12n
0659
(K12n
0659
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 11 10 2 5 3 6 8 4
Solving Sequence
5,12
4
1,9
3 8 2 7 11 6 10
c
4
c
12
c
3
c
8
c
2
c
7
c
11
c
5
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.74446 × 10
123
u
53
− 1.80068 × 10
124
u
52
+ ··· + 2.83000 × 10
124
b − 8.02256 × 10
125
,
1.03240 × 10
126
u
53
+ 4.93019 × 10
126
u
52
+ ··· + 1.38670 × 10
126
a + 2.28691 × 10
128
,
u
54
+ 5u
53
+ ··· + 528u + 49i
I
u
2
= h2u
17
+ 16u
16
+ ··· + b + 43, 11u
17
− 31u
16
+ ··· + a − 24, u
18
− 2u
17
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 72 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−3.74 × 10
123
u
53
− 1.80 × 10
124
u
52
+ · · · + 2.83 × 10
124
b − 8.02 ×
10
125
, 1.03 × 10
126
u
53
+ 4.93 × 10
126
u
52
+ · · · + 1.39 × 10
126
a + 2.29 ×
10
128
, u
54
+ 5u
53
+ · · · + 528u + 49i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
1
=
u
u
3
+ u
a
9
=
−0.744500u
53
− 3.55533u
52
+ ··· − 1001.93u − 164.918
0.132313u
53
+ 0.636282u
52
+ ··· + 178.673u + 28.3483
a
3
=
0.980752u
53
+ 4.70300u
52
+ ··· + 1409.41u + 228.585
−0.0620997u
53
− 0.294145u
52
+ ··· − 86.5558u − 14.5888
a
8
=
−0.612187u
53
− 2.91905u
52
+ ··· − 823.256u − 136.569
0.132313u
53
+ 0.636282u
52
+ ··· + 178.673u + 28.3483
a
2
=
2.27754u
53
+ 10.9226u
52
+ ··· + 3266.86u + 527.076
−0.155250u
53
− 0.741079u
52
+ ··· − 221.237u − 36.9171
a
7
=
2.69305u
53
+ 12.8497u
52
+ ··· + 3650.99u + 598.393
−0.178103u
53
− 0.850344u
52
+ ··· − 239.834u − 38.4779
a
11
=
−1.22947u
53
− 5.89896u
52
+ ··· − 1731.81u − 275.141
0.129646u
53
+ 0.617545u
52
+ ··· + 192.287u + 31.3383
a
6
=
−1.12462u
53
− 5.37150u
52
+ ··· − 1476.98u − 234.162
0.0650075u
53
+ 0.315357u
52
+ ··· + 100.049u + 15.3130
a
10
=
−1.86297u
53
− 8.89331u
52
+ ··· − 2509.47u − 410.424
0.218460u
53
+ 1.04761u
52
+ ··· + 297.149u + 47.1762
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.164546u
53
− 0.781563u
52
+ ··· − 246.802u − 54.5462
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 57u
53
+ ··· + 4309293u + 130321
c
2
, c
7
u
54
+ u
53
+ ··· + 1811u − 361
c
3
, c
9
u
54
− u
53
+ ··· − 171u − 37
c
4
, c
12
u
54
+ 5u
53
+ ··· + 528u + 49
c
5
, c
6
, c
10
u
54
+ u
53
+ ··· + 146u − 143
c
8
u
54
+ 3u
53
+ ··· − 53u − 11
c
11
u
54
− 6u
52
+ ··· − 2734u + 439
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
− 121y
53
+ ··· + 1173617520891y + 16983563041
c
2
, c
7
y
54
− 57y
53
+ ··· − 4309293y + 130321
c
3
, c
9
y
54
− 3y
53
+ ··· − 82743y + 1369
c
4
, c
12
y
54
+ 43y
53
+ ··· − 40056y + 2401
c
5
, c
6
, c
10
y
54
+ 43y
53
+ ··· + 236656y + 20449
c
8
y
54
+ 17y
53
+ ··· + 1393y + 121
c
11
y
54
− 12y
53
+ ··· − 2068032y + 192721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234320 + 0.969892I
a = −0.148625 + 1.288510I
b = 0.475743 − 1.092990I
3.14147 + 2.14385I −8.00000 − 2.27953I
u = −0.234320 − 0.969892I
a = −0.148625 − 1.288510I
b = 0.475743 + 1.092990I
3.14147 − 2.14385I −8.00000 + 2.27953I
u = 0.027994 + 0.970519I
a = −0.553301 − 0.417496I
b = 0.36927 + 1.64804I
3.04092 − 2.63323I −6.79514 + 3.39134I
u = 0.027994 − 0.970519I
a = −0.553301 + 0.417496I
b = 0.36927 − 1.64804I
3.04092 + 2.63323I −6.79514 − 3.39134I
u = −0.782902 + 0.567024I
a = −0.515595 + 1.182860I
b = −0.368436 + 0.517578I
−2.46486 − 3.78662I −6.40927 + 1.45545I
u = −0.782902 − 0.567024I
a = −0.515595 − 1.182860I
b = −0.368436 − 0.517578I
−2.46486 + 3.78662I −6.40927 − 1.45545I
u = −0.362509 + 1.006200I
a = −1.74365 + 0.26534I
b = 1.03182 + 1.06263I
2.07901 − 4.91557I −8.00000 + 0.I
u = −0.362509 − 1.006200I
a = −1.74365 − 0.26534I
b = 1.03182 − 1.06263I
2.07901 + 4.91557I −8.00000 + 0.I
u = 0.562881 + 1.010060I
a = 1.70829 + 0.19125I
b = −1.08761 + 0.91934I
0.36171 + 5.69112I 0
u = 0.562881 − 1.010060I
a = 1.70829 − 0.19125I
b = −1.08761 − 0.91934I
0.36171 − 5.69112I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.311601 + 1.189300I
a = 1.261750 − 0.239301I
b = −0.846614 − 0.808655I
−3.40881 − 2.20781I 0
u = −0.311601 − 1.189300I
a = 1.261750 + 0.239301I
b = −0.846614 + 0.808655I
−3.40881 + 2.20781I 0
u = 0.475047 + 0.535369I
a = 0.075261 + 0.763788I
b = −0.550857 − 1.221260I
2.01849 − 1.23122I −3.26105 − 1.16198I
u = 0.475047 − 0.535369I
a = 0.075261 − 0.763788I
b = −0.550857 + 1.221260I
2.01849 + 1.23122I −3.26105 + 1.16198I
u = 0.465598 + 1.208790I
a = −1.173780 + 0.049718I
b = 0.795766 − 0.488765I
−1.16225 + 2.99382I 0
u = 0.465598 − 1.208790I
a = −1.173780 − 0.049718I
b = 0.795766 + 0.488765I
−1.16225 − 2.99382I 0
u = −0.665299 + 1.133700I
a = 0.975711 − 0.647626I
b = −0.441264 − 0.844294I
−4.11326 − 2.05845I 0
u = −0.665299 − 1.133700I
a = 0.975711 + 0.647626I
b = −0.441264 + 0.844294I
−4.11326 + 2.05845I 0
u = 0.039718 + 1.317490I
a = −1.060890 − 0.018811I
b = 0.932021 + 0.518191I
−2.35880 + 2.03182I 0
u = 0.039718 − 1.317490I
a = −1.060890 + 0.018811I
b = 0.932021 − 0.518191I
−2.35880 − 2.03182I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.352052 + 0.575861I
a = 0.49680 − 1.33952I
b = 0.143466 − 1.197570I
8.88135 + 1.75033I −0.23249 − 5.30216I
u = 0.352052 − 0.575861I
a = 0.49680 + 1.33952I
b = 0.143466 + 1.197570I
8.88135 − 1.75033I −0.23249 + 5.30216I
u = 0.103091 + 1.329410I
a = 1.221790 + 0.330306I
b = −0.717176 + 1.156320I
−6.43910 + 4.65775I 0
u = 0.103091 − 1.329410I
a = 1.221790 − 0.330306I
b = −0.717176 − 1.156320I
−6.43910 − 4.65775I 0
u = 0.655732 + 0.001796I
a = −0.426767 − 0.217995I
b = −0.216342 + 0.945304I
2.33536 + 1.33301I −3.31811 − 4.81791I
u = 0.655732 − 0.001796I
a = −0.426767 + 0.217995I
b = −0.216342 − 0.945304I
2.33536 − 1.33301I −3.31811 + 4.81791I
u = −0.099058 + 1.403950I
a = −1.200600 + 0.034439I
b = 1.00529 − 0.99657I
−11.55370 − 1.21518I 0
u = −0.099058 − 1.403950I
a = −1.200600 − 0.034439I
b = 1.00529 + 0.99657I
−11.55370 + 1.21518I 0
u = 1.383890 + 0.257220I
a = 0.042622 + 0.310020I
b = 0.327830 + 0.748998I
4.07354 − 1.34058I 0
u = 1.383890 − 0.257220I
a = 0.042622 − 0.310020I
b = 0.327830 − 0.748998I
4.07354 + 1.34058I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.304294 + 0.499465I
a = 1.02836 + 1.02465I
b = 0.511575 − 0.716466I
3.32556 + 1.82215I −7.68501 − 4.30894I
u = −0.304294 − 0.499465I
a = 1.02836 − 1.02465I
b = 0.511575 + 0.716466I
3.32556 − 1.82215I −7.68501 + 4.30894I
u = −0.29988 + 1.38353I
a = 1.167220 − 0.318667I
b = −1.25222 + 0.74442I
−8.06461 − 7.14617I 0
u = −0.29988 − 1.38353I
a = 1.167220 + 0.318667I
b = −1.25222 − 0.74442I
−8.06461 + 7.14617I 0
u = −1.44175 + 0.12669I
a = 0.163034 − 0.101692I
b = −0.564264 − 0.875736I
−1.51180 − 7.69812I 0
u = −1.44175 − 0.12669I
a = 0.163034 + 0.101692I
b = −0.564264 + 0.875736I
−1.51180 + 7.69812I 0
u = 0.41538 + 1.39497I
a = 0.473978 − 0.650086I
b = 0.037314 + 0.438841I
5.88808 + 0.92042I 0
u = 0.41538 − 1.39497I
a = 0.473978 + 0.650086I
b = 0.037314 − 0.438841I
5.88808 − 0.92042I 0
u = 0.25489 + 1.47796I
a = 0.911154 − 0.269340I
b = −0.801265 + 0.938714I
−3.02616 + 3.86573I 0
u = 0.25489 − 1.47796I
a = 0.911154 + 0.269340I
b = −0.801265 − 0.938714I
−3.02616 − 3.86573I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.56773 + 1.48140I
a = −1.040690 + 0.016279I
b = 0.752725 − 1.177120I
−0.36984 + 8.31182I 0
u = 0.56773 − 1.48140I
a = −1.040690 − 0.016279I
b = 0.752725 + 1.177120I
−0.36984 − 8.31182I 0
u = −0.63065 + 1.50296I
a = 1.250760 + 0.035031I
b = −0.91992 − 1.19790I
−6.5506 − 14.8339I 0
u = −0.63065 − 1.50296I
a = 1.250760 − 0.035031I
b = −0.91992 + 1.19790I
−6.5506 + 14.8339I 0
u = −0.149852 + 0.300455I
a = −1.23317 + 5.69132I
b = −0.541979 − 0.188288I
−2.60231 − 4.18203I −11.45087 − 0.72915I
u = −0.149852 − 0.300455I
a = −1.23317 − 5.69132I
b = −0.541979 + 0.188288I
−2.60231 + 4.18203I −11.45087 + 0.72915I
u = −0.51673 + 1.64071I
a = −1.063790 − 0.161215I
b = 0.980622 + 0.969393I
−11.5956 − 8.4499I 0
u = −0.51673 − 1.64071I
a = −1.063790 + 0.161215I
b = 0.980622 − 0.969393I
−11.5956 + 8.4499I 0
u = −1.48162 + 0.91100I
a = −0.133736 − 0.101440I
b = 0.190419 + 0.615231I
−4.30577 − 1.29948I 0
u = −1.48162 − 0.91100I
a = −0.133736 + 0.101440I
b = 0.190419 − 0.615231I
−4.30577 + 1.29948I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30454 + 1.73276I
a = 0.825545 + 0.324392I
b = −0.878673 − 0.649779I
−8.04995 − 1.38990I 0
u = −0.30454 − 1.73276I
a = 0.825545 − 0.324392I
b = −0.878673 + 0.649779I
−8.04995 + 1.38990I 0
u = −0.221783
a = −1.37508
b = −0.409309
−0.627945 −15.7990
u = −0.216213
a = −7.73007
b = 0.674840
−6.62446 −17.2110
10
II. I
u
2
=
h2u
17
+16u
16
+· · ·+b+43, 11u
17
−31u
16
+· · ·+a−24, u
18
−2u
17
+· · ·−2u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
1
=
u
u
3
+ u
a
9
=
−11u
17
+ 31u
16
+ ··· − 48u + 24
−2u
17
− 16u
16
+ ··· + 60u − 43
a
3
=
−3u
17
+ 10u
16
+ ··· + 32u
2
− 9u
u
16
− 2u
15
+ ··· − 2u + 2
a
8
=
−13u
17
+ 15u
16
+ ··· + 12u − 19
−2u
17
− 16u
16
+ ··· + 60u − 43
a
2
=
−7u
17
+ 19u
16
+ ··· − 34u + 6
u
17
− u
16
+ ··· − 5u
2
+ 7u
a
7
=
11u
17
− 8u
16
+ ··· − 10u + 19
−2u
17
+ 8u
16
+ ··· − 12u + 4
a
11
=
−12u
17
+ 17u
16
+ ··· + 4u − 11
u
16
+ 4u
14
+ ··· + 2u + 5
a
6
=
19u
17
− 56u
16
+ ··· + 94u − 30
19u
17
− 41u
16
+ ··· + 58u − 13
a
10
=
35u
17
− 51u
16
+ ··· + 16u + 31
9u
17
− 10u
16
+ ··· − 7u + 10
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −116u
17
+ 218u
16
− 732u
15
+ 1098u
14
− 2099u
13
+ 3132u
12
− 4657u
11
+ 6171u
10
−
6988u
9
+ 6776u
8
− 6308u
7
+ 4541u
6
− 4126u
5
+ 2176u
4
− 1742u
3
+ 599u
2
− 297u + 39
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 14u
17
+ ··· − 11u + 1
c
2
u
18
− 7u
16
+ ··· + u + 1
c
3
u
18
+ 6u
16
+ ··· − u + 1
c
4
u
18
− 2u
17
+ ··· − 2u + 1
c
5
, c
6
u
18
+ 11u
16
+ ··· − 4u + 1
c
7
u
18
− 7u
16
+ ··· − u + 1
c
8
u
18
− 2u
17
+ ··· − 3u + 1
c
9
u
18
+ 6u
16
+ ··· + u + 1
c
10
u
18
+ 11u
16
+ ··· + 4u + 1
c
11
u
18
− u
17
+ ··· − 11u
2
+ 1
c
12
u
18
+ 2u
17
+ ··· + 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 22y
17
+ ··· + y + 1
c
2
, c
7
y
18
− 14y
17
+ ··· − 11y + 1
c
3
, c
9
y
18
+ 12y
17
+ ··· + 11y + 1
c
4
, c
12
y
18
+ 10y
17
+ ··· + 14y + 1
c
5
, c
6
, c
10
y
18
+ 22y
17
+ ··· + 14y + 1
c
8
y
18
+ 12y
17
+ ··· + 11y + 1
c
11
y
18
− y
17
+ ··· − 22y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.433983 + 1.043760I
a = 1.76917 + 0.06570I
b = −1.10704 + 1.10280I
2.38044 + 5.58075I −3.29349 − 9.18069I
u = 0.433983 − 1.043760I
a = 1.76917 − 0.06570I
b = −1.10704 − 1.10280I
2.38044 − 5.58075I −3.29349 + 9.18069I
u = 1.109000 + 0.375523I
a = −0.336175 − 0.040796I
b = −0.330973 − 0.824788I
4.68841 − 1.16029I 1.77241 + 1.34126I
u = 1.109000 − 0.375523I
a = −0.336175 + 0.040796I
b = −0.330973 + 0.824788I
4.68841 + 1.16029I 1.77241 − 1.34126I
u = −0.527284 + 0.639053I
a = −1.03264 + 2.28395I
b = 0.542663 + 0.578885I
−2.36972 − 4.87568I −7.53244 + 9.08177I
u = −0.527284 − 0.639053I
a = −1.03264 − 2.28395I
b = 0.542663 − 0.578885I
−2.36972 + 4.87568I −7.53244 − 9.08177I
u = 0.030219 + 0.770891I
a = 0.89608 − 1.10632I
b = −0.275066 − 1.229750I
8.30714 − 1.03793I −7.10521 − 1.06063I
u = 0.030219 − 0.770891I
a = 0.89608 + 1.10632I
b = −0.275066 + 1.229750I
8.30714 + 1.03793I −7.10521 + 1.06063I
u = 0.441547 + 1.178770I
a = −1.208310 + 0.169945I
b = 0.835779 − 0.722556I
−1.27644 + 3.83272I −8.04046 − 6.78992I
u = 0.441547 − 1.178770I
a = −1.208310 − 0.169945I
b = 0.835779 + 0.722556I
−1.27644 − 3.83272I −8.04046 + 6.78992I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.090717 + 0.687766I
a = −0.811399 − 0.398978I
b = 0.37619 + 1.36678I
1.34686 − 1.58107I −12.80363 + 3.25466I
u = 0.090717 − 0.687766I
a = −0.811399 + 0.398978I
b = 0.37619 − 1.36678I
1.34686 + 1.58107I −12.80363 − 3.25466I
u = 0.186640 + 0.604958I
a = 0.03137 + 1.98200I
b = −0.47824 − 1.53175I
4.32414 − 2.28815I 0.92523 + 2.22693I
u = 0.186640 − 0.604958I
a = 0.03137 − 1.98200I
b = −0.47824 + 1.53175I
4.32414 + 2.28815I 0.92523 − 2.22693I
u = −0.93428 + 1.11326I
a = 0.409560 − 0.526106I
b = −0.240017 − 0.368514I
−5.08793 − 1.14055I −13.57284 + 0.84904I
u = −0.93428 − 1.11326I
a = 0.409560 + 0.526106I
b = −0.240017 + 0.368514I
−5.08793 + 1.14055I −13.57284 − 0.84904I
u = 0.16946 + 1.46145I
a = 0.282355 − 0.799726I
b = −0.323299 + 0.565718I
5.78138 + 1.58656I −4.84957 − 7.40440I
u = 0.16946 − 1.46145I
a = 0.282355 + 0.799726I
b = −0.323299 − 0.565718I
5.78138 − 1.58656I −4.84957 + 7.40440I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 14u
17
+ ··· − 11u + 1)
· (u
54
+ 57u
53
+ ··· + 4309293u + 130321)
c
2
(u
18
− 7u
16
+ ··· + u + 1)(u
54
+ u
53
+ ··· + 1811u − 361)
c
3
(u
18
+ 6u
16
+ ··· − u + 1)(u
54
− u
53
+ ··· − 171u − 37)
c
4
(u
18
− 2u
17
+ ··· − 2u + 1)(u
54
+ 5u
53
+ ··· + 528u + 49)
c
5
, c
6
(u
18
+ 11u
16
+ ··· − 4u + 1)(u
54
+ u
53
+ ··· + 146u − 143)
c
7
(u
18
− 7u
16
+ ··· − u + 1)(u
54
+ u
53
+ ··· + 1811u − 361)
c
8
(u
18
− 2u
17
+ ··· − 3u + 1)(u
54
+ 3u
53
+ ··· − 53u − 11)
c
9
(u
18
+ 6u
16
+ ··· + u + 1)(u
54
− u
53
+ ··· − 171u − 37)
c
10
(u
18
+ 11u
16
+ ··· + 4u + 1)(u
54
+ u
53
+ ··· + 146u − 143)
c
11
(u
18
− u
17
+ ··· − 11u
2
+ 1)(u
54
− 6u
52
+ ··· − 2734u + 439)
c
12
(u
18
+ 2u
17
+ ··· + 2u + 1)(u
54
+ 5u
53
+ ··· + 528u + 49)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 22y
17
+ ··· + y + 1)
· (y
54
− 121y
53
+ ··· + 1173617520891y + 16983563041)
c
2
, c
7
(y
18
− 14y
17
+ ··· − 11y + 1)
· (y
54
− 57y
53
+ ··· − 4309293y + 130321)
c
3
, c
9
(y
18
+ 12y
17
+ ··· + 11y + 1)(y
54
− 3y
53
+ ··· − 82743y + 1369)
c
4
, c
12
(y
18
+ 10y
17
+ ··· + 14y + 1)(y
54
+ 43y
53
+ ··· − 40056y + 2401)
c
5
, c
6
, c
10
(y
18
+ 22y
17
+ ··· + 14y + 1)(y
54
+ 43y
53
+ ··· + 236656y + 20449)
c
8
(y
18
+ 12y
17
+ ··· + 11y + 1)(y
54
+ 17y
53
+ ··· + 1393y + 121)
c
11
(y
18
− y
17
+ ··· − 22y + 1)(y
54
− 12y
53
+ ··· − 2068032y + 192721)
17
