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

Symbolics

Substitution:
1->132314
2->13232314
3->13314
4->14
Abelianisation:
2 2 2 1
1 2 0 0
2 3 2 0
1 1 1 1

Characteristic polynomial:

(z4 - 7z3 + 11z2 - 7z + 1)

Eigenvalues:

5.107 0 0 0
0 0.84861+0.52902i 0 0
0 0 0.84861-0.52902i 0
0 0 0 0.19581