{\displaystyle {\begin{array}{llll}4^{0}&=1&=0\times 7+1&\equiv 1{\pmod {7}}\\4^{1}&=4&=0\times 7+4&\equiv 4{\pmod {7}}\\4^{2}&=16&=2\times 7+2&\equiv 2{\pmod {7}}\\4^{3}&=64&=9\times 7+1&\equiv 1{\pmod {7}}\\4^{4}&=256&=36\times 7+4&\equiv 4{\pmod {7}}\\4^{5}&=1024&=146\times 7+2&\equiv 2{\pmod {7}}\\\vdots \end{array}}}