12n
0335
(K12n
0335
)
A knot diagram
1
Linearized knot diagam
3 5 8 11 2 4 3 7 12 1 4 10
Solving Sequence
3,5
2 6
1,11
4 7 8 9 10 12
c
2
c
5
c
1
c
4
c
6
c
7
c
8
c
10
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.35069 × 10
64
u
54
+ 3.81695 × 10
64
u
53
+ ··· + 1.37855 × 10
64
b + 9.95905 × 10
64
,
− 5.59560 × 10
64
u
54
+ 1.78086 × 10
65
u
53
+ ··· + 4.13566 × 10
64
a + 2.40656 × 10
66
,
u
55
− 3u
54
+ ··· − 180u + 36i
I
u
2
= h−bau + b
2
− 2ba + bu − au + 2b + 2u, a
2
− a − 1, u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 63 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−1.35 × 10
64
u
54
+ 3.82 × 10
64
u
53
+ · · · + 1.38 × 10
64
b + 9.96 ×
10
64
, −5.60 × 10
64
u
54
+ 1.78 × 10
65
u
53
+ · · · + 4.14 × 10
64
a + 2.41 ×
10
66
, u
55
− 3u
54
+ · · · − 180u + 36i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
1.35301u
54
− 4.30610u
53
+ ··· + 353.805u − 58.1904
0.979787u
54
− 2.76881u
53
+ ··· + 110.400u − 7.22427
a
4
=
1.20076u
54
− 2.20679u
53
+ ··· − 306.550u + 94.2856
0.569068u
54
− 0.988169u
53
+ ··· − 149.680u + 43.2863
a
7
=
2.77967u
54
− 6.78822u
53
+ ··· − 70.9703u + 69.9144
0.436392u
54
− 0.768297u
53
+ ··· − 104.002u + 31.7186
a
8
=
2.34328u
54
− 6.01992u
53
+ ··· + 33.0317u + 38.1958
0.436392u
54
− 0.768297u
53
+ ··· − 104.002u + 31.7186
a
9
=
2.64631u
54
− 8.83637u
53
+ ··· + 788.120u − 127.191
0.0484147u
54
− 0.320036u
53
+ ··· + 86.8216u − 17.2120
a
10
=
2.08439u
54
− 6.60302u
53
+ ··· + 525.581u − 84.0141
0.459586u
54
− 1.41002u
53
+ ··· + 83.1692u − 10.7895
a
12
=
−2.48557u
54
+ 8.51354u
53
+ ··· − 805.408u + 134.995
−0.122323u
54
+ 0.796684u
53
+ ··· − 177.994u + 38.7845
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.07522u
54
− 3.77605u
53
+ ··· − 430.874u + 130.101
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 23u
54
+ ··· − 2664u − 1296
c
2
, c
5
u
55
+ 3u
54
+ ··· − 180u − 36
c
3
, c
7
u
55
+ 3u
54
+ ··· + 2u
2
− 9
c
4
, c
11
u
55
− u
54
+ ··· − 4u + 1
c
6
u
55
+ 9u
54
+ ··· + 711666u − 322299
c
8
u
55
+ 17u
54
+ ··· + 36u + 81
c
9
, c
10
, c
12
u
55
− 5u
54
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
+ 27y
54
+ ··· + 195397920y −1679616
c
2
, c
5
y
55
+ 23y
54
+ ··· − 2664y −1296
c
3
, c
7
y
55
− 17y
54
+ ··· + 36y −81
c
4
, c
11
y
55
+ 15y
54
+ ··· + 20y −1
c
6
y
55
− 77y
54
+ ··· + 1247977937268y −103876645401
c
8
y
55
+ 47y
54
+ ··· + 545940y −6561
c
9
, c
10
, c
12
y
55
− 45y
54
+ ··· − 76y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059953 + 1.012980I
a = 0.039284 + 0.228627I
b = 3.38648 − 7.92146I
−3.35243 + 2.03755I 55.1037 + 12.6479I
u = −0.059953 − 1.012980I
a = 0.039284 − 0.228627I
b = 3.38648 + 7.92146I
−3.35243 − 2.03755I 55.1037 − 12.6479I
u = 0.503627 + 0.897107I
a = 0.934263 − 0.027824I
b = 1.02333 + 1.27124I
−2.25554 + 4.57545I −5.65078 − 7.74410I
u = 0.503627 − 0.897107I
a = 0.934263 + 0.027824I
b = 1.02333 − 1.27124I
−2.25554 − 4.57545I −5.65078 + 7.74410I
u = −0.749649 + 0.722966I
a = −1.365230 + 0.185901I
b = −1.50650 + 0.41105I
1.75202 + 1.88837I −2.61590 − 0.91978I
u = −0.749649 − 0.722966I
a = −1.365230 − 0.185901I
b = −1.50650 − 0.41105I
1.75202 − 1.88837I −2.61590 + 0.91978I
u = −0.364761 + 0.993866I
a = 0.008868 + 0.879146I
b = 1.02933 − 1.07956I
−4.91412 − 2.97553I −9.62258 + 3.34712I
u = −0.364761 − 0.993866I
a = 0.008868 − 0.879146I
b = 1.02933 + 1.07956I
−4.91412 + 2.97553I −9.62258 − 3.34712I
u = 0.258557 + 1.030090I
a = −0.830582 − 0.163972I
b = −1.38989 − 0.45028I
−3.67536 + 0.88537I −11.38095 + 0.I
u = 0.258557 − 1.030090I
a = −0.830582 + 0.163972I
b = −1.38989 + 0.45028I
−3.67536 − 0.88537I −11.38095 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718519 + 0.847961I
a = −1.296050 − 0.245653I
b = −1.49635 − 0.46822I
1.59469 + 3.95590I 0. − 4.38344I
u = 0.718519 − 0.847961I
a = −1.296050 + 0.245653I
b = −1.49635 + 0.46822I
1.59469 − 3.95590I 0. + 4.38344I
u = 0.177488 + 1.115120I
a = 1.338900 + 0.369569I
b = 0.511338 + 0.177719I
−11.38140 − 0.95537I −13.23793 + 0.I
u = 0.177488 − 1.115120I
a = 1.338900 − 0.369569I
b = 0.511338 − 0.177719I
−11.38140 + 0.95537I −13.23793 + 0.I
u = 0.715954 + 0.884530I
a = −0.021837 − 1.295710I
b = 0.555987 + 0.117408I
1.48173 + 1.52459I 0
u = 0.715954 − 0.884530I
a = −0.021837 + 1.295710I
b = 0.555987 − 0.117408I
1.48173 − 1.52459I 0
u = −0.629070 + 0.579280I
a = 0.899218 + 0.140744I
b = 0.684898 − 0.590344I
0.99052 − 1.29254I 2.78379 + 2.92308I
u = −0.629070 − 0.579280I
a = 0.899218 − 0.140744I
b = 0.684898 + 0.590344I
0.99052 + 1.29254I 2.78379 − 2.92308I
u = 0.962772 + 0.634354I
a = −0.348395 + 1.141660I
b = −0.848577 + 0.156761I
6.13413 − 3.62958I 0
u = 0.962772 − 0.634354I
a = −0.348395 − 1.141660I
b = −0.848577 − 0.156761I
6.13413 + 3.62958I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.072657 + 1.156240I
a = −0.250058 − 0.246628I
b = −0.995895 − 0.128359I
−1.49791 − 2.22374I 0
u = −0.072657 − 1.156240I
a = −0.250058 + 0.246628I
b = −0.995895 + 0.128359I
−1.49791 + 2.22374I 0
u = −0.937527 + 0.741922I
a = −0.383327 − 1.039020I
b = −0.900494 − 0.104724I
6.37472 − 2.61690I 0
u = −0.937527 − 0.741922I
a = −0.383327 + 1.039020I
b = −0.900494 + 0.104724I
6.37472 + 2.61690I 0
u = 1.152520 + 0.350922I
a = 0.578184 − 0.918755I
b = 1.052210 − 0.449986I
2.57652 − 8.84046I 0
u = 1.152520 − 0.350922I
a = 0.578184 + 0.918755I
b = 1.052210 + 0.449986I
2.57652 + 8.84046I 0
u = −0.701046 + 0.984062I
a = 0.061127 + 1.262660I
b = 0.749098 − 0.104477I
0.95535 − 7.42151I 0
u = −0.701046 − 0.984062I
a = 0.061127 − 1.262660I
b = 0.749098 + 0.104477I
0.95535 + 7.42151I 0
u = −1.159080 + 0.396377I
a = 0.586340 + 0.734811I
b = 0.989615 + 0.342386I
3.69536 + 2.42722I 0
u = −1.159080 − 0.396377I
a = 0.586340 − 0.734811I
b = 0.989615 − 0.342386I
3.69536 − 2.42722I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203618 + 0.681460I
a = −0.591078 − 0.840978I
b = −0.472677 + 0.984550I
−2.07887 + 0.90467I −6.07000 + 0.56339I
u = 0.203618 − 0.681460I
a = −0.591078 + 0.840978I
b = −0.472677 − 0.984550I
−2.07887 − 0.90467I −6.07000 − 0.56339I
u = 0.110493 + 0.692074I
a = 0.739047 − 0.175124I
b = −0.665968 + 0.952652I
−1.59698 − 1.61659I −1.44406 − 0.65784I
u = 0.110493 − 0.692074I
a = 0.739047 + 0.175124I
b = −0.665968 − 0.952652I
−1.59698 + 1.61659I −1.44406 + 0.65784I
u = −0.801899 + 1.028120I
a = 1.117420 + 0.073109I
b = 1.48706 − 0.77147I
5.47096 − 3.75621I 0
u = −0.801899 − 1.028120I
a = 1.117420 − 0.073109I
b = 1.48706 + 0.77147I
5.47096 + 3.75621I 0
u = 0.763372 + 1.097560I
a = 1.130030 − 0.021844I
b = 1.57911 + 0.85143I
4.68957 + 9.94524I 0
u = 0.763372 − 1.097560I
a = 1.130030 + 0.021844I
b = 1.57911 − 0.85143I
4.68957 − 9.94524I 0
u = 0.132026 + 0.646971I
a = 2.61608 + 0.55117I
b = 0.941369 + 0.117297I
−9.42726 + 2.36390I −1.16452 − 4.84130I
u = 0.132026 − 0.646971I
a = 2.61608 − 0.55117I
b = 0.941369 − 0.117297I
−9.42726 − 2.36390I −1.16452 + 4.84130I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.738573 + 1.127370I
a = −0.861984 − 0.010078I
b = −0.82426 − 1.30675I
−6.84994 + 8.00995I 0
u = 0.738573 − 1.127370I
a = −0.861984 + 0.010078I
b = −0.82426 + 1.30675I
−6.84994 − 8.00995I 0
u = 1.085430 + 0.809644I
a = −0.259628 − 0.401649I
b = 0.278041 − 0.746527I
−5.33599 − 1.38467I 0
u = 1.085430 − 0.809644I
a = −0.259628 + 0.401649I
b = 0.278041 + 0.746527I
−5.33599 + 1.38467I 0
u = 0.71206 + 1.27104I
a = −1.045930 + 0.191194I
b = −1.50069 − 1.14574I
−0.2861 + 15.4592I 0
u = 0.71206 − 1.27104I
a = −1.045930 − 0.191194I
b = −1.50069 + 1.14574I
−0.2861 − 15.4592I 0
u = −0.74916 + 1.25256I
a = −0.978931 − 0.217150I
b = −1.36649 + 1.02579I
1.06335 − 9.19388I 0
u = −0.74916 − 1.25256I
a = −0.978931 + 0.217150I
b = −1.36649 − 1.02579I
1.06335 + 9.19388I 0
u = −0.87172 + 1.17361I
a = −0.522134 − 0.089230I
b = −0.540213 + 0.695522I
−1.56919 − 4.20311I 0
u = −0.87172 − 1.17361I
a = −0.522134 + 0.089230I
b = −0.540213 − 0.695522I
−1.56919 + 4.20311I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.422680
a = −1.62609
b = −1.25011
−2.48655 −1.11980
u = 0.383224 + 0.053506I
a = 0.13292 + 2.07512I
b = −0.541303 − 0.058971I
−0.85477 − 1.49574I −2.42286 + 5.05757I
u = 0.383224 − 0.053506I
a = 0.13292 − 2.07512I
b = −0.541303 + 0.058971I
−0.85477 + 1.49574I −2.42286 − 5.05757I
u = 0.18963 + 1.71301I
a = 0.303194 + 0.184743I
b = −0.0935061 + 0.0909681I
−4.31137 − 3.46877I 0
u = 0.18963 − 1.71301I
a = 0.303194 − 0.184743I
b = −0.0935061 − 0.0909681I
−4.31137 + 3.46877I 0
10
II. I
u
2
= h−bau + b
2
− 2ba + bu − au + 2b + 2u, a
2
− a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−1
a
6
=
u
0
a
1
=
0
−1
a
11
=
a
b
a
4
=
−au − u
−bau + u
a
7
=
2bau + bu − au
−ba + u + 1
a
8
=
2bau + ba + bu − au − u − 1
−ba + u + 1
a
9
=
−a − 1
−ba + 1
a
10
=
a
b − a
a
12
=
−a − 1
−ba + a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4bau + 4u − 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
c
2
, c
5
(u
2
+ 1)
4
c
3
, c
6
, c
7
(u
4
− u
2
+ 1)
2
c
4
, c
11
(u
4
+ 3u
2
+ 1)
2
c
8
(u
2
+ u + 1)
4
c
9
, c
10
(u
2
+ u − 1)
4
c
12
(u
2
− u − 1)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
c
2
, c
5
(y + 1)
8
c
3
, c
6
, c
7
(y
2
− y + 1)
4
c
4
, c
11
(y
2
+ 3y + 1)
4
c
8
(y
2
+ y + 1)
4
c
9
, c
10
, c
12
(y
2
− 3y + 1)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.618034
b = −0.216775 − 0.809017I
−2.63189 − 2.02988I −10.00000 + 3.46410I
u = 1.000000I
a = −0.618034
b = −3.01929 − 0.80902I
−2.63189 + 2.02988I −10.00000 − 3.46410I
u = 1.000000I
a = 1.61803
b = 1.153270 + 0.309017I
−10.52760 + 2.02988I −10.00000 − 3.46410I
u = 1.000000I
a = 1.61803
b = 0.082801 + 0.309017I
−10.52760 − 2.02988I −10.00000 + 3.46410I
u = − 1.000000I
a = −0.618034
b = −0.216775 + 0.809017I
−2.63189 + 2.02988I −10.00000 − 3.46410I
u = − 1.000000I
a = −0.618034
b = −3.01929 + 0.80902I
−2.63189 − 2.02988I −10.00000 + 3.46410I
u = − 1.000000I
a = 1.61803
b = 1.153270 − 0.309017I
−10.52760 − 2.02988I −10.00000 + 3.46410I
u = − 1.000000I
a = 1.61803
b = 0.082801 − 0.309017I
−10.52760 + 2.02988I −10.00000 − 3.46410I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
55
+ 23u
54
+ ··· − 2664u − 1296)
c
2
, c
5
((u
2
+ 1)
4
)(u
55
+ 3u
54
+ ··· − 180u − 36)
c
3
, c
7
((u
4
− u
2
+ 1)
2
)(u
55
+ 3u
54
+ ··· + 2u
2
− 9)
c
4
, c
11
((u
4
+ 3u
2
+ 1)
2
)(u
55
− u
54
+ ··· − 4u + 1)
c
6
((u
4
− u
2
+ 1)
2
)(u
55
+ 9u
54
+ ··· + 711666u − 322299)
c
8
((u
2
+ u + 1)
4
)(u
55
+ 17u
54
+ ··· + 36u + 81)
c
9
, c
10
((u
2
+ u − 1)
4
)(u
55
− 5u
54
+ ··· + 4u + 1)
c
12
((u
2
− u − 1)
4
)(u
55
− 5u
54
+ ··· + 4u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
55
+ 27y
54
+ ··· + 1.95398 × 10
8
y −1679616)
c
2
, c
5
((y + 1)
8
)(y
55
+ 23y
54
+ ··· − 2664y −1296)
c
3
, c
7
((y
2
− y + 1)
4
)(y
55
− 17y
54
+ ··· + 36y −81)
c
4
, c
11
((y
2
+ 3y + 1)
4
)(y
55
+ 15y
54
+ ··· + 20y −1)
c
6
(y
2
− y + 1)
4
· (y
55
− 77y
54
+ ··· + 1247977937268y −103876645401)
c
8
((y
2
+ y + 1)
4
)(y
55
+ 47y
54
+ ··· + 545940y −6561)
c
9
, c
10
, c
12
((y
2
− 3y + 1)
4
)(y
55
− 45y
54
+ ··· − 76y −1)
16
