12n
0661
(K12n
0661
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 11 10 2 6 3 8 5 4
Solving Sequence
5,12
4
1,9
3 11 6 8 2 7 10
c
4
c
12
c
3
c
11
c
5
c
8
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.88753 × 10
16
u
26
− 7.56446 × 10
16
u
25
+ ··· + 3.81765 × 10
17
b − 2.36711 × 10
17
,
7.72254 × 10
17
u
26
+ 1.53152 × 10
18
u
25
+ ··· + 3.81765 × 10
17
a + 1.17596 × 10
19
, u
27
+ 2u
26
+ ··· + 13u + 1i
I
u
2
= h−u
12
+ u
11
− 8u
10
+ 7u
9
− 24u
8
+ 17u
7
− 33u
6
+ 15u
5
− 19u
4
− 2u
2
+ b − 4u,
u
12
− u
11
+ 8u
10
− 7u
9
+ 24u
8
− 17u
7
+ 33u
6
− 15u
5
+ 20u
4
− u
3
+ 5u
2
+ a + 2u + 2,
u
13
− u
12
+ 9u
11
− 8u
10
+ 31u
9
− 23u
8
+ 50u
7
− 26u
6
+ 36u
5
− 5u
4
+ 8u
3
+ 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 40 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−1.89 × 10
16
u
26
− 7.56 × 10
16
u
25
+ · · · + 3.82 × 10
17
b − 2.37 ×
10
17
, 7.72 × 10
17
u
26
+ 1.53 × 10
18
u
25
+ · · · + 3.82 × 10
17
a + 1.18 ×
10
19
, u
27
+ 2u
26
+ · · · + 13u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
1
=
u
u
3
+ u
a
9
=
−2.02285u
26
− 4.01168u
25
+ ··· + 52.8694u − 30.8031
0.0494422u
26
+ 0.198144u
25
+ ··· − 4.98870u + 0.620042
a
3
=
2.30870u
26
+ 4.40950u
25
+ ··· − 64.8476u + 32.0288
−0.147916u
26
− 0.156483u
25
+ ··· + 5.40884u − 0.571583
a
11
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
8
=
−1.84488u
26
− 3.63901u
25
+ ··· + 46.6032u − 30.4259
−0.0335197u
26
+ 0.124979u
25
+ ··· − 3.47040u + 0.729526
a
2
=
5.51519u
26
+ 10.4146u
25
+ ··· − 140.640u + 79.5005
−0.539565u
26
− 0.738431u
25
+ ··· + 12.0070u − 1.51404
a
7
=
6.44254u
26
+ 12.6459u
25
+ ··· − 163.824u + 94.6771
0.187806u
26
+ 0.130509u
25
+ ··· + 3.17687u − 2.60252
a
10
=
−4.41532u
26
− 8.66985u
25
+ ··· + 116.266u − 63.9888
−0.0901988u
26
− 0.0255952u
25
+ ··· + 1.47740u + 1.99746
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
512696248127693729
381765450474394411
u
26
−
1173688396623260553
381765450474394411
u
25
+ ··· +
23974986416882589793
381765450474394411
u −
7032162693009829437
381765450474394411
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 43u
26
+ ··· + 32307u + 14641
c
2
, c
7
u
27
+ u
26
+ ··· − 451u − 121
c
3
, c
9
u
27
− u
26
+ ··· + 57u + 173
c
4
, c
5
, c
11
c
12
u
27
+ 2u
26
+ ··· + 13u + 1
c
6
u
27
− 30u
25
+ ··· + 20449u − 8017
c
8
u
27
− 5u
26
+ ··· − 38u + 7
c
10
u
27
− 22u
25
+ ··· + 125u − 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 111y
26
+ ··· + 6730511623y −214358881
c
2
, c
7
y
27
− 43y
26
+ ··· + 32307y −14641
c
3
, c
9
y
27
− 11y
26
+ ··· + 147185y −29929
c
4
, c
5
, c
11
c
12
y
27
+ 38y
26
+ ··· + 237y −1
c
6
y
27
− 60y
26
+ ··· − 129367431y −64272289
c
8
y
27
− 7y
26
+ ··· + 1402y −49
c
10
y
27
− 44y
26
+ ··· − 965y −441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.038928 + 1.096540I
a = 0.339795 − 0.956003I
b = −0.047794 + 0.583517I
−1.18227 + 2.78711I −8.53482 − 4.99224I
u = 0.038928 − 1.096540I
a = 0.339795 + 0.956003I
b = −0.047794 − 0.583517I
−1.18227 − 2.78711I −8.53482 + 4.99224I
u = −0.060221 + 1.114710I
a = −0.818699 + 1.150860I
b = 0.00282 − 2.15523I
−11.46510 − 0.44076I −9.43738 − 0.19503I
u = −0.060221 − 1.114710I
a = −0.818699 − 1.150860I
b = 0.00282 + 2.15523I
−11.46510 + 0.44076I −9.43738 + 0.19503I
u = −1.18869
a = −0.494164
b = 0.786510
−9.76195 −9.69870
u = −0.319861 + 0.734406I
a = 1.137130 − 0.483412I
b = 0.082638 − 0.422987I
−2.86657 − 2.08543I −10.74476 + 3.06559I
u = −0.319861 − 0.734406I
a = 1.137130 + 0.483412I
b = 0.082638 + 0.422987I
−2.86657 + 2.08543I −10.74476 − 3.06559I
u = 0.374600 + 0.697774I
a = −0.765943 − 0.335826I
b = 0.067516 + 0.335617I
−0.19323 + 1.53182I −2.51900 − 3.03384I
u = 0.374600 − 0.697774I
a = −0.765943 + 0.335826I
b = 0.067516 − 0.335617I
−0.19323 − 1.53182I −2.51900 + 3.03384I
u = 0.445707 + 1.146890I
a = −0.198922 + 0.327688I
b = 0.275375 + 0.416461I
−0.824285 + 1.070290I −8.64760 + 1.85610I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.445707 − 1.146890I
a = −0.198922 − 0.327688I
b = 0.275375 − 0.416461I
−0.824285 − 1.070290I −8.64760 − 1.85610I
u = −0.803778 + 1.109510I
a = −0.585598 + 0.655588I
b = −0.0328420 − 0.1176830I
−13.1170 − 6.5745I −9.22636 + 4.44172I
u = −0.803778 − 1.109510I
a = −0.585598 − 0.655588I
b = −0.0328420 + 0.1176830I
−13.1170 + 6.5745I −9.22636 − 4.44172I
u = −0.11687 + 1.62312I
a = −1.64946 + 0.43051I
b = 3.21083 − 0.53420I
−11.01260 − 3.84052I −10.07314 + 2.86056I
u = −0.11687 − 1.62312I
a = −1.64946 − 0.43051I
b = 3.21083 + 0.53420I
−11.01260 + 3.84052I −10.07314 − 2.86056I
u = 0.11486 + 1.65386I
a = 1.306150 − 0.183873I
b = −2.63732 + 0.04241I
−8.53404 + 3.33702I −6.52566 + 0.I
u = 0.11486 − 1.65386I
a = 1.306150 + 0.183873I
b = −2.63732 − 0.04241I
−8.53404 − 3.33702I −6.52566 + 0.I
u = 0.314955 + 0.040141I
a = −1.52461 − 0.75675I
b = −0.092808 + 1.092340I
2.49846 + 1.59988I 3.26170 − 4.46285I
u = 0.314955 − 0.040141I
a = −1.52461 + 0.75675I
b = −0.092808 − 1.092340I
2.49846 − 1.59988I 3.26170 + 4.46285I
u = −0.291278
a = −0.909250
b = −0.503041
−0.940177 −10.5360
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02099 + 1.78831I
a = 1.199340 + 0.558142I
b = −2.31418 − 0.09316I
17.2683 − 0.8391I 0
u = −0.02099 − 1.78831I
a = 1.199340 − 0.558142I
b = −2.31418 + 0.09316I
17.2683 + 0.8391I 0
u = −0.23930 + 1.77241I
a = 1.50180 + 0.12267I
b = −2.92542 − 0.18853I
16.5332 − 10.9055I 0
u = −0.23930 − 1.77241I
a = 1.50180 − 0.12267I
b = −2.92542 + 0.18853I
16.5332 + 10.9055I 0
u = 0.04590 + 1.81690I
a = −1.197200 − 0.034284I
b = 2.33171 − 0.21126I
−12.44700 + 3.08894I 0
u = 0.04590 − 1.81690I
a = −1.197200 + 0.034284I
b = 2.33171 + 0.21126I
−12.44700 − 3.08894I 0
u = −0.0678774
a = −33.0841
b = 0.875475
−7.70070 −21.8510
7
II.
I
u
2
= h−u
12
+u
11
+· · ·+b−4u, u
12
−u
11
+· · ·+a+2, u
13
−u
12
+· · ·+6u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
1
=
u
u
3
+ u
a
9
=
−u
12
+ u
11
+ ··· − 2u − 2
u
12
− u
11
+ 8u
10
− 7u
9
+ 24u
8
− 17u
7
+ 33u
6
− 15u
5
+ 19u
4
+ 2u
2
+ 4u
a
3
=
u
12
− u
11
+ ··· + 9u
2
+ 4u
u
9
− u
8
+ 6u
7
− 5u
6
+ 12u
5
− 7u
4
+ 9u
3
+ u + 2
a
11
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
8
=
−u
12
+ u
11
+ ··· + u − 2
2u
12
− 2u
11
+ ··· + 2u
2
+ 5u
a
2
=
2u
12
− 3u
11
+ ··· + u − 1
u
11
+ 7u
9
+ 17u
7
+ u
6
+ 17u
5
+ 4u
4
+ 10u
3
+ 5u
2
+ 5u + 2
a
7
=
u
12
− u
11
+ ··· − 6u + 3
−u
12
− 6u
10
+ ··· − 2u − 1
a
10
=
−u
10
+ 2u
9
− 8u
8
+ 13u
7
− 24u
6
+ 29u
5
− 31u
4
+ 23u
3
− 13u
2
+ 3u
−u
12
+ 2u
11
+ ··· − 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
12
−4u
11
+ 19u
10
−31u
9
+ 70u
8
−87u
7
+ 119u
6
−101u
5
+ 82u
4
−37u
3
+ 7u
2
+ u −11
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 12u
12
+ ··· + 6u − 1
c
2
u
13
− 6u
11
+ ··· + 3u
2
− 1
c
3
u
13
+ 4u
11
+ u
10
+ 3u
9
+ 3u
8
− 3u
7
+ u
6
− u
5
− 5u
4
+ 2u
3
− 4u
2
− 1
c
4
, c
5
u
13
− u
12
+ ··· + 6u
2
+ 1
c
6
u
13
− u
12
+ ··· − 4u + 1
c
7
u
13
− 6u
11
+ ··· − 3u
2
+ 1
c
8
u
13
+ 4u
12
+ ··· − u − 1
c
9
u
13
+ 4u
11
− u
10
+ 3u
9
− 3u
8
− 3u
7
− u
6
− u
5
+ 5u
4
+ 2u
3
+ 4u
2
+ 1
c
10
u
13
+ 5u
12
+ ··· + 4u + 1
c
11
, c
12
u
13
+ u
12
+ ··· − 6u
2
− 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 16y
12
+ ··· − 10y −1
c
2
, c
7
y
13
− 12y
12
+ ··· + 6y −1
c
3
, c
9
y
13
+ 8y
12
+ ··· − 8y −1
c
4
, c
5
, c
11
c
12
y
13
+ 17y
12
+ ··· − 12y −1
c
6
y
13
− 5y
12
+ ··· − 4y −1
c
8
y
13
+ 4y
12
+ ··· + 5y −1
c
10
y
13
− 17y
12
+ ··· − 10y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.133548 + 1.037260I
a = −0.533043 + 0.773593I
b = 0.502915 − 0.004440I
−0.15268 + 2.04240I −3.65004 − 2.96160I
u = 0.133548 − 1.037260I
a = −0.533043 − 0.773593I
b = 0.502915 + 0.004440I
−0.15268 − 2.04240I −3.65004 + 2.96160I
u = 0.595022 + 0.705190I
a = −0.707954 − 0.450630I
b = 0.334443 − 0.017859I
−0.95065 + 2.25169I −8.21474 − 6.15376I
u = 0.595022 − 0.705190I
a = −0.707954 + 0.450630I
b = 0.334443 + 0.017859I
−0.95065 − 2.25169I −8.21474 + 6.15376I
u = −0.18499 + 1.50758I
a = −1.06900 + 1.10979I
b = 1.96964 − 2.19015I
−12.75340 − 2.45911I −12.84063 + 2.25061I
u = −0.18499 − 1.50758I
a = −1.06900 − 1.10979I
b = 1.96964 + 2.19015I
−12.75340 + 2.45911I −12.84063 − 2.25061I
u = −0.458933
a = −3.86284
b = 0.172095
−7.33687 0.945020
u = 0.01093 + 1.55303I
a = 0.566263 − 0.677012I
b = −1.203680 + 0.099823I
−4.99307 − 1.29173I −8.47906 + 1.03783I
u = 0.01093 − 1.55303I
a = 0.566263 + 0.677012I
b = −1.203680 − 0.099823I
−4.99307 + 1.29173I −8.47906 − 1.03783I
u = 0.047246 + 0.397006I
a = −1.63460 − 0.77504I
b = 0.15026 + 1.40825I
1.86356 − 1.48404I −10.17394 + 1.43832I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047246 − 0.397006I
a = −1.63460 + 0.77504I
b = 0.15026 − 1.40825I
1.86356 + 1.48404I −10.17394 − 1.43832I
u = 0.12770 + 1.61697I
a = 1.309750 − 0.068445I
b = −2.83963 + 0.06093I
−8.95416 + 4.67635I −7.61410 − 5.21153I
u = 0.12770 − 1.61697I
a = 1.309750 + 0.068445I
b = −2.83963 − 0.06093I
−8.95416 − 4.67635I −7.61410 + 5.21153I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 12u
12
+ ··· + 6u − 1)(u
27
+ 43u
26
+ ··· + 32307u + 14641)
c
2
(u
13
− 6u
11
+ ··· + 3u
2
− 1)(u
27
+ u
26
+ ··· − 451u − 121)
c
3
(u
13
+ 4u
11
+ u
10
+ 3u
9
+ 3u
8
− 3u
7
+ u
6
− u
5
− 5u
4
+ 2u
3
− 4u
2
− 1)
· (u
27
− u
26
+ ··· + 57u + 173)
c
4
, c
5
(u
13
− u
12
+ ··· + 6u
2
+ 1)(u
27
+ 2u
26
+ ··· + 13u + 1)
c
6
(u
13
− u
12
+ ··· − 4u + 1)(u
27
− 30u
25
+ ··· + 20449u − 8017)
c
7
(u
13
− 6u
11
+ ··· − 3u
2
+ 1)(u
27
+ u
26
+ ··· − 451u − 121)
c
8
(u
13
+ 4u
12
+ ··· − u − 1)(u
27
− 5u
26
+ ··· − 38u + 7)
c
9
(u
13
+ 4u
11
− u
10
+ 3u
9
− 3u
8
− 3u
7
− u
6
− u
5
+ 5u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
27
− u
26
+ ··· + 57u + 173)
c
10
(u
13
+ 5u
12
+ ··· + 4u + 1)(u
27
− 22u
25
+ ··· + 125u − 21)
c
11
, c
12
(u
13
+ u
12
+ ··· − 6u
2
− 1)(u
27
+ 2u
26
+ ··· + 13u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
− 16y
12
+ ··· − 10y −1)
· (y
27
− 111y
26
+ ··· + 6730511623y −214358881)
c
2
, c
7
(y
13
− 12y
12
+ ··· + 6y −1)(y
27
− 43y
26
+ ··· + 32307y −14641)
c
3
, c
9
(y
13
+ 8y
12
+ ··· − 8y −1)(y
27
− 11y
26
+ ··· + 147185y −29929)
c
4
, c
5
, c
11
c
12
(y
13
+ 17y
12
+ ··· − 12y −1)(y
27
+ 38y
26
+ ··· + 237y −1)
c
6
(y
13
− 5y
12
+ ··· − 4y −1)
· (y
27
− 60y
26
+ ··· − 129367431y −64272289)
c
8
(y
13
+ 4y
12
+ ··· + 5y −1)(y
27
− 7y
26
+ ··· + 1402y −49)
c
10
(y
13
− 17y
12
+ ··· − 10y −1)(y
27
− 44y
26
+ ··· − 965y −441)
14
