12a
0311
(K12a
0311
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 12 2 11 1 4 5 7 9
Solving Sequence
4,9
10 5
1,11
8 3 7 12 6 2
c
9
c
4
c
10
c
8
c
3
c
7
c
12
c
5
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.08905 × 10
49
u
39
− 1.01301 × 10
50
u
38
+ ··· + 2.88391 × 10
51
b − 2.25929 × 10
51
,
− 4.64639 × 10
50
u
39
+ 1.25973 × 10
51
u
38
+ ··· + 2.30713 × 10
52
a + 9.26479 × 10
51
,
u
40
− 3u
39
+ ··· − 192u
2
− 32i
I
u
2
= h3u
30
a − 3u
30
+ ··· + 5a + 11, −112u
30
a − 102u
30
+ ··· − 77a − 491, u
31
+ u
30
+ ··· + 2u + 1i
I
u
3
= hb + 1, 8a
2
− 2au + 8a − u + 3, u
2
− 2i
I
u
4
= hb + u, 3a − 5u + 1, u
2
+ 1i
I
v
1
= ha, b − 1, 4v
2
+ 2v + 1i
* 5 irreducible components of dim
C
= 0, with total 110 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
= h4.09 × 10
49
u
39
− 1.01 × 10
50
u
38
+ · · · + 2.88 × 10
51
b − 2.26 ×
10
51
, −4.65 × 10
50
u
39
+ 1.26 × 10
51
u
38
+ · · · + 2.31 × 10
52
a + 9.26 ×
10
51
, u
40
− 3u
39
+ · · · − 192u
2
− 32i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
0.0201393u
39
− 0.0546018u
38
+ ··· − 3.01826u − 0.401572
−0.0141788u
39
+ 0.0351264u
38
+ ··· + 1.72761u + 0.783414
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
−0.000995231u
39
+ 0.00708915u
38
+ ··· + 0.246219u + 1.21626
0.0112644u
39
− 0.0355065u
38
+ ··· − 1.56872u − 0.703111
a
3
=
0.00214826u
39
− 0.00643004u
38
+ ··· + 1.27576u − 0.435663
−0.00982399u
39
+ 0.0113860u
38
+ ··· − 0.302904u + 0.425293
a
7
=
0.00280373u
39
− 0.0167005u
38
+ ··· − 1.93511u + 0.195727
−0.00183607u
39
− 0.0121602u
38
+ ··· − 0.993431u − 0.862558
a
12
=
0.00596044u
39
− 0.0194753u
38
+ ··· − 1.29065u + 0.381841
−0.0141788u
39
+ 0.0351264u
38
+ ··· + 1.72761u + 0.783414
a
6
=
0.00328746u
39
+ 0.00123723u
38
+ ··· − 0.904111u + 0.0108409
0.00995923u
39
− 0.0198393u
38
+ ··· − 0.266449u + 0.780010
a
2
=
0.00639471u
39
− 0.0181709u
38
+ ··· − 0.259320u + 0.0460362
−0.00105452u
39
+ 0.0113351u
38
+ ··· + 0.871003u + 0.956721
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.102467u
39
− 0.211834u
38
+ ··· − 12.5141u + 4.58841
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 12u
39
+ ··· − 6305u + 64
c
2
, c
6
u
40
− 2u
39
+ ··· + 57u − 8
c
3
, c
5
64(64u
40
− 32u
39
+ ··· + 40u − 8)
c
4
, c
9
, c
10
u
40
+ 3u
39
+ ··· − 192u
2
− 32
c
7
, c
8
, c
11
c
12
u
40
− 2u
39
+ ··· + 19u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 20y
39
+ ··· − 35596225y + 4096
c
2
, c
6
y
40
+ 12y
39
+ ··· − 6305y + 64
c
3
, c
5
4096(4096y
40
+ 3072y
39
+ ··· − 1312y + 64)
c
4
, c
9
, c
10
y
40
− 35y
39
+ ··· + 12288y + 1024
c
7
, c
8
, c
11
c
12
y
40
+ 14y
39
+ ··· + 115y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.440137 + 0.904158I
a = −0.46183 − 1.85321I
b = −0.513797 + 1.310640I
6.8384 + 13.5929I −4.21050 − 9.23121I
u = −0.440137 − 0.904158I
a = −0.46183 + 1.85321I
b = −0.513797 − 1.310640I
6.8384 − 13.5929I −4.21050 + 9.23121I
u = 0.429948 + 0.950952I
a = −0.40500 + 1.76947I
b = −0.420528 − 1.284740I
8.33666 − 7.25783I −2.07869 + 5.28616I
u = 0.429948 − 0.950952I
a = −0.40500 − 1.76947I
b = −0.420528 + 1.284740I
8.33666 + 7.25783I −2.07869 − 5.28616I
u = −0.187511 + 0.912417I
a = 0.02873 − 1.86648I
b = −0.409629 + 0.962631I
−0.05063 + 5.82607I −8.03423 − 8.68283I
u = −0.187511 − 0.912417I
a = 0.02873 + 1.86648I
b = −0.409629 − 0.962631I
−0.05063 − 5.82607I −8.03423 + 8.68283I
u = −0.808683 + 0.827619I
a = −0.582063 − 1.047810I
b = 0.378612 + 1.207320I
5.82044 − 7.81253I −4.24739 + 6.17178I
u = −0.808683 − 0.827619I
a = −0.582063 + 1.047810I
b = 0.378612 − 1.207320I
5.82044 + 7.81253I −4.24739 − 6.17178I
u = 1.199590 + 0.427748I
a = 0.411698 − 1.287580I
b = 0.387145 + 0.855456I
−3.26360 − 1.49706I −11.41293 + 5.34755I
u = 1.199590 − 0.427748I
a = 0.411698 + 1.287580I
b = 0.387145 − 0.855456I
−3.26360 + 1.49706I −11.41293 − 5.34755I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907718 + 0.908783I
a = −0.490822 + 1.072100I
b = 0.255927 − 1.148880I
7.10406 + 1.09362I −1.87527 − 4.00746I
u = 0.907718 − 0.908783I
a = −0.490822 − 1.072100I
b = 0.255927 + 1.148880I
7.10406 − 1.09362I −1.87527 + 4.00746I
u = −0.227717 + 1.277080I
a = 0.170112 + 1.366760I
b = −0.110689 − 0.909064I
4.51263 − 0.64388I −12.6147 + 10.6040I
u = −0.227717 − 1.277080I
a = 0.170112 − 1.366760I
b = −0.110689 + 0.909064I
4.51263 + 0.64388I −12.6147 − 10.6040I
u = −1.337180 + 0.093481I
a = −0.568363 − 0.175872I
b = −1.40862 − 0.31480I
−5.44648 − 0.82010I −6.94084 − 0.88214I
u = −1.337180 − 0.093481I
a = −0.568363 + 0.175872I
b = −1.40862 + 0.31480I
−5.44648 + 0.82010I −6.94084 + 0.88214I
u = 1.363060 + 0.137405I
a = −0.477079 + 0.243693I
b = −1.40170 + 0.49884I
−6.07938 − 4.11851I −9.52490 + 6.62129I
u = 1.363060 − 0.137405I
a = −0.477079 − 0.243693I
b = −1.40170 − 0.49884I
−6.07938 + 4.11851I −9.52490 − 6.62129I
u = −0.527569 + 0.240579I
a = −0.374770 − 0.519466I
b = 0.732459 + 0.494483I
−2.68524 − 2.28522I −15.8983 + 1.9193I
u = −0.527569 − 0.240579I
a = −0.374770 + 0.519466I
b = 0.732459 − 0.494483I
−2.68524 + 2.28522I −15.8983 − 1.9193I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43224
a = −0.492239
b = −0.887681
−6.54259 −14.4120
u = 1.47203 + 0.11321I
a = −0.308809 + 0.057755I
b = −0.961493 + 0.650737I
−9.12443 + 0.78989I −16.6960 − 1.5011I
u = 1.47203 − 0.11321I
a = −0.308809 − 0.057755I
b = −0.961493 − 0.650737I
−9.12443 − 0.78989I −16.6960 + 1.5011I
u = 1.44029 + 0.35968I
a = 0.89871 − 1.21509I
b = 0.577709 + 1.136010I
−5.34996 − 10.39560I −11.35294 + 7.92882I
u = 1.44029 − 0.35968I
a = 0.89871 + 1.21509I
b = 0.577709 − 1.136010I
−5.34996 + 10.39560I −11.35294 − 7.92882I
u = −1.42057 + 0.48007I
a = 0.631676 + 1.097510I
b = 0.374302 − 1.088160I
0.17053 + 6.80496I −8.00000 − 8.25092I
u = −1.42057 − 0.48007I
a = 0.631676 − 1.097510I
b = 0.374302 + 1.088160I
0.17053 − 6.80496I −8.00000 + 8.25092I
u = −1.51413 + 0.15368I
a = −0.505558 − 0.545335I
b = −0.073480 + 0.597284I
−4.25095 − 1.64346I −8.00000 + 0.I
u = −1.51413 − 0.15368I
a = −0.505558 + 0.545335I
b = −0.073480 − 0.597284I
−4.25095 + 1.64346I −8.00000 + 0.I
u = 1.50913 + 0.33966I
a = 1.10053 − 1.00347I
b = 0.63668 + 1.33597I
0.5699 − 18.1001I 0. + 9.77509I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50913 − 0.33966I
a = 1.10053 + 1.00347I
b = 0.63668 − 1.33597I
0.5699 + 18.1001I 0. − 9.77509I
u = −1.50745 + 0.35840I
a = 1.01596 + 0.98674I
b = 0.57197 − 1.32042I
2.12914 + 11.97580I 0
u = −1.50745 − 0.35840I
a = 1.01596 − 0.98674I
b = 0.57197 + 1.32042I
2.12914 − 11.97580I 0
u = 0.398385
a = 0.194086
b = 0.411087
−0.650198 −15.0380
u = 0.060206 + 0.390625I
a = 1.81385 − 0.89243I
b = −0.311880 + 0.206339I
−0.52443 − 1.67679I −4.14197 + 2.11677I
u = 0.060206 − 0.390625I
a = 1.81385 + 0.89243I
b = −0.311880 − 0.206339I
−0.52443 + 1.67679I −4.14197 − 2.11677I
u = −0.085016 + 0.355683I
a = −0.687889 − 0.084642I
b = 1.230980 + 0.116031I
−1.36201 + 2.26426I 3.25236 − 9.63689I
u = −0.085016 − 0.355683I
a = −0.687889 + 0.084642I
b = 1.230980 − 0.116031I
−1.36201 − 2.26426I 3.25236 + 9.63689I
u = 1.69092 + 0.00044I
a = −0.185011 + 0.410776I
b = −0.295674 − 0.847006I
−3.61784 − 4.35903I 0
u = 1.69092 − 0.00044I
a = −0.185011 − 0.410776I
b = −0.295674 + 0.847006I
−3.61784 + 4.35903I 0
8
II. I
u
2
= h3u
30
a − 3u
30
+ · · · + 5a + 11, −112u
30
a − 102u
30
+ · · · − 77a −
491, u
31
+ u
30
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
a
−0.187500au
30
+ 0.187500u
30
+ ··· − 0.312500a − 0.687500
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
0.187500au
30
+ 1.52679u
30
+ ··· − 0.687500a + 2.11607
0.187500au
30
− 0.187500u
30
+ ··· + 0.312500a + 0.687500
a
3
=
0.830357au
30
− 1.21811u
30
+ ··· + 2.09821a + 0.554847
−0.625000au
30
− 0.232143u
30
+ ··· − 0.375000a − 1.33929
a
7
=
0.187500au
30
+ 1.52679u
30
+ ··· − 0.687500a + 1.11607
1
a
12
=
−0.187500au
30
+ 0.187500u
30
+ ··· + 0.687500a − 0.687500
−0.187500au
30
+ 0.187500u
30
+ ··· − 0.312500a − 0.687500
a
6
=
0.232143au
30
− 2.41582u
30
+ ··· + 1.33929a − 1.13520
−0.312500au
30
− 0.830357u
30
+ ··· − 0.187500a − 2.09821
a
2
=
−0.758929au
30
− 0.547194u
30
+ ··· + 1.54464a − 1.87117
−0.562500au
30
− 0.00892857u
30
+ ··· − 0.937500a − 1.20536
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
28
− 52u
26
+ 4u
25
+ 292u
24
− 48u
23
− 916u
22
+ 244u
21
+
1732u
20
− 672u
19
− 1988u
18
+ 1056u
17
+ 1360u
16
− 896u
15
− 644u
14
+ 332u
13
+
420u
12
− 60u
11
− 288u
10
+ 84u
9
+ 88u
8
− 16u
6
− 44u
5
+ 4u
2
− 16u − 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
31
+ 11u
30
+ ··· − 4u − 1)
2
c
2
, c
6
(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
c
3
, c
5
49(49u
62
− 259u
61
+ ··· − 1.07072 × 10
7
u + 1308800)
c
4
, c
9
, c
10
(u
31
− u
30
+ ··· + 2u − 1)
2
c
7
, c
8
, c
11
c
12
u
62
+ 5u
61
+ ··· + 101u + 10
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
31
+ 19y
30
+ ··· − 8y −1)
2
c
2
, c
6
(y
31
+ 11y
30
+ ··· − 4y −1)
2
c
3
, c
5
2401
· (2401y
62
+ 64827y
61
+ ··· − 13911596441600y + 1712957440000)
c
4
, c
9
, c
10
(y
31
− 29y
30
+ ··· − 4y −1)
2
c
7
, c
8
, c
11
c
12
y
62
+ 39y
61
+ ··· + 1299y + 100
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.196790 + 0.189244I
a = 1.281310 + 0.314655I
b = 0.736083 − 1.151530I
3.79282 + 0.40298I −4.92930 − 0.52831I
u = −1.196790 + 0.189244I
a = 0.029998 − 0.447048I
b = 0.31189 + 1.51073I
3.79282 + 0.40298I −4.92930 − 0.52831I
u = −1.196790 − 0.189244I
a = 1.281310 − 0.314655I
b = 0.736083 + 1.151530I
3.79282 − 0.40298I −4.92930 + 0.52831I
u = −1.196790 − 0.189244I
a = 0.029998 + 0.447048I
b = 0.31189 − 1.51073I
3.79282 − 0.40298I −4.92930 + 0.52831I
u = 0.371332 + 0.681959I
a = 0.437240 + 0.099266I
b = −1.025610 + 0.013746I
2.81425 − 8.17190I −6.44268 + 8.00325I
u = 0.371332 + 0.681959I
a = 0.40027 − 1.90954I
b = 0.52071 + 1.33060I
2.81425 − 8.17190I −6.44268 + 8.00325I
u = 0.371332 − 0.681959I
a = 0.437240 − 0.099266I
b = −1.025610 − 0.013746I
2.81425 + 8.17190I −6.44268 − 8.00325I
u = 0.371332 − 0.681959I
a = 0.40027 + 1.90954I
b = 0.52071 − 1.33060I
2.81425 + 8.17190I −6.44268 − 8.00325I
u = 0.434998 + 0.611250I
a = 0.553711 − 0.502128I
b = −0.543967 + 0.395556I
−1.60703 − 1.99617I −11.89924 + 3.62729I
u = 0.434998 + 0.611250I
a = 0.48079 − 1.60306I
b = 0.423951 + 0.864140I
−1.60703 − 1.99617I −11.89924 + 3.62729I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.434998 − 0.611250I
a = 0.553711 + 0.502128I
b = −0.543967 − 0.395556I
−1.60703 + 1.99617I −11.89924 − 3.62729I
u = 0.434998 − 0.611250I
a = 0.48079 + 1.60306I
b = 0.423951 − 0.864140I
−1.60703 + 1.99617I −11.89924 − 3.62729I
u = 1.239060 + 0.217665I
a = 1.244900 − 0.296015I
b = 0.843023 + 1.049800I
3.41810 − 5.89464I −5.94513 + 6.44091I
u = 1.239060 + 0.217665I
a = −0.213070 + 0.516323I
b = 0.20988 − 1.57615I
3.41810 − 5.89464I −5.94513 + 6.44091I
u = 1.239060 − 0.217665I
a = 1.244900 + 0.296015I
b = 0.843023 − 1.049800I
3.41810 + 5.89464I −5.94513 − 6.44091I
u = 1.239060 − 0.217665I
a = −0.213070 − 0.516323I
b = 0.20988 + 1.57615I
3.41810 + 5.89464I −5.94513 − 6.44091I
u = 0.529247 + 0.517876I
a = 0.053894 − 1.405920I
b = 0.588857 − 0.075465I
2.14842 + 4.14236I −8.20039 − 2.04013I
u = 0.529247 + 0.517876I
a = 1.44126 − 0.83676I
b = −0.264698 + 1.158750I
2.14842 + 4.14236I −8.20039 − 2.04013I
u = 0.529247 − 0.517876I
a = 0.053894 + 1.405920I
b = 0.588857 + 0.075465I
2.14842 − 4.14236I −8.20039 + 2.04013I
u = 0.529247 − 0.517876I
a = 1.44126 + 0.83676I
b = −0.264698 − 1.158750I
2.14842 − 4.14236I −8.20039 + 2.04013I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343506 + 0.654959I
a = 0.213125 − 0.091385I
b = −0.878890 + 0.145845I
4.01963 + 2.73446I −4.23310 − 3.38925I
u = −0.343506 + 0.654959I
a = 0.47531 + 1.96420I
b = 0.362702 − 1.325630I
4.01963 + 2.73446I −4.23310 − 3.38925I
u = −0.343506 − 0.654959I
a = 0.213125 + 0.091385I
b = −0.878890 − 0.145845I
4.01963 − 2.73446I −4.23310 + 3.38925I
u = −0.343506 − 0.654959I
a = 0.47531 − 1.96420I
b = 0.362702 + 1.325630I
4.01963 − 2.73446I −4.23310 + 3.38925I
u = −1.26234
a = 1.24705 + 1.05057I
b = 0.323876 − 1.146600I
0.537061 −5.58210
u = −1.26234
a = 1.24705 − 1.05057I
b = 0.323876 + 1.146600I
0.537061 −5.58210
u = −0.028009 + 0.652167I
a = −0.30680 − 1.72943I
b = −0.573998 + 1.285130I
7.28578 + 2.71284I −0.10058 − 3.44665I
u = −0.028009 + 0.652167I
a = −0.19450 + 1.96096I
b = −0.45397 − 1.38921I
7.28578 + 2.71284I −0.10058 − 3.44665I
u = −0.028009 − 0.652167I
a = −0.30680 + 1.72943I
b = −0.573998 − 1.285130I
7.28578 − 2.71284I −0.10058 + 3.44665I
u = −0.028009 − 0.652167I
a = −0.19450 − 1.96096I
b = −0.45397 + 1.38921I
7.28578 − 2.71284I −0.10058 + 3.44665I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.358560 + 0.080822I
a = −0.49901 + 2.29998I
b = 0.076735 − 1.182270I
−1.93424 − 2.56488I −13.16453 + 4.43258I
u = 1.358560 + 0.080822I
a = 2.36676 + 0.38002I
b = 0.267326 + 0.813715I
−1.93424 − 2.56488I −13.16453 + 4.43258I
u = 1.358560 − 0.080822I
a = −0.49901 − 2.29998I
b = 0.076735 + 1.182270I
−1.93424 + 2.56488I −13.16453 − 4.43258I
u = 1.358560 − 0.080822I
a = 2.36676 − 0.38002I
b = 0.267326 − 0.813715I
−1.93424 + 2.56488I −13.16453 − 4.43258I
u = −0.464772 + 0.428483I
a = −0.21337 + 1.49668I
b = 0.274726 + 0.400923I
3.29780 + 0.92992I −6.40372 − 3.68841I
u = −0.464772 + 0.428483I
a = 1.87218 + 1.29697I
b = −0.052308 − 1.171690I
3.29780 + 0.92992I −6.40372 − 3.68841I
u = −0.464772 − 0.428483I
a = −0.21337 − 1.49668I
b = 0.274726 − 0.400923I
3.29780 − 0.92992I −6.40372 + 3.68841I
u = −0.464772 − 0.428483I
a = 1.87218 − 1.29697I
b = −0.052308 + 1.171690I
3.29780 − 0.92992I −6.40372 + 3.68841I
u = 1.43568 + 0.18978I
a = −0.939070 + 0.829544I
b = −0.275288 − 1.076150I
−2.60250 − 3.33239I −9.23670 + 3.21859I
u = 1.43568 + 0.18978I
a = 0.289833 + 0.332892I
b = 0.521278 − 0.041093I
−2.60250 − 3.33239I −9.23670 + 3.21859I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43568 − 0.18978I
a = −0.939070 − 0.829544I
b = −0.275288 + 1.076150I
−2.60250 + 3.33239I −9.23670 − 3.21859I
u = 1.43568 − 0.18978I
a = 0.289833 − 0.332892I
b = 0.521278 + 0.041093I
−2.60250 + 3.33239I −9.23670 − 3.21859I
u = 1.43808 + 0.24908I
a = −0.968905 + 0.795580I
b = −0.61976 − 1.34317I
−1.70250 − 6.04082I −8.35365 + 3.16093I
u = 1.43808 + 0.24908I
a = 0.393198 − 0.274074I
b = 1.120860 − 0.098271I
−1.70250 − 6.04082I −8.35365 + 3.16093I
u = 1.43808 − 0.24908I
a = −0.968905 − 0.795580I
b = −0.61976 + 1.34317I
−1.70250 + 6.04082I −8.35365 − 3.16093I
u = 1.43808 − 0.24908I
a = 0.393198 + 0.274074I
b = 1.120860 + 0.098271I
−1.70250 + 6.04082I −8.35365 − 3.16093I
u = −1.45066 + 0.25754I
a = −1.008450 − 0.802446I
b = −0.73854 + 1.34705I
−3.04348 + 11.60290I −10.34947 − 7.70694I
u = −1.45066 + 0.25754I
a = 0.334822 + 0.373412I
b = 1.219230 + 0.204321I
−3.04348 + 11.60290I −10.34947 − 7.70694I
u = −1.45066 − 0.25754I
a = −1.008450 + 0.802446I
b = −0.73854 − 1.34705I
−3.04348 − 11.60290I −10.34947 + 7.70694I
u = −1.45066 − 0.25754I
a = 0.334822 − 0.373412I
b = 1.219230 − 0.204321I
−3.04348 − 11.60290I −10.34947 + 7.70694I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46473 + 0.17711I
a = −0.752786 − 0.694476I
b = −0.144612 + 0.731261I
−4.22211 − 1.64856I −12.01509 + 2.12263I
u = −1.46473 + 0.17711I
a = −0.319336 − 0.515774I
b = 0.172653 + 0.424747I
−4.22211 − 1.64856I −12.01509 + 2.12263I
u = −1.46473 − 0.17711I
a = −0.752786 + 0.694476I
b = −0.144612 − 0.731261I
−4.22211 + 1.64856I −12.01509 − 2.12263I
u = −1.46473 − 0.17711I
a = −0.319336 + 0.515774I
b = 0.172653 − 0.424747I
−4.22211 + 1.64856I −12.01509 − 2.12263I
u = −1.46230 + 0.22292I
a = −0.948019 − 0.877022I
b = −0.641859 + 1.045060I
−7.71400 + 5.04935I −15.1253 − 3.4252I
u = −1.46230 + 0.22292I
a = 0.090986 + 0.159142I
b = 0.881829 + 0.374398I
−7.71400 + 5.04935I −15.1253 − 3.4252I
u = −1.46230 − 0.22292I
a = −0.948019 + 0.877022I
b = −0.641859 − 1.045060I
−7.71400 − 5.04935I −15.1253 + 3.4252I
u = −1.46230 − 0.22292I
a = 0.090986 − 0.159142I
b = 0.881829 − 0.374398I
−7.71400 − 5.04935I −15.1253 + 3.4252I
u = −0.265022 + 0.399657I
a = −1.88467 + 0.97391I
b = −0.124163 + 0.695584I
3.18273 + 1.02630I −5.81008 − 6.41690I
u = −0.265022 + 0.399657I
a = 1.75565 + 3.19567I
b = −0.017948 − 1.157170I
3.18273 + 1.02630I −5.81008 − 6.41690I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.265022 − 0.399657I
a = −1.88467 − 0.97391I
b = −0.124163 − 0.695584I
3.18273 − 1.02630I −5.81008 + 6.41690I
u = −0.265022 − 0.399657I
a = 1.75565 − 3.19567I
b = −0.017948 + 1.157170I
3.18273 − 1.02630I −5.81008 + 6.41690I
18
III. I
u
3
= hb + 1, 8a
2
− 2au + 8a − u + 3, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
2
a
5
=
−u
−u
a
1
=
a
−1
a
11
=
−1
0
a
8
=
a + 1
−1
a
3
=
au +
1
2
a +
5
8
u +
1
4
−au
a
7
=
a
−1
a
12
=
a − 1
−1
a
6
=
−2au +
1
2
a −
11
8
u +
1
4
−au − u
a
2
=
au + 2a +
3
8
u
−au + 2a −
1
2
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8au + 4u − 16
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
16(16u
4
+ 16u
3
− 4u
2
− 4u + 7)
c
4
, c
9
, c
10
(u
2
− 2)
2
c
5
16(16u
4
− 16u
3
− 4u
2
+ 4u + 7)
c
6
(u
2
+ u + 1)
2
c
7
, c
8
(u + 1)
4
c
11
, c
12
(u − 1)
4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
256(256y
4
− 384y
3
+ 368y
2
− 72y + 49)
c
4
, c
9
, c
10
(y −2)
4
c
7
, c
8
, c
11
c
12
(y −1)
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.323223 + 0.306186I
b = −1.00000
−6.57974 − 2.02988I −14.0000 + 3.4641I
u = 1.41421
a = −0.323223 − 0.306186I
b = −1.00000
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = −0.676777 + 0.306186I
b = −1.00000
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = −0.676777 − 0.306186I
b = −1.00000
−6.57974 − 2.02988I −14.0000 + 3.4641I
22
IV. I
u
4
= hb + u, 3a − 5u + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
5
=
−u
2u
a
1
=
5
3
u −
1
3
−u
a
11
=
2
−3
a
8
=
−
1
3
u −
2
3
1
a
3
=
1
3
u −
4
9
1
3
u +
1
3
a
7
=
−
7
3
u −
2
3
3u + 1
a
12
=
2
3
u −
1
3
−u
a
6
=
−u −
5
9
5
3
u +
2
3
a
2
=
4
3
u +
1
9
−
4
3
u −
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u + 1)
2
c
3
9(9u
2
+ 6u + 5)
c
4
, c
7
, c
8
c
9
, c
10
, c
11
c
12
u
2
+ 1
c
5
9(9u
2
− 6u + 5)
c
6
(u − 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y −1)
2
c
3
, c
5
81(81y
2
+ 54y + 25)
c
4
, c
7
, c
8
c
9
, c
10
, c
11
c
12
(y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.33333 + 1.66667I
b = − 1.000000I
4.93480 0
u = − 1.000000I
a = −0.33333 − 1.66667I
b = 1.000000I
4.93480 0
26
V. I
v
1
= ha, b − 1, 4v
2
+ 2v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
10
=
1
0
a
5
=
v
0
a
1
=
0
1
a
11
=
1
0
a
8
=
1
−1
a
3
=
2v
−v
a
7
=
0
−1
a
12
=
1
1
a
6
=
2v
v
a
2
=
2v + 1
−v +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7v −
25
2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
4(4u
2
− 2u + 1)
c
4
, c
9
, c
10
u
2
c
5
4(4u
2
+ 2u + 1)
c
7
, c
8
(u − 1)
2
c
11
, c
12
(u + 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
2
+ y + 1
c
3
, c
5
16(16y
2
+ 4y + 1)
c
4
, c
9
, c
10
y
2
c
7
, c
8
, c
11
c
12
(y − 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.250000 + 0.433013I
a = 0
b = 1.00000
−1.64493 + 2.02988I −14.2500 + 3.0311I
v = −0.250000 − 0.433013I
a = 0
b = 1.00000
−1.64493 − 2.02988I −14.2500 − 3.0311I
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
2
)(u
2
− u + 1)
3
(u
31
+ 11u
30
+ ··· − 4u − 1)
2
· (u
40
+ 12u
39
+ ··· − 6305u + 64)
c
2
((u + 1)
2
)(u
2
− u + 1)
2
(u
2
+ u + 1)(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
· (u
40
− 2u
39
+ ··· + 57u − 8)
c
3
1806336(4u
2
− 2u + 1)(9u
2
+ 6u + 5)(16u
4
+ 16u
3
+ ··· − 4u + 7)
· (64u
40
− 32u
39
+ ··· + 40u − 8)
· (49u
62
− 259u
61
+ ··· − 10707200u + 1308800)
c
4
, c
9
, c
10
u
2
(u
2
− 2)
2
(u
2
+ 1)(u
31
− u
30
+ ··· + 2u − 1)
2
· (u
40
+ 3u
39
+ ··· − 192u
2
− 32)
c
5
1806336(4u
2
+ 2u + 1)(9u
2
− 6u + 5)(16u
4
− 16u
3
+ ··· + 4u + 7)
· (64u
40
− 32u
39
+ ··· + 40u − 8)
· (49u
62
− 259u
61
+ ··· − 10707200u + 1308800)
c
6
((u − 1)
2
)(u
2
− u + 1)(u
2
+ u + 1)
2
(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
· (u
40
− 2u
39
+ ··· + 57u − 8)
c
7
, c
8
((u − 1)
2
)(u + 1)
4
(u
2
+ 1)(u
40
− 2u
39
+ ··· + 19u − 7)
· (u
62
+ 5u
61
+ ··· + 101u + 10)
c
11
, c
12
((u − 1)
4
)(u + 1)
2
(u
2
+ 1)(u
40
− 2u
39
+ ··· + 19u − 7)
· (u
62
+ 5u
61
+ ··· + 101u + 10)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
2
+ y + 1)
3
(y
31
+ 19y
30
+ ··· − 8y − 1)
2
· (y
40
+ 20y
39
+ ··· − 35596225y + 4096)
c
2
, c
6
((y − 1)
2
)(y
2
+ y + 1)
3
(y
31
+ 11y
30
+ ··· − 4y − 1)
2
· (y
40
+ 12y
39
+ ··· − 6305y + 64)
c
3
, c
5
3262849744896(16y
2
+ 4y + 1)(81y
2
+ 54y + 25)
· (256y
4
− 384y
3
+ 368y
2
− 72y + 49)
· (4096y
40
+ 3072y
39
+ ··· − 1312y + 64)
· (2401y
62
+ 64827y
61
+ ··· − 13911596441600y + 1712957440000)
c
4
, c
9
, c
10
y
2
(y − 2)
4
(y + 1)
2
(y
31
− 29y
30
+ ··· − 4y − 1)
2
· (y
40
− 35y
39
+ ··· + 12288y + 1024)
c
7
, c
8
, c
11
c
12
((y − 1)
6
)(y + 1)
2
(y
40
+ 14y
39
+ ··· + 115y + 49)
· (y
62
+ 39y
61
+ ··· + 1299y + 100)
32
