12n
0847
(K12n
0847
)
A knot diagram
1
Linearized knot diagam
4 7 8 9 1 12 10 1 2 3 7 6
Solving Sequence
1,5 6,9
4 2 10 8 3 12 7 11
c
5
c
4
c
1
c
9
c
8
c
3
c
12
c
6
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
10
− 5u
9
− 28u
8
− 131u
7
− 313u
6
− 576u
5
− 809u
4
− 779u
3
− 575u
2
+ 58b − 246u − 70,
− 35u
10
− 222u
9
+ ··· + 232a − 556,
u
11
+ 6u
10
+ 23u
9
+ 62u
8
+ 128u
7
+ 210u
6
+ 269u
5
+ 270u
4
+ 202u
3
+ 108u
2
+ 44u + 8i
I
u
2
= hau + b, 8u
6
a − 3u
6
+ ··· + 28a − 18, u
7
+ 4u
6
+ 11u
5
+ 20u
4
+ 26u
3
+ 25u
2
+ 14u + 4i
I
u
3
= h−a
3
u + 2a
3
− 7a
2
u + 5a
2
− 12au + 6b − 9u − 9, a
4
− 2a
3
u + 3a
3
− 4a
2
u + 3a
2
− 7au + 2a − 2u + 1,
u
2
− u + 1i
I
u
4
= h−au + b − u, a
2
+ a − 2u + 2, u
2
− u + 1i
I
u
5
= hu
12
− u
11
+ 8u
10
− 8u
9
+ 25u
8
− 24u
7
+ 42u
6
− 36u
5
+ 42u
4
− 31u
3
+ 22u
2
+ 2b − 13u + 5,
− 5u
15
− 55u
13
+ ··· + 38a − 247, u
16
+ 11u
14
+ 51u
12
+ 134u
10
+ 226u
8
+ 256u
6
+ 191u
4
+ 88u
2
+ 19i
I
u
6
= ha
3
u + a
3
+ a
2
u − 5a
2
− 6au + 3b + 3a + 6u + 3, a
4
+ a
3
u − 3a
3
− 2a
2
u + 2a
2
+ 2au + 2a − u − 1,
u
2
− u + 1i
I
u
7
= h−au + b + u − 1, a
2
− au − 2u + 1, u
2
− u + 1i
I
u
8
= hb − u + 1, a − 1, u
2
− u + 1i
I
u
9
= hb + u, a + u, u
2
− u + 1i
I
u
10
= hb + u + 1, a + u, u
2
+ u + 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
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).
1
* 11 irreducible components of dim
C
= 0, with total 73 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h3u
10
− 5u
9
+ · · · + 58b − 70, −35u
10
− 222u
9
+ · · · + 232a −
556, u
11
+ 6u
10
+ · · · + 44u + 8i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
0.150862u
10
+ 0.956897u
9
+ ··· + 6.37931u + 2.39655
−0.0517241u
10
+ 0.0862069u
9
+ ··· + 4.24138u + 1.20690
a
4
=
0.314655u
10
+ 1.51724u
9
+ ··· + 9.94828u + 3.74138
0.370690u
10
+ 1.96552u
9
+ ··· + 11.1034u + 2.51724
a
2
=
−0.193966u
10
− 0.801724u
9
+ ··· − 1.34483u + 0.775862
−0.620690u
10
− 3.46552u
9
+ ··· − 22.1034u − 4.51724
a
10
=
0.150862u
10
+ 0.706897u
9
+ ··· + 4.87931u + 1.39655
0.698276u
10
+ 2.58621u
9
+ ··· + 12.2414u + 3.20690
a
8
=
0.150862u
10
+ 0.956897u
9
+ ··· + 6.37931u + 2.39655
−0.448276u
10
− 1.58621u
9
+ ··· + 0.758621u + 0.793103
a
3
=
0.564655u
10
+ 2.76724u
9
+ ··· + 11.4483u + 2.74138
0.620690u
10
+ 3.46552u
9
+ ··· + 32.1034u + 6.51724
a
12
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
55
58
u
10
−
162
29
u
9
−
1217
58
u
8
−
1588
29
u
7
−
3216
29
u
6
−
5073
29
u
5
−
12583
58
u
4
−
5972
29
u
3
−
4159
29
u
2
−
2124
29
u−
702
29
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
11
− 5u
10
+ ··· + 5u + 7
c
2
, c
4
, c
8
c
10
u
11
+ u
10
+ 6u
9
+ 4u
8
+ 14u
7
+ 4u
6
+ 8u
5
− 5u
3
− 3u
2
+ u + 1
c
3
, c
9
u
11
− 2u
10
+ ··· − 9u + 24
c
5
, c
6
, c
11
c
12
u
11
+ 6u
10
+ ··· + 44u + 8
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
11
+ 5y
10
+ ··· − 31y −49
c
2
, c
4
, c
8
c
10
y
11
+ 11y
10
+ ··· + 7y −1
c
3
, c
9
y
11
− 22y
10
+ ··· + 4305y −576
c
5
, c
6
, c
11
c
12
y
11
+ 10y
10
+ ··· + 208y −64
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077559 + 0.704837I
a = 0.121802 − 0.808314I
b = −0.560282 − 0.148542I
0.79523 + 1.67374I 1.92464 − 5.47847I
u = −0.077559 − 0.704837I
a = 0.121802 + 0.808314I
b = −0.560282 + 0.148542I
0.79523 − 1.67374I 1.92464 + 5.47847I
u = −1.377920 + 0.101637I
a = −0.324451 + 1.135490I
b = −0.33166 + 1.59759I
−11.42710 − 8.15511I −7.08884 + 4.54839I
u = −1.377920 − 0.101637I
a = −0.324451 − 1.135490I
b = −0.33166 − 1.59759I
−11.42710 + 8.15511I −7.08884 − 4.54839I
u = −0.72850 + 1.42389I
a = −0.649822 + 0.893927I
b = 0.79946 + 1.57650I
−7.3754 + 15.4551I −4.41387 − 7.80880I
u = −0.72850 − 1.42389I
a = −0.649822 − 0.893927I
b = 0.79946 − 1.57650I
−7.3754 − 15.4551I −4.41387 + 7.80880I
u = −0.361176
a = 1.44545
b = 0.522063
−1.26726 −9.58390
u = 0.08198 + 1.70897I
a = −0.264638 + 0.259315I
b = 0.464855 + 0.430999I
9.26814 + 1.07224I 1.58191 − 6.79260I
u = 0.08198 − 1.70897I
a = −0.264638 − 0.259315I
b = 0.464855 − 0.430999I
9.26814 − 1.07224I 1.58191 + 6.79260I
u = −0.71742 + 1.60214I
a = 0.644383 − 0.371812I
b = −0.133405 − 1.299140I
−6.25408 − 0.69480I −6.21186 + 0.79724I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.71742 − 1.60214I
a = 0.644383 + 0.371812I
b = −0.133405 + 1.299140I
−6.25408 + 0.69480I −6.21186 − 0.79724I
7
II. I
u
2
= hau + b, 8u
6
a − 3u
6
+ · · · + 28a − 18, u
7
+ 4u
6
+ · · · + 14u + 4i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
a
−au
a
4
=
−
1
2
u
6
a − 2u
5
a + ··· − 4a +
5
2
−
1
2
u
6
− u
5
+ ··· − 2a −
3
2
u
a
2
=
−
1
2
u
6
−
3
2
u
5
+ ··· − a −
3
2
1
2
u
6
+ u
5
+ ··· − au +
5
2
u
a
10
=
−
1
2
u
6
a +
1
4
u
6
+ ··· +
21
4
u +
5
2
−u
6
a − 3u
5
a + ··· − 2a − 1
a
8
=
a
u
2
a − au
a
3
=
1
2
u
5
+ u
4
+ ··· − a +
5
2
−u
5
a −
1
2
u
6
+ ··· − au −
3
2
u
a
12
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
6
− 3u
5
− 11u
4
− 21u
3
− 30u
2
− 28u − 14
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
14
− 8u
13
+ ··· − 21u + 3
c
2
, c
4
, c
8
c
10
u
14
+ 8u
12
+ ··· − 3u + 1
c
3
, c
9
(u
7
+ u
6
− 2u
5
− 2u
4
− u
3
− 3u
2
− 1)
2
c
5
, c
6
, c
11
c
12
(u
7
+ 4u
6
+ 11u
5
+ 20u
4
+ 26u
3
+ 25u
2
+ 14u + 4)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
14
+ 2y
13
+ ··· − 33y + 9
c
2
, c
4
, c
8
c
10
y
14
+ 16y
13
+ ··· − 3y + 1
c
3
, c
9
(y
7
− 5y
6
+ 6y
5
+ 6y
4
− 9y
3
− 13y
2
− 6y −1)
2
c
5
, c
6
, c
11
c
12
(y
7
+ 6y
6
+ 13y
5
− 48y
3
− 57y
2
− 4y −16)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.532984 + 0.464109I
a = 0.595528 − 0.213565I
b = 0.218289 − 0.390217I
−0.57333 + 1.84126I −2.97768 − 3.50098I
u = −0.532984 + 0.464109I
a = 0.58819 − 1.42915I
b = −0.349784 − 1.034700I
−0.57333 + 1.84126I −2.97768 − 3.50098I
u = −0.532984 − 0.464109I
a = 0.595528 + 0.213565I
b = 0.218289 + 0.390217I
−0.57333 − 1.84126I −2.97768 + 3.50098I
u = −0.532984 − 0.464109I
a = 0.58819 + 1.42915I
b = −0.349784 + 1.034700I
−0.57333 − 1.84126I −2.97768 + 3.50098I
u = −1.33180
a = 0.228400 + 1.212910I
b = 0.30418 + 1.61536I
−12.0300 −7.93040
u = −1.33180
a = 0.228400 − 1.212910I
b = 0.30418 − 1.61536I
−12.0300 −7.93040
u = −0.11506 + 1.49422I
a = −0.755700 + 0.587068I
b = 0.79026 + 1.19673I
5.82905 + 4.07787I 5.41510 + 4.51647I
u = −0.11506 + 1.49422I
a = −0.095547 − 0.221715I
b = −0.342285 + 0.117257I
5.82905 + 4.07787I 5.41510 + 4.51647I
u = −0.11506 − 1.49422I
a = −0.755700 − 0.587068I
b = 0.79026 − 1.19673I
5.82905 − 4.07787I 5.41510 − 4.51647I
u = −0.11506 − 1.49422I
a = −0.095547 + 0.221715I
b = −0.342285 − 0.117257I
5.82905 − 4.07787I 5.41510 − 4.51647I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.68606 + 1.48551I
a = 0.668554 − 0.820572I
b = −0.76030 − 1.55610I
−7.46541 + 7.10242I −5.97220 − 3.89199I
u = −0.68606 + 1.48551I
a = −0.729428 + 0.430875I
b = 0.139642 + 1.379180I
−7.46541 + 7.10242I −5.97220 − 3.89199I
u = −0.68606 − 1.48551I
a = 0.668554 + 0.820572I
b = −0.76030 + 1.55610I
−7.46541 − 7.10242I −5.97220 + 3.89199I
u = −0.68606 − 1.48551I
a = −0.729428 − 0.430875I
b = 0.139642 − 1.379180I
−7.46541 − 7.10242I −5.97220 + 3.89199I
12
III.
I
u
3
= h−a
3
u − 7a
2
u + · · · + 5a
2
− 9, −2a
3
u − 4a
2
u + · · · + 2a + 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u − 1
a
9
=
a
1
6
a
3
u +
7
6
a
2
u + ··· −
5
6
a
2
+
3
2
a
4
=
1
3
a
3
u +
5
6
a
2
u + ··· + a + 1
1
2
a
3
u + 4a
2
u + ··· − a +
3
2
a
2
=
1
6
a
3
u +
7
6
a
2
u + ··· −
5
6
a
2
−
1
2
−
1
2
a
3
u − a
2
u + ··· − a −
1
2
a
10
=
1
2
a
3
−
3
2
a
2
u + a
2
− au − a −
1
2
u − 1
4
3
a
3
u +
4
3
a
2
u + ··· + 4a + 4
a
8
=
a
1
6
a
3
u +
7
6
a
2
u + ··· − a +
3
2
a
3
=
2
3
a
3
u +
13
6
a
2
u + ··· −
4
3
a
2
+ 1
−a
3
u − a
2
u − 2a
2
+ au − 3a + u − 2
a
12
=
u
u − 1
a
7
=
u
u − 2
a
11
=
2u − 1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 18
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
+ u
3
− 2u + 1)
2
c
2
, c
4
, c
8
c
10
u
8
+ 5u
7
+ 12u
6
+ 20u
5
+ 28u
4
+ 33u
3
+ 36u
2
+ 6u + 3
c
3
, c
9
(u
4
+ 2u
3
− 3u
2
− 4u + 7)
2
c
5
, c
6
, c
11
c
12
(u
2
− u + 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
4
− y
3
+ 6y
2
− 4y + 1)
2
c
2
, c
4
, c
8
c
10
y
8
− y
7
+ 14y
5
+ 274y
4
+ 759y
3
+ 1068y
2
+ 180y + 9
c
3
, c
9
(y
4
− 10y
3
+ 39y
2
− 58y + 49)
2
c
5
, c
6
, c
11
c
12
(y
2
+ y + 1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.91531 − 1.09688I
b = 0.87030 − 1.52885I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 0.500000 + 0.866025I
a = −0.293656 − 0.109216I
b = 2.06972 + 0.74483I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 0.500000 + 0.866025I
a = 0.88888 + 1.51813I
b = −0.49226 + 1.34112I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 0.500000 + 0.866025I
a = −1.67991 + 1.42001I
b = 0.052244 + 0.308922I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 0.500000 − 0.866025I
a = −0.91531 + 1.09688I
b = 0.87030 + 1.52885I
−3.28987 + 6.08965I −12.0000 − 10.3923I
u = 0.500000 − 0.866025I
a = −0.293656 + 0.109216I
b = 2.06972 − 0.74483I
−3.28987 + 6.08965I −12.0000 − 10.3923I
u = 0.500000 − 0.866025I
a = 0.88888 − 1.51813I
b = −0.49226 − 1.34112I
−3.28987 + 6.08965I −12.0000 − 10.3923I
u = 0.500000 − 0.866025I
a = −1.67991 − 1.42001I
b = 0.052244 − 0.308922I
−3.28987 + 6.08965I −12.0000 − 10.3923I
16
IV. I
u
4
= h−au + b − u, a
2
+ a − 2u + 2, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u − 1
a
9
=
a
au + u
a
4
=
−1
au − a − u − 1
a
2
=
−u
−a − u + 1
a
10
=
−au + a − 1
au + a − 2u + 2
a
8
=
a
2au − a + u
a
3
=
−au + a − 2u + 1
au + 2
a
12
=
u
u − 1
a
7
=
u
u − 2
a
11
=
2u − 1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
+ u + 1)
2
c
2
, c
4
, c
8
c
10
u
4
+ u
3
+ 3u
2
+ 4u + 4
c
3
, c
9
u
4
+ 3u
2
− 6u + 3
c
5
, c
6
, c
11
c
12
(u
2
− u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
(y
2
+ y + 1)
2
c
2
, c
4
, c
8
c
10
y
4
+ 5y
3
+ 9y
2
+ 8y + 16
c
3
, c
9
y
4
+ 6y
3
+ 15y
2
− 18y + 9
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.254141 + 1.148360I
b = −0.36744 + 1.66030I
− 6.08965I 0. + 10.39230I
u = 0.500000 + 0.866025I
a = −1.25414 − 1.14836I
b = 0.867438 − 0.794273I
− 6.08965I 0. + 10.39230I
u = 0.500000 − 0.866025I
a = 0.254141 − 1.148360I
b = −0.36744 − 1.66030I
6.08965I 0. − 10.39230I
u = 0.500000 − 0.866025I
a = −1.25414 + 1.14836I
b = 0.867438 + 0.794273I
6.08965I 0. − 10.39230I
20
V. I
u
5
= hu
12
− u
11
+ · · · + 2b + 5, −5u
15
− 55u
13
+ · · · + 38a − 247, u
16
+
11u
14
+ · · · + 88u
2
+ 19i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
9
=
0.131579u
15
+ 1.44737u
13
+ ··· + 0.578947u + 6.50000
−
1
2
u
12
+
1
2
u
11
+ ··· +
13
2
u −
5
2
a
4
=
−0.0789474u
15
− 0.368421u
13
+ ··· + 6.55263u + 6.50000
1
2
u
14
+
1
2
u
13
+ ··· +
11
2
u +
3
2
a
2
=
−0.131579u
15
− 0.947368u
13
+ ··· + 8.42105u + 9
1
2
u
15
+ u
14
+ ··· +
23
2
u +
5
2
a
10
=
3
38
u
15
+
1
2
u
14
+ ··· +
94
19
u + 12
1
2
u
15
+
1
2
u
14
+ ··· +
7
2
u −
3
2
a
8
=
0.131579u
15
+ 1.44737u
13
+ ··· + 0.578947u + 6.50000
−
1
2
u
13
−
7
2
u
11
+ ··· + 4u −
5
2
a
3
=
−0.131579u
15
+ 0.500000u
14
+ ··· + 14.9211u + 11.5000
u
15
+
1
2
u
14
+ ··· +
23
2
u − 7
a
12
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
14
− 56u
12
− 216u
10
− 468u
8
− 639u
6
− 555u
4
− 288u
2
− 73
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
16
− 7u
15
+ ··· + u + 1
c
2
, c
4
, c
8
c
10
u
16
− u
15
+ ··· − 3u + 1
c
3
, c
9
(u
8
− 4u
6
+ 6u
4
+ 3u
3
− 2u
2
− 4u − 1)
2
c
5
, c
6
, c
11
c
12
u
16
+ 11u
14
+ 51u
12
+ 134u
10
+ 226u
8
+ 256u
6
+ 191u
4
+ 88u
2
+ 19
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
16
+ 7y
15
+ ··· − 11y + 1
c
2
, c
4
, c
8
c
10
y
16
+ 7y
15
+ ··· + 9y + 1
c
3
, c
9
(y
8
− 8y
7
+ 28y
6
− 52y
5
+ 50y
4
− 25y
3
+ 16y
2
− 12y + 1)
2
c
5
, c
6
, c
11
c
12
(y
8
+ 11y
7
+ 51y
6
+ 134y
5
+ 226y
4
+ 256y
3
+ 191y
2
+ 88y + 19)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.450136 + 0.896465I
a = 0.94613 + 1.22806I
b = −0.67503 + 1.40096I
−2.63935 − 5.65917I −1.08017 + 3.20273I
u = 0.450136 − 0.896465I
a = 0.94613 − 1.22806I
b = −0.67503 − 1.40096I
−2.63935 + 5.65917I −1.08017 − 3.20273I
u = −0.450136 + 0.896465I
a = −0.841491 − 0.713776I
b = 1.018660 − 0.433071I
−2.63935 + 5.65917I −1.08017 − 3.20273I
u = −0.450136 − 0.896465I
a = −0.841491 + 0.713776I
b = 1.018660 + 0.433071I
−2.63935 − 5.65917I −1.08017 + 3.20273I
u = 0.539427 + 0.986711I
a = 0.988608 + 0.489509I
b = 0.050278 + 1.239530I
−2.28512 + 1.91134I −2.25611 − 2.12602I
u = 0.539427 − 0.986711I
a = 0.988608 − 0.489509I
b = 0.050278 − 1.239530I
−2.28512 − 1.91134I −2.25611 + 2.12602I
u = −0.539427 + 0.986711I
a = 0.628905 + 0.629308I
b = −0.960194 + 0.281082I
−2.28512 − 1.91134I −2.25611 + 2.12602I
u = −0.539427 − 0.986711I
a = 0.628905 − 0.629308I
b = −0.960194 − 0.281082I
−2.28512 + 1.91134I −2.25611 − 2.12602I
u = 0.846388I
a = 1.181140 + 0.332598I
b = −0.281507 + 0.999702I
−1.93059 −6.07620
u = − 0.846388I
a = 1.181140 − 0.332598I
b = −0.281507 − 0.999702I
−1.93059 −6.07620
24
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04760 + 1.50314I
a = −0.799076 − 0.569432I
b = 0.81790 − 1.22823I
5.58575 − 4.39316I −7.09441 + 10.90971I
u = 0.04760 − 1.50314I
a = −0.799076 + 0.569432I
b = 0.81790 + 1.22823I
5.58575 + 4.39316I −7.09441 − 10.90971I
u = −0.04760 + 1.50314I
a = 0.247325 − 0.146593I
b = 0.208575 + 0.378743I
5.58575 + 4.39316I −7.09441 − 10.90971I
u = −0.04760 − 1.50314I
a = 0.247325 + 0.146593I
b = 0.208575 − 0.378743I
5.58575 − 4.39316I −7.09441 + 10.90971I
u = 1.78942I
a = −0.351537 − 0.179565I
b = 0.321316 − 0.629047I
8.83269 −4.06250
u = − 1.78942I
a = −0.351537 + 0.179565I
b = 0.321316 + 0.629047I
8.83269 −4.06250
25
VI. I
u
6
= ha
3
u + a
2
u + · · · + 3a + 3, a
3
u − 2a
2
u + · · · + 2a − 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u − 1
a
9
=
a
−
1
3
a
3
u −
1
3
a
2
u + ··· − a − 1
a
4
=
−
2
3
a
3
u +
4
3
a
2
u + ··· − a + 1
a
3
u + a
3
− 4a
2
− 3au + 3a + 5u
a
2
=
−
1
3
a
3
u −
1
3
a
2
u + ··· +
5
3
a
2
− a
−a
3
u + 2a
2
u + a
2
− a − u − 1
a
10
=
a
2
u − au − a + 1
−
2
3
a
3
u +
7
3
a
2
u + ··· −
5
3
a
2
+ 2a
a
8
=
a
−
1
3
a
3
u −
1
3
a
2
u + ··· − 2a − 1
a
3
=
−
4
3
a
3
u +
5
3
a
2
u + ··· − 2a + 2
a
3
+ 2a
2
u − 2a
2
− 2au + 2u − 1
a
12
=
u
u − 1
a
7
=
u
u − 2
a
11
=
2u − 1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 10
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
+ u
3
− 2u + 1)
2
c
2
, c
4
, c
8
c
10
u
8
− 4u
7
+ 9u
6
− 16u
5
+ 22u
4
− 18u
3
+ 18u
2
− 6u + 3
c
3
, c
9
(u
4
− u
3
− 3u
2
+ 2u + 4)
2
c
5
, c
6
, c
11
c
12
(u
2
− u + 1)
4
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
4
− y
3
+ 6y
2
− 4y + 1)
2
c
2
, c
4
, c
8
c
10
y
8
+ 2y
7
− 3y
6
+ 32y
5
+ 190y
4
+ 330y
3
+ 240y
2
+ 72y + 9
c
3
, c
9
(y
4
− 7y
3
+ 21y
2
− 28y + 16)
2
c
5
, c
6
, c
11
c
12
(y
2
+ y + 1)
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.968092 − 0.487878I
b = −0.08797 − 1.50359I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = 0.521310 + 0.118664I
b = −1.81567 − 0.80000I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = 1.34613 + 0.67561I
b = 0.061531 + 1.082330I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = 1.60065 − 1.17242I
b = −0.157889 − 0.510800I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.968092 + 0.487878I
b = −0.08797 + 1.50359I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = 0.521310 − 0.118664I
b = −1.81567 + 0.80000I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = 1.34613 − 0.67561I
b = 0.061531 − 1.082330I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = 1.60065 + 1.17242I
b = −0.157889 + 0.510800I
−3.28987 − 2.02988I −12.00000 + 3.46410I
29
VII. I
u
7
= h−au + b + u − 1, a
2
− au − 2u + 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u − 1
a
9
=
a
au − u + 1
a
4
=
u − 1
a − 2u − 1
a
2
=
u − 1
a − u − 1
a
10
=
a − u
2au − a − 2u + 3
a
8
=
a
2au − a − u + 1
a
3
=
au − a + u − 1
−au − u − 1
a
12
=
u
u − 1
a
7
=
u
u − 2
a
11
=
2u − 1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 14
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u + 1)
4
c
2
, c
4
, c
8
c
10
u
4
+ u
3
+ 4u
2
+ 3
c
3
, c
9
(u
2
+ u + 1)
2
c
5
, c
6
, c
11
c
12
(u
2
− u + 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y − 1)
4
c
2
, c
4
, c
8
c
10
y
4
+ 7y
3
+ 22y
2
+ 24y + 9
c
3
, c
5
, c
6
c
9
, c
11
, c
12
(y
2
+ y + 1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.705919 − 0.586193I
b = 0.65470 − 1.77047I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = 1.20592 + 1.45222I
b = −0.154699 + 0.904441I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.705919 + 0.586193I
b = 0.65470 + 1.77047I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 1.20592 − 1.45222I
b = −0.154699 − 0.904441I
−3.28987 + 2.02988I −12.00000 − 3.46410I
33
VIII. I
u
8
= hb − u + 1, a − 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u − 1
a
9
=
1
u − 1
a
4
=
u
−u
a
2
=
1
u − 1
a
10
=
1
u − 1
a
8
=
1
2u − 2
a
3
=
2
3u − 2
a
12
=
u
u − 1
a
7
=
u
u − 2
a
11
=
2u − 1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 2
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
+ u + 1
c
2
, c
4
, c
5
c
6
, c
8
, c
10
c
11
, c
12
u
2
− u + 1
c
3
u
2
− 3u + 3
c
9
u
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y
2
+ y + 1
c
3
y
2
− 3y + 9
c
9
y
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = −0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = 0.500000 − 0.866025I
a = 1.00000
b = −0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
37
IX. I
u
9
= hb + u, a + u, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u − 1
a
9
=
−u
−u
a
4
=
u
u − 1
a
2
=
1
2u
a
10
=
−2u + 2
u + 2
a
8
=
−u
−u + 1
a
3
=
u
u − 1
a
12
=
u
u − 1
a
7
=
u
u − 2
a
11
=
2u − 1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 2
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
+ u + 1
c
2
, c
4
, c
5
c
6
, c
8
, c
10
c
11
, c
12
u
2
− u + 1
c
3
u
2
c
9
u
2
− 3u + 3
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y
2
+ y + 1
c
3
y
2
c
9
y
2
− 3y + 9
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
41
X. I
u
10
= hb + u + 1, a + u, u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
−u − 1
a
9
=
−u
−u − 1
a
4
=
0
u
a
2
=
0
u
a
10
=
−u
−u − 2
a
8
=
−u
−u − 2
a
3
=
1
−u − 1
a
12
=
u
u + 1
a
7
=
−u
−u − 2
a
11
=
2u + 1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 2
42
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
2
− u + 1
c
5
, c
6
, c
11
c
12
u
2
+ u + 1
43
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y
2
+ y + 1
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
45
XI. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
1
=
−1
0
a
5
=
1
0
a
6
=
1
0
a
9
=
0
b
a
4
=
1
−b − 1
a
2
=
b
−b
a
10
=
−1
b + 1
a
8
=
−b
b
a
3
=
0
−b
a
12
=
−1
0
a
7
=
1
0
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b + 4
46
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
2
− u + 1
c
2
, c
4
, c
8
c
10
u
2
+ u + 1
c
5
, c
6
, c
11
c
12
u
2
47
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
y
2
+ y + 1
c
5
, c
6
, c
11
c
12
y
2
48
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
4.05977I 0. − 6.92820I
49
XII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
(u + 1)
4
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
4
+ u
3
− 2u + 1)
4
· (u
11
− 5u
10
+ ··· + 5u + 7)(u
14
− 8u
13
+ ··· − 21u + 3)
· (u
16
− 7u
15
+ ··· + u + 1)
c
2
, c
4
, c
8
c
10
((u
2
− u + 1)
3
)(u
2
+ u + 1)(u
4
+ u
3
+ ··· + 4u + 4)(u
4
+ u
3
+ 4u
2
+ 3)
· (u
8
− 4u
7
+ 9u
6
− 16u
5
+ 22u
4
− 18u
3
+ 18u
2
− 6u + 3)
· (u
8
+ 5u
7
+ 12u
6
+ 20u
5
+ 28u
4
+ 33u
3
+ 36u
2
+ 6u + 3)
· (u
11
+ u
10
+ 6u
9
+ 4u
8
+ 14u
7
+ 4u
6
+ 8u
5
− 5u
3
− 3u
2
+ u + 1)
· (u
14
+ 8u
12
+ ··· − 3u + 1)(u
16
− u
15
+ ··· − 3u + 1)
c
3
, c
9
u
2
(u
2
− 3u + 3)(u
2
− u + 1)
2
(u
2
+ u + 1)
2
(u
4
+ 3u
2
− 6u + 3)
· (u
4
− u
3
− 3u
2
+ 2u + 4)
2
(u
4
+ 2u
3
− 3u
2
− 4u + 7)
2
· (u
7
+ u
6
− 2u
5
− 2u
4
− u
3
− 3u
2
− 1)
2
· ((u
8
− 4u
6
+ ··· − 4u − 1)
2
)(u
11
− 2u
10
+ ··· − 9u + 24)
c
5
, c
6
, c
11
c
12
u
2
(u
2
− u + 1)
14
(u
2
+ u + 1)
· (u
7
+ 4u
6
+ 11u
5
+ 20u
4
+ 26u
3
+ 25u
2
+ 14u + 4)
2
· (u
11
+ 6u
10
+ ··· + 44u + 8)
· (u
16
+ 11u
14
+ 51u
12
+ 134u
10
+ 226u
8
+ 256u
6
+ 191u
4
+ 88u
2
+ 19)
50
XIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
(y − 1)
4
(y
2
+ y + 1)
5
(y
4
− y
3
+ 6y
2
− 4y + 1)
4
· (y
11
+ 5y
10
+ ··· − 31y − 49)(y
14
+ 2y
13
+ ··· − 33y + 9)
· (y
16
+ 7y
15
+ ··· − 11y + 1)
c
2
, c
4
, c
8
c
10
((y
2
+ y + 1)
4
)(y
4
+ 5y
3
+ ··· + 8y + 16)(y
4
+ 7y
3
+ ··· + 24y + 9)
· (y
8
− y
7
+ 14y
5
+ 274y
4
+ 759y
3
+ 1068y
2
+ 180y + 9)
· (y
8
+ 2y
7
− 3y
6
+ 32y
5
+ 190y
4
+ 330y
3
+ 240y
2
+ 72y + 9)
· (y
11
+ 11y
10
+ ··· + 7y − 1)(y
14
+ 16y
13
+ ··· − 3y + 1)
· (y
16
+ 7y
15
+ ··· + 9y + 1)
c
3
, c
9
y
2
(y
2
− 3y + 9)(y
2
+ y + 1)
4
(y
4
− 10y
3
+ 39y
2
− 58y + 49)
2
· (y
4
− 7y
3
+ 21y
2
− 28y + 16)
2
(y
4
+ 6y
3
+ 15y
2
− 18y + 9)
· (y
7
− 5y
6
+ 6y
5
+ 6y
4
− 9y
3
− 13y
2
− 6y − 1)
2
· (y
8
− 8y
7
+ 28y
6
− 52y
5
+ 50y
4
− 25y
3
+ 16y
2
− 12y + 1)
2
· (y
11
− 22y
10
+ ··· + 4305y − 576)
c
5
, c
6
, c
11
c
12
y
2
(y
2
+ y + 1)
15
(y
7
+ 6y
6
+ 13y
5
− 48y
3
− 57y
2
− 4y − 16)
2
· (y
8
+ 11y
7
+ 51y
6
+ 134y
5
+ 226y
4
+ 256y
3
+ 191y
2
+ 88y + 19)
2
· (y
11
+ 10y
10
+ ··· + 208y − 64)
51
