12a
1013
(K12a
1013
)
A knot diagram
1
Linearized knot diagam
4 6 1 9 10 11 12 3 5 2 7 8
Solving Sequence
4,9
5 10
2,6
11 1 3 8 12 7
c
4
c
9
c
5
c
10
c
1
c
3
c
8
c
12
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.11706 × 10
59
u
58
+ 1.07231 × 10
60
u
57
+ ··· + 4.86975 × 10
59
b + 9.72469 × 10
59
,
− 2.05091 × 10
60
u
58
+ 3.51655 × 10
60
u
57
+ ··· + 4.86975 × 10
59
a + 1.34143 × 10
60
, u
59
− 3u
58
+ ··· + 3u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 59 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−6.12 × 10
59
u
58
+ 1.07 × 10
60
u
57
+ · · · + 4.87 × 10
59
b + 9.72 ×
10
59
, −2.05 × 10
60
u
58
+ 3.52 × 10
60
u
57
+ · · · + 4.87 × 10
59
a + 1.34 ×
10
60
, u
59
− 3u
58
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
4.21152u
58
− 7.22122u
57
+ ··· − 12.4594u − 2.75461
1.25613u
58
− 2.20198u
57
+ ··· − 0.819175u − 1.99696
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
−9.15963u
58
+ 16.8081u
57
+ ··· + 1.60609u + 10.4724
−6.32014u
58
+ 10.8093u
57
+ ··· + 5.10432u + 4.56009
a
1
=
5.46765u
58
− 9.42320u
57
+ ··· − 13.2786u − 4.75157
1.25613u
58
− 2.20198u
57
+ ··· − 0.819175u − 1.99696
a
3
=
4.39790u
58
− 7.52436u
57
+ ··· − 12.3770u − 2.98622
1.32770u
58
− 2.27810u
57
+ ··· − 0.861136u − 2.06309
a
8
=
12.1066u
58
− 24.6727u
57
+ ··· − 15.8303u − 1.97288
4.64955u
58
− 6.59987u
57
+ ··· − 1.46326u − 3.70154
a
12
=
10.5375u
58
− 10.9059u
57
+ ··· − 11.6889u − 15.2433
0.324061u
58
− 0.967105u
57
+ ··· − 0.188037u − 0.274138
a
7
=
8.66021u
58
− 9.05645u
57
+ ··· − 8.23792u − 4.80111
0.825077u
58
− 1.28802u
57
+ ··· − 0.769376u − 1.21854
(ii) Obstruction class = −1
(iii) Cusp Shapes = −26.5735u
58
+ 37.2947u
57
+ ··· + 9.09129u + 20.6511
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
59
− u
58
+ ··· − 46u + 1
c
2
u
59
− 5u
58
+ ··· + 4u + 1
c
4
, c
5
, c
9
u
59
+ 3u
58
+ ··· − 3u
2
− 1
c
6
, c
7
, c
11
c
12
u
59
− u
58
+ ··· + 3u
2
+ 1
c
8
u
59
− 49u
58
+ ··· + 67362u − 16529
c
10
u
59
+ 53u
58
+ ··· + 256u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
59
− 41y
58
+ ··· + 1910y −1
c
2
y
59
+ 3y
58
+ ··· + 270y −1
c
4
, c
5
, c
9
y
59
− 57y
58
+ ··· − 6y −1
c
6
, c
7
, c
11
c
12
y
59
− 73y
58
+ ··· − 6y −1
c
8
y
59
− 2169y
58
+ ··· + 18247485862y −273207841
c
10
y
59
− 2137y
58
+ ··· + 12906y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475350 + 0.860447I
a = 0.496568 + 0.839468I
b = 1.272020 − 0.381627I
−5.19566 + 7.84726I 0
u = 0.475350 − 0.860447I
a = 0.496568 − 0.839468I
b = 1.272020 + 0.381627I
−5.19566 − 7.84726I 0
u = −0.496786 + 0.831191I
a = 0.452243 − 1.016940I
b = 1.41446 + 0.46980I
−14.4117 − 10.5302I 0
u = −0.496786 − 0.831191I
a = 0.452243 + 1.016940I
b = 1.41446 − 0.46980I
−14.4117 + 10.5302I 0
u = −0.642055 + 0.817094I
a = −0.098059 − 0.497244I
b = 1.325190 − 0.298324I
−14.0087 + 5.0802I 0
u = −0.642055 − 0.817094I
a = −0.098059 + 0.497244I
b = 1.325190 + 0.298324I
−14.0087 − 5.0802I 0
u = −0.439918 + 0.966336I
a = 0.481104 − 0.534588I
b = 1.100680 + 0.202044I
−1.85929 − 3.33269I 0
u = −0.439918 − 0.966336I
a = 0.481104 + 0.534588I
b = 1.100680 − 0.202044I
−1.85929 + 3.33269I 0
u = 1.13498
a = 0.740239
b = 0.378809
−4.07948 0
u = 0.727904 + 0.915102I
a = 0.087669 + 0.413864I
b = 1.132370 + 0.126938I
−4.55152 − 2.10422I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727904 − 0.915102I
a = 0.087669 − 0.413864I
b = 1.132370 − 0.126938I
−4.55152 + 2.10422I 0
u = 1.21857
a = 1.69323
b = −1.89392
−10.6108 0
u = −1.26436
a = 1.11134
b = −1.65979
−1.59640 0
u = −1.316980 + 0.152107I
a = 1.03120 + 1.96585I
b = −1.40555 − 1.05122I
−8.95609 − 4.55404I 0
u = −1.316980 − 0.152107I
a = 1.03120 − 1.96585I
b = −1.40555 + 1.05122I
−8.95609 + 4.55404I 0
u = −0.381236 + 0.552080I
a = −0.167585 + 0.667792I
b = −0.208595 − 1.152770I
−9.30665 − 4.95113I −6.99238 + 6.51896I
u = −0.381236 − 0.552080I
a = −0.167585 − 0.667792I
b = −0.208595 + 1.152770I
−9.30665 + 4.95113I −6.99238 − 6.51896I
u = 1.334770 + 0.126781I
a = 0.82384 − 1.77989I
b = −1.22573 + 0.84622I
−0.05622 + 3.78887I 0
u = 1.334770 − 0.126781I
a = 0.82384 + 1.77989I
b = −1.22573 − 0.84622I
−0.05622 − 3.78887I 0
u = 0.407640 + 0.491215I
a = 0.007046 − 0.614145I
b = −0.124106 + 0.847511I
−0.95048 + 3.54930I −4.43989 − 9.05516I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407640 − 0.491215I
a = 0.007046 + 0.614145I
b = −0.124106 − 0.847511I
−0.95048 − 3.54930I −4.43989 + 9.05516I
u = 1.364330 + 0.022066I
a = −1.08977 − 1.29712I
b = −1.114170 + 0.098313I
2.05873 + 0.05448I 0
u = 1.364330 − 0.022066I
a = −1.08977 + 1.29712I
b = −1.114170 − 0.098313I
2.05873 − 0.05448I 0
u = −1.365210 + 0.084494I
a = 0.52896 + 1.73722I
b = −1.000010 − 0.478965I
2.93987 − 2.06641I 0
u = −1.365210 − 0.084494I
a = 0.52896 − 1.73722I
b = −1.000010 + 0.478965I
2.93987 + 2.06641I 0
u = 1.38545
a = 1.11296
b = 0.0228314
−3.92767 0
u = −0.488282 + 0.360464I
a = 0.329573 + 0.368478I
b = 0.087132 − 0.424414I
0.926561 − 0.875889I 4.21577 + 2.97992I
u = −0.488282 − 0.360464I
a = 0.329573 − 0.368478I
b = 0.087132 + 0.424414I
0.926561 + 0.875889I 4.21577 − 2.97992I
u = −1.42001
a = 32.7779
b = −1.00219
−5.59723 0
u = −0.367886 + 0.436129I
a = 2.08179 + 0.08994I
b = −0.257332 + 0.613928I
−9.13968 + 1.69764I −6.18348 + 2.07569I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.367886 − 0.436129I
a = 2.08179 − 0.08994I
b = −0.257332 − 0.613928I
−9.13968 − 1.69764I −6.18348 − 2.07569I
u = 0.117896 + 0.543965I
a = −0.454546 − 0.643164I
b = −1.53639 + 0.58516I
−13.38520 + 2.05056I −13.15743 − 3.37772I
u = 0.117896 − 0.543965I
a = −0.454546 + 0.643164I
b = −1.53639 − 0.58516I
−13.38520 − 2.05056I −13.15743 + 3.37772I
u = 1.44862 + 0.19565I
a = −0.40513 − 1.85474I
b = 0.04576 + 1.43936I
−3.39872 + 7.68478I 0
u = 1.44862 − 0.19565I
a = −0.40513 + 1.85474I
b = 0.04576 − 1.43936I
−3.39872 − 7.68478I 0
u = −1.46045 + 0.17666I
a = −0.31469 + 1.57531I
b = 0.099782 − 1.188640I
5.11240 − 6.01691I 0
u = −1.46045 − 0.17666I
a = −0.31469 − 1.57531I
b = 0.099782 + 1.188640I
5.11240 + 6.01691I 0
u = 1.48347 + 0.15220I
a = −0.239639 − 1.190530I
b = 0.220135 + 0.883885I
7.36971 + 2.90930I 0
u = 1.48347 − 0.15220I
a = −0.239639 + 1.190530I
b = 0.220135 − 0.883885I
7.36971 − 2.90930I 0
u = −0.120295 + 0.487779I
a = −0.692408 + 0.804530I
b = −1.316860 − 0.433488I
−4.56753 − 1.60582I −13.6627 + 4.6604I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.120295 − 0.487779I
a = −0.692408 − 0.804530I
b = −1.316860 + 0.433488I
−4.56753 + 1.60582I −13.6627 − 4.6604I
u = −1.51362 + 0.08542I
a = 0.043229 + 0.571042I
b = 0.282289 − 0.378928I
4.55593 − 0.22771I 0
u = −1.51362 − 0.08542I
a = 0.043229 − 0.571042I
b = 0.282289 + 0.378928I
4.55593 + 0.22771I 0
u = 0.471023
a = 4.79719
b = −1.27746
−11.4096 1.93000
u = 1.49877 + 0.32931I
a = −0.218270 + 1.315670I
b = 1.192200 − 0.489021I
4.33779 + 7.88058I 0
u = 1.49877 − 0.32931I
a = −0.218270 − 1.315670I
b = 1.192200 + 0.489021I
4.33779 − 7.88058I 0
u = −1.48704 + 0.38777I
a = −0.131122 − 0.943356I
b = 1.072210 + 0.305514I
2.27021 − 3.30917I 0
u = −1.48704 − 0.38777I
a = −0.131122 + 0.943356I
b = 1.072210 − 0.305514I
2.27021 + 3.30917I 0
u = 0.261111 + 0.381583I
a = 1.47093 − 0.33575I
b = −0.143895 − 0.219363I
−1.184200 − 0.687771I −5.69781 + 0.37912I
u = 0.261111 − 0.381583I
a = 1.47093 + 0.33575I
b = −0.143895 + 0.219363I
−1.184200 + 0.687771I −5.69781 − 0.37912I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51346 + 0.31095I
a = −0.38347 − 1.52566I
b = 1.32664 + 0.57039I
1.22146 − 12.09350I 0
u = −1.51346 − 0.31095I
a = −0.38347 + 1.52566I
b = 1.32664 − 0.57039I
1.22146 + 12.09350I 0
u = 1.52191 + 0.30160I
a = −0.52248 + 1.67114I
b = 1.43503 − 0.62232I
−7.8780 + 14.6651I 0
u = 1.52191 − 0.30160I
a = −0.52248 − 1.67114I
b = 1.43503 + 0.62232I
−7.8780 − 14.6651I 0
u = 0.131491 + 0.330288I
a = −1.50228 − 2.45162I
b = −1.005580 + 0.138537I
−1.78580 + 0.58489I −5.41482 + 2.56044I
u = 0.131491 − 0.330288I
a = −1.50228 + 2.45162I
b = −1.005580 − 0.138537I
−1.78580 − 0.58489I −5.41482 − 2.56044I
u = −0.340698
a = 6.50413
b = −1.09163
−2.98842 17.3980
u = 1.72747 + 0.35363I
a = −0.483202 + 0.301946I
b = 1.093980 + 0.049807I
−6.28102 − 0.67182I 0
u = 1.72747 − 0.35363I
a = −0.483202 − 0.301946I
b = 1.093980 − 0.049807I
−6.28102 + 0.67182I 0
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u
59
− u
58
+ ··· − 46u + 1
c
2
u
59
− 5u
58
+ ··· + 4u + 1
c
4
, c
5
, c
9
u
59
+ 3u
58
+ ··· − 3u
2
− 1
c
6
, c
7
, c
11
c
12
u
59
− u
58
+ ··· + 3u
2
+ 1
c
8
u
59
− 49u
58
+ ··· + 67362u − 16529
c
10
u
59
+ 53u
58
+ ··· + 256u + 19
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
59
− 41y
58
+ ··· + 1910y −1
c
2
y
59
+ 3y
58
+ ··· + 270y −1
c
4
, c
5
, c
9
y
59
− 57y
58
+ ··· − 6y −1
c
6
, c
7
, c
11
c
12
y
59
− 73y
58
+ ··· − 6y −1
c
8
y
59
− 2169y
58
+ ··· + 18247485862y −273207841
c
10
y
59
− 2137y
58
+ ··· + 12906y −361
12
