mat = {{-351, -260, -148, -159,   1},
       {-197, -106,    6,   -5, 155},
       {-194, -103,    9,   -2, 158},
       {-104,  -13,   99,   88, 248},
       {  28,  119,  231,  220, 380}};
Map[Min[Abs[#]] &, Transpose[mat]]