12a
0180
(K12a
0180
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 11 12 10 4 1 8 7
Solving Sequence
2,6
5 3
1,10
11 7 4 9 8 12
c
5
c
2
c
1
c
10
c
6
c
4
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h40u
91
+ 119u
90
+ ··· + 4b + 23, 27u
91
+ 64u
90
+ ··· + 4a − 3, u
92
+ 4u
91
+ ··· + 2u + 1i
I
u
2
= h−au + b, a
3
− a
2
u + a
2
+ 1, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 98 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
= h40u
91
+ 119u
90
+ · · · + 4b + 23, 27u
91
+ 64u
90
+ · · · + 4a − 3, u
92
+
4u
91
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−
27
4
u
91
− 16u
90
+ ··· −
25
2
u +
3
4
−10u
91
−
119
4
u
90
+ ··· −
53
4
u −
23
4
a
11
=
−
23
4
u
91
−
57
4
u
90
+ ··· −
45
4
u +
3
2
−5u
91
−
63
4
u
90
+ ··· −
29
4
u −
19
4
a
7
=
1
4
u
90
+
3
4
u
89
+ ··· +
17
4
u +
1
4
−
1
4
u
91
− u
90
+ ··· +
1
2
u −
1
4
a
4
=
u
2
+ 1
u
2
a
9
=
−
25
4
u
91
− 12u
90
+ ··· −
17
2
u +
21
4
−13u
91
−
161
4
u
90
+ ··· −
71
4
u −
25
4
a
8
=
−
9
4
u
91
− 12u
90
+ ··· −
27
2
u −
19
4
−2u
91
−
33
4
u
90
+ ··· −
23
4
u −
21
4
a
12
=
−
7
2
u
91
−
23
2
u
90
+ ··· − 5u −
3
2
5
4
u
91
+
5
4
u
90
+ ··· +
1
4
u −
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
91
−
51
2
u
90
+ ··· − 11u − 19
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
92
+ 32u
91
+ ··· + 18u + 1
c
2
, c
5
u
92
+ 4u
91
+ ··· + 2u + 1
c
3
, c
9
u
92
+ u
91
+ ··· + 32u + 64
c
6
u
92
+ 3u
91
+ ··· − 3u + 1
c
7
, c
11
, c
12
u
92
− 3u
91
+ ··· − 5u + 1
c
8
u
92
− 35u
91
+ ··· − 70656u + 4096
c
10
u
92
− 21u
91
+ ··· − 69583u + 3971
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
92
+ 60y
91
+ ··· + 102y + 1
c
2
, c
5
y
92
+ 32y
91
+ ··· + 18y + 1
c
3
, c
9
y
92
− 35y
91
+ ··· − 70656y + 4096
c
6
y
92
− y
91
+ ··· − y + 1
c
7
, c
11
, c
12
y
92
+ 83y
91
+ ··· − y + 1
c
8
y
92
+ 33y
91
+ ··· + 368050176y + 16777216
c
10
y
92
+ 19y
91
+ ··· + 418605695y + 15768841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642901 + 0.753810I
a = −0.876838 + 1.051680I
b = −0.464572 + 0.257031I
1.04598 + 1.86380I 0
u = 0.642901 − 0.753810I
a = −0.876838 − 1.051680I
b = −0.464572 − 0.257031I
1.04598 − 1.86380I 0
u = 0.749706 + 0.679211I
a = −0.90313 + 1.74816I
b = −0.562272 + 0.756692I
5.20706 − 4.55365I 0
u = 0.749706 − 0.679211I
a = −0.90313 − 1.74816I
b = −0.562272 − 0.756692I
5.20706 + 4.55365I 0
u = −0.645279 + 0.737552I
a = −0.06859 + 2.02630I
b = 1.37252 + 1.60110I
3.89595 − 4.10626I 0
u = −0.645279 − 0.737552I
a = −0.06859 − 2.02630I
b = 1.37252 − 1.60110I
3.89595 + 4.10626I 0
u = −0.049139 + 1.019310I
a = −0.872887 − 0.623692I
b = −0.15815 + 1.67459I
−0.33973 − 4.46873I 0
u = −0.049139 − 1.019310I
a = −0.872887 + 0.623692I
b = −0.15815 − 1.67459I
−0.33973 + 4.46873I 0
u = 0.412618 + 0.938002I
a = −0.362557 − 0.742830I
b = 0.324219 − 0.150659I
−0.51240 + 2.59373I 0
u = 0.412618 − 0.938002I
a = −0.362557 + 0.742830I
b = 0.324219 + 0.150659I
−0.51240 − 2.59373I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.712042 + 0.666319I
a = 0.75389 − 1.59404I
b = 0.428516 − 0.657966I
−0.094959 − 1.238240I 0
u = 0.712042 − 0.666319I
a = 0.75389 + 1.59404I
b = 0.428516 + 0.657966I
−0.094959 + 1.238240I 0
u = −0.728596 + 0.640611I
a = 0.81559 + 1.89435I
b = 1.46254 + 1.23253I
2.50023 + 3.17652I 0
u = −0.728596 − 0.640611I
a = 0.81559 − 1.89435I
b = 1.46254 − 1.23253I
2.50023 − 3.17652I 0
u = −0.795374 + 0.654252I
a = 1.14573 + 1.56142I
b = 1.51632 + 1.07301I
3.26408 + 3.00564I 0
u = −0.795374 − 0.654252I
a = 1.14573 − 1.56142I
b = 1.51632 − 1.07301I
3.26408 − 3.00564I 0
u = −0.014222 + 1.030500I
a = 0.739894 + 0.598341I
b = −0.04915 − 1.60139I
−5.29884 − 0.89429I 0
u = −0.014222 − 1.030500I
a = 0.739894 − 0.598341I
b = −0.04915 + 1.60139I
−5.29884 + 0.89429I 0
u = −0.821306 + 0.634726I
a = −1.38974 − 1.60955I
b = −1.62649 − 1.06033I
1.86179 + 6.99768I 0
u = −0.821306 − 0.634726I
a = −1.38974 + 1.60955I
b = −1.62649 + 1.06033I
1.86179 − 6.99768I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673042 + 0.683931I
a = −0.38646 − 1.98387I
b = −1.42101 − 1.36108I
−0.476840 − 0.461750I 0
u = −0.673042 − 0.683931I
a = −0.38646 + 1.98387I
b = −1.42101 + 1.36108I
−0.476840 + 0.461750I 0
u = −0.839105 + 0.634467I
a = 1.52117 + 1.56007I
b = 1.68190 + 1.02254I
7.34278 + 10.67130I 0
u = −0.839105 − 0.634467I
a = 1.52117 − 1.56007I
b = 1.68190 − 1.02254I
7.34278 − 10.67130I 0
u = 0.039095 + 1.055240I
a = −0.543732 − 0.565851I
b = 0.38416 + 1.48804I
−3.00342 + 2.65278I 0
u = 0.039095 − 1.055240I
a = −0.543732 + 0.565851I
b = 0.38416 − 1.48804I
−3.00342 − 2.65278I 0
u = 0.188853 + 1.042670I
a = 0.263413 + 0.793199I
b = −0.765362 − 0.731153I
3.26367 + 1.72100I 0
u = 0.188853 − 1.042670I
a = 0.263413 − 0.793199I
b = −0.765362 + 0.731153I
3.26367 − 1.72100I 0
u = 0.721414 + 0.781773I
a = 1.32688 − 1.25004I
b = 0.798901 − 0.328279I
6.63463 + 3.78818I 0
u = 0.721414 − 0.781773I
a = 1.32688 + 1.25004I
b = 0.798901 + 0.328279I
6.63463 − 3.78818I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.081609 + 1.063250I
a = −0.416314 − 0.600758I
b = 0.58404 + 1.31940I
−2.82546 + 2.65048I 0
u = 0.081609 − 1.063250I
a = −0.416314 + 0.600758I
b = 0.58404 − 1.31940I
−2.82546 − 2.65048I 0
u = −0.818744 + 0.695134I
a = −1.14533 − 1.17271I
b = −1.44066 − 0.90346I
9.90058 + 1.48370I 0
u = −0.818744 − 0.695134I
a = −1.14533 + 1.17271I
b = −1.44066 + 0.90346I
9.90058 − 1.48370I 0
u = 0.099843 + 1.107390I
a = 0.291232 + 0.526476I
b = −0.88134 − 1.37902I
−4.54378 + 6.35161I 0
u = 0.099843 − 1.107390I
a = 0.291232 − 0.526476I
b = −0.88134 + 1.37902I
−4.54378 − 6.35161I 0
u = 0.426898 + 1.032290I
a = 0.518448 + 0.965826I
b = −0.611894 + 0.416777I
4.53905 + 4.83419I 0
u = 0.426898 − 1.032290I
a = 0.518448 − 0.965826I
b = −0.611894 − 0.416777I
4.53905 − 4.83419I 0
u = 0.114031 + 1.124140I
a = −0.219078 − 0.521026I
b = 1.02893 + 1.35358I
0.73255 + 9.96253I 0
u = 0.114031 − 1.124140I
a = −0.219078 + 0.521026I
b = 1.02893 − 1.35358I
0.73255 − 9.96253I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772457 + 0.851923I
a = −0.248090 + 0.203737I
b = 0.364833 + 0.912372I
6.36426 − 0.95080I 0
u = −0.772457 − 0.851923I
a = −0.248090 − 0.203737I
b = 0.364833 − 0.912372I
6.36426 + 0.95080I 0
u = 0.637017 + 0.962931I
a = −1.54501 − 0.19549I
b = −0.539132 − 0.678725I
0.37562 + 3.13774I 0
u = 0.637017 − 0.962931I
a = −1.54501 + 0.19549I
b = −0.539132 + 0.678725I
0.37562 − 3.13774I 0
u = 0.694063 + 0.930779I
a = 1.84149 − 0.23992I
b = 0.901783 + 0.492338I
6.17703 + 1.63040I 0
u = 0.694063 − 0.930779I
a = 1.84149 + 0.23992I
b = 0.901783 − 0.492338I
6.17703 − 1.63040I 0
u = −0.648923 + 0.963875I
a = 2.28705 − 0.13460I
b = 1.01494 − 2.14469I
3.17860 − 0.96592I 0
u = −0.648923 − 0.963875I
a = 2.28705 + 0.13460I
b = 1.01494 + 2.14469I
3.17860 + 0.96592I 0
u = −0.802483 + 0.845550I
a = −0.0670920 − 0.0220836I
b = −0.473225 − 0.660175I
12.43660 + 1.84019I 0
u = −0.802483 − 0.845550I
a = −0.0670920 + 0.0220836I
b = −0.473225 + 0.660175I
12.43660 − 1.84019I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.765102 + 0.886692I
a = 0.599881 + 0.042043I
b = −0.024561 − 0.934324I
6.25915 − 4.83547I 0
u = −0.765102 − 0.886692I
a = 0.599881 − 0.042043I
b = −0.024561 + 0.934324I
6.25915 + 4.83547I 0
u = 0.553881 + 1.032230I
a = 1.13450 + 0.85900I
b = −0.089633 + 0.904418I
−1.78862 + 0.40226I 0
u = 0.553881 − 1.032230I
a = 1.13450 − 0.85900I
b = −0.089633 − 0.904418I
−1.78862 − 0.40226I 0
u = 0.610961 + 1.007840I
a = −1.47890 − 0.58939I
b = −0.310480 − 0.915611I
0.41714 + 3.43049I 0
u = 0.610961 − 1.007840I
a = −1.47890 + 0.58939I
b = −0.310480 + 0.915611I
0.41714 − 3.43049I 0
u = −0.660076 + 0.985183I
a = −2.30310 − 0.12522I
b = −1.23552 + 1.96251I
−1.38714 − 4.73913I 0
u = −0.660076 − 0.985183I
a = −2.30310 + 0.12522I
b = −1.23552 − 1.96251I
−1.38714 + 4.73913I 0
u = 0.536811 + 1.057780I
a = −1.05323 − 1.03593I
b = 0.274468 − 0.980206I
3.32573 − 2.90799I 0
u = 0.536811 − 1.057780I
a = −1.05323 + 1.03593I
b = 0.274468 + 0.980206I
3.32573 + 2.90799I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624857 + 0.519885I
a = −0.14823 + 1.43468I
b = 0.095485 + 0.593880I
1.75392 + 1.44567I 0.46845 − 3.19830I
u = 0.624857 − 0.519885I
a = −0.14823 − 1.43468I
b = 0.095485 − 0.593880I
1.75392 − 1.44567I 0.46845 + 3.19830I
u = −0.785281 + 0.904484I
a = −0.567595 − 0.371017I
b = −0.119757 + 0.699012I
12.2566 − 7.7782I 0
u = −0.785281 − 0.904484I
a = −0.567595 + 0.371017I
b = −0.119757 − 0.699012I
12.2566 + 7.7782I 0
u = 0.672023 + 0.995544I
a = 1.91013 + 0.33190I
b = 0.739155 + 0.926686I
−1.07653 + 6.57366I 0
u = 0.672023 − 0.995544I
a = 1.91013 − 0.33190I
b = 0.739155 − 0.926686I
−1.07653 − 6.57366I 0
u = 0.736653 + 0.303470I
a = 0.66833 + 1.37235I
b = 0.734474 + 0.760338I
5.51098 + 7.56145I 4.66571 − 6.73887I
u = 0.736653 − 0.303470I
a = 0.66833 − 1.37235I
b = 0.734474 − 0.760338I
5.51098 − 7.56145I 4.66571 + 6.73887I
u = −0.674913 + 1.007430I
a = 2.31488 + 0.39215I
b = 1.45352 − 1.75153I
1.41878 − 8.56226I 0
u = −0.674913 − 1.007430I
a = 2.31488 − 0.39215I
b = 1.45352 + 1.75153I
1.41878 + 8.56226I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689741 + 0.998409I
a = −2.06247 − 0.29732I
b = −0.866938 − 0.961930I
4.24777 + 10.04400I 0
u = 0.689741 − 0.998409I
a = −2.06247 + 0.29732I
b = −0.866938 + 0.961930I
4.24777 − 10.04400I 0
u = 0.691350 + 0.323647I
a = −0.472036 − 1.315920I
b = −0.615510 − 0.679209I
0.16035 + 4.18611I −0.08760 − 7.00112I
u = 0.691350 − 0.323647I
a = −0.472036 + 1.315920I
b = −0.615510 + 0.679209I
0.16035 − 4.18611I −0.08760 + 7.00112I
u = −0.701167 + 1.022500I
a = 2.22562 + 0.67703I
b = 1.58021 − 1.43553I
2.15321 − 8.65286I 0
u = −0.701167 − 1.022500I
a = 2.22562 − 0.67703I
b = 1.58021 + 1.43553I
2.15321 + 8.65286I 0
u = −0.725895 + 1.009800I
a = −1.95020 − 0.77200I
b = −1.39984 + 1.17166I
8.94198 − 7.27847I 0
u = −0.725895 − 1.009800I
a = −1.95020 + 0.77200I
b = −1.39984 − 1.17166I
8.94198 + 7.27847I 0
u = −0.705585 + 1.038540I
a = −2.31317 − 0.81730I
b = −1.75526 + 1.36554I
0.64185 − 12.72570I 0
u = −0.705585 − 1.038540I
a = −2.31317 + 0.81730I
b = −1.75526 − 1.36554I
0.64185 + 12.72570I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712363 + 1.045250I
a = 2.32087 + 0.91166I
b = 1.82414 − 1.28144I
6.0961 − 16.4704I 0
u = −0.712363 − 1.045250I
a = 2.32087 − 0.91166I
b = 1.82414 + 1.28144I
6.0961 + 16.4704I 0
u = 0.681181 + 0.155183I
a = −0.743363 − 0.691642I
b = −0.901052 − 0.360806I
7.13244 − 0.93823I 7.68047 − 0.32038I
u = 0.681181 − 0.155183I
a = −0.743363 + 0.691642I
b = −0.901052 + 0.360806I
7.13244 + 0.93823I 7.68047 + 0.32038I
u = −0.049709 + 0.669880I
a = 0.47868 + 1.58539I
b = 0.718536 − 0.314667I
2.15512 + 1.97107I −2.70295 − 3.91920I
u = −0.049709 − 0.669880I
a = 0.47868 − 1.58539I
b = 0.718536 + 0.314667I
2.15512 − 1.97107I −2.70295 + 3.91920I
u = 0.566211 + 0.246218I
a = 0.240340 + 0.887725I
b = 0.601429 + 0.361363I
1.35924 + 0.87136I 4.15219 − 0.94788I
u = 0.566211 − 0.246218I
a = 0.240340 − 0.887725I
b = 0.601429 − 0.361363I
1.35924 − 0.87136I 4.15219 + 0.94788I
u = −0.340858 + 0.208082I
a = 0.08860 + 2.84168I
b = 0.482748 + 0.817580I
3.41520 − 3.40175I −0.01797 + 2.25502I
u = −0.340858 − 0.208082I
a = 0.08860 − 2.84168I
b = 0.482748 − 0.817580I
3.41520 + 3.40175I −0.01797 − 2.25502I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154137 + 0.306851I
a = 0.15053 − 2.39095I
b = −0.555962 − 0.393546I
−1.248290 − 0.494452I −7.01028 + 0.72799I
u = −0.154137 − 0.306851I
a = 0.15053 + 2.39095I
b = −0.555962 + 0.393546I
−1.248290 + 0.494452I −7.01028 − 0.72799I
14
II. I
u
2
= h−au + b, a
3
− a
2
u + a
2
+ 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
10
=
a
au
a
11
=
−au + a
au
a
7
=
a
2
+ 1
a
2
u − a
2
a
4
=
u
u − 1
a
9
=
a
au
a
8
=
a
au
a
12
=
a
2
u − au + a + u − 1
a
2
u − a
2
+ au − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
2
u − 3au − a − 3u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
, c
8
, c
9
u
6
c
6
, c
10
(u
3
+ u
2
− 1)
2
c
7
(u
3
− u
2
+ 2u − 1)
2
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
8
, c
9
y
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.083790 + 0.387453I
b = −0.877439 − 0.744862I
3.02413 − 0.79824I 1.45566 − 0.28364I
u = 0.500000 + 0.866025I
a = 0.206350 + 1.132320I
b = −0.877439 + 0.744862I
3.02413 + 4.85801I −2.09851 − 6.80481I
u = 0.500000 + 0.866025I
a = 0.377439 − 0.653743I
b = 0.754878
−1.11345 + 2.02988I −5.85715 − 2.43783I
u = 0.500000 − 0.866025I
a = −1.083790 − 0.387453I
b = −0.877439 + 0.744862I
3.02413 + 0.79824I 1.45566 + 0.28364I
u = 0.500000 − 0.866025I
a = 0.206350 − 1.132320I
b = −0.877439 − 0.744862I
3.02413 − 4.85801I −2.09851 + 6.80481I
u = 0.500000 − 0.866025I
a = 0.377439 + 0.653743I
b = 0.754878
−1.11345 − 2.02988I −5.85715 + 2.43783I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
3
)(u
92
+ 32u
91
+ ··· + 18u + 1)
c
2
((u
2
+ u + 1)
3
)(u
92
+ 4u
91
+ ··· + 2u + 1)
c
3
, c
9
u
6
(u
92
+ u
91
+ ··· + 32u + 64)
c
5
((u
2
− u + 1)
3
)(u
92
+ 4u
91
+ ··· + 2u + 1)
c
6
((u
3
+ u
2
− 1)
2
)(u
92
+ 3u
91
+ ··· − 3u + 1)
c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
92
− 3u
91
+ ··· − 5u + 1)
c
8
u
6
(u
92
− 35u
91
+ ··· − 70656u + 4096)
c
10
((u
3
+ u
2
− 1)
2
)(u
92
− 21u
91
+ ··· − 69583u + 3971)
c
11
, c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
92
− 3u
91
+ ··· − 5u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
92
+ 60y
91
+ ··· + 102y + 1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
92
+ 32y
91
+ ··· + 18y + 1)
c
3
, c
9
y
6
(y
92
− 35y
91
+ ··· − 70656y + 4096)
c
6
((y
3
− y
2
+ 2y −1)
2
)(y
92
− y
91
+ ··· − y + 1)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
92
+ 83y
91
+ ··· − y + 1)
c
8
y
6
(y
92
+ 33y
91
+ ··· + 3.68050 × 10
8
y + 1.67772 × 10
7
)
c
10
((y
3
− y
2
+ 2y −1)
2
)(y
92
+ 19y
91
+ ··· + 4.18606 × 10
8
y + 1.57688 × 10
7
)
20
