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In this paper, we present the fast computational algorithms for the Jacobisums of orders $l^2$ and $2l^{2}$ with odd prime $l$ by formulating them interms of the minimum number of cyclotomic numbers of the corresponding orders.We also implement two additional algorithms to validate these formulae, whichare also useful for the demonstration of the minimality of cyclotomic numbersrequired.

Computation of Jacobi sums of order l^2 and 2l^2 with prime l