Improved πN partial waves,consistent with analyticity and unitarity

Partial wave dispersion relations in a new formulation and fixed-s dispersion relations are used to calculate the long range contributions to the real parts of πN amplitudes. Recent results from a double spectral function calculation are applied for constraining the imaginary parts. We propose to use the new partial waves as starting values in future phase shift analyses and to treat our prediction for the tail of high partial waves as part of the input. — The differences between our new partial waves and the Karlsruhe-Helsinki 80 and CMU-LBL 80 solutions are discussed. Concerning measurable quantities, the new parital waves lead to significant changes in the forward logarithmic slopes of differential cross sections. — Thel-dependence of our partial waves is discussed up to large values ofl. We find a systematic even-l, odd-l splitting at all energies.