LMFDB - p-adic field search results

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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 544 matches)

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Label	$n$	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	$\#\Aut(K/\Q_p)$	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
19.1.1.0a1.1	$1$	$x + 17$	$19$	$1$	$1$	$0$	Trivial (as 1T1)	$1$	$1$	$[\ ]$	$[\ ]$	$[\ ]$	$[\ ]$	$[\ ]$	$[\ ]$	$1$	$t + 17$	$x - 19$	$[0]$	$[\ ]$		undefined
19.2.1.0a1.1	$2$	$x^{2} + 18 x + 2$	$19$	$2$	$1$	$0$	$C_2$ (as 2T1)	$2$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{2}$	$[\ ]^{2}$	$[\ ]$	$[\ ]$	$2$	$t^{2} + 18 t + 2$	$x - 19$	$[0]$	$[\ ]$		undefined
19.1.2.1a1.1	$2$	$x^{2} + 19$	$19$	$1$	$2$	$1$	$C_2$ (as 2T1)	$1$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}$	$[\ ]_{2}$	$[\ ]$	$[\ ]$	$2$	$t + 17$	$x^{2} + 19$	$[0]$	$[1]$	$z + 2$	undefined
19.1.2.1a1.2	$2$	$x^{2} + 38$	$19$	$1$	$2$	$1$	$C_2$ (as 2T1)	$1$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}$	$[\ ]_{2}$	$[\ ]$	$[\ ]$	$2$	$t + 17$	$x^{2} + 38$	$[0]$	$[1]$	$z + 2$	undefined
19.3.1.0a1.1	$3$	$x^{3} + 4 x + 17$	$19$	$3$	$1$	$0$	$C_3$ (as 3T1)	$3$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{3}$	$[\ ]^{3}$	$[\ ]$	$[\ ]$	$3$	$t^{3} + 4 t + 17$	$x - 19$	$[0]$	$[\ ]$		undefined
19.1.3.2a1.1	$3$	$x^{3} + 19$	$19$	$1$	$3$	$2$	$C_3$ (as 3T1)	$1$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}$	$[\ ]_{3}$	$[\ ]$	$[\ ]$	$3$	$t + 17$	$x^{3} + 19$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.1.3.2a1.2	$3$	$x^{3} + 38$	$19$	$1$	$3$	$2$	$C_3$ (as 3T1)	$1$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}$	$[\ ]_{3}$	$[\ ]$	$[\ ]$	$3$	$t + 17$	$x^{3} + 38$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.1.3.2a1.3	$3$	$x^{3} + 76$	$19$	$1$	$3$	$2$	$C_3$ (as 3T1)	$1$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}$	$[\ ]_{3}$	$[\ ]$	$[\ ]$	$3$	$t + 17$	$x^{3} + 76$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.4.1.0a1.1	$4$	$x^{4} + 2 x^{2} + 11 x + 2$	$19$	$4$	$1$	$0$	$C_4$ (as 4T1)	$4$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{4}$	$[\ ]^{4}$	$[\ ]$	$[\ ]$	$4$	$t^{4} + 2 t^{2} + 11 t + 2$	$x - 19$	$[0]$	$[\ ]$		undefined
19.2.2.2a1.1	$4$	$( x^{2} + 18 x + 2 )^{2} + 19 x$	$19$	$2$	$2$	$2$	$C_4$ (as 4T1)	$2$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{2}$	$[\ ]_{2}^{2}$	$[\ ]$	$[\ ]$	$4$	$t^{2} + 18 t + 2$	$x^{2} + 19 t$	$[0]$	$[1]$	$z + 2$	undefined
19.2.2.2a1.2	$4$	$( x^{2} + 18 x + 2 )^{2} + 19$	$19$	$2$	$2$	$2$	$C_2^2$ (as 4T2)	$2$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{2}$	$[\ ]_{2}^{2}$	$[\ ]$	$[\ ]$	$4$	$t^{2} + 18 t + 2$	$x^{2} + 19$	$[0]$	$[1]$	$z + 2$	undefined
19.1.4.3a1.1	$4$	$x^{4} + 19$	$19$	$1$	$4$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]$	$[\ ]$	$[\ ]_{4}^{2}$	$[\ ]_{4}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$2$	$t + 17$	$x^{4} + 19$	$[0]$	$[2]$	$z^3 + 4 z^2 + 6 z + 4$	undefined
19.1.4.3a1.2	$4$	$x^{4} + 38$	$19$	$1$	$4$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]$	$[\ ]$	$[\ ]_{4}^{2}$	$[\ ]_{4}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$2$	$t + 17$	$x^{4} + 38$	$[0]$	$[2]$	$z^3 + 4 z^2 + 6 z + 4$	undefined
19.5.1.0a1.1	$5$	$x^{5} + 5 x + 17$	$19$	$5$	$1$	$0$	$C_5$ (as 5T1)	$5$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{5}$	$[\ ]^{5}$	$[\ ]$	$[\ ]$	$5$	$t^{5} + 5 t + 17$	$x - 19$	$[0]$	$[\ ]$		undefined
19.1.5.4a1.1	$5$	$x^{5} + 19$	$19$	$1$	$5$	$4$	$D_{5}$ (as 5T2)	$2$	$5$	$[\ ]$	$[\ ]$	$[\ ]_{5}^{2}$	$[\ ]_{5}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$1$	$t + 17$	$x^{5} + 19$	$[0]$	$[2]$	$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$	undefined
19.6.1.0a1.1	$6$	$x^{6} + 17 x^{3} + 17 x^{2} + 6 x + 2$	$19$	$6$	$1$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{6}$	$[\ ]^{6}$	$[\ ]$	$[\ ]$	$6$	$t^{6} + 17 t^{3} + 17 t^{2} + 6 t + 2$	$x - 19$	$[0]$	$[\ ]$		undefined
19.3.2.3a1.1	$6$	$( x^{3} + 4 x + 17 )^{2} + 19 x$	$19$	$3$	$2$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{3}$	$[\ ]_{2}^{3}$	$[\ ]$	$[\ ]$	$6$	$t^{3} + 4 t + 17$	$x^{2} + 19 t$	$[0]$	$[1]$	$z + 2$	undefined
19.3.2.3a1.2	$6$	$( x^{3} + 4 x + 17 )^{2} + 19$	$19$	$3$	$2$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{3}$	$[\ ]_{2}^{3}$	$[\ ]$	$[\ ]$	$6$	$t^{3} + 4 t + 17$	$x^{2} + 19$	$[0]$	$[1]$	$z + 2$	undefined
19.2.3.4a1.1	$6$	$( x^{2} + 18 x + 2 )^{3} + 19 x$	$19$	$2$	$3$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{2}$	$[\ ]_{3}^{2}$	$[\ ]$	$[\ ]$	$6$	$t^{2} + 18 t + 2$	$x^{3} + 19 t$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.2.3.4a1.2	$6$	$( x^{2} + 18 x + 2 )^{3} + 19$	$19$	$2$	$3$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{2}$	$[\ ]_{3}^{2}$	$[\ ]$	$[\ ]$	$6$	$t^{2} + 18 t + 2$	$x^{3} + 19$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.2.3.4a1.3	$6$	$( x^{2} + 18 x + 2 )^{3} + 19 x + 323$	$19$	$2$	$3$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{2}$	$[\ ]_{3}^{2}$	$[\ ]$	$[\ ]$	$6$	$t^{2} + 18 t + 2$	$x^{3} + 19 t + 323$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.1.6.5a1.1	$6$	$x^{6} + 19$	$19$	$1$	$6$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]$	$[\ ]$	$[\ ]_{6}$	$[\ ]_{6}$	$[\ ]$	$[\ ]$	$6$	$t + 17$	$x^{6} + 19$	$[0]$	$[1]$	$z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$	undefined
19.1.6.5a1.2	$6$	$x^{6} + 38$	$19$	$1$	$6$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]$	$[\ ]$	$[\ ]_{6}$	$[\ ]_{6}$	$[\ ]$	$[\ ]$	$6$	$t + 17$	$x^{6} + 38$	$[0]$	$[1]$	$z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$	undefined
19.1.6.5a1.3	$6$	$x^{6} + 76$	$19$	$1$	$6$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]$	$[\ ]$	$[\ ]_{6}$	$[\ ]_{6}$	$[\ ]$	$[\ ]$	$6$	$t + 17$	$x^{6} + 76$	$[0]$	$[1]$	$z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$	undefined
19.1.6.5a1.4	$6$	$x^{6} + 152$	$19$	$1$	$6$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]$	$[\ ]$	$[\ ]_{6}$	$[\ ]_{6}$	$[\ ]$	$[\ ]$	$6$	$t + 17$	$x^{6} + 152$	$[0]$	$[1]$	$z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$	undefined
19.1.6.5a1.5	$6$	$x^{6} + 247$	$19$	$1$	$6$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]$	$[\ ]$	$[\ ]_{6}$	$[\ ]_{6}$	$[\ ]$	$[\ ]$	$6$	$t + 17$	$x^{6} + 247$	$[0]$	$[1]$	$z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$	undefined
19.1.6.5a1.6	$6$	$x^{6} + 304$	$19$	$1$	$6$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]$	$[\ ]$	$[\ ]_{6}$	$[\ ]_{6}$	$[\ ]$	$[\ ]$	$6$	$t + 17$	$x^{6} + 304$	$[0]$	$[1]$	$z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$	undefined
19.7.1.0a1.1	$7$	$x^{7} + 6 x + 17$	$19$	$7$	$1$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{7}$	$[\ ]^{7}$	$[\ ]$	$[\ ]$	$7$	$t^{7} + 6 t + 17$	$x - 19$	$[0]$	$[\ ]$		undefined
19.1.7.6a1.1	$7$	$x^{7} + 19$	$19$	$1$	$7$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]$	$[\ ]_{7}^{6}$	$[\ ]_{7}^{6}$	$[\ ]^{6}$	$[\ ]^{6}$	$1$	$t + 17$	$x^{7} + 19$	$[0]$	$[6]$	$z^6 + 7 z^5 + 2 z^4 + 16 z^3 + 16 z^2 + 2 z + 7$	undefined
19.8.1.0a1.1	$8$	$x^{8} + x^{4} + 12 x^{3} + 10 x^{2} + 3 x + 2$	$19$	$8$	$1$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{8}$	$[\ ]^{8}$	$[\ ]$	$[\ ]$	$8$	$t^{8} + t^{4} + 12 t^{3} + 10 t^{2} + 3 t + 2$	$x - 19$	$[0]$	$[\ ]$		undefined
19.4.2.4a1.1	$8$	$( x^{4} + 2 x^{2} + 11 x + 2 )^{2} + 19 x$	$19$	$4$	$2$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{4}$	$[\ ]_{2}^{4}$	$[\ ]$	$[\ ]$	$8$	$t^{4} + 2 t^{2} + 11 t + 2$	$x^{2} + 19 t$	$[0]$	$[1]$	$z + 2$	undefined
19.4.2.4a1.2	$8$	$( x^{4} + 2 x^{2} + 11 x + 2 )^{2} + 19$	$19$	$4$	$2$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{4}$	$[\ ]_{2}^{4}$	$[\ ]$	$[\ ]$	$8$	$t^{4} + 2 t^{2} + 11 t + 2$	$x^{2} + 19$	$[0]$	$[1]$	$z + 2$	undefined
19.2.4.6a1.1	$8$	$( x^{2} + 18 x + 2 )^{4} + 19 x$	$19$	$2$	$4$	$6$	$C_8:C_2$ (as 8T7)	$4$	$4$	$[\ ]$	$[\ ]$	$[\ ]_{4}^{4}$	$[\ ]_{4}^{4}$	$[\ ]^{2}$	$[\ ]^{2}$	$4$	$t^{2} + 18 t + 2$	$x^{4} + 342 t + 323$	$[0]$	$[1]$	$z^3 + 4 z^2 + 6 z + 4$	undefined
19.2.4.6a1.2	$8$	$( x^{2} + 18 x + 2 )^{4} + 19$	$19$	$2$	$4$	$6$	$D_4$ (as 8T4)	$2$	$4$	$[\ ]$	$[\ ]$	$[\ ]_{4}^{2}$	$[\ ]_{4}^{2}$	$[\ ]$	$[\ ]$	$8$	$t^{2} + 18 t + 2$	$x^{4} + 19$	$[0]$	$[1]$	$z^3 + 4 z^2 + 6 z + 4$	undefined
19.2.4.6a1.3	$8$	$( x^{2} + 18 x + 2 )^{4} + 19 x + 323$	$19$	$2$	$4$	$6$	$Q_8$ (as 8T5)	$2$	$4$	$[\ ]$	$[\ ]$	$[\ ]_{4}^{2}$	$[\ ]_{4}^{2}$	$[\ ]$	$[\ ]$	$8$	$t^{2} + 18 t + 2$	$x^{4} + 19 t + 323$	$[0]$	$[1]$	$z^3 + 4 z^2 + 6 z + 4$	undefined
19.1.8.7a1.1	$8$	$x^{8} + 19$	$19$	$1$	$8$	$7$	$QD_{16}$ (as 8T8)	$2$	$8$	$[\ ]$	$[\ ]$	$[\ ]_{8}^{2}$	$[\ ]_{8}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$2$	$t + 17$	$x^{8} + 19$	$[0]$	$[2]$	$z^7 + 8 z^6 + 9 z^5 + 18 z^4 + 13 z^3 + 18 z^2 + 9 z + 8$	undefined
19.1.8.7a1.2	$8$	$x^{8} + 38$	$19$	$1$	$8$	$7$	$QD_{16}$ (as 8T8)	$2$	$8$	$[\ ]$	$[\ ]$	$[\ ]_{8}^{2}$	$[\ ]_{8}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$2$	$t + 17$	$x^{8} + 38$	$[0]$	$[2]$	$z^7 + 8 z^6 + 9 z^5 + 18 z^4 + 13 z^3 + 18 z^2 + 9 z + 8$	undefined
19.9.1.0a1.1	$9$	$x^{9} + 11 x^{3} + 14 x^{2} + 16 x + 17$	$19$	$9$	$1$	$0$	$C_9$ (as 9T1)	$9$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{9}$	$[\ ]^{9}$	$[\ ]$	$[\ ]$	$9$	$t^{9} + 11 t^{3} + 14 t^{2} + 16 t + 17$	$x - 19$	$[0]$	$[\ ]$		undefined
19.3.3.6a1.1	$9$	$( x^{3} + 4 x + 17 )^{3} + 19 x^{2}$	$19$	$3$	$3$	$6$	$C_9$ (as 9T1)	$3$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{3}$	$[\ ]_{3}^{3}$	$[\ ]$	$[\ ]$	$9$	$t^{3} + 4 t + 17$	$x^{3} + 19 t^{2}$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.3.3.6a1.2	$9$	$( x^{3} + 4 x + 17 )^{3} + 19 x$	$19$	$3$	$3$	$6$	$C_9$ (as 9T1)	$3$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{3}$	$[\ ]_{3}^{3}$	$[\ ]$	$[\ ]$	$9$	$t^{3} + 4 t + 17$	$x^{3} + 19 t$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.3.3.6a1.3	$9$	$( x^{3} + 4 x + 17 )^{3} + 19$	$19$	$3$	$3$	$6$	$C_3^2$ (as 9T2)	$3$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{3}$	$[\ ]_{3}^{3}$	$[\ ]$	$[\ ]$	$9$	$t^{3} + 4 t + 17$	$x^{3} + 19$	$[0]$	$[1]$	$z^2 + 3 z + 3$	undefined
19.1.9.8a1.1	$9$	$x^{9} + 19$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 19$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.2	$9$	$x^{9} + 38$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 38$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.3	$9$	$x^{9} + 76$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 76$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.4	$9$	$x^{9} + 133$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 133$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.5	$9$	$x^{9} + 152$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 152$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.6	$9$	$x^{9} + 171$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 171$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.7	$9$	$x^{9} + 247$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 247$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.8	$9$	$x^{9} + 266$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 266$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined
19.1.9.8a1.9	$9$	$x^{9} + 304$	$19$	$1$	$9$	$8$	$C_9$ (as 9T1)	$1$	$9$	$[\ ]$	$[\ ]$	$[\ ]_{9}$	$[\ ]_{9}$	$[\ ]$	$[\ ]$	$9$	$t + 17$	$x^{9} + 304$	$[0]$	$[1]$	$z^8 + 9 z^7 + 17 z^6 + 8 z^5 + 12 z^4 + 12 z^3 + 8 z^2 + 17 z + 9$	undefined

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