12n
0382
(K12n
0382
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 5 12 5 9 7 8
Solving Sequence
2,5
6
3,12
7 8 9 10 1 4 11
c
5
c
2
c
6
c
7
c
8
c
9
c
1
c
4
c
11
c
3
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−579753405694973u
23
− 472990592837092u
22
+ ··· + 1971269389223473b + 4407120302352329,
2.83690 × 10
15
u
23
+ 6.39000 × 10
15
u
22
+ ··· + 2.16840 × 10
16
a − 5.46780 × 10
16
, u
24
+ 2u
23
+ ··· − 7u − 11i
I
u
2
= h−u
14
+ u
13
+ 3u
12
− 4u
11
− 6u
10
+ 9u
9
+ 7u
8
− 13u
7
− 6u
6
+ 12u
5
+ 2u
4
− 7u
3
+ b + u,
− 2u
14
+ u
13
+ 5u
12
− 4u
11
− 10u
10
+ 8u
9
+ 10u
8
− 10u
7
− 8u
6
+ 7u
5
− 2u
3
+ u
2
+ a − u,
u
15
− u
14
− 3u
13
+ 4u
12
+ 6u
11
− 9u
10
− 7u
9
+ 13u
8
+ 6u
7
− 13u
6
− 2u
5
+ 8u
4
− 3u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 39 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−5.80 × 10
14
u
23
− 4.73 × 10
14
u
22
+ · · · + 1.97 × 10
15
b + 4.41 ×
10
15
, 2.84 × 10
15
u
23
+ 6.39 × 10
15
u
22
+ · · · + 2.17 × 10
16
a − 5.47 ×
10
16
, u
24
+ 2u
23
+ · · · − 7u − 11i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
−0.130829u
23
− 0.294688u
22
+ ··· − 1.59763u + 2.52159
0.294102u
23
+ 0.239942u
22
+ ··· + 0.00494916u − 2.23568
a
7
=
−0.534965u
23
− 0.416078u
22
+ ··· − 0.624684u + 5.43098
−0.310244u
23
− 0.272323u
22
+ ··· − 0.324549u + 2.64692
a
8
=
−0.224721u
23
− 0.143755u
22
+ ··· − 0.300135u + 2.78406
−0.310244u
23
− 0.272323u
22
+ ··· − 0.324549u + 2.64692
a
9
=
0.201549u
23
+ 0.249559u
22
+ ··· − 0.113316u − 1.36979
−0.111431u
23
− 0.128131u
22
+ ··· − 0.277454u + 1.05051
a
10
=
0.312979u
23
+ 0.377690u
22
+ ··· + 0.164138u − 2.42030
−0.111431u
23
− 0.128131u
22
+ ··· − 0.277454u + 1.05051
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
0.0617504u
23
− 0.0392309u
22
+ ··· − 2.06682u + 0.542106
0.194220u
23
+ 0.176940u
22
+ ··· + 0.957672u − 1.78638
a
11
=
−0.0302642u
23
+ 0.0123334u
22
+ ··· + 0.976733u − 1.03269
0.119247u
23
+ 0.191200u
22
+ ··· + 0.994406u − 1.82283
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2580377549362014
1971269389223473
u
23
+
3507150554528052
1971269389223473
u
22
+ ··· +
45898132692487883
1971269389223473
u −
44289338047701926
1971269389223473
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 16u
23
+ ··· + 819u + 121
c
2
, c
5
u
24
+ 2u
23
+ ··· − 7u − 11
c
3
u
24
+ 26u
22
+ ··· + 39u − 11
c
4
, c
9
u
24
+ u
23
+ ··· + 51u + 43
c
6
, c
11
u
24
− 2u
23
+ ··· − 472u − 163
c
7
u
24
− 3u
23
+ ··· + 9u + 1
c
8
, c
12
u
24
+ 4u
23
+ ··· − 138u − 23
c
10
u
24
− 7u
23
+ ··· − 667u + 1849
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 8y
23
+ ··· + 75809y + 14641
c
2
, c
5
y
24
− 16y
23
+ ··· − 819y + 121
c
3
y
24
+ 52y
23
+ ··· − 1015y + 121
c
4
, c
9
y
24
+ 7y
23
+ ··· + 667y + 1849
c
6
, c
11
y
24
+ 36y
23
+ ··· − 234846y + 26569
c
7
y
24
− 47y
23
+ ··· + 113y + 1
c
8
, c
12
y
24
+ 34y
23
+ ··· − 65412y + 529
c
10
y
24
+ 35y
23
+ ··· − 209766481y + 3418801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.840681 + 0.490024I
a = −0.724162 + 0.569771I
b = −0.34121 + 1.49688I
−2.96579 + 0.05300I −5.61914 − 0.01464I
u = −0.840681 − 0.490024I
a = −0.724162 − 0.569771I
b = −0.34121 − 1.49688I
−2.96579 − 0.05300I −5.61914 + 0.01464I
u = −1.022560 + 0.295401I
a = −1.05742 + 2.52587I
b = 0.33303 + 1.71764I
−3.54040 + 2.95826I −5.57765 − 4.27465I
u = −1.022560 − 0.295401I
a = −1.05742 − 2.52587I
b = 0.33303 − 1.71764I
−3.54040 − 2.95826I −5.57765 + 4.27465I
u = 0.962010 + 0.650431I
a = −0.070965 − 1.233660I
b = −0.070549 − 0.869894I
7.79911 − 2.52001I −0.51262 + 2.53374I
u = 0.962010 − 0.650431I
a = −0.070965 + 1.233660I
b = −0.070549 + 0.869894I
7.79911 + 2.52001I −0.51262 − 2.53374I
u = −0.927407 + 0.744557I
a = 0.713189 + 0.275798I
b = −0.014139 − 0.602418I
8.76252 + 2.82949I −3.38778 − 2.96422I
u = −0.927407 − 0.744557I
a = 0.713189 − 0.275798I
b = −0.014139 + 0.602418I
8.76252 − 2.82949I −3.38778 + 2.96422I
u = 1.133700 + 0.502318I
a = 0.53485 + 1.45879I
b = −1.02104 + 1.23446I
−2.58040 − 6.55097I −3.00232 + 8.95233I
u = 1.133700 − 0.502318I
a = 0.53485 − 1.45879I
b = −1.02104 − 1.23446I
−2.58040 + 6.55097I −3.00232 − 8.95233I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759420
a = −0.396801
b = −0.537831
−1.01372 −11.2860
u = −0.238482 + 1.223910I
a = 0.037299 − 0.531429I
b = 0.12489 − 1.74552I
−9.56824 − 4.63986I −2.53665 + 1.77990I
u = −0.238482 − 1.223910I
a = 0.037299 + 0.531429I
b = 0.12489 + 1.74552I
−9.56824 + 4.63986I −2.53665 − 1.77990I
u = 1.25828
a = −1.11711
b = 0.135805
−0.844274 −6.82360
u = 0.264664 + 0.670266I
a = −0.018243 − 0.736439I
b = 0.587531 + 0.857775I
−0.06550 + 2.02589I 0.03613 − 4.27604I
u = 0.264664 − 0.670266I
a = −0.018243 + 0.736439I
b = 0.587531 − 0.857775I
−0.06550 − 2.02589I 0.03613 + 4.27604I
u = −1.330090 + 0.222342I
a = −0.92490 + 1.09593I
b = 0.094519 + 1.136320I
−4.70867 + 0.81596I −5.59655 − 0.54882I
u = −1.330090 − 0.222342I
a = −0.92490 − 1.09593I
b = 0.094519 − 1.136320I
−4.70867 − 0.81596I −5.59655 + 0.54882I
u = 0.538622 + 0.352121I
a = 0.147046 + 1.001000I
b = 0.216583 − 0.106477I
0.98010 − 1.26540I 3.01329 + 5.29615I
u = 0.538622 − 0.352121I
a = 0.147046 − 1.001000I
b = 0.216583 + 0.106477I
0.98010 + 1.26540I 3.01329 − 5.29615I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.34887 + 0.69749I
a = 1.08996 − 1.58558I
b = −0.23003 − 1.81299I
−13.0253 + 11.4321I −3.86498 − 4.79478I
u = −1.34887 − 0.69749I
a = 1.08996 + 1.58558I
b = −0.23003 + 1.81299I
−13.0253 − 11.4321I −3.86498 + 4.79478I
u = 1.55966 + 0.42079I
a = −0.69697 − 1.79236I
b = 0.02142 − 1.78671I
−15.5246 − 1.3214I −5.39704 + 0.62510I
u = 1.55966 − 0.42079I
a = −0.69697 + 1.79236I
b = 0.02142 + 1.78671I
−15.5246 + 1.3214I −5.39704 − 0.62510I
7
II.
I
u
2
= h−u
14
+u
13
+· · ·+b+u, −2u
14
+u
13
+· · ·+a−u, u
15
−u
14
+· · ·−3u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
2u
14
− u
13
+ ··· − u
2
+ u
u
14
− u
13
+ ··· + 7u
3
− u
a
7
=
−u
14
− u
13
+ ··· − u + 3
−u
12
+ 3u
10
− u
9
− 6u
8
+ 2u
7
+ 7u
6
− 3u
5
− 6u
4
+ 2u
3
+ 2u
2
− u
a
8
=
−u
14
− u
13
+ ··· − 9u
2
+ 3
−u
12
+ 3u
10
− u
9
− 6u
8
+ 2u
7
+ 7u
6
− 3u
5
− 6u
4
+ 2u
3
+ 2u
2
− u
a
9
=
−u
14
− 2u
13
+ ··· + 2u + 2
−u
13
+ 3u
11
− u
10
− 7u
9
+ 2u
8
+ 9u
7
− 4u
6
− 9u
5
+ 3u
4
+ 4u
3
− 2u
2
− u
a
10
=
−u
14
− u
13
+ ··· + 3u + 2
−u
13
+ 3u
11
− u
10
− 7u
9
+ 2u
8
+ 9u
7
− 4u
6
− 9u
5
+ 3u
4
+ 4u
3
− 2u
2
− u
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−u
14
+ 5u
12
+ ··· + 3u + 4
−u
14
+ 3u
12
− 7u
10
+ 10u
8
− 11u
6
+ 7u
4
− 3u
2
+ u + 2
a
11
=
4u
14
− 11u
12
+ ··· − u − 1
u
14
− 3u
12
+ ··· + 3u
3
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
12
− u
11
+ 3u
10
+ u
9
− 5u
8
− 4u
7
+ 7u
6
+ 4u
5
− 7u
4
− 3u
3
+ 5u
2
− 2u − 4
8
(iv) u-Polynomials at the component
9
Crossings u-Polynomials at each crossing
c
1
u
15
− 7u
14
+ ··· + 6u − 1
c
2
u
15
+ u
14
+ ··· + 3u
2
− 1
c
3
u
15
− u
14
+ ··· − 2u − 1
c
4
u
15
+ 8u
13
+ ··· + 4u + 1
c
5
u
15
− u
14
+ ··· − 3u
2
+ 1
c
6
u
15
− u
14
+ ··· + 3u + 1
c
7
u
15
+ 2u
14
+ ··· + 4u + 1
c
8
u
15
+ 3u
14
+ ··· − u + 1
c
9
u
15
+ 8u
13
+ ··· + 4u − 1
c
10
u
15
− 16u
14
+ ··· + 4u + 1
c
11
u
15
+ u
14
+ ··· + 3u − 1
c
12
u
15
− 3u
14
+ ··· − u − 1
10
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 9y
14
+ ··· − 14y −1
c
2
, c
5
y
15
− 7y
14
+ ··· + 6y −1
c
3
y
15
+ 29y
14
+ ··· − 14y −1
c
4
, c
9
y
15
+ 16y
14
+ ··· + 4y −1
c
6
, c
11
y
15
− 3y
14
+ ··· + y −1
c
7
y
15
− 2y
14
+ ··· + 18y −1
c
8
, c
12
y
15
− y
14
+ ··· + 3y −1
c
10
y
15
− 20y
14
+ ··· + 252y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899781 + 0.286994I
a = −0.44937 + 1.89015I
b = 0.304958 + 0.973459I
6.68911 − 1.23661I −4.15485 − 0.98307I
u = 0.899781 − 0.286994I
a = −0.44937 − 1.89015I
b = 0.304958 − 0.973459I
6.68911 + 1.23661I −4.15485 + 0.98307I
u = −0.893982
a = 0.674370
b = −0.525910
0.237359 1.17550
u = −0.896890 + 0.731944I
a = −0.254396 − 0.626802I
b = 0.153159 + 0.059677I
9.57728 + 2.79903I 7.57416 − 2.89020I
u = −0.896890 − 0.731944I
a = −0.254396 + 0.626802I
b = 0.153159 − 0.059677I
9.57728 − 2.79903I 7.57416 + 2.89020I
u = −1.107400 + 0.432221I
a = −1.13757 + 1.78331I
b = −0.01538 + 1.93584I
−4.12042 + 1.58492I −8.26166 − 0.30703I
u = −1.107400 − 0.432221I
a = −1.13757 − 1.78331I
b = −0.01538 − 1.93584I
−4.12042 − 1.58492I −8.26166 + 0.30703I
u = 0.550933 + 0.586599I
a = 0.901557 − 0.875340I
b = 0.45418 + 1.47368I
−1.53674 + 1.05029I −3.10144 − 0.84326I
u = 0.550933 − 0.586599I
a = 0.901557 + 0.875340I
b = 0.45418 − 1.47368I
−1.53674 − 1.05029I −3.10144 + 0.84326I
u = 1.096940 + 0.544029I
a = 1.21180 + 1.50559I
b = −0.72158 + 1.69669I
−3.32611 − 5.65603I −6.88663 + 4.31157I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.096940 − 0.544029I
a = 1.21180 − 1.50559I
b = −0.72158 − 1.69669I
−3.32611 + 5.65603I −6.88663 − 4.31157I
u = 0.914301 + 0.849307I
a = −0.569444 − 0.431437I
b = −0.039917 − 0.985105I
6.12893 − 3.15877I −4.60445 + 3.34743I
u = 0.914301 − 0.849307I
a = −0.569444 + 0.431437I
b = −0.039917 + 0.985105I
6.12893 + 3.15877I −4.60445 − 3.34743I
u = −0.510671 + 0.420907I
a = −1.53976 + 1.37826I
b = 0.12754 + 1.51005I
−2.01618 + 2.10877I −1.65286 − 2.85205I
u = −0.510671 − 0.420907I
a = −1.53976 − 1.37826I
b = 0.12754 − 1.51005I
−2.01618 − 2.10877I −1.65286 + 2.85205I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 7u
14
+ ··· + 6u − 1)(u
24
+ 16u
23
+ ··· + 819u + 121)
c
2
(u
15
+ u
14
+ ··· + 3u
2
− 1)(u
24
+ 2u
23
+ ··· − 7u − 11)
c
3
(u
15
− u
14
+ ··· − 2u − 1)(u
24
+ 26u
22
+ ··· + 39u − 11)
c
4
(u
15
+ 8u
13
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· + 51u + 43)
c
5
(u
15
− u
14
+ ··· − 3u
2
+ 1)(u
24
+ 2u
23
+ ··· − 7u − 11)
c
6
(u
15
− u
14
+ ··· + 3u + 1)(u
24
− 2u
23
+ ··· − 472u − 163)
c
7
(u
15
+ 2u
14
+ ··· + 4u + 1)(u
24
− 3u
23
+ ··· + 9u + 1)
c
8
(u
15
+ 3u
14
+ ··· − u + 1)(u
24
+ 4u
23
+ ··· − 138u − 23)
c
9
(u
15
+ 8u
13
+ ··· + 4u − 1)(u
24
+ u
23
+ ··· + 51u + 43)
c
10
(u
15
− 16u
14
+ ··· + 4u + 1)(u
24
− 7u
23
+ ··· − 667u + 1849)
c
11
(u
15
+ u
14
+ ··· + 3u − 1)(u
24
− 2u
23
+ ··· − 472u − 163)
c
12
(u
15
− 3u
14
+ ··· − u − 1)(u
24
+ 4u
23
+ ··· − 138u − 23)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 9y
14
+ ··· − 14y −1)(y
24
− 8y
23
+ ··· + 75809y + 14641)
c
2
, c
5
(y
15
− 7y
14
+ ··· + 6y −1)(y
24
− 16y
23
+ ··· − 819y + 121)
c
3
(y
15
+ 29y
14
+ ··· − 14y −1)(y
24
+ 52y
23
+ ··· − 1015y + 121)
c
4
, c
9
(y
15
+ 16y
14
+ ··· + 4y −1)(y
24
+ 7y
23
+ ··· + 667y + 1849)
c
6
, c
11
(y
15
− 3y
14
+ ··· + y −1)(y
24
+ 36y
23
+ ··· − 234846y + 26569)
c
7
(y
15
− 2y
14
+ ··· + 18y −1)(y
24
− 47y
23
+ ··· + 113y + 1)
c
8
, c
12
(y
15
− y
14
+ ··· + 3y −1)(y
24
+ 34y
23
+ ··· − 65412y + 529)
c
10
(y
15
− 20y
14
+ ··· + 252y −1)
· (y
24
+ 35y
23
+ ··· − 209766481y + 3418801)
16
