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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
109.1.1.0a1.1 $x + 103$ $109$ $1$ $1$ $0$ Trivial (as 1T1) $1$ $1$ $[\ ]$ $[\ ]$ $[\ ]$ $[\ ]$ $[\ ]$ $[\ ]$ $t + 103$ $x - 109$ $[0]$ $[\ ]$ undefined
109.2.1.0a1.1 $x^{2} + 108 x + 6$ $109$ $2$ $1$ $0$ $C_2$ (as 2T1) $2$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{2}$ $[\ ]^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x - 109$ $[0]$ $[\ ]$ undefined
109.1.2.1a1.1 $x^{2} + 109$ $109$ $1$ $2$ $1$ $C_2$ (as 2T1) $1$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}$ $[\ ]_{2}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{2} + 109$ $[0]$ $[1]$ $z + 2$ undefined
109.1.2.1a1.2 $x^{2} + 654$ $109$ $1$ $2$ $1$ $C_2$ (as 2T1) $1$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}$ $[\ ]_{2}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{2} + 654$ $[0]$ $[1]$ $z + 2$ undefined
109.3.1.0a1.1 $x^{3} + x + 103$ $109$ $3$ $1$ $0$ $C_3$ (as 3T1) $3$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{3}$ $[\ ]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 103$ $x - 109$ $[0]$ $[\ ]$ undefined
109.1.3.2a1.1 $x^{3} + 109$ $109$ $1$ $3$ $2$ $C_3$ (as 3T1) $1$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}$ $[\ ]_{3}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{3} + 109$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.1.3.2a1.2 $x^{3} + 654$ $109$ $1$ $3$ $2$ $C_3$ (as 3T1) $1$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}$ $[\ ]_{3}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{3} + 654$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.1.3.2a1.3 $x^{3} + 3924$ $109$ $1$ $3$ $2$ $C_3$ (as 3T1) $1$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}$ $[\ ]_{3}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{3} + 3924$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.4.1.0a1.1 $x^{4} + 11 x^{2} + 98 x + 6$ $109$ $4$ $1$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{4}$ $[\ ]^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 11 t^{2} + 98 t + 6$ $x - 109$ $[0]$ $[\ ]$ undefined
109.2.2.2a1.1 $( x^{2} + 108 x + 6 )^{2} + 109 x$ $109$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{2}$ $[\ ]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{2} + 109 t$ $[0]$ $[1]$ $z + 2$ undefined
109.2.2.2a1.2 $( x^{2} + 108 x + 6 )^{2} + 109$ $109$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{2}$ $[\ ]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{2} + 109$ $[0]$ $[1]$ $z + 2$ undefined
109.1.4.3a1.1 $x^{4} + 109$ $109$ $1$ $4$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}$ $[\ ]_{4}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{4} + 109$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.1.4.3a1.2 $x^{4} + 654$ $109$ $1$ $4$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}$ $[\ ]_{4}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{4} + 654$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.1.4.3a1.3 $x^{4} + 3924$ $109$ $1$ $4$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}$ $[\ ]_{4}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{4} + 3924$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.1.4.3a1.4 $x^{4} + 11663$ $109$ $1$ $4$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}$ $[\ ]_{4}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{4} + 11663$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.5.1.0a1.1 $x^{5} + 4 x + 103$ $109$ $5$ $1$ $0$ $C_5$ (as 5T1) $5$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{5}$ $[\ ]^{5}$ $[\ ]$ $[\ ]$ $t^{5} + 4 t + 103$ $x - 109$ $[0]$ $[\ ]$ undefined
109.1.5.4a1.1 $x^{5} + 109$ $109$ $1$ $5$ $4$ $D_{5}$ (as 5T2) $2$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{2}$ $[\ ]_{5}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 103$ $x^{5} + 109$ $[0]$ $[2]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
109.6.1.0a1.1 $x^{6} + 107 x^{3} + 102 x^{2} + 66 x + 6$ $109$ $6$ $1$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{6}$ $[\ ]^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 107 t^{3} + 102 t^{2} + 66 t + 6$ $x - 109$ $[0]$ $[\ ]$ undefined
109.3.2.3a1.1 $( x^{3} + x + 103 )^{2} + 109 x$ $109$ $3$ $2$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{3}$ $[\ ]_{2}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 103$ $x^{2} + 109 t$ $[0]$ $[1]$ $z + 2$ undefined
109.3.2.3a1.2 $( x^{3} + x + 103 )^{2} + 109$ $109$ $3$ $2$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{3}$ $[\ ]_{2}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 103$ $x^{2} + 109$ $[0]$ $[1]$ $z + 2$ undefined
109.2.3.4a1.1 $( x^{2} + 108 x + 6 )^{3} + 109 x$ $109$ $2$ $3$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{2}$ $[\ ]_{3}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{3} + 109 t$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.2.3.4a1.2 $( x^{2} + 108 x + 6 )^{3} + 109$ $109$ $2$ $3$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{2}$ $[\ ]_{3}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{3} + 109$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.2.3.4a1.3 $( x^{2} + 108 x + 6 )^{3} + 109 x + 11227$ $109$ $2$ $3$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{2}$ $[\ ]_{3}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{3} + 109 t + 11227$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.1.6.5a1.1 $x^{6} + 109$ $109$ $1$ $6$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}$ $[\ ]_{6}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{6} + 109$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
109.1.6.5a1.2 $x^{6} + 654$ $109$ $1$ $6$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}$ $[\ ]_{6}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{6} + 654$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
109.1.6.5a1.3 $x^{6} + 3924$ $109$ $1$ $6$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}$ $[\ ]_{6}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{6} + 3924$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
109.1.6.5a1.4 $x^{6} + 4033$ $109$ $1$ $6$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}$ $[\ ]_{6}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{6} + 4033$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
109.1.6.5a1.5 $x^{6} + 10573$ $109$ $1$ $6$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}$ $[\ ]_{6}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{6} + 10573$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
109.1.6.5a1.6 $x^{6} + 11663$ $109$ $1$ $6$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}$ $[\ ]_{6}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{6} + 11663$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
109.7.1.0a1.1 $x^{7} + 14 x + 103$ $109$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 14 t + 103$ $x - 109$ $[0]$ $[\ ]$ undefined
109.1.7.6a1.1 $x^{7} + 109$ $109$ $1$ $7$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}^{3}$ $[\ ]_{7}^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $t + 103$ $x^{7} + 109$ $[0]$ $[3]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
109.8.1.0a1.1 $x^{8} + x^{4} + 102 x^{3} + 34 x^{2} + 86 x + 6$ $109$ $8$ $1$ $0$ $C_8$ (as 8T1) $8$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{8}$ $[\ ]^{8}$ $[\ ]$ $[\ ]$ $t^{8} + t^{4} + 102 t^{3} + 34 t^{2} + 86 t + 6$ $x - 109$ $[0]$ $[\ ]$ undefined
109.4.2.4a1.1 $( x^{4} + 11 x^{2} + 98 x + 6 )^{2} + 109 x$ $109$ $4$ $2$ $4$ $C_8$ (as 8T1) $4$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{4}$ $[\ ]_{2}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 11 t^{2} + 98 t + 6$ $x^{2} + 109 t$ $[0]$ $[1]$ $z + 2$ undefined
109.4.2.4a1.2 $( x^{4} + 11 x^{2} + 98 x + 6 )^{2} + 109$ $109$ $4$ $2$ $4$ $C_4\times C_2$ (as 8T2) $4$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{4}$ $[\ ]_{2}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 11 t^{2} + 98 t + 6$ $x^{2} + 109$ $[0]$ $[1]$ $z + 2$ undefined
109.2.4.6a1.1 $( x^{2} + 108 x + 6 )^{4} + 109 x$ $109$ $2$ $4$ $6$ $C_8$ (as 8T1) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{4} + 109 t$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.2.4.6a1.2 $( x^{2} + 108 x + 6 )^{4} + 109$ $109$ $2$ $4$ $6$ $C_4\times C_2$ (as 8T2) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{4} + 109$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.2.4.6a1.3 $( x^{2} + 108 x + 6 )^{4} + 109 x + 11227$ $109$ $2$ $4$ $6$ $C_4\times C_2$ (as 8T2) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{4} + 109 t + 11227$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.2.4.6a1.4 $( x^{2} + 108 x + 6 )^{4} + 11336 x + 11227$ $109$ $2$ $4$ $6$ $C_8$ (as 8T1) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 108 t + 6$ $x^{4} + 11336 t + 11227$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
109.1.8.7a1.1 $x^{8} + 109$ $109$ $1$ $8$ $7$ $C_8:C_2$ (as 8T7) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 103$ $x^{8} + 109$ $[0]$ $[2]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
109.1.8.7a1.2 $x^{8} + 654$ $109$ $1$ $8$ $7$ $C_8:C_2$ (as 8T7) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 103$ $x^{8} + 654$ $[0]$ $[2]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
109.1.8.7a1.3 $x^{8} + 3924$ $109$ $1$ $8$ $7$ $C_8:C_2$ (as 8T7) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 103$ $x^{8} + 3924$ $[0]$ $[2]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
109.1.8.7a1.4 $x^{8} + 11663$ $109$ $1$ $8$ $7$ $C_8:C_2$ (as 8T7) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 103$ $x^{8} + 11663$ $[0]$ $[2]$ $z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ undefined
109.9.1.0a1.1 $x^{9} + 93 x^{2} + 87 x + 103$ $109$ $9$ $1$ $0$ $C_9$ (as 9T1) $9$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{9}$ $[\ ]^{9}$ $[\ ]$ $[\ ]$ $t^{9} + 93 t^{2} + 87 t + 103$ $x - 109$ $[0]$ $[\ ]$ undefined
109.3.3.6a1.1 $( x^{3} + x + 103 )^{3} + 109 x^{2}$ $109$ $3$ $3$ $6$ $C_9$ (as 9T1) $3$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{3}$ $[\ ]_{3}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 103$ $x^{3} + 109 t^{2}$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.3.3.6a1.2 $( x^{3} + x + 103 )^{3} + 109 x$ $109$ $3$ $3$ $6$ $C_9$ (as 9T1) $3$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{3}$ $[\ ]_{3}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 103$ $x^{3} + 109 t$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.3.3.6a1.3 $( x^{3} + x + 103 )^{3} + 109$ $109$ $3$ $3$ $6$ $C_3^2$ (as 9T2) $3$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{3}$ $[\ ]_{3}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 103$ $x^{3} + 109$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
109.1.9.8a1.1 $x^{9} + 109$ $109$ $1$ $9$ $8$ $C_9$ (as 9T1) $1$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}$ $[\ ]_{9}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{9} + 109$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 17 z^4 + 17 z^3 + 84 z^2 + 36 z + 9$ undefined
109.1.9.8a1.2 $x^{9} + 436$ $109$ $1$ $9$ $8$ $C_9$ (as 9T1) $1$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}$ $[\ ]_{9}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{9} + 436$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 17 z^4 + 17 z^3 + 84 z^2 + 36 z + 9$ undefined
109.1.9.8a1.3 $x^{9} + 654$ $109$ $1$ $9$ $8$ $C_9$ (as 9T1) $1$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}$ $[\ ]_{9}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{9} + 654$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 17 z^4 + 17 z^3 + 84 z^2 + 36 z + 9$ undefined
109.1.9.8a1.4 $x^{9} + 2616$ $109$ $1$ $9$ $8$ $C_9$ (as 9T1) $1$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}$ $[\ ]_{9}$ $[\ ]$ $[\ ]$ $t + 103$ $x^{9} + 2616$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 17 z^4 + 17 z^3 + 84 z^2 + 36 z + 9$ undefined
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