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

Symbolics

Substitution:
1->114
2->121214
3->12131213121312131214
4->1213121312131214
Abelianisation:
2 3 10 8
0 2 5 4
0 0 4 3
1 1 1 1

Characteristic polynomial:

(z4 - 9z3 + 13z2 - 9z + 1)

Eigenvalues:

7.4064 0 0 0
0 0.72931+0.68418i 0 0
0 0 0.72931-0.68418i 0
0 0 0 0.13502