12n
0563
(K12n
0563
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 2 10 4 1 5 9 4
Solving Sequence
4,11 5,9
12 1 3 8 10 6 7 2
c
4
c
11
c
12
c
3
c
8
c
10
c
5
c
7
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.39160 × 10
54
u
47
− 3.95222 × 10
54
u
46
+ ··· + 7.49953 × 10
54
b − 2.89856 × 10
55
,
1.44654 × 10
55
u
47
− 1.62245 × 10
55
u
46
+ ··· + 7.49953 × 10
54
a + 4.83415 × 10
55
, u
48
− u
47
+ ··· + 3u + 1i
I
u
2
= h−u
3
+ b − 2u, −u
12
− u
11
− 8u
10
− 7u
9
− 25u
8
− 17u
7
− 39u
6
− 17u
5
− 32u
4
− 6u
3
− 14u
2
+ a + u − 4,
u
13
+ 8u
11
+ 25u
9
− u
8
+ 40u
7
− 5u
6
+ 36u
5
− 8u
4
+ 18u
3
− 5u
2
+ 5u − 1i
* 2 irreducible components of dim
C
= 0, with total 61 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−2.39×10
54
u
47
−3.95×10
54
u
46
+· · ·+7.50×10
54
b−2.90×10
55
, 1.45×
10
55
u
47
−1.62×10
55
u
46
+· · ·+7.50×10
54
a+4.83×10
55
, u
48
−u
47
+· · ·+3u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
−1.92884u
47
+ 2.16340u
46
+ ··· − 4.69127u − 6.44593
0.318900u
47
+ 0.526995u
46
+ ··· + 7.68737u + 3.86499
a
12
=
5.32722u
47
− 7.71278u
46
+ ··· + 5.69560u + 4.89101
−1.65263u
47
+ 2.15021u
46
+ ··· − 2.13909u + 0.429005
a
1
=
3.67459u
47
− 5.56258u
46
+ ··· + 3.55651u + 5.32002
−1.65263u
47
+ 2.15021u
46
+ ··· − 2.13909u + 0.429005
a
3
=
−0.429005u
47
− 1.22363u
46
+ ··· − 12.6538u − 3.42610
−0.741759u
47
+ 0.279846u
46
+ ··· − 3.69494u + 0.760160
a
8
=
−1.60994u
47
+ 2.69040u
46
+ ··· + 2.99610u − 2.58094
0.318900u
47
+ 0.526995u
46
+ ··· + 7.68737u + 3.86499
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−1.84566u
47
+ 2.55030u
46
+ ··· − 1.55830u − 4.58260
0.553995u
47
+ 0.491959u
46
+ ··· + 10.8786u + 5.49084
a
2
=
1.85623u
47
− 3.48934u
46
+ ··· − 4.22125u + 2.81550
−0.399504u
47
− 1.07854u
46
+ ··· − 11.0873u − 2.93213
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7.73136u
47
− 12.6807u
46
+ ··· − 1.90430u + 10.9470
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 14u
47
+ ··· + 1783u + 121
c
2
, c
6
u
48
− 2u
47
+ ··· − 21u − 11
c
3
, c
8
u
48
− u
47
+ ··· + 56u − 1
c
4
, c
5
, c
10
u
48
− u
47
+ ··· + 3u + 1
c
7
u
48
− 8u
47
+ ··· − 28403u + 7979
c
9
u
48
+ 4u
47
+ ··· − 231u − 49
c
11
u
48
− 2u
47
+ ··· + 2483u − 169
c
12
u
48
+ 5u
47
+ ··· + 2615u + 313
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 46y
47
+ ··· + 485517y + 14641
c
2
, c
6
y
48
− 14y
47
+ ··· − 1783y + 121
c
3
, c
8
y
48
+ 55y
47
+ ··· − 3490y + 1
c
4
, c
5
, c
10
y
48
+ 35y
47
+ ··· − y + 1
c
7
y
48
+ 46y
47
+ ··· + 1653354871y + 63664441
c
9
y
48
+ 2y
47
+ ··· + 7105y + 2401
c
11
y
48
+ 58y
47
+ ··· − 2857283y + 28561
c
12
y
48
− 69y
47
+ ··· − 5964955y + 97969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435520 + 0.942072I
a = −1.076810 − 0.546005I
b = −0.075623 − 0.253208I
0.84017 + 1.53001I −4.48166 − 1.67187I
u = −0.435520 − 0.942072I
a = −1.076810 + 0.546005I
b = −0.075623 + 0.253208I
0.84017 − 1.53001I −4.48166 + 1.67187I
u = −0.154361 + 1.095650I
a = 0.750842 − 0.363346I
b = 0.920518 − 0.093530I
−4.71668 − 2.11923I −10.82328 + 3.73003I
u = −0.154361 − 1.095650I
a = 0.750842 + 0.363346I
b = 0.920518 + 0.093530I
−4.71668 + 2.11923I −10.82328 − 3.73003I
u = 0.443963 + 1.034950I
a = −0.551533 − 0.438377I
b = −1.052700 + 0.633094I
1.19625 + 2.65861I −4.00000 − 4.52024I
u = 0.443963 − 1.034950I
a = −0.551533 + 0.438377I
b = −1.052700 − 0.633094I
1.19625 − 2.65861I −4.00000 + 4.52024I
u = −0.376782 + 0.764505I
a = −1.67330 + 2.06393I
b = −0.050763 − 1.300670I
4.54023 − 1.72963I 4.64800 + 3.11123I
u = −0.376782 − 0.764505I
a = −1.67330 − 2.06393I
b = −0.050763 + 1.300670I
4.54023 + 1.72963I 4.64800 − 3.11123I
u = 0.625304 + 0.996638I
a = −0.815699 − 0.738147I
b = −0.21810 + 1.41293I
1.47522 + 0.81061I 0
u = 0.625304 − 0.996638I
a = −0.815699 + 0.738147I
b = −0.21810 − 1.41293I
1.47522 − 0.81061I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.179960 + 0.123958I
a = −0.19080 + 1.69727I
b = 0.16078 − 1.62361I
11.96410 + 1.32500I 0
u = −1.179960 − 0.123958I
a = −0.19080 − 1.69727I
b = 0.16078 + 1.62361I
11.96410 − 1.32500I 0
u = −0.269250 + 1.162830I
a = 0.839939 − 0.658536I
b = 0.20024 + 1.60053I
1.26689 − 2.36269I 0
u = −0.269250 − 1.162830I
a = 0.839939 + 0.658536I
b = 0.20024 − 1.60053I
1.26689 + 2.36269I 0
u = −0.427605 + 1.128960I
a = 0.534297 − 0.374229I
b = 1.308210 + 0.533677I
0.10991 − 8.23975I 0
u = −0.427605 − 1.128960I
a = 0.534297 + 0.374229I
b = 1.308210 − 0.533677I
0.10991 + 8.23975I 0
u = 0.352885 + 1.172480I
a = 1.53487 + 0.77490I
b = 0.397307 − 1.278340I
−0.92113 + 6.80242I 0
u = 0.352885 − 1.172480I
a = 1.53487 − 0.77490I
b = 0.397307 + 1.278340I
−0.92113 − 6.80242I 0
u = 1.226860 + 0.007840I
a = 0.12427 + 1.63006I
b = −0.18772 − 1.63918I
11.45140 − 7.76917I 0
u = 1.226860 − 0.007840I
a = 0.12427 − 1.63006I
b = −0.18772 + 1.63918I
11.45140 + 7.76917I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376298 + 1.187320I
a = 0.913505 − 0.477894I
b = 0.057189 − 0.405233I
0.12397 + 4.49470I 0
u = 0.376298 − 1.187320I
a = 0.913505 + 0.477894I
b = 0.057189 + 0.405233I
0.12397 − 4.49470I 0
u = 0.580032 + 0.452436I
a = −0.92293 − 1.44096I
b = −0.33652 + 1.50463I
2.95847 + 4.00692I −2.67836 − 6.96933I
u = 0.580032 − 0.452436I
a = −0.92293 + 1.44096I
b = −0.33652 − 1.50463I
2.95847 − 4.00692I −2.67836 + 6.96933I
u = −0.151969 + 0.640678I
a = 1.79473 + 2.00434I
b = −0.128016 − 1.103990I
2.23261 − 4.69663I −2.29866 + 7.37362I
u = −0.151969 − 0.640678I
a = 1.79473 − 2.00434I
b = −0.128016 + 1.103990I
2.23261 + 4.69663I −2.29866 − 7.37362I
u = −0.024639 + 0.631913I
a = 1.292480 − 0.327555I
b = 0.44857 + 1.55247I
3.50058 + 0.55008I −1.118536 − 0.349377I
u = −0.024639 − 0.631913I
a = 1.292480 + 0.327555I
b = 0.44857 − 1.55247I
3.50058 − 0.55008I −1.118536 + 0.349377I
u = 0.219879 + 0.581123I
a = −0.507645 − 0.541214I
b = −0.194376 + 0.350188I
−0.254703 + 1.031080I −4.07316 − 6.58896I
u = 0.219879 − 0.581123I
a = −0.507645 + 0.541214I
b = −0.194376 − 0.350188I
−0.254703 − 1.031080I −4.07316 + 6.58896I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.65049 + 1.32174I
a = −0.96287 + 1.04566I
b = −0.36043 − 1.58899I
8.28567 − 7.72804I 0
u = −0.65049 − 1.32174I
a = −0.96287 − 1.04566I
b = −0.36043 + 1.58899I
8.28567 + 7.72804I 0
u = −0.08747 + 1.49239I
a = 0.207043 + 0.731169I
b = −0.048453 − 0.802768I
−7.65194 − 1.77181I 0
u = −0.08747 − 1.49239I
a = 0.207043 − 0.731169I
b = −0.048453 + 0.802768I
−7.65194 + 1.77181I 0
u = 0.498135 + 0.056251I
a = −1.178220 + 0.256245I
b = 0.343725 + 0.931868I
3.49281 + 1.01877I 0.423557 − 0.776578I
u = 0.498135 − 0.056251I
a = −1.178220 − 0.256245I
b = 0.343725 − 0.931868I
3.49281 − 1.01877I 0.423557 + 0.776578I
u = 0.62518 + 1.40469I
a = 0.905325 + 0.965225I
b = 0.41416 − 1.62727I
7.1315 + 14.2674I 0
u = 0.62518 − 1.40469I
a = 0.905325 − 0.965225I
b = 0.41416 + 1.62727I
7.1315 − 14.2674I 0
u = −0.382314 + 0.212503I
a = 0.083866 + 0.833170I
b = −0.701403 + 1.054330I
2.71637 + 4.57604I −0.11105 − 6.10786I
u = −0.382314 − 0.212503I
a = 0.083866 − 0.833170I
b = −0.701403 − 1.054330I
2.71637 − 4.57604I −0.11105 + 6.10786I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426711
a = 0.214040
b = −0.725860
−1.65788 −3.70660
u = −0.404609
a = −2.82616
b = 0.0167904
−2.55057 7.13390
u = 0.66628 + 1.45057I
a = −0.816215 − 0.730920I
b = −0.03431 + 1.50514I
6.99328 − 1.08384I 0
u = 0.66628 − 1.45057I
a = −0.816215 + 0.730920I
b = −0.03431 − 1.50514I
6.99328 + 1.08384I 0
u = −0.57241 + 1.49585I
a = 0.805241 − 0.729040I
b = 0.03707 + 1.53975I
6.90676 − 4.94555I 0
u = −0.57241 − 1.49585I
a = 0.805241 + 0.729040I
b = 0.03707 − 1.53975I
6.90676 + 4.94555I 0
u = 0.01361 + 1.60580I
a = 0.215681 + 0.206965I
b = −0.044827 − 0.676036I
−8.07717 + 1.45463I 0
u = 0.01361 − 1.60580I
a = 0.215681 − 0.206965I
b = −0.044827 + 0.676036I
−8.07717 − 1.45463I 0
9
II. I
u
2
= h−u
3
+ b − 2u, −u
12
− u
11
+ · · · + a − 4, u
13
+ 8u
11
+ · · · + 5u − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
u
12
+ u
11
+ ··· − u + 4
u
3
+ 2u
a
12
=
−u
12
− u
11
+ ··· − 3u − 3
u
11
+ 7u
9
+ 18u
7
− u
6
+ 22u
5
− 4u
4
+ 14u
3
− 4u
2
+ 4u − 1
a
1
=
−u
12
− 8u
10
+ ··· + u − 4
u
11
+ 7u
9
+ 18u
7
− u
6
+ 22u
5
− 4u
4
+ 14u
3
− 4u
2
+ 4u − 1
a
3
=
−u
12
− 7u
10
− 18u
8
+ u
7
− 22u
6
+ 4u
5
− 14u
4
+ 4u
3
− 4u
2
+ u − 1
−u
6
− 4u
4
− 4u
2
a
8
=
u
12
+ u
11
+ ··· + u + 4
u
3
+ 2u
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
12
+ u
11
+ ··· + 2u + 4
−u
9
− 5u
7
− 8u
5
− 4u
3
+ u
a
2
=
−u
12
− 8u
10
− 25u
8
+ u
7
− 40u
6
+ 5u
5
− 36u
4
+ 7u
3
− 18u
2
+ 3u − 5
−u
11
− 7u
9
− 18u
7
− 21u
5
− 11u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
11
− 5u
10
− 15u
9
− 30u
8
− 42u
7
− 65u
6
− 51u
5
− 68u
4
− 23u
3
− 38u
2
− 2u − 16
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 5u
12
+ ··· + 5u − 1
c
2
u
13
− u
12
+ ··· + u − 1
c
3
u
13
+ 8u
11
+ ··· + 2u − 3
c
4
, c
5
u
13
+ 8u
11
+ ··· + 5u − 1
c
6
u
13
+ u
12
+ ··· + u + 1
c
7
u
13
+ 3u
12
+ ··· − 3u − 1
c
8
u
13
+ 8u
11
+ ··· + 2u + 3
c
9
u
13
+ 3u
12
− 4u
10
+ 2u
9
+ u
8
− 4u
7
+ 3u
6
− u
5
− 2u
4
+ 2u
3
− 2u
2
+ u − 1
c
10
u
13
+ 8u
11
+ ··· + 5u + 1
c
11
u
13
+ u
12
+ ··· − 3u + 1
c
12
u
13
− 2u
11
+ 3u
10
+ 3u
9
+ u
8
+ 10u
7
+ 2u
6
− 4u
5
+ 5u
4
− 2u
3
+ 5u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 11y
12
+ ··· − 7y − 1
c
2
, c
6
y
13
− 5y
12
+ ··· + 5y − 1
c
3
, c
8
y
13
+ 16y
12
+ ··· − 20y − 9
c
4
, c
5
, c
10
y
13
+ 16y
12
+ ··· + 15y − 1
c
7
y
13
− y
12
+ ··· + 3y − 1
c
9
y
13
− 9y
12
+ ··· − 3y − 1
c
11
y
13
+ 3y
12
+ ··· + 9y − 1
c
12
y
13
− 4y
12
+ ··· + 25y − 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.406397 + 0.828070I
a = 0.623860 − 1.154070I
b = −0.04391 + 1.49862I
3.19757 − 2.07962I −2.23765 + 3.84644I
u = −0.406397 − 0.828070I
a = 0.623860 + 1.154070I
b = −0.04391 − 1.49862I
3.19757 + 2.07962I −2.23765 − 3.84644I
u = −0.405399 + 1.034180I
a = 0.943206 − 0.498481I
b = 0.42334 + 1.47217I
2.52863 − 1.04333I −0.891974 + 0.899946I
u = −0.405399 − 1.034180I
a = 0.943206 + 0.498481I
b = 0.42334 − 1.47217I
2.52863 + 1.04333I −0.891974 − 0.899946I
u = 0.276046 + 1.147950I
a = −1.238510 + 0.159643I
b = −0.518180 + 1.045570I
0.33288 + 6.03810I −3.21578 − 6.43497I
u = 0.276046 − 1.147950I
a = −1.238510 − 0.159643I
b = −0.518180 − 1.045570I
0.33288 − 6.03810I −3.21578 + 6.43497I
u = 0.351249 + 0.612687I
a = −0.00263 − 1.64078I
b = 0.350273 + 1.222150I
2.13932 − 3.61205I −3.50656 + 0.16807I
u = 0.351249 − 0.612687I
a = −0.00263 + 1.64078I
b = 0.350273 − 1.222150I
2.13932 + 3.61205I −3.50656 − 0.16807I
u = 0.05874 + 1.54134I
a = −0.078914 + 0.461676I
b = −0.300983 − 0.563189I
−8.64883 + 1.03612I −15.2263 + 1.7097I
u = 0.05874 − 1.54134I
a = −0.078914 − 0.461676I
b = −0.300983 + 0.563189I
−8.64883 − 1.03612I −15.2263 − 1.7097I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02035 + 1.65258I
a = −0.017867 + 0.348906I
b = −0.126034 − 1.206020I
−6.33652 − 2.53081I −3.17775 + 4.10072I
u = 0.02035 − 1.65258I
a = −0.017867 − 0.348906I
b = −0.126034 + 1.206020I
−6.33652 + 2.53081I −3.17775 − 4.10072I
u = 0.210812
a = 4.54171
b = 0.430994
−2.87546 −18.4880
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 5u
12
+ ··· + 5u − 1)(u
48
+ 14u
47
+ ··· + 1783u + 121)
c
2
(u
13
− u
12
+ ··· + u − 1)(u
48
− 2u
47
+ ··· − 21u − 11)
c
3
(u
13
+ 8u
11
+ ··· + 2u − 3)(u
48
− u
47
+ ··· + 56u − 1)
c
4
, c
5
(u
13
+ 8u
11
+ ··· + 5u − 1)(u
48
− u
47
+ ··· + 3u + 1)
c
6
(u
13
+ u
12
+ ··· + u + 1)(u
48
− 2u
47
+ ··· − 21u − 11)
c
7
(u
13
+ 3u
12
+ ··· − 3u − 1)(u
48
− 8u
47
+ ··· − 28403u + 7979)
c
8
(u
13
+ 8u
11
+ ··· + 2u + 3)(u
48
− u
47
+ ··· + 56u − 1)
c
9
(u
13
+ 3u
12
− 4u
10
+ 2u
9
+ u
8
− 4u
7
+ 3u
6
− u
5
− 2u
4
+ 2u
3
− 2u
2
+ u − 1)
· (u
48
+ 4u
47
+ ··· − 231u − 49)
c
10
(u
13
+ 8u
11
+ ··· + 5u + 1)(u
48
− u
47
+ ··· + 3u + 1)
c
11
(u
13
+ u
12
+ ··· − 3u + 1)(u
48
− 2u
47
+ ··· + 2483u − 169)
c
12
(u
13
− 2u
11
+ 3u
10
+ 3u
9
+ u
8
+ 10u
7
+ 2u
6
− 4u
5
+ 5u
4
− 2u
3
+ 5u − 1)
· (u
48
+ 5u
47
+ ··· + 2615u + 313)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
+ 11y
12
+ ··· − 7y − 1)(y
48
+ 46y
47
+ ··· + 485517y + 14641)
c
2
, c
6
(y
13
− 5y
12
+ ··· + 5y − 1)(y
48
− 14y
47
+ ··· − 1783y + 121)
c
3
, c
8
(y
13
+ 16y
12
+ ··· − 20y − 9)(y
48
+ 55y
47
+ ··· − 3490y + 1)
c
4
, c
5
, c
10
(y
13
+ 16y
12
+ ··· + 15y − 1)(y
48
+ 35y
47
+ ··· − y + 1)
c
7
(y
13
− y
12
+ ··· + 3y − 1)
· (y
48
+ 46y
47
+ ··· + 1653354871y + 63664441)
c
9
(y
13
− 9y
12
+ ··· − 3y − 1)(y
48
+ 2y
47
+ ··· + 7105y + 2401)
c
11
(y
13
+ 3y
12
+ ··· + 9y − 1)(y
48
+ 58y
47
+ ··· − 2857283y + 28561)
c
12
(y
13
− 4y
12
+ ··· + 25y − 1)(y
48
− 69y
47
+ ··· − 5964955y + 97969)
16
