12n
0460
(K12n
0460
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 7 2 12 11 12 4 5 9
Solving Sequence
8,11 5,9
12 1 4 3 7 6 2 10
c
8
c
11
c
12
c
4
c
3
c
7
c
5
c
2
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1248355972972u
23
− 21816995305526u
22
+ ··· + 1521391151543b − 18832007879252,
− 18832007879252u
23
− 332734361961676u
22
+ ··· + 7606955757715a − 305928879409436,
u
24
+ 18u
23
+ ··· + 63u + 5i
I
u
2
= h−u
13
+ 3u
12
− 2u
11
− 9u
10
+ 22u
9
− 16u
8
− 20u
7
+ 55u
6
− 50u
5
− u
4
+ 46u
3
− 53u
2
+ b + 28u − 8,
8u
13
− 69u
12
+ ··· + 13a − 164, u
14
− 7u
13
+ ··· − 66u + 13i
I
u
3
= hu
11
− 3u
10
+ 5u
9
− 4u
8
+ 4u
7
− 5u
6
+ 7u
5
− 4u
4
+ 3u
3
− 2au − 3u
2
+ 2b + 5u − 4,
− 4u
11
a + u
11
+ ··· + 4a + 24,
u
12
− 3u
11
+ 7u
10
− 10u
9
+ 16u
8
− 19u
7
+ 25u
6
− 22u
5
+ 23u
4
− 15u
3
+ 15u
2
− 6u + 4i
I
v
1
= ha, v
2
+ b − 2v + 2, v
4
− 3v
3
+ 5v
2
− 3v + 1i
I
v
2
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 67 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.25 × 10
12
u
23
− 2.18 × 10
13
u
22
+ · · · + 1.52 × 10
12
b − 1.88 ×
10
13
, −1.88 × 10
13
u
23
− 3.33 × 10
14
u
22
+ · · · + 7.61 × 10
12
a − 3.06 ×
10
14
, u
24
+ 18u
23
+ · · · + 63u + 5i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
2.47563u
23
+ 43.7408u
22
+ ··· + 399.917u + 40.2170
0.820536u
23
+ 14.3402u
22
+ ··· + 115.748u + 12.3781
a
9
=
1
u
2
a
12
=
0.136050u
23
+ 2.29322u
22
+ ··· + 6.95177u + 1.65823
0.155672u
23
+ 2.68503u
22
+ ··· + 7.91289u + 0.680248
a
1
=
0.174665u
23
+ 2.79784u
22
+ ··· + 5.73760u + 1.56012
0.452229u
23
+ 7.79322u
22
+ ··· + 19.7188u + 1.63255
a
4
=
1.65509u
23
+ 29.4006u
22
+ ··· + 284.170u + 27.8388
0.820536u
23
+ 14.3402u
22
+ ··· + 115.748u + 12.3781
a
3
=
2.38937u
23
+ 42.1061u
22
+ ··· + 383.557u + 38.2617
1.17675u
23
+ 20.7176u
22
+ ··· + 144.303u + 14.9358
a
7
=
−0.812939u
23
− 13.6447u
22
+ ··· − 40.9787u − 2.36243
−1.10529u
23
− 18.9019u
22
+ ··· − 56.9798u − 4.84305
a
6
=
0.822628u
23
+ 13.5628u
22
+ ··· + 65.4774u + 5.93289
2.10151u
23
+ 36.5939u
22
+ ··· + 173.676u + 16.6453
a
2
=
0.778150u
23
+ 13.1980u
22
+ ··· + 46.3607u + 3.84960
1.56119u
23
+ 26.8336u
22
+ ··· + 93.3811u + 7.91527
a
10
=
−0.0582376u
23
− 0.896432u
22
+ ··· + 2.25306u + 1.07610
0.0386155u
23
+ 0.504620u
22
+ ··· − 1.21417u − 0.0981103
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
12998513265738
1521391151543
u
23
+
228690626935746
1521391151543
u
22
+ ··· +
1512678087445189
1521391151543
u +
140722368482773
1521391151543
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
24
+ 5u
23
+ ··· + 4u + 25
c
2
, c
6
u
24
− 5u
23
+ ··· − 24u + 5
c
3
u
24
+ 32u
22
+ ··· + 3u + 1
c
4
, c
11
u
24
+ u
23
+ ··· + 4u + 1
c
7
u
24
− 27u
23
+ ··· − 6144u + 1024
c
8
u
24
− 18u
23
+ ··· − 63u + 5
c
9
, c
12
u
24
− 26u
22
+ ··· + 17u + 1
c
10
u
24
+ 12u
22
+ ··· + 19u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
24
+ 33y
23
+ ··· − 7216y + 625
c
2
, c
6
y
24
+ 5y
23
+ ··· + 4y + 25
c
3
y
24
+ 64y
23
+ ··· + 7y + 1
c
4
, c
11
y
24
− 9y
23
+ ··· − 16y + 1
c
7
y
24
− 15y
23
+ ··· + 29884416y
2
+ 1048576
c
8
y
24
+ 50y
22
+ ··· + 101y + 25
c
9
, c
12
y
24
− 52y
23
+ ··· − 117y + 1
c
10
y
24
+ 24y
23
+ ··· + 4311y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.401173 + 1.000390I
a = 0.287799 − 1.279530I
b = −1.164570 − 0.801223I
4.97730 + 3.76182I 7.47515 − 2.42928I
u = −0.401173 − 1.000390I
a = 0.287799 + 1.279530I
b = −1.164570 + 0.801223I
4.97730 − 3.76182I 7.47515 + 2.42928I
u = −0.895129 + 0.707186I
a = −0.642012 − 0.323894I
b = −0.803737 + 0.164096I
3.40541 + 0.54338I 9.96762 + 0.I
u = −0.895129 − 0.707186I
a = −0.642012 + 0.323894I
b = −0.803737 − 0.164096I
3.40541 − 0.54338I 9.96762 + 0.I
u = −0.634153 + 0.969164I
a = −0.099094 + 1.257220I
b = 1.15561 + 0.89330I
3.19488 + 9.64059I 5.12102 − 7.65493I
u = −0.634153 − 0.969164I
a = −0.099094 − 1.257220I
b = 1.15561 − 0.89330I
3.19488 − 9.64059I 5.12102 + 7.65493I
u = −0.388319 + 0.539618I
a = −0.22109 + 1.74704I
b = 0.856878 + 0.797713I
−1.96075 + 3.03649I 1.72656 − 2.94326I
u = −0.388319 − 0.539618I
a = −0.22109 − 1.74704I
b = 0.856878 − 0.797713I
−1.96075 − 3.03649I 1.72656 + 2.94326I
u = 0.264551 + 0.575187I
a = −0.414815 + 0.746478I
b = 0.539104 + 0.041115I
−0.61911 − 1.60676I −1.07516 + 5.36024I
u = 0.264551 − 0.575187I
a = −0.414815 − 0.746478I
b = 0.539104 − 0.041115I
−0.61911 + 1.60676I −1.07516 − 5.36024I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666916 + 1.239860I
a = 0.329991 + 0.358310I
b = 0.664331 − 0.170181I
3.42032 − 4.04799I 0. + 7.82789I
u = −0.666916 − 1.239860I
a = 0.329991 − 0.358310I
b = 0.664331 + 0.170181I
3.42032 + 4.04799I 0. − 7.82789I
u = −0.053583 + 0.452097I
a = 0.55903 − 2.05204I
b = −0.897767 − 0.362690I
1.51247 + 0.42081I 8.19848 − 1.31600I
u = −0.053583 − 0.452097I
a = 0.55903 + 2.05204I
b = −0.897767 + 0.362690I
1.51247 − 0.42081I 8.19848 + 1.31600I
u = −0.359542 + 0.101893I
a = −0.10927 + 2.29685I
b = 0.194744 + 0.836947I
0.17995 − 2.31205I −1.12278 + 4.62522I
u = −0.359542 − 0.101893I
a = −0.10927 − 2.29685I
b = 0.194744 − 0.836947I
0.17995 + 2.31205I −1.12278 − 4.62522I
u = −0.93950 + 1.42997I
a = 0.065784 − 0.924691I
b = −1.26048 − 0.96281I
15.4724 + 7.4151I 0
u = −0.93950 − 1.42997I
a = 0.065784 + 0.924691I
b = −1.26048 + 0.96281I
15.4724 − 7.4151I 0
u = −1.02696 + 1.40305I
a = −0.027606 + 0.911387I
b = 1.25037 + 0.97469I
15.0388 + 14.5096I 0
u = −1.02696 − 1.40305I
a = −0.027606 − 0.911387I
b = 1.25037 − 0.97469I
15.0388 − 14.5096I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.96069 + 1.10463I
a = −0.366729 + 0.020741I
b = −0.696132 + 0.445764I
12.99680 + 2.23230I 0
u = −1.96069 − 1.10463I
a = −0.366729 − 0.020741I
b = −0.696132 − 0.445764I
12.99680 − 2.23230I 0
u = −1.93859 + 1.28607I
a = 0.338018 + 0.004948I
b = 0.661642 − 0.425123I
13.11360 − 4.55126I 0
u = −1.93859 − 1.28607I
a = 0.338018 − 0.004948I
b = 0.661642 + 0.425123I
13.11360 + 4.55126I 0
7
II. I
u
2
= h−u
13
+ 3u
12
+ · · · + b − 8, 8u
13
− 69u
12
+ · · · + 13a − 164, u
14
−
7u
13
+ · · · − 66u + 13i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
−0.615385u
13
+ 5.30769u
12
+ ··· − 54.0769u + 12.6154
u
13
− 3u
12
+ ··· − 28u + 8
a
9
=
1
u
2
a
12
=
−0.923077u
13
+ 5.46154u
12
+ ··· − 40.6154u + 6.92308
−u
13
+ 6u
12
+ ··· − 53u + 12
a
1
=
−0.923077u
13
+ 5.46154u
12
+ ··· − 39.6154u + 5.92308
−u
13
+ 6u
12
+ ··· − 53u + 12
a
4
=
−1.61538u
13
+ 8.30769u
12
+ ··· − 26.0769u + 4.61538
u
13
− 3u
12
+ ··· − 28u + 8
a
3
=
3.38462u
13
− 18.6923u
12
+ ··· + 122.923u − 26.3846
11u
13
− 64u
12
+ ··· + 435u − 96
a
7
=
1.92308u
13
− 12.4615u
12
+ ··· + 134.615u − 31.9231
−u
12
+ 5u
11
+ ··· + 40u − 12
a
6
=
−4.38462u
13
+ 20.6923u
12
+ ··· − 6.92308u − 5.61538
−19u
13
+ 111u
12
+ ··· − 752u + 161
a
2
=
0.923077u
13
− 6.46154u
12
+ ··· + 80.6154u − 20.9231
−2u
12
+ 10u
11
+ ··· + 82u − 25
a
10
=
0.0769231u
13
− 0.538462u
12
+ ··· + 13.3846u − 4.07692
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14u
13
+ 87u
12
− 228u
11
+ 253u
10
+ 151u
9
− 946u
8
+ 1451u
7
−
907u
6
− 571u
5
+ 1908u
4
− 2143u
3
+ 1430u
2
− 580u + 122
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
14
− 4u
13
+ ··· − 11u + 1
c
2
u
14
− 2u
13
+ ··· − u + 1
c
3
u
14
− u
13
+ ··· − 4u + 1
c
4
, c
11
u
14
+ u
12
+ ··· + u + 1
c
6
u
14
+ 2u
13
+ ··· + u + 1
c
7
u
14
− 5u
13
+ ··· + 2u + 1
c
8
u
14
− 7u
13
+ ··· − 66u + 13
c
9
u
14
+ 7u
13
+ ··· + 2u + 1
c
10
u
14
− u
13
+ ··· + u
2
+ 1
c
12
u
14
− 7u
13
+ ··· − 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 16y
13
+ ··· − 29y + 1
c
2
, c
6
y
14
+ 4y
13
+ ··· + 11y + 1
c
3
y
14
+ 7y
13
+ ··· − 2y + 1
c
4
, c
11
y
14
+ 2y
13
+ ··· + 7y + 1
c
7
y
14
− 15y
13
+ ··· − 6y + 1
c
8
y
14
− 5y
13
+ ··· + 168y + 169
c
9
, c
12
y
14
− 5y
13
+ ··· + 14y + 1
c
10
y
14
+ 7y
13
+ ··· + 2y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.849111 + 0.715901I
a = 0.019947 + 1.052460I
b = −0.736521 + 0.907937I
−3.07370 − 3.80425I −5.63446 + 5.71514I
u = 0.849111 − 0.715901I
a = 0.019947 − 1.052460I
b = −0.736521 − 0.907937I
−3.07370 + 3.80425I −5.63446 − 5.71514I
u = 0.313761 + 1.089880I
a = −0.549742 − 0.549016I
b = 0.425872 − 0.771411I
1.77746 − 4.05505I 3.41727 + 6.24011I
u = 0.313761 − 1.089880I
a = −0.549742 + 0.549016I
b = 0.425872 + 0.771411I
1.77746 + 4.05505I 3.41727 − 6.24011I
u = 0.311775 + 0.708424I
a = 0.892105 + 0.945635I
b = −0.391774 + 0.926814I
0.73793 + 1.30082I 2.62476 + 1.43148I
u = 0.311775 − 0.708424I
a = 0.892105 − 0.945635I
b = −0.391774 − 0.926814I
0.73793 − 1.30082I 2.62476 − 1.43148I
u = 1.119030 + 0.593759I
a = −0.391744 + 0.935712I
b = −0.993957 + 0.814483I
1.54894 − 8.36056I 3.10198 + 6.93573I
u = 1.119030 − 0.593759I
a = −0.391744 − 0.935712I
b = −0.993957 − 0.814483I
1.54894 + 8.36056I 3.10198 − 6.93573I
u = 1.189000 + 0.649257I
a = 0.371944 − 0.816978I
b = 0.972669 − 0.729899I
2.10101 − 2.72257I 4.91037 + 2.51501I
u = 1.189000 − 0.649257I
a = 0.371944 + 0.816978I
b = 0.972669 + 0.729899I
2.10101 + 2.72257I 4.91037 − 2.51501I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.381310 + 0.146372I
a = −0.063316 + 0.461767I
b = 0.019869 − 0.647110I
12.91060 − 3.47104I 5.96925 + 1.99685I
u = −1.381310 − 0.146372I
a = −0.063316 − 0.461767I
b = 0.019869 + 0.647110I
12.91060 + 3.47104I 5.96925 − 1.99685I
u = 1.09864 + 1.09539I
a = 0.028499 − 0.613967I
b = 0.703842 − 0.643310I
−1.19786 − 3.68086I −0.88917 + 6.15653I
u = 1.09864 − 1.09539I
a = 0.028499 + 0.613967I
b = 0.703842 + 0.643310I
−1.19786 + 3.68086I −0.88917 − 6.15653I
12
III. I
u
3
=
hu
11
−3u
10
+· · ·+2b −4, −4u
11
a+u
11
+· · ·+4a +24, u
12
−3u
11
+· · ·−6u +4i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
a
−
1
2
u
11
+
3
2
u
10
+ ··· −
5
2
u + 2
a
9
=
1
u
2
a
12
=
1
2
u
11
a −
1
4
u
11
+ ··· − 2a +
1
2
1
a
1
=
3
2
u
11
a −
1
4
u
11
+ ··· − 2a +
3
2
−u
11
a + 3u
10
a + ··· − 4au + 1
a
4
=
1
2
u
11
−
3
2
u
10
+ ··· + a − 2
−
1
2
u
11
+
3
2
u
10
+ ··· −
5
2
u + 2
a
3
=
u
11
− 3u
10
+ ··· + a + 2u
−
1
2
u
11
+
3
2
u
10
+ ··· −
9
2
u + 2
a
7
=
1
2
u
11
a −
1
4
u
11
+ ··· − 2a +
3
2
1
a
6
=
−
1
2
u
11
a +
1
2
u
11
+ ··· + 2a −
1
2
au
a
2
=
−u
10
a −
1
4
u
11
+ ··· − 4a +
3
2
−
1
2
u
11
+
3
2
u
10
+ ··· + 2a + 2
a
10
=
3
2
u
11
a −
1
4
u
11
+ ··· − 2a +
1
2
−u
11
a + 3u
10
a + ··· + u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1
2
u
11
+
5
2
u
10
−
5
2
u
9
+ 4u
8
− 2u
7
+
19
2
u
6
−
7
2
u
5
+ 12u
4
−
3
2
u
3
+
29
2
u
2
−
5
2
u + 16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
12
+ 2u
11
+ ··· + 6u + 1)
2
c
2
, c
6
(u
12
+ 2u
11
+ ··· + 2u + 1)
2
c
3
u
24
+ 20u
22
+ ··· − 1035u + 22
c
4
, c
11
u
24
+ 2u
23
+ ··· − 7u + 16
c
7
(u + 1)
24
c
8
(u
12
+ 3u
11
+ ··· + 6u + 4)
2
c
9
, c
12
u
24
− 5u
23
+ ··· + 8613u + 4448
c
10
u
24
+ 2u
23
+ ··· + 1443u + 5011
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
12
+ 18y
11
+ ··· + 6y + 1)
2
c
2
, c
6
(y
12
+ 2y
11
+ ··· + 6y + 1)
2
c
3
y
24
+ 40y
23
+ ··· − 489721y + 484
c
4
, c
11
y
24
+ 38y
22
+ ··· − 2737y + 256
c
7
(y −1)
24
c
8
(y
12
+ 5y
11
+ ··· + 84y + 16)
2
c
9
, c
12
y
24
− 37y
23
+ ··· + 4661479y + 19784704
c
10
y
24
+ 20y
23
+ ··· + 194809963y + 25110121
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595557 + 0.863954I
a = −0.141148 − 0.929948I
b = 1.07056 − 1.49446I
13.6814 + 5.8161I 7.09681 − 5.45294I
u = −0.595557 + 0.863954I
a = 1.75162 + 0.03168I
b = −0.887493 − 0.431892I
13.6814 + 5.8161I 7.09681 − 5.45294I
u = −0.595557 − 0.863954I
a = −0.141148 + 0.929948I
b = 1.07056 + 1.49446I
13.6814 − 5.8161I 7.09681 + 5.45294I
u = −0.595557 − 0.863954I
a = 1.75162 − 0.03168I
b = −0.887493 + 0.431892I
13.6814 − 5.8161I 7.09681 + 5.45294I
u = −0.521857 + 0.963930I
a = 0.105818 + 0.886399I
b = −1.08284 + 1.48890I
14.05920 − 1.29677I 8.02075 − 0.64369I
u = −0.521857 + 0.963930I
a = −1.66482 − 0.22205I
b = 0.909648 + 0.360572I
14.05920 − 1.29677I 8.02075 − 0.64369I
u = −0.521857 − 0.963930I
a = 0.105818 − 0.886399I
b = −1.08284 − 1.48890I
14.05920 + 1.29677I 8.02075 + 0.64369I
u = −0.521857 − 0.963930I
a = −1.66482 + 0.22205I
b = 0.909648 − 0.360572I
14.05920 + 1.29677I 8.02075 + 0.64369I
u = 0.380152 + 1.069420I
a = −0.102983 + 0.676971I
b = −1.04377 + 1.20002I
3.57471 − 4.01356I 9.35409 + 5.50726I
u = 0.380152 + 1.069420I
a = −0.688213 − 1.220660I
b = 0.763114 − 0.147220I
3.57471 − 4.01356I 9.35409 + 5.50726I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.380152 − 1.069420I
a = −0.102983 − 0.676971I
b = −1.04377 − 1.20002I
3.57471 + 4.01356I 9.35409 − 5.50726I
u = 0.380152 − 1.069420I
a = −0.688213 + 1.220660I
b = 0.763114 + 0.147220I
3.57471 + 4.01356I 9.35409 − 5.50726I
u = 0.246665 + 0.748766I
a = 0.218149 − 0.727778I
b = 1.29103 − 1.21568I
2.20338 + 1.32744I 9.73221 + 1.32386I
u = 0.246665 + 0.748766I
a = 0.95223 + 2.03791I
b = −0.598745 + 0.016175I
2.20338 + 1.32744I 9.73221 + 1.32386I
u = 0.246665 − 0.748766I
a = 0.218149 + 0.727778I
b = 1.29103 + 1.21568I
2.20338 − 1.32744I 9.73221 − 1.32386I
u = 0.246665 − 0.748766I
a = 0.95223 − 2.03791I
b = −0.598745 − 0.016175I
2.20338 − 1.32744I 9.73221 − 1.32386I
u = 1.005850 + 0.842159I
a = −0.170941 + 0.863353I
b = −0.453719 + 0.571135I
−1.51202 − 2.72726I −2.43929 − 0.47681I
u = 1.005850 + 0.842159I
a = −0.014301 − 0.555838I
b = 0.899022 − 0.724448I
−1.51202 − 2.72726I −2.43929 − 0.47681I
u = 1.005850 − 0.842159I
a = −0.170941 − 0.863353I
b = −0.453719 − 0.571135I
−1.51202 + 2.72726I −2.43929 + 0.47681I
u = 1.005850 − 0.842159I
a = −0.014301 + 0.555838I
b = 0.899022 + 0.724448I
−1.51202 + 2.72726I −2.43929 + 0.47681I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.98474 + 1.10667I
a = −0.168174 − 0.749804I
b = 0.797372 − 0.556358I
−0.75285 − 4.59014I 2.73542 + 11.41867I
u = 0.98474 + 1.10667I
a = −0.077239 + 0.651782I
b = −0.664181 + 0.924478I
−0.75285 − 4.59014I 2.73542 + 11.41867I
u = 0.98474 − 1.10667I
a = −0.168174 + 0.749804I
b = 0.797372 + 0.556358I
−0.75285 + 4.59014I 2.73542 − 11.41867I
u = 0.98474 − 1.10667I
a = −0.077239 − 0.651782I
b = −0.664181 − 0.924478I
−0.75285 + 4.59014I 2.73542 − 11.41867I
18
IV. I
v
1
= ha, v
2
+ b − 2v + 2, v
4
− 3v
3
+ 5v
2
− 3v + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
v
0
a
5
=
0
−v
2
+ 2v − 2
a
9
=
1
0
a
12
=
v
−1
a
1
=
v − 1
−1
a
4
=
v
2
− 2v + 2
−v
2
+ 2v − 2
a
3
=
0
−v
2
+ 2v − 2
a
7
=
−v + 1
1
a
6
=
−v
3
+ 2v
2
− 3v + 1
−v
3
+ 2v
2
− 2v
a
2
=
v − 1
v
3
− 3v
2
+ 5v − 3
a
10
=
v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7v
3
+ 21v
2
− 28v + 14
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
4
, c
10
c
11
u
4
− u
3
− u
2
+ u + 1
c
7
, c
9
(u + 1)
4
c
8
u
4
c
12
(u − 1)
4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
10
c
11
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
7
, c
9
, c
12
(y − 1)
4
c
8
y
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.378256 + 0.440597I
a = 0
b = −1.192440 + 0.547877I
1.64493 + 2.02988I 3.50000 − 6.06218I
v = 0.378256 − 0.440597I
a = 0
b = −1.192440 − 0.547877I
1.64493 − 2.02988I 3.50000 + 6.06218I
v = 1.12174 + 1.30662I
a = 0
b = 0.692440 − 0.318148I
1.64493 − 2.02988I 3.50000 + 6.06218I
v = 1.12174 − 1.30662I
a = 0
b = 0.692440 + 0.318148I
1.64493 + 2.02988I 3.50000 − 6.06218I
22
V. I
v
2
= ha, b + 1, v − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
1
0
a
5
=
0
−1
a
9
=
1
0
a
12
=
1
−1
a
1
=
0
−1
a
4
=
1
−1
a
3
=
0
−1
a
7
=
0
1
a
6
=
0
−1
a
2
=
0
−1
a
10
=
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
u
c
3
, c
4
, c
7
c
9
, c
10
, c
11
c
12
u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
y
c
3
, c
4
, c
7
c
9
, c
10
, c
11
c
12
y − 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
1.64493 6.00000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u(u
2
− u + 1)
2
(u
12
+ 2u
11
+ ··· + 6u + 1)
2
· (u
14
− 4u
13
+ ··· − 11u + 1)(u
24
+ 5u
23
+ ··· + 4u + 25)
c
2
u(u
2
+ u + 1)
2
(u
12
+ 2u
11
+ ··· + 2u + 1)
2
(u
14
− 2u
13
+ ··· − u + 1)
· (u
24
− 5u
23
+ ··· − 24u + 5)
c
3
(u − 1)(u
4
− u
3
− u
2
+ u + 1)(u
14
− u
13
+ ··· − 4u + 1)
· (u
24
+ 20u
22
+ ··· − 1035u + 22)(u
24
+ 32u
22
+ ··· + 3u + 1)
c
4
, c
11
(u − 1)(u
4
− u
3
− u
2
+ u + 1)(u
14
+ u
12
+ ··· + u + 1)
· (u
24
+ u
23
+ ··· + 4u + 1)(u
24
+ 2u
23
+ ··· − 7u + 16)
c
6
u(u
2
− u + 1)
2
(u
12
+ 2u
11
+ ··· + 2u + 1)
2
(u
14
+ 2u
13
+ ··· + u + 1)
· (u
24
− 5u
23
+ ··· − 24u + 5)
c
7
(u − 1)(u + 1)
28
(u
14
− 5u
13
+ ··· + 2u + 1)
· (u
24
− 27u
23
+ ··· − 6144u + 1024)
c
8
u
5
(u
12
+ 3u
11
+ ··· + 6u + 4)
2
(u
14
− 7u
13
+ ··· − 66u + 13)
· (u
24
− 18u
23
+ ··· − 63u + 5)
c
9
(u − 1)(u + 1)
4
(u
14
+ 7u
13
+ ··· + 2u + 1)(u
24
− 26u
22
+ ··· + 17u + 1)
· (u
24
− 5u
23
+ ··· + 8613u + 4448)
c
10
(u − 1)(u
4
− u
3
− u
2
+ u + 1)(u
14
− u
13
+ ··· + u
2
+ 1)
· (u
24
+ 12u
22
+ ··· + 19u + 16)(u
24
+ 2u
23
+ ··· + 1443u + 5011)
c
12
((u − 1)
5
)(u
14
− 7u
13
+ ··· − 2u + 1)(u
24
− 26u
22
+ ··· + 17u + 1)
· (u
24
− 5u
23
+ ··· + 8613u + 4448)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y(y
2
+ y + 1)
2
(y
12
+ 18y
11
+ ··· + 6y + 1)
2
· (y
14
+ 16y
13
+ ··· − 29y + 1)(y
24
+ 33y
23
+ ··· − 7216y + 625)
c
2
, c
6
y(y
2
+ y + 1)
2
(y
12
+ 2y
11
+ ··· + 6y + 1)
2
· (y
14
+ 4y
13
+ ··· + 11y + 1)(y
24
+ 5y
23
+ ··· + 4y + 25)
c
3
(y − 1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
14
+ 7y
13
+ ··· − 2y + 1)
· (y
24
+ 40y
23
+ ··· − 489721y + 484)(y
24
+ 64y
23
+ ··· + 7y + 1)
c
4
, c
11
(y − 1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
14
+ 2y
13
+ ··· + 7y + 1)
· (y
24
+ 38y
22
+ ··· − 2737y + 256)(y
24
− 9y
23
+ ··· − 16y + 1)
c
7
((y − 1)
29
)(y
14
− 15y
13
+ ··· − 6y + 1)
· (y
24
− 15y
23
+ ··· + 29884416y
2
+ 1048576)
c
8
y
5
(y
12
+ 5y
11
+ ··· + 84y + 16)
2
(y
14
− 5y
13
+ ··· + 168y + 169)
· (y
24
+ 50y
22
+ ··· + 101y + 25)
c
9
, c
12
((y − 1)
5
)(y
14
− 5y
13
+ ··· + 14y + 1)(y
24
− 52y
23
+ ··· − 117y + 1)
· (y
24
− 37y
23
+ ··· + 4661479y + 19784704)
c
10
(y − 1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
14
+ 7y
13
+ ··· + 2y + 1)
· (y
24
+ 20y
23
+ ··· + 194809963y + 25110121)
· (y
24
+ 24y
23
+ ··· + 4311y + 256)
28
