  We give the first explicit computations of rational homotopy groups of spaces
of "long knots" in Euclidean spaces. We define a spectral sequence which
converges to these rational homotopy groups whose E^1 term is defined in terms
of braid Lie algebras. For odd k we establish a vanishing line for this
spectral sequence, show the Euler characteristic of the rows of this E^1 term
is zero, and make calculations of E^2 in a finite range.
