LMFDB - Embedded newform 560.2.cz.c.157.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(157,560)] 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, 9, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.157"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [360,2,-24,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == 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			157.15
Character	$\chi$	$=$	560.157
Dual form			560.2.cz.c.453.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26510 - 0.632072i) q^{2} +(-1.02960 - 0.594438i) q^{3} +(1.20097 + 1.59927i) q^{4} +(-2.17918 + 0.501194i) q^{5} +(0.926818 + 1.40280i) q^{6} +(1.72211 + 2.00856i) q^{7} +(-0.508498 - 2.78234i) q^{8} +(-0.793287 - 1.37401i) q^{9} +(3.07367 + 0.743332i) q^{10} +(-1.35178 - 5.04493i) q^{11} +(-0.285848 - 2.36051i) q^{12} +0.338561i q^{13} +(-0.909095 - 3.62954i) q^{14} +(2.54160 + 0.779356i) q^{15} +(-1.11534 + 3.84136i) q^{16} +(0.708048 + 2.64247i) q^{17} +(0.135115 + 2.23968i) q^{18} +(-0.563156 + 2.10173i) q^{19} +(-3.41867 - 2.88317i) q^{20} +(-0.579117 - 3.09170i) q^{21} +(-1.47861 + 7.23678i) q^{22} +(-2.30639 + 8.60756i) q^{23} +(-1.13038 + 3.16696i) q^{24} +(4.49761 - 2.18438i) q^{25} +(0.213995 - 0.428315i) q^{26} +5.45287i q^{27} +(-1.14403 + 5.16635i) q^{28} +(0.974217 - 0.974217i) q^{29} +(-2.72278 - 2.59244i) q^{30} +(4.53120 + 2.61609i) q^{31} +(3.83903 - 4.15474i) q^{32} +(-1.60710 + 5.99779i) q^{33} +(0.774477 - 3.79053i) q^{34} +(-4.75947 - 3.51390i) q^{35} +(1.24471 - 2.91883i) q^{36} +(4.34409 + 7.52418i) q^{37} +(2.04089 - 2.30295i) q^{38} +(0.201254 - 0.348581i) q^{39} +(2.50260 + 5.80836i) q^{40} +7.36805 q^{41} +(-1.22153 + 4.27736i) q^{42} -7.04252i q^{43} +(6.44476 - 8.22068i) q^{44} +(2.41736 + 2.59663i) q^{45} +(8.35841 - 9.43164i) q^{46} +(-6.64469 - 1.78044i) q^{47} +(3.43180 - 3.29205i) q^{48} +(-1.06865 + 6.91795i) q^{49} +(-7.07062 - 0.0793451i) q^{50} +(0.841781 - 3.14157i) q^{51} +(-0.541451 + 0.406602i) q^{52} +(7.23243 + 4.17565i) 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} +(-1.84826 + 0.616710i) q^{58} +(1.11590 + 4.16461i) q^{59} +(1.80599 + 5.00069i) q^{60} +(-0.0354146 - 0.00948932i) q^{61} +(-4.07888 - 6.17366i) q^{62} +(1.39366 - 3.95958i) q^{63} +(-7.48286 + 2.82963i) q^{64} +(-0.169685 - 0.737784i) q^{65} +(5.82419 - 6.57202i) q^{66} +(-7.17522 - 4.14262i) q^{67} +(-3.37568 + 4.30589i) q^{68} +(7.49131 - 7.49131i) q^{69} +(3.80018 + 7.45377i) q^{70} +5.62686i q^{71} +(-3.41959 + 2.90588i) q^{72} +(3.43244 + 12.8100i) q^{73} +(-0.739897 - 12.2646i) q^{74} +(-5.92920 - 0.424519i) q^{75} +(-4.03757 + 1.62347i) q^{76} +(7.80513 - 11.4031i) q^{77} +(-0.474935 + 0.313785i) q^{78} +(-8.98265 + 5.18614i) q^{79} +(0.505250 - 8.92999i) q^{80} +(0.861529 - 1.49221i) q^{81} +(-9.32135 - 4.65714i) q^{82} +17.3283i q^{83} +(4.24896 - 4.63920i) q^{84} +(-2.86735 - 5.40354i) q^{85} +(-4.45138 + 8.90951i) q^{86} +(-1.58216 + 0.423939i) q^{87} +(-13.3493 + 6.32646i) q^{88} +(1.59534 - 0.921068i) q^{89} +(-1.41696 - 4.81294i) q^{90} +(-0.680021 + 0.583041i) q^{91} +(-16.5357 + 6.64889i) q^{92} +(-3.11020 - 5.38703i) q^{93} +(7.28085 + 6.45236i) q^{94} +(0.173842 - 4.86228i) q^{95} +(-6.42239 + 1.99564i) q^{96} +(8.15823 - 8.15823i) q^{97} +(5.72459 - 8.07645i) q^{98} +(-5.85945 + 5.85945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Character values

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

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

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 $

$2$	−1.26510	−	0.632072i	−0.894563	−	0.446942i
$2$	−1.26510	−	0.632072i	−0.894563	−	0.446942i
$3$	−1.02960	−	0.594438i	−0.594438	−	0.343199i	0.172412	−	0.985025i	$-0.444844\pi$
$3$	−1.02960	−	0.594438i	−0.594438	−	0.343199i	−0.766850	+	0.641826i	$0.778177\pi$
$4$	1.20097	+	1.59927i	0.600485	+	0.799636i
$5$	−2.17918	+	0.501194i	−0.974557	+	0.224141i
$5$	−2.17918	+	0.501194i	−0.974557	+	0.224141i
$6$	0.926818	+	1.40280i	0.378372	+	0.572692i
$7$	1.72211	+	2.00856i	0.650898	+	0.759165i
$7$	1.72211	+	2.00856i	0.650898	+	0.759165i
$8$	−0.508498	−	2.78234i	−0.179781	−	0.983707i
$9$	−0.793287	−	1.37401i	−0.264429	−	0.458005i
$10$	3.07367	+	0.743332i	0.971980	+	0.235062i
$11$	−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	$-0.371897\pi$
$12$	−0.285848	−	2.36051i	−0.0825172	−	0.681420i
$13$			0.338561i			0.0939000i	0.998897	+	0.0469500i	$0.0149501\pi$
$13$			0.338561i			0.0939000i	−0.998897	+	0.0469500i	$0.985050\pi$
$14$	−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
$17$	0.708048	+	2.64247i	0.171727	+	0.640893i	0.997086	+	0.0762852i	$0.0243060\pi$
$17$	0.708048	+	2.64247i	0.171727	+	0.640893i	−0.825359	+	0.564608i	$0.809027\pi$
$18$	0.135115	+	2.23968i	0.0318469	+	0.527898i
$19$	−0.563156	+	2.10173i	−0.129197	+	0.482169i	−0.999954	−	0.00954318i	$-0.996962\pi$
$19$	−0.563156	+	2.10173i	−0.129197	+	0.482169i	0.870758	+	0.491713i	$0.163629\pi$
$20$	−3.41867	−	2.88317i	−0.764438	−	0.644697i
$21$	−0.579117	−	3.09170i	−0.126374	−	0.674664i
$22$	−1.47861	+	7.23678i	−0.315241	+	1.54289i
$23$	−2.30639	+	8.60756i	−0.480915	+	1.79480i	0.116874	+	0.993147i	$0.462713\pi$
$23$	−2.30639	+	8.60756i	−0.480915	+	1.79480i	−0.597789	+	0.801653i	$0.703954\pi$
$24$	−1.13038	+	3.16696i	−0.230738	+	0.646453i
$25$	4.49761	−	2.18438i	0.899522	−	0.436876i
$26$	0.213995	−	0.428315i	0.0419679	−	0.0839994i
$27$			5.45287i			1.04940i
$28$	−1.14403	+	5.16635i	−0.216201	+	0.976349i
$29$	0.974217	−	0.974217i	0.180908	−	0.180908i	−0.610844	−	0.791751i	$-0.709170\pi$
$29$	0.974217	−	0.974217i	0.180908	−	0.180908i	0.791751	+	0.610844i	$0.209170\pi$
$30$	−2.72278	−	2.59244i	−0.497109	−	0.473312i
$31$	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	$0.510970\pi$
$32$	3.83903	−	4.15474i	0.678651	−	0.734461i
$33$	−1.60710	+	5.99779i	−0.279761	+	1.04408i
$34$	0.774477	−	3.79053i	0.132822	−	0.650071i
$35$	−4.75947	−	3.51390i	−0.804497	−	0.593957i
$36$	1.24471	−	2.91883i	0.207451	−	0.486472i
$37$	4.34409	+	7.52418i	0.714164	+	1.23697i	0.963281	+	0.268495i	$0.0865262\pi$
$37$	4.34409	+	7.52418i	0.714164	+	1.23697i	−0.249117	+	0.968473i	$0.580140\pi$
$38$	2.04089	−	2.30295i	0.331077	−	0.373587i
$39$	0.201254	−	0.348581i	0.0322264	−	0.0558177i
$40$	2.50260	+	5.80836i	0.395696	+	0.918382i
$41$	7.36805			1.15070			0.575348	−	0.817909i	$-0.304867\pi$
$41$	7.36805			1.15070			0.575348	+	0.817909i	$0.304867\pi$
$42$	−1.22153	+	4.27736i	−0.188487	+	0.660011i
$43$		−	7.04252i		−	1.07397i	−0.843590	−	0.536987i	$-0.819562\pi$
$43$		−	7.04252i		−	1.07397i	0.843590	−	0.536987i	$-0.180438\pi$
$44$	6.44476	−	8.22068i	0.971583	−	1.23931i
$45$	2.41736	+	2.59663i	0.360359	+	0.387082i
$46$	8.35841	−	9.43164i	1.23238	−	1.39062i
$47$	−6.64469	−	1.78044i	−0.969227	−	0.259704i	−0.260726	−	0.965413i	$-0.583962\pi$
$47$	−6.64469	−	1.78044i	−0.969227	−	0.259704i	−0.708501	+	0.705709i	$0.750628\pi$
$48$	3.43180	−	3.29205i	0.495337	−	0.475166i
$49$	−1.06865	+	6.91795i	−0.152664	+	0.988278i
$50$	−7.07062	−	0.0793451i	−0.999937	−	0.0112211i
$51$	0.841781	−	3.14157i	0.117873	−	0.439908i
$52$	−0.541451	+	0.406602i	−0.0750858	+	0.0563856i
$53$	7.23243	+	4.17565i	0.993451	+	0.573569i	0.906304	−	0.422626i	$-0.138892\pi$
$53$	7.23243	+	4.17565i	0.993451	+	0.573569i	0.0871469	+	0.996195i	$0.472225\pi$
$54$	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
$58$	−1.84826	+	0.616710i	−0.242688	+	0.0809780i
$59$	1.11590	+	4.16461i	0.145278	+	0.542186i	0.999743	+	0.0226764i	$0.00721873\pi$
$59$	1.11590	+	4.16461i	0.145278	+	0.542186i	−0.854465	+	0.519510i	$0.826115\pi$
$60$	1.80599	+	5.00069i	0.233152	+	0.645587i
$61$	−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	$0.584080\pi$
$62$	−4.07888	−	6.17366i	−0.518018	−	0.784056i
$63$	1.39366	−	3.95958i	0.175585	−	0.498860i
$64$	−7.48286	+	2.82963i	−0.935358	+	0.353704i
$65$	−0.169685	−	0.737784i	−0.0210468	−	0.0915109i
$66$	5.82419	−	6.57202i	0.716908	−	0.808960i
$67$	−7.17522	−	4.14262i	−0.876593	−	0.506101i	−0.00705957	−	0.999975i	$-0.502247\pi$
$67$	−7.17522	−	4.14262i	−0.876593	−	0.506101i	−0.869534	+	0.493874i	$0.835580\pi$
$68$	−3.37568	+	4.30589i	−0.409362	+	0.522166i
$69$	7.49131	−	7.49131i	0.901847	−	0.901847i
$70$	3.80018	+	7.45377i	0.454209	+	0.890895i
$71$			5.62686i			0.667785i	0.942611	+	0.333893i	$0.108362\pi$
$71$			5.62686i			0.667785i	−0.942611	+	0.333893i	$0.891638\pi$
$72$	−3.41959	+	2.90588i	−0.403003	+	0.342461i
$73$	3.43244	+	12.8100i	0.401737	+	1.49930i	0.809996	+	0.586436i	$0.199469\pi$
$73$	3.43244	+	12.8100i	0.401737	+	1.49930i	−0.408259	+	0.912866i	$0.633864\pi$
$74$	−0.739897	−	12.2646i	−0.0860113	−	1.42574i
$75$	−5.92920	−	0.424519i	−0.684645	−	0.0490192i
$76$	−4.03757	+	1.62347i	−0.463141	+	0.186225i
$77$	7.80513	−	11.4031i	0.889477	−	1.29950i
$78$	−0.474935	+	0.313785i	−0.0537758	+	0.0355291i
$79$	−8.98265	+	5.18614i	−1.01063	+	0.583486i	−0.911375	−	0.411576i	$-0.864978\pi$
$79$	−8.98265	+	5.18614i	−1.01063	+	0.583486i	−0.0992520	+	0.995062i	$0.531645\pi$
$80$	0.505250	−	8.92999i	0.0564887	−	0.998403i
$81$	0.861529	−	1.49221i	0.0957254	−	0.165801i
$82$	−9.32135	−	4.65714i	−1.02937	−	0.514295i
$83$			17.3283i			1.90203i	0.309140	+	0.951016i	$0.399959\pi$
$83$			17.3283i			1.90203i	−0.309140	+	0.951016i	$0.600041\pi$
$84$	4.24896	−	4.63920i	0.463600	−	0.506179i
$85$	−2.86735	−	5.40354i	−0.311008	−	0.586096i
$86$	−4.45138	+	8.90951i	−0.480004	+	0.960737i
$87$	−1.58216	+	0.423939i	−0.169626	+	0.0454510i
$88$	−13.3493	+	6.32646i	−1.42304	+	0.674403i
$89$	1.59534	−	0.921068i	0.169105	−	0.0976330i	−0.413059	−	0.910704i	$-0.635540\pi$
$89$	1.59534	−	0.921068i	0.169105	−	0.0976330i	0.582164	+	0.813071i	$0.302206\pi$
$90$	−1.41696	−	4.81294i	−0.149360	−	0.507329i
$91$	−0.680021	+	0.583041i	−0.0712856	+	0.0611193i
$92$	−16.5357	+	6.64889i	−1.72397	+	0.693194i
$93$	−3.11020	−	5.38703i	−0.322513	−	0.558609i
$94$	7.28085	+	6.45236i	0.750962	+	0.665510i
$95$	0.173842	−	4.86228i	0.0178358	−	0.498860i
$96$	−6.42239	+	1.99564i	−0.655482	+	0.203679i
$97$	8.15823	−	8.15823i	0.828343	−	0.828343i	−0.158944	−	0.987288i	$-0.550809\pi$
$97$	8.15823	−	8.15823i	0.828343	−	0.828343i	0.987288	+	0.158944i	$0.0508091\pi$
$98$	5.72459	−	8.07645i	0.578271	−	0.815845i
$99$	−5.85945	+	5.85945i	−0.588897	+	0.588897i
$100$	8.89491	+	4.56952i	0.889491	+	0.456952i
$101$	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	$0.186432\pi$
$102$	−3.05064	+	3.44234i	−0.302058	+	0.340843i
$103$	14.6063	+	3.91374i	1.43920	+	0.385633i	0.892254	−	0.451535i	$-0.149123\pi$
$103$	14.6063	+	3.91374i	1.43920	+	0.385633i	0.546947	+	0.837167i	$0.315790\pi$
$104$	0.941993	−	0.172158i	0.0923700	−	0.0168814i
$105$	2.81154	+	6.44710i	0.274378	+	0.629173i
$106$	−6.51046	−	9.85404i	−0.632352	−	0.957109i
$107$	1.64441	+	2.84821i	0.158971	+	0.275347i	0.934498	−	0.355968i	$-0.115849\pi$
$107$	1.64441	+	2.84821i	0.158971	+	0.275347i	−0.775527	+	0.631315i	$0.782516\pi$
$108$	−8.72061	+	6.54873i	−0.839141	+	0.630152i
$109$	−0.998398	−	3.72607i	−0.0956292	−	0.356893i	0.901485	−	0.432811i	$-0.142478\pi$
$109$	−0.998398	−	3.72607i	−0.0956292	−	0.356893i	−0.997114	+	0.0759175i	$0.975811\pi$
$110$	−0.404882	−	16.5113i	−0.0386040	−	1.57429i
$111$		−	10.3292i		−	0.980401i
$112$	−9.63634	+	4.37503i	−0.910549	+	0.413401i
$113$	−2.41198	+	2.41198i	−0.226900	+	0.226900i	−0.811396	−	0.584496i	$-0.801292\pi$
$113$	−2.41198	+	2.41198i	−0.226900	+	0.226900i	0.584496	+	0.811396i	$0.301292\pi$
$114$	−3.47026	+	1.15792i	−0.325019	+	0.108449i
$115$	0.711965	−	19.9133i	0.0663911	−	1.85693i
$116$	2.72804	+	0.388031i	0.253292	+	0.0360278i
$117$	0.465188	−	0.268576i	0.0430066	−	0.0248299i
$118$	1.22060	−	5.97399i	0.112365	−	0.549951i
$119$	−4.08823	+	5.97279i	−0.374767	+	0.547525i
$120$	0.876038	−	7.46790i	0.0799710	−	0.681723i
$121$	−14.0977	+	8.13931i	−1.28161	+	0.739937i
$122$	0.0388052	+	0.0343895i	0.00351326	+	0.00311348i
$123$	−7.58612	−	4.37985i	−0.684018	−	0.394918i
$124$	1.25800	+	10.3885i	0.112972	+	0.932912i
$125$	−8.70628	+	7.01432i	−0.778713	+	0.627380i
$126$	−4.26586	+	4.12838i	−0.380033	+	0.367785i
$127$	−10.0750	−	10.0750i	−0.894015	−	0.894015i	0.100883	−	0.994898i	$-0.467833\pi$
$127$	−10.0750	−	10.0750i	−0.894015	−	0.894015i	−0.994898	+	0.100883i	$0.967833\pi$
$128$	11.2551	+	1.14993i	0.994821	+	0.101640i
$129$	−4.18634	+	7.25095i	−0.368587	+	0.638411i
$130$	−0.251664	+	1.04063i	−0.0220724	+	0.0912689i
$131$	−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	$0.726177\pi$
$132$	−11.5222	+	4.63298i	−1.00288	+	0.403249i
$133$	−5.19127	+	2.48828i	−0.450140	+	0.215761i
$134$	6.45897	+	9.77609i	0.557970	+	0.844526i
$135$	−2.73295	−	11.8828i	−0.235215	−	1.02270i
$136$	6.99222	−	3.31372i	0.599578	−	0.284149i
$137$	−1.87540	−	6.99909i	−0.160226	−	0.597972i	−0.998601	−	0.0528780i	$-0.983161\pi$
$137$	−1.87540	−	6.99909i	−0.160226	−	0.597972i	0.838375	−	0.545094i	$-0.183506\pi$
$138$	−14.2123	+	4.74223i	−1.20983	+	0.403686i
$139$	−8.63230	+	8.63230i	−0.732183	+	0.732183i	−0.971052	−	0.238869i	$-0.923223\pi$
$139$	−8.63230	+	8.63230i	−0.732183	+	0.732183i	0.238869	+	0.971052i	$0.423223\pi$
$140$	−0.0963076	−	11.8318i	−0.00813948	−	0.999967i
$141$	5.78299	+	5.78299i	0.487015	+	0.487015i
$142$	3.55658	−	7.11856i	0.298461	−	0.597376i
$143$	1.70802	−	0.457662i	0.142832	−	0.0382716i
$144$	6.16286	−	1.51481i	0.513572	−	0.126234i
$145$	−1.63472	+	2.61126i	−0.135756	+	0.216853i
$146$	3.75447	−	18.3756i	0.310722	−	1.52077i
$147$	5.21257	−	6.48745i	0.429925	−	0.535076i
$148$	−6.81609	+	15.9837i	−0.560279	+	1.31385i
$149$	3.48375	−	13.0015i	0.285400	−	1.06513i	−0.663147	−	0.748489i	$-0.730780\pi$
$149$	3.48375	−	13.0015i	0.285400	−	1.06513i	0.948547	−	0.316637i	$-0.102554\pi$
$150$	7.23272	+	4.28474i	0.590549	+	0.349847i
$151$	−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	$0.736445\pi$
$152$	6.13409	+	0.498170i	0.497540	+	0.0404069i
$153$	3.06911	−	3.06911i	0.248122	−	0.248122i
$154$	−17.0819	+	9.49267i	−1.37650	+	0.764941i
$155$	−11.1854	−	3.42991i	−0.898437	−	0.275497i
$156$	0.799176	−	0.0967771i	0.0639853	−	0.00774837i
$157$	−0.624693	+	1.08200i	−0.0498559	+	0.0863529i	−0.889876	−	0.456202i	$-0.849210\pi$
$157$	−0.624693	+	1.08200i	−0.0498559	+	0.0863529i	0.840020	+	0.542555i	$0.182543\pi$
$158$	14.6420	−	0.883317i	1.16485	−	0.0702729i
$159$	−4.96432	−	8.59846i	−0.393697	−	0.681902i
$160$	−6.28359	+	10.9780i	−0.496761	+	0.867887i
$161$	−21.2607	+	10.1907i	−1.67558	+	0.803137i
$162$	−2.03311	+	1.34325i	−0.159736	+	0.105536i
$163$	−9.41453	−	16.3064i	−0.737403	−	1.27722i	−0.953661	−	0.300883i	$-0.902719\pi$
$163$	−9.41453	−	16.3064i	−0.737403	−	1.27722i	0.216258	−	0.976336i	$-0.430615\pi$
$164$	8.84882	+	11.7835i	0.690977	+	0.920138i
$165$	0.496101	−	13.8757i	0.0386214	−	1.08022i
$166$	10.9528	−	21.9221i	0.850099	−	1.70149i
$167$	−8.22686	−	8.22686i	−0.636614	−	0.636614i	0.313105	−	0.949719i	$-0.398631\pi$
$167$	−8.22686	−	8.22686i	−0.636614	−	0.636614i	−0.949719	+	0.313105i	$0.898631\pi$
$168$	−8.30769	+	3.18342i	−0.640952	+	0.245606i
$169$	12.8854			0.991183
$170$	0.212072	+	8.64840i	0.0162652	+	0.663302i
$171$	3.33455	−	0.893489i	0.254999	−	0.0683268i
$172$	11.2629	−	8.45786i	0.858788	−	0.644906i
$173$	−15.4392	+	8.91380i	−1.17382	+	0.677704i	−0.954576	−	0.297967i	$-0.903692\pi$
$173$	−15.4392	+	8.91380i	−1.17382	+	0.677704i	−0.219241	+	0.975671i	$0.570358\pi$
$174$	2.26956	+	0.463713i	0.172055	+	0.0351540i
$175$	12.1329	+	5.27198i	0.917158	+	0.398524i
$176$	20.8871	+	0.434113i	1.57442	+	0.0327225i
$177$	1.32667	−	4.95120i	0.0997187	−	0.372155i
$178$	−2.60045	+	0.156879i	−0.194912	+	0.0117586i
$179$	2.35237	+	8.77917i	0.175824	+	0.656186i	0.996410	+	0.0846617i	$0.0269809\pi$
$179$	2.35237	+	8.77917i	0.175824	+	0.656186i	−0.820585	+	0.571524i	$0.806352\pi$
$180$	−1.24953	+	6.98449i	−0.0931345	+	0.520593i
$181$	−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	$0.807567\pi$
$182$	1.22882	−	0.307784i	0.0910862	−	0.0228145i
$183$	0.0308220	+	0.0308220i	0.00227843	+	0.00227843i
$184$	25.1220	+	2.04024i	1.85202	+	0.150408i
$185$	−13.2376	−	14.2193i	−0.973248	−	1.04542i
$186$	0.529739	+	8.78102i	0.0388423	+	0.643856i
$187$	12.3739	−	7.14410i	0.904872	−	0.522428i
$188$	−5.13267	−	12.7649i	−0.374338	−	0.930977i
$189$	−10.9524	+	9.39046i	−0.796672	+	0.683055i
$190$	−3.29324	+	6.04141i	−0.238917	+	0.438290i
$191$	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	$0.760949\pi$
$192$	9.38637	+	1.53472i	0.677403	+	0.110759i
$193$	−1.03952	−	3.87953i	−0.0748260	−	0.279254i	0.918368	−	0.395728i	$-0.129508\pi$
$193$	−1.03952	−	3.87953i	−0.0748260	−	0.279254i	−0.993194	+	0.116473i	$0.962841\pi$
$194$	−15.4776	+	5.16442i	−1.11123	+	0.370784i
$195$	−0.263860	+	0.860487i	−0.0188954	+	0.0616208i
$196$	−12.3471	+	6.59919i	−0.881935	+	0.471371i
$197$	2.28106			0.162519			0.0812596	−	0.996693i	$-0.474106\pi$
$197$	2.28106			0.162519			0.0812596	+	0.996693i	$0.474106\pi$
$198$	11.1164	−	3.70921i	0.790008	−	0.263602i
$199$	−0.322024	−	0.185920i	−0.0228276	−	0.0131795i	0.488543	−	0.872540i	$-0.337529\pi$
$199$	−0.322024	−	0.185920i	−0.0228276	−	0.0131795i	−0.511370	+	0.859360i	$0.670862\pi$
$200$	−8.36472	−	11.4031i	−0.591475	−	0.806323i
$201$	4.92506	+	8.53045i	0.347387	+	0.601692i
$202$	−18.4329	−	3.76619i	−1.29693	−	0.264988i
$203$	3.63449	+	0.279064i	0.255091	+	0.0195864i
$204$	6.03518	−	2.42670i	0.422547	−	0.169903i
$205$	−16.0563	+	3.69283i	−1.12142	+	0.257918i
$206$	−16.0047	−	14.1835i	−1.11510	−	0.988212i
$207$	13.6565	−	3.65926i	0.949195	−	0.254336i
$208$	−1.30053	−	0.377610i	−0.0901758	−	0.0261825i
$209$	11.3643			0.786087
$210$	0.518146	−	9.93334i	0.0357555	−	0.685466i
$211$	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	$0.633703\pi$
$212$	2.00795	+	16.5815i	0.137906	+	1.13882i
$213$	3.34482	−	5.79340i	0.229183	−	0.396957i
$214$	−0.280081	−	4.64266i	−0.0191459	−	0.317366i
$215$	3.52967	+	15.3469i	0.240721	+	1.04665i
$216$	15.1717	−	2.77277i	1.03231	−	0.188663i
$217$	2.54866	+	13.6064i	0.173014	+	0.923663i
$218$	−1.09207	+	5.34493i	−0.0739642	+	0.362004i
$219$	4.08074	−	15.2295i	0.275751	−	1.02912i
$220$	−9.92409	+	21.1444i	−0.669082	+	1.42555i
$221$	−0.894638	+	0.239718i	−0.0601799	+	0.0161251i
$222$	−6.52877	+	13.0675i	−0.438183	+	0.877030i
$223$	16.2456	+	16.2456i	1.08788	+	1.08788i	0.995746	+	0.0921383i	$0.0293702\pi$
$223$	16.2456	+	16.2456i	1.08788	+	1.08788i	0.0921383	+	0.995746i	$0.470630\pi$
$224$	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
$227$	−1.40700	+	2.43700i	−0.0933859	+	0.161749i	−0.908934	−	0.416940i	$-0.863102\pi$
$227$	−1.40700	+	2.43700i	−0.0933859	+	0.161749i	0.815548	+	0.578690i	$0.196436\pi$
$228$	5.12212	+	0.728559i	0.339221	+	0.0482500i
$229$	7.23657	+	1.93903i	0.478206	+	0.128135i	0.489867	−	0.871797i	$-0.337045\pi$
$229$	7.23657	+	1.93903i	0.478206	+	0.128135i	−0.0116613	+	0.999932i	$0.503712\pi$
$230$	−13.4874	+	24.7424i	−0.889330	+	1.63147i
$231$	−14.8146	+	7.10091i	−0.974726	+	0.467206i
$232$	−3.20599	−	2.21522i	−0.210484	−	0.145436i
$233$	1.05610	−	3.94140i	0.0691871	−	0.258210i	−0.922665	−	0.385602i	$-0.873994\pi$
$233$	1.05610	−	3.94140i	0.0691871	−	0.258210i	0.991852	+	0.127392i	$0.0406606\pi$
$234$	−0.758270	+	0.0457447i	−0.0495697	+	0.00299042i
$235$	15.3723	+	0.549608i	1.00278	+	0.0358525i
$236$	−5.32017	+	6.78621i	−0.346314	+	0.441745i
$237$	12.3313			0.801007
$238$	8.94726	−	4.97214i	0.579965	−	0.322296i
$239$		−	14.9500i		−	0.967032i	−0.875335	−	0.483516i	$-0.839359\pi$
$239$		−	14.9500i		−	0.967032i	0.875335	−	0.483516i	$-0.160641\pi$
$240$	−5.82853	+	8.89395i	−0.376230	+	0.574102i
$241$	−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	$0.674056\pi$
$242$	22.9797	−	1.38631i	1.47719	−	0.0891154i
$243$	12.3929	−	7.15505i	0.795006	−	0.458997i
$244$	−0.0273559	−	0.0680340i	−0.00175128	−	0.00435543i
$245$	−1.13846	−	15.6110i	−0.0727336	−	0.997351i
$246$	6.82885	+	10.3359i	0.435391	+	0.658995i
$247$	−0.711563	−	0.190663i	−0.0452757	−	0.0121316i
$248$	4.97475	−	13.9376i	0.315897	−	0.885040i
$249$	10.3006	−	17.8412i	0.652775	−	1.13064i
$250$	15.4479	−	3.37085i	0.977011	−	0.213191i
$251$	−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	$0.795561\pi$
$252$	8.00618	−	2.52649i	0.504342	−	0.159154i
$253$	46.5422			2.92609
$254$	6.37782	+	19.1141i	0.400180	+	1.19933i
$255$	−0.259852	+	7.26792i	−0.0162725	+	0.455135i
$256$	−13.5120	−	8.56882i	−0.844503	−	0.535551i
$257$	−17.0217	−	4.56094i	−1.06178	−	0.284504i	−0.314669	−	0.949201i	$-0.601894\pi$
$257$	−17.0217	−	4.56094i	−1.06178	−	0.284504i	−0.747112	+	0.664698i	$0.768560\pi$
$258$	9.87927	−	6.52714i	0.615057	−	0.406362i
$259$	−7.63178	+	21.6829i	−0.474216	+	1.34731i
$260$	0.976130	−	1.15743i	0.0605370	−	0.0717807i
$261$	−2.11142	−	0.565754i	−0.130694	−	0.0350193i
$262$	10.5112	+	9.31515i	0.649386	+	0.575492i
$263$	16.6353	−	4.45741i	1.02578	−	0.274856i	0.293569	−	0.955938i	$-0.405157\pi$
$263$	16.6353	−	4.45741i	1.02578	−	0.274856i	0.732207	+	0.681082i	$0.238490\pi$
$264$	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
$267$	−2.19007			−0.134030
$268$	−1.99207	−	16.4503i	−0.121685	−	1.00486i
$269$	−3.76940	+	1.01001i	−0.229824	+	0.0615812i	−0.371893	−	0.928276i	$-0.621291\pi$
$269$	−3.76940	+	1.01001i	−0.229824	+	0.0615812i	0.142069	+	0.989857i	$0.454625\pi$
$270$	−4.05329	+	16.7603i	−0.246676	+	1.02000i
$271$	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	$0.0820359\pi$
$272$	−10.9404	−	0.227383i	−0.663358	−	0.0137871i
$273$	1.04673	−	0.196066i	0.0633509	−	0.0118665i
$274$	−2.05135	+	10.0400i	−0.123927	+	0.606536i
$275$	−17.0998	−	19.7373i	−1.03116	−	1.19020i
$276$	20.9775	+	2.98379i	1.26270	+	0.179603i
$277$	−13.2070	+	22.8753i	−0.793535	+	1.37444i	0.130231	+	0.991484i	$0.458428\pi$
$277$	−13.2070	+	22.8753i	−0.793535	+	1.37444i	−0.923766	+	0.382959i	$0.874905\pi$
$278$	16.3770	−	5.46452i	0.982227	−	0.327740i
$279$		−	8.30124i		−	0.496982i
$280$	−7.35669	+	15.0293i	−0.439646	+	0.898171i
$281$			26.4543i			1.57813i	0.614310	+	0.789065i	$0.289434\pi$
$281$			26.4543i			1.57813i	−0.614310	+	0.789065i	$0.710566\pi$
$282$	−3.66081	−	10.9713i	−0.217998	−	0.653333i
$283$	−12.9068	+	22.3552i	−0.767230	+	1.32888i	0.171829	+	0.985127i	$0.445032\pi$
$283$	−12.9068	+	22.3552i	−0.767230	+	1.32888i	−0.939059	+	0.343755i	$0.888301\pi$
$284$	−8.99888	+	6.75770i	−0.533985	+	0.400995i
$285$	−3.06931	+	4.90285i	−0.181810	+	0.290420i
$286$	−2.45009	−	0.500600i	−0.144877	−	0.0296011i
$287$	12.6886	+	14.7992i	0.748986	+	0.873569i
$288$	−8.75412	−	1.97898i	−0.515842	−	0.116612i
$289$	8.24111	−	4.75801i	0.484771	−	0.279883i
$290$	3.71859	−	2.27026i	0.218363	−	0.133314i
$291$	−13.2493	+	3.55013i	−0.776685	+	0.208112i
$292$	−16.3645	+	20.8739i	−0.957658	+	1.22155i
$293$	0.188136			0.0109910			0.00549551	−	0.999985i	$-0.498251\pi$
$293$	0.188136			0.0109910			0.00549551	+	0.999985i	$0.498251\pi$
$294$	−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
$297$	27.5093	−	7.37110i	1.59625	−	0.427715i
$298$	−12.6252	+	14.2463i	−0.731358	+	0.825265i
$299$	−2.91419	−	0.780854i	−0.168532	−	0.0451579i
$300$	−6.44188	−	9.99223i	−0.371922	−	0.576902i
$301$	14.1453	−	12.1280i	0.815324	−	0.699047i
$302$	4.16640	+	6.30613i	0.239749	+	0.362877i
$303$	−15.2771	−	4.09347i	−0.877644	−	0.235164i
$304$	−7.44538	−	4.50742i	−0.427022	−	0.258518i
$305$	0.0819307	+	0.00292928i	0.00469134	+	0.000167730i
$306$	−5.82263	+	1.94284i	−0.332858	+	0.111065i
$307$	−4.83012			−0.275670			−0.137835	−	0.990455i	$-0.544014\pi$
$307$	−4.83012			−0.275670			−0.137835	+	0.990455i	$0.544014\pi$
$308$	27.6104	−	1.21225i	1.57325	−	0.0690745i
$309$	−12.7121	−	12.7121i	−0.723167	−	0.723167i
$310$	11.9828	+	11.4092i	0.680577	+	0.647998i
$311$	−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	$0.253235\pi$
$312$	−1.07221	−	0.382704i	−0.0607019	−	0.0216663i
$313$	−29.6134	−	7.93489i	−1.67385	−	0.448506i	−0.707704	−	0.706509i	$-0.750269\pi$
$313$	−29.6134	−	7.93489i	−1.67385	−	0.448506i	−0.966144	+	0.258002i	$0.916936\pi$
$314$	1.47420	−	0.973990i	0.0831940	−	0.0549654i
$315$	−1.05252	+	9.32710i	−0.0593027	+	0.525523i
$316$	−19.0819	−	8.13730i	−1.07344	−	0.457759i
$317$	−0.125967	+	0.0727273i	−0.00707504	+	0.00408477i	−0.503533	−	0.863976i	$-0.667967\pi$
$317$	−0.125967	+	0.0727273i	−0.00707504	+	0.00408477i	0.496458	+	0.868061i	$0.334634\pi$
$318$	0.845537	+	14.0157i	0.0474154	+	0.785964i
$319$	−6.23178	−	3.59792i	−0.348913	−	0.201445i
$320$	14.8883	−	9.91663i	0.832279	−	0.554356i
$321$		−	3.91000i		−	0.218235i
$322$	33.3382	+	0.546031i	1.85786	+	0.0304291i
$323$	−5.95250			−0.331206
$324$	3.42112	−	0.414284i	0.190062	−	0.0230158i
$325$	0.739546	+	1.52272i	0.0410227	+	0.0844651i
$326$	1.60351	+	26.5800i	0.0888102	+	1.47213i
$327$	−1.18697	+	4.42984i	−0.0656397	+	0.244971i
$328$	−3.74664	−	20.5004i	−0.206874	−	1.13195i
$329$	−7.86678	−	16.4124i	−0.433710	−	0.904844i
$330$	−9.39806	+	17.2406i	−0.517346	+	0.949066i
$331$	−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	$0.640034\pi$
$332$	−27.7127	+	20.8108i	−1.52093	+	1.14214i
$333$	6.89222	−	11.9377i	0.377691	−	0.654181i
$334$	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	0.660426	−	0.750892i	$-0.270376\pi$
$337$	−1.66073	−	1.66073i	−0.0904659	−	0.0904659i	−0.750892	+	0.660426i	$0.770376\pi$
$338$	−16.3013	−	8.14448i	−0.886675	−	0.443001i
$339$	3.91714	−	1.04960i	0.212750	−	0.0570062i
$340$	5.19812	−	11.0752i	0.281907	−	0.600635i
$341$	7.07278	−	26.3960i	0.383012	−	1.42942i
$342$	−4.78330	−	0.977317i	−0.258651	−	0.0528473i
$343$	−15.7355	+	9.76704i	−0.849635	+	0.527371i
$344$	−19.5947	+	3.58111i	−1.05648	+	0.193080i
$345$	−12.5703	+	20.0795i	−0.676761	+	1.08104i
$346$	25.1663	−	1.51822i	1.35295	−	0.0816202i
$347$	8.39542	−	14.5413i	0.450689	−	0.780617i	−0.547739	−	0.836649i	$-0.684512\pi$
$347$	8.39542	−	14.5413i	0.450689	−	0.780617i	0.998429	+	0.0560318i	$0.0178448\pi$
$348$	−2.57812	−	2.02117i	−0.138202	−	0.108346i
$349$	−1.46526	−	1.46526i	−0.0784338	−	0.0784338i	0.666802	−	0.745235i	$-0.267663\pi$
$349$	−1.46526	−	1.46526i	−0.0784338	−	0.0784338i	−0.745235	+	0.666802i	$0.767663\pi$
$350$	−12.0170	−	14.3384i	−0.642338	−	0.766421i
$351$	−1.84613			−0.0985391
$352$	−26.1499	−	13.7513i	−1.39379	−	0.732948i
$353$	−9.23892	+	2.47556i	−0.491738	+	0.131761i	−0.496163	−	0.868229i	$-0.665258\pi$
$353$	−9.23892	+	2.47556i	−0.491738	+	0.131761i	0.00442496	+	0.999990i	$0.498591\pi$
$354$	−4.80789	+	5.42523i	−0.255537	+	0.288348i
$355$	−2.82015	−	12.2619i	−0.149678	−	0.650795i
$356$	3.38899	+	1.44520i	0.179616	+	0.0765954i
$357$	7.75968	−	3.71937i	0.410686	−	0.196850i
$358$	2.57307	−	12.5934i	0.135991	−	0.665583i
$359$	9.74169	+	16.8731i	0.514147	+	0.890528i	0.999865	+	0.0164129i	$0.00522461\pi$
$359$	9.74169	+	16.8731i	0.514147	+	0.890528i	−0.485719	+	0.874115i	$0.661442\pi$
$360$	5.99548	−	8.04630i	0.315990	−	0.424077i
$361$	12.3544	+	7.13280i	0.650230	+	0.375410i
$362$	2.16636	+	6.49251i	0.113861	+	0.341239i
$363$	19.3533			1.01578
$364$	−1.74913	−	0.387324i	−0.0916791	−	0.0203013i
$365$	−13.9002	−	26.1950i	−0.727570	−	1.37111i
$366$	−0.0195113	−	0.0584746i	−0.00101987	−	0.00305652i
$367$	−2.63310	−	9.82688i	−0.137447	−	0.512959i	−0.999976	−	0.00695103i	$-0.997787\pi$
$367$	−2.63310	−	9.82688i	−0.137447	−	0.512959i	0.862529	−	0.506008i	$-0.168879\pi$
$368$	−30.4923	−	18.4600i	−1.58952	−	0.962294i
$369$	−5.84498	−	10.1238i	−0.304278	−	0.527024i
$370$	7.75933	+	26.3560i	0.403389	+	1.37018i
$371$	4.06802	+	21.7177i	0.211201	+	1.12753i
$372$	4.88006	−	11.4437i	0.253019	−	0.593330i
$373$	−4.15444	+	2.39857i	−0.215109	+	0.124193i	−0.603683	−	0.797224i	$-0.706301\pi$
$373$	−4.15444	+	2.39857i	−0.215109	+	0.124193i	0.388575	+	0.921417i	$0.372968\pi$
$374$	−20.1699	+	1.21680i	−1.04296	+	0.0629194i
$375$	13.1335	−	2.04658i	0.678213	−	0.105685i
$376$	−1.57498	+	19.3931i	−0.0812234	+	1.00012i
$377$	0.329832	+	0.329832i	0.0169872	+	0.0169872i
$378$	19.7914	−	4.95718i	1.01796	−	0.254970i
$379$	−4.22575	−	4.22575i	−0.217062	−	0.217062i	0.590197	−	0.807259i	$-0.299050\pi$
$379$	−4.22575	−	4.22575i	−0.217062	−	0.217062i	−0.807259	+	0.590197i	$0.799050\pi$
$380$	7.98489	−	5.56144i	0.409616	−	0.285296i
$381$	4.38424	+	16.3622i	0.224612	+	0.838262i
$382$	−0.530680	−	8.79663i	−0.0271519	−	0.450075i
$383$	−3.87586	+	14.4649i	−0.198047	+	0.739122i	0.793410	+	0.608688i	$0.208304\pi$
$383$	−3.87586	+	14.4649i	−0.198047	+	0.739122i	−0.991457	+	0.130434i	$0.958363\pi$
$384$	−10.9047	−	7.87443i	−0.556476	−	0.401840i
$385$	−11.2936	+	28.7612i	−0.575574	+	1.46581i
$386$	−1.13704	+	5.56505i	−0.0578740	+	0.283254i
$387$	−9.67652	+	5.58674i	−0.491885	+	0.283990i
$388$	22.8450	+	3.24943i	1.15978	+	0.164965i
$389$	−12.8771	+	3.45041i	−0.652895	+	0.174943i	−0.570037	−	0.821619i	$-0.693071\pi$
$389$	−12.8771	+	3.45041i	−0.652895	+	0.174943i	−0.0828575	+	0.996561i	$0.526405\pi$
$390$	0.877699	−	0.921827i	0.0444440	−	0.0466785i
$391$	−24.3783			−1.23286
$392$	19.7915	−	0.544413i	0.999622	−	0.0274970i
$393$	8.34879	+	8.34879i	0.421141	+	0.421141i
$394$	−2.88578	−	1.44180i	−0.145384	−	0.0726366i
$395$	16.9755	−	15.8036i	0.854131	−	0.795163i
$396$	−16.4079	−	2.33382i	−0.824527	−	0.117279i
$397$	13.9805	+	24.2150i	0.701663	+	1.21532i	0.967883	+	0.251403i	$0.0808919\pi$
$397$	13.9805	+	24.2150i	0.701663	+	1.21532i	−0.266220	+	0.963912i	$0.585775\pi$
$398$	0.289878	+	0.438750i	0.0145303	+	0.0219926i
$399$	6.82404	+	0.523964i	0.341629	+	0.0262310i
$400$	3.37463	+	19.7132i	0.168732	+	0.985662i
$401$	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	$0.682758\pi$
$402$	−0.838849	−	13.9049i	−0.0418380	−	0.693513i
$403$	−0.885706	+	1.53409i	−0.0441202	+	0.0764184i
$404$	20.9390	+	16.4155i	1.04175	+	0.816703i
$405$	−1.12953	+	3.68358i	−0.0561270	+	0.183039i
$406$	−4.42161	−	2.65030i	−0.219441	−	0.131532i
$407$	32.0867	−	32.0867i	1.59048	−	1.59048i
$408$	−9.16896	−	0.744642i	−0.453931	−	0.0368653i
$409$	2.11431	+	1.22070i	0.104546	+	0.0603597i	0.551361	−	0.834267i	$-0.314109\pi$
$409$	2.11431	+	1.22070i	0.104546	+	0.0603597i	−0.446815	+	0.894626i	$0.647442\pi$
$410$	22.6470	+	5.47691i	1.11845	+	0.270485i
$411$	−2.22962	+	8.32104i	−0.109979	+	0.410447i
$412$	11.2826	+	28.0597i	0.555853	+	1.38240i
$413$	−6.44317	+	9.41330i	−0.317048	+	0.463198i
$414$	−19.5898	−	4.00257i	−0.962788	−	0.196716i
$415$	−8.68487	−	37.7615i	−0.426323	−	1.85364i
$416$	1.40663	+	1.29975i	0.0689659	+	0.0637253i
$417$	14.0192	−	3.75642i	0.686521	−	0.183953i
$418$	−14.3770	−	7.18307i	−0.703204	−	0.351336i
$419$	18.1866	+	18.1866i	0.888473	+	0.888473i	0.994376	−	0.105903i	$-0.0337734\pi$
$419$	18.1866	+	18.1866i	0.888473	+	0.888473i	−0.105903	+	0.994376i	$0.533773\pi$
$420$	−6.93409	+	12.2392i	−0.338349	+	0.597212i
$421$	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	$-0.136759\pi$
$422$	−4.64616	−	13.9244i	−0.226171	−	0.677828i
$423$	2.82480	+	10.5423i	0.137346	+	0.512584i
$424$	7.94040	−	22.2464i	0.385620	−	1.08038i
$425$	8.95668	+	10.3382i	0.434463	+	0.501474i
$426$	−7.89338	+	5.21508i	−0.382436	+	0.252671i
$427$	−0.0419281	−	0.0874742i	−0.00202904	−	0.00423317i
$428$	−2.58016	+	6.05048i	−0.124717	+	0.292461i
$429$	−2.03062	−	0.544103i	−0.0980392	−	0.0262695i
$430$	5.23493	−	21.6464i	0.252451	−	1.04388i
$431$	−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	$0.273831\pi$
$432$	−20.9464	−	6.08179i	−1.00778	−	0.292610i
$433$	−13.7552	−	13.7552i	−0.661032	−	0.661032i	0.294591	−	0.955623i	$-0.404816\pi$
$433$	−13.7552	−	13.7552i	−0.661032	−	0.661032i	−0.955623	+	0.294591i	$0.904816\pi$
$434$	5.37590	−	18.8244i	0.258052	−	0.903602i
$435$	3.23533	−	1.71681i	0.155122	−	0.0823146i
$436$	4.75996	−	6.07162i	0.227961	−	0.290778i
$437$	−16.7919	−	9.69480i	−0.803265	−	0.463765i
$438$	−14.7887	+	16.6876i	−0.706633	+	0.797365i
$439$	15.7697	−	9.10464i	0.752647	−	0.434541i	−0.0740025	−	0.997258i	$-0.523577\pi$
$439$	15.7697	−	9.10464i	0.752647	−	0.434541i	0.826650	+	0.562717i	$0.190244\pi$
$440$	25.9198	−	20.4771i	1.23568	−	0.976207i
$441$	10.3531	−	4.01958i	0.493005	−	0.191409i
$442$	1.28333	+	0.262208i	0.0610417	+	0.0124720i
$443$	14.8209	−	8.55684i	0.704161	−	0.406548i	−0.104734	−	0.994500i	$-0.533399\pi$
$443$	14.8209	−	8.55684i	0.704161	−	0.406548i	0.808895	+	0.587953i	$0.200066\pi$
$444$	16.5191	−	12.4050i	0.783964	−	0.588717i
$445$	−3.01488	+	2.80674i	−0.142919	+	0.133052i
$446$	−10.2840	−	30.8207i	−0.486960	−	1.45940i
$447$	−11.3155	+	11.3155i	−0.535203	+	0.535203i
$448$	−18.5698	−	10.1568i	−0.877342	−	0.479866i
$449$			13.5321i			0.638618i	0.947651	+	0.319309i	$0.103451\pi$
$449$			13.5321i			0.638618i	−0.947651	+	0.319309i	$0.896549\pi$
$450$	5.50001	+	9.77808i	0.259273	+	0.460943i
$451$	−9.96002	−	37.1713i	−0.468999	−	1.75033i
$452$	−6.75414	−	0.960694i	−0.317688	−	0.0451873i
$453$	3.17694	+	5.50262i	0.149266	+	0.258536i
$454$	3.32036	−	2.19373i	0.155832	−	0.102957i
$455$	1.18967	−	1.61137i	0.0557725	−	0.0755422i
$456$	−6.01951	−	4.15925i	−0.281889	−	0.194775i
$457$	14.1882	+	3.80171i	0.663695	+	0.177837i	0.574913	−	0.818214i	$-0.305036\pi$
$457$	14.1882	+	3.80171i	0.663695	+	0.177837i	0.0887822	+	0.996051i	$0.471702\pi$
$458$	−7.92939	−	7.02710i	−0.370516	−	0.328355i
$459$	−14.4090	+	3.86089i	−0.672556	+	0.180211i
$460$	32.7019	−	22.7767i	1.52473	−	1.06197i
$461$	−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	$0.286708\pi$
$462$	23.2302	+	0.380478i	1.08077	+	0.0177014i
$463$	3.01354	−	3.01354i	0.140051	−	0.140051i	−0.633605	−	0.773656i	$-0.718426\pi$
$463$	3.01354	−	3.01354i	0.140051	−	0.140051i	0.773656	+	0.633605i	$0.218426\pi$
$464$	2.65573	+	4.82890i	0.123289	+	0.224176i
$465$	9.47763	+	10.1805i	0.439515	+	0.472108i
$466$	−3.82732	+	4.31875i	−0.177297	+	0.200062i
$467$	10.9168	+	18.9085i	0.505171	+	0.874982i	0.999982	+	0.00598173i	$0.00190405\pi$
$467$	10.9168	+	18.9085i	0.505171	+	0.874982i	−0.494811	+	0.869001i	$0.664763\pi$
$468$	0.988203	+	0.421409i	0.0456797	+	0.0194796i
$469$	−4.03584	−	21.5459i	−0.186358	−	0.994899i
$470$	−19.1001	−	10.4117i	−0.881023	−	0.480256i
$471$	1.28636	−	0.742682i	0.0592725	−	0.0342210i
$472$	11.0199	−	5.22252i	0.507234	−	0.240386i
$473$	−35.5290	+	9.51997i	−1.63363	+	0.437729i
$474$	−15.6004	−	7.79429i	−0.716551	−	0.358004i
$475$	2.05812	+	10.6829i	0.0944328	+	0.490165i
$476$	−14.4620	+	0.634963i	−0.662863	+	0.0291035i
$477$		−	13.2499i		−	0.606673i
$478$	−9.44944	+	18.9132i	−0.432208	+	0.865071i
$479$	−2.99347	+	5.18484i	−0.136775	+	0.236901i	−0.926274	−	0.376850i	$-0.877007\pi$
$479$	−2.99347	+	5.18484i	−0.136775	+	0.236901i	0.789499	+	0.613752i	$0.210340\pi$
$480$	12.9953	−	7.56771i	0.593152	−	0.345417i
$481$	−2.54740	+	1.47074i	−0.116151	+	0.0670600i
$482$	0.561870	+	0.850429i	0.0255925	+	0.0387360i
$483$	27.9476	+	2.14588i	1.27166	+	0.0976409i
$484$	−29.9479	−	12.7710i	−1.36127	−	0.580499i
$485$	−13.6894	+	21.8671i	−0.621602	+	0.992933i
$486$	−20.2008	+	1.21867i	−0.916327	+	0.0552799i
$487$	3.60084	+	13.4385i	0.163170	+	0.608958i	0.998267	+	0.0588549i	$0.0187449\pi$
$487$	3.60084	+	13.4385i	0.163170	+	0.608958i	−0.835097	+	0.550103i	$0.814588\pi$
$488$	−0.00839428	+	0.103361i	−0.000379991	+	0.00467893i
$489$			22.3854i			1.01230i
$490$	−8.42701	+	20.4691i	−0.380694	+	0.924701i
$491$	−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	$0.480773\pi$
$492$	−2.10614	−	17.3923i	−0.0949523	−	0.784107i
$493$	3.26413	+	1.88455i	0.147009	+	0.0848757i
$494$	0.779688	+	0.690967i	0.0350798	+	0.0310881i
$495$	9.83204	−	15.7055i	0.441917	−	0.705909i
$496$	−15.1031	+	14.4881i	−0.678151	+	0.650536i
$497$	−11.3019	+	9.69009i	−0.506960	+	0.434660i
$498$	−24.3083	+	16.0602i	−1.08928	+	0.719676i
$499$	−2.79984	−	0.750216i	−0.125338	−	0.0335843i	0.195605	−	0.980683i	$-0.437333\pi$
$499$	−2.79984	−	0.750216i	−0.125338	−	0.0335843i	−0.320943	+	0.947099i	$0.604000\pi$
$500$	−21.6738	−	5.49970i	−0.969281	−	0.245954i
$501$	3.57999	+	13.3607i	0.159942	+	0.596912i
$502$	2.02318	+	6.06340i	0.0902988	+	0.270623i
$503$	12.8172	−	12.8172i	0.571492	−	0.571492i	−0.361053	−	0.932545i	$-0.617583\pi$
$503$	12.8172	−	12.8172i	0.571492	−	0.571492i	0.932545	+	0.361053i	$0.117583\pi$
$504$	−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
$507$	−13.2667	−	7.65956i	−0.589197	−	0.340173i
$508$	4.01289	−	28.2126i	0.178043	−	1.25173i
$509$	2.27292	−	8.48264i	0.100745	−	0.375986i	−0.897083	−	0.441863i	$-0.854318\pi$
$509$	2.27292	−	8.48264i	0.100745	−	0.375986i	0.997828	+	0.0658766i	$0.0209844\pi$
$510$	4.92259	−	9.03043i	0.217976	−	0.399874i
$511$	−19.8187	+	28.9546i	−0.876729	+	1.28088i
$512$	11.6780	+	19.3810i	0.516100	+	0.856528i
$513$	−11.4604	−	3.07082i	−0.505991	−	0.135580i
$514$	18.6513	+	16.5290i	0.822674	+	0.729061i
$515$	−33.7912	−	1.20814i	−1.48902	−	0.0532372i
$516$	−16.6239	+	2.01309i	−0.731827	+	0.0886214i
$517$			35.9287i			1.58014i
$518$	23.3601	−	22.6072i	1.02638	−	0.993305i
$519$	21.1948			0.930349
$520$	−1.96648	+	0.847283i	−0.0862360	+	0.0371558i
$521$	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	$0.0640684\pi$
$522$	2.31357	+	2.05031i	0.101262	+	0.0897395i
$523$	−12.8739	−	22.2982i	−0.562936	−	0.975034i	−0.997238	−	0.0742670i	$-0.976338\pi$
$523$	−12.8739	−	22.2982i	−0.562936	−	0.975034i	0.434302	−	0.900767i	$-0.356995\pi$
$524$	−7.40994	−	18.4285i	−0.323705	−	0.805052i
$525$	−9.35808	−	12.6402i	−0.408420	−	0.551665i
$526$	−23.8628	−	4.87561i	−1.04047	−	0.212587i
$527$	−3.70463	+	13.8259i	−0.161376	+	0.602265i
$528$	−21.2472	−	12.8630i	−0.924666	−	0.559791i
$529$	−48.8520	−	28.2047i	−2.12400	−	1.22629i
$530$	19.1262	+	18.2107i	0.830790	+	0.791021i
$531$	4.83700	−	4.83700i	0.209908	−	0.209908i
$532$	−10.2140	−	5.31390i	−0.442833	−	0.230387i
$533$			2.49454i			0.108050i
$534$	2.77066	+	1.38428i	0.119898	+	0.0599037i
$535$	−5.01097	−	5.38257i	−0.216643	−	0.232709i
$536$	−7.87760	+	22.0704i	−0.340260	+	0.953298i
$537$	2.79668	−	10.4373i	0.120685	−	0.450404i
$538$	5.40707	+	1.10477i	0.233116	+	0.0476299i
$539$	36.3451	−	3.96031i	1.56550	−	0.170583i
$540$	15.7216	−	18.6416i	0.676548	−	0.802205i
$541$	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	$0.0348458\pi$
$542$	−32.9981	+	1.99070i	−1.41739	+	0.0855078i
$543$	1.48920	+	5.55777i	0.0639077	+	0.238507i
$544$	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
$547$		−	13.3169i		−	0.569388i	−0.958618	−	0.284694i	$-0.908108\pi$
$547$		−	13.3169i		−	0.569388i	0.958618	−	0.284694i	$-0.0918920\pi$
$548$	8.94114	−	11.4050i	0.381946	−	0.487196i
$549$	0.0150555	+	0.0561879i	0.000642554	+	0.00239804i
$550$	9.15767	+	35.7780i	0.390484	+	1.52558i
$551$	1.49890	+	2.59617i	0.0638554	+	0.110601i
$552$	−24.6527	−	17.0341i	−1.04929	−	0.725018i
$553$	−25.8858	−	9.11110i	−1.10078	−	0.387444i
$554$	31.1671	−	20.5918i	1.32416	−	0.874861i
$555$	5.17692	+	22.5091i	0.219748	+	0.955456i
$556$	−24.1725	−	3.43825i	−1.02514	−	0.145814i
$557$	8.75764	+	5.05622i	0.371073	+	0.214239i	0.673927	−	0.738798i	$-0.264606\pi$
$557$	8.75764	+	5.05622i	0.371073	+	0.214239i	−0.302854	+	0.953037i	$0.597940\pi$
$558$	−5.24698	+	10.5019i	−0.222122	+	0.444582i
$559$	2.38432			0.100846
$560$	18.8065	−	14.3636i	0.794722	−	0.606974i
$561$	−16.9869			−0.717187
$562$	16.7210	−	33.4674i	0.705332	−	1.41174i
$563$	−18.9085	−	10.9168i	−0.796897	−	0.460088i	0.0454883	−	0.998965i	$-0.485516\pi$
$563$	−18.9085	−	10.9168i	−0.796897	−	0.460088i	−0.842385	+	0.538876i	$0.818849\pi$
$564$	−2.30337	+	16.1938i	−0.0969892	+	0.681880i
$565$	4.04726	−	6.46501i	0.170270	−	0.271985i
$566$	30.4586	−	20.1237i	1.28027	−	0.845861i
$567$	4.48085	−	0.839323i	0.188178	−	0.0352483i
$568$	15.6559	−	2.86125i	0.656905	−	0.120055i
$569$	−6.69251	−	11.5918i	−0.280564	−	0.485952i	0.690959	−	0.722894i	$-0.257188\pi$
$569$	−6.69251	−	11.5918i	−0.280564	−	0.485952i	−0.971524	+	0.236942i	$0.923855\pi$
$570$	6.98195	−	4.26259i	0.292442	−	0.178540i
$571$	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	$0.798173\pi$
$572$	2.78320	+	2.18194i	0.116372	+	0.0912317i
$573$		−	7.40843i		−	0.309492i
$574$	−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
$577$	3.27239	+	12.2127i	0.136231	+	0.508422i	0.999990	+	0.00451610i	$0.00143752\pi$
$577$	3.27239	+	12.2127i	0.136231	+	0.508422i	−0.863759	+	0.503906i	$0.831896\pi$
$578$	−13.4333	+	0.810397i	−0.558750	+	0.0337081i
$579$	−1.23586	+	4.61228i	−0.0513604	+	0.191680i
$580$	−6.13936	+	0.521692i	−0.254923	+	0.0216621i
$581$	−34.8051	+	29.8414i	−1.44396	+	1.23803i
$582$	19.0056	+	3.88320i	0.787808	+	0.160964i
$583$	11.2891	−	42.1317i	0.467549	−	1.74492i
$584$	33.8965	−	16.0641i	1.40265	−	0.664737i
$585$	−0.879117	+	0.818424i	−0.0363470	+	0.0338377i
$586$	−0.238011	−	0.118915i	−0.00983216	−	0.00491235i
$587$		−	27.4813i		−	1.13428i	−0.823623	−	0.567138i	$-0.808051\pi$
$587$		−	27.4813i		−	1.13428i	0.823623	−	0.567138i	$-0.191949\pi$
$588$	16.6353	+	0.545072i	0.686030	+	0.0224784i
$589$	−8.05008	+	8.05008i	−0.331698	+	0.331698i
$590$	0.334232	+	13.6301i	0.0137601	+	0.561144i
$591$	−2.34858	−	1.35595i	−0.0966075	−	0.0557764i
$592$	−33.7482	+	8.29519i	−1.38704	+	0.340930i
$593$	3.53372	−	13.1880i	0.145113	−	0.541568i	−0.854638	−	0.519225i	$-0.826221\pi$
$593$	3.53372	−	13.1880i	0.145113	−	0.541568i	0.999750	−	0.0223429i	$-0.00711256\pi$
$594$	−39.4612	−	8.06266i	−1.61911	−	0.330815i
$595$	5.91544	−	15.0648i	0.242509	−	0.617595i
$596$	24.9768	−	10.0430i	1.02309	−	0.411377i
$597$	0.221036	+	0.382846i	0.00904641	+	0.0156688i
$598$	3.19319	+	2.82983i	0.130579	+	0.115721i
$599$	−18.2328	+	31.5801i	−0.744970	+	1.29033i	0.205238	+	0.978712i	$0.434203\pi$
$599$	−18.2328	+	31.5801i	−0.744970	+	1.29033i	−0.950209	+	0.311615i	$0.899130\pi$
$600$	1.83383	+	16.7129i	0.0748658	+	0.682303i
$601$	32.7250			1.33488			0.667440	−	0.744664i	$-0.267390\pi$
$601$	32.7250			1.33488			0.667440	+	0.744664i	$0.267390\pi$
$602$	−25.5611	+	6.40232i	−1.04179	+	0.260939i
$603$			13.1451i			0.535312i
$604$	−1.28499	−	10.6114i	−0.0522857	−	0.431770i
$605$	26.6420	−	24.8027i	1.08315	−	1.00837i
$606$	16.7397	+	14.8349i	0.680003	+	0.602625i
$607$	−4.59463	−	1.23113i	−0.186490	−	0.0499700i	0.164365	−	0.986400i	$-0.447442\pi$
$607$	−4.59463	−	1.23113i	−0.186490	−	0.0499700i	−0.350855	+	0.936430i	$0.614109\pi$
$608$	6.57016	+	10.4084i	0.266455	+	0.422115i
$609$	−3.57617	−	2.44780i	−0.144914	−	0.0991899i
$610$	−0.101799	−	0.0554919i	−0.00412173	−	0.00224680i
$611$	0.602787	−	2.24963i	0.0243862	−	0.0910104i
$612$	8.59424	+	1.22243i	0.347402	+	0.0494137i
$613$	22.5305	+	13.0080i	0.909997	+	0.525387i	0.880430	−	0.474176i	$-0.157254\pi$
$613$	22.5305	+	13.0080i	0.909997	+	0.525387i	0.0295666	+	0.999563i	$0.490587\pi$
$614$	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	$-0.637423\pi$
$617$	12.1665	−	12.1665i	0.489805	−	0.489805i	0.908245	+	0.418440i	$0.137423\pi$
$618$	8.04716	+	24.1171i	0.323704	+	0.970132i
$619$	9.53814	+	35.5968i	0.383370	+	1.43076i	0.840720	+	0.541470i	$0.182132\pi$
$619$	9.53814	+	35.5968i	0.383370	+	1.43076i	−0.457350	+	0.889287i	$0.651201\pi$
$620$	−7.94805	−	22.0078i	−0.319201	−	0.883854i
$621$	−46.9359	−	12.5764i	−1.88347	−	0.504675i
$622$	11.1793	−	7.38605i	0.448249	−	0.296154i
$623$	4.59737	+	1.61815i	0.184190	+	0.0648298i
$624$	1.11456	+	1.16187i	0.0446181	+	0.0465121i
$625$	15.4570	−	19.6490i	0.618279	−	0.785959i
$626$	32.4486	+	28.7562i	1.29691	+	1.14933i
$627$	−11.7007	−	6.75539i	−0.467280	−	0.269784i
$628$	−2.48065	+	0.300397i	−0.0989886	+	0.0119871i
$629$	−16.8066	+	16.8066i	−0.670123	+	0.670123i
$630$	7.22694	−	11.1345i	0.287928	−	0.443608i
$631$		−	11.4540i		−	0.455976i	−0.973664	−	0.227988i	$-0.926785\pi$
$631$		−	11.4540i		−	0.455976i	0.973664	−	0.227988i	$-0.0732147\pi$
$632$	18.9973	+	22.3557i	0.755671	+	0.889261i
$633$	−3.19386	−	11.9197i	−0.126945	−	0.473764i
$634$	0.205331	−	0.0123871i	0.00815472	−	0.000491955i
$635$	27.0048	+	16.9057i	1.07165	+	0.670883i
$636$	7.78926	−	18.2658i	0.308864	−	0.724286i
$637$	−2.34215	−	0.361803i	−0.0927993	−	0.0143352i
$638$	5.60970	+	8.49068i	0.222090	+	0.336149i
$639$	7.73138	−	4.46372i	0.305849	−	0.176582i
$640$	−25.1032	+	3.13510i	−0.992291	+	0.123926i
$641$	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	$-0.0610774\pi$
$642$	−2.47140	+	4.94656i	−0.0975385	+	0.195225i
$643$			5.80713i			0.229011i	0.993423	+	0.114505i	$0.0365283\pi$
$643$			5.80713i			0.229011i	−0.993423	+	0.114505i	$0.963472\pi$
$644$	−41.8311	−	21.7629i	−1.64838	−	0.857579i
$645$	5.48863	−	17.8993i	0.216115	−	0.704783i
$646$	7.53052	+	3.76240i	0.296284	+	0.148030i
$647$	−34.6435	+	9.28270i	−1.36198	+	0.364941i	−0.864542	−	0.502561i	$-0.832391\pi$
$647$	−34.6435	+	9.28270i	−1.36198	+	0.364941i	−0.497435	+	0.867501i	$0.665725\pi$
$648$	−4.58993	−	1.63828i	−0.180309	−	0.0643578i
$649$	19.5017	−	11.2593i	0.765509	−	0.441967i
$650$	0.0268632	−	2.39384i	0.00105366	−	0.0938941i
$651$	5.46407	−	15.5241i	0.214154	−	0.608438i
$652$	14.7719	−	34.6400i	0.578511	−	1.35661i
$653$	25.1399	+	43.5436i	0.983800	+	1.70399i	0.647153	+	0.762360i	$0.275959\pi$
$653$	25.1399	+	43.5436i	0.983800	+	1.70399i	0.336646	+	0.941631i	$0.390707\pi$
$654$	4.30162	−	4.85395i	0.168207	−	0.189804i
$655$	22.1927	+	0.793460i	0.867140	+	0.0310030i
$656$	−8.21787	+	28.3033i	−0.320854	+	1.10506i
$657$	14.8783	−	14.8783i	0.580456	−	0.580456i
$658$	−0.421514	+	25.7357i	−0.0164323	+	1.00328i
$659$	2.76732	−	2.76732i	0.107799	−	0.107799i	−0.651150	−	0.758949i	$-0.725713\pi$
$659$	2.76732	−	2.76732i	0.107799	−	0.107799i	0.758949	+	0.651150i	$0.225713\pi$
$660$	22.7868	−	15.8709i	0.886976	−	0.617775i
$661$	−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	$0.814594\pi$
$662$	6.82392	+	6.04743i	0.265219	+	0.235040i
$663$	1.06361	+	0.284994i	0.0413073	+	0.0110683i
$664$	48.2134	−	8.81142i	1.87104	−	0.341950i
$665$	10.0656	−	8.02423i	0.390326	−	0.311166i
$666$	−16.2648	+	10.7460i	−0.630250	+	0.416400i
$667$	6.13871	+	10.6325i	0.237692	+	0.411694i
$668$	3.27676	−	23.0372i	0.126782	−	0.891336i
$669$	−7.06941	−	26.3834i	−0.273319	−	1.02004i
$670$	−18.9749	−	18.0666i	−0.733066	−	0.697975i
$671$			0.191492i			0.00739246i
$672$	−15.0684	−	9.46305i	−0.581278	−	0.365045i
$673$	32.1014	−	32.1014i	1.23742	−	1.23742i	0.276364	−	0.961053i	$-0.410870\pi$
$673$	32.1014	−	32.1014i	1.23742	−	1.23742i	0.961053	−	0.276364i	$-0.0891296\pi$
$674$	1.05130	+	3.15070i	0.0404944	+	0.121361i
$675$	11.9111	+	24.5249i	0.458460	+	0.943962i
$676$	15.4750	+	20.6072i	0.595191	+	0.792585i
$677$	3.74171	−	2.16028i	0.143806	−	0.0830262i	−0.426371	−	0.904548i	$-0.640208\pi$
$677$	3.74171	−	2.16028i	0.143806	−	0.0830262i	0.570176	+	0.821522i	$0.306875\pi$
$678$	−5.61901	−	1.14807i	−0.215797	−	0.0440913i
$679$	30.4357	+	2.33692i	1.16802	+	0.0896827i
$680$	−13.5764	+	10.7256i	−0.520633	+	0.411309i
$681$	2.89729	−	1.67275i	0.111024	−	0.0640999i
$682$	−25.6319	+	28.9231i	−0.981497	+	1.10752i
$683$	−18.8179	−	10.8645i	−0.720047	−	0.415719i	0.0947229	−	0.995504i	$-0.469804\pi$
$683$	−18.8179	−	10.8645i	−0.720047	−	0.415719i	−0.814770	+	0.579784i	$0.803137\pi$
$684$	5.43363	+	4.25979i	0.207760	+	0.162877i
$685$	7.59473	+	14.3123i	0.290180	+	0.546845i
$686$	26.0805	−	2.41037i	0.995756	−	0.0920284i
$687$	−6.29811	−	6.29811i	−0.240288	−	0.240288i
$688$	27.0528	+	7.85479i	1.03138	+	0.299461i
$689$	−1.41371	+	2.44862i	−0.0538581	+	0.0932850i
$690$	28.5944	−	17.4573i	1.08857	−	0.664588i
$691$	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	$0.347742\pi$
$692$	−32.7976	−	13.9862i	−1.24678	−	0.531675i
$693$	−21.8597	−	1.67843i	−0.830382	−	0.0637584i
$694$	−19.8122	+	13.0897i	−0.752061	+	0.496879i
$695$	14.4848	−	23.1378i	0.549441	−	0.877665i
$696$	1.98407	+	4.18654i	0.0752059	+	0.158691i
$697$	5.21693	+	19.4699i	0.197605	+	0.737474i
$698$	0.927558	+	2.77986i	0.0351086	+	0.105219i
$699$	−3.43027	+	3.43027i	−0.129745	+	0.129745i
$700$	6.13989	+	25.7352i	0.232066	+	0.972700i
$701$	−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	$0.756273\pi$
$702$	2.33554	+	1.16689i	0.0881494	+	0.0440413i
$703$	−18.2602	+	4.89280i	−0.688696	+	0.184536i
$704$	24.3905	+	33.9254i	0.919251	+	1.27861i
$705$	−15.5005	−	9.70374i	−0.583784	−	0.365464i
$706$	13.2529	+	2.70782i	0.498780	+	0.101910i
$707$	29.0449	+	19.8805i	1.09235	+	0.747685i
$708$	9.51161	−	3.82455i	0.357468	−	0.143735i
$709$	−2.78474	+	10.3928i	−0.104583	+	0.390309i	−0.998298	−	0.0583270i	$-0.981423\pi$
$709$	−2.78474	+	10.3928i	−0.104583	+	0.390309i	0.893715	+	0.448636i	$0.148090\pi$
$710$	−4.18263	+	17.2951i	−0.156971	+	0.649074i
$711$	14.2516	+	8.22819i	0.534479	+	0.308581i
$712$	−3.37395	−	3.97041i	−0.126444	−	0.148797i
$713$	−32.9688	+	32.9688i	−1.23469	+	1.23469i
$714$	−12.1677	−	0.199289i	−0.455365	−	0.00745822i
$715$	−3.49269	+	1.85337i	−0.130619	+	0.0693122i
$716$	−11.2151	+	14.3056i	−0.419129	+	0.534625i
$717$	−8.88682	+	15.3924i	−0.331884	+	0.574841i
$718$	−1.65923	−	27.5036i	−0.0619220	−	1.02643i
$719$	−10.8607	−	18.8112i	−0.405034	−	0.701539i	0.589292	−	0.807920i	$-0.299407\pi$
$719$	−10.8607	−	18.8112i	−0.405034	−	0.701539i	−0.994325	+	0.106381i	$0.966074\pi$
$720$	−12.6707	+	6.38983i	−0.472211	+	0.238135i
$721$	17.2927	+	36.0776i	0.644013	+	1.34360i
$722$	−11.1211	−	16.8326i	−0.413885	−	0.626443i
$723$	0.428434	+	0.742070i	0.0159336	+	0.0275979i
$724$	1.36306	−	9.58299i	0.0506579	−	0.356149i
$725$	2.25359	−	6.50971i	0.0836961	−	0.241764i
$726$	−24.4839	−	12.2326i	−0.908681	−	0.453996i
$727$	−18.0505	−	18.0505i	−0.669457	−	0.669457i	0.288134	−	0.957590i	$-0.406965\pi$
$727$	−18.0505	−	18.0505i	−0.669457	−	0.669457i	−0.957590	+	0.288134i	$0.906965\pi$
$728$	1.96801	+	1.59558i	0.0729393	+	0.0591360i
$729$	−22.1821			−0.821559
$730$	1.02807	+	41.9253i	0.0380507	+	1.55173i
$731$	18.6096	−	4.98644i	0.688303	−	0.184430i
$732$	−0.0122764	+	0.0863090i	−0.000453749	+	0.00319007i
$733$	3.68394	−	2.12692i	0.136069	−	0.0785597i	−0.430420	−	0.902629i	$-0.641635\pi$
$733$	3.68394	−	2.12692i	0.136069	−	0.0785597i	0.566489	+	0.824069i	$0.308301\pi$
$734$	−2.88014	+	14.0963i	−0.106308	+	0.520305i
$735$	−8.10762	+	16.7498i	−0.299054	+	0.617826i
$736$	26.9079	+	42.6271i	0.991837	+	1.57126i
$737$	−11.1999	+	41.7984i	−0.412552	+	1.53966i
$738$	0.995534	+	16.5021i	0.0366461	+	0.607451i
$739$	2.60666	+	9.72820i	0.0958877	+	0.357858i	0.997153	−	0.0754108i	$-0.0240268\pi$
$739$	2.60666	+	9.72820i	0.0958877	+	0.357858i	−0.901265	+	0.433269i	$0.857360\pi$
$740$	6.84251	−	38.2475i	0.251536	−	1.40601i
$741$	0.619286	+	0.619286i	0.0227500	+	0.0227500i
$742$	8.58070	−	30.0464i	0.315007	−	1.10304i
$743$	−10.2002	−	10.2002i	−0.374209	−	0.374209i	0.494799	−	0.869008i	$-0.335242\pi$
$743$	−10.2002	−	10.2002i	−0.374209	−	0.374209i	−0.869008	+	0.494799i	$0.835242\pi$
$744$	−13.4070	+	11.3929i	−0.491526	+	0.417686i
$745$	−1.07541	+	30.0786i	−0.0393999	+	1.10200i
$746$	6.77186	−	0.408531i	0.247936	−	0.0149574i
$747$	23.8094	−	13.7464i	0.871140	−	0.502953i
$748$	26.2861	+	11.2094i	0.961115	+	0.409858i
$749$	−2.88894	+	8.20784i	−0.105559	+	0.299908i
$750$	−17.9089	−	5.71220i	−0.653939	−	0.208580i
$751$	−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	$0.860056\pi$
$752$	14.2504	−	23.5388i	0.519657	−	0.858372i
$753$	1.39077	+	5.19044i	0.0506826	+	0.189150i
$754$	−0.208794	−	0.625749i	−0.00760383	−	0.0227884i
$755$	11.4254	+	3.50350i	0.415814	+	0.127505i
$756$	−28.1714	−	6.23824i	−1.02459	−	0.226882i
$757$	−6.23131			−0.226481			−0.113240	−	0.993568i	$-0.536123\pi$
$757$	−6.23131			−0.226481			−0.113240	+	0.993568i	$0.536123\pi$
$758$	2.67503	+	8.01699i	0.0971616	+	0.291190i
$759$	−47.9197	−	27.6665i	−1.73938	−	1.00423i
$760$	−13.6169	+	1.98877i	−0.493938	+	0.0721403i
$761$	−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	$0.966931\pi$
$762$	4.79557	−	23.4710i	0.173725	−	0.850266i
$763$	5.76470	−	8.42207i	0.208696	−	0.304899i
$764$	−4.88873	+	11.4641i	−0.176868	+	0.414755i
$765$	−5.14990	+	8.22634i	−0.186195	+	0.297424i
$766$	14.0462	−	15.8498i	0.507511	−	0.572676i
$767$	−1.40998	+	0.377802i	−0.0509113	+	0.0136416i
$768$	8.81832	+	16.8545i	0.318204	+	0.608184i
$769$	17.4560			0.629478			0.314739	−	0.949178i	$-0.398083\pi$
$769$	17.4560			0.629478			0.314739	+	0.949178i	$0.398083\pi$
$770$	32.4667	−	29.2475i	1.17002	−	1.05401i
$771$	14.8142	+	14.8142i	0.533522	+	0.533522i
$772$	4.95599	−	6.32167i	0.178370	−	0.227522i
$773$	−25.9124	+	44.8816i	−0.932004	+	1.61428i	−0.152113	+	0.988363i	$0.548608\pi$
$773$	−25.9124	+	44.8816i	−0.932004	+	1.61428i	−0.779891	+	0.625915i	$0.784726\pi$
$774$	15.7730	−	0.951549i	0.566949	−	0.0342027i
$775$	26.0941	+	1.86828i	0.937328	+	0.0671107i
$776$	−26.8474	−	18.5506i	−0.963767	−	0.665926i
$777$	20.7468	−	17.7880i	0.744286	−	0.638141i
$778$	18.4718	+	3.77413i	0.662245	+	0.135309i
$779$	−4.14937	+	15.4856i	−0.148666	+	0.554831i
$780$	−1.69304	+	0.611437i	−0.0606206	+	0.0218929i
$781$	28.3871	−	7.60630i	1.01577	−	0.272175i
$782$	30.8410	+	15.4088i	1.10287	+	0.551018i
$783$	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
$787$	6.90250	−	11.9555i	0.246048	−	0.426167i	−0.716378	−	0.697712i	$-0.754201\pi$
$787$	6.90250	−	11.9555i	0.246048	−	0.426167i	0.962426	+	0.271545i	$0.0875347\pi$
$788$	2.73949	+	3.64804i	0.0975904	+	0.129956i
$789$	−19.7773	−	5.29931i	−0.704091	−	0.188660i
$790$	−31.4647	+	9.26338i	−1.11947	+	0.329576i
$791$	−8.99833	−	0.690911i	−0.319944	−	0.0245660i
$792$	19.2825	+	13.3235i	0.685174	+	0.473429i
$793$	0.00321272	−	0.0119900i	0.000114087	−	0.000425778i
$794$	−2.38120	−	39.4711i	−0.0845057	−	1.40078i
$795$	15.1276	+	16.2495i	0.536522	+	0.576309i
$796$	−0.0894038	−	0.738288i	−0.00316883	−	0.0261679i
$797$	18.6758			0.661532			0.330766	−	0.943713i	$-0.392693\pi$
$797$	18.6758			0.661532			0.330766	+	0.943713i	$0.392693\pi$
$798$	−8.30193	−	4.97615i	−0.293885	−	0.176154i
$799$		−	18.8190i		−	0.665769i
$800$	8.19093	−	27.0723i	0.289593	−	0.957150i
$801$	−2.53112	−	1.46134i	−0.0894327	−	0.0516340i
$802$	−1.55392	−	25.7580i	−0.0548708	−	0.909545i
$803$	59.9858	−	34.6328i	2.11685	−	1.22217i
$804$	−7.72765	+	18.1213i	−0.272533	+	0.639090i
$805$	41.2232	−	32.8630i	1.45293	−	1.15827i
$806$	2.09016	−	1.38095i	0.0736229	−	0.0486419i
$807$	4.48135	+	1.20077i	0.157751	+	0.0422692i
$808$	−16.1142	−	34.0023i	−0.566896	−	1.19620i
$809$	15.9456	−	27.6186i	0.560617	−	0.971018i	−0.436825	−	0.899546i	$-0.643897\pi$
$809$	15.9456	−	27.6186i	0.560617	−	0.971018i	0.997443	−	0.0714713i	$-0.0227694\pi$
$810$	3.75726	−	3.94617i	0.132017	−	0.138654i
$811$	−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	$0.837150\pi$
$812$	3.91862	+	6.14768i	0.137516	+	0.215741i
$813$	−27.7907			−0.974662
$814$	−60.8741	+	20.3119i	−2.13363	+	0.711931i
$815$	28.6886	+	30.8161i	1.00492	+	1.07944i
$816$	11.1290	+	6.73749i	0.389594	+	0.235859i
$817$	14.8015	+	3.96604i	0.517837	+	0.138754i
$818$	−1.90325	−	2.88071i	−0.0665457	−	0.100722i
$819$	1.34056	+	0.471840i	0.0468429	+	0.0164874i
$820$	−25.1890	−	21.2434i	−0.879636	−	0.741851i
$821$	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	$0.210493\pi$
$822$	8.08019	−	9.11770i	0.281829	−	0.318016i
$823$	−28.7366	+	7.69994i	−1.00169	+	0.268403i	−0.722155	−	0.691731i	$-0.756848\pi$
$823$	−28.7366	+	7.69994i	−1.00169	+	0.268403i	−0.279539	+	0.960134i	$0.590182\pi$
$824$	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
$827$	17.4174			0.605664			0.302832	−	0.953044i	$-0.402068\pi$
$827$	17.4174			0.605664			0.302832	+	0.953044i	$0.402068\pi$
$828$	22.2532	+	17.4458i	0.773354	+	0.606285i
$829$	−44.0036	+	11.7907i	−1.52831	+	0.409509i	−0.922466	−	0.386078i	$-0.873830\pi$
$829$	−44.0036	+	11.7907i	−1.52831	+	0.409509i	−0.605840	+	0.795586i	$0.707163\pi$
$830$	−12.8807	+	53.2616i	−0.447096	+	1.84874i
$831$	27.1959	−	15.7015i	0.943414	−	0.544680i
$832$	−0.958003	−	2.53341i	−0.0332128	−	0.0878301i
$833$	−19.0371	+	2.07436i	−0.659597	+	0.0718724i
$834$	−20.1100	−	4.10885i	−0.696353	−	0.142278i
$835$	22.0510	+	13.8045i	0.763107	+	0.477725i
$836$	13.6482	+	18.1746i	0.472034	+	0.628583i
$837$	−14.2652	+	24.7080i	−0.493077	+	0.854034i
$838$	−11.5127	−	34.5031i	−0.397699	−	1.19189i
$839$			46.4476i			1.60355i	0.597626	+	0.801775i	$0.296111\pi$
$839$			46.4476i			1.60355i	−0.597626	+	0.801775i	$0.703889\pi$
$840$	16.5084	−	11.1010i	0.569594	−	0.383021i
$841$			27.1018i			0.934545i
$842$	−51.6037	+	17.2186i	−1.77838	+	0.593393i
$843$	15.7254	−	27.2372i	0.541612	−	0.938100i
$844$	−2.92334	+	20.5525i	−0.100626	+	0.707445i
$845$	−28.0795	+	6.45808i	−0.965964	+	0.222165i
$846$	3.08982	−	15.1226i	0.106230	−	0.519924i
$847$	−40.6262	−	14.2993i	−1.39593	−	0.491330i
$848$	−24.1068	+	23.1251i	−0.827829	+	0.794119i
$849$	26.5776	−	15.3446i	0.912141	−	0.526625i
$850$	−4.79667	−	18.7401i	−0.164524	−	0.642780i
$851$	−74.7840	+	20.0383i	−2.56356	+	0.686905i
$852$	13.2822	−	1.60843i	0.455042	−	0.0551038i
$853$	23.5379			0.805923			0.402962	−	0.915217i	$-0.367981\pi$
$853$	23.5379			0.805923			0.402962	+	0.915217i	$0.367981\pi$
$854$	−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
$857$	−32.9015	+	8.81593i	−1.12389	+	0.301146i	−0.772458	−	0.635066i	$-0.780973\pi$
$857$	−32.9015	+	8.81593i	−1.12389	+	0.301146i	−0.351435	+	0.936212i	$0.614306\pi$
$858$	2.22503	+	1.97184i	0.0759613	+	0.0673176i
$859$	−42.0449	−	11.2659i	−1.43455	−	0.384388i	−0.543931	−	0.839130i	$-0.683065\pi$
$859$	−42.0449	−	11.2659i	−1.43455	−	0.384388i	−0.890623	+	0.454742i	$0.849731\pi$
$860$	−20.3048	+	24.0761i	−0.692388	+	0.820987i
$861$	−4.26696	−	22.7798i	−0.145418	−	0.776334i
$862$	16.1843	−	10.6928i	0.551241	−	0.364199i
$863$	−35.1188	−	9.41004i	−1.19546	−	0.320322i	−0.394416	−	0.918932i	$-0.629053\pi$
$863$	−35.1188	−	9.41004i	−1.19546	−	0.320322i	−0.801040	+	0.598610i	$0.795720\pi$
$864$	22.6552	+	20.9337i	0.770747	+	0.712180i
$865$	29.1771	−	27.1628i	0.992051	−	0.923561i
$866$	8.70746	+	26.0960i	0.295892	+	0.886777i
$867$	−11.3134			−0.384222
$868$	−18.6995	+	20.4169i	−0.634701	+	0.692994i
$869$	38.3063	+	38.3063i	1.29945	+	1.29945i
$870$	−5.17817	+	0.126977i	−0.175556	+	0.00430492i
$871$	1.40253	−	2.42925i	0.0475229	−	0.0823121i
$872$	−9.85953	+	4.67259i	−0.333886	+	0.158234i
$873$	−17.6814	−	4.73770i	−0.598423	−	0.160347i
$874$	15.1157	+	22.8786i	0.511295	+	0.773880i
$875$	−29.0819	−	5.40765i	−0.983148	−	0.182812i
$876$	29.2570	−	11.7640i	0.988504	−	0.397470i
$877$	−43.1848	+	24.9327i	−1.45825	+	0.841919i	−0.998925	−	0.0463511i	$-0.985241\pi$
$877$	−43.1848	+	24.9327i	−1.45825	+	0.841919i	−0.459321	+	0.888270i	$0.651907\pi$
$878$	−25.7051	+	1.55073i	−0.867505	+	0.0523345i
$879$	−0.193704	−	0.111835i	−0.00653348	−	0.00377211i
$880$	−45.7341	+	9.52247i	−1.54170	+	0.321002i
$881$		−	15.9710i		−	0.538076i	−0.963129	−	0.269038i	$-0.913294\pi$
$881$		−	15.9710i		−	0.538076i	0.963129	−	0.269038i	$-0.0867058\pi$
$882$	−15.6384	−	1.45872i	−0.526572	−	0.0491176i
$883$	44.1081			1.48435			0.742177	−	0.670204i	$-0.233793\pi$
$883$	44.1081			1.48435			0.742177	+	0.670204i	$0.233793\pi$
$884$	−1.45781	−	1.14288i	−0.0490314	−	0.0384390i
$885$	−0.409534	+	11.4545i	−0.0137663	+	0.385038i
$886$	−24.1585	+	1.45742i	−0.811620	+	0.0489631i
$887$	−2.45408	+	9.15875i	−0.0824000	+	0.307521i	−0.994809	−	0.101758i	$-0.967553\pi$
$887$	−2.45408	+	9.15875i	−0.0824000	+	0.307521i	0.912409	+	0.409279i	$0.134220\pi$
$888$	−28.7393	+	5.25236i	−0.964427	+	0.176258i
$889$	2.88599	−	37.5867i	0.0967929	−	1.26062i
$890$	5.58820	−	1.64519i	0.187317	−	0.0551471i
$891$	−8.69270	−	2.32920i	−0.291216	−	0.0780312i
$892$	−6.47062	+	45.4916i	−0.216652	+	1.52317i
$893$	7.48399	−	12.9627i	0.250442	−	0.433779i
$894$	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
$898$	8.55323	−	17.1195i	0.285425	−	0.571284i
$899$	6.96301	−	1.86573i	0.232229	−	0.0622257i
$900$	−0.777639	−	15.8467i	−0.0259213	−	0.528223i
$901$	−5.91311	+	22.0680i	−0.196994	+	0.735193i
$902$	−10.8945	+	53.3210i	−0.362746	+	1.77539i
$903$	−21.7733	+	4.07844i	−0.724572	+	0.135722i
$904$	7.93745	+	5.48448i	0.263996	+	0.182411i
$905$	9.17276	+	5.74239i	0.304913	+	0.190883i
$906$	−0.541105	−	8.96943i	−0.0179770	−	0.297989i
$907$	15.3940	−	26.6632i	0.511150	−	0.885337i	−0.488767	−	0.872414i	$-0.662553\pi$
$907$	15.3940	−	26.6632i	0.511150	−	0.885337i	0.999916	−	0.0129227i	$-0.00411354\pi$
$908$	−5.58719	+	0.676586i	−0.185417	+	0.0224533i
$909$	−14.9247	−	14.9247i	−0.495020	−	0.495020i
$910$	−2.52356	+	1.28659i	−0.0836551	+	0.0426502i
$911$	−27.3255			−0.905336			−0.452668	−	0.891679i	$-0.649528\pi$
$911$	−27.3255			−0.905336			−0.452668	+	0.891679i	$0.649528\pi$
$912$	4.98635	+	9.06664i	0.165115	+	0.300226i
$913$	87.4202	−	23.4242i	2.89319	−	0.775227i
$914$	−15.5466	−	13.7775i	−0.514235	−	0.455719i
$915$	−0.0826142	−	0.0517187i	−0.00273114	−	0.00170977i
$916$	5.58987	+	13.9020i	0.184694	+	0.459333i
$917$	−11.3571	−	23.6943i	−0.375046	−	0.782454i
$918$	20.6693	+	4.22312i	0.682188	+	0.139384i
$919$	−13.9169	−	24.1047i	−0.459075	−	0.795141i	0.539838	−	0.841769i	$-0.318486\pi$
$919$	−13.9169	−	24.1047i	−0.459075	−	0.795141i	−0.998912	+	0.0466285i	$0.985152\pi$
$920$	−55.7677	+	8.14495i	−1.83861	+	0.268531i
$921$	4.97308	+	2.87121i	0.163869	+	0.0946095i
$922$	6.62855	−	2.21175i	0.218300	−	0.0728402i
$923$	−1.90504			−0.0627050
$924$	−29.1481	−	15.1645i	−0.958903	−	0.498876i
$925$	35.9737	+	24.3517i	1.18281	+	0.800679i
$926$	−5.71722	+	1.90767i	−0.187879	+	0.0626898i
$927$	−6.20945	−	23.1740i	−0.203945	−	0.761133i
$928$	−0.307569	−	7.78766i	−0.0100964	−	0.255643i
$929$	17.1128	+	29.6403i	0.561453	+	0.972466i	0.997370	+	0.0724786i	$0.0230909\pi$
$929$	17.1128	+	29.6403i	0.561453	+	0.972466i	−0.435917	+	0.899987i	$0.643576\pi$
$930$	−5.55539	−	18.8699i	−0.182168	−	0.618768i
$931$	−13.9378	−	6.14189i	−0.456794	−	0.201292i
$932$	7.57171	−	3.04453i	0.248020	−	0.0997268i
$933$	9.75487	−	5.63198i	0.319360	−	0.184383i
$934$	−1.85939	−	30.8215i	−0.0608410	−	1.00851i
$935$	−23.3844	+	21.7700i	−0.764752	+	0.711955i
$936$	−0.983818	−	1.15774i	−0.0321571	−	0.0378420i
$937$	−39.3051	−	39.3051i	−1.28404	−	1.28404i	−0.938348	−	0.345692i	$-0.887644\pi$
$937$	−39.3051	−	39.3051i	−1.28404	−	1.28404i	−0.345692	−	0.938348i	$-0.612356\pi$
$938$	−8.51282	+	29.8088i	−0.277954	+	0.973291i
$939$	25.7731	+	25.7731i	0.841072	+	0.841072i
$940$	17.5827	+	25.2445i	0.573484	+	0.823385i
$941$	−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	$-0.224748\pi$
$942$	−2.09681	+	0.126496i	−0.0683177	+	0.00412145i
$943$	−16.9936	+	63.4209i	−0.553387	+	2.06527i
$944$	−17.2424	−	0.358362i	−0.561191	−	0.0116637i
$945$	19.1608	−	25.9527i	0.623301	−	0.844243i
$946$	50.9651	+	10.4131i	1.65702	+	0.338560i
$947$	−32.3182	+	18.6589i	−1.05020	+	0.606334i	−0.922706	−	0.385505i	$-0.874027\pi$
$947$	−32.3182	+	18.6589i	−1.05020	+	0.606334i	−0.127496	+	0.991839i	$0.540694\pi$
$948$	14.8096	+	19.7212i	0.480993	+	0.640514i
$949$	−4.33698	+	1.16209i	−0.140784	+	0.0377231i
$950$	4.14863	−	14.8158i	0.134599	−	0.480689i
$951$	0.172928			0.00560756
$952$	18.6972	+	8.33770i	0.605980	+	0.270226i
$953$	−20.1360	−	20.1360i	−0.652269	−	0.652269i	0.301270	−	0.953539i	$-0.402589\pi$
$953$	−20.1360	−	20.1360i	−0.652269	−	0.652269i	−0.953539	+	0.301270i	$0.902589\pi$
$954$	−8.37492	+	16.7625i	−0.271148	+	0.542708i
$955$	−9.49447	−	10.1986i	−0.307234	−	0.330018i
$956$	23.9090	−	17.9545i	0.773274	−	0.580689i
$957$	4.27748	+	7.40882i	0.138271	+	0.239493i
$958$	7.06423	−	4.66727i	0.228235	−	0.150793i
$959$	10.8285	−	15.8201i	0.349669	−	0.510857i
$960$	−21.2237	+	1.35997i	−0.684993	+	0.0438930i
$961$	−1.81216	−	3.13874i	−0.0584566	−	0.101250i
$962$	4.15233	−	0.250501i	0.133877	−	0.00807646i
$963$	2.60898	−	4.51889i	0.0840733	−	0.145619i
$964$	−0.173291	−	1.43102i	−0.00558133	−	0.0460901i
$965$	4.20968	+	7.93317i	0.135515	+	0.255378i
$966$	−34.0003	−	20.3797i	−1.09394	−	0.655705i
$967$	17.4747	−	17.4747i	0.561948	−	0.561948i	−0.367912	−	0.929860i	$-0.619927\pi$
$967$	17.4747	−	17.4747i	0.561948	−	0.561948i	0.929860	+	0.367912i	$0.119927\pi$
$968$	29.8150	+	35.0858i	0.958290	+	1.12770i
$969$	6.12867	+	3.53839i	0.196881	+	0.113669i
$970$	31.1400	−	19.0115i	0.999846	−	0.610421i
$971$	−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	$0.937884\pi$
$972$	26.3264	+	11.2266i	0.844419	+	0.360094i
$973$	−32.2043	−	2.47272i	−1.03242	−	0.0792717i
$974$	3.93868	−	19.2771i	0.126203	−	0.617679i
$975$	0.143725	−	2.00740i	0.00460290	−	0.0642882i
$976$	0.0759511	−	0.125456i	0.00243114	−	0.00401576i
$977$	28.9478	−	7.75655i	0.926123	−	0.248154i	0.235922	−	0.971772i	$-0.424189\pi$
$977$	28.9478	−	7.75655i	0.926123	−	0.248154i	0.690201	+	0.723618i	$0.257522\pi$
$978$	14.1492	−	28.3199i	0.452441	−	0.905569i
$979$	−6.80327	−	6.80327i	−0.217434	−	0.217434i
$980$	23.5990	−	20.5691i	0.753842	−	0.657055i
$981$	−4.32766	+	4.32766i	−0.138172	+	0.138172i
$982$	39.4241	−	13.1547i	1.25808	−	0.419783i
$983$	−5.22937	−	19.5163i	−0.166791	−	0.622473i	−0.997805	−	0.0662210i	$-0.978906\pi$
$983$	−5.22937	−	19.5163i	−0.166791	−	0.622473i	0.831014	−	0.556252i	$-0.187761\pi$
$984$	−8.32872	+	23.3343i	−0.265510	+	0.743871i
$985$	−4.97084	+	1.14326i	−0.158384	+	0.0364272i
$986$	−2.93829	−	4.44731i	−0.0935743	−	0.141631i
$987$	−1.65653	+	21.5744i	−0.0527280	+	0.686722i
$988$	−0.549645	−	1.36696i	−0.0174865	−	0.0434889i
$989$	60.6189	+	16.2428i	1.92757	+	0.516490i
$990$	−22.3655	+	13.6545i	−0.710823	+	0.433969i
$991$	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	$0.00651426\pi$
$992$	28.2646	−	8.78270i	0.897401	−	0.278851i
$993$	5.42006	+	5.42006i	0.172001	+	0.172001i
$994$	20.4229	−	5.11535i	0.647775	−	0.162249i
$995$	0.794928	+	0.243757i	0.0252009	+	0.00772761i
$996$	40.9037	−	4.95327i	1.29608	−	0.156950i
$997$	−46.9572	−	27.1107i	−1.48715	−	0.858606i	−0.487256	−	0.873259i	$-0.662002\pi$
$997$	−46.9572	−	27.1107i	−1.48715	−	0.858606i	−0.999893	+	0.0146537i	$0.995335\pi$
$998$	3.06790	+	2.71880i	0.0971127	+	0.0860622i
$999$	−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.cz.c.157.15	yes	360
5.3	odd	4		560.2.ch.c.493.32	yes	360
7.5	odd	6	inner	560.2.cz.c.397.46	yes	360
16.5	even	4		560.2.ch.c.437.89	yes	360
35.33	even	12		560.2.ch.c.173.89	yes	360
80.53	odd	4	inner	560.2.cz.c.213.46	yes	360
112.5	odd	12		560.2.ch.c.117.32	✓	360
560.453	even	12	inner	560.2.cz.c.453.15	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.32	✓	360	112.5	odd	12
560.2.ch.c.173.89	yes	360	35.33	even	12
560.2.ch.c.437.89	yes	360	16.5	even	4
560.2.ch.c.493.32	yes	360	5.3	odd	4
560.2.cz.c.157.15	yes	360	1.1	even	1	trivial
560.2.cz.c.213.46	yes	360	80.53	odd	4	inner
560.2.cz.c.397.46	yes	360	7.5	odd	6	inner
560.2.cz.c.453.15	yes	360	560.453	even	12	inner

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.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26510 - 0.632072i) q^{2} +(-1.02960 - 0.594438i) q^{3} +(1.20097 + 1.59927i) q^{4} +(-2.17918 + 0.501194i) q^{5} +(0.926818 + 1.40280i) q^{6} +(1.72211 + 2.00856i) q^{7} +(-0.508498 - 2.78234i) q^{8} +(-0.793287 - 1.37401i) q^{9} +(3.07367 + 0.743332i) q^{10} +(-1.35178 - 5.04493i) q^{11} +(-0.285848 - 2.36051i) q^{12} +0.338561i q^{13} +(-0.909095 - 3.62954i) q^{14} +(2.54160 + 0.779356i) q^{15} +(-1.11534 + 3.84136i) q^{16} +(0.708048 + 2.64247i) q^{17} +(0.135115 + 2.23968i) q^{18} +(-0.563156 + 2.10173i) q^{19} +(-3.41867 - 2.88317i) q^{20} +(-0.579117 - 3.09170i) q^{21} +(-1.47861 + 7.23678i) q^{22} +(-2.30639 + 8.60756i) q^{23} +(-1.13038 + 3.16696i) q^{24} +(4.49761 - 2.18438i) q^{25} +(0.213995 - 0.428315i) q^{26} +5.45287i q^{27} +(-1.14403 + 5.16635i) q^{28} +(0.974217 - 0.974217i) q^{29} +(-2.72278 - 2.59244i) q^{30} +(4.53120 + 2.61609i) q^{31} +(3.83903 - 4.15474i) q^{32} +(-1.60710 + 5.99779i) q^{33} +(0.774477 - 3.79053i) q^{34} +(-4.75947 - 3.51390i) q^{35} +(1.24471 - 2.91883i) q^{36} +(4.34409 + 7.52418i) q^{37} +(2.04089 - 2.30295i) q^{38} +(0.201254 - 0.348581i) q^{39} +(2.50260 + 5.80836i) q^{40} +7.36805 q^{41} +(-1.22153 + 4.27736i) q^{42} -7.04252i q^{43} +(6.44476 - 8.22068i) q^{44} +(2.41736 + 2.59663i) q^{45} +(8.35841 - 9.43164i) q^{46} +(-6.64469 - 1.78044i) q^{47} +(3.43180 - 3.29205i) q^{48} +(-1.06865 + 6.91795i) q^{49} +(-7.07062 - 0.0793451i) q^{50} +(0.841781 - 3.14157i) q^{51} +(-0.541451 + 0.406602i) q^{52} +(7.23243 + 4.17565i) 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} +(-1.84826 + 0.616710i) q^{58} +(1.11590 + 4.16461i) q^{59} +(1.80599 + 5.00069i) q^{60} +(-0.0354146 - 0.00948932i) q^{61} +(-4.07888 - 6.17366i) q^{62} +(1.39366 - 3.95958i) q^{63} +(-7.48286 + 2.82963i) q^{64} +(-0.169685 - 0.737784i) q^{65} +(5.82419 - 6.57202i) q^{66} +(-7.17522 - 4.14262i) q^{67} +(-3.37568 + 4.30589i) q^{68} +(7.49131 - 7.49131i) q^{69} +(3.80018 + 7.45377i) q^{70} +5.62686i q^{71} +(-3.41959 + 2.90588i) q^{72} +(3.43244 + 12.8100i) q^{73} +(-0.739897 - 12.2646i) q^{74} +(-5.92920 - 0.424519i) q^{75} +(-4.03757 + 1.62347i) q^{76} +(7.80513 - 11.4031i) q^{77} +(-0.474935 + 0.313785i) q^{78} +(-8.98265 + 5.18614i) q^{79} +(0.505250 - 8.92999i) q^{80} +(0.861529 - 1.49221i) q^{81} +(-9.32135 - 4.65714i) q^{82} +17.3283i q^{83} +(4.24896 - 4.63920i) q^{84} +(-2.86735 - 5.40354i) q^{85} +(-4.45138 + 8.90951i) q^{86} +(-1.58216 + 0.423939i) q^{87} +(-13.3493 + 6.32646i) q^{88} +(1.59534 - 0.921068i) q^{89} +(-1.41696 - 4.81294i) q^{90} +(-0.680021 + 0.583041i) q^{91} +(-16.5357 + 6.64889i) q^{92} +(-3.11020 - 5.38703i) q^{93} +(7.28085 + 6.45236i) q^{94} +(0.173842 - 4.86228i) q^{95} +(-6.42239 + 1.99564i) q^{96} +(8.15823 - 8.15823i) q^{97} +(5.72459 - 8.07645i) q^{98} +(-5.85945 + 5.85945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Introduction

L-functions

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