11a
155
(K11a
155
)
A knot diagram
1
Linearized knot diagam
5 1 11 8 2 4 10 6 3 7 9
Solving Sequence
2,6
5 1
3,9
10 8 4 7 11
c
5
c
1
c
2
c
9
c
8
c
4
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h634617868812u
44
+ 5120393538096u
43
+ ··· + 30290494853b − 88597448899,
19298245499249u
44
+ 173772806942140u
43
+ ··· + 302904948530a − 151790191623698,
u
45
+ 10u
44
+ ··· − 62u − 10i
I
u
2
= h9u
29
− 22u
28
+ ··· + 2b + 15, −15u
29
a + 21u
29
+ ··· − 25a + 47, u
30
− 3u
29
+ ··· + 6u − 1i
I
u
3
= h−10u
15
+ 19u
14
+ ··· + b + 11, −33u
15
+ 77u
14
+ ··· + 2a + 60,
u
16
− 3u
15
+ u
14
+ 8u
13
− 11u
12
− 3u
11
+ 16u
10
− 5u
9
− 12u
8
+ 4u
7
+ 18u
6
− 18u
5
− u
4
+ 9u
3
− u
2
− 4u + 2i
I
u
4
= hb + a + 1, a
2
+ 2a + 2, u + 1i
I
u
5
= hb
2
+ 1, a − 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 125 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
=
h6.35×10
11
u
44
+5.12×10
12
u
43
+· · ·+3.03×10
10
b−8.86×10
10
, 1.93×10
13
u
44
+
1.74 × 10
14
u
43
+ · · · + 3.03 × 10
11
a − 1.52 × 10
14
, u
45
+ 10u
44
+ · · · − 62u − 10i
(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
9
=
−63.7106u
44
− 573.688u
43
+ ··· + 2769.67u + 501.115
−20.9511u
44
− 169.043u
43
+ ··· + 154.125u + 2.92493
a
10
=
−27.4817u
44
− 253.810u
43
+ ··· + 1512.06u + 294.306
−21.4161u
44
− 184.268u
43
+ ··· + 590.907u + 90.3501
a
8
=
−42.7595u
44
− 404.645u
43
+ ··· + 2615.55u + 498.190
−20.9511u
44
− 169.043u
43
+ ··· + 154.125u + 2.92493
a
4
=
−0.151903u
44
+ 14.1733u
43
+ ··· − 560.112u − 114.459
21.5585u
44
+ 195.648u
43
+ ··· − 991.029u − 171.620
a
7
=
−31.1941u
44
− 298.498u
43
+ ··· + 2176.62u + 428.069
−6.32145u
44
− 47.9083u
43
+ ··· − 67.2357u − 22.6589
a
11
=
32.4369u
44
+ 282.562u
43
+ ··· − 863.523u − 114.918
4.19050u
44
+ 26.6301u
43
+ ··· + 372.503u + 93.7023
a
11
=
32.4369u
44
+ 282.562u
43
+ ··· − 863.523u − 114.918
4.19050u
44
+ 26.6301u
43
+ ··· + 372.503u + 93.7023
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
3963758068051
30290494853
u
44
+
32549076872033
30290494853
u
43
+ ··· −
27811268065342
30290494853
u +
968878849396
30290494853
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
45
+ 10u
44
+ ··· − 62u − 10
c
2
u
45
+ 18u
44
+ ··· + 1884u + 100
c
3
, c
6
u
45
+ 3u
44
+ ··· + 6u − 1
c
4
, c
9
u
45
− u
44
+ ··· + 8u − 1
c
7
, c
10
u
45
+ 11u
44
+ ··· − 398u − 26
c
8
, c
11
u
45
+ 2u
44
+ ··· − 3u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
45
− 18y
44
+ ··· + 1884y −100
c
2
y
45
+ 18y
44
+ ··· + 438256y −10000
c
3
, c
6
y
45
+ 33y
44
+ ··· − 36y −1
c
4
, c
9
y
45
− 7y
44
+ ··· + 20y −1
c
7
, c
10
y
45
+ 23y
44
+ ··· + 14052y −676
c
8
, c
11
y
45
+ 14y
44
+ ··· − 123y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.901122 + 0.391026I
a = −2.22398 − 0.09634I
b = −0.507989 − 0.720972I
−4.13007 + 2.02494I 0. − 5.73901I
u = −0.901122 − 0.391026I
a = −2.22398 + 0.09634I
b = −0.507989 + 0.720972I
−4.13007 − 2.02494I 0. + 5.73901I
u = −0.576298 + 0.870424I
a = −0.93549 + 1.15916I
b = −1.09116 + 1.03701I
2.66346 − 6.40405I 5.00000 + 4.59149I
u = −0.576298 − 0.870424I
a = −0.93549 − 1.15916I
b = −1.09116 − 1.03701I
2.66346 + 6.40405I 5.00000 − 4.59149I
u = −0.848723 + 0.610214I
a = −2.00602 + 1.35310I
b = −1.58039 − 0.17618I
3.17854 + 2.40398I 17.2523 − 3.9170I
u = −0.848723 − 0.610214I
a = −2.00602 − 1.35310I
b = −1.58039 + 0.17618I
3.17854 − 2.40398I 17.2523 + 3.9170I
u = 0.801098 + 0.511169I
a = −0.632677 − 0.499625I
b = 0.08297 + 1.43190I
−2.91066 − 1.58558I 0.87322 + 3.50523I
u = 0.801098 − 0.511169I
a = −0.632677 + 0.499625I
b = 0.08297 − 1.43190I
−2.91066 + 1.58558I 0.87322 − 3.50523I
u = 0.913441 + 0.533170I
a = 0.586441 + 0.383102I
b = −0.28087 − 1.44457I
−3.30005 − 2.64955I 0
u = 0.913441 − 0.533170I
a = 0.586441 − 0.383102I
b = −0.28087 + 1.44457I
−3.30005 + 2.64955I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.523749 + 0.936187I
a = 0.920068 − 0.987167I
b = 1.07979 − 1.07052I
−0.63452 − 12.54830I 5.00000 + 6.69848I
u = −0.523749 − 0.936187I
a = 0.920068 + 0.987167I
b = 1.07979 + 1.07052I
−0.63452 + 12.54830I 5.00000 − 6.69848I
u = −0.238075 + 0.894367I
a = −0.175446 − 0.518756I
b = −0.415208 − 0.426850I
1.09089 + 2.34622I 6.24165 − 8.56728I
u = −0.238075 − 0.894367I
a = −0.175446 + 0.518756I
b = −0.415208 + 0.426850I
1.09089 − 2.34622I 6.24165 + 8.56728I
u = −0.960767 + 0.492160I
a = 1.083620 − 0.193384I
b = 0.391029 + 0.437334I
−1.62646 + 1.74137I 0
u = −0.960767 − 0.492160I
a = 1.083620 + 0.193384I
b = 0.391029 − 0.437334I
−1.62646 − 1.74137I 0
u = 1.086040 + 0.097856I
a = −0.337473 − 0.512143I
b = 0.602346 + 1.260120I
−8.25548 + 0.14518I −5.86924 + 0.I
u = 1.086040 − 0.097856I
a = −0.337473 + 0.512143I
b = 0.602346 − 1.260120I
−8.25548 − 0.14518I −5.86924 + 0.I
u = 0.675748 + 0.600812I
a = 0.487260 + 0.009850I
b = −0.361960 − 0.696002I
1.72135 + 0.10542I 9.89084 − 0.57623I
u = 0.675748 − 0.600812I
a = 0.487260 − 0.009850I
b = −0.361960 + 0.696002I
1.72135 − 0.10542I 9.89084 + 0.57623I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960223 + 0.625182I
a = −0.287488 − 0.184192I
b = 0.092459 + 0.799602I
0.86875 − 4.99777I 0
u = 0.960223 − 0.625182I
a = −0.287488 + 0.184192I
b = 0.092459 − 0.799602I
0.86875 + 4.99777I 0
u = 1.155300 + 0.090732I
a = 0.136153 − 0.470997I
b = −0.479381 + 1.128020I
−3.98808 − 5.11963I 0
u = 1.155300 − 0.090732I
a = 0.136153 + 0.470997I
b = −0.479381 − 1.128020I
−3.98808 + 5.11963I 0
u = −0.503146 + 0.661088I
a = 1.36514 − 1.24377I
b = 0.943060 − 0.848825I
−3.52213 − 1.72391I 1.61111 + 1.48880I
u = −0.503146 − 0.661088I
a = 1.36514 + 1.24377I
b = 0.943060 + 0.848825I
−3.52213 + 1.72391I 1.61111 − 1.48880I
u = −0.464268 + 1.091500I
a = 0.334880 + 0.281474I
b = 0.504214 + 0.379227I
−1.04118 + 7.01442I 0
u = −0.464268 − 1.091500I
a = 0.334880 − 0.281474I
b = 0.504214 − 0.379227I
−1.04118 − 7.01442I 0
u = −0.887945 + 0.799772I
a = 0.877042 + 0.320791I
b = 0.449189 + 0.781343I
−1.90231 + 0.74732I 0
u = −0.887945 − 0.799772I
a = 0.877042 − 0.320791I
b = 0.449189 − 0.781343I
−1.90231 − 0.74732I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036610 + 0.611989I
a = 2.03296 − 0.73494I
b = 1.16696 + 1.08790I
−5.03326 + 6.70507I 0
u = −1.036610 − 0.611989I
a = 2.03296 + 0.73494I
b = 1.16696 − 1.08790I
−5.03326 − 6.70507I 0
u = −1.077580 + 0.695430I
a = −1.83741 + 0.52861I
b = −1.15966 − 1.26459I
1.13119 + 12.21450I 0
u = −1.077580 − 0.695430I
a = −1.83741 − 0.52861I
b = −1.15966 + 1.26459I
1.13119 − 12.21450I 0
u = 1.283260 + 0.065802I
a = −0.167563 + 0.367408I
b = 0.576462 − 1.035600I
−7.63721 − 10.29470I 0
u = 1.283260 − 0.065802I
a = −0.167563 − 0.367408I
b = 0.576462 + 1.035600I
−7.63721 + 10.29470I 0
u = −1.121770 + 0.698957I
a = 1.70890 − 0.60391I
b = 1.12635 + 1.27279I
−2.4765 + 18.5384I 0
u = −1.121770 − 0.698957I
a = 1.70890 + 0.60391I
b = 1.12635 − 1.27279I
−2.4765 − 18.5384I 0
u = −1.046500 + 0.828865I
a = −0.567749 − 0.408140I
b = 0.007330 − 0.774890I
−2.28132 + 5.64431I 0
u = −1.046500 − 0.828865I
a = −0.567749 + 0.408140I
b = 0.007330 + 0.774890I
−2.28132 − 5.64431I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.317060 + 0.458673I
a = −0.374157 + 0.197877I
b = −0.070789 − 0.321439I
−4.37062 − 0.52471I 0
u = −1.317060 − 0.458673I
a = −0.374157 − 0.197877I
b = −0.070789 + 0.321439I
−4.37062 + 0.52471I 0
u = −0.554028 + 0.236204I
a = 1.09200 + 1.81024I
b = 0.284535 + 0.576144I
−3.33768 + 0.83512I 2.33619 − 3.83248I
u = −0.554028 − 0.236204I
a = 1.09200 − 1.81024I
b = 0.284535 − 0.576144I
−3.33768 − 0.83512I 2.33619 + 3.83248I
u = 0.365045
a = 1.44199
b = −0.718548
1.11526 5.80750
9
II. I
u
2
= h9u
29
− 22u
28
+ · · · + 2b + 15, −15u
29
a + 21u
29
+ · · · − 25a +
47, u
30
− 3u
29
+ · · · + 6u − 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
9
=
a
−
9
2
u
29
+ 11u
28
+ ··· +
65
2
u −
15
2
a
10
=
−
1
2
u
29
+ u
28
+ ··· + a −
1
2
−5u
29
+ 11u
28
+ ··· + 31u − 7
a
8
=
9
2
u
29
− 11u
28
+ ··· + a +
15
2
−
9
2
u
29
+ 11u
28
+ ··· +
65
2
u −
15
2
a
4
=
3u
29
a −
1
2
u
29
+ ··· + 5a −
13
2
−
5
2
u
29
a + 6u
28
a + ··· −
7
2
a + 1
a
7
=
−u
29
a +
11
2
u
29
+ ··· −
67
2
u +
15
2
1
2
u
29
a −
1
2
u
29
+ ··· +
1
2
a +
1
2
a
11
=
−
9
2
u
29
a + 5u
29
+ ··· −
15
2
a + 8
1
a
11
=
−
9
2
u
29
a + 5u
29
+ ··· −
15
2
a + 8
1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
25u
29
−52u
28
−102u
27
+385u
26
+29u
25
−1217u
24
+842u
23
+2204u
22
−3082u
21
−2095u
20
+
6222u
19
−293u
18
−8211u
17
+4523u
16
+7118u
15
−8008u
14
−3146u
13
+8424u
12
−1074u
11
−
5710u
10
+3096u
9
+2146u
8
−2516u
7
+20u
6
+1054u
5
−509u
4
−102u
3
+231u
2
−129u +29
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
30
− 3u
29
+ ··· + 6u − 1)
2
c
2
(u
30
+ 13u
29
+ ··· + 8u + 1)
2
c
3
, c
6
u
60
+ 7u
59
+ ··· + 2u
2
+ 2
c
4
, c
9
u
60
− u
59
+ ··· + 64u + 94
c
7
, c
10
(u
30
− 9u
29
+ ··· − 14u + 1)
2
c
8
, c
11
u
60
+ 9u
59
+ ··· + 16u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
30
− 13y
29
+ ··· − 8y + 1)
2
c
2
(y
30
+ 11y
29
+ ··· − 52y + 1)
2
c
3
, c
6
y
60
− 7y
59
+ ··· + 8y + 4
c
4
, c
9
y
60
+ y
59
+ ··· − 322944y + 8836
c
7
, c
10
(y
30
+ 19y
29
+ ··· − 76y + 1)
2
c
8
, c
11
y
60
− 21y
59
+ ··· + 26y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465809 + 0.917860I
a = −0.989163 − 0.559689I
b = −1.128460 − 0.357199I
2.56109 + 3.64354I 6.72804 − 6.05682I
u = 0.465809 + 0.917860I
a = 0.752661 + 0.348017I
b = 0.715413 + 0.742706I
2.56109 + 3.64354I 6.72804 − 6.05682I
u = 0.465809 − 0.917860I
a = −0.989163 + 0.559689I
b = −1.128460 + 0.357199I
2.56109 − 3.64354I 6.72804 + 6.05682I
u = 0.465809 − 0.917860I
a = 0.752661 − 0.348017I
b = 0.715413 − 0.742706I
2.56109 − 3.64354I 6.72804 + 6.05682I
u = 0.558834 + 0.876988I
a = 0.968989 + 0.487384I
b = 0.838815 + 0.150681I
3.22316 + 0.83801I 8.60335 + 3.08812I
u = 0.558834 + 0.876988I
a = −0.669745 − 0.519770I
b = −0.929490 − 0.703123I
3.22316 + 0.83801I 8.60335 + 3.08812I
u = 0.558834 − 0.876988I
a = 0.968989 − 0.487384I
b = 0.838815 − 0.150681I
3.22316 − 0.83801I 8.60335 − 3.08812I
u = 0.558834 − 0.876988I
a = −0.669745 + 0.519770I
b = −0.929490 + 0.703123I
3.22316 − 0.83801I 8.60335 − 3.08812I
u = −0.847173 + 0.604187I
a = −1.63142 + 1.20812I
b = −1.55381 + 0.24780I
3.14397 + 2.38497I 13.36478 − 4.30077I
u = −0.847173 + 0.604187I
a = −2.00619 + 1.33601I
b = −1.312340 − 0.515721I
3.14397 + 2.38497I 13.36478 − 4.30077I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847173 − 0.604187I
a = −1.63142 − 1.20812I
b = −1.55381 − 0.24780I
3.14397 − 2.38497I 13.36478 + 4.30077I
u = −0.847173 − 0.604187I
a = −2.00619 − 1.33601I
b = −1.312340 + 0.515721I
3.14397 − 2.38497I 13.36478 + 4.30077I
u = −0.745543 + 0.602909I
a = 1.51667 − 0.00542I
b = 0.884770 − 0.652787I
−0.67785 − 3.97386I 7.94279 + 4.15081I
u = −0.745543 + 0.602909I
a = 2.27309 − 0.86759I
b = 1.47023 + 1.29190I
−0.67785 − 3.97386I 7.94279 + 4.15081I
u = −0.745543 − 0.602909I
a = 1.51667 + 0.00542I
b = 0.884770 + 0.652787I
−0.67785 + 3.97386I 7.94279 − 4.15081I
u = −0.745543 − 0.602909I
a = 2.27309 + 0.86759I
b = 1.47023 − 1.29190I
−0.67785 + 3.97386I 7.94279 − 4.15081I
u = 0.713795 + 0.638334I
a = 0.029316 − 1.007750I
b = −0.94994 − 1.09157I
1.88688 + 0.24232I 9.09491 − 2.16089I
u = 0.713795 + 0.638334I
a = 0.835125 + 0.889030I
b = 0.060739 − 0.151129I
1.88688 + 0.24232I 9.09491 − 2.16089I
u = 0.713795 − 0.638334I
a = 0.029316 + 1.007750I
b = −0.94994 + 1.09157I
1.88688 − 0.24232I 9.09491 + 2.16089I
u = 0.713795 − 0.638334I
a = 0.835125 − 0.889030I
b = 0.060739 + 0.151129I
1.88688 − 0.24232I 9.09491 + 2.16089I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.08167
a = 0.611909 + 0.400488I
b = −0.054055 − 0.901769I
−3.22581 2.05120
u = −1.08167
a = 0.611909 − 0.400488I
b = −0.054055 + 0.901769I
−3.22581 2.05120
u = −0.925201 + 0.599544I
a = 0.61119 − 1.65490I
b = 1.98046 − 1.05095I
−1.23358 + 8.73775I 5.61249 − 11.31082I
u = −0.925201 + 0.599544I
a = 1.59922 − 1.72063I
b = 0.688071 + 0.730989I
−1.23358 + 8.73775I 5.61249 − 11.31082I
u = −0.925201 − 0.599544I
a = 0.61119 + 1.65490I
b = 1.98046 + 1.05095I
−1.23358 − 8.73775I 5.61249 + 11.31082I
u = −0.925201 − 0.599544I
a = 1.59922 + 1.72063I
b = 0.688071 − 0.730989I
−1.23358 − 8.73775I 5.61249 + 11.31082I
u = 0.924590 + 0.653430I
a = 1.005020 − 0.317199I
b = 0.498803 + 0.002851I
1.26794 − 5.30680I 7.85803 + 7.71597I
u = 0.924590 + 0.653430I
a = −1.49774 − 0.11122I
b = −0.63001 + 1.49389I
1.26794 − 5.30680I 7.85803 + 7.71597I
u = 0.924590 − 0.653430I
a = 1.005020 + 0.317199I
b = 0.498803 − 0.002851I
1.26794 + 5.30680I 7.85803 − 7.71597I
u = 0.924590 − 0.653430I
a = −1.49774 + 0.11122I
b = −0.63001 − 1.49389I
1.26794 + 5.30680I 7.85803 − 7.71597I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.124040 + 0.295901I
a = −0.767708 − 0.518887I
b = 0.756590 − 1.163210I
−6.35917 − 1.51698I −5.73393 + 4.15289I
u = −1.124040 + 0.295901I
a = −0.132232 − 1.158150I
b = −0.090567 + 0.917835I
−6.35917 − 1.51698I −5.73393 + 4.15289I
u = −1.124040 − 0.295901I
a = −0.767708 + 0.518887I
b = 0.756590 + 1.163210I
−6.35917 + 1.51698I −5.73393 − 4.15289I
u = −1.124040 − 0.295901I
a = −0.132232 + 1.158150I
b = −0.090567 − 0.917835I
−6.35917 + 1.51698I −5.73393 − 4.15289I
u = 1.038780 + 0.527286I
a = −1.95032 − 0.50890I
b = −0.239703 + 0.469994I
−4.86450 − 8.50956I −3.55516 + 9.18354I
u = 1.038780 + 0.527286I
a = 1.75849 + 1.10412I
b = 1.55854 − 1.25381I
−4.86450 − 8.50956I −3.55516 + 9.18354I
u = 1.038780 − 0.527286I
a = −1.95032 + 0.50890I
b = −0.239703 − 0.469994I
−4.86450 + 8.50956I −3.55516 − 9.18354I
u = 1.038780 − 0.527286I
a = 1.75849 − 1.10412I
b = 1.55854 + 1.25381I
−4.86450 + 8.50956I −3.55516 − 9.18354I
u = 0.732793 + 0.306914I
a = 1.20279 + 1.71252I
b = 1.76689 + 0.33137I
−3.29232 + 4.72419I −2.23057 − 5.99691I
u = 0.732793 + 0.306914I
a = −2.56826 − 1.14965I
b = 0.264277 + 0.040198I
−3.29232 + 4.72419I −2.23057 − 5.99691I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.732793 − 0.306914I
a = 1.20279 − 1.71252I
b = 1.76689 − 0.33137I
−3.29232 − 4.72419I −2.23057 + 5.99691I
u = 0.732793 − 0.306914I
a = −2.56826 + 1.14965I
b = 0.264277 − 0.040198I
−3.29232 − 4.72419I −2.23057 + 5.99691I
u = 1.079960 + 0.689143I
a = 1.130380 + 0.499207I
b = 0.937068 − 0.464969I
1.63470 − 6.63134I 6.37041 + 2.21697I
u = 1.079960 + 0.689143I
a = −1.29810 − 0.61868I
b = −0.900147 + 1.041850I
1.63470 − 6.63134I 6.37041 + 2.21697I
u = 1.079960 − 0.689143I
a = 1.130380 − 0.499207I
b = 0.937068 + 0.464969I
1.63470 + 6.63134I 6.37041 − 2.21697I
u = 1.079960 − 0.689143I
a = −1.29810 + 0.61868I
b = −0.900147 − 1.041850I
1.63470 + 6.63134I 6.37041 − 2.21697I
u = −1.282760 + 0.075226I
a = 0.017934 + 0.588411I
b = 0.166675 − 0.656060I
−3.74409 − 0.89949I 6.49053 + 7.17366I
u = −1.282760 + 0.075226I
a = 0.226648 + 0.251346I
b = −0.352903 + 0.385022I
−3.74409 − 0.89949I 6.49053 + 7.17366I
u = −1.282760 − 0.075226I
a = 0.017934 − 0.588411I
b = 0.166675 + 0.656060I
−3.74409 + 0.89949I 6.49053 − 7.17366I
u = −1.282760 − 0.075226I
a = 0.226648 − 0.251346I
b = −0.352903 − 0.385022I
−3.74409 + 0.89949I 6.49053 − 7.17366I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.137130 + 0.675479I
a = −1.090570 − 0.732508I
b = −1.218040 + 0.657607I
0.51955 − 9.49431I 3.22449 + 10.41133I
u = 1.137130 + 0.675479I
a = 1.28316 + 0.67182I
b = 0.703634 − 0.963772I
0.51955 − 9.49431I 3.22449 + 10.41133I
u = 1.137130 − 0.675479I
a = −1.090570 + 0.732508I
b = −1.218040 − 0.657607I
0.51955 + 9.49431I 3.22449 − 10.41133I
u = 1.137130 − 0.675479I
a = 1.28316 − 0.67182I
b = 0.703634 + 0.963772I
0.51955 + 9.49431I 3.22449 − 10.41133I
u = 0.119467 + 0.501758I
a = −1.45451 + 0.75312I
b = 0.234328 − 0.691794I
−2.87297 + 4.49922I 1.43690 − 3.81618I
u = 0.119467 + 0.501758I
a = 1.75119 + 1.39246I
b = 1.134470 + 0.760585I
−2.87297 + 4.49922I 1.43690 − 3.81618I
u = 0.119467 − 0.501758I
a = −1.45451 − 0.75312I
b = 0.234328 + 0.691794I
−2.87297 − 4.49922I 1.43690 + 3.81618I
u = 0.119467 − 0.501758I
a = 1.75119 − 1.39246I
b = 1.134470 − 0.760585I
−2.87297 − 4.49922I 1.43690 + 3.81618I
u = 0.388799
a = 1.48217 + 0.72234I
b = −0.800318 + 0.171653I
1.10095 3.53460
u = 0.388799
a = 1.48217 − 0.72234I
b = −0.800318 − 0.171653I
1.10095 3.53460
18
III. I
u
3
= h−10u
15
+ 19u
14
+ · · · + b + 11, −33u
15
+ 77u
14
+ · · · + 2a +
60, u
16
− 3u
15
+ · · · − 4u + 2i
(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
9
=
33
2
u
15
−
77
2
u
14
+ ··· +
91
2
u − 30
10u
15
− 19u
14
+ ··· + 25u − 11
a
10
=
19
2
u
15
−
47
2
u
14
+ ··· +
55
2
u − 20
6u
15
− 12u
14
+ ··· + 16u − 7
a
8
=
13
2
u
15
−
39
2
u
14
+ ··· +
41
2
u − 19
10u
15
− 19u
14
+ ··· + 25u − 11
a
4
=
11
2
u
15
−
23
2
u
14
+ ··· +
29
2
u − 10
u
15
− 2u
14
+ ··· + 3u − 1
a
7
=
−
13
2
u
15
+
35
2
u
14
+ ··· −
33
2
u + 22
−4u
15
+ 9u
14
+ ··· − 10u + 9
a
11
=
3
2
u
15
−
9
2
u
14
+ ··· +
5
2
u − 5
2u
15
− 4u
14
+ ··· + 5u − 3
a
11
=
3
2
u
15
−
9
2
u
14
+ ··· +
5
2
u − 5
2u
15
− 4u
14
+ ··· + 5u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 19u
15
− 35u
14
− 36u
13
+ 134u
12
− 27u
11
− 175u
10
+ 112u
9
+
138u
8
− 122u
7
− 150u
6
+ 223u
5
+ 17u
4
− 127u
3
+ 17u
2
+ 48u − 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 3u
15
+ ··· + 4u + 2
c
2
u
16
+ 7u
15
+ ··· + 20u + 4
c
3
, c
6
u
16
+ u
15
+ ··· − u + 1
c
4
, c
9
u
16
− u
15
+ ··· + u + 1
c
5
u
16
− 3u
15
+ ··· − 4u + 2
c
7
u
16
+ 8u
15
+ ··· + 8u + 2
c
8
, c
11
u
16
− 2u
15
+ ··· + u + 1
c
10
u
16
− 8u
15
+ ··· − 8u + 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
− 7y
15
+ ··· − 20y + 4
c
2
y
16
+ 5y
15
+ ··· + 152y + 16
c
3
, c
6
y
16
− 3y
15
+ ··· + 7y + 1
c
4
, c
9
y
16
+ 5y
15
+ ··· + 3y + 1
c
7
, c
10
y
16
+ 6y
15
+ ··· + 60y + 4
c
8
, c
11
y
16
− 14y
15
+ ··· − 3y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689293 + 0.763114I
a = −0.200102 − 0.255774I
b = 0.580738 − 0.214333I
−1.38765 + 6.29654I 2.79421 − 6.76591I
u = −0.689293 − 0.763114I
a = −0.200102 + 0.255774I
b = 0.580738 + 0.214333I
−1.38765 − 6.29654I 2.79421 + 6.76591I
u = 0.473849 + 0.927712I
a = −0.723983 − 0.407509I
b = −0.783823 − 0.487449I
3.03599 + 2.03669I 8.11091 − 4.27164I
u = 0.473849 − 0.927712I
a = −0.723983 + 0.407509I
b = −0.783823 + 0.487449I
3.03599 − 2.03669I 8.11091 + 4.27164I
u = 0.852260 + 0.603148I
a = −2.18456 − 1.53912I
b = −1.72380 + 0.17458I
2.86661 − 2.38019I −8.79056 + 1.99021I
u = 0.852260 − 0.603148I
a = −2.18456 + 1.53912I
b = −1.72380 − 0.17458I
2.86661 + 2.38019I −8.79056 − 1.99021I
u = 1.005380 + 0.533825I
a = 1.61565 + 1.42534I
b = 1.220740 − 0.473289I
−3.32457 − 8.40901I 2.63588 + 9.00013I
u = 1.005380 − 0.533825I
a = 1.61565 − 1.42534I
b = 1.220740 + 0.473289I
−3.32457 + 8.40901I 2.63588 − 9.00013I
u = 0.715961 + 0.473787I
a = 2.39912 + 1.28920I
b = 1.290250 + 0.060612I
−2.29078 + 4.25970I 4.83496 − 2.62787I
u = 0.715961 − 0.473787I
a = 2.39912 − 1.28920I
b = 1.290250 − 0.060612I
−2.29078 − 4.25970I 4.83496 + 2.62787I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626207 + 0.332321I
a = 0.808873 + 0.220135I
b = −0.899157 + 0.405601I
1.184990 + 0.634317I 3.24186 − 9.95937I
u = −0.626207 − 0.332321I
a = 0.808873 − 0.220135I
b = −0.899157 − 0.405601I
1.184990 − 0.634317I 3.24186 + 9.95937I
u = 1.127500 + 0.689959I
a = −1.129520 − 0.528510I
b = −0.832964 + 0.802424I
1.07036 − 7.95714I 3.97297 + 7.06689I
u = 1.127500 − 0.689959I
a = −1.129520 + 0.528510I
b = −0.832964 − 0.802424I
1.07036 + 7.95714I 3.97297 − 7.06689I
u = −1.359450 + 0.241171I
a = −0.085477 + 0.135112I
b = 0.148019 − 0.502182I
−4.44482 − 0.90663I −9.80023 + 8.74691I
u = −1.359450 − 0.241171I
a = −0.085477 − 0.135112I
b = 0.148019 + 0.502182I
−4.44482 + 0.90663I −9.80023 − 8.74691I
23
IV. I
u
4
= hb + a + 1, a
2
+ 2a + 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
9
=
a
−a − 1
a
10
=
a − 1
−a
a
8
=
2a + 1
−a − 1
a
4
=
−3a − 3
a + 1
a
7
=
−2
1
a
11
=
−a − 3
1
a
11
=
−a − 3
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
4
u
2
+ 2u + 2
c
6
, c
7
, c
8
c
10
, c
11
u
2
+ 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
(y −1)
2
c
3
, c
4
y
2
+ 4
c
6
, c
7
, c
8
c
10
, c
11
(y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000 + 1.00000I
b = − 1.000000I
−4.93480 −4.00000
u = −1.00000
a = −1.00000 − 1.00000I
b = 1.000000I
−4.93480 −4.00000
27
V. I
u
5
= hb
2
+ 1, a − 1, 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
9
=
1
b
a
10
=
b + 2
−1
a
8
=
−b + 1
b
a
4
=
−b + 2
b − 1
a
7
=
−3b + 2
2b
a
11
=
−b − 1
1
a
11
=
−b − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
7
, c
8
c
10
, c
11
u
2
+ 1
c
6
, c
9
u
2
+ 2u + 2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y −1)
2
c
3
, c
7
, c
8
c
10
, c
11
(y + 1)
2
c
6
, c
9
y
2
+ 4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 1.000000I
−4.93480 −4.00000
u = −1.00000
a = 1.00000
b = − 1.000000I
−4.93480 −4.00000
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
16
+ 3u
15
+ ··· + 4u + 2)(u
30
− 3u
29
+ ··· + 6u − 1)
2
· (u
45
+ 10u
44
+ ··· − 62u − 10)
c
2
((u + 1)
4
)(u
16
+ 7u
15
+ ··· + 20u + 4)(u
30
+ 13u
29
+ ··· + 8u + 1)
2
· (u
45
+ 18u
44
+ ··· + 1884u + 100)
c
3
, c
6
(u
2
+ 1)(u
2
+ 2u + 2)(u
16
+ u
15
+ ··· − u + 1)(u
45
+ 3u
44
+ ··· + 6u − 1)
· (u
60
+ 7u
59
+ ··· + 2u
2
+ 2)
c
4
, c
9
((u − 1)
2
)(u
2
+ 2u + 2)(u
16
− u
15
+ ··· + u + 1)(u
45
− u
44
+ ··· + 8u − 1)
· (u
60
− u
59
+ ··· + 64u + 94)
c
5
((u + 1)
4
)(u
16
− 3u
15
+ ··· − 4u + 2)(u
30
− 3u
29
+ ··· + 6u − 1)
2
· (u
45
+ 10u
44
+ ··· − 62u − 10)
c
7
((u
2
+ 1)
2
)(u
16
+ 8u
15
+ ··· + 8u + 2)(u
30
− 9u
29
+ ··· − 14u + 1)
2
· (u
45
+ 11u
44
+ ··· − 398u − 26)
c
8
, c
11
((u
2
+ 1)
2
)(u
16
− 2u
15
+ ··· + u + 1)(u
45
+ 2u
44
+ ··· − 3u − 2)
· (u
60
+ 9u
59
+ ··· + 16u + 1)
c
10
((u
2
+ 1)
2
)(u
16
− 8u
15
+ ··· − 8u + 2)(u
30
− 9u
29
+ ··· − 14u + 1)
2
· (u
45
+ 11u
44
+ ··· − 398u − 26)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y −1)
4
)(y
16
− 7y
15
+ ··· − 20y + 4)(y
30
− 13y
29
+ ··· − 8y + 1)
2
· (y
45
− 18y
44
+ ··· + 1884y −100)
c
2
((y −1)
4
)(y
16
+ 5y
15
+ ··· + 152y + 16)
· (y
30
+ 11y
29
+ ··· − 52y + 1)
2
· (y
45
+ 18y
44
+ ··· + 438256y −10000)
c
3
, c
6
((y + 1)
2
)(y
2
+ 4)(y
16
− 3y
15
+ ··· + 7y + 1)(y
45
+ 33y
44
+ ··· − 36y −1)
· (y
60
− 7y
59
+ ··· + 8y + 4)
c
4
, c
9
((y −1)
2
)(y
2
+ 4)(y
16
+ 5y
15
+ ··· + 3y + 1)(y
45
− 7y
44
+ ··· + 20y −1)
· (y
60
+ y
59
+ ··· − 322944y + 8836)
c
7
, c
10
((y + 1)
4
)(y
16
+ 6y
15
+ ··· + 60y + 4)(y
30
+ 19y
29
+ ··· − 76y + 1)
2
· (y
45
+ 23y
44
+ ··· + 14052y −676)
c
8
, c
11
((y + 1)
4
)(y
16
− 14y
15
+ ··· − 3y + 1)(y
45
+ 14y
44
+ ··· − 123y −4)
· (y
60
− 21y
59
+ ··· + 26y + 1)
33
