11a
330
(K11a
330
)
A knot diagram
1
Linearized knot diagam
10 6 1 8 9 2 11 5 3 7 4
Solving Sequence
4,8
5 9
6,11
1 3 2 7 10
c
4
c
8
c
5
c
11
c
3
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.12011 × 10
74
u
58
+ 2.75629 × 10
74
u
57
+ ··· + 3.44884 × 10
73
b − 1.05135 × 10
76
,
− 1.49619 × 10
76
u
58
+ 3.79895 × 10
76
u
57
+ ··· + 1.62096 × 10
75
a − 1.57571 × 10
78
,
u
59
− 3u
58
+ ··· − 68u − 47i
I
u
2
= hu
13
− u
12
− 7u
11
+ 8u
10
+ 16u
9
− 22u
8
− 10u
7
+ 23u
6
− 7u
5
− 5u
4
+ 7u
3
− 3u
2
+ b − u + 1,
− u
14
+ 2u
13
+ ··· + a + 2,
u
15
− 2u
14
− 7u
13
+ 16u
12
+ 15u
11
− 46u
10
− 3u
9
+ 54u
8
− 25u
7
− 16u
6
+ 26u
5
− 12u
4
− 6u
3
+ 7u
2
− 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 74 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−1.12 × 10
74
u
58
+ 2.76 × 10
74
u
57
+ · · · + 3.45 × 10
73
b − 1.05 ×
10
76
, −1.50 × 10
76
u
58
+ 3.80 × 10
76
u
57
+ · · · + 1.62 × 10
75
a − 1.58 ×
10
78
, u
59
− 3u
58
+ · · · − 68u − 47i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
9.23031u
58
− 23.4365u
57
+ ··· + 3493.41u + 972.086
3.24779u
58
− 7.99193u
57
+ ··· + 1122.55u + 304.842
a
1
=
5.98251u
58
− 15.4445u
57
+ ··· + 2370.86u + 667.245
3.24779u
58
− 7.99193u
57
+ ··· + 1122.55u + 304.842
a
3
=
2.41804u
58
− 6.03112u
57
+ ··· + 1112.39u + 331.970
3.35170u
58
− 8.54361u
57
+ ··· + 1242.14u + 331.682
a
2
=
5.18004u
58
− 13.0960u
57
+ ··· + 2212.35u + 639.499
2.03204u
58
− 5.19353u
57
+ ··· + 732.562u + 188.668
a
7
=
3.24999u
58
− 7.66870u
57
+ ··· + 1187.04u + 318.226
2.73447u
58
− 7.36256u
57
+ ··· + 1055.99u + 271.177
a
10
=
−0.648359u
58
+ 1.03490u
57
+ ··· + 370.690u + 121.526
2.37556u
58
− 5.68960u
57
+ ··· + 673.282u + 160.207
a
10
=
−0.648359u
58
+ 1.03490u
57
+ ··· + 370.690u + 121.526
2.37556u
58
− 5.68960u
57
+ ··· + 673.282u + 160.207
(ii) Obstruction class = −1
(iii) Cusp Shapes = −19.2036u
58
+ 48.6512u
57
+ ··· − 6597.80u − 1810.72
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 8u
58
+ ··· + 7075u + 1561
c
2
, c
6
u
59
+ 2u
58
+ ··· − u + 1
c
3
, c
11
u
59
− 3u
58
+ ··· − 44u + 1
c
4
, c
5
, c
8
u
59
− 3u
58
+ ··· − 68u − 47
c
7
, c
10
u
59
− 30u
57
+ ··· + 331u − 19
c
9
u
59
− 2u
58
+ ··· + 2319u + 2117
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
− 28y
58
+ ··· + 51101495y −2436721
c
2
, c
6
y
59
+ 48y
58
+ ··· + 143y −1
c
3
, c
11
y
59
+ 51y
58
+ ··· + 564y −1
c
4
, c
5
, c
8
y
59
− 69y
58
+ ··· + 52564y −2209
c
7
, c
10
y
59
− 60y
58
+ ··· + 84595y −361
c
9
y
59
− 32y
58
+ ··· + 164317887y −4481689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663884 + 0.670936I
a = −1.15868 + 0.88811I
b = −0.33009 + 1.44308I
5.56188 + 5.09196I 0
u = 0.663884 − 0.670936I
a = −1.15868 − 0.88811I
b = −0.33009 − 1.44308I
5.56188 − 5.09196I 0
u = −1.072730 + 0.002898I
a = −0.708113 + 0.180531I
b = −0.679774 − 0.774687I
1.97600 − 2.55273I 0
u = −1.072730 − 0.002898I
a = −0.708113 − 0.180531I
b = −0.679774 + 0.774687I
1.97600 + 2.55273I 0
u = 0.481157 + 0.783711I
a = 0.87764 − 1.18816I
b = −0.033355 − 1.312050I
4.90675 − 0.17949I 0
u = 0.481157 − 0.783711I
a = 0.87764 + 1.18816I
b = −0.033355 + 1.312050I
4.90675 + 0.17949I 0
u = 0.912889 + 0.065447I
a = 0.654408 + 0.408442I
b = −0.109027 − 0.587707I
1.58471 + 0.10901I 0
u = 0.912889 − 0.065447I
a = 0.654408 − 0.408442I
b = −0.109027 + 0.587707I
1.58471 − 0.10901I 0
u = 0.547371 + 0.629034I
a = 0.275474 + 0.246041I
b = 0.362689 + 1.069460I
4.32344 − 1.31427I 8.87224 + 0.I
u = 0.547371 − 0.629034I
a = 0.275474 − 0.246041I
b = 0.362689 − 1.069460I
4.32344 + 1.31427I 8.87224 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655609 + 0.435361I
a = 1.52726 + 0.50194I
b = 0.899285 + 0.164244I
5.22435 − 5.58403I 7.88408 + 6.48040I
u = −0.655609 − 0.435361I
a = 1.52726 − 0.50194I
b = 0.899285 − 0.164244I
5.22435 + 5.58403I 7.88408 − 6.48040I
u = 0.566889 + 0.487295I
a = 1.27041 + 0.78556I
b = 0.293328 − 1.120330I
4.51202 + 5.11815I 8.89658 − 7.24819I
u = 0.566889 − 0.487295I
a = 1.27041 − 0.78556I
b = 0.293328 + 1.120330I
4.51202 − 5.11815I 8.89658 + 7.24819I
u = −0.462881 + 0.565944I
a = −0.55152 − 1.59437I
b = 0.0819864 − 0.0135157I
4.44971 + 2.14107I 5.59927 + 1.54259I
u = −0.462881 − 0.565944I
a = −0.55152 + 1.59437I
b = 0.0819864 + 0.0135157I
4.44971 − 2.14107I 5.59927 − 1.54259I
u = −0.870656 + 0.926885I
a = 0.986934 + 0.667144I
b = 0.31968 + 1.41732I
10.3757 − 9.8566I 0
u = −0.870656 − 0.926885I
a = 0.986934 − 0.667144I
b = 0.31968 − 1.41732I
10.3757 + 9.8566I 0
u = 0.415938 + 0.579248I
a = 0.846887 + 0.499107I
b = 0.574644 + 0.026281I
1.35011 + 1.88524I 3.00000 − 3.83760I
u = 0.415938 − 0.579248I
a = 0.846887 − 0.499107I
b = 0.574644 − 0.026281I
1.35011 − 1.88524I 3.00000 + 3.83760I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.647619 + 0.225990I
a = 1.90147 + 0.85004I
b = 0.42877 + 1.41249I
9.17648 + 0.45587I 13.79187 + 0.50236I
u = −0.647619 − 0.225990I
a = 1.90147 − 0.85004I
b = 0.42877 − 1.41249I
9.17648 − 0.45587I 13.79187 − 0.50236I
u = 1.31990
a = 0.0472574
b = −0.674808
2.77979 0
u = −0.507724 + 1.289270I
a = −0.303043 − 0.951975I
b = 0.042705 − 1.359630I
9.00112 + 2.68298I 0
u = −0.507724 − 1.289270I
a = −0.303043 + 0.951975I
b = 0.042705 + 1.359630I
9.00112 − 2.68298I 0
u = −1.44030 + 0.20799I
a = 0.221441 − 0.421025I
b = 0.542037 + 0.003122I
7.30101 − 4.74836I 0
u = −1.44030 − 0.20799I
a = 0.221441 + 0.421025I
b = 0.542037 − 0.003122I
7.30101 + 4.74836I 0
u = −0.485094 + 0.213274I
a = −3.30156 − 0.35475I
b = 0.001691 − 1.297030I
8.58837 − 2.03485I 15.0115 + 3.6514I
u = −0.485094 − 0.213274I
a = −3.30156 + 0.35475I
b = 0.001691 + 1.297030I
8.58837 + 2.03485I 15.0115 − 3.6514I
u = −0.486013 + 0.140699I
a = −0.526562 + 0.989442I
b = −0.351844 − 0.983970I
0.77762 − 2.37468I −0.58026 + 5.71266I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486013 − 0.140699I
a = −0.526562 − 0.989442I
b = −0.351844 + 0.983970I
0.77762 + 2.37468I −0.58026 − 5.71266I
u = −1.50589
a = 0.891008
b = 0.701190
7.41921 0
u = 0.453128
a = −2.33221
b = −1.18104
0.221271 19.3560
u = 0.452712
a = 1.61649
b = 0.0591731
0.981228 11.9020
u = 1.55236 + 0.02522I
a = −0.133426 − 0.715380I
b = −0.19113 + 1.40151I
7.75920 + 2.91351I 0
u = 1.55236 − 0.02522I
a = −0.133426 + 0.715380I
b = −0.19113 − 1.40151I
7.75920 − 2.91351I 0
u = 1.56343 + 0.06205I
a = −1.285730 − 0.513846I
b = −0.270263 + 1.324280I
15.6947 + 3.0236I 0
u = 1.56343 − 0.06205I
a = −1.285730 + 0.513846I
b = −0.270263 − 1.324280I
15.6947 − 3.0236I 0
u = −1.56748
a = −0.881028
b = −1.73811
7.31990 0
u = −1.57638 + 0.12949I
a = 0.436873 − 0.982897I
b = 0.186350 + 1.361050I
11.80620 − 7.29433I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57638 − 0.12949I
a = 0.436873 + 0.982897I
b = 0.186350 − 1.361050I
11.80620 + 7.29433I 0
u = −1.58483 + 0.22376I
a = 0.987123 − 0.209265I
b = 0.273747 + 1.367090I
11.87830 − 3.53773I 0
u = −1.58483 − 0.22376I
a = 0.987123 + 0.209265I
b = 0.273747 − 1.367090I
11.87830 + 3.53773I 0
u = 1.59540 + 0.14328I
a = −0.915820 + 0.268097I
b = −0.698680 + 0.076811I
11.68030 + 0.45414I 0
u = 1.59540 − 0.14328I
a = −0.915820 − 0.268097I
b = −0.698680 − 0.076811I
11.68030 − 0.45414I 0
u = −0.020007 + 0.394814I
a = −0.649909 + 1.080940I
b = −0.564266 + 0.401283I
−0.96759 + 1.06374I −3.58491 − 4.50505I
u = −0.020007 − 0.394814I
a = −0.649909 − 1.080940I
b = −0.564266 − 0.401283I
−0.96759 − 1.06374I −3.58491 + 4.50505I
u = 1.60361 + 0.11834I
a = 0.911699 + 0.052547I
b = 1.42194 − 0.25243I
12.9698 + 7.5955I 0
u = 1.60361 − 0.11834I
a = 0.911699 − 0.052547I
b = 1.42194 + 0.25243I
12.9698 − 7.5955I 0
u = 1.60729 + 0.06441I
a = 0.887442 + 0.078089I
b = 0.81025 − 1.62623I
17.0188 + 0.6284I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60729 − 0.06441I
a = 0.887442 − 0.078089I
b = 0.81025 + 1.62623I
17.0188 − 0.6284I 0
u = −1.60407 + 0.19460I
a = −0.938387 + 0.141608I
b = −0.58039 − 1.68597I
13.1880 − 8.2730I 0
u = −1.60407 − 0.19460I
a = −0.938387 − 0.141608I
b = −0.58039 + 1.68597I
13.1880 + 8.2730I 0
u = −1.63522 + 0.16039I
a = 0.003749 + 0.275010I
b = 0.23042 − 1.41743I
12.00310 − 1.72842I 0
u = −1.63522 − 0.16039I
a = 0.003749 − 0.275010I
b = 0.23042 + 1.41743I
12.00310 + 1.72842I 0
u = 1.68149 + 0.27693I
a = 1.006940 + 0.127051I
b = 0.53294 − 1.57371I
18.8364 + 14.4187I 0
u = 1.68149 − 0.27693I
a = 1.006940 − 0.127051I
b = 0.53294 + 1.57371I
18.8364 − 14.4187I 0
u = 1.78123 + 0.42255I
a = −0.759705 + 0.078407I
b = −0.27686 + 1.40310I
16.5334 + 4.0342I 0
u = 1.78123 − 0.42255I
a = −0.759705 − 0.078407I
b = −0.27686 − 1.40310I
16.5334 − 4.0342I 0
10
II.
I
u
2
= hu
13
−u
12
+· · ·+b+1, −u
14
+2u
13
+· · ·+a+2, u
15
−2u
14
+· · ·−2u−1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
u
14
− 2u
13
+ ··· + 6u − 2
−u
13
+ u
12
+ ··· + u − 1
a
1
=
u
14
− u
13
+ ··· + 5u − 1
−u
13
+ u
12
+ ··· + u − 1
a
3
=
u
8
− 5u
6
+ u
5
+ 7u
4
− 3u
3
− u
2
+ 2u − 1
−u
13
+ u
12
+ ··· + u − 1
a
2
=
u
8
− u
7
− 5u
6
+ 5u
5
+ 7u
4
− 7u
3
− u
2
+ 2u − 2
−u
14
+ 9u
12
+ ··· − 2u − 2
a
7
=
−u
14
+ 2u
13
+ ··· − 5u + 2
−u
14
+ u
13
+ ··· + 3u
2
− 2u
a
10
=
u
5
− 3u
3
+ 2u
u
14
− u
13
+ ··· + u
2
+ 2u
a
10
=
u
5
− 3u
3
+ 2u
u
14
− u
13
+ ··· + u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
14
− 7u
13
− 19u
12
+ 53u
11
+ 30u
10
− 141u
9
+ 29u
8
+ 144u
7
−
109u
6
− 21u
5
+ 76u
4
− 46u
3
− 2u
2
+ 24u + 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 3u
14
+ ··· + 5u − 1
c
2
u
15
+ u
14
+ ··· − u − 1
c
3
u
15
+ 2u
14
+ ··· + 2u + 1
c
4
, c
5
u
15
− 2u
14
+ ··· − 2u − 1
c
6
u
15
− u
14
+ ··· − u + 1
c
7
u
15
− 3u
14
+ ··· + 3u + 1
c
8
u
15
+ 2u
14
+ ··· − 2u + 1
c
9
u
15
− u
14
+ ··· − 7u − 1
c
10
u
15
+ 3u
14
+ ··· + 3u − 1
c
11
u
15
− 2u
14
+ ··· + 2u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 5y
14
+ ··· + 13y −1
c
2
, c
6
y
15
+ 11y
14
+ ··· − 23y −1
c
3
, c
11
y
15
+ 10y
14
+ ··· − 6y −1
c
4
, c
5
, c
8
y
15
− 18y
14
+ ··· + 18y −1
c
7
, c
10
y
15
− 17y
14
+ ··· + 17y −1
c
9
y
15
− 5y
14
+ ··· + 57y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859236 + 0.096648I
a = −0.290049 − 0.225922I
b = −0.455127 + 0.900633I
1.37447 + 1.85175I 6.24665 + 0.44232I
u = −0.859236 − 0.096648I
a = −0.290049 + 0.225922I
b = −0.455127 − 0.900633I
1.37447 − 1.85175I 6.24665 − 0.44232I
u = 0.147449 + 0.698939I
a = 0.14152 − 2.06872I
b = 0.102496 − 1.303930I
7.44398 − 1.12715I 9.32440 + 0.18246I
u = 0.147449 − 0.698939I
a = 0.14152 + 2.06872I
b = 0.102496 + 1.303930I
7.44398 + 1.12715I 9.32440 − 0.18246I
u = −1.28962
a = 0.514199
b = −0.581197
3.36193 14.4310
u = 0.488833 + 0.456106I
a = 0.60478 − 1.47650I
b = 0.258245 + 0.780965I
5.17256 − 2.76956I 12.90399 + 4.24420I
u = 0.488833 − 0.456106I
a = 0.60478 + 1.47650I
b = 0.258245 − 0.780965I
5.17256 + 2.76956I 12.90399 − 4.24420I
u = 1.318060 + 0.189471I
a = −0.574725 − 0.296326I
b = 0.214298 − 0.558537I
8.33813 + 5.13031I 13.01330 − 4.52627I
u = 1.318060 − 0.189471I
a = −0.574725 + 0.296326I
b = 0.214298 + 0.558537I
8.33813 − 5.13031I 13.01330 + 4.52627I
u = 1.52270
a = −0.865968
b = −1.27999
6.18333 5.55830
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54689 + 0.23410I
a = −0.914905 − 0.329736I
b = −0.15368 + 1.44939I
12.76520 + 4.69419I 12.91855 − 3.93139I
u = 1.54689 − 0.23410I
a = −0.914905 + 0.329736I
b = −0.15368 − 1.44939I
12.76520 − 4.69419I 12.91855 + 3.93139I
u = −1.62956 + 0.11015I
a = 1.018690 − 0.151448I
b = 0.429910 + 1.194280I
14.4815 − 1.9499I 11.70621 + 0.15719I
u = −1.62956 − 0.11015I
a = 1.018690 + 0.151448I
b = 0.429910 − 1.194280I
14.4815 + 1.9499I 11.70621 − 0.15719I
u = −0.257945
a = −3.61884
b = −0.931093
−0.131193 −4.21560
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 3u
14
+ ··· + 5u − 1)(u
59
+ 8u
58
+ ··· + 7075u + 1561)
c
2
(u
15
+ u
14
+ ··· − u − 1)(u
59
+ 2u
58
+ ··· − u + 1)
c
3
(u
15
+ 2u
14
+ ··· + 2u + 1)(u
59
− 3u
58
+ ··· − 44u + 1)
c
4
, c
5
(u
15
− 2u
14
+ ··· − 2u − 1)(u
59
− 3u
58
+ ··· − 68u − 47)
c
6
(u
15
− u
14
+ ··· − u + 1)(u
59
+ 2u
58
+ ··· − u + 1)
c
7
(u
15
− 3u
14
+ ··· + 3u + 1)(u
59
− 30u
57
+ ··· + 331u − 19)
c
8
(u
15
+ 2u
14
+ ··· − 2u + 1)(u
59
− 3u
58
+ ··· − 68u − 47)
c
9
(u
15
− u
14
+ ··· − 7u − 1)(u
59
− 2u
58
+ ··· + 2319u + 2117)
c
10
(u
15
+ 3u
14
+ ··· + 3u − 1)(u
59
− 30u
57
+ ··· + 331u − 19)
c
11
(u
15
− 2u
14
+ ··· + 2u − 1)(u
59
− 3u
58
+ ··· − 44u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 5y
14
+ ··· + 13y −1)
· (y
59
− 28y
58
+ ··· + 51101495y −2436721)
c
2
, c
6
(y
15
+ 11y
14
+ ··· − 23y −1)(y
59
+ 48y
58
+ ··· + 143y −1)
c
3
, c
11
(y
15
+ 10y
14
+ ··· − 6y −1)(y
59
+ 51y
58
+ ··· + 564y −1)
c
4
, c
5
, c
8
(y
15
− 18y
14
+ ··· + 18y −1)(y
59
− 69y
58
+ ··· + 52564y −2209)
c
7
, c
10
(y
15
− 17y
14
+ ··· + 17y −1)(y
59
− 60y
58
+ ··· + 84595y −361)
c
9
(y
15
− 5y
14
+ ··· + 57y −1)
· (y
59
− 32y
58
+ ··· + 164317887y −4481689)
17
