11a
27
(K11a
27
)
A knot diagram
1
Linearized knot diagam
5 1 11 2 9 3 4 10 6 8 7
Solving Sequence
5,9
6
2,10
1 3 4 8 7 11
c
5
c
9
c
1
c
2
c
4
c
8
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.81141 × 10
45
u
72
− 2.55560 × 10
45
u
71
+ ··· + 5.58876 × 10
45
b + 1.50088 × 10
46
,
1.50317 × 10
47
u
72
+ 3.46308 × 10
47
u
71
+ ··· + 5.58876 × 10
45
a + 2.41035 × 10
47
, u
73
+ 3u
72
+ ··· + 8u + 1i
I
u
2
= hb + a + 1, a
2
+ 3a + 3, u + 1i
* 2 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
= h−5.81×10
45
u
72
−2.56×10
45
u
71
+· · ·+5.59×10
45
b+1.50×10
46
, 1.50×
10
47
u
72
+3.46×10
47
u
71
+· · ·+5.59×10
45
a+2.41×10
47
, u
73
+3u
72
+· · ·+8u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
2
=
−26.8963u
72
− 61.9652u
71
+ ··· − 262.686u − 43.1285
1.03984u
72
+ 0.457276u
71
+ ··· − 8.76067u − 2.68554
a
10
=
u
−u
3
+ u
a
1
=
−27.9361u
72
− 62.4224u
71
+ ··· − 253.925u − 40.4429
1.03984u
72
+ 0.457276u
71
+ ··· − 8.76067u − 2.68554
a
3
=
−55.1885u
72
− 128.039u
71
+ ··· − 541.292u − 84.5791
−0.557631u
72
− 3.16857u
71
+ ··· − 25.1345u − 4.27345
a
4
=
52.9421u
72
+ 122.525u
71
+ ··· + 513.869u + 80.0761
−0.291491u
72
+ 0.944537u
71
+ ··· + 12.7180u + 2.20055
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
54.1305u
72
+ 120.249u
71
+ ··· + 492.164u + 73.9005
−11.1367u
72
− 24.4194u
71
+ ··· − 88.7848u − 13.4461
a
11
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
11
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −73.5210u
72
− 182.862u
71
+ ··· − 811.040u − 125.700
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
73
+ 2u
72
+ ··· + 7u − 1
c
2
u
73
+ 32u
72
+ ··· + 131u − 1
c
3
u
73
+ 7u
72
+ ··· + 12u + 4
c
5
, c
9
u
73
− 3u
72
+ ··· + 8u − 1
c
6
u
73
+ 34u
71
+ ··· − 149u − 41
c
7
u
73
− 2u
72
+ ··· − 784u − 224
c
8
, c
10
u
73
− 23u
72
+ ··· − 2u − 1
c
11
u
73
− 7u
72
+ ··· − u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
73
+ 32y
72
+ ··· + 131y −1
c
2
y
73
+ 20y
72
+ ··· + 19907y −1
c
3
y
73
+ 15y
72
+ ··· − 344y −16
c
5
, c
9
y
73
− 23y
72
+ ··· − 2y −1
c
6
y
73
+ 68y
72
+ ··· − 11173y −1681
c
7
y
73
+ 84y
72
+ ··· − 1858304y −50176
c
8
, c
10
y
73
+ 57y
72
+ ··· + 254y −1
c
11
y
73
+ 5y
72
+ ··· − 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872133 + 0.330890I
a = 0.347576 − 0.582681I
b = −0.093427 − 1.105170I
−1.56864 + 4.14463I 0. − 8.01358I
u = 0.872133 − 0.330890I
a = 0.347576 + 0.582681I
b = −0.093427 + 1.105170I
−1.56864 − 4.14463I 0. + 8.01358I
u = −0.827433 + 0.687248I
a = −0.757692 − 0.116396I
b = −0.903670 − 0.847810I
−0.261500 + 0.649592I 0
u = −0.827433 − 0.687248I
a = −0.757692 + 0.116396I
b = −0.903670 + 0.847810I
−0.261500 − 0.649592I 0
u = 0.917251 + 0.028799I
a = 0.957675 + 0.465286I
b = −0.899692 − 0.482863I
4.06916 + 1.66774I 17.5628 − 3.8525I
u = 0.917251 − 0.028799I
a = 0.957675 − 0.465286I
b = −0.899692 + 0.482863I
4.06916 − 1.66774I 17.5628 + 3.8525I
u = 0.744709 + 0.796357I
a = −0.254774 + 0.121438I
b = 0.525153 + 0.176233I
−3.74839 + 1.23253I 0
u = 0.744709 − 0.796357I
a = −0.254774 − 0.121438I
b = 0.525153 − 0.176233I
−3.74839 − 1.23253I 0
u = −0.797947 + 0.753369I
a = −0.64416 − 1.83433I
b = −0.572115 − 1.246620I
−3.09906 + 2.70236I 0
u = −0.797947 − 0.753369I
a = −0.64416 + 1.83433I
b = −0.572115 + 1.246620I
−3.09906 − 2.70236I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.077830 + 0.219114I
a = −0.690643 + 0.625004I
b = 0.817817 − 0.515578I
4.44539 + 5.47964I 0
u = 1.077830 − 0.219114I
a = −0.690643 − 0.625004I
b = 0.817817 + 0.515578I
4.44539 − 5.47964I 0
u = 0.887299 + 0.116247I
a = 1.69631 − 0.07268I
b = −0.704741 − 1.080540I
2.29836 + 4.22810I 12.1430 − 9.3439I
u = 0.887299 − 0.116247I
a = 1.69631 + 0.07268I
b = −0.704741 + 1.080540I
2.29836 − 4.22810I 12.1430 + 9.3439I
u = −0.880598 + 0.669028I
a = −0.700925 + 0.813755I
b = −0.964342 − 0.090780I
0.69933 − 2.58301I 0
u = −0.880598 − 0.669028I
a = −0.700925 − 0.813755I
b = −0.964342 + 0.090780I
0.69933 + 2.58301I 0
u = 0.875902 + 0.690173I
a = −0.191233 + 0.289860I
b = −0.386326 − 0.616731I
−2.40217 + 4.04097I 0
u = 0.875902 − 0.690173I
a = −0.191233 − 0.289860I
b = −0.386326 + 0.616731I
−2.40217 − 4.04097I 0
u = 0.668112 + 0.895781I
a = −0.28502 − 1.45618I
b = 0.465696 − 1.063540I
−6.08025 − 2.66865I 0
u = 0.668112 − 0.895781I
a = −0.28502 + 1.45618I
b = 0.465696 + 1.063540I
−6.08025 + 2.66865I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.720415 + 0.855626I
a = 0.314675 − 0.528100I
b = 0.910054 − 0.387571I
−2.75982 + 5.17856I 0
u = −0.720415 − 0.855626I
a = 0.314675 + 0.528100I
b = 0.910054 + 0.387571I
−2.75982 − 5.17856I 0
u = 0.876241 + 0.702164I
a = −0.81649 − 1.39051I
b = −0.484219 + 0.695912I
−2.39394 + 1.31325I 0
u = 0.876241 − 0.702164I
a = −0.81649 + 1.39051I
b = −0.484219 − 0.695912I
−2.39394 − 1.31325I 0
u = 0.846597 + 0.756952I
a = 0.55091 + 3.03768I
b = −0.468658 + 0.954426I
−3.36772 + 0.28806I 0
u = 0.846597 − 0.756952I
a = 0.55091 − 3.03768I
b = −0.468658 − 0.954426I
−3.36772 − 0.28806I 0
u = −1.070550 + 0.396975I
a = −1.34075 − 0.70080I
b = 0.606073 − 0.641390I
3.44487 − 1.41386I 0
u = −1.070550 − 0.396975I
a = −1.34075 + 0.70080I
b = 0.606073 + 0.641390I
3.44487 + 1.41386I 0
u = −0.853435
a = −0.672147
b = −0.0841487
1.41721 6.25420
u = −0.914329 + 0.693377I
a = 0.55780 + 1.40502I
b = −0.961681 + 0.764182I
0.01661 − 5.97370I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.914329 − 0.693377I
a = 0.55780 − 1.40502I
b = −0.961681 − 0.764182I
0.01661 + 5.97370I 0
u = −0.720406 + 0.896299I
a = −0.02381 + 1.65621I
b = 0.636841 + 1.154700I
−5.08354 + 10.84060I 0
u = −0.720406 − 0.896299I
a = −0.02381 − 1.65621I
b = 0.636841 − 1.154700I
−5.08354 − 10.84060I 0
u = 1.123670 + 0.265577I
a = −1.65424 + 0.52442I
b = 0.645150 + 1.076090I
2.75520 + 10.95230I 0
u = 1.123670 − 0.265577I
a = −1.65424 − 0.52442I
b = 0.645150 − 1.076090I
2.75520 − 10.95230I 0
u = −0.797794 + 0.839281I
a = −0.62268 − 2.20338I
b = 0.105796 − 1.302560I
−8.72144 + 2.03741I 0
u = −0.797794 − 0.839281I
a = −0.62268 + 2.20338I
b = 0.105796 + 1.302560I
−8.72144 − 2.03741I 0
u = −0.056905 + 0.832963I
a = −0.18731 − 1.57099I
b = 0.574495 − 1.065490I
−1.24065 − 7.33132I 0.88010 + 7.59105I
u = −0.056905 − 0.832963I
a = −0.18731 + 1.57099I
b = 0.574495 + 1.065490I
−1.24065 + 7.33132I 0.88010 − 7.59105I
u = 0.905677 + 0.743212I
a = 2.49650 − 3.26714I
b = −0.502055 − 0.950824I
−3.18426 + 5.39888I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.905677 − 0.743212I
a = 2.49650 + 3.26714I
b = −0.502055 + 0.950824I
−3.18426 − 5.39888I 0
u = −0.938472 + 0.730607I
a = 1.29738 + 2.34162I
b = −0.629103 + 1.251780I
−2.67029 − 8.34069I 0
u = −0.938472 − 0.730607I
a = 1.29738 − 2.34162I
b = −0.629103 − 1.251780I
−2.67029 + 8.34069I 0
u = −0.806104 + 0.030256I
a = 5.61862 − 2.98084I
b = −0.522576 + 0.858340I
1.30311 − 2.11076I −42.0323 − 9.8539I
u = −0.806104 − 0.030256I
a = 5.61862 + 2.98084I
b = −0.522576 − 0.858340I
1.30311 + 2.11076I −42.0323 + 9.8539I
u = −1.190620 + 0.080673I
a = −1.223050 − 0.005386I
b = 0.407136 − 0.888931I
1.11279 − 1.68465I 0
u = −1.190620 − 0.080673I
a = −1.223050 + 0.005386I
b = 0.407136 + 0.888931I
1.11279 + 1.68465I 0
u = −1.160110 + 0.331877I
a = −0.225821 − 0.129343I
b = 0.563847 + 0.978910I
2.41837 + 3.22713I 0
u = −1.160110 − 0.331877I
a = −0.225821 + 0.129343I
b = 0.563847 − 0.978910I
2.41837 − 3.22713I 0
u = 0.824162 + 0.902915I
a = −0.54627 + 1.78979I
b = 0.371133 + 1.036080I
−6.72947 + 4.09633I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.824162 − 0.902915I
a = −0.54627 − 1.78979I
b = 0.371133 − 1.036080I
−6.72947 − 4.09633I 0
u = 0.992368 + 0.723251I
a = −0.057932 + 0.453335I
b = 0.527464 − 0.346793I
−2.97910 + 4.50576I 0
u = 0.992368 − 0.723251I
a = −0.057932 − 0.453335I
b = 0.527464 + 0.346793I
−2.97910 − 4.50576I 0
u = −0.967923 + 0.779823I
a = 1.03339 + 1.85240I
b = 0.064735 + 1.326810I
−8.19243 − 8.08051I 0
u = −0.967923 − 0.779823I
a = 1.03339 − 1.85240I
b = 0.064735 − 1.326810I
−8.19243 + 8.08051I 0
u = −1.016430 + 0.755785I
a = 0.517773 − 0.711242I
b = 0.940848 + 0.419552I
−1.84899 − 11.18430I 0
u = −1.016430 − 0.755785I
a = 0.517773 + 0.711242I
b = 0.940848 − 0.419552I
−1.84899 + 11.18430I 0
u = −0.113221 + 0.709986I
a = 0.039506 + 0.618995I
b = 0.666738 + 0.436647I
0.57464 − 2.49330I 4.09751 + 3.36278I
u = −0.113221 − 0.709986I
a = 0.039506 − 0.618995I
b = 0.666738 − 0.436647I
0.57464 + 2.49330I 4.09751 − 3.36278I
u = 0.973348 + 0.835610I
a = 0.473684 − 1.300630I
b = 0.312134 − 1.005540I
−6.25965 + 2.30457I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973348 − 0.835610I
a = 0.473684 + 1.300630I
b = 0.312134 + 1.005540I
−6.25965 − 2.30457I 0
u = 0.215926 + 0.677273I
a = −0.84700 + 1.57866I
b = 0.190301 + 1.027280I
−3.66692 − 0.65369I −3.56200 + 0.87256I
u = 0.215926 − 0.677273I
a = −0.84700 − 1.57866I
b = 0.190301 − 1.027280I
−3.66692 + 0.65369I −3.56200 − 0.87256I
u = −1.034210 + 0.773016I
a = −1.54749 − 2.00996I
b = 0.658496 − 1.157870I
−4.1062 − 17.0192I 0
u = −1.034210 − 0.773016I
a = −1.54749 + 2.00996I
b = 0.658496 + 1.157870I
−4.1062 + 17.0192I 0
u = 1.058980 + 0.756530I
a = −1.57025 + 1.58679I
b = 0.518936 + 1.050430I
−4.88061 + 8.78731I 0
u = 1.058980 − 0.756530I
a = −1.57025 − 1.58679I
b = 0.518936 − 1.050430I
−4.88061 − 8.78731I 0
u = −0.435959 + 0.300456I
a = −1.39456 + 1.09197I
b = −0.359968 + 0.467827I
0.76514 − 1.25127I 5.38460 + 5.06088I
u = −0.435959 − 0.300456I
a = −1.39456 − 1.09197I
b = −0.359968 − 0.467827I
0.76514 + 1.25127I 5.38460 − 5.06088I
u = −0.447418 + 0.138876I
a = −2.53496 − 1.47336I
b = −0.487905 − 0.725427I
0.75785 + 1.41365I 4.07014 − 4.97652I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447418 − 0.138876I
a = −2.53496 + 1.47336I
b = −0.487905 + 0.725427I
0.75785 − 1.41365I 4.07014 + 4.97652I
u = −0.036644 + 0.286524I
a = −1.94866 + 1.84629I
b = −0.526291 + 0.983825I
−0.16446 − 2.80927I 2.04943 + 2.04126I
u = −0.036644 − 0.286524I
a = −1.94866 − 1.84629I
b = −0.526291 − 0.983825I
−0.16446 + 2.80927I 2.04943 − 2.04126I
12
II. I
u
2
= hb + a + 1, a
2
+ 3a + 3, u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
−1
a
6
=
1
−1
a
2
=
a
−a − 1
a
10
=
−1
0
a
1
=
2a + 1
−a − 1
a
3
=
2a + 4
−a − 2
a
4
=
2a + 4
−a − 2
a
8
=
1
−1
a
7
=
2a + 3
−a − 2
a
11
=
−2
1
a
11
=
−2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 15
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
2
+ u + 1
c
3
u
2
c
4
, c
6
, c
7
u
2
− u + 1
c
5
, c
8
(u + 1)
2
c
9
, c
10
, c
11
(u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
y
2
+ y + 1
c
3
y
2
c
5
, c
8
, c
9
c
10
, c
11
(y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.50000 + 0.86603I
b = 0.500000 − 0.866025I
1.64493 − 2.02988I 9.00000 + 3.46410I
u = −1.00000
a = −1.50000 − 0.86603I
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 9.00000 − 3.46410I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
73
+ 2u
72
+ ··· + 7u − 1)
c
2
(u
2
+ u + 1)(u
73
+ 32u
72
+ ··· + 131u − 1)
c
3
u
2
(u
73
+ 7u
72
+ ··· + 12u + 4)
c
4
(u
2
− u + 1)(u
73
+ 2u
72
+ ··· + 7u − 1)
c
5
((u + 1)
2
)(u
73
− 3u
72
+ ··· + 8u − 1)
c
6
(u
2
− u + 1)(u
73
+ 34u
71
+ ··· − 149u − 41)
c
7
(u
2
− u + 1)(u
73
− 2u
72
+ ··· − 784u − 224)
c
8
((u + 1)
2
)(u
73
− 23u
72
+ ··· − 2u − 1)
c
9
((u − 1)
2
)(u
73
− 3u
72
+ ··· + 8u − 1)
c
10
((u − 1)
2
)(u
73
− 23u
72
+ ··· − 2u − 1)
c
11
((u − 1)
2
)(u
73
− 7u
72
+ ··· − u
2
− 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
73
+ 32y
72
+ ··· + 131y −1)
c
2
(y
2
+ y + 1)(y
73
+ 20y
72
+ ··· + 19907y −1)
c
3
y
2
(y
73
+ 15y
72
+ ··· − 344y −16)
c
5
, c
9
((y −1)
2
)(y
73
− 23y
72
+ ··· − 2y −1)
c
6
(y
2
+ y + 1)(y
73
+ 68y
72
+ ··· − 11173y −1681)
c
7
(y
2
+ y + 1)(y
73
+ 84y
72
+ ··· − 1858304y −50176)
c
8
, c
10
((y −1)
2
)(y
73
+ 57y
72
+ ··· + 254y −1)
c
11
((y −1)
2
)(y
73
+ 5y
72
+ ··· − 2y −1)
18
