LMFDB - Embedded newform 558.2.bd.a.389.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(65,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.65"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.bd (of order $30$, 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:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			389.4
Character	$\chi$	$=$	558.389
Dual form			558.2.bd.a.383.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.743145 + 0.669131i) q^{2} +(-1.32974 + 1.10986i) q^{3} +(0.104528 - 0.994522i) q^{4} +3.99463i q^{5} +(0.245544 - 1.71456i) q^{6} +(-2.97653 - 2.16258i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.536406 - 2.95166i) q^{9} +(-2.67293 - 2.96858i) q^{10} +(-0.190195 + 1.80959i) q^{11} +(0.964788 + 1.43847i) q^{12} +(-2.79097 + 0.906841i) q^{13} +(3.65904 - 0.384581i) q^{14} +(-4.43349 - 5.31180i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-6.23297 - 2.77510i) q^{17} +(1.57642 + 2.55243i) q^{18} +(5.45186 - 1.15883i) q^{19} +(3.97274 + 0.417552i) q^{20} +(6.35817 - 0.427883i) q^{21} +(-1.06951 - 1.47205i) q^{22} +(4.38448 + 1.95210i) q^{23} +(-1.67950 - 0.423419i) q^{24} -10.9570 q^{25} +(1.46730 - 2.54144i) q^{26} +(2.56265 + 4.52027i) q^{27} +(-2.46186 + 2.73417i) q^{28} +(1.17897 + 1.30938i) q^{29} +(6.84902 + 0.980857i) q^{30} +(-0.256868 - 5.56184i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.75548 - 2.61737i) q^{33} +(6.48890 - 2.10837i) q^{34} +(8.63868 - 11.8901i) q^{35} +(-2.87942 - 0.842000i) q^{36} +(-0.233268 + 0.134677i) q^{37} +(-3.27611 + 4.50918i) q^{38} +(2.70479 - 4.30346i) q^{39} +(-3.23172 + 2.34798i) q^{40} +(-5.31777 - 1.72785i) q^{41} +(-4.43873 + 4.57243i) q^{42} +(2.99571 + 0.973364i) q^{43} +(1.77979 + 0.378306i) q^{44} +(11.7908 + 2.14274i) q^{45} +(-4.56451 + 1.48310i) q^{46} +(2.47676 - 11.6522i) q^{47} +(1.53143 - 0.809142i) q^{48} +(2.01988 + 6.21655i) q^{49} +(8.14266 - 7.33168i) q^{50} +(11.3682 - 3.22759i) q^{51} +(0.610138 + 2.87047i) q^{52} +(0.0546502 + 0.519962i) q^{53} +(-4.92907 - 1.64446i) q^{54} +(-7.22862 - 0.759758i) q^{55} -3.67919i q^{56} +(-5.96340 + 7.59176i) q^{57} +(-1.75230 - 0.184174i) q^{58} +(1.51276 - 7.11697i) q^{59} +(-5.74613 + 3.85397i) q^{60} +(-4.97228 - 2.87075i) q^{61} +(3.91248 + 3.96137i) q^{62} +(-7.97981 + 7.62567i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.62249 - 11.1489i) q^{65} +(3.05594 + 0.770434i) q^{66} -9.06915 q^{67} +(-3.41142 + 5.90874i) q^{68} +(-7.99677 + 2.27040i) q^{69} +(1.53625 + 14.6165i) q^{70} +(-2.44508 + 0.256988i) q^{71} +(2.70323 - 1.30098i) q^{72} +(1.40666 + 3.15942i) q^{73} +(0.0832352 - 0.256172i) q^{74} +(14.5700 - 12.1608i) q^{75} +(-0.582606 - 5.54312i) q^{76} +(4.47949 - 4.97498i) q^{77} +(0.869525 + 5.00795i) q^{78} +(1.40890 + 1.93918i) q^{79} +(0.830529 - 3.90733i) q^{80} +(-8.42454 - 3.16657i) q^{81} +(5.10803 - 2.27424i) q^{82} +(-8.18324 + 1.73940i) q^{83} +(0.239070 - 6.36807i) q^{84} +(11.0855 - 24.8984i) q^{85} +(-2.87755 + 1.28117i) q^{86} +(-3.02096 - 0.432636i) q^{87} +(-1.57578 + 0.909777i) q^{88} +(8.96437 + 6.51300i) q^{89} +(-10.1960 + 6.29719i) q^{90} +(10.2685 + 3.33644i) q^{91} +(2.39971 - 4.15641i) q^{92} +(6.51445 + 7.11070i) q^{93} +(5.95627 + 10.3166i) q^{94} +(4.62908 + 21.7781i) q^{95} +(-0.596655 + 1.62604i) q^{96} +(-12.9705 + 5.77484i) q^{97} +(-5.66075 - 3.26823i) q^{98} +(5.23925 + 1.53206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} + 4 q^{9} - 16 q^{15} + 32 q^{16} + 16 q^{18} - 4 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} - 268 q^{25} + 12 q^{26} - 18 q^{28} + 18 q^{30} + 22 q^{31} + 60 q^{33} - 4 q^{36}+ \cdots - 138 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 + 4 * q^9 - 16 * q^15 + 32 * q^16 + 16 * q^18 - 4 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 - 268 * q^25 + 12 * q^26 - 18 * q^28 + 18 * q^30 + 22 * q^31 + 60 * q^33 - 4 * q^36 + 72 * q^37 + 8 * q^39 + 6 * q^42 + 10 * q^43 - 24 * q^45 - 54 * q^47 + 10 * q^48 - 60 * q^49 + 28 * q^51 + 90 * q^53 - 96 * q^57 - 18 * q^58 + 6 * q^59 - 10 * q^60 - 42 * q^61 + 90 * q^62 + 124 * q^63 + 64 * q^64 + 120 * q^65 - 12 * q^66 - 16 * q^67 - 24 * q^69 - 6 * q^70 + 6 * q^71 + 8 * q^72 + 42 * q^73 - 48 * q^74 - 6 * q^76 - 90 * q^77 + 20 * q^78 - 10 * q^79 - 6 * q^80 + 8 * q^81 + 174 * q^83 - 2 * q^84 - 96 * q^86 + 100 * q^87 + 36 * q^89 - 176 * q^90 - 10 * q^91 + 18 * q^92 - 92 * q^93 - 150 * q^95 - 18 * q^97 + 48 * q^98 - 138 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.743145	+	0.669131i	−0.525483	+	0.473147i
$2$	−0.743145	+	0.669131i	−0.525483	+	0.473147i
$3$	−1.32974	+	1.10986i	−0.767725	+	0.640780i
$3$	−1.32974	+	1.10986i	−0.767725	+	0.640780i
$4$	0.104528	−	0.994522i	0.0522642	−	0.497261i
$5$			3.99463i			1.78645i	0.449609	+	0.893225i	$0.351563\pi$
$5$			3.99463i			1.78645i	−0.449609	+	0.893225i	$0.648437\pi$
$6$	0.245544	−	1.71456i	0.100243	−	0.699965i
$7$	−2.97653	−	2.16258i	−1.12502	−	0.817377i	−0.140060	−	0.990143i	$-0.544730\pi$
$7$	−2.97653	−	2.16258i	−1.12502	−	0.817377i	−0.984963	+	0.172766i	$0.944730\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.536406	−	2.95166i	0.178802	−	0.983885i
$10$	−2.67293	−	2.96858i	−0.845253	−	0.938749i
$11$	−0.190195	+	1.80959i	−0.0573460	+	0.545611i	0.927701	+	0.373324i	$0.121782\pi$
$11$	−0.190195	+	1.80959i	−0.0573460	+	0.545611i	−0.985047	+	0.172286i	$0.944885\pi$
$12$	0.964788	+	1.43847i	0.278510	+	0.415249i
$13$	−2.79097	+	0.906841i	−0.774076	+	0.251512i	−0.669309	−	0.742984i	$-0.733410\pi$
$13$	−2.79097	+	0.906841i	−0.774076	+	0.251512i	−0.104767	+	0.994497i	$0.533410\pi$
$14$	3.65904	−	0.384581i	0.977919	−	0.102783i
$15$	−4.43349	−	5.31180i	−1.14472	−	1.37150i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	−6.23297	−	2.77510i	−1.51172	−	0.673059i	−0.527423	−	0.849603i	$-0.676842\pi$
$17$	−6.23297	−	2.77510i	−1.51172	−	0.673059i	−0.984293	+	0.176543i	$0.943508\pi$
$18$	1.57642	+	2.55243i	0.371565	+	0.601614i
$19$	5.45186	−	1.15883i	1.25074	−	0.265853i	0.465503	−	0.885046i	$-0.345873\pi$
$19$	5.45186	−	1.15883i	1.25074	−	0.265853i	0.785239	+	0.619193i	$0.212540\pi$
$20$	3.97274	+	0.417552i	0.888332	+	0.0933675i
$21$	6.35817	−	0.427883i	1.38747	−	0.0933718i
$22$	−1.06951	−	1.47205i	−0.228020	−	0.313842i
$23$	4.38448	+	1.95210i	0.914228	+	0.407040i	0.809270	−	0.587436i	$-0.199863\pi$
$23$	4.38448	+	1.95210i	0.914228	+	0.407040i	0.104957	+	0.994477i	$0.466529\pi$
$24$	−1.67950	−	0.423419i	−0.342826	−	0.0864301i
$25$	−10.9570			−2.19141
$26$	1.46730	−	2.54144i	0.287761	−	0.498417i
$27$	2.56265	+	4.52027i	0.493183	+	0.869925i
$28$	−2.46186	+	2.73417i	−0.465248	+	0.516710i
$29$	1.17897	+	1.30938i	0.218930	+	0.243146i	0.842598	−	0.538543i	$-0.181025\pi$
$29$	1.17897	+	1.30938i	0.218930	+	0.243146i	−0.623668	+	0.781689i	$0.714358\pi$
$30$	6.84902	+	0.980857i	1.25045	+	0.179079i
$31$	−0.256868	−	5.56184i	−0.0461349	−	0.998935i
$31$	−0.256868	−	5.56184i	−0.0461349	−	0.998935i
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.75548	−	2.61737i	−0.305590	−	0.455625i
$34$	6.48890	−	2.10837i	1.11284	−	0.361583i
$35$	8.63868	−	11.8901i	1.46020	−	2.00980i
$36$	−2.87942	−	0.842000i	−0.479903	−	0.140333i
$37$	−0.233268	+	0.134677i	−0.0383490	+	0.0221408i	−0.519052	−	0.854743i	$-0.673715\pi$
$37$	−0.233268	+	0.134677i	−0.0383490	+	0.0221408i	0.480703	+	0.876884i	$0.340382\pi$
$38$	−3.27611	+	4.50918i	−0.531456	+	0.731486i
$39$	2.70479	−	4.30346i	0.433113	−	0.689105i
$40$	−3.23172	+	2.34798i	−0.510980	+	0.371249i
$41$	−5.31777	−	1.72785i	−0.830497	−	0.269845i	−0.137242	−	0.990538i	$-0.543824\pi$
$41$	−5.31777	−	1.72785i	−0.830497	−	0.269845i	−0.693255	+	0.720693i	$0.743824\pi$
$42$	−4.43873	+	4.57243i	−0.684911	+	0.705541i
$43$	2.99571	+	0.973364i	0.456841	+	0.148437i	0.528392	−	0.849000i	$-0.322795\pi$
$43$	2.99571	+	0.973364i	0.456841	+	0.148437i	−0.0715515	+	0.997437i	$0.522795\pi$
$44$	1.77979	+	0.378306i	0.268314	+	0.0570318i
$45$	11.7908	+	2.14274i	1.75766	+	0.319421i
$46$	−4.56451	+	1.48310i	−0.673001	+	0.218671i
$47$	2.47676	−	11.6522i	0.361272	−	1.69965i	−0.303687	−	0.952772i	$-0.598218\pi$
$47$	2.47676	−	11.6522i	0.361272	−	1.69965i	0.664959	−	0.746880i	$-0.268449\pi$
$48$	1.53143	−	0.809142i	0.221043	−	0.116790i
$49$	2.01988	+	6.21655i	0.288554	+	0.888079i
$50$	8.14266	−	7.33168i	1.15155	−	1.03686i
$51$	11.3682	−	3.22759i	1.59186	−	0.451953i
$52$	0.610138	+	2.87047i	0.0846109	+	0.398063i
$53$	0.0546502	+	0.519962i	0.00750678	+	0.0714222i	0.997634	−	0.0687499i	$-0.0219011\pi$
$53$	0.0546502	+	0.519962i	0.00750678	+	0.0714222i	−0.990127	+	0.140172i	$0.955234\pi$
$54$	−4.92907	−	1.64446i	−0.670762	−	0.223783i
$55$	−7.22862	−	0.759758i	−0.974706	−	0.102446i
$56$		−	3.67919i		−	0.491653i
$57$	−5.96340	+	7.59176i	−0.789872	+	1.00555i
$58$	−1.75230	−	0.184174i	−0.230088	−	0.0241832i
$59$	1.51276	−	7.11697i	0.196944	−	0.926550i	−0.763008	−	0.646389i	$-0.776279\pi$
$59$	1.51276	−	7.11697i	0.196944	−	0.926550i	0.959953	−	0.280162i	$-0.0903881\pi$
$60$	−5.74613	+	3.85397i	−0.741822	+	0.497545i
$61$	−4.97228	−	2.87075i	−0.636635	−	0.367562i	0.146682	−	0.989184i	$-0.453141\pi$
$61$	−4.97228	−	2.87075i	−0.636635	−	0.367562i	−0.783317	+	0.621622i	$0.786474\pi$
$62$	3.91248	+	3.96137i	0.496886	+	0.503095i
$63$	−7.97981	+	7.62567i	−1.00536	+	0.960745i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.62249	−	11.1489i	−0.449315	−	1.38285i
$66$	3.05594	+	0.770434i	0.376160	+	0.0948338i
$67$	−9.06915			−1.10797			−0.553987	−	0.832526i	$-0.686894\pi$
$67$	−9.06915			−1.10797			−0.553987	+	0.832526i	$0.686894\pi$
$68$	−3.41142	+	5.90874i	−0.413695	+	0.716541i
$69$	−7.99677	+	2.27040i	−0.962698	+	0.273324i
$70$	1.53625	+	14.6165i	0.183618	+	1.74700i
$71$	−2.44508	+	0.256988i	−0.290177	+	0.0304989i	−0.248499	−	0.968632i	$-0.579937\pi$
$71$	−2.44508	+	0.256988i	−0.290177	+	0.0304989i	−0.0416786	+	0.999131i	$0.513271\pi$
$72$	2.70323	−	1.30098i	0.318579	−	0.153322i
$73$	1.40666	+	3.15942i	0.164637	+	0.369782i	0.976959	−	0.213428i	$-0.0684630\pi$
$73$	1.40666	+	3.15942i	0.164637	+	0.369782i	−0.812321	+	0.583210i	$0.801796\pi$
$74$	0.0832352	−	0.256172i	0.00967589	−	0.0297793i
$75$	14.5700	−	12.1608i	1.68240	−	1.40421i
$76$	−0.582606	−	5.54312i	−0.0668294	−	0.635840i
$77$	4.47949	−	4.97498i	0.510485	−	0.566951i
$78$	0.869525	+	5.00795i	0.0984543	+	0.567039i
$79$	1.40890	+	1.93918i	0.158513	+	0.218175i	0.880885	−	0.473330i	$-0.156948\pi$
$79$	1.40890	+	1.93918i	0.158513	+	0.218175i	−0.722372	+	0.691505i	$0.756948\pi$
$80$	0.830529	−	3.90733i	0.0928560	−	0.436853i
$81$	−8.42454	−	3.16657i	−0.936060	−	0.351841i
$82$	5.10803	−	2.27424i	0.564088	−	0.251148i
$83$	−8.18324	+	1.73940i	−0.898227	+	0.190924i	−0.633814	−	0.773486i	$-0.718511\pi$
$83$	−8.18324	+	1.73940i	−0.898227	+	0.190924i	−0.264413	+	0.964410i	$0.585178\pi$
$84$	0.239070	−	6.36807i	0.0260847	−	0.694813i
$85$	11.0855	−	24.8984i	1.20239	−	2.70061i
$86$	−2.87755	+	1.28117i	−0.310294	+	0.138152i
$87$	−3.02096	−	0.432636i	−0.323881	−	0.0463835i
$88$	−1.57578	+	0.909777i	−0.167979	+	0.0969825i
$89$	8.96437	+	6.51300i	0.950221	+	0.690376i	0.950859	−	0.309623i	$-0.100203\pi$
$89$	8.96437	+	6.51300i	0.950221	+	0.690376i	−0.000637767		1.00000i	$0.500203\pi$
$90$	−10.1960	+	6.29719i	−1.07475	+	0.663782i
$91$	10.2685	+	3.33644i	1.07643	+	0.349754i
$92$	2.39971	−	4.15641i	0.250187	−	0.433336i
$93$	6.51445	+	7.11070i	0.675517	+	0.737345i
$94$	5.95627	+	10.3166i	0.614343	+	1.06407i
$95$	4.62908	+	21.7781i	0.474934	+	2.23439i
$96$	−0.596655	+	1.62604i	−0.0608959	+	0.165957i
$97$	−12.9705	+	5.77484i	−1.31696	+	0.586347i	−0.940407	−	0.340050i	$-0.889556\pi$
$97$	−12.9705	+	5.77484i	−1.31696	+	0.586347i	−0.376549	+	0.926397i	$0.622889\pi$
$98$	−5.66075	−	3.26823i	−0.571822	−	0.330142i
$99$	5.23925	+	1.53206i	0.526565	+	0.153978i
$100$	−1.14532	+	10.8970i	−0.114532	+	1.08970i
$101$	−15.3859	+	1.61713i	−1.53096	+	0.160910i	−0.832212	−	0.554458i	$-0.812926\pi$
$101$	−15.3859	+	1.61713i	−1.53096	+	0.160910i	−0.698747	+	0.715369i	$0.746259\pi$
$102$	−6.28853	+	10.0054i	−0.622657	+	0.990679i
$103$	3.83169	−	11.7927i	0.377548	−	1.16197i	−0.564196	−	0.825641i	$-0.690814\pi$
$103$	3.83169	−	11.7927i	0.377548	−	1.16197i	0.941744	−	0.336332i	$-0.109186\pi$
$104$	−2.37414	−	1.72491i	−0.232804	−	0.169142i
$105$	1.70923	+	25.3985i	0.166804	+	2.47864i
$106$	−0.388535	−	0.349839i	−0.0377379	−	0.0339793i
$107$	−7.64068	+	17.1612i	−0.738652	+	1.65904i	0.0133766	+	0.999911i	$0.495742\pi$
$107$	−7.64068	+	17.1612i	−0.738652	+	1.65904i	−0.752029	+	0.659130i	$0.770925\pi$
$108$	4.76337	−	2.07612i	0.458356	−	0.199775i
$109$	0.868081	+	2.67168i	0.0831471	+	0.255900i	0.983984	−	0.178257i	$-0.0570460\pi$
$109$	0.868081	+	2.67168i	0.0831471	+	0.255900i	−0.900837	+	0.434158i	$0.857046\pi$
$110$	5.88029	−	4.27228i	0.560663	−	0.407346i
$111$	0.160712	−	0.437981i	0.0152541	−	0.0415713i
$112$	2.46186	+	2.73417i	0.232624	+	0.258355i
$113$	0.490567	−	0.675208i	0.0461487	−	0.0635182i	−0.785319	−	0.619091i	$-0.787501\pi$
$113$	0.490567	−	0.675208i	0.0461487	−	0.0635182i	0.831468	+	0.555573i	$0.187501\pi$
$114$	−0.648205	−	9.63207i	−0.0607100	−	0.902126i
$115$	−7.79790	+	17.5144i	−0.727158	+	1.63322i
$116$	1.42545	−	1.03565i	0.132349	−	0.0961574i
$117$	1.17959	+	8.72442i	0.109053	+	0.806573i
$118$	3.63798	+	6.30117i	0.334903	+	0.580070i
$119$	12.5513	+	21.7394i	1.15057	+	1.99285i
$120$	1.69140	−	6.70897i	0.154403	−	0.612442i
$121$	7.52120	+	1.59868i	0.683745	+	0.145335i
$122$	5.61603	−	1.19372i	0.508452	−	0.108075i
$123$	8.98892	−	3.60442i	0.810504	−	0.324999i
$124$	−5.55822	−	0.325909i	−0.499143	−	0.0292675i
$125$		−	23.7961i		−	2.12839i
$126$	0.827582	−	11.0065i	0.0737268	−	0.980538i
$127$	−15.0663	−	13.5657i	−1.33692	−	1.20377i	−0.960816	−	0.277186i	$-0.910598\pi$
$127$	−15.0663	−	13.5657i	−1.33692	−	1.20377i	−0.376100	−	0.926579i	$-0.622735\pi$
$128$	−0.406737	−	0.913545i	−0.0359508	−	0.0807468i
$129$	−5.06380	+	2.03051i	−0.445843	+	0.178776i
$130$	10.1521	+	5.86131i	0.890397	+	0.514071i
$131$	2.86053	+	6.42486i	0.249926	+	0.561343i	0.994324	−	0.106393i	$-0.0339302\pi$
$131$	2.86053	+	6.42486i	0.249926	+	0.561343i	−0.744398	+	0.667736i	$0.767264\pi$
$132$	−2.78652	+	1.47228i	−0.242536	+	0.128145i
$133$	−18.7337	−	8.34077i	−1.62442	−	0.723236i
$134$	6.73969	−	6.06845i	0.582221	−	0.524234i
$135$	−18.0568	+	10.2368i	−1.55408	+	0.881047i
$136$	−1.41855	−	6.67374i	−0.121639	−	0.572268i
$137$	−8.20254	+	9.10984i	−0.700790	+	0.778306i	−0.983502	−	0.180899i	$-0.942099\pi$
$137$	−8.20254	+	9.10984i	−0.700790	+	0.778306i	0.282712	+	0.959205i	$0.408766\pi$
$138$	4.42357	−	7.03812i	0.376559	−	0.599125i
$139$	−14.1982	−	12.7841i	−1.20427	−	1.08433i	−0.994299	−	0.106626i	$-0.965995\pi$
$139$	−14.1982	−	12.7841i	−1.20427	−	1.08433i	−0.209975	−	0.977707i	$-0.567338\pi$
$140$	−10.9220	−	9.83421i	−0.923078	−	0.831143i
$141$	9.63894	+	18.2433i	0.811745	+	1.53636i
$142$	1.64509	−	1.82706i	0.138053	−	0.153323i
$143$	−1.11018	−	5.22298i	−0.0928377	−	0.436767i
$144$	−1.13837	+	2.77563i	−0.0948640	+	0.231302i
$145$	−5.23049	+	4.70956i	−0.434369	+	0.391107i
$146$	−3.15942	−	1.40666i	−0.261475	−	0.116416i
$147$	−9.58544	−	6.02459i	−0.790593	−	0.496900i
$148$	0.109556	+	0.246068i	0.00900548	+	0.0202266i
$149$	−8.00725	−	4.62299i	−0.655980	−	0.378730i	0.134764	−	0.990878i	$-0.456972\pi$
$149$	−8.00725	−	4.62299i	−0.655980	−	0.378730i	−0.790743	+	0.612148i	$0.790306\pi$
$150$	−2.69044	+	18.7865i	−0.219673	+	1.53391i
$151$	−1.57850	−	3.54537i	−0.128457	−	0.288518i	0.837855	−	0.545893i	$-0.183809\pi$
$151$	−1.57850	−	3.54537i	−0.128457	−	0.288518i	−0.966312	+	0.257374i	$0.917143\pi$
$152$	4.14203	+	3.72950i	0.335963	+	0.302503i
$153$	−11.5345	+	16.9090i	−0.932511	+	1.36701i
$154$			6.69449i			0.539457i
$155$	22.2174	−	1.02609i	1.78455	−	0.0824177i
$156$	−3.99715	−	3.13981i	−0.320029	−	0.251386i
$157$	−1.66311	+	0.353505i	−0.132731	+	0.0282128i	−0.273798	−	0.961787i	$-0.588280\pi$
$157$	−1.66311	+	0.353505i	−0.132731	+	0.0282128i	0.141067	+	0.990000i	$0.454947\pi$
$158$	−2.34458	−	0.498355i	−0.186525	−	0.0396470i
$159$	−0.649757	−	0.630758i	−0.0515291	−	0.0500224i
$160$	1.99731	+	3.45945i	0.157901	+	0.273493i
$161$	−8.82899	−	15.2923i	−0.695822	−	1.20520i
$162$	8.37950	−	3.28389i	0.658356	−	0.258007i
$163$	−9.30011	+	6.75692i	−0.728441	+	0.529243i	−0.889070	−	0.457772i	$-0.848648\pi$
$163$	−9.30011	+	6.75692i	−0.728441	+	0.529243i	0.160629	+	0.987015i	$0.448648\pi$
$164$	−2.27424	+	5.10803i	−0.177588	+	0.398870i
$165$	10.4554	−	7.01250i	0.813951	−	0.545922i
$166$	4.91744	−	6.76828i	0.381668	−	0.525320i
$167$	−1.47073	−	1.63341i	−0.113809	−	0.126397i	0.683548	−	0.729905i	$-0.260436\pi$
$167$	−1.47073	−	1.63341i	−0.113809	−	0.126397i	−0.797357	+	0.603508i	$0.793769\pi$
$168$	4.08340	+	4.89236i	0.315041	+	0.377454i
$169$	−3.55007	+	2.57927i	−0.273082	+	0.198406i
$170$	8.42215	+	25.9207i	0.645949	+	1.98803i
$171$	−0.496052	−	16.7136i	−0.0379340	−	1.27812i
$172$	1.28117	−	2.87755i	0.0976881	−	0.219411i
$173$	−12.9629	−	11.6718i	−0.985550	−	0.887394i	0.00809292	−	0.999967i	$-0.497424\pi$
$173$	−12.9629	−	11.6718i	−0.985550	−	0.887394i	−0.993643	+	0.112574i	$0.964091\pi$
$174$	2.53450	−	1.69991i	0.192140	−	0.128870i
$175$	32.6139	+	23.6954i	2.46538	+	1.79120i
$176$	0.562273	−	1.73050i	0.0423829	−	0.130441i
$177$	5.88729	+	11.1427i	0.442516	+	0.837534i
$178$	−11.0199	+	1.15824i	−0.825974	+	0.0868134i
$179$	−2.33143	+	22.1820i	−0.174259	+	1.65796i	0.462292	+	0.886728i	$0.347027\pi$
$179$	−2.33143	+	22.1820i	−0.174259	+	1.65796i	−0.636551	+	0.771235i	$0.719639\pi$
$180$	3.36347	−	11.5022i	0.250698	−	0.857322i
$181$	8.50152	+	4.90836i	0.631913	+	0.364835i	0.781493	−	0.623914i	$-0.214459\pi$
$181$	8.50152	+	4.90836i	0.631913	+	0.364835i	−0.149579	+	0.988750i	$0.547792\pi$
$182$	−9.86352	+	4.39152i	−0.731132	+	0.325521i
$183$	9.79797	−	1.70121i	0.724287	−	0.125757i
$184$	0.997854	+	4.69453i	0.0735628	+	0.346086i
$185$	−0.537986	−	0.931818i	−0.0395535	−	0.0685086i
$186$	−9.59916	−	0.925262i	−0.703845	−	0.0678435i
$187$	6.20725	−	10.7513i	0.453919	−	0.786211i
$188$	−11.3295	−	3.68118i	−0.826289	−	0.268478i
$189$	2.14760	−	18.9966i	0.156215	−	1.38180i
$190$	−18.0125	−	13.0868i	−1.30676	−	0.949419i
$191$	−8.80265	+	5.08221i	−0.636937	+	0.367736i	−0.783434	−	0.621475i	$-0.786534\pi$
$191$	−8.80265	+	5.08221i	−0.636937	+	0.367736i	0.146497	+	0.989211i	$0.453200\pi$
$192$	−0.644631	−	1.60762i	−0.0465223	−	0.116020i
$193$	3.29022	−	1.46490i	0.236836	−	0.105446i	−0.284887	−	0.958561i	$-0.591956\pi$
$193$	3.29022	−	1.46490i	0.236836	−	0.105446i	0.521723	+	0.853115i	$0.325290\pi$
$194$	5.77484	−	12.9705i	0.414610	−	0.931228i
$195$	17.1907	+	10.8046i	1.23105	+	0.773735i
$196$	6.39363	−	1.35901i	0.456688	−	0.0970720i
$197$	4.11116	−	1.83041i	0.292908	−	0.130411i	−0.255022	−	0.966935i	$-0.582083\pi$
$197$	4.11116	−	1.83041i	0.292908	−	0.130411i	0.547930	+	0.836524i	$0.315416\pi$
$198$	−4.91867	+	2.36720i	−0.349555	+	0.168229i
$199$	1.71065	−	8.04796i	0.121265	−	0.570505i	−0.874998	−	0.484127i	$-0.839137\pi$
$199$	1.71065	−	8.04796i	0.121265	−	0.570505i	0.996262	−	0.0863781i	$-0.0275293\pi$
$200$	−6.44038	−	8.86442i	−0.455404	−	0.626809i
$201$	12.0596	−	10.0655i	0.850618	−	0.709967i
$202$	10.3519	−	11.4970i	0.728358	−	0.808924i
$203$	−0.677611	−	6.44704i	−0.0475590	−	0.452493i
$204$	−2.02161	−	11.6433i	−0.141541	−	0.815193i
$205$	6.90211	−	21.2425i	0.482064	−	1.48364i
$206$	5.04338	+	11.3276i	0.351389	+	0.789232i
$207$	8.11378	−	11.8944i	0.563947	−	0.826715i
$208$	2.91852	−	0.306749i	0.202363	−	0.0212692i
$209$	1.06008	+	10.0860i	0.0733274	+	0.697664i
$210$	−18.2651	−	17.7311i	−1.26041	−	1.22356i
$211$	1.40728	−	2.43749i	0.0968814	−	0.167803i	−0.813511	−	0.581550i	$-0.802447\pi$
$211$	1.40728	−	2.43749i	0.0968814	−	0.167803i	0.910392	+	0.413746i	$0.135780\pi$
$212$	0.522826			0.0359078
$213$	2.96609	−	3.05543i	0.203233	−	0.209355i
$214$	−5.80498	−	17.8659i	−0.396821	−	1.22129i
$215$	−3.88822	+	11.9667i	−0.265175	+	0.816124i
$216$	−2.15068	+	4.73018i	−0.146335	+	0.321848i
$217$	−11.2633	+	17.1105i	−0.764604	+	1.16153i
$218$	−2.43281	−	1.40458i	−0.164771	−	0.0951305i
$219$	−5.37702	−	2.63999i	−0.363345	−	0.178394i
$220$	−1.51119	+	7.10960i	−0.101885	+	0.479329i
$221$	19.9126	+	2.09290i	1.33947	+	0.140784i
$222$	0.173634	+	0.433021i	0.0116536	+	0.0290624i
$223$		−	17.2102i		−	1.15248i	−0.817280	−	0.576241i	$-0.804519\pi$
$223$		−	17.2102i		−	1.15248i	0.817280	−	0.576241i	$-0.195481\pi$
$224$	−3.65904	−	0.384581i	−0.244480	−	0.0256959i
$225$	−5.87742	+	32.3414i	−0.391828	+	2.15609i
$226$	0.0872398	+	0.830031i	0.00580310	+	0.0552129i
$227$	1.47359	+	6.93272i	0.0978059	+	0.460140i	0.999608	+	0.0279916i	$0.00891117\pi$
$227$	1.47359	+	6.93272i	0.0978059	+	0.460140i	−0.901802	+	0.432149i	$0.857755\pi$
$228$	6.92682	+	6.72429i	0.458740	+	0.445327i
$229$	−2.00192	+	1.80254i	−0.132291	+	0.119115i	−0.732620	−	0.680638i	$-0.761703\pi$
$229$	−2.00192	+	1.80254i	−0.132291	+	0.119115i	0.600329	+	0.799753i	$0.295036\pi$
$230$	−5.92443	−	18.2335i	−0.390645	−	1.20228i
$231$	−0.435001	+	11.5870i	−0.0286210	+	0.762371i
$232$	−0.366330	+	1.72345i	−0.0240507	+	0.113150i
$233$	15.9091	−	5.16917i	1.04224	−	0.338643i	0.262620	−	0.964899i	$-0.415413\pi$
$233$	15.9091	−	5.16917i	1.04224	−	0.338643i	0.779618	+	0.626256i	$0.215413\pi$
$234$	−6.71438	−	5.69421i	−0.438933	−	0.372242i
$235$	46.5463	+	9.89372i	3.03634	+	0.645395i
$236$	−6.91985	−	2.24840i	−0.450444	−	0.146358i
$237$	−4.02569	−	1.01492i	−0.261496	−	0.0659260i
$238$	−23.8739	−	7.75710i	−1.54752	−	0.502818i
$239$	−2.48684	+	1.80680i	−0.160860	+	0.116872i	−0.665303	−	0.746573i	$-0.731698\pi$
$239$	−2.48684	+	1.80680i	−0.160860	+	0.116872i	0.504443	+	0.863445i	$0.331698\pi$
$240$	3.23222	+	6.11750i	0.208639	+	0.394883i
$241$	11.7859	−	16.2219i	0.759196	−	1.04494i	−0.238085	−	0.971244i	$-0.576520\pi$
$241$	11.7859	−	16.2219i	0.759196	−	1.04494i	0.997281	−	0.0736990i	$-0.0234804\pi$
$242$	−6.65907	+	3.84461i	−0.428061	+	0.247141i
$243$	14.7169	−	5.13938i	0.944089	−	0.329691i
$244$	−3.37477	+	4.64497i	−0.216047	+	0.297364i
$245$	−24.8328	+	8.06866i	−1.58651	+	0.515488i
$246$	−4.26825	+	8.69336i	−0.272133	+	0.554269i
$247$	−14.1651	+	8.17822i	−0.901304	+	0.520368i
$248$	4.34864	−	3.47698i	0.276139	−	0.220788i
$249$	8.95106	−	11.3952i	0.567250	−	0.722143i
$250$	15.9227	+	17.6839i	1.00704	+	1.11843i
$251$	6.45508	−	7.16909i	0.407441	−	0.452509i	−0.504145	−	0.863619i	$-0.668192\pi$
$251$	6.45508	−	7.16909i	0.407441	−	0.452509i	0.911586	+	0.411110i	$0.134859\pi$
$252$	6.74978	+	8.73319i	0.425196	+	0.550139i
$253$	−4.36639	+	7.56282i	−0.274513	+	0.475470i
$254$	20.2737			1.27208
$255$	12.8930	+	45.4116i	0.807392	+	2.84379i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−16.5173	−	22.7342i	−1.03032	−	1.41812i	−0.904705	−	0.426039i	$-0.859909\pi$
$257$	−16.5173	−	22.7342i	−1.03032	−	1.41812i	−0.125618	−	0.992079i	$-0.540091\pi$
$258$	2.40447	−	4.89731i	0.149696	−	0.304893i
$259$	0.985579	+	0.103589i	0.0612409	+	0.00643668i
$260$	−11.4665	+	2.43727i	−0.711120	+	0.151153i
$261$	4.49725	−	2.77756i	0.278373	−	0.171927i
$262$	−6.42486	−	2.86053i	−0.396929	−	0.176724i
$263$	23.4834	+	4.99156i	1.44805	+	0.307792i	0.863822	−	0.503797i	$-0.168064\pi$
$263$	23.4834	+	4.99156i	1.44805	+	0.307792i	0.584228	+	0.811590i	$0.301397\pi$
$264$	1.08565	−	2.95866i	0.0668169	−	0.182093i
$265$	−2.07705	+	0.218307i	−0.127592	+	0.0134105i
$266$	19.5029	−	6.33688i	1.19580	−	0.388539i
$267$	−19.1488	+	1.28865i	−1.17189	+	0.0788641i
$268$	−0.947984	+	9.01947i	−0.0579074	+	0.550952i
$269$	11.6789	+	12.9708i	0.712076	+	0.790841i	0.985249	−	0.171124i	$-0.0547399\pi$
$269$	11.6789	+	12.9708i	0.712076	+	0.790841i	−0.273173	+	0.961965i	$0.588073\pi$
$270$	6.56900	−	19.6898i	0.399777	−	1.19828i
$271$	−9.83879	−	13.5419i	−0.597664	−	0.822614i	0.397828	−	0.917460i	$-0.369764\pi$
$271$	−9.83879	−	13.5419i	−0.597664	−	0.822614i	−0.995492	+	0.0948460i	$0.969764\pi$
$272$	5.51979	+	4.01036i	0.334686	+	0.243164i
$273$	−17.3574	+	6.96006i	−1.05052	+	0.421242i
$274$		−	12.2585i		−	0.740563i
$275$	2.08397	−	19.8277i	0.125668	−	1.19565i
$276$	1.42207	+	8.19029i	0.0855986	+	0.492997i
$277$	10.3125	−	9.28541i	0.619618	−	0.557906i	−0.298402	−	0.954440i	$-0.596454\pi$
$277$	10.3125	−	9.28541i	0.619618	−	0.557906i	0.918020	+	0.396534i	$0.129787\pi$
$278$	19.1055			1.14587
$279$	−16.5544	−	2.22522i	−0.991086	−	0.133220i
$280$	14.6970			0.878314
$281$	14.1174	−	12.7114i	0.842175	−	0.758298i	−0.130258	−	0.991480i	$-0.541581\pi$
$281$	14.1174	−	12.7114i	0.842175	−	0.758298i	0.972433	+	0.233182i	$0.0749139\pi$
$282$	−19.3703	−	7.10768i	−1.15348	−	0.423256i
$283$	1.47556	−	14.0390i	0.0877127	−	0.834530i	−0.858897	−	0.512148i	$-0.828850\pi$
$283$	1.47556	−	14.0390i	0.0877127	−	0.834530i	0.946610	−	0.322382i	$-0.104484\pi$
$284$			2.45855i			0.145888i
$285$	−30.3262	−	23.8215i	−1.79637	−	1.41107i
$286$	4.31988	+	3.13857i	0.255440	+	0.185588i
$287$	12.0919	+	16.6431i	0.713763	+	0.982410i
$288$	−1.01129	−	2.82441i	−0.0595906	−	0.166430i
$289$	19.7735	+	21.9607i	1.16315	+	1.29180i
$290$	0.735705	−	6.99977i	0.0432021	−	0.411040i
$291$	10.8381	−	22.0745i	0.635340	−	1.29403i
$292$	3.28915	−	1.06871i	0.192483	−	0.0625414i
$293$	−8.98202	+	0.944049i	−0.524735	+	0.0551519i	−0.363193	−	0.931714i	$-0.618313\pi$
$293$	−8.98202	+	0.944049i	−0.524735	+	0.0551519i	−0.161542	+	0.986866i	$0.551647\pi$
$294$	11.1546	−	1.93676i	0.650550	−	0.112954i
$295$	28.4296	+	6.04290i	1.65524	+	0.351831i
$296$	−0.246068	−	0.109556i	−0.0143024	−	0.00636784i
$297$	−8.66721	+	3.77761i	−0.502923	+	0.219199i
$298$	9.04393	−	1.92235i	0.523901	−	0.111359i
$299$	−14.0072	−	1.47222i	−0.810057	−	0.0851405i
$300$	−10.5712	−	15.7613i	−0.610329	−	0.909980i
$301$	−6.81184	−	9.37569i	−0.392628	−	0.540406i
$302$	3.54537	+	1.57850i	0.204013	+	0.0908326i
$303$	18.6645	−	19.2267i	1.07225	−	1.10454i
$304$	−5.57366			−0.319671
$305$	11.4676	−	19.8624i	0.656631	−	1.13732i
$306$	−2.74250	−	20.2839i	−0.156778	−	1.15956i
$307$	−10.8003	+	11.9949i	−0.616405	+	0.684587i	−0.967823	−	0.251632i	$-0.919033\pi$
$307$	−10.8003	+	11.9949i	−0.616405	+	0.684587i	0.351418	+	0.936219i	$0.385699\pi$
$308$	−4.47949	−	4.97498i	−0.255243	−	0.283476i
$309$	7.99318	+	19.9339i	0.454716	+	1.13400i
$310$	−15.8242	+	15.6289i	−0.898754	+	0.887662i
$311$	−20.1026	+	11.6062i	−1.13991	+	0.658129i	−0.946409	−	0.322970i	$-0.895319\pi$
$311$	−20.1026	+	11.6062i	−1.13991	+	0.658129i	−0.193504	+	0.981099i	$0.561985\pi$
$312$	5.07141	−	0.341288i	0.287112	−	0.0193216i
$313$	−23.3848	+	7.59818i	−1.32179	+	0.429474i	−0.883108	−	0.469170i	$-0.844553\pi$
$313$	−23.3848	+	7.59818i	−1.32179	+	0.429474i	−0.438678	+	0.898644i	$0.644553\pi$
$314$	0.999391	−	1.37554i	0.0563989	−	0.0776264i
$315$	−30.4617	−	31.8763i	−1.71632	−	1.79603i
$316$	2.07583	−	1.19848i	0.116774	−	0.0674197i
$317$	−18.7564	+	25.8159i	−1.05346	+	1.44997i	−0.167694	+	0.985839i	$0.553632\pi$
$317$	−18.7564	+	25.8159i	−1.05346	+	1.44997i	−0.885768	+	0.464127i	$0.846368\pi$
$318$	0.904923	+	0.0339727i	0.0507456	+	0.00190510i
$319$	−2.59367	+	1.88442i	−0.145218	+	0.105507i
$320$	−3.79911	−	1.23441i	−0.212377	−	0.0690055i
$321$	−8.88654	−	31.3001i	−0.495998	−	1.74700i
$322$	16.7937	+	5.45661i	0.935878	+	0.304085i
$323$	−37.1971	−	7.90649i	−2.06970	−	0.439929i
$324$	−4.02983	+	8.04739i	−0.223879	+	0.447077i
$325$	30.5807	−	9.93629i	1.69631	−	0.551166i
$326$	2.39006	−	11.2444i	0.132373	−	0.622767i
$327$	−4.11952	−	2.58918i	−0.227810	−	0.143182i
$328$	−1.72785	−	5.31777i	−0.0954045	−	0.293625i
$329$	−32.5710	+	29.3270i	−1.79570	+	1.61685i
$330$	−3.07759	+	12.2073i	−0.169416	+	0.671991i
$331$	3.77202	+	17.7459i	0.207329	+	0.975405i	0.951555	+	0.307478i	$0.0994850\pi$
$331$	3.77202	+	17.7459i	0.207329	+	0.975405i	−0.744227	+	0.667927i	$0.767182\pi$
$332$	0.874491	+	8.32022i	0.0479939	+	0.456632i
$333$	0.272395	+	0.760768i	0.0149271	+	0.0416899i
$334$	2.18594	+	0.229751i	0.119609	+	0.0125714i
$335$		−	36.2279i		−	1.97934i
$336$	−6.30819	−	0.903405i	−0.344140	−	0.0492848i
$337$	28.3412	+	2.97878i	1.54384	+	0.162265i	0.837829	−	0.545932i	$-0.183824\pi$
$337$	28.3412	+	2.97878i	1.54384	+	0.162265i	0.706015	+	0.708197i	$0.250491\pi$
$338$	0.912342	−	4.29223i	0.0496249	−	0.233467i
$339$	0.0970628	+	1.44231i	0.00527173	+	0.0783357i
$340$	−23.6032	−	13.6273i	−1.28006	−	0.739045i
$341$	10.1135	+	0.593009i	0.547675	+	0.0321132i
$342$	11.5522	+	12.0887i	0.624673	+	0.653682i
$343$	−0.527003	+	1.62195i	−0.0284555	+	0.0875770i
$344$	0.973364	+	2.99571i	0.0524803	+	0.161518i
$345$	−9.06939	−	31.9441i	−0.488280	−	1.71981i
$346$	17.4433			0.937757
$347$	0.931699	−	1.61375i	0.0500162	−	0.0866306i	−0.839933	−	0.542690i	$-0.817406\pi$
$347$	0.931699	−	1.61375i	0.0500162	−	0.0866306i	0.889950	+	0.456059i	$0.150739\pi$
$348$	−0.746043	+	2.95919i	−0.0399921	+	0.158629i
$349$	−1.10429	−	10.5066i	−0.0591112	−	0.562405i	−0.983494	−	0.180940i	$-0.942086\pi$
$349$	−1.10429	−	10.5066i	−0.0591112	−	0.562405i	0.924383	−	0.381466i	$-0.124581\pi$
$350$	−40.0922	+	4.21386i	−2.14302	+	0.225240i
$351$	−11.2515	−	10.2920i	−0.600558	−	0.549347i
$352$	0.740079	+	1.66224i	0.0394463	+	0.0885979i
$353$	−4.65611	+	14.3300i	−0.247820	+	0.762711i	0.747340	+	0.664442i	$0.231331\pi$
$353$	−4.65611	+	14.3300i	−0.247820	+	0.762711i	−0.995160	+	0.0982695i	$0.968669\pi$
$354$	−11.8310	−	4.34124i	−0.628811	−	0.230734i
$355$	−1.02657	−	9.76717i	−0.0544847	−	0.518388i
$356$	7.41435	−	8.23447i	0.392960	−	0.436426i
$357$	−40.8177	−	14.9775i	−2.16030	−	0.792696i
$358$	−13.1101	−	18.0445i	−0.692890	−	0.953681i
$359$	4.06667	−	19.1322i	0.214631	−	1.00976i	−0.730461	−	0.682954i	$-0.760695\pi$
$359$	4.06667	−	19.1322i	0.214631	−	1.00976i	0.945092	−	0.326804i	$-0.105972\pi$
$360$	5.19692	+	10.7984i	0.273902	+	0.569125i
$361$	11.0225	−	4.90753i	0.580132	−	0.258291i
$362$	−9.60220	+	2.04101i	−0.504680	+	0.107273i
$363$	−11.7755	+	6.22168i	−0.618056	+	0.326553i
$364$	4.39152	−	9.86352i	0.230178	−	0.516989i
$365$	−12.6207	+	5.61909i	−0.660597	+	0.294117i
$366$	−6.14298	+	7.82037i	−0.321099	+	0.408777i
$367$	0.315855	−	0.182359i	0.0164875	−	0.00951907i	−0.491734	−	0.870746i	$-0.663637\pi$
$367$	0.315855	−	0.182359i	0.0164875	−	0.00951907i	0.508221	+	0.861227i	$0.330303\pi$
$368$	−3.88281	−	2.82102i	−0.202405	−	0.147056i
$369$	−7.95250	+	14.7694i	−0.413991	+	0.768864i
$370$	1.02331	+	0.332493i	0.0531993	+	0.0172855i
$371$	0.961789	−	1.66587i	0.0499336	−	0.0864875i
$372$	7.75269	−	5.73549i	0.401958	−	0.297371i
$373$	17.9414	+	31.0754i	0.928971	+	1.60902i	0.785047	+	0.619436i	$0.212639\pi$
$373$	17.9414	+	31.0754i	0.928971	+	1.60902i	0.143923	+	0.989589i	$0.454028\pi$
$374$	2.58112	+	12.1432i	0.133467	+	0.627911i
$375$	26.4104	+	31.6426i	1.36383	+	1.63402i
$376$	10.8827	−	4.84527i	0.561230	−	0.249876i
$377$	−4.47788	−	2.58531i	−0.230623	−	0.133150i
$378$	11.1153	+	15.5543i	0.571707	+	0.800026i
$379$	0.790371	−	7.51988i	0.0405987	−	0.386270i	−0.955289	−	0.295674i	$-0.904456\pi$
$379$	0.790371	−	7.51988i	0.0405987	−	0.386270i	0.995888	−	0.0905967i	$-0.0288774\pi$
$380$	22.1427	−	2.32729i	1.13590	−	0.119388i
$381$	35.0903	+	1.31736i	1.79773	+	0.0674906i
$382$	3.14098	−	9.66694i	0.160706	−	0.494604i
$383$	12.9918	+	9.43912i	0.663852	+	0.482316i	0.867961	−	0.496632i	$-0.165430\pi$
$383$	12.9918	+	9.43912i	0.663852	+	0.482316i	−0.204110	+	0.978948i	$0.565430\pi$
$384$	1.55476	+	0.763354i	0.0793412	+	0.0389547i
$385$	19.8732	+	17.8939i	1.01283	+	0.911956i
$386$	−1.46490	+	3.29022i	−0.0745616	+	0.167468i
$387$	4.47995	−	8.32017i	0.227729	−	0.422938i
$388$	4.38742	+	13.5031i	0.222738	+	0.685516i
$389$	−8.17866	+	5.94215i	−0.414675	+	0.301279i	−0.775492	−	0.631358i	$-0.782498\pi$
$389$	−8.17866	+	5.94215i	−0.414675	+	0.301279i	0.360817	+	0.932637i	$0.382498\pi$
$390$	−20.0049	+	3.47343i	−1.01299	+	0.175884i
$391$	−21.9111	−	24.3347i	−1.10809	−	1.23066i
$392$	−3.84204	+	5.28812i	−0.194052	+	0.267090i
$393$	−10.9345	−	5.36858i	−0.551572	−	0.270809i
$394$	−1.83041	+	4.11116i	−0.0922145	+	0.207117i
$395$	−7.74629	+	5.62801i	−0.389758	+	0.283176i
$396$	2.07132	−	5.05041i	0.104088	−	0.253792i
$397$	9.95928	+	17.2500i	0.499842	+	0.865752i	1.00000		0.000182426i	$-5.80679e-5\pi$
$397$	9.95928	+	17.2500i	0.499842	+	0.865752i	−0.500158	+	0.865934i	$0.666725\pi$
$398$	4.11388	+	7.12545i	0.206210	+	0.357166i
$399$	34.1680	−	9.70078i	1.71054	−	0.485647i
$400$	10.7176	+	2.27809i	0.535880	+	0.113905i
$401$	−1.26697	+	0.269303i	−0.0632694	+	0.0134483i	−0.239438	−	0.970912i	$-0.576963\pi$
$401$	−1.26697	+	0.269303i	−0.0632694	+	0.0134483i	0.176168	+	0.984360i	$0.443630\pi$
$402$	−2.22688	+	15.5496i	−0.111067	+	0.775543i
$403$	5.76061	+	15.2900i	0.286957	+	0.761648i
$404$			15.4707i			0.769696i
$405$	12.6493	−	33.6529i	0.628547	−	1.67222i
$406$	4.81747	+	4.33767i	0.239087	+	0.215275i
$407$	−0.199344	−	0.447733i	−0.00988110	−	0.0221933i
$408$	9.29323	+	7.29993i	0.460083	+	0.361400i
$409$	−24.6644	−	14.2400i	−1.21958	−	0.704124i	−0.254750	−	0.967007i	$-0.581993\pi$
$409$	−24.6644	−	14.2400i	−1.21958	−	0.704124i	−0.964828	+	0.262883i	$0.915327\pi$
$410$	9.08475	+	20.4047i	0.448664	+	1.00771i
$411$	0.796545	−	21.2174i	0.0392907	−	1.04658i
$412$	−11.3276	−	5.04338i	−0.558071	−	0.248469i
$413$	−19.8938	+	17.9124i	−0.978908	+	0.881413i
$414$	1.92917	+	14.2684i	0.0948134	+	0.701254i
$415$	−6.94825	−	32.6890i	−0.341076	−	1.60464i
$416$	−1.96363	+	2.18083i	−0.0962749	+	0.106924i
$417$	33.0685	+	1.24146i	1.61937	+	0.0607945i
$418$	−7.53665	−	6.78603i	−0.368630	−	0.331916i
$419$	−10.0153	−	9.01782i	−0.489279	−	0.440549i	0.387195	−	0.921998i	$-0.373444\pi$
$419$	−10.0153	−	9.01782i	−0.489279	−	0.440549i	−0.876474	+	0.481449i	$0.840111\pi$
$420$	25.4380	+	0.954997i	1.24125	+	0.0465991i
$421$	−14.5232	+	16.1296i	−0.707817	+	0.786110i	−0.984600	−	0.174822i	$-0.944065\pi$
$421$	−14.5232	+	16.1296i	−0.707817	+	0.786110i	0.276783	+	0.960932i	$0.410732\pi$
$422$	0.585181	+	2.75306i	0.0284862	+	0.134017i
$423$	−33.0648	−	13.5609i	−1.60767	−	0.659351i
$424$	−0.388535	+	0.349839i	−0.0188689	+	0.0169897i
$425$	68.2948	+	30.4068i	3.31278	+	1.47495i
$426$	−0.159754	+	4.25533i	−0.00774011	+	0.206171i
$427$	8.59194	+	19.2978i	0.415793	+	0.933886i
$428$	16.2686	+	9.39266i	0.786371	+	0.454011i
$429$	7.27304	+	5.71304i	0.351145	+	0.275828i
$430$	−5.11779	−	11.4947i	−0.246802	−	0.554325i
$431$	−1.37801	−	1.24077i	−0.0663765	−	0.0597657i	0.635275	−	0.772286i	$-0.280887\pi$
$431$	−1.37801	−	1.24077i	−0.0663765	−	0.0597657i	−0.701651	+	0.712521i	$0.747554\pi$
$432$	−1.56684	−	4.95429i	−0.0753846	−	0.238364i
$433$			22.4664i			1.07967i	0.841772	+	0.539833i	$0.181513\pi$
$433$			22.4664i			1.07967i	−0.841772	+	0.539833i	$0.818487\pi$
$434$	−3.07886	−	20.2522i	−0.147790	−	0.972136i
$435$	1.72822	−	12.0676i	0.0828618	−	0.578598i
$436$	2.74778	−	0.584059i	0.131595	−	0.0279714i
$437$	26.1657	+	5.56169i	1.25168	+	0.266052i
$438$	5.76240	−	1.63603i	0.275338	−	0.0781725i
$439$	−5.24529	−	9.08511i	−0.250344	−	0.433608i	0.713277	−	0.700883i	$-0.247210\pi$
$439$	−5.24529	−	9.08511i	−0.250344	−	0.433608i	−0.963620	+	0.267274i	$0.913877\pi$
$440$	−3.63422	−	6.29465i	−0.173254	−	0.300086i
$441$	19.4326	−	2.62739i	0.925362	−	0.125114i
$442$	−16.1984	+	11.7688i	−0.770477	+	0.559785i
$443$	16.5318	−	37.1310i	0.785449	−	1.76415i	0.155002	−	0.987914i	$-0.450462\pi$
$443$	16.5318	−	37.1310i	0.785449	−	1.76415i	0.630447	−	0.776232i	$-0.282872\pi$
$444$	−0.418783	−	0.205613i	−0.0198746	−	0.00975796i
$445$	−26.0170	+	35.8093i	−1.23332	+	1.69752i
$446$	11.5159	+	12.7897i	0.545293	+	0.605609i
$447$	15.7784	−	2.73959i	0.746294	−	0.129578i
$448$	2.97653	−	2.16258i	0.140628	−	0.102172i
$449$	11.6658	+	35.9035i	0.550541	+	1.69439i	0.707437	+	0.706777i	$0.249851\pi$
$449$	11.6658	+	35.9035i	0.550541	+	1.69439i	−0.156895	+	0.987615i	$0.550149\pi$
$450$	−17.2728	−	27.9671i	−0.814249	−	1.31838i
$451$	4.13811	−	9.29434i	0.194856	−	0.437653i
$452$	−0.620231	−	0.558459i	−0.0291732	−	0.0262677i
$453$	6.03388	+	2.96250i	0.283496	+	0.139190i
$454$	−5.73399	−	4.16598i	−0.269109	−	0.195519i
$455$	−13.3278	+	41.0189i	−0.624819	+	1.92300i
$456$	−9.64706	−	0.362171i	−0.451765	−	0.0169602i
$457$	16.2797	−	1.71107i	0.761534	−	0.0800405i	0.284203	−	0.958764i	$-0.408271\pi$
$457$	16.2797	−	1.71107i	0.761534	−	0.0800405i	0.477331	+	0.878724i	$0.341604\pi$
$458$	0.281584	−	2.67910i	0.0131576	−	0.125186i
$459$	−3.42877	−	35.2863i	−0.160041	−	1.64702i
$460$	16.6033	+	9.58593i	0.774133	+	0.446946i
$461$	−4.62910	+	2.06101i	−0.215599	+	0.0959907i	−0.511694	−	0.859168i	$-0.670982\pi$
$461$	−4.62910	+	2.06101i	−0.215599	+	0.0959907i	0.296096	+	0.955158i	$0.404315\pi$
$462$	−7.42997	−	8.90192i	−0.345673	−	0.414155i
$463$	3.39859	+	15.9891i	0.157946	+	0.743077i	0.983811	+	0.179209i	$0.0573539\pi$
$463$	3.39859	+	15.9891i	0.157946	+	0.743077i	−0.825865	+	0.563868i	$0.809313\pi$
$464$	−0.880974	−	1.52589i	−0.0408982	−	0.0708377i
$465$	−28.4046	+	26.0228i	−1.31723	+	1.20678i
$466$	−8.36389	+	14.4867i	−0.387450	+	0.671083i
$467$	15.1534	+	4.92365i	0.701218	+	0.227839i	0.637861	−	0.770151i	$-0.279819\pi$
$467$	15.1534	+	4.92365i	0.701218	+	0.227839i	0.0633568	+	0.997991i	$0.479819\pi$
$468$	8.79992	−	0.261178i	0.406777	−	0.0120729i
$469$	26.9946	+	19.6127i	1.24650	+	0.905632i
$470$	−41.2108	+	23.7931i	−1.90091	+	1.09749i
$471$	1.81916	−	2.31589i	0.0838224	−	0.106711i
$472$	6.64693	−	2.95940i	0.305950	−	0.136218i
$473$	−2.33115	+	5.23586i	−0.107187	+	0.240745i
$474$	3.67078	−	1.93948i	0.168605	−	0.0890832i
$475$	−59.7362	+	12.6973i	−2.74088	+	0.582593i
$476$	22.9323	−	10.2101i	1.05110	−	0.467980i
$477$	1.56406	+	0.117602i	0.0716135	+	0.00538463i
$478$	0.639101	−	3.00673i	0.0292318	−	0.137525i
$479$	2.55001	+	3.50979i	0.116513	+	0.160366i	0.863290	−	0.504708i	$-0.168400\pi$
$479$	2.55001	+	3.50979i	0.116513	+	0.160366i	−0.746777	+	0.665074i	$0.768400\pi$
$480$	−6.49542	−	2.38341i	−0.296474	−	0.108787i
$481$	0.528913	−	0.587418i	0.0241164	−	0.0267839i
$482$	2.09594	+	19.9415i	0.0954673	+	0.908311i
$483$	28.7126	+	10.5357i	1.30647	+	0.479392i
$484$	2.37610	−	7.31289i	0.108005	−	0.332404i
$485$	−23.0683	−	51.8123i	−1.04748	−	2.35268i
$486$	−7.49787	+	13.6668i	−0.340110	+	0.619940i
$487$	−5.52383	+	0.580578i	−0.250309	+	0.0263085i	−0.228852	−	0.973461i	$-0.573497\pi$
$487$	−5.52383	+	0.580578i	−0.250309	+	0.0263085i	−0.0214569	+	0.999770i	$0.506830\pi$
$488$	−0.600150	−	5.71004i	−0.0271675	−	0.258482i
$489$	4.86744	−	19.3068i	0.220113	−	0.873083i
$490$	13.0554	−	22.6126i	0.589782	−	1.02153i
$491$	−40.5228			−1.82877			−0.914385	−	0.404846i	$-0.867325\pi$
$491$	−40.5228			−1.82877			−0.914385	+	0.404846i	$0.867325\pi$
$492$	−2.64507	−	9.31644i	−0.119249	−	0.420018i
$493$	−3.71484	−	11.4331i	−0.167308	−	0.514921i
$494$	5.05442	−	15.5559i	0.227409	−	0.699893i
$495$	−6.12002	+	20.9288i	−0.275074	+	0.940682i
$496$	−0.905116	+	5.49370i	−0.0406409	+	0.246675i
$497$	7.83361	+	4.52274i	0.351385	+	0.202872i
$498$	0.972956	+	14.4577i	0.0435992	+	0.647866i
$499$	−5.75074	+	27.0551i	−0.257438	+	1.21115i	0.639428	+	0.768851i	$0.279171\pi$
$499$	−5.75074	+	27.0551i	−0.257438	+	1.21115i	−0.896867	+	0.442301i	$0.854162\pi$
$500$	−23.6657	−	2.48737i	−1.05836	−	0.111239i
$501$	3.76856	+	0.539700i	0.168367	+	0.0241120i
$502$			9.64696i			0.430565i
$503$	12.1879	+	1.28100i	0.543433	+	0.0571171i	0.372268	−	0.928125i	$-0.378580\pi$
$503$	12.1879	+	1.28100i	0.543433	+	0.0571171i	0.171165	+	0.985242i	$0.445247\pi$
$504$	−10.8597	−	1.97354i	−0.483730	−	0.0879085i
$505$	−6.45982	−	61.4611i	−0.287458	−	2.73498i
$506$	−1.81565	−	8.54195i	−0.0807154	−	0.379736i
$507$	1.85802	−	7.36985i	0.0825174	−	0.327307i
$508$	−15.0663	+	13.5657i	−0.668458	+	0.601883i
$509$	0.442135	+	1.36075i	0.0195973	+	0.0603143i	0.960377	−	0.278704i	$-0.0899050\pi$
$509$	0.442135	+	1.36075i	0.0195973	+	0.0603143i	−0.940780	+	0.339019i	$0.889905\pi$
$510$	−39.9677	−	25.1203i	−1.76980	−	1.11235i
$511$	2.64550	−	12.4461i	0.117030	−	0.550584i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	19.2094	+	21.6742i	0.848117	+	0.956938i
$514$	27.4869	+	5.84252i	1.21239	+	0.257702i
$515$	47.1076	+	15.3062i	2.07581	+	0.674471i
$516$	1.49007	+	5.24831i	0.0655967	+	0.231044i
$517$	20.6146	+	6.69810i	0.906631	+	0.294582i
$518$	−0.801743	+	0.582500i	−0.0352265	+	0.0255936i
$519$	30.1914	+	1.13345i	1.32526	+	0.0497529i
$520$	6.89039	−	9.48380i	0.302163	−	0.415892i
$521$	−25.1927	+	14.5450i	−1.10371	+	0.637229i	−0.937194	−	0.348809i	$-0.886586\pi$
$521$	−25.1927	+	14.5450i	−1.10371	+	0.637229i	−0.166520	+	0.986038i	$0.553253\pi$
$522$	−1.48356	+	5.07338i	−0.0649336	+	0.222056i
$523$	−1.25130	+	1.72227i	−0.0547155	+	0.0753094i	−0.835498	−	0.549494i	$-0.814821\pi$
$523$	−1.25130	+	1.72227i	−0.0547155	+	0.0753094i	0.780782	+	0.624803i	$0.214821\pi$
$524$	6.68867	−	2.17328i	0.292196	−	0.0949403i
$525$	−69.6667	+	4.68833i	−3.04050	+	0.204615i
$526$	−20.7916	+	12.0040i	−0.906556	+	0.523400i
$527$	−13.8336	+	35.3796i	−0.602600	+	1.54116i
$528$	1.17294	+	2.92515i	0.0510457	+	0.127301i
$529$	0.0229936	+	0.0255369i	0.000999720	+	0.00111030i
$530$	1.39747	−	1.55205i	0.0607024	−	0.0674169i
$531$	−20.1954	−	8.28273i	−0.876405	−	0.359440i
$532$	−10.2533	+	17.7592i	−0.444536	+	0.769959i
$533$	16.4086			0.710737
$534$	13.3681	−	13.7707i	0.578492	−	0.595917i
$535$	−68.5528	−	30.5217i	−2.96379	−	1.31957i
$536$	−5.33071	−	7.33710i	−0.230252	−	0.316914i
$537$	−21.5188	−	32.0839i	−0.928607	−	1.38452i
$538$	−17.3583	−	1.82443i	−0.748368	−	0.0786566i
$539$	−11.6336	+	2.47279i	−0.501093	+	0.106511i
$540$	8.29332	+	19.0279i	0.356888	+	0.818830i
$541$	−33.7185	−	15.0124i	−1.44967	−	0.645435i	−0.477272	−	0.878756i	$-0.658374\pi$
$541$	−33.7185	−	15.0124i	−1.44967	−	0.645435i	−0.972400	+	0.233320i	$0.925041\pi$
$542$	16.3730	+	3.48018i	0.703279	+	0.149487i
$543$	−16.7524	+	2.90870i	−0.718915	+	0.124824i
$544$	−6.78545	+	0.713180i	−0.290924	+	0.0305773i
$545$	−10.6724	+	3.46766i	−0.457153	+	0.148538i
$546$	8.24190	−	16.7867i	0.352721	−	0.718406i
$547$	1.72982	−	16.4581i	0.0739618	−	0.703699i	−0.893221	−	0.449618i	$-0.851560\pi$
$547$	1.72982	−	16.4581i	0.0739618	−	0.703699i	0.967183	−	0.254081i	$-0.0817731\pi$
$548$	8.20254	+	9.10984i	0.350395	+	0.389153i
$549$	−11.1406	+	13.1366i	−0.475470	+	0.560655i
$550$	11.7186	+	16.1293i	0.499683	+	0.687755i
$551$	7.94494	+	5.77234i	0.338466	+	0.245910i
$552$	−6.53718	−	5.13502i	−0.278241	−	0.218561i
$553$		−	8.81887i		−	0.375017i
$554$	−1.45052	+	13.8008i	−0.0616268	+	0.586340i
$555$	1.74957	+	0.641984i	0.0742651	+	0.0272507i
$556$	−14.1982	+	12.7841i	−0.602137	+	0.542167i
$557$	−28.9517			−1.22672			−0.613362	−	0.789802i	$-0.710183\pi$
$557$	−28.9517			−1.22672			−0.613362	+	0.789802i	$0.710183\pi$
$558$	13.7913	−	9.42340i	0.583832	−	0.398924i
$559$	−9.24361			−0.390963
$560$	−10.9220	+	9.83421i	−0.461539	+	0.415571i
$561$	3.67843	+	21.1856i	0.155303	+	0.894456i
$562$	−1.98571	+	18.8928i	−0.0837623	+	0.796945i
$563$			4.09987i			0.172789i	0.996261	+	0.0863945i	$0.0275346\pi$
$563$			4.09987i			0.172789i	−0.996261	+	0.0863945i	$0.972465\pi$
$564$	19.1509	−	7.67920i	0.806397	−	0.323353i
$565$	2.69720	+	1.95963i	0.113472	+	0.0824424i
$566$	8.29735	+	11.4203i	0.348764	+	0.480032i
$567$	18.2279	+	27.6441i	0.765502	+	1.16094i
$568$	−1.64509	−	1.82706i	−0.0690264	−	0.0766616i
$569$	1.48607	−	14.1390i	0.0622994	−	0.592739i	−0.918186	−	0.396149i	$-0.870346\pi$
$569$	1.48607	−	14.1390i	0.0622994	−	0.592739i	0.980486	−	0.196590i	$-0.0629869\pi$
$570$	38.4765	−	2.58934i	1.61160	−	0.108455i
$571$	31.0268	−	10.0812i	1.29843	−	0.421886i	0.423396	−	0.905945i	$-0.360838\pi$
$571$	31.0268	−	10.0812i	1.29843	−	0.421886i	0.875035	+	0.484059i	$0.160838\pi$
$572$	−5.31041	+	0.558147i	−0.222039	+	0.0233373i
$573$	6.06465	−	16.5277i	0.253355	−	0.690457i
$574$	−20.1224	−	4.27716i	−0.839894	−	0.178525i
$575$	−48.0409	−	21.3892i	−2.00344	−	0.891991i
$576$	2.64143	+	1.42226i	0.110060	+	0.0592610i
$577$	21.7832	−	4.63016i	0.906847	−	0.192756i	0.269199	−	0.963085i	$-0.413241\pi$
$577$	21.7832	−	4.63016i	0.906847	−	0.192756i	0.637647	+	0.770328i	$0.279908\pi$
$578$	−29.3891	−	3.08892i	−1.22243	−	0.128482i
$579$	−2.74929	+	5.59964i	−0.114257	+	0.232713i
$580$	4.13702	+	5.69412i	0.171780	+	0.236436i
$581$	28.1192	+	12.5195i	1.16658	+	0.519396i
$582$	6.71647	+	23.6567i	0.278407	+	0.980600i
$583$	−0.951309			−0.0393992
$584$	−1.72921	+	2.99507i	−0.0715551	+	0.123937i
$585$	−34.8508	+	4.71202i	−1.44090	+	0.194818i
$586$	6.04325	−	6.71171i	0.249644	−	0.277258i
$587$	5.32785	+	5.91718i	0.219904	+	0.244228i	0.842995	−	0.537921i	$-0.180790\pi$
$587$	5.32785	+	5.91718i	0.219904	+	0.244228i	−0.623091	+	0.782149i	$0.714124\pi$
$588$	−6.99354	+	8.90318i	−0.288409	+	0.367161i
$589$	−7.84562	−	30.0247i	−0.323273	−	1.23714i
$590$	−25.1708	+	14.5324i	−1.03627	+	0.598289i
$591$	−3.43526	+	6.99678i	−0.141308	+	0.287809i
$592$	0.256172	−	0.0832352i	0.0105286	−	0.00342094i
$593$	12.4578	−	17.1467i	0.511580	−	0.704129i	−0.472605	−	0.881274i	$-0.656686\pi$
$593$	12.4578	−	17.1467i	0.511580	−	0.704129i	0.984185	+	0.177145i	$0.0566862\pi$
$594$	3.91328	−	8.60681i	0.160564	−	0.353142i
$595$	−86.8408	+	50.1376i	−3.56013	+	2.05544i
$596$	−5.43465	+	7.48015i	−0.222612	+	0.306399i
$597$	6.65743	+	12.6003i	0.272470	+	0.515694i
$598$	11.3945	−	8.27858i	0.465955	−	0.338536i
$599$	3.84315	+	1.24872i	0.157027	+	0.0510211i	0.386476	−	0.922300i	$-0.373692\pi$
$599$	3.84315	+	1.24872i	0.157027	+	0.0510211i	−0.229449	+	0.973321i	$0.573692\pi$
$600$	18.4023	+	4.63942i	0.751271	+	0.189403i
$601$	41.2383	+	13.3991i	1.68215	+	0.546562i	0.985326	−	0.170684i	$-0.0545976\pi$
$601$	41.2383	+	13.3991i	1.68215	+	0.546562i	0.696820	+	0.717246i	$0.254598\pi$
$602$	11.3357	+	2.40949i	0.462010	+	0.0982033i
$603$	−4.86475	+	26.7690i	−0.198108	+	1.09012i
$604$	−3.69095	+	1.19926i	−0.150183	+	0.0487973i
$605$	−6.38613	+	30.0444i	−0.259633	+	1.22148i
$606$	−1.00527	+	26.7772i	−0.0408363	+	1.08775i
$607$	−7.34328	−	22.6003i	−0.298055	−	0.917317i	−0.982178	−	0.187952i	$-0.939815\pi$
$607$	−7.34328	−	22.6003i	−0.298055	−	0.917317i	0.684124	−	0.729366i	$-0.260185\pi$
$608$	4.14203	−	3.72950i	0.167982	−	0.151251i
$609$	8.05638	+	7.82081i	0.326461	+	0.316915i
$610$	4.76848	+	22.4339i	0.193070	+	0.908324i
$611$	3.65416	+	34.7670i	0.147832	+	1.40652i
$612$	15.6107	+	13.2388i	0.631024	+	0.535147i
$613$	5.10632	+	0.536695i	0.206242	+	0.0216769i	0.207086	−	0.978323i	$-0.433602\pi$
$613$	5.10632	+	0.536695i	0.206242	+	0.0216769i	−0.000843949		1.00000i	$0.500269\pi$
$614$		−	16.1408i		−	0.651388i
$615$	14.3983	+	35.9074i	0.580595	+	1.44792i
$616$	6.65782	+	0.699765i	0.268251	+	0.0281943i
$617$	−1.48394	+	6.98141i	−0.0597414	+	0.281061i	−0.997871	−	0.0652242i	$-0.979224\pi$
$617$	−1.48394	+	6.98141i	−0.0597414	+	0.281061i	0.938129	+	0.346285i	$0.112557\pi$
$618$	−19.2785	−	9.46530i	−0.775494	−	0.380750i
$619$	38.3647	+	22.1499i	1.54201	+	0.890279i	0.998712	+	0.0507382i	$0.0161574\pi$
$619$	38.3647	+	22.1499i	1.54201	+	0.890279i	0.543297	+	0.839541i	$0.317176\pi$
$620$	1.30189	−	22.2030i	0.0522850	−	0.891694i
$621$	2.41192	+	24.8216i	0.0967869	+	0.996055i
$622$	7.17305	−	22.0764i	0.287613	−	0.885182i
$623$	−12.5979	−	38.7723i	−0.504723	−	1.55338i
$624$	−3.54042	+	3.64706i	−0.141730	+	0.145999i
$625$	40.2713			1.61085
$626$	12.2941	−	21.2940i	0.491371	−	0.851080i
$627$	−12.6037	−	12.2352i	−0.503344	−	0.488627i
$628$	0.177726	+	1.69095i	0.00709204	+	0.0674763i
$629$	1.82769	−	0.192098i	0.0728749	−	0.00765946i
$630$	43.9669	+	3.30588i	1.75168	+	0.131709i
$631$	4.94385	+	11.1041i	0.196812	+	0.442046i	0.984811	−	0.173630i	$-0.0555496\pi$
$631$	4.94385	+	11.1041i	0.196812	+	0.442046i	−0.787999	+	0.615676i	$0.788883\pi$
$632$	−0.740701	+	2.27964i	−0.0294635	+	0.0906793i
$633$	0.833959	+	4.80311i	0.0331469	+	0.190906i
$634$	−3.33553	−	31.7354i	−0.132471	−	1.26037i
$635$	54.1901	−	60.1842i	2.15047	−	2.38834i
$636$	−0.695221	+	0.580265i	−0.0275673	+	0.0230090i
$637$	−11.2749	−	15.5185i	−0.446726	−	0.614865i
$638$	0.666556	−	3.13590i	0.0263892	−	0.124151i
$639$	−0.553015	+	7.35488i	−0.0218769	+	0.290955i
$640$	3.64927	−	1.62476i	0.144250	−	0.0642243i
$641$	9.90656	−	2.10570i	0.391286	−	0.0831703i	−0.00806764	−	0.999967i	$-0.502568\pi$
$641$	9.90656	−	2.10570i	0.391286	−	0.0831703i	0.399353	+	0.916797i	$0.369235\pi$
$642$	27.5478	+	17.3142i	1.08723	+	0.683338i
$643$	−12.7593	+	28.6578i	−0.503177	+	1.13015i	0.466223	+	0.884667i	$0.345614\pi$
$643$	−12.7593	+	28.6578i	−0.503177	+	1.13015i	−0.969400	+	0.245486i	$0.921052\pi$
$644$	−16.1314	+	7.18214i	−0.635665	+	0.283016i
$645$	−8.11111	−	20.2280i	−0.319375	−	0.796477i
$646$	32.9333	−	19.0141i	1.29574	−	0.748098i
$647$	17.0165	+	12.3632i	0.668986	+	0.486047i	0.869686	−	0.493606i	$-0.164321\pi$
$647$	17.0165	+	12.3632i	0.668986	+	0.486047i	−0.200699	+	0.979653i	$0.564321\pi$
$648$	−2.39001	−	8.67686i	−0.0938884	−	0.340859i
$649$	12.5910	+	4.09108i	0.494242	+	0.160589i
$650$	−16.0772	+	27.8466i	−0.630602	+	1.09223i
$651$	−4.01303	−	35.2532i	−0.157283	−	1.38168i
$652$	5.74778	+	9.95545i	0.225101	+	0.389886i
$653$	−5.86283	−	27.5824i	−0.229430	−	1.07938i	−0.930500	−	0.366292i	$-0.880627\pi$
$653$	−5.86283	−	27.5824i	−0.229430	−	1.07938i	0.701070	−	0.713093i	$-0.252706\pi$
$654$	4.79390	−	0.832360i	0.187456	−	0.0325478i
$655$	−25.6649	+	11.4268i	−1.00281	+	0.446480i
$656$	4.84233	+	2.79572i	0.189061	+	0.109154i
$657$	10.0801	−	2.45725i	0.393260	−	0.0958666i
$658$	4.58133	−	43.5885i	0.178599	−	1.69926i
$659$	−15.0142	+	1.57805i	−0.584869	+	0.0614722i	−0.392342	−	0.919820i	$-0.628335\pi$
$659$	−15.0142	+	1.57805i	−0.584869	+	0.0614722i	−0.192527	+	0.981292i	$0.561668\pi$
$660$	−5.88120	−	11.1311i	−0.228925	−	0.433278i
$661$	4.12097	−	12.6830i	0.160287	−	0.493313i	−0.838371	−	0.545100i	$-0.816492\pi$
$661$	4.12097	−	12.6830i	0.160287	−	0.493313i	0.998658	+	0.0517870i	$0.0164917\pi$
$662$	−14.6775	−	10.6638i	−0.570457	−	0.414462i
$663$	−28.8014	+	19.3173i	−1.11855	+	0.750220i
$664$	−6.21719	−	5.59798i	−0.241274	−	0.217244i
$665$	33.3182	−	74.8340i	1.29203	−	2.90194i
$666$	−0.711482	−	0.383094i	−0.0275694	−	0.0148446i
$667$	2.61315	+	8.04243i	0.101181	+	0.311404i
$668$	−1.77820	+	1.29194i	−0.0688006	+	0.0499866i
$669$	19.1010	+	22.8851i	0.738487	+	0.884788i
$670$	24.2412	+	26.9225i	0.936518	+	1.04011i
$671$	6.14057	−	8.45177i	0.237054	−	0.326277i
$672$	5.29240	−	3.54964i	0.204159	−	0.136930i
$673$	−2.62444	+	5.89458i	−0.101165	+	0.227219i	−0.957036	−	0.289970i	$-0.906355\pi$
$673$	−2.62444	+	5.89458i	−0.101165	+	0.227219i	0.855871	+	0.517189i	$0.173021\pi$
$674$	−23.0548	+	16.7503i	−0.888038	+	0.645198i
$675$	−28.0791	−	49.5287i	−1.08076	−	1.90636i
$676$	2.19406	+	3.80023i	0.0843870	+	0.146163i
$677$	−7.42334	−	12.8576i	−0.285302	−	0.494158i	0.687380	−	0.726298i	$-0.258761\pi$
$677$	−7.42334	−	12.8576i	−0.285302	−	0.494158i	−0.972682	+	0.232140i	$0.925427\pi$
$678$	−1.03723	−	1.00690i	−0.0398345	−	0.0386697i
$679$	51.0957	+	10.8607i	1.96087	+	0.416796i
$680$	26.6591	−	5.66656i	1.02233	−	0.217303i
$681$	−9.65386	−	7.58321i	−0.369937	−	0.290589i
$682$	−7.91258	+	6.32654i	−0.302988	+	0.242256i
$683$		−	5.95093i		−	0.227706i	−0.993498	−	0.113853i	$-0.963681\pi$
$683$		−	5.95093i		−	0.227706i	0.993498	−	0.113853i	$-0.0363193\pi$
$684$	−16.6739	−	1.25371i	−0.637542	−	0.0479369i
$685$	−36.3904	−	32.7661i	−1.39041	−	1.25193i
$686$	−0.693656	−	1.55798i	−0.0264839	−	0.0594838i
$687$	0.661460	−	4.61877i	0.0252363	−	0.176217i
$688$	−2.72787	−	1.57494i	−0.103999	−	0.0600439i
$689$	−0.624050	−	1.40164i	−0.0237744	−	0.0533982i
$690$	28.1147	+	17.6705i	1.07031	+	0.672704i
$691$	33.9304	+	15.1068i	1.29077	+	0.574689i	0.933254	−	0.359217i	$-0.116956\pi$
$691$	33.9304	+	15.1068i	1.29077	+	0.574689i	0.357518	+	0.933906i	$0.383623\pi$
$692$	−12.9629	+	11.6718i	−0.492775	+	0.443697i
$693$	−12.2816	−	15.8905i	−0.466539	−	0.603631i
$694$	0.387422	+	1.82268i	0.0147063	+	0.0691879i
$695$	51.0677	−	56.7164i	1.93711	−	2.15138i
$696$	−1.42567	−	2.69831i	−0.0540398	−	0.102279i
$697$	28.3505	+	25.5269i	1.07385	+	0.966902i
$698$	7.85093	+	7.06901i	0.297162	+	0.267566i
$699$	−15.4178	+	24.5305i	−0.583155	+	0.927830i
$700$	26.9747	−	29.9584i	1.01955	−	1.13232i
$701$	−7.23689	−	34.0469i	−0.273334	−	1.28593i	−0.873801	−	0.486284i	$-0.838352\pi$
$701$	−7.23689	−	34.0469i	−0.273334	−	1.28593i	0.600467	−	0.799650i	$-0.294981\pi$
$702$	15.2482	+	0.119756i	0.575505	+	0.00451991i
$703$	−1.11568	+	1.00456i	−0.0420785	+	0.0378877i
$704$	−1.66224	−	0.740079i	−0.0626482	−	0.0278928i
$705$	−72.8750	+	38.5040i	−2.74463	+	1.45014i
$706$	−6.12851	−	13.7648i	−0.230649	−	0.518047i
$707$	49.2939	+	28.4598i	1.85389	+	1.07034i
$708$	11.6970	−	4.69032i	0.439600	−	0.176273i
$709$	−8.10643	−	18.2073i	−0.304443	−	0.683791i	0.694934	−	0.719074i	$-0.255434\pi$
$709$	−8.10643	−	18.2073i	−0.304443	−	0.683791i	−0.999377	+	0.0352824i	$0.988767\pi$
$710$	7.29841	+	6.57151i	0.273904	+	0.246625i
$711$	6.47953	−	3.11839i	0.243001	−	0.116949i
$712$			11.0806i			0.415262i
$713$	9.73101	−	24.8872i	0.364429	−	0.932033i
$714$	40.3554	−	16.1819i	1.51026	−	0.605591i
$715$	20.8638	−	4.43474i	0.780263	−	0.165850i
$716$	21.8168	+	4.63731i	0.815333	+	0.173304i
$717$	1.30155	−	5.16262i	0.0486073	−	0.192802i
$718$	9.77981	+	16.9391i	0.364979	+	0.632162i
$719$	20.1698	+	34.9352i	0.752208	+	1.30286i	0.946751	+	0.321968i	$0.104344\pi$
$719$	20.1698	+	34.9352i	0.752208	+	1.30286i	−0.194543	+	0.980894i	$0.562322\pi$
$720$	−11.0876	−	4.54735i	−0.413210	−	0.169470i
$721$	−36.9078	+	26.8151i	−1.37452	+	0.998647i
$722$	−4.90753	+	11.0225i	−0.182640	+	0.410215i
$723$	2.33193	+	34.6516i	0.0867256	+	1.28871i
$724$	5.77012	−	7.94189i	0.214445	−	0.295158i
$725$	−12.9180	−	14.3469i	−0.479764	−	0.532832i
$726$	4.58782	−	12.5030i	0.170270	−	0.464029i
$727$	2.83316	−	2.05841i	0.105076	−	0.0763423i	−0.534006	−	0.845480i	$-0.679314\pi$
$727$	2.83316	−	2.05841i	0.105076	−	0.0763423i	0.639083	+	0.769138i	$0.279314\pi$
$728$	3.33644	+	10.2685i	0.123657	+	0.380577i
$729$	−13.8656	+	23.1678i	−0.513541	+	0.858065i
$730$	5.61909	−	12.6207i	0.207972	−	0.467113i
$731$	−15.9710	−	14.3803i	−0.590707	−	0.531875i
$732$	−0.667725	−	9.92212i	−0.0246798	−	0.366732i
$733$	−16.4239	−	11.9327i	−0.606631	−	0.440743i	0.241595	−	0.970377i	$-0.422329\pi$
$733$	−16.4239	−	11.9327i	−0.606631	−	0.440743i	−0.848226	+	0.529634i	$0.822329\pi$
$734$	−0.112704	+	0.346868i	−0.00415999	+	0.0128031i
$735$	24.0660	−	38.2902i	0.887688	−	1.41236i
$736$	4.77312	−	0.501675i	0.175940	−	0.0184920i
$737$	1.72491	−	16.4114i	0.0635378	−	0.604522i
$738$	−3.97280	−	16.2971i	−0.146241	−	0.599903i
$739$	−23.8970	−	13.7969i	−0.879066	−	0.507529i	−0.00871556	−	0.999962i	$-0.502774\pi$
$739$	−23.8970	−	13.7969i	−0.879066	−	0.507529i	−0.870350	+	0.492433i	$0.836108\pi$
$740$	−0.982948	+	0.437637i	−0.0361339	+	0.0160879i
$741$	9.75916	−	26.5962i	0.358512	−	0.977037i
$742$	0.399934	+	1.88154i	0.0146820	+	0.0690736i
$743$	−7.24353	−	12.5462i	−0.265739	−	0.460274i	0.702018	−	0.712160i	$-0.252283\pi$
$743$	−7.24353	−	12.5462i	−0.265739	−	0.460274i	−0.967757	+	0.251885i	$0.918949\pi$
$744$	−1.92358	+	9.44986i	−0.0705218	+	0.346449i
$745$	18.4671	−	31.9860i	0.676582	−	1.17188i
$746$	−34.1266	−	11.0884i	−1.24946	−	0.405975i
$747$	0.744574	+	25.0871i	0.0272425	+	0.917889i
$748$	−10.0435	−	7.29706i	−0.367228	−	0.266807i
$749$	59.8552	−	34.5574i	2.18706	−	1.26270i
$750$	−40.7998	−	5.84300i	−1.48980	−	0.213356i
$751$	1.63213	−	0.726672i	0.0595574	−	0.0265166i	−0.376742	−	0.926318i	$-0.622956\pi$
$751$	1.63213	−	0.726672i	0.0595574	−	0.0265166i	0.436299	+	0.899802i	$0.356289\pi$
$752$	−4.84527	+	10.8827i	−0.176689	+	0.396849i
$753$	−0.626850	+	16.6973i	−0.0228437	+	0.608482i
$754$	5.05762	−	1.07503i	0.184188	−	0.0391503i
$755$	14.1624	−	6.30553i	0.515424	−	0.229482i
$756$	−18.6681	−	4.12152i	−0.678952	−	0.149898i
$757$	4.82146	−	22.6832i	0.175239	−	0.824434i	−0.799426	−	0.600764i	$-0.794863\pi$
$757$	4.82146	−	22.6832i	0.175239	−	0.824434i	0.974665	−	0.223670i	$-0.0718037\pi$
$758$	4.44442	+	6.11722i	0.161429	+	0.222188i
$759$	−2.58753	−	14.9027i	−0.0939215	−	0.540932i
$760$	−14.8980	+	16.5459i	−0.540406	+	0.600182i
$761$	3.76536	+	35.8250i	0.136494	+	1.29866i	0.821538	+	0.570154i	$0.193116\pi$
$761$	3.76536	+	35.8250i	0.136494	+	1.29866i	−0.685044	+	0.728502i	$0.740217\pi$
$762$	−26.9587	+	22.5010i	−0.976610	+	0.815126i
$763$	3.19384	−	9.82963i	0.115625	−	0.355856i
$764$	4.13424	+	9.28566i	0.149572	+	0.335943i
$765$	−67.5451	−	46.0761i	−2.44210	−	1.66588i
$766$	−15.9708	+	1.67860i	−0.577049	+	0.0606503i
$767$	2.23190	+	21.2351i	0.0805891	+	0.766754i
$768$	−1.66620	+	0.473058i	−0.0601237	+	0.0170700i
$769$	−22.7843	+	39.4636i	−0.821623	+	1.42309i	0.0828508	+	0.996562i	$0.473598\pi$
$769$	−22.7843	+	39.4636i	−0.821623	+	1.42309i	−0.904473	+	0.426530i	$0.859736\pi$
$770$	−26.7420			−0.963714
$771$	47.1955	+	11.8985i	1.69971	+	0.428514i
$772$	−1.11296	−	3.42532i	−0.0400561	−	0.123280i
$773$	2.97401	−	9.15308i	0.106968	−	0.329213i	−0.883219	−	0.468960i	$-0.844629\pi$
$773$	2.97401	−	9.15308i	0.106968	−	0.329213i	0.990187	+	0.139747i	$0.0446288\pi$
$774$	2.23803	+	9.18076i	0.0804444	+	0.329996i
$775$	2.81451	+	60.9412i	0.101100	+	2.18907i
$776$	−12.2958	−	7.09900i	−0.441394	−	0.254839i
$777$	−1.42553	+	0.956113i	−0.0511407	+	0.0343004i
$778$	2.10186	−	9.88847i	0.0753553	−	0.354519i
$779$	−30.9940	−	3.25760i	−1.11048	−	0.116716i
$780$	12.5423	−	15.9671i	0.449088	−	0.571715i
$781$		−	4.47346i		−	0.160073i
$782$	32.5662	+	3.42285i	1.16456	+	0.122401i
$783$	−2.89745	+	8.68477i	−0.103547	+	0.310368i
$784$	−0.683247	−	6.50066i	−0.0244017	−	0.232167i
$785$	−1.41212	−	6.64350i	−0.0504007	−	0.237117i
$786$	11.7182	−	3.32696i	0.417974	−	0.118669i
$787$	−25.9358	+	23.3527i	−0.924510	+	0.832433i	−0.986182	−	0.165664i	$-0.947023\pi$
$787$	−25.9358	+	23.3527i	−0.924510	+	0.832433i	0.0616722	+	0.998096i	$0.480357\pi$
$788$	−1.39065	−	4.27997i	−0.0495397	−	0.152467i
$789$	−36.7667	+	19.4259i	−1.30893	+	0.691582i
$790$	1.99074	−	9.36571i	0.0708275	−	0.333217i
$791$	−2.92038	+	0.948888i	−0.103837	+	0.0337386i
$792$	1.84009	+	5.13917i	0.0653847	+	0.182612i
$793$	16.4808	+	3.50310i	0.585251	+	0.124399i
$794$	−18.9437	−	6.15517i	−0.672286	−	0.218439i
$795$	2.51964	−	2.59554i	0.0893626	−	0.0920541i
$796$	−7.82506	−	2.54252i	−0.277352	−	0.0901171i
$797$	23.4796	−	17.0589i	0.831691	−	0.604259i	−0.0883462	−	0.996090i	$-0.528158\pi$
$797$	23.4796	−	17.0589i	0.831691	−	0.604259i	0.920037	+	0.391831i	$0.128158\pi$
$798$	−18.9007	+	30.0719i	−0.669077	+	1.06454i
$799$	−47.7736	+	65.7547i	−1.69011	+	2.32623i
$800$	−9.48907	+	5.47851i	−0.335489	+	0.193695i
$801$	24.0327	−	22.9661i	0.849152	−	0.811468i
$802$	0.761343	−	1.04790i	0.0268840	−	0.0370026i
$803$	−5.98478	+	1.94457i	−0.211198	+	0.0686224i
$804$	−8.74981	−	13.0457i	−0.308582	−	0.460085i
$805$	61.0868	−	35.2685i	2.15303	−	1.24305i
$806$	−14.5120	−	7.50807i	−0.511162	−	0.264460i
$807$	−29.9257	−	4.28570i	−1.05343	−	0.150864i
$808$	−10.3519	−	11.4970i	−0.364179	−	0.404462i
$809$	−20.5313	+	22.8023i	−0.721842	+	0.801687i	−0.986692	−	0.162603i	$-0.948011\pi$
$809$	−20.5313	+	22.8023i	−0.721842	+	0.801687i	0.264849	+	0.964290i	$0.414678\pi$
$810$	13.1179	+	33.4730i	0.460917	+	1.17612i
$811$	12.7302	−	22.0493i	0.447016	−	0.774255i	−0.551174	−	0.834390i	$-0.685820\pi$
$811$	12.7302	−	22.0493i	0.447016	−	0.774255i	0.998190	+	0.0601354i	$0.0191533\pi$
$812$	−6.48255			−0.227493
$813$	28.1127	+	7.08751i	0.985956	+	0.248570i
$814$	0.447733	+	0.199344i	0.0156930	+	0.00698699i
$815$	−26.9914	−	37.1504i	−0.945467	−	1.30132i
$816$	−11.7908	+	0.793482i	−0.412761	+	0.0277774i
$817$	17.4601	+	1.83513i	0.610852	+	0.0642032i
$818$	27.8577	−	5.92133i	0.974021	−	0.207035i
$819$	15.3561	−	28.5194i	0.536587	−	0.996550i
$820$	−20.4047	−	9.08475i	−0.712562	−	0.317253i
$821$	−5.85713	−	1.24497i	−0.204415	−	0.0434498i	0.104566	−	0.994518i	$-0.466655\pi$
$821$	−5.85713	−	1.24497i	−0.204415	−	0.0434498i	−0.308981	+	0.951068i	$0.599988\pi$
$822$	13.6053	+	16.3006i	0.474538	+	0.568548i
$823$	30.6368	−	3.22006i	1.06793	−	0.112244i	0.445781	−	0.895142i	$-0.352926\pi$
$823$	30.6368	−	3.22006i	1.06793	−	0.112244i	0.622150	+	0.782898i	$0.286259\pi$
$824$	11.7927	−	3.83169i	0.410819	−	0.133483i
$825$	19.2349	+	28.6785i	0.669673	+	0.998459i
$826$	2.79819	−	26.6230i	0.0973616	−	0.926334i
$827$	−24.2860	−	26.9724i	−0.844509	−	0.937922i	0.154235	−	0.988034i	$-0.450709\pi$
$827$	−24.2860	−	26.9724i	−0.844509	−	0.937922i	−0.998744	+	0.0501124i	$0.984042\pi$
$828$	−10.9811	−	9.31263i	−0.381619	−	0.323636i
$829$	−9.73863	−	13.4041i	−0.338236	−	0.465543i	0.605689	−	0.795702i	$-0.292898\pi$
$829$	−9.73863	−	13.4041i	−0.338236	−	0.465543i	−0.943925	+	0.330159i	$0.892898\pi$
$830$	27.0367	+	19.6433i	0.938459	+	0.681830i
$831$	−3.40738	+	23.7926i	−0.118201	+	0.825357i
$832$		−	2.93460i		−	0.101739i
$833$	4.66168	−	44.3529i	0.161518	−	1.53674i
$834$	−25.4054	+	21.2045i	−0.879715	+	0.734253i
$835$	6.52488	−	5.87503i	0.225803	−	0.203314i
$836$	10.1416			0.350753
$837$	24.4827	−	15.4142i	0.846246	−	0.532792i
$838$	13.4769			0.465552
$839$	−14.9809	+	13.4889i	−0.517198	+	0.465687i	−0.885910	−	0.463857i	$-0.846465\pi$
$839$	−14.9809	+	13.4889i	−0.517198	+	0.465687i	0.368713	+	0.929543i	$0.379799\pi$
$840$	−19.5432	+	16.3117i	−0.674303	+	0.562806i
$841$	2.70682	−	25.7537i	0.0933387	−	0.888058i
$842$		−	21.7046i		−	0.747989i
$843$	−4.66457	+	32.5712i	−0.160656	+	1.12181i
$844$	−2.27703	−	1.65436i	−0.0783787	−	0.0569454i
$845$	−10.3032	−	14.1812i	−0.354442	−	0.487848i
$846$	33.6459	−	12.0470i	1.15677	−	0.414184i
$847$	−18.9298	−	21.0237i	−0.650436	−	0.722382i
$848$	0.0546502	−	0.519962i	0.00187669	−	0.0178556i
$849$	13.6192	+	20.3058i	0.467411	+	0.696894i
$850$	−71.0990	+	23.1015i	−2.43868	+	0.792374i
$851$	−1.28566	+	0.135129i	−0.0440719	+	0.00463215i
$852$	−2.72865	−	3.26922i	−0.0934821	−	0.112002i
$853$	−18.0766	−	3.84230i	−0.618931	−	0.131558i	−0.112234	−	0.993682i	$-0.535800\pi$
$853$	−18.0766	−	3.84230i	−0.618931	−	0.131558i	−0.506697	+	0.862124i	$0.669134\pi$
$854$	−19.2978	−	8.59194i	−0.660357	−	0.294010i
$855$	66.7646	−	1.98154i	2.28330	−	0.0677673i
$856$	−18.3748	+	3.90569i	−0.628038	+	0.133494i
$857$	−9.58913	−	1.00786i	−0.327558	−	0.0344278i	−0.0606779	−	0.998157i	$-0.519326\pi$
$857$	−9.58913	−	1.00786i	−0.327558	−	0.0344278i	−0.266881	+	0.963730i	$0.585993\pi$
$858$	−9.22769	+	0.620992i	−0.315028	+	0.0212003i
$859$	−15.4051	−	21.2033i	−0.525614	−	0.723446i	0.460840	−	0.887483i	$-0.347548\pi$
$859$	−15.4051	−	21.2033i	−0.525614	−	0.723446i	−0.986454	+	0.164037i	$0.947548\pi$
$860$	11.4947	+	5.11779i	0.391967	+	0.174515i
$861$	−34.5506	−	8.71057i	−1.17748	−	0.296856i
$862$	1.85430			0.0631577
$863$	−0.363083	+	0.628878i	−0.0123595	+	0.0214073i	−0.872139	−	0.489258i	$-0.837268\pi$
$863$	−0.363083	+	0.628878i	−0.0123595	+	0.0214073i	0.859780	+	0.510665i	$0.170601\pi$
$864$	4.47946	+	2.63334i	0.152394	+	0.0895880i
$865$	46.6246	−	51.7819i	1.58528	−	1.76064i
$866$	−15.0330	−	16.6958i	−0.510841	−	0.567346i
$867$	−50.6669	−	7.25608i	−1.72074	−	0.246429i
$868$	15.8394	+	12.9901i	0.537624	+	0.440914i
$869$	−3.77708	+	2.18070i	−0.128129	+	0.0739750i
$870$	6.79049	+	10.1244i	0.230219	+	0.343249i
$871$	25.3117	−	8.22428i	0.857655	−	0.278669i
$872$	−1.65119	+	2.27267i	−0.0559163	+	0.0769622i
$873$	10.0879	+	41.3821i	0.341423	+	1.40057i
$874$	−23.1664	+	13.3751i	−0.783616	+	0.452421i
$875$	−51.4609	+	70.8298i	−1.73970	+	2.39448i
$876$	−3.18758	+	5.07161i	−0.107698	+	0.171354i
$877$	−28.1619	+	20.4608i	−0.950959	+	0.690912i	−0.951033	−	0.309088i	$-0.899976\pi$
$877$	−28.1619	+	20.4608i	−0.950959	+	0.690912i	7.48058e−5		1.00000i	$0.499976\pi$
$878$	9.97713	+	3.24177i	0.336712	+	0.109404i
$879$	10.8960	−	11.2242i	0.367512	−	0.378581i
$880$	6.91269	+	2.24607i	0.233027	+	0.0757150i
$881$	−37.7956	−	8.03370i	−1.27337	−	0.270662i	−0.478845	−	0.877899i	$-0.658944\pi$
$881$	−37.7956	−	8.03370i	−1.27337	−	0.270662i	−0.794521	+	0.607237i	$0.792278\pi$
$882$	−12.6832	+	14.9555i	−0.427064	+	0.503577i
$883$	38.0691	−	12.3694i	1.28113	−	0.416263i	0.412149	−	0.911116i	$-0.364778\pi$
$883$	38.0691	−	12.3694i	1.28113	−	0.416263i	0.868977	+	0.494853i	$0.164778\pi$
$884$	4.16287	−	19.5847i	0.140012	−	0.658706i
$885$	−44.5107	+	23.5175i	−1.49621	+	0.790533i
$886$	12.5600	+	38.6556i	0.421961	+	1.29866i
$887$	38.3115	−	34.4958i	1.28637	−	1.15826i	0.308007	−	0.951384i	$-0.400338\pi$
$887$	38.3115	−	34.4958i	1.28637	−	1.15826i	0.978368	−	0.206873i	$-0.0663287\pi$
$888$	0.448798	−	0.127420i	0.0150607	−	0.00427595i
$889$	15.5083	+	72.9608i	0.520132	+	2.44703i
$890$	−4.62672	−	44.0203i	−0.155088	−	1.47556i
$891$	7.33249	−	14.6427i	0.245648	−	0.490547i
$892$	−17.1159	−	1.79896i	−0.573084	−	0.0602335i
$893$		−	66.3964i		−	2.22187i
$894$	−9.89252	+	12.5937i	−0.330855	+	0.421198i
$895$	−88.6089	−	9.31317i	−2.96187	−	0.311305i
$896$	−0.764947	+	3.59879i	−0.0255551	+	0.120227i
$897$	20.2599	−	13.5884i	0.676457	−	0.453704i
$898$	−32.6935	−	18.8756i	−1.09100	−	0.629887i
$899$	6.97973	−	6.89360i	0.232787	−	0.229914i
$900$	31.5498	+	9.22581i	1.05166	+	0.307527i
$901$	1.10231	−	3.39256i	0.0367233	−	0.113023i
$902$	3.14391	+	9.67597i	0.104681	+	0.322175i
$903$	19.4637	+	4.90700i	0.647711	+	0.163295i
$904$	0.834603			0.0277585
$905$	−19.6070	+	33.9604i	−0.651760	+	1.12888i
$906$	−6.46634	+	1.83589i	−0.214830	+	0.0609933i
$907$	1.13512	+	10.7999i	0.0376909	+	0.358605i	0.997071	+	0.0764870i	$0.0243704\pi$
$907$	1.13512	+	10.7999i	0.0376909	+	0.358605i	−0.959380	+	0.282118i	$0.908963\pi$
$908$	7.04877	−	0.740856i	0.233922	−	0.0245862i
$909$	−3.47991	+	46.2814i	−0.115421	+	1.53506i
$910$	−17.5425	−	39.4010i	−0.581527	−	1.30613i
$911$	5.96260	−	18.3510i	0.197550	−	0.607996i	−0.802388	−	0.596803i	$-0.796437\pi$
$911$	5.96260	−	18.3510i	0.197550	−	0.607996i	0.999937	−	0.0111926i	$-0.00356277\pi$
$912$	7.41150	−	6.18600i	0.245419	−	0.204839i
$913$	−1.59118	−	15.1391i	−0.0526605	−	0.501031i
$914$	−10.9533	+	12.1648i	−0.362302	+	0.402377i
$915$	6.79570	+	39.1392i	0.224659	+	1.29390i
$916$	1.58341	+	2.17937i	0.0523173	+	0.0720085i
$917$	5.37979	−	25.3099i	0.177656	−	0.835807i
$918$	26.1592	+	23.9285i	0.863382	+	0.789759i
$919$	−25.6455	+	11.4181i	−0.845968	+	0.376649i	−0.783496	−	0.621397i	$-0.786565\pi$
$919$	−25.6455	+	11.4181i	−0.845968	+	0.376649i	−0.0624726	+	0.998047i	$0.519899\pi$
$920$	−18.7529	+	3.98605i	−0.618265	+	0.131416i
$921$	1.04881	−	27.9369i	0.0345595	−	0.920554i
$922$	2.06101	−	4.62910i	0.0678757	−	0.152451i
$923$	6.59109	−	2.93454i	0.216949	−	0.0965917i
$924$	11.4781	+	1.64379i	0.377601	+	0.0540768i
$925$	2.55592	−	1.47566i	0.0840383	−	0.0485195i
$926$	−13.2244	−	9.60812i	−0.434582	−	0.315742i
$927$	−32.7527	−	17.6355i	−1.07574	−	0.579227i
$928$	1.67571	+	0.544472i	0.0550079	+	0.0178732i
$929$	−23.8838	+	41.3680i	−0.783602	+	1.35724i	0.146228	+	0.989251i	$0.453287\pi$
$929$	−23.8838	+	41.3680i	−0.783602	+	1.35724i	−0.929831	+	0.367988i	$0.880047\pi$
$930$	3.69607	−	38.3450i	0.121199	−	1.25738i
$931$	18.2160	+	31.5511i	0.597006	+	1.03404i
$932$	−3.47790	−	16.3622i	−0.113922	−	0.535963i
$933$	13.8498	−	37.7444i	0.453423	−	1.23570i
$934$	−14.5558	+	6.48065i	−0.476279	+	0.212053i
$935$	42.9473	+	24.7956i	1.40453	+	0.810904i
$936$	−6.36486	+	6.08239i	−0.208042	+	0.198809i
$937$	1.88936	−	17.9761i	0.0617227	−	0.587252i	−0.919327	−	0.393495i	$-0.871266\pi$
$937$	1.88936	−	17.9761i	0.0617227	−	0.587252i	0.981049	−	0.193757i	$-0.0620675\pi$
$938$	−33.1844	+	3.48782i	−1.08351	+	0.113881i
$939$	22.6627	−	36.0575i	0.739569	−	1.17669i
$940$	14.7049	−	45.2571i	0.479622	−	1.47612i
$941$	−4.80441	−	3.49061i	−0.156619	−	0.113791i	0.506715	−	0.862113i	$-0.330859\pi$
$941$	−4.80441	−	3.49061i	−0.156619	−	0.113791i	−0.663335	+	0.748323i	$0.730859\pi$
$942$	0.197738	+	2.93830i	0.00644264	+	0.0957350i
$943$	−19.9427	−	17.9565i	−0.649425	−	0.584745i
$944$	−2.95940	+	6.64693i	−0.0963203	+	0.216339i
$945$	75.8845	+	8.57884i	2.46852	+	0.279070i
$946$	−1.77109	−	5.45085i	−0.0575830	−	0.177222i
$947$	−17.5047	+	12.7179i	−0.568825	+	0.413275i	−0.834678	−	0.550738i	$-0.814346\pi$
$947$	−17.5047	+	12.7179i	−0.568825	+	0.413275i	0.265853	+	0.964014i	$0.414346\pi$
$948$	−1.43016	+	3.89755i	−0.0464493	+	0.126586i
$949$	−6.79104	−	7.54222i	−0.220447	−	0.244831i
$950$	35.8965	−	49.4072i	1.16463	−	1.60298i
$951$	−3.71110	−	55.1454i	−0.120341	−	1.78821i
$952$	−10.2101	+	22.9323i	−0.330912	+	0.743240i
$953$	−6.27380	+	4.55818i	−0.203228	+	0.147654i	−0.684745	−	0.728783i	$-0.740086\pi$
$953$	−6.27380	+	4.55818i	−0.203228	+	0.147654i	0.481516	+	0.876437i	$0.340086\pi$
$954$	−1.24102	+	0.959166i	−0.0401794	+	0.0310542i
$955$	−20.3015	−	35.1633i	−0.656942	−	1.13786i
$956$	1.53695	+	2.66208i	0.0497086	+	0.0860978i
$957$	1.35746	−	5.38440i	0.0438806	−	0.174053i
$958$	−4.24353	−	0.901990i	−0.137102	−	0.0291420i
$959$	44.1158	−	9.37711i	1.42457	−	0.302803i
$960$	6.42185	−	2.57506i	0.207264	−	0.0831097i
$961$	−30.8680	+	2.85732i	−0.995743	+	0.0921715i
$962$			0.790448i			0.0254851i
$963$	46.5556	+	31.7580i	1.50023	+	1.02339i
$964$	−14.9011	−	13.4170i	−0.479931	−	0.432132i
$965$	5.85173	+	13.1432i	0.188374	+	0.423095i
$966$	−28.3874	+	11.3829i	−0.913348	+	0.366238i
$967$	−2.61976	−	1.51252i	−0.0842457	−	0.0486393i	0.457285	−	0.889320i	$-0.348822\pi$
$967$	−2.61976	−	1.51252i	−0.0842457	−	0.0486393i	−0.541531	+	0.840681i	$0.682155\pi$
$968$	3.12749	+	7.02446i	0.100521	+	0.225775i
$969$	58.2375	−	30.7701i	1.87086	−	0.988479i
$970$	51.8123	+	23.0683i	1.66359	+	0.740680i
$971$	27.5978	−	24.8492i	0.885655	−	0.797447i	−0.0945319	−	0.995522i	$-0.530135\pi$
$971$	27.5978	−	24.8492i	0.885655	−	0.797447i	0.980187	+	0.198074i	$0.0634688\pi$
$972$	−3.57289	−	15.1735i	−0.114600	−	0.486690i
$973$	14.6147	+	68.7569i	0.468527	+	2.20425i
$974$	3.71652	−	4.12762i	0.119085	−	0.132257i
$975$	−29.6365	+	47.1531i	−0.949126	+	1.51011i
$976$	4.26676	+	3.84181i	0.136576	+	0.122973i
$977$	−14.2634	−	12.8429i	−0.456328	−	0.410880i	0.408649	−	0.912692i	$-0.366000\pi$
$977$	−14.2634	−	12.8429i	−0.456328	−	0.410880i	−0.864977	+	0.501812i	$0.832667\pi$
$978$	9.30155	+	17.6047i	0.297431	+	0.562936i
$979$	−13.4908	+	14.9831i	−0.431168	+	0.478861i
$980$	5.42873	+	25.5402i	0.173414	+	0.815851i
$981$	8.35152	−	1.12917i	0.266643	−	0.0360517i
$982$	30.1143	−	27.1151i	0.960987	−	0.865277i
$983$	−6.98951	−	3.11193i	−0.222931	−	0.0992551i	0.292232	−	0.956347i	$-0.405602\pi$
$983$	−6.98951	−	3.11193i	−0.222931	−	0.0992551i	−0.515163	+	0.857092i	$0.672269\pi$
$984$	8.19959	+	5.15357i	0.261393	+	0.164290i
$985$	7.31178	+	16.4225i	0.232973	+	0.523265i
$986$	10.4109	+	6.01074i	0.331551	+	0.191421i
$987$	10.7619	−	75.1466i	0.342553	−	2.39194i
$988$	6.65277	+	14.9424i	0.211653	+	0.475380i
$989$	11.2345	+	10.1156i	0.357237	+	0.321657i
$990$	−9.45607	−	19.6483i	−0.300534	−	0.624462i
$991$			6.57463i			0.208850i	0.994533	+	0.104425i	$0.0333002\pi$
$991$			6.57463i			0.208850i	−0.994533	+	0.104425i	$0.966700\pi$
$992$	−3.00337	−	4.68826i	−0.0953572	−	0.148852i
$993$	−24.7114	−	19.4110i	−0.784191	−	0.615990i
$994$	−8.84781	+	1.88066i	−0.280635	+	0.0596509i
$995$	32.1486	+	6.83339i	1.01918	+	0.216633i
$996$	−10.3972	−	10.0932i	−0.329446	−	0.319814i
$997$	−5.28352	−	9.15132i	−0.167331	−	0.289825i	0.770150	−	0.637863i	$-0.220181\pi$
$997$	−5.28352	−	9.15132i	−0.167331	−	0.289825i	−0.937481	+	0.348038i	$0.886848\pi$
$998$	−13.8298	−	23.9538i	−0.437773	−	0.758246i
$999$	−1.20656	−	0.709302i	−0.0381740	−	0.0224413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.bd.a.389.4	yes	256
9.5	odd	6		558.2.bh.a.203.27	yes	256
31.11	odd	30		558.2.bh.a.11.27	yes	256
279.104	even	30	inner	558.2.bd.a.383.4	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.bd.a.383.4	✓	256	279.104	even	30	inner
558.2.bd.a.389.4	yes	256	1.1	even	1	trivial
558.2.bh.a.11.27	yes	256	31.11	odd	30
558.2.bh.a.203.27	yes	256	9.5	odd	6

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.bd (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743145 + 0.669131i) q^{2} +(-1.32974 + 1.10986i) q^{3} +(0.104528 - 0.994522i) q^{4} +3.99463i q^{5} +(0.245544 - 1.71456i) q^{6} +(-2.97653 - 2.16258i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.536406 - 2.95166i) q^{9} +(-2.67293 - 2.96858i) q^{10} +(-0.190195 + 1.80959i) q^{11} +(0.964788 + 1.43847i) q^{12} +(-2.79097 + 0.906841i) q^{13} +(3.65904 - 0.384581i) q^{14} +(-4.43349 - 5.31180i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-6.23297 - 2.77510i) q^{17} +(1.57642 + 2.55243i) q^{18} +(5.45186 - 1.15883i) q^{19} +(3.97274 + 0.417552i) q^{20} +(6.35817 - 0.427883i) q^{21} +(-1.06951 - 1.47205i) q^{22} +(4.38448 + 1.95210i) q^{23} +(-1.67950 - 0.423419i) q^{24} -10.9570 q^{25} +(1.46730 - 2.54144i) q^{26} +(2.56265 + 4.52027i) q^{27} +(-2.46186 + 2.73417i) q^{28} +(1.17897 + 1.30938i) q^{29} +(6.84902 + 0.980857i) q^{30} +(-0.256868 - 5.56184i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.75548 - 2.61737i) q^{33} +(6.48890 - 2.10837i) q^{34} +(8.63868 - 11.8901i) q^{35} +(-2.87942 - 0.842000i) q^{36} +(-0.233268 + 0.134677i) q^{37} +(-3.27611 + 4.50918i) q^{38} +(2.70479 - 4.30346i) q^{39} +(-3.23172 + 2.34798i) q^{40} +(-5.31777 - 1.72785i) q^{41} +(-4.43873 + 4.57243i) q^{42} +(2.99571 + 0.973364i) q^{43} +(1.77979 + 0.378306i) q^{44} +(11.7908 + 2.14274i) q^{45} +(-4.56451 + 1.48310i) q^{46} +(2.47676 - 11.6522i) q^{47} +(1.53143 - 0.809142i) q^{48} +(2.01988 + 6.21655i) q^{49} +(8.14266 - 7.33168i) q^{50} +(11.3682 - 3.22759i) q^{51} +(0.610138 + 2.87047i) q^{52} +(0.0546502 + 0.519962i) q^{53} +(-4.92907 - 1.64446i) q^{54} +(-7.22862 - 0.759758i) q^{55} -3.67919i q^{56} +(-5.96340 + 7.59176i) q^{57} +(-1.75230 - 0.184174i) q^{58} +(1.51276 - 7.11697i) q^{59} +(-5.74613 + 3.85397i) q^{60} +(-4.97228 - 2.87075i) q^{61} +(3.91248 + 3.96137i) q^{62} +(-7.97981 + 7.62567i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.62249 - 11.1489i) q^{65} +(3.05594 + 0.770434i) q^{66} -9.06915 q^{67} +(-3.41142 + 5.90874i) q^{68} +(-7.99677 + 2.27040i) q^{69} +(1.53625 + 14.6165i) q^{70} +(-2.44508 + 0.256988i) q^{71} +(2.70323 - 1.30098i) q^{72} +(1.40666 + 3.15942i) q^{73} +(0.0832352 - 0.256172i) q^{74} +(14.5700 - 12.1608i) q^{75} +(-0.582606 - 5.54312i) q^{76} +(4.47949 - 4.97498i) q^{77} +(0.869525 + 5.00795i) q^{78} +(1.40890 + 1.93918i) q^{79} +(0.830529 - 3.90733i) q^{80} +(-8.42454 - 3.16657i) q^{81} +(5.10803 - 2.27424i) q^{82} +(-8.18324 + 1.73940i) q^{83} +(0.239070 - 6.36807i) q^{84} +(11.0855 - 24.8984i) q^{85} +(-2.87755 + 1.28117i) q^{86} +(-3.02096 - 0.432636i) q^{87} +(-1.57578 + 0.909777i) q^{88} +(8.96437 + 6.51300i) q^{89} +(-10.1960 + 6.29719i) q^{90} +(10.2685 + 3.33644i) q^{91} +(2.39971 - 4.15641i) q^{92} +(6.51445 + 7.11070i) q^{93} +(5.95627 + 10.3166i) q^{94} +(4.62908 + 21.7781i) q^{95} +(-0.596655 + 1.62604i) q^{96} +(-12.9705 + 5.77484i) q^{97} +(-5.66075 - 3.26823i) q^{98} +(5.23925 + 1.53206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} + 4 q^{9} - 16 q^{15} + 32 q^{16} + 16 q^{18} - 4 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} - 268 q^{25} + 12 q^{26} - 18 q^{28} + 18 q^{30} + 22 q^{31} + 60 q^{33} - 4 q^{36}+ \cdots - 138 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 + 4 * q^9 - 16 * q^15 + 32 * q^16 + 16 * q^18 - 4 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 - 268 * q^25 + 12 * q^26 - 18 * q^28 + 18 * q^30 + 22 * q^31 + 60 * q^33 - 4 * q^36 + 72 * q^37 + 8 * q^39 + 6 * q^42 + 10 * q^43 - 24 * q^45 - 54 * q^47 + 10 * q^48 - 60 * q^49 + 28 * q^51 + 90 * q^53 - 96 * q^57 - 18 * q^58 + 6 * q^59 - 10 * q^60 - 42 * q^61 + 90 * q^62 + 124 * q^63 + 64 * q^64 + 120 * q^65 - 12 * q^66 - 16 * q^67 - 24 * q^69 - 6 * q^70 + 6 * q^71 + 8 * q^72 + 42 * q^73 - 48 * q^74 - 6 * q^76 - 90 * q^77 + 20 * q^78 - 10 * q^79 - 6 * q^80 + 8 * q^81 + 174 * q^83 - 2 * q^84 - 96 * q^86 + 100 * q^87 + 36 * q^89 - 176 * q^90 - 10 * q^91 + 18 * q^92 - 92 * q^93 - 150 * q^95 - 18 * q^97 + 48 * q^98 - 138 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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