11a
324
(K11a
324
)
A knot diagram
1
Linearized knot diagam
7 9 1 8 10 2 11 3 6 5 4
Solving Sequence
6,9 3,10
2 7 1 5 11 8 4
c
9
c
2
c
6
c
1
c
5
c
10
c
8
c
4
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
20
− 59u
19
+ ··· + 16b + 720, −35u
20
+ 367u
19
+ ··· + 32a − 1520, u
21
− 11u
20
+ ··· + 368u − 32i
I
u
2
= h−6.48197 × 10
26
a
9
u
3
− 2.24957 × 10
27
a
8
u
3
+ ··· + 6.21716 × 10
28
a + 6.82138 × 10
28
,
2a
9
u
3
− 3a
8
u
3
+ ··· − 72a + 3, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
3
= h−u
6
− 4u
4
+ u
3
− 4u
2
+ b + u, −u
6
− u
5
− 4u
4
− 3u
3
− 3u
2
+ a − 3u + 1,
u
12
+ 8u
10
− u
9
+ 24u
8
− 4u
7
+ 32u
6
− 4u
5
+ 16u
4
+ u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 73 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
= h5u
20
− 59u
19
+ · · · + 16b + 720, −35u
20
+ 367u
19
+ · · · + 32a −
1520, u
21
− 11u
20
+ · · · + 368u − 32i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
3
=
1.09375u
20
− 11.4688u
19
+ ··· − 488.500u + 47.5000
−
5
16
u
20
+
59
16
u
19
+ ··· + 425u − 45
a
10
=
1
−u
2
a
2
=
1.40625u
20
− 15.1563u
19
+ ··· − 913.500u + 92.5000
−
5
16
u
20
+
59
16
u
19
+ ··· + 425u − 45
a
7
=
−
5
4
u
20
+
51
4
u
19
+ ··· + 360u −
63
2
u
20
−
21
2
u
19
+ ··· −
855
2
u + 40
a
1
=
27
16
u
20
−
139
8
u
19
+ ··· − 939u + 95
−
23
16
u
20
+
231
16
u
19
+ ··· + 456u − 44
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
1
4
u
20
−
9
4
u
19
+ ··· +
137
2
u −
15
2
−u
20
+
21
2
u
19
+ ··· +
857
2
u − 40
a
4
=
−
3
4
u
20
+
15
2
u
19
+ ··· +
763
4
u − 16
1
4
u
20
−
9
4
u
19
+ ··· − 143u + 16
a
4
=
−
3
4
u
20
+
15
2
u
19
+ ··· +
763
4
u − 16
1
4
u
20
−
9
4
u
19
+ ··· − 143u + 16
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1
2
u
19
−
9
2
u
18
+
51
2
u
17
−
209
2
u
16
+340u
15
−
1825
2
u
14
+2073u
13
−
8087
2
u
12
+6835u
11
−10051u
10
+
25731
2
u
9
−
28567
2
u
8
+ 13650u
7
−
22155
2
u
6
+ 7480u
5
− 4054u
4
+
3327
2
u
3
− 455u
2
+ 52u + 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
21
+ 10u
19
+ ··· + 2u − 1
c
3
, c
11
u
21
− 13u
20
+ ··· + 208u − 16
c
4
, c
7
u
21
+ u
19
+ ··· − 2u
2
− 1
c
5
, c
9
, c
10
u
21
− 11u
20
+ ··· + 368u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
21
+ 20y
20
+ ··· + 10y −1
c
3
, c
11
y
21
+ 13y
20
+ ··· + 3968y −256
c
4
, c
7
y
21
+ 2y
20
+ ··· − 4y −1
c
5
, c
9
, c
10
y
21
+ 21y
20
+ ··· + 4864y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.833412 + 0.782147I
a = 0.687594 − 0.745251I
b = −0.40300 − 1.39208I
−3.62928 + 10.88750I 3.73824 − 7.98574I
u = 0.833412 − 0.782147I
a = 0.687594 + 0.745251I
b = −0.40300 + 1.39208I
−3.62928 − 10.88750I 3.73824 + 7.98574I
u = 1.112700 + 0.364278I
a = 0.359904 − 0.202646I
b = 0.131151 − 1.261410I
−2.28517 − 4.65043I 4.06472 + 5.66819I
u = 1.112700 − 0.364278I
a = 0.359904 + 0.202646I
b = 0.131151 + 1.261410I
−2.28517 + 4.65043I 4.06472 − 5.66819I
u = 0.344675 + 0.678605I
a = 0.431309 − 0.926685I
b = −0.592900 − 0.573194I
1.84838 + 1.63594I 8.69775 − 4.82521I
u = 0.344675 − 0.678605I
a = 0.431309 + 0.926685I
b = −0.592900 + 0.573194I
1.84838 − 1.63594I 8.69775 + 4.82521I
u = 0.133089 + 1.297270I
a = 0.112115 + 0.615559I
b = 0.400211 + 0.336613I
−3.40974 + 1.83530I 7.00245 − 4.90716I
u = 0.133089 − 1.297270I
a = 0.112115 − 0.615559I
b = 0.400211 − 0.336613I
−3.40974 − 1.83530I 7.00245 + 4.90716I
u = 0.609486 + 0.268410I
a = −0.040658 + 0.537694I
b = 0.672784 − 0.348826I
3.15197 + 1.79452I 11.79217 − 1.79291I
u = 0.609486 − 0.268410I
a = −0.040658 − 0.537694I
b = 0.672784 + 0.348826I
3.15197 − 1.79452I 11.79217 + 1.79291I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.039590 + 0.860809I
a = −0.542621 + 0.649922I
b = 0.181872 + 1.313600I
−6.77144 + 3.85307I −1.71548 − 7.56695I
u = 1.039590 − 0.860809I
a = −0.542621 − 0.649922I
b = 0.181872 − 1.313600I
−6.77144 − 3.85307I −1.71548 + 7.56695I
u = 0.221176 + 1.373870I
a = −0.661614 − 0.256686I
b = −0.596408 + 0.187921I
−2.03502 + 4.78161I 6.69466 − 0.24839I
u = 0.221176 − 1.373870I
a = −0.661614 + 0.256686I
b = −0.596408 − 0.187921I
−2.03502 − 4.78161I 6.69466 + 0.24839I
u = 0.400789
a = 0.530955
b = −0.355136
0.646030 15.4450
u = 0.26372 + 1.64197I
a = −0.42059 + 1.78410I
b = 0.57970 + 1.59171I
−11.6624 + 15.0339I 2.04142 − 7.27394I
u = 0.26372 − 1.64197I
a = −0.42059 − 1.78410I
b = 0.57970 − 1.59171I
−11.6624 − 15.0339I 2.04142 + 7.27394I
u = 0.29003 + 1.67173I
a = 0.47249 − 1.61270I
b = −0.44648 − 1.50505I
−15.0973 + 8.6991I −1.14624 − 4.73883I
u = 0.29003 − 1.67173I
a = 0.47249 + 1.61270I
b = −0.44648 + 1.50505I
−15.0973 − 8.6991I −1.14624 + 4.73883I
u = 0.45173 + 1.85181I
a = −0.413403 + 1.215080I
b = 0.250641 + 1.241720I
−8.95857 + 2.10992I −13.39192 − 3.92736I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.45173 − 1.85181I
a = −0.413403 − 1.215080I
b = 0.250641 − 1.241720I
−8.95857 − 2.10992I −13.39192 + 3.92736I
7
II. I
u
2
= h−6.48 × 10
26
a
9
u
3
− 2.25 × 10
27
a
8
u
3
+ · · · + 6.22 × 10
28
a + 6.82 ×
10
28
, 2a
9
u
3
− 3a
8
u
3
+ · · · − 72a + 3, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
3
=
a
0.0165355a
9
u
3
+ 0.0573866a
8
u
3
+ ··· − 1.58600a − 1.74014
a
10
=
1
−u
2
a
2
=
−0.0165355a
9
u
3
− 0.0573866a
8
u
3
+ ··· + 2.58600a + 1.74014
0.0165355a
9
u
3
+ 0.0573866a
8
u
3
+ ··· − 1.58600a − 1.74014
a
7
=
0.000922235a
9
u
3
+ 0.0578207a
8
u
3
+ ··· + 0.0532973a + 0.490016
−0.0143278a
9
u
3
+ 0.00178663a
8
u
3
+ ··· − 0.336225a − 0.132170
a
1
=
0.0530326a
9
u
3
+ 0.0145794a
8
u
3
+ ··· − 2.36649a + 0.337689
0.0257401a
9
u
3
+ 0.0549904a
8
u
3
+ ··· − 2.07867a − 0.923136
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
8
=
0.00177082a
9
u
3
− 0.000877393a
8
u
3
+ ··· + 0.0216790a + 0.476649
−0.0288170a
9
u
3
− 0.0447707a
8
u
3
+ ··· + 0.194187a + 0.627577
a
4
=
−0.0109816a
9
u
3
− 0.0176154a
8
u
3
+ ··· + 0.0681560a + 1.02747
−0.0127258a
9
u
3
− 0.00892781a
8
u
3
+ ··· + 0.0628627a + 1.84822
a
4
=
−0.0109816a
9
u
3
− 0.0176154a
8
u
3
+ ··· + 0.0681560a + 1.02747
−0.0127258a
9
u
3
− 0.00892781a
8
u
3
+ ··· + 0.0628627a + 1.84822
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0146198a
9
u
3
− 0.0649565a
8
u
3
+ ··· − 0.385084a + 9.99651
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
40
+ u
39
+ ··· + 2894u + 361
c
3
, c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
8
c
4
, c
7
u
40
− 5u
39
+ ··· − 90u + 19
c
5
, c
9
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
10
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
40
+ 35y
39
+ ··· − 529984y + 130321
c
3
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
8
c
4
, c
7
y
40
+ 7y
39
+ ··· + 9304y + 361
c
5
, c
9
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
10
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.825694 + 0.761391I
b = 0.486624 − 0.146803I
−2.32272 − 1.41510I 3.30788 + 4.90874I
u = −0.395123 + 0.506844I
a = −1.176830 − 0.099414I
b = 0.56198 − 1.34282I
−4.39470 − 2.94568I 2.34185 + 9.33939I
u = −0.395123 + 0.506844I
a = 1.124900 + 0.392414I
b = −0.22676 + 1.56517I
−4.39470 + 0.11547I 2.34185 + 0.47809I
u = −0.395123 + 0.506844I
a = −0.093009 − 0.749116I
b = −0.618982 − 0.887013I
1.14877 + 2.98573I 6.57105 + 1.41016I
u = −0.395123 + 0.506844I
a = 0.582300 − 0.394023I
b = −1.069750 + 0.079546I
1.14877 − 5.81594I 6.57105 + 8.40733I
u = −0.395123 + 0.506844I
a = 0.58749 + 1.48072I
b = −0.058215 + 1.023990I
−2.32272 − 1.41510I 3.30788 + 4.90874I
u = −0.395123 + 0.506844I
a = 0.77408 − 1.82030I
b = 0.277716 − 0.212100I
1.14877 + 2.98573I 6.57105 + 1.41016I
u = −0.395123 + 0.506844I
a = −2.19803 + 0.07064I
b = −0.060334 − 1.148470I
−4.39470 + 0.11547I 2.34185 + 0.47809I
u = −0.395123 + 0.506844I
a = 2.12871 + 0.77761I
b = −0.056830 + 1.372610I
−4.39470 − 2.94568I 2.34185 + 9.33939I
u = −0.395123 + 0.506844I
a = −0.70829 − 2.26113I
b = 0.412739 − 1.024450I
1.14877 − 5.81594I 6.57105 + 8.40733I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 − 0.506844I
a = −0.825694 − 0.761391I
b = 0.486624 + 0.146803I
−2.32272 + 1.41510I 3.30788 − 4.90874I
u = −0.395123 − 0.506844I
a = −1.176830 + 0.099414I
b = 0.56198 + 1.34282I
−4.39470 + 2.94568I 2.34185 − 9.33939I
u = −0.395123 − 0.506844I
a = 1.124900 − 0.392414I
b = −0.22676 − 1.56517I
−4.39470 − 0.11547I 2.34185 − 0.47809I
u = −0.395123 − 0.506844I
a = −0.093009 + 0.749116I
b = −0.618982 + 0.887013I
1.14877 − 2.98573I 6.57105 − 1.41016I
u = −0.395123 − 0.506844I
a = 0.582300 + 0.394023I
b = −1.069750 − 0.079546I
1.14877 + 5.81594I 6.57105 − 8.40733I
u = −0.395123 − 0.506844I
a = 0.58749 − 1.48072I
b = −0.058215 − 1.023990I
−2.32272 + 1.41510I 3.30788 − 4.90874I
u = −0.395123 − 0.506844I
a = 0.77408 + 1.82030I
b = 0.277716 + 0.212100I
1.14877 − 2.98573I 6.57105 − 1.41016I
u = −0.395123 − 0.506844I
a = −2.19803 − 0.07064I
b = −0.060334 + 1.148470I
−4.39470 − 0.11547I 2.34185 − 0.47809I
u = −0.395123 − 0.506844I
a = 2.12871 − 0.77761I
b = −0.056830 − 1.372610I
−4.39470 + 2.94568I 2.34185 − 9.33939I
u = −0.395123 − 0.506844I
a = −0.70829 + 2.26113I
b = 0.412739 + 1.024450I
1.14877 + 5.81594I 6.57105 − 8.40733I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = 0.768262 − 0.287452I
b = 1.62038 − 0.20838I
−5.85298 − 7.56480I 2.91758 + 6.06338I
u = −0.10488 + 1.55249I
a = −0.098548 + 0.494298I
b = 0.686422 + 0.233614I
−5.85298 + 1.23687I 2.91758 − 0.93379I
u = −0.10488 + 1.55249I
a = −0.159807 + 0.282979I
b = −1.077640 + 0.318986I
−9.32446 − 3.16396I −0.34560 + 2.56480I
u = −0.10488 + 1.55249I
a = 0.20232 + 1.69625I
b = 0.322385 + 1.246000I
−5.85298 + 1.23687I 2.91758 − 0.93379I
u = −0.10488 + 1.55249I
a = 0.95740 + 1.43668I
b = −0.300846 + 1.175150I
−11.39640 − 1.63338I −1.31162 − 1.86585I
u = −0.10488 + 1.55249I
a = −0.08180 + 1.73380I
b = −1.02050 + 1.63272I
−11.39640 − 4.69454I −1.31162 + 6.99545I
u = −0.10488 + 1.55249I
a = −0.22855 − 2.06799I
b = 0.53799 − 1.92599I
−11.39640 − 1.63338I −1.31162 − 1.86585I
u = −0.10488 + 1.55249I
a = −0.21085 − 2.10586I
b = 0.04036 − 1.42870I
−9.32446 − 3.16396I −0.34560 + 2.56480I
u = −0.10488 + 1.55249I
a = −0.83572 − 2.03035I
b = 0.25538 − 1.44672I
−11.39640 − 4.69454I −1.31162 + 6.99545I
u = −0.10488 + 1.55249I
a = −0.00833 + 2.34458I
b = −0.212128 + 1.314620I
−5.85298 − 7.56480I 2.91758 + 6.06338I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 − 1.55249I
a = 0.768262 + 0.287452I
b = 1.62038 + 0.20838I
−5.85298 + 7.56480I 2.91758 − 6.06338I
u = −0.10488 − 1.55249I
a = −0.098548 − 0.494298I
b = 0.686422 − 0.233614I
−5.85298 − 1.23687I 2.91758 + 0.93379I
u = −0.10488 − 1.55249I
a = −0.159807 − 0.282979I
b = −1.077640 − 0.318986I
−9.32446 + 3.16396I −0.34560 − 2.56480I
u = −0.10488 − 1.55249I
a = 0.20232 − 1.69625I
b = 0.322385 − 1.246000I
−5.85298 − 1.23687I 2.91758 + 0.93379I
u = −0.10488 − 1.55249I
a = 0.95740 − 1.43668I
b = −0.300846 − 1.175150I
−11.39640 + 1.63338I −1.31162 + 1.86585I
u = −0.10488 − 1.55249I
a = −0.08180 − 1.73380I
b = −1.02050 − 1.63272I
−11.39640 + 4.69454I −1.31162 − 6.99545I
u = −0.10488 − 1.55249I
a = −0.22855 + 2.06799I
b = 0.53799 + 1.92599I
−11.39640 + 1.63338I −1.31162 + 1.86585I
u = −0.10488 − 1.55249I
a = −0.21085 + 2.10586I
b = 0.04036 + 1.42870I
−9.32446 + 3.16396I −0.34560 − 2.56480I
u = −0.10488 − 1.55249I
a = −0.83572 + 2.03035I
b = 0.25538 + 1.44672I
−11.39640 + 4.69454I −1.31162 − 6.99545I
u = −0.10488 − 1.55249I
a = −0.00833 − 2.34458I
b = −0.212128 − 1.314620I
−5.85298 + 7.56480I 2.91758 − 6.06338I
14
III. I
u
3
= h−u
6
− 4u
4
+ u
3
− 4u
2
+ b + u, −u
6
− u
5
− 4u
4
− 3u
3
− 3u
2
+ a −
3u + 1, u
12
+ 8u
10
+ · · · + u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
3
=
u
6
+ u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 3u − 1
u
6
+ 4u
4
− u
3
+ 4u
2
− u
a
10
=
1
−u
2
a
2
=
u
5
+ 4u
3
− u
2
+ 4u − 1
u
6
+ 4u
4
− u
3
+ 4u
2
− u
a
7
=
u
11
+ 8u
9
− 2u
8
+ 24u
7
− 10u
6
+ 33u
5
− 16u
4
+ 18u
3
− 8u
2
+ u
−u
9
− 6u
7
+ u
6
− 12u
5
+ 2u
4
− 8u
3
+ u − 1
a
1
=
u
11
+ 7u
9
− u
8
+ 18u
7
− 3u
6
+ 20u
5
− u
4
+ 8u
3
+ 3u
2
+ 2
−u
10
− 6u
8
+ 2u
7
− 12u
6
+ 7u
5
− 9u
4
+ 7u
3
− 2u
2
+ 2u − 1
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
11
+ 7u
9
− 2u
8
+ 18u
7
− 9u
6
+ 21u
5
− 14u
4
+ 10u
3
− 8u
2
+ u
−u
9
− 6u
7
+ u
6
− 12u
5
+ 2u
4
− 8u
3
− 1
a
4
=
−u
10
− 7u
8
+ u
7
− 17u
6
+ 4u
5
− 16u
4
+ 5u
3
− 5u
2
+ 3u − 1
−u
11
− 7u
9
+ u
8
− 18u
7
+ 4u
6
− 20u
5
+ 6u
4
− 8u
3
+ 4u
2
a
4
=
−u
10
− 7u
8
+ u
7
− 17u
6
+ 4u
5
− 16u
4
+ 5u
3
− 5u
2
+ 3u − 1
−u
11
− 7u
9
+ u
8
− 18u
7
+ 4u
6
− 20u
5
+ 6u
4
− 8u
3
+ 4u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
11
+ 3u
10
+ 8u
9
+ 18u
8
+ 20u
7
+ 38u
6
+ 22u
5
+ 35u
4
+ 17u
3
+ 13u
2
+ 8u + 5
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
12
+ 6u
10
− u
9
+ 15u
8
− 4u
7
+ 17u
6
− 5u
5
+ 9u
4
− 4u
3
+ 4u
2
− u + 1
c
2
, c
6
u
12
+ 6u
10
+ u
9
+ 15u
8
+ 4u
7
+ 17u
6
+ 5u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ u + 1
c
3
u
12
+ 2u
11
+ ··· + 3u + 2
c
4
, c
7
u
12
+ u
10
+ u
9
+ 7u
8
+ 5u
6
+ 4u
5
+ 7u
4
+ u
3
+ 3u
2
+ 3u + 1
c
5
u
12
+ 8u
10
+ u
9
+ 24u
8
+ 4u
7
+ 32u
6
+ 4u
5
+ 16u
4
+ u
2
+ 1
c
9
, c
10
u
12
+ 8u
10
− u
9
+ 24u
8
− 4u
7
+ 32u
6
− 4u
5
+ 16u
4
+ u
2
+ 1
c
11
u
12
− 2u
11
+ ··· − 3u + 2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
12
+ 12y
11
+ ··· + 7y + 1
c
3
, c
11
y
12
+ 10y
11
+ ··· + 27y + 4
c
4
, c
7
y
12
+ 2y
11
+ ··· − 3y + 1
c
5
, c
9
, c
10
y
12
+ 16y
11
+ ··· + 2y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230605 + 1.156080I
a = −0.567331 − 0.745762I
b = −0.020024 − 0.653910I
−4.31667 + 1.17027I −1.62350 − 1.30347I
u = 0.230605 − 1.156080I
a = −0.567331 + 0.745762I
b = −0.020024 + 0.653910I
−4.31667 − 1.17027I −1.62350 + 1.30347I
u = 0.140093 + 1.297660I
a = 0.853374 + 0.043040I
b = 0.508580 + 0.397736I
−2.44663 + 5.70307I 2.68049 − 6.99360I
u = 0.140093 − 1.297660I
a = 0.853374 − 0.043040I
b = 0.508580 − 0.397736I
−2.44663 − 5.70307I 2.68049 + 6.99360I
u = 0.378668 + 0.342829I
a = −0.32614 + 2.14787I
b = −0.468199 + 0.625265I
0.94072 − 3.94879I 4.00078 + 7.18659I
u = 0.378668 − 0.342829I
a = −0.32614 − 2.14787I
b = −0.468199 − 0.625265I
0.94072 + 3.94879I 4.00078 − 7.18659I
u = −0.365297 + 0.317056I
a = −2.00440 + 0.48099I
b = 0.219991 − 1.387990I
−4.41748 − 1.96789I 2.03835 + 0.71750I
u = −0.365297 − 0.317056I
a = −2.00440 − 0.48099I
b = 0.219991 + 1.387990I
−4.41748 + 1.96789I 2.03835 − 0.71750I
u = −0.09322 + 1.52595I
a = 0.48519 + 1.85935I
b = −0.55494 + 1.55922I
−10.83690 − 3.47795I 2.93008 + 1.05575I
u = −0.09322 − 1.52595I
a = 0.48519 − 1.85935I
b = −0.55494 − 1.55922I
−10.83690 + 3.47795I 2.93008 − 1.05575I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.29085 + 1.69584I
a = −0.440697 − 1.320550I
b = 0.314595 − 1.264580I
−8.53189 − 1.98164I 5.47380 − 1.06952I
u = −0.29085 − 1.69584I
a = −0.440697 + 1.320550I
b = 0.314595 + 1.264580I
−8.53189 + 1.98164I 5.47380 + 1.06952I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
12
+ 6u
10
− u
9
+ 15u
8
− 4u
7
+ 17u
6
− 5u
5
+ 9u
4
− 4u
3
+ 4u
2
− u + 1)
· (u
21
+ 10u
19
+ ··· + 2u − 1)(u
40
+ u
39
+ ··· + 2894u + 361)
c
2
, c
6
(u
12
+ 6u
10
+ u
9
+ 15u
8
+ 4u
7
+ 17u
6
+ 5u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ u + 1)
· (u
21
+ 10u
19
+ ··· + 2u − 1)(u
40
+ u
39
+ ··· + 2894u + 361)
c
3
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
8
)(u
12
+ 2u
11
+ ··· + 3u + 2)
· (u
21
− 13u
20
+ ··· + 208u − 16)
c
4
, c
7
(u
12
+ u
10
+ u
9
+ 7u
8
+ 5u
6
+ 4u
5
+ 7u
4
+ u
3
+ 3u
2
+ 3u + 1)
· (u
21
+ u
19
+ ··· − 2u
2
− 1)(u
40
− 5u
39
+ ··· − 90u + 19)
c
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
10
· (u
12
+ 8u
10
+ u
9
+ 24u
8
+ 4u
7
+ 32u
6
+ 4u
5
+ 16u
4
+ u
2
+ 1)
· (u
21
− 11u
20
+ ··· + 368u − 32)
c
9
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
10
· (u
12
+ 8u
10
− u
9
+ 24u
8
− 4u
7
+ 32u
6
− 4u
5
+ 16u
4
+ u
2
+ 1)
· (u
21
− 11u
20
+ ··· + 368u − 32)
c
11
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
8
)(u
12
− 2u
11
+ ··· − 3u + 2)
· (u
21
− 13u
20
+ ··· + 208u − 16)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
12
+ 12y
11
+ ··· + 7y + 1)(y
21
+ 20y
20
+ ··· + 10y −1)
· (y
40
+ 35y
39
+ ··· − 529984y + 130321)
c
3
, c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
8
)(y
12
+ 10y
11
+ ··· + 27y + 4)
· (y
21
+ 13y
20
+ ··· + 3968y −256)
c
4
, c
7
(y
12
+ 2y
11
+ ··· − 3y + 1)(y
21
+ 2y
20
+ ··· − 4y −1)
· (y
40
+ 7y
39
+ ··· + 9304y + 361)
c
5
, c
9
, c
10
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
10
)(y
12
+ 16y
11
+ ··· + 2y + 1)
· (y
21
+ 21y
20
+ ··· + 4864y −1024)
21
