12n
0708
(K12n
0708
)
A knot diagram
1
Linearized knot diagam
4 11 7 10 3 11 12 1 4 5 3 8
Solving Sequence
3,7 4,11
12 8 2 1 6 5 10 9
c
3
c
11
c
7
c
2
c
1
c
6
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.10576 × 10
47
u
33
− 8.01097 × 10
47
u
32
+ ··· + 1.80128 × 10
49
b + 1.32887 × 10
49
,
− 1.30799 × 10
49
u
33
+ 3.04903 × 10
49
u
32
+ ··· + 8.46601 × 10
50
a + 1.20480 × 10
51
,
u
34
− 3u
33
+ ··· + 119u − 47i
I
u
2
= hu
8
+ 2u
7
− u
6
− 2u
5
+ u
4
+ b − 1, −u
8
− 2u
7
+ u
6
+ 2u
5
− u
4
− u
3
− u
2
+ a + u + 1,
u
10
+ 2u
9
− u
8
− u
7
+ 2u
6
− u
5
+ u
4
− 2u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 44 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h1.11 × 10
47
u
33
− 8.01 × 10
47
u
32
+ · · · + 1.80 × 10
49
b + 1.33 ×
10
49
, −1.31 × 10
49
u
33
+ 3.05 × 10
49
u
32
+ · · · + 8.47 × 10
50
a + 1.20 ×
10
51
, u
34
− 3u
33
+ · · · + 119u − 47i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
0.0154499u
33
− 0.0360149u
32
+ ··· + 0.941098u − 1.42310
−0.00613876u
33
+ 0.0444738u
32
+ ··· + 2.98012u − 0.737735
a
12
=
0.00931114u
33
+ 0.00845885u
32
+ ··· + 3.92122u − 2.16083
−0.00613876u
33
+ 0.0444738u
32
+ ··· + 2.98012u − 0.737735
a
8
=
0.00533206u
33
− 0.0235388u
32
+ ··· − 3.14642u + 1.53400
0.0239032u
33
− 0.0742285u
32
+ ··· − 2.18646u + 0.793400
a
2
=
0.0232060u
33
− 0.0633719u
32
+ ··· − 1.53624u + 0.592137
−0.00632519u
33
+ 0.0366325u
32
+ ··· + 3.07109u − 0.769781
a
1
=
0.0236972u
33
− 0.0414540u
32
+ ··· + 1.18747u − 0.471217
−0.000941418u
33
− 0.00268565u
32
+ ··· + 0.310591u + 0.329618
a
6
=
−0.0248174u
33
+ 0.0762449u
32
+ ··· + 3.20943u − 0.350085
0.00624624u
33
− 0.0255551u
32
+ ··· − 2.16938u + 1.09068
a
5
=
−0.0185712u
33
+ 0.0506897u
32
+ ··· + 1.04004u + 0.740599
0.00624624u
33
− 0.0255551u
32
+ ··· − 2.16938u + 1.09068
a
10
=
0.0156673u
33
− 0.0416737u
32
+ ··· + 3.51356u − 2.20491
−0.0217802u
33
+ 0.0517956u
32
+ ··· − 0.173101u + 1.00253
a
9
=
0.0250751u
33
− 0.0635130u
32
+ ··· + 3.23816u − 1.45281
−0.0328754u
33
+ 0.0519114u
32
+ ··· − 0.490626u + 1.30257
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.338570u
33
+ 0.808896u
32
+ ··· + 19.1088u + 0.740160
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
− 4u
33
+ ··· + 612u − 536
c
2
, c
11
u
34
− 2u
33
+ ··· + 22u + 1
c
3
u
34
+ 3u
33
+ ··· − 119u − 47
c
4
, c
9
, c
10
u
34
+ u
33
+ ··· − 3u − 1
c
5
u
34
− 2u
33
+ ··· − 30u + 25
c
6
u
34
− u
33
+ ··· − 80u − 8
c
7
, c
8
, c
12
u
34
+ 2u
33
+ ··· − 11u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
+ 52y
33
+ ··· + 3454640y + 287296
c
2
, c
11
y
34
− 40y
33
+ ··· − 426y + 1
c
3
y
34
+ 7y
33
+ ··· + 23815y + 2209
c
4
, c
9
, c
10
y
34
− 23y
33
+ ··· − 9y + 1
c
5
y
34
+ 44y
33
+ ··· − 27550y + 625
c
6
y
34
+ 53y
33
+ ··· − 6560y + 64
c
7
, c
8
, c
12
y
34
− 44y
33
+ ··· − 261y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.469797 + 0.926681I
a = 0.173533 + 0.105962I
b = −0.73202 + 1.30784I
6.31099 − 6.15435I 0.40584 + 7.42268I
u = 0.469797 − 0.926681I
a = 0.173533 − 0.105962I
b = −0.73202 − 1.30784I
6.31099 + 6.15435I 0.40584 − 7.42268I
u = 0.055016 + 0.907256I
a = −2.57529 + 0.34754I
b = 1.334640 − 0.108463I
2.75863 − 1.86345I 3.58957 + 3.82529I
u = 0.055016 − 0.907256I
a = −2.57529 − 0.34754I
b = 1.334640 + 0.108463I
2.75863 + 1.86345I 3.58957 − 3.82529I
u = −0.597332 + 0.940180I
a = 0.729498 − 0.532364I
b = −1.41321 − 0.68276I
8.66900 + 2.33850I 4.06570 − 4.09223I
u = −0.597332 − 0.940180I
a = 0.729498 + 0.532364I
b = −1.41321 + 0.68276I
8.66900 − 2.33850I 4.06570 + 4.09223I
u = 0.548448 + 0.661548I
a = −0.395572 + 0.002411I
b = 0.361280 − 0.917030I
−0.97085 − 3.73329I −3.26740 + 7.90292I
u = 0.548448 − 0.661548I
a = −0.395572 − 0.002411I
b = 0.361280 + 0.917030I
−0.97085 + 3.73329I −3.26740 − 7.90292I
u = −0.838637
a = −1.95743
b = 0.627035
−4.25399 2.99560
u = 0.526405 + 1.043420I
a = −0.384792 + 1.231010I
b = −0.333049 + 0.008900I
6.57922 + 1.93235I 0.558019 − 0.700654I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526405 − 1.043420I
a = −0.384792 − 1.231010I
b = −0.333049 − 0.008900I
6.57922 − 1.93235I 0.558019 + 0.700654I
u = −0.572947 + 1.025320I
a = 0.483665 − 1.056480I
b = −1.052410 − 0.236751I
8.94084 + 2.54032I 3.06411 − 2.90404I
u = −0.572947 − 1.025320I
a = 0.483665 + 1.056480I
b = −1.052410 + 0.236751I
8.94084 − 2.54032I 3.06411 + 2.90404I
u = 0.001919 + 0.788798I
a = −1.54872 + 0.07110I
b = 1.52564 + 0.31114I
2.45487 + 1.58321I 5.81072 − 4.19715I
u = 0.001919 − 0.788798I
a = −1.54872 − 0.07110I
b = 1.52564 − 0.31114I
2.45487 − 1.58321I 5.81072 + 4.19715I
u = 0.758673
a = 0.528592
b = −0.0495765
−0.995684 −12.7630
u = 0.603373 + 0.439110I
a = 0.858658 − 0.248549I
b = 0.056009 + 0.383780I
−1.379030 − 0.087279I −5.81206 − 0.48445I
u = 0.603373 − 0.439110I
a = 0.858658 + 0.248549I
b = 0.056009 − 0.383780I
−1.379030 + 0.087279I −5.81206 + 0.48445I
u = −0.716829 + 1.057590I
a = 1.24846 − 0.72721I
b = −1.51816 − 0.17886I
8.00595 + 3.00523I 3.73808 − 2.90092I
u = −0.716829 − 1.057590I
a = 1.24846 + 0.72721I
b = −1.51816 + 0.17886I
8.00595 − 3.00523I 3.73808 + 2.90092I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691711 + 1.120790I
a = 1.60001 + 0.60370I
b = −1.48377 + 0.32078I
5.01121 − 8.11532I 0.18101 + 6.85241I
u = 0.691711 − 1.120790I
a = 1.60001 − 0.60370I
b = −1.48377 − 0.32078I
5.01121 + 8.11532I 0.18101 − 6.85241I
u = 0.881012 + 0.992412I
a = 1.080060 + 0.559009I
b = −1.51362 − 0.11800I
4.18213 + 1.75454I 1.44552 − 1.15085I
u = 0.881012 − 0.992412I
a = 1.080060 − 0.559009I
b = −1.51362 + 0.11800I
4.18213 − 1.75454I 1.44552 + 1.15085I
u = −0.202533 + 0.473694I
a = −0.566502 + 0.966055I
b = 0.571429 + 0.385434I
1.190200 + 0.722922I 4.39709 − 2.39918I
u = −0.202533 − 0.473694I
a = −0.566502 − 0.966055I
b = 0.571429 − 0.385434I
1.190200 − 0.722922I 4.39709 + 2.39918I
u = −1.48547
a = 0.692495
b = −0.738006
−7.70081 −22.1680
u = −1.49245
a = −0.0553962
b = 0.874161
−3.40883 −1.08290
u = 1.13577 + 1.43590I
a = −1.174670 − 0.437080I
b = 1.65946 − 0.37041I
14.0582 − 11.9947I 0
u = 1.13577 − 1.43590I
a = −1.174670 + 0.437080I
b = 1.65946 + 0.37041I
14.0582 + 11.9947I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.29108 + 1.38239I
a = −1.068980 + 0.541449I
b = 1.65562 + 0.16606I
18.1169 + 4.9950I 0
u = −1.29108 − 1.38239I
a = −1.068980 − 0.541449I
b = 1.65562 − 0.16606I
18.1169 − 4.9950I 0
u = 1.49621 + 1.30271I
a = −0.882637 − 0.559769I
b = 1.52536 + 0.01034I
13.07780 + 1.99862I 0
u = 1.49621 − 1.30271I
a = −0.882637 + 0.559769I
b = 1.52536 − 0.01034I
13.07780 − 1.99862I 0
8
II.
I
u
2
= hu
8
+2u
7
−u
6
−2u
5
+u
4
+b−1, −u
8
−2u
7
+· · ·+a+1, u
10
+2u
9
+· · ·+u−1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
u
8
+ 2u
7
− u
6
− 2u
5
+ u
4
+ u
3
+ u
2
− u − 1
−u
8
− 2u
7
+ u
6
+ 2u
5
− u
4
+ 1
a
12
=
u
3
+ u
2
− u
−u
8
− 2u
7
+ u
6
+ 2u
5
− u
4
+ 1
a
8
=
u
7
+ 2u
6
− u
5
− 2u
4
+ u
3
u
9
+ 2u
8
− u
7
− u
6
+ 2u
5
− 2u
4
+ u
2
− u + 1
a
2
=
u
9
+ 3u
8
+ u
7
− 2u
6
+ u
5
+ u
4
+ u
2
− 2u − 1
−u
3
− u
2
+ u + 1
a
1
=
u
9
+ 3u
8
+ u
7
− 2u
6
+ u
5
+ u
4
− u
3
− u − 1
−u
5
− u
4
− u
2
+ u + 1
a
6
=
−2u
9
− 4u
8
+ 3u
7
+ 4u
6
− 5u
5
+ u
4
− u
2
+ 5u − 2
u
9
+ 2u
8
− u
7
− u
6
+ 2u
5
− u
4
+ u
3
− 2u + 1
a
5
=
−u
9
− 2u
8
+ 2u
7
+ 3u
6
− 3u
5
+ u
3
− u
2
+ 3u − 1
u
9
+ 2u
8
− u
7
− u
6
+ 2u
5
− u
4
+ u
3
− 2u + 1
a
10
=
u
7
+ u
6
− 2u
5
+ u
3
+ 2u − 2
u
9
+ u
8
− 3u
7
− u
6
+ 3u
5
+ u
3
− u
2
− u + 1
a
9
=
u
2
+ u − 1
−u
7
− u
6
+ 2u
5
+ u
4
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
9
+ 4u
8
+ 3u
7
+ 4u
6
− 4u
5
− u
4
+ 7u
3
− 3u
2
+ 2u − 4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 3u
9
+ 6u
8
+ 6u
7
+ u
6
− 11u
5
− 14u
4
− u
3
+ 8u
2
+ 3u − 1
c
2
u
10
+ 3u
9
− 2u
8
− 14u
7
− 5u
6
+ 23u
5
+ 16u
4
− 15u
3
− 11u
2
+ 4u + 1
c
3
u
10
+ 2u
9
− u
8
− u
7
+ 2u
6
− u
5
+ u
4
− 2u
2
+ u − 1
c
4
u
10
− 6u
8
− u
7
+ 13u
6
+ 4u
5
− 13u
4
− 5u
3
+ 6u
2
+ 3u − 1
c
5
u
10
+ u
9
+ 2u
8
− u
6
− u
5
− 2u
4
− u
3
+ u
2
+ 2u − 1
c
6
u
10
+ 2u
8
− 2u
7
− u
6
− 4u
5
− 2u
4
+ 3u
3
− 2u
2
+ 3u + 1
c
7
, c
8
u
10
+ u
9
− 6u
8
− 6u
7
+ 11u
6
+ 11u
5
− 4u
4
− 5u
3
− 4u
2
− u + 1
c
9
, c
10
u
10
− 6u
8
+ u
7
+ 13u
6
− 4u
5
− 13u
4
+ 5u
3
+ 6u
2
− 3u − 1
c
11
u
10
− 3u
9
− 2u
8
+ 14u
7
− 5u
6
− 23u
5
+ 16u
4
+ 15u
3
− 11u
2
− 4u + 1
c
12
u
10
− u
9
− 6u
8
+ 6u
7
+ 11u
6
− 11u
5
− 4u
4
+ 5u
3
− 4u
2
+ u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 3y
9
+ ··· − 25y + 1
c
2
, c
11
y
10
− 13y
9
+ ··· − 38y + 1
c
3
y
10
− 6y
9
+ 9y
8
+ y
7
− 4y
6
+ y
5
− 3y
4
− 6y
3
+ 2y
2
+ 3y + 1
c
4
, c
9
, c
10
y
10
− 12y
9
+ ··· − 21y + 1
c
5
y
10
+ 3y
9
+ 2y
8
− 6y
7
− 3y
6
+ y
5
− 4y
4
+ y
3
+ 9y
2
− 6y + 1
c
6
y
10
+ 4y
9
+ 2y
8
− 12y
7
− 27y
6
− 6y
5
+ 48y
4
+ 21y
3
− 18y
2
− 13y + 1
c
7
, c
8
, c
12
y
10
− 13y
9
+ ··· − 9y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748756 + 0.648482I
a = 0.375274 + 0.762613I
b = −1.50876 + 0.37799I
8.36725 − 1.33489I 1.94242 − 2.46421I
u = 0.748756 − 0.648482I
a = 0.375274 − 0.762613I
b = −1.50876 − 0.37799I
8.36725 + 1.33489I 1.94242 + 2.46421I
u = 0.937843
a = 0.283456
b = 0.483130
−0.498447 5.48800
u = −0.186579 + 0.862945I
a = 1.14726 − 1.04811I
b = −1.26022 − 0.68934I
6.77164 + 4.55155I 1.99946 − 3.34420I
u = −0.186579 − 0.862945I
a = 1.14726 + 1.04811I
b = −1.26022 + 0.68934I
6.77164 − 4.55155I 1.99946 + 3.34420I
u = −1.12602
a = 1.14998
b = −0.183747
−5.01118 −8.63130
u = 0.213691 + 0.628245I
a = −2.16352 − 0.71377I
b = 1.357540 + 0.192129I
1.63959 + 1.30650I −4.90826 − 0.15548I
u = 0.213691 − 0.628245I
a = −2.16352 + 0.71377I
b = 1.357540 − 0.192129I
1.63959 − 1.30650I −4.90826 + 0.15548I
u = −1.55268
a = −0.662730
b = 0.883015
−7.45391 10.7450
u = −1.81088
a = 0.511259
b = −1.35950
−0.854207 1.33140
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 3u
9
+ 6u
8
+ 6u
7
+ u
6
− 11u
5
− 14u
4
− u
3
+ 8u
2
+ 3u − 1)
· (u
34
− 4u
33
+ ··· + 612u − 536)
c
2
(u
10
+ 3u
9
− 2u
8
− 14u
7
− 5u
6
+ 23u
5
+ 16u
4
− 15u
3
− 11u
2
+ 4u + 1)
· (u
34
− 2u
33
+ ··· + 22u + 1)
c
3
(u
10
+ 2u
9
− u
8
− u
7
+ 2u
6
− u
5
+ u
4
− 2u
2
+ u − 1)
· (u
34
+ 3u
33
+ ··· − 119u − 47)
c
4
(u
10
− 6u
8
− u
7
+ 13u
6
+ 4u
5
− 13u
4
− 5u
3
+ 6u
2
+ 3u − 1)
· (u
34
+ u
33
+ ··· − 3u − 1)
c
5
(u
10
+ u
9
+ 2u
8
− u
6
− u
5
− 2u
4
− u
3
+ u
2
+ 2u − 1)
· (u
34
− 2u
33
+ ··· − 30u + 25)
c
6
(u
10
+ 2u
8
− 2u
7
− u
6
− 4u
5
− 2u
4
+ 3u
3
− 2u
2
+ 3u + 1)
· (u
34
− u
33
+ ··· − 80u − 8)
c
7
, c
8
(u
10
+ u
9
− 6u
8
− 6u
7
+ 11u
6
+ 11u
5
− 4u
4
− 5u
3
− 4u
2
− u + 1)
· (u
34
+ 2u
33
+ ··· − 11u − 1)
c
9
, c
10
(u
10
− 6u
8
+ u
7
+ 13u
6
− 4u
5
− 13u
4
+ 5u
3
+ 6u
2
− 3u − 1)
· (u
34
+ u
33
+ ··· − 3u − 1)
c
11
(u
10
− 3u
9
− 2u
8
+ 14u
7
− 5u
6
− 23u
5
+ 16u
4
+ 15u
3
− 11u
2
− 4u + 1)
· (u
34
− 2u
33
+ ··· + 22u + 1)
c
12
(u
10
− u
9
− 6u
8
+ 6u
7
+ 11u
6
− 11u
5
− 4u
4
+ 5u
3
− 4u
2
+ u + 1)
· (u
34
+ 2u
33
+ ··· − 11u − 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 3y
9
+ ··· − 25y + 1)(y
34
+ 52y
33
+ ··· + 3454640y + 287296)
c
2
, c
11
(y
10
− 13y
9
+ ··· − 38y + 1)(y
34
− 40y
33
+ ··· − 426y + 1)
c
3
(y
10
− 6y
9
+ 9y
8
+ y
7
− 4y
6
+ y
5
− 3y
4
− 6y
3
+ 2y
2
+ 3y + 1)
· (y
34
+ 7y
33
+ ··· + 23815y + 2209)
c
4
, c
9
, c
10
(y
10
− 12y
9
+ ··· − 21y + 1)(y
34
− 23y
33
+ ··· − 9y + 1)
c
5
(y
10
+ 3y
9
+ 2y
8
− 6y
7
− 3y
6
+ y
5
− 4y
4
+ y
3
+ 9y
2
− 6y + 1)
· (y
34
+ 44y
33
+ ··· − 27550y + 625)
c
6
(y
10
+ 4y
9
+ 2y
8
− 12y
7
− 27y
6
− 6y
5
+ 48y
4
+ 21y
3
− 18y
2
− 13y + 1)
· (y
34
+ 53y
33
+ ··· − 6560y + 64)
c
7
, c
8
, c
12
(y
10
− 13y
9
+ ··· − 9y + 1)(y
34
− 44y
33
+ ··· − 261y + 1)
14
