12a
0088
(K12a
0088
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 4 11 12 1 7 6
Solving Sequence
4,7 8,11
9 12 10 3 6 1 2 5
c
7
c
8
c
11
c
9
c
3
c
6
c
12
c
1
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.50265 × 10
167
u
75
+ 1.62291 × 10
168
u
74
+ ··· + 2.17923 × 10
168
b − 2.92816 × 10
168
,
1.34711 × 10
170
u
75
+ 3.31466 × 10
170
u
74
+ ··· + 5.57883 × 10
170
a + 2.14734 × 10
172
,
u
76
+ 5u
75
+ ··· − 1504u − 256i
I
u
2
= h5.40539 × 10
57
au
53
+ 5.21405 × 10
57
u
53
+ ··· + 2.28078 × 10
59
a + 9.87330 × 10
58
,
2.49928 × 10
59
au
53
+ 5.44370 × 10
58
u
53
+ ··· − 9.46034 × 10
59
a + 3.73776 × 10
60
, u
54
− 2u
53
+ ··· − 36u + 8i
I
u
3
= h768246826u
22
− 1643416610u
21
+ ··· + 219374557b + 473494586,
99816722u
22
+ 500697163u
21
+ ··· + 219374557a + 85184191, u
23
− 2u
22
+ ··· + u − 1i
I
u
4
= h−u
2
a + b + 1, −4u
2
a + a
2
− 2au + 8u
2
− 5a + 3u + 15, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, 16v
3
− 48v
2
+ b + 51v −13, 4v
4
− 13v
3
+ 16v
2
− 7v + 1i
I
v
2
= ha, b
2
− bv + v
2
− b + 2v + 2, v
3
+ 2v
2
+ 3v + 1i
* 6 irreducible components of dim
C
= 0, with total 223 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
= h3.50 × 10
167
u
75
+ 1.62 × 10
168
u
74
+ · · · + 2.18 × 10
168
b − 2.93 ×
10
168
, 1.35 × 10
170
u
75
+ 3.31 × 10
170
u
74
+ · · · + 5.58 × 10
170
a + 2.15 ×
10
172
, u
76
+ 5u
75
+ · · · − 1504u − 256i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−0.241468u
75
− 0.594150u
74
+ ··· − 211.857u − 38.4908
−0.160728u
75
− 0.744715u
74
+ ··· + 69.1978u + 1.34366
a
9
=
0.429938u
75
+ 2.37634u
74
+ ··· − 882.782u − 147.812
−0.499536u
75
− 2.13504u
74
+ ··· + 443.772u + 61.6431
a
12
=
−0.402196u
75
− 1.33887u
74
+ ··· − 142.659u − 37.1472
−0.160728u
75
− 0.744715u
74
+ ··· + 69.1978u + 1.34366
a
10
=
−0.249605u
75
− 1.21879u
74
+ ··· + 592.443u + 125.818
−0.221325u
75
− 1.11335u
74
+ ··· + 502.440u + 98.4113
a
3
=
u
u
3
+ u
a
6
=
−0.0578480u
75
− 0.146509u
74
+ ··· − 107.825u − 25.7212
0.212028u
75
+ 0.991418u
74
+ ··· − 455.593u − 89.2052
a
1
=
−0.449045u
75
− 1.77037u
74
+ ··· + 239.294u + 44.5157
0.126005u
75
+ 0.424987u
74
+ ··· − 38.9179u + 13.2441
a
2
=
−0.0856491u
75
− 0.525662u
74
+ ··· + 361.435u + 92.6534
0.762094u
75
+ 3.29215u
74
+ ··· − 684.443u − 85.1196
a
5
=
−0.627609u
75
− 2.95001u
74
+ ··· + 877.437u + 152.834
−0.178564u
75
− 1.17964u
74
+ ··· + 638.143u + 108.319
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.630979u
75
+ 1.28928u
74
+ ··· + 1959.31u + 521.805
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 41u
75
+ ··· + 2881u + 256
c
2
, c
4
u
76
− 7u
75
+ ··· + 47u − 16
c
3
, c
7
u
76
+ 5u
75
+ ··· − 1504u − 256
c
5
, c
11
u
76
+ 8u
74
+ ··· + 9u + 1
c
6
, c
12
u
76
− u
75
+ ··· + 39u
2
+ 1
c
8
, c
10
u
76
− 12u
75
+ ··· + 133u + 1
c
9
u
76
− 41u
75
+ ··· − 60u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 5y
75
+ ··· + 3372927y + 65536
c
2
, c
4
y
76
− 41y
75
+ ··· − 2881y + 256
c
3
, c
7
y
76
+ 27y
75
+ ··· + 429056y + 65536
c
5
, c
11
y
76
+ 16y
75
+ ··· + 3y + 1
c
6
, c
12
y
76
+ 33y
75
+ ··· + 78y + 1
c
8
, c
10
y
76
− 32y
75
+ ··· − 14137y + 1
c
9
y
76
− y
75
+ ··· − 2152y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549536 + 0.837058I
a = 0.845110 − 0.407169I
b = −0.178093 − 0.944673I
−0.70430 + 2.22063I −4.00000 − 2.40787I
u = −0.549536 − 0.837058I
a = 0.845110 + 0.407169I
b = −0.178093 + 0.944673I
−0.70430 − 2.22063I −4.00000 + 2.40787I
u = −0.534703 + 0.821833I
a = −2.35677 + 1.04410I
b = 0.843511 + 0.558212I
−1.29584 + 3.21450I 0. − 6.87712I
u = −0.534703 − 0.821833I
a = −2.35677 − 1.04410I
b = 0.843511 − 0.558212I
−1.29584 − 3.21450I 0. + 6.87712I
u = 0.759718 + 0.688270I
a = 0.935380 + 0.629384I
b = 0.043562 + 0.961316I
−4.35465 + 1.27364I −11.13502 + 0.I
u = 0.759718 − 0.688270I
a = 0.935380 − 0.629384I
b = 0.043562 − 0.961316I
−4.35465 − 1.27364I −11.13502 + 0.I
u = −0.543650 + 0.875704I
a = 0.605225 + 0.025956I
b = −0.802405 + 0.766317I
−1.11422 + 1.13570I 0
u = −0.543650 − 0.875704I
a = 0.605225 − 0.025956I
b = −0.802405 − 0.766317I
−1.11422 − 1.13570I 0
u = −0.322297 + 0.995461I
a = −1.81898 + 0.11870I
b = 0.34869 + 1.43027I
3.50146 + 1.04648I 0
u = −0.322297 − 0.995461I
a = −1.81898 − 0.11870I
b = 0.34869 − 1.43027I
3.50146 − 1.04648I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249573 + 1.025490I
a = −1.02779 − 1.02684I
b = 0.671426 + 1.086410I
3.74651 − 0.84202I 0
u = 0.249573 − 1.025490I
a = −1.02779 + 1.02684I
b = 0.671426 − 1.086410I
3.74651 + 0.84202I 0
u = −0.942865 + 0.574311I
a = 0.549283 − 0.089509I
b = −0.906887 + 0.543363I
−0.77364 − 5.79215I 0
u = −0.942865 − 0.574311I
a = 0.549283 + 0.089509I
b = −0.906887 − 0.543363I
−0.77364 + 5.79215I 0
u = 1.048700 + 0.401936I
a = 0.024944 + 0.209686I
b = 0.92021 + 1.12910I
−0.42875 + 9.40339I 0
u = 1.048700 − 0.401936I
a = 0.024944 − 0.209686I
b = 0.92021 − 1.12910I
−0.42875 − 9.40339I 0
u = −0.870102 + 0.778626I
a = −0.051774 + 0.644784I
b = −0.087691 + 0.221674I
−1.14182 − 1.42017I 0
u = −0.870102 − 0.778626I
a = −0.051774 − 0.644784I
b = −0.087691 − 0.221674I
−1.14182 + 1.42017I 0
u = −0.545284 + 1.039170I
a = 2.19429 − 0.30840I
b = −0.92575 − 1.21687I
−3.30756 + 11.46430I 0
u = −0.545284 − 1.039170I
a = 2.19429 + 0.30840I
b = −0.92575 + 1.21687I
−3.30756 − 11.46430I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.167100 + 0.155073I
a = 0.043810 − 0.223231I
b = 0.839575 − 0.688649I
0.51141 − 6.92640I 0
u = 1.167100 − 0.155073I
a = 0.043810 + 0.223231I
b = 0.839575 + 0.688649I
0.51141 + 6.92640I 0
u = 0.148668 + 1.178760I
a = −1.46069 − 0.70930I
b = 0.769528 + 0.092030I
6.21669 − 0.96301I 0
u = 0.148668 − 1.178760I
a = −1.46069 + 0.70930I
b = 0.769528 − 0.092030I
6.21669 + 0.96301I 0
u = 0.674334 + 0.448142I
a = −1.35043 − 2.51371I
b = −0.110418 − 1.345250I
−0.288936 + 0.954845I −3.45501 − 0.61503I
u = 0.674334 − 0.448142I
a = −1.35043 + 2.51371I
b = −0.110418 + 1.345250I
−0.288936 − 0.954845I −3.45501 + 0.61503I
u = 0.090164 + 1.190440I
a = −1.73541 + 0.36304I
b = 0.873499 − 0.228563I
6.33414 − 4.20661I 0
u = 0.090164 − 1.190440I
a = −1.73541 − 0.36304I
b = 0.873499 + 0.228563I
6.33414 + 4.20661I 0
u = 0.671344 + 0.990709I
a = 0.733082 + 0.470181I
b = −0.165628 + 1.094830I
−3.41824 − 6.71246I 0
u = 0.671344 − 0.990709I
a = 0.733082 − 0.470181I
b = −0.165628 − 1.094830I
−3.41824 + 6.71246I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.513328 + 1.083880I
a = −0.552384 + 0.890997I
b = 0.875161 − 0.948192I
2.06843 + 5.63444I 0
u = −0.513328 − 1.083880I
a = −0.552384 − 0.890997I
b = 0.875161 + 0.948192I
2.06843 − 5.63444I 0
u = 0.574053 + 1.067600I
a = −1.42494 − 0.53905I
b = 0.26031 − 1.60832I
1.52029 − 5.80875I 0
u = 0.574053 − 1.067600I
a = −1.42494 + 0.53905I
b = 0.26031 + 1.60832I
1.52029 + 5.80875I 0
u = −0.287591 + 1.179520I
a = 0.483184 − 0.893572I
b = −0.732134 + 0.541466I
−1.84706 − 4.49374I 0
u = −0.287591 − 1.179520I
a = 0.483184 + 0.893572I
b = −0.732134 − 0.541466I
−1.84706 + 4.49374I 0
u = 0.690543 + 0.999672I
a = −0.589202 − 0.783524I
b = 0.301551 − 0.247279I
2.88500 − 2.68678I 0
u = 0.690543 − 0.999672I
a = −0.589202 + 0.783524I
b = 0.301551 + 0.247279I
2.88500 + 2.68678I 0
u = −0.699409 + 0.350504I
a = 1.60704 − 0.79835I
b = −0.493017 − 0.809392I
−0.142387 − 1.055050I −3.33641 + 2.59143I
u = −0.699409 − 0.350504I
a = 1.60704 + 0.79835I
b = −0.493017 + 0.809392I
−0.142387 + 1.055050I −3.33641 − 2.59143I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.515478 + 0.580446I
a = 0.032805 − 0.203339I
b = 0.66210 − 1.25035I
−4.78300 − 7.06905I −7.80289 − 1.26591I
u = −0.515478 − 0.580446I
a = 0.032805 + 0.203339I
b = 0.66210 + 1.25035I
−4.78300 + 7.06905I −7.80289 + 1.26591I
u = 0.570610 + 1.085870I
a = −1.79848 − 0.58609I
b = 0.971934 − 0.503577I
3.56430 − 6.64037I 0
u = 0.570610 − 1.085870I
a = −1.79848 + 0.58609I
b = 0.971934 + 0.503577I
3.56430 + 6.64037I 0
u = 0.710587 + 0.275739I
a = 0.647280 + 0.156114I
b = −0.724323 − 0.488591I
1.39169 + 1.83140I 2.48492 − 3.08758I
u = 0.710587 − 0.275739I
a = 0.647280 − 0.156114I
b = −0.724323 + 0.488591I
1.39169 − 1.83140I 2.48492 + 3.08758I
u = −0.005633 + 0.749278I
a = 0.759884 − 0.112506I
b = −0.535024 − 0.788844I
0.58588 + 2.17509I 0.99878 − 4.48209I
u = −0.005633 − 0.749278I
a = 0.759884 + 0.112506I
b = −0.535024 + 0.788844I
0.58588 − 2.17509I 0.99878 + 4.48209I
u = −1.096060 + 0.618310I
a = 0.021905 − 0.204802I
b = 0.96307 − 1.25920I
−2.6086 − 14.3887I 0
u = −1.096060 − 0.618310I
a = 0.021905 + 0.204802I
b = 0.96307 + 1.25920I
−2.6086 + 14.3887I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.241380 + 0.326765I
a = 0.092812 + 0.222898I
b = 0.752664 + 0.357810I
−0.52408 + 1.59823I 0
u = −1.241380 − 0.326765I
a = 0.092812 − 0.222898I
b = 0.752664 − 0.357810I
−0.52408 − 1.59823I 0
u = −0.712245 + 1.112630I
a = −1.57891 + 0.72399I
b = 1.020770 + 0.563999I
0.91919 + 11.86730I 0
u = −0.712245 − 1.112630I
a = −1.57891 − 0.72399I
b = 1.020770 − 0.563999I
0.91919 − 11.86730I 0
u = 0.664498 + 0.126009I
a = 0.761790 − 0.349521I
b = −0.534517 + 0.389943I
1.53863 − 1.56496I 2.77557 + 5.59966I
u = 0.664498 − 0.126009I
a = 0.761790 + 0.349521I
b = −0.534517 − 0.389943I
1.53863 + 1.56496I 2.77557 − 5.59966I
u = −0.448393 + 0.486769I
a = 0.037563 + 0.208706I
b = 0.427971 + 1.046490I
−4.52487 + 8.10749I −9.9914 − 16.1587I
u = −0.448393 − 0.486769I
a = 0.037563 − 0.208706I
b = 0.427971 − 1.046490I
−4.52487 − 8.10749I −9.9914 + 16.1587I
u = −0.806382 + 1.072400I
a = −0.651665 + 0.578005I
b = 0.302382 + 0.451184I
−0.25078 + 7.82050I 0
u = −0.806382 − 1.072400I
a = −0.651665 − 0.578005I
b = 0.302382 − 0.451184I
−0.25078 − 7.82050I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581027 + 1.227070I
a = 0.711403 − 0.432566I
b = −1.065000 − 0.075580I
2.89056 + 4.52244I 0
u = −0.581027 − 1.227070I
a = 0.711403 + 0.432566I
b = −1.065000 + 0.075580I
2.89056 − 4.52244I 0
u = 0.411624 + 1.304930I
a = 0.682737 + 0.476482I
b = −1.009490 − 0.186740I
4.80206 + 1.17927I 0
u = 0.411624 − 1.304930I
a = 0.682737 − 0.476482I
b = −1.009490 + 0.186740I
4.80206 − 1.17927I 0
u = 0.669960 + 1.194300I
a = 1.72554 + 0.41974I
b = −1.02542 + 1.29041I
2.0692 − 15.5390I 0
u = 0.669960 − 1.194300I
a = 1.72554 − 0.41974I
b = −1.02542 − 1.29041I
2.0692 + 15.5390I 0
u = −0.361514 + 0.505095I
a = 0.80173 + 3.10297I
b = 0.404732 − 0.566973I
−0.585059 − 0.657581I −1.22456 − 4.09128I
u = −0.361514 − 0.505095I
a = 0.80173 − 3.10297I
b = 0.404732 + 0.566973I
−0.585059 + 0.657581I −1.22456 + 4.09128I
u = −0.016174 + 1.400090I
a = 1.148900 + 0.537673I
b = −1.129950 − 0.781701I
6.69611 + 5.81599I 0
u = −0.016174 − 1.400090I
a = 1.148900 − 0.537673I
b = −1.129950 + 0.781701I
6.69611 − 5.81599I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.217621 + 1.385380I
a = 1.38478 − 0.35279I
b = −1.13894 + 0.96013I
6.25917 − 11.81910I 0
u = 0.217621 − 1.385380I
a = 1.38478 + 0.35279I
b = −1.13894 − 0.96013I
6.25917 + 11.81910I 0
u = −0.784462 + 1.172880I
a = 1.63321 − 0.61623I
b = −1.01050 − 1.36256I
−0.8005 + 21.1725I 0
u = −0.784462 − 1.172880I
a = 1.63321 + 0.61623I
b = −1.01050 + 1.36256I
−0.8005 − 21.1725I 0
u = −0.580251
a = 0.875154
b = 0.303114
−1.10369 −8.83920
u = 1.69710
a = 0.0860815
b = 0.341992
−10.2758 0
12
II. I
u
2
= h5.41 × 10
57
au
53
+ 5.21 × 10
57
u
53
+ · · · + 2.28 × 10
59
a + 9.87 ×
10
58
, 2.50 × 10
59
au
53
+ 5.44 × 10
58
u
53
+ · · · − 9.46 × 10
59
a + 3.74 ×
10
60
, u
54
− 2u
53
+ · · · − 36u + 8i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
a
−0.458633au
53
− 0.442398u
53
+ ··· − 19.3518a − 8.37724
a
9
=
2.27949au
53
− 2.11457u
53
+ ··· + 7.43511a + 28.2829
1.87139au
53
− 0.860803u
53
+ ··· − 1.82953a + 4.71620
a
12
=
−0.458633au
53
− 0.442398u
53
+ ··· − 18.3518a − 8.37724
−0.458633au
53
− 0.442398u
53
+ ··· − 19.3518a − 8.37724
a
10
=
1.37832au
53
− 1.40854u
53
+ ··· + 34.5330a − 6.74800
2.23912au
53
− 0.154776u
53
+ ··· + 29.8168a − 30.3147
a
3
=
u
u
3
+ u
a
6
=
0.730020au
53
− 2.75574u
53
+ ··· − 13.5603a + 44.1083
−1.84049au
53
+ 2.57051u
53
+ ··· − 28.0074a + 14.4472
a
1
=
−1.75778u
53
+ 1.27837u
52
+ ··· + 33.8023u − 15.5886
−0.860803u
53
+ 1.49544u
52
+ ··· − 25.3987u + 3.71620
a
2
=
−1.43663u
53
+ 1.00275u
52
+ ··· + 24.6995u − 12.0758
−0.583121u
53
+ 1.21655u
52
+ ··· − 23.8703u + 4.29557
a
5
=
−0.838088u
53
+ 1.23708u
52
+ ··· − 7.27521u − 1.40738
0.919688u
53
− 0.0412944u
52
+ ··· − 41.0775u + 14.1812
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.77654u
53
− 8.12192u
52
+ ··· + 368.132u − 110.252
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
(u
54
+ 27u
53
+ ··· + 13u + 1)
2
c
2
(u
54
− 5u
53
+ ··· − 9u + 1)
2
c
3
(u
54
− 2u
53
+ ··· − 36u + 8)
2
c
4
(u
54
+ 5u
53
+ ··· + 9u + 1)
2
c
5
u
108
− 5u
107
+ ··· + 132577u + 8777
c
6
u
108
− 9u
107
+ ··· − 9u + 1
c
7
(u
54
+ 2u
53
+ ··· + 36u + 8)
2
c
8
u
108
+ 8u
107
+ ··· + 23502u + 2087
c
9
(u
54
+ 26u
53
+ ··· + 4u + 8)
2
c
10
u
108
− 8u
107
+ ··· − 23502u + 2087
c
11
u
108
+ 5u
107
+ ··· − 132577u + 8777
c
12
u
108
+ 9u
107
+ ··· + 9u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
54
+ 5y
53
+ ··· − 29y + 1)
2
c
2
, c
4
(y
54
− 27y
53
+ ··· − 13y + 1)
2
c
3
, c
7
(y
54
+ 24y
53
+ ··· + 560y + 64)
2
c
5
, c
11
y
108
+ 7y
107
+ ··· + 4652443229y + 77035729
c
6
, c
12
y
108
− 25y
107
+ ··· + 13y + 1
c
8
, c
10
y
108
+ 36y
107
+ ··· − 214112262y + 4355569
c
9
(y
54
− 8y
53
+ ··· − 1552y + 64)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779920 + 0.570390I
a = −0.546537 − 0.411913I
b = −1.14839 + 1.23174I
−4.00101 − 5.38237I −10.98553 + 6.99111I
u = −0.779920 + 0.570390I
a = 2.18669 − 1.50175I
b = 0.066826 − 0.680570I
−4.00101 − 5.38237I −10.98553 + 6.99111I
u = −0.779920 − 0.570390I
a = −0.546537 + 0.411913I
b = −1.14839 − 1.23174I
−4.00101 + 5.38237I −10.98553 − 6.99111I
u = −0.779920 − 0.570390I
a = 2.18669 + 1.50175I
b = 0.066826 + 0.680570I
−4.00101 + 5.38237I −10.98553 − 6.99111I
u = 0.757774 + 0.710612I
a = 1.120360 + 0.276815I
b = 0.019976 + 1.052380I
−4.34597 + 1.29421I −11.39281 − 0.62282I
u = 0.757774 + 0.710612I
a = 0.801891 + 0.977290I
b = −0.001869 + 0.958331I
−4.34597 + 1.29421I −11.39281 − 0.62282I
u = 0.757774 − 0.710612I
a = 1.120360 − 0.276815I
b = 0.019976 − 1.052380I
−4.34597 − 1.29421I −11.39281 + 0.62282I
u = 0.757774 − 0.710612I
a = 0.801891 − 0.977290I
b = −0.001869 − 0.958331I
−4.34597 − 1.29421I −11.39281 + 0.62282I
u = −0.096612 + 0.955980I
a = 0.442956 + 0.941110I
b = −0.374086 + 1.012740I
1.05179 − 4.60277I 0.63962 + 8.77941I
u = −0.096612 + 0.955980I
a = −1.81719 + 1.39132I
b = 1.52214 − 0.66718I
1.05179 − 4.60277I 0.63962 + 8.77941I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096612 − 0.955980I
a = 0.442956 − 0.941110I
b = −0.374086 − 1.012740I
1.05179 + 4.60277I 0.63962 − 8.77941I
u = −0.096612 − 0.955980I
a = −1.81719 − 1.39132I
b = 1.52214 + 0.66718I
1.05179 + 4.60277I 0.63962 − 8.77941I
u = 0.952377 + 0.432650I
a = 0.164151 − 1.210680I
b = 1.61972 − 0.49258I
−0.44506 + 5.91935I −0.51840 − 8.32205I
u = 0.952377 + 0.432650I
a = 0.525169 − 0.136759I
b = −0.664923 − 0.908885I
−0.44506 + 5.91935I −0.51840 − 8.32205I
u = 0.952377 − 0.432650I
a = 0.164151 + 1.210680I
b = 1.61972 + 0.49258I
−0.44506 − 5.91935I −0.51840 + 8.32205I
u = 0.952377 − 0.432650I
a = 0.525169 + 0.136759I
b = −0.664923 + 0.908885I
−0.44506 − 5.91935I −0.51840 + 8.32205I
u = 0.455169 + 0.961144I
a = −0.365363 + 1.102460I
b = −0.081873 + 0.843018I
−0.12183 − 5.97761I −4.00000 + 8.19191I
u = 0.455169 + 0.961144I
a = −2.42444 − 0.34562I
b = 1.33653 − 1.18106I
−0.12183 − 5.97761I −4.00000 + 8.19191I
u = 0.455169 − 0.961144I
a = −0.365363 − 1.102460I
b = −0.081873 − 0.843018I
−0.12183 + 5.97761I −4.00000 − 8.19191I
u = 0.455169 − 0.961144I
a = −2.42444 + 0.34562I
b = 1.33653 + 1.18106I
−0.12183 + 5.97761I −4.00000 − 8.19191I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569426 + 0.734780I
a = 0.610216 + 0.018160I
b = −0.151643 − 1.078860I
−0.80723 + 2.33552I −5.88993 − 3.53014I
u = −0.569426 + 0.734780I
a = 1.14217 − 0.86449I
b = 0.103486 − 0.822957I
−0.80723 + 2.33552I −5.88993 − 3.53014I
u = −0.569426 − 0.734780I
a = 0.610216 − 0.018160I
b = −0.151643 + 1.078860I
−0.80723 − 2.33552I −5.88993 + 3.53014I
u = −0.569426 − 0.734780I
a = 1.14217 + 0.86449I
b = 0.103486 + 0.822957I
−0.80723 − 2.33552I −5.88993 + 3.53014I
u = 0.455009 + 0.987507I
a = 0.500230 − 0.558620I
b = −0.508840 − 1.095180I
−0.249845 + 0.317495I −1.32073 − 1.40260I
u = 0.455009 + 0.987507I
a = −0.89712 − 1.38052I
b = 1.73704 + 0.33821I
−0.249845 + 0.317495I −1.32073 − 1.40260I
u = 0.455009 − 0.987507I
a = 0.500230 + 0.558620I
b = −0.508840 + 1.095180I
−0.249845 − 0.317495I −1.32073 + 1.40260I
u = 0.455009 − 0.987507I
a = −0.89712 + 1.38052I
b = 1.73704 − 0.33821I
−0.249845 − 0.317495I −1.32073 + 1.40260I
u = −0.644738 + 0.638414I
a = −1.15005 − 1.14919I
b = −0.063925 − 0.543421I
−4.17995 + 3.05166I −11.84908 − 5.39236I
u = −0.644738 + 0.638414I
a = −2.69152 + 1.94111I
b = 1.01017 + 1.26228I
−4.17995 + 3.05166I −11.84908 − 5.39236I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644738 − 0.638414I
a = −1.15005 + 1.14919I
b = −0.063925 + 0.543421I
−4.17995 − 3.05166I −11.84908 + 5.39236I
u = −0.644738 − 0.638414I
a = −2.69152 − 1.94111I
b = 1.01017 − 1.26228I
−4.17995 − 3.05166I −11.84908 + 5.39236I
u = −0.898521 + 0.000623I
a = 0.606239 + 1.114270I
b = 1.23475 + 0.82345I
0.66383 − 1.91540I 1.02934 + 3.88232I
u = −0.898521 + 0.000623I
a = 0.536412 − 0.025774I
b = −0.535058 + 0.806364I
0.66383 − 1.91540I 1.02934 + 3.88232I
u = −0.898521 − 0.000623I
a = 0.606239 − 1.114270I
b = 1.23475 − 0.82345I
0.66383 + 1.91540I 1.02934 − 3.88232I
u = −0.898521 − 0.000623I
a = 0.536412 + 0.025774I
b = −0.535058 − 0.806364I
0.66383 + 1.91540I 1.02934 − 3.88232I
u = −1.058910 + 0.331265I
a = 0.321241 − 0.092722I
b = 0.912601 − 0.910871I
−2.20953 − 1.16569I −10.93449 + 2.51536I
u = −1.058910 + 0.331265I
a = 0.264198 + 0.040376I
b = 0.005058 + 0.590723I
−2.20953 − 1.16569I −10.93449 + 2.51536I
u = −1.058910 − 0.331265I
a = 0.321241 + 0.092722I
b = 0.912601 + 0.910871I
−2.20953 + 1.16569I −10.93449 − 2.51536I
u = −1.058910 − 0.331265I
a = 0.264198 − 0.040376I
b = 0.005058 − 0.590723I
−2.20953 + 1.16569I −10.93449 − 2.51536I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.593455 + 0.981746I
a = −0.119753 − 0.293048I
b = −0.90054 + 1.52672I
−3.14034 + 1.80316I −8.88688 + 0.I
u = −0.593455 + 0.981746I
a = 1.79119 − 0.43016I
b = −0.211247 − 0.403872I
−3.14034 + 1.80316I −8.88688 + 0.I
u = −0.593455 − 0.981746I
a = −0.119753 + 0.293048I
b = −0.90054 − 1.52672I
−3.14034 − 1.80316I −8.88688 + 0.I
u = −0.593455 − 0.981746I
a = 1.79119 + 0.43016I
b = −0.211247 + 0.403872I
−3.14034 − 1.80316I −8.88688 + 0.I
u = 0.500064 + 1.038010I
a = −1.210770 + 0.466175I
b = 0.130321 − 0.706851I
−4.95586 − 3.24816I −10.98398 + 5.99558I
u = 0.500064 + 1.038010I
a = 1.89780 + 0.13802I
b = −0.92533 + 1.13551I
−4.95586 − 3.24816I −10.98398 + 5.99558I
u = 0.500064 − 1.038010I
a = −1.210770 − 0.466175I
b = 0.130321 + 0.706851I
−4.95586 + 3.24816I −10.98398 − 5.99558I
u = 0.500064 − 1.038010I
a = 1.89780 − 0.13802I
b = −0.92533 − 1.13551I
−4.95586 + 3.24816I −10.98398 − 5.99558I
u = 0.369166 + 0.762326I
a = 0.054840 + 0.518456I
b = −0.76552 − 1.30977I
−0.87009 + 2.42239I −5.58442 − 1.37916I
u = 0.369166 + 0.762326I
a = 2.34391 − 0.03059I
b = 0.052646 + 0.249590I
−0.87009 + 2.42239I −5.58442 − 1.37916I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369166 − 0.762326I
a = 0.054840 − 0.518456I
b = −0.76552 + 1.30977I
−0.87009 − 2.42239I −5.58442 + 1.37916I
u = 0.369166 − 0.762326I
a = 2.34391 + 0.03059I
b = 0.052646 − 0.249590I
−0.87009 − 2.42239I −5.58442 + 1.37916I
u = 0.294834 + 0.782948I
a = 1.68203 + 2.22690I
b = −1.37054 − 0.47532I
−1.29037 − 3.59873I 0.83433 + 8.18799I
u = 0.294834 + 0.782948I
a = −3.57533 + 0.73898I
b = 0.593015 − 0.902081I
−1.29037 − 3.59873I 0.83433 + 8.18799I
u = 0.294834 − 0.782948I
a = 1.68203 − 2.22690I
b = −1.37054 + 0.47532I
−1.29037 + 3.59873I 0.83433 − 8.18799I
u = 0.294834 − 0.782948I
a = −3.57533 − 0.73898I
b = 0.593015 + 0.902081I
−1.29037 + 3.59873I 0.83433 − 8.18799I
u = 0.646249 + 0.980172I
a = 1.084690 + 0.681880I
b = −0.181695 + 0.835391I
−3.48158 − 6.62830I 0
u = 0.646249 + 0.980172I
a = 0.413024 + 0.182955I
b = −0.004625 + 1.236960I
−3.48158 − 6.62830I 0
u = 0.646249 − 0.980172I
a = 1.084690 − 0.681880I
b = −0.181695 − 0.835391I
−3.48158 + 6.62830I 0
u = 0.646249 − 0.980172I
a = 0.413024 − 0.182955I
b = −0.004625 − 1.236960I
−3.48158 + 6.62830I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.451052 + 0.617789I
a = 0.265713 + 0.095410I
b = 0.444907 + 1.288670I
−6.36701 − 0.76274I −10.03524 + 6.11129I
u = 0.451052 + 0.617789I
a = 0.252945 − 0.068814I
b = 0.054706 − 1.116220I
−6.36701 − 0.76274I −10.03524 + 6.11129I
u = 0.451052 − 0.617789I
a = 0.265713 − 0.095410I
b = 0.444907 − 1.288670I
−6.36701 + 0.76274I −10.03524 − 6.11129I
u = 0.451052 − 0.617789I
a = 0.252945 + 0.068814I
b = 0.054706 + 1.116220I
−6.36701 + 0.76274I −10.03524 − 6.11129I
u = −0.641738 + 1.056980I
a = −0.471302 − 0.849262I
b = 0.069476 − 0.851789I
−2.50992 + 10.76960I 0
u = −0.641738 + 1.056980I
a = −1.92569 + 0.64152I
b = 1.36326 + 1.36762I
−2.50992 + 10.76960I 0
u = −0.641738 − 1.056980I
a = −0.471302 + 0.849262I
b = 0.069476 + 0.851789I
−2.50992 − 10.76960I 0
u = −0.641738 − 1.056980I
a = −1.92569 − 0.64152I
b = 1.36326 − 1.36762I
−2.50992 − 10.76960I 0
u = 1.102160 + 0.586805I
a = 0.307854 + 0.128871I
b = 1.00243 + 1.23954I
−4.19042 + 6.13400I 0
u = 1.102160 + 0.586805I
a = 0.250979 − 0.042259I
b = −0.235865 − 0.712137I
−4.19042 + 6.13400I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.102160 − 0.586805I
a = 0.307854 − 0.128871I
b = 1.00243 − 1.23954I
−4.19042 − 6.13400I 0
u = 1.102160 − 0.586805I
a = 0.250979 + 0.042259I
b = −0.235865 + 0.712137I
−4.19042 − 6.13400I 0
u = −0.472614 + 1.158010I
a = 0.99275 − 1.16340I
b = −1.81462 + 0.61246I
4.11063 + 6.40964I 0
u = −0.472614 + 1.158010I
a = −1.92873 − 0.00523I
b = 0.748662 + 0.886711I
4.11063 + 6.40964I 0
u = −0.472614 − 1.158010I
a = 0.99275 + 1.16340I
b = −1.81462 − 0.61246I
4.11063 − 6.40964I 0
u = −0.472614 − 1.158010I
a = −1.92873 + 0.00523I
b = 0.748662 − 0.886711I
4.11063 − 6.40964I 0
u = 0.078227 + 1.284350I
a = −1.064300 − 0.850256I
b = 0.621006 + 0.613338I
5.85323 + 3.01512I 0
u = 0.078227 + 1.284350I
a = 1.55121 − 0.41035I
b = −1.56159 + 1.19226I
5.85323 + 3.01512I 0
u = 0.078227 − 1.284350I
a = −1.064300 + 0.850256I
b = 0.621006 − 0.613338I
5.85323 − 3.01512I 0
u = 0.078227 − 1.284350I
a = 1.55121 + 0.41035I
b = −1.56159 − 1.19226I
5.85323 − 3.01512I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.656223 + 1.160370I
a = 0.703467 + 1.147860I
b = −1.94805 − 0.47340I
1.81679 − 11.78100I 0
u = 0.656223 + 1.160370I
a = −1.81280 − 0.37772I
b = 0.777645 − 0.964665I
1.81679 − 11.78100I 0
u = 0.656223 − 1.160370I
a = 0.703467 − 1.147860I
b = −1.94805 + 0.47340I
1.81679 + 11.78100I 0
u = 0.656223 − 1.160370I
a = −1.81280 + 0.37772I
b = 0.777645 + 0.964665I
1.81679 + 11.78100I 0
u = −0.345070 + 1.307630I
a = −0.550201 + 0.825654I
b = 0.469133 − 0.497629I
5.03083 + 2.64174I 0
u = −0.345070 + 1.307630I
a = 1.53204 + 0.03564I
b = −1.43336 − 1.54275I
5.03083 + 2.64174I 0
u = −0.345070 − 1.307630I
a = −0.550201 − 0.825654I
b = 0.469133 + 0.497629I
5.03083 − 2.64174I 0
u = −0.345070 − 1.307630I
a = 1.53204 − 0.03564I
b = −1.43336 + 1.54275I
5.03083 − 2.64174I 0
u = −0.649103 + 1.211340I
a = −1.053210 − 0.044604I
b = 0.356104 + 0.677357I
0.54257 + 7.21886I 0
u = −0.649103 + 1.211340I
a = 1.52378 − 0.35546I
b = −1.12243 − 1.33335I
0.54257 + 7.21886I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649103 − 1.211340I
a = −1.053210 + 0.044604I
b = 0.356104 − 0.677357I
0.54257 − 7.21886I 0
u = −0.649103 − 1.211340I
a = 1.52378 + 0.35546I
b = −1.12243 + 1.33335I
0.54257 − 7.21886I 0
u = 0.772624 + 1.184220I
a = −1.129680 − 0.107049I
b = 0.417617 − 0.784997I
−2.25293 − 12.88510I 0
u = 0.772624 + 1.184220I
a = 1.47480 + 0.53096I
b = −1.05832 + 1.46391I
−2.25293 − 12.88510I 0
u = 0.772624 − 1.184220I
a = −1.129680 + 0.107049I
b = 0.417617 + 0.784997I
−2.25293 + 12.88510I 0
u = 0.772624 − 1.184220I
a = 1.47480 − 0.53096I
b = −1.05832 − 1.46391I
−2.25293 + 12.88510I 0
u = −0.057491 + 0.582953I
a = 0.512804 + 0.305125I
b = −0.483117 − 1.147310I
−0.59659 + 2.59685I −2.11326 − 1.51803I
u = −0.057491 + 0.582953I
a = 1.71484 − 1.07386I
b = 0.316819 − 0.233190I
−0.59659 + 2.59685I −2.11326 − 1.51803I
u = −0.057491 − 0.582953I
a = 0.512804 − 0.305125I
b = −0.483117 + 1.147310I
−0.59659 − 2.59685I −2.11326 + 1.51803I
u = −0.057491 − 0.582953I
a = 1.71484 + 1.07386I
b = 0.316819 + 0.233190I
−0.59659 − 2.59685I −2.11326 + 1.51803I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13785 + 1.44570I
a = 1.236400 + 0.016643I
b = −1.72191 − 0.41184I
4.37573 + 3.10323I 0
u = −0.13785 + 1.44570I
a = −0.408161 − 0.060273I
b = 0.149121 + 0.107651I
4.37573 + 3.10323I 0
u = −0.13785 − 1.44570I
a = 1.236400 − 0.016643I
b = −1.72191 + 0.41184I
4.37573 − 3.10323I 0
u = −0.13785 − 1.44570I
a = −0.408161 + 0.060273I
b = 0.149121 − 0.107651I
4.37573 − 3.10323I 0
u = 0.454526 + 0.087615I
a = −4.46751 + 1.04008I
b = −0.932183 + 0.533345I
−2.10388 − 3.56800I −11.4713 + 10.3154I
u = 0.454526 + 0.087615I
a = −0.69936 − 10.38270I
b = 0.566414 − 0.846383I
−2.10388 − 3.56800I −11.4713 + 10.3154I
u = 0.454526 − 0.087615I
a = −4.46751 − 1.04008I
b = −0.932183 − 0.533345I
−2.10388 + 3.56800I −11.4713 − 10.3154I
u = 0.454526 − 0.087615I
a = −0.69936 + 10.38270I
b = 0.566414 + 0.846383I
−2.10388 + 3.56800I −11.4713 − 10.3154I
28
III.
I
u
3
= h7.68 × 10
8
u
22
− 1.64 × 10
9
u
21
+ · · · + 2.19 × 10
8
b + 4.73 × 10
8
, 9.98 ×
10
7
u
22
+ 5.01 × 10
8
u
21
+ · · · + 2.19 × 10
8
a + 8.52 × 10
7
, u
23
− 2u
22
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−0.455006u
22
− 2.28238u
21
+ ··· + 15.9748u − 0.388305
−3.50199u
22
+ 7.49137u
21
+ ··· + 4.99452u − 2.15838
a
9
=
4.35627u
22
− 6.70780u
21
+ ··· − 0.0136713u + 7.77709
−1.25289u
22
− 0.137979u
21
+ ··· − 1.63786u + 3.49215
a
12
=
−3.95699u
22
+ 5.20899u
21
+ ··· + 20.9693u − 2.54669
−3.50199u
22
+ 7.49137u
21
+ ··· + 4.99452u − 2.15838
a
10
=
−2.70410u
22
+ 5.34697u
21
+ ··· + 22.6072u − 5.03883
−3.50199u
22
+ 7.49137u
21
+ ··· + 4.99452u − 2.15838
a
3
=
u
u
3
+ u
a
6
=
−0.183963u
22
+ 5.46982u
21
+ ··· + 20.1132u − 4.93168
0.287587u
22
− 1.11829u
21
+ ··· − 3.64799u + 1.60975
a
1
=
−4.46729u
22
+ 6.23510u
21
+ ··· − 0.291338u + 2.94351
−0.317644u
22
+ 0.661174u
21
+ ··· + 0.830704u − 0.543116
a
2
=
−2.87416u
22
+ 4.03399u
21
+ ··· − 1.67830u + 1.79215
0.926368u
22
− 1.25360u
21
+ ··· + 0.0517189u − 0.709319
a
5
=
2.53832u
22
− 3.92528u
21
+ ··· + 2.88986u − 0.787148
−1.92897u
22
+ 2.30982u
21
+ ··· + 2.59852u + 2.15636
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
68196543
219374557
u
22
−
1083749507
219374557
u
21
+ ··· +
791711183
219374557
u +
3834368197
219374557
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 14u
22
+ ··· + 3u − 1
c
2
u
23
+ 4u
22
+ ··· + 5u + 1
c
3
u
23
+ 2u
22
+ ··· + u + 1
c
4
u
23
− 4u
22
+ ··· + 5u − 1
c
5
, c
11
u
23
− 3u
21
+ ··· + 3u − 1
c
6
, c
12
u
23
− 3u
22
+ ··· + 3u
2
− 1
c
7
u
23
− 2u
22
+ ··· + u − 1
c
8
, c
10
u
23
+ 6u
22
+ ··· + 13u + 1
c
9
u
23
− 17u
22
+ ··· + 300u − 23
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 6y
22
+ ··· − 41y −1
c
2
, c
4
y
23
− 14y
22
+ ··· + 3y −1
c
3
, c
7
y
23
+ 6y
22
+ ··· − 13y −1
c
5
, c
11
y
23
− 6y
22
+ ··· + 13y −1
c
6
, c
12
y
23
− 13y
22
+ ··· + 6y −1
c
8
, c
10
y
23
+ 18y
22
+ ··· + 57y −1
c
9
y
23
+ 7y
22
+ ··· − 11982y −529
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932863 + 0.470918I
a = 0.165631 + 0.569254I
b = −0.942354 − 0.581737I
−2.12811 + 5.87189I −6.72516 − 8.17983I
u = 0.932863 − 0.470918I
a = 0.165631 − 0.569254I
b = −0.942354 + 0.581737I
−2.12811 − 5.87189I −6.72516 + 8.17983I
u = −1.073630 + 0.038473I
a = −0.312655 + 0.111696I
b = −0.704508 − 0.377525I
−1.15055 + 1.78087I −6.33794 − 6.21242I
u = −1.073630 − 0.038473I
a = −0.312655 − 0.111696I
b = −0.704508 + 0.377525I
−1.15055 − 1.78087I −6.33794 + 6.21242I
u = −0.623187 + 0.884614I
a = 0.385194 − 0.749681I
b = −0.424608 − 0.856790I
−2.47835 + 7.69486I −4.03051 − 10.74975I
u = −0.623187 − 0.884614I
a = 0.385194 + 0.749681I
b = −0.424608 + 0.856790I
−2.47835 − 7.69486I −4.03051 + 10.74975I
u = 0.536099 + 0.942930I
a = 0.862482 + 0.264107I
b = −0.921933 − 0.844990I
−1.91947 − 0.51386I −6.81021 − 1.61545I
u = 0.536099 − 0.942930I
a = 0.862482 − 0.264107I
b = −0.921933 + 0.844990I
−1.91947 + 0.51386I −6.81021 + 1.61545I
u = −0.201305 + 0.782124I
a = 1.52028 − 0.00897I
b = −0.782793 + 0.837361I
−0.03284 − 3.45587I −1.65858 + 6.73564I
u = −0.201305 − 0.782124I
a = 1.52028 + 0.00897I
b = −0.782793 − 0.837361I
−0.03284 + 3.45587I −1.65858 − 6.73564I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257132 + 0.709937I
a = 0.99695 + 1.29898I
b = −0.624537 + 0.822387I
−0.16869 − 3.94739I −0.48697 + 6.43488I
u = 0.257132 − 0.709937I
a = 0.99695 − 1.29898I
b = −0.624537 − 0.822387I
−0.16869 + 3.94739I −0.48697 − 6.43488I
u = −0.512945 + 1.136410I
a = −1.56269 + 0.20096I
b = 1.038430 + 0.524944I
2.34569 + 6.47513I −1.59916 − 6.72206I
u = −0.512945 − 1.136410I
a = −1.56269 − 0.20096I
b = 1.038430 − 0.524944I
2.34569 − 6.47513I −1.59916 + 6.72206I
u = 0.380344 + 0.634981I
a = −3.73066 − 0.26533I
b = 0.829525 − 0.651884I
−2.81772 − 3.60187I −6.08859 + 9.71801I
u = 0.380344 − 0.634981I
a = −3.73066 + 0.26533I
b = 0.829525 + 0.651884I
−2.81772 + 3.60187I −6.08859 − 9.71801I
u = 0.683735 + 1.137110I
a = −1.47522 − 0.45757I
b = 1.093930 − 0.601085I
−0.10268 − 11.79120I −5.66079 + 10.41521I
u = 0.683735 − 1.137110I
a = −1.47522 + 0.45757I
b = 1.093930 + 0.601085I
−0.10268 + 11.79120I −5.66079 − 10.41521I
u = −0.068461 + 1.365630I
a = −1.000100 − 0.079711I
b = 0.952194 + 0.115441I
4.77834 + 2.95935I 4.00300 − 4.77864I
u = −0.068461 − 1.365630I
a = −1.000100 + 0.079711I
b = 0.952194 − 0.115441I
4.77834 − 2.95935I 4.00300 + 4.77864I
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162072 + 0.546076I
a = 0.69002 + 4.98557I
b = 0.661666 − 0.636100I
−2.70546 − 3.71170I −1.066993 + 0.373005I
u = −0.162072 − 0.546076I
a = 0.69002 − 4.98557I
b = 0.661666 + 0.636100I
−2.70546 + 3.71170I −1.066993 − 0.373005I
u = 1.70286
a = −0.0784597
b = −0.350038
−10.2694 627.920
34
IV.
I
u
4
= h−u
2
a + b + 1, −4u
2
a + a
2
− 2au + 8u
2
− 5a + 3u + 15, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
a
u
2
a − 1
a
9
=
a + 1
u
2
a + u
2
− 1
a
12
=
u
2
a + a − 1
u
2
a − 1
a
10
=
a + 1
u
2
a + u
2
− 1
a
3
=
u
−u
2
− u − 1
a
6
=
−u
2
a + 3u
2
− a + 2u + 7
u
2
a − au + 2u
2
− a − u
a
1
=
−1
−u
2
a
2
=
−u
2
− 1
−u
2
− u − 1
a
5
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u − 4
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
11
c
12
u
6
+ 3u
5
+ 5u
4
+ 5u
3
+ 5u
2
+ 3u + 1
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
8
, c
10
(u + 1)
6
c
9
u
6
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
11
c
12
y
6
+ y
5
+ 5y
4
+ 9y
3
+ 5y
2
+ y + 1
c
8
, c
10
(y −1)
6
c
9
y
6
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.732199 + 0.502992I
b = 0.500000 − 0.424452I
4.66906 + 2.82812I −3.78492 − 1.30714I
u = −0.215080 + 1.307140I
a = −1.347400 − 0.137827I
b = 1.16236 + 0.98673I
4.66906 + 2.82812I −3.78492 − 1.30714I
u = −0.215080 − 1.307140I
a = −0.732199 − 0.502992I
b = 0.500000 + 0.424452I
4.66906 − 2.82812I −3.78492 + 1.30714I
u = −0.215080 − 1.307140I
a = −1.347400 + 0.137827I
b = 1.16236 − 0.98673I
4.66906 − 2.82812I −3.78492 + 1.30714I
u = −0.569840
a = 2.57960 + 3.03873I
b = −0.162359 + 0.986732I
0.531480 −3.43020
u = −0.569840
a = 2.57960 − 3.03873I
b = −0.162359 − 0.986732I
0.531480 −3.43020
38
V. I
v
1
= ha, 16v
3
− 48v
2
+ b + 51v − 13, 4v
4
− 13v
3
+ 16v
2
− 7v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−16v
3
+ 48v
2
− 51v + 13
a
9
=
1
20v
3
− 57v
2
+ 58v − 13
a
12
=
−16v
3
+ 48v
2
− 51v + 13
−16v
3
+ 48v
2
− 51v + 13
a
10
=
16v
3
− 48v
2
+ 51v − 13
36v
3
− 105v
2
+ 109v − 27
a
3
=
v
0
a
6
=
−20v
3
+ 57v
2
− 58v + 14
−36v
3
+ 105v
2
− 109v + 27
a
1
=
−1
4v
3
− 13v
2
+ 16v − 7
a
2
=
v − 1
4v
3
− 13v
2
+ 16v − 7
a
5
=
1
−4v
3
+ 13v
2
− 16v + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 68v
3
− 192v
2
+ 197v − 49
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
8
, c
10
u
4
+ u
2
+ u + 1
c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
8
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.28654 + 0.69736I
a = 0
b = −0.547424 + 0.585652I
−0.66484 − 1.39709I −2.80605 + 5.27044I
v = 1.28654 − 0.69736I
a = 0
b = −0.547424 − 0.585652I
−0.66484 + 1.39709I −2.80605 − 5.27044I
v = 0.338459 + 0.046758I
a = 0
b = 0.547424 − 1.120870I
−4.26996 − 7.64338I −1.41270 + 4.22005I
v = 0.338459 − 0.046758I
a = 0
b = 0.547424 + 1.120870I
−4.26996 + 7.64338I −1.41270 − 4.22005I
42
VI. I
v
2
= ha, b
2
− bv + v
2
− b + 2v + 2, v
3
+ 2v
2
+ 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
b
a
9
=
1
−bv + v
2
− b + 2v + 2
a
12
=
b
b
a
10
=
−v
2
b − bv − b + 1
−v
2
b − 2bv + v
2
− 2b + 2v + 2
a
3
=
v
0
a
6
=
bv − v
2
+ b − 2v − 1
v
2
b + 2bv − v
2
+ 2b − 2v − 2
a
1
=
−bv + v
2
+ v + 1
v
2
+ 2v + 3
a
2
=
−bv + v
2
+ 2v + 1
v
2
+ 2v + 3
a
5
=
bv − v
2
− v − 1
−v
2
− 2v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = v − 7
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
10
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
(u
3
− u
2
+ 1)
2
c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
9
(y
3
− y
2
+ 2y − 1)
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.78492 + 1.30714I
a = 0
b = −0.498832 + 1.001300I
−1.91067 − 2.82812I −7.78492 + 1.30714I
v = −0.78492 + 1.30714I
a = 0
b = 0.713912 + 0.305839I
−1.91067 − 2.82812I −7.78492 + 1.30714I
v = −0.78492 − 1.30714I
a = 0
b = −0.498832 − 1.001300I
−1.91067 + 2.82812I −7.78492 − 1.30714I
v = −0.78492 − 1.30714I
a = 0
b = 0.713912 − 0.305839I
−1.91067 + 2.82812I −7.78492 − 1.30714I
v = −0.430160
a = 0
b = 0.284920 + 1.115140I
−6.04826 −7.43020
v = −0.430160
a = 0
b = 0.284920 − 1.115140I
−6.04826 −7.43020
46
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
3
− u
2
+ 2u − 1)
2
(u
23
− 14u
22
+ ··· + 3u − 1)
· (u
76
+ 41u
75
+ ··· + 2881u + 256)
c
2
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
23
+ 4u
22
+ ··· + 5u + 1)
· (u
76
− 7u
75
+ ··· + 47u − 16)
c
3
u
10
(u
3
− u
2
+ 2u − 1)
2
(u
23
+ 2u
22
+ ··· + u + 1)
· (u
76
+ 5u
75
+ ··· − 1504u − 256)
c
4
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
23
− 4u
22
+ ··· + 5u − 1)
· (u
76
− 7u
75
+ ··· + 47u − 16)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
6
+ 3u
5
+ ··· + 3u + 1)(u
23
− 3u
21
+ ··· + 3u − 1)
· (u
76
+ 8u
74
+ ··· + 9u + 1)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
6
+ 3u
5
+ ··· + 3u + 1)(u
23
− 3u
22
+ ··· + 3u
2
− 1)
· (u
76
− u
75
+ ··· + 39u
2
+ 1)
c
7
u
10
(u
3
+ u
2
+ 2u + 1)
2
(u
23
− 2u
22
+ ··· + u − 1)
· (u
76
+ 5u
75
+ ··· − 1504u − 256)
c
8
, c
10
(u + 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
23
+ 6u
22
+ ··· + 13u + 1)(u
76
− 12u
75
+ ··· + 133u + 1)
c
9
u
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
23
− 17u
22
+ ··· + 300u − 23)(u
76
− 41u
75
+ ··· − 60u + 4)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
6
+ 3u
5
+ ··· + 3u + 1)(u
23
− 3u
21
+ ··· + 3u − 1)
· (u
76
+ 8u
74
+ ··· + 9u + 1)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
6
+ 3u
5
+ ··· + 3u + 1)(u
23
− 3u
22
+ ··· + 3u
2
− 1)
· (u
76
− u
75
+ ··· + 39u
2
+ 1)
47
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
23
− 6y
22
+ ··· − 41y − 1)
· (y
76
− 5y
75
+ ··· + 3372927y + 65536)
c
2
, c
4
((y − 1)
10
)(y
3
− y
2
+ 2y − 1)
2
(y
23
− 14y
22
+ ··· + 3y − 1)
· (y
76
− 41y
75
+ ··· − 2881y + 256)
c
3
, c
7
y
10
(y
3
+ 3y
2
+ 2y − 1)
2
(y
23
+ 6y
22
+ ··· − 13y − 1)
· (y
76
+ 27y
75
+ ··· + 429056y + 65536)
c
5
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ y
5
+ 5y
4
+ 9y
3
+ 5y
2
+ y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)(y
23
− 6y
22
+ ··· + 13y − 1)
· (y
76
+ 16y
75
+ ··· + 3y + 1)
c
6
, c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
6
+ y
5
+ 5y
4
+ 9y
3
+ 5y
2
+ y + 1)(y
23
− 13y
22
+ ··· + 6y − 1)
· (y
76
+ 33y
75
+ ··· + 78y + 1)
c
8
, c
10
(y − 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
23
+ 18y
22
+ ··· + 57y − 1)(y
76
− 32y
75
+ ··· − 14137y + 1)
c
9
y
6
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
23
+ 7y
22
+ ··· − 11982y − 529)(y
76
− y
75
+ ··· − 2152y + 16)
48
