11a
25
(K11a
25
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 8 3 10 11 5 6 9
Solving Sequence
1,4
2
5,9
10 11 8 6 7 3
c
1
c
4
c
9
c
11
c
8
c
5
c
7
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.14096 × 10
69
u
81
− 5.58994 × 10
69
u
80
+ ··· + 1.56549 × 10
69
b + 2.41728 × 10
69
,
− 1.59096 × 10
68
u
81
− 1.08869 × 10
69
u
80
+ ··· + 9.78432 × 10
67
a + 1.01297 × 10
69
, u
82
+ 6u
81
+ ··· − 8u − 1i
I
u
2
= hb
5
− b
4
− 2b
3
+ b
2
+ b + 1, a − 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 87 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−1.14×10
69
u
81
−5.59×10
69
u
80
+· · ·+1.57×10
69
b+2.42×10
69
, −1.59×
10
68
u
81
−1.09×10
69
u
80
+· · ·+9.78×10
67
a+1.01×10
69
, u
82
+6u
81
+· · ·−8u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
1.62603u
81
+ 11.1269u
80
+ ··· − 32.4970u − 10.3530
0.728817u
81
+ 3.57073u
80
+ ··· − 2.46718u − 1.54411
a
10
=
−2.60869u
81
− 11.2390u
80
+ ··· − 2.43637u − 5.89186
5.06035u
81
+ 21.3826u
80
+ ··· − 12.4229u − 2.96275
a
11
=
1.50444u
81
+ 10.5800u
80
+ ··· − 34.0990u − 11.2965
1.80874u
81
+ 9.46187u
80
+ ··· − 11.7179u − 3.24701
a
8
=
−0.393237u
81
− 2.05370u
80
+ ··· + 5.46852u + 3.40029
−2.58681u
81
− 15.0269u
80
+ ··· + 30.1392u + 5.36022
a
6
=
3.69251u
81
+ 18.0231u
80
+ ··· − 19.9154u − 0.624870
−2.07099u
81
− 5.98340u
80
+ ··· − 5.40373u − 0.423689
a
7
=
−2.73425u
81
− 10.6085u
80
+ ··· − 4.73671u − 3.63574
−4.68430u
81
− 29.2185u
80
+ ··· + 55.5656u + 7.41855
a
3
=
−u
2
+ 1
u
2
a
3
=
−u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11.3752u
81
+ 53.0887u
80
+ ··· − 66.0984u − 14.2656
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
82
− 6u
81
+ ··· + 8u − 1
c
2
u
82
+ 42u
81
+ ··· + 32u + 1
c
3
, c
6
u
82
− u
81
+ ··· + 160u + 32
c
5
u
82
− 6u
81
+ ··· + 2u − 1
c
7
u
82
+ 14u
81
+ ··· + 2u + 1
c
8
, c
11
u
82
− 2u
81
+ ··· + 14u + 1
c
9
u
82
+ 2u
81
+ ··· − 20520u − 1647
c
10
u
82
− 2u
81
+ ··· − 2362u − 484
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
82
− 42y
81
+ ··· − 32y + 1
c
2
y
82
+ 2y
81
+ ··· − 484y + 1
c
3
, c
6
y
82
− 33y
81
+ ··· − 19968y + 1024
c
5
y
82
− 14y
81
+ ··· − 6y + 1
c
7
y
82
+ 6y
81
+ ··· + 14y + 1
c
8
, c
11
y
82
− 58y
81
+ ··· + 14y + 1
c
9
y
82
+ 50y
81
+ ··· − 261288342y + 2712609
c
10
y
82
+ 90y
81
+ ··· + 10862436y + 234256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.573215 + 0.805489I
a = −0.878259 − 0.430787I
b = 1.087480 + 0.153969I
−2.85407 − 3.43010I 0
u = 0.573215 − 0.805489I
a = −0.878259 + 0.430787I
b = 1.087480 − 0.153969I
−2.85407 + 3.43010I 0
u = −0.196895 + 0.993276I
a = −0.292028 − 0.361855I
b = 1.062450 + 0.212626I
0.01560 − 3.91593I 0
u = −0.196895 − 0.993276I
a = −0.292028 + 0.361855I
b = 1.062450 − 0.212626I
0.01560 + 3.91593I 0
u = −0.268436 + 0.946194I
a = −0.613930 − 1.004810I
b = 1.36047 + 0.56106I
−1.22744 − 12.16920I 0
u = −0.268436 − 0.946194I
a = −0.613930 + 1.004810I
b = 1.36047 − 0.56106I
−1.22744 + 12.16920I 0
u = −0.725256 + 0.718006I
a = −0.294348 − 0.999996I
b = 0.372669 + 0.922938I
5.22827 + 3.35824I 0
u = −0.725256 − 0.718006I
a = −0.294348 + 0.999996I
b = 0.372669 − 0.922938I
5.22827 − 3.35824I 0
u = 0.974615 + 0.396279I
a = 0.549380 + 0.539251I
b = −0.054094 − 0.154978I
−1.87549 − 1.38403I 0
u = 0.974615 − 0.396279I
a = 0.549380 − 0.539251I
b = −0.054094 + 0.154978I
−1.87549 + 1.38403I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.030350 + 0.222684I
a = 0.939397 + 0.259886I
b = 1.42187 − 0.12543I
−7.77694 + 4.95365I 0
u = −1.030350 − 0.222684I
a = 0.939397 − 0.259886I
b = 1.42187 + 0.12543I
−7.77694 − 4.95365I 0
u = 1.06725
a = 2.54402
b = −1.09577
−3.80714 0
u = −1.056730 + 0.265244I
a = 0.834912 + 0.256843I
b = 1.46239 + 0.32296I
−8.00907 − 3.75643I 0
u = −1.056730 − 0.265244I
a = 0.834912 − 0.256843I
b = 1.46239 − 0.32296I
−8.00907 + 3.75643I 0
u = 1.045010 + 0.319225I
a = −4.54540 + 3.18845I
b = −1.043930 − 0.027951I
−3.74856 − 1.03244I 0
u = 1.045010 − 0.319225I
a = −4.54540 − 3.18845I
b = −1.043930 + 0.027951I
−3.74856 + 1.03244I 0
u = −0.870879 + 0.677783I
a = 0.74524 + 1.23544I
b = 0.528336 − 0.760241I
4.80113 + 1.92406I 0
u = −0.870879 − 0.677783I
a = 0.74524 − 1.23544I
b = 0.528336 + 0.760241I
4.80113 − 1.92406I 0
u = −0.319570 + 0.836317I
a = 0.19390 + 1.45588I
b = 0.041190 − 1.176220I
2.93914 − 6.11947I 0. + 6.25574I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.319570 − 0.836317I
a = 0.19390 − 1.45588I
b = 0.041190 + 1.176220I
2.93914 + 6.11947I 0. − 6.25574I
u = −0.415240 + 0.792411I
a = 0.436581 + 0.572912I
b = 0.116621 − 0.310795I
2.44851 − 1.57419I 0
u = −0.415240 − 0.792411I
a = 0.436581 − 0.572912I
b = 0.116621 + 0.310795I
2.44851 + 1.57419I 0
u = −1.023160 + 0.461176I
a = 0.803227 + 0.138120I
b = −0.516137 − 1.108300I
−1.65757 + 0.93442I 0
u = −1.023160 − 0.461176I
a = 0.803227 − 0.138120I
b = −0.516137 + 1.108300I
−1.65757 − 0.93442I 0
u = 1.105680 + 0.199763I
a = 0.993090 − 0.249534I
b = −0.182502 − 0.012960I
−2.36954 − 0.63816I 0
u = 1.105680 − 0.199763I
a = 0.993090 + 0.249534I
b = −0.182502 + 0.012960I
−2.36954 + 0.63816I 0
u = −0.728926 + 0.864243I
a = −0.678740 − 0.135292I
b = 0.948714 + 0.407094I
3.48456 − 2.48996I 0
u = −0.728926 − 0.864243I
a = −0.678740 + 0.135292I
b = 0.948714 − 0.407094I
3.48456 + 2.48996I 0
u = 1.044580 + 0.476716I
a = −1.16454 + 1.08799I
b = −0.055196 − 1.089590I
−1.46560 − 5.42569I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.044580 − 0.476716I
a = −1.16454 − 1.08799I
b = −0.055196 + 1.089590I
−1.46560 + 5.42569I 0
u = −1.035010 + 0.523379I
a = 0.703329 + 0.786738I
b = −0.586949 − 0.306956I
−0.96667 + 4.63901I 0
u = −1.035010 − 0.523379I
a = 0.703329 − 0.786738I
b = −0.586949 + 0.306956I
−0.96667 − 4.63901I 0
u = 0.822458 + 0.162075I
a = 4.35993 + 0.23976I
b = −0.924124 − 0.155896I
−2.85067 − 0.96287I −12.24182 − 4.62200I
u = 0.822458 − 0.162075I
a = 4.35993 − 0.23976I
b = −0.924124 + 0.155896I
−2.85067 + 0.96287I −12.24182 + 4.62200I
u = 1.099040 + 0.390529I
a = −0.93956 + 2.37638I
b = −1.39410 − 0.58186I
−5.73183 − 3.04738I 0
u = 1.099040 − 0.390529I
a = −0.93956 − 2.37638I
b = −1.39410 + 0.58186I
−5.73183 + 3.04738I 0
u = 0.373251 + 0.739288I
a = −1.15126 + 1.02585I
b = 1.294620 − 0.433035I
−3.71598 + 6.06156I −4.81312 − 3.61533I
u = 0.373251 − 0.739288I
a = −1.15126 − 1.02585I
b = 1.294620 + 0.433035I
−3.71598 − 6.06156I −4.81312 + 3.61533I
u = 1.146840 + 0.310629I
a = −0.262041 + 1.031410I
b = −1.43309 + 0.47733I
−5.91812 + 0.62603I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.146840 − 0.310629I
a = −0.262041 − 1.031410I
b = −1.43309 − 0.47733I
−5.91812 − 0.62603I 0
u = −0.898916 + 0.791063I
a = −0.192333 + 1.289610I
b = 1.085630 − 0.509853I
2.97750 + 8.50086I 0
u = −0.898916 − 0.791063I
a = −0.192333 − 1.289610I
b = 1.085630 + 0.509853I
2.97750 − 8.50086I 0
u = −1.098860 + 0.495683I
a = −0.251893 − 0.866876I
b = −1.67621 − 0.41894I
−5.00012 + 4.29669I 0
u = −1.098860 − 0.495683I
a = −0.251893 + 0.866876I
b = −1.67621 + 0.41894I
−5.00012 − 4.29669I 0
u = −1.095490 + 0.542489I
a = −2.14444 − 2.01164I
b = −1.121470 + 0.103386I
−2.13971 + 6.01246I 0
u = −1.095490 − 0.542489I
a = −2.14444 + 2.01164I
b = −1.121470 − 0.103386I
−2.13971 − 6.01246I 0
u = −0.505284 + 0.582244I
a = 0.71509 − 2.39987I
b = −0.783636 + 0.165518I
0.603497 − 0.216471I −2.65199 + 5.07001I
u = −0.505284 − 0.582244I
a = 0.71509 + 2.39987I
b = −0.783636 − 0.165518I
0.603497 + 0.216471I −2.65199 − 5.07001I
u = −0.616890 + 0.459273I
a = 0.003549 − 1.194610I
b = −0.817286 + 0.838746I
−0.34685 + 2.85468I −2.55427 − 7.34325I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616890 − 0.459273I
a = 0.003549 + 1.194610I
b = −0.817286 − 0.838746I
−0.34685 − 2.85468I −2.55427 + 7.34325I
u = 1.218450 + 0.212469I
a = 0.801155 + 0.005540I
b = −0.111866 + 0.982814I
−2.09067 + 2.95787I 0
u = 1.218450 − 0.212469I
a = 0.801155 − 0.005540I
b = −0.111866 − 0.982814I
−2.09067 − 2.95787I 0
u = −0.256433 + 0.716128I
a = 0.900304 + 0.838602I
b = −1.31960 − 0.71550I
−1.85423 − 3.78257I −5.86247 + 6.02702I
u = −0.256433 − 0.716128I
a = 0.900304 − 0.838602I
b = −1.31960 + 0.71550I
−1.85423 + 3.78257I −5.86247 − 6.02702I
u = −0.359004 + 0.663764I
a = −1.33923 + 1.95181I
b = −1.037470 − 0.112404I
−0.006489 − 1.319230I 7.9750 − 14.9866I
u = −0.359004 − 0.663764I
a = −1.33923 − 1.95181I
b = −1.037470 + 0.112404I
−0.006489 + 1.319230I 7.9750 + 14.9866I
u = 1.110380 + 0.566495I
a = 0.44194 − 2.14286I
b = 1.36225 + 0.50910I
−5.89382 − 11.02700I 0
u = 1.110380 − 0.566495I
a = 0.44194 + 2.14286I
b = 1.36225 − 0.50910I
−5.89382 + 11.02700I 0
u = −1.133180 + 0.536226I
a = −0.86085 − 1.76202I
b = −1.46595 + 0.77759I
−4.37377 + 8.54127I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.133180 − 0.536226I
a = −0.86085 + 1.76202I
b = −1.46595 − 0.77759I
−4.37377 − 8.54127I 0
u = −1.114120 + 0.596036I
a = 0.049404 − 0.567613I
b = −0.017201 + 0.444698I
0.34729 + 6.79546I 0
u = −1.114120 − 0.596036I
a = 0.049404 + 0.567613I
b = −0.017201 − 0.444698I
0.34729 − 6.79546I 0
u = −1.153020 + 0.586404I
a = −1.007640 − 0.736012I
b = −0.025777 + 1.279070I
0.45408 + 11.38860I 0
u = −1.153020 − 0.586404I
a = −1.007640 + 0.736012I
b = −0.025777 − 1.279070I
0.45408 − 11.38860I 0
u = 1.174900 + 0.635746I
a = 0.105656 − 1.081020I
b = 1.099320 + 0.078865I
−4.70519 − 2.39134I 0
u = 1.174900 − 0.635746I
a = 0.105656 + 1.081020I
b = 1.099320 − 0.078865I
−4.70519 + 2.39134I 0
u = −1.210680 + 0.603160I
a = 0.73287 + 1.83631I
b = 1.41333 − 0.57602I
−4.0922 + 17.7863I 0
u = −1.210680 − 0.603160I
a = 0.73287 − 1.83631I
b = 1.41333 + 0.57602I
−4.0922 − 17.7863I 0
u = 1.336130 + 0.262407I
a = 0.643768 − 0.141253I
b = 1.34855 − 0.46968I
−6.58899 + 8.11200I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.336130 − 0.262407I
a = 0.643768 + 0.141253I
b = 1.34855 + 0.46968I
−6.58899 − 8.11200I 0
u = −1.237190 + 0.595619I
a = 0.557202 + 1.248800I
b = 1.190570 − 0.263500I
−3.13741 + 9.59200I 0
u = −1.237190 − 0.595619I
a = 0.557202 − 1.248800I
b = 1.190570 + 0.263500I
−3.13741 − 9.59200I 0
u = 0.455771 + 0.389865I
a = 0.61679 − 2.10839I
b = 0.014957 + 0.768895I
0.28541 + 1.54658I −0.57343 − 2.06881I
u = 0.455771 − 0.389865I
a = 0.61679 + 2.10839I
b = 0.014957 − 0.768895I
0.28541 − 1.54658I −0.57343 + 2.06881I
u = −0.222834 + 0.492928I
a = 0.02494 − 1.67474I
b = −1.49404 + 0.24932I
−2.65606 − 0.12519I −6.98986 + 0.10633I
u = −0.222834 − 0.492928I
a = 0.02494 + 1.67474I
b = −1.49404 − 0.24932I
−2.65606 + 0.12519I −6.98986 − 0.10633I
u = 1.44028 + 0.24640I
a = 0.584787 − 0.199933I
b = 1.115110 + 0.022821I
−5.52870 − 0.86398I 0
u = 1.44028 − 0.24640I
a = 0.584787 + 0.199933I
b = 1.115110 − 0.022821I
−5.52870 + 0.86398I 0
u = 0.216654 + 0.255543I
a = 1.94220 + 1.20034I
b = −0.047106 − 0.410466I
0.041508 − 1.376630I 0.16544 + 4.98668I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.216654 − 0.255543I
a = 1.94220 − 1.20034I
b = −0.047106 + 0.410466I
0.041508 + 1.376630I 0.16544 − 4.98668I
u = −0.197051
a = −4.66830
b = −1.34181
−2.55123 −4.11150
13
II. I
u
2
= hb
5
− b
4
− 2b
3
+ b
2
+ b + 1, a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
1
b
a
10
=
−b + 1
b
a
11
=
−b + 1
−b
2
a
8
=
−b
2
+ b + 1
−b
3
+ b
a
6
=
0
−b
4
− b
3
+ b
2
+ 2b + 1
a
7
=
0
−b
4
− b
3
+ b
2
+ 2b + 1
a
3
=
0
1
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3b
4
+ 7b
3
+ 2b
2
− 6b − 7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
6
u
5
c
5
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
7
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
8
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
9
, c
11
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
10
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
7
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
8
, c
9
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.21774
−4.04602 −15.9650
u = 1.00000
a = 1.00000
b = −0.309916 + 0.549911I
−1.97403 + 1.53058I −3.57269 − 4.45807I
u = 1.00000
a = 1.00000
b = −0.309916 − 0.549911I
−1.97403 − 1.53058I −3.57269 + 4.45807I
u = 1.00000
a = 1.00000
b = 1.41878 + 0.21917I
−7.51750 − 4.40083I −3.44484 + 1.78781I
u = 1.00000
a = 1.00000
b = 1.41878 − 0.21917I
−7.51750 + 4.40083I −3.44484 − 1.78781I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
82
− 6u
81
+ ··· + 8u − 1)
c
2
((u + 1)
5
)(u
82
+ 42u
81
+ ··· + 32u + 1)
c
3
, c
6
u
5
(u
82
− u
81
+ ··· + 160u + 32)
c
4
((u + 1)
5
)(u
82
− 6u
81
+ ··· + 8u − 1)
c
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
82
− 6u
81
+ ··· + 2u − 1)
c
7
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
82
+ 14u
81
+ ··· + 2u + 1)
c
8
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
82
− 2u
81
+ ··· + 14u + 1)
c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
82
+ 2u
81
+ ··· − 20520u − 1647)
c
10
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
82
− 2u
81
+ ··· − 2362u − 484)
c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
82
− 2u
81
+ ··· + 14u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
82
− 42y
81
+ ··· − 32y + 1)
c
2
((y −1)
5
)(y
82
+ 2y
81
+ ··· − 484y + 1)
c
3
, c
6
y
5
(y
82
− 33y
81
+ ··· − 19968y + 1024)
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
82
− 14y
81
+ ··· − 6y + 1)
c
7
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
82
+ 6y
81
+ ··· + 14y + 1)
c
8
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
82
− 58y
81
+ ··· + 14y + 1)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
82
+ 50y
81
+ ··· − 261288342y + 2712609)
c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
82
+ 90y
81
+ ··· + 10862436y + 234256)
19
