12n
0015
(K12n
0015
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 10 5 11 12 7 1 9
Solving Sequence
6,10
7
2,11
5 3 8 1 12 4 9
c
6
c
10
c
5
c
2
c
7
c
1
c
11
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.50022 × 10
125
u
64
+ 4.36424 × 10
125
u
63
+ ··· + 3.54215 × 10
125
b − 7.96745 × 10
124
,
− 2.95873 × 10
125
u
64
− 9.80937 × 10
125
u
63
+ ··· + 3.54215 × 10
125
a − 9.49669 × 10
125
, u
65
+ 3u
64
+ ··· − u
2
+ 1i
I
u
2
= hu
3
a − u
2
a + u
3
− au − u
2
+ b − a − u − 1, u
4
a − 2u
3
a − 4u
4
− u
2
a + 5u
3
+ a
2
+ 3au + 8u
2
+ a − 8u − 3,
u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 75 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
= h1.50 × 10
125
u
64
+ 4.36 × 10
125
u
63
+ · · · + 3.54 × 10
125
b − 7.97 ×
10
124
, −2.96 × 10
125
u
64
− 9.81 × 10
125
u
63
+ · · · + 3.54 × 10
125
a − 9.50 ×
10
125
, u
65
+ 3u
64
+ · · · − u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
0.835293u
64
+ 2.76933u
63
+ ··· + 1.71444u + 2.68105
−0.423534u
64
− 1.23209u
63
+ ··· + 1.25883u + 0.224932
a
11
=
u
−u
3
+ u
a
5
=
0.345381u
64
+ 0.473837u
63
+ ··· − 1.23941u + 2.97738
−0.310281u
64
− 0.952665u
63
+ ··· + 1.07920u − 0.578999
a
3
=
0.154488u
64
− 0.107654u
63
+ ··· − 1.02424u + 2.50407
−0.0606760u
64
− 0.279839u
63
+ ··· + 0.948980u − 0.490002
a
8
=
0.206883u
64
+ 0.609928u
63
+ ··· − 1.00346u − 0.732547
−0.383905u
64
− 1.05169u
63
+ ··· + 1.00690u − 0.344765
a
1
=
0.767182u
64
+ 2.19356u
63
+ ··· − 1.80348u − 0.398504
0.560299u
64
+ 1.58363u
63
+ ··· − 0.800020u + 0.334043
a
12
=
0.376922u
64
+ 0.519176u
63
+ ··· + 2.21285u + 0.877994
0.402208u
64
+ 0.524302u
63
+ ··· + 1.79239u − 0.116295
a
4
=
0.215164u
64
+ 0.172185u
63
+ ··· − 1.97322u + 2.99408
−0.0606760u
64
− 0.279839u
63
+ ··· + 0.948980u − 0.490002
a
9
=
0.323109u
64
+ 0.870589u
63
+ ··· − 0.236280u − 0.840533
−0.433466u
64
− 1.19898u
63
+ ··· + 1.89031u − 0.540767
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.36898u
64
− 8.01720u
63
+ ··· − 34.4288u − 0.224583
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 36u
64
+ ··· − 153u − 1
c
2
, c
5
u
65
+ 6u
64
+ ··· − 5u − 1
c
3
u
65
− 6u
64
+ ··· − 3141u − 1282
c
4
, c
7
u
65
+ 5u
64
+ ··· − 13312u
2
− 1024
c
6
, c
10
u
65
− 3u
64
+ ··· + u
2
− 1
c
8
u
65
+ 3u
64
+ ··· + 969u − 578
c
9
, c
12
u
65
− 3u
64
+ ··· + 8u − 1
c
11
u
65
− 29u
64
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 8y
64
+ ··· + 10327y −1
c
2
, c
5
y
65
+ 36y
64
+ ··· − 153y −1
c
3
y
65
− 52y
64
+ ··· − 241954815y −1643524
c
4
, c
7
y
65
+ 55y
64
+ ··· − 27262976y −1048576
c
6
, c
10
y
65
− 15y
64
+ ··· + 2y −1
c
8
y
65
+ 5y
64
+ ··· − 4574003y −334084
c
9
, c
12
y
65
+ 29y
64
+ ··· + 2y −1
c
11
y
65
+ 17y
64
+ ··· − 142y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628102 + 0.569155I
a = −0.40185 + 1.73582I
b = 0.448292 + 1.291450I
−1.16500 + 7.59687I 3.63163 − 10.87893I
u = 0.628102 − 0.569155I
a = −0.40185 − 1.73582I
b = 0.448292 − 1.291450I
−1.16500 − 7.59687I 3.63163 + 10.87893I
u = −0.565212 + 0.623133I
a = −0.32719 − 1.87544I
b = 0.344749 − 1.222650I
−2.37364 − 2.97409I 0.03419 + 4.98688I
u = −0.565212 − 0.623133I
a = −0.32719 + 1.87544I
b = 0.344749 + 1.222650I
−2.37364 + 2.97409I 0.03419 − 4.98688I
u = 0.072366 + 0.781453I
a = 1.19704 + 1.78785I
b = 0.152981 + 0.671120I
0.24332 − 1.46975I 2.96650 + 0.84122I
u = 0.072366 − 0.781453I
a = 1.19704 − 1.78785I
b = 0.152981 − 0.671120I
0.24332 + 1.46975I 2.96650 − 0.84122I
u = −0.340961 + 0.698038I
a = 0.19869 − 2.27298I
b = 0.233975 − 0.974531I
−1.64164 − 2.15616I −0.38705 + 4.35750I
u = −0.340961 − 0.698038I
a = 0.19869 + 2.27298I
b = 0.233975 + 0.974531I
−1.64164 + 2.15616I −0.38705 − 4.35750I
u = −0.725228 + 0.278028I
a = 1.95932 − 0.44335I
b = 0.208955 + 0.909618I
−1.41966 − 0.52874I 3.13856 + 2.24700I
u = −0.725228 − 0.278028I
a = 1.95932 + 0.44335I
b = 0.208955 − 0.909618I
−1.41966 + 0.52874I 3.13856 − 2.24700I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.765214 + 0.985370I
a = −0.15270 − 1.41131I
b = −0.264359 − 1.359580I
−7.96046 − 6.18775I 0
u = −0.765214 − 0.985370I
a = −0.15270 + 1.41131I
b = −0.264359 + 1.359580I
−7.96046 + 6.18775I 0
u = −0.855805 + 0.909432I
a = 0.197635 + 0.609389I
b = −0.821764 + 0.080284I
−2.89879 + 3.80873I 0
u = −0.855805 − 0.909432I
a = 0.197635 − 0.609389I
b = −0.821764 − 0.080284I
−2.89879 − 3.80873I 0
u = 0.897889 + 0.886104I
a = 0.138267 − 0.519755I
b = −0.856989 + 0.018873I
−4.61158 + 1.57498I 0
u = 0.897889 − 0.886104I
a = 0.138267 + 0.519755I
b = −0.856989 − 0.018873I
−4.61158 − 1.57498I 0
u = −0.977996 + 0.800120I
a = 0.160447 + 0.259314I
b = −0.781893 − 0.251942I
1.27467 − 2.98710I 0
u = −0.977996 − 0.800120I
a = 0.160447 − 0.259314I
b = −0.781893 + 0.251942I
1.27467 + 2.98710I 0
u = 0.734905 + 0.039492I
a = 0.217205 − 0.011467I
b = 0.883998 + 0.223037I
3.33660 + 2.97737I 14.6570 − 4.9725I
u = 0.734905 − 0.039492I
a = 0.217205 + 0.011467I
b = 0.883998 − 0.223037I
3.33660 − 2.97737I 14.6570 + 4.9725I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.677662 + 0.256690I
a = −0.554218 − 0.670994I
b = 0.850990 − 0.944246I
2.13495 − 5.98222I 10.3042 + 10.3831I
u = −0.677662 − 0.256690I
a = −0.554218 + 0.670994I
b = 0.850990 + 0.944246I
2.13495 + 5.98222I 10.3042 − 10.3831I
u = −0.697071 + 0.134831I
a = −0.208690 − 0.093719I
b = 0.865604 − 0.650193I
2.94313 − 0.27251I 13.63116 + 1.74028I
u = −0.697071 − 0.134831I
a = −0.208690 + 0.093719I
b = 0.865604 + 0.650193I
2.94313 + 0.27251I 13.63116 − 1.74028I
u = 0.783819 + 1.026080I
a = −0.143080 + 1.349990I
b = −0.323635 + 1.327820I
−9.37380 + 0.62790I 0
u = 0.783819 − 1.026080I
a = −0.143080 − 1.349990I
b = −0.323635 − 1.327820I
−9.37380 − 0.62790I 0
u = 0.583045 + 0.371142I
a = −0.94998 + 1.34055I
b = 0.642745 + 1.066730I
0.97209 + 2.48020I 8.17214 − 4.93777I
u = 0.583045 − 0.371142I
a = −0.94998 − 1.34055I
b = 0.642745 − 1.066730I
0.97209 − 2.48020I 8.17214 + 4.93777I
u = 0.980745 + 0.879226I
a = −0.009190 − 0.355180I
b = −0.952450 + 0.203308I
−4.36918 + 4.99205I 0
u = 0.980745 − 0.879226I
a = −0.009190 + 0.355180I
b = −0.952450 − 0.203308I
−4.36918 − 4.99205I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.674850
a = 0.446292
b = 0.463057
1.16666 8.48480
u = −1.326940 + 0.154775I
a = 0.982376 + 0.410900I
b = −0.273052 + 0.826180I
1.92758 − 1.33174I 0
u = −1.326940 − 0.154775I
a = 0.982376 − 0.410900I
b = −0.273052 − 0.826180I
1.92758 + 1.33174I 0
u = 0.580701 + 0.321504I
a = 2.76581 + 0.85928I
b = 0.345091 − 0.954683I
−0.87681 − 4.22656I 6.95306 + 2.39808I
u = 0.580701 − 0.321504I
a = 2.76581 − 0.85928I
b = 0.345091 + 0.954683I
−0.87681 + 4.22656I 6.95306 − 2.39808I
u = −1.003250 + 0.884542I
a = −0.060369 + 0.304416I
b = −0.985091 − 0.260120I
−2.47713 − 10.45070I 0
u = −1.003250 − 0.884542I
a = −0.060369 − 0.304416I
b = −0.985091 + 0.260120I
−2.47713 + 10.45070I 0
u = −0.745935 + 1.160500I
a = 0.000884 − 1.252980I
b = −0.361004 − 1.170190I
−2.81669 + 0.45437I 0
u = −0.745935 − 1.160500I
a = 0.000884 + 1.252980I
b = −0.361004 + 1.170190I
−2.81669 − 0.45437I 0
u = −1.127810 + 0.820945I
a = 1.24601 + 1.23918I
b = −0.420609 + 1.227310I
−6.79571 − 0.50966I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.127810 − 0.820945I
a = 1.24601 − 1.23918I
b = −0.420609 − 1.227310I
−6.79571 + 0.50966I 0
u = 0.849131 + 1.120280I
a = −0.118188 + 1.192840I
b = −0.451043 + 1.242660I
−8.41853 − 3.05895I 0
u = 0.849131 − 1.120280I
a = −0.118188 − 1.192840I
b = −0.451043 − 1.242660I
−8.41853 + 3.05895I 0
u = −0.195377 + 0.553421I
a = 1.205400 + 0.389629I
b = −0.0029121 + 0.1179000I
0.36359 − 1.66193I 2.56838 + 3.46511I
u = −0.195377 − 0.553421I
a = 1.205400 − 0.389629I
b = −0.0029121 − 0.1179000I
0.36359 + 1.66193I 2.56838 − 3.46511I
u = 1.12627 + 0.86481I
a = 1.18250 − 1.30489I
b = −0.470843 − 1.237780I
−8.27510 + 6.31962I 0
u = 1.12627 − 0.86481I
a = 1.18250 + 1.30489I
b = −0.470843 + 1.237780I
−8.27510 − 6.31962I 0
u = 0.534053 + 0.202971I
a = −1.58350 + 0.17037I
b = 0.633931 + 0.867673I
0.62677 + 2.45051I 2.30160 − 3.49944I
u = 0.534053 − 0.202971I
a = −1.58350 − 0.17037I
b = 0.633931 − 0.867673I
0.62677 − 2.45051I 2.30160 + 3.49944I
u = −0.88456 + 1.14555I
a = −0.116208 − 1.133810I
b = −0.494977 − 1.215640I
−6.25912 + 8.60016I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.88456 − 1.14555I
a = −0.116208 + 1.133810I
b = −0.494977 + 1.215640I
−6.25912 − 8.60016I 0
u = 1.45538 + 0.10222I
a = 0.757445 + 0.377705I
b = −0.361366 + 0.750604I
5.76923 + 2.96244I 0
u = 1.45538 − 0.10222I
a = 0.757445 − 0.377705I
b = −0.361366 − 0.750604I
5.76923 − 2.96244I 0
u = 1.11941 + 0.94502I
a = 1.03658 − 1.40534I
b = −0.576768 − 1.237090I
−7.52216 + 10.51980I 0
u = 1.11941 − 0.94502I
a = 1.03658 + 1.40534I
b = −0.576768 + 1.237090I
−7.52216 − 10.51980I 0
u = −1.11499 + 0.96636I
a = 0.99158 + 1.42922I
b = −0.608733 + 1.232920I
−5.4631 − 16.2041I 0
u = −1.11499 − 0.96636I
a = 0.99158 − 1.42922I
b = −0.608733 − 1.232920I
−5.4631 + 16.2041I 0
u = −1.17549 + 0.93342I
a = 1.01884 + 1.29137I
b = −0.543560 + 1.174510I
−1.47035 − 7.97117I 0
u = −1.17549 − 0.93342I
a = 1.01884 − 1.29137I
b = −0.543560 − 1.174510I
−1.47035 + 7.97117I 0
u = −0.039971 + 0.483137I
a = 4.26633 + 3.79248I
b = 0.520875 + 0.799810I
0.42197 + 3.98006I −11.1996 − 14.1267I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.039971 − 0.483137I
a = 4.26633 − 3.79248I
b = 0.520875 − 0.799810I
0.42197 − 3.98006I −11.1996 + 14.1267I
u = 1.51110 + 0.30215I
a = 0.932692 − 0.595477I
b = −0.344026 − 0.883021I
5.37755 + 6.09849I 0
u = 1.51110 − 0.30215I
a = 0.932692 + 0.595477I
b = −0.344026 + 0.883021I
5.37755 − 6.09849I 0
u = 0.199982 + 0.366065I
a = 7.44696 − 1.05122I
b = 0.531360 − 0.882027I
0.173552 − 0.278194I −17.0776 − 31.8991I
u = 0.199982 − 0.366065I
a = 7.44696 + 1.05122I
b = 0.531360 + 0.882027I
0.173552 + 0.278194I −17.0776 + 31.8991I
11
II. I
u
2
= hu
3
a − u
2
a + u
3
− au − u
2
+ b − a − u − 1, u
4
a − 4u
4
+ · · · + a −
3, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
a
−u
3
a + u
2
a − u
3
+ au + u
2
+ a + u + 1
a
11
=
u
−u
3
+ u
a
5
=
u
3
a + u
4
− u
2
a − u
3
− au − 2u
2
+ 2u
−u
3
a + u
2
a − u
3
+ au + u
2
+ a + u
a
3
=
u
4
− 2u
3
− u
2
+ a + 3u
−u
3
a + u
2
a − u
3
+ au + u
2
+ a + u
a
8
=
1
−u
2
a
1
=
−1
0
a
12
=
−u
3
+ 2u
−u
3
+ u
a
4
=
u
3
a + u
4
− u
2
a − u
3
− au − 2u
2
+ 2u
−u
3
a + u
2
a − u
3
+ au + u
2
+ a + u
a
9
=
−u
2
+ 1
u
4
− 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
a + 6u
3
a − u
4
− 4u
2
a + 2u
3
− 7au − 4u
2
− 5a + u + 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
, c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
8
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.837181 + 0.282010I
b = 0.500000 + 0.866025I
2.40108 + 2.02988I 6.80799 − 4.97460I
u = −1.21774
a = −0.837181 − 0.282010I
b = 0.500000 − 0.866025I
2.40108 − 2.02988I 6.80799 + 4.97460I
u = −0.309916 + 0.549911I
a = 2.00919 + 0.91819I
b = 0.500000 + 0.866025I
0.329100 + 0.499304I 7.97351 − 4.21865I
u = −0.309916 + 0.549911I
a = −1.70942 − 3.06513I
b = 0.500000 − 0.866025I
0.32910 − 3.56046I −1.93681 + 7.63956I
u = −0.309916 − 0.549911I
a = 2.00919 − 0.91819I
b = 0.500000 − 0.866025I
0.329100 − 0.499304I 7.97351 + 4.21865I
u = −0.309916 − 0.549911I
a = −1.70942 + 3.06513I
b = 0.500000 + 0.866025I
0.32910 + 3.56046I −1.93681 − 7.63956I
u = 1.41878 + 0.21917I
a = −0.858089 + 0.538616I
b = 0.500000 + 0.866025I
5.87256 + 6.43072I 12.8115 − 8.6504I
u = 1.41878 + 0.21917I
a = −0.604500 − 0.392206I
b = 0.500000 − 0.866025I
5.87256 + 2.37095I 8.34383 + 3.96169I
u = 1.41878 − 0.21917I
a = −0.858089 − 0.538616I
b = 0.500000 − 0.866025I
5.87256 − 6.43072I 12.8115 + 8.6504I
u = 1.41878 − 0.21917I
a = −0.604500 + 0.392206I
b = 0.500000 + 0.866025I
5.87256 − 2.37095I 8.34383 − 3.96169I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
65
+ 36u
64
+ ··· − 153u − 1)
c
2
((u
2
+ u + 1)
5
)(u
65
+ 6u
64
+ ··· − 5u − 1)
c
3
((u
2
− u + 1)
5
)(u
65
− 6u
64
+ ··· − 3141u − 1282)
c
4
, c
7
u
10
(u
65
+ 5u
64
+ ··· − 13312u
2
− 1024)
c
5
((u
2
− u + 1)
5
)(u
65
+ 6u
64
+ ··· − 5u − 1)
c
6
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
65
− 3u
64
+ ··· + u
2
− 1)
c
8
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
65
+ 3u
64
+ ··· + 969u − 578)
c
9
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
65
− 3u
64
+ ··· + 8u − 1)
c
10
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
65
− 3u
64
+ ··· + u
2
− 1)
c
11
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
65
− 29u
64
+ ··· + 2u + 1)
c
12
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
65
− 3u
64
+ ··· + 8u − 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
65
− 8y
64
+ ··· + 10327y −1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
65
+ 36y
64
+ ··· − 153y −1)
c
3
((y
2
+ y + 1)
5
)(y
65
− 52y
64
+ ··· − 2.41955 × 10
8
y −1643524)
c
4
, c
7
y
10
(y
65
+ 55y
64
+ ··· − 2.72630 × 10
7
y −1048576)
c
6
, c
10
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
65
− 15y
64
+ ··· + 2y −1)
c
8
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
65
+ 5y
64
+ ··· − 4574003y −334084)
c
9
, c
12
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
65
+ 29y
64
+ ··· + 2y −1)
c
11
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
65
+ 17y
64
+ ··· − 142y −1)
17
