12a
0050
(K12a
0050
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 4 11 12 6 1 8 9
Solving Sequence
8,11
12 9 1
4,7
3 2 6 10 5
c
11
c
8
c
12
c
7
c
3
c
1
c
6
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.41187 × 10
28
u
86
− 8.03613 × 10
28
u
85
+ ··· + 8.45678 × 10
26
b − 1.28690 × 10
28
,
− 1.57728 × 10
28
u
86
+ 4.79845 × 10
28
u
85
+ ··· + 1.26852 × 10
27
a − 9.45453 × 10
26
,
u
87
− 5u
86
+ ··· − 12u + 1i
I
u
2
= h−u
5
+ u
4
+ 3u
3
− u
2
+ b − 2u − 2, u
5
− u
4
− 3u
3
+ u
2
+ a + 2u + 2, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
u
3
= h5a
2
u + 9a
2
− 17au + 11b − 13a + 3u + 12, a
3
− 2a
2
u − a
2
− 2au + 3a − 7u + 3, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 99 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
= h2.41 × 10
28
u
86
− 8.04 × 10
28
u
85
+ · · · + 8.46 × 10
26
b − 1.29 ×
10
28
, −1.58 × 10
28
u
86
+ 4.80 × 10
28
u
85
+ · · · + 1.27 × 10
27
a − 9.45 ×
10
26
, u
87
− 5u
86
+ · · · − 12u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
9
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
12.4341u
86
− 37.8273u
85
+ ··· + 73.4069u + 0.745322
−28.5200u
86
+ 95.0259u
85
+ ··· − 184.859u + 15.2174
a
7
=
−u
u
a
3
=
−23.4679u
86
+ 86.4564u
85
+ ··· − 189.281u + 23.9765
7.38192u
86
− 29.2577u
85
+ ··· + 77.8285u − 8.01379
a
2
=
−12.9963u
86
+ 40.5794u
85
+ ··· − 77.7307u + 2.64155
23.6604u
86
− 78.3808u
85
+ ··· + 153.528u − 12.6789
a
6
=
35.4668u
86
− 123.526u
85
+ ··· + 266.381u − 20.1274
−44.3507u
86
+ 155.563u
85
+ ··· − 328.649u + 28.6288
a
10
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
5
=
−12.8929u
86
+ 44.8571u
85
+ ··· − 91.9941u + 11.8160
2.22886u
86
− 7.05574u
85
+ ··· + 16.1967u − 1.77867
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
10273217624408414786374874349
422838840952911474609384418
u
86
+
33680189062042541632794753137
422838840952911474609384418
u
85
+ ··· −
52187858752987512639204783279
422838840952911474609384418
u −
411818702336231626307587519
422838840952911474609384418
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
87
+ 41u
86
+ ··· + 1968u + 1
c
2
, c
4
u
87
− 9u
86
+ ··· + 42u + 1
c
3
, c
6
u
87
− 3u
86
+ ··· − 512u + 64
c
5
, c
9
u
87
− 2u
86
+ ··· − 224u − 64
c
7
, c
8
, c
11
c
12
u
87
− 5u
86
+ ··· − 12u + 1
c
10
u
87
+ 23u
86
+ ··· − 19872u + 337
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
87
+ 19y
86
+ ··· + 3775568y −1
c
2
, c
4
y
87
− 41y
86
+ ··· + 1968y −1
c
3
, c
6
y
87
+ 45y
86
+ ··· + 139264y −4096
c
5
, c
9
y
87
+ 40y
86
+ ··· + 29696y −4096
c
7
, c
8
, c
11
c
12
y
87
− 101y
86
+ ··· + 152y −1
c
10
y
87
− 5y
86
+ ··· + 506574140y −113569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.010010 + 0.280355I
a = −0.454171 + 0.318801I
b = −0.363009 − 1.195620I
1.86315 − 5.76624I 0
u = 1.010010 − 0.280355I
a = −0.454171 − 0.318801I
b = −0.363009 + 1.195620I
1.86315 + 5.76624I 0
u = 0.891141 + 0.294012I
a = 0.201900 − 0.412796I
b = 0.47945 + 1.39754I
3.78271 − 0.75026I 0
u = 0.891141 − 0.294012I
a = 0.201900 + 0.412796I
b = 0.47945 − 1.39754I
3.78271 + 0.75026I 0
u = −0.728506 + 0.562808I
a = −0.003687 − 0.438604I
b = −0.18441 + 1.95219I
−0.38906 − 13.27690I 0
u = −0.728506 − 0.562808I
a = −0.003687 + 0.438604I
b = −0.18441 − 1.95219I
−0.38906 + 13.27690I 0
u = −0.721882 + 0.517254I
a = 0.181711 + 0.389685I
b = 0.11772 − 1.87759I
2.10446 − 7.61105I 0
u = −0.721882 − 0.517254I
a = 0.181711 − 0.389685I
b = 0.11772 + 1.87759I
2.10446 + 7.61105I 0
u = −0.672458 + 0.516598I
a = 0.817277 − 0.015309I
b = 0.536901 + 0.326251I
−2.69044 − 6.81997I 0
u = −0.672458 − 0.516598I
a = 0.817277 + 0.015309I
b = 0.536901 − 0.326251I
−2.69044 + 6.81997I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.829810 + 0.126652I
a = −0.864661 − 0.893648I
b = 0.09823 + 1.44423I
−0.281846 − 0.813988I 0
u = 0.829810 − 0.126652I
a = −0.864661 + 0.893648I
b = 0.09823 − 1.44423I
−0.281846 + 0.813988I 0
u = −0.551676 + 0.628089I
a = 0.446283 − 0.209888I
b = 0.462139 − 0.044862I
−4.48506 − 0.94573I 0
u = −0.551676 − 0.628089I
a = 0.446283 + 0.209888I
b = 0.462139 + 0.044862I
−4.48506 + 0.94573I 0
u = −0.633849 + 0.504234I
a = −0.510764 − 0.726611I
b = 0.13756 + 1.96218I
−3.58375 − 4.13631I 0
u = −0.633849 − 0.504234I
a = −0.510764 + 0.726611I
b = 0.13756 − 1.96218I
−3.58375 + 4.13631I 0
u = 0.686979 + 0.423204I
a = −0.381993 − 0.202436I
b = 0.78804 + 1.56982I
3.84596 + 1.80001I 0
u = 0.686979 − 0.423204I
a = −0.381993 + 0.202436I
b = 0.78804 − 1.56982I
3.84596 − 1.80001I 0
u = 0.627329 + 0.490479I
a = 0.496057 + 0.013424I
b = −0.83681 − 1.57447I
2.05491 + 6.93244I 0
u = 0.627329 − 0.490479I
a = 0.496057 − 0.013424I
b = −0.83681 + 1.57447I
2.05491 − 6.93244I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.415376 + 0.656442I
a = −0.247896 + 0.519613I
b = −0.296944 + 0.491125I
−4.88363 − 3.37848I 0
u = −0.415376 − 0.656442I
a = −0.247896 − 0.519613I
b = −0.296944 − 0.491125I
−4.88363 + 3.37848I 0
u = −0.599038 + 0.447390I
a = −0.782862 − 0.244572I
b = −0.414912 − 0.371063I
−1.18861 − 2.16669I 0
u = −0.599038 − 0.447390I
a = −0.782862 + 0.244572I
b = −0.414912 + 0.371063I
−1.18861 + 2.16669I 0
u = −0.676449 + 0.299656I
a = 0.756567 − 0.237800I
b = 0.00819 − 1.44854I
4.62680 − 3.56560I 7.27157 + 9.65744I
u = −0.676449 − 0.299656I
a = 0.756567 + 0.237800I
b = 0.00819 + 1.44854I
4.62680 + 3.56560I 7.27157 − 9.65744I
u = −0.190684 + 0.682767I
a = 1.84849 + 0.10243I
b = −0.022296 + 0.386971I
−1.98497 + 9.09309I 0. − 5.78619I
u = −0.190684 − 0.682767I
a = 1.84849 − 0.10243I
b = −0.022296 − 0.386971I
−1.98497 − 9.09309I 0. + 5.78619I
u = 0.595986 + 0.335404I
a = 1.15247 + 0.88242I
b = 0.095803 − 1.019010I
−0.41312 + 1.89802I 2.53218 − 5.30507I
u = 0.595986 − 0.335404I
a = 1.15247 − 0.88242I
b = 0.095803 + 1.019010I
−0.41312 − 1.89802I 2.53218 + 5.30507I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.159142 + 0.620290I
a = −1.93738 − 0.18215I
b = 0.042132 − 0.161742I
0.45494 + 3.75851I 2.39831 − 2.27831I
u = −0.159142 − 0.620290I
a = −1.93738 + 0.18215I
b = 0.042132 + 0.161742I
0.45494 − 3.75851I 2.39831 + 2.27831I
u = −0.598200 + 0.200921I
a = −1.088720 + 0.625520I
b = −0.056104 + 1.282070I
4.04708 + 2.36658I 3.70340 + 8.40480I
u = −0.598200 − 0.200921I
a = −1.088720 − 0.625520I
b = −0.056104 − 1.282070I
4.04708 − 2.36658I 3.70340 − 8.40480I
u = −0.229873 + 0.585003I
a = −0.237608 + 0.897450I
b = 0.011505 + 0.833562I
−3.98249 + 3.05201I −2.80405 − 2.05356I
u = −0.229873 − 0.585003I
a = −0.237608 − 0.897450I
b = 0.011505 − 0.833562I
−3.98249 − 3.05201I −2.80405 + 2.05356I
u = −0.282835 + 0.551663I
a = 2.12272 + 0.04738I
b = −0.537227 + 0.031704I
−4.60787 + 0.49284I −2.55335 − 0.71964I
u = −0.282835 − 0.551663I
a = 2.12272 − 0.04738I
b = −0.537227 − 0.031704I
−4.60787 − 0.49284I −2.55335 + 0.71964I
u = 0.292776 + 0.514297I
a = 1.56985 + 0.81715I
b = 0.391728 − 0.558737I
1.08055 − 3.42442I 2.38420 + 1.79720I
u = 0.292776 − 0.514297I
a = 1.56985 − 0.81715I
b = 0.391728 + 0.558737I
1.08055 + 3.42442I 2.38420 − 1.79720I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350737 + 0.463289I
a = −0.205369 − 0.866134I
b = −0.160390 − 0.592063I
−1.92348 − 1.04705I −0.41462 + 4.62441I
u = −0.350737 − 0.463289I
a = −0.205369 + 0.866134I
b = −0.160390 + 0.592063I
−1.92348 + 1.04705I −0.41462 − 4.62441I
u = 1.41295 + 0.17256I
a = −0.516333 − 0.548345I
b = 0.201492 + 1.207130I
0.95643 + 6.36363I 0
u = 1.41295 − 0.17256I
a = −0.516333 + 0.548345I
b = 0.201492 − 1.207130I
0.95643 − 6.36363I 0
u = 1.42426 + 0.02648I
a = −0.79902 + 1.28037I
b = 0.25311 − 1.81147I
0.53938 + 1.34945I 0
u = 1.42426 − 0.02648I
a = −0.79902 − 1.28037I
b = 0.25311 + 1.81147I
0.53938 − 1.34945I 0
u = −1.46571 + 0.05632I
a = −0.051547 + 0.571568I
b = −0.189919 + 0.027666I
6.64268 + 1.76311I 0
u = −1.46571 − 0.05632I
a = −0.051547 − 0.571568I
b = −0.189919 − 0.027666I
6.64268 − 1.76311I 0
u = 1.47372 + 0.06877I
a = 0.188121 + 0.967063I
b = 0.32808 − 1.44311I
4.00953 + 2.73511I 0
u = 1.47372 − 0.06877I
a = 0.188121 − 0.967063I
b = 0.32808 + 1.44311I
4.00953 − 2.73511I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.487248 + 0.192015I
a = 1.60102 + 0.93973I
b = −1.32640 − 1.87157I
−1.041640 + 0.182607I 4.12606 − 13.21729I
u = 0.487248 − 0.192015I
a = 1.60102 − 0.93973I
b = −1.32640 + 1.87157I
−1.041640 − 0.182607I 4.12606 + 13.21729I
u = 0.509388
a = −0.679237
b = 0.383628
0.764590 13.1770
u = 0.131672 + 0.482233I
a = −1.86437 − 0.77008I
b = −0.267014 + 0.371744I
2.25594 + 1.34746I 3.93001 − 3.94443I
u = 0.131672 − 0.482233I
a = −1.86437 + 0.77008I
b = −0.267014 − 0.371744I
2.25594 − 1.34746I 3.93001 + 3.94443I
u = 1.52856 + 0.19143I
a = 0.408104 + 0.063979I
b = −0.616967 − 0.460387I
2.36054 + 3.92288I 0
u = 1.52856 − 0.19143I
a = 0.408104 − 0.063979I
b = −0.616967 + 0.460387I
2.36054 − 3.92288I 0
u = −1.57166 + 0.06729I
a = −2.08529 + 3.23114I
b = 1.90322 − 3.71902I
6.18518 − 1.19455I 0
u = −1.57166 − 0.06729I
a = −2.08529 − 3.23114I
b = 1.90322 + 3.71902I
6.18518 + 1.19455I 0
u = 1.57641 + 0.12488I
a = −0.571783 + 0.472057I
b = 1.289790 − 0.459669I
6.19157 + 4.23438I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57641 − 0.12488I
a = −0.571783 − 0.472057I
b = 1.289790 + 0.459669I
6.19157 − 4.23438I 0
u = −1.57932 + 0.09454I
a = −0.247972 + 0.844562I
b = −0.362527 − 0.626041I
7.02868 − 3.46437I 0
u = −1.57932 − 0.09454I
a = −0.247972 − 0.844562I
b = −0.362527 + 0.626041I
7.02868 + 3.46437I 0
u = 1.58242 + 0.06903I
a = −0.29201 − 2.76631I
b = 0.57137 + 3.68365I
11.55840 − 1.29646I 0
u = 1.58242 − 0.06903I
a = −0.29201 + 2.76631I
b = 0.57137 − 3.68365I
11.55840 + 1.29646I 0
u = −1.58519
a = 0.997201
b = −0.668948
8.07273 0
u = −1.58073 + 0.14082I
a = −1.78005 + 2.09338I
b = 1.45293 − 2.87581I
9.51389 − 9.24025I 0
u = −1.58073 − 0.14082I
a = −1.78005 − 2.09338I
b = 1.45293 + 2.87581I
9.51389 + 9.24025I 0
u = 1.58150 + 0.14435I
a = −0.90877 − 3.37832I
b = 0.76910 + 4.06653I
3.89012 + 6.50742I 0
u = 1.58150 − 0.14435I
a = −0.90877 + 3.37832I
b = 0.76910 − 4.06653I
3.89012 − 6.50742I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59599 + 0.09211I
a = 0.40709 + 2.92156I
b = −0.51286 − 3.84759I
12.39170 + 5.06306I 0
u = 1.59599 − 0.09211I
a = 0.40709 − 2.92156I
b = −0.51286 + 3.84759I
12.39170 − 5.06306I 0
u = 1.59413 + 0.15161I
a = 0.653822 − 0.295842I
b = −1.396300 + 0.079914I
4.96648 + 9.29592I 0
u = 1.59413 − 0.15161I
a = 0.653822 + 0.295842I
b = −1.396300 − 0.079914I
4.96648 − 9.29592I 0
u = −1.59938 + 0.11914I
a = 1.61226 − 2.32414I
b = −1.40674 + 3.07633I
11.62610 − 3.80327I 0
u = −1.59938 − 0.11914I
a = 1.61226 + 2.32414I
b = −1.40674 − 3.07633I
11.62610 + 3.80327I 0
u = −1.61679 + 0.03544I
a = 0.83922 − 1.17901I
b = −0.380596 + 1.248080I
8.04740 + 0.17742I 0
u = −1.61679 − 0.03544I
a = 0.83922 + 1.17901I
b = −0.380596 − 1.248080I
8.04740 − 0.17742I 0
u = 1.61192 + 0.15359I
a = 0.97184 + 2.89964I
b = −0.70154 − 3.73677I
10.0164 + 10.1316I 0
u = 1.61192 − 0.15359I
a = 0.97184 − 2.89964I
b = −0.70154 + 3.73677I
10.0164 − 10.1316I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61482 + 0.17017I
a = −1.12043 − 2.77461I
b = 0.75341 + 3.59107I
7.5322 + 16.0397I 0
u = 1.61482 − 0.17017I
a = −1.12043 + 2.77461I
b = 0.75341 − 3.59107I
7.5322 − 16.0397I 0
u = −1.65448 + 0.06893I
a = 0.76967 − 2.45752I
b = −0.91725 + 3.16651I
12.58290 − 0.59134I 0
u = −1.65448 − 0.06893I
a = 0.76967 + 2.45752I
b = −0.91725 − 3.16651I
12.58290 + 0.59134I 0
u = −1.67615 + 0.04835I
a = −0.48336 + 2.26752I
b = 0.78811 − 2.96006I
11.19340 + 4.66031I 0
u = −1.67615 − 0.04835I
a = −0.48336 − 2.26752I
b = 0.78811 + 2.96006I
11.19340 − 4.66031I 0
u = 0.0864028
a = 6.46516
b = −0.774246
−1.21024 −9.56520
13
II. I
u
2
= h−u
5
+ u
4
+ 3u
3
− u
2
+ b − 2u − 2, u
5
− u
4
− 3u
3
+ u
2
+ a + 2u +
2, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
9
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
−u
5
+ u
4
+ 3u
3
− u
2
− 2u − 2
u
5
− u
4
− 3u
3
+ u
2
+ 2u + 2
a
7
=
−u
u
a
3
=
−u
5
+ u
4
+ 3u
3
− u
2
− 2u − 2
u
5
− u
4
− 3u
3
+ u
2
+ 2u + 2
a
2
=
−u
5
+ u
4
+ 3u
3
− 2u
2
− 2u − 1
u
5
− 3u
3
− u
2
+ 2u + 2
a
6
=
−u
u
a
10
=
−u
5
+ 2u
3
+ u
u
5
− 3u
3
+ u
a
5
=
u
2
− 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
5
− 6u
4
− 38u
3
+ 5u
2
+ 33u + 27
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
, c
10
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
7
, c
8
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
9
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
11
, c
12
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
9
, c
10
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
c
7
, c
8
, c
11
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493180 + 0.575288I
a = −0.228804 + 0.434483I
b = 0.228804 − 0.434483I
−4.60518 − 1.97241I −0.89950 + 4.53432I
u = −0.493180 − 0.575288I
a = −0.228804 − 0.434483I
b = 0.228804 + 0.434483I
−4.60518 + 1.97241I −0.89950 − 4.53432I
u = 0.483672
a = −2.83358
b = 2.83358
−0.906083 39.7680
u = 1.52087 + 0.16310I
a = 0.636388 + 0.565801I
b = −0.636388 − 0.565801I
2.05064 + 4.59213I 1.73030 − 5.96315I
u = 1.52087 − 0.16310I
a = 0.636388 − 0.565801I
b = −0.636388 + 0.565801I
2.05064 − 4.59213I 1.73030 + 5.96315I
u = −1.53904
a = 2.01841
b = −2.01841
6.01515 6.57090
17
III. I
u
3
= h5a
2
u + 9a
2
− 17au + 11b − 13a + 3u + 12, a
3
− 2a
2
u − a
2
− 2au +
3a − 7u + 3, u
2
+ u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u − 1
a
9
=
u
−u + 1
a
1
=
u
−u
a
4
=
a
−0.454545a
2
u + 1.54545au + ··· + 1.18182a − 1.09091
a
7
=
−u
u
a
3
=
−0.0909091a
2
u + 0.909091au + ··· + 1.63636a − 0.818182
−0.363636a
2
u + 0.636364au + ··· + 0.545455a − 0.272727
a
2
=
0.363636a
2
u + 0.363636au + ··· + 0.454545a − 1.72727
−2u
a
6
=
0.0909091a
2
u + 0.0909091au + ··· + 0.363636a − 1.18182
0.272727a
2
u + 0.272727au + ··· + 0.0909091a − 0.545455
a
10
=
u
−u + 1
a
5
=
0.0909091a
2
u + 0.0909091au + ··· + 0.363636a − 1.18182
0.272727a
2
u + 0.272727au + ··· + 0.0909091a − 0.545455
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
20
11
a
2
u −
58
11
a
2
+
57
11
au +
107
11
a +
10
11
u −
59
11
18
(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
9
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
8
, c
10
(u
2
− u − 1)
3
c
11
, c
12
(u
2
+ u − 1)
3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
9
y
6
c
7
, c
8
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.290827 + 0.846791I
b = 0.057180 + 1.268210I
4.01109 − 2.82812I 3.00413 + 7.79836I
u = 0.618034
a = 0.290827 − 0.846791I
b = 0.057180 − 1.268210I
4.01109 + 2.82812I 3.00413 − 7.79836I
u = 0.618034
a = 1.65441
b = −0.732393
−0.126494 −0.918090
u = −1.61803
a = −2.26961
b = 1.91743
7.76919 −21.8890
u = −1.61803
a = 0.01677 + 2.51235I
b = −0.14970 − 3.32021I
11.90680 − 2.82812I 7.89941 + 3.17745I
u = −1.61803
a = 0.01677 − 2.51235I
b = −0.14970 + 3.32021I
11.90680 + 2.82812I 7.89941 − 3.17745I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
− u
2
+ 2u − 1)
2
(u
87
+ 41u
86
+ ··· + 1968u + 1)
c
2
((u − 1)
6
)(u
3
+ u
2
− 1)
2
(u
87
− 9u
86
+ ··· + 42u + 1)
c
3
u
6
(u
3
− u
2
+ 2u − 1)
2
(u
87
− 3u
86
+ ··· − 512u + 64)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)
2
(u
87
− 9u
86
+ ··· + 42u + 1)
c
5
u
6
(u
6
− u
5
+ ··· − u − 1)(u
87
− 2u
86
+ ··· − 224u − 64)
c
6
u
6
(u
3
+ u
2
+ 2u + 1)
2
(u
87
− 3u
86
+ ··· − 512u + 64)
c
7
, c
8
(u
2
− u − 1)
3
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
87
− 5u
86
+ ··· − 12u + 1)
c
9
u
6
(u
6
+ u
5
+ ··· + u − 1)(u
87
− 2u
86
+ ··· − 224u − 64)
c
10
(u
2
− u − 1)
3
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
87
+ 23u
86
+ ··· − 19872u + 337)
c
11
, c
12
(u
2
+ u − 1)
3
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
87
− 5u
86
+ ··· − 12u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
87
+ 19y
86
+ ··· + 3775568y − 1)
c
2
, c
4
((y − 1)
6
)(y
3
− y
2
+ 2y − 1)
2
(y
87
− 41y
86
+ ··· + 1968y − 1)
c
3
, c
6
y
6
(y
3
+ 3y
2
+ 2y − 1)
2
(y
87
+ 45y
86
+ ··· + 139264y − 4096)
c
5
, c
9
y
6
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
87
+ 40y
86
+ ··· + 29696y − 4096)
c
7
, c
8
, c
11
c
12
(y
2
− 3y + 1)
3
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
87
− 101y
86
+ ··· + 152y − 1)
c
10
(y
2
− 3y + 1)
3
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
87
− 5y
86
+ ··· + 506574140y − 113569)
23
