LMFDB - Embedded newform 680.2.co.a.99.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			99.9
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37562 + 0.328119i) q^{2} +(-1.63264 - 0.324753i) q^{3} +(1.78468 - 0.902737i) q^{4} +(0.608763 - 2.15161i) q^{5} +(2.35246 - 0.0889645i) q^{6} +(-0.693159 - 0.463154i) q^{7} +(-2.15883 + 1.82741i) q^{8} +(-0.211574 - 0.0876370i) q^{9} +(-0.131444 + 3.15954i) q^{10} +(5.70222 - 1.13424i) q^{11} +(-3.20691 + 0.894270i) q^{12} +(-0.791428 - 0.791428i) q^{13} +(1.10550 + 0.409686i) q^{14} +(-1.69263 + 3.31511i) q^{15} +(2.37013 - 3.22218i) q^{16} +(1.86239 - 3.67852i) q^{17} +(0.319802 + 0.0511338i) q^{18} +(1.74054 - 0.720955i) q^{19} +(-0.855890 - 4.38947i) q^{20} +(0.981272 + 0.981272i) q^{21} +(-7.47194 + 3.43130i) q^{22} +(0.716030 + 3.59973i) q^{23} +(4.11807 - 2.28243i) q^{24} +(-4.25882 - 2.61963i) q^{25} +(1.34839 + 0.829023i) q^{26} +(4.46923 + 2.98625i) q^{27} +(-1.65517 - 0.200839i) q^{28} +(-7.13568 + 4.76791i) q^{29} +(1.24067 - 5.11573i) q^{30} +(0.420894 - 2.11598i) q^{31} +(-2.20315 + 5.21020i) q^{32} -9.67805 q^{33} +(-1.35495 + 5.67134i) q^{34} +(-1.41849 + 1.20945i) q^{35} +(-0.456705 + 0.0345924i) q^{36} +(0.424529 - 2.13425i) q^{37} +(-2.15777 + 1.56287i) q^{38} +(1.03510 + 1.54914i) q^{39} +(2.61765 + 5.75742i) q^{40} +(-3.08795 - 2.06330i) q^{41} +(-1.67183 - 1.02789i) q^{42} +(1.72320 - 4.16017i) q^{43} +(9.15269 - 7.17186i) q^{44} +(-0.317359 + 0.401875i) q^{45} +(-2.16613 - 4.71692i) q^{46} +(-7.04908 - 7.04908i) q^{47} +(-4.91600 + 4.49097i) q^{48} +(-2.41283 - 5.82508i) q^{49} +(6.71808 + 2.20623i) q^{50} +(-4.23523 + 5.40090i) q^{51} +(-2.12689 - 0.697990i) q^{52} +(8.10860 - 3.35869i) q^{53} +(-7.12782 - 2.64151i) q^{54} +(1.03086 - 12.9594i) q^{55} +(2.34279 - 0.266814i) q^{56} +(-3.07582 + 0.611818i) q^{57} +(8.25156 - 8.90020i) q^{58} +(-4.00568 + 9.67056i) q^{59} +(-0.0281300 + 7.44440i) q^{60} +(-8.90360 - 5.94920i) q^{61} +(0.115302 + 3.04889i) q^{62} +(0.106065 + 0.158738i) q^{63} +(1.32113 - 7.89016i) q^{64} +(-2.18463 + 1.22105i) q^{65} +(13.3133 - 3.17556i) q^{66} +9.22896 q^{67} +(0.00302559 - 8.24621i) q^{68} -6.10961i q^{69} +(1.55447 - 2.12919i) q^{70} +(-2.73634 - 0.544291i) q^{71} +(0.616903 - 0.197440i) q^{72} +(-9.15520 - 13.7017i) q^{73} +(0.116297 + 3.07522i) q^{74} +(6.10240 + 5.66000i) q^{75} +(2.45547 - 2.85792i) q^{76} +(-4.47788 - 1.85480i) q^{77} +(-1.93221 - 1.79139i) q^{78} +(-0.721559 - 3.62752i) q^{79} +(-5.49002 - 7.06114i) q^{80} +(-5.84108 - 5.84108i) q^{81} +(4.92486 + 1.82511i) q^{82} +(-1.61962 + 0.670870i) q^{83} +(2.63708 + 0.865421i) q^{84} +(-6.78097 - 6.24647i) q^{85} +(-1.00544 + 6.28824i) q^{86} +(13.1984 - 5.46697i) q^{87} +(-10.2374 + 12.8689i) q^{88} +(-8.32848 + 8.32848i) q^{89} +(0.304703 - 0.656959i) q^{90} +(0.182032 + 0.915138i) q^{91} +(4.52749 + 5.77796i) q^{92} +(-1.37434 + 3.31795i) q^{93} +(12.0098 + 7.38394i) q^{94} +(-0.491636 - 4.18385i) q^{95} +(5.28898 - 7.79092i) q^{96} +(1.19945 - 0.801448i) q^{97} +(5.23046 + 7.22141i) q^{98} +(-1.30585 - 0.259749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

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 $

$2$	−1.37562	+	0.328119i	−0.972712	+	0.232015i
$2$	−1.37562	+	0.328119i	−0.972712	+	0.232015i
$3$	−1.63264	−	0.324753i	−0.942608	−	0.187496i	−0.300215	−	0.953872i	$-0.597058\pi$
$3$	−1.63264	−	0.324753i	−0.942608	−	0.187496i	−0.642393	+	0.766375i	$0.722058\pi$
$4$	1.78468	−	0.902737i	0.892338	−	0.451368i
$5$	0.608763	−	2.15161i	0.272247	−	0.962227i
$5$	0.608763	−	2.15161i	0.272247	−	0.962227i
$6$	2.35246	−	0.0889645i	0.960388	−	0.0363196i
$7$	−0.693159	−	0.463154i	−0.261990	−	0.175056i	0.417637	−	0.908614i	$-0.362858\pi$
$7$	−0.693159	−	0.463154i	−0.261990	−	0.175056i	−0.679627	+	0.733558i	$0.737858\pi$
$8$	−2.15883	+	1.82741i	−0.763263	+	0.646088i
$9$	−0.211574	−	0.0876370i	−0.0705248	−	0.0292123i
$10$	−0.131444	+	3.15954i	−0.0415663	+	0.999136i
$11$	5.70222	−	1.13424i	1.71928	−	0.341987i	0.765720	−	0.643175i	$-0.222383\pi$
$11$	5.70222	−	1.13424i	1.71928	−	0.341987i	0.953565	+	0.301188i	$0.0973831\pi$
$12$	−3.20691	+	0.894270i	−0.925754	+	0.258153i
$13$	−0.791428	−	0.791428i	−0.219503	−	0.219503i	0.588786	−	0.808289i	$-0.299606\pi$
$13$	−0.791428	−	0.791428i	−0.219503	−	0.219503i	−0.808289	+	0.588786i	$0.799606\pi$
$14$	1.10550	+	0.409686i	0.295456	+	0.109493i
$15$	−1.69263	+	3.31511i	−0.437036	+	0.855958i
$16$	2.37013	−	3.22218i	0.592533	−	0.805546i
$17$	1.86239	−	3.67852i	0.451696	−	0.892172i
$17$	1.86239	−	3.67852i	0.451696	−	0.892172i
$18$	0.319802	+	0.0511338i	0.0753780	+	0.0120523i
$19$	1.74054	−	0.720955i	0.399307	−	0.165398i	−0.173987	−	0.984748i	$-0.555665\pi$
$19$	1.74054	−	0.720955i	0.399307	−	0.165398i	0.573294	+	0.819349i	$0.305665\pi$
$20$	−0.855890	−	4.38947i	−0.191383	−	0.981515i
$21$	0.981272	+	0.981272i	0.214131	+	0.214131i
$22$	−7.47194	+	3.43130i	−1.59302	+	0.731555i
$23$	0.716030	+	3.59973i	0.149303	+	0.750595i	0.980792	+	0.195055i	$0.0624885\pi$
$23$	0.716030	+	3.59973i	0.149303	+	0.750595i	−0.831490	+	0.555540i	$0.812512\pi$
$24$	4.11807	−	2.28243i	0.840597	−	0.465898i
$25$	−4.25882	−	2.61963i	−0.851763	−	0.523927i
$26$	1.34839	+	0.829023i	0.264441	+	0.162585i
$27$	4.46923	+	2.98625i	0.860104	+	0.574703i
$28$	−1.65517	−	0.200839i	−0.312798	−	0.0379551i
$29$	−7.13568	+	4.76791i	−1.32506	+	0.885379i	−0.998216	−	0.0596986i	$-0.980986\pi$
$29$	−7.13568	+	4.76791i	−1.32506	+	0.885379i	−0.326847	+	0.945077i	$0.605986\pi$
$30$	1.24067	−	5.11573i	0.226515	−	0.934000i
$31$	0.420894	−	2.11598i	0.0755947	−	0.380040i	−0.924404	−	0.381414i	$-0.875437\pi$
$31$	0.420894	−	2.11598i	0.0755947	−	0.380040i	0.999999	+	0.00137362i	$0.000437238\pi$
$32$	−2.20315	+	5.21020i	−0.389465	+	0.921041i
$33$	−9.67805			−1.68473
$34$	−1.35495	+	5.67134i	−0.232372	+	0.972627i
$35$	−1.41849	+	1.20945i	−0.239769	+	0.204435i
$36$	−0.456705	+	0.0345924i	−0.0761175	+	0.00576541i
$37$	0.424529	−	2.13425i	0.0697921	−	0.350869i	−0.930072	−	0.367378i	$-0.880255\pi$
$37$	0.424529	−	2.13425i	0.0697921	−	0.350869i	0.999864	+	0.0165096i	$0.00525542\pi$
$38$	−2.15777	+	1.56287i	−0.350036	+	0.253531i
$39$	1.03510	+	1.54914i	0.165749	+	0.248061i
$40$	2.61765	+	5.75742i	0.413887	+	0.910328i
$41$	−3.08795	−	2.06330i	−0.482256	−	0.322233i	0.290567	−	0.956855i	$-0.406156\pi$
$41$	−3.08795	−	2.06330i	−0.482256	−	0.322233i	−0.772823	+	0.634621i	$0.781156\pi$
$42$	−1.67183	−	1.02789i	−0.257970	−	0.158606i
$43$	1.72320	−	4.16017i	0.262785	−	0.634420i	−0.736323	−	0.676630i	$-0.763440\pi$
$43$	1.72320	−	4.16017i	0.262785	−	0.634420i	0.999109	+	0.0422097i	$0.0134398\pi$
$44$	9.15269	−	7.17186i	1.37982	−	1.08120i
$45$	−0.317359	+	0.401875i	−0.0473091	+	0.0599079i
$46$	−2.16613	−	4.71692i	−0.319378	−	0.695472i
$47$	−7.04908	−	7.04908i	−1.02821	−	1.02821i	−0.999590	−	0.0286244i	$-0.990887\pi$
$47$	−7.04908	−	7.04908i	−1.02821	−	1.02821i	−0.0286244	−	0.999590i	$-0.509113\pi$
$48$	−4.91600	+	4.49097i	−0.709563	+	0.648216i
$49$	−2.41283	−	5.82508i	−0.344689	−	0.832154i
$50$	6.71808	+	2.20623i	0.950080	+	0.312008i
$51$	−4.23523	+	5.40090i	−0.593051	+	0.756277i
$52$	−2.12689	−	0.697990i	−0.294947	−	0.0967939i
$53$	8.10860	−	3.35869i	1.11380	−	0.461352i	0.251557	−	0.967843i	$-0.419058\pi$
$53$	8.10860	−	3.35869i	1.11380	−	0.461352i	0.862245	+	0.506491i	$0.169058\pi$
$54$	−7.12782	−	2.64151i	−0.969974	−	0.359463i
$55$	1.03086	−	12.9594i	0.139001	−	1.74745i
$56$	2.34279	−	0.266814i	0.313068	−	0.0356545i
$57$	−3.07582	+	0.611818i	−0.407402	+	0.0810373i
$58$	8.25156	−	8.90020i	1.08348	−	1.16865i
$59$	−4.00568	+	9.67056i	−0.521494	+	1.25900i	0.415480	+	0.909602i	$0.363614\pi$
$59$	−4.00568	+	9.67056i	−0.521494	+	1.25900i	−0.936975	+	0.349397i	$0.886386\pi$
$60$	−0.0281300	+	7.44440i	−0.00363157	+	0.961068i
$61$	−8.90360	−	5.94920i	−1.13999	−	0.761717i	−0.165513	−	0.986208i	$-0.552928\pi$
$61$	−8.90360	−	5.94920i	−1.13999	−	0.761717i	−0.974476	+	0.224491i	$0.927928\pi$
$62$	0.115302	+	3.04889i	0.0146433	+	0.387209i
$63$	0.106065	+	0.158738i	0.0133630	+	0.0199991i
$64$	1.32113	−	7.89016i	0.165141	−	0.986270i
$65$	−2.18463	+	1.22105i	−0.270970	+	0.151452i
$66$	13.3133	−	3.17556i	1.63876	−	0.390884i
$67$	9.22896			1.12750			0.563749	−	0.825946i	$-0.309359\pi$
$67$	9.22896			1.12750			0.563749	+	0.825946i	$0.309359\pi$
$68$	0.00302559	−	8.24621i	0.000366907	−	1.00000i
$69$		−	6.10961i		−	0.735511i
$70$	1.55447	−	2.12919i	0.185794	−	0.254487i
$71$	−2.73634	−	0.544291i	−0.324743	−	0.0645954i	0.0300266	−	0.999549i	$-0.490441\pi$
$71$	−2.73634	−	0.544291i	−0.324743	−	0.0645954i	−0.354770	+	0.934954i	$0.615441\pi$
$72$	0.616903	−	0.197440i	0.0727027	−	0.0232685i
$73$	−9.15520	−	13.7017i	−1.07154	−	1.60367i	−0.755780	−	0.654826i	$-0.772742\pi$
$73$	−9.15520	−	13.7017i	−1.07154	−	1.60367i	−0.315756	−	0.948840i	$-0.602258\pi$
$74$	0.116297	+	3.07522i	0.0135193	+	0.357487i
$75$	6.10240	+	5.66000i	0.704644	+	0.653560i
$76$	2.45547	−	2.85792i	0.281661	−	0.327826i
$77$	−4.47788	−	1.85480i	−0.510301	−	0.211374i
$78$	−1.93221	−	1.79139i	−0.218780	−	0.202835i
$79$	−0.721559	−	3.62752i	−0.0811818	−	0.408128i	−0.999912	−	0.0132432i	$-0.995784\pi$
$79$	−0.721559	−	3.62752i	−0.0811818	−	0.408128i	0.918731	−	0.394885i	$-0.129216\pi$
$80$	−5.49002	−	7.06114i	−0.613803	−	0.789459i
$81$	−5.84108	−	5.84108i	−0.649009	−	0.649009i
$82$	4.92486	+	1.82511i	0.543860	+	0.201549i
$83$	−1.61962	+	0.670870i	−0.177777	+	0.0736375i	−0.469796	−	0.882775i	$-0.655673\pi$
$83$	−1.61962	+	0.670870i	−0.177777	+	0.0736375i	0.292020	+	0.956412i	$0.405673\pi$
$84$	2.63708	+	0.865421i	0.287729	+	0.0944252i
$85$	−6.78097	−	6.24647i	−0.735500	−	0.677525i
$86$	−1.00544	+	6.28824i	−0.108419	+	0.678078i
$87$	13.1984	−	5.46697i	1.41502	−	0.586121i
$88$	−10.2374	+	12.8689i	−1.09131	+	1.37183i
$89$	−8.32848	+	8.32848i	−0.882818	+	0.882818i	−0.993820	−	0.111003i	$-0.964594\pi$
$89$	−8.32848	+	8.32848i	−0.882818	+	0.882818i	0.111003	+	0.993820i	$0.464594\pi$
$90$	0.304703	−	0.656959i	0.0321185	−	0.0692496i
$91$	0.182032	+	0.915138i	0.0190822	+	0.0959325i
$92$	4.52749	+	5.77796i	0.472023	+	0.602394i
$93$	−1.37434	+	3.31795i	−0.142512	+	0.344055i
$94$	12.0098	+	7.38394i	1.23872	+	0.761595i
$95$	−0.491636	−	4.18385i	−0.0504408	−	0.429254i
$96$	5.28898	−	7.79092i	0.539805	−	0.795158i
$97$	1.19945	−	0.801448i	0.121786	−	0.0813747i	−0.493185	−	0.869924i	$-0.664168\pi$
$97$	1.19945	−	0.801448i	0.121786	−	0.0813747i	0.614971	+	0.788550i	$0.289168\pi$
$98$	5.23046	+	7.22141i	0.528356	+	0.729473i
$99$	−1.30585	−	0.259749i	−0.131242	−	0.0261057i
$100$	−9.96544	−	0.830607i	−0.996544	−	0.0830607i
$101$	11.0712			1.10163			0.550813	−	0.834628i	$-0.314318\pi$
$101$	11.0712			1.10163			0.550813	+	0.834628i	$0.314318\pi$
$102$	4.05394	−	8.81926i	0.401400	−	0.873237i
$103$	−13.8536			−1.36504			−0.682518	−	0.730869i	$-0.739115\pi$
$103$	−13.8536			−1.36504			−0.682518	+	0.730869i	$0.739115\pi$
$104$	3.15483	+	0.262297i	0.309356	+	0.0257203i
$105$	2.70867	−	1.51395i	0.264339	−	0.147746i
$106$	−10.0523	+	7.28088i	−0.976368	+	0.707182i
$107$	0.207920	+	0.311175i	0.0201004	+	0.0300824i	0.841384	−	0.540438i	$-0.181741\pi$
$107$	0.207920	+	0.311175i	0.0201004	+	0.0300824i	−0.821283	+	0.570521i	$0.806741\pi$
$108$	10.6719	+	1.29494i	1.02691	+	0.124606i
$109$	0.544704	−	0.815206i	0.0521731	−	0.0780826i	−0.804466	−	0.593999i	$-0.797548\pi$
$109$	0.544704	−	0.815206i	0.0521731	−	0.0780826i	0.856639	+	0.515916i	$0.172548\pi$
$110$	2.83417	+	18.1655i	0.270227	+	1.73201i
$111$	−1.38621	+	3.34661i	−0.131573	+	0.317646i
$112$	−3.13525	+	1.13575i	−0.296253	+	0.107318i
$113$	2.90842	+	14.6216i	0.273601	+	1.37549i	0.836050	+	0.548654i	$0.184859\pi$
$113$	2.90842	+	14.6216i	0.273601	+	1.37549i	−0.562449	+	0.826832i	$0.690141\pi$
$114$	4.03041	−	1.85087i	0.377483	−	0.173349i
$115$	8.18109	+	0.650765i	0.762890	+	0.0606841i
$116$	−8.43071	+	14.9508i	−0.782772	+	1.38815i
$117$	0.0980875	+	0.236804i	0.00906819	+	0.0218925i
$118$	2.33720	−	14.6174i	0.215157	−	1.34564i
$119$	−2.99465	+	1.68723i	−0.274519	+	0.154668i
$120$	−2.40396	−	10.2499i	−0.219450	−	0.935685i
$121$	21.0661	−	8.72588i	1.91510	−	0.793262i
$122$	14.2000	+	5.26241i	1.28561	+	0.476436i
$123$	4.37146	+	4.37146i	0.394161	+	0.394161i
$124$	−1.15901	−	4.15629i	−0.104082	−	0.373245i
$125$	−8.22903	+	7.56856i	−0.736027	+	0.676952i
$126$	−0.197991	−	0.183561i	−0.0176384	−	0.0163529i
$127$	0.133794	−	0.323007i	0.0118723	−	0.0286623i	−0.917832	−	0.396969i	$-0.870062\pi$
$127$	0.133794	−	0.323007i	0.0118723	−	0.0286623i	0.929705	+	0.368306i	$0.120062\pi$
$128$	0.771535	+	11.2874i	0.0681947	+	0.997672i
$129$	−4.16440	+	6.23247i	−0.366655	+	0.548738i
$130$	2.60458	−	2.39652i	0.228437	−	0.210189i
$131$	−3.99977	−	5.98607i	−0.349461	−	0.523005i	0.614546	−	0.788881i	$-0.289339\pi$
$131$	−3.99977	−	5.98607i	−0.349461	−	0.523005i	−0.964007	+	0.265875i	$0.914339\pi$
$132$	−17.2722	+	8.73673i	−1.50335	+	0.760435i
$133$	−1.54038	−	0.306402i	−0.133568	−	0.0265684i
$134$	−12.6956	+	3.02820i	−1.09673	+	0.261597i
$135$	9.14593	−	7.79811i	0.787156	−	0.671155i
$136$	2.70158	+	11.3447i	0.231659	+	0.972797i
$137$			13.9544i			1.19220i	0.802909	+	0.596102i	$0.203284\pi$
$137$			13.9544i			1.19220i	−0.802909	+	0.596102i	$0.796716\pi$
$138$	2.00468	+	8.40452i	0.170650	+	0.715440i
$139$	−2.45988	+	12.3666i	−0.208644	+	1.04892i	0.724460	+	0.689317i	$0.242089\pi$
$139$	−2.45988	+	12.3666i	−0.208644	+	1.04892i	−0.933104	+	0.359608i	$0.882911\pi$
$140$	−1.43973	+	3.43901i	−0.121680	+	0.290649i
$141$	9.21944	+	13.7979i	0.776417	+	1.16199i
$142$	3.94276	−	0.149106i	0.330869	−	0.0125127i
$143$	−5.41057	−	3.61522i	−0.452454	−	0.302320i
$144$	−0.783842	+	0.474020i	−0.0653201	+	0.0395017i
$145$	5.91473	+	18.2557i	0.491191	+	1.51605i
$146$	17.0899	+	15.8444i	1.41437	+	1.31129i
$147$	2.04758	+	10.2939i	0.168881	+	0.849023i
$148$	−1.16902	−	4.19218i	−0.0960929	−	0.344595i
$149$	7.30705	−	7.30705i	0.598617	−	0.598617i	−0.341328	−	0.939944i	$-0.610877\pi$
$149$	7.30705	−	7.30705i	0.598617	−	0.598617i	0.939944	+	0.341328i	$0.110877\pi$
$150$	−10.2518	−	5.78371i	−0.837052	−	0.472238i
$151$	20.1723	−	8.35563i	1.64160	−	0.679972i	0.645139	−	0.764065i	$-0.276799\pi$
$151$	20.1723	−	8.35563i	1.64160	−	0.679972i	0.996458	+	0.0840929i	$0.0267993\pi$
$152$	−2.44006	+	4.73711i	−0.197915	+	0.384230i
$153$	−0.716408	+	0.615066i	−0.0579182	+	0.0497252i
$154$	6.76846	+	1.08222i	0.545418	+	0.0872080i
$155$	−4.29652	−	2.19372i	−0.345105	−	0.176204i
$156$	3.24578	+	1.83029i	0.259871	+	0.146540i
$157$	−8.46210	+	8.46210i	−0.675349	+	0.675349i	−0.958944	−	0.283595i	$-0.908473\pi$
$157$	−8.46210	+	8.46210i	−0.675349	+	0.675349i	0.283595	+	0.958944i	$0.408473\pi$
$158$	2.18285	+	4.75335i	0.173659	+	0.378156i
$159$	−14.3292	+	2.85026i	−1.13638	+	0.226040i
$160$	9.86910	+	7.91208i	0.780221	+	0.625505i
$161$	1.17091	−	2.82682i	0.0922803	−	0.222784i
$162$	9.95170	+	6.11855i	0.781879	+	0.480719i
$163$	3.21159	+	2.14592i	0.251551	+	0.168081i	0.674953	−	0.737861i	$-0.264164\pi$
$163$	3.21159	+	2.14592i	0.251551	+	0.168081i	−0.423401	+	0.905942i	$0.639164\pi$
$164$	−7.37360	−	0.894717i	−0.575781	−	0.0698657i
$165$	−5.89164	+	20.8234i	−0.458663	+	1.62110i
$166$	2.00786	−	1.45429i	0.155841	−	0.112875i
$167$	5.24869	+	1.04403i	0.406156	+	0.0807894i	0.393940	−	0.919136i	$-0.371112\pi$
$167$	5.24869	+	1.04403i	0.406156	+	0.0807894i	0.0122153	+	0.999925i	$0.496112\pi$
$168$	−3.91159	−	0.325216i	−0.301786	−	0.0250909i
$169$		−	11.7473i		−	0.903637i
$170$	11.3776	+	6.36782i	0.872626	+	0.488390i
$171$	−0.431436			−0.0329927
$172$	−0.680189	−	8.98015i	−0.0518639	−	0.684730i
$173$	2.81206	−	14.1372i	0.213797	−	1.07483i	−0.713544	−	0.700610i	$-0.752911\pi$
$173$	2.81206	−	14.1372i	0.213797	−	1.07483i	0.927341	−	0.374218i	$-0.122089\pi$
$174$	−16.3622	+	11.8511i	−1.24042	+	0.898433i
$175$	1.73874	+	3.78831i	0.131437	+	0.286369i
$176$	9.86028	−	21.0619i	0.743247	−	1.58760i
$177$	9.68039	−	14.4877i	0.727623	−	1.08896i
$178$	8.72411	−	14.1896i	0.653900	−	1.06355i
$179$	−18.5114	−	7.66769i	−1.38361	−	0.573110i	−0.438166	−	0.898894i	$-0.644372\pi$
$179$	−18.5114	−	7.66769i	−1.38361	−	0.573110i	−0.945444	+	0.325784i	$0.894372\pi$
$180$	−0.203595	+	1.00371i	−0.0151751	+	0.0748119i
$181$	0.438918	+	2.20659i	0.0326245	+	0.164015i	0.993663	−	0.112400i	$-0.0358537\pi$
$181$	0.438918	+	2.20659i	0.0326245	+	0.164015i	−0.961039	+	0.276414i	$0.910854\pi$
$182$	−0.550682	−	1.19916i	−0.0408193	−	0.0888874i
$183$	12.6044	+	12.6044i	0.931744	+	0.931744i
$184$	−8.12398	−	6.46273i	−0.598907	−	0.476439i
$185$	−4.33363	−	2.21267i	−0.318615	−	0.162679i
$186$	0.801889	−	5.01519i	0.0587974	−	0.367732i
$187$	6.44742	−	23.0881i	0.471482	−	1.68837i
$188$	−18.9438	−	6.21686i	−1.38162	−	0.453411i
$189$	−1.71480	−	4.13989i	−0.124733	−	0.301133i
$190$	2.04911	+	5.59408i	0.148658	+	0.405837i
$191$	11.3936	+	11.3936i	0.824410	+	0.824410i	0.986737	−	0.162327i	$-0.0519000\pi$
$191$	11.3936	+	11.3936i	0.824410	+	0.824410i	−0.162327	+	0.986737i	$0.551900\pi$
$192$	−4.71929	+	12.4528i	−0.340586	+	0.898702i
$193$	−9.84881	+	1.95905i	−0.708933	+	0.141015i	−0.536370	−	0.843983i	$-0.680205\pi$
$193$	−9.84881	+	1.95905i	−0.708933	+	0.141015i	−0.172563	+	0.984999i	$0.555205\pi$
$194$	−1.38702	+	1.49605i	−0.0995824	+	0.107410i
$195$	3.96327	−	1.28407i	0.283815	−	0.0919543i
$196$	−9.56462	−	8.21773i	−0.683187	−	0.586980i
$197$	9.58271	−	14.3415i	0.682740	−	1.02179i	−0.314623	−	0.949217i	$-0.601878\pi$
$197$	9.58271	−	14.3415i	0.682740	−	1.02179i	0.997363	−	0.0725757i	$-0.0231219\pi$
$198$	1.88158	−	0.0711568i	0.133718	−	0.00505690i
$199$	−10.4480	+	6.98112i	−0.740638	+	0.494878i	−0.867744	−	0.497011i	$-0.834431\pi$
$199$	−10.4480	+	6.98112i	−0.740638	+	0.494878i	0.127107	+	0.991889i	$0.459431\pi$
$200$	13.9812	−	2.12725i	0.988622	−	0.150420i
$201$	−15.0676	−	2.99714i	−1.06279	−	0.211402i
$202$	−15.2298	+	3.63268i	−1.07157	+	0.255594i
$203$	7.15444			0.502143
$204$	−2.68292	+	13.4622i	−0.187842	+	0.942539i
$205$	−6.31924	+	5.38798i	−0.441355	+	0.376313i
$206$	19.0573	−	4.54563i	1.32779	−	0.316709i
$207$	0.163976	−	0.824361i	0.0113971	−	0.0572970i
$208$	−4.42591	+	0.674338i	−0.306882	+	0.0467569i
$209$	9.10721	−	6.08524i	0.629959	−	0.420925i
$210$	−3.22935	+	2.97139i	−0.222847	+	0.205045i
$211$	2.18387	+	1.45921i	0.150344	+	0.100456i	0.628467	−	0.777836i	$-0.283683\pi$
$211$	2.18387	+	1.45921i	0.150344	+	0.100456i	−0.478123	+	0.878293i	$0.658683\pi$
$212$	11.4392	−	13.3141i	0.785648	−	0.914417i
$213$	4.29070	+	1.77727i	0.293994	+	0.121776i
$214$	−0.388122	−	0.359836i	−0.0265315	−	0.0245979i
$215$	−7.90203	−	6.24020i	−0.538914	−	0.425578i
$216$	−15.1054	+	1.72032i	−1.02779	+	0.117053i
$217$	−1.27177	+	1.27177i	−0.0863333	+	0.0863333i
$218$	−0.481821	+	1.30014i	−0.0326331	+	0.0880569i
$219$	10.4975	+	25.3432i	0.709356	+	1.71254i
$220$	−9.85920	−	24.0589i	−0.664707	−	1.62205i
$221$	−4.38523	+	1.43734i	−0.294982	+	0.0966856i
$222$	0.808815	−	5.05851i	0.0542841	−	0.339505i
$223$	0.651353	−	0.269799i	0.0436178	−	0.0180671i	−0.360768	−	0.932656i	$-0.617485\pi$
$223$	0.651353	−	0.269799i	0.0436178	−	0.0180671i	0.404386	+	0.914589i	$0.367485\pi$
$224$	3.94026	−	2.59110i	0.263269	−	0.173125i
$225$	0.671479	+	0.927477i	0.0447653	+	0.0618318i
$226$	−8.79852	−	19.1595i	−0.585269	−	1.27447i
$227$	19.3475	−	3.84845i	1.28414	−	0.255431i	0.494592	−	0.869125i	$-0.335317\pi$
$227$	19.3475	−	3.84845i	1.28414	−	0.255431i	0.789544	+	0.613694i	$0.210317\pi$
$228$	−4.93702	+	3.86855i	−0.326962	+	0.256201i
$229$	21.3164	+	8.82955i	1.40863	+	0.583473i	0.951976	−	0.306173i	$-0.0990485\pi$
$229$	21.3164	+	8.82955i	1.40863	+	0.583473i	0.456652	+	0.889645i	$0.349049\pi$
$230$	−11.4676	+	1.78917i	−0.756152	+	0.117974i
$231$	6.70843	+	4.48243i	0.441382	+	0.294922i
$232$	6.69182	−	23.3330i	0.439340	−	1.53188i
$233$	−0.420693	+	0.281098i	−0.0275605	+	0.0184153i	−0.569274	−	0.822148i	$-0.692776\pi$
$233$	−0.420693	+	0.281098i	−0.0275605	+	0.0184153i	0.541714	+	0.840563i	$0.317776\pi$
$234$	−0.212631	−	0.293569i	−0.0139001	−	0.0191912i
$235$	−19.4581	+	10.8756i	−1.26930	+	0.709448i
$236$	1.58114	+	20.8749i	0.102923	+	1.35884i
$237$			6.15679i			0.399926i
$238$	3.56590	−	3.30359i	0.231143	−	0.214140i
$239$			15.1718i			0.981381i	0.871334	+	0.490690i	$0.163255\pi$
$239$			15.1718i			0.981381i	−0.871334	+	0.490690i	$0.836745\pi$
$240$	6.67013	+	13.3112i	0.430555	+	0.859236i
$241$	0.733977	−	3.68995i	0.0472796	−	0.237691i	−0.949918	−	0.312498i	$-0.898834\pi$
$241$	0.733977	−	3.68995i	0.0472796	−	0.237691i	0.997198	+	0.0748074i	$0.0238342\pi$
$242$	−26.1159	+	18.9157i	−1.67880	+	1.21595i
$243$	−1.31924	−	1.97438i	−0.0846292	−	0.126657i
$244$	−21.2606	−	2.57977i	−1.36107	−	0.165153i
$245$	−14.0021	+	1.64536i	−0.894562	+	0.105118i
$246$	−7.44783	−	4.57912i	−0.474857	−	0.291954i
$247$	−1.94810	−	0.806927i	−0.123954	−	0.0513436i
$248$	2.95812	+	5.33719i	0.187841	+	0.338912i
$249$	2.86214	−	0.569314i	0.181381	−	0.0360788i
$250$	8.83665	−	13.1116i	0.558879	−	0.829249i
$251$	7.68901	+	7.68901i	0.485326	+	0.485326i	0.906828	−	0.421501i	$-0.138497\pi$
$251$	7.68901	+	7.68901i	0.485326	+	0.485326i	−0.421501	+	0.906828i	$0.638497\pi$
$252$	0.332591	+	0.187547i	0.0209512	+	0.0118143i
$253$	8.16593	+	19.7143i	0.513387	+	1.23943i
$254$	−0.0780651	+	0.488237i	−0.00489824	+	0.0306347i
$255$	9.04235	+	12.4004i	0.566254	+	0.776544i
$256$	−4.76495	−	15.2740i	−0.297809	−	0.954625i
$257$	−1.07291	−	2.59024i	−0.0669264	−	0.161575i	0.886877	−	0.462005i	$-0.152870\pi$
$257$	−1.07291	−	2.59024i	−0.0669264	−	0.161575i	−0.953804	+	0.300430i	$0.902870\pi$
$258$	3.68365	−	9.93994i	0.229334	−	0.618834i
$259$	−1.28275	+	1.28275i	−0.0797064	+	0.0797064i
$260$	−2.79657	+	4.15132i	−0.173436	+	0.257454i
$261$	1.92757	−	0.383418i	0.119314	−	0.0237330i
$262$	7.46631	+	6.92217i	0.461270	+	0.427653i
$263$	−8.89242	+	21.4682i	−0.548330	+	1.32379i	0.370390	+	0.928876i	$0.379224\pi$
$263$	−8.89242	+	21.4682i	−0.548330	+	1.32379i	−0.918720	+	0.394909i	$0.870776\pi$
$264$	20.8933	−	17.6858i	1.28589	−	1.08848i
$265$	−2.29037	−	19.4912i	−0.140696	−	1.19733i
$266$	2.21952	−	0.0839371i	0.136088	−	0.00514652i
$267$	16.3022	−	10.8928i	0.997676	−	0.666626i
$268$	16.4707	−	8.33132i	1.00611	−	0.508917i
$269$	3.10609	−	15.6154i	0.189382	−	0.952087i	−0.762818	−	0.646613i	$-0.776185\pi$
$269$	3.10609	−	15.6154i	0.189382	−	0.952087i	0.952200	−	0.305474i	$-0.0988150\pi$
$270$	−10.0226	+	13.7282i	−0.609958	+	0.835473i
$271$	25.3129			1.53765			0.768826	−	0.639458i	$-0.220841\pi$
$271$	25.3129			1.53765			0.768826	+	0.639458i	$0.220841\pi$
$272$	−7.43876	−	14.7195i	−0.451041	−	0.892503i
$273$		−	1.55321i		−	0.0940046i
$274$	−4.57870	−	19.1960i	−0.276610	−	1.15967i
$275$	−27.2560	−	10.1072i	−1.64360	−	0.609488i
$276$	−5.51537	−	10.9037i	−0.331986	−	0.656324i
$277$	−11.1341	+	7.43956i	−0.668983	+	0.447000i	−0.843123	−	0.537721i	$-0.819285\pi$
$277$	−11.1341	+	7.43956i	−0.668983	+	0.447000i	0.174140	+	0.984721i	$0.444285\pi$
$278$	−0.673871	−	17.8190i	−0.0404161	−	1.06871i
$279$	−0.274488	+	0.410800i	−0.0164332	+	0.0245940i
$280$	0.852124	−	5.20319i	0.0509241	−	0.310950i
$281$	16.8511	+	6.97996i	1.00525	+	0.416389i	0.823721	−	0.566996i	$-0.191894\pi$
$281$	16.8511	+	6.97996i	1.00525	+	0.416389i	0.181532	+	0.983385i	$0.441894\pi$
$282$	−17.2098	−	15.9556i	−1.02483	−	0.950141i
$283$	1.44073	+	7.24303i	0.0856424	+	0.430554i	0.999689	+	0.0249440i	$0.00794074\pi$
$283$	1.44073	+	7.24303i	0.0856424	+	0.430554i	−0.914046	+	0.405610i	$0.867059\pi$
$284$	−5.37482	+	1.49881i	−0.318937	+	0.0889379i
$285$	−0.556051	+	6.99040i	−0.0329376	+	0.414075i
$286$	8.62912	+	3.19787i	0.510251	+	0.189094i
$287$	1.18481	+	2.86039i	0.0699373	+	0.168844i
$288$	0.922735	−	0.909267i	0.0543727	−	0.0535791i
$289$	−10.0630	−	13.7017i	−0.591942	−	0.805981i
$290$	−14.1265	−	23.1722i	−0.829536	−	1.36072i
$291$	−2.21855	+	0.918954i	−0.130054	+	0.0538700i
$292$	−28.7081	−	16.1884i	−1.68002	−	0.947355i
$293$	10.5333	−	10.5333i	0.615365	−	0.615365i	−0.328974	−	0.944339i	$-0.606703\pi$
$293$	10.5333	−	10.5333i	0.615365	−	0.615365i	0.944339	+	0.328974i	$0.106703\pi$
$294$	−6.19430	−	13.4886i	−0.361259	−	0.786672i
$295$	18.3687	+	14.5057i	1.06947	+	0.844555i
$296$	2.98367	+	5.38328i	0.173422	+	0.312897i
$297$	28.8717	+	11.9590i	1.67531	+	0.693934i
$298$	−7.65416	+	12.4493i	−0.443393	+	0.721170i
$299$	2.28224	−	3.41561i	0.131985	−	0.197530i
$300$	16.0003	+	4.59240i	0.923777	+	0.265142i
$301$	−3.12125	+	2.08555i	−0.179906	+	0.120209i
$302$	−25.0078	+	18.1131i	−1.43904	+	1.04229i
$303$	−18.0754	−	3.59541i	−1.03840	−	0.206551i
$304$	1.80226	−	7.31710i	0.103367	−	0.419664i
$305$	−18.2205	+	15.5354i	−1.04330	+	0.889554i
$306$	0.783692	−	1.08117i	0.0448007	−	0.0618062i
$307$		−	3.32653i		−	0.189855i	−0.995484	−	0.0949274i	$-0.969738\pi$
$307$		−	3.32653i		−	0.189855i	0.995484	−	0.0949274i	$-0.0302619\pi$
$308$	−9.66595	+	0.732133i	−0.550769	+	0.0417172i
$309$	22.6180	+	4.49900i	1.28669	+	0.255939i
$310$	6.63019	+	1.60796i	0.376570	+	0.0913263i
$311$	−16.9690	−	25.3959i	−0.962225	−	1.44007i	−0.896913	−	0.442206i	$-0.854196\pi$
$311$	−16.9690	−	25.3959i	−0.962225	−	1.44007i	−0.0653113	−	0.997865i	$-0.520804\pi$
$312$	−5.06553	−	1.45278i	−0.286779	−	0.0822473i
$313$	−1.75723	+	2.62988i	−0.0993246	+	0.148650i	−0.877803	−	0.479021i	$-0.840992\pi$
$313$	−1.75723	+	2.62988i	−0.0993246	+	0.148650i	0.778479	+	0.627671i	$0.215992\pi$
$314$	8.86407	−	14.4172i	0.500229	−	0.813611i
$315$	0.406110	−	0.131577i	0.0228817	−	0.00741352i
$316$	−4.56245	−	5.82257i	−0.256658	−	0.327545i
$317$	6.68042	−	1.32882i	0.375210	−	0.0746339i	−0.00388305	−	0.999992i	$-0.501236\pi$
$317$	6.68042	−	1.32882i	0.375210	−	0.0746339i	0.379093	+	0.925359i	$0.376236\pi$
$318$	18.7764	−	8.62257i	1.05293	−	0.483530i
$319$	−35.2813	+	35.2813i	−1.97537	+	1.97537i
$320$	−16.1723	−	7.64579i	−0.904057	−	0.427413i
$321$	−0.238405	−	0.575560i	−0.0133065	−	0.0321247i
$322$	−0.683191	+	4.27283i	−0.0380728	+	0.238115i
$323$	0.589516	−	7.74531i	0.0328015	−	0.430961i
$324$	−15.6974	−	5.15147i	−0.872077	−	0.286193i
$325$	1.29729	+	5.44380i	0.0719609	+	0.301967i
$326$	−5.12205	−	1.89819i	−0.283684	−	0.105131i
$327$	−1.15405	+	1.15405i	−0.0638190	+	0.0638190i
$328$	10.4369	−	1.18863i	0.576279	−	0.0656310i
$329$	1.62132	+	8.15095i	0.0893865	+	0.449376i
$330$	1.27212	−	30.5782i	0.0700281	−	1.68328i
$331$	6.62845	−	16.0025i	0.364332	−	0.879576i	−0.630324	−	0.776332i	$-0.717078\pi$
$331$	6.62845	−	16.0025i	0.364332	−	0.879576i	0.994656	−	0.103244i	$-0.0329222\pi$
$332$	−2.28488	+	2.65938i	−0.125399	+	0.145952i
$333$	−0.276859	+	0.414348i	−0.0151718	+	0.0227062i
$334$	−7.56278	+	0.286006i	−0.413817	+	0.0156496i
$335$	5.61825	−	19.8571i	0.306958	−	1.08491i
$336$	5.48758	−	0.836095i	0.299372	−	0.0456127i
$337$	3.69834	−	18.5928i	0.201461	−	1.01282i	−0.739204	−	0.673481i	$-0.764798\pi$
$337$	3.69834	−	18.5928i	0.201461	−	1.01282i	0.940666	−	0.339334i	$-0.110202\pi$
$338$	3.85451	+	16.1598i	0.209658	+	0.878979i
$339$		−	24.8164i		−	1.34784i
$340$	−17.7408	−	5.02650i	−0.962127	−	0.272600i
$341$		−	12.5432i		−	0.679250i
$342$	0.593493	−	0.141563i	0.0320924	−	0.00765482i
$343$	−2.16390	+	10.8787i	−0.116840	+	0.587393i
$344$	3.88224	+	12.1301i	0.209317	+	0.654012i
$345$	−13.1455	−	3.71930i	−0.707728	−	0.200240i
$346$	0.770348	+	20.3701i	0.0414142	+	1.09510i
$347$	−3.35404	+	5.01968i	−0.180054	+	0.269470i	−0.910508	−	0.413492i	$-0.864309\pi$
$347$	−3.35404	+	5.01968i	−0.180054	+	0.269470i	0.730453	+	0.682963i	$0.239309\pi$
$348$	18.6197	−	21.6715i	0.998119	−	1.16171i
$349$	11.8464	−	28.5999i	0.634126	−	1.53092i	−0.200265	−	0.979742i	$-0.564180\pi$
$349$	11.8464	−	28.5999i	0.634126	−	1.53092i	0.834391	−	0.551173i	$-0.185820\pi$
$350$	−3.63487	−	4.64077i	−0.194292	−	0.248060i
$351$	−1.17368	−	5.90047i	−0.0626462	−	0.314944i
$352$	−6.65320	+	32.2086i	−0.354617	+	1.71672i
$353$	2.09608	−	2.09608i	0.111563	−	0.111563i	−0.649122	−	0.760685i	$-0.724863\pi$
$353$	2.09608	−	2.09608i	0.111563	−	0.111563i	0.760685	+	0.649122i	$0.224863\pi$
$354$	−8.56286	+	23.1060i	−0.455111	+	1.22807i
$355$	−2.83688	+	5.55617i	−0.150566	+	0.294891i
$356$	−7.34521	+	22.3821i	−0.389295	+	1.18625i
$357$	5.43714	−	1.78212i	0.287764	−	0.0943196i
$358$	27.9807	+	4.47388i	1.47882	+	0.236452i
$359$	−4.72206	−	11.4001i	−0.249221	−	0.601673i	0.748917	−	0.662663i	$-0.230574\pi$
$359$	−4.72206	−	11.4001i	−0.249221	−	0.601673i	−0.998138	+	0.0609908i	$0.980574\pi$
$360$	−0.0492652	−	1.44753i	−0.00259650	−	0.0762913i
$361$	−10.9253	+	10.9253i	−0.575017	+	0.575017i
$362$	−1.32781	−	2.89142i	−0.0697882	−	0.151970i
$363$	−37.2273	+	7.40497i	−1.95393	+	0.388660i
$364$	1.15100	+	1.46890i	0.0603287	+	0.0769911i
$365$	−35.0541	+	11.3573i	−1.83481	+	0.594468i
$366$	−21.4746	−	13.2031i	−1.12250	−	0.690140i
$367$	4.02147	−	6.01856i	0.209919	−	0.314166i	−0.711537	−	0.702649i	$-0.752001\pi$
$367$	4.02147	−	6.01856i	0.209919	−	0.314166i	0.921456	+	0.388482i	$0.127001\pi$
$368$	13.2961	+	6.22465i	0.693106	+	0.324482i
$369$	0.472509	+	0.707160i	0.0245978	+	0.0368133i
$370$	6.68746	+	1.62185i	0.347664	+	0.0843161i
$371$	−7.17614	−	1.42742i	−0.372567	−	0.0741081i
$372$	0.542485	+	7.16213i	0.0281265	+	0.371339i
$373$		−	31.5176i		−	1.63192i	−0.578108	−	0.815960i	$-0.696209\pi$
$373$		−	31.5176i		−	1.63192i	0.578108	−	0.815960i	$-0.303791\pi$
$374$	−1.29356	+	33.8761i	−0.0668884	+	1.75169i
$375$	15.8930	−	9.68436i	0.820711	−	0.500098i
$376$	28.0994	+	2.33623i	1.44912	+	0.120482i
$377$	9.42083	+	1.87392i	0.485198	+	0.0965118i
$378$	3.71729	+	5.13227i	0.191197	+	0.263975i
$379$	17.5749	−	11.7432i	0.902763	−	0.603207i	−0.0151950	−	0.999885i	$-0.504837\pi$
$379$	17.5749	−	11.7432i	0.902763	−	0.603207i	0.917958	+	0.396678i	$0.129837\pi$
$380$	−4.65432	−	7.02299i	−0.238762	−	0.360272i
$381$	−0.323336	+	0.483906i	−0.0165650	+	0.0247913i
$382$	−19.4117	−	11.9348i	−0.993189	−	0.610638i
$383$	1.91773	+	0.794351i	0.0979916	+	0.0405895i	0.431141	−	0.902285i	$-0.358111\pi$
$383$	1.91773	+	0.794351i	0.0979916	+	0.0405895i	−0.333149	+	0.942874i	$0.608111\pi$
$384$	2.40597	−	18.6788i	0.122779	−	0.953200i
$385$	−6.71676	+	8.50549i	−0.342318	+	0.433480i
$386$	12.9054	−	5.92650i	0.656869	−	0.301651i
$387$	−0.729170	+	0.729170i	−0.0370658	+	0.0370658i
$388$	1.41713	−	2.51311i	0.0719441	−	0.127584i
$389$	20.3375	−	8.42405i	1.03115	−	0.427117i	0.198023	−	0.980197i	$-0.436548\pi$
$389$	20.3375	−	8.42405i	1.03115	−	0.427117i	0.833128	+	0.553081i	$0.186548\pi$
$390$	−5.03063	+	3.06682i	−0.254736	+	0.155295i
$391$	14.5752	+	4.07016i	0.737099	+	0.205837i
$392$	15.8537	+	8.16615i	0.800733	+	0.412453i
$393$	4.58620	+	11.0721i	0.231343	+	0.558512i
$394$	−8.47646	+	22.8728i	−0.427038	+	1.15232i
$395$	−8.24426	−	0.655790i	−0.414814	−	0.0329964i
$396$	−2.56500	+	0.715268i	−0.128896	+	0.0359435i
$397$	1.97679	+	9.93798i	0.0992121	+	0.498773i	0.998156	+	0.0607083i	$0.0193359\pi$
$397$	1.97679	+	9.93798i	0.0992121	+	0.498773i	−0.898943	+	0.438065i	$0.855664\pi$
$398$	12.0818	−	13.0316i	0.605608	−	0.653214i
$399$	2.41540	+	1.00049i	0.120921	+	0.0500871i
$400$	−18.5349	+	7.51381i	−0.926745	+	0.375691i
$401$	3.25735	−	4.87497i	0.162664	−	0.243444i	−0.741179	−	0.671307i	$-0.765733\pi$
$401$	3.25735	−	4.87497i	0.162664	−	0.243444i	0.903844	+	0.427863i	$0.140733\pi$
$402$	21.7108	−	0.821050i	1.08283	−	0.0409502i
$403$	−2.00775	+	1.34153i	−0.100013	+	0.0668266i
$404$	19.7585	−	9.99439i	0.983023	−	0.497240i
$405$	−16.1235	+	9.01187i	−0.801185	+	0.447804i
$406$	−9.84181	+	2.34751i	−0.488441	+	0.116505i
$407$		−	12.6515i		−	0.627111i
$408$	−0.726502	−	19.3992i	−0.0359672	−	0.960401i
$409$	27.3786			1.35378			0.676891	−	0.736083i	$-0.263327\pi$
$409$	27.3786			1.35378			0.676891	+	0.736083i	$0.263327\pi$
$410$	6.92498	−	9.48530i	0.342000	−	0.468445i
$411$	4.53173	−	22.7826i	0.223534	−	1.12378i
$412$	−24.7242	+	12.5062i	−1.21807	+	0.616134i
$413$	7.25553	−	4.84799i	0.357021	−	0.238554i
$414$	0.0449203	+	1.18781i	0.00220771	+	0.0583778i
$415$	0.457481	+	3.89319i	0.0224569	+	0.191109i
$416$	5.86712	−	2.37986i	0.287659	−	0.116682i
$417$	8.03221	−	19.3915i	0.393339	−	0.949605i
$418$	−10.5314	+	11.3592i	−0.515107	+	0.555599i
$419$	29.1455	−	5.79740i	1.42385	−	0.283221i	0.577736	−	0.816223i	$-0.303936\pi$
$419$	29.1455	−	5.79740i	1.42385	−	0.283221i	0.846114	+	0.533002i	$0.178936\pi$
$420$	3.46740	−	5.14712i	0.169192	−	0.251154i
$421$	−25.4046	+	25.4046i	−1.23814	+	1.23814i	−0.277385	+	0.960759i	$0.589468\pi$
$421$	−25.4046	+	25.4046i	−1.23814	+	1.23814i	−0.960759	+	0.277385i	$0.910532\pi$
$422$	−3.48297	−	1.29076i	−0.169548	−	0.0628331i
$423$	0.873645	+	2.10917i	0.0424781	+	0.102551i
$424$	−11.3674	+	22.0686i	−0.552050	+	1.07175i
$425$	−17.5680	+	10.7874i	−0.852171	+	0.523264i
$426$	−6.48554	−	1.03699i	−0.314226	−	0.0502422i
$427$	3.41622	+	8.24748i	0.165322	+	0.399124i
$428$	0.651979	+	0.367648i	0.0315146	+	0.0177710i
$429$	7.65948	+	7.65948i	0.369803	+	0.369803i
$430$	12.9177	+	5.99136i	0.622949	+	0.288929i
$431$	−18.7201	+	3.72365i	−0.901713	+	0.179362i	−0.624112	−	0.781335i	$-0.714539\pi$
$431$	−18.7201	+	3.72365i	−0.901713	+	0.179362i	−0.277601	+	0.960696i	$0.589539\pi$
$432$	20.2149	−	7.32290i	0.972590	−	0.352323i
$433$	8.72685	+	3.61478i	0.419386	+	0.173715i	0.582389	−	0.812910i	$-0.302118\pi$
$433$	8.72685	+	3.61478i	0.419386	+	0.173715i	−0.163003	+	0.986626i	$0.552118\pi$
$434$	1.33218	−	2.16677i	0.0639468	−	0.104008i
$435$	−3.72805	−	31.7259i	−0.178746	−	1.52114i
$436$	0.236202	−	1.94660i	0.0113120	−	0.0932254i
$437$	3.84152	+	5.74924i	0.183765	+	0.275024i
$438$	−22.7562	−	31.4183i	−1.08733	−	1.50122i
$439$	5.40393	−	27.1674i	0.257916	−	1.29663i	−0.606996	−	0.794705i	$-0.707626\pi$
$439$	5.40393	−	27.1674i	0.257916	−	1.29663i	0.864912	−	0.501924i	$-0.167374\pi$
$440$	21.4567	+	29.8610i	1.02291	+	1.42357i
$441$			1.44389i			0.0687567i
$442$	5.56080	−	3.41611i	0.264500	−	0.162488i
$443$			22.1171i			1.05081i	0.850851	+	0.525407i	$0.176087\pi$
$443$			22.1171i			1.05081i	−0.850851	+	0.525407i	$0.823913\pi$
$444$	0.547171	+	7.22399i	0.0259676	+	0.342835i
$445$	12.8495	+	22.9897i	0.609127	+	1.08982i
$446$	−0.807490	+	0.584864i	−0.0382358	+	0.0276941i
$447$	−14.3028	+	9.55683i	−0.676499	+	0.452022i
$448$	−4.57011	+	4.85725i	−0.215918	+	0.229483i
$449$	−4.73128	−	3.16134i	−0.223283	−	0.149193i	0.438898	−	0.898537i	$-0.355369\pi$
$449$	−4.73128	−	3.16134i	−0.223283	−	0.149193i	−0.662181	+	0.749344i	$0.730369\pi$
$450$	−1.22803	−	1.05553i	−0.0578897	−	0.0497583i
$451$	−19.9484	−	8.26291i	−0.939335	−	0.389085i
$452$	18.3901	+	23.4693i	0.864995	+	1.10390i
$453$	−35.6477	+	7.09077i	−1.67487	+	0.333153i
$454$	−25.3521	+	11.6423i	−1.18983	+	0.546400i
$455$	2.07983	+	0.165440i	0.0975040	+	0.00775596i
$456$	5.52213	−	6.94160i	0.258598	−	0.325070i
$457$	−6.25534	+	2.59105i	−0.292612	+	0.121204i	−0.524161	−	0.851619i	$-0.675621\pi$
$457$	−6.25534	+	2.59105i	−0.292612	+	0.121204i	0.231548	+	0.972823i	$0.425621\pi$
$458$	−32.2205	−	5.15180i	−1.50556	−	0.240728i
$459$	19.3084	−	10.8786i	0.901240	−	0.507770i
$460$	15.1881	−	6.22397i	0.708147	−	0.290194i
$461$	5.47495	+	13.2177i	0.254994	+	0.615610i	0.998594	−	0.0530153i	$-0.0168832\pi$
$461$	5.47495	+	13.2177i	0.254994	+	0.615610i	−0.743600	+	0.668625i	$0.766883\pi$
$462$	−10.6990	−	3.96497i	−0.497764	−	0.184467i
$463$	−10.7407	+	10.7407i	−0.499164	+	0.499164i	−0.911178	−	0.412014i	$-0.864825\pi$
$463$	−10.7407	+	10.7407i	−0.499164	+	0.499164i	0.412014	+	0.911178i	$0.364825\pi$
$464$	−1.54942	+	34.2931i	−0.0719302	+	1.59202i
$465$	6.30227	+	4.97688i	0.292261	+	0.230797i
$466$	0.486481	−	0.524722i	0.0225358	−	0.0243073i
$467$	−8.36974	−	3.46686i	−0.387305	−	0.160427i	0.180530	−	0.983570i	$-0.442219\pi$
$467$	−8.36974	−	3.46686i	−0.387305	−	0.160427i	−0.567835	+	0.823142i	$0.692219\pi$
$468$	0.388826	+	0.334071i	0.0179735	+	0.0154424i
$469$	−6.39714	−	4.27443i	−0.295392	−	0.197375i
$470$	23.1985	−	21.3453i	1.07007	−	0.984587i
$471$	16.5637	−	11.0675i	0.763215	−	0.509964i
$472$	−9.02450	−	28.1971i	−0.415386	−	1.29788i
$473$	5.10742	−	25.6767i	0.234839	−	1.18062i
$474$	−2.02016	−	8.46941i	−0.0927891	−	0.389013i
$475$	−9.30128	−	1.48916i	−0.426772	−	0.0683275i
$476$	−3.82136	+	5.71454i	−0.175152	+	0.261925i
$477$	−2.00992			−0.0920278
$478$	−4.97815	−	20.8706i	−0.227695	−	0.954601i
$479$	−5.04342	−	1.00320i	−0.230440	−	0.0458374i	0.0785195	−	0.996913i	$-0.474981\pi$
$479$	−5.04342	−	1.00320i	−0.230440	−	0.0458374i	−0.308959	+	0.951075i	$0.599981\pi$
$480$	−13.5433	−	16.1226i	−0.618162	−	0.735894i
$481$	−2.02509	+	1.35312i	−0.0923361	+	0.0616970i
$482$	0.201069	+	5.31681i	0.00915845	+	0.242174i
$483$	−2.82969	+	4.23493i	−0.128755	+	0.192696i
$484$	29.7191	−	34.5901i	1.35087	−	1.57228i
$485$	−0.994219	−	3.06864i	−0.0451451	−	0.139340i
$486$	2.46261	+	2.28313i	0.111706	+	0.103565i
$487$	−21.5019	+	4.27700i	−0.974345	+	0.193809i	−0.656494	−	0.754331i	$-0.727961\pi$
$487$	−21.5019	+	4.27700i	−0.974345	+	0.193809i	−0.317851	+	0.948141i	$0.602961\pi$
$488$	30.0930	−	3.42722i	1.36225	−	0.155143i
$489$	−4.54649	−	4.54649i	−0.205600	−	0.205600i
$490$	18.7217	−	6.85776i	0.845762	−	0.309802i
$491$	4.12613	+	9.96135i	0.186210	+	0.449550i	0.989224	−	0.146410i	$-0.0467719\pi$
$491$	4.12613	+	9.96135i	0.186210	+	0.449550i	−0.803014	+	0.595960i	$0.796772\pi$
$492$	11.7479	+	3.85536i	0.529637	+	0.173813i
$493$	4.24943	+	35.1285i	0.191385	+	1.58211i
$494$	2.94461	+	0.470820i	0.132484	+	0.0211832i
$495$	−1.35383	+	2.65154i	−0.0608500	+	0.119178i
$496$	−5.82049	−	6.37134i	−0.261348	−	0.286082i
$497$	1.64463	+	1.64463i	0.0737715	+	0.0737715i
$498$	−3.75042	+	1.72228i	−0.168060	+	0.0771774i
$499$	6.07923	+	30.5623i	0.272144	+	1.36816i	0.838906	+	0.544277i	$0.183196\pi$
$499$	6.07923	+	30.5623i	0.272144	+	1.36816i	−0.566762	+	0.823881i	$0.691804\pi$
$500$	−7.85373	+	20.9361i	−0.351230	+	0.936289i
$501$	−8.23019	−	3.40906i	−0.367698	−	0.152305i
$502$	−13.1001	−	8.05427i	−0.584686	−	0.359480i
$503$	22.4258	−	33.5626i	0.999917	−	1.49648i	0.137359	−	0.990521i	$-0.456139\pi$
$503$	22.4258	−	33.5626i	0.999917	−	1.49648i	0.862557	−	0.505960i	$-0.168861\pi$
$504$	−0.519057	−	0.148864i	−0.0231206	−	0.00663093i
$505$	6.73974	−	23.8209i	0.299915	−	1.06002i
$506$	−17.7019	−	24.4400i	−0.786944	−	1.08649i
$507$	−3.81497	+	19.1791i	−0.169429	+	0.851776i
$508$	−0.0528118	−	0.697244i	−0.00234314	−	0.0309352i
$509$	3.05215			0.135284			0.0676420	−	0.997710i	$-0.478452\pi$
$509$	3.05215			0.135284			0.0676420	+	0.997710i	$0.478452\pi$
$510$	−16.5077	−	14.0913i	−0.730973	−	0.623974i
$511$			13.7378i			0.607722i
$512$	11.5665	+	19.4478i	0.511170	+	0.859479i
$513$	9.93183	+	1.97556i	0.438501	+	0.0872233i
$514$	2.32583	+	3.21115i	0.102588	+	0.141638i
$515$	−8.43355	+	29.8075i	−0.371627	+	1.31347i
$516$	−1.80583	+	14.8823i	−0.0794971	+	0.655156i
$517$	−48.1908	−	32.2001i	−2.11943	−	1.41616i
$518$	1.34369	−	2.18548i	0.0590383	−	0.0960245i
$519$	−9.18218	+	22.1677i	−0.403053	+	0.973056i
$520$	2.48490	−	6.62826i	0.108970	−	0.290669i
$521$	−17.7129	+	3.52331i	−0.776014	+	0.154359i	−0.567182	−	0.823593i	$-0.691966\pi$
$521$	−17.7129	+	3.52331i	−0.776014	+	0.154359i	−0.208832	+	0.977951i	$0.566966\pi$
$522$	−2.52581	+	1.15991i	−0.110552	+	0.0507680i
$523$	29.3743	−	29.3743i	1.28445	−	1.28445i	0.346338	−	0.938110i	$-0.387425\pi$
$523$	29.3743	−	29.3743i	1.28445	−	1.28445i	0.938110	−	0.346338i	$-0.112575\pi$
$524$	−12.5421	−	7.07246i	−0.547905	−	0.308962i
$525$	−1.60848	−	6.74963i	−0.0701999	−	0.294578i
$526$	5.18848	−	32.4499i	0.226229	−	1.41488i
$527$	−6.99979	−	5.48904i	−0.304916	−	0.239106i
$528$	−22.9383	+	31.1845i	−0.998260	+	1.35713i
$529$	8.80389	−	3.64669i	0.382778	−	0.158552i
$530$	9.54611	+	26.0610i	0.414657	+	1.13202i
$531$	1.69500	−	1.69500i	0.0735566	−	0.0735566i
$532$	−3.02569	+	0.843735i	−0.131180	+	0.0365805i
$533$	0.810934	+	4.07684i	0.0351254	+	0.176587i
$534$	−18.8515	+	20.3334i	−0.815784	+	0.879911i
$535$	0.796099	−	0.257931i	0.0344184	−	0.0111513i
$536$	−19.9238	+	16.8651i	−0.860577	+	0.728462i
$537$	27.7325	+	18.5303i	1.19675	+	0.799640i
$538$	0.850898	+	22.5000i	0.0366848	+	0.970046i
$539$	−20.3655	−	30.4792i	−0.877205	−	1.31283i
$540$	9.28287	−	22.1735i	0.399471	−	0.954194i
$541$	5.37119	−	27.0028i	0.230926	−	1.16094i	−0.675102	−	0.737724i	$-0.735901\pi$
$541$	5.37119	−	27.0028i	0.230926	−	1.16094i	0.906028	−	0.423218i	$-0.139099\pi$
$542$	−34.8211	+	8.30567i	−1.49569	+	0.356759i
$543$		−	3.74512i		−	0.160719i
$544$	15.0627	+	17.8077i	0.645808	+	0.763500i
$545$	−1.42241	−	1.66825i	−0.0609293	−	0.0714602i
$546$	0.509639	+	2.13663i	0.0218105	+	0.0914394i
$547$	−7.27286	−	1.44666i	−0.310965	−	0.0618548i	0.0371408	−	0.999310i	$-0.488175\pi$
$547$	−7.27286	−	1.44666i	−0.310965	−	0.0618548i	−0.348106	+	0.937455i	$0.613175\pi$
$548$	12.5971	+	24.9040i	0.538123	+	1.06385i
$549$	1.36240	+	2.03898i	0.0581460	+	0.0870216i
$550$	40.8104	+	4.96048i	1.74016	+	0.211515i
$551$	−8.98249	+	13.4432i	−0.382667	+	0.572702i
$552$	11.1648	+	13.1896i	0.475204	+	0.561388i
$553$	−1.17995	+	2.84864i	−0.0501765	+	0.121137i
$554$	12.8752	−	13.8873i	0.547017	−	0.590017i
$555$	6.35671	+	5.01987i	0.269827	+	0.213081i
$556$	6.77374	+	24.2911i	0.287271	+	1.03017i
$557$	10.0735	+	10.0735i	0.426827	+	0.426827i	0.887546	−	0.460719i	$-0.152408\pi$
$557$	10.0735	+	10.0735i	0.426827	+	0.426827i	−0.460719	+	0.887546i	$0.652408\pi$
$558$	0.242800	−	0.655171i	0.0102786	−	0.0277356i
$559$	−4.65626	+	1.92869i	−0.196939	+	0.0815748i
$560$	0.535065	+	7.43722i	0.0226106	+	0.314280i
$561$	−18.0243	+	35.6009i	−0.760987	+	1.50307i
$562$	−25.4710	−	4.07261i	−1.07443	−	0.171793i
$563$	4.99118	+	12.0498i	0.210353	+	0.507837i	0.993478	−	0.114028i	$-0.0363753\pi$
$563$	4.99118	+	12.0498i	0.210353	+	0.507837i	−0.783125	+	0.621865i	$0.786375\pi$
$564$	28.9095	+	16.3020i	1.21731	+	0.686437i
$565$	33.2305	+	2.64332i	1.39802	+	0.111205i
$566$	−4.35848	−	9.49095i	−0.183201	−	0.398934i
$567$	1.34348	+	6.75412i	0.0564208	+	0.283646i
$568$	6.90194	−	3.82538i	0.289599	−	0.160509i
$569$	0.930557	−	2.24656i	0.0390110	−	0.0941808i	−0.903173	−	0.429276i	$-0.858769\pi$
$569$	0.930557	−	2.24656i	0.0390110	−	0.0941808i	0.942184	+	0.335096i	$0.108769\pi$
$570$	−1.52877	−	9.79860i	−0.0640330	−	0.410418i
$571$	−18.9840	+	28.4116i	−0.794457	+	1.18899i	0.184079	+	0.982911i	$0.441070\pi$
$571$	−18.9840	+	28.4116i	−0.794457	+	1.18899i	−0.978536	+	0.206077i	$0.933930\pi$
$572$	−12.9197	−	1.56768i	−0.540200	−	0.0655482i
$573$	−14.9016	−	22.3017i	−0.622521	−	0.931669i
$574$	−2.56840	−	3.54606i	−0.107203	−	0.148010i
$575$	6.38053	−	17.2063i	0.266086	−	0.717553i
$576$	−0.970987	+	1.55358i	−0.0404578	+	0.0647323i
$577$	−23.8173			−0.991525			−0.495763	−	0.868458i	$-0.665111\pi$
$577$	−23.8173			−0.991525			−0.495763	+	0.868458i	$0.665111\pi$
$578$	18.3387	+	15.5465i	0.762789	+	0.646648i
$579$	16.7158			0.694685
$580$	27.0360	+	27.2411i	1.12261	+	1.13112i
$581$	1.43337	+	0.285116i	0.0594663	+	0.0118286i
$582$	2.75036	−	1.99208i	0.114006	−	0.0825745i
$583$	42.4275	−	28.3491i	1.75717	−	1.17410i
$584$	44.8033	+	12.8494i	1.85397	+	0.531714i
$585$	0.569221	−	0.0668881i	0.0235344	−	0.00276548i
$586$	−11.0337	+	17.9461i	−0.455798	+	0.741347i
$587$	3.23779	−	7.81671i	0.133638	−	0.322630i	−0.842868	−	0.538120i	$-0.819135\pi$
$587$	3.23779	−	7.81671i	0.133638	−	0.322630i	0.976506	+	0.215490i	$0.0691348\pi$
$588$	12.9469	+	16.5228i	0.533921	+	0.681387i
$589$	−0.792941	−	3.98639i	−0.0326726	−	0.164256i
$590$	−30.0280	−	13.9272i	−1.23623	−	0.573376i
$591$	−20.3026	+	20.3026i	−0.835138	+	0.835138i
$592$	−5.87076	−	6.42637i	−0.241287	−	0.264122i
$593$	4.27413	−	1.77040i	0.175518	−	0.0727018i	−0.293194	−	0.956053i	$-0.594718\pi$
$593$	4.27413	−	1.77040i	0.175518	−	0.0727018i	0.468712	+	0.883351i	$0.344718\pi$
$594$	−43.6405	−	6.97777i	−1.79059	−	0.286301i
$595$	1.80721	+	7.47044i	0.0740885	+	0.306258i
$596$	6.44437	−	19.6370i	0.263972	−	0.804365i
$597$	19.3250	−	8.00467i	0.790919	−	0.327609i
$598$	−2.01877	+	5.44744i	−0.0825536	+	0.222762i
$599$	11.0817	+	11.0817i	0.452784	+	0.452784i	0.896278	−	0.443493i	$-0.146261\pi$
$599$	11.0817	+	11.0817i	0.452784	+	0.452784i	−0.443493	+	0.896278i	$0.646261\pi$
$600$	−23.5172	−	1.06740i	−0.960086	−	0.0435765i
$601$	1.82261	+	9.16287i	0.0743457	+	0.373761i	0.999989	−	0.00463542i	$-0.00147551\pi$
$601$	1.82261	+	9.16287i	0.0743457	+	0.373761i	−0.925644	+	0.378397i	$0.876476\pi$
$602$	3.60935	−	3.89308i	0.147106	−	0.158670i
$603$	−1.95261	−	0.808798i	−0.0795165	−	0.0329368i
$604$	28.4580	−	33.1224i	1.15794	−	1.34773i
$605$	−5.95038	−	50.6380i	−0.241917	−	2.05873i
$606$	26.0446	−	0.984944i	1.05799	−	0.0400106i
$607$	−5.89991	−	8.82984i	−0.239470	−	0.358392i	0.692195	−	0.721710i	$-0.256644\pi$
$607$	−5.89991	−	8.82984i	−0.239470	−	0.358392i	−0.931665	+	0.363318i	$0.881644\pi$
$608$	−0.0783461	+	10.6569i	−0.00317735	+	0.432195i
$609$	−11.6807	−	2.32343i	−0.473324	−	0.0941501i
$610$	19.9671	−	27.3493i	0.808443	−	1.10734i
$611$			11.1577i			0.451391i
$612$	−0.723313	+	1.74442i	−0.0292382	+	0.0705141i
$613$	16.7399			0.676117			0.338058	−	0.941125i	$-0.390230\pi$
$613$	16.7399			0.676117			0.338058	+	0.941125i	$0.390230\pi$
$614$	1.09150	+	4.57604i	0.0440493	+	0.184674i
$615$	12.0668	−	6.74447i	0.486582	−	0.271963i
$616$	13.0565	−	4.17872i	0.526060	−	0.168366i
$617$	3.40826	+	5.10083i	0.137211	+	0.205351i	0.893711	−	0.448642i	$-0.148092\pi$
$617$	3.40826	+	5.10083i	0.137211	+	0.205351i	−0.756500	+	0.653994i	$0.773092\pi$
$618$	−32.5900	+	1.23248i	−1.31096	+	0.0495775i
$619$	−28.5423	−	19.0713i	−1.14721	−	0.766542i	−0.171409	−	0.985200i	$-0.554832\pi$
$619$	−28.5423	−	19.0713i	−1.14721	−	0.766542i	−0.975801	+	0.218658i	$0.929832\pi$
$620$	−9.64825	−	0.0364577i	−0.387483	−	0.00146418i
$621$	−7.54957	+	18.2263i	−0.302954	+	0.731395i
$622$	31.6759	+	29.3674i	1.27009	+	1.17752i
$623$	9.63034	−	1.91559i	0.385831	−	0.0767466i
$624$	7.44494	+	0.336376i	0.298036	+	0.0134658i
$625$	11.2750	+	22.3131i	0.451001	+	0.892523i
$626$	1.55437	−	4.19431i	0.0621252	−	0.167638i
$627$	−16.8450	+	6.97744i	−0.672726	+	0.278652i
$628$	−7.46305	+	22.7411i	−0.297808	+	0.907470i
$629$	−7.06025	−	5.53644i	−0.281510	−	0.220753i
$630$	−0.515481	+	0.314253i	−0.0205373	+	0.0125201i
$631$	−12.2226	−	29.5081i	−0.486576	−	1.17470i	−0.956432	−	0.291955i	$-0.905694\pi$
$631$	−12.2226	−	29.5081i	−0.486576	−	1.17470i	0.469856	−	0.882743i	$-0.344306\pi$
$632$	8.18671	+	6.51264i	0.325650	+	0.259059i
$633$	−3.09159	−	3.09159i	−0.122880	−	0.122880i
$634$	−8.75373	+	4.01993i	−0.347655	+	0.159652i
$635$	−0.613536	−	0.484507i	−0.0243474	−	0.0192271i
$636$	−23.0000	+	18.0223i	−0.912008	+	0.714630i
$637$	−2.70055	+	6.51970i	−0.107000	+	0.258320i
$638$	36.9573	−	60.1102i	1.46315	−	2.37979i
$639$	0.531238	+	0.354962i	0.0210155	+	0.0140421i
$640$	24.7557	+	5.21129i	0.978553	+	0.205994i
$641$	23.6681	+	35.4218i	0.934835	+	1.39908i	0.916846	+	0.399241i	$0.130726\pi$
$641$	23.6681	+	35.4218i	0.934835	+	1.39908i	0.0179883	+	0.999838i	$0.494274\pi$
$642$	0.516808	+	0.713529i	0.0203968	+	0.0281607i
$643$	−4.35047	+	21.8713i	−0.171566	+	0.862519i	0.795100	+	0.606478i	$0.207418\pi$
$643$	−4.35047	+	21.8713i	−0.171566	+	0.862519i	−0.966666	+	0.256041i	$0.917582\pi$
$644$	−0.462185	−	6.10197i	−0.0182126	−	0.240451i
$645$	10.8747	+	12.7542i	0.428190	+	0.502198i
$646$	1.73044	+	10.8481i	0.0680831	+	0.426811i
$647$	47.1213			1.85253			0.926265	−	0.376873i	$-0.123001\pi$
$647$	47.1213			1.85253			0.926265	+	0.376873i	$0.123001\pi$
$648$	23.2840	+	1.93587i	0.914681	+	0.0760480i
$649$	−11.8725	+	59.6871i	−0.466036	+	2.34292i
$650$	−3.57080	−	7.06294i	−0.140058	−	0.277031i
$651$	2.48936	−	1.66334i	0.0975656	−	0.0651913i
$652$	7.66885	+	0.930543i	0.300335	+	0.0364429i
$653$	21.1895	+	14.1584i	0.829208	+	0.554059i	0.896178	−	0.443696i	$-0.146333\pi$
$653$	21.1895	+	14.1584i	0.829208	+	0.554059i	−0.0669691	+	0.997755i	$0.521333\pi$
$654$	1.20887	−	1.96620i	0.0472705	−	0.0768845i
$655$	−15.3146	+	4.96182i	−0.598390	+	0.193874i
$656$	−13.9672	+	5.05964i	−0.545327	+	0.197546i
$657$	0.736228	+	3.70127i	0.0287230	+	0.144400i
$658$	−4.90482	−	10.6806i	−0.191210	−	0.416375i
$659$	6.54117	+	6.54117i	0.254808	+	0.254808i	0.822938	−	0.568130i	$-0.192333\pi$
$659$	6.54117	+	6.54117i	0.254808	+	0.254808i	−0.568130	+	0.822938i	$0.692333\pi$
$660$	8.28335	+	42.4815i	0.322429	+	1.65359i
$661$	−33.4301	+	13.8472i	−1.30028	+	0.538594i	−0.922034	−	0.387110i	$-0.873473\pi$
$661$	−33.4301	+	13.8472i	−1.30028	+	0.538594i	−0.378248	+	0.925704i	$0.623473\pi$
$662$	−3.86752	+	24.1883i	−0.150315	+	0.940105i
$663$	7.62630	−	0.922541i	0.296181	−	0.0358285i
$664$	2.27054	−	4.40802i	0.0881141	−	0.171064i
$665$	−1.59698	+	3.12777i	−0.0619284	+	0.121290i
$666$	0.244897	−	0.660830i	0.00948958	−	0.0256066i
$667$	−22.2725	−	22.2725i	−0.862396	−	0.862396i
$668$	10.3097	−	2.87493i	0.398894	−	0.111234i
$669$	−1.15105	+	0.228957i	−0.0445020	+	0.00885201i
$670$	−1.21309	+	29.1593i	−0.0468659	+	1.12652i
$671$	−57.5181	−	23.8248i	−2.22046	−	0.919746i
$672$	−7.27450	+	2.95073i	−0.280620	+	0.113827i
$673$	28.9785	+	19.3628i	1.11704	+	0.746382i	0.970086	−	0.242762i	$-0.0780533\pi$
$673$	28.9785	+	19.3628i	1.11704	+	0.746382i	0.146953	+	0.989143i	$0.453053\pi$
$674$	1.01314	+	26.7902i	0.0390247	+	1.03192i
$675$	−11.2108	−	24.4256i	−0.431503	−	0.940143i
$676$	−10.6047	−	20.9651i	−0.407873	−	0.806350i
$677$	1.66393	+	0.330977i	0.0639501	+	0.0127205i	0.226962	−	0.973904i	$-0.427121\pi$
$677$	1.66393	+	0.330977i	0.0639501	+	0.0127205i	−0.163012	+	0.986624i	$0.552121\pi$
$678$	8.14275	+	34.1380i	0.312720	+	1.31106i
$679$	−1.20260			−0.0461517
$680$	26.0539	+	1.09348i	0.999120	+	0.0419329i
$681$	−32.8373			−1.25833
$682$	4.11565	+	17.2546i	0.157596	+	0.660715i
$683$	−42.2258	−	8.39924i	−1.61573	−	0.321388i	−0.697239	−	0.716838i	$-0.745588\pi$
$683$	−42.2258	−	8.39924i	−1.61573	−	0.321388i	−0.918487	+	0.395450i	$0.870588\pi$
$684$	−0.769973	+	0.389473i	−0.0294407	+	0.0148919i
$685$	30.0243	+	8.49491i	1.14717	+	0.324574i
$686$	−0.592790	−	15.6750i	−0.0226328	−	0.598473i
$687$	−31.9347	−	21.3381i	−1.21838	−	0.814099i
$688$	−9.32063	−	15.4126i	−0.355346	−	0.587601i
$689$	−9.07553	−	3.75921i	−0.345750	−	0.143214i
$690$	19.3036	+	0.803072i	0.734875	+	0.0305724i
$691$	25.6422	−	5.10054i	0.975474	−	0.194034i	0.318480	−	0.947930i	$-0.396828\pi$
$691$	25.6422	−	5.10054i	0.975474	−	0.194034i	0.656994	+	0.753896i	$0.271828\pi$
$692$	−7.74353	−	27.7688i	−0.294365	−	1.05561i
$693$	0.784855	+	0.784855i	0.0298142	+	0.0298142i
$694$	2.96684	−	8.00571i	0.112620	−	0.303892i
$695$	25.1107	+	12.8210i	0.952502	+	0.486330i
$696$	−18.5028	+	35.9212i	−0.701348	+	1.36159i
$697$	−13.3408	+	7.51640i	−0.505321	+	0.284704i
$698$	−6.91208	+	43.2297i	−0.261626	+	1.63627i
$699$	0.778129	−	0.322312i	0.0294315	−	0.0121909i
$700$	6.52294	+	5.19128i	0.246544	+	0.196212i
$701$	−12.2153	−	12.2153i	−0.461367	−	0.461367i	0.437736	−	0.899103i	$-0.355780\pi$
$701$	−12.2153	−	12.2153i	−0.461367	−	0.461367i	−0.899103	+	0.437736i	$0.855780\pi$
$702$	3.55060	+	7.73172i	0.134009	+	0.291815i
$703$	−0.799790	−	4.02082i	−0.0301646	−	0.151648i
$704$	−1.41597	−	46.4899i	−0.0533662	−	1.75215i
$705$	35.3000	−	11.4370i	1.32948	−	0.430741i
$706$	−2.19565	+	3.57117i	−0.0826342	+	0.134403i
$707$	−7.67411	−	5.12768i	−0.288615	−	0.192846i
$708$	4.19775	−	34.5947i	0.157761	−	1.30015i
$709$	−10.7630	+	7.19160i	−0.404213	+	0.270086i	−0.741014	−	0.671489i	$-0.765655\pi$
$709$	−10.7630	+	7.19160i	−0.404213	+	0.270086i	0.336802	+	0.941576i	$0.390655\pi$
$710$	2.07939	−	8.57403i	0.0780380	−	0.321778i
$711$	−0.165242	+	0.830726i	−0.00619705	+	0.0311547i
$712$	2.76025	−	33.1994i	0.103445	−	1.24420i
$713$	7.91831			0.296543
$714$	−6.89470	+	4.23555i	−0.258028	+	0.158512i
$715$	−11.0723	+	9.44059i	−0.414080	+	0.353058i
$716$	−39.9588	+	3.02662i	−1.49333	+	0.113110i
$717$	4.92708	−	24.7701i	0.184005	−	0.925057i
$718$	10.2364	+	14.1328i	0.382018	+	0.527431i
$719$	9.50829	+	14.2302i	0.354599	+	0.530695i	0.965292	−	0.261172i	$-0.0841090\pi$
$719$	9.50829	+	14.2302i	0.354599	+	0.530695i	−0.610693	+	0.791868i	$0.709109\pi$
$720$	0.542732	+	1.97508i	0.0202264	+	0.0736071i
$721$	9.60275	+	6.41635i	0.357625	+	0.238957i
$722$	11.4443	−	18.6139i	0.425913	−	0.692739i
$723$	−2.39665	+	5.78602i	−0.0891323	+	0.215184i
$724$	2.77530	+	3.54182i	0.103143	+	0.131631i
$725$	42.8797	−	1.61277i	1.59251	−	0.0598969i
$726$	48.7810	−	22.4014i	1.81043	−	0.831395i
$727$	29.4063	+	29.4063i	1.09062	+	1.09062i	0.995462	+	0.0951573i	$0.0303354\pi$
$727$	29.4063	+	29.4063i	1.09062	+	1.09062i	0.0951573	+	0.995462i	$0.469665\pi$
$728$	−2.06531	−	1.64298i	−0.0765456	−	0.0608930i
$729$	10.9962	+	26.5471i	0.407266	+	0.983226i
$730$	44.4946	−	27.1253i	1.64682	−	1.00395i
$731$	−12.0940	−	14.0867i	−0.447313	−	0.521015i
$732$	33.8732	+	11.1163i	1.25199	+	0.410870i
$733$	6.92433	−	2.86815i	0.255756	−	0.105938i	−0.251122	−	0.967955i	$-0.580799\pi$
$733$	6.92433	−	2.86815i	0.255756	−	0.105938i	0.506878	+	0.862018i	$0.330799\pi$
$734$	−3.55722	+	9.59879i	−0.131300	+	0.354298i
$735$	23.3948	+	1.86094i	0.862930	+	0.0686418i
$736$	−20.3328	−	4.20007i	−0.749477	−	0.154817i
$737$	52.6256	−	10.4679i	1.93849	−	0.385589i
$738$	−0.882027	−	0.817746i	−0.0324679	−	0.0301016i
$739$	−3.22954	+	7.79680i	−0.118801	+	0.286810i	−0.972082	−	0.234640i	$-0.924609\pi$
$739$	−3.22954	+	7.79680i	−0.118801	+	0.286810i	0.853282	+	0.521450i	$0.174609\pi$
$740$	−9.73158	−	0.0367726i	−0.357740	−	0.00135179i
$741$	2.91850	+	1.95008i	0.107214	+	0.0716378i
$742$	10.3400	−	0.391035i	0.379594	−	0.0143554i
$743$	18.5833	+	27.8119i	0.681755	+	1.02032i	0.997444	+	0.0714560i	$0.0227645\pi$
$743$	18.5833	+	27.8119i	0.681755	+	1.02032i	−0.315688	+	0.948863i	$0.602235\pi$
$744$	−3.09629	−	9.67439i	−0.113515	−	0.354680i
$745$	−11.2736	−	20.1701i	−0.413034	−	0.738977i
$746$	10.3415	+	43.3564i	0.378631	+	1.58739i
$747$	0.401464			0.0146888
$748$	−9.33595	−	47.0251i	−0.341356	−	1.71941i
$749$		−	0.311993i		−	0.0114000i
$750$	−18.6851	+	18.5368i	−0.682285	+	0.676869i
$751$	9.20356	+	1.83070i	0.335843	+	0.0668033i	0.360131	−	0.932902i	$-0.382732\pi$
$751$	9.20356	+	1.83070i	0.335843	+	0.0668033i	−0.0242883	+	0.999705i	$0.507732\pi$
$752$	−39.4207	+	6.00619i	−1.43753	+	0.219023i
$753$	−10.0564	−	15.0505i	−0.366475	−	0.548469i
$754$	−13.5744	+	0.513351i	−0.494350	+	0.0186951i
$755$	−5.69790	−	48.4894i	−0.207368	−	1.76471i
$756$	−6.79759	−	5.84035i	−0.247226	−	0.212411i
$757$	19.9150	+	8.24908i	0.723825	+	0.299818i	0.714012	−	0.700134i	$-0.246876\pi$
$757$	19.9150	+	8.24908i	0.723825	+	0.299818i	0.00981312	+	0.999952i	$0.496876\pi$
$758$	−20.3233	+	21.9209i	−0.738175	+	0.796202i
$759$	−6.92978	−	34.8383i	−0.251535	−	1.26455i
$760$	8.70697	+	8.13381i	0.315835	+	0.295044i
$761$	−0.0488229	−	0.0488229i	−0.00176983	−	0.00176983i	0.706221	−	0.707991i	$-0.250398\pi$
$761$	−0.0488229	−	0.0488229i	−0.00176983	−	0.00176983i	−0.707991	+	0.706221i	$0.750398\pi$
$762$	0.286009	−	0.771765i	0.0103610	−	0.0279581i
$763$	−0.755132	+	0.312786i	−0.0273376	+	0.0113236i
$764$	30.6192	+	10.0484i	1.10776	+	0.363539i
$765$	0.887258	+	1.91586i	0.0320789	+	0.0692680i
$766$	−2.89872	−	0.463482i	−0.104735	−	0.0167463i
$767$	10.8237	−	4.48334i	0.390823	−	0.161884i
$768$	2.81918	+	26.4845i	0.101728	+	0.955676i
$769$	15.4153	−	15.4153i	0.555889	−	0.555889i	−0.372245	−	0.928134i	$-0.621412\pi$
$769$	15.4153	−	15.4153i	0.555889	−	0.555889i	0.928134	+	0.372245i	$0.121412\pi$
$770$	6.44890	−	13.9042i	0.232402	−	0.501074i
$771$	0.910495	+	4.57737i	0.0327907	+	0.164850i
$772$	−15.8084	+	12.3871i	−0.568957	+	0.445823i
$773$	4.95940	−	11.9730i	0.178377	−	0.430640i	−0.809249	−	0.587465i	$-0.800126\pi$
$773$	4.95940	−	11.9730i	0.178377	−	0.430640i	0.987626	+	0.156825i	$0.0501258\pi$
$774$	0.763808	−	1.24232i	0.0274545	−	0.0446542i
$775$	−7.33559	+	7.90896i	−0.263502	+	0.284098i
$776$	−1.12484	+	3.92208i	−0.0403795	+	0.140795i
$777$	2.51086	−	1.67770i	0.0900766	−	0.0601872i
$778$	−25.2126	+	18.2614i	−0.903915	+	0.654704i
$779$	−6.86224	−	1.36498i	−0.245865	−	0.0489057i
$780$	5.91397	−	5.86944i	0.211754	−	0.210160i
$781$	−16.2205			−0.580417
$782$	−21.3855	−	0.816605i	−0.764743	−	0.0292017i
$783$	−46.1292			−1.64852
$784$	−24.4882	−	6.03163i	−0.874578	−	0.215415i
$785$	13.0557	+	23.3585i	0.465977	+	0.833701i
$786$	−9.94184	−	13.7262i	−0.354614	−	0.489596i
$787$	24.1128	+	36.0874i	0.859529	+	1.28638i	0.956690	+	0.291108i	$0.0940237\pi$
$787$	24.1128	+	36.0874i	0.859529	+	1.28638i	−0.0971613	+	0.995269i	$0.530976\pi$
$788$	4.15539	−	34.2457i	0.148030	−	1.21995i
$789$	21.4900	−	32.1621i	0.765065	−	1.14500i
$790$	11.5562	−	1.80298i	0.411150	−	0.0641472i
$791$	4.75606	−	11.4822i	0.169106	−	0.408258i
$792$	3.29377	−	1.82556i	0.117039	−	0.0648685i
$793$	2.33820	+	11.7549i	0.0830318	+	0.417429i
$794$	−5.98016	−	13.0223i	−0.212228	−	0.462144i
$795$	−2.59046	+	32.5659i	−0.0918741	+	1.15500i
$796$	−12.3441	+	21.8908i	−0.437527	+	0.775899i
$797$	−17.1467	−	41.3959i	−0.607368	−	1.46632i	−0.865852	−	0.500301i	$-0.833223\pi$
$797$	−17.1467	−	41.3959i	−0.607368	−	1.46632i	0.258483	−	0.966016i	$-0.416777\pi$
$798$	−3.65095	−	0.583758i	−0.129242	−	0.0206648i
$799$	−39.0583	+	12.8021i	−1.38178	+	0.452904i
$800$	23.0316	−	16.4178i	0.814290	−	0.580458i
$801$	2.49198	−	1.03221i	0.0880497	−	0.0364714i
$802$	−2.88131	+	7.77492i	−0.101743	+	0.274542i
$803$	−67.7461	−	67.7461i	−2.39071	−	2.39071i
$804$	−29.5964	+	8.25318i	−1.04379	+	0.291067i
$805$	−5.36939	−	4.24019i	−0.189246	−	0.149447i
$806$	2.32172	−	2.50423i	0.0817791	−	0.0882076i
$807$	−10.1423	+	24.4857i	−0.357026	+	0.861936i
$808$	−23.9009	+	20.2317i	−0.840831	+	0.711747i
$809$	17.6459	−	26.4089i	0.620395	−	0.928487i	−0.379599	−	0.925151i	$-0.623938\pi$
$809$	17.6459	−	26.4089i	0.620395	−	0.928487i	0.999994	−	0.00333595i	$-0.00106187\pi$
$810$	19.2229	−	17.6874i	0.675425	−	0.621471i
$811$	9.57167	+	14.3250i	0.336107	+	0.503019i	0.960571	−	0.278034i	$-0.0896828\pi$
$811$	9.57167	+	14.3250i	0.336107	+	0.503019i	−0.624465	+	0.781053i	$0.714683\pi$
$812$	12.7684	−	6.45858i	0.448081	−	0.226652i
$813$	−41.3271	−	8.22046i	−1.44940	−	0.288304i
$814$	4.15120	+	17.4037i	0.145499	+	0.609999i
$815$	6.57226	−	5.60372i	0.230216	−	0.196290i
$816$	7.36463	+	26.4475i	0.257814	+	0.925849i
$817$		−	8.48329i		−	0.296793i
$818$	−37.6626	+	8.98344i	−1.31684	+	0.314098i
$819$	0.0416866	−	0.209573i	0.00145665	−	0.00732306i
$820$	−6.41385	+	15.3204i	−0.223981	+	0.535012i
$821$	−6.48511	−	9.70566i	−0.226332	−	0.338730i	0.700872	−	0.713287i	$-0.252795\pi$
$821$	−6.48511	−	9.70566i	−0.226332	−	0.338730i	−0.927204	+	0.374558i	$0.877795\pi$
$822$	1.24144	+	32.8271i	0.0433003	+	1.14498i
$823$	−36.6784	−	24.5077i	−1.27853	−	0.854286i	−0.284008	−	0.958822i	$-0.591664\pi$
$823$	−36.6784	−	24.5077i	−1.27853	−	0.854286i	−0.994521	+	0.104536i	$0.966664\pi$
$824$	29.9076	−	25.3162i	1.04188	−	0.881932i
$825$	41.2170	+	25.3530i	1.43499	+	0.882677i
$826$	−8.39015	+	9.04968i	−0.291931	+	0.314879i
$827$	−5.60228	−	28.1646i	−0.194810	−	0.979377i	−0.947196	−	0.320655i	$-0.896097\pi$
$827$	−5.60228	−	28.1646i	−0.194810	−	0.979377i	0.752386	−	0.658723i	$-0.228903\pi$
$828$	−0.451538	−	1.61924i	−0.0156920	−	0.0562726i
$829$	15.8570	−	15.8570i	0.550735	−	0.550735i	−0.375918	−	0.926653i	$-0.622673\pi$
$829$	15.8570	−	15.8570i	0.550735	−	0.550735i	0.926653	+	0.375918i	$0.122673\pi$
$830$	−1.90675	−	5.20545i	−0.0661844	−	0.180684i
$831$	20.5940	−	8.53033i	0.714399	−	0.295914i
$832$	−7.29007	+	5.19891i	−0.252738	+	0.180240i
$833$	−25.9213	−	1.97294i	−0.898119	−	0.0683582i
$834$	−4.68658	+	29.3109i	−0.162283	+	1.01495i
$835$	5.44154	−	10.6575i	0.188312	−	0.368819i
$836$	10.7600	−	19.0816i	0.372144	−	0.659951i
$837$	8.19990	−	8.19990i	0.283430	−	0.283430i
$838$	−38.1910	+	17.5382i	−1.31928	+	0.605848i
$839$	−24.2657	+	4.82675i	−0.837746	+	0.166638i	−0.595276	−	0.803521i	$-0.702957\pi$
$839$	−24.2657	+	4.82675i	−0.837746	+	0.166638i	−0.242469	+	0.970159i	$0.577957\pi$
$840$	−3.08097	+	8.21822i	−0.106303	+	0.283556i
$841$	17.0872	−	41.2521i	0.589213	−	1.42249i
$842$	26.6114	−	43.2829i	0.917089	−	1.49163i
$843$	−25.2451	−	16.8682i	−0.869488	−	0.580973i
$844$	5.21478	+	0.632765i	0.179500	+	0.0217807i
$845$	−25.2755	−	7.15131i	−0.869505	−	0.246012i
$846$	−1.89386	−	2.61476i	−0.0651124	−	0.0898972i
$847$	−18.6436	−	3.70845i	−0.640602	−	0.127424i
$848$	8.39613	−	34.0880i	0.288324	−	1.17059i
$849$		−	12.2932i		−	0.421901i
$850$	20.6273	−	20.6037i	0.707512	−	0.706702i
$851$	7.98670			0.273780
$852$	9.26192	−	0.701531i	0.317308	−	0.0240340i
$853$	0.290228	−	1.45907i	0.00993722	−	0.0499578i	−0.975499	−	0.220006i	$-0.929392\pi$
$853$	0.290228	−	1.45907i	0.00993722	−	0.0499578i	0.985436	+	0.170048i	$0.0543923\pi$
$854$	−7.40559	−	10.2245i	−0.253414	−	0.349875i
$855$	−0.262642	+	0.928280i	−0.00898217	+	0.0317465i
$856$	−1.01751	−	0.291819i	−0.0347778	−	0.00997416i
$857$	−18.2073	+	27.2491i	−0.621948	+	0.930811i	0.378040	+	0.925789i	$0.376598\pi$
$857$	−18.2073	+	27.2491i	−0.621948	+	0.930811i	−0.999987	+	0.00502126i	$0.998402\pi$
$858$	−13.0498	−	8.02333i	−0.445512	−	0.273912i
$859$	−26.0345	−	10.7838i	−0.888285	−	0.367940i	−0.108581	−	0.994088i	$-0.534631\pi$
$859$	−26.0345	−	10.7838i	−0.888285	−	0.367940i	−0.779704	+	0.626148i	$0.784631\pi$
$860$	−19.7358	−	4.00328i	−0.672986	−	0.136511i
$861$	−1.00546	−	5.05477i	−0.0342659	−	0.172266i
$862$	24.5299	−	11.2648i	0.835493	−	0.383679i
$863$	13.8563	+	13.8563i	0.471675	+	0.471675i	0.902456	−	0.430782i	$-0.141762\pi$
$863$	13.8563	+	13.8563i	0.471675	+	0.471675i	−0.430782	+	0.902456i	$0.641762\pi$
$864$	−25.4053	+	16.7064i	−0.864306	+	0.568365i
$865$	−28.7057	−	14.6566i	−0.976024	−	0.498340i
$866$	−13.1909	−	2.10913i	−0.448246	−	0.0716710i
$867$	11.9797	+	25.6380i	0.406851	+	0.870711i
$868$	−1.12162	+	3.41777i	−0.0380703	+	0.116007i
$869$	−8.22898	−	19.8665i	−0.279149	−	0.673925i
$870$	15.5383	+	42.4196i	0.526797	+	1.43816i
$871$	−7.30405	−	7.30405i	−0.247488	−	0.247488i
$872$	0.313793	+	2.75529i	0.0106264	+	0.0933060i
$873$	−0.324010	+	0.0644495i	−0.0109661	+	0.00218129i
$874$	−7.17092	−	6.64831i	−0.242560	−	0.224883i
$875$	9.20944	−	1.43491i	0.311336	−	0.0485087i
$876$	41.6129	+	35.7530i	1.40597	+	1.20798i
$877$	−18.1713	+	27.1952i	−0.613600	+	0.918318i	−0.999992	−	0.00401720i	$-0.998721\pi$
$877$	−18.1713	+	27.1952i	−0.613600	+	0.918318i	0.386392	+	0.922335i	$0.373721\pi$
$878$	1.48038	+	39.1452i	0.0499604	+	1.32109i
$879$	−20.6179	+	13.7765i	−0.695426	+	0.464669i
$880$	−39.3144	−	34.0371i	−1.32529	−	1.14739i
$881$	11.5198	+	2.29144i	0.388113	+	0.0772004i	0.385290	−	0.922796i	$-0.374101\pi$
$881$	11.5198	+	2.29144i	0.388113	+	0.0772004i	0.00282289	+	0.999996i	$0.499101\pi$
$882$	−0.473768	−	1.98625i	−0.0159526	−	0.0668804i
$883$	58.1126			1.95564			0.977822	−	0.209437i	$-0.0671631\pi$
$883$	58.1126			1.95564			0.977822	+	0.209437i	$0.0671631\pi$
$884$	−6.52867	+	6.52388i	−0.219583	+	0.219422i
$885$	−25.2788	−	29.6480i	−0.849738	−	0.996606i
$886$	−7.25704	−	30.4247i	−0.243805	−	1.02214i
$887$	7.28884	−	36.6435i	0.244735	−	1.23037i	−0.641496	−	0.767126i	$-0.721686\pi$
$887$	7.28884	−	36.6435i	0.244735	−	1.23037i	0.886232	−	0.463242i	$-0.153314\pi$
$888$	−3.12303	−	9.75795i	−0.104802	−	0.327455i
$889$	−0.242343	+	0.161928i	−0.00812792	+	0.00543090i
$890$	−25.2195	−	27.4089i	−0.845359	−	0.918750i
$891$	−39.9323	−	26.6819i	−1.33778	−	0.893879i
$892$	0.918896	−	1.06951i	0.0307669	−	0.0358097i
$893$	−17.3513	−	7.18714i	−0.580639	−	0.240508i
$894$	16.5395	−	17.8396i	0.553163	−	0.596646i
$895$	−27.7669	+	35.1615i	−0.928146	+	1.17532i
$896$	4.69300	−	8.18128i	0.156782	−	0.273318i
$897$	−4.83531	+	4.83531i	−0.161446	+	0.161446i
$898$	7.54576	+	2.79639i	0.251805	+	0.0933167i
$899$	7.08542	+	17.1057i	0.236312	+	0.570507i
$900$	2.03564	+	1.04908i	0.0678547	+	0.0349692i
$901$	2.74636	−	36.0828i	0.0914944	−	1.20209i
$902$	30.1527	+	4.82118i	1.00398	+	0.160528i
$903$	5.77319	−	2.39133i	0.192120	−	0.0795785i
$904$	−32.9985	−	26.2508i	−1.09751	−	0.873087i
$905$	5.01491	+	0.398911i	0.166701	+	0.0132603i
$906$	46.7112	−	21.4509i	1.55187	−	0.712659i
$907$	−2.92881	+	0.582577i	−0.0972496	+	0.0193442i	−0.243475	−	0.969907i	$-0.578287\pi$
$907$	−2.92881	+	0.582577i	−0.0972496	+	0.0193442i	0.146226	+	0.989251i	$0.453287\pi$
$908$	31.0548	−	24.3339i	1.03059	−	0.807549i
$909$	−2.34238	−	0.970248i	−0.0776920	−	0.0321811i
$910$	−2.91535	+	0.454850i	−0.0966428	+	0.0150781i
$911$	3.19147	+	2.13247i	0.105738	+	0.0706520i	0.607315	−	0.794461i	$-0.292247\pi$
$911$	3.19147	+	2.13247i	0.105738	+	0.0706520i	−0.501577	+	0.865113i	$0.667247\pi$
$912$	−5.31870	+	11.3609i	−0.176120	+	0.376198i
$913$	−8.47452	+	5.66249i	−0.280466	+	0.187401i
$914$	7.75481	−	5.61680i	0.256506	−	0.185787i
$915$	34.7928	−	19.4466i	1.15021	−	0.642885i
$916$	46.0136	−	3.48524i	1.52033	−	0.115155i
$917$			6.00181i			0.198197i
$918$	−22.9916	+	21.3003i	−0.758836	+	0.703016i
$919$			16.3150i			0.538183i	0.963115	+	0.269091i	$0.0867234\pi$
$919$			16.3150i			0.538183i	−0.963115	+	0.269091i	$0.913277\pi$
$920$	−18.8508	+	13.5453i	−0.621493	+	0.446576i
$921$	−1.08030	+	5.43104i	−0.0355971	+	0.178959i
$922$	−11.8684	−	16.3861i	−0.390866	−	0.539648i
$923$	1.73484	+	2.59638i	0.0571031	+	0.0854608i
$924$	16.0188	+	1.94373i	0.526981	+	0.0639442i
$925$	−7.39895	+	7.97727i	−0.243276	+	0.262291i
$926$	11.2509	−	18.2994i	0.369729	−	0.601356i
$927$	2.93107	+	1.21409i	0.0962688	+	0.0398759i
$928$	−9.12080	−	47.6827i	−0.299405	−	1.56526i
$929$	−36.9267	+	7.34518i	−1.21153	+	0.240987i	−0.759195	−	0.650863i	$-0.774407\pi$
$929$	−36.9267	+	7.34518i	−1.21153	+	0.240987i	−0.452331	+	0.891850i	$0.649407\pi$
$930$	−10.3026	−	4.77841i	−0.337834	−	0.156690i
$931$	−8.39924	−	8.39924i	−0.275274	−	0.275274i
$932$	−0.497042	+	0.881443i	−0.0162812	+	0.0288726i
$933$	19.4570	+	46.9733i	0.636993	+	1.53784i
$934$	12.6511	+	2.02282i	0.413958	+	0.0661886i
$935$	−45.7516	−	27.9275i	−1.49624	−	0.913327i
$936$	−0.644493	−	0.331975i	−0.0210659	−	0.0108509i
$937$	−18.9469	−	45.7418i	−0.618967	−	1.49432i	−0.852905	−	0.522067i	$-0.825161\pi$
$937$	−18.9469	−	45.7418i	−0.618967	−	1.49432i	0.233938	−	0.972252i	$-0.424839\pi$
$938$	10.2026	+	3.78098i	0.333126	+	0.123453i
$939$	3.72300	−	3.72300i	0.121495	−	0.121495i
$940$	−24.9085	+	36.9750i	−0.812426	+	1.20599i
$941$	−13.6880	+	2.72272i	−0.446216	+	0.0887580i	−0.413084	−	0.910693i	$-0.635548\pi$
$941$	−13.6880	+	2.72272i	−0.446216	+	0.0887580i	−0.0331326	+	0.999451i	$0.510548\pi$
$942$	−19.1539	+	20.6596i	−0.624069	+	0.673125i
$943$	5.21625	−	12.5932i	0.169865	−	0.410089i
$944$	21.6663	+	35.8275i	0.705179	+	1.16609i
$945$	−9.95131	+	1.16936i	−0.323716	+	0.0380393i
$946$	1.39915	+	36.9974i	0.0454903	+	1.20289i
$947$	−5.29279	+	3.53653i	−0.171992	+	0.114922i	−0.638587	−	0.769550i	$-0.720481\pi$
$947$	−5.29279	+	3.53653i	−0.171992	+	0.114922i	0.466595	+	0.884471i	$0.345481\pi$
$948$	5.55796	+	10.9879i	0.180514	+	0.356869i
$949$	−3.59825	+	18.0896i	−0.116804	+	0.587214i
$950$	13.2837	−	1.00340i	0.430979	−	0.0325547i
$951$	−11.3383			−0.367670
$952$	3.38171	−	9.11491i	0.109602	−	0.295416i
$953$		−	32.3758i		−	1.04876i	−0.851486	−	0.524378i	$-0.824298\pi$
$953$		−	32.3758i		−	1.04876i	0.851486	−	0.524378i	$-0.175702\pi$
$954$	2.76489	−	0.659493i	0.0895166	−	0.0213519i
$955$	31.4504	−	17.5785i	1.01771	−	0.568827i
$956$	13.6961	+	27.0767i	0.442964	+	0.875723i
$957$	69.0595	−	46.1441i	2.23238	−	1.49163i
$958$	7.26702	−	0.274821i	0.234787	−	0.00887907i
$959$	6.46303	−	9.67261i	0.208702	−	0.312345i
$960$	23.9206	+	17.7349i	0.772033	+	0.572390i
$961$	24.3401	+	10.0820i	0.785163	+	0.325225i
$962$	2.34177	−	2.52585i	0.0755018	−	0.0814368i
$963$	−0.0167202	−	0.0840581i	−0.000538801	−	0.00270873i
$964$	−2.02115	−	7.24796i	−0.0650967	−	0.233441i
$965$	−1.78048	+	22.3833i	−0.0573158	+	0.720545i
$966$	2.50302	−	6.75414i	0.0805335	−	0.217311i
$967$	5.62174	+	13.5721i	0.180783	+	0.436448i	0.988128	−	0.153631i	$-0.0490966\pi$
$967$	5.62174	+	13.5721i	0.180783	+	0.436448i	−0.807345	+	0.590079i	$0.799097\pi$
$968$	−29.5325	+	57.3343i	−0.949212	+	1.84279i
$969$	−3.47778	+	12.4539i	−0.111723	+	0.400077i
$970$	2.37455	+	3.89507i	0.0762422	+	0.125063i
$971$	3.01986	−	1.25087i	0.0969118	−	0.0401422i	−0.333701	−	0.942679i	$-0.608298\pi$
$971$	3.01986	−	1.25087i	0.0969118	−	0.0401422i	0.430613	+	0.902537i	$0.358298\pi$
$972$	−4.13676	−	2.33270i	−0.132687	−	0.0748214i
$973$	7.43275	−	7.43275i	0.238283	−	0.238283i
$974$	28.1752	−	12.9387i	0.902790	−	0.414584i
$975$	−0.350129	−	9.30908i	−0.0112131	−	0.298129i
$976$	−40.2721	+	14.5887i	−1.28908	+	0.466972i
$977$	18.0342	+	7.47000i	0.576964	+	0.238986i	0.652031	−	0.758192i	$-0.273917\pi$
$977$	18.0342	+	7.47000i	0.576964	+	0.238986i	−0.0750671	+	0.997178i	$0.523917\pi$
$978$	7.74605	+	4.76247i	0.247691	+	0.152287i
$979$	−38.0443	+	56.9374i	−1.21590	+	1.81973i
$980$	−23.5039	+	15.5767i	−0.750804	+	0.497578i
$981$	−0.186688	+	0.124741i	−0.00596047	+	0.00398266i
$982$	−8.94451	−	12.3492i	−0.285431	−	0.394079i
$983$	8.06269	+	1.60377i	0.257160	+	0.0511523i	0.321986	−	0.946744i	$-0.395649\pi$
$983$	8.06269	+	1.60377i	0.257160	+	0.0511523i	−0.0648267	+	0.997897i	$0.520649\pi$
$984$	−17.4257	−	1.44880i	−0.555511	−	0.0461860i
$985$	−25.0237	−	29.3488i	−0.797323	−	0.935131i
$986$	−17.3719	−	46.9292i	−0.553235	−	1.49453i
$987$		−	13.8341i		−	0.440345i
$988$	−4.20516	+	0.318514i	−0.133784	+	0.0101333i
$989$	16.2093	+	3.22424i	0.515427	+	0.102525i
$990$	0.992334	−	4.09173i	0.0315384	−	0.130044i
$991$	31.0051	+	46.4024i	0.984910	+	1.47402i	0.877366	+	0.479822i	$0.159299\pi$
$991$	31.0051	+	46.4024i	0.984910	+	1.47402i	0.107544	+	0.994200i	$0.465701\pi$
$992$	10.0974	+	6.85474i	0.320591	+	0.217638i
$993$	−16.0188	+	23.9738i	−0.508340	+	0.760785i
$994$	−2.80202	−	1.72275i	−0.0888746	−	0.0546423i
$995$	8.66027	+	26.7298i	0.274549	+	0.847391i
$996$	4.59404	−	3.59980i	0.145568	−	0.114064i
$997$	−8.05985	+	1.60320i	−0.255258	+	0.0507740i	−0.321060	−	0.947059i	$-0.604039\pi$
$997$	−8.05985	+	1.60320i	−0.255258	+	0.0507740i	0.0658025	+	0.997833i	$0.479039\pi$
$998$	−18.3908	−	40.0475i	−0.582151	−	1.26768i
$999$	8.27072	−	8.27072i	0.261674	−	0.261674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.99.9	✓	832
5.4	even	2	inner	680.2.co.a.99.96	yes	832
8.3	odd	2	inner	680.2.co.a.99.88	yes	832
17.11	odd	16	inner	680.2.co.a.419.17	yes	832
40.19	odd	2	inner	680.2.co.a.99.17	yes	832
85.79	odd	16	inner	680.2.co.a.419.88	yes	832
136.11	even	16	inner	680.2.co.a.419.96	yes	832
680.419	even	16	inner	680.2.co.a.419.9	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.9	✓	832	1.1	even	1	trivial
680.2.co.a.99.17	yes	832	40.19	odd	2	inner
680.2.co.a.99.88	yes	832	8.3	odd	2	inner
680.2.co.a.99.96	yes	832	5.4	even	2	inner
680.2.co.a.419.9	yes	832	680.419	even	16	inner
680.2.co.a.419.17	yes	832	17.11	odd	16	inner
680.2.co.a.419.88	yes	832	85.79	odd	16	inner
680.2.co.a.419.96	yes	832	136.11	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37562 + 0.328119i) q^{2} +(-1.63264 - 0.324753i) q^{3} +(1.78468 - 0.902737i) q^{4} +(0.608763 - 2.15161i) q^{5} +(2.35246 - 0.0889645i) q^{6} +(-0.693159 - 0.463154i) q^{7} +(-2.15883 + 1.82741i) q^{8} +(-0.211574 - 0.0876370i) q^{9} +(-0.131444 + 3.15954i) q^{10} +(5.70222 - 1.13424i) q^{11} +(-3.20691 + 0.894270i) q^{12} +(-0.791428 - 0.791428i) q^{13} +(1.10550 + 0.409686i) q^{14} +(-1.69263 + 3.31511i) q^{15} +(2.37013 - 3.22218i) q^{16} +(1.86239 - 3.67852i) q^{17} +(0.319802 + 0.0511338i) q^{18} +(1.74054 - 0.720955i) q^{19} +(-0.855890 - 4.38947i) q^{20} +(0.981272 + 0.981272i) q^{21} +(-7.47194 + 3.43130i) q^{22} +(0.716030 + 3.59973i) q^{23} +(4.11807 - 2.28243i) q^{24} +(-4.25882 - 2.61963i) q^{25} +(1.34839 + 0.829023i) q^{26} +(4.46923 + 2.98625i) q^{27} +(-1.65517 - 0.200839i) q^{28} +(-7.13568 + 4.76791i) q^{29} +(1.24067 - 5.11573i) q^{30} +(0.420894 - 2.11598i) q^{31} +(-2.20315 + 5.21020i) q^{32} -9.67805 q^{33} +(-1.35495 + 5.67134i) q^{34} +(-1.41849 + 1.20945i) q^{35} +(-0.456705 + 0.0345924i) q^{36} +(0.424529 - 2.13425i) q^{37} +(-2.15777 + 1.56287i) q^{38} +(1.03510 + 1.54914i) q^{39} +(2.61765 + 5.75742i) q^{40} +(-3.08795 - 2.06330i) q^{41} +(-1.67183 - 1.02789i) q^{42} +(1.72320 - 4.16017i) q^{43} +(9.15269 - 7.17186i) q^{44} +(-0.317359 + 0.401875i) q^{45} +(-2.16613 - 4.71692i) q^{46} +(-7.04908 - 7.04908i) q^{47} +(-4.91600 + 4.49097i) q^{48} +(-2.41283 - 5.82508i) q^{49} +(6.71808 + 2.20623i) q^{50} +(-4.23523 + 5.40090i) q^{51} +(-2.12689 - 0.697990i) q^{52} +(8.10860 - 3.35869i) q^{53} +(-7.12782 - 2.64151i) q^{54} +(1.03086 - 12.9594i) q^{55} +(2.34279 - 0.266814i) q^{56} +(-3.07582 + 0.611818i) q^{57} +(8.25156 - 8.90020i) q^{58} +(-4.00568 + 9.67056i) q^{59} +(-0.0281300 + 7.44440i) q^{60} +(-8.90360 - 5.94920i) q^{61} +(0.115302 + 3.04889i) q^{62} +(0.106065 + 0.158738i) q^{63} +(1.32113 - 7.89016i) q^{64} +(-2.18463 + 1.22105i) q^{65} +(13.3133 - 3.17556i) q^{66} +9.22896 q^{67} +(0.00302559 - 8.24621i) q^{68} -6.10961i q^{69} +(1.55447 - 2.12919i) q^{70} +(-2.73634 - 0.544291i) q^{71} +(0.616903 - 0.197440i) q^{72} +(-9.15520 - 13.7017i) q^{73} +(0.116297 + 3.07522i) q^{74} +(6.10240 + 5.66000i) q^{75} +(2.45547 - 2.85792i) q^{76} +(-4.47788 - 1.85480i) q^{77} +(-1.93221 - 1.79139i) q^{78} +(-0.721559 - 3.62752i) q^{79} +(-5.49002 - 7.06114i) q^{80} +(-5.84108 - 5.84108i) q^{81} +(4.92486 + 1.82511i) q^{82} +(-1.61962 + 0.670870i) q^{83} +(2.63708 + 0.865421i) q^{84} +(-6.78097 - 6.24647i) q^{85} +(-1.00544 + 6.28824i) q^{86} +(13.1984 - 5.46697i) q^{87} +(-10.2374 + 12.8689i) q^{88} +(-8.32848 + 8.32848i) q^{89} +(0.304703 - 0.656959i) q^{90} +(0.182032 + 0.915138i) q^{91} +(4.52749 + 5.77796i) q^{92} +(-1.37434 + 3.31795i) q^{93} +(12.0098 + 7.38394i) q^{94} +(-0.491636 - 4.18385i) q^{95} +(5.28898 - 7.79092i) q^{96} +(1.19945 - 0.801448i) q^{97} +(5.23046 + 7.22141i) q^{98} +(-1.30585 - 0.259749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

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