  We search points in a Vogel plane with regular universal expression for
character of adjoint representation. This gives seven patterns of singularities
cancellation, each giving a certain Diophantine equation of third order on
three variables. Solutions of these equations are classical series of simple
Lie algebras (including an "odd symplectic" one), $D_{2,1,\lambda}$
superalgebra, the straight line of three-dimensional algebras, and a number of
isolated solutions, including exceptional simple Lie algebras. One of these
Diophantine equations, namely knm=4k+4n+2m+12 contains all simple Lie algebras,
except SO(2N+1). Isolated solutions contain, beside exceptional simple Lie
algebras, so called $E_{71/2}$ algebra and also two other similar (unknown)
objects with positive dimensions. In addition, there are 47 isolated solutions
in "unphysical semiplane" with negative dimensions. Isolated solutions mainly
lie on a few straight lines in Vogel plane. All solutions give an integers in
universal dimension formulae for first three symmetric powers of adjoint
representation.
