11a
316
(K11a
316
)
A knot diagram
1
Linearized knot diagam
9 6 1 11 8 2 10 3 7 4 5
Solving Sequence
4,10
11
5,8
6 1 3 2 7 9
c
10
c
4
c
5
c
11
c
3
c
2
c
7
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.80623 × 10
32
u
61
− 5.14761 × 10
32
u
60
+ ··· + 4.61017 × 10
32
b − 1.10416 × 10
32
,
− 6.91332 × 10
32
u
61
− 7.53652 × 10
32
u
60
+ ··· + 2.30509 × 10
33
a − 2.31132 × 10
33
, u
62
− 2u
61
+ ··· + 3u + 1i
I
u
2
= hb − 1, 5a + u − 2, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 64 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
= h1.81×10
32
u
61
−5.15×10
32
u
60
+· · ·+4.61×10
32
b−1.10×10
32
, −6.91×
10
32
u
61
−7.54×10
32
u
60
+· · ·+2.31×10
33
a−2.31×10
33
, u
62
−2u
61
+· · ·+3u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
8
=
0.299916u
61
+ 0.326952u
60
+ ··· − 3.67552u + 1.00270
−0.391793u
61
+ 1.11658u
60
+ ··· − 0.782541u + 0.239505
a
6
=
−1.37364u
61
+ 0.955447u
60
+ ··· + 15.8721u + 3.35880
0.226500u
61
− 0.438184u
60
+ ··· + 5.26406u + 0.574836
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
2
=
0.403303u
61
+ 1.11034u
60
+ ··· + 3.59385u − 1.62323
0.435823u
61
− 0.0545467u
60
+ ··· − 0.0437745u − 1.01330
a
7
=
0.691708u
61
− 0.789625u
60
+ ··· − 2.89298u + 0.763197
−0.391793u
61
+ 1.11658u
60
+ ··· − 0.782541u + 0.239505
a
9
=
0.210043u
61
+ 0.259417u
60
+ ··· − 3.20318u + 1.25041
−0.348888u
61
+ 0.656606u
60
+ ··· + 0.331553u + 0.825406
a
9
=
0.210043u
61
+ 0.259417u
60
+ ··· − 3.20318u + 1.25041
−0.348888u
61
+ 0.656606u
60
+ ··· + 0.331553u + 0.825406
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.89183u
61
− 9.68250u
60
+ ··· − 4.68341u + 13.0328
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
62
+ 7u
61
+ ··· + 100038u − 28017)
c
2
, c
6
u
62
+ 2u
61
+ ··· − u + 1
c
3
u
62
− 6u
61
+ ··· + 795u − 117
c
4
, c
10
, c
11
u
62
+ 2u
61
+ ··· − 3u + 1
c
5
5(5u
62
− 14u
61
+ ··· + 61755u + 8377)
c
7
, c
9
u
62
+ 3u
61
+ ··· + 214u − 25
c
8
u
62
+ u
61
+ ··· + 280u − 100
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
62
− 1309y
61
+ ··· − 1.54576 × 10
10
y + 7.84952 × 10
8
)
c
2
, c
6
y
62
+ 42y
61
+ ··· − 25y + 1
c
3
y
62
+ 18y
61
+ ··· − 440613y + 13689
c
4
, c
10
, c
11
y
62
− 54y
61
+ ··· − 25y + 1
c
5
25(25y
62
− 286y
61
+ ··· − 1.29244 × 10
9
y + 7.01741 × 10
7
)
c
7
, c
9
y
62
− 49y
61
+ ··· − 22596y + 625
c
8
y
62
− 15y
61
+ ··· − 413000y + 10000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.887619 + 0.514849I
a = −0.168834 − 0.676664I
b = −1.351070 − 0.186432I
6.81266 + 5.56177I 4.66163 − 5.86539I
u = −0.887619 − 0.514849I
a = −0.168834 + 0.676664I
b = −1.351070 + 0.186432I
6.81266 − 5.56177I 4.66163 + 5.86539I
u = −0.956988 + 0.457534I
a = −0.411794 − 0.142908I
b = −1.44265 + 0.39962I
7.18631 − 7.01551I 0
u = −0.956988 − 0.457534I
a = −0.411794 + 0.142908I
b = −1.44265 − 0.39962I
7.18631 + 7.01551I 0
u = −0.268927 + 0.858943I
a = 0.487450 − 0.791896I
b = −1.326860 + 0.042366I
8.77447 − 0.73219I 8.26642 + 0.24787I
u = −0.268927 − 0.858943I
a = 0.487450 + 0.791896I
b = −1.326860 − 0.042366I
8.77447 + 0.73219I 8.26642 − 0.24787I
u = 0.981110 + 0.511433I
a = −0.156001 + 0.318273I
b = −1.245360 − 0.167604I
2.26101 + 1.03760I 0
u = 0.981110 − 0.511433I
a = −0.156001 − 0.318273I
b = −1.245360 + 0.167604I
2.26101 − 1.03760I 0
u = 0.216176 + 0.854810I
a = 0.879762 + 0.839368I
b = −1.284170 + 0.305083I
4.62237 − 5.84398I 3.48358 + 6.22366I
u = 0.216176 − 0.854810I
a = 0.879762 − 0.839368I
b = −1.284170 − 0.305083I
4.62237 + 5.84398I 3.48358 − 6.22366I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.222629 + 0.830394I
a = 0.97517 − 1.10506I
b = −1.47365 − 0.48988I
9.4690 + 11.6120I 5.02297 − 7.15875I
u = −0.222629 − 0.830394I
a = 0.97517 + 1.10506I
b = −1.47365 + 0.48988I
9.4690 − 11.6120I 5.02297 + 7.15875I
u = −1.133930 + 0.168026I
a = 1.26618 − 0.92935I
b = 0.586572 − 1.058950I
1.22471 − 2.22328I 0
u = −1.133930 − 0.168026I
a = 1.26618 + 0.92935I
b = 0.586572 + 1.058950I
1.22471 + 2.22328I 0
u = 1.233700 + 0.140829I
a = 1.11356 + 0.95442I
b = 0.498573 + 0.517622I
−2.34840 − 0.48442I 0
u = 1.233700 − 0.140829I
a = 1.11356 − 0.95442I
b = 0.498573 − 0.517622I
−2.34840 + 0.48442I 0
u = 1.228560 + 0.275128I
a = 1.155710 − 0.633770I
b = 1.77170 + 0.45104I
4.49072 − 1.35832I 0
u = 1.228560 − 0.275128I
a = 1.155710 + 0.633770I
b = 1.77170 − 0.45104I
4.49072 + 1.35832I 0
u = −0.154976 + 0.717888I
a = −0.542160 + 0.195736I
b = 0.278710 + 1.257500I
3.96361 + 5.62230I 4.59110 − 7.16807I
u = −0.154976 − 0.717888I
a = −0.542160 − 0.195736I
b = 0.278710 − 1.257500I
3.96361 − 5.62230I 4.59110 + 7.16807I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.046542 + 0.724748I
a = −1.208990 − 0.366912I
b = 1.66460 − 0.64188I
8.09797 − 2.26515I 10.09980 + 3.27421I
u = 0.046542 − 0.724748I
a = −1.208990 + 0.366912I
b = 1.66460 + 0.64188I
8.09797 + 2.26515I 10.09980 − 3.27421I
u = −1.263000 + 0.236260I
a = −0.487348 + 0.065309I
b = 1.210290 − 0.144045I
−0.11388 + 2.17095I 0
u = −1.263000 − 0.236260I
a = −0.487348 − 0.065309I
b = 1.210290 + 0.144045I
−0.11388 − 2.17095I 0
u = −1.288710 + 0.185153I
a = 2.28058 − 2.74209I
b = 0.864085 + 0.005366I
0.03983 + 2.79266I 0
u = −1.288710 − 0.185153I
a = 2.28058 + 2.74209I
b = 0.864085 − 0.005366I
0.03983 − 2.79266I 0
u = 0.179463 + 0.661396I
a = −0.055951 − 0.244113I
b = 0.050410 − 0.678849I
0.49280 − 2.22863I −1.88873 + 4.27642I
u = 0.179463 − 0.661396I
a = −0.055951 + 0.244113I
b = 0.050410 + 0.678849I
0.49280 + 2.22863I −1.88873 − 4.27642I
u = −1.293980 + 0.298379I
a = 0.30932 + 2.31869I
b = 1.60267 + 0.81560I
3.91657 + 5.96640I 0
u = −1.293980 − 0.298379I
a = 0.30932 − 2.31869I
b = 1.60267 − 0.81560I
3.91657 − 5.96640I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.301670 + 0.265672I
a = −0.14106 − 2.23111I
b = 1.118260 − 0.376395I
−0.57816 − 4.41700I 0
u = 1.301670 − 0.265672I
a = −0.14106 + 2.23111I
b = 1.118260 + 0.376395I
−0.57816 + 4.41700I 0
u = −0.042843 + 0.662429I
a = −1.81923 + 1.14582I
b = 1.139070 + 0.251694I
3.63336 + 1.04794I 2.34672 − 0.35139I
u = −0.042843 − 0.662429I
a = −1.81923 − 1.14582I
b = 1.139070 − 0.251694I
3.63336 − 1.04794I 2.34672 + 0.35139I
u = 1.334310 + 0.246440I
a = 1.069770 − 0.893080I
b = 0.231740 − 0.094385I
−1.00664 − 2.96825I 0
u = 1.334310 − 0.246440I
a = 1.069770 + 0.893080I
b = 0.231740 + 0.094385I
−1.00664 + 2.96825I 0
u = −0.115133 + 0.619794I
a = 1.22726 + 1.09164I
b = 0.413434 − 0.098972I
3.55015 − 0.20409I 5.98628 − 1.19975I
u = −0.115133 − 0.619794I
a = 1.22726 − 1.09164I
b = 0.413434 + 0.098972I
3.55015 + 0.20409I 5.98628 + 1.19975I
u = 1.372160 + 0.035845I
a = 0.47764 + 1.70860I
b = −0.237289 + 0.862746I
−4.26849 + 2.33228I 0
u = 1.372160 − 0.035845I
a = 0.47764 − 1.70860I
b = −0.237289 − 0.862746I
−4.26849 − 2.33228I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.354390 + 0.299440I
a = −0.88402 − 1.77945I
b = 0.150670 − 1.364490I
−0.80126 − 9.32026I 0
u = 1.354390 − 0.299440I
a = −0.88402 + 1.77945I
b = 0.150670 + 1.364490I
−0.80126 + 9.32026I 0
u = −1.364120 + 0.277183I
a = −0.491592 + 1.171990I
b = −0.043760 + 0.847969I
−4.39333 + 5.67407I 0
u = −1.364120 − 0.277183I
a = −0.491592 − 1.171990I
b = −0.043760 − 0.847969I
−4.39333 − 5.67407I 0
u = −1.41802 + 0.08070I
a = −0.165441 − 1.216540I
b = −0.566676 − 0.567301I
−7.01139 + 2.01626I 0
u = −1.41802 − 0.08070I
a = −0.165441 + 1.216540I
b = −0.566676 + 0.567301I
−7.01139 − 2.01626I 0
u = 1.39937 + 0.34656I
a = −0.28769 + 2.13431I
b = −1.47028 + 0.55396I
4.3271 − 15.8582I 0
u = 1.39937 − 0.34656I
a = −0.28769 − 2.13431I
b = −1.47028 − 0.55396I
4.3271 + 15.8582I 0
u = −1.39672 + 0.35868I
a = −0.16352 − 1.69873I
b = −1.286260 − 0.404733I
−0.48145 + 10.21060I 0
u = −1.39672 − 0.35868I
a = −0.16352 + 1.69873I
b = −1.286260 + 0.404733I
−0.48145 − 10.21060I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.463287 + 0.297906I
a = 0.788454 + 0.539829I
b = −0.250407 + 0.311008I
−1.008560 − 0.666322I −7.37810 + 3.95165I
u = 0.463287 − 0.297906I
a = 0.788454 − 0.539829I
b = −0.250407 − 0.311008I
−1.008560 + 0.666322I −7.37810 − 3.95165I
u = −0.550158 + 0.016824I
a = 1.33228 + 1.00368I
b = 0.256229 + 0.735207I
1.45921 + 2.58594I −1.55168 − 3.98149I
u = −0.550158 − 0.016824I
a = 1.33228 − 1.00368I
b = 0.256229 − 0.735207I
1.45921 − 2.58594I −1.55168 + 3.98149I
u = 1.42814 + 0.36734I
a = −0.564087 + 1.146080I
b = −1.270380 + 0.067319I
3.38499 − 3.70672I 0
u = 1.42814 − 0.36734I
a = −0.564087 − 1.146080I
b = −1.270380 − 0.067319I
3.38499 + 3.70672I 0
u = 1.50001 + 0.04160I
a = −1.29195 + 0.81714I
b = −1.205330 + 0.382950I
−1.16526 − 6.77623I 0
u = 1.50001 − 0.04160I
a = −1.29195 − 0.81714I
b = −1.205330 − 0.382950I
−1.16526 + 6.77623I 0
u = 0.239018 + 0.279647I
a = 3.12607 − 0.97399I
b = 1.190070 − 0.194532I
4.30759 − 0.97665I −0.516718 + 1.197110I
u = 0.239018 − 0.279647I
a = 3.12607 + 0.97399I
b = 1.190070 + 0.194532I
4.30759 + 0.97665I −0.516718 − 1.197110I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63921
a = −0.771484
b = −1.04713
−7.12923 0
u = −0.201088
a = 2.67242
b = 0.901231
1.30954 9.93960
11
II. I
u
2
= hb − 1, 5a + u − 2, u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
−u + 1
a
5
=
−u
−u + 1
a
8
=
−
1
5
u +
2
5
1
a
6
=
−u +
1
5
−
4
5
u +
8
5
a
1
=
u
u
a
3
=
2u − 1
3u − 1
a
2
=
4
5
u
3
5
u −
1
5
a
7
=
−
1
5
u −
3
5
1
a
9
=
−
1
5
u +
2
5
1
a
9
=
−
1
5
u +
2
5
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
72
5
u − 13
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
2
− 1)
c
2
, c
10
, c
11
u
2
+ u − 1
c
3
u
2
+ 3u + 1
c
4
, c
6
u
2
− u − 1
c
5
5(5u
2
+ 5u + 1)
c
7
(u + 1)
2
c
8
u
2
c
9
(u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(5y −1)
2
c
2
, c
4
, c
6
c
10
, c
11
y
2
− 3y + 1
c
3
y
2
− 7y + 1
c
5
25(25y
2
− 15y + 1)
c
7
, c
9
(y −1)
2
c
8
y
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.276393
b = 1.00000
0.657974 −4.10030
u = −1.61803
a = 0.723607
b = 1.00000
−7.23771 −36.3000
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
25(5u
2
− 1)(5u
62
+ 7u
61
+ ··· + 100038u − 28017)
c
2
(u
2
+ u − 1)(u
62
+ 2u
61
+ ··· − u + 1)
c
3
(u
2
+ 3u + 1)(u
62
− 6u
61
+ ··· + 795u − 117)
c
4
(u
2
− u − 1)(u
62
+ 2u
61
+ ··· − 3u + 1)
c
5
25(5u
2
+ 5u + 1)(5u
62
− 14u
61
+ ··· + 61755u + 8377)
c
6
(u
2
− u − 1)(u
62
+ 2u
61
+ ··· − u + 1)
c
7
((u + 1)
2
)(u
62
+ 3u
61
+ ··· + 214u − 25)
c
8
u
2
(u
62
+ u
61
+ ··· + 280u − 100)
c
9
((u − 1)
2
)(u
62
+ 3u
61
+ ··· + 214u − 25)
c
10
, c
11
(u
2
+ u − 1)(u
62
+ 2u
61
+ ··· − 3u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
625(5y −1)
2
· (25y
62
− 1309y
61
+ ··· − 15457580352y + 784952289)
c
2
, c
6
(y
2
− 3y + 1)(y
62
+ 42y
61
+ ··· − 25y + 1)
c
3
(y
2
− 7y + 1)(y
62
+ 18y
61
+ ··· − 440613y + 13689)
c
4
, c
10
, c
11
(y
2
− 3y + 1)(y
62
− 54y
61
+ ··· − 25y + 1)
c
5
625(25y
2
− 15y + 1)
· (25y
62
− 286y
61
+ ··· − 1292437581y + 70174129)
c
7
, c
9
((y −1)
2
)(y
62
− 49y
61
+ ··· − 22596y + 625)
c
8
y
2
(y
62
− 15y
61
+ ··· − 413000y + 10000)
17
