They are complex and linear in the variables. Say six of those equations (out of 1549) are like:
$a_{\{1,2\}}=a_{\{2,1\}}+i,a_{\{1,3\}}=a_{\{3,1\}},a_{\{1,4\}}=a_{\{4,1\}},a_{\{1,5\}}=a_{\{5,1\}},a_{\{1,6\}}=a_{\{6,1\}},a_{\{2,1\}}=a_{\{1,2\}}-i,a_{\{2,3\}}=a_{\{3,2\}}$
while solving for all
$a_{\{\cdot,\cdot\}}$ totaling to about 1329.