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too complicated to be written here. Click on the link to download a text file. 

X(3), X(4), X(20) antipoints, see Table 77 

See Q125 for general explanations where Q131 is Q(X2071). The radial center is X(3). The tangent at X(3) is the Euler line. Any line passing through O meets Q131 again at three (real or not, distinct or not) points M1, M2, M3 such that the centroid/isobarycenter of {O, M1, M2, M3} is O. This is obviously true with the Euler line. 
