LMFDB - Embedded newform 289.2.d.f.134.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(110,289)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			134.4
Character	$\chi$	$=$	289.134
Dual form			289.2.d.f.110.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.614932	−	0.788580i	$-0.289183\pi$
$2$	−0.245576	−	0.245576i	−0.173648	−	0.173648i	−0.788580	+	0.614932i	$0.789183\pi$
$3$	0.336526	+	0.812446i	0.194293	+	0.469066i	0.990762	−	0.135614i	$-0.0433008\pi$
$3$	0.336526	+	0.812446i	0.194293	+	0.469066i	−0.796468	+	0.604680i	$0.793301\pi$
$4$		−	1.87939i		−	0.939693i
$5$	−2.16862	+	0.898271i	−0.969836	+	0.401719i	−0.810651	−	0.585530i	$-0.800887\pi$
$5$	−2.16862	+	0.898271i	−0.969836	+	0.401719i	−0.159185	+	0.987249i	$0.550887\pi$
$6$	0.116874	−	0.282160i	0.0477137	−	0.115191i
$7$	−1.73633	−	0.719210i	−0.656269	−	0.271836i	0.0295984	−	0.999562i	$-0.490577\pi$
$7$	−1.73633	−	0.719210i	−0.656269	−	0.271836i	−0.685868	+	0.727726i	$0.740577\pi$
$8$	−0.952682	+	0.952682i	−0.336824	+	0.336824i
$9$	1.57450	−	1.57450i	0.524834	−	0.524834i
$10$	0.753153	+	0.311966i	0.238168	+	0.0986524i
$11$	1.93798	−	4.67869i	0.584322	−	1.41068i	−0.304538	−	0.952500i	$-0.598502\pi$
$11$	1.93798	−	4.67869i	0.584322	−	1.41068i	0.888860	−	0.458178i	$-0.151498\pi$
$12$	1.52690	−	0.632462i	0.440778	−	0.182576i
$13$		−	4.71688i		−	1.30823i	−0.756396	−	0.654114i	$-0.773042\pi$
$13$		−	4.71688i		−	1.30823i	0.756396	−	0.654114i	$-0.226958\pi$
$14$	0.249779	+	0.603020i	0.0667562	+	0.161164i
$15$	−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	0.678376	−	0.734715i	$-0.262684\pi$
$19$	−0.245576	−	0.245576i	−0.0563389	−	0.0563389i	−0.734715	+	0.678376i	$0.762684\pi$
$20$	1.68820	+	4.07567i	0.377493	+	0.911348i
$21$		−	1.65270i		−	0.360650i
$22$	−1.62489	+	0.673052i	−0.346428	+	0.143495i
$23$	−0.678620	+	1.63833i	−0.141502	+	0.341616i	−0.978704	−	0.205278i	$-0.934190\pi$
$23$	−0.678620	+	1.63833i	−0.141502	+	0.341616i	0.837202	+	0.546894i	$0.184190\pi$
$24$	−1.09461	−	0.453400i	−0.223435	−	0.0925500i
$25$	0.360483	−	0.360483i	0.0720966	−	0.0720966i
$26$	−1.15835	+	1.15835i	−0.227171	+	0.227171i
$27$	4.24640	+	1.75892i	0.817219	+	0.338503i
$28$	−1.35167	+	3.26322i	−0.255442	+	0.616691i
$29$	−2.05719	+	0.852114i	−0.382010	+	0.158234i	−0.565421	−	0.824803i	$-0.691286\pi$
$29$	−2.05719	+	0.852114i	−0.382010	+	0.158234i	0.183411	+	0.983036i	$0.441286\pi$
$30$			0.716881i			0.130884i
$31$	−0.743769	−	1.79562i	−0.133585	−	0.322503i	0.842906	−	0.538061i	$-0.180843\pi$
$31$	−0.743769	−	1.79562i	−0.133585	−	0.322503i	−0.976491	+	0.215558i	$0.930843\pi$
$32$	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
$37$	−2.36125	−	5.70056i	−0.388187	−	0.937167i	−0.990324	−	0.138774i	$-0.955684\pi$
$37$	−2.36125	−	5.70056i	−0.388187	−	0.937167i	0.602137	−	0.798393i	$-0.294316\pi$
$38$			0.120615i			0.0195663i
$39$	3.83221	−	1.58735i	0.613645	−	0.254180i
$40$	1.21024	−	2.92177i	0.191355	−	0.461973i
$41$	4.77668	+	1.97857i	0.745993	+	0.309000i	0.723105	−	0.690738i	$-0.242714\pi$
$41$	4.77668	+	1.97857i	0.745993	+	0.309000i	0.0228873	+	0.999738i	$0.492714\pi$
$42$	−0.405864	+	0.405864i	−0.0626261	+	0.0626261i
$43$	1.04344	−	1.04344i	0.159124	−	0.159124i	−0.623055	−	0.782178i	$-0.714109\pi$
$43$	1.04344	−	1.04344i	0.159124	−	0.159124i	0.782178	+	0.623055i	$0.214109\pi$
$44$	−8.79306	−	3.64221i	−1.32560	−	0.549083i
$45$	−2.00016	+	4.82882i	−0.298167	+	0.719839i
$46$	0.568987	−	0.235682i	0.0838925	−	0.0347494i
$47$			8.53209i			1.24453i	0.782805	+	0.622267i	$0.213788\pi$
$47$			8.53209i			1.24453i	−0.782805	+	0.622267i	$0.786212\pi$
$48$	−1.10746	−	2.67365i	−0.159848	−	0.385908i
$49$	−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	$0.00491477\pi$
$53$	7.39164	+	7.39164i	1.01532	+	1.01532i	0.0154396	+	0.999881i	$0.495085\pi$
$54$	−0.610865	−	1.47476i	−0.0831282	−	0.200689i
$55$			11.8871i			1.60286i
$56$	2.33935	−	0.968988i	0.312608	−	0.129487i
$57$	0.116874	−	0.282160i	0.0154804	−	0.0373729i
$58$	0.714453	+	0.295936i	0.0938123	+	0.0388583i
$59$	3.54101	−	3.54101i	0.461000	−	0.461000i	−0.437983	−	0.898983i	$-0.644307\pi$
$59$	3.54101	−	3.54101i	0.461000	−	0.461000i	0.898983	+	0.437983i	$0.144307\pi$
$60$	−2.74314	+	2.74314i	−0.354138	+	0.354138i
$61$	0.170726	+	0.0707170i	0.0218592	+	0.00905439i	0.393586	−	0.919288i	$-0.371234\pi$
$61$	0.170726	+	0.0707170i	0.0218592	+	0.00905439i	−0.371727	+	0.928342i	$0.621234\pi$
$62$	−0.258308	+	0.623612i	−0.0328052	+	0.0791988i
$63$	−3.86624	+	1.60145i	−0.487101	+	0.201764i
$64$			5.24897i			0.656121i
$65$	4.23704	+	10.2291i	0.525540	+	1.26877i
$66$	−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
$71$	−3.79671	−	9.16606i	−0.450586	−	1.08781i	−0.972100	−	0.234568i	$-0.924632\pi$
$71$	−3.79671	−	9.16606i	−0.450586	−	1.08781i	0.521513	−	0.853243i	$-0.325368\pi$
$72$			3.00000i			0.353553i
$73$	10.0718	−	4.17189i	1.17882	−	0.488283i	0.294721	−	0.955584i	$-0.404773\pi$
$73$	10.0718	−	4.17189i	1.17882	−	0.488283i	0.884098	+	0.467301i	$0.154773\pi$
$74$	−0.820054	+	1.97978i	−0.0953293	+	0.230145i
$75$	0.414185	+	0.171561i	0.0478260	+	0.0198102i
$76$	−0.461531	+	0.461531i	−0.0529413	+	0.0529413i
$77$	−6.72992	+	6.72992i	−0.766945	+	0.766945i
$78$	−1.33091	−	0.551282i	−0.150696	−	0.0624204i
$79$	−1.69673	+	4.09626i	−0.190897	+	0.460866i	−0.990129	−	0.140156i	$-0.955240\pi$
$79$	−1.69673	+	4.09626i	−0.190897	+	0.460866i	0.799233	+	0.601022i	$0.205240\pi$
$80$	7.13662	−	2.95608i	0.797898	−	0.330500i
$81$		−	2.63816i		−	0.293128i
$82$	−0.687149	−	1.65892i	−0.0758829	−	0.183198i
$83$	9.60373	+	9.60373i	1.05415	+	1.05415i	0.998448	+	0.0556982i	$0.0177385\pi$
$83$	9.60373	+	9.60373i	1.05415	+	1.05415i	0.0556982	+	0.998448i	$0.482262\pi$
$84$	−3.10607			−0.338900
$85$		0			0
$86$	−0.512489			−0.0552631
$87$	−1.38459	−	1.38459i	−0.148444	−	0.148444i
$88$	2.61103	+	6.30358i	0.278337	+	0.671964i
$89$		−	6.32770i		−	0.670734i	−0.942087	−	0.335367i	$-0.891140\pi$
$89$		−	6.32770i		−	0.670734i	0.942087	−	0.335367i	$-0.108860\pi$
$90$	1.67703	−	0.694650i	0.176775	−	0.0732225i
$91$	−3.39243	+	8.19004i	−0.355623	+	0.858550i
$92$	3.07906	+	1.27539i	0.321014	+	0.132968i
$93$	1.20854	−	1.20854i	0.125320	−	0.125320i
$94$	2.09527	−	2.09527i	0.216111	−	0.216111i
$95$	0.753153	+	0.311966i	0.0772719	+	0.0320071i
$96$	−1.29142	+	3.11776i	−0.131805	+	0.318205i
$97$	−8.57019	+	3.54989i	−0.870171	+	0.360437i	−0.772677	−	0.634799i	$-0.781083\pi$
$97$	−8.57019	+	3.54989i	−0.870171	+	0.360437i	−0.0974943	+	0.995236i	$0.531083\pi$
$98$			1.20439i			0.121662i
$99$	−4.31526	−	10.4180i	−0.433700	−	1.04704i
$100$	−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
$105$	1.48458	+	3.58408i	0.144880	+	0.349771i
$106$		−	3.63041i		−	0.352617i
$107$	−14.4091	+	5.96843i	−1.39298	+	0.576990i	−0.947919	−	0.318511i	$-0.896817\pi$
$107$	−14.4091	+	5.96843i	−1.39298	+	0.576990i	−0.445058	+	0.895502i	$0.646817\pi$
$108$	3.30568	−	7.98062i	0.318089	−	0.767935i
$109$	1.72917	+	0.716247i	0.165625	+	0.0686041i	0.463955	−	0.885859i	$-0.346430\pi$
$109$	1.72917	+	0.716247i	0.165625	+	0.0686041i	−0.298331	+	0.954463i	$0.596430\pi$
$110$	2.91919	−	2.91919i	0.278334	−	0.278334i
$111$	3.83678	−	3.83678i	0.364171	−	0.364171i
$112$	5.71400	+	2.36682i	0.539923	+	0.223643i
$113$	4.63575	−	11.1917i	0.436095	−	1.05283i	−0.541191	−	0.840900i	$-0.682026\pi$
$113$	4.63575	−	11.1917i	0.436095	−	1.05283i	0.977286	−	0.211927i	$-0.0679738\pi$
$114$	−0.0979930	+	0.0405900i	−0.00917788	+	0.00380160i
$115$		−	4.16250i		−	0.388155i
$116$	1.60145	+	3.86624i	0.148691	+	0.358972i
$117$	−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
$122$	−0.0245598	−	0.0592925i	−0.00222354	−	0.00536809i
$123$			4.54664i			0.409956i
$124$	−3.37466	+	1.39783i	−0.303053	+	0.125529i
$125$	4.03342	−	9.73753i	0.360760	−	0.870951i
$126$	1.34273	+	0.556178i	0.119620	+	0.0495483i
$127$	−8.15989	+	8.15989i	−0.724073	+	0.724073i	−0.969432	−	0.245359i	$-0.921094\pi$
$127$	−8.15989	+	8.15989i	−0.724073	+	0.724073i	0.245359	+	0.969432i	$0.421094\pi$
$128$	6.71606	−	6.71606i	0.593621	−	0.593621i
$129$	1.19889	+	0.496595i	0.105556	+	0.0437228i
$130$	1.47151	−	3.55254i	0.129060	−	0.311578i
$131$	17.8998	−	7.41435i	1.56392	−	0.647795i	0.578151	−	0.815929i	$-0.303774\pi$
$131$	17.8998	−	7.41435i	1.56392	−	0.647795i	0.985764	+	0.168134i	$0.0537743\pi$
$132$		−	8.36959i		−	0.728479i
$133$	0.249779	+	0.603020i	0.0216586	+	0.0522884i
$134$	−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
$139$	4.46976	+	10.7910i	0.379120	+	0.915277i	0.992131	+	0.125203i	$0.0399581\pi$
$139$	4.46976	+	10.7910i	0.379120	+	0.915277i	−0.613011	+	0.790074i	$0.710042\pi$
$140$		−	8.29086i		−	0.700706i
$141$	−6.93186	+	2.87127i	−0.583768	+	0.241805i
$142$	−1.31858	+	3.18334i	−0.110653	+	0.267140i
$143$	−22.0688	−	9.14121i	−1.84549	−	0.764426i
$144$	−5.18146	+	5.18146i	−0.431789	+	0.431789i
$145$	3.69582	−	3.69582i	0.306921	−	0.306921i
$146$	−3.49791	−	1.44888i	−0.289489	−	0.119910i
$147$	1.16704	−	2.81749i	0.0962561	−	0.232383i
$148$	−10.7136	+	4.43770i	−0.880649	+	0.364777i
$149$		−	8.46791i		−	0.693718i	−0.937917	−	0.346859i	$-0.887248\pi$
$149$		−	8.46791i		−	0.693718i	0.937917	−	0.346859i	$-0.112752\pi$
$150$	−0.0595825	−	0.143845i	−0.00486489	−	0.0117449i
$151$	−9.73439	−	9.73439i	−0.792174	−	0.792174i	0.189674	−	0.981847i	$-0.439257\pi$
$151$	−9.73439	−	9.73439i	−0.792174	−	0.792174i	−0.981847	+	0.189674i	$0.939257\pi$
$152$	0.467911			0.0379526
$153$		0			0
$154$	3.30541			0.266357
$155$	3.22590	+	3.22590i	0.259111	+	0.259111i
$156$	−2.98325	−	7.20220i	−0.238851	−	0.576638i
$157$		−	17.9786i		−	1.43485i	−0.696635	−	0.717426i	$-0.745320\pi$
$157$		−	17.9786i		−	1.43485i	0.696635	−	0.717426i	$-0.254680\pi$
$158$	1.42262	−	0.589267i	0.113177	−	0.0468796i
$159$	−3.51783	+	8.49279i	−0.278982	+	0.673522i
$160$	−8.32207	−	3.44711i	−0.657917	−	0.272518i
$161$	2.35661	−	2.35661i	0.185727	−	0.185727i
$162$	−0.647867	+	0.647867i	−0.0509012	+	0.0509012i
$163$	6.68373	+	2.76849i	0.523511	+	0.216845i	0.628758	−	0.777601i	$-0.283564\pi$
$163$	6.68373	+	2.76849i	0.523511	+	0.216845i	−0.105248	+	0.994446i	$0.533564\pi$
$164$	3.71849	−	8.97723i	0.290365	−	0.701004i
$165$	−9.65765	+	4.00033i	−0.751847	+	0.311425i
$166$		−	4.71688i		−	0.366101i
$167$	1.95401	+	4.71739i	0.151206	+	0.365043i	0.981273	−	0.192620i	$-0.0616984\pi$
$167$	1.95401	+	4.71739i	0.151206	+	0.365043i	−0.830068	+	0.557662i	$0.811698\pi$
$168$	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
$173$	4.90816	+	11.8493i	0.373160	+	0.900889i	0.993211	+	0.116327i	$0.0371121\pi$
$173$	4.90816	+	11.8493i	0.373160	+	0.900889i	−0.620051	+	0.784562i	$0.712888\pi$
$174$			0.680045i			0.0515541i
$175$	−0.885179	+	0.366653i	−0.0669132	+	0.0277164i
$176$	−6.37761	+	15.3969i	−0.480730	+	1.16059i
$177$	4.06852	+	1.68524i	0.305809	+	0.126670i
$178$	−1.55393	+	1.55393i	−0.116472	+	0.116472i
$179$	−3.02024	+	3.02024i	−0.225743	+	0.225743i	−0.810912	−	0.585169i	$-0.801028\pi$
$179$	−3.02024	+	3.02024i	−0.225743	+	0.225743i	0.585169	+	0.810912i	$0.301028\pi$
$180$	9.07522	+	3.75908i	0.676427	+	0.280185i
$181$	0.177128	−	0.427626i	0.0131658	−	0.0317852i	−0.917160	−	0.398519i	$-0.869524\pi$
$181$	0.177128	−	0.427626i	0.0131658	−	0.0317852i	0.930326	+	0.366734i	$0.119524\pi$
$182$	2.84437	−	1.17818i	0.210839	−	0.0873323i
$183$			0.162504i			0.0120126i
$184$	−0.914302	−	2.20732i	−0.0674032	−	0.162726i
$185$	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
$190$	−0.108345	−	0.261567i	−0.00786016	−	0.0189761i
$191$		−	1.43107i		−	0.103549i	−0.998659	−	0.0517745i	$-0.983512\pi$
$191$		−	1.43107i		−	0.103549i	0.998659	−	0.0517745i	$-0.0164877\pi$
$192$	−4.26451	+	1.76642i	−0.307764	+	0.127480i
$193$	9.46170	−	22.8426i	0.681068	−	1.64424i	−0.0809733	−	0.996716i	$-0.525803\pi$
$193$	9.46170	−	22.8426i	0.681068	−	1.64424i	0.762042	−	0.647528i	$-0.224197\pi$
$194$	2.97640	+	1.23286i	0.213693	+	0.0885145i
$195$	−6.88473	+	6.88473i	−0.493026	+	0.493026i
$196$	−4.60860	+	4.60860i	−0.329186	+	0.329186i
$197$	−10.8662	−	4.50092i	−0.774183	−	0.320677i	−0.0396173	−	0.999215i	$-0.512614\pi$
$197$	−10.8662	−	4.50092i	−0.774183	−	0.320677i	−0.734565	+	0.678538i	$0.762614\pi$
$198$	−1.49867	+	3.61812i	−0.106506	+	0.257128i
$199$	18.9582	−	7.85275i	1.34391	−	0.556667i	0.409321	−	0.912390i	$-0.365766\pi$
$199$	18.9582	−	7.85275i	1.34391	−	0.556667i	0.934591	+	0.355723i	$0.115766\pi$
$200$			0.686852i			0.0485678i
$201$	0.823921	+	1.98912i	0.0581149	+	0.140302i
$202$	−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
$207$	1.51107	+	3.64804i	0.105027	+	0.253557i
$208$			15.5226i			1.07630i
$209$	−1.62489	+	0.673052i	−0.112396	+	0.0465560i
$210$	0.515588	−	1.24474i	0.0355790	−	0.0858952i
$211$	20.0646	+	8.31105i	1.38131	+	0.572156i	0.944831	−	0.327559i	$-0.106226\pi$
$211$	20.0646	+	8.31105i	1.38131	+	0.572156i	0.436477	+	0.899716i	$0.356226\pi$
$212$	13.8917	−	13.8917i	0.954089	−	0.954089i
$213$	6.16924	−	6.16924i	0.422709	−	0.422709i
$214$	5.00422	+	2.07281i	0.342081	+	0.141695i
$215$	−1.32554	+	3.20013i	−0.0904008	+	0.218247i
$216$	−5.72115	+	2.36978i	−0.389275	+	0.161243i
$217$			3.65270i			0.247962i
$218$	−0.248750	−	0.600536i	−0.0168475	−	0.0406734i
$219$	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	0.998550	−	0.0538286i	$-0.0171425\pi$
$223$	14.1077	+	14.1077i	0.944722	+	0.944722i	−0.0538286	+	0.998550i	$0.517142\pi$
$224$	−2.75996	−	6.66314i	−0.184408	−	0.445200i
$225$		−	1.13516i		−	0.0756775i
$226$	−3.88684	+	1.60998i	−0.258549	+	0.107094i
$227$	−1.61555	+	3.90028i	−0.107228	+	0.258870i	−0.968382	−	0.249474i	$-0.919742\pi$
$227$	−1.61555	+	3.90028i	−0.107228	+	0.258870i	0.861154	+	0.508344i	$0.169742\pi$
$228$	−0.530286	−	0.219652i	−0.0351191	−	0.0145468i
$229$	10.2571	−	10.2571i	0.677806	−	0.677806i	−0.281697	−	0.959503i	$-0.590897\pi$
$229$	10.2571	−	10.2571i	0.677806	−	0.677806i	0.959503	+	0.281697i	$0.0908974\pi$
$230$	−1.02221	+	1.02221i	−0.0674025	+	0.0674025i
$231$	−7.73249	−	3.20290i	−0.508760	−	0.210735i
$232$	1.14805	−	2.77164i	0.0753732	−	0.181967i
$233$	−4.73712	+	1.96218i	−0.310339	+	0.128547i	−0.532417	−	0.846482i	$-0.678716\pi$
$233$	−4.73712	+	1.96218i	−0.310339	+	0.128547i	0.222078	+	0.975029i	$0.428716\pi$
$234$			3.64765i			0.238454i
$235$	−7.66413	−	18.5029i	−0.499953	−	1.20699i
$236$	−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
$241$	−6.93288	−	16.7375i	−0.446586	−	1.07815i	−0.973592	−	0.228293i	$-0.926686\pi$
$241$	−6.93288	−	16.7375i	−0.446586	−	1.07815i	0.527006	−	0.849861i	$-0.323314\pi$
$242$			5.08647i			0.326970i
$243$	14.8825	−	6.16455i	0.954716	−	0.395456i
$244$	0.132905	−	0.320860i	0.00850834	−	0.0205410i
$245$	7.52058	+	3.11513i	0.480472	+	0.199018i
$246$	1.11654	−	1.11654i	0.0711882	−	0.0711882i
$247$	−1.15835	+	1.15835i	−0.0737041	+	0.0737041i
$248$	2.41923	+	1.00208i	0.153621	+	0.0636320i
$249$	−4.57060	+	11.0344i	−0.289650	+	0.699278i
$250$	−3.38181	+	1.40079i	−0.213884	+	0.0885938i
$251$			29.6810i			1.87345i	0.350070	+	0.936723i	$0.386158\pi$
$251$			29.6810i			1.87345i	−0.350070	+	0.936723i	$0.613842\pi$
$252$	3.00974	+	7.26616i	0.189596	+	0.457725i
$253$	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	0.524900	−	0.851164i	$-0.324103\pi$
$257$	−5.23042	−	5.23042i	−0.326264	−	0.326264i	−0.851164	+	0.524900i	$0.824103\pi$
$258$	−0.172466	−	0.416369i	−0.0107373	−	0.0259220i
$259$			11.5963i			0.720557i
$260$	19.2245	−	7.96303i	1.19225	−	0.493846i
$261$	−1.89739	+	4.58070i	−0.117445	+	0.283538i
$262$	−6.21655	−	2.57498i	−0.384059	−	0.159083i
$263$	−16.3984	+	16.3984i	−1.01117	+	1.01117i	−0.0112290	+	0.999937i	$0.503574\pi$
$263$	−16.3984	+	16.3984i	−1.01117	+	1.01117i	−0.999937	+	0.0112290i	$0.996426\pi$
$264$	−4.24264	+	4.24264i	−0.261116	+	0.261116i
$265$	−22.6694	−	9.38996i	−1.39257	−	0.576821i
$266$	0.0867473	−	0.209426i	0.00531882	−	0.0128408i
$267$	5.14091	−	2.12944i	0.314619	−	0.130319i
$268$		−	4.60132i		−	0.281070i
$269$	6.08724	+	14.6959i	0.371146	+	0.896025i	0.993557	+	0.113334i	$0.0361531\pi$
$269$	6.08724	+	14.6959i	0.371146	+	0.896025i	−0.622411	+	0.782690i	$0.713847\pi$
$270$	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
$275$	−0.987981	−	2.38520i	−0.0595775	−	0.143833i
$276$			2.93077i			0.176412i
$277$	15.5265	−	6.43127i	0.932894	−	0.386417i	0.136118	−	0.990693i	$-0.456537\pi$
$277$	15.5265	−	6.43127i	0.932894	−	0.386417i	0.796776	+	0.604275i	$0.206537\pi$
$278$	1.55233	−	3.74766i	0.0931026	−	0.224770i
$279$	−3.99827	−	1.65614i	−0.239370	−	0.0991504i
$280$	−4.20273	+	4.20273i	−0.251161	+	0.251161i
$281$	−20.0259	+	20.0259i	−1.19464	+	1.19464i	−0.218897	+	0.975748i	$0.570246\pi$
$281$	−20.0259	+	20.0259i	−1.19464	+	1.19464i	−0.975748	+	0.218897i	$0.929754\pi$
$282$	2.40741	+	0.997182i	0.143359	+	0.0593813i
$283$	−12.3356	+	29.7807i	−0.733274	+	1.77028i	−0.101910	+	0.994794i	$0.532495\pi$
$283$	−12.3356	+	29.7807i	−0.733274	+	1.77028i	−0.631364	+	0.775487i	$0.717505\pi$
$284$	−17.2266	+	7.13548i	−1.02221	+	0.423413i
$285$			0.716881i			0.0424644i
$286$	3.17471	+	7.66442i	0.187724	+	0.453207i
$287$	−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
$292$	−7.84059	−	18.9289i	−0.458836	−	1.10773i
$293$			13.9709i			0.816189i	0.912940	+	0.408094i	$0.133807\pi$
$293$			13.9709i			0.816189i	−0.912940	+	0.408094i	$0.866193\pi$
$294$	−0.978504	+	0.405310i	−0.0570675	+	0.0236381i
$295$	−4.49831	+	10.8599i	−0.261902	+	0.632287i
$296$	7.68035	+	3.18130i	0.446411	+	0.184910i
$297$	16.4588	−	16.4588i	0.955039	−	0.955039i
$298$	−2.07951	+	2.07951i	−0.120463	+	0.120463i
$299$	7.72782	+	3.20097i	0.446911	+	0.185117i
$300$	0.322429	−	0.778413i	0.0186155	−	0.0449417i
$301$	−2.56221	+	1.06130i	−0.147683	+	0.0611725i
$302$			4.78106i			0.275119i
$303$	2.37238	+	5.72744i	0.136290	+	0.329033i
$304$	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
$309$	1.78312	+	4.30483i	0.101438	+	0.244893i
$310$		−	1.58441i		−	0.0899883i
$311$	−2.16862	+	0.898271i	−0.122971	+	0.0509363i	−0.443321	−	0.896363i	$-0.646200\pi$
$311$	−2.16862	+	0.898271i	−0.122971	+	0.0509363i	0.320349	+	0.947299i	$0.396200\pi$
$312$	−2.13864	+	5.16312i	−0.121076	+	0.292304i
$313$	−13.9768	−	5.78937i	−0.790014	−	0.327235i	−0.0490649	−	0.998796i	$-0.515624\pi$
$313$	−13.9768	−	5.78937i	−0.790014	−	0.327235i	−0.740949	+	0.671561i	$0.765624\pi$
$314$	−4.41512	+	4.41512i	−0.249159	+	0.249159i
$315$	6.94587	−	6.94587i	0.391356	−	0.391356i
$316$	7.69846	+	3.18880i	0.433072	+	0.179384i
$317$	−3.95611	+	9.55088i	−0.222197	+	0.536431i	−0.995188	−	0.0979863i	$-0.968760\pi$
$317$	−3.95611	+	9.55088i	−0.222197	+	0.536431i	0.772991	+	0.634417i	$0.218760\pi$
$318$	2.94952	−	1.22173i	0.165401	−	0.0685112i
$319$			11.2763i			0.631352i
$320$	−4.71500	−	11.3830i	−0.263577	−	0.636330i
$321$	−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
$326$	−0.961488	−	2.32124i	−0.0532519	−	0.128561i
$327$			1.64590i			0.0910183i
$328$	−6.43561	+	2.66572i	−0.355347	+	0.147190i
$329$	6.13636	−	14.8145i	0.338308	−	0.816749i
$330$	3.35407	+	1.38930i	0.184635	+	0.0764784i
$331$	12.9094	−	12.9094i	0.709567	−	0.709567i	−0.256877	−	0.966444i	$-0.582693\pi$
$331$	12.9094	−	12.9094i	0.709567	−	0.709567i	0.966444	+	0.256877i	$0.0826935\pi$
$332$	18.0491	−	18.0491i	0.990573	−	0.990573i
$333$	−12.6933	−	5.25775i	−0.695591	−	0.288123i
$334$	0.678620	−	1.63833i	0.0371324	−	0.0896456i
$335$	−5.30945	+	2.19925i	−0.290086	+	0.120158i
$336$			5.43882i			0.296712i
$337$	−6.31246	−	15.2396i	−0.343862	−	0.830155i	−0.997318	−	0.0731911i	$-0.976682\pi$
$337$	−6.31246	−	15.2396i	−0.343862	−	0.830155i	0.653456	−	0.756964i	$-0.273318\pi$
$338$	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
$343$	7.52862	+	18.1757i	0.406507	+	0.981396i
$344$			1.98814i			0.107193i
$345$	3.38181	−	1.40079i	0.182071	−	0.0754161i
$346$	1.70459	−	4.11523i	0.0916391	−	0.221236i
$347$	19.0063	+	7.87265i	1.02031	+	0.422626i	0.829205	−	0.558944i	$-0.188793\pi$
$347$	19.0063	+	7.87265i	1.02031	+	0.422626i	0.191104	+	0.981570i	$0.438793\pi$
$348$	−2.60218	+	2.60218i	−0.139492	+	0.139492i
$349$	−4.54264	+	4.54264i	−0.243162	+	0.243162i	−0.818157	−	0.574995i	$-0.805004\pi$
$349$	−4.54264	+	4.54264i	−0.243162	+	0.243162i	0.574995	+	0.818157i	$0.305004\pi$
$350$	0.307419	+	0.127337i	0.0164323	+	0.00680647i
$351$	8.29659	−	20.0297i	0.442839	−	1.06911i
$352$	17.9545	−	7.43698i	0.956976	−	0.396392i
$353$		−	27.1685i		−	1.44603i	−0.690831	−	0.723016i	$-0.742755\pi$
$353$		−	27.1685i		−	1.44603i	0.690831	−	0.723016i	$-0.257245\pi$
$354$	−0.585276	−	1.41298i	−0.0311071	−	0.0750991i
$355$	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	0.317685	−	0.948196i	$-0.397094\pi$
$359$	−11.9465	−	11.9465i	−0.630511	−	0.630511i	−0.948196	+	0.317685i	$0.897094\pi$
$360$	−2.69481	−	6.50586i	−0.142029	−	0.342889i
$361$		−	18.8794i		−	0.993652i
$362$	−0.148513	+	0.0615160i	−0.00780566	+	0.00323321i
$363$	4.92873	−	11.8990i	0.258691	−	0.624536i
$364$	15.3922	+	6.37568i	0.806773	+	0.334176i
$365$	−18.0945	+	18.0945i	−0.947108	+	0.947108i
$366$	0.0399070	−	0.0399070i	0.00208597	−	0.00208597i
$367$	1.37428	+	0.569246i	0.0717369	+	0.0297144i	0.418263	−	0.908326i	$-0.362639\pi$
$367$	1.37428	+	0.569246i	0.0717369	+	0.0297144i	−0.346526	+	0.938040i	$0.612639\pi$
$368$	2.23324	−	5.39152i	0.116416	−	0.281053i
$369$	10.6362	−	4.40564i	0.553696	−	0.229348i
$370$		−	5.03003i		−	0.261499i
$371$	−7.51816	−	18.1504i	−0.390323	−	0.942324i
$372$	−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
$377$	4.01932	+	9.70350i	0.207006	+	0.499756i
$378$			3.00000i			0.154303i
$379$	−18.6601	+	7.72928i	−0.958507	+	0.397027i	−0.806422	−	0.591341i	$-0.798599\pi$
$379$	−18.6601	+	7.72928i	−0.958507	+	0.397027i	−0.152085	+	0.988367i	$0.548599\pi$
$380$	0.586305	−	1.41547i	0.0300768	−	0.0726119i
$381$	−9.37549	−	3.88345i	−0.480321	−	0.198955i
$382$	−0.351437	+	0.351437i	−0.0179811	+	0.0179811i
$383$	6.02828	−	6.02828i	0.308031	−	0.308031i	−0.536114	−	0.844145i	$-0.680108\pi$
$383$	6.02828	−	6.02828i	0.308031	−	0.308031i	0.844145	+	0.536114i	$0.180108\pi$
$384$	7.71656	+	3.19631i	0.393784	+	0.163111i
$385$	8.54934	−	20.6399i	0.435714	−	1.05191i
$386$	−7.93314	+	3.28602i	−0.403786	+	0.167254i
$387$		−	3.28581i		−	0.167027i
$388$	6.67161	+	16.1067i	0.338700	+	0.817694i
$389$	−9.13315	−	9.13315i	−0.463069	−	0.463069i	0.436591	−	0.899660i	$-0.356186\pi$
$389$	−9.13315	−	9.13315i	−0.463069	−	0.463069i	−0.899660	+	0.436591i	$0.856186\pi$
$390$	3.38144			0.171226
$391$		0			0
$392$	4.67230			0.235987
$393$	12.0475	+	12.0475i	0.607717	+	0.607717i
$394$	1.56315	+	3.77378i	0.0787504	+	0.190120i
$395$		−	10.4074i		−	0.523651i
$396$	−19.5793	+	8.11003i	−0.983899	+	0.407544i
$397$	−9.27048	+	22.3809i	−0.465272	+	1.12327i	0.500932	+	0.865487i	$0.332991\pi$
$397$	−9.27048	+	22.3809i	−0.465272	+	1.12327i	−0.966204	+	0.257779i	$0.917009\pi$
$398$	−6.58412	−	2.72723i	−0.330032	−	0.136704i
$399$	−0.405864	+	0.405864i	−0.0203186	+	0.0203186i
$400$	−1.18630	+	1.18630i	−0.0593150	+	0.0593150i
$401$	23.5932	+	9.77264i	1.17819	+	0.488022i	0.883892	−	0.467691i	$-0.154914\pi$
$401$	23.5932	+	9.77264i	1.17819	+	0.488022i	0.294298	+	0.955714i	$0.404914\pi$
$402$	0.286145	−	0.690814i	0.0142716	−	0.0344547i
$403$	−8.46972	+	3.50827i	−0.421907	+	0.174759i
$404$		−	13.2490i		−	0.659161i
$405$	2.36978	+	5.72115i	0.117755	+	0.284286i
$406$	−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
$411$	−0.150868	−	0.364228i	−0.00744178	−	0.0179661i
$412$		−	9.95811i		−	0.490601i
$413$	−8.69507	+	3.60162i	−0.427856	+	0.177224i
$414$	0.524789	−	1.26695i	0.0257920	−	0.0622673i
$415$	−29.4536	−	12.2001i	−1.44582	−	0.598878i
$416$	12.7994	−	12.7994i	0.627540	−	0.627540i
$417$	−7.26288	+	7.26288i	−0.355665	+	0.355665i
$418$	0.564319	+	0.233749i	0.0276017	+	0.0114330i
$419$	0.502520	−	1.21319i	0.0245497	−	0.0592682i	−0.911129	−	0.412121i	$-0.864788\pi$
$419$	0.502520	−	1.21319i	0.0245497	−	0.0592682i	0.935679	+	0.352852i	$0.114788\pi$
$420$	6.73588	−	2.79009i	0.328677	−	0.136143i
$421$		−	8.01548i		−	0.390651i	−0.980739	−	0.195325i	$-0.937424\pi$
$421$		−	8.01548i		−	0.390651i	0.980739	−	0.195325i	$-0.0625763\pi$
$422$	−2.88640	−	6.96838i	−0.140508	−	0.339215i
$423$	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
$428$	11.2170	+	27.0802i	0.542193	+	1.30897i
$429$		−	21.0060i		−	1.01418i
$430$	1.11139	−	0.460354i	0.0535961	−	0.0222002i
$431$	−5.63577	+	13.6060i	−0.271466	+	0.655376i	−0.999546	−	0.0301153i	$-0.990413\pi$
$431$	−5.63577	+	13.6060i	−0.271466	+	0.655376i	0.728081	+	0.685491i	$0.240413\pi$
$432$	−13.9743	−	5.78834i	−0.672339	−	0.278492i
$433$	−5.82743	+	5.82743i	−0.280048	+	0.280048i	−0.833128	−	0.553080i	$-0.813452\pi$
$433$	−5.82743	+	5.82743i	−0.280048	+	0.280048i	0.553080	+	0.833128i	$0.313452\pi$
$434$	0.897015	−	0.897015i	0.0430581	−	0.0430581i
$435$	4.24640	+	1.75892i	0.203599	+	0.0843335i
$436$	1.34610	−	3.24978i	0.0644667	−	0.155636i
$437$	0.568987	−	0.235682i	0.0272183	−	0.0112742i
$438$		−	3.32945i		−	0.159087i
$439$	15.2906	+	36.9149i	0.729782	+	1.76185i	0.643323	+	0.765595i	$0.277555\pi$
$439$	15.2906	+	36.9149i	0.729782	+	1.76185i	0.0864590	+	0.996255i	$0.472445\pi$
$440$	−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
$445$	5.68399	+	13.7224i	0.269447	+	0.650502i
$446$		−	6.92902i		−	0.328098i
$447$	6.87972	−	2.84967i	0.325400	−	0.134785i
$448$	3.77511	−	9.11392i	0.178357	−	0.430592i
$449$	−9.45289	−	3.91552i	−0.446109	−	0.184785i	0.148308	−	0.988941i	$-0.452617\pi$
$449$	−9.45289	−	3.91552i	−0.446109	−	0.184785i	−0.594417	+	0.804157i	$0.702617\pi$
$450$	−0.278768	+	0.278768i	−0.0131413	+	0.0131413i
$451$	18.5142	−	18.5142i	0.871800	−	0.871800i
$452$	−21.0335	−	8.71237i	−0.989333	−	0.409795i
$453$	4.63279	−	11.1845i	0.217668	−	0.525496i
$454$	1.35455	−	0.561074i	0.0635723	−	0.0263325i
$455$		−	20.8084i		−	0.975513i
$456$	0.157464	+	0.380153i	0.00737394	+	0.0178023i
$457$	−8.32309	−	8.32309i	−0.389338	−	0.389338i	0.485113	−	0.874451i	$-0.338778\pi$
$457$	−8.32309	−	8.32309i	−0.389338	−	0.389338i	−0.874451	+	0.485113i	$0.838778\pi$
$458$	−5.03777			−0.235400
$459$		0			0
$460$	−7.82295			−0.364747
$461$	−13.7888	−	13.7888i	−0.642208	−	0.642208i	0.308890	−	0.951098i	$-0.400043\pi$
$461$	−13.7888	−	13.7888i	−0.642208	−	0.642208i	−0.951098	+	0.308890i	$0.900043\pi$
$462$	1.11236	+	2.68547i	0.0517515	+	0.124939i
$463$		−	1.43107i		−	0.0665077i	−0.999447	−	0.0332538i	$-0.989413\pi$
$463$		−	1.43107i		−	0.0665077i	0.999447	−	0.0332538i	$-0.0105870\pi$
$464$	6.76991	−	2.80419i	0.314285	−	0.130181i
$465$	−1.53527	+	3.70647i	−0.0711965	+	0.171884i
$466$	1.64518	+	0.681458i	0.0762117	+	0.0315679i
$467$	−7.55865	+	7.55865i	−0.349772	+	0.349772i	−0.860025	−	0.510252i	$-0.829552\pi$
$467$	−7.55865	+	7.55865i	−0.349772	+	0.349772i	0.510252	+	0.860025i	$0.329552\pi$
$468$	−13.9577	+	13.9577i	−0.645195	+	0.645195i
$469$	−4.25106	−	1.76085i	−0.196296	−	0.0813084i
$470$	−2.66172	+	6.42597i	−0.122776	+	0.296408i
$471$	14.6067	−	6.05028i	0.673040	−	0.278782i
$472$			6.74691i			0.310552i
$473$	−2.85978	−	6.90412i	−0.131493	−	0.317452i
$474$	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
$479$	−14.8740	−	35.9089i	−0.679608	−	1.64072i	−0.764731	−	0.644350i	$-0.777128\pi$
$479$	−14.8740	−	35.9089i	−0.679608	−	1.64072i	0.0851226	−	0.996370i	$-0.472872\pi$
$480$		−	7.92127i		−	0.361555i
$481$	−26.8889	+	11.1377i	−1.22603	+	0.507837i
$482$	−2.40776	+	5.81286i	−0.109671	+	0.264768i
$483$	2.70768	+	1.12156i	0.123204	+	0.0510326i
$484$	−19.4633	+	19.4633i	−0.884696	+	0.884696i
$485$	15.3967	−	15.3967i	0.699129	−	0.699129i
$486$	−5.16866	−	2.14093i	−0.234455	−	0.0971144i
$487$	14.1645	−	34.1962i	0.641857	−	1.54958i	−0.182316	−	0.983240i	$-0.558359\pi$
$487$	14.1645	−	34.1962i	0.641857	−	1.54958i	0.824172	−	0.566339i	$-0.191641\pi$
$488$	−0.230019	+	0.0952768i	−0.0104125	+	0.00431298i
$489$			6.36184i			0.287693i
$490$	−1.08187	−	2.61187i	−0.0488740	−	0.117992i
$491$	−17.9729	−	17.9729i	−0.811104	−	0.811104i	0.173696	−	0.984799i	$-0.444429\pi$
$491$	−17.9729	−	17.9729i	−0.811104	−	0.811104i	−0.984799	+	0.173696i	$0.944429\pi$
$492$	8.54488			0.385233
$493$		0			0
$494$	0.568926			0.0255972
$495$	18.7163	+	18.7163i	0.841235	+	0.841235i
$496$	2.44764	+	5.90913i	0.109902	+	0.265328i
$497$			18.6459i			0.836383i
$498$	3.83221	−	1.58735i	0.171726	−	0.0711310i
$499$	8.35164	−	20.1626i	0.373871	−	0.902604i	−0.619216	−	0.785221i	$-0.712549\pi$
$499$	8.35164	−	20.1626i	0.373871	−	0.902604i	0.993087	−	0.117383i	$-0.0374505\pi$
$500$	−18.3006	−	7.58035i	−0.818427	−	0.339003i
$501$	−3.17505	+	3.17505i	−0.141851	+	0.141851i
$502$	7.28892	−	7.28892i	0.325321	−	0.325321i
$503$	30.8918	+	12.7958i	1.37740	+	0.570537i	0.943784	−	0.330562i	$-0.107238\pi$
$503$	30.8918	+	12.7958i	1.37740	+	0.570537i	0.433614	+	0.901099i	$0.357238\pi$
$504$	2.15763	−	5.20898i	0.0961084	−	0.232026i
$505$	−15.2880	+	6.33248i	−0.680305	+	0.281792i
$506$		−	3.11886i		−	0.138650i
$507$	−3.11252	−	7.51429i	−0.138232	−	0.333721i
$508$	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
$513$	−0.610865	−	1.47476i	−0.0269703	−	0.0651122i
$514$			2.56893i			0.113310i
$515$	−11.4906	+	4.75958i	−0.506338	+	0.209732i
$516$	0.933294	−	2.25317i	0.0410860	−	0.0991903i
$517$	39.9190	+	16.5350i	1.75564	+	0.727208i
$518$	2.84776	−	2.84776i	0.125123	−	0.125123i
$519$	−7.97523	+	7.97523i	−0.350074	+	0.350074i
$520$	−13.7817	−	5.70855i	−0.604366	−	0.250336i
$521$	−13.5979	+	32.8282i	−0.595735	+	1.43823i	0.282155	+	0.959369i	$0.408951\pi$
$521$	−13.5979	+	32.8282i	−0.595735	+	1.43823i	−0.877890	+	0.478862i	$0.841049\pi$
$522$	1.59086	−	0.658956i	0.0696300	−	0.0288417i
$523$			11.8307i			0.517320i	0.965968	+	0.258660i	$0.0832809\pi$
$523$			11.8307i			0.517320i	−0.965968	+	0.258660i	$0.916719\pi$
$524$	−13.9344	−	33.6407i	−0.608728	−	1.46960i
$525$	−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
$530$	3.26110	+	7.87299i	0.141653	+	0.341981i
$531$		−	11.1506i		−	0.483897i
$532$	1.13331	−	0.469431i	0.0491350	−	0.0203524i
$533$	9.33267	−	22.5310i	0.404243	−	0.975928i
$534$	−1.78542	−	0.739545i	−0.0772627	−	0.0320032i
$535$	25.8865	−	25.8865i	1.11917	−	1.11917i
$536$	−2.33246	+	2.33246i	−0.100747	+	0.100747i
$537$	−3.47017	−	1.43739i	−0.149749	−	0.0620280i
$538$	2.11408	−	5.10383i	0.0911443	−	0.220042i
$539$	−16.2253	+	6.72073i	−0.698872	+	0.289482i
$540$			20.2763i			0.872554i
$541$	2.12714	+	5.13538i	0.0914531	+	0.220787i	0.962987	−	0.269548i	$-0.0868743\pi$
$541$	2.12714	+	5.13538i	0.0914531	+	0.220787i	−0.871534	+	0.490335i	$0.836874\pi$
$542$	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
$547$	−1.92285	−	4.64217i	−0.0822152	−	0.198485i	0.877426	−	0.479712i	$-0.159259\pi$
$547$	−1.92285	−	4.64217i	−0.0822152	−	0.198485i	−0.959641	+	0.281227i	$0.909259\pi$
$548$			0.842549i			0.0359919i
$549$	0.380153	−	0.157464i	0.0162245	−	0.00672041i
$550$	−0.343122	+	0.828370i	−0.0146308	+	0.0353218i
$551$	0.714453	+	0.295936i	0.0304367	+	0.0126073i
$552$	1.48564	−	1.48564i	0.0632331	−	0.0632331i
$553$	5.89214	−	5.89214i	0.250559	−	0.250559i
$554$	−5.39228	−	2.23356i	−0.229096	−	0.0948947i
$555$	−4.87404	+	11.7670i	−0.206891	+	0.499480i
$556$	20.2804	−	8.40040i	0.860079	−	0.356256i
$557$		−	3.86659i		−	0.163833i	−0.996639	−	0.0819164i	$-0.973896\pi$
$557$		−	3.86659i		−	0.163833i	0.996639	−	0.0819164i	$-0.0261040\pi$
$558$	0.575171	+	1.38858i	0.0243489	+	0.0587835i
$559$	−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	0.131784	−	0.991278i	$-0.457929\pi$
$563$	−20.3938	−	20.3938i	−0.859494	−	0.859494i	−0.991278	+	0.131784i	$0.957929\pi$
$564$	5.39622	+	13.0276i	0.227222	+	0.548563i
$565$			28.4347i			1.19626i
$566$	10.3427	−	4.28410i	0.434738	−	0.180074i
$567$	−1.89739	+	4.58070i	−0.0796828	+	0.192371i
$568$	12.3494	+	5.11529i	0.518169	+	0.214633i
$569$	1.52846	−	1.52846i	0.0640764	−	0.0640764i	−0.674342	−	0.738419i	$-0.735573\pi$
$569$	1.52846	−	1.52846i	0.0640764	−	0.0640764i	0.738419	+	0.674342i	$0.235573\pi$
$570$	0.176049	−	0.176049i	0.00737386	−	0.00737386i
$571$	−5.28389	−	2.18866i	−0.221124	−	0.0915926i	0.269371	−	0.963036i	$-0.413184\pi$
$571$	−5.28389	−	2.18866i	−0.221124	−	0.0915926i	−0.490495	+	0.871444i	$0.663184\pi$
$572$	−17.1799	+	41.4758i	−0.718326	+	1.73419i
$573$	1.16267	−	0.481594i	0.0485713	−	0.0201189i
$574$			3.37464i			0.140855i
$575$	0.345960	+	0.835222i	0.0144275	+	0.0348312i
$576$	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
$581$	−9.76810	−	23.5823i	−0.405249	−	0.978358i
$582$			2.83305i			0.117434i
$583$	48.9080	−	20.2584i	2.02556	−	0.839016i
$584$	−5.62077	+	13.5697i	−0.232589	+	0.561520i
$585$	22.7770	+	9.43454i	0.941713	+	0.390070i
$586$	3.43091	−	3.43091i	0.141730	−	0.141730i
$587$	−14.7211	+	14.7211i	−0.607606	+	0.607606i	−0.942320	−	0.334714i	$-0.891360\pi$
$587$	−14.7211	+	14.7211i	−0.607606	+	0.607606i	0.334714	+	0.942320i	$0.391360\pi$
$588$	−5.29515	−	2.19332i	−0.218368	−	0.0904511i
$589$	−0.258308	+	0.623612i	−0.0106434	+	0.0256955i
$590$	3.77160	−	1.56225i	0.155274	−	0.0643167i
$591$		−	10.3429i		−	0.425448i
$592$	7.77054	+	18.7598i	0.319367	+	0.771021i
$593$	14.5886	+	14.5886i	0.599081	+	0.599081i	0.940068	−	0.340987i	$-0.110761\pi$
$593$	14.5886	+	14.5886i	0.599081	+	0.599081i	−0.340987	+	0.940068i	$0.610761\pi$
$594$	−8.08378			−0.331681
$595$		0			0
$596$	−15.9145			−0.651882
$597$	12.7599	+	12.7599i	0.522227	+	0.522227i
$598$	−1.11168	−	2.68384i	−0.0454602	−	0.109751i
$599$			31.8212i			1.30018i	0.759858	+	0.650089i	$0.225269\pi$
$599$			31.8212i			1.30018i	−0.759858	+	0.650089i	$0.774731\pi$
$600$	−0.558030	+	0.231144i	−0.0227815	+	0.00943640i
$601$	−18.4137	+	44.4547i	−0.751112	+	1.81335i	−0.198079	+	0.980186i	$0.563470\pi$
$601$	−18.4137	+	44.4547i	−0.751112	+	1.81335i	−0.553033	+	0.833159i	$0.686530\pi$
$602$	0.889847	+	0.368587i	0.0362675	+	0.0150225i
$603$	3.85487	−	3.85487i	0.156982	−	0.156982i
$604$	−18.2947	+	18.2947i	−0.744400	+	0.744400i
$605$	31.7614	+	13.1560i	1.29128	+	0.534867i
$606$	0.823921	−	1.98912i	0.0334695	−	0.0808025i
$607$	−14.2976	+	5.92228i	−0.580323	+	0.240378i	−0.653481	−	0.756943i	$-0.726692\pi$
$607$	−14.2976	+	5.92228i	−0.580323	+	0.240378i	0.0731581	+	0.997320i	$0.476692\pi$
$608$		−	1.33275i		−	0.0540501i
$609$	1.40829	+	3.39992i	0.0570669	+	0.137772i
$610$	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
$615$	−4.08411	−	9.85992i	−0.164687	−	0.397590i
$616$		−	12.8229i		−	0.516651i
$617$	25.5050	−	10.5645i	1.02679	−	0.425311i	0.195238	−	0.980756i	$-0.437452\pi$
$617$	25.5050	−	10.5645i	1.02679	−	0.425311i	0.831553	+	0.555445i	$0.187452\pi$
$618$	0.619270	−	1.49505i	0.0249107	−	0.0601398i
$619$	−13.7040	−	5.67636i	−0.550808	−	0.228152i	0.0898809	−	0.995953i	$-0.471351\pi$
$619$	−13.7040	−	5.67636i	−0.550808	−	0.228152i	−0.640689	+	0.767800i	$0.721351\pi$
$620$	6.06272	−	6.06272i	0.243485	−	0.243485i
$621$	−5.76338	+	5.76338i	−0.231276	+	0.231276i
$622$	0.753153	+	0.311966i	0.0301987	+	0.0125087i
$623$	−4.55094	+	10.9869i	−0.182330	+	0.440182i
$624$	−12.6113	+	5.22376i	−0.504855	+	0.209118i
$625$			27.2891i			1.09156i
$626$	2.01063	+	4.85408i	0.0803608	+	0.194008i
$627$	−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	0.999173	−	0.0406672i	$-0.0129483\pi$
$631$	24.0774	+	24.0774i	0.958506	+	0.958506i	−0.0406672	+	0.999173i	$0.512948\pi$
$632$	−2.28599	−	5.51888i	−0.0909320	−	0.219529i
$633$			19.0983i			0.759090i
$634$	3.31699	−	1.37394i	0.131734	−	0.0545662i
$635$	10.3659	−	25.0255i	0.411358	−	0.993106i
$636$	15.9612	+	6.61136i	0.632904	+	0.262157i
$637$	−11.5667	+	11.5667i	−0.458288	+	0.458288i
$638$	2.76919	−	2.76919i	0.109633	−	0.109633i
$639$	−20.4099	−	8.45406i	−0.807403	−	0.334437i
$640$	−8.53173	+	20.5974i	−0.337246	+	0.814184i
$641$	−13.8796	+	5.74914i	−0.548213	+	0.227077i	−0.639559	−	0.768742i	$-0.720883\pi$
$641$	−13.8796	+	5.74914i	−0.548213	+	0.227077i	0.0913460	+	0.995819i	$0.470883\pi$
$642$			4.76321i			0.187989i
$643$	−6.81099	−	16.4432i	−0.268599	−	0.648456i	0.730819	−	0.682572i	$-0.239138\pi$
$643$	−6.81099	−	16.4432i	−0.268599	−	0.648456i	−0.999418	+	0.0341158i	$0.989138\pi$
$644$	−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
$649$	−9.70489	−	23.4297i	−0.380950	−	0.919695i
$650$			0.835132i			0.0327566i
$651$	−2.96762	+	1.22923i	−0.116310	+	0.0481773i
$652$	5.20307	−	12.5613i	0.203768	−	0.491939i
$653$	−28.2064	−	11.6835i	−1.10380	−	0.457209i	−0.245002	−	0.969523i	$-0.578788\pi$
$653$	−28.2064	−	11.6835i	−1.10380	−	0.457209i	−0.858798	+	0.512314i	$0.828788\pi$
$654$	0.404192	−	0.404192i	0.0158052	−	0.0158052i
$655$	−32.1578	+	32.1578i	−1.25651	+	1.25651i
$656$	−15.7194	−	6.51119i	−0.613739	−	0.254219i
$657$	9.28947	−	22.4268i	0.362417	−	0.874951i
$658$	−5.14502	+	2.13114i	−0.200574	+	0.0830803i
$659$			9.83481i			0.383110i	0.981482	+	0.191555i	$0.0613530\pi$
$659$			9.83481i			0.383110i	−0.981482	+	0.191555i	$0.938647\pi$
$660$	7.51816	+	18.1504i	0.292644	+	0.706505i
$661$	8.79367	+	8.79367i	0.342034	+	0.342034i	0.857132	−	0.515097i	$-0.172244\pi$
$661$	8.79367	+	8.79367i	0.342034	+	0.342034i	−0.515097	+	0.857132i	$0.672244\pi$
$662$	−6.34049			−0.246430
$663$		0			0
$664$	−18.2986			−0.710123
$665$	−1.08335	−	1.08335i	−0.0420105	−	0.0420105i
$666$	1.82600	+	4.40835i	0.0707560	+	0.170820i
$667$		−	3.94862i		−	0.152891i
$668$	8.86579	−	3.67233i	0.343028	−	0.142087i
$669$	−6.71414	+	16.2094i	−0.259583	+	0.626690i
$670$	1.84395	+	0.763791i	0.0712382	+	0.0295078i
$671$	0.661726	−	0.661726i	0.0255457	−	0.0255457i
$672$	4.48464	−	4.48464i	0.172999	−	0.172999i
$673$	−11.6517	−	4.82631i	−0.449141	−	0.186040i	0.146635	−	0.989191i	$-0.453156\pi$
$673$	−11.6517	−	4.82631i	−0.449141	−	0.186040i	−0.595777	+	0.803150i	$0.703156\pi$
$674$	−2.19229	+	5.29267i	−0.0844440	+	0.203866i
$675$	2.16481	−	0.896695i	0.0833237	−	0.0345138i
$676$			17.3824i			0.668553i
$677$	−1.74083	−	4.20273i	−0.0669054	−	0.161524i	0.886890	−	0.461980i	$-0.152861\pi$
$677$	−1.74083	−	4.20273i	−0.0669054	−	0.161524i	−0.953796	+	0.300456i	$0.902861\pi$
$678$	−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
$683$	−1.86272	−	4.49701i	−0.0712751	−	0.172073i	0.884227	−	0.467057i	$-0.154686\pi$
$683$	−1.86272	−	4.49701i	−0.0712751	−	0.172073i	−0.955502	+	0.294984i	$0.904686\pi$
$684$			1.45336i			0.0555707i
$685$	0.972215	−	0.402705i	0.0371464	−	0.0153866i
$686$	2.61466	−	6.31235i	0.0998283	−	0.241007i
$687$	11.7851	+	4.88154i	0.449629	+	0.186242i
$688$	−3.43383	+	3.43383i	−0.130913	+	0.130913i
$689$	34.8655	−	34.8655i	1.32827	−	1.32827i
$690$	−1.17449	−	0.486490i	−0.0447121	−	0.0185203i
$691$	2.11111	−	5.09668i	0.0803106	−	0.193887i	−0.878624	−	0.477514i	$-0.841538\pi$
$691$	2.11111	−	5.09668i	0.0803106	−	0.193887i	0.958935	+	0.283627i	$0.0915379\pi$
$692$	22.2695	−	9.22432i	0.846559	−	0.350656i
$693$			21.1925i			0.805038i
$694$	−2.73414	−	6.60080i	−0.103787	−	0.250563i
$695$	−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
$700$	0.689083	+	1.66359i	0.0260449	+	0.0628779i
$701$			22.3233i			0.843138i	0.906796	+	0.421569i	$0.138520\pi$
$701$			22.3233i			0.843138i	−0.906796	+	0.421569i	$0.861480\pi$
$702$	−6.95626	+	2.88138i	−0.262547	+	0.108751i
$703$	−0.820054	+	1.97978i	−0.0309289	+	0.0746690i
$704$	24.5583	+	10.1724i	0.925576	+	0.383386i
$705$	12.4534	−	12.4534i	0.469022	−	0.469022i
$706$	−6.67192	+	6.67192i	−0.251101	+	0.251101i
$707$	−12.2405	−	5.07016i	−0.460350	−	0.190683i
$708$	3.16721	−	7.64631i	0.119031	−	0.287366i
$709$	32.1294	−	13.3084i	1.20665	−	0.499809i	0.313505	−	0.949587i	$-0.398497\pi$
$709$	32.1294	−	13.3084i	1.20665	−	0.499809i	0.893140	+	0.449778i	$0.148497\pi$
$710$		−	8.08790i		−	0.303533i
$711$	3.77807	+	9.12107i	0.141689	+	0.342067i
$712$	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
$717$	−5.33404	−	12.8775i	−0.199203	−	0.480919i
$718$			5.86753i			0.218974i
$719$	3.92640	−	1.62637i	0.146430	−	0.0606533i	−0.308265	−	0.951301i	$-0.599748\pi$
$719$	3.92640	−	1.62637i	0.146430	−	0.0606533i	0.454695	+	0.890647i	$0.349748\pi$
$720$	6.58226	−	15.8910i	0.245306	−	0.592222i
$721$	−9.20009	−	3.81080i	−0.342629	−	0.141922i
$722$	−4.63632	+	4.63632i	−0.172546	+	0.172546i
$723$	11.2652	−	11.2652i	0.418957	−	0.418957i
$724$	−0.803673	−	0.332892i	−0.0298683	−	0.0123718i
$725$	−0.434408	+	1.04875i	−0.0161335	+	0.0389497i
$726$	−4.13248	+	1.71173i	−0.153371	+	0.0635282i
$727$		−	29.1644i		−	1.08165i	−0.841136	−	0.540823i	$-0.818113\pi$
$727$		−	29.1644i		−	1.08165i	0.841136	−	0.540823i	$-0.181887\pi$
$728$	−4.57060	−	11.0344i	−0.169398	−	0.408963i
$729$	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	0.713645	−	0.700508i	$-0.247043\pi$
$733$	0.355670	+	0.355670i	0.0131370	+	0.0131370i	−0.700508	+	0.713645i	$0.747043\pi$
$734$	−0.197697	−	0.477283i	−0.00729713	−	0.0176168i
$735$			7.15839i			0.264041i
$736$	−6.28709	+	2.60420i	−0.231745	+	0.0959921i
$737$	4.74477	−	11.4549i	0.174776	−	0.421946i
$738$	−3.69390	−	1.53006i	−0.135974	−	0.0563224i
$739$	10.5770	−	10.5770i	0.389081	−	0.389081i	−0.485279	−	0.874359i	$-0.661282\pi$
$739$	10.5770	−	10.5770i	0.389081	−	0.389081i	0.874359	+	0.485279i	$0.161282\pi$
$740$	19.2474	−	19.2474i	0.707547	−	0.707547i
$741$	−1.33091	−	0.551282i	−0.0488923	−	0.0202519i
$742$	−2.61103	+	6.30358i	−0.0958539	+	0.231412i
$743$	−21.5962	+	8.94544i	−0.792288	+	0.328177i	−0.741863	−	0.670551i	$-0.766058\pi$
$743$	−21.5962	+	8.94544i	−0.792288	+	0.328177i	−0.0504250	+	0.998728i	$0.516058\pi$
$744$			2.30272i			0.0844218i
$745$	7.60648	+	18.3637i	0.278680	+	0.672793i
$746$	−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
$751$	6.51675	+	15.7328i	0.237800	+	0.574099i	0.997055	−	0.0766940i	$-0.0244365\pi$
$751$	6.51675	+	15.7328i	0.237800	+	0.574099i	−0.759255	+	0.650793i	$0.774436\pi$
$752$		−	28.0779i		−	1.02390i
$753$	−24.1142	+	9.98843i	−0.878770	+	0.363998i
$754$	1.39590	−	3.36999i	0.0508355	−	0.122728i
$755$	29.8543	+	12.3661i	1.08651	+	0.450047i
$756$	−11.4795	+	11.4795i	−0.417504	+	0.417504i
$757$	−11.5786	+	11.5786i	−0.420832	+	0.420832i	−0.885490	−	0.464658i	$-0.846177\pi$
$757$	−11.5786	+	11.5786i	−0.420832	+	0.420832i	0.464658	+	0.885490i	$0.346177\pi$
$758$	6.48060	+	2.68435i	0.235386	+	0.0975000i
$759$	−3.02214	+	7.29609i	−0.109697	+	0.264831i
$760$	−1.01472	+	0.420311i	−0.0368078	+	0.0152463i
$761$			18.8803i			0.684411i	0.939625	+	0.342206i	$0.111174\pi$
$761$			18.8803i			0.684411i	−0.939625	+	0.342206i	$0.888826\pi$
$762$	1.34871	+	3.25607i	0.0488586	+	0.117955i
$763$	−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
$768$	2.42277	+	5.84908i	0.0874241	+	0.211060i
$769$		−	27.4766i		−	0.990831i	−0.868656	−	0.495416i	$-0.835016\pi$
$769$		−	27.4766i		−	0.990831i	0.868656	−	0.495416i	$-0.164984\pi$
$770$	−7.16817	+	2.96915i	−0.258323	+	0.107001i
$771$	2.48926	−	6.00960i	0.0896485	−	0.216431i
$772$	−42.9300	−	17.7822i	−1.54508	−	0.639995i
$773$	7.00344	−	7.00344i	0.251896	−	0.251896i	−0.569851	−	0.821748i	$-0.692999\pi$
$773$	7.00344	−	7.00344i	0.251896	−	0.251896i	0.821748	+	0.569851i	$0.192999\pi$
$774$	−0.806914	+	0.806914i	−0.0290039	+	0.0290039i
$775$	−0.915406	−	0.379174i	−0.0328824	−	0.0136203i
$776$	4.78275	−	11.5466i	0.171691	−	0.414498i
$777$	−9.42134	+	3.90245i	−0.337989	+	0.140000i
$778$			4.48576i			0.160822i
$779$	−0.687149	−	1.65892i	−0.0246197	−	0.0594371i
$780$	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
$785$	16.1497	+	38.9888i	0.576408	+	1.39157i
$786$		−	5.91716i		−	0.211058i
$787$	−46.9741	+	19.4573i	−1.67445	+	0.693578i	−0.999037	−	0.0438650i	$-0.986033\pi$
$787$	−46.9741	+	19.4573i	−1.67445	+	0.693578i	−0.675409	+	0.737443i	$0.736033\pi$
$788$	−8.45895	+	20.4217i	−0.301338	+	0.727494i
$789$	−18.8413	−	7.80430i	−0.670766	−	0.277841i
$790$	−2.55579	+	2.55579i	−0.0909310	+	0.0909310i
$791$	−16.0984	+	16.0984i	−0.572392	+	0.572392i
$792$	14.0361	+	5.81393i	0.498750	+	0.206589i
$793$	0.333564	−	0.805294i	0.0118452	−	0.0285968i
$794$	7.77281	−	3.21960i	0.275847	−	0.114259i
$795$		−	21.5776i		−	0.765279i
$796$	−14.7583	−	35.6298i	−0.523096	−	1.26286i
$797$	3.80883	+	3.80883i	0.134916	+	0.134916i	0.771340	−	0.636424i	$-0.219587\pi$
$797$	3.80883	+	3.80883i	0.134916	+	0.134916i	−0.636424	+	0.771340i	$0.719587\pi$
$798$	0.199340			0.00705658
$799$		0			0
$800$	1.95636			0.0691676
$801$	−9.96297	−	9.96297i	−0.352024	−	0.352024i
$802$	−3.39400	−	8.19385i	−0.119846	−	0.289335i
$803$		−	55.2080i		−	1.94825i
$804$	3.73832	−	1.54846i	0.131841	−	0.0546101i
$805$	−2.99371	+	7.22746i	−0.105515	+	0.254735i
$806$	2.94150	+	1.21841i	0.103610	+	0.0429167i
$807$	−9.89111	+	9.89111i	−0.348184	+	0.348184i
$808$	−6.71606	+	6.71606i	−0.236270	+	0.236270i
$809$	44.9762	+	18.6298i	1.58128	+	0.654988i	0.988616	−	0.150462i	$-0.0480762\pi$
$809$	44.9762	+	18.6298i	1.58128	+	0.654988i	0.592664	+	0.805450i	$0.298076\pi$
$810$	0.823016	−	1.98694i	0.0289178	−	0.0698138i
$811$	−14.7156	+	6.09541i	−0.516736	+	0.214039i	−0.625782	−	0.779998i	$-0.715220\pi$
$811$	−14.7156	+	6.09541i	−0.516736	+	0.214039i	0.109047	+	0.994037i	$0.465220\pi$
$812$		−	7.86484i		−	0.276002i
$813$	−5.72094	−	13.8116i	−0.200642	−	0.484393i
$814$	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
$819$	7.55385	+	18.2366i	0.263953	+	0.637239i
$820$			22.8084i			0.796504i
$821$	15.7993	−	6.54427i	0.551399	−	0.228397i	−0.0895477	−	0.995983i	$-0.528542\pi$
$821$	15.7993	−	6.54427i	0.551399	−	0.228397i	0.640946	+	0.767586i	$0.278542\pi$
$822$	−0.0523960	+	0.126495i	−0.00182752	+	0.00441203i
$823$	5.19467	+	2.15170i	0.181075	+	0.0750037i	0.471379	−	0.881931i	$-0.343756\pi$
$823$	5.19467	+	2.15170i	0.181075	+	0.0750037i	−0.290304	+	0.956934i	$0.593756\pi$
$824$	−5.04788	+	5.04788i	−0.175851	+	0.175851i
$825$	1.60536	−	1.60536i	0.0558915	−	0.0558915i
$826$	3.01977	+	1.25083i	0.105071	+	0.0435219i
$827$	6.83500	−	16.5012i	0.237676	−	0.573801i	−0.759365	−	0.650664i	$-0.774490\pi$
$827$	6.83500	−	16.5012i	0.237676	−	0.573801i	0.997042	+	0.0768632i	$0.0244905\pi$
$828$	6.85608	−	2.83988i	0.238265	−	0.0986927i
$829$		−	35.8161i		−	1.24395i	−0.783039	−	0.621973i	$-0.786331\pi$
$829$		−	35.8161i		−	1.24395i	0.783039	−	0.621973i	$-0.213669\pi$
$830$	4.23704	+	10.2291i	0.147070	+	0.355058i
$831$	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
$836$	1.26492	+	3.05380i	0.0437483	+	0.105618i
$837$		−	8.93313i		−	0.308774i
$838$	−0.421337	+	0.174523i	−0.0145548	+	0.00602881i
$839$	−13.6899	+	33.0502i	−0.472626	+	1.14102i	0.490372	+	0.871513i	$0.336861\pi$
$839$	−13.6899	+	33.0502i	−0.472626	+	1.14102i	−0.962998	+	0.269508i	$0.913139\pi$
$840$	−4.82882	−	2.00016i	−0.166610	−	0.0690122i
$841$	−17.0002	+	17.0002i	−0.586213	+	0.586213i
$842$	−1.96841	+	1.96841i	−0.0678358	+	0.0678358i
$843$	−23.0092	−	9.53072i	−0.792479	−	0.328255i
$844$	15.6197	−	37.7092i	0.537651	−	1.29800i
$845$	20.0575	−	8.30809i	0.689999	−	0.285807i
$846$		−	6.59802i		−	0.226845i
$847$	10.5335	+	25.4300i	0.361934	+	0.873787i
$848$	−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
$853$	−4.23511	−	10.2245i	−0.145007	−	0.350079i	0.834643	−	0.550792i	$-0.185674\pi$
$853$	−4.23511	−	10.2245i	−0.145007	−	0.350079i	−0.979650	+	0.200713i	$0.935674\pi$
$854$			0.120615i			0.00412735i
$855$	1.67703	−	0.694650i	0.0573533	−	0.0237565i
$856$	8.04125	−	19.4133i	0.274844	−	0.663533i
$857$	−25.0137	−	10.3610i	−0.854451	−	0.353925i	−0.0879160	−	0.996128i	$-0.528021\pi$
$857$	−25.0137	−	10.3610i	−0.854451	−	0.353925i	−0.766535	+	0.642203i	$0.778021\pi$
$858$	−5.15856	+	5.15856i	−0.176110	+	0.176110i
$859$	36.5772	−	36.5772i	1.24800	−	1.24800i	0.291393	−	0.956603i	$-0.405881\pi$
$859$	36.5772	−	36.5772i	1.24800	−	1.24800i	0.956603	−	0.291393i	$-0.0941189\pi$
$860$	6.01427	+	2.49119i	0.205085	+	0.0849490i
$861$	3.26998	−	7.89444i	0.111441	−	0.269042i
$862$	4.72530	−	1.95728i	0.160944	−	0.0666653i
$863$		−	45.4712i		−	1.54786i	−0.633272	−	0.773929i	$-0.718289\pi$
$863$		−	45.4712i		−	1.54786i	0.633272	−	0.773929i	$-0.281711\pi$
$864$	6.74983	+	16.2955i	0.229634	+	0.554385i
$865$	−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
$870$	−0.610865	−	1.47476i	−0.0207103	−	0.0499990i
$871$		−	11.5484i		−	0.391302i
$872$	−2.32971	+	0.964997i	−0.0788939	+	0.0326789i
$873$	−7.90448	+	19.0831i	−0.267526	+	0.645865i
$874$	−0.197607	−	0.0818515i	−0.00668416	−	0.00276867i
$875$	−14.0067	+	14.0067i	−0.473511	+	0.473511i
$876$	12.7401	−	12.7401i	0.430448	−	0.430448i
$877$	34.6301	+	14.3443i	1.16938	+	0.484372i	0.880987	−	0.473141i	$-0.156880\pi$
$877$	34.6301	+	14.3443i	1.16938	+	0.484372i	0.288390	+	0.957513i	$0.406880\pi$
$878$	5.31038	−	12.8204i	0.179217	−	0.432667i
$879$	−11.3506	+	4.70157i	−0.382846	+	0.158580i
$880$		−	39.1189i		−	1.31870i
$881$	−6.96324	−	16.8108i	−0.234598	−	0.566369i	0.762110	−	0.647447i	$-0.224163\pi$
$881$	−6.96324	−	16.8108i	−0.234598	−	0.566369i	−0.996708	+	0.0810787i	$0.974163\pi$
$882$	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
$887$	9.10152	+	21.9730i	0.305599	+	0.737782i	0.999837	+	0.0180364i	$0.00574146\pi$
$887$	9.10152	+	21.9730i	0.305599	+	0.737782i	−0.694238	+	0.719745i	$0.744259\pi$
$888$			7.31046i			0.245323i
$889$	20.0369	−	8.29956i	0.672016	−	0.278358i
$890$	1.97403	−	4.76573i	0.0661696	−	0.159748i
$891$	−12.3431	−	5.11268i	−0.413510	−	0.171281i
$892$	26.5138	−	26.5138i	0.887748	−	0.887748i
$893$	2.09527	−	2.09527i	0.0701156	−	0.0701156i
$894$	−2.38930	−	0.989681i	−0.0799102	−	0.0330999i
$895$	3.83675	−	9.26273i	0.128248	−	0.309619i
$896$	−16.4915	+	6.83101i	−0.550943	+	0.228208i
$897$			7.35565i			0.245598i
$898$	1.35984	+	3.28295i	0.0453786	+	0.109554i
$899$	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
$904$	6.24573	+	15.0785i	0.207730	+	0.501505i
$905$			1.08647i			0.0361154i
$906$	−3.88435	+	1.60895i	−0.129049	+	0.0534538i
$907$	14.3587	−	34.6650i	0.476774	−	1.15103i	−0.484340	−	0.874880i	$-0.660940\pi$
$907$	14.3587	−	34.6650i	0.476774	−	1.15103i	0.961114	−	0.276154i	$-0.0890599\pi$
$908$	7.33012	+	3.03624i	0.243259	+	0.100761i
$909$	11.0997	−	11.0997i	0.368152	−	0.368152i
$910$	−5.11004	+	5.11004i	−0.169396	+	0.169396i
$911$	−13.6409	−	5.65023i	−0.451942	−	0.187200i	0.145089	−	0.989419i	$-0.453653\pi$
$911$	−13.6409	−	5.65023i	−0.451942	−	0.187200i	−0.597031	+	0.802218i	$0.703653\pi$
$912$	−0.384617	+	0.928547i	−0.0127359	+	0.0307473i
$913$	63.5447	−	26.3211i	2.10302	−	0.871100i
$914$			4.08790i			0.135216i
$915$	−0.145973	−	0.352409i	−0.00482570	−	0.0116503i
$916$	−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
$921$	3.04544	+	7.35234i	0.100351	+	0.242268i
$922$			6.77238i			0.223037i
$923$	−43.2352	+	17.9086i	−1.42310	+	0.589469i
$924$	−6.01949	+	14.5323i	−0.198027	+	0.478078i
$925$	−2.90615	−	1.20377i	−0.0955536	−	0.0395796i
$926$	−0.351437	+	0.351437i	−0.0115489	+	0.0115489i
$927$	8.34265	−	8.34265i	0.274009	−	0.274009i
$928$	−7.89444	−	3.26998i	−0.259148	−	0.107343i
$929$	4.31036	−	10.4061i	0.141418	−	0.341414i	−0.837262	−	0.546801i	$-0.815845\pi$
$929$	4.31036	−	10.4061i	0.141418	−	0.341414i	0.978681	+	0.205387i	$0.0658453\pi$
$930$	1.28725	−	0.533194i	0.0422104	−	0.0174841i
$931$			1.20439i			0.0394724i
$932$	3.68769	+	8.90287i	0.120794	+	0.291623i
$933$	−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	0.678870	−	0.734258i	$-0.262470\pi$
$937$	−1.69546	−	1.69546i	−0.0553884	−	0.0553884i	−0.734258	+	0.678870i	$0.762470\pi$
$938$	0.611536	+	1.47638i	0.0199674	+	0.0482055i
$939$		−	13.3037i		−	0.434148i
$940$	−34.7740	+	14.4039i	−1.13420	+	0.469802i
$941$	13.1565	−	31.7627i	0.428891	−	1.03543i	−0.550749	−	0.834671i	$-0.685658\pi$
$941$	13.1565	−	31.7627i	0.428891	−	1.03543i	0.979640	−	0.200763i	$-0.0643422\pi$
$942$	−5.07285	−	2.10124i	−0.165282	−	0.0684622i
$943$	−6.48310	+	6.48310i	−0.211119	+	0.211119i
$944$	−11.6530	+	11.6530i	−0.379271	+	0.379271i
$945$	18.7329	+	7.75941i	0.609380	+	0.252414i
$946$	−0.993191	+	2.39778i	−0.0322914	+	0.0779584i
$947$	−18.9667	+	7.85626i	−0.616335	+	0.255294i	−0.668934	−	0.743321i	$-0.733249\pi$
$947$	−18.9667	+	7.85626i	−0.616335	+	0.255294i	0.0525996	+	0.998616i	$0.483249\pi$
$948$			7.32770i			0.237993i
$949$	−19.6783	−	47.5076i	−0.638785	−	1.54216i
$950$	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
$955$	1.28549	+	3.10346i	0.0415976	+	0.100425i
$956$			29.7888i			0.963439i
$957$	−9.16139	+	3.79477i	−0.296146	+	0.122668i
$958$	−5.16567	+	12.4710i	−0.166895	+	0.402921i
$959$	0.778413	+	0.322429i	0.0251363	+	0.0104118i
$960$	7.66137	−	7.66137i	0.247270	−	0.247270i
$961$	19.2493	−	19.2493i	0.620944	−	0.620944i
$962$	9.33841	+	3.86810i	0.301082	+	0.124712i
$963$	−13.2898	+	32.0844i	−0.428258	+	1.03391i
$964$	−31.4561	+	13.0296i	−1.01313	+	0.419654i
$965$			58.0360i			1.86825i
$966$	−0.389513	−	0.940367i	−0.0125324	−	0.0302558i
$967$	2.77656	+	2.77656i	0.0892882	+	0.0892882i	0.750340	−	0.661052i	$-0.229890\pi$
$967$	2.77656	+	2.77656i	0.0892882	+	0.0892882i	−0.661052	+	0.750340i	$0.729890\pi$
$968$	19.7324			0.634222
$969$		0			0
$970$	−7.56212			−0.242805
$971$	3.00805	+	3.00805i	0.0965329	+	0.0965329i	0.753724	−	0.657191i	$-0.228256\pi$
$971$	3.00805	+	3.00805i	0.0965329	+	0.0965329i	−0.657191	+	0.753724i	$0.728256\pi$
$972$	−11.5856	−	27.9700i	−0.371607	−	0.897140i
$973$		−	21.9513i		−	0.703726i
$974$	−11.8762	+	4.91929i	−0.380539	+	0.157624i
$975$	0.809233	−	1.95366i	0.0259162	−	0.0625673i
$976$	−0.561835	−	0.232720i	−0.0179839	−	0.00744918i
$977$	−34.3252	+	34.3252i	−1.09816	+	1.09816i	−0.103534	+	0.994626i	$0.533015\pi$
$977$	−34.3252	+	34.3252i	−1.09816	+	1.09816i	−0.994626	+	0.103534i	$0.966985\pi$
$978$	1.56231	−	1.56231i	0.0499573	−	0.0499573i
$979$	−29.6053	−	12.2629i	−0.946190	−	0.391925i
$980$	5.85452	−	14.1341i	0.187016	−	0.451496i
$981$	3.85032	−	1.59485i	0.122931	−	0.0509198i
$982$			8.82739i			0.281693i
$983$	13.4168	+	32.3910i	0.427929	+	1.03311i	0.979943	+	0.199277i	$0.0638593\pi$
$983$	13.4168	+	32.3910i	0.427929	+	1.03311i	−0.552014	+	0.833835i	$0.686141\pi$
$984$	−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
$989$	1.00141	+	2.41761i	0.0318429	+	0.0768755i
$990$		−	9.19253i		−	0.292158i
$991$	49.1499	−	20.3585i	1.56130	−	0.646711i	0.575983	−	0.817461i	$-0.304619\pi$
$991$	49.1499	−	20.3585i	1.56130	−	0.646711i	0.985314	+	0.170751i	$0.0546193\pi$
$992$	2.85421	−	6.89068i	0.0906213	−	0.218779i
$993$	14.8326	+	6.14386i	0.470698	+	0.194970i
$994$	4.57898	−	4.57898i	0.145236	−	0.145236i
$995$	−34.0593	+	34.0593i	−1.07975	+	1.07975i
$996$	20.7379	+	8.58993i	0.657106	+	0.272182i
$997$	−8.64074	+	20.8606i	−0.273655	+	0.660662i	−0.999634	−	0.0270551i	$-0.991387\pi$
$997$	−8.64074	+	20.8606i	−0.273655	+	0.660662i	0.725979	+	0.687717i	$0.241387\pi$
$998$	−7.00241	+	2.90049i	−0.221657	+	0.0918135i
$999$		−	28.3601i		−	0.897274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.f.134.4		24
17.2	even	8	inner	289.2.d.f.179.4		24
17.3	odd	16		289.2.b.d.288.4		6
17.4	even	4	inner	289.2.d.f.155.4		24
17.5	odd	16		289.2.a.e.1.2	yes	3
17.6	odd	16		289.2.c.d.251.4		12
17.7	odd	16		289.2.c.d.38.4		12
17.8	even	8	inner	289.2.d.f.110.4		24
17.9	even	8	inner	289.2.d.f.110.3		24
17.10	odd	16		289.2.c.d.38.3		12
17.11	odd	16		289.2.c.d.251.3		12
17.12	odd	16		289.2.a.d.1.2	✓	3
17.13	even	4	inner	289.2.d.f.155.3		24
17.14	odd	16		289.2.b.d.288.3		6
17.15	even	8	inner	289.2.d.f.179.3		24
17.16	even	2	inner	289.2.d.f.134.3		24
51.5	even	16		2601.2.a.w.1.2		3
51.29	even	16		2601.2.a.x.1.2		3
68.39	even	16		4624.2.a.bd.1.3		3
68.63	even	16		4624.2.a.bg.1.1		3
85.29	odd	16		7225.2.a.t.1.2		3
85.39	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	17.12	odd	16
289.2.a.e.1.2	yes	3	17.5	odd	16
289.2.b.d.288.3		6	17.14	odd	16
289.2.b.d.288.4		6	17.3	odd	16
289.2.c.d.38.3		12	17.10	odd	16
289.2.c.d.38.4		12	17.7	odd	16
289.2.c.d.251.3		12	17.11	odd	16
289.2.c.d.251.4		12	17.6	odd	16
289.2.d.f.110.3		24	17.9	even	8	inner
289.2.d.f.110.4		24	17.8	even	8	inner
289.2.d.f.134.3		24	17.16	even	2	inner
289.2.d.f.134.4		24	1.1	even	1	trivial
289.2.d.f.155.3		24	17.13	even	4	inner
289.2.d.f.155.4		24	17.4	even	4	inner
289.2.d.f.179.3		24	17.15	even	8	inner
289.2.d.f.179.4		24	17.2	even	8	inner
2601.2.a.w.1.2		3	51.5	even	16
2601.2.a.x.1.2		3	51.29	even	16
4624.2.a.bd.1.3		3	68.39	even	16
4624.2.a.bg.1.1		3	68.63	even	16
7225.2.a.s.1.2		3	85.39	odd	16
7225.2.a.t.1.2		3	85.29	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 $\F_{q}$

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

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