12n
0797
(K12n
0797
)
A knot diagram
1
Linearized knot diagam
4 7 10 9 11 2 12 5 1 2 8 7
Solving Sequence
8,11
12
2,7
3 1 6 5 10 4 9
c
11
c
7
c
2
c
12
c
6
c
5
c
10
c
3
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.07960 × 10
91
u
54
+ 2.94820 × 10
91
u
53
+ ··· + 1.60845 × 10
93
b 8.75300 × 10
93
,
3.49565 × 10
93
u
54
+ 1.25650 × 10
94
u
53
+ ··· + 2.58961 × 10
95
a + 8.81973 × 10
95
,
u
55
+ 2u
54
+ ··· + 547u + 161i
I
u
2
= h2u
25
88u
24
+ ··· + 46b 59, 91u
25
+ 215u
24
+ ··· + 46a + 66, u
26
u
25
+ ··· + 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 81 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
=
h2.08×10
91
u
54
+2.95×10
91
u
53
+· · ·+1.61×10
93
b8.75×10
93
, 3.50×10
93
u
54
+
1.26 × 10
94
u
53
+ · · · + 2.59 × 10
95
a + 8.82 × 10
95
, u
55
+ 2u
54
+ · · · + 547u + 161i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
0.0134987u
54
0.0485208u
53
+ ··· 12.9886u 3.40581
0.0129292u
54
0.0183294u
53
+ ··· + 18.5763u + 5.44188
a
7
=
u
u
3
+ u
a
3
=
0.0187035u
54
0.0547457u
53
+ ··· 3.27141u 0.392712
0.0151382u
54
0.0181689u
53
+ ··· + 26.8425u + 7.78127
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
0.0211190u
54
0.0418297u
53
+ ··· 8.19248u + 0.487545
0.0160121u
54
+ 0.0367680u
53
+ ··· + 6.73323u 0.603776
a
5
=
0.00510696u
54
0.00506179u
53
+ ··· 1.45925u 0.116231
0.0160121u
54
+ 0.0367680u
53
+ ··· + 6.73323u 0.603776
a
10
=
0.0168284u
54
+ 0.0417284u
53
+ ··· + 17.8209u + 3.35274
0.0107121u
54
+ 0.00850273u
53
+ ··· 25.3078u 6.73136
a
4
=
0.00524703u
54
+ 0.0251477u
53
+ ··· + 38.4021u + 9.27761
0.0246750u
54
+ 0.0506644u
53
+ ··· 1.69128u 1.40430
a
9
=
0.0213925u
54
+ 0.0472947u
53
+ ··· + 8.93888u + 0.875826
0.00408564u
54
0.00772075u
53
+ ··· 24.1554u 5.78092
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0784770u
54
0.193082u
53
+ ··· 68.0047u 10.6801
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
6u
54
+ ··· + 138u 7
c
2
, c
6
u
55
u
54
+ ··· 6215u + 4261
c
3
u
55
22u
53
+ ··· 425241u + 68743
c
4
, c
8
u
55
+ 3u
54
+ ··· + 40u + 8
c
5
u
55
+ u
54
+ ··· + 518u + 691
c
7
, c
11
, c
12
u
55
+ 2u
54
+ ··· + 547u + 161
c
9
u
55
+ 6u
54
+ ··· + 3961u + 547
c
10
u
55
45u
53
+ ··· + 42944u + 11864
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
+ 10y
54
+ ··· + 9314y 49
c
2
, c
6
y
55
+ 81y
54
+ ··· 714727097y 18156121
c
3
y
55
44y
54
+ ··· + 161699281125y 4725600049
c
4
, c
8
y
55
+ 51y
54
+ ··· 16448y 64
c
5
y
55
+ 83y
54
+ ··· 17632722y 477481
c
7
, c
11
, c
12
y
55
+ 68y
54
+ ··· 615593y 25921
c
9
y
55
+ 24y
54
+ ··· 5301057y 299209
c
10
y
55
90y
54
+ ··· + 3812472192y 140754496
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.490040 + 0.753457I
a = 0.887738 0.559278I
b = 1.50685 0.03038I
6.13669 4.64981I 5.28628 + 6.18804I
u = 0.490040 0.753457I
a = 0.887738 + 0.559278I
b = 1.50685 + 0.03038I
6.13669 + 4.64981I 5.28628 6.18804I
u = 0.570071 + 0.997038I
a = 0.88532 + 1.33081I
b = 0.537901 + 0.521935I
1.18456 2.16066I 0
u = 0.570071 0.997038I
a = 0.88532 1.33081I
b = 0.537901 0.521935I
1.18456 + 2.16066I 0
u = 0.251956 + 0.785395I
a = 1.08299 1.33546I
b = 1.61042 0.04562I
9.54903 0.14815I 1.97076 + 0.45693I
u = 0.251956 0.785395I
a = 1.08299 + 1.33546I
b = 1.61042 + 0.04562I
9.54903 + 0.14815I 1.97076 0.45693I
u = 0.116882 + 1.178060I
a = 0.104386 0.227431I
b = 0.646640 0.042880I
2.57075 + 2.07006I 0
u = 0.116882 1.178060I
a = 0.104386 + 0.227431I
b = 0.646640 + 0.042880I
2.57075 2.07006I 0
u = 0.636334 + 1.002860I
a = 0.811613 0.985736I
b = 0.254278 1.303390I
0.34669 + 2.38010I 0
u = 0.636334 1.002860I
a = 0.811613 + 0.985736I
b = 0.254278 + 1.303390I
0.34669 2.38010I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.516300 + 0.607161I
a = 0.551523 + 0.748786I
b = 1.57349 0.23422I
5.55349 + 1.15098I 7.02981 + 2.01750I
u = 0.516300 0.607161I
a = 0.551523 0.748786I
b = 1.57349 + 0.23422I
5.55349 1.15098I 7.02981 2.01750I
u = 0.635640 + 0.408514I
a = 0.049474 0.375979I
b = 0.244897 + 0.404452I
3.21037 3.81410I 3.00876 + 4.44084I
u = 0.635640 0.408514I
a = 0.049474 + 0.375979I
b = 0.244897 0.404452I
3.21037 + 3.81410I 3.00876 4.44084I
u = 0.578207 + 0.479856I
a = 0.433436 + 0.026732I
b = 0.483722 + 0.114833I
3.53350 0.19360I 3.73389 + 2.78818I
u = 0.578207 0.479856I
a = 0.433436 0.026732I
b = 0.483722 0.114833I
3.53350 + 0.19360I 3.73389 2.78818I
u = 0.084715 + 0.743739I
a = 0.86276 2.38888I
b = 0.302921 + 0.216438I
1.83611 + 5.00955I 1.41995 4.51640I
u = 0.084715 0.743739I
a = 0.86276 + 2.38888I
b = 0.302921 0.216438I
1.83611 5.00955I 1.41995 + 4.51640I
u = 0.206657 + 0.671508I
a = 0.30812 + 1.43958I
b = 0.371827 + 1.206250I
1.53161 4.54582I 1.70666 + 0.80391I
u = 0.206657 0.671508I
a = 0.30812 1.43958I
b = 0.371827 1.206250I
1.53161 + 4.54582I 1.70666 0.80391I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.223556 + 0.606477I
a = 0.602584 + 1.250130I
b = 1.89077 + 0.29080I
8.94290 1.49383I 1.30346 + 4.21129I
u = 0.223556 0.606477I
a = 0.602584 1.250130I
b = 1.89077 0.29080I
8.94290 + 1.49383I 1.30346 4.21129I
u = 1.116550 + 0.829939I
a = 0.054400 + 0.756088I
b = 2.34708 + 0.06527I
12.4197 + 8.7555I 0
u = 1.116550 0.829939I
a = 0.054400 0.756088I
b = 2.34708 0.06527I
12.4197 8.7555I 0
u = 0.129598 + 1.407450I
a = 0.933650 0.404509I
b = 0.363613 + 1.022520I
4.96026 + 2.94833I 0
u = 0.129598 1.407450I
a = 0.933650 + 0.404509I
b = 0.363613 1.022520I
4.96026 2.94833I 0
u = 1.29784 + 0.63122I
a = 0.058295 0.824045I
b = 2.36846 0.46156I
11.71150 0.95890I 0
u = 1.29784 0.63122I
a = 0.058295 + 0.824045I
b = 2.36846 + 0.46156I
11.71150 + 0.95890I 0
u = 0.18355 + 1.46859I
a = 0.384347 0.500239I
b = 0.278834 0.427014I
4.72513 + 1.63928I 0
u = 0.18355 1.46859I
a = 0.384347 + 0.500239I
b = 0.278834 + 0.427014I
4.72513 1.63928I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.22442 + 1.46665I
a = 0.758599 0.218438I
b = 0.711269 + 0.025399I
9.77580 3.16441I 0
u = 0.22442 1.46665I
a = 0.758599 + 0.218438I
b = 0.711269 0.025399I
9.77580 + 3.16441I 0
u = 0.22595 + 1.46861I
a = 0.078711 + 0.724552I
b = 0.246015 0.635654I
9.28337 6.93920I 0
u = 0.22595 1.46861I
a = 0.078711 0.724552I
b = 0.246015 + 0.635654I
9.28337 + 6.93920I 0
u = 0.295289 + 0.365913I
a = 0.546011 1.002610I
b = 0.236263 0.861145I
0.63078 + 1.39813I 4.91291 6.55485I
u = 0.295289 0.365913I
a = 0.546011 + 1.002610I
b = 0.236263 + 0.861145I
0.63078 1.39813I 4.91291 + 6.55485I
u = 0.426697
a = 1.04155
b = 0.354185
0.877261 10.1120
u = 0.06992 + 1.64735I
a = 2.21340 + 0.12521I
b = 2.70602 0.87673I
17.0119 2.6386I 0
u = 0.06992 1.64735I
a = 2.21340 0.12521I
b = 2.70602 + 0.87673I
17.0119 + 2.6386I 0
u = 0.14782 + 1.66795I
a = 1.88593 0.44797I
b = 2.33419 0.02631I
13.66400 1.40536I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.14782 1.66795I
a = 1.88593 + 0.44797I
b = 2.33419 + 0.02631I
13.66400 + 1.40536I 0
u = 0.194738 + 0.240755I
a = 1.82364 + 2.49499I
b = 0.421348 0.103727I
1.054960 0.149529I 3.90095 3.89450I
u = 0.194738 0.240755I
a = 1.82364 2.49499I
b = 0.421348 + 0.103727I
1.054960 + 0.149529I 3.90095 + 3.89450I
u = 0.15421 + 1.68561I
a = 1.84022 + 0.35608I
b = 2.13772 + 0.11444I
14.7179 7.2096I 0
u = 0.15421 1.68561I
a = 1.84022 0.35608I
b = 2.13772 0.11444I
14.7179 + 7.2096I 0
u = 0.08151 + 1.71479I
a = 1.71136 + 0.13502I
b = 2.00460 + 0.60101I
18.6220 1.5785I 0
u = 0.08151 1.71479I
a = 1.71136 0.13502I
b = 2.00460 0.60101I
18.6220 + 1.5785I 0
u = 0.04620 + 1.72945I
a = 0.847700 + 0.629686I
b = 1.26083 1.76289I
10.49490 3.28765I 0
u = 0.04620 1.72945I
a = 0.847700 0.629686I
b = 1.26083 + 1.76289I
10.49490 + 3.28765I 0
u = 0.01411 + 1.75354I
a = 0.705957 0.124688I
b = 0.83820 + 1.26974I
11.23260 + 4.25408I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.01411 1.75354I
a = 0.705957 + 0.124688I
b = 0.83820 1.26974I
11.23260 4.25408I 0
u = 0.36581 + 1.72020I
a = 1.56485 0.63201I
b = 2.36197 0.69629I
18.7497 + 14.4065I 0
u = 0.36581 1.72020I
a = 1.56485 + 0.63201I
b = 2.36197 + 0.69629I
18.7497 14.4065I 0
u = 0.46563 + 1.76753I
a = 1.33286 + 0.60148I
b = 2.24415 + 0.96108I
19.3972 + 5.7935I 0
u = 0.46563 1.76753I
a = 1.33286 0.60148I
b = 2.24415 0.96108I
19.3972 5.7935I 0
10
II. I
u
2
= h2u
25
88u
24
+ · · · + 46b 59, 91u
25
+ 215u
24
+ · · · + 46a +
66, u
26
u
25
+ · · · + 4u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
1.97826u
25
4.67391u
24
+ ··· + 2.36957u 1.43478
0.0434783u
25
+ 1.91304u
24
+ ··· + 6.47826u + 1.28261
a
7
=
u
u
3
+ u
a
3
=
3.63043u
25
8.30435u
24
+ ··· 1.86957u 2.76087
1.13043u
25
+ 4.67391u
24
+ ··· + 8.50000u + 1.93478
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
3.23913u
25
+ 2.80435u
24
+ ··· 13.1522u 2.23913
0.652174u
25
+ 0.434783u
24
+ ··· + 2.69565u + 0.586957
a
5
=
2.58696u
25
+ 3.23913u
24
+ ··· 10.4565u 1.65217
0.652174u
25
+ 0.434783u
24
+ ··· + 2.69565u + 0.586957
a
10
=
0.543478u
25
2.43478u
24
+ ··· 4.95652u 1.58696
1.52174u
25
1.21739u
24
+ ··· + 2.52174u 0.0434783
a
4
=
0.717391u
25
+ 0.760870u
24
+ ··· + 0.195652u + 0.652174
1.04348u
25
+ 4.84783u
24
+ ··· + 7.54348u + 2.36957
a
9
=
u
25
2u
24
+ ··· 4u 2
1.54348u
25
1.32609u
24
+ ··· + 1.93478u 0.0652174
(ii) Obstruction class = 1
(iii) Cusp Shapes =
55
23
u
25
266
23
u
24
+ ··· +
1
23
u
274
23
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
9u
25
+ ··· 3u + 1
c
2
u
26
+ 7u
24
+ ··· 6u
2
+ 1
c
3
u
26
+ u
25
+ ··· + 7u
2
+ 1
c
4
u
26
+ 2u
25
+ ··· + 8u + 8
c
5
u
26
+ 18u
24
+ ··· + 155u + 19
c
6
u
26
+ 7u
24
+ ··· 6u
2
+ 1
c
7
u
26
+ u
25
+ ··· 4u + 1
c
8
u
26
2u
25
+ ··· 8u + 8
c
9
u
26
+ u
25
+ ··· 6u + 1
c
10
u
26
3u
25
+ ··· 16u + 8
c
11
, c
12
u
26
u
25
+ ··· + 4u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
y
25
+ ··· 3y + 1
c
2
, c
6
y
26
+ 14y
25
+ ··· 12y + 1
c
3
y
26
7y
25
+ ··· + 14y + 1
c
4
, c
8
y
26
+ 20y
25
+ ··· + 768y + 64
c
5
y
26
+ 36y
25
+ ··· 3239y + 361
c
7
, c
11
, c
12
y
26
+ 29y
25
+ ··· + 8y + 1
c
9
y
26
+ y
25
+ ··· + 72y + 1
c
10
y
26
17y
25
+ ··· + 448y + 64
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.531767 + 0.924726I
a = 0.95660 1.36911I
b = 0.314180 0.738123I
1.60523 + 2.14875I 18.0536 1.1189I
u = 0.531767 0.924726I
a = 0.95660 + 1.36911I
b = 0.314180 + 0.738123I
1.60523 2.14875I 18.0536 + 1.1189I
u = 0.155520 + 1.184120I
a = 0.297405 0.783721I
b = 0.964857 + 0.167882I
7.99337 + 3.58193I 0.53526 3.16458I
u = 0.155520 1.184120I
a = 0.297405 + 0.783721I
b = 0.964857 0.167882I
7.99337 3.58193I 0.53526 + 3.16458I
u = 0.278958 + 0.724589I
a = 0.996507 + 0.135576I
b = 1.332660 + 0.342920I
6.25488 1.92335I 0.90199 + 3.47352I
u = 0.278958 0.724589I
a = 0.996507 0.135576I
b = 1.332660 0.342920I
6.25488 + 1.92335I 0.90199 3.47352I
u = 0.930098 + 0.802820I
a = 0.474244 + 0.914716I
b = 0.060489 + 1.338220I
0.53288 3.32357I 2.37998 + 5.27576I
u = 0.930098 0.802820I
a = 0.474244 0.914716I
b = 0.060489 1.338220I
0.53288 + 3.32357I 2.37998 5.27576I
u = 0.028031 + 1.276740I
a = 1.00372 1.53912I
b = 0.172185 + 0.709515I
3.91194 + 5.18636I 1.06606 5.83088I
u = 0.028031 1.276740I
a = 1.00372 + 1.53912I
b = 0.172185 0.709515I
3.91194 5.18636I 1.06606 + 5.83088I
14
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.499919 + 0.469085I
a = 0.20979 + 1.55488I
b = 1.84433 + 0.13564I
8.18136 + 0.02481I 4.35136 0.00061I
u = 0.499919 0.469085I
a = 0.20979 1.55488I
b = 1.84433 0.13564I
8.18136 0.02481I 4.35136 + 0.00061I
u = 0.075484 + 1.330840I
a = 0.140603 + 1.168060I
b = 0.453510 0.455888I
2.64528 + 0.49890I 3.27837 + 0.91499I
u = 0.075484 1.330840I
a = 0.140603 1.168060I
b = 0.453510 + 0.455888I
2.64528 0.49890I 3.27837 0.91499I
u = 0.251257 + 1.313020I
a = 0.585820 0.404742I
b = 1.356040 + 0.081601I
11.21190 2.85234I 3.32067 + 2.75617I
u = 0.251257 1.313020I
a = 0.585820 + 0.404742I
b = 1.356040 0.081601I
11.21190 + 2.85234I 3.32067 2.75617I
u = 0.15611 + 1.42827I
a = 0.770422 + 0.144555I
b = 0.483139 + 0.795468I
4.00781 + 2.36685I 6.55320 2.61997I
u = 0.15611 1.42827I
a = 0.770422 0.144555I
b = 0.483139 0.795468I
4.00781 2.36685I 6.55320 + 2.61997I
u = 0.017031 + 0.451525I
a = 1.36632 + 2.82567I
b = 0.178221 + 0.877402I
0.91017 5.01353I 11.92997 + 6.89384I
u = 0.017031 0.451525I
a = 1.36632 2.82567I
b = 0.178221 0.877402I
0.91017 + 5.01353I 11.92997 6.89384I
15
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.20761 + 1.53663I
a = 0.015459 + 0.437458I
b = 0.167651 1.040590I
8.40386 6.76860I 5.77206 + 3.99737I
u = 0.20761 1.53663I
a = 0.015459 0.437458I
b = 0.167651 + 1.040590I
8.40386 + 6.76860I 5.77206 3.99737I
u = 0.09600 + 1.68071I
a = 1.97843 0.05589I
b = 2.47796 0.70763I
16.3295 2.2416I 3.78517 + 0.I
u = 0.09600 1.68071I
a = 1.97843 + 0.05589I
b = 2.47796 + 0.70763I
16.3295 + 2.2416I 3.78517 + 0.I
u = 0.276043 + 0.143761I
a = 1.97897 2.35981I
b = 0.510160 0.524360I
1.33535 + 0.64782I 10.78419 5.87862I
u = 0.276043 0.143761I
a = 1.97897 + 2.35981I
b = 0.510160 + 0.524360I
1.33535 0.64782I 10.78419 + 5.87862I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
9u
25
+ ··· 3u + 1)(u
55
6u
54
+ ··· + 138u 7)
c
2
(u
26
+ 7u
24
+ ··· 6u
2
+ 1)(u
55
u
54
+ ··· 6215u + 4261)
c
3
(u
26
+ u
25
+ ··· + 7u
2
+ 1)(u
55
22u
53
+ ··· 425241u + 68743)
c
4
(u
26
+ 2u
25
+ ··· + 8u + 8)(u
55
+ 3u
54
+ ··· + 40u + 8)
c
5
(u
26
+ 18u
24
+ ··· + 155u + 19)(u
55
+ u
54
+ ··· + 518u + 691)
c
6
(u
26
+ 7u
24
+ ··· 6u
2
+ 1)(u
55
u
54
+ ··· 6215u + 4261)
c
7
(u
26
+ u
25
+ ··· 4u + 1)(u
55
+ 2u
54
+ ··· + 547u + 161)
c
8
(u
26
2u
25
+ ··· 8u + 8)(u
55
+ 3u
54
+ ··· + 40u + 8)
c
9
(u
26
+ u
25
+ ··· 6u + 1)(u
55
+ 6u
54
+ ··· + 3961u + 547)
c
10
(u
26
3u
25
+ ··· 16u + 8)(u
55
45u
53
+ ··· + 42944u + 11864)
c
11
, c
12
(u
26
u
25
+ ··· + 4u + 1)(u
55
+ 2u
54
+ ··· + 547u + 161)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
y
25
+ ··· 3y + 1)(y
55
+ 10y
54
+ ··· + 9314y 49)
c
2
, c
6
(y
26
+ 14y
25
+ ··· 12y + 1)
· (y
55
+ 81y
54
+ ··· 714727097y 18156121)
c
3
(y
26
7y
25
+ ··· + 14y + 1)
· (y
55
44y
54
+ ··· + 161699281125y 4725600049)
c
4
, c
8
(y
26
+ 20y
25
+ ··· + 768y + 64)(y
55
+ 51y
54
+ ··· 16448y 64)
c
5
(y
26
+ 36y
25
+ ··· 3239y + 361)
· (y
55
+ 83y
54
+ ··· 17632722y 477481)
c
7
, c
11
, c
12
(y
26
+ 29y
25
+ ··· + 8y + 1)(y
55
+ 68y
54
+ ··· 615593y 25921)
c
9
(y
26
+ y
25
+ ··· + 72y + 1)(y
55
+ 24y
54
+ ··· 5301057y 299209)
c
10
(y
26
17y
25
+ ··· + 448y + 64)
· (y
55
90y
54
+ ··· + 3812472192y 140754496)
18