12a
0100
(K12a
0100
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 4 11 6 1 7 9
Solving Sequence
4,7 8,11
9 12 1 3 2 6 10 5
c
7
c
8
c
11
c
12
c
3
c
1
c
6
c
9
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.87861 × 10
82
u
47
+ 1.04155 × 10
83
u
46
+ ··· + 3.05135 × 10
83
b − 3.51869 × 10
84
,
− 3.38702 × 10
82
u
47
− 2.61769 × 10
83
u
46
+ ··· + 2.44108 × 10
84
a + 1.57211 × 10
85
,
u
48
+ 6u
47
+ ··· − 608u − 128i
I
u
2
= h34725u
16
a
3
− 26335u
16
a
2
+ ··· − 126824a + 31474, −2u
16
a
3
+ 23u
16
a
2
+ ··· + 842a + 2659,
u
17
+ 2u
16
+ ··· − 2u − 2i
I
u
3
= h338183u
20
− 78918u
19
+ ··· + 334723b + 221323,
− 2123279u
20
+ 2034822u
19
+ ··· + 334723a + 4096060, u
21
− u
20
+ ··· − 2u + 1i
I
u
4
= h−1746a
5
u − 3784a
4
u + ··· + 44299a − 6066,
a
6
− 4a
5
u + 4a
5
− 10a
4
u − 6a
4
+ 18a
3
u − 27a
3
+ 33a
2
u + 3a
2
− 27au + 26a + 4u − 7, u
2
− u + 1i
I
u
5
= h30a
5
u − 47a
4
u + ··· + 104a − 142, a
6
− 4a
5
+ 4a
4
− a
3
u − a
3
− a
2
u + 5a
2
− a + 2u, u
2
− u + 1i
I
v
1
= ha, −8v
2
+ b + 26v −7, 4v
3
− 14v
2
+ 7v −1i
I
v
2
= ha, b
4
− b
3
+ 2b
2
− 2b + 1, v + 1i
* 7 irreducible components of dim
C
= 0, with total 168 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
= h1.88 × 10
82
u
47
+ 1.04 × 10
83
u
46
+ · · · + 3.05 × 10
83
b − 3.52 ×
10
84
, −3.39 × 10
82
u
47
− 2.62 × 10
83
u
46
+ · · · + 2.44 × 10
84
a + 1.57 ×
10
85
, u
48
+ 6u
47
+ · · · − 608u − 128i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
0.0138751u
47
+ 0.107235u
46
+ ··· − 25.5601u − 6.44022
−0.0615666u
47
− 0.341342u
46
+ ··· + 44.5324u + 11.5316
a
9
=
0.0773618u
47
+ 0.445624u
46
+ ··· − 51.2591u − 9.84291
0.0862284u
47
+ 0.487720u
46
+ ··· − 62.1112u − 12.9461
a
12
=
−0.0476915u
47
− 0.234107u
46
+ ··· + 18.9724u + 5.09137
−0.0615666u
47
− 0.341342u
46
+ ··· + 44.5324u + 11.5316
a
1
=
−0.0708863u
47
− 0.354435u
46
+ ··· + 15.5178u + 0.0840131
−0.109737u
47
− 0.627104u
46
+ ··· + 72.2764u + 12.8045
a
3
=
u
u
3
+ u
a
2
=
−0.0947782u
47
− 0.492160u
46
+ ··· + 28.6120u + 2.50397
−0.123753u
47
− 0.710763u
46
+ ··· + 85.7340u + 15.9448
a
6
=
−0.116272u
47
− 0.613951u
46
+ ··· + 58.0413u + 11.2491
−0.126215u
47
− 0.696047u
46
+ ··· + 77.0279u + 15.8185
a
10
=
0.0714285u
47
+ 0.418715u
46
+ ··· − 65.5831u − 16.3972
0.123594u
47
+ 0.671965u
46
+ ··· − 88.7374u − 22.0222
a
5
=
0.0124958u
47
+ 0.0938805u
46
+ ··· − 22.7356u − 3.64759
0.0833820u
47
+ 0.448316u
46
+ ··· − 38.2534u − 3.73160
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.109672u
47
− 0.524268u
46
+ ··· − 20.2898u − 35.2434
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 25u
47
+ ··· + 18800u + 256
c
2
, c
4
u
48
− 3u
47
+ ··· + 76u + 16
c
3
, c
7
u
48
+ 6u
47
+ ··· − 608u − 128
c
5
, c
6
, c
9
c
11
u
48
+ 19u
46
+ ··· − u − 1
c
8
, c
10
u
48
− 3u
47
+ ··· − 23u + 1
c
12
u
48
− 51u
47
+ ··· − 285212672u + 8388608
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
− y
47
+ ··· − 279621376y + 65536
c
2
, c
4
y
48
− 25y
47
+ ··· − 18800y + 256
c
3
, c
7
y
48
+ 18y
47
+ ··· − 158720y + 16384
c
5
, c
6
, c
9
c
11
y
48
+ 38y
47
+ ··· − 31y + 1
c
8
, c
10
y
48
+ 5y
47
+ ··· − 237y + 1
c
12
y
48
+ 5y
47
+ ··· − 5875790138834944y + 70368744177664
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191047 + 1.007770I
a = 0.728739 + 0.164163I
b = −0.607742 − 0.383050I
1.84375 + 0.90076I 5.50791 − 3.88202I
u = 0.191047 − 1.007770I
a = 0.728739 − 0.164163I
b = −0.607742 + 0.383050I
1.84375 − 0.90076I 5.50791 + 3.88202I
u = −0.824028 + 0.494777I
a = 0.775855 − 0.447940I
b = −0.719486 − 0.096265I
−0.84172 − 2.79098I 2.56303 + 3.67085I
u = −0.824028 − 0.494777I
a = 0.775855 + 0.447940I
b = −0.719486 + 0.096265I
−0.84172 + 2.79098I 2.56303 − 3.67085I
u = −0.061009 + 1.092180I
a = −1.55932 + 0.14388I
b = 0.586610 + 0.474683I
4.73028 − 1.19532I 7.39057 − 1.46823I
u = −0.061009 − 1.092180I
a = −1.55932 − 0.14388I
b = 0.586610 − 0.474683I
4.73028 + 1.19532I 7.39057 + 1.46823I
u = 0.449465 + 1.031100I
a = −1.28963 − 0.62914I
b = 0.789520 + 0.202426I
3.26311 − 3.26704I 7.67341 + 2.61304I
u = 0.449465 − 1.031100I
a = −1.28963 + 0.62914I
b = 0.789520 − 0.202426I
3.26311 + 3.26704I 7.67341 − 2.61304I
u = 0.333088 + 1.109900I
a = −1.33371 − 0.49028I
b = 0.463573 − 0.639486I
3.87618 − 3.65220I 3.08711 + 8.05406I
u = 0.333088 − 1.109900I
a = −1.33371 + 0.49028I
b = 0.463573 + 0.639486I
3.87618 + 3.65220I 3.08711 − 8.05406I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538501 + 1.036350I
a = 0.711782 − 0.232849I
b = −0.803519 + 0.258105I
0.15510 + 3.68398I 2.64964 − 1.96684I
u = −0.538501 − 1.036350I
a = 0.711782 + 0.232849I
b = −0.803519 − 0.258105I
0.15510 − 3.68398I 2.64964 + 1.96684I
u = 1.066610 + 0.483181I
a = −0.048708 + 0.338357I
b = 0.44345 + 1.38767I
−7.17044 + 7.50868I −1.58512 − 3.77436I
u = 1.066610 − 0.483181I
a = −0.048708 − 0.338357I
b = 0.44345 − 1.38767I
−7.17044 − 7.50868I −1.58512 + 3.77436I
u = −0.593763 + 0.555003I
a = −0.050418 − 0.332210I
b = 0.32635 − 1.49374I
−11.74940 − 4.76001I −6.57262 − 2.96707I
u = −0.593763 − 0.555003I
a = −0.050418 + 0.332210I
b = 0.32635 + 1.49374I
−11.74940 + 4.76001I −6.57262 + 2.96707I
u = −0.601845 + 1.052800I
a = 2.05390 + 0.10513I
b = −0.46620 − 1.43355I
−10.21060 + 9.59449I −3.60142 − 6.18831I
u = −0.601845 − 1.052800I
a = 2.05390 − 0.10513I
b = −0.46620 + 1.43355I
−10.21060 − 9.59449I −3.60142 + 6.18831I
u = −0.485413 + 0.601421I
a = −1.28070 + 1.69925I
b = 0.627305 − 0.012830I
−1.262120 + 0.607533I 3.19613 − 5.27342I
u = −0.485413 − 0.601421I
a = −1.28070 − 1.69925I
b = 0.627305 + 0.012830I
−1.262120 − 0.607533I 3.19613 + 5.27342I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.635379 + 1.085340I
a = −1.035040 + 0.645312I
b = 0.890242 − 0.142272I
0.95191 + 8.23122I 3.50123 − 7.17855I
u = −0.635379 − 1.085340I
a = −1.035040 − 0.645312I
b = 0.890242 + 0.142272I
0.95191 − 8.23122I 3.50123 + 7.17855I
u = −1.096040 + 0.664816I
a = −0.054336 − 0.338178I
b = 0.49492 − 1.44926I
−9.5879 − 12.5892I −3.60578 + 7.24500I
u = −1.096040 − 0.664816I
a = −0.054336 + 0.338178I
b = 0.49492 + 1.44926I
−9.5879 + 12.5892I −3.60578 − 7.24500I
u = 0.638998 + 0.071034I
a = 1.28773 − 1.29641I
b = −0.345569 − 0.223570I
0.673431 + 0.110718I 7.7390 − 14.7279I
u = 0.638998 − 0.071034I
a = 1.28773 + 1.29641I
b = −0.345569 + 0.223570I
0.673431 − 0.110718I 7.7390 + 14.7279I
u = 0.710349 + 1.174450I
a = 1.68838 + 0.12583I
b = −0.53527 + 1.45440I
−4.9700 − 13.8549I 0
u = 0.710349 − 1.174450I
a = 1.68838 − 0.12583I
b = −0.53527 − 1.45440I
−4.9700 + 13.8549I 0
u = −0.420346 + 0.423788I
a = −0.053647 + 0.334365I
b = 0.17258 + 1.45355I
−11.27470 + 5.48110I −7.3979 − 14.4496I
u = −0.420346 − 0.423788I
a = −0.053647 − 0.334365I
b = 0.17258 − 1.45355I
−11.27470 − 5.48110I −7.3979 + 14.4496I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.806830 + 1.155070I
a = 1.66382 − 0.32906I
b = −0.54117 − 1.49832I
−7.9747 + 19.4545I 0
u = −0.806830 − 1.155070I
a = 1.66382 + 0.32906I
b = −0.54117 + 1.49832I
−7.9747 − 19.4545I 0
u = 0.33726 + 1.38273I
a = 1.048030 − 0.444775I
b = −0.535063 + 1.197840I
−0.00671 − 10.39530I 0
u = 0.33726 − 1.38273I
a = 1.048030 + 0.444775I
b = −0.535063 − 1.197840I
−0.00671 + 10.39530I 0
u = −0.22239 + 1.42242I
a = 0.721683 + 0.463533I
b = −0.458297 − 1.049830I
1.00442 + 4.31512I 0
u = −0.22239 − 1.42242I
a = 0.721683 − 0.463533I
b = −0.458297 + 1.049830I
1.00442 − 4.31512I 0
u = −0.89457 + 1.16056I
a = −1.001830 + 0.221515I
b = 0.118376 + 1.224700I
−5.81153 + 10.03740I 0
u = −0.89457 − 1.16056I
a = −1.001830 − 0.221515I
b = 0.118376 − 1.224700I
−5.81153 − 10.03740I 0
u = 1.47382 + 0.09648I
a = −0.023063 − 0.280597I
b = 0.214306 − 1.129300I
−5.30932 − 4.33878I 0
u = 1.47382 − 0.09648I
a = −0.023063 + 0.280597I
b = 0.214306 + 1.129300I
−5.30932 + 4.33878I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.90750 + 1.20267I
a = −0.791351 − 0.168123I
b = 0.072284 − 1.150090I
−2.35143 − 4.21639I 0
u = 0.90750 − 1.20267I
a = −0.791351 + 0.168123I
b = 0.072284 + 1.150090I
−2.35143 + 4.21639I 0
u = −0.441911
a = 1.53998
b = 0.237250
−1.26980 −9.92780
u = −1.32729 + 0.82837I
a = −0.162773 + 0.297503I
b = 0.006720 + 1.165660I
−7.13142 − 2.34962I 0
u = −1.32729 − 0.82837I
a = −0.162773 − 0.297503I
b = 0.006720 − 1.165660I
−7.13142 + 2.34962I 0
u = −0.55430 + 1.47189I
a = −0.471137 − 0.489578I
b = −0.089207 + 1.159830I
−7.97723 − 1.25475I 0
u = −0.55430 − 1.47189I
a = −0.471137 + 0.489578I
b = −0.089207 − 1.159830I
−7.97723 + 1.25475I 0
u = 0.349047
a = 1.28651
b = −0.446661
0.908064 11.6320
9
II. I
u
2
= h3.47 × 10
4
a
3
u
16
− 2.63 × 10
4
a
2
u
16
+ · · · − 1.27 × 10
5
a + 3.15 ×
10
4
, −2u
16
a
3
+ 23u
16
a
2
+ · · · + 842a + 2659, u
17
+ 2u
16
+ · · · − 2u − 2i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
a
−1.15889a
3
u
16
+ 0.878888a
2
u
16
+ ··· + 4.23255a − 1.05039
a
9
=
0.454445a
3
u
16
− 0.378888a
2
u
16
+ ··· − 1.44961a + 3.55039
−0.295555a
2
u
16
− 0.352223u
16
+ ··· + 0.565879a
2
+ 1.21706
a
12
=
−1.15889a
3
u
16
+ 0.878888a
2
u
16
+ ··· + 5.23255a − 1.05039
−1.15889a
3
u
16
+ 0.878888a
2
u
16
+ ··· + 4.23255a − 1.05039
a
1
=
−
1
2
u
16
−
1
4
u
15
+ ··· −
1
2
u −
1
2
−
1
2
u
16
−
1
2
u
15
+ ··· −
3
4
u
2
+
1
2
a
3
=
u
u
3
+ u
a
2
=
−
1
4
u
16
−
3
4
u
14
+ ··· −
3
2
u −
1
2
−
1
4
u
16
−
1
2
u
14
+ ··· −
1
2
u
2
− u
a
6
=
−0.811107a
3
u
16
+ 1.06778a
2
u
16
+ ··· + 0.418636a − 4.13176
−0.356661a
3
u
16
+ 0.688893a
2
u
16
+ ··· − 1.03097a − 2.58136
a
10
=
0.908891a
3
u
16
− 0.795555a
2
u
16
+ ··· + 1.93412a − 1.28294
0.158891a
3
u
16
− 0.212221a
2
u
16
+ ··· + 4.10079a − 0.616273
a
5
=
−
1
2
u
16
− u
15
+ ··· −
11
4
u
2
+
1
2
−
3
4
u
15
−
3
4
u
14
+ ··· +
1
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
12718
7491
u
16
a
3
+
4539
2497
u
16
a
2
+ ··· +
82924
7491
a −
17808
2497
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 8u
16
+ ··· + 3u + 1)
4
c
2
, c
4
(u
17
− 2u
16
+ ··· − u + 1)
4
c
3
, c
7
(u
17
+ 2u
16
+ ··· − 2u − 2)
4
c
5
, c
6
, c
9
c
11
u
68
− 2u
67
+ ··· + 942u + 61
c
8
, c
10
u
68
+ 18u
67
+ ··· + 8600u + 373
c
12
(u
2
+ u + 1)
34
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ 4y
16
+ ··· − 13y −1)
4
c
2
, c
4
(y
17
− 8y
16
+ ··· + 3y −1)
4
c
3
, c
7
(y
17
+ 6y
16
+ ··· + 8y −4)
4
c
5
, c
6
, c
9
c
11
y
68
+ 54y
67
+ ··· + 221616y + 3721
c
8
, c
10
y
68
+ 14y
67
+ ··· + 20523884y + 139129
c
12
(y
2
+ y + 1)
34
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.742615 + 0.650908I
a = −0.858913 − 0.213402I
b = −0.66649 + 1.56071I
−8.59404 − 3.25712I −8.14847 + 4.31915I
u = −0.742615 + 0.650908I
a = −0.17250 − 1.68551I
b = −0.040339 − 1.225610I
−8.59404 + 0.80264I −8.14847 − 2.60905I
u = −0.742615 + 0.650908I
a = −2.43226 + 1.27156I
b = 0.59407 + 1.60818I
−8.59404 + 0.80264I −8.14847 − 2.60905I
u = −0.742615 + 0.650908I
a = 2.51978 − 1.83542I
b = 0.058310 − 1.272450I
−8.59404 − 3.25712I −8.14847 + 4.31915I
u = −0.742615 − 0.650908I
a = −0.858913 + 0.213402I
b = −0.66649 − 1.56071I
−8.59404 + 3.25712I −8.14847 − 4.31915I
u = −0.742615 − 0.650908I
a = −0.17250 + 1.68551I
b = −0.040339 + 1.225610I
−8.59404 − 0.80264I −8.14847 + 2.60905I
u = −0.742615 − 0.650908I
a = −2.43226 − 1.27156I
b = 0.59407 − 1.60818I
−8.59404 − 0.80264I −8.14847 + 2.60905I
u = −0.742615 − 0.650908I
a = 2.51978 + 1.83542I
b = 0.058310 + 1.272450I
−8.59404 + 3.25712I −8.14847 − 4.31915I
u = −0.834865 + 0.265014I
a = −0.016132 + 0.733452I
b = 0.960620 − 0.161520I
−2.31524 − 2.46376I 0.56834 + 2.58870I
u = −0.834865 + 0.265014I
a = 0.284668 − 0.665934I
b = 0.509050 − 0.033729I
−2.31524 + 1.59601I 0.56834 − 4.33950I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.834865 + 0.265014I
a = 0.475849 + 0.326477I
b = −0.232899 + 1.178170I
−2.31524 − 2.46376I 0.56834 + 2.58870I
u = −0.834865 + 0.265014I
a = 0.403399 − 0.262157I
b = 0.007533 − 1.104820I
−2.31524 + 1.59601I 0.56834 − 4.33950I
u = −0.834865 − 0.265014I
a = −0.016132 − 0.733452I
b = 0.960620 + 0.161520I
−2.31524 + 2.46376I 0.56834 − 2.58870I
u = −0.834865 − 0.265014I
a = 0.284668 + 0.665934I
b = 0.509050 + 0.033729I
−2.31524 − 1.59601I 0.56834 + 4.33950I
u = −0.834865 − 0.265014I
a = 0.475849 − 0.326477I
b = −0.232899 − 1.178170I
−2.31524 + 2.46376I 0.56834 − 2.58870I
u = −0.834865 − 0.265014I
a = 0.403399 + 0.262157I
b = 0.007533 + 1.104820I
−2.31524 − 1.59601I 0.56834 + 4.33950I
u = 0.976738 + 0.562668I
a = 0.453582 + 0.523609I
b = 0.097566 + 0.148491I
−4.32437 + 2.61783I −2.43915 − 0.65285I
u = 0.976738 + 0.562668I
a = −0.163065 − 0.655845I
b = 1.225180 + 0.226983I
−4.32437 + 6.67759I −2.43915 − 7.58105I
u = 0.976738 + 0.562668I
a = 0.462635 − 0.371400I
b = −0.336705 − 1.223300I
−4.32437 + 6.67759I −2.43915 − 7.58105I
u = 0.976738 + 0.562668I
a = 0.286253 + 0.249449I
b = 0.321037 + 1.119110I
−4.32437 + 2.61783I −2.43915 − 0.65285I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.976738 − 0.562668I
a = 0.453582 − 0.523609I
b = 0.097566 − 0.148491I
−4.32437 − 2.61783I −2.43915 + 0.65285I
u = 0.976738 − 0.562668I
a = −0.163065 + 0.655845I
b = 1.225180 − 0.226983I
−4.32437 − 6.67759I −2.43915 + 7.58105I
u = 0.976738 − 0.562668I
a = 0.462635 + 0.371400I
b = −0.336705 + 1.223300I
−4.32437 − 6.67759I −2.43915 + 7.58105I
u = 0.976738 − 0.562668I
a = 0.286253 − 0.249449I
b = 0.321037 − 1.119110I
−4.32437 − 2.61783I −2.43915 + 0.65285I
u = −0.003992 + 0.842342I
a = 0.823514 + 0.703163I
b = −0.188923 + 1.380570I
−3.62498 − 3.49944I 1.63583 + 8.12938I
u = −0.003992 + 0.842342I
a = 0.354576 + 0.342592I
b = −0.17222 − 1.57777I
−3.62498 + 0.56033I 1.63583 + 1.20118I
u = −0.003992 + 0.842342I
a = −1.14706 + 1.36568I
b = 0.865544 − 1.043820I
−3.62498 − 3.49944I 1.63583 + 8.12938I
u = −0.003992 + 0.842342I
a = 1.59887 − 1.09681I
b = 0.125548 + 0.823426I
−3.62498 + 0.56033I 1.63583 + 1.20118I
u = −0.003992 − 0.842342I
a = 0.823514 − 0.703163I
b = −0.188923 − 1.380570I
−3.62498 + 3.49944I 1.63583 − 8.12938I
u = −0.003992 − 0.842342I
a = 0.354576 − 0.342592I
b = −0.17222 + 1.57777I
−3.62498 − 0.56033I 1.63583 − 1.20118I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003992 − 0.842342I
a = −1.14706 − 1.36568I
b = 0.865544 + 1.043820I
−3.62498 + 3.49944I 1.63583 − 8.12938I
u = −0.003992 − 0.842342I
a = 1.59887 + 1.09681I
b = 0.125548 − 0.823426I
−3.62498 − 0.56033I 1.63583 − 1.20118I
u = −0.656745 + 1.004700I
a = 0.146155 − 1.227280I
b = −0.025709 − 1.355530I
−7.51458 + 8.60052I −5.26005 − 9.89862I
u = −0.656745 + 1.004700I
a = −0.376762 − 0.223958I
b = −0.55941 + 1.77505I
−7.51458 + 4.54075I −5.26005 − 2.97041I
u = −0.656745 + 1.004700I
a = −1.80331 + 0.32050I
b = 0.84173 + 1.60733I
−7.51458 + 8.60052I −5.26005 − 9.89862I
u = −0.656745 + 1.004700I
a = 1.99063 − 0.75779I
b = −0.066671 − 1.194250I
−7.51458 + 4.54075I −5.26005 − 2.97041I
u = −0.656745 − 1.004700I
a = 0.146155 + 1.227280I
b = −0.025709 + 1.355530I
−7.51458 − 8.60052I −5.26005 + 9.89862I
u = −0.656745 − 1.004700I
a = −0.376762 + 0.223958I
b = −0.55941 − 1.77505I
−7.51458 − 4.54075I −5.26005 + 2.97041I
u = −0.656745 − 1.004700I
a = −1.80331 − 0.32050I
b = 0.84173 − 1.60733I
−7.51458 − 8.60052I −5.26005 + 9.89862I
u = −0.656745 − 1.004700I
a = 1.99063 + 0.75779I
b = −0.066671 + 1.194250I
−7.51458 − 4.54075I −5.26005 + 2.97041I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.110097 + 1.246510I
a = −0.537569 + 0.828636I
b = 0.247183 − 0.880435I
3.09988 + 0.68177I 3.84242 + 0.32700I
u = −0.110097 + 1.246510I
a = 1.147850 − 0.201747I
b = −0.922464 − 0.394135I
3.09988 + 0.68177I 3.84242 + 0.32700I
u = −0.110097 + 1.246510I
a = 1.301120 + 0.007909I
b = −1.089750 + 0.222504I
3.09988 + 4.74154I 3.84242 − 6.60120I
u = −0.110097 + 1.246510I
a = −1.063350 − 0.849870I
b = 0.323575 + 0.999592I
3.09988 + 4.74154I 3.84242 − 6.60120I
u = −0.110097 − 1.246510I
a = −0.537569 − 0.828636I
b = 0.247183 + 0.880435I
3.09988 − 0.68177I 3.84242 − 0.32700I
u = −0.110097 − 1.246510I
a = 1.147850 + 0.201747I
b = −0.922464 + 0.394135I
3.09988 − 0.68177I 3.84242 − 0.32700I
u = −0.110097 − 1.246510I
a = 1.301120 − 0.007909I
b = −1.089750 − 0.222504I
3.09988 − 4.74154I 3.84242 + 6.60120I
u = −0.110097 − 1.246510I
a = −1.063350 + 0.849870I
b = 0.323575 − 0.999592I
3.09988 − 4.74154I 3.84242 + 6.60120I
u = −0.578864 + 1.116300I
a = 1.204300 − 0.022501I
b = −0.488361 − 1.049000I
0.11501 + 3.48170I 2.25126 − 0.38080I
u = −0.578864 + 1.116300I
a = 1.27173 − 0.65139I
b = −1.312600 − 0.151182I
0.11501 + 7.54146I 2.25126 − 7.30900I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578864 + 1.116300I
a = −0.194398 − 0.198117I
b = 0.042359 − 0.283882I
0.11501 + 3.48170I 2.25126 − 0.38080I
u = −0.578864 + 1.116300I
a = −1.96774 − 0.11289I
b = 0.381291 + 1.203870I
0.11501 + 7.54146I 2.25126 − 7.30900I
u = −0.578864 − 1.116300I
a = 1.204300 + 0.022501I
b = −0.488361 + 1.049000I
0.11501 − 3.48170I 2.25126 + 0.38080I
u = −0.578864 − 1.116300I
a = 1.27173 + 0.65139I
b = −1.312600 + 0.151182I
0.11501 − 7.54146I 2.25126 + 7.30900I
u = −0.578864 − 1.116300I
a = −0.194398 + 0.198117I
b = 0.042359 + 0.283882I
0.11501 − 3.48170I 2.25126 + 0.38080I
u = −0.578864 − 1.116300I
a = −1.96774 + 0.11289I
b = 0.381291 − 1.203870I
0.11501 − 7.54146I 2.25126 + 7.30900I
u = 0.718492 + 1.129370I
a = 1.275350 + 0.228864I
b = −0.553021 + 1.205800I
−2.53156 − 8.80385I −1.10622 + 3.94851I
u = 0.718492 + 1.129370I
a = 1.097970 + 0.736493I
b = −1.40257 + 0.22167I
−2.53156 − 12.86360I −1.10622 + 10.87671I
u = 0.718492 + 1.129370I
a = −0.420731 + 0.192335I
b = 0.164364 + 0.168623I
−2.53156 − 8.80385I −1.10622 + 3.94851I
u = 0.718492 + 1.129370I
a = −1.89005 − 0.20697I
b = 0.406612 − 1.245470I
−2.53156 − 12.86360I −1.10622 + 10.87671I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718492 − 1.129370I
a = 1.275350 − 0.228864I
b = −0.553021 − 1.205800I
−2.53156 + 8.80385I −1.10622 − 3.94851I
u = 0.718492 − 1.129370I
a = 1.097970 − 0.736493I
b = −1.40257 − 0.22167I
−2.53156 + 12.86360I −1.10622 − 10.87671I
u = 0.718492 − 1.129370I
a = −0.420731 − 0.192335I
b = 0.164364 − 0.168623I
−2.53156 + 8.80385I −1.10622 − 3.94851I
u = 0.718492 − 1.129370I
a = −1.89005 + 0.20697I
b = 0.406612 + 1.245470I
−2.53156 + 12.86360I −1.10622 − 10.87671I
u = 0.463897
a = −4.47126 + 2.76907I
b = −0.397720 + 1.155250I
−6.19292 − 2.02988I −10.68792 + 3.46410I
u = 0.463897
a = −4.47126 − 2.76907I
b = −0.397720 − 1.155250I
−6.19292 + 2.02988I −10.68792 − 3.46410I
u = 0.463897
a = −0.58311 + 11.52350I
b = 0.284280 + 1.351730I
−6.19292 + 2.02988I −10.68792 − 3.46410I
u = 0.463897
a = −0.58311 − 11.52350I
b = 0.284280 − 1.351730I
−6.19292 − 2.02988I −10.68792 + 3.46410I
19
III.
I
u
3
= h3.38 × 10
5
u
20
− 7.89 × 10
4
u
19
+ · · · + 3.35 × 10
5
b + 2.21 × 10
5
, −2.12 ×
10
6
u
20
+ 2.03 × 10
6
u
19
+ · · · + 3.35 × 10
5
a + 4.10 × 10
6
, u
21
− u
20
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
6.34339u
20
− 6.07912u
19
+ ··· + 17.6956u − 12.2372
−1.01034u
20
+ 0.235771u
19
+ ··· − 2.20402u − 0.661212
a
9
=
0.312375u
20
+ 2.96012u
19
+ ··· + 3.86554u + 11.9528
1.35474u
20
− 1.24479u
19
+ ··· + 3.63887u − 1.82860
a
12
=
5.33305u
20
− 5.84335u
19
+ ··· + 15.4916u − 12.8984
−1.01034u
20
+ 0.235771u
19
+ ··· − 2.20402u − 0.661212
a
1
=
−1.24963u
20
+ 0.461943u
19
+ ··· − 4.25896u + 0.00811417
−0.0988130u
20
+ 0.262465u
19
+ ··· + 0.213051u + 0.0131213
a
3
=
u
u
3
+ u
a
2
=
−1.47255u
20
+ 1.20487u
19
+ ··· − 4.89251u + 0.996355
−0.180295u
20
+ 0.767210u
19
+ ··· + 0.842431u + 0.481356
a
6
=
4.42387u
20
− 1.98590u
19
+ ··· + 22.5450u + 0.373646
−0.411406u
20
+ 0.417725u
19
+ ··· − 3.61084u − 0.603057
a
10
=
4.98866u
20
− 4.83433u
19
+ ··· + 14.0567u − 9.40856
−1.01034u
20
+ 0.235771u
19
+ ··· − 2.20402u − 0.661212
a
5
=
1.34293u
20
− 0.354687u
19
+ ··· + 4.79776u − 0.782680
0.0932980u
20
+ 0.107256u
19
+ ··· + 0.538795u − 0.774566
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2811940
334723
u
20
−
1365409
334723
u
19
+ ··· +
14890533
334723
u −
3065752
334723
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 11u
20
+ ··· + 2u − 1
c
2
u
21
+ 3u
20
+ ··· − 4u − 1
c
3
u
21
+ u
20
+ ··· − 2u − 1
c
4
u
21
− 3u
20
+ ··· − 4u + 1
c
5
, c
11
u
21
+ 12u
19
+ ··· + 5u − 1
c
6
, c
9
u
21
+ 12u
19
+ ··· + 5u + 1
c
7
u
21
− u
20
+ ··· − 2u + 1
c
8
, c
10
u
21
− 3u
20
+ ··· − 3u + 1
c
12
u
21
+ 3u
20
+ ··· − 3u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ y
20
+ ··· − 6y −1
c
2
, c
4
y
21
− 11y
20
+ ··· + 2y −1
c
3
, c
7
y
21
+ 9y
20
+ ··· − 6y −1
c
5
, c
6
, c
9
c
11
y
21
+ 24y
20
+ ··· + 99y −1
c
8
, c
10
y
21
+ 3y
20
+ ··· − 3y −1
c
12
y
21
+ 3y
20
+ ··· − 3y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.490243 + 0.937388I
a = 0.514333 + 0.625527I
b = −0.528540 − 1.286100I
−5.52103 − 1.78110I −3.65173 + 3.65315I
u = 0.490243 − 0.937388I
a = 0.514333 − 0.625527I
b = −0.528540 + 1.286100I
−5.52103 + 1.78110I −3.65173 − 3.65315I
u = −0.156277 + 1.122180I
a = −1.217350 + 0.179026I
b = 0.410410 + 0.113082I
4.06250 + 2.43837I 5.17498 − 3.14519I
u = −0.156277 − 1.122180I
a = −1.217350 − 0.179026I
b = 0.410410 − 0.113082I
4.06250 − 2.43837I 5.17498 + 3.14519I
u = −0.130234 + 0.829741I
a = 1.35637 − 0.71728I
b = −0.43014 + 1.34934I
−3.93501 − 2.17155I 0.14652 + 1.48581I
u = −0.130234 − 0.829741I
a = 1.35637 + 0.71728I
b = −0.43014 − 1.34934I
−3.93501 + 2.17155I 0.14652 − 1.48581I
u = −0.659203 + 0.963090I
a = 1.009120 − 0.683478I
b = −0.18280 − 1.48861I
−7.11068 + 6.86906I −4.04608 − 5.76368I
u = −0.659203 − 0.963090I
a = 1.009120 + 0.683478I
b = −0.18280 + 1.48861I
−7.11068 − 6.86906I −4.04608 + 5.76368I
u = 0.410688 + 0.721803I
a = 1.56660 + 0.92039I
b = −0.280481 + 1.376890I
−4.50106 − 2.68972I 0.55053 + 1.78075I
u = 0.410688 − 0.721803I
a = 1.56660 − 0.92039I
b = −0.280481 − 1.376890I
−4.50106 + 2.68972I 0.55053 − 1.78075I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.156740 + 0.305908I
a = −0.338936 − 0.137814I
b = −0.304972 − 1.054660I
−5.35947 + 3.69430I −6.58451 − 3.53350I
u = 1.156740 − 0.305908I
a = −0.338936 + 0.137814I
b = −0.304972 + 1.054660I
−5.35947 − 3.69430I −6.58451 + 3.53350I
u = −0.730687 + 0.973520I
a = 1.040580 − 0.020751I
b = 0.089617 − 1.248120I
−7.52481 − 1.55740I −4.73995 + 2.30181I
u = −0.730687 − 0.973520I
a = 1.040580 + 0.020751I
b = 0.089617 + 1.248120I
−7.52481 + 1.55740I −4.73995 − 2.30181I
u = 0.731610 + 1.181440I
a = −1.096200 − 0.010581I
b = 0.526976 − 0.918183I
−2.90296 − 10.25050I −2.57335 + 9.34499I
u = 0.731610 − 1.181440I
a = −1.096200 + 0.010581I
b = 0.526976 + 0.918183I
−2.90296 + 10.25050I −2.57335 − 9.34499I
u = −0.640346 + 1.260900I
a = −0.845339 − 0.135710I
b = 0.381374 + 0.865230I
−0.24350 + 4.56805I −0.64289 − 8.18526I
u = −0.640346 − 1.260900I
a = −0.845339 + 0.135710I
b = 0.381374 − 0.865230I
−0.24350 − 4.56805I −0.64289 + 8.18526I
u = −0.549197
a = 3.01565
b = −0.100536
0.498833 −32.6110
u = 0.302066 + 0.377168I
a = −8.99701 + 2.20814I
b = 0.368826 − 1.244610I
−6.69180 − 1.84270I −6.8280 + 14.0564I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302066 − 0.377168I
a = −8.99701 − 2.20814I
b = 0.368826 + 1.244610I
−6.69180 + 1.84270I −6.8280 − 14.0564I
25
IV. I
u
4
= h−1746a
5
u − 3784a
4
u + · · · + 44299a − 6066, −4a
5
u − 10a
4
u +
· · · + 26a − 7, u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u − 1
a
11
=
a
0.232583a
5
u + 0.504063a
4
u + ··· − 5.90103a + 0.808046
a
9
=
−0.285067a
5
u − 0.983216a
4
u + ··· + 4.04822a + 0.452911
−0.273611a
5
u − 0.980152a
4
u + ··· + 4.54909a + 0.472093
a
12
=
0.232583a
5
u + 0.504063a
4
u + ··· − 4.90103a + 0.808046
0.232583a
5
u + 0.504063a
4
u + ··· − 5.90103a + 0.808046
a
1
=
−0.0166511a
5
u + 0.332756a
4
u + ··· − 1.12335a + 0.344212
0.0410284a
5
u + 0.476089a
4
u + ··· − 0.648062a + 0.719861
a
3
=
u
u − 1
a
2
=
0.136806a
5
u + 0.490076a
4
u + ··· − 2.27454a + 1.76395
0.189290a
5
u + 0.969229a
4
u + ··· − 2.42174a + 2.50300
a
6
=
0.309445a
5
u + 1.79206a
4
u + ··· − 4.81964a − 1.38884
0.0243772a
5
u + 0.808845a
4
u + ··· − 0.771413a − 2.93593
a
10
=
−0.131877a
5
u − 0.244572a
4
u + ··· + 2.58306a + 0.686160
−0.0492873a
5
u − 0.455042a
4
u + ··· − 1.08512a + 1.49887
a
5
=
−0.148262a
5
u − 0.493140a
4
u + ··· + 1.77368a − 1.78314
−0.131610a
5
u − 0.825896a
4
u + ··· + 2.89703a − 2.12735
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u − 6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
2
c
2
, c
4
(u
6
− 2u
4
+ u
3
+ u
2
− u + 1)
2
c
3
, c
7
(u
2
− u + 1)
6
c
5
, c
6
, c
9
c
11
u
12
+ 6u
10
+ ··· − 2u + 4
c
8
, c
10
u
12
+ 4u
11
+ ··· + 14u + 13
c
12
(u
2
+ u + 1)
6
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
2
c
2
, c
4
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
c
3
, c
7
, c
12
(y
2
+ y + 1)
6
c
5
, c
6
, c
9
c
11
y
12
+ 12y
11
+ ··· + 228y + 16
c
8
, c
10
y
12
+ 8y
11
+ ··· + 558y + 169
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.800900 + 0.692255I
b = 0.020130 − 0.405138I
−4.93480 − 4.05977I −2.00000 + 6.92820I
u = 0.500000 + 0.866025I
a = 0.37705 + 1.39893I
b = −0.086959 + 1.331210I
−4.93480 − 4.05977I −2.00000 + 6.92820I
u = 0.500000 + 0.866025I
a = 0.296620 + 0.036933I
b = 0.12517 + 1.51446I
−4.93480 − 4.05977I −2.00000 + 6.92820I
u = 0.500000 + 0.866025I
a = 1.72107 + 0.97581I
b = −1.127070 + 0.261490I
−4.93480 − 4.05977I −2.00000 + 6.92820I
u = 0.500000 + 0.866025I
a = −2.29509 + 0.00735I
b = 0.77338 − 1.47468I
−4.93480 − 4.05977I −2.00000 + 6.92820I
u = 0.500000 + 0.866025I
a = −2.90055 + 0.35282I
b = 0.295351 − 1.227340I
−4.93480 − 4.05977I −2.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = 0.800900 − 0.692255I
b = 0.020130 + 0.405138I
−4.93480 + 4.05977I −2.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = 0.37705 − 1.39893I
b = −0.086959 − 1.331210I
−4.93480 + 4.05977I −2.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = 0.296620 − 0.036933I
b = 0.12517 − 1.51446I
−4.93480 + 4.05977I −2.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = 1.72107 − 0.97581I
b = −1.127070 − 0.261490I
−4.93480 + 4.05977I −2.00000 − 6.92820I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −2.29509 − 0.00735I
b = 0.77338 + 1.47468I
−4.93480 + 4.05977I −2.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = −2.90055 − 0.35282I
b = 0.295351 + 1.227340I
−4.93480 + 4.05977I −2.00000 − 6.92820I
30
V.
I
u
5
= h30a
5
u−47a
4
u+· · ·+104a − 142, −a
3
u−a
2
u+· · ·+5a
2
−a, u
2
−u +1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u − 1
a
11
=
a
−0.189873a
5
u + 0.297468a
4
u + ··· − 0.658228a + 0.898734
a
9
=
0.462025a
5
u − 1.74051a
4
u + ··· − 1.03165a + 1.37975
0.0506329a
5
u − 0.0126582a
4
u + ··· + 0.708861a + 1.49367
a
12
=
−0.189873a
5
u + 0.297468a
4
u + ··· + 0.341772a + 0.898734
−0.189873a
5
u + 0.297468a
4
u + ··· − 0.658228a + 0.898734
a
1
=
−0.101266a
5
u + 0.0253165a
4
u + ··· − 1.41772a + 1.01266
0.0253165a
5
u − 0.00632911a
4
u + ··· − 0.645570a + 0.746835
a
3
=
u
u − 1
a
2
=
−0.0822785a
5
u + 0.145570a
4
u + ··· + 0.348101a + 0.822785
0.481013a
5
u − 1.62025a
4
u + ··· − 0.265823a + 1.18987
a
6
=
−0.139241a
5
u + 0.284810a
4
u + ··· + 1.05063a − 1.60759
0.322785a
5
u − 1.45570a
4
u + ··· + 0.0189873a − 2.22785
a
10
=
0.151899a
5
u − 1.03797a
4
u + ··· − 0.873418a + 0.481013
−0.354430a
5
u + 1.08861a
4
u + ··· − 1.96203a + 1.54430
a
5
=
−0.455696a
5
u + 1.61392a
4
u + ··· − 0.379747a − 0.443038
−0.354430a
5
u + 1.58861a
4
u + ··· + 1.03797a − 1.45570
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
2
c
2
, c
4
(u
6
− 2u
4
+ u
3
+ u
2
− u + 1)
2
c
3
, c
7
(u
2
− u + 1)
6
c
5
, c
6
, c
9
c
11
u
12
+ 6u
10
+ ··· − 8u + 1
c
8
, c
10
u
12
+ 4u
11
+ ··· + 14u + 4
c
12
(u
2
+ u + 1)
6
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
2
c
2
, c
4
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
c
3
, c
7
, c
12
(y
2
+ y + 1)
6
c
5
, c
6
, c
9
c
11
y
12
+ 12y
11
+ ··· − 30y + 1
c
8
, c
10
y
12
+ 8y
11
+ ··· + 132y + 16
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.458927 − 0.846317I
b = 1.154960 + 0.679619I
−4.93480 −2.00000
u = 0.500000 + 0.866025I
a = −0.120980 + 0.945900I
b = −0.227005 + 0.048397I
−4.93480 −2.00000
u = 0.500000 + 0.866025I
a = 0.541662 − 0.468758I
b = −0.266914 − 1.360110I
−4.93480 −2.00000
u = 0.500000 + 0.866025I
a = −0.375061 + 0.467634I
b = −0.48176 − 1.66531I
−4.93480 −2.00000
u = 0.500000 + 0.866025I
a = 1.86135 − 0.58876I
b = −0.193588 + 1.154820I
−4.93480 −2.00000
u = 0.500000 + 0.866025I
a = 2.55196 + 0.49030I
b = 0.014308 + 1.142590I
−4.93480 −2.00000
u = 0.500000 − 0.866025I
a = −0.458927 + 0.846317I
b = 1.154960 − 0.679619I
−4.93480 −2.00000
u = 0.500000 − 0.866025I
a = −0.120980 − 0.945900I
b = −0.227005 − 0.048397I
−4.93480 −2.00000
u = 0.500000 − 0.866025I
a = 0.541662 + 0.468758I
b = −0.266914 + 1.360110I
−4.93480 −2.00000
u = 0.500000 − 0.866025I
a = −0.375061 − 0.467634I
b = −0.48176 + 1.66531I
−4.93480 −2.00000
34
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 1.86135 + 0.58876I
b = −0.193588 − 1.154820I
−4.93480 −2.00000
u = 0.500000 − 0.866025I
a = 2.55196 − 0.49030I
b = 0.014308 − 1.142590I
−4.93480 −2.00000
35
VI. I
v
1
= ha, −8v
2
+ b + 26v − 7, 4v
3
− 14v
2
+ 7v − 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
8v
2
− 26v + 7
a
9
=
1
−4v
2
+ 12v − 1
a
12
=
8v
2
− 26v + 7
8v
2
− 26v + 7
a
1
=
−1
−4v
2
+ 14v − 7
a
3
=
v
0
a
2
=
v − 1
−4v
2
+ 14v − 7
a
6
=
4v
2
− 12v + 2
4v
2
− 12v + 1
a
10
=
−8v
2
+ 26v − 7
−20v
2
+ 64v − 16
a
5
=
1
4v
2
− 14v + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13v
2
− 38v + 13
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
10
u
3
+ 2u + 1
c
9
, c
11
u
3
+ 2u − 1
c
12
u
3
− 3u
2
+ 5u − 2
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
3
+ 4y
2
+ 4y − 1
c
12
y
3
+ y
2
+ 13y − 4
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.283866 + 0.068399I
a = 0
b = 0.22670 − 1.46771I
−11.08570 − 5.13794I 3.19982 − 2.09434I
v = 0.283866 − 0.068399I
a = 0
b = 0.22670 + 1.46771I
−11.08570 + 5.13794I 3.19982 + 2.09434I
v = 2.93227
a = 0
b = −0.453398
−0.857735 13.3500
39
VII. I
v
2
= ha, b
4
− b
3
+ 2b
2
− 2b + 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
b
a
9
=
1
−b
2
a
12
=
b
b
a
1
=
b
3
+ 2b
1
a
3
=
−1
0
a
2
=
b
3
+ 2b − 1
1
a
6
=
b
2
+ 1
b
2
a
10
=
−2b
3
+ b
2
− 3b + 3
−b
3
− b + 1
a
5
=
−b
3
− 2b
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b
3
− 4b
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
8
c
10
u
4
− u
3
+ 2u
2
− 2u + 1
c
9
, c
11
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
12
(u
2
+ u + 1)
2
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
4
+ 3y
3
+ 2y
2
+ 1
c
12
(y
2
+ y + 1)
2
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 0.621744 + 0.440597I
−4.93480 + 2.02988I −2.00000 − 3.46410I
v = −1.00000
a = 0
b = 0.621744 − 0.440597I
−4.93480 − 2.02988I −2.00000 + 3.46410I
v = −1.00000
a = 0
b = −0.121744 + 1.306620I
−4.93480 − 2.02988I −2.00000 + 3.46410I
v = −1.00000
a = 0
b = −0.121744 − 1.306620I
−4.93480 + 2.02988I −2.00000 − 3.46410I
43
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
4
· ((u
17
+ 8u
16
+ ··· + 3u + 1)
4
)(u
21
− 11u
20
+ ··· + 2u − 1)
· (u
48
+ 25u
47
+ ··· + 18800u + 256)
c
2
((u − 1)
7
)(u
6
− 2u
4
+ ··· − u + 1)
4
(u
17
− 2u
16
+ ··· − u + 1)
4
· (u
21
+ 3u
20
+ ··· − 4u − 1)(u
48
− 3u
47
+ ··· + 76u + 16)
c
3
u
7
(u
2
− u + 1)
12
(u
17
+ 2u
16
+ ··· − 2u − 2)
4
(u
21
+ u
20
+ ··· − 2u − 1)
· (u
48
+ 6u
47
+ ··· − 608u − 128)
c
4
((u + 1)
7
)(u
6
− 2u
4
+ ··· − u + 1)
4
(u
17
− 2u
16
+ ··· − u + 1)
4
· (u
21
− 3u
20
+ ··· − 4u + 1)(u
48
− 3u
47
+ ··· + 76u + 16)
c
5
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
+ 6u
10
+ ··· − 2u + 4)
· (u
12
+ 6u
10
+ ··· − 8u + 1)(u
21
+ 12u
19
+ ··· + 5u − 1)
· (u
48
+ 19u
46
+ ··· − u − 1)(u
68
− 2u
67
+ ··· + 942u + 61)
c
6
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
+ 6u
10
+ ··· − 2u + 4)
· (u
12
+ 6u
10
+ ··· − 8u + 1)(u
21
+ 12u
19
+ ··· + 5u + 1)
· (u
48
+ 19u
46
+ ··· − u − 1)(u
68
− 2u
67
+ ··· + 942u + 61)
c
7
u
7
(u
2
− u + 1)
12
(u
17
+ 2u
16
+ ··· − 2u − 2)
4
(u
21
− u
20
+ ··· − 2u + 1)
· (u
48
+ 6u
47
+ ··· − 608u − 128)
c
8
, c
10
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
+ 4u
11
+ ··· + 14u + 13)
· (u
12
+ 4u
11
+ ··· + 14u + 4)(u
21
− 3u
20
+ ··· − 3u + 1)
· (u
48
− 3u
47
+ ··· − 23u + 1)(u
68
+ 18u
67
+ ··· + 8600u + 373)
c
9
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
12
+ 6u
10
+ ··· − 2u + 4)
· (u
12
+ 6u
10
+ ··· − 8u + 1)(u
21
+ 12u
19
+ ··· + 5u + 1)
· (u
48
+ 19u
46
+ ··· − u − 1)(u
68
− 2u
67
+ ··· + 942u + 61)
c
11
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
12
+ 6u
10
+ ··· − 2u + 4)
· (u
12
+ 6u
10
+ ··· − 8u + 1)(u
21
+ 12u
19
+ ··· + 5u − 1)
· (u
48
+ 19u
46
+ ··· − u − 1)(u
68
− 2u
67
+ ··· + 942u + 61)
c
12
((u
2
+ u + 1)
48
)(u
3
− 3u
2
+ 5u − 2)(u
21
+ 3u
20
+ ··· − 3u − 1)
· (u
48
− 51u
47
+ ··· − 285212672u + 8388608)
44
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
7
(y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
4
· ((y
17
+ 4y
16
+ ··· − 13y − 1)
4
)(y
21
+ y
20
+ ··· − 6y − 1)
· (y
48
− y
47
+ ··· − 279621376y + 65536)
c
2
, c
4
(y − 1)
7
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
4
· ((y
17
− 8y
16
+ ··· + 3y − 1)
4
)(y
21
− 11y
20
+ ··· + 2y − 1)
· (y
48
− 25y
47
+ ··· − 18800y + 256)
c
3
, c
7
y
7
(y
2
+ y + 1)
12
(y
17
+ 6y
16
+ ··· + 8y − 4)
4
· (y
21
+ 9y
20
+ ··· − 6y − 1)(y
48
+ 18y
47
+ ··· − 158720y + 16384)
c
5
, c
6
, c
9
c
11
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
12
+ 12y
11
+ ··· + 228y + 16)
· (y
12
+ 12y
11
+ ··· − 30y + 1)(y
21
+ 24y
20
+ ··· + 99y − 1)
· (y
48
+ 38y
47
+ ··· − 31y + 1)(y
68
+ 54y
67
+ ··· + 221616y + 3721)
c
8
, c
10
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
12
+ 8y
11
+ ··· + 132y + 16)
· (y
12
+ 8y
11
+ ··· + 558y + 169)(y
21
+ 3y
20
+ ··· − 3y − 1)
· (y
48
+ 5y
47
+ ··· − 237y + 1)
· (y
68
+ 14y
67
+ ··· + 20523884y + 139129)
c
12
((y
2
+ y + 1)
48
)(y
3
+ y
2
+ 13y − 4)(y
21
+ 3y
20
+ ··· − 3y − 1)
· (y
48
+ 5y
47
+ ··· − 5875790138834944y + 70368744177664)
45
