12n
0485
(K12n
0485
)
A knot diagram
1
Linearized knot diagam
3 6 12 11 2 10 5 12 3 7 8 10
Solving Sequence
6,10
7
3,11
2 1 5 8 4 12 9
c
6
c
10
c
2
c
1
c
5
c
7
c
4
c
12
c
8
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.68088 × 10
114
u
49
+ 4.16169 × 10
114
u
48
+ ··· + 7.67515 × 10
115
b + 4.28407 × 10
115
,
− 6.82277 × 10
115
u
49
− 1.30399 × 10
116
u
48
+ ··· + 5.37260 × 10
116
a + 7.15218 × 10
117
,
u
50
+ 2u
49
+ ··· − 457u − 23i
I
u
2
= h−326316u
14
− 428568u
13
+ ··· + 738005b − 1963248,
− 516082u
14
− 337061u
13
+ ··· + 738005a − 2248216,
u
15
+ u
14
− 6u
13
− 13u
12
+ 11u
11
+ 48u
10
+ 15u
9
− 72u
8
− 69u
7
+ 41u
6
+ 80u
5
+ u
4
− 39u
3
− 6u
2
+ 7u − 1i
* 2 irreducible components of dim
C
= 0, with total 65 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
= h1.68 × 10
114
u
49
+ 4.16 × 10
114
u
48
+ · · · + 7.68 × 10
115
b + 4.28 ×
10
115
, −6.82 × 10
115
u
49
− 1.30 × 10
116
u
48
+ · · · + 5.37 × 10
116
a + 7.15 ×
10
117
, u
50
+ 2u
49
+ · · · − 457u − 23i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
0.126992u
49
+ 0.242711u
48
+ ··· − 212.139u − 13.3123
−0.0219003u
49
− 0.0542229u
48
+ ··· − 4.04389u − 0.558174
a
11
=
−u
−u
3
+ u
a
2
=
0.105092u
49
+ 0.188488u
48
+ ··· − 216.183u − 13.8705
−0.0219003u
49
− 0.0542229u
48
+ ··· − 4.04389u − 0.558174
a
1
=
−0.0244401u
49
− 0.0544173u
48
+ ··· + 64.2416u + 6.94455
0.0202777u
49
+ 0.0488855u
48
+ ··· − 0.453421u − 0.822925
a
5
=
0.125355u
49
+ 0.236460u
48
+ ··· − 229.828u − 15.6829
0.0231342u
49
+ 0.0609480u
48
+ ··· + 55.0377u + 2.61238
a
8
=
−0.121315u
49
− 0.239466u
48
+ ··· + 307.315u + 24.6209
0.0144984u
49
+ 0.0160292u
48
+ ··· − 43.7020u − 2.79868
a
4
=
0.111866u
49
+ 0.205756u
48
+ ··· − 237.020u − 15.8895
0.0326281u
49
+ 0.0837666u
48
+ ··· + 60.2174u + 2.73337
a
12
=
−0.0244401u
49
− 0.0544173u
48
+ ··· + 64.2416u + 6.94455
0.0232371u
49
+ 0.0518221u
48
+ ··· − 3.54599u − 0.950278
a
9
=
−0.143868u
49
− 0.280796u
48
+ ··· + 334.339u + 27.3191
0.0289298u
49
+ 0.0544418u
48
+ ··· − 28.4198u − 2.35108
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.270594u
49
− 0.467859u
48
+ ··· − 63.7985u − 8.23325
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 38u
49
+ ··· − 888u + 361
c
2
, c
5
u
50
− 19u
48
+ ··· + 86u + 19
c
3
u
50
− 9u
49
+ ··· + 7672u + 449
c
4
u
50
− 3u
49
+ ··· − 316u − 239
c
6
, c
10
u
50
+ 2u
49
+ ··· − 457u − 23
c
7
u
50
− 5u
49
+ ··· − 18u + 1
c
8
, c
11
u
50
− 3u
49
+ ··· + 7u + 1
c
9
u
50
− u
49
+ ··· − 48u − 119
c
12
u
50
+ 3u
49
+ ··· − 36385u − 1997
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 42y
49
+ ··· + 7137572y + 130321
c
2
, c
5
y
50
− 38y
49
+ ··· + 888y + 361
c
3
y
50
− 85y
49
+ ··· − 26826128y + 201601
c
4
y
50
+ 31y
49
+ ··· + 1567408y + 57121
c
6
, c
10
y
50
− 50y
49
+ ··· − 75863y + 529
c
7
y
50
+ 7y
49
+ ··· − 88y + 1
c
8
, c
11
y
50
− 9y
49
+ ··· − 19y + 1
c
9
y
50
+ 57y
49
+ ··· + 139782y + 14161
c
12
y
50
+ 95y
49
+ ··· − 251387363y + 3988009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.962392
a = −1.01045
b = −1.32074
−2.96141 2.27250
u = −0.914795 + 0.294994I
a = 0.348985 − 1.244120I
b = −0.336309 + 0.574877I
−1.75231 + 1.61093I −2.00000 − 4.17914I
u = −0.914795 − 0.294994I
a = 0.348985 + 1.244120I
b = −0.336309 − 0.574877I
−1.75231 − 1.61093I −2.00000 + 4.17914I
u = 0.188071 + 0.934572I
a = −1.32544 − 0.55559I
b = −0.330034 + 0.374073I
−3.45737 − 4.06670I − 60.298116 + 0.10I
u = 0.188071 − 0.934572I
a = −1.32544 + 0.55559I
b = −0.330034 − 0.374073I
−3.45737 + 4.06670I − 60.298116 + 0.10I
u = −1.063020 + 0.238205I
a = 0.513483 − 0.668053I
b = −0.219406 + 0.431806I
−1.88900 + 1.18238I 0
u = −1.063020 − 0.238205I
a = 0.513483 + 0.668053I
b = −0.219406 − 0.431806I
−1.88900 − 1.18238I 0
u = −1.12876
a = −2.19559
b = −1.15007
−3.84446 56.7750
u = −0.201542 + 1.118180I
a = −0.163469 + 0.515966I
b = 0.939070 − 0.303988I
−0.56528 + 3.67939I 0. − 8.30272I
u = −0.201542 − 1.118180I
a = −0.163469 − 0.515966I
b = 0.939070 + 0.303988I
−0.56528 − 3.67939I 0. + 8.30272I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.133680 + 0.426918I
a = 0.19890 − 1.42670I
b = −1.125150 + 0.186429I
−3.75163 + 1.13848I 0
u = −1.133680 − 0.426918I
a = 0.19890 + 1.42670I
b = −1.125150 − 0.186429I
−3.75163 − 1.13848I 0
u = 1.166960 + 0.482292I
a = −0.242984 + 0.621460I
b = 0.025892 − 0.730255I
−1.46117 − 5.17618I 0
u = 1.166960 − 0.482292I
a = −0.242984 − 0.621460I
b = 0.025892 + 0.730255I
−1.46117 + 5.17618I 0
u = 1.161870 + 0.501646I
a = 0.174398 − 0.201602I
b = 0.852089 − 0.342703I
2.18914 + 1.57391I 0
u = 1.161870 − 0.501646I
a = 0.174398 + 0.201602I
b = 0.852089 + 0.342703I
2.18914 − 1.57391I 0
u = 0.279120 + 0.649040I
a = 0.526491 − 0.708843I
b = 0.200176 + 0.379822I
1.27220 + 0.82528I 4.71608 − 1.63337I
u = 0.279120 − 0.649040I
a = 0.526491 + 0.708843I
b = 0.200176 − 0.379822I
1.27220 − 0.82528I 4.71608 + 1.63337I
u = −1.406050 + 0.128958I
a = −0.090166 + 1.145330I
b = 1.49695 − 0.61870I
−13.59260 − 1.25874I 0
u = −1.406050 − 0.128958I
a = −0.090166 − 1.145330I
b = 1.49695 + 0.61870I
−13.59260 + 1.25874I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40806 + 0.28799I
a = −0.208667 + 0.877622I
b = −0.799188 − 0.695079I
−1.71585 − 2.64303I 0
u = −1.40806 − 0.28799I
a = −0.208667 − 0.877622I
b = −0.799188 + 0.695079I
−1.71585 + 2.64303I 0
u = 1.38930 + 0.44579I
a = 0.530144 − 0.813142I
b = 1.290420 + 0.327880I
−5.44067 − 9.04729I 0
u = 1.38930 − 0.44579I
a = 0.530144 + 0.813142I
b = 1.290420 − 0.327880I
−5.44067 + 9.04729I 0
u = 0.499788 + 0.001448I
a = −0.058887 − 0.899672I
b = 0.908853 + 0.846009I
4.40130 − 3.14257I −9.86497 + 6.30227I
u = 0.499788 − 0.001448I
a = −0.058887 + 0.899672I
b = 0.908853 − 0.846009I
4.40130 + 3.14257I −9.86497 − 6.30227I
u = −1.47559 + 0.28198I
a = −0.081256 + 1.075060I
b = 0.042685 − 1.259730I
−9.03640 + 8.03955I 0
u = −1.47559 − 0.28198I
a = −0.081256 − 1.075060I
b = 0.042685 + 1.259730I
−9.03640 − 8.03955I 0
u = −0.187501 + 0.455490I
a = −3.04218 + 1.68708I
b = 1.382520 + 0.000995I
−9.25542 + 3.21801I −8.68028 − 2.26278I
u = −0.187501 − 0.455490I
a = −3.04218 − 1.68708I
b = 1.382520 − 0.000995I
−9.25542 − 3.21801I −8.68028 + 2.26278I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50019 + 0.27239I
a = −0.051146 − 1.185010I
b = 1.44274 + 0.53398I
−15.1134 − 6.2855I 0
u = 1.50019 − 0.27239I
a = −0.051146 + 1.185010I
b = 1.44274 − 0.53398I
−15.1134 + 6.2855I 0
u = 1.53985 + 0.12206I
a = −0.124852 − 1.057310I
b = −0.048220 + 1.175680I
−10.37170 + 0.19283I 0
u = 1.53985 − 0.12206I
a = −0.124852 + 1.057310I
b = −0.048220 − 1.175680I
−10.37170 − 0.19283I 0
u = 1.54597 + 0.25810I
a = −0.163723 − 0.343395I
b = −1.314650 + 0.219888I
−5.75356 − 1.82353I 0
u = 1.54597 − 0.25810I
a = −0.163723 + 0.343395I
b = −1.314650 − 0.219888I
−5.75356 + 1.82353I 0
u = −1.37962 + 0.95465I
a = −0.320379 + 0.766815I
b = 1.42544 − 0.21562I
−7.41648 + 4.49387I 0
u = −1.37962 − 0.95465I
a = −0.320379 − 0.766815I
b = 1.42544 + 0.21562I
−7.41648 − 4.49387I 0
u = −0.176458 + 0.261015I
a = 2.19741 − 2.19418I
b = −0.984299 − 0.645971I
2.84989 − 2.54700I 0.20027 + 2.87410I
u = −0.176458 − 0.261015I
a = 2.19741 + 2.19418I
b = −0.984299 + 0.645971I
2.84989 + 2.54700I 0.20027 − 2.87410I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67091 + 0.40185I
a = 0.133031 + 0.469663I
b = 1.308980 − 0.234411I
−6.47062 + 3.76881I 0
u = −1.67091 − 0.40185I
a = 0.133031 − 0.469663I
b = 1.308980 + 0.234411I
−6.47062 − 3.76881I 0
u = −1.73086 + 0.55706I
a = 0.105414 − 0.948189I
b = −1.46194 + 0.56733I
−13.8255 + 14.4892I 0
u = −1.73086 − 0.55706I
a = 0.105414 + 0.948189I
b = −1.46194 − 0.56733I
−13.8255 − 14.4892I 0
u = 1.81370 + 0.37242I
a = 0.097510 + 0.883592I
b = −1.40613 − 0.59107I
−14.6308 − 6.0935I 0
u = 1.81370 − 0.37242I
a = 0.097510 − 0.883592I
b = −1.40613 + 0.59107I
−14.6308 + 6.0935I 0
u = −0.1120250 + 0.0235911I
a = 5.77586 − 3.15149I
b = −0.849378 + 0.151074I
−1.45480 + 0.34218I −6.89829 + 0.51719I
u = −0.1120250 − 0.0235911I
a = 5.77586 + 3.15149I
b = −0.849378 − 0.151074I
−1.45480 − 0.34218I −6.89829 − 0.51719I
u = 0.85847 + 1.91212I
a = 0.591928 + 0.361934I
b = −1.205700 − 0.185859I
−6.19255 − 6.25623I 0
u = 0.85847 − 1.91212I
a = 0.591928 − 0.361934I
b = −1.205700 + 0.185859I
−6.19255 + 6.25623I 0
9
II.
I
u
2
= h−3.26 × 10
5
u
14
− 4.29 × 10
5
u
13
+ · · · + 7.38 × 10
5
b − 1.96 × 10
6
, −5.16 ×
10
5
u
14
− 3.37× 10
5
u
13
+ · · · + 7.38 × 10
5
a −2.25 × 10
6
, u
15
+ u
14
+ · · · + 7u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
0.699293u
14
+ 0.456719u
13
+ ··· − 8.14388u + 3.04634
0.442160u
14
+ 0.580712u
13
+ ··· − 4.70877u + 2.66021
a
11
=
−u
−u
3
+ u
a
2
=
1.14145u
14
+ 1.03743u
13
+ ··· − 12.8527u + 5.70655
0.442160u
14
+ 0.580712u
13
+ ··· − 4.70877u + 2.66021
a
1
=
0.701112u
14
+ 0.979793u
13
+ ··· − 10.1395u + 6.46055
−0.0843436u
14
− 0.544892u
13
+ ··· + 10.4553u − 0.463978
a
5
=
−1.76423u
14
− 2.44279u
13
+ ··· + 26.2734u − 5.77124
−1.06494u
14
− 0.986071u
13
+ ··· + 11.1296u − 3.72490
a
8
=
−0.840260u
14
− 0.979408u
13
+ ··· + 8.72051u − 6.30081
0.440341u
14
+ 0.0576378u
13
+ ··· − 2.71316u − 0.753996
a
4
=
−1.45570u
14
− 2.40598u
13
+ ··· + 25.6851u − 5.33526
−0.956101u
14
− 1.06517u
13
+ ··· + 13.9285u − 4.43261
a
12
=
0.701112u
14
+ 0.979793u
13
+ ··· − 10.1395u + 6.46055
−0.446840u
14
− 0.697475u
13
+ ··· + 9.20568u − 0.185297
a
9
=
0.159740u
14
+ 0.0205920u
13
+ ··· + 2.72051u − 0.300808
−0.757426u
14
− 0.700316u
13
+ ··· + 2.84871u − 0.699293
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
337434
738005
u
14
−
617487
738005
u
13
+ ··· +
14750433
738005
u +
4380108
738005
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
15
− 9u
14
+ ··· + 14u − 1
c
2
u
15
+ u
14
+ ··· − 2u − 1
c
3
u
15
+ 4u
14
+ ··· + 14u + 1
c
4
u
15
+ 6u
13
+ ··· + 2u + 1
c
5
u
15
− u
14
+ ··· − 2u + 1
c
6
u
15
+ u
14
+ ··· + 7u − 1
c
7
u
15
+ 2u
14
+ ··· − 2u − 1
c
8
u
15
− 4u
14
+ ··· + u + 1
c
9
u
15
+ 7u
13
+ ··· − 4u − 1
c
10
u
15
− u
14
+ ··· + 7u + 1
c
11
u
15
+ 4u
14
+ ··· + u − 1
c
12
u
15
+ 4u
13
+ ··· − 9u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 3y
14
+ ··· + 26y −1
c
2
, c
5
y
15
− 9y
14
+ ··· + 14y −1
c
3
y
15
− 12y
14
+ ··· + 22y −1
c
4
y
15
+ 12y
14
+ ··· − 26y −1
c
6
, c
10
y
15
− 13y
14
+ ··· + 37y −1
c
7
y
15
+ 8y
14
+ ··· − 14y −1
c
8
, c
11
y
15
− 12y
14
+ ··· + 17y −1
c
9
y
15
+ 14y
14
+ ··· − 24y −1
c
12
y
15
+ 8y
14
+ ··· + 17y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.922745 + 0.460995I
a = 0.114369 − 0.538469I
b = −0.929425 − 0.375212I
1.64110 − 1.53234I −7.81691 + 0.84164I
u = −0.922745 − 0.460995I
a = 0.114369 + 0.538469I
b = −0.929425 + 0.375212I
1.64110 + 1.53234I −7.81691 − 0.84164I
u = 0.938945 + 0.177818I
a = 0.86597 + 1.32539I
b = −0.704339 − 0.269006I
−2.57188 − 0.93465I −11.79565 − 6.05051I
u = 0.938945 − 0.177818I
a = 0.86597 − 1.32539I
b = −0.704339 + 0.269006I
−2.57188 + 0.93465I −11.79565 + 6.05051I
u = −1.076890 + 0.164965I
a = 0.145601 − 1.209410I
b = −0.923532 + 0.993400I
1.02111 + 3.57074I −2.62126 − 3.81898I
u = −1.076890 − 0.164965I
a = 0.145601 + 1.209410I
b = −0.923532 − 0.993400I
1.02111 − 3.57074I −2.62126 + 3.81898I
u = 1.13583
a = −1.56273
b = −1.20582
−3.97180 −19.0140
u = −0.711260 + 0.972886I
a = 0.705794 − 0.758936I
b = 0.517765 − 0.027190I
−3.96515 + 4.70743I −6.56405 − 7.08888I
u = −0.711260 − 0.972886I
a = 0.705794 + 0.758936I
b = 0.517765 + 0.027190I
−3.96515 − 4.70743I −6.56405 + 7.08888I
u = −1.32192 + 1.13798I
a = −0.384571 + 0.713684I
b = 1.383610 − 0.124672I
−7.69386 + 5.20657I −7.68973 − 8.44911I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32192 − 1.13798I
a = −0.384571 − 0.713684I
b = 1.383610 + 0.124672I
−7.69386 − 5.20657I −7.68973 + 8.44911I
u = 0.214145 + 0.072034I
a = 0.182763 − 1.288960I
b = 0.913178 − 0.795560I
4.77103 + 2.99420I 9.45142 + 0.57526I
u = 0.214145 − 0.072034I
a = 0.182763 + 1.288960I
b = 0.913178 + 0.795560I
4.77103 − 2.99420I 9.45142 − 0.57526I
u = 1.81182 + 0.31886I
a = 0.151436 + 0.671996I
b = 0.845655 − 0.567560I
−1.08605 + 2.26406I 3.04312 − 0.55917I
u = 1.81182 − 0.31886I
a = 0.151436 − 0.671996I
b = 0.845655 + 0.567560I
−1.08605 − 2.26406I 3.04312 + 0.55917I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 9u
14
+ ··· + 14u − 1)(u
50
+ 38u
49
+ ··· − 888u + 361)
c
2
(u
15
+ u
14
+ ··· − 2u − 1)(u
50
− 19u
48
+ ··· + 86u + 19)
c
3
(u
15
+ 4u
14
+ ··· + 14u + 1)(u
50
− 9u
49
+ ··· + 7672u + 449)
c
4
(u
15
+ 6u
13
+ ··· + 2u + 1)(u
50
− 3u
49
+ ··· − 316u − 239)
c
5
(u
15
− u
14
+ ··· − 2u + 1)(u
50
− 19u
48
+ ··· + 86u + 19)
c
6
(u
15
+ u
14
+ ··· + 7u − 1)(u
50
+ 2u
49
+ ··· − 457u − 23)
c
7
(u
15
+ 2u
14
+ ··· − 2u − 1)(u
50
− 5u
49
+ ··· − 18u + 1)
c
8
(u
15
− 4u
14
+ ··· + u + 1)(u
50
− 3u
49
+ ··· + 7u + 1)
c
9
(u
15
+ 7u
13
+ ··· − 4u − 1)(u
50
− u
49
+ ··· − 48u − 119)
c
10
(u
15
− u
14
+ ··· + 7u + 1)(u
50
+ 2u
49
+ ··· − 457u − 23)
c
11
(u
15
+ 4u
14
+ ··· + u − 1)(u
50
− 3u
49
+ ··· + 7u + 1)
c
12
(u
15
+ 4u
13
+ ··· − 9u + 1)(u
50
+ 3u
49
+ ··· − 36385u − 1997)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 3y
14
+ ··· + 26y −1)(y
50
− 42y
49
+ ··· + 7137572y + 130321)
c
2
, c
5
(y
15
− 9y
14
+ ··· + 14y −1)(y
50
− 38y
49
+ ··· + 888y + 361)
c
3
(y
15
− 12y
14
+ ··· + 22y −1)
· (y
50
− 85y
49
+ ··· − 26826128y + 201601)
c
4
(y
15
+ 12y
14
+ ··· − 26y −1)(y
50
+ 31y
49
+ ··· + 1567408y + 57121)
c
6
, c
10
(y
15
− 13y
14
+ ··· + 37y −1)(y
50
− 50y
49
+ ··· − 75863y + 529)
c
7
(y
15
+ 8y
14
+ ··· − 14y −1)(y
50
+ 7y
49
+ ··· − 88y + 1)
c
8
, c
11
(y
15
− 12y
14
+ ··· + 17y −1)(y
50
− 9y
49
+ ··· − 19y + 1)
c
9
(y
15
+ 14y
14
+ ··· − 24y −1)(y
50
+ 57y
49
+ ··· + 139782y + 14161)
c
12
(y
15
+ 8y
14
+ ··· + 17y −1)
· (y
50
+ 95y
49
+ ··· − 251387363y + 3988009)
18
