10
106
(K10a
95
)
A knot diagram
1
Linearized knot diagam
8 6 9 7 2 10 1 3 4 5
Solving Sequence
3,8
9 4
6,10
2 1 5 7
c
8
c
3
c
9
c
2
c
1
c
5
c
7
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.48988 × 10
22
u
38
− 3.35873 × 10
21
u
37
+ ··· + 1.23445 × 10
23
b − 2.68996 × 10
23
,
7.60416 × 10
23
u
38
− 5.87608 × 10
23
u
37
+ ··· + 1.23445 × 10
23
a − 3.17189 × 10
24
, u
39
− u
38
+ ··· − 12u + 1i
I
u
2
= hu
4
+ u
3
− 2u
2
+ b − u + 1, u
6
− u
5
− 4u
4
+ 4u
3
+ 3u
2
+ a − 3u + 1, u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1i
I
u
3
= hu
3
+ b − u, a + u, u
4
− u
3
− 1i
I
u
4
= hb, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 51 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
= h−4.49×10
22
u
38
−3.36×10
21
u
37
+· · ·+1.23×10
23
b−2.69×10
23
, 7.60×
10
23
u
38
−5.88×10
23
u
37
+· · ·+1.23×10
23
a−3.17×10
24
, u
39
−u
38
+· · ·−12u+1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
−6.15999u
38
+ 4.76010u
37
+ ··· − 199.096u + 25.6949
0.363717u
38
+ 0.0272084u
37
+ ··· − 15.2996u + 2.17908
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
6.10160u
38
− 5.05142u
37
+ ··· + 243.206u − 37.0950
−1.08737u
38
+ 0.953945u
37
+ ··· − 39.0834u + 4.92208
a
1
=
5.01423u
38
− 4.09747u
37
+ ··· + 204.123u − 32.1729
−1.08737u
38
+ 0.953945u
37
+ ··· − 39.0834u + 4.92208
a
5
=
3.85842u
38
− 3.05742u
37
+ ··· + 127.285u − 20.9953
0.129593u
38
+ 0.0772817u
37
+ ··· − 8.16390u + 2.14319
a
7
=
−5.60239u
38
+ 4.54940u
37
+ ··· − 197.298u + 25.4505
0.341348u
38
+ 0.0105311u
37
+ ··· − 12.5393u + 1.90327
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1385017988288929065913488
123444509404697939971901
u
38
+
961354782874772297950502
123444509404697939971901
u
37
+ ··· −
42223327798922175146355847
123444509404697939971901
u +
4715398000555894355706065
123444509404697939971901
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
39
− 5u
38
+ ··· − 30u + 4
c
2
, c
5
u
39
− 2u
38
+ ··· − 3u + 1
c
3
, c
8
, c
9
u
39
− u
38
+ ··· − 12u + 1
c
4
u
39
− 3u
38
+ ··· + 145u − 47
c
6
u
39
− 3u
38
+ ··· − 10u − 19
c
10
u
39
+ u
38
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
39
− 27y
38
+ ··· + 44y −16
c
2
, c
5
y
39
− 18y
38
+ ··· + 9y −1
c
3
, c
8
, c
9
y
39
− 43y
38
+ ··· + 34y −1
c
4
y
39
− 11y
38
+ ··· + 39261y −2209
c
6
y
39
+ 9y
38
+ ··· − 4118y −361
c
10
y
39
+ y
38
+ ··· + 76y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526234 + 0.893865I
a = 0.080741 + 1.260370I
b = 0.77528 − 1.59615I
−0.67462 + 9.52466I −2.84539 − 8.01548I
u = −0.526234 − 0.893865I
a = 0.080741 − 1.260370I
b = 0.77528 + 1.59615I
−0.67462 − 9.52466I −2.84539 + 8.01548I
u = −0.891332
a = 0.948472
b = −0.173901
−1.64188 −6.13450
u = −0.753681 + 0.913845I
a = −0.775515 − 0.367156I
b = −0.034229 + 1.332130I
−1.18856 − 3.53262I 0. + 6.78010I
u = −0.753681 − 0.913845I
a = −0.775515 + 0.367156I
b = −0.034229 − 1.332130I
−1.18856 + 3.53262I 0. − 6.78010I
u = 0.449207 + 0.638779I
a = −0.54432 + 1.40207I
b = 0.02023 − 1.45003I
3.29761 − 4.06547I 1.75322 + 6.53958I
u = 0.449207 − 0.638779I
a = −0.54432 − 1.40207I
b = 0.02023 + 1.45003I
3.29761 + 4.06547I 1.75322 − 6.53958I
u = 0.587174 + 0.474790I
a = −0.976192 − 0.745918I
b = −0.028896 − 0.602541I
−3.42290 − 4.16688I −6.75958 + 5.97205I
u = 0.587174 − 0.474790I
a = −0.976192 + 0.745918I
b = −0.028896 + 0.602541I
−3.42290 + 4.16688I −6.75958 − 5.97205I
u = 0.556467 + 0.391333I
a = 1.46828 − 1.00646I
b = 0.434310 + 0.698478I
2.85501 + 0.22937I 3.06420 + 0.82307I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.556467 − 0.391333I
a = 1.46828 + 1.00646I
b = 0.434310 − 0.698478I
2.85501 − 0.22937I 3.06420 − 0.82307I
u = 1.345600 + 0.177030I
a = −0.659060 + 0.853206I
b = −0.77984 − 1.42084I
−3.63229 − 5.60644I 0
u = 1.345600 − 0.177030I
a = −0.659060 − 0.853206I
b = −0.77984 + 1.42084I
−3.63229 + 5.60644I 0
u = 1.357030 + 0.066004I
a = 0.377431 + 0.276144I
b = 0.13369 − 1.70062I
−4.94271 − 3.13295I 0
u = 1.357030 − 0.066004I
a = 0.377431 − 0.276144I
b = 0.13369 + 1.70062I
−4.94271 + 3.13295I 0
u = 1.347220 + 0.243173I
a = −0.228876 + 0.363453I
b = −0.82451 − 1.40522I
−5.00065 − 3.66933I 0
u = 1.347220 − 0.243173I
a = −0.228876 − 0.363453I
b = −0.82451 + 1.40522I
−5.00065 + 3.66933I 0
u = −1.379580 + 0.070494I
a = 0.730492 + 0.504077I
b = 0.243999 − 0.841162I
−2.64947 + 1.12815I 0
u = −1.379580 − 0.070494I
a = 0.730492 − 0.504077I
b = 0.243999 + 0.841162I
−2.64947 − 1.12815I 0
u = −0.123207 + 0.595163I
a = 0.73822 − 1.95025I
b = −0.332572 + 1.082270I
0.96132 + 2.87976I 1.76496 − 6.23197I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.123207 − 0.595163I
a = 0.73822 + 1.95025I
b = −0.332572 − 1.082270I
0.96132 − 2.87976I 1.76496 + 6.23197I
u = −1.43879 + 0.06242I
a = −0.797689 − 0.378346I
b = −1.78940 + 1.48271I
−6.97221 + 3.87850I 0
u = −1.43879 − 0.06242I
a = −0.797689 + 0.378346I
b = −1.78940 − 1.48271I
−6.97221 − 3.87850I 0
u = −0.241634 + 0.442757I
a = 0.755226 − 0.616591I
b = −0.040932 + 0.380173I
−0.205812 + 1.182100I −2.82912 − 5.35064I
u = −0.241634 − 0.442757I
a = 0.755226 + 0.616591I
b = −0.040932 − 0.380173I
−0.205812 − 1.182100I −2.82912 + 5.35064I
u = −1.50425 + 0.21931I
a = −0.643325 − 0.432545I
b = −0.52587 + 1.73147I
−3.11282 + 7.19611I 0
u = −1.50425 − 0.21931I
a = −0.643325 + 0.432545I
b = −0.52587 − 1.73147I
−3.11282 − 7.19611I 0
u = −1.51467 + 0.17480I
a = −0.366164 + 0.848258I
b = 0.067693 − 0.170797I
−10.26840 + 6.64183I 0
u = −1.51467 − 0.17480I
a = −0.366164 − 0.848258I
b = 0.067693 + 0.170797I
−10.26840 − 6.64183I 0
u = −1.51667 + 0.36861I
a = 0.642404 + 0.518029I
b = 1.68758 − 1.24610I
−7.37640 + 4.84807I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51667 − 0.36861I
a = 0.642404 − 0.518029I
b = 1.68758 + 1.24610I
−7.37640 − 4.84807I 0
u = 1.54379 + 0.31697I
a = 0.708936 − 0.642910I
b = 1.36593 + 1.52871I
−7.3816 − 13.9330I 0
u = 1.54379 − 0.31697I
a = 0.708936 + 0.642910I
b = 1.36593 − 1.52871I
−7.3816 + 13.9330I 0
u = 1.63152 + 0.09989I
a = −0.115695 − 0.351183I
b = −0.353674 + 0.058988I
−10.12000 − 0.22050I 0
u = 1.63152 − 0.09989I
a = −0.115695 + 0.351183I
b = −0.353674 − 0.058988I
−10.12000 + 0.22050I 0
u = 1.64295
a = 0.177919
b = −0.647125
−10.0861 0
u = 0.207051 + 0.164027I
a = −1.65178 + 3.06553I
b = −0.98385 − 1.41829I
−1.44889 − 3.00326I −6.47920 + 9.13782I
u = 0.207051 − 0.164027I
a = −1.65178 − 3.06553I
b = −0.98385 + 1.41829I
−1.44889 + 3.00326I −6.47920 − 9.13782I
u = 0.195697
a = 7.38738
b = −0.248837
2.69998 9.09120
8
II. I
u
2
= hu
4
+ u
3
− 2u
2
+ b − u + 1, u
6
− u
5
− 4u
4
+ 4u
3
+ 3u
2
+ a − 3u +
1, u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
−u
6
+ u
5
+ 4u
4
− 4u
3
− 3u
2
+ 3u − 1
−u
4
− u
3
+ 2u
2
+ u − 1
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
6
− 4u
4
+ 2u
3
+ 4u
2
− 4u + 1
−u
2
+ 1
a
1
=
u
6
− 4u
4
+ 2u
3
+ 3u
2
− 4u + 2
−u
2
+ 1
a
5
=
u
6
− u
5
− 3u
4
+ 4u
3
− 3u + 2
−u
4
− u
3
+ 2u
2
+ u
a
7
=
−u
6
+ u
5
+ 3u
4
− 4u
3
− u
2
+ 3u − 1
−u
4
+ 2u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
6
+ 4u
5
+ 7u
4
− 13u
3
− 4u
2
+ 7u − 9
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− u
6
− 3u
5
+ 2u
4
+ 3u
3
− 3u
2
− u + 1
c
2
u
7
− u
6
− 3u
5
+ 3u
4
+ 2u
3
− 3u
2
− u + 1
c
3
u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1
c
4
u
7
− 2u
5
+ 4u
4
− u
3
− 3u
2
+ 3u − 1
c
5
u
7
+ u
6
− 3u
5
− 3u
4
+ 2u
3
+ 3u
2
− u − 1
c
6
u
7
+ u
4
− 2u
3
− 1
c
7
u
7
+ u
6
− 3u
5
− 2u
4
+ 3u
3
+ 3u
2
− u − 1
c
8
, c
9
u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1
c
10
u
7
+ 2u
4
− u
3
− 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
7
− 7y
6
+ 19y
5
− 30y
4
+ 29y
3
− 19y
2
+ 7y −1
c
2
, c
5
y
7
− 7y
6
+ 19y
5
− 29y
4
+ 30y
3
− 19y
2
+ 7y −1
c
3
, c
8
, c
9
y
7
− 8y
6
+ 24y
5
− 33y
4
+ 20y
3
− 6y
2
+ 4y −1
c
4
y
7
− 4y
6
+ 2y
5
− 6y
4
+ 13y
3
− 7y
2
+ 3y −1
c
6
y
7
− 4y
5
− y
4
+ 4y
3
+ 2y
2
− 1
c
10
y
7
− 2y
5
− 4y
4
+ y
3
+ 4y
2
− 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.25920
a = 1.35619
b = 0.394456
−0.400829 2.74790
u = 0.401963 + 0.546430I
a = 1.019580 − 0.650467I
b = −0.40274 + 1.44367I
−1.17508 + 2.13385I −3.11487 − 0.61129I
u = 0.401963 − 0.546430I
a = 1.019580 + 0.650467I
b = −0.40274 − 1.44367I
−1.17508 − 2.13385I −3.11487 + 0.61129I
u = 1.346460 + 0.204423I
a = −0.556014 + 0.539828I
b = −1.21748 − 1.74792I
−4.73997 − 4.82255I −6.63814 + 6.34253I
u = 1.346460 − 0.204423I
a = −0.556014 − 0.539828I
b = −1.21748 + 1.74792I
−4.73997 + 4.82255I −6.63814 − 6.34253I
u = −0.552010
a = −2.60549
b = −0.867226
2.28642 −11.4800
u = −1.68564
a = 0.322173
b = −0.286793
−9.79470 9.23770
12
III. I
u
3
= hu
3
+ b − u, a + u, u
4
− u
3
− 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
3
+ 2u
2
− 1
a
2
=
−u
3
−1
a
1
=
−u
3
− 1
−1
a
5
=
u
3
+ 1
−u
3
+ u
2
+ u
a
7
=
−u
3
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u + 1)
4
c
2
, c
5
u
4
+ u
3
− 2u
2
+ 1
c
3
, c
6
, c
8
c
9
u
4
− u
3
− 1
c
4
u
4
− u
3
− 2u
2
+ 1
c
10
u
4
+ u
2
+ 4u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)
4
c
2
, c
4
, c
5
y
4
− 5y
3
+ 6y
2
− 4y + 1
c
3
, c
6
, c
8
c
9
y
4
− y
3
− 2y
2
+ 1
c
10
y
4
+ 2y
3
+ 3y
2
− 14y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219447 + 0.914474I
a = −0.219447 − 0.914474I
b = 0.75943 + 1.54710I
−1.64493 −6.00000
u = 0.219447 − 0.914474I
a = −0.219447 + 0.914474I
b = 0.75943 − 1.54710I
−1.64493 −6.00000
u = −0.819173
a = 0.819173
b = −0.269472
−1.64493 −6.00000
u = 1.38028
a = −1.38028
b = −1.24938
−1.64493 −6.00000
16
IV. I
u
4
= hb, a − 1, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
8
=
1
0
a
9
=
1
1
a
4
=
1
0
a
6
=
1
0
a
10
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
0
1
a
7
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
9
u + 1
c
4
u − 1
c
10
u
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
y −1
c
10
y
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
−1.64493 −6.00000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)
5
(u
7
− u
6
− 3u
5
+ 2u
4
+ 3u
3
− 3u
2
− u + 1)
· (u
39
− 5u
38
+ ··· − 30u + 4)
c
2
(u + 1)(u
4
+ u
3
− 2u
2
+ 1)(u
7
− u
6
+ ··· − u + 1)
· (u
39
− 2u
38
+ ··· − 3u + 1)
c
3
(u + 1)(u
4
− u
3
− 1)(u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1)
· (u
39
− u
38
+ ··· − 12u + 1)
c
4
(u − 1)(u
4
− u
3
− 2u
2
+ 1)(u
7
− 2u
5
+ 4u
4
− u
3
− 3u
2
+ 3u − 1)
· (u
39
− 3u
38
+ ··· + 145u − 47)
c
5
(u + 1)(u
4
+ u
3
− 2u
2
+ 1)(u
7
+ u
6
+ ··· − u − 1)
· (u
39
− 2u
38
+ ··· − 3u + 1)
c
6
(u + 1)(u
4
− u
3
− 1)(u
7
+ u
4
− 2u
3
− 1)(u
39
− 3u
38
+ ··· − 10u − 19)
c
7
(u + 1)
5
(u
7
+ u
6
− 3u
5
− 2u
4
+ 3u
3
+ 3u
2
− u − 1)
· (u
39
− 5u
38
+ ··· − 30u + 4)
c
8
, c
9
(u + 1)(u
4
− u
3
− 1)(u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1)
· (u
39
− u
38
+ ··· − 12u + 1)
c
10
u(u
4
+ u
2
+ 4u + 1)(u
7
+ 2u
4
− u
3
− 1)(u
39
+ u
38
+ ··· + 6u + 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)
5
(y
7
− 7y
6
+ 19y
5
− 30y
4
+ 29y
3
− 19y
2
+ 7y −1)
· (y
39
− 27y
38
+ ··· + 44y −16)
c
2
, c
5
(y −1)(y
4
− 5y
3
+ 6y
2
− 4y + 1)
· (y
7
− 7y
6
+ 19y
5
− 29y
4
+ 30y
3
− 19y
2
+ 7y −1)
· (y
39
− 18y
38
+ ··· + 9y −1)
c
3
, c
8
, c
9
(y −1)(y
4
− y
3
− 2y
2
+ 1)(y
7
− 8y
6
+ ··· + 4y −1)
· (y
39
− 43y
38
+ ··· + 34y −1)
c
4
(y −1)(y
4
− 5y
3
+ 6y
2
− 4y + 1)
· (y
7
− 4y
6
+ 2y
5
− 6y
4
+ 13y
3
− 7y
2
+ 3y −1)
· (y
39
− 11y
38
+ ··· + 39261y −2209)
c
6
(y −1)(y
4
− y
3
− 2y
2
+ 1)(y
7
− 4y
5
− y
4
+ 4y
3
+ 2y
2
− 1)
· (y
39
+ 9y
38
+ ··· − 4118y −361)
c
10
y(y
4
+ 2y
3
+ 3y
2
− 14y + 1)(y
7
− 2y
5
− 4y
4
+ y
3
+ 4y
2
− 1)
· (y
39
+ y
38
+ ··· + 76y −1)
22
