12a
1014
(K12a
1014
)
A knot diagram
1
Linearized knot diagam
4 6 1 9 10 11 12 3 5 2 8 7
Solving Sequence
5,10 2,6
3 11 7 9 4 1 8 12
c
5
c
2
c
10
c
6
c
9
c
4
c
1
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.48028 × 10
137
u
87
− 1.90470 × 10
137
u
86
+ ··· + 7.25646 × 10
137
b + 2.50630 × 10
137
,
2.11941 × 10
137
u
87
+ 7.24817 × 10
137
u
86
+ ··· + 7.25646 × 10
137
a − 8.34303 × 10
136
, u
88
+ 2u
87
+ ··· + 4u
2
+ 1i
I
u
2
= h7b − u + 2, 7a − 3u − 1, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 90 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−2.48 × 10
137
u
87
− 1.90 × 10
137
u
86
+ · · · + 7.26 × 10
137
b + 2.51 ×
10
137
, 2.12 × 10
137
u
87
+ 7.25 × 10
137
u
86
+ · · · + 7.26 × 10
137
a − 8.34 ×
10
136
, u
88
+ 2u
87
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−0.292072u
87
− 0.998857u
86
+ ··· + 4.58008u + 0.114974
0.341803u
87
+ 0.262483u
86
+ ··· − 0.159539u − 0.345389
a
6
=
1
−u
2
a
3
=
−0.264668u
87
− 0.894639u
86
+ ··· + 4.71261u + 0.184298
0.325117u
87
+ 0.233773u
86
+ ··· − 0.132136u − 0.295978
a
11
=
−0.138518u
87
+ 2.23892u
86
+ ··· − 0.340831u − 3.88428
3.10091u
87
+ 1.52591u
86
+ ··· − 1.72649u + 2.45169
a
7
=
−0.963044u
87
− 0.180143u
86
+ ··· + 3.28975u + 3.23650
2.30375u
87
+ 1.20769u
86
+ ··· − 1.34975u + 1.52417
a
9
=
−u
u
a
4
=
−u
2
+ 1
u
2
a
1
=
−0.215669u
87
− 0.801951u
86
+ ··· + 4.52640u − 1.04103
0.321531u
87
+ 0.203061u
86
+ ··· − 0.215669u − 0.370612
a
8
=
2.84777u
87
+ 3.42425u
86
+ ··· − 8.89289u − 1.49021
−3.51383u
87
− 2.67370u
86
+ ··· + 1.69517u − 2.18337
a
12
=
0.209783u
87
+ 1.31979u
86
+ ··· + 1.71885u − 2.35314
1.79542u
87
+ 1.30105u
86
+ ··· − 0.315595u + 1.00197
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.67403u
87
− 4.82309u
86
+ ··· − 7.57749u − 3.42504
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
88
− 3u
87
+ ··· − 295u + 49
c
2
u
88
− 7u
87
+ ··· − 980u + 196
c
4
, c
5
, c
9
u
88
+ 2u
87
+ ··· + 4u
2
+ 1
c
6
u
88
− 2u
87
+ ··· − 218u + 65
c
7
, c
11
, c
12
u
88
+ 2u
87
+ ··· + 2u + 1
c
8
7(7u
88
− 36u
87
+ ··· − 40832u + 4553)
c
10
7(7u
88
+ 71u
87
+ ··· + 449u + 1459)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
88
− 53y
87
+ ··· − 18915y + 2401
c
2
y
88
− 15y
87
+ ··· − 201880y + 38416
c
4
, c
5
, c
9
y
88
− 82y
87
+ ··· + 8y + 1
c
6
y
88
− 34y
87
+ ··· + 196616y + 4225
c
7
, c
11
, c
12
y
88
+ 74y
87
+ ··· + 8y + 1
c
8
49(49y
88
+ 3926y
87
+ ··· − 8.10942 × 10
8
y + 2.07298 × 10
7
)
c
10
49(49y
88
+ 4003y
87
+ ··· − 2854063y + 2128681)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465025 + 0.870255I
a = 0.208785 + 1.159280I
b = 0.309065 − 0.370721I
−2.82358 + 4.12952I 0
u = 0.465025 − 0.870255I
a = 0.208785 − 1.159280I
b = 0.309065 + 0.370721I
−2.82358 − 4.12952I 0
u = 0.678542 + 0.774022I
a = −0.907312 + 0.128470I
b = 0.806388 + 0.235769I
0.40735 − 7.71051I 0
u = 0.678542 − 0.774022I
a = −0.907312 − 0.128470I
b = 0.806388 − 0.235769I
0.40735 + 7.71051I 0
u = −0.474169 + 0.840049I
a = 0.241987 − 1.390130I
b = 0.299699 + 0.471165I
−5.23953 − 8.76456I 0
u = −0.474169 − 0.840049I
a = 0.241987 + 1.390130I
b = 0.299699 − 0.471165I
−5.23953 + 8.76456I 0
u = 0.475214 + 0.823836I
a = 0.31410 + 1.52013I
b = 0.268780 − 0.528112I
−0.16472 + 13.04760I 0
u = 0.475214 − 0.823836I
a = 0.31410 − 1.52013I
b = 0.268780 + 0.528112I
−0.16472 − 13.04760I 0
u = 0.224097 + 1.032390I
a = 0.478233 + 0.326886I
b = 0.155332 − 0.081088I
−1.55925 + 2.49981I 0
u = 0.224097 − 1.032390I
a = 0.478233 − 0.326886I
b = 0.155332 + 0.081088I
−1.55925 − 2.49981I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.709608 + 0.809911I
a = −0.732695 − 0.187189I
b = 0.708824 − 0.197729I
−4.61019 + 3.28116I 0
u = −0.709608 − 0.809911I
a = −0.732695 + 0.187189I
b = 0.708824 + 0.197729I
−4.61019 − 3.28116I 0
u = −0.355788 + 0.802924I
a = 0.877968 − 0.955168I
b = 0.043536 + 0.303056I
5.68213 − 4.42760I 0
u = −0.355788 − 0.802924I
a = 0.877968 + 0.955168I
b = 0.043536 − 0.303056I
5.68213 + 4.42760I 0
u = 0.807583 + 0.884999I
a = −0.454813 + 0.140604I
b = 0.533679 + 0.217858I
−2.00805 + 1.65292I 0
u = 0.807583 − 0.884999I
a = −0.454813 − 0.140604I
b = 0.533679 − 0.217858I
−2.00805 − 1.65292I 0
u = −0.590432 + 0.529783I
a = −0.598808 + 0.811973I
b = 0.588467 − 0.662727I
6.79240 + 0.03358I 6.01227 + 1.06957I
u = −0.590432 − 0.529783I
a = −0.598808 − 0.811973I
b = 0.588467 + 0.662727I
6.79240 − 0.03358I 6.01227 − 1.06957I
u = −1.248020 + 0.027660I
a = 0.971817 + 0.039767I
b = 0.385149 + 0.317525I
1.89898 − 3.61624I 0
u = −1.248020 − 0.027660I
a = 0.971817 − 0.039767I
b = 0.385149 − 0.317525I
1.89898 + 3.61624I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25038
a = 1.00048
b = 0.302083
−2.00769 0
u = 0.428355 + 0.546083I
a = −0.42999 − 1.60423I
b = 0.289935 + 1.063610I
3.81209 + 7.45383I 1.39315 − 8.57538I
u = 0.428355 − 0.546083I
a = −0.42999 + 1.60423I
b = 0.289935 − 1.063610I
3.81209 − 7.45383I 1.39315 + 8.57538I
u = 1.313290 + 0.118441I
a = 0.193456 + 0.100801I
b = 0.78076 − 1.74527I
2.98306 + 0.50959I 0
u = 1.313290 − 0.118441I
a = 0.193456 − 0.100801I
b = 0.78076 + 1.74527I
2.98306 − 0.50959I 0
u = −1.331540 + 0.136013I
a = −0.065593 − 0.153457I
b = 0.93450 + 1.99969I
−0.39006 − 4.02805I 0
u = −1.331540 − 0.136013I
a = −0.065593 + 0.153457I
b = 0.93450 − 1.99969I
−0.39006 + 4.02805I 0
u = −0.411528 + 0.511958I
a = −0.21256 + 1.56445I
b = 0.162302 − 0.967337I
−1.04299 − 3.88125I −3.63273 + 8.23421I
u = −0.411528 − 0.511958I
a = −0.21256 − 1.56445I
b = 0.162302 + 0.967337I
−1.04299 + 3.88125I −3.63273 − 8.23421I
u = 1.340780 + 0.150050I
a = −0.236604 + 0.147537I
b = 1.04400 − 2.12368I
3.97725 + 7.70239I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.340780 − 0.150050I
a = −0.236604 − 0.147537I
b = 1.04400 + 2.12368I
3.97725 − 7.70239I 0
u = 1.365900 + 0.082318I
a = 0.164386 + 0.923797I
b = 0.34928 − 2.67036I
2.94649 + 2.04332I 0
u = 1.365900 − 0.082318I
a = 0.164386 − 0.923797I
b = 0.34928 + 2.67036I
2.94649 − 2.04332I 0
u = −1.369380 + 0.013705I
a = 2.54977 − 0.95313I
b = −4.25386 + 2.03407I
2.02967 − 0.01294I 0
u = −1.369380 − 0.013705I
a = 2.54977 + 0.95313I
b = −4.25386 − 2.03407I
2.02967 + 0.01294I 0
u = 0.470844 + 0.373071I
a = 0.094395 − 0.945702I
b = 0.220554 + 0.530322I
0.905268 + 0.924263I 4.02456 − 3.18187I
u = 0.470844 − 0.373071I
a = 0.094395 + 0.945702I
b = 0.220554 − 0.530322I
0.905268 − 0.924263I 4.02456 + 3.18187I
u = 0.302426 + 0.510200I
a = 1.92897 + 0.17179I
b = −0.256677 − 0.037097I
3.59262 − 4.05238I 1.82011 + 0.64734I
u = 0.302426 − 0.510200I
a = 1.92897 − 0.17179I
b = −0.256677 + 0.037097I
3.59262 + 4.05238I 1.82011 − 0.64734I
u = −1.368850 + 0.325549I
a = −0.276046 + 0.686310I
b = 0.70201 − 1.59031I
8.47086 + 0.96250I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.368850 − 0.325549I
a = −0.276046 − 0.686310I
b = 0.70201 + 1.59031I
8.47086 − 0.96250I 0
u = 1.409890 + 0.029155I
a = −0.65909 + 5.45104I
b = 1.81784 − 11.09350I
6.42235 − 2.77134I 0
u = 1.409890 − 0.029155I
a = −0.65909 − 5.45104I
b = 1.81784 + 11.09350I
6.42235 + 2.77134I 0
u = −1.42533 + 0.08102I
a = −0.911301 − 0.787379I
b = 1.90182 + 2.04497I
7.54516 − 3.10813I 0
u = −1.42533 − 0.08102I
a = −0.911301 + 0.787379I
b = 1.90182 − 2.04497I
7.54516 + 3.10813I 0
u = 0.320807 + 0.471107I
a = 0.23879 − 1.74609I
b = −0.233979 + 0.856786I
1.63354 + 0.85045I −1.53895 − 5.23910I
u = 0.320807 − 0.471107I
a = 0.23879 + 1.74609I
b = −0.233979 − 0.856786I
1.63354 − 0.85045I −1.53895 + 5.23910I
u = −1.44185 + 0.14310I
a = −0.570195 − 0.619847I
b = 0.69295 + 2.11347I
7.32098 − 3.04286I 0
u = −1.44185 − 0.14310I
a = −0.570195 + 0.619847I
b = 0.69295 − 2.11347I
7.32098 + 3.04286I 0
u = −0.154069 + 0.519282I
a = 0.60767 + 1.59884I
b = −1.070580 − 0.771606I
−0.68368 − 5.30063I −6.18473 + 7.46843I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154069 − 0.519282I
a = 0.60767 − 1.59884I
b = −1.070580 + 0.771606I
−0.68368 + 5.30063I −6.18473 − 7.46843I
u = 1.46093 + 0.18393I
a = −0.577303 + 0.740047I
b = 0.18603 − 2.36742I
5.02748 + 6.44830I 0
u = 1.46093 − 0.18393I
a = −0.577303 − 0.740047I
b = 0.18603 + 2.36742I
5.02748 − 6.44830I 0
u = −1.46509 + 0.19462I
a = −0.579534 − 0.802604I
b = 0.04047 + 2.47187I
9.9418 − 10.1764I 0
u = −1.46509 − 0.19462I
a = −0.579534 + 0.802604I
b = 0.04047 − 2.47187I
9.9418 + 10.1764I 0
u = 0.122670 + 0.505532I
a = 0.52604 − 1.34952I
b = −1.130960 + 0.595578I
−4.89818 + 1.73906I −12.21356 − 4.35527I
u = 0.122670 − 0.505532I
a = 0.52604 + 1.34952I
b = −1.130960 − 0.595578I
−4.89818 − 1.73906I −12.21356 + 4.35527I
u = −1.47349 + 0.15116I
a = −0.509337 − 0.629558I
b = 0.34252 + 1.90298I
7.23343 − 2.97184I 0
u = −1.47349 − 0.15116I
a = −0.509337 + 0.629558I
b = 0.34252 − 1.90298I
7.23343 + 2.97184I 0
u = −0.079421 + 0.507840I
a = 0.548744 + 0.934759I
b = −1.259470 − 0.407517I
−1.26799 + 1.70875I −7.72525 − 0.49338I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.079421 − 0.507840I
a = 0.548744 − 0.934759I
b = −1.259470 + 0.407517I
−1.26799 − 1.70875I −7.72525 + 0.49338I
u = 1.43573 + 0.38529I
a = −0.007478 − 0.595504I
b = 0.08476 + 1.51582I
2.71814 + 2.73664I 0
u = 1.43573 − 0.38529I
a = −0.007478 + 0.595504I
b = 0.08476 − 1.51582I
2.71814 − 2.73664I 0
u = −0.269583 + 0.412174I
a = 1.78564 + 0.30892I
b = −0.214649 − 0.070213I
−1.25437 + 0.85817I −4.51635 − 0.02662I
u = −0.269583 − 0.412174I
a = 1.78564 − 0.30892I
b = −0.214649 + 0.070213I
−1.25437 − 0.85817I −4.51635 + 0.02662I
u = 1.48155 + 0.30360I
a = 0.245807 − 1.043490I
b = −0.22891 + 2.56472I
11.6500 + 8.4676I 0
u = 1.48155 − 0.30360I
a = 0.245807 + 1.043490I
b = −0.22891 − 2.56472I
11.6500 − 8.4676I 0
u = 1.50563 + 0.17910I
a = −0.348456 + 0.721440I
b = −0.27315 − 1.84088I
13.58050 + 2.56939I 0
u = 1.50563 − 0.17910I
a = −0.348456 − 0.721440I
b = −0.27315 + 1.84088I
13.58050 − 2.56939I 0
u = 1.52367
a = −0.523082
b = 0.691833
4.13126 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48453 + 0.34451I
a = 0.225794 + 0.730825I
b = −0.33907 − 1.91530I
4.19421 − 7.28551I 0
u = −1.48453 − 0.34451I
a = 0.225794 − 0.730825I
b = −0.33907 + 1.91530I
4.19421 + 7.28551I 0
u = 0.346362 + 0.322667I
a = 2.52356 − 1.29399I
b = −0.324707 + 0.186840I
1.98288 + 1.74756I −0.63361 − 6.31369I
u = 0.346362 − 0.322667I
a = 2.52356 + 1.29399I
b = −0.324707 − 0.186840I
1.98288 − 1.74756I −0.63361 + 6.31369I
u = −1.51013 + 0.31460I
a = 0.512292 + 0.870667I
b = −0.85109 − 2.34807I
3.54515 − 8.41526I 0
u = −1.51013 − 0.31460I
a = 0.512292 − 0.870667I
b = −0.85109 + 2.34807I
3.54515 + 8.41526I 0
u = −1.51365 + 0.29904I
a = 0.637562 + 1.039300I
b = −1.01287 − 2.74790I
6.2721 − 17.1376I 0
u = −1.51365 − 0.29904I
a = 0.637562 − 1.039300I
b = −1.01287 + 2.74790I
6.2721 + 17.1376I 0
u = 1.51356 + 0.30479I
a = 0.604525 − 0.961803I
b = −0.98748 + 2.57780I
1.18596 + 12.92690I 0
u = 1.51356 − 0.30479I
a = 0.604525 + 0.961803I
b = −0.98748 − 2.57780I
1.18596 − 12.92690I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.410125 + 0.089016I
a = 5.23763 + 1.01500I
b = −0.285000 − 0.082453I
0.82913 + 3.21823I 9.71233 + 3.98519I
u = −0.410125 − 0.089016I
a = 5.23763 − 1.01500I
b = −0.285000 + 0.082453I
0.82913 − 3.21823I 9.71233 − 3.98519I
u = 1.58966
a = −0.306266
b = 0.155878
4.11849 0
u = 0.374898
a = 6.14886
b = −0.307864
−3.21214 11.9970
u = −1.61970 + 0.13613I
a = −0.090455 − 0.279218I
b = −0.411048 + 0.524774I
8.41962 + 4.25598I 0
u = −1.61970 − 0.13613I
a = −0.090455 + 0.279218I
b = −0.411048 − 0.524774I
8.41962 − 4.25598I 0
u = −0.132203 + 0.327967I
a = −0.85319 + 2.73462I
b = −0.650413 − 0.230842I
−1.78272 − 0.58271I −5.55303 − 2.81973I
u = −0.132203 − 0.327967I
a = −0.85319 − 2.73462I
b = −0.650413 + 0.230842I
−1.78272 + 0.58271I −5.55303 + 2.81973I
13
II. I
u
2
= h7b − u + 2, 7a − 3u − 1, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
3
7
u +
1
7
1
7
u −
2
7
a
6
=
1
u + 1
a
3
=
3
7
u +
1
7
1
7
u −
2
7
a
11
=
5
49
u −
3
49
46
49
u −
8
49
a
7
=
−
8
49
u +
44
49
−
5
49
u +
3
49
a
9
=
−u
u
a
4
=
u + 2
−u − 1
a
1
=
−
4
7
u −
13
7
8
7
u +
5
7
a
8
=
−
47
49
u −
11
49
38
49
u −
13
49
a
12
=
16
49
u −
39
49
59
49
u +
43
49
(ii) Obstruction class = 1
(iii) Cusp Shapes =
52
49
u +
155
49
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
u
2
c
3
(u + 1)
2
c
4
, c
5
, c
6
c
11
, c
12
u
2
+ u + 1
c
7
, c
9
u
2
− u + 1
c
8
7(7u
2
− 3u + 3)
c
10
7(7u
2
− 4u + 1)
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
2
c
2
y
2
c
4
, c
5
, c
6
c
7
, c
9
, c
11
c
12
y
2
+ y + 1
c
8
49(49y
2
+ 33y + 9)
c
10
49(49y
2
− 2y + 1)
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.071429 + 0.371154I
b = −0.357143 + 0.123718I
−1.64493 − 2.02988I 2.63265 + 0.91905I
u = −0.500000 − 0.866025I
a = −0.071429 − 0.371154I
b = −0.357143 − 0.123718I
−1.64493 + 2.02988I 2.63265 − 0.91905I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
88
− 3u
87
+ ··· − 295u + 49)
c
2
u
2
(u
88
− 7u
87
+ ··· − 980u + 196)
c
3
((u + 1)
2
)(u
88
− 3u
87
+ ··· − 295u + 49)
c
4
, c
5
(u
2
+ u + 1)(u
88
+ 2u
87
+ ··· + 4u
2
+ 1)
c
6
(u
2
+ u + 1)(u
88
− 2u
87
+ ··· − 218u + 65)
c
7
(u
2
− u + 1)(u
88
+ 2u
87
+ ··· + 2u + 1)
c
8
49(7u
2
− 3u + 3)(7u
88
− 36u
87
+ ··· − 40832u + 4553)
c
9
(u
2
− u + 1)(u
88
+ 2u
87
+ ··· + 4u
2
+ 1)
c
10
49(7u
2
− 4u + 1)(7u
88
+ 71u
87
+ ··· + 449u + 1459)
c
11
, c
12
(u
2
+ u + 1)(u
88
+ 2u
87
+ ··· + 2u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
2
)(y
88
− 53y
87
+ ··· − 18915y + 2401)
c
2
y
2
(y
88
− 15y
87
+ ··· − 201880y + 38416)
c
4
, c
5
, c
9
(y
2
+ y + 1)(y
88
− 82y
87
+ ··· + 8y + 1)
c
6
(y
2
+ y + 1)(y
88
− 34y
87
+ ··· + 196616y + 4225)
c
7
, c
11
, c
12
(y
2
+ y + 1)(y
88
+ 74y
87
+ ··· + 8y + 1)
c
8
2401(49y
2
+ 33y + 9)
· (49y
88
+ 3926y
87
+ ··· − 810942196y + 20729809)
c
10
2401(49y
2
− 2y + 1)(49y
88
+ 4003y
87
+ ··· − 2854063y + 2128681)
19
