12n
0070
(K12n
0070
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 9 4 5 11 6 12 8 10
Solving Sequence
5,9
6
3,10
2 1 4 7 12 11 8
c
5
c
9
c
2
c
1
c
4
c
6
c
12
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.79874 × 10
43
u
47
+ 4.02119 × 10
43
u
46
+ ··· + 8.11774 × 10
44
b + 8.69331 × 10
44
,
8.37339 × 10
44
u
47
− 7.89584 × 10
44
u
46
+ ··· + 8.11774 × 10
44
a + 8.23673 × 10
44
, u
48
− 2u
47
+ ··· + u − 1i
I
u
2
= hb + 1, −u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ a + 2u + 1, 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 57 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−2.80×10
43
u
47
+4.02×10
43
u
46
+· · ·+8.12×10
44
b+8.69×10
44
, 8.37×
10
44
u
47
−7.90×10
44
u
46
+· · ·+8.12×10
44
a+8.24×10
44
, u
48
−2u
47
+· · ·+u−1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
3
=
−1.03149u
47
+ 0.972665u
46
+ ··· + 7.94786u − 1.01466
0.0344769u
47
− 0.0495358u
46
+ ··· + 0.0738871u − 1.07090
a
10
=
−u
−u
3
+ u
a
2
=
−0.997016u
47
+ 0.923129u
46
+ ··· + 8.02175u − 2.08556
0.0344769u
47
− 0.0495358u
46
+ ··· + 0.0738871u − 1.07090
a
1
=
0.0331947u
47
− 0.0856097u
46
+ ··· + 0.0573894u − 1.12853
0.0134332u
47
− 0.0242057u
46
+ ··· + 0.0350763u − 0.0500498
a
4
=
−1.02750u
47
+ 0.980811u
46
+ ··· + 7.96292u − 0.995240
0.0271246u
47
− 0.0401768u
46
+ ··· + 0.0617487u − 1.05477
a
7
=
0.0331947u
47
− 0.0856097u
46
+ ··· + 0.0573894u − 1.12853
0.0231038u
47
− 0.00484707u
46
+ ··· + 0.0173387u + 0.0308295
a
12
=
0.00227898u
47
− 0.0424799u
46
+ ··· − 0.0132823u − 1.06795
0.0555135u
47
− 0.0910188u
46
+ ··· + 0.0935339u − 0.129332
a
11
=
−0.00405982u
47
+ 0.347568u
46
+ ··· − 0.370675u + 0.256769
0.0520834u
47
− 0.385513u
46
+ ··· + 0.537247u + 0.0988580
a
8
=
0.0100910u
47
− 0.0807626u
46
+ ··· + 0.0400507u − 1.15936
0.0231038u
47
− 0.00484707u
46
+ ··· + 0.0173387u + 0.0308295
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.65697u
47
+ 10.4260u
46
+ ··· + 9.56539u − 4.59345
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 10u
47
+ ··· + 29u + 1
c
2
, c
4
u
48
− 10u
47
+ ··· + 9u − 1
c
3
, c
6
u
48
+ 5u
47
+ ··· + 2560u + 512
c
5
, c
9
u
48
+ 2u
47
+ ··· − u − 1
c
7
u
48
− 10u
47
+ ··· − 284463u − 118529
c
8
, c
11
u
48
− 2u
47
+ ··· + 5u + 1
c
10
, c
12
u
48
− 18u
47
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 66y
47
+ ··· − 29y + 1
c
2
, c
4
y
48
− 10y
47
+ ··· − 29y + 1
c
3
, c
6
y
48
− 57y
47
+ ··· − 6553600y + 262144
c
5
, c
9
y
48
− 10y
47
+ ··· − 5y + 1
c
7
y
48
+ 46y
47
+ ··· + 130798249663y + 14049123841
c
8
, c
11
y
48
+ 18y
47
+ ··· − 5y + 1
c
10
, c
12
y
48
+ 26y
47
+ ··· − 305y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.896760 + 0.394007I
a = 1.195670 + 0.370079I
b = 0.334698 − 0.383487I
1.62098 + 2.77574I 0.84836 − 5.23754I
u = −0.896760 − 0.394007I
a = 1.195670 − 0.370079I
b = 0.334698 + 0.383487I
1.62098 − 2.77574I 0.84836 + 5.23754I
u = 0.974989
a = 1.02044
b = 0.393396
−1.61952 −5.35010
u = −0.120610 + 0.916069I
a = 0.235604 − 0.115451I
b = 0.343969 + 0.103094I
−0.93576 − 2.61420I −0.93985 + 3.31089I
u = −0.120610 − 0.916069I
a = 0.235604 + 0.115451I
b = 0.343969 − 0.103094I
−0.93576 + 2.61420I −0.93985 − 3.31089I
u = −0.738807 + 0.549894I
a = 0.165480 − 1.227210I
b = −0.486703 + 1.024080I
−0.48319 + 6.71552I −4.51681 − 9.54041I
u = −0.738807 − 0.549894I
a = 0.165480 + 1.227210I
b = −0.486703 − 1.024080I
−0.48319 − 6.71552I −4.51681 + 9.54041I
u = −0.599663 + 0.680544I
a = 0.187949 − 0.890060I
b = −0.049207 + 0.720509I
2.76925 + 1.42198I 2.53709 − 3.03057I
u = −0.599663 − 0.680544I
a = 0.187949 + 0.890060I
b = −0.049207 − 0.720509I
2.76925 − 1.42198I 2.53709 + 3.03057I
u = 0.697412 + 0.490405I
a = 0.242589 + 1.252710I
b = −0.620253 − 0.841171I
−1.49634 − 1.82392I −7.12758 + 4.49809I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697412 − 0.490405I
a = 0.242589 − 1.252710I
b = −0.620253 + 0.841171I
−1.49634 + 1.82392I −7.12758 − 4.49809I
u = 0.741862 + 0.199966I
a = −0.024215 + 0.937984I
b = −1.35488 − 0.46391I
−3.92122 − 4.12814I −11.08539 + 6.80823I
u = 0.741862 − 0.199966I
a = −0.024215 − 0.937984I
b = −1.35488 + 0.46391I
−3.92122 + 4.12814I −11.08539 − 6.80823I
u = −0.732347 + 0.133432I
a = −0.169686 − 0.690549I
b = −1.41588 + 0.30582I
−4.22436 − 0.79348I −12.24074 + 0.40151I
u = −0.732347 − 0.133432I
a = −0.169686 + 0.690549I
b = −1.41588 − 0.30582I
−4.22436 + 0.79348I −12.24074 − 0.40151I
u = −0.837259 + 0.941864I
a = −0.544783 − 0.719252I
b = 0.782990 + 1.125810I
5.63113 + 1.53351I 0
u = −0.837259 − 0.941864I
a = −0.544783 + 0.719252I
b = 0.782990 − 1.125810I
5.63113 − 1.53351I 0
u = 0.861555 + 0.923996I
a = −0.593554 + 0.787088I
b = 0.79140 − 1.22798I
7.43222 − 6.89004I 0
u = 0.861555 − 0.923996I
a = −0.593554 − 0.787088I
b = 0.79140 + 1.22798I
7.43222 + 6.89004I 0
u = −0.517390 + 0.487120I
a = 1.92274 − 0.32819I
b = −0.312068 − 0.327759I
−0.09198 − 2.92294I −2.75678 + 1.45029I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.517390 − 0.487120I
a = 1.92274 + 0.32819I
b = −0.312068 + 0.327759I
−0.09198 + 2.92294I −2.75678 − 1.45029I
u = 0.871406 + 0.978758I
a = −0.658628 + 0.639461I
b = 0.95026 − 1.11406I
11.29790 + 0.41096I 0
u = 0.871406 − 0.978758I
a = −0.658628 − 0.639461I
b = 0.95026 + 1.11406I
11.29790 − 0.41096I 0
u = 1.002820 + 0.849357I
a = 0.72578 − 1.44875I
b = 0.939578 + 1.008210I
6.96696 + 0.32370I 0
u = 1.002820 − 0.849357I
a = 0.72578 + 1.44875I
b = 0.939578 − 1.008210I
6.96696 − 0.32370I 0
u = 1.271800 + 0.367688I
a = 0.720656 − 0.331546I
b = 0.681047 + 0.240011I
−5.31134 − 1.83633I 0
u = 1.271800 − 0.367688I
a = 0.720656 + 0.331546I
b = 0.681047 − 0.240011I
−5.31134 + 1.83633I 0
u = −0.844944 + 1.021610I
a = −0.595460 − 0.519471I
b = 0.959842 + 0.954036I
5.10392 − 1.89300I 0
u = −0.844944 − 1.021610I
a = −0.595460 + 0.519471I
b = 0.959842 − 0.954036I
5.10392 + 1.89300I 0
u = −1.030920 + 0.851423I
a = 0.63113 + 1.38478I
b = 0.990071 − 0.940352I
5.00640 + 5.09433I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.030920 − 0.851423I
a = 0.63113 − 1.38478I
b = 0.990071 + 0.940352I
5.00640 − 5.09433I 0
u = −1.266230 + 0.463136I
a = 0.690484 + 0.432110I
b = 0.720279 − 0.304393I
−4.61107 + 7.74308I 0
u = −1.266230 − 0.463136I
a = 0.690484 − 0.432110I
b = 0.720279 + 0.304393I
−4.61107 − 7.74308I 0
u = 0.867259 + 1.032790I
a = −0.651865 + 0.488809I
b = 1.034680 − 0.958036I
6.65683 + 7.53345I 0
u = 0.867259 − 1.032790I
a = −0.651865 − 0.488809I
b = 1.034680 + 0.958036I
6.65683 − 7.53345I 0
u = 0.516744 + 0.394217I
a = 0.62833 + 1.70615I
b = −0.701706 − 0.277894I
−0.88029 − 1.27188I −6.26432 + 4.55192I
u = 0.516744 − 0.394217I
a = 0.62833 − 1.70615I
b = −0.701706 + 0.277894I
−0.88029 + 1.27188I −6.26432 − 4.55192I
u = 1.029070 + 0.891394I
a = 0.52071 − 1.51346I
b = 1.09974 + 1.00345I
10.77840 − 7.27793I 0
u = 1.029070 − 0.891394I
a = 0.52071 + 1.51346I
b = 1.09974 − 1.00345I
10.77840 + 7.27793I 0
u = 0.421301 + 0.450001I
a = 1.94355 + 1.59209I
b = −0.639240 + 0.073730I
−0.95094 − 1.38886I −6.78496 + 5.34534I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.421301 − 0.450001I
a = 1.94355 − 1.59209I
b = −0.639240 − 0.073730I
−0.95094 + 1.38886I −6.78496 − 5.34534I
u = −1.062880 + 0.898984I
a = 0.39761 + 1.42135I
b = 1.16352 − 0.90692I
4.39176 + 8.90399I 0
u = −1.062880 − 0.898984I
a = 0.39761 − 1.42135I
b = 1.16352 + 0.90692I
4.39176 − 8.90399I 0
u = 1.059770 + 0.914043I
a = 0.35101 − 1.47183I
b = 1.20972 + 0.93066I
6.0154 − 14.6316I 0
u = 1.059770 − 0.914043I
a = 0.35101 + 1.47183I
b = 1.20972 − 0.93066I
6.0154 + 14.6316I 0
u = −0.501063
a = −2.33906
b = −1.11935
−2.23585 −0.442570
u = 0.069842 + 0.433647I
a = 7.33822 + 1.47455I
b = −1.058890 + 0.041997I
−1.95643 + 2.20437I 21.2973 + 12.8131I
u = 0.069842 − 0.433647I
a = 7.33822 − 1.47455I
b = −1.058890 − 0.041997I
−1.95643 − 2.20437I 21.2973 − 12.8131I
9
II. I
u
2
= hb + 1, −u
8
+ 3u
6
+ u
5
− 4u
4
− 2u
3
+ u
2
+ a + 2u + 1, u
9
+ u
8
−
2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
3
=
u
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− 2u − 1
−1
a
10
=
−u
−u
3
+ u
a
2
=
u
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− 2u − 2
−1
a
1
=
−1
0
a
4
=
u
8
− 3u
6
− u
5
+ 4u
4
+ 2u
3
− u
2
− 2u − 1
−1
a
7
=
1
u
2
a
12
=
−u
4
+ u
2
− 1
−u
6
+ 2u
4
− u
2
a
11
=
−u
7
+ 2u
5
− 2u
3
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u
3
− 1
a
8
=
−u
2
+ 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
− 6u
7
+ 2u
6
+ 13u
5
+ 2u
4
− 13u
3
− 5u
2
− 4u − 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
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
7
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
8
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
10
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
11
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
12
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = −0.457852 − 1.072010I
b = −1.00000
0.13850 + 2.09337I −2.03658 − 4.61282I
u = −0.772920 − 0.510351I
a = −0.457852 + 1.072010I
b = −1.00000
0.13850 − 2.09337I −2.03658 + 4.61282I
u = 0.825933
a = −1.46592
b = −1.00000
−2.84338 −15.2670
u = 1.173910 + 0.391555I
a = −0.522253 + 0.392004I
b = −1.00000
−6.01628 − 1.33617I −12.05808 − 1.14063I
u = 1.173910 − 0.391555I
a = −0.522253 − 0.392004I
b = −1.00000
−6.01628 + 1.33617I −12.05808 + 1.14063I
u = −0.141484 + 0.739668I
a = 1.63880 − 0.65075I
b = −1.00000
−2.26187 − 2.45442I −8.82413 + 4.82524I
u = −0.141484 − 0.739668I
a = 1.63880 + 0.65075I
b = −1.00000
−2.26187 + 2.45442I −8.82413 − 4.82524I
u = −1.172470 + 0.500383I
a = −0.425734 − 0.444312I
b = −1.00000
−5.24306 + 7.08493I −9.44791 − 3.65320I
u = −1.172470 − 0.500383I
a = −0.425734 + 0.444312I
b = −1.00000
−5.24306 − 7.08493I −9.44791 + 3.65320I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
48
+ 10u
47
+ ··· + 29u + 1)
c
2
((u − 1)
9
)(u
48
− 10u
47
+ ··· + 9u − 1)
c
3
, c
6
u
9
(u
48
+ 5u
47
+ ··· + 2560u + 512)
c
4
((u + 1)
9
)(u
48
− 10u
47
+ ··· + 9u − 1)
c
5
(u
9
+ u
8
+ ··· − u − 1)(u
48
+ 2u
47
+ ··· − u − 1)
c
7
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
48
− 10u
47
+ ··· − 284463u − 118529)
c
8
(u
9
+ u
8
+ ··· + u − 1)(u
48
− 2u
47
+ ··· + 5u + 1)
c
9
(u
9
− u
8
+ ··· − u + 1)(u
48
+ 2u
47
+ ··· − u − 1)
c
10
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
48
− 18u
47
+ ··· + 5u + 1)
c
11
(u
9
− u
8
+ ··· + u + 1)(u
48
− 2u
47
+ ··· + 5u + 1)
c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
48
− 18u
47
+ ··· + 5u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
48
+ 66y
47
+ ··· − 29y + 1)
c
2
, c
4
((y −1)
9
)(y
48
− 10y
47
+ ··· − 29y + 1)
c
3
, c
6
y
9
(y
48
− 57y
47
+ ··· − 6553600y + 262144)
c
5
, c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
48
− 10y
47
+ ··· − 5y + 1)
c
7
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
48
+ 46y
47
+ ··· + 130798249663y + 14049123841)
c
8
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
48
+ 18y
47
+ ··· − 5y + 1)
c
10
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
48
+ 26y
47
+ ··· − 305y + 1)
15
