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

Symbolics

Substitution:
1->114
2->121214
3->1213121312131214
4->121312131214
Abelianisation:
2 3 8 6
0 2 4 3
0 0 3 2
1 1 1 1

Characteristic polynomial:

(z4 - 8z3 + 12z2 - 8z + 1)

Eigenvalues:

6.2905 0 0 0
0 0.77526+0.63165i 0 0
0 0 0.77526-0.63165i 0
0 0 0 0.15897