10
102
(K10a
97
)
A knot diagram
1
Linearized knot diagam
5 6 9 8 10 3 1 4 2 7
Solving Sequence
2,6
3
7,10
5 1 9 4 8
c
2
c
6
c
5
c
1
c
9
c
3
c
8
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.25484 × 10
39
u
42
+ 2.20978 × 10
39
u
41
+ ··· + 2.97870 × 10
39
b − 1.19885 × 10
39
,
− 3.16887 × 10
39
u
42
− 4.11086 × 10
36
u
41
+ ··· + 2.97870 × 10
39
a + 2.58687 × 10
40
,
u
43
− 12u
41
+ ··· − 7u − 1i
I
u
2
= hu
6
− 3u
4
− u
3
+ 6u
2
+ b − 3, −u
6
− u
5
+ u
4
+ 2u
3
− 2u
2
+ a − u − 1, u
7
+ u
6
− 2u
5
− 3u
4
+ 3u
3
+ 3u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 50 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−2.25 × 10
39
u
42
+ 2.21 × 10
39
u
41
+ · · · + 2.98 × 10
39
b − 1.20 ×
10
39
, −3.17 × 10
39
u
42
− 4.11 × 10
36
u
41
+ · · · + 2.98 × 10
39
a + 2.59 ×
10
40
, u
43
− 12u
41
+ · · · − 7u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
−u
−u
3
+ u
a
10
=
1.06384u
42
+ 0.00138009u
41
+ ··· − 8.11372u − 8.68458
0.756988u
42
− 0.741862u
41
+ ··· − 0.408776u + 0.402477
a
5
=
−0.534324u
42
− 0.672258u
41
+ ··· + 3.56812u + 10.8345
−0.489904u
42
+ 0.404335u
41
+ ··· + 3.17936u − 0.269339
a
1
=
1.67244u
42
− 0.522788u
41
+ ··· − 8.92616u − 9.02482
0.644047u
42
− 0.551896u
41
+ ··· − 2.65691u + 0.218556
a
9
=
1.82083u
42
− 0.740482u
41
+ ··· − 8.52249u − 8.28210
0.756988u
42
− 0.741862u
41
+ ··· − 0.408776u + 0.402477
a
4
=
−0.891489u
42
+ 1.06089u
41
+ ··· + 7.38092u − 2.51083
−0.892905u
42
+ 0.445547u
41
+ ··· + 7.63273u + 1.57813
a
8
=
0.580848u
42
+ 1.18966u
41
+ ··· − 4.91202u − 10.4146
−0.291565u
42
+ 0.524997u
41
+ ··· + 0.716241u + 0.694269
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.56001u
42
− 2.01639u
41
+ ··· − 29.9474u − 1.29868
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
− 3u
42
+ ··· − 1000u + 419
c
2
, c
6
u
43
− 12u
41
+ ··· − 7u − 1
c
3
, c
4
, c
8
u
43
+ u
42
+ ··· + 10u − 1
c
5
u
43
+ u
42
+ ··· + 2u − 1
c
7
, c
10
u
43
− 17u
41
+ ··· + 85u − 19
c
9
u
43
− 7u
42
+ ··· + 18u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
− 17y
42
+ ··· + 2566222y −175561
c
2
, c
6
y
43
− 24y
42
+ ··· + 29y −1
c
3
, c
4
, c
8
y
43
+ 45y
42
+ ··· + 28y −1
c
5
y
43
+ y
42
+ ··· + 8y −1
c
7
, c
10
y
43
− 34y
42
+ ··· + 4299y −361
c
9
y
43
+ y
42
+ ··· + 68y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179428 + 0.966528I
a = −0.758038 + 0.845663I
b = 0.655485 − 0.701109I
3.68686 + 3.98038I 2.52488 − 5.84737I
u = 0.179428 − 0.966528I
a = −0.758038 − 0.845663I
b = 0.655485 + 0.701109I
3.68686 − 3.98038I 2.52488 + 5.84737I
u = 0.873967 + 0.439410I
a = −1.86520 − 0.23703I
b = −0.248002 − 0.538074I
8.42806 − 4.73173I 3.14920 + 6.15524I
u = 0.873967 − 0.439410I
a = −1.86520 + 0.23703I
b = −0.248002 + 0.538074I
8.42806 + 4.73173I 3.14920 − 6.15524I
u = −0.894503 + 0.382311I
a = 1.176590 + 0.347821I
b = 1.61995 − 0.69095I
8.00794 − 0.59552I 3.42142 − 0.64701I
u = −0.894503 − 0.382311I
a = 1.176590 − 0.347821I
b = 1.61995 + 0.69095I
8.00794 + 0.59552I 3.42142 + 0.64701I
u = −0.937588 + 0.179486I
a = −0.339877 − 1.370130I
b = −0.908003 + 0.652924I
−1.78551 + 0.79823I −3.86305 + 0.92711I
u = −0.937588 − 0.179486I
a = −0.339877 + 1.370130I
b = −0.908003 − 0.652924I
−1.78551 − 0.79823I −3.86305 − 0.92711I
u = 1.005980 + 0.308159I
a = −0.113439 + 0.394153I
b = 0.524877 − 0.944675I
0.85124 − 2.72416I 2.00505 + 5.61413I
u = 1.005980 − 0.308159I
a = −0.113439 − 0.394153I
b = 0.524877 + 0.944675I
0.85124 + 2.72416I 2.00505 − 5.61413I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.765516 + 0.410276I
a = −0.11829 − 1.69787I
b = −0.114903 + 1.388430I
8.79687 + 1.11797I 3.28924 + 1.64001I
u = 0.765516 − 0.410276I
a = −0.11829 + 1.69787I
b = −0.114903 − 1.388430I
8.79687 − 1.11797I 3.28924 − 1.64001I
u = −0.028174 + 0.866113I
a = 0.809304 + 0.674158I
b = −0.391438 − 1.141660I
6.04283 − 2.22576I 2.85072 + 2.97682I
u = −0.028174 − 0.866113I
a = 0.809304 − 0.674158I
b = −0.391438 + 1.141660I
6.04283 + 2.22576I 2.85072 − 2.97682I
u = −0.780496 + 0.342696I
a = −0.346122 − 0.358729I
b = 1.14579 + 1.89719I
8.42175 + 3.77684I 3.65503 − 8.57155I
u = −0.780496 − 0.342696I
a = −0.346122 + 0.358729I
b = 1.14579 − 1.89719I
8.42175 − 3.77684I 3.65503 + 8.57155I
u = −1.078720 + 0.416332I
a = 0.42969 + 1.53300I
b = 0.516989 − 0.937834I
0.60187 + 3.31941I 1.55391 − 4.71171I
u = −1.078720 − 0.416332I
a = 0.42969 − 1.53300I
b = 0.516989 + 0.937834I
0.60187 − 3.31941I 1.55391 + 4.71171I
u = 1.129000 + 0.367417I
a = −0.365298 + 0.935642I
b = −1.15401 − 0.92294I
−3.24498 − 4.34665I −5.96005 + 6.56486I
u = 1.129000 − 0.367417I
a = −0.365298 − 0.935642I
b = −1.15401 + 0.92294I
−3.24498 + 4.34665I −5.96005 − 6.56486I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.191130 + 0.116555I
a = 0.256373 + 0.200746I
b = 0.664648 − 0.107180I
−1.93492 + 0.03968I −6.28529 + 0.84629I
u = −1.191130 − 0.116555I
a = 0.256373 − 0.200746I
b = 0.664648 + 0.107180I
−1.93492 − 0.03968I −6.28529 − 0.84629I
u = −0.378773 + 1.211200I
a = −0.790261 − 0.487133I
b = 0.729066 + 0.956751I
10.42570 − 7.06955I 4.08198 + 5.07559I
u = −0.378773 − 1.211200I
a = −0.790261 + 0.487133I
b = 0.729066 − 0.956751I
10.42570 + 7.06955I 4.08198 − 5.07559I
u = −1.213920 + 0.493820I
a = −0.400742 − 0.782997I
b = −1.36620 + 1.30872I
2.55744 + 7.03361I 0. − 6.57917I
u = −1.213920 − 0.493820I
a = −0.400742 + 0.782997I
b = −1.36620 − 1.30872I
2.55744 − 7.03361I 0. + 6.57917I
u = −1.137270 + 0.679680I
a = 0.184669 − 0.702586I
b = −0.708630 + 0.391631I
−1.44466 + 3.00552I 0. − 9.20545I
u = −1.137270 − 0.679680I
a = 0.184669 + 0.702586I
b = −0.708630 − 0.391631I
−1.44466 − 3.00552I 0. + 9.20545I
u = 1.158150 + 0.671841I
a = 0.232978 − 0.277892I
b = 0.750511 + 0.201961I
1.98226 − 3.31409I 0
u = 1.158150 − 0.671841I
a = 0.232978 + 0.277892I
b = 0.750511 − 0.201961I
1.98226 + 3.31409I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.219040 + 0.557460I
a = 0.372924 − 1.203390I
b = 0.973714 + 1.002820I
0.51328 − 9.38930I 0
u = 1.219040 − 0.557460I
a = 0.372924 + 1.203390I
b = 0.973714 − 1.002820I
0.51328 + 9.38930I 0
u = −1.26281 + 0.69376I
a = 0.265003 + 1.100870I
b = 1.25438 − 1.17806I
7.5587 + 13.7273I 0
u = −1.26281 − 0.69376I
a = 0.265003 − 1.100870I
b = 1.25438 + 1.17806I
7.5587 − 13.7273I 0
u = 0.548716
a = 2.07278
b = 1.17742
2.69846 8.61990
u = 1.41987 + 0.31511I
a = 0.211755 + 0.472935I
b = 0.172064 + 0.048798I
1.65782 − 2.65936I 0
u = 1.41987 − 0.31511I
a = 0.211755 − 0.472935I
b = 0.172064 − 0.048798I
1.65782 + 2.65936I 0
u = 1.14071 + 0.96754I
a = 0.310323 + 0.683171I
b = −1.152640 − 0.275297I
3.92762 − 3.88689I 0
u = 1.14071 − 0.96754I
a = 0.310323 − 0.683171I
b = −1.152640 + 0.275297I
3.92762 + 3.88689I 0
u = −0.018931 + 0.428931I
a = 1.30275 − 0.64031I
b = −0.458147 + 0.443775I
−0.163307 + 1.128420I −2.36544 − 5.85154I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.018931 − 0.428931I
a = 1.30275 + 0.64031I
b = −0.458147 − 0.443775I
−0.163307 − 1.128420I −2.36544 + 5.85154I
u = −0.243711 + 0.078761I
a = −5.49149 − 1.45816I
b = 0.405795 + 0.070225I
2.85108 − 0.00109I 4.91718 − 0.42732I
u = −0.243711 − 0.078761I
a = −5.49149 + 1.45816I
b = 0.405795 − 0.070225I
2.85108 + 0.00109I 4.91718 + 0.42732I
9
II. I
u
2
= hu
6
− 3u
4
− u
3
+ 6u
2
+ b − 3, −u
6
− u
5
+ u
4
+ 2u
3
− 2u
2
+ a − u −
1, u
7
+ u
6
− 2u
5
− 3u
4
+ 3u
3
+ 3u
2
− u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
−u
−u
3
+ u
a
10
=
u
6
+ u
5
− u
4
− 2u
3
+ 2u
2
+ u + 1
−u
6
+ 3u
4
+ u
3
− 6u
2
+ 3
a
5
=
−2u
5
− 2u
4
+ 3u
3
+ 5u
2
− 4u − 3
−u
6
− u
5
+ 2u
4
+ 3u
3
− 3u
2
− 2u + 1
a
1
=
u
6
+ u
5
− u
4
− 2u
3
+ 2u
2
+ u + 2
−u
6
+ 3u
4
+ u
3
− 5u
2
+ 2
a
9
=
u
5
+ 2u
4
− u
3
− 4u
2
+ u + 4
−u
6
+ 3u
4
+ u
3
− 6u
2
+ 3
a
4
=
−4u
6
− 2u
5
+ 8u
4
+ 7u
3
− 14u
2
− 2u + 4
−u
6
+ 2u
4
+ u
3
− 3u
2
+ u
a
8
=
2u
6
+ 3u
5
− 3u
4
− 7u
3
+ 4u
2
+ 7u − 1
2u
6
+ u
5
− 4u
4
− 4u
3
+ 7u
2
+ 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
6
− 5u
5
+ 4u
4
+ 10u
3
− 2u
2
− 11u − 3
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
+ u
5
− u
4
+ 2u
3
+ 1
c
2
u
7
+ u
6
− 2u
5
− 3u
4
+ 3u
3
+ 3u
2
− u − 1
c
3
, c
4
u
7
+ 4u
5
+ 4u
3
+ u
2
+ 1
c
5
u
7
+ 2u
4
− u
3
+ u
2
+ 1
c
6
u
7
− u
6
− 2u
5
+ 3u
4
+ 3u
3
− 3u
2
− u + 1
c
7
u
7
− u
6
− 3u
5
+ 3u
4
+ 3u
3
− 2u
2
− u + 1
c
8
u
7
+ 4u
5
+ 4u
3
− u
2
− 1
c
9
u
7
− 2u
4
+ 2u
3
+ u
2
− 2u + 1
c
10
u
7
+ u
6
− 3u
5
− 3u
4
+ 3u
3
+ 2u
2
− u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
7
+ 2y
6
+ 5y
5
+ 3y
4
+ 4y
3
+ 2y
2
− 1
c
2
, c
6
y
7
− 5y
6
+ 16y
5
− 29y
4
+ 33y
3
− 21y
2
+ 7y − 1
c
3
, c
4
, c
8
y
7
+ 8y
6
+ 24y
5
+ 32y
4
+ 16y
3
− y
2
− 2y − 1
c
5
y
7
− 2y
5
− 4y
4
− 3y
3
− 5y
2
− 2y − 1
c
7
, c
10
y
7
− 7y
6
+ 21y
5
− 33y
4
+ 29y
3
− 16y
2
+ 5y − 1
c
9
y
7
+ 4y
5
− 8y
4
+ 8y
3
− 5y
2
+ 2y − 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060630 + 0.467862I
a = 0.094535 + 0.998646I
b = −0.498285 − 0.549564I
−1.05108 − 2.27150I −1.29108 + 1.27417I
u = 1.060630 − 0.467862I
a = 0.094535 − 0.998646I
b = −0.498285 + 0.549564I
−1.05108 + 2.27150I −1.29108 − 1.27417I
u = 0.719538
a = 2.07355
b = 0.931490
2.16696 −8.53360
u = −0.636439 + 0.197997I
a = 1.36182 − 0.54122I
b = 0.85369 + 1.27696I
8.25977 + 2.86772I 1.82451 − 0.48406I
u = −0.636439 − 0.197997I
a = 1.36182 + 0.54122I
b = 0.85369 − 1.27696I
8.25977 − 2.86772I 1.82451 + 0.48406I
u = −1.28396 + 0.82422I
a = 0.006867 − 0.472371I
b = −0.821146 + 0.390568I
1.57743 + 3.93356I −3.26663 − 8.37973I
u = −1.28396 − 0.82422I
a = 0.006867 + 0.472371I
b = −0.821146 − 0.390568I
1.57743 − 3.93356I −3.26663 + 8.37973I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
7
+ u
5
− u
4
+ 2u
3
+ 1)(u
43
− 3u
42
+ ··· − 1000u + 419)
c
2
(u
7
+ u
6
+ ··· − u − 1)(u
43
− 12u
41
+ ··· − 7u − 1)
c
3
, c
4
(u
7
+ 4u
5
+ 4u
3
+ u
2
+ 1)(u
43
+ u
42
+ ··· + 10u − 1)
c
5
(u
7
+ 2u
4
− u
3
+ u
2
+ 1)(u
43
+ u
42
+ ··· + 2u − 1)
c
6
(u
7
− u
6
+ ··· − u + 1)(u
43
− 12u
41
+ ··· − 7u − 1)
c
7
(u
7
− u
6
+ ··· − u + 1)(u
43
− 17u
41
+ ··· + 85u − 19)
c
8
(u
7
+ 4u
5
+ 4u
3
− u
2
− 1)(u
43
+ u
42
+ ··· + 10u − 1)
c
9
(u
7
− 2u
4
+ 2u
3
+ u
2
− 2u + 1)(u
43
− 7u
42
+ ··· + 18u − 1)
c
10
(u
7
+ u
6
+ ··· − u − 1)(u
43
− 17u
41
+ ··· + 85u − 19)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 2y
6
+ 5y
5
+ 3y
4
+ 4y
3
+ 2y
2
− 1)
· (y
43
− 17y
42
+ ··· + 2566222y − 175561)
c
2
, c
6
(y
7
− 5y
6
+ 16y
5
− 29y
4
+ 33y
3
− 21y
2
+ 7y − 1)
· (y
43
− 24y
42
+ ··· + 29y − 1)
c
3
, c
4
, c
8
(y
7
+ 8y
6
+ 24y
5
+ 32y
4
+ 16y
3
− y
2
− 2y − 1)
· (y
43
+ 45y
42
+ ··· + 28y − 1)
c
5
(y
7
− 2y
5
+ ··· − 2y − 1)(y
43
+ y
42
+ ··· + 8y − 1)
c
7
, c
10
(y
7
− 7y
6
+ 21y
5
− 33y
4
+ 29y
3
− 16y
2
+ 5y − 1)
· (y
43
− 34y
42
+ ··· + 4299y − 361)
c
9
(y
7
+ 4y
5
+ ··· + 2y − 1)(y
43
+ y
42
+ ··· + 68y − 1)
15
