12n
0773
(K12n
0773
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 10 3 11 12 2 5 8 9
Solving Sequence
8,11
12 9
1,5
4 2 3 7 6 10
c
11
c
8
c
12
c
4
c
1
c
3
c
7
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.99252 × 10
54
u
58
− 4.27398 × 10
53
u
57
+ ··· + 1.08123 × 10
55
b − 5.85001 × 10
54
,
− 8.90269 × 10
54
u
58
+ 1.21104 × 10
55
u
57
+ ··· + 1.08123 × 10
55
a − 4.30153 × 10
56
, u
59
− u
58
+ ··· + 32u + 1i
I
u
2
= h2u
14
− u
13
− 16u
12
+ 8u
11
+ 49u
10
− 26u
9
− 67u
8
+ 42u
7
+ 27u
6
− 31u
5
+ 22u
4
+ 7u
3
− 18u
2
+ b + 2,
− 2u
14
+ 2u
13
+ ··· + a + 1,
u
15
− 9u
13
+ 32u
11
− u
10
− 55u
9
+ 6u
8
+ 41u
7
− 13u
6
+ 13u
4
− 13u
3
− 6u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 74 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−2.99×10
54
u
58
−4.27×10
53
u
57
+· · ·+1.08×10
55
b−5.85×10
54
, −8.90×
10
54
u
58
+1.21×10
55
u
57
+· · ·+1.08×10
55
a−4.30×10
56
, u
59
−u
58
+· · ·+32u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
9
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
0.823385u
58
− 1.12006u
57
+ ··· − 182.375u + 39.7837
0.276770u
58
+ 0.0395289u
57
+ ··· − 0.767568u + 0.541051
a
4
=
1.10016u
58
− 1.08053u
57
+ ··· − 183.142u + 40.3248
0.276770u
58
+ 0.0395289u
57
+ ··· − 0.767568u + 0.541051
a
2
=
−0.483130u
58
− 1.09918u
57
+ ··· − 102.939u + 26.7972
0.581937u
58
+ 0.395648u
57
+ ··· − 24.3369u − 0.367973
a
3
=
1.22082u
58
− 0.989380u
57
+ ··· − 182.255u + 40.3858
−0.00126625u
58
− 0.0204342u
57
+ ··· + 7.01822u + 0.813889
a
7
=
−u
u
a
6
=
1.84485u
58
− 1.31590u
57
+ ··· − 229.979u + 52.0102
−0.472356u
58
− 0.328224u
57
+ ··· + 6.26065u + 0.900727
a
10
=
−1.94402u
58
+ 0.476904u
57
+ ··· + 139.733u − 20.1503
0.316358u
58
− 0.0242382u
57
+ ··· + 0.806174u − 0.303933
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.27874u
58
+ 0.721176u
57
+ ··· − 64.5120u − 5.58630
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
− 9u
58
+ ··· − 108u + 61
c
2
, c
6
u
59
− 2u
58
+ ··· + 5154u − 773
c
3
u
59
− u
58
+ ··· + 23u − 43
c
4
, c
5
, c
10
u
59
− u
58
+ ··· + 102u + 1
c
7
, c
8
, c
11
c
12
u
59
− u
58
+ ··· + 32u + 1
c
9
u
59
+ 2u
58
+ ··· + 1624u − 1291
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
− 33y
58
+ ··· + 229434y −3721
c
2
, c
6
y
59
− 40y
58
+ ··· + 18677570y −597529
c
3
y
59
+ 31y
58
+ ··· − 87965y −1849
c
4
, c
5
, c
10
y
59
+ 59y
58
+ ··· + 10138y −1
c
7
, c
8
, c
11
c
12
y
59
− 53y
58
+ ··· + 1298y −1
c
9
y
59
− 32y
58
+ ··· + 37592492y −1666681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264830 + 0.931382I
a = −0.880909 + 0.866071I
b = −0.36110 − 1.47905I
3.66563 − 9.89323I 7.43337 + 6.27116I
u = −0.264830 − 0.931382I
a = −0.880909 − 0.866071I
b = −0.36110 + 1.47905I
3.66563 + 9.89323I 7.43337 − 6.27116I
u = 0.119168 + 0.889846I
a = −0.474592 − 0.195483I
b = −0.924980 + 0.347695I
−2.19237 + 5.25619I 4.23819 − 5.61197I
u = 0.119168 − 0.889846I
a = −0.474592 + 0.195483I
b = −0.924980 − 0.347695I
−2.19237 − 5.25619I 4.23819 + 5.61197I
u = −0.056257 + 0.894737I
a = 0.654957 − 0.276427I
b = 0.165353 + 1.327120I
0.33927 − 2.65716I 7.07647 + 3.01945I
u = −0.056257 − 0.894737I
a = 0.654957 + 0.276427I
b = 0.165353 − 1.327120I
0.33927 + 2.65716I 7.07647 − 3.01945I
u = 1.110480 + 0.149176I
a = −0.444606 + 1.134310I
b = −0.394307 − 0.923884I
1.42201 + 0.91602I 0
u = 1.110480 − 0.149176I
a = −0.444606 − 1.134310I
b = −0.394307 + 0.923884I
1.42201 − 0.91602I 0
u = 0.876618
a = −0.237869
b = 0.547477
1.47441 6.10400
u = −0.946025 + 0.638857I
a = −0.59515 + 1.28359I
b = 0.31286 − 1.38423I
5.77333 + 4.51012I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.946025 − 0.638857I
a = −0.59515 − 1.28359I
b = 0.31286 + 1.38423I
5.77333 − 4.51012I 0
u = −1.140520 + 0.188136I
a = 0.22857 − 1.65457I
b = 0.284860 + 0.755221I
3.89321 − 2.91811I 0
u = −1.140520 − 0.188136I
a = 0.22857 + 1.65457I
b = 0.284860 − 0.755221I
3.89321 + 2.91811I 0
u = −0.102126 + 0.801805I
a = 0.688121 − 0.400215I
b = 0.498536 − 0.055398I
−4.03916 + 0.26803I −0.184983 + 0.165110I
u = −0.102126 − 0.801805I
a = 0.688121 + 0.400215I
b = 0.498536 + 0.055398I
−4.03916 − 0.26803I −0.184983 − 0.165110I
u = 0.373831 + 0.712271I
a = 1.14505 + 1.41925I
b = 0.142122 − 1.261840I
−0.31798 + 2.01882I 8.09002 − 3.66839I
u = 0.373831 − 0.712271I
a = 1.14505 − 1.41925I
b = 0.142122 + 1.261840I
−0.31798 − 2.01882I 8.09002 + 3.66839I
u = 1.115350 + 0.452791I
a = −0.361726 + 0.339593I
b = 0.824800 + 0.143591I
0.891108 − 0.463329I 0
u = 1.115350 − 0.452791I
a = −0.361726 − 0.339593I
b = 0.824800 − 0.143591I
0.891108 + 0.463329I 0
u = −1.22285
a = 2.11329
b = −0.00993937
6.34821 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069536 + 0.754894I
a = −0.723962 − 0.583814I
b = −0.659233 + 0.942112I
−0.414783 + 0.267178I 7.48415 + 0.42381I
u = 0.069536 − 0.754894I
a = −0.723962 + 0.583814I
b = −0.659233 − 0.942112I
−0.414783 − 0.267178I 7.48415 − 0.42381I
u = 1.246900 + 0.128101I
a = 0.84306 + 3.72917I
b = 0.08010 − 1.59038I
11.78010 + 4.24713I 0
u = 1.246900 − 0.128101I
a = 0.84306 − 3.72917I
b = 0.08010 + 1.59038I
11.78010 − 4.24713I 0
u = −1.201700 + 0.358369I
a = −0.431364 + 0.406062I
b = −0.609338 − 0.225740I
−0.66555 − 4.45229I 0
u = −1.201700 − 0.358369I
a = −0.431364 − 0.406062I
b = −0.609338 + 0.225740I
−0.66555 + 4.45229I 0
u = 1.25489
a = −0.0869145
b = −1.08085
6.69122 0
u = 1.244200 + 0.194794I
a = 2.26800 + 1.51808I
b = −0.014499 − 1.386050I
11.09980 − 0.10055I 0
u = 1.244200 − 0.194794I
a = 2.26800 − 1.51808I
b = −0.014499 + 1.386050I
11.09980 + 0.10055I 0
u = 1.238570 + 0.325666I
a = −0.680385 − 0.614714I
b = 0.919436 + 0.808126I
3.20240 + 3.63807I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.238570 − 0.325666I
a = −0.680385 + 0.614714I
b = 0.919436 − 0.808126I
3.20240 − 3.63807I 0
u = −1.197820 + 0.461395I
a = 0.413885 − 1.277320I
b = −0.062854 + 1.223650I
3.87163 − 2.16113I 0
u = −1.197820 − 0.461395I
a = 0.413885 + 1.277320I
b = −0.062854 − 1.223650I
3.87163 + 2.16113I 0
u = −1.278360 + 0.133753I
a = −0.40499 + 2.53862I
b = 0.15595 − 1.70029I
12.17270 + 0.50014I 0
u = −1.278360 − 0.133753I
a = −0.40499 − 2.53862I
b = 0.15595 + 1.70029I
12.17270 − 0.50014I 0
u = −1.280870 + 0.190846I
a = −0.94846 + 1.39858I
b = −0.41025 − 1.44460I
11.52880 − 5.38344I 0
u = −1.280870 − 0.190846I
a = −0.94846 − 1.39858I
b = −0.41025 + 1.44460I
11.52880 + 5.38344I 0
u = 1.310030 + 0.412002I
a = −1.39880 − 1.65413I
b = −0.20326 + 1.40973I
4.59729 + 7.32898I 0
u = 1.310030 − 0.412002I
a = −1.39880 + 1.65413I
b = −0.20326 − 1.40973I
4.59729 − 7.32898I 0
u = −1.351480 + 0.338312I
a = 0.63432 − 2.00827I
b = 0.466718 + 1.200170I
4.10202 − 4.20256I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.351480 − 0.338312I
a = 0.63432 + 2.00827I
b = 0.466718 − 1.200170I
4.10202 + 4.20256I 0
u = −1.350240 + 0.403220I
a = −0.077062 − 1.105780I
b = 0.962009 + 0.506118I
2.41229 − 9.89482I 0
u = −1.350240 − 0.403220I
a = −0.077062 + 1.105780I
b = 0.962009 − 0.506118I
2.41229 + 9.89482I 0
u = 1.364290 + 0.355675I
a = −0.206900 − 0.650879I
b = −0.400650 + 0.135843I
0.60420 + 3.90700I 0
u = 1.364290 − 0.355675I
a = −0.206900 + 0.650879I
b = −0.400650 − 0.135843I
0.60420 − 3.90700I 0
u = 0.039755 + 0.542419I
a = −0.31991 − 1.70017I
b = 0.203089 − 1.373340I
7.42461 + 2.75741I 6.63280 − 3.03516I
u = 0.039755 − 0.542419I
a = −0.31991 + 1.70017I
b = 0.203089 + 1.373340I
7.42461 − 2.75741I 6.63280 + 3.03516I
u = 1.43665 + 0.39904I
a = 1.11035 + 2.24747I
b = 0.35346 − 1.55119I
9.0502 + 14.6852I 0
u = 1.43665 − 0.39904I
a = 1.11035 − 2.24747I
b = 0.35346 + 1.55119I
9.0502 − 14.6852I 0
u = −1.48426 + 0.30904I
a = −1.02295 + 2.49547I
b = −0.143027 − 1.403930I
5.68590 − 5.85795I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48426 − 0.30904I
a = −1.02295 − 2.49547I
b = −0.143027 + 1.403930I
5.68590 + 5.85795I 0
u = 0.037620 + 0.395735I
a = −1.287690 + 0.574122I
b = −0.12095 − 1.59031I
8.09559 − 2.39337I 3.23244 + 2.80367I
u = 0.037620 − 0.395735I
a = −1.287690 − 0.574122I
b = −0.12095 + 1.59031I
8.09559 + 2.39337I 3.23244 − 2.80367I
u = −1.63857
a = 0.548716
b = −0.409341
10.4567 0
u = 0.152119 + 0.317487I
a = −0.986059 − 0.348852I
b = −0.207133 + 0.562199I
0.300017 + 0.906434I 6.10890 − 7.39998I
u = 0.152119 − 0.317487I
a = −0.986059 + 0.348852I
b = −0.207133 − 0.562199I
0.300017 − 0.906434I 6.10890 + 7.39998I
u = 1.67470 + 0.08059I
a = 0.33916 + 2.32988I
b = −0.161751 − 1.374090I
15.0554 − 2.0908I 0
u = 1.67470 − 0.08059I
a = 0.33916 − 2.32988I
b = −0.161751 + 1.374090I
15.0554 + 2.0908I 0
u = −0.0275139
a = 45.5029
b = 0.560752
2.83333 −3.70810
10
II.
I
u
2
= h2u
14
−u
13
+· · ·+b+2, −2u
14
+2u
13
+· · ·+a+1, u
15
−9u
13
+· · ·+2u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
9
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
2u
14
− 2u
13
+ ··· + u − 1
−2u
14
+ u
13
+ ··· + 18u
2
− 2
a
4
=
−u
13
+ u
12
+ ··· + u − 3
−2u
14
+ u
13
+ ··· + 18u
2
− 2
a
2
=
2u
13
− 2u
12
+ ··· − 16u
2
+ 3
u
14
− u
13
+ ··· − 10u
2
+ 3u
a
3
=
u
14
− u
13
+ ··· + 2u
2
− 3
−2u
14
+ u
13
+ ··· + 16u
2
− 2
a
7
=
−u
u
a
6
=
2u
13
− 3u
12
+ ··· − 11u + 2
2u
14
− 2u
13
+ ··· + 4u + 3
a
10
=
−3u
14
+ 2u
13
+ ··· + 42u
2
− 4
−u
12
+ 7u
10
− 18u
8
+ u
7
+ 19u
6
− 4u
5
− 3u
4
+ 5u
3
− 6u
2
− 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
14
− 2u
13
+ 16u
12
+ 15u
11
− 49u
10
− 41u
9
+ 70u
8
+ 45u
7
−
38u
6
− 5u
5
− 10u
4
− 22u
3
+ 10u
2
+ 5u + 15
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 2u
14
+ ··· + 6u + 1
c
2
u
15
− 3u
14
+ ··· + 2u
2
+ 1
c
3
u
15
+ u
13
+ ··· + u + 1
c
4
, c
5
u
15
+ 9u
13
+ ··· − 2u + 1
c
6
u
15
+ 3u
14
+ ··· − 2u
2
− 1
c
7
, c
8
u
15
− 9u
13
+ ··· + 2u − 1
c
9
u
15
+ u
14
+ ··· + u
2
+ 1
c
10
u
15
+ 9u
13
+ ··· − 2u − 1
c
11
, c
12
u
15
− 9u
13
+ ··· + 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 2y
14
+ ··· + 40y −1
c
2
, c
6
y
15
− 13y
14
+ ··· − 4y −1
c
3
y
15
+ 2y
14
+ ··· + 9y −1
c
4
, c
5
, c
10
y
15
+ 18y
14
+ ··· + 12y −1
c
7
, c
8
, c
11
c
12
y
15
− 18y
14
+ ··· + 16y −1
c
9
y
15
− 9y
14
+ ··· − 2y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.19201
a = −1.00785
b = −0.669803
5.66959 5.09880
u = −1.238320 + 0.078062I
a = −1.29573 + 2.90295I
b = −0.15885 − 1.58766I
11.83090 − 3.16023I 13.91924 + 0.52022I
u = −1.238320 − 0.078062I
a = −1.29573 − 2.90295I
b = −0.15885 + 1.58766I
11.83090 + 3.16023I 13.91924 − 0.52022I
u = 0.151779 + 0.741588I
a = −1.040030 − 0.584316I
b = −0.260278 + 0.958370I
−1.79394 + 1.02194I 2.84820 − 1.54812I
u = 0.151779 − 0.741588I
a = −1.040030 + 0.584316I
b = −0.260278 − 0.958370I
−1.79394 − 1.02194I 2.84820 + 1.54812I
u = 1.237890 + 0.308571I
a = −0.061952 − 0.614896I
b = 0.371777 + 0.708479I
1.57563 + 2.68429I 8.08777 − 2.30509I
u = 1.237890 − 0.308571I
a = −0.061952 + 0.614896I
b = 0.371777 − 0.708479I
1.57563 − 2.68429I 8.08777 + 2.30509I
u = −1.40336 + 0.36290I
a = 0.87716 − 1.84733I
b = 0.265089 + 1.156520I
3.20409 − 5.09393I 7.73695 + 4.78673I
u = −1.40336 − 0.36290I
a = 0.87716 + 1.84733I
b = 0.265089 − 1.156520I
3.20409 + 5.09393I 7.73695 − 4.78673I
u = 0.458300
a = −2.74392
b = 0.467982
3.24621 16.6550
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58675 + 0.04787I
a = 0.53316 + 2.42451I
b = −0.12509 − 1.45929I
15.8645 − 1.5465I 16.0962 − 0.3491I
u = 1.58675 − 0.04787I
a = 0.53316 − 2.42451I
b = −0.12509 + 1.45929I
15.8645 + 1.5465I 16.0962 + 0.3491I
u = −1.60528
a = 0.693477
b = −0.282393
10.6979 25.1980
u = −0.357259 + 0.149534I
a = −2.48346 + 0.24716I
b = 0.14946 − 1.51822I
8.86003 + 2.31551I 14.8358 − 1.2107I
u = −0.357259 − 0.149534I
a = −2.48346 − 0.24716I
b = 0.14946 + 1.51822I
8.86003 − 2.31551I 14.8358 + 1.2107I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 2u
14
+ ··· + 6u + 1)(u
59
− 9u
58
+ ··· − 108u + 61)
c
2
(u
15
− 3u
14
+ ··· + 2u
2
+ 1)(u
59
− 2u
58
+ ··· + 5154u − 773)
c
3
(u
15
+ u
13
+ ··· + u + 1)(u
59
− u
58
+ ··· + 23u − 43)
c
4
, c
5
(u
15
+ 9u
13
+ ··· − 2u + 1)(u
59
− u
58
+ ··· + 102u + 1)
c
6
(u
15
+ 3u
14
+ ··· − 2u
2
− 1)(u
59
− 2u
58
+ ··· + 5154u − 773)
c
7
, c
8
(u
15
− 9u
13
+ ··· + 2u − 1)(u
59
− u
58
+ ··· + 32u + 1)
c
9
(u
15
+ u
14
+ ··· + u
2
+ 1)(u
59
+ 2u
58
+ ··· + 1624u − 1291)
c
10
(u
15
+ 9u
13
+ ··· − 2u − 1)(u
59
− u
58
+ ··· + 102u + 1)
c
11
, c
12
(u
15
− 9u
13
+ ··· + 2u + 1)(u
59
− u
58
+ ··· + 32u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 2y
14
+ ··· + 40y −1)(y
59
− 33y
58
+ ··· + 229434y −3721)
c
2
, c
6
(y
15
− 13y
14
+ ··· − 4y −1)
· (y
59
− 40y
58
+ ··· + 18677570y −597529)
c
3
(y
15
+ 2y
14
+ ··· + 9y −1)(y
59
+ 31y
58
+ ··· − 87965y −1849)
c
4
, c
5
, c
10
(y
15
+ 18y
14
+ ··· + 12y −1)(y
59
+ 59y
58
+ ··· + 10138y −1)
c
7
, c
8
, c
11
c
12
(y
15
− 18y
14
+ ··· + 16y −1)(y
59
− 53y
58
+ ··· + 1298y −1)
c
9
(y
15
− 9y
14
+ ··· − 2y −1)
· (y
59
− 32y
58
+ ··· + 37592492y −1666681)
17
