11a
3
(K11a
3
)
A knot diagram
1
Linearized knot diagam
5 1 7 2 3 10 4 11 6 8 9
Solving Sequence
1,5
2 3 6
4,9
11 8 7 10
c
1
c
2
c
5
c
4
c
11
c
8
c
7
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4.73407 × 10
19
u
65
− 1.78062 × 10
20
u
64
+ ··· + 6.92121 × 10
19
b − 9.60242 × 10
19
,
2.00992 × 10
19
u
65
− 1.27810 × 10
20
u
64
+ ··· + 6.92121 × 10
19
a + 5.30233 × 10
20
, u
66
− 4u
65
+ ··· − 14u + 1i
I
u
2
= hb − 1, u
4
− u
3
+ 2u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
3
= h−au + b + u, a
2
− au − 3a + 2, u
2
+ u + 1i
* 3 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
=
h4.73×10
19
u
65
−1.78×10
20
u
64
+· · ·+6.92×10
19
b−9.60×10
19
, 2.01×10
19
u
65
−
1.28 × 10
20
u
64
+ · · · + 6.92 × 10
19
a + 5.30 × 10
20
, u
66
− 4u
65
+ · · · − 14u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
6
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
4
=
−u
u
3
+ u
a
9
=
−0.290400u
65
+ 1.84665u
64
+ ··· + 17.1503u − 7.66099
−0.683994u
65
+ 2.57271u
64
+ ··· − 8.88365u + 1.38739
a
11
=
0.477604u
65
− 0.313880u
64
+ ··· + 9.01518u − 4.46864
−1.76402u
65
+ 7.20916u
64
+ ··· − 25.9654u + 2.45043
a
8
=
0.352013u
65
− 2.74835u
64
+ ··· + 30.8461u − 5.72790
1.33994u
65
− 5.22709u
64
+ ··· + 16.3365u − 0.873918
a
7
=
0.996758u
65
− 2.80838u
64
+ ··· + 21.4371u − 5.07963
−1.17865u
65
+ 4.19945u
64
+ ··· − 8.87499u + 0.996758
a
10
=
0.773579u
65
− 2.81719u
64
+ ··· + 35.3229u − 9.01284
−0.443910u
65
+ 1.66335u
64
+ ··· − 5.63834u + 1.19827
a
10
=
0.773579u
65
− 2.81719u
64
+ ··· + 35.3229u − 9.01284
−0.443910u
65
+ 1.66335u
64
+ ··· − 5.63834u + 1.19827
(ii) Obstruction class = −1
(iii) Cusp Shapes =
88536532098082237941
69212056571253139646
u
65
−
346942669555547012397
69212056571253139646
u
64
+ ··· −
2682685309410699867097
69212056571253139646
u +
417517236906079889612
34606028285626569823
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
66
+ 4u
65
+ ··· + 14u + 1
c
2
u
66
+ 32u
65
+ ··· − 86u + 1
c
3
, c
7
u
66
+ 2u
65
+ ··· − 16u − 16
c
5
u
66
− 4u
65
+ ··· + 4020u + 977
c
6
, c
9
u
66
− 3u
65
+ ··· − 96u + 32
c
8
, c
10
, c
11
u
66
+ 8u
65
+ ··· − 12u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
66
+ 32y
65
+ ··· − 86y + 1
c
2
y
66
+ 8y
65
+ ··· − 8342y + 1
c
3
, c
7
y
66
− 30y
65
+ ··· − 2688y + 256
c
5
y
66
− 16y
65
+ ··· − 97788750y + 954529
c
6
, c
9
y
66
− 39y
65
+ ··· − 7680y + 1024
c
8
, c
10
, c
11
y
66
− 64y
65
+ ··· − 92y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447737 + 0.886933I
a = 1.92832 + 1.33209I
b = 0.960667 + 0.075689I
1.35276 − 1.84672I 28.2718 + 21.5804I
u = −0.447737 − 0.886933I
a = 1.92832 − 1.33209I
b = 0.960667 − 0.075689I
1.35276 + 1.84672I 28.2718 − 21.5804I
u = −0.801015 + 0.661180I
a = 2.30437 + 0.57137I
b = −1.45947 + 0.22980I
7.91868 − 6.59447I 0. + 6.00646I
u = −0.801015 − 0.661180I
a = 2.30437 − 0.57137I
b = −1.45947 − 0.22980I
7.91868 + 6.59447I 0. − 6.00646I
u = 0.860042 + 0.369782I
a = 2.14032 + 0.32890I
b = −1.47569 + 0.33459I
6.19769 − 10.10890I 7.50011 + 5.44756I
u = 0.860042 − 0.369782I
a = 2.14032 − 0.32890I
b = −1.47569 − 0.33459I
6.19769 + 10.10890I 7.50011 − 5.44756I
u = −0.668703 + 0.641624I
a = −0.453771 + 0.163173I
b = 0.430801 − 0.625032I
1.84919 − 3.47096I 5.53731 + 7.57944I
u = −0.668703 − 0.641624I
a = −0.453771 − 0.163173I
b = 0.430801 + 0.625032I
1.84919 + 3.47096I 5.53731 − 7.57944I
u = −0.375168 + 1.011290I
a = 1.006090 + 0.919127I
b = 0.091003 + 0.416704I
−1.05484 − 1.47223I 0
u = −0.375168 − 1.011290I
a = 1.006090 − 0.919127I
b = 0.091003 − 0.416704I
−1.05484 + 1.47223I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511878 + 0.976459I
a = 1.64988 − 1.32112I
b = −1.66385 + 0.06802I
8.80229 + 2.61597I 0
u = 0.511878 − 0.976459I
a = 1.64988 + 1.32112I
b = −1.66385 − 0.06802I
8.80229 − 2.61597I 0
u = 0.246513 + 1.075850I
a = −0.702183 − 0.085805I
b = 1.331250 − 0.286376I
−1.20633 − 0.98148I 0
u = 0.246513 − 1.075850I
a = −0.702183 + 0.085805I
b = 1.331250 + 0.286376I
−1.20633 + 0.98148I 0
u = −0.593695 + 0.930839I
a = 0.633018 − 0.417893I
b = 0.444003 + 0.428029I
0.99829 − 1.41928I 0
u = −0.593695 − 0.930839I
a = 0.633018 + 0.417893I
b = 0.444003 − 0.428029I
0.99829 + 1.41928I 0
u = 0.895716
a = 1.28200
b = −1.26436
0.335750 9.51520
u = 0.323236 + 1.068020I
a = −0.71514 + 1.43717I
b = 1.056090 + 0.536731I
−1.87944 + 1.86021I 0
u = 0.323236 − 1.068020I
a = −0.71514 − 1.43717I
b = 1.056090 − 0.536731I
−1.87944 − 1.86021I 0
u = 0.583954 + 0.630467I
a = 2.47273 − 1.26841I
b = −1.58923 − 0.11013I
9.82684 + 1.74748I 11.13070 + 1.76182I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583954 − 0.630467I
a = 2.47273 + 1.26841I
b = −1.58923 + 0.11013I
9.82684 − 1.74748I 11.13070 − 1.76182I
u = 0.779756 + 0.337981I
a = −0.457305 + 0.348225I
b = 0.360992 − 0.860365I
0.29837 − 5.77580I 4.51138 + 5.26923I
u = 0.779756 − 0.337981I
a = −0.457305 − 0.348225I
b = 0.360992 + 0.860365I
0.29837 + 5.77580I 4.51138 − 5.26923I
u = −0.553417 + 1.013290I
a = −1.98755 − 2.54381I
b = 1.277910 − 0.085579I
2.55061 − 3.21838I 0
u = −0.553417 − 1.013290I
a = −1.98755 + 2.54381I
b = 1.277910 + 0.085579I
2.55061 + 3.21838I 0
u = −0.350315 + 0.758669I
a = 0.903762 − 0.185239I
b = −0.0960512 − 0.0497974I
−0.23109 − 1.44442I −1.44757 + 4.95270I
u = −0.350315 − 0.758669I
a = 0.903762 + 0.185239I
b = −0.0960512 + 0.0497974I
−0.23109 + 1.44442I −1.44757 − 4.95270I
u = −0.633698 + 0.542548I
a = −3.20205 + 0.42108I
b = 1.320010 − 0.014248I
3.94155 − 1.44668I 7.42047 + 3.11484I
u = −0.633698 − 0.542548I
a = −3.20205 − 0.42108I
b = 1.320010 + 0.014248I
3.94155 + 1.44668I 7.42047 − 3.11484I
u = 0.221525 + 1.144870I
a = 0.415305 − 0.704627I
b = 0.220112 − 0.840668I
−4.39164 − 2.99363I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.221525 − 1.144870I
a = 0.415305 + 0.704627I
b = 0.220112 + 0.840668I
−4.39164 + 2.99363I 0
u = −0.763032 + 0.307439I
a = 1.74149 − 0.72557I
b = −1.46443 − 0.20883I
8.22126 + 3.50783I 9.72944 − 1.69161I
u = −0.763032 − 0.307439I
a = 1.74149 + 0.72557I
b = −1.46443 + 0.20883I
8.22126 − 3.50783I 9.72944 + 1.69161I
u = −0.263556 + 1.157410I
a = −0.512295 − 0.085483I
b = −1.378620 − 0.146836I
3.75032 + 0.51941I 0
u = −0.263556 − 1.157410I
a = −0.512295 + 0.085483I
b = −1.378620 + 0.146836I
3.75032 − 0.51941I 0
u = −0.527326 + 1.065790I
a = −0.79696 − 1.22027I
b = 0.329323 − 0.680569I
0.11788 − 5.06683I 0
u = −0.527326 − 1.065790I
a = −0.79696 + 1.22027I
b = 0.329323 + 0.680569I
0.11788 + 5.06683I 0
u = 0.721013 + 0.363719I
a = −2.95924 − 0.12833I
b = 1.41518 − 0.16379I
3.08928 − 3.39261I 6.58379 + 2.75306I
u = 0.721013 − 0.363719I
a = −2.95924 + 0.12833I
b = 1.41518 + 0.16379I
3.08928 + 3.39261I 6.58379 − 2.75306I
u = −0.711073 + 0.974927I
a = 1.58757 + 1.06886I
b = −1.44305 − 0.18150I
6.98766 + 0.95393I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711073 − 0.974927I
a = 1.58757 − 1.06886I
b = −1.44305 + 0.18150I
6.98766 − 0.95393I 0
u = 0.363610 + 1.151710I
a = 0.015002 + 0.368525I
b = −0.207558 + 0.642919I
−6.04161 + 2.45340I 0
u = 0.363610 − 1.151710I
a = 0.015002 − 0.368525I
b = −0.207558 − 0.642919I
−6.04161 − 2.45340I 0
u = 0.536106 + 1.092070I
a = 0.109685 + 0.492756I
b = 0.901979 − 0.712422I
−0.40126 + 5.25319I 0
u = 0.536106 − 1.092070I
a = 0.109685 − 0.492756I
b = 0.901979 + 0.712422I
−0.40126 − 5.25319I 0
u = 0.156166 + 1.218030I
a = 0.085968 + 0.372608I
b = −1.40723 + 0.32906I
0.79611 − 7.18319I 0
u = 0.156166 − 1.218030I
a = 0.085968 − 0.372608I
b = −1.40723 − 0.32906I
0.79611 + 7.18319I 0
u = 0.563876 + 1.106240I
a = −1.90945 + 1.84534I
b = 1.46658 + 0.20344I
0.91936 + 8.30279I 0
u = 0.563876 − 1.106240I
a = −1.90945 − 1.84534I
b = 1.46658 − 0.20344I
0.91936 − 8.30279I 0
u = 0.492275 + 1.150200I
a = 0.949530 − 0.599065I
b = −0.409340 − 0.495814I
−5.17298 + 5.63394I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.492275 − 1.150200I
a = 0.949530 + 0.599065I
b = −0.409340 + 0.495814I
−5.17298 − 5.63394I 0
u = −0.563535 + 1.134560I
a = 0.88677 + 2.16349I
b = −1.43841 + 0.26048I
5.80147 − 8.50464I 0
u = −0.563535 − 1.134560I
a = 0.88677 − 2.16349I
b = −1.43841 − 0.26048I
5.80147 + 8.50464I 0
u = 0.575045 + 1.130160I
a = −1.128290 + 0.629597I
b = 0.356915 + 0.930272I
−2.03842 + 10.86450I 0
u = 0.575045 − 1.130160I
a = −1.128290 − 0.629597I
b = 0.356915 − 0.930272I
−2.03842 − 10.86450I 0
u = 0.712768 + 0.146826I
a = 0.827880 − 0.176126I
b = −0.256675 + 0.450186I
−2.30399 − 1.13049I −0.90491 + 1.23607I
u = 0.712768 − 0.146826I
a = 0.827880 + 0.176126I
b = −0.256675 − 0.450186I
−2.30399 + 1.13049I −0.90491 − 1.23607I
u = 0.626648 + 0.353158I
a = −1.406460 + 0.110890I
b = 0.808652 + 0.620740I
1.72098 − 0.65765I 7.06140 + 0.81107I
u = 0.626648 − 0.353158I
a = −1.406460 − 0.110890I
b = 0.808652 − 0.620740I
1.72098 + 0.65765I 7.06140 − 0.81107I
u = −0.578683 + 0.421784I
a = −0.654555 + 0.516153I
b = 0.475930 + 0.593283I
1.99483 + 0.60906I 7.48413 − 1.51323I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578683 − 0.421784I
a = −0.654555 − 0.516153I
b = 0.475930 − 0.593283I
1.99483 − 0.60906I 7.48413 + 1.51323I
u = 0.611501 + 1.147440I
a = 1.49873 − 1.96189I
b = −1.48463 − 0.36648I
3.8588 + 15.5500I 0
u = 0.611501 − 1.147440I
a = 1.49873 + 1.96189I
b = −1.48463 + 0.36648I
3.8588 − 15.5500I 0
u = 0.444892 + 1.249160I
a = 0.162825 − 0.849550I
b = −1.218660 − 0.058791I
−3.53690 + 4.73542I 0
u = 0.444892 − 1.249160I
a = 0.162825 + 0.849550I
b = −1.218660 + 0.058791I
−3.53690 − 4.73542I 0
u = 0.104581
a = −6.15002
b = 0.755340
1.11358 9.06930
11
II. I
u
2
= hb − 1, u
4
− u
3
+ 2u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
6
=
−u
4
− u
2
− 1
u
4
− u
3
+ u
2
+ 1
a
4
=
−u
u
3
+ u
a
9
=
−u
4
+ u
3
− 2u
2
+ u − 1
1
a
11
=
−u
4
+ u
3
− 2u
2
+ u
1
a
8
=
−1
0
a
7
=
−u
4
− u
2
− 1
u
4
− u
3
+ u
2
+ 1
a
10
=
−u
4
+ u
3
− 2u
2
+ u − 1
1
a
10
=
−u
4
+ u
3
− 2u
2
+ u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
4
+ 5u
3
− 4u
2
+ 3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
3
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
5
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
, c
9
u
5
c
8
(u + 1)
5
c
10
, c
11
(u − 1)
5
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
3
, c
5
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
, c
9
y
5
c
8
, c
10
, c
11
(y −1)
5
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.428550 + 1.039280I
b = 1.00000
1.31583 − 1.53058I 8.47842 − 1.00973I
u = −0.339110 − 0.822375I
a = 0.428550 − 1.039280I
b = 1.00000
1.31583 + 1.53058I 8.47842 + 1.00973I
u = 0.766826
a = −1.30408
b = 1.00000
−0.756147 1.86520
u = 0.455697 + 1.200150I
a = −0.276511 + 0.728237I
b = 1.00000
−4.22763 + 4.40083I −2.41100 − 1.19010I
u = 0.455697 − 1.200150I
a = −0.276511 − 0.728237I
b = 1.00000
−4.22763 − 4.40083I −2.41100 + 1.19010I
15
III. I
u
3
= h−au + b + u, a
2
− au − 3a + 2, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
6
=
−1
0
a
4
=
−u
u + 1
a
9
=
a
au − u
a
11
=
au − a − 2u + 1
−au + u + 1
a
8
=
−a − u
−au + u + 1
a
7
=
−a − u
−au + u + 1
a
10
=
au + a − u
au − u
a
10
=
au + a − u
au − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3au − 6a + 10u + 14
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
7
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
8
(u
2
− u − 1)
2
c
9
, c
10
, c
11
(u
2
+ u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
7
y
4
c
6
, c
8
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.690983 − 0.535233I
b = 0.618034
0.98696 − 2.02988I 4.50000 + 9.27358I
u = −0.500000 + 0.866025I
a = 1.80902 + 1.40126I
b = −1.61803
8.88264 − 2.02988I 4.50000 − 2.34537I
u = −0.500000 − 0.866025I
a = 0.690983 + 0.535233I
b = 0.618034
0.98696 + 2.02988I 4.50000 − 9.27358I
u = −0.500000 − 0.866025I
a = 1.80902 − 1.40126I
b = −1.61803
8.88264 + 2.02988I 4.50000 + 2.34537I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
5
− u
4
+ ··· + u − 1)(u
66
+ 4u
65
+ ··· + 14u + 1)
c
2
((u
2
+ u + 1)
2
)(u
5
+ 3u
4
+ ··· − u − 1)(u
66
+ 32u
65
+ ··· − 86u + 1)
c
3
u
4
(u
5
+ u
4
+ ··· + u − 1)(u
66
+ 2u
65
+ ··· − 16u − 16)
c
4
((u
2
− u + 1)
2
)(u
5
+ u
4
+ ··· + u + 1)(u
66
+ 4u
65
+ ··· + 14u + 1)
c
5
(u
2
+ u + 1)
2
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
· (u
66
− 4u
65
+ ··· + 4020u + 977)
c
6
u
5
(u
2
− u − 1)
2
(u
66
− 3u
65
+ ··· − 96u + 32)
c
7
u
4
(u
5
− u
4
+ ··· + u + 1)(u
66
+ 2u
65
+ ··· − 16u − 16)
c
8
((u + 1)
5
)(u
2
− u − 1)
2
(u
66
+ 8u
65
+ ··· − 12u − 1)
c
9
u
5
(u
2
+ u − 1)
2
(u
66
− 3u
65
+ ··· − 96u + 32)
c
10
, c
11
((u − 1)
5
)(u
2
+ u − 1)
2
(u
66
+ 8u
65
+ ··· − 12u − 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
5
+ 3y
4
+ ··· − y −1)(y
66
+ 32y
65
+ ··· − 86y + 1)
c
2
(y
2
+ y + 1)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
66
+ 8y
65
+ ··· − 8342y + 1)
c
3
, c
7
y
4
(y
5
− 5y
4
+ ··· − y −1)(y
66
− 30y
65
+ ··· − 2688y + 256)
c
5
(y
2
+ y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
66
− 16y
65
+ ··· − 97788750y + 954529)
c
6
, c
9
y
5
(y
2
− 3y + 1)
2
(y
66
− 39y
65
+ ··· − 7680y + 1024)
c
8
, c
10
, c
11
((y −1)
5
)(y
2
− 3y + 1)
2
(y
66
− 64y
65
+ ··· − 92y + 1)
21
