LMFDB - Embedded newform 84.2.n.a.23.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [84,2,Mod(11,84)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("84.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.n (of order $6$, degree $2$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	84.23
Dual form			84.2.n.a.11.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.162204 - 1.40488i) q^{2} +(-0.373317 - 1.69134i) q^{3} +(-1.94738 + 0.455755i) q^{4} +(0.432549 + 0.249732i) q^{5} +(-2.31558 + 0.798808i) q^{6} +(0.261928 - 2.63275i) q^{7} +(0.956154 + 2.66191i) q^{8} +(-2.72127 + 1.26281i) q^{9} +(0.280683 - 0.648187i) q^{10} +(0.695249 + 1.20421i) q^{11} +(1.49783 + 3.12354i) q^{12} +2.75054 q^{13} +(-3.74119 + 0.0590654i) q^{14} +(0.260904 - 0.824817i) q^{15} +(3.58458 - 1.77505i) q^{16} +(5.04311 - 2.91164i) q^{17} +(2.21550 + 3.61822i) q^{18} +(2.14907 + 1.24076i) q^{19} +(-0.956154 - 0.289187i) q^{20} +(-4.55067 + 0.539842i) q^{21} +(1.57899 - 1.17207i) q^{22} +(-2.53203 + 4.38560i) q^{23} +(4.14525 - 2.61092i) q^{24} +(-2.37527 - 4.11408i) q^{25} +(-0.446148 - 3.86417i) q^{26} +(3.15174 + 4.13116i) q^{27} +(0.689816 + 5.24635i) q^{28} +6.32275i q^{29} +(-1.20109 - 0.232751i) q^{30} +(-5.98869 + 3.45757i) q^{31} +(-3.07517 - 4.74798i) q^{32} +(1.77718 - 1.62545i) q^{33} +(-4.90852 - 6.61269i) q^{34} +(0.770780 - 1.07338i) q^{35} +(4.72381 - 3.69941i) q^{36} +(-3.67154 + 6.35929i) q^{37} +(1.39454 - 3.22044i) q^{38} +(-1.02682 - 4.65209i) q^{39} +(-0.251182 + 1.39019i) q^{40} -5.74438i q^{41} +(1.49655 + 6.30558i) q^{42} +3.52627i q^{43} +(-1.90274 - 2.02819i) q^{44} +(-1.49245 - 0.133360i) q^{45} +(6.57194 + 2.84583i) q^{46} +(2.53203 - 4.38560i) q^{47} +(-4.34041 - 5.40008i) q^{48} +(-6.86279 - 1.37918i) q^{49} +(-5.39452 + 4.00429i) q^{50} +(-6.80726 - 7.44266i) q^{51} +(-5.35634 + 1.25357i) q^{52} +(-4.54223 + 2.62246i) q^{53} +(5.29257 - 5.09791i) q^{54} +0.694505i q^{55} +(7.25860 - 1.82009i) q^{56} +(1.29627 - 4.09801i) q^{57} +(8.88271 - 1.02558i) q^{58} +(1.57587 + 2.72949i) q^{59} +(-0.132166 + 1.72514i) q^{60} +(2.45426 - 4.25091i) q^{61} +(5.82886 + 7.85256i) q^{62} +(2.61190 + 7.49520i) q^{63} +(-6.17154 + 5.09039i) q^{64} +(1.18974 + 0.686897i) q^{65} +(-2.57183 - 2.23307i) q^{66} +(9.30445 - 5.37193i) q^{67} +(-8.49386 + 7.96850i) q^{68} +(8.36279 + 2.64530i) q^{69} +(-1.63300 - 0.908747i) q^{70} +4.54224 q^{71} +(-5.96345 - 6.03633i) q^{72} +(4.98752 + 8.63864i) q^{73} +(9.52959 + 4.12657i) q^{74} +(-6.07159 + 5.55325i) q^{75} +(-4.75054 - 1.43679i) q^{76} +(3.35249 - 1.51500i) q^{77} +(-6.36908 + 2.19715i) q^{78} +(-1.84576 - 1.06565i) q^{79} +(1.99379 + 0.127386i) q^{80} +(5.81061 - 6.87291i) q^{81} +(-8.07016 + 0.931761i) q^{82} -12.0165 q^{83} +(8.61584 - 3.12526i) q^{84} +2.90852 q^{85} +(4.95398 - 0.571975i) q^{86} +(10.6939 - 2.36039i) q^{87} +(-2.54073 + 3.00210i) q^{88} +(-2.12318 - 1.22582i) q^{89} +(0.0547257 + 2.11834i) q^{90} +(0.720443 - 7.24148i) q^{91} +(2.93206 - 9.69440i) q^{92} +(8.08361 + 8.83814i) q^{93} +(-6.57194 - 2.84583i) q^{94} +(0.619718 + 1.07338i) q^{95} +(-6.88244 + 6.97367i) q^{96} +0.526031 q^{97} +(-0.824419 + 9.86511i) q^{98} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.162204	−	1.40488i	−0.114696	−	0.993401i
$2$	−0.162204	−	1.40488i	−0.114696	−	0.993401i
$3$	−0.373317	−	1.69134i	−0.215535	−	0.976496i
$3$	−0.373317	−	1.69134i	−0.215535	−	0.976496i
$4$	−1.94738	+	0.455755i	−0.973690	+	0.227877i
$5$	0.432549	+	0.249732i	0.193442	+	0.111684i	0.593593	−	0.804766i	$-0.297709\pi$
$5$	0.432549	+	0.249732i	0.193442	+	0.111684i	−0.400151	+	0.916449i	$0.631042\pi$
$6$	−2.31558	+	0.798808i	−0.945331	+	0.326112i
$7$	0.261928	−	2.63275i	0.0989995	−	0.995087i
$7$	0.261928	−	2.63275i	0.0989995	−	0.995087i
$8$	0.956154	+	2.66191i	0.338051	+	0.941128i
$9$	−2.72127	+	1.26281i	−0.907090	+	0.420938i
$10$	0.280683	−	0.648187i	0.0887597	−	0.204975i
$11$	0.695249	+	1.20421i	0.209626	+	0.363082i	0.951597	−	0.307350i	$-0.0994422\pi$
$11$	0.695249	+	1.20421i	0.209626	+	0.363082i	−0.741971	+	0.670432i	$0.766109\pi$
$12$	1.49783	+	3.12354i	0.432385	+	0.901689i
$13$	2.75054			0.762861			0.381431	−	0.924397i	$-0.375432\pi$
$13$	2.75054			0.762861			0.381431	+	0.924397i	$0.375432\pi$
$14$	−3.74119	+	0.0590654i	−0.999875	+	0.0157859i
$15$	0.260904	−	0.824817i	0.0673652	−	0.212967i
$16$	3.58458	−	1.77505i	0.896144	−	0.443764i
$17$	5.04311	−	2.91164i	1.22313	−	0.706177i	0.257550	−	0.966265i	$-0.417085\pi$
$17$	5.04311	−	2.91164i	1.22313	−	0.706177i	0.965585	+	0.260088i	$0.0837515\pi$
$18$	2.21550	+	3.61822i	0.522199	+	0.852824i
$19$	2.14907	+	1.24076i	0.493030	+	0.284651i	0.725831	−	0.687874i	$-0.241456\pi$
$19$	2.14907	+	1.24076i	0.493030	+	0.284651i	−0.232801	+	0.972524i	$0.574789\pi$
$20$	−0.956154	−	0.289187i	−0.213802	−	0.0646643i
$21$	−4.55067	+	0.539842i	−0.993037	+	0.117803i
$22$	1.57899	−	1.17207i	0.336643	−	0.249886i
$23$	−2.53203	+	4.38560i	−0.527964	+	0.914460i	0.471505	+	0.881863i	$0.343711\pi$
$23$	−2.53203	+	4.38560i	−0.527964	+	0.914460i	−0.999469	+	0.0325966i	$0.989622\pi$
$24$	4.14525	−	2.61092i	0.846146	−	0.532952i
$25$	−2.37527	−	4.11408i	−0.475054	−	0.822817i
$26$	−0.446148	−	3.86417i	−0.0874968	−	0.757827i
$27$	3.15174	+	4.13116i	0.606553	+	0.795043i
$28$	0.689816	+	5.24635i	0.130363	+	0.991466i
$29$			6.32275i			1.17411i	0.809549	+	0.587053i	$0.199712\pi$
$29$			6.32275i			1.17411i	−0.809549	+	0.587053i	$0.800288\pi$
$30$	−1.20109	−	0.232751i	−0.219288	−	0.0424943i
$31$	−5.98869	+	3.45757i	−1.07560	+	0.620998i	−0.929706	−	0.368302i	$-0.879939\pi$
$31$	−5.98869	+	3.45757i	−1.07560	+	0.620998i	−0.145894	+	0.989300i	$0.546606\pi$
$32$	−3.07517	−	4.74798i	−0.543619	−	0.839332i
$33$	1.77718	−	1.62545i	0.309367	−	0.282955i
$34$	−4.90852	−	6.61269i	−0.841805	−	1.13407i
$35$	0.770780	−	1.07338i	0.130286	−	0.181435i
$36$	4.72381	−	3.69941i	0.787302	−	0.616568i
$37$	−3.67154	+	6.35929i	−0.603598	+	1.04546i	0.388674	+	0.921375i	$0.372933\pi$
$37$	−3.67154	+	6.35929i	−0.603598	+	1.04546i	−0.992271	+	0.124086i	$0.960400\pi$
$38$	1.39454	−	3.22044i	0.226224	−	0.522425i
$39$	−1.02682	−	4.65209i	−0.164423	−	0.744931i
$40$	−0.251182	+	1.39019i	−0.0397153	+	0.219808i
$41$		−	5.74438i		−	0.897121i	−0.893753	−	0.448560i	$-0.851937\pi$
$41$		−	5.74438i		−	0.897121i	0.893753	−	0.448560i	$-0.148063\pi$
$42$	1.49655	+	6.30558i	0.230923	+	0.972972i
$43$			3.52627i			0.537751i	0.963175	+	0.268875i	$0.0866520\pi$
$43$			3.52627i			0.537751i	−0.963175	+	0.268875i	$0.913348\pi$
$44$	−1.90274	−	2.02819i	−0.286848	−	0.305760i
$45$	−1.49245	−	0.133360i	−0.222481	−	0.0198802i
$46$	6.57194	+	2.84583i	0.968980	+	0.419595i
$47$	2.53203	−	4.38560i	0.369334	−	0.639705i	−0.620128	−	0.784501i	$-0.712919\pi$
$47$	2.53203	−	4.38560i	0.369334	−	0.639705i	0.989462	+	0.144796i	$0.0462526\pi$
$48$	−4.34041	−	5.40008i	−0.626484	−	0.779435i
$49$	−6.86279	−	1.37918i	−0.980398	−	0.197026i
$50$	−5.39452	+	4.00429i	−0.762900	+	0.566292i
$51$	−6.80726	−	7.44266i	−0.953207	−	1.04218i
$52$	−5.35634	+	1.25357i	−0.742790	+	0.173839i
$53$	−4.54223	+	2.62246i	−0.623923	+	0.360222i	−0.778395	−	0.627775i	$-0.783966\pi$
$53$	−4.54223	+	2.62246i	−0.623923	+	0.360222i	0.154472	+	0.987997i	$0.450632\pi$
$54$	5.29257	−	5.09791i	0.720227	−	0.693738i
$55$			0.694505i			0.0936470i
$56$	7.25860	−	1.82009i	0.969971	−	0.243219i
$57$	1.29627	−	4.09801i	0.171696	−	0.542794i
$58$	8.88271	−	1.02558i	1.16636	−	0.134665i
$59$	1.57587	+	2.72949i	0.205161	+	0.355349i	0.950184	−	0.311689i	$-0.100895\pi$
$59$	1.57587	+	2.72949i	0.205161	+	0.355349i	−0.745023	+	0.667039i	$0.767562\pi$
$60$	−0.132166	+	1.72514i	−0.0170626	+	0.222715i
$61$	2.45426	−	4.25091i	0.314236	−	0.544273i	−0.665039	−	0.746809i	$-0.731585\pi$
$61$	2.45426	−	4.25091i	0.314236	−	0.544273i	0.979275	+	0.202536i	$0.0649183\pi$
$62$	5.82886	+	7.85256i	0.740267	+	0.997276i
$63$	2.61190	+	7.49520i	0.329068	+	0.944306i
$64$	−6.17154	+	5.09039i	−0.771443	+	0.636299i
$65$	1.18974	+	0.686897i	0.147569	+	0.0851991i
$66$	−2.57183	−	2.23307i	−0.316571	−	0.274871i
$67$	9.30445	−	5.37193i	1.13672	−	0.656286i	0.191104	−	0.981570i	$-0.438793\pi$
$67$	9.30445	−	5.37193i	1.13672	−	0.656286i	0.945616	+	0.325284i	$0.105460\pi$
$68$	−8.49386	+	7.96850i	−1.03003	+	0.966322i
$69$	8.36279	+	2.64530i	1.00676	+	0.318457i
$70$	−1.63300	−	0.908747i	−0.195181	−	0.108616i
$71$	4.54224			0.539065			0.269532	−	0.962991i	$-0.413131\pi$
$71$	4.54224			0.539065			0.269532	+	0.962991i	$0.413131\pi$
$72$	−5.96345	−	6.03633i	−0.702799	−	0.711389i
$73$	4.98752	+	8.63864i	0.583745	+	1.01108i	0.995031	+	0.0995695i	$0.0317466\pi$
$73$	4.98752	+	8.63864i	0.583745	+	1.01108i	−0.411286	+	0.911507i	$0.634920\pi$
$74$	9.52959	+	4.12657i	1.10779	+	0.479704i
$75$	−6.07159	+	5.55325i	−0.701087	+	0.641234i
$76$	−4.75054	−	1.43679i	−0.544924	−	0.164811i
$77$	3.35249	−	1.51500i	0.382051	−	0.172651i
$78$	−6.36908	+	2.19715i	−0.721156	+	0.248778i
$79$	−1.84576	−	1.06565i	−0.207664	−	0.119895i	0.392561	−	0.919726i	$-0.371589\pi$
$79$	−1.84576	−	1.06565i	−0.207664	−	0.119895i	−0.600225	+	0.799831i	$0.704922\pi$
$80$	1.99379	+	0.127386i	0.222913	+	0.0142422i
$81$	5.81061	−	6.87291i	0.645623	−	0.763656i
$82$	−8.07016	+	0.931761i	−0.891200	+	0.102896i
$83$	−12.0165			−1.31899			−0.659493	−	0.751710i	$-0.729229\pi$
$83$	−12.0165			−1.31899			−0.659493	+	0.751710i	$0.729229\pi$
$84$	8.61584	−	3.12526i	0.940065	−	0.340994i
$85$	2.90852			0.315474
$86$	4.95398	−	0.571975i	0.534202	−	0.0616776i
$87$	10.6939	−	2.36039i	1.14651	−	0.253060i
$88$	−2.54073	+	3.00210i	−0.270842	+	0.320025i
$89$	−2.12318	−	1.22582i	−0.225056	−	0.129936i	0.383233	−	0.923652i	$-0.374811\pi$
$89$	−2.12318	−	1.22582i	−0.225056	−	0.129936i	−0.608289	+	0.793715i	$0.708144\pi$
$90$	0.0547257	+	2.11834i	0.00576860	+	0.223293i
$91$	0.720443	−	7.24148i	0.0755229	−	0.759114i
$92$	2.93206	−	9.69440i	0.305688	−	1.01071i
$93$	8.08361	+	8.83814i	0.838231	+	0.916473i
$94$	−6.57194	−	2.84583i	−0.677844	−	0.293525i
$95$	0.619718	+	1.07338i	0.0635817	+	0.110127i
$96$	−6.88244	+	6.97367i	−0.702436	+	0.711747i
$97$	0.526031			0.0534104			0.0267052	−	0.999643i	$-0.491498\pi$
$97$	0.526031			0.0534104			0.0267052	+	0.999643i	$0.491498\pi$
$98$	−0.824419	+	9.86511i	−0.0832789	+	0.996526i
$99$	−3.41265	−	2.39900i	−0.342984	−	0.241109i
$100$	6.50056	+	6.92914i	0.650056	+	0.692914i
$101$	−13.9396	+	8.04803i	−1.38704	+	0.800809i	−0.992981	−	0.118275i	$-0.962264\pi$
$101$	−13.9396	+	8.04803i	−1.38704	+	0.800809i	−0.394061	+	0.919084i	$0.628930\pi$
$102$	−9.35188	+	10.7706i	−0.925974	+	1.06645i
$103$	−1.62521	−	0.938316i	−0.160137	−	0.0924550i	0.417790	−	0.908544i	$-0.362805\pi$
$103$	−1.62521	−	0.938316i	−0.160137	−	0.0924550i	−0.577927	+	0.816089i	$0.696138\pi$
$104$	2.62993	+	7.32168i	0.257886	+	0.717950i
$105$	−2.10320	−	0.902940i	−0.205252	−	0.0881179i
$106$	4.42101	+	5.95591i	0.429406	+	0.578490i
$107$	3.63924	−	6.30335i	0.351819	−	0.609368i	−0.634749	−	0.772718i	$-0.718897\pi$
$107$	3.63924	−	6.30335i	0.351819	−	0.609368i	0.986568	+	0.163350i	$0.0522300\pi$
$108$	−8.02044	−	6.60852i	−0.771767	−	0.635905i
$109$	0.921005	+	1.59523i	0.0882163	+	0.152795i	0.906757	−	0.421653i	$-0.138550\pi$
$109$	0.921005	+	1.59523i	0.0882163	+	0.152795i	−0.818541	+	0.574448i	$0.805217\pi$
$110$	0.975696	−	0.112651i	0.0930290	−	0.0107409i
$111$	12.1264	+	3.83579i	1.15099	+	0.364077i
$112$	−3.73438	−	9.90224i	−0.352866	−	0.935674i
$113$		−	10.2728i		−	0.966382i	−0.875515	−	0.483191i	$-0.839478\pi$
$113$		−	10.2728i		−	0.966382i	0.875515	−	0.483191i	$-0.160522\pi$
$114$	−5.96747	−	1.15640i	−0.558905	−	0.108306i
$115$	−2.19045	+	1.26466i	−0.204260	+	0.117930i
$116$	−2.88162	−	12.3128i	−0.267552	−	1.14321i
$117$	−7.48495	+	3.47341i	−0.691983	+	0.321117i
$118$	3.57899	−	2.65665i	0.329473	−	0.244564i
$119$	−6.34471	−	14.0399i	−0.581618	−	1.28704i
$120$	2.44505	−	0.0941473i	0.223202	−	0.00859443i
$121$	4.53326	−	7.85183i	0.412114	−	0.713803i
$122$	−6.37011	−	2.75843i	−0.576723	−	0.249737i
$123$	−9.71570	+	2.14447i	−0.876035	+	0.193361i
$124$	10.0864	−	9.46258i	0.905790	−	0.849764i
$125$		−	4.87005i		−	0.435590i
$126$	10.1062	−	4.88516i	0.900332	−	0.435204i
$127$			1.51224i			0.134190i	0.997747	+	0.0670949i	$0.0213730\pi$
$127$			1.51224i			0.134190i	−0.997747	+	0.0670949i	$0.978627\pi$
$128$	8.15244	+	7.84460i	0.720581	+	0.693371i
$129$	5.96412	−	1.31642i	0.525111	−	0.115904i
$130$	0.772028	−	1.78286i	0.0677113	−	0.156367i
$131$	3.32518	−	5.75939i	0.290523	−	0.503200i	−0.683411	−	0.730034i	$-0.739504\pi$
$131$	3.32518	−	5.75939i	0.290523	−	0.503200i	0.973933	+	0.226834i	$0.0728375\pi$
$132$	−2.72003	+	3.97533i	−0.236748	+	0.346008i
$133$	3.82953	−	5.33298i	0.332062	−	0.462428i
$134$	−9.05614	−	12.2003i	−0.782331	−	1.05395i
$135$	0.331598	+	2.57402i	0.0285394	+	0.221537i
$136$	12.5725	+	10.6403i	1.07809	+	0.912402i
$137$	−10.5583	+	6.09586i	−0.902060	+	0.520805i	−0.877868	−	0.478903i	$-0.841035\pi$
$137$	−10.5583	+	6.09586i	−0.902060	+	0.520805i	−0.0241922	+	0.999707i	$0.507701\pi$
$138$	2.35985	−	12.1778i	0.200884	−	1.03664i
$139$			0.0477837i			0.00405296i	0.999998	+	0.00202648i	$0.000645050\pi$
$139$			0.0477837i			0.00405296i	−0.999998	+	0.00202648i	$0.999355\pi$
$140$	−1.01180	+	2.44157i	−0.0855129	+	0.206350i
$141$	−8.36279	−	2.64530i	−0.704274	−	0.222774i
$142$	−0.736770	−	6.38131i	−0.0618283	−	0.535507i
$143$	1.91231	+	3.31221i	0.159915	+	0.276981i
$144$	−7.51303	+	9.35705i	−0.626086	+	0.779754i
$145$	−1.57899	+	2.73490i	−0.131128	+	0.227121i
$146$	11.3273	−	8.40809i	0.937451	−	0.695859i
$147$	0.229323	+	12.1222i	0.0189143	+	0.999821i
$148$	4.25161	−	14.0573i	0.349480	−	1.15550i
$149$	−1.98650	−	1.14691i	−0.162740	−	0.0939583i	0.416418	−	0.909173i	$-0.363285\pi$
$149$	−1.98650	−	1.14691i	−0.162740	−	0.0939583i	−0.579158	+	0.815215i	$0.696619\pi$
$150$	8.78648	+	7.62910i	0.717413	+	0.622914i
$151$	−11.3759	+	6.56789i	−0.925759	+	0.534487i	−0.885468	−	0.464701i	$-0.846162\pi$
$151$	−11.3759	+	6.56789i	−0.925759	+	0.534487i	−0.0402913	+	0.999188i	$0.512829\pi$
$152$	−1.24797	+	6.90699i	−0.101223	+	0.560231i
$153$	−10.0468	+	14.2919i	−0.812236	+	1.15543i
$154$	−2.67219	−	4.46410i	−0.215331	−	0.359728i
$155$	−3.45387			−0.277421
$156$	4.11982	+	8.59141i	0.329850	+	0.687864i
$157$	−4.20480	−	7.28292i	−0.335579	−	0.581241i	0.648017	−	0.761626i	$-0.275599\pi$
$157$	−4.20480	−	7.28292i	−0.335579	−	0.581241i	−0.983596	+	0.180386i	$0.942265\pi$
$158$	−1.19772	+	2.76592i	−0.0952855	+	0.220045i
$159$	6.13116	+	6.70345i	0.486232	+	0.531618i
$160$	−0.144439	−	2.82170i	−0.0114189	−	0.223075i
$161$	10.8830	+	7.81491i	0.857700	+	0.615901i
$162$	−10.5981	−	7.04840i	−0.832667	−	0.553774i
$163$	10.7040	+	6.17993i	0.838399	+	0.484050i	0.856720	−	0.515782i	$-0.172499\pi$
$163$	10.7040	+	6.17993i	0.838399	+	0.484050i	−0.0183210	+	0.999832i	$0.505832\pi$
$164$	2.61803	+	11.1865i	0.204433	+	0.873517i
$165$	1.17464	−	0.259270i	0.0914459	−	0.0201842i
$166$	1.94913	+	16.8818i	0.151282	+	1.31028i
$167$	2.36549			0.183047			0.0915237	−	0.995803i	$-0.470826\pi$
$167$	2.36549			0.183047			0.0915237	+	0.995803i	$0.470826\pi$
$168$	−5.78815	−	11.5973i	−0.446565	−	0.894751i
$169$	−5.43456			−0.418043
$170$	−0.471774	−	4.08613i	−0.0361834	−	0.313392i
$171$	−7.41504	−	0.662584i	−0.567043	−	0.0506691i
$172$	−1.60711	−	6.86698i	−0.122541	−	0.523602i
$173$	8.28769	+	4.78490i	0.630102	+	0.363789i	0.780791	−	0.624792i	$-0.214816\pi$
$173$	8.28769	+	4.78490i	0.630102	+	0.363789i	−0.150690	+	0.988581i	$0.548149\pi$
$174$	−5.05067	−	14.6408i	−0.382890	−	1.10992i
$175$	−11.4535	+	5.17590i	−0.865805	+	0.391261i
$176$	4.62971	+	3.08247i	0.348977	+	0.232350i
$177$	4.02820	−	3.68430i	0.302778	−	0.276929i
$178$	−1.37774	+	3.18164i	−0.103266	+	0.238474i
$179$	10.3771	+	17.9736i	0.775619	+	1.34341i	0.934446	+	0.356105i	$0.115895\pi$
$179$	10.3771	+	17.9736i	0.775619	+	1.34341i	−0.158827	+	0.987306i	$0.550771\pi$
$180$	2.96714	−	0.420487i	0.221158	−	0.0313412i
$181$	−6.43456			−0.478277			−0.239138	−	0.970985i	$-0.576865\pi$
$181$	−6.43456			−0.478277			−0.239138	+	0.970985i	$0.576865\pi$
$182$	−10.2903	+	0.162461i	−0.762766	+	0.0120424i
$183$	−8.10595	−	2.56406i	−0.599209	−	0.189541i
$184$	−14.0951	−	2.54672i	−1.03910	−	0.187747i
$185$	−3.17624	+	1.83380i	−0.233522	+	0.134824i
$186$	11.1053	−	12.7901i	0.814283	−	0.937815i
$187$	7.01244	+	4.04864i	0.512801	+	0.296066i
$188$	−2.93206	+	9.69440i	−0.213842	+	0.707037i
$189$	11.7019	−	7.21570i	0.851186	−	0.524865i
$190$	1.40745	−	1.04474i	0.102107	−	0.0757932i
$191$	−8.76689	+	15.1847i	−0.634350	+	1.09873i	0.352303	+	0.935886i	$0.385399\pi$
$191$	−8.76689	+	15.1847i	−0.634350	+	1.09873i	−0.986652	+	0.162840i	$0.947935\pi$
$192$	10.9135	+	8.53785i	0.787616	+	0.616166i
$193$	1.09255	+	1.89234i	0.0786432	+	0.136214i	0.902665	−	0.430344i	$-0.141608\pi$
$193$	1.09255	+	1.89234i	0.0786432	+	0.136214i	−0.824022	+	0.566558i	$0.808275\pi$
$194$	−0.0853244	−	0.739011i	−0.00612593	−	0.0530579i
$195$	0.717627	−	2.26869i	0.0513903	−	0.162464i
$196$	13.9930	−	0.441950i	0.999502	−	0.0315679i
$197$		−	6.27706i		−	0.447222i	−0.974678	−	0.223611i	$-0.928215\pi$
$197$		−	6.27706i		−	0.447222i	0.974678	−	0.223611i	$-0.0717845\pi$
$198$	−2.81676	+	5.18349i	−0.200179	+	0.368375i
$199$	0.749564	−	0.432761i	0.0531352	−	0.0306776i	−0.473197	−	0.880957i	$-0.656900\pi$
$199$	0.749564	−	0.432761i	0.0531352	−	0.0306776i	0.526332	+	0.850279i	$0.323567\pi$
$200$	8.68021	−	10.2564i	0.613783	−	0.725240i
$201$	−12.5593	−	13.7316i	−0.885863	−	0.968550i
$202$	13.5676	+	18.2781i	0.954612	+	1.28604i
$203$	16.6462	+	1.65611i	1.16834	+	0.116236i
$204$	16.6484	+	11.3912i	1.16562	+	0.797547i
$205$	1.43456	−	2.48472i	0.100194	−	0.173541i
$206$	−1.05461	+	2.43543i	−0.0734779	+	0.169684i
$207$	1.35213	−	15.1319i	0.0939798	−	1.05174i
$208$	9.85950	−	4.88235i	0.683633	−	0.338530i
$209$			3.45056i			0.238680i
$210$	−0.927375	+	3.10121i	−0.0639950	+	0.214004i
$211$		−	3.90417i		−	0.268774i	−0.990929	−	0.134387i	$-0.957094\pi$
$211$		−	3.90417i		−	0.268774i	0.990929	−	0.134387i	$-0.0429065\pi$
$212$	7.65024	−	7.17706i	0.525421	−	0.492922i
$213$	−1.69570	−	7.68248i	−0.116187	−	0.526395i
$214$	−9.44576	−	4.09027i	−0.645699	−	0.279605i
$215$	−0.880622	+	1.52528i	−0.0600580	+	0.104023i
$216$	−7.98324	+	12.3397i	−0.543191	+	0.839609i
$217$	7.53433	+	16.6724i	0.511463	+	1.13179i
$218$	2.09171	−	1.55265i	0.141669	−	0.105159i
$219$	12.7490	−	11.6605i	0.861495	−	0.787947i
$220$	−0.316524	−	1.35246i	−0.0213400	−	0.0911831i
$221$	13.8713	−	8.00858i	0.933082	−	0.538715i
$222$	3.42188	−	17.6583i	0.229662	−	1.18515i
$223$		−	23.5017i		−	1.57379i	−0.617085	−	0.786896i	$-0.711687\pi$
$223$		−	23.5017i		−	1.57379i	0.617085	−	0.786896i	$-0.288313\pi$
$224$	−13.3057	+	6.85254i	−0.889027	+	0.457855i
$225$	11.6591	+	8.19601i	0.777271	+	0.546401i
$226$	−14.4320	+	1.66629i	−0.960004	+	0.110840i
$227$	−9.58391	−	16.5998i	−0.636107	−	1.10177i	−0.986280	−	0.165084i	$-0.947210\pi$
$227$	−9.58391	−	16.5998i	−0.636107	−	1.10177i	0.350173	−	0.936685i	$-0.386123\pi$
$228$	−0.656651	+	8.57115i	−0.0434878	+	0.567639i
$229$	−5.73805	+	9.93860i	−0.379181	+	0.656761i	−0.990943	−	0.134281i	$-0.957128\pi$
$229$	−5.73805	+	9.93860i	−0.379181	+	0.656761i	0.611762	+	0.791042i	$0.290461\pi$
$230$	2.13199	+	2.87219i	0.140579	+	0.189386i
$231$	−3.81393	−	5.10462i	−0.250938	−	0.335859i
$232$	−16.8306	+	6.04552i	−1.10498	+	0.396908i
$233$	−17.5088	−	10.1087i	−1.14704	−	0.662245i	−0.198877	−	0.980025i	$-0.563729\pi$
$233$	−17.5088	−	10.1087i	−1.14704	−	0.662245i	−0.948164	+	0.317780i	$0.897063\pi$
$234$	6.09382	+	9.95205i	0.398365	+	0.650586i
$235$	2.19045	−	1.26466i	0.142889	−	0.0824971i
$236$	−4.31280	−	4.59714i	−0.280739	−	0.299248i
$237$	−1.11332	+	3.51963i	−0.0723181	+	0.228625i
$238$	−18.6953	+	11.1909i	−1.21183	+	0.725398i
$239$	6.90774			0.446824			0.223412	−	0.974724i	$-0.428280\pi$
$239$	6.90774			0.446824			0.223412	+	0.974724i	$0.428280\pi$
$240$	−0.528863	−	3.41974i	−0.0341380	−	0.220743i
$241$	−4.03326	−	6.98581i	−0.259805	−	0.449995i	0.706385	−	0.707828i	$-0.250325\pi$
$241$	−4.03326	−	6.98581i	−0.259805	−	0.449995i	−0.966190	+	0.257833i	$0.916992\pi$
$242$	−11.7662	−	5.09509i	−0.756360	−	0.327525i
$243$	−13.7936	−	7.26194i	−0.884862	−	0.465854i
$244$	−2.84201	+	9.39667i	−0.181941	+	0.601560i
$245$	−2.62406	−	2.31042i	−0.167645	−	0.147608i
$246$	4.58866	+	13.3016i	0.292562	+	0.848076i
$247$	5.91109	+	3.41277i	0.376113	+	0.217149i
$248$	−14.9299	−	12.6354i	−0.948047	−	0.802348i
$249$	4.48598	+	20.3241i	0.284287	+	1.28799i
$250$	−6.84183	+	0.789941i	−0.432716	+	0.0499603i
$251$	−20.4073			−1.28810			−0.644048	−	0.764985i	$-0.722746\pi$
$251$	−20.4073			−1.28810			−0.644048	+	0.764985i	$0.722746\pi$
$252$	−8.50233	−	13.4056i	−0.535596	−	0.844474i
$253$	−7.04155			−0.442699
$254$	2.12452	−	0.245292i	0.133304	−	0.0153910i
$255$	−1.08580	−	4.91931i	−0.0679956	−	0.308059i
$256$	9.69836	−	12.7256i	0.606148	−	0.795352i
$257$	23.5645	+	13.6050i	1.46991	+	0.848655i	0.999430	−	0.0337537i	$-0.0107462\pi$
$257$	23.5645	+	13.6050i	1.46991	+	0.848655i	0.470484	+	0.882409i	$0.344080\pi$
$258$	−2.81681	−	8.16535i	−0.175367	−	0.508352i
$259$	15.7808	+	11.3319i	0.980570	+	0.704133i
$260$	−2.62993	−	0.795420i	−0.163102	−	0.0493299i
$261$	−7.98445	−	17.2059i	−0.494225	−	1.06502i
$262$	−8.63061	−	3.73729i	−0.533201	−	0.230891i
$263$	−1.80247	−	3.12196i	−0.111145	−	0.192508i	0.805087	−	0.593156i	$-0.202118\pi$
$263$	−1.80247	−	3.12196i	−0.111145	−	0.192508i	−0.916232	+	0.400648i	$0.868785\pi$
$264$	6.02607	+	3.17650i	0.370879	+	0.195500i
$265$	−2.61965			−0.160924
$266$	−8.11336	−	4.51500i	−0.497462	−	0.276833i
$267$	−1.28066	+	4.04864i	−0.0783749	+	0.247772i
$268$	−15.6710	+	14.7017i	−0.957260	+	0.898051i
$269$	22.6598	−	13.0827i	1.38160	−	0.797664i	0.389247	−	0.921134i	$-0.372735\pi$
$269$	22.6598	−	13.0827i	1.38160	−	0.797664i	0.992348	+	0.123469i	$0.0394020\pi$
$270$	3.56241	−	0.883373i	0.216801	−	0.0537604i
$271$	−19.9722	−	11.5309i	−1.21322	−	0.700455i	−0.249764	−	0.968307i	$-0.580353\pi$
$271$	−19.9722	−	11.5309i	−1.21322	−	0.700455i	−0.963460	+	0.267851i	$0.913686\pi$
$272$	12.9091	−	19.3888i	0.782729	−	1.17562i
$273$	−12.5168	+	1.48485i	−0.757549	+	0.0898675i
$274$	10.2766	+	13.8444i	0.620830	+	0.836373i
$275$	3.30281	−	5.72063i	0.199167	−	0.344967i
$276$	−17.4911	−	1.34003i	−1.05284	−	0.0806600i
$277$	10.1455	+	17.5725i	0.609585	+	1.05583i	0.991309	+	0.131555i	$0.0419971\pi$
$277$	10.1455	+	17.5725i	0.609585	+	1.05583i	−0.381724	+	0.924276i	$0.624670\pi$
$278$	0.0671305	−	0.00775071i	0.00402622	−	0.000464857i
$279$	11.9306	−	16.9716i	0.714264	−	1.01606i
$280$	3.59423	+	1.02543i	0.214797	+	0.0612811i
$281$			27.6637i			1.65028i	0.564929	+	0.825140i	$0.308904\pi$
$281$			27.6637i			1.65028i	−0.564929	+	0.825140i	$0.691096\pi$
$282$	−2.35985	+	12.1778i	−0.140527	+	0.725177i
$283$	15.0435	−	8.68535i	0.894242	−	0.516291i	0.0189142	−	0.999821i	$-0.493979\pi$
$283$	15.0435	−	8.68535i	0.894242	−	0.516291i	0.875328	+	0.483530i	$0.160646\pi$
$284$	−8.84547	+	2.07015i	−0.524882	+	0.122841i
$285$	1.58411	−	1.44887i	0.0938343	−	0.0858235i
$286$	4.34308	−	3.22382i	0.256812	−	0.190628i
$287$	−15.1235	−	1.50461i	−0.892714	−	0.0888146i
$288$	14.3642	+	9.03716i	0.846417	+	0.532520i
$289$	8.45533	−	14.6451i	0.497373	−	0.861474i
$290$	4.09833	+	1.77469i	0.240662	+	0.104213i
$291$	−0.196376	−	0.889698i	−0.0115118	−	0.0521550i
$292$	−13.6497	−	14.5496i	−0.798788	−	0.851452i
$293$		−	19.9672i		−	1.16650i	−0.812294	−	0.583248i	$-0.801782\pi$
$293$		−	19.9672i		−	1.16650i	0.812294	−	0.583248i	$-0.198218\pi$
$294$	16.9930	−	2.28844i	0.991054	−	0.133465i
$295$			1.57418i			0.0916525i
$296$	−20.4384	−	3.69285i	−1.18796	−	0.214643i
$297$	−2.78353	+	6.66754i	−0.161517	+	0.386890i
$298$	−1.28905	+	2.97683i	−0.0746726	+	0.172443i
$299$	−6.96442	+	12.0627i	−0.402763	+	0.697606i
$300$	9.29278	−	13.5814i	0.536519	−	0.784124i
$301$	9.28379	+	0.923629i	0.535109	+	0.0532371i
$302$	11.0723	+	14.9165i	0.637141	+	0.858346i
$303$	18.8159	+	20.5722i	1.08094	+	1.18184i
$304$	9.90592	+	0.632903i	0.568144	+	0.0362995i
$305$	2.12318	−	1.22582i	0.121573	−	0.0701901i
$306$	21.7080	+	11.7964i	1.24096	+	0.674353i
$307$			14.1529i			0.807746i	0.914815	+	0.403873i	$0.132336\pi$
$307$			14.1529i			0.807746i	−0.914815	+	0.403873i	$0.867664\pi$
$308$	−5.83809	+	4.47820i	−0.332656	+	0.255169i
$309$	−0.980294	+	3.09908i	−0.0557670	+	0.176300i
$310$	0.560231	+	4.85227i	0.0318190	+	0.275591i
$311$	12.2774	+	21.2652i	0.696190	+	1.20584i	0.969778	+	0.243990i	$0.0784563\pi$
$311$	12.2774	+	21.2652i	0.696190	+	1.20584i	−0.273588	+	0.961847i	$0.588210\pi$
$312$	11.4017	−	7.18142i	0.645492	−	0.406568i
$313$	−0.0260312	+	0.0450873i	−0.00147137	+	0.00254848i	−0.866760	−	0.498725i	$-0.833802\pi$
$313$	−0.0260312	+	0.0450873i	−0.00147137	+	0.00254848i	0.865289	+	0.501274i	$0.167135\pi$
$314$	−9.54960	+	7.08856i	−0.538915	+	0.400031i
$315$	−0.742018	+	3.89432i	−0.0418080	+	0.219420i
$316$	4.08007	+	1.23401i	0.229522	+	0.0694185i
$317$	5.86864	+	3.38826i	0.329616	+	0.190304i	0.655671	−	0.755047i	$-0.272386\pi$
$317$	5.86864	+	3.38826i	0.329616	+	0.190304i	−0.326055	+	0.945351i	$0.605719\pi$
$318$	8.42305	−	9.70087i	0.472341	−	0.543998i
$319$	−7.61390	+	4.39589i	−0.426297	+	0.246122i
$320$	−3.94073	+	0.660611i	−0.220293	+	0.0369293i
$321$	−12.0197	−	3.80205i	−0.670875	−	0.212210i
$322$	9.21375	−	16.5569i	0.513462	−	0.922681i
$323$	14.4507			0.804056
$324$	−8.18310	+	16.0324i	−0.454617	+	0.890687i
$325$	−6.53326	−	11.3159i	−0.362400	−	0.627695i
$326$	6.94584	−	16.0402i	0.384695	−	0.888384i
$327$	2.35425	−	2.15326i	0.130190	−	0.119076i
$328$	15.2910	−	5.49251i	0.844305	−	0.303273i
$329$	−10.8830	−	7.81491i	−0.599999	−	0.430850i
$330$	−0.554776	−	1.60818i	−0.0305394	−	0.0885274i
$331$	−15.4949	−	8.94598i	−0.851676	−	0.491715i	0.00953987	−	0.999954i	$-0.496963\pi$
$331$	−15.4949	−	8.94598i	−0.851676	−	0.491715i	−0.861216	+	0.508239i	$0.830297\pi$
$332$	23.4008	−	5.47659i	1.28428	−	0.300567i
$333$	1.96065	−	21.9418i	0.107443	−	1.20240i
$334$	−0.383693	−	3.32324i	−0.0209947	−	0.181839i
$335$	5.36618			0.293185
$336$	−15.3540	+	10.0128i	−0.837627	+	0.546242i
$337$	7.09362			0.386414			0.193207	−	0.981158i	$-0.438111\pi$
$337$	7.09362			0.386414			0.193207	+	0.981158i	$0.438111\pi$
$338$	0.881507	+	7.63490i	0.0479476	+	0.415284i
$339$	−17.3748	+	3.83500i	−0.943668	+	0.208289i
$340$	−5.66400	+	1.32557i	−0.307174	+	0.0718893i
$341$	−8.32726	−	4.80775i	−0.450946	−	0.260354i
$342$	0.271898	+	10.5247i	0.0147026	+	0.569112i
$343$	−5.42861	+	17.7068i	−0.293118	+	0.956076i
$344$	−9.38661	+	3.37165i	−0.506092	+	0.181787i
$345$	2.95670	+	3.23268i	0.159183	+	0.174042i
$346$	5.37792	−	12.4194i	0.289119	−	0.667669i
$347$	4.59539	+	7.95946i	0.246694	+	0.427286i	0.962606	−	0.270904i	$-0.0873225\pi$
$347$	4.59539	+	7.95946i	0.246694	+	0.427286i	−0.715913	+	0.698190i	$0.753989\pi$
$348$	−19.7494	+	9.47038i	−1.05868	+	0.507666i
$349$	−22.1330			−1.18475			−0.592377	−	0.805661i	$-0.701810\pi$
$349$	−22.1330			−1.18475			−0.592377	+	0.805661i	$0.701810\pi$
$350$	9.12933	+	15.2513i	0.487983	+	0.815215i
$351$	8.66898	+	11.3629i	0.462716	+	0.606507i
$352$	3.57954	−	7.00417i	0.190790	−	0.373324i
$353$	−9.28947	+	5.36328i	−0.494429	+	0.285458i	−0.726410	−	0.687262i	$-0.758813\pi$
$353$	−9.28947	+	5.36328i	−0.494429	+	0.285458i	0.231981	+	0.972720i	$0.425479\pi$
$354$	−5.82939	−	5.06153i	−0.309829	−	0.269017i
$355$	1.96474	+	1.13434i	0.104278	+	0.0602047i
$356$	4.69330	+	1.41948i	0.248745	+	0.0752325i
$357$	−21.3777	+	15.9724i	−1.13143	+	0.845349i
$358$	23.5676	−	17.4939i	1.24559	−	0.924584i
$359$	−1.80247	+	3.12196i	−0.0951305	+	0.164771i	−0.909663	−	0.415347i	$-0.863660\pi$
$359$	−1.80247	+	3.12196i	−0.0951305	+	0.164771i	0.814533	+	0.580118i	$0.196993\pi$
$360$	−1.07202	−	4.10027i	−0.0565002	−	0.216103i
$361$	−6.42101	−	11.1215i	−0.337948	−	0.585342i
$362$	1.04371	+	9.03978i	0.0548562	+	0.475120i
$363$	−14.9725	−	4.73606i	−0.785851	−	0.248579i
$364$	1.89736	+	14.4303i	0.0994489	+	0.756351i
$365$			4.98218i			0.260779i
$366$	−2.28738	+	11.8038i	−0.119563	+	0.616994i
$367$	13.0134	−	7.51328i	0.679293	−	0.392190i	−0.120295	−	0.992738i	$-0.538384\pi$
$367$	13.0134	−	7.51328i	0.679293	−	0.392190i	0.799589	+	0.600548i	$0.205051\pi$
$368$	−1.29156	+	20.2150i	−0.0673274	+	1.05378i
$369$	7.25407	+	15.6320i	0.377632	+	0.813769i
$370$	3.09148	+	4.16479i	0.160718	+	0.216517i
$371$	5.71454	+	12.6455i	0.296684	+	0.656520i
$372$	−19.7699	−	13.5271i	−1.02502	−	0.701346i
$373$	−1.32846	+	2.30096i	−0.0687850	+	0.119139i	−0.898367	−	0.439246i	$-0.855246\pi$
$373$	−1.32846	+	2.30096i	−0.0687850	+	0.119139i	0.829582	+	0.558385i	$0.188579\pi$
$374$	4.55040	−	10.5083i	0.235296	−	0.543374i
$375$	−8.23691	+	1.81807i	−0.425352	+	0.0938848i
$376$	14.0951	+	2.54672i	0.726898	+	0.131337i
$377$			17.3909i			0.895679i
$378$	−12.0353	−	15.2693i	−0.619028	−	0.785369i
$379$		−	17.7150i		−	0.909957i	−0.890502	−	0.454979i	$-0.849647\pi$
$379$		−	17.7150i		−	0.909957i	0.890502	−	0.454979i	$-0.150353\pi$
$380$	−1.69603	−	1.80785i	−0.0870043	−	0.0927405i
$381$	2.55772	−	0.564546i	0.131036	−	0.0289226i
$382$	22.7547	+	9.85342i	1.16423	+	0.504145i
$383$	16.4609	−	28.5111i	0.841111	−	1.45685i	−0.0478445	−	0.998855i	$-0.515235\pi$
$383$	16.4609	−	28.5111i	0.841111	−	1.45685i	0.888956	−	0.457993i	$-0.151431\pi$
$384$	10.2244	−	16.7171i	0.521764	−	0.853090i
$385$	1.82846	+	0.181910i	0.0931869	+	0.00927101i
$386$	2.48130	−	1.84184i	0.126295	−	0.0937473i
$387$	−4.45301	−	9.59592i	−0.226359	−	0.487788i
$388$	−1.02438	+	0.239741i	−0.0520051	+	0.0121710i
$389$	−5.90821	+	3.41111i	−0.299558	+	0.172950i	−0.642244	−	0.766500i	$-0.721997\pi$
$389$	−5.90821	+	3.41111i	−0.299558	+	0.172950i	0.342686	+	0.939450i	$0.388663\pi$
$390$	−3.30364	−	0.640190i	−0.167286	−	0.0324173i
$391$			29.4894i			1.49134i
$392$	−2.89061	−	19.5868i	−0.145998	−	0.989285i
$393$	−10.9824	−	3.47394i	−0.553991	−	0.175237i
$394$	−8.81852	+	1.01816i	−0.444271	+	0.0512944i
$395$	−0.532254	−	0.921890i	−0.0267806	−	0.0463853i
$396$	7.73908	+	3.11644i	0.388903	+	0.156607i
$397$	10.4221	−	18.0516i	0.523069	−	0.905982i	−0.476571	−	0.879136i	$-0.658120\pi$
$397$	10.4221	−	18.0516i	0.523069	−	0.905982i	0.999640	−	0.0268459i	$-0.00854633\pi$
$398$	−0.729560	−	0.982853i	−0.0365695	−	0.0492660i
$399$	−10.4495	−	4.48615i	−0.523130	−	0.224588i
$400$	−15.8170	−	10.5310i	−0.790852	−	0.526551i
$401$	3.31292	+	1.91271i	0.165439	+	0.0955164i	0.580434	−	0.814308i	$-0.302883\pi$
$401$	3.31292	+	1.91271i	0.165439	+	0.0955164i	−0.414994	+	0.909824i	$0.636216\pi$
$402$	−17.2541	+	19.8716i	−0.860554	+	0.991105i
$403$	−16.4721	+	9.51017i	−0.820534	+	0.473735i
$404$	23.4778	−	22.0256i	1.16806	−	1.09582i
$405$	4.22976	−	1.52177i	0.210178	−	0.0756175i
$406$	−0.373456	−	23.6546i	−0.0185343	−	1.17396i
$407$	−10.2105			−0.506118
$408$	13.3029	−	25.2367i	0.658592	−	1.24940i
$409$	1.93456	+	3.35075i	0.0956576	+	0.165684i	0.909883	−	0.414865i	$-0.136171\pi$
$409$	1.93456	+	3.35075i	0.0956576	+	0.165684i	−0.814225	+	0.580549i	$0.802838\pi$
$410$	−3.72343	−	1.61235i	−0.183887	−	0.0796282i
$411$	14.2518	+	15.5821i	0.702989	+	0.768607i
$412$	3.59255	+	1.08656i	0.176992	+	0.0535310i
$413$	7.59884	−	3.43395i	0.373914	−	0.168974i
$414$	−21.4778	+	0.554862i	−1.05558	+	0.0272700i
$415$	−5.19774	−	3.00092i	−0.255147	−	0.147309i
$416$	−8.45837	−	13.0595i	−0.414706	−	0.640294i
$417$	0.0808186	−	0.0178385i	0.00395770	−	0.000873554i
$418$	4.84763	−	0.559695i	0.237105	−	0.0273756i
$419$	−13.5133			−0.660170			−0.330085	−	0.943951i	$-0.607077\pi$
$419$	−13.5133			−0.660170			−0.330085	+	0.943951i	$0.607077\pi$
$420$	4.50725	+	0.799823i	0.219931	+	0.0390274i
$421$	11.3825			0.554749			0.277374	−	0.960762i	$-0.410536\pi$
$421$	11.3825			0.554749			0.277374	+	0.960762i	$0.410536\pi$
$422$	−5.48489	+	0.633271i	−0.267000	+	0.0308272i
$423$	−1.35213	+	15.1319i	−0.0657430	+	0.735736i
$424$	−11.3238	−	9.58353i	−0.549933	−	0.465418i
$425$	−23.9575	−	13.8319i	−1.16211	−	0.670944i
$426$	−10.5179	+	3.62838i	−0.509595	+	0.175796i
$427$	−10.5488	−	7.57490i	−0.510490	−	0.366575i
$428$	−4.21420	+	13.9336i	−0.203701	+	0.673507i
$429$	4.88819	−	4.47087i	0.236004	−	0.215856i
$430$	2.28568	+	0.989763i	0.110225	+	0.0477306i
$431$	−12.9623	−	22.4513i	−0.624370	−	1.08144i	−0.988662	−	0.150155i	$-0.952023\pi$
$431$	−12.9623	−	22.4513i	−0.624370	−	1.08144i	0.364293	−	0.931284i	$-0.381311\pi$
$432$	18.6307	+	9.21395i	0.896370	+	0.443307i
$433$	23.3825			1.12369			0.561845	−	0.827242i	$-0.310092\pi$
$433$	23.3825			1.12369			0.561845	+	0.827242i	$0.310092\pi$
$434$	22.2006	−	13.2892i	1.06566	−	0.637900i
$435$	5.21511	+	1.64963i	0.250046	+	0.0790939i
$436$	−2.52058	−	2.68676i	−0.120714	−	0.128673i
$437$	−10.8830	+	6.28330i	−0.520604	+	0.300571i
$438$	−18.4496	−	16.0194i	−0.881556	−	0.765435i
$439$	15.3054	+	8.83658i	0.730487	+	0.421747i	0.818600	−	0.574364i	$-0.194750\pi$
$439$	15.3054	+	8.83658i	0.730487	+	0.421747i	−0.0881133	+	0.996110i	$0.528084\pi$
$440$	−1.84871	+	0.664053i	−0.0881338	+	0.0316575i
$441$	20.4171	−	4.91328i	0.972245	−	0.233966i
$442$	−13.5011	−	18.1884i	−0.642180	−	0.865136i
$443$	17.5681	−	30.4288i	0.834685	−	1.44572i	−0.0596013	−	0.998222i	$-0.518983\pi$
$443$	17.5681	−	30.4288i	0.834685	−	1.44572i	0.894286	−	0.447495i	$-0.147684\pi$
$444$	−25.3629	−	1.94309i	−1.20367	−	0.0922150i
$445$	−0.612252	−	1.06045i	−0.0290235	−	0.0502702i
$446$	−33.0171	+	3.81208i	−1.56341	+	0.180507i
$447$	−1.19822	+	3.78801i	−0.0566737	+	0.179167i
$448$	11.7852	+	17.5815i	0.556801	+	0.830646i
$449$		−	5.52733i		−	0.260851i	−0.991458	−	0.130425i	$-0.958366\pi$
$449$		−	5.52733i		−	0.260851i	0.991458	−	0.130425i	$-0.0416343\pi$
$450$	9.62327	−	17.7090i	0.453645	−	0.834811i
$451$	6.91742	−	3.99377i	0.325728	−	0.188059i
$452$	4.68187	+	20.0050i	0.220216	+	0.940956i
$453$	15.3554	+	16.7887i	0.721458	+	0.788800i
$454$	−21.7662	+	16.1568i	−1.02154	+	0.758277i
$455$	2.12006	−	2.95238i	0.0993899	−	0.138410i
$456$	12.1480	−	0.467760i	0.568880	−	0.0219049i
$457$	−11.9761	+	20.7432i	−0.560219	+	0.970327i	0.437258	+	0.899336i	$0.355950\pi$
$457$	−11.9761	+	20.7432i	−0.560219	+	0.970327i	−0.997477	+	0.0709914i	$0.977384\pi$
$458$	14.8933	+	6.44920i	0.695918	+	0.301351i
$459$	27.9231	+	11.6572i	1.30334	+	0.544110i
$460$	3.68926	−	3.46107i	0.172013	−	0.161373i
$461$			2.99679i			0.139574i	0.997562	+	0.0697871i	$0.0222320\pi$
$461$			2.99679i			0.139574i	−0.997562	+	0.0697871i	$0.977768\pi$
$462$	−6.55275	+	6.18611i	−0.304861	+	0.287804i
$463$		−	22.4152i		−	1.04172i	−0.853642	−	0.520861i	$-0.825611\pi$
$463$		−	22.4152i		−	1.04172i	0.853642	−	0.520861i	$-0.174389\pi$
$464$	11.2232	+	22.6644i	0.521025	+	1.05217i
$465$	1.28939	+	5.84167i	0.0597939	+	0.270901i
$466$	−11.3616	+	26.2375i	−0.526314	+	1.21543i
$467$	−6.03065	+	10.4454i	−0.279065	+	0.483355i	−0.971153	−	0.238459i	$-0.923358\pi$
$467$	−6.03065	+	10.4454i	−0.279065	+	0.483355i	0.692088	+	0.721814i	$0.256691\pi$
$468$	12.9930	−	10.1753i	0.600602	−	0.470356i
$469$	−11.7059	−	25.9034i	−0.540527	−	1.19611i
$470$	−2.13199	−	2.87219i	−0.0983414	−	0.132484i
$471$	−10.7482	+	9.83059i	−0.495250	+	0.452969i
$472$	−5.75888	+	6.80464i	−0.265074	+	0.313209i
$473$	−4.24635	+	2.45163i	−0.195248	+	0.112726i
$474$	5.12525	+	0.993187i	0.235410	+	0.0456186i
$475$		−	11.7886i		−	0.540898i
$476$	18.7543	+	24.4494i	0.859602	+	1.12064i
$477$	9.04895	−	12.8724i	0.414323	−	0.589386i
$478$	−1.12046	−	9.70455i	−0.0512488	−	0.443876i
$479$	−6.70352	−	11.6108i	−0.306292	−	0.530513i	0.671256	−	0.741225i	$-0.265755\pi$
$479$	−6.70352	−	11.6108i	−0.306292	−	0.530513i	−0.977548	+	0.210713i	$0.932422\pi$
$480$	−4.71854	+	1.29769i	−0.215371	+	0.0592310i
$481$	−10.0987	+	17.4915i	−0.460461	+	0.797542i
$482$	−9.16001	+	6.79937i	−0.417227	+	0.309703i
$483$	9.15487	−	21.3243i	0.416561	−	0.970288i
$484$	−5.24946	+	17.3566i	−0.238612	+	0.788934i
$485$	0.227534	+	0.131367i	0.0103318	+	0.00596507i
$486$	−7.96478	+	20.5563i	−0.361290	+	0.932454i
$487$	10.5727	−	6.10416i	0.479095	−	0.276606i	−0.240944	−	0.970539i	$-0.577457\pi$
$487$	10.5727	−	6.10416i	0.479095	−	0.276606i	0.720039	+	0.693933i	$0.244124\pi$
$488$	13.6622	+	2.46851i	0.618458	+	0.111744i
$489$	6.45640	−	20.4111i	0.291969	−	0.923023i
$490$	−2.82024	+	4.06126i	−0.127405	+	0.183469i
$491$	−39.8981			−1.80058			−0.900288	−	0.435294i	$-0.856644\pi$
$491$	−39.8981			−1.80058			−0.900288	+	0.435294i	$0.856644\pi$
$492$	17.9428	−	8.60408i	0.808924	−	0.387902i
$493$	18.4096	+	31.8864i	0.829126	+	1.43609i
$494$	3.83573	−	8.85794i	0.172578	−	0.398537i
$495$	−0.877029	−	1.88993i	−0.0394195	−	0.0849462i
$496$	−15.3295	+	23.0242i	−0.688316	+	1.03382i
$497$	1.18974	−	11.9586i	0.0533672	−	0.536417i
$498$	27.8253	−	9.59891i	1.24688	−	0.430138i
$499$	−7.33971	−	4.23758i	−0.328571	−	0.189700i	0.326636	−	0.945150i	$-0.394085\pi$
$499$	−7.33971	−	4.23758i	−0.328571	−	0.189700i	−0.655206	+	0.755450i	$0.727418\pi$
$500$	2.21955	+	9.48383i	0.0992611	+	0.424130i
$501$	−0.883079	−	4.00086i	−0.0394531	−	0.178745i
$502$	3.31014	+	28.6698i	0.147739	+	1.27959i
$503$	42.5519			1.89730			0.948648	−	0.316334i	$-0.102452\pi$
$503$	42.5519			1.89730			0.948648	+	0.316334i	$0.102452\pi$
$504$	−17.4542	+	14.1192i	−0.777471	+	0.628919i
$505$	−8.03941			−0.357749
$506$	1.14217	+	9.89254i	0.0507756	+	0.439777i
$507$	2.02881	+	9.19169i	0.0901027	+	0.408217i
$508$	−0.689212	−	2.94491i	−0.0305788	−	0.130659i
$509$	−14.9018	−	8.60356i	−0.660511	−	0.381346i	0.131961	−	0.991255i	$-0.457873\pi$
$509$	−14.9018	−	8.60356i	−0.660511	−	0.381346i	−0.792472	+	0.609909i	$0.791206\pi$
$510$	−6.73492	+	2.32335i	−0.298227	+	0.102880i
$511$	24.0498	−	10.8682i	1.06390	−	0.480781i
$512$	−19.4511	−	11.5609i	−0.859626	−	0.510924i
$513$	1.64751	+	12.7887i	0.0727392	+	0.564636i
$514$	15.2911	−	35.3121i	0.674462	−	1.55755i
$515$	−0.468656	−	0.811735i	−0.0206514	−	0.0357693i
$516$	−11.0144	+	5.28174i	−0.484884	+	0.232515i
$517$	7.04155			0.309687
$518$	13.3603	−	24.0082i	0.587019	−	1.05486i
$519$	4.99896	−	15.8036i	0.219430	−	0.693701i
$520$	−0.690884	+	3.82376i	−0.0302973	+	0.167683i
$521$	9.47744	−	5.47180i	0.415214	−	0.239724i	−0.277814	−	0.960635i	$-0.589610\pi$
$521$	9.47744	−	5.47180i	0.415214	−	0.239724i	0.693028	+	0.720911i	$0.256276\pi$
$522$	−22.8771	+	14.0081i	−1.00130	+	0.613117i
$523$	−4.79287	−	2.76716i	−0.209578	−	0.121000i	0.391537	−	0.920162i	$-0.371943\pi$
$523$	−4.79287	−	2.76716i	−0.209578	−	0.121000i	−0.601115	+	0.799162i	$0.705277\pi$
$524$	−3.85053	+	12.7312i	−0.168211	+	0.556164i
$525$	13.0300	+	17.4396i	0.568676	+	0.761125i
$526$	−4.09362	+	3.03864i	−0.178490	+	0.132491i
$527$	−20.1344	+	34.8739i	−0.877069	+	1.51913i
$528$	3.48515	−	8.98115i	0.151672	−	0.390854i
$529$	−1.32230	−	2.29030i	−0.0574915	−	0.0995782i
$530$	0.424917	+	3.68029i	0.0184572	+	0.159862i
$531$	−7.73521	−	5.43764i	−0.335679	−	0.235974i
$532$	−5.02702	+	12.1307i	−0.217949	+	0.525931i
$533$		−	15.8001i		−	0.684379i
$534$	5.89558	+	1.14246i	0.255127	+	0.0494393i
$535$	3.14830	−	1.81767i	0.136113	−	0.0785848i
$536$	23.1961	+	19.6312i	1.00192	+	0.847940i
$537$	26.5256	−	24.2610i	1.14466	−	1.04694i
$538$	−22.0551	−	29.7123i	−0.950863	−	1.28099i
$539$	−3.11052	−	9.22309i	−0.133980	−	0.397267i
$540$	−1.81887	−	4.86147i	−0.0782717	−	0.209204i
$541$	−6.26409	+	10.8497i	−0.269314	+	0.466466i	−0.968685	−	0.248293i	$-0.920130\pi$
$541$	−6.26409	+	10.8497i	−0.269314	+	0.466466i	0.699371	+	0.714759i	$0.253464\pi$
$542$	−12.9600	+	29.9289i	−0.556681	+	1.28556i
$543$	2.40213	+	10.8830i	0.103085	+	0.467035i
$544$	−29.3329	−	14.9908i	−1.25764	−	0.642725i
$545$			0.920019i			0.0394093i
$546$	4.11631	+	17.3437i	0.176162	+	0.742243i
$547$			37.4911i			1.60300i	0.597992	+	0.801502i	$0.295966\pi$
$547$			37.4911i			1.60300i	−0.597992	+	0.801502i	$0.704034\pi$
$548$	17.7829	−	16.6830i	0.759647	−	0.712661i
$549$	−1.31061	+	14.6671i	−0.0559354	+	0.625978i
$550$	−8.57253	−	3.71214i	−0.365534	−	0.158286i
$551$	−7.84505	+	13.5880i	−0.334210	+	0.578869i
$552$	0.954556	+	24.7903i	0.0406286	+	1.05515i
$553$	−3.28905	+	4.58030i	−0.139864	+	0.194774i
$554$	23.0417	−	17.1036i	0.978947	−	0.726661i
$555$	4.28733	+	4.68752i	0.181987	+	0.198974i
$556$	−0.0217777	−	0.0930531i	−0.000923578	−	0.00394633i
$557$	−26.0411	+	15.0348i	−1.10340	+	0.637046i	−0.937111	−	0.349031i	$-0.886511\pi$
$557$	−26.0411	+	15.0348i	−1.10340	+	0.637046i	−0.166286	+	0.986078i	$0.553177\pi$
$558$	−25.7782	−	14.0082i	−1.09128	−	0.593013i
$559$			9.69912i			0.410229i
$560$	0.857607	−	5.21580i	0.0362405	−	0.220408i
$561$	4.22976	−	13.3719i	0.178581	−	0.564560i
$562$	38.8642	−	4.48717i	1.63939	−	0.189280i
$563$	−3.41956	−	5.92285i	−0.144117	−	0.249618i	0.784926	−	0.619589i	$-0.212701\pi$
$563$	−3.41956	−	5.92285i	−0.144117	−	0.249618i	−0.929043	+	0.369971i	$0.879368\pi$
$564$	17.4911	+	1.34003i	0.736509	+	0.0564252i
$565$	2.56544	−	4.44348i	0.107929	−	0.186939i
$566$	−14.6420	−	19.7255i	−0.615449	−	0.829124i
$567$	−16.5727	−	17.0981i	−0.695988	−	0.718053i
$568$	4.34308	+	12.0910i	0.182232	+	0.507329i
$569$	29.0006	+	16.7435i	1.21577	+	0.701924i	0.964010	−	0.265866i	$-0.0856578\pi$
$569$	29.0006	+	16.7435i	1.21577	+	0.701924i	0.251759	+	0.967790i	$0.418991\pi$
$570$	−2.29243	−	1.99047i	−0.0960195	−	0.0833715i
$571$	24.2464	−	13.9986i	1.01468	−	0.585825i	0.102121	−	0.994772i	$-0.467437\pi$
$571$	24.2464	−	13.9986i	1.01468	−	0.585825i	0.912558	+	0.408947i	$0.134104\pi$
$572$	−5.23354	−	5.57859i	−0.218826	−	0.233253i
$573$	28.9553	+	9.15909i	1.20963	+	0.382627i
$574$	0.339294	+	21.4908i	0.0141619	+	0.897009i
$575$	24.0570			1.00324
$576$	10.3662	−	21.6458i	0.431925	−	0.901909i
$577$	−18.8181	−	32.5939i	−0.783409	−	1.35690i	−0.929945	−	0.367698i	$-0.880146\pi$
$577$	−18.8181	−	32.5939i	−0.783409	−	1.35690i	0.146537	−	0.989205i	$-0.453187\pi$
$578$	−21.9461	−	9.50325i	−0.912836	−	0.395283i
$579$	2.79273	−	2.55431i	0.116062	−	0.106154i
$580$	1.82846	−	6.04552i	0.0759227	−	0.251027i
$581$	−3.14747	+	31.6366i	−0.130579	+	1.31251i
$582$	−1.21807	+	0.420198i	−0.0504905	+	0.0174178i
$583$	−6.31596	−	3.64652i	−0.261580	−	0.151023i
$584$	−18.2264	+	21.5362i	−0.754216	+	0.891174i
$585$	−4.10503	−	0.366812i	−0.169722	−	0.0151658i
$586$	−28.0515	+	3.23876i	−1.15880	+	0.133792i
$587$	19.7791			0.816373			0.408186	−	0.912899i	$-0.366161\pi$
$587$	19.7791			0.816373			0.408186	+	0.912899i	$0.366161\pi$
$588$	−5.97132	−	23.5020i	−0.246253	−	0.969206i
$589$	−17.1601			−0.707071
$590$	2.21154	−	0.255339i	0.0910477	−	0.0105121i
$591$	−10.6167	+	2.34333i	−0.436711	+	0.0963919i
$592$	−1.87282	+	29.3126i	−0.0769724	+	1.20474i
$593$	−19.5061	−	11.2619i	−0.801020	−	0.462469i	0.0428074	−	0.999083i	$-0.486370\pi$
$593$	−19.5061	−	11.2619i	−0.801020	−	0.462469i	−0.843828	+	0.536614i	$0.819703\pi$
$594$	9.81860	+	2.82902i	0.402862	+	0.116076i
$595$	0.761825	−	7.65743i	0.0312318	−	0.313924i
$596$	4.39118	+	1.32811i	0.179870	+	0.0544013i
$597$	−1.01177	−	1.10621i	−0.0414091	−	0.0452742i
$598$	18.0764	+	7.82756i	0.739198	+	0.320093i
$599$	−13.3658	−	23.1503i	−0.546113	−	0.945895i	−0.998536	−	0.0540915i	$-0.982774\pi$
$599$	−13.3658	−	23.1503i	−0.546113	−	0.945895i	0.452423	−	0.891803i	$-0.350560\pi$
$600$	−20.5876	−	10.8523i	−0.840486	−	0.443042i
$601$	31.1478			1.27055			0.635273	−	0.772288i	$-0.280888\pi$
$601$	31.1478			1.27055			0.635273	+	0.772288i	$0.280888\pi$
$602$	−0.208280	−	13.1924i	−0.00848887	−	0.537684i
$603$	−18.5362	+	26.3682i	−0.754851	+	1.07380i
$604$	19.1599	−	17.9748i	0.779605	−	0.731384i
$605$	3.92171	−	2.26420i	0.159440	−	0.0920529i
$606$	25.8494	−	29.7709i	1.05006	−	1.20936i
$607$	−10.8934	−	6.28933i	−0.442151	−	0.255276i	0.262358	−	0.964970i	$-0.415500\pi$
$607$	−10.8934	−	6.28933i	−0.442151	−	0.255276i	−0.704510	+	0.709694i	$0.748833\pi$
$608$	−0.717627	−	14.0193i	−0.0291036	−	0.568558i
$609$	−3.41329	−	28.7727i	−0.138313	−	1.16593i
$610$	−2.06651	−	2.78398i	−0.0836707	−	0.112720i
$611$	6.96442	−	12.0627i	0.281750	−	0.488006i
$612$	13.0514	−	32.4106i	0.527570	−	1.31012i
$613$	−2.27131	−	3.93403i	−0.0917374	−	0.158894i	0.816505	−	0.577339i	$-0.195909\pi$
$613$	−2.27131	−	3.93403i	−0.0917374	−	0.158894i	−0.908242	+	0.418445i	$0.862575\pi$
$614$	19.8831	−	2.29565i	0.802415	−	0.0926449i
$615$	−4.73806	−	1.49873i	−0.191057	−	0.0604348i
$616$	7.23830	+	7.47544i	0.291639	+	0.301194i
$617$		−	35.4652i		−	1.42777i	−0.700261	−	0.713887i	$-0.746933\pi$
$617$		−	35.4652i		−	1.42777i	0.700261	−	0.713887i	$-0.253067\pi$
$618$	4.51284	+	0.874513i	0.181533	+	0.0351781i
$619$	−35.9030	+	20.7286i	−1.44306	+	0.833153i	−0.998053	−	0.0623719i	$-0.980134\pi$
$619$	−35.9030	+	20.7286i	−1.44306	+	0.833153i	−0.445011	+	0.895525i	$0.646800\pi$
$620$	6.72599	−	1.57412i	0.270122	−	0.0632180i
$621$	−26.0979	+	3.36206i	−1.04727	+	0.134915i
$622$	27.8836	−	20.6976i	1.11803	−	0.829900i
$623$	−3.78339	+	5.26873i	−0.151578	+	0.211087i
$624$	−11.9384	−	14.8531i	−0.477920	−	0.594600i
$625$	−10.6601	+	18.4639i	−0.426405	+	0.738556i
$626$	0.0675646	+	0.0292573i	0.00270043	+	0.00116936i
$627$	5.83608	−	1.28815i	0.233071	−	0.0514439i
$628$	11.5076	+	12.2663i	0.459202	+	0.489477i
$629$			42.7609i			1.70499i
$630$	5.59141	+	0.410774i	0.222767	+	0.0163656i
$631$			22.2919i			0.887428i	0.896168	+	0.443714i	$0.146339\pi$
$631$			22.2919i			0.887428i	−0.896168	+	0.443714i	$0.853661\pi$
$632$	1.07183	−	5.93217i	0.0426353	−	0.235969i
$633$	−6.60328	+	1.45749i	−0.262457	+	0.0579301i
$634$	3.80819	−	8.79434i	0.151242	−	0.349268i
$635$	−0.377656	+	0.654119i	−0.0149868	+	0.0259579i
$636$	−14.9948	−	10.2599i	−0.594583	−	0.406830i
$637$	−18.8763	−	3.79350i	−0.747908	−	0.150304i
$638$	7.41070	+	9.98359i	0.293393	+	0.395254i
$639$	−12.3607	+	5.73600i	−0.488980	+	0.226913i
$640$	1.56728	+	5.42910i	0.0619522	+	0.214604i
$641$	29.5411	−	17.0555i	1.16680	−	0.673653i	0.213877	−	0.976861i	$-0.431391\pi$
$641$	29.5411	−	17.0555i	1.16680	−	0.673653i	0.952925	+	0.303207i	$0.0980575\pi$
$642$	−3.39178	+	17.5030i	−0.133863	+	0.690787i
$643$			24.2299i			0.955533i	0.878487	+	0.477766i	$0.158553\pi$
$643$			24.2299i			0.955533i	−0.878487	+	0.477766i	$0.841447\pi$
$644$	−24.7550	−	10.2586i	−0.975483	−	0.404247i
$645$	2.90852	+	0.920019i	0.114523	+	0.0362257i
$646$	−2.34395	−	20.3015i	−0.0922217	−	0.798750i
$647$	0.714092	+	1.23684i	0.0280738	+	0.0486253i	0.879721	−	0.475490i	$-0.157729\pi$
$647$	0.714092	+	1.23684i	0.0280738	+	0.0486253i	−0.851647	+	0.524116i	$0.824396\pi$
$648$	23.8509	+	8.89576i	0.936952	+	0.349459i
$649$	−2.19125	+	3.79535i	−0.0860140	+	0.148981i
$650$	−14.8378	+	11.0139i	−0.581987	+	0.432002i
$651$	25.3860	−	18.9672i	0.994955	−	0.743383i
$652$	−23.6612	−	7.15630i	−0.926644	−	0.280262i
$653$	−4.35426	−	2.51393i	−0.170395	−	0.0983778i	0.412377	−	0.911013i	$-0.364699\pi$
$653$	−4.35426	−	2.51393i	−0.170395	−	0.0983778i	−0.582772	+	0.812636i	$0.698032\pi$
$654$	−3.40694	−	2.95817i	−0.133222	−	0.115674i
$655$	2.87661	−	1.66081i	0.112398	−	0.0648933i
$656$	−10.1966	−	20.5912i	−0.398110	−	0.803949i
$657$	−24.4814	−	17.2097i	−0.955109	−	0.671416i
$658$	−9.21375	+	16.5569i	−0.359190	+	0.645456i
$659$	19.7930			0.771025			0.385512	−	0.922703i	$-0.374025\pi$
$659$	19.7930			0.771025			0.385512	+	0.922703i	$0.374025\pi$
$660$	−2.16931	+	1.04025i	−0.0844404	+	0.0404916i
$661$	11.3306	+	19.6252i	0.440709	+	0.763331i	0.997742	−	0.0671595i	$-0.0213936\pi$
$661$	11.3306	+	19.6252i	0.440709	+	0.763331i	−0.557033	+	0.830490i	$0.688060\pi$
$662$	−10.0547	+	23.2195i	−0.390787	+	0.902453i
$663$	−18.7236	−	20.4713i	−0.727165	−	0.795039i
$664$	−11.4897	−	31.9870i	−0.445885	−	1.24134i
$665$	2.98828	−	1.35042i	0.115880	−	0.0523669i
$666$	−31.1437	+	0.804573i	−1.20679	+	0.0311766i
$667$	−27.7290	−	16.0094i	−1.07367	−	0.619885i
$668$	−4.60652	+	1.07808i	−0.178231	+	0.0417124i
$669$	−39.7495	+	8.77360i	−1.53680	+	0.339207i
$670$	−0.870415	−	7.53884i	−0.0336271	−	0.291251i
$671$	6.82530			0.263488
$672$	16.5572	+	19.9464i	0.638710	+	0.769448i
$673$	−11.2766			−0.434680			−0.217340	−	0.976096i	$-0.569738\pi$
$673$	−11.2766			−0.434680			−0.217340	+	0.976096i	$0.569738\pi$
$674$	−1.15061	−	9.96568i	−0.0443200	−	0.383864i
$675$	9.50972	−	22.7792i	0.366029	−	0.876770i
$676$	10.5831	−	2.47682i	0.407044	−	0.0952625i
$677$	8.73729	+	5.04448i	0.335801	+	0.193875i	0.658414	−	0.752656i	$-0.271228\pi$
$677$	8.73729	+	5.04448i	0.335801	+	0.193875i	−0.322612	+	0.946531i	$0.604561\pi$
$678$	8.20598	+	23.7874i	0.315149	+	0.913551i
$679$	0.137782	−	1.38491i	0.00528760	−	0.0531480i
$680$	2.78100	+	7.74223i	0.106646	+	0.296901i
$681$	−24.4981	+	22.4067i	−0.938770	+	0.858625i
$682$	−5.40360	+	12.4786i	−0.206914	+	0.477832i
$683$	3.11743	+	5.39955i	0.119285	+	0.206608i	0.919485	−	0.393126i	$-0.128606\pi$
$683$	3.11743	+	5.39955i	0.119285	+	0.206608i	−0.800199	+	0.599734i	$0.795273\pi$
$684$	14.7419	−	2.08914i	0.563670	−	0.0798802i
$685$	−6.08933			−0.232662
$686$	25.7565	+	4.75444i	0.983386	+	0.181525i
$687$	18.9517	+	5.99476i	0.723052	+	0.228714i
$688$	6.25932	+	12.6402i	0.238634	+	0.481902i
$689$	−12.4936	+	7.21316i	−0.475967	+	0.274799i
$690$	4.06194	−	4.67816i	0.154635	−	0.178095i
$691$	14.7810	+	8.53381i	0.562295	+	0.324641i	0.754066	−	0.656798i	$-0.228090\pi$
$691$	14.7810	+	8.53381i	0.562295	+	0.324641i	−0.191771	+	0.981440i	$0.561423\pi$
$692$	−18.3200	−	5.54087i	−0.696423	−	0.210632i
$693$	−7.20985	+	8.35630i	−0.273879	+	0.317429i
$694$	10.4367	−	7.74704i	0.396172	−	0.294074i
$695$	−0.0119331	+	0.0206688i	−0.000452650	+	0.000784012i
$696$	16.5082	+	26.2094i	0.625741	+	0.993464i
$697$	−16.7256	−	28.9695i	−0.633526	−	1.09730i
$698$	3.59007	+	31.0943i	0.135886	+	1.17694i
$699$	−10.5610	+	33.3872i	−0.399452	+	1.26282i
$700$	19.9454	−	15.2994i	0.753866	−	0.578264i
$701$			21.4324i			0.809489i	0.914430	+	0.404744i	$0.132640\pi$
$701$			21.4324i			0.809489i	−0.914430	+	0.404744i	$0.867360\pi$
$702$	14.5574	−	14.0220i	0.549433	−	0.529226i
$703$	−15.7808	+	9.11104i	−0.595183	+	0.343629i
$704$	−10.4206	−	3.89272i	−0.392743	−	0.146712i
$705$	−2.95670	−	3.23268i	−0.111356	−	0.121750i
$706$	9.04155	+	12.1807i	0.340283	+	0.458425i
$707$	17.5373	+	38.8075i	0.659559	+	1.45951i
$708$	−6.16529	+	9.01060i	−0.231706	+	0.338639i
$709$	4.27131	−	7.39813i	0.160412	−	0.277843i	−0.774604	−	0.632446i	$-0.782051\pi$
$709$	4.27131	−	7.39813i	0.160412	−	0.277843i	0.935017	+	0.354604i	$0.115384\pi$
$710$	1.27493	−	2.94422i	0.0478472	−	0.110495i
$711$	6.36852	+	0.569070i	0.238838	+	0.0213418i
$712$	1.23293	−	6.82378i	0.0462061	−	0.255732i
$713$		−	35.0186i		−	1.31146i
$714$	25.9069	+	27.4423i	0.969540	+	1.02700i
$715$			1.91026i			0.0714396i
$716$	−28.3997	−	30.2721i	−1.06135	−	1.13132i
$717$	−2.57878	−	11.6833i	−0.0963061	−	0.436322i
$718$	4.67835	+	2.02585i	0.174594	+	0.0756042i
$719$	−13.7366	+	23.7924i	−0.512287	+	0.887308i	0.487611	+	0.873061i	$0.337868\pi$
$719$	−13.7366	+	23.7924i	−0.512287	+	0.887308i	−0.999899	+	0.0142470i	$0.995465\pi$
$720$	−5.58651	+	2.17114i	−0.208197	+	0.0809134i
$721$	−2.89604	+	4.03301i	−0.107854	+	0.150197i
$722$	−14.5829	+	10.8247i	−0.542719	+	0.402854i
$723$	−10.3097	+	9.42953i	−0.383422	+	0.350688i
$724$	12.5305	−	2.93258i	0.465693	−	0.108988i
$725$	26.0123	−	15.0182i	0.966074	−	0.557763i
$726$	−4.22501	+	21.8027i	−0.156805	+	0.809176i
$727$		−	45.7930i		−	1.69837i	−0.528096	−	0.849185i	$-0.677094\pi$
$727$		−	45.7930i		−	1.69837i	0.528096	−	0.849185i	$-0.322906\pi$
$728$	19.9650	−	5.00622i	0.739953	−	0.185543i
$729$	−7.13303	+	26.0407i	−0.264186	+	0.964472i
$730$	6.99937	−	0.808129i	0.259058	−	0.0299102i
$731$	10.2672	+	17.7834i	0.379747	+	0.657741i
$732$	16.9539	+	1.29887i	0.626636	+	0.0480076i
$733$	21.6466	−	37.4930i	0.799535	−	1.38483i	−0.120385	−	0.992727i	$-0.538413\pi$
$733$	21.6466	−	37.4930i	0.799535	−	1.38483i	0.919919	−	0.392107i	$-0.128254\pi$
$734$	−12.6661	−	17.0636i	−0.467514	−	0.629828i
$735$	−2.92811	+	5.30071i	−0.108005	+	0.195520i
$736$	28.6091	−	1.46446i	1.05455	−	0.0539807i
$737$	12.9378	+	7.46966i	0.476571	+	0.275148i
$738$	20.7844	−	12.7267i	0.765086	−	0.468476i
$739$	4.48246	−	2.58795i	0.164890	−	0.0951993i	−0.415284	−	0.909692i	$-0.636318\pi$
$739$	4.48246	−	2.58795i	0.164890	−	0.0951993i	0.580174	+	0.814492i	$0.302984\pi$
$740$	5.34958	−	5.01870i	0.196655	−	0.184491i
$741$	3.56544	−	11.2717i	0.130980	−	0.414077i
$742$	16.8384	−	10.0794i	0.618159	−	0.370026i
$743$	−49.5492			−1.81778			−0.908891	−	0.417034i	$-0.863070\pi$
$743$	−49.5492			−1.81778			−0.908891	+	0.417034i	$0.863070\pi$
$744$	−15.7972	+	29.9685i	−0.579153	+	1.09870i
$745$	−0.572839	−	0.992187i	−0.0209872	−	0.0363509i
$746$	3.44806	+	1.49310i	0.126242	+	0.0546664i
$747$	32.7002	−	15.1746i	1.19644	−	0.555211i
$748$	−15.5011	−	4.68828i	−0.566775	−	0.171420i
$749$	−15.6420	−	11.2323i	−0.571544	−	0.410418i
$750$	3.89023	+	11.2770i	0.142051	+	0.411777i
$751$	26.4899	+	15.2939i	0.966630	+	0.558084i	0.898207	−	0.439572i	$-0.144870\pi$
$751$	26.4899	+	15.2939i	0.966630	+	0.558084i	0.0684228	+	0.997656i	$0.478203\pi$
$752$	1.29156	−	20.2150i	0.0470985	−	0.737165i
$753$	7.61838	+	34.5156i	0.277629	+	1.25782i
$754$	24.4322	−	2.82088i	0.889769	−	0.102730i
$755$	−6.56086			−0.238774
$756$	−19.4994	+	19.3849i	−0.709186	+	0.705021i
$757$	46.4533			1.68837			0.844187	−	0.536049i	$-0.180084\pi$
$757$	46.4533			1.68837			0.844187	+	0.536049i	$0.180084\pi$
$758$	−24.8874	+	2.87344i	−0.903952	+	0.104368i
$759$	2.62873	+	11.9097i	0.0954169	+	0.432294i
$760$	−2.26470	+	2.67595i	−0.0821495	+	0.0970670i
$761$	34.1633	+	19.7242i	1.23842	+	0.715002i	0.968771	−	0.247956i	$-0.0797589\pi$
$761$	34.1633	+	19.7242i	1.23842	+	0.715002i	0.269649	+	0.962959i	$0.413092\pi$
$762$	−1.20799	−	3.50172i	−0.0437609	−	0.126854i
$763$	4.44108	−	2.00694i	0.160778	−	0.0726563i
$764$	10.1520	−	33.5659i	0.367285	−	1.21437i
$765$	−7.91488	+	3.67292i	−0.286163	+	0.132795i
$766$	−42.7247	−	18.5010i	−1.54371	−	0.668467i
$767$	4.33449	+	7.50756i	0.156509	+	0.271082i
$768$	−25.1440	−	11.6525i	−0.907304	−	0.420475i
$769$	39.7256			1.43254			0.716270	−	0.697823i	$-0.245848\pi$
$769$	39.7256			1.43254			0.716270	+	0.697823i	$0.245848\pi$
$770$	−0.0410212	−	2.59827i	−0.00147830	−	0.0936353i
$771$	14.2136	−	44.9346i	0.511891	−	1.61828i
$772$	−2.99005	−	3.18718i	−0.107614	−	0.114709i
$773$	18.9935	−	10.9659i	0.683149	−	0.394416i	−0.117891	−	0.993026i	$-0.537613\pi$
$773$	18.9935	−	10.9659i	0.683149	−	0.394416i	0.801040	+	0.598610i	$0.204280\pi$
$774$	−12.7588	+	7.81245i	−0.458606	+	0.280813i
$775$	28.4495	+	16.4253i	1.02194	+	0.590015i
$776$	0.502967	+	1.40025i	0.0180554	+	0.0502660i
$777$	13.2749	−	30.9211i	0.476236	−	1.10929i
$778$	5.75054	+	7.74704i	0.206167	+	0.277745i
$779$	7.12742	−	12.3451i	0.255366	−	0.442307i
$780$	−0.363527	+	4.74506i	−0.0130164	+	0.169900i
$781$	3.15799	+	5.46980i	0.113002	+	0.195725i
$782$	41.4291	−	4.78330i	1.48150	−	0.171051i
$783$	−26.1203	+	19.9277i	−0.933464	+	0.712157i
$784$	−27.0483	+	7.23803i	−0.966011	+	0.258501i
$785$		−	4.20029i		−	0.149915i
$786$	−3.09908	+	15.9925i	−0.110540	+	0.570434i
$787$	−4.36864	+	2.52223i	−0.155725	+	0.0899080i	−0.575838	−	0.817564i	$-0.695324\pi$
$787$	−4.36864	+	2.52223i	−0.155725	+	0.0899080i	0.420112	+	0.907472i	$0.361991\pi$
$788$	2.86080	+	12.2238i	0.101912	+	0.435456i
$789$	−4.60741	+	4.21406i	−0.164028	+	0.150025i
$790$	−1.20881	+	0.897287i	−0.0430076	+	0.0319240i
$791$	−27.0457	−	2.69073i	−0.961634	−	0.0956714i
$792$	3.12291	−	11.3780i	0.110968	−	0.404299i
$793$	6.75054	−	11.6923i	0.239719	−	0.415205i
$794$	−27.0508	−	11.7137i	−0.959997	−	0.415705i
$795$	0.977959	+	4.43072i	0.0346846	+	0.157141i
$796$	−1.26245	+	1.18437i	−0.0447465	+	0.0419788i
$797$			28.3335i			1.00362i	0.864977	+	0.501812i	$0.167333\pi$
$797$			28.3335i			1.00362i	−0.864977	+	0.501812i	$0.832667\pi$
$798$	−4.60755	+	15.4080i	−0.163106	+	0.545437i
$799$		−	29.4894i		−	1.04326i
$800$	−12.2292	+	23.9292i	−0.432369	+	0.846026i
$801$	7.32571	+	0.654602i	0.258841	+	0.0231292i
$802$	2.14977	−	4.96450i	0.0759109	−	0.175303i
$803$	−6.93514	+	12.0120i	−0.244736	+	0.423895i
$804$	30.7159	+	21.0166i	1.08327	+	0.741200i
$805$	2.75579	+	6.09816i	0.0971288	+	0.214932i
$806$	16.0325	+	21.5987i	0.564721	+	0.760783i
$807$	−30.5866	−	33.4415i	−1.07670	−	1.17720i
$808$	−34.7515	−	29.4108i	−1.22256	−	1.03467i
$809$	17.5088	−	10.1087i	0.615577	−	0.355404i	−0.159568	−	0.987187i	$-0.551010\pi$
$809$	17.5088	−	10.1087i	0.615577	−	0.355404i	0.775145	+	0.631783i	$0.217677\pi$
$810$	−2.82399	−	5.69547i	−0.0992250	−	0.200118i
$811$		−	1.33368i		−	0.0468317i	−0.999726	−	0.0234158i	$-0.992546\pi$
$811$		−	1.33368i		−	0.0468317i	0.999726	−	0.0234158i	$-0.00745418\pi$
$812$	−33.1713	+	4.36154i	−1.16409	+	0.153060i
$813$	−12.0468	+	38.0845i	−0.422500	+	1.33568i
$814$	1.65619	+	14.3446i	0.0580495	+	0.502778i
$815$	3.08666	+	5.34625i	0.108121	+	0.187271i
$816$	−37.6123	−	14.5955i	−1.31669	−	0.510945i
$817$	−4.37527	+	7.57819i	−0.153071	+	0.265127i
$818$	4.39361	−	3.26133i	0.153619	−	0.114030i
$819$	7.18412	+	20.6158i	0.251033	+	0.720375i
$820$	−1.66120	+	5.49251i	−0.0580117	+	0.191807i
$821$	−4.59977	−	2.65568i	−0.160533	−	0.0926838i	0.417581	−	0.908640i	$-0.362878\pi$
$821$	−4.59977	−	2.65568i	−0.160533	−	0.0926838i	−0.578114	+	0.815956i	$0.696211\pi$
$822$	19.5793	−	22.5495i	0.682905	−	0.786506i
$823$	13.2508	−	7.65035i	0.461894	−	0.266675i	−0.250946	−	0.968001i	$-0.580742\pi$
$823$	13.2508	−	7.65035i	0.461894	−	0.266675i	0.712840	+	0.701326i	$0.247408\pi$
$824$	0.943763	−	5.22334i	0.0328775	−	0.181964i
$825$	−10.9085	−	3.45056i	−0.379786	−	0.120133i
$826$	−6.05686	−	10.1185i	−0.210745	−	0.352066i
$827$	0.288306			0.0100254			0.00501270	−	0.999987i	$-0.498404\pi$
$827$	0.288306			0.0100254			0.00501270	+	0.999987i	$0.498404\pi$
$828$	4.26330	+	30.0837i	0.148160	+	1.04548i
$829$	20.5551	+	35.6025i	0.713908	+	1.23653i	0.963379	+	0.268143i	$0.0864100\pi$
$829$	20.5551	+	35.6025i	0.713908	+	1.23653i	−0.249471	+	0.968382i	$0.580257\pi$
$830$	−3.37284	+	7.78897i	−0.117073	+	0.270359i
$831$	25.9337	−	23.7196i	0.899629	−	0.822825i
$832$	−16.9750	+	14.0013i	−0.588504	+	0.485408i
$833$	−38.6255	+	13.0266i	−1.33829	+	0.451345i
$834$	−0.0381700	−	0.110647i	−0.00132172	−	0.00383139i
$835$	1.02319	+	0.590740i	0.0354090	+	0.0204434i
$836$	−1.57261	−	6.71956i	−0.0543898	−	0.232401i
$837$	−33.1586	−	13.8429i	−1.14613	−	0.478480i
$838$	2.19192	+	18.9846i	0.0757186	+	0.655814i
$839$	25.7705			0.889695			0.444848	−	0.895606i	$-0.353258\pi$
$839$	25.7705			0.889695			0.444848	+	0.895606i	$0.353258\pi$
$840$	0.392562	−	6.46189i	0.0135447	−	0.222956i
$841$	−10.9772			−0.378523
$842$	−1.84629	−	15.9910i	−0.0636272	−	0.551088i
$843$	46.7888	−	10.3273i	1.61149	−	0.355693i
$844$	1.77934	+	7.60289i	0.0612475	+	0.261702i
$845$	−2.35071	−	1.35718i	−0.0808669	−	0.0466885i
$846$	21.4778	−	0.554862i	0.738421	−	0.0190766i
$847$	−19.4846	−	13.9916i	−0.669497	−	0.480756i
$848$	−11.6270	+	17.4631i	−0.399271	+	0.599685i
$849$	−20.3059	−	22.2013i	−0.696896	−	0.761945i
$850$	−15.5461	+	35.9010i	−0.533227	+	1.23139i
$851$	−18.5929	−	32.2038i	−0.637355	−	1.10393i
$852$	6.80349	+	14.1879i	0.233084	+	0.486069i
$853$	−51.4656			−1.76215			−0.881074	−	0.472978i	$-0.843179\pi$
$853$	−51.4656			−1.76215			−0.881074	+	0.472978i	$0.843179\pi$
$854$	−8.93078	+	16.0484i	−0.305605	+	0.549166i
$855$	−3.04190	−	2.13838i	−0.104031	−	0.0731309i
$856$	20.2586	+	3.66036i	0.692426	+	0.125109i
$857$	30.8099	−	17.7881i	1.05245	−	0.607631i	0.129114	−	0.991630i	$-0.458787\pi$
$857$	30.8099	−	17.7881i	1.05245	−	0.607631i	0.923334	+	0.383999i	$0.125453\pi$
$858$	−7.07392	−	6.14212i	−0.241500	−	0.209689i
$859$	−44.4334	−	25.6536i	−1.51605	−	0.875290i	−0.999823	−	0.0188372i	$-0.994004\pi$
$859$	−44.4334	−	25.6536i	−1.51605	−	0.875290i	−0.516225	−	0.856453i	$-0.672663\pi$
$860$	1.01975	−	3.37165i	0.0347732	−	0.114972i
$861$	3.10106	+	26.1407i	0.105684	+	0.890874i
$862$	−29.4388	+	21.8521i	−1.00269	+	0.744286i
$863$	5.89152	−	10.2044i	0.200550	−	0.347362i	−0.748156	−	0.663523i	$-0.769061\pi$
$863$	5.89152	−	10.2044i	0.200550	−	0.347362i	0.948706	+	0.316161i	$0.102394\pi$
$864$	9.92253	−	27.6685i	0.337571	−	0.941300i
$865$	2.38989	+	4.13941i	0.0812587	+	0.140744i
$866$	−3.79273	−	32.8496i	−0.128882	−	1.11628i
$867$	−27.9263	−	8.83360i	−0.948428	−	0.300005i
$868$	−22.2707	−	29.0336i	−0.755917	−	0.985466i
$869$		−	2.96357i		−	0.100532i
$870$	1.47163	−	7.59419i	0.0498928	−	0.257467i
$871$	25.5922	−	14.7757i	0.867160	−	0.500655i
$872$	−3.36573	+	3.97692i	−0.113978	+	0.134675i
$873$	−1.43147	+	0.664279i	−0.0484480	+	0.0224824i
$874$	10.5925	+	14.2701i	0.358298	+	0.482694i
$875$	−12.8216	−	1.27560i	−0.433450	−	0.0431232i
$876$	−19.5127	+	28.5179i	−0.659273	+	0.963531i
$877$	−0.664314	+	1.15063i	−0.0224323	+	0.0388539i	−0.877024	−	0.480447i	$-0.840474\pi$
$877$	−0.664314	+	1.15063i	−0.0224323	+	0.0388539i	0.854591	+	0.519301i	$0.173808\pi$
$878$	9.93174	−	22.9356i	0.335180	−	0.774039i
$879$	−33.7713	+	7.45409i	−1.13908	+	0.251420i
$880$	1.23278	+	2.48950i	0.0415571	+	0.0839212i
$881$		−	23.8258i		−	0.802713i	−0.915922	−	0.401356i	$-0.868539\pi$
$881$		−	23.8258i		−	0.802713i	0.915922	−	0.401356i	$-0.131461\pi$
$882$	−10.2143	−	27.8867i	−0.343934	−	0.938994i
$883$		−	30.2235i		−	1.01710i	−0.861032	−	0.508551i	$-0.830181\pi$
$883$		−	30.2235i		−	1.01710i	0.861032	−	0.508551i	$-0.169819\pi$
$884$	−23.3627	+	21.9176i	−0.785772	+	0.737170i
$885$	2.66248	−	0.587670i	0.0894983	−	0.0197543i
$886$	−45.5985	−	19.7454i	−1.53191	−	0.663359i
$887$	10.9556	−	18.9756i	0.367852	−	0.637138i	−0.621377	−	0.783511i	$-0.713427\pi$
$887$	10.9556	−	18.9756i	0.367852	−	0.637138i	0.989229	+	0.146373i	$0.0467600\pi$
$888$	1.38415	+	35.9470i	0.0464489	+	1.20630i
$889$	3.98136	+	0.396099i	0.133531	+	0.0132847i
$890$	−1.39050	+	1.03215i	−0.0466096	+	0.0345978i
$891$	12.3162	+	2.21879i	0.412609	+	0.0743323i
$892$	10.7110	+	45.7668i	0.358632	+	1.53239i
$893$	10.8830	−	6.28330i	0.364185	−	0.210262i
$894$	5.51606	+	1.06892i	0.184485	+	0.0357500i
$895$			10.3660i			0.346496i
$896$	22.7882	−	19.4087i	0.761302	−	0.648398i
$897$	23.0021	+	7.27599i	0.768019	+	0.242938i
$898$	−7.76524	+	0.896555i	−0.259129	+	0.0299184i
$899$	−21.8614	−	37.8650i	−0.729117	−	1.26287i
$900$	−26.4400	−	10.6471i	−0.881333	−	0.354902i
$901$	−15.2713	+	26.4507i	−0.508761	+	0.881200i
$902$	−6.73281	−	9.07034i	−0.224178	−	0.302009i
$903$	−1.90363	−	16.0469i	−0.0633487	−	0.534006i
$904$	27.3452	−	9.82235i	0.909489	−	0.326687i
$905$	−2.78326	−	1.60692i	−0.0925187	−	0.0534157i
$906$	21.0954	−	24.2956i	0.700846	−	0.807169i
$907$	−42.4039	+	24.4819i	−1.40800	+	0.812907i	−0.995195	−	0.0979134i	$-0.968783\pi$
$907$	−42.4039	+	24.4819i	−1.40800	+	0.812907i	−0.412802	+	0.910821i	$0.635450\pi$
$908$	26.2290	+	27.9583i	0.870439	+	0.927827i
$909$	27.7702	−	39.5040i	0.921081	−	1.31026i
$910$	−4.49162	−	2.49954i	−0.148896	−	0.0828590i
$911$	51.8251			1.71704			0.858522	−	0.512777i	$-0.171383\pi$
$911$	51.8251			1.71704			0.858522	+	0.512777i	$0.171383\pi$
$912$	−2.62759	−	16.9906i	−0.0870083	−	0.562614i
$913$	−8.35449	−	14.4704i	−0.276493	−	0.478900i
$914$	31.0843	+	13.4604i	1.02818	+	0.445229i
$915$	−2.86589	−	3.13340i	−0.0947435	−	0.103587i
$916$	6.64461	−	21.9694i	0.219544	−	0.725889i
$917$	−14.2921	−	10.2629i	−0.471966	−	0.338912i
$918$	11.8477	−	41.1194i	0.391033	−	1.35714i
$919$	43.7375	+	25.2518i	1.44277	+	0.832981i	0.998034	−	0.0626826i	$-0.0199656\pi$
$919$	43.7375	+	25.2518i	1.44277	+	0.832981i	0.444732	+	0.895664i	$0.353299\pi$
$920$	−5.46081	−	4.62158i	−0.180038	−	0.152369i
$921$	23.9373	−	5.28350i	0.788761	−	0.174097i
$922$	4.21013	−	0.486091i	0.138653	−	0.0160086i
$923$	12.4936			0.411232
$924$	9.75362	+	8.20242i	0.320871	+	0.269840i
$925$	34.8836			1.14696
$926$	−31.4907	+	3.63583i	−1.03485	+	0.119481i
$927$	5.60755	+	0.501073i	0.184176	+	0.0164574i
$928$	30.0203	−	19.4435i	0.985464	−	0.638266i
$929$	1.07011	+	0.617830i	0.0351093	+	0.0202703i	0.517452	−	0.855712i	$-0.326881\pi$
$929$	1.07011	+	0.617830i	0.0351093	+	0.0202703i	−0.482343	+	0.875983i	$0.660214\pi$
$930$	7.99770	−	2.75898i	0.262255	−	0.0904705i
$931$	−13.0374	−	11.4791i	−0.427282	−	0.376211i
$932$	38.7034	+	11.7058i	1.26777	+	0.383436i
$933$	31.3833	−	28.7040i	1.02744	−	0.939727i
$934$	15.6527	+	6.77806i	0.512173	+	0.221785i
$935$	2.02215	+	3.50247i	0.0661314	+	0.114543i
$936$	−16.4027	−	16.6031i	−0.536138	−	0.542691i
$937$	−29.4139			−0.960909			−0.480455	−	0.877020i	$-0.659528\pi$
$937$	−29.4139			−0.960909			−0.480455	+	0.877020i	$0.659528\pi$
$938$	−34.4924	+	20.6470i	−1.12622	+	0.674148i
$939$	0.0859759	+	0.0271957i	0.00280572	+	0.000887499i
$940$	−3.68926	+	3.46107i	−0.120331	+	0.112888i
$941$	−38.8530	+	22.4318i	−1.26657	+	0.731256i	−0.974338	−	0.225090i	$-0.927732\pi$
$941$	−38.8530	+	22.4318i	−1.26657	+	0.731256i	−0.292235	+	0.956346i	$0.594399\pi$
$942$	15.5542	+	13.5054i	0.506783	+	0.440028i
$943$	25.1925	+	14.5449i	0.820381	+	0.473647i
$944$	10.4938	+	6.98680i	0.341545	+	0.227401i
$945$	6.86362	−	0.198808i	0.223274	−	0.00646722i
$946$	4.13303	+	5.56796i	0.134376	+	0.181030i
$947$	−8.77882	+	15.2054i	−0.285273	+	0.494108i	−0.972675	−	0.232169i	$-0.925418\pi$
$947$	−8.77882	+	15.2054i	−0.285273	+	0.494108i	0.687402	+	0.726277i	$0.258751\pi$
$948$	0.563974	−	7.36146i	0.0183170	−	0.239089i
$949$	13.7183	+	23.7609i	0.445316	+	0.771311i
$950$	−16.5616	+	1.91216i	−0.537328	+	0.0620386i
$951$	3.53984	−	11.1908i	0.114787	−	0.362886i
$952$	31.3065	−	30.3134i	1.01465	−	0.982462i
$953$			37.1546i			1.20356i	0.798663	+	0.601778i	$0.205541\pi$
$953$			37.1546i			1.20356i	−0.798663	+	0.601778i	$0.794459\pi$
$954$	−19.5519	−	10.6247i	−0.633018	−	0.343989i
$955$	−7.58422	+	4.37875i	−0.245420	+	0.141693i
$956$	−13.4520	+	3.14823i	−0.435068	+	0.101821i
$957$	10.2773	+	11.2366i	0.332219	+	0.363229i
$958$	−15.2245	+	11.3010i	−0.491881	+	0.365118i
$959$	13.2834	+	29.3942i	0.428943	+	0.949188i
$960$	2.58846	+	6.41850i	0.0835422	+	0.207156i
$961$	8.40960	−	14.5658i	0.271277	−	0.469866i
$962$	26.2115	+	11.3503i	0.845092	+	0.365948i
$963$	−1.94340	+	21.7488i	−0.0626252	+	0.700845i
$964$	11.0381	+	11.7658i	0.355513	+	0.378952i
$965$			1.09138i			0.0351326i
$966$	−31.4430	−	9.40262i	−1.01166	−	0.302524i
$967$			53.9045i			1.73345i	0.498786	+	0.866725i	$0.333779\pi$
$967$			53.9045i			1.73345i	−0.498786	+	0.866725i	$0.666221\pi$
$968$	25.2354	+	4.55957i	0.811095	+	0.146550i
$969$	−5.39468	−	24.4410i	−0.173302	−	0.785158i
$970$	0.147648	−	0.340967i	0.00474069	−	0.0109478i
$971$	−19.1783	+	33.2177i	−0.615460	+	1.06601i	0.374844	+	0.927088i	$0.377696\pi$
$971$	−19.1783	+	33.2177i	−0.615460	+	1.06601i	−0.990304	+	0.138920i	$0.955637\pi$
$972$	30.1711	+	7.85526i	0.967738	+	0.251957i
$973$	0.125803	+	0.0125159i	0.00403305	+	0.000401242i
$974$	−10.2906	−	13.8633i	−0.329731	−	0.444208i
$975$	−16.7001	+	15.2744i	−0.534832	+	0.489172i
$976$	1.25190	−	19.5941i	0.0400722	−	0.627193i
$977$	−15.5907	+	9.00127i	−0.498789	+	0.287976i	−0.728214	−	0.685350i	$-0.759649\pi$
$977$	−15.5907	+	9.00127i	−0.498789	+	0.287976i	0.229424	+	0.973327i	$0.426316\pi$
$978$	−29.7224	−	5.75971i	−0.950419	−	0.184175i
$979$		−	3.40899i		−	0.108952i
$980$	6.16304	+	3.30334i	0.196871	+	0.105521i
$981$	−4.52078	−	3.17799i	−0.144337	−	0.101465i
$982$	6.47163	+	56.0521i	0.206518	+	1.78869i
$983$	6.87845	+	11.9138i	0.219388	+	0.379992i	0.954621	−	0.297823i	$-0.0962605\pi$
$983$	6.87845	+	11.9138i	0.219388	+	0.379992i	−0.735233	+	0.677815i	$0.762927\pi$
$984$	−14.9981	−	23.8119i	−0.478122	−	0.759095i
$985$	1.56758	−	2.71514i	0.0499474	−	0.0865114i
$986$	41.8104	−	31.0354i	1.33151	−	0.988368i
$987$	−9.15487	+	21.3243i	−0.291403	+	0.678759i
$988$	−13.0665	−	3.95195i	−0.415701	−	0.125728i
$989$	−15.4648	−	8.92860i	−0.491751	−	0.283913i
$990$	−2.51287	+	1.53868i	−0.0798644	+	0.0489023i
$991$	−1.60779	+	0.928258i	−0.0510731	+	0.0294871i	−0.525319	−	0.850905i	$-0.676054\pi$
$991$	−1.60779	+	0.928258i	−0.0510731	+	0.0294871i	0.474246	+	0.880392i	$0.342721\pi$
$992$	34.8327	+	17.8015i	1.10594	+	0.565200i
$993$	−9.34619	+	29.5468i	−0.296593	+	0.937640i
$994$	−16.9934	+	0.268289i	−0.538998	+	0.00850962i
$995$	0.432298			0.0137048
$996$	−17.9987	−	37.5342i	−0.570310	−	1.18932i
$997$	−30.1748	−	52.2642i	−0.955644	−	1.65522i	−0.732888	−	0.680350i	$-0.761828\pi$
$997$	−30.1748	−	52.2642i	−0.955644	−	1.65522i	−0.222756	−	0.974874i	$-0.571505\pi$
$998$	−4.76277	+	10.9988i	−0.150763	+	0.348160i
$999$	−37.8430	+	4.87513i	−1.19730	+	0.154242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.n.a.23.6	yes	24
3.2	odd	2	inner	84.2.n.a.23.7	yes	24
4.3	odd	2	inner	84.2.n.a.23.2	yes	24
7.2	even	3		588.2.e.e.491.4		12
7.3	odd	6		588.2.n.e.263.11		24
7.4	even	3	inner	84.2.n.a.11.11	yes	24
7.5	odd	6		588.2.e.d.491.4		12
7.6	odd	2		588.2.n.e.275.6		24
12.11	even	2	inner	84.2.n.a.23.11	yes	24
21.2	odd	6		588.2.e.e.491.9		12
21.5	even	6		588.2.e.d.491.9		12
21.11	odd	6	inner	84.2.n.a.11.2	✓	24
21.17	even	6		588.2.n.e.263.2		24
21.20	even	2		588.2.n.e.275.7		24
28.3	even	6		588.2.n.e.263.7		24
28.11	odd	6	inner	84.2.n.a.11.7	yes	24
28.19	even	6		588.2.e.d.491.10		12
28.23	odd	6		588.2.e.e.491.10		12
28.27	even	2		588.2.n.e.275.2		24
84.11	even	6	inner	84.2.n.a.11.6	yes	24
84.23	even	6		588.2.e.e.491.3		12
84.47	odd	6		588.2.e.d.491.3		12
84.59	odd	6		588.2.n.e.263.6		24
84.83	odd	2		588.2.n.e.275.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.2	✓	24	21.11	odd	6	inner
84.2.n.a.11.6	yes	24	84.11	even	6	inner
84.2.n.a.11.7	yes	24	28.11	odd	6	inner
84.2.n.a.11.11	yes	24	7.4	even	3	inner
84.2.n.a.23.2	yes	24	4.3	odd	2	inner
84.2.n.a.23.6	yes	24	1.1	even	1	trivial
84.2.n.a.23.7	yes	24	3.2	odd	2	inner
84.2.n.a.23.11	yes	24	12.11	even	2	inner
588.2.e.d.491.3		12	84.47	odd	6
588.2.e.d.491.4		12	7.5	odd	6
588.2.e.d.491.9		12	21.5	even	6
588.2.e.d.491.10		12	28.19	even	6
588.2.e.e.491.3		12	84.23	even	6
588.2.e.e.491.4		12	7.2	even	3
588.2.e.e.491.9		12	21.2	odd	6
588.2.e.e.491.10		12	28.23	odd	6
588.2.n.e.263.2		24	21.17	even	6
588.2.n.e.263.6		24	84.59	odd	6
588.2.n.e.263.7		24	28.3	even	6
588.2.n.e.263.11		24	7.3	odd	6
588.2.n.e.275.2		24	28.27	even	2
588.2.n.e.275.6		24	7.6	odd	2
588.2.n.e.275.7		24	21.20	even	2
588.2.n.e.275.11		24	84.83	odd	2

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.162204 - 1.40488i) q^{2} +(-0.373317 - 1.69134i) q^{3} +(-1.94738 + 0.455755i) q^{4} +(0.432549 + 0.249732i) q^{5} +(-2.31558 + 0.798808i) q^{6} +(0.261928 - 2.63275i) q^{7} +(0.956154 + 2.66191i) q^{8} +(-2.72127 + 1.26281i) q^{9} +(0.280683 - 0.648187i) q^{10} +(0.695249 + 1.20421i) q^{11} +(1.49783 + 3.12354i) q^{12} +2.75054 q^{13} +(-3.74119 + 0.0590654i) q^{14} +(0.260904 - 0.824817i) q^{15} +(3.58458 - 1.77505i) q^{16} +(5.04311 - 2.91164i) q^{17} +(2.21550 + 3.61822i) q^{18} +(2.14907 + 1.24076i) q^{19} +(-0.956154 - 0.289187i) q^{20} +(-4.55067 + 0.539842i) q^{21} +(1.57899 - 1.17207i) q^{22} +(-2.53203 + 4.38560i) q^{23} +(4.14525 - 2.61092i) q^{24} +(-2.37527 - 4.11408i) q^{25} +(-0.446148 - 3.86417i) q^{26} +(3.15174 + 4.13116i) q^{27} +(0.689816 + 5.24635i) q^{28} +6.32275i q^{29} +(-1.20109 - 0.232751i) q^{30} +(-5.98869 + 3.45757i) q^{31} +(-3.07517 - 4.74798i) q^{32} +(1.77718 - 1.62545i) q^{33} +(-4.90852 - 6.61269i) q^{34} +(0.770780 - 1.07338i) q^{35} +(4.72381 - 3.69941i) q^{36} +(-3.67154 + 6.35929i) q^{37} +(1.39454 - 3.22044i) q^{38} +(-1.02682 - 4.65209i) q^{39} +(-0.251182 + 1.39019i) q^{40} -5.74438i q^{41} +(1.49655 + 6.30558i) q^{42} +3.52627i q^{43} +(-1.90274 - 2.02819i) q^{44} +(-1.49245 - 0.133360i) q^{45} +(6.57194 + 2.84583i) q^{46} +(2.53203 - 4.38560i) q^{47} +(-4.34041 - 5.40008i) q^{48} +(-6.86279 - 1.37918i) q^{49} +(-5.39452 + 4.00429i) q^{50} +(-6.80726 - 7.44266i) q^{51} +(-5.35634 + 1.25357i) q^{52} +(-4.54223 + 2.62246i) q^{53} +(5.29257 - 5.09791i) q^{54} +0.694505i q^{55} +(7.25860 - 1.82009i) q^{56} +(1.29627 - 4.09801i) q^{57} +(8.88271 - 1.02558i) q^{58} +(1.57587 + 2.72949i) q^{59} +(-0.132166 + 1.72514i) q^{60} +(2.45426 - 4.25091i) q^{61} +(5.82886 + 7.85256i) q^{62} +(2.61190 + 7.49520i) q^{63} +(-6.17154 + 5.09039i) q^{64} +(1.18974 + 0.686897i) q^{65} +(-2.57183 - 2.23307i) q^{66} +(9.30445 - 5.37193i) q^{67} +(-8.49386 + 7.96850i) q^{68} +(8.36279 + 2.64530i) q^{69} +(-1.63300 - 0.908747i) q^{70} +4.54224 q^{71} +(-5.96345 - 6.03633i) q^{72} +(4.98752 + 8.63864i) q^{73} +(9.52959 + 4.12657i) q^{74} +(-6.07159 + 5.55325i) q^{75} +(-4.75054 - 1.43679i) q^{76} +(3.35249 - 1.51500i) q^{77} +(-6.36908 + 2.19715i) q^{78} +(-1.84576 - 1.06565i) q^{79} +(1.99379 + 0.127386i) q^{80} +(5.81061 - 6.87291i) q^{81} +(-8.07016 + 0.931761i) q^{82} -12.0165 q^{83} +(8.61584 - 3.12526i) q^{84} +2.90852 q^{85} +(4.95398 - 0.571975i) q^{86} +(10.6939 - 2.36039i) q^{87} +(-2.54073 + 3.00210i) q^{88} +(-2.12318 - 1.22582i) q^{89} +(0.0547257 + 2.11834i) q^{90} +(0.720443 - 7.24148i) q^{91} +(2.93206 - 9.69440i) q^{92} +(8.08361 + 8.83814i) q^{93} +(-6.57194 - 2.84583i) q^{94} +(0.619718 + 1.07338i) q^{95} +(-6.88244 + 6.97367i) q^{96} +0.526031 q^{97} +(-0.824419 + 9.86511i) q^{98} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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