12n
0183
(K12n
0183
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 9 12 3 11 6 1 7
Solving Sequence
5,10
6
3,11
2 1 4 9 7 12 8
c
5
c
10
c
2
c
1
c
4
c
9
c
6
c
12
c
7
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.20523 × 10
32
u
62
− 1.33633 × 10
32
u
61
+ ··· + 4.02644 × 10
32
b + 1.46507 × 10
32
,
1.44947 × 10
32
u
62
− 4.60820 × 10
30
u
61
+ ··· + 1.34215 × 10
32
a − 2.19191 × 10
32
, u
63
+ 2u
62
+ ··· + 4u + 1i
I
u
2
= hb + 1, 2u
8
+ u
7
− 5u
6
− 3u
5
+ 4u
4
+ 3u
3
+ 2u
2
+ a − 2, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 72 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−1.21×10
32
u
62
−1.34×10
32
u
61
+· · ·+4.03×10
32
b+1.47×10
32
, 1.45×
10
32
u
62
−4.61×10
30
u
61
+· · ·+1.34×10
32
a−2.19×10
32
, u
63
+2u
62
+· · ·+4u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−1.07996u
62
+ 0.0343346u
61
+ ··· − 1.91121u + 1.63313
0.299329u
62
+ 0.331888u
61
+ ··· + 1.56778u − 0.363863
a
11
=
−u
−u
3
+ u
a
2
=
−0.780635u
62
+ 0.366222u
61
+ ··· − 0.343427u + 1.26927
0.299329u
62
+ 0.331888u
61
+ ··· + 1.56778u − 0.363863
a
1
=
0.498188u
62
+ 0.716504u
61
+ ··· + 2.18592u − 0.0731899
0.197906u
62
+ 0.176045u
61
+ ··· + 1.05588u + 0.392848
a
4
=
−1.09042u
62
− 0.00217631u
61
+ ··· − 1.99896u + 1.59173
0.208603u
62
+ 0.265857u
61
+ ··· + 1.12023u − 0.513655
a
9
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
0.153458u
62
+ 0.0698033u
61
+ ··· + 2.02811u − 0.0419731
0.369503u
62
+ 0.349046u
61
+ ··· + 2.10549u + 0.618121
a
8
=
−0.445304u
62
− 0.752007u
61
+ ··· − 4.41211u − 0.301292
0.301712u
62
+ 0.446342u
61
+ ··· + 1.60552u + 0.343270
(ii) Obstruction class = −1
(iii) Cusp Shapes = 20.7017u
62
+ 25.9299u
61
+ ··· + 68.1832u + 9.80994
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 20u
62
+ ··· − 54u + 1
c
2
, c
4
u
63
− 10u
62
+ ··· − 6u + 1
c
3
, c
8
u
63
+ u
62
+ ··· + 5632u + 512
c
5
, c
10
u
63
+ 2u
62
+ ··· + 4u + 1
c
6
u
63
+ 6u
62
+ ··· + 1272u + 117
c
7
, c
12
u
63
+ 2u
62
+ ··· + 4u + 1
c
9
u
63
+ 28u
62
+ ··· + 6u + 1
c
11
u
63
− 36u
62
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 56y
62
+ ··· + 398y −1
c
2
, c
4
y
63
− 20y
62
+ ··· − 54y −1
c
3
, c
8
y
63
+ 57y
62
+ ··· + 10485760y −262144
c
5
, c
10
y
63
− 28y
62
+ ··· + 6y −1
c
6
y
63
− 4y
62
+ ··· + 236682y −13689
c
7
, c
12
y
63
+ 36y
62
+ ··· + 6y −1
c
9
y
63
+ 16y
62
+ ··· − 14y −1
c
11
y
63
− 16y
62
+ ··· + 90y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926110 + 0.366074I
a = −0.476922 + 0.252194I
b = −1.244610 + 0.271873I
−3.07412 − 1.36938I −14.1533 + 4.8337I
u = 0.926110 − 0.366074I
a = −0.476922 − 0.252194I
b = −1.244610 − 0.271873I
−3.07412 + 1.36938I −14.1533 − 4.8337I
u = −0.560970 + 0.838273I
a = −0.54543 + 1.39738I
b = 0.991983 − 0.885226I
8.30126 + 6.53190I −3.98974 − 5.60044I
u = −0.560970 − 0.838273I
a = −0.54543 − 1.39738I
b = 0.991983 + 0.885226I
8.30126 − 6.53190I −3.98974 + 5.60044I
u = 0.568620 + 0.802904I
a = −0.24496 − 1.43112I
b = 0.765553 + 0.905015I
4.93754 − 1.39094I −6.19355 + 2.18855I
u = 0.568620 − 0.802904I
a = −0.24496 + 1.43112I
b = 0.765553 − 0.905015I
4.93754 + 1.39094I −6.19355 − 2.18855I
u = −0.839102 + 0.489407I
a = 3.31553 + 9.53794I
b = −0.982885 + 0.004271I
0.04887 + 2.03557I −112.9138 + 23.7044I
u = −0.839102 − 0.489407I
a = 3.31553 − 9.53794I
b = −0.982885 − 0.004271I
0.04887 − 2.03557I −112.9138 − 23.7044I
u = −0.447997 + 0.861723I
a = −0.71326 − 1.29092I
b = 1.18245 + 0.86510I
7.62161 − 10.39330I −4.76838 + 5.34490I
u = −0.447997 − 0.861723I
a = −0.71326 + 1.29092I
b = 1.18245 − 0.86510I
7.62161 + 10.39330I −4.76838 − 5.34490I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772884 + 0.566946I
a = 0.741522 − 0.337818I
b = 0.0483031 + 0.1203760I
1.79771 − 2.20109I −2.95390 + 4.60864I
u = 0.772884 − 0.566946I
a = 0.741522 + 0.337818I
b = 0.0483031 − 0.1203760I
1.79771 + 2.20109I −2.95390 − 4.60864I
u = −0.529043 + 0.791579I
a = −0.17601 + 1.78351I
b = 0.710973 − 1.169850I
9.18780 − 3.10441I −2.77684 + 1.28013I
u = −0.529043 − 0.791579I
a = −0.17601 − 1.78351I
b = 0.710973 + 1.169850I
9.18780 + 3.10441I −2.77684 − 1.28013I
u = 0.427955 + 0.848872I
a = −0.482691 + 1.203200I
b = 1.039060 − 0.804035I
4.08395 + 4.95084I −7.20670 − 2.70270I
u = 0.427955 − 0.848872I
a = −0.482691 − 1.203200I
b = 1.039060 + 0.804035I
4.08395 − 4.95084I −7.20670 + 2.70270I
u = −0.916546 + 0.249573I
a = 0.527016 − 0.043315I
b = −1.008620 − 0.698143I
−1.65763 − 1.62708I −12.47188 + 3.53384I
u = −0.916546 − 0.249573I
a = 0.527016 + 0.043315I
b = −1.008620 + 0.698143I
−1.65763 + 1.62708I −12.47188 − 3.53384I
u = 0.972660 + 0.400781I
a = −0.570758 + 1.097760I
b = −1.45853 + 0.06110I
−3.33869 − 1.43594I −8.00000 + 0.I
u = 0.972660 − 0.400781I
a = −0.570758 − 1.097760I
b = −1.45853 − 0.06110I
−3.33869 + 1.43594I −8.00000 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439813 + 0.813829I
a = −0.22505 − 1.43226I
b = 0.872307 + 0.941914I
8.68256 − 0.17840I −3.11591 − 0.13366I
u = −0.439813 − 0.813829I
a = −0.22505 + 1.43226I
b = 0.872307 − 0.941914I
8.68256 + 0.17840I −3.11591 + 0.13366I
u = 0.946126 + 0.549853I
a = 1.30038 + 1.55435I
b = −0.476073 − 0.045942I
1.19543 − 2.08630I 0
u = 0.946126 − 0.549853I
a = 1.30038 − 1.55435I
b = −0.476073 + 0.045942I
1.19543 + 2.08630I 0
u = −1.003650 + 0.458888I
a = −0.56877 − 1.84841I
b = −1.42816 + 0.42370I
−2.91315 + 4.52729I 0
u = −1.003650 − 0.458888I
a = −0.56877 + 1.84841I
b = −1.42816 − 0.42370I
−2.91315 − 4.52729I 0
u = 1.111750 + 0.078744I
a = 0.931682 − 0.009722I
b = 0.606356 − 0.865246I
3.30246 − 1.91069I 0
u = 1.111750 − 0.078744I
a = 0.931682 + 0.009722I
b = 0.606356 + 0.865246I
3.30246 + 1.91069I 0
u = −0.992246 + 0.519940I
a = −0.33704 − 1.95730I
b = −0.879799 + 0.608584I
−1.95839 + 4.15867I 0
u = −0.992246 − 0.519940I
a = −0.33704 + 1.95730I
b = −0.879799 − 0.608584I
−1.95839 − 4.15867I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027300 + 0.547178I
a = −0.62187 + 1.64598I
b = −0.674886 − 1.080260I
0.27233 − 7.55007I 0
u = 1.027300 − 0.547178I
a = −0.62187 − 1.64598I
b = −0.674886 + 1.080260I
0.27233 + 7.55007I 0
u = 0.105288 + 0.803613I
a = 0.163733 + 0.190487I
b = 0.635693 − 0.133199I
−1.46958 + 2.74391I −2.52412 − 4.27240I
u = 0.105288 − 0.803613I
a = 0.163733 − 0.190487I
b = 0.635693 + 0.133199I
−1.46958 − 2.74391I −2.52412 + 4.27240I
u = −1.190260 + 0.105981I
a = 0.841204 + 0.034521I
b = 0.922740 + 0.637535I
−1.51798 − 2.46440I 0
u = −1.190260 − 0.105981I
a = 0.841204 − 0.034521I
b = 0.922740 − 0.637535I
−1.51798 + 2.46440I 0
u = 1.205040 + 0.067480I
a = 0.816284 + 0.015394I
b = 1.112880 − 0.749697I
1.77097 + 7.99701I 0
u = 1.205040 − 0.067480I
a = 0.816284 − 0.015394I
b = 1.112880 + 0.749697I
1.77097 − 7.99701I 0
u = 1.039570 + 0.658560I
a = −0.914741 + 0.261872I
b = 0.622398 − 0.949236I
3.52241 − 4.08840I 0
u = 1.039570 − 0.658560I
a = −0.914741 − 0.261872I
b = 0.622398 + 0.949236I
3.52241 + 4.08840I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.059960 + 0.641966I
a = −1.231410 − 0.420346I
b = 0.637529 + 1.260300I
7.59858 + 8.49760I 0
u = −1.059960 − 0.641966I
a = −1.231410 + 0.420346I
b = 0.637529 − 1.260300I
7.59858 − 8.49760I 0
u = −1.057440 + 0.680554I
a = −1.002810 + 0.058966I
b = 0.898990 + 0.875767I
6.80806 − 0.88135I 0
u = −1.057440 − 0.680554I
a = −1.002810 − 0.058966I
b = 0.898990 − 0.875767I
6.80806 + 0.88135I 0
u = 0.568628 + 0.459189I
a = 1.57734 + 0.31772I
b = −0.253084 − 0.388928I
2.13125 − 2.17129I −3.22626 + 3.56149I
u = 0.568628 − 0.459189I
a = 1.57734 − 0.31772I
b = −0.253084 + 0.388928I
2.13125 + 2.17129I −3.22626 − 3.56149I
u = −1.206380 + 0.395280I
a = 0.870666 + 0.422612I
b = 0.706799 − 0.004491I
−5.38670 + 1.34424I 0
u = −1.206380 − 0.395280I
a = 0.870666 − 0.422612I
b = 0.706799 + 0.004491I
−5.38670 − 1.34424I 0
u = −1.109200 + 0.619508I
a = 1.24867 + 1.72679I
b = 0.939930 − 0.857494I
6.67687 + 5.54473I 0
u = −1.109200 − 0.619508I
a = 1.24867 − 1.72679I
b = 0.939930 + 0.857494I
6.67687 − 5.54473I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452256 + 0.561618I
a = 1.40155 − 1.36845I
b = −0.506448 + 0.882679I
1.87503 + 3.06479I −4.36652 − 4.78234I
u = 0.452256 − 0.561618I
a = 1.40155 + 1.36845I
b = −0.506448 − 0.882679I
1.87503 − 3.06479I −4.36652 + 4.78234I
u = 1.124570 + 0.631526I
a = 0.93240 − 1.80350I
b = 1.123120 + 0.773338I
1.99016 − 10.45010I 0
u = 1.124570 − 0.631526I
a = 0.93240 + 1.80350I
b = 1.123120 − 0.773338I
1.99016 + 10.45010I 0
u = −1.120990 + 0.642900I
a = 0.86354 + 2.02077I
b = 1.24190 − 0.85165I
5.5911 + 15.9697I 0
u = −1.120990 − 0.642900I
a = 0.86354 − 2.02077I
b = 1.24190 + 0.85165I
5.5911 − 15.9697I 0
u = 1.198640 + 0.490741I
a = 0.872834 − 0.659332I
b = 0.755641 + 0.177473I
−4.71317 − 7.47420I 0
u = 1.198640 − 0.490741I
a = 0.872834 + 0.659332I
b = 0.755641 − 0.177473I
−4.71317 + 7.47420I 0
u = −0.575685 + 0.399556I
a = 1.31366 + 0.78416I
b = −0.548676 − 0.386355I
−0.700698 − 0.064745I −10.52169 + 0.11838I
u = −0.575685 − 0.399556I
a = 1.31366 − 0.78416I
b = −0.548676 + 0.386355I
−0.700698 + 0.064745I −10.52169 − 0.11838I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.505150
a = 1.23248
b = −0.339414
−0.801265 −12.3320
u = −0.145540 + 0.342331I
a = 2.27747 + 0.36324I
b = −1.183120 − 0.244413I
−1.04760 − 1.10754I −6.89009 + 0.60196I
u = −0.145540 − 0.342331I
a = 2.27747 − 0.36324I
b = −1.183120 + 0.244413I
−1.04760 + 1.10754I −6.89009 − 0.60196I
11
II.
I
u
2
= hb +1, 2u
8
+u
7
+· · · + a −2, u
9
+u
8
−2u
7
−3u
6
+u
5
+3u
4
+2u
3
−u −1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−2u
8
− u
7
+ 5u
6
+ 3u
5
− 4u
4
− 3u
3
− 2u
2
+ 2
−1
a
11
=
−u
−u
3
+ u
a
2
=
−2u
8
− u
7
+ 5u
6
+ 3u
5
− 4u
4
− 3u
3
− 2u
2
+ 1
−1
a
1
=
−1
0
a
4
=
−2u
8
− u
7
+ 5u
6
+ 3u
5
− 4u
4
− 3u
3
− 2u
2
+ 2
−1
a
9
=
u
3
u
5
− u
3
+ u
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
−u
3
−u
3
+ u
a
8
=
u
3
u
5
− u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
8
− 5u
7
− 10u
6
+ 8u
5
+ 10u
4
− 8u
3
+ 4u
2
− 8u − 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
, c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
7
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 1.67861 + 2.31573I
b = −1.00000
0.13850 + 2.09337I 0.6725 − 14.2088I
u = −0.772920 − 0.510351I
a = 1.67861 − 2.31573I
b = −1.00000
0.13850 − 2.09337I 0.6725 + 14.2088I
u = 0.825933
a = −0.871015
b = −1.00000
−2.84338 −13.8440
u = 1.173910 + 0.391555I
a = −0.893484 + 0.630694I
b = −1.00000
−6.01628 − 1.33617I −18.6190 + 0.6500I
u = 1.173910 − 0.391555I
a = −0.893484 − 0.630694I
b = −1.00000
−6.01628 + 1.33617I −18.6190 − 0.6500I
u = −0.141484 + 0.739668I
a = 0.309843 + 0.043204I
b = −1.00000
−2.26187 − 2.45442I −11.89962 + 1.90984I
u = −0.141484 − 0.739668I
a = 0.309843 − 0.043204I
b = −1.00000
−2.26187 + 2.45442I −11.89962 − 1.90984I
u = −1.172470 + 0.500383I
a = −0.659464 − 0.874093I
b = −1.00000
−5.24306 + 7.08493I −15.2318 − 2.9321I
u = −1.172470 − 0.500383I
a = −0.659464 + 0.874093I
b = −1.00000
−5.24306 − 7.08493I −15.2318 + 2.9321I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
63
+ 20u
62
+ ··· − 54u + 1)
c
2
((u − 1)
9
)(u
63
− 10u
62
+ ··· − 6u + 1)
c
3
, c
8
u
9
(u
63
+ u
62
+ ··· + 5632u + 512)
c
4
((u + 1)
9
)(u
63
− 10u
62
+ ··· − 6u + 1)
c
5
(u
9
+ u
8
+ ··· − u − 1)(u
63
+ 2u
62
+ ··· + 4u + 1)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
63
+ 6u
62
+ ··· + 1272u + 117)
c
7
(u
9
+ u
8
+ ··· + u − 1)(u
63
+ 2u
62
+ ··· + 4u + 1)
c
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
63
+ 28u
62
+ ··· + 6u + 1)
c
10
(u
9
− u
8
+ ··· − u + 1)(u
63
+ 2u
62
+ ··· + 4u + 1)
c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
63
− 36u
62
+ ··· + 6u + 1)
c
12
(u
9
− u
8
+ ··· + u + 1)(u
63
+ 2u
62
+ ··· + 4u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
63
+ 56y
62
+ ··· + 398y −1)
c
2
, c
4
((y −1)
9
)(y
63
− 20y
62
+ ··· − 54y −1)
c
3
, c
8
y
9
(y
63
+ 57y
62
+ ··· + 1.04858 × 10
7
y −262144)
c
5
, c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
63
− 28y
62
+ ··· + 6y −1)
c
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
63
− 4y
62
+ ··· + 236682y −13689)
c
7
, c
12
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
63
+ 36y
62
+ ··· + 6y −1)
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
63
+ 16y
62
+ ··· − 14y −1)
c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
63
− 16y
62
+ ··· + 90y −1)
17
