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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (1-50 of 2622 matches)

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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
11.1.1.0a1.1 $x + 9$ $11$ $1$ $1$ $0$ Trivial (as 1T1) $1$ $1$ $[\ ]$ $[\ ]$ $[\ ]$ $[\ ]$ $[\ ]$ $[\ ]$ $t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
11.2.1.0a1.1 $x^{2} + 7 x + 2$ $11$ $2$ $1$ $0$ $C_2$ (as 2T1) $2$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{2}$ $[\ ]^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x - 11$ $[0]$ $[\ ]$ undefined
11.1.2.1a1.1 $x^{2} + 11$ $11$ $1$ $2$ $1$ $C_2$ (as 2T1) $1$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}$ $[\ ]_{2}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{2} + 11$ $[0]$ $[1]$ $z + 2$ undefined
11.1.2.1a1.2 $x^{2} + 22$ $11$ $1$ $2$ $1$ $C_2$ (as 2T1) $1$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}$ $[\ ]_{2}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{2} + 22$ $[0]$ $[1]$ $z + 2$ undefined
11.3.1.0a1.1 $x^{3} + 2 x + 9$ $11$ $3$ $1$ $0$ $C_3$ (as 3T1) $3$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{3}$ $[\ ]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
11.1.3.2a1.1 $x^{3} + 11$ $11$ $1$ $3$ $2$ $S_3$ (as 3T2) $2$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{2}$ $[\ ]_{3}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{3} + 11$ $[0]$ $[2]$ $z^2 + 3 z + 3$ undefined
11.4.1.0a1.1 $x^{4} + 8 x^{2} + 10 x + 2$ $11$ $4$ $1$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{4}$ $[\ ]^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 8 t^{2} + 10 t + 2$ $x - 11$ $[0]$ $[\ ]$ undefined
11.2.2.2a1.1 $( x^{2} + 7 x + 2 )^{2} + 11 x$ $11$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{2}$ $[\ ]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{2} + 11 t$ $[0]$ $[1]$ $z + 2$ undefined
11.2.2.2a1.2 $( x^{2} + 7 x + 2 )^{2} + 11$ $11$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{2}$ $[\ ]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{2} + 11$ $[0]$ $[1]$ $z + 2$ undefined
11.1.4.3a1.1 $x^{4} + 11$ $11$ $1$ $4$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{4} + 11$ $[0]$ $[2]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
11.1.4.3a1.2 $x^{4} + 22$ $11$ $1$ $4$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{4} + 22$ $[0]$ $[2]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
11.5.1.0a1.1 $x^{5} + 10 x^{2} + 9$ $11$ $5$ $1$ $0$ $C_5$ (as 5T1) $5$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{5}$ $[\ ]^{5}$ $[\ ]$ $[\ ]$ $t^{5} + 10 t^{2} + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
11.1.5.4a1.1 $x^{5} + 11$ $11$ $1$ $5$ $4$ $C_5$ (as 5T1) $1$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}$ $[\ ]_{5}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{5} + 11$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.1.5.4a1.2 $x^{5} + 22$ $11$ $1$ $5$ $4$ $C_5$ (as 5T1) $1$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}$ $[\ ]_{5}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{5} + 22$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.1.5.4a1.3 $x^{5} + 44$ $11$ $1$ $5$ $4$ $C_5$ (as 5T1) $1$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}$ $[\ ]_{5}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{5} + 44$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.1.5.4a1.4 $x^{5} + 55$ $11$ $1$ $5$ $4$ $C_5$ (as 5T1) $1$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}$ $[\ ]_{5}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{5} + 55$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.1.5.4a1.5 $x^{5} + 88$ $11$ $1$ $5$ $4$ $C_5$ (as 5T1) $1$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}$ $[\ ]_{5}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{5} + 88$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.6.1.0a1.1 $x^{6} + 3 x^{4} + 4 x^{3} + 6 x^{2} + 7 x + 2$ $11$ $6$ $1$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{6}$ $[\ ]^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 3 t^{4} + 4 t^{3} + 6 t^{2} + 7 t + 2$ $x - 11$ $[0]$ $[\ ]$ undefined
11.3.2.3a1.1 $( x^{3} + 2 x + 9 )^{2} + 11 x$ $11$ $3$ $2$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{3}$ $[\ ]_{2}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 9$ $x^{2} + 11 t$ $[0]$ $[1]$ $z + 2$ undefined
11.3.2.3a1.2 $( x^{3} + 2 x + 9 )^{2} + 11$ $11$ $3$ $2$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{3}$ $[\ ]_{2}^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 9$ $x^{2} + 11$ $[0]$ $[1]$ $z + 2$ undefined
11.2.3.4a1.1 $( x^{2} + 7 x + 2 )^{3} + 11 x$ $11$ $2$ $3$ $4$ $S_3\times C_3$ (as 6T5) $6$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{6}$ $[\ ]_{3}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 7 t + 2$ $x^{3} + 44 t + 99$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
11.2.3.4a1.2 $( x^{2} + 7 x + 2 )^{3} + 11$ $11$ $2$ $3$ $4$ $S_3$ (as 6T2) $2$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{2}$ $[\ ]_{3}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{3} + 11$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
11.1.6.5a1.1 $x^{6} + 11$ $11$ $1$ $6$ $5$ $D_{6}$ (as 6T3) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{6} + 11$ $[0]$ $[2]$ $z^5 + 6 z^4 + 4 z^3 + 9 z^2 + 4 z + 6$ undefined
11.1.6.5a1.2 $x^{6} + 22$ $11$ $1$ $6$ $5$ $D_{6}$ (as 6T3) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{6} + 22$ $[0]$ $[2]$ $z^5 + 6 z^4 + 4 z^3 + 9 z^2 + 4 z + 6$ undefined
11.7.1.0a1.1 $x^{7} + 4 x + 9$ $11$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 4 t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
11.1.7.6a1.1 $x^{7} + 11$ $11$ $1$ $7$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}^{3}$ $[\ ]_{7}^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $t + 9$ $x^{7} + 11$ $[0]$ $[3]$ $z^6 + 7 z^5 + 10 z^4 + 2 z^3 + 2 z^2 + 10 z + 7$ undefined
11.8.1.0a1.1 $x^{8} + 7 x^{4} + 7 x^{3} + x^{2} + 7 x + 2$ $11$ $8$ $1$ $0$ $C_8$ (as 8T1) $8$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{8}$ $[\ ]^{8}$ $[\ ]$ $[\ ]$ $t^{8} + 7 t^{4} + 7 t^{3} + t^{2} + 7 t + 2$ $x - 11$ $[0]$ $[\ ]$ undefined
11.4.2.4a1.1 $( x^{4} + 8 x^{2} + 10 x + 2 )^{2} + 11 x$ $11$ $4$ $2$ $4$ $C_8$ (as 8T1) $4$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{4}$ $[\ ]_{2}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 8 t^{2} + 10 t + 2$ $x^{2} + 11 t$ $[0]$ $[1]$ $z + 2$ undefined
11.4.2.4a1.2 $( x^{4} + 8 x^{2} + 10 x + 2 )^{2} + 11$ $11$ $4$ $2$ $4$ $C_4\times C_2$ (as 8T2) $4$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{4}$ $[\ ]_{2}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 8 t^{2} + 10 t + 2$ $x^{2} + 11$ $[0]$ $[1]$ $z + 2$ undefined
11.2.4.6a1.1 $( x^{2} + 7 x + 2 )^{4} + 11 x$ $11$ $2$ $4$ $6$ $C_8:C_2$ (as 8T7) $4$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{4}$ $[\ ]_{4}^{4}$ $[\ ]^{2}$ $[\ ]^{2}$ $t^{2} + 7 t + 2$ $x^{4} + 33 t + 33$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
11.2.4.6a1.2 $( x^{2} + 7 x + 2 )^{4} + 11$ $11$ $2$ $4$ $6$ $D_4$ (as 8T4) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{4} + 11$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
11.2.4.6a1.3 $( x^{2} + 7 x + 2 )^{4} + 44 x + 99$ $11$ $2$ $4$ $6$ $Q_8$ (as 8T5) $2$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{2}$ $[\ ]_{4}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{4} + 44 t + 99$ $[0]$ $[1]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
11.1.8.7a1.1 $x^{8} + 11$ $11$ $1$ $8$ $7$ $QD_{16}$ (as 8T8) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{8} + 11$ $[0]$ $[2]$ $z^7 + 8 z^6 + 6 z^5 + z^4 + 4 z^3 + z^2 + 6 z + 8$ undefined
11.1.8.7a1.2 $x^{8} + 22$ $11$ $1$ $8$ $7$ $QD_{16}$ (as 8T8) $2$ $8$ $[\ ]$ $[\ ]$ $[\ ]_{8}^{2}$ $[\ ]_{8}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 9$ $x^{8} + 22$ $[0]$ $[2]$ $z^7 + 8 z^6 + 6 z^5 + z^4 + 4 z^3 + z^2 + 6 z + 8$ undefined
11.9.1.0a1.1 $x^{9} + 9 x^{2} + 8 x + 9$ $11$ $9$ $1$ $0$ $C_9$ (as 9T1) $9$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{9}$ $[\ ]^{9}$ $[\ ]$ $[\ ]$ $t^{9} + 9 t^{2} + 8 t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
11.3.3.6a1.1 $( x^{3} + 2 x + 9 )^{3} + 11$ $11$ $3$ $3$ $6$ $S_3\times C_3$ (as 9T4) $6$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{6}$ $[\ ]_{3}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $t^{3} + 2 t + 9$ $x^{3} + 11$ $[0]$ $[2]$ $z^2 + 3 z + 3$ undefined
11.1.9.8a1.1 $x^{9} + 11$ $11$ $1$ $9$ $8$ $(C_9:C_3):C_2$ (as 9T10) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $t + 9$ $x^{9} + 11$ $[0]$ $[6]$ $z^8 + 9 z^7 + 3 z^6 + 7 z^5 + 5 z^4 + 5 z^3 + 7 z^2 + 3 z + 9$ undefined
11.10.1.0a1.1 $x^{10} + 7 x^{5} + 8 x^{4} + 10 x^{3} + 6 x^{2} + 6 x + 2$ $11$ $10$ $1$ $0$ $C_{10}$ (as 10T1) $10$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{10}$ $[\ ]^{10}$ $[\ ]$ $[\ ]$ $t^{10} + 7 t^{5} + 8 t^{4} + 10 t^{3} + 6 t^{2} + 6 t + 2$ $x - 11$ $[0]$ $[\ ]$ undefined
11.5.2.5a1.1 $( x^{5} + 10 x^{2} + 9 )^{2} + 11 x$ $11$ $5$ $2$ $5$ $C_{10}$ (as 10T1) $5$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{5}$ $[\ ]_{2}^{5}$ $[\ ]$ $[\ ]$ $t^{5} + 10 t^{2} + 9$ $x^{2} + 11 t$ $[0]$ $[1]$ $z + 2$ undefined
11.5.2.5a1.2 $( x^{5} + 10 x^{2} + 9 )^{2} + 11$ $11$ $5$ $2$ $5$ $C_{10}$ (as 10T1) $5$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{5}$ $[\ ]_{2}^{5}$ $[\ ]$ $[\ ]$ $t^{5} + 10 t^{2} + 9$ $x^{2} + 11$ $[0]$ $[1]$ $z + 2$ undefined
11.2.5.8a1.1 $( x^{2} + 7 x + 2 )^{5} + 11 x$ $11$ $2$ $5$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{2}$ $[\ ]_{5}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{5} + 11 t$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.2.5.8a1.2 $( x^{2} + 7 x + 2 )^{5} + 11$ $11$ $2$ $5$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{2}$ $[\ ]_{5}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{5} + 11$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.2.5.8a1.3 $( x^{2} + 7 x + 2 )^{5} + 33 x + 33$ $11$ $2$ $5$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{2}$ $[\ ]_{5}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{5} + 33 t + 33$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.2.5.8a1.4 $( x^{2} + 7 x + 2 )^{5} + 44 x + 55$ $11$ $2$ $5$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{2}$ $[\ ]_{5}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{5} + 44 t + 55$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.2.5.8a1.5 $( x^{2} + 7 x + 2 )^{5} + 44 x + 99$ $11$ $2$ $5$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{2}$ $[\ ]_{5}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 7 t + 2$ $x^{5} + 44 t + 99$ $[0]$ $[1]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
11.1.10.9a1.1 $x^{10} + 11$ $11$ $1$ $10$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]$ $[\ ]_{10}$ $[\ ]_{10}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{10} + 11$ $[0]$ $[1]$ $z^9 + 10 z^8 + z^7 + 10 z^6 + z^5 + 10 z^4 + z^3 + 10 z^2 + z + 10$ $[1]$
11.1.10.9a1.2 $x^{10} + 22$ $11$ $1$ $10$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]$ $[\ ]_{10}$ $[\ ]_{10}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{10} + 22$ $[0]$ $[1]$ $z^9 + 10 z^8 + z^7 + 10 z^6 + z^5 + 10 z^4 + z^3 + 10 z^2 + z + 10$ undefined
11.1.10.9a1.3 $x^{10} + 33$ $11$ $1$ $10$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]$ $[\ ]_{10}$ $[\ ]_{10}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{10} + 33$ $[0]$ $[1]$ $z^9 + 10 z^8 + z^7 + 10 z^6 + z^5 + 10 z^4 + z^3 + 10 z^2 + z + 10$ undefined
11.1.10.9a1.4 $x^{10} + 44$ $11$ $1$ $10$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]$ $[\ ]_{10}$ $[\ ]_{10}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{10} + 44$ $[0]$ $[1]$ $z^9 + 10 z^8 + z^7 + 10 z^6 + z^5 + 10 z^4 + z^3 + 10 z^2 + z + 10$ undefined
11.1.10.9a1.5 $x^{10} + 55$ $11$ $1$ $10$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]$ $[\ ]_{10}$ $[\ ]_{10}$ $[\ ]$ $[\ ]$ $t + 9$ $x^{10} + 55$ $[0]$ $[1]$ $z^9 + 10 z^8 + z^7 + 10 z^6 + z^5 + 10 z^4 + z^3 + 10 z^2 + z + 10$ undefined
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