12n
0319
(K12n
0319
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 4 11 12 1 6 4 9
Solving Sequence
4,6 7,12
11 8 9 3 2 1 5 10
c
6
c
11
c
7
c
8
c
3
c
2
c
1
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.38952 × 10
93
u
31
− 2.15372 × 10
94
u
30
+ ··· + 2.56436 × 10
95
b − 7.20111 × 10
95
,
− 8.99453 × 10
94
u
31
+ 7.55251 × 10
95
u
30
+ ··· + 1.28218 × 10
96
a + 7.93300 × 10
96
,
u
32
− 8u
31
+ ··· − 300u − 25i
I
u
2
= h−255u
11
− 694u
10
+ ··· + b − 720, −583u
11
− 1385u
10
+ ··· + a − 850,
u
12
+ 3u
11
− u
10
− 7u
9
+ 19u
8
+ 99u
7
+ 234u
6
+ 343u
5
+ 314u
4
+ 179u
3
+ 62u
2
+ 12u + 1i
* 2 irreducible components of dim
C
= 0, with total 44 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
= h2.39 × 10
93
u
31
− 2.15 × 10
94
u
30
+ · · · + 2.56 × 10
95
b − 7.20 ×
10
95
, −8.99 × 10
94
u
31
+ 7.55 × 10
95
u
30
+ · · · + 1.28 × 10
96
a + 7.93 ×
10
96
, u
32
− 8u
31
+ · · · − 300u − 25i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
12
=
0.0701502u
31
− 0.589036u
30
+ ··· − 53.1722u − 6.18711
−0.00931818u
31
+ 0.0839867u
30
+ ··· + 19.4660u + 2.80815
a
11
=
0.0701502u
31
− 0.589036u
30
+ ··· − 53.1722u − 6.18711
0.00428886u
31
− 0.0294728u
30
+ ··· + 12.8694u + 2.11228
a
8
=
0.139715u
31
− 1.09759u
30
+ ··· − 162.772u − 15.3667
−0.0410233u
31
+ 0.326903u
30
+ ··· + 50.9224u + 5.87488
a
9
=
−0.114284u
31
+ 0.997908u
30
+ ··· − 72.2217u − 7.58056
0.0357130u
31
− 0.298486u
30
+ ··· − 4.59855u + 0.151481
a
3
=
0.00605923u
31
− 0.0127608u
30
+ ··· − 57.1169u − 6.41631
0.00341044u
31
− 0.0414358u
30
+ ··· + 35.9729u + 4.57856
a
2
=
0.00946966u
31
− 0.0541966u
30
+ ··· − 21.1440u − 1.83775
0.00341044u
31
− 0.0414358u
30
+ ··· + 35.9729u + 4.57856
a
1
=
0.102606u
31
− 0.898043u
30
+ ··· + 90.8067u + 10.9018
−0.0317497u
31
+ 0.264273u
30
+ ··· + 7.01197u + 0.281882
a
5
=
0.0314017u
31
− 0.300910u
30
+ ··· + 57.4657u + 7.12226
−0.00733120u
31
+ 0.0774930u
30
+ ··· − 38.6716u − 4.73528
a
10
=
0.0658613u
31
− 0.559563u
30
+ ··· − 66.0416u − 8.29939
0.00428886u
31
− 0.0294728u
30
+ ··· + 12.8694u + 2.11228
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.253355u
31
− 2.01113u
30
+ ··· − 403.608u − 50.8053
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 27u
31
+ ··· + 673u + 1
c
2
, c
5
u
32
+ u
31
+ ··· − 23u + 1
c
3
u
32
+ 2u
31
+ ··· − 42u − 19
c
4
, c
11
u
32
− u
31
+ ··· + 10u − 1
c
6
u
32
− 8u
31
+ ··· − 300u − 25
c
7
u
32
− 3u
31
+ ··· + 1686u + 41
c
8
, c
9
, c
12
u
32
+ 3u
31
+ ··· + 15u − 29
c
10
u
32
+ 3u
31
+ ··· − 37856u − 9991
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 35y
31
+ ··· − 466213y + 1
c
2
, c
5
y
32
− 27y
31
+ ··· − 673y + 1
c
3
y
32
− 6y
31
+ ··· − 2866y + 361
c
4
, c
11
y
32
+ 45y
31
+ ··· − 158y + 1
c
6
y
32
− 82y
31
+ ··· + 6850y + 625
c
7
y
32
+ 61y
31
+ ··· − 2599876y + 1681
c
8
, c
9
, c
12
y
32
− 43y
31
+ ··· − 24875y + 841
c
10
y
32
+ 69y
31
+ ··· − 909927994y + 99820081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197289 + 0.790742I
a = −1.185250 + 0.678056I
b = 0.453864 − 0.396921I
−1.17179 − 1.02205I −9.29559 − 0.44678I
u = −0.197289 − 0.790742I
a = −1.185250 − 0.678056I
b = 0.453864 + 0.396921I
−1.17179 + 1.02205I −9.29559 + 0.44678I
u = −0.299086 + 1.150790I
a = 0.0080471 + 0.0961297I
b = 0.628217 + 0.060085I
2.11287 + 2.53091I 5.79491 − 0.47582I
u = −0.299086 − 1.150790I
a = 0.0080471 − 0.0961297I
b = 0.628217 − 0.060085I
2.11287 − 2.53091I 5.79491 + 0.47582I
u = 0.192167 + 0.775949I
a = 1.404300 − 0.081966I
b = 0.364013 − 1.054130I
−6.40829 + 3.07693I −7.10952 − 3.47095I
u = 0.192167 − 0.775949I
a = 1.404300 + 0.081966I
b = 0.364013 + 1.054130I
−6.40829 − 3.07693I −7.10952 + 3.47095I
u = −1.20877
a = −0.173934
b = −2.03957
−6.85965 −17.0320
u = −0.727605
a = 1.88288
b = −0.166504
−7.46881 −13.7170
u = −0.650840
a = −0.792502
b = −0.0256764
−1.50430 −6.06880
u = −0.303065 + 0.488280I
a = −1.67068 + 0.64751I
b = −1.052950 − 0.482581I
−1.17553 + 2.30017I −10.81580 − 3.72452I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303065 − 0.488280I
a = −1.67068 − 0.64751I
b = −1.052950 + 0.482581I
−1.17553 − 2.30017I −10.81580 + 3.72452I
u = 0.350721
a = 1.62466
b = −0.817925
−2.83439 1.03330
u = −0.089144 + 0.338495I
a = −2.77884 + 3.13257I
b = −0.124470 − 1.064190I
−11.30980 + 7.23064I −10.49848 − 5.56490I
u = −0.089144 − 0.338495I
a = −2.77884 − 3.13257I
b = −0.124470 + 1.064190I
−11.30980 − 7.23064I −10.49848 + 5.56490I
u = −0.084309 + 0.271616I
a = −1.52532 + 1.43742I
b = −0.027514 + 0.487501I
−0.193873 + 1.035160I −3.30197 − 6.61105I
u = −0.084309 − 0.271616I
a = −1.52532 − 1.43742I
b = −0.027514 − 0.487501I
−0.193873 − 1.035160I −3.30197 + 6.61105I
u = −0.263547 + 0.101009I
a = −0.39229 − 3.09375I
b = −0.088766 + 1.320520I
−3.69901 + 3.15402I −10.25267 − 6.17085I
u = −0.263547 − 0.101009I
a = −0.39229 + 3.09375I
b = −0.088766 − 1.320520I
−3.69901 − 3.15402I −10.25267 + 6.17085I
u = −0.09080 + 2.11846I
a = 0.508788 − 0.094674I
b = 1.05942 + 1.08265I
−10.49350 + 1.26769I 0
u = −0.09080 − 2.11846I
a = 0.508788 + 0.094674I
b = 1.05942 − 1.08265I
−10.49350 − 1.26769I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.12482 + 0.01926I
a = 0.001205 + 0.868470I
b = −0.29154 − 1.72481I
−12.56270 − 0.83637I 0
u = 2.12482 − 0.01926I
a = 0.001205 − 0.868470I
b = −0.29154 + 1.72481I
−12.56270 + 0.83637I 0
u = −2.36872 + 0.16438I
a = 0.084723 − 0.669788I
b = −0.11322 + 2.10961I
−7.72510 − 2.29615I 0
u = −2.36872 − 0.16438I
a = 0.084723 + 0.669788I
b = −0.11322 − 2.10961I
−7.72510 + 2.29615I 0
u = 2.59941 + 0.20248I
a = −0.035870 − 0.679734I
b = 0.71473 + 2.13119I
18.4946 − 2.1635I 0
u = 2.59941 − 0.20248I
a = −0.035870 + 0.679734I
b = 0.71473 − 2.13119I
18.4946 + 2.1635I 0
u = −2.80747 + 0.15741I
a = 0.002410 − 0.627895I
b = 0.69377 + 2.39073I
−16.6434 + 4.8981I 0
u = −2.80747 − 0.15741I
a = 0.002410 + 0.627895I
b = 0.69377 − 2.39073I
−16.6434 − 4.8981I 0
u = 3.02521 + 0.40807I
a = 0.006648 + 0.594266I
b = 0.55522 − 2.49269I
17.8060 − 11.5990I 0
u = 3.02521 − 0.40807I
a = 0.006648 − 0.594266I
b = 0.55522 + 2.49269I
17.8060 + 11.5990I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 3.68008 + 0.58451I
a = 0.101580 + 0.427871I
b = 0.25407 − 2.77344I
−11.97980 + 5.22512I 0
u = 3.68008 − 0.58451I
a = 0.101580 − 0.427871I
b = 0.25407 + 2.77344I
−11.97980 − 5.22512I 0
8
II. I
u
2
= h−255u
11
− 694u
10
+ · · · + b − 720, −583u
11
− 1385u
10
+ · · · + a −
850, u
12
+ 3u
11
+ · · · + 12u + 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
12
=
583u
11
+ 1385u
10
+ ··· + 9095u + 850
255u
11
+ 694u
10
+ ··· + 6836u + 720
a
11
=
583u
11
+ 1385u
10
+ ··· + 9095u + 850
465u
11
+ 1211u
10
+ ··· + 10621u + 1084
a
8
=
−12u
11
− 34u
10
+ ··· − 515u − 70
−256u
11
− 640u
10
+ ··· − 5120u − 513
a
9
=
429u
11
+ 1141u
10
+ ··· + 10869u + 1129
u
11
+ 10u
10
+ ··· + 332u + 47
a
3
=
−47u
11
− 140u
10
+ ··· − 1937u − 232
−u
11
− 3u
10
+ ··· − 62u − 11
a
2
=
−48u
11
− 143u
10
+ ··· − 1999u − 243
−u
11
− 3u
10
+ ··· − 62u − 11
a
1
=
382u
11
+ 1008u
10
+ ··· + 9202u + 932
48u
11
+ 135u
10
+ ··· + 1679u + 197
a
5
=
−195u
11
− 538u
10
+ ··· − 6031u − 673
−10u
11
− 29u
10
+ ··· − 441u − 59
a
10
=
118u
11
+ 174u
10
+ ··· − 1526u − 234
465u
11
+ 1211u
10
+ ··· + 10621u + 1084
(ii) Obstruction class = 1
(iii) Cusp Shapes = −557u
11
− 1504u
10
+ 1049u
9
+ 3665u
8
− 11818u
7
− 51768u
6
−
113824u
5
− 153844u
4
− 122639u
3
− 56077u
2
− 13659u − 1383
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 8u
11
+ ··· − 11u + 1
c
2
u
12
− 4u
10
+ u
9
+ 8u
8
− 3u
7
− 11u
6
+ 4u
5
+ 10u
4
− 4u
3
− 5u
2
+ u + 1
c
3
u
12
+ u
11
+ 3u
10
+ 2u
9
+ u
8
− u
7
− 2u
6
− 5u
5
+ 2u
4
− 2u
3
+ 2u
2
− 1
c
4
u
12
+ 8u
10
+ 23u
8
− u
7
+ 26u
6
− 5u
5
+ 5u
4
− 7u
3
− 6u
2
− 2u − 1
c
5
u
12
− 4u
10
− u
9
+ 8u
8
+ 3u
7
− 11u
6
− 4u
5
+ 10u
4
+ 4u
3
− 5u
2
− u + 1
c
6
u
12
+ 3u
11
+ ··· + 12u + 1
c
7
u
12
+ 4u
10
+ ··· − 8u + 1
c
8
, c
9
u
12
+ 4u
11
+ ··· − u + 1
c
10
u
12
+ 4u
11
+ ··· − 2u + 1
c
11
u
12
+ 8u
10
+ 23u
8
+ u
7
+ 26u
6
+ 5u
5
+ 5u
4
+ 7u
3
− 6u
2
+ 2u − 1
c
12
u
12
− 4u
11
+ ··· + u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 12y
10
+ ··· − 15y + 1
c
2
, c
5
y
12
− 8y
11
+ ··· − 11y + 1
c
3
y
12
+ 5y
11
+ 7y
10
+ 7y
8
+ 35y
7
+ 16y
6
− 39y
5
− 26y
4
+ 8y
3
− 4y + 1
c
4
, c
11
y
12
+ 16y
11
+ ··· + 8y + 1
c
6
y
12
− 11y
11
+ ··· − 20y + 1
c
7
y
12
+ 8y
11
+ ··· − 22y + 1
c
8
, c
9
, c
12
y
12
− 16y
11
+ ··· + 23y + 1
c
10
y
12
+ 4y
11
+ ··· − 20y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614910
a = −0.756088
b = 0.764925
−3.38826 −14.4840
u = −0.215601 + 1.381410I
a = 0.288748 − 0.106147I
b = 0.283384 + 0.092414I
1.69154 + 2.70631I −11.02847 − 6.50238I
u = −0.215601 − 1.381410I
a = 0.288748 + 0.106147I
b = 0.283384 − 0.092414I
1.69154 − 2.70631I −11.02847 + 6.50238I
u = −0.484089 + 0.123501I
a = 0.24097 − 1.98728I
b = −0.879338 + 0.481043I
−0.12267 − 1.98013I −3.12844 + 2.86006I
u = −0.484089 − 0.123501I
a = 0.24097 + 1.98728I
b = −0.879338 − 0.481043I
−0.12267 + 1.98013I −3.12844 − 2.86006I
u = −0.445198 + 0.198592I
a = −1.35255 + 2.90526I
b = 0.766353 − 0.473864I
−5.28947 − 3.09904I −8.62038 + 2.82123I
u = −0.445198 − 0.198592I
a = −1.35255 − 2.90526I
b = 0.766353 + 0.473864I
−5.28947 + 3.09904I −8.62038 − 2.82123I
u = −0.438663
a = 1.76179
b = 1.21224
−6.05655 −5.50250
u = −2.04805 + 0.64643I
a = −0.276703 + 0.652409I
b = −0.25152 − 2.07706I
−9.00537 − 2.27031I −12.11846 + 2.13201I
u = −2.04805 − 0.64643I
a = −0.276703 − 0.652409I
b = −0.25152 + 2.07706I
−9.00537 + 2.27031I −12.11846 − 2.13201I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 2.21973 + 1.41604I
a = −0.403311 − 0.470237I
b = −0.90746 + 1.60507I
−12.16040 + 3.87633I −12.61114 − 1.47831I
u = 2.21973 − 1.41604I
a = −0.403311 + 0.470237I
b = −0.90746 − 1.60507I
−12.16040 − 3.87633I −12.61114 + 1.47831I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
− 8u
11
+ ··· − 11u + 1)(u
32
+ 27u
31
+ ··· + 673u + 1)
c
2
(u
12
− 4u
10
+ u
9
+ 8u
8
− 3u
7
− 11u
6
+ 4u
5
+ 10u
4
− 4u
3
− 5u
2
+ u + 1)
· (u
32
+ u
31
+ ··· − 23u + 1)
c
3
(u
12
+ u
11
+ 3u
10
+ 2u
9
+ u
8
− u
7
− 2u
6
− 5u
5
+ 2u
4
− 2u
3
+ 2u
2
− 1)
· (u
32
+ 2u
31
+ ··· − 42u − 19)
c
4
(u
12
+ 8u
10
+ 23u
8
− u
7
+ 26u
6
− 5u
5
+ 5u
4
− 7u
3
− 6u
2
− 2u − 1)
· (u
32
− u
31
+ ··· + 10u − 1)
c
5
(u
12
− 4u
10
− u
9
+ 8u
8
+ 3u
7
− 11u
6
− 4u
5
+ 10u
4
+ 4u
3
− 5u
2
− u + 1)
· (u
32
+ u
31
+ ··· − 23u + 1)
c
6
(u
12
+ 3u
11
+ ··· + 12u + 1)(u
32
− 8u
31
+ ··· − 300u − 25)
c
7
(u
12
+ 4u
10
+ ··· − 8u + 1)(u
32
− 3u
31
+ ··· + 1686u + 41)
c
8
, c
9
(u
12
+ 4u
11
+ ··· − u + 1)(u
32
+ 3u
31
+ ··· + 15u − 29)
c
10
(u
12
+ 4u
11
+ ··· − 2u + 1)(u
32
+ 3u
31
+ ··· − 37856u − 9991)
c
11
(u
12
+ 8u
10
+ 23u
8
+ u
7
+ 26u
6
+ 5u
5
+ 5u
4
+ 7u
3
− 6u
2
+ 2u − 1)
· (u
32
− u
31
+ ··· + 10u − 1)
c
12
(u
12
− 4u
11
+ ··· + u + 1)(u
32
+ 3u
31
+ ··· + 15u − 29)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
12
− 12y
10
+ ··· − 15y + 1)(y
32
− 35y
31
+ ··· − 466213y + 1)
c
2
, c
5
(y
12
− 8y
11
+ ··· − 11y + 1)(y
32
− 27y
31
+ ··· − 673y + 1)
c
3
(y
12
+ 5y
11
+ 7y
10
+ 7y
8
+ 35y
7
+ 16y
6
− 39y
5
− 26y
4
+ 8y
3
− 4y + 1)
· (y
32
− 6y
31
+ ··· − 2866y + 361)
c
4
, c
11
(y
12
+ 16y
11
+ ··· + 8y + 1)(y
32
+ 45y
31
+ ··· − 158y + 1)
c
6
(y
12
− 11y
11
+ ··· − 20y + 1)(y
32
− 82y
31
+ ··· + 6850y + 625)
c
7
(y
12
+ 8y
11
+ ··· − 22y + 1)(y
32
+ 61y
31
+ ··· − 2599876y + 1681)
c
8
, c
9
, c
12
(y
12
− 16y
11
+ ··· + 23y + 1)(y
32
− 43y
31
+ ··· − 24875y + 841)
c
10
(y
12
+ 4y
11
+ ··· − 20y + 1)
· (y
32
+ 69y
31
+ ··· − 909927994y + 99820081)
15
