A Complex Puzzle

Normal sudoku rules somewhat apply.

Choose and place 6 pairwise distinct digits, each taking values of the form x+iy, where x and y are from the set [-1,0,1], such that no value may be repeated in any row, column or marked 2x3 box. The 6 digits are the same for the entire grid.

Values along a marked contour must sum to the sum of the values placed in all marked singularities contained by the contour. Singularities are given by small black dots in some cells.

Values separated by an "=" have identical moduli. Not all =s are given.

Values in a killer cage cannot repeat and sum to the given total.