11a
70
(K11a
70
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 9 4 11 6 3 7 10
Solving Sequence
7,11 3,8
4 6 10 1 2 9 5
c
7
c
3
c
6
c
10
c
11
c
2
c
9
c
5
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.79690 × 10
82
u
74
+ 7.20239 × 10
82
u
73
+ ··· + 6.04541 × 10
81
b − 1.44668 × 10
82
,
− 3.67725 × 10
81
u
74
+ 1.14897 × 10
82
u
73
+ ··· + 6.04541 × 10
81
a − 2.36959 × 10
81
, u
75
− 5u
74
+ ··· − 5u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 75 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−1.80 × 10
82
u
74
+ 7.20 × 10
82
u
73
+ · · · + 6.05 × 10
81
b − 1.45 ×
10
82
, −3.68 × 10
81
u
74
+ 1.15 × 10
82
u
73
+ · · · + 6.05 × 10
81
a − 2.37 ×
10
81
, u
75
− 5u
74
+ · · · − 5u
2
− 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
0.608272u
74
− 1.90056u
73
+ ··· + 1.36502u + 0.391965
2.97234u
74
− 11.9138u
73
+ ··· + 0.909081u + 2.39302
a
8
=
1
u
2
a
4
=
−0.754990u
74
+ 3.70568u
73
+ ··· + 1.06421u − 0.860252
2.28904u
74
− 8.56988u
73
+ ··· − 0.454181u + 1.18295
a
6
=
0.735779u
74
− 2.59000u
73
+ ··· − 1.30849u + 3.10168
2.66733u
74
− 13.8183u
73
+ ··· − 1.11611u + 0.260040
a
10
=
u
u
a
1
=
−u
3
−u
3
+ u
a
2
=
−0.780163u
74
+ 4.52362u
73
+ ··· − 0.0143966u − 1.25921
2.96332u
74
− 10.7355u
73
+ ··· − 1.40070u + 1.40206
a
9
=
−0.742503u
74
+ 5.31417u
73
+ ··· + 6.61688u + 2.14994
−0.526551u
74
+ 1.38417u
73
+ ··· − 1.71851u + 1.60740
a
5
=
1.78437u
74
− 6.22270u
73
+ ··· + 5.32082u + 2.42275
2.41956u
74
− 10.4227u
73
+ ··· + 0.784371u + 2.69916
a
5
=
1.78437u
74
− 6.22270u
73
+ ··· + 5.32082u + 2.42275
2.41956u
74
− 10.4227u
73
+ ··· + 0.784371u + 2.69916
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.56995u
74
+ 12.8202u
73
+ ··· + 11.6536u − 1.36638
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
75
+ u
74
+ ··· + 16u + 1
c
2
u
75
+ 31u
74
+ ··· + 54u − 1
c
3
u
75
+ u
74
+ ··· − 10u + 1
c
5
, c
8
u
75
+ 5u
74
+ ··· + 5u
2
+ 1
c
6
u
75
+ u
74
+ ··· + 30u − 1
c
7
, c
10
u
75
+ 5u
74
+ ··· + 5u
2
+ 1
c
9
u
75
+ 11u
74
+ ··· − 828u + 297
c
11
u
75
+ 29u
74
+ ··· − 10u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
75
+ 31y
74
+ ··· + 54y −1
c
2
y
75
+ 27y
74
+ ··· − 1370y −1
c
3
y
75
− 5y
74
+ ··· − 18y −1
c
5
, c
8
y
75
+ 47y
74
+ ··· − 10y −1
c
6
y
75
− 121y
74
+ ··· + 18y −1
c
7
, c
10
y
75
− 29y
74
+ ··· − 10y −1
c
9
y
75
+ 111y
74
+ ··· − 4790502y −88209
c
11
y
75
+ 35y
74
+ ··· + 118y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791299 + 0.626157I
a = −1.136250 − 0.194648I
b = −1.55325 − 0.23650I
2.07598 + 0.79958I 0
u = 0.791299 − 0.626157I
a = −1.136250 + 0.194648I
b = −1.55325 + 0.23650I
2.07598 − 0.79958I 0
u = 0.944435 + 0.356346I
a = −0.956319 − 0.093515I
b = −0.272280 − 1.297540I
−2.28865 − 1.17947I 0
u = 0.944435 − 0.356346I
a = −0.956319 + 0.093515I
b = −0.272280 + 1.297540I
−2.28865 + 1.17947I 0
u = −0.868230 + 0.530776I
a = −2.18646 + 8.50420I
b = 6.91289 + 6.22470I
−1.67548 + 0.05018I 33.6456 + 61.6621I
u = −0.868230 − 0.530776I
a = −2.18646 − 8.50420I
b = 6.91289 − 6.22470I
−1.67548 − 0.05018I 33.6456 − 61.6621I
u = −0.901384 + 0.490863I
a = −4.06027 − 6.10797I
b = −7.63991 − 0.14270I
−1.69112 + 4.00680I 36.1919 − 36.8000I
u = −0.901384 − 0.490863I
a = −4.06027 + 6.10797I
b = −7.63991 + 0.14270I
−1.69112 − 4.00680I 36.1919 + 36.8000I
u = 0.567539 + 0.856472I
a = −1.019940 + 0.924823I
b = −1.54560 − 0.33056I
1.74716 + 5.71342I 0
u = 0.567539 − 0.856472I
a = −1.019940 − 0.924823I
b = −1.54560 + 0.33056I
1.74716 − 5.71342I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964338
a = 0.506841
b = −0.214290
−1.61136 −5.58450
u = 0.765824 + 0.583007I
a = 0.303385 − 1.001710I
b = −0.196885 − 0.062255I
1.55349 + 0.61348I − 60.10 + 1.237316I
u = 0.765824 − 0.583007I
a = 0.303385 + 1.001710I
b = −0.196885 + 0.062255I
1.55349 − 0.61348I − 60.10 − 1.237316I
u = −0.829499 + 0.630475I
a = 1.18877 + 1.25117I
b = 1.88802 + 0.62955I
2.48636 + 2.32410I 0
u = −0.829499 − 0.630475I
a = 1.18877 − 1.25117I
b = 1.88802 − 0.62955I
2.48636 − 2.32410I 0
u = −0.850863 + 0.627859I
a = 0.87390 + 1.79384I
b = 1.54353 + 0.99983I
2.42103 + 2.60653I 0
u = −0.850863 − 0.627859I
a = 0.87390 − 1.79384I
b = 1.54353 − 0.99983I
2.42103 − 2.60653I 0
u = 0.526837 + 0.922838I
a = 0.942081 − 1.033130I
b = 1.51134 + 0.47807I
−0.14883 + 11.48980I 0
u = 0.526837 − 0.922838I
a = 0.942081 + 1.033130I
b = 1.51134 − 0.47807I
−0.14883 − 11.48980I 0
u = −0.607991 + 0.890820I
a = 0.599024 + 0.851155I
b = 1.207750 − 0.075419I
5.04527 − 0.07914I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.607991 − 0.890820I
a = 0.599024 − 0.851155I
b = 1.207750 + 0.075419I
5.04527 + 0.07914I 0
u = 0.263630 + 0.876603I
a = −0.375992 − 0.459802I
b = −0.020158 − 0.411851I
0.37773 − 1.86497I 0. + 5.71221I
u = 0.263630 − 0.876603I
a = −0.375992 + 0.459802I
b = −0.020158 + 0.411851I
0.37773 + 1.86497I 0. − 5.71221I
u = 0.886820 + 0.625610I
a = −0.02345 + 1.84145I
b = −0.251662 + 1.256830I
1.78310 − 5.71290I 0
u = 0.886820 − 0.625610I
a = −0.02345 − 1.84145I
b = −0.251662 − 1.256830I
1.78310 + 5.71290I 0
u = 0.914521 + 0.590451I
a = 0.119679 + 0.166270I
b = 0.970439 − 0.336294I
1.08449 − 5.28857I 0
u = 0.914521 − 0.590451I
a = 0.119679 − 0.166270I
b = 0.970439 + 0.336294I
1.08449 + 5.28857I 0
u = 0.932597 + 0.568367I
a = 0.013751 + 1.184380I
b = −0.884923 + 0.749244I
−1.83222 − 2.08698I 0
u = 0.932597 − 0.568367I
a = 0.013751 − 1.184380I
b = −0.884923 − 0.749244I
−1.83222 + 2.08698I 0
u = −0.685629 + 0.592250I
a = −0.46109 − 2.41463I
b = −0.744705 − 1.183340I
−0.17676 − 3.45478I −1.78652 + 5.40342I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.685629 − 0.592250I
a = −0.46109 + 2.41463I
b = −0.744705 + 1.183340I
−0.17676 + 3.45478I −1.78652 − 5.40342I
u = −0.515117 + 0.972701I
a = −0.527100 − 0.786396I
b = −0.995231 + 0.207120I
4.01125 − 5.34018I 0
u = −0.515117 − 0.972701I
a = −0.527100 + 0.786396I
b = −0.995231 − 0.207120I
4.01125 + 5.34018I 0
u = 0.445298 + 1.029250I
a = 0.435633 + 0.502400I
b = −0.295800 + 0.460901I
−0.63449 − 6.30730I 0
u = 0.445298 − 1.029250I
a = 0.435633 − 0.502400I
b = −0.295800 − 0.460901I
−0.63449 + 6.30730I 0
u = −0.955518 + 0.606406I
a = −1.62212 − 0.44289I
b = −2.45993 − 0.12029I
−0.99272 + 8.24278I 0
u = −0.955518 − 0.606406I
a = −1.62212 + 0.44289I
b = −2.45993 + 0.12029I
−0.99272 − 8.24278I 0
u = −1.128430 + 0.127839I
a = 0.202502 + 0.566795I
b = −0.874006 + 0.102629I
−9.45607 − 1.38465I 0
u = −1.128430 − 0.127839I
a = 0.202502 − 0.566795I
b = −0.874006 − 0.102629I
−9.45607 + 1.38465I 0
u = −1.145380 + 0.069325I
a = −0.679931 + 0.226099I
b = 0.221937 − 0.116509I
−4.70899 + 4.40582I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.145380 − 0.069325I
a = −0.679931 − 0.226099I
b = 0.221937 + 0.116509I
−4.70899 − 4.40582I 0
u = −1.043790 + 0.518555I
a = −1.00385 − 1.21751I
b = −1.48625 − 0.73116I
−2.22532 + 5.04203I 0
u = −1.043790 − 0.518555I
a = −1.00385 + 1.21751I
b = −1.48625 + 0.73116I
−2.22532 − 5.04203I 0
u = −0.742052 + 0.333850I
a = −0.49225 − 1.85952I
b = −1.13591 − 1.35983I
−0.76010 − 1.33278I −0.332802 + 0.983014I
u = −0.742052 − 0.333850I
a = −0.49225 + 1.85952I
b = −1.13591 + 1.35983I
−0.76010 + 1.33278I −0.332802 − 0.983014I
u = 0.795402 + 0.062224I
a = 1.62950 − 0.64233I
b = 1.09692 − 1.47817I
−3.90324 + 3.60828I −10.09775 − 4.41571I
u = 0.795402 − 0.062224I
a = 1.62950 + 0.64233I
b = 1.09692 + 1.47817I
−3.90324 − 3.60828I −10.09775 + 4.41571I
u = 1.055580 + 0.589429I
a = 0.72557 − 1.95839I
b = 1.62317 − 1.88315I
−6.54687 − 8.38886I 0
u = 1.055580 − 0.589429I
a = 0.72557 + 1.95839I
b = 1.62317 + 1.88315I
−6.54687 + 8.38886I 0
u = 0.397886 + 0.666525I
a = 1.49281 − 1.20707I
b = 1.199140 + 0.038507I
−4.74813 + 3.53322I −6.97223 − 3.25767I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397886 − 0.666525I
a = 1.49281 + 1.20707I
b = 1.199140 − 0.038507I
−4.74813 − 3.53322I −6.97223 + 3.25767I
u = 0.873447 + 0.870694I
a = 0.395339 + 0.623453I
b = −0.437516 + 0.908419I
−2.26517 − 1.56796I 0
u = 0.873447 − 0.870694I
a = 0.395339 − 0.623453I
b = −0.437516 − 0.908419I
−2.26517 + 1.56796I 0
u = −1.263390 + 0.059974I
a = 0.451522 − 0.021954I
b = −0.367243 + 0.519313I
−7.03947 + 9.35177I 0
u = −1.263390 − 0.059974I
a = 0.451522 + 0.021954I
b = −0.367243 − 0.519313I
−7.03947 − 9.35177I 0
u = 1.075430 + 0.686951I
a = −0.61564 + 1.81999I
b = −1.83957 + 1.40797I
0.20150 − 11.45470I 0
u = 1.075430 − 0.686951I
a = −0.61564 − 1.81999I
b = −1.83957 − 1.40797I
0.20150 + 11.45470I 0
u = −1.065960 + 0.707388I
a = 0.59448 + 1.33761I
b = 1.59308 + 0.92121I
3.62731 + 5.97807I 0
u = −1.065960 − 0.707388I
a = 0.59448 − 1.33761I
b = 1.59308 − 0.92121I
3.62731 − 5.97807I 0
u = 1.115700 + 0.695740I
a = 0.64039 − 1.78540I
b = 2.05325 − 1.45013I
−1.9580 − 17.4335I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.115700 − 0.695740I
a = 0.64039 + 1.78540I
b = 2.05325 + 1.45013I
−1.9580 + 17.4335I 0
u = 1.311660 + 0.204711I
a = −0.138053 + 0.165335I
b = 0.348061 + 0.219302I
−3.70859 − 2.85030I 0
u = 1.311660 − 0.204711I
a = −0.138053 − 0.165335I
b = 0.348061 − 0.219302I
−3.70859 + 2.85030I 0
u = −1.131880 + 0.708785I
a = −0.553642 − 1.238480I
b = −1.58959 − 1.00695I
2.10726 + 11.44930I 0
u = −1.131880 − 0.708785I
a = −0.553642 + 1.238480I
b = −1.58959 + 1.00695I
2.10726 − 11.44930I 0
u = 1.254070 + 0.541848I
a = 0.006977 − 0.440278I
b = −0.005491 − 0.633191I
−3.53974 + 0.15240I 0
u = 1.254070 − 0.541848I
a = 0.006977 + 0.440278I
b = −0.005491 + 0.633191I
−3.53974 − 0.15240I 0
u = 1.115880 + 0.819454I
a = −0.230622 − 0.569677I
b = 0.335742 − 0.951701I
−3.00033 − 5.17857I 0
u = 1.115880 − 0.819454I
a = −0.230622 + 0.569677I
b = 0.335742 + 0.951701I
−3.00033 + 5.17857I 0
u = 0.006554 + 0.393735I
a = 0.770227 − 0.359535I
b = −0.550817 − 0.498112I
−0.147876 − 1.356400I −1.90597 + 4.54012I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.006554 − 0.393735I
a = 0.770227 + 0.359535I
b = −0.550817 + 0.498112I
−0.147876 + 1.356400I −1.90597 − 4.54012I
u = −0.287824 + 0.229163I
a = −3.06974 + 2.15753I
b = 0.908382 + 0.915708I
−1.13072 + 3.27384I −6.63565 − 1.70507I
u = −0.287824 − 0.229163I
a = −3.06974 − 2.15753I
b = 0.908382 − 0.915708I
−1.13072 − 3.27384I −6.63565 + 1.70507I
u = 0.000354 + 0.340693I
a = 1.51373 − 0.61491I
b = −0.659750 − 0.404961I
−0.148374 − 1.372820I −2.72639 + 4.45702I
u = 0.000354 − 0.340693I
a = 1.51373 + 0.61491I
b = −0.659750 + 0.404961I
−0.148374 + 1.372820I −2.72639 − 4.45702I
12
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
75
+ u
74
+ ··· + 16u + 1
c
2
u
75
+ 31u
74
+ ··· + 54u − 1
c
3
u
75
+ u
74
+ ··· − 10u + 1
c
5
, c
8
u
75
+ 5u
74
+ ··· + 5u
2
+ 1
c
6
u
75
+ u
74
+ ··· + 30u − 1
c
7
, c
10
u
75
+ 5u
74
+ ··· + 5u
2
+ 1
c
9
u
75
+ 11u
74
+ ··· − 828u + 297
c
11
u
75
+ 29u
74
+ ··· − 10u + 1
13
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
75
+ 31y
74
+ ··· + 54y −1
c
2
y
75
+ 27y
74
+ ··· − 1370y −1
c
3
y
75
− 5y
74
+ ··· − 18y −1
c
5
, c
8
y
75
+ 47y
74
+ ··· − 10y −1
c
6
y
75
− 121y
74
+ ··· + 18y −1
c
7
, c
10
y
75
− 29y
74
+ ··· − 10y −1
c
9
y
75
+ 111y
74
+ ··· − 4790502y −88209
c
11
y
75
+ 35y
74
+ ··· + 118y −1
14
