11a
329
(K11a
329
)
A knot diagram
1
Linearized knot diagam
9 6 1 8 10 2 5 11 3 7 4
Solving Sequence
4,8 5,11
9 1 2 3 7 6 10
c
4
c
8
c
11
c
1
c
3
c
7
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 7480949u
26
+ 102501940u
25
+ ··· + 35850519a + 58313900, u
27
+ u
26
+ ··· + 4u − 1i
I
u
2
= h−1.25488 × 10
119
u
63
− 5.93390 × 10
119
u
62
+ ··· + 1.36032 × 10
119
b − 4.57609 × 10
119
,
− 7.61826 × 10
119
u
63
− 3.45060 × 10
120
u
62
+ ··· + 4.08097 × 10
119
a + 8.20476 × 10
119
,
u
64
+ 5u
63
+ ··· + 9u + 1i
I
u
3
= hb + u, u
2
+ a + u, u
3
+ u − 1i
I
u
4
= hb + u, −2u
7
+ u
6
− 7u
5
+ u
4
− 10u
3
+ a − 7u, u
8
− u
7
+ 4u
6
− 2u
5
+ 6u
4
− 2u
3
+ 5u
2
− u + 1i
I
u
5
= hu
6
− u
5
+ 3u
4
− 7u
3
+ 6u
2
+ 2b − 10u + 5, −5u
7
− 22u
5
+ 12u
4
− 41u
3
+ 24u
2
+ 6a − 27u + 11,
u
8
+ 5u
6
− 3u
5
+ 10u
4
− 9u
3
+ 9u
2
− 7u + 3i
* 5 irreducible components of dim
C
= 0, with total 110 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
= hb − u, 7.48 × 10
6
u
26
+ 1.03 × 10
8
u
25
+ · · · + 3.59 × 10
7
a + 5.83 ×
10
7
, u
27
+ u
26
+ · · · + 4u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
−0.208671u
26
− 2.85915u
25
+ ··· + 7.44217u − 1.62658
u
a
9
=
−3.27801u
26
+ 5.32766u
25
+ ··· + 46.4586u − 8.94242
1.20999u
26
− 3.00055u
25
+ ··· − 9.39324u + 2.65048
a
1
=
−0.208671u
26
− 2.85915u
25
+ ··· + 6.44217u − 1.62658
u
a
2
=
−2.58876u
26
− 0.102742u
25
+ ··· − 3.92105u − 2.07685
0.977408u
26
+ 0.220438u
25
+ ··· − 3.89929u + 0.517993
a
3
=
2.65048u
26
+ 3.86047u
25
+ ··· + 0.791902u + 1.20867
−u
2
a
7
=
u
u
3
+ u
a
6
=
3.03935u
26
+ 5.72431u
25
+ ··· + 8.43055u − 4.17643
−0.810224u
26
− 2.02363u
25
+ ··· − 2.57059u + 0.767074
a
10
=
−0.606939u
26
− 0.979932u
25
+ ··· + 15.1011u − 3.18665
0.175698u
26
− 1.25035u
25
+ ··· − 0.849262u + 0.717414
a
10
=
−0.606939u
26
− 0.979932u
25
+ ··· + 15.1011u − 3.18665
0.175698u
26
− 1.25035u
25
+ ··· − 0.849262u + 0.717414
(ii) Obstruction class = −1
(iii) Cusp Shapes =
26113891
3983391
u
26
+
16946267
3983391
u
25
+ ··· −
13443049
442599
u −
51593591
3983391
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
27
− 2u
26
+ ··· − 10u + 3
c
2
, c
6
u
27
+ 8u
26
+ ··· + 110u + 12
c
3
, c
4
, c
7
c
11
u
27
− u
26
+ ··· + 4u + 1
c
5
, c
9
u
27
+ 12u
25
+ ··· + 15u
2
+ 1
c
8
u
27
− 20u
26
+ ··· − 1284u + 180
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
27
+ 4y
26
+ ··· + 4y −9
c
2
, c
6
y
27
+ 14y
26
+ ··· + 700y −144
c
3
, c
4
, c
7
c
11
y
27
+ 27y
26
+ ··· − 4y −1
c
5
, c
9
y
27
+ 24y
26
+ ··· − 30y −1
c
8
y
27
− 2y
26
+ ··· + 561816y −32400
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886580 + 0.019207I
a = −1.057340 + 0.497197I
b = −0.886580 + 0.019207I
0.96030 + 6.99778I −11.49841 − 6.31594I
u = −0.886580 − 0.019207I
a = −1.057340 − 0.497197I
b = −0.886580 − 0.019207I
0.96030 − 6.99778I −11.49841 + 6.31594I
u = −0.236028 + 1.095620I
a = −0.798201 + 0.061958I
b = −0.236028 + 1.095620I
4.10301 − 1.11169I −6.68347 + 2.36909I
u = −0.236028 − 1.095620I
a = −0.798201 − 0.061958I
b = −0.236028 − 1.095620I
4.10301 + 1.11169I −6.68347 − 2.36909I
u = 0.868007 + 0.115359I
a = 0.768649 − 0.417549I
b = 0.868007 + 0.115359I
−2.19193 + 1.02446I −11.23776 − 6.18138I
u = 0.868007 − 0.115359I
a = 0.768649 + 0.417549I
b = 0.868007 − 0.115359I
−2.19193 − 1.02446I −11.23776 + 6.18138I
u = −0.003006 + 1.229040I
a = 1.65700 − 1.48184I
b = −0.003006 + 1.229040I
9.55943 + 6.00813I −1.22265 − 6.13894I
u = −0.003006 − 1.229040I
a = 1.65700 + 1.48184I
b = −0.003006 − 1.229040I
9.55943 − 6.00813I −1.22265 + 6.13894I
u = −0.045846 + 1.255570I
a = −1.24858 − 0.95153I
b = −0.045846 + 1.255570I
6.76407 − 1.62647I −5.58254 + 2.60825I
u = −0.045846 − 1.255570I
a = −1.24858 + 0.95153I
b = −0.045846 − 1.255570I
6.76407 + 1.62647I −5.58254 − 2.60825I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029913 + 1.343500I
a = 0.37553 − 1.49753I
b = −0.029913 + 1.343500I
9.97119 − 1.49427I 0.080207 + 0.920031I
u = −0.029913 − 1.343500I
a = 0.37553 + 1.49753I
b = −0.029913 − 1.343500I
9.97119 + 1.49427I 0.080207 − 0.920031I
u = 0.524847 + 1.241400I
a = 0.633730 − 0.220695I
b = 0.524847 + 1.241400I
2.50522 − 4.33326I −7.76207 − 3.39042I
u = 0.524847 − 1.241400I
a = 0.633730 + 0.220695I
b = 0.524847 − 1.241400I
2.50522 + 4.33326I −7.76207 + 3.39042I
u = −0.580317 + 0.090563I
a = −0.597417 + 1.252030I
b = −0.580317 + 0.090563I
3.08469 − 2.64958I −9.08747 + 2.09938I
u = −0.580317 − 0.090563I
a = −0.597417 − 1.252030I
b = −0.580317 − 0.090563I
3.08469 + 2.64958I −9.08747 − 2.09938I
u = 0.10388 + 1.45531I
a = 0.370550 − 0.378802I
b = 0.10388 + 1.45531I
10.25310 − 0.47528I −1.44372 + 0.I
u = 0.10388 − 1.45531I
a = 0.370550 + 0.378802I
b = 0.10388 − 1.45531I
10.25310 + 0.47528I −1.44372 + 0.I
u = −0.45771 + 1.48529I
a = −0.908211 − 0.286969I
b = −0.45771 + 1.48529I
12.64960 + 6.10710I −1.83403 − 3.86721I
u = −0.45771 − 1.48529I
a = −0.908211 + 0.286969I
b = −0.45771 − 1.48529I
12.64960 − 6.10710I −1.83403 + 3.86721I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.47966 + 1.48279I
a = −1.135590 − 0.392236I
b = −0.47966 + 1.48279I
10.7046 + 17.4305I −4.97020 − 8.80041I
u = −0.47966 − 1.48279I
a = −1.135590 + 0.392236I
b = −0.47966 − 1.48279I
10.7046 − 17.4305I −4.97020 + 8.80041I
u = 0.47037 + 1.48644I
a = 1.021560 − 0.423137I
b = 0.47037 + 1.48644I
7.11389 − 11.36350I −6.87134 + 6.73077I
u = 0.47037 − 1.48644I
a = 1.021560 + 0.423137I
b = 0.47037 − 1.48644I
7.11389 + 11.36350I −6.87134 − 6.73077I
u = 0.275286
a = −0.867193
b = 0.275286
−0.622366 −16.1230
u = 0.114320 + 0.213263I
a = −1.14807 + 5.10834I
b = 0.114320 + 0.213263I
−1.14394 + 1.30778I −18.3250 − 4.6536I
u = 0.114320 − 0.213263I
a = −1.14807 − 5.10834I
b = 0.114320 − 0.213263I
−1.14394 − 1.30778I −18.3250 + 4.6536I
7
II. I
u
2
= h−1.25 × 10
119
u
63
− 5.93 × 10
119
u
62
+ · · · + 1.36 × 10
119
b − 4.58 ×
10
119
, −7.62 × 10
119
u
63
− 3.45 × 10
120
u
62
+ · · · + 4.08 × 10
119
a + 8.20 ×
10
119
, u
64
+ 5u
63
+ · · · + 9u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
1.86678u
63
+ 8.45535u
62
+ ··· + 13.0919u − 2.01050
0.922490u
63
+ 4.36213u
62
+ ··· + 19.0193u + 3.36397
a
9
=
−2.07092u
63
− 9.95817u
62
+ ··· − 51.5217u − 6.64500
−0.765928u
63
− 3.73638u
62
+ ··· − 20.4529u − 4.25401
a
1
=
0.944287u
63
+ 4.09322u
62
+ ··· − 5.92732u − 5.37447
0.922490u
63
+ 4.36213u
62
+ ··· + 19.0193u + 3.36397
a
2
=
−1.92058u
63
− 9.65347u
62
+ ··· − 55.0762u − 11.3256
0.0555653u
63
+ 0.244446u
62
+ ··· + 4.82412u + 0.229347
a
3
=
5.08294u
63
+ 24.8391u
62
+ ··· + 104.384u + 17.2019
−0.828932u
63
− 4.33500u
62
+ ··· − 13.7757u + 0.631299
a
7
=
u
u
3
+ u
a
6
=
−3.21107u
63
− 15.6228u
62
+ ··· − 65.7787u − 11.6119
0.348757u
63
+ 1.59825u
62
+ ··· + 16.3904u + 1.14200
a
10
=
1.54638u
63
+ 7.15847u
62
+ ··· + 9.16166u − 2.57721
0.647718u
63
+ 2.94801u
62
+ ··· + 12.6636u + 2.49217
a
10
=
1.54638u
63
+ 7.15847u
62
+ ··· + 9.16166u − 2.57721
0.647718u
63
+ 2.94801u
62
+ ··· + 12.6636u + 2.49217
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.07366u
63
− 4.33095u
62
+ ··· + 40.1271u + 1.41454
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
64
+ 2u
63
+ ··· − 126u + 177
c
2
, c
6
(u
32
− 3u
31
+ ··· − 10u + 3)
2
c
3
, c
4
, c
7
c
11
u
64
− 5u
63
+ ··· − 9u + 1
c
5
, c
9
u
64
− u
63
+ ··· − 16935u + 15481
c
8
(u
32
+ 10u
31
+ ··· + 99u + 19)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
64
+ 4y
63
+ ··· + 305202y + 31329
c
2
, c
6
(y
32
+ 21y
31
+ ··· + 74y + 9)
2
c
3
, c
4
, c
7
c
11
y
64
+ 49y
63
+ ··· − 3y + 1
c
5
, c
9
y
64
+ 11y
63
+ ··· + 3729627377y + 239661361
c
8
(y
32
+ 18y
31
+ ··· + 3461y + 361)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.920222 + 0.395412I
a = −0.129317 + 1.135090I
b = −0.151131 + 1.300520I
3.42651 + 2.86570I −5.40728 − 4.03056I
u = 0.920222 − 0.395412I
a = −0.129317 − 1.135090I
b = −0.151131 − 1.300520I
3.42651 − 2.86570I −5.40728 + 4.03056I
u = −0.063212 + 0.940817I
a = 0.717133 + 0.574436I
b = 0.804979 − 0.202940I
−0.168876 + 0.846731I −12.88022 − 0.77932I
u = −0.063212 − 0.940817I
a = 0.717133 − 0.574436I
b = 0.804979 + 0.202940I
−0.168876 − 0.846731I −12.88022 + 0.77932I
u = 0.294249 + 1.039510I
a = −1.105040 + 0.363187I
b = −0.685111 − 0.128372I
1.25382 − 4.32436I 0
u = 0.294249 − 1.039510I
a = −1.105040 − 0.363187I
b = −0.685111 + 0.128372I
1.25382 + 4.32436I 0
u = 0.804979 + 0.202940I
a = −0.872180 − 0.573156I
b = −0.063212 − 0.940817I
−0.168876 − 0.846731I −12.88022 + 0.77932I
u = 0.804979 − 0.202940I
a = −0.872180 + 0.573156I
b = −0.063212 + 0.940817I
−0.168876 + 0.846731I −12.88022 − 0.77932I
u = −0.271195 + 1.153980I
a = 1.63456 + 0.62464I
b = 0.336277 − 1.364760I
4.73825 + 4.95632I 0
u = −0.271195 − 1.153980I
a = 1.63456 − 0.62464I
b = 0.336277 + 1.364760I
4.73825 − 4.95632I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.053296 + 1.199700I
a = 0.715928 + 0.774703I
b = 0.42436 − 1.68610I
5.82389 + 3.48280I 0
u = −0.053296 − 1.199700I
a = 0.715928 − 0.774703I
b = 0.42436 + 1.68610I
5.82389 − 3.48280I 0
u = −0.087790 + 1.202470I
a = −0.397620 + 0.281730I
b = −1.04393 − 1.82190I
8.11459 + 3.37630I 0
u = −0.087790 − 1.202470I
a = −0.397620 − 0.281730I
b = −1.04393 + 1.82190I
8.11459 − 3.37630I 0
u = −0.612602 + 0.471856I
a = 0.025706 + 1.164300I
b = 0.232794 + 1.231510I
2.52109 − 1.66996I −6.36037 − 2.48874I
u = −0.612602 − 0.471856I
a = 0.025706 − 1.164300I
b = 0.232794 − 1.231510I
2.52109 + 1.66996I −6.36037 + 2.48874I
u = 0.452635 + 1.145970I
a = −1.69479 + 0.14216I
b = −0.297614 − 1.338770I
5.87133 − 7.92548I 0
u = 0.452635 − 1.145970I
a = −1.69479 − 0.14216I
b = −0.297614 + 1.338770I
5.87133 + 7.92548I 0
u = −0.201492 + 1.219100I
a = −0.686845 + 0.005818I
b = −1.382930 + 0.232456I
6.90028 + 0.03721I 0
u = −0.201492 − 1.219100I
a = −0.686845 − 0.005818I
b = −1.382930 − 0.232456I
6.90028 − 0.03721I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.197290 + 0.312647I
a = −0.707406 + 0.535648I
b = −0.398045 + 1.299040I
5.08314 + 11.58170I 0
u = −1.197290 − 0.312647I
a = −0.707406 − 0.535648I
b = −0.398045 − 1.299040I
5.08314 − 11.58170I 0
u = 0.232794 + 1.231510I
a = −0.633433 + 0.339154I
b = −0.612602 + 0.471856I
2.52109 − 1.66996I 0
u = 0.232794 − 1.231510I
a = −0.633433 − 0.339154I
b = −0.612602 − 0.471856I
2.52109 + 1.66996I 0
u = −0.339847 + 1.221780I
a = 0.956485 − 0.589998I
b = 0.120701 − 0.199374I
6.38478 + 6.22988I 0
u = −0.339847 − 1.221780I
a = 0.956485 + 0.589998I
b = 0.120701 + 0.199374I
6.38478 − 6.22988I 0
u = 0.276431 + 1.243720I
a = −0.639083 − 0.172102I
b = −0.230618 + 0.105542I
2.72784 − 2.52152I 0
u = 0.276431 − 1.243720I
a = −0.639083 + 0.172102I
b = −0.230618 − 0.105542I
2.72784 + 2.52152I 0
u = 0.397836 + 1.218830I
a = 0.644295 − 0.250433I
b = 1.211970 + 0.440132I
1.24375 − 5.55297I 0
u = 0.397836 − 1.218830I
a = 0.644295 + 0.250433I
b = 1.211970 − 0.440132I
1.24375 + 5.55297I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.211970 + 0.440132I
a = 0.590869 + 0.351158I
b = 0.397836 + 1.218830I
1.24375 − 5.55297I 0
u = 1.211970 − 0.440132I
a = 0.590869 − 0.351158I
b = 0.397836 − 1.218830I
1.24375 + 5.55297I 0
u = −0.685111 + 0.128372I
a = 1.26615 − 1.28343I
b = 0.294249 − 1.039510I
1.25382 + 4.32436I −10.17044 − 8.05596I
u = −0.685111 − 0.128372I
a = 1.26615 + 1.28343I
b = 0.294249 + 1.039510I
1.25382 − 4.32436I −10.17044 + 8.05596I
u = −0.151131 + 1.300520I
a = 0.803730 + 0.343215I
b = 0.920222 + 0.395412I
3.42651 + 2.86570I 0
u = −0.151131 − 1.300520I
a = 0.803730 − 0.343215I
b = 0.920222 − 0.395412I
3.42651 − 2.86570I 0
u = 0.090336 + 1.330560I
a = −0.986962 + 0.344993I
b = −0.62803 − 1.48659I
11.25570 − 7.19139I 0
u = 0.090336 − 1.330560I
a = −0.986962 − 0.344993I
b = −0.62803 + 1.48659I
11.25570 + 7.19139I 0
u = −0.398045 + 1.299040I
a = −0.753479 − 0.292200I
b = −1.197290 + 0.312647I
5.08314 + 11.58170I 0
u = −0.398045 − 1.299040I
a = −0.753479 + 0.292200I
b = −1.197290 − 0.312647I
5.08314 − 11.58170I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.297614 + 1.338770I
a = 1.48376 + 0.36485I
b = 0.452635 − 1.145970I
5.87133 + 7.92548I 0
u = −0.297614 − 1.338770I
a = 1.48376 − 0.36485I
b = 0.452635 + 1.145970I
5.87133 − 7.92548I 0
u = −1.382930 + 0.232456I
a = −0.191453 + 0.574145I
b = −0.201492 + 1.219100I
6.90028 + 0.03721I 0
u = −1.382930 − 0.232456I
a = −0.191453 − 0.574145I
b = −0.201492 − 1.219100I
6.90028 − 0.03721I 0
u = 0.336277 + 1.364760I
a = −1.38413 + 0.51193I
b = −0.271195 − 1.153980I
4.73825 − 4.95632I 0
u = 0.336277 − 1.364760I
a = −1.38413 − 0.51193I
b = −0.271195 + 1.153980I
4.73825 + 4.95632I 0
u = −0.39852 + 1.36564I
a = 0.121970 − 0.518027I
b = −0.214549 + 0.185839I
5.08106 − 2.21530I 0
u = −0.39852 − 1.36564I
a = 0.121970 + 0.518027I
b = −0.214549 − 0.185839I
5.08106 + 2.21530I 0
u = −0.269264 + 0.401570I
a = 1.63873 + 1.71309I
b = 0.463669 + 0.019406I
−1.16995 + 1.22634I −14.0955 − 5.1640I
u = −0.269264 − 0.401570I
a = 1.63873 − 1.71309I
b = 0.463669 − 0.019406I
−1.16995 − 1.22634I −14.0955 + 5.1640I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.463669 + 0.019406I
a = −2.41332 + 0.52542I
b = −0.269264 + 0.401570I
−1.16995 + 1.22634I −14.0955 − 5.1640I
u = 0.463669 − 0.019406I
a = −2.41332 − 0.52542I
b = −0.269264 − 0.401570I
−1.16995 − 1.22634I −14.0955 + 5.1640I
u = −0.62803 + 1.48659I
a = 0.863992 + 0.003752I
b = 0.090336 − 1.330560I
11.25570 + 7.19139I 0
u = −0.62803 − 1.48659I
a = 0.863992 − 0.003752I
b = 0.090336 + 1.330560I
11.25570 − 7.19139I 0
u = −0.214549 + 0.185839I
a = −0.89406 − 2.51300I
b = −0.39852 + 1.36564I
5.08106 − 2.21530I −7.36537 + 6.15916I
u = −0.214549 − 0.185839I
a = −0.89406 + 2.51300I
b = −0.39852 − 1.36564I
5.08106 + 2.21530I −7.36537 − 6.15916I
u = 0.42436 + 1.68610I
a = −0.591850 + 0.424891I
b = −0.053296 − 1.199700I
5.82389 − 3.48280I 0
u = 0.42436 − 1.68610I
a = −0.591850 − 0.424891I
b = −0.053296 + 1.199700I
5.82389 + 3.48280I 0
u = −0.230618 + 0.105542I
a = −1.51626 + 2.95895I
b = 0.276431 + 1.243720I
2.72784 − 2.52152I −6.98017 + 1.90432I
u = −0.230618 − 0.105542I
a = −1.51626 − 2.95895I
b = 0.276431 − 1.243720I
2.72784 + 2.52152I −6.98017 − 1.90432I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.120701 + 0.199374I
a = −4.14581 − 4.49501I
b = −0.339847 − 1.221780I
6.38478 − 6.22988I −5.40289 + 5.47727I
u = 0.120701 − 0.199374I
a = −4.14581 + 4.49501I
b = −0.339847 + 1.221780I
6.38478 + 6.22988I −5.40289 − 5.47727I
u = −1.04393 + 1.82190I
a = 0.279733 + 0.006501I
b = −0.087790 − 1.202470I
8.11459 − 3.37630I 0
u = −1.04393 − 1.82190I
a = 0.279733 − 0.006501I
b = −0.087790 + 1.202470I
8.11459 + 3.37630I 0
17
III. I
u
3
= hb + u, u
2
+ a + u, u
3
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
−u
2
− u
−u
a
9
=
u
2
− 2u
u
2
+ u − 1
a
1
=
−u
2
−u
a
2
=
u
2
+ u − 1
−u
2
+ u − 1
a
3
=
u
−u
2
a
7
=
u
1
a
6
=
u
2
− u + 1
u
2
a
10
=
−u
0
a
10
=
−u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
− 9u − 9
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
u
3
+ u + 1
c
2
, c
4
, c
11
u
3
+ u − 1
c
5
, c
9
u
3
− 3u
2
+ 4u − 1
c
8
u
3
− u
2
+ 4u − 3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
10
, c
11
y
3
+ 2y
2
+ y −1
c
5
, c
9
y
3
− y
2
+ 10y −1
c
8
y
3
+ 7y
2
+ 10y −9
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.341164 + 1.161540I
a = 1.57395 − 0.36899I
b = 0.341164 − 1.161540I
7.76697 + 7.91583I −2.23117 − 8.07622I
u = −0.341164 − 1.161540I
a = 1.57395 + 0.36899I
b = 0.341164 + 1.161540I
7.76697 − 7.91583I −2.23117 + 8.07622I
u = 0.682328
a = −1.14790
b = −0.682328
−2.37447 −16.5380
21
IV. I
u
4
= hb + u, −2u
7
+ u
6
− 7u
5
+ u
4
− 10u
3
+ a − 7u, u
8
− u
7
+ 4u
6
−
2u
5
+ 6u
4
− 2u
3
+ 5u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
2u
7
− u
6
+ 7u
5
− u
4
+ 10u
3
+ 7u
−u
a
9
=
4u
7
− 2u
6
+ 12u
5
− u
4
+ 16u
3
+ 10u + 1
−u
6
− 2u
4
− u
3
− 3u
2
− 1
a
1
=
2u
7
− u
6
+ 7u
5
− u
4
+ 10u
3
+ 8u
−u
a
2
=
−u
6
− u
5
− 3u
4
− 2u
3
− 5u
2
− 2u − 3
−u
7
− 2u
5
− u
4
− 2u
3
− u
2
− u
a
3
=
u
7
− u
6
+ 3u
5
− 2u
4
+ 4u
3
− 2u
2
+ 2u − 1
−u
2
a
7
=
u
u
3
+ u
a
6
=
u
7
− 2u
6
+ 5u
5
− 5u
4
+ 7u
3
− 6u
2
+ 6u − 3
u
2
a
10
=
3u
7
− 2u
6
+ 10u
5
− 2u
4
+ 13u
3
− u
2
+ 9u
0
a
10
=
3u
7
− 2u
6
+ 10u
5
− 2u
4
+ 13u
3
− u
2
+ 9u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
6
+ u
5
− 2u
4
+ 3u
3
+ 2u
2
+ 7u + 1
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
+ 2u
7
+ 2u
6
+ 3u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1
c
2
u
8
+ 3u
7
+ 6u
6
+ 8u
5
+ 8u
4
+ 7u
3
+ 5u
2
+ 2u + 1
c
3
, c
7
u
8
+ u
7
+ 4u
6
+ 2u
5
+ 6u
4
+ 2u
3
+ 5u
2
+ u + 1
c
4
, c
11
u
8
− u
7
+ 4u
6
− 2u
5
+ 6u
4
− 2u
3
+ 5u
2
− u + 1
c
5
, c
9
u
8
+ 3u
7
+ 4u
6
+ 5u
5
+ 5u
4
+ 4u
3
+ 4u
2
+ 2u + 1
c
6
u
8
− 3u
7
+ 6u
6
− 8u
5
+ 8u
4
− 7u
3
+ 5u
2
− 2u + 1
c
8
u
8
− 6u
7
+ 19u
6
− 35u
5
+ 38u
4
− 25u
3
+ 10u
2
− 2u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
8
− 2y
6
− 3y
5
+ y
4
+ 7y
3
+ 9y
2
+ 5y + 1
c
2
, c
6
y
8
+ 3y
7
+ 4y
6
+ 2y
4
+ 11y
3
+ 13y
2
+ 6y + 1
c
3
, c
4
, c
7
c
11
y
8
+ 7y
7
+ 24y
6
+ 50y
5
+ 68y
4
+ 60y
3
+ 33y
2
+ 9y + 1
c
5
, c
9
y
8
− y
7
− 4y
6
− y
5
+ 7y
4
+ 12y
3
+ 10y
2
+ 4y + 1
c
8
y
8
+ 2y
7
+ 17y
6
− 61y
5
+ 52y
4
+ 33y
3
+ 76y
2
+ 16y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506251 + 0.960489I
a = 0.249506 − 0.196383I
b = 0.506251 − 0.960489I
5.85877 − 1.31073I −1.64360 + 0.98117I
u = −0.506251 − 0.960489I
a = 0.249506 + 0.196383I
b = 0.506251 + 0.960489I
5.85877 + 1.31073I −1.64360 − 0.98117I
u = 0.302896 + 1.275450I
a = −1.64863 + 0.55513I
b = −0.302896 − 1.275450I
5.44517 − 5.83722I −3.39356 + 6.57107I
u = 0.302896 − 1.275450I
a = −1.64863 − 0.55513I
b = −0.302896 + 1.275450I
5.44517 + 5.83722I −3.39356 − 6.57107I
u = 0.584835 + 1.175860I
a = −0.684107 + 0.080025I
b = −0.584835 − 1.175860I
2.64533 − 4.83456I −3.93301 + 10.95748I
u = 0.584835 − 1.175860I
a = −0.684107 − 0.080025I
b = −0.584835 + 1.175860I
2.64533 + 4.83456I −3.93301 − 10.95748I
u = 0.118520 + 0.521695I
a = 0.08323 + 2.62717I
b = −0.118520 − 0.521695I
−0.789792 + 1.148200I 0.97016 + 3.66325I
u = 0.118520 − 0.521695I
a = 0.08323 − 2.62717I
b = −0.118520 + 0.521695I
−0.789792 − 1.148200I 0.97016 − 3.66325I
25
V. I
u
5
= hu
6
− u
5
+ 3u
4
− 7u
3
+ 6u
2
+ 2b − 10u + 5, −5u
7
− 22u
5
+ · · · +
6a + 11, u
8
+ 5u
6
− 3u
5
+ 10u
4
− 9u
3
+ 9u
2
− 7u + 3i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
5
6
u
7
+
11
3
u
5
+ ··· +
9
2
u −
11
6
−
1
2
u
6
+
1
2
u
5
+ ··· + 5u −
5
2
a
9
=
−
1
6
u
7
−
1
3
u
5
+ ··· +
3
2
u +
1
6
1
2
u
7
+ 2u
5
+ ··· +
5
2
u +
1
2
a
1
=
5
6
u
7
+
1
2
u
6
+ ··· −
1
2
u +
2
3
−
1
2
u
6
+
1
2
u
5
+ ··· + 5u −
5
2
a
2
=
2
3
u
7
+ u
6
+ ··· − 3u +
13
3
−
1
2
u
7
−
1
2
u
6
+ ··· +
5
2
u + 1
a
3
=
−
7
6
u
7
+ u
6
+ ··· −
13
2
u +
19
6
u
7
−
1
2
u
6
+ ··· + 4u +
1
2
a
7
=
u
u
3
+ u
a
6
=
1
6
u
7
+ 2u
6
+ ··· −
9
2
u +
5
6
u
7
− u
6
+ 5u
5
− 6u
4
+ 13u
3
− 11u
2
+ 11u − 5
a
10
=
5
6
u
7
+ u
6
+ ··· −
3
2
u +
7
6
−
1
2
u
6
+
1
2
u
5
+ ··· + 6u −
5
2
a
10
=
5
6
u
7
+ u
6
+ ··· −
3
2
u +
7
6
−
1
2
u
6
+
1
2
u
5
+ ··· + 6u −
5
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5
2
u
7
−
1
2
u
6
+
13
2
u
5
−
21
2
u
4
+ 5u
3
− 13u
2
−
1
2
u − 9
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
− 5u
7
+ 9u
6
− 3u
5
− 8u
4
+ 7u
3
+ 3u
2
− 2u + 1
c
2
(u
4
− u
3
+ 2u
2
+ 1)
2
c
3
, c
7
u
8
+ 5u
6
+ 3u
5
+ 10u
4
+ 9u
3
+ 9u
2
+ 7u + 3
c
4
, c
11
u
8
+ 5u
6
− 3u
5
+ 10u
4
− 9u
3
+ 9u
2
− 7u + 3
c
5
, c
9
u
8
+ 2u
6
+ 2u
5
+ 3u
4
+ 4u
3
+ 7u
2
+ 7u + 3
c
6
(u
4
+ u
3
+ 2u
2
+ 1)
2
c
8
(u
4
+ u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
8
− 7y
7
+ 35y
6
− 77y
5
+ 142y
4
− 91y
3
+ 21y
2
+ 2y + 1
c
2
, c
6
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
c
3
, c
4
, c
7
c
11
y
8
+ 10y
7
+ 45y
6
+ 109y
5
+ 142y
4
+ 87y
3
+ 15y
2
+ 5y + 9
c
5
, c
9
y
8
+ 4y
7
+ 10y
6
+ 22y
5
+ 27y
4
+ 10y
3
+ 11y
2
− 7y + 9
c
8
(y
4
+ 2y
2
− y + 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.095575 + 1.200900I
a = 0.307939 − 0.630003I
b = 0.63156 + 1.63091I
7.71788 + 3.38562I −9.43066 − 4.92823I
u = −0.095575 − 1.200900I
a = 0.307939 + 0.630003I
b = 0.63156 − 1.63091I
7.71788 − 3.38562I −9.43066 + 4.92823I
u = 0.154365 + 1.248590I
a = −0.807775 + 0.482499I
b = −0.572771 + 0.314492I
2.15173 − 2.37936I −12.06934 + 4.77691I
u = 0.154365 − 1.248590I
a = −0.807775 − 0.482499I
b = −0.572771 − 0.314492I
2.15173 + 2.37936I −12.06934 − 4.77691I
u = 0.572771 + 0.314492I
a = −0.28741 + 1.78865I
b = −0.154365 + 1.248590I
2.15173 + 2.37936I −12.06934 − 4.77691I
u = 0.572771 − 0.314492I
a = −0.28741 − 1.78865I
b = −0.154365 − 1.248590I
2.15173 − 2.37936I −12.06934 + 4.77691I
u = −0.63156 + 1.63091I
a = −0.379420 − 0.298919I
b = 0.095575 + 1.200900I
7.71788 − 3.38562I −9.43066 + 4.92823I
u = −0.63156 − 1.63091I
a = −0.379420 + 0.298919I
b = 0.095575 − 1.200900I
7.71788 + 3.38562I −9.43066 − 4.92823I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
3
+ u + 1)(u
8
− 5u
7
+ 9u
6
− 3u
5
− 8u
4
+ 7u
3
+ 3u
2
− 2u + 1)
· (u
8
+ 2u
7
+ 2u
6
+ 3u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
27
− 2u
26
+ ··· − 10u + 3)(u
64
+ 2u
63
+ ··· − 126u + 177)
c
2
(u
3
+ u − 1)(u
4
− u
3
+ 2u
2
+ 1)
2
· (u
8
+ 3u
7
+ 6u
6
+ 8u
5
+ 8u
4
+ 7u
3
+ 5u
2
+ 2u + 1)
· (u
27
+ 8u
26
+ ··· + 110u + 12)(u
32
− 3u
31
+ ··· − 10u + 3)
2
c
3
, c
7
(u
3
+ u + 1)(u
8
+ 5u
6
+ 3u
5
+ 10u
4
+ 9u
3
+ 9u
2
+ 7u + 3)
· (u
8
+ u
7
+ ··· + u + 1)(u
27
− u
26
+ ··· + 4u + 1)
· (u
64
− 5u
63
+ ··· − 9u + 1)
c
4
, c
11
(u
3
+ u − 1)(u
8
+ 5u
6
− 3u
5
+ 10u
4
− 9u
3
+ 9u
2
− 7u + 3)
· (u
8
− u
7
+ ··· − u + 1)(u
27
− u
26
+ ··· + 4u + 1)
· (u
64
− 5u
63
+ ··· − 9u + 1)
c
5
, c
9
(u
3
− 3u
2
+ 4u − 1)(u
8
+ 2u
6
+ 2u
5
+ 3u
4
+ 4u
3
+ 7u
2
+ 7u + 3)
· (u
8
+ 3u
7
+ 4u
6
+ 5u
5
+ 5u
4
+ 4u
3
+ 4u
2
+ 2u + 1)
· (u
27
+ 12u
25
+ ··· + 15u
2
+ 1)(u
64
− u
63
+ ··· − 16935u + 15481)
c
6
(u
3
+ u + 1)(u
4
+ u
3
+ 2u
2
+ 1)
2
· (u
8
− 3u
7
+ 6u
6
− 8u
5
+ 8u
4
− 7u
3
+ 5u
2
− 2u + 1)
· (u
27
+ 8u
26
+ ··· + 110u + 12)(u
32
− 3u
31
+ ··· − 10u + 3)
2
c
8
(u
3
− u
2
+ 4u − 3)(u
4
+ u + 1)
2
· (u
8
− 6u
7
+ 19u
6
− 35u
5
+ 38u
4
− 25u
3
+ 10u
2
− 2u + 1)
· (u
27
− 20u
26
+ ··· − 1284u + 180)(u
32
+ 10u
31
+ ··· + 99u + 19)
2
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
+ 2y
2
+ y −1)(y
8
− 2y
6
− 3y
5
+ y
4
+ 7y
3
+ 9y
2
+ 5y + 1)
· (y
8
− 7y
7
+ 35y
6
− 77y
5
+ 142y
4
− 91y
3
+ 21y
2
+ 2y + 1)
· (y
27
+ 4y
26
+ ··· + 4y −9)(y
64
+ 4y
63
+ ··· + 305202y + 31329)
c
2
, c
6
(y
3
+ 2y
2
+ y −1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
· (y
8
+ 3y
7
+ 4y
6
+ 2y
4
+ 11y
3
+ 13y
2
+ 6y + 1)
· (y
27
+ 14y
26
+ ··· + 700y −144)(y
32
+ 21y
31
+ ··· + 74y + 9)
2
c
3
, c
4
, c
7
c
11
(y
3
+ 2y
2
+ y −1)
· (y
8
+ 7y
7
+ 24y
6
+ 50y
5
+ 68y
4
+ 60y
3
+ 33y
2
+ 9y + 1)
· (y
8
+ 10y
7
+ 45y
6
+ 109y
5
+ 142y
4
+ 87y
3
+ 15y
2
+ 5y + 9)
· (y
27
+ 27y
26
+ ··· − 4y −1)(y
64
+ 49y
63
+ ··· − 3y + 1)
c
5
, c
9
(y
3
− y
2
+ 10y −1)(y
8
− y
7
+ ··· + 4y + 1)
· (y
8
+ 4y
7
+ 10y
6
+ 22y
5
+ 27y
4
+ 10y
3
+ 11y
2
− 7y + 9)
· (y
27
+ 24y
26
+ ··· − 30y −1)
· (y
64
+ 11y
63
+ ··· + 3729627377y + 239661361)
c
8
(y
3
+ 7y
2
+ 10y −9)(y
4
+ 2y
2
− y + 1)
2
· (y
8
+ 2y
7
+ 17y
6
− 61y
5
+ 52y
4
+ 33y
3
+ 76y
2
+ 16y + 1)
· (y
27
− 2y
26
+ ··· + 561816y −32400)
· (y
32
+ 18y
31
+ ··· + 3461y + 361)
2
31
