12a
1007
(K12a
1007
)
A knot diagram
1
Linearized knot diagam
4 6 12 1 9 10 11 2 3 7 8 5
Solving Sequence
7,10
11 8
3,12
4 6 2 1 9 5
c
10
c
7
c
11
c
3
c
6
c
2
c
1
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.73105 × 10
74
u
73
+ 1.04551 × 10
75
u
72
+ ··· + 6.63560 × 10
73
b + 5.79542 × 10
74
,
2.90380 × 10
74
u
73
− 1.11784 × 10
75
u
72
+ ··· + 6.63560 × 10
73
a − 7.84843 × 10
74
, u
74
− 4u
73
+ ··· + 3u + 1i
I
u
2
= hb + a, a
3
+ a
2
− 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 77 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−2.73×10
74
u
73
+1.05×10
75
u
72
+· · ·+6.64×10
73
b+5.80×10
74
, 2.90×
10
74
u
73
−1.12×10
75
u
72
+· · ·+6.64×10
73
a−7.85×10
74
, u
74
−4u
73
+· · ·+3u+1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
3
+ u
a
3
=
−4.37609u
73
+ 16.8460u
72
+ ··· + 52.4768u + 11.8278
4.11576u
73
− 15.7560u
72
+ ··· − 45.0010u − 8.73384
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
−6.70751u
73
+ 23.6093u
72
+ ··· + 56.6250u + 12.6818
7.05505u
73
− 24.6502u
72
+ ··· − 59.0346u − 11.9969
a
6
=
−u
u
a
2
=
−5.25069u
73
+ 18.6857u
72
+ ··· + 52.3624u + 11.8764
4.99036u
73
− 17.5957u
72
+ ··· − 44.8866u − 8.78248
a
1
=
6.92512u
73
− 21.5547u
72
+ ··· − 40.4571u − 7.72040
−6.48591u
73
+ 20.1000u
72
+ ··· + 34.5039u + 7.98169
a
9
=
3.64853u
73
− 11.8343u
72
+ ··· − 31.7013u − 7.77982
−6.07450u
73
+ 18.8967u
72
+ ··· + 44.3898u + 8.64309
a
5
=
1.21712u
73
− 5.23446u
72
+ ··· − 18.5691u − 4.25242
−1.21712u
73
+ 5.23446u
72
+ ··· + 18.5691u + 3.25242
(ii) Obstruction class = −1
(iii) Cusp Shapes = 90.9880u
73
− 311.861u
72
+ ··· − 727.709u − 161.363
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
74
− 2u
73
+ ··· + 14u − 1
c
2
u
74
− 5u
73
+ ··· − 4u + 8
c
3
u
74
+ 2u
73
+ ··· + 316u − 113
c
5
u
74
+ 4u
73
+ ··· − 3u − 1
c
6
, c
7
, c
10
c
11
u
74
− 4u
73
+ ··· + 3u + 1
c
8
u
74
+ 29u
72
+ ··· − 10528u − 1472
c
9
u
74
+ 2u
73
+ ··· − 1674u + 189
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
74
+ 66y
73
+ ··· − 86y + 1
c
2
y
74
− 21y
73
+ ··· + 176y + 64
c
3
y
74
− 6y
73
+ ··· − 1391446y + 12769
c
5
y
74
− 8y
73
+ ··· − 11y + 1
c
6
, c
7
, c
10
c
11
y
74
− 88y
73
+ ··· − 11y + 1
c
8
y
74
+ 58y
73
+ ··· − 88558592y + 2166784
c
9
y
74
+ 90y
73
+ ··· − 75006y + 35721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942093 + 0.309194I
a = 0.82178 − 1.53663I
b = 0.512844 + 1.053040I
9.22994 − 3.76689I 0
u = −0.942093 − 0.309194I
a = 0.82178 + 1.53663I
b = 0.512844 − 1.053040I
9.22994 + 3.76689I 0
u = −0.829214 + 0.539612I
a = 0.454823 − 1.201050I
b = 0.93839 + 1.08699I
0.17157 − 8.96993I 0
u = −0.829214 − 0.539612I
a = 0.454823 + 1.201050I
b = 0.93839 − 1.08699I
0.17157 + 8.96993I 0
u = 0.759294 + 0.675735I
a = −0.727541 − 0.427353I
b = 0.083007 + 0.966573I
6.66017 + 4.10483I 0
u = 0.759294 − 0.675735I
a = −0.727541 + 0.427353I
b = 0.083007 − 0.966573I
6.66017 − 4.10483I 0
u = −0.875516 + 0.576026I
a = −0.378694 + 1.296850I
b = −0.94555 − 1.18981I
5.52475 − 12.85780I 0
u = −0.875516 − 0.576026I
a = −0.378694 − 1.296850I
b = −0.94555 + 1.18981I
5.52475 + 12.85780I 0
u = −0.783161 + 0.448813I
a = −0.672469 + 1.120440I
b = −0.846780 − 0.934444I
1.93066 − 4.73106I 0
u = −0.783161 − 0.448813I
a = −0.672469 − 1.120440I
b = −0.846780 + 0.934444I
1.93066 + 4.73106I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.019360 + 0.418934I
a = −0.652930 − 0.054022I
b = 0.195417 + 0.497499I
1.233780 − 0.643810I 0
u = 1.019360 − 0.418934I
a = −0.652930 + 0.054022I
b = 0.195417 − 0.497499I
1.233780 + 0.643810I 0
u = 0.683679 + 0.520772I
a = 0.646846 + 0.414647I
b = 0.063130 − 0.851636I
1.52626 + 1.62659I 0
u = 0.683679 − 0.520772I
a = 0.646846 − 0.414647I
b = 0.063130 + 0.851636I
1.52626 − 1.62659I 0
u = −0.042815 + 0.820802I
a = −0.022920 − 0.248405I
b = 0.752740 − 0.872074I
2.99294 + 8.23725I 0
u = −0.042815 − 0.820802I
a = −0.022920 + 0.248405I
b = 0.752740 + 0.872074I
2.99294 − 8.23725I 0
u = 1.041600 + 0.561025I
a = 0.843277 + 0.134056I
b = −0.345412 − 0.645126I
6.23102 − 3.52690I 0
u = 1.041600 − 0.561025I
a = 0.843277 − 0.134056I
b = −0.345412 + 0.645126I
6.23102 + 3.52690I 0
u = 0.804616
a = 0.0596040
b = −0.470934
1.37963 7.78020
u = 0.278147 + 0.701699I
a = −0.531426 − 0.183780I
b = −0.370065 + 0.993896I
5.32512 + 0.61066I 6.95537 − 3.49676I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.278147 − 0.701699I
a = −0.531426 + 0.183780I
b = −0.370065 − 0.993896I
5.32512 − 0.61066I 6.95537 + 3.49676I
u = −0.076491 + 0.743872I
a = −0.068451 + 0.435127I
b = −0.708862 + 0.765875I
−2.10901 + 4.69253I −2.35074 − 6.40585I
u = −0.076491 − 0.743872I
a = −0.068451 − 0.435127I
b = −0.708862 − 0.765875I
−2.10901 − 4.69253I −2.35074 + 6.40585I
u = −0.697142 + 0.254994I
a = −0.84682 − 2.27846I
b = 0.394907 + 0.369057I
4.36563 − 5.67177I 5.66664 + 10.45565I
u = −0.697142 − 0.254994I
a = −0.84682 + 2.27846I
b = 0.394907 − 0.369057I
4.36563 + 5.67177I 5.66664 − 10.45565I
u = 1.232420 + 0.264639I
a = 0.554960 − 0.396105I
b = −0.260746 − 0.134724I
4.38603 + 1.61993I 0
u = 1.232420 − 0.264639I
a = 0.554960 + 0.396105I
b = −0.260746 + 0.134724I
4.38603 − 1.61993I 0
u = 0.679946 + 0.082464I
a = −0.43115 + 3.67418I
b = 0.41590 − 3.16791I
4.22903 + 3.00667I −23.7815 + 12.2873I
u = 0.679946 − 0.082464I
a = −0.43115 − 3.67418I
b = 0.41590 + 3.16791I
4.22903 − 3.00667I −23.7815 − 12.2873I
u = −0.581096 + 0.313903I
a = −1.213140 + 0.596613I
b = −0.822786 − 0.504890I
1.22795 − 4.09761I 0.86435 + 10.33100I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581096 − 0.313903I
a = −1.213140 − 0.596613I
b = −0.822786 + 0.504890I
1.22795 + 4.09761I 0.86435 − 10.33100I
u = 0.590590 + 0.079779I
a = 0.28668 − 3.05361I
b = −0.11712 + 2.48646I
−0.097330 + 0.250762I −5.7725 + 24.0060I
u = 0.590590 − 0.079779I
a = 0.28668 + 3.05361I
b = −0.11712 − 2.48646I
−0.097330 − 0.250762I −5.7725 − 24.0060I
u = −0.178104 + 0.556859I
a = 0.277771 − 1.018920I
b = 0.587211 − 0.511483I
−0.013339 + 1.302490I −1.19820 − 1.15705I
u = −0.178104 − 0.556859I
a = 0.277771 + 1.018920I
b = 0.587211 + 0.511483I
−0.013339 − 1.302490I −1.19820 + 1.15705I
u = −0.516630 + 0.230004I
a = 0.36605 + 2.44705I
b = −0.314688 − 0.080344I
−1.24147 − 1.91408I −5.09899 + 10.28622I
u = −0.516630 − 0.230004I
a = 0.36605 − 2.44705I
b = −0.314688 + 0.080344I
−1.24147 + 1.91408I −5.09899 − 10.28622I
u = 0.458807 + 0.180216I
a = −0.85511 + 2.71233I
b = 0.70245 − 1.70843I
3.88920 − 2.27458I 1.22488 + 8.50227I
u = 0.458807 − 0.180216I
a = −0.85511 − 2.71233I
b = 0.70245 + 1.70843I
3.88920 + 2.27458I 1.22488 − 8.50227I
u = −1.55302 + 0.02610I
a = −0.25871 − 2.13725I
b = 0.68489 + 1.79511I
10.61670 − 2.04355I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55302 − 0.02610I
a = −0.25871 + 2.13725I
b = 0.68489 − 1.79511I
10.61670 + 2.04355I 0
u = −0.048697 + 0.438598I
a = 0.930836 − 0.918696I
b = 0.383488 − 0.579860I
−0.060405 + 1.403310I −0.47421 − 3.22545I
u = −0.048697 − 0.438598I
a = 0.930836 + 0.918696I
b = 0.383488 + 0.579860I
−0.060405 − 1.403310I −0.47421 + 3.22545I
u = 1.57754
a = −0.226280
b = −1.08206
5.13843 0
u = 1.58226 + 0.03011I
a = −0.26906 + 1.71184I
b = 0.025820 − 0.468816I
6.03750 + 2.63879I 0
u = 1.58226 − 0.03011I
a = −0.26906 − 1.71184I
b = 0.025820 + 0.468816I
6.03750 − 2.63879I 0
u = 1.58916 + 0.05016I
a = 0.069893 + 0.879917I
b = 1.086110 − 0.532337I
8.67348 + 5.20861I 0
u = 1.58916 − 0.05016I
a = 0.069893 − 0.879917I
b = 1.086110 + 0.532337I
8.67348 − 5.20861I 0
u = −1.60397 + 0.01496I
a = 0.74114 − 3.10611I
b = −0.95392 + 2.77699I
7.59534 − 0.55477I 0
u = −1.60397 − 0.01496I
a = 0.74114 + 3.10611I
b = −0.95392 − 2.77699I
7.59534 + 0.55477I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62084 + 0.05971I
a = 0.56755 − 1.69860I
b = −0.050518 + 0.593462I
12.4082 + 6.7857I 0
u = 1.62084 − 0.05971I
a = 0.56755 + 1.69860I
b = −0.050518 − 0.593462I
12.4082 − 6.7857I 0
u = −1.62819 + 0.02954I
a = −0.25981 + 3.45963I
b = 0.38510 − 3.04819I
12.34910 − 3.46973I 0
u = −1.62819 − 0.02954I
a = −0.25981 − 3.45963I
b = 0.38510 + 3.04819I
12.34910 + 3.46973I 0
u = −1.62870 + 0.15990I
a = −0.270266 + 1.334690I
b = −0.344859 − 1.144900I
9.47696 − 4.24095I 0
u = −1.62870 − 0.15990I
a = −0.270266 − 1.334690I
b = −0.344859 + 1.144900I
9.47696 + 4.24095I 0
u = 1.64161 + 0.12775I
a = −0.15420 + 1.69986I
b = 1.04989 − 1.20464I
10.27170 + 6.92583I 0
u = 1.64161 − 0.12775I
a = −0.15420 − 1.69986I
b = 1.04989 + 1.20464I
10.27170 − 6.92583I 0
u = −1.65700 + 0.08518I
a = −0.092227 − 1.003530I
b = 0.633049 + 0.868120I
10.43250 − 0.92808I 0
u = −1.65700 − 0.08518I
a = −0.092227 + 1.003530I
b = 0.633049 − 0.868120I
10.43250 + 0.92808I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65340 + 0.15594I
a = 0.23581 − 1.86604I
b = −1.08403 + 1.37222I
8.6605 + 11.6416I 0
u = 1.65340 − 0.15594I
a = 0.23581 + 1.86604I
b = −1.08403 − 1.37222I
8.6605 − 11.6416I 0
u = −1.65535 + 0.20131I
a = 0.461400 − 1.305450I
b = 0.191063 + 1.136940I
14.8889 − 7.4681I 0
u = −1.65535 − 0.20131I
a = 0.461400 + 1.305450I
b = 0.191063 − 1.136940I
14.8889 + 7.4681I 0
u = −0.288235 + 0.161328I
a = 2.08965 + 0.60336I
b = 0.851960 + 0.035687I
−1.79590 + 0.04835I −7.72033 + 2.40236I
u = −0.288235 − 0.161328I
a = 2.08965 − 0.60336I
b = 0.851960 − 0.035687I
−1.79590 − 0.04835I −7.72033 − 2.40236I
u = 1.67485 + 0.08494I
a = −0.18727 − 1.73912I
b = −0.731206 + 1.134850I
18.3117 + 5.3180I 0
u = 1.67485 − 0.08494I
a = −0.18727 + 1.73912I
b = −0.731206 − 1.134850I
18.3117 − 5.3180I 0
u = 1.67017 + 0.16856I
a = −0.22476 + 1.98140I
b = 1.04949 − 1.47622I
14.2321 + 15.7575I 0
u = 1.67017 − 0.16856I
a = −0.22476 − 1.98140I
b = 1.04949 + 1.47622I
14.2321 − 15.7575I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.051463 + 0.297579I
a = −0.80704 − 2.13227I
b = −1.056030 + 0.299059I
2.60707 + 3.62012I −0.482860 − 0.752061I
u = −0.051463 − 0.297579I
a = −0.80704 + 2.13227I
b = −1.056030 − 0.299059I
2.60707 − 3.62012I −0.482860 + 0.752061I
u = −1.73032 + 0.09654I
a = −0.341147 + 0.686921I
b = −0.257783 − 0.605681I
16.1715 + 1.0241I 0
u = −1.73032 − 0.09654I
a = −0.341147 − 0.686921I
b = −0.257783 + 0.605681I
16.1715 − 1.0241I 0
12
II. I
u
2
= hb + a, a
3
+ a
2
− 1, u − 1i
(i) Arc colorings
a
7
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
8
=
1
0
a
3
=
a
−a
a
12
=
0
−1
a
4
=
a
0
a
6
=
−1
1
a
2
=
a
−a
a
1
=
a
2
+ a − 1
−a
a
9
=
a
2
+ 1
−a
2
a
5
=
a
2
−a
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
2
− 5a + 1
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
3
− u
2
+ 2u − 1
c
2
u
3
c
3
, c
8
, c
9
u
3
− u
2
+ 1
c
4
u
3
+ u
2
+ 2u + 1
c
5
, c
6
, c
7
(u + 1)
3
c
10
, c
11
(u − 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
y
3
c
3
, c
8
, c
9
y
3
− y
2
+ 2y −1
c
5
, c
6
, c
7
c
10
, c
11
(y −1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.877439 + 0.744862I
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 5.17211 − 2.41717I
u = 1.00000
a = −0.877439 − 0.744862I
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 5.17211 + 2.41717I
u = 1.00000
a = 0.754878
b = −0.754878
0.531480 −3.34420
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
3
− u
2
+ 2u − 1)(u
74
− 2u
73
+ ··· + 14u − 1)
c
2
u
3
(u
74
− 5u
73
+ ··· − 4u + 8)
c
3
(u
3
− u
2
+ 1)(u
74
+ 2u
73
+ ··· + 316u − 113)
c
4
(u
3
+ u
2
+ 2u + 1)(u
74
− 2u
73
+ ··· + 14u − 1)
c
5
((u + 1)
3
)(u
74
+ 4u
73
+ ··· − 3u − 1)
c
6
, c
7
((u + 1)
3
)(u
74
− 4u
73
+ ··· + 3u + 1)
c
8
(u
3
− u
2
+ 1)(u
74
+ 29u
72
+ ··· − 10528u − 1472)
c
9
(u
3
− u
2
+ 1)(u
74
+ 2u
73
+ ··· − 1674u + 189)
c
10
, c
11
((u − 1)
3
)(u
74
− 4u
73
+ ··· + 3u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
74
+ 66y
73
+ ··· − 86y + 1)
c
2
y
3
(y
74
− 21y
73
+ ··· + 176y + 64)
c
3
(y
3
− y
2
+ 2y −1)(y
74
− 6y
73
+ ··· − 1391446y + 12769)
c
5
((y −1)
3
)(y
74
− 8y
73
+ ··· − 11y + 1)
c
6
, c
7
, c
10
c
11
((y −1)
3
)(y
74
− 88y
73
+ ··· − 11y + 1)
c
8
(y
3
− y
2
+ 2y −1)(y
74
+ 58y
73
+ ··· − 8.85586 × 10
7
y + 2166784)
c
9
(y
3
− y
2
+ 2y −1)(y
74
+ 90y
73
+ ··· − 75006y + 35721)
18
