12a
0245
(K12a
0245
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 1 11 5 12 8 4 9
Solving Sequence
4,10 5,12
9 1 8 11 7 3 2 6
c
4
c
9
c
12
c
8
c
11
c
7
c
3
c
1
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.30829 × 10
182
u
45
+ 3.21690 × 10
182
u
44
+ ··· + 2.91664 × 10
185
b + 1.81261 × 10
186
,
2.74927 × 10
182
u
45
− 1.01973 × 10
183
u
44
+ ··· + 5.83327 × 10
185
a − 1.27181 × 10
187
,
u
46
− 3u
45
+ ··· − 30720u + 8192i
I
u
2
= h−u
31
− u
30
+ ··· − a − 2, 2u
31
+ u
30
+ ··· + a
2
+ 3, u
32
+ u
31
+ ··· + 2u + 1i
I
u
3
= hu
2
a − u
3
− u
2
+ b − a, a
2
− au − u, u
4
+ u
3
+ 1i
I
u
4
= hb + 1, a
2
− a + 2, u − 1i
I
u
5
= hb − u − 1, a − 1, u
2
+ 1i
I
v
1
= ha, v
5
+ 2v
4
− 16v
2
+ 64b − 16v + 32, v
6
+ 2v
5
− 16v
3
− 16v
2
+ 32v + 64i
* 6 irreducible components of dim
C
= 0, with total 128 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−1.31 × 10
182
u
45
+ 3.22 × 10
182
u
44
+ · · · + 2.92 × 10
185
b + 1.81 ×
10
186
, 2.75 × 10
182
u
45
− 1.02 × 10
183
u
44
+ · · · + 5.83 × 10
185
a − 1.27 ×
10
187
, u
46
− 3u
45
+ · · · − 30720u + 8192i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
−0.000471309u
45
+ 0.00174813u
44
+ ··· − 24.9228u + 21.8026
0.000448560u
45
− 0.00110295u
44
+ ··· + 13.9436u − 6.21474
a
9
=
0.000919870u
45
− 0.00285108u
44
+ ··· + 38.8664u − 28.0174
0.000859527u
45
− 0.00194940u
44
+ ··· + 24.2892u − 6.96411
a
1
=
−0.000531652u
45
+ 0.00264982u
44
+ ··· − 40.4999u + 42.8559
0.000478275u
45
− 0.00119240u
44
+ ··· + 14.5999u − 7.27524
a
8
=
0.000471309u
45
− 0.00174813u
44
+ ··· + 24.9228u − 21.8026
0.000991814u
45
− 0.00227861u
44
+ ··· + 28.0713u − 8.95256
a
11
=
−0.000919870u
45
+ 0.00285108u
44
+ ··· − 38.8664u + 28.0174
0.000448560u
45
− 0.00110295u
44
+ ··· + 13.9436u − 6.21474
a
7
=
0.000531652u
45
− 0.00264982u
44
+ ··· + 40.4999u − 42.8559
0.00185134u
45
− 0.00422801u
44
+ ··· + 51.3606u − 15.9167
a
3
=
0.00115169u
45
− 0.00185933u
44
+ ··· + 29.6103u + 9.69006
0.00179201u
45
− 0.00442512u
44
+ ··· + 55.3750u − 28.2489
a
2
=
−0.000177162u
45
+ 0.00141815u
44
+ ··· − 33.1849u + 22.5187
0.000323331u
45
− 0.00109532u
44
+ ··· + 8.96510u − 11.5651
a
6
=
0.00269326u
45
− 0.00782283u
44
+ ··· + 106.019u − 66.8639
−0.00167414u
45
+ 0.00452784u
44
+ ··· − 49.4479u + 36.0030
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000526625u
45
− 0.00139921u
44
+ ··· + 30.9656u + 16.8615
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 22u
45
+ ··· + 65u + 16
c
2
, c
5
u
46
+ 2u
45
+ ··· + 15u + 4
c
3
u
46
+ 2u
45
+ ··· + 419884u + 136336
c
4
u
46
+ 3u
45
+ ··· + 30720u + 8192
c
6
u
46
+ 2u
44
+ ··· + 2032u + 448
c
7
, c
9
, c
10
c
12
u
46
+ 6u
45
+ ··· − 6u + 1
c
8
, c
11
64(64u
46
− 96u
45
+ ··· − 8u
2
+ 2)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 6y
45
+ ··· + 3391y + 256
c
2
, c
5
y
46
− 22y
45
+ ··· − 65y + 16
c
3
y
46
− 30y
45
+ ··· − 205613722768y + 18587504896
c
4
y
46
− 11y
45
+ ··· − 1572864000y + 67108864
c
6
y
46
+ 4y
45
+ ··· + 910080y + 200704
c
7
, c
9
, c
10
c
12
y
46
+ 26y
45
+ ··· − 12y + 1
c
8
, c
11
4096(4096y
46
− 93184y
45
+ ··· − 32y + 4)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.401792 + 0.789673I
a = 1.034950 + 0.489117I
b = −0.098777 + 0.739250I
−3.37451 + 5.47103I −6.94202 − 5.47084I
u = −0.401792 − 0.789673I
a = 1.034950 − 0.489117I
b = −0.098777 − 0.739250I
−3.37451 − 5.47103I −6.94202 + 5.47084I
u = 0.239618 + 0.727911I
a = −0.877973 + 0.679500I
b = 0.064614 + 0.618606I
−1.23789 − 1.34787I −5.39091 + 2.19254I
u = 0.239618 − 0.727911I
a = −0.877973 − 0.679500I
b = 0.064614 − 0.618606I
−1.23789 + 1.34787I −5.39091 − 2.19254I
u = −0.078679 + 0.719346I
a = −0.451493 + 0.580682I
b = −0.063814 + 0.526016I
−0.697121 − 1.212220I −4.01044 + 6.14816I
u = −0.078679 − 0.719346I
a = −0.451493 − 0.580682I
b = −0.063814 − 0.526016I
−0.697121 + 1.212220I −4.01044 − 6.14816I
u = −0.433643 + 0.566016I
a = 1.33364 + 0.69018I
b = −0.273046 + 0.628978I
−4.26962 − 1.33304I −9.23410 + 6.58879I
u = −0.433643 − 0.566016I
a = 1.33364 − 0.69018I
b = −0.273046 − 0.628978I
−4.26962 + 1.33304I −9.23410 − 6.58879I
u = 0.672328 + 0.122077I
a = −2.03352 + 0.16905I
b = 0.811410 + 0.208117I
−1.01846 + 6.05975I 5.32943 − 7.91016I
u = 0.672328 − 0.122077I
a = −2.03352 − 0.16905I
b = 0.811410 − 0.208117I
−1.01846 − 6.05975I 5.32943 + 7.91016I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.645073 + 0.070271I
a = 2.10420 + 0.11324I
b = −0.777175 + 0.116055I
0.827180 − 1.119400I 9.81417 + 2.37316I
u = −0.645073 − 0.070271I
a = 2.10420 − 0.11324I
b = −0.777175 − 0.116055I
0.827180 + 1.119400I 9.81417 − 2.37316I
u = 0.520537 + 0.295551I
a = 0.413738 + 0.318781I
b = 0.371984 + 0.476647I
−1.97267 − 1.37276I −2.57483 + 1.51766I
u = 0.520537 − 0.295551I
a = 0.413738 − 0.318781I
b = 0.371984 − 0.476647I
−1.97267 + 1.37276I −2.57483 − 1.51766I
u = 0.502594 + 0.228503I
a = −2.11877 + 0.56848I
b = 0.525503 + 0.309703I
−3.39297 − 0.50689I 1.54331 − 8.55618I
u = 0.502594 − 0.228503I
a = −2.11877 − 0.56848I
b = 0.525503 − 0.309703I
−3.39297 + 0.50689I 1.54331 + 8.55618I
u = 0.532699 + 0.084051I
a = 0.573143 + 0.199439I
b = 0.707726 + 0.345489I
−0.46138 + 5.41462I 2.43162 − 4.62417I
u = 0.532699 − 0.084051I
a = 0.573143 − 0.199439I
b = 0.707726 − 0.345489I
−0.46138 − 5.41462I 2.43162 + 4.62417I
u = −0.478597 + 0.061203I
a = −0.523519 + 0.112067I
b = −0.641497 + 0.184230I
1.49547 − 0.77471I 6.52139 + 0.61017I
u = −0.478597 − 0.061203I
a = −0.523519 − 0.112067I
b = −0.641497 − 0.184230I
1.49547 + 0.77471I 6.52139 − 0.61017I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32298 + 1.00419I
a = −0.244934 − 0.868893I
b = −1.59181 − 1.00368I
7.9562 + 18.9510I 0
u = 1.32298 − 1.00419I
a = −0.244934 + 0.868893I
b = −1.59181 + 1.00368I
7.9562 − 18.9510I 0
u = 1.36201 + 0.97857I
a = −0.221655 − 0.833836I
b = −1.46345 − 0.96268I
4.87739 + 11.08340I 0
u = 1.36201 − 0.97857I
a = −0.221655 + 0.833836I
b = −1.46345 + 0.96268I
4.87739 − 11.08340I 0
u = −1.33866 + 1.01035I
a = 0.250581 − 0.854142I
b = 1.57565 − 0.95478I
10.1320 − 13.6218I 0
u = −1.33866 − 1.01035I
a = 0.250581 + 0.854142I
b = 1.57565 + 0.95478I
10.1320 + 13.6218I 0
u = −1.38555 + 1.03866I
a = 0.272974 − 0.808895I
b = 1.53500 − 0.79923I
11.2953 − 10.4811I 0
u = −1.38555 − 1.03866I
a = 0.272974 + 0.808895I
b = 1.53500 + 0.79923I
11.2953 + 10.4811I 0
u = −1.57230 + 0.77246I
a = 0.085159 − 0.690200I
b = 0.913569 − 0.867748I
0.59144 − 10.81880I 0
u = −1.57230 − 0.77246I
a = 0.085159 + 0.690200I
b = 0.913569 + 0.867748I
0.59144 + 10.81880I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41374 + 1.05421I
a = −0.282174 − 0.781521I
b = −1.49805 − 0.71794I
10.12260 + 5.12502I 0
u = 1.41374 − 1.05421I
a = −0.282174 + 0.781521I
b = −1.49805 + 0.71794I
10.12260 − 5.12502I 0
u = 1.69696 + 0.85231I
a = −0.124053 − 0.627843I
b = −0.899624 − 0.686359I
3.79825 + 6.24987I 0
u = 1.69696 − 0.85231I
a = −0.124053 + 0.627843I
b = −0.899624 + 0.686359I
3.79825 − 6.24987I 0
u = −1.88174 + 0.67526I
a = 0.052037 − 0.556937I
b = 0.669760 − 0.655489I
−0.19317 − 2.26026I 0
u = −1.88174 − 0.67526I
a = 0.052037 + 0.556937I
b = 0.669760 + 0.655489I
−0.19317 + 2.26026I 0
u = 1.15493 + 1.84484I
a = −0.522503 − 0.223781I
b = −0.696453 + 0.457576I
6.20944 − 9.54624I 0
u = 1.15493 − 1.84484I
a = −0.522503 + 0.223781I
b = −0.696453 − 0.457576I
6.20944 + 9.54624I 0
u = 1.71157 + 1.45820I
a = −0.345297 − 0.457141I
b = −0.959259 − 0.047672I
9.03151 + 5.36539I 0
u = 1.71157 − 1.45820I
a = −0.345297 + 0.457141I
b = −0.959259 + 0.047672I
9.03151 − 5.36539I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.29479 + 1.87645I
a = 0.478230 − 0.255335I
b = 0.724784 + 0.367690I
8.41076 + 3.99047I 0
u = −1.29479 − 1.87645I
a = 0.478230 + 0.255335I
b = 0.724784 − 0.367690I
8.41076 − 3.99047I 0
u = −1.65453 + 1.63052I
a = 0.382255 − 0.391673I
b = 0.882553 + 0.091874I
9.95002 + 0.24033I 0
u = −1.65453 − 1.63052I
a = 0.382255 + 0.391673I
b = 0.882553 − 0.091874I
9.95002 − 0.24033I 0
u = 1.53540 + 2.28777I
a = −0.360009 − 0.207800I
b = −0.569607 + 0.219649I
2.65240 − 1.11142I 0
u = 1.53540 − 2.28777I
a = −0.360009 + 0.207800I
b = −0.569607 − 0.219649I
2.65240 + 1.11142I 0
9
II.
I
u
2
= h−u
31
−u
30
+· · ·−a−2, 2u
31
+u
30
+· · ·+a
2
+3, u
32
+u
31
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
a
u
31
+ u
30
+ ··· + a + 2
a
9
=
u
31
+ u
30
+ ··· + u + 2
u
31
+ u
30
+ ··· − a + 2
a
1
=
−u
5
− u
u
7
− u
5
+ 2u
3
− u
a
8
=
a − u
u
31
+ u
30
+ ··· − a + 2
a
11
=
−u
31
− u
30
+ ··· − u − 2
u
31
+ u
30
+ ··· + a + 2
a
7
=
u
5
+ u
−u
5
+ u
3
− u
a
3
=
−u
10
+ u
8
− 2u
6
+ u
4
− u
2
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
2
=
−u
27
+ 4u
25
+ ··· + 10u
5
− 5u
3
u
27
− 5u
25
+ ··· + 3u
3
− u
a
6
=
−u
17
+ 2u
15
− 5u
13
+ 6u
11
− 7u
9
+ 6u
7
− 2u
5
+ 2u
3
+ u
u
19
− 3u
17
+ 8u
15
− 13u
13
+ 17u
11
− 17u
9
+ 12u
7
− 8u
5
+ 3u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
30
+ 20u
28
+ 4u
27
−68u
26
−20u
25
+ 156u
24
+ 68u
23
−276u
22
−160u
21
+ 380u
20
+
292u
19
− 404u
18
− 428u
17
+ 328u
16
+ 504u
15
− 160u
14
− 496u
13
− 8u
12
+ 392u
11
+
124u
10
− 252u
9
− 156u
8
+ 120u
7
+ 116u
6
− 28u
5
− 64u
4
− 4u
3
+ 16u
2
+ 12u − 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
32
+ 15u
31
+ ··· + 2u + 1)
2
c
2
, c
5
(u
32
+ u
31
+ ··· − u
2
+ 1)
2
c
3
(u
32
+ 4u
31
+ ··· + 28u + 4)
2
c
4
(u
32
− u
31
+ ··· − 2u + 1)
2
c
6
(u
32
+ 3u
31
+ ··· + 2u + 3)
2
c
7
, c
9
, c
10
c
12
u
64
− 11u
63
+ ··· + 4u + 1
c
8
, c
11
u
64
+ u
63
+ ··· − 8574468u + 1426351
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
32
+ 5y
31
+ ··· + 2y + 1)
2
c
2
, c
5
(y
32
− 15y
31
+ ··· − 2y + 1)
2
c
3
(y
32
− 20y
31
+ ··· − 184y + 16)
2
c
4
(y
32
− 11y
31
+ ··· − 2y + 1)
2
c
6
(y
32
+ 5y
31
+ ··· + 164y + 9)
2
c
7
, c
9
, c
10
c
12
y
64
+ 43y
63
+ ··· − 58y + 1
c
8
, c
11
y
64
− 33y
63
+ ··· − 47292589687204y + 2034477175201
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613006 + 0.792175I
a = −0.991143 + 0.568727I
b = −1.182060 + 0.538855I
2.22015 + 7.30693I −2.17644 − 4.86883I
u = −0.613006 + 0.792175I
a = 0.378138 + 0.223448I
b = 0.86730 + 1.43651I
2.22015 + 7.30693I −2.17644 − 4.86883I
u = −0.613006 − 0.792175I
a = −0.991143 − 0.568727I
b = −1.182060 − 0.538855I
2.22015 − 7.30693I −2.17644 + 4.86883I
u = −0.613006 − 0.792175I
a = 0.378138 − 0.223448I
b = 0.86730 − 1.43651I
2.22015 − 7.30693I −2.17644 + 4.86883I
u = −0.674958 + 0.742403I
a = −0.814727 + 0.619700I
b = −0.843215 + 0.599874I
−0.345747 + 0.057794I −5.67435 + 0.61686I
u = −0.674958 + 0.742403I
a = 0.139769 + 0.122703I
b = 0.700606 + 1.011950I
−0.345747 + 0.057794I −5.67435 + 0.61686I
u = −0.674958 − 0.742403I
a = −0.814727 − 0.619700I
b = −0.843215 − 0.599874I
−0.345747 − 0.057794I −5.67435 − 0.61686I
u = −0.674958 − 0.742403I
a = 0.139769 − 0.122703I
b = 0.700606 − 1.011950I
−0.345747 − 0.057794I −5.67435 − 0.61686I
u = 0.600521 + 0.762759I
a = 0.990953 + 0.630677I
b = 1.150690 + 0.671706I
4.27947 − 2.26361I 1.018945 + 0.670058I
u = 0.600521 + 0.762759I
a = −0.390433 + 0.132083I
b = −0.99299 + 1.32833I
4.27947 − 2.26361I 1.018945 + 0.670058I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600521 − 0.762759I
a = 0.990953 − 0.630677I
b = 1.150690 − 0.671706I
4.27947 + 2.26361I 1.018945 − 0.670058I
u = 0.600521 − 0.762759I
a = −0.390433 − 0.132083I
b = −0.99299 − 1.32833I
4.27947 + 2.26361I 1.018945 − 0.670058I
u = −0.849583 + 0.407230I
a = −0.257323 − 0.869065I
b = 1.44423 − 0.10517I
3.39887 − 4.15286I 2.01286 + 7.18864I
u = −0.849583 + 0.407230I
a = −0.592259 + 1.276300I
b = −0.188985 + 0.615704I
3.39887 − 4.15286I 2.01286 + 7.18864I
u = −0.849583 − 0.407230I
a = −0.257323 + 0.869065I
b = 1.44423 + 0.10517I
3.39887 + 4.15286I 2.01286 − 7.18864I
u = −0.849583 − 0.407230I
a = −0.592259 − 1.276300I
b = −0.188985 − 0.615704I
3.39887 + 4.15286I 2.01286 − 7.18864I
u = −1.093530 + 0.032199I
a = −0.548154 − 1.299260I
b = 1.111940 + 0.241357I
10.01990 − 1.36697I 7.90065 + 0.55023I
u = −1.093530 + 0.032199I
a = −0.54538 + 1.33146I
b = 0.926137 − 0.270830I
10.01990 − 1.36697I 7.90065 + 0.55023I
u = −1.093530 − 0.032199I
a = −0.548154 + 1.299260I
b = 1.111940 − 0.241357I
10.01990 + 1.36697I 7.90065 − 0.55023I
u = −1.093530 − 0.032199I
a = −0.54538 − 1.33146I
b = 0.926137 + 0.270830I
10.01990 + 1.36697I 7.90065 − 0.55023I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098860 + 0.059621I
a = 0.552832 − 1.283140I
b = −1.188240 + 0.238476I
8.24887 + 6.50568I 4.96918 − 5.51070I
u = 1.098860 + 0.059621I
a = 0.54603 + 1.34276I
b = −0.842777 − 0.296157I
8.24887 + 6.50568I 4.96918 − 5.51070I
u = 1.098860 − 0.059621I
a = 0.552832 + 1.283140I
b = −1.188240 − 0.238476I
8.24887 − 6.50568I 4.96918 + 5.51070I
u = 1.098860 − 0.059621I
a = 0.54603 − 1.34276I
b = −0.842777 + 0.296157I
8.24887 − 6.50568I 4.96918 + 5.51070I
u = −0.858258 + 0.694285I
a = −0.353853 + 0.953789I
b = −0.696175 + 0.858994I
0.68161 − 2.66625I −1.77705 + 3.31297I
u = −0.858258 + 0.694285I
a = −0.504405 − 0.259504I
b = 0.637544 − 0.224845I
0.68161 − 2.66625I −1.77705 + 3.31297I
u = −0.858258 − 0.694285I
a = −0.353853 − 0.953789I
b = −0.696175 − 0.858994I
0.68161 + 2.66625I −1.77705 − 3.31297I
u = −0.858258 − 0.694285I
a = −0.504405 + 0.259504I
b = 0.637544 + 0.224845I
0.68161 + 2.66625I −1.77705 − 3.31297I
u = 0.828553 + 0.741140I
a = 0.286437 + 0.827841I
b = 0.593381 + 0.962196I
−2.41066 − 0.95663I −6.35494 + 0.97622I
u = 0.828553 + 0.741140I
a = 0.542115 − 0.086700I
b = −0.309214 − 0.140871I
−2.41066 − 0.95663I −6.35494 + 0.97622I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.828553 − 0.741140I
a = 0.286437 − 0.827841I
b = 0.593381 − 0.962196I
−2.41066 + 0.95663I −6.35494 − 0.97622I
u = 0.828553 − 0.741140I
a = 0.542115 + 0.086700I
b = −0.309214 + 0.140871I
−2.41066 + 0.95663I −6.35494 − 0.97622I
u = 0.891994 + 0.729689I
a = 0.253631 + 0.984227I
b = 0.796465 + 0.944428I
−2.21840 + 6.53878I −5.61404 − 6.99151I
u = 0.891994 + 0.729689I
a = 0.638363 − 0.254538I
b = −0.532638 − 0.469112I
−2.21840 + 6.53878I −5.61404 − 6.99151I
u = 0.891994 − 0.729689I
a = 0.253631 − 0.984227I
b = 0.796465 − 0.944428I
−2.21840 − 6.53878I −5.61404 + 6.99151I
u = 0.891994 − 0.729689I
a = 0.638363 + 0.254538I
b = −0.532638 + 0.469112I
−2.21840 − 6.53878I −5.61404 + 6.99151I
u = 1.022970 + 0.630121I
a = 0.702017 − 0.598737I
b = −1.234440 − 0.678426I
6.32371 + 5.05352I 4.11469 − 5.31459I
u = 1.022970 + 0.630121I
a = 0.320956 + 1.228860I
b = 0.988094 + 0.453551I
6.32371 + 5.05352I 4.11469 − 5.31459I
u = 1.022970 − 0.630121I
a = 0.702017 + 0.598737I
b = −1.234440 + 0.678426I
6.32371 − 5.05352I 4.11469 + 5.31459I
u = 1.022970 − 0.630121I
a = 0.320956 − 1.228860I
b = 0.988094 − 0.453551I
6.32371 − 5.05352I 4.11469 + 5.31459I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997643 + 0.681461I
a = −0.726980 − 0.495574I
b = 1.016280 − 0.754097I
0.62565 − 5.49753I −3.62281 + 4.60034I
u = −0.997643 + 0.681461I
a = −0.270663 + 1.177040I
b = −1.043920 + 0.650978I
0.62565 − 5.49753I −3.62281 + 4.60034I
u = −0.997643 − 0.681461I
a = −0.726980 + 0.495574I
b = 1.016280 + 0.754097I
0.62565 + 5.49753I −3.62281 − 4.60034I
u = −0.997643 − 0.681461I
a = −0.270663 − 1.177040I
b = −1.043920 − 0.650978I
0.62565 + 5.49753I −3.62281 − 4.60034I
u = −0.416995 + 0.648442I
a = 0.866981 − 0.198915I
b = 1.88993 + 1.31188I
3.37910 − 4.79464I −1.29089 + 5.61871I
u = −0.416995 + 0.648442I
a = −1.28398 + 0.84736I
b = −1.35726 + 1.45293I
3.37910 − 4.79464I −1.29089 + 5.61871I
u = −0.416995 − 0.648442I
a = 0.866981 + 0.198915I
b = 1.88993 − 1.31188I
3.37910 + 4.79464I −1.29089 − 5.61871I
u = −0.416995 − 0.648442I
a = −1.28398 − 0.84736I
b = −1.35726 − 1.45293I
3.37910 + 4.79464I −1.29089 − 5.61871I
u = 1.031610 + 0.673233I
a = 0.763322 − 0.549290I
b = −1.14586 − 0.83030I
5.55363 + 7.72193I 2.98438 − 5.32873I
u = 1.031610 + 0.673233I
a = 0.268289 + 1.222520I
b = 1.122660 + 0.546584I
5.55363 + 7.72193I 2.98438 − 5.32873I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031610 − 0.673233I
a = 0.763322 + 0.549290I
b = −1.14586 + 0.83030I
5.55363 − 7.72193I 2.98438 + 5.32873I
u = 1.031610 − 0.673233I
a = 0.268289 − 1.222520I
b = 1.122660 − 0.546584I
5.55363 − 7.72193I 2.98438 + 5.32873I
u = −1.036490 + 0.686644I
a = −0.786050 − 0.537663I
b = 1.12365 − 0.88821I
3.48615 − 12.88870I −0.12323 + 9.41526I
u = −1.036490 + 0.686644I
a = −0.250444 + 1.224310I
b = −1.171630 + 0.573964I
3.48615 − 12.88870I −0.12323 + 9.41526I
u = −1.036490 − 0.686644I
a = −0.786050 + 0.537663I
b = 1.12365 + 0.88821I
3.48615 + 12.88870I −0.12323 − 9.41526I
u = −1.036490 − 0.686644I
a = −0.250444 − 1.224310I
b = −1.171630 − 0.573964I
3.48615 + 12.88870I −0.12323 − 9.41526I
u = 0.730192 + 0.168194I
a = 0.156002 − 1.338560I
b = −1.55205 − 0.40149I
4.45908 + 0.19319I 5.20830 − 0.78328I
u = 0.730192 + 0.168194I
a = 0.57419 + 1.50676I
b = −0.646114 + 0.904532I
4.45908 + 0.19319I 5.20830 − 0.78328I
u = 0.730192 − 0.168194I
a = 0.156002 + 1.338560I
b = −1.55205 + 0.40149I
4.45908 − 0.19319I 5.20830 + 0.78328I
u = 0.730192 − 0.168194I
a = 0.57419 − 1.50676I
b = −0.646114 − 0.904532I
4.45908 − 0.19319I 5.20830 + 0.78328I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164238 + 0.469611I
a = 1.84018 − 0.39005I
b = 2.92010 + 1.71566I
1.64661 + 1.19641I −5.57525 − 0.85209I
u = −0.164238 + 0.469611I
a = −2.00442 + 0.85967I
b = −1.86144 + 2.61422I
1.64661 + 1.19641I −5.57525 − 0.85209I
u = −0.164238 − 0.469611I
a = 1.84018 + 0.39005I
b = 2.92010 − 1.71566I
1.64661 − 1.19641I −5.57525 + 0.85209I
u = −0.164238 − 0.469611I
a = −2.00442 − 0.85967I
b = −1.86144 − 2.61422I
1.64661 − 1.19641I −5.57525 + 0.85209I
19
III. I
u
3
= hu
2
a − u
3
− u
2
+ b − a, a
2
− au − u, u
4
+ u
3
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
a
−u
2
a + u
3
+ u
2
+ a
a
9
=
u
2
a + u
2
u
3
a + u
2
a + u
3
+ u
2
+ u + 1
a
1
=
−u
3
− 1
u
3
+ u
2
− u
a
8
=
a − u
u
3
+ u
2
− a + u
a
11
=
u
2
a − u
3
− u
2
−u
2
a + u
3
+ u
2
+ a
a
7
=
u
3
+ 1
−1
a
3
=
−u
3
1
a
2
=
−u
u
3
− u
a
6
=
u
2
+ 1
u
3
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 2u
2
+ 1)
2
c
2
, c
5
(u
4
+ u
3
+ 1)
2
c
3
(u − 1)
8
c
4
(u
4
− u
3
+ 1)
2
c
6
(u
4
− u
2
− 2u + 3)
2
c
7
, c
9
, c
10
c
12
u
8
− u
7
+ 3u
6
− 5u
5
+ 4u
4
− 5u
3
+ 3u
2
+ 1
c
8
, c
11
u
8
− 3u
6
+ 14u
4
+ 6u
3
− 18u
2
− 10u + 19
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
c
2
, c
4
, c
5
(y
4
− y
3
+ 2y
2
+ 1)
2
c
3
(y −1)
8
c
6
(y
4
− 2y
3
+ 7y
2
− 10y + 9)
2
c
7
, c
9
, c
10
c
12
y
8
+ 5y
7
+ 7y
6
− 5y
5
− 14y
4
+ 5y
3
+ 17y
2
+ 6y + 1
c
8
, c
11
y
8
− 6y
7
+ 37y
6
− 120y
5
+ 342y
4
− 654y
3
+ 976y
2
− 784y + 361
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518913 + 0.666610I
a = 1.107930 + 0.828053I
b = 1.14766 + 1.14065I
4.93480 2.00000
u = 0.518913 + 0.666610I
a = −0.589021 − 0.161444I
b = −1.53098 + 1.15189I
4.93480 2.00000
u = 0.518913 − 0.666610I
a = 1.107930 − 0.828053I
b = 1.14766 − 1.14065I
4.93480 2.00000
u = 0.518913 − 0.666610I
a = −0.589021 + 0.161444I
b = −1.53098 − 1.15189I
4.93480 2.00000
u = −1.018910 + 0.602565I
a = −0.667444 − 0.634184I
b = 1.28901 − 0.59560I
4.93480 2.00000
u = −1.018910 + 0.602565I
a = −0.351469 + 1.236750I
b = −0.905690 + 0.400260I
4.93480 2.00000
u = −1.018910 − 0.602565I
a = −0.667444 + 0.634184I
b = 1.28901 + 0.59560I
4.93480 2.00000
u = −1.018910 − 0.602565I
a = −0.351469 − 1.236750I
b = −0.905690 − 0.400260I
4.93480 2.00000
23
IV. I
u
4
= hb + 1, a
2
− a + 2, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
5
=
1
−1
a
12
=
a
−1
a
9
=
a − 2
−a + 1
a
1
=
−2
1
a
8
=
a − 1
−a
a
11
=
a + 1
−1
a
7
=
2
−1
a
3
=
−1
1
a
2
=
−1
0
a
6
=
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u + 1)
2
c
2
, c
3
, c
5
c
8
, c
11
(u − 1)
2
c
6
u
2
c
7
, c
9
, c
10
c
12
u
2
− u + 2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
c
11
(y −1)
2
c
6
y
2
c
7
, c
9
, c
10
c
12
y
2
+ 3y + 4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.50000 + 1.32288I
b = −1.00000
4.93480 2.00000
u = 1.00000
a = 0.50000 − 1.32288I
b = −1.00000
4.93480 2.00000
27
V. I
u
5
= hb − u − 1, a − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
1
a
12
=
1
u + 1
a
9
=
u
2u − 1
a
1
=
0
−1
a
8
=
1
u
a
11
=
−u
u + 1
a
7
=
0
1
a
3
=
1
1
a
2
=
1
0
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u − 1)
2
c
4
, c
7
, c
9
c
10
, c
12
u
2
+ 1
c
5
(u + 1)
2
c
6
u
2
c
8
u
2
− 2u + 2
c
11
u
2
+ 2u + 2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y −1)
2
c
4
, c
7
, c
9
c
10
, c
12
(y + 1)
2
c
6
y
2
c
8
, c
11
y
2
+ 4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.00000 + 1.00000I
1.64493 0
u = − 1.000000I
a = 1.00000
b = 1.00000 − 1.00000I
1.64493 0
31
VI.
I
v
1
= ha, v
5
+ 2v
4
− 16v
2
+ 64b − 16v + 32, v
6
+ 2v
5
− 16v
3
− 16v
2
+ 32v + 64i
(i) Arc colorings
a
4
=
1
0
a
10
=
v
0
a
5
=
1
0
a
12
=
0
−
1
64
v
5
−
1
32
v
4
+ ··· +
1
4
v −
1
2
a
9
=
v
1
64
v
5
+
1
32
v
4
+ ··· −
1
4
v +
1
2
a
1
=
−v
−
1
32
v
5
−
1
16
v
4
+ ··· +
1
2
v − 1
a
8
=
−
1
64
v
5
−
1
32
v
4
+ ··· +
5
4
v −
1
2
1
64
v
5
+
1
32
v
4
+ ··· −
1
4
v +
1
2
a
11
=
1
64
v
5
+
1
32
v
4
+ ··· −
1
4
v +
1
2
−
1
64
v
5
−
1
32
v
4
+ ··· +
1
4
v −
1
2
a
7
=
−
1
32
v
5
−
1
16
v
4
+ ··· +
3
2
v − 1
1
32
v
5
+
1
16
v
4
+ ··· −
1
2
v + 1
a
3
=
−
1
32
v
5
+
1
8
v
3
+ ··· −
1
2
v − 3
1
32
v
5
−
1
8
v
3
−
1
2
v
2
+
1
2
v + 2
a
2
=
−
1
16
v
4
+
1
8
v
3
+
1
4
v
2
− 2
−
1
8
v
3
+ 1
a
6
=
1
32
v
5
+
1
16
v
4
+ ··· +
1
2
v + 1
−
1
32
v
5
+
1
4
v
2
−
1
2
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
17
128
v
5
+
1
32
v
3
+
9
8
v
2
−
1
8
v −
13
2
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
5
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
4
u
6
c
7
, c
9
(u − 1)
6
c
8
64(64u
6
+ 32u
5
− 16u
4
− 16u
3
+ 2u + 1)
c
10
, c
12
(u + 1)
6
c
11
64(64u
6
− 32u
5
− 16u
4
+ 16u
3
− 2u + 1)
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
5
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
4
y
6
c
7
, c
9
, c
10
c
12
(y − 1)
6
c
8
, c
11
4096(4096y
6
− 3072y
5
+ 1280y
4
− 256y
3
+ 32y
2
− 4y + 1)
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.46557 + 0.76250I
a = 0
b = −0.536975 − 0.279376I
−1.64493 + 5.69302I −5.77678 − 3.57560I
v = −1.46557 − 0.76250I
a = 0
b = −0.536975 + 0.279376I
−1.64493 − 5.69302I −5.77678 + 3.57560I
v = 1.83596 + 0.54142I
a = 0
b = 0.501096 − 0.147771I
0.245672 − 0.924305I −3.59017 − 1.04572I
v = 1.83596 − 0.54142I
a = 0
b = 0.501096 + 0.147771I
0.245672 + 0.924305I −3.59017 + 1.04572I
v = −1.37039 + 2.12652I
a = 0
b = −0.214122 − 0.332266I
−3.53554 − 0.92430I −5.00805 + 6.48027I
v = −1.37039 − 2.12652I
a = 0
b = −0.214122 + 0.332266I
−3.53554 + 0.92430I −5.00805 − 6.48027I
35
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u + 1)
2
(u
4
+ u
3
+ 2u
2
+ 1)
2
· (u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
32
+ 15u
31
+ ··· + 2u + 1)
2
· (u
46
+ 22u
45
+ ··· + 65u + 16)
c
2
(u − 1)
4
(u
4
+ u
3
+ 1)
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
· ((u
32
+ u
31
+ ··· − u
2
+ 1)
2
)(u
46
+ 2u
45
+ ··· + 15u + 4)
c
3
((u − 1)
12
)(u
6
− u
5
+ ··· − u + 1)(u
32
+ 4u
31
+ ··· + 28u + 4)
2
· (u
46
+ 2u
45
+ ··· + 419884u + 136336)
c
4
u
6
(u + 1)
2
(u
2
+ 1)(u
4
− u
3
+ 1)
2
(u
32
− u
31
+ ··· − 2u + 1)
2
· (u
46
+ 3u
45
+ ··· + 30720u + 8192)
c
5
(u − 1)
2
(u + 1)
2
(u
4
+ u
3
+ 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
· ((u
32
+ u
31
+ ··· − u
2
+ 1)
2
)(u
46
+ 2u
45
+ ··· + 15u + 4)
c
6
u
4
(u
4
− u
2
− 2u + 3)
2
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· ((u
32
+ 3u
31
+ ··· + 2u + 3)
2
)(u
46
+ 2u
44
+ ··· + 2032u + 448)
c
7
, c
9
((u − 1)
6
)(u
2
+ 1)(u
2
− u + 2)(u
8
− u
7
+ ··· + 3u
2
+ 1)
· (u
46
+ 6u
45
+ ··· − 6u + 1)(u
64
− 11u
63
+ ··· + 4u + 1)
c
8
4096(u − 1)
2
(u
2
− 2u + 2)(64u
6
+ 32u
5
− 16u
4
− 16u
3
+ 2u + 1)
· (u
8
− 3u
6
+ 14u
4
+ 6u
3
− 18u
2
− 10u + 19)
· (64u
46
− 96u
45
+ ··· − 8u
2
+ 2)
· (u
64
+ u
63
+ ··· − 8574468u + 1426351)
c
10
, c
12
((u + 1)
6
)(u
2
+ 1)(u
2
− u + 2)(u
8
− u
7
+ ··· + 3u
2
+ 1)
· (u
46
+ 6u
45
+ ··· − 6u + 1)(u
64
− 11u
63
+ ··· + 4u + 1)
c
11
4096(u − 1)
2
(u
2
+ 2u + 2)(64u
6
− 32u
5
− 16u
4
+ 16u
3
− 2u + 1)
· (u
8
− 3u
6
+ 14u
4
+ 6u
3
− 18u
2
− 10u + 19)
· (64u
46
− 96u
45
+ ··· − 8u
2
+ 2)
· (u
64
+ u
63
+ ··· − 8574468u + 1426351)
36
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
4
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· ((y
32
+ 5y
31
+ ··· + 2y + 1)
2
)(y
46
+ 6y
45
+ ··· + 3391y + 256)
c
2
, c
5
(y − 1)
4
(y
4
− y
3
+ 2y
2
+ 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· ((y
32
− 15y
31
+ ··· − 2y + 1)
2
)(y
46
− 22y
45
+ ··· − 65y + 16)
c
3
(y − 1)
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
32
− 20y
31
+ ··· − 184y + 16)
2
· (y
46
− 30y
45
+ ··· − 205613722768y + 18587504896)
c
4
y
6
(y − 1)
2
(y + 1)
2
(y
4
− y
3
+ 2y
2
+ 1)
2
(y
32
− 11y
31
+ ··· − 2y + 1)
2
· (y
46
− 11y
45
+ ··· − 1572864000y + 67108864)
c
6
y
4
(y
4
− 2y
3
+ 7y
2
− 10y + 9)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
32
+ 5y
31
+ ··· + 164y + 9)
2
· (y
46
+ 4y
45
+ ··· + 910080y + 200704)
c
7
, c
9
, c
10
c
12
(y − 1)
6
(y + 1)
2
(y
2
+ 3y + 4)
· (y
8
+ 5y
7
+ 7y
6
− 5y
5
− 14y
4
+ 5y
3
+ 17y
2
+ 6y + 1)
· (y
46
+ 26y
45
+ ··· − 12y + 1)(y
64
+ 43y
63
+ ··· − 58y + 1)
c
8
, c
11
16777216(y − 1)
2
(y
2
+ 4)
· (4096y
6
− 3072y
5
+ 1280y
4
− 256y
3
+ 32y
2
− 4y + 1)
· (y
8
− 6y
7
+ 37y
6
− 120y
5
+ 342y
4
− 654y
3
+ 976y
2
− 784y + 361)
· (4096y
46
− 93184y
45
+ ··· − 32y + 4)
· (y
64
− 33y
63
+ ··· − 47292589687204y + 2034477175201)
37
