10
94
(K10a
91
)
A knot diagram
1
Linearized knot diagam
5 6 8 1 9 3 10 2 7 4
Solving Sequence
4,10
1 5
2,8
3 7 6 9
c
10
c
4
c
1
c
3
c
7
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.74096 × 10
15
u
34
+ 8.22209 × 10
17
u
33
+ ··· + 6.62181 × 10
18
b + 7.90428 × 10
18
,
− 4.09728 × 10
18
u
34
− 3.86755 × 10
18
u
33
+ ··· + 6.62181 × 10
18
a − 2.70054 × 10
18
, u
35
+ 3u
34
+ ··· + 3u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 35 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−9.74 × 10
15
u
34
+ 8.22 × 10
17
u
33
+ · · · + 6.62 × 10
18
b + 7.90 ×
10
18
, −4.10 × 10
18
u
34
− 3.87 × 10
18
u
33
+ · · · + 6.62 × 10
18
a − 2.70 ×
10
18
, u
35
+ 3u
34
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
1
=
1
u
2
a
5
=
−u
−u
3
+ u
a
2
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
0.618755u
34
+ 0.584062u
33
+ ··· − 9.67919u + 0.407825
0.00147104u
34
− 0.124167u
33
+ ··· + 0.203436u − 1.19367
a
3
=
1.09583u
34
+ 3.07364u
33
+ ··· − 2.42964u − 5.58169
−1.19271u
34
− 2.87858u
33
+ ··· + 1.54761u + 0.464135
a
7
=
0.620226u
34
+ 0.459895u
33
+ ··· − 9.47575u − 0.785850
0.00147104u
34
− 0.124167u
33
+ ··· + 0.203436u − 1.19367
a
6
=
2.14790u
34
+ 6.59302u
33
+ ··· − 8.38643u − 4.87814
−0.134603u
34
− 0.623769u
33
+ ··· + 1.93231u − 0.272284
a
9
=
0.561562u
34
+ 0.370987u
33
+ ··· − 9.79383u + 0.358105
0.0974274u
34
+ 0.171295u
33
+ ··· + 0.0892870u − 1.18951
(ii) Obstruction class = −1
(iii) Cusp Shapes =
28372200930047336304
6621809224193386385
u
34
+
75749700395542932768
6621809224193386385
u
33
+ ··· −
95288194958111912596
6621809224193386385
u −
24995006422002411154
6621809224193386385
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
u
35
+ 3u
34
+ ··· + 3u
2
− 1
c
2
, c
6
u
35
− u
34
+ ··· − 3u
2
+ 1
c
3
u
35
+ 17u
34
+ ··· + 214u + 23
c
5
u
35
− 13u
34
+ ··· + 12u − 7
c
7
, c
9
u
35
− u
34
+ ··· − 2u + 1
c
8
u
35
− 3u
34
+ ··· + 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
y
35
− 37y
34
+ ··· + 6y −1
c
2
, c
6
y
35
− 21y
34
+ ··· + 6y −1
c
3
y
35
− 233y
34
+ ··· + 5914y −529
c
5
y
35
− 237y
34
+ ··· + 942y −49
c
7
, c
9
y
35
− 25y
34
+ ··· − 70y −1
c
8
y
35
+ 3y
34
+ ··· + 34y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638742 + 0.763228I
a = −0.32878 − 1.37864I
b = 1.265670 + 0.500696I
−0.17363 − 9.53352I −2.89594 + 8.02980I
u = 0.638742 − 0.763228I
a = −0.32878 + 1.37864I
b = 1.265670 − 0.500696I
−0.17363 + 9.53352I −2.89594 − 8.02980I
u = 0.421188 + 0.899484I
a = −0.792986 − 0.007441I
b = 1.102020 − 0.318172I
0.51201 + 4.13357I −2.56649 − 6.25203I
u = 0.421188 − 0.899484I
a = −0.792986 + 0.007441I
b = 1.102020 + 0.318172I
0.51201 − 4.13357I −2.56649 + 6.25203I
u = −0.708907 + 0.871150I
a = −0.370730 + 0.784435I
b = 1.164500 − 0.178894I
−3.73588 + 3.17966I −9.01884 − 7.80623I
u = −0.708907 − 0.871150I
a = −0.370730 − 0.784435I
b = 1.164500 + 0.178894I
−3.73588 − 3.17966I −9.01884 + 7.80623I
u = 0.555117 + 0.428217I
a = 1.29244 − 0.80829I
b = 0.267299 + 0.532419I
2.98343 + 0.70642I 1.79862 + 1.96555I
u = 0.555117 − 0.428217I
a = 1.29244 + 0.80829I
b = 0.267299 − 0.532419I
2.98343 − 0.70642I 1.79862 − 1.96555I
u = 0.420666 + 0.556962I
a = −0.213994 + 1.367610I
b = 0.122551 − 0.993553I
3.42076 − 4.23935I 1.57284 + 6.50170I
u = 0.420666 − 0.556962I
a = −0.213994 − 1.367610I
b = 0.122551 + 0.993553I
3.42076 + 4.23935I 1.57284 − 6.50170I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.369300 + 0.067601I
a = 0.631419 − 0.279359I
b = 0.030418 + 0.167299I
−3.14805 + 0.11237I −2.00000 + 0.I
u = −1.369300 − 0.067601I
a = 0.631419 + 0.279359I
b = 0.030418 − 0.167299I
−3.14805 − 0.11237I −2.00000 + 0.I
u = 1.42805
a = −11.1085
b = −1.01279
−4.96247 155.290
u = −0.505143 + 0.260157I
a = 0.63134 − 1.66041I
b = −1.106350 + 0.599174I
−1.17815 + 2.75086I −5.83679 − 7.59594I
u = −0.505143 − 0.260157I
a = 0.63134 + 1.66041I
b = −1.106350 − 0.599174I
−1.17815 − 2.75086I −5.83679 + 7.59594I
u = 1.46072 + 0.11973I
a = −0.027998 + 0.767434I
b = −0.361779 − 0.871354I
−5.91469 − 2.99202I 0
u = 1.46072 − 0.11973I
a = −0.027998 − 0.767434I
b = −0.361779 + 0.871354I
−5.91469 + 2.99202I 0
u = −0.291602 + 0.421032I
a = 0.608613 − 0.956903I
b = −0.142845 + 0.366228I
−0.134869 + 1.085580I −2.08723 − 6.10429I
u = −0.291602 − 0.421032I
a = 0.608613 + 0.956903I
b = −0.142845 − 0.366228I
−0.134869 − 1.085580I −2.08723 + 6.10429I
u = −1.48666 + 0.16089I
a = −0.270075 − 0.598911I
b = −0.023905 + 1.336550I
−2.83088 + 6.77803I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48666 − 0.16089I
a = −0.270075 + 0.598911I
b = −0.023905 − 1.336550I
−2.83088 − 6.77803I 0
u = −1.50842 + 0.01996I
a = −0.634805 − 0.360863I
b = −1.60295 + 0.26970I
−8.87322 + 0.26521I 0
u = −1.50842 − 0.01996I
a = −0.634805 + 0.360863I
b = −1.60295 − 0.26970I
−8.87322 − 0.26521I 0
u = 1.51371 + 0.06175I
a = −0.323814 + 0.778359I
b = −1.42288 − 0.85959I
−7.88737 − 3.84000I 0
u = 1.51371 − 0.06175I
a = −0.323814 − 0.778359I
b = −1.42288 + 0.85959I
−7.88737 + 3.84000I 0
u = 0.458527 + 0.023050I
a = −0.364039 + 0.257321I
b = −1.252630 − 0.041449I
−2.28660 − 0.00327I −6.71199 − 0.85350I
u = 0.458527 − 0.023050I
a = −0.364039 − 0.257321I
b = −1.252630 + 0.041449I
−2.28660 + 0.00327I −6.71199 + 0.85350I
u = −1.57609 + 0.25528I
a = 0.520584 + 1.107560I
b = 1.42500 − 0.57684I
−7.4557 + 13.3116I 0
u = −1.57609 − 0.25528I
a = 0.520584 − 1.107560I
b = 1.42500 + 0.57684I
−7.4557 − 13.3116I 0
u = 1.59602 + 0.26769I
a = 0.394220 − 0.908500I
b = 1.38166 + 0.35942I
−11.27950 − 7.30532I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59602 − 0.26769I
a = 0.394220 + 0.908500I
b = 1.38166 − 0.35942I
−11.27950 + 7.30532I 0
u = −0.151482 + 0.347444I
a = 5.01455 − 1.87194I
b = −0.984898 − 0.180613I
−0.118043 − 0.668153I 2.12828 − 10.66433I
u = −0.151482 − 0.347444I
a = 5.01455 + 1.87194I
b = −0.984898 + 0.180613I
−0.118043 + 0.668153I 2.12828 + 10.66433I
u = −1.68110 + 0.33608I
a = 0.288307 + 0.479751I
b = 1.145510 − 0.065819I
−6.16860 + 1.10468I 0
u = −1.68110 − 0.33608I
a = 0.288307 − 0.479751I
b = 1.145510 + 0.065819I
−6.16860 − 1.10468I 0
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
u
35
+ 3u
34
+ ··· + 3u
2
− 1
c
2
, c
6
u
35
− u
34
+ ··· − 3u
2
+ 1
c
3
u
35
+ 17u
34
+ ··· + 214u + 23
c
5
u
35
− 13u
34
+ ··· + 12u − 7
c
7
, c
9
u
35
− u
34
+ ··· − 2u + 1
c
8
u
35
− 3u
34
+ ··· + 4u − 1
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
y
35
− 37y
34
+ ··· + 6y −1
c
2
, c
6
y
35
− 21y
34
+ ··· + 6y −1
c
3
y
35
− 233y
34
+ ··· + 5914y −529
c
5
y
35
− 237y
34
+ ··· + 942y −49
c
7
, c
9
y
35
− 25y
34
+ ··· − 70y −1
c
8
y
35
+ 3y
34
+ ··· + 34y −1
10
