LMFDB - Embedded newform 880.2.s.b.67.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(67,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.13
Character	$\chi$	$=$	880.67
Dual form			880.2.s.b.683.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31123 + 0.529799i) q^{2} +0.968673i q^{3} +(1.43863 - 1.38937i) q^{4} +(-1.36191 - 1.77347i) q^{5} +(-0.513202 - 1.27015i) q^{6} +(-3.54228 - 3.54228i) q^{7} +(-1.15028 + 2.58396i) q^{8} +2.06167 q^{9} +(2.72536 + 1.60388i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(1.34585 + 1.39356i) q^{12} -4.30151 q^{13} +(6.52142 + 2.76803i) q^{14} +(1.71791 - 1.31925i) q^{15} +(0.139291 - 3.99757i) q^{16} +(1.99094 + 1.99094i) q^{17} +(-2.70332 + 1.09227i) q^{18} +(-0.375520 - 0.375520i) q^{19} +(-4.42329 - 0.659151i) q^{20} +(3.43131 - 3.43131i) q^{21} +(1.30180 + 0.552552i) q^{22} +(-1.82819 + 1.82819i) q^{23} +(-2.50302 - 1.11424i) q^{24} +(-1.29038 + 4.83062i) q^{25} +(5.64025 - 2.27894i) q^{26} +4.90311i q^{27} +(-10.0176 - 0.174473i) q^{28} +(0.379539 - 0.379539i) q^{29} +(-1.55363 + 2.63998i) q^{30} +9.27533i q^{31} +(1.93527 + 5.31552i) q^{32} +(0.684955 - 0.684955i) q^{33} +(-3.66538 - 1.55578i) q^{34} +(-1.45784 + 11.1064i) q^{35} +(2.96598 - 2.86443i) q^{36} +6.95184 q^{37} +(0.691342 + 0.293442i) q^{38} -4.16676i q^{39} +(6.14915 - 1.47916i) q^{40} +8.37549i q^{41} +(-2.68132 + 6.31712i) q^{42} -5.64862 q^{43} +(-1.99970 - 0.0348281i) q^{44} +(-2.80782 - 3.65631i) q^{45} +(1.42859 - 3.36574i) q^{46} +(7.02444 - 7.02444i) q^{47} +(3.87234 + 0.134928i) q^{48} +18.0955i q^{49} +(-0.867284 - 7.01768i) q^{50} +(-1.92857 + 1.92857i) q^{51} +(-6.18827 + 5.97640i) q^{52} +8.87618i q^{53} +(-2.59766 - 6.42908i) q^{54} +(-0.291012 + 2.21705i) q^{55} +(13.2277 - 5.07852i) q^{56} +(0.363756 - 0.363756i) q^{57} +(-0.296582 + 0.698741i) q^{58} +(7.74804 - 7.74804i) q^{59} +(0.638502 - 4.28473i) q^{60} +(-4.43760 - 4.43760i) q^{61} +(-4.91406 - 12.1620i) q^{62} +(-7.30301 - 7.30301i) q^{63} +(-5.35373 - 5.94454i) q^{64} +(5.85829 + 7.62859i) q^{65} +(-0.535243 + 1.26102i) q^{66} -11.8337 q^{67} +(5.63039 + 0.0980628i) q^{68} +(-1.77092 - 1.77092i) q^{69} +(-3.97260 - 15.3353i) q^{70} -7.91956 q^{71} +(-2.37149 + 5.32728i) q^{72} +(4.91595 + 4.91595i) q^{73} +(-9.11543 + 3.68308i) q^{74} +(-4.67930 - 1.24995i) q^{75} +(-1.06197 - 0.0184960i) q^{76} +5.00954i q^{77} +(2.20754 + 5.46356i) q^{78} +0.0761695 q^{79} +(-7.27927 + 5.19733i) q^{80} +1.43551 q^{81} +(-4.43733 - 10.9822i) q^{82} -6.77763i q^{83} +(0.169007 - 9.70373i) q^{84} +(0.819379 - 6.24237i) q^{85} +(7.40662 - 2.99263i) q^{86} +(0.367649 + 0.367649i) q^{87} +(2.64051 - 1.01377i) q^{88} +2.28095 q^{89} +(5.61880 + 3.30667i) q^{90} +(15.2371 + 15.2371i) q^{91} +(-0.0900462 + 5.17011i) q^{92} -8.98476 q^{93} +(-5.48909 + 12.9322i) q^{94} +(-0.154547 + 1.17740i) q^{95} +(-5.14900 + 1.87464i) q^{96} +(-6.40065 - 6.40065i) q^{97} +(-9.58695 - 23.7272i) q^{98} +(-1.45782 - 1.45782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 8 q^{5} - 4 q^{7} + 12 q^{8} - 240 q^{9} + 16 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} + 8 q^{17} - 12 q^{18} - 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} - 12 q^{25} + 8 q^{26} + 36 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 236 * q + 8 * q^5 - 4 * q^7 + 12 * q^8 - 240 * q^9 + 16 * q^13 - 12 * q^14 + 4 * q^15 - 8 * q^16 + 8 * q^17 - 12 * q^18 - 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 - 12 * q^25 + 8 * q^26 + 36 * q^28 - 8 * q^29 + 40 * q^32 - 4 * q^33 + 44 * q^34 - 12 * q^35 - 32 * q^36 + 4 * q^37 - 44 * q^38 - 40 * q^40 - 60 * q^42 - 16 * q^43 - 40 * q^46 + 48 * q^47 - 112 * q^48 - 28 * q^51 + 108 * q^52 - 24 * q^56 + 16 * q^57 - 28 * q^58 - 8 * q^59 + 100 * q^60 - 24 * q^61 + 36 * q^62 + 24 * q^63 - 32 * q^65 - 4 * q^66 - 56 * q^67 - 36 * q^68 - 48 * q^69 + 164 * q^70 - 4 * q^71 + 12 * q^72 - 8 * q^73 - 72 * q^75 - 24 * q^76 + 152 * q^78 - 40 * q^79 - 24 * q^80 + 244 * q^81 + 40 * q^82 + 104 * q^84 - 24 * q^85 + 72 * q^86 - 140 * q^87 + 32 * q^88 - 36 * q^89 + 72 * q^90 + 12 * q^91 + 12 * q^93 + 16 * q^94 + 36 * q^95 + 72 * q^96 + 20 * q^97 - 64 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.31123	+	0.529799i	−0.927177	+	0.374624i
$2$	−1.31123	+	0.529799i	−0.927177	+	0.374624i
$3$			0.968673i			0.559264i	0.960107	+	0.279632i	$0.0902124\pi$
$3$			0.968673i			0.559264i	−0.960107	+	0.279632i	$0.909788\pi$
$4$	1.43863	−	1.38937i	0.719313	−	0.694686i
$5$	−1.36191	−	1.77347i	−0.609067	−	0.793119i
$5$	−1.36191	−	1.77347i	−0.609067	−	0.793119i
$6$	−0.513202	−	1.27015i	−0.209514	−	0.518536i
$7$	−3.54228	−	3.54228i	−1.33885	−	1.33885i	−0.897171	−	0.441684i	$-0.854381\pi$
$7$	−3.54228	−	3.54228i	−1.33885	−	1.33885i	−0.441684	−	0.897171i	$-0.645619\pi$
$8$	−1.15028	+	2.58396i	−0.406684	+	0.913569i
$9$	2.06167			0.687224
$10$	2.72536	+	1.60388i	0.861834	+	0.507190i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	1.34585	+	1.39356i	0.388513	+	0.402286i
$13$	−4.30151			−1.19302			−0.596512	−	0.802604i	$-0.703447\pi$
$13$	−4.30151			−1.19302			−0.596512	+	0.802604i	$0.703447\pi$
$14$	6.52142	+	2.76803i	1.74292	+	0.739787i
$15$	1.71791	−	1.31925i	0.443563	−	0.340629i
$16$	0.139291	−	3.99757i	0.0348228	−	0.999394i
$17$	1.99094	+	1.99094i	0.482875	+	0.482875i	0.906049	−	0.423174i	$-0.139084\pi$
$17$	1.99094	+	1.99094i	0.482875	+	0.482875i	−0.423174	+	0.906049i	$0.639084\pi$
$18$	−2.70332	+	1.09227i	−0.637178	+	0.257451i
$19$	−0.375520	−	0.375520i	−0.0861502	−	0.0861502i	0.662718	−	0.748869i	$-0.269403\pi$
$19$	−0.375520	−	0.375520i	−0.0861502	−	0.0861502i	−0.748869	+	0.662718i	$0.769403\pi$
$20$	−4.42329	−	0.659151i	−0.989078	−	0.147391i
$21$	3.43131	−	3.43131i	0.748773	−	0.748773i
$22$	1.30180	+	0.552552i	0.277545	+	0.117805i
$23$	−1.82819	+	1.82819i	−0.381203	+	0.381203i	−0.871536	−	0.490332i	$-0.836875\pi$
$23$	−1.82819	+	1.82819i	−0.381203	+	0.381203i	0.490332	+	0.871536i	$0.336875\pi$
$24$	−2.50302	−	1.11424i	−0.510926	−	0.227444i
$25$	−1.29038	+	4.83062i	−0.258075	+	0.966125i
$26$	5.64025	−	2.27894i	1.10614	−	0.446936i
$27$			4.90311i			0.943603i
$28$	−10.0176	−	0.174473i	−1.89314	−	0.0329723i
$29$	0.379539	−	0.379539i	0.0704787	−	0.0704787i	−0.670989	−	0.741467i	$-0.734130\pi$
$29$	0.379539	−	0.379539i	0.0704787	−	0.0704787i	0.741467	+	0.670989i	$0.234130\pi$
$30$	−1.55363	+	2.63998i	−0.283653	+	0.481993i
$31$			9.27533i			1.66590i	0.553350	+	0.832949i	$0.313349\pi$
$31$			9.27533i			1.66590i	−0.553350	+	0.832949i	$0.686651\pi$
$32$	1.93527	+	5.31552i	0.342110	+	0.939660i
$33$	0.684955	−	0.684955i	0.119235	−	0.119235i
$34$	−3.66538	−	1.55578i	−0.628607	−	0.266814i
$35$	−1.45784	+	11.1064i	−0.246419	+	1.87732i
$36$	2.96598	−	2.86443i	0.494329	−	0.477405i
$37$	6.95184			1.14288			0.571438	−	0.820645i	$-0.306386\pi$
$37$	6.95184			1.14288			0.571438	+	0.820645i	$0.306386\pi$
$38$	0.691342	+	0.293442i	0.112150	+	0.0476025i
$39$		−	4.16676i		−	0.667215i
$40$	6.14915	−	1.47916i	0.972267	−	0.233876i
$41$			8.37549i			1.30803i	0.756481	+	0.654016i	$0.226917\pi$
$41$			8.37549i			1.30803i	−0.756481	+	0.654016i	$0.773083\pi$
$42$	−2.68132	+	6.31712i	−0.413736	+	0.974753i
$43$	−5.64862			−0.861406			−0.430703	−	0.902494i	$-0.641734\pi$
$43$	−5.64862			−0.861406			−0.430703	+	0.902494i	$0.641734\pi$
$44$	−1.99970	−	0.0348281i	−0.301466	−	0.00525054i
$45$	−2.80782	−	3.65631i	−0.418565	−	0.545050i
$46$	1.42859	−	3.36574i	0.210635	−	0.496251i
$47$	7.02444	−	7.02444i	1.02462	−	1.02462i	0.0249314	−	0.999689i	$-0.492063\pi$
$47$	7.02444	−	7.02444i	1.02462	−	1.02462i	0.999689	−	0.0249314i	$-0.00793672\pi$
$48$	3.87234	+	0.134928i	0.558925	+	0.0194752i
$49$			18.0955i			2.58506i
$50$	−0.867284	−	7.01768i	−0.122653	−	0.992450i
$51$	−1.92857	+	1.92857i	−0.270054	+	0.270054i
$52$	−6.18827	+	5.97640i	−0.858158	+	0.828777i
$53$			8.87618i			1.21924i	0.792695	+	0.609618i	$0.208677\pi$
$53$			8.87618i			1.21924i	−0.792695	+	0.609618i	$0.791323\pi$
$54$	−2.59766	−	6.42908i	−0.353497	−	0.874887i
$55$	−0.291012	+	2.21705i	−0.0392401	+	0.298947i
$56$	13.2277	−	5.07852i	1.76763	−	0.678645i
$57$	0.363756	−	0.363756i	0.0481807	−	0.0481807i
$58$	−0.296582	+	0.698741i	−0.0389431	+	0.0917492i
$59$	7.74804	−	7.74804i	1.00871	−	1.00871i	0.00874707	−	0.999962i	$-0.497216\pi$
$59$	7.74804	−	7.74804i	1.00871	−	1.00871i	0.999962	−	0.00874707i	$-0.00278431\pi$
$60$	0.638502	−	4.28473i	0.0824303	−	0.553156i
$61$	−4.43760	−	4.43760i	−0.568176	−	0.568176i	0.363441	−	0.931617i	$-0.381602\pi$
$61$	−4.43760	−	4.43760i	−0.568176	−	0.568176i	−0.931617	+	0.363441i	$0.881602\pi$
$62$	−4.91406	−	12.1620i	−0.624086	−	1.54458i
$63$	−7.30301	−	7.30301i	−0.920093	−	0.920093i
$64$	−5.35373	−	5.94454i	−0.669216	−	0.743068i
$65$	5.85829	+	7.62859i	0.726631	+	0.946210i
$66$	−0.535243	+	1.26102i	−0.0658838	+	0.155221i
$67$	−11.8337			−1.44572			−0.722860	−	0.690994i	$-0.757173\pi$
$67$	−11.8337			−1.44572			−0.722860	+	0.690994i	$0.757173\pi$
$68$	5.63039	+	0.0980628i	0.682785	+	0.0118919i
$69$	−1.77092	−	1.77092i	−0.213193	−	0.213193i
$70$	−3.97260	−	15.3353i	−0.474817	−	1.83292i
$71$	−7.91956			−0.939878			−0.469939	−	0.882699i	$-0.655724\pi$
$71$	−7.91956			−0.939878			−0.469939	+	0.882699i	$0.655724\pi$
$72$	−2.37149	+	5.32728i	−0.279483	+	0.627827i
$73$	4.91595	+	4.91595i	0.575369	+	0.575369i	0.933624	−	0.358255i	$-0.116628\pi$
$73$	4.91595	+	4.91595i	0.575369	+	0.575369i	−0.358255	+	0.933624i	$0.616628\pi$
$74$	−9.11543	+	3.68308i	−1.05965	+	0.428149i
$75$	−4.67930	−	1.24995i	−0.540319	−	0.144332i
$76$	−1.06197	−	0.0184960i	−0.121816	−	0.00212164i
$77$			5.00954i			0.570890i
$78$	2.20754	+	5.46356i	0.249955	+	0.618626i
$79$	0.0761695			0.00856974			0.00428487	−	0.999991i	$-0.498636\pi$
$79$	0.0761695			0.00856974			0.00428487	+	0.999991i	$0.498636\pi$
$80$	−7.27927	+	5.19733i	−0.813847	+	0.581079i
$81$	1.43551			0.159501
$82$	−4.43733	−	10.9822i	−0.490021	−	1.21278i
$83$		−	6.77763i		−	0.743942i	−0.928244	−	0.371971i	$-0.878682\pi$
$83$		−	6.77763i		−	0.743942i	0.928244	−	0.371971i	$-0.121318\pi$
$84$	0.169007	−	9.70373i	0.0184402	−	1.05876i
$85$	0.819379	−	6.24237i	0.0888742	−	0.677080i
$86$	7.40662	−	2.99263i	0.798676	−	0.322704i
$87$	0.367649	+	0.367649i	0.0394162	+	0.0394162i
$88$	2.64051	−	1.01377i	0.281479	−	0.108068i
$89$	2.28095			0.241780			0.120890	−	0.992666i	$-0.461425\pi$
$89$	2.28095			0.241780			0.120890	+	0.992666i	$0.461425\pi$
$90$	5.61880	+	3.30667i	0.592273	+	0.348553i
$91$	15.2371	+	15.2371i	1.59729	+	1.59729i
$92$	−0.0900462	+	5.17011i	−0.00938797	+	0.539021i
$93$	−8.98476			−0.931676
$94$	−5.48909	+	12.9322i	−0.566156	+	1.33385i
$95$	−0.154547	+	1.17740i	−0.0158561	+	0.120799i
$96$	−5.14900	+	1.87464i	−0.525518	+	0.191330i
$97$	−6.40065	−	6.40065i	−0.649888	−	0.649888i	0.303078	−	0.952966i	$-0.401986\pi$
$97$	−6.40065	−	6.40065i	−0.649888	−	0.649888i	−0.952966	+	0.303078i	$0.901986\pi$
$98$	−9.58695	−	23.7272i	−0.968428	−	2.39681i
$99$	−1.45782	−	1.45782i	−0.146517	−	0.146517i
$100$	4.85516	+	8.74228i	0.485516	+	0.874228i
$101$	1.29250	−	1.29250i	0.128608	−	0.128608i	−0.639873	−	0.768481i	$-0.721013\pi$
$101$	1.29250	−	1.29250i	0.128608	−	0.128608i	0.768481	+	0.639873i	$0.221013\pi$
$102$	1.50704	−	3.55055i	0.149219	−	0.351557i
$103$	−14.0525	+	14.0525i	−1.38463	+	1.38463i	−0.548439	+	0.836191i	$0.684778\pi$
$103$	−14.0525	+	14.0525i	−1.38463	+	1.38463i	−0.836191	+	0.548439i	$0.815222\pi$
$104$	4.94793	−	11.1149i	0.485184	−	1.08991i
$105$	−10.7585	−	1.41217i	−1.04992	−	0.137813i
$106$	−4.70259	−	11.6387i	−0.456756	−	1.13045i
$107$		−	3.50473i		−	0.338815i	−0.985546	−	0.169408i	$-0.945815\pi$
$107$		−	3.50473i		−	0.338815i	0.985546	−	0.169408i	$-0.0541855\pi$
$108$	6.81224	+	7.05374i	0.655508	+	0.678746i
$109$	−1.20652	+	1.20652i	−0.115563	+	0.115563i	−0.762524	−	0.646960i	$-0.776040\pi$
$109$	−1.20652	+	1.20652i	−0.115563	+	0.115563i	0.646960	+	0.762524i	$0.276040\pi$
$110$	−0.793008	−	3.06123i	−0.0756104	−	0.291877i
$111$			6.73406i			0.639169i
$112$	−14.6539	+	13.6671i	−1.38467	+	1.29142i
$113$	−5.14221	+	5.14221i	−0.483738	+	0.483738i	−0.906323	−	0.422585i	$-0.861123\pi$
$113$	−5.14221	+	5.14221i	−0.483738	+	0.483738i	0.422585	+	0.906323i	$0.361123\pi$
$114$	−0.284249	+	0.669684i	−0.0266224	+	0.0627217i
$115$	5.73206	+	0.752396i	0.534518	+	0.0701613i
$116$	0.0186940	−	1.07334i	0.00173569	−	0.0996568i
$117$	−8.86830			−0.819875
$118$	−6.05453	+	14.2643i	−0.557364	+	1.31314i
$119$		−	14.1050i		−	1.29300i
$120$	1.43282	+	5.95652i	0.130798	+	0.543753i
$121$			1.00000i			0.0909091i
$122$	8.16973	+	3.46766i	0.739653	+	0.313947i
$123$	−8.11312			−0.731535
$124$	12.8869	+	13.3437i	1.15728	+	1.19830i
$125$	10.3243	−	4.29046i	0.923437	−	0.383750i
$126$	13.4450	+	5.70677i	1.19778	+	0.508400i
$127$	−2.52103	+	2.52103i	−0.223705	+	0.223705i	−0.810057	−	0.586352i	$-0.800564\pi$
$127$	−2.52103	+	2.52103i	−0.223705	+	0.223705i	0.586352	+	0.810057i	$0.300564\pi$
$128$	10.1694	+	4.95824i	0.898853	+	0.438251i
$129$		−	5.47167i		−	0.481753i
$130$	−11.7232	−	6.89909i	−1.02819	−	0.605090i
$131$	−10.3223	+	10.3223i	−0.901862	+	0.901862i	−0.995597	−	0.0937349i	$-0.970119\pi$
$131$	−10.3223	+	10.3223i	−0.901862	+	0.901862i	0.0937349	+	0.995597i	$0.470119\pi$
$132$	0.0337371	−	1.93705i	0.00293644	−	0.168599i
$133$			2.66039i			0.230685i
$134$	15.5167	−	6.26950i	1.34044	−	0.541602i
$135$	8.69550	−	6.67761i	0.748390	−	0.574717i
$136$	−7.43466	+	2.85439i	−0.637517	+	0.244762i
$137$	3.63741	−	3.63741i	0.310765	−	0.310765i	−0.534441	−	0.845206i	$-0.679478\pi$
$137$	3.63741	−	3.63741i	0.310765	−	0.310765i	0.845206	+	0.534441i	$0.179478\pi$
$138$	3.26030	+	1.38384i	0.277535	+	0.117800i
$139$	−7.75684	+	7.75684i	−0.657927	+	0.657927i	−0.954889	−	0.296962i	$-0.904026\pi$
$139$	−7.75684	+	7.75684i	−0.657927	+	0.657927i	0.296962	+	0.954889i	$0.404026\pi$
$140$	13.3336	+	18.0034i	1.12690	+	1.52157i
$141$	6.80439	+	6.80439i	0.573033	+	0.573033i
$142$	10.3843	−	4.19577i	0.871433	−	0.352101i
$143$	3.04163	+	3.04163i	0.254354	+	0.254354i
$144$	0.287173	−	8.24169i	0.0239311	−	0.686807i
$145$	−1.19000	−	0.156201i	−0.0988242	−	0.0129717i
$146$	−9.05039	−	3.84146i	−0.749016	−	0.317921i
$147$	−17.5286			−1.44573
$148$	10.0011	−	9.65869i	0.822086	−	0.793940i
$149$	−6.81099	−	6.81099i	−0.557978	−	0.557978i	0.370753	−	0.928731i	$-0.379100\pi$
$149$	−6.81099	−	6.81099i	−0.557978	−	0.557978i	−0.928731	+	0.370753i	$0.879100\pi$
$150$	6.79784	−	0.840115i	0.555041	−	0.0685951i
$151$	−16.0972			−1.30997			−0.654984	−	0.755643i	$-0.727325\pi$
$151$	−16.0972			−1.30997			−0.654984	+	0.755643i	$0.727325\pi$
$152$	1.40228	−	0.538378i	0.113740	−	0.0436682i
$153$	4.10468	+	4.10468i	0.331843	+	0.331843i
$154$	−2.65405	−	6.56863i	−0.213869	−	0.529316i
$155$	16.4495	−	12.6322i	1.32126	−	1.01464i
$156$	−5.78918	−	5.99441i	−0.463505	−	0.479937i
$157$			2.85663i			0.227984i	0.993482	+	0.113992i	$0.0363639\pi$
$157$			2.85663i			0.227984i	−0.993482	+	0.113992i	$0.963636\pi$
$158$	−0.0998754	+	0.0403545i	−0.00794566	+	0.00321043i
$159$	−8.59811			−0.681875
$160$	6.79123	−	10.6714i	0.536894	−	0.843650i
$161$	12.9519			1.02075
$162$	−1.88228	+	0.760531i	−0.147886	+	0.0597530i
$163$		−	4.98714i		−	0.390623i	−0.980741	−	0.195311i	$-0.937428\pi$
$163$		−	4.98714i		−	0.390623i	0.980741	−	0.195311i	$-0.0625718\pi$
$164$	11.6367	+	12.0492i	0.908672	+	0.940885i
$165$	−2.14760	−	0.281896i	−0.167190	−	0.0219455i
$166$	3.59078	+	8.88701i	0.278699	+	0.689766i
$167$	11.5108	+	11.5108i	0.890732	+	0.890732i	0.994592	−	0.103860i	$-0.0331194\pi$
$167$	11.5108	+	11.5108i	0.890732	+	0.890732i	−0.103860	+	0.994592i	$0.533119\pi$
$168$	4.91942	+	12.8133i	0.379542	+	0.988570i
$169$	5.50299			0.423307
$170$	2.23281	+	8.61927i	0.171249	+	0.661068i
$171$	−0.774200	−	0.774200i	−0.0592045	−	0.0592045i
$172$	−8.12625	+	7.84803i	−0.619621	+	0.598407i
$173$	22.3069			1.69597			0.847983	−	0.530024i	$-0.177817\pi$
$173$	22.3069			1.69597			0.847983	+	0.530024i	$0.177817\pi$
$174$	−0.676852	−	0.287291i	−0.0513120	−	0.0217795i
$175$	21.6823	−	12.5405i	1.63903	−	0.947976i
$176$	−2.92521	+	2.72822i	−0.220496	+	0.205647i
$177$	7.50532	+	7.50532i	0.564134	+	0.564134i
$178$	−2.99084	+	1.20845i	−0.224173	+	0.0905768i
$179$	−2.65733	−	2.65733i	−0.198618	−	0.198618i	0.600789	−	0.799407i	$-0.294853\pi$
$179$	−2.65733	−	2.65733i	−0.198618	−	0.198618i	−0.799407	+	0.600789i	$0.794853\pi$
$180$	−9.11938	−	1.35895i	−0.679718	−	0.101290i
$181$	−14.6139	+	14.6139i	−1.08624	+	1.08624i	−0.0903306	+	0.995912i	$0.528792\pi$
$181$	−14.6139	+	14.6139i	−1.08624	+	1.08624i	−0.995912	+	0.0903306i	$0.971208\pi$
$182$	−28.0520	−	11.9067i	−2.07935	−	0.882584i
$183$	4.29858	−	4.29858i	0.317761	−	0.317761i
$184$	−2.62105	−	6.82689i	−0.193226	−	0.503285i
$185$	−9.46782	−	12.3289i	−0.696088	−	0.906436i
$186$	11.7811	−	4.76012i	0.863829	−	0.349029i
$187$		−	2.81562i		−	0.205899i
$188$	0.345985	−	19.8651i	0.0252335	−	1.44881i
$189$	17.3682	−	17.3682i	1.26335	−	1.26335i
$190$	−0.421140	−	1.62572i	−0.0305527	−	0.117942i
$191$		−	12.7138i		−	0.919941i	−0.887934	−	0.459970i	$-0.847860\pi$
$191$		−	12.7138i		−	0.919941i	0.887934	−	0.459970i	$-0.152140\pi$
$192$	5.75832	−	5.18601i	0.415571	−	0.374268i
$193$	10.2753	−	10.2753i	0.739633	−	0.739633i	−0.232874	−	0.972507i	$-0.574813\pi$
$193$	10.2753	−	10.2753i	0.739633	−	0.739633i	0.972507	+	0.232874i	$0.0748129\pi$
$194$	11.7838	+	5.00164i	0.846025	+	0.359097i
$195$	−7.38961	+	5.67477i	−0.529181	+	0.406379i
$196$	25.1413	+	26.0326i	1.79581	+	1.85947i
$197$	−8.59048			−0.612046			−0.306023	−	0.952024i	$-0.598998\pi$
$197$	−8.59048			−0.612046			−0.306023	+	0.952024i	$0.598998\pi$
$198$	2.68389	+	1.13918i	0.190736	+	0.0809581i
$199$		−	14.3479i		−	1.01709i	−0.861034	−	0.508547i	$-0.830183\pi$
$199$		−	14.3479i		−	1.01709i	0.861034	−	0.508547i	$-0.169817\pi$
$200$	−10.9979	−	8.89084i	−0.777666	−	0.628677i
$201$		−	11.4630i		−	0.808539i
$202$	−1.00999	+	2.37952i	−0.0710629	+	0.167423i
$203$	−2.68887			−0.188721
$204$	−0.0949908	+	5.45401i	−0.00665069	+	0.381857i
$205$	14.8537	−	11.4067i	1.03743	−	0.796679i
$206$	10.9810	−	25.8709i	0.765080	−	1.80251i
$207$	−3.76912	+	3.76912i	−0.261972	+	0.261972i
$208$	−0.599163	+	17.1956i	−0.0415445	+	1.19230i
$209$			0.531066i			0.0367346i
$210$	14.8549	−	3.84815i	1.02509	−	0.265548i
$211$	4.90551	−	4.90551i	0.337709	−	0.337709i	−0.517795	−	0.855505i	$-0.673247\pi$
$211$	4.90551	−	4.90551i	0.337709	−	0.337709i	0.855505	+	0.517795i	$0.173247\pi$
$212$	12.3323	+	12.7695i	0.846987	+	0.877013i
$213$		−	7.67146i		−	0.525640i
$214$	1.85680	+	4.59550i	0.126929	+	0.314142i
$215$	7.69294	+	10.0176i	0.524654	+	0.683198i
$216$	−12.6694	−	5.63993i	−0.862047	−	0.383748i
$217$	32.8558	−	32.8558i	2.23040	−	2.23040i
$218$	0.942806	−	2.22123i	0.0638549	−	0.150441i
$219$	−4.76195	+	4.76195i	−0.321783	+	0.321783i
$220$	2.66165	+	3.59383i	0.179448	+	0.242296i
$221$	−8.56407	−	8.56407i	−0.576082	−	0.576082i
$222$	−3.56770	−	8.82988i	−0.239448	−	0.592623i
$223$	15.5434	+	15.5434i	1.04086	+	1.04086i	0.999129	+	0.0417323i	$0.0132877\pi$
$223$	15.5434	+	15.5434i	1.04086	+	1.04086i	0.0417323	+	0.999129i	$0.486712\pi$
$224$	11.9738	−	25.6843i	0.800032	−	1.71610i
$225$	−2.66033	+	9.95916i	−0.177356	+	0.663944i
$226$	4.01826	−	9.46693i	0.267291	−	0.629731i
$227$	−1.98420			−0.131696			−0.0658481	−	0.997830i	$-0.520975\pi$
$227$	−1.98420			−0.131696			−0.0658481	+	0.997830i	$0.520975\pi$
$228$	0.0179166	−	1.02870i	0.00118656	−	0.0681275i
$229$	−0.822989	−	0.822989i	−0.0543846	−	0.0543846i	0.679391	−	0.733776i	$-0.262244\pi$
$229$	−0.822989	−	0.822989i	−0.0543846	−	0.0543846i	−0.733776	+	0.679391i	$0.762244\pi$
$230$	−7.91465	+	2.05028i	−0.521877	+	0.135191i
$231$	−4.85260			−0.319278
$232$	0.544140	+	1.41729i	0.0357246	+	0.0930497i
$233$	−1.04122	−	1.04122i	−0.0682126	−	0.0682126i	0.672177	−	0.740390i	$-0.265359\pi$
$233$	−1.04122	−	1.04122i	−0.0682126	−	0.0682126i	−0.740390	+	0.672177i	$0.765359\pi$
$234$	11.6283	−	4.69842i	0.760169	−	0.307145i
$235$	−22.0243	−	2.89093i	−1.43671	−	0.188584i
$236$	0.381625	−	21.9114i	0.0248417	−	1.42631i
$237$			0.0737833i			0.00479274i
$238$	7.47279	+	18.4948i	0.484389	+	1.19884i
$239$	−8.71593			−0.563786			−0.281893	−	0.959446i	$-0.590962\pi$
$239$	−8.71593			−0.563786			−0.281893	+	0.959446i	$0.590962\pi$
$240$	−5.03451	−	7.05124i	−0.324976	−	0.455155i
$241$	22.3635			1.44056			0.720279	−	0.693685i	$-0.244014\pi$
$241$	22.3635			1.44056			0.720279	+	0.693685i	$0.244014\pi$
$242$	−0.529799	−	1.31123i	−0.0340568	−	0.0842888i
$243$			16.0999i			1.03281i
$244$	−12.5495	−	0.218571i	−0.803401	−	0.0139926i
$245$	32.0917	−	24.6445i	2.05026	−	1.57448i
$246$	10.6381	−	4.29832i	0.678262	−	0.274051i
$247$	1.61530	+	1.61530i	0.102779	+	0.102779i
$248$	−23.9671	−	10.6692i	−1.52191	−	0.677494i
$249$	6.56531			0.416060
$250$	−11.2645	+	11.0956i	−0.712427	+	0.701746i
$251$	−2.92039	−	2.92039i	−0.184333	−	0.184333i	0.608908	−	0.793241i	$-0.291608\pi$
$251$	−2.92039	−	2.92039i	−0.184333	−	0.184333i	−0.793241	+	0.608908i	$0.791608\pi$
$252$	−20.6529	−	0.359706i	−1.30101	−	0.0226593i
$253$	2.58545			0.162546
$254$	1.97000	−	4.64127i	0.123609	−	0.291219i
$255$	6.04682	+	0.793711i	0.378667	+	0.0497041i
$256$	−15.9612	−	1.11366i	−0.997575	−	0.0696035i
$257$	20.8635	+	20.8635i	1.30143	+	1.30143i	0.927429	+	0.374000i	$0.122014\pi$
$257$	20.8635	+	20.8635i	1.30143	+	1.30143i	0.374000	+	0.927429i	$0.377986\pi$
$258$	2.89888	+	7.17459i	0.180477	+	0.446670i
$259$	−24.6253	−	24.6253i	−1.53014	−	1.53014i
$260$	19.0268	+	2.83535i	1.17999	+	0.175841i
$261$	0.782485	−	0.782485i	0.0484346	−	0.0484346i
$262$	8.06611	−	19.0036i	0.498326	−	1.17405i
$263$	−18.0331	+	18.0331i	−1.11197	+	1.11197i	−0.119087	+	0.992884i	$0.537997\pi$
$263$	−18.0331	+	18.0331i	−1.11197	+	1.11197i	−0.992884	+	0.119087i	$0.962003\pi$
$264$	0.982011	+	2.55779i	0.0604386	+	0.157421i
$265$	15.7416	−	12.0886i	0.967000	−	0.742597i
$266$	−1.40947	−	3.48838i	−0.0864203	−	0.213886i
$267$			2.20950i			0.135219i
$268$	−17.0243	+	16.4415i	−1.03993	+	1.00432i
$269$	−14.2539	+	14.2539i	−0.869078	+	0.869078i	−0.992370	−	0.123293i	$-0.960655\pi$
$269$	−14.2539	+	14.2539i	−0.869078	+	0.869078i	0.123293	+	0.992370i	$0.460655\pi$
$270$	−7.86397	+	13.3627i	−0.478586	+	0.813230i
$271$			26.0562i			1.58280i	0.611298	+	0.791401i	$0.290648\pi$
$271$			26.0562i			1.58280i	−0.611298	+	0.791401i	$0.709352\pi$
$272$	8.23627	−	7.68163i	0.499397	−	0.465767i
$273$	−14.7598	+	14.7598i	−0.893304	+	0.893304i
$274$	−2.84237	+	6.69656i	−0.171714	+	0.404554i
$275$	4.32820	−	2.50333i	0.261000	−	0.150957i
$276$	−5.00815	−	0.0872254i	−0.301455	−	0.00525035i
$277$	−16.6064			−0.997783			−0.498891	−	0.866665i	$-0.666259\pi$
$277$	−16.6064			−0.997783			−0.498891	+	0.866665i	$0.666259\pi$
$278$	6.06141	−	14.2805i	0.363539	−	0.856490i
$279$			19.1227i			1.14485i
$280$	−27.0216	−	16.5424i	−1.61485	−	0.988598i
$281$			22.9574i			1.36953i	0.728766	+	0.684763i	$0.240094\pi$
$281$			22.9574i			1.36953i	−0.728766	+	0.684763i	$0.759906\pi$
$282$	−12.5271	−	5.31713i	−0.745975	−	0.316631i
$283$	−9.30787			−0.553295			−0.276648	−	0.960971i	$-0.589223\pi$
$283$	−9.30787			−0.553295			−0.276648	+	0.960971i	$0.589223\pi$
$284$	−11.3933	+	11.0032i	−0.676067	+	0.652920i
$285$	−1.14052	−	0.149705i	−0.0675583	−	0.00886776i
$286$	−5.59971	−	2.37681i	−0.331118	−	0.140544i
$287$	29.6683	−	29.6683i	1.75127	−	1.75127i
$288$	3.98989	+	10.9589i	0.235106	+	0.645757i
$289$		−	9.07228i		−	0.533663i
$290$	1.64311	−	0.425647i	0.0964870	−	0.0249948i
$291$	6.20014	−	6.20014i	0.363459	−	0.363459i
$292$	13.9023	+	0.242132i	0.813571	+	0.0141697i
$293$		−	5.40172i		−	0.315572i	−0.987473	−	0.157786i	$-0.949564\pi$
$293$		−	5.40172i		−	0.315572i	0.987473	−	0.157786i	$-0.0504356\pi$
$294$	22.9839	−	9.28662i	1.34045	−	0.541607i
$295$	−24.2931	−	3.18873i	−1.41440	−	0.185655i
$296$	−7.99654	+	17.9633i	−0.464789	+	1.04410i
$297$	3.46702	−	3.46702i	0.201177	−	0.201177i
$298$	12.5392	+	5.32230i	0.726377	+	0.308312i
$299$	7.86396	−	7.86396i	0.454785	−	0.454785i
$300$	−8.46841	+	4.70307i	−0.488924	+	0.271532i
$301$	20.0090	+	20.0090i	1.15330	+	1.15330i
$302$	21.1070	−	8.52825i	1.21457	−	0.490746i
$303$	1.25201	+	1.25201i	0.0719260	+	0.0719260i
$304$	−1.55348	+	1.44886i	−0.0890980	+	0.0830980i
$305$	−1.82631	+	13.9136i	−0.104574	+	0.796689i
$306$	−7.55681	−	3.20750i	−0.431994	−	0.183361i
$307$	−29.9151			−1.70735			−0.853673	−	0.520809i	$-0.825630\pi$
$307$	−29.9151			−1.70735			−0.853673	+	0.520809i	$0.825630\pi$
$308$	6.96011	+	7.20685i	0.396589	+	0.410648i
$309$	−13.6122	−	13.6122i	−0.774373	−	0.774373i
$310$	−14.8765	+	25.2786i	−0.844927	+	1.43573i
$311$	27.6784			1.56950			0.784749	−	0.619813i	$-0.212792\pi$
$311$	27.6784			1.56950			0.784749	+	0.619813i	$0.212792\pi$
$312$	10.7667	+	4.79292i	0.609547	+	0.271346i
$313$	−5.65587	−	5.65587i	−0.319689	−	0.319689i	0.528959	−	0.848647i	$-0.322583\pi$
$313$	−5.65587	−	5.65587i	−0.319689	−	0.319689i	−0.848647	+	0.528959i	$0.822583\pi$
$314$	−1.51344	−	3.74569i	−0.0854085	−	0.211382i
$315$	−3.00558	+	22.8977i	−0.169345	+	1.29014i
$316$	0.109579	−	0.105828i	0.00616432	−	0.00595328i
$317$			12.2258i			0.686670i	0.939213	+	0.343335i	$0.111557\pi$
$317$			12.2258i			0.686670i	−0.939213	+	0.343335i	$0.888443\pi$
$318$	11.2741	−	4.55527i	0.632218	−	0.255447i
$319$	−0.536749			−0.0300522
$320$	−3.25113	+	17.5906i	−0.181744	+	0.983346i
$321$	3.39494			0.189487
$322$	−16.9828	+	6.86189i	−0.946417	+	0.382398i
$323$		−	1.49528i		−	0.0831996i
$324$	2.06516	−	1.99446i	0.114731	−	0.110803i
$325$	5.55057	−	20.7790i	0.307890	−	1.15261i
$326$	2.64218	+	6.53927i	0.146337	+	0.362176i
$327$	−1.16872	−	1.16872i	−0.0646304	−	0.0646304i
$328$	−21.6420	−	9.63413i	−1.19498	−	0.531956i
$329$	−49.7651			−2.74364
$330$	2.96533	−	0.768166i	0.163236	−	0.0422861i
$331$	−3.19094	−	3.19094i	−0.175390	−	0.175390i	0.613953	−	0.789343i	$-0.289578\pi$
$331$	−3.19094	−	3.19094i	−0.175390	−	0.175390i	−0.789343	+	0.613953i	$0.789578\pi$
$332$	−9.41665	−	9.75048i	−0.516806	−	0.535127i
$333$	14.3324			0.785412
$334$	−21.1917	−	8.99484i	−1.15956	−	0.492176i
$335$	16.1165	+	20.9867i	0.880540	+	1.14663i
$336$	−13.2390	−	14.1949i	−0.722244	−	0.774393i
$337$	−2.20238	−	2.20238i	−0.119971	−	0.119971i	0.644572	−	0.764543i	$-0.277035\pi$
$337$	−2.20238	−	2.20238i	−0.119971	−	0.119971i	−0.764543	+	0.644572i	$0.777035\pi$
$338$	−7.21566	+	2.91548i	−0.392480	+	0.158581i
$339$	−4.98112	−	4.98112i	−0.270537	−	0.270537i
$340$	−7.49420	−	10.1189i	−0.406430	−	0.548773i
$341$	6.55865	−	6.55865i	0.355171	−	0.355171i
$342$	1.42532	+	0.604980i	0.0770725	+	0.0327136i
$343$	39.3032	−	39.3032i	2.12217	−	2.12217i
$344$	6.49747	−	14.5958i	0.350320	−	0.786954i
$345$	−0.728826	+	5.55250i	−0.0392387	+	0.298936i
$346$	−29.2494	+	11.8182i	−1.57246	+	0.635350i
$347$			13.2278i			0.710104i	0.934847	+	0.355052i	$0.115537\pi$
$347$			13.2278i			0.710104i	−0.934847	+	0.355052i	$0.884463\pi$
$348$	1.03971	+	0.0181084i	0.0557344	+	0.000970710i
$349$	0.412836	−	0.412836i	0.0220986	−	0.0220986i	−0.695971	−	0.718070i	$-0.745026\pi$
$349$	0.412836	−	0.412836i	0.0220986	−	0.0220986i	0.718070	+	0.695971i	$0.245026\pi$
$350$	−21.7864	+	27.9307i	−1.16453	+	1.49296i
$351$		−	21.0908i		−	1.12574i
$352$	2.39020	−	5.12708i	0.127398	−	0.273274i
$353$	−15.6419	+	15.6419i	−0.832533	+	0.832533i	−0.987863	−	0.155330i	$-0.950356\pi$
$353$	−15.6419	+	15.6419i	−0.832533	+	0.832533i	0.155330	+	0.987863i	$0.450356\pi$
$354$	−13.8175	−	5.86486i	−0.734391	−	0.311714i
$355$	10.7858	+	14.0451i	0.572449	+	0.745435i
$356$	3.28144	−	3.16909i	0.173916	−	0.167961i
$357$	13.6631			0.723127
$358$	4.89221	+	2.07651i	0.258561	+	0.109747i
$359$			12.9290i			0.682368i	0.939996	+	0.341184i	$0.110828\pi$
$359$			12.9290i			0.682368i	−0.939996	+	0.341184i	$0.889172\pi$
$360$	12.6775	−	3.04954i	0.668165	−	0.160725i
$361$		−	18.7180i		−	0.985156i
$362$	11.4197	−	26.9045i	0.600206	−	1.41407i
$363$	−0.968673			−0.0508422
$364$	43.0906	+	0.750496i	2.25856	+	0.0393367i
$365$	2.02318	−	15.4134i	0.105898	−	0.806774i
$366$	−3.35903	+	7.91380i	−0.175579	+	0.413661i
$367$	11.0937	−	11.0937i	0.579084	−	0.579084i	−0.355567	−	0.934651i	$-0.615712\pi$
$367$	11.0937	−	11.0937i	0.579084	−	0.579084i	0.934651	+	0.355567i	$0.115712\pi$
$368$	7.05366	+	7.56296i	0.367697	+	0.394247i
$369$			17.2675i			0.898911i
$370$	18.9463	+	11.1499i	0.984969	+	0.579655i
$371$	31.4419	−	31.4419i	1.63238	−	1.63238i
$372$	−12.9257	+	12.4832i	−0.670167	+	0.647222i
$373$			14.9930i			0.776306i	0.921595	+	0.388153i	$0.126887\pi$
$373$			14.9930i			0.776306i	−0.921595	+	0.388153i	$0.873113\pi$
$374$	1.49171	+	3.69191i	0.0771346	+	0.190904i
$375$	4.15605	+	10.0009i	0.214618	+	0.516445i
$376$	10.0709	+	26.2310i	0.519365	+	1.35276i
$377$	−1.63259	+	1.63259i	−0.0840828	+	0.0840828i
$378$	−13.5719	+	31.9752i	−0.698066	+	1.64463i
$379$	−3.25104	+	3.25104i	−0.166995	+	0.166995i	−0.785657	−	0.618662i	$-0.787675\pi$
$379$	−3.25104	+	3.25104i	−0.166995	+	0.166995i	0.618662	+	0.785657i	$0.287675\pi$
$380$	1.41351	+	1.90856i	0.0725116	+	0.0979071i
$381$	−2.44205	−	2.44205i	−0.125110	−	0.125110i
$382$	6.73578	+	16.6707i	0.344632	+	0.852948i
$383$	−1.98197	−	1.98197i	−0.101274	−	0.101274i	0.654654	−	0.755928i	$-0.272814\pi$
$383$	−1.98197	−	1.98197i	−0.101274	−	0.101274i	−0.755928	+	0.654654i	$0.772814\pi$
$384$	−4.80291	+	9.85079i	−0.245098	+	0.502696i
$385$	8.88425	−	6.82256i	0.452783	−	0.347710i
$386$	−8.02941	+	18.9171i	−0.408686	+	0.962855i
$387$	−11.6456			−0.591979
$388$	−18.1010	−	0.315260i	−0.918941	−	0.0160049i
$389$	−9.95105	−	9.95105i	−0.504538	−	0.504538i	0.408307	−	0.912845i	$-0.366119\pi$
$389$	−9.95105	−	9.95105i	−0.504538	−	0.504538i	−0.912845	+	0.408307i	$0.866119\pi$
$390$	6.68296	−	11.3559i	0.338405	−	0.575029i
$391$	−7.27964			−0.368147
$392$	−46.7580	−	20.8148i	−2.36163	−	1.05130i
$393$	−9.99892	−	9.99892i	−0.504379	−	0.504379i
$394$	11.2641	−	4.55122i	0.567475	−	0.229287i
$395$	−0.103736	−	0.135084i	−0.00521954	−	0.00679682i
$396$	−4.12272	−	0.0718042i	−0.207174	−	0.00360830i
$397$		−	30.9856i		−	1.55513i	−0.628806	−	0.777563i	$-0.716456\pi$
$397$		−	30.9856i		−	1.55513i	0.628806	−	0.777563i	$-0.283544\pi$
$398$	7.60149	+	18.8133i	0.381028	+	0.943026i
$399$	−2.57705			−0.129014
$400$	19.1310	+	5.83124i	0.956552	+	0.291562i
$401$	−13.1510			−0.656730			−0.328365	−	0.944551i	$-0.606498\pi$
$401$	−13.1510			−0.656730			−0.328365	+	0.944551i	$0.606498\pi$
$402$	6.07309	+	15.0306i	0.302898	+	0.749658i
$403$		−	39.8979i		−	1.98746i
$404$	0.0636613	−	3.65518i	0.00316727	−	0.181852i
$405$	−1.95504	−	2.54583i	−0.0971468	−	0.126503i
$406$	3.52571	−	1.42456i	0.174978	−	0.0706996i
$407$	−4.91569	−	4.91569i	−0.243662	−	0.243662i
$408$	−2.76497	−	7.20176i	−0.136886	−	0.356540i
$409$	−27.4765			−1.35862			−0.679312	−	0.733850i	$-0.737721\pi$
$409$	−27.4765			−1.35862			−0.679312	+	0.733850i	$0.737721\pi$
$410$	−13.4333	+	22.8262i	−0.663421	+	1.12731i
$411$	3.52346	+	3.52346i	0.173799	+	0.173799i
$412$	−0.692145	+	39.7403i	−0.0340996	+	1.95786i
$413$	−54.8914			−2.70103
$414$	2.94529	−	6.93905i	0.144753	−	0.341035i
$415$	−12.0199	+	9.23056i	−0.590034	+	0.453110i
$416$	−8.32457	−	22.8648i	−0.408146	−	1.12104i
$417$	−7.51385	−	7.51385i	−0.367955	−	0.367955i
$418$	−0.281358	−	0.696347i	−0.0137617	−	0.0340595i
$419$	2.35053	+	2.35053i	0.114831	+	0.114831i	0.762187	−	0.647356i	$-0.224125\pi$
$419$	2.35053	+	2.35053i	0.114831	+	0.114831i	−0.647356	+	0.762187i	$0.724125\pi$
$420$	−17.4394	+	12.9159i	−0.850957	+	0.630233i
$421$	−22.4056	+	22.4056i	−1.09198	+	1.09198i	−0.0966640	+	0.995317i	$0.530817\pi$
$421$	−22.4056	+	22.4056i	−1.09198	+	1.09198i	−0.995317	+	0.0966640i	$0.969183\pi$
$422$	−3.83330	+	9.03116i	−0.186602	+	0.439630i
$423$	14.4821	−	14.4821i	0.704144	−	0.704144i
$424$	−22.9357	−	10.2101i	−1.11386	−	0.495844i
$425$	−12.1866	+	7.04844i	−0.591136	+	0.341899i
$426$	4.06433	+	10.0590i	0.196918	+	0.487361i
$427$			31.4384i			1.52141i
$428$	−4.86938	−	5.04200i	−0.235370	−	0.243714i
$429$	−2.94634	+	2.94634i	−0.142251	+	0.142251i
$430$	−15.3945	−	9.05968i	−0.742389	−	0.436897i
$431$		−	11.5082i		−	0.554330i	−0.960822	−	0.277165i	$-0.910605\pi$
$431$		−	11.5082i		−	0.554330i	0.960822	−	0.277165i	$-0.0893948\pi$
$432$	19.6005	+	0.682960i	0.943031	+	0.0328589i
$433$	12.3465	−	12.3465i	0.593336	−	0.593336i	−0.345195	−	0.938531i	$-0.612187\pi$
$433$	12.3465	−	12.3465i	0.593336	−	0.593336i	0.938531	+	0.345195i	$0.112187\pi$
$434$	−25.6744	+	60.4883i	−1.23241	+	2.90353i
$435$	0.151307	−	1.15272i	0.00725463	−	0.0552688i
$436$	−0.0594263	+	3.41203i	−0.00284600	+	0.163407i
$437$	1.37304			0.0656815
$438$	3.72112	−	8.76687i	0.177802	−	0.418897i
$439$			10.0389i			0.479133i	0.970880	+	0.239566i	$0.0770053\pi$
$439$			10.0389i			0.479133i	−0.970880	+	0.239566i	$0.922995\pi$
$440$	−5.39403	−	3.30218i	−0.257150	−	0.157425i
$441$			37.3069i			1.77652i
$442$	15.7667	+	6.69219i	0.749944	+	0.318315i
$443$	4.71195			0.223871			0.111936	−	0.993715i	$-0.464295\pi$
$443$	4.71195			0.223871			0.111936	+	0.993715i	$0.464295\pi$
$444$	9.35612	+	9.68780i	0.444022	+	0.459763i
$445$	−3.10646	−	4.04519i	−0.147260	−	0.191761i
$446$	−28.6157	−	12.1460i	−1.35499	−	0.575130i
$447$	6.59763	−	6.59763i	0.312057	−	0.312057i
$448$	−2.09283	+	40.0216i	−0.0988768	+	1.89084i
$449$		−	19.8615i		−	0.937322i	−0.883378	−	0.468661i	$-0.844737\pi$
$449$		−	19.8615i		−	0.937322i	0.883378	−	0.468661i	$-0.155263\pi$
$450$	−1.78806	−	14.4682i	−0.0842898	−	0.682035i
$451$	5.92237	−	5.92237i	0.278873	−	0.278873i
$452$	−0.253276	+	14.5422i	−0.0119131	+	0.684005i
$453$		−	15.5929i		−	0.732617i
$454$	2.60174	−	1.05123i	0.122106	−	0.0493366i
$455$	6.27089	−	47.7743i	0.293984	−	2.23969i
$456$	0.521513	+	1.35835i	0.0244221	+	0.0636107i
$457$	9.98488	−	9.98488i	0.467073	−	0.467073i	−0.433892	−	0.900965i	$-0.642860\pi$
$457$	9.98488	−	9.98488i	0.467073	−	0.467073i	0.900965	+	0.433892i	$0.142860\pi$
$458$	1.51514	+	0.643105i	0.0707980	+	0.0300503i
$459$	−9.76181	+	9.76181i	−0.455642	+	0.455642i
$460$	9.29166	−	6.88155i	0.433226	−	0.320854i
$461$	−15.9385	−	15.9385i	−0.742328	−	0.742328i	0.230697	−	0.973026i	$-0.425899\pi$
$461$	−15.9385	−	15.9385i	−0.742328	−	0.742328i	−0.973026	+	0.230697i	$0.925899\pi$
$462$	6.36286	−	2.57090i	0.296027	−	0.119609i
$463$	6.09074	+	6.09074i	0.283061	+	0.283061i	0.834328	−	0.551268i	$-0.185856\pi$
$463$	6.09074	+	6.09074i	0.283061	+	0.283061i	−0.551268	+	0.834328i	$0.685856\pi$
$464$	−1.46437	−	1.57010i	−0.0679816	−	0.0728902i
$465$	12.2365	+	15.9342i	0.567453	+	0.738930i
$466$	1.91691	+	0.813637i	0.0887992	+	0.0376910i
$467$	−4.10332			−0.189879			−0.0949394	−	0.995483i	$-0.530266\pi$
$467$	−4.10332			−0.189879			−0.0949394	+	0.995483i	$0.530266\pi$
$468$	−12.7582	+	12.3214i	−0.589747	+	0.569556i
$469$	41.9184	+	41.9184i	1.93561	+	1.93561i
$470$	30.4105	−	7.87780i	1.40273	−	0.363376i
$471$	−2.76715			−0.127503
$472$	11.1083	+	28.9330i	0.511299	+	1.33175i
$473$	3.99418	+	3.99418i	0.183652	+	0.183652i
$474$	−0.0390903	−	0.0967466i	−0.00179548	−	0.00444372i
$475$	2.29856	−	1.32943i	0.105465	−	0.0609986i
$476$	−19.5970	−	20.2918i	−0.898228	−	0.930071i
$477$			18.2998i			0.837889i
$478$	11.4285	−	4.61769i	0.522730	−	0.211208i
$479$	1.42277			0.0650081			0.0325041	−	0.999472i	$-0.489652\pi$
$479$	1.42277			0.0650081			0.0325041	+	0.999472i	$0.489652\pi$
$480$	10.3371	+	6.57848i	0.471823	+	0.300265i
$481$	−29.9034			−1.36348
$482$	−29.3236	+	11.8481i	−1.33565	+	0.539668i
$483$			12.5461i			0.570869i
$484$	1.38937	+	1.43863i	0.0631533	+	0.0653921i
$485$	−2.63421	+	20.0685i	−0.119613	+	0.911263i
$486$	−8.52969	−	21.1105i	−0.386914	−	0.957594i
$487$	−19.9637	−	19.9637i	−0.904639	−	0.904639i	0.0911938	−	0.995833i	$-0.470932\pi$
$487$	−19.9637	−	19.9637i	−0.904639	−	0.904639i	−0.995833	+	0.0911938i	$0.970932\pi$
$488$	16.5711	−	6.36213i	0.750137	−	0.288000i
$489$	4.83091			0.218461
$490$	−29.0229	+	49.3166i	−1.31112	+	2.22790i
$491$	3.53662	+	3.53662i	0.159605	+	0.159605i	0.782392	−	0.622786i	$-0.213999\pi$
$491$	3.53662	+	3.53662i	0.159605	+	0.159605i	−0.622786	+	0.782392i	$0.713999\pi$
$492$	−11.6717	+	11.2721i	−0.526203	+	0.508187i
$493$	1.51128			0.0680648
$494$	−2.97381	−	1.26224i	−0.133798	−	0.0567910i
$495$	−0.599971	+	4.57083i	−0.0269667	+	0.205444i
$496$	37.0788	+	1.29197i	1.66489	+	0.0580113i
$497$	28.0533	+	28.0533i	1.25836	+	1.25836i
$498$	−8.60861	+	3.47829i	−0.385761	+	0.155866i
$499$	12.5398	+	12.5398i	0.561359	+	0.561359i	0.929693	−	0.368335i	$-0.120072\pi$
$499$	12.5398	+	12.5398i	0.561359	+	0.561359i	−0.368335	+	0.929693i	$0.620072\pi$
$500$	8.89183	−	20.5167i	0.397655	−	0.917535i
$501$	−11.1502	+	11.1502i	−0.498154	+	0.498154i
$502$	5.37650	+	2.28207i	0.239965	+	0.101854i
$503$	−8.91290	+	8.91290i	−0.397407	+	0.397407i	−0.877317	−	0.479911i	$-0.840669\pi$
$503$	−8.91290	+	8.91290i	−0.397407	+	0.397407i	0.479911	+	0.877317i	$0.340669\pi$
$504$	27.2712	−	10.4702i	1.21476	−	0.466381i
$505$	−4.05248	−	0.531932i	−0.180333	−	0.0236707i
$506$	−3.39010	+	1.36977i	−0.150708	+	0.0608935i
$507$			5.33060i			0.236740i
$508$	−0.124172	+	7.12946i	−0.00550923	+	0.316318i
$509$	1.13747	−	1.13747i	0.0504177	−	0.0504177i	−0.681448	−	0.731866i	$-0.738650\pi$
$509$	1.13747	−	1.13747i	0.0504177	−	0.0504177i	0.731866	+	0.681448i	$0.238650\pi$
$510$	−8.34925	+	2.16286i	−0.369711	+	0.0957732i
$511$		−	34.8273i		−	1.54067i
$512$	21.5187	−	6.99597i	0.951003	−	0.309181i
$513$	1.84122	−	1.84122i	0.0812916	−	0.0812916i
$514$	−38.4102	−	16.3033i	−1.69420	−	0.719108i
$515$	44.0598	+	5.78333i	1.94151	+	0.254844i
$516$	−7.60218	−	7.87168i	−0.334667	−	0.346532i
$517$	−9.93406			−0.436900
$518$	45.3359	+	19.2429i	1.99194	+	0.845485i
$519$			21.6081i			0.948492i
$520$	−26.4506	+	6.36262i	−1.15994	+	0.279019i
$521$			26.7296i			1.17105i	0.810656	+	0.585523i	$0.199111\pi$
$521$			26.7296i			1.17105i	−0.810656	+	0.585523i	$0.800889\pi$
$522$	−0.611455	+	1.44058i	−0.0267627	+	0.0630523i
$523$	−32.5929			−1.42519			−0.712595	−	0.701576i	$-0.752480\pi$
$523$	−32.5929			−1.42519			−0.712595	+	0.701576i	$0.752480\pi$
$524$	−0.508418	+	29.1914i	−0.0222103	+	1.27523i
$525$	12.1477	+	21.0030i	0.530168	+	0.916648i
$526$	14.0916	−	33.1994i	0.614422	−	1.44756i
$527$	−18.4667	+	18.4667i	−0.804420	+	0.804420i
$528$	−2.64275	−	2.83357i	−0.115011	−	0.123315i
$529$			16.3155i			0.709368i
$530$	−14.2363	+	24.1908i	−0.618385	+	1.05078i
$531$	15.9739	−	15.9739i	0.693209	−	0.693209i
$532$	3.69628	+	3.82731i	0.160254	+	0.165935i
$533$		−	36.0273i		−	1.56051i
$534$	−1.17059	−	2.89715i	−0.0506563	−	0.125372i
$535$	−6.21553	+	4.77315i	−0.268721	+	0.206361i
$536$	13.6121	−	30.5779i	0.587951	−	1.32077i
$537$	2.57408	−	2.57408i	0.111080	−	0.111080i
$538$	11.1384	−	26.2418i	0.480211	−	1.13137i
$539$	12.7954	−	12.7954i	0.551138	−	0.551138i
$540$	3.23189	−	21.6879i	0.139078	−	0.933298i
$541$	1.80463	+	1.80463i	0.0775871	+	0.0775871i	0.744835	−	0.667248i	$-0.232528\pi$
$541$	1.80463	+	1.80463i	0.0775871	+	0.0775871i	−0.667248	+	0.744835i	$0.732528\pi$
$542$	−13.8045	−	34.1656i	−0.592956	−	1.46754i
$543$	−14.1561	−	14.1561i	−0.607496	−	0.607496i
$544$	−6.72989	+	14.4359i	−0.288542	+	0.618935i
$545$	3.78290	+	0.496546i	0.162041	+	0.0212697i
$546$	11.5337	−	27.1732i	0.493597	−	1.16290i
$547$	−2.96479			−0.126765			−0.0633827	−	0.997989i	$-0.520189\pi$
$547$	−2.96479			−0.126765			−0.0633827	+	0.997989i	$0.520189\pi$
$548$	0.179158	−	10.2866i	0.00765327	−	0.439421i
$549$	−9.14888	−	9.14888i	−0.390465	−	0.390465i
$550$	−4.34899	+	5.57551i	−0.185441	+	0.237741i
$551$	−0.285049			−0.0121435
$552$	6.61302	−	2.53894i	0.281469	−	0.108064i
$553$	−0.269813	−	0.269813i	−0.0114736	−	0.0114736i
$554$	21.7748	−	8.79806i	0.925121	−	0.373794i
$555$	11.9426	−	9.17122i	0.506937	−	0.389297i
$556$	−0.382059	+	21.9363i	−0.0162029	+	0.930308i
$557$		−	36.2460i		−	1.53579i	−0.640574	−	0.767897i	$-0.721303\pi$
$557$		−	36.2460i		−	1.53579i	0.640574	−	0.767897i	$-0.278697\pi$
$558$	−10.1312	−	25.0742i	−0.428887	−	1.06147i
$559$	24.2976			1.02768
$560$	44.1956	+	7.37483i	1.86760	+	0.311643i
$561$	2.72742			0.115152
$562$	−12.1628	−	30.1024i	−0.513058	−	1.26979i
$563$		−	29.5787i		−	1.24659i	−0.781986	−	0.623297i	$-0.785793\pi$
$563$		−	29.5787i		−	1.24659i	0.781986	−	0.623297i	$-0.214207\pi$
$564$	19.2428	+	0.335146i	0.810268	+	0.0141122i
$565$	16.1228	+	2.11629i	0.678291	+	0.0890330i
$566$	12.2047	−	4.93130i	0.513002	−	0.207278i
$567$	−5.08497	−	5.08497i	−0.213549	−	0.213549i
$568$	9.10968	−	20.4638i	0.382234	−	0.858644i
$569$	−5.34932			−0.224255			−0.112127	−	0.993694i	$-0.535767\pi$
$569$	−5.34932			−0.224255			−0.112127	+	0.993694i	$0.535767\pi$
$570$	1.57479	−	0.407947i	0.0659606	−	0.0170870i
$571$	1.03508	+	1.03508i	0.0433166	+	0.0433166i	0.728433	−	0.685117i	$-0.240249\pi$
$571$	1.03508	+	1.03508i	0.0433166	+	0.0433166i	−0.685117	+	0.728433i	$0.740249\pi$
$572$	8.60172	+	0.149814i	0.359656	+	0.00626402i
$573$	12.3156			0.514490
$574$	−23.1836	+	54.6201i	−0.967666	+	2.27980i
$575$	−6.47223	−	11.1903i	−0.269911	−	0.466669i
$576$	−11.0376	−	12.2557i	−0.459901	−	0.510654i
$577$	−31.5558	−	31.5558i	−1.31368	−	1.31368i	−0.918678	−	0.395006i	$-0.870742\pi$
$577$	−31.5558	−	31.5558i	−1.31368	−	1.31368i	−0.395006	−	0.918678i	$-0.629258\pi$
$578$	4.80648	+	11.8958i	0.199923	+	0.494800i
$579$	9.95342	+	9.95342i	0.413650	+	0.413650i
$580$	−1.92899	+	1.42864i	−0.0800968	+	0.0593210i
$581$	−24.0083	+	24.0083i	−0.996030	+	0.996030i
$582$	−4.84496	+	11.4146i	−0.200830	+	0.473151i
$583$	6.27640	−	6.27640i	0.259942	−	0.259942i
$584$	−18.3573	+	7.04794i	−0.759632	+	0.291646i
$585$	12.0779	+	15.7277i	0.499359	+	0.650258i
$586$	2.86182	+	7.08287i	0.118221	+	0.292591i
$587$			22.3536i			0.922632i	0.887236	+	0.461316i	$0.152623\pi$
$587$			22.3536i			0.922632i	−0.887236	+	0.461316i	$0.847377\pi$
$588$	−25.2171	+	24.3537i	−1.03993	+	1.00433i
$589$	3.48307	−	3.48307i	0.143518	−	0.143518i
$590$	33.5431	−	8.68929i	1.38095	−	0.357733i
$591$		−	8.32136i		−	0.342295i
$592$	0.968332	−	27.7905i	0.0397982	−	1.14218i
$593$	−16.7760	+	16.7760i	−0.688909	+	0.688909i	−0.961991	−	0.273082i	$-0.911957\pi$
$593$	−16.7760	+	16.7760i	−0.688909	+	0.688909i	0.273082	+	0.961991i	$0.411957\pi$
$594$	−2.70922	+	6.38287i	−0.111161	+	0.261892i
$595$	−25.0147	+	19.2097i	−1.02550	+	0.787523i
$596$	−19.2615	−	0.335472i	−0.788981	−	0.0137414i
$597$	13.8984			0.568824
$598$	−6.14511	+	14.4778i	−0.251292	+	0.592039i
$599$			7.43792i			0.303905i	0.988388	+	0.151953i	$0.0485561\pi$
$599$			7.43792i			0.303905i	−0.988388	+	0.151953i	$0.951444\pi$
$600$	8.61232	−	10.6533i	0.351596	−	0.434921i
$601$			13.1297i			0.535571i	0.963479	+	0.267786i	$0.0862919\pi$
$601$			13.1297i			0.535571i	−0.963479	+	0.267786i	$0.913708\pi$
$602$	−36.8370	−	15.6356i	−1.50136	−	0.637258i
$603$	−24.3973			−0.993534
$604$	−23.1578	+	22.3649i	−0.942277	+	0.910016i
$605$	1.77347	−	1.36191i	0.0721017	−	0.0553697i
$606$	−2.30498	−	0.978353i	−0.0936334	−	0.0397429i
$607$	9.37589	−	9.37589i	0.380556	−	0.380556i	−0.490747	−	0.871302i	$-0.663276\pi$
$607$	9.37589	−	9.37589i	0.380556	−	0.380556i	0.871302	+	0.490747i	$0.163276\pi$
$608$	1.26935	−	2.72282i	0.0514790	−	0.110425i
$609$		−	2.60463i		−	0.105545i
$610$	−4.97669	−	19.2114i	−0.201500	−	0.777847i
$611$	−30.2157	+	30.2157i	−1.22240	+	1.22240i
$612$	11.6080	+	0.202173i	0.469226	+	0.00817237i
$613$		−	7.12271i		−	0.287684i	−0.989601	−	0.143842i	$-0.954054\pi$
$613$		−	7.12271i		−	0.287684i	0.989601	−	0.143842i	$-0.0459457\pi$
$614$	39.2255	−	15.8490i	1.58301	−	0.639614i
$615$	11.0494	+	14.3884i	0.445554	+	0.580194i
$616$	−12.9445	−	5.76235i	−0.521547	−	0.232172i
$617$	9.03935	−	9.03935i	0.363911	−	0.363911i	−0.501340	−	0.865250i	$-0.667159\pi$
$617$	9.03935	−	9.03935i	0.363911	−	0.363911i	0.865250	+	0.501340i	$0.167159\pi$
$618$	25.0605	+	10.6370i	1.00808	+	0.427882i
$619$	13.7808	−	13.7808i	0.553898	−	0.553898i	−0.373666	−	0.927564i	$-0.621899\pi$
$619$	13.7808	−	13.7808i	0.553898	−	0.553898i	0.927564	+	0.373666i	$0.121899\pi$
$620$	6.11385	−	41.0275i	0.245538	−	1.64770i
$621$	−8.96379	−	8.96379i	−0.359705	−	0.359705i
$622$	−36.2926	+	14.6640i	−1.45520	+	0.587972i
$623$	−8.07976	−	8.07976i	−0.323709	−	0.323709i
$624$	−16.6569	−	0.580393i	−0.666811	−	0.0232343i
$625$	−21.6699	−	12.4666i	−0.866794	−	0.498666i
$626$	10.4126	+	4.41965i	0.416171	+	0.176645i
$627$	−0.514429			−0.0205443
$628$	3.96893	+	4.10963i	0.158377	+	0.163992i
$629$	13.8407	+	13.8407i	0.551866	+	0.551866i
$630$	−8.19021	−	31.6165i	−0.326306	−	1.25963i
$631$	−35.5466			−1.41509			−0.707545	−	0.706669i	$-0.750197\pi$
$631$	−35.5466			−1.41509			−0.707545	+	0.706669i	$0.750197\pi$
$632$	−0.0876159	+	0.196819i	−0.00348518	+	0.00782904i
$633$	4.75184	+	4.75184i	0.188868	+	0.188868i
$634$	−6.47723	−	16.0308i	−0.257243	−	0.636665i
$635$	7.90438	+	1.03754i	0.313676	+	0.0411734i
$636$	−12.3695	+	11.9460i	−0.490482	+	0.473689i
$637$		−	77.8378i		−	3.08404i
$638$	0.703800	−	0.284369i	0.0278637	−	0.0112583i
$639$	−16.3275			−0.645907
$640$	−5.05652	−	24.7877i	−0.199877	−	0.979821i
$641$	−37.4693			−1.47995			−0.739974	−	0.672635i	$-0.765162\pi$
$641$	−37.4693			−1.47995			−0.739974	+	0.672635i	$0.765162\pi$
$642$	−4.45153	+	1.79864i	−0.175688	+	0.0709865i
$643$		−	9.90852i		−	0.390754i	−0.980728	−	0.195377i	$-0.937407\pi$
$643$		−	9.90852i		−	0.390754i	0.980728	−	0.195377i	$-0.0625930\pi$
$644$	18.6329	−	17.9950i	0.734240	−	0.709102i
$645$	−9.70382	+	7.45194i	−0.382088	+	0.293420i
$646$	0.792198	+	1.96065i	0.0311686	+	0.0771407i
$647$	0.680016	+	0.680016i	0.0267342	+	0.0267342i	0.720348	−	0.693613i	$-0.243982\pi$
$647$	0.680016	+	0.680016i	0.0267342	+	0.0267342i	−0.693613	+	0.720348i	$0.743982\pi$
$648$	−1.65123	+	3.70930i	−0.0648665	+	0.145715i
$649$	−10.9574			−0.430115
$650$	3.73063	+	30.1866i	0.146327	+	1.18402i
$651$	31.8265	+	31.8265i	1.24738	+	1.24738i
$652$	−6.92899	−	7.17463i	−0.271360	−	0.280980i
$653$	20.1591			0.788887			0.394443	−	0.918920i	$-0.370937\pi$
$653$	20.1591			0.788887			0.394443	+	0.918920i	$0.370937\pi$
$654$	2.15165	+	0.913271i	0.0841360	+	0.0357117i
$655$	32.3643	+	4.24817i	1.26458	+	0.165990i
$656$	33.4817	+	1.16663i	1.30724	+	0.0455494i
$657$	10.1351	+	10.1351i	0.395407	+	0.395407i
$658$	65.2532	−	26.3655i	2.54384	−	1.02783i
$659$	3.79896	+	3.79896i	0.147987	+	0.147987i	0.777218	−	0.629231i	$-0.216630\pi$
$659$	3.79896	+	3.79896i	0.147987	+	0.147987i	−0.629231	+	0.777218i	$0.716630\pi$
$660$	−3.48125	+	2.57827i	−0.135507	+	0.100359i
$661$	−11.3438	+	11.3438i	−0.441223	+	0.441223i	−0.892423	−	0.451200i	$-0.850996\pi$
$661$	−11.3438	+	11.3438i	−0.441223	+	0.441223i	0.451200	+	0.892423i	$0.350996\pi$
$662$	5.87459	+	2.49348i	0.228323	+	0.0969120i
$663$	8.29578	−	8.29578i	0.322182	−	0.322182i
$664$	17.5132	+	7.79615i	0.679642	+	0.302549i
$665$	4.71812	−	3.62323i	0.182961	−	0.140503i
$666$	−18.7930	+	7.59330i	−0.728215	+	0.294234i
$667$			1.38774i			0.0537334i
$668$	32.5525	+	0.566957i	1.25949	+	0.0219362i
$669$	−15.0564	+	15.0564i	−0.582116	+	0.582116i
$670$	−32.2512	−	18.9798i	−1.24597	−	0.733255i
$671$			6.27571i			0.242271i
$672$	24.8797	+	11.5987i	0.959755	+	0.447429i
$673$	31.2162	−	31.2162i	1.20330	−	1.20330i	0.230138	−	0.973158i	$-0.426082\pi$
$673$	31.2162	−	31.2162i	1.20330	−	1.20330i	0.973158	−	0.230138i	$-0.0739177\pi$
$674$	4.05463	+	1.72100i	0.156179	+	0.0662903i
$675$	−23.6851	−	6.32685i	−0.911638	−	0.243521i
$676$	7.91675	−	7.64570i	0.304490	−	0.294065i
$677$	7.05047			0.270972			0.135486	−	0.990779i	$-0.456740\pi$
$677$	7.05047			0.270972			0.135486	+	0.990779i	$0.456740\pi$
$678$	9.17036	+	3.89238i	0.352186	+	0.149486i
$679$			45.3458i			1.74021i
$680$	15.1875	+	9.29770i	0.582416	+	0.356551i
$681$		−	1.92204i		−	0.0736529i
$682$	−5.12510	+	12.0746i	−0.196250	+	0.462362i
$683$	−43.5420			−1.66609			−0.833044	−	0.553207i	$-0.813404\pi$
$683$	−43.5420			−1.66609			−0.833044	+	0.553207i	$0.813404\pi$
$684$	−2.18943	−	0.0381327i	−0.0837151	−	0.00145804i
$685$	−11.4047	−	1.49699i	−0.435750	−	0.0571969i
$686$	−30.7126	+	72.3581i	−1.17261	+	2.76264i
$687$	0.797207	−	0.797207i	0.0304153	−	0.0304153i
$688$	−0.786804	+	22.5808i	−0.0299966	+	0.860884i
$689$		−	38.1810i		−	1.45458i
$690$	−1.98605	−	7.66671i	−0.0756077	−	0.291867i
$691$	21.9198	−	21.9198i	0.833868	−	0.833868i	−0.154176	−	0.988043i	$-0.549272\pi$
$691$	21.9198	−	21.9198i	0.833868	−	0.833868i	0.988043	+	0.154176i	$0.0492721\pi$
$692$	32.0914	−	30.9926i	1.21993	−	1.17816i
$693$			10.3280i			0.392329i
$694$	−7.00806	−	17.3446i	−0.266022	−	0.658392i
$695$	24.3207	+	3.19235i	0.922536	+	0.121093i
$696$	−1.37289	+	0.527094i	−0.0520393	+	0.0199795i
$697$	−16.6751	+	16.6751i	−0.631616	+	0.631616i
$698$	−0.322601	+	0.760041i	−0.0122106	+	0.0287680i
$699$	1.00860	−	1.00860i	0.0381488	−	0.0381488i
$700$	13.7692	−	48.1659i	0.520428	−	1.82050i
$701$	−4.64186	−	4.64186i	−0.175321	−	0.175321i	0.613992	−	0.789312i	$-0.289563\pi$
$701$	−4.64186	−	4.64186i	−0.175321	−	0.175321i	−0.789312	+	0.613992i	$0.789563\pi$
$702$	11.1739	+	27.6548i	0.421730	+	1.04376i
$703$	−2.61056	−	2.61056i	−0.0984590	−	0.0984590i
$704$	−0.417769	+	7.98908i	−0.0157452	+	0.301100i
$705$	2.80037	−	21.3344i	0.105468	−	0.803499i
$706$	12.2230	−	28.7971i	0.460018	−	1.08379i
$707$	−9.15678			−0.344376
$708$	21.2250	+	0.369670i	0.797685	+	0.0138930i
$709$	−15.1255	−	15.1255i	−0.568050	−	0.568050i	0.363532	−	0.931582i	$-0.381571\pi$
$709$	−15.1255	−	15.1255i	−0.568050	−	0.568050i	−0.931582	+	0.363532i	$0.881571\pi$
$710$	−21.5836	−	12.7020i	−0.810019	−	0.476697i
$711$	0.157037			0.00588933
$712$	−2.62372	+	5.89389i	−0.0983282	+	0.220883i
$713$	−16.9570	−	16.9570i	−0.635046	−	0.635046i
$714$	−17.9154	+	7.23869i	−0.670467	+	0.270901i
$715$	1.25179	−	9.53666i	0.0468143	−	0.356651i
$716$	−7.51492	−	0.130885i	−0.280846	−	0.00489141i
$717$		−	8.44288i		−	0.315305i
$718$	−6.84979	−	16.9529i	−0.255632	−	0.632676i
$719$	32.8584			1.22541			0.612705	−	0.790312i	$-0.290081\pi$
$719$	32.8584			1.22541			0.612705	+	0.790312i	$0.290081\pi$
$720$	−15.0075	+	10.7152i	−0.559296	+	0.399331i
$721$	99.5554			3.70764
$722$	9.91676	+	24.5435i	0.369064	+	0.913414i
$723$			21.6629i			0.805652i
$724$	−0.719799	+	41.3281i	−0.0267511	+	1.53595i
$725$	1.34366	+	2.32316i	0.0499024	+	0.0862800i
$726$	1.27015	−	0.513202i	0.0471397	−	0.0190467i
$727$	9.17445	+	9.17445i	0.340261	+	0.340261i	0.856466	−	0.516204i	$-0.172655\pi$
$727$	9.17445	+	9.17445i	0.340261	+	0.340261i	−0.516204	+	0.856466i	$0.672655\pi$
$728$	−56.8991	+	21.8453i	−2.10882	+	0.809640i
$729$	−11.2890			−0.418110
$730$	5.51316	+	21.2823i	0.204051	+	0.787694i
$731$	−11.2461	−	11.2461i	−0.415952	−	0.415952i
$732$	0.211724	−	12.1564i	0.00782555	−	0.449313i
$733$	10.7442			0.396845			0.198422	−	0.980117i	$-0.436418\pi$
$733$	10.7442			0.396845			0.198422	+	0.980117i	$0.436418\pi$
$734$	−8.66888	+	20.4237i	−0.319974	+	0.753852i
$735$	23.8724	+	31.0864i	0.880548	+	1.14664i
$736$	−13.2558	−	6.17973i	−0.488615	−	0.227788i
$737$	8.36771	+	8.36771i	0.308229	+	0.308229i
$738$	−9.14831	−	22.6416i	−0.336754	−	0.833450i
$739$	−10.4333	−	10.4333i	−0.383795	−	0.383795i	0.488672	−	0.872467i	$-0.337481\pi$
$739$	−10.4333	−	10.4333i	−0.383795	−	0.383795i	−0.872467	+	0.488672i	$0.837481\pi$
$740$	−30.7500	−	4.58232i	−1.13039	−	0.168449i
$741$	−1.56470	+	1.56470i	−0.0574808	+	0.0574808i
$742$	−24.5695	+	57.8853i	−0.901976	+	2.12504i
$743$	29.2878	−	29.2878i	1.07447	−	1.07447i	0.0774721	−	0.996995i	$-0.475315\pi$
$743$	29.2878	−	29.2878i	1.07447	−	1.07447i	0.996995	−	0.0774721i	$-0.0246849\pi$
$744$	10.3350	−	23.2163i	0.378898	−	0.851150i
$745$	−2.80309	+	21.3551i	−0.102697	+	0.782389i
$746$	−7.94325	−	19.6592i	−0.290823	−	0.719773i
$747$		−	13.9733i		−	0.511255i
$748$	−3.91194	−	4.05063i	−0.143035	−	0.148106i
$749$	−12.4147	+	12.4147i	−0.453625	+	0.453625i
$750$	−10.7480	−	10.9116i	−0.392461	−	0.398435i
$751$		−	35.6860i		−	1.30220i	−0.758992	−	0.651100i	$-0.774308\pi$
$751$		−	35.6860i		−	1.30220i	0.758992	−	0.651100i	$-0.225692\pi$
$752$	−27.1023	−	29.0592i	−0.988319	−	1.05968i
$753$	2.82890	−	2.82890i	0.103091	−	0.103091i
$754$	1.27575	−	3.00564i	0.0464601	−	0.109459i
$755$	21.9230	+	28.5478i	0.797858	+	1.03896i
$756$	0.855458	−	49.1171i	0.0311127	−	1.78637i
$757$	−13.9404			−0.506672			−0.253336	−	0.967378i	$-0.581528\pi$
$757$	−13.9404			−0.506672			−0.253336	+	0.967378i	$0.581528\pi$
$758$	2.54045	−	5.98525i	0.0922734	−	0.217394i
$759$			2.50445i			0.0909059i
$760$	−2.86459	−	1.75368i	−0.103909	−	0.0636126i
$761$		−	11.5808i		−	0.419805i	−0.977722	−	0.209902i	$-0.932685\pi$
$761$		−	11.5808i		−	0.419805i	0.977722	−	0.209902i	$-0.0673146\pi$
$762$	4.49587	+	1.90828i	0.162868	+	0.0691298i
$763$	8.54764			0.309445
$764$	−17.6642	−	18.2905i	−0.639070	−	0.661726i
$765$	1.68929	−	12.8697i	0.0610765	−	0.465306i
$766$	3.64885	+	1.54876i	0.131838	+	0.0559591i
$767$	−33.3283	+	33.3283i	−1.20341	+	1.20341i
$768$	1.07877	−	15.4612i	0.0389267	−	0.557907i
$769$			33.2627i			1.19948i	0.800194	+	0.599742i	$0.204730\pi$
$769$			33.2627i			1.19948i	−0.800194	+	0.599742i	$0.795270\pi$
$770$	−8.03467	+	13.6528i	−0.289550	+	0.492012i
$771$	−20.2099	+	20.2099i	−0.727842	+	0.727842i
$772$	0.506104	−	29.0586i	0.0182151	−	1.04584i
$773$		−	26.1597i		−	0.940899i	−0.882427	−	0.470450i	$-0.844092\pi$
$773$		−	26.1597i		−	0.940899i	0.882427	−	0.470450i	$-0.155908\pi$
$774$	15.2700	−	6.16983i	0.548869	−	0.221770i
$775$	−44.8056	−	11.9687i	−1.60947	−	0.429927i
$776$	23.9016	−	9.17653i	0.858016	−	0.329418i
$777$	23.8539	−	23.8539i	0.855754	−	0.855754i
$778$	18.3201	+	7.77602i	0.656809	+	0.278784i
$779$	3.14517	−	3.14517i	0.112687	−	0.112687i
$780$	−2.74652	+	18.4308i	−0.0983414	+	0.659928i
$781$	5.59997	+	5.59997i	0.200383	+	0.200383i
$782$	9.54525	−	3.85674i	0.341337	−	0.137917i
$783$	1.86092	+	1.86092i	0.0665039	+	0.0665039i
$784$	72.3379	+	2.52054i	2.58350	+	0.0900193i
$785$	5.06615	−	3.89049i	0.180819	−	0.138858i
$786$	18.4083	+	7.81343i	0.656601	+	0.278696i
$787$	43.1704			1.53886			0.769430	−	0.638731i	$-0.220540\pi$
$787$	43.1704			1.53886			0.769430	+	0.638731i	$0.220540\pi$
$788$	−12.3585	+	11.9354i	−0.440253	+	0.425180i
$789$	−17.4682	−	17.4682i	−0.621885	−	0.621885i
$790$	0.207589	+	0.122166i	0.00738569	+	0.00434649i
$791$	36.4302			1.29531
$792$	5.44386	−	2.09006i	0.193439	−	0.0742671i
$793$	19.0884	+	19.0884i	0.677848	+	0.677848i
$794$	16.4162	+	40.6292i	0.582588	+	1.44188i
$795$	11.7099	+	15.2485i	0.415307	+	0.540808i
$796$	−19.9345	−	20.6412i	−0.706561	−	0.731609i
$797$			54.8263i			1.94205i	0.238981	+	0.971024i	$0.423187\pi$
$797$			54.8263i			1.94205i	−0.238981	+	0.971024i	$0.576813\pi$
$798$	3.37910	−	1.36532i	0.119619	−	0.0483318i
$799$	27.9706			0.989527
$800$	−28.1745	+	2.48953i	−0.996119	+	0.0880182i
$801$	4.70257			0.166157
$802$	17.2439	−	6.96739i	0.608904	−	0.246027i
$803$		−	6.95221i		−	0.245338i
$804$	−15.9264	−	16.4910i	−0.561681	−	0.581593i
$805$	−17.6394	−	22.9698i	−0.621706	−	0.809577i
$806$	21.1379	+	52.3152i	0.744550	+	1.84272i
$807$	−13.8074	−	13.8074i	−0.486044	−	0.486044i
$808$	1.85304	+	4.82650i	0.0651897	+	0.169796i
$809$	−3.42635			−0.120464			−0.0602320	−	0.998184i	$-0.519184\pi$
$809$	−3.42635			−0.120464			−0.0602320	+	0.998184i	$0.519184\pi$
$810$	3.91228	+	2.30238i	0.137463	+	0.0808973i
$811$	14.0779	+	14.0779i	0.494341	+	0.494341i	0.909671	−	0.415330i	$-0.136334\pi$
$811$	14.0779	+	14.0779i	0.494341	+	0.494341i	−0.415330	+	0.909671i	$0.636334\pi$
$812$	−3.86827	+	3.73583i	−0.135750	+	0.131102i
$813$	−25.2399			−0.885204
$814$	9.04991	+	3.84126i	0.317199	+	0.134636i
$815$	−8.84453	+	6.79206i	−0.309810	+	0.237915i
$816$	7.44099	+	7.97825i	0.260487	+	0.279295i
$817$	2.12117	+	2.12117i	0.0742104	+	0.0742104i
$818$	36.0278	−	14.5570i	1.25968	−	0.508973i
$819$	31.4140	+	31.4140i	1.09769	+	1.09769i
$820$	5.52072	−	37.0473i	0.192792	−	1.29375i
$821$	−12.0176	+	12.0176i	−0.419419	+	0.419419i	−0.885003	−	0.465585i	$-0.845844\pi$
$821$	−12.0176	+	12.0176i	−0.419419	+	0.419419i	0.465585	+	0.885003i	$0.345844\pi$
$822$	−6.48678	−	2.75333i	−0.226252	−	0.0960333i
$823$	17.3877	−	17.3877i	0.606098	−	0.606098i	−0.335826	−	0.941924i	$-0.609015\pi$
$823$	17.3877	−	17.3877i	0.606098	−	0.606098i	0.941924	+	0.335826i	$0.109015\pi$
$824$	−20.1468	−	52.4752i	−0.701848	−	1.82806i
$825$	2.42491	+	4.19261i	0.0844246	+	0.145968i
$826$	71.9750	−	29.0814i	2.50433	−	1.01187i
$827$			31.1539i			1.08333i	0.840595	+	0.541664i	$0.182205\pi$
$827$			31.1539i			1.08333i	−0.840595	+	0.541664i	$0.817795\pi$
$828$	−0.185646	+	10.6591i	−0.00645164	+	0.370428i
$829$	8.37029	−	8.37029i	0.290712	−	0.290712i	−0.546649	−	0.837362i	$-0.684097\pi$
$829$	8.37029	−	8.37029i	0.290712	−	0.290712i	0.837362	+	0.546649i	$0.184097\pi$
$830$	10.8705	−	18.4715i	0.377320	−	0.641155i
$831$		−	16.0862i		−	0.558024i
$832$	23.0291	+	25.5705i	0.798391	+	0.886498i
$833$	−36.0270	+	36.0270i	−1.24826	+	1.24826i
$834$	13.8332	+	5.87152i	0.479004	+	0.203314i
$835$	4.73730	−	36.0907i	0.163941	−	1.24897i
$836$	0.737848	+	0.764005i	0.0255190	+	0.0264237i
$837$	−45.4779			−1.57195
$838$	−4.32738	−	1.83677i	−0.149487	−	0.0634501i
$839$		−	9.70278i		−	0.334977i	−0.985874	−	0.167489i	$-0.946434\pi$
$839$		−	9.70278i		−	0.334977i	0.985874	−	0.167489i	$-0.0535658\pi$
$840$	16.0242	−	26.1751i	0.552887	−	0.903127i
$841$			28.7119i			0.990066i
$842$	17.5083	−	41.2492i	0.603377	−	1.42154i
$843$	−22.2383			−0.765926
$844$	0.241618	−	13.8728i	0.00831683	−	0.477520i
$845$	−7.49460	−	9.75938i	−0.257822	−	0.335733i
$846$	−11.3167	+	26.6619i	−0.389076	+	0.916655i
$847$	3.54228	−	3.54228i	0.121714	−	0.121714i
$848$	35.4832	+	1.23637i	1.21850	+	0.0424573i
$849$		−	9.01628i		−	0.309438i
$850$	12.2451	−	15.6985i	0.420003	−	0.538455i
$851$	−12.7093	+	12.7093i	−0.435668	+	0.435668i
$852$	−10.6585	−	11.0364i	−0.365155	−	0.378100i
$853$			51.4133i			1.76036i	0.474643	+	0.880178i	$0.342577\pi$
$853$			51.4133i			1.76036i	−0.474643	+	0.880178i	$0.657423\pi$
$854$	−16.6560	−	41.2229i	−0.569958	−	1.41062i
$855$	−0.318624	+	2.42741i	−0.0108967	+	0.0830157i
$856$	9.05610	+	4.03141i	0.309531	+	0.137791i
$857$	−9.23247	+	9.23247i	−0.315375	+	0.315375i	−0.846988	−	0.531613i	$-0.821586\pi$
$857$	−9.23247	+	9.23247i	−0.315375	+	0.315375i	0.531613	+	0.846988i	$0.321586\pi$
$858$	2.30235	−	5.42429i	0.0786010	−	0.185182i
$859$	34.0340	−	34.0340i	1.16122	−	1.16122i	0.177017	−	0.984208i	$-0.443355\pi$
$859$	34.0340	−	34.0340i	1.16122	−	1.16122i	0.984208	−	0.177017i	$-0.0566448\pi$
$860$	24.9855	+	3.72330i	0.851998	+	0.126963i
$861$	28.7389	+	28.7389i	0.979419	+	0.979419i
$862$	6.09702	+	15.0898i	0.207665	+	0.513961i
$863$	−3.78597	−	3.78597i	−0.128876	−	0.128876i	0.639727	−	0.768603i	$-0.279048\pi$
$863$	−3.78597	−	3.78597i	−0.128876	−	0.128876i	−0.768603	+	0.639727i	$0.779048\pi$
$864$	−26.0626	+	9.48882i	−0.886666	+	0.322816i
$865$	−30.3802	−	39.5606i	−1.03296	−	1.34510i
$866$	−9.64791	+	22.7303i	−0.327849	+	0.772406i
$867$	8.78807			0.298459
$868$	1.61829	−	92.9161i	0.0549284	−	3.15378i
$869$	−0.0538600	−	0.0538600i	−0.00182707	−	0.00182707i
$870$	0.412313	+	1.59164i	0.0139787	+	0.0539617i
$871$	50.9029			1.72478
$872$	−1.72977	−	4.50543i	−0.0585774	−	0.152573i
$873$	−13.1960	−	13.1960i	−0.446619	−	0.446619i
$874$	−1.80037	+	0.727436i	−0.0608984	+	0.0246059i
$875$	−51.7697	−	21.3737i	−1.75013	−	0.722562i
$876$	−0.234547	+	13.4668i	−0.00792461	+	0.455001i
$877$			27.7561i			0.937256i	0.883395	+	0.468628i	$0.155252\pi$
$877$			27.7561i			0.937256i	−0.883395	+	0.468628i	$0.844748\pi$
$878$	−5.31862	−	13.1633i	−0.179495	−	0.444241i
$879$	5.23250			0.176488
$880$	8.82229	+	1.47216i	0.297399	+	0.0496264i
$881$	−24.3755			−0.821233			−0.410616	−	0.911808i	$-0.634686\pi$
$881$	−24.3755			−0.821233			−0.410616	+	0.911808i	$0.634686\pi$
$882$	−19.7651	−	48.9178i	−0.665527	−	1.64715i
$883$			34.8381i			1.17240i	0.810168	+	0.586198i	$0.199376\pi$
$883$			34.8381i			1.17240i	−0.810168	+	0.586198i	$0.800624\pi$
$884$	−24.2192	−	0.421818i	−0.814579	−	0.0141873i
$885$	3.08884	−	23.5320i	0.103830	−	0.791021i
$886$	−6.17843	+	2.49639i	−0.207568	+	0.0838677i
$887$	18.0090	+	18.0090i	0.604683	+	0.604683i	0.941552	−	0.336868i	$-0.109368\pi$
$887$	18.0090	+	18.0090i	0.604683	+	0.604683i	−0.336868	+	0.941552i	$0.609368\pi$
$888$	−17.4006	−	7.74603i	−0.583925	−	0.259940i
$889$	17.8603			0.599017
$890$	6.21641	+	3.65836i	0.208375	+	0.122629i
$891$	−1.01506	−	1.01506i	−0.0340057	−	0.0340057i
$892$	43.9566	+	0.765580i	1.47178	+	0.0256335i
$893$	−5.27564			−0.176543
$894$	−5.15556	+	12.1464i	−0.172428	+	0.406236i
$895$	−1.09363	+	8.33175i	−0.0365561	+	0.278500i
$896$	−18.4592	−	53.5861i	−0.616680	−	1.79019i
$897$	7.61761	+	7.61761i	0.254345	+	0.254345i
$898$	10.5226	+	26.0429i	0.351144	+	0.869063i
$899$	3.52035	+	3.52035i	0.117410	+	0.117410i
$900$	10.0098	+	18.0237i	0.333659	+	0.600790i
$901$	−17.6720	+	17.6720i	−0.588739	+	0.588739i
$902$	−4.62790	+	10.9032i	−0.154092	+	0.363038i
$903$	−19.3822	+	19.3822i	−0.644998	+	0.644998i
$904$	−7.37231	−	19.2022i	−0.245199	−	0.638657i
$905$	45.8202	+	6.01440i	1.52311	+	0.199925i
$906$	8.26109	+	20.4458i	0.274456	+	0.679266i
$907$		−	22.6254i		−	0.751265i	−0.926769	−	0.375633i	$-0.877425\pi$
$907$		−	22.6254i		−	0.751265i	0.926769	−	0.375633i	$-0.122575\pi$
$908$	−2.85453	+	2.75679i	−0.0947307	+	0.0914874i
$909$	2.66471	−	2.66471i	0.0883828	−	0.0883828i
$910$	17.0882	+	65.9652i	0.566468	+	2.18672i
$911$			22.0552i			0.730721i	0.930866	+	0.365361i	$0.119054\pi$
$911$			22.0552i			0.730721i	−0.930866	+	0.365361i	$0.880946\pi$
$912$	−1.40347	−	1.50481i	−0.0464737	−	0.0498293i
$913$	−4.79251	+	4.79251i	−0.158609	+	0.158609i
$914$	−7.80245	+	18.3824i	−0.258082	+	0.608036i
$915$	−13.4777	−	1.76910i	−0.445559	−	0.0584845i
$916$	−2.32741	−	0.0405358i	−0.0768998	−	0.00133934i
$917$	73.1288			2.41493
$918$	7.62814	−	17.9717i	0.251766	−	0.593156i
$919$			14.3755i			0.474204i	0.971485	+	0.237102i	$0.0761975\pi$
$919$			14.3755i			0.474204i	−0.971485	+	0.237102i	$0.923803\pi$
$920$	−8.53762	+	13.9460i	−0.281477	+	0.459785i
$921$		−	28.9780i		−	0.954857i
$922$	29.3431	+	12.4547i	0.966364	+	0.410175i
$923$	34.0661			1.12130
$924$	−6.98108	+	6.74207i	−0.229661	+	0.221798i
$925$	−8.97049	+	33.5817i	−0.294948	+	1.10416i
$926$	−11.2132	−	4.75947i	−0.368489	−	0.156406i
$927$	−28.9716	+	28.9716i	−0.951551	+	0.951551i
$928$	2.75196	+	1.28294i	0.0903374	+	0.0421145i
$929$		−	15.7454i		−	0.516590i	−0.966066	−	0.258295i	$-0.916839\pi$
$929$		−	15.7454i		−	0.516590i	0.966066	−	0.258295i	$-0.0831607\pi$
$930$	−24.4867	−	14.4104i	−0.802950	−	0.472537i
$931$	6.79521	−	6.79521i	0.222704	−	0.222704i
$932$	−2.94457	−	0.0512847i	−0.0964526	−	0.00167989i
$933$			26.8113i			0.877763i
$934$	5.38037	−	2.17393i	0.176051	−	0.0711332i
$935$	−4.99341	+	3.83464i	−0.163302	+	0.125406i
$936$	10.2010	−	22.9154i	0.333430	−	0.749012i
$937$	32.1678	−	32.1678i	1.05088	−	1.05088i	0.0522417	−	0.998634i	$-0.483363\pi$
$937$	32.1678	−	32.1678i	1.05088	−	1.05088i	0.998634	−	0.0522417i	$-0.0166366\pi$
$938$	−77.1727	−	32.7561i	−2.51978	−	1.06953i
$939$	5.47869	−	5.47869i	0.178790	−	0.178790i
$940$	−35.7013	+	26.4410i	−1.16445	+	0.862410i
$941$	40.8515	+	40.8515i	1.33172	+	1.33172i	0.903830	+	0.427892i	$0.140744\pi$
$941$	40.8515	+	40.8515i	1.33172	+	1.33172i	0.427892	+	0.903830i	$0.359256\pi$
$942$	3.62835	−	1.46603i	0.118218	−	0.0477659i
$943$	−15.3120	−	15.3120i	−0.498626	−	0.498626i
$944$	−29.8941	−	32.0526i	−0.972971	−	1.04322i
$945$	−54.4558	−	7.14792i	−1.77145	−	0.232522i
$946$	−7.35338	−	3.12116i	−0.239079	−	0.101478i
$947$	3.20627			0.104190			0.0520949	−	0.998642i	$-0.483410\pi$
$947$	3.20627			0.104190			0.0520949	+	0.998642i	$0.483410\pi$
$948$	0.102512	+	0.106147i	0.00332945	+	0.00344748i
$949$	−21.1460	−	21.1460i	−0.686429	−	0.686429i
$950$	−2.30960	+	2.96096i	−0.0749332	+	0.0960663i
$951$	−11.8428			−0.384030
$952$	36.4467	+	16.2246i	1.18124	+	0.525842i
$953$	7.93144	+	7.93144i	0.256925	+	0.256925i	0.823802	−	0.566877i	$-0.191849\pi$
$953$	7.93144	+	7.93144i	0.256925	+	0.256925i	−0.566877	+	0.823802i	$0.691849\pi$
$954$	−9.69520	−	23.9951i	−0.313894	−	0.776871i
$955$	−22.5476	+	17.3152i	−0.729623	+	0.560305i
$956$	−12.5390	+	12.1097i	−0.405539	+	0.391654i
$957$		−	0.519935i		−	0.0168071i
$958$	−1.86558	+	0.753783i	−0.0602740	+	0.0243536i
$959$	−25.7694			−0.832138
$960$	−17.0396	−	3.14929i	−0.549950	−	0.101643i
$961$	−55.0317			−1.77522
$962$	39.2101	−	15.8428i	1.26419	−	0.510792i
$963$		−	7.22561i		−	0.232842i
$964$	32.1727	−	31.0712i	1.03621	−	1.00074i
$965$	−32.2170	−	4.22884i	−1.03710	−	0.136131i
$966$	−6.64693	−	16.4508i	−0.213862	−	0.529297i
$967$	12.7137	+	12.7137i	0.408846	+	0.408846i	0.881336	−	0.472490i	$-0.156645\pi$
$967$	12.7137	+	12.7137i	0.408846	+	0.408846i	−0.472490	+	0.881336i	$0.656645\pi$
$968$	−2.58396	−	1.15028i	−0.0830517	−	0.0369713i
$969$	1.44844			0.0465305
$970$	−7.17822	−	27.7099i	−0.230479	−	0.889712i
$971$	20.4492	+	20.4492i	0.656246	+	0.656246i	0.954490	−	0.298244i	$-0.0964009\pi$
$971$	20.4492	+	20.4492i	0.656246	+	0.656246i	−0.298244	+	0.954490i	$0.596401\pi$
$972$	22.3687	+	23.1617i	0.717476	+	0.742911i
$973$	54.9538			1.76174
$974$	36.7536	+	15.6001i	1.17766	+	0.499861i
$975$	20.1280	+	5.37669i	0.644613	+	0.172192i
$976$	−18.3578	+	17.1215i	−0.587617	+	0.548046i
$977$	−22.4877	−	22.4877i	−0.719447	−	0.719447i	0.249045	−	0.968492i	$-0.419883\pi$
$977$	−22.4877	−	22.4877i	−0.719447	−	0.719447i	−0.968492	+	0.249045i	$0.919883\pi$
$978$	−6.33441	+	2.55941i	−0.202552	+	0.0818409i
$979$	−1.61288	−	1.61288i	−0.0515477	−	0.0515477i
$980$	11.9276	−	80.0415i	0.381015	−	2.55683i
$981$	−2.48744	+	2.48744i	−0.0794180	+	0.0794180i
$982$	−6.51101	−	2.76361i	−0.207775	−	0.0881904i
$983$	15.2792	−	15.2792i	0.487330	−	0.487330i	−0.420133	−	0.907463i	$-0.638016\pi$
$983$	15.2792	−	15.2792i	0.487330	−	0.487330i	0.907463	+	0.420133i	$0.138016\pi$
$984$	9.33233	−	20.9640i	0.297504	−	0.668308i
$985$	11.6995	+	15.2349i	0.372777	+	0.485425i
$986$	−1.98163	+	0.800676i	−0.0631081	+	0.0254987i
$987$		−	48.2061i		−	1.53442i
$988$	4.56808	+	0.0795608i	0.145330	+	0.00253117i
$989$	10.3267	−	10.3267i	0.328371	−	0.328371i
$990$	−1.63492	−	6.31126i	−0.0519613	−	0.200585i
$991$			13.8514i			0.440004i	0.975499	+	0.220002i	$0.0706065\pi$
$991$			13.8514i			0.440004i	−0.975499	+	0.220002i	$0.929394\pi$
$992$	−49.3032	+	17.9502i	−1.56538	+	0.569921i
$993$	3.09098	−	3.09098i	0.0980891	−	0.0980891i
$994$	−51.6467	−	21.9216i	−1.63814	−	0.695310i
$995$	−25.4455	+	19.5406i	−0.806677	+	0.619478i
$996$	9.44503	−	9.12166i	0.299277	−	0.289031i
$997$	−20.6795			−0.654925			−0.327463	−	0.944864i	$-0.606194\pi$
$997$	−20.6795			−0.654925			−0.327463	+	0.944864i	$0.606194\pi$
$998$	−23.0861	−	9.79894i	−0.730777	−	0.310180i
$999$			34.0856i			1.07842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.s.b.67.13	✓	236
5.3	odd	4		880.2.bk.b.243.75	yes	236
16.11	odd	4		880.2.bk.b.507.75	yes	236
80.43	even	4	inner	880.2.s.b.683.13	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.13	✓	236	1.1	even	1	trivial
880.2.s.b.683.13	yes	236	80.43	even	4	inner
880.2.bk.b.243.75	yes	236	5.3	odd	4
880.2.bk.b.507.75	yes	236	16.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31123 + 0.529799i) q^{2} +0.968673i q^{3} +(1.43863 - 1.38937i) q^{4} +(-1.36191 - 1.77347i) q^{5} +(-0.513202 - 1.27015i) q^{6} +(-3.54228 - 3.54228i) q^{7} +(-1.15028 + 2.58396i) q^{8} +2.06167 q^{9} +(2.72536 + 1.60388i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(1.34585 + 1.39356i) q^{12} -4.30151 q^{13} +(6.52142 + 2.76803i) q^{14} +(1.71791 - 1.31925i) q^{15} +(0.139291 - 3.99757i) q^{16} +(1.99094 + 1.99094i) q^{17} +(-2.70332 + 1.09227i) q^{18} +(-0.375520 - 0.375520i) q^{19} +(-4.42329 - 0.659151i) q^{20} +(3.43131 - 3.43131i) q^{21} +(1.30180 + 0.552552i) q^{22} +(-1.82819 + 1.82819i) q^{23} +(-2.50302 - 1.11424i) q^{24} +(-1.29038 + 4.83062i) q^{25} +(5.64025 - 2.27894i) q^{26} +4.90311i q^{27} +(-10.0176 - 0.174473i) q^{28} +(0.379539 - 0.379539i) q^{29} +(-1.55363 + 2.63998i) q^{30} +9.27533i q^{31} +(1.93527 + 5.31552i) q^{32} +(0.684955 - 0.684955i) q^{33} +(-3.66538 - 1.55578i) q^{34} +(-1.45784 + 11.1064i) q^{35} +(2.96598 - 2.86443i) q^{36} +6.95184 q^{37} +(0.691342 + 0.293442i) q^{38} -4.16676i q^{39} +(6.14915 - 1.47916i) q^{40} +8.37549i q^{41} +(-2.68132 + 6.31712i) q^{42} -5.64862 q^{43} +(-1.99970 - 0.0348281i) q^{44} +(-2.80782 - 3.65631i) q^{45} +(1.42859 - 3.36574i) q^{46} +(7.02444 - 7.02444i) q^{47} +(3.87234 + 0.134928i) q^{48} +18.0955i q^{49} +(-0.867284 - 7.01768i) q^{50} +(-1.92857 + 1.92857i) q^{51} +(-6.18827 + 5.97640i) q^{52} +8.87618i q^{53} +(-2.59766 - 6.42908i) q^{54} +(-0.291012 + 2.21705i) q^{55} +(13.2277 - 5.07852i) q^{56} +(0.363756 - 0.363756i) q^{57} +(-0.296582 + 0.698741i) q^{58} +(7.74804 - 7.74804i) q^{59} +(0.638502 - 4.28473i) q^{60} +(-4.43760 - 4.43760i) q^{61} +(-4.91406 - 12.1620i) q^{62} +(-7.30301 - 7.30301i) q^{63} +(-5.35373 - 5.94454i) q^{64} +(5.85829 + 7.62859i) q^{65} +(-0.535243 + 1.26102i) q^{66} -11.8337 q^{67} +(5.63039 + 0.0980628i) q^{68} +(-1.77092 - 1.77092i) q^{69} +(-3.97260 - 15.3353i) q^{70} -7.91956 q^{71} +(-2.37149 + 5.32728i) q^{72} +(4.91595 + 4.91595i) q^{73} +(-9.11543 + 3.68308i) q^{74} +(-4.67930 - 1.24995i) q^{75} +(-1.06197 - 0.0184960i) q^{76} +5.00954i q^{77} +(2.20754 + 5.46356i) q^{78} +0.0761695 q^{79} +(-7.27927 + 5.19733i) q^{80} +1.43551 q^{81} +(-4.43733 - 10.9822i) q^{82} -6.77763i q^{83} +(0.169007 - 9.70373i) q^{84} +(0.819379 - 6.24237i) q^{85} +(7.40662 - 2.99263i) q^{86} +(0.367649 + 0.367649i) q^{87} +(2.64051 - 1.01377i) q^{88} +2.28095 q^{89} +(5.61880 + 3.30667i) q^{90} +(15.2371 + 15.2371i) q^{91} +(-0.0900462 + 5.17011i) q^{92} -8.98476 q^{93} +(-5.48909 + 12.9322i) q^{94} +(-0.154547 + 1.17740i) q^{95} +(-5.14900 + 1.87464i) q^{96} +(-6.40065 - 6.40065i) q^{97} +(-9.58695 - 23.7272i) q^{98} +(-1.45782 - 1.45782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 8 q^{5} - 4 q^{7} + 12 q^{8} - 240 q^{9} + 16 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} + 8 q^{17} - 12 q^{18} - 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} - 12 q^{25} + 8 q^{26} + 36 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 236 * q + 8 * q^5 - 4 * q^7 + 12 * q^8 - 240 * q^9 + 16 * q^13 - 12 * q^14 + 4 * q^15 - 8 * q^16 + 8 * q^17 - 12 * q^18 - 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 - 12 * q^25 + 8 * q^26 + 36 * q^28 - 8 * q^29 + 40 * q^32 - 4 * q^33 + 44 * q^34 - 12 * q^35 - 32 * q^36 + 4 * q^37 - 44 * q^38 - 40 * q^40 - 60 * q^42 - 16 * q^43 - 40 * q^46 + 48 * q^47 - 112 * q^48 - 28 * q^51 + 108 * q^52 - 24 * q^56 + 16 * q^57 - 28 * q^58 - 8 * q^59 + 100 * q^60 - 24 * q^61 + 36 * q^62 + 24 * q^63 - 32 * q^65 - 4 * q^66 - 56 * q^67 - 36 * q^68 - 48 * q^69 + 164 * q^70 - 4 * q^71 + 12 * q^72 - 8 * q^73 - 72 * q^75 - 24 * q^76 + 152 * q^78 - 40 * q^79 - 24 * q^80 + 244 * q^81 + 40 * q^82 + 104 * q^84 - 24 * q^85 + 72 * q^86 - 140 * q^87 + 32 * q^88 - 36 * q^89 + 72 * q^90 + 12 * q^91 + 12 * q^93 + 16 * q^94 + 36 * q^95 + 72 * q^96 + 20 * q^97 - 64 * q^98 - 8 * q^99

Introduction

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