12n
0295
(K12n
0295
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 10 2 12 5 6 9 1 8
Solving Sequence
6,9
10
3,11
2 7 1 5 8 4 12
c
9
c
10
c
2
c
6
c
1
c
5
c
8
c
4
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.06469 × 10
32
u
66
− 1.40021 × 10
32
u
65
+ ··· + 2.98795 × 10
31
b − 4.19610 × 10
32
,
− 1.94960 × 10
31
u
66
− 3.90032 × 10
31
u
65
+ ··· + 2.98795 × 10
31
a − 2.08028 × 10
32
, u
67
− u
66
+ ··· − 4u + 4i
I
u
2
= hu
3
a − u
2
a + au − u
2
+ b − 2a + u − 1, u
3
a + 2a
2
+ 2au − u
2
− 2, u
4
+ 2u
2
+ 2i
I
v
1
= ha, b + v, v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 77 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
= h1.06×10
32
u
66
−1.40×10
32
u
65
+· · ·+2.99×10
31
b−4.20×10
32
, −1.95×
10
31
u
66
−3.90×10
31
u
65
+· · ·+2.99×10
31
a−2.08×10
32
, u
67
−u
66
+· · ·−4u+4i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
0.652488u
66
+ 1.30535u
65
+ ··· + 3.13714u + 6.96225
−3.56329u
66
+ 4.68621u
65
+ ··· − 16.7518u + 14.0434
a
11
=
u
2
+ 1
u
2
a
2
=
0.652488u
66
+ 1.30535u
65
+ ··· + 3.13714u + 6.96225
−2.60763u
66
+ 2.64905u
65
+ ··· − 11.5304u + 6.21206
a
7
=
−3.25872u
66
+ 3.19768u
65
+ ··· − 14.7929u + 8.57622
2.29504u
66
− 0.672961u
65
+ ··· + 9.68506u − 2.51477
a
1
=
0.0915661u
66
− 1.99663u
65
+ ··· + 2.63606u − 7.72366
−4.93115u
66
+ 4.21632u
65
+ ··· − 21.8384u + 11.2155
a
5
=
u
u
3
+ u
a
8
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
−u
7
− 2u
5
− 2u
3
−u
9
− 3u
7
− 3u
5
+ u
a
12
=
0.709744u
66
− 1.32832u
65
+ ··· + 4.54050u − 3.81522
−5.57978u
66
+ 5.85739u
65
+ ··· − 26.2200u + 17.2657
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.44470u
66
− 8.34775u
65
+ ··· + 29.7826u − 28.7599
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
+ 38u
66
+ ··· − 4u − 1
c
2
, c
6
u
67
− 2u
66
+ ··· + 6u − 1
c
3
u
67
+ 2u
66
+ ··· + 734u − 173
c
4
, c
8
u
67
− u
66
+ ··· − 52u − 548
c
5
, c
9
u
67
+ u
66
+ ··· − 4u − 4
c
7
, c
12
u
67
− 3u
66
+ ··· − 15u − 13
c
10
u
67
− 31u
66
+ ··· − 80u + 16
c
11
u
67
− 23u
66
+ ··· + 3501u − 169
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
− 10y
66
+ ··· + 84y −1
c
2
, c
6
y
67
+ 38y
66
+ ··· − 4y −1
c
3
y
67
− 58y
66
+ ··· − 506856y −29929
c
4
, c
8
y
67
− y
66
+ ··· − 3289680y −300304
c
5
, c
9
y
67
+ 31y
66
+ ··· − 80y −16
c
7
, c
12
y
67
− 23y
66
+ ··· + 3501y −169
c
10
y
67
+ 15y
66
+ ··· − 3328y −256
c
11
y
67
+ 57y
66
+ ··· + 203921y −28561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293686 + 0.958960I
a = −0.848658 − 0.410982I
b = −1.26966 − 0.89610I
3.60658 − 1.32410I 10.41239 + 2.57758I
u = −0.293686 − 0.958960I
a = −0.848658 + 0.410982I
b = −1.26966 + 0.89610I
3.60658 + 1.32410I 10.41239 − 2.57758I
u = −0.797556 + 0.595964I
a = 0.370623 − 1.314420I
b = −0.92158 − 2.06820I
−8.62301 + 6.67427I 0. − 5.42994I
u = −0.797556 − 0.595964I
a = 0.370623 + 1.314420I
b = −0.92158 + 2.06820I
−8.62301 − 6.67427I 0. + 5.42994I
u = 0.390812 + 0.942541I
a = −0.614053 − 0.918919I
b = −0.27889 − 2.74791I
2.87894 − 3.62568I 4.00000 + 3.66828I
u = 0.390812 − 0.942541I
a = −0.614053 + 0.918919I
b = −0.27889 + 2.74791I
2.87894 + 3.62568I 4.00000 − 3.66828I
u = 0.369468 + 0.905859I
a = −1.161530 + 0.100804I
b = 1.70277 + 0.10484I
2.70033 + 0.62241I 6.92862 + 0.I
u = 0.369468 − 0.905859I
a = −1.161530 − 0.100804I
b = 1.70277 − 0.10484I
2.70033 − 0.62241I 6.92862 + 0.I
u = −0.625687 + 0.815726I
a = −0.866747 + 0.736378I
b = 0.96397 + 1.91289I
−4.18859 + 2.44849I 0
u = −0.625687 − 0.815726I
a = −0.866747 − 0.736378I
b = 0.96397 − 1.91289I
−4.18859 − 2.44849I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827360 + 0.500431I
a = −0.371421 − 1.339800I
b = 0.97307 − 1.82972I
−8.90984 + 0.43271I −1.022530 + 0.496680I
u = 0.827360 − 0.500431I
a = −0.371421 + 1.339800I
b = 0.97307 + 1.82972I
−8.90984 − 0.43271I −1.022530 − 0.496680I
u = −0.828153 + 0.492617I
a = −1.081770 + 0.896752I
b = 1.05437 + 1.68616I
−8.86607 − 3.17955I −0.988573 + 0.950602I
u = −0.828153 − 0.492617I
a = −1.081770 − 0.896752I
b = 1.05437 − 1.68616I
−8.86607 + 3.17955I −0.988573 − 0.950602I
u = 0.773593 + 0.535367I
a = 0.820590 − 0.525886I
b = 0.506080 + 0.187810I
−4.83958 − 1.65195I 2.33033 + 2.39714I
u = 0.773593 − 0.535367I
a = 0.820590 + 0.525886I
b = 0.506080 − 0.187810I
−4.83958 + 1.65195I 2.33033 − 2.39714I
u = 0.846926 + 0.407345I
a = 1.10299 + 0.93182I
b = −1.17325 + 1.47521I
−7.51011 + 10.16540I 0.84901 − 5.51887I
u = 0.846926 − 0.407345I
a = 1.10299 − 0.93182I
b = −1.17325 − 1.47521I
−7.51011 − 10.16540I 0.84901 + 5.51887I
u = −0.808297 + 0.434822I
a = −0.798749 − 0.636743I
b = −0.374659 + 0.223488I
−4.26028 − 4.81071I 3.21364 + 2.49973I
u = −0.808297 − 0.434822I
a = −0.798749 + 0.636743I
b = −0.374659 − 0.223488I
−4.26028 + 4.81071I 3.21364 − 2.49973I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.393391 + 1.042260I
a = −0.204574 + 0.462109I
b = −0.204935 − 0.456540I
4.35771 + 3.46092I 0
u = −0.393391 − 1.042260I
a = −0.204574 − 0.462109I
b = −0.204935 + 0.456540I
4.35771 − 3.46092I 0
u = −0.102031 + 1.124100I
a = −0.074288 + 0.720806I
b = −0.252101 + 1.022590I
1.05983 − 2.64924I 0
u = −0.102031 − 1.124100I
a = −0.074288 − 0.720806I
b = −0.252101 − 1.022590I
1.05983 + 2.64924I 0
u = 0.499688 + 1.012210I
a = 0.890259 − 0.218223I
b = 0.757089 − 0.307916I
1.97793 − 2.12988I 0
u = 0.499688 − 1.012210I
a = 0.890259 + 0.218223I
b = 0.757089 + 0.307916I
1.97793 + 2.12988I 0
u = 0.548320 + 0.997805I
a = 0.696251 + 0.717636I
b = −2.01408 + 2.32374I
1.30273 − 5.96282I 0
u = 0.548320 − 0.997805I
a = 0.696251 − 0.717636I
b = −2.01408 − 2.32374I
1.30273 + 5.96282I 0
u = −0.003645 + 1.165290I
a = 1.040750 + 0.337542I
b = −0.279122 + 0.832538I
−2.94562 − 1.34587I 0
u = −0.003645 − 1.165290I
a = 1.040750 − 0.337542I
b = −0.279122 − 0.832538I
−2.94562 + 1.34587I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298119 + 0.774004I
a = 0.239287 + 0.602551I
b = −0.040611 + 0.560440I
0.401806 − 1.265690I 4.47035 + 5.10756I
u = 0.298119 − 0.774004I
a = 0.239287 − 0.602551I
b = −0.040611 − 0.560440I
0.401806 + 1.265690I 4.47035 − 5.10756I
u = −0.545451 + 1.036140I
a = 0.346086 − 0.872759I
b = −0.02443 − 2.31994I
1.87665 + 7.41999I 0
u = −0.545451 − 1.036140I
a = 0.346086 + 0.872759I
b = −0.02443 + 2.31994I
1.87665 − 7.41999I 0
u = −0.414664 + 1.113320I
a = −0.322911 − 0.117417I
b = −0.009462 − 1.064340I
4.31530 + 3.66992I 0
u = −0.414664 − 1.113320I
a = −0.322911 + 0.117417I
b = −0.009462 + 1.064340I
4.31530 − 3.66992I 0
u = 0.563544 + 0.577917I
a = 1.109400 + 0.643464I
b = −0.66998 + 2.28277I
0.05661 + 1.47287I −0.156482 − 0.461455I
u = 0.563544 − 0.577917I
a = 1.109400 − 0.643464I
b = −0.66998 − 2.28277I
0.05661 − 1.47287I −0.156482 + 0.461455I
u = 0.123549 + 1.190490I
a = −1.043430 + 0.330545I
b = 0.286253 + 1.175820I
−2.02431 + 7.56304I 0
u = 0.123549 − 1.190490I
a = −1.043430 − 0.330545I
b = 0.286253 − 1.175820I
−2.02431 − 7.56304I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.670786 + 1.018810I
a = 1.078320 − 0.268018I
b = −0.60969 − 1.60312I
−7.35703 − 1.17039I 0
u = −0.670786 − 1.018810I
a = 1.078320 + 0.268018I
b = −0.60969 + 1.60312I
−7.35703 + 1.17039I 0
u = 0.431796 + 1.142180I
a = 0.842437 − 0.007900I
b = 0.311709 − 0.277350I
2.39569 − 1.20414I 0
u = 0.431796 − 1.142180I
a = 0.842437 + 0.007900I
b = 0.311709 + 0.277350I
2.39569 + 1.20414I 0
u = 0.632532 + 1.049100I
a = −0.410549 + 0.627513I
b = −1.004620 + 0.513716I
−3.30409 − 3.65847I 0
u = 0.632532 − 1.049100I
a = −0.410549 − 0.627513I
b = −1.004620 − 0.513716I
−3.30409 + 3.65847I 0
u = −0.491913 + 1.123810I
a = 0.487065 − 0.297919I
b = 0.64193 − 2.20537I
3.73381 + 3.87247I 0
u = −0.491913 − 1.123810I
a = 0.487065 + 0.297919I
b = 0.64193 + 2.20537I
3.73381 − 3.87247I 0
u = 0.442549 + 1.167140I
a = −0.668713 − 0.591003I
b = −0.37959 − 2.23277I
2.29737 − 6.96304I 0
u = 0.442549 − 1.167140I
a = −0.668713 + 0.591003I
b = −0.37959 + 2.23277I
2.29737 + 6.96304I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.649361 + 1.084610I
a = −1.014350 − 0.308144I
b = 0.43011 − 1.87121I
−7.15571 − 5.94368I 0
u = 0.649361 − 1.084610I
a = −1.014350 + 0.308144I
b = 0.43011 + 1.87121I
−7.15571 + 5.94368I 0
u = −0.646127 + 1.088570I
a = −0.663411 + 0.842579I
b = 0.88041 + 3.02440I
−7.07599 + 8.68070I 0
u = −0.646127 − 1.088570I
a = −0.663411 − 0.842579I
b = 0.88041 − 3.02440I
−7.07599 − 8.68070I 0
u = −0.570732 + 0.461256I
a = 1.41705 − 0.34329I
b = −0.533167 − 0.314158I
0.23654 − 2.91363I 0.64103 + 4.67783I
u = −0.570732 − 0.461256I
a = 1.41705 + 0.34329I
b = −0.533167 + 0.314158I
0.23654 + 2.91363I 0.64103 − 4.67783I
u = −0.617183 + 1.107590I
a = 0.503682 + 0.559159I
b = 1.252870 + 0.595770I
−2.25041 + 10.15140I 0
u = −0.617183 − 1.107590I
a = 0.503682 − 0.559159I
b = 1.252870 − 0.595770I
−2.25041 − 10.15140I 0
u = 0.713940 + 0.055087I
a = −0.56556 − 1.40057I
b = 0.473278 − 0.746286I
−0.93797 + 2.72253I −0.22585 − 4.76234I
u = 0.713940 − 0.055087I
a = −0.56556 + 1.40057I
b = 0.473278 + 0.746286I
−0.93797 − 2.72253I −0.22585 + 4.76234I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621904 + 1.131010I
a = 0.619371 + 0.849174I
b = −0.63824 + 3.33873I
−5.3362 − 15.6199I 0
u = 0.621904 − 1.131010I
a = 0.619371 − 0.849174I
b = −0.63824 − 3.33873I
−5.3362 + 15.6199I 0
u = −0.622131 + 0.231767I
a = 0.260574 − 1.086710I
b = −1.188230 − 0.194967I
1.188580 + 0.490539I 2.76633 + 0.06990I
u = −0.622131 − 0.231767I
a = 0.260574 + 1.086710I
b = −1.188230 + 0.194967I
1.188580 − 0.490539I 2.76633 − 0.06990I
u = 0.484230 + 0.413310I
a = 0.14617 + 1.58952I
b = −0.135120 + 0.584183I
0.34718 − 1.92926I −0.50268 + 2.96380I
u = 0.484230 − 0.413310I
a = 0.14617 − 1.58952I
b = −0.135120 − 0.584183I
0.34718 + 1.92926I −0.50268 − 2.96380I
u = −0.572521
a = 0.479617
b = −0.464996
1.36152 7.18480
11
II.
I
u
2
= hu
3
a−u
2
a+au−u
2
+b−2a+u−1, u
3
a+2a
2
+2au−u
2
−2, u
4
+2u
2
+2i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
a
−u
3
a + u
2
a − au + u
2
+ 2a − u + 1
a
11
=
u
2
+ 1
u
2
a
2
=
a
−u
3
a + 2u
2
a − au + u
2
+ 2a − u + 1
a
7
=
1
2
u
3
+ a + u
u
2
a + u
3
+ u
2
+ 2a + u + 1
a
1
=
1
2
u
3
+ a + u
u
2
a + u
3
+ u
2
+ 2a + u + 1
a
5
=
u
u
3
+ u
a
8
=
−u
2
− 1
−u
2
a
4
=
0
−u
a
12
=
1
2
u
3
+ u
2
+ a + u + 1
u
2
a + u
3
+ 2u
2
+ 2a + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4au + 4u
2
+ 16
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
4
c
3
, c
6
(u
2
+ u + 1)
4
c
4
, c
8
(u
4
− 2u
2
+ 2)
2
c
5
, c
9
(u
4
+ 2u
2
+ 2)
2
c
7
(u − 1)
8
c
10
(u
2
− 2u + 2)
4
c
11
, c
12
(u + 1)
8
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
4
c
4
, c
8
(y
2
− 2y + 2)
4
c
5
, c
9
(y
2
+ 2y + 2)
4
c
7
, c
11
, c
12
(y −1)
8
c
10
(y
2
+ 4)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455090 + 1.098680I
a = 0.833702 − 0.109759I
b = 1.354400 + 0.125259I
4.11234 − 5.69375I 10.00000 + 7.46410I
u = 0.455090 + 1.098680I
a = −0.511905 − 0.667128I
b = −1.16589 − 1.77772I
4.11234 − 1.63398I 10.00000 + 0.53590I
u = 0.455090 − 1.098680I
a = 0.833702 + 0.109759I
b = 1.354400 − 0.125259I
4.11234 + 5.69375I 10.00000 − 7.46410I
u = 0.455090 − 1.098680I
a = −0.511905 + 0.667128I
b = −1.16589 + 1.77772I
4.11234 + 1.63398I 10.00000 − 0.53590I
u = −0.455090 + 1.098680I
a = −0.833702 − 0.109759I
b = 0.377654 − 0.874741I
4.11234 + 5.69375I 10.00000 − 7.46410I
u = −0.455090 + 1.098680I
a = 0.511905 − 0.667128I
b = −0.56616 − 2.77772I
4.11234 + 1.63398I 10.00000 − 0.53590I
u = −0.455090 − 1.098680I
a = −0.833702 + 0.109759I
b = 0.377654 + 0.874741I
4.11234 − 5.69375I 10.00000 + 7.46410I
u = −0.455090 − 1.098680I
a = 0.511905 + 0.667128I
b = −0.56616 + 2.77772I
4.11234 − 1.63398I 10.00000 + 0.53590I
15
III. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
6
=
v
0
a
9
=
1
0
a
10
=
1
0
a
3
=
0
−v
a
11
=
1
0
a
2
=
−1
−v
a
7
=
1
1
a
1
=
−1
−1
a
5
=
v
0
a
8
=
1
0
a
4
=
v
0
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
, c
10
u
2
c
7
, c
11
(u + 1)
2
c
12
(u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
, c
10
y
2
c
7
, c
11
, c
12
(y − 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
1.64493 − 2.02988I 6.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
1.64493 + 2.02988I 6.00000 − 3.46410I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
67
+ 38u
66
+ ··· − 4u − 1)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)(u
67
− 2u
66
+ ··· + 6u − 1)
c
3
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
67
+ 2u
66
+ ··· + 734u − 173)
c
4
, c
8
u
2
(u
4
− 2u
2
+ 2)
2
(u
67
− u
66
+ ··· − 52u − 548)
c
5
, c
9
u
2
(u
4
+ 2u
2
+ 2)
2
(u
67
+ u
66
+ ··· − 4u − 4)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
67
− 2u
66
+ ··· + 6u − 1)
c
7
((u − 1)
8
)(u + 1)
2
(u
67
− 3u
66
+ ··· − 15u − 13)
c
10
u
2
(u
2
− 2u + 2)
4
(u
67
− 31u
66
+ ··· − 80u + 16)
c
11
((u + 1)
10
)(u
67
− 23u
66
+ ··· + 3501u − 169)
c
12
((u − 1)
2
)(u + 1)
8
(u
67
− 3u
66
+ ··· − 15u − 13)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
67
− 10y
66
+ ··· + 84y − 1)
c
2
, c
6
((y
2
+ y + 1)
5
)(y
67
+ 38y
66
+ ··· − 4y − 1)
c
3
((y
2
+ y + 1)
5
)(y
67
− 58y
66
+ ··· − 506856y − 29929)
c
4
, c
8
y
2
(y
2
− 2y + 2)
4
(y
67
− y
66
+ ··· − 3289680y − 300304)
c
5
, c
9
y
2
(y
2
+ 2y + 2)
4
(y
67
+ 31y
66
+ ··· − 80y − 16)
c
7
, c
12
((y − 1)
10
)(y
67
− 23y
66
+ ··· + 3501y − 169)
c
10
y
2
(y
2
+ 4)
4
(y
67
+ 15y
66
+ ··· − 3328y − 256)
c
11
((y − 1)
10
)(y
67
+ 57y
66
+ ··· + 203921y − 28561)
21
