11a
148
(K11a
148
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 2 5 11 3 7 4 9
Solving Sequence
2,6
1 3 5
7,9
10 4 8 11
c
1
c
2
c
5
c
6
c
9
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h35u
24
+ 168u
23
+ ··· + 2b − 32, −27u
24
− 155u
23
+ ··· + 2a + 101, u
25
+ 6u
24
+ ··· + 2u − 4i
I
u
2
= h2016599941u
10
a
3
− 15792956111u
10
a
2
+ ··· + 42968527616a + 47798397673,
2u
10
a
3
+ 5u
10
a
2
+ ··· − 11a − 4, u
11
− u
10
+ 2u
9
− u
8
+ 4u
7
− 2u
6
+ 4u
5
− u
4
+ 3u
3
+ u
2
+ 1i
I
u
3
= h−u
11
+ u
10
− 3u
9
+ u
8
− 6u
7
+ 2u
6
− 9u
5
+ 2u
4
− 7u
3
+ b − 4u,
u
11
− 2u
10
+ 4u
9
− 4u
8
+ 7u
7
− 8u
6
+ 11u
5
− 11u
4
+ 9u
3
− 7u
2
+ a + 4u − 4,
u
12
− u
11
+ 3u
10
− 2u
9
+ 6u
8
− 4u
7
+ 9u
6
− 5u
5
+ 8u
4
− 3u
3
+ 5u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 81 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
= h35u
24
+ 168u
23
+ · · · + 2b − 32, −27u
24
− 155u
23
+ · · · + 2a +
101, u
25
+ 6u
24
+ · · · + 2u − 4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
9
=
27
2
u
24
+
155
2
u
23
+ ··· + 39u −
101
2
−
35
2
u
24
− 84u
23
+ ··· +
53
2
u + 16
a
10
=
7
2
u
24
+
37
2
u
23
+ ··· + 7u −
21
2
−
9
2
u
24
− 17u
23
+ ··· +
39
2
u − 6
a
4
=
−
3
4
u
24
− u
23
+ ··· +
17
4
u − 2
−
5
2
u
24
− 16u
23
+ ··· −
21
2
u + 11
a
8
=
−u
24
−
7
2
u
23
+ ··· +
3
2
u −
5
2
3
2
u
24
+ 6u
23
+ ··· +
17
2
u − 4
a
11
=
−
17
4
u
24
− 24u
23
+ ··· −
37
4
u + 16
9
2
u
24
+ 21u
23
+ ··· −
27
2
u − 1
a
11
=
−
17
4
u
24
− 24u
23
+ ··· −
37
4
u + 16
9
2
u
24
+ 21u
23
+ ··· −
27
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −15u
24
− 91u
23
− 314u
22
− 764u
21
− 1477u
20
− 2371u
19
− 3183u
18
− 3544u
17
−
3125u
16
− 1943u
15
− 107u
14
+ 1758u
13
+ 3237u
12
+ 3576u
11
+ 3208u
10
+ 1906u
9
+
604u
8
− 914u
7
− 1457u
6
− 1716u
5
− 1155u
4
− 780u
3
− 197u
2
− 64u + 58
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
25
− 6u
24
+ ··· + 2u + 4
c
2
, c
6
u
25
+ 8u
24
+ ··· + 92u − 16
c
3
, c
4
, c
8
c
10
u
25
+ 11u
23
+ ··· + u + 1
c
7
u
25
+ 25u
24
+ ··· + 22528u + 2048
c
9
, c
11
u
25
+ 2u
24
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
25
+ 8y
24
+ ··· + 92y −16
c
2
, c
6
y
25
+ 20y
24
+ ··· + 34416y −256
c
3
, c
4
, c
8
c
10
y
25
+ 22y
24
+ ··· − y −1
c
7
y
25
+ 5y
24
+ ··· − 6291456y −4194304
c
9
, c
11
y
25
+ 10y
24
+ ··· + y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547785 + 0.829347I
a = −0.132188 + 1.028140I
b = 0.342369 − 0.476494I
−1.27014 + 2.16528I −1.04869 − 7.02425I
u = 0.547785 − 0.829347I
a = −0.132188 − 1.028140I
b = 0.342369 + 0.476494I
−1.27014 − 2.16528I −1.04869 + 7.02425I
u = 0.909758 + 0.111933I
a = 0.448280 + 0.761789I
b = −0.191053 − 0.377973I
7.60221 − 5.64749I 1.55411 + 4.80712I
u = 0.909758 − 0.111933I
a = 0.448280 − 0.761789I
b = −0.191053 + 0.377973I
7.60221 + 5.64749I 1.55411 − 4.80712I
u = 0.172465 + 0.850743I
a = 1.05588 + 0.98070I
b = −0.068333 − 0.860826I
−2.99666 + 1.65679I −15.0147 − 0.6856I
u = 0.172465 − 0.850743I
a = 1.05588 − 0.98070I
b = −0.068333 + 0.860826I
−2.99666 − 1.65679I −15.0147 + 0.6856I
u = −0.772738 + 0.848455I
a = −1.04991 + 1.28098I
b = 2.14935 + 0.25094I
2.58604 − 0.70386I −5.85928 − 0.49941I
u = −0.772738 − 0.848455I
a = −1.04991 − 1.28098I
b = 2.14935 − 0.25094I
2.58604 + 0.70386I −5.85928 + 0.49941I
u = −0.261992 + 0.786193I
a = −0.562785 − 0.125344I
b = 0.120830 + 0.426313I
−0.450467 − 1.265120I −5.40648 + 4.55979I
u = −0.261992 − 0.786193I
a = −0.562785 + 0.125344I
b = 0.120830 − 0.426313I
−0.450467 + 1.265120I −5.40648 − 4.55979I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387681 + 1.123210I
a = −0.918133 − 0.226616I
b = 0.438533 + 0.451507I
4.17221 + 10.11180I −4.52201 − 8.50269I
u = 0.387681 − 1.123210I
a = −0.918133 + 0.226616I
b = 0.438533 − 0.451507I
4.17221 − 10.11180I −4.52201 + 8.50269I
u = −0.764005 + 0.915174I
a = 0.34371 − 1.87642I
b = −2.17540 + 1.02852I
2.38356 − 5.10130I −6.46922 + 5.59973I
u = −0.764005 − 0.915174I
a = 0.34371 + 1.87642I
b = −2.17540 − 1.02852I
2.38356 + 5.10130I −6.46922 − 5.59973I
u = −0.928755 + 0.776951I
a = 0.99963 − 1.17470I
b = −2.38197 − 0.23867I
13.0505 + 9.3478I −0.12461 − 3.78791I
u = −0.928755 − 0.776951I
a = 0.99963 + 1.17470I
b = −2.38197 + 0.23867I
13.0505 − 9.3478I −0.12461 + 3.78791I
u = −0.993283 + 0.737833I
a = −0.375273 + 0.709529I
b = 1.332200 − 0.192203I
11.57130 − 0.60521I 2.81259 + 0.07964I
u = −0.993283 − 0.737833I
a = −0.375273 − 0.709529I
b = 1.332200 + 0.192203I
11.57130 + 0.60521I 2.81259 − 0.07964I
u = 0.205874 + 1.279220I
a = 0.297105 − 0.434123I
b = −0.360870 + 0.141760I
2.70932 − 1.76563I 1.67735 + 6.00861I
u = 0.205874 − 1.279220I
a = 0.297105 + 0.434123I
b = −0.360870 − 0.141760I
2.70932 + 1.76563I 1.67735 − 6.00861I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.815577 + 1.026240I
a = −0.83474 + 1.97424I
b = 2.55672 − 0.85139I
12.2597 − 15.7728I −1.36713 + 8.34320I
u = −0.815577 − 1.026240I
a = −0.83474 − 1.97424I
b = 2.55672 + 0.85139I
12.2597 + 15.7728I −1.36713 − 8.34320I
u = −0.834263 + 1.074420I
a = 0.617688 − 1.026740I
b = −1.46448 + 0.32121I
10.51100 − 6.06025I 0.84273 + 5.20676I
u = −0.834263 − 1.074420I
a = 0.617688 + 1.026740I
b = −1.46448 − 0.32121I
10.51100 + 6.06025I 0.84273 − 5.20676I
u = 0.294100
a = −1.77854
b = 0.404195
−0.887194 −11.1490
7
II. I
u
2
= h2.02 × 10
9
a
3
u
10
− 1.58 × 10
10
a
2
u
10
+ · · · + 4.30 × 10
10
a + 4.78 ×
10
10
, 2u
10
a
3
+ 5u
10
a
2
+ · · · − 11a − 4, u
11
− u
10
+ · · · + u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
9
=
a
−0.0501087a
3
u
10
+ 0.392425a
2
u
10
+ ··· − 1.06769a − 1.18770
a
10
=
0.0730076a
3
u
10
+ 0.0208690a
2
u
10
+ ··· + 1.15943a − 0.436827
−0.0458109a
3
u
10
+ 0.201699a
2
u
10
+ ··· − 1.42746a − 1.14085
a
4
=
−0.101413a
3
u
10
+ 0.463802a
2
u
10
+ ··· − 0.220601a − 0.144396
−0.00665696a
3
u
10
− 0.286527a
2
u
10
+ ··· − 0.381572a − 2.85287
a
8
=
0.0552205a
3
u
10
+ 0.0271607a
2
u
10
+ ··· + 0.272604a − 0.228788
−0.0458109a
3
u
10
+ 0.201699a
2
u
10
+ ··· − 1.42746a − 1.14085
a
11
=
−0.113164a
3
u
10
+ 0.205988a
2
u
10
+ ··· − 0.610611a + 0.745692
0.204647a
3
u
10
+ 0.121534a
2
u
10
+ ··· − 0.319396a + 1.27947
a
11
=
−0.113164a
3
u
10
+ 0.205988a
2
u
10
+ ··· − 0.610611a + 0.745692
0.204647a
3
u
10
+ 0.121534a
2
u
10
+ ··· − 0.319396a + 1.27947
(ii) Obstruction class = −1
(iii) Cusp Shapes =
601490176
3658590779
u
10
a
3
+
5167626756
3658590779
u
10
a
2
+ ···−
9844699240
3658590779
a −
14836404290
3658590779
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
4
c
2
, c
6
(u
11
+ 3u
10
+ ··· − 2u − 1)
4
c
3
, c
4
, c
8
c
10
u
44
+ u
43
+ ··· − 10u + 1
c
7
(u
2
− u + 1)
22
c
9
, c
11
u
44
− 13u
43
+ ··· − 7082u + 793
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
11
+ 3y
10
+ ··· − 2y −1)
4
c
2
, c
6
(y
11
+ 11y
10
+ ··· + 6y −1)
4
c
3
, c
4
, c
8
c
10
y
44
+ 39y
43
+ ··· − 72y + 1
c
7
(y
2
+ y + 1)
22
c
9
, c
11
y
44
+ 19y
43
+ ··· + 14956920y + 628849
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274458 + 0.988557I
a = −0.761443 − 0.782702I
b = 0.437204 + 0.625252I
−0.246814 − 0.916836I −7.79937 + 0.65377I
u = −0.274458 + 0.988557I
a = 1.150000 + 0.163504I
b = −0.078138 + 0.311249I
−0.24681 − 4.97660I −7.79937 + 7.58197I
u = −0.274458 + 0.988557I
a = −1.07620 + 0.93707I
b = 0.763501 − 0.929299I
−0.24681 − 4.97660I −7.79937 + 7.58197I
u = −0.274458 + 0.988557I
a = −0.228586 + 0.296333I
b = −0.244639 + 0.277316I
−0.246814 − 0.916836I −7.79937 + 0.65377I
u = −0.274458 − 0.988557I
a = −0.761443 + 0.782702I
b = 0.437204 − 0.625252I
−0.246814 + 0.916836I −7.79937 − 0.65377I
u = −0.274458 − 0.988557I
a = 1.150000 − 0.163504I
b = −0.078138 − 0.311249I
−0.24681 + 4.97660I −7.79937 − 7.58197I
u = −0.274458 − 0.988557I
a = −1.07620 − 0.93707I
b = 0.763501 + 0.929299I
−0.24681 + 4.97660I −7.79937 − 7.58197I
u = −0.274458 − 0.988557I
a = −0.228586 − 0.296333I
b = −0.244639 − 0.277316I
−0.246814 + 0.916836I −7.79937 − 0.65377I
u = 0.838197 + 0.796762I
a = 0.259768 + 0.864513I
b = −1.65309 − 0.61568I
6.91185 + 0.61290I −1.20869 − 2.83037I
u = 0.838197 + 0.796762I
a = 0.03670 − 1.50054I
b = 1.36614 + 0.90157I
6.91185 + 0.61290I −1.20869 − 2.83037I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838197 + 0.796762I
a = 0.69454 + 1.55821I
b = −2.43426 + 0.15762I
6.91185 − 3.44687I −1.20869 + 4.09783I
u = 0.838197 + 0.796762I
a = −1.39359 − 1.49694I
b = 2.82533 − 0.05206I
6.91185 − 3.44687I −1.20869 + 4.09783I
u = 0.838197 − 0.796762I
a = 0.259768 − 0.864513I
b = −1.65309 + 0.61568I
6.91185 − 0.61290I −1.20869 + 2.83037I
u = 0.838197 − 0.796762I
a = 0.03670 + 1.50054I
b = 1.36614 − 0.90157I
6.91185 − 0.61290I −1.20869 + 2.83037I
u = 0.838197 − 0.796762I
a = 0.69454 − 1.55821I
b = −2.43426 − 0.15762I
6.91185 + 3.44687I −1.20869 − 4.09783I
u = 0.838197 − 0.796762I
a = −1.39359 + 1.49694I
b = 2.82533 + 0.05206I
6.91185 + 3.44687I −1.20869 − 4.09783I
u = −0.813506 + 0.895281I
a = −0.053255 + 1.073330I
b = 2.14570 − 1.02655I
10.57740 − 1.01164I 2.06121 − 0.64168I
u = −0.813506 + 0.895281I
a = 1.18879 − 1.57660I
b = −1.85365 − 0.68950I
10.57740 − 5.07141I 2.06121 + 6.28652I
u = −0.813506 + 0.895281I
a = 1.96101 − 0.26916I
b = −2.56967 − 1.24825I
10.57740 − 5.07141I 2.06121 + 6.28652I
u = −0.813506 + 0.895281I
a = 0.07683 + 2.57735I
b = 1.74410 − 1.83528I
10.57740 − 1.01164I 2.06121 − 0.64168I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.813506 − 0.895281I
a = −0.053255 − 1.073330I
b = 2.14570 + 1.02655I
10.57740 + 1.01164I 2.06121 + 0.64168I
u = −0.813506 − 0.895281I
a = 1.18879 + 1.57660I
b = −1.85365 + 0.68950I
10.57740 + 5.07141I 2.06121 − 6.28652I
u = −0.813506 − 0.895281I
a = 1.96101 + 0.26916I
b = −2.56967 + 1.24825I
10.57740 + 5.07141I 2.06121 − 6.28652I
u = −0.813506 − 0.895281I
a = 0.07683 − 2.57735I
b = 1.74410 + 1.83528I
10.57740 + 1.01164I 2.06121 + 0.64168I
u = 0.783273 + 0.973706I
a = 1.036200 + 0.662931I
b = −1.80909 + 0.34245I
6.36658 + 5.44535I −2.22908 − 2.09050I
u = 0.783273 + 0.973706I
a = −0.89046 − 1.26486I
b = 1.58433 − 0.03492I
6.36658 + 5.44535I −2.22908 − 2.09050I
u = 0.783273 + 0.973706I
a = −0.58020 − 1.92757I
b = 2.64742 + 0.71348I
6.36658 + 9.50512I −2.22908 − 9.01871I
u = 0.783273 + 0.973706I
a = 1.02861 + 2.35476I
b = −2.80137 − 1.06189I
6.36658 + 9.50512I −2.22908 − 9.01871I
u = 0.783273 − 0.973706I
a = 1.036200 − 0.662931I
b = −1.80909 − 0.34245I
6.36658 − 5.44535I −2.22908 + 2.09050I
u = 0.783273 − 0.973706I
a = −0.89046 + 1.26486I
b = 1.58433 + 0.03492I
6.36658 − 5.44535I −2.22908 + 2.09050I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783273 − 0.973706I
a = −0.58020 + 1.92757I
b = 2.64742 − 0.71348I
6.36658 − 9.50512I −2.22908 + 9.01871I
u = 0.783273 − 0.973706I
a = 1.02861 − 2.35476I
b = −2.80137 + 1.06189I
6.36658 − 9.50512I −2.22908 + 9.01871I
u = 0.267638 + 0.666716I
a = −0.382603 − 0.064806I
b = −0.65101 − 1.57425I
4.63007 + 3.16118I −2.01220 − 9.52195I
u = 0.267638 + 0.666716I
a = 0.02805 − 2.21970I
b = 0.74533 + 1.93262I
4.63007 − 0.89859I −2.01220 − 2.59375I
u = 0.267638 + 0.666716I
a = −2.48453 + 0.39943I
b = −0.398387 − 0.438790I
4.63007 − 0.89859I −2.01220 − 2.59375I
u = 0.267638 + 0.666716I
a = 3.18724 − 1.15243I
b = −0.816152 + 1.127800I
4.63007 + 3.16118I −2.01220 − 9.52195I
u = 0.267638 − 0.666716I
a = −0.382603 + 0.064806I
b = −0.65101 + 1.57425I
4.63007 − 3.16118I −2.01220 + 9.52195I
u = 0.267638 − 0.666716I
a = 0.02805 + 2.21970I
b = 0.74533 − 1.93262I
4.63007 + 0.89859I −2.01220 + 2.59375I
u = 0.267638 − 0.666716I
a = −2.48453 − 0.39943I
b = −0.398387 + 0.438790I
4.63007 + 0.89859I −2.01220 + 2.59375I
u = 0.267638 − 0.666716I
a = 3.18724 + 1.15243I
b = −0.816152 − 1.127800I
4.63007 − 3.16118I −2.01220 + 9.52195I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602288
a = −0.778528 + 0.855239I
b = 0.012044 − 0.807490I
2.73943 + 2.02988I −1.62374 − 3.46410I
u = −0.602288
a = −0.778528 − 0.855239I
b = 0.012044 + 0.807490I
2.73943 − 2.02988I −1.62374 + 3.46410I
u = −0.602288
a = 0.48164 + 1.36946I
b = −0.461645 − 0.028759I
2.73943 − 2.02988I −1.62374 + 3.46410I
u = −0.602288
a = 0.48164 − 1.36946I
b = −0.461645 + 0.028759I
2.73943 + 2.02988I −1.62374 − 3.46410I
15
III.
I
u
3
= h−u
11
+u
10
+· · · + b − 4u, u
11
−2u
10
+· · · + a − 4, u
12
−u
11
+· · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
9
=
−u
11
+ 2u
10
+ ··· − 4u + 4
u
11
− u
10
+ 3u
9
− u
8
+ 6u
7
− 2u
6
+ 9u
5
− 2u
4
+ 7u
3
+ 4u
a
10
=
−u
11
+ 2u
10
+ ··· − 3u + 4
2u
11
− 2u
10
+ ··· + 5u − 1
a
4
=
3u
11
− 3u
10
+ ··· + 9u − 1
−u
11
− 2u
9
− u
8
− 4u
7
− 2u
6
− 4u
5
− 4u
4
− 2u
3
− 4u
2
− u − 3
a
8
=
u
10
− u
9
+ 2u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 3u
3
+ 4u
2
− u + 3
u
11
− u
10
+ 3u
9
− u
8
+ 5u
7
− 2u
6
+ 8u
5
− 2u
4
+ 6u
3
+ 4u
a
11
=
−2u
11
+ u
10
− 4u
9
+ u
8
− 8u
7
+ 2u
6
− 10u
5
+ u
4
− 6u
3
− 2u
2
− 4u − 2
u
10
− u
9
+ 2u
8
− 2u
7
+ 4u
6
− 4u
5
+ 5u
4
− 5u
3
+ 4u
2
− 3u + 2
a
11
=
−2u
11
+ u
10
− 4u
9
+ u
8
− 8u
7
+ 2u
6
− 10u
5
+ u
4
− 6u
3
− 2u
2
− 4u − 2
u
10
− u
9
+ 2u
8
− 2u
7
+ 4u
6
− 4u
5
+ 5u
4
− 5u
3
+ 4u
2
− 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
10
− 5u
9
+ 4u
8
− 9u
7
+ 6u
6
− 15u
5
+ 9u
4
− 17u
3
+ 6u
2
− 5u − 3
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− u
11
+ ··· − u + 1
c
2
, c
6
u
12
+ 5u
11
+ ··· + 9u + 1
c
3
, c
10
u
12
+ 7u
10
+ ··· − 4u + 1
c
4
, c
8
u
12
+ 7u
10
+ ··· + 4u + 1
c
5
u
12
+ u
11
+ ··· + u + 1
c
7
u
12
+ 2u
11
+ 4u
10
+ u
9
− 2u
8
− 5u
7
− 6u
6
− 3u
5
+ 3u
3
+ 3u
2
+ 2u + 1
c
9
, c
11
u
12
− 2u
11
+ 3u
10
− 3u
9
+ 3u
7
− 6u
6
+ 5u
5
− 2u
4
− u
3
+ 4u
2
− 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
+ 5y
11
+ ··· + 9y + 1
c
2
, c
6
y
12
+ 9y
11
+ ··· − 11y + 1
c
3
, c
4
, c
8
c
10
y
12
+ 14y
11
+ ··· + 14y + 1
c
7
y
12
+ 4y
11
+ ··· + 2y + 1
c
9
, c
11
y
12
+ 2y
11
+ ··· + 4y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429976 + 0.814812I
a = −0.081378 + 0.968613I
b = −0.252948 − 0.481751I
−1.76614 − 1.77242I −11.74681 + 0.90385I
u = −0.429976 − 0.814812I
a = −0.081378 − 0.968613I
b = −0.252948 + 0.481751I
−1.76614 + 1.77242I −11.74681 − 0.90385I
u = 0.796369 + 0.772849I
a = −0.03503 + 1.67593I
b = −2.00388 − 1.18404I
7.61677 − 1.25384I 1.08380 + 0.96345I
u = 0.796369 − 0.772849I
a = −0.03503 − 1.67593I
b = −2.00388 + 1.18404I
7.61677 + 1.25384I 1.08380 − 0.96345I
u = 0.111695 + 1.124500I
a = 0.025899 − 0.751777I
b = 0.396961 + 0.440767I
2.20710 − 1.19387I −6.38204 − 1.53253I
u = 0.111695 − 1.124500I
a = 0.025899 + 0.751777I
b = 0.396961 − 0.440767I
2.20710 + 1.19387I −6.38204 + 1.53253I
u = −0.839842 + 0.897845I
a = −0.241344 − 0.625397I
b = 0.269373 + 0.299156I
10.06100 − 3.11950I 0.49742 + 2.52128I
u = −0.839842 − 0.897845I
a = −0.241344 + 0.625397I
b = 0.269373 − 0.299156I
10.06100 + 3.11950I 0.49742 − 2.52128I
u = 0.752518 + 0.986539I
a = −1.33320 − 1.17743I
b = 2.13710 − 0.37562I
6.95919 + 7.10303I −0.32122 − 6.73031I
u = 0.752518 − 0.986539I
a = −1.33320 + 1.17743I
b = 2.13710 + 0.37562I
6.95919 − 7.10303I −0.32122 + 6.73031I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.109236 + 0.556796I
a = 2.66505 − 0.92579I
b = −0.04661 + 1.52320I
4.53093 + 2.25781I −3.63115 − 0.42527I
u = 0.109236 − 0.556796I
a = 2.66505 + 0.92579I
b = −0.04661 − 1.52320I
4.53093 − 2.25781I −3.63115 + 0.42527I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
4
· (u
12
− u
11
+ ··· − u + 1)(u
25
− 6u
24
+ ··· + 2u + 4)
c
2
, c
6
((u
11
+ 3u
10
+ ··· − 2u − 1)
4
)(u
12
+ 5u
11
+ ··· + 9u + 1)
· (u
25
+ 8u
24
+ ··· + 92u − 16)
c
3
, c
10
(u
12
+ 7u
10
+ ··· − 4u + 1)(u
25
+ 11u
23
+ ··· + u + 1)
· (u
44
+ u
43
+ ··· − 10u + 1)
c
4
, c
8
(u
12
+ 7u
10
+ ··· + 4u + 1)(u
25
+ 11u
23
+ ··· + u + 1)
· (u
44
+ u
43
+ ··· − 10u + 1)
c
5
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
4
· (u
12
+ u
11
+ ··· + u + 1)(u
25
− 6u
24
+ ··· + 2u + 4)
c
7
(u
2
− u + 1)
22
· (u
12
+ 2u
11
+ 4u
10
+ u
9
− 2u
8
− 5u
7
− 6u
6
− 3u
5
+ 3u
3
+ 3u
2
+ 2u + 1)
· (u
25
+ 25u
24
+ ··· + 22528u + 2048)
c
9
, c
11
(u
12
− 2u
11
+ 3u
10
− 3u
9
+ 3u
7
− 6u
6
+ 5u
5
− 2u
4
− u
3
+ 4u
2
− 2u + 1)
· (u
25
+ 2u
24
+ ··· − 3u + 1)(u
44
− 13u
43
+ ··· − 7082u + 793)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
11
+ 3y
10
+ ··· − 2y − 1)
4
)(y
12
+ 5y
11
+ ··· + 9y + 1)
· (y
25
+ 8y
24
+ ··· + 92y − 16)
c
2
, c
6
((y
11
+ 11y
10
+ ··· + 6y − 1)
4
)(y
12
+ 9y
11
+ ··· − 11y + 1)
· (y
25
+ 20y
24
+ ··· + 34416y − 256)
c
3
, c
4
, c
8
c
10
(y
12
+ 14y
11
+ ··· + 14y + 1)(y
25
+ 22y
24
+ ··· − y − 1)
· (y
44
+ 39y
43
+ ··· − 72y + 1)
c
7
((y
2
+ y + 1)
22
)(y
12
+ 4y
11
+ ··· + 2y + 1)
· (y
25
+ 5y
24
+ ··· − 6291456y − 4194304)
c
9
, c
11
(y
12
+ 2y
11
+ ··· + 4y + 1)(y
25
+ 10y
24
+ ··· + y − 1)
· (y
44
+ 19y
43
+ ··· + 14956920y + 628849)
22
