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

Symbolics

Substitution:
1->14
2->14224
3->14232324
4->142324
Abelianisation:
1 1 1 1
0 2 3 2
0 0 2 1
1 2 2 2

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