12n
0734
(K12n
0734
)
A knot diagram
1
Linearized knot diagam
4 11 7 1 11 2 5 12 2 7 8 9
Solving Sequence
2,11 3,7
4 1 6 5 8 10 9 12
c
2
c
3
c
1
c
6
c
5
c
7
c
10
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.93981 × 10
179
u
58
+ 4.60320 × 10
178
u
57
+ ··· + 2.85555 × 10
182
b + 1.72195 × 10
182
,
8.20063 × 10
181
u
58
+ 3.02434 × 10
181
u
57
+ ··· + 1.74189 × 10
184
a 1.14409 × 10
185
,
u
59
+ u
58
+ ··· + 386u + 244i
I
u
2
= h−659021u
16
928037u
15
+ ··· + 963035b 442908,
299324u
16
63918u
15
+ ··· + 963035a 1083657, u
17
+ 4u
15
+ ··· + 2u 1i
* 2 irreducible components of dim
C
= 0, with total 76 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
= h5.94 × 10
179
u
58
+ 4.60 × 10
178
u
57
+ · · · + 2.86 × 10
182
b + 1.72 ×
10
182
, 8.20 × 10
181
u
58
+ 3.02 × 10
181
u
57
+ · · · + 1.74 × 10
184
a 1.14 ×
10
185
, u
59
+ u
58
+ · · · + 386u + 244i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
0.00470791u
58
0.00173624u
57
+ ··· + 17.8688u + 6.56814
0.00208009u
58
0.000161202u
57
+ ··· + 5.50343u 0.603017
a
4
=
0.00503808u
58
+ 0.00882567u
57
+ ··· + 27.3491u + 5.92936
0.00537009u
58
+ 0.00348580u
57
+ ··· + 2.87966u + 2.25203
a
1
=
0.00261013u
58
0.00116710u
57
+ ··· + 12.3671u + 6.44607
0.000615613u
58
+ 0.00164482u
57
+ ··· + 1.81783u + 0.0786874
a
6
=
0.00678800u
58
0.00189745u
57
+ ··· + 23.3723u + 5.96512
0.00208009u
58
0.000161202u
57
+ ··· + 5.50343u 0.603017
a
5
=
0.00678800u
58
0.00189745u
57
+ ··· + 23.3723u + 5.96512
0.00278773u
58
0.000245605u
57
+ ··· + 5.27195u 1.79631
a
8
=
0.00902786u
58
0.0115764u
57
+ ··· 31.0968u 6.01473
0.00179571u
58
0.00195730u
57
+ ··· + 3.71563u + 2.05425
a
10
=
0.00972417u
58
0.0103974u
57
+ ··· 24.0644u 0.306697
0.00277555u
58
0.00259612u
57
+ ··· + 0.647903u + 1.39356
a
9
=
0.0124997u
58
0.0129935u
57
+ ··· 23.4165u + 1.08686
0.00277555u
58
0.00259612u
57
+ ··· + 0.647903u + 1.39356
a
12
=
0.0159522u
58
+ 0.0183199u
57
+ ··· + 42.8385u + 5.19776
0.00330850u
58
+ 0.00353952u
57
+ ··· 2.63085u 2.59425
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0183261u
58
+ 0.0259595u
57
+ ··· + 60.0353u + 1.14679
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
59
6u
58
+ ··· 493u + 47
c
2
u
59
+ u
58
+ ··· + 386u + 244
c
3
u
59
2u
58
+ ··· + 1473477u + 77047
c
5
u
59
7u
57
+ ··· 2336u + 439
c
6
u
59
2u
58
+ ··· 4481u + 1539
c
7
u
59
15u
58
+ ··· + 72u 4
c
8
, c
11
, c
12
u
59
+ 6u
58
+ ··· + 2u + 1
c
9
u
59
2u
58
+ ··· + 2746719u + 257651
c
10
u
59
+ 2u
58
+ ··· 394u + 149
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
59
+ 40y
58
+ ··· 8213y 2209
c
2
y
59
+ 73y
58
+ ··· 1655140y 59536
c
3
y
59
+ 38y
58
+ ··· + 2137083856067y 5936240209
c
5
y
59
14y
58
+ ··· + 6258510y 192721
c
6
y
59
+ 76y
58
+ ··· + 38959813y 2368521
c
7
y
59
y
58
+ ··· + 1240y 16
c
8
, c
11
, c
12
y
59
58y
58
+ ··· 112y 1
c
9
y
59
+ 44y
58
+ ··· 140722482637y 66384037801
c
10
y
59
82y
58
+ ··· + 910368y 22201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.688572 + 0.799657I
a = 0.403897 0.429993I
b = 1.319730 + 0.029746I
5.51450 + 1.11046I 8.00000 + 0.I
u = 0.688572 0.799657I
a = 0.403897 + 0.429993I
b = 1.319730 0.029746I
5.51450 1.11046I 8.00000 + 0.I
u = 0.458695 + 0.730749I
a = 0.541463 + 0.804889I
b = 0.180739 + 0.082078I
1.92960 1.37995I 8.00000 + 0.I
u = 0.458695 0.730749I
a = 0.541463 0.804889I
b = 0.180739 0.082078I
1.92960 + 1.37995I 8.00000 + 0.I
u = 0.263108 + 0.751221I
a = 0.543851 0.807976I
b = 1.51685 0.53259I
2.99977 6.73475I 8.47764 + 5.04092I
u = 0.263108 0.751221I
a = 0.543851 + 0.807976I
b = 1.51685 + 0.53259I
2.99977 + 6.73475I 8.47764 5.04092I
u = 1.248950 + 0.106397I
a = 0.205733 0.100828I
b = 0.629743 0.803792I
6.50171 1.29569I 0
u = 1.248950 0.106397I
a = 0.205733 + 0.100828I
b = 0.629743 + 0.803792I
6.50171 + 1.29569I 0
u = 0.739660
a = 0.474782
b = 0.311743
0.974720 8.42250
u = 0.839226 + 1.015310I
a = 0.149446 + 1.228250I
b = 0.449432 0.919016I
0.28824 + 3.32242I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.839226 1.015310I
a = 0.149446 1.228250I
b = 0.449432 + 0.919016I
0.28824 3.32242I 0
u = 0.621367 + 0.148005I
a = 1.42430 + 1.76510I
b = 0.411559 0.511446I
1.67239 2.74169I 5.07241 + 2.45099I
u = 0.621367 0.148005I
a = 1.42430 1.76510I
b = 0.411559 + 0.511446I
1.67239 + 2.74169I 5.07241 2.45099I
u = 0.087984 + 1.365300I
a = 0.68821 + 1.42066I
b = 0.72763 1.73513I
4.68182 + 3.93350I 0
u = 0.087984 1.365300I
a = 0.68821 1.42066I
b = 0.72763 + 1.73513I
4.68182 3.93350I 0
u = 0.581835 + 0.198470I
a = 0.560192 + 0.121209I
b = 0.808875 + 0.059387I
1.109630 0.030440I 3.69972 2.46994I
u = 0.581835 0.198470I
a = 0.560192 0.121209I
b = 0.808875 0.059387I
1.109630 + 0.030440I 3.69972 + 2.46994I
u = 1.233130 + 0.644677I
a = 0.214064 0.343399I
b = 0.159650 + 0.596710I
2.01774 3.63891I 0
u = 1.233130 0.644677I
a = 0.214064 + 0.343399I
b = 0.159650 0.596710I
2.01774 + 3.63891I 0
u = 0.347764 + 0.493636I
a = 0.498777 0.775233I
b = 0.612320 0.444426I
3.01321 1.32546I 3.35867 + 3.08161I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.347764 0.493636I
a = 0.498777 + 0.775233I
b = 0.612320 + 0.444426I
3.01321 + 1.32546I 3.35867 3.08161I
u = 0.162857 + 0.510371I
a = 0.524139 + 0.787944I
b = 1.157400 + 0.627551I
2.64810 + 4.11685I 1.10051 4.77583I
u = 0.162857 0.510371I
a = 0.524139 0.787944I
b = 1.157400 0.627551I
2.64810 4.11685I 1.10051 + 4.77583I
u = 0.508925 + 0.043509I
a = 0.515449 0.759347I
b = 0.785003 0.994869I
0.49587 2.96712I 13.62136 + 1.03116I
u = 0.508925 0.043509I
a = 0.515449 + 0.759347I
b = 0.785003 + 0.994869I
0.49587 + 2.96712I 13.62136 1.03116I
u = 0.07223 + 1.50932I
a = 0.418282 1.323470I
b = 0.35654 + 2.00494I
9.26707 1.87361I 0
u = 0.07223 1.50932I
a = 0.418282 + 1.323470I
b = 0.35654 2.00494I
9.26707 + 1.87361I 0
u = 1.38402 + 0.62460I
a = 0.178185 + 0.088283I
b = 0.290901 0.757014I
3.68149 + 7.78233I 0
u = 1.38402 0.62460I
a = 0.178185 0.088283I
b = 0.290901 + 0.757014I
3.68149 7.78233I 0
u = 0.61536 + 1.42764I
a = 0.209800 + 0.892422I
b = 0.504159 0.898602I
1.35128 2.05230I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.61536 1.42764I
a = 0.209800 0.892422I
b = 0.504159 + 0.898602I
1.35128 + 2.05230I 0
u = 0.03547 + 1.56073I
a = 0.16653 + 1.40982I
b = 0.15839 2.37746I
5.41563 + 0.15050I 0
u = 0.03547 1.56073I
a = 0.16653 1.40982I
b = 0.15839 + 2.37746I
5.41563 0.15050I 0
u = 0.012840 + 0.401825I
a = 2.04510 0.24675I
b = 0.128940 0.325332I
0.635898 + 1.219670I 5.93174 6.56340I
u = 0.012840 0.401825I
a = 2.04510 + 0.24675I
b = 0.128940 + 0.325332I
0.635898 1.219670I 5.93174 + 6.56340I
u = 0.24053 + 1.61358I
a = 0.196266 + 1.036510I
b = 0.298352 1.176050I
1.07758 1.94960I 0
u = 0.24053 1.61358I
a = 0.196266 1.036510I
b = 0.298352 + 1.176050I
1.07758 + 1.94960I 0
u = 0.257140 + 0.250978I
a = 4.22445 1.73413I
b = 0.657455 + 0.553233I
4.50098 + 6.76243I 7.82043 2.26611I
u = 0.257140 0.250978I
a = 4.22445 + 1.73413I
b = 0.657455 0.553233I
4.50098 6.76243I 7.82043 + 2.26611I
u = 0.089742 + 0.315657I
a = 3.52034 + 1.67931I
b = 0.042107 + 0.701564I
6.63125 3.43002I 9.55405 + 4.93953I
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.089742 0.315657I
a = 3.52034 1.67931I
b = 0.042107 0.701564I
6.63125 + 3.43002I 9.55405 4.93953I
u = 0.27509 + 1.69404I
a = 0.131857 1.009020I
b = 0.04091 + 1.65776I
5.77005 0.91747I 0
u = 0.27509 1.69404I
a = 0.131857 + 1.009020I
b = 0.04091 1.65776I
5.77005 + 0.91747I 0
u = 0.55649 + 1.67541I
a = 0.476397 0.752620I
b = 0.44696 + 1.44326I
5.71622 + 1.79000I 0
u = 0.55649 1.67541I
a = 0.476397 + 0.752620I
b = 0.44696 1.44326I
5.71622 1.79000I 0
u = 0.33397 + 1.77298I
a = 0.357603 + 0.882444I
b = 0.27226 1.80631I
10.07080 + 0.99686I 0
u = 0.33397 1.77298I
a = 0.357603 0.882444I
b = 0.27226 + 1.80631I
10.07080 0.99686I 0
u = 0.35811 + 1.82702I
a = 0.104148 + 0.922751I
b = 0.29686 1.79295I
6.29629 + 5.09762I 0
u = 0.35811 1.82702I
a = 0.104148 0.922751I
b = 0.29686 + 1.79295I
6.29629 5.09762I 0
u = 0.41543 + 1.87910I
a = 0.025261 1.080380I
b = 0.56533 + 1.90237I
4.8121 + 14.9606I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.41543 1.87910I
a = 0.025261 + 1.080380I
b = 0.56533 1.90237I
4.8121 14.9606I 0
u = 0.48235 + 1.86660I
a = 0.129952 0.874599I
b = 0.56255 + 1.76211I
0.40098 8.52654I 0
u = 0.48235 1.86660I
a = 0.129952 + 0.874599I
b = 0.56255 1.76211I
0.40098 + 8.52654I 0
u = 0.37322 + 1.91053I
a = 0.000180 + 1.063390I
b = 0.40489 1.80934I
10.8864 10.4301I 0
u = 0.37322 1.91053I
a = 0.000180 1.063390I
b = 0.40489 + 1.80934I
10.8864 + 10.4301I 0
u = 0.14111 + 1.94684I
a = 0.183559 0.886815I
b = 0.20310 + 2.12857I
6.56818 3.53126I 0
u = 0.14111 1.94684I
a = 0.183559 + 0.886815I
b = 0.20310 2.12857I
6.56818 + 3.53126I 0
u = 0.31032 + 1.96443I
a = 0.035948 1.052330I
b = 0.26686 + 1.60207I
9.61428 + 4.66443I 0
u = 0.31032 1.96443I
a = 0.035948 + 1.052330I
b = 0.26686 1.60207I
9.61428 4.66443I 0
10
II.
I
u
2
= h−6.59 × 10
5
u
16
9.28 × 10
5
u
15
+ · · · + 9.63 × 10
5
b 4.43 × 10
5
, 2.99 ×
10
5
u
16
6.39×10
4
u
15
+· · · +9.63×10
5
a1.08×10
6
, u
17
+4u
15
+· · · +2u 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
0.310813u
16
+ 0.0663714u
15
+ ··· 1.72241u + 1.12525
0.684317u
16
+ 0.963659u
15
+ ··· 1.05249u + 0.459909
a
4
=
0.310813u
16
0.0663714u
15
+ ··· + 1.72241u + 0.874748
0.310813u
16
+ 0.0663714u
15
+ ··· 1.72241u + 1.12525
a
1
=
0.354199u
16
+ 0.713554u
15
+ ··· + 0.491844u 0.731715
0.995130u
16
1.03003u
15
+ ··· + 2.77490u 0.585160
a
6
=
0.995130u
16
+ 1.03003u
15
+ ··· 2.77490u + 1.58516
0.684317u
16
+ 0.963659u
15
+ ··· 1.05249u + 0.459909
a
5
=
0.995130u
16
+ 1.03003u
15
+ ··· 2.77490u + 1.58516
1.48635u
16
+ 1.77288u
15
+ ··· 2.11742u + 1.48994
a
8
=
1.87286u
16
+ 0.769039u
15
+ ··· 2.81009u + 2.81349
2.27571u
16
+ 1.58348u
15
+ ··· 2.69896u + 1.66310
a
10
=
1.03003u
16
0.802032u
15
+ ··· + 1.40510u 0.995130
0.742846u
16
0.862875u
15
+ ··· + 1.07766u 0.491219
a
9
=
1.77288u
16
1.66491u
15
+ ··· + 2.48276u 1.48635
0.742846u
16
0.862875u
15
+ ··· + 1.07766u 0.491219
a
12
=
1.08780u
16
0.279503u
15
+ ··· + 3.29700u 2.89828
0.917296u
16
0.947080u
15
+ ··· + 2.92780u 0.487479
(ii) Obstruction class = 1
(iii) Cusp Shapes =
48633
963035
u
16
201324
963035
u
15
+ ··· +
2698689
963035
u
5677206
963035
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
5u
16
+ ··· + 24u 5
c
2
u
17
+ 4u
15
+ ··· + 2u 1
c
3
u
17
3u
16
+ ··· + 6u 1
c
4
u
17
+ 5u
16
+ ··· + 24u + 5
c
5
u
17
u
16
+ ··· u 1
c
6
u
17
+ u
16
+ ··· 3u
2
+ 1
c
7
u
17
+ 2u
16
+ ··· 3u 1
c
8
u
17
+ u
16
+ ··· u 1
c
9
u
17
u
16
+ ··· + 6u 1
c
10
u
17
+ 5u
16
+ ··· + 23u + 5
c
11
, c
12
u
17
u
16
+ ··· u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
+ 11y
16
+ ··· 144y 25
c
2
y
17
+ 8y
16
+ ··· + 2y 1
c
3
y
17
3y
16
+ ··· + 4y 1
c
5
y
17
3y
16
+ ··· 17y 1
c
6
y
17
+ 15y
16
+ ··· + 6y 1
c
7
y
17
6y
16
+ ··· + 19y 1
c
8
, c
11
, c
12
y
17
19y
16
+ ··· + 17y 1
c
9
y
17
+ 15y
16
+ ··· + 40y 1
c
10
y
17
11y
16
+ ··· + 29y 25
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.943516 + 0.217153I
a = 0.305598 + 1.090860I
b = 0.402187 0.424132I
1.02446 4.01073I 9.58562 + 8.03441I
u = 0.943516 0.217153I
a = 0.305598 1.090860I
b = 0.402187 + 0.424132I
1.02446 + 4.01073I 9.58562 8.03441I
u = 0.783718 + 0.432402I
a = 0.531720 1.180930I
b = 0.643590 0.074918I
5.37250 + 7.81586I 13.0076 6.4890I
u = 0.783718 0.432402I
a = 0.531720 + 1.180930I
b = 0.643590 + 0.074918I
5.37250 7.81586I 13.0076 + 6.4890I
u = 0.817030 + 0.365305I
a = 0.934805 + 0.650996I
b = 0.515260 + 0.566112I
7.37347 + 2.42280I 13.78303 1.70443I
u = 0.817030 0.365305I
a = 0.934805 0.650996I
b = 0.515260 0.566112I
7.37347 2.42280I 13.78303 + 1.70443I
u = 0.780176
a = 1.11145
b = 1.12388
4.50362 7.25140
u = 0.628918 + 0.321070I
a = 0.752042 0.357337I
b = 0.685836 0.180128I
1.45511 0.44387I 13.3170 + 6.4333I
u = 0.628918 0.321070I
a = 0.752042 + 0.357337I
b = 0.685836 + 0.180128I
1.45511 + 0.44387I 13.3170 6.4333I
u = 0.218331 + 0.434310I
a = 0.162367 1.304580I
b = 0.837927 + 0.880938I
1.31011 + 3.21669I 4.26897 3.76271I
14
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.218331 0.434310I
a = 0.162367 + 1.304580I
b = 0.837927 0.880938I
1.31011 3.21669I 4.26897 + 3.76271I
u = 0.16034 + 1.55364I
a = 0.412465 1.224420I
b = 0.08339 + 2.23448I
5.22091 1.95313I 7.30585 + 2.22273I
u = 0.16034 1.55364I
a = 0.412465 + 1.224420I
b = 0.08339 2.23448I
5.22091 + 1.95313I 7.30585 2.22273I
u = 0.08691 + 1.63349I
a = 0.307317 + 1.147970I
b = 0.08394 1.85355I
8.57737 + 1.44400I 6.54282 + 0.32634I
u = 0.08691 1.63349I
a = 0.307317 1.147970I
b = 0.08394 + 1.85355I
8.57737 1.44400I 6.54282 0.32634I
u = 0.88290 + 1.41099I
a = 0.022475 0.754741I
b = 0.453346 + 0.788668I
1.32490 2.54139I 11.5634 + 9.6256I
u = 0.88290 1.41099I
a = 0.022475 + 0.754741I
b = 0.453346 0.788668I
1.32490 + 2.54139I 11.5634 9.6256I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
5u
16
+ ··· + 24u 5)(u
59
6u
58
+ ··· 493u + 47)
c
2
(u
17
+ 4u
15
+ ··· + 2u 1)(u
59
+ u
58
+ ··· + 386u + 244)
c
3
(u
17
3u
16
+ ··· + 6u 1)(u
59
2u
58
+ ··· + 1473477u + 77047)
c
4
(u
17
+ 5u
16
+ ··· + 24u + 5)(u
59
6u
58
+ ··· 493u + 47)
c
5
(u
17
u
16
+ ··· u 1)(u
59
7u
57
+ ··· 2336u + 439)
c
6
(u
17
+ u
16
+ ··· 3u
2
+ 1)(u
59
2u
58
+ ··· 4481u + 1539)
c
7
(u
17
+ 2u
16
+ ··· 3u 1)(u
59
15u
58
+ ··· + 72u 4)
c
8
(u
17
+ u
16
+ ··· u 1)(u
59
+ 6u
58
+ ··· + 2u + 1)
c
9
(u
17
u
16
+ ··· + 6u 1)(u
59
2u
58
+ ··· + 2746719u + 257651)
c
10
(u
17
+ 5u
16
+ ··· + 23u + 5)(u
59
+ 2u
58
+ ··· 394u + 149)
c
11
, c
12
(u
17
u
16
+ ··· u + 1)(u
59
+ 6u
58
+ ··· + 2u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
17
+ 11y
16
+ ··· 144y 25)(y
59
+ 40y
58
+ ··· 8213y 2209)
c
2
(y
17
+ 8y
16
+ ··· + 2y 1)(y
59
+ 73y
58
+ ··· 1655140y 59536)
c
3
(y
17
3y
16
+ ··· + 4y 1)
· (y
59
+ 38y
58
+ ··· + 2137083856067y 5936240209)
c
5
(y
17
3y
16
+ ··· 17y 1)(y
59
14y
58
+ ··· + 6258510y 192721)
c
6
(y
17
+ 15y
16
+ ··· + 6y 1)
· (y
59
+ 76y
58
+ ··· + 38959813y 2368521)
c
7
(y
17
6y
16
+ ··· + 19y 1)(y
59
y
58
+ ··· + 1240y 16)
c
8
, c
11
, c
12
(y
17
19y
16
+ ··· + 17y 1)(y
59
58y
58
+ ··· 112y 1)
c
9
(y
17
+ 15y
16
+ ··· + 40y 1)
· (y
59
+ 44y
58
+ ··· 140722482637y 66384037801)
c
10
(y
17
11y
16
+ ··· + 29y 25)(y
59
82y
58
+ ··· + 910368y 22201)
17