\begin{table}%t4
  \caption{\label{tab:table4}Direction cosines relative to the ERF after the application of the local astrometric corrections$^{a}$. }
\small%\centerline
 {
\begin{tabular}{lrccccc}
\hline \hline
      Solution & $N$ & A1 & A2 & A3 & A4 & A5 \\
      \hline 
BU6 & 2616 & --33.7 $\pm$ 6.3 & --8.0 $\pm$ 6.1 & 50.8 $\pm$ 5.3 & 40.5 $\pm$ 10.7 & 2.6 $\pm$ 5.3 \\
BN6 & 244 & --5.5 $\pm$ 12.9 & 31.8 $\pm$ 14.1 & 123.0 $\pm$ 25.2  & 1.5 $\pm$ 12.8 & \\
BT6 & 3764 & --23.8 $\pm$ 5.1 & 1.5 $\pm$ 4.7 & 23.7 $\pm$ 4.6 & 27.5 $\pm$ 9.7 & --21.0 $\pm$ 4.3 \\
BU4 & 2522 & --37.5 $\pm$ 6.3 & --4.9 $\pm$ 6.2 & 48.6 $\pm$ 5.4 & 42.1 $\pm$ 10.7 & 0.0 $\pm$ 5.4 \\
BN4 & 240 & --0.4 $\pm$ 12.9 & 34.7 $\pm$ 14.1 & 118.9 $\pm$ 25.4 & --0.3 $\pm$ 12.8 & \\
BT4 & 3762 & --24.6 $\pm$ 5.1 & 1.4 $\pm$ 4.7 & 24.3 $\pm$ 4.6 & 24.7 $\pm$ 9.6 & --21.7 $\pm$ 4.3 \\
GU6 & 3238 & --7.0 $\pm$ 5.8 & --3.1 $\pm$ 5.3 & 30.4 $\pm$ 4.7 & 100.8 $\pm$ 9.3 & 15.2 $\pm$ 4.8 \\
GN6 & 300 & --7.2 $\pm$ 13.2 & 16.3 $\pm$ 14.2 & --43.4 $\pm$ 25.1 & --4.7 $\pm$ 13.1 & \\
GT6 & 3940 & --4.0 $\pm$ 4.7 & --4.9 $\pm$ 4.4 & 8.7 $\pm$ 4.3 & 30.2 $\pm$  8.7 & --6.1 $\pm$ 4.0 \\
GU4 & 3240 & --7.7 $\pm$ 5.8 & --2.5 $\pm$ 5.3 & 29.4 $\pm$ 4.7 & 99.1 $\pm$ 9.3 & 14.7 $\pm$ 4.8 \\
GN4 & 308 & --7.1 $\pm$ 13.1 & 15.7 $\pm$ 14.0 & --40.4 $\pm$ 24.7 & --6.8 $\pm$ 12.9 & \\
GT4 & 3938 & --3.7 $\pm$ 4.7 & --6.0 $\pm$ 4.4 & 8.7 $\pm$ 4.3 & 30.1 $\pm$ 8.7 & --6.3 $\pm$ 4.0 \\
SU6 & 480 & --5.3 $\pm$ 4.7 & --14.6 $\pm$ 4.8 & --4.8 $\pm$ 3.7 & 16.6 $\pm$ 4.1 & \\
SN6 & 74 & --5.0 $\pm$ 11.6 & 14.8 $\pm$ 13.9 & 32.0 $\pm$ 17.8 & 9.8 $\pm$ 13.1 & \\
ST6 & 600 & --13.9 $\pm$ 5.5 & --14.6 $\pm$ 6.0 & --5.1 $\pm$ 4.9 & 20.1 $\pm$ 5.3 & \\
SU4 & 478 & --5.5 $\pm$ 4.5 & --12.8 $\pm$ 4.6 & --5.2 $\pm$ 3.5 & 16.3 $\pm$ 4.0 & \\
SN4 & 74 & --6.2 $\pm$ 11.4 & 13.1 $\pm$ 13.8 & 33.2 $\pm$ 17.6 & 9.5 $\pm$ 13.0 & \\
ST4 & 600 & --14.3 $\pm$ 5.5 & --14.2 $\pm$ 6.0 & --4.7 $\pm$ 4.9 & 19.2 $\pm$  5.3 & \\
\hline 
      \end{tabular}}
  \medskip
$^{a}$ Direction cosines A1, A2, and A3 from the comparison of the equatorial positions as found for each family of solutions and as given by the radio interferometry for the ERF~objects. The equatorial bias~A4 (north of declination~$-$20$^\circ$) and A5 (south of declination~$-$20$^\circ$), when applicable, are also presented. The solutions nomenclature is formed by one letter designating the quasar position input catalog, followed by one letter designating the stellar reference frame, 
and by the codes~$6$ and~$4$ informing whether the algorithm is of the six or four-parameter models.
$N$~is the number of equations used to derive the direction cosines and equatorial biases. All angular values are in milli-arcsec.
\end{table}