11a
10
(K11a
10
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 3 11 10 4 6 7 8
Solving Sequence
6,11 3,7
5 10 8 1 2 9 4
c
6
c
5
c
10
c
7
c
11
c
2
c
9
c
3
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
58
− 8u
57
+ ··· + 2b + 1, u
58
+ 6u
57
+ ··· + 2a − 4, u
59
+ 3u
58
+ ··· − 3u − 1i
I
u
2
= h−au + b, u
2
a + a
2
− au + 2u
2
+ 2a − u + 3, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 65 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−3u
58
−8u
57
+· · ·+2b+1, u
58
+6u
57
+· · ·+2a−4, u
59
+3u
58
+· · ·−3u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−
1
2
u
58
− 3u
57
+ ··· + 2u + 2
3
2
u
58
+ 4u
57
+ ··· −
5
2
u −
1
2
a
7
=
1
u
2
a
5
=
−
1
2
u
58
− u
57
+ ··· + 6u + 1
−
1
2
u
58
− u
57
+ ··· +
3
2
u +
1
2
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
3u
58
+ 5u
57
+ ··· −
7
2
u −
1
2
7
2
u
58
+ 10u
57
+ ··· −
13
2
u −
5
2
a
9
=
u
3
+ 2u
u
3
+ u
a
4
=
7
2
u
58
+ 6u
57
+ ··· − 4u − 1
9
2
u
58
+ 13u
57
+ ··· −
19
2
u −
7
2
a
4
=
7
2
u
58
+ 6u
57
+ ··· − 4u − 1
9
2
u
58
+ 13u
57
+ ··· −
19
2
u −
7
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
58
+
13
2
u
57
+ ··· − 5u −
1
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
59
+ 4u
58
+ ··· − 4u − 1
c
2
u
59
+ 30u
58
+ ··· − 4u − 1
c
3
, c
8
u
59
+ u
58
+ ··· + 32u + 64
c
5
u
59
− 4u
58
+ ··· − 22u − 137
c
6
, c
7
, c
10
u
59
− 3u
58
+ ··· − 3u + 1
c
9
, c
11
u
59
+ 3u
58
+ ··· − 67u + 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
59
+ 30y
58
+ ··· − 4y −1
c
2
y
59
+ 2y
58
+ ··· + 24y −1
c
3
, c
8
y
59
+ 35y
58
+ ··· − 35840y −4096
c
5
y
59
− 26y
58
+ ··· − 288860y −18769
c
6
, c
7
, c
10
y
59
+ 49y
58
+ ··· − 9y −1
c
9
, c
11
y
59
− 43y
58
+ ··· − 79169y −5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856020 + 0.073484I
a = −1.65134 − 0.50020I
b = −0.984871 + 0.337502I
−10.46570 + 1.43686I −11.55835 − 0.61012I
u = −0.856020 − 0.073484I
a = −1.65134 + 0.50020I
b = −0.984871 − 0.337502I
−10.46570 − 1.43686I −11.55835 + 0.61012I
u = −0.847080 + 0.128915I
a = −2.75122 − 0.10346I
b = −1.61866 + 0.64547I
−8.54972 + 10.26440I −9.15841 − 6.91772I
u = −0.847080 − 0.128915I
a = −2.75122 + 0.10346I
b = −1.61866 − 0.64547I
−8.54972 − 10.26440I −9.15841 + 6.91772I
u = −0.829204 + 0.107730I
a = 2.27299 − 0.15394I
b = 1.31540 − 0.76071I
−5.74133 + 5.06975I −6.65758 − 3.49400I
u = −0.829204 − 0.107730I
a = 2.27299 + 0.15394I
b = 1.31540 + 0.76071I
−5.74133 − 5.06975I −6.65758 + 3.49400I
u = 0.131822 + 1.175380I
a = −0.041304 + 1.180220I
b = 0.142720 + 0.203347I
1.39618 − 2.09190I 0
u = 0.131822 − 1.175380I
a = −0.041304 − 1.180220I
b = 0.142720 − 0.203347I
1.39618 + 2.09190I 0
u = −0.410091 + 1.123290I
a = −0.975892 − 0.863707I
b = −1.57994 − 0.54447I
−5.50561 − 5.74082I 0
u = −0.410091 − 1.123290I
a = −0.975892 + 0.863707I
b = −1.57994 + 0.54447I
−5.50561 + 5.74082I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796588 + 0.044117I
a = 2.81269 + 0.63796I
b = 1.175990 + 0.375378I
−4.83655 − 3.88458I −8.90529 + 3.78678I
u = 0.796588 − 0.044117I
a = 2.81269 − 0.63796I
b = 1.175990 − 0.375378I
−4.83655 + 3.88458I −8.90529 − 3.78678I
u = −0.379560 + 1.151180I
a = 0.596247 + 0.686778I
b = 1.32673 + 0.59766I
−2.55192 − 0.70368I 0
u = −0.379560 − 1.151180I
a = 0.596247 − 0.686778I
b = 1.32673 − 0.59766I
−2.55192 + 0.70368I 0
u = −0.754668 + 0.026465I
a = 0.58720 − 1.61512I
b = 0.31567 − 1.50166I
−2.49974 + 2.68394I −8.69632 − 3.80104I
u = −0.754668 − 0.026465I
a = 0.58720 + 1.61512I
b = 0.31567 + 1.50166I
−2.49974 − 2.68394I −8.69632 + 3.80104I
u = −0.409182 + 1.194340I
a = −0.691302 − 0.078308I
b = −1.089200 − 0.246358I
−7.01962 + 3.10038I 0
u = −0.409182 − 1.194340I
a = −0.691302 + 0.078308I
b = −1.089200 + 0.246358I
−7.01962 − 3.10038I 0
u = 0.486405 + 0.550204I
a = −1.088040 + 0.443756I
b = −1.261210 − 0.450390I
−3.53532 − 5.79141I −7.16103 + 7.27058I
u = 0.486405 − 0.550204I
a = −1.088040 − 0.443756I
b = −1.261210 + 0.450390I
−3.53532 + 5.79141I −7.16103 − 7.27058I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730409
a = −1.99609
b = −0.729874
−1.92594 −4.78130
u = 0.342721 + 1.230370I
a = 1.28582 − 1.39129I
b = 1.069880 − 0.258043I
−1.186550 − 0.224277I 0
u = 0.342721 − 1.230370I
a = 1.28582 + 1.39129I
b = 1.069880 + 0.258043I
−1.186550 + 0.224277I 0
u = 0.573054 + 0.406970I
a = −0.64175 + 1.45528I
b = −1.081700 + 0.295661I
−3.99025 + 1.99015I −8.92828 − 0.31986I
u = 0.573054 − 0.406970I
a = −0.64175 − 1.45528I
b = −1.081700 − 0.295661I
−3.99025 − 1.99015I −8.92828 + 0.31986I
u = −0.042991 + 1.296740I
a = 0.612344 + 1.253280I
b = 0.970255 − 0.994207I
4.23548 + 3.29913I 0
u = −0.042991 − 1.296740I
a = 0.612344 − 1.253280I
b = 0.970255 + 0.994207I
4.23548 − 3.29913I 0
u = −0.312666 + 1.260280I
a = −0.947892 + 0.316493I
b = 0.51778 + 1.49782I
1.31708 + 1.15944I 0
u = −0.312666 − 1.260280I
a = −0.947892 − 0.316493I
b = 0.51778 − 1.49782I
1.31708 − 1.15944I 0
u = 0.308900 + 1.284590I
a = −1.32494 + 0.68919I
b = −0.810078 − 0.293298I
2.08956 − 3.75051I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.308900 − 1.284590I
a = −1.32494 − 0.68919I
b = −0.810078 + 0.293298I
2.08956 + 3.75051I 0
u = 0.007860 + 1.322200I
a = −0.505680 − 1.017660I
b = −0.342454 + 1.026550I
5.58829 − 1.44801I 0
u = 0.007860 − 1.322200I
a = −0.505680 + 1.017660I
b = −0.342454 − 1.026550I
5.58829 + 1.44801I 0
u = −0.324436 + 1.292440I
a = 1.260280 + 0.208066I
b = 0.14207 − 1.55287I
1.62049 + 6.58252I 0
u = −0.324436 − 1.292440I
a = 1.260280 − 0.208066I
b = 0.14207 + 1.55287I
1.62049 − 6.58252I 0
u = 0.349284 + 1.299200I
a = 1.86046 − 0.79136I
b = 1.262440 + 0.472314I
−0.64183 − 8.01411I 0
u = 0.349284 − 1.299200I
a = 1.86046 + 0.79136I
b = 1.262440 − 0.472314I
−0.64183 + 8.01411I 0
u = 0.247609 + 1.341690I
a = −0.878663 − 0.254927I
b = −0.010321 − 0.575786I
3.12629 − 3.79302I 0
u = 0.247609 − 1.341690I
a = −0.878663 + 0.254927I
b = −0.010321 + 0.575786I
3.12629 + 3.79302I 0
u = 0.616427 + 0.135220I
a = −0.772422 − 1.104090I
b = −0.025567 − 0.410528I
−1.53739 − 0.64054I −8.33837 + 0.19638I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.616427 − 0.135220I
a = −0.772422 + 1.104090I
b = −0.025567 + 0.410528I
−1.53739 + 0.64054I −8.33837 − 0.19638I
u = −0.385237 + 1.320760I
a = −0.84823 − 1.32751I
b = −0.882451 + 0.394924I
−6.10402 + 5.89251I 0
u = −0.385237 − 1.320760I
a = −0.84823 + 1.32751I
b = −0.882451 − 0.394924I
−6.10402 − 5.89251I 0
u = 0.090653 + 1.377440I
a = −0.326353 − 0.822204I
b = 0.672970 + 0.735433I
4.93456 − 3.07605I 0
u = 0.090653 − 1.377440I
a = −0.326353 + 0.822204I
b = 0.672970 − 0.735433I
4.93456 + 3.07605I 0
u = −0.363885 + 1.340010I
a = 1.36573 + 1.29503I
b = 1.28712 − 0.87319I
−1.19374 + 9.36497I 0
u = −0.363885 − 1.340010I
a = 1.36573 − 1.29503I
b = 1.28712 + 0.87319I
−1.19374 − 9.36497I 0
u = 0.406682 + 0.444506I
a = 0.364648 − 0.579230I
b = 0.813057 + 0.301724I
−0.77600 − 1.53921I −3.61158 + 4.49048I
u = 0.406682 − 0.444506I
a = 0.364648 + 0.579230I
b = 0.813057 − 0.301724I
−0.77600 + 1.53921I −3.61158 − 4.49048I
u = −0.371273 + 1.354390I
a = −1.46770 − 1.56354I
b = −1.62445 + 0.72234I
−3.8828 + 14.6473I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.371273 − 1.354390I
a = −1.46770 + 1.56354I
b = −1.62445 − 0.72234I
−3.8828 − 14.6473I 0
u = 0.190850 + 1.391990I
a = 0.542814 + 0.866023I
b = −0.845987 + 0.391644I
1.68472 − 0.64264I 0
u = 0.190850 − 1.391990I
a = 0.542814 − 0.866023I
b = −0.845987 − 0.391644I
1.68472 + 0.64264I 0
u = 0.10837 + 1.41748I
a = 0.253825 + 0.832571I
b = −1.231490 − 0.673169I
2.74503 − 7.63920I 0
u = 0.10837 − 1.41748I
a = 0.253825 − 0.832571I
b = −1.231490 + 0.673169I
2.74503 + 7.63920I 0
u = −0.007745 + 0.362586I
a = −1.362500 + 0.139689I
b = 0.062326 + 0.756000I
0.56495 − 1.37410I 1.41861 + 4.46189I
u = −0.007745 − 0.362586I
a = −1.362500 − 0.139689I
b = 0.062326 − 0.756000I
0.56495 + 1.37410I 1.41861 − 4.46189I
u = −0.228387 + 0.196319I
a = 2.95823 − 0.48432I
b = 0.678923 − 0.739397I
−0.26736 + 2.47932I 1.42598 − 4.73162I
u = −0.228387 − 0.196319I
a = 2.95823 + 0.48432I
b = 0.678923 + 0.739397I
−0.26736 − 2.47932I 1.42598 + 4.73162I
10
II. I
u
2
= h−au + b, u
2
a + a
2
− au + 2u
2
+ 2a − u + 3, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
a
au
a
7
=
1
u
2
a
5
=
u
2
+ a − u + 3
au + 1
a
10
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
1
=
−1
0
a
2
=
au + a
au
a
9
=
u
2
+ 1
u
2
− u + 1
a
4
=
a
au
a
4
=
a
au
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
a − 4au − 3u
2
+ a + 3u − 8
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
8
u
6
c
4
(u
2
− u + 1)
3
c
6
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
9
, c
11
(u
3
− u
2
+ 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
8
y
6
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
11
(y
3
− y
2
+ 2y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.706350 + 0.266290I
b = −0.500000 − 0.866025I
3.02413 − 4.85801I −2.09851 + 6.80481I
u = 0.215080 + 1.307140I
a = 0.583789 + 0.478572I
b = −0.500000 + 0.866025I
3.02413 − 0.79824I 1.45566 − 0.28364I
u = 0.215080 − 1.307140I
a = −0.706350 − 0.266290I
b = −0.500000 + 0.866025I
3.02413 + 4.85801I −2.09851 − 6.80481I
u = 0.215080 − 1.307140I
a = 0.583789 − 0.478572I
b = −0.500000 − 0.866025I
3.02413 + 0.79824I 1.45566 + 0.28364I
u = 0.569840
a = −0.87744 + 1.51977I
b = −0.500000 + 0.866025I
−1.11345 + 2.02988I −5.85715 − 2.43783I
u = 0.569840
a = −0.87744 − 1.51977I
b = −0.500000 − 0.866025I
−1.11345 − 2.02988I −5.85715 + 2.43783I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
59
+ 4u
58
+ ··· − 4u − 1)
c
2
((u
2
+ u + 1)
3
)(u
59
+ 30u
58
+ ··· − 4u − 1)
c
3
, c
8
u
6
(u
59
+ u
58
+ ··· + 32u + 64)
c
4
((u
2
− u + 1)
3
)(u
59
+ 4u
58
+ ··· − 4u − 1)
c
5
((u
2
+ u + 1)
3
)(u
59
− 4u
58
+ ··· − 22u − 137)
c
6
, c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
59
− 3u
58
+ ··· − 3u + 1)
c
9
, c
11
((u
3
− u
2
+ 1)
2
)(u
59
+ 3u
58
+ ··· − 67u + 73)
c
10
((u
3
+ u
2
+ 2u + 1)
2
)(u
59
− 3u
58
+ ··· − 3u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
59
+ 30y
58
+ ··· − 4y −1)
c
2
((y
2
+ y + 1)
3
)(y
59
+ 2y
58
+ ··· + 24y −1)
c
3
, c
8
y
6
(y
59
+ 35y
58
+ ··· − 35840y −4096)
c
5
((y
2
+ y + 1)
3
)(y
59
− 26y
58
+ ··· − 288860y −18769)
c
6
, c
7
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
59
+ 49y
58
+ ··· − 9y −1)
c
9
, c
11
((y
3
− y
2
+ 2y −1)
2
)(y
59
− 43y
58
+ ··· − 79169y −5329)
16
