11a
261
(K11a
261
)
A knot diagram
1
Linearized knot diagam
8 5 1 2 11 10 3 4 6 7 9
Solving Sequence
6,9
10 7 11
1,4
3 5 8 2
c
9
c
6
c
10
c
11
c
3
c
5
c
8
c
1
c
2
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.81838 × 10
20
u
64
+ 3.28868 × 10
20
u
63
+ ··· + 3.16246 × 10
20
b + 3.28868 × 10
20
,
2.56145 × 10
20
u
64
+ 1.23301 × 10
20
u
63
+ ··· + 4.74369 × 10
20
a + 1.66504 × 10
21
, u
65
− 2u
64
+ ··· − 5u + 1i
I
u
2
= hb − 1, a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 66 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−5.82×10
20
u
64
+3.29×10
20
u
63
+· · ·+3.16×10
20
b+3.29×10
20
, 2.56×
10
20
u
64
+1.23×10
20
u
63
+· · ·+4.74×10
20
a+1.67×10
21
, u
65
−2u
64
+· · ·−5u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
7
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
4
=
−0.539970u
64
− 0.259927u
63
+ ··· − 1.96576u − 3.51002
1.83982u
64
− 1.03991u
63
+ ··· + 6.70956u − 1.03991
a
3
=
−0.573322u
64
− 0.227294u
63
+ ··· − 0.674829u − 3.39334
2.04123u
64
− 1.24062u
63
+ ··· + 7.59641u − 1.24062
a
5
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
1.65099u
64
− 0.842590u
63
+ ··· + 10.1209u + 2.47153
−2.24504u
64
+ 1.44254u
63
+ ··· − 7.30269u + 1.44504
a
2
=
0.606671u
64
+ 0.193473u
63
+ ··· − 0.0581858u + 3.37667
−2.24028u
64
+ 1.44014u
63
+ ··· − 7.57737u + 1.44014
a
2
=
0.606671u
64
+ 0.193473u
63
+ ··· − 0.0581858u + 3.37667
−2.24028u
64
+ 1.44014u
63
+ ··· − 7.57737u + 1.44014
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1129105924074689745576
158123107034570359949
u
64
−
1258714178007543158198
158123107034570359949
u
63
+ ··· +
58838764609619796866
3364321426267454467
u −
281566083191392405996
158123107034570359949
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
− 4u
64
+ ··· − u + 1
c
2
, c
4
u
65
+ 2u
64
+ ··· − 3u + 1
c
3
u
65
− 11u
64
+ ··· + 6u − 2
c
5
u
65
+ 3u
64
+ ··· − 288u + 288
c
6
, c
9
, c
10
u
65
− 2u
64
+ ··· − 5u + 1
c
7
u
65
+ 18u
63
+ ··· − 5599u + 599
c
8
u
65
− 2u
64
+ ··· + 875u + 199
c
11
u
65
− 12u
64
+ ··· + 15361u − 937
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 12y
64
+ ··· + 5y −1
c
2
, c
4
y
65
− 48y
64
+ ··· + 65y −1
c
3
y
65
+ 9y
64
+ ··· − 32y −4
c
5
y
65
− 15y
64
+ ··· + 2689344y −82944
c
6
, c
9
, c
10
y
65
− 60y
64
+ ··· + 5y −1
c
7
y
65
+ 36y
64
+ ··· + 25490581y −358801
c
8
y
65
+ 76y
64
+ ··· + 46837y −39601
c
11
y
65
+ 40y
64
+ ··· + 64331905y −877969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.678260 + 0.569072I
a = −0.016122 + 0.492515I
b = 0.137240 − 0.682876I
4.77180 + 0.79551I 17.2605 − 1.0216I
u = 0.678260 − 0.569072I
a = −0.016122 − 0.492515I
b = 0.137240 + 0.682876I
4.77180 − 0.79551I 17.2605 + 1.0216I
u = 1.14092
a = −0.115125
b = 0.758312
1.93638 0
u = 0.382954 + 0.760163I
a = 0.794021 + 0.280590I
b = 0.046721 − 0.656714I
3.78970 + 3.79443I 12.5834 − 7.8440I
u = 0.382954 − 0.760163I
a = 0.794021 − 0.280590I
b = 0.046721 + 0.656714I
3.78970 − 3.79443I 12.5834 + 7.8440I
u = 1.125870 + 0.332132I
a = −0.689757 + 0.119579I
b = 0.687361 + 0.619577I
2.88797 − 1.12159I 0
u = 1.125870 − 0.332132I
a = −0.689757 − 0.119579I
b = 0.687361 − 0.619577I
2.88797 + 1.12159I 0
u = −0.614901 + 0.535330I
a = −0.761912 + 0.631452I
b = 0.88334 − 1.27623I
5.66757 + 7.97706I 9.36287 − 3.39629I
u = −0.614901 − 0.535330I
a = −0.761912 − 0.631452I
b = 0.88334 + 1.27623I
5.66757 − 7.97706I 9.36287 + 3.39629I
u = −0.366460 + 0.727085I
a = −1.42890 + 1.39175I
b = −0.95536 − 1.32953I
4.76852 − 12.28510I 7.44035 + 8.76560I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.366460 − 0.727085I
a = −1.42890 − 1.39175I
b = −0.95536 + 1.32953I
4.76852 + 12.28510I 7.44035 − 8.76560I
u = −1.191650 + 0.175560I
a = −0.880003 + 0.405987I
b = −0.699401 − 0.545647I
0.37120 − 4.07451I 0
u = −1.191650 − 0.175560I
a = −0.880003 − 0.405987I
b = −0.699401 + 0.545647I
0.37120 + 4.07451I 0
u = 1.235000 + 0.041141I
a = −0.79341 − 1.31957I
b = 0.31476 + 2.40619I
3.95963 + 0.42107I 0
u = 1.235000 − 0.041141I
a = −0.79341 + 1.31957I
b = 0.31476 − 2.40619I
3.95963 − 0.42107I 0
u = 0.049713 + 0.754423I
a = −0.714482 + 0.300281I
b = −0.855140 + 0.797416I
−0.40517 + 5.06438I 3.95497 − 7.18299I
u = 0.049713 − 0.754423I
a = −0.714482 − 0.300281I
b = −0.855140 − 0.797416I
−0.40517 − 5.06438I 3.95497 + 7.18299I
u = −0.339899 + 0.663108I
a = 1.64239 − 1.16141I
b = 0.781935 + 0.829638I
0.09522 − 6.44593I 5.03058 + 9.01119I
u = −0.339899 − 0.663108I
a = 1.64239 + 1.16141I
b = 0.781935 − 0.829638I
0.09522 + 6.44593I 5.03058 − 9.01119I
u = −1.235770 + 0.297333I
a = 0.406289 − 1.235280I
b = 0.943698 + 0.958823I
3.56058 − 8.86995I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.235770 − 0.297333I
a = 0.406289 + 1.235280I
b = 0.943698 − 0.958823I
3.56058 + 8.86995I 0
u = −0.380812 + 0.610143I
a = 0.06444 + 1.61329I
b = −0.058355 − 0.809391I
4.44968 − 3.80628I 12.2239 + 7.2828I
u = −0.380812 − 0.610143I
a = 0.06444 − 1.61329I
b = −0.058355 + 0.809391I
4.44968 + 3.80628I 12.2239 − 7.2828I
u = −1.288300 + 0.091889I
a = 0.31534 − 2.36850I
b = 0.348122 + 0.973758I
5.10270 − 3.01321I 0
u = −1.288300 − 0.091889I
a = 0.31534 + 2.36850I
b = 0.348122 − 0.973758I
5.10270 + 3.01321I 0
u = 1.283700 + 0.210832I
a = 0.005363 − 0.773420I
b = −0.480767 − 0.212588I
1.09839 + 1.94254I 0
u = 1.283700 − 0.210832I
a = 0.005363 + 0.773420I
b = −0.480767 + 0.212588I
1.09839 − 1.94254I 0
u = −0.419028 + 0.549280I
a = −1.77640 + 1.52917I
b = 0.042992 − 0.667229I
4.67294 + 0.09706I 13.36415 + 0.53030I
u = −0.419028 − 0.549280I
a = −1.77640 − 1.52917I
b = 0.042992 + 0.667229I
4.67294 − 0.09706I 13.36415 − 0.53030I
u = 0.301362 + 0.621548I
a = −0.934672 − 0.857687I
b = −0.837815 + 0.659025I
0.29568 + 2.24337I 4.30616 − 2.82871I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.301362 − 0.621548I
a = −0.934672 + 0.857687I
b = −0.837815 − 0.659025I
0.29568 − 2.24337I 4.30616 + 2.82871I
u = −1.31305
a = 2.73258
b = −0.192967
6.69568 0
u = −0.492722 + 0.447883I
a = −0.018732 − 0.417872I
b = −0.662214 + 0.833663I
0.86536 + 2.71020I 7.15754 − 3.04555I
u = −0.492722 − 0.447883I
a = −0.018732 + 0.417872I
b = −0.662214 − 0.833663I
0.86536 − 2.71020I 7.15754 + 3.04555I
u = 0.345537 + 0.561912I
a = 3.53045 + 1.22785I
b = −0.07014 − 3.28534I
2.29780 + 1.66494I −17.5253 + 6.6293I
u = 0.345537 − 0.561912I
a = 3.53045 − 1.22785I
b = −0.07014 + 3.28534I
2.29780 − 1.66494I −17.5253 − 6.6293I
u = −0.051518 + 0.628248I
a = 1.04887 − 0.98256I
b = 0.564358 − 0.403906I
−3.01841 + 1.08766I −2.25646 − 1.14539I
u = −0.051518 − 0.628248I
a = 1.04887 + 0.98256I
b = 0.564358 + 0.403906I
−3.01841 − 1.08766I −2.25646 + 1.14539I
u = −1.41925 + 0.19367I
a = 1.52410 − 1.19809I
b = −0.66039 + 1.31268I
6.55173 − 3.43032I 0
u = −1.41925 − 0.19367I
a = 1.52410 + 1.19809I
b = −0.66039 − 1.31268I
6.55173 + 3.43032I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358057 + 0.432304I
a = −0.856983 + 0.012393I
b = 0.337227 + 0.939608I
0.927115 + 0.969009I 7.33388 − 5.10467I
u = 0.358057 − 0.432304I
a = −0.856983 − 0.012393I
b = 0.337227 − 0.939608I
0.927115 − 0.969009I 7.33388 + 5.10467I
u = −1.42039 + 0.24290I
a = −0.13396 − 1.83660I
b = 1.027690 + 0.777107I
5.81492 − 5.42387I 0
u = −1.42039 − 0.24290I
a = −0.13396 + 1.83660I
b = 1.027690 − 0.777107I
5.81492 + 5.42387I 0
u = −1.43036 + 0.22015I
a = −2.83053 + 4.42260I
b = −0.01146 − 3.25716I
7.99318 − 4.57389I 0
u = −1.43036 − 0.22015I
a = −2.83053 − 4.42260I
b = −0.01146 + 3.25716I
7.99318 + 4.57389I 0
u = 1.43947 + 0.17545I
a = −0.61970 − 1.47828I
b = 0.652456 + 0.963631I
6.93022 − 0.40426I 0
u = 1.43947 − 0.17545I
a = −0.61970 + 1.47828I
b = 0.652456 − 0.963631I
6.93022 + 0.40426I 0
u = 1.43628 + 0.25338I
a = −0.74240 − 2.08871I
b = −0.828861 + 0.874237I
5.79461 + 9.79626I 0
u = 1.43628 − 0.25338I
a = −0.74240 + 2.08871I
b = −0.828861 − 0.874237I
5.79461 − 9.79626I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44643 + 0.20811I
a = 1.52474 + 1.92775I
b = 0.076180 − 0.648466I
10.64080 + 2.70423I 0
u = 1.44643 − 0.20811I
a = 1.52474 − 1.92775I
b = 0.076180 + 0.648466I
10.64080 − 2.70423I 0
u = 1.44458 + 0.23052I
a = 0.00727 + 2.22521I
b = −0.008684 − 0.861520I
10.31070 + 6.89598I 0
u = 1.44458 − 0.23052I
a = 0.00727 − 2.22521I
b = −0.008684 + 0.861520I
10.31070 − 6.89598I 0
u = 1.45377 + 0.27698I
a = 0.60639 + 2.76642I
b = 0.97235 − 1.38618I
10.6167 + 15.9423I 0
u = 1.45377 − 0.27698I
a = 0.60639 − 2.76642I
b = 0.97235 + 1.38618I
10.6167 − 15.9423I 0
u = −1.46439 + 0.28501I
a = −0.788256 + 1.075800I
b = −0.145502 − 0.724051I
9.73502 − 7.58811I 0
u = −1.46439 − 0.28501I
a = −0.788256 − 1.075800I
b = −0.145502 + 0.724051I
9.73502 + 7.58811I 0
u = 1.49064 + 0.14963I
a = 1.32087 + 1.93888I
b = −0.77806 − 1.33217I
12.49300 − 5.62787I 0
u = 1.49064 − 0.14963I
a = 1.32087 − 1.93888I
b = −0.77806 + 1.33217I
12.49300 + 5.62787I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50530 + 0.13452I
a = 0.26995 + 1.42007I
b = −0.180993 − 0.917016I
11.93110 − 3.09362I 0
u = −1.50530 − 0.13452I
a = 0.26995 − 1.42007I
b = −0.180993 + 0.917016I
11.93110 + 3.09362I 0
u = 0.113883 + 0.422940I
a = −1.56859 − 0.39304I
b = −0.431618 + 1.169140I
0.92611 + 1.21767I 5.78394 − 3.84378I
u = 0.113883 − 0.422940I
a = −1.56859 + 0.39304I
b = −0.431618 − 1.169140I
0.92611 − 1.21767I 5.78394 + 3.84378I
u = 0.242610
a = −5.62882
b = 1.13132
2.24319 1.34300
11
II. I
u
2
= hb − 1, a + 1, u − 1i
(i) Arc colorings
a
6
=
0
1
a
9
=
1
0
a
10
=
1
−1
a
7
=
1
0
a
11
=
0
−1
a
1
=
1
−1
a
4
=
−1
1
a
3
=
−1
1
a
5
=
0
1
a
8
=
2
−1
a
2
=
−1
0
a
2
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
9
, c
10
c
11
u − 1
c
2
, c
6
u + 1
c
3
, c
5
u
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y −1
c
3
, c
5
y
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 1.00000
3.28987 12.0000
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
65
− 4u
64
+ ··· − u + 1)
c
2
(u + 1)(u
65
+ 2u
64
+ ··· − 3u + 1)
c
3
u(u
65
− 11u
64
+ ··· + 6u − 2)
c
4
(u − 1)(u
65
+ 2u
64
+ ··· − 3u + 1)
c
5
u(u
65
+ 3u
64
+ ··· − 288u + 288)
c
6
(u + 1)(u
65
− 2u
64
+ ··· − 5u + 1)
c
7
(u − 1)(u
65
+ 18u
63
+ ··· − 5599u + 599)
c
8
(u − 1)(u
65
− 2u
64
+ ··· + 875u + 199)
c
9
, c
10
(u − 1)(u
65
− 2u
64
+ ··· − 5u + 1)
c
11
(u − 1)(u
65
− 12u
64
+ ··· + 15361u − 937)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
65
− 12y
64
+ ··· + 5y −1)
c
2
, c
4
(y −1)(y
65
− 48y
64
+ ··· + 65y −1)
c
3
y(y
65
+ 9y
64
+ ··· − 32y −4)
c
5
y(y
65
− 15y
64
+ ··· + 2689344y −82944)
c
6
, c
9
, c
10
(y −1)(y
65
− 60y
64
+ ··· + 5y −1)
c
7
(y −1)(y
65
+ 36y
64
+ ··· + 2.54906 × 10
7
y −358801)
c
8
(y −1)(y
65
+ 76y
64
+ ··· + 46837y −39601)
c
11
(y −1)(y
65
+ 40y
64
+ ··· + 6.43319 × 10
7
y −877969)
17
