LMFDB - Embedded newform 560.2.ch.c.493.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(117,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 3, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.117"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ch (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [360,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$90$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.32
Character	$\chi$	$=$	560.493
Dual form			560.2.ch.c.117.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.632072 + 1.26510i) q^{2} +(0.594438 - 1.02960i) q^{3} +(-1.20097 - 1.59927i) q^{4} +(1.63662 + 1.52363i) q^{5} +(0.926818 + 1.40280i) q^{6} +(2.00856 - 1.72211i) q^{7} +(2.78234 - 0.508498i) q^{8} +(0.793287 + 1.37401i) q^{9} +(-2.96202 + 1.10745i) q^{10} +(-1.35178 - 5.04493i) q^{11} +(-2.36051 + 0.285848i) q^{12} -0.338561 q^{13} +(0.909095 + 3.62954i) q^{14} +(2.54160 - 0.779356i) q^{15} +(-1.11534 + 3.84136i) q^{16} +(2.64247 - 0.708048i) q^{17} +(-2.23968 + 0.135115i) q^{18} +(0.563156 - 2.10173i) q^{19} +(0.471167 - 4.44725i) q^{20} +(-0.579117 - 3.09170i) q^{21} +(7.23678 + 1.47861i) q^{22} +(-8.60756 - 2.30639i) q^{23} +(1.13038 - 3.16696i) q^{24} +(0.357076 + 4.98723i) q^{25} +(0.213995 - 0.428315i) q^{26} +5.45287 q^{27} +(-5.16635 - 1.14403i) q^{28} +(-0.974217 + 0.974217i) q^{29} +(-0.620507 + 3.70799i) q^{30} +(4.53120 + 2.61609i) q^{31} +(-4.15474 - 3.83903i) q^{32} +(-5.99779 - 1.60710i) q^{33} +(-0.774477 + 3.79053i) q^{34} +(5.91113 + 0.241863i) q^{35} +(1.24471 - 2.91883i) q^{36} +(7.52418 - 4.34409i) q^{37} +(2.30295 + 2.04089i) q^{38} +(-0.201254 + 0.348581i) q^{39} +(5.32841 + 3.40705i) q^{40} +7.36805 q^{41} +(4.27736 + 1.22153i) q^{42} +7.04252 q^{43} +(-6.44476 + 8.22068i) q^{44} +(-0.795182 + 3.45742i) q^{45} +(8.35841 - 9.43164i) q^{46} +(-1.78044 + 6.64469i) q^{47} +(3.29205 + 3.43180i) q^{48} +(1.06865 - 6.91795i) q^{49} +(-6.53506 - 2.70055i) q^{50} +(0.841781 - 3.14157i) q^{51} +(0.406602 + 0.541451i) q^{52} +(-4.17565 + 7.23243i) q^{53} +(-3.44660 + 6.89844i) q^{54} +(5.47426 - 10.3163i) q^{55} +(4.71282 - 5.81286i) q^{56} +(-1.82917 - 1.82917i) q^{57} +(-0.616710 - 1.84826i) q^{58} +(-1.11590 - 4.16461i) q^{59} +(-4.29879 - 3.12872i) q^{60} +(-0.0354146 - 0.00948932i) q^{61} +(-6.17366 + 4.07888i) q^{62} +(3.95958 + 1.39366i) q^{63} +(7.48286 - 2.82963i) q^{64} +(-0.554097 - 0.515844i) q^{65} +(5.82419 - 6.57202i) q^{66} +(-4.14262 + 7.17522i) q^{67} +(-4.30589 - 3.37568i) q^{68} +(-7.49131 + 7.49131i) q^{69} +(-4.04224 + 7.32532i) q^{70} +5.62686i q^{71} +(2.90588 + 3.41959i) q^{72} +(-12.8100 + 3.43244i) q^{73} +(0.739897 + 12.2646i) q^{74} +(5.34710 + 2.59696i) q^{75} +(-4.03757 + 1.62347i) q^{76} +(-11.4031 - 7.80513i) q^{77} +(-0.313785 - 0.474935i) q^{78} +(8.98265 - 5.18614i) q^{79} +(-7.67821 + 4.58749i) q^{80} +(0.861529 - 1.49221i) q^{81} +(-4.65714 + 9.32135i) q^{82} -17.3283 q^{83} +(-4.24896 + 4.63920i) q^{84} +(5.40354 + 2.86735i) q^{85} +(-4.45138 + 8.90951i) q^{86} +(0.423939 + 1.58216i) q^{87} +(-6.32646 - 13.3493i) q^{88} +(-1.59534 + 0.921068i) q^{89} +(-3.87139 - 3.19133i) q^{90} +(-0.680021 + 0.583041i) q^{91} +(6.64889 + 16.5357i) q^{92} +(5.38703 - 3.11020i) q^{93} +(-7.28085 - 6.45236i) q^{94} +(4.12394 - 2.58169i) q^{95} +(-6.42239 + 1.99564i) q^{96} +(-8.15823 - 8.15823i) q^{97} +(8.07645 + 5.72459i) q^{98} +(5.85945 - 5.85945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.632072	+	1.26510i	−0.446942	+	0.894563i
$2$	−0.632072	+	1.26510i	−0.446942	+	0.894563i
$3$	0.594438	−	1.02960i	0.343199	−	0.594438i	−0.641826	−	0.766850i	$-0.721823\pi$
$3$	0.594438	−	1.02960i	0.343199	−	0.594438i	0.985025	+	0.172412i	$0.0551562\pi$
$4$	−1.20097	−	1.59927i	−0.600485	−	0.799636i
$5$	1.63662	+	1.52363i	0.731920	+	0.681390i
$5$	1.63662	+	1.52363i	0.731920	+	0.681390i
$6$	0.926818	+	1.40280i	0.378372	+	0.572692i
$7$	2.00856	−	1.72211i	0.759165	−	0.650898i
$7$	2.00856	−	1.72211i	0.759165	−	0.650898i
$8$	2.78234	−	0.508498i	0.983707	−	0.179781i
$9$	0.793287	+	1.37401i	0.264429	+	0.458005i
$10$	−2.96202	+	1.10745i	−0.936672	+	0.350207i
$11$	−1.35178	−	5.04493i	−0.407578	−	1.52110i	−0.799250	−	0.600998i	$-0.794770\pi$
$11$	−1.35178	−	5.04493i	−0.407578	−	1.52110i	0.391672	−	0.920105i	$-0.371897\pi$
$12$	−2.36051	+	0.285848i	−0.681420	+	0.0825172i
$13$	−0.338561			−0.0939000			−0.0469500	−	0.998897i	$-0.514950\pi$
$13$	−0.338561			−0.0939000			−0.0469500	+	0.998897i	$0.514950\pi$
$14$	0.909095	+	3.62954i	0.242966	+	0.970035i
$15$	2.54160	−	0.779356i	0.656238	−	0.201229i
$16$	−1.11534	+	3.84136i	−0.278834	+	0.960339i
$17$	2.64247	−	0.708048i	0.640893	−	0.171727i	0.0762852	−	0.997086i	$-0.475694\pi$
$17$	2.64247	−	0.708048i	0.640893	−	0.171727i	0.564608	+	0.825359i	$0.309027\pi$
$18$	−2.23968	+	0.135115i	−0.527898	+	0.0318469i
$19$	0.563156	−	2.10173i	0.129197	−	0.482169i	−0.870758	−	0.491713i	$-0.836371\pi$
$19$	0.563156	−	2.10173i	0.129197	−	0.482169i	0.999954	+	0.00954318i	$0.00303773\pi$
$20$	0.471167	−	4.44725i	0.105356	−	0.994435i
$21$	−0.579117	−	3.09170i	−0.126374	−	0.674664i
$22$	7.23678	+	1.47861i	1.54289	+	0.315241i
$23$	−8.60756	−	2.30639i	−1.79480	−	0.480915i	−0.801653	−	0.597789i	$-0.796046\pi$
$23$	−8.60756	−	2.30639i	−1.79480	−	0.480915i	−0.993147	+	0.116874i	$0.962713\pi$
$24$	1.13038	−	3.16696i	0.230738	−	0.646453i
$25$	0.357076	+	4.98723i	0.0714151	+	0.997447i
$26$	0.213995	−	0.428315i	0.0419679	−	0.0839994i
$27$	5.45287			1.04940
$28$	−5.16635	−	1.14403i	−0.976349	−	0.216201i
$29$	−0.974217	+	0.974217i	−0.180908	+	0.180908i	−0.791751	−	0.610844i	$-0.790830\pi$
$29$	−0.974217	+	0.974217i	−0.180908	+	0.180908i	0.610844	+	0.791751i	$0.290830\pi$
$30$	−0.620507	+	3.70799i	−0.113289	+	0.676984i
$31$	4.53120	+	2.61609i	0.813827	+	0.469863i	0.848283	−	0.529543i	$-0.177636\pi$
$31$	4.53120	+	2.61609i	0.813827	+	0.469863i	−0.0344558	+	0.999406i	$0.510970\pi$
$32$	−4.15474	−	3.83903i	−0.734461	−	0.678651i
$33$	−5.99779	−	1.60710i	−1.04408	−	0.279761i
$34$	−0.774477	+	3.79053i	−0.132822	+	0.650071i
$35$	5.91113	+	0.241863i	0.999164	+	0.0408824i
$36$	1.24471	−	2.91883i	0.207451	−	0.486472i
$37$	7.52418	−	4.34409i	1.23697	−	0.714164i	0.268495	−	0.963281i	$-0.413474\pi$
$37$	7.52418	−	4.34409i	1.23697	−	0.714164i	0.968473	+	0.249117i	$0.0801404\pi$
$38$	2.30295	+	2.04089i	0.373587	+	0.331077i
$39$	−0.201254	+	0.348581i	−0.0322264	+	0.0558177i
$40$	5.32841	+	3.40705i	0.842496	+	0.538702i
$41$	7.36805			1.15070			0.575348	−	0.817909i	$-0.304867\pi$
$41$	7.36805			1.15070			0.575348	+	0.817909i	$0.304867\pi$
$42$	4.27736	+	1.22153i	0.660011	+	0.188487i
$43$	7.04252			1.07397			0.536987	−	0.843590i	$-0.319562\pi$
$43$	7.04252			1.07397			0.536987	+	0.843590i	$0.319562\pi$
$44$	−6.44476	+	8.22068i	−0.971583	+	1.23931i
$45$	−0.795182	+	3.45742i	−0.118539	+	0.515402i
$46$	8.35841	−	9.43164i	1.23238	−	1.39062i
$47$	−1.78044	+	6.64469i	−0.259704	+	0.969227i	0.705709	+	0.708501i	$0.250628\pi$
$47$	−1.78044	+	6.64469i	−0.259704	+	0.969227i	−0.965413	+	0.260726i	$0.916038\pi$
$48$	3.29205	+	3.43180i	0.475166	+	0.495337i
$49$	1.06865	−	6.91795i	0.152664	−	0.988278i
$50$	−6.53506	−	2.70055i	−0.924197	−	0.381916i
$51$	0.841781	−	3.14157i	0.117873	−	0.439908i
$52$	0.406602	+	0.541451i	0.0563856	+	0.0750858i
$53$	−4.17565	+	7.23243i	−0.573569	+	0.993451i	0.422626	+	0.906304i	$0.361108\pi$
$53$	−4.17565	+	7.23243i	−0.573569	+	0.993451i	−0.996195	+	0.0871469i	$0.972225\pi$
$54$	−3.44660	+	6.89844i	−0.469023	+	0.938759i
$55$	5.47426	−	10.3163i	0.738150	−	1.39105i
$56$	4.71282	−	5.81286i	0.629777	−	0.776776i
$57$	−1.82917	−	1.82917i	−0.242280	−	0.242280i
$58$	−0.616710	−	1.84826i	−0.0809780	−	0.242688i
$59$	−1.11590	−	4.16461i	−0.145278	−	0.542186i	−0.999743	−	0.0226764i	$-0.992781\pi$
$59$	−1.11590	−	4.16461i	−0.145278	−	0.542186i	0.854465	−	0.519510i	$-0.173885\pi$
$60$	−4.29879	−	3.12872i	−0.554971	−	0.403917i
$61$	−0.0354146	−	0.00948932i	−0.00453438	−	0.00121498i	0.256551	−	0.966531i	$-0.417414\pi$
$61$	−0.0354146	−	0.00948932i	−0.00453438	−	0.00121498i	−0.261086	+	0.965316i	$0.584080\pi$
$62$	−6.17366	+	4.07888i	−0.784056	+	0.518018i
$63$	3.95958	+	1.39366i	0.498860	+	0.175585i
$64$	7.48286	−	2.82963i	0.935358	−	0.353704i
$65$	−0.554097	−	0.515844i	−0.0687273	−	0.0639825i
$66$	5.82419	−	6.57202i	0.716908	−	0.808960i
$67$	−4.14262	+	7.17522i	−0.506101	+	0.876593i	0.493874	+	0.869534i	$0.335580\pi$
$67$	−4.14262	+	7.17522i	−0.506101	+	0.876593i	−0.999975	+	0.00705957i	$0.997753\pi$
$68$	−4.30589	−	3.37568i	−0.522166	−	0.409362i
$69$	−7.49131	+	7.49131i	−0.901847	+	0.901847i
$70$	−4.04224	+	7.32532i	−0.483140	+	0.875543i
$71$			5.62686i			0.667785i	0.942611	+	0.333893i	$0.108362\pi$
$71$			5.62686i			0.667785i	−0.942611	+	0.333893i	$0.891638\pi$
$72$	2.90588	+	3.41959i	0.342461	+	0.403003i
$73$	−12.8100	+	3.43244i	−1.49930	+	0.401737i	−0.912866	−	0.408259i	$-0.866136\pi$
$73$	−12.8100	+	3.43244i	−1.49930	+	0.401737i	−0.586436	+	0.809996i	$0.699469\pi$
$74$	0.739897	+	12.2646i	0.0860113	+	1.42574i
$75$	5.34710	+	2.59696i	0.617430	+	0.299871i
$76$	−4.03757	+	1.62347i	−0.463141	+	0.186225i
$77$	−11.4031	−	7.80513i	−1.29950	−	0.889477i
$78$	−0.313785	−	0.474935i	−0.0355291	−	0.0537758i
$79$	8.98265	−	5.18614i	1.01063	−	0.583486i	0.0992520	−	0.995062i	$-0.468355\pi$
$79$	8.98265	−	5.18614i	1.01063	−	0.583486i	0.911375	+	0.411576i	$0.135022\pi$
$80$	−7.67821	+	4.58749i	−0.858450	+	0.512897i
$81$	0.861529	−	1.49221i	0.0957254	−	0.165801i
$82$	−4.65714	+	9.32135i	−0.514295	+	1.02937i
$83$	−17.3283			−1.90203			−0.951016	−	0.309140i	$-0.899959\pi$
$83$	−17.3283			−1.90203			−0.951016	+	0.309140i	$0.899959\pi$
$84$	−4.24896	+	4.63920i	−0.463600	+	0.506179i
$85$	5.40354	+	2.86735i	0.586096	+	0.311008i
$86$	−4.45138	+	8.90951i	−0.480004	+	0.960737i
$87$	0.423939	+	1.58216i	0.0454510	+	0.169626i
$88$	−6.32646	−	13.3493i	−0.674403	−	1.42304i
$89$	−1.59534	+	0.921068i	−0.169105	+	0.0976330i	−0.582164	−	0.813071i	$-0.697794\pi$
$89$	−1.59534	+	0.921068i	−0.169105	+	0.0976330i	0.413059	+	0.910704i	$0.364460\pi$
$90$	−3.87139	−	3.19133i	−0.408080	−	0.336395i
$91$	−0.680021	+	0.583041i	−0.0712856	+	0.0611193i
$92$	6.64889	+	16.5357i	0.693194	+	1.72397i
$93$	5.38703	−	3.11020i	0.558609	−	0.322513i
$94$	−7.28085	−	6.45236i	−0.750962	−	0.665510i
$95$	4.12394	−	2.58169i	0.423107	−	0.264876i
$96$	−6.42239	+	1.99564i	−0.655482	+	0.203679i
$97$	−8.15823	−	8.15823i	−0.828343	−	0.828343i	0.158944	−	0.987288i	$-0.449191\pi$
$97$	−8.15823	−	8.15823i	−0.828343	−	0.828343i	−0.987288	+	0.158944i	$0.949191\pi$
$98$	8.07645	+	5.72459i	0.815845	+	0.578271i
$99$	5.85945	−	5.85945i	0.588897	−	0.588897i
$100$	7.54710	−	6.56058i	0.754710	−	0.656058i
$101$	12.8500	−	3.44315i	1.27862	−	0.342606i	0.445294	−	0.895384i	$-0.353099\pi$
$101$	12.8500	−	3.44315i	1.27862	−	0.342606i	0.833328	+	0.552778i	$0.186432\pi$
$102$	3.44234	+	3.05064i	0.340843	+	0.302058i
$103$	−3.91374	+	14.6063i	−0.385633	+	1.43920i	0.451535	+	0.892254i	$0.350877\pi$
$103$	−3.91374	+	14.6063i	−0.385633	+	1.43920i	−0.837167	+	0.546947i	$0.815790\pi$
$104$	−0.941993	+	0.172158i	−0.0923700	+	0.0168814i
$105$	3.76282	−	5.94231i	0.367214	−	0.579910i
$106$	−6.51046	−	9.85404i	−0.632352	−	0.957109i
$107$	2.84821	−	1.64441i	0.275347	−	0.158971i	−0.355968	−	0.934498i	$-0.615849\pi$
$107$	2.84821	−	1.64441i	0.275347	−	0.158971i	0.631315	+	0.775527i	$0.282516\pi$
$108$	−6.54873	−	8.72061i	−0.630152	−	0.839141i
$109$	0.998398	+	3.72607i	0.0956292	+	0.356893i	0.997114	−	0.0759175i	$-0.0241886\pi$
$109$	0.998398	+	3.72607i	0.0956292	+	0.356893i	−0.901485	+	0.432811i	$0.857522\pi$
$110$	9.59102	+	13.4461i	0.914468	+	1.28204i
$111$		−	10.3292i		−	0.980401i
$112$	4.37503	+	9.63634i	0.413401	+	0.910549i
$113$	−2.41198	−	2.41198i	−0.226900	−	0.226900i	0.584496	−	0.811396i	$-0.301292\pi$
$113$	−2.41198	−	2.41198i	−0.226900	−	0.226900i	−0.811396	+	0.584496i	$0.801292\pi$
$114$	3.47026	−	1.15792i	0.325019	−	0.108449i
$115$	−10.5732	−	16.8895i	−0.985960	−	1.57495i
$116$	2.72804	+	0.388031i	0.253292	+	0.0360278i
$117$	−0.268576	−	0.465188i	−0.0248299	−	0.0430066i
$118$	5.97399	+	1.22060i	0.549951	+	0.112365i
$119$	4.08823	−	5.97279i	0.374767	−	0.547525i
$120$	6.67530	−	3.46083i	0.609369	−	0.315929i
$121$	−14.0977	+	8.13931i	−1.28161	+	0.739937i
$122$	0.0343895	−	0.0388052i	0.00311348	−	0.00351326i
$123$	4.37985	−	7.58612i	0.394918	−	0.684018i
$124$	−1.25800	−	10.3885i	−0.112972	−	0.932912i
$125$	−7.01432	+	8.70628i	−0.627380	+	0.778713i
$126$	−4.26586	+	4.12838i	−0.380033	+	0.367785i
$127$	−10.0750	+	10.0750i	−0.894015	+	0.894015i	−0.994898	−	0.100883i	$-0.967833\pi$
$127$	−10.0750	+	10.0750i	−0.894015	+	0.894015i	0.100883	+	0.994898i	$0.467833\pi$
$128$	−1.14993	+	11.2551i	−0.101640	+	0.994821i
$129$	4.18634	−	7.25095i	0.368587	−	0.638411i
$130$	1.00282	−	0.374940i	0.0879535	−	0.0328844i
$131$	−9.59281	−	2.57039i	−0.838128	−	0.224576i	−0.185872	−	0.982574i	$-0.559511\pi$
$131$	−9.59281	−	2.57039i	−0.838128	−	0.224576i	−0.652256	+	0.757998i	$0.726177\pi$
$132$	4.63298	+	11.5222i	0.403249	+	1.00288i
$133$	−2.48828	−	5.19127i	−0.215761	−	0.450140i
$134$	−6.45897	−	9.77609i	−0.557970	−	0.844526i
$135$	8.92429	+	8.30818i	0.768081	+	0.715054i
$136$	6.99222	−	3.31372i	0.599578	−	0.284149i
$137$	−6.99909	+	1.87540i	−0.597972	+	0.160226i	−0.545094	−	0.838375i	$-0.683506\pi$
$137$	−6.99909	+	1.87540i	−0.597972	+	0.160226i	−0.0528780	+	0.998601i	$0.516839\pi$
$138$	−4.74223	−	14.2123i	−0.403686	−	1.20983i
$139$	8.63230	−	8.63230i	0.732183	−	0.732183i	−0.238869	−	0.971052i	$-0.576777\pi$
$139$	8.63230	−	8.63230i	0.732183	−	0.732183i	0.971052	+	0.238869i	$0.0767767\pi$
$140$	−6.71229	−	9.74398i	−0.567292	−	0.823516i
$141$	5.78299	+	5.78299i	0.487015	+	0.487015i
$142$	−7.11856	−	3.55658i	−0.597376	−	0.298461i
$143$	0.457662	+	1.70802i	0.0382716	+	0.142832i
$144$	−6.16286	+	1.51481i	−0.513572	+	0.126234i
$145$	−3.07878	+	0.110076i	−0.255679	+	0.00914133i
$146$	3.75447	−	18.3756i	0.310722	−	1.52077i
$147$	−6.48745	−	5.21257i	−0.535076	−	0.429925i
$148$	−15.9837	−	6.81609i	−1.31385	−	0.560279i
$149$	−3.48375	+	13.0015i	−0.285400	+	1.06513i	0.663147	+	0.748489i	$0.269220\pi$
$149$	−3.48375	+	13.0015i	−0.285400	+	1.06513i	−0.948547	+	0.316637i	$0.897446\pi$
$150$	−6.66517	+	5.12317i	−0.544209	+	0.418305i
$151$	−4.62842	−	2.67222i	−0.376656	−	0.217462i	0.299707	−	0.954031i	$-0.403111\pi$
$151$	−4.62842	−	2.67222i	−0.376656	−	0.217462i	−0.676362	+	0.736569i	$0.736445\pi$
$152$	0.498170	−	6.13409i	0.0404069	−	0.497540i
$153$	3.06911	+	3.06911i	0.248122	+	0.248122i
$154$	17.0819	−	9.49267i	1.37650	−	0.764941i
$155$	3.42991	+	11.1854i	0.275497	+	0.898437i
$156$	0.799176	−	0.0967771i	0.0639853	−	0.00774837i
$157$	1.08200	+	0.624693i	0.0863529	+	0.0498559i	0.542555	−	0.840020i	$-0.317457\pi$
$157$	1.08200	+	0.624693i	0.0863529	+	0.0498559i	−0.456202	+	0.889876i	$0.650790\pi$
$158$	0.883317	+	14.6420i	0.0702729	+	1.16485i
$159$	4.96432	+	8.59846i	0.393697	+	0.681902i
$160$	−0.950466	−	12.6134i	−0.0751409	−	0.997173i
$161$	−21.2607	+	10.1907i	−1.67558	+	0.803137i
$162$	1.34325	+	2.03311i	0.105536	+	0.159736i
$163$	16.3064	−	9.41453i	1.27722	−	0.737403i	0.300883	−	0.953661i	$-0.402719\pi$
$163$	16.3064	−	9.41453i	1.27722	−	0.737403i	0.976336	+	0.216258i	$0.0693852\pi$
$164$	−8.84882	−	11.7835i	−0.690977	−	0.920138i
$165$	−7.36749	−	11.7687i	−0.573558	−	0.916190i
$166$	10.9528	−	21.9221i	0.850099	−	1.70149i
$167$	−8.22686	+	8.22686i	−0.636614	+	0.636614i	−0.949719	−	0.313105i	$-0.898631\pi$
$167$	−8.22686	+	8.22686i	−0.636614	+	0.636614i	0.313105	+	0.949719i	$0.398631\pi$
$168$	−3.18342	−	8.30769i	−0.245606	−	0.640952i
$169$	−12.8854			−0.991183
$170$	−7.04292	+	5.02366i	−0.540167	+	0.385297i
$171$	3.33455	−	0.893489i	0.254999	−	0.0683268i
$172$	−8.45786	−	11.2629i	−0.644906	−	0.858788i
$173$	−8.91380	−	15.4392i	−0.677704	−	1.17382i	−0.975671	−	0.219241i	$-0.929642\pi$
$173$	−8.91380	−	15.4392i	−0.677704	−	1.17382i	0.297967	−	0.954576i	$-0.403692\pi$
$174$	−2.26956	−	0.463713i	−0.172055	−	0.0351540i
$175$	9.30579	+	9.40225i	0.703452	+	0.710743i
$176$	20.8871	+	0.434113i	1.57442	+	0.0327225i
$177$	−4.95120	−	1.32667i	−0.372155	−	0.0997187i
$178$	−0.156879	−	2.60045i	−0.0117586	−	0.194912i
$179$	−2.35237	−	8.77917i	−0.175824	−	0.656186i	−0.996410	−	0.0846617i	$-0.973019\pi$
$179$	−2.35237	−	8.77917i	−0.175824	−	0.656186i	0.820585	−	0.571524i	$-0.193648\pi$
$180$	6.48435	−	2.88055i	0.483315	−	0.214704i
$181$	−3.42220	−	3.42220i	−0.254370	−	0.254370i	0.568389	−	0.822760i	$-0.307567\pi$
$181$	−3.42220	−	3.42220i	−0.254370	−	0.254370i	−0.822760	+	0.568389i	$0.807567\pi$
$182$	−0.307784	−	1.22882i	−0.0228145	−	0.0910862i
$183$	−0.0308220	+	0.0308220i	−0.00227843	+	0.00227843i
$184$	−25.1220	−	2.04024i	−1.85202	−	0.150408i
$185$	18.9331	+	4.35447i	1.39199	+	0.320147i
$186$	0.529739	+	8.78102i	0.0388423	+	0.643856i
$187$	−7.14410	−	12.3739i	−0.522428	−	0.904872i
$188$	12.7649	−	5.13267i	0.930977	−	0.374338i
$189$	10.9524	−	9.39046i	0.796672	−	0.683055i
$190$	0.659483	+	6.84902i	0.0478439	+	0.496880i
$191$	3.11573	+	5.39660i	0.225446	+	0.390485i	0.956453	−	0.291885i	$-0.0942826\pi$
$191$	3.11573	+	5.39660i	0.225446	+	0.390485i	−0.731007	+	0.682370i	$0.760949\pi$
$192$	1.53472	−	9.38637i	0.110759	−	0.677403i
$193$	3.87953	−	1.03952i	0.279254	−	0.0748260i	−0.116473	−	0.993194i	$-0.537159\pi$
$193$	3.87953	−	1.03952i	0.279254	−	0.0748260i	0.395728	+	0.918368i	$0.370492\pi$
$194$	15.4776	−	5.16442i	1.11123	−	0.370784i
$195$	−0.860487	+	0.263860i	−0.0616208	+	0.0188954i
$196$	−12.3471	+	6.59919i	−0.881935	+	0.471371i
$197$		−	2.28106i		−	0.162519i	−0.996693	−	0.0812596i	$-0.974106\pi$
$197$		−	2.28106i		−	0.162519i	0.996693	−	0.0812596i	$-0.0258943\pi$
$198$	3.70921	+	11.1164i	0.263602	+	0.790008i
$199$	0.322024	+	0.185920i	0.0228276	+	0.0131795i	0.511370	−	0.859360i	$-0.329138\pi$
$199$	0.322024	+	0.185920i	0.0228276	+	0.0131795i	−0.488543	+	0.872540i	$0.662471\pi$
$200$	3.52950	+	13.6946i	0.249574	+	0.968356i
$201$	4.92506	+	8.53045i	0.347387	+	0.601692i
$202$	−3.76619	+	18.4329i	−0.264988	+	1.29693i
$203$	−0.279064	+	3.63449i	−0.0195864	+	0.255091i
$204$	−6.03518	+	2.42670i	−0.422547	+	0.169903i
$205$	12.0587	+	11.2262i	0.842218	+	0.784073i
$206$	−16.0047	−	14.1835i	−1.11510	−	0.988212i
$207$	−3.65926	−	13.6565i	−0.254336	−	0.949195i
$208$	0.377610	−	1.30053i	0.0261825	−	0.0901758i
$209$	−11.3643			−0.786087
$210$	5.13926	+	8.51632i	0.354643	+	0.587682i
$211$	7.33954	+	7.33954i	0.505274	+	0.505274i	0.913072	−	0.407798i	$-0.133703\pi$
$211$	7.33954	+	7.33954i	0.505274	+	0.505274i	−0.407798	+	0.913072i	$0.633703\pi$
$212$	16.5815	−	2.00795i	1.13882	−	0.137906i
$213$	5.79340	+	3.34482i	0.396957	+	0.229183i
$214$	0.280081	+	4.64266i	0.0191459	+	0.317366i
$215$	11.5260	+	10.7302i	0.786064	+	0.731795i
$216$	15.1717	−	2.77277i	1.03231	−	0.188663i
$217$	13.6064	−	2.54866i	0.923663	−	0.173014i
$218$	−5.34493	−	1.09207i	−0.362004	−	0.0739642i
$219$	−4.08074	+	15.2295i	−0.275751	+	1.02912i
$220$	−23.0730	+	3.63471i	−1.55558	+	0.245052i
$221$	−0.894638	+	0.239718i	−0.0601799	+	0.0161251i
$222$	13.0675	+	6.52877i	0.877030	+	0.438183i
$223$	−16.2456	+	16.2456i	−1.08788	+	1.08788i	−0.0921383	+	0.995746i	$0.529370\pi$
$223$	−16.2456	+	16.2456i	−1.08788	+	1.08788i	−0.995746	+	0.0921383i	$0.970630\pi$
$224$	−14.9563	−	0.556001i	−0.999310	−	0.0371493i
$225$	−6.56926	+	4.44694i	−0.437951	+	0.296462i
$226$	4.57595	−	1.52686i	0.304388	−	0.101565i
$227$	2.43700	+	1.40700i	0.161749	+	0.0933859i	0.578690	−	0.815548i	$-0.303564\pi$
$227$	2.43700	+	1.40700i	0.161749	+	0.0933859i	−0.416940	+	0.908934i	$0.636898\pi$
$228$	−0.728559	+	5.12212i	−0.0482500	+	0.339221i
$229$	−7.23657	−	1.93903i	−0.478206	−	0.128135i	0.0116613	−	0.999932i	$-0.496288\pi$
$229$	−7.23657	−	1.93903i	−0.478206	−	0.128135i	−0.489867	+	0.871797i	$0.662955\pi$
$230$	28.0500	−	2.70089i	1.84956	−	0.178091i
$231$	−14.8146	+	7.10091i	−0.974726	+	0.467206i
$232$	−2.21522	+	3.20599i	−0.145436	+	0.210484i
$233$	3.94140	+	1.05610i	0.258210	+	0.0691871i	0.385602	−	0.922665i	$-0.373994\pi$
$233$	3.94140	+	1.05610i	0.258210	+	0.0691871i	−0.127392	+	0.991852i	$0.540661\pi$
$234$	0.758270	−	0.0457447i	0.0495697	−	0.00299042i
$235$	−13.0380	+	8.16211i	−0.850504	+	0.532438i
$236$	−5.32017	+	6.78621i	−0.346314	+	0.441745i
$237$		−	12.3313i		−	0.801007i
$238$	4.97214	+	8.94726i	0.322296	+	0.579965i
$239$			14.9500i			0.967032i	0.875335	+	0.483516i	$0.160641\pi$
$239$			14.9500i			0.967032i	−0.875335	+	0.483516i	$0.839359\pi$
$240$	0.159043	+	10.6324i	0.0102662	+	0.686321i
$241$	−0.624178	−	0.360369i	−0.0402068	−	0.0232134i	0.479762	−	0.877399i	$-0.340723\pi$
$241$	−0.624178	−	0.360369i	−0.0402068	−	0.0232134i	−0.519969	+	0.854185i	$0.674056\pi$
$242$	−1.38631	−	22.9797i	−0.0891154	−	1.47719i
$243$	7.15505	+	12.3929i	0.458997	+	0.795006i
$244$	0.0273559	+	0.0680340i	0.00175128	+	0.00435543i
$245$	12.2894	−	9.69385i	0.785141	−	0.619317i
$246$	6.82885	+	10.3359i	0.435391	+	0.658995i
$247$	−0.190663	+	0.711563i	−0.0121316	+	0.0452757i
$248$	13.9376	+	4.97475i	0.885040	+	0.315897i
$249$	−10.3006	+	17.8412i	−0.652775	+	1.13064i
$250$	−6.58078	−	14.3768i	−0.416205	−	0.909271i
$251$	−3.19601	−	3.19601i	−0.201731	−	0.201731i	0.599011	−	0.800741i	$-0.295561\pi$
$251$	−3.19601	−	3.19601i	−0.201731	−	0.201731i	−0.800741	+	0.599011i	$0.795561\pi$
$252$	−2.52649	−	8.00618i	−0.159154	−	0.504342i
$253$			46.5422i			2.92609i
$254$	−6.37782	−	19.1141i	−0.400180	−	1.19933i
$255$	6.16428	−	3.85900i	0.386022	−	0.241660i
$256$	−13.5120	−	8.56882i	−0.844503	−	0.535551i
$257$	−4.56094	+	17.0217i	−0.284504	+	1.06178i	0.664698	+	0.747112i	$0.268560\pi$
$257$	−4.56094	+	17.0217i	−0.284504	+	1.06178i	−0.949201	+	0.314669i	$0.898106\pi$
$258$	6.52714	+	9.87927i	0.406362	+	0.615057i
$259$	7.63178	−	21.6829i	0.474216	−	1.34731i
$260$	−0.159519	+	1.50567i	−0.00989295	+	0.0933774i
$261$	−2.11142	−	0.565754i	−0.130694	−	0.0350193i
$262$	9.31515	−	10.5112i	0.575492	−	0.649386i
$263$	4.45741	+	16.6353i	0.274856	+	1.02578i	0.955938	+	0.293569i	$0.0948431\pi$
$263$	4.45741	+	16.6353i	0.274856	+	1.02578i	−0.681082	+	0.732207i	$0.738490\pi$
$264$	−17.5051	−	1.42165i	−1.07737	−	0.0874964i
$265$	−17.8535	+	5.47461i	−1.09673	+	0.336303i
$266$	8.14026	+	0.133326i	0.499112	+	0.00817473i
$267$			2.19007i			0.134030i
$268$	16.4503	−	1.99207i	1.00486	−	0.121685i
$269$	3.76940	−	1.01001i	0.229824	−	0.0615812i	−0.142069	−	0.989857i	$-0.545375\pi$
$269$	3.76940	−	1.01001i	0.229824	−	0.0615812i	0.371893	+	0.928276i	$0.378709\pi$
$270$	−16.1515	+	6.03879i	−0.982948	+	0.367509i
$271$	20.2439	−	11.6878i	1.22973	−	0.709983i	0.262754	−	0.964863i	$-0.415369\pi$
$271$	20.2439	−	11.6878i	1.22973	−	0.709983i	0.966973	+	0.254880i	$0.0820359\pi$
$272$	−0.227383	+	10.9404i	−0.0137871	+	0.663358i
$273$	0.196066	+	1.04673i	0.0118665	+	0.0633509i
$274$	2.05135	−	10.0400i	0.123927	−	0.606536i
$275$	24.6775	−	8.54309i	1.48811	−	0.515167i
$276$	20.9775	+	2.98379i	1.26270	+	0.179603i
$277$	22.8753	+	13.2070i	1.37444	+	0.793535i	0.991484	−	0.130231i	$-0.0415719\pi$
$277$	22.8753	+	13.2070i	1.37444	+	0.793535i	0.382959	+	0.923766i	$0.374905\pi$
$278$	5.46452	+	16.3770i	0.327740	+	0.982227i
$279$			8.30124i			0.496982i
$280$	16.5698	−	2.33285i	0.990234	−	0.139415i
$281$			26.4543i			1.57813i	0.614310	+	0.789065i	$0.289434\pi$
$281$			26.4543i			1.57813i	−0.614310	+	0.789065i	$0.710566\pi$
$282$	−10.9713	+	3.66081i	−0.653333	+	0.217998i
$283$	−22.3552	−	12.9068i	−1.32888	−	0.767230i	−0.343755	−	0.939059i	$-0.611699\pi$
$283$	−22.3552	−	12.9068i	−1.32888	−	0.767230i	−0.985127	+	0.171829i	$0.945032\pi$
$284$	8.99888	−	6.75770i	0.533985	−	0.400995i
$285$	−0.206677	−	5.78065i	−0.0122425	−	0.342416i
$286$	−2.45009	−	0.500600i	−0.144877	−	0.0296011i
$287$	14.7992	−	12.6886i	0.873569	−	0.748986i
$288$	1.97898	−	8.75412i	0.116612	−	0.515842i
$289$	−8.24111	+	4.75801i	−0.484771	+	0.279883i
$290$	1.80675	−	3.96455i	0.106096	−	0.232806i
$291$	−13.2493	+	3.55013i	−0.776685	+	0.208112i
$292$	20.8739	+	16.3645i	1.22155	+	0.957658i
$293$			0.188136i			0.0109910i	0.999985	+	0.00549551i	$0.00174928\pi$
$293$			0.188136i			0.0109910i	−0.999985	+	0.00549551i	$0.998251\pi$
$294$	10.6950	−	4.91257i	0.623743	−	0.286507i
$295$	4.51903	−	8.51613i	0.263108	−	0.495828i
$296$	18.7259	−	15.9128i	1.08842	−	0.924911i
$297$	−7.37110	−	27.5093i	−0.427715	−	1.59625i
$298$	−14.2463	−	12.6252i	−0.825265	−	0.731358i
$299$	2.91419	+	0.780854i	0.168532	+	0.0451579i
$300$	−2.26847	−	11.6703i	−0.130970	−	0.673787i
$301$	14.1453	−	12.1280i	0.815324	−	0.699047i
$302$	6.30613	−	4.16640i	0.362877	−	0.239749i
$303$	4.09347	−	15.2771i	0.235164	−	0.877644i
$304$	7.44538	+	4.50742i	0.427022	+	0.258518i
$305$	−0.0435022	−	0.0694894i	−0.00249093	−	0.00397895i
$306$	−5.82263	+	1.94284i	−0.332858	+	0.111065i
$307$			4.83012i			0.275670i	0.990455	+	0.137835i	$0.0440143\pi$
$307$			4.83012i			0.275670i	−0.990455	+	0.137835i	$0.955986\pi$
$308$	1.21225	+	27.6104i	0.0690745	+	1.57325i
$309$	12.7121	+	12.7121i	0.723167	+	0.723167i
$310$	−16.3187	−	2.73082i	−0.926839	−	0.155100i
$311$	−4.73723	+	8.20512i	−0.268624	+	0.465270i	−0.968507	−	0.248988i	$-0.919902\pi$
$311$	−4.73723	+	8.20512i	−0.268624	+	0.465270i	0.699883	+	0.714257i	$0.253235\pi$
$312$	−0.382704	+	1.07221i	−0.0216663	+	0.0607019i
$313$	7.93489	−	29.6134i	0.448506	−	1.67385i	−0.258002	−	0.966144i	$-0.583064\pi$
$313$	7.93489	−	29.6134i	0.448506	−	1.67385i	0.706509	−	0.707704i	$-0.250269\pi$
$314$	−1.47420	+	0.973990i	−0.0831940	+	0.0549654i
$315$	4.35690	+	8.31385i	0.245484	+	0.468432i
$316$	−19.0819	−	8.13730i	−1.07344	−	0.457759i
$317$	0.0727273	+	0.125967i	0.00408477	+	0.00707504i	0.868061	−	0.496458i	$-0.165366\pi$
$317$	0.0727273	+	0.125967i	0.00408477	+	0.00707504i	−0.863976	+	0.503533i	$0.832033\pi$
$318$	−14.0157	+	0.845537i	−0.785964	+	0.0474154i
$319$	6.23178	+	3.59792i	0.348913	+	0.201445i
$320$	16.5579	+	6.77010i	0.925618	+	0.378460i
$321$		−	3.91000i		−	0.218235i
$322$	0.546031	−	33.3382i	0.0304291	−	1.85786i
$323$		−	5.95250i		−	0.331206i
$324$	−3.42112	+	0.414284i	−0.190062	+	0.0230158i
$325$	−0.120892	−	1.68848i	−0.00670588	−	0.0936602i
$326$	1.60351	+	26.5800i	0.0888102	+	1.47213i
$327$	4.42984	+	1.18697i	0.244971	+	0.0656397i
$328$	20.5004	−	3.74664i	1.13195	−	0.206874i
$329$	7.86678	+	16.4124i	0.433710	+	0.904844i
$330$	19.5454	−	1.88199i	1.07594	−	0.103600i
$331$	−6.22769	−	1.66870i	−0.342305	−	0.0917202i	0.0835714	−	0.996502i	$-0.473367\pi$
$331$	−6.22769	−	1.66870i	−0.342305	−	0.0917202i	−0.425876	+	0.904782i	$0.640034\pi$
$332$	20.8108	+	27.7127i	1.14214	+	1.52093i
$333$	11.9377	+	6.89222i	0.654181	+	0.377691i
$334$	−5.20786	−	15.6078i	−0.284961	−	0.854020i
$335$	−17.7123	+	5.43131i	−0.967728	+	0.296744i
$336$	12.5222	+	1.22370i	0.683144	+	0.0667580i
$337$	−1.66073	+	1.66073i	−0.0904659	+	0.0904659i	−0.750892	−	0.660426i	$-0.770376\pi$
$337$	−1.66073	+	1.66073i	−0.0904659	+	0.0904659i	0.660426	+	0.750892i	$0.270376\pi$
$338$	8.14448	−	16.3013i	0.443001	−	0.886675i
$339$	−3.91714	+	1.04960i	−0.212750	+	0.0570062i
$340$	−1.90382	−	12.0853i	−0.103249	−	0.655419i
$341$	7.07278	−	26.3960i	0.383012	−	1.42942i
$342$	−0.977317	+	4.78330i	−0.0528473	+	0.258651i
$343$	−9.76704	−	15.7355i	−0.527371	−	0.849635i
$344$	19.5947	−	3.58111i	1.05648	−	0.193080i
$345$	−23.6745	+	0.846438i	−1.27459	+	0.0455707i
$346$	25.1663	−	1.51822i	1.35295	−	0.0816202i
$347$	−14.5413	−	8.39542i	−0.780617	−	0.450689i	0.0560318	−	0.998429i	$-0.482155\pi$
$347$	−14.5413	−	8.39542i	−0.780617	−	0.450689i	−0.836649	+	0.547739i	$0.815488\pi$
$348$	2.02117	−	2.57812i	0.108346	−	0.138202i
$349$	1.46526	+	1.46526i	0.0784338	+	0.0784338i	0.745235	−	0.666802i	$-0.232337\pi$
$349$	1.46526	+	1.46526i	0.0784338	+	0.0784338i	−0.666802	+	0.745235i	$0.732337\pi$
$350$	−17.7767	+	5.82989i	−0.950207	+	0.311621i
$351$	−1.84613			−0.0985391
$352$	−13.7513	+	26.1499i	−0.732948	+	1.39379i
$353$	−2.47556	−	9.23892i	−0.131761	−	0.491738i	0.868229	−	0.496163i	$-0.165258\pi$
$353$	−2.47556	−	9.23892i	−0.131761	−	0.491738i	−0.999990	+	0.00442496i	$0.998591\pi$
$354$	4.80789	−	5.42523i	0.255537	−	0.288348i
$355$	−8.57328	+	9.20905i	−0.455022	+	0.488766i
$356$	3.38899	+	1.44520i	0.179616	+	0.0765954i
$357$	−3.71937	−	7.75968i	−0.196850	−	0.410686i
$358$	12.5934	+	2.57307i	0.665583	+	0.135991i
$359$	−9.74169	−	16.8731i	−0.514147	−	0.890528i	−0.999865	−	0.0164129i	$-0.994775\pi$
$359$	−9.74169	−	16.8731i	−0.514147	−	0.890528i	0.485719	−	0.874115i	$-0.338558\pi$
$360$	−0.454377	+	10.0241i	−0.0239477	+	0.528316i
$361$	12.3544	+	7.13280i	0.650230	+	0.375410i
$362$	6.49251	−	2.16636i	0.341239	−	0.113861i
$363$			19.3533i			1.01578i
$364$	1.74913	+	0.387324i	0.0916791	+	0.0203013i
$365$	−26.1950	−	13.9002i	−1.37111	−	0.727570i
$366$	−0.0195113	−	0.0584746i	−0.00101987	−	0.00305652i
$367$	−9.82688	+	2.63310i	−0.512959	+	0.137447i	−0.506008	−	0.862529i	$-0.668879\pi$
$367$	−9.82688	+	2.63310i	−0.512959	+	0.137447i	−0.00695103	+	0.999976i	$0.502213\pi$
$368$	18.4600	−	30.4923i	0.962294	−	1.58952i
$369$	5.84498	+	10.1238i	0.304278	+	0.527024i
$370$	−17.4759	+	21.1999i	−0.908529	+	1.10213i
$371$	4.06802	+	21.7177i	0.211201	+	1.12753i
$372$	−11.4437	−	4.88006i	−0.593330	−	0.253019i
$373$	−2.39857	−	4.15444i	−0.124193	−	0.215109i	0.797224	−	0.603683i	$-0.206301\pi$
$373$	−2.39857	−	4.15444i	−0.124193	−	0.215109i	−0.921417	+	0.388575i	$0.872968\pi$
$374$	20.1699	−	1.21680i	1.04296	−	0.0629194i
$375$	4.79438	+	12.3973i	0.247580	+	0.640192i
$376$	−1.57498	+	19.3931i	−0.0812234	+	1.00012i
$377$	0.329832	−	0.329832i	0.0169872	−	0.0169872i
$378$	4.95718	+	19.7914i	0.254970	+	1.01796i
$379$	4.22575	+	4.22575i	0.217062	+	0.217062i	0.807259	−	0.590197i	$-0.200950\pi$
$379$	4.22575	+	4.22575i	0.217062	+	0.217062i	−0.590197	+	0.807259i	$0.700950\pi$
$380$	−9.08156	−	3.49476i	−0.465874	−	0.179277i
$381$	4.38424	+	16.3622i	0.224612	+	0.838262i
$382$	−8.79663	+	0.530680i	−0.450075	+	0.0271519i
$383$	−14.4649	−	3.87586i	−0.739122	−	0.198047i	−0.130434	−	0.991457i	$-0.541637\pi$
$383$	−14.4649	−	3.87586i	−0.739122	−	0.198047i	−0.608688	+	0.793410i	$0.708304\pi$
$384$	10.9047	+	7.87443i	0.556476	+	0.401840i
$385$	−6.77040	−	30.1482i	−0.345051	−	1.53649i
$386$	−1.13704	+	5.56505i	−0.0578740	+	0.283254i
$387$	5.58674	+	9.67652i	0.283990	+	0.491885i
$388$	−3.24943	+	22.8450i	−0.164965	+	1.15978i
$389$	12.8771	−	3.45041i	0.652895	−	0.174943i	0.0828575	−	0.996561i	$-0.473595\pi$
$389$	12.8771	−	3.45041i	0.652895	−	0.174943i	0.570037	+	0.821619i	$0.306929\pi$
$390$	0.210080	−	1.25538i	0.0106378	−	0.0635688i
$391$	−24.3783			−1.23286
$392$	−0.544413	−	19.7915i	−0.0274970	−	0.999622i
$393$	−8.34879	+	8.34879i	−0.421141	+	0.421141i
$394$	2.88578	+	1.44180i	0.145384	+	0.0726366i
$395$	22.6030	+	5.19852i	1.13728	+	0.261566i
$396$	−16.4079	−	2.33382i	−0.824527	−	0.117279i
$397$	24.2150	−	13.9805i	1.21532	−	0.701663i	0.251403	−	0.967883i	$-0.419108\pi$
$397$	24.2150	−	13.9805i	1.21532	−	0.701663i	0.963912	+	0.266220i	$0.0857748\pi$
$398$	−0.438750	+	0.289878i	−0.0219926	+	0.0145303i
$399$	−6.82404	−	0.523964i	−0.341629	−	0.0262310i
$400$	−19.5560	−	4.19079i	−0.977800	−	0.209540i
$401$	9.12337	+	15.8021i	0.455599	+	0.789121i	0.998722	−	0.0505317i	$-0.0160916\pi$
$401$	9.12337	+	15.8021i	0.455599	+	0.789121i	−0.543123	+	0.839653i	$0.682758\pi$
$402$	−13.9049	+	0.838849i	−0.693513	+	0.0418380i
$403$	−1.53409	−	0.885706i	−0.0764184	−	0.0441202i
$404$	−20.9390	−	16.4155i	−1.04175	−	0.816703i
$405$	3.68358	−	1.12953i	0.183039	−	0.0561270i
$406$	−4.42161	−	2.65030i	−0.219441	−	0.131532i
$407$	−32.0867	−	32.0867i	−1.59048	−	1.59048i
$408$	0.744642	−	9.16896i	0.0368653	−	0.453931i
$409$	−2.11431	−	1.22070i	−0.104546	−	0.0603597i	0.446815	−	0.894626i	$-0.352558\pi$
$409$	−2.11431	−	1.22070i	−0.104546	−	0.0603597i	−0.551361	+	0.834267i	$0.685891\pi$
$410$	−21.8243	+	8.15976i	−1.07783	+	0.402982i
$411$	−2.22962	+	8.32104i	−0.109979	+	0.410447i
$412$	28.0597	−	11.2826i	1.38240	−	0.555853i
$413$	−9.41330	−	6.44317i	−0.463198	−	0.317048i
$414$	19.5898	+	4.00257i	0.962788	+	0.196716i
$415$	−28.3600	−	26.4021i	−1.39214	−	1.29603i
$416$	1.40663	+	1.29975i	0.0689659	+	0.0637253i
$417$	−3.75642	−	14.0192i	−0.183953	−	0.686521i
$418$	7.18307	−	14.3770i	0.351336	−	0.703204i
$419$	−18.1866	−	18.1866i	−0.888473	−	0.888473i	0.105903	−	0.994376i	$-0.466227\pi$
$419$	−18.1866	−	18.1866i	−0.888473	−	0.888473i	−0.994376	+	0.105903i	$0.966227\pi$
$420$	−14.0224	+	1.11877i	−0.684223	+	0.0545902i
$421$	27.2003	−	27.2003i	1.32566	−	1.32566i	0.416546	−	0.909115i	$-0.363241\pi$
$421$	27.2003	−	27.2003i	1.32566	−	1.32566i	0.909115	−	0.416546i	$-0.136759\pi$
$422$	−13.9244	+	4.64616i	−0.677828	+	0.226171i
$423$	−10.5423	+	2.82480i	−0.512584	+	0.137346i
$424$	−7.94040	+	22.2464i	−0.385620	+	1.08038i
$425$	4.47476	+	12.9258i	0.217058	+	0.626993i
$426$	−7.89338	+	5.21508i	−0.382436	+	0.252671i
$427$	−0.0874742	+	0.0419281i	−0.00423317	+	0.00202904i
$428$	−6.05048	−	2.58016i	−0.292461	−	0.124717i
$429$	2.03062	+	0.544103i	0.0980392	+	0.0262695i
$430$	−20.8601	+	7.79925i	−1.00596	+	0.376113i
$431$	−6.85811	+	11.8786i	−0.330343	+	0.572172i	−0.982579	−	0.185845i	$-0.940498\pi$
$431$	−6.85811	+	11.8786i	−0.330343	+	0.572172i	0.652236	+	0.758016i	$0.273831\pi$
$432$	−6.08179	+	20.9464i	−0.292610	+	1.00778i
$433$	13.7552	−	13.7552i	0.661032	−	0.661032i	−0.294591	−	0.955623i	$-0.595184\pi$
$433$	13.7552	−	13.7552i	0.661032	−	0.661032i	0.955623	+	0.294591i	$0.0951836\pi$
$434$	−5.37590	+	18.8244i	−0.258052	+	0.903602i
$435$	−1.71681	+	3.23533i	−0.0823146	+	0.155122i
$436$	4.75996	−	6.07162i	0.227961	−	0.290778i
$437$	−9.69480	+	16.7919i	−0.463765	+	0.803265i
$438$	−16.6876	−	14.7887i	−0.797365	−	0.706633i
$439$	−15.7697	+	9.10464i	−0.752647	+	0.434541i	−0.826650	−	0.562717i	$-0.809756\pi$
$439$	−15.7697	+	9.10464i	−0.752647	+	0.434541i	0.0740025	+	0.997258i	$0.476423\pi$
$440$	9.98547	−	31.4871i	0.476039	−	1.50109i
$441$	10.3531	−	4.01958i	0.493005	−	0.191409i
$442$	0.262208	−	1.28333i	0.0124720	−	0.0610417i
$443$	8.55684	+	14.8209i	0.406548	+	0.704161i	0.994500	−	0.104734i	$-0.0333992\pi$
$443$	8.55684	+	14.8209i	0.406548	+	0.704161i	−0.587953	+	0.808895i	$0.700066\pi$
$444$	−16.5191	+	12.4050i	−0.783964	+	0.588717i
$445$	−4.01434	−	0.923268i	−0.190298	−	0.0437671i
$446$	−10.2840	−	30.8207i	−0.486960	−	1.45940i
$447$	11.3155	+	11.3155i	0.535203	+	0.535203i
$448$	10.1568	−	18.5698i	0.479866	−	0.877342i
$449$		−	13.5321i		−	0.638618i	−0.947651	−	0.319309i	$-0.896549\pi$
$449$		−	13.5321i		−	0.638618i	0.947651	−	0.319309i	$-0.103451\pi$
$450$	−1.47359	−	11.1216i	−0.0694655	−	0.524276i
$451$	−9.96002	−	37.1713i	−0.468999	−	1.75033i
$452$	−0.960694	+	6.75414i	−0.0451873	+	0.317688i
$453$	−5.50262	+	3.17694i	−0.258536	+	0.149266i
$454$	−3.32036	+	2.19373i	−0.155832	+	0.102957i
$455$	−2.00128	−	0.0818855i	−0.0938215	−	0.00383885i
$456$	−6.01951	−	4.15925i	−0.281889	−	0.194775i
$457$	3.80171	−	14.1882i	0.177837	−	0.663695i	−0.818214	−	0.574913i	$-0.805036\pi$
$457$	3.80171	−	14.1882i	0.177837	−	0.663695i	0.996051	−	0.0887822i	$-0.0282975\pi$
$458$	7.02710	−	7.92939i	0.328355	−	0.370516i
$459$	14.4090	−	3.86089i	0.672556	−	0.180211i
$460$	−14.3127	+	37.1932i	−0.667332	+	1.73414i
$461$	−3.49391	+	3.49391i	−0.162727	+	0.162727i	−0.783774	−	0.621046i	$-0.786708\pi$
$461$	−3.49391	+	3.49391i	−0.162727	+	0.162727i	0.621046	+	0.783774i	$0.286708\pi$
$462$	0.380478	−	23.2302i	0.0177014	−	1.08077i
$463$	3.01354	+	3.01354i	0.140051	+	0.140051i	0.773656	−	0.633605i	$-0.218426\pi$
$463$	3.01354	+	3.01354i	0.140051	+	0.140051i	−0.633605	+	0.773656i	$0.718426\pi$
$464$	−2.65573	−	4.82890i	−0.123289	−	0.224176i
$465$	13.5554	+	3.11763i	0.628615	+	0.144577i
$466$	−3.82732	+	4.31875i	−0.177297	+	0.200062i
$467$	18.9085	−	10.9168i	0.874982	−	0.505171i	0.00598173	−	0.999982i	$-0.498096\pi$
$467$	18.9085	−	10.9168i	0.874982	−	0.505171i	0.869001	+	0.494811i	$0.164763\pi$
$468$	−0.421409	+	0.988203i	−0.0194796	+	0.0456797i
$469$	4.03584	+	21.5459i	0.186358	+	0.994899i
$470$	−2.08498	−	21.6534i	−0.0961728	−	0.998798i
$471$	1.28636	−	0.742682i	0.0592725	−	0.0342210i
$472$	−5.22252	−	11.0199i	−0.240386	−	0.507234i
$473$	−9.51997	−	35.5290i	−0.437729	−	1.63363i
$474$	15.6004	+	7.79429i	0.716551	+	0.358004i
$475$	10.6829	+	2.05812i	0.490165	+	0.0944328i
$476$	−14.4620	+	0.634963i	−0.662863	+	0.0291035i
$477$	−13.2499			−0.606673
$478$	−18.9132	−	9.44944i	−0.865071	−	0.432208i
$479$	2.99347	−	5.18484i	0.136775	−	0.236901i	−0.789499	−	0.613752i	$-0.789660\pi$
$479$	2.99347	−	5.18484i	0.136775	−	0.236901i	0.926274	+	0.376850i	$0.122993\pi$
$480$	−13.5517	−	6.51926i	−0.618546	−	0.297562i
$481$	−2.54740	+	1.47074i	−0.116151	+	0.0670600i
$482$	0.850429	−	0.561870i	0.0387360	−	0.0255925i
$483$	−2.14588	+	27.9476i	−0.0976409	+	1.27166i
$484$	29.9479	+	12.7710i	1.36127	+	0.580499i
$485$	−0.921794	−	25.7821i	−0.0418565	−	1.17071i
$486$	−20.2008	+	1.21867i	−0.916327	+	0.0552799i
$487$	13.4385	−	3.60084i	0.608958	−	0.163170i	0.0588549	−	0.998267i	$-0.481255\pi$
$487$	13.4385	−	3.60084i	0.608958	−	0.163170i	0.550103	+	0.835097i	$0.314588\pi$
$488$	−0.103361	−	0.00839428i	−0.00467893	−	0.000379991i
$489$		−	22.3854i		−	1.01230i
$490$	4.49593	+	21.6746i	0.203106	+	0.979157i
$491$	−20.7805	+	20.7805i	−0.937809	+	0.937809i	−0.998176	−	0.0603676i	$-0.980773\pi$
$491$	−20.7805	+	20.7805i	−0.937809	+	0.937809i	0.0603676	+	0.998176i	$0.480773\pi$
$492$	−17.3923	+	2.10614i	−0.784107	+	0.0949523i
$493$	−1.88455	+	3.26413i	−0.0848757	+	0.147009i
$494$	−0.779688	−	0.690967i	−0.0350798	−	0.0310881i
$495$	18.5174	−	0.662055i	0.832294	−	0.0297572i
$496$	−15.1031	+	14.4881i	−0.678151	+	0.650536i
$497$	9.69009	+	11.3019i	0.434660	+	0.506960i
$498$	−16.0602	−	24.3083i	−0.719676	−	1.08928i
$499$	2.79984	+	0.750216i	0.125338	+	0.0335843i	0.320943	−	0.947099i	$-0.396000\pi$
$499$	2.79984	+	0.750216i	0.125338	+	0.0335843i	−0.195605	+	0.980683i	$0.562667\pi$
$500$	22.3477	+	0.761818i	0.999419	+	0.0340695i
$501$	3.57999	+	13.3607i	0.159942	+	0.596912i
$502$	6.06340	−	2.02318i	0.270623	−	0.0902988i
$503$	12.8172	+	12.8172i	0.571492	+	0.571492i	0.932545	−	0.361053i	$-0.117583\pi$
$503$	12.8172	+	12.8172i	0.571492	+	0.571492i	−0.361053	+	0.932545i	$0.617583\pi$
$504$	11.7256	+	1.86421i	0.522298	+	0.0830385i
$505$	26.2767	+	13.9436i	1.16930	+	0.620481i
$506$	−58.8807	−	29.4180i	−2.61757	−	1.30779i
$507$	−7.65956	+	13.2667i	−0.340173	+	0.589197i
$508$	28.2126	+	4.01289i	1.25173	+	0.178043i
$509$	−2.27292	+	8.48264i	−0.100745	+	0.375986i	−0.997828	−	0.0658766i	$-0.979016\pi$
$509$	−2.27292	+	8.48264i	−0.100745	+	0.375986i	0.897083	+	0.441863i	$0.145682\pi$
$510$	0.985765	+	10.2376i	0.0436504	+	0.453329i
$511$	−19.8187	+	28.9546i	−0.876729	+	1.28088i
$512$	19.3810	−	11.6780i	0.856528	−	0.516100i
$513$	3.07082	−	11.4604i	0.135580	−	0.505991i
$514$	−18.6513	−	16.5290i	−0.822674	−	0.729061i
$515$	−28.6600	+	17.9419i	−1.26291	+	0.790614i
$516$	−16.6239	+	2.01309i	−0.731827	+	0.0886214i
$517$	35.9287			1.58014
$518$	22.6072	+	23.3601i	0.993305	+	1.02638i
$519$	−21.1948			−0.930349
$520$	−1.80399	−	1.15350i	−0.0791104	−	0.0505842i
$521$	7.23040	−	12.5234i	0.316770	−	0.548661i	−0.663042	−	0.748582i	$-0.730735\pi$
$521$	7.23040	−	12.5234i	0.316770	−	0.548661i	0.979812	+	0.199921i	$0.0640684\pi$
$522$	2.05031	−	2.31357i	0.0897395	−	0.101262i
$523$	22.2982	−	12.8739i	0.975034	−	0.562936i	0.0742670	−	0.997238i	$-0.476338\pi$
$523$	22.2982	−	12.8739i	0.975034	−	0.562936i	0.900767	+	0.434302i	$0.143005\pi$
$524$	7.40994	+	18.4285i	0.323705	+	0.805052i
$525$	15.2122	−	3.99216i	0.663916	−	0.174232i
$526$	−23.8628	−	4.87561i	−1.04047	−	0.212587i
$527$	13.8259	+	3.70463i	0.602265	+	0.161376i
$528$	12.8630	−	21.2472i	0.559791	−	0.924666i
$529$	48.8520	+	28.2047i	2.12400	+	1.22629i
$530$	4.35877	−	26.0469i	0.189333	−	1.13141i
$531$	4.83700	−	4.83700i	0.209908	−	0.209908i
$532$	−5.31390	+	10.2140i	−0.230387	+	0.442833i
$533$	−2.49454			−0.108050
$534$	−2.77066	−	1.38428i	−0.119898	−	0.0599037i
$535$	7.16693	+	1.64834i	0.309853	+	0.0712640i
$536$	−7.87760	+	22.0704i	−0.340260	+	0.953298i
$537$	−10.4373	−	2.79668i	−0.450404	−	0.120685i
$538$	−1.10477	+	5.40707i	−0.0476299	+	0.233116i
$539$	−36.3451	+	3.96031i	−1.56550	+	0.170583i
$540$	2.56921	−	24.2502i	0.110561	−	1.04356i
$541$	1.82694	−	6.81823i	0.0785463	−	0.293139i	−0.915468	−	0.402391i	$-0.868179\pi$
$541$	1.82694	−	6.81823i	0.0785463	−	0.293139i	0.994014	+	0.109253i	$0.0348458\pi$
$542$	1.99070	+	32.9981i	0.0855078	+	1.41739i
$543$	−5.55777	+	1.48920i	−0.238507	+	0.0639077i
$544$	−13.6970	−	7.20277i	−0.587254	−	0.308816i
$545$	−4.04317	+	7.61938i	−0.173190	+	0.326378i
$546$	−1.44815	−	0.413564i	−0.0619750	−	0.0176989i
$547$	−13.3169			−0.569388			−0.284694	−	0.958618i	$-0.591892\pi$
$547$	−13.3169			−0.569388			−0.284694	+	0.958618i	$0.591892\pi$
$548$	11.4050	+	8.94114i	0.487196	+	0.381946i
$549$	−0.0150555	−	0.0561879i	−0.000642554	−	0.00239804i
$550$	−4.79009	+	36.6195i	−0.204250	+	1.56146i
$551$	1.49890	+	2.59617i	0.0638554	+	0.110601i
$552$	−17.0341	+	24.6527i	−0.725018	+	1.04929i
$553$	9.11110	−	25.8858i	0.387444	−	1.10078i
$554$	−31.1671	+	20.5918i	−1.32416	+	0.874861i
$555$	15.7379	−	16.9050i	0.668035	−	0.717576i
$556$	−24.1725	−	3.43825i	−1.02514	−	0.145814i
$557$	5.05622	−	8.75764i	0.214239	−	0.371073i	−0.738798	−	0.673927i	$-0.764606\pi$
$557$	5.05622	−	8.75764i	0.214239	−	0.371073i	0.953037	+	0.302854i	$0.0979395\pi$
$558$	−10.5019	−	5.24698i	−0.444582	−	0.222122i
$559$	−2.38432			−0.100846
$560$	−7.52199	+	22.4370i	−0.317862	+	0.948137i
$561$	−16.9869			−0.717187
$562$	−33.4674	−	16.7210i	−1.41174	−	0.705332i
$563$	10.9168	−	18.9085i	0.460088	−	0.796897i	−0.538876	−	0.842385i	$-0.681151\pi$
$563$	10.9168	−	18.9085i	0.460088	−	0.796897i	0.998965	+	0.0454883i	$0.0144844\pi$
$564$	2.30337	−	16.1938i	0.0969892	−	0.681880i
$565$	−0.272529	−	7.62249i	−0.0114654	−	0.320681i
$566$	30.4586	−	20.1237i	1.28027	−	0.845861i
$567$	−0.839323	−	4.48085i	−0.0352483	−	0.188178i
$568$	2.86125	+	15.6559i	0.120055	+	0.656905i
$569$	6.69251	+	11.5918i	0.280564	+	0.485952i	0.971524	−	0.236942i	$-0.0761450\pi$
$569$	6.69251	+	11.5918i	0.280564	+	0.485952i	−0.690959	+	0.722894i	$0.742812\pi$
$570$	7.44375	+	3.39232i	0.311784	+	0.142089i
$571$	4.49896	+	16.7903i	0.188276	+	0.702654i	0.993906	+	0.110235i	$0.0351603\pi$
$571$	4.49896	+	16.7903i	0.188276	+	0.702654i	−0.805630	+	0.592419i	$0.798173\pi$
$572$	2.18194	−	2.78320i	0.0912317	−	0.116372i
$573$	7.40843			0.309492
$574$	6.69826	+	26.7426i	0.279580	+	1.11622i
$575$	8.42895	−	43.7515i	0.351511	−	1.82456i
$576$	9.82401	+	8.03684i	0.409334	+	0.334869i
$577$	12.2127	−	3.27239i	0.508422	−	0.136231i	0.00451610	−	0.999990i	$-0.498562\pi$
$577$	12.2127	−	3.27239i	0.508422	−	0.136231i	0.503906	+	0.863759i	$0.331896\pi$
$578$	−0.810397	−	13.4333i	−0.0337081	−	0.558750i
$579$	1.23586	−	4.61228i	0.0513604	−	0.191680i
$580$	3.87356	+	4.79160i	0.160841	+	0.198960i
$581$	−34.8051	+	29.8414i	−1.44396	+	1.23803i
$582$	3.88320	−	19.0056i	0.160964	−	0.787808i
$583$	42.1317	+	11.2891i	1.74492	+	0.467549i
$584$	−33.8965	+	16.0641i	−1.40265	+	0.664737i
$585$	0.269218	−	1.17055i	0.0111308	−	0.0483963i
$586$	−0.238011	−	0.118915i	−0.00983216	−	0.00491235i
$587$	−27.4813			−1.13428			−0.567138	−	0.823623i	$-0.691949\pi$
$587$	−27.4813			−1.13428			−0.567138	+	0.823623i	$0.691949\pi$
$588$	−0.545072	+	16.6353i	−0.0224784	+	0.686030i
$589$	8.05008	−	8.05008i	0.331698	−	0.331698i
$590$	7.91743	+	11.0998i	0.325956	+	0.456973i
$591$	−2.34858	−	1.35595i	−0.0966075	−	0.0557764i
$592$	8.29519	+	33.7482i	0.340930	+	1.38704i
$593$	13.1880	+	3.53372i	0.541568	+	0.145113i	0.519225	−	0.854638i	$-0.326221\pi$
$593$	13.1880	+	3.53372i	0.541568	+	0.145113i	0.0223429	+	0.999750i	$0.492887\pi$
$594$	39.4612	+	8.06266i	1.61911	+	0.330815i
$595$	15.7912	−	3.54625i	0.647378	−	0.145382i
$596$	24.9768	−	10.0430i	1.02309	−	0.411377i
$597$	0.382846	−	0.221036i	0.0156688	−	0.00904641i
$598$	−2.82983	+	3.19319i	−0.115721	+	0.130579i
$599$	18.2328	−	31.5801i	0.744970	−	1.29033i	−0.205238	−	0.978712i	$-0.565797\pi$
$599$	18.2328	−	31.5801i	0.744970	−	1.29033i	0.950209	−	0.311615i	$-0.100870\pi$
$600$	16.1980	+	4.50664i	0.661281	+	0.183983i
$601$	32.7250			1.33488			0.667440	−	0.744664i	$-0.267390\pi$
$601$	32.7250			1.33488			0.667440	+	0.744664i	$0.267390\pi$
$602$	6.40232	+	25.5611i	0.260939	+	1.04179i
$603$	−13.1451			−0.535312
$604$	1.28499	+	10.6114i	0.0522857	+	0.431770i
$605$	−35.4740	−	8.15875i	−1.44222	−	0.331700i
$606$	16.7397	+	14.8349i	0.680003	+	0.602625i
$607$	−1.23113	+	4.59463i	−0.0499700	+	0.186490i	−0.986400	−	0.164365i	$-0.947442\pi$
$607$	−1.23113	+	4.59463i	−0.0499700	+	0.186490i	0.936430	+	0.350855i	$0.114109\pi$
$608$	−10.4084	+	6.57016i	−0.422115	+	0.266455i
$609$	3.57617	+	2.44780i	0.144914	+	0.0991899i
$610$	0.115408	−	0.0111124i	0.00467272	−	0.000449930i
$611$	0.602787	−	2.24963i	0.0243862	−	0.0910104i
$612$	1.22243	−	8.59424i	0.0494137	−	0.347402i
$613$	−13.0080	+	22.5305i	−0.525387	+	0.909997i	0.474176	+	0.880430i	$0.342746\pi$
$613$	−13.0080	+	22.5305i	−0.525387	+	0.909997i	−0.999563	+	0.0295666i	$0.990587\pi$
$614$	−6.11060	−	3.05298i	−0.246604	−	0.123208i
$615$	18.7266	−	5.74234i	0.755131	−	0.231553i
$616$	−35.6962	−	15.9181i	−1.43824	−	0.641358i
$617$	−12.1665	−	12.1665i	−0.489805	−	0.489805i	0.418440	−	0.908245i	$-0.362577\pi$
$617$	−12.1665	−	12.1665i	−0.489805	−	0.489805i	−0.908245	+	0.418440i	$0.862577\pi$
$618$	−24.1171	+	8.04716i	−0.970132	+	0.323704i
$619$	−9.53814	−	35.5968i	−0.383370	−	1.43076i	−0.840720	−	0.541470i	$-0.817868\pi$
$619$	−9.53814	−	35.5968i	−0.383370	−	1.43076i	0.457350	−	0.889287i	$-0.348799\pi$
$620$	13.7693	−	18.9187i	0.552990	−	0.759795i
$621$	−46.9359	−	12.5764i	−1.88347	−	0.504675i
$622$	−7.38605	−	11.1793i	−0.296154	−	0.448249i
$623$	−1.61815	+	4.59737i	−0.0648298	+	0.184190i
$624$	−1.11456	−	1.16187i	−0.0446181	−	0.0465121i
$625$	−24.7450	+	3.56164i	−0.989800	+	0.142466i
$626$	32.4486	+	28.7562i	1.29691	+	1.14933i
$627$	−6.75539	+	11.7007i	−0.269784	+	0.467280i
$628$	−0.300397	−	2.48065i	−0.0119871	−	0.0989886i
$629$	16.8066	−	16.8066i	0.670123	−	0.670123i
$630$	−13.2717	+	0.256985i	−0.528759	+	0.0102385i
$631$		−	11.4540i		−	0.455976i	−0.973664	−	0.227988i	$-0.926785\pi$
$631$		−	11.4540i		−	0.455976i	0.973664	−	0.227988i	$-0.0732147\pi$
$632$	22.3557	−	18.9973i	0.889261	−	0.755671i
$633$	11.9197	−	3.19386i	0.473764	−	0.126945i
$634$	−0.205331	+	0.0123871i	−0.00815472	+	0.000491955i
$635$	−31.8397	+	1.13837i	−1.26352	+	0.0451749i
$636$	7.78926	−	18.2658i	0.308864	−	0.724286i
$637$	−0.361803	+	2.34215i	−0.0143352	+	0.0927993i
$638$	−8.49068	+	5.60970i	−0.336149	+	0.222090i
$639$	−7.73138	+	4.46372i	−0.305849	+	0.176582i
$640$	−19.0307	+	16.6683i	−0.752254	+	0.658873i
$641$	16.6081	−	28.7660i	0.655979	−	1.13619i	−0.325668	−	0.945484i	$-0.605589\pi$
$641$	16.6081	−	28.7660i	0.655979	−	1.13619i	0.981647	−	0.190705i	$-0.0610774\pi$
$642$	4.94656	+	2.47140i	0.195225	+	0.0975385i
$643$	−5.80713			−0.229011			−0.114505	−	0.993423i	$-0.536528\pi$
$643$	−5.80713			−0.229011			−0.114505	+	0.993423i	$0.536528\pi$
$644$	41.8311	+	21.7629i	1.64838	+	0.857579i
$645$	17.8993	−	5.48863i	0.704783	−	0.216115i
$646$	7.53052	+	3.76240i	0.296284	+	0.148030i
$647$	9.28270	+	34.6435i	0.364941	+	1.36198i	0.867501	+	0.497435i	$0.165725\pi$
$647$	9.28270	+	34.6435i	0.364941	+	1.36198i	−0.502561	+	0.864542i	$0.667609\pi$
$648$	1.63828	−	4.58993i	0.0643578	−	0.180309i
$649$	−19.5017	+	11.2593i	−0.765509	+	0.441967i
$650$	2.21252	+	0.914302i	0.0867821	+	0.0358619i
$651$	5.46407	−	15.5241i	0.214154	−	0.608438i
$652$	−34.6400	−	14.7719i	−1.35661	−	0.578511i
$653$	−43.5436	+	25.1399i	−1.70399	+	0.983800i	−0.762360	+	0.647153i	$0.775959\pi$
$653$	−43.5436	+	25.1399i	−1.70399	+	0.983800i	−0.941631	+	0.336646i	$0.890707\pi$
$654$	−4.30162	+	4.85395i	−0.168207	+	0.189804i
$655$	−11.7835	−	18.8227i	−0.460419	−	0.735464i
$656$	−8.21787	+	28.3033i	−0.320854	+	1.10506i
$657$	−14.8783	−	14.8783i	−0.580456	−	0.580456i
$658$	−25.7357	−	0.421514i	−1.00328	−	0.0164323i
$659$	−2.76732	+	2.76732i	−0.107799	+	0.107799i	−0.758949	−	0.651150i	$-0.774287\pi$
$659$	−2.76732	+	2.76732i	−0.107799	+	0.107799i	0.651150	+	0.758949i	$0.274287\pi$
$660$	−9.97315	+	25.9164i	−0.388204	+	1.00880i
$661$	−47.1359	+	12.6300i	−1.83337	+	0.491251i	−0.998268	−	0.0588369i	$-0.981261\pi$
$661$	−47.1359	+	12.6300i	−1.83337	+	0.491251i	−0.835107	+	0.550088i	$0.814594\pi$
$662$	6.04743	−	6.82392i	0.235040	−	0.265219i
$663$	−0.284994	+	1.06361i	−0.0110683	+	0.0413073i
$664$	−48.2134	+	8.81142i	−1.87104	+	0.341950i
$665$	3.83722	−	12.2874i	0.148801	−	0.476484i
$666$	−16.2648	+	10.7460i	−0.630250	+	0.416400i
$667$	10.6325	−	6.13871i	0.411694	−	0.237692i
$668$	23.0372	+	3.27676i	0.891336	+	0.126782i
$669$	7.06941	+	26.3834i	0.273319	+	1.02004i
$670$	4.32430	−	25.8409i	0.167062	−	0.998321i
$671$			0.191492i			0.00739246i
$672$	−9.46305	+	15.0684i	−0.365045	+	0.581278i
$673$	32.1014	+	32.1014i	1.23742	+	1.23742i	0.961053	+	0.276364i	$0.0891296\pi$
$673$	32.1014	+	32.1014i	1.23742	+	1.23742i	0.276364	+	0.961053i	$0.410870\pi$
$674$	−1.05130	−	3.15070i	−0.0404944	−	0.121361i
$675$	1.94709	+	27.1947i	0.0749434	+	1.04673i
$676$	15.4750	+	20.6072i	0.595191	+	0.792585i
$677$	−2.16028	−	3.74171i	−0.0830262	−	0.143806i	0.821522	−	0.570176i	$-0.193125\pi$
$677$	−2.16028	−	3.74171i	−0.0830262	−	0.143806i	−0.904548	+	0.426371i	$0.859792\pi$
$678$	1.14807	−	5.61901i	0.0440913	−	0.215797i
$679$	−30.4357	−	2.33692i	−1.16802	−	0.0896827i
$680$	16.4925	+	5.23027i	0.632460	+	0.200572i
$681$	2.89729	−	1.67275i	0.111024	−	0.0640999i
$682$	28.9231	+	25.6319i	1.10752	+	0.981497i
$683$	10.8645	−	18.8179i	0.415719	−	0.720047i	−0.579784	−	0.814770i	$-0.696863\pi$
$683$	10.8645	−	18.8179i	0.415719	−	0.720047i	0.995504	+	0.0947229i	$0.0301965\pi$
$684$	−5.43363	−	4.25979i	−0.207760	−	0.162877i
$685$	−14.3123	−	7.59473i	−0.546845	−	0.290180i
$686$	26.0805	−	2.41037i	0.995756	−	0.0920284i
$687$	−6.29811	+	6.29811i	−0.240288	+	0.240288i
$688$	−7.85479	+	27.0528i	−0.299461	+	1.03138i
$689$	1.41371	−	2.44862i	0.0538581	−	0.0932850i
$690$	13.8931	−	30.4856i	0.528902	−	1.16057i
$691$	34.2469	+	9.17643i	1.30281	+	0.349088i	0.842514	−	0.538675i	$-0.181075\pi$
$691$	34.2469	+	9.17643i	1.30281	+	0.349088i	0.460301	+	0.887763i	$0.347742\pi$
$692$	−13.9862	+	32.7976i	−0.531675	+	1.24678i
$693$	1.67843	−	21.8597i	0.0637584	−	0.830382i
$694$	19.8122	−	13.0897i	0.752061	−	0.496879i
$695$	27.2803	−	0.975359i	1.03480	−	0.0369975i
$696$	1.98407	+	4.18654i	0.0752059	+	0.158691i
$697$	19.4699	−	5.21693i	0.737474	−	0.197605i
$698$	−2.77986	+	0.927558i	−0.105219	+	0.0351086i
$699$	3.43027	−	3.43027i	0.129745	−	0.129745i
$700$	3.86076	−	26.1743i	0.145923	−	0.989296i
$701$	−0.737800	−	0.737800i	−0.0278663	−	0.0278663i	0.693036	−	0.720903i	$-0.256273\pi$
$701$	−0.737800	−	0.737800i	−0.0278663	−	0.0278663i	−0.720903	+	0.693036i	$0.756273\pi$
$702$	1.16689	−	2.33554i	0.0440413	−	0.0881494i
$703$	−4.89280	−	18.2602i	−0.184536	−	0.688696i
$704$	−24.3905	−	33.9254i	−0.919251	−	1.27861i
$705$	0.653416	+	18.2757i	0.0246091	+	0.688304i
$706$	13.2529	+	2.70782i	0.498780	+	0.101910i
$707$	19.8805	−	29.0449i	0.747685	−	1.09235i
$708$	3.82455	+	9.51161i	0.143735	+	0.357468i
$709$	2.78474	−	10.3928i	0.104583	−	0.390309i	−0.893715	−	0.448636i	$-0.851910\pi$
$709$	2.78474	−	10.3928i	0.104583	−	0.390309i	0.998298	+	0.0583270i	$0.0185766\pi$
$710$	−6.23148	−	16.6669i	−0.233863	−	0.625496i
$711$	14.2516	+	8.22819i	0.534479	+	0.308581i
$712$	−3.97041	+	3.37395i	−0.148797	+	0.126444i
$713$	−32.9688	−	32.9688i	−1.23469	−	1.23469i
$714$	12.1677	+	0.199289i	0.455365	+	0.00745822i
$715$	−1.85337	+	3.49269i	−0.0693122	+	0.130619i
$716$	−11.2151	+	14.3056i	−0.419129	+	0.534625i
$717$	15.3924	+	8.88682i	0.574841	+	0.331884i
$718$	27.5036	−	1.65923i	1.02643	−	0.0619220i
$719$	10.8607	+	18.8112i	0.405034	+	0.701539i	0.994325	−	0.106381i	$-0.0339264\pi$
$719$	10.8607	+	18.8112i	0.405034	+	0.701539i	−0.589292	+	0.807920i	$0.700593\pi$
$720$	−12.3943	−	6.91077i	−0.461908	−	0.257549i
$721$	17.2927	+	36.0776i	0.644013	+	1.34360i
$722$	−16.8326	+	11.1211i	−0.626443	+	0.413885i
$723$	−0.742070	+	0.428434i	−0.0275979	+	0.0159336i
$724$	−1.36306	+	9.58299i	−0.0506579	+	0.356149i
$725$	−5.20652	−	4.51078i	−0.193365	−	0.167526i
$726$	−24.4839	−	12.2326i	−0.908681	−	0.453996i
$727$	−18.0505	+	18.0505i	−0.669457	+	0.669457i	−0.957590	−	0.288134i	$-0.906965\pi$
$727$	−18.0505	+	18.0505i	−0.669457	+	0.669457i	0.288134	+	0.957590i	$0.406965\pi$
$728$	−1.59558	+	1.96801i	−0.0591360	+	0.0729393i
$729$	22.1821			0.821559
$730$	34.1423	−	24.3535i	1.26366	−	0.901362i
$731$	18.6096	−	4.98644i	0.688303	−	0.184430i
$732$	0.0863090	+	0.0122764i	0.00319007	+	0.000453749i
$733$	2.12692	+	3.68394i	0.0785597	+	0.136069i	0.902629	−	0.430420i	$-0.141635\pi$
$733$	2.12692	+	3.68394i	0.0785597	+	0.136069i	−0.824069	+	0.566489i	$0.808301\pi$
$734$	2.88014	−	14.0963i	0.106308	−	0.520305i
$735$	−2.67547	−	18.4155i	−0.0986861	−	0.679266i
$736$	26.9079	+	42.6271i	0.991837	+	1.57126i
$737$	41.7984	+	11.1999i	1.53966	+	0.412552i
$738$	−16.5021	+	0.995534i	−0.607451	+	0.0366461i
$739$	−2.60666	−	9.72820i	−0.0958877	−	0.357858i	0.901265	−	0.433269i	$-0.142640\pi$
$739$	−2.60666	−	9.72820i	−0.0958877	−	0.357858i	−0.997153	+	0.0754108i	$0.975973\pi$
$740$	−15.7741	−	35.5087i	−0.579867	−	1.30533i
$741$	0.619286	+	0.619286i	0.0227500	+	0.0227500i
$742$	−30.0464	−	8.58070i	−1.10304	−	0.315007i
$743$	10.2002	−	10.2002i	0.374209	−	0.374209i	−0.494799	−	0.869008i	$-0.664758\pi$
$743$	10.2002	−	10.2002i	0.374209	−	0.374209i	0.869008	+	0.494799i	$0.164758\pi$
$744$	13.4070	−	11.3929i	0.491526	−	0.417686i
$745$	−25.5112	+	15.9706i	−0.934656	+	0.585119i
$746$	6.77186	−	0.408531i	0.247936	−	0.0149574i
$747$	−13.7464	−	23.8094i	−0.502953	−	0.871140i
$748$	−11.2094	+	26.2861i	−0.409858	+	0.961115i
$749$	2.88894	−	8.20784i	0.105559	−	0.299908i
$750$	−18.7142	−	1.77058i	−0.683346	−	0.0646525i
$751$	−2.29798	−	3.98021i	−0.0838544	−	0.145240i	0.821048	−	0.570859i	$-0.193390\pi$
$751$	−2.29798	−	3.98021i	−0.0838544	−	0.145240i	−0.904902	+	0.425619i	$0.860056\pi$
$752$	−23.5388	−	14.2504i	−0.858372	−	0.519657i
$753$	−5.19044	+	1.39077i	−0.189150	+	0.0506826i
$754$	0.208794	+	0.625749i	0.00760383	+	0.0227884i
$755$	−3.50350	−	11.4254i	−0.127505	−	0.415814i
$756$	−28.1714	−	6.23824i	−1.02459	−	0.226882i
$757$			6.23131i			0.226481i	0.993568	+	0.113240i	$0.0361230\pi$
$757$			6.23131i			0.226481i	−0.993568	+	0.113240i	$0.963877\pi$
$758$	−8.01699	+	2.67503i	−0.291190	+	0.0971616i
$759$	47.9197	+	27.6665i	1.73938	+	1.00423i
$760$	10.1614	−	9.28017i	0.368594	−	0.336627i
$761$	−11.2413	−	19.4704i	−0.407495	−	0.705802i	0.587113	−	0.809505i	$-0.300264\pi$
$761$	−11.2413	−	19.4704i	−0.407495	−	0.705802i	−0.994608	+	0.103702i	$0.966931\pi$
$762$	−23.4710	−	4.79557i	−0.850266	−	0.173725i
$763$	8.42207	+	5.76470i	0.304899	+	0.208696i
$764$	4.88873	−	11.4641i	0.176868	−	0.414755i
$765$	0.346776	+	9.69917i	0.0125377	+	0.350674i
$766$	14.0462	−	15.8498i	0.507511	−	0.572676i
$767$	0.377802	+	1.40998i	0.0136416	+	0.0509113i
$768$	−16.8545	+	8.81832i	−0.608184	+	0.318204i
$769$	−17.4560			−0.629478			−0.314739	−	0.949178i	$-0.601917\pi$
$769$	−17.4560			−0.629478			−0.314739	+	0.949178i	$0.601917\pi$
$770$	42.4199	+	10.4906i	1.52871	+	0.378054i
$771$	14.8142	+	14.8142i	0.533522	+	0.533522i
$772$	−6.32167	−	4.95599i	−0.227522	−	0.178370i
$773$	−44.8816	−	25.9124i	−1.61428	−	0.932004i	−0.988363	−	0.152113i	$-0.951392\pi$
$773$	−44.8816	−	25.9124i	−1.61428	−	0.932004i	−0.625915	−	0.779891i	$-0.715274\pi$
$774$	−15.7730	+	0.951549i	−0.566949	+	0.0342027i
$775$	−11.4291	+	23.5323i	−0.410544	+	0.845305i
$776$	−26.8474	−	18.5506i	−0.963767	−	0.665926i
$777$	−17.7880	−	20.7468i	−0.638141	−	0.744286i
$778$	−3.77413	+	18.4718i	−0.135309	+	0.662245i
$779$	4.14937	−	15.4856i	0.148666	−	0.554831i
$780$	1.45540	+	1.05926i	0.0521118	+	0.0379278i
$781$	28.3871	−	7.60630i	1.01577	−	0.272175i
$782$	15.4088	−	30.8410i	0.551018	−	1.10287i
$783$	−5.31227	+	5.31227i	−0.189845	+	0.189845i
$784$	25.3824	+	11.8209i	0.906514	+	0.422175i
$785$	0.819023	+	2.67096i	0.0292322	+	0.0953306i
$786$	−5.28505	−	15.8391i	−0.188511	−	0.564963i
$787$	−11.9555	−	6.90250i	−0.426167	−	0.246048i	0.271545	−	0.962426i	$-0.412465\pi$
$787$	−11.9555	−	6.90250i	−0.426167	−	0.246048i	−0.697712	+	0.716378i	$0.745799\pi$
$788$	−3.64804	+	2.73949i	−0.129956	+	0.0975904i
$789$	19.7773	+	5.29931i	0.704091	+	0.188660i
$790$	−20.8634	+	25.3093i	−0.742286	+	0.900464i
$791$	−8.99833	−	0.690911i	−0.319944	−	0.0245660i
$792$	13.3235	−	19.2825i	0.473429	−	0.685174i
$793$	0.0119900	+	0.00321272i	0.000425778	+	0.000114087i
$794$	2.38120	+	39.4711i	0.0845057	+	1.40078i
$795$	−4.97618	+	21.6363i	−0.176487	+	0.767359i
$796$	−0.0894038	−	0.738288i	−0.00316883	−	0.0261679i
$797$		−	18.6758i		−	0.661532i	−0.943713	−	0.330766i	$-0.892693\pi$
$797$		−	18.6758i		−	0.661532i	0.943713	−	0.330766i	$-0.107307\pi$
$798$	4.97615	−	8.30193i	0.176154	−	0.293885i
$799$			18.8190i			0.665769i
$800$	17.6626	−	22.0915i	0.624467	−	0.781052i
$801$	−2.53112	−	1.46134i	−0.0894327	−	0.0516340i
$802$	−25.7580	+	1.55392i	−0.909545	+	0.0548708i
$803$	34.6328	+	59.9858i	1.22217	+	2.11685i
$804$	7.72765	−	18.1213i	0.272533	−	0.639090i
$805$	−50.3226	−	15.7152i	−1.77364	−	0.553889i
$806$	2.09016	−	1.38095i	0.0736229	−	0.0486419i
$807$	1.20077	−	4.48135i	0.0422692	−	0.157751i
$808$	34.0023	−	16.1142i	1.19620	−	0.566896i
$809$	−15.9456	+	27.6186i	−0.560617	+	0.971018i	0.436825	+	0.899546i	$0.356103\pi$
$809$	−15.9456	+	27.6186i	−0.560617	+	0.971018i	−0.997443	+	0.0714713i	$0.977231\pi$
$810$	−0.899311	+	5.37406i	−0.0315986	+	0.188825i
$811$	−10.8894	−	10.8894i	−0.382379	−	0.382379i	0.489580	−	0.871959i	$-0.337150\pi$
$811$	−10.8894	−	10.8894i	−0.382379	−	0.382379i	−0.871959	+	0.489580i	$0.837150\pi$
$812$	6.14768	−	3.91862i	0.215741	−	0.137516i
$813$		−	27.7907i		−	0.974662i
$814$	60.8741	−	20.3119i	2.13363	−	0.711931i
$815$	41.0318	+	9.43702i	1.43728	+	0.330564i
$816$	11.1290	+	6.73749i	0.389594	+	0.235859i
$817$	3.96604	−	14.8015i	0.138754	−	0.517837i
$818$	2.88071	−	1.90325i	0.100722	−	0.0665457i
$819$	−1.34056	−	0.471840i	−0.0468429	−	0.0164874i
$820$	3.47159	−	32.7675i	0.121233	−	1.14429i
$821$	50.9951	+	13.6641i	1.77974	+	0.476881i	0.990537	−	0.137248i	$-0.0438258\pi$
$821$	50.9951	+	13.6641i	1.77974	+	0.476881i	0.789206	+	0.614129i	$0.210493\pi$
$822$	−9.11770	−	8.08019i	−0.318016	−	0.281829i
$823$	−7.69994	−	28.7366i	−0.268403	−	1.00169i	−0.960134	−	0.279539i	$-0.909818\pi$
$823$	−7.69994	−	28.7366i	−0.268403	−	1.00169i	0.691731	−	0.722155i	$-0.256848\pi$
$824$	−3.46211	+	42.6298i	−0.120608	+	1.48508i
$825$	5.87334	−	30.4862i	0.204483	−	1.06139i
$826$	14.1011	−	7.83624i	0.490642	−	0.272658i
$827$		−	17.4174i		−	0.605664i	−0.953044	−	0.302832i	$-0.902068\pi$
$827$		−	17.4174i		−	0.605664i	0.953044	−	0.302832i	$-0.0979321\pi$
$828$	−17.4458	+	22.2532i	−0.606285	+	0.773354i
$829$	44.0036	−	11.7907i	1.52831	−	0.409509i	0.605840	−	0.795586i	$-0.292837\pi$
$829$	44.0036	−	11.7907i	1.52831	−	0.409509i	0.922466	+	0.386078i	$0.126170\pi$
$830$	51.3269	−	19.1903i	1.78158	−	0.666105i
$831$	27.1959	−	15.7015i	0.943414	−	0.544680i
$832$	−2.53341	+	0.958003i	−0.0878301	+	0.0332128i
$833$	−2.07436	−	19.0371i	−0.0718724	−	0.659597i
$834$	20.1100	+	4.10885i	0.696353	+	0.142278i
$835$	−25.9990	+	0.929548i	−0.899733	+	0.0321683i
$836$	13.6482	+	18.1746i	0.472034	+	0.628583i
$837$	24.7080	+	14.2652i	0.854034	+	0.493077i
$838$	34.5031	−	11.5127i	1.19189	−	0.397699i
$839$		−	46.4476i		−	1.60355i	−0.597626	−	0.801775i	$-0.703889\pi$
$839$		−	46.4476i		−	1.60355i	0.597626	−	0.801775i	$-0.296111\pi$
$840$	7.44781	−	18.4469i	0.256974	−	0.636480i
$841$			27.1018i			0.934545i
$842$	17.2186	+	51.6037i	0.593393	+	1.77838i
$843$	27.2372	+	15.7254i	0.938100	+	0.541612i
$844$	2.92334	−	20.5525i	0.100626	−	0.707445i
$845$	−21.0885	−	19.6326i	−0.725467	−	0.675382i
$846$	3.08982	−	15.1226i	0.106230	−	0.519924i
$847$	−14.2993	+	40.6262i	−0.491330	+	1.39593i
$848$	−23.1251	−	24.1068i	−0.794119	−	0.827829i
$849$	−26.5776	+	15.3446i	−0.912141	+	0.526625i
$850$	−19.1808	−	2.50899i	−0.657897	−	0.0860577i
$851$	−74.7840	+	20.0383i	−2.56356	+	0.686905i
$852$	−1.60843	−	13.2822i	−0.0551038	−	0.455042i
$853$			23.5379i			0.805923i	0.915217	+	0.402962i	$0.132019\pi$
$853$			23.5379i			0.805923i	−0.915217	+	0.402962i	$0.867981\pi$
$854$	0.00224657	−	0.137165i	7.68761e−5	−	0.00469370i
$855$	6.81875	+	3.61833i	0.233196	+	0.123744i
$856$	7.08851	−	6.02363i	0.242280	−	0.205883i
$857$	8.81593	+	32.9015i	0.301146	+	1.12389i	0.936212	+	0.351435i	$0.114306\pi$
$857$	8.81593	+	32.9015i	0.301146	+	1.12389i	−0.635066	+	0.772458i	$0.719027\pi$
$858$	−1.97184	+	2.22503i	−0.0673176	+	0.0759613i
$859$	42.0449	+	11.2659i	1.43455	+	0.384388i	0.890623	−	0.454742i	$-0.150269\pi$
$859$	42.0449	+	11.2659i	1.43455	+	0.384388i	0.543931	+	0.839130i	$0.316935\pi$
$860$	3.31821	−	31.3198i	0.113150	−	1.06800i
$861$	−4.26696	−	22.7798i	−0.145418	−	0.776334i
$862$	−10.6928	−	16.1843i	−0.364199	−	0.551241i
$863$	9.41004	−	35.1188i	0.320322	−	1.19546i	−0.598610	−	0.801040i	$-0.704280\pi$
$863$	9.41004	−	35.1188i	0.320322	−	1.19546i	0.918932	−	0.394416i	$-0.129053\pi$
$864$	−22.6552	−	20.9337i	−0.770747	−	0.712180i
$865$	8.93509	−	38.8495i	0.303802	−	1.32092i
$866$	8.70746	+	26.0960i	0.295892	+	0.886777i
$867$			11.3134i			0.384222i
$868$	−20.4169	−	18.6995i	−0.692994	−	0.634701i
$869$	−38.3063	−	38.3063i	−1.29945	−	1.29945i
$870$	−3.00788	−	4.21690i	−0.101977	−	0.142966i
$871$	1.40253	−	2.42925i	0.0475229	−	0.0823121i
$872$	4.67259	+	9.85953i	0.158234	+	0.333886i
$873$	4.73770	−	17.6814i	0.160347	−	0.598423i
$874$	−15.1157	−	22.8786i	−0.511295	−	0.773880i
$875$	0.904493	+	29.5666i	0.0305774	+	0.999532i
$876$	29.2570	−	11.7640i	0.988504	−	0.397470i
$877$	24.9327	+	43.1848i	0.841919	+	1.45825i	0.888270	+	0.459321i	$0.151907\pi$
$877$	24.9327	+	43.1848i	0.841919	+	1.45825i	−0.0463511	+	0.998925i	$0.514759\pi$
$878$	−1.55073	−	25.7051i	−0.0523345	−	0.867505i
$879$	0.193704	+	0.111835i	0.00653348	+	0.00377211i
$880$	33.5228	+	32.5347i	1.13005	+	1.09675i
$881$		−	15.9710i		−	0.538076i	−0.963129	−	0.269038i	$-0.913294\pi$
$881$		−	15.9710i		−	0.538076i	0.963129	−	0.269038i	$-0.0867058\pi$
$882$	−1.45872	+	15.6384i	−0.0491176	+	0.526572i
$883$			44.1081i			1.48435i	0.670204	+	0.742177i	$0.266207\pi$
$883$			44.1081i			1.48435i	−0.670204	+	0.742177i	$0.733793\pi$
$884$	1.45781	+	1.14288i	0.0490314	+	0.0384390i
$885$	−6.08190	−	9.71509i	−0.204441	−	0.326569i
$886$	−24.1585	+	1.45742i	−0.811620	+	0.0489631i
$887$	9.15875	+	2.45408i	0.307521	+	0.0824000i	0.409279	−	0.912409i	$-0.365780\pi$
$887$	9.15875	+	2.45408i	0.307521	+	0.0824000i	−0.101758	+	0.994809i	$0.532447\pi$
$888$	−5.25236	−	28.7393i	−0.176258	−	0.964427i
$889$	−2.88599	+	37.5867i	−0.0967929	+	1.26062i
$890$	3.70538	−	4.49498i	0.124205	−	0.150672i
$891$	−8.69270	−	2.32920i	−0.291216	−	0.0780312i
$892$	45.4916	+	6.47062i	1.52317	+	0.216652i
$893$	12.9627	+	7.48399i	0.433779	+	0.250442i
$894$	−21.4674	+	7.16304i	−0.717977	+	0.239568i
$895$	9.52629	−	17.9523i	0.318429	−	0.600081i
$896$	17.0729	+	24.5869i	0.570365	+	0.821391i
$897$	2.53627	−	2.53627i	0.0846835	−	0.0846835i
$898$	17.1195	+	8.55323i	0.571284	+	0.285425i
$899$	−6.96301	+	1.86573i	−0.232229	+	0.0622257i
$900$	15.0014	+	5.16540i	0.500045	+	0.172180i
$901$	−5.91311	+	22.0680i	−0.196994	+	0.735193i
$902$	53.3210	+	10.8945i	1.77539	+	0.362746i
$903$	−4.07844	−	21.7733i	−0.135722	−	0.724572i
$904$	−7.93745	−	5.48448i	−0.263996	−	0.182411i
$905$	−0.386672	−	10.8150i	−0.0128534	−	0.359504i
$906$	−0.541105	−	8.96943i	−0.0179770	−	0.297989i
$907$	−26.6632	−	15.3940i	−0.885337	−	0.511150i	−0.0129227	−	0.999916i	$-0.504114\pi$
$907$	−26.6632	−	15.3940i	−0.885337	−	0.511150i	−0.872414	+	0.488767i	$0.837447\pi$
$908$	−0.676586	−	5.58719i	−0.0224533	−	0.185417i
$909$	14.9247	+	14.9247i	0.495020	+	0.495020i
$910$	1.36855	−	2.48007i	0.0453669	−	0.0822135i
$911$	−27.3255			−0.905336			−0.452668	−	0.891679i	$-0.649528\pi$
$911$	−27.3255			−0.905336			−0.452668	+	0.891679i	$0.649528\pi$
$912$	9.06664	−	4.98635i	0.300226	−	0.165115i
$913$	23.4242	+	87.4202i	0.775227	+	2.89319i
$914$	15.5466	+	13.7775i	0.514235	+	0.455719i
$915$	−0.0974054	+	0.00348255i	−0.00322012	+	0.000115130i
$916$	5.58987	+	13.9020i	0.184694	+	0.459333i
$917$	−23.6943	+	11.3571i	−0.782454	+	0.375046i
$918$	−4.22312	+	20.6693i	−0.139384	+	0.682188i
$919$	13.9169	+	24.1047i	0.459075	+	0.795141i	0.998912	−	0.0466285i	$-0.0148477\pi$
$919$	13.9169	+	24.1047i	0.459075	+	0.795141i	−0.539838	+	0.841769i	$0.681514\pi$
$920$	−38.0066	−	41.6158i	−1.25304	−	1.37203i
$921$	4.97308	+	2.87121i	0.163869	+	0.0946095i
$922$	−2.21175	−	6.62855i	−0.0728402	−	0.218300i
$923$		−	1.90504i		−	0.0627050i
$924$	29.1481	+	15.1645i	0.958903	+	0.498876i
$925$	24.3517	+	35.9737i	0.800679	+	1.18281i
$926$	−5.71722	+	1.90767i	−0.187879	+	0.0626898i
$927$	−23.1740	+	6.20945i	−0.761133	+	0.203945i
$928$	7.78766	−	0.307569i	0.255643	−	0.0100964i
$929$	−17.1128	−	29.6403i	−0.561453	−	0.972466i	−0.997370	−	0.0724786i	$-0.976909\pi$
$929$	−17.1128	−	29.6403i	−0.561453	−	0.972466i	0.435917	−	0.899987i	$-0.356424\pi$
$930$	−12.5121	+	15.1784i	−0.410287	+	0.497718i
$931$	−13.9378	−	6.14189i	−0.456794	−	0.201292i
$932$	−3.04453	−	7.57171i	−0.0997268	−	0.248020i
$933$	5.63198	+	9.75487i	0.184383	+	0.319360i
$934$	1.85939	+	30.8215i	0.0608410	+	1.00851i
$935$	7.16116	−	31.1365i	0.234195	−	1.01827i
$936$	−0.983818	−	1.15774i	−0.0321571	−	0.0378420i
$937$	−39.3051	+	39.3051i	−1.28404	+	1.28404i	−0.345692	+	0.938348i	$0.612356\pi$
$937$	−39.3051	+	39.3051i	−1.28404	+	1.28404i	−0.938348	+	0.345692i	$0.887644\pi$
$938$	−29.8088	−	8.51282i	−0.973291	−	0.277954i
$939$	−25.7731	−	25.7731i	−0.841072	−	0.841072i
$940$	28.7117	+	11.0488i	0.936471	+	0.360372i
$941$	−6.82472	−	25.4702i	−0.222480	−	0.830305i	−0.983399	−	0.181458i	$-0.941918\pi$
$941$	−6.82472	−	25.4702i	−0.222480	−	0.830305i	0.760919	−	0.648847i	$-0.224748\pi$
$942$	0.126496	+	2.09681i	0.00412145	+	0.0683177i
$943$	−63.4209	−	16.9936i	−2.06527	−	0.553387i
$944$	17.2424	+	0.358362i	0.561191	+	0.0116637i
$945$	32.2326	+	1.31885i	1.04853	+	0.0429021i
$946$	50.9651	+	10.4131i	1.65702	+	0.338560i
$947$	18.6589	+	32.3182i	0.606334	+	1.05020i	0.991839	+	0.127496i	$0.0406940\pi$
$947$	18.6589	+	32.3182i	0.606334	+	1.05020i	−0.385505	+	0.922706i	$0.625973\pi$
$948$	−19.7212	+	14.8096i	−0.640514	+	0.480993i
$949$	4.33698	−	1.16209i	0.140784	−	0.0377231i
$950$	−9.35608	+	12.2141i	−0.303551	+	0.396277i
$951$	0.172928			0.00560756
$952$	8.33770	−	18.6972i	0.270226	−	0.605980i
$953$	20.1360	−	20.1360i	0.652269	−	0.652269i	−0.301270	−	0.953539i	$-0.597411\pi$
$953$	20.1360	−	20.1360i	0.652269	−	0.652269i	0.953539	+	0.301270i	$0.0974106\pi$
$954$	8.37492	−	16.7625i	0.271148	−	0.542708i
$955$	−3.12317	+	13.5794i	−0.101064	+	0.439421i
$956$	23.9090	−	17.9545i	0.773274	−	0.580689i
$957$	7.40882	−	4.27748i	0.239493	−	0.138271i
$958$	4.66727	+	7.06423i	0.150793	+	0.228235i
$959$	−10.8285	+	15.8201i	−0.349669	+	0.510857i
$960$	16.8131	−	13.0236i	0.542642	−	0.420335i
$961$	−1.81216	−	3.13874i	−0.0584566	−	0.101250i
$962$	−0.250501	−	4.15233i	−0.00807646	−	0.133877i
$963$	4.51889	+	2.60898i	0.145619	+	0.0840733i
$964$	0.173291	+	1.43102i	0.00558133	+	0.0460901i
$965$	7.93317	+	4.20968i	0.255378	+	0.135515i
$966$	−34.0003	−	20.3797i	−1.09394	−	0.655705i
$967$	−17.4747	−	17.4747i	−0.561948	−	0.561948i	0.367912	−	0.929860i	$-0.380073\pi$
$967$	−17.4747	−	17.4747i	−0.561948	−	0.561948i	−0.929860	+	0.367912i	$0.880073\pi$
$968$	−35.0858	+	29.8150i	−1.12770	+	0.958290i
$969$	−6.12867	−	3.53839i	−0.196881	−	0.113669i
$970$	33.1997	+	15.1300i	1.06598	+	0.485795i
$971$	−7.11668	+	26.5598i	−0.228385	+	0.852344i	0.752635	+	0.658438i	$0.228782\pi$
$971$	−7.11668	+	26.5598i	−0.228385	+	0.852344i	−0.981020	+	0.193906i	$0.937884\pi$
$972$	11.2266	−	26.3264i	0.360094	−	0.844419i
$973$	2.47272	−	32.2043i	0.0792717	−	1.03242i
$974$	−3.93868	+	19.2771i	−0.126203	+	0.617679i
$975$	−1.81032	−	0.879229i	−0.0579766	−	0.0281579i
$976$	0.0759511	−	0.125456i	0.00243114	−	0.00401576i
$977$	−7.75655	−	28.9478i	−0.248154	−	0.926123i	−0.971772	−	0.235922i	$-0.924189\pi$
$977$	−7.75655	−	28.9478i	−0.248154	−	0.926123i	0.723618	−	0.690201i	$-0.242478\pi$
$978$	28.3199	+	14.1492i	0.905569	+	0.452441i
$979$	6.80327	+	6.80327i	0.217434	+	0.217434i
$980$	−30.2623	−	8.01206i	−0.966694	−	0.255936i
$981$	−4.32766	+	4.32766i	−0.138172	+	0.138172i
$982$	−13.1547	−	39.4241i	−0.419783	−	1.25808i
$983$	19.5163	−	5.22937i	0.622473	−	0.166791i	0.0662210	−	0.997805i	$-0.478906\pi$
$983$	19.5163	−	5.22937i	0.622473	−	0.166791i	0.556252	+	0.831014i	$0.312239\pi$
$984$	8.32872	−	23.3343i	0.265510	−	0.743871i
$985$	3.47551	−	3.73324i	0.110739	−	0.118951i
$986$	−2.93829	−	4.44731i	−0.0935743	−	0.141631i
$987$	21.5744	+	1.65653i	0.686722	+	0.0527280i
$988$	1.36696	−	0.549645i	0.0434889	−	0.0174865i
$989$	−60.6189	−	16.2428i	−1.92757	−	0.516490i
$990$	−10.8667	+	23.8448i	−0.345368	+	0.757839i
$991$	15.1789	−	26.2906i	0.482173	−	0.835148i	−0.517617	−	0.855612i	$-0.673181\pi$
$991$	15.1789	−	26.2906i	0.482173	−	0.835148i	0.999791	+	0.0204637i	$0.00651426\pi$
$992$	−8.78270	−	28.2646i	−0.278851	−	0.897401i
$993$	−5.42006	+	5.42006i	−0.172001	+	0.172001i
$994$	−20.4229	+	5.11535i	−0.647775	+	0.162249i
$995$	0.243757	+	0.794928i	0.00772761	+	0.0252009i
$996$	40.9037	−	4.95327i	1.29608	−	0.156950i
$997$	−27.1107	+	46.9572i	−0.858606	+	1.48715i	0.0146537	+	0.999893i	$0.495335\pi$
$997$	−27.1107	+	46.9572i	−0.858606	+	1.48715i	−0.873259	+	0.487256i	$0.837998\pi$
$998$	−2.71880	+	3.06790i	−0.0860622	+	0.0971127i
$999$	41.0284	−	23.6877i	1.29808	−	0.749447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ch.c.493.32	yes	360
5.2	odd	4		560.2.cz.c.157.15	yes	360
7.5	odd	6	inner	560.2.ch.c.173.89	yes	360
16.5	even	4		560.2.cz.c.213.46	yes	360
35.12	even	12		560.2.cz.c.397.46	yes	360
80.37	odd	4	inner	560.2.ch.c.437.89	yes	360
112.5	odd	12		560.2.cz.c.453.15	yes	360
560.117	even	12	inner	560.2.ch.c.117.32	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.32	✓	360	560.117	even	12	inner
560.2.ch.c.173.89	yes	360	7.5	odd	6	inner
560.2.ch.c.437.89	yes	360	80.37	odd	4	inner
560.2.ch.c.493.32	yes	360	1.1	even	1	trivial
560.2.cz.c.157.15	yes	360	5.2	odd	4
560.2.cz.c.213.46	yes	360	16.5	even	4
560.2.cz.c.397.46	yes	360	35.12	even	12
560.2.cz.c.453.15	yes	360	112.5	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.632072 + 1.26510i) q^{2} +(0.594438 - 1.02960i) q^{3} +(-1.20097 - 1.59927i) q^{4} +(1.63662 + 1.52363i) q^{5} +(0.926818 + 1.40280i) q^{6} +(2.00856 - 1.72211i) q^{7} +(2.78234 - 0.508498i) q^{8} +(0.793287 + 1.37401i) q^{9} +(-2.96202 + 1.10745i) q^{10} +(-1.35178 - 5.04493i) q^{11} +(-2.36051 + 0.285848i) q^{12} -0.338561 q^{13} +(0.909095 + 3.62954i) q^{14} +(2.54160 - 0.779356i) q^{15} +(-1.11534 + 3.84136i) q^{16} +(2.64247 - 0.708048i) q^{17} +(-2.23968 + 0.135115i) q^{18} +(0.563156 - 2.10173i) q^{19} +(0.471167 - 4.44725i) q^{20} +(-0.579117 - 3.09170i) q^{21} +(7.23678 + 1.47861i) q^{22} +(-8.60756 - 2.30639i) q^{23} +(1.13038 - 3.16696i) q^{24} +(0.357076 + 4.98723i) q^{25} +(0.213995 - 0.428315i) q^{26} +5.45287 q^{27} +(-5.16635 - 1.14403i) q^{28} +(-0.974217 + 0.974217i) q^{29} +(-0.620507 + 3.70799i) q^{30} +(4.53120 + 2.61609i) q^{31} +(-4.15474 - 3.83903i) q^{32} +(-5.99779 - 1.60710i) q^{33} +(-0.774477 + 3.79053i) q^{34} +(5.91113 + 0.241863i) q^{35} +(1.24471 - 2.91883i) q^{36} +(7.52418 - 4.34409i) q^{37} +(2.30295 + 2.04089i) q^{38} +(-0.201254 + 0.348581i) q^{39} +(5.32841 + 3.40705i) q^{40} +7.36805 q^{41} +(4.27736 + 1.22153i) q^{42} +7.04252 q^{43} +(-6.44476 + 8.22068i) q^{44} +(-0.795182 + 3.45742i) q^{45} +(8.35841 - 9.43164i) q^{46} +(-1.78044 + 6.64469i) q^{47} +(3.29205 + 3.43180i) q^{48} +(1.06865 - 6.91795i) q^{49} +(-6.53506 - 2.70055i) q^{50} +(0.841781 - 3.14157i) q^{51} +(0.406602 + 0.541451i) q^{52} +(-4.17565 + 7.23243i) q^{53} +(-3.44660 + 6.89844i) q^{54} +(5.47426 - 10.3163i) q^{55} +(4.71282 - 5.81286i) q^{56} +(-1.82917 - 1.82917i) q^{57} +(-0.616710 - 1.84826i) q^{58} +(-1.11590 - 4.16461i) q^{59} +(-4.29879 - 3.12872i) q^{60} +(-0.0354146 - 0.00948932i) q^{61} +(-6.17366 + 4.07888i) q^{62} +(3.95958 + 1.39366i) q^{63} +(7.48286 - 2.82963i) q^{64} +(-0.554097 - 0.515844i) q^{65} +(5.82419 - 6.57202i) q^{66} +(-4.14262 + 7.17522i) q^{67} +(-4.30589 - 3.37568i) q^{68} +(-7.49131 + 7.49131i) q^{69} +(-4.04224 + 7.32532i) q^{70} +5.62686i q^{71} +(2.90588 + 3.41959i) q^{72} +(-12.8100 + 3.43244i) q^{73} +(0.739897 + 12.2646i) q^{74} +(5.34710 + 2.59696i) q^{75} +(-4.03757 + 1.62347i) q^{76} +(-11.4031 - 7.80513i) q^{77} +(-0.313785 - 0.474935i) q^{78} +(8.98265 - 5.18614i) q^{79} +(-7.67821 + 4.58749i) q^{80} +(0.861529 - 1.49221i) q^{81} +(-4.65714 + 9.32135i) q^{82} -17.3283 q^{83} +(-4.24896 + 4.63920i) q^{84} +(5.40354 + 2.86735i) q^{85} +(-4.45138 + 8.90951i) q^{86} +(0.423939 + 1.58216i) q^{87} +(-6.32646 - 13.3493i) q^{88} +(-1.59534 + 0.921068i) q^{89} +(-3.87139 - 3.19133i) q^{90} +(-0.680021 + 0.583041i) q^{91} +(6.64889 + 16.5357i) q^{92} +(5.38703 - 3.11020i) q^{93} +(-7.28085 - 6.45236i) q^{94} +(4.12394 - 2.58169i) q^{95} +(-6.42239 + 1.99564i) q^{96} +(-8.15823 - 8.15823i) q^{97} +(8.07645 + 5.72459i) q^{98} +(5.85945 - 5.85945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Introduction

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