12n
0016
(K12n
0016
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 4 12 6 8 9 11
Solving Sequence
4,7
8
5,10
11 6 3 2 1 9 12
c
7
c
4
c
10
c
6
c
3
c
2
c
1
c
9
c
11
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, 224074u
9
+ 244456u
8
+ Β·Β·Β· + 85463a + 346296,
u
10
+ u
9
βˆ’ 7u
8
βˆ’ 14u
7
+ 16u
6
+ 17u
5
βˆ’ 3u
4
βˆ’ 10u
3
βˆ’ 3u
2
+ u βˆ’ 1i
I
u
2
= h5.86389 Γ— 10
37
u
19
+ 1.09059 Γ— 10
38
u
18
+ Β·Β·Β· + 1.52045 Γ— 10
41
b βˆ’ 1.97465 Γ— 10
40
,
βˆ’ 1.68947 Γ— 10
39
u
19
βˆ’ 3.22641 Γ— 10
39
u
18
+ Β·Β·Β· + 1.21636 Γ— 10
42
a βˆ’ 1.00257 Γ— 10
42
,
u
20
+ 2u
19
+ Β·Β·Β· βˆ’ 2048u + 1024i
I
u
3
= hb, u
4
a βˆ’ 2u
3
a βˆ’ 3u
4
βˆ’ u
2
a + 3u
3
+ a
2
+ 3au + 7u
2
βˆ’ 5u βˆ’ 4, u
5
βˆ’ u
4
βˆ’ 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, 8286v
9
βˆ’ 14092v
8
+ Β·Β·Β· + 8095b + 12581,
v
10
βˆ’ v
9
βˆ’ 2v
8
βˆ’ 19v
7
+ 12v
6
+ 35v
5
+ 50v
4
+ 34v
3
+ 17v
2
+ 5v + 1i
* 4 irreducible components of dim
C
= 0, with total 50 representations.
1
The image of knot diagram is generated by the software β€œDraw 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, 224074u
9
+244456u
8
+Β· Β· Β·+85463a+346296, u
10
+u
9
+Β· Β· Β·+uβˆ’1i
(i) Arc colorings
a
4
=
ξ€’
0
u

a
7
=
ξ€’
1
0

a
8
=
ξ€’
1
u
2

a
5
=
ξ€’
βˆ’u
βˆ’u
3
+ u

a
10
=
ξ€’
βˆ’2.62188u
9
βˆ’ 2.86037u
8
+ Β·Β·Β· + 12.1063u βˆ’ 4.05200
βˆ’u

a
11
=
ξ€’
βˆ’2.43179u
9
βˆ’ 2.58767u
8
+ Β·Β·Β· + 10.7229u βˆ’ 4.29049
0.0122626u
9
βˆ’ 0.0607046u
8
+ Β·Β·Β· βˆ’ 0.892515u + 0.0826088

a
6
=
ξ€’
βˆ’0.238489u
9
βˆ’ 0.0483952u
8
+ Β·Β·Β· βˆ’ 1.43012u βˆ’ 1.62188
βˆ’u
2

a
3
=
ξ€’
βˆ’0.367925u
9
βˆ’ 0.606110u
8
+ Β·Β·Β· + 3.87427u + 0.559587
βˆ’0.0122626u
9
+ 0.0607046u
8
+ Β·Β·Β· + 0.892515u βˆ’ 0.0826088

a
2
=
ξ€’
βˆ’0.404257u
9
βˆ’ 0.758316u
8
+ Β·Β·Β· + 4.08826u + 0.692697
βˆ’0.122310u
9
βˆ’ 0.00902145u
8
+ Β·Β·Β· + 0.758071u βˆ’ 0.331594

a
1
=
ξ€’
0.238489u
9
+ 0.0483952u
8
+ Β·Β·Β· + 1.43012u + 1.62188
βˆ’0.0826088u
9
βˆ’ 0.0948715u
8
+ Β·Β·Β· + 0.428583u βˆ’ 0.190094

a
9
=
ξ€’
βˆ’2.81198u
9
βˆ’ 3.13308u
8
+ Β·Β·Β· + 13.4897u βˆ’ 3.81351
u
3
βˆ’ u

a
12
=
ξ€’
βˆ’1.14164u
9
βˆ’ 0.462949u
8
+ Β·Β·Β· βˆ’ 5.42663u βˆ’ 7.69845
0.122310u
9
+ 0.00902145u
8
+ Β·Β·Β· βˆ’ 0.758071u + 0.331594

(ii) Obstruction class = βˆ’1
(iii) Cusp Shapes = βˆ’
765256
85463
u
9
βˆ’
1261184
85463
u
8
+
4740376
85463
u
7
+
14048256
85463
u
6
βˆ’
4533392
85463
u
5
βˆ’
19248384
85463
u
4
βˆ’
7535280
85463
u
3
+
7955648
85463
u
2
+
7424384
85463
u +
490522
85463
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
10
+ 5u
9
+ 13u
8
+ 12u
7
βˆ’ 12u
6
βˆ’ 51u
5
βˆ’ 65u
4
βˆ’ 44u
3
βˆ’ 13u
2
+ u + 1
c
2
, c
5
, c
8
c
11
u
10
+ 3u
9
+ 7u
8
+ 10u
7
+ 12u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 5u
2
+ 3u + 1
c
3
, c
10
u
10
βˆ’ 3u
9
βˆ’ 9u
8
+ 36u
7
βˆ’ 12u
6
βˆ’ 7u
5
βˆ’ 23u
4
+ 13u
3
+ 16u
2
+ 3u + 2
c
4
, c
6
, c
7
c
9
u
10
+ u
9
βˆ’ 7u
8
βˆ’ 14u
7
+ 16u
6
+ 17u
5
βˆ’ 3u
4
βˆ’ 10u
3
βˆ’ 3u
2
+ u βˆ’ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
10
+ y
9
+ Β·Β·Β· βˆ’ 27y + 1
c
2
, c
5
, c
8
c
11
y
10
+ 5y
9
+ 13y
8
+ 12y
7
βˆ’ 12y
6
βˆ’ 51y
5
βˆ’ 65y
4
βˆ’ 44y
3
βˆ’ 13y
2
+ y + 1
c
3
, c
10
y
10
βˆ’ 27y
9
+ Β·Β·Β· + 55y + 4
c
4
, c
6
, c
7
c
9
y
10
βˆ’ 15y
9
+ Β·Β·Β· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
βˆ’1(vol +
√
βˆ’1CS) Cusp shape
u = 1.051110 + 0.169733I
a = 0.075124 + 0.218323I
b = βˆ’1.051110 βˆ’ 0.169733I
βˆ’6.66754 βˆ’ 7.26680I βˆ’14.1481 + 8.5135I
u = 1.051110 βˆ’ 0.169733I
a = 0.075124 βˆ’ 0.218323I
b = βˆ’1.051110 + 0.169733I
βˆ’6.66754 + 7.26680I βˆ’14.1481 βˆ’ 8.5135I
u = βˆ’0.766019
a = 0.342395
b = 0.766019
βˆ’1.35955 βˆ’6.41950
u = βˆ’0.505971 + 0.548673I
a = 0.308348 + 0.874136I
b = 0.505971 βˆ’ 0.548673I
βˆ’1.23733 + 1.36545I βˆ’9.59143 βˆ’ 3.61875I
u = βˆ’0.505971 βˆ’ 0.548673I
a = 0.308348 βˆ’ 0.874136I
b = 0.505971 + 0.548673I
βˆ’1.23733 βˆ’ 1.36545I βˆ’9.59143 + 3.61875I
u = 0.171353 + 0.321669I
a = βˆ’4.31436 + 8.42917I
b = βˆ’0.171353 βˆ’ 0.321669I
βˆ’0.16069 βˆ’ 3.80568I 19.6494 + 42.7056I
u = 0.171353 βˆ’ 0.321669I
a = βˆ’4.31436 βˆ’ 8.42917I
b = βˆ’0.171353 + 0.321669I
βˆ’0.16069 + 3.80568I 19.6494 βˆ’ 42.7056I
u = βˆ’2.11995 + 1.24678I
a = 0.704601 + 0.550226I
b = 2.11995 βˆ’ 1.24678I
17.3702 + 13.6949I βˆ’8.24581 βˆ’ 5.79353I
u = βˆ’2.11995 βˆ’ 1.24678I
a = 0.704601 βˆ’ 0.550226I
b = 2.11995 + 1.24678I
17.3702 βˆ’ 13.6949I βˆ’8.24581 + 5.79353I
u = 2.57293
a = βˆ’0.889824
b = βˆ’2.57293
βˆ’13.9598 βˆ’4.90870
5
II. I
u
2
= h5.86 Γ— 10
37
u
19
+ 1.09 Γ— 10
38
u
18
+ Β· Β· Β· + 1.52 Γ— 10
41
b βˆ’ 1.97 Γ—
10
40
, βˆ’1.69 Γ— 10
39
u
19
βˆ’ 3.23 Γ— 10
39
u
18
+ Β· Β· Β· + 1.22 Γ— 10
42
a βˆ’ 1.00 Γ—
10
42
, u
20
+ 2u
19
+ Β· Β· Β· βˆ’ 2048u + 1024i
(i) Arc colorings
a
4
=
ξ€’
0
u

a
7
=
ξ€’
1
0

a
8
=
ξ€’
1
u
2

a
5
=
ξ€’
βˆ’u
βˆ’u
3
+ u

a
10
=
ξ€’
0.00138896u
19
+ 0.00265251u
18
+ Β·Β·Β· + 3.64638u + 0.824235
βˆ’0.000385667u
19
βˆ’ 0.000717282u
18
+ Β·Β·Β· βˆ’ 1.18247u + 0.129872

a
11
=
ξ€’
0.00151255u
19
+ 0.00313681u
18
+ Β·Β·Β· + 3.14973u + 0.822778
βˆ’0.000451559u
19
βˆ’ 0.000899794u
18
+ Β·Β·Β· βˆ’ 0.823414u βˆ’ 0.112935

a
6
=
ξ€’
0.000295502u
19
+ 0.000835151u
18
+ Β·Β·Β· βˆ’ 2.41530u + 0.836394
βˆ’1.74761 Γ— 10
βˆ’6
u
19
βˆ’ 0.0000459509u
18
+ Β·Β·Β· + 0.619191u + 0.0512561

a
3
=
ξ€’
βˆ’0.000175793u
19
βˆ’ 0.000736748u
18
+ Β·Β·Β· + 3.47292u βˆ’ 1.24551
0.000101127u
19
+ 0.000225173u
18
+ Β·Β·Β· + 0.697375u + 0.189635

a
2
=
ξ€’
βˆ’0.000515937u
19
βˆ’ 0.00143281u
18
+ Β·Β·Β· + 3.99150u βˆ’ 1.66721
0.000576429u
19
+ 0.00110414u
18
+ Β·Β·Β· + 0.494790u + 0.627482

a
1
=
ξ€’
βˆ’0.000293754u
19
βˆ’ 0.000789200u
18
+ Β·Β·Β· + 1.79611u βˆ’ 0.887650
0.000158683u
19
+ 0.000288930u
18
+ Β·Β·Β· + 0.506931u + 0.257788

a
9
=
ξ€’
0.00144125u
19
+ 0.00289745u
18
+ Β·Β·Β· + 2.51554u + 1.04162
βˆ’0.000525250u
19
βˆ’ 0.000988354u
18
+ Β·Β·Β· βˆ’ 1.00784u + 0.125174

a
12
=
ξ€’
0.000756916u
19
+ 0.00212323u
18
+ Β·Β·Β· βˆ’ 1.07571u + 3.13147
βˆ’0.000291771u
19
βˆ’ 0.000735805u
18
+ Β·Β·Β· βˆ’ 0.338968u βˆ’ 0.810783

(ii) Obstruction class = βˆ’1
(iii) Cusp Shapes = βˆ’0.00176167u
19
βˆ’ 0.00309564u
18
+ Β·Β·Β· βˆ’ 12.6991u βˆ’ 1.09946
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
20
+ 19u
19
+ Β·Β·Β· + 175u + 1
c
2
, c
5
, c
8
c
11
u
20
+ 5u
19
+ Β·Β·Β· + 5u + 1
c
3
, c
10
u
20
βˆ’ 5u
19
+ Β·Β·Β· + 2619u + 641
c
4
, c
6
, c
7
c
9
u
20
+ 2u
19
+ Β·Β·Β· βˆ’ 2048u + 1024
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
20
βˆ’ 29y
19
+ Β·Β·Β· βˆ’ 13889y + 1
c
2
, c
5
, c
8
c
11
y
20
+ 19y
19
+ Β·Β·Β· + 175y + 1
c
3
, c
10
y
20
βˆ’ 53y
19
+ Β·Β·Β· + 71819743y + 410881
c
4
, c
6
, c
7
c
9
y
20
βˆ’ 50y
19
+ Β·Β·Β· + 4194304y + 1048576
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
βˆ’1(vol +
√
βˆ’1CS) Cusp shape
u = βˆ’0.804594 + 0.696559I
a = βˆ’0.002315 βˆ’ 0.280709I
b = βˆ’1.396170 βˆ’ 0.196408I
βˆ’4.73849 + 3.00338I βˆ’7.64371 βˆ’ 3.35763I
u = βˆ’0.804594 βˆ’ 0.696559I
a = βˆ’0.002315 + 0.280709I
b = βˆ’1.396170 + 0.196408I
βˆ’4.73849 βˆ’ 3.00338I βˆ’7.64371 + 3.35763I
u = βˆ’0.257283 + 0.651285I
a = βˆ’1.12449 βˆ’ 2.84653I
b = 0.257283 + 0.651285I
βˆ’0.537213 βˆ’6 βˆ’ 1.350198 + 0.10I
u = βˆ’0.257283 βˆ’ 0.651285I
a = βˆ’1.12449 + 2.84653I
b = 0.257283 βˆ’ 0.651285I
βˆ’0.537213 βˆ’6 βˆ’ 1.350198 + 0.10I
u = 1.396170 + 0.196408I
a = 0.160795 + 0.137994I
b = 0.804594 βˆ’ 0.696559I
βˆ’4.73849 + 3.00338I βˆ’7.64371 βˆ’ 3.35763I
u = 1.396170 βˆ’ 0.196408I
a = 0.160795 βˆ’ 0.137994I
b = 0.804594 + 0.696559I
βˆ’4.73849 βˆ’ 3.00338I βˆ’7.64371 + 3.35763I
u = βˆ’0.204722 + 0.532348I
a = 1.241470 + 0.214157I
b = βˆ’0.241836 βˆ’ 0.217250I
βˆ’0.35106 + 1.66079I βˆ’2.53678 βˆ’ 3.96410I
u = βˆ’0.204722 βˆ’ 0.532348I
a = 1.241470 βˆ’ 0.214157I
b = βˆ’0.241836 + 0.217250I
βˆ’0.35106 βˆ’ 1.66079I βˆ’2.53678 + 3.96410I
u = 0.241836 + 0.217250I
a = 0.42599 + 2.16885I
b = 0.204722 βˆ’ 0.532348I
βˆ’0.35106 + 1.66079I βˆ’2.53678 βˆ’ 3.96410I
u = 0.241836 βˆ’ 0.217250I
a = 0.42599 βˆ’ 2.16885I
b = 0.204722 + 0.532348I
βˆ’0.35106 βˆ’ 1.66079I βˆ’2.53678 + 3.96410I
9
Solutions to I
u
2
√
βˆ’1(vol +
√
βˆ’1CS) Cusp shape
u = βˆ’0.55408 + 2.01462I
a = βˆ’0.191665 βˆ’ 0.696885I
b = 0.55408 + 2.01462I
βˆ’4.58401 βˆ’9.53898 + 0.I
u = βˆ’0.55408 βˆ’ 2.01462I
a = βˆ’0.191665 + 0.696885I
b = 0.55408 βˆ’ 2.01462I
βˆ’4.58401 βˆ’9.53898 + 0.I
u = 2.55394 + 0.67960I
a = 0.797707 βˆ’ 0.266076I
b = 2.56756 + 0.95364I
βˆ’18.4617 βˆ’ 6.7670I βˆ’6.82707 + 2.49268I
u = 2.55394 βˆ’ 0.67960I
a = 0.797707 + 0.266076I
b = 2.56756 βˆ’ 0.95364I
βˆ’18.4617 + 6.7670I βˆ’6.82707 βˆ’ 2.49268I
u = βˆ’2.56756 + 0.95364I
a = βˆ’0.741704 βˆ’ 0.329004I
b = βˆ’2.55394 + 0.67960I
βˆ’18.4617 + 6.7670I βˆ’6.82707 βˆ’ 2.49268I
u = βˆ’2.56756 βˆ’ 0.95364I
a = βˆ’0.741704 + 0.329004I
b = βˆ’2.55394 βˆ’ 0.67960I
βˆ’18.4617 βˆ’ 6.7670I βˆ’6.82707 + 2.49268I
u = 2.62678 + 1.73277I
a = βˆ’0.171297 + 0.112997I
b = βˆ’2.62678 + 1.73277I
βˆ’12.4152 βˆ’9.95005 + 0.I
u = 2.62678 βˆ’ 1.73277I
a = βˆ’0.171297 βˆ’ 0.112997I
b = βˆ’2.62678 βˆ’ 1.73277I
βˆ’12.4152 βˆ’9.95005 + 0.I
u = βˆ’3.43049 + 0.37740I
a = 0.605506 + 0.066614I
b = 3.43049 + 0.37740I
15.2909 βˆ’9.14565 + 0.I
u = βˆ’3.43049 βˆ’ 0.37740I
a = 0.605506 βˆ’ 0.066614I
b = 3.43049 βˆ’ 0.37740I
15.2909 βˆ’9.14565 + 0.I
10
III. I
u
3
= hb, u
4
a βˆ’ 3u
4
+ Β· Β· Β· + a
2
βˆ’ 4, u
5
βˆ’ u
4
βˆ’ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
ξ€’
0
u

a
7
=
ξ€’
1
0

a
8
=
ξ€’
1
u
2

a
5
=
ξ€’
βˆ’u
βˆ’u
3
+ u

a
10
=
ξ€’
a
0

a
11
=
ξ€’
u
2
a + a
u
4
a

a
6
=
ξ€’
1
0

a
3
=
ξ€’
u
u

a
2
=
ξ€’
u
4
βˆ’ u
2
βˆ’ 1
u
4
βˆ’ 2u
2

a
1
=
ξ€’
βˆ’1
βˆ’u
2

a
9
=
ξ€’
a
0

a
12
=
ξ€’
u
4
+ u
2
a βˆ’ 2u
3
βˆ’ u
2
+ a + 3u
u
4
a

(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
a + 3u
3
a + 3u
4
βˆ’ 5u
2
a + u
3
βˆ’ 5au βˆ’ 7u
2
βˆ’ a βˆ’ 3u βˆ’ 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
βˆ’ 3u
4
+ 4u
3
βˆ’ u
2
βˆ’ u + 1)
2
c
2
(u
5
βˆ’ u
4
+ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
c
3
, c
4
(u
5
+ u
4
βˆ’ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
9
u
10
c
7
(u
5
βˆ’ u
4
βˆ’ 2u
3
+ u
2
+ u + 1)
2
c
8
, c
10
, c
12
(u
2
+ u + 1)
5
c
11
(u
2
βˆ’ u + 1)
5
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
βˆ’ y
4
+ 8y
3
βˆ’ 3y
2
+ 3y βˆ’ 1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
βˆ’ y βˆ’ 1)
2
c
3
, c
4
, c
7
(y
5
βˆ’ 5y
4
+ 8y
3
βˆ’ 3y
2
βˆ’ y βˆ’ 1)
2
c
6
, c
9
y
10
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
5
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
βˆ’1(vol +
√
βˆ’1CS) Cusp shape
u = βˆ’1.21774
a = βˆ’0.337181 + 0.584015I
b = 0
βˆ’2.40108 + 2.02988I βˆ’6.80799 βˆ’ 1.95361I
u = βˆ’1.21774
a = βˆ’0.337181 βˆ’ 0.584015I
b = 0
βˆ’2.40108 βˆ’ 2.02988I βˆ’6.80799 + 1.95361I
u = βˆ’0.309916 + 0.549911I
a = 2.50919 + 0.05217I
b = 0
βˆ’0.32910 + 3.56046I βˆ’7.97351 βˆ’ 2.70956I
u = βˆ’0.309916 + 0.549911I
a = βˆ’1.20942 βˆ’ 2.19910I
b = 0
βˆ’0.329100 βˆ’ 0.499304I 1.93681 βˆ’ 0.71136I
u = βˆ’0.309916 βˆ’ 0.549911I
a = 2.50919 βˆ’ 0.05217I
b = 0
βˆ’0.32910 βˆ’ 3.56046I βˆ’7.97351 + 2.70956I
u = βˆ’0.309916 βˆ’ 0.549911I
a = βˆ’1.20942 + 2.19910I
b = 0
βˆ’0.329100 + 0.499304I 1.93681 + 0.71136I
u = 1.41878 + 0.21917I
a = βˆ’0.358089 βˆ’ 0.327409I
b = 0
βˆ’5.87256 βˆ’ 6.43072I βˆ’8.34383 + 2.96651I
u = 1.41878 + 0.21917I
a = βˆ’0.104500 + 0.473819I
b = 0
βˆ’5.87256 βˆ’ 2.37095I βˆ’12.81148 + 1.72217I
u = 1.41878 βˆ’ 0.21917I
a = βˆ’0.358089 + 0.327409I
b = 0
βˆ’5.87256 + 6.43072I βˆ’8.34383 βˆ’ 2.96651I
u = 1.41878 βˆ’ 0.21917I
a = βˆ’0.104500 βˆ’ 0.473819I
b = 0
βˆ’5.87256 + 2.37095I βˆ’12.81148 βˆ’ 1.72217I
14
IV. I
v
1
= ha, 8286v
9
βˆ’ 14092v
8
+ Β· Β· Β· + 8095b + 12581, v
10
βˆ’ v
9
+ Β· Β· Β· + 5v + 1i
(i) Arc colorings
a
4
=
ξ€’
v
0

a
7
=
ξ€’
1
0

a
8
=
ξ€’
1
0

a
5
=
ξ€’
v
0

a
10
=
ξ€’
0
βˆ’1.02359v
9
+ 1.74083v
8
+ Β·Β·Β· βˆ’ 2.14256v βˆ’ 1.55417

a
11
=
ξ€’
1.02359v
9
βˆ’ 1.74083v
8
+ Β·Β·Β· + 2.14256v + 1.55417
βˆ’1.02359v
9
+ 1.74083v
8
+ Β·Β·Β· βˆ’ 2.14256v βˆ’ 1.55417

a
6
=
ξ€’
1
0.566770v
9
βˆ’ 0.910562v
8
+ Β·Β·Β· + 1.12069v βˆ’ 2.46844

a
3
=
ξ€’
0.343792v
9
βˆ’ 0.433107v
8
+ Β·Β·Β· + 6.30229v + 0.566770
βˆ’1.56677v
9
+ 1.91056v
8
+ Β·Β·Β· βˆ’ 18.1207v βˆ’ 2.53156

a
2
=
ξ€’
0.433107v
9
βˆ’ 0.556763v
8
+ Β·Β·Β· + 6.45448v + 0.910562
βˆ’1.56677v
9
+ 1.91056v
8
+ Β·Β·Β· βˆ’ 18.1207v βˆ’ 2.53156

a
1
=
ξ€’
βˆ’1
βˆ’0.566770v
9
+ 0.910562v
8
+ Β·Β·Β· βˆ’ 1.12069v + 2.46844

a
9
=
ξ€’
βˆ’1.02359v
9
+ 1.74083v
8
+ Β·Β·Β· βˆ’ 2.14256v βˆ’ 1.55417
βˆ’0.515256v
9
+ 0.785300v
8
+ Β·Β·Β· βˆ’ 0.966523v + 2.10241

a
12
=
ξ€’
βˆ’1.96479v
9
+ 3.18777v
8
+ Β·Β·Β· βˆ’ 3.92341v + 1.99444
1.39802v
9
βˆ’ 2.27721v
8
+ Β·Β·Β· + 2.80272v βˆ’ 0.526004

(ii) Obstruction class = 1
(iii) Cusp Shapes
= βˆ’
4097
1619
v
9
+
9450
1619
v
8
+
1665
1619
v
7
+
67341
1619
v
6
βˆ’
147227
1619
v
5
βˆ’
55323
1619
v
4
βˆ’
14483
1619
v
3
+
69031
1619
v
2
+
28097
1619
vβˆ’
3358
1619
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
βˆ’ u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
+ u
4
βˆ’ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
c
8
(u
5
βˆ’ u
4
+ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
c
9
, c
10
(u
5
βˆ’ u
4
βˆ’ 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
βˆ’ u βˆ’ 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
9
, c
10
(y
5
βˆ’ 5y
4
+ 8y
3
βˆ’ 3y
2
βˆ’ y βˆ’ 1)
2
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
βˆ’ y βˆ’ 1)
2
c
12
(y
5
βˆ’ y
4
+ 8y
3
βˆ’ 3y
2
+ 3y βˆ’ 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
βˆ’1(vol +
√
βˆ’1CS) Cusp shape
v = βˆ’0.337181 + 0.584015I
a = 0
b = 1.21774
βˆ’2.40108 + 2.02988I βˆ’6.80799 βˆ’ 1.95361I
v = βˆ’0.337181 βˆ’ 0.584015I
a = 0
b = 1.21774
βˆ’2.40108 βˆ’ 2.02988I βˆ’6.80799 + 1.95361I
v = βˆ’0.104500 + 0.473819I
a = 0
b = βˆ’1.41878 βˆ’ 0.21917I
βˆ’5.87256 βˆ’ 2.37095I βˆ’12.81148 + 1.72217I
v = βˆ’0.104500 βˆ’ 0.473819I
a = 0
b = βˆ’1.41878 + 0.21917I
βˆ’5.87256 + 2.37095I βˆ’12.81148 βˆ’ 1.72217I
v = βˆ’0.358089 + 0.327409I
a = 0
b = βˆ’1.41878 + 0.21917I
βˆ’5.87256 + 6.43072I βˆ’8.34383 βˆ’ 2.96651I
v = βˆ’0.358089 βˆ’ 0.327409I
a = 0
b = βˆ’1.41878 βˆ’ 0.21917I
βˆ’5.87256 βˆ’ 6.43072I βˆ’8.34383 + 2.96651I
v = βˆ’1.20942 + 2.19910I
a = 0
b = 0.309916 + 0.549911I
βˆ’0.32910 βˆ’ 3.56046I βˆ’7.97351 + 2.70956I
v = βˆ’1.20942 βˆ’ 2.19910I
a = 0
b = 0.309916 βˆ’ 0.549911I
βˆ’0.32910 + 3.56046I βˆ’7.97351 βˆ’ 2.70956I
v = 2.50919 + 0.05217I
a = 0
b = 0.309916 βˆ’ 0.549911I
βˆ’0.329100 βˆ’ 0.499304I 1.93681 βˆ’ 0.71136I
v = 2.50919 βˆ’ 0.05217I
a = 0
b = 0.309916 + 0.549911I
βˆ’0.329100 + 0.499304I 1.93681 + 0.71136I
18
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
βˆ’ u + 1)
5
(u
5
βˆ’ 3u
4
+ 4u
3
βˆ’ u
2
βˆ’ u + 1)
2
Β· (u
10
+ 5u
9
+ 13u
8
+ 12u
7
βˆ’ 12u
6
βˆ’ 51u
5
βˆ’ 65u
4
βˆ’ 44u
3
βˆ’ 13u
2
+ u + 1)
Β· (u
20
+ 19u
19
+ Β·Β·Β· + 175u + 1)
c
2
, c
8
(u
2
+ u + 1)
5
(u
5
βˆ’ u
4
+ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
Β· (u
10
+ 3u
9
+ 7u
8
+ 10u
7
+ 12u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 5u
2
+ 3u + 1)
Β· (u
20
+ 5u
19
+ Β·Β·Β· + 5u + 1)
c
3
(u
2
βˆ’ u + 1)
5
(u
5
+ u
4
βˆ’ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
Β· (u
10
βˆ’ 3u
9
βˆ’ 9u
8
+ 36u
7
βˆ’ 12u
6
βˆ’ 7u
5
βˆ’ 23u
4
+ 13u
3
+ 16u
2
+ 3u + 2)
Β· (u
20
βˆ’ 5u
19
+ Β·Β·Β· + 2619u + 641)
c
4
, c
6
u
10
(u
5
+ u
4
βˆ’ 2u
3
βˆ’ u
2
+ u βˆ’ 1)
2
Β· (u
10
+ u
9
βˆ’ 7u
8
βˆ’ 14u
7
+ 16u
6
+ 17u
5
βˆ’ 3u
4
βˆ’ 10u
3
βˆ’ 3u
2
+ u βˆ’ 1)
Β· (u
20
+ 2u
19
+ Β·Β·Β· βˆ’ 2048u + 1024)
c
5
, c
11
(u
2
βˆ’ u + 1)
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
Β· (u
10
+ 3u
9
+ 7u
8
+ 10u
7
+ 12u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 5u
2
+ 3u + 1)
Β· (u
20
+ 5u
19
+ Β·Β·Β· + 5u + 1)
c
7
, c
9
u
10
(u
5
βˆ’ u
4
βˆ’ 2u
3
+ u
2
+ u + 1)
2
Β· (u
10
+ u
9
βˆ’ 7u
8
βˆ’ 14u
7
+ 16u
6
+ 17u
5
βˆ’ 3u
4
βˆ’ 10u
3
βˆ’ 3u
2
+ u βˆ’ 1)
Β· (u
20
+ 2u
19
+ Β·Β·Β· βˆ’ 2048u + 1024)
c
10
(u
2
+ u + 1)
5
(u
5
βˆ’ u
4
βˆ’ 2u
3
+ u
2
+ u + 1)
2
Β· (u
10
βˆ’ 3u
9
βˆ’ 9u
8
+ 36u
7
βˆ’ 12u
6
βˆ’ 7u
5
βˆ’ 23u
4
+ 13u
3
+ 16u
2
+ 3u + 2)
Β· (u
20
βˆ’ 5u
19
+ Β·Β·Β· + 2619u + 641)
c
12
(u
2
+ u + 1)
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
βˆ’ u βˆ’ 1)
2
Β· (u
10
+ 5u
9
+ 13u
8
+ 12u
7
βˆ’ 12u
6
βˆ’ 51u
5
βˆ’ 65u
4
βˆ’ 44u
3
βˆ’ 13u
2
+ u + 1)
Β· (u
20
+ 19u
19
+ Β·Β·Β· + 175u + 1)
19
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y
2
+ y + 1)
5
(y
5
βˆ’ y
4
+ 8y
3
βˆ’ 3y
2
+ 3y βˆ’ 1)
2
Β· (y
10
+ y
9
+ Β·Β·Β· βˆ’ 27y + 1)(y
20
βˆ’ 29y
19
+ Β·Β·Β· βˆ’ 13889y + 1)
c
2
, c
5
, c
8
c
11
(y
2
+ y + 1)
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
βˆ’ y βˆ’ 1)
2
Β· (y
10
+ 5y
9
+ 13y
8
+ 12y
7
βˆ’ 12y
6
βˆ’ 51y
5
βˆ’ 65y
4
βˆ’ 44y
3
βˆ’ 13y
2
+ y + 1)
Β· (y
20
+ 19y
19
+ Β·Β·Β· + 175y + 1)
c
3
, c
10
(y
2
+ y + 1)
5
(y
5
βˆ’ 5y
4
+ 8y
3
βˆ’ 3y
2
βˆ’ y βˆ’ 1)
2
Β· (y
10
βˆ’ 27y
9
+ Β·Β·Β· + 55y + 4)
Β· (y
20
βˆ’ 53y
19
+ Β·Β·Β· + 71819743y + 410881)
c
4
, c
6
, c
7
c
9
y
10
(y
5
βˆ’ 5y
4
+ Β·Β·Β· βˆ’ y βˆ’ 1)
2
(y
10
βˆ’ 15y
9
+ Β·Β·Β· + 5y + 1)
Β· (y
20
βˆ’ 50y
19
+ Β·Β·Β· + 4194304y + 1048576)
20