10
115
(K10a
94
)
A knot diagram
1
Linearized knot diagam
7 5 1 10 2 9 3 4 6 8
Solving Sequence
2,6
5
3,10
4 9 7 1 8
c
5
c
2
c
4
c
9
c
6
c
1
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.34331 × 10
115
u
65
+ 6.48169 × 10
115
u
64
+ ··· + 2.86473 × 10
116
b + 1.11198 × 10
117
,
− 1.40951 × 10
118
u
65
− 8.70781 × 10
118
u
64
+ ··· + 1.42377 × 10
119
a − 1.81835 × 10
120
,
u
66
+ 3u
65
+ ··· − 77u + 21i
I
u
2
= h−u
11
− 5u
10
− 15u
9
− 32u
8
− 51u
7
− 64u
6
− 63u
5
− 49u
4
− 32u
3
− 17u
2
+ b − 8u − 2,
u
11
+ 3u
10
+ 7u
9
+ 12u
8
+ 15u
7
+ 18u
6
+ 17u
5
+ 16u
4
+ 14u
3
+ 5u
2
+ a + 3u − 1,
u
12
+ 4u
11
+ 11u
10
+ 22u
9
+ 33u
8
+ 41u
7
+ 40u
6
+ 33u
5
+ 24u
4
+ 13u
3
+ 8u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 78 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
= h1.34 × 10
115
u
65
+ 6.48 × 10
115
u
64
+ · · · + 2.86 × 10
116
b + 1.11 ×
10
117
, −1.41 × 10
118
u
65
− 8.71 × 10
118
u
64
+ · · · + 1.42 × 10
119
a − 1.82 ×
10
120
, u
66
+ 3u
65
+ · · · − 77u + 21i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
0.0989985u
65
+ 0.611601u
64
+ ··· − 38.4442u + 12.7714
−0.0468913u
65
− 0.226258u
64
+ ··· + 9.77991u − 3.88162
a
4
=
−0.0379845u
65
+ 0.367680u
64
+ ··· − 94.1129u + 27.5594
0.0238215u
65
− 0.0620212u
64
+ ··· + 22.0119u − 6.47645
a
9
=
0.145890u
65
+ 0.837859u
64
+ ··· − 48.2241u + 16.6530
−0.0468913u
65
− 0.226258u
64
+ ··· + 9.77991u − 3.88162
a
7
=
0.183485u
65
+ 0.376814u
64
+ ··· + 44.2181u − 10.0787
−0.0938407u
65
− 0.227660u
64
+ ··· − 10.9063u + 3.96108
a
1
=
0.431722u
65
+ 1.24657u
64
+ ··· + 41.2616u − 2.40760
0.0228165u
65
+ 0.142911u
64
+ ··· + 2.85831u − 3.07897
a
8
=
0.137406u
65
+ 0.154946u
64
+ ··· + 52.6432u − 12.3398
−0.106962u
65
− 0.276610u
64
+ ··· − 13.8597u + 4.46596
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.703263u
65
+ 1.38008u
64
+ ··· + 130.121u − 35.8005
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ u
65
+ ··· − 1128u + 193
c
2
, c
5
u
66
+ 3u
65
+ ··· − 77u + 21
c
3
u
66
− 5u
65
+ ··· − 7u + 3
c
4
u
66
− u
65
+ ··· + 1128u + 193
c
6
, c
9
u
66
− 3u
65
+ ··· + 77u + 21
c
7
u
66
− u
65
+ ··· − 31u + 3
c
8
u
66
+ u
65
+ ··· + 31u + 3
c
10
u
66
+ 5u
65
+ ··· + 7u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
66
+ 5y
65
+ ··· + 1235072y + 37249
c
2
, c
5
, c
6
c
9
y
66
+ 35y
65
+ ··· + 7259y + 441
c
3
, c
10
y
66
+ y
65
+ ··· + 149y + 9
c
7
, c
8
y
66
+ 3y
65
+ ··· − 31y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662737 + 0.747286I
a = 1.84867 − 0.18714I
b = 0.643705 + 0.913849I
−2.10904 + 4.58826I −5.96198 − 6.80019I
u = −0.662737 − 0.747286I
a = 1.84867 + 0.18714I
b = 0.643705 − 0.913849I
−2.10904 − 4.58826I −5.96198 + 6.80019I
u = −0.759989 + 0.676773I
a = 0.352294 − 0.243482I
b = 0.355245 − 1.033540I
−2.30167 + 0.78056I −4.09013 − 4.30344I
u = −0.759989 − 0.676773I
a = 0.352294 + 0.243482I
b = 0.355245 + 1.033540I
−2.30167 − 0.78056I −4.09013 + 4.30344I
u = 0.287386 + 0.983998I
a = −1.48006 − 0.92224I
b = −1.303580 − 0.315783I
4.24208 − 0.93364I 15.9161 + 3.0658I
u = 0.287386 − 0.983998I
a = −1.48006 + 0.92224I
b = −1.303580 + 0.315783I
4.24208 + 0.93364I 15.9161 − 3.0658I
u = 0.458890 + 0.841270I
a = 1.79291 − 0.60912I
b = 0.396945 − 1.221130I
−3.75920 + 1.29912I −3.74536 + 0.15014I
u = 0.458890 − 0.841270I
a = 1.79291 + 0.60912I
b = 0.396945 + 1.221130I
−3.75920 − 1.29912I −3.74536 − 0.15014I
u = −0.149058 + 1.034510I
a = −1.68613 + 0.22740I
b = −1.334980 + 0.373687I
4.29717 + 0.35366I 9.83486 + 1.20455I
u = −0.149058 − 1.034510I
a = −1.68613 − 0.22740I
b = −1.334980 − 0.373687I
4.29717 − 0.35366I 9.83486 − 1.20455I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355245 + 1.033540I
a = −0.362934 − 0.639915I
b = −0.759989 − 0.676773I
2.30167 + 0.78056I 0
u = 0.355245 − 1.033540I
a = −0.362934 + 0.639915I
b = −0.759989 + 0.676773I
2.30167 − 0.78056I 0
u = 0.643705 + 0.913849I
a = −1.20470 − 0.82212I
b = −0.662737 + 0.747286I
2.10904 − 4.58826I 0
u = 0.643705 − 0.913849I
a = −1.20470 + 0.82212I
b = −0.662737 − 0.747286I
2.10904 + 4.58826I 0
u = 0.360202 + 1.059140I
a = −2.20455 + 0.76831I
b = −0.342978 + 1.152930I
−2.39843 − 6.38163I 0
u = 0.360202 − 1.059140I
a = −2.20455 − 0.76831I
b = −0.342978 − 1.152930I
−2.39843 + 6.38163I 0
u = 0.359059 + 0.750855I
a = −0.298810 + 0.451021I
b = 0.08218 + 1.58909I
−4.14504 − 4.87522I −2.26179 + 9.07875I
u = 0.359059 − 0.750855I
a = −0.298810 − 0.451021I
b = 0.08218 − 1.58909I
−4.14504 + 4.87522I −2.26179 − 9.07875I
u = −0.783137 + 0.250577I
a = 0.259092 + 0.291154I
b = −0.271930 − 1.178510I
−3.01082 + 3.10826I −5.64725 − 5.61918I
u = −0.783137 − 0.250577I
a = 0.259092 − 0.291154I
b = −0.271930 + 1.178510I
−3.01082 − 3.10826I −5.64725 + 5.61918I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.009834 + 0.802079I
a = −2.12400 − 0.10197I
b = −0.596579 + 1.045740I
0.88395 − 2.01054I 3.45858 + 2.97810I
u = −0.009834 − 0.802079I
a = −2.12400 + 0.10197I
b = −0.596579 − 1.045740I
0.88395 + 2.01054I 3.45858 − 2.97810I
u = −0.342978 + 1.152930I
a = 1.61910 − 0.70992I
b = 0.360202 + 1.059140I
2.39843 + 6.38163I 0
u = −0.342978 − 1.152930I
a = 1.61910 + 0.70992I
b = 0.360202 − 1.059140I
2.39843 − 6.38163I 0
u = −0.596579 + 1.045740I
a = 1.260790 + 0.175394I
b = −0.009834 + 0.802079I
−0.88395 + 2.01054I 0
u = −0.596579 − 1.045740I
a = 1.260790 − 0.175394I
b = −0.009834 − 0.802079I
−0.88395 − 2.01054I 0
u = −0.271930 + 1.178510I
a = −0.965808 − 0.442503I
b = −0.783137 − 0.250577I
3.01082 + 3.10826I 0
u = −0.271930 − 1.178510I
a = −0.965808 + 0.442503I
b = −0.783137 + 0.250577I
3.01082 − 3.10826I 0
u = 0.687231 + 0.358682I
a = 0.443779 + 0.395345I
b = −0.430277 − 1.187340I
−1.38542 + 3.12807I 0.18739 − 5.83461I
u = 0.687231 − 0.358682I
a = 0.443779 − 0.395345I
b = −0.430277 + 1.187340I
−1.38542 − 3.12807I 0.18739 + 5.83461I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542734 + 1.105870I
a = −1.71563 − 0.08154I
b = −0.68953 + 1.34019I
0.80844 − 7.87674I 0
u = 0.542734 − 1.105870I
a = −1.71563 + 0.08154I
b = −0.68953 − 1.34019I
0.80844 + 7.87674I 0
u = 1.195210 + 0.323364I
a = 0.164442 − 0.141775I
b = 0.499077 + 1.182910I
−3.08497 + 10.03660I 0
u = 1.195210 − 0.323364I
a = 0.164442 + 0.141775I
b = 0.499077 − 1.182910I
−3.08497 − 10.03660I 0
u = 0.734419 + 0.105022I
a = 0.549959 + 1.225450I
b = 0.734419 − 0.105022I
5.41602I 0. − 4.57520I
u = 0.734419 − 0.105022I
a = 0.549959 − 1.225450I
b = 0.734419 + 0.105022I
− 5.41602I 0. + 4.57520I
u = −0.430277 + 1.187340I
a = 1.052010 − 0.353445I
b = 0.687231 − 0.358682I
1.38542 + 3.12807I 0
u = −0.430277 − 1.187340I
a = 1.052010 + 0.353445I
b = 0.687231 + 0.358682I
1.38542 − 3.12807I 0
u = 0.499077 + 1.182910I
a = 1.205270 + 0.532515I
b = 1.195210 + 0.323364I
3.08497 − 10.03660I 0
u = 0.499077 − 1.182910I
a = 1.205270 − 0.532515I
b = 1.195210 − 0.323364I
3.08497 + 10.03660I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396945 + 1.221130I
a = 1.047550 + 0.443482I
b = 0.458890 − 0.841270I
3.75920 + 1.29912I 0
u = 0.396945 − 1.221130I
a = 1.047550 − 0.443482I
b = 0.458890 + 0.841270I
3.75920 − 1.29912I 0
u = −0.610321 + 0.270672I
a = 0.749139 − 0.428729I
b = 0.290517 − 0.266226I
−1.36445 + 0.78938I −4.43693 − 1.27648I
u = −0.610321 − 0.270672I
a = 0.749139 + 0.428729I
b = 0.290517 + 0.266226I
−1.36445 − 0.78938I −4.43693 + 1.27648I
u = −0.448635 + 1.259820I
a = −1.39053 − 0.45102I
b = −0.71942 − 1.28265I
1.26966 + 7.40298I 0
u = −0.448635 − 1.259820I
a = −1.39053 + 0.45102I
b = −0.71942 + 1.28265I
1.26966 − 7.40298I 0
u = −1.303580 + 0.315783I
a = 0.334582 + 0.347965I
b = 0.287386 − 0.983998I
−4.24208 − 0.93364I 0
u = −1.303580 − 0.315783I
a = 0.334582 − 0.347965I
b = 0.287386 + 0.983998I
−4.24208 + 0.93364I 0
u = −0.043435 + 0.637728I
a = −4.04261 − 0.04501I
b = −0.043435 − 0.637728I
− 4.25960I − 60.10 − 0.329447I
u = −0.043435 − 0.637728I
a = −4.04261 + 0.04501I
b = −0.043435 + 0.637728I
4.25960I − 60.10 + 0.329447I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.334980 + 0.373687I
a = 0.207880 − 0.197593I
b = −0.149058 + 1.034510I
−4.29717 − 0.35366I 0
u = −1.334980 − 0.373687I
a = 0.207880 + 0.197593I
b = −0.149058 − 1.034510I
−4.29717 + 0.35366I 0
u = 0.280686 + 0.541514I
a = 0.076389 + 1.010860I
b = −0.198274 − 1.381690I
−4.11853 + 3.35398I −7.32610 + 2.92910I
u = 0.280686 − 0.541514I
a = 0.076389 − 1.010860I
b = −0.198274 + 1.381690I
−4.11853 − 3.35398I −7.32610 − 2.92910I
u = −0.198274 + 1.381690I
a = 0.457708 − 0.947576I
b = 0.280686 − 0.541514I
4.11853 + 3.35398I 0
u = −0.198274 − 1.381690I
a = 0.457708 + 0.947576I
b = 0.280686 + 0.541514I
4.11853 − 3.35398I 0
u = 0.68120 + 1.28817I
a = 1.52199 − 0.01935I
b = 0.68120 − 1.28817I
− 16.6380I 0
u = 0.68120 − 1.28817I
a = 1.52199 + 0.01935I
b = 0.68120 + 1.28817I
16.6380I 0
u = −0.71942 + 1.28265I
a = −0.971050 − 0.037443I
b = −0.448635 − 1.259820I
−1.26966 + 7.40298I 0
u = −0.71942 − 1.28265I
a = −0.971050 + 0.037443I
b = −0.448635 + 1.259820I
−1.26966 − 7.40298I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.68953 + 1.34019I
a = 1.43294 + 0.02037I
b = 0.542734 + 1.105870I
−0.80844 + 7.87674I 0
u = −0.68953 − 1.34019I
a = 1.43294 − 0.02037I
b = 0.542734 − 1.105870I
−0.80844 − 7.87674I 0
u = 0.08218 + 1.58909I
a = 0.412708 + 0.473001I
b = 0.359059 + 0.750855I
4.14504 + 4.87522I 0
u = 0.08218 − 1.58909I
a = 0.412708 − 0.473001I
b = 0.359059 − 0.750855I
4.14504 − 4.87522I 0
u = 0.290517 + 0.266226I
a = 0.824282 + 0.013319I
b = −0.610321 − 0.270672I
1.36445 + 0.78938I 4.43693 − 1.27648I
u = 0.290517 − 0.266226I
a = 0.824282 − 0.013319I
b = −0.610321 + 0.270672I
1.36445 − 0.78938I 4.43693 + 1.27648I
11
II.
I
u
2
= h−u
11
−5u
10
+· · ·+b−2, u
11
+3u
10
+· · ·+a−1, u
12
+4u
11
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
−u
11
− 3u
10
+ ··· − 3u + 1
u
11
+ 5u
10
+ ··· + 8u + 2
a
4
=
u
11
+ 5u
10
+ ··· + 14u + 5
−u
10
− 4u
9
+ ··· − 6u − 4
a
9
=
−2u
11
− 8u
10
+ ··· − 11u − 1
u
11
+ 5u
10
+ ··· + 8u + 2
a
7
=
−2u
11
− 10u
10
+ ··· − 14u − 5
−2u
11
− 6u
10
+ ··· + 2u + 4
a
1
=
−u
10
− 4u
9
+ ··· − 11u − 6
−u
11
− 3u
10
+ ··· + 2u + 4
a
8
=
−3u
11
− 13u
10
+ ··· − 15u − 4
−u
11
− 2u
10
+ ··· + 4u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 6u
11
+26u
10
+70u
9
+137u
8
+198u
7
+228u
6
+208u
5
+155u
4
+112u
3
+67u
2
+34u +12
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 2u
10
+ u
8
− 6u
7
+ 12u
5
+ 4u
4
− 8u
3
+ u
2
+ 3u + 3
c
2
, c
9
u
12
− 4u
11
+ ··· − 2u + 1
c
3
u
12
+ 2u
11
− u
9
+ 6u
8
+ 12u
7
+ 2u
6
− 11u
5
− 5u
4
+ u
3
+ u
2
+ 1
c
4
u
12
− 2u
10
+ u
8
+ 6u
7
− 12u
5
+ 4u
4
+ 8u
3
+ u
2
− 3u + 3
c
5
, c
6
u
12
+ 4u
11
+ ··· + 2u + 1
c
7
u
12
+ 3u
10
+ u
9
+ 3u
8
+ 4u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u
3
+ 3u
2
+ 1
c
8
u
12
+ 3u
10
− u
9
+ 3u
8
− 4u
7
+ 3u
6
− 4u
5
+ 3u
4
− u
3
+ 3u
2
+ 1
c
10
u
12
− 2u
11
+ u
9
+ 6u
8
− 12u
7
+ 2u
6
+ 11u
5
− 5u
4
− u
3
+ u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
12
− 4y
11
+ ··· − 3y + 9
c
2
, c
5
, c
6
c
9
y
12
+ 6y
11
+ ··· + 12y + 1
c
3
, c
10
y
12
− 4y
11
+ ··· + 2y + 1
c
7
, c
8
y
12
+ 6y
11
+ ··· + 6y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238381 + 0.958097I
a = −1.64769 + 0.58255I
b = −1.340910 + 0.230586I
3.76649 + 0.96528I −2.46025 − 6.19259I
u = −0.238381 − 0.958097I
a = −1.64769 − 0.58255I
b = −1.340910 − 0.230586I
3.76649 − 0.96528I −2.46025 + 6.19259I
u = 0.275611 + 0.671814I
a = 3.49684 + 1.04213I
b = 0.275611 − 0.671814I
− 4.91597I 0. + 11.11517I
u = 0.275611 − 0.671814I
a = 3.49684 − 1.04213I
b = 0.275611 + 0.671814I
4.91597I 0. − 11.11517I
u = −0.540477 + 1.222060I
a = −1.42814 − 0.09893I
b = −0.540477 − 1.222060I
6.92803I 0. − 5.92253I
u = −0.540477 − 1.222060I
a = −1.42814 + 0.09893I
b = −0.540477 + 1.222060I
− 6.92803I 0. + 5.92253I
u = −1.340910 + 0.230586I
a = −0.144225 − 0.306569I
b = −0.238381 + 0.958097I
−3.76649 − 0.96528I 2.46025 + 6.19259I
u = −1.340910 − 0.230586I
a = −0.144225 + 0.306569I
b = −0.238381 − 0.958097I
−3.76649 + 0.96528I 2.46025 − 6.19259I
u = −0.09726 + 1.42673I
a = −0.530300 + 0.558704I
b = −0.058582 + 0.533279I
3.74262 + 3.79217I −1.40025 − 6.58435I
u = −0.09726 − 1.42673I
a = −0.530300 − 0.558704I
b = −0.058582 − 0.533279I
3.74262 − 3.79217I −1.40025 + 6.58435I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.058582 + 0.533279I
a = 1.253520 − 0.119688I
b = −0.09726 + 1.42673I
−3.74262 − 3.79217I 1.40025 + 6.58435I
u = −0.058582 − 0.533279I
a = 1.253520 + 0.119688I
b = −0.09726 − 1.42673I
−3.74262 + 3.79217I 1.40025 − 6.58435I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
− 2u
10
+ u
8
− 6u
7
+ 12u
5
+ 4u
4
− 8u
3
+ u
2
+ 3u + 3)
· (u
66
+ u
65
+ ··· − 1128u + 193)
c
2
(u
12
− 4u
11
+ ··· − 2u + 1)(u
66
+ 3u
65
+ ··· − 77u + 21)
c
3
(u
12
+ 2u
11
− u
9
+ 6u
8
+ 12u
7
+ 2u
6
− 11u
5
− 5u
4
+ u
3
+ u
2
+ 1)
· (u
66
− 5u
65
+ ··· − 7u + 3)
c
4
(u
12
− 2u
10
+ u
8
+ 6u
7
− 12u
5
+ 4u
4
+ 8u
3
+ u
2
− 3u + 3)
· (u
66
− u
65
+ ··· + 1128u + 193)
c
5
(u
12
+ 4u
11
+ ··· + 2u + 1)(u
66
+ 3u
65
+ ··· − 77u + 21)
c
6
(u
12
+ 4u
11
+ ··· + 2u + 1)(u
66
− 3u
65
+ ··· + 77u + 21)
c
7
(u
12
+ 3u
10
+ u
9
+ 3u
8
+ 4u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u
3
+ 3u
2
+ 1)
· (u
66
− u
65
+ ··· − 31u + 3)
c
8
(u
12
+ 3u
10
− u
9
+ 3u
8
− 4u
7
+ 3u
6
− 4u
5
+ 3u
4
− u
3
+ 3u
2
+ 1)
· (u
66
+ u
65
+ ··· + 31u + 3)
c
9
(u
12
− 4u
11
+ ··· − 2u + 1)(u
66
− 3u
65
+ ··· + 77u + 21)
c
10
(u
12
− 2u
11
+ u
9
+ 6u
8
− 12u
7
+ 2u
6
+ 11u
5
− 5u
4
− u
3
+ u
2
+ 1)
· (u
66
+ 5u
65
+ ··· + 7u + 3)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
12
− 4y
11
+ ··· − 3y + 9)(y
66
+ 5y
65
+ ··· + 1235072y + 37249)
c
2
, c
5
, c
6
c
9
(y
12
+ 6y
11
+ ··· + 12y + 1)(y
66
+ 35y
65
+ ··· + 7259y + 441)
c
3
, c
10
(y
12
− 4y
11
+ ··· + 2y + 1)(y
66
+ y
65
+ ··· + 149y + 9)
c
7
, c
8
(y
12
+ 6y
11
+ ··· + 6y + 1)(y
66
+ 3y
65
+ ··· − 31y + 9)
18
