12n
0754
(K12n
0754
)
A knot diagram
1
Linearized knot diagam
4 6 8 10 3 10 2 12 1 6 5 9
Solving Sequence
6,10
7
3,11
2 8 5 12 4 1 9
c
6
c
10
c
2
c
7
c
5
c
11
c
4
c
1
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.68814 × 10
39
u
31
+ 4.43259 × 10
39
u
30
+ ··· + 1.03715 × 10
39
b + 8.81961 × 10
39
,
− 2.68814 × 10
39
u
31
− 4.43259 × 10
39
u
30
+ ··· + 1.03715 × 10
39
a − 9.85676 × 10
39
, u
32
+ 2u
31
+ ··· + 3u + 1i
I
u
2
= h−9.65086 × 10
81
u
35
− 1.35252 × 10
82
u
34
+ ··· + 5.32581 × 10
85
b + 4.57159 × 10
85
,
− 7.17774 × 10
84
u
35
− 2.27336 × 10
85
u
34
+ ··· + 7.05055 × 10
87
a + 1.28066 × 10
88
,
u
36
+ 2u
35
+ ··· − 345u + 1721i
I
u
3
= h−588u
14
− 1117u
13
+ ··· + 1513b + 3572, 588u
14
+ 1117u
13
+ ··· + 1513a − 2059,
u
15
+ 3u
14
+ 3u
13
− 7u
11
− 16u
10
− 14u
9
+ 2u
8
+ 26u
7
+ 50u
6
+ 59u
5
+ 48u
4
+ 30u
3
+ 13u
2
+ 4u + 1i
I
u
4
= hb, a − 1, u − 1i
I
u
5
= hb, a − u − 2, u
2
+ u − 1i
* 5 irreducible components of dim
C
= 0, with total 86 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
= h2.69×10
39
u
31
+4.43×10
39
u
30
+· · ·+1.04×10
39
b+8.82×10
39
, −2.69×
10
39
u
31
−4.43×10
39
u
30
+· · ·+1.04×10
39
a−9.86×10
39
, u
32
+2u
31
+· · ·+3u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
2.59186u
31
+ 4.27384u
30
+ ··· + 0.0225842u + 9.50373
−2.59186u
31
− 4.27384u
30
+ ··· − 0.0225842u − 8.50373
a
11
=
−u
u
a
2
=
1
−2.59186u
31
− 4.27384u
30
+ ··· − 0.0225842u − 8.50373
a
8
=
−2.59186u
31
− 4.27384u
30
+ ··· − 0.0225842u − 7.50373
0.934704u
31
+ 1.45438u
30
+ ··· + 1.23689u + 2.26933
a
5
=
3.21748u
31
+ 5.20620u
30
+ ··· + 1.12168u + 10.8632
−0.625617u
31
− 0.932359u
30
+ ··· − 1.09909u − 1.35945
a
12
=
−0.835399u
31
− 1.31731u
30
+ ··· − 0.385321u − 1.44477
−1.30325u
31
− 2.20760u
30
+ ··· + 2.32421u − 4.36458
a
4
=
3.21748u
31
+ 5.20620u
30
+ ··· + 1.12168u + 10.8632
−0.182315u
31
− 0.176177u
30
+ ··· − 0.630287u − 0.130685
a
1
=
1.47940u
31
+ 2.41530u
30
+ ··· − 0.101041u + 4.07523
0.504058u
31
+ 0.994655u
30
+ ··· − 0.583979u + 1.83194
a
9
=
−1.16297u
31
− 1.83866u
30
+ ··· − 0.347165u − 4.48853
0.540348u
31
+ 0.679881u
30
+ ··· + 0.438800u + 2.01562
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.53130u
31
+ 14.3893u
30
+ ··· + 9.88172u + 20.4373
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
32
− 2u
30
+ ··· + 6u
2
+ 1
c
2
, c
5
u
32
− 9u
31
+ ··· − 12u + 9
c
4
u
32
− 2u
31
+ ··· + 22u + 4
c
6
, c
10
u
32
− 2u
31
+ ··· − 3u + 1
c
7
u
32
+ 31u
31
+ ··· + 1966080u + 131072
c
8
, c
9
, c
12
u
32
− 10u
31
+ ··· + 24u + 9
c
11
u
32
− 2u
31
+ ··· − 926u + 233
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
32
− 4y
31
+ ··· + 12y + 1
c
2
, c
5
y
32
+ 13y
31
+ ··· − 630y + 81
c
4
y
32
+ 2y
31
+ ··· − 188y + 16
c
6
, c
10
y
32
− 40y
31
+ ··· − 11y + 1
c
7
y
32
+ 3y
31
+ ··· − 51539607552y + 17179869184
c
8
, c
9
, c
12
y
32
− 34y
31
+ ··· + 1260y + 81
c
11
y
32
+ 30y
31
+ ··· + 118794y + 54289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727787 + 0.359428I
a = 1.50645 + 0.30685I
b = −0.506447 − 0.306846I
3.01151 − 0.12453I 2.01930 − 0.65952I
u = −0.727787 − 0.359428I
a = 1.50645 − 0.30685I
b = −0.506447 + 0.306846I
3.01151 + 0.12453I 2.01930 + 0.65952I
u = −1.088820 + 0.491186I
a = 0.429547 + 0.223085I
b = 0.570453 − 0.223085I
2.15764 − 0.43132I 3.87708 + 2.50521I
u = −1.088820 − 0.491186I
a = 0.429547 − 0.223085I
b = 0.570453 + 0.223085I
2.15764 + 0.43132I 3.87708 − 2.50521I
u = 0.123243 + 0.684919I
a = 1.074160 + 0.889657I
b = −0.074156 − 0.889657I
1.24572 − 1.59798I −0.69901 + 4.34280I
u = 0.123243 − 0.684919I
a = 1.074160 − 0.889657I
b = −0.074156 + 0.889657I
1.24572 + 1.59798I −0.69901 − 4.34280I
u = −0.181903 + 0.562687I
a = 1.76402 − 0.20287I
b = −0.764020 + 0.202871I
3.20927 + 1.51045I 1.61636 − 4.36798I
u = −0.181903 − 0.562687I
a = 1.76402 + 0.20287I
b = −0.764020 − 0.202871I
3.20927 − 1.51045I 1.61636 + 4.36798I
u = 0.570063 + 0.113911I
a = 1.10156 − 1.54628I
b = −0.10156 + 1.54628I
9.84884 + 5.18562I 1.41138 − 2.71485I
u = 0.570063 − 0.113911I
a = 1.10156 + 1.54628I
b = −0.10156 − 1.54628I
9.84884 − 5.18562I 1.41138 + 2.71485I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097390 + 0.483297I
a = 1.44762 − 1.17049I
b = −0.447624 + 1.170490I
5.83833 + 4.06602I 6.43607 − 3.22823I
u = 0.097390 − 0.483297I
a = 1.44762 + 1.17049I
b = −0.447624 − 1.170490I
5.83833 − 4.06602I 6.43607 + 3.22823I
u = −1.30092 + 0.76651I
a = 0.565351 − 1.100220I
b = 0.434649 + 1.100220I
4.66242 − 4.30535I 0
u = −1.30092 − 0.76651I
a = 0.565351 + 1.100220I
b = 0.434649 − 1.100220I
4.66242 + 4.30535I 0
u = −1.58301 + 0.10612I
a = −0.040653 − 0.769050I
b = 1.040650 + 0.769050I
−5.78170 + 5.02185I 0
u = −1.58301 − 0.10612I
a = −0.040653 + 0.769050I
b = 1.040650 − 0.769050I
−5.78170 − 5.02185I 0
u = 1.59789 + 0.07572I
a = 0.152087 + 0.822987I
b = 0.847913 − 0.822987I
−4.90783 − 0.17419I 0
u = 1.59789 − 0.07572I
a = 0.152087 − 0.822987I
b = 0.847913 + 0.822987I
−4.90783 + 0.17419I 0
u = 1.59468 + 0.12683I
a = −0.176743 + 0.703049I
b = 1.176740 − 0.703049I
0.33699 − 8.78781I 0
u = 1.59468 − 0.12683I
a = −0.176743 − 0.703049I
b = 1.176740 + 0.703049I
0.33699 + 8.78781I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.224964 + 0.303301I
a = 1.60702 + 0.01432I
b = −0.607019 − 0.014324I
−1.277390 − 0.391091I −8.45483 + 1.44760I
u = 0.224964 − 0.303301I
a = 1.60702 − 0.01432I
b = −0.607019 + 0.014324I
−1.277390 + 0.391091I −8.45483 − 1.44760I
u = −0.329013 + 0.018023I
a = 1.16462 + 1.38080I
b = −0.164619 − 1.380800I
3.64918 − 3.45629I −10.02596 + 4.62950I
u = −0.329013 − 0.018023I
a = 1.16462 − 1.38080I
b = −0.164619 + 1.380800I
3.64918 + 3.45629I −10.02596 − 4.62950I
u = −1.74543 + 0.37989I
a = 0.439100 + 0.949102I
b = 0.560900 − 0.949102I
4.10800 + 2.16881I 0
u = −1.74543 − 0.37989I
a = 0.439100 − 0.949102I
b = 0.560900 + 0.949102I
4.10800 − 2.16881I 0
u = 1.71462 + 0.67318I
a = 0.120504 − 1.186710I
b = 0.87950 + 1.18671I
1.9107 − 16.1447I 0
u = 1.71462 − 0.67318I
a = 0.120504 + 1.186710I
b = 0.87950 − 1.18671I
1.9107 + 16.1447I 0
u = −1.72533 + 0.66821I
a = 0.136057 + 1.096830I
b = 0.863943 − 1.096830I
−4.72526 + 11.94950I 0
u = −1.72533 − 0.66821I
a = 0.136057 − 1.096830I
b = 0.863943 + 1.096830I
−4.72526 − 11.94950I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75936 + 0.67100I
a = 0.209299 − 0.991283I
b = 0.790701 + 0.991283I
−4.36968 − 6.32073I 0
u = 1.75936 − 0.67100I
a = 0.209299 + 0.991283I
b = 0.790701 − 0.991283I
−4.36968 + 6.32073I 0
8
II. I
u
2
= h−9.65 × 10
81
u
35
− 1.35 × 10
82
u
34
+ · · · + 5.33 × 10
85
b + 4.57 ×
10
85
, −7.18 × 10
84
u
35
− 2.27 × 10
85
u
34
+ · · · + 7.05 × 10
87
a + 1.28 ×
10
88
, u
36
+ 2u
35
+ · · · − 345u + 1721i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
0.00101804u
35
+ 0.00322437u
34
+ ··· − 3.03218u − 1.81639
0.000181209u
35
+ 0.000253957u
34
+ ··· − 1.69137u − 0.858384
a
11
=
−u
u
a
2
=
0.00119925u
35
+ 0.00347833u
34
+ ··· − 4.72355u − 2.67478
0.000181209u
35
+ 0.000253957u
34
+ ··· − 1.69137u − 0.858384
a
8
=
0.00119925u
35
+ 0.00347833u
34
+ ··· − 4.72355u − 1.67478
0.000181209u
35
+ 0.000253957u
34
+ ··· − 1.69137u − 0.858384
a
5
=
0.00122718u
35
+ 0.00328059u
34
+ ··· − 1.81467u + 0.516616
−0.000330064u
35
− 0.00139754u
34
+ ··· + 0.178060u + 0.705552
a
12
=
0.000158903u
35
+ 0.00143193u
34
+ ··· − 0.847012u − 2.41702
0.00166960u
35
+ 0.00517909u
34
+ ··· − 0.901484u − 2.62550
a
4
=
0.00122718u
35
+ 0.00328059u
34
+ ··· − 1.81467u + 0.516616
0.000525501u
35
+ 0.00101205u
34
+ ··· − 1.64888u − 0.716369
a
1
=
0.000933234u
35
+ 0.00308935u
34
+ ··· + 1.23389u − 4.21048
0.00191049u
35
+ 0.00584877u
34
+ ··· − 0.657755u − 3.18542
a
9
=
0.000694411u
35
+ 0.00104134u
34
+ ··· − 2.62227u + 2.26900
−0.000527487u
35
− 0.00143426u
34
+ ··· + 0.446693u + 1.57292
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00480094u
35
+ 0.0143993u
34
+ ··· − 10.3752u − 14.3937
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
36
− 3u
35
+ ··· − 26u + 1
c
2
, c
5
(u
18
+ 7u
17
+ ··· + 3u + 2)
2
c
4
u
36
+ 4u
34
+ ··· − 81u + 7
c
6
, c
10
u
36
− 2u
35
+ ··· + 345u + 1721
c
7
(u − 1)
36
c
8
, c
9
, c
12
(u
18
+ 2u
17
+ ··· + 2u + 1)
2
c
11
u
36
− 2u
35
+ ··· − 107951u + 18799
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
36
+ 13y
35
+ ··· − 238y + 1
c
2
, c
5
(y
18
+ 3y
17
+ ··· + 27y + 4)
2
c
4
y
36
+ 8y
35
+ ··· + 24785y + 49
c
6
, c
10
y
36
− 24y
35
+ ··· − 23369735y + 2961841
c
7
(y −1)
36
c
8
, c
9
, c
12
(y
18
− 18y
17
+ ··· + 6y + 1)
2
c
11
y
36
+ 20y
35
+ ··· + 3655697641y + 353402401
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.951328 + 0.265633I
a = −1.00770 + 1.00856I
b = −0.799005 − 0.432049I
−0.749045 − 0.267600I −5.91340 + 2.02101I
u = 0.951328 − 0.265633I
a = −1.00770 − 1.00856I
b = −0.799005 + 0.432049I
−0.749045 + 0.267600I −5.91340 − 2.02101I
u = −0.648013 + 0.675517I
a = 0.627478 − 0.216336I
b = 0.186015 − 0.679590I
1.71945 − 1.37809I 3.91287 − 1.41254I
u = −0.648013 − 0.675517I
a = 0.627478 + 0.216336I
b = 0.186015 + 0.679590I
1.71945 + 1.37809I 3.91287 + 1.41254I
u = 0.823523 + 0.347145I
a = −0.079307 + 0.626674I
b = 0.172943 + 0.911158I
8.82842 + 4.51784I 4.44915 − 1.04065I
u = 0.823523 − 0.347145I
a = −0.079307 − 0.626674I
b = 0.172943 − 0.911158I
8.82842 − 4.51784I 4.44915 + 1.04065I
u = 0.078059 + 1.130100I
a = 0.369477 + 1.291370I
b = 0.186015 − 0.679590I
1.71945 − 1.37809I 3.91287 − 1.41254I
u = 0.078059 − 1.130100I
a = 0.369477 − 1.291370I
b = 0.186015 + 0.679590I
1.71945 + 1.37809I 3.91287 + 1.41254I
u = −1.207030 + 0.342060I
a = −0.344195 − 1.035250I
b = −1.007410 + 0.797418I
−4.69253 + 2.67585I −11.48246 + 0.04874I
u = −1.207030 − 0.342060I
a = −0.344195 + 1.035250I
b = −1.007410 − 0.797418I
−4.69253 − 2.67585I −11.48246 − 0.04874I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.304090 + 0.242334I
a = −0.172903 + 0.923671I
b = −1.20068 − 1.01012I
−1.01052 − 4.22577I −7.20649 + 4.92260I
u = 1.304090 − 0.242334I
a = −0.172903 − 0.923671I
b = −1.20068 + 1.01012I
−1.01052 + 4.22577I −7.20649 − 4.92260I
u = 1.339670 + 0.120163I
a = −0.297280 + 0.744568I
b = −0.80875 − 1.24243I
1.72404 − 6.10285I −0.03303 + 7.78532I
u = 1.339670 − 0.120163I
a = −0.297280 − 0.744568I
b = −0.80875 + 1.24243I
1.72404 + 6.10285I −0.03303 − 7.78532I
u = −0.456738 + 1.298950I
a = −0.13350 − 1.55902I
b = 0.172943 + 0.911158I
8.82842 + 4.51784I 4.44915 − 1.04065I
u = −0.456738 − 1.298950I
a = −0.13350 + 1.55902I
b = 0.172943 − 0.911158I
8.82842 − 4.51784I 4.44915 + 1.04065I
u = −1.41435 + 0.18193I
a = −0.123524 − 0.807920I
b = −0.92905 + 1.08318I
−3.82636 + 4.39821I −4.26128 − 12.11852I
u = −1.41435 − 0.18193I
a = −0.123524 + 0.807920I
b = −0.92905 − 1.08318I
−3.82636 − 4.39821I −4.26128 + 12.11852I
u = 0.329048 + 0.415115I
a = 2.16953 + 1.12232I
b = 0.370956 + 0.584694I
1.15682 − 3.56504I −0.39209 + 9.87971I
u = 0.329048 − 0.415115I
a = 2.16953 − 1.12232I
b = 0.370956 − 0.584694I
1.15682 + 3.56504I −0.39209 − 9.87971I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43862 + 0.58080I
a = 0.039810 + 1.315730I
b = −0.92905 − 1.08318I
−3.82636 − 4.39821I −4.26128 + 12.11852I
u = 1.43862 − 0.58080I
a = 0.039810 − 1.315730I
b = −0.92905 + 1.08318I
−3.82636 + 4.39821I −4.26128 − 12.11852I
u = −0.353911 + 0.263917I
a = 1.82923 − 2.67302I
b = 0.514983 − 0.621068I
7.54180 + 7.47357I 0.42672 − 8.56588I
u = −0.353911 − 0.263917I
a = 1.82923 + 2.67302I
b = 0.514983 + 0.621068I
7.54180 − 7.47357I 0.42672 + 8.56588I
u = 0.12734 + 1.61628I
a = −0.099767 − 0.766912I
b = 0.370956 + 0.584694I
1.15682 − 3.56504I −0.39209 + 9.87971I
u = 0.12734 − 1.61628I
a = −0.099767 + 0.766912I
b = 0.370956 − 0.584694I
1.15682 + 3.56504I −0.39209 − 9.87971I
u = −1.42189 + 0.79988I
a = 0.05695 − 1.58085I
b = −0.80875 + 1.24243I
1.72404 + 6.10285I 0. − 7.78532I
u = −1.42189 − 0.79988I
a = 0.05695 + 1.58085I
b = −0.80875 − 1.24243I
1.72404 − 6.10285I 0. + 7.78532I
u = 1.71277 + 0.17526I
a = 0.289764 + 0.671140I
b = −1.007410 − 0.797418I
−4.69253 − 2.67585I −11.48246 + 0.I
u = 1.71277 − 0.17526I
a = 0.289764 − 0.671140I
b = −1.007410 + 0.797418I
−4.69253 + 2.67585I −11.48246 + 0.I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03972 + 1.78449I
a = −0.371574 + 0.822587I
b = 0.514983 − 0.621068I
7.54180 + 7.47357I 0. − 8.56588I
u = 0.03972 − 1.78449I
a = −0.371574 − 0.822587I
b = 0.514983 + 0.621068I
7.54180 − 7.47357I 0. + 8.56588I
u = −1.77033 + 0.44561I
a = 0.475535 − 1.055760I
b = −1.20068 + 1.01012I
−1.01052 + 4.22577I 0. − 4.92260I
u = −1.77033 − 0.44561I
a = 0.475535 + 1.055760I
b = −1.20068 − 1.01012I
−1.01052 − 4.22577I 0. + 4.92260I
u = −1.87191 + 0.06853I
a = 0.296661 + 0.271754I
b = −0.799005 − 0.432049I
−0.749045 − 0.267600I 0
u = −1.87191 − 0.06853I
a = 0.296661 − 0.271754I
b = −0.799005 + 0.432049I
−0.749045 + 0.267600I 0
15
III. I
u
3
= h−588u
14
− 1117u
13
+ · · · + 1513b + 3572, 588u
14
+ 1117u
13
+ · · · +
1513a − 2059, u
15
+ 3u
14
+ · · · + 4u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−0.388632u
14
− 0.738268u
13
+ ··· + 5.77859u + 1.36087
0.388632u
14
+ 0.738268u
13
+ ··· − 5.77859u − 2.36087
a
11
=
−u
u
a
2
=
−1
0.388632u
14
+ 0.738268u
13
+ ··· − 5.77859u − 2.36087
a
8
=
−0.388632u
14
− 0.738268u
13
+ ··· + 5.77859u + 3.36087
0.815598u
14
+ 1.94052u
13
+ ··· + 7.27759u + 1.09980
a
5
=
1.51091u
14
+ 3.39061u
13
+ ··· + 0.177132u − 0.688698
−1.12227u
14
− 2.65235u
13
+ ··· − 5.95572u − 0.672174
a
12
=
−0.881031u
14
− 2.28420u
13
+ ··· − 5.34038u − 0.967614
−0.688698u
14
− 2.57700u
13
+ ··· − 5.30734u − 0.931923
a
4
=
1.51091u
14
+ 3.39061u
13
+ ··· + 0.177132u − 0.688698
−0.967614u
14
− 2.02181u
13
+ ··· − 2.89822u + 0.469927
a
1
=
0.747521u
14
+ 2.04759u
13
+ ··· − 3.22208u − 2.47984
−1.99802u
14
− 4.83807u
13
+ ··· − 5.42234u − 0.216127
a
9
=
1.55254u
14
+ 3.79114u
13
+ ··· + 4.30800u + 1.77264
−0.0647720u
14
+ 1.04362u
13
+ ··· + 10.7964u + 3.06015
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
11241
1513
u
14
−
26858
1513
u
13
+ ··· −
17389
1513
u +
5791
1513
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
15
+ u
14
+ ··· − u − 1
c
2
u
15
− 6u
14
+ ··· + 19u − 5
c
4
u
15
− u
14
+ ··· − 2u + 1
c
5
u
15
+ 6u
14
+ ··· + 19u + 5
c
6
u
15
+ 3u
14
+ ··· + 4u + 1
c
7
u
15
+ 3u
14
+ ··· + 19u + 7
c
8
, c
9
u
15
− 3u
14
+ ··· − 5u + 1
c
10
u
15
− 3u
14
+ ··· + 4u − 1
c
11
u
15
− u
14
+ ··· + 37u − 7
c
12
u
15
+ 3u
14
+ ··· − 5u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
15
+ 9y
14
+ ··· − y −1
c
2
, c
5
y
15
+ 10y
14
+ ··· − 199y −25
c
4
y
15
+ 7y
14
+ ··· + 10y −1
c
6
, c
10
y
15
− 3y
14
+ ··· − 10y −1
c
7
y
15
+ 3y
14
+ ··· + 795y −49
c
8
, c
9
, c
12
y
15
− 17y
14
+ ··· + 19y −1
c
11
y
15
+ 11y
14
+ ··· + 1817y −49
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.987374 + 0.467890I
a = −0.579345 + 1.158540I
b = −0.420655 − 1.158540I
4.31997 − 4.13409I −3.46958 + 1.84906I
u = −0.987374 − 0.467890I
a = −0.579345 − 1.158540I
b = −0.420655 + 1.158540I
4.31997 + 4.13409I −3.46958 − 1.84906I
u = 0.117054 + 1.115160I
a = −1.179320 + 0.743611I
b = 0.179315 − 0.743611I
8.59029 + 6.53866I 6.63406 − 4.93610I
u = 0.117054 − 1.115160I
a = −1.179320 − 0.743611I
b = 0.179315 + 0.743611I
8.59029 − 6.53866I 6.63406 + 4.93610I
u = −0.233685 + 0.729101I
a = −1.02361 − 1.31637I
b = 0.023606 + 1.316370I
11.04790 + 5.60149I 8.37859 − 4.59557I
u = −0.233685 − 0.729101I
a = −1.02361 + 1.31637I
b = 0.023606 − 1.316370I
11.04790 − 5.60149I 8.37859 + 4.59557I
u = −0.073575 + 1.235960I
a = −0.884526 − 0.744696I
b = −0.115474 + 0.744696I
1.89869 − 2.15293I 7.70740 + 10.20235I
u = −0.073575 − 1.235960I
a = −0.884526 + 0.744696I
b = −0.115474 − 0.744696I
1.89869 + 2.15293I 7.70740 − 10.20235I
u = −0.690497
a = −0.235710
b = −0.764290
0.864751 −3.54690
u = −1.42824 + 0.34324I
a = 0.158166 − 1.046720I
b = −1.15817 + 1.04672I
−0.00542 + 4.12317I 3.00102 − 3.07740I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42824 − 0.34324I
a = 0.158166 + 1.046720I
b = −1.15817 − 1.04672I
−0.00542 − 4.12317I 3.00102 + 3.07740I
u = 1.46796 + 0.35294I
a = −0.028861 + 0.971059I
b = −0.971139 − 0.971059I
−4.05276 − 3.56193I −5.72461 + 2.61288I
u = 1.46796 − 0.35294I
a = −0.028861 − 0.971059I
b = −0.971139 + 0.971059I
−4.05276 + 3.56193I −5.72461 − 2.61288I
u = −0.016884 + 0.466920I
a = −0.84466 + 1.26589I
b = −0.155342 − 1.265890I
4.08794 − 3.40468I 8.74659 + 3.38159I
u = −0.016884 − 0.466920I
a = −0.84466 − 1.26589I
b = −0.155342 + 1.265890I
4.08794 + 3.40468I 8.74659 − 3.38159I
20
IV. I
u
4
= hb, a − 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
3
=
1
0
a
11
=
−1
1
a
2
=
1
0
a
8
=
0
1
a
5
=
1
0
a
12
=
0
1
a
4
=
1
1
a
1
=
0
−1
a
9
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
10
c
11
u + 1
c
2
, c
5
, c
8
c
9
, c
12
u
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
10
c
11
y −1
c
2
, c
5
, c
8
c
9
, c
12
y
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
−1.64493 −6.00000
24
V. I
u
5
= hb, a − u − 2, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u + 1
a
3
=
u + 2
0
a
11
=
−u
u
a
2
=
u + 2
0
a
8
=
−u − 1
−u + 1
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u + 1
a
1
=
u + 1
u − 1
a
9
=
−u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
(u − 1)
2
c
2
, c
5
u
2
c
4
, c
6
u
2
+ u − 1
c
7
, c
8
, c
9
(u + 1)
2
c
10
, c
11
u
2
− u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
8
, c
9
, c
12
(y −1)
2
c
2
, c
5
y
2
c
4
, c
6
, c
10
c
11
y
2
− 3y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.61803
b = 0
0 5.00000
u = −1.61803
a = 0.381966
b = 0
0 5.00000
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
2
)(u + 1)(u
15
+ u
14
+ ··· − u − 1)(u
32
− 2u
30
+ ··· + 6u
2
+ 1)
· (u
36
− 3u
35
+ ··· − 26u + 1)
c
2
u
3
(u
15
− 6u
14
+ ··· + 19u − 5)(u
18
+ 7u
17
+ ··· + 3u + 2)
2
· (u
32
− 9u
31
+ ··· − 12u + 9)
c
4
(u + 1)(u
2
+ u − 1)(u
15
− u
14
+ ··· − 2u + 1)(u
32
− 2u
31
+ ··· + 22u + 4)
· (u
36
+ 4u
34
+ ··· − 81u + 7)
c
5
u
3
(u
15
+ 6u
14
+ ··· + 19u + 5)(u
18
+ 7u
17
+ ··· + 3u + 2)
2
· (u
32
− 9u
31
+ ··· − 12u + 9)
c
6
(u + 1)(u
2
+ u − 1)(u
15
+ 3u
14
+ ··· + 4u + 1)(u
32
− 2u
31
+ ··· − 3u + 1)
· (u
36
− 2u
35
+ ··· + 345u + 1721)
c
7
((u − 1)
36
)(u + 1)
3
(u
15
+ 3u
14
+ ··· + 19u + 7)
· (u
32
+ 31u
31
+ ··· + 1966080u + 131072)
c
8
, c
9
u(u + 1)
2
(u
15
− 3u
14
+ ··· − 5u + 1)(u
18
+ 2u
17
+ ··· + 2u + 1)
2
· (u
32
− 10u
31
+ ··· + 24u + 9)
c
10
(u + 1)(u
2
− u − 1)(u
15
− 3u
14
+ ··· + 4u − 1)(u
32
− 2u
31
+ ··· − 3u + 1)
· (u
36
− 2u
35
+ ··· + 345u + 1721)
c
11
(u + 1)(u
2
− u − 1)(u
15
− u
14
+ ··· + 37u − 7)
· (u
32
− 2u
31
+ ··· − 926u + 233)(u
36
− 2u
35
+ ··· − 107951u + 18799)
c
12
u(u − 1)
2
(u
15
+ 3u
14
+ ··· − 5u − 1)(u
18
+ 2u
17
+ ··· + 2u + 1)
2
· (u
32
− 10u
31
+ ··· + 24u + 9)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
3
)(y
15
+ 9y
14
+ ··· − y −1)(y
32
− 4y
31
+ ··· + 12y + 1)
· (y
36
+ 13y
35
+ ··· − 238y + 1)
c
2
, c
5
y
3
(y
15
+ 10y
14
+ ··· − 199y −25)(y
18
+ 3y
17
+ ··· + 27y + 4)
2
· (y
32
+ 13y
31
+ ··· − 630y + 81)
c
4
(y −1)(y
2
− 3y + 1)(y
15
+ 7y
14
+ ··· + 10y −1)
· (y
32
+ 2y
31
+ ··· − 188y + 16)(y
36
+ 8y
35
+ ··· + 24785y + 49)
c
6
, c
10
(y −1)(y
2
− 3y + 1)(y
15
− 3y
14
+ ··· − 10y −1)
· (y
32
− 40y
31
+ ··· − 11y + 1)
· (y
36
− 24y
35
+ ··· − 23369735y + 2961841)
c
7
((y −1)
39
)(y
15
+ 3y
14
+ ··· + 795y −49)
· (y
32
+ 3y
31
+ ··· − 51539607552y + 17179869184)
c
8
, c
9
, c
12
y(y −1)
2
(y
15
− 17y
14
+ ··· + 19y −1)(y
18
− 18y
17
+ ··· + 6y + 1)
2
· (y
32
− 34y
31
+ ··· + 1260y + 81)
c
11
(y −1)(y
2
− 3y + 1)(y
15
+ 11y
14
+ ··· + 1817y −49)
· (y
32
+ 30y
31
+ ··· + 118794y + 54289)
· (y
36
+ 20y
35
+ ··· + 3655697641y + 353402401)
30
