self-test passed A: Klein and cyclic 2-part identities verified on 200 random sign arrays B: Z[C_9], x x* = 9: 34802 candidates, 108 solutions, Delta orders {1: 36, 3: 72} B: Z[i][C_9], x x* = 9: 32041636 candidates, 432 solutions, Delta orders {1: 144, 3: 288} C: two (36,15,6) Hadamard difference sets verified (C2xC2xC3xC3 and C4xC3xC3) C: Klein, projected to C2xC2xC3: Delta(c), Delta(d_i) = [([-1, 0], 2), ([1, 0], 1), ([-1, 0], 2), ([-1, 0], 2)] C: R_i = [[-1, 0], [1, 0], [1, 0]] (the argument needs all R_i = 1; it fails, as it must) D: x = -i + (1+i)X + (1+i)X**2 in Z[i][C_3], x x* = 5; x(1)/x(rho) integral? False E: abelian groups of order 4u**2, u odd in [3,105]: 424 no cyclic odd Sylow (Lander silent): 204 covered, all odd Sylow cyclic (unconditional): 104 covered via self-conjugacy: 53 Lander hypothesis but not covered: 63 F: u odd, not a prime power, u <= 200000, not excluded by the exponent bound and the field descent bound: circulant C_{4u**2}: [11715, 16401, 82005] Klein C2 x C_{2u**2}: [11715, 16401, 82005] all checks passed in 47.1 s