12a
0331
(K12a
0331
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 9 2 4 7 12 1 5 10
Solving Sequence
4,11
5
8,12
3 7 9 10 1 2 6
c
4
c
11
c
3
c
7
c
8
c
9
c
12
c
1
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.20578 × 10
55
u
43
+ 2.72261 × 10
53
u
42
+ ··· + 2.20839 × 10
56
b + 3.82813 × 10
56
,
− 2.53459 × 10
56
u
43
+ 3.60015 × 10
56
u
42
+ ··· + 1.76671 × 10
57
a − 8.03449 × 10
57
,
u
44
− 3u
43
+ ··· + 48u − 64i
I
u
2
= h−2.99662 × 10
27
au
31
+ 3.45285 × 10
27
u
31
+ ··· − 2.16166 × 10
28
a + 2.56649 × 10
28
,
1.55146 × 10
23
au
31
− 3.42612 × 10
25
u
31
+ ··· − 8.65692 × 10
25
a + 2.42878 × 10
26
, u
32
+ u
31
+ ··· − 4u + 8i
I
u
3
= hu
9
− 2u
7
+ u
5
+ 2u
3
+ b − u, u
9
+ u
8
− 2u
7
− 3u
6
+ 4u
4
+ 4u
3
− u
2
+ a − 3u − 1, u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1i
I
v
1
= ha, 2v
3
+ v
2
+ b + 3v + 1, 2v
4
+ 3v
3
+ 4v
2
+ 3v + 1i
I
v
2
= ha, v
2
b + b
2
+ bv −b −v, v
3
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 128 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
= h−1.21 × 10
55
u
43
+ 2.72 × 10
53
u
42
+ · · · + 2.21 × 10
56
b + 3.83 ×
10
56
, −2.53 × 10
56
u
43
+ 3.60 × 10
56
u
42
+ · · · + 1.77 × 10
57
a − 8.03 ×
10
57
, u
44
− 3u
43
+ · · · + 48u − 64i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
0.143464u
43
− 0.203777u
42
+ ··· − 2.64743u + 4.54771
0.0546002u
43
− 0.00123285u
42
+ ··· − 3.22478u − 1.73345
a
12
=
u
−u
3
+ u
a
3
=
0.175427u
43
− 0.255448u
42
+ ··· − 3.94058u + 6.06949
−0.309915u
43
+ 0.609208u
42
+ ··· − 5.06054u − 19.6604
a
7
=
0.0888638u
43
− 0.202544u
42
+ ··· + 0.577349u + 6.28116
0.0546002u
43
− 0.00123285u
42
+ ··· − 3.22478u − 1.73345
a
9
=
−0.655567u
43
+ 1.17863u
42
+ ··· − 3.12523u − 34.9827
0.525900u
43
− 0.919790u
42
+ ··· + 0.385297u + 25.9781
a
10
=
−0.329361u
43
+ 0.580992u
42
+ ··· − 2.08842u − 17.7466
0.412425u
43
− 0.700514u
42
+ ··· − 1.16828u + 18.8318
a
1
=
0.218186u
43
− 0.385243u
42
+ ··· − 0.618559u + 10.5245
−0.437381u
43
+ 0.793391u
42
+ ··· − 3.74379u − 24.4582
a
2
=
0.571987u
43
− 1.16565u
42
+ ··· + 8.28123u + 36.6401
0.409286u
43
− 0.759210u
42
+ ··· + 1.85925u + 22.1877
a
6
=
0.649605u
43
− 1.17009u
42
+ ··· + 4.76265u + 36.5187
−0.587692u
43
+ 0.983287u
42
+ ··· + 4.35683u − 26.2754
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.19362u
43
− 2.33566u
42
+ ··· + 21.5478u + 85.7392
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
44
+ 18u
43
+ ··· + 11u + 1
c
2
, c
3
, c
6
c
7
u
44
+ 9u
42
+ ··· − 3u + 1
c
4
, c
11
u
44
+ 3u
43
+ ··· − 48u − 64
c
5
u
44
− 18u
43
+ ··· − 28060u + 2284
c
9
, c
10
, c
12
u
44
+ 5u
43
+ ··· − 11u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
44
+ 30y
43
+ ··· − 117y + 1
c
2
, c
3
, c
6
c
7
y
44
+ 18y
43
+ ··· + 11y + 1
c
4
, c
11
y
44
− 27y
43
+ ··· − 8448y + 4096
c
5
y
44
+ 20y
43
+ ··· − 118969272y + 5216656
c
9
, c
10
, c
12
y
44
− 43y
43
+ ··· − 337y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877125 + 0.508540I
a = −0.830235 + 0.263996I
b = −0.552748 + 0.993827I
0.33144 − 5.53133I 8.20557 + 5.60912I
u = 0.877125 − 0.508540I
a = −0.830235 − 0.263996I
b = −0.552748 − 0.993827I
0.33144 + 5.53133I 8.20557 − 5.60912I
u = 0.551521 + 0.892173I
a = −0.37219 + 2.31116I
b = 0.518404 + 0.942737I
0.87743 + 2.97747I 7.43344 − 5.22549I
u = 0.551521 − 0.892173I
a = −0.37219 − 2.31116I
b = 0.518404 − 0.942737I
0.87743 − 2.97747I 7.43344 + 5.22549I
u = 0.918562 + 0.190781I
a = −0.06947 + 2.14622I
b = 0.493005 + 1.143320I
0.04036 + 8.34489I 9.07426 − 8.42771I
u = 0.918562 − 0.190781I
a = −0.06947 − 2.14622I
b = 0.493005 − 1.143320I
0.04036 − 8.34489I 9.07426 + 8.42771I
u = 0.777804 + 0.489896I
a = 0.447932 − 1.235890I
b = −0.107092 − 0.599664I
−1.23908 + 2.01870I 5.50350 − 5.95724I
u = 0.777804 − 0.489896I
a = 0.447932 + 1.235890I
b = −0.107092 + 0.599664I
−1.23908 − 2.01870I 5.50350 + 5.95724I
u = −0.553221 + 0.710651I
a = −0.18276 − 2.17276I
b = 0.513691 − 1.049330I
−3.34564 − 6.15513I 1.18529 + 7.20651I
u = −0.553221 − 0.710651I
a = −0.18276 + 2.17276I
b = 0.513691 + 1.049330I
−3.34564 + 6.15513I 1.18529 − 7.20651I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.939623 + 0.583661I
a = −0.850904 − 1.023730I
b = −0.456389 − 0.953909I
−2.18540 + 1.24012I 4.01532 − 2.37646I
u = −0.939623 − 0.583661I
a = −0.850904 + 1.023730I
b = −0.456389 + 0.953909I
−2.18540 − 1.24012I 4.01532 + 2.37646I
u = −1.121990 + 0.460726I
a = 0.18892 + 1.42239I
b = −0.139239 + 0.731129I
3.74404 − 4.98999I 12.7872 + 7.5818I
u = −1.121990 − 0.460726I
a = 0.18892 − 1.42239I
b = −0.139239 − 0.731129I
3.74404 + 4.98999I 12.7872 − 7.5818I
u = 1.210230 + 0.107374I
a = 1.233610 − 0.619919I
b = −0.644818 − 1.118720I
2.28709 + 7.54168I 8.78911 − 4.76693I
u = 1.210230 − 0.107374I
a = 1.233610 + 0.619919I
b = −0.644818 + 1.118720I
2.28709 − 7.54168I 8.78911 + 4.76693I
u = 1.220140 + 0.130546I
a = −0.879775 + 0.046540I
b = 0.791200 + 0.653166I
5.30527 + 3.52676I 12.39571 − 5.60505I
u = 1.220140 − 0.130546I
a = −0.879775 − 0.046540I
b = 0.791200 − 0.653166I
5.30527 − 3.52676I 12.39571 + 5.60505I
u = 1.22786
a = −0.226705
b = −0.764455
6.46619 15.1390
u = −1.221210 + 0.277116I
a = −0.290071 − 0.491123I
b = 0.815287 + 0.556119I
4.99655 − 1.77857I 12.03283 + 0.90771I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.221210 − 0.277116I
a = −0.290071 + 0.491123I
b = 0.815287 − 0.556119I
4.99655 + 1.77857I 12.03283 − 0.90771I
u = −0.187852 + 0.707638I
a = −0.10739 + 2.04695I
b = 0.584108 + 1.123780I
−2.10344 + 8.47320I 0.86513 − 7.32488I
u = −0.187852 − 0.707638I
a = −0.10739 − 2.04695I
b = 0.584108 − 1.123780I
−2.10344 − 8.47320I 0.86513 + 7.32488I
u = 0.077200 + 1.270820I
a = −0.344452 − 0.637993I
b = −0.813481 − 0.606549I
7.29308 + 0.83298I 12.93302 − 2.35138I
u = 0.077200 − 1.270820I
a = −0.344452 + 0.637993I
b = −0.813481 + 0.606549I
7.29308 − 0.83298I 12.93302 + 2.35138I
u = 1.147950 + 0.576653I
a = −0.63200 + 1.38012I
b = −0.366262 + 0.944615I
2.90580 + 2.45908I 8.37655 + 2.48976I
u = 1.147950 − 0.576653I
a = −0.63200 − 1.38012I
b = −0.366262 − 0.944615I
2.90580 − 2.45908I 8.37655 − 2.48976I
u = −0.373154 + 0.590810I
a = 1.32152 + 1.14412I
b = 0.140186 + 0.443282I
1.43845 + 0.81939I 7.07317 − 0.59629I
u = −0.373154 − 0.590810I
a = 1.32152 − 1.14412I
b = 0.140186 − 0.443282I
1.43845 − 0.81939I 7.07317 + 0.59629I
u = 0.286301 + 1.271350I
a = −0.06998 − 1.96322I
b = 0.646714 − 1.143430I
3.83652 − 10.39040I 6.00000 + 6.99388I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.286301 − 1.271350I
a = −0.06998 + 1.96322I
b = 0.646714 + 1.143430I
3.83652 + 10.39040I 6.00000 − 6.99388I
u = −1.232470 + 0.449409I
a = 1.48422 + 1.42635I
b = −0.636544 + 1.161000I
1.13812 − 12.94230I 6.00000 + 9.65030I
u = −1.232470 − 0.449409I
a = 1.48422 − 1.42635I
b = −0.636544 − 1.161000I
1.13812 + 12.94230I 6.00000 − 9.65030I
u = −0.572137
a = 0.404331
b = −0.317872
0.742706 14.0290
u = −0.041980 + 0.544402I
a = −0.201901 + 0.667917I
b = −0.626567 + 0.580076I
1.43276 − 1.29168I 5.31163 + 3.20971I
u = −0.041980 − 0.544402I
a = −0.201901 − 0.667917I
b = −0.626567 − 0.580076I
1.43276 + 1.29168I 5.31163 − 3.20971I
u = 1.37733 + 0.68948I
a = 1.13789 − 1.81742I
b = −0.643082 − 1.192500I
7.3537 + 17.3599I 0
u = 1.37733 − 0.68948I
a = 1.13789 + 1.81742I
b = −0.643082 + 1.192500I
7.3537 − 17.3599I 0
u = 1.44068 + 0.58329I
a = 0.168597 + 0.266784I
b = 0.891958 − 0.507832I
11.72660 + 5.76056I 0
u = 1.44068 − 0.58329I
a = 0.168597 − 0.266784I
b = 0.891958 + 0.507832I
11.72660 − 5.76056I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53910 + 0.28678I
a = 0.364929 − 0.791054I
b = −0.714050 − 1.079210I
10.37340 + 4.75111I 0
u = −1.53910 − 0.28678I
a = 0.364929 + 0.791054I
b = −0.714050 + 1.079210I
10.37340 − 4.75111I 0
u = −1.50213 + 0.47642I
a = −0.542791 − 0.639449I
b = 0.846882 − 0.739073I
12.5656 − 7.1187I 0
u = −1.50213 − 0.47642I
a = −0.542791 + 0.639449I
b = 0.846882 + 0.739073I
12.5656 + 7.1187I 0
9
II.
I
u
2
= h−3.00×10
27
au
31
+3.45×10
27
u
31
+· · ·−2.16×10
28
a+2.57×10
28
, 1.55×
10
23
au
31
−3.43×10
25
u
31
+· · ·−8.66×10
25
a+2.43×10
26
, u
32
+u
31
+· · ·−4u+8i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
a
2.08262au
31
− 2.39969u
31
+ ··· + 15.0233a − 17.8368
a
12
=
u
−u
3
+ u
a
3
=
−3.47308au
31
− 0.402645u
31
+ ··· − 21.9512a + 5.83712
4.59499au
31
− 0.207407u
31
+ ··· + 30.2057a − 1.17201
a
7
=
−2.08262au
31
+ 2.39969u
31
+ ··· − 14.0233a + 17.8368
2.08262au
31
− 2.39969u
31
+ ··· + 15.0233a − 17.8368
a
9
=
7.54748u
31
− 1.20115u
30
+ ··· − 67.8623u + 47.3131
−5.97373u
31
+ 1.04734u
30
+ ··· + 53.1575u − 38.4575
a
10
=
3.55221u
31
− 0.611351u
30
+ ··· − 33.0310u + 22.4678
−4.23845u
31
+ 0.712986u
30
+ ··· + 37.6864u − 26.6223
a
1
=
−2.80108u
31
+ 0.304585u
30
+ ··· + 25.6455u − 15.7816
4.74639u
31
− 0.896566u
30
+ ··· − 42.2168u + 31.5315
a
2
=
−2.39969au
31
− 3.10645u
31
+ ··· − 17.8368a − 27.5448
1
a
6
=
5.78721u
31
− 1.13313u
30
+ ··· − 51.3179u + 39.9500
−5.87276u
31
+ 1.39777u
30
+ ··· + 51.5961u − 39.7880
(ii) Obstruction class = −1
(iii) Cusp Shapes =
11025781239134800397292311
6007819644609133159819012
u
31
−
4547387949457051047751187
6007819644609133159819012
u
30
+ ··· −
27712897715167341742192775
3003909822304566579909506
u +
37908238938466571310198751
1501954911152283289954753
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
64
+ 34u
63
+ ··· + 2888u + 289
c
2
, c
3
, c
6
c
7
u
64
− 2u
63
+ ··· + 6u + 17
c
4
, c
11
(u
32
− u
31
+ ··· + 4u + 8)
2
c
5
(u
32
+ 6u
31
+ ··· − 29u + 19)
2
c
9
, c
10
, c
12
(u
32
+ 4u
31
+ ··· − 2u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
64
− 10y
63
+ ··· + 2113164y + 83521
c
2
, c
3
, c
6
c
7
y
64
+ 34y
63
+ ··· + 2888y + 289
c
4
, c
11
(y
32
− 21y
31
+ ··· − 400y + 64)
2
c
5
(y
32
+ 18y
31
+ ··· − 14597y + 361)
2
c
9
, c
10
, c
12
(y
32
− 32y
31
+ ··· + 10y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994786 + 0.117498I
a = 0.605972 − 0.777809I
b = −0.086371 − 1.233020I
−1.56769 + 0.51232I 8.14141 + 0.14369I
u = 0.994786 + 0.117498I
a = 1.64444 − 1.08920I
b = −0.371286 + 0.809217I
−1.56769 + 0.51232I 8.14141 + 0.14369I
u = 0.994786 − 0.117498I
a = 0.605972 + 0.777809I
b = −0.086371 + 1.233020I
−1.56769 − 0.51232I 8.14141 − 0.14369I
u = 0.994786 − 0.117498I
a = 1.64444 + 1.08920I
b = −0.371286 − 0.809217I
−1.56769 − 0.51232I 8.14141 − 0.14369I
u = 1.06664
a = −0.57970 + 2.22749I
b = 0.386184 + 1.203090I
−0.726839 7.36180
u = 1.06664
a = −0.57970 − 2.22749I
b = 0.386184 − 1.203090I
−0.726839 7.36180
u = −1.080820 + 0.181795I
a = 0.410379 + 0.315421I
b = 0.704804 + 0.067726I
2.97866 − 3.96490I 11.15642 + 4.13069I
u = −1.080820 + 0.181795I
a = 0.31340 + 1.97047I
b = −0.382987 + 1.136630I
2.97866 − 3.96490I 11.15642 + 4.13069I
u = −1.080820 − 0.181795I
a = 0.410379 − 0.315421I
b = 0.704804 − 0.067726I
2.97866 + 3.96490I 11.15642 − 4.13069I
u = −1.080820 − 0.181795I
a = 0.31340 − 1.97047I
b = −0.382987 − 1.136630I
2.97866 + 3.96490I 11.15642 − 4.13069I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.134937 + 1.098550I
a = −1.05581 − 1.06392I
b = 0.438430 − 0.887152I
0.19293 − 1.78898I 7.34736 + 3.66370I
u = 0.134937 + 1.098550I
a = −0.09148 + 2.94336I
b = 0.134755 + 1.267700I
0.19293 − 1.78898I 7.34736 + 3.66370I
u = 0.134937 − 1.098550I
a = −1.05581 + 1.06392I
b = 0.438430 + 0.887152I
0.19293 + 1.78898I 7.34736 − 3.66370I
u = 0.134937 − 1.098550I
a = −0.09148 − 2.94336I
b = 0.134755 − 1.267700I
0.19293 + 1.78898I 7.34736 − 3.66370I
u = −0.636893 + 0.594211I
a = 1.273170 + 0.270032I
b = 0.455758 + 0.730375I
1.60801 + 1.11555I 10.11098 + 0.26189I
u = −0.636893 + 0.594211I
a = 0.73961 + 1.69841I
b = −0.501791 + 0.546256I
1.60801 + 1.11555I 10.11098 + 0.26189I
u = −0.636893 − 0.594211I
a = 1.273170 − 0.270032I
b = 0.455758 − 0.730375I
1.60801 − 1.11555I 10.11098 − 0.26189I
u = −0.636893 − 0.594211I
a = 0.73961 − 1.69841I
b = −0.501791 − 0.546256I
1.60801 − 1.11555I 10.11098 − 0.26189I
u = −1.100670 + 0.347474I
a = −0.692111 − 1.106880I
b = −0.174423 − 1.282110I
−2.17989 − 4.05552I 5.42840 + 6.80075I
u = −1.100670 + 0.347474I
a = 2.31612 + 0.53329I
b = −0.463156 + 0.945799I
−2.17989 − 4.05552I 5.42840 + 6.80075I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.100670 − 0.347474I
a = −0.692111 + 1.106880I
b = −0.174423 + 1.282110I
−2.17989 + 4.05552I 5.42840 − 6.80075I
u = −1.100670 − 0.347474I
a = 2.31612 − 0.53329I
b = −0.463156 − 0.945799I
−2.17989 + 4.05552I 5.42840 − 6.80075I
u = 0.646992 + 0.531527I
a = 0.519557 − 0.623716I
b = 0.433001 − 0.304309I
−1.44328 + 2.03195I 4.06352 − 4.09496I
u = 0.646992 + 0.531527I
a = 0.56058 − 1.76408I
b = −0.311585 − 0.887175I
−1.44328 + 2.03195I 4.06352 − 4.09496I
u = 0.646992 − 0.531527I
a = 0.519557 + 0.623716I
b = 0.433001 + 0.304309I
−1.44328 − 2.03195I 4.06352 + 4.09496I
u = 0.646992 − 0.531527I
a = 0.56058 + 1.76408I
b = −0.311585 + 0.887175I
−1.44328 − 2.03195I 4.06352 + 4.09496I
u = −1.202960 + 0.001367I
a = −1.087730 − 0.207618I
b = 0.670268 − 0.984132I
4.30187 − 1.96238I 11.59391 + 0.38403I
u = −1.202960 + 0.001367I
a = 0.589667 + 0.223844I
b = −0.860542 − 0.449534I
4.30187 − 1.96238I 11.59391 + 0.38403I
u = −1.202960 − 0.001367I
a = −1.087730 + 0.207618I
b = 0.670268 + 0.984132I
4.30187 + 1.96238I 11.59391 − 0.38403I
u = −1.202960 − 0.001367I
a = 0.589667 − 0.223844I
b = −0.860542 + 0.449534I
4.30187 + 1.96238I 11.59391 − 0.38403I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198859 + 1.266490I
a = 0.609392 − 0.394183I
b = 0.892109 − 0.416609I
6.03039 + 4.72345I 11.29654 − 3.13438I
u = −0.198859 + 1.266490I
a = 0.11900 − 1.60692I
b = −0.672303 − 1.023730I
6.03039 + 4.72345I 11.29654 − 3.13438I
u = −0.198859 − 1.266490I
a = 0.609392 + 0.394183I
b = 0.892109 + 0.416609I
6.03039 − 4.72345I 11.29654 + 3.13438I
u = −0.198859 − 1.266490I
a = 0.11900 + 1.60692I
b = −0.672303 + 1.023730I
6.03039 − 4.72345I 11.29654 + 3.13438I
u = 1.227290 + 0.381073I
a = 0.026410 − 0.616452I
b = −0.902498 + 0.379655I
3.49706 + 7.28997I 9.63030 − 6.08966I
u = 1.227290 + 0.381073I
a = −1.48730 + 1.05175I
b = 0.657960 + 1.053360I
3.49706 + 7.28997I 9.63030 − 6.08966I
u = 1.227290 − 0.381073I
a = 0.026410 + 0.616452I
b = −0.902498 − 0.379655I
3.49706 − 7.28997I 9.63030 + 6.08966I
u = 1.227290 − 0.381073I
a = −1.48730 − 1.05175I
b = 0.657960 − 1.053360I
3.49706 − 7.28997I 9.63030 + 6.08966I
u = 0.151614 + 0.623104I
a = 0.575026 + 0.389652I
b = 0.772697 + 0.348527I
0.16780 − 3.36417I 3.62130 + 3.50479I
u = 0.151614 + 0.623104I
a = 0.25504 + 1.68992I
b = −0.557905 + 1.003080I
0.16780 − 3.36417I 3.62130 + 3.50479I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.151614 − 0.623104I
a = 0.575026 − 0.389652I
b = 0.772697 − 0.348527I
0.16780 + 3.36417I 3.62130 − 3.50479I
u = 0.151614 − 0.623104I
a = 0.25504 − 1.68992I
b = −0.557905 − 1.003080I
0.16780 + 3.36417I 3.62130 − 3.50479I
u = −0.313036 + 0.506372I
a = −1.29037 + 2.02439I
b = 0.333105 + 1.047930I
−4.53431 + 0.51964I −2.41959 − 1.56914I
u = −0.313036 + 0.506372I
a = −0.77520 − 2.85106I
b = 0.236452 − 1.173590I
−4.53431 + 0.51964I −2.41959 − 1.56914I
u = −0.313036 − 0.506372I
a = −1.29037 − 2.02439I
b = 0.333105 − 1.047930I
−4.53431 − 0.51964I −2.41959 + 1.56914I
u = −0.313036 − 0.506372I
a = −0.77520 + 2.85106I
b = 0.236452 + 1.173590I
−4.53431 − 0.51964I −2.41959 + 1.56914I
u = −1.36499 + 0.44637I
a = 0.602581 + 0.409536I
b = −0.524339 − 0.670875I
5.04731 − 3.47045I 10.19300 + 0.53804I
u = −1.36499 + 0.44637I
a = 0.49345 + 1.70348I
b = −0.009584 + 1.306260I
5.04731 − 3.47045I 10.19300 + 0.53804I
u = −1.36499 − 0.44637I
a = 0.602581 − 0.409536I
b = −0.524339 + 0.670875I
5.04731 + 3.47045I 10.19300 − 0.53804I
u = −1.36499 − 0.44637I
a = 0.49345 − 1.70348I
b = −0.009584 − 1.306260I
5.04731 + 3.47045I 10.19300 − 0.53804I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35714 + 0.57417I
a = −0.60974 + 1.69144I
b = −0.195124 + 1.338750I
4.07948 + 7.82848I 8.18330 − 6.10894I
u = 1.35714 + 0.57417I
a = 1.62920 − 1.07081I
b = −0.542275 − 0.975573I
4.07948 + 7.82848I 8.18330 − 6.10894I
u = 1.35714 − 0.57417I
a = −0.60974 − 1.69144I
b = −0.195124 − 1.338750I
4.07948 − 7.82848I 8.18330 + 6.10894I
u = 1.35714 − 0.57417I
a = 1.62920 + 1.07081I
b = −0.542275 + 0.975573I
4.07948 − 7.82848I 8.18330 + 6.10894I
u = 0.476060
a = 4.34064 + 4.91932I
b = −0.135427 − 1.027140I
−2.06962 14.0180
u = 0.476060
a = 4.34064 − 4.91932I
b = −0.135427 + 1.027140I
−2.06962 14.0180
u = −1.40531 + 0.64765I
a = −0.341520 + 0.430658I
b = −0.957793 − 0.351336I
9.9177 − 11.5375I 11.79347 + 6.25344I
u = −1.40531 + 0.64765I
a = −1.11355 − 1.52043I
b = 0.676309 − 1.102780I
9.9177 − 11.5375I 11.79347 + 6.25344I
u = −1.40531 − 0.64765I
a = −0.341520 − 0.430658I
b = −0.957793 + 0.351336I
9.9177 + 11.5375I 11.79347 − 6.25344I
u = −1.40531 − 0.64765I
a = −1.11355 + 1.52043I
b = 0.676309 + 1.102780I
9.9177 + 11.5375I 11.79347 − 6.25344I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51942 + 0.37951I
a = −0.285426 − 0.453571I
b = 0.761601 − 0.938114I
11.95810 + 1.18611I 13.66994 + 0.I
u = 1.51942 + 0.37951I
a = 0.286276 − 0.384305I
b = −0.904045 − 0.555037I
11.95810 + 1.18611I 13.66994 + 0.I
u = 1.51942 − 0.37951I
a = −0.285426 + 0.453571I
b = 0.761601 + 0.938114I
11.95810 − 1.18611I 13.66994 + 0.I
u = 1.51942 − 0.37951I
a = 0.286276 + 0.384305I
b = −0.904045 + 0.555037I
11.95810 − 1.18611I 13.66994 + 0.I
19
III.
I
u
3
= hu
9
−2u
7
+u
5
+2u
3
+b−u, u
9
+u
8
+· · ·+a−1, u
10
−3u
8
+4u
6
−u
4
−u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
−u
9
− u
8
+ 2u
7
+ 3u
6
− 4u
4
− 4u
3
+ u
2
+ 3u + 1
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
a
12
=
u
−u
3
+ u
a
3
=
−u
9
− u
8
+ 2u
7
+ 3u
6
− 2u
5
− 4u
4
+ u
2
− u
−1
a
7
=
−u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ 2u + 1
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
a
9
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
0
a
10
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
1
=
u
7
− 2u
5
+ 2u
3
−u
9
+ 3u
7
− 3u
5
+ u
a
2
=
−u
9
− u
8
+ 3u
7
+ 3u
6
− 4u
5
− 4u
4
+ 2u
3
+ u
2
− u
−u
9
+ 3u
7
− 3u
5
+ u − 1
a
6
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
8
+ 8u
6
− 8u
4
− 4u
2
+ 4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
6
c
7
(u
2
+ 1)
5
c
4
, c
11
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
5
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
c
8
(u + 1)
10
c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y −1)
10
c
2
, c
3
, c
6
c
7
(y + 1)
10
c
4
, c
11
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
5
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
c
9
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822375 + 0.339110I
a = 0.005676 − 0.212799I
b = − 1.000000I
−2.96077 − 1.53058I 0.51511 + 4.43065I
u = −0.822375 − 0.339110I
a = 0.005676 + 0.212799I
b = 1.000000I
−2.96077 + 1.53058I 0.51511 − 4.43065I
u = 0.822375 + 0.339110I
a = 1.78720 − 1.99432I
b = − 1.000000I
−2.96077 + 1.53058I 0.51511 − 4.43065I
u = 0.822375 − 0.339110I
a = 1.78720 + 1.99432I
b = 1.000000I
−2.96077 − 1.53058I 0.51511 + 4.43065I
u = 0.766826I
a = −1.70062 + 3.70062I
b = 1.000000I
−0.888787 1.48110
u = − 0.766826I
a = −1.70062 − 3.70062I
b = − 1.000000I
−0.888787 1.48110
u = −1.200150 + 0.455697I
a = 0.85660 + 1.94886I
b = 1.000000I
2.58269 − 4.40083I 4.74431 + 3.49859I
u = −1.200150 − 0.455697I
a = 0.85660 − 1.94886I
b = − 1.000000I
2.58269 + 4.40083I 4.74431 − 3.49859I
u = 1.200150 + 0.455697I
a = 0.051139 + 1.143400I
b = 1.000000I
2.58269 + 4.40083I 4.74431 − 3.49859I
u = 1.200150 − 0.455697I
a = 0.051139 − 1.143400I
b = − 1.000000I
2.58269 − 4.40083I 4.74431 + 3.49859I
23
IV. I
v
1
= ha, 2v
3
+ v
2
+ b + 3v + 1, 2v
4
+ 3v
3
+ 4v
2
+ 3v + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
v
0
a
5
=
1
0
a
8
=
0
−2v
3
− v
2
− 3v − 1
a
12
=
v
0
a
3
=
1
−4v
3
− 4v
2
− 5v − 3
a
7
=
2v
3
+ v
2
+ 3v + 1
−2v
3
− v
2
− 3v − 1
a
9
=
2v
2
+ v + 2
−2v
3
− 3v
2
− 4v − 3
a
10
=
2v
2
+ 2v + 2
−2v
3
− 3v
2
− 4v − 3
a
1
=
−2v
2
− v − 2
2v
3
+ 3v
2
+ 4v + 3
a
2
=
4v
3
+ 2v
2
+ 4v + 1
−4v
3
− 2v
2
− 4v
a
6
=
−4v
3
− 6v
2
− 6v − 4
6v
3
+ 7v
2
+ 9v + 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10v
3
+ 7v + 9
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
3
u
4
+ u
2
+ u + 1
c
4
, c
11
u
4
c
5
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
6
, c
7
u
4
+ u
2
− u + 1
c
8
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
9
, c
10
(u + 1)
4
c
12
(u − 1)
4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
3
, c
6
c
7
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
4
, c
11
y
4
c
5
y
4
− y
3
+ 2y
2
+ 7y + 4
c
9
, c
10
, c
12
(y − 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.173850 + 1.069070I
a = 0
b = −0.547424 − 0.585652I
2.62503 + 1.39709I 13.6914 − 3.7657I
v = −0.173850 − 1.069070I
a = 0
b = −0.547424 + 0.585652I
2.62503 − 1.39709I 13.6914 + 3.7657I
v = −0.576150 + 0.307015I
a = 0
b = 0.547424 − 1.120870I
−0.98010 − 7.64338I 4.68363 + 4.91712I
v = −0.576150 − 0.307015I
a = 0
b = 0.547424 + 1.120870I
−0.98010 + 7.64338I 4.68363 − 4.91712I
27
V. I
v
2
= ha, v
2
b + b
2
+ bv − b − v, v
3
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
v
0
a
5
=
1
0
a
8
=
0
b
a
12
=
v
0
a
3
=
1
−v
2
b − bv + b + v
a
7
=
−b
b
a
9
=
v
2
+ b − 1
−v
2
+ 1
a
10
=
v
2
+ b + v − 1
−v
2
+ 1
a
1
=
−v
2
− b + 1
v
2
− 1
a
2
=
−v
2
b − bv − v
2
+ 2
−1
a
6
=
−v
2
b + v
2
+ b + v
−v
2
− v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v
2
+ v + 9
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
3
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
4
, c
11
u
6
c
5
(u
3
− u
2
+ 1)
2
c
6
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
9
, c
10
(u + 1)
6
c
12
(u − 1)
6
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
3
, c
6
c
7
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
4
, c
11
y
6
c
5
(y
3
− y
2
+ 2y − 1)
2
c
9
, c
10
, c
12
(y − 1)
6
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.662359 + 0.562280I
a = 0
b = −0.498832 − 1.001300I
1.37919 + 2.82812I 9.17211 − 2.41717I
v = 0.662359 + 0.562280I
a = 0
b = 0.713912 − 0.305839I
1.37919 + 2.82812I 9.17211 − 2.41717I
v = 0.662359 − 0.562280I
a = 0
b = −0.498832 + 1.001300I
1.37919 − 2.82812I 9.17211 + 2.41717I
v = 0.662359 − 0.562280I
a = 0
b = 0.713912 + 0.305839I
1.37919 − 2.82812I 9.17211 + 2.41717I
v = −1.32472
a = 0
b = 0.284920 + 1.115140I
−2.75839 0.655770
v = −1.32472
a = 0
b = 0.284920 − 1.115140I
−2.75839 0.655770
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
44
+ 18u
43
+ ··· + 11u + 1)(u
64
+ 34u
63
+ ··· + 2888u + 289)
c
2
, c
3
(u
2
+ 1)
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
44
+ 9u
42
+ ··· − 3u + 1)(u
64
− 2u
63
+ ··· + 6u + 17)
c
4
, c
11
u
10
(u
10
− 3u
8
+ ··· − u
2
+ 1)(u
32
− u
31
+ ··· + 4u + 8)
2
· (u
44
+ 3u
43
+ ··· − 48u − 64)
c
5
((u
3
− u
2
+ 1)
2
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
10
+ u
8
+ ··· + 3u
2
+ 1)
· ((u
32
+ 6u
31
+ ··· − 29u + 19)
2
)(u
44
− 18u
43
+ ··· − 28060u + 2284)
c
6
, c
7
(u
2
+ 1)
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
44
+ 9u
42
+ ··· − 3u + 1)(u
64
− 2u
63
+ ··· + 6u + 17)
c
8
(u + 1)
10
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
44
+ 18u
43
+ ··· + 11u + 1)(u
64
+ 34u
63
+ ··· + 2888u + 289)
c
9
, c
10
((u + 1)
10
)(u
5
− u
4
+ ··· + u + 1)
2
(u
32
+ 4u
31
+ ··· − 2u − 1)
2
· (u
44
+ 5u
43
+ ··· − 11u − 4)
c
12
((u − 1)
10
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
32
+ 4u
31
+ ··· − 2u − 1)
2
· (u
44
+ 5u
43
+ ··· − 11u − 4)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y − 1)
10
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
44
+ 30y
43
+ ··· − 117y + 1)
· (y
64
− 10y
63
+ ··· + 2113164y + 83521)
c
2
, c
3
, c
6
c
7
(y + 1)
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
44
+ 18y
43
+ ··· + 11y + 1)(y
64
+ 34y
63
+ ··· + 2888y + 289)
c
4
, c
11
y
10
(y
5
− 3y
4
+ ··· − y + 1)
2
(y
32
− 21y
31
+ ··· − 400y + 64)
2
· (y
44
− 27y
43
+ ··· − 8448y + 4096)
c
5
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
· (y
32
+ 18y
31
+ ··· − 14597y + 361)
2
· (y
44
+ 20y
43
+ ··· − 118969272y + 5216656)
c
9
, c
10
, c
12
(y − 1)
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· ((y
32
− 32y
31
+ ··· + 10y + 1)
2
)(y
44
− 43y
43
+ ··· − 337y + 16)
33
