lifted relations from the above. Otherwise, it is called a *non-standard* relation.

The main goal of this paper is to provide some numerical evidence concerning the (in)completeness of the standard relations. Namely, these relations in general are not enough to cover all the $\Q$-linear relation between MPVs (see Remark \[rem:Ta:bN\] and Remark \[rem:wt2\]); however, when the level is a prime $\le 47$ and weight $w=2$ using a result of Goncharov we can show that the standard relations are complete under the assumption of Grothendieck’s period conjecture (see [@Zocta]). We further find that when weight $w=2$ and $N=25$ or $N=49$, the standard relations are complete. However, when $N$ is a 2-power or 3-power or has at least two distinct prime factors, we know that the standard relations are often incomplete by comparing our results with those of Deligne and Goncharov [@DG]. Moreover, we don’t know how to obtain the non-standard relations except that when $N=4$, we discover recently that octahedral symmetry of ${{\mathbb P}}^1-(\{0,\infty\}\cup \mmu_4)$ can produce some (presumably all) new relations not covered by the standard ones (see op. cit.)

Most of the MPV identities in this paper are discovered with the help of MAPLE using symbolic computations. We have 