11n
130
(K11n
130
)
A knot diagram
1
Linearized knot diagam
7 1 10 8 9 2 11 1 7 4 5
Solving Sequence
5,11 1,8
9 4 7 2 3 6 10
c
11
c
8
c
4
c
7
c
1
c
2
c
6
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.64498 × 10
39
u
36
− 5.83142 × 10
39
u
35
+ ··· + 9.36297 × 10
38
b − 1.79289 × 10
40
,
8.32208 × 10
40
u
36
+ 2.24302 × 10
41
u
35
+ ··· + 1.02993 × 10
40
a + 1.49267 × 10
42
, u
37
+ 2u
36
+ ··· − 8u − 11i
I
u
2
= h5u
10
+ 19u
9
+ 8u
8
+ 9u
7
+ 20u
6
+ 86u
5
+ 142u
4
+ 71u
3
− 71u
2
+ 67b + 39u + 64,
5u
10
− 48u
9
+ 8u
8
+ 76u
7
− 47u
6
− 249u
5
+ 75u
4
+ 138u
3
− 4u
2
+ 67a − 95u + 131,
u
11
+ u
10
− u
9
+ 7u
7
+ 6u
6
− u
5
− u
4
+ 5u
3
+ 2u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 48 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−2.64 × 10
39
u
36
− 5.83 × 10
39
u
35
+ · · · + 9.36 × 10
38
b − 1.79 ×
10
40
, 8.32 × 10
40
u
36
+ 2.24 × 10
41
u
35
+ · · · + 1.03 × 10
40
a + 1.49 ×
10
42
, u
37
+ 2u
36
+ · · · − 8u − 11i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−8.08027u
36
− 21.7785u
35
+ ··· − 344.393u − 144.929
2.82494u
36
+ 6.22818u
35
+ ··· + 78.1053u + 19.1487
a
9
=
−1.86142u
36
− 6.80771u
35
+ ··· − 132.462u − 63.9835
5.72773u
36
+ 12.8467u
35
+ ··· + 166.777u + 47.0123
a
4
=
−14.5710u
36
− 35.2438u
35
+ ··· − 475.357u − 170.402
−4.84473u
36
− 12.7993u
35
+ ··· − 193.507u − 68.6348
a
7
=
−5.25533u
36
− 15.5503u
35
+ ··· − 266.288u − 125.781
2.82494u
36
+ 6.22818u
35
+ ··· + 78.1053u + 19.1487
a
2
=
7.55117u
36
+ 20.4537u
35
+ ··· + 318.954u + 177.930
4.57906u
36
+ 12.5897u
35
+ ··· + 193.139u + 107.947
a
3
=
7.22065u
36
+ 17.5684u
35
+ ··· + 251.689u + 128.847
4.47610u
36
+ 11.7558u
35
+ ··· + 171.709u + 83.4806
a
6
=
−9.28201u
36
− 21.1993u
35
+ ··· − 266.287u − 108.443
0.126287u
36
+ 2.51101u
35
+ ··· + 72.2964u + 34.4863
a
10
=
2.42894u
36
+ 8.72585u
35
+ ··· + 164.941u + 113.830
2.47797u
36
+ 5.69993u
35
+ ··· + 64.9436u + 35.7552
a
10
=
2.42894u
36
+ 8.72585u
35
+ ··· + 164.941u + 113.830
2.47797u
36
+ 5.69993u
35
+ ··· + 64.9436u + 35.7552
(ii) Obstruction class = −1
(iii) Cusp Shapes = −28.2238u
36
− 73.9995u
35
+ ··· − 1024.01u − 467.975
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
37
+ 24u
35
+ ··· − 4u + 1
c
2
u
37
+ 48u
36
+ ··· + 8u − 1
c
3
, c
10
u
37
− u
36
+ ··· + 6u + 1
c
4
u
37
− 3u
36
+ ··· + 12u + 1
c
5
u
37
− u
36
+ ··· + 1746u + 367
c
7
u
37
+ 4u
36
+ ··· − 8u + 1
c
8
u
37
+ 10u
35
+ ··· − 75u + 23
c
9
u
37
+ 6u
36
+ ··· − 6703u + 583
c
11
u
37
+ 2u
36
+ ··· − 8u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
37
+ 48y
36
+ ··· + 8y −1
c
2
y
37
− 112y
36
+ ··· − 100y −1
c
3
, c
10
y
37
− 17y
36
+ ··· + 22y −1
c
4
y
37
− 3y
36
+ ··· + 24y −1
c
5
y
37
− 53y
36
+ ··· + 2094316y −134689
c
7
y
37
+ 2y
36
+ ··· − 56y
2
− 1
c
8
y
37
+ 20y
36
+ ··· − 44975y −529
c
9
y
37
− 66y
36
+ ··· + 4068905y −339889
c
11
y
37
− 10y
36
+ ··· + 2308y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.601373 + 0.797904I
a = 0.100319 − 0.818260I
b = −0.125544 + 0.666416I
0.33153 + 1.56965I 1.84729 − 2.87829I
u = −0.601373 − 0.797904I
a = 0.100319 + 0.818260I
b = −0.125544 − 0.666416I
0.33153 − 1.56965I 1.84729 + 2.87829I
u = −0.756589 + 0.697163I
a = 0.048994 − 0.966661I
b = −0.592884 + 1.189630I
0.52746 + 2.09006I 0.36189 − 3.60216I
u = −0.756589 − 0.697163I
a = 0.048994 + 0.966661I
b = −0.592884 − 1.189630I
0.52746 − 2.09006I 0.36189 + 3.60216I
u = 0.746755 + 0.717340I
a = 0.24852 − 1.52698I
b = 0.832075 + 0.932954I
3.60755 − 4.86664I 5.83345 + 5.56346I
u = 0.746755 − 0.717340I
a = 0.24852 + 1.52698I
b = 0.832075 − 0.932954I
3.60755 + 4.86664I 5.83345 − 5.56346I
u = −0.850079 + 0.415638I
a = 0.200244 + 0.592775I
b = −1.43302 − 1.13498I
−9.44422 + 4.54412I −2.91144 − 6.06217I
u = −0.850079 − 0.415638I
a = 0.200244 − 0.592775I
b = −1.43302 + 1.13498I
−9.44422 − 4.54412I −2.91144 + 6.06217I
u = 0.833991 + 0.353566I
a = 0.238282 + 1.378690I
b = 0.48049 − 1.49168I
−9.78588 + 0.61235I −3.21523 + 0.70893I
u = 0.833991 − 0.353566I
a = 0.238282 − 1.378690I
b = 0.48049 + 1.49168I
−9.78588 − 0.61235I −3.21523 − 0.70893I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820454 + 0.302238I
a = 0.649750 − 0.760838I
b = 0.367432 − 0.280099I
−0.44492 + 2.47536I −1.10953 − 5.85952I
u = −0.820454 − 0.302238I
a = 0.649750 + 0.760838I
b = 0.367432 + 0.280099I
−0.44492 − 2.47536I −1.10953 + 5.85952I
u = −0.709146 + 0.450731I
a = −2.09178 − 0.67084I
b = −1.020550 + 0.314178I
−8.92085 − 1.02999I −3.37249 − 2.08147I
u = −0.709146 − 0.450731I
a = −2.09178 + 0.67084I
b = −1.020550 − 0.314178I
−8.92085 + 1.02999I −3.37249 + 2.08147I
u = 0.698049 + 0.369328I
a = 2.57924 + 1.16241I
b = 0.291961 + 0.320467I
−9.27666 − 3.59094I −4.07946 + 9.46699I
u = 0.698049 − 0.369328I
a = 2.57924 − 1.16241I
b = 0.291961 − 0.320467I
−9.27666 + 3.59094I −4.07946 − 9.46699I
u = 0.518070 + 1.102540I
a = 0.461824 − 0.300576I
b = −0.066504 + 0.656363I
1.17632 + 1.49794I 4.03696 − 6.33192I
u = 0.518070 − 1.102540I
a = 0.461824 + 0.300576I
b = −0.066504 − 0.656363I
1.17632 − 1.49794I 4.03696 + 6.33192I
u = 1.223990 + 0.280649I
a = −0.445468 + 0.076745I
b = 0.380103 − 0.218592I
2.40459 + 0.03773I 9.51019 + 3.78756I
u = 1.223990 − 0.280649I
a = −0.445468 − 0.076745I
b = 0.380103 + 0.218592I
2.40459 − 0.03773I 9.51019 − 3.78756I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.658844
a = −1.02220
b = −1.22072
−2.54226 −10.2460
u = −0.599605 + 0.263744I
a = 0.44406 + 1.78040I
b = 0.98175 − 1.24775I
1.39846 + 3.05009I −3.20830 − 2.79125I
u = −0.599605 − 0.263744I
a = 0.44406 − 1.78040I
b = 0.98175 + 1.24775I
1.39846 − 3.05009I −3.20830 + 2.79125I
u = 0.649301 + 0.015184I
a = −0.789959 + 0.549138I
b = −1.202670 − 0.218143I
−2.53052 − 0.01603I −8.01901 − 0.30181I
u = 0.649301 − 0.015184I
a = −0.789959 − 0.549138I
b = −1.202670 + 0.218143I
−2.53052 + 0.01603I −8.01901 + 0.30181I
u = 1.070020 + 0.832774I
a = −0.089943 + 0.968954I
b = −1.00403 − 1.22232I
−0.20513 − 8.27502I 0. + 7.41109I
u = 1.070020 − 0.832774I
a = −0.089943 − 0.968954I
b = −1.00403 + 1.22232I
−0.20513 + 8.27502I 0. − 7.41109I
u = −1.026120 + 0.886327I
a = 0.287552 + 1.044070I
b = 0.813618 − 0.738930I
−0.93685 + 5.16140I 0. − 5.99788I
u = −1.026120 − 0.886327I
a = 0.287552 − 1.044070I
b = 0.813618 + 0.738930I
−0.93685 − 5.16140I 0. + 5.99788I
u = −1.23107 + 0.72507I
a = 0.147341 + 0.177104I
b = 0.605243 − 0.552824I
−0.70258 + 2.95006I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23107 − 0.72507I
a = 0.147341 − 0.177104I
b = 0.605243 + 0.552824I
−0.70258 − 2.95006I 0
u = −1.24432 + 0.89792I
a = −0.179117 − 1.081050I
b = −1.10074 + 1.15043I
−9.0036 + 13.3479I 0
u = −1.24432 − 0.89792I
a = −0.179117 + 1.081050I
b = −1.10074 − 1.15043I
−9.0036 − 13.3479I 0
u = −0.64511 + 1.54806I
a = 0.463658 + 0.370863I
b = −0.511435 − 0.791669I
−6.92057 − 5.26122I 0
u = −0.64511 − 1.54806I
a = 0.463658 − 0.370863I
b = −0.511435 + 0.791669I
−6.92057 + 5.26122I 0
u = 1.41428 + 1.03844I
a = −0.080599 − 0.633894I
b = 0.915060 + 0.595859I
−12.51050 − 5.12964I 0
u = 1.41428 − 1.03844I
a = −0.080599 + 0.633894I
b = 0.915060 − 0.595859I
−12.51050 + 5.12964I 0
8
II. I
u
2
=
h5u
10
+19u
9
+· · ·+67b+64, 5u
10
−48u
9
+· · ·+67a+131, u
11
+u
10
+· · ·−u−1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−0.0746269u
10
+ 0.716418u
9
+ ··· + 1.41791u − 1.95522
−0.0746269u
10
− 0.283582u
9
+ ··· − 0.582090u − 0.955224
a
9
=
0.835821u
10
+ 0.776119u
9
+ ··· + 0.119403u − 3.70149
0.343284u
10
+ 0.104478u
9
+ ··· − 0.522388u − 1.80597
a
4
=
1.47761u
10
+ 0.0149254u
9
+ ··· − 4.07463u − 0.686567
−0.850746u
10
− 0.432836u
9
+ ··· − 0.835821u + 0.910448
a
7
=
−0.149254u
10
+ 0.432836u
9
+ ··· + 0.835821u − 2.91045
−0.0746269u
10
− 0.283582u
9
+ ··· − 0.582090u − 0.955224
a
2
=
2.74627u
10
+ 0.835821u
9
+ ··· − 4.17910u − 2.44776
0.791045u
10
− 0.194030u
9
+ ··· − 2.02985u − 0.0746269
a
3
=
2.80597u
10
+ 1.46269u
9
+ ··· − 1.31343u − 4.28358
0.179104u
10
− 0.119403u
9
+ ··· − 1.40299u + 0.492537
a
6
=
−1.37313u
10
− 2.41791u
9
+ ··· − 6.91045u + 4.22388
−0.820896u
10
− 1.11940u
9
+ ··· − 2.40299u + 1.49254
a
10
=
0.611940u
10
− 0.0746269u
9
+ ··· − 3.62687u + 2.43284
−0.567164u
10
+ 0.0447761u
9
+ ··· + 0.776119u + 0.940299
a
10
=
0.611940u
10
− 0.0746269u
9
+ ··· − 3.62687u + 2.43284
−0.567164u
10
+ 0.0447761u
9
+ ··· + 0.776119u + 0.940299
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
76
67
u
10
+
61
67
u
9
+
68
67
u
8
−
24
67
u
7
+
371
67
u
6
+
731
67
u
5
+
470
67
u
4
−
167
67
u
3
+
569
67
u
2
+
700
67
u +
209
67
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ u
10
+ ··· + 3u + 1
c
2
u
11
+ 11u
10
+ ··· − 3u − 1
c
3
u
11
− 5u
9
− 2u
8
+ 11u
7
+ 9u
6
− 12u
5
− 15u
4
+ 5u
3
+ 11u
2
+ u − 3
c
4
u
11
− 2u
9
− 3u
8
+ 7u
7
+ 6u
6
− 3u
5
− 12u
4
+ 3u
3
+ 6u
2
− u − 1
c
5
u
11
− 3u
9
+ 3u
8
− u
7
− 5u
6
+ 12u
5
− 15u
4
+ 13u
3
− 8u
2
+ 3u − 1
c
6
u
11
− u
10
+ ··· + 3u − 1
c
7
u
11
+ u
10
+ u
9
− 3u
8
− u
7
− 3u
6
+ 2u
5
− 5u
4
− 2u
2
+ u − 1
c
8
u
11
− u
10
+ 2u
9
+ 3u
8
− 4u
7
+ 4u
6
+ 5u
5
− 8u
4
+ u
3
+ 5u
2
− 4u − 3
c
9
u
11
+ 7u
10
+ ··· + 8u + 1
c
10
u
11
− 5u
9
+ 2u
8
+ 11u
7
− 9u
6
− 12u
5
+ 15u
4
+ 5u
3
− 11u
2
+ u + 3
c
11
u
11
+ u
10
− u
9
+ 7u
7
+ 6u
6
− u
5
− u
4
+ 5u
3
+ 2u
2
− u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
11
+ 11y
10
+ ··· − 3y −1
c
2
y
11
− 17y
10
+ ··· + y −1
c
3
, c
10
y
11
− 10y
10
+ ··· + 67y −9
c
4
y
11
− 4y
10
+ ··· + 13y −1
c
5
y
11
− 6y
10
+ ··· − 7y −1
c
7
y
11
+ y
10
+ ··· − 3y −1
c
8
y
11
+ 3y
10
+ ··· + 46y −9
c
9
y
11
− 7y
10
+ ··· + 2y −1
c
11
y
11
− 3y
10
+ ··· + 5y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.575448 + 0.685098I
a = −0.28148 − 1.48144I
b = 0.594339 + 1.201490I
2.53579 − 3.27380I 4.40962 + 3.96450I
u = 0.575448 − 0.685098I
a = −0.28148 + 1.48144I
b = 0.594339 − 1.201490I
2.53579 + 3.27380I 4.40962 − 3.96450I
u = −0.931149 + 0.725260I
a = 0.483405 + 1.197060I
b = 1.05505 − 1.01633I
2.26337 + 5.93413I 0.97958 − 6.14906I
u = −0.931149 − 0.725260I
a = 0.483405 − 1.197060I
b = 1.05505 + 1.01633I
2.26337 − 5.93413I 0.97958 + 6.14906I
u = −1.132080 + 0.689250I
a = −0.322254 − 0.191452I
b = 0.468519 + 0.646535I
2.10419 − 0.48851I 1.91182 + 5.66309I
u = −1.132080 − 0.689250I
a = −0.322254 + 0.191452I
b = 0.468519 − 0.646535I
2.10419 + 0.48851I 1.91182 − 5.66309I
u = −0.470761 + 0.380594I
a = −2.42373 + 0.15412I
b = −0.537257 − 0.676495I
−9.12876 + 2.79567I −1.55052 + 0.06651I
u = −0.470761 − 0.380594I
a = −2.42373 − 0.15412I
b = −0.537257 + 0.676495I
−9.12876 − 2.79567I −1.55052 − 0.06651I
u = 0.547799
a = −1.41244
b = −1.39693
−2.17580 12.3110
u = 1.18464 + 1.06749I
a = −0.249721 + 0.403821I
b = −0.382185 − 0.494093I
0.02345 − 3.01225I 6.59416 + 5.79825I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18464 − 1.06749I
a = −0.249721 − 0.403821I
b = −0.382185 + 0.494093I
0.02345 + 3.01225I 6.59416 − 5.79825I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ u
10
+ ··· + 3u + 1)(u
37
+ 24u
35
+ ··· − 4u + 1)
c
2
(u
11
+ 11u
10
+ ··· − 3u − 1)(u
37
+ 48u
36
+ ··· + 8u − 1)
c
3
(u
11
− 5u
9
− 2u
8
+ 11u
7
+ 9u
6
− 12u
5
− 15u
4
+ 5u
3
+ 11u
2
+ u − 3)
· (u
37
− u
36
+ ··· + 6u + 1)
c
4
(u
11
− 2u
9
− 3u
8
+ 7u
7
+ 6u
6
− 3u
5
− 12u
4
+ 3u
3
+ 6u
2
− u − 1)
· (u
37
− 3u
36
+ ··· + 12u + 1)
c
5
(u
11
− 3u
9
+ 3u
8
− u
7
− 5u
6
+ 12u
5
− 15u
4
+ 13u
3
− 8u
2
+ 3u − 1)
· (u
37
− u
36
+ ··· + 1746u + 367)
c
6
(u
11
− u
10
+ ··· + 3u − 1)(u
37
+ 24u
35
+ ··· − 4u + 1)
c
7
(u
11
+ u
10
+ u
9
− 3u
8
− u
7
− 3u
6
+ 2u
5
− 5u
4
− 2u
2
+ u − 1)
· (u
37
+ 4u
36
+ ··· − 8u + 1)
c
8
(u
11
− u
10
+ 2u
9
+ 3u
8
− 4u
7
+ 4u
6
+ 5u
5
− 8u
4
+ u
3
+ 5u
2
− 4u − 3)
· (u
37
+ 10u
35
+ ··· − 75u + 23)
c
9
(u
11
+ 7u
10
+ ··· + 8u + 1)(u
37
+ 6u
36
+ ··· − 6703u + 583)
c
10
(u
11
− 5u
9
+ 2u
8
+ 11u
7
− 9u
6
− 12u
5
+ 15u
4
+ 5u
3
− 11u
2
+ u + 3)
· (u
37
− u
36
+ ··· + 6u + 1)
c
11
(u
11
+ u
10
− u
9
+ 7u
7
+ 6u
6
− u
5
− u
4
+ 5u
3
+ 2u
2
− u − 1)
· (u
37
+ 2u
36
+ ··· − 8u − 11)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
11
+ 11y
10
+ ··· − 3y −1)(y
37
+ 48y
36
+ ··· + 8y −1)
c
2
(y
11
− 17y
10
+ ··· + y −1)(y
37
− 112y
36
+ ··· − 100y −1)
c
3
, c
10
(y
11
− 10y
10
+ ··· + 67y −9)(y
37
− 17y
36
+ ··· + 22y −1)
c
4
(y
11
− 4y
10
+ ··· + 13y −1)(y
37
− 3y
36
+ ··· + 24y −1)
c
5
(y
11
− 6y
10
+ ··· − 7y −1)(y
37
− 53y
36
+ ··· + 2094316y −134689)
c
7
(y
11
+ y
10
+ ··· − 3y −1)(y
37
+ 2y
36
+ ··· − 56y
2
− 1)
c
8
(y
11
+ 3y
10
+ ··· + 46y −9)(y
37
+ 20y
36
+ ··· − 44975y −529)
c
9
(y
11
− 7y
10
+ ··· + 2y −1)(y
37
− 66y
36
+ ··· + 4068905y −339889)
c
11
(y
11
− 3y
10
+ ··· + 5y −1)(y
37
− 10y
36
+ ··· + 2308y −121)
15
