12a
0179
(K12a
0179
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 11 12 10 4 1 7 8
Solving Sequence
3,9
4
5,10
2 6 1 11 8 12 7
c
3
c
9
c
2
c
5
c
1
c
10
c
8
c
12
c
7
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.71708 × 10
39
u
70
+ 1.91637 × 10
39
u
69
+ ··· + 7.55053 × 10
39
b − 5.39067 × 10
40
,
2.23600 × 10
39
u
70
+ 3.25449 × 10
37
u
69
+ ··· + 7.55053 × 10
39
a + 2.20656 × 10
40
, u
71
− u
70
+ ··· + 32u − 16i
I
v
1
= ha, −v
3
+ 2v
2
+ 2b − 2v + 1, v
4
− v
3
+ 2v
2
+ v + 1i
* 2 irreducible components of dim
C
= 0, with total 75 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−2.72 × 10
39
u
70
+ 1.92 × 10
39
u
69
+ · · · + 7.55 × 10
39
b − 5.39 ×
10
40
, 2.24 × 10
39
u
70
+ 3.25 × 10
37
u
69
+ · · · + 7.55 × 10
39
a + 2.21 ×
10
40
, u
71
− u
70
+ · · · + 32u − 16i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
5
=
−0.296138u
70
− 0.00431028u
69
+ ··· + 12.0993u − 2.92239
0.359852u
70
− 0.253806u
69
+ ··· − 4.10423u + 7.13946
a
10
=
u
−u
3
+ u
a
2
=
−0.0672794u
70
− 0.0679694u
69
+ ··· + 9.94426u − 3.79346
−0.204932u
70
− 0.00949976u
69
+ ··· − 0.840329u − 3.24825
a
6
=
−0.0672794u
70
− 0.0679694u
69
+ ··· + 9.94426u − 3.79346
0.114199u
70
− 0.134587u
69
+ ··· − 2.41116u + 5.41223
a
1
=
−0.272212u
70
− 0.0774692u
69
+ ··· + 9.10394u − 7.04171
−0.204932u
70
− 0.00949976u
69
+ ··· − 0.840329u − 3.24825
a
11
=
0.0361174u
70
− 0.0228612u
69
+ ··· + 12.0016u − 6.74339
−0.0426249u
70
− 0.173546u
69
+ ··· − 2.35671u + 4.17575
a
8
=
−u
3
u
5
− u
3
+ u
a
12
=
−0.169607u
70
+ 0.0192873u
69
+ ··· + 9.80052u − 8.54872
−0.197794u
70
+ 0.101478u
69
+ ··· − 2.00512u − 2.63268
a
7
=
0.184380u
70
− 0.0878898u
69
+ ··· − 13.0143u + 10.6308
0.288200u
70
− 0.111556u
69
+ ··· + 0.409843u + 3.14069
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.56249u
70
− 0.499654u
69
+ ··· − 24.3357u + 56.8547
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
71
+ 25u
70
+ ··· − 24u − 1
c
2
, c
5
u
71
+ 3u
70
+ ··· − 12u
2
− 1
c
3
, c
9
u
71
+ u
70
+ ··· + 32u + 16
c
6
, c
7
, c
11
c
12
u
71
+ 3u
70
+ ··· − 2u + 1
c
8
u
71
− 25u
70
+ ··· + 3712u − 256
c
10
u
71
− 21u
70
+ ··· + 30122u − 2513
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
71
+ 45y
70
+ ··· + 32y −1
c
2
, c
5
y
71
+ 25y
70
+ ··· − 24y −1
c
3
, c
9
y
71
− 25y
70
+ ··· + 3712y −256
c
6
, c
7
, c
11
c
12
y
71
− 83y
70
+ ··· + 4y −1
c
8
y
71
+ 35y
70
+ ··· − 1695744y −65536
c
10
y
71
− 23y
70
+ ··· + 38952656y −6315169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.898695 + 0.447888I
a = −0.48166 + 1.64393I
b = 0.704202 − 0.678389I
−0.156625 − 0.128245I −2.60256 + 0.62828I
u = 0.898695 − 0.447888I
a = −0.48166 − 1.64393I
b = 0.704202 + 0.678389I
−0.156625 + 0.128245I −2.60256 − 0.62828I
u = 0.485356 + 0.866096I
a = 0.723279 − 0.275133I
b = −0.695289 − 0.658546I
−0.181303 − 0.963321I −2.97724 + 2.47393I
u = 0.485356 − 0.866096I
a = 0.723279 + 0.275133I
b = −0.695289 + 0.658546I
−0.181303 + 0.963321I −2.97724 − 2.47393I
u = −0.046756 + 1.006700I
a = 0.664918 − 0.351532I
b = −0.707383 − 0.856092I
−4.78280 + 2.70516I −3.93532 − 3.08025I
u = −0.046756 − 1.006700I
a = 0.664918 + 0.351532I
b = −0.707383 + 0.856092I
−4.78280 − 2.70516I −3.93532 + 3.08025I
u = 0.814841 + 0.602433I
a = −2.85625 + 1.03972I
b = 0.633904 + 0.996625I
−9.92867 + 3.79379I −6.79831 − 6.12485I
u = 0.814841 − 0.602433I
a = −2.85625 − 1.03972I
b = 0.633904 − 0.996625I
−9.92867 − 3.79379I −6.79831 + 6.12485I
u = 1.03416
a = 0.792535
b = −0.659001
−4.08496 0
u = 0.915846 + 0.508550I
a = 0.777578 − 0.138252I
b = −0.671992 − 0.337720I
0.04777 + 3.88882I 0. − 7.52926I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.915846 − 0.508550I
a = 0.777578 + 0.138252I
b = −0.671992 + 0.337720I
0.04777 − 3.88882I 0. + 7.52926I
u = −0.749394 + 0.742501I
a = 0.927602 + 1.023970I
b = −0.002922 + 1.034700I
−5.23643 + 0.49136I −10.35637 + 0.I
u = −0.749394 − 0.742501I
a = 0.927602 − 1.023970I
b = −0.002922 − 1.034700I
−5.23643 − 0.49136I −10.35637 + 0.I
u = 0.842164 + 0.647596I
a = 0.860044 − 0.892957I
b = −0.080620 − 1.043370I
−2.69671 + 2.52237I 0
u = 0.842164 − 0.647596I
a = 0.860044 + 0.892957I
b = −0.080620 + 1.043370I
−2.69671 − 2.52237I 0
u = −0.744352 + 0.553739I
a = 0.651043 − 0.469715I
b = −0.561912 − 1.022170I
−1.79172 + 0.68850I −5.62900 + 3.38039I
u = −0.744352 − 0.553739I
a = 0.651043 + 0.469715I
b = −0.561912 + 1.022170I
−1.79172 − 0.68850I −5.62900 − 3.38039I
u = −0.913780 + 0.144906I
a = 0.731500 + 0.609419I
b = −0.338962 + 1.033540I
−7.19330 − 3.32362I −5.12286 + 4.83275I
u = −0.913780 − 0.144906I
a = 0.731500 − 0.609419I
b = −0.338962 − 1.033540I
−7.19330 + 3.32362I −5.12286 − 4.83275I
u = 0.895328 + 0.614559I
a = 0.627473 + 0.478230I
b = −0.571721 + 1.063660I
−9.66637 + 1.00404I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.895328 − 0.614559I
a = 0.627473 − 0.478230I
b = −0.571721 − 1.063660I
−9.66637 − 1.00404I 0
u = −0.580986 + 0.928128I
a = 0.629379 − 0.415842I
b = −0.663444 − 0.995696I
−1.18425 + 6.22847I 0
u = −0.580986 − 0.928128I
a = 0.629379 + 0.415842I
b = −0.663444 + 0.995696I
−1.18425 − 6.22847I 0
u = 0.438808 + 0.779885I
a = 0.657294 + 0.414809I
b = −0.631199 + 0.953782I
0.39399 − 3.06003I −0.75932 + 1.65602I
u = 0.438808 − 0.779885I
a = 0.657294 − 0.414809I
b = −0.631199 − 0.953782I
0.39399 + 3.06003I −0.75932 − 1.65602I
u = 0.731479 + 0.831783I
a = 0.88446 − 1.13386I
b = 0.038927 − 1.065800I
−13.52330 − 2.24339I 0
u = 0.731479 − 0.831783I
a = 0.88446 + 1.13386I
b = 0.038927 + 1.065800I
−13.52330 + 2.24339I 0
u = −0.955053 + 0.565034I
a = −2.56607 − 0.59068I
b = 0.670926 − 0.992762I
−1.10321 − 5.18739I 0
u = −0.955053 − 0.565034I
a = −2.56607 + 0.59068I
b = 0.670926 + 0.992762I
−1.10321 + 5.18739I 0
u = −0.821890 + 0.297804I
a = 0.838078 + 0.097095I
b = −0.543921 + 0.231319I
1.32332 − 0.80569I 4.20345 + 1.04258I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821890 − 0.297804I
a = 0.838078 − 0.097095I
b = −0.543921 − 0.231319I
1.32332 + 0.80569I 4.20345 − 1.04258I
u = −0.595799 + 0.966991I
a = 0.704626 + 0.251056I
b = −0.754441 + 0.629987I
−7.86275 + 2.84728I 0
u = −0.595799 − 0.966991I
a = 0.704626 − 0.251056I
b = −0.754441 − 0.629987I
−7.86275 − 2.84728I 0
u = −0.943340 + 0.686884I
a = 0.769346 + 0.904490I
b = −0.091008 + 1.099760I
−4.63880 − 5.93106I 0
u = −0.943340 − 0.686884I
a = 0.769346 − 0.904490I
b = −0.091008 − 1.099760I
−4.63880 + 5.93106I 0
u = −0.995858 + 0.614315I
a = 0.744700 + 0.143172I
b = −0.745958 + 0.363151I
−7.64756 − 5.89043I 0
u = −0.995858 − 0.614315I
a = 0.744700 − 0.143172I
b = −0.745958 − 0.363151I
−7.64756 + 5.89043I 0
u = −1.185220 + 0.024512I
a = −1.68390 − 0.91780I
b = 0.763748 + 0.846463I
6.09381 + 0.94811I 0
u = −1.185220 − 0.024512I
a = −1.68390 + 0.91780I
b = 0.763748 − 0.846463I
6.09381 − 0.94811I 0
u = 1.190440 + 0.117078I
a = −1.91536 − 0.66291I
b = 0.755383 + 0.886674I
5.97207 + 4.78145I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.190440 − 0.117078I
a = −1.91536 + 0.66291I
b = 0.755383 − 0.886674I
5.97207 − 4.78145I 0
u = 0.660911 + 1.000500I
a = 0.615402 + 0.416919I
b = −0.678388 + 1.018840I
−9.01807 − 8.30674I 0
u = 0.660911 − 1.000500I
a = 0.615402 − 0.416919I
b = −0.678388 − 1.018840I
−9.01807 + 8.30674I 0
u = −0.639037 + 0.480316I
a = 0.63082 − 2.00324I
b = 0.578600 + 0.637489I
−8.84566 + 1.15303I −4.74959 + 2.27232I
u = −0.639037 − 0.480316I
a = 0.63082 + 2.00324I
b = 0.578600 − 0.637489I
−8.84566 − 1.15303I −4.74959 − 2.27232I
u = −1.066010 + 0.557376I
a = −0.553984 − 1.154100I
b = 0.783980 + 0.661621I
3.27242 − 2.74628I 0
u = −1.066010 − 0.557376I
a = −0.553984 + 1.154100I
b = 0.783980 − 0.661621I
3.27242 + 2.74628I 0
u = −0.216560 + 0.759366I
a = 0.723009 + 0.336172I
b = −0.635057 + 0.763179I
1.00588 − 1.89636I 0.54641 + 5.25437I
u = −0.216560 − 0.759366I
a = 0.723009 − 0.336172I
b = −0.635057 − 0.763179I
1.00588 + 1.89636I 0.54641 − 5.25437I
u = 1.217720 + 0.204604I
a = −1.28956 + 1.01899I
b = 0.788740 − 0.796172I
−0.028361 + 1.390240I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.217720 − 0.204604I
a = −1.28956 − 1.01899I
b = 0.788740 + 0.796172I
−0.028361 − 1.390240I 0
u = 0.998362 + 0.733734I
a = 0.720523 − 0.920806I
b = −0.086327 − 1.133430I
−12.6856 + 8.1034I 0
u = 0.998362 − 0.733734I
a = 0.720523 + 0.920806I
b = −0.086327 + 1.133430I
−12.6856 − 8.1034I 0
u = 1.075840 + 0.632701I
a = −2.18572 + 0.55812I
b = 0.698464 + 1.015000I
2.20770 + 8.35369I 0
u = 1.075840 − 0.632701I
a = −2.18572 − 0.55812I
b = 0.698464 − 1.015000I
2.20770 − 8.35369I 0
u = −1.223810 + 0.275921I
a = −1.99796 + 0.29578I
b = 0.754446 − 0.931385I
−0.43731 − 7.18811I 0
u = −1.223810 − 0.275921I
a = −1.99796 − 0.29578I
b = 0.754446 + 0.931385I
−0.43731 + 7.18811I 0
u = −0.422944 + 0.589272I
a = 1.234610 − 0.617787I
b = 0.389148 + 0.464716I
−8.91534 + 1.12808I −7.69562 + 1.51946I
u = −0.422944 − 0.589272I
a = 1.234610 + 0.617787I
b = 0.389148 − 0.464716I
−8.91534 − 1.12808I −7.69562 − 1.51946I
u = 1.093130 + 0.656674I
a = −0.464088 + 1.005390I
b = 0.811468 − 0.632359I
1.65039 + 6.56883I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.093130 − 0.656674I
a = −0.464088 − 1.005390I
b = 0.811468 + 0.632359I
1.65039 − 6.56883I 0
u = −1.098940 + 0.711938I
a = −2.03891 − 0.66504I
b = 0.700760 − 1.035720I
0.43518 − 12.25320I 0
u = −1.098940 − 0.711938I
a = −2.03891 + 0.66504I
b = 0.700760 + 1.035720I
0.43518 + 12.25320I 0
u = −1.106240 + 0.731732I
a = −0.410040 − 0.912009I
b = 0.831200 + 0.610202I
−6.25111 − 9.04376I 0
u = −1.106240 − 0.731732I
a = −0.410040 + 0.912009I
b = 0.831200 − 0.610202I
−6.25111 + 9.04376I 0
u = 1.106610 + 0.773513I
a = −1.94318 + 0.74250I
b = 0.700048 + 1.051230I
−7.5826 + 14.7744I 0
u = 1.106610 − 0.773513I
a = −1.94318 − 0.74250I
b = 0.700048 − 1.051230I
−7.5826 − 14.7744I 0
u = 0.595380 + 0.063159I
a = 0.766930 − 0.508281I
b = −0.410411 − 0.925666I
−0.52089 + 2.54938I 1.55851 − 8.99527I
u = 0.595380 − 0.063159I
a = 0.766930 + 0.508281I
b = −0.410411 + 0.925666I
−0.52089 − 2.54938I 1.55851 + 8.99527I
u = 0.327964 + 0.426910I
a = 1.107820 + 0.038370I
b = 0.096513 − 0.298186I
−1.159260 − 0.383261I −7.97768 + 0.90492I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.327964 − 0.426910I
a = 1.107820 − 0.038370I
b = 0.096513 + 0.298186I
−1.159260 + 0.383261I −7.97768 − 0.90492I
12
II. I
v
1
= ha, −v
3
+ 2v
2
+ 2b − 2v + 1, v
4
− v
3
+ 2v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
2
v
3
− v
2
+ v −
1
2
a
10
=
v
0
a
2
=
1
−
1
2
v
3
+ v
2
− v −
1
2
a
6
=
1
2
v
3
− v
2
+ v −
1
2
1
2
v
3
− v
2
+ v +
1
2
a
1
=
−
1
2
v
3
+ v
2
− v +
1
2
−
1
2
v
3
+ v
2
− v −
1
2
a
11
=
0
−
1
2
v
3
− v −
1
2
a
8
=
v
0
a
12
=
−v
−
1
2
v
3
+ v
2
− v −
1
2
a
7
=
1
2
v
3
− v
2
+ v −
1
2
1
2
v
3
+ v +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = v
3
− 3v
2
+ v − 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
8
, c
9
u
4
c
6
, c
7
, c
10
(u
2
+ u − 1)
2
c
11
, c
12
(u
2
− u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
8
, c
9
y
4
c
6
, c
7
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.309017 + 0.535233I
a = 0
b = −0.500000 + 0.866025I
−0.98696 − 2.02988I −6.50000 + 1.52761I
v = −0.309017 − 0.535233I
a = 0
b = −0.500000 − 0.866025I
−0.98696 + 2.02988I −6.50000 − 1.52761I
v = 0.80902 + 1.40126I
a = 0
b = −0.500000 − 0.866025I
−8.88264 + 2.02988I −6.50000 − 5.40059I
v = 0.80902 − 1.40126I
a = 0
b = −0.500000 + 0.866025I
−8.88264 − 2.02988I −6.50000 + 5.40059I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
2
)(u
71
+ 25u
70
+ ··· − 24u − 1)
c
2
((u
2
+ u + 1)
2
)(u
71
+ 3u
70
+ ··· − 12u
2
− 1)
c
3
, c
9
u
4
(u
71
+ u
70
+ ··· + 32u + 16)
c
5
((u
2
− u + 1)
2
)(u
71
+ 3u
70
+ ··· − 12u
2
− 1)
c
6
, c
7
((u
2
+ u − 1)
2
)(u
71
+ 3u
70
+ ··· − 2u + 1)
c
8
u
4
(u
71
− 25u
70
+ ··· + 3712u − 256)
c
10
((u
2
+ u − 1)
2
)(u
71
− 21u
70
+ ··· + 30122u − 2513)
c
11
, c
12
((u
2
− u − 1)
2
)(u
71
+ 3u
70
+ ··· − 2u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
71
+ 45y
70
+ ··· + 32y − 1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
71
+ 25y
70
+ ··· − 24y − 1)
c
3
, c
9
y
4
(y
71
− 25y
70
+ ··· + 3712y − 256)
c
6
, c
7
, c
11
c
12
((y
2
− 3y + 1)
2
)(y
71
− 83y
70
+ ··· + 4y − 1)
c
8
y
4
(y
71
+ 35y
70
+ ··· − 1695744y − 65536)
c
10
((y
2
− 3y + 1)
2
)(y
71
− 23y
70
+ ··· + 3.89527 × 10
7
y − 6315169)
18
