0.687149i	0.0594371	−	0.0246197i
$780$	−12.9391	−	12.9391i	−0.463293	−	0.463293i
$781$	−50.2431			−1.79784
$782$		0			0
$783$	−10.2344			−0.365748
$784$	−8.06979	−	8.06979i	−0.288207	−	0.288207i
$785$	−38.9888	+	16.1497i	−1.39157	+	0.576408i
$786$		−	5.91716i		−	0.211058i
$787$	−19.4573	−	46.9741i	−0.693578	−	1.67445i	−0.737443	−	0.675409i	$-0.763967\pi$
$787$	−19.4573	−	46.9741i	−0.693578	−	1.67445i	0.0438650	−	0.999037i	$-0.486033\pi$
$788$	20.4217	+	8.45895i	0.727494	+	0.301338i
$789$	−7.80430	+	18.8413i	−0.277841	+	0.670766i
$790$	2.55579	−	2.55579i	0.0909310	−	0.0909310i
$791$	16.0984	−	16.0984i	0.572392	−	0.572392i
$792$	5.81393	−	14.0361i	0.206589	−	0.498750i
$793$	−0.805294	−	0.333564i	−0.0285968	−	0.0118452i
$794$	3.21960	+	7.77281i	0.114259	+	0.275847i
$795$		−	21.5776i		−	0.765279i
$796$	35.6298	−	14.7583i	1.26286	−	0.523096i
$797$	−3.80883	−	3.80883i	−0.134916	−	0.134916i	0.636424	−	0.771340i	$-0.280413\pi$
$797$	−3.80883	−	3.80883i	−0.134916	−	0.134916i	−0.771340	+	0.636424i	$0.780413\pi$
$798$	0.199340			0.00705658
$799$		0			0
$800$	1.95636			0.0691676
$801$	9.96297	+	9.96297i	0.352024	+	0.352024i
$802$	8.19385	−	3.39400i	0.289335	−	0.119846i
$803$		−	55.2080i		−	1.94825i
$804$	1.54846	+	3.73832i	0.0546101	+	0.131841i
$805$	7.22746	+	2.99371i	0.254735	+	0.105515i
$806$	1.21841	−	2.94150i	0.0429167	−	0.103610i
$807$	9.89111	−	9.89111i	0.348184	−	0.348184i
$808$	6.71606	−	6.71606i	0.236270	−	0.236270i
$809$	18.6298	−	44.9762i	0.654988	−	1.58128i	−0.150462	−	0.988616i	$-0.548076\pi$
$809$	18.6298	−	44.9762i	0.654988	−	1.58128i	0.805450	−	0.592664i	$-0.201924\pi$
$810$	−1.98694	−	0.823016i	−0.0698138	−	0.0289178i
$811$	−6.09541	−	14.7156i	−0.214039	−	0.516736i	0.779998	−	0.625782i	$-0.215220\pi$
$811$	−6.09541	−	14.7156i	−0.214039	−	0.516736i	−0.994037	+	0.109047i	$0.965220\pi$
$812$		−	7.86484i		−	0.276002i
$813$	13.8116	−	5.72094i	0.484393	−	0.200642i
$814$	−7.67355	−	7.67355i	−0.268958	−	0.268958i
$815$	−16.9813			−0.594830
$816$		0			0
$817$	−0.512489			−0.0179297
$818$	2.54228	+	2.54228i	0.0888889	+	0.0888889i
$819$	−18.2366	+	7.55385i	−0.637239	+	0.263953i
$820$			22.8084i			0.796504i
$821$	6.54427	+	15.7993i	0.228397	+	0.551399i	0.995983	−	0.0895477i	$-0.0285421\pi$
$821$	6.54427	+	15.7993i	0.228397	+	0.551399i	−0.767586	+	0.640946i	$0.778542\pi$
$822$	0.126495	+	0.0523960i	0.00441203	+	0.00182752i
$823$	2.15170	−	5.19467i	0.0750037	−	0.181075i	−0.881931	−	0.471379i	$-0.843756\pi$
$823$	2.15170	−	5.19467i	0.0750037	−	0.181075i	0.956934	+	0.290304i	$0.0937564\pi$
$824$	5.04788	−	5.04788i	0.175851	−	0.175851i
$825$	−1.60536	+	1.60536i	−0.0558915	+	0.0558915i
$826$	1.25083	−	3.01977i	0.0435219	−	0.105071i
$827$	−16.5012	−	6.83500i	−0.573801	−	0.237676i	0.0768632	−	0.997042i	$-0.475510\pi$
$827$	−16.5012	−	6.83500i	−0.573801	−	0.237676i	−0.650664	+	0.759365i	$0.725510\pi$
$828$	2.83988	+	6.85608i	0.0986927	+	0.238265i
$829$		−	35.8161i		−	1.24395i	−0.783039	−	0.621973i	$-0.786331\pi$
$829$		−	35.8161i		−	1.24395i	0.783039	−	0.621973i	$-0.213669\pi$
$830$	−10.2291	+	4.23704i	−0.355058	+	0.147070i
$831$	−10.4501	−	10.4501i	−0.362510	−	0.362510i
$832$	24.7588			0.858356
$833$		0			0
$834$	3.56717			0.123521
$835$	8.47499	+	8.47499i	0.293289	+	0.293289i
$836$	−3.05380	+	1.26492i	−0.105618	+	0.0437483i
$837$		−	8.93313i		−	0.308774i
$838$	−0.174523	−	0.421337i	−0.00602881	−	0.0145548i
$839$	33.0502	+	13.6899i	1.14102	+	0.472626i	0.871513	−	0.490372i	$-0.163139\pi$
$839$	33.0502	+	13.6899i	1.14102	+	0.472626i	0.269508	+	0.962998i	$0.413139\pi$
$840$	−2.00016	+	4.82882i	−0.0690122	+	0.166610i
$841$	17.0002	−	17.0002i	0.586213	−	0.586213i
$842$	1.96841	−	1.96841i	0.0678358	−	0.0678358i
$843$	−9.53072	+	23.0092i	−0.328255	+	0.792479i
$844$	−37.7092	−	15.6197i	−1.29800	−	0.537651i
$845$	8.30809	+	20.0575i	0.285807	+	0.689999i
$846$		−	6.59802i		−	0.226845i
$847$	−25.4300	+	10.5335i	−0.873787	+	0.361934i
$848$	24.3249	+	24.3249i	0.835319	+	0.835319i
$849$	−28.3465			−0.972849
$850$		0			0
$851$	10.9418			0.375080
$852$	11.5944	+	11.5944i	0.397217	+	0.397217i
$853$	10.2245	−	4.23511i	0.350079	−	0.145007i	−0.200713	−	0.979650i	$-0.564326\pi$
$853$	10.2245	−	4.23511i	0.350079	−	0.145007i	0.550792	+	0.834643i	$0.314326\pi$
$854$			0.120615i			0.00412735i
$855$	0.694650	+	1.67703i	0.0237565	+	0.0573533i
$856$	−19.4133	−	8.04125i	−0.663533	−	0.274844i
$857$	−10.3610	+	25.0137i	−0.353925	+	0.854451i	0.642203	+	0.766535i	$0.278021\pi$
$857$	−10.3610	+	25.0137i	−0.353925	+	0.854451i	−0.996128	+	0.0879160i	$0.971979\pi$
$858$	5.15856	−	5.15856i	0.176110	−	0.176110i
$859$	−36.5772	+	36.5772i	−1.24800	+	1.24800i	−0.291393	+	0.956603i	$0.594119\pi$
$859$	−36.5772	+	36.5772i	−1.24800	+	1.24800i	−0.956603	+	0.291393i	$0.905881\pi$
$860$	2.49119	−	6.01427i	0.0849490	−	0.205085i
$861$	−7.89444	−	3.26998i	−0.269042	−	0.111441i
$862$	1.95728	+	4.72530i	0.0666653	+	0.160944i
$863$		−	45.4712i		−	1.54786i	−0.633272	−	0.773929i	$-0.718289\pi$
$863$		−	45.4712i		−	1.54786i	0.633272	−	0.773929i	$-0.281711\pi$
$864$	−16.2955	+	6.74983i	−0.554385	+	0.229634i
$865$	21.2879	+	21.2879i	0.723809	+	0.723809i
$866$	2.86215			0.0972598
$867$		0			0
$868$	6.86484			0.233008
$869$	−15.8769	−	15.8769i	−0.538588	−	0.538588i
$870$	1.47476	−	0.610865i	0.0499990	−	0.0207103i
$871$		−	11.5484i		−	0.391302i
$872$	−0.964997	−	2.32971i	−0.0326789	−	0.0788939i
$873$	19.0831	+	7.90448i	0.645865	+	0.267526i
$874$	−0.0818515	+	0.197607i	−0.00276867	+	0.00668416i
$875$	14.0067	−	14.0067i	0.473511	−	0.473511i
$876$	−12.7401	+	12.7401i	−0.430448	+	0.430448i
$877$	14.3443	−	34.6301i	0.484372	−	1.16938i	−0.473141	−	0.880987i	$-0.656880\pi$
$877$	14.3443	−	34.6301i	0.484372	−	1.16938i	0.957513	−	0.288390i	$-0.0931200\pi$
$878$	−12.8204	−	5.31038i	−0.432667	−	0.179217i
$879$	−4.70157	−	11.3506i	−0.158580	−	0.382846i
$880$		−	39.1189i		−	1.31870i
$881$	16.8108	−	6.96324i	0.566369	−	0.234598i	−0.0810787	−	0.996708i	$-0.525837\pi$
$881$	16.8108	−	6.96324i	0.566369	−	0.234598i	0.647447	+	0.762110i	$0.275837\pi$
$882$	−1.89632	−	1.89632i	−0.0638524	−	0.0638524i
$883$	−0.397860			−0.0133891			−0.00669453	−	0.999978i	$-0.502131\pi$
$883$	−0.397860			−0.0133891			−0.00669453	+	0.999978i	$0.502131\pi$
$884$		0			0
$885$	−10.3369			−0.347470
$886$	3.42486	+	3.42486i	0.115060	+	0.115060i
$887$	−21.9730	+	9.10152i	−0.737782	+	0.305599i	−0.719745	−	0.694238i	$-0.755741\pi$
$887$	−21.9730	+	9.10152i	−0.737782	+	0.305599i	−0.0180364	+	0.999837i	$0.505741\pi$
$888$			7.31046i			0.245323i
$889$	8.29956	+	20.0369i	0.278358	+	0.672016i
$890$	−4.76573	−	1.97403i	−0.159748	−	0.0661696i
$891$	−5.11268	+	12.3431i	−0.171281	+	0.413510i
$892$	−26.5138	+	26.5138i	−0.887748	+	0.887748i
$893$	−2.09527	+	2.09527i	−0.0701156	+	0.0701156i
$894$	−0.989681	+	2.38930i	−0.0330999	+	0.0799102i
$895$	−9.26273	−	3.83675i	−0.309619	−	0.128248i
$896$	−6.83101	−	16.4915i	−0.228208	−	0.550943i
$897$			7.35565i			0.245598i
$898$	−3.28295	+	1.35984i	−0.109554	+	0.0453786i
$899$	−3.06014	−	3.06014i	−0.102061	−	0.102061i
$900$	−2.13341			−0.0711136
$901$		0			0
$902$	−9.09327			−0.302773
$903$	1.72450	+	1.72450i	0.0573879	+	0.0573879i
$904$	−15.0785	+	6.24573i	−0.501505	+	0.207730i
$905$			1.08647i			0.0361154i
$906$	−1.60895	−	3.88435i	−0.0534538	−	0.129049i
$907$	−34.6650	−	14.3587i	−1.15103	−	0.476774i	−0.276154	−	0.961114i	$-0.589060\pi$
$907$	−34.6650	−	14.3587i	−1.15103	−	0.476774i	−0.874880	+	0.484340i	$0.839060\pi$
$908$	3.03624	−	7.33012i	0.100761	−	0.243259i
$909$	−11.0997	+	11.0997i	−0.368152	+	0.368152i
$910$	5.11004	−	5.11004i	0.169396	−	0.169396i
$911$	−5.65023	+	13.6409i	−0.187200	+	0.451942i	−0.989419	−	0.145089i	$-0.953653\pi$
$911$	−5.65023	+	13.6409i	−0.187200	+	0.451942i	0.802218	+	0.597031i	$0.203653\pi$
$912$	0.928547	+	0.384617i	0.0307473	+	0.0127359i
$913$	26.3211	+	63.5447i	0.871100	+	2.10302i
$914$			4.08790i			0.135216i
$915$	0.352409	−	0.145973i	0.0116503	−	0.00482570i
$916$	19.2770	+	19.2770i	0.636929	+	0.636929i
$917$	−36.4124			−1.20244
$918$		0			0
$919$	−48.5476			−1.60144			−0.800718	−	0.599041i	$-0.795549\pi$
$919$	−48.5476			−1.60144			−0.800718	+	0.599041i	$0.795549\pi$
$920$	−3.96554	−	3.96554i	−0.130740	−	0.130740i
$921$	−7.35234	+	3.04544i	−0.242268	+	0.100351i
$922$			6.77238i			0.223037i
$923$	−17.9086	−	43.2352i	−0.589469	−	1.42310i
$924$	14.5323	+	6.01949i	0.478078	+	0.198027i
$925$	−1.20377	+	2.90615i	−0.0395796	+	0.0955536i
$926$	0.351437	−	0.351437i	0.0115489	−	0.0115489i
$927$	−8.34265	+	8.34265i	−0.274009	+	0.274009i
$928$	−3.26998	+	7.89444i	−0.107343	+	0.259148i
$929$	−10.4061	−	4.31036i	−0.341414	−	0.141418i	0.205387	−	0.978681i	$-0.434155\pi$
$929$	−10.4061	−	4.31036i	−0.341414	−	0.141418i	−0.546801	+	0.837262i	$0.684155\pi$
$930$	0.533194	+	1.28725i	0.0174841	+	0.0422104i
$931$			1.20439i			0.0394724i
$932$	−8.90287	+	3.68769i	−0.291623	+	0.120794i
$933$	1.45959	+	1.45959i	0.0477850	+	0.0477850i
$934$	3.71244			0.121475
$935$		0			0
$936$	14.1506			0.462528
$937$	1.69546	+	1.69546i	0.0553884	+	0.0553884i	0.734258	−	0.678870i	$-0.237530\pi$
$937$	1.69546	+	1.69546i	0.0553884	+	0.0553884i	−0.678870	+	0.734258i	$0.737530\pi$
$938$	−1.47638	+	0.611536i	−0.0482055	+	0.0199674i
$939$		−	13.3037i		−	0.434148i
$940$	−14.4039	−	34.7740i	−0.469802	−	1.13420i
$941$	−31.7627	−	13.1565i	−1.03543	−	0.428891i	−0.200763	−	0.979640i	$-0.564342\pi$
$941$	−31.7627	−	13.1565i	−1.03543	−	0.428891i	−0.834671	+	0.550749i	$0.814342\pi$
$942$	−2.10124	+	5.07285i	−0.0684622	+	0.165282i
$943$	6.48310	−	6.48310i	0.211119	−	0.211119i
$944$	11.6530	−	11.6530i	0.379271	−	0.379271i
$945$	7.75941	−	18.7329i	0.252414	−	0.609380i
$946$	2.39778	+	0.993191i	0.0779584	+	0.0322914i
$947$	−7.85626	−	18.9667i	−0.255294	−	0.616335i	0.743321	−	0.668934i	$-0.233249\pi$
$947$	−7.85626	−	18.9667i	−0.255294	−	0.616335i	−0.998616	+	0.0525996i	$0.983249\pi$
$948$			7.32770i			0.237993i
$949$	47.5076	−	19.6783i	1.54216	−	0.638785i
$950$	−0.0434796	−	0.0434796i	−0.00141066	−	0.00141066i
$951$	−9.09091			−0.294793
$952$		0			0
$953$	16.5517			0.536162			0.268081	−	0.963396i	$-0.413611\pi$
$953$	16.5517			0.536162			0.268081	+	0.963396i	$0.413611\pi$
$954$	5.71609	+	5.71609i	0.185065	+	0.185065i
$955$	−3.10346	+	1.28549i	−0.100425	+	0.0415976i
$956$			29.7888i			0.963439i
$957$	−3.79477	−	9.16139i	−0.122668	−	0.296146i
$958$	12.4710	+	5.16567i	0.402921	+	0.166895i
$959$	0.322429	−	0.778413i	0.0104118	−	0.0251363i
$960$	−7.66137	+	7.66137i	−0.247270	+	0.247270i
$961$	−19.2493	+	19.2493i	−0.620944	+	0.620944i
$962$	3.86810	−	9.33841i	0.124712	−	0.301082i
$963$	32.0844	+	13.2898i	1.03391	+	0.428258i
$964$	−13.0296	−	31.4561i	−0.419654	−	1.01313i
$965$			58.0360i			1.86825i
$966$	0.940367	−	0.389513i	0.0302558	−	0.0125324i
$967$	−2.77656	−	2.77656i	−0.0892882	−	0.0892882i	0.661052	−	0.750340i	$-0.270110\pi$
$967$	−2.77656	−	2.77656i	−0.0892882	−	0.0892882i	−0.750340	+	0.661052i	$0.770110\pi$
$968$	19.7324			0.634222
$969$		0			0
$970$	−7.56212			−0.242805
$971$	−3.00805	−	3.00805i	−0.0965329	−	0.0965329i	0.657191	−	0.753724i	$-0.271744\pi$
$971$	−3.00805	−	3.00805i	−0.0965329	−	0.0965329i	−0.753724	+	0.657191i	$0.771744\pi$
$972$	27.9700	−	11.5856i	0.897140	−	0.371607i
$973$		−	21.9513i		−	0.703726i
$974$	−4.91929	−	11.8762i	−0.157624	−	0.380539i
$975$	−1.95366	−	0.809233i	−0.0625673	−	0.0259162i
$976$	−0.232720	+	0.561835i	−0.00744918	+	0.0179839i
$977$	34.3252	−	34.3252i	1.09816	−	1.09816i	0.103534	−	0.994626i	$-0.466985\pi$
$977$	34.3252	−	34.3252i	1.09816	−	1.09816i	0.994626	−	0.103534i	$-0.0330150\pi$
$978$	−1.56231	+	1.56231i	−0.0499573	+	0.0499573i
$979$	−12.2629	+	29.6053i	−0.391925	+	0.946190i
$980$	−14.1341	−	5.85452i	−0.451496	−	0.187016i
$981$	1.59485	+	3.85032i	0.0509198	+	0.122931i
$982$			8.82739i			0.281693i
$983$	−32.3910	+	13.4168i	−1.03311	+	0.427929i	−0.833835	−	0.552014i	$-0.813859\pi$
$983$	−32.3910	+	13.4168i	−1.03311	+	0.427929i	−0.199277	+	0.979943i	$0.563859\pi$
$984$	4.33150	+	4.33150i	0.138083	+	0.138083i
$985$	27.6076			0.879652
$986$		0			0
$987$	14.1010			0.448840
$988$	−2.17699	−	2.17699i	−0.0692592	−	0.0692592i
$989$	−2.41761	+	1.00141i	−0.0768755	+	0.0318429i
$990$		−	9.19253i		−	0.292158i
$991$	20.3585	+	49.1499i	0.646711	+	1.56130i	0.817461	+	0.575983i	$0.195381\pi$
$991$	20.3585	+	49.1499i	0.646711	+	1.56130i	−0.170751	+	0.985314i	$0.554619\pi$
$992$	−6.89068	−	2.85421i	−0.218779	−	0.0906213i
$993$	6.14386	−	14.8326i	0.194970	−	0.470698i
$994$	−4.57898	+	4.57898i	−0.145236	+	0.145236i
$995$	34.0593	−	34.0593i	1.07975	−	1.07975i
$996$	8.58993	−	20.7379i	0.272182	−	0.657106i
$997$	20.8606	+	8.64074i	0.660662	+	0.273655i	0.687717	−	0.725979i	$-0.258613\pi$
$997$	20.8606	+	8.64074i	0.660662	+	0.273655i	−0.0270551	+	0.999634i	$0.508613\pi$
$998$	−2.90049	−	7.00241i	−0.0918135	−	0.221657i
$999$		−	28.3601i		−	0.897274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.f.155.3		24
17.2	even	8	inner	289.2.d.f.110.3		24
17.3	odd	16		289.2.a.e.1.2	yes	3
17.4	even	4	inner	289.2.d.f.134.4		24
17.5	odd	16		289.2.b.d.288.3		6
17.6	odd	16		289.2.c.d.38.3		12
17.7	odd	16		289.2.c.d.251.4		12
17.8	even	8	inner	289.2.d.f.179.4		24
17.9	even	8	inner	289.2.d.f.179.3		24
17.10	odd	16		289.2.c.d.251.3		12
17.11	odd	16		289.2.c.d.38.4		12
17.12	odd	16		289.2.b.d.288.4		6
17.13	even	4	inner	289.2.d.f.134.3		24
17.14	odd	16		289.2.a.d.1.2	✓	3
17.15	even	8	inner	289.2.d.f.110.4		24
17.16	even	2	inner	289.2.d.f.155.4		24
51.14	even	16		2601.2.a.x.1.2		3
51.20	even	16		2601.2.a.w.1.2		3
68.3	even	16		4624.2.a.bd.1.3		3
68.31	even	16		4624.2.a.bg.1.1		3
85.14	odd	16		7225.2.a.t.1.2		3
85.54	odd	16		7225.2.a.s.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.2	✓	3	17.14	odd	16
289.2.a.e.1.2	yes	3	17.3	odd	16
289.2.b.d.288.3		6	17.5	odd	16
289.2.b.d.288.4		6	17.12	odd	16
289.2.c.d.38.3		12	17.6	odd	16
289.2.c.d.38.4		12	17.11	odd	16
289.2.c.d.251.3		12	17.10	odd	16
289.2.c.d.251.4		12	17.7	odd	16
289.2.d.f.110.3		24	17.2	even	8	inner
289.2.d.f.110.4		24	17.15	even	8	inner
289.2.d.f.134.3		24	17.13	even	4	inner
289.2.d.f.134.4		24	17.4	even	4	inner
289.2.d.f.155.3		24	1.1	even	1	trivial
289.2.d.f.155.4		24	17.16	even	2	inner
289.2.d.f.179.3		24	17.9	even	8	inner
289.2.d.f.179.4		24	17.8	even	8	inner
2601.2.a.w.1.2		3	51.20	even	16
2601.2.a.x.1.2		3	51.14	even	16
4624.2.a.bd.1.3		3	68.3	even	16
4624.2.a.bg.1.1		3	68.31	even	16
7225.2.a.s.1.2		3	85.54	odd	16
7225.2.a.t.1.2		3	85.14	odd	16

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.245576 + 0.245576i) q^{2} +(-0.812446 + 0.336526i) q^{3} -1.87939i q^{4} +(-0.898271 - 2.16862i) q^{5} +(-0.282160 - 0.116874i) q^{6} +(-0.719210 + 1.73633i) q^{7} +(0.952682 - 0.952682i) q^{8} +(-1.57450 + 1.57450i) q^{9} +(0.311966 - 0.753153i) q^{10} +(-4.67869 - 1.93798i) q^{11} +(0.632462 + 1.52690i) q^{12} -4.71688i q^{13} +(-0.603020 + 0.249779i) q^{14} +(1.45959 + 1.45959i) q^{15} -3.29086 q^{16} -0.773318 q^{18} +(0.245576 + 0.245576i) q^{19} +(-4.07567 + 1.68820i) q^{20} -1.65270i q^{21} +(-0.673052 - 1.62489i) q^{22} +(1.63833 + 0.678620i) q^{23} +(-0.453400 + 1.09461i) q^{24} +(-0.360483 + 0.360483i) q^{25} +(1.15835 - 1.15835i) q^{26} +(1.75892 - 4.24640i) q^{27} +(3.26322 + 1.35167i) q^{28} +(-0.852114 - 2.05719i) q^{29} +0.716881i q^{30} +(1.79562 - 0.743769i) q^{31} +(-2.71352 - 2.71352i) q^{32} +4.45336 q^{33} +4.41147 q^{35} +(2.95910 + 2.95910i) q^{36} +(5.70056 - 2.36125i) q^{37} +0.120615i q^{38} +(1.58735 + 3.83221i) q^{39} +(-2.92177 - 1.21024i) q^{40} +(1.97857 - 4.77668i) q^{41} +(0.405864 - 0.405864i) q^{42} +(-1.04344 + 1.04344i) q^{43} +(-3.64221 + 8.79306i) q^{44} +(4.82882 + 2.00016i) q^{45} +(0.235682 + 0.568987i) q^{46} +8.53209i q^{47} +(2.67365 - 1.10746i) q^{48} +(2.45218 + 2.45218i) q^{49} -0.177052 q^{50} -8.86484 q^{52} +(-7.39164 - 7.39164i) q^{53} +(1.47476 - 0.610865i) q^{54} +11.8871i q^{55} +(0.968988 + 2.33935i) q^{56} +(-0.282160 - 0.116874i) q^{57} +(0.295936 - 0.714453i) q^{58} +(-3.54101 + 3.54101i) q^{59} +(2.74314 - 2.74314i) q^{60} +(0.0707170 - 0.170726i) q^{61} +(0.623612 + 0.258308i) q^{62} +(-1.60145 - 3.86624i) q^{63} +5.24897i q^{64} +(-10.2291 + 4.23704i) q^{65} +(1.09364 + 1.09364i) q^{66} +2.44831 q^{67} -1.55943 q^{69} +(1.08335 + 1.08335i) q^{70} +(9.16606 - 3.79671i) q^{71} +3.00000i q^{72} +(4.17189 + 10.0718i) q^{73} +(1.97978 + 0.820054i) q^{74} +(0.171561 - 0.414185i) q^{75} +(0.461531 - 0.461531i) q^{76} +(6.72992 - 6.72992i) q^{77} +(-0.551282 + 1.33091i) q^{78} +(4.09626 + 1.69673i) q^{79} +(2.95608 + 7.13662i) q^{80} -2.63816i q^{81} +(1.65892 - 0.687149i) q^{82} +(-9.60373 - 9.60373i) q^{83} -3.10607 q^{84} -0.512489 q^{86} +(1.38459 + 1.38459i) q^{87} +(-6.30358 + 2.61103i) q^{88} -6.32770i q^{89} +(0.694650 + 1.67703i) q^{90} +(8.19004 + 3.39243i) q^{91} +(1.27539 - 3.07906i) q^{92} +(-1.20854 + 1.20854i) q^{93} +(-2.09527 + 2.09527i) q^{94} +(0.311966 - 0.753153i) q^{95} +(3.11776 + 1.29142i) q^{96} +(-3.54989 - 8.57019i) q^{97} +1.20439i q^{98} +(10.4180 - 4.31526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{16} - 72 q^{18} + 24 q^{35} - 168 q^{50} - 24 q^{52} + 72 q^{67} + 168 q^{69} + 24 q^{84} + 48 q^{86}+O(q^{100}) \) 24 * q + 48 * q^16 - 72 * q^18 + 24 * q^35 - 168 * q^50 - 24 * q^52 + 72 * q^67 + 168 * q^69 + 24 * q^84 + 48 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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