12n
0362
(K12n
0362
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 12 2 10 1 12 7 6 4
Solving Sequence
2,7
6
3,11
12 1 5 10 8 4 9
c
6
c
2
c
11
c
1
c
5
c
10
c
7
c
3
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h6.22856 × 10
22
u
28
+ 9.17947 × 10
22
u
27
+ ··· + 6.05360 × 10
22
b − 3.78443 × 10
23
,
4.23380 × 10
22
u
28
+ 6.00251 × 10
22
u
27
+ ··· + 1.81608 × 10
23
a − 2.84140 × 10
23
, u
29
+ u
28
+ ··· − 7u + 3i
I
u
2
= h25u
13
+ 21u
12
+ ··· + 38b + 39, 28u
13
+ 22u
12
+ ··· + 38a + 125,
u
14
+ 2u
12
+ u
11
+ 2u
10
+ 4u
9
+ 5u
7
+ 3u
6
+ 9u
4
− 4u
3
+ 6u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 43 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
= h6.23 × 10
22
u
28
+ 9.18 × 10
22
u
27
+ · · · + 6.05 × 10
22
b − 3.78 × 10
23
, 4.23 ×
10
22
u
28
+6.00×10
22
u
27
+· · ·+1.82×10
23
a−2.84×10
23
, u
29
+u
28
+· · ·−7u+3i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−0.233129u
28
− 0.330520u
27
+ ··· + 0.142332u + 1.56458
−1.02890u
28
− 1.51637u
27
+ ··· − 2.22286u + 6.25155
a
12
=
−1.28168u
28
− 1.86932u
27
+ ··· − 2.09818u + 7.52395
−1.33350u
28
− 1.99028u
27
+ ··· − 2.50900u + 7.72231
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
−1.13087u
28
− 1.69160u
27
+ ··· − 3.73374u + 6.87479
−0.452599u
28
− 0.697647u
27
+ ··· − 2.84372u + 2.78730
a
10
=
−1.26203u
28
− 1.84689u
27
+ ··· − 2.08053u + 7.81613
−1.02890u
28
− 1.51637u
27
+ ··· − 2.22286u + 6.25155
a
8
=
−1.46451u
28
− 2.20169u
27
+ ··· − 3.99392u + 9.36262
−0.583764u
28
− 0.939441u
27
+ ··· − 2.53644u + 3.54213
a
4
=
1.44243u
28
+ 2.20325u
27
+ ··· + 5.47310u − 7.92054
0.146798u
28
+ 0.344443u
27
+ ··· + 2.49249u − 0.145976
a
9
=
−1.51831u
28
− 2.23503u
27
+ ··· − 3.75421u + 9.70241
−0.975943u
28
− 1.42608u
27
+ ··· − 2.71519u + 6.24874
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
284585492999900700617379
60535961828035184424854
u
28
−
234964149766130199530131
30267980914017592212427
u
27
+ ··· −
730227845218527654431241
60535961828035184424854
u +
888664531849357631011752
30267980914017592212427
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− u
28
+ ··· + 73u − 9
c
2
, c
6
u
29
− u
28
+ ··· − 7u − 3
c
3
u
29
+ 15u
25
+ ··· + 32u − 11
c
4
u
29
− 24u
27
+ ··· − 306u − 49
c
5
, c
11
u
29
− 3u
28
+ ··· − 6023859u − 792917
c
7
, c
10
u
29
− 4u
28
+ ··· + 590u − 1097
c
8
u
29
− u
28
+ ··· + 2101u − 503
c
9
u
29
+ 6u
28
+ ··· + 8024u − 1461
c
12
u
29
+ 2u
27
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 51y
28
+ ··· + 1909y −81
c
2
, c
6
y
29
− y
28
+ ··· + 73y −9
c
3
y
29
+ 30y
27
+ ··· − 538y −121
c
4
y
29
− 48y
28
+ ··· + 26604y −2401
c
5
, c
11
y
29
− 99y
28
+ ··· + 5243889665927y −628717368889
c
7
, c
10
y
29
+ 50y
28
+ ··· + 4466238y −1203409
c
8
y
29
+ 31y
28
+ ··· − 4491917y −253009
c
9
y
29
− 62y
28
+ ··· − 12595514y −2134521
c
12
y
29
+ 4y
28
+ ··· + 12y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373209 + 0.987492I
a = −0.104866 − 0.390683I
b = 0.354634 + 0.496131I
−0.91018 − 2.91066I 5.01825 + 3.66237I
u = −0.373209 − 0.987492I
a = −0.104866 + 0.390683I
b = 0.354634 − 0.496131I
−0.91018 + 2.91066I 5.01825 − 3.66237I
u = −0.676723 + 0.657927I
a = 1.37413 − 1.24981I
b = −0.587705 − 0.859816I
3.33766 − 4.86187I 6.31556 + 7.79080I
u = −0.676723 − 0.657927I
a = 1.37413 + 1.24981I
b = −0.587705 + 0.859816I
3.33766 + 4.86187I 6.31556 − 7.79080I
u = −1.003850 + 0.405083I
a = 0.881641 − 0.955047I
b = −1.52183 + 1.81794I
4.69261 + 0.54758I 8.30748 − 0.23720I
u = −1.003850 − 0.405083I
a = 0.881641 + 0.955047I
b = −1.52183 − 1.81794I
4.69261 − 0.54758I 8.30748 + 0.23720I
u = 0.690839 + 0.852823I
a = −1.58706 − 0.12680I
b = 1.168090 − 0.519664I
−1.72733 + 5.06544I −0.06902 − 8.02609I
u = 0.690839 − 0.852823I
a = −1.58706 + 0.12680I
b = 1.168090 + 0.519664I
−1.72733 − 5.06544I −0.06902 + 8.02609I
u = 0.301765 + 1.063800I
a = 0.115276 − 1.216510I
b = 0.350185 + 0.484209I
−3.69483 + 0.73314I −5.00047 + 1.33936I
u = 0.301765 − 1.063800I
a = 0.115276 + 1.216510I
b = 0.350185 − 0.484209I
−3.69483 − 0.73314I −5.00047 − 1.33936I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.746264 + 0.430998I
a = 0.459246 + 0.593245I
b = −1.06802 − 1.95662I
4.83649 + 4.86751I 7.86120 − 7.38894I
u = 0.746264 − 0.430998I
a = 0.459246 − 0.593245I
b = −1.06802 + 1.95662I
4.83649 − 4.86751I 7.86120 + 7.38894I
u = −1.17492
a = 1.30562
b = −1.24715
2.83868 −0.284290
u = 0.785504 + 0.193075I
a = −0.69313 + 1.26338I
b = 0.123042 + 0.893877I
5.21089 − 2.34623I 11.13604 + 2.03452I
u = 0.785504 − 0.193075I
a = −0.69313 − 1.26338I
b = 0.123042 − 0.893877I
5.21089 + 2.34623I 11.13604 − 2.03452I
u = −0.636133 + 0.449347I
a = 0.946998 − 0.046552I
b = −0.353642 − 0.116483I
1.14437 − 0.87641I 6.31209 + 2.91044I
u = −0.636133 − 0.449347I
a = 0.946998 + 0.046552I
b = −0.353642 + 0.116483I
1.14437 + 0.87641I 6.31209 − 2.91044I
u = −0.193861 + 0.669195I
a = −1.12680 − 1.16765I
b = 0.873432 + 0.640443I
−1.76493 − 2.37343I −1.52317 + 0.50273I
u = −0.193861 − 0.669195I
a = −1.12680 + 1.16765I
b = 0.873432 − 0.640443I
−1.76493 + 2.37343I −1.52317 − 0.50273I
u = 0.510226 + 0.048164I
a = 0.823085 − 0.113650I
b = 0.302073 − 0.906163I
−0.71888 + 2.03179I 1.45662 − 4.22219I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510226 − 0.048164I
a = 0.823085 + 0.113650I
b = 0.302073 + 0.906163I
−0.71888 − 2.03179I 1.45662 + 4.22219I
u = 1.15086 + 1.05205I
a = 1.35233 − 1.13268I
b = −0.61827 + 2.28433I
17.8200 + 4.6744I 4.90361 − 1.93865I
u = 1.15086 − 1.05205I
a = 1.35233 + 1.13268I
b = −0.61827 − 2.28433I
17.8200 − 4.6744I 4.90361 + 1.93865I
u = 1.06456 + 1.14906I
a = −1.02725 + 1.45432I
b = 0.02209 − 2.23942I
17.4581 + 3.4840I 4.59551 − 2.22003I
u = 1.06456 − 1.14906I
a = −1.02725 − 1.45432I
b = 0.02209 + 2.23942I
17.4581 − 3.4840I 4.59551 + 2.22003I
u = −1.14088 + 1.11108I
a = 1.45432 + 1.41280I
b = −0.63801 − 2.49907I
17.2047 − 12.2799I 4.10699 + 5.81074I
u = −1.14088 − 1.11108I
a = 1.45432 − 1.41280I
b = −0.63801 + 2.49907I
17.2047 + 12.2799I 4.10699 − 5.81074I
u = −1.13790 + 1.15169I
a = −1.18740 − 1.61441I
b = 0.21751 + 2.42455I
17.1162 + 3.8820I 4.22145 − 2.11285I
u = −1.13790 − 1.15169I
a = −1.18740 + 1.61441I
b = 0.21751 − 2.42455I
17.1162 − 3.8820I 4.22145 + 2.11285I
7
II. I
u
2
= h25u
13
+ 21u
12
+ · · · + 38b + 39, 28u
13
+ 22u
12
+ · · · + 38a +
125, u
14
+ 2u
12
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−0.736842u
13
− 0.578947u
12
+ ··· − 0.0789474u − 3.28947
−0.657895u
13
− 0.552632u
12
+ ··· − 2.05263u − 1.02632
a
12
=
−1.86842u
13
− 1.28947u
12
+ ··· − 2.28947u − 4.89474
−0.394737u
13
− 0.131579u
12
+ ··· − 1.63158u − 0.315789
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
3.65789u
13
+ 1.55263u
12
+ ··· + 7.55263u + 6.52632
−
1
2
u
9
+ u
8
+ ··· +
3
2
u −
1
2
a
10
=
−1.39474u
13
− 1.13158u
12
+ ··· − 2.13158u − 4.31579
−0.657895u
13
− 0.552632u
12
+ ··· − 2.05263u − 1.02632
a
8
=
2.02632u
13
+ 0.342105u
12
+ ··· + 6.34211u + 1.92105
0.921053u
13
− 0.526316u
12
+ ··· + 2.47368u − 1.26316
a
4
=
−0.315789u
13
+ 0.894737u
12
+ ··· − 6.10526u + 4.44737
1.15789u
13
+ 0.0526316u
12
+ ··· + 2.55263u − 0.473684
a
9
=
2.21053u
13
+ 0.736842u
12
+ ··· + 6.73684u + 2.36842
0.394737u
13
− 0.868421u
12
+ ··· + 1.13158u − 1.68421
(ii) Obstruction class = 1
(iii) Cusp Shapes =
275
38
u
13
+
117
38
u
12
+ 10u
11
+
389
38
u
10
+
191
19
u
9
+
993
38
u
8
+
61
19
u
7
+
643
38
u
6
+
1071
38
u
5
−
175
38
u
4
+
1549
38
u
3
−
105
19
u
2
+
49
19
u +
201
38
8
(iv) u-Polynomials at the component
9
Crossings u-Polynomials at each crossing
c
1
u
14
− 4u
13
+ ··· − 11u + 1
c
2
u
14
+ 2u
12
− u
11
+ 2u
10
− 4u
9
− 5u
7
+ 3u
6
+ 9u
4
+ 4u
3
+ 6u
2
+ u + 1
c
3
u
14
− u
13
− 3u
12
+ 4u
11
+ 4u
10
− 7u
9
+ 6u
7
− 6u
6
− 2u
5
+ 9u
4
− 5u
2
+ 1
c
4
u
14
+ u
13
+ ··· − 8u + 1
c
5
u
14
+ 2u
13
+ ··· − 9u + 1
c
6
u
14
+ 2u
12
+ u
11
+ 2u
10
+ 4u
9
+ 5u
7
+ 3u
6
+ 9u
4
− 4u
3
+ 6u
2
− u + 1
c
7
u
14
+ u
13
+ ··· + 2u + 1
c
8
u
14
+ 6u
13
+ ··· + 3u + 1
c
9
u
14
+ 15u
13
+ ··· + 430u + 67
c
10
u
14
− u
13
+ ··· − 2u + 1
c
11
u
14
− 2u
13
+ ··· + 9u + 1
c
12
u
14
+ u
13
+ ··· + 4u
2
+ 1
10
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ 12y
12
+ ··· − 29y + 1
c
2
, c
6
y
14
+ 4y
13
+ ··· + 11y + 1
c
3
y
14
− 7y
13
+ ··· − 10y + 1
c
4
y
14
− 15y
13
+ ··· − 36y + 1
c
5
, c
11
y
14
+ 2y
13
+ ··· − 3y + 1
c
7
, c
10
y
14
+ 3y
13
+ ··· + 2y + 1
c
8
y
14
+ 12y
13
+ ··· + 5y + 1
c
9
y
14
− 13y
13
+ ··· + 12482y + 4489
c
12
y
14
+ 5y
13
+ ··· + 8y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.083441 + 1.078120I
a = −0.61041 − 1.75239I
b = 0.359465 + 0.927829I
−3.38940 − 1.96463I −3.36465 + 3.16114I
u = −0.083441 − 1.078120I
a = −0.61041 + 1.75239I
b = 0.359465 − 0.927829I
−3.38940 + 1.96463I −3.36465 − 3.16114I
u = 0.897543 + 0.628482I
a = −0.569463 − 0.217274I
b = 0.362370 − 1.134100I
2.05951 + 4.06327I 2.33224 − 4.24956I
u = 0.897543 − 0.628482I
a = −0.569463 + 0.217274I
b = 0.362370 + 1.134100I
2.05951 − 4.06327I 2.33224 + 4.24956I
u = 0.330516 + 0.759270I
a = −1.019620 + 0.347965I
b = 0.931938 − 0.797201I
−1.80322 + 3.24685I −4.21171 − 8.28864I
u = 0.330516 − 0.759270I
a = −1.019620 − 0.347965I
b = 0.931938 + 0.797201I
−1.80322 − 3.24685I −4.21171 + 8.28864I
u = 0.605820 + 1.045230I
a = 0.540931 − 0.356236I
b = 0.280794 + 0.717818I
0.55352 + 1.43715I 2.87679 − 0.95272I
u = 0.605820 − 1.045230I
a = 0.540931 + 0.356236I
b = 0.280794 − 0.717818I
0.55352 − 1.43715I 2.87679 + 0.95272I
u = −1.201470 + 0.299412I
a = 0.998346 − 0.558650I
b = −1.21886 + 1.14220I
3.33918 + 0.87099I 2.89094 − 4.11825I
u = −1.201470 − 0.299412I
a = 0.998346 + 0.558650I
b = −1.21886 − 1.14220I
3.33918 − 0.87099I 2.89094 + 4.11825I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.555233 + 1.209370I
a = 1.330610 − 0.277547I
b = −0.600887 − 0.417434I
0.03234 − 6.71387I 0.87198 + 7.20748I
u = −0.555233 − 1.209370I
a = 1.330610 + 0.277547I
b = −0.600887 + 0.417434I
0.03234 + 6.71387I 0.87198 − 7.20748I
u = 0.006261 + 0.511967I
a = −2.67040 + 0.41495I
b = −0.614823 − 0.394790I
4.14287 + 3.38328I 6.10441 − 3.17614I
u = 0.006261 − 0.511967I
a = −2.67040 − 0.41495I
b = −0.614823 + 0.394790I
4.14287 − 3.38328I 6.10441 + 3.17614I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− 4u
13
+ ··· − 11u + 1)(u
29
− u
28
+ ··· + 73u − 9)
c
2
(u
14
+ 2u
12
− u
11
+ 2u
10
− 4u
9
− 5u
7
+ 3u
6
+ 9u
4
+ 4u
3
+ 6u
2
+ u + 1)
· (u
29
− u
28
+ ··· − 7u − 3)
c
3
(u
14
− u
13
− 3u
12
+ 4u
11
+ 4u
10
− 7u
9
+ 6u
7
− 6u
6
− 2u
5
+ 9u
4
− 5u
2
+ 1)
· (u
29
+ 15u
25
+ ··· + 32u − 11)
c
4
(u
14
+ u
13
+ ··· − 8u + 1)(u
29
− 24u
27
+ ··· − 306u − 49)
c
5
(u
14
+ 2u
13
+ ··· − 9u + 1)(u
29
− 3u
28
+ ··· − 6023859u − 792917)
c
6
(u
14
+ 2u
12
+ u
11
+ 2u
10
+ 4u
9
+ 5u
7
+ 3u
6
+ 9u
4
− 4u
3
+ 6u
2
− u + 1)
· (u
29
− u
28
+ ··· − 7u − 3)
c
7
(u
14
+ u
13
+ ··· + 2u + 1)(u
29
− 4u
28
+ ··· + 590u − 1097)
c
8
(u
14
+ 6u
13
+ ··· + 3u + 1)(u
29
− u
28
+ ··· + 2101u − 503)
c
9
(u
14
+ 15u
13
+ ··· + 430u + 67)(u
29
+ 6u
28
+ ··· + 8024u − 1461)
c
10
(u
14
− u
13
+ ··· − 2u + 1)(u
29
− 4u
28
+ ··· + 590u − 1097)
c
11
(u
14
− 2u
13
+ ··· + 9u + 1)(u
29
− 3u
28
+ ··· − 6023859u − 792917)
c
12
(u
14
+ u
13
+ ··· + 4u
2
+ 1)(u
29
+ 2u
27
+ ··· + 6u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
14
+ 12y
12
+ ··· − 29y + 1)(y
29
+ 51y
28
+ ··· + 1909y −81)
c
2
, c
6
(y
14
+ 4y
13
+ ··· + 11y + 1)(y
29
− y
28
+ ··· + 73y −9)
c
3
(y
14
− 7y
13
+ ··· − 10y + 1)(y
29
+ 30y
27
+ ··· − 538y −121)
c
4
(y
14
− 15y
13
+ ··· − 36y + 1)(y
29
− 48y
28
+ ··· + 26604y −2401)
c
5
, c
11
(y
14
+ 2y
13
+ ··· − 3y + 1)
· (y
29
− 99y
28
+ ··· + 5243889665927y −628717368889)
c
7
, c
10
(y
14
+ 3y
13
+ ··· + 2y + 1)(y
29
+ 50y
28
+ ··· + 4466238y −1203409)
c
8
(y
14
+ 12y
13
+ ··· + 5y + 1)(y
29
+ 31y
28
+ ··· − 4491917y −253009)
c
9
(y
14
− 13y
13
+ ··· + 12482y + 4489)
· (y
29
− 62y
28
+ ··· − 12595514y −2134521)
c
12
(y
14
+ 5y
13
+ ··· + 8y + 1)(y
29
+ 4y
28
+ ··· + 12y −1)
16
