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Triangles containing the origin II

Problem 456

Published on Sunday, 26th January 2014, 01:00 am; Solved by 231

Define:
xn = (1248n mod 32323) - 16161
yn = (8421n mod 30103) - 15051
Pn = {(x1, y1), (x2, y2), ..., (xn, yn)}

For example, P8 = {(-14913, -6630), (-10161, 5625), (5226, 11896), (8340, -10778), (15852, -5203), (-15165, 11295), (-1427, -14495), (12407, 1060)}.

Let C(n) be the number of triangles whose vertices are in Pn which contain the origin in the interior.

Examples:
C(8) = 20
C(600) = 8950634
C(40 000) = 2666610948988

Find C(2 000 000).