12n
0792
(K12n
0792
)
A knot diagram
1
Linearized knot diagam
4 5 11 9 3 12 1 5 1 4 6 7
Solving Sequence
6,11
12 7
1,4
3 5 2 10 9 8
c
11
c
6
c
12
c
3
c
5
c
2
c
10
c
9
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h3.07628 × 10
46
u
52
− 1.00351 × 10
47
u
51
+ ··· + 3.48741 × 10
47
b + 1.73101 × 10
48
,
− 1.34583 × 10
48
u
52
+ 5.85153 × 10
47
u
51
+ ··· + 6.62608 × 10
48
a − 2.02004 × 10
48
, u
53
+ u
52
+ ··· + 2u + 19i
I
u
2
= hu
10
− 7u
8
+ u
7
+ 17u
6
− 5u
5
− 16u
4
+ 7u
3
+ 4u
2
+ b − 2u,
− u
10
+ 7u
8
− u
7
− 17u
6
+ 5u
5
+ 16u
4
− 7u
3
− 5u
2
+ a + 2u + 2,
u
14
− 10u
12
+ u
11
+ 39u
10
− 8u
9
− 74u
8
+ 23u
7
+ 69u
6
− 28u
5
− 28u
4
+ 13u
3
+ 4u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 67 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
= h3.08×10
46
u
52
−1.00×10
47
u
51
+· · ·+3.49×10
47
b+1.73×10
48
, −1.35×
10
48
u
52
+5.85×10
47
u
51
+· · ·+6.63×10
48
a−2.02×10
48
, u
53
+u
52
+· · ·+2u+19i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
0.203111u
52
− 0.0883105u
51
+ ··· − 9.46298u + 0.304862
−0.0882110u
52
+ 0.287753u
51
+ ··· − 1.72583u − 4.96359
a
3
=
0.114900u
52
+ 0.199442u
51
+ ··· − 11.1888u − 4.65873
−0.0882110u
52
+ 0.287753u
51
+ ··· − 1.72583u − 4.96359
a
5
=
0.0908917u
52
+ 0.0768978u
51
+ ··· − 7.10988u − 3.08929
0.0260187u
52
+ 0.0838960u
51
+ ··· − 5.33771u − 3.10420
a
2
=
0.0279811u
52
+ 0.0401943u
51
+ ··· + 3.61598u + 4.82383
−0.0143374u
52
− 0.198875u
51
+ ··· + 4.54528u + 3.00459
a
10
=
−0.109349u
52
+ 0.187204u
51
+ ··· − 5.22764u − 4.01238
0.272728u
52
+ 0.00219298u
51
+ ··· − 4.61603u − 0.998578
a
9
=
0.0602843u
52
+ 0.218936u
51
+ ··· − 9.13144u − 3.51075
0.120808u
52
− 0.0288635u
51
+ ··· − 1.02731u − 0.112491
a
8
=
u
3
− 2u
−u
5
+ 3u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0556426u
52
+ 0.289899u
51
+ ··· + 16.8530u + 6.93721
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
− 8u
52
+ ··· − 25u + 1
c
2
, c
5
u
53
− 18u
51
+ ··· − u + 683
c
3
, c
10
u
53
− u
52
+ ··· + 996u − 745
c
4
, c
8
u
53
+ 2u
52
+ ··· − 13u − 1
c
6
, c
7
, c
11
c
12
u
53
− u
52
+ ··· + 2u − 19
c
9
u
53
+ 3u
52
+ ··· + 26u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
− 36y
52
+ ··· + 47y −1
c
2
, c
5
y
53
− 36y
52
+ ··· + 10124793y −466489
c
3
, c
10
y
53
+ 31y
52
+ ··· − 10501844y −555025
c
4
, c
8
y
53
+ 22y
52
+ ··· + 167y −1
c
6
, c
7
, c
11
c
12
y
53
− 65y
52
+ ··· + 5324y −361
c
9
y
53
− 33y
52
+ ··· + 392y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.976765 + 0.204315I
a = −0.695066 − 1.196400I
b = −0.341850 + 0.765716I
3.70234 + 2.85475I 7.56242 − 7.71874I
u = 0.976765 − 0.204315I
a = −0.695066 + 1.196400I
b = −0.341850 − 0.765716I
3.70234 − 2.85475I 7.56242 + 7.71874I
u = 0.830103 + 0.663239I
a = 0.622792 + 0.940843I
b = 0.68077 − 1.27126I
1.17909 + 10.63840I 4.37034 − 8.18411I
u = 0.830103 − 0.663239I
a = 0.622792 − 0.940843I
b = 0.68077 + 1.27126I
1.17909 − 10.63840I 4.37034 + 8.18411I
u = −0.672364 + 0.631114I
a = 0.755869 − 0.889133I
b = 0.567716 + 1.241920I
−0.25800 − 4.19233I 2.11175 + 4.57513I
u = −0.672364 − 0.631114I
a = 0.755869 + 0.889133I
b = 0.567716 − 1.241920I
−0.25800 + 4.19233I 2.11175 − 4.57513I
u = 0.161033 + 0.868640I
a = 0.204873 − 0.301193I
b = −0.433829 − 1.023470I
−0.84645 − 5.58131I 2.80981 + 5.18997I
u = 0.161033 − 0.868640I
a = 0.204873 + 0.301193I
b = −0.433829 + 1.023470I
−0.84645 + 5.58131I 2.80981 − 5.18997I
u = −0.583775 + 0.645996I
a = −0.843622 − 0.123449I
b = −0.267716 − 0.980072I
5.12894 − 2.24975I 9.33045 + 6.74363I
u = −0.583775 − 0.645996I
a = −0.843622 + 0.123449I
b = −0.267716 + 0.980072I
5.12894 + 2.24975I 9.33045 − 6.74363I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15898
a = 0.0546397
b = −0.526356
2.43214 4.06270
u = −0.339714 + 0.732403I
a = 0.493441 + 0.206248I
b = −0.444967 + 0.968163I
−1.276670 − 0.383611I 1.90948 + 0.44922I
u = −0.339714 − 0.732403I
a = 0.493441 − 0.206248I
b = −0.444967 − 0.968163I
−1.276670 + 0.383611I 1.90948 − 0.44922I
u = −1.24740
a = 0.350546
b = −0.846371
2.39687 0
u = −1.155310 + 0.491746I
a = −0.678424 + 0.467706I
b = −0.016892 − 0.866092I
3.21605 + 0.86609I 0
u = −1.155310 − 0.491746I
a = −0.678424 − 0.467706I
b = −0.016892 + 0.866092I
3.21605 − 0.86609I 0
u = 0.605946 + 0.390778I
a = 0.00427 − 2.23076I
b = −0.582765 + 0.683402I
−2.25202 + 4.47982I 2.34770 − 7.54811I
u = 0.605946 − 0.390778I
a = 0.00427 + 2.23076I
b = −0.582765 − 0.683402I
−2.25202 − 4.47982I 2.34770 + 7.54811I
u = −0.586170 + 0.296342I
a = 0.123031 + 0.435024I
b = 1.287910 − 0.486685I
−1.61768 − 3.77662I 4.85409 + 6.48122I
u = −0.586170 − 0.296342I
a = 0.123031 − 0.435024I
b = 1.287910 + 0.486685I
−1.61768 + 3.77662I 4.85409 − 6.48122I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554932 + 0.317475I
a = 1.47164 + 1.23287I
b = 0.06112 − 1.65085I
7.37545 + 1.13740I 0.82605 − 7.31172I
u = 0.554932 − 0.317475I
a = 1.47164 − 1.23287I
b = 0.06112 + 1.65085I
7.37545 − 1.13740I 0.82605 + 7.31172I
u = 0.575786 + 0.115234I
a = −2.26792 − 0.59441I
b = −0.322176 + 0.846567I
4.61254 + 0.39900I 8.15479 + 2.26046I
u = 0.575786 − 0.115234I
a = −2.26792 + 0.59441I
b = −0.322176 − 0.846567I
4.61254 − 0.39900I 8.15479 − 2.26046I
u = 1.41745 + 0.25332I
a = −0.761883 − 0.551649I
b = 0.350041 + 0.716405I
4.28909 + 3.91504I 0
u = 1.41745 − 0.25332I
a = −0.761883 + 0.551649I
b = 0.350041 − 0.716405I
4.28909 − 3.91504I 0
u = 0.339035 + 0.441644I
a = 0.355817 − 0.338282I
b = 1.014180 + 0.427589I
−3.02796 − 1.52327I −0.96904 − 2.19439I
u = 0.339035 − 0.441644I
a = 0.355817 + 0.338282I
b = 1.014180 − 0.427589I
−3.02796 + 1.52327I −0.96904 + 2.19439I
u = −1.44940
a = 0.732573
b = −1.34519
2.55697 0
u = −0.437530 + 0.311081I
a = 0.50768 + 2.81489I
b = −0.600329 − 0.687466I
−2.04690 + 1.54353I 2.73867 + 2.39570I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437530 − 0.311081I
a = 0.50768 − 2.81489I
b = −0.600329 + 0.687466I
−2.04690 − 1.54353I 2.73867 − 2.39570I
u = 1.53217 + 0.05661I
a = −0.47460 + 2.01391I
b = 0.137826 − 1.140700I
4.62893 − 0.36463I 0
u = 1.53217 − 0.05661I
a = −0.47460 − 2.01391I
b = 0.137826 + 1.140700I
4.62893 + 0.36463I 0
u = −1.58165 + 0.08978I
a = −0.45673 + 2.22859I
b = −0.21483 − 1.85848I
14.7556 − 2.6131I 0
u = −1.58165 − 0.08978I
a = −0.45673 − 2.22859I
b = −0.21483 + 1.85848I
14.7556 + 2.6131I 0
u = −1.58814 + 0.03812I
a = 0.298490 − 1.206380I
b = 0.771676 + 1.000330I
12.15160 − 0.98530I 0
u = −1.58814 − 0.03812I
a = 0.298490 + 1.206380I
b = 0.771676 − 1.000330I
12.15160 + 0.98530I 0
u = −0.186420 + 0.366698I
a = 0.872470 − 0.246646I
b = 0.207209 + 0.429467I
0.043197 − 0.918878I 0.91856 + 7.38780I
u = −0.186420 − 0.366698I
a = 0.872470 + 0.246646I
b = 0.207209 − 0.429467I
0.043197 + 0.918878I 0.91856 − 7.38780I
u = 1.59148 + 0.08142I
a = 1.024970 + 0.427099I
b = −1.73010 − 0.47903I
5.91981 + 5.13315I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59148 − 0.08142I
a = 1.024970 − 0.427099I
b = −1.73010 + 0.47903I
5.91981 − 5.13315I 0
u = −1.59036 + 0.10324I
a = −0.30768 − 2.00866I
b = 0.244184 + 1.036970I
5.27677 − 6.23867I 0
u = −1.59036 − 0.10324I
a = −0.30768 + 2.00866I
b = 0.244184 − 1.036970I
5.27677 + 6.23867I 0
u = 1.58933 + 0.17527I
a = 0.218478 + 1.130000I
b = 0.758755 − 1.104590I
12.49110 + 5.20174I 0
u = 1.58933 − 0.17527I
a = 0.218478 − 1.130000I
b = 0.758755 + 1.104590I
12.49110 − 5.20174I 0
u = 1.59648 + 0.19044I
a = −0.24628 − 1.91486I
b = −0.64701 + 1.53101I
7.34850 + 7.24137I 0
u = 1.59648 − 0.19044I
a = −0.24628 + 1.91486I
b = −0.64701 − 1.53101I
7.34850 − 7.24137I 0
u = −1.65850 + 0.20486I
a = −0.11064 + 1.82637I
b = −0.83022 − 1.52276I
9.5991 − 13.9965I 0
u = −1.65850 − 0.20486I
a = −0.11064 − 1.82637I
b = −0.83022 + 1.52276I
9.5991 + 13.9965I 0
u = −1.70641 + 0.05300I
a = 0.16970 − 1.44726I
b = 0.601076 + 0.977119I
13.21480 − 3.88400I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70641 − 0.05300I
a = 0.16970 + 1.44726I
b = 0.601076 − 0.977119I
13.21480 + 3.88400I 0
u = 1.74373 + 0.08356I
a = −0.007459 + 1.240060I
b = 0.609167 − 1.102060I
13.60250 + 1.24707I 0
u = 1.74373 − 0.08356I
a = −0.007459 − 1.240060I
b = 0.609167 + 1.102060I
13.60250 − 1.24707I 0
10
II.
I
u
2
= hu
10
−7u
8
+· · ·+b−2u, −u
10
+7u
8
+· · ·+a+2, u
14
−10u
12
+· · ·−2u+1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
u
10
− 7u
8
+ u
7
+ 17u
6
− 5u
5
− 16u
4
+ 7u
3
+ 5u
2
− 2u − 2
−u
10
+ 7u
8
− u
7
− 17u
6
+ 5u
5
+ 16u
4
− 7u
3
− 4u
2
+ 2u
a
3
=
u
2
− 2
−u
10
+ 7u
8
− u
7
− 17u
6
+ 5u
5
+ 16u
4
− 7u
3
− 4u
2
+ 2u
a
5
=
−u
5
+ 4u
3
− 4u
u
13
− 9u
11
+ ··· + 4u
2
+ u
a
2
=
−u
8
+ 6u
6
− 12u
4
+ 9u
2
− 2
u
4
− 3u
2
+ 1
a
10
=
u
12
− 9u
10
+ ··· + 6u + 1
u
6
− 4u
4
+ u
3
+ 4u
2
− 2u
a
9
=
u
12
− 9u
10
+ u
9
+ 31u
8
− 7u
7
− 50u
6
+ 17u
5
+ 36u
4
− 17u
3
− 8u
2
+ 6u
−u
8
+ 6u
6
− 11u
4
+ u
3
+ 6u
2
− 2u
a
8
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
12
+ 2u
11
+ 8u
10
−17u
9
−24u
8
+ 51u
7
+ 35u
6
−64u
5
−28u
4
+ 35u
3
+ 12u
2
−14u + 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 3u
13
+ ··· + u + 3
c
2
u
14
+ 3u
13
+ ··· + 3u + 1
c
3
u
14
+ 4u
12
− 2u
11
+ 4u
10
− 5u
9
− u
8
+ 2u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u + 1
c
4
u
14
+ u
13
+ ··· + u + 1
c
5
u
14
− 3u
13
+ ··· − 3u + 1
c
6
, c
7
u
14
− 10u
12
+ ··· + 2u + 1
c
8
u
14
− u
13
+ ··· − u + 1
c
9
u
14
+ 2u
13
− 2u
11
− 3u
10
− 2u
9
+ 2u
8
− u
6
+ 5u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ 1
c
10
u
14
+ 4u
12
+ 2u
11
+ 4u
10
+ 5u
9
− u
8
+ 2u
6
− 2u
5
− 3u
4
− 2u
3
+ 2u + 1
c
11
, c
12
u
14
− 10u
12
+ ··· − 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 3y
13
+ ··· + 29y + 9
c
2
, c
5
y
14
− 11y
13
+ ··· + 3y + 1
c
3
, c
10
y
14
+ 8y
13
+ ··· − 4y + 1
c
4
, c
8
y
14
+ 11y
13
+ ··· + 13y + 1
c
6
, c
7
, c
11
c
12
y
14
− 20y
13
+ ··· + 4y + 1
c
9
y
14
− 4y
13
+ ··· + 8y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.740673 + 0.377978I
a = −1.370460 − 0.189280I
b = −0.223815 + 0.749196I
4.48989 + 1.36379I 6.88457 − 3.36739I
u = 0.740673 − 0.377978I
a = −1.370460 + 0.189280I
b = −0.223815 − 0.749196I
4.48989 − 1.36379I 6.88457 + 3.36739I
u = 1.281420 + 0.169138I
a = 0.311837 + 0.481666I
b = −0.698412 − 0.048193I
1.64857 − 0.94774I 1.25930 + 3.51308I
u = 1.281420 − 0.169138I
a = 0.311837 − 0.481666I
b = −0.698412 + 0.048193I
1.64857 + 0.94774I 1.25930 − 3.51308I
u = −0.652748 + 0.218469I
a = −1.44503 + 1.25753I
b = −0.17662 − 1.54274I
7.87230 − 0.75737I 12.39129 − 1.00527I
u = −0.652748 − 0.218469I
a = −1.44503 − 1.25753I
b = −0.17662 + 1.54274I
7.87230 + 0.75737I 12.39129 + 1.00527I
u = −1.45319 + 0.14529I
a = 0.854026 − 0.775035I
b = −0.763381 + 0.352765I
3.23638 − 4.38255I 2.20346 + 3.96328I
u = −1.45319 − 0.14529I
a = 0.854026 + 0.775035I
b = −0.763381 − 0.352765I
3.23638 + 4.38255I 2.20346 − 3.96328I
u = 1.64929 + 0.07227I
a = 0.25018 + 1.82900I
b = 0.46476 − 1.59062I
16.0636 + 1.9139I 11.41509 − 0.37585I
u = 1.64929 − 0.07227I
a = 0.25018 − 1.82900I
b = 0.46476 + 1.59062I
16.0636 − 1.9139I 11.41509 + 0.37585I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.131123 + 0.302892I
a = −2.85944 − 0.08111I
b = 0.784890 + 0.160547I
−2.23411 + 2.69440I 1.91591 − 3.21763I
u = 0.131123 − 0.302892I
a = −2.85944 + 0.08111I
b = 0.784890 − 0.160547I
−2.23411 − 2.69440I 1.91591 + 3.21763I
u = −1.69657 + 0.08296I
a = 0.258886 − 1.138930I
b = 0.612578 + 0.857416I
13.33660 − 3.11372I 9.93038 − 0.27629I
u = −1.69657 − 0.08296I
a = 0.258886 + 1.138930I
b = 0.612578 − 0.857416I
13.33660 + 3.11372I 9.93038 + 0.27629I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− 3u
13
+ ··· + u + 3)(u
53
− 8u
52
+ ··· − 25u + 1)
c
2
(u
14
+ 3u
13
+ ··· + 3u + 1)(u
53
− 18u
51
+ ··· − u + 683)
c
3
(u
14
+ 4u
12
− 2u
11
+ 4u
10
− 5u
9
− u
8
+ 2u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u + 1)
· (u
53
− u
52
+ ··· + 996u − 745)
c
4
(u
14
+ u
13
+ ··· + u + 1)(u
53
+ 2u
52
+ ··· − 13u − 1)
c
5
(u
14
− 3u
13
+ ··· − 3u + 1)(u
53
− 18u
51
+ ··· − u + 683)
c
6
, c
7
(u
14
− 10u
12
+ ··· + 2u + 1)(u
53
− u
52
+ ··· + 2u − 19)
c
8
(u
14
− u
13
+ ··· − u + 1)(u
53
+ 2u
52
+ ··· − 13u − 1)
c
9
(u
14
+ 2u
13
− 2u
11
− 3u
10
− 2u
9
+ 2u
8
− u
6
+ 5u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
53
+ 3u
52
+ ··· + 26u − 1)
c
10
(u
14
+ 4u
12
+ 2u
11
+ 4u
10
+ 5u
9
− u
8
+ 2u
6
− 2u
5
− 3u
4
− 2u
3
+ 2u + 1)
· (u
53
− u
52
+ ··· + 996u − 745)
c
11
, c
12
(u
14
− 10u
12
+ ··· − 2u + 1)(u
53
− u
52
+ ··· + 2u − 19)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
14
− 3y
13
+ ··· + 29y + 9)(y
53
− 36y
52
+ ··· + 47y −1)
c
2
, c
5
(y
14
− 11y
13
+ ··· + 3y + 1)
· (y
53
− 36y
52
+ ··· + 10124793y −466489)
c
3
, c
10
(y
14
+ 8y
13
+ ··· − 4y + 1)(y
53
+ 31y
52
+ ··· − 1.05018 × 10
7
y −555025)
c
4
, c
8
(y
14
+ 11y
13
+ ··· + 13y + 1)(y
53
+ 22y
52
+ ··· + 167y −1)
c
6
, c
7
, c
11
c
12
(y
14
− 20y
13
+ ··· + 4y + 1)(y
53
− 65y
52
+ ··· + 5324y −361)
c
9
(y
14
− 4y
13
+ ··· + 8y + 1)(y
53
− 33y
52
+ ··· + 392y −1)
17
