A new numeric-analytical method for calculating the spectral-angular characteristics of coherent radiation, occurring under the distribution of relativistic electrons in the atomic chain is developed. Calculation of the Fourier integrals which is the most difficult and important stage of the problem is performed analytically using the particle trajectory which is determined numerically from the motion equations in the real chain potential. Analysis of radiation features is conducted with regard to non-dipolarity and quantum recoil under irradiation. 13 refs.; 5 figs.