Joe Root to an outstanding innings of 156 runs from Aaron Finch. Root came in with England 37/3 and he managed to score 90* off 49 balls but England lost by 39 runs. In the second T20I Joe batted at number 7 but only faced 1 ball scoring 1 run before England's innings finished. England won the match and drew the series, Root finished with 91 runs (both matches he was not out) and 1 wicket. The third ODI was abandoned in England's 15th over, Root had made 12 runs before being caught. In the fourth ODI Root was bowled for 0,
Root of unity modulo n a primitive formula_25-th root of unity because there is the smaller exponent formula_72. That is, by exponentiating "x" one can obtain formula_84 different primitive "k"-th roots of unity, but these may not be all such roots. However, finding all of them is not so easy. You may want to know, in what integer residue class rings you have a primitive "k"-th root of unity. You need it for instance if you want to compute a Discrete Fourier Transform (more precisely a Number theoretic transform) of a formula_25-dimensional integer vector. In order to perform the inverse transform, you also need to