11n
185
(K11n
185
)
A knot diagram
1
Linearized knot diagam
6 5 1 10 8 4 3 2 4 5 7
Solving Sequence
5,10 7,11
1 4 3 8 2 6 9
c
10
c
11
c
4
c
3
c
7
c
2
c
6
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−25u
13
− 100u
12
+ ··· + 32b − 4, −u
13
+ 44u
12
+ ··· + 64a + 284,
u
14
+ 6u
13
+ 14u
12
+ 8u
11
− 35u
10
− 98u
9
− 105u
8
+ 154u
6
+ 224u
5
+ 168u
4
+ 74u
3
+ 26u
2
+ 16u + 8i
I
u
2
= hau + b, u
5
a + 2u
4
a + 3u
5
+ 2u
3
a + 9u
4
− u
2
a + 8u
3
+ 4a
2
− au − u
2
− 10u − 7,
u
6
+ 4u
5
+ 6u
4
+ 3u
3
− 3u
2
− 6u − 4i
I
u
3
= h−10a
3
u
2
− 36a
2
u
2
+ ··· − 289a − 111,
a
3
u
2
+ a
4
− 2a
3
u + 3a
2
u
2
+ a
3
− 2a
2
u + u
2
a + 3a
2
− 5au + 6u
2
+ 4a − 6u + 1, u
3
− u
2
+ 1i
I
u
4
= h−2452292589a
7
u
2
+ 1959398184a
6
u
2
+ ··· − 9164004134a − 16046840503,
− a
7
u
2
+ 10a
6
u
2
+ ··· + 116a + 33, u
3
− u
2
+ 1i
I
u
5
= h6u
17
+ 4u
16
+ ··· + 2b + 46, 23u
17
+ 12u
16
+ ··· + 4a + 112,
u
18
− 8u
16
+ 29u
14
− 68u
12
+ 115u
10
− 141u
8
+ 126u
6
− 79u
4
+ 28u
2
− 4i
I
u
6
= h−u
2
+ b − u + 1, −u
2
+ a + 1, u
3
+ u
2
− 1i
I
u
7
= h−au − u
2
+ b + u − 1, −u
2
a + a
2
+ 2au + u
2
− a + 1, u
3
− u
2
+ 1i
I
v
1
= ha, b + 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 90 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−25u
13
− 100u
12
+ · · · + 32b − 4, −u
13
+ 44u
12
+ · · · + 64a +
284, u
14
+ 6u
13
+ · · · + 16u + 8i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
0.0156250u
13
− 0.687500u
12
+ ··· − 3.40625u − 4.43750
25
32
u
13
+
25
8
u
12
+ ··· +
75
16
u +
1
8
a
11
=
1
u
2
a
1
=
0.265625u
13
+ 1.56250u
12
+ ··· + 2.59375u + 3.06250
1
32
u
13
+
5
8
u
12
+ ··· +
35
16
u +
17
8
a
4
=
u
u
a
3
=
0.765625u
13
+ 3.81250u
12
+ ··· + 8.09375u + 4.56250
1.34375u
13
+ 6.37500u
12
+ ··· + 11.0625u + 6.37500
a
8
=
−0.234375u
13
− 0.937500u
12
+ ··· − 0.406250u − 0.937500
1
32
u
13
+
5
8
u
12
+ ··· +
35
16
u +
17
8
a
2
=
0.765625u
13
+ 3.81250u
12
+ ··· + 8.09375u + 4.56250
25
32
u
13
+
25
8
u
12
+ ··· +
75
16
u +
1
8
a
6
=
0.578125u
13
+ 2.56250u
12
+ ··· + 2.96875u + 1.81250
1.34375u
13
+ 6.37500u
12
+ ··· + 11.0625u + 6.37500
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
11
8
u
13
−
13
2
u
12
−
49
4
u
11
−
1
2
u
10
+
361
8
u
9
+
183
2
u
8
+
491
8
u
7
−
247
4
u
6
−
673
4
u
5
−
307
2
u
4
− 60u
3
−
23
4
u
2
−
33
4
u −
31
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
14
− u
13
+ ··· + 2u
2
+ 2
c
2
, c
6
, c
8
c
11
u
14
− u
13
+ ··· − u + 1
c
3
, c
5
u
14
− 7u
13
+ ··· − 25u + 11
c
4
, c
9
, c
10
u
14
− 6u
13
+ ··· − 16u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
14
+ 3y
13
+ ··· + 8y + 4
c
2
, c
6
, c
8
c
11
y
14
+ 11y
13
+ ··· + 21y + 1
c
3
, c
5
y
14
− 7y
13
+ ··· − 493y + 121
c
4
, c
9
, c
10
y
14
− 8y
13
+ ··· + 160y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667935 + 1.025090I
a = −0.285457 − 0.894080I
b = −1.107180 − 0.304570I
4.32333 + 2.75562I −3.35979 − 3.59185I
u = −0.667935 − 1.025090I
a = −0.285457 + 0.894080I
b = −1.107180 + 0.304570I
4.32333 − 2.75562I −3.35979 + 3.59185I
u = −0.536682 + 1.118280I
a = 0.636097 + 0.907281I
b = 1.355980 − 0.224415I
3.36641 − 10.30200I −6.23771 + 5.94221I
u = −0.536682 − 1.118280I
a = 0.636097 − 0.907281I
b = 1.355980 + 0.224415I
3.36641 + 10.30200I −6.23771 − 5.94221I
u = −1.069760 + 0.720252I
a = −0.777184 − 0.841410I
b = −1.43743 − 0.34034I
3.01100 + 3.56965I −5.19675 − 2.89817I
u = −1.069760 − 0.720252I
a = −0.777184 + 0.841410I
b = −1.43743 + 0.34034I
3.01100 − 3.56965I −5.19675 + 2.89817I
u = −1.344910 + 0.179800I
a = 0.609809 − 0.501435I
b = 0.729978 − 0.784026I
−5.73092 + 3.41357I −11.64336 + 0.09610I
u = −1.344910 − 0.179800I
a = 0.609809 + 0.501435I
b = 0.729978 + 0.784026I
−5.73092 − 3.41357I −11.64336 − 0.09610I
u = −1.19710 + 0.78285I
a = 0.78383 + 1.31732I
b = 1.96958 + 0.96334I
1.2941 + 17.1000I −8.51485 − 9.31216I
u = −1.19710 − 0.78285I
a = 0.78383 − 1.31732I
b = 1.96958 − 0.96334I
1.2941 − 17.1000I −8.51485 + 9.31216I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.252591 + 0.403462I
a = −0.828123 − 0.088481I
b = 0.173478 + 0.356466I
−0.81174 − 1.19027I −7.67312 + 5.52205I
u = 0.252591 − 0.403462I
a = −0.828123 + 0.088481I
b = 0.173478 − 0.356466I
−0.81174 + 1.19027I −7.67312 − 5.52205I
u = 1.56380 + 0.03954I
a = 0.111030 − 0.272749I
b = −0.184413 + 0.422135I
−4.62975 + 6.18029I −7.37442 − 7.53018I
u = 1.56380 − 0.03954I
a = 0.111030 + 0.272749I
b = −0.184413 − 0.422135I
−4.62975 − 6.18029I −7.37442 + 7.53018I
6
II.
I
u
2
= hau + b, u
5
a + 3u
5
+ · · · + 4a
2
− 7, u
6
+ 4u
5
+ 6u
4
+ 3u
3
− 3u
2
− 6u − 4i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
a
−au
a
11
=
1
u
2
a
1
=
1
2
u
5
a −
1
4
u
5
+ ··· − a + 1
u
5
a −
1
2
u
5
+ ··· − 2a + 1
a
4
=
u
u
a
3
=
−
1
4
u
5
−
1
2
u
4
+ ··· + a + 1
−
3
2
u
5
− 3u
4
+ ··· +
7
2
u + 3
a
8
=
−
1
2
u
5
a +
1
4
u
5
+ ··· + a −
3
2
−u
5
a − 2u
4
a + u
5
− u
3
a + 3u
4
+ u
2
a + 3u
3
+ 2au + 2a − 2u − 3
a
2
=
−
1
4
u
5
−
1
2
u
4
+ ··· + a + 1
−
1
2
u
5
− u
4
− u
3
+ au +
1
2
u
2
+
3
2
u + 1
a
6
=
−u
3
a − u
2
a + a
−u
3
a − u
2
a − au
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14u
5
− 31u
4
− 31u
3
+ 5u
2
+ 28u + 30
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
− 2u
4
− u
3
+ 3u
2
+ u − 1)
2
c
2
, c
6
, c
8
c
11
u
12
− u
11
+ ··· − 7u + 1
c
3
, c
5
u
12
− 5u
11
+ ··· + 42u − 7
c
4
, c
9
, c
10
(u
6
− 4u
5
+ 6u
4
− 3u
3
− 3u
2
+ 6u − 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
− 4y
5
+ 10y
4
− 15y
3
+ 15y
2
− 7y + 1)
2
c
2
, c
6
, c
8
c
11
y
12
+ y
11
+ ··· − 59y + 1
c
3
, c
5
y
12
− 5y
11
+ ··· + 154y + 49
c
4
, c
9
, c
10
(y
6
− 4y
5
+ 6y
4
− 5y
3
− 3y
2
− 12y + 16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.977719
a = −0.332086 + 0.227752I
b = 0.324687 − 0.222678I
−0.985708 −7.65430
u = 0.977719
a = −0.332086 − 0.227752I
b = 0.324687 + 0.222678I
−0.985708 −7.65430
u = −0.429813 + 1.015170I
a = −0.575835 − 1.071170I
b = −1.334920 + 0.124164I
4.79788 − 2.68180I −2.86354 + 2.82727I
u = −0.429813 + 1.015170I
a = 0.024967 + 0.780798I
b = 0.803370 + 0.310252I
4.79788 − 2.68180I −2.86354 + 2.82727I
u = −0.429813 − 1.015170I
a = −0.575835 + 1.071170I
b = −1.334920 − 0.124164I
4.79788 + 2.68180I −2.86354 − 2.82727I
u = −0.429813 − 1.015170I
a = 0.024967 − 0.780798I
b = 0.803370 − 0.310252I
4.79788 + 2.68180I −2.86354 − 2.82727I
u = −1.23275 + 0.71927I
a = 0.626848 + 0.640690I
b = 1.233580 + 0.338935I
2.32551 + 9.01899I −7.13133 − 8.44417I
u = −1.23275 + 0.71927I
a = −0.93315 − 1.29101I
b = −2.07892 − 0.92030I
2.32551 + 9.01899I −7.13133 − 8.44417I
u = −1.23275 − 0.71927I
a = 0.626848 − 0.640690I
b = 1.233580 − 0.338935I
2.32551 − 9.01899I −7.13133 + 8.44417I
u = −1.23275 − 0.71927I
a = −0.93315 + 1.29101I
b = −2.07892 + 0.92030I
2.32551 − 9.01899I −7.13133 + 8.44417I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.65260
a = 1.75945
b = 2.90767
−9.97120 78.6440
u = −1.65260
a = 0.119054
b = 0.196749
−9.97120 78.6440
11
III. I
u
3
=
h−10a
3
u
2
−36a
2
u
2
+· · · − 289a − 111, a
3
u
2
+3a
2
u
2
+· · · + 4a + 1, u
3
−u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
a
0.0332226a
3
u
2
+ 0.119601a
2
u
2
+ ··· + 0.960133a + 0.368771
a
11
=
1
u
2
a
1
=
−0.249169a
3
u
2
− 0.897010a
2
u
2
+ ··· − 0.700997a − 0.265781
−0.205980a
3
u
2
− 0.541528a
2
u
2
+ ··· − 0.152824a − 0.0863787
a
4
=
u
u
a
3
=
−0.189369a
3
u
2
− 0.481728a
2
u
2
+ ··· − 0.172757a − 0.401993
−0.146179a
3
u
2
− 0.126246a
2
u
2
+ ··· + 0.375415a − 0.222591
a
8
=
0.0431894a
3
u
2
+ 0.355482a
2
u
2
+ ··· + 0.548173a + 0.179402
−0.176080a
3
u
2
+ 0.166113a
2
u
2
+ ··· + 0.611296a + 0.345515
a
2
=
−0.189369a
3
u
2
− 0.481728a
2
u
2
+ ··· − 0.172757a − 0.401993
−au
a
6
=
0.0431894a
3
u
2
+ 0.355482a
2
u
2
+ ··· + 0.548173a + 0.179402
0.0764120a
3
u
2
+ 0.475083a
2
u
2
+ ··· + 0.508306a + 0.548173
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
24
301
a
3
u
2
−
352
301
a
3
u −
568
301
a
2
u
2
+
104
301
a
3
−
304
301
a
2
u +
512
301
u
2
a +
856
301
a
2
−
1320
301
au +
80
301
u
2
+
992
301
a +
772
301
u −
146
301
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
12
− 3u
11
+ ··· + 30u + 25
c
2
, c
6
, c
8
c
11
u
12
− u
11
+ ··· + 4u + 7
c
3
, c
5
(u
2
+ u + 1)
6
c
4
, c
9
, c
10
(u
3
+ u
2
− 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
12
− 9y
11
+ ··· − 100y + 625
c
2
, c
6
, c
8
c
11
y
12
+ 3y
11
+ ··· + 208y + 49
c
3
, c
5
(y
2
+ y + 1)
6
c
4
, c
9
, c
10
(y
3
− y
2
+ 2y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.163500 − 0.426968I
b = 1.65706 − 0.08153I
3.02413 + 1.23164I −2.49024 − 3.94876I
u = 0.877439 + 0.744862I
a = −0.014457 + 1.385720I
b = −1.70063 + 1.21638I
3.02413 − 6.88789I −2.49024 + 9.90765I
u = 0.877439 + 0.744862I
a = −1.05173 + 0.98574I
b = −1.33894 − 0.49201I
3.02413 + 1.23164I −2.49024 − 3.94876I
u = 0.877439 + 0.744862I
a = 0.44248 − 1.76191I
b = 1.04486 − 1.20512I
3.02413 − 6.88789I −2.49024 + 9.90765I
u = 0.877439 − 0.744862I
a = 1.163500 + 0.426968I
b = 1.65706 + 0.08153I
3.02413 − 1.23164I −2.49024 + 3.94876I
u = 0.877439 − 0.744862I
a = −0.014457 − 1.385720I
b = −1.70063 − 1.21638I
3.02413 + 6.88789I −2.49024 − 9.90765I
u = 0.877439 − 0.744862I
a = −1.05173 − 0.98574I
b = −1.33894 + 0.49201I
3.02413 − 1.23164I −2.49024 + 3.94876I
u = 0.877439 − 0.744862I
a = 0.44248 + 1.76191I
b = 1.04486 + 1.20512I
3.02413 + 6.88789I −2.49024 − 9.90765I
u = −0.754878
a = −0.03389 + 1.64154I
b = −1.136780 + 0.774104I
−1.11345 − 4.05977I −9.01951 + 6.92820I
u = −0.754878
a = −0.03389 − 1.64154I
b = −1.136780 − 0.774104I
−1.11345 + 4.05977I −9.01951 − 6.92820I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −1.50591 + 1.02547I
b = −0.025581 + 1.239160I
−1.11345 − 4.05977I −9.01951 + 6.92820I
u = −0.754878
a = −1.50591 − 1.02547I
b = −0.025581 − 1.239160I
−1.11345 + 4.05977I −9.01951 − 6.92820I
16
IV. I
u
4
= h−2.45 × 10
9
a
7
u
2
+ 1.96 × 10
9
a
6
u
2
+ · · · − 9.16 × 10
9
a − 1.60 ×
10
10
, −a
7
u
2
+ 10a
6
u
2
+ · · · + 116a + 33, u
3
− u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
a
0.405041a
7
u
2
− 0.323630a
6
u
2
+ ··· + 1.51360a + 2.65043
a
11
=
1
u
2
a
1
=
−0.523501a
7
u
2
− 0.0850496a
6
u
2
+ ··· − 0.741341a − 0.113356
−0.280191a
7
u
2
− 0.209408a
6
u
2
+ ··· + 2.44721a + 3.96214
a
4
=
u
u
a
3
=
−0.0502811a
7
u
2
− 0.392110a
6
u
2
+ ··· + 1.40914a + 0.793861
−0.124389a
7
u
2
− 0.527176a
6
u
2
+ ··· + 9.80960a + 8.21031
a
8
=
−0.232267a
7
u
2
+ 0.0446991a
6
u
2
+ ··· + 0.0658781a − 1.11663
0.338024a
7
u
2
+ 0.201586a
6
u
2
+ ··· + 2.61051a − 0.410883
a
2
=
−0.0502811a
7
u
2
− 0.392110a
6
u
2
+ ··· + 1.40914a + 0.793861
0.342964a
7
u
2
− 0.298685a
6
u
2
+ ··· + 10.1678a + 8.72007
a
6
=
0.107236a
7
u
2
− 0.103911a
6
u
2
+ ··· + 1.36281a + 1.46016
0.512277a
7
u
2
− 0.427541a
6
u
2
+ ··· + 1.87642a + 4.11059
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
8159408
12909239
a
7
u
2
−
2809816
1844177
a
6
u
2
+ ··· +
257953072
12909239
a −
2299186
12909239
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
12
+ u
11
+ ··· − 4u + 1)
2
c
2
, c
6
, c
8
c
11
u
24
+ u
23
+ ··· + 94u + 19
c
3
, c
5
(u
4
+ u
3
− 2u + 1)
6
c
4
, c
9
, c
10
(u
3
+ u
2
− 1)
8
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
12
+ 3y
11
+ ··· − 8y + 1)
2
c
2
, c
6
, c
8
c
11
y
24
− 15y
23
+ ··· + 6136y + 361
c
3
, c
5
(y
4
− y
3
+ 6y
2
− 4y + 1)
6
c
4
, c
9
, c
10
(y
3
− y
2
+ 2y −1)
8
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.781244 − 0.526293I
b = −1.57291 − 0.16189I
−0.26574 − 6.88789I −14.4902 + 9.9077I
u = 0.877439 + 0.744862I
a = −0.931824 + 0.522997I
b = −0.957160 − 0.116334I
−0.265740 + 1.231640I −14.4902 − 3.9488I
u = 0.877439 + 0.744862I
a = 0.699396 − 0.461137I
b = 1.207180 + 0.235183I
−0.265740 + 1.231640I −14.4902 − 3.9488I
u = 0.877439 + 0.744862I
a = −0.065722 + 1.213540I
b = 0.418059 + 0.300929I
−0.265740 + 1.231640I −14.4902 − 3.9488I
u = 0.877439 + 0.744862I
a = 1.132860 − 0.777183I
b = 0.293478 + 1.043710I
−0.26574 − 6.88789I −14.4902 + 9.9077I
u = 0.877439 + 0.744862I
a = −0.222091 + 1.383150I
b = −1.23772 + 1.32475I
−0.26574 − 6.88789I −14.4902 + 9.9077I
u = 0.877439 + 0.744862I
a = −0.446111 + 0.035743I
b = 0.961588 − 1.015860I
−0.265740 + 1.231640I −14.4902 − 3.9488I
u = 0.877439 + 0.744862I
a = 0.07494 − 1.57340I
b = 1.22513 − 1.04820I
−0.26574 − 6.88789I −14.4902 + 9.9077I
u = 0.877439 − 0.744862I
a = −0.781244 + 0.526293I
b = −1.57291 + 0.16189I
−0.26574 + 6.88789I −14.4902 − 9.9077I
u = 0.877439 − 0.744862I
a = −0.931824 − 0.522997I
b = −0.957160 + 0.116334I
−0.265740 − 1.231640I −14.4902 + 3.9488I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = 0.699396 + 0.461137I
b = 1.207180 − 0.235183I
−0.265740 − 1.231640I −14.4902 + 3.9488I
u = 0.877439 − 0.744862I
a = −0.065722 − 1.213540I
b = 0.418059 − 0.300929I
−0.265740 − 1.231640I −14.4902 + 3.9488I
u = 0.877439 − 0.744862I
a = 1.132860 + 0.777183I
b = 0.293478 − 1.043710I
−0.26574 + 6.88789I −14.4902 − 9.9077I
u = 0.877439 − 0.744862I
a = −0.222091 − 1.383150I
b = −1.23772 − 1.32475I
−0.26574 + 6.88789I −14.4902 − 9.9077I
u = 0.877439 − 0.744862I
a = −0.446111 − 0.035743I
b = 0.961588 + 1.015860I
−0.265740 − 1.231640I −14.4902 + 3.9488I
u = 0.877439 − 0.744862I
a = 0.07494 + 1.57340I
b = 1.22513 + 1.04820I
−0.26574 + 6.88789I −14.4902 − 9.9077I
u = −0.754878
a = −0.421556 + 0.043844I
b = 1.135590 + 0.509778I
−4.40332 − 4.05977I −21.0195 + 6.9282I
u = −0.754878
a = −0.421556 − 0.043844I
b = 1.135590 − 0.509778I
−4.40332 + 4.05977I −21.0195 − 6.9282I
u = −0.754878
a = 1.50433 + 0.67531I
b = −0.318223 + 0.033097I
−4.40332 − 4.05977I −21.0195 + 6.9282I
u = −0.754878
a = 1.50433 − 0.67531I
b = −0.318223 − 0.033097I
−4.40332 + 4.05977I −21.0195 − 6.9282I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = 0.28531 + 2.98501I
b = 0.12962 + 3.24360I
−4.40332 − 4.05977I −21.0195 + 6.9282I
u = −0.754878
a = 0.28531 − 2.98501I
b = 0.12962 − 3.24360I
−4.40332 + 4.05977I −21.0195 − 6.9282I
u = −0.754878
a = 0.17171 + 4.29685I
b = 0.21537 + 2.25332I
−4.40332 − 4.05977I −21.0195 + 6.9282I
u = −0.754878
a = 0.17171 − 4.29685I
b = 0.21537 − 2.25332I
−4.40332 + 4.05977I −21.0195 − 6.9282I
22
V. I
u
5
= h6u
17
+ 4u
16
+ · · · + 2b + 46, 23u
17
+ 12u
16
+ · · · + 4a + 112, u
18
−
8u
16
+ · · · + 28u
2
− 4i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
−
23
4
u
17
− 3u
16
+ ··· − 57u − 28
−3u
17
− 2u
16
+ ··· − 28u − 23
a
11
=
1
u
2
a
1
=
3
4
u
17
− u
16
+ ··· + 3u − 14
−u
17
+
1
2
u
16
+ ··· − 15u + 3
a
4
=
u
u
a
3
=
11
4
u
17
− u
16
+ ··· + 29u − 5
−2u
17
+
3
2
u
16
+ ··· − 17u + 19
a
8
=
−
7
4
u
17
−
3
2
u
16
+ ··· − 18u − 17
−u
17
−
1
2
u
16
+ ··· − 15u − 3
a
2
=
11
4
u
17
− u
16
+ ··· + 29u − 5
−3u
17
+ 2u
16
+ ··· − 28u + 23
a
6
=
−
19
4
u
17
−
5
2
u
16
+ ··· − 46u − 24
−2u
17
−
3
2
u
16
+ ··· − 17u − 19
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
16
+ 3 u
14
+ 4 u
12
−33u
10
+ 92 u
8
−152u
6
+ 155u
4
−108u
2
+ 24
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
18
+ 2u
16
− u
14
− u
12
+ 12u
10
+ u
8
− 20u
6
+ u
4
+ 20u
2
− 4
c
2
, c
8
u
18
− 5u
16
+ ··· + 5u + 1
c
3
u
18
+ 10u
17
+ ··· + 4u + 1
c
4
, c
9
, c
10
u
18
− 8u
16
+ ··· + 28u
2
− 4
c
5
u
18
− 10u
17
+ ··· − 4u + 1
c
6
, c
11
u
18
− 5u
16
+ ··· − 5u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
9
+ 2y
8
− y
7
− y
6
+ 12y
5
+ y
4
− 20y
3
+ y
2
+ 20y −4)
2
c
2
, c
6
, c
8
c
11
y
18
− 10y
17
+ ··· − 9y + 1
c
3
, c
5
y
18
− 10y
17
+ ··· − 2y + 1
c
4
, c
9
, c
10
(y
9
− 8y
8
+ 29y
7
− 68y
6
+ 115y
5
− 141y
4
+ 126y
3
− 79y
2
+ 28y −4)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.876962 + 0.699049I
a = 0.19361 − 1.61044I
b = 1.29556 − 1.27695I
0.75125 − 6.53634I −5.69189 + 6.84556I
u = 0.876962 − 0.699049I
a = 0.19361 + 1.61044I
b = 1.29556 + 1.27695I
0.75125 + 6.53634I −5.69189 − 6.84556I
u = −0.876962 + 0.699049I
a = −0.270200 − 0.490177I
b = 0.579612 + 0.240984I
0.75125 + 6.53634I −5.69189 − 6.84556I
u = −0.876962 − 0.699049I
a = −0.270200 + 0.490177I
b = 0.579612 − 0.240984I
0.75125 − 6.53634I −5.69189 + 6.84556I
u = −0.955338 + 0.726047I
a = 0.179005 + 0.581867I
b = −0.593473 − 0.425914I
0.516726 − 1.138040I −1.96620 + 2.22050I
u = −0.955338 − 0.726047I
a = 0.179005 − 0.581867I
b = −0.593473 + 0.425914I
0.516726 + 1.138040I −1.96620 − 2.22050I
u = 0.955338 + 0.726047I
a = 0.860786 − 0.442427I
b = 1.143560 + 0.202303I
0.516726 + 1.138040I −1.96620 − 2.22050I
u = 0.955338 − 0.726047I
a = 0.860786 + 0.442427I
b = 1.143560 − 0.202303I
0.516726 − 1.138040I −1.96620 + 2.22050I
u = 1.256610 + 0.086547I
a = −0.55265 − 1.53743I
b = −0.56141 − 1.97978I
−6.35463 − 4.54485I −17.3071 + 6.6446I
u = 1.256610 − 0.086547I
a = −0.55265 + 1.53743I
b = −0.56141 + 1.97978I
−6.35463 + 4.54485I −17.3071 − 6.6446I
26
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.256610 + 0.086547I
a = −0.325560 + 0.123216I
b = 0.398439 − 0.183010I
−6.35463 + 4.54485I −17.3071 − 6.6446I
u = −1.256610 − 0.086547I
a = −0.325560 − 0.123216I
b = 0.398439 + 0.183010I
−6.35463 − 4.54485I −17.3071 + 6.6446I
u = 0.649819 + 0.050171I
a = 0.20068 + 4.09044I
b = −0.07481 + 2.66812I
−3.88718 + 3.93091I −2.97598 − 2.31585I
u = 0.649819 − 0.050171I
a = 0.20068 − 4.09044I
b = −0.07481 − 2.66812I
−3.88718 − 3.93091I −2.97598 + 2.31585I
u = −0.649819 + 0.050171I
a = 1.139310 + 0.512299I
b = −0.766045 − 0.275742I
−3.88718 − 3.93091I −2.97598 + 2.31585I
u = −0.649819 − 0.050171I
a = 1.139310 − 0.512299I
b = −0.766045 + 0.275742I
−3.88718 + 3.93091I −2.97598 − 2.31585I
u = 1.63875
a = −1.79237
b = −2.93725
−10.0162 −99.1180
u = −1.63875
a = −0.0575881
b = 0.0943725
−10.0162 −99.1180
27
VI. I
u
6
= h−u
2
+ b − u + 1, −u
2
+ a + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
u
2
− 1
u
2
+ u − 1
a
11
=
1
u
2
a
1
=
u
u
a
4
=
u
u
a
3
=
u
u
a
8
=
0
u
a
2
=
u
u
2
+ u − 1
a
6
=
0
u
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
u
3
+ u
2
+ 2u + 1
c
3
, c
5
u
3
c
4
, c
9
, c
10
u
3
− u
2
+ 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
y
3
+ 3y
2
+ 2y −1
c
3
, c
5
y
3
c
4
, c
9
, c
10
y
3
− y
2
+ 2y −1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.78492 − 1.30714I
b = −1.66236 − 0.56228I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = −0.78492 + 1.30714I
b = −1.66236 + 0.56228I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.754878
a = −0.430160
b = 0.324718
−1.11345 −9.01950
31
VII. I
u
7
= h−au − u
2
+ b + u − 1, −u
2
a + a
2
+ 2au + u
2
− a + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
7
=
a
au + u
2
− u + 1
a
11
=
1
u
2
a
1
=
au + u
2
− a − 2u + 1
au + 2u
2
− a − 3u + 1
a
4
=
u
u
a
3
=
au + u
2
− a − u + 1
au + 2u
2
− a − 2u + 1
a
8
=
u
2
− u
au + 2u
2
− a − 3u + 1
a
2
=
au + u
2
− a − u + 1
au + u
2
− u + 1
a
6
=
u
2
− u
au + 2u
2
− a − 2u + 1
a
9
=
−u
2
+ 1
−u
2
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 18
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
2
, c
6
, c
8
c
11
u
6
+ u
5
+ 2u
4
− 4u
2
+ 2u − 1
c
3
, c
5
(u + 1)
6
c
4
, c
9
, c
10
(u
3
+ u
2
− 1)
2
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
6
, c
8
c
11
y
6
+ 3y
5
− 4y
4
− 22y
3
+ 12y
2
+ 4y + 1
c
3
, c
5
(y −1)
6
c
4
, c
9
, c
10
(y
3
− y
2
+ 2y −1)
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.256475 − 1.286130I
b = 1.52067 − 0.37518I
−0.26574 − 2.82812I −14.4902 + 2.9794I
u = 0.877439 + 0.744862I
a = −0.796273 + 1.103550I
b = −1.18303 + 0.93746I
−0.26574 − 2.82812I −14.4902 + 2.9794I
u = 0.877439 − 0.744862I
a = 0.256475 + 1.286130I
b = 1.52067 + 0.37518I
−0.26574 + 2.82812I −14.4902 − 2.9794I
u = 0.877439 − 0.744862I
a = −0.796273 − 1.103550I
b = −1.18303 − 0.93746I
−0.26574 + 2.82812I −14.4902 − 2.9794I
u = −0.754878
a = 0.644735
b = 1.83802
−4.40332 −21.0200
u = −0.754878
a = 2.43486
b = 0.486696
−4.40332 −21.0200
35
VIII. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
10
=
1
0
a
7
=
0
−1
a
11
=
1
0
a
1
=
1
1
a
4
=
−1
0
a
3
=
0
1
a
8
=
0
−1
a
2
=
1
1
a
6
=
−1
−1
a
9
=
1
0
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
9
, c
10
u
c
2
, c
5
, c
8
u − 1
c
3
, c
6
, c
11
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
9
, c
10
y
c
2
, c
3
, c
5
c
6
, c
8
, c
11
y −1
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
39
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u(u
3
+ u
2
+ 2u + 1)
3
(u
6
− 2u
4
− u
3
+ 3u
2
+ u − 1)
2
· (u
12
− 3u
11
+ ··· + 30u + 25)(u
12
+ u
11
+ ··· − 4u + 1)
2
· (u
14
− u
13
+ ··· + 2u
2
+ 2)
· (u
18
+ 2u
16
− u
14
− u
12
+ 12u
10
+ u
8
− 20u
6
+ u
4
+ 20u
2
− 4)
c
2
, c
8
(u − 1)(u
3
+ u
2
+ 2u + 1)(u
6
+ u
5
+ 2u
4
− 4u
2
+ 2u − 1)
· (u
12
− u
11
+ ··· − 7u + 1)(u
12
− u
11
+ ··· + 4u + 7)
· (u
14
− u
13
+ ··· − u + 1)(u
18
− 5u
16
+ ··· + 5u + 1)
· (u
24
+ u
23
+ ··· + 94u + 19)
c
3
u
3
(u + 1)
7
(u
2
+ u + 1)
6
(u
4
+ u
3
− 2u + 1)
6
· (u
12
− 5u
11
+ ··· + 42u − 7)(u
14
− 7u
13
+ ··· − 25u + 11)
· (u
18
+ 10u
17
+ ··· + 4u + 1)
c
4
, c
9
, c
10
u(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
14
(u
6
− 4u
5
+ 6u
4
− 3u
3
− 3u
2
+ 6u − 4)
2
· (u
14
− 6u
13
+ ··· − 16u + 8)(u
18
− 8u
16
+ ··· + 28u
2
− 4)
c
5
u
3
(u − 1)(u + 1)
6
(u
2
+ u + 1)
6
(u
4
+ u
3
− 2u + 1)
6
· (u
12
− 5u
11
+ ··· + 42u − 7)(u
14
− 7u
13
+ ··· − 25u + 11)
· (u
18
− 10u
17
+ ··· − 4u + 1)
c
6
, c
11
(u + 1)(u
3
+ u
2
+ 2u + 1)(u
6
+ u
5
+ 2u
4
− 4u
2
+ 2u − 1)
· (u
12
− u
11
+ ··· − 7u + 1)(u
12
− u
11
+ ··· + 4u + 7)
· (u
14
− u
13
+ ··· − u + 1)(u
18
− 5u
16
+ ··· − 5u + 1)
· (u
24
+ u
23
+ ··· + 94u + 19)
40
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y
3
+ 3y
2
+ 2y −1)
3
(y
6
− 4y
5
+ 10y
4
− 15y
3
+ 15y
2
− 7y + 1)
2
· (y
9
+ 2y
8
− y
7
− y
6
+ 12y
5
+ y
4
− 20y
3
+ y
2
+ 20y −4)
2
· (y
12
− 9y
11
+ ··· − 100y + 625)(y
12
+ 3y
11
+ ··· − 8y + 1)
2
· (y
14
+ 3y
13
+ ··· + 8y + 4)
c
2
, c
6
, c
8
c
11
(y −1)(y
3
+ 3y
2
+ 2y −1)(y
6
+ 3y
5
+ ··· + 4y + 1)
· (y
12
+ y
11
+ ··· − 59y + 1)(y
12
+ 3y
11
+ ··· + 208y + 49)
· (y
14
+ 11y
13
+ ··· + 21y + 1)(y
18
− 10y
17
+ ··· − 9y + 1)
· (y
24
− 15y
23
+ ··· + 6136y + 361)
c
3
, c
5
y
3
(y −1)
7
(y
2
+ y + 1)
6
(y
4
− y
3
+ 6y
2
− 4y + 1)
6
· (y
12
− 5y
11
+ ··· + 154y + 49)(y
14
− 7y
13
+ ··· − 493y + 121)
· (y
18
− 10y
17
+ ··· − 2y + 1)
c
4
, c
9
, c
10
y(y
3
− y
2
+ 2y −1)
15
(y
6
− 4y
5
+ 6y
4
− 5y
3
− 3y
2
− 12y + 16)
2
· (y
9
− 8y
8
+ 29y
7
− 68y
6
+ 115y
5
− 141y
4
+ 126y
3
− 79y
2
+ 28y −4)
2
· (y
14
− 8y
13
+ ··· + 160y + 64)
41
