12a
0572
(K12a
0572
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 6 12 4 1 8 5
Solving Sequence
3,9
4 10
5,7
2 1 11 6 12 8
c
3
c
9
c
4
c
2
c
1
c
10
c
6
c
12
c
8
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.15099 × 10
151
u
95
+ 6.01892 × 10
150
u
94
+ ··· + 4.57032 × 10
151
b − 4.06184 × 10
152
,
9.03162 × 10
152
u
95
+ 5.47605 × 10
150
u
94
+ ··· + 1.32539 × 10
153
a − 1.93189 × 10
154
,
u
96
+ u
95
+ ··· − 254u − 29i
I
u
2
= h6u
22
− 63u
20
+ ··· + b − 7, −5u
22
+ 8u
21
+ ··· + a + 1, u
24
− 12u
22
+ ··· − 2u + 1i
I
u
3
= h−u
10
+ 2u
8
+ u
6
− u
5
− 2u
4
+ u
3
− u
2
+ b + u − 1, u
13
− 2u
11
− u
9
+ 2u
7
+ 2u
5
+ a − u,
u
15
− 3u
13
+ u
10
+ 5u
9
− 2u
8
− u
6
− u
5
+ 2u
4
− 3u
3
+ u
2
− 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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
= h2.15 × 10
151
u
95
+ 6.02 × 10
150
u
94
+ · · · + 4.57 × 10
151
b − 4.06 ×
10
152
, 9.03 × 10
152
u
95
+ 5.48 × 10
150
u
94
+ · · · + 1.33 × 10
153
a − 1.93 ×
10
154
, u
96
+ u
95
+ · · · − 254u − 29i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−0.681430u
95
− 0.00413165u
94
+ ··· + 99.7765u + 14.5760
−0.470644u
95
− 0.131696u
94
+ ··· + 59.7808u + 8.88743
a
2
=
−1.65395u
95
+ 0.429407u
94
+ ··· + 386.874u + 50.3558
1.07387u
95
− 0.384746u
94
+ ··· − 206.119u − 26.2557
a
1
=
−0.580085u
95
+ 0.0446613u
94
+ ··· + 180.755u + 24.1002
1.07387u
95
− 0.384746u
94
+ ··· − 206.119u − 26.2557
a
11
=
−0.454721u
95
+ 0.151308u
94
+ ··· + 126.982u + 19.7118
−0.351241u
95
+ 0.320756u
94
+ ··· + 93.4406u + 11.4080
a
6
=
0.308554u
95
+ 0.0963542u
94
+ ··· + 42.1533u + 2.60418
−1.17149u
95
− 0.204140u
94
+ ··· + 153.030u + 21.0519
a
12
=
−0.888517u
95
+ 0.0913258u
94
+ ··· + 249.933u + 33.1094
1.29641u
95
− 0.491042u
94
+ ··· − 246.556u − 30.8209
a
8
=
0.922646u
95
− 0.276868u
94
+ ··· − 54.9860u − 3.07145
0.00159182u
95
− 0.299162u
94
+ ··· − 85.6322u − 10.7903
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.21551u
95
+ 2.24153u
94
+ ··· + 978.183u + 121.935
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
96
+ 30u
95
+ ··· + 140u + 16
c
2
, c
6
u
96
+ 4u
95
+ ··· − 14u + 4
c
3
, c
4
, c
9
u
96
− u
95
+ ··· + 254u − 29
c
5
u
96
+ u
95
+ ··· − 128495u − 83681
c
8
, c
11
u
96
− 5u
95
+ ··· + 50782u + 9913
c
10
u
96
− 11u
95
+ ··· + 3726u − 783
c
12
u
96
− 4u
95
+ ··· + 994u − 121
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
96
+ 78y
95
+ ··· − 64624y + 256
c
2
, c
6
y
96
− 30y
95
+ ··· − 140y + 16
c
3
, c
4
, c
9
y
96
− 99y
95
+ ··· + 618y + 841
c
5
y
96
− 43y
95
+ ··· − 297276786777y + 7002509761
c
8
, c
11
y
96
− 67y
95
+ ··· − 2596436838y + 98267569
c
10
y
96
+ 5y
95
+ ··· − 16105230y + 613089
c
12
y
96
+ 14y
95
+ ··· + 401770y + 14641
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.385743 + 0.920287I
a = −0.26339 − 2.22738I
b = 1.018312 + 0.780274I
7.3635 − 13.1198I 0
u = 0.385743 − 0.920287I
a = −0.26339 + 2.22738I
b = 1.018312 − 0.780274I
7.3635 + 13.1198I 0
u = 0.663242 + 0.767263I
a = −0.093897 − 0.238168I
b = 0.979786 − 0.185667I
−0.04698 + 2.47024I 0
u = 0.663242 − 0.767263I
a = −0.093897 + 0.238168I
b = 0.979786 + 0.185667I
−0.04698 − 2.47024I 0
u = −0.354084 + 0.893077I
a = −1.21039 − 1.32767I
b = 0.746214 + 0.886048I
8.21230 + 6.94201I 0
u = −0.354084 − 0.893077I
a = −1.21039 + 1.32767I
b = 0.746214 − 0.886048I
8.21230 − 6.94201I 0
u = 0.135681 + 0.893536I
a = 0.68169 + 1.79557I
b = −0.865194 − 0.590369I
1.68985 − 2.34367I 0
u = 0.135681 − 0.893536I
a = 0.68169 − 1.79557I
b = −0.865194 + 0.590369I
1.68985 + 2.34367I 0
u = 0.471081 + 0.760470I
a = −0.013155 + 1.084280I
b = −1.075187 − 0.289861I
0.38982 − 7.56346I 0
u = 0.471081 − 0.760470I
a = −0.013155 − 1.084280I
b = −1.075187 + 0.289861I
0.38982 + 7.56346I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935682 + 0.714738I
a = 0.04944 − 1.74878I
b = −0.760190 + 0.824141I
6.56134 − 1.43456I 0
u = −0.935682 − 0.714738I
a = 0.04944 + 1.74878I
b = −0.760190 − 0.824141I
6.56134 + 1.43456I 0
u = −0.468471 + 0.659668I
a = 0.40771 + 2.35136I
b = 0.943827 − 0.759298I
2.98434 + 7.28558I 0
u = −0.468471 − 0.659668I
a = 0.40771 − 2.35136I
b = 0.943827 + 0.759298I
2.98434 − 7.28558I 0
u = 0.924493 + 0.776710I
a = 0.657518 − 1.023712I
b = −0.986223 + 0.755241I
5.86427 + 7.35566I 0
u = 0.924493 − 0.776710I
a = 0.657518 + 1.023712I
b = −0.986223 − 0.755241I
5.86427 − 7.35566I 0
u = 0.412450 + 0.664332I
a = −1.38768 + 0.63963I
b = 0.809782 − 0.789448I
3.39395 − 1.44923I 0
u = 0.412450 − 0.664332I
a = −1.38768 − 0.63963I
b = 0.809782 + 0.789448I
3.39395 + 1.44923I 0
u = −0.334080 + 0.660105I
a = 0.066401 + 1.330555I
b = −0.025158 − 0.783113I
3.89051 + 3.95952I 2.70271 − 5.67794I
u = −0.334080 − 0.660105I
a = 0.066401 − 1.330555I
b = −0.025158 + 0.783113I
3.89051 − 3.95952I 2.70271 + 5.67794I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.265687 + 0.164608I
a = −0.305186 + 0.194936I
b = 0.618688 + 0.905355I
4.18322 + 1.97592I 0
u = −1.265687 − 0.164608I
a = −0.305186 − 0.194936I
b = 0.618688 − 0.905355I
4.18322 − 1.97592I 0
u = −1.270790 + 0.120676I
a = −0.100143 − 0.807864I
b = 0.999396 + 0.869415I
3.52668 − 3.66382I 0
u = −1.270790 − 0.120676I
a = −0.100143 + 0.807864I
b = 0.999396 − 0.869415I
3.52668 + 3.66382I 0
u = −0.609687 + 0.366846I
a = 1.58577 + 0.87904I
b = 0.007089 − 0.413591I
2.89097 − 0.23399I 2.30056 − 1.02334I
u = −0.609687 − 0.366846I
a = 1.58577 − 0.87904I
b = 0.007089 + 0.413591I
2.89097 + 0.23399I 2.30056 + 1.02334I
u = 1.29120
a = −1.61139
b = −1.30175
−2.81463 0
u = 1.295518 + 0.112046I
a = 1.12403 − 1.32519I
b = −0.867065 + 0.855609I
3.57768 − 1.08471I 0
u = 1.295518 − 0.112046I
a = 1.12403 + 1.32519I
b = −0.867065 − 0.855609I
3.57768 + 1.08471I 0
u = −1.294278 + 0.128891I
a = 0.27458 − 2.17732I
b = −0.938756 + 0.826704I
3.35105 + 7.33768I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.294278 − 0.128891I
a = 0.27458 + 2.17732I
b = −0.938756 − 0.826704I
3.35105 − 7.33768I 0
u = 1.294428 + 0.156264I
a = 0.096525 − 1.097000I
b = 0.834667 + 0.951948I
4.05073 − 2.99694I 0
u = 1.294428 − 0.156264I
a = 0.096525 + 1.097000I
b = 0.834667 − 0.951948I
4.05073 + 2.99694I 0
u = 1.331300 + 0.160981I
a = 1.30482 − 1.22682I
b = 1.084050 + 0.751190I
2.77719 − 8.10147I 0
u = 1.331300 − 0.160981I
a = 1.30482 + 1.22682I
b = 1.084050 − 0.751190I
2.77719 + 8.10147I 0
u = −0.460716 + 0.424248I
a = −1.31371 − 0.93039I
b = −0.910181 + 0.209562I
−2.75688 + 3.28834I −10.53288 − 7.33652I
u = −0.460716 − 0.424248I
a = −1.31371 + 0.93039I
b = −0.910181 − 0.209562I
−2.75688 − 3.28834I −10.53288 + 7.33652I
u = −1.352914 + 0.252649I
a = −0.120568 + 0.331321I
b = −6 − 0.394137 − 6.10I
−4.97451 + 3.66414I 0
u = −1.352914 − 0.252649I
a = −0.120568 − 0.331321I
b = −6 − 0.394137 + 6.10I
−4.97451 − 3.66414I 0
u = −1.368542 + 0.152756I
a = −0.0128781 − 0.1160252I
b = −0.309216 + 0.563548I
−5.22850 + 3.47859I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.368542 − 0.152756I
a = −0.0128781 + 0.1160252I
b = −0.309216 − 0.563548I
−5.22850 − 3.47859I 0
u = 0.193262 + 0.570422I
a = 1.32752 + 1.93198I
b = −0.784388 − 0.291616I
1.13940 − 2.20728I −0.01228 + 7.32813I
u = 0.193262 − 0.570422I
a = 1.32752 − 1.93198I
b = −0.784388 + 0.291616I
1.13940 + 2.20728I −0.01228 − 7.32813I
u = 1.381065 + 0.233970I
a = −0.576924 + 0.538644I
b = 0.559104 − 0.738166I
−2.50654 − 1.42565I 0
u = 1.381065 − 0.233970I
a = −0.576924 − 0.538644I
b = 0.559104 + 0.738166I
−2.50654 + 1.42565I 0
u = −1.395635 + 0.184655I
a = 0.127249 + 1.274073I
b = 0.723765 − 0.418716I
−3.90744 + 4.87063I 0
u = −1.395635 − 0.184655I
a = 0.127249 − 1.274073I
b = 0.723765 + 0.418716I
−3.90744 − 4.87063I 0
u = 1.409053 + 0.067170I
a = −1.28444 − 0.74008I
b = −1.025047 + 0.466204I
−7.26522 + 0.62596I 0
u = 1.409053 − 0.067170I
a = −1.28444 + 0.74008I
b = −1.025047 − 0.466204I
−7.26522 − 0.62596I 0
u = 1.411271 + 0.017367I
a = −0.206449 + 0.766721I
b = 0.419657 − 0.629449I
−3.05064 − 0.91419I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.411271 − 0.017367I
a = −0.206449 − 0.766721I
b = 0.419657 + 0.629449I
−3.05064 + 0.91419I 0
u = −1.37464 + 0.44446I
a = −0.914447 − 0.786391I
b = 0.823552 + 0.765190I
−1.32824 + 2.49262I 0
u = −1.37464 − 0.44446I
a = −0.914447 + 0.786391I
b = 0.823552 − 0.765190I
−1.32824 − 2.49262I 0
u = −1.43821 + 0.17375I
a = −0.726188 + 0.114938I
b = −1.239035 − 0.341309I
−5.83118 + 2.77682I 0
u = −1.43821 − 0.17375I
a = −0.726188 − 0.114938I
b = −1.239035 + 0.341309I
−5.83118 − 2.77682I 0
u = 1.43393 + 0.24614I
a = −0.332589 + 0.576994I
b = −0.041356 − 0.913366I
−1.78579 − 7.25616I 0
u = 1.43393 − 0.24614I
a = −0.332589 − 0.576994I
b = −0.041356 + 0.913366I
−1.78579 + 7.25616I 0
u = 0.366601 + 0.388801I
a = −0.438408 + 0.713928I
b = 1.123777 − 0.216649I
−0.005958 − 0.537835I −2.51261 + 8.87589I
u = 0.366601 − 0.388801I
a = −0.438408 − 0.713928I
b = 1.123777 + 0.216649I
−0.005958 + 0.537835I −2.51261 − 8.87589I
u = −0.003669 + 0.531412I
a = 1.52604 − 1.37366I
b = −0.751294 + 0.914167I
8.07625 + 0.55686I 5.81445 − 0.47058I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003669 − 0.531412I
a = 1.52604 + 1.37366I
b = −0.751294 − 0.914167I
8.07625 − 0.55686I 5.81445 + 0.47058I
u = 1.46464 + 0.16428I
a = 1.64834 − 0.63689I
b = 1.016207 + 0.168687I
−8.98408 − 5.52910I 0
u = 1.46464 − 0.16428I
a = 1.64834 + 0.63689I
b = 1.016207 − 0.168687I
−8.98408 + 5.52910I 0
u = −1.45673 + 0.24384I
a = 0.662498 − 0.031069I
b = −0.756340 − 0.799979I
−2.60853 + 4.75653I 0
u = −1.45673 − 0.24384I
a = 0.662498 + 0.031069I
b = −0.756340 + 0.799979I
−2.60853 − 4.75653I 0
u = 0.242107 + 0.457342I
a = 0.346810 − 0.285860I
b = 0.029135 + 0.383175I
−0.180616 − 1.192610I −2.62815 + 5.38719I
u = 0.242107 − 0.457342I
a = 0.346810 + 0.285860I
b = 0.029135 − 0.383175I
−0.180616 + 1.192610I −2.62815 − 5.38719I
u = 1.41615 + 0.44982I
a = 0.37692 − 2.00054I
b = 0.926604 + 0.743757I
−1.64583 − 8.20716I 0
u = 1.41615 − 0.44982I
a = 0.37692 + 2.00054I
b = 0.926604 − 0.743757I
−1.64583 + 8.20716I 0
u = 1.47921 + 0.24044I
a = −1.18070 + 1.68873I
b = −0.980661 − 0.745233I
−3.29263 − 10.57900I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47921 − 0.24044I
a = −1.18070 − 1.68873I
b = −0.980661 + 0.745233I
−3.29263 + 10.57900I 0
u = −1.47057 + 0.30015I
a = 0.63167 + 1.55832I
b = 1.032637 − 0.650837I
−3.88087 + 6.72339I 0
u = −1.47057 − 0.30015I
a = 0.63167 − 1.55832I
b = 1.032637 + 0.650837I
−3.88087 − 6.72339I 0
u = 1.46946 + 0.34201I
a = 0.833509 − 0.383063I
b = −0.723681 + 0.925712I
2.37021 − 11.38420I 0
u = 1.46946 − 0.34201I
a = 0.833509 + 0.383063I
b = −0.723681 − 0.925712I
2.37021 + 11.38420I 0
u = −0.037275 + 0.487405I
a = −3.41330 − 1.79895I
b = 0.925692 + 0.789261I
7.25080 − 5.19343I 5.91357 + 5.53961I
u = −0.037275 − 0.487405I
a = −3.41330 + 1.79895I
b = 0.925692 − 0.789261I
7.25080 + 5.19343I 5.91357 − 5.53961I
u = −0.067495 + 0.481964I
a = 0.27248 − 2.68237I
b = −1.028324 + 0.803320I
7.21452 + 5.77752I 4.21585 − 6.14634I
u = −0.067495 − 0.481964I
a = 0.27248 + 2.68237I
b = −1.028324 − 0.803320I
7.21452 − 5.77752I 4.21585 + 6.14634I
u = 1.47665 + 0.33190I
a = −1.11324 + 0.88392I
b = −0.860610 − 0.096616I
−6.57609 − 4.45340I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47665 − 0.33190I
a = −1.11324 − 0.88392I
b = −0.860610 + 0.096616I
−6.57609 + 4.45340I 0
u = −1.49158 + 0.27180I
a = 0.963012 + 0.994212I
b = 1.166353 − 0.296461I
−5.94258 + 11.30370I 0
u = −1.49158 − 0.27180I
a = 0.963012 − 0.994212I
b = 1.166353 + 0.296461I
−5.94258 − 11.30370I 0
u = −1.52409 + 0.10872I
a = −1.003222 − 0.242752I
b = −1.076996 + 0.004087I
−7.97132 + 0.35100I 0
u = −1.52409 − 0.10872I
a = −1.003222 + 0.242752I
b = −1.076996 − 0.004087I
−7.97132 − 0.35100I 0
u = −1.48800 + 0.35029I
a = −0.76078 − 1.82949I
b = −1.046910 + 0.786981I
1.3548 + 17.6950I 0
u = −1.48800 − 0.35029I
a = −0.76078 + 1.82949I
b = −1.046910 − 0.786981I
1.3548 − 17.6950I 0
u = 1.53649 + 0.18899I
a = 0.307601 + 0.690125I
b = 0.842267 − 0.634755I
−3.81769 − 0.61012I 0
u = 1.53649 − 0.18899I
a = 0.307601 − 0.690125I
b = 0.842267 + 0.634755I
−3.81769 + 0.61012I 0
u = −1.55102 + 0.07225I
a = 0.550455 + 0.954771I
b = 0.955630 − 0.640179I
−4.21474 + 5.49448I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55102 − 0.07225I
a = 0.550455 − 0.954771I
b = 0.955630 + 0.640179I
−4.21474 − 5.49448I 0
u = 0.048709 + 0.427693I
a = −0.64547 − 5.01194I
b = 0.851952 + 0.811537I
7.48000 − 0.80563I 7.00203 + 0.00027I
u = 0.048709 − 0.427693I
a = −0.64547 + 5.01194I
b = 0.851952 − 0.811537I
7.48000 + 0.80563I 7.00203 − 0.00027I
u = −0.280585
a = 8.03312
b = −0.424011
2.75406 10.2700
u = −0.234009 + 0.143150I
a = 2.34923 − 1.26936I
b = 0.870682 + 0.397620I
−1.89063 − 1.44912I −11.79295 + 4.30313I
u = −0.234009 − 0.143150I
a = 2.34923 + 1.26936I
b = 0.870682 − 0.397620I
−1.89063 + 1.44912I −11.79295 − 4.30313I
14
II. I
u
2
=
h6u
22
−63u
20
+· · ·+b−7, −5u
22
+8u
21
+· · ·+a+1, u
24
−12u
22
+· · ·−2u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
5u
22
− 8u
21
+ ··· − 17u − 1
−6u
22
+ 63u
20
+ ··· − 12u + 7
a
2
=
−3u
23
+ 33u
21
+ ··· + 12u + 2
u
23
− 11u
21
+ ··· − 4u − 1
a
1
=
−2u
23
+ 22u
21
+ ··· + 8u + 1
u
23
− 11u
21
+ ··· − 4u − 1
a
11
=
6u
23
− u
22
+ ··· − 10u + 1
−4u
23
+ 2u
22
+ ··· + 4u − 1
a
6
=
−u
23
+ 5u
22
+ ··· + 9u
2
+ 1
5u
23
− 6u
22
+ ··· − 17u + 6
a
12
=
−2u
23
+ 23u
21
+ ··· + 12u + 2
u
23
− 11u
21
+ ··· − 3u − 1
a
8
=
−2u
21
+ 21u
19
+ ··· − 12u − 2
4u
23
− u
22
+ ··· − 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −29u
23
+ 5u
22
+ 318u
21
−90u
20
−1450u
19
+ 599u
18
+ 3346u
17
−
2009u
16
− 3368u
15
+ 3585u
14
− 1230u
13
− 2820u
12
+ 6649u
11
− 769u
10
− 6023u
9
+
3223u
8
+ 1245u
7
− 2244u
6
+ 1017u
5
+ 536u
4
− 588u
3
− 6u
2
+ 101u − 16
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 10u
23
+ ··· − 17u + 1
c
2
u
24
− 5u
22
+ ··· + u + 1
c
3
, c
4
u
24
− 12u
22
+ ··· − 2u + 1
c
5
u
24
+ 2u
22
+ ··· + u + 1
c
6
u
24
− 5u
22
+ ··· − u + 1
c
7
u
24
+ 10u
23
+ ··· + 17u + 1
c
8
u
24
− 4u
23
+ ··· − 10u
2
+ 1
c
9
u
24
− 12u
22
+ ··· + 2u + 1
c
10
u
24
− 2u
22
+ ··· − 2u + 1
c
11
u
24
+ 4u
23
+ ··· − 10u
2
+ 1
c
12
u
24
+ u
23
+ ··· + 2u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
24
+ 18y
23
+ ··· − 21y + 1
c
2
, c
6
y
24
− 10y
23
+ ··· − 17y + 1
c
3
, c
4
, c
9
y
24
− 24y
23
+ ··· − 24y + 1
c
5
y
24
+ 4y
23
+ ··· − 3y + 1
c
8
, c
11
y
24
− 24y
23
+ ··· − 20y + 1
c
10
y
24
− 4y
23
+ ··· − 28y + 1
c
12
y
24
− 3y
23
+ ··· + 4y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069435 + 1.036046I
a = 0.66638 + 1.80021I
b = −0.860609 − 0.627483I
1.15922 − 2.45672I −11.76507 + 4.05548I
u = 0.069435 − 1.036046I
a = 0.66638 − 1.80021I
b = −0.860609 + 0.627483I
1.15922 + 2.45672I −11.76507 − 4.05548I
u = −1.26306
a = 2.58666
b = −0.487477
−0.321029 3.90020
u = −1.269120 + 0.063695I
a = −1.094285 − 0.360186I
b = 0.813850 + 0.867940I
3.72041 − 0.09960I −1.49510 + 1.82581I
u = −1.269120 − 0.063695I
a = −1.094285 + 0.360186I
b = 0.813850 − 0.867940I
3.72041 + 0.09960I −1.49510 − 1.82581I
u = 1.276910 + 0.085066I
a = 0.59170 − 1.89272I
b = 0.981897 + 0.822707I
3.20923 − 6.17817I −2.91423 + 3.11588I
u = 1.276910 − 0.085066I
a = 0.59170 + 1.89272I
b = 0.981897 − 0.822707I
3.20923 + 6.17817I −2.91423 − 3.11588I
u = 0.175388 + 0.682644I
a = 0.0032504 + 0.1060193I
b = 0.815552 − 0.258376I
−0.861346 + 1.121530I −4.71985 − 4.56886I
u = 0.175388 − 0.682644I
a = 0.0032504 − 0.1060193I
b = 0.815552 + 0.258376I
−0.861346 − 1.121530I −4.71985 + 4.56886I
u = 1.32213
a = −1.90954
b = −1.19053
−3.32254 −13.3090
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.359653 + 0.243941I
a = −0.214460 + 0.497603I
b = −0.619154 − 0.305928I
−4.95628 − 4.46849I −8.98806 + 8.25419I
u = 1.359653 − 0.243941I
a = −0.214460 − 0.497603I
b = −0.619154 + 0.305928I
−4.95628 + 4.46849I −8.98806 − 8.25419I
u = 0.549549 + 0.222442I
a = 1.280952 − 0.200355I
b = −0.960666 + 0.781636I
6.01195 + 5.07639I −2.15298 − 3.37252I
u = 0.549549 − 0.222442I
a = 1.280952 + 0.200355I
b = −0.960666 − 0.781636I
6.01195 − 5.07639I −2.15298 + 3.37252I
u = −0.557552 + 0.168075I
a = −1.11190 − 2.42975I
b = −0.816870 + 0.818962I
6.45585 + 0.92731I −1.82788 − 1.97146I
u = −0.557552 − 0.168075I
a = −1.11190 + 2.42975I
b = −0.816870 − 0.818962I
6.45585 − 0.92731I −1.82788 + 1.97146I
u = −1.45171 + 0.18695I
a = −0.907638 + 0.094328I
b = −1.044657 − 0.280230I
−6.58300 + 1.87441I −9.74769 + 0.34982I
u = −1.45171 − 0.18695I
a = −0.907638 − 0.094328I
b = −1.044657 + 0.280230I
−6.58300 − 1.87441I −9.74769 − 0.34982I
u = 1.42146 + 0.35631I
a = −0.581803 + 0.538929I
b = 0.732013 − 0.646391I
−3.46309 − 2.54519I −7.17375 + 1.89556I
u = 1.42146 − 0.35631I
a = −0.581803 − 0.538929I
b = 0.732013 + 0.646391I
−3.46309 + 2.54519I −7.17375 − 1.89556I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533598
a = 4.89543
b = 0.561007
2.43421 −16.1970
u = −1.49694 + 0.35016I
a = 0.65568 + 1.58456I
b = 0.974519 − 0.627765I
−4.23792 + 7.53826I −7.73528 − 9.46189I
u = −1.49694 − 0.35016I
a = 0.65568 − 1.58456I
b = 0.974519 + 0.627765I
−4.23792 − 7.53826I −7.73528 + 9.46189I
u = 0.320367
a = −2.14829
b = 1.08525
0.299325 3.64630
20
III. I
u
3
= h−u
10
+ 2u
8
+ · · · + b − 1, u
13
− 2u
11
− u
9
+ 2u
7
+ 2u
5
+ a −
u, u
15
− 3u
13
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−u
13
+ 2u
11
+ u
9
− 2u
7
− 2u
5
+ u
u
10
− 2u
8
− u
6
+ u
5
+ 2u
4
− u
3
+ u
2
− u + 1
a
2
=
−u
5
+ 2u
3
+ u
u
5
− u
3
− u
a
1
=
u
3
u
5
− u
3
− u
a
11
=
u
5
− u
u
7
− u
5
− 2u
3
+ u
a
6
=
u
8
− u
6
− u
4
+ 1
u
10
− 2u
8
− u
6
+ 2u
4
+ u
2
a
12
=
u
u
3
− u
a
8
=
−u
3
−u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
10
+ 8u
8
+ 4u
6
− 4u
5
− 8u
4
+ 4u
3
− 4u
2
+ 4u − 10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
+ u
2
+ 2u + 1)
5
c
2
, c
6
(u
3
− u
2
+ 1)
5
c
3
, c
4
, c
9
c
12
u
15
− 3u
13
− u
10
+ 5u
9
+ 2u
8
+ u
6
− u
5
− 2u
4
− 3u
3
− u
2
− 2u − 1
c
5
u
15
+ 3u
13
+ ··· − 6u − 5
c
8
, c
11
u
15
+ 6u
14
+ ··· + 2u + 1
c
10
u
15
− 6u
14
+ ··· + 2u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
+ 3y
2
+ 2y −1)
5
c
2
, c
6
(y
3
− y
2
+ 2y −1)
5
c
3
, c
4
, c
9
c
12
y
15
− 6y
14
+ ··· + 2y −1
c
5
y
15
+ 6y
14
+ ··· + 386y −25
c
8
, c
10
, c
11
y
15
− 18y
14
+ ··· + 18y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.026418 + 1.041933I
a = 0.90685 − 2.00655I
b = −0.877439 + 0.744862I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.026418 − 1.041933I
a = 0.90685 + 2.00655I
b = −0.877439 − 0.744862I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.157973 + 0.852017I
a = 0.119316 + 0.734848I
b = 0.754878
−1.11345 −9.01951 + 0.I
u = −0.157973 − 0.852017I
a = 0.119316 − 0.734848I
b = 0.754878
−1.11345 −9.01951 + 0.I
u = −0.481476 + 0.711290I
a = 0.700991 + 1.048286I
b = −0.877439 − 0.744862I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.481476 − 0.711290I
a = 0.700991 − 1.048286I
b = −0.877439 + 0.744862I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.543595 + 0.631377I
a = 0.06407 + 1.78637I
b = −0.877439 − 0.744862I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.543595 − 0.631377I
a = 0.06407 − 1.78637I
b = −0.877439 + 0.744862I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 1.17217
a = −1.56369
b = 0.754878
−1.11345 −9.01950
u = 1.306364 + 0.163068I
a = 1.155741 + 0.437932I
b = −0.877439 + 0.744862I
3.02413 + 2.82812I −2.49024 − 2.97945I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.306364 − 0.163068I
a = 1.155741 − 0.437932I
b = −0.877439 − 0.744862I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −1.33954
a = 3.75398
b = 0.754878
−1.11345 −9.01950
u = −1.342065 + 0.137666I
a = −1.75226 − 2.13243I
b = −0.877439 + 0.744862I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −1.342065 − 0.137666I
a = −1.75226 + 2.13243I
b = −0.877439 − 0.744862I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.483314
a = 0.420282
b = 0.754878
−1.11345 −9.01950
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
5
)(u
24
− 10u
23
+ ··· − 17u + 1)
· (u
96
+ 30u
95
+ ··· + 140u + 16)
c
2
((u
3
− u
2
+ 1)
5
)(u
24
− 5u
22
+ ··· + u + 1)(u
96
+ 4u
95
+ ··· − 14u + 4)
c
3
, c
4
(u
15
− 3u
13
− u
10
+ 5u
9
+ 2u
8
+ u
6
− u
5
− 2u
4
− 3u
3
− u
2
− 2u − 1)
· (u
24
− 12u
22
+ ··· − 2u + 1)(u
96
− u
95
+ ··· + 254u − 29)
c
5
(u
15
+ 3u
13
+ ··· − 6u − 5)(u
24
+ 2u
22
+ ··· + u + 1)
· (u
96
+ u
95
+ ··· − 128495u − 83681)
c
6
((u
3
− u
2
+ 1)
5
)(u
24
− 5u
22
+ ··· − u + 1)(u
96
+ 4u
95
+ ··· − 14u + 4)
c
7
((u
3
+ u
2
+ 2u + 1)
5
)(u
24
+ 10u
23
+ ··· + 17u + 1)
· (u
96
+ 30u
95
+ ··· + 140u + 16)
c
8
(u
15
+ 6u
14
+ ··· + 2u + 1)(u
24
− 4u
23
+ ··· − 10u
2
+ 1)
· (u
96
− 5u
95
+ ··· + 50782u + 9913)
c
9
(u
15
− 3u
13
− u
10
+ 5u
9
+ 2u
8
+ u
6
− u
5
− 2u
4
− 3u
3
− u
2
− 2u − 1)
· (u
24
− 12u
22
+ ··· + 2u + 1)(u
96
− u
95
+ ··· + 254u − 29)
c
10
(u
15
− 6u
14
+ ··· + 2u − 1)(u
24
− 2u
22
+ ··· − 2u + 1)
· (u
96
− 11u
95
+ ··· + 3726u − 783)
c
11
(u
15
+ 6u
14
+ ··· + 2u + 1)(u
24
+ 4u
23
+ ··· − 10u
2
+ 1)
· (u
96
− 5u
95
+ ··· + 50782u + 9913)
c
12
(u
15
− 3u
13
− u
10
+ 5u
9
+ 2u
8
+ u
6
− u
5
− 2u
4
− 3u
3
− u
2
− 2u − 1)
· (u
24
+ u
23
+ ··· + 2u
2
+ 1)(u
96
− 4u
95
+ ··· + 994u − 121)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
3
+ 3y
2
+ 2y −1)
5
)(y
24
+ 18y
23
+ ··· − 21y + 1)
· (y
96
+ 78y
95
+ ··· − 64624y + 256)
c
2
, c
6
((y
3
− y
2
+ 2y −1)
5
)(y
24
− 10y
23
+ ··· − 17y + 1)
· (y
96
− 30y
95
+ ··· − 140y + 16)
c
3
, c
4
, c
9
(y
15
− 6y
14
+ ··· + 2y −1)(y
24
− 24y
23
+ ··· − 24y + 1)
· (y
96
− 99y
95
+ ··· + 618y + 841)
c
5
(y
15
+ 6y
14
+ ··· + 386y −25)(y
24
+ 4y
23
+ ··· − 3y + 1)
· (y
96
− 43y
95
+ ··· − 297276786777y + 7002509761)
c
8
, c
11
(y
15
− 18y
14
+ ··· + 18y −1)(y
24
− 24y
23
+ ··· − 20y + 1)
· (y
96
− 67y
95
+ ··· − 2596436838y + 98267569)
c
10
(y
15
− 18y
14
+ ··· + 18y −1)(y
24
− 4y
23
+ ··· − 28y + 1)
· (y
96
+ 5y
95
+ ··· − 16105230y + 613089)
c
12
(y
15
− 6y
14
+ ··· + 2y −1)(y
24
− 3y
23
+ ··· + 4y + 1)
· (y
96
+ 14y
95
+ ··· + 401770y + 14641)
27
