11a
72
(K11a
72
)
A knot diagram
1
Linearized knot diagam
5 1 10 9 2 3 4 11 7 8 6
Solving Sequence
2,6
5 1 3
7,9
4 11 8 10
c
5
c
1
c
2
c
6
c
4
c
11
c
8
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.34803 × 10
24
u
76
− 2.11084 × 10
24
u
75
+ ··· + 9.10663 × 10
24
b + 2.06273 × 10
24
,
2.74420 × 10
25
u
76
− 4.20119 × 10
25
u
75
+ ··· + 9.10663 × 10
24
a + 1.31742 × 10
25
, u
77
− 2u
76
+ ··· − u − 1i
I
u
2
= hb + 1, a − 2, u + 1i
* 2 irreducible components of dim
C
= 0, with total 78 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
= h9.35 × 10
24
u
76
− 2.11 × 10
24
u
75
+ · · · + 9.11 × 10
24
b + 2.06 × 10
24
, 2.74 ×
10
25
u
76
−4.20×10
25
u
75
+· · ·+9.11×10
24
a+1.32×10
25
, u
77
−2u
76
+· · ·−u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
7
=
u
8
− u
6
+ u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
9
=
−3.01341u
76
+ 4.61333u
75
+ ··· − 6.55819u − 1.44666
−1.02651u
76
+ 0.231791u
75
+ ··· + 2.18024u − 0.226508
a
4
=
−4.68917u
76
+ 6.28660u
75
+ ··· − 16.1580u − 3.80329
0.0425498u
76
− 0.839980u
75
+ ··· + 2.36327u + 0.839980
a
11
=
u
3
−u
3
+ u
a
8
=
−2.84647u
76
+ 4.44668u
75
+ ··· − 6.17515u − 1.26334
−0.993730u
76
+ 0.182343u
75
+ ··· + 1.42940u − 0.193730
a
10
=
−2.78104u
76
+ 4.37995u
75
+ ··· − 7.68244u − 1.12997
−1.05786u
76
+ 0.320078u
75
+ ··· + 2.03322u − 0.257856
a
10
=
−2.78104u
76
+ 4.37995u
75
+ ··· − 7.68244u − 1.12997
−1.05786u
76
+ 0.320078u
75
+ ··· + 2.03322u − 0.257856
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
98621680931509431399030560
4553313053666260493091767
u
76
+
105996530335693508948090410
4553313053666260493091767
u
75
+
··· −
186890667880794717580337970
4553313053666260493091767
u −
85143874290832413279068140
4553313053666260493091767
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
77
+ 2u
76
+ ··· − u + 1
c
2
u
77
+ 36u
76
+ ··· − u + 1
c
3
u
77
− 4u
76
+ ··· − 1931u + 431
c
4
u
77
− 2u
76
+ ··· + 22949u + 1393
c
6
u
77
− 22u
75
+ ··· − 44155u + 8353
c
7
u
77
+ 4u
76
+ ··· + u + 1
c
8
, c
10
u
77
+ 2u
76
+ ··· − u + 1
c
9
u
77
− 13u
76
+ ··· + 2u + 2
c
11
u
77
+ 3u
76
+ ··· + 523u
2
+ 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
77
− 36y
76
+ ··· − y −1
c
2
y
77
+ 12y
76
+ ··· − 69y −1
c
3
y
77
− 92y
76
+ ··· + 8518895y −185761
c
4
y
77
− 48y
76
+ ··· + 99292559y −1940449
c
6
y
77
− 44y
76
+ ··· + 683599815y −69772609
c
7
y
77
+ 12y
76
+ ··· − y −1
c
8
, c
10
y
77
− 56y
76
+ ··· − 21y −1
c
9
y
77
+ 9y
76
+ ··· − 40y −4
c
11
y
77
+ 9y
76
+ ··· − 33472y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.633423 + 0.760124I
a = −0.611333 − 0.236752I
b = −0.164228 + 0.298926I
7.04838 + 0.24930I 0
u = −0.633423 − 0.760124I
a = −0.611333 + 0.236752I
b = −0.164228 − 0.298926I
7.04838 − 0.24930I 0
u = −0.976497 + 0.154539I
a = 1.94444 + 0.74223I
b = −1.75615 + 0.52296I
1.58545 − 1.56270I 0
u = −0.976497 − 0.154539I
a = 1.94444 − 0.74223I
b = −1.75615 − 0.52296I
1.58545 + 1.56270I 0
u = 0.980965 + 0.263279I
a = −5.16701 + 1.31783I
b = 2.20127 + 1.66225I
−0.098989 − 0.629989I 0
u = 0.980965 − 0.263279I
a = −5.16701 − 1.31783I
b = 2.20127 − 1.66225I
−0.098989 + 0.629989I 0
u = 0.602244 + 0.740774I
a = 0.487640 − 0.874753I
b = 0.138617 + 0.833361I
7.76295 − 8.98786I 5.03981 + 6.60179I
u = 0.602244 − 0.740774I
a = 0.487640 + 0.874753I
b = 0.138617 − 0.833361I
7.76295 + 8.98786I 5.03981 − 6.60179I
u = 1.001230 + 0.352341I
a = 2.57836 + 0.25405I
b = −0.34696 − 2.11296I
−0.63003 − 1.40723I 0
u = 1.001230 − 0.352341I
a = 2.57836 − 0.25405I
b = −0.34696 + 2.11296I
−0.63003 + 1.40723I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986878 + 0.427459I
a = −1.09537 + 1.40681I
b = −0.15416 − 2.04505I
0.14403 + 4.20779I 0
u = −0.986878 − 0.427459I
a = −1.09537 − 1.40681I
b = −0.15416 + 2.04505I
0.14403 − 4.20779I 0
u = −0.857333 + 0.345143I
a = 1.55446 + 0.57642I
b = −1.251310 − 0.537113I
2.25018 + 1.60092I 4.93810 − 3.13192I
u = −0.857333 − 0.345143I
a = 1.55446 − 0.57642I
b = −1.251310 + 0.537113I
2.25018 − 1.60092I 4.93810 + 3.13192I
u = −0.390473 + 0.833868I
a = −0.426341 + 0.195318I
b = −0.962283 − 0.945326I
5.65147 − 3.46025I 8.06773 + 5.13180I
u = −0.390473 − 0.833868I
a = −0.426341 − 0.195318I
b = −0.962283 + 0.945326I
5.65147 + 3.46025I 8.06773 − 5.13180I
u = 1.057940 + 0.262256I
a = 0.163573 + 0.640731I
b = 0.273950 − 0.088341I
−2.24047 − 0.49207I 0
u = 1.057940 − 0.262256I
a = 0.163573 − 0.640731I
b = 0.273950 + 0.088341I
−2.24047 + 0.49207I 0
u = −1.081720 + 0.191062I
a = 1.184630 + 0.277945I
b = −0.759225 + 0.986911I
−2.82137 − 3.73074I 0
u = −1.081720 − 0.191062I
a = 1.184630 − 0.277945I
b = −0.759225 − 0.986911I
−2.82137 + 3.73074I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387547 + 0.806255I
a = 0.563280 + 0.658078I
b = 1.72067 − 1.45490I
6.58364 + 11.91200I 3.84588 − 6.37900I
u = 0.387547 − 0.806255I
a = 0.563280 − 0.658078I
b = 1.72067 + 1.45490I
6.58364 − 11.91200I 3.84588 + 6.37900I
u = 0.541842 + 0.673198I
a = 0.09318 + 1.41546I
b = 0.631068 − 0.608537I
2.59107 − 3.68436I 3.37129 + 6.54731I
u = 0.541842 − 0.673198I
a = 0.09318 − 1.41546I
b = 0.631068 + 0.608537I
2.59107 + 3.68436I 3.37129 − 6.54731I
u = 0.483139 + 0.708206I
a = −0.886828 + 0.978020I
b = −0.0147570 − 0.0914207I
6.41209 − 0.81622I 9.40053 + 2.76203I
u = 0.483139 − 0.708206I
a = −0.886828 − 0.978020I
b = −0.0147570 + 0.0914207I
6.41209 + 0.81622I 9.40053 − 2.76203I
u = 0.440637 + 0.729674I
a = −1.102280 − 0.664605I
b = −1.33147 + 1.25437I
6.18768 + 3.22828I 8.64527 − 4.04810I
u = 0.440637 − 0.729674I
a = −1.102280 + 0.664605I
b = −1.33147 − 1.25437I
6.18768 − 3.22828I 8.64527 + 4.04810I
u = 0.392152 + 0.748358I
a = −0.246077 − 1.227730I
b = −1.38993 + 0.56100I
1.81609 + 5.99286I 1.94012 − 6.31838I
u = 0.392152 − 0.748358I
a = −0.246077 + 1.227730I
b = −1.38993 − 0.56100I
1.81609 − 5.99286I 1.94012 + 6.31838I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.150190 + 0.154691I
a = −1.66372 − 1.56905I
b = 1.70843 + 0.15475I
1.48123 − 9.38293I 0
u = −1.150190 − 0.154691I
a = −1.66372 + 1.56905I
b = 1.70843 − 0.15475I
1.48123 + 9.38293I 0
u = −1.097430 + 0.397998I
a = −2.20501 − 0.41756I
b = 1.71177 − 0.97354I
−4.75169 + 4.63385I 0
u = −1.097430 − 0.397998I
a = −2.20501 + 0.41756I
b = 1.71177 + 0.97354I
−4.75169 − 4.63385I 0
u = 1.019250 + 0.569973I
a = −0.968680 + 0.492416I
b = 1.56760 + 0.09910I
1.17732 − 1.14110I 0
u = 1.019250 − 0.569973I
a = −0.968680 − 0.492416I
b = 1.56760 − 0.09910I
1.17732 + 1.14110I 0
u = −0.966449 + 0.658776I
a = −0.544919 + 0.354770I
b = −0.060655 + 0.135899I
6.05588 + 5.10252I 0
u = −0.966449 − 0.658776I
a = −0.544919 − 0.354770I
b = −0.060655 − 0.135899I
6.05588 − 5.10252I 0
u = 0.988060 + 0.637942I
a = 1.037290 + 0.762523I
b = −0.344734 − 0.328832I
6.61756 + 3.75380I 0
u = 0.988060 − 0.637942I
a = 1.037290 − 0.762523I
b = −0.344734 + 0.328832I
6.61756 − 3.75380I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.441519 + 0.688569I
a = −0.640475 − 0.410726I
b = 3.57366 − 0.54646I
3.93132 − 1.04131I −17.5631 − 6.0870I
u = −0.441519 − 0.688569I
a = −0.640475 + 0.410726I
b = 3.57366 + 0.54646I
3.93132 + 1.04131I −17.5631 + 6.0870I
u = −1.048020 + 0.551434I
a = 1.50338 + 1.61813I
b = −2.00955 − 0.35919I
0.78969 + 4.81154I 0
u = −1.048020 − 0.551434I
a = 1.50338 − 1.61813I
b = −2.00955 + 0.35919I
0.78969 − 4.81154I 0
u = 1.098860 + 0.457057I
a = −1.34783 + 1.20877I
b = 1.55693 + 0.45145I
−4.35858 − 2.73970I 0
u = 1.098860 − 0.457057I
a = −1.34783 − 1.20877I
b = 1.55693 − 0.45145I
−4.35858 + 2.73970I 0
u = −0.490723 + 0.637155I
a = 0.495475 + 0.840231I
b = −1.195810 − 0.341182I
2.43954 − 0.14027I 3.53078 + 1.38098I
u = −0.490723 − 0.637155I
a = 0.495475 − 0.840231I
b = −1.195810 + 0.341182I
2.43954 + 0.14027I 3.53078 − 1.38098I
u = −0.385008 + 0.703290I
a = 0.458055 − 0.514268I
b = 0.110246 + 0.984199I
1.91834 − 1.76256I 1.60352 − 0.19237I
u = −0.385008 − 0.703290I
a = 0.458055 + 0.514268I
b = 0.110246 − 0.984199I
1.91834 + 1.76256I 1.60352 + 0.19237I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799179
a = 0.890054
b = 0.0869293
−1.30832 −7.95820
u = 1.056810 + 0.584937I
a = −0.203663 − 0.214512I
b = 0.316267 − 0.635080I
4.71591 − 4.15265I 0
u = 1.056810 − 0.584937I
a = −0.203663 + 0.214512I
b = 0.316267 + 0.635080I
4.71591 + 4.15265I 0
u = 1.204850 + 0.137903I
a = 0.838912 − 0.786254I
b = −1.002720 + 0.299954I
0.272573 + 0.769014I 0
u = 1.204850 − 0.137903I
a = 0.838912 + 0.786254I
b = −1.002720 − 0.299954I
0.272573 − 0.769014I 0
u = −1.072810 + 0.570326I
a = −2.14473 − 4.53419I
b = 3.85106 + 0.99547I
2.07576 + 5.91007I 0
u = −1.072810 − 0.570326I
a = −2.14473 + 4.53419I
b = 3.85106 − 0.99547I
2.07576 − 5.91007I 0
u = 1.080330 + 0.586452I
a = 2.30172 − 0.66834I
b = −2.15681 − 1.66870I
4.30053 − 8.25445I 0
u = 1.080330 − 0.586452I
a = 2.30172 + 0.66834I
b = −2.15681 + 1.66870I
4.30053 + 8.25445I 0
u = 1.169410 + 0.384995I
a = 0.36891 − 1.39572I
b = −1.18116 + 0.86341I
−2.52184 + 1.07600I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.169410 − 0.384995I
a = 0.36891 + 1.39572I
b = −1.18116 − 0.86341I
−2.52184 − 1.07600I 0
u = −1.096480 + 0.564671I
a = −1.317570 + 0.511258I
b = 0.728265 − 1.085450I
−0.15987 + 6.64038I 0
u = −1.096480 − 0.564671I
a = −1.317570 − 0.511258I
b = 0.728265 + 1.085450I
−0.15987 − 6.64038I 0
u = −1.156250 + 0.450661I
a = 1.72500 − 0.52320I
b = −0.61479 + 1.66456I
−2.08535 + 9.31159I 0
u = −1.156250 − 0.450661I
a = 1.72500 + 0.52320I
b = −0.61479 − 1.66456I
−2.08535 − 9.31159I 0
u = 1.103350 + 0.581743I
a = 1.78047 − 1.06989I
b = −2.32561 − 0.37152I
−0.27685 − 11.04150I 0
u = 1.103350 − 0.581743I
a = 1.78047 + 1.06989I
b = −2.32561 + 0.37152I
−0.27685 + 11.04150I 0
u = −0.055639 + 0.747611I
a = −0.219020 − 0.528181I
b = −0.662916 − 1.064330I
1.12267 − 5.01345I 1.50910 + 6.72977I
u = −0.055639 − 0.747611I
a = −0.219020 + 0.528181I
b = −0.662916 + 1.064330I
1.12267 + 5.01345I 1.50910 − 6.72977I
u = 1.122420 + 0.599973I
a = −2.78774 + 0.73339I
b = 2.40366 + 1.65651I
4.3964 − 17.1730I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122420 − 0.599973I
a = −2.78774 − 0.73339I
b = 2.40366 − 1.65651I
4.3964 + 17.1730I 0
u = −1.128570 + 0.611450I
a = 1.63288 + 0.43606I
b = −1.35747 + 1.10949I
3.44557 + 8.83292I 0
u = −1.128570 − 0.611450I
a = 1.63288 − 0.43606I
b = −1.35747 − 1.10949I
3.44557 − 8.83292I 0
u = 0.075487 + 0.572572I
a = 0.631910 − 0.139374I
b = 1.047670 + 0.274040I
−1.67112 − 1.17907I −4.23336 + 1.76718I
u = 0.075487 − 0.572572I
a = 0.631910 + 0.139374I
b = 1.047670 − 0.274040I
−1.67112 + 1.17907I −4.23336 − 1.76718I
u = −0.190674 + 0.306614I
a = 2.29001 + 1.56288I
b = −0.541888 + 1.030790I
1.87411 − 0.91268I 3.90518 + 0.39794I
u = −0.190674 − 0.306614I
a = 2.29001 − 1.56288I
b = −0.541888 − 1.030790I
1.87411 + 0.91268I 3.90518 − 0.39794I
12
II. I
u
2
= hb + 1, a − 2, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
5
=
1
−1
a
1
=
−1
0
a
3
=
1
−1
a
7
=
2
−1
a
9
=
2
−1
a
4
=
−1
0
a
11
=
−1
0
a
8
=
3
−1
a
10
=
2
−1
a
10
=
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
10
u − 1
c
2
, c
5
, c
6
c
7
, c
8
u + 1
c
9
, c
11
u
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
y −1
c
9
, c
11
y
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.00000
b = −1.00000
0 0
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
77
+ 2u
76
+ ··· − u + 1)
c
2
(u + 1)(u
77
+ 36u
76
+ ··· − u + 1)
c
3
(u − 1)(u
77
− 4u
76
+ ··· − 1931u + 431)
c
4
(u − 1)(u
77
− 2u
76
+ ··· + 22949u + 1393)
c
5
(u + 1)(u
77
+ 2u
76
+ ··· − u + 1)
c
6
(u + 1)(u
77
− 22u
75
+ ··· − 44155u + 8353)
c
7
(u + 1)(u
77
+ 4u
76
+ ··· + u + 1)
c
8
(u + 1)(u
77
+ 2u
76
+ ··· − u + 1)
c
9
u(u
77
− 13u
76
+ ··· + 2u + 2)
c
10
(u − 1)(u
77
+ 2u
76
+ ··· − u + 1)
c
11
u(u
77
+ 3u
76
+ ··· + 523u
2
+ 32)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)(y
77
− 36y
76
+ ··· − y −1)
c
2
(y −1)(y
77
+ 12y
76
+ ··· − 69y −1)
c
3
(y −1)(y
77
− 92y
76
+ ··· + 8518895y −185761)
c
4
(y −1)(y
77
− 48y
76
+ ··· + 9.92926 × 10
7
y −1940449)
c
6
(y −1)(y
77
− 44y
76
+ ··· + 6.83600 × 10
8
y −6.97726 × 10
7
)
c
7
(y −1)(y
77
+ 12y
76
+ ··· − y −1)
c
8
, c
10
(y −1)(y
77
− 56y
76
+ ··· − 21y −1)
c
9
y(y
77
+ 9y
76
+ ··· − 40y −4)
c
11
y(y
77
+ 9y
76
+ ··· − 33472y −1024)
18
