12n
0265
(K12n
0265
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 11 3 12 5 7 6
Solving Sequence
3,8 9,11
7 12 10 6 1 5 2 4
c
8
c
7
c
11
c
9
c
6
c
12
c
5
c
2
c
4
c
1
, c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.44371 × 10
49
u
24
− 2.09348 × 10
50
u
23
+ ··· + 2.28036 × 10
53
b − 8.49453 × 10
51
,
− 3.67178 × 10
50
u
24
+ 2.53945 × 10
51
u
23
+ ··· + 1.82429 × 10
54
a − 1.58059 × 10
54
,
u
25
− 7u
24
+ ··· − 768u − 1024i
I
u
2
= h1765a
5
u
4
− 1502a
4
u
4
+ ··· + 17362a − 4182, −2a
5
u
4
+ 22a
4
u
4
+ ··· − 398a − 265,
u
5
+ u
4
+ 5u
3
+ u
2
+ 2u − 2i
I
u
3
= h94430u
13
− 176465u
12
+ ··· + 3057583b − 933114,
11442968u
13
− 3792535u
12
+ ··· + 3057583a + 15949942,
u
14
+ 3u
12
+ 3u
11
− 5u
10
− 4u
9
− 11u
8
− 8u
7
+ 12u
6
− 8u
5
+ 20u
4
+ 6u
2
+ u + 1i
I
v
1
= ha, 8v
3
− 12v
2
+ b + 10v −3, 8v
4
− 12v
3
+ 12v
2
− 5v + 1i
I
v
2
= ha, b
6
− b
5
+ 2b
4
− 2b
3
+ 2b
2
− 2b + 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 79 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
= h2.44 × 10
49
u
24
− 2.09 × 10
50
u
23
+ · · · + 2.28 × 10
53
b − 8.49 ×
10
51
, −3.67 × 10
50
u
24
+ 2.54 × 10
51
u
23
+ · · · + 1.82 × 10
54
a − 1.58 ×
10
54
, u
25
− 7u
24
+ · · · − 768u − 1024i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
0.000201272u
24
− 0.00139202u
23
+ ··· + 0.373312u + 0.866413
−0.000107163u
24
+ 0.000918045u
23
+ ··· + 0.329212u + 0.0372508
a
7
=
0.000229394u
24
− 0.00150305u
23
+ ··· + 0.0571684u + 0.797253
0.000436197u
24
− 0.00314869u
23
+ ··· + 0.195357u − 0.517398
a
12
=
0.000142173u
24
− 0.000866042u
23
+ ··· + 0.288083u + 0.794249
0.0000403596u
24
− 0.000408965u
23
+ ··· + 0.135333u − 0.227239
a
10
=
0.000280396u
24
− 0.00189155u
23
+ ··· + 0.798559u + 1.20818
−0.000127304u
24
+ 0.00120796u
23
+ ··· + 0.0853997u + 0.470901
a
6
=
0.000729995u
24
− 0.00506873u
23
+ ··· + 0.566298u + 0.385020
0.000193200u
24
− 0.00159495u
23
+ ··· − 0.270058u − 0.454462
a
1
=
0.000602735u
24
− 0.00397878u
23
+ ··· + 0.982564u + 0.885973
−0.000178179u
24
+ 0.00103362u
23
+ ··· − 0.219803u − 0.141734
a
5
=
0.000548097u
24
− 0.00349779u
23
+ ··· + 0.400564u + 0.781569
−0.0000546374u
24
+ 0.000480983u
23
+ ··· − 0.582000u − 0.104403
a
2
=
0.000602735u
24
− 0.00397878u
23
+ ··· + 0.982564u + 0.885973
0.0000546374u
24
− 0.000480983u
23
+ ··· + 0.582000u + 0.104403
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00281397u
24
+ 0.0194032u
23
+ ··· − 9.17416u + 2.20110
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
+ 25u
24
+ ··· − 39680u + 4096
c
2
, c
4
u
25
− 5u
24
+ ··· − 272u + 64
c
3
, c
8
u
25
+ 7u
24
+ ··· − 768u + 1024
c
5
, c
7
, c
10
c
11
u
25
+ 16u
23
+ ··· − 4u − 1
c
6
, c
12
u
25
− u
24
+ ··· − 3u − 1
c
9
u
25
− 17u
24
+ ··· + 304u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 45y
24
+ ··· + 260374528y −16777216
c
2
, c
4
y
25
− 25y
24
+ ··· − 39680y −4096
c
3
, c
8
y
25
+ 15y
24
+ ··· + 3473408y −1048576
c
5
, c
7
, c
10
c
11
y
25
+ 32y
24
+ ··· + 6y −1
c
6
, c
12
y
25
− 19y
24
+ ··· − 27y −1
c
9
y
25
+ 3y
24
+ ··· + 6912y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239284 + 0.960930I
a = 0.533027 − 0.309402I
b = 0.493247 + 0.016890I
−0.98698 − 2.00436I 0.63223 + 3.08678I
u = −0.239284 − 0.960930I
a = 0.533027 + 0.309402I
b = 0.493247 − 0.016890I
−0.98698 + 2.00436I 0.63223 − 3.08678I
u = 0.966851
a = 0.382684
b = −0.452501
−3.00634 −1.07640
u = 1.116350 + 0.182242I
a = 0.381438 − 0.739225I
b = −0.224461 − 0.800052I
0.48422 + 3.81324I 7.26566 − 4.06355I
u = 1.116350 − 0.182242I
a = 0.381438 + 0.739225I
b = −0.224461 + 0.800052I
0.48422 − 3.81324I 7.26566 + 4.06355I
u = −0.697727 + 0.198752I
a = −0.164828 + 0.368624I
b = 0.521134 + 1.221040I
−3.96011 + 7.15054I 0.209463 − 0.912602I
u = −0.697727 − 0.198752I
a = −0.164828 − 0.368624I
b = 0.521134 − 1.221040I
−3.96011 − 7.15054I 0.209463 + 0.912602I
u = 0.407422 + 1.271680I
a = 0.154193 + 0.247049I
b = 0.470617 + 0.132952I
−7.17114 + 4.86761I 3.67428 + 1.38704I
u = 0.407422 − 1.271680I
a = 0.154193 − 0.247049I
b = 0.470617 − 0.132952I
−7.17114 − 4.86761I 3.67428 − 1.38704I
u = 0.356543 + 0.532418I
a = 1.40268 − 0.66297I
b = 0.145873 − 0.427689I
−1.84591 − 0.75519I −5.74786 − 0.43805I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356543 − 0.532418I
a = 1.40268 + 0.66297I
b = 0.145873 + 0.427689I
−1.84591 + 0.75519I −5.74786 + 0.43805I
u = −0.481170 + 0.308405I
a = 0.517741 + 0.397349I
b = −0.458678 + 0.410360I
0.898356 − 0.808185I 6.63316 + 4.13450I
u = −0.481170 − 0.308405I
a = 0.517741 − 0.397349I
b = −0.458678 − 0.410360I
0.898356 + 0.808185I 6.63316 − 4.13450I
u = −1.24876 + 0.83504I
a = 0.202515 − 0.510317I
b = −0.516721 − 1.100670I
−0.688755 − 0.842359I −3.27794 − 2.99522I
u = −1.24876 − 0.83504I
a = 0.202515 + 0.510317I
b = −0.516721 + 1.100670I
−0.688755 + 0.842359I −3.27794 + 2.99522I
u = −0.19971 + 2.12744I
a = 0.089187 + 1.142770I
b = −0.29018 + 1.74806I
−12.2506 − 8.8129I −5.58581 + 4.80434I
u = −0.19971 − 2.12744I
a = 0.089187 − 1.142770I
b = −0.29018 − 1.74806I
−12.2506 + 8.8129I −5.58581 − 4.80434I
u = 1.03266 + 1.89173I
a = 0.583269 − 0.980042I
b = −0.67321 − 1.74414I
19.0826 + 15.6197I −5.76128 − 6.47974I
u = 1.03266 − 1.89173I
a = 0.583269 + 0.980042I
b = −0.67321 + 1.74414I
19.0826 − 15.6197I −5.76128 + 6.47974I
u = −0.58061 + 2.17440I
a = −0.286368 − 1.009020I
b = 0.12493 − 1.68098I
−11.69760 + 0.19520I −6.36512 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58061 − 2.17440I
a = −0.286368 + 1.009020I
b = 0.12493 + 1.68098I
−11.69760 − 0.19520I −6.36512 + 0.I
u = 1.23926 + 1.89887I
a = −0.567788 + 0.851816I
b = 0.55518 + 1.55240I
−19.1706 + 7.3377I −6.38194 − 3.47918I
u = 1.23926 − 1.89887I
a = −0.567788 − 0.851816I
b = 0.55518 − 1.55240I
−19.1706 − 7.3377I −6.38194 + 3.47918I
u = 2.31161 + 0.19224I
a = −0.036412 + 0.377901I
b = 0.07852 + 1.79165I
−14.6508 + 4.4763I −6.63166 − 2.50646I
u = 2.31161 − 0.19224I
a = −0.036412 − 0.377901I
b = 0.07852 − 1.79165I
−14.6508 − 4.4763I −6.63166 + 2.50646I
7
II. I
u
2
= h1765a
5
u
4
− 1502a
4
u
4
+ · · · + 17362a − 4182, −2a
5
u
4
+ 22a
4
u
4
+
· · · − 398a − 265, u
5
+ u
4
+ 5u
3
+ u
2
+ 2u − 2i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
a
−1.22230a
5
u
4
+ 1.04017a
4
u
4
+ ··· − 12.0235a + 2.89612
a
7
=
−0.407202a
5
u
4
+ 1.61911a
4
u
4
+ ··· − 12.4986a + 10.4488
1.02216a
5
u
4
+ 0.364266a
4
u
4
+ ··· + 4.14958a − 2.79778
a
12
=
−1.26593a
5
u
4
+ 0.393352a
4
u
4
+ ··· − 13.1371a + 0.155125
−1.72022a
5
u
4
− 3.92521a
4
u
4
+ ··· + 10.4017a − 6.69252
a
10
=
0.0117729a
5
u
4
− 0.395429a
4
u
4
+ ··· + 4.60249a − 1.10665
−1.61150a
5
u
4
+ 0.450831a
4
u
4
+ ··· − 6.61773a + 1.48061
a
6
=
−0.407202a
5
u
4
+ 1.61911a
4
u
4
+ ··· − 12.4986a + 9.18560
1.02216a
5
u
4
+ 0.364266a
4
u
4
+ ··· + 4.14958a − 3.21884
a
1
=
1
4
u
4
+
1
2
u
3
+ ··· +
1
2
u −
1
2
1
4
u
4
+
3
2
u
3
+
7
4
u
2
+ u −
1
2
a
5
=
1
4
u
4
+
3
4
u
2
−
1
2
u −
1
2
−
1
2
u
3
−
1
2
u
2
− u
a
2
=
1
4
u
4
+
1
2
u
3
+ ··· +
1
2
u −
1
2
1
2
u
3
+
1
2
u
2
+ u
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
588
361
a
4
u
4
+
53
19
u
4
a
3
+ ··· +
434
19
a −
9308
361
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 8u
4
+ 22u
3
+ 25u
2
+ 15u + 1)
6
c
2
, c
4
(u
5
− 2u
4
− 2u
3
+ 3u
2
+ 3u − 1)
6
c
3
, c
8
(u
5
− u
4
+ 5u
3
− u
2
+ 2u + 2)
6
c
5
, c
7
, c
10
c
11
u
30
− 2u
29
+ ··· + 4896u + 1161
c
6
, c
12
u
30
− 6u
29
+ ··· − 2892u + 367
c
9
(u
3
+ u
2
− 1)
10
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 20y
4
+ 114y
3
+ 19y
2
+ 175y −1)
6
c
2
, c
4
(y
5
− 8y
4
+ 22y
3
− 25y
2
+ 15y −1)
6
c
3
, c
8
(y
5
+ 9y
4
+ 27y
3
+ 23y
2
+ 8y −4)
6
c
5
, c
7
, c
10
c
11
y
30
+ 30y
29
+ ··· + 10260108y + 1347921
c
6
, c
12
y
30
− 10y
29
+ ··· − 2032180y + 134689
c
9
(y
3
− y
2
+ 2y −1)
10
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.375669 + 0.888717I
a = −0.218883 + 0.638145I
b = −0.936331 − 0.693043I
−3.76205 + 3.93704I −6.85572 − 5.02057I
u = −0.375669 + 0.888717I
a = −1.341030 + 0.088898I
b = 0.131979 + 0.509733I
−3.76205 − 1.71921I −6.85572 + 0.93832I
u = −0.375669 + 0.888717I
a = −1.69246 − 1.78412I
b = −0.22064 − 1.80276I
−7.89964 + 1.10891I −13.38499 − 2.04112I
u = −0.375669 + 0.888717I
a = 0.48486 + 2.82858I
b = 0.03993 + 1.45055I
−7.89964 + 1.10891I −13.38499 − 2.04112I
u = −0.375669 + 0.888717I
a = −1.51063 − 2.46477I
b = 0.607737 − 1.057200I
−3.76205 − 1.71921I −6.85572 + 0.93832I
u = −0.375669 + 0.888717I
a = 2.15895 + 2.52617I
b = 0.060199 + 0.974637I
−3.76205 + 3.93704I −6.85572 − 5.02057I
u = −0.375669 − 0.888717I
a = −0.218883 − 0.638145I
b = −0.936331 + 0.693043I
−3.76205 − 3.93704I −6.85572 + 5.02057I
u = −0.375669 − 0.888717I
a = −1.341030 − 0.088898I
b = 0.131979 − 0.509733I
−3.76205 + 1.71921I −6.85572 − 0.93832I
u = −0.375669 − 0.888717I
a = −1.69246 + 1.78412I
b = −0.22064 + 1.80276I
−7.89964 − 1.10891I −13.38499 + 2.04112I
u = −0.375669 − 0.888717I
a = 0.48486 − 2.82858I
b = 0.03993 − 1.45055I
−7.89964 − 1.10891I −13.38499 + 2.04112I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.375669 − 0.888717I
a = −1.51063 + 2.46477I
b = 0.607737 + 1.057200I
−3.76205 + 1.71921I −6.85572 − 0.93832I
u = −0.375669 − 0.888717I
a = 2.15895 − 2.52617I
b = 0.060199 − 0.974637I
−3.76205 − 3.93704I −6.85572 + 5.02057I
u = 0.504107
a = 0.528054 + 0.820274I
b = 0.237566 − 1.254220I
−4.84461 −2.07647 + 0.I
u = 0.504107
a = 0.528054 − 0.820274I
b = 0.237566 + 1.254220I
−4.84461 −2.07647 + 0.I
u = 0.504107
a = 0.538593 + 0.918461I
b = −0.429107 + 0.992688I
−0.70702 − 2.82812I 4.45279 + 2.97945I
u = 0.504107
a = 0.538593 − 0.918461I
b = −0.429107 − 0.992688I
−0.70702 + 2.82812I 4.45279 − 2.97945I
u = 0.504107
a = −0.13998 + 1.50412I
b = 0.608440 + 0.097206I
−0.70702 − 2.82812I 4.45279 + 2.97945I
u = 0.504107
a = −0.13998 − 1.50412I
b = 0.608440 − 0.097206I
−0.70702 + 2.82812I 4.45279 − 2.97945I
u = −0.37638 + 2.02979I
a = 0.221103 + 0.952099I
b = −1.08899 + 2.05323I
−17.9582 − 4.1249I −12.12555 + 2.15443I
u = −0.37638 + 2.02979I
a = 0.136635 + 1.070190I
b = 0.16428 + 1.80622I
−13.82060 − 1.29678I −5.59629 − 0.82502I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.37638 + 2.02979I
a = −0.681231 − 0.969436I
b = 0.46229 − 1.40963I
−17.9582 − 4.1249I −12.12555 + 2.15443I
u = −0.37638 + 2.02979I
a = −0.131733 − 1.324220I
b = 0.14268 − 1.60991I
−13.8206 − 6.9530I −5.59629 + 5.13388I
u = −0.37638 + 2.02979I
a = −0.350074 − 0.021260I
b = 1.075530 − 0.125738I
−13.82060 − 1.29678I −5.59629 − 0.82502I
u = −0.37638 + 2.02979I
a = −0.002169 + 0.262200I
b = −1.85557 + 0.41527I
−13.8206 − 6.9530I −5.59629 + 5.13388I
u = −0.37638 − 2.02979I
a = 0.221103 − 0.952099I
b = −1.08899 − 2.05323I
−17.9582 + 4.1249I −12.12555 − 2.15443I
u = −0.37638 − 2.02979I
a = 0.136635 − 1.070190I
b = 0.16428 − 1.80622I
−13.82060 + 1.29678I −5.59629 + 0.82502I
u = −0.37638 − 2.02979I
a = −0.681231 + 0.969436I
b = 0.46229 + 1.40963I
−17.9582 + 4.1249I −12.12555 − 2.15443I
u = −0.37638 − 2.02979I
a = −0.131733 + 1.324220I
b = 0.14268 + 1.60991I
−13.8206 + 6.9530I −5.59629 − 5.13388I
u = −0.37638 − 2.02979I
a = −0.350074 + 0.021260I
b = 1.075530 + 0.125738I
−13.82060 + 1.29678I −5.59629 + 0.82502I
u = −0.37638 − 2.02979I
a = −0.002169 − 0.262200I
b = −1.85557 − 0.41527I
−13.8206 + 6.9530I −5.59629 − 5.13388I
13
III.
I
u
3
= h9.44 × 10
4
u
13
− 1.76 × 10
5
u
12
+ · · · + 3.06 × 10
6
b − 9.33 × 10
5
, 1.14 ×
10
7
u
13
− 3.79 × 10
6
u
12
+ · · · + 3.06 × 10
6
a + 1.59 × 10
7
, u
14
+ 3u
12
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
−3.74249u
13
+ 1.24037u
12
+ ··· − 13.2443u − 5.21652
−0.0308839u
13
+ 0.0577139u
12
+ ··· − 1.36605u + 0.305180
a
7
=
−2.42006u
13
− 0.985121u
12
+ ··· + 2.65790u − 6.80147
−0.316204u
13
− 0.0156306u
12
+ ··· − 1.02247u − 0.0647390
a
12
=
−1.65230u
13
− 0.528076u
12
+ ··· − 3.28689u − 9.41576
0.0490374u
13
− 0.177945u
12
+ ··· − 2.06678u − 0.528005
a
10
=
−3.08993u
13
+ 1.27423u
12
+ ··· − 12.9284u − 3.82414
−0.0308839u
13
+ 0.0577139u
12
+ ··· − 1.36605u + 0.305180
a
6
=
−1.81654u
13
− 0.773320u
12
+ ··· + 5.04060u − 5.88109
−0.349611u
13
+ 0.0608824u
12
+ ··· − 0.207156u + 0.147062
a
1
=
−0.721149u
13
+ 0.347374u
12
+ ··· − 3.07386u − 0.461186
−0.0528928u
13
+ 0.242971u
12
+ ··· + 0.414713u + 0.501461
a
5
=
0.671228u
13
− 0.305180u
12
+ ··· + 3.86235u + 0.615272
−0.0499215u
13
+ 0.0421941u
12
+ ··· + 0.788488u + 0.154087
a
2
=
−0.721149u
13
+ 0.347374u
12
+ ··· − 3.07386u − 0.461186
−0.0499215u
13
+ 0.0421941u
12
+ ··· + 0.788488u + 0.154087
a
4
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
9599746
3057583
u
13
−
14270512
3057583
u
12
+ ··· +
101040801
3057583
u −
56545536
3057583
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 14u
13
+ ··· − 5u + 1
c
2
u
14
+ 6u
13
+ ··· − 3u + 1
c
3
u
14
+ 3u
12
+ ··· − u + 1
c
4
u
14
− 6u
13
+ ··· + 3u + 1
c
5
, c
11
u
14
+ 7u
12
+ ··· − 3u + 1
c
6
, c
12
u
14
− 3u
13
+ ··· − 6u + 1
c
7
, c
10
u
14
+ 7u
12
+ ··· + 3u + 1
c
8
u
14
+ 3u
12
+ ··· + u + 1
c
9
u
14
− 5u
13
+ ··· + 2u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 22y
13
+ ··· + 143y + 1
c
2
, c
4
y
14
− 14y
13
+ ··· − 5y + 1
c
3
, c
8
y
14
+ 6y
13
+ ··· + 11y + 1
c
5
, c
7
, c
10
c
11
y
14
+ 14y
13
+ ··· + 9y + 1
c
6
, c
12
y
14
− 5y
13
+ ··· − 10y + 1
c
9
y
14
+ 5y
13
+ ··· + 4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139126 + 0.855284I
a = 0.02309 − 2.89055I
b = 0.10927 − 1.56543I
−7.24127 − 0.77135I −2.53833 − 3.61425I
u = 0.139126 − 0.855284I
a = 0.02309 + 2.89055I
b = 0.10927 + 1.56543I
−7.24127 + 0.77135I −2.53833 + 3.61425I
u = −0.352449 + 1.175430I
a = −0.266214 + 0.045704I
b = −0.341781 + 0.418746I
−7.50206 − 5.05550I −15.3583 + 8.9418I
u = −0.352449 − 1.175430I
a = −0.266214 − 0.045704I
b = −0.341781 − 0.418746I
−7.50206 + 5.05550I −15.3583 − 8.9418I
u = 1.229090 + 0.054546I
a = 0.515481 − 0.846913I
b = −0.262265 − 0.901818I
0.04153 + 3.93339I −9.88151 − 7.52594I
u = 1.229090 − 0.054546I
a = 0.515481 + 0.846913I
b = −0.262265 + 0.901818I
0.04153 − 3.93339I −9.88151 + 7.52594I
u = 0.196848 + 0.556043I
a = −2.17999 − 0.00411I
b = −0.381345 − 0.641179I
−2.19156 + 3.21998I −4.00004 − 4.18914I
u = 0.196848 − 0.556043I
a = −2.17999 + 0.00411I
b = −0.381345 + 0.641179I
−2.19156 − 3.21998I −4.00004 + 4.18914I
u = −1.40215 + 0.37579I
a = 0.298006 − 0.417984I
b = −0.283501 − 1.095790I
−0.69469 − 1.77882I −3.04716 + 4.98028I
u = −1.40215 − 0.37579I
a = 0.298006 + 0.417984I
b = −0.283501 + 1.095790I
−0.69469 + 1.77882I −3.04716 − 4.98028I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.229849 + 0.360057I
a = −9.97539 − 6.14831I
b = 0.420766 − 0.730987I
−3.49965 − 2.65520I −8.3154 + 25.3017I
u = −0.229849 − 0.360057I
a = −9.97539 + 6.14831I
b = 0.420766 + 0.730987I
−3.49965 + 2.65520I −8.3154 − 25.3017I
u = 0.41939 + 2.04733I
a = −0.414975 + 0.898851I
b = 0.73885 + 1.60027I
−16.7458 + 4.0257I −3.85923 − 1.44990I
u = 0.41939 − 2.04733I
a = −0.414975 − 0.898851I
b = 0.73885 − 1.60027I
−16.7458 − 4.0257I −3.85923 + 1.44990I
18
IV. I
v
1
= ha, 8v
3
− 12v
2
+ b + 10v − 3, 8v
4
− 12v
3
+ 12v
2
− 5v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
−8v
3
+ 12v
2
− 10v + 3
a
7
=
1
−8v
3
+ 8v
2
− 8v + 1
a
12
=
−8v
3
+ 12v
2
− 10v + 3
−8v
3
+ 8v
2
− 6v
a
10
=
8v
3
− 12v
2
+ 10v − 3
16v
3
− 16v
2
+ 14v − 2
a
6
=
−8v
3
+ 8v
2
− 8v + 2
−8v
3
+ 8v
2
− 8v + 1
a
1
=
−1
8v
3
− 12v
2
+ 12v − 5
a
5
=
1
−8v
3
+ 12v
2
− 12v + 5
a
2
=
v − 1
8v
3
− 12v
2
+ 12v − 5
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 72v
3
− 101v
2
+ 96v − 31
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
u
4
+ u
2
+ u + 1
c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
, c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.447562 + 0.776246I
a = 0
b = −0.547424 + 0.585652I
−0.66484 − 1.39709I 0.79646 + 4.25046I
v = 0.447562 − 0.776246I
a = 0
b = −0.547424 − 0.585652I
−0.66484 + 1.39709I 0.79646 − 4.25046I
v = 0.302438 + 0.253422I
a = 0
b = 0.547424 − 1.120870I
−4.26996 − 7.64338I −6.9215 + 12.6814I
v = 0.302438 − 0.253422I
a = 0
b = 0.547424 + 1.120870I
−4.26996 + 7.64338I −6.9215 − 12.6814I
22
V. I
v
2
= ha, b
6
− b
5
+ 2b
4
− 2b
3
+ 2b
2
− 2b + 1, v + 1i
(i) Arc colorings
a
3
=
−1
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
b
a
7
=
1
b
2
a
12
=
b
b
3
+ b
a
10
=
b
4
+ b
2
+ 1
b
5
+ 2b
3
− b
2
+ 2b − 1
a
6
=
b
2
+ 1
b
2
a
1
=
−b
5
− 2b
3
− b + 1
1
a
5
=
b
5
+ 2b
3
+ b − 1
−1
a
2
=
−b
5
− 2b
3
− b
1
a
4
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
3
+ 4b − 8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
(u
3
− u
2
+ 1)
2
c
10
, c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
9
(y
3
− y
2
+ 2y − 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.498832 + 1.001300I
−1.91067 − 2.82812I −4.49024 + 2.97945I
v = −1.00000
a = 0
b = −0.498832 − 1.001300I
−1.91067 + 2.82812I −4.49024 − 2.97945I
v = −1.00000
a = 0
b = 0.284920 + 1.115140I
−6.04826 −11.01951 + 0.I
v = −1.00000
a = 0
b = 0.284920 − 1.115140I
−6.04826 −11.01951 + 0.I
v = −1.00000
a = 0
b = 0.713912 + 0.305839I
−1.91067 − 2.82812I −4.49024 + 2.97945I
v = −1.00000
a = 0
b = 0.713912 − 0.305839I
−1.91067 + 2.82812I −4.49024 − 2.97945I
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
5
+ 8u
4
+ 22u
3
+ 25u
2
+ 15u + 1)
6
· (u
14
− 14u
13
+ ··· − 5u + 1)(u
25
+ 25u
24
+ ··· − 39680u + 4096)
c
2
((u − 1)
10
)(u
5
− 2u
4
+ ··· + 3u − 1)
6
(u
14
+ 6u
13
+ ··· − 3u + 1)
· (u
25
− 5u
24
+ ··· − 272u + 64)
c
3
u
10
(u
5
− u
4
+ ··· + 2u + 2)
6
(u
14
+ 3u
12
+ ··· − u + 1)
· (u
25
+ 7u
24
+ ··· − 768u + 1024)
c
4
((u + 1)
10
)(u
5
− 2u
4
+ ··· + 3u − 1)
6
(u
14
− 6u
13
+ ··· + 3u + 1)
· (u
25
− 5u
24
+ ··· − 272u + 64)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
14
+ 7u
12
+ ··· − 3u + 1)(u
25
+ 16u
23
+ ··· − 4u − 1)
· (u
30
− 2u
29
+ ··· + 4896u + 1161)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
14
− 3u
13
+ ··· − 6u + 1)(u
25
− u
24
+ ··· − 3u − 1)
· (u
30
− 6u
29
+ ··· − 2892u + 367)
c
7
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
14
+ 7u
12
+ ··· + 3u + 1)(u
25
+ 16u
23
+ ··· − 4u − 1)
· (u
30
− 2u
29
+ ··· + 4896u + 1161)
c
8
u
10
(u
5
− u
4
+ ··· + 2u + 2)
6
(u
14
+ 3u
12
+ ··· + u + 1)
· (u
25
+ 7u
24
+ ··· − 768u + 1024)
c
9
(u
3
− u
2
+ 1)
2
(u
3
+ u
2
− 1)
10
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
14
− 5u
13
+ ··· + 2u
2
+ 1)(u
25
− 17u
24
+ ··· + 304u − 32)
c
10
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
14
+ 7u
12
+ ··· + 3u + 1)(u
25
+ 16u
23
+ ··· − 4u − 1)
· (u
30
− 2u
29
+ ··· + 4896u + 1161)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
14
+ 7u
12
+ ··· − 3u + 1)(u
25
+ 16u
23
+ ··· − 4u − 1)
· (u
30
− 2u
29
+ ··· + 4896u + 1161)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
14
− 3u
13
+ ··· − 6u + 1)(u
25
− u
24
+ ··· − 3u − 1)
· (u
30
− 6u
29
+ ··· − 2892u + 367)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
(y
5
− 20y
4
+ 114y
3
+ 19y
2
+ 175y − 1)
6
· (y
14
− 22y
13
+ ··· + 143y + 1)
· (y
25
− 45y
24
+ ··· + 260374528y − 16777216)
c
2
, c
4
(y − 1)
10
(y
5
− 8y
4
+ 22y
3
− 25y
2
+ 15y − 1)
6
· (y
14
− 14y
13
+ ··· − 5y + 1)(y
25
− 25y
24
+ ··· − 39680y − 4096)
c
3
, c
8
y
10
(y
5
+ 9y
4
+ ··· + 8y − 4)
6
(y
14
+ 6y
13
+ ··· + 11y + 1)
· (y
25
+ 15y
24
+ ··· + 3473408y − 1048576)
c
5
, c
7
, c
10
c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
14
+ 14y
13
+ ··· + 9y + 1)(y
25
+ 32y
24
+ ··· + 6y − 1)
· (y
30
+ 30y
29
+ ··· + 10260108y + 1347921)
c
6
, c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
14
− 5y
13
+ ··· − 10y + 1)(y
25
− 19y
24
+ ··· − 27y − 1)
· (y
30
− 10y
29
+ ··· − 2032180y + 134689)
c
9
((y
3
− y
2
+ 2y − 1)
12
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
14
+ 5y
13
+ ··· + 4y + 1)
· (y
25
+ 3y
24
+ ··· + 6912y − 1024)
28
