12a
0148
(K12a
0148
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 12 1 4 8 7 6
Solving Sequence
3,9
4
5,10
6 2 1 8 11 12 7
c
3
c
9
c
5
c
2
c
1
c
8
c
10
c
12
c
7
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.42539 × 10
200
u
87
3.64946 × 10
199
u
86
+ ··· + 1.99958 × 10
199
b + 9.22932 × 10
202
,
3.50341 × 10
201
u
87
+ 1.47839 × 10
201
u
86
+ ··· + 1.59966 × 10
200
a + 1.35973 × 10
204
,
u
88
+ u
87
+ ··· + 896u + 256i
I
v
1
= ha, b 1, v
8
v
7
v
6
+ 2v
5
+ v
4
2v
3
+ 2v 1i
* 2 irreducible components of dim
C
= 0, with total 96 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
= h4.43 × 10
200
u
87
3.65 × 10
199
u
86
+ · · · + 2.00 × 10
199
b + 9.23 ×
10
202
, 3.50 × 10
201
u
87
+ 1.48 × 10
201
u
86
+ · · · + 1.60 × 10
200
a + 1.36 ×
10
204
, u
88
+ u
87
+ · · · + 896u + 256i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
21.9009u
87
9.24189u
86
+ ··· 17882.8u 8500.07
22.1316u
87
+ 1.82512u
86
+ ··· 13328.4u 4615.63
a
10
=
u
u
3
+ u
a
6
=
36.3315u
87
7.56623u
86
+ ··· 26362.6u 11326.7
20.1398u
87
+ 4.15579u
86
+ ··· 11071.2u 3319.07
a
2
=
21.9009u
87
9.24189u
86
+ ··· 17882.8u 8500.07
27.4223u
87
+ 3.72173u
86
+ ··· + 19064.3u + 7856.34
a
1
=
5.52139u
87
5.52016u
86
+ ··· + 1181.43u 643.728
27.4223u
87
+ 3.72173u
86
+ ··· + 19064.3u + 7856.34
a
8
=
57.6042u
87
9.93484u
86
+ ··· 40728.9u 17176.4
9.77552u
87
+ 1.20789u
86
+ ··· 5709.00u 1880.73
a
11
=
10.1990u
87
4.09790u
86
+ ··· + 4767.62u + 1155.77
16.1258u
87
3.46355u
86
+ ··· 11668.8u 5093.69
a
12
=
22.0367u
87
6.36866u
86
+ ··· + 11313.4u + 3063.28
4.70307u
87
3.57832u
86
+ ··· 4496.61u 2419.16
a
7
=
69.8135u
87
16.6900u
86
+ ··· 51473.6u 22702.9
35.6897u
87
+ 7.12445u
86
+ ··· 19702.9u 5719.85
(ii) Obstruction class = 1
(iii) Cusp Shapes = 61.0516u
87
11.3428u
86
+ ··· 43625.8u 18291.7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 39u
87
+ ··· + 48u + 1
c
2
, c
4
u
88
9u
87
+ ··· 16u + 1
c
3
, c
9
u
88
u
87
+ ··· 896u + 256
c
5
, c
8
u
88
+ 2u
87
+ ··· + 7868u + 1960
c
6
, c
7
, c
11
u
88
2u
87
+ ··· + 2u
2
+ 1
c
10
, c
12
u
88
+ 6u
87
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 29y
87
+ ··· 2128y + 1
c
2
, c
4
y
88
39y
87
+ ··· 48y + 1
c
3
, c
9
y
88
51y
87
+ ··· 1949696y + 65536
c
5
, c
8
y
88
66y
87
+ ··· + 35490896y + 3841600
c
6
, c
7
, c
11
y
88
74y
87
+ ··· + 4y + 1
c
10
, c
12
y
88
+ 46y
87
+ ··· + 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.00435
a = 0.429782
b = 1.32676
6.57645 0
u = 1.001690 + 0.149224I
a = 0.429739 + 0.012969I
b = 1.324880 0.070161I
2.39022 7.28873I 0
u = 1.001690 0.149224I
a = 0.429739 0.012969I
b = 1.324880 + 0.070161I
2.39022 + 7.28873I 0
u = 0.957734 + 0.153558I
a = 0.433584 0.013510I
b = 1.304120 + 0.071792I
2.38943 + 3.43455I 0
u = 0.957734 0.153558I
a = 0.433584 + 0.013510I
b = 1.304120 0.071792I
2.38943 3.43455I 0
u = 0.219203 + 1.015630I
a = 0.500350 + 0.146984I
b = 0.839830 0.540473I
1.67070 + 2.16357I 0
u = 0.219203 1.015630I
a = 0.500350 0.146984I
b = 0.839830 + 0.540473I
1.67070 2.16357I 0
u = 1.031030 + 0.152271I
a = 0.58647 + 1.56663I
b = 0.790418 0.559855I
1.37194 0.87864I 0
u = 1.031030 0.152271I
a = 0.58647 1.56663I
b = 0.790418 + 0.559855I
1.37194 + 0.87864I 0
u = 0.098155 + 1.040920I
a = 0.515677 0.169679I
b = 0.749756 + 0.575742I
0.582374 + 1.270130I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.098155 1.040920I
a = 0.515677 + 0.169679I
b = 0.749756 0.575742I
0.582374 1.270130I 0
u = 0.576718 + 0.732950I
a = 0.466275 0.078251I
b = 1.085910 + 0.350059I
1.59869 4.94887I 0
u = 0.576718 0.732950I
a = 0.466275 + 0.078251I
b = 1.085910 0.350059I
1.59869 + 4.94887I 0
u = 0.305706 + 1.023880I
a = 0.486178 + 0.137784I
b = 0.903940 0.539582I
1.49354 + 2.08175I 0
u = 0.305706 1.023880I
a = 0.486178 0.137784I
b = 0.903940 + 0.539582I
1.49354 2.08175I 0
u = 0.977964 + 0.448688I
a = 0.00055 1.99302I
b = 1.000140 + 0.501752I
0.69091 + 1.55122I 0
u = 0.977964 0.448688I
a = 0.00055 + 1.99302I
b = 1.000140 0.501752I
0.69091 1.55122I 0
u = 0.087736 + 1.086640I
a = 0.509047 + 0.178283I
b = 0.749823 0.612838I
4.24013 5.02346I 0
u = 0.087736 1.086640I
a = 0.509047 0.178283I
b = 0.749823 + 0.612838I
4.24013 + 5.02346I 0
u = 0.601343 + 0.667675I
a = 0.464910 + 0.069332I
b = 1.104160 0.313793I
5.59798 + 1.13427I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.601343 0.667675I
a = 0.464910 0.069332I
b = 1.104160 + 0.313793I
5.59798 1.13427I 0
u = 0.647327 + 0.605586I
a = 0.460593 0.060958I
b = 1.133740 + 0.282394I
1.76809 + 2.65293I 0
u = 0.647327 0.605586I
a = 0.460593 + 0.060958I
b = 1.133740 0.282394I
1.76809 2.65293I 0
u = 1.007440 + 0.484362I
a = 0.08958 + 1.91917I
b = 1.024270 0.519926I
4.28846 5.63711I 0
u = 1.007440 0.484362I
a = 0.08958 1.91917I
b = 1.024270 + 0.519926I
4.28846 + 5.63711I 0
u = 1.096010 + 0.287738I
a = 0.28422 1.63973I
b = 0.897374 + 0.592068I
1.01324 + 3.73408I 0
u = 1.096010 0.287738I
a = 0.28422 + 1.63973I
b = 0.897374 0.592068I
1.01324 3.73408I 0
u = 0.213348 + 1.117470I
a = 0.487187 0.162434I
b = 0.847254 + 0.615896I
8.14434 2.42174I 0
u = 0.213348 1.117470I
a = 0.487187 + 0.162434I
b = 0.847254 0.615896I
8.14434 + 2.42174I 0
u = 0.322387 + 1.091330I
a = 0.476315 0.145185I
b = 0.920976 + 0.585529I
1.11718 5.91216I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.322387 1.091330I
a = 0.476315 + 0.145185I
b = 0.920976 0.585529I
1.11718 + 5.91216I 0
u = 0.859307
a = 0.442580
b = 1.25948
0.232477 11.3810
u = 0.830025 + 0.174817I
a = 0.445016 + 0.015816I
b = 1.244270 0.079764I
0.314091 + 0.198621I 0
u = 0.830025 0.174817I
a = 0.445016 0.015816I
b = 1.244270 + 0.079764I
0.314091 0.198621I 0
u = 1.032070 + 0.514380I
a = 0.15414 1.85794I
b = 1.044350 + 0.534552I
0.12676 + 9.73288I 0
u = 1.032070 0.514380I
a = 0.15414 + 1.85794I
b = 1.044350 0.534552I
0.12676 9.73288I 0
u = 0.051824 + 0.840631I
a = 0.562713 + 0.136610I
b = 0.678195 0.407415I
2.05221 + 1.93040I 6.00000 3.49207I
u = 0.051824 0.840631I
a = 0.562713 0.136610I
b = 0.678195 + 0.407415I
2.05221 1.93040I 6.00000 + 3.49207I
u = 0.823823 + 0.171820I
a = 1.08150 + 2.00827I
b = 0.792131 0.385999I
0.29466 2.12175I 6.00000 + 4.57537I
u = 0.823823 0.171820I
a = 1.08150 2.00827I
b = 0.792131 + 0.385999I
0.29466 + 2.12175I 6.00000 4.57537I
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.164840 + 0.015673I
a = 0.519545 1.240270I
b = 0.712673 + 0.685914I
6.62329 0.64955I 0
u = 1.164840 0.015673I
a = 0.519545 + 1.240270I
b = 0.712673 0.685914I
6.62329 + 0.64955I 0
u = 0.322346 + 1.120770I
a = 0.472940 + 0.148909I
b = 0.923722 0.605700I
3.70264 + 9.83487I 0
u = 0.322346 1.120770I
a = 0.472940 0.148909I
b = 0.923722 + 0.605700I
3.70264 9.83487I 0
u = 0.691641 + 0.455798I
a = 0.853629 0.525545I
b = 0.150516 + 0.522993I
1.87270 5.60259I 6.00000 + 6.15186I
u = 0.691641 0.455798I
a = 0.853629 + 0.525545I
b = 0.150516 0.522993I
1.87270 + 5.60259I 6.00000 6.15186I
u = 0.776541 + 0.121597I
a = 1.41349 1.89153I
b = 0.746497 + 0.339237I
2.93128 1.87221I 6.00000 + 0.I
u = 0.776541 0.121597I
a = 1.41349 + 1.89153I
b = 0.746497 0.339237I
2.93128 + 1.87221I 6.00000 + 0.I
u = 0.735694 + 0.094036I
a = 1.70267 + 1.78739I
b = 0.720592 0.293311I
1.54881 + 5.88294I 11.49151 1.84085I
u = 0.735694 0.094036I
a = 1.70267 1.78739I
b = 0.720592 + 0.293311I
1.54881 5.88294I 11.49151 + 1.84085I
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.226590 + 0.300164I
a = 0.16868 + 1.45270I
b = 0.921134 0.679217I
6.02695 5.91537I 0
u = 1.226590 0.300164I
a = 0.16868 1.45270I
b = 0.921134 + 0.679217I
6.02695 + 5.91537I 0
u = 0.569700 + 0.462149I
a = 0.874864 + 0.418521I
b = 0.069835 0.444976I
2.39619 + 1.83979I 5.06407 4.03961I
u = 0.569700 0.462149I
a = 0.874864 0.418521I
b = 0.069835 + 0.444976I
2.39619 1.83979I 5.06407 + 4.03961I
u = 0.427991 + 0.540581I
a = 0.816176 0.306811I
b = 0.073526 + 0.403552I
1.16464 + 1.76346I 8.83454 + 0.17315I
u = 0.427991 0.540581I
a = 0.816176 + 0.306811I
b = 0.073526 0.403552I
1.16464 1.76346I 8.83454 0.17315I
u = 1.301580 + 0.388579I
a = 0.479272 + 0.832451I
b = 0.480564 0.902214I
6.52418 + 2.29472I 0
u = 1.301580 0.388579I
a = 0.479272 0.832451I
b = 0.480564 + 0.902214I
6.52418 2.29472I 0
u = 1.320800 + 0.324605I
a = 0.463895 + 0.875320I
b = 0.527305 0.891925I
6.81647 + 2.12430I 0
u = 1.320800 0.324605I
a = 0.463895 0.875320I
b = 0.527305 + 0.891925I
6.81647 2.12430I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.357440 + 0.262000I
a = 0.430943 0.915034I
b = 0.578746 + 0.894462I
4.81467 + 1.57988I 0
u = 1.357440 0.262000I
a = 0.430943 + 0.915034I
b = 0.578746 0.894462I
4.81467 1.57988I 0
u = 1.327820 + 0.430064I
a = 0.462500 0.806106I
b = 0.464521 + 0.933303I
4.02843 6.29523I 0
u = 1.327820 0.430064I
a = 0.462500 + 0.806106I
b = 0.464521 0.933303I
4.02843 + 6.29523I 0
u = 0.601538
a = 1.84428
b = 0.457784
5.87336 17.3130
u = 1.29156 + 0.57696I
a = 0.20838 + 1.42034I
b = 1.101120 0.689224I
5.07279 7.95878I 0
u = 1.29156 0.57696I
a = 0.20838 1.42034I
b = 1.101120 + 0.689224I
5.07279 + 7.95878I 0
u = 1.31363 + 0.52509I
a = 0.143157 1.398570I
b = 1.072430 + 0.707601I
3.30771 + 4.32222I 0
u = 1.31363 0.52509I
a = 0.143157 + 1.398570I
b = 1.072430 0.707601I
3.30771 4.32222I 0
u = 1.27396 + 0.62381I
a = 0.26980 + 1.43160I
b = 1.127130 0.674560I
4.55871 8.10417I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.27396 0.62381I
a = 0.26980 1.43160I
b = 1.127130 + 0.674560I
4.55871 + 8.10417I 0
u = 1.39560 + 0.25845I
a = 0.404256 + 0.910869I
b = 0.592938 0.917193I
9.80224 5.29054I 0
u = 1.39560 0.25845I
a = 0.404256 0.910869I
b = 0.592938 + 0.917193I
9.80224 + 5.29054I 0
u = 1.34834 + 0.44357I
a = 0.450169 + 0.798043I
b = 0.463781 0.950589I
8.92156 + 10.27380I 0
u = 1.34834 0.44357I
a = 0.450169 0.798043I
b = 0.463781 + 0.950589I
8.92156 10.27380I 0
u = 1.38667 + 0.36184I
a = 0.423626 0.845767I
b = 0.526559 + 0.945222I
13.55820 2.57088I 0
u = 1.38667 0.36184I
a = 0.423626 + 0.845767I
b = 0.526559 0.945222I
13.55820 + 2.57088I 0
u = 0.231987 + 0.508335I
a = 0.516989 0.041592I
b = 0.921836 + 0.154614I
1.61463 0.56356I 2.54529 + 2.25978I
u = 0.231987 0.508335I
a = 0.516989 + 0.041592I
b = 0.921836 0.154614I
1.61463 + 0.56356I 2.54529 2.25978I
u = 1.28815 + 0.64947I
a = 0.29632 1.40690I
b = 1.143350 + 0.680591I
1.95879 + 12.20550I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.28815 0.64947I
a = 0.29632 + 1.40690I
b = 1.143350 0.680591I
1.95879 12.20550I 0
u = 1.34931 + 0.52189I
a = 0.138486 + 1.357150I
b = 1.074410 0.729244I
8.33102 0.74805I 0
u = 1.34931 0.52189I
a = 0.138486 1.357150I
b = 1.074410 + 0.729244I
8.33102 + 0.74805I 0
u = 1.30005 + 0.66027I
a = 0.30494 + 1.38969I
b = 1.150650 0.686528I
6.8211 16.2526I 0
u = 1.30005 0.66027I
a = 0.30494 1.38969I
b = 1.150650 + 0.686528I
6.8211 + 16.2526I 0
u = 1.33561 + 0.60551I
a = 0.233965 1.363710I
b = 1.122210 + 0.712327I
11.7348 + 8.6310I 0
u = 1.33561 0.60551I
a = 0.233965 + 1.363710I
b = 1.122210 0.712327I
11.7348 8.6310I 0
u = 0.381782
a = 1.17518
b = 0.149070
0.622395 16.0480
13
II. I
v
1
= ha, b 1, v
8
v
7
v
6
+ 2v
5
+ v
4
2v
3
+ 2v 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
10
=
v
0
a
6
=
v
2
1
a
2
=
1
1
a
1
=
0
1
a
8
=
v
v
a
11
=
v
3
+ v
v
3
a
12
=
v
4
v
2
1
a
7
=
v
7
+ v
6
+ 2v
5
v
4
2v
3
+ 2v
2
+ 2v 1
v
7
+ 2v
5
2v
3
+ 2v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
7
+ v
6
5v
5
+ v
4
+ 4v
3
2v
2
2v + 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u 1)
8
c
3
, c
9
u
8
c
4
(u + 1)
8
c
5
, c
8
u
8
+ u
7
u
6
2u
5
+ u
4
+ 2u
3
2u 1
c
6
, c
7
u
8
u
7
3u
6
+ 2u
5
+ 3u
4
2u 1
c
10
, c
12
u
8
3u
7
+ 7u
6
10u
5
+ 11u
4
10u
3
+ 6u
2
4u + 1
c
11
u
8
+ u
7
3u
6
2u
5
+ 3u
4
+ 2u 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y 1)
8
c
3
, c
9
y
8
c
5
, c
8
y
8
3y
7
+ 7y
6
10y
5
+ 11y
4
10y
3
+ 6y
2
4y + 1
c
6
, c
7
, c
11
y
8
7y
7
+ 19y
6
22y
5
+ 3y
4
+ 14y
3
6y
2
4y + 1
c
10
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
17y
4
34y
3
22y
2
4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
1(vol +
1CS) Cusp shape
v = 0.570868 + 0.730671I
a = 0
b = 1.00000
0.604279 1.131230I 3.90459 + 0.80511I
v = 0.570868 0.730671I
a = 0
b = 1.00000
0.604279 + 1.131230I 3.90459 0.80511I
v = 0.855237 + 0.665892I
a = 0
b = 1.00000
3.80435 2.57849I 0.21961 + 3.88175I
v = 0.855237 0.665892I
a = 0
b = 1.00000
3.80435 + 2.57849I 0.21961 3.88175I
v = 1.09818
a = 0
b = 1.00000
4.85780 7.82890
v = 1.031810 + 0.655470I
a = 0
b = 1.00000
0.73474 + 6.44354I 4.50908 6.04101I
v = 1.031810 0.655470I
a = 0
b = 1.00000
0.73474 6.44354I 4.50908 + 6.04101I
v = 0.603304
a = 0
b = 1.00000
0.799899 4.78300
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u 1)
8
)(u
88
+ 39u
87
+ ··· + 48u + 1)
c
2
((u 1)
8
)(u
88
9u
87
+ ··· 16u + 1)
c
3
, c
9
u
8
(u
88
u
87
+ ··· 896u + 256)
c
4
((u + 1)
8
)(u
88
9u
87
+ ··· 16u + 1)
c
5
, c
8
(u
8
+ u
7
u
6
2u
5
+ u
4
+ 2u
3
2u 1)
· (u
88
+ 2u
87
+ ··· + 7868u + 1960)
c
6
, c
7
(u
8
u
7
3u
6
+ 2u
5
+ 3u
4
2u 1)(u
88
2u
87
+ ··· + 2u
2
+ 1)
c
10
, c
12
(u
8
3u
7
+ 7u
6
10u
5
+ 11u
4
10u
3
+ 6u
2
4u + 1)
· (u
88
+ 6u
87
+ ··· + 4u + 1)
c
11
(u
8
+ u
7
3u
6
2u
5
+ 3u
4
+ 2u 1)(u
88
2u
87
+ ··· + 2u
2
+ 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y 1)
8
)(y
88
+ 29y
87
+ ··· 2128y + 1)
c
2
, c
4
((y 1)
8
)(y
88
39y
87
+ ··· 48y + 1)
c
3
, c
9
y
8
(y
88
51y
87
+ ··· 1949696y + 65536)
c
5
, c
8
(y
8
3y
7
+ 7y
6
10y
5
+ 11y
4
10y
3
+ 6y
2
4y + 1)
· (y
88
66y
87
+ ··· + 35490896y + 3841600)
c
6
, c
7
, c
11
(y
8
7y
7
+ 19y
6
22y
5
+ 3y
4
+ 14y
3
6y
2
4y + 1)
· (y
88
74y
87
+ ··· + 4y + 1)
c
10
, c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
17y
4
34y
3
22y
2
4y + 1)
· (y
88
+ 46y
87
+ ··· + 4y + 1)
19