10
83
(K10a
87
)
A knot diagram
1
Linearized knot diagam
4 5 1 8 9 10 3 2 7 6
Solving Sequence
2,5 3,8
9 6 4 1 7 10
c
2
c
8
c
5
c
4
c
1
c
7
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.71392 × 10
63
u
40
+ 3.65753 × 10
64
u
39
+ ··· + 1.68092 × 10
63
b − 3.02213 × 10
63
,
− 6.85501 × 10
63
u
40
− 4.73991 × 10
64
u
39
+ ··· + 1.68092 × 10
63
a + 1.55757 × 10
64
, u
41
+ 7u
40
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 41 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
= h5.71×10
63
u
40
+3.66×10
64
u
39
+· · ·+1.68×10
63
b−3.02×10
63
, −6.86×
10
63
u
40
−4.74×10
64
u
39
+· · ·+1.68×10
63
a+1.56×10
64
, u
41
+7u
40
+· · ·−u−1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
8
=
4.07812u
40
+ 28.1982u
39
+ ··· + 2.31009u − 9.26617
−3.39928u
40
− 21.7591u
39
+ ··· + 7.35017u + 1.79790
a
9
=
0.678844u
40
+ 6.43917u
39
+ ··· + 9.66026u − 7.46827
−3.39928u
40
− 21.7591u
39
+ ··· + 7.35017u + 1.79790
a
6
=
8.89305u
40
+ 59.3831u
39
+ ··· − 6.00010u − 11.8860
4.09598u
40
+ 28.5050u
39
+ ··· + 3.04934u − 8.50322
a
4
=
1.80830u
40
+ 11.7114u
39
+ ··· − 1.62251u − 0.316229
2.98878u
40
+ 19.1668u
39
+ ··· − 5.42693u − 3.06653
a
1
=
1.80830u
40
+ 11.7114u
39
+ ··· − 1.62251u − 0.316229
−3.20007u
40
− 20.2893u
39
+ ··· + 6.28848u + 2.11978
a
7
=
1.67473u
40
+ 12.2834u
39
+ ··· + 5.93075u − 7.11966
−3.47210u
40
− 22.4391u
39
+ ··· + 5.85564u + 2.70675
a
10
=
−4.33853u
40
− 24.2279u
39
+ ··· + 19.3082u − 5.37875
−7.53934u
40
− 48.4715u
39
+ ··· + 11.8342u + 6.09444
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.0825u
40
− 65.2708u
39
+ ··· + 2.08186u + 7.14206
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
41
+ u
40
+ ··· + 7u − 1
c
2
u
41
− 7u
40
+ ··· − u + 1
c
4
u
41
+ 3u
40
+ ··· + u + 1
c
5
u
41
− u
40
+ ··· + 131u − 17
c
6
, c
9
, c
10
u
41
+ u
40
+ ··· + 3u − 1
c
7
u
41
− u
40
+ ··· + 289u + 77
c
8
u
41
− 3u
40
+ ··· − 129u + 31
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
41
− 29y
40
+ ··· − 7y −1
c
2
y
41
+ 3y
40
+ ··· − 7y −1
c
4
y
41
+ 7y
40
+ ··· − 3y −1
c
5
y
41
− 17y
40
+ ··· − 2627y −289
c
6
, c
9
, c
10
y
41
+ 35y
40
+ ··· − 3y −1
c
7
y
41
− 25y
40
+ ··· − 76331y −5929
c
8
y
41
− 45y
40
+ ··· + 24081y −961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866167 + 0.522972I
a = 1.35646 − 0.66908I
b = −0.725791 − 1.020460I
−4.89451 + 5.37316I 0.36580 − 6.73028I
u = −0.866167 − 0.522972I
a = 1.35646 + 0.66908I
b = −0.725791 + 1.020460I
−4.89451 − 5.37316I 0.36580 + 6.73028I
u = 0.631814 + 0.671299I
a = 0.943824 − 0.130258I
b = −0.620989 + 0.419528I
−0.99413 − 1.43665I −0.46376 + 2.78521I
u = 0.631814 − 0.671299I
a = 0.943824 + 0.130258I
b = −0.620989 − 0.419528I
−0.99413 + 1.43665I −0.46376 − 2.78521I
u = 1.134280 + 0.411388I
a = −0.871113 − 0.261658I
b = 0.321519 − 0.685150I
−6.90594 − 0.82118I −3.22724 + 0.I
u = 1.134280 − 0.411388I
a = −0.871113 + 0.261658I
b = 0.321519 + 0.685150I
−6.90594 + 0.82118I −3.22724 + 0.I
u = 0.465693 + 0.633658I
a = 0.05902 − 2.25820I
b = 0.580789 − 0.173369I
−0.29899 − 5.96215I 6.24062 + 8.95093I
u = 0.465693 − 0.633658I
a = 0.05902 + 2.25820I
b = 0.580789 + 0.173369I
−0.29899 + 5.96215I 6.24062 − 8.95093I
u = −0.326222 + 0.713161I
a = −2.26295 − 0.54539I
b = 0.755468 + 0.459159I
2.95137 + 3.82132I 10.20968 − 8.07346I
u = −0.326222 − 0.713161I
a = −2.26295 + 0.54539I
b = 0.755468 − 0.459159I
2.95137 − 3.82132I 10.20968 + 8.07346I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.801624 + 1.033830I
a = −1.213990 − 0.028195I
b = 1.161390 + 0.790188I
3.54673 + 5.39109I 0
u = −0.801624 − 1.033830I
a = −1.213990 + 0.028195I
b = 1.161390 − 0.790188I
3.54673 − 5.39109I 0
u = 0.344862 + 1.265380I
a = 0.614486 − 0.252898I
b = −0.953366 + 0.482315I
−1.46534 − 1.30012I 0
u = 0.344862 − 1.265380I
a = 0.614486 + 0.252898I
b = −0.953366 − 0.482315I
−1.46534 + 1.30012I 0
u = 0.119178 + 0.652646I
a = 1.53296 + 2.51289I
b = −0.639883 − 0.088284I
4.91037 − 1.30258I 16.3776 + 4.3347I
u = 0.119178 − 0.652646I
a = 1.53296 − 2.51289I
b = −0.639883 + 0.088284I
4.91037 + 1.30258I 16.3776 − 4.3347I
u = 0.020565 + 0.656018I
a = 0.658242 − 0.704684I
b = −1.62626 − 0.29430I
−2.00733 − 2.04071I 3.80481 + 5.50278I
u = 0.020565 − 0.656018I
a = 0.658242 + 0.704684I
b = −1.62626 + 0.29430I
−2.00733 + 2.04071I 3.80481 − 5.50278I
u = −0.453284 + 0.429541I
a = 0.257607 − 1.211290I
b = −0.541078 − 1.041380I
−3.37217 + 3.66290I 0.41021 − 1.40051I
u = −0.453284 − 0.429541I
a = 0.257607 + 1.211290I
b = −0.541078 + 1.041380I
−3.37217 − 3.66290I 0.41021 + 1.40051I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439287 + 0.430084I
a = −0.369850 + 0.809872I
b = 0.826171 − 0.878602I
1.92386 − 0.70569I 4.73633 − 1.49377I
u = −0.439287 − 0.430084I
a = −0.369850 − 0.809872I
b = 0.826171 + 0.878602I
1.92386 + 0.70569I 4.73633 + 1.49377I
u = 0.458556 + 0.245803I
a = −0.926842 + 0.254373I
b = 3.14697 − 0.02721I
−1.01770 + 3.12959I −11.2117 + 9.6931I
u = 0.458556 − 0.245803I
a = −0.926842 − 0.254373I
b = 3.14697 + 0.02721I
−1.01770 − 3.12959I −11.2117 − 9.6931I
u = −0.98309 + 1.11338I
a = 1.042320 − 0.030462I
b = −1.28757 − 0.91513I
5.88754 + 9.99849I 0
u = −0.98309 − 1.11338I
a = 1.042320 + 0.030462I
b = −1.28757 + 0.91513I
5.88754 − 9.99849I 0
u = −0.164101 + 0.449464I
a = −0.688933 + 1.140020I
b = 0.744682 + 0.591989I
1.35739 + 0.57043I 7.08701 − 0.51436I
u = −0.164101 − 0.449464I
a = −0.688933 − 1.140020I
b = 0.744682 − 0.591989I
1.35739 − 0.57043I 7.08701 + 0.51436I
u = 0.95044 + 1.21876I
a = −0.641001 + 0.045558I
b = 0.825830 − 0.718272I
1.17907 − 4.49890I 0
u = 0.95044 − 1.21876I
a = −0.641001 − 0.045558I
b = 0.825830 + 0.718272I
1.17907 + 4.49890I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11398 + 1.11513I
a = −0.963889 + 0.084455I
b = 1.33509 + 1.02179I
0.7775 + 14.2581I 0
u = −1.11398 − 1.11513I
a = −0.963889 − 0.084455I
b = 1.33509 − 1.02179I
0.7775 − 14.2581I 0
u = 0.387269
a = 1.11745
b = −3.36262
3.05082 −23.9460
u = −1.25742 + 1.12500I
a = 0.221918 − 0.430829I
b = −0.738517 + 0.066545I
5.25717 − 1.92366I 0
u = −1.25742 − 1.12500I
a = 0.221918 + 0.430829I
b = −0.738517 − 0.066545I
5.25717 + 1.92366I 0
u = −1.50650 + 0.79307I
a = −0.147496 + 0.451688I
b = 0.517015 + 0.004012I
1.64294 + 1.58754I 0
u = −1.50650 − 0.79307I
a = −0.147496 − 0.451688I
b = 0.517015 − 0.004012I
1.64294 − 1.58754I 0
u = 1.20335 + 1.23704I
a = 0.605373 + 0.022172I
b = −0.801305 + 0.846956I
−3.65031 − 8.13712I 0
u = 1.20335 − 1.23704I
a = 0.605373 − 0.022172I
b = −0.801305 − 0.846956I
−3.65031 + 8.13712I 0
u = −1.11069 + 1.42621I
a = −0.264870 + 0.387539I
b = 0.901140 − 0.076911I
1.04931 − 5.53805I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11069 − 1.42621I
a = −0.264870 − 0.387539I
b = 0.901140 + 0.076911I
1.04931 + 5.53805I 0
9
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u
41
+ u
40
+ ··· + 7u − 1
c
2
u
41
− 7u
40
+ ··· − u + 1
c
4
u
41
+ 3u
40
+ ··· + u + 1
c
5
u
41
− u
40
+ ··· + 131u − 17
c
6
, c
9
, c
10
u
41
+ u
40
+ ··· + 3u − 1
c
7
u
41
− u
40
+ ··· + 289u + 77
c
8
u
41
− 3u
40
+ ··· − 129u + 31
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
41
− 29y
40
+ ··· − 7y −1
c
2
y
41
+ 3y
40
+ ··· − 7y −1
c
4
y
41
+ 7y
40
+ ··· − 3y −1
c
5
y
41
− 17y
40
+ ··· − 2627y −289
c
6
, c
9
, c
10
y
41
+ 35y
40
+ ··· − 3y −1
c
7
y
41
− 25y
40
+ ··· − 76331y −5929
c
8
y
41
− 45y
40
+ ··· + 24081y −961
11
