12a
1236
(K12a
1236
)
A knot diagram
1
Linearized knot diagam
5 6 9 10 11 3 12 1 4 2 8 7
Solving Sequence
7,12
8 1
3,9
4 6 2 11 5 10
c
7
c
12
c
8
c
3
c
6
c
2
c
11
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.42131 × 10
123
u
103
− 8.31432 × 10
122
u
102
+ ··· + 7.88496 × 10
123
b − 1.31020 × 10
124
,
2.40145 × 10
123
u
103
+ 7.06011 × 10
121
u
102
+ ··· + 7.88496 × 10
123
a − 3.73579 × 10
124
,
u
104
+ 48u
102
+ ··· − 10u + 1i
I
u
2
= h−u
18
− u
17
+ ··· + b + 1, −3u
19
− 3u
18
+ ··· + a + 2, u
21
+ u
20
+ ··· − 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 125 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
= h1.42 × 10
123
u
103
− 8.31 × 10
122
u
102
+ · · · + 7.88 × 10
123
b − 1.31 ×
10
124
, 2.40 × 10
123
u
103
+ 7.06 × 10
121
u
102
+ · · · + 7.88 × 10
123
a − 3.74 ×
10
124
, u
104
+ 48u
102
+ · · · − 10u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
3
=
−0.304561u
103
− 0.00895389u
102
+ ··· − 5.28918u + 4.73786
−0.180256u
103
+ 0.105445u
102
+ ··· − 0.205229u + 1.66165
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
4
=
−0.503681u
103
− 0.0491159u
102
+ ··· − 5.68605u + 6.33520
−0.141227u
103
+ 0.133202u
102
+ ··· − 0.273063u + 1.70134
a
6
=
−0.754616u
103
− 0.358618u
102
+ ··· − 1.06064u + 8.36278
−0.163006u
103
+ 0.0997843u
102
+ ··· − 2.03954u + 3.07367
a
2
=
1.30230u
103
+ 0.259004u
102
+ ··· − 0.111082u − 10.0921
0.441501u
103
− 0.0875902u
102
+ ··· + 3.77303u − 3.80556
a
11
=
u
u
3
+ u
a
5
=
−0.873306u
103
− 0.247297u
102
+ ··· − 1.79375u + 8.39105
−0.0628994u
103
+ 0.0596347u
102
+ ··· − 1.54074u + 2.99062
a
10
=
0.688002u
103
− 0.203148u
102
+ ··· + 8.09484u − 9.31886
0.212943u
103
+ 0.326702u
102
+ ··· − 0.785101u − 2.66788
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.09066u
103
− 0.418692u
102
+ ··· − 10.7066u + 25.3820
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 7u
103
+ ··· − 906u + 1909
c
2
, c
6
u
104
+ 2u
103
+ ··· + 63u + 73
c
3
, c
4
, c
9
u
104
− u
103
+ ··· − 42u − 1
c
5
u
104
+ u
103
+ ··· − 106u + 1
c
7
, c
11
, c
12
u
104
+ 48u
102
+ ··· + 10u + 1
c
8
u
104
− u
101
+ ··· + 7744u + 457
c
10
u
104
− 5u
103
+ ··· − 39735u + 17047
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 23y
103
+ ··· + 88027842y + 3644281
c
2
, c
6
y
104
− 82y
103
+ ··· + 131957y + 5329
c
3
, c
4
, c
9
y
104
− 109y
103
+ ··· − 1178y + 1
c
5
y
104
+ 15y
103
+ ··· − 10638y + 1
c
7
, c
11
, c
12
y
104
+ 96y
103
+ ··· − 72y + 1
c
8
y
104
+ 106y
102
+ ··· − 16677012y + 208849
c
10
y
104
− 41y
103
+ ··· − 14746825375y + 290600209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.620118 + 0.789865I
a = 0.521286 + 0.592077I
b = −1.35459 − 0.45056I
9.56661 + 8.03524I 0
u = 0.620118 − 0.789865I
a = 0.521286 − 0.592077I
b = −1.35459 + 0.45056I
9.56661 − 8.03524I 0
u = −0.105335 + 1.030070I
a = 1.51620 − 0.42594I
b = −0.385243 + 0.617360I
5.10809 + 3.63975I 0
u = −0.105335 − 1.030070I
a = 1.51620 + 0.42594I
b = −0.385243 − 0.617360I
5.10809 − 3.63975I 0
u = −1.03778
a = −0.0269272
b = −1.07237
3.29245 0
u = −0.746382 + 0.602859I
a = 0.998714 − 0.840032I
b = −0.855899 − 0.402358I
3.94155 + 4.30366I 0
u = −0.746382 − 0.602859I
a = 0.998714 + 0.840032I
b = −0.855899 + 0.402358I
3.94155 − 4.30366I 0
u = 0.829680 + 0.352824I
a = 0.565617 + 1.157080I
b = −1.41176 + 0.56699I
8.2061 − 13.0082I 0
u = 0.829680 − 0.352824I
a = 0.565617 − 1.157080I
b = −1.41176 − 0.56699I
8.2061 + 13.0082I 0
u = −0.154977 + 1.099720I
a = −0.834959 − 0.027034I
b = 0.308767 + 0.799992I
0.087281 − 0.510738I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154977 − 1.099720I
a = −0.834959 + 0.027034I
b = 0.308767 − 0.799992I
0.087281 + 0.510738I 0
u = 0.191981 + 0.865189I
a = −0.082965 − 0.736955I
b = 1.340770 + 0.359873I
9.58062 − 0.35742I 0
u = 0.191981 − 0.865189I
a = −0.082965 + 0.736955I
b = 1.340770 − 0.359873I
9.58062 + 0.35742I 0
u = 0.857934
a = −0.114455
b = 0.723712
−1.60767 −15.4730
u = 0.367285 + 1.109370I
a = −0.960640 − 0.313248I
b = 0.861427 − 0.337448I
1.80378 − 4.43282I 0
u = 0.367285 − 1.109370I
a = −0.960640 + 0.313248I
b = 0.861427 + 0.337448I
1.80378 + 4.43282I 0
u = −0.408974 + 0.720777I
a = −1.010150 + 0.592828I
b = 1.171700 − 0.398512I
2.81966 − 4.74793I 3.70519 + 4.52321I
u = −0.408974 − 0.720777I
a = −1.010150 − 0.592828I
b = 1.171700 + 0.398512I
2.81966 + 4.74793I 3.70519 − 4.52321I
u = 0.043813 + 1.200940I
a = 1.50087 − 0.34043I
b = −1.093100 − 0.538555I
3.93615 + 1.11713I 0
u = 0.043813 − 1.200940I
a = 1.50087 + 0.34043I
b = −1.093100 + 0.538555I
3.93615 − 1.11713I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.695428 + 0.387530I
a = −0.813314 − 0.738577I
b = 0.910790 − 0.218196I
−0.45127 − 2.08949I −5.67320 + 7.54122I
u = 0.695428 − 0.387530I
a = −0.813314 + 0.738577I
b = 0.910790 + 0.218196I
−0.45127 + 2.08949I −5.67320 − 7.54122I
u = −0.735924 + 0.296284I
a = −0.80397 + 1.25813I
b = 1.303710 + 0.471076I
1.35265 + 8.84857I 1.14263 − 8.81074I
u = −0.735924 − 0.296284I
a = −0.80397 − 1.25813I
b = 1.303710 − 0.471076I
1.35265 − 8.84857I 1.14263 + 8.81074I
u = −0.705894 + 0.351680I
a = 0.188275 + 0.274678I
b = −0.551335 + 0.540399I
3.17492 + 0.39098I 0.93290 − 2.00106I
u = −0.705894 − 0.351680I
a = 0.188275 − 0.274678I
b = −0.551335 − 0.540399I
3.17492 − 0.39098I 0.93290 + 2.00106I
u = −0.722198 + 0.274964I
a = 0.19760 + 1.63490I
b = 1.194830 + 0.126529I
8.05202 + 4.22912I 6.55587 − 4.57124I
u = −0.722198 − 0.274964I
a = 0.19760 − 1.63490I
b = 1.194830 − 0.126529I
8.05202 − 4.22912I 6.55587 + 4.57124I
u = −0.771734
a = 0.759937
b = −0.790368
2.40158 5.63180
u = −0.246560 + 0.725443I
a = −0.446882 − 0.239528I
b = 1.329300 + 0.122327I
9.68887 − 0.42429I 9.29933 − 1.12741I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246560 − 0.725443I
a = −0.446882 + 0.239528I
b = 1.329300 − 0.122327I
9.68887 + 0.42429I 9.29933 + 1.12741I
u = 0.716700 + 0.247198I
a = 0.11399 − 1.50069I
b = 1.44713 − 0.71686I
7.66319 − 3.32471I 7.08153 + 4.25402I
u = 0.716700 − 0.247198I
a = 0.11399 + 1.50069I
b = 1.44713 + 0.71686I
7.66319 + 3.32471I 7.08153 − 4.25402I
u = 0.243166 + 1.243460I
a = 0.202575 + 0.189137I
b = −0.284679 + 0.591002I
1.66136 − 3.20269I 0
u = 0.243166 − 1.243460I
a = 0.202575 − 0.189137I
b = −0.284679 − 0.591002I
1.66136 + 3.20269I 0
u = 0.665439 + 0.274419I
a = −0.332478 − 0.928461I
b = 0.011124 − 1.285510I
3.67182 − 6.63904I 1.49843 + 7.92289I
u = 0.665439 − 0.274419I
a = −0.332478 + 0.928461I
b = 0.011124 + 1.285510I
3.67182 + 6.63904I 1.49843 − 7.92289I
u = −0.080589 + 1.296550I
a = −0.078900 − 0.672379I
b = −0.614973 + 0.771669I
4.80034 − 1.11455I 0
u = −0.080589 − 1.296550I
a = −0.078900 + 0.672379I
b = −0.614973 − 0.771669I
4.80034 + 1.11455I 0
u = 0.698700 + 0.022216I
a = −0.527324 − 0.318258I
b = −0.041523 − 0.373581I
−2.08518 − 0.19609I −5.25700 − 1.07973I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.698700 − 0.022216I
a = −0.527324 + 0.318258I
b = −0.041523 + 0.373581I
−2.08518 + 0.19609I −5.25700 + 1.07973I
u = −0.682573 + 0.149623I
a = 0.368074 − 0.719379I
b = 0.042810 − 0.956572I
−2.61203 + 3.75303I −4.16251 − 7.39345I
u = −0.682573 − 0.149623I
a = 0.368074 + 0.719379I
b = 0.042810 + 0.956572I
−2.61203 − 3.75303I −4.16251 + 7.39345I
u = 0.071296 + 1.310970I
a = −0.071099 − 0.804873I
b = −0.427448 + 0.028098I
4.95252 − 1.57160I 0
u = 0.071296 − 1.310970I
a = −0.071099 + 0.804873I
b = −0.427448 − 0.028098I
4.95252 + 1.57160I 0
u = 0.303223 + 1.286920I
a = −0.587063 + 0.148446I
b = 0.088712 − 0.174045I
1.98304 − 3.83783I 0
u = 0.303223 − 1.286920I
a = −0.587063 − 0.148446I
b = 0.088712 + 0.174045I
1.98304 + 3.83783I 0
u = −0.573315 + 1.219970I
a = 0.718100 − 0.491528I
b = −1.111370 − 0.127817I
7.02373 + 5.61735I 0
u = −0.573315 − 1.219970I
a = 0.718100 + 0.491528I
b = −1.111370 + 0.127817I
7.02373 − 5.61735I 0
u = −0.273407 + 1.343450I
a = 0.849372 + 0.471844I
b = −0.087968 − 1.038730I
2.09247 + 7.22215I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273407 − 1.343450I
a = 0.849372 − 0.471844I
b = −0.087968 + 1.038730I
2.09247 − 7.22215I 0
u = 0.569902 + 0.259753I
a = 1.47098 + 1.16159I
b = −1.250830 + 0.290569I
1.59615 − 3.09335I 3.07050 + 7.96279I
u = 0.569902 − 0.259753I
a = 1.47098 − 1.16159I
b = −1.250830 − 0.290569I
1.59615 + 3.09335I 3.07050 − 7.96279I
u = 0.064615 + 1.389110I
a = −2.69390 − 0.27554I
b = 1.130990 − 0.439667I
9.11640 − 3.79729I 0
u = 0.064615 − 1.389110I
a = −2.69390 + 0.27554I
b = 1.130990 + 0.439667I
9.11640 + 3.79729I 0
u = −0.217418 + 1.379800I
a = 1.97103 − 0.92033I
b = −1.399880 + 0.080986I
6.95103 + 2.47096I 0
u = −0.217418 − 1.379800I
a = 1.97103 + 0.92033I
b = −1.399880 − 0.080986I
6.95103 − 2.47096I 0
u = 0.131274 + 1.392020I
a = −2.35695 − 1.10644I
b = 2.03046 + 0.39544I
15.1827 − 1.2684I 0
u = 0.131274 − 1.392020I
a = −2.35695 + 1.10644I
b = 2.03046 − 0.39544I
15.1827 + 1.2684I 0
u = −0.212116 + 1.389820I
a = 2.20201 − 0.82635I
b = −1.35433 − 0.67085I
6.99266 + 5.38612I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.212116 − 1.389820I
a = 2.20201 + 0.82635I
b = −1.35433 + 0.67085I
6.99266 − 5.38612I 0
u = 0.20338 + 1.40110I
a = 2.12985 + 1.61341I
b = −1.160280 + 0.081319I
7.27022 − 2.24226I 0
u = 0.20338 − 1.40110I
a = 2.12985 − 1.61341I
b = −1.160280 − 0.081319I
7.27022 + 2.24226I 0
u = 0.16109 + 1.40977I
a = 0.120261 − 0.660060I
b = 0.673479 + 1.217030I
10.51900 + 1.46499I 0
u = 0.16109 − 1.40977I
a = 0.120261 + 0.660060I
b = 0.673479 − 1.217030I
10.51900 − 1.46499I 0
u = 0.22769 + 1.40184I
a = 2.73223 + 0.77856I
b = −1.384850 + 0.232626I
6.91603 − 6.05149I 0
u = 0.22769 − 1.40184I
a = 2.73223 − 0.77856I
b = −1.384850 − 0.232626I
6.91603 + 6.05149I 0
u = −0.12690 + 1.41514I
a = −2.49800 + 0.06442I
b = 1.57856 − 0.11426I
15.7422 + 0.8659I 0
u = −0.12690 − 1.41514I
a = −2.49800 − 0.06442I
b = 1.57856 + 0.11426I
15.7422 − 0.8659I 0
u = −0.14866 + 1.41986I
a = −0.023453 − 0.800359I
b = 0.363945 − 0.398775I
10.64610 + 5.13547I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14866 − 1.41986I
a = −0.023453 + 0.800359I
b = 0.363945 + 0.398775I
10.64610 − 5.13547I 0
u = −0.516954 + 0.237865I
a = 0.35640 − 1.91087I
b = −1.132780 − 0.585934I
1.79267 + 2.64792I 4.98022 − 10.27183I
u = −0.516954 − 0.237865I
a = 0.35640 + 1.91087I
b = −1.132780 + 0.585934I
1.79267 − 2.64792I 4.98022 + 10.27183I
u = 0.28290 + 1.40368I
a = −1.99965 − 0.89852I
b = 1.55247 − 0.88840I
12.9310 − 6.9544I 0
u = 0.28290 − 1.40368I
a = −1.99965 + 0.89852I
b = 1.55247 + 0.88840I
12.9310 + 6.9544I 0
u = −0.09297 + 1.42903I
a = −2.51248 + 0.76287I
b = 1.187870 − 0.152148I
9.54976 − 3.46045I 0
u = −0.09297 − 1.42903I
a = −2.51248 − 0.76287I
b = 1.187870 + 0.152148I
9.54976 + 3.46045I 0
u = 0.26025 + 1.41053I
a = −0.868443 + 0.711871I
b = 0.07049 − 1.49738I
9.05860 − 10.01860I 0
u = 0.26025 − 1.41053I
a = −0.868443 − 0.711871I
b = 0.07049 + 1.49738I
9.05860 + 10.01860I 0
u = 0.485179 + 0.270736I
a = 0.79040 + 2.38823I
b = −1.031660 − 0.077777I
1.91959 + 0.37712I 4.44701 + 1.12327I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.485179 − 0.270736I
a = 0.79040 − 2.38823I
b = −1.031660 + 0.077777I
1.91959 − 0.37712I 4.44701 − 1.12327I
u = −0.28329 + 1.41670I
a = −1.37473 + 1.49910I
b = 1.209200 + 0.265954I
13.4608 + 7.8834I 0
u = −0.28329 − 1.41670I
a = −1.37473 − 1.49910I
b = 1.209200 − 0.265954I
13.4608 − 7.8834I 0
u = −0.28789 + 1.42366I
a = −2.29994 + 0.99344I
b = 1.40281 + 0.46662I
6.8492 + 12.5656I 0
u = −0.28789 − 1.42366I
a = −2.29994 − 0.99344I
b = 1.40281 − 0.46662I
6.8492 − 12.5656I 0
u = −0.26439 + 1.43129I
a = 0.265359 − 0.325520I
b = −0.403032 + 0.743808I
8.85482 + 3.89445I 0
u = −0.26439 − 1.43129I
a = 0.265359 + 0.325520I
b = −0.403032 − 0.743808I
8.85482 − 3.89445I 0
u = 0.28315 + 1.44885I
a = −1.83399 − 0.74117I
b = 1.153810 − 0.253328I
5.41763 − 5.72105I 0
u = 0.28315 − 1.44885I
a = −1.83399 + 0.74117I
b = 1.153810 + 0.253328I
5.41763 + 5.72105I 0
u = 0.32355 + 1.46124I
a = 2.04944 + 0.92269I
b = −1.49181 + 0.61857I
14.0185 − 17.1862I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32355 − 1.46124I
a = 2.04944 − 0.92269I
b = −1.49181 − 0.61857I
14.0185 + 17.1862I 0
u = −0.452341 + 0.213983I
a = 0.041623 − 0.568597I
b = −1.074090 + 0.183023I
1.92002 − 0.19899I 4.99423 − 1.13661I
u = −0.452341 − 0.213983I
a = 0.041623 + 0.568597I
b = −1.074090 − 0.183023I
1.92002 + 0.19899I 4.99423 + 1.13661I
u = 0.138678 + 0.436669I
a = −0.715549 − 0.443071I
b = 0.071608 + 0.401000I
0.005210 − 1.077320I 0.04464 + 5.68876I
u = 0.138678 − 0.436669I
a = −0.715549 + 0.443071I
b = 0.071608 − 0.401000I
0.005210 + 1.077320I 0.04464 − 5.68876I
u = 0.239830 + 0.371764I
a = 2.59875 + 1.03140I
b = 0.386909 + 0.764730I
4.93361 + 3.39110I 3.79128 − 1.57942I
u = 0.239830 − 0.371764I
a = 2.59875 − 1.03140I
b = 0.386909 − 0.764730I
4.93361 − 3.39110I 3.79128 + 1.57942I
u = −0.30421 + 1.53966I
a = 1.68761 − 0.61965I
b = −1.070700 − 0.438021I
10.85890 + 8.30683I 0
u = −0.30421 − 1.53966I
a = 1.68761 + 0.61965I
b = −1.070700 + 0.438021I
10.85890 − 8.30683I 0
u = 0.07246 + 1.57674I
a = 1.88538 + 0.43170I
b = −1.44750 − 0.25587I
17.7577 + 5.8198I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07246 − 1.57674I
a = 1.88538 − 0.43170I
b = −1.44750 + 0.25587I
17.7577 − 5.8198I 0
u = −0.125299 + 0.374525I
a = 2.66492 − 2.42690I
b = 0.281850 + 0.291258I
4.91367 + 3.46621I 5.63596 − 0.30210I
u = −0.125299 − 0.374525I
a = 2.66492 + 2.42690I
b = 0.281850 − 0.291258I
4.91367 − 3.46621I 5.63596 + 0.30210I
u = 0.107145
a = 4.42125
b = 1.77125
10.1182 26.4200
15
II.
I
u
2
= h−u
18
−u
17
+· · ·+b+1, −3u
19
−3u
18
+· · ·+a+2, u
21
+u
20
+· · ·−2u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
3
=
3u
19
+ 3u
18
+ ··· − 5u − 2
u
18
+ u
17
+ ··· + 3u − 1
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
4
=
−u
20
+ u
19
+ ··· − u − 2
u
20
+ 10u
18
+ ··· + 3u − 1
a
6
=
u
20
− 2u
19
+ ··· + u + 2
3u
19
+ 2u
18
+ ··· − 5u + 1
a
2
=
3u
20
+ 2u
19
+ ··· − 2u + 1
−3u
20
− 27u
18
+ ··· − 5u + 1
a
11
=
u
u
3
+ u
a
5
=
u
20
− 2u
19
+ ··· + u + 2
−u
20
+ 2u
19
+ ··· − 5u + 1
a
10
=
u
20
+ u
19
+ ··· + u − 1
−u
20
+ u
19
+ ··· + 2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
20
− 2u
19
+ 16u
18
− 15u
17
+ 96u
16
− 41u
15
+ 289u
14
− 34u
13
+ 451u
12
+ 56u
11
+
269u
10
+ 149u
9
− 182u
8
+ 129u
7
− 343u
6
+ 62u
5
− 122u
4
+ 39u
3
+ 2u
2
+ 21u − 13
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 2u
19
+ ··· − 4u
3
+ 1
c
2
u
21
− 3u
20
+ ··· − 3u + 1
c
3
, c
4
u
21
− 12u
19
+ ··· + 6u
2
− 1
c
5
u
21
+ 2u
19
+ ··· + 4u
3
+ 1
c
6
u
21
+ 3u
20
+ ··· − 3u − 1
c
7
u
21
+ u
20
+ ··· − 2u − 1
c
8
u
21
− u
20
+ ··· + 5u
2
− 1
c
9
u
21
− 12u
19
+ ··· − 6u
2
+ 1
c
10
u
21
− 6u
19
+ ··· − 3u + 1
c
11
, c
12
u
21
− u
20
+ ··· − 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 4y
20
+ ··· + 4y
2
− 1
c
2
, c
6
y
21
− 21y
20
+ ··· + 17y −1
c
3
, c
4
, c
9
y
21
− 24y
20
+ ··· + 12y −1
c
5
y
21
+ 4y
20
+ ··· + 8y
2
− 1
c
7
, c
11
, c
12
y
21
+ 21y
20
+ ··· + 14y −1
c
8
y
21
− 7y
20
+ ··· + 10y −1
c
10
y
21
− 12y
20
+ ··· + 9y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984366
a = 0.662312
b = −0.673716
1.82676 −9.91440
u = 0.815366
a = 0.226730
b = 0.766209
−1.25146 8.97490
u = −0.094643 + 1.210930I
a = −1.35923 − 0.59174I
b = −0.506081 + 0.505228I
7.46274 − 2.59275I 6.09158 + 2.39408I
u = −0.094643 − 1.210930I
a = −1.35923 + 0.59174I
b = −0.506081 − 0.505228I
7.46274 + 2.59275I 6.09158 − 2.39408I
u = −0.400308 + 1.163200I
a = 1.350780 + 0.065188I
b = −0.595239 − 0.197957I
5.26942 + 5.01003I 4.18148 − 7.46302I
u = −0.400308 − 1.163200I
a = 1.350780 − 0.065188I
b = −0.595239 + 0.197957I
5.26942 − 5.01003I 4.18148 + 7.46302I
u = 0.118068 + 1.275040I
a = −0.419472 − 0.038310I
b = 0.926190 + 0.562953I
4.92913 + 0.08626I 7.93219 + 1.76829I
u = 0.118068 − 1.275040I
a = −0.419472 + 0.038310I
b = 0.926190 − 0.562953I
4.92913 − 0.08626I 7.93219 − 1.76829I
u = 0.334075 + 1.250500I
a = −0.462448 − 0.306608I
b = 0.714711 − 0.169866I
2.56546 − 4.14061I 10.62678 + 5.20457I
u = 0.334075 − 1.250500I
a = −0.462448 + 0.306608I
b = 0.714711 + 0.169866I
2.56546 + 4.14061I 10.62678 − 5.20457I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.470586 + 0.411070I
a = 1.31709 − 2.30799I
b = −0.731585 − 0.450596I
4.93789 + 4.21985I 6.56409 − 9.36044I
u = −0.470586 − 0.411070I
a = 1.31709 + 2.30799I
b = −0.731585 + 0.450596I
4.93789 − 4.21985I 6.56409 + 9.36044I
u = −0.121197 + 1.370090I
a = 2.48838 − 0.58106I
b = −1.85728 + 0.21135I
14.5696 + 1.5143I 3.79993 − 5.22180I
u = −0.121197 − 1.370090I
a = 2.48838 + 0.58106I
b = −1.85728 − 0.21135I
14.5696 − 1.5143I 3.79993 + 5.22180I
u = 0.197775 + 1.398750I
a = −2.38843 − 0.88230I
b = 1.312150 − 0.340653I
6.65693 − 4.31329I 6.76497 + 2.43690I
u = 0.197775 − 1.398750I
a = −2.38843 + 0.88230I
b = 1.312150 + 0.340653I
6.65693 + 4.31329I 6.76497 − 2.43690I
u = −0.26074 + 1.46036I
a = 1.58165 − 0.83966I
b = −0.996753 − 0.582614I
11.05480 + 7.28682I 8.35637 − 3.98505I
u = −0.26074 − 1.46036I
a = 1.58165 + 0.83966I
b = −0.996753 + 0.582614I
11.05480 − 7.28682I 8.35637 + 3.98505I
u = 0.426638 + 0.185914I
a = −1.15995 − 2.17038I
b = 1.086900 − 0.393442I
1.44452 − 1.88456I −0.318304 + 1.212914I
u = 0.426638 − 0.185914I
a = −1.15995 + 2.17038I
b = 1.086900 + 0.393442I
1.44452 + 1.88456I −0.318304 − 1.212914I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289165
a = 0.214232
b = −1.79851
9.94852 −21.0590
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 2u
19
+ ··· − 4u
3
+ 1)(u
104
+ 7u
103
+ ··· − 906u + 1909)
c
2
(u
21
− 3u
20
+ ··· − 3u + 1)(u
104
+ 2u
103
+ ··· + 63u + 73)
c
3
, c
4
(u
21
− 12u
19
+ ··· + 6u
2
− 1)(u
104
− u
103
+ ··· − 42u − 1)
c
5
(u
21
+ 2u
19
+ ··· + 4u
3
+ 1)(u
104
+ u
103
+ ··· − 106u + 1)
c
6
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
104
+ 2u
103
+ ··· + 63u + 73)
c
7
(u
21
+ u
20
+ ··· − 2u − 1)(u
104
+ 48u
102
+ ··· + 10u + 1)
c
8
(u
21
− u
20
+ ··· + 5u
2
− 1)(u
104
− u
101
+ ··· + 7744u + 457)
c
9
(u
21
− 12u
19
+ ··· − 6u
2
+ 1)(u
104
− u
103
+ ··· − 42u − 1)
c
10
(u
21
− 6u
19
+ ··· − 3u + 1)(u
104
− 5u
103
+ ··· − 39735u + 17047)
c
11
, c
12
(u
21
− u
20
+ ··· − 2u + 1)(u
104
+ 48u
102
+ ··· + 10u + 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 4y
20
+ ··· + 4y
2
− 1)
· (y
104
+ 23y
103
+ ··· + 88027842y + 3644281)
c
2
, c
6
(y
21
− 21y
20
+ ··· + 17y −1)(y
104
− 82y
103
+ ··· + 131957y + 5329)
c
3
, c
4
, c
9
(y
21
− 24y
20
+ ··· + 12y −1)(y
104
− 109y
103
+ ··· − 1178y + 1)
c
5
(y
21
+ 4y
20
+ ··· + 8y
2
− 1)(y
104
+ 15y
103
+ ··· − 10638y + 1)
c
7
, c
11
, c
12
(y
21
+ 21y
20
+ ··· + 14y −1)(y
104
+ 96y
103
+ ··· − 72y + 1)
c
8
(y
21
− 7y
20
+ ··· + 10y −1)
· (y
104
+ 106y
102
+ ··· − 16677012y + 208849)
c
10
(y
21
− 12y
20
+ ··· + 9y −1)
· (y
104
− 41y
103
+ ··· − 14746825375y + 290600209)
23
