LMFDB - Embedded newform 560.2.ch.c.173.89

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			173.89
Character	$\chi$	$=$	560.173
Dual form			560.2.ch.c.437.89

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41165 - 0.0851614i) q^{2} +(-0.594438 - 1.02960i) q^{3} +(1.98550 - 0.240436i) q^{4} +(-0.501194 + 2.17918i) q^{5} +(-0.926818 - 1.40280i) q^{6} +(-1.72211 + 2.00856i) q^{7} +(2.78234 - 0.508498i) q^{8} +(0.793287 - 1.37401i) q^{9} +(-0.521928 + 3.11891i) q^{10} +(5.04493 + 1.35178i) q^{11} +(-1.42781 - 1.90133i) q^{12} +0.338561 q^{13} +(-2.25996 + 2.98204i) q^{14} +(2.54160 - 0.779356i) q^{15} +(3.88438 - 0.954768i) q^{16} +(0.708048 - 2.64247i) q^{17} +(1.00283 - 2.00718i) q^{18} +(2.10173 - 0.563156i) q^{19} +(-0.471167 + 4.44725i) q^{20} +(3.09170 + 0.579117i) q^{21} +(7.23678 + 1.47861i) q^{22} +(2.30639 + 8.60756i) q^{23} +(-2.17748 - 2.56242i) q^{24} +(-4.49761 - 2.18438i) q^{25} +(0.477929 - 0.0288323i) q^{26} -5.45287 q^{27} +(-2.93632 + 4.40205i) q^{28} +(-0.974217 + 0.974217i) q^{29} +(3.52147 - 1.31662i) q^{30} +(4.53120 - 2.61609i) q^{31} +(5.40207 - 1.67859i) q^{32} +(-1.60710 - 5.99779i) q^{33} +(0.774477 - 3.79053i) q^{34} +(-3.51390 - 4.75947i) q^{35} +(1.24471 - 2.91883i) q^{36} +(-7.52418 - 4.34409i) q^{37} +(2.91894 - 0.973964i) q^{38} +(-0.201254 - 0.348581i) q^{39} +(-0.286388 + 6.31807i) q^{40} -7.36805 q^{41} +(4.41371 + 0.554215i) q^{42} +7.04252 q^{43} +(10.3417 + 1.47098i) q^{44} +(2.59663 + 2.41736i) q^{45} +(3.98884 + 11.9544i) q^{46} +(-6.64469 + 1.78044i) q^{47} +(-3.29205 - 3.43180i) q^{48} +(-1.06865 - 6.91795i) q^{49} +(-6.53506 - 2.70055i) q^{50} +(-3.14157 + 0.841781i) q^{51} +(0.672212 - 0.0814022i) q^{52} +(-4.17565 - 7.23243i) q^{53} +(-7.69752 + 0.464374i) q^{54} +(-5.47426 + 10.3163i) q^{55} +(-3.77016 + 6.46420i) q^{56} +(-1.82917 - 1.82917i) q^{57} +(-1.29228 + 1.45822i) q^{58} +(-4.16461 - 1.11590i) q^{59} +(4.85895 - 2.15850i) q^{60} +(-0.00948932 - 0.0354146i) q^{61} +(6.17366 - 4.07888i) q^{62} +(1.39366 + 3.95958i) q^{63} +(7.48286 - 2.82963i) q^{64} +(-0.169685 + 0.737784i) q^{65} +(-2.77944 - 8.32990i) q^{66} +(-4.14262 - 7.17522i) q^{67} +(0.770481 - 5.41685i) q^{68} +(7.49131 - 7.49131i) q^{69} +(-5.36570 - 6.41944i) q^{70} +5.62686i q^{71} +(1.50851 - 4.22636i) q^{72} +(-3.43244 + 12.8100i) q^{73} +(-10.9914 - 5.49155i) q^{74} +(0.424519 + 5.92920i) 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} +(0.133776 + 8.94327i) q^{80} +(0.861529 + 1.49221i) q^{81} +(-10.4011 + 0.627474i) q^{82} +17.3283 q^{83} +(6.27779 + 0.406478i) q^{84} +(5.40354 + 2.86735i) q^{85} +(9.94155 - 0.599751i) q^{86} +(1.58216 + 0.423939i) q^{87} +(14.7241 + 1.19579i) q^{88} +(-1.59534 - 0.921068i) q^{89} +(3.87139 + 3.19133i) q^{90} +(-0.583041 + 0.680021i) q^{91} +(6.64889 + 16.5357i) q^{92} +(-5.38703 - 3.11020i) q^{93} +(-9.22833 + 3.07922i) q^{94} +(0.173842 + 4.86228i) q^{95} +(-4.93947 - 4.56413i) q^{96} +(8.15823 + 8.15823i) q^{97} +(-2.09770 - 9.67469i) 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.41165	−	0.0851614i	0.998185	−	0.0602182i
$2$	1.41165	−	0.0851614i	0.998185	−	0.0602182i
$3$	−0.594438	−	1.02960i	−0.343199	−	0.594438i	0.641826	−	0.766850i	$-0.278177\pi$
$3$	−0.594438	−	1.02960i	−0.343199	−	0.594438i	−0.985025	+	0.172412i	$0.944844\pi$
$4$	1.98550	−	0.240436i	0.992748	−	0.120218i
$5$	−0.501194	+	2.17918i	−0.224141	+	0.974557i
$5$	−0.501194	+	2.17918i	−0.224141	+	0.974557i
$6$	−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
$8$	2.78234	−	0.508498i	0.983707	−	0.179781i
$9$	0.793287	−	1.37401i	0.264429	−	0.458005i
$10$	−0.521928	+	3.11891i	−0.165048	+	0.986286i
$11$	5.04493	+	1.35178i	1.52110	+	0.407578i	0.920105	−	0.391672i	$-0.128103\pi$
$11$	5.04493	+	1.35178i	1.52110	+	0.407578i	0.600998	+	0.799250i	$0.294770\pi$
$12$	−1.42781	−	1.90133i	−0.412172	−	0.548868i
$13$	0.338561			0.0939000			0.0469500	−	0.998897i	$-0.485050\pi$
$13$	0.338561			0.0939000			0.0469500	+	0.998897i	$0.485050\pi$
$14$	−2.25996	+	2.98204i	−0.604001	+	0.796984i
$15$	2.54160	−	0.779356i	0.656238	−	0.201229i
$16$	3.88438	−	0.954768i	0.971095	−	0.238692i
$17$	0.708048	−	2.64247i	0.171727	−	0.640893i	−0.825359	−	0.564608i	$-0.809027\pi$
$17$	0.708048	−	2.64247i	0.171727	−	0.640893i	0.997086	−	0.0762852i	$-0.0243060\pi$
$18$	1.00283	−	2.00718i	0.236369	−	0.473097i
$19$	2.10173	−	0.563156i	0.482169	−	0.129197i	−0.00954318	−	0.999954i	$-0.503038\pi$
$19$	2.10173	−	0.563156i	0.482169	−	0.129197i	0.491713	+	0.870758i	$0.336371\pi$
$20$	−0.471167	+	4.44725i	−0.105356	+	0.994435i
$21$	3.09170	+	0.579117i	0.674664	+	0.126374i
$22$	7.23678	+	1.47861i	1.54289	+	0.315241i
$23$	2.30639	+	8.60756i	0.480915	+	1.79480i	0.597789	+	0.801653i	$0.296046\pi$
$23$	2.30639	+	8.60756i	0.480915	+	1.79480i	−0.116874	+	0.993147i	$0.537287\pi$
$24$	−2.17748	−	2.56242i	−0.444476	−	0.523052i
$25$	−4.49761	−	2.18438i	−0.899522	−	0.436876i
$26$	0.477929	−	0.0288323i	0.0937296	−	0.00565449i
$27$	−5.45287			−1.04940
$28$	−2.93632	+	4.40205i	−0.554912	+	0.831909i
$29$	−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	$0.290830\pi$
$30$	3.52147	−	1.31662i	0.642930	−	0.240381i
$31$	4.53120	−	2.61609i	0.813827	−	0.469863i	−0.0344558	−	0.999406i	$-0.510970\pi$
$31$	4.53120	−	2.61609i	0.813827	−	0.469863i	0.848283	+	0.529543i	$0.177636\pi$
$32$	5.40207	−	1.67859i	0.954959	−	0.296736i
$33$	−1.60710	−	5.99779i	−0.279761	−	1.04408i
$34$	0.774477	−	3.79053i	0.132822	−	0.650071i
$35$	−3.51390	−	4.75947i	−0.593957	−	0.804497i
$36$	1.24471	−	2.91883i	0.207451	−	0.486472i
$37$	−7.52418	−	4.34409i	−1.23697	−	0.714164i	−0.268495	−	0.963281i	$-0.586526\pi$
$37$	−7.52418	−	4.34409i	−1.23697	−	0.714164i	−0.968473	+	0.249117i	$0.919860\pi$
$38$	2.91894	−	0.973964i	0.473514	−	0.157998i
$39$	−0.201254	−	0.348581i	−0.0322264	−	0.0558177i
$40$	−0.286388	+	6.31807i	−0.0452820	+	0.998974i
$41$	−7.36805			−1.15070			−0.575348	−	0.817909i	$-0.695133\pi$
$41$	−7.36805			−1.15070			−0.575348	+	0.817909i	$0.695133\pi$
$42$	4.41371	+	0.554215i	0.681050	+	0.0855172i
$43$	7.04252			1.07397			0.536987	−	0.843590i	$-0.319562\pi$
$43$	7.04252			1.07397			0.536987	+	0.843590i	$0.319562\pi$
$44$	10.3417	+	1.47098i	1.55907	+	0.221759i
$45$	2.59663	+	2.41736i	0.387082	+	0.360359i
$46$	3.98884	+	11.9544i	0.588122	+	1.76258i
$47$	−6.64469	+	1.78044i	−0.969227	+	0.259704i	−0.708501	−	0.705709i	$-0.750628\pi$
$47$	−6.64469	+	1.78044i	−0.969227	+	0.259704i	−0.260726	+	0.965413i	$0.583962\pi$
$48$	−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
$51$	−3.14157	+	0.841781i	−0.439908	+	0.117873i
$52$	0.672212	−	0.0814022i	0.0932190	−	0.0112885i
$53$	−4.17565	−	7.23243i	−0.573569	−	0.993451i	−0.996195	−	0.0871469i	$-0.972225\pi$
$53$	−4.17565	−	7.23243i	−0.573569	−	0.993451i	0.422626	−	0.906304i	$-0.361108\pi$
$54$	−7.69752	+	0.464374i	−1.04750	+	0.0631933i
$55$	−5.47426	+	10.3163i	−0.738150	+	1.39105i
$56$	−3.77016	+	6.46420i	−0.503809	+	0.863815i
$57$	−1.82917	−	1.82917i	−0.242280	−	0.242280i
$58$	−1.29228	+	1.45822i	−0.169685	+	0.191473i
$59$	−4.16461	−	1.11590i	−0.542186	−	0.145278i	−0.0226764	−	0.999743i	$-0.507219\pi$
$59$	−4.16461	−	1.11590i	−0.542186	−	0.145278i	−0.519510	+	0.854465i	$0.673885\pi$
$60$	4.85895	−	2.15850i	0.627288	−	0.278661i
$61$	−0.00948932	−	0.0354146i	−0.00121498	−	0.00453438i	0.965316	−	0.261086i	$-0.0840805\pi$
$61$	−0.00948932	−	0.0354146i	−0.00121498	−	0.00453438i	−0.966531	+	0.256551i	$0.917414\pi$
$62$	6.17366	−	4.07888i	0.784056	−	0.518018i
$63$	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
$66$	−2.77944	−	8.32990i	−0.342126	−	1.02534i
$67$	−4.14262	−	7.17522i	−0.506101	−	0.876593i	−0.999975	−	0.00705957i	$-0.997753\pi$
$67$	−4.14262	−	7.17522i	−0.506101	−	0.876593i	0.493874	−	0.869534i	$-0.335580\pi$
$68$	0.770481	−	5.41685i	0.0934346	−	0.656890i
$69$	7.49131	−	7.49131i	0.901847	−	0.901847i
$70$	−5.36570	−	6.41944i	−0.641324	−	0.767270i
$71$			5.62686i			0.667785i	0.942611	+	0.333893i	$0.108362\pi$
$71$			5.62686i			0.667785i	−0.942611	+	0.333893i	$0.891638\pi$
$72$	1.50851	−	4.22636i	0.177780	−	0.498082i
$73$	−3.43244	+	12.8100i	−0.401737	+	1.49930i	0.408259	+	0.912866i	$0.366136\pi$
$73$	−3.43244	+	12.8100i	−0.401737	+	1.49930i	−0.809996	+	0.586436i	$0.800531\pi$
$74$	−10.9914	−	5.49155i	−1.27773	−	0.638380i
$75$	0.424519	+	5.92920i	0.0490192	+	0.684645i
$76$	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	$-0.531645\pi$
$79$	−8.98265	−	5.18614i	−1.01063	−	0.583486i	−0.911375	+	0.411576i	$0.864978\pi$
$80$	0.133776	+	8.94327i	0.0149566	+	0.999888i
$81$	0.861529	+	1.49221i	0.0957254	+	0.165801i
$82$	−10.4011	+	0.627474i	−1.14861	+	0.0692929i
$83$	17.3283			1.90203			0.951016	−	0.309140i	$-0.100041\pi$
$83$	17.3283			1.90203			0.951016	+	0.309140i	$0.100041\pi$
$84$	6.27779	+	0.406478i	0.684963	+	0.0443504i
$85$	5.40354	+	2.86735i	0.586096	+	0.311008i
$86$	9.94155	−	0.599751i	1.07203	−	0.0646728i
$87$	1.58216	+	0.423939i	0.169626	+	0.0454510i
$88$	14.7241	+	1.19579i	1.56959	+	0.127472i
$89$	−1.59534	−	0.921068i	−0.169105	−	0.0976330i	0.413059	−	0.910704i	$-0.364460\pi$
$89$	−1.59534	−	0.921068i	−0.169105	−	0.0976330i	−0.582164	+	0.813071i	$0.697794\pi$
$90$	3.87139	+	3.19133i	0.408080	+	0.336395i
$91$	−0.583041	+	0.680021i	−0.0611193	+	0.0712856i
$92$	6.64889	+	16.5357i	0.693194	+	1.72397i
$93$	−5.38703	−	3.11020i	−0.558609	−	0.322513i
$94$	−9.22833	+	3.07922i	−0.951829	+	0.317597i
$95$	0.173842	+	4.86228i	0.0178358	+	0.498860i
$96$	−4.93947	−	4.56413i	−0.504132	−	0.465824i
$97$	8.15823	+	8.15823i	0.828343	+	0.828343i	0.987288	−	0.158944i	$-0.0508091\pi$
$97$	8.15823	+	8.15823i	0.828343	+	0.828343i	−0.158944	+	0.987288i	$0.550809\pi$
$98$	−2.09770	−	9.67469i	−0.211899	−	0.977291i
$99$	5.85945	−	5.85945i	0.588897	−	0.588897i
$100$	−9.45518	−	3.25569i	−0.945518	−	0.325569i
$101$	3.44315	−	12.8500i	0.342606	−	1.27862i	−0.552778	−	0.833328i	$-0.686432\pi$
$101$	3.44315	−	12.8500i	0.342606	−	1.27862i	0.895384	−	0.445294i	$-0.146901\pi$
$102$	−4.36310	+	1.45584i	−0.432011	+	0.144149i
$103$	−14.6063	+	3.91374i	−1.43920	+	0.385633i	−0.892254	−	0.451535i	$-0.850877\pi$
$103$	−14.6063	+	3.91374i	−1.43920	+	0.385633i	−0.546947	+	0.837167i	$0.684210\pi$
$104$	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
$107$	−2.84821	−	1.64441i	−0.275347	−	0.158971i	0.355968	−	0.934498i	$-0.384151\pi$
$107$	−2.84821	−	1.64441i	−0.275347	−	0.158971i	−0.631315	+	0.775527i	$0.717484\pi$
$108$	−10.8266	+	1.31106i	−1.04179	+	0.126157i
$109$	−3.72607	−	0.998398i	−0.356893	−	0.0956292i	0.0759175	−	0.997114i	$-0.475811\pi$
$109$	−3.72607	−	0.998398i	−0.356893	−	0.0956292i	−0.432811	+	0.901485i	$0.642478\pi$
$110$	−6.84918	+	15.0291i	−0.653044	+	1.43297i
$111$			10.3292i			0.980401i
$112$	−4.77164	+	9.44624i	−0.450877	+	0.892586i
$113$	−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	$0.801292\pi$
$114$	−2.73792	−	2.42637i	−0.256429	−	0.227250i
$115$	−19.9133	+	0.711965i	−1.85693	+	0.0663911i
$116$	−1.70007	+	2.16854i	−0.157847	+	0.201344i
$117$	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
$122$	−0.0164115	−	0.0491848i	−0.00148583	−	0.00445299i
$123$	4.37985	+	7.58612i	0.394918	+	0.684018i
$124$	8.36767	−	6.28369i	0.751439	−	0.564292i
$125$	7.01432	−	8.70628i	0.627380	−	0.778713i
$126$	2.30456	+	5.47084i	0.205307	+	0.487381i
$127$	−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	$0.467833\pi$
$128$	10.3222	−	4.63169i	0.912361	−	0.409387i
$129$	−4.18634	−	7.25095i	−0.368587	−	0.638411i
$130$	−0.176705	+	1.05594i	−0.0154980	+	0.0926122i
$131$	−2.57039	−	9.59281i	−0.224576	−	0.838128i	−0.982574	−	0.185872i	$-0.940489\pi$
$131$	−2.57039	−	9.59281i	−0.224576	−	0.838128i	0.757998	−	0.652256i	$-0.226177\pi$
$132$	−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
$135$	2.73295	−	11.8828i	0.235215	−	1.02270i
$136$	0.626341	−	7.71230i	0.0537083	−	0.661324i
$137$	1.87540	−	6.99909i	0.160226	−	0.597972i	−0.838375	−	0.545094i	$-0.816494\pi$
$137$	1.87540	−	6.99909i	0.160226	−	0.597972i	0.998601	−	0.0528780i	$-0.0168395\pi$
$138$	9.93711	−	11.2131i	0.845903	−	0.954518i
$139$	−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	$0.423223\pi$
$140$	−8.12117	−	8.60503i	−0.686364	−	0.727258i
$141$	5.78299	+	5.78299i	0.487015	+	0.487015i
$142$	0.479191	+	7.94314i	0.0402128	+	0.666574i
$143$	1.70802	+	0.457662i	0.142832	+	0.0382716i
$144$	1.76957	−	6.09460i	0.147464	−	0.507883i
$145$	−1.63472	−	2.61126i	−0.135756	−	0.216853i
$146$	−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
$149$	13.0015	−	3.48375i	1.06513	−	0.285400i	0.316637	−	0.948547i	$-0.397446\pi$
$149$	13.0015	−	3.48375i	1.06513	−	0.285400i	0.748489	+	0.663147i	$0.230780\pi$
$150$	1.10421	+	8.33379i	0.0901583	+	0.680451i
$151$	4.62842	−	2.67222i	0.376656	−	0.217462i	−0.299707	−	0.954031i	$-0.596889\pi$
$151$	4.62842	−	2.67222i	0.376656	−	0.217462i	0.676362	+	0.736569i	$0.263555\pi$
$152$	5.56136	−	2.63562i	0.451086	−	0.213777i
$153$	−3.06911	−	3.06911i	−0.248122	−	0.248122i
$154$	−15.4324	+	11.9892i	−1.24358	+	0.966116i
$155$	3.42991	+	11.1854i	0.275497	+	0.898437i
$156$	−0.483399	−	0.643718i	−0.0387029	−	0.0515387i
$157$	1.08200	−	0.624693i	0.0863529	−	0.0498559i	−0.456202	−	0.889876i	$-0.650790\pi$
$157$	1.08200	−	0.624693i	0.0863529	−	0.0498559i	0.542555	+	0.840020i	$0.317457\pi$
$158$	−13.1220	−	6.55602i	−1.04393	−	0.521569i
$159$	−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	$-0.597281\pi$
$163$	−16.3064	−	9.41453i	−1.27722	−	0.737403i	−0.976336	+	0.216258i	$0.930615\pi$
$164$	−14.6292	+	1.77154i	−1.14235	+	0.138334i
$165$	13.8757	−	0.496101i	1.08022	−	0.0386214i
$166$	24.4615	−	1.47571i	1.89858	−	0.114537i
$167$	8.22686	−	8.22686i	0.636614	−	0.636614i	−0.313105	−	0.949719i	$-0.601369\pi$
$167$	8.22686	−	8.22686i	0.636614	−	0.636614i	0.949719	+	0.313105i	$0.101369\pi$
$168$	8.89664	+	0.0391785i	0.686391	+	0.00302269i
$169$	−12.8854			−0.991183
$170$	7.87207	+	3.58752i	0.603761	+	0.275150i
$171$	0.893489	−	3.33455i	0.0683268	−	0.254999i
$172$	13.9829	−	1.69327i	1.06619	−	0.129111i
$173$	8.91380	−	15.4392i	0.677704	−	1.17382i	−0.297967	−	0.954576i	$-0.596308\pi$
$173$	8.91380	−	15.4392i	0.677704	−	1.17382i	0.975671	−	0.219241i	$-0.0703582\pi$
$174$	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
$178$	−2.33049	−	1.16436i	−0.174678	−	0.0872726i
$179$	8.77917	+	2.35237i	0.656186	+	0.175824i	0.571524	−	0.820585i	$-0.306352\pi$
$179$	8.77917	+	2.35237i	0.656186	+	0.175824i	0.0846617	+	0.996410i	$0.473019\pi$
$180$	5.73681	+	4.17533i	0.427596	+	0.311211i
$181$	3.42220	+	3.42220i	0.254370	+	0.254370i	0.822760	−	0.568389i	$-0.192433\pi$
$181$	3.42220	+	3.42220i	0.254370	+	0.254370i	−0.568389	+	0.822760i	$0.692433\pi$
$182$	−0.765136	+	1.00960i	−0.0567157	+	0.0748367i
$183$	−0.0308220	+	0.0308220i	−0.00227843	+	0.00227843i
$184$	10.7941	+	22.7764i	0.795751	+	1.67910i
$185$	13.2376	−	14.2193i	0.973248	−	1.04542i
$186$	−7.86946	−	3.93174i	−0.577017	−	0.288289i
$187$	7.14410	−	12.3739i	0.522428	−	0.904872i
$188$	−12.7649	+	5.13267i	−0.930977	+	0.374338i
$189$	9.39046	−	10.9524i	0.683055	−	0.796672i
$190$	0.659483	+	6.84902i	0.0478439	+	0.496880i
$191$	3.11573	−	5.39660i	0.225446	−	0.390485i	−0.731007	−	0.682370i	$-0.760949\pi$
$191$	3.11573	−	5.39660i	0.225446	−	0.390485i	0.956453	+	0.291885i	$0.0942826\pi$
$192$	−7.36147	−	6.02229i	−0.531269	−	0.434621i
$193$	−1.03952	+	3.87953i	−0.0748260	+	0.279254i	−0.993194	−	0.116473i	$-0.962841\pi$
$193$	−1.03952	+	3.87953i	−0.0748260	+	0.279254i	0.918368	+	0.395728i	$0.129508\pi$
$194$	12.2113	+	10.8218i	0.876721	+	0.776959i
$195$	0.860487	−	0.263860i	0.0616208	−	0.0188954i
$196$	−3.78512	−	13.4786i	−0.270366	−	0.962758i
$197$		−	2.28106i		−	0.162519i	−0.996693	−	0.0812596i	$-0.974106\pi$
$197$		−	2.28106i		−	0.162519i	0.996693	−	0.0812596i	$-0.0258943\pi$
$198$	7.77247	−	8.77047i	0.552366	−	0.623290i
$199$	0.322024	−	0.185920i	0.0228276	−	0.0131795i	−0.488543	−	0.872540i	$-0.662471\pi$
$199$	0.322024	−	0.185920i	0.0228276	−	0.0131795i	0.511370	+	0.859360i	$0.329138\pi$
$200$	−13.6246	−	3.79067i	−0.963408	−	0.268041i
$201$	−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
$205$	3.69283	−	16.0563i	0.257918	−	1.12142i
$206$	−20.2856	+	6.76872i	−1.41337	+	0.471599i
$207$	13.6565	+	3.65926i	0.949195	+	0.254336i
$208$	1.31510	−	0.323247i	0.0911858	−	0.0224132i
$209$	11.3643			0.786087
$210$	−3.41986	+	9.34047i	−0.235992	+	0.644554i
$211$	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	$0.633703\pi$
$212$	−10.0297	−	13.3560i	−0.688840	−	0.917293i
$213$	5.79340	−	3.34482i	0.396957	−	0.229183i
$214$	−4.16070	−	2.07877i	−0.284420	−	0.142102i
$215$	−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
$218$	−5.34493	−	1.09207i	−0.362004	−	0.0739642i
$219$	15.2295	−	4.08074i	1.02912	−	0.275751i
$220$	−8.38872	+	21.7991i	−0.565568	+	1.46970i
$221$	0.239718	−	0.894638i	0.0161251	−	0.0601799i
$222$	0.879646	+	14.5811i	0.0590380	+	0.978622i
$223$	16.2456	−	16.2456i	1.08788	−	1.08788i	0.0921383	−	0.995746i	$-0.470630\pi$
$223$	16.2456	−	16.2456i	1.08788	−	1.08788i	0.995746	−	0.0921383i	$-0.0293702\pi$
$224$	−5.93141	+	13.7411i	−0.396309	+	0.918117i
$225$	−6.56926	+	4.44694i	−0.437951	+	0.296462i
$226$	−3.61028	−	3.19946i	−0.240152	−	0.212825i
$227$	2.43700	−	1.40700i	0.161749	−	0.0933859i	−0.416940	−	0.908934i	$-0.636898\pi$
$227$	2.43700	−	1.40700i	0.161749	−	0.0933859i	0.578690	+	0.815548i	$0.303564\pi$
$228$	−4.07161	−	3.19201i	−0.269649	−	0.211396i
$229$	−1.93903	−	7.23657i	−0.128135	−	0.478206i	0.871797	−	0.489867i	$-0.162955\pi$
$229$	−1.93903	−	7.23657i	−0.128135	−	0.478206i	−0.999932	+	0.0116613i	$0.996288\pi$
$230$	−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
$233$	−1.05610	−	3.94140i	−0.0691871	−	0.258210i	0.922665	−	0.385602i	$-0.126006\pi$
$233$	−1.05610	−	3.94140i	−0.0691871	−	0.258210i	−0.991852	+	0.127392i	$0.959339\pi$
$234$	0.339519	−	0.679553i	0.0221950	−	0.0444238i
$235$	−0.549608	−	15.3723i	−0.0358525	−	1.00278i
$236$	−8.53712	−	1.21430i	−0.555719	−	0.0790443i
$237$			12.3313i			0.801007i
$238$	6.27979	+	8.08332i	0.407058	+	0.523964i
$239$			14.9500i			0.967032i	0.875335	+	0.483516i	$0.160641\pi$
$239$			14.9500i			0.967032i	−0.875335	+	0.483516i	$0.839359\pi$
$240$	9.12844	−	5.45395i	0.589238	−	0.352051i
$241$	−0.624178	+	0.360369i	−0.0402068	+	0.0232134i	−0.519969	−	0.854185i	$-0.674056\pi$
$241$	−0.624178	+	0.360369i	−0.0402068	+	0.0232134i	0.479762	+	0.877399i	$0.340723\pi$
$242$	20.5941	+	10.2893i	1.32384	+	0.661418i
$243$	−7.15505	+	12.3929i	−0.458997	+	0.795006i
$244$	−0.0273559	−	0.0680340i	−0.00175128	−	0.00435543i
$245$	15.6110	+	1.13846i	0.997351	+	0.0727336i
$246$	6.82885	+	10.3359i	0.435391	+	0.658995i
$247$	0.711563	−	0.190663i	0.0452757	−	0.0121316i
$248$	11.2771	−	9.58296i	0.716095	−	0.608519i
$249$	−10.3006	−	17.8412i	−0.652775	−	1.13064i
$250$	9.16031	−	12.8875i	0.579349	−	0.815080i
$251$	3.19601	+	3.19601i	0.201731	+	0.201731i	0.800741	−	0.599011i	$-0.204439\pi$
$251$	3.19601	+	3.19601i	0.201731	+	0.201731i	−0.599011	+	0.800741i	$0.704439\pi$
$252$	3.71913	+	7.52663i	0.234283	+	0.474133i
$253$			46.5422i			2.92609i
$254$	−13.3644	+	15.0804i	−0.838557	+	0.946229i
$255$	−0.259852	−	7.26792i	−0.0162725	−	0.455135i
$256$	14.1768	−	7.41736i	0.886052	−	0.463585i
$257$	−17.0217	+	4.56094i	−1.06178	+	0.284504i	−0.747112	−	0.664698i	$-0.768560\pi$
$257$	−17.0217	+	4.56094i	−1.06178	+	0.284504i	−0.314669	+	0.949201i	$0.601894\pi$
$258$	−6.52714	−	9.87927i	−0.406362	−	0.615057i
$259$	21.6829	−	7.63178i	1.34731	−	0.474216i
$260$	−0.159519	+	1.50567i	−0.00989295	+	0.0933774i
$261$	0.565754	+	2.11142i	0.0350193	+	0.130694i
$262$	−4.44542	−	13.3228i	−0.274639	−	0.823083i
$263$	−16.6353	−	4.45741i	−1.02578	−	0.274856i	−0.293569	−	0.955938i	$-0.594843\pi$
$263$	−16.6353	−	4.45741i	−1.02578	−	0.274856i	−0.732207	+	0.681082i	$0.761510\pi$
$264$	−7.52138	−	15.8707i	−0.462909	−	0.976774i
$265$	17.8535	−	5.47461i	1.09673	−	0.336303i
$266$	−3.07048	+	7.54015i	−0.188263	+	0.462316i
$267$			2.19007i			0.134030i
$268$	−9.95033	−	13.2503i	−0.607813	−	0.809393i
$269$	1.01001	−	3.76940i	0.0615812	−	0.229824i	−0.928276	−	0.371893i	$-0.878709\pi$
$269$	1.01001	−	3.76940i	0.0615812	−	0.229824i	0.989857	+	0.142069i	$0.0453754\pi$
$270$	2.84600	−	17.0070i	0.173202	−	1.03501i
$271$	20.2439	+	11.6878i	1.22973	+	0.709983i	0.966973	−	0.254880i	$-0.0820359\pi$
$271$	20.2439	+	11.6878i	1.22973	+	0.709983i	0.262754	+	0.964863i	$0.415369\pi$
$272$	0.227383	−	10.9404i	0.0137871	−	0.663358i
$273$	1.04673	+	0.196066i	0.0633509	+	0.0118665i
$274$	2.05135	−	10.0400i	0.123927	−	0.606536i
$275$	−19.7373	−	17.0998i	−1.19020	−	1.03116i
$276$	13.0728	−	16.6751i	0.786889	−	1.00372i
$277$	−22.8753	+	13.2070i	−1.37444	+	0.793535i	−0.991484	−	0.130231i	$-0.958428\pi$
$277$	−22.8753	+	13.2070i	−1.37444	+	0.793535i	−0.382959	+	0.923766i	$0.625095\pi$
$278$	−11.4506	+	12.9209i	−0.686763	+	0.774945i
$279$		−	8.30124i		−	0.496982i
$280$	−12.1970	−	11.4557i	−0.728913	−	0.684607i
$281$			26.4543i			1.57813i	0.614310	+	0.789065i	$0.289434\pi$
$281$			26.4543i			1.57813i	−0.614310	+	0.789065i	$0.710566\pi$
$282$	8.65602	+	7.67105i	0.515459	+	0.456804i
$283$	−22.3552	+	12.9068i	−1.32888	+	0.767230i	−0.985127	−	0.171829i	$-0.945032\pi$
$283$	−22.3552	+	12.9068i	−1.32888	+	0.767230i	−0.343755	+	0.939059i	$0.611699\pi$
$284$	1.35290	+	11.1721i	0.0802797	+	0.662942i
$285$	4.90285	−	3.06931i	0.290420	−	0.181810i
$286$	2.45009	+	0.500600i	0.144877	+	0.0296011i
$287$	12.6886	−	14.7992i	0.748986	−	0.873569i
$288$	1.97898	−	8.75412i	0.116612	−	0.515842i
$289$	8.24111	+	4.75801i	0.484771	+	0.279883i
$290$	−2.53002	−	3.54696i	−0.148568	−	0.208285i
$291$	3.55013	−	13.2493i	0.208112	−	0.776685i
$292$	−3.73510	+	26.2596i	−0.218580	+	1.53672i
$293$		−	0.188136i		−	0.0109910i	−0.999985	−	0.00549551i	$-0.998251\pi$
$293$		−	0.188136i		−	0.0109910i	0.999985	−	0.00549551i	$-0.00174928\pi$
$294$	−8.71408	+	7.91078i	−0.508215	+	0.461366i
$295$	4.51903	−	8.51613i	0.263108	−	0.495828i
$296$	−23.1438	−	8.26071i	−1.34521	−	0.480144i
$297$	−27.5093	−	7.37110i	−1.59625	−	0.427715i
$298$	18.0569	−	6.02505i	1.04601	−	0.349022i
$299$	0.780854	+	2.91419i	0.0451579	+	0.168532i
$300$	2.26847	+	11.6703i	0.130970	+	0.673787i
$301$	−12.1280	+	14.1453i	−0.699047	+	0.815324i
$302$	6.30613	−	4.16640i	0.362877	−	0.239749i
$303$	−15.2771	+	4.09347i	−0.877644	+	0.235164i
$304$	7.62623	−	4.19418i	0.437394	−	0.240552i
$305$	0.0819307	−	0.00292928i	0.00469134	−	0.000167730i
$306$	−4.59386	−	4.07113i	−0.262614	−	0.232731i
$307$		−	4.83012i		−	0.275670i	−0.990455	−	0.137835i	$-0.955986\pi$
$307$		−	4.83012i		−	0.275670i	0.990455	−	0.137835i	$-0.0440143\pi$
$308$	−20.7641	+	18.2388i	−1.18315	+	1.03925i
$309$	12.7121	+	12.7121i	0.723167	+	0.723167i
$310$	5.79438	+	15.4978i	0.329099	+	0.880216i
$311$	4.73723	+	8.20512i	0.268624	+	0.465270i	0.968507	−	0.248988i	$-0.0800979\pi$
$311$	4.73723	+	8.20512i	0.268624	+	0.465270i	−0.699883	+	0.714257i	$0.746765\pi$
$312$	−0.737209	−	0.867536i	−0.0417363	−	0.0491146i
$313$	29.6134	−	7.93489i	1.67385	−	0.448506i	0.707704	−	0.706509i	$-0.249731\pi$
$313$	29.6134	−	7.93489i	1.67385	−	0.448506i	0.966144	+	0.258002i	$0.0830642\pi$
$314$	1.47420	−	0.973990i	0.0831940	−	0.0549654i
$315$	−9.32710	+	1.05252i	−0.525523	+	0.0593027i
$316$	−19.0819	−	8.13730i	−1.07344	−	0.457759i
$317$	0.0727273	−	0.125967i	0.00408477	−	0.00707504i	−0.863976	−	0.503533i	$-0.832033\pi$
$317$	0.0727273	−	0.125967i	0.00408477	−	0.00707504i	0.868061	+	0.496458i	$0.165366\pi$
$318$	−6.27562	+	12.5608i	−0.351919	+	0.704373i
$319$	−6.23178	+	3.59792i	−0.348913	+	0.201445i
$320$	2.41589	+	17.7247i	0.135053	+	0.990838i
$321$			3.91000i			0.218235i
$322$	−30.8804	−	12.5750i	−1.72090	−	0.700779i
$323$		−	5.95250i		−	0.331206i
$324$	2.06934	+	2.75564i	0.114963	+	0.153091i
$325$	−1.52272	−	0.739546i	−0.0844651	−	0.0410227i
$326$	−23.8207	−	11.9013i	−1.31931	−	0.659153i
$327$	1.18697	+	4.42984i	0.0656397	+	0.244971i
$328$	−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
$331$	1.66870	+	6.22769i	0.0917202	+	0.342305i	0.996502	−	0.0835714i	$-0.0266327\pi$
$331$	1.66870	+	6.22769i	0.0917202	+	0.342305i	−0.904782	+	0.425876i	$0.859966\pi$
$332$	34.4053	−	4.16635i	1.88824	−	0.228658i
$333$	−11.9377	+	6.89222i	−0.654181	+	0.377691i
$334$	10.9128	−	12.3140i	0.597123	−	0.673794i
$335$	17.7123	−	5.43131i	0.967728	−	0.296744i
$336$	12.5623	−	0.702344i	0.685327	−	0.0383160i
$337$	−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	$0.270376\pi$
$338$	−18.1896	+	1.09734i	−0.989384	+	0.0596872i
$339$	−1.04960	+	3.91714i	−0.0570062	+	0.212750i
$340$	11.4181	+	4.39391i	0.619234	+	0.238293i
$341$	26.3960	−	7.07278i	1.42942	−	0.383012i
$342$	0.977317	−	4.78330i	0.0528473	−	0.258651i
$343$	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
$346$	11.2683	−	22.5538i	0.605789	−	1.21250i
$347$	14.5413	−	8.39542i	0.780617	−	0.450689i	−0.0560318	−	0.998429i	$-0.517845\pi$
$347$	14.5413	−	8.39542i	0.780617	−	0.450689i	0.836649	+	0.547739i	$0.184512\pi$
$348$	3.24330	+	0.461321i	0.173859	+	0.0247294i
$349$	−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	$0.767663\pi$
$350$	16.6783	−	8.47542i	0.891495	−	0.453030i
$351$	−1.84613			−0.0985391
$352$	29.5221	−	1.16596i	1.57354	−	0.0621458i
$353$	−9.23892	−	2.47556i	−0.491738	−	0.131761i	0.00442496	−	0.999990i	$-0.498591\pi$
$353$	−9.23892	−	2.47556i	−0.491738	−	0.131761i	−0.496163	+	0.868229i	$0.665258\pi$
$354$	2.29444	+	6.87637i	0.121948	+	0.365475i
$355$	−12.2619	−	2.82015i	−0.650795	−	0.149678i
$356$	−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	0.485719	+	0.874115i	$0.338558\pi$
$359$	−9.74169	+	16.8731i	−0.514147	+	0.890528i	−0.999865	+	0.0164129i	$0.994775\pi$
$360$	8.45393	+	5.40554i	0.445561	+	0.284897i
$361$	−12.3544	+	7.13280i	−0.650230	+	0.375410i
$362$	5.12238	+	4.53950i	0.269226	+	0.238591i
$363$		−	19.3533i		−	1.01578i
$364$	−0.994123	+	1.49036i	−0.0521062	+	0.0781162i
$365$	−26.1950	−	13.9002i	−1.37111	−	0.727570i
$366$	−0.0408849	+	0.0461346i	−0.00213709	+	0.00241149i
$367$	−2.63310	+	9.82688i	−0.137447	+	0.512959i	0.862529	+	0.506008i	$0.168879\pi$
$367$	−2.63310	+	9.82688i	−0.137447	+	0.512959i	−0.999976	+	0.00695103i	$0.997787\pi$
$368$	17.1771	+	31.2330i	0.895419	+	1.62813i
$369$	−5.84498	+	10.1238i	−0.304278	+	0.527024i
$370$	17.4759	−	21.1999i	0.908529	−	1.10213i
$371$	21.7177	+	4.06802i	1.12753	+	0.211201i
$372$	−11.4437	−	4.88006i	−0.593330	−	0.253019i
$373$	−2.39857	+	4.15444i	−0.124193	+	0.215109i	−0.921417	−	0.388575i	$-0.872968\pi$
$373$	−2.39857	+	4.15444i	−0.124193	+	0.215109i	0.797224	+	0.603683i	$0.206301\pi$
$374$	9.03117	−	18.0760i	0.466991	−	0.934690i
$375$	−13.1335	−	2.04658i	−0.678213	−	0.105685i
$376$	−17.5824	+	8.33260i	−0.906745	+	0.429721i
$377$	−0.329832	+	0.329832i	−0.0169872	+	0.0169872i
$378$	12.3233	−	16.2607i	0.633842	−	0.836358i
$379$	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	$0.700950\pi$
$380$	1.51423	+	9.61224i	0.0776783	+	0.493098i
$381$	16.3622	+	4.38424i	0.838262	+	0.224612i
$382$	3.93873	−	7.88344i	0.201523	−	0.403352i
$383$	−3.87586	−	14.4649i	−0.198047	−	0.739122i	−0.991457	−	0.130434i	$-0.958363\pi$
$383$	−3.87586	−	14.4649i	−0.198047	−	0.739122i	0.793410	−	0.608688i	$-0.208304\pi$
$384$	−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
$387$	5.58674	−	9.67652i	0.283990	−	0.491885i
$388$	18.1597	+	14.2366i	0.921917	+	0.722754i
$389$	−3.45041	+	12.8771i	−0.174943	+	0.652895i	0.821619	+	0.570037i	$0.193071\pi$
$389$	−3.45041	+	12.8771i	−0.174943	+	0.652895i	−0.996561	+	0.0828575i	$0.973595\pi$
$390$	1.19223	−	0.445757i	0.0603711	−	0.0225718i
$391$	24.3783			1.23286
$392$	−6.49111	−	18.7047i	−0.327850	−	0.944730i
$393$	−8.34879	+	8.34879i	−0.421141	+	0.421141i
$394$	−0.194259	−	3.22006i	−0.00978661	−	0.162224i
$395$	15.8036	−	16.9755i	0.795163	−	0.854131i
$396$	10.2251	−	13.0427i	0.513830	−	0.655422i
$397$	24.2150	+	13.9805i	1.21532	+	0.701663i	0.963912	−	0.266220i	$-0.0857748\pi$
$397$	24.2150	+	13.9805i	1.21532	+	0.701663i	0.251403	+	0.967883i	$0.419108\pi$
$398$	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	−0.543123	−	0.839653i	$-0.682758\pi$
$401$	9.12337	−	15.8021i	0.455599	−	0.789121i	0.998722	+	0.0505317i	$0.0160916\pi$
$402$	−6.22598	+	12.4614i	−0.310524	+	0.621519i
$403$	1.53409	−	0.885706i	0.0764184	−	0.0441202i
$404$	3.74675	−	26.3415i	0.186408	−	1.31054i
$405$	−3.68358	+	1.12953i	−0.183039	+	0.0561270i
$406$	−0.703457	−	5.10685i	−0.0349120	−	0.253449i
$407$	−32.0867	−	32.0867i	−1.59048	−	1.59048i
$408$	−8.31288	+	3.93960i	−0.411549	+	0.195039i
$409$	−2.11431	+	1.22070i	−0.104546	+	0.0603597i	−0.551361	−	0.834267i	$-0.685891\pi$
$409$	−2.11431	+	1.22070i	−0.104546	+	0.0603597i	0.446815	+	0.894626i	$0.352558\pi$
$410$	3.84559	−	22.9803i	0.189920	−	1.13492i
$411$	−8.32104	+	2.22962i	−0.410447	+	0.109979i
$412$	−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
$415$	−8.68487	+	37.7615i	−0.426323	+	1.85364i
$416$	1.82893	−	0.568307i	0.0896707	−	0.0278635i
$417$	14.0192	+	3.75642i	0.686521	+	0.183953i
$418$	16.0424	−	0.967802i	0.784661	−	0.0473368i
$419$	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	$0.533773\pi$
$420$	−4.03218	+	13.4767i	−0.196750	+	0.657595i
$421$	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	$-0.136759\pi$
$422$	10.9859	+	9.73579i	0.534784	+	0.473931i
$423$	−2.82480	+	10.5423i	−0.137346	+	0.512584i
$424$	−15.2958	−	17.9998i	−0.742827	−	0.874147i
$425$	−8.95668	+	10.3382i	−0.434463	+	0.501474i
$426$	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
$429$	−0.544103	−	2.03062i	−0.0262695	−	0.0980392i
$430$	−3.67569	+	21.9650i	−0.177257	+	1.05925i
$431$	−6.85811	−	11.8786i	−0.330343	−	0.572172i	0.652236	−	0.758016i	$-0.273831\pi$
$431$	−6.85811	−	11.8786i	−0.330343	−	0.572172i	−0.982579	+	0.185845i	$0.940498\pi$
$432$	−21.1810	+	5.20622i	−1.01907	+	0.250484i
$433$	−13.7552	+	13.7552i	−0.661032	+	0.661032i	−0.955623	−	0.294591i	$-0.904816\pi$
$433$	−13.7552	+	13.7552i	−0.661032	+	0.661032i	0.294591	+	0.955623i	$0.404816\pi$
$434$	−2.43907	+	19.4245i	−0.117079	+	0.932405i
$435$	−1.71681	+	3.23533i	−0.0823146	+	0.155122i
$436$	−7.63815	−	1.08643i	−0.365801	−	0.0520308i
$437$	9.69480	+	16.7919i	0.463765	+	0.803265i
$438$	21.1512	−	7.05754i	1.01064	−	0.337222i
$439$	−15.7697	−	9.10464i	−0.752647	−	0.434541i	0.0740025	−	0.997258i	$-0.476423\pi$
$439$	−15.7697	−	9.10464i	−0.752647	−	0.434541i	−0.826650	+	0.562717i	$0.809756\pi$
$440$	−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	−0.587953	−	0.808895i	$-0.700066\pi$
$443$	8.55684	−	14.8209i	0.406548	−	0.704161i	0.994500	+	0.104734i	$0.0333992\pi$
$444$	2.48350	+	20.5085i	0.117862	+	0.973291i
$445$	2.80674	−	3.01488i	0.133052	−	0.142919i
$446$	21.5495	−	24.3165i	1.02040	−	1.15142i
$447$	−11.3155	−	11.3155i	−0.535203	−	0.535203i
$448$	−7.20285	+	19.9027i	−0.340302	+	0.940316i
$449$		−	13.5321i		−	0.638618i	−0.947651	−	0.319309i	$-0.896549\pi$
$449$		−	13.5321i		−	0.638618i	0.947651	−	0.319309i	$-0.103451\pi$
$450$	−8.89478	+	6.83695i	−0.419304	+	0.322297i
$451$	−37.1713	−	9.96002i	−1.75033	−	0.468999i
$452$	−5.36891	−	4.20906i	−0.252532	−	0.197977i
$453$	−5.50262	−	3.17694i	−0.258536	−	0.149266i
$454$	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	$-0.694964\pi$
$457$	−14.1882	+	3.80171i	−0.663695	+	0.177837i	−0.0887822	+	0.996051i	$0.528298\pi$
$458$	−3.35350	−	10.0503i	−0.156699	−	0.469622i
$459$	−3.86089	+	14.4090i	−0.180211	+	0.672556i
$460$	−39.3666	+	6.20148i	−1.83548	+	0.289145i
$461$	3.49391	−	3.49391i	0.162727	−	0.162727i	−0.621046	−	0.783774i	$-0.713292\pi$
$461$	3.49391	−	3.49391i	0.162727	−	0.162727i	0.783774	+	0.621046i	$0.213292\pi$
$462$	21.5177	+	8.76235i	1.00109	+	0.407662i
$463$	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	$0.718426\pi$
$464$	−2.85408	+	4.71438i	−0.132497	+	0.218860i
$465$	9.47763	−	10.1805i	0.439515	−	0.472108i
$466$	−1.82649	−	5.47393i	−0.0846105	−	0.253575i
$467$	18.9085	+	10.9168i	0.874982	+	0.505171i	0.869001	−	0.494811i	$-0.164763\pi$
$467$	18.9085	+	10.9168i	0.874982	+	0.505171i	0.00598173	+	0.999982i	$0.498096\pi$
$468$	0.421409	−	0.988203i	0.0194796	−	0.0456797i
$469$	21.5459	+	4.03584i	0.994899	+	0.186358i
$470$	−2.08498	−	21.6534i	−0.0961728	−	0.998798i
$471$	−1.28636	−	0.742682i	−0.0592725	−	0.0342210i
$472$	−12.1548	−	0.987132i	−0.559470	−	0.0454364i
$473$	35.5290	+	9.51997i	1.63363	+	0.437729i
$474$	1.05015	+	17.4075i	0.0482352	+	0.799553i
$475$	−10.6829	−	2.05812i	−0.490165	−	0.0944328i
$476$	9.55323	+	10.8760i	0.437872	+	0.498500i
$477$	−13.2499			−0.606673
$478$	1.27316	+	21.1041i	0.0582329	+	0.965278i
$479$	−2.99347	−	5.18484i	−0.136775	−	0.236901i	0.789499	−	0.613752i	$-0.210340\pi$
$479$	−2.99347	−	5.18484i	−0.136775	−	0.236901i	−0.926274	+	0.376850i	$0.877007\pi$
$480$	12.4217	−	8.47645i	0.566969	−	0.386895i
$481$	−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
$485$	−21.8671	+	13.6894i	−0.992933	+	0.621602i
$486$	−9.04501	+	18.1038i	−0.410290	+	0.821203i
$487$	−3.60084	+	13.4385i	−0.163170	+	0.608958i	0.835097	+	0.550103i	$0.185412\pi$
$487$	−3.60084	+	13.4385i	−0.163170	+	0.608958i	−0.998267	+	0.0588549i	$0.981255\pi$
$488$	−0.0444108	−	0.0937103i	−0.00201038	−	0.00424207i
$489$			22.3854i			1.01230i
$490$	22.1342	+	0.277650i	0.999921	+	0.0125429i
$491$	−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	$0.480773\pi$
$492$	10.5201	+	14.0091i	0.474285	+	0.631581i
$493$	1.88455	+	3.26413i	0.0848757	+	0.147009i
$494$	0.988239	−	0.329746i	0.0444630	−	0.0148360i
$495$	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
$498$	−16.0602	−	24.3083i	−0.719676	−	1.08928i
$499$	−0.750216	−	2.79984i	−0.0335843	−	0.125338i	0.947099	−	0.320943i	$-0.104000\pi$
$499$	−0.750216	−	2.79984i	−0.0335843	−	0.125338i	−0.980683	+	0.195605i	$0.937333\pi$
$500$	11.8336	−	18.9728i	0.529215	−	0.848488i
$501$	−13.3607	−	3.57999i	−0.596912	−	0.159942i
$502$	4.78382	+	4.23947i	0.213512	+	0.189217i
$503$	−12.8172	−	12.8172i	−0.571492	−	0.571492i	0.361053	−	0.932545i	$-0.382417\pi$
$503$	−12.8172	−	12.8172i	−0.571492	−	0.571492i	−0.932545	+	0.361053i	$0.882417\pi$
$504$	5.89108	+	10.3082i	0.262410	+	0.459165i
$505$	26.2767	+	13.9436i	1.16930	+	0.620481i
$506$	3.96360	+	65.7012i	0.176204	+	2.92078i
$507$	7.65956	+	13.2667i	0.340173	+	0.589197i
$508$	−17.5815	+	22.4263i	−0.780055	+	0.995008i
$509$	−8.48264	+	2.27292i	−0.375986	+	0.100745i	−0.441863	−	0.897083i	$-0.645682\pi$
$509$	−8.48264	+	2.27292i	−0.375986	+	0.100745i	0.0658766	+	0.997828i	$0.479016\pi$
$510$	−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
$513$	−11.4604	+	3.07082i	−0.505991	+	0.135580i
$514$	−23.6402	+	7.88802i	−1.04272	+	0.347926i
$515$	−1.20814	−	33.7912i	−0.0532372	−	1.48902i
$516$	−10.0553	−	13.3902i	−0.442662	−	0.589470i
$517$	−35.9287			−1.58014
$518$	29.9586	−	12.6199i	1.31631	−	0.554488i
$519$	−21.1948			−0.930349
$520$	−0.0969600	+	2.13905i	−0.00425198	+	0.0938037i
$521$	−7.23040	−	12.5234i	−0.316770	−	0.548661i	0.663042	−	0.748582i	$-0.269265\pi$
$521$	−7.23040	−	12.5234i	−0.316770	−	0.548661i	−0.979812	+	0.199921i	$0.935932\pi$
$522$	0.978456	+	2.93240i	0.0428259	+	0.128348i
$523$	22.2982	+	12.8739i	0.975034	+	0.562936i	0.900767	−	0.434302i	$-0.143005\pi$
$523$	22.2982	+	12.8739i	0.975034	+	0.562936i	0.0742670	+	0.997238i	$0.476338\pi$
$524$	−7.40994	−	18.4285i	−0.323705	−	0.805052i
$525$	−12.6402	−	9.35808i	−0.551665	−	0.408420i
$526$	−23.8628	−	4.87561i	−1.04047	−	0.212587i
$527$	−3.70463	−	13.8259i	−0.161376	−	0.602265i
$528$	−11.9691	−	21.7633i	−0.520888	−	0.947126i
$529$	−48.8520	+	28.2047i	−2.12400	+	1.22629i
$530$	24.7367	−	9.24865i	1.07449	−	0.401736i
$531$	−4.83700	+	4.83700i	−0.209908	+	0.209908i
$532$	−3.69230	+	10.9055i	−0.160081	+	0.472814i
$533$	−2.49454			−0.108050
$534$	0.186509	+	3.09161i	0.00807105	+	0.133787i
$535$	5.01097	−	5.38257i	0.216643	−	0.232709i
$536$	−15.1748	−	17.8574i	−0.655450	−	0.771323i
$537$	−2.79668	−	10.4373i	−0.120685	−	0.450404i
$538$	1.10477	−	5.40707i	0.0476299	−	0.233116i
$539$	3.96031	−	36.3451i	0.170583	−	1.56550i
$540$	2.56921	−	24.2502i	0.110561	−	1.04356i
$541$	−6.81823	+	1.82694i	−0.293139	+	0.0785463i	−0.402391	−	0.915468i	$-0.631821\pi$
$541$	−6.81823	+	1.82694i	−0.293139	+	0.0785463i	0.109253	+	0.994014i	$0.465154\pi$
$542$	29.5725	+	14.7751i	1.27025	+	0.634643i
$543$	1.48920	−	5.55777i	0.0639077	−	0.238507i
$544$	−0.610714	−	15.4633i	−0.0261842	−	0.662985i
$545$	4.04317	−	7.61938i	0.173190	−	0.326378i
$546$	1.49431	+	0.187636i	0.0639505	+	0.00803006i
$547$	−13.3169			−0.569388			−0.284694	−	0.958618i	$-0.591892\pi$
$547$	−13.3169			−0.569388			−0.284694	+	0.958618i	$0.591892\pi$
$548$	2.04077	−	14.3476i	0.0871772	−	0.612898i
$549$	−0.0561879	−	0.0150555i	−0.00239804	−	0.000642554i
$550$	−29.3183	−	22.4581i	−1.25014	−	0.957616i
$551$	−1.49890	+	2.59617i	−0.0638554	+	0.110601i
$552$	17.0341	−	24.6527i	0.725018	−	1.04929i
$553$	25.8858	−	9.11110i	1.10078	−	0.387444i
$554$	−31.1671	+	20.5918i	−1.32416	+	0.874861i
$555$	−22.5091	−	5.17692i	−0.955456	−	0.219748i
$556$	−15.0639	+	19.2149i	−0.638851	+	0.814894i
$557$	5.05622	+	8.75764i	0.214239	+	0.371073i	0.953037	−	0.302854i	$-0.0979395\pi$
$557$	5.05622	+	8.75764i	0.214239	+	0.371073i	−0.738798	+	0.673927i	$0.764606\pi$
$558$	−0.706945	−	11.7184i	−0.0299274	−	0.496080i
$559$	2.38432			0.100846
$560$	−18.1935	−	15.1326i	−0.768816	−	0.639470i
$561$	−16.9869			−0.717187
$562$	2.25288	+	37.3441i	0.0950321	+	1.57527i
$563$	−10.9168	−	18.9085i	−0.460088	−	0.796897i	0.538876	−	0.842385i	$-0.318849\pi$
$563$	−10.9168	−	18.9085i	−0.460088	−	0.796897i	−0.998965	+	0.0454883i	$0.985516\pi$
$564$	12.8725	+	10.0917i	0.542031	+	0.424935i
$565$	6.46501	−	4.04726i	0.271985	−	0.170270i
$566$	−30.4586	+	20.1237i	−1.28027	+	0.845861i
$567$	−4.48085	−	0.839323i	−0.188178	−	0.0352483i
$568$	2.86125	+	15.6559i	0.120055	+	0.656905i
$569$	6.69251	−	11.5918i	0.280564	−	0.485952i	−0.690959	−	0.722894i	$-0.742812\pi$
$569$	6.69251	−	11.5918i	0.280564	−	0.485952i	0.971524	+	0.236942i	$0.0761450\pi$
$570$	6.65971	−	4.75032i	0.278945	−	0.198969i
$571$	−16.7903	−	4.49896i	−0.702654	−	0.188276i	−0.110235	−	0.993906i	$-0.535160\pi$
$571$	−16.7903	−	4.49896i	−0.702654	−	0.188276i	−0.592419	+	0.805630i	$0.701827\pi$
$572$	3.50130	+	0.498017i	0.146397	+	0.0208231i
$573$	−7.40843			−0.309492
$574$	16.6515	−	21.9718i	0.695022	−	0.917086i
$575$	8.42895	−	43.7515i	0.351511	−	1.82456i
$576$	2.04811	−	12.5263i	0.0853378	−	0.521928i
$577$	3.27239	−	12.2127i	0.136231	−	0.508422i	−0.863759	−	0.503906i	$-0.831896\pi$
$577$	3.27239	−	12.2127i	0.136231	−	0.508422i	0.999990	−	0.00451610i	$-0.00143752\pi$
$578$	12.0387	+	6.01481i	0.500746	+	0.250183i
$579$	4.61228	−	1.23586i	0.191680	−	0.0513604i
$580$	−3.87356	−	4.79160i	−0.160841	−	0.198960i
$581$	−29.8414	+	34.8051i	−1.23803	+	1.44396i
$582$	3.88320	−	19.0056i	0.160964	−	0.787808i
$583$	−11.2891	−	42.1317i	−0.467549	−	1.74492i
$584$	−3.03635	+	37.3873i	−0.125645	+	1.54710i
$585$	0.879117	+	0.818424i	0.0363470	+	0.0338377i
$586$	−0.0160219	−	0.265582i	−0.000661859	−	0.0109711i
$587$	27.4813			1.13428			0.567138	−	0.823623i	$-0.308051\pi$
$587$	27.4813			1.13428			0.567138	+	0.823623i	$0.308051\pi$
$588$	−11.6275	+	11.9093i	−0.479510	+	0.491133i
$589$	8.05008	−	8.05008i	0.331698	−	0.331698i
$590$	5.65403	−	12.4066i	0.232773	−	0.510772i
$591$	−2.34858	+	1.35595i	−0.0966075	+	0.0557764i
$592$	−33.3744	−	9.69025i	−1.37168	−	0.398267i
$593$	3.53372	+	13.1880i	0.145113	+	0.541568i	0.999750	+	0.0223429i	$0.00711256\pi$
$593$	3.53372	+	13.1880i	0.145113	+	0.541568i	−0.854638	+	0.519225i	$0.826221\pi$
$594$	−39.4612	−	8.06266i	−1.61911	−	0.330815i
$595$	−15.0648	+	5.91544i	−0.617595	+	0.242509i
$596$	24.9768	−	10.0430i	1.02309	−	0.411377i
$597$	−0.382846	−	0.221036i	−0.0156688	−	0.00904641i
$598$	1.35047	+	4.04730i	0.0552246	+	0.165506i
$599$	18.2328	+	31.5801i	0.744970	+	1.29033i	0.950209	+	0.311615i	$0.100870\pi$
$599$	18.2328	+	31.5801i	0.744970	+	1.29033i	−0.205238	+	0.978712i	$0.565797\pi$
$600$	4.19614	+	16.2812i	0.171307	+	0.664677i
$601$	−32.7250			−1.33488			−0.667440	−	0.744664i	$-0.732610\pi$
$601$	−32.7250			−1.33488			−0.667440	+	0.744664i	$0.732610\pi$
$602$	−15.9158	+	21.0011i	−0.648681	+	0.855940i
$603$	−13.1451			−0.535312
$604$	8.54721	−	6.41852i	0.347781	−	0.261166i
$605$	−24.8027	+	26.6420i	−1.00837	+	1.08315i
$606$	−21.2172	+	7.07956i	−0.861890	+	0.287587i
$607$	−4.59463	+	1.23113i	−0.186490	+	0.0499700i	−0.350855	−	0.936430i	$-0.614109\pi$
$607$	−4.59463	+	1.23113i	−0.186490	+	0.0499700i	0.164365	+	0.986400i	$0.447442\pi$
$608$	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
$611$	−2.24963	+	0.602787i	−0.0910104	+	0.0243862i
$612$	−6.83162	−	5.35577i	−0.276152	−	0.216494i
$613$	−13.0080	−	22.5305i	−0.525387	−	0.909997i	−0.999563	−	0.0295666i	$-0.990587\pi$
$613$	−13.0080	−	22.5305i	−0.525387	−	0.909997i	0.474176	−	0.880430i	$-0.342746\pi$
$614$	−0.411340	−	6.81843i	−0.0166003	−	0.275170i
$615$	−18.7266	+	5.74234i	−0.755131	+	0.231553i
$616$	−27.7584	+	27.5150i	−1.11842	+	1.10861i
$617$	−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	$0.862577\pi$
$618$	19.0276	+	16.8624i	0.765402	+	0.678306i
$619$	−35.5968	−	9.53814i	−1.43076	−	0.383370i	−0.541470	−	0.840720i	$-0.682132\pi$
$619$	−35.5968	−	9.53814i	−1.43076	−	0.383370i	−0.889287	+	0.457350i	$0.848799\pi$
$620$	9.49944	+	21.3840i	0.381507	+	0.858801i
$621$	−12.5764	−	46.9359i	−0.504675	−	1.88347i
$622$	7.38605	+	11.1793i	0.296154	+	0.448249i
$623$	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
$626$	41.1279	−	13.7232i	1.64380	−	0.548489i
$627$	−6.75539	−	11.7007i	−0.269784	−	0.467280i
$628$	1.99811	−	1.50048i	0.0797331	−	0.0598755i
$629$	−16.8066	+	16.8066i	−0.670123	+	0.670123i
$630$	−13.0769	+	2.28009i	−0.520998	+	0.0908411i
$631$		−	11.4540i		−	0.455976i	−0.973664	−	0.227988i	$-0.926785\pi$
$631$		−	11.4540i		−	0.455976i	0.973664	−	0.227988i	$-0.0732147\pi$
$632$	−27.6300	−	9.86195i	−1.09906	−	0.392287i
$633$	3.19386	−	11.9197i	0.126945	−	0.473764i
$634$	0.0919378	−	0.184015i	0.00365132	−	0.00730818i
$635$	−16.9057	−	27.0048i	−0.670883	−	1.07165i
$636$	−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
$640$	4.91984	+	24.8152i	0.194474	+	0.980908i
$641$	16.6081	+	28.7660i	0.655979	+	1.13619i	0.981647	+	0.190705i	$0.0610774\pi$
$641$	16.6081	+	28.7660i	0.655979	+	1.13619i	−0.325668	+	0.945484i	$0.605589\pi$
$642$	0.332981	+	5.51955i	0.0131417	+	0.217839i
$643$	5.80713			0.229011			0.114505	−	0.993423i	$-0.463472\pi$
$643$	5.80713			0.229011			0.114505	+	0.993423i	$0.463472\pi$
$644$	−44.6632	−	15.1217i	−1.75998	−	0.595878i
$645$	17.8993	−	5.48863i	0.704783	−	0.216115i
$646$	−0.506923	−	8.40282i	−0.0199446	−	0.330605i
$647$	34.6435	+	9.28270i	1.36198	+	0.364941i	0.864542	−	0.502561i	$-0.167609\pi$
$647$	34.6435	+	9.28270i	1.36198	+	0.364941i	0.497435	+	0.867501i	$0.334275\pi$
$648$	3.15585	+	3.71376i	0.123974	+	0.145890i
$649$	−19.5017	−	11.2593i	−0.765509	−	0.441967i
$650$	−2.21252	−	0.914302i	−0.0867821	−	0.0358619i
$651$	15.5241	−	5.46407i	0.608438	−	0.214154i
$652$	−34.6400	−	14.7719i	−1.35661	−	0.578511i
$653$	43.5436	+	25.1399i	1.70399	+	0.983800i	0.941631	+	0.336646i	$0.109293\pi$
$653$	43.5436	+	25.1399i	1.70399	+	0.983800i	0.762360	+	0.647153i	$0.224041\pi$
$654$	2.05284	+	6.15228i	0.0802723	+	0.240573i
$655$	22.1927	−	0.793460i	0.867140	−	0.0310030i
$656$	−28.6203	+	7.03478i	−1.11744	+	0.274662i
$657$	14.8783	+	14.8783i	0.580456	+	0.580456i
$658$	9.70742	−	23.8384i	0.378435	−	0.929319i
$659$	−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	$0.274287\pi$
$660$	27.4309	−	4.32122i	1.06775	−	0.168203i
$661$	−12.6300	+	47.1359i	−0.491251	+	1.83337i	0.0588369	+	0.998268i	$0.481261\pi$
$661$	−12.6300	+	47.1359i	−0.491251	+	1.83337i	−0.550088	+	0.835107i	$0.685406\pi$
$662$	2.88598	+	8.64919i	0.112167	+	0.336160i
$663$	−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
$667$	−10.6325	−	6.13871i	−0.411694	−	0.237692i
$668$	14.3564	−	18.3124i	0.555464	−	0.708529i
$669$	−26.3834	−	7.06941i	−1.02004	−	0.273319i
$670$	24.5410	−	9.17550i	0.948102	−	0.354480i
$671$		−	0.191492i		−	0.00739246i
$672$	17.6737	−	2.06128i	0.681776	−	0.0795157i
$673$	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	$0.410870\pi$
$674$	−2.20294	+	2.48580i	−0.0848541	+	0.0957495i
$675$	24.5249	+	11.9111i	0.943962	+	0.458460i
$676$	−25.5839	+	3.09810i	−0.983994	+	0.119158i
$677$	2.16028	−	3.74171i	0.0830262	−	0.143806i	−0.821522	−	0.570176i	$-0.806875\pi$
$677$	2.16028	−	3.74171i	0.0830262	−	0.143806i	0.904548	+	0.426371i	$0.140208\pi$
$678$	−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
$682$	36.6595	−	12.2322i	1.40376	−	0.468394i
$683$	10.8645	+	18.8179i	0.415719	+	0.720047i	0.995504	−	0.0947229i	$-0.0301965\pi$
$683$	10.8645	+	18.8179i	0.415719	+	0.720047i	−0.579784	+	0.814770i	$0.696863\pi$
$684$	0.972275	−	6.83556i	0.0371759	−	0.261364i
$685$	14.3123	+	7.59473i	0.546845	+	0.290180i
$686$	23.0447	+	12.4476i	0.879851	+	0.475250i
$687$	−6.29811	+	6.29811i	−0.240288	+	0.240288i
$688$	27.3558	−	6.72397i	1.04293	−	0.256349i
$689$	−1.41371	−	2.44862i	−0.0538581	−	0.0932850i
$690$	19.4548	+	27.2746i	0.740631	+	1.03833i
$691$	9.17643	+	34.2469i	0.349088	+	1.30281i	0.887763	+	0.460301i	$0.152258\pi$
$691$	9.17643	+	34.2469i	0.349088	+	1.30281i	−0.538675	+	0.842514i	$0.681075\pi$
$692$	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
$695$	−14.4848	−	23.1378i	−0.549441	−	0.877665i
$696$	4.61769	+	0.375018i	0.175033	+	0.0142150i
$697$	−5.21693	+	19.4699i	−0.197605	+	0.737474i
$698$	−2.19322	−	1.94365i	−0.0830146	−	0.0735683i
$699$	−3.43027	+	3.43027i	−0.129745	+	0.129745i
$700$	22.8222	−	13.3847i	0.862596	−	0.505893i
$701$	−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	$0.756273\pi$
$702$	−2.60608	+	0.157219i	−0.0983603	+	0.00593385i
$703$	−18.2602	−	4.89280i	−0.688696	−	0.184536i
$704$	41.5755	−	4.16007i	1.56694	−	0.156788i
$705$	−15.5005	+	9.70374i	−0.583784	+	0.365464i
$706$	−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
$709$	−10.3928	+	2.78474i	−0.390309	+	0.104583i	−0.448636	−	0.893715i	$-0.648090\pi$
$709$	−10.3928	+	2.78474i	−0.390309	+	0.104583i	0.0583270	+	0.998298i	$0.481423\pi$
$710$	−17.5497	−	2.93682i	−0.658627	−	0.110217i
$711$	−14.2516	+	8.22819i	−0.534479	+	0.308581i
$712$	−4.90713	−	1.75150i	−0.183903	−	0.0656403i
$713$	32.9688	+	32.9688i	1.23469	+	1.23469i
$714$	4.58961	−	11.2707i	0.171762	−	0.421794i
$715$	−1.85337	+	3.49269i	−0.0693122	+	0.130619i
$716$	17.9966	+	2.55980i	0.672564	+	0.0956641i
$717$	15.3924	−	8.88682i	0.574841	−	0.331884i
$718$	−12.3149	+	24.6485i	−0.459588	+	0.919873i
$719$	−10.8607	+	18.8112i	−0.405034	+	0.701539i	−0.994325	−	0.106381i	$-0.966074\pi$
$719$	−10.8607	+	18.8112i	−0.405034	+	0.701539i	0.589292	+	0.807920i	$0.299407\pi$
$720$	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
$724$	7.61758	+	5.97194i	0.283105	+	0.221945i
$725$	6.50971	−	2.25359i	0.241764	−	0.0836961i
$726$	−1.64815	−	27.3200i	−0.0611686	−	1.01394i
$727$	18.0505	−	18.0505i	0.669457	−	0.669457i	−0.288134	−	0.957590i	$-0.593035\pi$
$727$	18.0505	−	18.0505i	0.669457	−	0.669457i	0.957590	+	0.288134i	$0.0930347\pi$
$728$	−1.27643	+	2.18853i	−0.0473076	+	0.0811122i
$729$	22.1821			0.821559
$730$	−38.1619	−	17.3914i	−1.41243	−	0.643684i
$731$	4.98644	−	18.6096i	0.184430	−	0.688303i
$732$	−0.0537862	+	0.0686076i	−0.00198799	+	0.00253581i
$733$	−2.12692	+	3.68394i	−0.0785597	+	0.136069i	−0.902629	−	0.430420i	$-0.858365\pi$
$733$	−2.12692	+	3.68394i	−0.0785597	+	0.136069i	0.824069	+	0.566489i	$0.191699\pi$
$734$	−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
$738$	−7.38890	+	14.7890i	−0.271989	+	0.544391i
$739$	9.72820	+	2.60666i	0.357858	+	0.0958877i	0.433269	−	0.901265i	$-0.357360\pi$
$739$	9.72820	+	2.60666i	0.357858	+	0.0958877i	−0.0754108	+	0.997153i	$0.524027\pi$
$740$	22.8644	−	31.4151i	0.840512	−	1.15484i
$741$	−0.619286	−	0.619286i	−0.0227500	−	0.0227500i
$742$	31.0042	+	3.89310i	1.13820	+	0.142920i
$743$	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	$0.164758\pi$
$744$	−16.5701	−	5.91436i	−0.607489	−	0.216831i
$745$	1.07541	+	30.0786i	0.0393999	+	1.10200i
$746$	−3.03213	+	6.06887i	−0.111014	+	0.222197i
$747$	13.7464	−	23.8094i	0.502953	−	0.871140i
$748$	11.2094	−	26.2861i	0.409858	−	0.961115i
$749$	8.20784	−	2.88894i	0.299908	−	0.105559i
$750$	−18.7142	−	1.77058i	−0.683346	−	0.0646525i
$751$	−2.29798	+	3.98021i	−0.0838544	+	0.145240i	−0.904902	−	0.425619i	$-0.860056\pi$
$751$	−2.29798	+	3.98021i	−0.0838544	+	0.145240i	0.821048	+	0.570859i	$0.193390\pi$
$752$	−24.1106	+	13.2600i	−0.879223	+	0.483544i
$753$	1.39077	−	5.19044i	0.0506826	−	0.189150i
$754$	−0.437517	+	0.493695i	−0.0159334	+	0.0179793i
$755$	3.50350	+	11.4254i	0.127505	+	0.415814i
$756$	16.0114	−	24.0038i	0.582327	−	0.873009i
$757$			6.23131i			0.226481i	0.993568	+	0.113240i	$0.0361230\pi$
$757$			6.23131i			0.226481i	−0.993568	+	0.113240i	$0.963877\pi$
$758$	6.32514	+	5.60540i	0.229739	+	0.203597i
$759$	47.9197	−	27.6665i	1.73938	−	1.00423i
$760$	2.95615	+	13.4401i	0.107231	+	0.487525i
$761$	11.2413	−	19.4704i	0.407495	−	0.705802i	−0.587113	−	0.809505i	$-0.699736\pi$
$761$	11.2413	−	19.4704i	0.407495	−	0.705802i	0.994608	+	0.103702i	$0.0330690\pi$
$762$	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
$765$	8.22634	−	5.14990i	0.297424	−	0.186195i
$766$	−6.70320	−	20.0893i	−0.242196	−	0.725855i
$767$	−1.40998	−	0.377802i	−0.0509113	−	0.0136416i
$768$	−16.0641	−	10.1873i	−0.579665	−	0.367601i
$769$	17.4560			0.629478			0.314739	−	0.949178i	$-0.398083\pi$
$769$	17.4560			0.629478			0.314739	+	0.949178i	$0.398083\pi$
$770$	−18.3919	−	39.6389i	−0.662798	−	1.42849i
$771$	14.8142	+	14.8142i	0.533522	+	0.533522i
$772$	−1.13118	+	7.95272i	−0.0407120	+	0.286225i
$773$	−44.8816	+	25.9124i	−1.61428	+	0.932004i	−0.625915	+	0.779891i	$0.715274\pi$
$773$	−44.8816	+	25.9124i	−1.61428	+	0.932004i	−0.988363	+	0.152113i	$0.951392\pi$
$774$	7.06244	−	14.1356i	0.253854	−	0.508094i
$775$	−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
$778$	−3.77413	+	18.4718i	−0.135309	+	0.662245i
$779$	−15.4856	+	4.14937i	−0.554831	+	0.148666i
$780$	1.64505	−	0.730784i	0.0589023	−	0.0261663i
$781$	−7.60630	+	28.3871i	−0.272175	+	1.01577i
$782$	34.4135	−	2.07609i	1.23062	−	0.0742407i
$783$	5.31227	−	5.31227i	0.189845	−	0.189845i
$784$	−10.7561	−	25.8516i	−0.384145	−	0.923273i
$785$	0.819023	+	2.67096i	0.0292322	+	0.0953306i
$786$	−11.0746	+	12.4965i	−0.395016	+	0.445737i
$787$	−11.9555	+	6.90250i	−0.426167	+	0.246048i	−0.697712	−	0.716378i	$-0.745799\pi$
$787$	−11.9555	+	6.90250i	−0.426167	+	0.246048i	0.271545	+	0.962426i	$0.412465\pi$
$788$	−0.548449	−	4.52904i	−0.0195377	−	0.161340i
$789$	5.29931	+	19.7773i	0.188660	+	0.704091i
$790$	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
$793$	−0.00321272	−	0.0119900i	−0.000114087	−	0.000425778i
$794$	35.3736	+	17.6734i	1.25536	+	0.627205i
$795$	−16.2495	−	15.1276i	−0.576309	−	0.536522i
$796$	0.594674	−	0.446570i	0.0210777	−	0.0158283i
$797$			18.6758i			0.661532i	0.943713	+	0.330766i	$0.107307\pi$
$797$			18.6758i			0.661532i	−0.943713	+	0.330766i	$0.892693\pi$
$798$	9.58852	−	1.32080i	0.339430	−	0.0467557i
$799$			18.8190i			0.665769i
$800$	−27.9631	−	4.25051i	−0.988644	−	0.150278i
$801$	−2.53112	+	1.46134i	−0.0894327	+	0.0516340i
$802$	11.5333	−	23.0840i	0.407253	−	0.815125i
$803$	−34.6328	+	59.9858i	−1.22217	+	2.11685i
$804$	−7.72765	+	18.1213i	−0.272533	+	0.639090i
$805$	32.8630	−	41.2232i	1.15827	−	1.45293i
$806$	2.09016	−	1.38095i	0.0736229	−	0.0486419i
$807$	−4.48135	+	1.20077i	−0.157751	+	0.0422692i
$808$	3.04582	−	37.5039i	0.107152	−	1.31938i
$809$	−15.9456	−	27.6186i	−0.560617	−	0.971018i	−0.997443	−	0.0714713i	$-0.977231\pi$
$809$	−15.9456	−	27.6186i	−0.560617	−	0.971018i	0.436825	−	0.899546i	$-0.356103\pi$
$810$	−5.10373	+	1.90820i	−0.179327	+	0.0670474i
$811$	10.8894	+	10.8894i	0.382379	+	0.382379i	0.871959	−	0.489580i	$-0.162850\pi$
$811$	10.8894	+	10.8894i	0.382379	+	0.382379i	−0.489580	+	0.871959i	$0.662850\pi$
$812$	−1.42794	−	7.14916i	−0.0501109	−	0.250886i
$813$		−	27.7907i		−	0.974662i
$814$	−48.0276	−	42.5625i	−1.68337	−	1.49182i
$815$	28.6886	−	30.8161i	1.00492	−	1.07944i
$816$	−11.3993	+	6.26927i	−0.399057	+	0.219468i
$817$	14.8015	−	3.96604i	0.517837	−	0.138754i
$818$	−2.88071	+	1.90325i	−0.100722	+	0.0665457i
$819$	0.471840	+	1.34056i	0.0164874	+	0.0468429i
$820$	3.47159	−	32.7675i	0.121233	−	1.14429i
$821$	−13.6641	−	50.9951i	−0.476881	−	1.77974i	−0.614129	−	0.789206i	$-0.710493\pi$
$821$	−13.6641	−	50.9951i	−0.476881	−	1.77974i	0.137248	−	0.990537i	$-0.456174\pi$
$822$	−11.5565	+	3.85606i	−0.403079	+	0.134496i
$823$	28.7366	+	7.69994i	1.00169	+	0.268403i	0.722155	−	0.691731i	$-0.243152\pi$
$823$	28.7366	+	7.69994i	1.00169	+	0.268403i	0.279539	+	0.960134i	$0.409818\pi$
$824$	−38.6496	+	18.3166i	−1.34642	+	0.638090i
$825$	−5.87334	+	30.4862i	−0.204483	+	1.06139i
$826$	12.7395	−	9.89713i	0.443265	−	0.344365i
$827$		−	17.4174i		−	0.605664i	−0.953044	−	0.302832i	$-0.902068\pi$
$827$		−	17.4174i		−	0.605664i	0.953044	−	0.302832i	$-0.0979321\pi$
$828$	27.9948	+	3.98192i	0.972886	+	0.138381i
$829$	11.7907	−	44.0036i	0.409509	−	1.52831i	−0.386078	−	0.922466i	$-0.626170\pi$
$829$	11.7907	−	44.0036i	0.409509	−	1.52831i	0.795586	−	0.605840i	$-0.207163\pi$
$830$	−9.04415	+	54.0455i	−0.313927	+	1.87595i
$831$	27.1959	+	15.7015i	0.943414	+	0.544680i
$832$	2.53341	−	0.958003i	0.0878301	−	0.0332128i
$833$	−19.0371	−	2.07436i	−0.659597	−	0.0718724i
$834$	20.1100	+	4.10885i	0.696353	+	0.142278i
$835$	13.8045	+	22.0510i	0.477725	+	0.763107i
$836$	22.5638	−	2.73239i	0.780386	−	0.0945017i
$837$	−24.7080	+	14.2652i	−0.854034	+	0.493077i
$838$	27.2218	+	24.1243i	0.940363	+	0.833359i
$839$			46.4476i			1.60355i	0.597626	+	0.801775i	$0.296111\pi$
$839$			46.4476i			1.60355i	−0.597626	+	0.801775i	$0.703889\pi$
$840$	−4.54432	+	19.3677i	−0.156794	+	0.668250i
$841$			27.1018i			0.934545i
$842$	36.0808	−	40.7136i	1.24343	−	1.40308i
$843$	27.2372	−	15.7254i	0.938100	−	0.541612i
$844$	16.3373	+	12.8079i	0.562353	+	0.440867i
$845$	6.45808	−	28.0795i	0.222165	−	0.965964i
$846$	−3.08982	+	15.1226i	−0.106230	+	0.519924i
$847$	−40.6262	+	14.2993i	−1.39593	+	0.491330i
$848$	−23.1251	−	24.1068i	−0.794119	−	0.827829i
$849$	26.5776	+	15.3446i	0.912141	+	0.526625i
$850$	−11.7633	+	15.3566i	−0.403477	+	0.526727i
$851$	20.0383	−	74.7840i	0.686905	−	2.56356i
$852$	10.6985	−	8.03406i	0.366526	−	0.275242i
$853$		−	23.5379i		−	0.805923i	−0.915217	−	0.402962i	$-0.867981\pi$
$853$		−	23.5379i		−	0.805923i	0.915217	−	0.402962i	$-0.132019\pi$
$854$	0.127053	+	0.0517383i	0.00434768	+	0.00177045i
$855$	6.81875	+	3.61833i	0.233196	+	0.123744i
$856$	−8.76087	−	3.12701i	−0.299440	−	0.106879i
$857$	32.9015	+	8.81593i	1.12389	+	0.301146i	0.772458	−	0.635066i	$-0.219027\pi$
$857$	32.9015	+	8.81593i	1.12389	+	0.301146i	0.351435	+	0.936212i	$0.385694\pi$
$858$	−0.941012	−	2.82018i	−0.0321256	−	0.0962794i
$859$	11.2659	+	42.0449i	0.384388	+	1.43455i	0.839130	+	0.543931i	$0.183065\pi$
$859$	11.2659	+	42.0449i	0.384388	+	1.43455i	−0.454742	+	0.890623i	$0.650269\pi$
$860$	−3.31821	+	31.3198i	−0.113150	+	1.06800i
$861$	−22.7798	−	4.26696i	−0.776334	−	0.145418i
$862$	−10.6928	−	16.1843i	−0.364199	−	0.551241i
$863$	−35.1188	+	9.41004i	−1.19546	+	0.320322i	−0.801040	−	0.598610i	$-0.795720\pi$
$863$	−35.1188	+	9.41004i	−1.19546	+	0.320322i	−0.394416	+	0.918932i	$0.629053\pi$
$864$	−29.4567	+	9.15315i	−1.00214	+	0.311397i
$865$	29.1771	+	27.1628i	0.992051	+	0.923561i
$866$	−18.2461	+	20.5889i	−0.620026	+	0.699638i
$867$		−	11.3134i		−	0.384222i
$868$	−1.78889	+	27.6282i	−0.0607189	+	0.937763i
$869$	−38.3063	−	38.3063i	−1.29945	−	1.29945i
$870$	−2.14800	+	4.71335i	−0.0728241	+	0.159798i
$871$	−1.40253	−	2.42925i	−0.0475229	−	0.0823121i
$872$	−10.8749	−	0.883186i	−0.368270	−	0.0299085i
$873$	17.6814	−	4.73770i	0.598423	−	0.160347i
$874$	15.1157	+	22.8786i	0.511295	+	0.773880i
$875$	5.40765	+	29.0819i	0.182812	+	0.983148i
$876$	29.2570	−	11.7640i	0.988504	−	0.397470i
$877$	24.9327	−	43.1848i	0.841919	−	1.45825i	−0.0463511	−	0.998925i	$-0.514759\pi$
$877$	24.9327	−	43.1848i	0.841919	−	1.45825i	0.888270	−	0.459321i	$-0.151907\pi$
$878$	−23.0366	−	11.5096i	−0.777448	−	0.388429i
$879$	−0.193704	+	0.111835i	−0.00653348	+	0.00377211i
$880$	−11.4145	+	45.2990i	−0.384782	+	1.52703i
$881$			15.9710i			0.538076i	0.963129	+	0.269038i	$0.0867058\pi$
$881$			15.9710i			0.538076i	−0.963129	+	0.269038i	$0.913294\pi$
$882$	−14.9572	−	4.79254i	−0.503636	−	0.161373i
$883$			44.1081i			1.48435i	0.670204	+	0.742177i	$0.266207\pi$
$883$			44.1081i			1.48435i	−0.670204	+	0.742177i	$0.733793\pi$
$884$	0.260855	−	1.83394i	0.00877351	−	0.0616819i
$885$	−11.4545	+	0.409534i	−0.385038	+	0.0137663i
$886$	10.8171	−	21.6506i	0.363406	−	0.727365i
$887$	2.45408	+	9.15875i	0.0824000	+	0.307521i	0.994809	−	0.101758i	$-0.0324469\pi$
$887$	2.45408	+	9.15875i	0.0824000	+	0.307521i	−0.912409	+	0.409279i	$0.865780\pi$
$888$	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
$891$	2.32920	+	8.69270i	0.0780312	+	0.291216i
$892$	28.3495	−	36.1615i	0.949212	−	1.21078i
$893$	−12.9627	+	7.48399i	−0.433779	+	0.250442i
$894$	−16.9371	−	15.0098i	−0.566460	−	0.502002i
$895$	−9.52629	+	17.9523i	−0.318429	+	0.600081i
$896$	−8.47293	+	28.7090i	−0.283061	+	0.959102i
$897$	2.53627	−	2.53627i	0.0846835	−	0.0846835i
$898$	−1.15241	−	19.1025i	−0.0384564	−	0.637459i
$899$	−1.86573	+	6.96301i	−0.0622257	+	0.232229i
$900$	−11.9740	+	10.4089i	−0.399135	+	0.346962i
$901$	−22.0680	+	5.91311i	−0.735193	+	0.196994i
$902$	−53.3210	−	10.8945i	−1.77539	−	0.362746i
$903$	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
$906$	−8.03831	−	4.01610i	−0.267055	−	0.133426i
$907$	26.6632	−	15.3940i	0.885337	−	0.511150i	0.0129227	−	0.999916i	$-0.495886\pi$
$907$	26.6632	−	15.3940i	0.885337	−	0.511150i	0.872414	+	0.488767i	$0.162553\pi$
$908$	4.50035	−	3.37953i	0.149349	−	0.112154i
$909$	−14.9247	−	14.9247i	−0.495020	−	0.495020i
$910$	−1.81662	−	2.17337i	−0.0602203	−	0.0720466i
$911$	−27.3255			−0.905336			−0.452668	−	0.891679i	$-0.649528\pi$
$911$	−27.3255			−0.905336			−0.452668	+	0.891679i	$0.649528\pi$
$912$	−8.85163	−	5.35876i	−0.293107	−	0.177446i
$913$	87.4202	+	23.4242i	2.89319	+	0.775227i
$914$	−19.7050	+	6.57496i	−0.651782	+	0.217480i
$915$	−0.0517187	−	0.0826142i	−0.00170977	−	0.00273114i
$916$	−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	−0.539838	−	0.841769i	$-0.681514\pi$
$919$	13.9169	−	24.1047i	0.459075	−	0.795141i	0.998912	+	0.0466285i	$0.0148477\pi$
$920$	−55.0437	+	12.1068i	−1.81474	+	0.399150i
$921$	−4.97308	+	2.87121i	−0.163869	+	0.0946095i
$922$	4.63462	−	5.22971i	0.152633	−	0.172231i
$923$			1.90504i			0.0627050i
$924$	31.1215	+	10.5369i	1.02382	+	0.346638i
$925$	24.3517	+	35.9737i	0.800679	+	1.18281i
$926$	4.51070	+	3.99742i	0.148231	+	0.131363i
$927$	−6.20945	+	23.1740i	−0.203945	+	0.761133i
$928$	−3.62747	+	6.89810i	−0.119078	+	0.226441i
$929$	17.1128	−	29.6403i	0.561453	−	0.972466i	−0.435917	−	0.899987i	$-0.643576\pi$
$929$	17.1128	−	29.6403i	0.561453	−	0.972466i	0.997370	−	0.0724786i	$-0.0230909\pi$
$930$	12.5121	−	15.1784i	0.410287	−	0.497718i
$931$	−6.14189	−	13.9378i	−0.201292	−	0.456794i
$932$	−3.04453	−	7.57171i	−0.0997268	−	0.248020i
$933$	5.63198	−	9.75487i	0.184383	−	0.319360i
$934$	27.6219	+	13.8005i	0.903815	+	0.451565i
$935$	23.3844	+	21.7700i	0.764752	+	0.711955i
$936$	0.510724	−	1.43088i	0.0166935	−	0.0467698i
$937$	39.3051	−	39.3051i	1.28404	−	1.28404i	0.345692	−	0.938348i	$-0.387644\pi$
$937$	39.3051	−	39.3051i	1.28404	−	1.28404i	0.938348	−	0.345692i	$-0.112356\pi$
$938$	30.7590	+	3.86230i	1.00432	+	0.126109i
$939$	−25.7731	−	25.7731i	−0.841072	−	0.841072i
$940$	−4.78729	−	30.3894i	−0.156144	−	0.991194i
$941$	−25.4702	−	6.82472i	−0.830305	−	0.222480i	−0.181458	−	0.983399i	$-0.558082\pi$
$941$	−25.4702	−	6.82472i	−0.830305	−	0.222480i	−0.648847	+	0.760919i	$0.724748\pi$
$942$	−1.87914	−	0.938856i	−0.0612256	−	0.0305896i
$943$	−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
$947$	18.6589	−	32.3182i	0.606334	−	1.05020i	−0.385505	−	0.922706i	$-0.625973\pi$
$947$	18.6589	−	32.3182i	0.606334	−	1.05020i	0.991839	−	0.127496i	$-0.0406940\pi$
$948$	2.96489	+	24.4838i	0.0962953	+	0.795198i
$949$	−1.16209	+	4.33698i	−0.0377231	+	0.140784i
$950$	−15.2558	−	1.99556i	−0.494962	−	0.0647446i
$951$	−0.172928			−0.00560756
$952$	14.4120	+	14.5395i	0.467096	+	0.471228i
$953$	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	$0.0974106\pi$
$954$	−18.7043	+	1.12838i	−0.605573	+	0.0365328i
$955$	10.1986	+	9.49447i	0.330018	+	0.307234i
$956$	3.59450	+	29.6831i	0.116255	+	0.960019i
$957$	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
$962$	−3.72128	−	1.85923i	−0.119979	−	0.0599439i
$963$	−4.51889	+	2.60898i	−0.145619	+	0.0840733i
$964$	−1.15266	+	0.865586i	−0.0371246	+	0.0278786i
$965$	−7.93317	−	4.20968i	−0.255378	−	0.135515i
$966$	5.40928	+	39.2695i	0.174041	+	1.26347i
$967$	−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	$0.880073\pi$
$968$	43.3634	+	15.4777i	1.39375	+	0.497472i
$969$	−6.12867	+	3.53839i	−0.196881	+	0.113669i
$970$	−29.7028	+	21.1868i	−0.953699	+	0.680266i
$971$	−26.5598	+	7.11668i	−0.852344	+	0.228385i	−0.658438	−	0.752635i	$-0.728782\pi$
$971$	−26.5598	+	7.11668i	−0.852344	+	0.228385i	−0.193906	+	0.981020i	$0.562116\pi$
$972$	−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
$975$	0.143725	+	2.00740i	0.00460290	+	0.0642882i
$976$	−0.0706729	−	0.128504i	−0.00226218	−	0.00411331i
$977$	28.9478	+	7.75655i	0.926123	+	0.248154i	0.690201	−	0.723618i	$-0.257522\pi$
$977$	28.9478	+	7.75655i	0.926123	+	0.248154i	0.235922	+	0.971772i	$0.424189\pi$
$978$	1.90637	+	31.6003i	0.0609591	+	1.01047i
$979$	−6.80327	−	6.80327i	−0.217434	−	0.217434i
$980$	31.2693	−	1.49304i	0.998862	−	0.0476933i
$981$	−4.32766	+	4.32766i	−0.138172	+	0.138172i
$982$	−27.5650	+	31.1044i	−0.879634	+	0.992580i
$983$	5.22937	−	19.5163i	0.166791	−	0.622473i	−0.831014	−	0.556252i	$-0.812239\pi$
$983$	5.22937	−	19.5163i	0.166791	−	0.622473i	0.997805	−	0.0662210i	$-0.0210942\pi$
$984$	16.0438	+	18.8800i	0.511457	+	0.601874i
$985$	4.97084	+	1.14326i	0.158384	+	0.0364272i
$986$	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
$989$	16.2428	+	60.6189i	0.516490	+	1.92757i
$990$	15.2169	+	21.3333i	0.483624	+	0.678017i
$991$	15.1789	+	26.2906i	0.482173	+	0.835148i	0.999791	−	0.0204637i	$-0.00651426\pi$
$991$	15.1789	+	26.2906i	0.482173	+	0.835148i	−0.517617	+	0.855612i	$0.673181\pi$
$992$	20.0865	−	21.7383i	0.637747	−	0.690193i
$993$	5.42006	−	5.42006i	0.172001	−	0.172001i
$994$	−16.7795	−	12.7165i	−0.532214	−	0.403343i
$995$	0.243757	+	0.794928i	0.00772761	+	0.0252009i
$996$	−24.7415	−	32.9470i	−0.783964	−	1.04397i
$997$	27.1107	+	46.9572i	0.858606	+	1.48715i	0.873259	+	0.487256i	$0.162002\pi$
$997$	27.1107	+	46.9572i	0.858606	+	1.48715i	−0.0146537	+	0.999893i	$0.504665\pi$
$998$	−1.29748	−	3.88850i	−0.0410710	−	0.123088i
$999$	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.173.89	yes	360
5.2	odd	4		560.2.cz.c.397.46	yes	360
7.3	odd	6	inner	560.2.ch.c.493.32	yes	360
16.5	even	4		560.2.cz.c.453.15	yes	360
35.17	even	12		560.2.cz.c.157.15	yes	360
80.37	odd	4	inner	560.2.ch.c.117.32	✓	360
112.101	odd	12		560.2.cz.c.213.46	yes	360
560.437	even	12	inner	560.2.ch.c.437.89	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.32	✓	360	80.37	odd	4	inner
560.2.ch.c.173.89	yes	360	1.1	even	1	trivial
560.2.ch.c.437.89	yes	360	560.437	even	12	inner
560.2.ch.c.493.32	yes	360	7.3	odd	6	inner
560.2.cz.c.157.15	yes	360	35.17	even	12
560.2.cz.c.213.46	yes	360	112.101	odd	12
560.2.cz.c.397.46	yes	360	5.2	odd	4
560.2.cz.c.453.15	yes	360	16.5	even	4

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+(1.41165 - 0.0851614i) q^{2} +(-0.594438 - 1.02960i) q^{3} +(1.98550 - 0.240436i) q^{4} +(-0.501194 + 2.17918i) q^{5} +(-0.926818 - 1.40280i) q^{6} +(-1.72211 + 2.00856i) q^{7} +(2.78234 - 0.508498i) q^{8} +(0.793287 - 1.37401i) q^{9} +(-0.521928 + 3.11891i) q^{10} +(5.04493 + 1.35178i) q^{11} +(-1.42781 - 1.90133i) q^{12} +0.338561 q^{13} +(-2.25996 + 2.98204i) q^{14} +(2.54160 - 0.779356i) q^{15} +(3.88438 - 0.954768i) q^{16} +(0.708048 - 2.64247i) q^{17} +(1.00283 - 2.00718i) q^{18} +(2.10173 - 0.563156i) q^{19} +(-0.471167 + 4.44725i) q^{20} +(3.09170 + 0.579117i) q^{21} +(7.23678 + 1.47861i) q^{22} +(2.30639 + 8.60756i) q^{23} +(-2.17748 - 2.56242i) q^{24} +(-4.49761 - 2.18438i) q^{25} +(0.477929 - 0.0288323i) q^{26} -5.45287 q^{27} +(-2.93632 + 4.40205i) q^{28} +(-0.974217 + 0.974217i) q^{29} +(3.52147 - 1.31662i) q^{30} +(4.53120 - 2.61609i) q^{31} +(5.40207 - 1.67859i) q^{32} +(-1.60710 - 5.99779i) q^{33} +(0.774477 - 3.79053i) q^{34} +(-3.51390 - 4.75947i) q^{35} +(1.24471 - 2.91883i) q^{36} +(-7.52418 - 4.34409i) q^{37} +(2.91894 - 0.973964i) q^{38} +(-0.201254 - 0.348581i) q^{39} +(-0.286388 + 6.31807i) q^{40} -7.36805 q^{41} +(4.41371 + 0.554215i) q^{42} +7.04252 q^{43} +(10.3417 + 1.47098i) q^{44} +(2.59663 + 2.41736i) q^{45} +(3.98884 + 11.9544i) q^{46} +(-6.64469 + 1.78044i) q^{47} +(-3.29205 - 3.43180i) q^{48} +(-1.06865 - 6.91795i) q^{49} +(-6.53506 - 2.70055i) q^{50} +(-3.14157 + 0.841781i) q^{51} +(0.672212 - 0.0814022i) q^{52} +(-4.17565 - 7.23243i) q^{53} +(-7.69752 + 0.464374i) q^{54} +(-5.47426 + 10.3163i) q^{55} +(-3.77016 + 6.46420i) q^{56} +(-1.82917 - 1.82917i) q^{57} +(-1.29228 + 1.45822i) q^{58} +(-4.16461 - 1.11590i) q^{59} +(4.85895 - 2.15850i) q^{60} +(-0.00948932 - 0.0354146i) q^{61} +(6.17366 - 4.07888i) q^{62} +(1.39366 + 3.95958i) q^{63} +(7.48286 - 2.82963i) q^{64} +(-0.169685 + 0.737784i) q^{65} +(-2.77944 - 8.32990i) q^{66} +(-4.14262 - 7.17522i) q^{67} +(0.770481 - 5.41685i) q^{68} +(7.49131 - 7.49131i) q^{69} +(-5.36570 - 6.41944i) q^{70} +5.62686i q^{71} +(1.50851 - 4.22636i) q^{72} +(-3.43244 + 12.8100i) q^{73} +(-10.9914 - 5.49155i) q^{74} +(0.424519 + 5.92920i) 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} +(0.133776 + 8.94327i) q^{80} +(0.861529 + 1.49221i) q^{81} +(-10.4011 + 0.627474i) q^{82} +17.3283 q^{83} +(6.27779 + 0.406478i) q^{84} +(5.40354 + 2.86735i) q^{85} +(9.94155 - 0.599751i) q^{86} +(1.58216 + 0.423939i) q^{87} +(14.7241 + 1.19579i) q^{88} +(-1.59534 - 0.921068i) q^{89} +(3.87139 + 3.19133i) q^{90} +(-0.583041 + 0.680021i) q^{91} +(6.64889 + 16.5357i) q^{92} +(-5.38703 - 3.11020i) q^{93} +(-9.22833 + 3.07922i) q^{94} +(0.173842 + 4.86228i) q^{95} +(-4.93947 - 4.56413i) q^{96} +(8.15823 + 8.15823i) q^{97} +(-2.09770 - 9.67469i) 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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