12n
0778
(K12n
0778
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 2 10 11 1 3 7 4 8
Solving Sequence
3,9
4
7,10
11 6 2 1 5 8 12
c
3
c
9
c
10
c
6
c
2
c
1
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.19719 × 10
90
u
58
+ 3.18845 × 10
90
u
57
+ ··· + 8.27618 × 10
90
b + 5.36600 × 10
91
,
1.26061 × 10
91
u
58
+ 1.72237 × 10
91
u
57
+ ··· + 2.48285 × 10
91
a + 4.55960 × 10
92
, u
59
+ u
58
+ ··· − 18u − 9i
I
u
2
= hu
16
− u
15
+ ··· + 5b − 9, 7u
16
+ 3u
15
+ ··· + 5a − 28, u
17
+ 10u
15
+ ··· − 5u + 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
= h2.20 × 10
90
u
58
+ 3.19 × 10
90
u
57
+ · · · + 8.28 × 10
90
b + 5.37 × 10
91
, 1.26 ×
10
91
u
58
+1.72×10
91
u
57
+· · ·+2.48×10
91
a+4.56×10
92
, u
59
+u
58
+· · ·−18u−9i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
−0.507725u
58
− 0.693705u
57
+ ··· − 47.3340u − 18.3644
−0.265483u
58
− 0.385257u
57
+ ··· − 20.1693u − 6.48366
a
10
=
u
u
a
11
=
−1.18361u
58
− 1.61569u
57
+ ··· − 147.188u − 26.2949
0.331778u
58
+ 0.515855u
57
+ ··· + 42.4239u + 9.96083
a
6
=
−0.503583u
58
− 0.697011u
57
+ ··· − 43.9621u − 17.7685
−0.261341u
58
− 0.388563u
57
+ ··· − 16.7974u − 5.88781
a
2
=
1.73974u
58
+ 2.35435u
57
+ ··· + 193.814u + 32.6618
0.0168231u
58
+ 0.0480879u
57
+ ··· − 16.3637u − 3.47890
a
1
=
1.92664u
58
+ 2.62835u
57
+ ··· + 204.171u + 34.7144
−0.0640961u
58
− 0.0778894u
57
+ ··· − 19.6136u − 4.26282
a
5
=
1.23803u
58
+ 1.74157u
57
+ ··· + 163.964u + 31.2786
−0.729025u
58
− 0.985396u
57
+ ··· − 80.2851u − 18.3600
a
8
=
0.155964u
58
+ 0.116373u
57
+ ··· + 20.0247u − 5.23157
−0.846484u
58
− 1.22210u
57
+ ··· − 89.6127u − 19.8092
a
12
=
0.979045u
58
+ 1.35615u
57
+ ··· + 123.194u + 20.2228
−0.337866u
58
− 0.511247u
57
+ ··· − 39.5933u − 9.46607
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.7456u
58
− 14.9438u
57
+ ··· − 1129.44u − 248.422
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
− 6u
58
+ ··· − 172u − 188
c
2
, c
5
u
59
+ 2u
58
+ ··· + 16404u + 3277
c
3
, c
9
u
59
− u
58
+ ··· − 18u + 9
c
4
, c
11
u
59
− 3u
58
+ ··· − 326u − 59
c
6
, c
7
, c
10
u
59
+ u
58
+ ··· + 55u − 1
c
8
, c
12
u
59
− 2u
58
+ ··· + 4u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
+ 2y
58
+ ··· + 493568y −35344
c
2
, c
5
y
59
− 44y
58
+ ··· + 376032834y −10738729
c
3
, c
9
y
59
+ 61y
58
+ ··· + 5274y −81
c
4
, c
11
y
59
− 35y
58
+ ··· + 302746y −3481
c
6
, c
7
, c
10
y
59
− 59y
58
+ ··· + 3505y −1
c
8
, c
12
y
59
− 24y
58
+ ··· + 7920y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.946714 + 0.326161I
a = 1.56057 − 0.12495I
b = 0.311162 + 0.580467I
−1.56439 + 3.00160I 0
u = 0.946714 − 0.326161I
a = 1.56057 + 0.12495I
b = 0.311162 − 0.580467I
−1.56439 − 3.00160I 0
u = 0.274423 + 0.933293I
a = 1.093080 + 0.183487I
b = 0.284590 + 0.978686I
−1.31018 − 2.27927I 0
u = 0.274423 − 0.933293I
a = 1.093080 − 0.183487I
b = 0.284590 − 0.978686I
−1.31018 + 2.27927I 0
u = 0.432068 + 0.950149I
a = 0.769405 + 0.539694I
b = 0.959480 + 0.704692I
0.84211 − 1.52559I 0
u = 0.432068 − 0.950149I
a = 0.769405 − 0.539694I
b = 0.959480 − 0.704692I
0.84211 + 1.52559I 0
u = 0.352097 + 0.878149I
a = −0.045510 − 0.420512I
b = 0.39071 − 1.47323I
−3.75832 + 2.49847I −12.64369 + 0.I
u = 0.352097 − 0.878149I
a = −0.045510 + 0.420512I
b = 0.39071 + 1.47323I
−3.75832 − 2.49847I −12.64369 + 0.I
u = −1.13422
a = −1.26893
b = −0.0814501
−6.98624 0
u = 0.561179 + 1.012900I
a = −0.302808 − 0.673820I
b = 0.31273 − 1.54903I
−3.67169 + 2.45859I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.561179 − 1.012900I
a = −0.302808 + 0.673820I
b = 0.31273 + 1.54903I
−3.67169 − 2.45859I 0
u = −1.044970 + 0.554481I
a = 1.284180 − 0.118622I
b = 0.348427 − 0.902142I
−2.53248 − 9.55354I 0
u = −1.044970 − 0.554481I
a = 1.284180 + 0.118622I
b = 0.348427 + 0.902142I
−2.53248 + 9.55354I 0
u = 0.694897 + 0.309169I
a = −0.655382 − 0.922102I
b = −0.492656 + 0.163283I
2.70885 + 5.61589I −3.30287 − 6.43944I
u = 0.694897 − 0.309169I
a = −0.655382 + 0.922102I
b = −0.492656 − 0.163283I
2.70885 − 5.61589I −3.30287 + 6.43944I
u = −0.377570 + 1.203860I
a = 0.551178 − 0.618257I
b = 0.836117 − 0.754276I
0.14649 − 4.50904I 0
u = −0.377570 − 1.203860I
a = 0.551178 + 0.618257I
b = 0.836117 + 0.754276I
0.14649 + 4.50904I 0
u = −0.727540 + 0.051837I
a = −0.190027 + 0.786244I
b = −0.397472 − 0.225985I
3.62930 + 0.50765I −0.833668 + 0.393936I
u = −0.727540 − 0.051837I
a = −0.190027 − 0.786244I
b = −0.397472 + 0.225985I
3.62930 − 0.50765I −0.833668 − 0.393936I
u = −0.219875 + 1.257510I
a = 0.364413 + 0.342316I
b = −0.279945 + 0.897413I
−0.40003 − 2.91377I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.219875 − 1.257510I
a = 0.364413 − 0.342316I
b = −0.279945 − 0.897413I
−0.40003 + 2.91377I 0
u = −1.000700 + 0.859170I
a = −0.917675 + 0.566007I
b = −0.110854 + 1.175290I
−3.32365 + 2.74478I 0
u = −1.000700 − 0.859170I
a = −0.917675 − 0.566007I
b = −0.110854 − 1.175290I
−3.32365 − 2.74478I 0
u = −0.037604 + 1.359730I
a = 0.67112 − 2.28060I
b = 0.72572 − 3.32571I
−4.27309 + 0.18450I 0
u = −0.037604 − 1.359730I
a = 0.67112 + 2.28060I
b = 0.72572 + 3.32571I
−4.27309 − 0.18450I 0
u = −0.225882 + 0.585977I
a = 0.581173 − 0.021516I
b = 0.153517 + 0.402501I
−0.260694 − 1.053330I −4.12893 + 6.41098I
u = −0.225882 − 0.585977I
a = 0.581173 + 0.021516I
b = 0.153517 − 0.402501I
−0.260694 + 1.053330I −4.12893 − 6.41098I
u = 0.122554 + 1.388830I
a = −0.994864 − 0.157474I
b = −0.458238 − 0.081576I
−7.26872 + 1.86522I 0
u = 0.122554 − 1.388830I
a = −0.994864 + 0.157474I
b = −0.458238 + 0.081576I
−7.26872 − 1.86522I 0
u = −0.064719 + 1.399950I
a = 0.551474 − 0.867993I
b = −0.18042 − 1.60402I
−4.84282 − 1.75534I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.064719 − 1.399950I
a = 0.551474 + 0.867993I
b = −0.18042 + 1.60402I
−4.84282 + 1.75534I 0
u = 0.15765 + 1.41350I
a = −1.30737 + 1.31318I
b = −1.20152 + 2.27783I
−11.48850 + 1.95356I 0
u = 0.15765 − 1.41350I
a = −1.30737 − 1.31318I
b = −1.20152 − 2.27783I
−11.48850 − 1.95356I 0
u = −0.20549 + 1.40769I
a = 0.45179 + 1.89171I
b = 0.54915 + 3.15852I
−15.4308 − 2.6517I 0
u = −0.20549 − 1.40769I
a = 0.45179 − 1.89171I
b = 0.54915 − 3.15852I
−15.4308 + 2.6517I 0
u = 0.12784 + 1.44950I
a = 0.49772 + 2.72782I
b = 0.51248 + 3.68045I
−4.61048 + 6.42427I 0
u = 0.12784 − 1.44950I
a = 0.49772 − 2.72782I
b = 0.51248 − 3.68045I
−4.61048 − 6.42427I 0
u = 0.24147 + 1.45902I
a = 0.195740 − 0.333338I
b = −0.532485 − 0.754762I
−3.05183 + 8.97120I 0
u = 0.24147 − 1.45902I
a = 0.195740 + 0.333338I
b = −0.532485 + 0.754762I
−3.05183 − 8.97120I 0
u = −0.513897
a = 3.15603
b = −0.176822
−10.6596 6.98370
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.35908 + 1.48621I
a = 0.31558 − 1.94989I
b = 0.33758 − 3.01668I
−7.41483 + 7.70510I 0
u = 0.35908 − 1.48621I
a = 0.31558 + 1.94989I
b = 0.33758 + 3.01668I
−7.41483 − 7.70510I 0
u = −0.44114 + 1.47669I
a = −0.464833 − 1.280610I
b = −0.53565 − 2.19843I
−11.91740 − 5.70509I 0
u = −0.44114 − 1.47669I
a = −0.464833 + 1.280610I
b = −0.53565 + 2.19843I
−11.91740 + 5.70509I 0
u = 0.389493 + 0.220844I
a = −2.44087 + 0.94073I
b = −0.754459 − 1.051460I
0.98362 + 4.60612I −4.20164 − 5.47950I
u = 0.389493 − 0.220844I
a = −2.44087 − 0.94073I
b = −0.754459 + 1.051460I
0.98362 − 4.60612I −4.20164 + 5.47950I
u = 0.421815
a = 1.90314
b = 0.0611523
−1.31886 −6.37980
u = 0.00552 + 1.58194I
a = −0.499227 − 0.232760I
b = −0.087958 − 0.208511I
−7.88129 − 1.40424I 0
u = 0.00552 − 1.58194I
a = −0.499227 + 0.232760I
b = −0.087958 + 0.208511I
−7.88129 + 1.40424I 0
u = 0.404606
a = 1.10231
b = 1.14381
−2.55057 7.13820
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12585 + 1.62496I
a = −0.95051 + 2.36181I
b = −0.86504 + 3.19856I
−12.17070 + 4.62001I 0
u = 0.12585 − 1.62496I
a = −0.95051 − 2.36181I
b = −0.86504 − 3.19856I
−12.17070 − 4.62001I 0
u = −0.37010 + 1.59094I
a = 0.35752 + 2.03746I
b = 0.31522 + 3.03288I
−9.4757 − 14.7159I 0
u = −0.37010 − 1.59094I
a = 0.35752 − 2.03746I
b = 0.31522 − 3.03288I
−9.4757 + 14.7159I 0
u = 0.365225
a = −2.32338
b = 1.24588
−6.61235 −20.0250
u = −0.17738 + 1.74654I
a = −0.46710 − 2.03444I
b = −0.40433 − 2.83686I
−12.58460 − 1.90611I 0
u = −0.17738 − 1.74654I
a = −0.46710 + 2.03444I
b = −0.40433 + 2.83686I
−12.58460 + 1.90611I 0
u = −0.169630 + 0.056480I
a = −7.62669 + 0.37534I
b = −0.832136 − 0.476957I
0.101047 − 0.878351I −4.40864 + 3.72300I
u = −0.169630 − 0.056480I
a = −7.62669 − 0.37534I
b = −0.832136 + 0.476957I
0.101047 + 0.878351I −4.40864 − 3.72300I
10
II.
I
u
2
= hu
16
−u
15
+· · ·+5b−9, 7u
16
+3u
15
+· · ·+5a −28, u
17
+10u
15
+· · ·−5u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
−
7
5
u
16
−
3
5
u
15
+ ··· −
43
5
u +
28
5
−
1
5
u
16
+
1
5
u
15
+ ··· −
14
5
u +
9
5
a
10
=
u
u
a
11
=
−
3
5
u
16
−
2
5
u
15
+ ··· −
12
5
u +
2
5
u
10
+ u
9
+ 6u
8
+ 5u
7
+ 12u
6
+ 9u
5
+ 9u
4
+ 7u
3
+ 2u
2
+ 2u − 1
a
6
=
−
6
5
u
16
−
4
5
u
15
+ ··· −
29
5
u +
24
5
u
2
+ 1
a
2
=
7
5
u
16
+
3
5
u
15
+ ··· +
43
5
u −
23
5
−u
4
− 2u
2
− 1
a
1
=
9
5
u
16
+
1
5
u
15
+ ··· +
51
5
u −
31
5
3
5
u
16
−
3
5
u
15
+ ··· +
12
5
u −
7
5
a
5
=
3
5
u
16
−
3
5
u
15
+ ··· +
22
5
u −
2
5
−u
6
− 3u
4
− 2u
2
a
8
=
−
2
5
u
16
+
2
5
u
15
+ ··· −
3
5
u +
8
5
−
6
5
u
16
+
1
5
u
15
+ ··· −
34
5
u +
14
5
a
12
=
−
6
5
u
16
−
4
5
u
15
+ ··· −
9
5
u −
1
5
−
2
5
u
16
−
3
5
u
15
+ ··· +
17
5
u −
7
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
5
u
16
+
9
5
u
15
−
19
5
u
14
+
89
5
u
13
+
17
5
u
12
+
344
5
u
11
+
259
5
u
10
+
653
5
u
9
+
586
5
u
8
+
608
5
u
7
+
539
5
u
6
+
196
5
u
5
+
152
5
u
4
−
76
5
u
3
−
79
5
u
2
−
66
5
u −
84
5
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− u
16
+ ··· − 8u − 16
c
2
u
17
+ 3u
16
+ ··· + u − 1
c
3
u
17
+ 10u
15
+ ··· − 5u + 1
c
4
u
17
− 2u
15
+ ··· + u − 1
c
5
u
17
− 3u
16
+ ··· + u + 1
c
6
, c
7
u
17
− 10u
15
+ ··· − 2u + 3
c
8
u
17
− u
16
+ ··· + u − 1
c
9
u
17
+ 10u
15
+ ··· − 5u − 1
c
10
u
17
− 10u
15
+ ··· − 2u − 3
c
11
u
17
− 2u
15
+ ··· + u + 1
c
12
u
17
+ u
16
+ ··· + u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 3y
16
+ ··· + 160y −256
c
2
, c
5
y
17
− 13y
16
+ ··· − 5y −1
c
3
, c
9
y
17
+ 20y
16
+ ··· + 15y −1
c
4
, c
11
y
17
− 4y
16
+ ··· + 31y −1
c
6
, c
7
, c
10
y
17
− 20y
16
+ ··· + 106y −9
c
8
, c
12
y
17
− 13y
16
+ ··· + 17y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.370270 + 0.882724I
a = 1.126790 + 0.849720I
b = 0.40061 + 1.62836I
−0.37700 − 2.96750I −6.68021 + 5.04813I
u = 0.370270 − 0.882724I
a = 1.126790 − 0.849720I
b = 0.40061 − 1.62836I
−0.37700 + 2.96750I −6.68021 − 5.04813I
u = 0.283380 + 1.034670I
a = −0.474819 + 0.656137I
b = −0.579943 − 0.171953I
−0.92109 + 5.46786I −10.23763 − 6.06003I
u = 0.283380 − 1.034670I
a = −0.474819 − 0.656137I
b = −0.579943 + 0.171953I
−0.92109 − 5.46786I −10.23763 + 6.06003I
u = −0.294785 + 1.165370I
a = 0.149035 − 1.322070I
b = −0.44174 − 2.16688I
−2.15159 − 2.40927I −6.43861 + 2.42877I
u = −0.294785 − 1.165370I
a = 0.149035 + 1.322070I
b = −0.44174 + 2.16688I
−2.15159 + 2.40927I −6.43861 − 2.42877I
u = −0.310109 + 0.708925I
a = −0.022884 − 1.244910I
b = −0.0010927 + 0.1277530I
−0.506795 + 0.007742I −9.18842 + 1.72914I
u = −0.310109 − 0.708925I
a = −0.022884 + 1.244910I
b = −0.0010927 − 0.1277530I
−0.506795 − 0.007742I −9.18842 − 1.72914I
u = −0.755533
a = −1.11126
b = 0.596176
−6.01295 −4.57530
u = 0.18150 + 1.49267I
a = −0.58896 + 1.91094I
b = −0.59908 + 3.05192I
−16.2398 + 2.2995I −16.2678 + 0.0594I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18150 − 1.49267I
a = −0.58896 − 1.91094I
b = −0.59908 − 3.05192I
−16.2398 − 2.2995I −16.2678 − 0.0594I
u = 0.02507 + 1.52816I
a = −0.859007 − 0.246531I
b = −0.489948 − 0.467465I
−8.73985 + 0.88822I −14.9978 − 0.1467I
u = 0.02507 − 1.52816I
a = −0.859007 + 0.246531I
b = −0.489948 + 0.467465I
−8.73985 − 0.88822I −14.9978 + 0.1467I
u = 0.421302
a = −3.52887
b = 0.468060
−10.9243 −23.7490
u = −0.21106 + 1.61530I
a = −0.94194 − 1.94202I
b = −0.90243 − 2.76465I
−12.16690 − 3.74722I −13.50510 + 0.26507I
u = −0.21106 − 1.61530I
a = −0.94194 + 1.94202I
b = −0.90243 + 2.76465I
−12.16690 + 3.74722I −13.50510 − 0.26507I
u = 0.245686
a = 2.86368
b = 1.16302
−2.84280 −21.0440
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− u
16
+ ··· − 8u − 16)(u
59
− 6u
58
+ ··· − 172u − 188)
c
2
(u
17
+ 3u
16
+ ··· + u − 1)(u
59
+ 2u
58
+ ··· + 16404u + 3277)
c
3
(u
17
+ 10u
15
+ ··· − 5u + 1)(u
59
− u
58
+ ··· − 18u + 9)
c
4
(u
17
− 2u
15
+ ··· + u − 1)(u
59
− 3u
58
+ ··· − 326u − 59)
c
5
(u
17
− 3u
16
+ ··· + u + 1)(u
59
+ 2u
58
+ ··· + 16404u + 3277)
c
6
, c
7
(u
17
− 10u
15
+ ··· − 2u + 3)(u
59
+ u
58
+ ··· + 55u − 1)
c
8
(u
17
− u
16
+ ··· + u − 1)(u
59
− 2u
58
+ ··· + 4u + 19)
c
9
(u
17
+ 10u
15
+ ··· − 5u − 1)(u
59
− u
58
+ ··· − 18u + 9)
c
10
(u
17
− 10u
15
+ ··· − 2u − 3)(u
59
+ u
58
+ ··· + 55u − 1)
c
11
(u
17
− 2u
15
+ ··· + u + 1)(u
59
− 3u
58
+ ··· − 326u − 59)
c
12
(u
17
+ u
16
+ ··· + u + 1)(u
59
− 2u
58
+ ··· + 4u + 19)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 3y
16
+ ··· + 160y −256)(y
59
+ 2y
58
+ ··· + 493568y −35344)
c
2
, c
5
(y
17
− 13y
16
+ ··· − 5y −1)
· (y
59
− 44y
58
+ ··· + 376032834y −10738729)
c
3
, c
9
(y
17
+ 20y
16
+ ··· + 15y −1)(y
59
+ 61y
58
+ ··· + 5274y −81)
c
4
, c
11
(y
17
− 4y
16
+ ··· + 31y −1)(y
59
− 35y
58
+ ··· + 302746y −3481)
c
6
, c
7
, c
10
(y
17
− 20y
16
+ ··· + 106y −9)(y
59
− 59y
58
+ ··· + 3505y −1)
c
8
, c
12
(y
17
− 13y
16
+ ··· + 17y −1)(y
59
− 24y
58
+ ··· + 7920y −361)
17
