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Table 2:

Parameters from the non-coplanar analysis.
Orbital parameters          
Parameter Planet b Planet c Planet d    
m $\rm 2.64^{+0.11}_{-0.09}$  $M_{\rm Jup}$ $\rm0.78^{+0.05}_{-0.03}$  $M_{\rm Jup}$ $\rm 8.41^{+0.78}_{-0.75}$  $M_{\oplus}$    
a  (AU) $\rm0.20700^{+0.00010}_{-0.00009}$ $\rm0.13062^{+0.00005}_{-0.00005}$ $\rm0.0208069^{+0.0000004}_{-0.0000004}$    
e $\rm0.0363^{+0.0028}_{-0.0026}$ $\rm0.2683^{+0.0058}_{-0.0052}$ 0.0 (Fixed)    
$\omega$  ( $\hbox{$^\circ$ }$) $\rm 188.2^{+4.9}_{-4.0}$ $\rm 200.4^{+1.8}_{-1.9}$ 0.0 (Fixed)    
M  ( $\hbox{$^\circ$ }$) $\rm 163.1^{+4.0}_{-4.9}$ $\rm 309.1^{+1.9}_{-1.7}$ $\rm 312.2^{+4.9}_{-5.0}$    
i  ( $\hbox{$^\circ$ }$) $\rm 47.2^{+2.2}_{-2.4}$ $\rm 51.1^{+3.6}_{-3.9}$ 47.2 (Tied)    
$\Omega$  ( $\hbox{$^\circ$ }$) $\rm 252.3^{+8.4}_{-7.7}$ $\rm 249.4^{+7.1}_{-8.4}$ 252.3 (Tied)    
Astrometric parameters          
Star $\xi$ $\eta$ $\pi_{\rm abs}$ $\mu_{\alpha}$ $\mu_{\delta}$
  (arcsec) (arcsec) (mas) $\rm (mas~yr^{-1}$) $\rm (mas~yr^{-1}$)
GJ 876 $\rm 51.9001^{+0.0004}_{-0.0004}$ $\rm 730.3929^{+0.0003}_{-0.0003}$ $\rm 215.5^{+0.4}_{-0.5}$ $\rm 955.7^{+1.7}_{-1.7}$ $\rm -673.4^{+1.1}_{-1.1}$
Ref-2 $\rm -27.8463^{+0.0003}_{-0.0003}$ $\rm 767.6817^{+0.0005}_{-0.0005}$ $\rm 1.0^{+0.3}_{-0.3}$ $\rm 5.5^{+1.6}_{-1.7}$ $\rm -16.0^{+1.2}_{-1.1}$
Ref-3 $\rm -226.2855^{+0.0005}_{-0.0005}$ $\rm 759.8752^{+0.0007}_{-0.0007}$ $\rm 3.1^{+0.4}_{-0.4}$ $\rm 14.2^{+2.0}_{-2.0}$ $\rm 2.4^{+1.6}_{-1.7}$
Ref-4 $\rm -297.4706^{+0.0005}_{-0.0005}$ $\rm 639.3754^{+0.0005}_{-0.0005}$ $\rm 2.3^{+0.6}_{-0.6}$ $\rm -39.8^{+2.2}_{-2.2}$ $\rm -43.0^{+1.2}_{-1.2}$
Ref-5 $\rm 450.9640^{+0.0006}_{-0.0006}$ $\rm 635.2999^{+0.0004}_{-0.0004}$ $\rm 4.7^{+0.6}_{-0.7}$ $\rm 7.3^{+3.0}_{-3.3}$ $\rm -1.2^{+2.4}_{-2.2}$
Ref-6 $\rm 351.6679^{+0.0005}_{-0.0005}$ $\rm 594.2625^{+0.0005}_{-0.0005}$ $\rm 1.9^{+0.3}_{-0.3}$ $\rm -13.1^{+2.4}_{-2.7}$ $\rm -3.8^{+2.3}_{-2.1}$
Fit information          
Parameter Value        
$\chi ^{2}$ 855.8        
d.o.f. 841        
Radial velocity rms (m s-1) 4.2        
Astrometry rms (mas) 0.9        
Note: Planet d's inclination and longitude of the ascending node were tied to those of planet b. The orbital parameters are osculating and valid at HJD 2 452 490.0. The coordinates ($\xi$ and $\eta$) are relative positions in the reference frame of the constraint plate. To convert to the RA - Dec reference frame, the coordinates should be rotated about the inverse of the determined roll angle ( $26.07\hbox{$^\circ$ }^{~+0.04\hbox{$^\circ$ }}_{~-0.04\hbox{$^\circ$ }}$). The $\chi ^{2}$ and rms shown are for the best-fit model.

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