12n
0323
(K12n
0323
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 4 10 12 6 4 9 8
Solving Sequence
4,6 7,10
8 11 3 2 1 5 9 12
c
6
c
7
c
10
c
3
c
2
c
1
c
5
c
9
c
11
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.93292 × 10
96
u
38
− 8.20410 × 10
95
u
37
+ ··· + 4.97642 × 10
96
b − 4.64235 × 10
97
,
− 1.86317 × 10
97
u
38
− 7.56639 × 10
95
u
37
+ ··· + 4.97642 × 10
96
a − 1.47890 × 10
98
,
u
39
− 27u
37
+ ··· + 23u − 1i
I
u
2
= h193u
12
+ 451u
11
+ ··· + b + 265, −473u
12
− 1171u
11
+ ··· + a − 874,
u
13
+ 3u
12
− u
11
− 13u
10
− 22u
9
− 18u
8
+ 21u
7
+ 83u
6
+ 131u
5
+ 138u
4
+ 97u
3
+ 42u
2
+ 10u + 1i
* 2 irreducible components of dim
C
= 0, with total 52 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−5.93 × 10
96
u
38
− 8.20 × 10
95
u
37
+ · · · + 4.98 × 10
96
b − 4.64 ×
10
97
, −1.86 × 10
97
u
38
− 7.57 × 10
95
u
37
+ · · · + 4.98 × 10
96
a − 1.48 ×
10
98
, u
39
− 27u
37
+ · · · + 23u − 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
3.74399u
38
+ 0.152045u
37
+ ··· − 535.809u + 29.7183
1.19221u
38
+ 0.164860u
37
+ ··· − 144.637u + 9.32870
a
8
=
−12.4725u
38
− 2.14316u
37
+ ··· + 1137.22u − 63.9305
0.330558u
38
+ 0.0519417u
37
+ ··· − 31.6927u + 2.63188
a
11
=
3.74399u
38
+ 0.152045u
37
+ ··· − 535.809u + 29.7183
1.24585u
38
+ 0.181271u
37
+ ··· − 144.884u + 9.17665
a
3
=
−8.97456u
38
− 1.43150u
37
+ ··· + 889.416u − 63.1649
−1.50003u
38
− 0.226969u
37
+ ··· + 156.223u − 8.24024
a
2
=
−10.4746u
38
− 1.65847u
37
+ ··· + 1045.64u − 71.4051
−1.50003u
38
− 0.226969u
37
+ ··· + 156.223u − 8.24024
a
1
=
−31.1624u
38
− 4.81610u
37
+ ··· + 3104.14u − 177.973
−0.404984u
38
− 0.0547518u
37
+ ··· + 61.2052u − 2.70494
a
5
=
−4.84811u
38
− 0.726842u
37
+ ··· + 500.726u − 13.4811
2.04459u
38
+ 0.303981u
37
+ ··· − 209.069u + 11.7457
a
9
=
2.55178u
38
− 0.0128147u
37
+ ··· − 391.172u + 20.3896
1.19221u
38
+ 0.164860u
37
+ ··· − 144.637u + 9.32870
a
12
=
11.7457u
38
+ 2.04459u
37
+ ··· − 1039.19u + 61.0824
0.0960919u
38
+ 0.00947475u
37
+ ··· − 14.9880u + 0.00924794
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.40504u
38
+ 0.306842u
37
+ ··· − 347.511u + 22.5697
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 16u
38
+ ··· + 329u + 1
c
2
, c
5
u
39
+ 4u
38
+ ··· + 15u − 1
c
3
u
39
+ 10u
37
+ ··· + 249u − 171
c
4
, c
10
u
39
+ u
38
+ ··· + 7u − 1
c
6
u
39
− 27u
37
+ ··· + 23u − 1
c
7
u
39
+ 2u
38
+ ··· − 4549u − 567
c
8
, c
11
, c
12
u
39
+ 4u
38
+ ··· − 79u − 29
c
9
u
39
+ 17u
37
+ ··· − 4121u − 2447
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 24y
38
+ ··· + 99345y −1
c
2
, c
5
y
39
− 16y
38
+ ··· + 329y −1
c
3
y
39
+ 20y
38
+ ··· − 233145y −29241
c
4
, c
10
y
39
+ 49y
38
+ ··· − 47y −1
c
6
y
39
− 54y
38
+ ··· + 67y −1
c
7
y
39
+ 40y
38
+ ··· + 13389307y −321489
c
8
, c
11
, c
12
y
39
+ 22y
38
+ ··· − 13189y −841
c
9
y
39
+ 34y
38
+ ··· − 55732411y −5987809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994299 + 0.272414I
a = 0.463680 − 0.927259I
b = 1.018090 − 0.678656I
−0.629315 + 0.697668I −0.69777 + 1.96847I
u = −0.994299 − 0.272414I
a = 0.463680 + 0.927259I
b = 1.018090 + 0.678656I
−0.629315 − 0.697668I −0.69777 − 1.96847I
u = 0.649416 + 0.545046I
a = 0.543557 + 0.859256I
b = 0.932275 + 0.703931I
−0.04361 + 5.03289I −0.70677 − 5.74773I
u = 0.649416 − 0.545046I
a = 0.543557 − 0.859256I
b = 0.932275 − 0.703931I
−0.04361 − 5.03289I −0.70677 + 5.74773I
u = −1.003940 + 0.692341I
a = 0.328055 − 0.842205I
b = −1.78302 − 0.03484I
−1.32978 − 3.67485I 0
u = −1.003940 − 0.692341I
a = 0.328055 + 0.842205I
b = −1.78302 + 0.03484I
−1.32978 + 3.67485I 0
u = −0.639274 + 0.192301I
a = 0.756843 − 0.681921I
b = 0.300034 − 0.398633I
−1.39152 + 0.61829I −4.65215 − 1.06818I
u = −0.639274 − 0.192301I
a = 0.756843 + 0.681921I
b = 0.300034 + 0.398633I
−1.39152 − 0.61829I −4.65215 + 1.06818I
u = 0.593939 + 0.218894I
a = 0.976981 + 0.875107I
b = −1.005710 + 0.276370I
1.53232 − 0.33929I 2.22376 + 1.90694I
u = 0.593939 − 0.218894I
a = 0.976981 − 0.875107I
b = −1.005710 − 0.276370I
1.53232 + 0.33929I 2.22376 − 1.90694I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09219 + 1.41774I
a = 0.1177060 + 0.0003338I
b = −0.544510 − 0.762381I
3.32998 + 1.36180I 0
u = 0.09219 − 1.41774I
a = 0.1177060 − 0.0003338I
b = −0.544510 + 0.762381I
3.32998 − 1.36180I 0
u = −1.58355 + 0.07109I
a = 0.242255 + 1.000940I
b = 0.550049 + 1.295150I
−2.17716 + 0.58502I 0
u = −1.58355 − 0.07109I
a = 0.242255 − 1.000940I
b = 0.550049 − 1.295150I
−2.17716 − 0.58502I 0
u = 1.52238 + 0.49770I
a = −0.599371 − 0.810262I
b = 0.202320 − 1.285620I
−8.76356 + 1.01188I 0
u = 1.52238 − 0.49770I
a = −0.599371 + 0.810262I
b = 0.202320 + 1.285620I
−8.76356 − 1.01188I 0
u = −0.45538 + 1.56426I
a = −0.0753063 − 0.0530697I
b = −0.505804 + 0.964655I
2.41500 + 4.97539I 0
u = −0.45538 − 1.56426I
a = −0.0753063 + 0.0530697I
b = −0.505804 − 0.964655I
2.41500 − 4.97539I 0
u = −0.164690 + 0.303209I
a = 0.604983 + 0.898851I
b = 0.880121 + 0.762617I
−4.06684 + 2.90659I 6.73557 + 0.48460I
u = −0.164690 − 0.303209I
a = 0.604983 − 0.898851I
b = 0.880121 − 0.762617I
−4.06684 − 2.90659I 6.73557 − 0.48460I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65134 + 0.17017I
a = 0.210060 − 1.091670I
b = 0.59401 − 1.30121I
−2.82025 − 6.80896I 0
u = 1.65134 − 0.17017I
a = 0.210060 + 1.091670I
b = 0.59401 + 1.30121I
−2.82025 + 6.80896I 0
u = 0.316011
a = 1.69045
b = −0.597495
1.11789 11.2670
u = 1.78797 + 0.23546I
a = −0.175928 − 1.026470I
b = 0.426419 − 1.281700I
−9.84094 − 3.14577I 0
u = 1.78797 − 0.23546I
a = −0.175928 + 1.026470I
b = 0.426419 + 1.281700I
−9.84094 + 3.14577I 0
u = 0.147459 + 0.018240I
a = 8.93744 + 0.12975I
b = −0.052132 − 0.818099I
2.82165 + 0.44220I 0.165551 − 1.251212I
u = 0.147459 − 0.018240I
a = 8.93744 − 0.12975I
b = −0.052132 + 0.818099I
2.82165 − 0.44220I 0.165551 + 1.251212I
u = 0.0757690 + 0.1010380I
a = −9.82475 + 6.73299I
b = 0.096930 − 1.077780I
1.58306 + 6.33307I −2.17277 − 5.35202I
u = 0.0757690 − 0.1010380I
a = −9.82475 − 6.73299I
b = 0.096930 + 1.077780I
1.58306 − 6.33307I −2.17277 + 5.35202I
u = −1.81753 + 0.76879I
a = −0.361839 + 0.599956I
b = 0.192205 + 1.129990I
−8.14778 + 2.96891I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.81753 − 0.76879I
a = −0.361839 − 0.599956I
b = 0.192205 − 1.129990I
−8.14778 − 2.96891I 0
u = 1.99569 + 0.16593I
a = 0.098834 + 0.938233I
b = 0.13027 + 2.53503I
−12.47920 − 1.55057I 0
u = 1.99569 − 0.16593I
a = 0.098834 − 0.938233I
b = 0.13027 − 2.53503I
−12.47920 + 1.55057I 0
u = −1.97927 + 0.41282I
a = 0.025347 − 0.879507I
b = −0.64583 − 1.82989I
−4.36641 + 6.38323I 0
u = −1.97927 − 0.41282I
a = 0.025347 + 0.879507I
b = −0.64583 + 1.82989I
−4.36641 − 6.38323I 0
u = 2.03401 + 0.41923I
a = −0.017030 + 0.900973I
b = −0.90609 + 1.73968I
−6.3597 − 13.3871I 0
u = 2.03401 − 0.41923I
a = −0.017030 − 0.900973I
b = −0.90609 − 1.73968I
−6.3597 + 13.3871I 0
u = −2.07024 + 0.28134I
a = −0.096745 + 0.760848I
b = 0.419131 + 1.090140I
−9.04262 + 0.68757I 0
u = −2.07024 − 0.28134I
a = −0.096745 − 0.760848I
b = 0.419131 − 1.090140I
−9.04262 − 0.68757I 0
8
II. I
u
2
= h193u
12
+ 451u
11
+ · · · + b + 265, −473u
12
− 1171u
11
+ · · · + a −
874, u
13
+ 3u
12
+ · · · + 10u + 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
473u
12
+ 1171u
11
+ ··· + 7192u + 874
−193u
12
− 451u
11
+ ··· − 2345u − 265
a
8
=
−8u
12
− 24u
11
+ ··· − 273u − 46
512u
12
+ 1280u
11
+ ··· + 8192u + 1023
a
11
=
473u
12
+ 1171u
11
+ ··· + 7192u + 874
−320u
12
− 768u
11
+ ··· − 4352u − 513
a
3
=
−47u
12
− 124u
11
+ ··· − 1013u − 142
−u
12
− 3u
11
+ ··· − 42u − 9
a
2
=
−48u
12
− 127u
11
+ ··· − 1055u − 151
−u
12
− 3u
11
+ ··· − 42u − 9
a
1
=
122u
12
+ 318u
11
+ ··· + 2113u + 256
30u
12
+ 83u
11
+ ··· + 719u + 103
a
5
=
−103u
12
− 278u
11
+ ··· − 2217u − 303
−8u
12
− 23u
11
+ ··· − 239u − 39
a
9
=
666u
12
+ 1622u
11
+ ··· + 9537u + 1139
−193u
12
− 451u
11
+ ··· − 2345u − 265
a
12
=
−39u
12
− 109u
11
+ ··· − 1000u − 151
192u
12
+ 512u
11
+ ··· + 3840u + 511
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1726u
12
+ 4212u
11
− 4090u
10
− 20161u
9
− 26665u
8
− 16081u
7
+
45309u
6
+ 117921u
5
+ 159920u
4
+ 148350u
3
+ 83989u
2
+ 25167u + 3051
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 9u
12
+ ··· + 14u − 1
c
2
u
13
+ 3u
12
+ ··· − 2u − 1
c
3
u
13
− u
12
+ ··· + 4u − 1
c
4
u
13
+ 6u
11
+ ··· + 2u − 1
c
5
u
13
− 3u
12
+ ··· − 2u + 1
c
6
u
13
+ 3u
12
+ ··· + 10u + 1
c
7
u
13
+ u
12
+ ··· + 2u
2
+ 1
c
8
u
13
+ 3u
12
+ ··· + 2u + 1
c
9
u
13
− u
12
+ ··· + 4u − 1
c
10
u
13
+ 6u
11
+ ··· + 2u + 1
c
11
, c
12
u
13
− 3u
12
+ ··· + 2u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− y
12
+ ··· + 30y −1
c
2
, c
5
y
13
− 9y
12
+ ··· + 14y −1
c
3
y
13
+ 3y
12
+ ··· − 12y −1
c
4
, c
10
y
13
+ 12y
12
+ ··· − 10y −1
c
6
y
13
− 11y
12
+ ··· + 16y −1
c
7
y
13
+ 11y
12
+ ··· − 4y −1
c
8
, c
11
, c
12
y
13
+ 9y
12
+ ··· − 16y −1
c
9
y
13
+ 9y
12
+ ··· − 2y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.299683 + 1.053320I
a = 0.593765 + 0.622158I
b = −0.346775 − 0.499880I
4.03587 + 0.38376I 4.73339 + 0.12017I
u = −0.299683 − 1.053320I
a = 0.593765 − 0.622158I
b = −0.346775 + 0.499880I
4.03587 − 0.38376I 4.73339 − 0.12017I
u = 0.044736 + 1.203680I
a = 0.410218 − 0.674956I
b = −0.125085 + 0.679786I
3.18980 + 5.96021I 3.63825 − 5.77074I
u = 0.044736 − 1.203680I
a = 0.410218 + 0.674956I
b = −0.125085 − 0.679786I
3.18980 − 5.96021I 3.63825 + 5.77074I
u = −0.647940
a = 1.04389
b = −0.521466
0.639171 −8.02710
u = −0.515856 + 0.039018I
a = 0.102601 + 0.741557I
b = 0.957371 − 0.646629I
−4.52059 − 3.12580I −8.05352 + 6.05122I
u = −0.515856 − 0.039018I
a = 0.102601 − 0.741557I
b = 0.957371 + 0.646629I
−4.52059 + 3.12580I −8.05352 − 6.05122I
u = −0.448017 + 0.119182I
a = −0.19232 − 2.52486I
b = −1.181340 − 0.032991I
−0.43607 − 1.97707I −0.56144 + 3.20484I
u = −0.448017 − 0.119182I
a = −0.19232 + 2.52486I
b = −1.181340 + 0.032991I
−0.43607 + 1.97707I −0.56144 − 3.20484I
u = −1.92525 + 0.43385I
a = −0.245558 + 0.767619I
b = 0.294055 + 1.035630I
−9.09336 + 1.74394I −4.69358 − 2.80316I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.92525 − 0.43385I
a = −0.245558 − 0.767619I
b = 0.294055 − 1.035630I
−9.09336 − 1.74394I −4.69358 + 2.80316I
u = 1.96804 + 0.29336I
a = −0.190656 − 0.923645I
b = 0.16250 − 2.23453I
−13.23440 − 0.87223I −6.54954 − 0.63082I
u = 1.96804 − 0.29336I
a = −0.190656 + 0.923645I
b = 0.16250 + 2.23453I
−13.23440 + 0.87223I −6.54954 + 0.63082I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 9u
12
+ ··· + 14u − 1)(u
39
+ 16u
38
+ ··· + 329u + 1)
c
2
(u
13
+ 3u
12
+ ··· − 2u − 1)(u
39
+ 4u
38
+ ··· + 15u − 1)
c
3
(u
13
− u
12
+ ··· + 4u − 1)(u
39
+ 10u
37
+ ··· + 249u − 171)
c
4
(u
13
+ 6u
11
+ ··· + 2u − 1)(u
39
+ u
38
+ ··· + 7u − 1)
c
5
(u
13
− 3u
12
+ ··· − 2u + 1)(u
39
+ 4u
38
+ ··· + 15u − 1)
c
6
(u
13
+ 3u
12
+ ··· + 10u + 1)(u
39
− 27u
37
+ ··· + 23u − 1)
c
7
(u
13
+ u
12
+ ··· + 2u
2
+ 1)(u
39
+ 2u
38
+ ··· − 4549u − 567)
c
8
(u
13
+ 3u
12
+ ··· + 2u + 1)(u
39
+ 4u
38
+ ··· − 79u − 29)
c
9
(u
13
− u
12
+ ··· + 4u − 1)(u
39
+ 17u
37
+ ··· − 4121u − 2447)
c
10
(u
13
+ 6u
11
+ ··· + 2u + 1)(u
39
+ u
38
+ ··· + 7u − 1)
c
11
, c
12
(u
13
− 3u
12
+ ··· + 2u − 1)(u
39
+ 4u
38
+ ··· − 79u − 29)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
− y
12
+ ··· + 30y −1)(y
39
+ 24y
38
+ ··· + 99345y −1)
c
2
, c
5
(y
13
− 9y
12
+ ··· + 14y −1)(y
39
− 16y
38
+ ··· + 329y −1)
c
3
(y
13
+ 3y
12
+ ··· − 12y −1)(y
39
+ 20y
38
+ ··· − 233145y −29241)
c
4
, c
10
(y
13
+ 12y
12
+ ··· − 10y −1)(y
39
+ 49y
38
+ ··· − 47y −1)
c
6
(y
13
− 11y
12
+ ··· + 16y −1)(y
39
− 54y
38
+ ··· + 67y −1)
c
7
(y
13
+ 11y
12
+ ··· − 4y −1)
· (y
39
+ 40y
38
+ ··· + 13389307y −321489)
c
8
, c
11
, c
12
(y
13
+ 9y
12
+ ··· − 16y −1)(y
39
+ 22y
38
+ ··· − 13189y −841)
c
9
(y
13
+ 9y
12
+ ··· − 2y −1)
· (y
39
+ 34y
38
+ ··· − 55732411y −5987809)
15
