LMFDB - Embedded newform 560.2.t.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40839 + 0.128258i) q^{2} -0.748637i q^{3} +(1.96710 - 0.361275i) q^{4} +(0.813660 + 2.08278i) q^{5} +(0.0960190 + 1.05437i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.72410 + 0.761111i) q^{8} +2.43954 q^{9} +O(q^{10})$	\(q+(-1.40839 + 0.128258i) q^{2} -0.748637i q^{3} +(1.96710 - 0.361275i) q^{4} +(0.813660 + 2.08278i) q^{5} +(0.0960190 + 1.05437i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.72410 + 0.761111i) q^{8} +2.43954 q^{9} +(-1.41308 - 2.82899i) q^{10} +(2.70593 - 2.70593i) q^{11} +(-0.270463 - 1.47264i) q^{12} +0.698675 q^{13} +(0.905187 - 1.08657i) q^{14} +(1.55924 - 0.609136i) q^{15} +(3.73896 - 1.42133i) q^{16} +(-2.35913 + 2.35913i) q^{17} +(-3.43582 + 0.312892i) q^{18} +(-3.87334 + 3.87334i) q^{19} +(2.35300 + 3.80307i) q^{20} +(0.529366 + 0.529366i) q^{21} +(-3.46393 + 4.15805i) q^{22} +(3.18870 + 3.18870i) q^{23} +(0.569796 + 2.03936i) q^{24} +(-3.67592 + 3.38934i) q^{25} +(-0.984004 + 0.0896109i) q^{26} -4.07224i q^{27} +(-1.13549 + 1.64641i) q^{28} +(6.19414 + 6.19414i) q^{29} +(-2.11789 + 1.05788i) q^{30} -9.99650i q^{31} +(-5.08360 + 2.48133i) q^{32} +(-2.02576 - 2.02576i) q^{33} +(3.01998 - 3.62514i) q^{34} +(-2.04809 - 0.897401i) q^{35} +(4.79882 - 0.881345i) q^{36} +6.25950 q^{37} +(4.95837 - 5.95195i) q^{38} -0.523054i q^{39} +(-3.80171 - 5.05440i) q^{40} +1.60083i q^{41} +(-0.813447 - 0.677656i) q^{42} -0.343061 q^{43} +(4.34525 - 6.30042i) q^{44} +(1.98496 + 5.08102i) q^{45} +(-4.89990 - 4.08195i) q^{46} +(5.90808 + 5.90808i) q^{47} +(-1.06406 - 2.79912i) q^{48} -1.00000i q^{49} +(4.74239 - 5.24497i) q^{50} +(1.76613 + 1.76613i) q^{51} +(1.37436 - 0.252413i) q^{52} +3.36204i q^{53} +(0.522299 + 5.73529i) q^{54} +(7.83755 + 3.43414i) q^{55} +(1.38804 - 2.46441i) q^{56} +(2.89973 + 2.89973i) q^{57} +(-9.51819 - 7.92929i) q^{58} +(4.29827 + 4.29827i) q^{59} +(2.84712 - 1.76155i) q^{60} +(-1.44702 + 1.44702i) q^{61} +(1.28214 + 14.0789i) q^{62} +(-1.72502 + 1.72502i) q^{63} +(6.84142 - 4.14668i) q^{64} +(0.568484 + 1.45518i) q^{65} +(3.11287 + 2.59323i) q^{66} -1.61316 q^{67} +(-3.78835 + 5.49293i) q^{68} +(2.38718 - 2.38718i) q^{69} +(2.99960 + 1.00120i) q^{70} +14.8236 q^{71} +(-6.64555 + 1.85676i) q^{72} +(4.93985 - 4.93985i) q^{73} +(-8.81579 + 0.802833i) q^{74} +(2.53739 + 2.75193i) q^{75} +(-6.21991 + 9.01859i) q^{76} +3.82676i q^{77} +(0.0670860 + 0.736661i) q^{78} -7.67064 q^{79} +(6.00255 + 6.63095i) q^{80} +4.27000 q^{81} +(-0.205320 - 2.25458i) q^{82} -6.65978i q^{83} +(1.23256 + 0.850069i) q^{84} +(-6.83306 - 2.99401i) q^{85} +(0.483162 - 0.0440005i) q^{86} +(4.63716 - 4.63716i) q^{87} +(-5.31171 + 9.43073i) q^{88} -16.9082 q^{89} +(-3.44727 - 6.90145i) q^{90} +(-0.494038 + 0.494038i) q^{91} +(7.42450 + 5.12050i) q^{92} -7.48375 q^{93} +(-9.07862 - 7.56309i) q^{94} +(-11.2189 - 4.91573i) q^{95} +(1.85761 + 3.80577i) q^{96} +(2.63601 - 2.63601i) q^{97} +(0.128258 + 1.40839i) q^{98} +(6.60123 - 6.60123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.40839	+	0.128258i	−0.995879	+	0.0906924i
$2$	−1.40839	+	0.128258i	−0.995879	+	0.0906924i
$3$		−	0.748637i		−	0.432226i	−0.976368	−	0.216113i	$-0.930662\pi$
$3$		−	0.748637i		−	0.432226i	0.976368	−	0.216113i	$-0.0693379\pi$
$4$	1.96710	−	0.361275i	0.983550	−	0.180637i
$5$	0.813660	+	2.08278i	0.363880	+	0.931446i
$5$	0.813660	+	2.08278i	0.363880	+	0.931446i
$6$	0.0960190	+	1.05437i	0.0391996	+	0.430444i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−2.72410	+	0.761111i	−0.963114	+	0.269093i
$9$	2.43954			0.813181
$10$	−1.41308	−	2.82899i	−0.446855	−	0.894606i
$11$	2.70593	−	2.70593i	0.815869	−	0.815869i	−0.169638	−	0.985506i	$-0.554260\pi$
$11$	2.70593	−	2.70593i	0.815869	−	0.815869i	0.985506	+	0.169638i	$0.0542598\pi$
$12$	−0.270463	−	1.47264i	−0.0780761	−	0.425115i
$13$	0.698675			0.193778			0.0968888	−	0.995295i	$-0.469111\pi$
$13$	0.698675			0.193778			0.0968888	+	0.995295i	$0.469111\pi$
$14$	0.905187	−	1.08657i	0.241921	−	0.290398i
$15$	1.55924	−	0.609136i	0.402595	−	0.157278i
$16$	3.73896	−	1.42133i	0.934740	−	0.355331i
$17$	−2.35913	+	2.35913i	−0.572173	+	0.572173i	−0.932735	−	0.360562i	$-0.882585\pi$
$17$	−2.35913	+	2.35913i	−0.572173	+	0.572173i	0.360562	+	0.932735i	$0.382585\pi$
$18$	−3.43582	+	0.312892i	−0.809830	+	0.0737493i
$19$	−3.87334	+	3.87334i	−0.888606	+	0.888606i	−0.994389	−	0.105783i	$-0.966265\pi$
$19$	−3.87334	+	3.87334i	−0.888606	+	0.888606i	0.105783	+	0.994389i	$0.466265\pi$
$20$	2.35300	+	3.80307i	0.526148	+	0.850393i
$21$	0.529366	+	0.529366i	0.115517	+	0.115517i
$22$	−3.46393	+	4.15805i	−0.738513	+	0.886500i
$23$	3.18870	+	3.18870i	0.664891	+	0.664891i	0.956529	−	0.291638i	$-0.0942003\pi$
$23$	3.18870	+	3.18870i	0.664891	+	0.664891i	−0.291638	+	0.956529i	$0.594200\pi$
$24$	0.569796	+	2.03936i	0.116309	+	0.416283i
$25$	−3.67592	+	3.38934i	−0.735183	+	0.677869i
$26$	−0.984004	+	0.0896109i	−0.192979	+	0.0175742i
$27$		−	4.07224i		−	0.783703i
$28$	−1.13549	+	1.64641i	−0.214587	+	0.311142i
$29$	6.19414	+	6.19414i	1.15022	+	1.15022i	0.986508	+	0.163716i	$0.0523480\pi$
$29$	6.19414	+	6.19414i	1.15022	+	1.15022i	0.163716	+	0.986508i	$0.447652\pi$
$30$	−2.11789	+	1.05788i	−0.386672	+	0.193142i
$31$		−	9.99650i		−	1.79542i	−0.440582	−	0.897712i	$-0.645228\pi$
$31$		−	9.99650i		−	1.79542i	0.440582	−	0.897712i	$-0.354772\pi$
$32$	−5.08360	+	2.48133i	−0.898662	+	0.438641i
$33$	−2.02576	−	2.02576i	−0.352639	−	0.352639i
$34$	3.01998	−	3.62514i	0.517923	−	0.621706i
$35$	−2.04809	−	0.897401i	−0.346190	−	0.151688i
$36$	4.79882	−	0.881345i	0.799804	−	0.146891i
$37$	6.25950			1.02906			0.514528	−	0.857474i	$-0.327967\pi$
$37$	6.25950			1.02906			0.514528	+	0.857474i	$0.327967\pi$
$38$	4.95837	−	5.95195i	0.804354	−	0.965534i
$39$		−	0.523054i		−	0.0837556i
$40$	−3.80171	−	5.05440i	−0.601104	−	0.799171i
$41$			1.60083i			0.250008i	0.992156	+	0.125004i	$0.0398943\pi$
$41$			1.60083i			0.250008i	−0.992156	+	0.125004i	$0.960106\pi$
$42$	−0.813447	−	0.677656i	−0.125518	−	0.104565i
$43$	−0.343061			−0.0523163			−0.0261582	−	0.999658i	$-0.508327\pi$
$43$	−0.343061			−0.0523163			−0.0261582	+	0.999658i	$0.508327\pi$
$44$	4.34525	−	6.30042i	0.655071	−	0.949824i
$45$	1.98496	+	5.08102i	0.295900	+	0.757434i
$46$	−4.89990	−	4.08195i	−0.722451	−	0.601850i
$47$	5.90808	+	5.90808i	0.861782	+	0.861782i	0.991545	−	0.129763i	$-0.0414216\pi$
$47$	5.90808	+	5.90808i	0.861782	+	0.861782i	−0.129763	+	0.991545i	$0.541422\pi$
$48$	−1.06406	−	2.79912i	−0.153583	−	0.404019i
$49$		−	1.00000i		−	0.142857i
$50$	4.74239	−	5.24497i	0.670676	−	0.741751i
$51$	1.76613	+	1.76613i	0.247308	+	0.247308i
$52$	1.37436	−	0.252413i	0.190590	−	0.0350035i
$53$			3.36204i			0.461811i	0.972976	+	0.230906i	$0.0741689\pi$
$53$			3.36204i			0.461811i	−0.972976	+	0.230906i	$0.925831\pi$
$54$	0.522299	+	5.73529i	0.0710759	+	0.780474i
$55$	7.83755	+	3.43414i	1.05682	+	0.463060i
$56$	1.38804	−	2.46441i	0.185485	−	0.329321i
$57$	2.89973	+	2.89973i	0.384078	+	0.384078i
$58$	−9.51819	−	7.92929i	−1.24980	−	1.04117i
$59$	4.29827	+	4.29827i	0.559587	+	0.559587i	0.929190	−	0.369603i	$-0.120506\pi$
$59$	4.29827	+	4.29827i	0.559587	+	0.559587i	−0.369603	+	0.929190i	$0.620506\pi$
$60$	2.84712	−	1.76155i	0.367562	−	0.227415i
$61$	−1.44702	+	1.44702i	−0.185272	+	0.185272i	−0.793649	−	0.608376i	$-0.791821\pi$
$61$	−1.44702	+	1.44702i	−0.185272	+	0.185272i	0.608376	+	0.793649i	$0.291821\pi$
$62$	1.28214	+	14.0789i	0.162831	+	1.78803i
$63$	−1.72502	+	1.72502i	−0.217332	+	0.217332i
$64$	6.84142	−	4.14668i	0.855178	−	0.518335i
$65$	0.568484	+	1.45518i	0.0705117	+	0.180493i
$66$	3.11287	+	2.59323i	0.383168	+	0.319204i
$67$	−1.61316			−0.197078			−0.0985392	−	0.995133i	$-0.531417\pi$
$67$	−1.61316			−0.197078			−0.0985392	+	0.995133i	$0.531417\pi$
$68$	−3.78835	+	5.49293i	−0.459405	+	0.666116i
$69$	2.38718	−	2.38718i	0.287383	−	0.287383i
$70$	2.99960	+	1.00120i	0.358521	+	0.119667i
$71$	14.8236			1.75924			0.879620	−	0.475678i	$-0.157797\pi$
$71$	14.8236			1.75924			0.879620	+	0.475678i	$0.157797\pi$
$72$	−6.64555	+	1.85676i	−0.783186	+	0.218822i
$73$	4.93985	−	4.93985i	0.578165	−	0.578165i	−0.356232	−	0.934397i	$-0.615939\pi$
$73$	4.93985	−	4.93985i	0.578165	−	0.578165i	0.934397	+	0.356232i	$0.115939\pi$
$74$	−8.81579	+	0.802833i	−1.02481	+	0.0933275i
$75$	2.53739	+	2.75193i	0.292992	+	0.317765i
$76$	−6.21991	+	9.01859i	−0.713473	+	1.03450i
$77$			3.82676i			0.436100i
$78$	0.0670860	+	0.736661i	0.00759600	+	0.0834105i
$79$	−7.67064			−0.863014			−0.431507	−	0.902110i	$-0.642018\pi$
$79$	−7.67064			−0.863014			−0.431507	+	0.902110i	$0.642018\pi$
$80$	6.00255	+	6.63095i	0.671105	+	0.741362i
$81$	4.27000			0.474444
$82$	−0.205320	−	2.25458i	−0.0226738	−	0.248977i
$83$		−	6.65978i		−	0.731006i	−0.930810	−	0.365503i	$-0.880897\pi$
$83$		−	6.65978i		−	0.731006i	0.930810	−	0.365503i	$-0.119103\pi$
$84$	1.23256	+	0.850069i	0.134484	+	0.0927502i
$85$	−6.83306	−	2.99401i	−0.741150	−	0.324746i
$86$	0.483162	−	0.0440005i	0.0521007	−	0.00474469i
$87$	4.63716	−	4.63716i	0.497156	−	0.497156i
$88$	−5.31171	+	9.43073i	−0.566230	+	1.00532i
$89$	−16.9082			−1.79227			−0.896133	−	0.443786i	$-0.853635\pi$
$89$	−16.9082			−1.79227			−0.896133	+	0.443786i	$0.853635\pi$
$90$	−3.44727	−	6.90145i	−0.363374	−	0.727477i
$91$	−0.494038	+	0.494038i	−0.0517892	+	0.0517892i
$92$	7.42450	+	5.12050i	0.774057	+	0.533849i
$93$	−7.48375			−0.776029
$94$	−9.07862	−	7.56309i	−0.936388	−	0.780074i
$95$	−11.2189	−	4.91573i	−1.15103	−	0.504343i
$96$	1.85761	+	3.80577i	0.189592	+	0.388425i
$97$	2.63601	−	2.63601i	0.267646	−	0.267646i	−0.560505	−	0.828151i	$-0.689393\pi$
$97$	2.63601	−	2.63601i	0.267646	−	0.267646i	0.828151	+	0.560505i	$0.189393\pi$
$98$	0.128258	+	1.40839i	0.0129561	+	0.142268i
$99$	6.60123	−	6.60123i	0.663449	−	0.663449i
$100$	−6.00641	+	7.99519i	−0.600641	+	0.799519i
$101$	6.12623	+	6.12623i	0.609582	+	0.609582i	0.942837	−	0.333255i	$-0.108147\pi$
$101$	6.12623	+	6.12623i	0.609582	+	0.609582i	−0.333255	+	0.942837i	$0.608147\pi$
$102$	−2.71391	−	2.26087i	−0.268717	−	0.223860i
$103$	−12.0712	−	12.0712i	−1.18941	−	1.18941i	−0.977230	−	0.212183i	$-0.931943\pi$
$103$	−12.0712	−	12.0712i	−1.18941	−	1.18941i	−0.212183	−	0.977230i	$-0.568057\pi$
$104$	−1.90326	+	0.531769i	−0.186630	+	0.0521443i
$105$	−0.671827	+	1.53328i	−0.0655636	+	0.149632i
$106$	−0.431210	−	4.73504i	−0.0418828	−	0.459908i
$107$			0.617402i			0.0596865i	0.999555	+	0.0298433i	$0.00950081\pi$
$107$			0.617402i			0.0596865i	−0.999555	+	0.0298433i	$0.990499\pi$
$108$	−1.47120	−	8.01051i	−0.141566	−	0.770811i
$109$	3.89734	+	3.89734i	0.373297	+	0.373297i	0.868677	−	0.495379i	$-0.164971\pi$
$109$	3.89734	+	3.89734i	0.373297	+	0.373297i	−0.495379	+	0.868677i	$0.664971\pi$
$110$	−11.4788	−	3.83136i	−1.09446	−	0.365306i
$111$		−	4.68609i		−	0.444784i
$112$	−1.63882	+	3.64887i	−0.154854	+	0.344786i
$113$	−0.492430	−	0.492430i	−0.0463239	−	0.0463239i	0.683565	−	0.729889i	$-0.260428\pi$
$113$	−0.492430	−	0.492430i	−0.0463239	−	0.0463239i	−0.729889	+	0.683565i	$0.760428\pi$
$114$	−4.45585	−	3.71202i	−0.417328	−	0.347663i
$115$	−4.04684	+	9.23588i	−0.377370	+	0.861250i
$116$	14.4223	+	9.94671i	1.33908	+	0.923529i
$117$	1.70445			0.157576
$118$	−6.60491	−	5.50233i	−0.608031	−	0.506531i
$119$		−	3.33631i		−	0.305839i
$120$	−3.78391	+	2.84610i	−0.345422	+	0.259812i
$121$		−	3.64412i		−	0.331284i
$122$	1.85237	−	2.22356i	0.167706	−	0.201312i
$123$	1.19844			0.108060
$124$	−3.61148	−	19.6641i	−0.324321	−	1.76589i
$125$	−10.0502	−	4.89834i	−0.898916	−	0.438121i
$126$	2.20824	−	2.65074i	0.196726	−	0.236146i
$127$	−5.37279	−	5.37279i	−0.476758	−	0.476758i	0.427335	−	0.904093i	$-0.359452\pi$
$127$	−5.37279	−	5.37279i	−0.476758	−	0.476758i	−0.904093	+	0.427335i	$0.859452\pi$
$128$	−9.10351	+	6.71760i	−0.804644	+	0.593757i
$129$			0.256828i			0.0226125i
$130$	−0.987284	−	1.97655i	−0.0865905	−	0.173355i
$131$	−1.95814	−	1.95814i	−0.171083	−	0.171083i	0.616372	−	0.787455i	$-0.288602\pi$
$131$	−1.95814	−	1.95814i	−0.171083	−	0.171083i	−0.787455	+	0.616372i	$0.788602\pi$
$132$	−4.71673	−	3.25301i	−0.410538	−	0.283139i
$133$		−	5.47773i		−	0.474980i
$134$	2.27195	−	0.206901i	0.196266	−	0.0178735i
$135$	8.48157	−	3.31342i	0.729977	−	0.285174i
$136$	4.63094	−	8.22205i	0.397100	−	0.705035i
$137$	−16.4822	−	16.4822i	−1.40817	−	1.40817i	−0.769386	−	0.638784i	$-0.779438\pi$
$137$	−16.4822	−	16.4822i	−1.40817	−	1.40817i	−0.638784	−	0.769386i	$-0.720562\pi$
$138$	−3.05590	+	3.66825i	−0.260135	+	0.312262i
$139$	1.41113	+	1.41113i	0.119690	+	0.119690i	0.764415	−	0.644725i	$-0.223028\pi$
$139$	1.41113	+	1.41113i	0.119690	+	0.119690i	−0.644725	+	0.764415i	$0.723028\pi$
$140$	−4.35300	−	1.02535i	−0.367896	−	0.0866583i
$141$	4.42301	−	4.42301i	0.372484	−	0.372484i
$142$	−20.8774	+	1.90125i	−1.75199	+	0.159550i
$143$	1.89057	−	1.89057i	0.158097	−	0.158097i
$144$	9.12136	−	3.46739i	0.760113	−	0.288949i
$145$	−7.86109	+	17.9409i	−0.652828	+	1.48991i
$146$	−6.32363	+	7.59078i	−0.523347	+	0.628218i
$147$	−0.748637			−0.0617465
$148$	12.3131	−	2.26140i	1.01213	−	0.185886i
$149$	1.47746	−	1.47746i	0.121038	−	0.121038i	−0.643993	−	0.765031i	$-0.722723\pi$
$149$	1.47746	−	1.47746i	0.121038	−	0.121038i	0.765031	+	0.643993i	$0.222723\pi$
$150$	−3.92658	−	3.55033i	−0.320604	−	0.289883i
$151$	−11.1926			−0.910838			−0.455419	−	0.890277i	$-0.650511\pi$
$151$	−11.1926			−0.910838			−0.455419	+	0.890277i	$0.650511\pi$
$152$	7.60332	−	13.4994i	0.616711	−	1.09495i
$153$	−5.75519	+	5.75519i	−0.465280	+	0.465280i
$154$	−0.490815	−	5.38956i	−0.0395510	−	0.434303i
$155$	20.8205	−	8.13375i	1.67234	−	0.653319i
$156$	−0.188966	−	1.02890i	−0.0151294	−	0.0823778i
$157$			15.6763i			1.25111i	0.780181	+	0.625554i	$0.215127\pi$
$157$			15.6763i			1.25111i	−0.780181	+	0.625554i	$0.784873\pi$
$158$	10.8032	−	0.983824i	0.859458	−	0.0782688i
$159$	2.51694			0.199607
$160$	−9.30437	−	8.56905i	−0.735575	−	0.677443i
$161$	−4.50951			−0.355399
$162$	−6.01380	+	0.547663i	−0.472489	+	0.0430285i
$163$			4.83443i			0.378662i	0.981913	+	0.189331i	$0.0606319\pi$
$163$			4.83443i			0.378662i	−0.981913	+	0.189331i	$0.939368\pi$
$164$	0.578339	+	3.14899i	0.0451607	+	0.245895i
$165$	2.57092	−	5.86748i	0.200146	−	0.456783i
$166$	0.854173	+	9.37954i	0.0662967	+	0.727993i
$167$	9.97035	−	9.97035i	0.771529	−	0.771529i	−0.206845	−	0.978374i	$-0.566320\pi$
$167$	9.97035	−	9.97035i	0.771529	−	0.771529i	0.978374	+	0.206845i	$0.0663196\pi$
$168$	−1.84495	−	1.03914i	−0.142341	−	0.0801713i
$169$	−12.5119			−0.962450
$170$	10.0076	+	3.34032i	0.767547	+	0.256191i
$171$	−9.44919	+	9.44919i	−0.722597	+	0.722597i
$172$	−0.674835	+	0.123939i	−0.0514557	+	0.00945028i
$173$	−24.2405			−1.84297			−0.921486	−	0.388413i	$-0.873023\pi$
$173$	−24.2405			−1.84297			−0.921486	+	0.388413i	$0.873023\pi$
$174$	−5.93616	+	7.12567i	−0.450019	+	0.540196i
$175$	0.202638	−	4.99589i	0.0153180	−	0.377654i
$176$	6.27136	−	13.9634i	0.472722	−	1.05253i
$177$	3.21784	−	3.21784i	0.241868	−	0.241868i
$178$	23.8133	−	2.16862i	1.78488	−	0.162545i
$179$	0.485802	−	0.485802i	0.0363105	−	0.0363105i	−0.688718	−	0.725029i	$-0.741826\pi$
$179$	0.485802	−	0.485802i	0.0363105	−	0.0363105i	0.725029	+	0.688718i	$0.241826\pi$
$180$	5.74025	+	9.27776i	0.427853	+	0.691524i
$181$	0.681574	+	0.681574i	0.0506610	+	0.0506610i	0.731983	−	0.681322i	$-0.238595\pi$
$181$	0.681574	+	0.681574i	0.0506610	+	0.0506610i	−0.681322	+	0.731983i	$0.738595\pi$
$182$	0.632431	−	0.759160i	0.0468789	−	0.0562727i
$183$	1.08329	+	1.08329i	0.0800794	+	0.0800794i
$184$	−11.1133	−	6.25939i	−0.819283	−	0.461448i
$185$	5.09310	+	13.0371i	0.374452	+	0.958509i
$186$	10.5400	−	0.959854i	0.772831	−	0.0703799i
$187$			12.7673i			0.933635i
$188$	13.7562	+	9.48734i	1.00328	+	0.691936i
$189$	2.87951	+	2.87951i	0.209454	+	0.209454i
$190$	16.4310	+	5.48432i	1.19203	+	0.397874i
$191$		−	3.97104i		−	0.287335i	−0.989626	−	0.143667i	$-0.954110\pi$
$191$		−	3.97104i		−	0.287335i	0.989626	−	0.143667i	$-0.0458895\pi$
$192$	−3.10436	−	5.12174i	−0.224038	−	0.369630i
$193$	−17.1933	−	17.1933i	−1.23760	−	1.23760i	−0.960978	−	0.276625i	$-0.910784\pi$
$193$	−17.1933	−	17.1933i	−1.23760	−	1.23760i	−0.276625	−	0.960978i	$-0.589216\pi$
$194$	−3.37443	+	4.05061i	−0.242270	+	0.290817i
$195$	1.08940	−	0.425588i	0.0780139	−	0.0304770i
$196$	−0.361275	−	1.96710i	−0.0258053	−	0.140507i
$197$	24.4403			1.74130			0.870650	−	0.491902i	$-0.163698\pi$
$197$	24.4403			1.74130			0.870650	+	0.491902i	$0.163698\pi$
$198$	−8.45042	+	10.1437i	−0.600545	+	0.720885i
$199$		−	20.2544i		−	1.43580i	−0.696149	−	0.717898i	$-0.745105\pi$
$199$		−	20.2544i		−	1.43580i	0.696149	−	0.717898i	$-0.254895\pi$
$200$	7.43389	−	12.0307i	0.525655	−	0.850698i
$201$			1.20767i			0.0851823i
$202$	−9.41383	−	7.84235i	−0.662355	−	0.551786i
$203$	−8.75984			−0.614820
$204$	4.11221	+	2.83610i	0.287912	+	0.198566i
$205$	−3.33417	+	1.30253i	−0.232868	+	0.0909727i
$206$	18.5492	+	15.4527i	1.29238	+	1.07664i
$207$	7.77898	+	7.77898i	0.540677	+	0.540677i
$208$	2.61232	−	0.993045i	0.181132	−	0.0688553i
$209$			20.9620i			1.44997i
$210$	0.749537	−	2.24561i	0.0517229	−	0.154962i
$211$	−7.46207	−	7.46207i	−0.513710	−	0.513710i	0.401951	−	0.915661i	$-0.368332\pi$
$211$	−7.46207	−	7.46207i	−0.513710	−	0.513710i	−0.915661	+	0.401951i	$0.868332\pi$
$212$	1.21462	+	6.61346i	0.0834203	+	0.454214i
$213$		−	11.0975i		−	0.760388i
$214$	−0.0791870	−	0.869540i	−0.00541311	−	0.0594405i
$215$	−0.279135	−	0.714520i	−0.0190369	−	0.0487298i
$216$	3.09943	+	11.0932i	0.210889	+	0.754796i
$217$	7.06859	+	7.06859i	0.479847	+	0.479847i
$218$	−5.98882	−	4.98909i	−0.405614	−	0.337904i
$219$	−3.69815	−	3.69815i	−0.249898	−	0.249898i
$220$	16.6579	+	3.92379i	1.12308	+	0.264542i
$221$	−1.64826	+	1.64826i	−0.110874	+	0.110874i
$222$	0.601030	+	6.59982i	0.0403385	+	0.442951i
$223$	−1.03447	+	1.03447i	−0.0692731	+	0.0692731i	−0.740895	−	0.671621i	$-0.765598\pi$
$223$	−1.03447	+	1.03447i	−0.0692731	+	0.0692731i	0.671621	+	0.740895i	$0.265598\pi$
$224$	1.84009	−	5.34921i	0.122946	−	0.357409i
$225$	−8.96755	+	8.26845i	−0.597837	+	0.551230i
$226$	0.756689	+	0.630373i	0.0503342	+	0.0419318i
$227$	−15.3206			−1.01686			−0.508430	−	0.861103i	$-0.669774\pi$
$227$	−15.3206			−1.01686			−0.508430	+	0.861103i	$0.669774\pi$
$228$	6.75165	+	4.65646i	0.447139	+	0.308381i
$229$	9.55785	−	9.55785i	0.631600	−	0.631600i	−0.316869	−	0.948469i	$-0.602632\pi$
$229$	9.55785	−	9.55785i	0.631600	−	0.631600i	0.948469	+	0.316869i	$0.102632\pi$
$230$	4.51493	−	13.5267i	0.297706	−	0.891925i
$231$	2.86486			0.188494
$232$	−21.5879	−	12.1590i	−1.41731	−	0.798279i
$233$	11.6690	−	11.6690i	0.764464	−	0.764464i	−0.212662	−	0.977126i	$-0.568213\pi$
$233$	11.6690	−	11.6690i	0.764464	−	0.764464i	0.977126	+	0.212662i	$0.0682134\pi$
$234$	−2.40052	+	0.218610i	−0.156927	+	0.0142910i
$235$	−7.49804	+	17.1124i	−0.489118	+	1.11629i
$236$	10.0080	+	6.90227i	0.651464	+	0.449300i
$237$			5.74252i			0.373017i
$238$	0.427910	+	4.69881i	0.0277373	+	0.304579i
$239$	−23.2444			−1.50356			−0.751779	−	0.659415i	$-0.770804\pi$
$239$	−23.2444			−1.50356			−0.751779	+	0.659415i	$0.770804\pi$
$240$	4.96417	−	4.49373i	0.320436	−	0.290069i
$241$	−18.7709			−1.20914			−0.604569	−	0.796553i	$-0.706655\pi$
$241$	−18.7709			−1.20914			−0.604569	+	0.796553i	$0.706655\pi$
$242$	0.467389	+	5.13232i	0.0300449	+	0.329918i
$243$		−	15.4134i		−	0.988770i
$244$	−2.32367	+	3.36921i	−0.148757	+	0.215692i
$245$	2.08278	−	0.813660i	0.133064	−	0.0519828i
$246$	−1.68787	+	0.153710i	−0.107614	+	0.00980019i
$247$	−2.70621	+	2.70621i	−0.172192	+	0.172192i
$248$	7.60845	+	27.2315i	0.483137	+	1.72920i
$249$	−4.98576			−0.315959
$250$	14.7828	+	5.60973i	0.934946	+	0.354790i
$251$	−7.67878	+	7.67878i	−0.484680	+	0.484680i	−0.906623	−	0.421942i	$-0.861348\pi$
$251$	−7.67878	+	7.67878i	−0.484680	+	0.484680i	0.421942	+	0.906623i	$0.361348\pi$
$252$	−2.77008	+	4.01649i	−0.174498	+	0.253015i
$253$	17.2568			1.08493
$254$	8.25606	+	6.87785i	0.518032	+	0.431555i
$255$	−2.24143	+	5.11548i	−0.140363	+	0.320344i
$256$	11.9597	−	10.6286i	0.747479	−	0.664285i
$257$	7.52405	−	7.52405i	0.469338	−	0.469338i	−0.432362	−	0.901700i	$-0.642320\pi$
$257$	7.52405	−	7.52405i	0.469338	−	0.469338i	0.901700	+	0.432362i	$0.142320\pi$
$258$	−0.0329404	−	0.361713i	−0.00205078	−	0.0225193i
$259$	−4.42613	+	4.42613i	−0.275027	+	0.275027i
$260$	1.64398	+	2.65711i	0.101956	+	0.164787i
$261$	15.1109	+	15.1109i	0.935340	+	0.935340i
$262$	3.00896	+	2.50666i	0.185894	+	0.154862i
$263$	14.0969	+	14.0969i	0.869250	+	0.869250i	0.992389	−	0.123140i	$-0.0392963\pi$
$263$	14.0969	+	14.0969i	0.869250	+	0.869250i	−0.123140	+	0.992389i	$0.539296\pi$
$264$	7.06019	+	3.97654i	0.434525	+	0.244739i
$265$	−7.00237	+	2.73555i	−0.430152	+	0.168044i
$266$	0.702565	+	7.71476i	0.0430771	+	0.473022i
$267$			12.6581i			0.774663i
$268$	−3.17324	+	0.582792i	−0.193836	+	0.0355997i
$269$	−1.01292	−	1.01292i	−0.0617590	−	0.0617590i	0.675553	−	0.737312i	$-0.263905\pi$
$269$	−1.01292	−	1.01292i	−0.0617590	−	0.0617590i	−0.737312	+	0.675553i	$0.763905\pi$
$270$	−11.5203	+	5.75440i	−0.701106	+	0.350202i
$271$		−	0.953759i		−	0.0579367i	−0.999580	−	0.0289684i	$-0.990778\pi$
$271$		−	0.953759i		−	0.0579367i	0.999580	−	0.0289684i	$-0.00922221\pi$
$272$	−5.46760	+	12.1738i	−0.331522	+	0.738144i
$273$	0.369855	+	0.369855i	0.0223846	+	0.0223846i
$274$	25.3273	+	21.0993i	1.53008	+	1.27466i
$275$	−0.775446	+	19.1181i	−0.0467612	+	1.15286i
$276$	3.83340	−	5.55825i	0.230743	−	0.334567i
$277$	24.5340			1.47410			0.737051	−	0.675837i	$-0.236218\pi$
$277$	24.5340			1.47410			0.737051	+	0.675837i	$0.236218\pi$
$278$	−2.16840	−	1.80643i	−0.130052	−	0.108342i
$279$		−	24.3869i		−	1.46001i
$280$	6.26222	+	0.885785i	0.374239	+	0.0529358i
$281$		−	12.7498i		−	0.760588i	−0.924866	−	0.380294i	$-0.875823\pi$
$281$		−	12.7498i		−	0.760588i	0.924866	−	0.380294i	$-0.124177\pi$
$282$	−5.66201	+	6.79659i	−0.337168	+	0.404731i
$283$	18.2003			1.08189			0.540946	−	0.841057i	$-0.318066\pi$
$283$	18.2003			1.08189			0.540946	+	0.841057i	$0.318066\pi$
$284$	29.1595	−	5.35539i	1.73030	−	0.317784i
$285$	−3.68009	+	8.39888i	−0.217990	+	0.497506i
$286$	−2.42016	+	2.90513i	−0.143107	+	0.171784i
$287$	−1.13196	−	1.13196i	−0.0668173	−	0.0668173i
$288$	−12.4017	+	6.05331i	−0.730775	+	0.356694i
$289$			5.86903i			0.345237i
$290$	8.77037	−	26.2760i	0.515014	−	1.54298i
$291$	−1.97341	−	1.97341i	−0.115684	−	0.115684i
$292$	7.93253	−	11.5018i	0.464216	−	0.673092i
$293$		−	6.91227i		−	0.403819i	−0.979404	−	0.201910i	$-0.935285\pi$
$293$		−	6.91227i		−	0.403819i	0.979404	−	0.201910i	$-0.0647148\pi$
$294$	1.05437	−	0.0960190i	0.0614921	−	0.00559994i
$295$	−5.45501	+	12.4497i	−0.317603	+	0.724848i
$296$	−17.0515	+	4.76417i	−0.991098	+	0.276912i
$297$	−11.0192	−	11.0192i	−0.639399	−	0.639399i
$298$	−1.89134	+	2.27033i	−0.109562	+	0.131517i
$299$	2.22787	+	2.22787i	0.128841	+	0.128841i
$300$	5.98549	+	4.49662i	0.345573	+	0.259612i
$301$	0.242581	−	0.242581i	0.0139821	−	0.0139821i
$302$	15.7634	−	1.43554i	0.907084	−	0.0826060i
$303$	4.58632	−	4.58632i	0.263477	−	0.263477i
$304$	−8.97700	+	19.9876i	−0.514866	+	1.14637i
$305$	−4.19121	−	1.83644i	−0.239988	−	0.105154i
$306$	7.36738	−	8.84368i	0.421165	−	0.505560i
$307$	−1.78101			−0.101647			−0.0508237	−	0.998708i	$-0.516185\pi$
$307$	−1.78101			−0.101647			−0.0508237	+	0.998708i	$0.516185\pi$
$308$	1.38251	+	7.52762i	0.0787759	+	0.428926i
$309$	−9.03696	+	9.03696i	−0.514095	+	0.514095i
$310$	−28.2800	+	14.1259i	−1.60620	+	0.802295i
$311$	−29.7070			−1.68453			−0.842264	−	0.539065i	$-0.818778\pi$
$311$	−29.7070			−1.68453			−0.842264	+	0.539065i	$0.818778\pi$
$312$	0.398102	+	1.42485i	0.0225381	+	0.0806662i
$313$	6.35049	−	6.35049i	0.358951	−	0.358951i	−0.504475	−	0.863426i	$-0.668314\pi$
$313$	6.35049	−	6.35049i	0.358951	−	0.358951i	0.863426	+	0.504475i	$0.168314\pi$
$314$	−2.01062	−	22.0783i	−0.113466	−	1.24595i
$315$	−4.99640	−	2.18925i	−0.281515	−	0.123350i
$316$	−15.0889	+	2.77121i	−0.848818	+	0.155893i
$317$		−	25.9529i		−	1.45766i	−0.684696	−	0.728829i	$-0.740065\pi$
$317$		−	25.9529i		−	1.45766i	0.684696	−	0.728829i	$-0.259935\pi$
$318$	−3.54483	+	0.322819i	−0.198784	+	0.0181028i
$319$	33.5218			1.87686
$320$	14.2032	+	10.8752i	0.793983	+	0.607940i
$321$	0.462210			0.0257980
$322$	6.35113	−	0.578382i	0.353934	−	0.0322320i
$323$		−	18.2754i		−	1.01687i
$324$	8.39951	−	1.54264i	0.466640	−	0.0857023i
$325$	−2.56827	+	2.36805i	−0.142462	+	0.131356i
$326$	−0.620056	−	6.80874i	−0.0343417	−	0.377101i
$327$	2.91769	−	2.91769i	0.161349	−	0.161349i
$328$	−1.21841	−	4.36082i	−0.0672754	−	0.240786i
$329$	−8.35529			−0.460642
$330$	−2.86830	+	8.59342i	−0.157895	+	0.473052i
$331$	11.1288	−	11.1288i	0.611694	−	0.611694i	−0.331693	−	0.943387i	$-0.607620\pi$
$331$	11.1288	−	11.1288i	0.611694	−	0.611694i	0.943387	+	0.331693i	$0.107620\pi$
$332$	−2.40601	−	13.1005i	−0.132047	−	0.718981i
$333$	15.2703			0.836808
$334$	−12.7633	+	15.3209i	−0.698377	+	0.838321i
$335$	−1.31256	−	3.35984i	−0.0717128	−	0.183568i
$336$	2.73168	+	1.22688i	0.149025	+	0.0669317i
$337$	19.7222	−	19.7222i	1.07433	−	1.07433i	0.0773285	−	0.997006i	$-0.475361\pi$
$337$	19.7222	−	19.7222i	1.07433	−	1.07433i	0.997006	−	0.0773285i	$-0.0246390\pi$
$338$	17.6215	−	1.60475i	0.958484	−	0.0872869i
$339$	−0.368651	+	0.368651i	−0.0200224	+	0.0200224i
$340$	−14.5230	−	3.42090i	−0.787619	−	0.185524i
$341$	−27.0498	−	27.0498i	−1.46483	−	1.46483i
$342$	12.0962	−	14.5200i	0.654086	−	0.785154i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	0.934532	−	0.261108i	0.0503866	−	0.0140780i
$345$	6.91432	+	3.02961i	0.372254	+	0.163109i
$346$	34.1400	−	3.10905i	1.83538	−	0.167143i
$347$			32.1830i			1.72767i	0.503771	+	0.863837i	$0.331946\pi$
$347$			32.1830i			1.72767i	−0.503771	+	0.863837i	$0.668054\pi$
$348$	7.44647	−	10.7971i	0.399173	−	0.578783i
$349$	13.0769	+	13.0769i	0.699990	+	0.699990i	0.964408	−	0.264418i	$-0.0851798\pi$
$349$	13.0769	+	13.0769i	0.699990	+	0.699990i	−0.264418	+	0.964408i	$0.585180\pi$
$350$	0.355373	+	7.06213i	0.0189955	+	0.377487i
$351$		−	2.84517i		−	0.151864i
$352$	−7.04157	+	20.4702i	−0.375317	+	1.09106i
$353$	14.8283	+	14.8283i	0.789232	+	0.789232i	0.981368	−	0.192136i	$-0.0615414\pi$
$353$	14.8283	+	14.8283i	0.789232	+	0.789232i	−0.192136	+	0.981368i	$0.561541\pi$
$354$	−4.11925	+	4.94468i	−0.218936	+	0.262807i
$355$	12.0614	+	30.8743i	0.640151	+	1.63864i
$356$	−33.2601	+	6.10850i	−1.76278	+	0.323750i
$357$	−2.49768			−0.132192
$358$	−0.621888	+	0.746504i	−0.0328678	+	0.0394540i
$359$		−	34.9596i		−	1.84510i	−0.385883	−	0.922548i	$-0.626103\pi$
$359$		−	34.9596i		−	1.84510i	0.385883	−	0.922548i	$-0.373897\pi$
$360$	−9.27444	−	12.3304i	−0.488806	−	0.649871i
$361$		−	11.0056i		−	0.579241i
$362$	−1.04734	−	0.872501i	−0.0550468	−	0.0458577i
$363$	−2.72812			−0.143189
$364$	−0.793338	+	1.15030i	−0.0415822	+	0.0602924i
$365$	14.3079	+	6.26924i	0.748912	+	0.328147i
$366$	−1.66464	−	1.38675i	−0.0870120	−	0.0724868i
$367$	1.80475	+	1.80475i	0.0942073	+	0.0942073i	0.752640	−	0.658433i	$-0.228780\pi$
$367$	1.80475	+	1.80475i	0.0942073	+	0.0942073i	−0.658433	+	0.752640i	$0.728780\pi$
$368$	16.4546	+	7.39025i	0.857757	+	0.385244i
$369$			3.90529i			0.203301i
$370$	−8.84517	−	17.7081i	−0.459839	−	0.920599i
$371$	−2.37732	−	2.37732i	−0.123424	−	0.123424i
$372$	−14.7213	+	2.70369i	−0.763263	+	0.140180i
$373$			2.25752i			0.116890i	0.998291	+	0.0584450i	$0.0186142\pi$
$373$			2.25752i			0.116890i	−0.998291	+	0.0584450i	$0.981386\pi$
$374$	−1.63751	−	17.9812i	−0.0846736	−	0.929788i
$375$	−3.66708	+	7.52394i	−0.189367	+	0.388535i
$376$	−20.5909	−	11.5975i	−1.06189	−	0.598095i
$377$	4.32769	+	4.32769i	0.222888	+	0.222888i
$378$	−4.42478	−	3.68614i	−0.227586	−	0.189595i
$379$	−3.34090	−	3.34090i	−0.171610	−	0.171610i	0.616076	−	0.787687i	$-0.288721\pi$
$379$	−3.34090	−	3.34090i	−0.171610	−	0.171610i	−0.787687	+	0.616076i	$0.788721\pi$
$380$	−23.8446	−	5.61662i	−1.22320	−	0.288127i
$381$	−4.02227	+	4.02227i	−0.206067	+	0.206067i
$382$	0.509319	+	5.59276i	0.0260591	+	0.286150i
$383$	−5.72029	+	5.72029i	−0.292293	+	0.292293i	−0.837986	−	0.545692i	$-0.816267\pi$
$383$	−5.72029	+	5.72029i	−0.292293	+	0.292293i	0.545692	+	0.837986i	$0.316267\pi$
$384$	5.02904	+	6.81522i	0.256637	+	0.347788i
$385$	−7.97029	+	3.11368i	−0.406204	+	0.158688i
$386$	26.4200	+	22.0096i	1.34474	+	1.12026i
$387$	−0.836912			−0.0425426
$388$	4.23297	−	6.13761i	0.214896	−	0.311590i
$389$	−22.9021	+	22.9021i	−1.16118	+	1.16118i	−0.176966	+	0.984217i	$0.556628\pi$
$389$	−22.9021	+	22.9021i	−1.16118	+	1.16118i	−0.984217	+	0.176966i	$0.943372\pi$
$390$	−1.47972	+	0.739117i	−0.0749283	+	0.0374266i
$391$	−15.0451			−0.760865
$392$	0.761111	+	2.72410i	0.0384419	+	0.137588i
$393$	−1.46593	+	1.46593i	−0.0739465	+	0.0739465i
$394$	−34.4214	+	3.13468i	−1.73412	+	0.157923i
$395$	−6.24129	−	15.9762i	−0.314033	−	0.803851i
$396$	10.6004	−	15.3701i	0.532691	−	0.772379i
$397$		−	27.0842i		−	1.35932i	−0.733528	−	0.679659i	$-0.762128\pi$
$397$		−	27.0842i		−	1.35932i	0.733528	−	0.679659i	$-0.237872\pi$
$398$	2.59779	+	28.5260i	0.130216	+	1.42988i
$399$	−4.10083			−0.205298
$400$	−8.92675	+	17.8973i	−0.446337	+	0.894865i
$401$	29.0471			1.45055			0.725273	−	0.688462i	$-0.241714\pi$
$401$	29.0471			1.45055			0.725273	+	0.688462i	$0.241714\pi$
$402$	−0.154894	−	1.70086i	−0.00772539	−	0.0848313i
$403$		−	6.98431i		−	0.347913i
$404$	14.2641	+	9.83765i	0.709668	+	0.489441i
$405$	3.47433	+	8.89345i	0.172641	+	0.441919i
$406$	12.3372	−	1.12352i	0.612287	−	0.0557595i
$407$	16.9378	−	16.9378i	0.839574	−	0.839574i
$408$	−6.15533	−	3.46689i	−0.304734	−	0.171637i
$409$	27.1069			1.34035			0.670174	−	0.742204i	$-0.266219\pi$
$409$	27.1069			1.34035			0.670174	+	0.742204i	$0.266219\pi$
$410$	4.52874	−	2.26210i	0.223658	−	0.111717i
$411$	−12.3392	+	12.3392i	−0.608647	+	0.608647i
$412$	−28.1063	−	19.3843i	−1.38470	−	0.954995i
$413$	−6.07867			−0.299112
$414$	−11.9535	−	9.95808i	−0.587484	−	0.489413i
$415$	13.8708	−	5.41879i	0.680892	−	0.265998i
$416$	−3.55179	+	1.73364i	−0.174141	+	0.0849988i
$417$	1.05642	−	1.05642i	0.0517333	−	0.0517333i
$418$	−2.68855	−	29.5226i	−0.131501	−	1.44400i
$419$	−12.1138	+	12.1138i	−0.591797	+	0.591797i	−0.938116	−	0.346320i	$-0.887431\pi$
$419$	−12.1138	+	12.1138i	−0.591797	+	0.591797i	0.346320	+	0.938116i	$0.387431\pi$
$420$	−0.767618	+	3.25882i	−0.0374559	+	0.159014i
$421$	−7.40481	−	7.40481i	−0.360889	−	0.360889i	0.503251	−	0.864140i	$-0.332137\pi$
$421$	−7.40481	−	7.40481i	−0.360889	−	0.360889i	−0.864140	+	0.503251i	$0.832137\pi$
$422$	11.4665	+	9.55240i	0.558183	+	0.465004i
$423$	14.4130	+	14.4130i	0.700785	+	0.700785i
$424$	−2.55888	−	9.15852i	−0.124270	−	0.444777i
$425$	0.676062	−	16.6678i	0.0327938	−	0.808509i
$426$	1.42335	+	15.6296i	0.0689614	+	0.757255i
$427$		−	2.04640i		−	0.0990322i
$428$	0.223052	+	1.21449i	0.0107816	+	0.0587047i
$429$	−1.41535	−	1.41535i	−0.0683336	−	0.0683336i
$430$	0.484773	+	0.970518i	0.0233778	+	0.0468025i
$431$			24.5730i			1.18364i	0.806069	+	0.591821i	$0.201591\pi$
$431$			24.5730i			1.18364i	−0.806069	+	0.591821i	$0.798409\pi$
$432$	−5.78798	−	15.2260i	−0.278474	−	0.732559i
$433$	−2.50750	−	2.50750i	−0.120503	−	0.120503i	0.644284	−	0.764787i	$-0.277156\pi$
$433$	−2.50750	−	2.50750i	−0.120503	−	0.120503i	−0.764787	+	0.644284i	$0.777156\pi$
$434$	−10.8619	−	9.04870i	−0.521389	−	0.434351i
$435$	13.4312	+	5.88510i	0.643979	+	0.282169i
$436$	9.07446	+	6.25844i	0.434588	+	0.299725i
$437$	−24.7019			−1.18165
$438$	5.68274	+	4.73410i	0.271532	+	0.226204i
$439$			7.63676i			0.364483i	0.983254	+	0.182241i	$0.0583352\pi$
$439$			7.63676i			0.364483i	−0.983254	+	0.182241i	$0.941665\pi$
$440$	−23.9640	−	3.38969i	−1.14244	−	0.161597i
$441$		−	2.43954i		−	0.116169i
$442$	2.10999	−	2.53279i	0.100362	−	0.120473i
$443$	−11.6730			−0.554603			−0.277301	−	0.960783i	$-0.589440\pi$
$443$	−11.6730			−0.554603			−0.277301	+	0.960783i	$0.589440\pi$
$444$	−1.69297	−	9.21801i	−0.0803446	−	0.437467i
$445$	−13.7575	−	35.2160i	−0.652169	−	1.66940i
$446$	1.32425	−	1.58961i	0.0627051	−	0.0752702i
$447$	−1.10608	−	1.10608i	−0.0523159	−	0.0523159i
$448$	−1.90547	+	7.76976i	−0.0900249	+	0.367087i
$449$		−	31.6739i		−	1.49478i	−0.664384	−	0.747391i	$-0.731306\pi$
$449$		−	31.6739i		−	1.49478i	0.664384	−	0.747391i	$-0.268694\pi$
$450$	11.5693	−	12.7953i	0.545381	−	0.603177i
$451$	4.33173	+	4.33173i	0.203973	+	0.203973i
$452$	−1.14656	−	0.790756i	−0.0539297	−	0.0371940i
$453$			8.37916i			0.393687i
$454$	21.5772	−	1.96499i	1.01267	−	0.0922215i
$455$	−1.43095	−	0.626992i	−0.0670839	−	0.0293938i
$456$	−10.1062	−	5.69213i	−0.473264	−	0.266558i
$457$	−15.3604	−	15.3604i	−0.718529	−	0.718529i	0.249775	−	0.968304i	$-0.419643\pi$
$457$	−15.3604	−	15.3604i	−0.718529	−	0.718529i	−0.968304	+	0.249775i	$0.919643\pi$
$458$	−12.2353	+	14.6870i	−0.571716	+	0.686279i
$459$	9.60694	+	9.60694i	0.448414	+	0.448414i
$460$	−4.62385	+	19.6299i	−0.215588	+	0.915249i
$461$	−6.76553	+	6.76553i	−0.315102	+	0.315102i	−0.846882	−	0.531780i	$-0.821523\pi$
$461$	−6.76553	+	6.76553i	−0.315102	+	0.315102i	0.531780	+	0.846882i	$0.321523\pi$
$462$	−4.03482	+	0.367442i	−0.187717	+	0.0170949i
$463$	−21.9571	+	21.9571i	−1.02043	+	1.02043i	−0.0206456	+	0.999787i	$0.506572\pi$
$463$	−21.9571	+	21.9571i	−1.02043	+	1.02043i	−0.999787	+	0.0206456i	$0.993428\pi$
$464$	31.9636	+	14.3558i	1.48387	+	0.666450i
$465$	−6.08923	−	15.5870i	−0.282381	−	0.722829i
$466$	−14.9378	+	17.9311i	−0.691982	+	0.830644i
$467$	−27.3191			−1.26418			−0.632089	−	0.774896i	$-0.717802\pi$
$467$	−27.3191			−1.26418			−0.632089	+	0.774896i	$0.717802\pi$
$468$	3.35282	−	0.615774i	0.154984	−	0.0284641i
$469$	1.14067	−	1.14067i	0.0526714	−	0.0526714i
$470$	8.36533	−	25.0625i	0.385864	−	1.15605i
$471$	11.7359			0.540761
$472$	−14.9804	−	8.43745i	−0.689528	−	0.388365i
$473$	−0.928300	+	0.928300i	−0.0426833	+	0.0426833i
$474$	−0.736527	−	8.08769i	−0.0338298	−	0.371480i
$475$	1.11000	−	27.3662i	0.0509301	−	1.25565i
$476$	−1.20532	−	6.56286i	−0.0552459	−	0.300808i
$477$			8.20183i			0.375536i
$478$	32.7371	−	2.98130i	1.49736	−	0.136361i
$479$	−25.2092			−1.15184			−0.575919	−	0.817507i	$-0.695356\pi$
$479$	−25.2092			−1.15184			−0.575919	+	0.817507i	$0.695356\pi$
$480$	−6.41511	+	6.96560i	−0.292808	+	0.317935i
$481$	4.37335			0.199408
$482$	26.4366	−	2.40752i	1.20415	−	0.109660i
$483$			3.37598i			0.153613i
$484$	−1.31653	−	7.16835i	−0.0598422	−	0.325834i
$485$	7.63503	+	3.34540i	0.346689	+	0.151907i
$486$	1.97690	+	21.7080i	0.0896739	+	0.984696i
$487$	−7.18291	+	7.18291i	−0.325489	+	0.325489i	−0.850868	−	0.525380i	$-0.823923\pi$
$487$	−7.18291	+	7.18291i	−0.325489	+	0.325489i	0.525380	+	0.850868i	$0.323923\pi$
$488$	2.84049	−	5.04318i	0.128583	−	0.228294i
$489$	3.61923			0.163667
$490$	−2.82899	+	1.41308i	−0.127801	+	0.0638365i
$491$	−4.02148	+	4.02148i	−0.181487	+	0.181487i	−0.792003	−	0.610517i	$-0.790962\pi$
$491$	−4.02148	+	4.02148i	−0.181487	+	0.181487i	0.610517	+	0.792003i	$0.290962\pi$
$492$	2.35745	−	0.432966i	0.106282	−	0.0195196i
$493$	−29.2255			−1.31625
$494$	3.46429	−	4.15848i	0.155866	−	0.187099i
$495$	19.1201	+	8.37774i	0.859382	+	0.376551i
$496$	−14.2083	−	37.3765i	−0.637971	−	1.67826i
$497$	−10.4819	+	10.4819i	−0.470176	+	0.470176i
$498$	7.02187	−	0.639465i	0.314657	−	0.0286551i
$499$	−3.07126	+	3.07126i	−0.137488	+	0.137488i	−0.772501	−	0.635013i	$-0.780995\pi$
$499$	−3.07126	+	3.07126i	−0.137488	+	0.137488i	0.635013	+	0.772501i	$0.280995\pi$
$500$	−21.5394	−	6.00464i	−0.963270	−	0.268536i
$501$	−7.46417	−	7.46417i	−0.333474	−	0.333474i
$502$	9.82982	−	11.7996i	0.438726	−	0.526640i
$503$	19.7873	+	19.7873i	0.882274	+	0.882274i	0.993765	−	0.111491i	$-0.0355628\pi$
$503$	19.7873	+	19.7873i	0.882274	+	0.882274i	−0.111491	+	0.993765i	$0.535563\pi$
$504$	3.38619	−	6.01205i	0.150833	−	0.267798i
$505$	−7.77489	+	17.7442i	−0.345978	+	0.789607i
$506$	−24.3043	+	2.21333i	−1.08046	+	0.0983946i
$507$			9.36683i			0.415996i
$508$	−12.5099	−	8.62776i	−0.555035	−	0.382795i
$509$	5.73530	+	5.73530i	0.254213	+	0.254213i	0.822695	−	0.568483i	$-0.192469\pi$
$509$	5.73530	+	5.73530i	0.254213	+	0.254213i	−0.568483	+	0.822695i	$0.692469\pi$
$510$	2.50069	−	7.49205i	0.110732	−	0.331754i
$511$			6.98600i			0.309042i
$512$	−15.4806	+	16.5030i	−0.684153	+	0.729338i
$513$	15.7732	+	15.7732i	0.696403	+	0.696403i
$514$	−9.63174	+	11.5618i	−0.424838	+	0.509969i
$515$	15.3198	−	34.9635i	0.675071	−	1.54068i
$516$	0.0927855	+	0.505207i	0.00408465	+	0.0222405i
$517$	31.9737			1.40620
$518$	5.66601	−	6.80139i	0.248950	−	0.298836i
$519$			18.1473i			0.796579i
$520$	−2.65616	−	3.53138i	−0.116480	−	0.154861i
$521$		−	15.1020i		−	0.661630i	−0.943696	−	0.330815i	$-0.892676\pi$
$521$		−	15.1020i		−	0.661630i	0.943696	−	0.330815i	$-0.107324\pi$
$522$	−23.2200	−	19.3438i	−1.01631	−	0.846657i
$523$	−1.39618			−0.0610507			−0.0305254	−	0.999534i	$-0.509718\pi$
$523$	−1.39618			−0.0610507			−0.0305254	+	0.999534i	$0.509718\pi$
$524$	−4.55927	−	3.14442i	−0.199173	−	0.137365i
$525$	−3.74011	−	0.151702i	−0.163232	−	0.00662082i
$526$	−21.6619	−	18.0458i	−0.944502	−	0.786833i
$527$	23.5830	+	23.5830i	1.02729	+	1.02729i
$528$	−10.4535	−	4.69497i	−0.454930	−	0.204322i
$529$		−	2.66433i		−	0.115841i
$530$	9.51118	−	4.75083i	0.413139	−	0.206363i
$531$	10.4858	+	10.4858i	0.455046	+	0.455046i
$532$	−1.97897	−	10.7753i	−0.0857991	−	0.467166i
$533$			1.11846i			0.0484459i
$534$	−1.62351	−	17.8275i	−0.0702560	−	0.771471i
$535$	−1.28591	+	0.502355i	−0.0555948	+	0.0217187i
$536$	4.39440	−	1.22779i	0.189809	−	0.0530325i
$537$	−0.363689	−	0.363689i	−0.0156943	−	0.0156943i
$538$	1.55650	+	1.29667i	0.0671056	+	0.0559034i
$539$	−2.70593	−	2.70593i	−0.116553	−	0.116553i
$540$	15.4870	−	9.58200i	0.666456	−	0.412344i
$541$	28.0653	−	28.0653i	1.20662	−	1.20662i	0.234508	−	0.972114i	$-0.424652\pi$
$541$	28.0653	−	28.0653i	1.20662	−	1.20662i	0.972114	−	0.234508i	$-0.0753480\pi$
$542$	0.122328	+	1.34326i	0.00525442	+	0.0576980i
$543$	0.510251	−	0.510251i	0.0218970	−	0.0218970i
$544$	6.13910	−	17.8466i	0.263212	−	0.765168i
$545$	−4.94618	+	11.2884i	−0.211871	+	0.483542i
$546$	−0.568335	−	0.473461i	−0.0243225	−	0.0202623i
$547$	12.7462			0.544986			0.272493	−	0.962158i	$-0.412152\pi$
$547$	12.7462			0.544986			0.272493	+	0.962158i	$0.412152\pi$
$548$	−38.3767	−	26.4675i	−1.63937	−	1.13064i
$549$	−3.53007	+	3.53007i	−0.150660	+	0.150660i
$550$	−1.35993	−	27.0251i	−0.0579876	−	1.15235i
$551$	−47.9841			−2.04419
$552$	−4.68601	+	8.31983i	−0.199450	+	0.354115i
$553$	5.42396	−	5.42396i	0.230650	−	0.230650i
$554$	−34.5533	+	3.14669i	−1.46803	+	0.133690i
$555$	9.76008	−	3.81288i	0.414292	−	0.161848i
$556$	3.28564	+	2.26603i	0.139342	+	0.0961009i
$557$		−	8.53733i		−	0.361738i	−0.983507	−	0.180869i	$-0.942109\pi$
$557$		−	8.53733i		−	0.361738i	0.983507	−	0.180869i	$-0.0578910\pi$
$558$	3.12782	+	34.3462i	0.132411	+	1.45399i
$559$	−0.239688			−0.0101377
$560$	−8.93323	−	0.444345i	−0.377498	−	0.0187770i
$561$	9.55805			0.403541
$562$	1.63527	+	17.9566i	0.0689795	+	0.757453i
$563$		−	20.6774i		−	0.871448i	−0.900080	−	0.435724i	$-0.856492\pi$
$563$		−	20.6774i		−	0.871448i	0.900080	−	0.435724i	$-0.143508\pi$
$564$	7.10258	−	10.2984i	0.299072	−	0.433641i
$565$	0.624951	−	1.42629i	0.0262919	−	0.0600045i
$566$	−25.6330	+	2.33434i	−1.07743	+	0.0981194i
$567$	−3.01934	+	3.01934i	−0.126801	+	0.126801i
$568$	−40.3810	+	11.2824i	−1.69435	+	0.473399i
$569$	−27.5440			−1.15471			−0.577353	−	0.816495i	$-0.695914\pi$
$569$	−27.5440			−1.15471			−0.577353	+	0.816495i	$0.695914\pi$
$570$	4.10576	−	12.3009i	0.171971	−	0.515226i
$571$	−24.9107	+	24.9107i	−1.04248	+	1.04248i	−0.0434217	+	0.999057i	$0.513826\pi$
$571$	−24.9107	+	24.9107i	−1.04248	+	1.04248i	−0.999057	+	0.0434217i	$0.986174\pi$
$572$	3.03592	−	4.40194i	0.126938	−	0.184055i
$573$	−2.97287			−0.124193
$574$	1.73942	+	1.44905i	0.0726018	+	0.0604821i
$575$	−22.5290	−	0.913796i	−0.939525	−	0.0381079i
$576$	16.6899	−	10.1160i	0.695414	−	0.421500i
$577$	4.85451	−	4.85451i	0.202096	−	0.202096i	−0.598802	−	0.800897i	$-0.704356\pi$
$577$	4.85451	−	4.85451i	0.202096	−	0.202096i	0.800897	+	0.598802i	$0.204356\pi$
$578$	−0.752752	−	8.26586i	−0.0313104	−	0.343814i
$579$	−12.8716	+	12.8716i	−0.534924	+	0.534924i
$580$	−8.98194	+	38.1316i	−0.372955	+	1.58333i
$581$	4.70918	+	4.70918i	0.195370	+	0.195370i
$582$	3.03243	+	2.52622i	0.125698	+	0.104715i
$583$	9.09744	+	9.09744i	0.376777	+	0.376777i
$584$	−9.69685	+	17.2164i	−0.401259	+	0.712419i
$585$	1.38684	+	3.54998i	0.0573388	+	0.146774i
$586$	0.886557	+	9.73515i	0.0366233	+	0.402155i
$587$		−	24.1564i		−	0.997040i	−0.866878	−	0.498520i	$-0.833877\pi$
$587$		−	24.1564i		−	0.997040i	0.866878	−	0.498520i	$-0.166123\pi$
$588$	−1.47264	+	0.270463i	−0.0607308	+	0.0111537i
$589$	38.7199	+	38.7199i	1.59543	+	1.59543i
$590$	6.08598	−	18.2336i	0.250556	−	0.750665i
$591$		−	18.2969i		−	0.752635i
$592$	23.4040	−	8.89679i	0.961899	−	0.365656i
$593$	12.4428	+	12.4428i	0.510964	+	0.510964i	0.914822	−	0.403858i	$-0.132331\pi$
$593$	12.4428	+	12.4428i	0.510964	+	0.510964i	−0.403858	+	0.914822i	$0.632331\pi$
$594$	16.9326	+	14.1060i	0.694753	+	0.578775i
$595$	6.94879	−	2.71462i	0.284873	−	0.111289i
$596$	2.37254	−	3.44008i	0.0971832	−	0.140911i
$597$	−15.1632			−0.620587
$598$	−3.42344	−	2.85195i	−0.139995	−	0.116625i
$599$			12.6013i			0.514876i	0.966295	+	0.257438i	$0.0828783\pi$
$599$			12.6013i			0.514876i	−0.966295	+	0.257438i	$0.917122\pi$
$600$	−9.00661	−	5.56528i	−0.367693	−	0.227202i
$601$			15.1571i			0.618269i	0.951018	+	0.309135i	$0.100039\pi$
$601$			15.1571i			0.618269i	−0.951018	+	0.309135i	$0.899961\pi$
$602$	−0.310534	+	0.372760i	−0.0126564	+	0.0151926i
$603$	−3.93536			−0.160260
$604$	−22.0169	+	4.04359i	−0.895854	+	0.164531i
$605$	7.58989	−	2.96507i	0.308573	−	0.120547i
$606$	−5.87107	+	7.04754i	−0.238496	+	0.286287i
$607$	11.2061	+	11.2061i	0.454840	+	0.454840i	0.896957	−	0.442117i	$-0.145772\pi$
$607$	11.2061	+	11.2061i	0.454840	+	0.454840i	−0.442117	+	0.896957i	$0.645772\pi$
$608$	10.0795	−	29.3016i	0.408778	−	1.18834i
$609$			6.55794i			0.265741i
$610$	6.13838	+	2.04886i	0.248536	+	0.0829559i
$611$	4.12783	+	4.12783i	0.166994	+	0.166994i
$612$	−9.24183	+	13.4002i	−0.373579	+	0.541673i
$613$		−	9.73641i		−	0.393250i	−0.980479	−	0.196625i	$-0.937002\pi$
$613$		−	9.73641i		−	0.393250i	0.980479	−	0.196625i	$-0.0629981\pi$
$614$	2.50834	−	0.228429i	0.101229	−	0.00921865i
$615$	0.975122	+	2.49608i	0.0393207	+	0.100652i
$616$	−2.91259	−	10.4245i	−0.117352	−	0.420014i
$617$	3.00564	+	3.00564i	0.121003	+	0.121003i	0.765015	−	0.644012i	$-0.222731\pi$
$617$	3.00564	+	3.00564i	0.121003	+	0.121003i	−0.644012	+	0.765015i	$0.722731\pi$
$618$	11.5685	−	13.8866i	0.465352	−	0.558601i
$619$	−22.6068	−	22.6068i	−0.908643	−	0.908643i	0.0875194	−	0.996163i	$-0.472106\pi$
$619$	−22.6068	−	22.6068i	−0.908643	−	0.908643i	−0.996163	+	0.0875194i	$0.972106\pi$
$620$	38.0174	−	23.5218i	1.52682	−	0.944659i
$621$	12.9852	−	12.9852i	0.521077	−	0.521077i
$622$	41.8389	−	3.81017i	1.67759	−	0.152774i
$623$	11.9559	−	11.9559i	0.479003	−	0.479003i
$624$	−0.743430	−	1.95568i	−0.0297610	−	0.0782898i
$625$	2.02471	−	24.9179i	0.0809884	−	0.996715i
$626$	−8.12944	+	9.75844i	−0.324918	+	0.390026i
$627$	15.6929			0.626715
$628$	5.66346	+	30.8369i	0.225997	+	1.23053i
$629$	−14.7670	+	14.7670i	−0.588797	+	0.588797i
$630$	7.31765	+	2.44248i	0.291542	+	0.0973105i
$631$	−0.637572			−0.0253813			−0.0126907	−	0.999919i	$-0.504040\pi$
$631$	−0.637572			−0.0253813			−0.0126907	+	0.999919i	$0.504040\pi$
$632$	20.8956	−	5.83821i	0.831181	−	0.232231i
$633$	−5.58638	+	5.58638i	−0.222039	+	0.222039i
$634$	3.32867	+	36.5516i	0.132198	+	1.45165i
$635$	6.81870	−	15.5619i	0.270592	−	0.617557i
$636$	4.95108	−	0.909308i	0.196323	−	0.0360564i
$637$		−	0.698675i		−	0.0276825i
$638$	−47.2117	+	4.29946i	−1.86913	+	0.170217i
$639$	36.1628			1.43058
$640$	−21.3984	−	13.4947i	−0.845846	−	0.533427i
$641$	21.7471			0.858959			0.429480	−	0.903077i	$-0.358697\pi$
$641$	21.7471			0.858959			0.429480	+	0.903077i	$0.358697\pi$
$642$	−0.650970	+	0.0592823i	−0.0256917	+	0.00233969i
$643$			28.5173i			1.12461i	0.826929	+	0.562307i	$0.190086\pi$
$643$			28.5173i			1.12461i	−0.826929	+	0.562307i	$0.809914\pi$
$644$	−8.87065	+	1.62917i	−0.349553	+	0.0641983i
$645$	−0.534916	+	0.208971i	−0.0210623	+	0.00822822i
$646$	2.34398	+	25.7388i	0.0922225	+	1.01268i
$647$	−7.02236	+	7.02236i	−0.276078	+	0.276078i	−0.831541	−	0.555463i	$-0.812541\pi$
$647$	−7.02236	+	7.02236i	−0.276078	+	0.276078i	0.555463	+	0.831541i	$0.312541\pi$
$648$	−11.6319	+	3.24994i	−0.456944	+	0.127670i
$649$	23.2616			0.913099
$650$	3.31339	−	3.66453i	0.129962	−	0.143735i
$651$	5.29181	−	5.29181i	0.207402	−	0.207402i
$652$	1.74656	+	9.50981i	0.0684005	+	0.372433i
$653$	9.41927			0.368604			0.184302	−	0.982870i	$-0.440997\pi$
$653$	9.41927			0.368604			0.184302	+	0.982870i	$0.440997\pi$
$654$	−3.73502	+	4.48345i	−0.146051	+	0.175317i
$655$	2.48510	−	5.67162i	0.0971010	−	0.221608i
$656$	2.27530	+	5.98544i	0.0888355	+	0.233692i
$657$	12.0510	−	12.0510i	0.470153	−	0.470153i
$658$	11.7675	−	1.07164i	0.458744	−	0.0417767i
$659$	4.29492	−	4.29492i	0.167306	−	0.167306i	−0.618488	−	0.785794i	$-0.712254\pi$
$659$	4.29492	−	4.29492i	0.167306	−	0.167306i	0.785794	+	0.618488i	$0.212254\pi$
$660$	2.93749	−	12.4707i	0.114342	−	0.485423i
$661$	8.86255	+	8.86255i	0.344713	+	0.344713i	0.858136	−	0.513423i	$-0.171623\pi$
$661$	8.86255	+	8.86255i	0.344713	+	0.344713i	−0.513423	+	0.858136i	$0.671623\pi$
$662$	−14.2463	+	17.1010i	−0.553697	+	0.664649i
$663$	1.23395	+	1.23395i	0.0479227	+	0.0479227i
$664$	5.06883	+	18.1419i	0.196709	+	0.704042i
$665$	11.4089	−	4.45701i	0.442418	−	0.172836i
$666$	−21.5065	+	1.95855i	−0.833360	+	0.0758921i
$667$			39.5026i			1.52955i
$668$	16.0106	−	23.2147i	0.619470	−	0.898204i
$669$	0.774441	+	0.774441i	0.0299416	+	0.0299416i
$670$	2.27952	+	4.56361i	0.0880655	+	0.176308i
$671$			7.83109i			0.302316i
$672$	−4.00462	−	1.37756i	−0.154481	−	0.0531404i
$673$	−12.1512	−	12.1512i	−0.468395	−	0.468395i	0.433000	−	0.901394i	$-0.357455\pi$
$673$	−12.1512	−	12.1512i	−0.468395	−	0.468395i	−0.901394	+	0.433000i	$0.857455\pi$
$674$	−25.2469	+	30.3059i	−0.972473	+	1.16734i
$675$	13.8022	+	14.9692i	0.531248	+	0.576165i
$676$	−24.6121	+	4.52021i	−0.946618	+	0.173854i
$677$	21.7242			0.834929			0.417465	−	0.908693i	$-0.362919\pi$
$677$	21.7242			0.834929			0.417465	+	0.908693i	$0.362919\pi$
$678$	0.471920	−	0.566485i	0.0181240	−	0.0217557i
$679$			3.72788i			0.143063i
$680$	20.8927	+	2.95525i	0.801199	+	0.113329i
$681$			11.4695i			0.439513i
$682$	41.5660	+	34.6272i	1.59164	+	1.32595i
$683$	28.3479			1.08470			0.542352	−	0.840151i	$-0.317534\pi$
$683$	28.3479			1.08470			0.542352	+	0.840151i	$0.317534\pi$
$684$	−15.1737	+	22.0012i	−0.580183	+	0.841239i
$685$	20.9178	−	47.7397i	0.799230	−	1.82404i
$686$	−1.08657	−	0.905187i	−0.0414855	−	0.0345602i
$687$	−7.15535	−	7.15535i	−0.272994	−	0.272994i
$688$	−1.28269	+	0.487602i	−0.0489022	+	0.0185896i
$689$			2.34897i			0.0894887i
$690$	−10.1266	−	3.38004i	−0.385513	−	0.128676i
$691$	5.59142	+	5.59142i	0.212708	+	0.212708i	0.805417	−	0.592709i	$-0.201942\pi$
$691$	5.59142	+	5.59142i	0.212708	+	0.212708i	−0.592709	+	0.805417i	$0.701942\pi$
$692$	−47.6835	+	8.75747i	−1.81265	+	0.332909i
$693$			9.33555i			0.354628i
$694$	−4.12774	−	45.3261i	−0.156687	−	1.72055i
$695$	−1.79089	+	4.08725i	−0.0679323	+	0.155038i
$696$	−9.10269	+	16.1615i	−0.345037	+	0.612599i
$697$	−3.77656	−	3.77656i	−0.143047	−	0.143047i
$698$	−20.0945	−	16.7401i	−0.760590	−	0.633622i
$699$	−8.73587	−	8.73587i	−0.330421	−	0.330421i
$700$	−1.40628	−	9.90063i	−0.0531524	−	0.374208i
$701$	−18.8421	+	18.8421i	−0.711655	+	0.711655i	−0.966881	−	0.255226i	$-0.917850\pi$
$701$	−18.8421	+	18.8421i	−0.711655	+	0.711655i	0.255226	+	0.966881i	$0.417850\pi$
$702$	0.364917	+	4.00710i	0.0137729	+	0.151238i
$703$	−24.2452	+	24.2452i	−0.914425	+	0.914425i
$704$	7.29178	−	29.7330i	0.274819	−	1.12061i
$705$	12.8110	+	5.61331i	0.482489	+	0.211410i
$706$	−22.7859	−	18.9821i	−0.857557	−	0.714403i
$707$	−8.66379			−0.325835
$708$	5.16729	−	7.49234i	0.194199	−	0.281580i
$709$	19.4072	−	19.4072i	0.728851	−	0.728851i	−0.241540	−	0.970391i	$-0.577652\pi$
$709$	19.4072	−	19.4072i	0.728851	−	0.728851i	0.970391	+	0.241540i	$0.0776524\pi$
$710$	−20.9470	−	41.9359i	−0.786125	−	1.57383i
$711$	−18.7129			−0.701787
$712$	46.0596	−	12.8690i	1.72616	−	0.482287i
$713$	31.8759	−	31.8759i	1.19376	−	1.19376i
$714$	3.51770	−	0.320349i	0.131647	−	0.0119888i
$715$	5.47590	+	2.39935i	0.204787	+	0.0897306i
$716$	0.780113	−	1.13113i	0.0291542	−	0.0422722i
$717$			17.4016i			0.649876i
$718$	4.48386	+	49.2366i	0.167336	+	1.83749i
$719$	12.3710			0.461359			0.230679	−	0.973030i	$-0.425905\pi$
$719$	12.3710			0.461359			0.230679	+	0.973030i	$0.425905\pi$
$720$	14.6435	+	16.1765i	0.545730	+	0.602862i
$721$	17.0713			0.635768
$722$	1.41156	+	15.5001i	0.0525328	+	0.576854i
$723$			14.0526i			0.522620i
$724$	1.58696	+	1.09449i	0.0589789	+	0.0406764i
$725$	−43.7632	−	1.77507i	−1.62533	−	0.0659246i
$726$	3.84225	−	0.349904i	0.142599	−	0.0129862i
$727$	−2.27279	+	2.27279i	−0.0842930	+	0.0842930i	−0.747996	−	0.663703i	$-0.768984\pi$
$727$	−2.27279	+	2.27279i	−0.0842930	+	0.0842930i	0.663703	+	0.747996i	$0.268984\pi$
$728$	0.969790	−	1.72183i	0.0359428	−	0.0638151i
$729$	1.27095			0.0470724
$730$	−20.9552	−	6.99439i	−0.775586	−	0.258874i
$731$	0.809325	−	0.809325i	0.0299340	−	0.0299340i
$732$	2.52232	+	1.73958i	0.0932275	+	0.0642968i
$733$	−30.3447			−1.12081			−0.560403	−	0.828220i	$-0.689354\pi$
$733$	−30.3447			−1.12081			−0.560403	+	0.828220i	$0.689354\pi$
$734$	−2.77326	−	2.31031i	−0.102363	−	0.0852752i
$735$	−0.609136	−	1.55924i	−0.0224683	−	0.0575135i
$736$	−24.1223	−	8.29788i	−0.889161	−	0.305864i
$737$	−4.36509	+	4.36509i	−0.160790	+	0.160790i
$738$	−0.500886	−	5.50016i	−0.0184379	−	0.202464i
$739$	−1.92003	+	1.92003i	−0.0706295	+	0.0706295i	−0.741539	−	0.670910i	$-0.765904\pi$
$739$	−1.92003	+	1.92003i	−0.0706295	+	0.0706295i	0.670910	+	0.741539i	$0.265904\pi$
$740$	14.7286	+	23.8053i	0.541435	+	0.875102i
$741$	2.02597	+	2.02597i	0.0744258	+	0.0744258i
$742$	3.65309	+	3.04327i	0.134109	+	0.111722i
$743$	−2.62063	−	2.62063i	−0.0961415	−	0.0961415i	0.657400	−	0.753542i	$-0.271656\pi$
$743$	−2.62063	−	2.62063i	−0.0961415	−	0.0961415i	−0.753542	+	0.657400i	$0.771656\pi$
$744$	20.3865	−	5.69596i	0.747404	−	0.208824i
$745$	4.27937	+	1.87507i	0.156784	+	0.0686973i
$746$	−0.289546	−	3.17946i	−0.0106010	−	0.116408i
$747$		−	16.2468i		−	0.594440i
$748$	4.61249	+	25.1145i	0.168649	+	0.918277i
$749$	−0.436569	−	0.436569i	−0.0159519	−	0.0159519i
$750$	4.19965	−	11.0669i	0.153350	−	0.404108i
$751$		−	40.9313i		−	1.49360i	−0.665047	−	0.746802i	$-0.731588\pi$
$751$		−	40.9313i		−	1.49360i	0.665047	−	0.746802i	$-0.268412\pi$
$752$	30.4874	+	13.6928i	1.11176	+	0.499324i
$753$	5.74862	+	5.74862i	0.209491	+	0.209491i
$754$	−6.65012	−	5.54000i	−0.242183	−	0.201755i
$755$	−9.10694	−	23.3116i	−0.331435	−	0.848396i
$756$	6.70458	+	4.62399i	0.243843	+	0.168173i
$757$	−11.0143			−0.400323			−0.200162	−	0.979763i	$-0.564147\pi$
$757$	−11.0143			−0.400323			−0.200162	+	0.979763i	$0.564147\pi$
$758$	5.13377	+	4.27677i	0.186467	+	0.155339i
$759$		−	12.9191i		−	0.468933i
$760$	34.3028	+	4.85210i	1.24429	+	0.176004i
$761$			18.1039i			0.656266i	0.944631	+	0.328133i	$0.106419\pi$
$761$			18.1039i			0.656266i	−0.944631	+	0.328133i	$0.893581\pi$
$762$	5.14901	−	6.18079i	0.186529	−	0.223907i
$763$	−5.51167			−0.199536
$764$	−1.43464	−	7.81144i	−0.0519033	−	0.282608i
$765$	−16.6696	−	7.30401i	−0.602689	−	0.264077i
$766$	7.32270	−	8.79005i	0.264580	−	0.317597i
$767$	3.00309	+	3.00309i	0.108435	+	0.108435i
$768$	−7.95694	−	8.95345i	−0.287121	−	0.323080i
$769$			49.2797i			1.77707i	0.458809	+	0.888535i	$0.348276\pi$
$769$			49.2797i			1.77707i	−0.458809	+	0.888535i	$0.651724\pi$
$770$	10.8259	−	5.40752i	0.390138	−	0.194874i
$771$	−5.63278	−	5.63278i	−0.202860	−	0.202860i
$772$	−40.0325	−	27.6095i	−1.44080	−	0.993687i
$773$			47.4141i			1.70537i	0.522428	+	0.852684i	$0.325026\pi$
$773$			47.4141i			1.70537i	−0.522428	+	0.852684i	$0.674974\pi$
$774$	1.17870	−	0.107341i	0.0423673	−	0.00385829i
$775$	33.8816	+	36.7463i	1.21706	+	1.31997i
$776$	−5.17445	+	9.18704i	−0.185752	+	0.329796i
$777$	3.31357	+	3.31357i	0.118874	+	0.118874i
$778$	29.3176	−	35.1924i	1.05109	−	1.26171i
$779$	−6.20056	−	6.20056i	−0.222158	−	0.222158i
$780$	1.98921	−	1.23075i	0.0712252	−	0.0440678i
$781$	40.1117	−	40.1117i	1.43531	−	1.43531i
$782$	21.1893	−	1.92966i	0.757729	−	0.0690046i
$783$	25.2240	−	25.2240i	0.901434	−	0.901434i
$784$	−1.42133	−	3.73896i	−0.0507616	−	0.133534i
$785$	−32.6503	+	12.7552i	−1.16534	+	0.455253i
$786$	1.87658	−	2.25262i	0.0669354	−	0.0803482i
$787$	2.69257			0.0959797			0.0479899	−	0.998848i	$-0.484718\pi$
$787$	2.69257			0.0959797			0.0479899	+	0.998848i	$0.484718\pi$
$788$	48.0765	−	8.82967i	1.71266	−	0.314544i
$789$	10.5534	−	10.5534i	0.375712	−	0.375712i
$790$	10.8392	+	21.7002i	0.385642	+	0.772058i
$791$	0.696401			0.0247612
$792$	−12.9581	+	23.0067i	−0.460447	+	0.817507i
$793$	−1.01100	+	1.01100i	−0.0359016	+	0.0359016i
$794$	3.47378	+	38.1450i	0.123280	+	1.35372i
$795$	2.04794	+	5.24223i	0.0726328	+	0.185923i
$796$	−7.31739	−	39.8424i	−0.259358	−	1.41218i
$797$			13.1937i			0.467345i	0.972315	+	0.233672i	$0.0750743\pi$
$797$			13.1937i			0.467345i	−0.972315	+	0.233672i	$0.924926\pi$
$798$	5.77556	−	0.525966i	0.204452	−	0.0186190i
$799$	−27.8758			−0.986176
$800$	10.2768	−	26.3512i	0.363341	−	0.931656i
$801$	−41.2483			−1.45744
$802$	−40.9096	+	3.72554i	−1.44457	+	0.131553i
$803$		−	26.7338i		−	0.943414i
$804$	0.436300	+	2.37560i	0.0153871	+	0.0837811i
$805$	−3.66921	−	9.39230i	−0.129323	−	0.331035i
$806$	0.895796	+	9.83660i	0.0315531	+	0.346479i
$807$	−0.758312	+	0.758312i	−0.0266938	+	0.0266938i
$808$	−21.3512	−	12.0257i	−0.751132	−	0.423063i
$809$	−49.9843			−1.75735			−0.878677	−	0.477417i	$-0.841573\pi$
$809$	−49.9843			−1.75735			−0.878677	+	0.477417i	$0.841573\pi$
$810$	−6.03385	−	12.0798i	−0.212008	−	0.424441i
$811$	22.4701	−	22.4701i	0.789033	−	0.789033i	−0.192303	−	0.981336i	$-0.561596\pi$
$811$	22.4701	−	22.4701i	0.789033	−	0.789033i	0.981336	+	0.192303i	$0.0615956\pi$
$812$	−17.2315	+	3.16471i	−0.604706	+	0.111059i
$813$	−0.714019			−0.0250417
$814$	−21.6825	+	26.0273i	−0.759971	+	0.912257i
$815$	−10.0690	+	3.93358i	−0.352703	+	0.137787i
$816$	9.11374	+	4.09325i	0.319045	+	0.143292i
$817$	1.32879	−	1.32879i	0.0464886	−	0.0464886i
$818$	−38.1769	+	3.47668i	−1.33482	+	0.121559i
$819$	−1.20523	+	1.20523i	−0.0421140	+	0.0421140i
$820$	−6.08807	+	3.76676i	−0.212605	+	0.131541i
$821$	−22.5772	−	22.5772i	−0.787950	−	0.787950i	0.193208	−	0.981158i	$-0.438111\pi$
$821$	−22.5772	−	22.5772i	−0.787950	−	0.787950i	−0.981158	+	0.193208i	$0.938111\pi$
$822$	15.7957	−	18.9609i	0.550939	−	0.661339i
$823$	12.5240	+	12.5240i	0.436558	+	0.436558i	0.890852	−	0.454294i	$-0.150108\pi$
$823$	12.5240	+	12.5240i	0.436558	+	0.436558i	−0.454294	+	0.890852i	$0.650108\pi$
$824$	42.0707	+	23.6957i	1.46560	+	0.825478i
$825$	14.3125	+	0.580528i	0.498298	+	0.0202114i
$826$	8.56112	−	0.779641i	0.297879	−	0.0271272i
$827$		−	34.5431i		−	1.20118i	−0.799557	−	0.600591i	$-0.794932\pi$
$827$		−	34.5431i		−	1.20118i	0.799557	−	0.600591i	$-0.205068\pi$
$828$	18.1124	+	12.4917i	0.629449	+	0.434116i
$829$	28.7341	+	28.7341i	0.997976	+	0.997976i	0.999998	−	0.00202179i	$-0.000643556\pi$
$829$	28.7341	+	28.7341i	0.997976	+	0.997976i	−0.00202179	+	0.999998i	$0.500644\pi$
$830$	−18.8405	+	9.41080i	−0.653962	+	0.326654i
$831$		−	18.3670i		−	0.637145i
$832$	4.77993	−	2.89718i	0.165714	−	0.100442i
$833$	2.35913	+	2.35913i	0.0817389	+	0.0817389i
$834$	−1.35236	+	1.62335i	−0.0468283	+	0.0562119i
$835$	28.8785	+	12.6535i	0.999381	+	0.437894i
$836$	7.57304	+	41.2343i	0.261919	+	1.42612i
$837$	−40.7082			−1.40708
$838$	15.5072	−	18.6146i	0.535686	−	0.643029i
$839$		−	33.1019i		−	1.14280i	−0.820670	−	0.571402i	$-0.806400\pi$
$839$		−	33.1019i		−	1.14280i	0.820670	−	0.571402i	$-0.193600\pi$
$840$	0.663131	−	4.68813i	0.0228802	−	0.161756i
$841$			47.7348i			1.64603i
$842$	11.3786	+	9.47910i	0.392131	+	0.326672i
$843$	−9.54495			−0.328745
$844$	−17.3745	−	11.9828i	−0.598055	−	0.412464i
$845$	−10.1804	−	26.0594i	−0.350216	−	0.896470i
$846$	−22.1477	−	18.4505i	−0.761453	−	0.634341i
$847$	2.57678	+	2.57678i	0.0885393	+	0.0885393i
$848$	4.77855	+	12.5705i	0.164096	+	0.431674i
$849$		−	13.6254i		−	0.467622i
$850$	1.18564	+	23.5615i	0.0406670	+	0.808152i
$851$	19.9597	+	19.9597i	0.684209	+	0.684209i
$852$	−4.00924	−	21.8299i	−0.137354	−	0.747880i
$853$		−	36.5654i		−	1.25198i	−0.779832	−	0.625988i	$-0.784696\pi$
$853$		−	36.5654i		−	1.25198i	0.779832	−	0.625988i	$-0.215304\pi$
$854$	0.262468	+	2.88212i	0.00898147	+	0.0986241i
$855$	−27.3690	−	11.9921i	−0.935999	−	0.410122i
$856$	−0.469911	−	1.68186i	−0.0160612	−	0.0574849i
$857$	10.3435	+	10.3435i	0.353326	+	0.353326i	0.861345	−	0.508020i	$-0.169622\pi$
$857$	10.3435	+	10.3435i	0.353326	+	0.353326i	−0.508020	+	0.861345i	$0.669622\pi$
$858$	2.17488	+	1.81182i	0.0742493	+	0.0618547i
$859$	27.0696	+	27.0696i	0.923604	+	0.923604i	0.997282	−	0.0736780i	$-0.0234737\pi$
$859$	27.0696	+	27.0696i	0.923604	+	0.923604i	−0.0736780	+	0.997282i	$0.523474\pi$
$860$	−0.807224	−	1.30469i	−0.0275261	−	0.0444895i
$861$	−0.847425	+	0.847425i	−0.0288802	+	0.0288802i
$862$	−3.15170	−	34.6083i	−0.107347	−	1.17876i
$863$	−15.3407	+	15.3407i	−0.522205	+	0.522205i	−0.918237	−	0.396032i	$-0.870387\pi$
$863$	−15.3407	+	15.3407i	−0.522205	+	0.522205i	0.396032	+	0.918237i	$0.370387\pi$
$864$	10.1046	+	20.7017i	0.343764	+	0.704285i
$865$	−19.7235	−	50.4875i	−0.670620	−	1.71663i
$866$	3.85314	+	3.20992i	0.130935	+	0.109078i
$867$	4.39377			0.149220
$868$	16.4583	+	11.3509i	0.558632	+	0.385276i
$869$	−20.7562	+	20.7562i	−0.704106	+	0.704106i
$870$	−19.6712	−	6.56582i	−0.666916	−	0.222602i
$871$	−1.12707			−0.0381894
$872$	−13.5830	−	7.65042i	−0.459980	−	0.259076i
$873$	6.43066	−	6.43066i	0.217645	−	0.217645i
$874$	34.7898	−	3.16823i	1.17678	−	0.107167i
$875$	10.5702	−	3.64291i	0.357338	−	0.123153i
$876$	−8.61068	−	5.93858i	−0.290928	−	0.200646i
$877$			19.8244i			0.669422i	0.942321	+	0.334711i	$0.108639\pi$
$877$			19.8244i			0.669422i	−0.942321	+	0.334711i	$0.891361\pi$
$878$	−0.979478	−	10.7555i	−0.0330558	−	0.362981i
$879$	−5.17478			−0.174541
$880$	34.1854	+	1.70040i	1.15239	+	0.0573206i
$881$	37.0294			1.24755			0.623776	−	0.781603i	$-0.285598\pi$
$881$	37.0294			1.24755			0.623776	+	0.781603i	$0.285598\pi$
$882$	0.312892	+	3.43582i	0.0105356	+	0.115690i
$883$		−	41.9391i		−	1.41136i	−0.708530	−	0.705681i	$-0.750641\pi$
$883$		−	41.9391i		−	1.41136i	0.708530	−	0.705681i	$-0.249359\pi$
$884$	−2.64682	+	3.83777i	−0.0890223	+	0.129078i
$885$	9.32028	+	4.08382i	0.313298	+	0.137276i
$886$	16.4401	−	1.49717i	0.552317	−	0.0502983i
$887$	−10.7615	+	10.7615i	−0.361337	+	0.361337i	−0.864305	−	0.502968i	$-0.832241\pi$
$887$	−10.7615	+	10.7615i	−0.361337	+	0.361337i	0.502968	+	0.864305i	$0.332241\pi$
$888$	3.56663	+	12.7654i	0.119688	+	0.428378i
$889$	7.59827			0.254838
$890$	23.8926	+	47.8332i	0.800883	+	1.60337i
$891$	11.5543	−	11.5543i	0.387084	−	0.387084i
$892$	−1.66118	+	2.40863i	−0.0556203	+	0.0806469i
$893$	−45.7681			−1.53157
$894$	1.69965	+	1.41593i	0.0568449	+	0.0473556i
$895$	1.40709	+	0.616539i	0.0470340	+	0.0206086i
$896$	1.68710	−	11.1872i	0.0563620	−	0.373739i
$897$	1.66786	−	1.66786i	0.0556884	−	0.0556884i
$898$	4.06244	+	44.6090i	0.135565	+	1.48862i
$899$	61.9198	−	61.9198i	2.06514	−	2.06514i
$900$	−14.6529	+	19.5046i	−0.488430	+	0.650154i
$901$	−7.93148	−	7.93148i	−0.264236	−	0.264236i
$902$	−6.65633	−	5.54517i	−0.221632	−	0.184634i
$903$	−0.181605	−	0.181605i	−0.00604343	−	0.00604343i
$904$	1.71622	+	0.966633i	0.0570807	+	0.0321497i
$905$	−0.864997	+	1.97414i	−0.0287535	+	0.0656225i
$906$	−1.07470	−	11.8011i	−0.0357045	−	0.392065i
$907$			15.5732i			0.517100i	0.965998	+	0.258550i	$0.0832447\pi$
$907$			15.5732i			0.517100i	−0.965998	+	0.258550i	$0.916755\pi$
$908$	−30.1371	+	5.53493i	−1.00013	+	0.183683i
$909$	14.9452	+	14.9452i	0.495701	+	0.495701i
$910$	2.09574	+	0.699515i	0.0694733	+	0.0231887i
$911$			42.1010i			1.39487i	0.716649	+	0.697434i	$0.245675\pi$
$911$			42.1010i			1.39487i	−0.716649	+	0.697434i	$0.754325\pi$
$912$	14.9634	+	6.72051i	0.495489	+	0.222538i
$913$	−18.0209	−	18.0209i	−0.596405	−	0.596405i
$914$	23.6035	+	19.6633i	0.780733	+	0.650403i
$915$	−1.37483	+	3.13769i	−0.0454504	+	0.103729i
$916$	15.3482	−	22.2542i	0.507120	−	0.735301i
$917$	2.76922			0.0914478
$918$	−14.7624	−	12.2981i	−0.487233	−	0.405898i
$919$			39.5198i			1.30364i	0.758374	+	0.651819i	$0.225994\pi$
$919$			39.5198i			1.30364i	−0.758374	+	0.651819i	$0.774006\pi$
$920$	3.99446	−	28.2395i	0.131693	−	0.931030i
$921$			1.33333i			0.0439346i
$922$	8.66074	−	10.3962i	0.285226	−	0.342381i
$923$	10.3569			0.340901
$924$	5.63546	−	1.03500i	0.185393	−	0.0340490i
$925$	−23.0094	+	21.2156i	−0.756544	+	0.697564i
$926$	28.1079	−	33.7402i	0.923682	−	1.10877i
$927$	−29.4483	−	29.4483i	−0.967208	−	0.967208i
$928$	−46.8583	−	16.1189i	−1.53820	−	0.529127i
$929$			44.9384i			1.47438i	0.675685	+	0.737190i	$0.263848\pi$
$929$			44.9384i			1.47438i	−0.675685	+	0.737190i	$0.736152\pi$
$930$	10.5751	+	21.1715i	0.346772	+	0.694240i
$931$	3.87334	+	3.87334i	0.126944	+	0.126944i
$932$	18.7384	−	27.1699i	0.613797	−	0.889979i
$933$			22.2397i			0.728096i
$934$	38.4759	−	3.50391i	1.25897	−	0.114651i
$935$	−26.5914	+	10.3882i	−0.869631	+	0.339731i
$936$	−4.64308	+	1.29727i	−0.151764	+	0.0424027i
$937$	4.24922	+	4.24922i	0.138816	+	0.138816i	0.773100	−	0.634284i	$-0.218705\pi$
$937$	4.24922	+	4.24922i	0.138816	+	0.138816i	−0.634284	+	0.773100i	$0.718705\pi$
$938$	−1.46021	+	1.75281i	−0.0476775	+	0.0572313i
$939$	−4.75421	−	4.75421i	−0.155148	−	0.155148i
$940$	−8.56713	+	36.3706i	−0.279429	+	1.18628i
$941$	23.2945	−	23.2945i	0.759380	−	0.759380i	−0.216829	−	0.976210i	$-0.569572\pi$
$941$	23.2945	−	23.2945i	0.759380	−	0.759380i	0.976210	+	0.216829i	$0.0695715\pi$
$942$	−16.5286	+	1.50523i	−0.538532	+	0.0490429i
$943$	−5.10457	+	5.10457i	−0.166228	+	0.166228i
$944$	22.1803	+	9.96183i	0.721908	+	0.324230i
$945$	−3.65443	+	8.34032i	−0.118879	+	0.271311i
$946$	1.18834	−	1.42647i	0.0386363	−	0.0463784i
$947$	−47.1721			−1.53289			−0.766444	−	0.642311i	$-0.777976\pi$
$947$	−47.1721			−1.53289			−0.766444	+	0.642311i	$0.777976\pi$
$948$	2.07463	+	11.2961i	0.0673808	+	0.366881i
$949$	3.45135	−	3.45135i	0.112035	−	0.112035i
$950$	1.94664	+	38.6845i	0.0631574	+	1.25509i
$951$	−19.4293			−0.630037
$952$	2.53930	+	9.08844i	0.0822993	+	0.294558i
$953$	4.76093	−	4.76093i	0.154222	−	0.154222i	−0.625779	−	0.780001i	$-0.715219\pi$
$953$	4.76093	−	4.76093i	0.154222	−	0.154222i	0.780001	+	0.625779i	$0.215219\pi$
$954$	−1.05195	−	11.5513i	−0.0340583	−	0.373989i
$955$	8.27079	−	3.23108i	0.267637	−	0.104555i
$956$	−45.7241	+	8.39763i	−1.47882	+	0.271599i
$957$		−	25.0957i		−	0.811228i
$958$	35.5043	−	3.23329i	1.14709	−	0.104463i
$959$	23.3094			0.752699
$960$	8.14155	−	10.6330i	0.262767	−	0.343180i
$961$	−68.9301			−2.22355
$962$	−6.15937	+	0.560919i	−0.198586	+	0.0180848i
$963$			1.50618i			0.0485359i
$964$	−36.9242	+	6.78144i	−1.18925	+	0.218415i
$965$	21.8203	−	49.7994i	0.702422	−	1.60310i
$966$	−0.432998	−	4.75469i	−0.0139315	−	0.152980i
$967$	−18.1663	+	18.1663i	−0.584189	+	0.584189i	−0.936052	−	0.351862i	$-0.885548\pi$
$967$	−18.1663	+	18.1663i	−0.584189	+	0.584189i	0.351862	+	0.936052i	$0.385548\pi$
$968$	2.77358	+	9.92694i	0.0891462	+	0.319064i
$969$	−13.6817			−0.439518
$970$	−11.1821	−	3.73236i	−0.359037	−	0.119839i
$971$	−17.8423	+	17.8423i	−0.572587	+	0.572587i	−0.932851	−	0.360263i	$-0.882687\pi$
$971$	−17.8423	+	17.8423i	−0.572587	+	0.572587i	0.360263	+	0.932851i	$0.382687\pi$
$972$	−5.56847	−	30.3197i	−0.178609	−	0.972505i
$973$	−1.99564			−0.0639772
$974$	9.19503	−	11.0376i	0.294628	−	0.353666i
$975$	1.77281	+	1.92270i	0.0567753	+	0.0615757i
$976$	−3.35367	+	7.46705i	−0.107348	+	0.239015i
$977$	24.9169	−	24.9169i	0.797162	−	0.797162i	−0.185485	−	0.982647i	$-0.559386\pi$
$977$	24.9169	−	24.9169i	0.797162	−	0.797162i	0.982647	+	0.185485i	$0.0593857\pi$
$978$	−5.09728	+	0.464197i	−0.162993	+	0.0148434i
$979$	−45.7524	+	45.7524i	−1.46225	+	1.46225i
$980$	3.80307	−	2.35300i	0.121485	−	0.0751640i
$981$	9.50772	+	9.50772i	0.303558	+	0.303558i
$982$	5.14800	−	6.17958i	0.164279	−	0.197198i
$983$	31.6443	+	31.6443i	1.00930	+	1.00930i	0.999956	+	0.00934120i	$0.00297344\pi$
$983$	31.6443	+	31.6443i	1.00930	+	1.00930i	0.00934120	+	0.999956i	$0.497027\pi$
$984$	−3.26467	+	0.912145i	−0.104074	+	0.0290781i
$985$	19.8861	+	50.9037i	0.633624	+	1.62193i
$986$	41.1608	−	3.74842i	1.31083	−	0.119374i
$987$			6.25508i			0.199101i
$988$	−4.34570	+	6.30107i	−0.138255	+	0.200464i
$989$	−1.09392	−	1.09392i	−0.0347846	−	0.0347846i
$990$	−28.0029	−	9.34677i	−0.889991	−	0.297060i
$991$			33.1918i			1.05437i	0.849750	+	0.527186i	$0.176753\pi$
$991$			33.1918i			1.05437i	−0.849750	+	0.527186i	$0.823247\pi$
$992$	24.8046	+	50.8182i	0.787547	+	1.61348i
$993$	−8.33143	−	8.33143i	−0.264390	−	0.264390i
$994$	13.4181	−	16.1069i	0.425597	−	0.510880i
$995$	42.1854	−	16.4802i	1.33737	−	0.522457i
$996$	−9.80748	+	1.80123i	−0.310762	+	0.0570741i
$997$	−12.9682			−0.410706			−0.205353	−	0.978688i	$-0.565834\pi$
$997$	−12.9682			−0.410706			−0.205353	+	0.978688i	$0.565834\pi$
$998$	3.93160	−	4.71943i	0.124453	−	0.149391i
$999$		−	25.4902i		−	0.806474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.3	✓	144
5.2	odd	4		560.2.bl.a.267.34	yes	144
16.3	odd	4		560.2.bl.a.323.34	yes	144
80.67	even	4	inner	560.2.t.a.547.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.3	✓	144	1.1	even	1	trivial
560.2.t.a.547.3	yes	144	80.67	even	4	inner
560.2.bl.a.267.34	yes	144	5.2	odd	4
560.2.bl.a.323.34	yes	144	16.3	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.40839 + 0.128258i) q^{2} -0.748637i q^{3} +(1.96710 - 0.361275i) q^{4} +(0.813660 + 2.08278i) q^{5} +(0.0960190 + 1.05437i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.72410 + 0.761111i) q^{8} +2.43954 q^{9} +O(q^{10})\)	\(q+(-1.40839 + 0.128258i) q^{2} -0.748637i q^{3} +(1.96710 - 0.361275i) q^{4} +(0.813660 + 2.08278i) q^{5} +(0.0960190 + 1.05437i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.72410 + 0.761111i) q^{8} +2.43954 q^{9} +(-1.41308 - 2.82899i) q^{10} +(2.70593 - 2.70593i) q^{11} +(-0.270463 - 1.47264i) q^{12} +0.698675 q^{13} +(0.905187 - 1.08657i) q^{14} +(1.55924 - 0.609136i) q^{15} +(3.73896 - 1.42133i) q^{16} +(-2.35913 + 2.35913i) q^{17} +(-3.43582 + 0.312892i) q^{18} +(-3.87334 + 3.87334i) q^{19} +(2.35300 + 3.80307i) q^{20} +(0.529366 + 0.529366i) q^{21} +(-3.46393 + 4.15805i) q^{22} +(3.18870 + 3.18870i) q^{23} +(0.569796 + 2.03936i) q^{24} +(-3.67592 + 3.38934i) q^{25} +(-0.984004 + 0.0896109i) q^{26} -4.07224i q^{27} +(-1.13549 + 1.64641i) q^{28} +(6.19414 + 6.19414i) q^{29} +(-2.11789 + 1.05788i) q^{30} -9.99650i q^{31} +(-5.08360 + 2.48133i) q^{32} +(-2.02576 - 2.02576i) q^{33} +(3.01998 - 3.62514i) q^{34} +(-2.04809 - 0.897401i) q^{35} +(4.79882 - 0.881345i) q^{36} +6.25950 q^{37} +(4.95837 - 5.95195i) q^{38} -0.523054i q^{39} +(-3.80171 - 5.05440i) q^{40} +1.60083i q^{41} +(-0.813447 - 0.677656i) q^{42} -0.343061 q^{43} +(4.34525 - 6.30042i) q^{44} +(1.98496 + 5.08102i) q^{45} +(-4.89990 - 4.08195i) q^{46} +(5.90808 + 5.90808i) q^{47} +(-1.06406 - 2.79912i) q^{48} -1.00000i q^{49} +(4.74239 - 5.24497i) q^{50} +(1.76613 + 1.76613i) q^{51} +(1.37436 - 0.252413i) q^{52} +3.36204i q^{53} +(0.522299 + 5.73529i) q^{54} +(7.83755 + 3.43414i) q^{55} +(1.38804 - 2.46441i) q^{56} +(2.89973 + 2.89973i) q^{57} +(-9.51819 - 7.92929i) q^{58} +(4.29827 + 4.29827i) q^{59} +(2.84712 - 1.76155i) q^{60} +(-1.44702 + 1.44702i) q^{61} +(1.28214 + 14.0789i) q^{62} +(-1.72502 + 1.72502i) q^{63} +(6.84142 - 4.14668i) q^{64} +(0.568484 + 1.45518i) q^{65} +(3.11287 + 2.59323i) q^{66} -1.61316 q^{67} +(-3.78835 + 5.49293i) q^{68} +(2.38718 - 2.38718i) q^{69} +(2.99960 + 1.00120i) q^{70} +14.8236 q^{71} +(-6.64555 + 1.85676i) q^{72} +(4.93985 - 4.93985i) q^{73} +(-8.81579 + 0.802833i) q^{74} +(2.53739 + 2.75193i) q^{75} +(-6.21991 + 9.01859i) q^{76} +3.82676i q^{77} +(0.0670860 + 0.736661i) q^{78} -7.67064 q^{79} +(6.00255 + 6.63095i) q^{80} +4.27000 q^{81} +(-0.205320 - 2.25458i) q^{82} -6.65978i q^{83} +(1.23256 + 0.850069i) q^{84} +(-6.83306 - 2.99401i) q^{85} +(0.483162 - 0.0440005i) q^{86} +(4.63716 - 4.63716i) q^{87} +(-5.31171 + 9.43073i) q^{88} -16.9082 q^{89} +(-3.44727 - 6.90145i) q^{90} +(-0.494038 + 0.494038i) q^{91} +(7.42450 + 5.12050i) q^{92} -7.48375 q^{93} +(-9.07862 - 7.56309i) q^{94} +(-11.2189 - 4.91573i) q^{95} +(1.85761 + 3.80577i) q^{96} +(2.63601 - 2.63601i) q^{97} +(0.128258 + 1.40839i) q^{98} +(6.60123 - 6.60123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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