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Jones polynomials of the prime knots with at most ten crossings
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Polynomials
$n$
$k$
knot 
$t^{-m}V_K(t)$
0
1
$K$:
1
comment: $0_1$, the unknot; $V=1$, and whether any nontrivial knot has $V=1$ is an open question
equals: One
3
1
$K$:
-t^3 + t^2 + 1
comment: $3_1$, the right-handed trefoil, the torus knot $T(2,3)$; $m=1$; determinant $3$, signature $-2$, alternating
3
1
$\bar K$:
t^3 + t - 1
comment: the mirror image of $3_1$, the left-handed trefoil; $m=-4$; signature $2$
4
1
$K$:
t^4 - t^3 + t^2 - t + 1
comment: $4_1$, the figure-eight knot; $m=-2$; determinant $5$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
5
1
$K$:
-t^5 + t^4 - t^3 + t^2 + 1
comment: $5_1$, the cinquefoil, the torus knot $T(2,5)$; $m=2$; determinant $5$, signature $-4$, alternating; the same polynomial as the mirror image of $10_{132}$
5
1
$\bar K$:
t^5 + t^3 - t^2 + t - 1
comment: the mirror image of $5_1$, the cinquefoil; $m=-7$; signature $4$; the same polynomial as $10_{132}$
5
2
$K$:
-t^5 + t^4 - t^3 + 2*t^2 - t + 1
comment: $5_2$, the three-twist knot; $m=1$; determinant $7$, signature $-2$, alternating
5
2
$\bar K$:
t^5 - t^4 + 2*t^3 - t^2 + t - 1
comment: the mirror image of $5_2$, the three-twist knot; $m=-6$; signature $2$
6
1
$K$:
t^6 - t^5 + t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $6_1$, the stevedore knot; $m=-2$; determinant $9$, signature $0$, alternating
6
1
$\bar K$:
t^6 - t^5 + 2*t^4 - 2*t^3 + t^2 - t + 1
comment: the mirror image of $6_1$, the stevedore knot; $m=-4$; signature $0$
6
2
$K$:
t^6 - 2*t^5 + 2*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $6_2$, the Miller Institute knot; $m=-1$; determinant $11$, signature $-2$, alternating
6
2
$\bar K$:
t^6 - t^5 + 2*t^4 - 2*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $6_2$, the Miller Institute knot; $m=-5$; signature $2$
6
3
$K$:
-t^6 + 2*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + 2*t - 1
comment: $6_3$; $m=-3$; determinant $13$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
7
1
$K$:
-t^7 + t^6 - t^5 + t^4 - t^3 + t^2 + 1
comment: $7_1$, the torus knot $T(2,7)$; $m=3$; determinant $7$, signature $-6$, alternating
7
1
$\bar K$:
t^7 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: the mirror image of $7_1$; $m=-10$; signature $6$
7
2
$K$:
-t^7 + t^6 - t^5 + 2*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $7_2$; $m=1$; determinant $11$, signature $-2$, alternating
7
2
$\bar K$:
t^7 - t^6 + 2*t^5 - 2*t^4 + 2*t^3 - t^2 + t - 1
comment: the mirror image of $7_2$; $m=-8$; signature $2$
7
3
$K$:
-t^7 + t^6 - 2*t^5 + 3*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $7_3$; $m=2$; determinant $13$, signature $-4$, alternating
7
3
$\bar K$:
t^7 - t^6 + 2*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: the mirror image of $7_3$; $m=-9$; signature $4$
7
4
$K$:
-t^7 + t^6 - 2*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 2*t + 1
comment: $7_4$, the endless knot; $m=1$; determinant $15$, signature $-2$, alternating
7
4
$\bar K$:
t^7 - 2*t^6 + 3*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: the mirror image of $7_4$, the endless knot; $m=-8$; signature $2$
7
5
$K$:
-t^7 + 2*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 3*t^2 - t + 1
comment: $7_5$; $m=2$; determinant $17$, signature $-4$, alternating
7
5
$\bar K$:
t^7 - t^6 + 3*t^5 - 3*t^4 + 3*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $7_5$; $m=-9$; signature $4$
7
6
$K$:
-t^7 + 2*t^6 - 3*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $7_6$; $m=-1$; determinant $19$, signature $-2$, alternating
7
6
$\bar K$:
t^7 - 2*t^6 + 3*t^5 - 3*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $7_6$; $m=-6$; signature $2$
7
7
$K$:
-t^7 + 3*t^6 - 3*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $7_7$; $m=-4$; determinant $21$, signature $0$, alternating
7
7
$\bar K$:
t^7 - 2*t^6 + 3*t^5 - 4*t^4 + 4*t^3 - 3*t^2 + 3*t - 1
comment: the mirror image of $7_7$; $m=-3$; signature $0$
8
1
$K$:
t^8 - t^7 + t^6 - 2*t^5 + 2*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $8_1$; $m=-2$; determinant $13$, signature $0$, alternating
8
1
$\bar K$:
t^8 - t^7 + 2*t^6 - 2*t^5 + 2*t^4 - 2*t^3 + t^2 - t + 1
comment: the mirror image of $8_1$; $m=-6$; signature $0$
8
2
$K$:
t^8 - 2*t^7 + 2*t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $8_2$; $m=0$; determinant $17$, signature $-4$, alternating
8
2
$\bar K$:
t^8 - t^7 + 2*t^6 - 2*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $8_2$; $m=-8$; signature $4$
8
3
$K$:
t^8 - t^7 + 2*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: $8_3$; $m=-4$; determinant $17$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
8
4
$K$:
t^8 - t^7 + 2*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $8_4$; $m=-5$; determinant $19$, signature $2$, alternating
8
4
$\bar K$:
t^8 - 2*t^7 + 3*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: the mirror image of $8_4$; $m=-3$; signature $-2$
8
5
$K$:
t^8 - 2*t^7 + 3*t^6 - 4*t^5 + 3*t^4 - 3*t^3 + 3*t^2 - t + 1
comment: $8_5$; $m=0$; determinant $21$, signature $-4$, alternating
8
5
$\bar K$:
t^8 - t^7 + 3*t^6 - 3*t^5 + 3*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $8_5$; $m=-8$; signature $4$
8
6
$K$:
t^8 - 2*t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - t + 1
comment: $8_6$; $m=-1$; determinant $23$, signature $-2$, alternating
8
6
$\bar K$:
t^8 - t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $8_6$; $m=-7$; signature $2$
8
7
$K$:
-t^8 + 2*t^7 - 2*t^6 + 4*t^5 - 4*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: $8_7$; $m=-6$; determinant $23$, signature $2$, alternating
8
7
$\bar K$:
-t^8 + 2*t^7 - 3*t^6 + 4*t^5 - 4*t^4 + 4*t^3 - 2*t^2 + 2*t - 1
comment: the mirror image of $8_7$; $m=-2$; signature $-2$
8
8
$K$:
-t^8 + 2*t^7 - 3*t^6 + 5*t^5 - 4*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: $8_8$; $m=-5$; determinant $25$, signature $0$, alternating; the same polynomial as the mirror image of $10_{129}$
8
8
$\bar K$:
-t^8 + 2*t^7 - 3*t^6 + 4*t^5 - 4*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $8_8$; $m=-3$; signature $0$; the same polynomial as $10_{129}$
8
9
$K$:
t^8 - 2*t^7 + 3*t^6 - 4*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $8_9$; $m=-4$; determinant $25$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
8
10
$K$:
-t^8 + 2*t^7 - 3*t^6 + 5*t^5 - 4*t^4 + 5*t^3 - 4*t^2 + 2*t - 1
comment: $8_{10}$; $m=-6$; determinant $27$, signature $2$, alternating
8
10
$\bar K$:
-t^8 + 2*t^7 - 4*t^6 + 5*t^5 - 4*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $8_{10}$; $m=-2$; signature $-2$
8
11
$K$:
t^8 - 2*t^7 + 3*t^6 - 5*t^5 + 5*t^4 - 4*t^3 + 4*t^2 - 2*t + 1
comment: $8_{11}$; $m=-1$; determinant $27$, signature $-2$, alternating
8
11
$\bar K$:
t^8 - 2*t^7 + 4*t^6 - 4*t^5 + 5*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $8_{11}$; $m=-7$; signature $2$
8
12
$K$:
t^8 - 2*t^7 + 4*t^6 - 5*t^5 + 5*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $8_{12}$; $m=-4$; determinant $29$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
8
13
$K$:
-t^8 + 3*t^7 - 4*t^6 + 5*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: $8_{13}$; $m=-5$; determinant $29$, signature $0$, alternating
8
13
$\bar K$:
-t^8 + 2*t^7 - 3*t^6 + 5*t^5 - 5*t^4 + 5*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $8_{13}$; $m=-3$; signature $0$
8
14
$K$:
t^8 - 3*t^7 + 4*t^6 - 5*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $8_{14}$; $m=-1$; determinant $31$, signature $-2$, alternating
8
14
$\bar K$:
t^8 - 2*t^7 + 4*t^6 - 5*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $8_{14}$; $m=-7$; signature $2$
8
15
$K$:
t^8 - 3*t^7 + 4*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 5*t^2 - 2*t + 1
comment: $8_{15}$; $m=2$; determinant $33$, signature $-4$, alternating
8
15
$\bar K$:
t^8 - 2*t^7 + 5*t^6 - 5*t^5 + 6*t^4 - 6*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $8_{15}$; $m=-10$; signature $4$
8
16
$K$:
-t^8 + 3*t^7 - 4*t^6 + 6*t^5 - 6*t^4 + 6*t^3 - 5*t^2 + 3*t - 1
comment: $8_{16}$; $m=-6$; determinant $35$, signature $2$, alternating; the same polynomial as $10_{156}$
8
16
$\bar K$:
-t^8 + 3*t^7 - 5*t^6 + 6*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $8_{16}$; $m=-2$; signature $-2$; the same polynomial as the mirror image of $10_{156}$
8
17
$K$:
t^8 - 3*t^7 + 5*t^6 - 6*t^5 + 7*t^4 - 6*t^3 + 5*t^2 - 3*t + 1
comment: $8_{17}$; $m=-4$; determinant $37$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
8
18
$K$:
t^8 - 4*t^7 + 6*t^6 - 7*t^5 + 9*t^4 - 7*t^3 + 6*t^2 - 4*t + 1
comment: $8_{18}$, the Carrick mat; $m=-4$; determinant $45$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
8
19
$K$:
-t^5 + t^2 + 1
comment: $8_{19}$, the torus knot $T(3,4)$; $m=3$; determinant $3$, signature $-6$, non-alternating
8
19
$\bar K$:
t^5 + t^3 - 1
comment: the mirror image of $8_{19}$; $m=-8$; signature $6$
8
20
$K$:
-t^6 + 2*t^5 - t^4 + 2*t^3 - t^2 + t - 1
comment: $8_{20}$; $m=-5$; determinant $9$, signature $0$, non-alternating
8
20
$\bar K$:
-t^6 + t^5 - t^4 + 2*t^3 - t^2 + 2*t - 1
comment: the mirror image of $8_{20}$; $m=-1$; signature $0$
8
21
$K$:
t^6 - 2*t^5 + 2*t^4 - 3*t^3 + 3*t^2 - 2*t + 2
comment: $8_{21}$; $m=1$; determinant $15$, signature $-2$, non-alternating
8
21
$\bar K$:
2*t^6 - 2*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $8_{21}$; $m=-7$; signature $2$
9
1
$K$:
-t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 + 1
comment: $9_1$, the torus knot $T(2,9)$; $m=4$; determinant $9$, signature $-8$, alternating
9
1
$\bar K$:
t^9 + t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: the mirror image of $9_1$; $m=-13$; signature $8$
9
2
$K$:
-t^9 + t^8 - t^7 + 2*t^6 - 2*t^5 + 2*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $9_2$; $m=1$; determinant $15$, signature $-2$, alternating
9
2
$\bar K$:
t^9 - t^8 + 2*t^7 - 2*t^6 + 2*t^5 - 2*t^4 + 2*t^3 - t^2 + t - 1
comment: the mirror image of $9_2$; $m=-10$; signature $2$
9
3
$K$:
-t^9 + t^8 - 2*t^7 + 3*t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $9_3$; $m=3$; determinant $19$, signature $-6$, alternating
9
3
$\bar K$:
t^9 - t^8 + 2*t^7 - 2*t^6 + 3*t^5 - 3*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: the mirror image of $9_3$; $m=-12$; signature $6$
9
4
$K$:
-t^9 + t^8 - 2*t^7 + 3*t^6 - 3*t^5 + 4*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: $9_4$; $m=2$; determinant $21$, signature $-4$, alternating
9
4
$\bar K$:
t^9 - t^8 + 2*t^7 - 3*t^6 + 4*t^5 - 3*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: the mirror image of $9_4$; $m=-11$; signature $4$
9
5
$K$:
-t^9 + t^8 - 2*t^7 + 3*t^6 - 3*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $9_5$; $m=1$; determinant $23$, signature $-2$, alternating
9
5
$\bar K$:
t^9 - 2*t^8 + 3*t^7 - 3*t^6 + 4*t^5 - 3*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: the mirror image of $9_5$; $m=-10$; signature $2$
9
6
$K$:
-t^9 + 2*t^8 - 3*t^7 + 4*t^6 - 5*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - t + 1
comment: $9_6$; $m=3$; determinant $27$, signature $-6$, alternating
9
6
$\bar K$:
t^9 - t^8 + 3*t^7 - 3*t^6 + 4*t^5 - 5*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $9_6$; $m=-12$; signature $6$
9
7
$K$:
-t^9 + 2*t^8 - 3*t^7 + 4*t^6 - 5*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - t + 1
comment: $9_7$; $m=2$; determinant $29$, signature $-4$, alternating
9
7
$\bar K$:
t^9 - t^8 + 3*t^7 - 4*t^6 + 5*t^5 - 5*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $9_7$; $m=-11$; signature $4$
9
8
$K$:
-t^9 + 2*t^8 - 3*t^7 + 5*t^6 - 5*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $9_8$; $m=-3$; determinant $31$, signature $-2$, alternating
9
8
$\bar K$:
t^9 - 2*t^8 + 3*t^7 - 4*t^6 + 5*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $9_8$; $m=-6$; signature $2$
9
9
$K$:
-t^9 + 2*t^8 - 4*t^7 + 5*t^6 - 5*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - t + 1
comment: $9_9$; $m=3$; determinant $31$, signature $-6$, alternating
9
9
$\bar K$:
t^9 - t^8 + 3*t^7 - 4*t^6 + 5*t^5 - 5*t^4 + 5*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $9_9$; $m=-12$; signature $6$
9
10
$K$:
-t^9 + t^8 - 3*t^7 + 5*t^6 - 5*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $9_{10}$; $m=2$; determinant $33$, signature $-4$, alternating
9
10
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 5*t^6 + 6*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + t - 1
comment: the mirror image of $9_{10}$; $m=-11$; signature $4$
9
11
$K$:
t^9 - 2*t^8 + 3*t^7 - 4*t^6 + 6*t^5 - 5*t^4 + 5*t^3 - 4*t^2 + 2*t - 1
comment: $9_{11}$; $m=-9$; determinant $33$, signature $4$, alternating
9
11
$\bar K$:
-t^9 + 2*t^8 - 4*t^7 + 5*t^6 - 5*t^5 + 6*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $9_{11}$; $m=0$; signature $-4$
9
12
$K$:
-t^9 + 2*t^8 - 3*t^7 + 5*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $9_{12}$; $m=-1$; determinant $35$, signature $-2$, alternating
9
12
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 5*t^6 + 6*t^5 - 6*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $9_{12}$; $m=-8$; signature $2$
9
13
$K$:
-t^9 + 2*t^8 - 4*t^7 + 5*t^6 - 6*t^5 + 7*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $9_{13}$; $m=2$; determinant $37$, signature $-4$, alternating
9
13
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 5*t^6 + 7*t^5 - 6*t^4 + 5*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $9_{13}$; $m=-11$; signature $4$
9
14
$K$:
-t^9 + 3*t^8 - 4*t^7 + 6*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: $9_{14}$; $m=-6$; determinant $37$, signature $0$, alternating
9
14
$\bar K$:
t^9 - 2*t^8 + 3*t^7 - 5*t^6 + 6*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $9_{14}$; $m=-3$; signature $0$
9
15
$K$:
t^9 - 2*t^8 + 4*t^7 - 6*t^6 + 7*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $9_{15}$; $m=-8$; determinant $39$, signature $2$, alternating
9
15
$\bar K$:
-t^9 + 2*t^8 - 4*t^7 + 6*t^6 - 6*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $9_{15}$; $m=-1$; signature $-2$
9
16
$K$:
-t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 7*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - t + 1
comment: $9_{16}$; $m=3$; determinant $39$, signature $-6$, alternating
9
16
$\bar K$:
t^9 - t^8 + 4*t^7 - 5*t^6 + 6*t^5 - 7*t^4 + 6*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{16}$; $m=-12$; signature $6$
9
17
$K$:
-t^9 + 3*t^8 - 4*t^7 + 6*t^6 - 7*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $9_{17}$; $m=-3$; determinant $39$, signature $-2$, alternating
9
17
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 5*t^6 + 6*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $9_{17}$; $m=-6$; signature $2$
9
18
$K$:
-t^9 + 2*t^8 - 4*t^7 + 6*t^6 - 7*t^5 + 7*t^4 - 6*t^3 + 5*t^2 - 2*t + 1
comment: $9_{18}$; $m=2$; determinant $41$, signature $-4$, alternating
9
18
$\bar K$:
t^9 - 2*t^8 + 5*t^7 - 6*t^6 + 7*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $9_{18}$; $m=-11$; signature $4$
9
19
$K$:
-t^9 + 3*t^8 - 4*t^7 + 6*t^6 - 7*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $9_{19}$; $m=-4$; determinant $41$, signature $0$, alternating
9
19
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 6*t^6 + 7*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $9_{19}$; $m=-5$; signature $0$
9
20
$K$:
-t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 7*t^5 + 7*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $9_{20}$; $m=0$; determinant $41$, signature $-4$, alternating
9
20
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 5*t^6 + 7*t^5 - 7*t^4 + 6*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{20}$; $m=-9$; signature $4$
9
21
$K$:
t^9 - 3*t^8 + 5*t^7 - 6*t^6 + 8*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $9_{21}$; $m=-8$; determinant $43$, signature $2$, alternating
9
21
$\bar K$:
-t^9 + 2*t^8 - 4*t^7 + 6*t^6 - 7*t^5 + 8*t^4 - 6*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $9_{21}$; $m=-1$; signature $-2$
9
22
$K$:
-t^9 + 3*t^8 - 5*t^7 + 7*t^6 - 7*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $9_{22}$; $m=-3$; determinant $43$, signature $-2$, alternating
9
22
$\bar K$:
t^9 - 2*t^8 + 4*t^7 - 6*t^6 + 7*t^5 - 7*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{22}$; $m=-6$; signature $2$
9
23
$K$:
-t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 8*t^5 + 8*t^4 - 6*t^3 + 5*t^2 - 2*t + 1
comment: $9_{23}$; $m=2$; determinant $45$, signature $-4$, alternating
9
23
$\bar K$:
t^9 - 2*t^8 + 5*t^7 - 6*t^6 + 8*t^5 - 8*t^4 + 6*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{23}$; $m=-11$; signature $4$
9
24
$K$:
-t^9 + 2*t^8 - 4*t^7 + 7*t^6 - 7*t^5 + 8*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: $9_{24}$; $m=-4$; determinant $45$, signature $0$, alternating
9
24
$\bar K$:
t^9 - 3*t^8 + 5*t^7 - 7*t^6 + 8*t^5 - 7*t^4 + 7*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $9_{24}$; $m=-5$; signature $0$
9
25
$K$:
-t^9 + 3*t^8 - 5*t^7 + 7*t^6 - 8*t^5 + 8*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $9_{25}$; $m=-1$; determinant $47$, signature $-2$, alternating
9
25
$\bar K$:
t^9 - 2*t^8 + 5*t^7 - 7*t^6 + 8*t^5 - 8*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{25}$; $m=-8$; signature $2$
9
26
$K$:
-t^9 + 3*t^8 - 4*t^7 + 7*t^6 - 8*t^5 + 8*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: $9_{26}$; $m=-7$; determinant $47$, signature $2$, alternating
9
26
$\bar K$:
t^9 - 3*t^8 + 5*t^7 - 7*t^6 + 8*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $9_{26}$; $m=-2$; signature $-2$
9
27
$K$:
-t^9 + 3*t^8 - 5*t^7 + 7*t^6 - 8*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: $9_{27}$; $m=-4$; determinant $49$, signature $0$, alternating
9
27
$\bar K$:
t^9 - 3*t^8 + 5*t^7 - 7*t^6 + 9*t^5 - 8*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{27}$; $m=-5$; signature $0$
9
28
$K$:
t^9 - 3*t^8 + 5*t^7 - 8*t^6 + 9*t^5 - 8*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: $9_{28}$; $m=-2$; determinant $51$, signature $-2$, alternating
9
28
$\bar K$:
-t^9 + 3*t^8 - 5*t^7 + 8*t^6 - 8*t^5 + 9*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $9_{28}$; $m=-7$; signature $2$
9
29
$K$:
t^9 - 3*t^8 + 5*t^7 - 7*t^6 + 9*t^5 - 8*t^4 + 8*t^3 - 6*t^2 + 3*t - 1
comment: $9_{29}$; $m=-6$; determinant $51$, signature $2$, alternating
9
29
$\bar K$:
-t^9 + 3*t^8 - 6*t^7 + 8*t^6 - 8*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $9_{29}$; $m=-3$; signature $-2$
9
30
$K$:
t^9 - 3*t^8 + 6*t^7 - 8*t^6 + 9*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: $9_{30}$; $m=-5$; determinant $53$, signature $0$, alternating
9
30
$\bar K$:
-t^9 + 3*t^8 - 5*t^7 + 8*t^6 - 9*t^5 + 9*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $9_{30}$; $m=-4$; signature $0$
9
31
$K$:
t^9 - 4*t^8 + 6*t^7 - 8*t^6 + 10*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: $9_{31}$; $m=-2$; determinant $55$, signature $-2$, alternating
9
31
$\bar K$:
-t^9 + 3*t^8 - 5*t^7 + 8*t^6 - 9*t^5 + 10*t^4 - 8*t^3 + 6*t^2 - 4*t + 1
comment: the mirror image of $9_{31}$; $m=-7$; signature $2$
9
32
$K$:
-t^9 + 4*t^8 - 6*t^7 + 9*t^6 - 10*t^5 + 10*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $9_{32}$; $m=-7$; determinant $59$, signature $2$, alternating
9
32
$\bar K$:
t^9 - 3*t^8 + 6*t^7 - 9*t^6 + 10*t^5 - 10*t^4 + 9*t^3 - 6*t^2 + 4*t - 1
comment: the mirror image of $9_{32}$; $m=-2$; signature $-2$
9
33
$K$:
t^9 - 4*t^8 + 7*t^7 - 9*t^6 + 11*t^5 - 10*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $9_{33}$; $m=-5$; determinant $61$, signature $0$, alternating
9
33
$\bar K$:
-t^9 + 3*t^8 - 6*t^7 + 9*t^6 - 10*t^5 + 11*t^4 - 9*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $9_{33}$; $m=-4$; signature $0$
9
34
$K$:
t^9 - 4*t^8 + 8*t^7 - 10*t^6 + 12*t^5 - 12*t^4 + 10*t^3 - 7*t^2 + 4*t - 1
comment: $9_{34}$; $m=-5$; determinant $69$, signature $0$, alternating
9
34
$\bar K$:
-t^9 + 4*t^8 - 7*t^7 + 10*t^6 - 12*t^5 + 12*t^4 - 10*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $9_{34}$; $m=-4$; signature $0$
9
35
$K$:
-t^9 + t^8 - 3*t^7 + 4*t^6 - 3*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $9_{35}$; $m=1$; determinant $27$, signature $-2$, alternating
9
35
$\bar K$:
t^9 - 2*t^8 + 3*t^7 - 4*t^6 + 5*t^5 - 3*t^4 + 4*t^3 - 3*t^2 + t - 1
comment: the mirror image of $9_{35}$; $m=-10$; signature $2$
9
36
$K$:
t^9 - 2*t^8 + 4*t^7 - 5*t^6 + 6*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $9_{36}$; $m=-9$; determinant $37$, signature $4$, alternating
9
36
$\bar K$:
-t^9 + 2*t^8 - 4*t^7 + 6*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $9_{36}$; $m=0$; signature $-4$
9
37
$K$:
-t^9 + 3*t^8 - 4*t^7 + 7*t^6 - 8*t^5 + 7*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $9_{37}$; $m=-4$; determinant $45$, signature $0$, alternating
9
37
$\bar K$:
t^9 - 2*t^8 + 5*t^7 - 7*t^6 + 7*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $9_{37}$; $m=-5$; signature $0$
9
38
$K$:
-t^9 + 3*t^8 - 6*t^7 + 8*t^6 - 10*t^5 + 10*t^4 - 8*t^3 + 7*t^2 - 3*t + 1
comment: $9_{38}$; $m=2$; determinant $57$, signature $-4$, alternating
9
38
$\bar K$:
t^9 - 3*t^8 + 7*t^7 - 8*t^6 + 10*t^5 - 10*t^4 + 8*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $9_{38}$; $m=-11$; signature $4$
9
39
$K$:
t^9 - 3*t^8 + 6*t^7 - 8*t^6 + 10*t^5 - 9*t^4 + 8*t^3 - 6*t^2 + 3*t - 1
comment: $9_{39}$; $m=-8$; determinant $55$, signature $2$, alternating
9
39
$\bar K$:
-t^9 + 3*t^8 - 6*t^7 + 8*t^6 - 9*t^5 + 10*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $9_{39}$; $m=-1$; signature $-2$
9
40
$K$:
t^9 - 4*t^8 + 8*t^7 - 11*t^6 + 13*t^5 - 13*t^4 + 11*t^3 - 8*t^2 + 5*t - 1
comment: $9_{40}$; $m=-2$; determinant $75$, signature $-2$, alternating
9
40
$\bar K$:
-t^9 + 5*t^8 - 8*t^7 + 11*t^6 - 13*t^5 + 13*t^4 - 11*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $9_{40}$; $m=-7$; signature $2$
9
41
$K$:
-t^9 + 3*t^8 - 5*t^7 + 8*t^6 - 8*t^5 + 8*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: $9_{41}$; $m=-6$; determinant $49$, signature $0$, alternating
9
41
$\bar K$:
t^9 - 3*t^8 + 5*t^7 - 7*t^6 + 8*t^5 - 8*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $9_{41}$; $m=-3$; signature $0$
9
42
$K$:
t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: $9_{42}$; $m=-3$; determinant $7$, signature $2$, non-alternating; chiral, yet $V(t)=V(1/t)$, so the mirror image has the same polynomial
9
42
$\bar K$:
t^6 - t^5 + t^4 - t^3 + t^2 - t + 1
comment: the mirror image of $9_{42}$; $m=-3$; signature $-2$; the same polynomial as $9_{42}$
9
43
$K$:
-t^7 + 2*t^6 - 2*t^5 + 2*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $9_{43}$; $m=0$; determinant $13$, signature $-4$, non-alternating
9
43
$\bar K$:
t^7 - t^6 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t^2 + 2*t - 1
comment: the mirror image of $9_{43}$; $m=-7$; signature $4$
9
44
$K$:
-t^7 + 2*t^6 - 2*t^5 + 3*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $9_{44}$; $m=-2$; determinant $17$, signature $0$, non-alternating
9
44
$\bar K$:
t^7 - 2*t^6 + 3*t^5 - 3*t^4 + 3*t^3 - 2*t^2 + 2*t - 1
comment: the mirror image of $9_{44}$; $m=-5$; signature $0$
9
45
$K$:
2*t^7 - 3*t^6 + 4*t^5 - 4*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: $9_{45}$; $m=-8$; determinant $23$, signature $2$, non-alternating
9
45
$\bar K$:
-t^7 + 2*t^6 - 3*t^5 + 4*t^4 - 4*t^3 + 4*t^2 - 3*t + 2
comment: the mirror image of $9_{45}$; $m=1$; signature $-2$
9
46
$K$:
2*t^6 - t^5 + t^4 - 2*t^3 + t^2 - t + 1
comment: $9_{46}$; $m=-6$; determinant $9$, signature $0$, non-alternating
9
46
$\bar K$:
t^6 - t^5 + t^4 - 2*t^3 + t^2 - t + 2
comment: the mirror image of $9_{46}$; $m=0$; signature $0$
9
47
$K$:
2*t^7 - 4*t^6 + 4*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + 3*t - 1
comment: $9_{47}$; $m=-2$; determinant $27$, signature $-2$, non-alternating
9
47
$\bar K$:
-t^7 + 3*t^6 - 3*t^5 + 5*t^4 - 5*t^3 + 4*t^2 - 4*t + 2
comment: the mirror image of $9_{47}$; $m=-5$; signature $2$
9
48
$K$:
t^7 - 3*t^6 + 4*t^5 - 4*t^4 + 6*t^3 - 4*t^2 + 3*t - 2
comment: $9_{48}$; $m=-6$; determinant $27$, signature $2$, non-alternating
9
48
$\bar K$:
-2*t^7 + 3*t^6 - 4*t^5 + 6*t^4 - 4*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $9_{48}$; $m=-1$; signature $-2$
9
49
$K$:
-2*t^7 + 3*t^6 - 4*t^5 + 5*t^4 - 4*t^3 + 4*t^2 - 2*t + 1
comment: $9_{49}$; $m=2$; determinant $25$, signature $-4$, non-alternating
9
49
$\bar K$:
t^7 - 2*t^6 + 4*t^5 - 4*t^4 + 5*t^3 - 4*t^2 + 3*t - 2
comment: the mirror image of $9_{49}$; $m=-9$; signature $4$
10
1
$K$:
t^10 - t^9 + t^8 - 2*t^7 + 2*t^6 - 2*t^5 + 2*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $10_1$; $m=-2$; determinant $17$, signature $0$, alternating
10
1
$\bar K$:
t^10 - t^9 + 2*t^8 - 2*t^7 + 2*t^6 - 2*t^5 + 2*t^4 - 2*t^3 + t^2 - t + 1
comment: the mirror image of $10_1$; $m=-8$; signature $0$
10
2
$K$:
t^10 - 2*t^9 + 2*t^8 - 3*t^7 + 3*t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $10_2$; $m=1$; determinant $23$, signature $-6$, alternating
10
2
$\bar K$:
t^10 - t^9 + 2*t^8 - 2*t^7 + 3*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $10_2$; $m=-11$; signature $6$
10
3
$K$:
t^10 - t^9 + 2*t^8 - 3*t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: $10_3$; $m=-4$; determinant $25$, signature $0$, alternating
10
3
$\bar K$:
t^10 - t^9 + 2*t^8 - 3*t^7 + 4*t^6 - 4*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: the mirror image of $10_3$; $m=-6$; signature $0$
10
4
$K$:
t^10 - t^9 + 2*t^8 - 3*t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $10_4$; $m=-5$; determinant $27$, signature $2$, alternating
10
4
$\bar K$:
t^10 - 2*t^9 + 3*t^8 - 3*t^7 + 4*t^6 - 4*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: the mirror image of $10_4$; $m=-5$; signature $-2$
10
5
$K$:
-t^10 + 2*t^9 - 2*t^8 + 4*t^7 - 4*t^6 + 5*t^5 - 5*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: $10_5$; $m=-9$; determinant $33$, signature $4$, alternating
10
5
$\bar K$:
-t^10 + 2*t^9 - 3*t^8 + 4*t^7 - 5*t^6 + 5*t^5 - 4*t^4 + 4*t^3 - 2*t^2 + 2*t - 1
comment: the mirror image of $10_5$; $m=-1$; signature $-4$
10
6
$K$:
t^10 - 2*t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 6*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - t + 1
comment: $10_6$; $m=0$; determinant $37$, signature $-4$, alternating
10
6
$\bar K$:
t^10 - t^9 + 3*t^8 - 4*t^7 + 5*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_6$; $m=-10$; signature $4$
10
7
$K$:
t^10 - 2*t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 7*t^5 + 7*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $10_7$; $m=-1$; determinant $43$, signature $-2$, alternating
10
7
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 5*t^7 + 7*t^6 - 7*t^5 + 6*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_7$; $m=-9$; signature $2$
10
8
$K$:
t^10 - 2*t^9 + 3*t^8 - 4*t^7 + 4*t^6 - 4*t^5 + 4*t^4 - 3*t^3 + 2*t^2 - t + 1
comment: $10_8$; $m=-2$; determinant $29$, signature $-4$, alternating
10
8
$\bar K$:
t^10 - t^9 + 2*t^8 - 3*t^7 + 4*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_8$; $m=-8$; signature $4$
10
9
$K$:
t^10 - 2*t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 6*t^5 + 6*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $10_9$; $m=-3$; determinant $39$, signature $-2$, alternating
10
9
$\bar K$:
t^10 - 2*t^9 + 3*t^8 - 4*t^7 + 6*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_9$; $m=-7$; signature $2$
10
10
$K$:
-t^10 + 3*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 7*t^5 - 6*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: $10_{10}$; $m=-7$; determinant $45$, signature $0$, alternating
10
10
$\bar K$:
-t^10 + 2*t^9 - 3*t^8 + 5*t^7 - 6*t^6 + 7*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $10_{10}$; $m=-3$; signature $0$
10
11
$K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 7*t^6 - 7*t^5 + 6*t^4 - 5*t^3 + 3*t^2 - t + 1
comment: $10_{11}$; $m=-3$; determinant $43$, signature $-2$, alternating
10
11
$\bar K$:
t^10 - t^9 + 3*t^8 - 5*t^7 + 6*t^6 - 7*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{11}$; $m=-7$; signature $2$
10
12
$K$:
-t^10 + 2*t^9 - 3*t^8 + 6*t^7 - 7*t^6 + 8*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $10_{12}$; $m=-8$; determinant $47$, signature $2$, alternating
10
12
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 8*t^5 - 7*t^4 + 6*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $10_{12}$; $m=-2$; signature $-2$
10
13
$K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 9*t^5 + 8*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{13}$; $m=-4$; determinant $53$, signature $0$, alternating
10
13
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 8*t^6 - 9*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{13}$; $m=-6$; signature $0$
10
14
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 9*t^6 - 9*t^5 + 9*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{14}$; $m=0$; determinant $57$, signature $-4$, alternating
10
14
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 9*t^6 - 9*t^5 + 9*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{14}$; $m=-10$; signature $4$
10
15
$K$:
-t^10 + 2*t^9 - 3*t^8 + 5*t^7 - 6*t^6 + 7*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $10_{15}$; $m=-6$; determinant $43$, signature $2$, alternating
10
15
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 6*t^6 + 7*t^5 - 6*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $10_{15}$; $m=-4$; signature $-2$
10
16
$K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 7*t^6 - 8*t^5 + 7*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $10_{16}$; $m=-3$; determinant $47$, signature $-2$, alternating
10
16
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 5*t^7 + 7*t^6 - 8*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{16}$; $m=-7$; signature $2$
10
17
$K$:
-t^10 + 2*t^9 - 3*t^8 + 5*t^7 - 6*t^6 + 7*t^5 - 6*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: $10_{17}$; $m=-5$; determinant $41$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
18
$K$:
t^10 - 3*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 9*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{18}$; $m=-3$; determinant $55$, signature $-2$, alternating
10
18
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 9*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{18}$; $m=-7$; signature $2$
10
19
$K$:
-t^10 + 3*t^9 - 5*t^8 + 7*t^7 - 8*t^6 + 8*t^5 - 7*t^4 + 6*t^3 - 3*t^2 + 2*t - 1
comment: $10_{19}$; $m=-4$; determinant $51$, signature $-2$, alternating
10
19
$\bar K$:
-t^10 + 2*t^9 - 3*t^8 + 6*t^7 - 7*t^6 + 8*t^5 - 8*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{19}$; $m=-6$; signature $2$
10
20
$K$:
t^10 - 2*t^9 + 3*t^8 - 4*t^7 + 5*t^6 - 6*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - t + 1
comment: $10_{20}$; $m=-1$; determinant $35$, signature $-2$, alternating
10
20
$\bar K$:
t^10 - t^9 + 3*t^8 - 4*t^7 + 5*t^6 - 6*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{20}$; $m=-9$; signature $2$
10
21
$K$:
t^10 - 2*t^9 + 3*t^8 - 6*t^7 + 7*t^6 - 7*t^5 + 7*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $10_{21}$; $m=0$; determinant $45$, signature $-4$, alternating
10
21
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 5*t^7 + 7*t^6 - 7*t^5 + 7*t^4 - 6*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{21}$; $m=-10$; signature $4$
10
22
$K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 7*t^6 - 8*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{22}$; $m=-4$; determinant $49$, signature $0$, alternating; the same polynomial as the mirror image of $10_{35}$
10
22
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 8*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{22}$; $m=-6$; signature $0$; the same polynomial as $10_{35}$
10
23
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 9*t^6 + 10*t^5 - 9*t^4 + 7*t^3 - 4*t^2 + 2*t - 1
comment: $10_{23}$; $m=-8$; determinant $59$, signature $2$, alternating
10
23
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 7*t^7 - 9*t^6 + 10*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{23}$; $m=-2$; signature $-2$
10
24
$K$:
t^10 - 2*t^9 + 4*t^8 - 7*t^7 + 8*t^6 - 9*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{24}$; $m=-1$; determinant $55$, signature $-2$, alternating
10
24
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 9*t^5 + 8*t^4 - 7*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{24}$; $m=-9$; signature $2$
10
25
$K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 10*t^6 - 11*t^5 + 10*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{25}$; $m=0$; determinant $65$, signature $-4$, alternating; the same polynomial as $10_{56}$
10
25
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 10*t^6 - 11*t^5 + 10*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{25}$; $m=-10$; signature $4$; the same polynomial as the mirror image of $10_{56}$
10
26
$K$:
t^10 - 2*t^9 + 4*t^8 - 7*t^7 + 9*t^6 - 10*t^5 + 10*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: $10_{26}$; $m=-4$; determinant $61$, signature $0$, alternating
10
26
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 10*t^6 - 10*t^5 + 9*t^4 - 7*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{26}$; $m=-6$; signature $0$
10
27
$K$:
-t^10 + 3*t^9 - 5*t^8 + 9*t^7 - 11*t^6 + 12*t^5 - 11*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $10_{27}$; $m=-8$; determinant $71$, signature $2$, alternating
10
27
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 11*t^6 + 12*t^5 - 11*t^4 + 9*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{27}$; $m=-2$; signature $-2$
10
28
$K$:
-t^10 + 3*t^9 - 5*t^8 + 7*t^7 - 8*t^6 + 9*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $10_{28}$; $m=-7$; determinant $53$, signature $0$, alternating
10
28
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 9*t^5 - 8*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{28}$; $m=-3$; signature $0$
10
29
$K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 10*t^6 - 11*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{29}$; $m=-3$; determinant $63$, signature $-2$, alternating
10
29
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 11*t^5 + 10*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{29}$; $m=-7$; signature $2$
10
30
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 11*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: $10_{30}$; $m=-1$; determinant $67$, signature $-2$, alternating
10
30
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 11*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{30}$; $m=-9$; signature $2$
10
31
$K$:
-t^10 + 3*t^9 - 5*t^8 + 7*t^7 - 9*t^6 + 10*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 2*t - 1
comment: $10_{31}$; $m=-5$; determinant $57$, signature $0$, alternating
10
31
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 7*t^7 - 8*t^6 + 10*t^5 - 9*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{31}$; $m=-5$; signature $0$
10
32
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 11*t^6 - 11*t^5 + 11*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $10_{32}$; $m=-4$; determinant $69$, signature $0$, alternating
10
32
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 11*t^6 - 11*t^5 + 11*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{32}$; $m=-6$; signature $0$
10
33
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 10*t^6 + 11*t^5 - 10*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: $10_{33}$; $m=-5$; determinant $65$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
34
$K$:
-t^10 + 2*t^9 - 3*t^8 + 5*t^7 - 5*t^6 + 6*t^5 - 5*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: $10_{34}$; $m=-7$; determinant $37$, signature $0$, alternating
10
34
$\bar K$:
-t^10 + 2*t^9 - 3*t^8 + 4*t^7 - 5*t^6 + 6*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $10_{34}$; $m=-3$; signature $0$
10
35
$K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 8*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{35}$; $m=-6$; determinant $49$, signature $0$, alternating; the same polynomial as the mirror image of $10_{22}$
10
35
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 7*t^6 - 8*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{35}$; $m=-4$; signature $0$; the same polynomial as $10_{22}$
10
36
$K$:
t^10 - 3*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 8*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{36}$; $m=-1$; determinant $51$, signature $-2$, alternating
10
36
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 8*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $10_{36}$; $m=-9$; signature $2$
10
37
$K$:
-t^10 + 2*t^9 - 4*t^8 + 7*t^7 - 8*t^6 + 9*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 2*t - 1
comment: $10_{37}$; $m=-5$; determinant $53$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
38
$K$:
t^10 - 3*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 10*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{38}$; $m=-1$; determinant $59$, signature $-2$, alternating
10
38
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 10*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{38}$; $m=-9$; signature $2$
10
39
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 10*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{39}$; $m=0$; determinant $61$, signature $-4$, alternating
10
39
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 10*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{39}$; $m=-10$; signature $4$
10
40
$K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 11*t^6 + 13*t^5 - 12*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $10_{40}$; $m=-8$; determinant $75$, signature $2$, alternating; the same polynomial as $10_{103}$
10
40
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 12*t^6 + 13*t^5 - 11*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{40}$; $m=-2$; signature $-2$; the same polynomial as the mirror image of $10_{103}$
10
41
$K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 11*t^6 - 12*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: $10_{41}$; $m=-3$; determinant $71$, signature $-2$, alternating; the same polynomial as $10_{94}$
10
41
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 12*t^5 + 11*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{41}$; $m=-7$; signature $2$; the same polynomial as the mirror image of $10_{94}$
10
42
$K$:
-t^10 + 4*t^9 - 7*t^8 + 10*t^7 - 13*t^6 + 14*t^5 - 12*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: $10_{42}$; $m=-5$; determinant $81$, signature $0$, alternating
10
42
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 12*t^6 + 14*t^5 - 13*t^4 + 10*t^3 - 7*t^2 + 4*t - 1
comment: the mirror image of $10_{42}$; $m=-5$; signature $0$
10
43
$K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 11*t^6 + 13*t^5 - 11*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $10_{43}$; $m=-5$; determinant $73$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$; the same polynomial as $10_{91}$, the mirror image of $10_{91}$
10
44
$K$:
t^10 - 4*t^9 + 7*t^8 - 10*t^7 + 13*t^6 - 13*t^5 + 12*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $10_{44}$; $m=-3$; determinant $79$, signature $-2$, alternating
10
44
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 12*t^6 - 13*t^5 + 13*t^4 - 10*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{44}$; $m=-7$; signature $2$
10
45
$K$:
-t^10 + 4*t^9 - 7*t^8 + 11*t^7 - 14*t^6 + 15*t^5 - 14*t^4 + 11*t^3 - 7*t^2 + 4*t - 1
comment: $10_{45}$; $m=-5$; determinant $89$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
46
$K$:
t^10 - 2*t^9 + 3*t^8 - 4*t^7 + 4*t^6 - 5*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - t + 1
comment: $10_{46}$; $m=1$; determinant $31$, signature $-6$, alternating
10
46
$\bar K$:
t^10 - t^9 + 3*t^8 - 3*t^7 + 4*t^6 - 5*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{46}$; $m=-11$; signature $6$
10
47
$K$:
-t^10 + 2*t^9 - 3*t^8 + 5*t^7 - 5*t^6 + 7*t^5 - 6*t^4 + 5*t^3 - 4*t^2 + 2*t - 1
comment: $10_{47}$; $m=-9$; determinant $41$, signature $4$, alternating
10
47
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 5*t^7 - 6*t^6 + 7*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $10_{47}$; $m=-1$; signature $-4$
10
48
$K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 9*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $10_{48}$; $m=-5$; determinant $49$, signature $0$, alternating; chiral, yet $V(t)=V(1/t)$, so the mirror image has the same polynomial
10
48
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 9*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $10_{48}$; $m=-5$; signature $0$; the same polynomial as $10_{48}$
10
49
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 9*t^6 - 10*t^5 + 9*t^4 - 6*t^3 + 5*t^2 - 2*t + 1
comment: $10_{49}$; $m=3$; determinant $59$, signature $-6$, alternating
10
49
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 6*t^7 + 9*t^6 - 10*t^5 + 9*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{49}$; $m=-13$; signature $6$
10
50
$K$:
t^10 - 2*t^9 + 4*t^8 - 7*t^7 + 8*t^6 - 9*t^5 + 8*t^4 - 6*t^3 + 5*t^2 - 2*t + 1
comment: $10_{50}$; $m=0$; determinant $53$, signature $-4$, alternating
10
50
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 6*t^7 + 8*t^6 - 9*t^5 + 8*t^4 - 7*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{50}$; $m=-10$; signature $4$
10
51
$K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 10*t^6 + 12*t^5 - 10*t^4 + 8*t^3 - 5*t^2 + 2*t - 1
comment: $10_{51}$; $m=-8$; determinant $67$, signature $2$, alternating
10
51
$\bar K$:
-t^10 + 2*t^9 - 5*t^8 + 8*t^7 - 10*t^6 + 12*t^5 - 10*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{51}$; $m=-2$; signature $-2$
10
52
$K$:
-t^10 + 3*t^9 - 6*t^8 + 8*t^7 - 9*t^6 + 10*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 2*t - 1
comment: $10_{52}$; $m=-4$; determinant $59$, signature $-2$, alternating
10
52
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 7*t^7 - 8*t^6 + 10*t^5 - 9*t^4 + 8*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{52}$; $m=-6$; signature $2$
10
53
$K$:
t^10 - 3*t^9 + 5*t^8 - 9*t^7 + 11*t^6 - 12*t^5 + 12*t^4 - 9*t^3 + 7*t^2 - 3*t + 1
comment: $10_{53}$; $m=2$; determinant $73$, signature $-4$, alternating
10
53
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 9*t^7 + 12*t^6 - 12*t^5 + 11*t^4 - 9*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{53}$; $m=-12$; signature $4$
10
54
$K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 6*t^6 + 8*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $10_{54}$; $m=-6$; determinant $47$, signature $2$, alternating
10
54
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 8*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $10_{54}$; $m=-4$; signature $-2$
10
55
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 9*t^6 - 10*t^5 + 10*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{55}$; $m=2$; determinant $61$, signature $-4$, alternating
10
55
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 10*t^6 - 10*t^5 + 9*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{55}$; $m=-12$; signature $4$
10
56
$K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 10*t^6 - 11*t^5 + 10*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{56}$; $m=0$; determinant $65$, signature $-4$, alternating; the same polynomial as $10_{25}$
10
56
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 10*t^6 - 11*t^5 + 10*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{56}$; $m=-10$; signature $4$; the same polynomial as the mirror image of $10_{25}$
10
57
$K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 12*t^6 + 14*t^5 - 12*t^4 + 10*t^3 - 7*t^2 + 3*t - 1
comment: $10_{57}$; $m=-8$; determinant $79$, signature $2$, alternating
10
57
$\bar K$:
-t^10 + 3*t^9 - 7*t^8 + 10*t^7 - 12*t^6 + 14*t^5 - 12*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{57}$; $m=-2$; signature $-2$
10
58
$K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 10*t^6 - 11*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 2*t + 1
comment: $10_{58}$; $m=-4$; determinant $65$, signature $0$, alternating
10
58
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 11*t^5 + 10*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{58}$; $m=-6$; signature $0$
10
59
$K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 12*t^6 - 12*t^5 + 12*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $10_{59}$; $m=-3$; determinant $75$, signature $-2$, alternating; the same polynomial as $10_{106}$
10
59
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 12*t^6 - 12*t^5 + 12*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{59}$; $m=-7$; signature $2$; the same polynomial as the mirror image of $10_{106}$
10
60
$K$:
t^10 - 4*t^9 + 8*t^8 - 11*t^7 + 14*t^6 - 14*t^5 + 13*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: $10_{60}$; $m=-6$; determinant $85$, signature $0$, alternating; the same polynomial as the mirror image of $10_{86}$
10
60
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 13*t^6 - 14*t^5 + 14*t^4 - 11*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{60}$; $m=-4$; signature $0$; the same polynomial as $10_{86}$
10
61
$K$:
t^10 - 2*t^9 + 3*t^8 - 4*t^7 + 5*t^6 - 5*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - t + 1
comment: $10_{61}$; $m=-2$; determinant $33$, signature $-4$, alternating
10
61
$\bar K$:
t^10 - t^9 + 3*t^8 - 4*t^7 + 4*t^6 - 5*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{61}$; $m=-8$; signature $4$
10
62
$K$:
-t^10 + 2*t^9 - 3*t^8 + 6*t^7 - 6*t^6 + 7*t^5 - 7*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: $10_{62}$; $m=-9$; determinant $45$, signature $4$, alternating
10
62
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 6*t^7 - 7*t^6 + 7*t^5 - 6*t^4 + 6*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $10_{62}$; $m=-1$; signature $-4$
10
63
$K$:
t^10 - 3*t^9 + 4*t^8 - 7*t^7 + 9*t^6 - 9*t^5 + 9*t^4 - 7*t^3 + 5*t^2 - 2*t + 1
comment: $10_{63}$; $m=2$; determinant $57$, signature $-4$, alternating
10
63
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 7*t^7 + 9*t^6 - 9*t^5 + 9*t^4 - 7*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $10_{63}$; $m=-12$; signature $4$
10
64
$K$:
t^10 - 2*t^9 + 4*t^8 - 7*t^7 + 8*t^6 - 8*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{64}$; $m=-3$; determinant $51$, signature $-2$, alternating
10
64
$\bar K$:
t^10 - 2*t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 8*t^5 + 8*t^4 - 7*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{64}$; $m=-7$; signature $2$
10
65
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 10*t^6 + 11*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 2*t - 1
comment: $10_{65}$; $m=-8$; determinant $63$, signature $2$, alternating
10
65
$\bar K$:
-t^10 + 2*t^9 - 5*t^8 + 8*t^7 - 9*t^6 + 11*t^5 - 10*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{65}$; $m=-2$; signature $-2$
10
66
$K$:
t^10 - 4*t^9 + 7*t^8 - 10*t^7 + 12*t^6 - 13*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 2*t + 1
comment: $10_{66}$; $m=3$; determinant $75$, signature $-6$, alternating
10
66
$\bar K$:
t^10 - 2*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 13*t^5 + 12*t^4 - 10*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{66}$; $m=-13$; signature $6$
10
67
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 10*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 2*t + 1
comment: $10_{67}$; $m=-1$; determinant $63$, signature $-2$, alternating
10
67
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 10*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{67}$; $m=-9$; signature $2$
10
68
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 9*t^6 + 9*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 2*t - 1
comment: $10_{68}$; $m=-7$; determinant $57$, signature $0$, alternating
10
68
$\bar K$:
-t^10 + 2*t^9 - 4*t^8 + 7*t^7 - 8*t^6 + 9*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{68}$; $m=-3$; signature $0$
10
69
$K$:
-t^10 + 4*t^9 - 7*t^8 + 11*t^7 - 14*t^6 + 15*t^5 - 13*t^4 + 11*t^3 - 7*t^2 + 3*t - 1
comment: $10_{69}$; $m=-8$; determinant $87$, signature $2$, alternating
10
69
$\bar K$:
-t^10 + 3*t^9 - 7*t^8 + 11*t^7 - 13*t^6 + 15*t^5 - 14*t^4 + 11*t^3 - 7*t^2 + 4*t - 1
comment: the mirror image of $10_{69}$; $m=-2$; signature $-2$
10
70
$K$:
t^10 - 2*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 11*t^5 + 11*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $10_{70}$; $m=-7$; determinant $67$, signature $2$, alternating
10
70
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 11*t^6 - 11*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 2*t + 1
comment: the mirror image of $10_{70}$; $m=-3$; signature $-2$
10
71
$K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 12*t^6 + 13*t^5 - 12*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: $10_{71}$; $m=-5$; determinant $77$, signature $0$, alternating; chiral, yet $V(t)=V(1/t)$, so the mirror image has the same polynomial; the same polynomial as $10_{104}$, the mirror image of $10_{104}$
10
71
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 12*t^6 + 13*t^5 - 12*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{71}$; $m=-5$; signature $0$; the same polynomial as $10_{71}$, $10_{104}$, the mirror image of $10_{104}$
10
72
$K$:
t^10 - 4*t^9 + 7*t^8 - 10*t^7 + 12*t^6 - 12*t^5 + 11*t^4 - 8*t^3 + 5*t^2 - 2*t + 1
comment: $10_{72}$; $m=0$; determinant $73$, signature $-4$, alternating
10
72
$\bar K$:
t^10 - 2*t^9 + 5*t^8 - 8*t^7 + 11*t^6 - 12*t^5 + 12*t^4 - 10*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{72}$; $m=-10$; signature $4$
10
73
$K$:
-t^10 + 4*t^9 - 7*t^8 + 11*t^7 - 13*t^6 + 14*t^5 - 13*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: $10_{73}$; $m=-8$; determinant $83$, signature $2$, alternating; the same polynomial as $10_{83}$
10
73
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 13*t^6 + 14*t^5 - 13*t^4 + 11*t^3 - 7*t^2 + 4*t - 1
comment: the mirror image of $10_{73}$; $m=-2$; signature $-2$; the same polynomial as the mirror image of $10_{83}$
10
74
$K$:
t^10 - 2*t^9 + 4*t^8 - 8*t^7 + 9*t^6 - 10*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: $10_{74}$; $m=-1$; determinant $63$, signature $-2$, alternating
10
74
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 10*t^5 + 9*t^4 - 8*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{74}$; $m=-9$; signature $2$
10
75
$K$:
t^10 - 4*t^9 + 7*t^8 - 10*t^7 + 14*t^6 - 13*t^5 + 12*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: $10_{75}$; $m=-6$; determinant $81$, signature $0$, alternating
10
75
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 12*t^6 - 13*t^5 + 14*t^4 - 10*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{75}$; $m=-4$; signature $0$
10
76
$K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 9*t^6 - 10*t^5 + 8*t^4 - 6*t^3 + 4*t^2 - t + 1
comment: $10_{76}$; $m=0$; determinant $57$, signature $-4$, alternating
10
76
$\bar K$:
t^10 - t^9 + 4*t^8 - 6*t^7 + 8*t^6 - 10*t^5 + 9*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{76}$; $m=-10$; signature $4$
10
77
$K$:
-t^10 + 2*t^9 - 4*t^8 + 8*t^7 - 9*t^6 + 11*t^5 - 10*t^4 + 8*t^3 - 6*t^2 + 3*t - 1
comment: $10_{77}$; $m=-8$; determinant $63$, signature $2$, alternating
10
77
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 8*t^7 - 10*t^6 + 11*t^5 - 9*t^4 + 8*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $10_{77}$; $m=-2$; signature $-2$
10
78
$K$:
t^10 - 3*t^9 + 5*t^8 - 9*t^7 + 11*t^6 - 11*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: $10_{78}$; $m=0$; determinant $69$, signature $-4$, alternating
10
78
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 11*t^5 + 11*t^4 - 9*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{78}$; $m=-10$; signature $4$
10
79
$K$:
-t^10 + 2*t^9 - 5*t^8 + 8*t^7 - 9*t^6 + 11*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 2*t - 1
comment: $10_{79}$; $m=-5$; determinant $61$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
80
$K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 11*t^6 - 12*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 2*t + 1
comment: $10_{80}$; $m=3$; determinant $71$, signature $-6$, alternating
10
80
$\bar K$:
t^10 - 2*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 12*t^5 + 11*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{80}$; $m=-13$; signature $6$
10
81
$K$:
-t^10 + 3*t^9 - 7*t^8 + 11*t^7 - 13*t^6 + 15*t^5 - 13*t^4 + 11*t^3 - 7*t^2 + 3*t - 1
comment: $10_{81}$; $m=-5$; determinant $85$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$; the same polynomial as $10_{109}$
10
82
$K$:
t^10 - 3*t^9 + 5*t^8 - 8*t^7 + 10*t^6 - 10*t^5 + 10*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: $10_{82}$; $m=-3$; determinant $63$, signature $-2$, alternating
10
82
$\bar K$:
t^10 - 3*t^9 + 5*t^8 - 7*t^7 + 10*t^6 - 10*t^5 + 10*t^4 - 8*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{82}$; $m=-7$; signature $2$
10
83
$K$:
-t^10 + 4*t^9 - 7*t^8 + 11*t^7 - 13*t^6 + 14*t^5 - 13*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: $10_{83}$; $m=-8$; determinant $83$, signature $2$, alternating; the same polynomial as $10_{73}$
10
83
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 13*t^6 + 14*t^5 - 13*t^4 + 11*t^3 - 7*t^2 + 4*t - 1
comment: the mirror image of $10_{83}$; $m=-2$; signature $-2$; the same polynomial as the mirror image of $10_{73}$
10
84
$K$:
-t^10 + 4*t^9 - 8*t^8 + 11*t^7 - 14*t^6 + 15*t^5 - 13*t^4 + 11*t^3 - 6*t^2 + 3*t - 1
comment: $10_{84}$; $m=-2$; determinant $87$, signature $-2$, alternating
10
84
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 11*t^7 - 13*t^6 + 15*t^5 - 14*t^4 + 11*t^3 - 8*t^2 + 4*t - 1
comment: the mirror image of $10_{84}$; $m=-8$; signature $2$
10
85
$K$:
-t^10 + 3*t^9 - 4*t^8 + 7*t^7 - 8*t^6 + 9*t^5 - 9*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: $10_{85}$; $m=-9$; determinant $57$, signature $4$, alternating
10
85
$\bar K$:
-t^10 + 3*t^9 - 5*t^8 + 7*t^7 - 9*t^6 + 9*t^5 - 8*t^4 + 7*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $10_{85}$; $m=-1$; signature $-4$
10
86
$K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 13*t^6 - 14*t^5 + 14*t^4 - 11*t^3 + 8*t^2 - 4*t + 1
comment: $10_{86}$; $m=-4$; determinant $85$, signature $0$, alternating; the same polynomial as the mirror image of $10_{60}$
10
86
$\bar K$:
t^10 - 4*t^9 + 8*t^8 - 11*t^7 + 14*t^6 - 14*t^5 + 13*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{86}$; $m=-6$; signature $0$; the same polynomial as $10_{60}$
10
87
$K$:
t^10 - 4*t^9 + 7*t^8 - 10*t^7 + 13*t^6 - 13*t^5 + 13*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: $10_{87}$; $m=-4$; determinant $81$, signature $0$, alternating
10
87
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 13*t^6 - 13*t^5 + 13*t^4 - 10*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{87}$; $m=-6$; signature $0$
10
88
$K$:
-t^10 + 4*t^9 - 8*t^8 + 13*t^7 - 16*t^6 + 17*t^5 - 16*t^4 + 13*t^3 - 8*t^2 + 4*t - 1
comment: $10_{88}$; $m=-5$; determinant $101$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
89
$K$:
-t^10 + 5*t^9 - 9*t^8 + 13*t^7 - 16*t^6 + 17*t^5 - 15*t^4 + 12*t^3 - 7*t^2 + 3*t - 1
comment: $10_{89}$; $m=-8$; determinant $99$, signature $2$, alternating
10
89
$\bar K$:
-t^10 + 3*t^9 - 7*t^8 + 12*t^7 - 15*t^6 + 17*t^5 - 16*t^4 + 13*t^3 - 9*t^2 + 5*t - 1
comment: the mirror image of $10_{89}$; $m=-2$; signature $-2$
10
90
$K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 12*t^6 - 13*t^5 + 12*t^4 - 10*t^3 + 7*t^2 - 3*t + 1
comment: $10_{90}$; $m=-4$; determinant $77$, signature $0$, alternating
10
90
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 10*t^7 + 12*t^6 - 13*t^5 + 12*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{90}$; $m=-6$; signature $0$
10
91
$K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 11*t^6 + 13*t^5 - 11*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $10_{91}$; $m=-5$; determinant $73$, signature $0$, alternating; chiral, yet $V(t)=V(1/t)$, so the mirror image has the same polynomial; the same polynomial as $10_{43}$
10
91
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 11*t^6 + 13*t^5 - 11*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{91}$; $m=-5$; signature $0$; the same polynomial as $10_{43}$, $10_{91}$
10
92
$K$:
t^10 - 4*t^9 + 8*t^8 - 12*t^7 + 14*t^6 - 15*t^5 + 14*t^4 - 10*t^3 + 7*t^2 - 3*t + 1
comment: $10_{92}$; $m=0$; determinant $89$, signature $-4$, alternating
10
92
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 10*t^7 + 14*t^6 - 15*t^5 + 14*t^4 - 12*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{92}$; $m=-10$; signature $4$
10
93
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 10*t^6 + 11*t^5 - 10*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $10_{93}$; $m=-6$; determinant $67$, signature $2$, alternating
10
93
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 10*t^6 + 11*t^5 - 10*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{93}$; $m=-4$; signature $-2$
10
94
$K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 11*t^6 - 12*t^5 + 11*t^4 - 8*t^3 + 6*t^2 - 3*t + 1
comment: $10_{94}$; $m=-3$; determinant $71$, signature $-2$, alternating; the same polynomial as $10_{41}$
10
94
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 8*t^7 + 11*t^6 - 12*t^5 + 11*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{94}$; $m=-7$; signature $2$; the same polynomial as the mirror image of $10_{41}$
10
95
$K$:
-t^10 + 4*t^9 - 8*t^8 + 12*t^7 - 14*t^6 + 16*t^5 - 14*t^4 + 11*t^3 - 7*t^2 + 3*t - 1
comment: $10_{95}$; $m=-8$; determinant $91$, signature $2$, alternating
10
95
$\bar K$:
-t^10 + 3*t^9 - 7*t^8 + 11*t^7 - 14*t^6 + 16*t^5 - 14*t^4 + 12*t^3 - 8*t^2 + 4*t - 1
comment: the mirror image of $10_{95}$; $m=-2$; signature $-2$
10
96
$K$:
t^10 - 4*t^9 + 9*t^8 - 12*t^7 + 15*t^6 - 16*t^5 + 14*t^4 - 11*t^3 + 7*t^2 - 3*t + 1
comment: $10_{96}$; $m=-6$; determinant $93$, signature $0$, alternating
10
96
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 11*t^7 + 14*t^6 - 16*t^5 + 15*t^4 - 12*t^3 + 9*t^2 - 4*t + 1
comment: the mirror image of $10_{96}$; $m=-4$; signature $0$
10
97
$K$:
t^10 - 4*t^9 + 7*t^8 - 11*t^7 + 14*t^6 - 14*t^5 + 14*t^4 - 11*t^3 + 7*t^2 - 3*t + 1
comment: $10_{97}$; $m=-1$; determinant $87$, signature $-2$, alternating
10
97
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 11*t^7 + 14*t^6 - 14*t^5 + 14*t^4 - 11*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{97}$; $m=-9$; signature $2$
10
98
$K$:
t^10 - 3*t^9 + 7*t^8 - 11*t^7 + 12*t^6 - 14*t^5 + 13*t^4 - 9*t^3 + 7*t^2 - 3*t + 1
comment: $10_{98}$; $m=0$; determinant $81$, signature $-4$, alternating
10
98
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 9*t^7 + 13*t^6 - 14*t^5 + 12*t^4 - 11*t^3 + 7*t^2 - 3*t + 1
comment: the mirror image of $10_{98}$; $m=-10$; signature $4$
10
99
$K$:
-t^10 + 3*t^9 - 7*t^8 + 10*t^7 - 12*t^6 + 15*t^5 - 12*t^4 + 10*t^3 - 7*t^2 + 3*t - 1
comment: $10_{99}$; $m=-5$; determinant $81$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
100
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 9*t^6 + 11*t^5 - 10*t^4 + 8*t^3 - 6*t^2 + 3*t - 1
comment: $10_{100}$; $m=-9$; determinant $65$, signature $4$, alternating
10
100
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 8*t^7 - 10*t^6 + 11*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{100}$; $m=-1$; signature $-4$
10
101
$K$:
t^10 - 4*t^9 + 7*t^8 - 11*t^7 + 13*t^6 - 14*t^5 + 14*t^4 - 10*t^3 + 7*t^2 - 3*t + 1
comment: $10_{101}$; $m=2$; determinant $85$, signature $-4$, alternating
10
101
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 10*t^7 + 14*t^6 - 14*t^5 + 13*t^4 - 11*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{101}$; $m=-12$; signature $4$
10
102
$K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 11*t^6 - 12*t^5 + 12*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $10_{102}$; $m=-4$; determinant $73$, signature $0$, alternating
10
102
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 12*t^6 - 12*t^5 + 11*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{102}$; $m=-6$; signature $0$
10
103
$K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 11*t^6 + 13*t^5 - 12*t^4 + 9*t^3 - 6*t^2 + 3*t - 1
comment: $10_{103}$; $m=-8$; determinant $75$, signature $2$, alternating; the same polynomial as $10_{40}$
10
103
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 9*t^7 - 12*t^6 + 13*t^5 - 11*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{103}$; $m=-2$; signature $-2$; the same polynomial as the mirror image of $10_{40}$
10
104
$K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 12*t^6 + 13*t^5 - 12*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: $10_{104}$; $m=-5$; determinant $77$, signature $0$, alternating; chiral, yet $V(t)=V(1/t)$, so the mirror image has the same polynomial; the same polynomial as $10_{71}$, the mirror image of $10_{71}$
10
104
$\bar K$:
-t^10 + 3*t^9 - 6*t^8 + 10*t^7 - 12*t^6 + 13*t^5 - 12*t^4 + 10*t^3 - 6*t^2 + 3*t - 1
comment: the mirror image of $10_{104}$; $m=-5$; signature $0$; the same polynomial as $10_{71}$, the mirror image of $10_{71}$, $10_{104}$
10
105
$K$:
t^10 - 4*t^9 + 8*t^8 - 12*t^7 + 15*t^6 - 15*t^5 + 14*t^4 - 11*t^3 + 7*t^2 - 3*t + 1
comment: $10_{105}$; $m=-3$; determinant $91$, signature $-2$, alternating
10
105
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 11*t^7 + 14*t^6 - 15*t^5 + 15*t^4 - 12*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{105}$; $m=-7$; signature $2$
10
106
$K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 12*t^6 - 12*t^5 + 12*t^4 - 9*t^3 + 6*t^2 - 3*t + 1
comment: $10_{106}$; $m=-3$; determinant $75$, signature $-2$, alternating; the same polynomial as $10_{59}$
10
106
$\bar K$:
t^10 - 3*t^9 + 6*t^8 - 9*t^7 + 12*t^6 - 12*t^5 + 12*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{106}$; $m=-7$; signature $2$; the same polynomial as the mirror image of $10_{59}$
10
107
$K$:
-t^10 + 4*t^9 - 8*t^8 + 12*t^7 - 15*t^6 + 16*t^5 - 14*t^4 + 12*t^3 - 7*t^2 + 3*t - 1
comment: $10_{107}$; $m=-5$; determinant $93$, signature $0$, alternating
10
107
$\bar K$:
-t^10 + 3*t^9 - 7*t^8 + 12*t^7 - 14*t^6 + 16*t^5 - 15*t^4 + 12*t^3 - 8*t^2 + 4*t - 1
comment: the mirror image of $10_{107}$; $m=-5$; signature $0$
10
108
$K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 10*t^6 + 10*t^5 - 9*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: $10_{108}$; $m=-4$; determinant $63$, signature $-2$, alternating
10
108
$\bar K$:
-t^10 + 3*t^9 - 5*t^8 + 8*t^7 - 9*t^6 + 10*t^5 - 10*t^4 + 8*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{108}$; $m=-6$; signature $2$
10
109
$K$:
-t^10 + 3*t^9 - 7*t^8 + 11*t^7 - 13*t^6 + 15*t^5 - 13*t^4 + 11*t^3 - 7*t^2 + 3*t - 1
comment: $10_{109}$; $m=-5$; determinant $85$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$; the same polynomial as $10_{81}$
10
110
$K$:
t^10 - 3*t^9 + 7*t^8 - 11*t^7 + 13*t^6 - 14*t^5 + 13*t^4 - 10*t^3 + 7*t^2 - 3*t + 1
comment: $10_{110}$; $m=-3$; determinant $83$, signature $-2$, alternating
10
110
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 10*t^7 + 13*t^6 - 14*t^5 + 13*t^4 - 11*t^3 + 7*t^2 - 3*t + 1
comment: the mirror image of $10_{110}$; $m=-7$; signature $2$
10
111
$K$:
t^10 - 3*t^9 + 6*t^8 - 10*t^7 + 12*t^6 - 13*t^5 + 12*t^4 - 9*t^3 + 7*t^2 - 3*t + 1
comment: $10_{111}$; $m=0$; determinant $77$, signature $-4$, alternating
10
111
$\bar K$:
t^10 - 3*t^9 + 7*t^8 - 9*t^7 + 12*t^6 - 13*t^5 + 12*t^4 - 10*t^3 + 6*t^2 - 3*t + 1
comment: the mirror image of $10_{111}$; $m=-10$; signature $4$
10
112
$K$:
t^10 - 4*t^9 + 7*t^8 - 10*t^7 + 14*t^6 - 14*t^5 + 14*t^4 - 11*t^3 + 7*t^2 - 4*t + 1
comment: $10_{112}$; $m=-7$; determinant $87$, signature $2$, alternating
10
112
$\bar K$:
t^10 - 4*t^9 + 7*t^8 - 11*t^7 + 14*t^6 - 14*t^5 + 14*t^4 - 10*t^3 + 7*t^2 - 4*t + 1
comment: the mirror image of $10_{112}$; $m=-3$; signature $-2$
10
113
$K$:
-t^10 + 5*t^9 - 10*t^8 + 14*t^7 - 18*t^6 + 19*t^5 - 17*t^4 + 14*t^3 - 8*t^2 + 4*t - 1
comment: $10_{113}$; $m=-2$; determinant $111$, signature $-2$, alternating
10
113
$\bar K$:
-t^10 + 4*t^9 - 8*t^8 + 14*t^7 - 17*t^6 + 19*t^5 - 18*t^4 + 14*t^3 - 10*t^2 + 5*t - 1
comment: the mirror image of $10_{113}$; $m=-8$; signature $2$
10
114
$K$:
t^10 - 4*t^9 + 8*t^8 - 12*t^7 + 15*t^6 - 15*t^5 + 15*t^4 - 11*t^3 + 7*t^2 - 4*t + 1
comment: $10_{114}$; $m=-6$; determinant $93$, signature $0$, alternating
10
114
$\bar K$:
t^10 - 4*t^9 + 7*t^8 - 11*t^7 + 15*t^6 - 15*t^5 + 15*t^4 - 12*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{114}$; $m=-4$; signature $0$
10
115
$K$:
-t^10 + 4*t^9 - 9*t^8 + 14*t^7 - 17*t^6 + 19*t^5 - 17*t^4 + 14*t^3 - 9*t^2 + 4*t - 1
comment: $10_{115}$; $m=-5$; determinant $109$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
116
$K$:
t^10 - 4*t^9 + 8*t^8 - 11*t^7 + 15*t^6 - 16*t^5 + 15*t^4 - 12*t^3 + 8*t^2 - 4*t + 1
comment: $10_{116}$; $m=-7$; determinant $95$, signature $2$, alternating
10
116
$\bar K$:
t^10 - 4*t^9 + 8*t^8 - 12*t^7 + 15*t^6 - 16*t^5 + 15*t^4 - 11*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{116}$; $m=-3$; signature $-2$
10
117
$K$:
-t^10 + 4*t^9 - 8*t^8 + 13*t^7 - 16*t^6 + 18*t^5 - 16*t^4 + 13*t^3 - 9*t^2 + 4*t - 1
comment: $10_{117}$; $m=-8$; determinant $103$, signature $2$, alternating
10
117
$\bar K$:
-t^10 + 4*t^9 - 9*t^8 + 13*t^7 - 16*t^6 + 18*t^5 - 16*t^4 + 13*t^3 - 8*t^2 + 4*t - 1
comment: the mirror image of $10_{117}$; $m=-2$; signature $-2$
10
118
$K$:
-t^10 + 4*t^9 - 8*t^8 + 12*t^7 - 15*t^6 + 17*t^5 - 15*t^4 + 12*t^3 - 8*t^2 + 4*t - 1
comment: $10_{118}$; $m=-5$; determinant $97$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
119
$K$:
t^10 - 4*t^9 + 9*t^8 - 13*t^7 + 16*t^6 - 17*t^5 + 16*t^4 - 12*t^3 + 8*t^2 - 4*t + 1
comment: $10_{119}$; $m=-6$; determinant $101$, signature $0$, alternating
10
119
$\bar K$:
t^10 - 4*t^9 + 8*t^8 - 12*t^7 + 16*t^6 - 17*t^5 + 16*t^4 - 13*t^3 + 9*t^2 - 4*t + 1
comment: the mirror image of $10_{119}$; $m=-4$; signature $0$
10
120
$K$:
t^10 - 4*t^9 + 8*t^8 - 13*t^7 + 16*t^6 - 18*t^5 + 17*t^4 - 13*t^3 + 10*t^2 - 4*t + 1
comment: $10_{120}$; $m=2$; determinant $105$, signature $-4$, alternating
10
120
$\bar K$:
t^10 - 4*t^9 + 10*t^8 - 13*t^7 + 17*t^6 - 18*t^5 + 16*t^4 - 13*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{120}$; $m=-12$; signature $4$
10
121
$K$:
-t^10 + 4*t^9 - 9*t^8 + 14*t^7 - 18*t^6 + 20*t^5 - 18*t^4 + 15*t^3 - 10*t^2 + 5*t - 1
comment: $10_{121}$; $m=-2$; determinant $115$, signature $-2$, alternating
10
121
$\bar K$:
-t^10 + 5*t^9 - 10*t^8 + 15*t^7 - 18*t^6 + 20*t^5 - 18*t^4 + 14*t^3 - 9*t^2 + 4*t - 1
comment: the mirror image of $10_{121}$; $m=-8$; signature $2$
10
122
$K$:
t^10 - 4*t^9 + 8*t^8 - 13*t^7 + 17*t^6 - 17*t^5 + 17*t^4 - 13*t^3 + 9*t^2 - 5*t + 1
comment: $10_{122}$; $m=-6$; determinant $105$, signature $0$, alternating
10
122
$\bar K$:
t^10 - 5*t^9 + 9*t^8 - 13*t^7 + 17*t^6 - 17*t^5 + 17*t^4 - 13*t^3 + 8*t^2 - 4*t + 1
comment: the mirror image of $10_{122}$; $m=-4$; signature $0$
10
123
$K$:
-t^10 + 5*t^9 - 10*t^8 + 15*t^7 - 19*t^6 + 21*t^5 - 19*t^4 + 15*t^3 - 10*t^2 + 5*t - 1
comment: $10_{123}$; $m=-5$; determinant $121$, signature $0$, alternating; amphichiral, so the mirror image is the same knot and $V(t)=V(1/t)$
10
124
$K$:
-t^6 + t^2 + 1
comment: $10_{124}$, the torus knot $T(3,5)$; $m=4$; determinant $1$, signature $-8$, non-alternating
10
124
$\bar K$:
t^6 + t^4 - 1
comment: the mirror image of $10_{124}$; $m=-10$; signature $8$
10
125
$K$:
-t^8 + t^7 - t^6 + 2*t^5 - t^4 + 2*t^3 - t^2 + t - 1
comment: $10_{125}$; $m=-4$; determinant $11$, signature $2$, non-alternating; chiral, yet $V(t)=V(1/t)$, so the mirror image has the same polynomial
10
125
$\bar K$:
-t^8 + t^7 - t^6 + 2*t^5 - t^4 + 2*t^3 - t^2 + t - 1
comment: the mirror image of $10_{125}$; $m=-4$; signature $-2$; the same polynomial as $10_{125}$
10
126
$K$:
-t^8 + 2*t^7 - 2*t^6 + 4*t^5 - 3*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: $10_{126}$; $m=-8$; determinant $19$, signature $2$, non-alternating
10
126
$\bar K$:
-t^8 + t^7 - 2*t^6 + 3*t^5 - 3*t^4 + 4*t^3 - 2*t^2 + 2*t - 1
comment: the mirror image of $10_{126}$; $m=0$; signature $-2$
10
127
$K$:
t^8 - 2*t^7 + 3*t^6 - 5*t^5 + 5*t^4 - 5*t^3 + 4*t^2 - 2*t + 2
comment: $10_{127}$; $m=2$; determinant $29$, signature $-4$, non-alternating
10
127
$\bar K$:
2*t^8 - 2*t^7 + 4*t^6 - 5*t^5 + 5*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{127}$; $m=-10$; signature $4$
10
128
$K$:
-t^7 + t^6 - 2*t^5 + 2*t^4 - t^3 + 2*t^2 - t + 1
comment: $10_{128}$; $m=3$; determinant $11$, signature $-6$, non-alternating
10
128
$\bar K$:
t^7 - t^6 + 2*t^5 - t^4 + 2*t^3 - 2*t^2 + t - 1
comment: the mirror image of $10_{128}$; $m=-10$; signature $6$
10
129
$K$:
-t^8 + 2*t^7 - 3*t^6 + 4*t^5 - 4*t^4 + 5*t^3 - 3*t^2 + 2*t - 1
comment: $10_{129}$; $m=-3$; determinant $25$, signature $0$, non-alternating; the same polynomial as the mirror image of $8_8$
10
129
$\bar K$:
-t^8 + 2*t^7 - 3*t^6 + 5*t^5 - 4*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: the mirror image of $10_{129}$; $m=-5$; signature $0$; the same polynomial as $8_8$
10
130
$K$:
-t^8 + 2*t^7 - 2*t^6 + 3*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + t - 1
comment: $10_{130}$; $m=-7$; determinant $17$, signature $0$, non-alternating
10
130
$\bar K$:
-t^8 + t^7 - 2*t^6 + 3*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + 2*t - 1
comment: the mirror image of $10_{130}$; $m=-1$; signature $0$
10
131
$K$:
t^8 - 2*t^7 + 3*t^6 - 5*t^5 + 5*t^4 - 5*t^3 + 5*t^2 - 3*t + 2
comment: $10_{131}$; $m=1$; determinant $31$, signature $-2$, non-alternating
10
131
$\bar K$:
2*t^8 - 3*t^7 + 5*t^6 - 5*t^5 + 5*t^4 - 5*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{131}$; $m=-9$; signature $2$
10
132
$K$:
t^5 + t^3 - t^2 + t - 1
comment: $10_{132}$; $m=-7$; determinant $5$, signature $0$, non-alternating; the same polynomial as the mirror image of $5_1$
10
132
$\bar K$:
-t^5 + t^4 - t^3 + t^2 + 1
comment: the mirror image of $10_{132}$; $m=2$; signature $0$; the same polynomial as $5_1$
10
133
$K$:
t^8 - 2*t^7 + 2*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 3*t^2 - t + 1
comment: $10_{133}$; $m=1$; determinant $19$, signature $-2$, non-alternating
10
133
$\bar K$:
t^8 - t^7 + 3*t^6 - 3*t^5 + 3*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $10_{133}$; $m=-9$; signature $2$
10
134
$K$:
t^8 - 3*t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - t + 1
comment: $10_{134}$; $m=3$; determinant $23$, signature $-6$, non-alternating
10
134
$\bar K$:
t^8 - t^7 + 3*t^6 - 3*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 3*t + 1
comment: the mirror image of $10_{134}$; $m=-11$; signature $6$
10
135
$K$:
-t^8 + 2*t^7 - 4*t^6 + 6*t^5 - 6*t^4 + 7*t^3 - 5*t^2 + 4*t - 2
comment: $10_{135}$; $m=-3$; determinant $37$, signature $0$, non-alternating
10
135
$\bar K$:
-2*t^8 + 4*t^7 - 5*t^6 + 7*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 2*t - 1
comment: the mirror image of $10_{135}$; $m=-5$; signature $0$
10
136
$K$:
t^7 - 2*t^6 + 2*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + 2*t - 1
comment: $10_{136}$; $m=-4$; determinant $15$, signature $2$, non-alternating
10
136
$\bar K$:
-t^7 + 2*t^6 - 2*t^5 + 3*t^4 - 2*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $10_{136}$; $m=-3$; signature $-2$
10
137
$K$:
t^8 - 2*t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 4*t^2 - 2*t + 1
comment: $10_{137}$; $m=-2$; determinant $25$, signature $0$, non-alternating; the same polynomial as the mirror image of $10_{155}$
10
137
$\bar K$:
t^8 - 2*t^7 + 4*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: the mirror image of $10_{137}$; $m=-6$; signature $0$; the same polynomial as $10_{155}$
10
138
$K$:
2*t^8 - 4*t^7 + 5*t^6 - 6*t^5 + 6*t^4 - 5*t^3 + 4*t^2 - 2*t + 1
comment: $10_{138}$; $m=-3$; determinant $35$, signature $-2$, non-alternating
10
138
$\bar K$:
t^8 - 2*t^7 + 4*t^6 - 5*t^5 + 6*t^4 - 6*t^3 + 5*t^2 - 4*t + 2
comment: the mirror image of $10_{138}$; $m=-5$; signature $2$
10
139
$K$:
-t^8 + t^7 - t^6 + t^5 - t^4 + t^2 + 1
comment: $10_{139}$; $m=4$; determinant $3$, signature $-6$, non-alternating
10
139
$\bar K$:
t^8 + t^6 - t^4 + t^3 - t^2 + t - 1
comment: the mirror image of $10_{139}$; $m=-12$; signature $6$
10
140
$K$:
-t^7 + t^6 - t^5 + 2*t^4 - t^3 + t^2 - t + 1
comment: $10_{140}$; $m=0$; determinant $9$, signature $0$, non-alternating
10
140
$\bar K$:
t^7 - t^6 + t^5 - t^4 + 2*t^3 - t^2 + t - 1
comment: the mirror image of $10_{140}$; $m=-7$; signature $0$
10
141
$K$:
t^8 - 2*t^7 + 2*t^6 - 3*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $10_{141}$; $m=-2$; determinant $21$, signature $0$, non-alternating
10
141
$\bar K$:
t^8 - 2*t^7 + 3*t^6 - 3*t^5 + 4*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $10_{141}$; $m=-6$; signature $0$
10
142
$K$:
-2*t^7 + 2*t^6 - 2*t^5 + 3*t^4 - 2*t^3 + 2*t^2 - t + 1
comment: $10_{142}$; $m=3$; determinant $15$, signature $-6$, non-alternating
10
142
$\bar K$:
t^7 - t^6 + 2*t^5 - 2*t^4 + 3*t^3 - 2*t^2 + 2*t - 2
comment: the mirror image of $10_{142}$; $m=-10$; signature $6$
10
143
$K$:
-t^8 + 3*t^7 - 3*t^6 + 5*t^5 - 5*t^4 + 4*t^3 - 3*t^2 + 2*t - 1
comment: $10_{143}$; $m=-8$; determinant $27$, signature $2$, non-alternating
10
143
$\bar K$:
-t^8 + 2*t^7 - 3*t^6 + 4*t^5 - 5*t^4 + 5*t^3 - 3*t^2 + 3*t - 1
comment: the mirror image of $10_{143}$; $m=0$; signature $-2$
10
144
$K$:
t^8 - 3*t^7 + 5*t^6 - 6*t^5 + 7*t^4 - 7*t^3 + 5*t^2 - 3*t + 2
comment: $10_{144}$; $m=-1$; determinant $39$, signature $-2$, non-alternating
10
144
$\bar K$:
2*t^8 - 3*t^7 + 5*t^6 - 7*t^5 + 7*t^4 - 6*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{144}$; $m=-7$; signature $2$
10
145
$K$:
t^8 + t^3 - t^2 + t - 1
comment: $10_{145}$; $m=-10$; determinant $3$, signature $2$, non-alternating
10
145
$\bar K$:
-t^8 + t^7 - t^6 + t^5 + 1
comment: the mirror image of $10_{145}$; $m=2$; signature $-2$
10
146
$K$:
-t^8 + 3*t^7 - 4*t^6 + 6*t^5 - 6*t^4 + 5*t^3 - 4*t^2 + 3*t - 1
comment: $10_{146}$; $m=-5$; determinant $33$, signature $0$, non-alternating
10
146
$\bar K$:
-t^8 + 3*t^7 - 4*t^6 + 5*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $10_{146}$; $m=-3$; signature $0$
10
147
$K$:
t^8 - 3*t^7 + 4*t^6 - 4*t^5 + 5*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $10_{147}$; $m=-3$; determinant $27$, signature $-2$, non-alternating
10
147
$\bar K$:
t^8 - 2*t^7 + 3*t^6 - 4*t^5 + 5*t^4 - 4*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $10_{147}$; $m=-5$; signature $2$
10
148
$K$:
-t^8 + 3*t^7 - 4*t^6 + 6*t^5 - 5*t^4 + 5*t^3 - 4*t^2 + 2*t - 1
comment: $10_{148}$; $m=-8$; determinant $31$, signature $2$, non-alternating
10
148
$\bar K$:
-t^8 + 2*t^7 - 4*t^6 + 5*t^5 - 5*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $10_{148}$; $m=0$; signature $-2$
10
149
$K$:
t^8 - 3*t^7 + 5*t^6 - 7*t^5 + 7*t^4 - 7*t^3 + 6*t^2 - 3*t + 2
comment: $10_{149}$; $m=2$; determinant $41$, signature $-4$, non-alternating
10
149
$\bar K$:
2*t^8 - 3*t^7 + 6*t^6 - 7*t^5 + 7*t^4 - 7*t^3 + 5*t^2 - 3*t + 1
comment: the mirror image of $10_{149}$; $m=-10$; signature $4$
10
150
$K$:
t^8 - 3*t^7 + 4*t^6 - 5*t^5 + 5*t^4 - 4*t^3 + 4*t^2 - 2*t + 1
comment: $10_{150}$; $m=0$; determinant $29$, signature $-4$, non-alternating
10
150
$\bar K$:
t^8 - 2*t^7 + 4*t^6 - 4*t^5 + 5*t^4 - 5*t^3 + 4*t^2 - 3*t + 1
comment: the mirror image of $10_{150}$; $m=-8$; signature $4$
10
151
$K$:
-t^8 + 3*t^7 - 5*t^6 + 7*t^5 - 7*t^4 + 8*t^3 - 6*t^2 + 4*t - 2
comment: $10_{151}$; $m=-6$; determinant $43$, signature $2$, non-alternating
10
151
$\bar K$:
-2*t^8 + 4*t^7 - 6*t^6 + 8*t^5 - 7*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{151}$; $m=-2$; signature $-2$
10
152
$K$:
t^9 - 2*t^8 + 2*t^7 - 3*t^6 + 2*t^5 - 2*t^4 + t^3 + t^2 + 1
comment: $10_{152}$; $m=4$; determinant $11$, signature $-6$, non-alternating
10
152
$\bar K$:
t^9 + t^7 + t^6 - 2*t^5 + 2*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $10_{152}$; $m=-13$; signature $6$
10
153
$K$:
-t^9 + t^8 - t^7 + t^6 + t^5 + t^3 - t^2 + t - 1
comment: $10_{153}$; $m=-5$; determinant $1$, signature $0$, non-alternating
10
153
$\bar K$:
-t^9 + t^8 - t^7 + t^6 + t^4 + t^3 - t^2 + t - 1
comment: the mirror image of $10_{153}$; $m=-4$; signature $0$
10
154
$K$:
t^9 - 2*t^8 + 2*t^7 - 3*t^6 + 2*t^5 - 2*t^4 + 2*t^3 + 1
comment: $10_{154}$; $m=3$; determinant $13$, signature $-4$, non-alternating
10
154
$\bar K$:
t^9 + 2*t^6 - 2*t^5 + 2*t^4 - 3*t^3 + 2*t^2 - 2*t + 1
comment: the mirror image of $10_{154}$; $m=-12$; signature $4$
10
155
$K$:
t^8 - 2*t^7 + 4*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 3*t^2 - 2*t + 1
comment: $10_{155}$; $m=-6$; determinant $25$, signature $0$, non-alternating; the same polynomial as the mirror image of $10_{137}$
10
155
$\bar K$:
t^8 - 2*t^7 + 3*t^6 - 4*t^5 + 4*t^4 - 4*t^3 + 4*t^2 - 2*t + 1
comment: the mirror image of $10_{155}$; $m=-2$; signature $0$; the same polynomial as $10_{137}$
10
156
$K$:
-t^8 + 3*t^7 - 4*t^6 + 6*t^5 - 6*t^4 + 6*t^3 - 5*t^2 + 3*t - 1
comment: $10_{156}$; $m=-6$; determinant $35$, signature $2$, non-alternating; the same polynomial as $8_{16}$
10
156
$\bar K$:
-t^8 + 3*t^7 - 5*t^6 + 6*t^5 - 6*t^4 + 6*t^3 - 4*t^2 + 3*t - 1
comment: the mirror image of $10_{156}$; $m=-2$; signature $-2$; the same polynomial as the mirror image of $8_{16}$
10
157
$K$:
2*t^8 - 4*t^7 + 7*t^6 - 8*t^5 + 9*t^4 - 8*t^3 + 6*t^2 - 4*t + 1
comment: $10_{157}$; $m=-10$; determinant $49$, signature $4$, non-alternating
10
157
$\bar K$:
t^8 - 4*t^7 + 6*t^6 - 8*t^5 + 9*t^4 - 8*t^3 + 7*t^2 - 4*t + 2
comment: the mirror image of $10_{157}$; $m=2$; signature $-4$
10
158
$K$:
2*t^8 - 4*t^7 + 6*t^6 - 8*t^5 + 8*t^4 - 7*t^3 + 6*t^2 - 3*t + 1
comment: $10_{158}$; $m=-4$; determinant $45$, signature $0$, non-alternating
10
158
$\bar K$:
t^8 - 3*t^7 + 6*t^6 - 7*t^5 + 8*t^4 - 8*t^3 + 6*t^2 - 4*t + 2
comment: the mirror image of $10_{158}$; $m=-4$; signature $0$
10
159
$K$:
-t^8 + 3*t^7 - 5*t^6 + 6*t^5 - 7*t^4 + 7*t^3 - 5*t^2 + 4*t - 1
comment: $10_{159}$; $m=0$; determinant $39$, signature $-2$, non-alternating
10
159
$\bar K$:
-t^8 + 4*t^7 - 5*t^6 + 7*t^5 - 7*t^4 + 6*t^3 - 5*t^2 + 3*t - 1
comment: the mirror image of $10_{159}$; $m=-8$; signature $2$
10
160
$K$:
-2*t^7 + 3*t^6 - 3*t^5 + 4*t^4 - 3*t^3 + 3*t^2 - 2*t + 1
comment: $10_{160}$; $m=0$; determinant $21$, signature $-4$, non-alternating
10
160
$\bar K$:
t^7 - 2*t^6 + 3*t^5 - 3*t^4 + 4*t^3 - 3*t^2 + 3*t - 2
comment: the mirror image of $10_{160}$; $m=-7$; signature $4$
10
161
$K$:
-t^8 + t^7 - t^6 + t^5 - t^4 + t^3 + 1
comment: $10_{161}$, the Perko pair, listed twice by Rolfsen as $10_{161}$ and $10_{162}$; $m=3$; determinant $5$, signature $-4$, non-alternating
10
161
$\bar K$:
t^8 + t^5 - t^4 + t^3 - t^2 + t - 1
comment: the mirror image of $10_{161}$, the Perko pair, listed twice by Rolfsen as $10_{161}$ and $10_{162}$; $m=-11$; signature $4$
10
162
$K$:
2*t^8 - 3*t^7 + 5*t^6 - 6*t^5 + 6*t^4 - 6*t^3 + 4*t^2 - 2*t + 1
comment: $10_{162}$; $m=-7$; determinant $35$, signature $2$, non-alternating
10
162
$\bar K$:
t^8 - 2*t^7 + 4*t^6 - 6*t^5 + 6*t^4 - 6*t^3 + 5*t^2 - 3*t + 2
comment: the mirror image of $10_{162}$; $m=-1$; signature $-2$
10
163
$K$:
-2*t^8 + 5*t^7 - 7*t^6 + 9*t^5 - 9*t^4 + 8*t^3 - 6*t^2 + 4*t - 1
comment: $10_{163}$; $m=-2$; determinant $51$, signature $-2$, non-alternating
10
163
$\bar K$:
-t^8 + 4*t^7 - 6*t^6 + 8*t^5 - 9*t^4 + 9*t^3 - 7*t^2 + 5*t - 2
comment: the mirror image of $10_{163}$; $m=-6$; signature $2$
10
164
$K$:
-2*t^8 + 5*t^7 - 6*t^6 + 8*t^5 - 8*t^4 + 7*t^3 - 5*t^2 + 3*t - 1
comment: $10_{164}$; $m=-5$; determinant $45$, signature $0$, non-alternating
10
164
$\bar K$:
-t^8 + 3*t^7 - 5*t^6 + 7*t^5 - 8*t^4 + 8*t^3 - 6*t^2 + 5*t - 2
comment: the mirror image of $10_{164}$; $m=-3$; signature $0$
10
165
$K$:
2*t^8 - 4*t^7 + 6*t^6 - 6*t^5 + 7*t^4 - 6*t^3 + 4*t^2 - 3*t + 1
comment: $10_{165}$; $m=-9$; determinant $39$, signature $2$, non-alternating
10
165
$\bar K$:
t^8 - 3*t^7 + 4*t^6 - 6*t^5 + 7*t^4 - 6*t^3 + 6*t^2 - 4*t + 2
comment: the mirror image of $10_{165}$; $m=1$; signature $-2$
Definition
The Jones polynomial $V_K(t)$ [8] of the unknot, of every prime knot $K=n_k$ with at most ten crossings, named as in the Rolfsen table [5] with Perko's correction [6] and drawn as in KnotInfo [14], and of its mirror image $\bar K$, listed as $t^{-m}V_K(t)$ with nonzero constant term.
Parameters
$n$
—   crossing number ($n=0$ or $3\leq n\leq 10$)
$k$
—   index in the Rolfsen table ($1\leq k\leq N(n)$, where $N(n)$ is the number of knots listed with $n$ crossings, $1,1,1,2,3,7,21,49,165$ for $n=0,3,4,\ldots,10$)
knot
—   the knot $K=n_k$ as KnotInfo draws it, or its mirror image $\bar K$ ($\bar K$ is listed for the 229 chiral knots only; the unknot and the 20 amphichiral knots are their own mirror images)
Formulas
(1)
$V(0_1)=1$ and $t^{-1}V(L_+)-t\,V(L_-)=(t^{1/2}-t^{-1/2})\,V(L_0)$ for three oriented link diagrams $L_+$, $L_-$ and $L_0$ that agree except at one crossing, which is positive in $L_+$, negative in $L_-$ and smoothed in $L_0$ [1] [8]. For a knot every exponent of $V$ is an integer.
(2)
$V_K(t)=\bigl((-A^3)^{-w(D)}\langle D\rangle\bigr)\big|_{A=t^{-1/4}}$ for any diagram $D$ of $K$, where $w(D)$ is the writhe of $D$ and $\langle D\rangle$ its Kauffman bracket [2] [8].
(3)
$V_{\bar K}(t)=V_K(t^{-1})$ for the mirror image $\bar K$ [8]. If the entry of $K$ is $P(t)=t^{-m}V_K(t)$, of degree $d$, the entry of $\bar K$ is $t^dP(t^{-1})$, the same coefficients in the opposite order, and the $m$ of $\bar K$ is $-m-d$.
(4)
$V_K(1)=1$, $V_K(\omega)=1$ for $\omega$ a primitive cube root of unity, and $|V_K(-1)|=\det K=|\Delta_K(-1)|$, where $\det K$ is the determinant of the knot and $\Delta_K$ its Alexander polynomial [12].
(5)
For an alternating knot the span of $V_K$, the difference between its highest and lowest exponents, is the crossing number $n$, its extreme coefficients are $\pm1$, and its coefficients $a_e$ satisfy $(-1)^ea_e\geq0$ for all $e$ or $(-1)^ea_e\leq0$ for all $e$ [2] [3] [4]; for a prime non-alternating knot the span is less than $n$ [3]. So the entry of an alternating knot has degree $n$.
(6)
$V_{T(p,q)}(t)=t^{(p-1)(q-1)/2}\,\dfrac{1-t^{p+1}-t^{q+1}+t^{p+q}}{1-t^2}$ for the right-handed torus knot $T(p,q)$ [10]. The torus knots here are $3_1=T(2,3)$, $5_1=T(2,5)$, $7_1=T(2,7)$, $9_1=T(2,9)$, $8_{19}=T(3,4)$ and $10_{124}=T(3,5)$, right-handed as KnotInfo draws them, so that $V_{3_1}=t+t^3-t^4$.
Comments
(7)
$V_K$ is a Laurent polynomial and the table holds polynomials, so the entry is $t^{-m}V_K(t)$ with $m$ the lowest exponent of $V_K$, and each entry's comment gives $m$. The right-handed trefoil has $V=t+t^3-t^4$ and the entry $-t^3+t^2+1$ with $m=1$; the left-handed trefoil has $V=-t^{-4}+t^{-3}+t^{-1}$ and the entry $t^3+t-1$ with $m=-4$. The variable is Jones's $t$, with $V(0_1)=1$ and the skein relation (1); the Knot Atlas [13] writes $q$ for it, and Kauffman's bracket variable $A$ [8] is $t^{-1/4}$. Sage's jones_polynomial() [15] and KnotInfo [14] use the same $t$, and Sage returns $V_K$ as a symbolic expression rather than a Laurent polynomial, because a link can have half-integer exponents.
(8)
The name $n_k$ names a knot only up to mirror image, and $V_{\bar K}(t)=V_K(t^{-1})$, so a table of Jones polynomials has to say which mirror image it draws. Here $K$ is the knot as KnotInfo [14] draws it, the closure of the braid in its braid notation, and $\bar K$ is its mirror image. The Knot Atlas [13], and Sage's Knots().from_table [15], which takes its braid words from the Knot Atlas, draw $\bar K$ for 139 of the 229 chiral knots: their $3_1$ is the left-handed trefoil where KnotInfo's is the right-handed one. Neither choice is wrong, which is why both mirror images are listed; the Alexander polynomial does not see the difference.
(9)
An amphichiral knot is isotopic to its mirror image, and its Jones polynomial satisfies $V(t)=V(t^{-1})$ [8]. Twenty knots here are amphichiral, $4_1$, $6_3$, $8_3$, $8_9$, $8_{12}$, $8_{17}$, $8_{18}$, $10_{17}$, $10_{33}$, $10_{37}$, $10_{43}$, $10_{45}$, $10_{79}$, $10_{81}$, $10_{88}$, $10_{99}$, $10_{109}$, $10_{115}$, $10_{118}$ and $10_{123}$, which is $1,1,5,13$ of them for $n=4,6,8,10$ [17], and each has a single entry. The converse fails: $9_{42}$, $10_{48}$, $10_{71}$, $10_{91}$, $10_{104}$ and $10_{125}$ are chiral although $V(t)=V(t^{-1})$ [9], so their two entries are equal.
(10)
The signature in each entry's comment is that of the knot listed, in the sign convention of KnotInfo [14], where the right-handed trefoil has signature $-2$; the mirror image has the opposite signature. The signature and the Jones polynomial are the two invariants here that see the mirror image; the determinant $|V(-1)|$ does not.
(11)
The numbering is Rolfsen's after Perko's correction [6]: the knots Rolfsen listed as $10_{161}$ and $10_{162}$ are one knot, so there are $165$ prime knots with ten crossings rather than $166$ [16], and Rolfsen's $10_{163}$ to $10_{166}$ are $10_{162}$ to $10_{165}$ here [11]. Sage's knot table, the Knot Atlas and KnotInfo all use this numbering. Within each crossing number the alternating knots come first: the non-alternating ones are $8_{19}$ to $8_{21}$, $9_{42}$ to $9_{49}$ and $10_{124}$ to $10_{165}$, and every prime knot with fewer than eight crossings is alternating.
(12)
The Jones polynomial does not determine the knot. Up to mirror image the 249 prime knots take 235 distinct polynomials, and 14 pairs share one: with the knots as KnotInfo draws them, $V_{8_{16}}=V_{10_{156}}$, $V_{10_{25}}=V_{10_{56}}$, $V_{10_{40}}=V_{10_{103}}$, $V_{10_{41}}=V_{10_{94}}$, $V_{10_{43}}=V_{10_{91}}$, $V_{10_{59}}=V_{10_{106}}$, $V_{10_{71}}=V_{10_{104}}$, $V_{10_{73}}=V_{10_{83}}$ and $V_{10_{81}}=V_{10_{109}}$, while $V_{5_1}(t)=V_{10_{132}}(t^{-1})$, $V_{8_8}(t)=V_{10_{129}}(t^{-1})$, $V_{10_{22}}(t)=V_{10_{35}}(t^{-1})$, $V_{10_{60}}(t)=V_{10_{86}}(t^{-1})$ and $V_{10_{137}}(t)=V_{10_{155}}(t^{-1})$. The 479 entries hold 448 distinct polynomials, and each entry's comment names the other entries with the same one. The unknot is the only knot here with $V=1$; whether a nontrivial knot with $V=1$ exists is an open question, and none has up to 24 crossings [7].
(13)
The Rolfsen table ends at ten crossings, and so do the names $n_k$. The 552 prime knots with eleven crossings are named $11a_1$ to $11a_{367}$ and $11n_1$ to $11n_{185}$ after Hoste and Thistlethwaite, alternating and non-alternating separately [14], which the parameters here cannot express; among them the Conway knot $11n_{34}$ and the Kinoshita–Terasaka knot $11n_{42}$ have the same Jones polynomial [8]. The Alexander polynomials of the knots listed here are in their own table; the HOMFLY-PT polynomials are not listed.
Programs
(P1)
Sage
B = BraidGroup(4)
K = Link(B([1, 1, 1, -2, -1, -1, -2, -3, 2, -3, -3]))   # 10_132, from KnotInfo's braid notation
V = K.jones_polynomial()                                # -t^(-7) + t^(-6) - t^(-5) + t^(-4) + t^(-2)
R.<t> = ZZ[]
c = V.coefficients(V.default_variable())               # [[coefficient, exponent], ...]
m = min(e for _, e in c)                                # -7
P = sum(ZZ(a) * t^(e - m) for a, e in c)                # t^5 + t^3 - t^2 + t - 1, the entry for K
Q = P.reverse()                                         # -t^5 + t^4 - t^3 + t^2 + 1, the entry for its mirror image
References
[1]
V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985), 103–111.
[2]
L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395–407.
[3]
K. Murasugi, Jones polynomials and classical conjectures in knot theory, Topology 26 (1987), 187–194.
[4]
M. B. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987), 297–309.
[5]
D. Rolfsen, Knots and Links, Publish or Perish, 1976, Appendix C: Table of knots and links.
[6]
K. A. Perko, On the classification of knots, Proc. Amer. Math. Soc. 45 (1974), 262–266.
[7]
R. E. Tuzun and A. S. Sikora, Verification of the Jones unknot conjecture up to 24 crossings, J. Knot Theory Ramifications 30 (2021), 2150020.
Links
Similar tables
Alexander polynomials of the prime knots with at most ten crossings —   the same knots; $|V_K(-1)|=|\Delta_K(-1)|$, and the Alexander polynomial does not see the mirror image
Data properties
Entries are of type: integral polynomial
How well the digits are known: exact
Table is complete: yes
How they were obtained:

Each polynomial is Sage's jones_polynomial() of the closure of KnotInfo's braid word for the knot, which evaluates a representation of the braid group.

more

The generator requires it to agree exactly with the Kauffman bracket state sum on the planar diagram of the same closure, and up to $t\mapsto t^{-1}$ with the Jones polynomial of Sage's Knots().from_table, whose braid word comes from the Knot Atlas; the entry of $\bar K$ is computed from the mirror image of the link and must equal $V_K(t^{-1})$. The value must satisfy $V(1)=1$, $V(\omega)=1$, $|V(-1)|=\det K$, the span and sign conditions for alternating and non-alternating knots, $V(t)=V(t^{-1})$ exactly for the 20 amphichiral and the six symmetric chiral knots, and the closed form for the six torus knots. Outside the generator all 249 polynomials of $K$ were compared with the jones_polynomial column of KnotInfo (package database_knotinfo 2026.9.1, computed from KnotInfo's own diagrams) and agree exactly, so the mirror entries agree with it under $t\mapsto t^{-1}$; $|V(-1)|$ was compared with $|\Delta(-1)|$ for KnotInfo's Alexander polynomials and $V(i)=(-1)^{\mathrm{Arf}}$ with its Arf invariants; and the determinant, signature, amphichirality and alternating facts in the comments were compared with KnotInfo's columns. Which mirror image the Knot Atlas draws was decided for every chiral knot: the Jones polynomial of Knots().from_table is $V_K(t^{-1})\neq V_K(t)$ for 137 of them; the signature Sage computes for the closure of KnotInfo's braid equals KnotInfo's column for all 249 knots, and for Knots().from_table it is the negative for $9_{42}$ and $10_{125}$; and for $10_{48}$, $10_{71}$, $10_{91}$ and $10_{104}$ Sage's knot table holds the same braid word as KnotInfo.



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