12n
0524
(K12n
0524
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 8 2 11 5 3 12 7 9
Solving Sequence
4,9 5,12
1 3 10 11 8 6 2 7
c
4
c
12
c
3
c
9
c
10
c
8
c
5
c
2
c
7
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1096u
18
+ 7571u
17
+ ··· + 2606b + 15844, 3961u
18
+ 29496u
17
+ ··· + 5212a + 60062,
u
19
+ 8u
18
+ ··· + 40u + 8i
I
u
2
= hu
22
− 7u
21
+ ··· + 4b − 16, −80u
22
a + 97u
22
+ ··· − 45a + 3, u
23
− 3u
22
+ ··· − 11u + 5i
I
u
3
= hu
9
− u
8
+ 5u
7
− 5u
6
+ 9u
5
− 7u
4
+ 7u
3
− 2u
2
+ b + u, u
8
− u
7
+ 5u
6
− 5u
5
+ 9u
4
− 7u
3
+ 7u
2
+ a − 2u + 1,
u
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 7u
5
+ 12u
4
− u
3
+ 4u
2
+ 2u + 1i
I
u
4
= hau + b + 1, u
4
a + u
4
+ 3u
2
a + a
2
+ 4u
2
+ 2a + 4, u
5
+ 3u
3
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 85 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
= h1096u
18
+ 7571u
17
+ · · · + 2606b + 15844, 3961u
18
+ 29496u
17
+
· · · + 5212a + 60062, u
19
+ 8u
18
+ · · · + 40u + 8i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−0.759977u
18
− 5.65925u
17
+ ··· − 37.0253u − 11.5238
−0.420568u
18
− 2.90522u
17
+ ··· − 18.8753u − 6.07982
a
1
=
−0.759977u
18
− 5.65925u
17
+ ··· − 37.0253u − 11.5238
−0.879893u
18
− 5.90982u
17
+ ··· − 29.6182u − 9.44436
a
3
=
−1.19052u
18
− 8.97371u
17
+ ··· − 54.1759u − 15.1274
−0.550460u
18
− 4.31504u
17
+ ··· − 31.4935u − 9.52417
a
10
=
1.44561u
18
+ 10.7231u
17
+ ··· + 56.3331u + 15.2068
0.930353u
18
+ 7.22487u
17
+ ··· + 56.1117u + 15.9685
a
11
=
0.640061u
18
+ 4.65867u
17
+ ··· + 21.6825u + 6.60322
0.550460u
18
+ 4.31504u
17
+ ··· + 32.4935u + 9.52417
a
8
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
−0.399079u
18
− 3.11992u
17
+ ··· − 23.7630u − 7.95165
−0.129893u
18
− 0.909823u
17
+ ··· − 2.11819u − 1.44436
a
7
=
0.879029u
18
+ 6.38162u
17
+ ··· + 29.0679u + 7.33653
−0.118764u
18
− 0.712970u
17
+ ··· + 2.14083u + 1.38987
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3773
1303
u
18
+
27698
1303
u
17
+ ··· +
165236
1303
u +
31950
1303
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
19
+ 11u
18
+ ··· − 9u − 1
c
2
, c
6
, c
7
c
11
u
19
− u
18
+ ··· − u + 1
c
3
, c
12
u
19
− u
18
+ ··· + 2u + 1
c
4
, c
5
, c
8
u
19
− 8u
18
+ ··· + 40u − 8
c
9
u
19
+ 17u
18
+ ··· + 672u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
19
+ 3y
18
+ ··· − 5y −1
c
2
, c
6
, c
7
c
11
y
19
+ 11y
18
+ ··· − 9y −1
c
3
, c
12
y
19
− 25y
18
+ ··· − 8y −1
c
4
, c
5
, c
8
y
19
+ 16y
18
+ ··· + 32y −64
c
9
y
19
− 9y
18
+ ··· − 7168y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616811 + 0.855089I
a = −1.021840 − 0.627553I
b = −1.166890 + 0.486679I
−3.17455 + 2.33222I −9.09826 − 1.94044I
u = −0.616811 − 0.855089I
a = −1.021840 + 0.627553I
b = −1.166890 − 0.486679I
−3.17455 − 2.33222I −9.09826 + 1.94044I
u = −1.120010 + 0.195383I
a = 1.52958 + 0.02914I
b = 1.71883 − 0.26621I
−9.12103 + 9.62063I −8.08284 − 6.41226I
u = −1.120010 − 0.195383I
a = 1.52958 − 0.02914I
b = 1.71883 + 0.26621I
−9.12103 − 9.62063I −8.08284 + 6.41226I
u = −0.678394 + 0.473924I
a = −0.638948 − 0.805280I
b = −0.815100 − 0.243485I
−3.94120 + 2.37372I −9.61488 − 3.89895I
u = −0.678394 − 0.473924I
a = −0.638948 + 0.805280I
b = −0.815100 + 0.243485I
−3.94120 − 2.37372I −9.61488 + 3.89895I
u = −0.643620
a = −2.20220
b = −1.41738
−2.91062 −2.04050
u = −0.283257 + 1.330640I
a = −0.629985 − 0.965924I
b = −1.46374 + 0.56468I
1.36748 + 3.35758I −0.130533 − 0.838590I
u = −0.283257 − 1.330640I
a = −0.629985 + 0.965924I
b = −1.46374 − 0.56468I
1.36748 − 3.35758I −0.130533 + 0.838590I
u = −0.72609 + 1.25708I
a = 0.602034 + 0.850739I
b = 1.50658 − 0.13910I
−5.96103 − 3.19218I −6.11033 + 3.75659I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.72609 − 1.25708I
a = 0.602034 − 0.850739I
b = 1.50658 + 0.13910I
−5.96103 + 3.19218I −6.11033 − 3.75659I
u = 0.344998 + 0.346579I
a = 0.494258 + 0.345842I
b = −0.050657 − 0.290614I
−0.136375 − 0.955727I −2.79406 + 6.93579I
u = 0.344998 − 0.346579I
a = 0.494258 − 0.345842I
b = −0.050657 + 0.290614I
−0.136375 + 0.955727I −2.79406 − 6.93579I
u = −0.20896 + 1.50540I
a = 0.164518 − 0.451521I
b = −0.645343 − 0.342017I
2.53796 + 5.54235I −7.14543 − 3.27743I
u = −0.20896 − 1.50540I
a = 0.164518 + 0.451521I
b = −0.645343 + 0.342017I
2.53796 − 5.54235I −7.14543 + 3.27743I
u = −0.49084 + 1.46047I
a = 0.735940 + 0.906077I
b = 1.68453 − 0.63008I
−3.8953 + 15.3465I −4.88591 − 8.00097I
u = −0.49084 − 1.46047I
a = 0.735940 − 0.906077I
b = 1.68453 + 0.63008I
−3.8953 − 15.3465I −4.88591 + 8.00097I
u = 0.10117 + 1.56824I
a = 0.115543 + 0.288337I
b = 0.440490 − 0.210371I
6.50755 − 2.80738I −1.61751 + 0.28698I
u = 0.10117 − 1.56824I
a = 0.115543 − 0.288337I
b = 0.440490 + 0.210371I
6.50755 + 2.80738I −1.61751 − 0.28698I
6
II. I
u
2
= hu
22
− 7u
21
+ · · · + 4b − 16, −80u
22
a + 97u
22
+ · · · − 45a + 3, u
23
−
3u
22
+ · · · − 11u + 5i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
a
−
1
4
u
22
+
7
4
u
21
+ ··· −
37
4
u + 4
a
1
=
a
−
1
4
u
22
+
7
4
u
21
+ ··· −
37
4
u + 4
a
3
=
0.350000u
22
− 2.05000u
21
+ ··· + 10.7000u − 3.85000
−u
22
a −
7
4
u
22
+ ··· −
5
4
a +
29
4
a
10
=
0.0500000u
22
− 1.15000u
21
+ ··· + 8.35000u − 4.55000
3
2
u
22
a −
3
2
u
22
+ ··· −
15
4
a −
13
4
a
11
=
−
1
4
u
22
a +
27
20
u
22
+ ··· + 4a −
31
10
−u
22
+
9
4
u
21
+ ··· +
33
4
u
2
−
7
4
a
8
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
1
2
u
21
a +
11
10
u
22
+ ··· +
5
2
a −
97
20
−
1
2
u
22
a − u
22
+ ··· − 7u + 1
a
7
=
3
4
u
22
a +
13
20
u
22
+ ··· − 2a −
29
10
3
4
u
22
a +
1
2
u
22
+ ··· +
5
4
a − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
21
−5u
20
+ 25u
19
−48u
18
+ 126u
17
−191u
16
+ 333u
15
−398u
14
+ 484u
13
−437u
12
+
341u
11
− 191u
10
+ 29u
9
+ 56u
8
− 78u
7
+ 72u
6
+ 8u
5
+ 13u
4
+ 23u
3
+ 6u
2
− 8u − 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
46
+ 26u
45
+ ··· + 2067u + 121
c
2
, c
6
, c
7
c
11
u
46
− 2u
45
+ ··· − 45u + 11
c
3
, c
12
u
46
− 2u
45
+ ··· + 117u + 7
c
4
, c
5
, c
8
(u
23
+ 3u
22
+ ··· − 11u − 5)
2
c
9
(u
23
− 8u
22
+ ··· − 26u + 5)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
46
− 6y
45
+ ··· − 691857y + 14641
c
2
, c
6
, c
7
c
11
y
46
+ 26y
45
+ ··· + 2067y + 121
c
3
, c
12
y
46
− 42y
45
+ ··· + 4707y + 49
c
4
, c
5
, c
8
(y
23
+ 21y
22
+ ··· + 51y − 25)
2
c
9
(y
23
− 32y
22
+ ··· + 36y − 25)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949457 + 0.274301I
a = −1.53072 + 0.32112I
b = −1.70279 − 0.29302I
−6.21980 − 4.08700I −6.45479 + 3.28019I
u = 0.949457 + 0.274301I
a = 1.73757 − 0.19337I
b = 1.54144 + 0.11499I
−6.21980 − 4.08700I −6.45479 + 3.28019I
u = 0.949457 − 0.274301I
a = −1.53072 − 0.32112I
b = −1.70279 + 0.29302I
−6.21980 + 4.08700I −6.45479 − 3.28019I
u = 0.949457 − 0.274301I
a = 1.73757 + 0.19337I
b = 1.54144 − 0.11499I
−6.21980 + 4.08700I −6.45479 − 3.28019I
u = 0.129915 + 1.043420I
a = −0.493058 + 0.848090I
b = −1.94953 − 0.23067I
−5.55917 − 0.57299I −3.52244 − 2.34138I
u = 0.129915 + 1.043420I
a = 0.44678 − 1.81277I
b = 0.948973 + 0.404288I
−5.55917 − 0.57299I −3.52244 − 2.34138I
u = 0.129915 − 1.043420I
a = −0.493058 − 0.848090I
b = −1.94953 + 0.23067I
−5.55917 + 0.57299I −3.52244 + 2.34138I
u = 0.129915 − 1.043420I
a = 0.44678 + 1.81277I
b = 0.948973 − 0.404288I
−5.55917 + 0.57299I −3.52244 + 2.34138I
u = 0.157565 + 1.169780I
a = 0.170495 − 0.884679I
b = −0.525087 + 1.299010I
2.81400 − 1.37485I −2.47637 + 0.94605I
u = 0.157565 + 1.169780I
a = −1.031300 − 0.587788I
b = −1.061750 − 0.060047I
2.81400 − 1.37485I −2.47637 + 0.94605I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157565 − 1.169780I
a = 0.170495 + 0.884679I
b = −0.525087 − 1.299010I
2.81400 + 1.37485I −2.47637 − 0.94605I
u = 0.157565 − 1.169780I
a = −1.031300 + 0.587788I
b = −1.061750 + 0.060047I
2.81400 + 1.37485I −2.47637 − 0.94605I
u = −0.297704 + 1.164290I
a = −0.315648 − 0.681415I
b = 0.02755 + 1.63095I
1.67762 + 7.26897I −4.60706 − 6.86727I
u = −0.297704 + 1.164290I
a = −1.309170 + 0.358408I
b = −0.887336 + 0.164646I
1.67762 + 7.26897I −4.60706 − 6.86727I
u = −0.297704 − 1.164290I
a = −0.315648 + 0.681415I
b = 0.02755 − 1.63095I
1.67762 − 7.26897I −4.60706 + 6.86727I
u = −0.297704 − 1.164290I
a = −1.309170 − 0.358408I
b = −0.887336 − 0.164646I
1.67762 − 7.26897I −4.60706 + 6.86727I
u = 0.701104 + 1.024510I
a = −0.679056 + 0.799381I
b = −1.62187 − 0.29006I
−4.06293 − 1.56405I −5.53705 + 2.00718I
u = 0.701104 + 1.024510I
a = 0.930638 − 0.946208I
b = 1.295060 + 0.135249I
−4.06293 − 1.56405I −5.53705 + 2.00718I
u = 0.701104 − 1.024510I
a = −0.679056 − 0.799381I
b = −1.62187 + 0.29006I
−4.06293 + 1.56405I −5.53705 − 2.00718I
u = 0.701104 − 1.024510I
a = 0.930638 + 0.946208I
b = 1.295060 − 0.135249I
−4.06293 + 1.56405I −5.53705 − 2.00718I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.700899
a = 2.31801 + 0.38865I
b = 1.62469 − 0.27240I
−11.2801 −11.1210
u = −0.700899
a = 2.31801 − 0.38865I
b = 1.62469 + 0.27240I
−11.2801 −11.1210
u = 0.098502 + 1.344050I
a = 0.866199 − 0.095805I
b = 0.845917 − 0.031157I
5.30060 − 3.06078I 0.29039 + 3.85817I
u = 0.098502 + 1.344050I
a = −0.022822 + 0.627708I
b = −0.214088 − 1.154780I
5.30060 − 3.06078I 0.29039 + 3.85817I
u = 0.098502 − 1.344050I
a = 0.866199 + 0.095805I
b = 0.845917 + 0.031157I
5.30060 + 3.06078I 0.29039 − 3.85817I
u = 0.098502 − 1.344050I
a = −0.022822 − 0.627708I
b = −0.214088 + 1.154780I
5.30060 + 3.06078I 0.29039 − 3.85817I
u = −0.314282 + 1.335820I
a = 0.636808 + 0.819242I
b = 1.79937 − 0.02411I
−7.00942 + 3.66737I −5.63248 − 4.77182I
u = −0.314282 + 1.335820I
a = 0.317399 + 1.272340I
b = 1.29450 − 0.59319I
−7.00942 + 3.66737I −5.63248 − 4.77182I
u = −0.314282 − 1.335820I
a = 0.636808 − 0.819242I
b = 1.79937 + 0.02411I
−7.00942 − 3.66737I −5.63248 + 4.77182I
u = −0.314282 − 1.335820I
a = 0.317399 − 1.272340I
b = 1.29450 + 0.59319I
−7.00942 − 3.66737I −5.63248 + 4.77182I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540846 + 0.315918I
a = 0.051854 − 0.150163I
b = −0.539179 − 1.227400I
−0.93518 − 3.99671I −9.62845 + 1.40973I
u = −0.540846 + 0.315918I
a = 0.24507 − 2.12626I
b = −0.0193942 − 0.0975969I
−0.93518 − 3.99671I −9.62845 + 1.40973I
u = −0.540846 − 0.315918I
a = 0.051854 + 0.150163I
b = −0.539179 + 1.227400I
−0.93518 + 3.99671I −9.62845 − 1.40973I
u = −0.540846 − 0.315918I
a = 0.24507 + 2.12626I
b = −0.0193942 + 0.0975969I
−0.93518 + 3.99671I −9.62845 − 1.40973I
u = 0.499495 + 0.232325I
a = 0.80490 + 1.31816I
b = −0.0999299 − 0.0558064I
0.125631 − 0.991368I −5.18428 + 5.58556I
u = 0.499495 + 0.232325I
a = 0.207202 + 0.015352I
b = −0.095801 − 0.845413I
0.125631 − 0.991368I −5.18428 + 5.58556I
u = 0.499495 − 0.232325I
a = 0.80490 − 1.31816I
b = −0.0999299 + 0.0558064I
0.125631 + 0.991368I −5.18428 − 5.58556I
u = 0.499495 − 0.232325I
a = 0.207202 − 0.015352I
b = −0.095801 + 0.845413I
0.125631 + 0.991368I −5.18428 − 5.58556I
u = 0.40672 + 1.44182I
a = −0.563943 + 0.961951I
b = −1.54904 − 0.71550I
−0.79781 − 8.96070I −2.64189 + 5.31157I
u = 0.40672 + 1.44182I
a = 0.740402 − 0.865507I
b = 1.61633 + 0.42186I
−0.79781 − 8.96070I −2.64189 + 5.31157I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.40672 − 1.44182I
a = −0.563943 − 0.961951I
b = −1.54904 + 0.71550I
−0.79781 + 8.96070I −2.64189 − 5.31157I
u = 0.40672 − 1.44182I
a = 0.740402 + 0.865507I
b = 1.61633 − 0.42186I
−0.79781 + 8.96070I −2.64189 − 5.31157I
u = 0.06052 + 1.52562I
a = 0.443758 − 0.312131I
b = 0.775017 − 0.227308I
5.50209 − 2.76341I −4.54493 + 5.66390I
u = 0.06052 + 1.52562I
a = 0.128639 + 0.513106I
b = −0.503049 − 0.658113I
5.50209 − 2.76341I −4.54493 + 5.66390I
u = 0.06052 − 1.52562I
a = 0.443758 + 0.312131I
b = 0.775017 + 0.227308I
5.50209 + 2.76341I −4.54493 − 5.66390I
u = 0.06052 − 1.52562I
a = 0.128639 − 0.513106I
b = −0.503049 + 0.658113I
5.50209 + 2.76341I −4.54493 − 5.66390I
14
III. I
u
3
= hu
9
− u
8
+ · · · + b + u, u
8
− u
7
+ · · · + a + 1, u
10
− u
9
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−u
8
+ u
7
− 5u
6
+ 5u
5
− 9u
4
+ 7u
3
− 7u
2
+ 2u − 1
−u
9
+ u
8
− 5u
7
+ 5u
6
− 9u
5
+ 7u
4
− 7u
3
+ 2u
2
− u
a
1
=
−u
8
+ u
7
− 5u
6
+ 5u
5
− 9u
4
+ 7u
3
− 7u
2
+ 2u − 1
−u
9
+ 2u
8
− 5u
7
+ 9u
6
− 9u
5
+ 12u
4
− 6u
3
+ 5u
2
+ u + 1
a
3
=
u
8
− u
7
+ 5u
6
− 4u
5
+ 8u
4
− 3u
3
+ 4u
2
+ 2u
u
9
− u
8
+ 5u
7
− 4u
6
+ 8u
5
− 3u
4
+ 4u
3
+ 2u
2
− u
a
10
=
2u
8
− u
7
+ 9u
6
− 4u
5
+ 13u
4
− 2u
3
+ 8u
2
+ 4u + 2
2u
9
− 2u
8
+ 10u
7
− 9u
6
+ 17u
5
− 10u
4
+ 11u
3
+ u − 1
a
11
=
−u
9
+ 2u
8
− 6u
7
+ 9u
6
− 12u
5
+ 11u
4
− 7u
3
+ 2u
2
+ 2u − 1
u
9
− u
8
+ 5u
7
− 4u
6
+ 8u
5
− 3u
4
+ 4u
3
+ 2u
2
a
8
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
u
8
− u
7
+ 5u
6
− 3u
5
+ 7u
4
+ 2u
2
+ 4u
u
9
+ 5u
7
+ 8u
5
+ 2u
4
+ 5u
3
+ 5u
2
+ u + 1
a
7
=
−u
9
+ u
8
− 6u
7
+ 6u
6
− 13u
5
+ 10u
4
− 12u
3
+ 4u
2
− 3u + 1
u
8
+ 4u
6
+ 5u
4
+ 2u
3
+ 3u
2
+ 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
9
− 4u
8
+ 24u
7
− 20u
6
+ 44u
5
− 28u
4
+ 40u
3
− 8u
2
+ 12u
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
10
− 7u
9
+ ··· − 8u + 1
c
2
, c
7
u
10
− u
9
+ 4u
8
− 3u
7
+ 7u
6
− 4u
5
+ 7u
4
− 3u
3
+ 4u
2
+ 1
c
3
, c
12
u
10
+ u
9
− 2u
8
− 4u
7
− 3u
6
+ u
5
+ 6u
4
+ 7u
3
+ 6u
2
+ 3u + 1
c
4
, c
5
u
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 7u
5
+ 12u
4
− u
3
+ 4u
2
+ 2u + 1
c
6
, c
11
u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 4u
5
+ 7u
4
+ 3u
3
+ 4u
2
+ 1
c
8
u
10
+ u
9
+ 6u
8
+ 5u
7
+ 13u
6
+ 7u
5
+ 12u
4
+ u
3
+ 4u
2
− 2u + 1
c
9
u
10
− 4u
9
+ 6u
8
− 10u
7
+ 17u
6
− 13u
5
+ 11u
4
− 7u
3
− 2u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
10
− y
9
− 19y
7
− 21y
6
+ 34y
5
+ 145y
4
+ 217y
3
+ 102y
2
− 4y + 1
c
2
, c
6
, c
7
c
11
y
10
+ 7y
9
+ ··· + 8y + 1
c
3
, c
12
y
10
− 5y
9
+ 6y
8
+ 6y
7
− 9y
6
− 9y
5
+ 6y
4
+ 11y
3
+ 6y
2
+ 3y + 1
c
4
, c
5
, c
8
y
10
+ 11y
9
+ ··· + 4y + 1
c
9
y
10
− 4y
9
+ ··· − 5y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.250000 + 0.998657I
a = 0.59595 − 1.38352I
b = 1.53065 + 0.24927I
−8.30263 − 0.98508I −8.00878 + 0.35212I
u = 0.250000 − 0.998657I
a = 0.59595 + 1.38352I
b = 1.53065 − 0.24927I
−8.30263 + 0.98508I −8.00878 − 0.35212I
u = 0.692359 + 0.857180I
a = −0.929090 + 0.709584I
b = −1.251510 − 0.305111I
−2.35435 − 2.60043I 0.40869 + 4.75693I
u = 0.692359 − 0.857180I
a = −0.929090 − 0.709584I
b = −1.251510 + 0.305111I
−2.35435 + 2.60043I 0.40869 − 4.75693I
u = −0.159586 + 1.376540I
a = 0.576417 − 0.085459I
b = 0.025649 + 0.807097I
3.84271 + 6.23098I −0.71193 − 5.55731I
u = −0.159586 − 1.376540I
a = 0.576417 + 0.085459I
b = 0.025649 − 0.807097I
3.84271 − 6.23098I −0.71193 + 5.55731I
u = 0.00345 + 1.56150I
a = −0.310078 + 0.314723I
b = −0.492510 − 0.483102I
6.88666 − 3.66525I 2.21222 + 7.64965I
u = 0.00345 − 1.56150I
a = −0.310078 − 0.314723I
b = −0.492510 + 0.483102I
6.88666 + 3.66525I 2.21222 − 7.64965I
u = −0.286221 + 0.289922I
a = −0.93320 + 1.99841I
b = −0.312283 − 0.842541I
−0.07240 − 4.46416I −0.40020 + 6.18186I
u = −0.286221 − 0.289922I
a = −0.93320 − 1.99841I
b = −0.312283 + 0.842541I
−0.07240 + 4.46416I −0.40020 − 6.18186I
18
IV. I
u
4
= hau + b + 1, u
4
a + u
4
+ 3u
2
a + a
2
+ 4u
2
+ 2a + 4, u
5
+ 3u
3
+ 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
a
−au − 1
a
1
=
a
u
2
a − au − 1
a
3
=
−u
3
− 2u
u
4
− au + 2u
2
+ u − 1
a
10
=
u
3
− u
2
+ 2u − 1
u
3
a − 2u
4
+ 2au − 4u
2
− a + 1
a
11
=
u
4
+ u
3
+ 2u
2
+ a + 2u + 1
−u
4
− 2u
2
a
8
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
−u
3
a − u
3
− au + a − 2u
u
4
+ u
2
a − au + 2u
2
+ u − 1
a
7
=
−u
3
a − u
2
a − 2au
u
2
a + u
3
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 3u
3
+ 8u
2
− 6u − 3
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
10
− 7u
9
+ ··· − 7u + 1
c
2
, c
7
u
10
− u
9
+ 4u
8
− 3u
7
+ 7u
6
− 3u
5
+ 7u
4
− 3u
3
+ 4u
2
− u + 1
c
3
, c
12
u
10
+ 5u
9
+ 8u
8
+ 2u
7
− 8u
6
− 10u
5
− 2u
4
+ 5u
3
+ 6u
2
+ 3u + 1
c
4
, c
5
(u
5
+ 3u
3
+ 2u − 1)
2
c
6
, c
11
u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 7u
4
+ 3u
3
+ 4u
2
+ u + 1
c
8
(u
5
+ 3u
3
+ 2u + 1)
2
c
9
(u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u − 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
10
− y
9
+ ··· − y + 1
c
2
, c
6
, c
7
c
11
y
10
+ 7y
9
+ ··· + 7y + 1
c
3
, c
12
y
10
− 9y
9
+ 28y
8
− 36y
7
+ 34y
6
− 20y
5
+ 12y
4
− 5y
3
+ 2y
2
+ 3y + 1
c
4
, c
5
, c
8
(y
5
+ 6y
4
+ 13y
3
+ 12y
2
+ 4y − 1)
2
c
9
(y
5
− 2y
4
− 3y
3
+ 4y
2
+ 8y − 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351694 + 0.989493I
a = −0.548693 − 0.777335I
b = −1.96214 + 0.26954I
−5.97351 + 1.36579I −9.71244 − 4.93711I
u = −0.351694 + 0.989493I
a = 0.86761 + 1.67460I
b = 0.962140 − 0.269544I
−5.97351 + 1.36579I −9.71244 − 4.93711I
u = −0.351694 − 0.989493I
a = −0.548693 + 0.777335I
b = −1.96214 − 0.26954I
−5.97351 − 1.36579I −9.71244 + 4.93711I
u = −0.351694 − 0.989493I
a = 0.86761 − 1.67460I
b = 0.962140 + 0.269544I
−5.97351 − 1.36579I −9.71244 + 4.93711I
u = 0.15201 + 1.49915I
a = 0.311870 + 0.594201I
b = −0.156612 − 0.557863I
5.78657 − 2.10101I 0.31723 − 3.66297I
u = 0.15201 + 1.49915I
a = −0.378818 + 0.066057I
b = −0.843388 + 0.557863I
5.78657 − 2.10101I 0.31723 − 3.66297I
u = 0.15201 − 1.49915I
a = 0.311870 − 0.594201I
b = −0.156612 + 0.557863I
5.78657 + 2.10101I 0.31723 + 3.66297I
u = 0.15201 − 1.49915I
a = −0.378818 − 0.066057I
b = −0.843388 − 0.557863I
5.78657 + 2.10101I 0.31723 + 3.66297I
u = 0.399372
a = −1.25197 + 1.75955I
b = −0.500000 − 0.702714I
0.373884 −4.20960
u = 0.399372
a = −1.25197 − 1.75955I
b = −0.500000 + 0.702714I
0.373884 −4.20960
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
10
− 7u
9
+ ··· − 7u + 1)(u
10
− 7u
9
+ ··· − 8u + 1)
· (u
19
+ 11u
18
+ ··· − 9u − 1)(u
46
+ 26u
45
+ ··· + 2067u + 121)
c
2
, c
7
(u
10
− u
9
+ 4u
8
− 3u
7
+ 7u
6
− 4u
5
+ 7u
4
− 3u
3
+ 4u
2
+ 1)
· (u
10
− u
9
+ 4u
8
− 3u
7
+ 7u
6
− 3u
5
+ 7u
4
− 3u
3
+ 4u
2
− u + 1)
· (u
19
− u
18
+ ··· − u + 1)(u
46
− 2u
45
+ ··· − 45u + 11)
c
3
, c
12
(u
10
+ u
9
− 2u
8
− 4u
7
− 3u
6
+ u
5
+ 6u
4
+ 7u
3
+ 6u
2
+ 3u + 1)
· (u
10
+ 5u
9
+ 8u
8
+ 2u
7
− 8u
6
− 10u
5
− 2u
4
+ 5u
3
+ 6u
2
+ 3u + 1)
· (u
19
− u
18
+ ··· + 2u + 1)(u
46
− 2u
45
+ ··· + 117u + 7)
c
4
, c
5
(u
5
+ 3u
3
+ 2u − 1)
2
· (u
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 7u
5
+ 12u
4
− u
3
+ 4u
2
+ 2u + 1)
· (u
19
− 8u
18
+ ··· + 40u − 8)(u
23
+ 3u
22
+ ··· − 11u − 5)
2
c
6
, c
11
(u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 7u
4
+ 3u
3
+ 4u
2
+ u + 1)
· (u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 4u
5
+ 7u
4
+ 3u
3
+ 4u
2
+ 1)
· (u
19
− u
18
+ ··· − u + 1)(u
46
− 2u
45
+ ··· − 45u + 11)
c
8
(u
5
+ 3u
3
+ 2u + 1)
2
· (u
10
+ u
9
+ 6u
8
+ 5u
7
+ 13u
6
+ 7u
5
+ 12u
4
+ u
3
+ 4u
2
− 2u + 1)
· (u
19
− 8u
18
+ ··· + 40u − 8)(u
23
+ 3u
22
+ ··· − 11u − 5)
2
c
9
(u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u − 1)
2
· (u
10
− 4u
9
+ 6u
8
− 10u
7
+ 17u
6
− 13u
5
+ 11u
4
− 7u
3
− 2u
2
+ u + 1)
· (u
19
+ 17u
18
+ ··· + 672u + 64)(u
23
− 8u
22
+ ··· − 26u + 5)
2
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
10
− y
9
− 19y
7
− 21y
6
+ 34y
5
+ 145y
4
+ 217y
3
+ 102y
2
− 4y + 1)
· (y
10
− y
9
+ ··· − y + 1)(y
19
+ 3y
18
+ ··· − 5y − 1)
· (y
46
− 6y
45
+ ··· − 691857y + 14641)
c
2
, c
6
, c
7
c
11
(y
10
+ 7y
9
+ ··· + 8y + 1)(y
10
+ 7y
9
+ ··· + 7y + 1)
· (y
19
+ 11y
18
+ ··· − 9y − 1)(y
46
+ 26y
45
+ ··· + 2067y + 121)
c
3
, c
12
(y
10
− 9y
9
+ 28y
8
− 36y
7
+ 34y
6
− 20y
5
+ 12y
4
− 5y
3
+ 2y
2
+ 3y + 1)
· (y
10
− 5y
9
+ 6y
8
+ 6y
7
− 9y
6
− 9y
5
+ 6y
4
+ 11y
3
+ 6y
2
+ 3y + 1)
· (y
19
− 25y
18
+ ··· − 8y − 1)(y
46
− 42y
45
+ ··· + 4707y + 49)
c
4
, c
5
, c
8
((y
5
+ 6y
4
+ 13y
3
+ 12y
2
+ 4y − 1)
2
)(y
10
+ 11y
9
+ ··· + 4y + 1)
· (y
19
+ 16y
18
+ ··· + 32y − 64)(y
23
+ 21y
22
+ ··· + 51y − 25)
2
c
9
((y
5
− 2y
4
− 3y
3
+ 4y
2
+ 8y − 1)
2
)(y
10
− 4y
9
+ ··· − 5y + 1)
· (y
19
− 9y
18
+ ··· − 7168y − 4096)(y
23
− 32y
22
+ ··· + 36y − 25)
2
24
