12n
0494
(K12n
0494
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 9 3 11 4 6 7
Solving Sequence
3,9
8 4
7,12
1 6 2 5 11 10
c
8
c
3
c
7
c
12
c
6
c
2
c
5
c
11
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
8
− 2u
6
− u
5
− 2u
4
− 2u
3
+ 2u
2
+ 4b − 2u,
− 3u
8
− 3u
7
− 8u
6
− 13u
5
− 17u
4
− 18u
3
− 12u
2
+ 8a − 12u − 10,
u
9
+ 3u
7
+ 3u
6
+ 4u
5
+ 7u
4
+ 2u
3
+ 8u
2
+ 2u + 2i
I
u
2
= h−55u
11
+ 144u
10
+ ··· + 246b + 197, −98u
11
+ 229u
10
+ ··· + 615a − 179,
u
12
− 3u
11
+ 8u
10
− 16u
9
+ 27u
8
− 42u
7
+ 48u
6
− 48u
5
+ 41u
4
− 29u
3
+ 22u
2
− 12u + 5i
I
u
3
= hu
3
+ u
2
+ 2b, u
3
+ 2u
2
+ 2a + u + 2, u
4
+ u
2
+ 2i
I
u
4
= h−2u
2
b + 2b
2
+ u
2
− 2b + u − 1, −u
2
+ a − 2, u
3
+ 2u − 1i
I
u
5
= h2u
2
b + b
2
+ bu + u
2
+ 2b − 2u − 1, u
3
+ u
2
+ a + 2u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
I
u
6
= hu
3
− u
2
+ 2b − u − 1, u
3
− u
2
+ a − 1, u
4
+ 1i
I
u
7
= h2b − u − 1, a − u, u
2
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 46 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
8
− 2u
6
− u
5
− 2u
4
− 2u
3
+ 2u
2
+ 4b − 2u, −3u
8
− 3u
7
+ · · · +
8a − 10, u
9
+ 3u
7
+ · · · + 2u + 2i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
12
=
3
8
u
8
+
3
8
u
7
+ ··· +
3
2
u +
5
4
1
4
u
8
+
1
2
u
6
+ ··· −
1
2
u
2
+
1
2
u
a
1
=
1
8
u
8
+
1
8
u
7
+ ··· +
1
2
u +
3
4
1
8
u
8
−
1
8
u
7
+ ··· + u +
1
4
a
6
=
−
3
8
u
8
+
1
8
u
7
+ ··· −
3
2
u +
3
4
−
1
4
u
8
−
1
2
u
6
+ ··· +
1
2
u
2
−
1
2
u
a
2
=
1
8
u
8
+
1
8
u
7
+ ··· +
1
2
u +
3
4
−
1
4
u
8
−
1
2
u
6
+ ··· −
1
2
u
2
+
1
2
u
a
5
=
−
1
2
u
8
+
1
2
u
7
+ ··· − 2u + 1
−u
5
− u
3
− u
a
11
=
1
2
u
8
+
1
2
u
7
+ ··· + 2u + 2
−u
2
a
10
=
1
2
u
8
+
1
2
u
7
+ ··· + 2u + 2
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7
2
u
8
+
1
2
u
7
+ 8u
6
+
21
2
u
5
+
19
2
u
4
+ 17u
3
+ 14u − 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 9u
8
+ 34u
7
+ 67u
6
+ 110u
5
+ 195u
4
+ 74u
3
+ 13u
2
+ 5u + 4
c
2
, c
5
, c
6
c
11
, c
12
u
9
+ 3u
8
− 3u
6
+ 8u
5
+ 7u
4
− 8u
3
− u
2
− u + 2
c
3
, c
4
, c
8
c
10
u
9
+ 3u
7
− 3u
6
+ 4u
5
− 7u
4
+ 2u
3
− 8u
2
+ 2u − 2
c
7
, c
9
u
9
+ 6u
8
+ 17u
7
+ 19u
6
− 10u
5
− 69u
4
− 104u
3
− 84u
2
− 28u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 13y
8
+ ··· − 79y −16
c
2
, c
5
, c
6
c
11
, c
12
y
9
− 9y
8
+ 34y
7
− 67y
6
+ 110y
5
− 195y
4
+ 74y
3
− 13y
2
+ 5y −4
c
3
, c
4
, c
8
c
10
y
9
+ 6y
8
+ 17y
7
+ 19y
6
− 10y
5
− 69y
4
− 104y
3
− 84y
2
− 28y −4
c
7
, c
9
y
9
− 2y
8
+ ··· + 112y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605578 + 0.988703I
a = −0.498037 − 1.109200I
b = 0.448043 − 0.671342I
−1.16289 + 6.06815I −4.01464 − 9.38796I
u = 0.605578 − 0.988703I
a = −0.498037 + 1.109200I
b = 0.448043 + 0.671342I
−1.16289 − 6.06815I −4.01464 + 9.38796I
u = −0.393682 + 1.170050I
a = −0.161336 + 1.318460I
b = 0.282547 + 0.651319I
−1.55283 − 2.10568I −8.24909 + 2.94817I
u = −0.393682 − 1.170050I
a = −0.161336 − 1.318460I
b = 0.282547 − 0.651319I
−1.55283 + 2.10568I −8.24909 − 2.94817I
u = −1.28577
a = 2.25673
b = 2.08230
−11.6795 −6.68460
u = −0.167967 + 0.528611I
a = 0.919569 + 0.464661I
b = 0.114544 + 0.334046I
−0.079794 − 1.130890I −1.24369 + 6.31560I
u = −0.167967 − 0.528611I
a = 0.919569 − 0.464661I
b = 0.114544 − 0.334046I
−0.079794 + 1.130890I −1.24369 − 6.31560I
u = 0.59896 + 1.45234I
a = −0.88856 + 1.33082I
b = −2.38628 + 0.41174I
18.5049 + 13.3202I −10.15028 − 5.68943I
u = 0.59896 − 1.45234I
a = −0.88856 − 1.33082I
b = −2.38628 − 0.41174I
18.5049 − 13.3202I −10.15028 + 5.68943I
5
II. I
u
2
= h−55u
11
+ 144u
10
+ · · · + 246b + 197, −98u
11
+ 229u
10
+ · · · +
615a − 179, u
12
− 3u
11
+ · · · − 12u + 5i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
12
=
0.159350u
11
− 0.372358u
10
+ ··· + 1.42439u + 0.291057
0.223577u
11
− 0.585366u
10
+ ··· + 2.53252u − 0.800813
a
1
=
−0.572358u
11
+ 1.05854u
10
+ ··· − 4.13659u + 3.06341
−0.231707u
11
+ 0.430894u
10
+ ··· − 1.06098u + 1.27236
a
6
=
0.139837u
11
− 0.143089u
10
+ ··· − 0.110569u + 0.289431
0.394309u
11
− 0.674797u
10
+ ··· + 2.29675u − 1.70325
a
2
=
−0.572358u
11
+ 1.05854u
10
+ ··· − 4.13659u + 3.06341
−1.05285u
11
+ 1.82927u
10
+ ··· − 6.10163u + 4.56504
a
5
=
−1.44390u
11
+ 2.63252u
10
+ ··· − 10.5870u + 6.54634
−2.73984u
11
+ 4.94309u
10
+ ··· − 17.7561u + 10.5772
a
11
=
−0.413008u
11
+ 0.686179u
10
+ ··· − 2.71220u + 3.35447
−0.829268u
11
+ 1.24390u
10
+ ··· − 4.56911u + 3.76423
a
10
=
−1.24228u
11
+ 1.93008u
10
+ ··· − 7.28130u + 6.11870
−3.35772u
11
+ 5.53659u
10
+ ··· − 19.9187u + 12.7480
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
146
123
u
11
+
114
41
u
10
−
1024
123
u
9
+
540
41
u
8
−
996
41
u
7
+
1288
41
u
6
−
1388
41
u
5
+
1156
41
u
4
−
1768
123
u
3
+
2074
123
u
2
−
470
123
u +
104
123
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 11u
5
+ 43u
4
+ 66u
3
+ 27u
2
+ 11u + 1)
2
c
2
, c
5
, c
6
c
11
, c
12
(u
6
− u
5
− 5u
4
+ 4u
3
+ 5u
2
+ u − 1)
2
c
3
, c
4
, c
8
c
10
u
12
+ 3u
11
+ ··· + 12u + 5
c
7
, c
9
u
12
+ 7u
11
+ ··· + 76u + 25
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 35y
5
+ 451y
4
− 2274y
3
− 637y
2
− 67y + 1)
2
c
2
, c
5
, c
6
c
11
, c
12
(y
6
− 11y
5
+ 43y
4
− 66y
3
+ 27y
2
− 11y + 1)
2
c
3
, c
4
, c
8
c
10
y
12
+ 7y
11
+ ··· + 76y + 25
c
7
, c
9
y
12
− 5y
11
+ ··· + 4124y + 625
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.187195 + 1.051250I
a = 0.042610 − 0.239290I
b = 0.799220 + 0.595347I
−3.90045 −12.16498 + 0.I
u = 0.187195 − 1.051250I
a = 0.042610 + 0.239290I
b = 0.799220 − 0.595347I
−3.90045 −12.16498 + 0.I
u = −0.461242 + 0.712140I
a = 0.931142 − 0.466748I
b = 0.0261039 − 0.1100110I
−0.02949 − 1.42716I −2.28345 + 4.88332I
u = −0.461242 − 0.712140I
a = 0.931142 + 0.466748I
b = 0.0261039 + 0.1100110I
−0.02949 + 1.42716I −2.28345 − 4.88332I
u = 0.497740 + 0.566185I
a = 0.790067 + 0.866041I
b = 0.349904 + 0.608879I
−0.02949 − 1.42716I −2.28345 + 4.88332I
u = 0.497740 − 0.566185I
a = 0.790067 − 0.866041I
b = 0.349904 − 0.608879I
−0.02949 + 1.42716I −2.28345 − 4.88332I
u = 1.256410 + 0.018334I
a = −2.14746 − 0.23652I
b = −2.02885 − 0.02831I
−16.3520 + 6.7708I −8.38492 − 2.96218I
u = 1.256410 − 0.018334I
a = −2.14746 + 0.23652I
b = −2.02885 + 0.02831I
−16.3520 − 6.7708I −8.38492 + 2.96218I
u = −0.61652 + 1.48694I
a = 0.83408 + 1.46579I
b = 2.18635 + 0.61399I
−16.3520 − 6.7708I −8.38492 + 2.96218I
u = −0.61652 − 1.48694I
a = 0.83408 − 1.46579I
b = 2.18635 − 0.61399I
−16.3520 + 6.7708I −8.38492 − 2.96218I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63641 + 1.48830I
a = −0.65044 + 1.52111I
b = −1.83272 + 0.63406I
18.5691 −10.49827 + 0.I
u = 0.63641 − 1.48830I
a = −0.65044 − 1.52111I
b = −1.83272 − 0.63406I
18.5691 −10.49827 + 0.I
10
III. I
u
3
= hu
3
+ u
2
+ 2b, u
3
+ 2u
2
+ 2a + u + 2, u
4
+ u
2
+ 2i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
12
=
−
1
2
u
3
− u
2
−
1
2
u − 1
−
1
2
u
3
−
1
2
u
2
a
1
=
−
1
2
u
3
−
1
2
u
−
1
2
u
3
+
1
2
u
2
a
6
=
−
1
2
u
3
−
1
2
u
−
1
2
u
3
+
1
2
u
2
a
2
=
−
1
2
u
3
−
1
2
u
−
1
2
u
3
+
1
2
u
2
+ u
a
5
=
0
−u
a
11
=
−u
2
− 1
−u
2
a
10
=
−1
−u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
8
c
10
u
4
+ u
2
+ 2
c
7
, c
9
(u
2
− u + 2)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
8
c
10
(y
2
+ y + 2)
2
c
7
, c
9
(y
2
+ 3y + 4)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = −0.02193 − 2.01465I
b = 1.066120 − 0.864054I
−2.46740 + 5.33349I −10.00000 − 5.29150I
u = 0.676097 − 0.978318I
a = −0.02193 + 2.01465I
b = 1.066120 + 0.864054I
−2.46740 − 5.33349I −10.00000 + 5.29150I
u = −0.676097 + 0.978318I
a = −0.978073 + 0.631100I
b = −0.566121 + 0.458821I
−2.46740 − 5.33349I −10.00000 + 5.29150I
u = −0.676097 − 0.978318I
a = −0.978073 − 0.631100I
b = −0.566121 − 0.458821I
−2.46740 + 5.33349I −10.00000 − 5.29150I
14
IV. I
u
4
= h−2u
2
b + 2b
2
+ u
2
− 2b + u − 1, −u
2
+ a − 2, u
3
+ 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
4
=
u
−u + 1
a
7
=
u
2
+ 1
u
2
a
12
=
u
2
+ 2
b
a
1
=
−bu + u
2
− b − u + 3
u
2
b − bu + b − 2u + 1
a
6
=
−u
2
b − bu + u
2
− 2b + 2
−b
a
2
=
−bu + u
2
− b − u + 3
bu + u
2
+ u
a
5
=
−u
2
+ 3u − 2
−u
2
− 3u + 1
a
11
=
u
2
+ u
−u
2
a
10
=
2u
2
+ u
−2u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 7u
5
+ 9u
4
+ 33u
3
+ 299u
2
+ 434u + 121
c
2
, c
5
, c
6
c
11
, c
12
u
6
+ 3u
5
+ u
4
+ 5u
3
+ 19u
2
+ 4u − 11
c
3
, c
4
, c
8
c
10
(u
3
+ 2u + 1)
2
c
7
, c
9
(u
3
+ 4u
2
+ 4u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 31y
5
+ 217y
4
− 1541y
3
+ 62935y
2
− 115998y + 14641
c
2
, c
5
, c
6
c
11
, c
12
y
6
− 7y
5
+ 9y
4
− 33y
3
+ 299y
2
− 434y + 121
c
3
, c
4
, c
8
c
10
(y
3
+ 4y
2
+ 4y −1)
2
c
7
, c
9
(y
3
− 8y
2
+ 24y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −0.102785 − 0.665457I
b = 0.811775 − 0.345273I
−12.73060 − 5.13794I −11.31793 + 3.20902I
u = −0.22670 + 1.46771I
a = −0.102785 − 0.665457I
b = −1.91456 − 0.32018I
−12.73060 − 5.13794I −11.31793 + 3.20902I
u = −0.22670 − 1.46771I
a = −0.102785 + 0.665457I
b = 0.811775 + 0.345273I
−12.73060 + 5.13794I −11.31793 − 3.20902I
u = −0.22670 − 1.46771I
a = −0.102785 + 0.665457I
b = −1.91456 + 0.32018I
−12.73060 + 5.13794I −11.31793 − 3.20902I
u = 0.453398
a = 2.20557
b = 1.33345
−2.50267 0.635870
u = 0.453398
a = 2.20557
b = −0.127877
−2.50267 0.635870
18
V.
I
u
5
= h2u
2
b+b
2
+bu+u
2
+2b−2u−1, u
3
+u
2
+a+2u+2, u
4
+u
3
+2u
2
+2u+1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
12
=
−u
3
− u
2
− 2u − 2
b
a
1
=
u
3
b + 2bu − u
2
− u − 2
u
3
b + u
2
b + u
3
+ 2bu + 2b
a
6
=
u
3
b + u
2
b + bu + u
2
+ 2b + 2
−u
3
b − 3u
3
− 2bu − u
2
− 4u − 2
a
2
=
u
3
b + 2bu − u
2
− u − 2
2u
3
b + u
2
b + u
3
+ 3bu + 3b + 2u + 1
a
5
=
−u
3
− 2u
2
− 2u − 3
2u
3
+ 4u + 1
a
11
=
u
3
+ 2u + 1
u
3
+ u
2
+ u + 2
a
10
=
2u
3
+ 3u + 2
2u
3
+ 2u
2
+ 3u + 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 5u
3
+ 10u
2
+ 12u + 9)
2
c
2
, c
5
, c
6
c
11
, c
12
(u
4
− u
3
− 2u
2
+ 3)
2
c
3
, c
4
, c
8
c
10
(u
4
− u
3
+ 2u
2
− 2u + 1)
2
c
7
, c
9
(u
4
+ 3u
3
+ 2u
2
+ 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 5y
3
− 2y
2
+ 36y + 81)
2
c
2
, c
5
, c
6
c
11
, c
12
(y
4
− 5y
3
+ 10y
2
− 12y + 9)
2
c
3
, c
4
, c
8
c
10
(y
4
+ 3y
3
+ 2y
2
+ 1)
2
c
7
, c
9
(y
4
− 5y
3
+ 6y
2
+ 4y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −1.070700 − 0.758745I
b = −0.134247 + 0.897284I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = −1.070700 − 0.758745I
b = −1.62889 − 0.24213I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = −1.070700 + 0.758745I
b = −0.134247 − 0.897284I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −1.070700 + 0.758745I
b = −1.62889 + 0.24213I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 0.070696 − 0.758745I
b = −0.95112 − 1.30886I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 0.070696 − 0.758745I
b = 2.21426 − 0.63406I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = 0.070696 + 0.758745I
b = −0.95112 + 1.30886I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.070696 + 0.758745I
b = 2.21426 + 0.63406I
−6.57974 − 2.02988I −8.00000 + 3.46410I
22
VI. I
u
6
= hu
3
− u
2
+ 2b − u − 1, u
3
− u
2
+ a − 1, u
4
+ 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
2
a
12
=
−u
3
+ u
2
+ 1
−
1
2
u
3
+
1
2
u
2
+
1
2
u +
1
2
a
1
=
−u
3
−
1
2
u
3
−
1
2
u
2
+
1
2
u +
1
2
a
6
=
u
3
1
2
u
3
+
1
2
u
2
−
1
2
u −
1
2
a
2
=
−u
3
−
1
2
u
3
−
1
2
u
2
+
3
2
u +
1
2
a
5
=
0
u
a
11
=
u
2
+ 1
u
2
a
10
=
u
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u − 1)
4
c
3
, c
4
, c
8
c
10
u
4
+ 1
c
5
, c
11
, c
12
(u + 1)
4
c
7
, c
9
(u
2
+ 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
8
c
10
(y
2
+ 1)
2
c
7
, c
9
(y + 1)
4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.70711 + 0.29289I
b = 1.207110 + 0.500000I
−1.64493 −8.00000
u = 0.707107 − 0.707107I
a = 1.70711 − 0.29289I
b = 1.207110 − 0.500000I
−1.64493 −8.00000
u = −0.707107 + 0.707107I
a = 0.29289 − 1.70711I
b = −0.207107 − 0.500000I
−1.64493 −8.00000
u = −0.707107 − 0.707107I
a = 0.29289 + 1.70711I
b = −0.207107 + 0.500000I
−1.64493 −8.00000
26
VII. I
u
7
= h2b − u − 1, a − u, u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
−1
a
4
=
u
0
a
7
=
0
−1
a
12
=
u
1
2
u +
1
2
a
1
=
u
3
2
u +
1
2
a
6
=
1
−
1
2
u −
1
2
a
2
=
u
1
2
u +
1
2
a
5
=
2
−u
a
11
=
2u
1
a
10
=
2u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
11
, c
12
u
2
+ 1
c
7
, c
9
(u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
11
, c
12
(y + 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.000000I
b = 0.500000 + 0.500000I
−1.64493 −8.00000
u = − 1.000000I
a = − 1.000000I
b = 0.500000 − 0.500000I
−1.64493 −8.00000
30
VIII. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
−1
0
a
9
=
1
0
a
8
=
1
0
a
4
=
−1
0
a
7
=
1
0
a
12
=
0
1
a
1
=
−1
1
a
6
=
1
−1
a
2
=
−2
1
a
5
=
−1
0
a
11
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
11
, c
12
u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y −1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
34
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u + 1)
2
(u
4
+ 5u
3
+ 10u
2
+ 12u + 9)
2
· (u
6
+ 7u
5
+ 9u
4
+ 33u
3
+ 299u
2
+ 434u + 121)
· (u
6
+ 11u
5
+ 43u
4
+ 66u
3
+ 27u
2
+ 11u + 1)
2
· (u
9
+ 9u
8
+ 34u
7
+ 67u
6
+ 110u
5
+ 195u
4
+ 74u
3
+ 13u
2
+ 5u + 4)
c
2
, c
6
(u − 1)
5
(u + 1)
4
(u
2
+ 1)(u
4
− u
3
− 2u
2
+ 3)
2
· (u
6
− u
5
− 5u
4
+ 4u
3
+ 5u
2
+ u − 1)
2
· (u
6
+ 3u
5
+ u
4
+ 5u
3
+ 19u
2
+ 4u − 11)
· (u
9
+ 3u
8
− 3u
6
+ 8u
5
+ 7u
4
− 8u
3
− u
2
− u + 2)
c
3
, c
4
, c
8
c
10
u(u
2
+ 1)(u
3
+ 2u + 1)
2
(u
4
+ 1)(u
4
+ u
2
+ 2)(u
4
− u
3
+ ··· − 2u + 1)
2
· (u
9
+ 3u
7
− 3u
6
+ 4u
5
− 7u
4
+ 2u
3
− 8u
2
+ 2u − 2)
· (u
12
+ 3u
11
+ ··· + 12u + 5)
c
5
, c
11
, c
12
(u − 1)
4
(u + 1)
5
(u
2
+ 1)(u
4
− u
3
− 2u
2
+ 3)
2
· (u
6
− u
5
− 5u
4
+ 4u
3
+ 5u
2
+ u − 1)
2
· (u
6
+ 3u
5
+ u
4
+ 5u
3
+ 19u
2
+ 4u − 11)
· (u
9
+ 3u
8
− 3u
6
+ 8u
5
+ 7u
4
− 8u
3
− u
2
− u + 2)
c
7
, c
9
u(u − 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
3
+ 4u
2
+ 4u − 1)
2
· (u
4
+ 3u
3
+ 2u
2
+ 1)
2
· (u
9
+ 6u
8
+ 17u
7
+ 19u
6
− 10u
5
− 69u
4
− 104u
3
− 84u
2
− 28u − 4)
· (u
12
+ 7u
11
+ ··· + 76u + 25)
35
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
11
(y
4
− 5y
3
− 2y
2
+ 36y + 81)
2
· (y
6
− 35y
5
+ 451y
4
− 2274y
3
− 637y
2
− 67y + 1)
2
· (y
6
− 31y
5
+ 217y
4
− 1541y
3
+ 62935y
2
− 115998y + 14641)
· (y
9
− 13y
8
+ ··· − 79y −16)
c
2
, c
5
, c
6
c
11
, c
12
(y −1)
9
(y + 1)
2
(y
4
− 5y
3
+ 10y
2
− 12y + 9)
2
· (y
6
− 11y
5
+ 43y
4
− 66y
3
+ 27y
2
− 11y + 1)
2
· (y
6
− 7y
5
+ 9y
4
− 33y
3
+ 299y
2
− 434y + 121)
· (y
9
− 9y
8
+ 34y
7
− 67y
6
+ 110y
5
− 195y
4
+ 74y
3
− 13y
2
+ 5y −4)
c
3
, c
4
, c
8
c
10
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
3
+ 4y
2
+ 4y −1)
2
· (y
4
+ 3y
3
+ 2y
2
+ 1)
2
· (y
9
+ 6y
8
+ 17y
7
+ 19y
6
− 10y
5
− 69y
4
− 104y
3
− 84y
2
− 28y −4)
· (y
12
+ 7y
11
+ ··· + 76y + 25)
c
7
, c
9
y(y −1)
2
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
3
− 8y
2
+ 24y −1)
2
· ((y
4
− 5y
3
+ 6y
2
+ 4y + 1)
2
)(y
9
− 2y
8
+ ··· + 112y −16)
· (y
12
− 5y
11
+ ··· + 4124y + 625)
36
