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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.2.8.48c1.117 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $48$ $D_{8}$ (as 16T13) $2$ $1$ $[2, 3, 4]$ $[1,2,3]$ $[2, 3, 4]^{2}$ $[1,2,3]^{2}$ $[\ ]$ $[\ ]$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ $[17, 10, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 15, 23]$
2.2.8.48c1.120 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $48$ $D_{8}$ (as 16T13) $2$ $1$ $[2, 3, 4]$ $[1,2,3]$ $[2, 3, 4]^{2}$ $[1,2,3]^{2}$ $[\ ]$ $[\ ]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ $[17, 10, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 15, 23]$
2.2.8.62a1.1281 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $62$ $D_{8}$ (as 16T13) $2$ $1$ $[3, 4, 5]$ $[2,3,4]$ $[3, 4, 5]^{2}$ $[2,3,4]^{2}$ $[\ ]$ $[\ ]$ $t^{2} + t + 1$ $x^{8} + 8 x^{2} + 16 x + 2$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.1285 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $62$ $D_{8}$ (as 16T13) $2$ $1$ $[3, 4, 5]$ $[2,3,4]$ $[3, 4, 5]^{2}$ $[2,3,4]^{2}$ $[\ ]$ $[\ ]$ $t^{2} + t + 1$ $x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 2$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.16.58m1.482 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 23, 39, 55]$
2.1.16.58m1.483 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 23, 39, 55]$
2.1.16.58m1.733 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 10$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 10$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 32, 48]$
2.1.16.58m1.734 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 26 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 10$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 26 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 10$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 32, 48]$
2.1.16.58m1.877 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 16 x^{5} + 4 x^{4} + 6$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 16 x^{5} + 4 x^{4} + 6$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58m1.878 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 26 x^{8} + 16 x^{5} + 4 x^{4} + 6$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 26 x^{8} + 16 x^{5} + 4 x^{4} + 6$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58m1.1060 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 14$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 14$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58m1.1061 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 14$ $2$ $1$ $16$ $58$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]$ $[1,2,\frac{5}{2},\frac{7}{2}]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 14$ $[43, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.587 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $2$ $1$ $16$ $64$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 11, 27, 43, 59]$
2.1.16.64g1.588 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 34$ $2$ $1$ $16$ $64$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 34$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 11, 27, 43, 59]$
2.1.16.64g1.640 $x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $2$ $1$ $16$ $64$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 11, 27, 43, 59]$
2.1.16.64g1.641 $x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 50$ $2$ $1$ $16$ $64$ $D_{8}$ (as 16T13) $1$ $1$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[2, 3, 4, 5]$ $[1,2,3,4]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 50$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 11, 27, 43, 59]$
7.2.8.14a1.2 $( x^{2} + 6 x + 3 )^{8} + 7$ $7$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{8} + 7$ $[0]$ $[1]$ $z^7 + z^6 + 1$ undefined
23.2.8.14a1.2 $( x^{2} + 21 x + 5 )^{8} + 23$ $23$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 21 t + 5$ $x^{8} + 23$ $[0]$ $[1]$ $z^7 + 8 z^6 + 5 z^5 + 10 z^4 + z^3 + 10 z^2 + 5 z + 8$ undefined
31.2.8.14a1.2 $( x^{2} + 29 x + 3 )^{8} + 31$ $31$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 29 t + 3$ $x^{8} + 31$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 25 z^4 + 8 z^3 + 25 z^2 + 28 z + 8$ undefined
47.2.8.14a1.2 $( x^{2} + 45 x + 5 )^{8} + 47$ $47$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 45 t + 5$ $x^{8} + 47$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 9 z^4 + 23 z^3 + 9 z^2 + 28 z + 8$ undefined
71.2.8.14a1.2 $( x^{2} + 69 x + 7 )^{8} + 71$ $71$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 69 t + 7$ $x^{8} + 71$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
79.2.8.14a1.2 $( x^{2} + 78 x + 3 )^{8} + 79$ $79$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 78 t + 3$ $x^{8} + 79$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
103.2.8.14a1.2 $( x^{2} + 102 x + 5 )^{8} + 103$ $103$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 102 t + 5$ $x^{8} + 103$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
127.2.8.14a1.2 $( x^{2} + 126 x + 3 )^{8} + 127$ $127$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 126 t + 3$ $x^{8} + 127$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
151.2.8.14a1.2 $( x^{2} + 149 x + 6 )^{8} + 151$ $151$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 149 t + 6$ $x^{8} + 151$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
167.2.8.14a1.2 $( x^{2} + 166 x + 5 )^{8} + 167$ $167$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 166 t + 5$ $x^{8} + 167$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
191.2.8.14a1.2 $( x^{2} + 190 x + 19 )^{8} + 191$ $191$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 190 t + 19$ $x^{8} + 191$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
199.2.8.14a1.2 $( x^{2} + 193 x + 3 )^{8} + 199$ $199$ $2$ $8$ $14$ $D_{8}$ (as 16T13) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 193 t + 3$ $x^{8} + 199$ $[0]$ $[1]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
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