Trilinears           cos(A + ω) : cos(B + ω) : cos(C + ω)

                                    = sin A - sin(A + 2ω) : sin B - sin(B + 2ω) : sin C - sin(C + 2ω)
                                    = cos A + cos(A + 2ω) : cos B + cos(B + 2ω) : cos C + cos(C + 2ω) (cf. X(39))
                                    = a(a²b² + a²c² - b⁴ - c⁴) : b(b²c² + b²a² - c⁴ - a⁴) : c(c²a² + c²b² - a⁴ - b⁴)       (M. Iliev, 5/13/07)

Barycentrics    sin A cos(A + ω) : sin B cos(B + ω) : sin C cos(C + ω)

As the isogonal conjugate of a point on the circumcircle, X(511) lies on the line at infinity.

X(511) lies on these lines:
1,256    2,51    3,6    4,69 5,141    20,185    22,184    23,110    24,1092    25,394    26,206    30,512    40,1045    55,611    56,613    66,68    67,265    74,691    98,385    107,450    111,352    114,325    125,858    140,143    155,159    171,181    186,249    287,401    298,1080    299,383    343,427    381,599    549,597

X(511) = orthopoint of X(512)
X(511) = isogonal conjugate of X(98)
X(511) = isotomic conjugate of X(290)
X(511) = anticomplementary conjugate of X(147)
X(511) = complementary conjugate of X(114)
X(511) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,114), (290,2), (297,232)
X(511) = cevapoint of X(385) and X(401)
X(511) = X(I)-cross conjugate of X(J) for these (I,J): (4,114), (290,2), (297,232)
X(511) = crosspoint of X(I) and X(J) for these (I,J): (2,290), (297,325)
X(511) = crosssum of X(I) and X(J) for these (I,J): (2,385), (6,237), (11,659), (523,868)
X(511) = crossdifference of any two points on line X(6)X(523)
X(511) = X(3)-Hirst inverse of X(6)
X(511) = X(I)-line conjugate of X(J) for these (I,J): (3,6), (30,523)