12n
0407
(K12n
0407
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 10 3 6 12 3 7 9
Solving Sequence
6,10 4,7
3 8 11 12 2 1 5 9
c
6
c
3
c
7
c
10
c
11
c
2
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.91368 × 10
38
u
28
+ 9.57768 × 10
38
u
27
+ ··· + 2.45804 × 10
41
b + 3.47957 × 10
40
,
2.07300 × 10
41
u
28
− 1.33160 × 10
41
u
27
+ ··· + 3.22003 × 10
43
a − 6.95309 × 10
43
,
u
29
− u
28
+ ··· + 138u − 131i
I
u
2
= h107u
10
+ 32u
9
+ 296u
8
− 244u
7
+ 366u
6
− 671u
5
+ 173u
4
− 379u
3
+ 801u
2
+ 137b − 343u + 11,
− 65u
10
− 22u
9
− 135u
8
+ 202u
7
− 29u
6
+ 487u
5
+ 78u
4
+ 115u
3
− 525u
2
+ 137a + 56u + 138,
u
11
+ 3u
9
− 3u
8
+ 5u
7
− 8u
6
+ 5u
5
− 6u
4
+ 9u
3
− 7u
2
+ 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 40 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
= h−7.91 × 10
38
u
28
+ 9.58 × 10
38
u
27
+ · · · + 2.46 × 10
41
b + 3.48 ×
10
40
, 2.07 × 10
41
u
28
− 1.33 × 10
41
u
27
+ · · · + 3.22 × 10
43
a − 6.95 ×
10
43
, u
29
− u
28
+ · · · + 138u − 131i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
4
=
−0.00643783u
28
+ 0.00413537u
27
+ ··· + 0.662423u + 2.15933
0.00321951u
28
− 0.00389647u
27
+ ··· − 1.02149u − 0.141559
a
7
=
1
u
2
a
3
=
−0.00643783u
28
+ 0.00413537u
27
+ ··· + 0.662423u + 2.15933
0.000740929u
28
+ 0.00319203u
27
+ ··· − 1.54711u − 0.443182
a
8
=
−0.00128485u
28
+ 0.00710786u
27
+ ··· − 1.02644u + 0.742688
0.00237299u
28
+ 0.00288909u
27
+ ··· + 0.812621u − 0.726496
a
11
=
0.00280137u
28
− 0.000100345u
27
+ ··· + 5.91373u − 1.91339
−0.00280112u
28
+ 0.00521011u
27
+ ··· + 0.914236u + 0.185519
a
12
=
−0.00302164u
28
+ 0.00557538u
27
+ ··· + 4.99373u − 1.74508
0.00526331u
28
− 0.00557686u
27
+ ··· + 0.171748u + 0.166224
a
2
=
−0.00569690u
28
+ 0.00732739u
27
+ ··· − 0.884682u + 1.71614
0.000740929u
28
+ 0.00319203u
27
+ ··· − 1.54711u − 0.443182
a
1
=
0.00343665u
28
+ 0.00333715u
27
+ ··· − 4.10542u + 1.78332
0.000428392u
28
− 0.00831580u
27
+ ··· − 1.31725u + 0.269050
a
5
=
−0.00619815u
28
+ 0.00185133u
27
+ ··· + 1.94172u + 1.98378
−0.00478198u
28
− 0.00236596u
27
+ ··· − 1.38469u + 1.09344
a
9
=
−0.00365784u
28
+ 0.00421878u
27
+ ··· − 1.83906u + 1.46918
0.00237299u
28
+ 0.00288909u
27
+ ··· + 0.812621u − 0.726496
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0105084u
28
+ 0.00112769u
27
+ ··· + 16.0288u − 8.53764
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 36u
28
+ ··· + 31u + 1
c
2
, c
5
u
29
+ 4u
28
+ ··· − u + 1
c
3
, c
10
u
29
− 2u
28
+ ··· + 8u + 1
c
4
u
29
+ 3u
28
+ ··· + 365u + 41
c
6
u
29
+ u
28
+ ··· + 138u + 131
c
7
u
29
− u
28
+ ··· + 19u + 1
c
8
u
29
− 6u
28
+ ··· − 2946u + 449
c
9
, c
12
u
29
− 3u
28
+ ··· + 4u + 1
c
11
u
29
− 2u
28
+ ··· + 814u + 143
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 76y
28
+ ··· − 661y −1
c
2
, c
5
y
29
− 36y
28
+ ··· + 31y −1
c
3
, c
10
y
29
− 34y
28
+ ··· − 44y −1
c
4
y
29
− 37y
28
+ ··· + 56719y −1681
c
6
y
29
+ 23y
28
+ ··· − 189770y −17161
c
7
y
29
+ 37y
28
+ ··· + 65y −1
c
8
y
29
− 28y
28
+ ··· + 5623920y −201601
c
9
, c
12
y
29
+ 13y
28
+ ··· + 10y −1
c
11
y
29
+ 22y
28
+ ··· − 104456y −20449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.436375 + 0.850418I
a = 0.1286560 − 0.0002151I
b = 1.78815 − 0.23286I
−9.19094 + 2.43845I −7.01904 + 1.26700I
u = 0.436375 − 0.850418I
a = 0.1286560 + 0.0002151I
b = 1.78815 + 0.23286I
−9.19094 − 2.43845I −7.01904 − 1.26700I
u = 0.078457 + 1.066260I
a = −1.46433 − 0.41449I
b = −0.0909103 − 0.0528598I
−8.13051 − 4.19111I −7.68221 + 3.19701I
u = 0.078457 − 1.066260I
a = −1.46433 + 0.41449I
b = −0.0909103 + 0.0528598I
−8.13051 + 4.19111I −7.68221 − 3.19701I
u = −0.879989 + 0.721780I
a = 0.260919 + 0.251520I
b = 0.184603 + 0.338556I
2.12073 + 2.71911I 0.73382 − 5.26127I
u = −0.879989 − 0.721780I
a = 0.260919 − 0.251520I
b = 0.184603 − 0.338556I
2.12073 − 2.71911I 0.73382 + 5.26127I
u = 0.790394 + 0.245974I
a = 0.525024 − 0.126942I
b = −0.706490 + 0.199595I
−0.940187 + 0.023179I −6.45467 + 0.13585I
u = 0.790394 − 0.245974I
a = 0.525024 + 0.126942I
b = −0.706490 − 0.199595I
−0.940187 − 0.023179I −6.45467 − 0.13585I
u = −0.943061 + 0.720483I
a = −0.789406 − 0.515771I
b = −0.664638 − 0.961832I
−5.68896 + 1.78021I −8.58741 − 3.28174I
u = −0.943061 − 0.720483I
a = −0.789406 + 0.515771I
b = −0.664638 + 0.961832I
−5.68896 − 1.78021I −8.58741 + 3.28174I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.312879 + 1.192260I
a = −0.476660 − 1.226750I
b = 0.44318 − 1.83008I
8.78516 + 1.46029I −3.70386 − 0.33063I
u = −0.312879 − 1.192260I
a = −0.476660 + 1.226750I
b = 0.44318 + 1.83008I
8.78516 − 1.46029I −3.70386 + 0.33063I
u = −0.083431 + 1.234000I
a = 0.437799 + 0.932870I
b = −0.83465 + 1.40051I
3.89818 + 0.55243I −6.20625 − 0.30214I
u = −0.083431 − 1.234000I
a = 0.437799 − 0.932870I
b = −0.83465 − 1.40051I
3.89818 − 0.55243I −6.20625 + 0.30214I
u = 0.711939
a = 0.565805
b = −0.540254
−0.970174 −8.63040
u = −0.550508 + 1.211630I
a = 0.440780 + 1.225810I
b = −0.10690 + 1.85218I
5.97141 + 2.47634I −8.54776 − 2.98261I
u = −0.550508 − 1.211630I
a = 0.440780 − 1.225810I
b = −0.10690 − 1.85218I
5.97141 − 2.47634I −8.54776 + 2.98261I
u = −0.612611 + 1.267610I
a = −0.070611 − 1.272500I
b = 0.21455 − 1.57150I
−3.65066 + 4.20226I −9.01127 − 2.33118I
u = −0.612611 − 1.267610I
a = −0.070611 + 1.272500I
b = 0.21455 + 1.57150I
−3.65066 − 4.20226I −9.01127 + 2.33118I
u = −0.106413 + 0.445417I
a = 2.15539 − 0.01946I
b = −0.057994 − 0.310123I
−0.73739 − 1.44881I −4.73223 + 5.89766I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.106413 − 0.445417I
a = 2.15539 + 0.01946I
b = −0.057994 + 0.310123I
−0.73739 + 1.44881I −4.73223 − 5.89766I
u = 1.49230 + 0.42245I
a = −0.772162 + 0.148645I
b = 0.356443 + 1.010820I
−4.96797 + 3.17574I −8.51023 − 2.94389I
u = 1.49230 − 0.42245I
a = −0.772162 − 0.148645I
b = 0.356443 − 1.010820I
−4.96797 − 3.17574I −8.51023 + 2.94389I
u = −0.35669 + 1.69215I
a = 0.107831 + 0.917859I
b = 0.15685 + 1.73182I
5.71858 + 1.14552I −8.18527 − 0.09349I
u = −0.35669 − 1.69215I
a = 0.107831 − 0.917859I
b = 0.15685 − 1.73182I
5.71858 − 1.14552I −8.18527 + 0.09349I
u = 0.81408 + 1.59165I
a = −0.213716 + 0.990636I
b = 0.46420 + 2.04047I
−1.05228 − 11.62150I −7.61445 + 5.40349I
u = 0.81408 − 1.59165I
a = −0.213716 − 0.990636I
b = 0.46420 − 2.04047I
−1.05228 + 11.62150I −7.61445 − 5.40349I
u = 0.37800 + 1.85458I
a = 0.073544 − 0.896135I
b = −0.37627 − 1.91342I
6.70498 − 5.94744I −6.16397 + 5.31814I
u = 0.37800 − 1.85458I
a = 0.073544 + 0.896135I
b = −0.37627 + 1.91342I
6.70498 + 5.94744I −6.16397 − 5.31814I
7
II. I
u
2
= h107u
10
+ 32u
9
+ · · · + 137b + 11, −65u
10
− 22u
9
+ · · · + 137a +
138, u
11
+ 3u
9
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
4
=
0.474453u
10
+ 0.160584u
9
+ ··· − 0.408759u − 1.00730
−0.781022u
10
− 0.233577u
9
+ ··· + 2.50365u − 0.0802920
a
7
=
1
u
2
a
3
=
0.474453u
10
+ 0.160584u
9
+ ··· − 0.408759u − 1.00730
−1.21898u
10
− 0.766423u
9
+ ··· + 2.49635u + 0.0802920
a
8
=
1.21898u
10
+ 0.766423u
9
+ ··· − 2.49635u − 0.0802920
−0.781022u
10
− 0.233577u
9
+ ··· + 2.50365u + 0.919708
a
11
=
−1.01460u
10
− 0.0510949u
9
+ ··· + 5.76642u − 0.861314
1.08759u
10
+ 0.306569u
9
+ ··· − 4.59854u + 1.16788
a
12
=
−1.78102u
10
− 0.233577u
9
+ ··· + 9.50365u − 2.08029
0.948905u
10
+ 0.321168u
9
+ ··· − 4.81752u + 0.985401
a
2
=
−0.744526u
10
− 0.605839u
9
+ ··· + 2.08759u − 0.927007
−1.21898u
10
− 0.766423u
9
+ ··· + 2.49635u + 0.0802920
a
1
=
−2.08029u
10
− 1.78102u
9
+ ··· + 0.715328u + 3.26277
1.16788u
10
+ 1.08759u
9
+ ··· − 0.313869u − 2.09489
a
5
=
−0.693431u
10
− 0.927007u
9
+ ··· − 0.0948905u + 1.08759
0.474453u
10
+ 0.160584u
9
+ ··· − 0.408759u − 2.00730
a
9
=
2u
10
+ u
9
+ 6u
8
− 3u
7
+ 7u
6
− 11u
5
+ 2u
4
− 7u
3
+ 12u
2
− 5u − 1
−0.781022u
10
− 0.233577u
9
+ ··· + 2.50365u + 0.919708
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
387
137
u
10
+
190
137
u
9
+
1278
137
u
8
−
524
137
u
7
+
1882
137
u
6
−
2126
137
u
5
+
1207
137
u
4
−
2002
137
u
3
+
2504
137
u
2
−
1891
137
u−
1005
137
8
(iv) u-Polynomials at the component
9
Crossings u-Polynomials at each crossing
c
1
u
11
− 13u
10
+ ··· + 52u − 9
c
2
u
11
+ 3u
10
+ ··· + 2u − 3
c
3
u
11
+ u
10
− 5u
9
− 5u
8
+ 5u
7
+ 6u
6
+ 4u
5
+ u
4
+ 3u
3
+ 6u
2
− u + 1
c
4
u
11
+ 2u
10
− u
9
+ u
8
+ 4u
7
− 7u
6
+ 6u
5
+ 4u
4
− 10u
3
+ 12u
2
− 4u + 1
c
5
u
11
− 3u
10
+ ··· + 2u + 3
c
6
u
11
+ 3u
9
− 3u
8
+ 5u
7
− 8u
6
+ 5u
5
− 6u
4
+ 9u
3
− 7u
2
+ 3u − 1
c
7
u
11
+ 4u
9
− 2u
8
− 2u
7
− 6u
6
− 19u
5
− 2u
4
+ 25u
3
+ 23u
2
+ 8u + 1
c
8
u
11
+ 5u
10
+ 8u
9
+ 5u
8
+ 3u
7
− u
5
− u
4
− 11u
3
+ 2u
2
+ 19u + 11
c
9
u
11
− 2u
10
+ ··· + u + 1
c
10
u
11
− u
10
− 5u
9
+ 5u
8
+ 5u
7
− 6u
6
+ 4u
5
− u
4
+ 3u
3
− 6u
2
− u − 1
c
11
u
11
+ u
10
+ 5u
9
+ 4u
8
+ 5u
7
+ 8u
6
− 3u
5
+ 14u
4
+ 6u
3
+ 2u
2
+ 7u + 3
c
12
u
11
+ 2u
10
+ ··· + u − 1
10
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 21y
10
+ ··· − 572y −81
c
2
, c
5
y
11
− 13y
10
+ ··· + 52y −9
c
3
, c
10
y
11
− 11y
10
+ ··· − 11y −1
c
4
y
11
− 6y
10
+ ··· − 8y −1
c
6
y
11
+ 6y
10
+ ··· − 5y −1
c
7
y
11
+ 8y
10
+ ··· + 18y −1
c
8
y
11
− 9y
10
+ ··· + 317y −121
c
9
, c
12
y
11
+ 8y
10
+ ··· + 7y −1
c
11
y
11
+ 9y
10
+ ··· + 37y −9
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.911705
a = −1.38521
b = −0.393018
−5.17789 −7.42590
u = −0.773965 + 0.836171I
a = 0.181088 − 0.296407I
b = −0.517402 + 0.043467I
1.53593 + 2.51523I −12.12476 − 1.29720I
u = −0.773965 − 0.836171I
a = 0.181088 + 0.296407I
b = −0.517402 − 0.043467I
1.53593 − 2.51523I −12.12476 + 1.29720I
u = 0.686714 + 0.364294I
a = 0.919009 + 0.465058I
b = −0.604594 − 0.175211I
−1.53391 + 0.85947I −12.42982 − 2.96274I
u = 0.686714 − 0.364294I
a = 0.919009 − 0.465058I
b = −0.604594 + 0.175211I
−1.53391 − 0.85947I −12.42982 + 2.96274I
u = 0.25449 + 1.39655I
a = 0.057934 − 1.204510I
b = 0.36465 − 1.77060I
7.50546 − 0.80130I −3.83965 + 0.29153I
u = 0.25449 − 1.39655I
a = 0.057934 + 1.204510I
b = 0.36465 + 1.77060I
7.50546 + 0.80130I −3.83965 − 0.29153I
u = 0.143684 + 0.483044I
a = −1.91917 + 0.41809I
b = 1.362770 + 0.233285I
−9.90480 + 3.35709I −12.00843 − 3.32581I
u = 0.143684 − 0.483044I
a = −1.91917 − 0.41809I
b = 1.362770 − 0.233285I
−9.90480 − 3.35709I −12.00843 + 3.32581I
u = −0.76677 + 1.46423I
a = 0.453746 + 0.894119I
b = −0.40891 + 1.90938I
8.27614 + 3.20665I −4.88437 − 3.50404I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.76677 − 1.46423I
a = 0.453746 − 0.894119I
b = −0.40891 − 1.90938I
8.27614 − 3.20665I −4.88437 + 3.50404I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
− 13u
10
+ ··· + 52u − 9)(u
29
+ 36u
28
+ ··· + 31u + 1)
c
2
(u
11
+ 3u
10
+ ··· + 2u − 3)(u
29
+ 4u
28
+ ··· − u + 1)
c
3
(u
11
+ u
10
− 5u
9
− 5u
8
+ 5u
7
+ 6u
6
+ 4u
5
+ u
4
+ 3u
3
+ 6u
2
− u + 1)
· (u
29
− 2u
28
+ ··· + 8u + 1)
c
4
(u
11
+ 2u
10
− u
9
+ u
8
+ 4u
7
− 7u
6
+ 6u
5
+ 4u
4
− 10u
3
+ 12u
2
− 4u + 1)
· (u
29
+ 3u
28
+ ··· + 365u + 41)
c
5
(u
11
− 3u
10
+ ··· + 2u + 3)(u
29
+ 4u
28
+ ··· − u + 1)
c
6
(u
11
+ 3u
9
− 3u
8
+ 5u
7
− 8u
6
+ 5u
5
− 6u
4
+ 9u
3
− 7u
2
+ 3u − 1)
· (u
29
+ u
28
+ ··· + 138u + 131)
c
7
(u
11
+ 4u
9
− 2u
8
− 2u
7
− 6u
6
− 19u
5
− 2u
4
+ 25u
3
+ 23u
2
+ 8u + 1)
· (u
29
− u
28
+ ··· + 19u + 1)
c
8
(u
11
+ 5u
10
+ 8u
9
+ 5u
8
+ 3u
7
− u
5
− u
4
− 11u
3
+ 2u
2
+ 19u + 11)
· (u
29
− 6u
28
+ ··· − 2946u + 449)
c
9
(u
11
− 2u
10
+ ··· + u + 1)(u
29
− 3u
28
+ ··· + 4u + 1)
c
10
(u
11
− u
10
− 5u
9
+ 5u
8
+ 5u
7
− 6u
6
+ 4u
5
− u
4
+ 3u
3
− 6u
2
− u − 1)
· (u
29
− 2u
28
+ ··· + 8u + 1)
c
11
(u
11
+ u
10
+ 5u
9
+ 4u
8
+ 5u
7
+ 8u
6
− 3u
5
+ 14u
4
+ 6u
3
+ 2u
2
+ 7u + 3)
· (u
29
− 2u
28
+ ··· + 814u + 143)
c
12
(u
11
+ 2u
10
+ ··· + u − 1)(u
29
− 3u
28
+ ··· + 4u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
− 21y
10
+ ··· − 572y −81)(y
29
− 76y
28
+ ··· − 661y −1)
c
2
, c
5
(y
11
− 13y
10
+ ··· + 52y −9)(y
29
− 36y
28
+ ··· + 31y −1)
c
3
, c
10
(y
11
− 11y
10
+ ··· − 11y −1)(y
29
− 34y
28
+ ··· − 44y −1)
c
4
(y
11
− 6y
10
+ ··· − 8y −1)(y
29
− 37y
28
+ ··· + 56719y −1681)
c
6
(y
11
+ 6y
10
+ ··· − 5y −1)(y
29
+ 23y
28
+ ··· − 189770y −17161)
c
7
(y
11
+ 8y
10
+ ··· + 18y −1)(y
29
+ 37y
28
+ ··· + 65y −1)
c
8
(y
11
− 9y
10
+ ··· + 317y −121)
· (y
29
− 28y
28
+ ··· + 5623920y −201601)
c
9
, c
12
(y
11
+ 8y
10
+ ··· + 7y −1)(y
29
+ 13y
28
+ ··· + 10y −1)
c
11
(y
11
+ 9y
10
+ ··· + 37y −9)(y
29
+ 22y
28
+ ··· − 104456y −20449)
16
