  A table of the families of alternating knots formed by conways is presented.
The Conway's function is shown with the use of linear algebra in terms of
natural numbers, called conways, that represent the number of crossings along a
direction, as it was used by J. Conway for the classification of knots. Colored
figures and tangles show the parts of the knots or tangles with a definite
handedness: all the colored parts of the knot family are associated to a
particular orientation. For example all the colored conways have a right hand
screw thread, and all the white conways have the opposite handedness. Figures
for six conways were colored with two different colors for forty two families
in order to show the dissection of the knot in two tangles corresponding to a
particular factorization of the Conway's function. The Conway's function of
each family is expressed as the internal product of two vectors corresponding
to each of two colored family 2-tangles, and with a full factorization which is
not unique.
