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X(2), X(3), X(6), X(13), X(15), X(18), X(298), X(470), X(1082), X(2992), X(5240), X(11127), X(11131), X(30471) midpoints of ABC imaginary foci of the Simmons inconic with real foci X(13), X(15) 3 (always real) mates of X(370) (blue points), see Table 10 

K341a is remarkable since it contains a good number of familiar centers and it is also anharmonically equivalent to the Neuberg cubic. See Table 20. It has the same asymptotic directions as K1053a = pK(X2, X621) which is its anticomplement. It meets the circumcircle at the same points as pK(X6, X298). It is the isotomic transform of K342a = pK(X300, X300), a member of the class CL007. Its isogonal transform is K1145a = pK(X3457, X13) = X(13) x K341a = spK(X298, X396). Simmons inconics are studied here. 
