12a
0080
(K12a
0080
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 7 12 1 6 10
Solving Sequence
4,7
8 9
3,11
6 12 5 2 1 10
c
7
c
8
c
3
c
6
c
11
c
5
c
2
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.47932 × 10
172
u
99
+ 4.76140 × 10
172
u
98
+ ··· + 7.64219 × 10
171
b − 7.86042 × 10
173
,
1.61477 × 10
173
u
99
+ 2.13974 × 10
173
u
98
+ ··· + 1.52844 × 10
172
a − 2.14797 × 10
174
,
u
100
+ 2u
99
+ ··· − 64u − 32i
I
u
2
= hb, −u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ a + 2u − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
v
1
= ha, 2v
4
− v
3
− 3v
2
+ b + 6v −2, v
5
− v
4
− v
3
+ 4v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 114 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
= h2.48 × 10
172
u
99
+ 4.76 × 10
172
u
98
+ · · · + 7.64 × 10
171
b − 7.86 ×
10
173
, 1.61 × 10
173
u
99
+ 2.14 × 10
173
u
98
+ · · · + 1.53 × 10
172
a − 2.15 ×
10
174
, u
100
+ 2u
99
+ · · · − 64u − 32i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
11
=
−10.5648u
99
− 13.9996u
98
+ ··· + 485.144u + 140.533
−3.24425u
99
− 6.23041u
98
+ ··· + 227.295u + 102.856
a
6
=
−1.62635u
99
− 12.7491u
98
+ ··· + 379.363u + 373.535
2.75906u
99
− 1.00208u
98
+ ··· + 17.4499u + 112.614
a
12
=
1.99211u
99
− 0.362984u
98
+ ··· + 11.6286u + 92.4955
4.80922u
99
+ 8.87550u
98
+ ··· − 249.660u − 114.564
a
5
=
−2.00742u
99
− 6.91461u
98
+ ··· + 214.739u + 175.776
−2.72976u
99
− 5.69852u
98
+ ··· + 201.086u + 122.708
a
2
=
−6.01213u
99
− 5.95088u
98
+ ··· + 236.170u + 39.7247
−9.17264u
99
− 20.1928u
98
+ ··· + 647.217u + 409.849
a
1
=
−0.722339u
99
+ 1.21609u
98
+ ··· − 13.6525u − 53.0678
−5.10774u
99
− 10.5309u
98
+ ··· + 348.261u + 207.853
a
10
=
−2.75020u
99
− 1.20374u
98
+ ··· + 54.2989u − 54.5712
−1.57899u
99
− 0.971002u
98
+ ··· + 14.8200u − 34.6674
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0436322u
99
+ 11.7279u
98
+ ··· − 467.357u − 260.647
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 53u
99
+ ··· + 7u + 1
c
2
, c
4
u
100
− 7u
99
+ ··· − 7u + 1
c
3
, c
7
u
100
+ 2u
99
+ ··· − 64u − 32
c
5
u
100
+ 3u
99
+ ··· − 618085u − 69121
c
6
, c
11
u
100
+ 2u
99
+ ··· + 512u + 512
c
8
u
100
− 36u
99
+ ··· − 13824u + 1024
c
9
, c
10
, c
12
u
100
+ 11u
99
+ ··· − 17u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
− 5y
99
+ ··· + 33y + 1
c
2
, c
4
y
100
− 53y
99
+ ··· − 7y + 1
c
3
, c
7
y
100
+ 36y
99
+ ··· + 13824y + 1024
c
5
y
100
− 37y
99
+ ··· − 377607258613y + 4777712641
c
6
, c
11
y
100
+ 60y
99
+ ··· − 2883584y + 262144
c
8
y
100
+ 48y
99
+ ··· − 60424192y + 1048576
c
9
, c
10
, c
12
y
100
− 97y
99
+ ··· − 201y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884881 + 0.443710I
a = −1.02731 + 1.13017I
b = −0.56926 + 1.31324I
6.60856 + 5.95419I 0
u = 0.884881 − 0.443710I
a = −1.02731 − 1.13017I
b = −0.56926 − 1.31324I
6.60856 − 5.95419I 0
u = 0.539252 + 0.807936I
a = 0.74537 − 1.84294I
b = 1.070410 − 0.257597I
0.28317 − 1.56689I 0
u = 0.539252 − 0.807936I
a = 0.74537 + 1.84294I
b = 1.070410 + 0.257597I
0.28317 + 1.56689I 0
u = −0.877511 + 0.546781I
a = 0.1165030 − 0.0622745I
b = −0.093715 − 1.021170I
−0.65453 − 1.60971I 0
u = −0.877511 − 0.546781I
a = 0.1165030 + 0.0622745I
b = −0.093715 + 1.021170I
−0.65453 + 1.60971I 0
u = −0.590496 + 0.849773I
a = 0.995509 + 0.498875I
b = 0.547653 + 1.013140I
−2.32363 + 0.91046I 0
u = −0.590496 − 0.849773I
a = 0.995509 − 0.498875I
b = 0.547653 − 1.013140I
−2.32363 − 0.91046I 0
u = −0.586412 + 0.852774I
a = −2.45305 − 0.96693I
b = −0.433519 + 1.091210I
−2.31645 + 3.75588I 0
u = −0.586412 − 0.852774I
a = −2.45305 + 0.96693I
b = −0.433519 − 1.091210I
−2.31645 − 3.75588I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707489 + 0.757410I
a = −0.528671 + 1.213530I
b = −0.622925 + 0.365302I
−4.51548 + 0.41476I 0
u = 0.707489 − 0.757410I
a = −0.528671 − 1.213530I
b = −0.622925 − 0.365302I
−4.51548 − 0.41476I 0
u = −0.131827 + 1.029980I
a = −0.230349 − 0.166934I
b = −0.542386 − 0.048973I
2.23387 + 2.24163I 0
u = −0.131827 − 1.029980I
a = −0.230349 + 0.166934I
b = −0.542386 + 0.048973I
2.23387 − 2.24163I 0
u = −0.595860 + 0.754704I
a = −1.05018 − 1.06069I
b = −0.610358 − 1.204840I
3.06706 − 2.97422I 0
u = −0.595860 − 0.754704I
a = −1.05018 + 1.06069I
b = −0.610358 + 1.204840I
3.06706 + 2.97422I 0
u = 0.942753 + 0.079467I
a = −0.94741 − 1.14825I
b = −0.42749 − 1.36141I
7.67217 − 4.88901I 0
u = 0.942753 − 0.079467I
a = −0.94741 + 1.14825I
b = −0.42749 + 1.36141I
7.67217 + 4.88901I 0
u = −0.982256 + 0.392199I
a = −0.89974 + 1.13851I
b = −0.31425 + 1.38095I
6.55088 + 0.63605I 0
u = −0.982256 − 0.392199I
a = −0.89974 − 1.13851I
b = −0.31425 − 1.38095I
6.55088 − 0.63605I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.561927 + 0.902740I
a = −1.93396 + 0.08705I
b = −0.980104 − 0.465605I
0.61325 − 2.85921I 0
u = 0.561927 − 0.902740I
a = −1.93396 − 0.08705I
b = −0.980104 + 0.465605I
0.61325 + 2.85921I 0
u = −0.586585 + 0.721651I
a = 1.253280 − 0.140571I
b = 0.579476 − 0.460487I
−1.10103 + 1.53124I 0
u = −0.586585 − 0.721651I
a = 1.253280 + 0.140571I
b = 0.579476 + 0.460487I
−1.10103 − 1.53124I 0
u = −0.273384 + 0.883080I
a = −1.55173 − 0.98026I
b = 0.361902 + 1.342250I
5.56558 − 3.02900I 0
u = −0.273384 − 0.883080I
a = −1.55173 + 0.98026I
b = 0.361902 − 1.342250I
5.56558 + 3.02900I 0
u = 0.846635 + 0.674153I
a = 1.294800 + 0.078123I
b = 0.636434 + 0.312379I
−4.33856 + 2.20835I 0
u = 0.846635 − 0.674153I
a = 1.294800 − 0.078123I
b = 0.636434 − 0.312379I
−4.33856 − 2.20835I 0
u = 0.933715 + 0.579457I
a = −2.11655 + 0.00733I
b = −1.132900 − 0.269644I
0.78239 + 4.13235I 0
u = 0.933715 − 0.579457I
a = −2.11655 − 0.00733I
b = −1.132900 + 0.269644I
0.78239 − 4.13235I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.592846 + 0.934567I
a = 2.56449 + 0.68884I
b = 0.61347 − 1.31069I
3.64044 + 7.68908I 0
u = −0.592846 − 0.934567I
a = 2.56449 − 0.68884I
b = 0.61347 + 1.31069I
3.64044 − 7.68908I 0
u = −0.604341 + 0.951748I
a = −0.517680 − 0.796306I
b = −0.642092 − 0.244132I
−0.38436 + 3.21470I 0
u = −0.604341 − 0.951748I
a = −0.517680 + 0.796306I
b = −0.642092 + 0.244132I
−0.38436 − 3.21470I 0
u = −0.595384 + 0.957685I
a = −0.577978 + 0.159926I
b = −0.399909 − 0.928636I
−0.19999 + 5.40810I 0
u = −0.595384 − 0.957685I
a = −0.577978 − 0.159926I
b = −0.399909 + 0.928636I
−0.19999 − 5.40810I 0
u = −0.952835 + 0.617965I
a = 0.825124 + 0.563092I
b = 0.438487 + 1.130360I
−1.85066 − 6.43010I 0
u = −0.952835 − 0.617965I
a = 0.825124 − 0.563092I
b = 0.438487 − 1.130360I
−1.85066 + 6.43010I 0
u = 0.353565 + 0.779804I
a = −0.737665 − 0.744402I
b = −0.386602 + 0.710932I
2.07371 − 1.25412I 5.06066 + 0.I
u = 0.353565 − 0.779804I
a = −0.737665 + 0.744402I
b = −0.386602 − 0.710932I
2.07371 + 1.25412I 5.06066 + 0.I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767779 + 0.856370I
a = −0.74522 + 1.20868I
b = −0.078209 + 0.988155I
2.51912 + 2.88295I 0
u = −0.767779 − 0.856370I
a = −0.74522 − 1.20868I
b = −0.078209 − 0.988155I
2.51912 − 2.88295I 0
u = 0.671240 + 0.936658I
a = 1.320780 + 0.169029I
b = 0.711534 + 0.469548I
−3.96383 − 5.71381I 0
u = 0.671240 − 0.936658I
a = 1.320780 − 0.169029I
b = 0.711534 − 0.469548I
−3.96383 + 5.71381I 0
u = −0.526480 + 0.660317I
a = 2.10099 + 1.07697I
b = 0.092237 − 0.872052I
−1.085510 − 0.755363I 0
u = −0.526480 − 0.660317I
a = 2.10099 − 1.07697I
b = 0.092237 + 0.872052I
−1.085510 + 0.755363I 0
u = 0.736743 + 0.396732I
a = 0.807808 − 0.420897I
b = 0.372239 − 1.034010I
0.58400 + 2.29834I 0. − 2.67935I
u = 0.736743 − 0.396732I
a = 0.807808 + 0.420897I
b = 0.372239 + 1.034010I
0.58400 − 2.29834I 0. + 2.67935I
u = 0.846193 + 0.820472I
a = −0.68816 − 1.35772I
b = 0.020735 − 0.965121I
−1.27779 + 1.44176I 0
u = 0.846193 − 0.820472I
a = −0.68816 + 1.35772I
b = 0.020735 + 0.965121I
−1.27779 − 1.44176I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531104 + 1.052380I
a = 1.124550 − 0.785137I
b = 0.075357 + 1.118830I
3.55316 − 2.32371I 0
u = 0.531104 − 1.052380I
a = 1.124550 + 0.785137I
b = 0.075357 − 1.118830I
3.55316 + 2.32371I 0
u = 0.062447 + 1.182640I
a = −0.047396 − 1.179770I
b = −0.152637 + 1.182900I
5.94496 − 0.00646I 0
u = 0.062447 − 1.182640I
a = −0.047396 + 1.179770I
b = −0.152637 − 1.182900I
5.94496 + 0.00646I 0
u = −1.010080 + 0.638749I
a = −1.06871 − 1.13966I
b = −0.63437 − 1.32583I
4.17046 − 10.49690I 0
u = −1.010080 − 0.638749I
a = −1.06871 + 1.13966I
b = −0.63437 + 1.32583I
4.17046 + 10.49690I 0
u = 0.160477 + 1.192630I
a = −0.670374 + 1.141510I
b = −0.246868 − 1.196250I
5.73999 − 5.17903I 0
u = 0.160477 − 1.192630I
a = −0.670374 − 1.141510I
b = −0.246868 + 1.196250I
5.73999 + 5.17903I 0
u = −0.111935 + 1.198360I
a = 0.498285 + 0.254723I
b = 1.237630 + 0.049174I
7.96158 + 2.61323I 0
u = −0.111935 − 1.198360I
a = 0.498285 − 0.254723I
b = 1.237630 − 0.049174I
7.96158 − 2.61323I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.575264 + 1.075480I
a = 0.94704 + 1.16772I
b = 1.197790 + 0.259387I
5.08931 + 4.99074I 0
u = −0.575264 − 1.075480I
a = 0.94704 − 1.16772I
b = 1.197790 − 0.259387I
5.08931 − 4.99074I 0
u = 0.778394 + 0.949746I
a = −0.655843 − 1.135800I
b = −0.110283 − 0.902804I
−0.85499 − 7.49455I 0
u = 0.778394 − 0.949746I
a = −0.655843 + 1.135800I
b = −0.110283 + 0.902804I
−0.85499 + 7.49455I 0
u = 0.764709 + 0.097850I
a = 0.600945 + 0.209636I
b = 0.169538 + 0.986881I
1.11462 − 1.94278I 1.85416 + 5.36837I
u = 0.764709 − 0.097850I
a = 0.600945 − 0.209636I
b = 0.169538 − 0.986881I
1.11462 + 1.94278I 1.85416 − 5.36837I
u = −0.723243 + 0.246375I
a = −2.19747 − 0.04350I
b = −1.020380 + 0.117035I
2.93963 − 0.21256I 2.00889 − 1.10009I
u = −0.723243 − 0.246375I
a = −2.19747 + 0.04350I
b = −1.020380 − 0.117035I
2.93963 + 0.21256I 2.00889 + 1.10009I
u = 0.613381 + 1.073800I
a = −1.83144 + 0.65617I
b = −0.429259 − 1.174990I
2.46078 − 7.41018I 0
u = 0.613381 − 1.073800I
a = −1.83144 − 0.65617I
b = −0.429259 + 1.174990I
2.46078 + 7.41018I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440467 + 1.158480I
a = −0.683720 − 0.005974I
b = 0.30408 − 1.45896I
11.17460 + 0.24489I 0
u = 0.440467 − 1.158480I
a = −0.683720 + 0.005974I
b = 0.30408 + 1.45896I
11.17460 − 0.24489I 0
u = −0.114937 + 0.750794I
a = −1.83320 − 0.55115I
b = −0.681621 + 0.459189I
2.54384 − 0.78639I 3.67508 + 0.13252I
u = −0.114937 − 0.750794I
a = −1.83320 + 0.55115I
b = −0.681621 − 0.459189I
2.54384 + 0.78639I 3.67508 − 0.13252I
u = −0.013659 + 1.255670I
a = 0.395183 + 0.654450I
b = 0.47616 − 1.45597I
12.99600 + 3.48911I 0
u = −0.013659 − 1.255670I
a = 0.395183 − 0.654450I
b = 0.47616 + 1.45597I
12.99600 − 3.48911I 0
u = 0.719929 + 1.031490I
a = −0.727686 + 0.780402I
b = −0.713876 + 0.248134I
−3.22846 − 8.05708I 0
u = 0.719929 − 1.031490I
a = −0.727686 − 0.780402I
b = −0.713876 − 0.248134I
−3.22846 + 8.05708I 0
u = 0.219681 + 1.258860I
a = 0.974040 − 0.677228I
b = 0.54021 + 1.43860I
12.5302 − 8.9696I 0
u = 0.219681 − 1.258860I
a = 0.974040 + 0.677228I
b = 0.54021 − 1.43860I
12.5302 + 8.9696I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688325 + 1.089100I
a = 1.220450 + 0.472444I
b = 0.154564 − 1.150210I
0.99382 + 7.40466I 0
u = −0.688325 − 1.089100I
a = 1.220450 − 0.472444I
b = 0.154564 + 1.150210I
0.99382 − 7.40466I 0
u = 0.655303 + 1.113300I
a = 2.11748 − 0.31037I
b = 0.65071 + 1.35252I
8.6068 − 11.5978I 0
u = 0.655303 − 1.113300I
a = 2.11748 + 0.31037I
b = 0.65071 − 1.35252I
8.6068 + 11.5978I 0
u = −0.611906 + 1.158220I
a = −0.735864 + 0.386210I
b = 0.22842 + 1.47970I
9.03534 + 5.08439I 0
u = −0.611906 − 1.158220I
a = −0.735864 − 0.386210I
b = 0.22842 − 1.47970I
9.03534 − 5.08439I 0
u = 0.714038 + 1.103300I
a = 1.19287 − 1.18198I
b = 1.219300 − 0.319619I
2.42053 − 10.18240I 0
u = 0.714038 − 1.103300I
a = 1.19287 + 1.18198I
b = 1.219300 + 0.319619I
2.42053 + 10.18240I 0
u = −0.737297 + 1.100470I
a = −1.88544 − 0.36854I
b = −0.473405 + 1.192110I
−0.32558 + 12.62840I 0
u = −0.737297 − 1.100470I
a = −1.88544 + 0.36854I
b = −0.473405 − 1.192110I
−0.32558 − 12.62840I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.018968 + 0.672758I
a = 1.090690 − 0.276318I
b = 0.505309 − 0.771691I
−0.25376 + 2.03673I 0.89306 − 5.76366I
u = −0.018968 − 0.672758I
a = 1.090690 + 0.276318I
b = 0.505309 + 0.771691I
−0.25376 − 2.03673I 0.89306 + 5.76366I
u = −0.766986 + 1.121400I
a = 2.18814 + 0.06503I
b = 0.68311 − 1.34178I
5.7212 + 16.9694I 0
u = −0.766986 − 1.121400I
a = 2.18814 − 0.06503I
b = 0.68311 + 1.34178I
5.7212 − 16.9694I 0
u = −0.401862 + 0.490171I
a = 2.62983 + 0.88459I
b = −0.042922 − 0.711367I
−1.040340 − 0.778197I −0.27027 − 2.61559I
u = −0.401862 − 0.490171I
a = 2.62983 − 0.88459I
b = −0.042922 + 0.711367I
−1.040340 + 0.778197I −0.27027 + 2.61559I
u = −0.153184 + 0.607610I
a = −0.937923 + 1.036010I
b = −0.437442 + 1.121800I
4.67145 + 4.93475I 7.38116 − 9.44071I
u = −0.153184 − 0.607610I
a = −0.937923 − 1.036010I
b = −0.437442 − 1.121800I
4.67145 − 4.93475I 7.38116 + 9.44071I
u = −0.554585
a = 1.16240
b = 0.265734
−1.12797 −9.40680
u = 0.369216
a = 9.89071
b = 0.314374
0.283296 −54.4150
14
II.
I
u
2
= hb, −u
8
+ 2u
7
+ · · · + a − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1 i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
11
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
0
a
6
=
1
0
a
12
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
0
a
5
=
u
4
+ u
2
+ 1
u
4
a
2
=
−u
6
− u
4
− 2u
2
− 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
1
=
−u
2
− 1
−u
2
a
10
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 4u
2
− 2u + 2
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
+ 4u
6
− 3u
5
+ 10u
4
− u
3
+ 7u
2
− 6u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
, c
11
u
9
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
, c
10
(u + 1)
9
c
12
(u − 1)
9
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
, c
11
y
9
c
9
, c
10
, c
12
(y −1)
9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −1.004430 + 0.297869I
b = 0
3.42837 + 2.09337I 6.19892 − 4.26451I
u = −0.140343 − 0.966856I
a = −1.004430 − 0.297869I
b = 0
3.42837 − 2.09337I 6.19892 + 4.26451I
u = −0.628449 + 0.875112I
a = −0.275254 + 0.816341I
b = 0
1.02799 + 2.45442I 0.00914 − 2.54651I
u = −0.628449 − 0.875112I
a = −0.275254 − 0.816341I
b = 0
1.02799 − 2.45442I 0.00914 + 2.54651I
u = 0.796005 + 0.733148I
a = 0.070080 − 0.850995I
b = 0
−2.72642 + 1.33617I −5.35644 − 0.59665I
u = 0.796005 − 0.733148I
a = 0.070080 + 0.850995I
b = 0
−2.72642 − 1.33617I −5.35644 + 0.59665I
u = 0.728966 + 0.986295I
a = −0.195086 − 0.635552I
b = 0
−1.95319 − 7.08493I −3.81555 + 4.89194I
u = 0.728966 − 0.986295I
a = −0.195086 + 0.635552I
b = 0
−1.95319 + 7.08493I −3.81555 − 4.89194I
u = −0.512358
a = 3.80937
b = 0
0.446489 9.92790
18
III. I
v
1
= ha, 2v
4
− v
3
− 3v
2
+ b + 6v − 2, v
5
− v
4
− v
3
+ 4v
2
− 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
11
=
0
−2v
4
+ v
3
+ 3v
2
− 6v + 2
a
6
=
1
−v
4
+ v
3
+ v
2
− 4v + 3
a
12
=
2v
4
− v
3
− 3v
2
+ 6v − 2
v
3
− v + 2
a
5
=
v
4
− v
3
− v
2
+ 4v − 2
−v
4
+ v
3
+ v
2
− 4v + 3
a
2
=
−v
4
+ v
3
+ v
2
− 3v + 2
v
4
− v
3
− v
2
+ 4v − 3
a
1
=
−v
4
+ v
3
+ v
2
− 4v + 2
v
4
− v
3
− v
2
+ 4v − 3
a
10
=
−2v
4
+ v
3
+ 3v
2
− 7v + 3
−v
3
+ 2v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = v
4
+ 2v
3
+ v
2
+ v − 1
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
, c
8
u
5
c
4
(u + 1)
5
c
5
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
9
, c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
5
c
3
, c
7
, c
8
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
6
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
9
, c
10
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.896438 + 0.890762I
a = 0
b = 0.339110 + 0.822375I
−1.31583 − 1.53058I −5.47076 + 5.40154I
v = 0.896438 − 0.890762I
a = 0
b = 0.339110 − 0.822375I
−1.31583 + 1.53058I −5.47076 − 5.40154I
v = 0.453870 + 0.402731I
a = 0
b = −0.455697 − 1.200150I
4.22763 − 4.40083I −0.88874 + 1.16747I
v = 0.453870 − 0.402731I
a = 0
b = −0.455697 + 1.200150I
4.22763 + 4.40083I −0.88874 − 1.16747I
v = −1.70062
a = 0
b = −0.766826
0.756147 −1.28100
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
100
+ 53u
99
+ ··· + 7u + 1)
c
2
(u − 1)
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
100
− 7u
99
+ ··· − 7u + 1)
c
3
u
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
100
+ 2u
99
+ ··· − 64u − 32)
c
4
(u + 1)
5
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
100
− 7u
99
+ ··· − 7u + 1)
c
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
100
+ 3u
99
+ ··· − 618085u − 69121)
c
6
u
9
(u
5
+ u
4
+ ··· + u + 1)(u
100
+ 2u
99
+ ··· + 512u + 512)
c
7
u
5
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
100
+ 2u
99
+ ··· − 64u − 32)
c
8
u
5
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
100
− 36u
99
+ ··· − 13824u + 1024)
c
9
, c
10
((u + 1)
9
)(u
5
− u
4
+ ··· + u + 1)(u
100
+ 11u
99
+ ··· − 17u − 1)
c
11
u
9
(u
5
− u
4
+ ··· + u − 1)(u
100
+ 2u
99
+ ··· + 512u + 512)
c
12
((u − 1)
9
)(u
5
+ u
4
+ ··· + u − 1)(u
100
+ 11u
99
+ ··· − 17u − 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
5
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
100
− 5y
99
+ ··· + 33y + 1)
c
2
, c
4
(y − 1)
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
100
− 53y
99
+ ··· − 7y + 1)
c
3
, c
7
y
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
100
+ 36y
99
+ ··· + 13824y + 1024)
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
100
− 37y
99
+ ··· − 377607258613y + 4777712641)
c
6
, c
11
y
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
· (y
100
+ 60y
99
+ ··· − 2883584y + 262144)
c
8
y
5
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
100
+ 48y
99
+ ··· − 60424192y + 1048576)
c
9
, c
10
, c
12
((y − 1)
9
)(y
5
− 5y
4
+ ··· − y − 1)(y
100
− 97y
99
+ ··· − 201y + 1)
24
