LMFDB - Embedded newform 289.2.d.f.134.3

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			134.3
Character	$\chi$	$=$	289.134
Dual form			289.2.d.f.110.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.245576 - 0.245576i) q^{2} +(-0.336526 - 0.812446i) q^{3} -1.87939i q^{4} +(2.16862 - 0.898271i) q^{5} +(-0.116874 + 0.282160i) q^{6} +(1.73633 + 0.719210i) q^{7} +(-0.952682 + 0.952682i) q^{8} +(1.57450 - 1.57450i) q^{9} +O(q^{10})$	\(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	0.796468	−	0.604680i	$-0.206699\pi$
$3$	−0.336526	−	0.812446i	−0.194293	−	0.469066i	−0.990762	+	0.135614i	$0.956699\pi$
$4$		−	1.87939i		−	0.939693i
$5$	2.16862	−	0.898271i	0.969836	−	0.401719i	0.159185	−	0.987249i	$-0.449113\pi$
$5$	2.16862	−	0.898271i	0.969836	−	0.401719i	0.810651	+	0.585530i	$0.199113\pi$
$6$	−0.116874	+	0.282160i	−0.0477137	+	0.115191i
$7$	1.73633	+	0.719210i	0.656269	+	0.271836i	0.685868	−	0.727726i	$-0.259423\pi$
$7$	1.73633	+	0.719210i	0.656269	+	0.271836i	−0.0295984	+	0.999562i	$0.509423\pi$
$8$	−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	$0.401498\pi$
$11$	−1.93798	+	4.67869i	−0.584322	+	1.41068i	−0.888860	+	0.458178i	$0.848502\pi$
$12$	−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	−0.837202	−	0.546894i	$-0.815810\pi$
$23$	0.678620	−	1.63833i	0.141502	−	0.341616i	0.978704	+	0.205278i	$0.0658100\pi$
$24$	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	−0.183411	−	0.983036i	$-0.558714\pi$
$29$	2.05719	−	0.852114i	0.382010	−	0.158234i	0.565421	+	0.824803i	$0.308714\pi$
$30$			0.716881i			0.130884i
$31$	0.743769	+	1.79562i	0.133585	+	0.322503i	0.976491	−	0.215558i	$-0.0691571\pi$
$31$	0.743769	+	1.79562i	0.133585	+	0.322503i	−0.842906	+	0.538061i	$0.819157\pi$
$32$	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	$0.0443161\pi$
$37$	2.36125	+	5.70056i	0.388187	+	0.937167i	−0.602137	+	0.798393i	$0.705684\pi$
$38$			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	−0.0228873	−	0.999738i	$-0.507286\pi$
$41$	−4.77668	−	1.97857i	−0.745993	−	0.309000i	−0.723105	+	0.690738i	$0.757286\pi$
$42$	−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	0.371727	−	0.928342i	$-0.378766\pi$
$61$	−0.170726	−	0.0707170i	−0.0218592	−	0.00905439i	−0.393586	+	0.919288i	$0.628766\pi$
$62$	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	$0.0753677\pi$
$71$	3.79671	+	9.16606i	0.450586	+	1.08781i	−0.521513	+	0.853243i	$0.674632\pi$
$72$			3.00000i			0.353553i
$73$	−10.0718	+	4.17189i	−1.17882	+	0.488283i	−0.884098	−	0.467301i	$-0.845227\pi$
$73$	−10.0718	+	4.17189i	−1.17882	+	0.488283i	−0.294721	+	0.955584i	$0.595227\pi$
$74$	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	−0.799233	−	0.601022i	$-0.794760\pi$
$79$	1.69673	−	4.09626i	0.190897	−	0.460866i	0.990129	+	0.140156i	$0.0447605\pi$
$80$	−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	0.0974943	−	0.995236i	$-0.468917\pi$
$97$	8.57019	−	3.54989i	0.870171	−	0.360437i	0.772677	+	0.634799i	$0.218917\pi$
$98$			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	0.445058	−	0.895502i	$-0.353183\pi$
$107$	14.4091	−	5.96843i	1.39298	−	0.576990i	0.947919	+	0.318511i	$0.103183\pi$
$108$	−3.30568	+	7.98062i	−0.318089	+	0.767935i
$109$	−1.72917	−	0.716247i	−0.165625	−	0.0686041i	0.298331	−	0.954463i	$-0.403570\pi$
$109$	−1.72917	−	0.716247i	−0.165625	−	0.0686041i	−0.463955	+	0.885859i	$0.653570\pi$
$110$	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	$0.317974\pi$
$113$	−4.63575	+	11.1917i	−0.436095	+	1.05283i	−0.977286	+	0.211927i	$0.932026\pi$
$114$	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	−0.985764	−	0.168134i	$-0.946226\pi$
$131$	−17.8998	+	7.41435i	−1.56392	+	0.647795i	−0.578151	+	0.815929i	$0.696226\pi$
$132$		−	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	$-0.960042\pi$
$139$	−4.46976	−	10.7910i	−0.379120	−	0.915277i	0.613011	−	0.790074i	$-0.289958\pi$
$140$		−	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	0.105248	−	0.994446i	$-0.466436\pi$
$163$	−6.68373	−	2.76849i	−0.523511	−	0.216845i	−0.628758	+	0.777601i	$0.716436\pi$
$164$	−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	0.830068	−	0.557662i	$-0.188302\pi$
$167$	−1.95401	−	4.71739i	−0.151206	−	0.365043i	−0.981273	+	0.192620i	$0.938302\pi$
$168$	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	$-0.962888\pi$
$173$	−4.90816	−	11.8493i	−0.373160	−	0.900889i	0.620051	−	0.784562i	$-0.287112\pi$
$174$			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	−0.930326	−	0.366734i	$-0.880476\pi$
$181$	−0.177128	+	0.427626i	−0.0131658	+	0.0317852i	0.917160	+	0.398519i	$0.130476\pi$
$182$	−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	$0.474197\pi$
$193$	−9.46170	+	22.8426i	−0.681068	+	1.64424i	−0.762042	+	0.647528i	$0.775803\pi$
$194$	−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	0.734565	−	0.678538i	$-0.237386\pi$
$197$	10.8662	+	4.50092i	0.774183	+	0.320677i	0.0396173	+	0.999215i	$0.487386\pi$
$198$	1.49867	−	3.61812i	0.106506	−	0.257128i
$199$	−18.9582	+	7.85275i	−1.34391	+	0.556667i	−0.934591	−	0.355723i	$-0.884234\pi$
$199$	−18.9582	+	7.85275i	−1.34391	+	0.556667i	−0.409321	+	0.912390i	$0.634234\pi$
$200$			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	−0.436477	−	0.899716i	$-0.643774\pi$
$211$	−20.0646	−	8.31105i	−1.38131	−	0.572156i	−0.944831	+	0.327559i	$0.893774\pi$
$212$	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	−0.861154	−	0.508344i	$-0.830258\pi$
$227$	1.61555	−	3.90028i	0.107228	−	0.258870i	0.968382	+	0.249474i	$0.0802577\pi$
$228$	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	−0.222078	−	0.975029i	$-0.571284\pi$
$233$	4.73712	−	1.96218i	0.310339	−	0.128547i	0.532417	+	0.846482i	$0.321284\pi$
$234$			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	$0.0733145\pi$
$241$	6.93288	+	16.7375i	0.446586	+	1.07815i	−0.527006	+	0.849861i	$0.676686\pi$
$242$			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	$-0.963847\pi$
$269$	−6.08724	−	14.6959i	−0.371146	−	0.896025i	0.622411	−	0.782690i	$-0.286153\pi$
$270$	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	−0.796776	−	0.604275i	$-0.793463\pi$
$277$	−15.5265	+	6.43127i	−0.932894	+	0.386417i	−0.136118	+	0.990693i	$0.543463\pi$
$278$	−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	$-0.467505\pi$
$283$	12.3356	−	29.7807i	0.733274	−	1.77028i	0.631364	−	0.775487i	$-0.282495\pi$
$284$	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	−0.320349	−	0.947299i	$-0.603800\pi$
$311$	2.16862	−	0.898271i	0.122971	−	0.0509363i	0.443321	+	0.896363i	$0.353800\pi$
$312$	2.13864	−	5.16312i	0.121076	−	0.292304i
$313$	13.9768	+	5.78937i	0.790014	+	0.327235i	0.740949	−	0.671561i	$-0.234376\pi$
$313$	13.9768	+	5.78937i	0.790014	+	0.327235i	0.0490649	+	0.998796i	$0.484376\pi$
$314$	−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	−0.772991	−	0.634417i	$-0.781240\pi$
$317$	3.95611	−	9.55088i	0.222197	−	0.536431i	0.995188	+	0.0979863i	$0.0312401\pi$
$318$	−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	$0.0233183\pi$
$337$	6.31246	+	15.2396i	0.343862	+	0.830155i	−0.653456	+	0.756964i	$0.726682\pi$
$338$	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	−0.191104	−	0.981570i	$-0.561207\pi$
$347$	−19.0063	−	7.87265i	−1.02031	−	0.422626i	−0.829205	+	0.558944i	$0.811207\pi$
$348$	−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	0.346526	−	0.938040i	$-0.387361\pi$
$367$	−1.37428	−	0.569246i	−0.0717369	−	0.0297144i	−0.418263	+	0.908326i	$0.637361\pi$
$368$	−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	0.152085	−	0.988367i	$-0.451401\pi$
$379$	18.6601	−	7.72928i	0.958507	−	0.397027i	0.806422	+	0.591341i	$0.201401\pi$
$380$	−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	$-0.667009\pi$
$397$	9.27048	−	22.3809i	0.465272	−	1.12327i	0.966204	−	0.257779i	$-0.0829907\pi$
$398$	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	−0.294298	−	0.955714i	$-0.595086\pi$
$401$	−23.5932	−	9.77264i	−1.17819	−	0.488022i	−0.883892	+	0.467691i	$0.845086\pi$
$402$	−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	−0.935679	−	0.352852i	$-0.885212\pi$
$419$	−0.502520	+	1.21319i	−0.0245497	+	0.0592682i	0.911129	+	0.412121i	$0.135212\pi$
$420$	−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	−0.728081	−	0.685491i	$-0.759587\pi$
$431$	5.63577	−	13.6060i	0.271466	−	0.655376i	0.999546	+	0.0301153i	$0.00958744\pi$
$432$	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	$-0.722445\pi$
$439$	−15.2906	−	36.9149i	−0.729782	−	1.76185i	−0.0864590	−	0.996255i	$-0.527555\pi$
$440$	−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	0.594417	−	0.804157i	$-0.297383\pi$
$449$	9.45289	+	3.91552i	0.446109	+	0.184785i	−0.148308	+	0.988941i	$0.547383\pi$
$450$	−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	$0.222872\pi$
$479$	14.8740	+	35.9089i	0.679608	+	1.64072i	−0.0851226	+	0.996370i	$0.527128\pi$
$480$		−	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	$0.441641\pi$
$487$	−14.1645	+	34.1962i	−0.641857	+	1.54958i	−0.824172	+	0.566339i	$0.808359\pi$
$488$	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	$0.287451\pi$
$499$	−8.35164	+	20.1626i	−0.373871	+	0.902604i	−0.993087	+	0.117383i	$0.962549\pi$
$500$	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	−0.433614	−	0.901099i	$-0.642762\pi$
$503$	−30.8918	−	12.7958i	−1.37740	−	0.570537i	−0.943784	+	0.330562i	$0.892762\pi$
$504$	−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	$-0.591049\pi$
$521$	13.5979	−	32.8282i	0.595735	−	1.43823i	0.877890	−	0.478862i	$-0.158951\pi$
$522$	−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	0.871534	−	0.490335i	$-0.163126\pi$
$541$	−2.12714	−	5.13538i	−0.0914531	−	0.220787i	−0.962987	+	0.269548i	$0.913126\pi$
$542$	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	0.959641	−	0.281227i	$-0.0907413\pi$
$547$	1.92285	+	4.64217i	0.0822152	+	0.198485i	−0.877426	+	0.479712i	$0.840741\pi$
$548$			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	0.490495	−	0.871444i	$-0.336816\pi$
$571$	5.28389	+	2.18866i	0.221124	+	0.0915926i	−0.269371	+	0.963036i	$0.586816\pi$
$572$	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	$-0.436530\pi$
$601$	18.4137	−	44.4547i	0.751112	−	1.81335i	0.553033	−	0.833159i	$-0.313470\pi$
$602$	−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	−0.0731581	−	0.997320i	$-0.523308\pi$
$607$	14.2976	−	5.92228i	0.580323	−	0.240378i	0.653481	+	0.756943i	$0.273308\pi$
$608$		−	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	−0.831553	−	0.555445i	$-0.812548\pi$
$617$	−25.5050	+	10.5645i	−1.02679	+	0.425311i	−0.195238	+	0.980756i	$0.562548\pi$
$618$	−0.619270	+	1.49505i	−0.0249107	+	0.0601398i
$619$	13.7040	+	5.67636i	0.550808	+	0.228152i	0.640689	−	0.767800i	$-0.278649\pi$
$619$	13.7040	+	5.67636i	0.550808	+	0.228152i	−0.0898809	+	0.995953i	$0.528649\pi$
$620$	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	−0.0913460	−	0.995819i	$-0.529117\pi$
$641$	13.8796	−	5.74914i	0.548213	−	0.227077i	0.639559	+	0.768742i	$0.279117\pi$
$642$			4.76321i			0.187989i
$643$	6.81099	+	16.4432i	0.268599	+	0.648456i	0.999418	−	0.0341158i	$-0.0108615\pi$
$643$	6.81099	+	16.4432i	0.268599	+	0.648456i	−0.730819	+	0.682572i	$0.760862\pi$
$644$	−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	0.858798	−	0.512314i	$-0.171212\pi$
$653$	28.2064	+	11.6835i	1.10380	+	0.457209i	0.245002	+	0.969523i	$0.421212\pi$
$654$	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	0.595777	−	0.803150i	$-0.296844\pi$
$673$	11.6517	+	4.82631i	0.449141	+	0.186040i	−0.146635	+	0.989191i	$0.546844\pi$
$674$	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	0.953796	−	0.300456i	$-0.0971390\pi$
$677$	1.74083	+	4.20273i	0.0669054	+	0.161524i	−0.886890	+	0.461980i	$0.847139\pi$
$678$	−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	0.955502	−	0.294984i	$-0.0953143\pi$
$683$	1.86272	+	4.49701i	0.0712751	+	0.172073i	−0.884227	+	0.467057i	$0.845314\pi$
$684$			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	−0.958935	−	0.283627i	$-0.908462\pi$
$691$	−2.11111	+	5.09668i	−0.0803106	+	0.193887i	0.878624	+	0.477514i	$0.158462\pi$
$692$	−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	−0.893140	−	0.449778i	$-0.851503\pi$
$709$	−32.1294	+	13.3084i	−1.20665	+	0.499809i	−0.313505	+	0.949587i	$0.601503\pi$
$710$		−	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	−0.454695	−	0.890647i	$-0.650252\pi$
$719$	−3.92640	+	1.62637i	−0.146430	+	0.0606533i	0.308265	+	0.951301i	$0.400252\pi$
$720$	−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	0.0504250	−	0.998728i	$-0.483942\pi$
$743$	21.5962	−	8.94544i	0.792288	−	0.328177i	0.741863	+	0.670551i	$0.233942\pi$
$744$			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	0.759255	−	0.650793i	$-0.225564\pi$
$751$	−6.51675	−	15.7328i	−0.237800	−	0.574099i	−0.997055	+	0.0766940i	$0.975564\pi$
$752$		−	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	0.675409	−	0.737443i	$-0.263967\pi$
$787$	46.9741	−	19.4573i	1.67445	−	0.693578i	0.999037	+	0.0438650i	$0.0139672\pi$
$788$	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	−0.592664	−	0.805450i	$-0.701924\pi$
$809$	−44.9762	−	18.6298i	−1.58128	−	0.654988i	−0.988616	+	0.150462i	$0.951924\pi$
$810$	−0.823016	+	1.98694i	−0.0289178	+	0.0698138i
$811$	14.7156	−	6.09541i	0.516736	−	0.214039i	−0.109047	−	0.994037i	$-0.534780\pi$
$811$	14.7156	−	6.09541i	0.516736	−	0.214039i	0.625782	+	0.779998i	$0.284780\pi$
$812$		−	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	−0.640946	−	0.767586i	$-0.721458\pi$
$821$	−15.7993	+	6.54427i	−0.551399	+	0.228397i	0.0895477	+	0.995983i	$0.471458\pi$
$822$	0.0523960	−	0.126495i	0.00182752	−	0.00441203i
$823$	−5.19467	−	2.15170i	−0.181075	−	0.0750037i	0.290304	−	0.956934i	$-0.406244\pi$
$823$	−5.19467	−	2.15170i	−0.181075	−	0.0750037i	−0.471379	+	0.881931i	$0.656244\pi$
$824$	−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	−0.997042	−	0.0768632i	$-0.975510\pi$
$827$	−6.83500	+	16.5012i	−0.237676	+	0.573801i	0.759365	+	0.650664i	$0.225510\pi$
$828$	−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	$-0.663139\pi$
$839$	13.6899	−	33.0502i	0.472626	−	1.14102i	0.962998	−	0.269508i	$-0.0868609\pi$
$840$	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	0.979650	−	0.200713i	$-0.0643259\pi$
$853$	4.23511	+	10.2245i	0.145007	+	0.350079i	−0.834643	+	0.550792i	$0.814326\pi$
$854$			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	0.766535	−	0.642203i	$-0.221979\pi$
$857$	25.0137	+	10.3610i	0.854451	+	0.353925i	0.0879160	+	0.996128i	$0.471979\pi$
$858$	−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	−0.288390	−	0.957513i	$-0.593120\pi$
$877$	−34.6301	−	14.3443i	−1.16938	−	0.484372i	−0.880987	+	0.473141i	$0.843120\pi$
$878$	−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	0.996708	−	0.0810787i	$-0.0258365\pi$
$881$	6.96324	+	16.8108i	0.234598	+	0.566369i	−0.762110	+	0.647447i	$0.775837\pi$
$882$	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	$-0.994259\pi$
$887$	−9.10152	−	21.9730i	−0.305599	−	0.737782i	0.694238	−	0.719745i	$-0.255741\pi$
$888$			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	$0.339060\pi$
$907$	−14.3587	+	34.6650i	−0.476774	+	1.15103i	−0.961114	+	0.276154i	$0.910940\pi$
$908$	−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	0.597031	−	0.802218i	$-0.296347\pi$
$911$	13.6409	+	5.65023i	0.451942	+	0.187200i	−0.145089	+	0.989419i	$0.546347\pi$
$912$	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	−0.978681	−	0.205387i	$-0.934155\pi$
$929$	−4.31036	+	10.4061i	−0.141418	+	0.341414i	0.837262	+	0.546801i	$0.184155\pi$
$930$	−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	$0.314342\pi$
$941$	−13.1565	+	31.7627i	−0.428891	+	1.03543i	−0.979640	+	0.200763i	$0.935658\pi$
$942$	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	−0.0525996	−	0.998616i	$-0.516751\pi$
$947$	18.9667	−	7.85626i	0.616335	−	0.255294i	0.668934	+	0.743321i	$0.266751\pi$
$948$			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	$-0.936141\pi$
$983$	−13.4168	−	32.3910i	−0.427929	−	1.03311i	0.552014	−	0.833835i	$-0.313859\pi$
$984$	−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	−0.985314	−	0.170751i	$-0.945381\pi$
$991$	−49.1499	+	20.3585i	−1.56130	+	0.646711i	−0.575983	+	0.817461i	$0.695381\pi$
$992$	−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	−0.725979	−	0.687717i	$-0.758613\pi$
$997$	8.64074	−	20.8606i	0.273655	−	0.660662i	0.999634	+	0.0270551i	$0.00861297\pi$
$998$	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.134.3		24
17.2	even	8	inner	289.2.d.f.179.3		24
17.3	odd	16		289.2.b.d.288.3		6
17.4	even	4	inner	289.2.d.f.155.3		24
17.5	odd	16		289.2.a.d.1.2	✓	3
17.6	odd	16		289.2.c.d.251.3		12
17.7	odd	16		289.2.c.d.38.3		12
17.8	even	8	inner	289.2.d.f.110.3		24
17.9	even	8	inner	289.2.d.f.110.4		24
17.10	odd	16		289.2.c.d.38.4		12
17.11	odd	16		289.2.c.d.251.4		12
17.12	odd	16		289.2.a.e.1.2	yes	3
17.13	even	4	inner	289.2.d.f.155.4		24
17.14	odd	16		289.2.b.d.288.4		6
17.15	even	8	inner	289.2.d.f.179.4		24
17.16	even	2	inner	289.2.d.f.134.4		24
51.5	even	16		2601.2.a.x.1.2		3
51.29	even	16		2601.2.a.w.1.2		3
68.39	even	16		4624.2.a.bg.1.1		3
68.63	even	16		4624.2.a.bd.1.3		3
85.29	odd	16		7225.2.a.s.1.2		3
85.39	odd	16		7225.2.a.t.1.2		3

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