11a
67
(K11a
67
)
A knot diagram
1
Linearized knot diagam
5 1 10 2 9 4 11 3 6 8 7
Solving Sequence
5,9
6
2,10
1 3 4 7 8 11
c
5
c
9
c
1
c
2
c
4
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.57965 × 10
100
u
65
+ 1.68003 × 10
101
u
64
+ ··· + 6.92347 × 10
99
b + 9.20330 × 10
100
,
− 2.47059 × 10
101
u
65
− 5.69947 × 10
101
u
64
+ ··· + 2.07704 × 10
100
a − 3.70163 × 10
101
,
u
66
+ 3u
65
+ ··· + 3u + 1i
I
u
2
= hb + u − 1, 3a + 2u + 2, u
2
− u + 1i
I
u
3
= hb − u, 3a − u + 2, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 70 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
= h7.58 × 10
100
u
65
+ 1.68 × 10
101
u
64
+ · · · + 6.92 × 10
99
b + 9.20 ×
10
100
, −2.47 × 10
101
u
65
− 5.70 × 10
101
u
64
+ · · · + 2.08 × 10
100
a − 3.70 ×
10
101
, u
66
+ 3u
65
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
2
=
11.8948u
65
+ 27.4403u
64
+ ··· + 27.6224u + 17.8216
−10.9478u
65
− 24.2657u
64
+ ··· − 22.9293u − 13.2929
a
10
=
−u
−u
3
+ u
a
1
=
22.8425u
65
+ 51.7060u
64
+ ··· + 50.5518u + 31.1145
−10.9478u
65
− 24.2657u
64
+ ··· − 22.9293u − 13.2929
a
3
=
6.57681u
65
+ 15.6596u
64
+ ··· + 17.0862u + 11.0579
−12.8649u
65
− 27.9088u
64
+ ··· − 26.2360u − 15.7081
a
4
=
0.307059u
65
+ 1.87504u
64
+ ··· + 3.31189u + 3.66520
−10.3782u
65
− 22.8004u
64
+ ··· − 21.2660u − 13.3401
a
7
=
−11.0251u
65
− 25.7638u
64
+ ··· − 23.1138u − 17.5999
15.7432u
65
+ 36.3559u
64
+ ··· + 35.5916u + 21.6869
a
8
=
9.82325u
65
+ 23.5692u
64
+ ··· + 22.4882u + 14.6165
−11.2402u
65
− 24.5385u
64
+ ··· − 20.0450u − 13.5642
a
11
=
7.80521u
65
+ 17.4313u
64
+ ··· + 12.8222u + 10.6919
−9.15300u
65
− 20.5993u
64
+ ··· − 19.6263u − 11.6363
a
11
=
7.80521u
65
+ 17.4313u
64
+ ··· + 12.8222u + 10.6919
−9.15300u
65
− 20.5993u
64
+ ··· − 19.6263u − 11.6363
(ii) Obstruction class = −1
(iii) Cusp Shapes = 47.6455u
65
+ 100.101u
64
+ ··· + 103.221u + 52.0421
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
66
+ 3u
65
+ ··· + 41u + 9
c
2
u
66
+ 31u
65
+ ··· + 677u + 81
c
3
u
66
− 3u
65
+ ··· + 720u + 432
c
5
, c
9
u
66
+ 3u
65
+ ··· + 3u + 1
c
6
9(9u
66
− 6u
65
+ ··· − 14606u + 2729)
c
7
, c
10
, c
11
u
66
+ 3u
65
+ ··· + 3u + 1
c
8
9(9u
66
− 39u
65
+ ··· + 10089u + 1177)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
66
+ 31y
65
+ ··· + 677y + 81
c
2
y
66
+ 11y
65
+ ··· − 42151y + 6561
c
3
y
66
+ 25y
65
+ ··· + 1835136y + 186624
c
5
, c
9
y
66
− 37y
65
+ ··· − 7y + 1
c
6
81(81y
66
− 1368y
65
+ ··· + 2.20603 × 10
8
y + 7447441)
c
7
, c
10
, c
11
y
66
+ 63y
65
+ ··· − 7y + 1
c
8
81(81y
66
+ 2655y
65
+ ··· − 3529607y + 1385329)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.027910 + 0.140250I
a = −1.56997 + 3.07061I
b = 0.494896 + 0.961583I
−1.87964 + 2.60684I 0
u = −1.027910 − 0.140250I
a = −1.56997 − 3.07061I
b = 0.494896 − 0.961583I
−1.87964 − 2.60684I 0
u = 0.267669 + 0.912838I
a = 0.795579 + 0.323644I
b = −0.587688 + 0.502670I
1.99050 + 1.28842I 6.23643 − 3.32220I
u = 0.267669 − 0.912838I
a = 0.795579 − 0.323644I
b = −0.587688 − 0.502670I
1.99050 − 1.28842I 6.23643 + 3.32220I
u = 0.929271 + 0.179840I
a = 3.08538 − 1.09458I
b = 0.381546 + 0.907422I
−7.08795 + 1.79943I 3.00000 + 0.I
u = 0.929271 − 0.179840I
a = 3.08538 + 1.09458I
b = 0.381546 − 0.907422I
−7.08795 − 1.79943I 3.00000 + 0.I
u = 1.027420 + 0.259721I
a = −0.63107 − 2.20262I
b = 0.578870 − 1.167110I
−1.62753 − 4.82509I 0
u = 1.027420 − 0.259721I
a = −0.63107 + 2.20262I
b = 0.578870 + 1.167110I
−1.62753 + 4.82509I 0
u = −0.126987 + 0.929394I
a = 0.648741 − 0.233480I
b = −0.807014 − 0.382013I
−3.85129 − 4.96920I 3.00000 + 2.88447I
u = −0.126987 − 0.929394I
a = 0.648741 + 0.233480I
b = −0.807014 + 0.382013I
−3.85129 + 4.96920I 3.00000 − 2.88447I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.878518 + 0.301881I
a = −0.17890 + 1.44186I
b = 0.925761 + 0.963630I
−3.68434 + 4.73747I 1.30727 − 7.90880I
u = −0.878518 − 0.301881I
a = −0.17890 − 1.44186I
b = 0.925761 − 0.963630I
−3.68434 − 4.73747I 1.30727 + 7.90880I
u = −0.093833 + 1.098820I
a = 0.625616 + 0.592154I
b = −0.595202 + 1.124180I
−6.06522 − 10.21100I 0
u = −0.093833 − 1.098820I
a = 0.625616 − 0.592154I
b = −0.595202 − 1.124180I
−6.06522 + 10.21100I 0
u = −1.063900 + 0.314595I
a = −0.42713 + 2.25061I
b = 0.54028 + 1.34674I
−7.07880 + 6.83377I 0
u = −1.063900 − 0.314595I
a = −0.42713 − 2.25061I
b = 0.54028 − 1.34674I
−7.07880 − 6.83377I 0
u = 1.142820 + 0.051839I
a = 1.52539 − 3.45312I
b = 0.364468 − 0.789088I
−6.72143 − 1.46998I 0
u = 1.142820 − 0.051839I
a = 1.52539 + 3.45312I
b = 0.364468 + 0.789088I
−6.72143 + 1.46998I 0
u = 0.263475 + 0.806064I
a = 0.756962 − 0.438726I
b = −0.155427 − 1.130610I
−8.91388 − 2.47472I −3.77224 + 2.13911I
u = 0.263475 − 0.806064I
a = 0.756962 + 0.438726I
b = −0.155427 + 1.130610I
−8.91388 + 2.47472I −3.77224 − 2.13911I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.804342 + 0.238052I
a = −0.138734 − 0.766058I
b = 0.811477 − 0.733493I
0.71398 − 2.89026I 7.98157 + 7.76196I
u = 0.804342 − 0.238052I
a = −0.138734 + 0.766058I
b = 0.811477 + 0.733493I
0.71398 + 2.89026I 7.98157 − 7.76196I
u = −0.667684 + 0.979193I
a = 0.993850 − 0.593955I
b = −0.401394 − 0.744321I
0.01721 + 3.43805I 0
u = −0.667684 − 0.979193I
a = 0.993850 + 0.593955I
b = −0.401394 + 0.744321I
0.01721 − 3.43805I 0
u = 0.158730 + 1.178700I
a = 0.617050 − 0.572268I
b = −0.537011 − 1.034030I
0.42286 + 5.79491I 0
u = 0.158730 − 1.178700I
a = 0.617050 + 0.572268I
b = −0.537011 + 1.034030I
0.42286 − 5.79491I 0
u = −0.420402 + 1.160070I
a = 0.577230 + 0.519941I
b = −0.417197 + 0.960057I
−0.683814 − 0.021668I 0
u = −0.420402 − 1.160070I
a = 0.577230 − 0.519941I
b = −0.417197 − 0.960057I
−0.683814 + 0.021668I 0
u = −1.148800 + 0.518145I
a = 0.060373 − 0.165749I
b = −0.626248 + 0.346796I
−1.69354 + 2.00274I 0
u = −1.148800 − 0.518145I
a = 0.060373 + 0.165749I
b = −0.626248 − 0.346796I
−1.69354 − 2.00274I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668822 + 0.298999I
a = 0.694866 + 0.620371I
b = 0.935300 + 0.273219I
−2.35847 + 1.56855I 4.39447 − 3.89698I
u = −0.668822 − 0.298999I
a = 0.694866 − 0.620371I
b = 0.935300 − 0.273219I
−2.35847 − 1.56855I 4.39447 + 3.89698I
u = −0.720655 + 0.061865I
a = 0.825120 + 0.868088I
b = 0.437299 − 0.709945I
−1.03551 − 1.38591I −5.22665 + 5.92733I
u = −0.720655 − 0.061865I
a = 0.825120 − 0.868088I
b = 0.437299 + 0.709945I
−1.03551 + 1.38591I −5.22665 − 5.92733I
u = 1.232360 + 0.377220I
a = 0.208644 + 0.679292I
b = −0.625470 + 0.073721I
−8.25951 + 0.62444I 0
u = 1.232360 − 0.377220I
a = 0.208644 − 0.679292I
b = −0.625470 − 0.073721I
−8.25951 − 0.62444I 0
u = −0.596410 + 0.337532I
a = 0.681963 + 0.070596I
b = 0.159471 + 0.573771I
−1.16566 + 1.36283I −2.49105 − 4.63362I
u = −0.596410 − 0.337532I
a = 0.681963 − 0.070596I
b = 0.159471 − 0.573771I
−1.16566 − 1.36283I −2.49105 + 4.63362I
u = −1.274710 + 0.356952I
a = −0.38689 + 1.90829I
b = −0.144965 + 1.388670I
−13.4953 + 6.4032I 0
u = −1.274710 − 0.356952I
a = −0.38689 − 1.90829I
b = −0.144965 − 1.388670I
−13.4953 − 6.4032I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.300980 + 0.293047I
a = −0.15525 − 1.89069I
b = −0.112571 − 1.208740I
−6.61424 − 3.82375I 0
u = 1.300980 − 0.293047I
a = −0.15525 + 1.89069I
b = −0.112571 + 1.208740I
−6.61424 + 3.82375I 0
u = 1.231140 + 0.533142I
a = −0.250791 + 0.196456I
b = −0.854961 − 0.385031I
−1.08969 − 6.56887I 0
u = 1.231140 − 0.533142I
a = −0.250791 − 0.196456I
b = −0.854961 + 0.385031I
−1.08969 + 6.56887I 0
u = −1.259040 + 0.522644I
a = −0.402514 − 0.295163I
b = −0.982154 + 0.351456I
−7.34078 + 10.21730I 0
u = −1.259040 − 0.522644I
a = −0.402514 + 0.295163I
b = −0.982154 − 0.351456I
−7.34078 − 10.21730I 0
u = 1.209140 + 0.641703I
a = 1.30879 + 1.40280I
b = −0.403574 + 1.119680I
−11.48110 − 3.00110I 0
u = 1.209140 − 0.641703I
a = 1.30879 − 1.40280I
b = −0.403574 − 1.119680I
−11.48110 + 3.00110I 0
u = 0.553080 + 0.247800I
a = 0.972098 − 0.300416I
b = 0.633036 + 0.187323I
1.191740 + 0.072864I 10.27225 + 0.64255I
u = 0.553080 − 0.247800I
a = 0.972098 + 0.300416I
b = 0.633036 − 0.187323I
1.191740 − 0.072864I 10.27225 − 0.64255I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32753 + 0.56696I
a = 0.97157 − 1.80452I
b = −0.644585 − 1.195850I
−9.9328 + 16.0998I 0
u = −1.32753 − 0.56696I
a = 0.97157 + 1.80452I
b = −0.644585 + 1.195850I
−9.9328 − 16.0998I 0
u = 1.33445 + 0.59375I
a = 0.95771 + 1.67943I
b = −0.613804 + 1.137650I
−3.35255 − 12.00270I 0
u = 1.33445 − 0.59375I
a = 0.95771 − 1.67943I
b = −0.613804 − 1.137650I
−3.35255 + 12.00270I 0
u = −1.43305 + 0.29093I
a = −0.02130 + 1.54098I
b = −0.300452 + 1.063620I
−5.41831 − 0.47417I 0
u = −1.43305 − 0.29093I
a = −0.02130 − 1.54098I
b = −0.300452 − 1.063620I
−5.41831 + 0.47417I 0
u = −1.31812 + 0.64627I
a = 1.01971 − 1.51040I
b = −0.539949 − 1.088430I
−3.79681 + 6.60858I 0
u = −1.31812 − 0.64627I
a = 1.01971 + 1.51040I
b = −0.539949 + 1.088430I
−3.79681 − 6.60858I 0
u = −0.429696 + 0.307998I
a = 1.167160 + 0.258396I
b = 0.850565 − 0.604928I
−2.64330 − 1.72779I 3.37557 + 1.36335I
u = −0.429696 − 0.307998I
a = 1.167160 − 0.258396I
b = 0.850565 + 0.604928I
−2.64330 + 1.72779I 3.37557 − 1.36335I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44535 + 0.41062I
a = −0.231500 − 1.341830I
b = −0.455012 − 1.123040I
−11.13050 + 4.68214I 0
u = 1.44535 − 0.41062I
a = −0.231500 + 1.341830I
b = −0.455012 + 1.123040I
−11.13050 − 4.68214I 0
u = −0.104871 + 0.408761I
a = 1.153220 − 0.114537I
b = 0.597692 − 1.092470I
−4.56797 − 3.83881I 1.28636 + 2.41019I
u = −0.104871 − 0.408761I
a = 1.153220 + 0.114537I
b = 0.597692 + 1.092470I
−4.56797 + 3.83881I 1.28636 − 2.41019I
u = 0.160720 + 0.228423I
a = 1.080360 − 0.013737I
b = 0.594015 + 0.896392I
0.45918 + 2.40111I 3.44791 − 1.32342I
u = 0.160720 − 0.228423I
a = 1.080360 + 0.013737I
b = 0.594015 − 0.896392I
0.45918 − 2.40111I 3.44791 + 1.32342I
11
II. I
u
2
= hb + u − 1, 3a + 2u + 2, u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u − 1
a
2
=
−
2
3
u −
2
3
−u + 1
a
10
=
−u
u + 1
a
1
=
1
3
u −
5
3
−u + 1
a
3
=
2
3
u −
1
3
−u
a
4
=
2
3
u −
1
3
−u
a
7
=
1.33333
4
3
u −
5
3
a
8
=
1
3
u
2
3
u −
1
3
a
11
=
−u −
1
3
2
3
u +
2
3
a
11
=
−u −
1
3
2
3
u +
2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes =
32
3
u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
9
u
2
+ u + 1
c
3
u
2
c
4
, c
5
, c
10
c
11
u
2
− u + 1
c
6
3(3u
2
+ 1)
c
8
3(3u
2
− 3u + 1)
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
y
2
c
6
9(3y + 1)
2
c
8
9(9y
2
− 3y + 1)
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.000000 − 0.577350I
b = 0.500000 − 0.866025I
− 4.05977I 0.33333 + 9.23760I
u = 0.500000 − 0.866025I
a = −1.000000 + 0.577350I
b = 0.500000 + 0.866025I
4.05977I 0.33333 − 9.23760I
15
III. I
u
3
= hb − u, 3a − u + 2, u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u − 1
a
2
=
1
3
u −
2
3
u
a
10
=
−u
u + 1
a
1
=
−
2
3
u −
2
3
u
a
3
=
−
1
3
u +
2
3
u − 1
a
4
=
−
1
3
u +
2
3
u − 1
a
7
=
1
3
u +
2
3
1
3
u −
2
3
a
8
=
−0.333333
2
3
u +
2
3
a
11
=
−
4
3
u +
1
3
5
3
u −
1
3
a
11
=
−
4
3
u +
1
3
5
3
u −
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5.33333
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
9
u
2
+ u + 1
c
3
u
2
c
4
, c
5
, c
10
c
11
u
2
− u + 1
c
6
, c
8
3(3u
2
+ 3u + 1)
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
y
2
c
6
, c
8
9(9y
2
− 3y + 1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 + 0.288675I
b = 0.500000 + 0.866025I
0 5.33330
u = 0.500000 − 0.866025I
a = −0.500000 − 0.288675I
b = 0.500000 − 0.866025I
0 5.33330
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
66
+ 3u
65
+ ··· + 41u + 9)
c
2
((u
2
+ u + 1)
2
)(u
66
+ 31u
65
+ ··· + 677u + 81)
c
3
u
4
(u
66
− 3u
65
+ ··· + 720u + 432)
c
4
((u
2
− u + 1)
2
)(u
66
+ 3u
65
+ ··· + 41u + 9)
c
5
((u
2
− u + 1)
2
)(u
66
+ 3u
65
+ ··· + 3u + 1)
c
6
81(3u
2
+ 1)(3u
2
+ 3u + 1)(9u
66
− 6u
65
+ ··· − 14606u + 2729)
c
7
((u
2
+ u + 1)
2
)(u
66
+ 3u
65
+ ··· + 3u + 1)
c
8
81(3u
2
− 3u + 1)(3u
2
+ 3u + 1)(9u
66
− 39u
65
+ ··· + 10089u + 1177)
c
9
((u
2
+ u + 1)
2
)(u
66
+ 3u
65
+ ··· + 3u + 1)
c
10
, c
11
((u
2
− u + 1)
2
)(u
66
+ 3u
65
+ ··· + 3u + 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
66
+ 31y
65
+ ··· + 677y + 81)
c
2
((y
2
+ y + 1)
2
)(y
66
+ 11y
65
+ ··· − 42151y + 6561)
c
3
y
4
(y
66
+ 25y
65
+ ··· + 1835136y + 186624)
c
5
, c
9
((y
2
+ y + 1)
2
)(y
66
− 37y
65
+ ··· − 7y + 1)
c
6
6561(3y + 1)
2
(9y
2
− 3y + 1)
· (81y
66
− 1368y
65
+ ··· + 220603054y + 7447441)
c
7
, c
10
, c
11
((y
2
+ y + 1)
2
)(y
66
+ 63y
65
+ ··· − 7y + 1)
c
8
6561(9y
2
− 3y + 1)
2
· (81y
66
+ 2655y
65
+ ··· − 3529607y + 1385329)
21
