Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q2 of degree 16

j Ramification Polygon Slopes Residual Polynomials #A Polynomials Extensions
1{(1,1), (16,0)}[ 1/15 ](z+1)11161616
3{(1,3), (16,0)}[ 1/5 ](z3+1)11161632
{(1,3), (2,2), (16,0)}[ 1, 1/7 ](z+1, z2+1)121616
5{(1,5), (16,0)}[ 1/3 ](z5+1)11161664
{(1,5), (2,2), (16,0)}[ 3, 1/7 ](z+1, z2+1)143232
{(1,5), (4,4), (16,0)}[ 1/3 ](z5+z+1)111616
7{(1,7), (16,0)}[ 7/15 ](z+1)111616128
{(1,7), (2,2), (16,0)}[ 5, 1/7 ](z+1, z2+1)186464
{(1,7), (2,6), (16,0)}[ 1, 3/7 ](z+1, z2+1)121616
{(1,7), (4,4), (16,0)}[ 1, 1/3 ](z3+1, z4+1)121616
{(1,7), (2,6), (4,4), (16,0)}[ 1, 1/3 ](z3+z+1, z4+1)111616
9{(1,9), (16,0)}[ 3/5 ](z3+1)123232256
{(1,9), (2,2), (16,0)}[ 7, 1/7 ](z+1, z2+1)116128128
{(1,9), (2,6), (16,0)}[ 3, 3/7 ](z+1, z2+1)143232
{(1,9), (4,4), (16,0)}[ 5/3, 1/3 ](z+1, z4+1)123232
{(1,9), (2,6), (4,4), (16,0)}[ 3, 1, 1/3 ](z+1, z2+1, z4+1)18 [!]3232
11{(1,11), (16,0)}[ 11/15 ](z+1)123232512
{(1,11), (2,2), (16,0)}[ 9, 1/7 ](z+1, z2+1)132256256
{(1,11), (2,6), (16,0)}[ 5, 3/7 ](z+1, z2+1)186464
{(1,11), (2,10), (16,0)}[ 1, 5/7 ](z+1, z2+1)143232
{(1,11), (4,4), (16,0)}[ 7/3, 1/3 ](z+1, z4+1)146464
{(1,11), (2,6), (4,4), (16,0)}[ 5, 1, 1/3 ](z+1, z2+1, z4+1)116 [!]6464
13{(1,13), (16,0)}[ 13/15 ](z+1)1464641024
{(1,13), (2,2), (16,0)}[ 11, 1/7 ](z+1, z2+1)164512512
{(1,13), (2,6), (16,0)}[ 7, 3/7 ](z+1, z2+1)116128128
{(1,13), (2,10), (16,0)}[ 3, 5/7 ](z+1, z2+1)186464
{(1,13), (4,4), (16,0)}[ 3, 1/3 ](z3+1, z4+1)186464
{(1,13), (2,6), (4,4), (16,0)}[ 7, 1, 1/3 ](z+1, z2+1, z4+1)132 [!]128128
{(1,13), (2,10), (4,4), (16,0)}[ 3, 1/3 ](z3+z+1, z4+1)146464
15{(1,15), (16,0)}[ 1 ](z15+1)1216162048
{(1,15), (2,2), (16,0)}[ 13, 1/7 ](z+1, z2+1)112810241024
{(1,15), (2,6), (16,0)}[ 9, 3/7 ](z+1, z2+1)132256256
{(1,15), (2,10), (16,0)}[ 5, 5/7 ](z+1, z2+1)116128128
{(1,15), (2,14), (16,0)}[ 1 ](z15+z+1)111616
{(1,15), (4,4), (16,0)}[ 11/3, 1/3 ](z+1, z4+1)18128128
{(1,15), (2,6), (4,4), (16,0)}[ 9, 1, 1/3 ](z+1, z2+1, z4+1)164 [!]256256
{(1,15), (2,10), (4,4), (16,0)}[ 5, 3, 1/3 ](z+1, z2+1, z4+1)132 [!]128128
{(1,15), (8,8), (16,0)}[ 1 ](z15+z7+1)111616
17{(1,17), (16,0)}[ 17/15 ](z+1)1232324096
{(1,17), (2,2), (16,0)}[ 15, 1/7 ](z+1, z2+1)1256 [!]20482048
{(1,17), (2,6), (16,0)}[ 11, 3/7 ](z+1, z2+1)164512512
{(1,17), (2,10), (16,0)}[ 7, 5/7 ](z+1, z2+1)132256256
{(1,17), (2,14), (16,0)}[ 3, 1 ](z+1, z14+1)18 [!]3232
{(1,17), (4,4), (16,0)}[ 13/3, 1/3 ](z+1, z4+1)116256256
{(1,17), (2,6), (4,4), (16,0)}[ 11, 1, 1/3 ](z+1, z2+1, z4+1)1128 [!]512512
{(1,17), (2,10), (4,4), (16,0)}[ 7, 3, 1/3 ](z+1, z2+1, z4+1)164 [!]256256
{(1,17), (8,8), (16,0)}[ 9/7, 1 ](z+1, z8+1)14 [!]3232
18{(1,18), (2,2), (16,0)}[ 16, 1/7 ](z+1, z2+1)1512 [!]409640964096
19{(1,19), (16,0)}[ 19/15 ](z+1)1464644096
{(1,19), (2,6), (16,0)}[ 13, 3/7 ](z+1, z2+1)1128 [!]10241024
{(1,19), (2,10), (16,0)}[ 9, 5/7 ](z+1, z2+1)164512512
{(1,19), (2,14), (16,0)}[ 5, 1 ](z+1, z14+1)116 [!]6464
{(1,19), (4,4), (16,0)}[ 5, 1/3 ](z3+1, z4+1)132256256
{(1,19), (2,6), (4,4), (16,0)}[ 13, 1, 1/3 ](z+1, z2+1, z4+1)1256 [!]10241024
{(1,19), (2,10), (4,4), (16,0)}[ 9, 3, 1/3 ](z+1, z2+1, z4+1)1128 [!]512512
{(1,19), (2,14), (4,4), (16,0)}[ 5, 1/3 ](z3+z+1, z4+1)116256256
{(1,19), (8,8), (16,0)}[ 11/7, 1 ](z+1, z8+1)18 [!]6464
21{(1,21), (16,0)}[ 7/5 ](z3+1)1464648192
{(1,21), (2,6), (16,0)}[ 15, 3/7 ](z+1, z2+1)1256 [!]20482048
{(1,21), (2,10), (16,0)}[ 11, 5/7 ](z+1, z2+1)1128 [!]10241024
{(1,21), (2,14), (16,0)}[ 7, 1 ](z+1, z14+1)132 [!]128128
{(1,21), (2,18), (16,0)}[ 3, 9/7 ](z+1, z2+1)186464
{(1,21), (4,4), (16,0)}[ 17/3, 1/3 ](z+1, z4+1)132512512
{(1,21), (2,6), (4,4), (16,0)}[ 15, 1, 1/3 ](z+1, z2+1, z4+1)1512 [!]20482048
{(1,21), (2,10), (4,4), (16,0)}[ 11, 3, 1/3 ](z+1, z2+1, z4+1)1256 [!]10241024
{(1,21), (2,14), (4,4), (16,0)}[ 7, 5, 1/3 ](z+1, z2+1, z4+1)1128 [!]512512
{(1,21), (8,8), (16,0)}[ 13/7, 1 ](z+1, z8+1)18 [!]6464
{(1,21), (2,18), (8,8), (16,0)}[ 3, 5/3, 1 ](z+1, z2+1, z8+1)116 [!]6464
22{(1,22), (2,6), (16,0)}[ 16, 3/7 ](z+1, z2+1)1512 [!]409640968192
{(1,22), (2,6), (4,4), (16,0)}[ 16, 1, 1/3 ](z+1, z2+1, z4+1)11024 [!]40964096
23{(1,23), (16,0)}[ 23/15 ](z+1)181281288192
{(1,23), (2,10), (16,0)}[ 13, 5/7 ](z+1, z2+1)1256 [!]20482048
{(1,23), (2,14), (16,0)}[ 9, 1 ](z+1, z14+1)164 [!]256256
{(1,23), (2,18), (16,0)}[ 5, 9/7 ](z+1, z2+1)116128128
{(1,23), (4,4), (16,0)}[ 19/3, 1/3 ](z+1, z4+1)16410241024
{(1,23), (2,10), (4,4), (16,0)}[ 13, 3, 1/3 ](z+1, z2+1, z4+1)1512 [!]20482048
{(1,23), (2,14), (4,4), (16,0)}[ 9, 5, 1/3 ](z+1, z2+1, z4+1)1256 [!]10241024
{(1,23), (4,12), (16,0)}[ 11/3, 1 ](z+1, z12+1)116 [!]128128
{(1,23), (2,18), (4,12), (16,0)}[ 5, 3, 1 ](z+1, z2+1, z12+1)164 [!]128128
{(1,23), (8,8), (16,0)}[ 15/7, 1 ](z+1, z8+1)116 [!]128128
{(1,23), (2,18), (8,8), (16,0)}[ 5, 5/3, 1 ](z+1, z2+1, z8+1)132 [!]128128
25{(1,25), (16,0)}[ 5/3 ](z5+1)14646416384
{(1,25), (2,10), (16,0)}[ 15, 5/7 ](z+1, z2+1)1512 [!]40964096
{(1,25), (2,14), (16,0)}[ 11, 1 ](z+1, z14+1)1128 [!]512512
{(1,25), (2,18), (16,0)}[ 7, 9/7 ](z+1, z2+1)132 [!]256256
{(1,25), (2,22), (16,0)}[ 3, 11/7 ](z+1, z2+1)116128128
{(1,25), (4,4), (16,0)}[ 7, 1/3 ](z3+1, z4+1)1128 [!]10241024
{(1,25), (2,10), (4,4), (16,0)}[ 15, 3, 1/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,25), (2,14), (4,4), (16,0)}[ 11, 5, 1/3 ](z+1, z2+1, z4+1)1512 [!]20482048
{(1,25), (2,18), (4,4), (16,0)}[ 7, 1/3 ](z3+z+1, z4+1)16410241024
{(1,25), (4,12), (16,0)}[ 13/3, 1 ](z+1, z12+1)132 [!]256256
{(1,25), (2,18), (4,12), (16,0)}[ 7, 3, 1 ](z+1, z2+1, z12+1)1128 [!]256256
{(1,25), (8,8), (16,0)}[ 17/7, 1 ](z+1, z8+1)116 [!]128128
{(1,25), (2,18), (8,8), (16,0)}[ 7, 5/3, 1 ](z+1, z2+1, z8+1)164 [!]256256
{(1,25), (2,22), (8,8), (16,0)}[ 3, 7/3, 1 ](z+1, z2+1, z8+1)132 [!]128128
26{(1,26), (2,10), (16,0)}[ 16, 5/7 ](z+1, z2+1)11024 [!]8192819216384
{(1,26), (2,10), (4,4), (16,0)}[ 16, 3, 1/3 ](z+1, z2+1, z4+1)12048 [!]81928192
27{(1,27), (16,0)}[ 9/5 ](z3+1)1812812816384
{(1,27), (2,14), (16,0)}[ 13, 1 ](z+1, z14+1)1256 [!]10241024
{(1,27), (2,18), (16,0)}[ 9, 9/7 ](z+1, z2+1)164 [!]512512
{(1,27), (2,22), (16,0)}[ 5, 11/7 ](z+1, z2+1)132 [!]256256
{(1,27), (4,4), (16,0)}[ 23/3, 1/3 ](z+1, z4+1)112820482048
{(1,27), (2,14), (4,4), (16,0)}[ 13, 5, 1/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,27), (2,18), (4,4), (16,0)}[ 9, 7, 1/3 ](z+1, z2+1, z4+1)1512 [!]20482048
{(1,27), (4,12), (16,0)}[ 5, 1 ](z3+1, z12+1)164 [!]256256
{(1,27), (2,18), (4,12), (16,0)}[ 9, 3, 1 ](z+1, z2+1, z12+1)1256 [!]512512
{(1,27), (2,22), (4,12), (16,0)}[ 5, 1 ](z3+z+1, z12+1)132 [!]256256
{(1,27), (8,8), (16,0)}[ 19/7, 1 ](z+1, z8+1)132 [!]256256
{(1,27), (2,18), (8,8), (16,0)}[ 9, 5/3, 1 ](z+1, z2+1, z8+1)1128 [!]512512
{(1,27), (2,22), (8,8), (16,0)}[ 5, 7/3, 1 ](z+1, z2+1, z8+1)164 [!]256256
29{(1,29), (16,0)}[ 29/15 ](z+1)1812812832768
{(1,29), (2,14), (16,0)}[ 15, 1 ](z+1, z14+1)1512 [!]20482048
{(1,29), (2,18), (16,0)}[ 11, 9/7 ](z+1, z2+1)1128 [!]10241024
{(1,29), (2,22), (16,0)}[ 7, 11/7 ](z+1, z2+1)164 [!]512512
{(1,29), (2,26), (16,0)}[ 3, 13/7 ](z+1, z2+1)116 [!]128128
{(1,29), (2,14), (4,4), (16,0)}[ 15, 5, 1/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,29), (2,18), (4,4), (16,0)}[ 11, 7, 1/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,29), (2,20), (4,4), (16,0)}[ 9, 8, 1/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,29), (4,12), (16,0)}[ 17/3, 1 ](z+1, z12+1)164 [!]512512
{(1,29), (2,18), (4,12), (16,0)}[ 11, 3, 1 ](z+1, z2+1, z12+1)1512 [!]10241024
{(1,29), (2,22), (4,12), (16,0)}[ 7, 5, 1 ](z+1, z2+1, z12+1)1256 [!]512512
{(1,29), (8,8), (16,0)}[ 3, 1 ](z7+1, z8+1)132 [!]128128
{(1,29), (2,18), (8,8), (16,0)}[ 11, 5/3, 1 ](z+1, z2+1, z8+1)1256 [!]10241024
{(1,29), (2,22), (8,8), (16,0)}[ 7, 7/3, 1 ](z+1, z2+1, z8+1)1128 [!]512512
{(1,29), (2,26), (8,8), (16,0)}[ 3, 1 ](z7+z+1, z8+1)116 [!]128128
30{(1,30), (2,14), (16,0)}[ 16, 1 ](z+1, z14+1)11024 [!]4096409632768
{(1,30), (2,14), (4,4), (16,0)}[ 16, 5, 1/3 ](z+1, z2+1, z4+1)14096 [!]1638416384
31{(1,31), (2,18), (16,0)}[ 13, 9/7 ](z+1, z2+1)12562048204832768
{(1,31), (2,22), (16,0)}[ 9, 11/7 ](z+1, z2+1)112810241024
{(1,31), (2,26), (16,0)}[ 5, 13/7 ](z+1, z2+1)132 [!]256256
{(1,31), (2,18), (4,4), (16,0)}[ 13, 7, 1/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,31), (2,20), (4,4), (16,0)}[ 11, 8, 1/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,31), (4,12), (16,0)}[ 19/3, 1 ](z+1, z12+1)1128 [!]10241024
{(1,31), (2,18), (4,12), (16,0)}[ 13, 3, 1 ](z+1, z2+1, z12+1)11024 [!]20482048
{(1,31), (2,22), (4,12), (16,0)}[ 9, 5, 1 ](z+1, z2+1, z12+1)1512 [!]10241024
{(1,31), (4,20), (16,0)}[ 11/3, 5/3 ](z+1, z4+1)116256256
{(1,31), (2,26), (4,20), (16,0)}[ 5, 3, 5/3 ](z+1, z2+1, z4+1)164 [!]256256
{(1,31), (8,8), (16,0)}[ 23/7, 1 ](z+1, z8+1)132 [!]256256
{(1,31), (2,18), (8,8), (16,0)}[ 13, 5/3, 1 ](z+1, z2+1, z8+1)1512 [!]20482048
{(1,31), (2,22), (8,8), (16,0)}[ 9, 7/3, 1 ](z+1, z2+1, z8+1)1256 [!]10241024
{(1,31), (2,26), (8,8), (16,0)}[ 5, 3, 1 ](z+1, z6+1, z8+1)1128 [!]256256
{(1,31), (4,20), (8,8), (16,0)}[ 11/3, 3, 1 ](z+1, z4+1, z8+1)164 [!]256256
33{(1,33), (2,18), (16,0)}[ 15, 9/7 ](z+1, z2+1)1512 [!]4096409665536
{(1,33), (2,22), (16,0)}[ 11, 11/7 ](z+1, z2+1)125620482048
{(1,33), (2,26), (16,0)}[ 7, 13/7 ](z+1, z2+1)164 [!]512512
{(1,33), (2,18), (4,4), (16,0)}[ 15, 7, 1/3 ](z+1, z2+1, z4+1)14096 [!]1638416384
{(1,33), (2,20), (4,4), (16,0)}[ 13, 8, 1/3 ](z+1, z2+1, z4+1)14096 [!]1638416384
{(1,33), (4,12), (16,0)}[ 7, 1 ](z3+1, z12+1)1256 [!]10241024
{(1,33), (2,18), (4,12), (16,0)}[ 15, 3, 1 ](z+1, z2+1, z12+1)12048 [!]40964096
{(1,33), (2,22), (4,12), (16,0)}[ 11, 5, 1 ](z+1, z2+1, z12+1)11024 [!]20482048
{(1,33), (2,26), (4,12), (16,0)}[ 7, 1 ](z3+z+1, z12+1)1128 [!]10241024
{(1,33), (4,20), (16,0)}[ 13/3, 5/3 ](z+1, z4+1)132512512
{(1,33), (2,26), (4,20), (16,0)}[ 7, 3, 5/3 ](z+1, z2+1, z4+1)1128 [!]512512
{(1,33), (8,8), (16,0)}[ 25/7, 1 ](z+1, z8+1)164 [!]512512
{(1,33), (2,18), (8,8), (16,0)}[ 15, 5/3, 1 ](z+1, z2+1, z8+1)11024 [!]40964096
{(1,33), (2,22), (8,8), (16,0)}[ 11, 7/3, 1 ](z+1, z2+1, z8+1)1512 [!]20482048
{(1,33), (2,26), (8,8), (16,0)}[ 7, 3, 1 ](z+1, z6+1, z8+1)1256 [!]512512
{(1,33), (4,20), (8,8), (16,0)}[ 13/3, 3, 1 ](z+1, z4+1, z8+1)1128 [!]512512
34{(1,34), (2,18), (16,0)}[ 16, 9/7 ](z+1, z2+1)11024 [!]8192819265536
{(1,34), (2,18), (4,4), (16,0)}[ 16, 7, 1/3 ](z+1, z2+1, z4+1)18192 [!]3276832768
{(1,34), (2,18), (4,12), (16,0)}[ 16, 3, 1 ](z+1, z2+1, z12+1)14096 [!]81928192
{(1,34), (2,18), (8,8), (16,0)}[ 16, 5/3, 1 ](z+1, z2+1, z8+1)12048 [!]81928192
35{(1,35), (2,22), (16,0)}[ 13, 11/7 ](z+1, z2+1)1512 [!]4096409665536
{(1,35), (2,26), (16,0)}[ 9, 13/7 ](z+1, z2+1)112810241024
{(1,35), (2,20), (4,4), (16,0)}[ 15, 8, 1/3 ](z+1, z2+1, z4+1)18192 [!]3276832768
{(1,35), (4,12), (16,0)}[ 23/3, 1 ](z+1, z12+1)1256 [!]20482048
{(1,35), (2,22), (4,12), (16,0)}[ 13, 5, 1 ](z+1, z2+1, z12+1)12048 [!]40964096
{(1,35), (2,26), (4,12), (16,0)}[ 9, 7, 1 ](z+1, z2+1, z12+1)11024 [!]20482048
{(1,35), (4,20), (16,0)}[ 5, 5/3 ](z3+1, z4+1)164512512
{(1,35), (2,26), (4,20), (16,0)}[ 9, 3, 5/3 ](z+1, z2+1, z4+1)1256 [!]10241024
{(1,35), (2,30), (4,20), (16,0)}[ 5, 5/3 ](z3+z+1, z4+1)132512512
{(1,35), (8,8), (16,0)}[ 27/7, 1 ](z+1, z8+1)164 [!]512512
{(1,35), (2,22), (8,8), (16,0)}[ 13, 7/3, 1 ](z+1, z2+1, z8+1)11024 [!]40964096
{(1,35), (2,26), (8,8), (16,0)}[ 9, 3, 1 ](z+1, z6+1, z8+1)1512 [!]10241024
{(1,35), (2,30), (8,8), (16,0)}[ 5, 11/3, 1 ](z+1, z2+1, z8+1)1128 [!]512512
{(1,35), (4,20), (8,8), (16,0)}[ 5, 3, 1 ](z3+1, z4+1, z8+1)1256 [!]512512
{(1,35), (2,30), (4,20), (8,8), (16,0)}[ 5, 3, 1 ](z3+z+1, z4+1, z8+1)1128 [!]512512
36{(1,36), (2,20), (4,4), (16,0)}[ 16, 8, 1/3 ](z+1, z2+1, z4+1)116384 [!]655366553665536
37{(1,37), (2,22), (16,0)}[ 15, 11/7 ](z+1, z2+1)11024 [!]8192819265536
{(1,37), (2,26), (16,0)}[ 11, 13/7 ](z+1, z2+1)1256 [!]20482048
{(1,37), (2,22), (4,12), (16,0)}[ 15, 5, 1 ](z+1, z2+1, z12+1)14096 [!]81928192
{(1,37), (2,26), (4,12), (16,0)}[ 11, 7, 1 ](z+1, z2+1, z12+1)12048 [!]40964096
{(1,37), (2,28), (4,12), (16,0)}[ 9, 8, 1 ](z+1, z2+1, z12+1)12048 [!]40964096
{(1,37), (4,20), (16,0)}[ 17/3, 5/3 ](z+1, z4+1)16410241024
{(1,37), (2,26), (4,20), (16,0)}[ 11, 3, 5/3 ](z+1, z2+1, z4+1)1512 [!]20482048
{(1,37), (2,30), (4,20), (16,0)}[ 7, 5, 5/3 ](z+1, z2+1, z4+1)1256 [!]10241024
{(1,37), (2,22), (8,8), (16,0)}[ 15, 7/3, 1 ](z+1, z2+1, z8+1)12048 [!]81928192
{(1,37), (2,26), (8,8), (16,0)}[ 11, 3, 1 ](z+1, z6+1, z8+1)11024 [!]20482048
{(1,37), (2,30), (8,8), (16,0)}[ 7, 11/3, 1 ](z+1, z2+1, z8+1)1256 [!]10241024
{(1,37), (4,20), (8,8), (16,0)}[ 17/3, 3, 1 ](z+1, z4+1, z8+1)1256 [!]10241024
{(1,37), (2,30), (4,20), (8,8), (16,0)}[ 7, 5, 3, 1 ](z+1, z2+1, z4+1, z8+1)11024 [!]10241024
38{(1,38), (2,22), (16,0)}[ 16, 11/7 ](z+1, z2+1)12048 [!]163841638465536
{(1,38), (2,22), (4,12), (16,0)}[ 16, 5, 1 ](z+1, z2+1, z12+1)18192 [!]1638416384
{(1,38), (2,22), (8,8), (16,0)}[ 16, 7/3, 1 ](z+1, z2+1, z8+1)14096 [!]1638416384
39{(1,39), (2,26), (16,0)}[ 13, 13/7 ](z+1, z2+1)1512 [!]4096409665536
{(1,39), (2,26), (4,12), (16,0)}[ 13, 7, 1 ](z+1, z2+1, z12+1)14096 [!]81928192
{(1,39), (2,28), (4,12), (16,0)}[ 11, 8, 1 ](z+1, z2+1, z12+1)14096 [!]81928192
{(1,39), (4,20), (16,0)}[ 19/3, 5/3 ](z+1, z4+1)112820482048
{(1,39), (2,26), (4,20), (16,0)}[ 13, 3, 5/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,39), (2,30), (4,20), (16,0)}[ 9, 5, 5/3 ](z+1, z2+1, z4+1)1512 [!]20482048
{(1,39), (2,26), (8,8), (16,0)}[ 13, 3, 1 ](z+1, z6+1, z8+1)12048 [!]40964096
{(1,39), (2,30), (8,8), (16,0)}[ 9, 11/3, 1 ](z+1, z2+1, z8+1)1512 [!]20482048
{(1,39), (4,20), (8,8), (16,0)}[ 19/3, 3, 1 ](z+1, z4+1, z8+1)1512 [!]20482048
{(1,39), (2,30), (4,20), (8,8), (16,0)}[ 9, 5, 3, 1 ](z+1, z2+1, z4+1, z8+1)12048 [!]20482048
{(1,39), (4,24), (8,8), (16,0)}[ 5, 4, 1 ](z3+1, z4+1, z8+1)1512 [!]10241024
{(1,39), (2,34), (4,24), (8,8), (16,0)}[ 5, 4, 1 ](z3+z+1, z4+1, z8+1)1256 [!]10241024
41{(1,41), (2,26), (16,0)}[ 15, 13/7 ](z+1, z2+1)11024 [!]81928192131072
{(1,41), (2,26), (4,12), (16,0)}[ 15, 7, 1 ](z+1, z2+1, z12+1)18192 [!]1638416384
{(1,41), (2,28), (4,12), (16,0)}[ 13, 8, 1 ](z+1, z2+1, z12+1)18192 [!]1638416384
{(1,41), (4,20), (16,0)}[ 7, 5/3 ](z3+1, z4+1)1256 [!]20482048
{(1,41), (2,26), (4,20), (16,0)}[ 15, 3, 5/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,41), (2,30), (4,20), (16,0)}[ 11, 5, 5/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,41), (2,34), (4,20), (16,0)}[ 7, 5/3 ](z3+z+1, z4+1)112820482048
{(1,41), (2,26), (8,8), (16,0)}[ 15, 3, 1 ](z+1, z6+1, z8+1)14096 [!]81928192
{(1,41), (2,30), (8,8), (16,0)}[ 11, 11/3, 1 ](z+1, z2+1, z8+1)11024 [!]40964096
{(1,41), (4,20), (8,8), (16,0)}[ 7, 3, 1 ](z3+1, z4+1, z8+1)11024 [!]20482048
{(1,41), (2,30), (4,20), (8,8), (16,0)}[ 11, 5, 3, 1 ](z+1, z2+1, z4+1, z8+1)14096 [!]40964096
{(1,41), (2,34), (4,20), (8,8), (16,0)}[ 7, 3, 1 ](z3+z+1, z4+1, z8+1)1512 [!]20482048
{(1,41), (4,24), (8,8), (16,0)}[ 17/3, 4, 1 ](z+1, z4+1, z8+1)1512 [!]20482048
{(1,41), (2,34), (4,24), (8,8), (16,0)}[ 7, 5, 4, 1 ](z+1, z2+1, z4+1, z8+1)12048 [!]20482048
42{(1,42), (2,26), (16,0)}[ 16, 13/7 ](z+1, z2+1)12048 [!]1638416384131072
{(1,42), (2,26), (4,12), (16,0)}[ 16, 7, 1 ](z+1, z2+1, z12+1)116384 [!]3276832768
{(1,42), (2,26), (4,20), (16,0)}[ 16, 3, 5/3 ](z+1, z2+1, z4+1)14096 [!]1638416384
{(1,42), (2,26), (8,8), (16,0)}[ 16, 3, 1 ](z+1, z6+1, z8+1)18192 [!]1638416384
43{(1,43), (2,28), (4,12), (16,0)}[ 15, 8, 1 ](z+1, z2+1, z12+1)116384 [!]3276832768131072
{(1,43), (4,20), (16,0)}[ 23/3, 5/3 ](z+1, z4+1)125640964096
{(1,43), (2,30), (4,20), (16,0)}[ 13, 5, 5/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,43), (2,34), (4,20), (16,0)}[ 9, 7, 5/3 ](z+1, z2+1, z4+1)11024 [!]40964096
{(1,43), (2,30), (8,8), (16,0)}[ 13, 11/3, 1 ](z+1, z2+1, z8+1)12048 [!]81928192
{(1,43), (4,20), (8,8), (16,0)}[ 23/3, 3, 1 ](z+1, z4+1, z8+1)11024 [!]40964096
{(1,43), (2,30), (4,20), (8,8), (16,0)}[ 13, 5, 3, 1 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,43), (2,34), (4,20), (8,8), (16,0)}[ 9, 7, 3, 1 ](z+1, z2+1, z4+1, z8+1)14096 [!]40964096
{(1,43), (4,24), (8,8), (16,0)}[ 19/3, 4, 1 ](z+1, z4+1, z8+1)11024 [!]40964096
{(1,43), (2,34), (4,24), (8,8), (16,0)}[ 9, 5, 4, 1 ](z+1, z2+1, z4+1, z8+1)14096 [!]40964096
44{(1,44), (2,28), (4,12), (16,0)}[ 16, 8, 1 ](z+1, z2+1, z12+1)132768 [!]6553665536131072
45{(1,45), (2,30), (4,20), (16,0)}[ 15, 5, 5/3 ](z+1, z2+1, z4+1)14096 [!]1638416384131072
{(1,45), (2,34), (4,20), (16,0)}[ 11, 7, 5/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,45), (2,36), (4,20), (16,0)}[ 9, 8, 5/3 ](z+1, z2+1, z4+1)12048 [!]81928192
{(1,45), (2,30), (8,8), (16,0)}[ 15, 11/3, 1 ](z+1, z2+1, z8+1)14096 [!]1638416384
{(1,45), (2,30), (4,20), (8,8), (16,0)}[ 15, 5, 3, 1 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,45), (2,34), (4,20), (8,8), (16,0)}[ 11, 7, 3, 1 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,45), (2,36), (4,20), (8,8), (16,0)}[ 9, 8, 3, 1 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,45), (4,24), (8,8), (16,0)}[ 7, 4, 1 ](z3+1, z4+1, z8+1)12048 [!]40964096
{(1,45), (2,34), (4,24), (8,8), (16,0)}[ 11, 5, 4, 1 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,45), (2,38), (4,24), (8,8), (16,0)}[ 7, 4, 1 ](z3+z+1, z4+1, z8+1)11024 [!]40964096
{(1,45), (2,30), (8,16), (16,0)}[ 15, 7/3, 2 ](z+1, z2+1, z8+1)14096 [!]1638416384
{(1,45), (2,34), (8,16), (16,0)}[ 11, 3, 2 ](z+1, z6+1, z8+1)12048 [!]40964096
{(1,45), (2,38), (8,16), (16,0)}[ 7, 11/3, 2 ](z+1, z2+1, z8+1)1512 [!]20482048
{(1,45), (4,28), (8,16), (16,0)}[ 17/3, 3, 2 ](z+1, z4+1, z8+1)1512 [!]20482048
{(1,45), (2,38), (4,28), (8,16), (16,0)}[ 7, 5, 3, 2 ](z+1, z2+1, z4+1, z8+1)12048 [!]20482048
46{(1,46), (2,30), (4,20), (16,0)}[ 16, 5, 5/3 ](z+1, z2+1, z4+1)18192 [!]3276832768131072
{(1,46), (2,30), (8,8), (16,0)}[ 16, 11/3, 1 ](z+1, z2+1, z8+1)18192 [!]3276832768
{(1,46), (2,30), (4,20), (8,8), (16,0)}[ 16, 5, 3, 1 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,46), (2,30), (8,16), (16,0)}[ 16, 7/3, 2 ](z+1, z2+1, z8+1)18192 [!]3276832768
47{(1,47), (2,34), (4,20), (16,0)}[ 13, 7, 5/3 ](z+1, z2+1, z4+1)14096 [!]1638416384131072
{(1,47), (2,36), (4,20), (16,0)}[ 11, 8, 5/3 ](z+1, z2+1, z4+1)14096 [!]1638416384
{(1,47), (2,34), (4,20), (8,8), (16,0)}[ 13, 7, 3, 1 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,47), (2,36), (4,20), (8,8), (16,0)}[ 11, 8, 3, 1 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,47), (4,24), (8,8), (16,0)}[ 23/3, 4, 1 ](z+1, z4+1, z8+1)12048 [!]81928192
{(1,47), (2,34), (4,24), (8,8), (16,0)}[ 13, 5, 4, 1 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,47), (2,38), (4,24), (8,8), (16,0)}[ 9, 7, 4, 1 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,47), (2,34), (8,16), (16,0)}[ 13, 3, 2 ](z+1, z6+1, z8+1)14096 [!]81928192
{(1,47), (2,38), (8,16), (16,0)}[ 9, 11/3, 2 ](z+1, z2+1, z8+1)11024 [!]40964096
{(1,47), (4,28), (8,16), (16,0)}[ 19/3, 3, 2 ](z+1, z4+1, z8+1)11024 [!]40964096
{(1,47), (2,38), (4,28), (8,16), (16,0)}[ 9, 5, 3, 2 ](z+1, z2+1, z4+1, z8+1)14096 [!]40964096
{(1,47), (4,32), (8,16), (16,0)}[ 5, 4, 2 ](z3+1, z4+1, z8+1)11024 [!]20482048
{(1,47), (2,42), (4,32), (8,16), (16,0)}[ 5, 4, 2 ](z3+z+1, z4+1, z8+1)1512 [!]20482048
49{(1,49), (2,34), (4,20), (16,0)}[ 15, 7, 5/3 ](z+1, z2+1, z4+1)18192 [!]3276832768262144
{(1,49), (2,36), (4,20), (16,0)}[ 13, 8, 5/3 ](z+1, z2+1, z4+1)18192 [!]3276832768
{(1,49), (2,34), (4,20), (8,8), (16,0)}[ 15, 7, 3, 1 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,49), (2,36), (4,20), (8,8), (16,0)}[ 13, 8, 3, 1 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,49), (2,34), (4,24), (8,8), (16,0)}[ 15, 5, 4, 1 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,49), (2,38), (4,24), (8,8), (16,0)}[ 11, 7, 4, 1 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,49), (2,40), (4,24), (8,8), (16,0)}[ 9, 8, 4, 1 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,49), (2,34), (8,16), (16,0)}[ 15, 3, 2 ](z+1, z6+1, z8+1)18192 [!]1638416384
{(1,49), (2,38), (8,16), (16,0)}[ 11, 11/3, 2 ](z+1, z2+1, z8+1)12048 [!]81928192
{(1,49), (4,28), (8,16), (16,0)}[ 7, 3, 2 ](z3+1, z4+1, z8+1)12048 [!]40964096
{(1,49), (2,38), (4,28), (8,16), (16,0)}[ 11, 5, 3, 2 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,49), (2,42), (4,28), (8,16), (16,0)}[ 7, 3, 2 ](z3+z+1, z4+1, z8+1)11024 [!]40964096
{(1,49), (4,32), (8,16), (16,0)}[ 17/3, 4, 2 ](z+1, z4+1, z8+1)11024 [!]40964096
{(1,49), (2,42), (4,32), (8,16), (16,0)}[ 7, 5, 4, 2 ](z+1, z2+1, z4+1, z8+1)14096 [!]40964096
50{(1,50), (2,34), (4,20), (16,0)}[ 16, 7, 5/3 ](z+1, z2+1, z4+1)116384 [!]6553665536262144
{(1,50), (2,34), (4,20), (8,8), (16,0)}[ 16, 7, 3, 1 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,50), (2,34), (4,24), (8,8), (16,0)}[ 16, 5, 4, 1 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,50), (2,34), (8,16), (16,0)}[ 16, 3, 2 ](z+1, z6+1, z8+1)116384 [!]3276832768
51{(1,51), (2,36), (4,20), (16,0)}[ 15, 8, 5/3 ](z+1, z2+1, z4+1)116384 [!]6553665536262144
{(1,51), (2,36), (4,20), (8,8), (16,0)}[ 15, 8, 3, 1 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,51), (2,38), (4,24), (8,8), (16,0)}[ 13, 7, 4, 1 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,51), (2,40), (4,24), (8,8), (16,0)}[ 11, 8, 4, 1 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,51), (2,38), (8,16), (16,0)}[ 13, 11/3, 2 ](z+1, z2+1, z8+1)14096 [!]1638416384
{(1,51), (4,28), (8,16), (16,0)}[ 23/3, 3, 2 ](z+1, z4+1, z8+1)12048 [!]81928192
{(1,51), (2,38), (4,28), (8,16), (16,0)}[ 13, 5, 3, 2 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,51), (2,42), (4,28), (8,16), (16,0)}[ 9, 7, 3, 2 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
{(1,51), (4,32), (8,16), (16,0)}[ 19/3, 4, 2 ](z+1, z4+1, z8+1)12048 [!]81928192
{(1,51), (2,42), (4,32), (8,16), (16,0)}[ 9, 5, 4, 2 ](z+1, z2+1, z4+1, z8+1)18192 [!]81928192
52{(1,52), (2,36), (4,20), (16,0)}[ 16, 8, 5/3 ](z+1, z2+1, z4+1)132768 [!]131072131072262144
{(1,52), (2,36), (4,20), (8,8), (16,0)}[ 16, 8, 3, 1 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072
53{(1,53), (2,38), (4,24), (8,8), (16,0)}[ 15, 7, 4, 1 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536262144
{(1,53), (2,40), (4,24), (8,8), (16,0)}[ 13, 8, 4, 1 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,53), (2,38), (8,16), (16,0)}[ 15, 11/3, 2 ](z+1, z2+1, z8+1)18192 [!]3276832768
{(1,53), (2,38), (4,28), (8,16), (16,0)}[ 15, 5, 3, 2 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,53), (2,42), (4,28), (8,16), (16,0)}[ 11, 7, 3, 2 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,53), (2,44), (4,28), (8,16), (16,0)}[ 9, 8, 3, 2 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,53), (4,32), (8,16), (16,0)}[ 7, 4, 2 ](z3+1, z4+1, z8+1)14096 [!]81928192
{(1,53), (2,42), (4,32), (8,16), (16,0)}[ 11, 5, 4, 2 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
{(1,53), (2,46), (4,32), (8,16), (16,0)}[ 7, 4, 2 ](z3+z+1, z4+1, z8+1)12048 [!]81928192
54{(1,54), (2,38), (4,24), (8,8), (16,0)}[ 16, 7, 4, 1 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072262144
{(1,54), (2,38), (8,16), (16,0)}[ 16, 11/3, 2 ](z+1, z2+1, z8+1)116384 [!]6553665536
{(1,54), (2,38), (4,28), (8,16), (16,0)}[ 16, 5, 3, 2 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
55{(1,55), (2,40), (4,24), (8,8), (16,0)}[ 15, 8, 4, 1 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072262144
{(1,55), (2,42), (4,28), (8,16), (16,0)}[ 13, 7, 3, 2 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,55), (2,44), (4,28), (8,16), (16,0)}[ 11, 8, 3, 2 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,55), (4,32), (8,16), (16,0)}[ 23/3, 4, 2 ](z+1, z4+1, z8+1)14096 [!]1638416384
{(1,55), (2,42), (4,32), (8,16), (16,0)}[ 13, 5, 4, 2 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,55), (2,46), (4,32), (8,16), (16,0)}[ 9, 7, 4, 2 ](z+1, z2+1, z4+1, z8+1)116384 [!]1638416384
56{(1,56), (2,40), (4,24), (8,8), (16,0)}[ 16, 8, 4, 1 ](z+1, z2+1, z4+1, z8+1)1262144 [!]262144262144262144
57{(1,57), (2,42), (4,28), (8,16), (16,0)}[ 15, 7, 3, 2 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536262144
{(1,57), (2,44), (4,28), (8,16), (16,0)}[ 13, 8, 3, 2 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,57), (2,42), (4,32), (8,16), (16,0)}[ 15, 5, 4, 2 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,57), (2,46), (4,32), (8,16), (16,0)}[ 11, 7, 4, 2 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
{(1,57), (2,48), (4,32), (8,16), (16,0)}[ 9, 8, 4, 2 ](z+1, z2+1, z4+1, z8+1)132768 [!]3276832768
58{(1,58), (2,42), (4,28), (8,16), (16,0)}[ 16, 7, 3, 2 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072262144
{(1,58), (2,42), (4,32), (8,16), (16,0)}[ 16, 5, 4, 2 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072
59{(1,59), (2,44), (4,28), (8,16), (16,0)}[ 15, 8, 3, 2 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072262144
{(1,59), (2,46), (4,32), (8,16), (16,0)}[ 13, 7, 4, 2 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
{(1,59), (2,48), (4,32), (8,16), (16,0)}[ 11, 8, 4, 2 ](z+1, z2+1, z4+1, z8+1)165536 [!]6553665536
60{(1,60), (2,44), (4,28), (8,16), (16,0)}[ 16, 8, 3, 2 ](z+1, z2+1, z4+1, z8+1)1262144 [!]262144262144262144
61{(1,61), (2,46), (4,32), (8,16), (16,0)}[ 15, 7, 4, 2 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072262144
{(1,61), (2,48), (4,32), (8,16), (16,0)}[ 13, 8, 4, 2 ](z+1, z2+1, z4+1, z8+1)1131072 [!]131072131072
62{(1,62), (2,46), (4,32), (8,16), (16,0)}[ 16, 7, 4, 2 ](z+1, z2+1, z4+1, z8+1)1262144 [!]262144262144262144
63{(1,63), (2,48), (4,32), (8,16), (16,0)}[ 15, 8, 4, 2 ](z+1, z2+1, z4+1, z8+1)1262144 [!]262144262144262144
64{(1,64), (2,48), (4,32), (8,16), (16,0)}[ 16, 8, 4, 2 ](z+1, z2+1, z4+1, z8+1)1524288 [!]524288524288524288