11a
254
(K11a
254
)
A knot diagram
1
Linearized knot diagam
4 7 1 2 8 3 10 11 6 5 9
Solving Sequence
7,10 3,8
2 6 5 11 4 1 9
c
7
c
2
c
6
c
5
c
10
c
4
c
1
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.04159 × 10
241
u
70
+ 7.02943 × 10
242
u
69
+ ··· + 6.12381 × 10
241
b + 8.22545 × 10
241
,
2.08888 × 10
242
u
70
− 2.32560 × 10
243
u
69
+ ··· + 6.12381 × 10
241
a + 2.43849 × 10
242
, u
71
− 12u
70
+ ··· − 2u + 1i
I
u
2
= hb, −u
5
+ 2u
4
+ u
3
− 3u
2
+ a + 2, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 77 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−6.04 × 10
241
u
70
+ 7.03 × 10
242
u
69
+ · · · + 6.12 × 10
241
b + 8.23 ×
10
241
, 2.09 × 10
242
u
70
− 2.33 × 10
243
u
69
+ · · · + 6.12 × 10
241
a + 2.44 ×
10
242
, u
71
− 12u
70
+ · · · − 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
−3.41108u
70
+ 37.9764u
69
+ ··· − 4.41767u − 3.98199
0.986573u
70
− 11.4788u
69
+ ··· + 1.16296u − 1.34319
a
8
=
1
−u
2
a
2
=
−4.39765u
70
+ 49.4552u
69
+ ··· − 5.58062u − 2.63880
0.986573u
70
− 11.4788u
69
+ ··· + 1.16296u − 1.34319
a
6
=
0.676294u
70
− 8.31654u
69
+ ··· + 9.11289u − 1.31962
0.0427928u
70
− 0.0844798u
69
+ ··· + 0.876884u + 1.75188
a
5
=
1.00267u
70
− 12.5483u
69
+ ··· + 9.31432u − 3.27251
0.304306u
70
− 3.13984u
69
+ ··· + 1.83385u + 1.43659
a
11
=
−1.46583u
70
+ 16.5432u
69
+ ··· − 16.5616u + 9.43161
0.491717u
70
− 5.73898u
69
+ ··· + 1.64593u − 1.66950
a
4
=
3.16529u
70
− 35.6825u
69
+ ··· + 7.81990u + 2.97070
−0.426948u
70
+ 5.06894u
69
+ ··· + 0.0537692u + 1.02327
a
1
=
−2.10032u
70
+ 24.1805u
69
+ ··· − 0.598859u + 2.20095
0.426948u
70
− 5.06894u
69
+ ··· − 0.0537692u − 1.02327
a
9
=
−0.0796172u
70
+ 0.485804u
69
+ ··· − 16.3067u + 8.04204
0.110458u
70
− 1.25495u
69
+ ··· + 2.09635u − 1.23648
a
9
=
−0.0796172u
70
+ 0.485804u
69
+ ··· − 16.3067u + 8.04204
0.110458u
70
− 1.25495u
69
+ ··· + 2.09635u − 1.23648
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.95513u
70
+ 59.1718u
69
+ ··· − 20.0129u + 21.2017
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
71
− 7u
70
+ ··· − 3u + 1
c
2
, c
6
u
71
− u
70
+ ··· + 320u + 64
c
5
u
71
+ 6u
70
+ ··· + 2u + 1
c
7
u
71
+ 12u
70
+ ··· − 2u − 1
c
8
, c
11
u
71
− 2u
70
+ ··· + 10u + 1
c
9
u
71
− 2u
70
+ ··· + 35022u + 3953
c
10
u
71
− 6u
70
+ ··· − 3424u + 319
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
71
− 67y
70
+ ··· − 45y −1
c
2
, c
6
y
71
+ 39y
70
+ ··· − 36864y −4096
c
5
y
71
+ 12y
70
+ ··· − 6y −1
c
7
y
71
+ 72y
69
+ ··· − 10y −1
c
8
, c
11
y
71
− 48y
70
+ ··· − 10y −1
c
9
y
71
− 48y
70
+ ··· − 314283574y −15626209
c
10
y
71
− 72y
70
+ ··· + 3210942y −101761
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621616 + 0.757699I
a = −0.520196 − 1.278890I
b = 0.77239 − 1.38072I
−8.79734 − 8.72585I 0
u = −0.621616 − 0.757699I
a = −0.520196 + 1.278890I
b = 0.77239 + 1.38072I
−8.79734 + 8.72585I 0
u = 0.513135 + 0.804698I
a = −0.625469 + 0.710978I
b = 0.343529 + 0.197975I
−1.92491 − 1.08364I 0
u = 0.513135 − 0.804698I
a = −0.625469 − 0.710978I
b = 0.343529 − 0.197975I
−1.92491 + 1.08364I 0
u = 0.573139 + 0.542700I
a = −1.36366 + 1.05846I
b = 0.579667 + 1.190180I
−5.36921 + 5.60292I −4.23205 − 1.95004I
u = 0.573139 − 0.542700I
a = −1.36366 − 1.05846I
b = 0.579667 − 1.190180I
−5.36921 − 5.60292I −4.23205 + 1.95004I
u = −0.775802 + 0.143132I
a = −0.189904 − 0.120697I
b = −0.590838 + 0.168836I
1.57443 − 0.30385I 7.03884 − 0.55864I
u = −0.775802 − 0.143132I
a = −0.189904 + 0.120697I
b = −0.590838 − 0.168836I
1.57443 + 0.30385I 7.03884 + 0.55864I
u = −0.050131 + 0.783968I
a = 0.86098 − 2.36171I
b = 0.357475 − 1.213820I
−6.99999 − 3.26565I −6.82531 + 6.65441I
u = −0.050131 − 0.783968I
a = 0.86098 + 2.36171I
b = 0.357475 + 1.213820I
−6.99999 + 3.26565I −6.82531 − 6.65441I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749759 + 0.966431I
a = 0.27470 + 1.81378I
b = −0.194327 + 0.887939I
−1.12559 − 1.87856I 0
u = −0.749759 − 0.966431I
a = 0.27470 − 1.81378I
b = −0.194327 − 0.887939I
−1.12559 + 1.87856I 0
u = 0.651616 + 0.380129I
a = 0.128462 − 0.217584I
b = −0.950465 − 0.547836I
0.16886 + 3.43064I 1.32233 − 8.48531I
u = 0.651616 − 0.380129I
a = 0.128462 + 0.217584I
b = −0.950465 + 0.547836I
0.16886 − 3.43064I 1.32233 + 8.48531I
u = 0.982401 + 0.777247I
a = 0.0103051 + 0.0993017I
b = 0.847736 − 0.223685I
−0.76386 + 6.94431I 0
u = 0.982401 − 0.777247I
a = 0.0103051 − 0.0993017I
b = 0.847736 + 0.223685I
−0.76386 − 6.94431I 0
u = 1.196400 + 0.406962I
a = −0.0962558 − 0.0436996I
b = 0.166256 + 0.769936I
−2.28261 + 6.08346I 0
u = 1.196400 − 0.406962I
a = −0.0962558 + 0.0436996I
b = 0.166256 − 0.769936I
−2.28261 − 6.08346I 0
u = −1.068610 + 0.686746I
a = −0.172216 + 0.127673I
b = 0.636931 + 0.433595I
2.34440 − 1.95014I 0
u = −1.068610 − 0.686746I
a = −0.172216 − 0.127673I
b = 0.636931 − 0.433595I
2.34440 + 1.95014I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509062 + 1.200470I
a = −0.098773 + 1.288770I
b = −0.04900 + 1.62786I
−14.7704 + 4.4090I 0
u = 0.509062 − 1.200470I
a = −0.098773 − 1.288770I
b = −0.04900 − 1.62786I
−14.7704 − 4.4090I 0
u = −0.585356 + 0.316293I
a = 2.37838 − 2.14743I
b = 0.472300 + 1.255780I
−8.04028 + 4.80757I 3.79140 + 4.67263I
u = −0.585356 − 0.316293I
a = 2.37838 + 2.14743I
b = 0.472300 − 1.255780I
−8.04028 − 4.80757I 3.79140 − 4.67263I
u = 0.894754 + 1.015750I
a = 0.46009 − 1.55526I
b = −0.280654 − 1.250440I
−5.52892 + 6.64078I 0
u = 0.894754 − 1.015750I
a = 0.46009 + 1.55526I
b = −0.280654 + 1.250440I
−5.52892 − 6.64078I 0
u = −0.378627 + 0.497963I
a = 0.36207 + 1.47520I
b = −0.55003 + 1.38741I
−2.62165 − 3.78828I −7.5138 + 12.3973I
u = −0.378627 − 0.497963I
a = 0.36207 − 1.47520I
b = −0.55003 − 1.38741I
−2.62165 + 3.78828I −7.5138 − 12.3973I
u = −0.214548 + 0.558917I
a = −1.15528 + 2.43443I
b = 0.021877 + 0.744451I
−1.31227 − 1.35935I −5.28068 + 4.63416I
u = −0.214548 − 0.558917I
a = −1.15528 − 2.43443I
b = 0.021877 − 0.744451I
−1.31227 + 1.35935I −5.28068 − 4.63416I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232241 + 0.550466I
a = −0.229573 − 1.365780I
b = 0.53215 − 1.35587I
−4.60632 + 2.57396I −14.4639 − 9.6502I
u = 0.232241 − 0.550466I
a = −0.229573 + 1.365780I
b = 0.53215 + 1.35587I
−4.60632 − 2.57396I −14.4639 + 9.6502I
u = 0.035331 + 0.546911I
a = −3.02113 + 2.09727I
b = −0.278145 + 0.620196I
−1.42339 − 1.14206I −7.64564 + 4.36852I
u = 0.035331 − 0.546911I
a = −3.02113 − 2.09727I
b = −0.278145 − 0.620196I
−1.42339 + 1.14206I −7.64564 − 4.36852I
u = −0.084299 + 0.536575I
a = 0.197726 + 0.218088I
b = 1.46733 + 0.55222I
−5.71064 − 0.88851I −19.3340 + 4.3203I
u = −0.084299 − 0.536575I
a = 0.197726 − 0.218088I
b = 1.46733 − 0.55222I
−5.71064 + 0.88851I −19.3340 − 4.3203I
u = 0.98379 + 1.07460I
a = −0.0372116 − 0.1123680I
b = −1.281980 + 0.428483I
−6.81481 + 9.66907I 0
u = 0.98379 − 1.07460I
a = −0.0372116 + 0.1123680I
b = −1.281980 − 0.428483I
−6.81481 − 9.66907I 0
u = −1.43299 + 0.26730I
a = 0.144509 − 0.036331I
b = −0.127147 − 0.930225I
−1.031500 − 0.354146I 0
u = −1.43299 − 0.26730I
a = 0.144509 + 0.036331I
b = −0.127147 + 0.930225I
−1.031500 + 0.354146I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.410100 + 0.311510I
a = −7.00348 + 3.46773I
b = 0.307554 + 0.337684I
−3.57140 − 0.57623I −2.3848 − 22.6336I
u = 0.410100 − 0.311510I
a = −7.00348 − 3.46773I
b = 0.307554 − 0.337684I
−3.57140 + 0.57623I −2.3848 + 22.6336I
u = −0.95336 + 1.14595I
a = 0.310856 − 0.085089I
b = −1.038550 − 0.330627I
−2.29132 − 4.25686I 0
u = −0.95336 − 1.14595I
a = 0.310856 + 0.085089I
b = −1.038550 + 0.330627I
−2.29132 + 4.25686I 0
u = 1.27141 + 0.80457I
a = −0.808425 + 1.120290I
b = 0.141043 + 0.976339I
−4.54539 + 0.34097I 0
u = 1.27141 − 0.80457I
a = −0.808425 − 1.120290I
b = 0.141043 − 0.976339I
−4.54539 − 0.34097I 0
u = 0.375079 + 0.308494I
a = 1.93835 − 0.93583I
b = −0.483446 − 0.898105I
−0.04861 + 2.05474I −0.05845 − 2.58157I
u = 0.375079 − 0.308494I
a = 1.93835 + 0.93583I
b = −0.483446 + 0.898105I
−0.04861 − 2.05474I −0.05845 + 2.58157I
u = 1.07563 + 1.06925I
a = −0.71329 + 1.38663I
b = 0.554582 + 1.234190I
−3.85560 + 12.20440I 0
u = 1.07563 − 1.06925I
a = −0.71329 − 1.38663I
b = 0.554582 − 1.234190I
−3.85560 − 12.20440I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340640 + 0.213069I
a = −6.49139 + 4.25195I
b = −0.311768 − 0.896973I
−2.19246 + 1.77118I 13.6954 + 18.4226I
u = −0.340640 − 0.213069I
a = −6.49139 − 4.25195I
b = −0.311768 + 0.896973I
−2.19246 − 1.77118I 13.6954 − 18.4226I
u = 0.124910 + 0.377859I
a = −0.37983 + 1.61319I
b = 0.831063 − 0.230779I
−2.61258 + 0.40782I −2.91513 + 1.25335I
u = 0.124910 − 0.377859I
a = −0.37983 − 1.61319I
b = 0.831063 + 0.230779I
−2.61258 − 0.40782I −2.91513 − 1.25335I
u = 1.18478 + 1.08230I
a = 0.735003 − 0.565771I
b = −1.045740 − 0.098007I
−6.35450 − 1.85292I 0
u = 1.18478 − 1.08230I
a = 0.735003 + 0.565771I
b = −1.045740 + 0.098007I
−6.35450 + 1.85292I 0
u = −1.13576 + 1.14489I
a = −0.65087 − 1.28968I
b = 0.483907 − 1.062650I
0.43763 − 6.35749I 0
u = −1.13576 − 1.14489I
a = −0.65087 + 1.28968I
b = 0.483907 + 1.062650I
0.43763 + 6.35749I 0
u = 1.04219 + 1.27794I
a = 0.078842 − 1.121010I
b = 0.313191 − 1.037600I
−4.09299 − 4.00272I 0
u = 1.04219 − 1.27794I
a = 0.078842 + 1.121010I
b = 0.313191 + 1.037600I
−4.09299 + 4.00272I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18923 + 1.15866I
a = 0.751838 − 1.187430I
b = −0.74894 − 1.32485I
−9.7419 + 16.8559I 0
u = 1.18923 − 1.15866I
a = 0.751838 + 1.187430I
b = −0.74894 + 1.32485I
−9.7419 − 16.8559I 0
u = −0.321575
a = −13.9658
b = 0.869697
−4.26740 40.4800
u = −0.32809 + 1.70346I
a = 0.134157 − 1.015440I
b = −0.269373 − 1.279760I
−7.91168 − 0.39314I 0
u = −0.32809 − 1.70346I
a = 0.134157 + 1.015440I
b = −0.269373 + 1.279760I
−7.91168 + 0.39314I 0
u = −1.33473 + 1.32716I
a = 0.619234 + 1.017330I
b = −0.627257 + 1.263310I
−5.26918 − 10.31530I 0
u = −1.33473 − 1.32716I
a = 0.619234 − 1.017330I
b = −0.627257 − 1.263310I
−5.26918 + 10.31530I 0
u = 1.80582 + 0.79238I
a = 0.682403 − 0.591220I
b = −0.414392 − 1.329890I
−11.03720 + 3.15602I 0
u = 1.80582 − 0.79238I
a = 0.682403 + 0.591220I
b = −0.414392 + 1.329890I
−11.03720 − 3.15602I 0
u = 1.16409 + 1.64419I
a = −0.028085 + 0.784646I
b = −0.52176 + 1.31571I
−10.25460 − 7.45224I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16409 − 1.64419I
a = −0.028085 − 0.784646I
b = −0.52176 − 1.31571I
−10.25460 + 7.45224I 0
12
II. I
u
2
= hb, −u
5
+ 2u
4
+ u
3
− 3u
2
+ a + 2, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
u
5
− 2u
4
− u
3
+ 3u
2
− 2
0
a
8
=
1
−u
2
a
2
=
u
5
− 2u
4
− u
3
+ 3u
2
− 2
0
a
6
=
1
0
a
5
=
−u
2
+ 1
u
4
a
11
=
−u
5
+ 2u
3
− u
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
4
=
u
5
− 2u
4
− u
3
+ 2u
2
− 1
u
4
a
1
=
u
2
− 1
−u
4
a
9
=
−u
u
a
9
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
− 7u
4
− 4u
3
+ 11u
2
− 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
6
u
6
c
3
, c
4
(u + 1)
6
c
5
, c
10
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
7
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
8
, c
9
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y −1)
6
c
2
, c
6
y
6
c
5
, c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
7
, c
8
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.344968 + 0.764807I
b = 0
0.245672 − 0.924305I 1.12292 + 1.33143I
u = −1.002190 − 0.295542I
a = 0.344968 − 0.764807I
b = 0
0.245672 + 0.924305I 1.12292 − 1.33143I
u = 0.428243 + 0.664531I
a = −1.68613 + 1.92635I
b = 0
−3.53554 − 0.92430I −6.82874 + 7.13914I
u = 0.428243 − 0.664531I
a = −1.68613 − 1.92635I
b = 0
−3.53554 + 0.92430I −6.82874 − 7.13914I
u = 1.073950 + 0.558752I
a = −0.158836 − 0.437639I
b = 0
−1.64493 + 5.69302I −0.29418 − 2.69056I
u = 1.073950 − 0.558752I
a = −0.158836 + 0.437639I
b = 0
−1.64493 − 5.69302I −0.29418 + 2.69056I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
71
− 7u
70
+ ··· − 3u + 1)
c
2
, c
6
u
6
(u
71
− u
70
+ ··· + 320u + 64)
c
3
, c
4
((u + 1)
6
)(u
71
− 7u
70
+ ··· − 3u + 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
71
+ 6u
70
+ ··· + 2u + 1)
c
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
71
+ 12u
70
+ ··· − 2u − 1)
c
8
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
71
− 2u
70
+ ··· + 10u + 1)
c
9
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
71
− 2u
70
+ ··· + 35022u + 3953)
c
10
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
71
− 6u
70
+ ··· − 3424u + 319)
c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
71
− 2u
70
+ ··· + 10u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
((y −1)
6
)(y
71
− 67y
70
+ ··· − 45y −1)
c
2
, c
6
y
6
(y
71
+ 39y
70
+ ··· − 36864y −4096)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
71
+ 12y
70
+ ··· − 6y −1)
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
71
+ 72y
69
+ ··· − 10y −1)
c
8
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
71
− 48y
70
+ ··· − 10y −1)
c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
71
− 48y
70
+ ··· − 314283574y −15626209)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
71
− 72y
70
+ ··· + 3210942y −101761)
18
