12n
0003
(K12n
0003
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 10 4 6 12 7 9 11
Solving Sequence
6,10 4,7
5 8 9 11 12 3 2 1
c
6
c
4
c
7
c
8
c
10
c
11
c
3
c
2
c
1
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.97857 × 10
48
u
47
− 8.37875 × 10
48
u
46
+ ··· + 1.28272 × 10
49
b + 5.04932 × 10
48
,
− 1.38689 × 10
49
u
47
− 4.12412 × 10
49
u
46
+ ··· + 1.28272 × 10
49
a − 7.42829 × 10
49
, u
48
+ 3u
47
+ ··· + 2u + 1i
I
u
2
= hu
2
a + b, u
5
a + u
5
− 2u
3
a − 2u
4
+ u
2
a − u
3
+ a
2
+ 2au + 3u
2
− a − 2, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 60 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−1.98×10
48
u
47
−8.38×10
48
u
46
+· · ·+1.28×10
49
b+5.05×10
48
, −1.39×
10
49
u
47
−4.12×10
49
u
46
+· · ·+1.28×10
49
a−7.43×10
49
, u
48
+3u
47
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
4
=
1.08121u
47
+ 3.21513u
46
+ ··· + 0.931628u + 5.79103
0.154247u
47
+ 0.653200u
46
+ ··· − 0.117415u − 0.393641
a
7
=
1
−u
2
a
5
=
0.794887u
47
+ 2.62840u
46
+ ··· − 0.210005u + 5.42589
0.264517u
47
+ 0.943944u
46
+ ··· + 0.140724u − 0.121410
a
8
=
0.138808u
47
+ 0.0569367u
46
+ ··· + 1.13835u − 1.23220
0.0866426u
47
+ 0.143205u
46
+ ··· − 0.0590538u + 0.156142
a
9
=
0.225450u
47
+ 0.200142u
46
+ ··· + 1.07929u − 1.07605
0.0866426u
47
+ 0.143205u
46
+ ··· − 0.0590538u + 0.156142
a
11
=
u
−u
3
+ u
a
12
=
0.197793u
47
+ 0.746837u
46
+ ··· − 0.411380u + 1.70840
0.497798u
47
+ 1.23878u
46
+ ··· + 1.17262u + 0.785808
a
3
=
1.23546u
47
+ 3.86833u
46
+ ··· + 0.814213u + 5.39739
0.154247u
47
+ 0.653200u
46
+ ··· − 0.117415u − 0.393641
a
2
=
−1.23812u
47
− 2.80513u
46
+ ··· − 9.14389u + 0.0144920
0.146826u
47
+ 0.655230u
46
+ ··· + 0.00400667u + 0.694477
a
1
=
0.138808u
47
+ 0.0569367u
46
+ ··· + 1.13835u − 1.23220
−0.270573u
47
− 0.659768u
46
+ ··· − 0.521111u − 0.515628
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7.13383u
47
+ 19.7832u
46
+ ··· + 16.2053u + 20.7902
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 31u
47
+ ··· + 24u + 1
c
2
, c
5
u
48
+ 7u
47
+ ··· + 12u + 1
c
3
u
48
− 7u
47
+ ··· + 12u
2
+ 1
c
4
, c
7
u
48
+ 3u
47
+ ··· − 8192u + 4096
c
6
, c
10
u
48
− 3u
47
+ ··· − 2u + 1
c
8
u
48
+ 9u
47
+ ··· − 23626848u + 3579401
c
9
, c
11
u
48
− 3u
47
+ ··· − 8u + 1
c
12
u
48
+ 29u
47
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
− 21y
47
+ ··· + 2824y + 1
c
2
, c
5
y
48
+ 31y
47
+ ··· + 24y + 1
c
3
y
48
− 73y
47
+ ··· + 24y + 1
c
4
, c
7
y
48
+ 65y
47
+ ··· + 184549376y + 16777216
c
6
, c
10
y
48
− 9y
47
+ ··· − 8y + 1
c
8
y
48
+ 83y
47
+ ··· + 697935129971156y + 12812111518801
c
9
, c
11
y
48
− 29y
47
+ ··· − 8y + 1
c
12
y
48
− 17y
47
+ ··· + 200y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888432 + 0.471966I
a = −0.334610 − 1.300970I
b = −0.050019 + 0.219961I
−4.63723 − 0.72636I −3.19086 − 0.34526I
u = 0.888432 − 0.471966I
a = −0.334610 + 1.300970I
b = −0.050019 − 0.219961I
−4.63723 + 0.72636I −3.19086 + 0.34526I
u = 0.636986 + 0.733622I
a = 0.279122 + 0.849564I
b = −0.813791 − 0.933020I
−5.67745 + 5.32167I −4.21900 − 6.97135I
u = 0.636986 − 0.733622I
a = 0.279122 − 0.849564I
b = −0.813791 + 0.933020I
−5.67745 − 5.32167I −4.21900 + 6.97135I
u = −1.035480 + 0.144515I
a = 0.398707 + 0.045146I
b = −0.005777 − 0.451241I
1.83509 − 0.11544I 4.43775 + 1.73282I
u = −1.035480 − 0.144515I
a = 0.398707 − 0.045146I
b = −0.005777 + 0.451241I
1.83509 + 0.11544I 4.43775 − 1.73282I
u = 0.468363 + 0.992714I
a = −0.028122 + 0.951893I
b = 0.197854 − 0.122368I
−3.89164 − 1.83510I −3.88038 + 1.67120I
u = 0.468363 − 0.992714I
a = −0.028122 − 0.951893I
b = 0.197854 + 0.122368I
−3.89164 + 1.83510I −3.88038 − 1.67120I
u = −0.438971 + 0.749800I
a = −0.150656 − 0.909768I
b = −0.434634 + 0.073940I
−1.87656 − 2.26693I −0.23419 + 4.23054I
u = −0.438971 − 0.749800I
a = −0.150656 + 0.909768I
b = −0.434634 − 0.073940I
−1.87656 + 2.26693I −0.23419 − 4.23054I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.055170 + 0.454319I
a = 0.350993 − 0.350907I
b = −0.229165 + 0.586958I
0.47415 + 4.77230I 2.90925 − 7.59230I
u = 1.055170 − 0.454319I
a = 0.350993 + 0.350907I
b = −0.229165 − 0.586958I
0.47415 − 4.77230I 2.90925 + 7.59230I
u = −1.157600 + 0.418766I
a = −0.250131 + 0.368235I
b = 0.366611 + 0.145765I
0.69730 − 2.30425I 0
u = −1.157600 − 0.418766I
a = −0.250131 − 0.368235I
b = 0.366611 − 0.145765I
0.69730 + 2.30425I 0
u = −0.617941 + 0.399224I
a = 0.060615 + 0.914870I
b = −1.57348 − 1.15912I
−1.23836 − 4.95401I 0.95024 + 9.76424I
u = −0.617941 − 0.399224I
a = 0.060615 − 0.914870I
b = −1.57348 + 1.15912I
−1.23836 + 4.95401I 0.95024 − 9.76424I
u = −0.690433 + 0.022710I
a = 0.340123 + 0.236436I
b = 0.710419 − 0.336425I
1.274320 − 0.061861I 8.91275 − 0.63325I
u = −0.690433 − 0.022710I
a = 0.340123 − 0.236436I
b = 0.710419 + 0.336425I
1.274320 + 0.061861I 8.91275 + 0.63325I
u = 0.952290 + 0.917135I
a = 0.86871 − 1.24612I
b = −2.02867 + 0.31602I
−5.72498 + 3.38721I 0
u = 0.952290 − 0.917135I
a = 0.86871 + 1.24612I
b = −2.02867 − 0.31602I
−5.72498 − 3.38721I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663259 + 0.139973I
a = 0.219248 − 1.384360I
b = 0.12321 + 1.65156I
0.85103 + 2.84744I 6.69474 − 7.55737I
u = 0.663259 − 0.139973I
a = 0.219248 + 1.384360I
b = 0.12321 − 1.65156I
0.85103 − 2.84744I 6.69474 + 7.55737I
u = −0.864759 + 1.001780I
a = −0.70764 − 1.33859I
b = 2.09539 + 0.70588I
−14.6682 − 3.0850I 0
u = −0.864759 − 1.001780I
a = −0.70764 + 1.33859I
b = 2.09539 − 0.70588I
−14.6682 + 3.0850I 0
u = −0.934317 + 0.943776I
a = 1.07851 + 1.19683I
b = −2.15162 + 0.09289I
−9.73534 + 1.58904I 0
u = −0.934317 − 0.943776I
a = 1.07851 − 1.19683I
b = −2.15162 − 0.09289I
−9.73534 − 1.58904I 0
u = 0.325135 + 0.583617I
a = 1.010560 − 0.435996I
b = −0.100686 − 0.124770I
−1.73157 − 0.74220I −3.53436 + 1.20207I
u = 0.325135 − 0.583617I
a = 1.010560 + 0.435996I
b = −0.100686 + 0.124770I
−1.73157 + 0.74220I −3.53436 − 1.20207I
u = 1.213470 + 0.584928I
a = −0.504959 − 0.128402I
b = 0.658444 − 0.124156I
−1.32166 + 7.73642I 0
u = 1.213470 − 0.584928I
a = −0.504959 + 0.128402I
b = 0.658444 + 0.124156I
−1.32166 − 7.73642I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.978343 + 0.926207I
a = 0.80633 + 1.44174I
b = −2.29946 − 0.61084I
−9.59881 − 8.46951I 0
u = −0.978343 − 0.926207I
a = 0.80633 − 1.44174I
b = −2.29946 + 0.61084I
−9.59881 + 8.46951I 0
u = 0.866755 + 1.048470I
a = −0.729094 + 1.119430I
b = 1.93255 − 0.26341I
−10.22760 − 1.78431I 0
u = 0.866755 − 1.048470I
a = −0.729094 − 1.119430I
b = 1.93255 + 0.26341I
−10.22760 + 1.78431I 0
u = −1.051530 + 0.891321I
a = −1.31485 − 1.07651I
b = 2.10442 − 0.11160I
−14.0441 − 3.8628I 0
u = −1.051530 − 0.891321I
a = −1.31485 + 1.07651I
b = 2.10442 + 0.11160I
−14.0441 + 3.8628I 0
u = −0.905222 + 1.060420I
a = −0.888396 − 1.029930I
b = 2.14464 − 0.04344I
−13.8372 + 7.1481I 0
u = −0.905222 − 1.060420I
a = −0.888396 + 1.029930I
b = 2.14464 + 0.04344I
−13.8372 − 7.1481I 0
u = 1.07786 + 0.91788I
a = −1.00742 + 1.16837I
b = 2.09175 − 0.23831I
−9.52196 + 8.95742I 0
u = 1.07786 − 0.91788I
a = −1.00742 − 1.16837I
b = 2.09175 + 0.23831I
−9.52196 − 8.95742I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06846 + 0.94471I
a = −0.91395 − 1.39925I
b = 2.30191 + 0.42350I
−13.2732 − 14.4519I 0
u = −1.06846 − 0.94471I
a = −0.91395 + 1.39925I
b = 2.30191 − 0.42350I
−13.2732 + 14.4519I 0
u = 0.518541 + 0.209657I
a = −0.15012 − 2.09948I
b = −0.571793 + 1.215850I
0.60718 + 2.45344I 2.01156 − 2.44263I
u = 0.518541 − 0.209657I
a = −0.15012 + 2.09948I
b = −0.571793 − 1.215850I
0.60718 − 2.45344I 2.01156 + 2.44263I
u = −0.097000 + 0.527699I
a = −0.97037 − 3.44326I
b = −0.320461 − 0.724196I
−1.36020 − 1.48509I −1.96785 + 10.33925I
u = −0.097000 − 0.527699I
a = −0.97037 + 3.44326I
b = −0.320461 + 0.724196I
−1.36020 + 1.48509I −1.96785 − 10.33925I
u = −0.326195 + 0.340981I
a = 4.53740 + 4.91757I
b = −0.647629 + 0.837735I
−1.80837 + 2.42279I 4.5070 + 19.1208I
u = −0.326195 − 0.340981I
a = 4.53740 − 4.91757I
b = −0.647629 − 0.837735I
−1.80837 − 2.42279I 4.5070 − 19.1208I
9
II. I
u
2
= hu
2
a + b, u
5
a + u
5
+ · · · − a − 2, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
4
=
a
−u
2
a
a
7
=
1
−u
2
a
5
=
a
−u
2
a
a
8
=
1
−u
2
a
9
=
−u
2
+ 1
−u
2
a
11
=
u
−u
3
+ u
a
12
=
−u
4
+ u
2
− 1
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
3
=
−u
2
a + a
−u
2
a
a
2
=
u
5
− u
2
a − 2u
3
+ u
2
+ a + 2u − 1
−u
2
a + 1
a
1
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
5
a + u
4
a + u
5
− 4u
3
a − 6u
4
+ 5u
2
a − u
3
+ 3au + 7u
2
− 2a − 4u − 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
7
u
12
c
6
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
9
, c
10
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
7
y
12
c
6
, c
9
, c
10
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
8
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.815127 − 0.417821I
b = −0.500000 + 0.866025I
1.89061 + 1.10558I 4.53097 − 2.95636I
u = −1.002190 + 0.295542I
a = −0.045720 + 0.914831I
b = −0.500000 − 0.866025I
1.89061 − 2.95419I 7.73749 + 4.22314I
u = −1.002190 − 0.295542I
a = 0.815127 + 0.417821I
b = −0.500000 − 0.866025I
1.89061 − 1.10558I 4.53097 + 2.95636I
u = −1.002190 − 0.295542I
a = −0.045720 − 0.914831I
b = −0.500000 + 0.866025I
1.89061 + 2.95419I 7.73749 − 4.22314I
u = 0.428243 + 0.664531I
a = 0.93136 − 1.30101I
b = −0.500000 − 0.866025I
−1.89061 − 2.95419I −0.76561 + 6.31197I
u = 0.428243 + 0.664531I
a = −1.59239 − 0.15607I
b = −0.500000 + 0.866025I
−1.89061 + 1.10558I −4.61123 − 3.09109I
u = 0.428243 − 0.664531I
a = 0.93136 + 1.30101I
b = −0.500000 + 0.866025I
−1.89061 + 2.95419I −0.76561 − 6.31197I
u = 0.428243 − 0.664531I
a = −1.59239 + 0.15607I
b = −0.500000 − 0.866025I
−1.89061 − 1.10558I −4.61123 + 3.09109I
u = 1.073950 + 0.558752I
a = 0.679704 + 0.059778I
b = −0.500000 − 0.866025I
3.66314I −0.57335 − 1.75283I
u = 1.073950 + 0.558752I
a = −0.288082 − 0.618530I
b = −0.500000 + 0.866025I
7.72290I 3.68173 − 7.68692I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = 0.679704 − 0.059778I
b = −0.500000 + 0.866025I
− 3.66314I −0.57335 + 1.75283I
u = 1.073950 − 0.558752I
a = −0.288082 + 0.618530I
b = −0.500000 − 0.866025I
− 7.72290I 3.68173 + 7.68692I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
48
+ 31u
47
+ ··· + 24u + 1)
c
2
((u
2
+ u + 1)
6
)(u
48
+ 7u
47
+ ··· + 12u + 1)
c
3
((u
2
− u + 1)
6
)(u
48
− 7u
47
+ ··· + 12u
2
+ 1)
c
4
, c
7
u
12
(u
48
+ 3u
47
+ ··· − 8192u + 4096)
c
5
((u
2
− u + 1)
6
)(u
48
+ 7u
47
+ ··· + 12u + 1)
c
6
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
48
− 3u
47
+ ··· − 2u + 1)
c
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
48
+ 9u
47
+ ··· − 23626848u + 3579401)
c
9
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
48
− 3u
47
+ ··· − 8u + 1)
c
10
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
48
− 3u
47
+ ··· − 2u + 1)
c
11
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
48
− 3u
47
+ ··· − 8u + 1)
c
12
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
)(u
48
+ 29u
47
+ ··· + 8u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
48
− 21y
47
+ ··· + 2824y + 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
48
+ 31y
47
+ ··· + 24y + 1)
c
3
((y
2
+ y + 1)
6
)(y
48
− 73y
47
+ ··· + 24y + 1)
c
4
, c
7
y
12
(y
48
+ 65y
47
+ ··· + 1.84549 × 10
8
y + 1.67772 × 10
7
)
c
6
, c
10
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
48
− 9y
47
+ ··· − 8y + 1)
c
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
48
+ 83y
47
+ ··· + 697935129971156y + 12812111518801)
c
9
, c
11
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
48
− 29y
47
+ ··· − 8y + 1)
c
12
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
48
− 17y
47
+ ··· + 200y + 1)
16
