K = {*12341-12-13-14-1}

Symbolics

Substitution:
1->142324
2->1423242324
3->1423323324
4->1423324
Abelianisation:
1 1 1 1
2 4 3 2
1 2 4 2
2 3 2 2

Characteristic polynomial:

(z4 - 11z3 + 21z2 - 11z + 1)

Eigenvalues:

8.7397 0 0 0
0 1.4618 0 0
0 0 0.68408 0
0 0 0 0.11442

Realisations:

Indices:Realisations:
3x2:realisation