12n
0480
(K12n
0480
)
A knot diagram
1
Linearized knot diagam
3 5 9 7 2 11 1 3 4 12 6 4
Solving Sequence
3,9
4
5,10
2 6 1 8 7 12 11
c
3
c
9
c
2
c
5
c
1
c
8
c
7
c
12
c
11
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
7
+ 4u
6
− 9u
5
+ 10u
4
− 6u
3
+ b − u + 1, −u
7
+ 4u
6
− 9u
5
+ 10u
4
− 7u
3
+ u
2
+ a − u,
u
8
− 5u
7
+ 13u
6
− 19u
5
+ 17u
4
− 8u
3
+ 3u
2
− 2u + 1i
I
u
2
= h−u
2
a − u
2
+ b, −u
7
a − u
6
a + u
7
− u
5
a + u
6
+ u
4
a + u
5
− 2u
3
a − 2u
4
+ u
3
+ a
2
− u
2
+ a − 1,
u
8
+ 2u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1i
I
u
3
= h−u
7
+ 3u
5
− 2u
3
+ b − u + 1, −u
7
+ 3u
5
− u
3
+ u
2
+ a − 3u, u
8
− u
7
− 3u
6
+ 3u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
4
= h5u
7
− 17u
6
+ 17u
5
+ 28u
4
− 71u
3
+ 8u
2
+ 8b + 112u − 104,
17u
7
− 57u
6
+ 61u
5
+ 92u
4
− 231u
3
+ 36u
2
+ 32a + 356u − 344,
u
8
− 5u
7
+ 9u
6
− 23u
4
+ 24u
3
+ 20u
2
− 56u + 32i
I
u
5
= h2u
11
+ 5u
10
+ 5u
9
− 2u
8
− 7u
7
− 8u
6
− 9u
5
+ 3u
4
− 4u
2
a − 2u
3
+ 7u
2
+ 4b − 7u + 1,
6u
11
a − 7u
11
+ ··· − 9a + 25, u
12
+ 3u
11
+ 4u
10
+ u
9
− 3u
8
− 5u
7
− 6u
6
+ 3u
3
− 3u
2
− 2u − 1i
I
u
6
= h−u
2
a − u
2
+ b, −u
3
a + u
3
+ a
2
+ 2au + 2u
2
+ a − u − 2, u
4
+ u
3
− u
2
− u − 1i
* 6 irreducible components of dim
C
= 0, with total 72 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−u
7
+ 4u
6
− 9u
5
+ 10u
4
− 6u
3
+ b − u + 1, −u
7
+ 4u
6
− 9u
5
+
10u
4
− 7u
3
+ u
2
+ a − u, u
8
− 5u
7
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
u
7
− 4u
6
+ 9u
5
− 10u
4
+ 7u
3
− u
2
+ u
u
7
− 4u
6
+ 9u
5
− 10u
4
+ 6u
3
+ u − 1
a
10
=
−u
−u
3
+ u
a
2
=
u
7
− 5u
6
+ 12u
5
− 15u
4
+ 10u
3
− 2u
2
+ u − 1
u
5
− 3u
4
+ 4u
3
− 2u
2
− 1
a
6
=
u
7
− 5u
6
+ 12u
5
− 15u
4
+ 10u
3
− 2u
2
+ u − 1
−u
7
+ 5u
6
− 11u
5
+ 13u
4
− 8u
3
+ 3u
2
− 2u + 1
a
1
=
u
7
− 5u
6
+ 13u
5
− 18u
4
+ 14u
3
− 4u
2
+ u − 2
u
5
− 3u
4
+ 4u
3
− 2u
2
− 1
a
8
=
u
u
a
7
=
u
7
− 4u
6
+ 9u
5
− 10u
4
+ 7u
3
− u
2
+ 2u − 1
u
7
− 4u
6
+ 9u
5
− 10u
4
+ 7u
3
− 2u
2
+ 2u − 1
a
12
=
u
7
− 4u
6
+ 9u
5
− 11u
4
+ 8u
3
− 2u
2
− 1
u
7
− 6u
6
+ 14u
5
− 18u
4
+ 11u
3
− 4u
2
+ 2u − 2
a
11
=
u
7
− 5u
6
+ 12u
5
− 16u
4
+ 11u
3
− 3u
2
− 2
−u
6
+ 3u
5
− 5u
4
+ 4u
3
− 2u
2
+ u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
7
− 30u
6
+ 72u
5
− 90u
4
+ 56u
3
− 4u
2
− 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
+ 3u
7
+ 8u
6
+ 15u
5
+ 19u
4
+ 24u
3
+ 18u
2
+ 4u + 1
c
2
, c
5
, c
6
c
11
u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 1
c
3
, c
4
, c
8
c
9
u
8
− 5u
7
+ 13u
6
− 19u
5
+ 17u
4
− 8u
3
+ 3u
2
− 2u + 1
c
7
, c
12
u
8
+ u
7
− 6u
6
− 9u
5
+ 11u
4
+ 13u
3
+ 9u
2
+ 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
8
+ 7y
7
+ 12y
6
− 29y
5
− 93y
4
+ 4y
3
+ 170y
2
+ 20y + 1
c
2
, c
5
, c
6
c
11
y
8
+ 3y
7
+ 8y
6
+ 15y
5
+ 19y
4
+ 24y
3
+ 18y
2
+ 4y + 1
c
3
, c
4
, c
8
c
9
y
8
+ y
7
+ 13y
6
+ 7y
5
+ 45y
4
− 12y
3
+ 11y
2
+ 2y + 1
c
7
, c
12
y
8
− 13y
7
+ 76y
6
− 221y
5
+ 245y
4
+ 53y
3
+ 51y
2
+ 14y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.652271 + 0.360769I
a = 0.732717 + 1.076160I
b = 0.005195 + 1.133280I
−4.98976 − 1.40911I −5.93719 + 4.96219I
u = 0.652271 − 0.360769I
a = 0.732717 − 1.076160I
b = 0.005195 − 1.133280I
−4.98976 + 1.40911I −5.93719 − 4.96219I
u = −0.260888 + 0.445572I
a = 0.965935 − 0.196423I
b = −0.302166 − 0.431430I
0.040580 + 1.038860I 0.71134 − 6.68770I
u = −0.260888 − 0.445572I
a = 0.965935 + 0.196423I
b = −0.302166 + 0.431430I
0.040580 − 1.038860I 0.71134 + 6.68770I
u = 0.89585 + 1.26725I
a = −0.831436 − 0.483431I
b = 0.962229 + 0.771104I
10.00520 − 2.02473I 3.02254 − 0.14098I
u = 0.89585 − 1.26725I
a = −0.831436 + 0.483431I
b = 0.962229 − 0.771104I
10.00520 + 2.02473I 3.02254 + 0.14098I
u = 1.21276 + 1.15424I
a = −1.367220 − 0.316333I
b = 0.834742 − 1.071900I
8.1034 − 15.2709I 0.20330 + 8.45960I
u = 1.21276 − 1.15424I
a = −1.367220 + 0.316333I
b = 0.834742 + 1.071900I
8.1034 + 15.2709I 0.20330 − 8.45960I
5
II. I
u
2
=
h−u
2
a−u
2
+b, −u
7
a+u
7
+· · ·+a−1, u
8
+2u
7
+3u
6
+u
5
+2u
4
+u
3
+2u
2
+u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
u
2
a + u
2
a
10
=
−u
−u
3
+ u
a
2
=
u
6
a + u
5
a + u
4
a − u
3
a + u
2
a + u
3
+ a
−u
7
a − 2u
6
a − 2u
5
a + u
5
− u
3
a + u
4
− u
2
a − au − u
2
− a
a
6
=
u
6
a + u
5
a + u
4
a − u
3
a + u
2
a + u
3
+ a
−u
6
a + u
7
− u
5
a + u
6
− 2u
4
a + u
5
− 2u
4
− u
2
a + u
2
− a
a
1
=
−u
7
a − u
6
a − u
5
a + u
4
a + u
5
− 2u
3
a + u
4
+ u
3
− au − u
2
−u
7
a − 2u
6
a − 2u
5
a + u
5
− u
3
a + u
4
− u
2
a − au − u
2
− a
a
8
=
u
u
a
7
=
−u
7
a + u
7
+ ··· − a + 1
au
a
12
=
u
7
+ u
6
+ u
5
− u
3
a − u
4
+ u
3
−u
7
a − u
6
a − u
7
− 2u
5
a + u
4
a − u
3
a + 3u
4
− u
3
− au + 1
a
11
=
−u
7
a + u
7
+ ··· − a + 1
−2u
7
− 3u
6
− 4u
5
+ u
3
a − 3u
3
− 2u
2
− 3u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7u
7
− 9u
6
− 8u
5
+ 13u
4
− 2u
3
+ 4u
2
− 5u + 4
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
16
+ 4u
15
+ ··· + 128u + 256
c
2
, c
5
, c
6
c
11
u
16
+ 4u
15
+ ··· + 48u + 16
c
3
, c
4
, c
8
c
9
(u
8
+ 2u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1)
2
c
7
, c
12
u
16
+ 2u
15
+ ··· + 2u + 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
16
+ 12y
15
+ ··· + 237568y + 65536
c
2
, c
5
, c
6
c
11
y
16
+ 4y
15
+ ··· + 128y + 256
c
3
, c
4
, c
8
c
9
(y
8
+ 2y
7
+ 9y
6
+ 11y
5
+ 12y
4
+ 11y
3
+ 6y
2
+ 3y + 1)
2
c
7
, c
12
y
16
− 34y
15
+ ··· + 34y + 1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.669857 + 0.618731I
a = 0.519643 + 0.618737I
b = −0.412772 + 1.300430I
−0.68359 − 8.02114I −3.38988 + 11.48011I
u = 0.669857 + 0.618731I
a = −2.17987 − 0.90212I
b = 0.670058 − 1.037450I
−0.68359 − 8.02114I −3.38988 + 11.48011I
u = 0.669857 − 0.618731I
a = 0.519643 − 0.618737I
b = −0.412772 − 1.300430I
−0.68359 + 8.02114I −3.38988 − 11.48011I
u = 0.669857 − 0.618731I
a = −2.17987 + 0.90212I
b = 0.670058 + 1.037450I
−0.68359 + 8.02114I −3.38988 − 11.48011I
u = −0.575075 + 0.604029I
a = −0.206518 + 1.127330I
b = 0.756093 − 0.589737I
0.63668 + 2.58489I −1.22299 − 5.26005I
u = −0.575075 + 0.604029I
a = 0.634679 − 0.563795I
b = −0.447489 − 1.116400I
0.63668 + 2.58489I −1.22299 − 5.26005I
u = −0.575075 − 0.604029I
a = −0.206518 − 1.127330I
b = 0.756093 + 0.589737I
0.63668 − 2.58489I −1.22299 + 5.26005I
u = −0.575075 − 0.604029I
a = 0.634679 + 0.563795I
b = −0.447489 + 1.116400I
0.63668 − 2.58489I −1.22299 + 5.26005I
u = −0.046597 + 0.820905I
a = 0.633387 − 0.032164I
b = −1.099630 − 0.103355I
4.09203 + 2.71750I 9.92245 − 2.29698I
u = −0.046597 + 0.820905I
a = −2.18872 − 1.14293I
b = 0.711041 + 0.858664I
4.09203 + 2.71750I 9.92245 − 2.29698I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046597 − 0.820905I
a = 0.633387 + 0.032164I
b = −1.099630 + 0.103355I
4.09203 − 2.71750I 9.92245 + 2.29698I
u = −0.046597 − 0.820905I
a = −2.18872 + 1.14293I
b = 0.711041 − 0.858664I
4.09203 − 2.71750I 9.92245 + 2.29698I
u = −1.04818 + 1.20777I
a = −0.761541 + 0.428484I
b = 0.999043 − 0.758029I
9.11436 + 8.57751I 1.69041 − 4.42296I
u = −1.04818 + 1.20777I
a = −1.45106 + 0.26117I
b = 0.823655 + 1.048040I
9.11436 + 8.57751I 1.69041 − 4.42296I
u = −1.04818 − 1.20777I
a = −0.761541 − 0.428484I
b = 0.999043 + 0.758029I
9.11436 − 8.57751I 1.69041 + 4.42296I
u = −1.04818 − 1.20777I
a = −1.45106 − 0.26117I
b = 0.823655 − 1.048040I
9.11436 − 8.57751I 1.69041 + 4.42296I
10
III. I
u
3
= h−u
7
+ 3u
5
− 2u
3
+ b − u + 1, −u
7
+ 3u
5
− u
3
+ u
2
+ a − 3u, u
8
−
u
7
− 3u
6
+ 3u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
u
7
− 3u
5
+ u
3
− u
2
+ 3u
u
7
− 3u
5
+ 2u
3
+ u − 1
a
10
=
−u
−u
3
+ u
a
2
=
u
7
− u
6
− 4u
5
+ 3u
4
+ 4u
3
− 2u
2
+ u − 1
u
5
+ u
4
− 2u
3
− 2u
2
− 1
a
6
=
−u
7
+ u
6
+ 4u
5
− 3u
4
− 4u
3
+ 2u
2
− u + 1
u
7
+ u
6
− 3u
5
− 3u
4
+ 2u
3
+ u
2
+ 1
a
1
=
u
7
− u
6
− 3u
5
+ 4u
4
+ 2u
3
− 4u
2
+ u − 2
u
5
+ u
4
− 2u
3
− 2u
2
− 1
a
8
=
u
u
a
7
=
−u
7
+ 3u
5
− u
3
+ u
2
− 2u − 1
−u
7
+ 3u
5
− u
3
− 2u + 1
a
12
=
u
7
− 3u
5
+ u
4
+ 2u
3
− 2u
2
− 1
u
7
− 2u
5
+ 2u
4
− u
3
− 4u
2
+ 2u − 2
a
11
=
−u
7
+ u
6
+ 4u
5
− 2u
4
− 3u
3
+ u
2
− 4u
u
6
+ u
5
− u
4
− 2u
3
− 2u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
7
− 2u
6
− 12u
5
+ 2u
4
+ 16u
3
+ 4u + 3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
− 3u
7
+ 8u
6
− 11u
5
+ 15u
4
− 12u
3
+ 10u
2
− 4u + 1
c
2
, c
6
u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ 1
c
3
u
8
− u
7
− 3u
6
+ 3u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1
c
4
, c
8
, c
9
u
8
+ u
7
− 3u
6
− 3u
5
+ u
4
+ 2u
3
+ 3u
2
+ 2u + 1
c
5
, c
11
u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 1
c
7
, c
12
u
8
− u
7
− u
5
+ 3u
4
− 3u
3
+ u
2
+ 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
8
+ 7y
7
+ 28y
6
+ 67y
5
+ 99y
4
+ 84y
3
+ 34y
2
+ 4y + 1
c
2
, c
5
, c
6
c
11
y
8
+ 3y
7
+ 8y
6
+ 11y
5
+ 15y
4
+ 12y
3
+ 10y
2
+ 4y + 1
c
3
, c
4
, c
8
c
9
y
8
− 7y
7
+ 17y
6
− 13y
5
− 7y
4
+ 8y
3
+ 3y
2
+ 2y + 1
c
7
, c
12
y
8
− y
7
+ 4y
6
− 5y
5
+ 5y
4
− 3y
3
+ 7y
2
+ 2y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030890 + 0.718197I
a = 0.622175 + 1.173170I
b = −0.783128 − 0.675988I
3.07236 + 3.68820I 4.98393 − 5.29986I
u = −0.030890 − 0.718197I
a = 0.622175 − 1.173170I
b = −0.783128 + 0.675988I
3.07236 − 3.68820I 4.98393 + 5.29986I
u = 0.472052 + 0.470170I
a = 1.52839 + 1.41091I
b = −0.621805 + 1.124830I
0.10782 − 7.15810I 2.37662 + 6.44391I
u = 0.472052 − 0.470170I
a = 1.52839 − 1.41091I
b = −0.621805 − 1.124830I
0.10782 + 7.15810I 2.37662 − 6.44391I
u = −1.40119 + 0.27682I
a = −0.990196 + 0.324197I
b = 0.269993 + 0.604062I
−5.44591 + 2.04290I −7.10763 + 1.33066I
u = −1.40119 − 0.27682I
a = −0.990196 − 0.324197I
b = 0.269993 − 0.604062I
−5.44591 − 2.04290I −7.10763 − 1.33066I
u = 1.46003 + 0.07298I
a = −0.660372 + 0.409353I
b = 0.634940 + 0.942808I
−4.31401 + 5.00304I −2.25292 − 6.22083I
u = 1.46003 − 0.07298I
a = −0.660372 − 0.409353I
b = 0.634940 − 0.942808I
−4.31401 − 5.00304I −2.25292 + 6.22083I
14
IV. I
u
4
=
h5u
7
−17u
6
+· · ·+8b−104, 17u
7
−57u
6
+· · ·+32a−344, u
8
−5u
7
+· · ·−56u+32i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
−0.531250u
7
+ 1.78125u
6
+ ··· − 11.1250u + 10.7500
−
5
8
u
7
+
17
8
u
6
+ ··· − 14u + 13
a
10
=
−u
−u
3
+ u
a
2
=
1
32
u
7
−
9
32
u
6
+ ··· +
19
8
u −
13
4
−
3
8
u
7
+
13
8
u
6
+ ··· −
23
2
u + 11
a
6
=
−
1
2
u
7
+
15
8
u
6
+ ··· − 13u +
27
2
−
3
8
u
7
+
7
8
u
6
+ ··· −
9
2
u + 4
a
1
=
−0.343750u
7
+ 1.34375u
6
+ ··· − 9.12500u + 7.75000
−
3
8
u
7
+
13
8
u
6
+ ··· −
23
2
u + 11
a
8
=
u
u
a
7
=
1
32
u
7
−
1
32
u
6
+ ··· +
7
8
u +
1
4
1
8
u
7
−
3
8
u
6
+ ··· + 3u − 1
a
12
=
−0.218750u
7
+ 0.968750u
6
+ ··· − 7.62500u + 8.75000
−
3
8
u
7
+
5
8
u
6
+ ··· −
3
2
u + 3
a
11
=
−0.218750u
7
+ 0.718750u
6
+ ··· − 5.12500u + 4.25000
−
5
8
u
7
+
15
8
u
6
+ ··· − 11u + 11
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
7
− 30u
6
+ 34u
5
+ 46u
4
− 132u
3
+ 26u
2
+ 204u − 198
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
2
, c
5
, c
6
c
11
(u
4
− u
3
+ u
2
+ 1)
2
c
3
, c
4
, c
8
c
9
u
8
− 5u
7
+ 9u
6
− 23u
4
+ 24u
3
+ 20u
2
− 56u + 32
c
7
, c
12
u
8
− 5u
6
− 7u
5
+ 3u
4
+ 20u
3
+ 23u
2
− 5u + 2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
5
, c
6
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
4
, c
8
c
9
y
8
− 7y
7
+ ··· − 1856y + 1024
c
7
, c
12
y
8
− 10y
7
+ 31y
6
− 33y
5
+ 63y
4
− 352y
3
+ 741y
2
+ 67y + 4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.307400 + 0.487823I
a = −0.954979 − 0.171241I
b = 0.351808 + 0.720342I
−5.35681 + 2.83021I −5.65348 − 9.81749I
u = −1.307400 − 0.487823I
a = −0.954979 + 0.171241I
b = 0.351808 − 0.720342I
−5.35681 − 2.83021I −5.65348 + 9.81749I
u = 1.408170 + 0.087291I
a = −0.681944 − 0.925546I
b = 0.351808 − 0.720342I
−5.35681 − 2.83021I −5.65348 + 9.81749I
u = 1.408170 − 0.087291I
a = −0.681944 + 0.925546I
b = 0.351808 + 0.720342I
−5.35681 + 2.83021I −5.65348 − 9.81749I
u = 1.30983 + 1.01957I
a = 1.331510 + 0.422810I
b = −0.851808 + 0.911292I
8.64668 − 6.32793I 1.65348 + 5.12960I
u = 1.30983 − 1.01957I
a = 1.331510 − 0.422810I
b = −0.851808 − 0.911292I
8.64668 + 6.32793I 1.65348 − 5.12960I
u = 1.08940 + 1.34521I
a = 0.680418 + 0.376735I
b = −0.851808 − 0.911292I
8.64668 + 6.32793I 1.65348 − 5.12960I
u = 1.08940 − 1.34521I
a = 0.680418 − 0.376735I
b = −0.851808 + 0.911292I
8.64668 − 6.32793I 1.65348 + 5.12960I
18
V. I
u
5
=
h2u
11
+5u
10
+· · ·+4b+1, 6u
11
a−7u
11
+· · ·−9a+25, u
12
+3u
11
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
−
1
2
u
11
−
5
4
u
10
+ ··· +
7
4
u −
1
4
a
10
=
−u
−u
3
+ u
a
2
=
−
1
2
u
11
a −
3
4
u
11
+ ··· +
1
2
a + 1
−
1
4
u
10
a +
3
4
u
11
+ ··· +
1
2
a − 1
a
6
=
−
1
4
u
10
a +
1
2
u
11
+ ··· + a −
11
4
1
4
u
10
a −
5
4
u
11
+ ··· −
1
4
a +
3
2
a
1
=
−
1
2
u
11
a −
3
2
u
10
a + ··· + a −
3
4
u
−
1
4
u
10
a +
3
4
u
11
+ ··· +
1
2
a − 1
a
8
=
u
u
a
7
=
−
1
4
u
11
a +
1
4
u
11
+ ··· +
7
4
au −
7
4
u
1
2
u
11
+
3
2
u
10
+ ··· −
7
4
u − 1
a
12
=
−
1
4
u
11
a − u
11
+ ··· +
1
2
a + 1
−
1
4
u
11
a + u
11
+ ··· +
1
2
a −
3
4
a
11
=
−
1
4
u
11
a +
1
4
u
11
+ ··· +
3
2
au − 3u
−
1
4
u
11
a +
3
4
u
11
+ ··· −
1
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
11
+ 2u
10
+ u
9
−3u
8
−5u
7
−5u
6
−4u
5
+ 7u
4
+ 5u
3
+ 6u
2
−4u −3
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
6
c
2
, c
5
, c
6
c
11
(u
4
− u
3
+ u
2
+ 1)
6
c
3
, c
4
, c
8
c
9
(u
12
+ 3u
11
+ 4u
10
+ u
9
− 3u
8
− 5u
7
− 6u
6
+ 3u
3
− 3u
2
− 2u − 1)
2
c
7
, c
12
u
24
+ 3u
23
+ ··· + 2368u + 1016
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
c
2
, c
5
, c
6
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
c
3
, c
4
, c
8
c
9
(y
12
− y
11
+ ··· + 2y + 1)
2
c
7
, c
12
y
24
− 3y
23
+ ··· − 1653152y + 1032256
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.535167 + 0.929438I
a = 0.528827 + 0.711224I
b = 0.351808 − 0.720342I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.535167 + 0.929438I
a = 1.197710 − 0.110412I
b = −0.851808 − 0.911292I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.535167 − 0.929438I
a = 0.528827 − 0.711224I
b = 0.351808 + 0.720342I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = −0.535167 − 0.929438I
a = 1.197710 + 0.110412I
b = −0.851808 + 0.911292I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = 0.056867 + 1.089550I
a = 0.929613 + 0.375044I
b = −0.851808 − 0.911292I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = 0.056867 + 1.089550I
a = 0.066659 − 1.093490I
b = 0.351808 + 0.720342I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = 0.056867 − 1.089550I
a = 0.929613 − 0.375044I
b = −0.851808 + 0.911292I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = 0.056867 − 1.089550I
a = 0.066659 + 1.093490I
b = 0.351808 − 0.720342I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = 1.15037
a = −1.58111 + 0.54433I
b = 0.351808 + 0.720342I
−5.35681 −5.65350
u = 1.15037
a = −1.58111 − 0.54433I
b = 0.351808 − 0.720342I
−5.35681 −5.65350
22
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.688565 + 0.422967I
a = 1.64391 + 0.26308I
b = −0.851808 + 0.911292I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = 0.688565 + 0.422967I
a = 0.24848 − 2.51053I
b = 0.351808 − 0.720342I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = 0.688565 − 0.422967I
a = 1.64391 − 0.26308I
b = −0.851808 − 0.911292I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = 0.688565 − 0.422967I
a = 0.24848 + 2.51053I
b = 0.351808 + 0.720342I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = −0.293143 + 0.369169I
a = 0.645814 − 1.117350I
b = −0.851808 + 0.911292I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = −0.293143 + 0.369169I
a = 0.25546 + 4.35284I
b = 0.351808 + 0.720342I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = −0.293143 − 0.369169I
a = 0.645814 + 1.117350I
b = −0.851808 − 0.911292I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.293143 − 0.369169I
a = 0.25546 − 4.35284I
b = 0.351808 − 0.720342I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −1.56338
a = −0.397494 + 0.294719I
b = 0.351808 + 0.720342I
−5.35681 −5.65350
u = −1.56338
a = −0.397494 − 0.294719I
b = 0.351808 − 0.720342I
−5.35681 −5.65350
23
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21061 + 1.15450I
a = 0.655793 − 0.383339I
b = −0.851808 + 0.911292I
8.64668 1.65348 + 0.I
u = −1.21061 + 1.15450I
a = 1.306340 − 0.414226I
b = −0.851808 − 0.911292I
8.64668 1.65348 + 0.I
u = −1.21061 − 1.15450I
a = 0.655793 + 0.383339I
b = −0.851808 − 0.911292I
8.64668 1.65348 + 0.I
u = −1.21061 − 1.15450I
a = 1.306340 + 0.414226I
b = −0.851808 + 0.911292I
8.64668 1.65348 + 0.I
24
VI.
I
u
6
= h−u
2
a−u
2
+b, −u
3
a+u
3
+a
2
+2au+2 u
2
+a−u−2, u
4
+u
3
−u
2
−u−1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
u
2
a + u
2
a
10
=
−u
−u
3
+ u
a
2
=
u
3
− a − 2u
−u
3
a − u
3
+ au + a + u
a
6
=
−u
3
+ a + 2u
u
2
a − au − u + 1
a
1
=
−u
3
a + au − u
−u
3
a − u
3
+ au + a + u
a
8
=
u
u
a
7
=
−u
3
a − u
2
a + u
3
+ au + u
2
+ a − u − 1
−au
a
12
=
−u
3
a − 2u
−2u
3
a − 2u
3
+ au + a + u
a
11
=
−u
3
a − u
2
a + a − 2u − 1
−u
3
a − u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
− 2u
2
− 11u − 1
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
− 3u
7
+ 8u
6
− 13u
5
+ 15u
4
− 13u
3
+ 8u
2
− 3u + 1
c
2
, c
6
u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ u
3
+ 2u
2
+ u + 1
c
3
(u
4
+ u
3
− u
2
− u − 1)
2
c
4
, c
8
, c
9
(u
4
− u
3
− u
2
+ u − 1)
2
c
5
, c
11
u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− u
3
+ 2u
2
− u + 1
c
7
, c
12
u
8
+ 2u
6
+ 4u
5
+ 2u
4
+ 2u
3
+ u
2
+ 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
8
+ 7y
7
+ 16y
6
+ 9y
5
− y
4
+ 9y
3
+ 16y
2
+ 7y + 1
c
2
, c
5
, c
6
c
11
y
8
+ 3y
7
+ 8y
6
+ 13y
5
+ 15y
4
+ 13y
3
+ 8y
2
+ 3y + 1
c
3
, c
4
, c
8
c
9
(y
4
− 3y
3
+ y
2
+ y + 1)
2
c
7
, c
12
y
8
+ 4y
7
+ 8y
6
− 6y
5
− 6y
4
+ 4y
3
+ 5y
2
+ 2y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.17872
a = −0.859870 + 0.705967I
b = 0.194695 + 0.980864I
−6.97792 −11.8320
u = 1.17872
a = −0.859870 − 0.705967I
b = 0.194695 − 0.980864I
−6.97792 −11.8320
u = −0.332924 + 0.670769I
a = 1.374520 − 0.115864I
b = −0.856931 − 1.021240I
2.07364 + 2.52742I 4.57778 − 6.72148I
u = −0.332924 + 0.670769I
a = −1.29620 − 1.30443I
b = −0.482162 + 0.574614I
2.07364 + 2.52742I 4.57778 − 6.72148I
u = −0.332924 − 0.670769I
a = 1.374520 + 0.115864I
b = −0.856931 + 1.021240I
2.07364 − 2.52742I 4.57778 + 6.72148I
u = −0.332924 − 0.670769I
a = −1.29620 + 1.30443I
b = −0.482162 − 0.574614I
2.07364 − 2.52742I 4.57778 + 6.72148I
u = −1.51288
a = −0.718456 + 0.334102I
b = 0.644397 + 0.764691I
−3.74910 0.676060
u = −1.51288
a = −0.718456 − 0.334102I
b = 0.644397 − 0.764691I
−3.74910 0.676060
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
8
· (u
8
− 3u
7
+ 8u
6
− 13u
5
+ 15u
4
− 13u
3
+ 8u
2
− 3u + 1)
· (u
8
− 3u
7
+ 8u
6
− 11u
5
+ 15u
4
− 12u
3
+ 10u
2
− 4u + 1)
· (u
8
+ 3u
7
+ 8u
6
+ 15u
5
+ 19u
4
+ 24u
3
+ 18u
2
+ 4u + 1)
· (u
16
+ 4u
15
+ ··· + 128u + 256)
c
2
, c
6
(u
4
− u
3
+ u
2
+ 1)
8
(u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ u
3
+ 2u
2
+ u + 1)
· (u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ 1)
· (u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 1)
· (u
16
+ 4u
15
+ ··· + 48u + 16)
c
3
(u
4
+ u
3
− u
2
− u − 1)
2
· (u
8
− 5u
7
+ 9u
6
− 23u
4
+ 24u
3
+ 20u
2
− 56u + 32)
· (u
8
− 5u
7
+ 13u
6
− 19u
5
+ 17u
4
− 8u
3
+ 3u
2
− 2u + 1)
· (u
8
− u
7
− 3u
6
+ 3u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
· (u
8
+ 2u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1)
2
· (u
12
+ 3u
11
+ 4u
10
+ u
9
− 3u
8
− 5u
7
− 6u
6
+ 3u
3
− 3u
2
− 2u − 1)
2
c
4
, c
8
, c
9
(u
4
− u
3
− u
2
+ u − 1)
2
· (u
8
− 5u
7
+ 9u
6
− 23u
4
+ 24u
3
+ 20u
2
− 56u + 32)
· (u
8
− 5u
7
+ 13u
6
− 19u
5
+ 17u
4
− 8u
3
+ 3u
2
− 2u + 1)
· (u
8
+ u
7
− 3u
6
− 3u
5
+ u
4
+ 2u
3
+ 3u
2
+ 2u + 1)
· (u
8
+ 2u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1)
2
· (u
12
+ 3u
11
+ 4u
10
+ u
9
− 3u
8
− 5u
7
− 6u
6
+ 3u
3
− 3u
2
− 2u − 1)
2
c
5
, c
11
(u
4
− u
3
+ u
2
+ 1)
8
(u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 1)
· (u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− u
3
+ 2u
2
− u + 1)
· (u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 7u
4
+ 4u
3
+ 2u
2
+ 1)
· (u
16
+ 4u
15
+ ··· + 48u + 16)
c
7
, c
12
(u
8
− 5u
6
− 7u
5
+ 3u
4
+ 20u
3
+ 23u
2
− 5u + 2)
· (u
8
+ 2u
6
+ ··· + u
2
+ 1)(u
8
− u
7
− u
5
+ 3u
4
− 3u
3
+ u
2
+ 1)
· (u
8
+ u
7
− 6u
6
− 9u
5
+ 11u
4
+ 13u
3
+ 9u
2
+ 2u + 1)
· (u
16
+ 2u
15
+ ··· + 2u + 1)(u
24
+ 3u
23
+ ··· + 2368u + 1016)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
8
· (y
8
+ 7y
7
+ 12y
6
− 29y
5
− 93y
4
+ 4y
3
+ 170y
2
+ 20y + 1)
· (y
8
+ 7y
7
+ 16y
6
+ 9y
5
− y
4
+ 9y
3
+ 16y
2
+ 7y + 1)
· (y
8
+ 7y
7
+ 28y
6
+ 67y
5
+ 99y
4
+ 84y
3
+ 34y
2
+ 4y + 1)
· (y
16
+ 12y
15
+ ··· + 237568y + 65536)
c
2
, c
5
, c
6
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
8
· (y
8
+ 3y
7
+ 8y
6
+ 11y
5
+ 15y
4
+ 12y
3
+ 10y
2
+ 4y + 1)
· (y
8
+ 3y
7
+ 8y
6
+ 13y
5
+ 15y
4
+ 13y
3
+ 8y
2
+ 3y + 1)
· (y
8
+ 3y
7
+ 8y
6
+ 15y
5
+ 19y
4
+ 24y
3
+ 18y
2
+ 4y + 1)
· (y
16
+ 4y
15
+ ··· + 128y + 256)
c
3
, c
4
, c
8
c
9
(y
4
− 3y
3
+ y
2
+ y + 1)
2
· (y
8
− 7y
7
+ 17y
6
− 13y
5
− 7y
4
+ 8y
3
+ 3y
2
+ 2y + 1)
· (y
8
− 7y
7
+ ··· − 1856y + 1024)
· (y
8
+ y
7
+ 13y
6
+ 7y
5
+ 45y
4
− 12y
3
+ 11y
2
+ 2y + 1)
· (y
8
+ 2y
7
+ 9y
6
+ 11y
5
+ 12y
4
+ 11y
3
+ 6y
2
+ 3y + 1)
2
· (y
12
− y
11
+ ··· + 2y + 1)
2
c
7
, c
12
(y
8
− 13y
7
+ 76y
6
− 221y
5
+ 245y
4
+ 53y
3
+ 51y
2
+ 14y + 1)
· (y
8
− 10y
7
+ 31y
6
− 33y
5
+ 63y
4
− 352y
3
+ 741y
2
+ 67y + 4)
· (y
8
− y
7
+ 4y
6
− 5y
5
+ 5y
4
− 3y
3
+ 7y
2
+ 2y + 1)
· (y
8
+ 4y
7
+ 8y
6
− 6y
5
− 6y
4
+ 4y
3
+ 5y
2
+ 2y + 1)
· (y
16
− 34y
15
+ ··· + 34y + 1)
· (y
24
− 3y
23
+ ··· − 1653152y + 1032256)
30
