12n
0269
(K12n
0269
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 10 12 4 7 6 1 7
Solving Sequence
2,6
5 3 1
4,11
10 7 9 8 12
c
5
c
2
c
1
c
4
c
10
c
6
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6075798104u
29
− 20035573492u
28
+ ··· + 94573295142b − 102785752178,
52900187657u
29
− 66435815226u
28
+ ··· + 189146590284a − 100941534777,
u
30
− 2u
29
+ ··· − 11u + 4i
I
u
2
= h3u
18
a − 3u
18
+ ··· − a − 1, 2u
18
− 3u
17
+ ··· − 4a + 5, u
19
− u
18
+ ··· + 2u + 1i
I
u
3
= h−u
3
+ au − u
2
+ b + 1, −2u
3
a − 4u
2
a + u
3
+ a
2
− 4au − 2u
2
− 4u − 5, u
4
+ u
3
+ u
2
+ 1i
I
u
4
= hb − 1, 2a + 2u + 1, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 78 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
=
h6.08×10
9
u
29
−2.00×10
10
u
28
+· · ·+9.46×10
10
b−1.03×10
11
, 5.29×10
10
u
29
−
6.64 × 10
10
u
28
+ · · · + 1.89 × 10
11
a − 1.01 × 10
11
, u
30
− 2u
29
+ · · · − 11u + 4i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
4
=
u
2
+ 1
u
2
a
11
=
−0.279678u
29
+ 0.351240u
28
+ ··· − 2.48757u + 0.533668
−0.0642443u
29
+ 0.211852u
28
+ ··· − 0.962626u + 1.08684
a
10
=
−0.343923u
29
+ 0.563092u
28
+ ··· − 3.45020u + 1.62051
−0.0642443u
29
+ 0.211852u
28
+ ··· − 0.962626u + 1.08684
a
7
=
−0.293504u
29
+ 0.578779u
28
+ ··· − 3.77569u + 2.01661
−0.0196924u
29
+ 0.238501u
28
+ ··· − 1.68736u + 1.14206
a
9
=
−0.642162u
29
+ 1.14610u
28
+ ··· − 7.29055u + 2.93572
−0.0853310u
29
+ 0.458919u
28
+ ··· − 2.98810u + 2.09785
a
8
=
−0.565573u
29
+ 1.10421u
28
+ ··· − 7.29137u + 2.70821
−0.0269374u
29
+ 0.494525u
28
+ ··· − 3.51309u + 2.26229
a
12
=
−0.298240u
29
+ 0.583012u
28
+ ··· − 3.84035u + 1.31521
−0.0210866u
29
+ 0.247066u
28
+ ··· − 1.02547u + 1.01102
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
13126781461
15762215857
u
29
−
346887419065
189146590284
u
28
+ ··· +
2455780116659
189146590284
u −
364257663059
47286647571
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
30
+ 10u
29
+ ··· − u + 16
c
2
, c
5
u
30
+ 2u
29
+ ··· + 11u + 4
c
3
, c
8
u
30
− 3u
29
+ ··· + 24u + 32
c
6
, c
7
, c
9
c
10
, c
12
u
30
+ 2u
29
+ ··· − u + 1
c
11
u
30
− 8u
29
+ ··· − 15u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
+ 22y
29
+ ··· + 3743y + 256
c
2
, c
5
y
30
+ 10y
29
+ ··· − y + 16
c
3
, c
8
y
30
− 15y
29
+ ··· − 6336y + 1024
c
6
, c
7
, c
9
c
10
, c
12
y
30
+ 8y
29
+ ··· + 15y + 1
c
11
y
30
+ 24y
29
+ ··· + 19y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460643 + 0.958497I
a = 1.032200 − 0.246838I
b = −0.299080 − 0.268098I
−0.32179 − 2.57657I 1.59153 + 5.16266I
u = −0.460643 − 0.958497I
a = 1.032200 + 0.246838I
b = −0.299080 + 0.268098I
−0.32179 + 2.57657I 1.59153 − 5.16266I
u = 0.117766 + 1.065450I
a = −2.08067 + 0.32615I
b = 0.868345 − 0.853291I
−5.22441 + 3.04204I −6.16892 − 2.76702I
u = 0.117766 − 1.065450I
a = −2.08067 − 0.32615I
b = 0.868345 + 0.853291I
−5.22441 − 3.04204I −6.16892 + 2.76702I
u = 0.892544 + 0.608188I
a = 0.357885 − 0.459993I
b = −0.660894 − 1.208280I
3.48880 − 10.37700I 3.38979 + 5.72342I
u = 0.892544 − 0.608188I
a = 0.357885 + 0.459993I
b = −0.660894 + 1.208280I
3.48880 + 10.37700I 3.38979 − 5.72342I
u = −0.835530 + 0.693005I
a = −0.118947 − 0.761630I
b = 0.596590 − 0.966034I
1.29700 + 3.10575I 1.45147 − 3.18731I
u = −0.835530 − 0.693005I
a = −0.118947 + 0.761630I
b = 0.596590 + 0.966034I
1.29700 − 3.10575I 1.45147 + 3.18731I
u = 0.513340 + 0.739634I
a = −1.14053 − 0.97145I
b = 1.145550 − 0.289264I
−1.57253 + 1.48061I 1.51311 + 5.82808I
u = 0.513340 − 0.739634I
a = −1.14053 + 0.97145I
b = 1.145550 + 0.289264I
−1.57253 − 1.48061I 1.51311 − 5.82808I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850935 + 0.293187I
a = 0.444169 − 0.489109I
b = −0.601963 − 1.009720I
1.66857 − 6.29086I 3.10303 + 6.83080I
u = −0.850935 − 0.293187I
a = 0.444169 + 0.489109I
b = −0.601963 + 1.009720I
1.66857 + 6.29086I 3.10303 − 6.83080I
u = 0.590492 + 0.982207I
a = −0.644113 − 1.170090I
b = 1.149850 + 0.591978I
−2.48088 + 3.02207I −2.21456 − 6.76782I
u = 0.590492 − 0.982207I
a = −0.644113 + 1.170090I
b = 1.149850 − 0.591978I
−2.48088 − 3.02207I −2.21456 + 6.76782I
u = −0.120227 + 1.185320I
a = 1.71764 + 0.85667I
b = −0.727551 − 1.085270I
−3.53890 − 9.16679I −2.72882 + 7.28806I
u = −0.120227 − 1.185320I
a = 1.71764 − 0.85667I
b = −0.727551 + 1.085270I
−3.53890 + 9.16679I −2.72882 − 7.28806I
u = −0.537667 + 0.602506I
a = 0.295236 + 0.519101I
b = 0.023047 + 0.423163I
0.81059 − 1.39109I 1.55512 + 4.14990I
u = −0.537667 − 0.602506I
a = 0.295236 − 0.519101I
b = 0.023047 − 0.423163I
0.81059 + 1.39109I 1.55512 − 4.14990I
u = −0.530973 + 1.119350I
a = 0.144119 − 0.924498I
b = −0.645054 + 0.883761I
−0.91910 + 1.29166I −0.69831 − 3.06877I
u = −0.530973 − 1.119350I
a = 0.144119 + 0.924498I
b = −0.645054 − 0.883761I
−0.91910 − 1.29166I −0.69831 + 3.06877I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.730890 + 1.026770I
a = −1.64352 + 1.06510I
b = 0.646060 + 1.041760I
0.26873 − 8.97735I 0.28174 + 7.42318I
u = −0.730890 − 1.026770I
a = −1.64352 − 1.06510I
b = 0.646060 − 1.041760I
0.26873 + 8.97735I 0.28174 − 7.42318I
u = 0.896688 + 0.897515I
a = 0.544249 + 0.743729I
b = −0.269532 + 0.876061I
9.52166 + 4.35690I 1.93733 − 9.19475I
u = 0.896688 − 0.897515I
a = 0.544249 − 0.743729I
b = −0.269532 − 0.876061I
9.52166 − 4.35690I 1.93733 + 9.19475I
u = 0.875554 + 0.943207I
a = −0.406635 − 0.439577I
b = −0.231064 − 0.841743I
9.37686 + 2.17701I 0.69666 + 4.17919I
u = 0.875554 − 0.943207I
a = −0.406635 + 0.439577I
b = −0.231064 + 0.841743I
9.37686 − 2.17701I 0.69666 − 4.17919I
u = 0.719689 + 1.077380I
a = 2.03341 + 0.65165I
b = −0.70309 + 1.23931I
2.0453 + 16.3438I 1.41001 − 9.88978I
u = 0.719689 − 1.077380I
a = 2.03341 − 0.65165I
b = −0.70309 − 1.23931I
2.0453 − 16.3438I 1.41001 + 9.88978I
u = 0.460792 + 0.211623I
a = −0.159496 − 1.172690I
b = 0.708800 − 0.487048I
−1.26041 + 1.13919I −3.24420 − 2.21188I
u = 0.460792 − 0.211623I
a = −0.159496 + 1.172690I
b = 0.708800 + 0.487048I
−1.26041 − 1.13919I −3.24420 + 2.21188I
7
II.
I
u
2
= h3u
18
a−3u
18
+· · ·−a−1, 2u
18
−3u
17
+· · ·−4a+5, u
19
−u
18
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
4
=
u
2
+ 1
u
2
a
11
=
a
−
3
2
u
18
a +
3
2
u
18
+ ··· +
1
2
a +
1
2
a
10
=
−
3
2
u
18
a +
3
2
u
18
+ ··· +
3
2
a +
1
2
−
3
2
u
18
a +
3
2
u
18
+ ··· +
1
2
a +
1
2
a
7
=
2u
17
a − u
17
+ ··· − a + 4
3
2
u
18
a −
3
2
u
18
+ ··· −
1
2
a −
1
2
a
9
=
−u
13
− 2u
11
− 3u
9
− 2u
7
+ u
−u
15
− 3u
13
− 6u
11
− 7u
9
− 6u
7
− 4u
5
− 2u
3
− u
a
8
=
u
18
+ 3u
16
+ 6u
14
+ 7u
12
+ 5u
10
+ 3u
8
− u
2
− 1
u
18
− u
17
+ ··· − 3u − 1
a
12
=
−
1
2
u
18
a +
3
2
u
18
+ ··· +
1
2
a −
1
2
−2u
18
a + 3u
18
+ ··· + au − 4u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
+ 4u
16
−12u
15
+ 12u
14
−28u
13
+ 24u
12
−36u
11
+ 32u
10
−
36u
9
+ 28u
8
− 28u
7
+ 28u
6
− 12u
5
+ 16u
4
− 12u
3
+ 12u
2
+ 4u + 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
19
+ 7u
18
+ ··· + 2u − 1)
2
c
2
, c
5
(u
19
+ u
18
+ ··· + 2u − 1)
2
c
3
, c
8
(u
19
+ u
18
+ ··· − u
2
+ 1)
2
c
6
, c
7
, c
9
c
10
, c
12
u
38
− 5u
37
+ ··· − 173u + 34
c
11
u
38
− 19u
37
+ ··· − 13387u + 1156
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
19
+ 11y
18
+ ··· + 42y −1)
2
c
2
, c
5
(y
19
+ 7y
18
+ ··· + 2y −1)
2
c
3
, c
8
(y
19
− 5y
18
+ ··· + 2y −1)
2
c
6
, c
7
, c
9
c
10
, c
12
y
38
+ 19y
37
+ ··· + 13387y + 1156
c
11
y
38
− y
37
+ ··· + 7530783y + 1336336
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.787239 + 0.559366I
a = 0.516479 + 0.470519I
b = −0.991761 + 0.337645I
0.85217 − 4.39903I 0.93348 + 2.80289I
u = 0.787239 + 0.559366I
a = −0.195675 + 0.232139I
b = 0.689098 + 1.130990I
0.85217 − 4.39903I 0.93348 + 2.80289I
u = 0.787239 − 0.559366I
a = 0.516479 − 0.470519I
b = −0.991761 − 0.337645I
0.85217 + 4.39903I 0.93348 − 2.80289I
u = 0.787239 − 0.559366I
a = −0.195675 − 0.232139I
b = 0.689098 − 1.130990I
0.85217 + 4.39903I 0.93348 − 2.80289I
u = 0.709462 + 0.766103I
a = 0.585393 + 0.482577I
b = −0.678167 − 0.996758I
6.91199 − 0.16816I 6.16829 + 0.91431I
u = 0.709462 + 0.766103I
a = 1.214050 + 0.700043I
b = −0.19863 + 1.44121I
6.91199 − 0.16816I 6.16829 + 0.91431I
u = 0.709462 − 0.766103I
a = 0.585393 − 0.482577I
b = −0.678167 + 0.996758I
6.91199 + 0.16816I 6.16829 − 0.91431I
u = 0.709462 − 0.766103I
a = 1.214050 − 0.700043I
b = −0.19863 − 1.44121I
6.91199 + 0.16816I 6.16829 − 0.91431I
u = −0.588600 + 0.865037I
a = −0.49489 − 2.57683I
b = 0.138356 − 1.097670I
3.75823 − 2.32534I −1.72826 + 3.09456I
u = −0.588600 + 0.865037I
a = −3.97835 + 1.04025I
b = 0.197824 + 0.975432I
3.75823 − 2.32534I −1.72826 + 3.09456I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588600 − 0.865037I
a = −0.49489 + 2.57683I
b = 0.138356 + 1.097670I
3.75823 + 2.32534I −1.72826 − 3.09456I
u = −0.588600 − 0.865037I
a = −3.97835 − 1.04025I
b = 0.197824 − 0.975432I
3.75823 + 2.32534I −1.72826 − 3.09456I
u = −0.745489 + 0.500016I
a = 0.352472 + 0.544649I
b = −0.564915 + 0.608349I
0.45606 − 1.53005I 0.20605 + 2.54963I
u = −0.745489 + 0.500016I
a = −0.147251 + 0.364183I
b = 0.536858 + 0.708989I
0.45606 − 1.53005I 0.20605 + 2.54963I
u = −0.745489 − 0.500016I
a = 0.352472 − 0.544649I
b = −0.564915 − 0.608349I
0.45606 + 1.53005I 0.20605 − 2.54963I
u = −0.745489 − 0.500016I
a = −0.147251 − 0.364183I
b = 0.536858 − 0.708989I
0.45606 + 1.53005I 0.20605 − 2.54963I
u = −0.021471 + 1.128170I
a = −1.52252 − 1.09613I
b = 0.800008 + 0.907616I
−5.01775 − 3.11880I −5.58624 + 2.69239I
u = −0.021471 + 1.128170I
a = 1.81596 − 0.53999I
b = −0.913287 + 0.607157I
−5.01775 − 3.11880I −5.58624 + 2.69239I
u = −0.021471 − 1.128170I
a = −1.52252 + 1.09613I
b = 0.800008 − 0.907616I
−5.01775 + 3.11880I −5.58624 − 2.69239I
u = −0.021471 − 1.128170I
a = 1.81596 + 0.53999I
b = −0.913287 − 0.607157I
−5.01775 + 3.11880I −5.58624 − 2.69239I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167515 + 0.839557I
a = 0.857565 − 0.800159I
b = −0.003570 + 1.177280I
1.87881 − 1.72326I −3.81965 + 5.18112I
u = −0.167515 + 0.839557I
a = 0.78439 + 2.81455I
b = −0.197548 − 0.604455I
1.87881 − 1.72326I −3.81965 + 5.18112I
u = −0.167515 − 0.839557I
a = 0.857565 + 0.800159I
b = −0.003570 − 1.177280I
1.87881 + 1.72326I −3.81965 − 5.18112I
u = −0.167515 − 0.839557I
a = 0.78439 − 2.81455I
b = −0.197548 + 0.604455I
1.87881 + 1.72326I −3.81965 − 5.18112I
u = 0.687512 + 0.928828I
a = −0.992722 − 0.197204I
b = −0.09297 − 1.48296I
6.41945 + 5.52702I 4.42794 − 7.00248I
u = 0.687512 + 0.928828I
a = 1.93781 + 0.22445I
b = −0.765375 + 0.868851I
6.41945 + 5.52702I 4.42794 − 7.00248I
u = 0.687512 − 0.928828I
a = −0.992722 + 0.197204I
b = −0.09297 + 1.48296I
6.41945 − 5.52702I 4.42794 + 7.00248I
u = 0.687512 − 0.928828I
a = 1.93781 − 0.22445I
b = −0.765375 − 0.868851I
6.41945 − 5.52702I 4.42794 + 7.00248I
u = −0.636878 + 1.050560I
a = −0.005727 + 0.813937I
b = 0.717895 − 0.570311I
−1.12421 − 3.71612I −2.19900 + 2.45937I
u = −0.636878 + 1.050560I
a = 1.69165 − 0.73976I
b = −0.636967 − 0.819328I
−1.12421 − 3.71612I −2.19900 + 2.45937I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636878 − 1.050560I
a = −0.005727 − 0.813937I
b = 0.717895 + 0.570311I
−1.12421 + 3.71612I −2.19900 − 2.45937I
u = −0.636878 − 1.050560I
a = 1.69165 + 0.73976I
b = −0.636967 + 0.819328I
−1.12421 + 3.71612I −2.19900 − 2.45937I
u = 0.666721 + 1.052350I
a = 0.652896 + 1.081010I
b = −1.105990 − 0.392926I
−0.60648 + 9.88550I −1.13872 − 7.31129I
u = 0.666721 + 1.052350I
a = −2.00964 − 0.51551I
b = 0.792055 − 1.166900I
−0.60648 + 9.88550I −1.13872 − 7.31129I
u = 0.666721 − 1.052350I
a = 0.652896 − 1.081010I
b = −1.105990 + 0.392926I
−0.60648 − 9.88550I −1.13872 + 7.31129I
u = 0.666721 − 1.052350I
a = −2.00964 + 0.51551I
b = 0.792055 + 1.166900I
−0.60648 − 9.88550I −1.13872 + 7.31129I
u = −0.381963
a = 2.43810 + 0.93795I
b = −0.222910 − 1.071950I
4.19724 7.47220
u = −0.381963
a = 2.43810 − 0.93795I
b = −0.222910 + 1.071950I
4.19724 7.47220
14
III. I
u
3
= h−u
3
+ au − u
2
+ b + 1, −2u
3
a + u
3
+ · · · + a
2
− 5, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
3
+ u
2
+ 1
a
4
=
u
2
+ 1
u
2
a
11
=
a
u
3
− au + u
2
− 1
a
10
=
u
3
− au + u
2
+ a − 1
u
3
− au + u
2
− 1
a
7
=
−u
3
a − u
2
a − 3u
3
− 5u
2
+ a − 5u − 1
−1
a
9
=
u
3
− au + u
2
− 1
0
a
8
=
−u
3
a − u
2
a − a − 1
−u
2
a + au − a + u
a
12
=
u
3
+ a
2u
3
− au + 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
2
(u
4
− u
3
+ u
2
+ 1)
2
c
3
, c
8
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
c
5
(u
4
+ u
3
+ u
2
+ 1)
2
c
6
, c
7
, c
9
c
10
, c
12
(u
2
+ 1)
4
c
11
(u + 1)
8
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
8
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
c
6
, c
7
, c
9
c
10
, c
12
(y + 1)
8
c
11
(y −1)
8
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −1.71161 + 1.80064I
b = 1.000000I
3.07886 + 1.41510I 4.17326 − 4.90874I
u = 0.351808 + 0.720342I
a = 0.53013 + 2.89548I
b = − 1.000000I
3.07886 + 1.41510I 4.17326 − 4.90874I
u = 0.351808 − 0.720342I
a = −1.71161 − 1.80064I
b = − 1.000000I
3.07886 − 1.41510I 4.17326 + 4.90874I
u = 0.351808 − 0.720342I
a = 0.53013 − 2.89548I
b = 1.000000I
3.07886 − 1.41510I 4.17326 + 4.90874I
u = −0.851808 + 0.911292I
a = −0.994913 + 0.491876I
b = 1.000000I
10.08060 − 3.16396I 7.82674 + 2.56480I
u = −0.851808 + 0.911292I
a = 0.176391 − 0.602971I
b = − 1.000000I
10.08060 − 3.16396I 7.82674 + 2.56480I
u = −0.851808 − 0.911292I
a = −0.994913 − 0.491876I
b = − 1.000000I
10.08060 + 3.16396I 7.82674 − 2.56480I
u = −0.851808 − 0.911292I
a = 0.176391 + 0.602971I
b = 1.000000I
10.08060 + 3.16396I 7.82674 − 2.56480I
18
IV. I
u
4
= hb − 1, 2a + 2u + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
4
=
u
u − 1
a
11
=
−u −
1
2
1
a
10
=
−u +
1
2
1
a
7
=
−u +
3
2
1
a
9
=
−2u + 2
2
a
8
=
−2u + 2
2
a
12
=
−u +
1
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
31
4
u + 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
8
u
2
c
6
, c
7
, c
11
(u − 1)
2
c
9
, c
10
, c
12
(u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
8
y
2
c
6
, c
7
, c
9
c
10
, c
11
, c
12
(y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.000000 − 0.866025I
b = 1.00000
−1.64493 + 2.02988I −1.87500 − 6.71170I
u = 0.500000 − 0.866025I
a = −1.000000 + 0.866025I
b = 1.00000
−1.64493 − 2.02988I −1.87500 + 6.71170I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
19
+ 7u
18
+ ··· + 2u − 1)
2
· (u
30
+ 10u
29
+ ··· − u + 16)
c
2
(u
2
+ u + 1)(u
4
− u
3
+ u
2
+ 1)
2
(u
19
+ u
18
+ ··· + 2u − 1)
2
· (u
30
+ 2u
29
+ ··· + 11u + 4)
c
3
, c
8
u
2
(u
8
− 5u
6
+ ··· − 2u
2
+ 1)(u
19
+ u
18
+ ··· − u
2
+ 1)
2
· (u
30
− 3u
29
+ ··· + 24u + 32)
c
5
(u
2
− u + 1)(u
4
+ u
3
+ u
2
+ 1)
2
(u
19
+ u
18
+ ··· + 2u − 1)
2
· (u
30
+ 2u
29
+ ··· + 11u + 4)
c
6
, c
7
((u − 1)
2
)(u
2
+ 1)
4
(u
30
+ 2u
29
+ ··· − u + 1)
· (u
38
− 5u
37
+ ··· − 173u + 34)
c
9
, c
10
, c
12
((u + 1)
2
)(u
2
+ 1)
4
(u
30
+ 2u
29
+ ··· − u + 1)
· (u
38
− 5u
37
+ ··· − 173u + 34)
c
11
((u − 1)
2
)(u + 1)
8
(u
30
− 8u
29
+ ··· − 15u + 1)
· (u
38
− 19u
37
+ ··· − 13387u + 1156)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
4
+ 5y
3
+ ··· + 2y + 1)
2
(y
19
+ 11y
18
+ ··· + 42y −1)
2
· (y
30
+ 22y
29
+ ··· + 3743y + 256)
c
2
, c
5
(y
2
+ y + 1)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
19
+ 7y
18
+ ··· + 2y −1)
2
· (y
30
+ 10y
29
+ ··· − y + 16)
c
3
, c
8
y
2
(y
4
− 5y
3
+ ··· − 2y + 1)
2
(y
19
− 5y
18
+ ··· + 2y −1)
2
· (y
30
− 15y
29
+ ··· − 6336y + 1024)
c
6
, c
7
, c
9
c
10
, c
12
((y −1)
2
)(y + 1)
8
(y
30
+ 8y
29
+ ··· + 15y + 1)
· (y
38
+ 19y
37
+ ··· + 13387y + 1156)
c
11
((y −1)
10
)(y
30
+ 24y
29
+ ··· + 19y + 1)
· (y
38
− y
37
+ ··· + 7530783y + 1336336)
24
