12a
0138
(K12a
0138
)
A knot diagram
1
Linearized knot diagam
3 5 8 9 2 10 11 1 12 7 6 4
Solving Sequence
6,10
7 11 8
2,12
5 3 1 9 4
c
6
c
10
c
7
c
11
c
5
c
2
c
1
c
9
c
4
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.19471 × 10
73
u
112
− 1.22414 × 10
74
u
111
+ ··· + 1.80916 × 10
73
b + 6.97020 × 10
73
,
− 1.81957 × 10
74
u
112
+ 3.28712 × 10
74
u
111
+ ··· + 1.80916 × 10
73
a − 1.87404 × 10
74
,
u
113
− 3u
112
+ ··· − 2u − 1i
I
u
2
= hb + a + 1, a
2
+ 3a + 3, u − 1i
* 2 irreducible components of dim
C
= 0, with total 115 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
= h7.19 × 10
73
u
112
− 1.22 × 10
74
u
111
+ · · · + 1.81 × 10
73
b + 6.97 ×
10
73
, −1.82 × 10
74
u
112
+ 3.29 × 10
74
u
111
+ · · · + 1.81 × 10
73
a − 1.87 ×
10
74
, u
113
− 3u
112
+ · · · − 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
10.0575u
112
− 18.1693u
111
+ ··· + 29.5396u + 10.3586
−3.97683u
112
+ 6.76633u
111
+ ··· − 13.0851u − 3.85273
a
12
=
u
3
− 2u
−u
3
+ u
a
5
=
21.7820u
112
− 39.2061u
111
+ ··· + 48.7260u + 19.4581
−3.21144u
112
+ 5.39167u
111
+ ··· − 11.0344u − 4.09903
a
3
=
18.8353u
112
− 34.2427u
111
+ ··· + 38.5483u + 15.7723
−3.75718u
112
+ 6.19544u
111
+ ··· − 11.7379u − 4.57583
a
1
=
−2.58530u
112
+ 4.46215u
111
+ ··· − 2.91973u − 2.46253
0.126934u
112
− 0.107623u
111
+ ··· − 0.558030u − 0.562200
a
9
=
−u
7
+ 4u
5
− 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
4
=
15.1071u
112
− 28.0166u
111
+ ··· + 31.2262u + 13.6875
6.59937u
112
− 12.6329u
111
+ ··· + 16.3813u + 4.92547
(ii) Obstruction class = −1
(iii) Cusp Shapes = −21.9603u
112
+ 39.6262u
111
+ ··· − 14.3575u − 5.90643
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
113
+ 48u
112
+ ··· + 55u − 1
c
2
, c
5
u
113
+ 2u
112
+ ··· − 5u − 1
c
3
u
113
+ 60u
111
+ ··· − 47u + 1
c
4
u
113
+ 2u
112
+ ··· + 1009u + 347
c
6
, c
7
, c
10
u
113
+ 3u
112
+ ··· − 2u + 1
c
8
u
113
+ 7u
112
+ ··· + u
2
+ 1
c
9
u
113
+ 23u
112
+ ··· + 6255814u + 309047
c
11
u
113
− 3u
112
+ ··· + 1280u − 1088
c
12
u
113
+ 11u
112
+ ··· + 12u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
113
+ 36y
112
+ ··· + 3831y −1
c
2
, c
5
y
113
+ 48y
112
+ ··· + 55y −1
c
3
y
113
+ 120y
112
+ ··· + 463y −1
c
4
y
113
+ 128y
112
+ ··· − 8247513y −120409
c
6
, c
7
, c
10
y
113
− 103y
112
+ ··· − 2y −1
c
8
y
113
+ 9y
112
+ ··· − 2y −1
c
9
y
113
+ 53y
112
+ ··· − 1833344062454y −95510048209
c
11
y
113
− 17y
112
+ ··· + 72743552y −1183744
c
12
y
113
+ 15y
112
+ ··· − 280y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939909 + 0.317543I
a = 1.46055 − 0.18139I
b = −0.368917 + 0.830267I
−2.13808 − 1.37165I 0
u = 0.939909 − 0.317543I
a = 1.46055 + 0.18139I
b = −0.368917 − 0.830267I
−2.13808 + 1.37165I 0
u = 0.752167 + 0.473634I
a = 0.826598 + 0.274339I
b = −0.455174 − 0.969053I
−2.81213 + 1.98997I 0
u = 0.752167 − 0.473634I
a = 0.826598 − 0.274339I
b = −0.455174 + 0.969053I
−2.81213 − 1.98997I 0
u = −1.118790 + 0.027576I
a = −0.980417 − 0.453269I
b = 0.925019 + 0.474762I
0.74089 + 1.69233I 0
u = −1.118790 − 0.027576I
a = −0.980417 + 0.453269I
b = 0.925019 − 0.474762I
0.74089 − 1.69233I 0
u = 0.579977 + 0.611709I
a = 1.344920 + 0.261692I
b = −0.423750 + 0.967531I
−2.99500 − 3.68548I 0
u = 0.579977 − 0.611709I
a = 1.344920 − 0.261692I
b = −0.423750 − 0.967531I
−2.99500 + 3.68548I 0
u = 1.15862
a = 0.574458
b = 0.129833
−1.97009 0
u = 0.323055 + 0.768075I
a = 2.28499 − 0.15615I
b = −0.514948 + 0.996717I
−1.39021 − 6.40201I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323055 − 0.768075I
a = 2.28499 + 0.15615I
b = −0.514948 − 0.996717I
−1.39021 + 6.40201I 0
u = −1.167310 + 0.082409I
a = −1.61291 − 0.08377I
b = 0.732275 + 1.080280I
−1.03203 + 4.35287I 0
u = −1.167310 − 0.082409I
a = −1.61291 + 0.08377I
b = 0.732275 − 1.080280I
−1.03203 − 4.35287I 0
u = 0.440456 + 0.694712I
a = 0.138212 + 0.304488I
b = −0.351572 − 0.923192I
−2.54432 − 0.78650I 0
u = 0.440456 − 0.694712I
a = 0.138212 − 0.304488I
b = −0.351572 + 0.923192I
−2.54432 + 0.78650I 0
u = −1.150760 + 0.263291I
a = 0.884861 − 0.795944I
b = −0.806370 + 0.549939I
1.48117 + 5.52965I 0
u = −1.150760 − 0.263291I
a = 0.884861 + 0.795944I
b = −0.806370 − 0.549939I
1.48117 − 5.52965I 0
u = −0.649038 + 0.499158I
a = 0.799156 − 0.174595I
b = −0.645108 + 1.123390I
−1.72359 − 10.60720I 0
u = −0.649038 − 0.499158I
a = 0.799156 + 0.174595I
b = −0.645108 − 1.123390I
−1.72359 + 10.60720I 0
u = −0.341872 + 0.735602I
a = 2.63336 − 0.13250I
b = −0.663628 − 1.137570I
−0.6241 + 14.8733I 0. − 10.48364I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.341872 − 0.735602I
a = 2.63336 + 0.13250I
b = −0.663628 + 1.137570I
−0.6241 − 14.8733I 0. + 10.48364I
u = 1.191890 + 0.019067I
a = −4.44997 + 2.27032I
b = 0.534866 − 0.855939I
−2.14131 − 2.15135I 0
u = 1.191890 − 0.019067I
a = −4.44997 − 2.27032I
b = 0.534866 + 0.855939I
−2.14131 + 2.15135I 0
u = −0.325971 + 0.717414I
a = 1.00912 − 1.43916I
b = −0.916275 + 0.452303I
1.46474 + 9.07915I 0. − 7.02875I
u = −0.325971 − 0.717414I
a = 1.00912 + 1.43916I
b = −0.916275 − 0.452303I
1.46474 − 9.07915I 0. + 7.02875I
u = −1.182760 + 0.306456I
a = 1.92843 − 0.18354I
b = −0.652135 − 1.054830I
−0.04028 + 10.99740I 0
u = −1.182760 − 0.306456I
a = 1.92843 + 0.18354I
b = −0.652135 + 1.054830I
−0.04028 − 10.99740I 0
u = −0.627370 + 0.450096I
a = 1.102860 − 0.068589I
b = −0.866470 − 0.442386I
0.32647 − 5.01240I −2.00000 + 1.72974I
u = −0.627370 − 0.450096I
a = 1.102860 + 0.068589I
b = −0.866470 + 0.442386I
0.32647 + 5.01240I −2.00000 − 1.72974I
u = −0.011515 + 0.764522I
a = 1.78598 − 1.34153I
b = −0.631765 + 1.016450I
3.55207 − 7.10523I 1.72920 + 7.58809I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.011515 − 0.764522I
a = 1.78598 + 1.34153I
b = −0.631765 − 1.016450I
3.55207 + 7.10523I 1.72920 − 7.58809I
u = −0.357793 + 0.666831I
a = −1.078110 − 0.253263I
b = −0.030920 + 1.288310I
−4.91041 + 6.36723I −6.53571 − 8.04968I
u = −0.357793 − 0.666831I
a = −1.078110 + 0.253263I
b = −0.030920 − 1.288310I
−4.91041 − 6.36723I −6.53571 + 8.04968I
u = 1.208510 + 0.330567I
a = 0.440418 + 0.637304I
b = −0.601288 − 0.975849I
−0.20340 + 3.14702I 0
u = 1.208510 − 0.330567I
a = 0.440418 − 0.637304I
b = −0.601288 + 0.975849I
−0.20340 − 3.14702I 0
u = 0.255939 + 0.693140I
a = 0.783379 + 1.097760I
b = −0.343556 − 0.527140I
−0.04039 − 2.38375I −1.98371 + 5.90852I
u = 0.255939 − 0.693140I
a = 0.783379 − 1.097760I
b = −0.343556 + 0.527140I
−0.04039 + 2.38375I −1.98371 − 5.90852I
u = −0.051929 + 0.725337I
a = 2.13698 + 0.72891I
b = −0.735643 − 0.596633I
4.81430 − 1.88544I 4.72473 + 1.60361I
u = −0.051929 − 0.725337I
a = 2.13698 − 0.72891I
b = −0.735643 + 0.596633I
4.81430 + 1.88544I 4.72473 − 1.60361I
u = −1.269840 + 0.138595I
a = −0.220884 + 0.428106I
b = 0.189644 + 1.136810I
−4.83804 + 4.63939I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.269840 − 0.138595I
a = −0.220884 − 0.428106I
b = 0.189644 − 1.136810I
−4.83804 − 4.63939I 0
u = −0.514108 + 0.503712I
a = 1.036330 − 0.361962I
b = −0.073302 − 1.239800I
−5.57728 − 2.46347I −8.69302 + 1.29328I
u = −0.514108 − 0.503712I
a = 1.036330 + 0.361962I
b = −0.073302 + 1.239800I
−5.57728 + 2.46347I −8.69302 − 1.29328I
u = 1.257620 + 0.290271I
a = 1.63911 + 0.39912I
b = −0.669510 + 0.656393I
0.76639 − 1.79202I 0
u = 1.257620 − 0.290271I
a = 1.63911 − 0.39912I
b = −0.669510 − 0.656393I
0.76639 + 1.79202I 0
u = −0.300733 + 0.634297I
a = −2.69044 + 0.24594I
b = 0.652286 + 1.200950I
0.19992 + 6.60671I 0.07217 − 12.10916I
u = −0.300733 − 0.634297I
a = −2.69044 − 0.24594I
b = 0.652286 − 1.200950I
0.19992 − 6.60671I 0.07217 + 12.10916I
u = 1.297840 + 0.027388I
a = 1.04790 − 1.63196I
b = 0.286338 − 0.747497I
−3.22613 − 1.48459I 0
u = 1.297840 − 0.027388I
a = 1.04790 + 1.63196I
b = 0.286338 + 0.747497I
−3.22613 + 1.48459I 0
u = 0.234136 + 0.628805I
a = 0.318271 + 0.979558I
b = 0.027002 − 0.471357I
−0.07346 − 2.33823I −3.38006 + 5.78977I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234136 − 0.628805I
a = 0.318271 − 0.979558I
b = 0.027002 + 0.471357I
−0.07346 + 2.33823I −3.38006 − 5.78977I
u = −0.253157 + 0.618984I
a = −2.34577 + 0.07324I
b = 0.933553 + 0.670622I
2.57361 + 4.20982I 6.47955 − 9.14983I
u = −0.253157 − 0.618984I
a = −2.34577 − 0.07324I
b = 0.933553 − 0.670622I
2.57361 − 4.20982I 6.47955 + 9.14983I
u = 0.310571 + 0.587049I
a = −4.65059 − 1.98552I
b = 0.509350 − 0.916675I
−0.38515 − 3.92427I 1.8807 − 17.6364I
u = 0.310571 − 0.587049I
a = −4.65059 + 1.98552I
b = 0.509350 + 0.916675I
−0.38515 + 3.92427I 1.8807 + 17.6364I
u = −0.215249 + 0.601538I
a = −1.05368 + 1.43755I
b = 0.901782 − 0.257745I
2.97908 + 0.86642I 8.54734 − 2.47415I
u = −0.215249 − 0.601538I
a = −1.05368 − 1.43755I
b = 0.901782 + 0.257745I
2.97908 − 0.86642I 8.54734 + 2.47415I
u = 0.258441 + 0.568603I
a = −0.24006 − 3.99969I
b = 0.492878 + 0.781115I
0.063611 + 0.181588I −10.94547 − 7.12456I
u = 0.258441 − 0.568603I
a = −0.24006 + 3.99969I
b = 0.492878 − 0.781115I
0.063611 − 0.181588I −10.94547 + 7.12456I
u = 0.449623 + 0.413218I
a = 0.972889 − 0.131299I
b = −0.283957 + 0.017994I
−1.09683 − 0.93427I −5.40273 + 3.78636I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.449623 − 0.413218I
a = 0.972889 + 0.131299I
b = −0.283957 − 0.017994I
−1.09683 + 0.93427I −5.40273 − 3.78636I
u = 0.342240 + 0.503546I
a = −0.76992 + 2.58082I
b = 0.455400 + 0.907374I
−0.692652 + 0.747510I 11.9814 + 9.3471I
u = 0.342240 − 0.503546I
a = −0.76992 − 2.58082I
b = 0.455400 − 0.907374I
−0.692652 − 0.747510I 11.9814 − 9.3471I
u = 1.388180 + 0.206751I
a = 0.197810 − 0.570262I
b = 0.878563 + 0.906512I
−3.29106 − 0.71548I 0
u = 1.388180 − 0.206751I
a = 0.197810 + 0.570262I
b = 0.878563 − 0.906512I
−3.29106 + 0.71548I 0
u = 1.389330 + 0.229302I
a = 0.032086 − 1.016630I
b = 0.985524 + 0.169001I
−2.15273 − 3.89237I 0
u = 1.389330 − 0.229302I
a = 0.032086 + 1.016630I
b = 0.985524 − 0.169001I
−2.15273 + 3.89237I 0
u = −1.395280 + 0.228734I
a = 0.022173 − 0.456532I
b = 0.318153 + 0.529929I
−5.25575 + 5.40772I 0
u = −1.395280 − 0.228734I
a = 0.022173 + 0.456532I
b = 0.318153 − 0.529929I
−5.25575 − 5.40772I 0
u = −1.40251 + 0.22262I
a = 0.20905 + 2.11697I
b = 0.515171 − 0.727283I
−5.25799 + 2.73945I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40251 − 0.22262I
a = 0.20905 − 2.11697I
b = 0.515171 + 0.727283I
−5.25799 − 2.73945I 0
u = 1.40136 + 0.23957I
a = −1.22459 − 0.93674I
b = 0.982381 − 0.722917I
−2.71907 − 7.34999I 0
u = 1.40136 − 0.23957I
a = −1.22459 + 0.93674I
b = 0.982381 + 0.722917I
−2.71907 + 7.34999I 0
u = 1.41292 + 0.18059I
a = 0.524545 + 1.034890I
b = 0.524820 + 1.235330I
−6.26506 + 1.08823I 0
u = 1.41292 − 0.18059I
a = 0.524545 − 1.034890I
b = 0.524820 − 1.235330I
−6.26506 − 1.08823I 0
u = −0.170323 + 0.538397I
a = −0.88005 + 2.08855I
b = 0.766888 − 0.937064I
1.75629 − 1.99035I 5.16557 + 2.88568I
u = −0.170323 − 0.538397I
a = −0.88005 − 2.08855I
b = 0.766888 + 0.937064I
1.75629 + 1.99035I 5.16557 − 2.88568I
u = −1.42218 + 0.20369I
a = −0.34383 − 2.55067I
b = 0.444068 − 0.949016I
−6.33252 + 1.92115I 0
u = −1.42218 − 0.20369I
a = −0.34383 + 2.55067I
b = 0.444068 + 0.949016I
−6.33252 − 1.92115I 0
u = −1.42009 + 0.23097I
a = −3.25951 + 2.43167I
b = 0.517759 + 0.941725I
−5.93096 + 6.95191I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42009 − 0.23097I
a = −3.25951 − 2.43167I
b = 0.517759 − 0.941725I
−5.93096 − 6.95191I 0
u = 1.41833 + 0.24594I
a = −1.85416 − 1.51461I
b = 0.656040 − 1.242250I
−5.30356 − 9.83245I 0
u = 1.41833 − 0.24594I
a = −1.85416 + 1.51461I
b = 0.656040 + 1.242250I
−5.30356 + 9.83245I 0
u = −1.41588 + 0.27350I
a = 0.329476 − 0.665678I
b = −0.512649 + 0.438397I
−5.41815 + 5.90992I 0
u = −1.41588 − 0.27350I
a = 0.329476 + 0.665678I
b = −0.512649 − 0.438397I
−5.41815 − 5.90992I 0
u = −1.43811 + 0.15525I
a = 0.504046 + 0.022616I
b = −0.539058 − 0.039985I
−7.11566 + 3.06003I 0
u = −1.43811 − 0.15525I
a = 0.504046 − 0.022616I
b = −0.539058 + 0.039985I
−7.11566 − 3.06003I 0
u = −0.398416 + 0.372308I
a = 0.101682 − 0.109041I
b = 0.571816 − 1.141880I
−0.63076 − 3.31553I −3.36731 + 5.22677I
u = −0.398416 − 0.372308I
a = 0.101682 + 0.109041I
b = 0.571816 + 1.141880I
−0.63076 + 3.31553I −3.36731 − 5.22677I
u = 1.43515 + 0.27776I
a = 0.055806 + 1.047710I
b = −0.943067 − 0.441627I
−4.17674 − 12.70210I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43515 − 0.27776I
a = 0.055806 − 1.047710I
b = −0.943067 + 0.441627I
−4.17674 + 12.70210I 0
u = 1.44154 + 0.25402I
a = −1.11991 − 1.00625I
b = −0.037074 − 1.326310I
−10.6833 − 9.7329I 0
u = 1.44154 − 0.25402I
a = −1.11991 + 1.00625I
b = −0.037074 + 1.326310I
−10.6833 + 9.7329I 0
u = 1.46055 + 0.12957I
a = 0.241626 + 0.379269I
b = −0.862769 + 0.364248I
−6.29480 + 3.09263I 0
u = 1.46055 − 0.12957I
a = 0.241626 − 0.379269I
b = −0.862769 − 0.364248I
−6.29480 − 3.09263I 0
u = 1.45869 + 0.17183I
a = 0.85005 + 1.43397I
b = −0.133037 + 1.269100I
−11.87960 + 0.03386I 0
u = 1.45869 − 0.17183I
a = 0.85005 − 1.43397I
b = −0.133037 − 1.269100I
−11.87960 − 0.03386I 0
u = −1.44081 + 0.29762I
a = 1.91997 − 0.94342I
b = −0.536367 − 1.027970I
−7.04207 + 10.26620I 0
u = −1.44081 − 0.29762I
a = 1.91997 + 0.94342I
b = −0.536367 + 1.027970I
−7.04207 − 10.26620I 0
u = 1.44413 + 0.28396I
a = 2.04970 + 1.30197I
b = −0.668248 + 1.151520I
−6.3507 − 18.5832I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44413 − 0.28396I
a = 2.04970 − 1.30197I
b = −0.668248 − 1.151520I
−6.3507 + 18.5832I 0
u = −1.47202 + 0.09733I
a = 0.561177 + 0.898504I
b = −0.393349 + 1.066740I
−9.91084 − 0.41010I 0
u = −1.47202 − 0.09733I
a = 0.561177 − 0.898504I
b = −0.393349 − 1.066740I
−9.91084 + 0.41010I 0
u = −1.46861 + 0.24755I
a = −0.266045 + 0.691177I
b = −0.284580 + 0.961432I
−8.69432 + 4.18913I 0
u = −1.46861 − 0.24755I
a = −0.266045 − 0.691177I
b = −0.284580 − 0.961432I
−8.69432 − 4.18913I 0
u = 1.48401 + 0.12840I
a = 0.317785 − 0.970044I
b = −0.615816 − 1.140620I
−8.61039 + 8.53738I 0
u = 1.48401 − 0.12840I
a = 0.317785 + 0.970044I
b = −0.615816 + 1.140620I
−8.61039 − 8.53738I 0
u = −1.49411 + 0.17396I
a = 0.808586 − 1.159040I
b = −0.424875 − 1.041320I
−9.76386 + 6.40779I 0
u = −1.49411 − 0.17396I
a = 0.808586 + 1.159040I
b = −0.424875 + 1.041320I
−9.76386 − 6.40779I 0
u = −0.379605 + 0.069470I
a = 0.480908 + 0.316543I
b = 0.705236 − 0.554147I
1.26265 − 1.49033I 1.18213 + 3.24989I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379605 − 0.069470I
a = 0.480908 − 0.316543I
b = 0.705236 + 0.554147I
1.26265 + 1.49033I 1.18213 − 3.24989I
u = 0.200253 + 0.310690I
a = 0.97283 + 1.24513I
b = 0.413444 − 0.932626I
−0.52263 − 2.65559I 2.07624 + 6.94674I
u = 0.200253 − 0.310690I
a = 0.97283 − 1.24513I
b = 0.413444 + 0.932626I
−0.52263 + 2.65559I 2.07624 − 6.94674I
16
II. I
u
2
= hb + a + 1, a
2
+ 3a + 3, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
−1
0
a
8
=
0
1
a
2
=
a
−a − 1
a
12
=
−1
0
a
5
=
2a + 4
−a − 2
a
3
=
a + 2
−a − 2
a
1
=
−1
0
a
9
=
−1
1
a
4
=
a + 2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
6
, c
7
, c
8
c
9
(u − 1)
2
c
10
(u + 1)
2
c
11
, c
12
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
y
2
+ y + 1
c
6
, c
7
, c
8
c
9
, c
10
(y −1)
2
c
11
, c
12
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.50000 + 0.86603I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
u = 1.00000
a = −1.50000 − 0.86603I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
113
+ 48u
112
+ ··· + 55u − 1)
c
2
(u
2
+ u + 1)(u
113
+ 2u
112
+ ··· − 5u − 1)
c
3
(u
2
− u + 1)(u
113
+ 60u
111
+ ··· − 47u + 1)
c
4
(u
2
− u + 1)(u
113
+ 2u
112
+ ··· + 1009u + 347)
c
5
(u
2
− u + 1)(u
113
+ 2u
112
+ ··· − 5u − 1)
c
6
, c
7
((u − 1)
2
)(u
113
+ 3u
112
+ ··· − 2u + 1)
c
8
((u − 1)
2
)(u
113
+ 7u
112
+ ··· + u
2
+ 1)
c
9
((u − 1)
2
)(u
113
+ 23u
112
+ ··· + 6255814u + 309047)
c
10
((u + 1)
2
)(u
113
+ 3u
112
+ ··· − 2u + 1)
c
11
u
2
(u
113
− 3u
112
+ ··· + 1280u − 1088)
c
12
u
2
(u
113
+ 11u
112
+ ··· + 12u + 4)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
113
+ 36y
112
+ ··· + 3831y −1)
c
2
, c
5
(y
2
+ y + 1)(y
113
+ 48y
112
+ ··· + 55y −1)
c
3
(y
2
+ y + 1)(y
113
+ 120y
112
+ ··· + 463y −1)
c
4
(y
2
+ y + 1)(y
113
+ 128y
112
+ ··· − 8247513y −120409)
c
6
, c
7
, c
10
((y −1)
2
)(y
113
− 103y
112
+ ··· − 2y −1)
c
8
((y −1)
2
)(y
113
+ 9y
112
+ ··· − 2y −1)
c
9
((y −1)
2
)(y
113
+ 53y
112
+ ··· − 1.83334 × 10
12
y −9.55100 × 10
10
)
c
11
y
2
(y
113
− 17y
112
+ ··· + 7.27436 × 10
7
y −1183744)
c
12
y
2
(y
113
+ 15y
112
+ ··· − 280y −16)
22
