12a
0428
(K12a
0428
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 5 11 12 1 7 4 9
Solving Sequence
9,12
1
4,10
3 2 8 5 11 7 6
c
12
c
9
c
3
c
1
c
8
c
4
c
11
c
7
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.80676 × 10
126
u
84
− 1.58226 × 10
127
u
83
+ ··· + 6.30962 × 10
126
b − 8.39340 × 10
126
,
− 8.84774 × 10
126
u
84
+ 5.87857 × 10
127
u
83
+ ··· + 6.30962 × 10
126
a + 7.56669 × 10
127
,
u
85
− 7u
84
+ ··· − 6u + 2i
I
u
2
= hb + 1, 2a + u − 4, u
2
− 2i
I
v
1
= ha, b − 1, v −1i
* 3 irreducible components of dim
C
= 0, with total 88 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
= h2.81 × 10
126
u
84
− 1.58 × 10
127
u
83
+ · · · + 6.31 × 10
126
b − 8.39 ×
10
126
, −8.85 × 10
126
u
84
+ 5.88 × 10
127
u
83
+ · · · + 6.31 × 10
126
a + 7.57 ×
10
127
, u
85
− 7u
84
+ · · · − 6u + 2i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
1.40226u
84
− 9.31684u
83
+ ··· − 23.5188u − 11.9923
−0.444839u
84
+ 2.50770u
83
+ ··· − 0.499951u + 1.33025
a
10
=
u
−u
3
+ u
a
3
=
1.47259u
84
− 9.46618u
83
+ ··· − 22.8706u − 13.0462
−0.418554u
84
+ 2.03469u
83
+ ··· − 1.76897u + 0.962317
a
2
=
−1.84257u
84
+ 11.7840u
83
+ ··· + 18.6397u + 10.0949
1.51198u
84
− 8.84490u
83
+ ··· + 3.89018u − 2.11365
a
8
=
−u
u
a
5
=
1.67889u
84
− 10.4912u
83
+ ··· − 20.9610u − 12.2067
−0.721468u
84
+ 3.68203u
83
+ ··· − 3.05782u + 1.54459
a
11
=
0.138261u
84
− 1.44715u
83
+ ··· − 8.35732u − 4.42866
0.360457u
84
− 2.01792u
83
+ ··· + 1.41000u − 0.981112
a
7
=
−0.138261u
84
+ 1.44715u
83
+ ··· + 8.35732u + 4.42866
−0.519401u
84
+ 2.66327u
83
+ ··· − 1.74245u − 0.0224697
a
6
=
1.22347u
84
− 7.56601u
83
+ ··· − 9.48559u − 3.57665
−1.38509u
84
+ 7.99231u
83
+ ··· − 3.90685u + 1.41003
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.04066u
84
+ 28.4088u
83
+ ··· + 78.3664u + 30.4352
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
85
+ 26u
84
+ ··· + 138u + 1
c
2
, c
5
u
85
+ 4u
84
+ ··· − 10u + 1
c
3
u
85
− 30u
84
+ ··· + 3982062u + 182711
c
4
u
85
+ 24u
84
+ ··· + 38u + 349
c
7
, c
10
u
85
+ 2u
84
+ ··· + 22u + 1
c
8
, c
9
, c
12
u
85
− 7u
84
+ ··· − 6u + 2
c
11
u
85
− 4u
84
+ ··· − 10u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
85
+ 70y
84
+ ··· + 18106y −1
c
2
, c
5
y
85
− 26y
84
+ ··· + 138y −1
c
3
y
85
− 266y
84
+ ··· + 5409686724738y −33383309521
c
4
y
85
− 258y
84
+ ··· − 3360822y −121801
c
7
, c
10
y
85
− 50y
84
+ ··· + 210y −1
c
8
, c
9
, c
12
y
85
− 91y
84
+ ··· + 84y −4
c
11
y
85
− 10y
84
+ ··· + 82y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350398 + 0.954037I
a = −0.219916 + 0.109779I
b = −0.615170 − 0.648027I
1.23620 + 1.62017I 0
u = −0.350398 − 0.954037I
a = −0.219916 − 0.109779I
b = −0.615170 + 0.648027I
1.23620 − 1.62017I 0
u = −0.689400 + 0.747068I
a = −0.820189 − 0.472975I
b = 0.887204 − 0.981521I
2.30710 − 7.08904I 0
u = −0.689400 − 0.747068I
a = −0.820189 + 0.472975I
b = 0.887204 + 0.981521I
2.30710 + 7.08904I 0
u = −0.663371 + 0.802333I
a = 0.809381 + 0.448944I
b = −0.903277 + 0.986202I
1.47284 − 13.12350I 0
u = −0.663371 − 0.802333I
a = 0.809381 − 0.448944I
b = −0.903277 − 0.986202I
1.47284 + 13.12350I 0
u = −0.443639 + 0.971475I
a = 0.188178 − 0.202759I
b = 0.625699 + 0.679357I
0.74636 + 7.39297I 0
u = −0.443639 − 0.971475I
a = 0.188178 + 0.202759I
b = 0.625699 − 0.679357I
0.74636 − 7.39297I 0
u = −0.582158 + 0.684632I
a = 0.424934 − 0.552027I
b = 0.520307 + 0.764862I
−4.75882 + 3.00452I 0
u = −0.582158 − 0.684632I
a = 0.424934 + 0.552027I
b = 0.520307 − 0.764862I
−4.75882 − 3.00452I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.483276 + 0.686746I
a = 0.721089 + 0.479217I
b = −0.894296 + 1.050870I
−5.01547 − 7.61885I 0
u = −0.483276 − 0.686746I
a = 0.721089 − 0.479217I
b = −0.894296 − 1.050870I
−5.01547 + 7.61885I 0
u = −0.780126 + 0.247893I
a = 0.24627 − 1.42990I
b = 0.260947 + 0.994313I
−3.10853 − 1.92390I 0
u = −0.780126 − 0.247893I
a = 0.24627 + 1.42990I
b = 0.260947 − 0.994313I
−3.10853 + 1.92390I 0
u = 0.352197 + 0.734345I
a = 0.228751 − 0.454302I
b = −0.622349 − 0.427633I
−0.61148 + 3.02035I 0
u = 0.352197 − 0.734345I
a = 0.228751 + 0.454302I
b = −0.622349 + 0.427633I
−0.61148 − 3.02035I 0
u = 0.718711 + 0.953380I
a = 0.334403 − 0.245488I
b = −0.690642 − 0.403366I
5.16840 + 6.32915I 0
u = 0.718711 − 0.953380I
a = 0.334403 + 0.245488I
b = −0.690642 + 0.403366I
5.16840 − 6.32915I 0
u = 0.797687 + 0.893769I
a = −0.365741 + 0.245017I
b = 0.687642 + 0.390239I
5.44394 + 0.44289I 0
u = 0.797687 − 0.893769I
a = −0.365741 − 0.245017I
b = 0.687642 − 0.390239I
5.44394 − 0.44289I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.523520 + 0.498463I
a = −0.694604 − 0.589082I
b = 0.805309 − 1.079360I
−1.28750 − 4.47163I 0. + 7.27748I
u = −0.523520 − 0.498463I
a = −0.694604 + 0.589082I
b = 0.805309 + 1.079360I
−1.28750 + 4.47163I 0. − 7.27748I
u = 1.312140 + 0.034317I
a = −0.288123 − 0.083227I
b = 0.282890 − 0.765202I
2.85614 + 1.44672I 0
u = 1.312140 − 0.034317I
a = −0.288123 + 0.083227I
b = 0.282890 + 0.765202I
2.85614 − 1.44672I 0
u = 0.633148 + 0.261587I
a = −0.599636 − 0.162415I
b = 1.010410 − 0.616700I
3.19350 + 0.56226I 3.06377 − 2.90425I
u = 0.633148 − 0.261587I
a = −0.599636 + 0.162415I
b = 1.010410 + 0.616700I
3.19350 − 0.56226I 3.06377 + 2.90425I
u = 0.540521 + 0.360690I
a = 0.590908 + 0.173669I
b = −1.095800 + 0.703881I
2.25501 + 6.33839I 0.16573 − 8.82951I
u = 0.540521 − 0.360690I
a = 0.590908 − 0.173669I
b = −1.095800 − 0.703881I
2.25501 − 6.33839I 0.16573 + 8.82951I
u = 0.550804 + 0.330376I
a = −0.605955 + 0.401645I
b = 0.664924 + 0.336752I
1.141080 + 0.674467I 6.05979 − 2.03685I
u = 0.550804 − 0.330376I
a = −0.605955 − 0.401645I
b = 0.664924 − 0.336752I
1.141080 − 0.674467I 6.05979 + 2.03685I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.373900 + 0.312502I
a = −0.546242 + 0.208542I
b = 0.540012 + 0.290386I
2.32626 + 1.44371I 0
u = 1.373900 − 0.312502I
a = −0.546242 − 0.208542I
b = 0.540012 − 0.290386I
2.32626 − 1.44371I 0
u = −1.40914
a = −16.7791
b = 0.101896
2.16646 0
u = −0.575916 + 0.039342I
a = −0.56776 + 1.38481I
b = 0.314595 + 0.853851I
4.04443 + 2.89490I 2.62420 − 5.69184I
u = −0.575916 − 0.039342I
a = −0.56776 − 1.38481I
b = 0.314595 − 0.853851I
4.04443 − 2.89490I 2.62420 + 5.69184I
u = −1.42933
a = −2.01148
b = 1.27671
3.31731 0
u = −1.43615 + 0.00633I
a = −1.07681 + 8.24758I
b = 0.026127 + 0.202391I
6.35829 − 2.84127I 0
u = −1.43615 − 0.00633I
a = −1.07681 − 8.24758I
b = 0.026127 − 0.202391I
6.35829 + 2.84127I 0
u = −0.302575 + 0.455380I
a = −1.49220 + 0.23122I
b = −0.383548 − 0.612585I
−1.80646 + 1.16535I −2.20309 + 0.49603I
u = −0.302575 − 0.455380I
a = −1.49220 − 0.23122I
b = −0.383548 + 0.612585I
−1.80646 − 1.16535I −2.20309 − 0.49603I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46581
a = 1.07213
b = −0.291522
3.38907 0
u = 1.47026 + 0.09843I
a = −1.90184 − 1.00109I
b = 1.48075 + 1.64599I
1.40995 + 2.41389I 0
u = 1.47026 − 0.09843I
a = −1.90184 + 1.00109I
b = 1.48075 − 1.64599I
1.40995 − 2.41389I 0
u = −0.301501 + 0.430647I
a = 0.540764 + 0.519219I
b = −0.87964 + 1.24285I
−4.44895 − 0.68347I −8.48630 + 5.94537I
u = −0.301501 − 0.430647I
a = 0.540764 − 0.519219I
b = −0.87964 − 1.24285I
−4.44895 + 0.68347I −8.48630 − 5.94537I
u = −1.47467
a = −2.37463
b = 2.10239
3.16776 0
u = −0.498452 + 0.140002I
a = 0.54620 − 1.67577I
b = −0.250598 − 0.735061I
3.84985 − 3.08699I 1.200909 + 0.416894I
u = −0.498452 − 0.140002I
a = 0.54620 + 1.67577I
b = −0.250598 + 0.735061I
3.84985 + 3.08699I 1.200909 − 0.416894I
u = −1.46964 + 0.20672I
a = −1.54329 − 0.13102I
b = 1.099320 − 0.617535I
5.32596 − 6.27686I 0
u = −1.46964 − 0.20672I
a = −1.54329 + 0.13102I
b = 1.099320 + 0.617535I
5.32596 + 6.27686I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50742 + 0.21678I
a = −1.88143 − 0.35406I
b = 1.30541 + 1.20213I
1.48847 + 10.87230I 0
u = 1.50742 − 0.21678I
a = −1.88143 + 0.35406I
b = 1.30541 − 1.20213I
1.48847 − 10.87230I 0
u = 1.52560 + 0.04894I
a = −0.732565 + 0.568243I
b = 0.60909 − 1.42456I
10.66790 + 3.82825I 0
u = 1.52560 − 0.04894I
a = −0.732565 − 0.568243I
b = 0.60909 + 1.42456I
10.66790 − 3.82825I 0
u = −1.52356 + 0.11089I
a = 1.64270 − 0.07825I
b = −1.262990 + 0.607994I
7.99831 − 2.36928I 0
u = −1.52356 − 0.11089I
a = 1.64270 + 0.07825I
b = −1.262990 − 0.607994I
7.99831 + 2.36928I 0
u = −1.53057 + 0.09366I
a = −1.58412 − 0.90265I
b = 1.53360 + 1.16611I
9.16879 − 7.92620I 0
u = −1.53057 − 0.09366I
a = −1.58412 + 0.90265I
b = 1.53360 − 1.16611I
9.16879 + 7.92620I 0
u = 1.52747 + 0.14748I
a = 1.72231 + 0.56923I
b = −1.26106 − 1.37468I
5.52175 + 6.80206I 0
u = 1.52747 − 0.14748I
a = 1.72231 − 0.56923I
b = −1.26106 + 1.37468I
5.52175 − 6.80206I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54188 + 0.01197I
a = 0.905976 − 0.683222I
b = −0.73000 + 1.51724I
11.17630 − 2.69311I 0
u = 1.54188 − 0.01197I
a = 0.905976 + 0.683222I
b = −0.73000 − 1.51724I
11.17630 + 2.69311I 0
u = 0.217769 + 0.395625I
a = −2.31457 + 3.78349I
b = 0.549464 + 0.358418I
1.33766 − 3.69180I −2.91564 − 6.56746I
u = 0.217769 − 0.395625I
a = −2.31457 − 3.78349I
b = 0.549464 − 0.358418I
1.33766 + 3.69180I −2.91564 + 6.56746I
u = 0.137119 + 0.429179I
a = 1.41458 − 3.63175I
b = −0.508025 − 0.397814I
1.61743 + 1.92054I −4.53145 − 10.20212I
u = 0.137119 − 0.429179I
a = 1.41458 + 3.63175I
b = −0.508025 + 0.397814I
1.61743 − 1.92054I −4.53145 + 10.20212I
u = −1.55025 + 0.05271I
a = 1.65971 + 0.68673I
b = −1.54955 − 0.98630I
10.50810 − 1.58318I 0
u = −1.55025 − 0.05271I
a = 1.65971 − 0.68673I
b = −1.54955 + 0.98630I
10.50810 + 1.58318I 0
u = 1.59322 + 0.24396I
a = 1.68399 + 0.21421I
b = −1.16060 − 1.17745I
9.8437 + 10.7875I 0
u = 1.59322 − 0.24396I
a = 1.68399 − 0.21421I
b = −1.16060 + 1.17745I
9.8437 − 10.7875I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58993 + 0.26792I
a = −1.71012 − 0.16860I
b = 1.16281 + 1.14841I
8.8777 + 17.1027I 0
u = 1.58993 − 0.26792I
a = −1.71012 + 0.16860I
b = 1.16281 − 1.14841I
8.8777 − 17.1027I 0
u = 1.61589
a = 0.698589
b = −0.487127
3.20256 0
u = −1.61442 + 0.28932I
a = −1.330270 − 0.024937I
b = 1.115990 − 0.750430I
12.8099 − 10.8246I 0
u = −1.61442 − 0.28932I
a = −1.330270 + 0.024937I
b = 1.115990 + 0.750430I
12.8099 + 10.8246I 0
u = −1.62338 + 0.25478I
a = 1.350760 − 0.010554I
b = −1.136210 + 0.748740I
13.4106 − 4.5882I 0
u = −1.62338 − 0.25478I
a = 1.350760 + 0.010554I
b = −1.136210 − 0.748740I
13.4106 + 4.5882I 0
u = 0.324337
a = 0.519295
b = −1.59336
−2.87826 11.9720
u = −0.046813 + 0.268057I
a = 0.91813 − 2.01039I
b = −0.329123 − 0.384605I
−1.299660 − 0.323757I −7.76191 + 0.15984I
u = −0.046813 − 0.268057I
a = 0.91813 + 2.01039I
b = −0.329123 + 0.384605I
−1.299660 + 0.323757I −7.76191 − 0.15984I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70664 + 0.39050I
a = −0.546221 + 0.106871I
b = 0.628527 + 0.166438I
7.66813 + 4.11619I 0
u = 1.70664 − 0.39050I
a = −0.546221 − 0.106871I
b = 0.628527 − 0.166438I
7.66813 − 4.11619I 0
u = 1.74211 + 0.33236I
a = 0.556958 − 0.093535I
b = −0.623304 − 0.141707I
7.76568 − 1.75662I 0
u = 1.74211 − 0.33236I
a = 0.556958 + 0.093535I
b = −0.623304 + 0.141707I
7.76568 + 1.75662I 0
u = 0.208276
a = −13.4536
b = 0.461304
−3.01471 42.1890
13
II. I
u
2
= hb + 1, 2a + u − 4, u
2
− 2i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−2
a
4
=
−
1
2
u + 2
−1
a
10
=
u
−u
a
3
=
1
2
u
−u + 1
a
2
=
1
2
u + 1
−u − 1
a
8
=
−u
u
a
5
=
1
2
u
−u + 1
a
11
=
1
2
u − 1
1
a
7
=
−
1
2
u − 1
u + 1
a
6
=
−1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
(u − 1)
2
c
3
u
2
− 2u − 1
c
4
u
2
+ 2u − 1
c
5
, c
6
, c
7
c
11
(u + 1)
2
c
8
, c
9
, c
12
u
2
− 2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
(y −1)
2
c
3
, c
4
y
2
− 6y + 1
c
8
, c
9
, c
12
(y −2)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 1.29289
b = −1.00000
1.64493 −4.00000
u = −1.41421
a = 2.70711
b = −1.00000
1.64493 −4.00000
17
III. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
1
0
a
1
=
1
0
a
4
=
0
1
a
10
=
1
0
a
3
=
−1
1
a
2
=
0
1
a
8
=
1
0
a
5
=
−1
1
a
11
=
1
1
a
7
=
0
−1
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
u − 1
c
3
, c
4
, c
5
c
6
, c
10
u + 1
c
8
, c
9
, c
12
u
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
10
, c
11
y −1
c
8
, c
9
, c
12
y
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
85
+ 26u
84
+ ··· + 138u + 1)
c
2
((u − 1)
3
)(u
85
+ 4u
84
+ ··· − 10u + 1)
c
3
(u + 1)(u
2
− 2u − 1)(u
85
− 30u
84
+ ··· + 3982062u + 182711)
c
4
(u + 1)(u
2
+ 2u − 1)(u
85
+ 24u
84
+ ··· + 38u + 349)
c
5
((u + 1)
3
)(u
85
+ 4u
84
+ ··· − 10u + 1)
c
6
((u + 1)
3
)(u
85
+ 26u
84
+ ··· + 138u + 1)
c
7
(u − 1)(u + 1)
2
(u
85
+ 2u
84
+ ··· + 22u + 1)
c
8
, c
9
, c
12
u(u
2
− 2)(u
85
− 7u
84
+ ··· − 6u + 2)
c
10
((u − 1)
2
)(u + 1)(u
85
+ 2u
84
+ ··· + 22u + 1)
c
11
(u − 1)(u + 1)
2
(u
85
− 4u
84
+ ··· − 10u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
3
)(y
85
+ 70y
84
+ ··· + 18106y −1)
c
2
, c
5
((y −1)
3
)(y
85
− 26y
84
+ ··· + 138y −1)
c
3
(y −1)(y
2
− 6y + 1)
· (y
85
− 266y
84
+ ··· + 5409686724738y −33383309521)
c
4
(y −1)(y
2
− 6y + 1)(y
85
− 258y
84
+ ··· − 3360822y −121801)
c
7
, c
10
((y −1)
3
)(y
85
− 50y
84
+ ··· + 210y −1)
c
8
, c
9
, c
12
y(y −2)
2
(y
85
− 91y
84
+ ··· + 84y −4)
c
11
((y −1)
3
)(y
85
− 10y
84
+ ··· + 82y −1)
23
