12a
0988
(K12a
0988
)
A knot diagram
1
Linearized knot diagam
4 6 11 10 9 3 12 1 5 2 7 8
Solving Sequence
7,12
8 1
3,9
6 2 5 11 4 10
c
7
c
12
c
8
c
6
c
2
c
5
c
11
c
3
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.41244 × 10
69
u
68
− 3.32508 × 10
69
u
67
+ ··· + 3.39317 × 10
69
b + 1.80676 × 10
70
,
1.05888 × 10
70
u
68
+ 2.32754 × 10
70
u
67
+ ··· + 2.37522 × 10
70
a − 1.91976 × 10
71
,
u
69
+ 4u
68
+ ··· + 118u − 28i
I
u
2
= h−u
3
+ b + 2u, u
16
− u
15
+ ··· + a − 2, u
17
− 12u
15
+ ··· + 10u
2
− 1i
I
u
3
= h−186a
4
u − 87a
4
− 392a
3
u − 230a
3
+ 1248a
2
u + 506a
2
+ 2922au + 241b + 1289a + 282u − 78,
a
5
+ 2a
4
+ a
3
u − 8a
3
+ 10a
2
u − 30a
2
+ 17au − 29a + 8u − 13, u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 96 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−1.41 × 10
69
u
68
− 3.33 × 10
69
u
67
+ · · · + 3.39 × 10
69
b + 1.81 ×
10
70
, 1.06 × 10
70
u
68
+ 2.33 × 10
70
u
67
+ · · · + 2.38 × 10
70
a − 1.92 ×
10
71
, u
69
+ 4u
68
+ · · · + 118u − 28i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−0.445803u
68
− 0.979926u
67
+ ··· − 37.8294u + 8.08246
0.416260u
68
+ 0.979934u
67
+ ··· + 31.7679u − 5.32469
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−0.337813u
68
− 0.689657u
67
+ ··· − 32.8264u + 7.20315
0.182878u
68
+ 0.451924u
67
+ ··· + 7.26000u − 0.225713
a
2
=
−0.279350u
68
− 0.735303u
67
+ ··· − 17.4605u + 4.28483
0.356355u
68
+ 0.862570u
67
+ ··· + 35.2557u − 6.44200
a
5
=
0.864573u
68
+ 2.07589u
67
+ ··· + 74.2680u − 16.1219
−1.15159u
68
− 2.66334u
67
+ ··· − 108.556u + 24.4015
a
11
=
−u
u
a
4
=
−0.201645u
68
− 0.481748u
67
+ ··· − 23.0572u + 4.77346
0.172103u
68
+ 0.481755u
67
+ ··· + 16.9956u − 2.01569
a
10
=
0.878887u
68
+ 2.21773u
67
+ ··· + 57.9452u − 9.67980
−0.809320u
68
− 1.99188u
67
+ ··· − 55.2577u + 11.7419
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.841314u
68
− 1.63044u
67
+ ··· − 102.614u + 28.7772
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
− 9u
68
+ ··· − 125u − 1
c
2
, c
6
u
69
− 4u
68
+ ··· + 1186u + 1279
c
3
u
69
+ 19u
67
+ ··· − 73191u + 47449
c
4
, c
5
, c
9
u
69
− 2u
68
+ ··· − 82u + 1
c
7
, c
8
, c
11
c
12
u
69
− 4u
68
+ ··· + 118u + 28
c
10
u
69
+ 4u
68
+ ··· + 171u − 29
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
+ 9y
68
+ ··· + 17785y −1
c
2
, c
6
y
69
− 52y
68
+ ··· + 50080220y −1635841
c
3
y
69
+ 38y
68
+ ··· − 35937183035y −2251407601
c
4
, c
5
, c
9
y
69
+ 70y
68
+ ··· + 6500y −1
c
7
, c
8
, c
11
c
12
y
69
− 84y
68
+ ··· + 6364y −784
c
10
y
69
− 14y
68
+ ··· + 39333y −841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885057 + 0.508714I
a = −1.25938 + 1.09741I
b = 1.313650 + 0.417375I
5.12644 + 8.14034I 0
u = 0.885057 − 0.508714I
a = −1.25938 − 1.09741I
b = 1.313650 − 0.417375I
5.12644 − 8.14034I 0
u = −1.016630 + 0.148616I
a = −1.354710 − 0.051330I
b = 1.152720 − 0.802920I
0.08436 − 3.60660I 0
u = −1.016630 − 0.148616I
a = −1.354710 + 0.051330I
b = 1.152720 + 0.802920I
0.08436 + 3.60660I 0
u = 0.636042 + 0.735204I
a = 0.771040 − 0.820398I
b = −1.385970 − 0.048806I
1.71288 + 2.51836I 0
u = 0.636042 − 0.735204I
a = 0.771040 + 0.820398I
b = −1.385970 + 0.048806I
1.71288 − 2.51836I 0
u = −0.896655 + 0.578537I
a = −0.888310 − 0.824652I
b = 1.234820 + 0.008364I
4.86851 − 0.44171I 0
u = −0.896655 − 0.578537I
a = −0.888310 + 0.824652I
b = 1.234820 − 0.008364I
4.86851 + 0.44171I 0
u = −0.906672 + 0.619011I
a = 1.24005 + 0.82717I
b = −1.36590 + 0.51916I
−0.78365 − 12.22400I 0
u = −0.906672 − 0.619011I
a = 1.24005 − 0.82717I
b = −1.36590 − 0.51916I
−0.78365 + 12.22400I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.044130 + 0.894273I
a = 0.0367545 − 0.0279078I
b = −1.218310 − 0.375774I
−3.41603 + 7.23977I 6.00000 − 5.79158I
u = −0.044130 − 0.894273I
a = 0.0367545 + 0.0279078I
b = −1.218310 + 0.375774I
−3.41603 − 7.23977I 6.00000 + 5.79158I
u = −0.769410 + 0.383812I
a = 1.04791 + 1.63891I
b = −1.180600 + 0.315893I
3.85880 − 3.01933I 9.96983 + 6.07662I
u = −0.769410 − 0.383812I
a = 1.04791 − 1.63891I
b = −1.180600 − 0.315893I
3.85880 + 3.01933I 9.96983 − 6.07662I
u = 0.836904 + 0.153168I
a = 1.49560 − 0.59674I
b = −1.343630 − 0.417966I
4.62859 + 1.66065I 18.4070 − 5.0043I
u = 0.836904 − 0.153168I
a = 1.49560 + 0.59674I
b = −1.343630 + 0.417966I
4.62859 − 1.66065I 18.4070 + 5.0043I
u = −0.709314 + 0.400333I
a = −0.178614 + 0.107335I
b = −0.011683 − 1.196020I
−5.11512 − 6.32617I 4.96847 + 7.99574I
u = −0.709314 − 0.400333I
a = −0.178614 − 0.107335I
b = −0.011683 + 1.196020I
−5.11512 + 6.32617I 4.96847 − 7.99574I
u = 0.746120 + 0.270176I
a = 0.431126 − 0.142662I
b = −0.078465 − 0.885255I
0.83816 + 3.48222I 8.75635 − 8.60776I
u = 0.746120 − 0.270176I
a = 0.431126 + 0.142662I
b = −0.078465 + 0.885255I
0.83816 − 3.48222I 8.75635 + 8.60776I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.22679
a = −1.24264
b = 0.596925
2.39981 0
u = 0.502427 + 0.575755I
a = 0.632278 + 0.570820I
b = 0.593291 − 0.256882I
−4.44506 + 2.24811I 4.48548 − 1.48739I
u = 0.502427 − 0.575755I
a = 0.632278 − 0.570820I
b = 0.593291 + 0.256882I
−4.44506 − 2.24811I 4.48548 + 1.48739I
u = −0.032139 + 0.742398I
a = 0.130428 − 0.345678I
b = 1.211830 − 0.239682I
2.35512 − 3.98609I 9.19250 + 6.28784I
u = −0.032139 − 0.742398I
a = 0.130428 + 0.345678I
b = 1.211830 + 0.239682I
2.35512 + 3.98609I 9.19250 − 6.28784I
u = 1.099620 + 0.619020I
a = 0.808964 − 0.837395I
b = −1.137280 + 0.162151I
−0.01258 − 2.07394I 0
u = 1.099620 − 0.619020I
a = 0.808964 + 0.837395I
b = −1.137280 − 0.162151I
−0.01258 + 2.07394I 0
u = 1.263810 + 0.241659I
a = 1.34299 + 0.51814I
b = −0.572476 − 0.299994I
−1.95538 − 0.27990I 0
u = 1.263810 − 0.241659I
a = 1.34299 − 0.51814I
b = −0.572476 + 0.299994I
−1.95538 + 0.27990I 0
u = 0.668449 + 0.182768I
a = −3.22718 − 0.46140I
b = 0.943084 + 0.285478I
−3.62595 + 4.73786I 7.87798 − 6.16232I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668449 − 0.182768I
a = −3.22718 + 0.46140I
b = 0.943084 − 0.285478I
−3.62595 − 4.73786I 7.87798 + 6.16232I
u = 0.412391 + 0.548973I
a = 0.155129 + 0.716030I
b = 0.736431 + 0.522225I
−4.65764 + 1.61626I 2.82750 − 4.30956I
u = 0.412391 − 0.548973I
a = 0.155129 − 0.716030I
b = 0.736431 − 0.522225I
−4.65764 − 1.61626I 2.82750 + 4.30956I
u = −0.219158 + 0.552429I
a = 1.53288 + 0.30165I
b = −0.223631 + 0.772688I
−6.59300 + 3.04852I 0.086786 − 0.536752I
u = −0.219158 − 0.552429I
a = 1.53288 − 0.30165I
b = −0.223631 − 0.772688I
−6.59300 − 3.04852I 0.086786 + 0.536752I
u = 1.49203
a = −0.152282
b = −0.616971
6.96786 0
u = −1.51224 + 0.16519I
a = −0.052321 − 0.516958I
b = 0.511789 + 0.054440I
2.17563 − 4.90185I 0
u = −1.51224 − 0.16519I
a = −0.052321 + 0.516958I
b = 0.511789 − 0.054440I
2.17563 + 4.90185I 0
u = −1.53515 + 0.04841I
a = −0.797218 − 0.049788I
b = 0.833772 − 0.898244I
1.47969 − 3.26450I 0
u = −1.53515 − 0.04841I
a = −0.797218 + 0.049788I
b = 0.833772 + 0.898244I
1.47969 + 3.26450I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.089185 + 0.433722I
a = −1.301320 − 0.439390I
b = −1.085960 − 0.017290I
1.86291 + 0.12476I 6.99819 + 0.57622I
u = −0.089185 − 0.433722I
a = −1.301320 + 0.439390I
b = −1.085960 + 0.017290I
1.86291 − 0.12476I 6.99819 − 0.57622I
u = 0.068174 + 0.406678I
a = −1.01773 + 1.10026I
b = 0.051644 + 0.523892I
−1.15029 − 1.08308I −0.94169 + 2.86009I
u = 0.068174 − 0.406678I
a = −1.01773 − 1.10026I
b = 0.051644 − 0.523892I
−1.15029 + 1.08308I −0.94169 − 2.86009I
u = −0.410283
a = −1.01651
b = −0.420595
0.822559 13.9630
u = 0.323738 + 0.194743I
a = −0.41274 − 1.81065I
b = 0.838599 − 0.702790I
−4.62796 − 3.27883I 5.32821 − 2.18413I
u = 0.323738 − 0.194743I
a = −0.41274 + 1.81065I
b = 0.838599 + 0.702790I
−4.62796 + 3.27883I 5.32821 + 2.18413I
u = −1.62231 + 0.04624I
a = −2.43198 + 0.36370I
b = 1.173720 − 0.075551I
4.39357 − 5.56424I 0
u = −1.62231 − 0.04624I
a = −2.43198 − 0.36370I
b = 1.173720 + 0.075551I
4.39357 + 5.56424I 0
u = 1.62794 + 0.10132I
a = −0.214550 − 0.885759I
b = 0.06305 + 1.51910I
2.96097 + 8.14106I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62794 − 0.10132I
a = −0.214550 + 0.885759I
b = 0.06305 − 1.51910I
2.96097 − 8.14106I 0
u = −1.63793 + 0.06004I
a = 0.303364 − 0.514810I
b = −0.104398 + 1.183180I
9.14294 − 4.64744I 0
u = −1.63793 − 0.06004I
a = 0.303364 + 0.514810I
b = −0.104398 − 1.183180I
9.14294 + 4.64744I 0
u = 1.64036 + 0.11039I
a = 1.66328 − 0.72027I
b = −1.267400 − 0.503838I
12.18870 + 4.90550I 0
u = 1.64036 − 0.11039I
a = 1.66328 + 0.72027I
b = −1.267400 + 0.503838I
12.18870 − 4.90550I 0
u = −1.63556 + 0.21597I
a = 1.85907 + 0.58231I
b = −1.50689 + 0.15630I
9.45657 − 6.06793I 0
u = −1.63556 − 0.21597I
a = 1.85907 − 0.58231I
b = −1.50689 − 0.15630I
9.45657 + 6.06793I 0
u = −1.66810 + 0.03752I
a = 1.97899 − 0.02011I
b = −1.57935 + 0.61268I
13.45550 − 2.36434I 0
u = −1.66810 − 0.03752I
a = 1.97899 + 0.02011I
b = −1.57935 − 0.61268I
13.45550 + 2.36434I 0
u = −1.67186 + 0.14663I
a = −1.88316 − 0.52112I
b = 1.42741 − 0.53981I
13.9239 − 10.7016I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67186 − 0.14663I
a = −1.88316 + 0.52112I
b = 1.42741 + 0.53981I
13.9239 + 10.7016I 0
u = 1.68319 + 0.18230I
a = 1.95034 − 0.37437I
b = −1.51510 − 0.60638I
8.0665 + 15.3703I 0
u = 1.68319 − 0.18230I
a = 1.95034 + 0.37437I
b = −1.51510 + 0.60638I
8.0665 − 15.3703I 0
u = 1.69652 + 0.15096I
a = −1.69943 + 0.46959I
b = 1.357260 + 0.214340I
13.8959 + 3.3008I 0
u = 1.69652 − 0.15096I
a = −1.69943 − 0.46959I
b = 1.357260 − 0.214340I
13.8959 − 3.3008I 0
u = 1.71146 + 0.04198I
a = −1.78409 − 0.38247I
b = 1.44052 + 0.94034I
9.75066 + 4.39705I 0
u = 1.71146 − 0.04198I
a = −1.78409 + 0.38247I
b = 1.44052 − 0.94034I
9.75066 − 4.39705I 0
u = −1.76323 + 0.10512I
a = 1.39968 + 0.49586I
b = −1.086220 + 0.160688I
10.33700 − 0.79826I 0
u = −1.76323 − 0.10512I
a = 1.39968 − 0.49586I
b = −1.086220 − 0.160688I
10.33700 + 0.79826I 0
11
II. I
u
2
= h−u
3
+ b + 2u, u
16
− u
15
+ · · · + a − 2, u
17
− 12u
15
+ · · · + 10u
2
− 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
16
+ u
15
+ ··· − 11u + 2
u
3
− 2u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−u
16
+ 12u
14
+ ··· − 3u + 3
u
6
− 4u
4
+ 4u
2
a
2
=
−u
16
+ 12u
14
+ ··· + 20u
2
− 5u
−u
9
+ 6u
7
− 12u
5
+ 9u
3
− 2u
a
5
=
−u
16
+ 11u
14
+ ··· − 2u + 3
u
11
− 7u
9
+ 17u
7
+ u
6
− 17u
5
− 4u
4
+ 7u
3
+ 4u
2
− u
a
11
=
−u
u
a
4
=
−u
16
+ 12u
14
+ ··· − 10u + 1
u
15
− 10u
13
+ ··· − 3u + 1
a
10
=
u
16
− 12u
14
+ ··· − 20u
2
+ u
u
13
− 9u
11
+ 31u
9
− 51u
7
+ 41u
5
− 15u
3
+ 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
16
−u
15
−39u
14
+ 14u
13
+ 203u
12
−80u
11
−541u
10
+ 235u
9
+
785u
8
− 372u
7
− 615u
6
+ 311u
5
+ 247u
4
− 130u
3
− 39u
2
+ 18u + 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 6u
14
+ ··· + 5u − 1
c
2
u
17
− 3u
16
+ ··· − 7u
2
+ 1
c
3
u
17
− u
16
+ ··· − 3u + 1
c
4
, c
5
u
17
− u
16
+ ··· − 2u + 1
c
6
u
17
+ 3u
16
+ ··· + 7u
2
− 1
c
7
, c
8
u
17
− 12u
15
+ ··· + 10u
2
− 1
c
9
u
17
+ u
16
+ ··· − 2u − 1
c
10
u
17
+ 3u
16
+ ··· − u − 1
c
11
, c
12
u
17
− 12u
15
+ ··· − 10u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 12y
15
+ ··· + 15y −1
c
2
, c
6
y
17
− 17y
16
+ ··· + 14y −1
c
3
y
17
− 3y
16
+ ··· + 3y −1
c
4
, c
5
, c
9
y
17
+ 17y
16
+ ··· − 10y −1
c
7
, c
8
, c
11
c
12
y
17
− 24y
16
+ ··· + 20y −1
c
10
y
17
− 3y
16
+ ··· + 3y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12483
a = −1.57050
b = 0.826480
2.87361 16.9180
u = 0.765149 + 0.421591I
a = 1.35270 − 0.57990I
b = −1.49033 − 0.17765I
0.68195 + 1.52103I 7.26853 − 3.12009I
u = 0.765149 − 0.421591I
a = 1.35270 + 0.57990I
b = −1.49033 + 0.17765I
0.68195 − 1.52103I 7.26853 + 3.12009I
u = 1.178570 + 0.219790I
a = 1.42225 − 0.62684I
b = −0.890871 + 0.465689I
−1.81193 − 2.25763I 5.66700 + 2.84264I
u = 1.178570 − 0.219790I
a = 1.42225 + 0.62684I
b = −0.890871 − 0.465689I
−1.81193 + 2.25763I 5.66700 − 2.84264I
u = −0.714795 + 0.288375I
a = −1.12109 − 1.23941I
b = 1.242710 − 0.158712I
3.77071 − 1.06837I 10.68484 + 0.89742I
u = −0.714795 − 0.288375I
a = −1.12109 + 1.23941I
b = 1.242710 + 0.158712I
3.77071 + 1.06837I 10.68484 − 0.89742I
u = 1.51456
a = 0.620258
b = 0.445096
6.54472 −0.282310
u = −1.51854 + 0.10060I
a = −0.238616 − 0.104806I
b = −0.418499 + 0.493694I
1.55012 − 5.50234I 4.53425 + 6.47331I
u = −1.51854 − 0.10060I
a = −0.238616 + 0.104806I
b = −0.418499 − 0.493694I
1.55012 + 5.50234I 4.53425 − 6.47331I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.284877 + 0.277612I
a = −1.61523 + 1.23649I
b = −0.612500 − 0.509030I
−4.75398 + 4.11120I 3.36378 − 6.09217I
u = 0.284877 − 0.277612I
a = −1.61523 − 1.23649I
b = −0.612500 + 0.509030I
−4.75398 − 4.11120I 3.36378 + 6.09217I
u = 1.66968 + 0.06964I
a = −1.69186 + 0.32947I
b = 1.291110 + 0.442823I
12.32780 + 2.39306I 10.46353 − 1.14209I
u = 1.66968 − 0.06964I
a = −1.69186 − 0.32947I
b = 1.291110 − 0.442823I
12.32780 − 2.39306I 10.46353 + 1.14209I
u = −0.300477
a = 3.94004
b = 0.573825
0.201181 −3.47720
u = −1.70957 + 0.08018I
a = 1.89695 − 0.09951I
b = −1.54432 + 0.54215I
9.74452 − 3.40985I 9.93902 + 0.00636I
u = −1.70957 − 0.08018I
a = 1.89695 + 0.09951I
b = −1.54432 − 0.54215I
9.74452 + 3.40985I 9.93902 − 0.00636I
16
III. I
u
3
=
h−186a
4
u−392a
3
u+· · ·+1289a−78, a
3
u+10a
2
u+· · ·−29a−13, u
2
−u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u − 1
a
1
=
u
−u − 1
a
3
=
a
0.771784a
4
u + 1.62656a
3
u + ··· − 5.34855a + 0.323651
a
9
=
−u
u
a
6
=
0.0829876a
4
u − 0.136929a
3
u + ··· − 2.32780a − 0.481328
−0.597510a
4
u − 0.614108a
3
u + ··· + 3.56017a + 0.265560
a
2
=
−1.35270a
4
u − 1.66805a
3
u + ··· + 9.64315a + 1.04564
1.86722a
4
u + 2.41909a
3
u + ··· − 10.8755a − 0.829876
a
5
=
1.35270a
4
u + 1.66805a
3
u + ··· − 9.64315a − 1.04564
−1.86722a
4
u − 2.41909a
3
u + ··· + 10.8755a + 0.829876
a
11
=
−u
u
a
4
=
−1.90456a
4
u − 4.20747a
3
u + ··· + 17.4730a + 0.846473
2.67635a
4
u + 5.83402a
3
u + ··· − 21.8216a − 0.522822
a
10
=
1.14938a
4
u + 1.15353a
3
u + ··· − 5.39004a − 0.0663900
−1.51037a
4
u − 2.10788a
3
u + ··· + 12.1660a + 1.56017
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 5u
5
− 4u
4
+ u
3
+ 7u
2
+ 3u + 1
c
2
, c
6
u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 5u
5
− 4u
4
− u
3
+ 7u
2
− 3u + 1
c
3
u
10
− 2u
8
− 4u
7
− 7u
6
− u
5
− 8u
4
+ u
3
− 9u
2
+ 5u − 5
c
4
, c
5
, c
9
c
10
u
10
+ 2u
8
− u
6
− u
5
− 2u
4
− u
3
+ u
2
+ u − 1
c
7
, c
8
, c
11
c
12
(u
2
+ u − 1)
5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
10
− 12y
9
+ ··· + 5y + 1
c
3
y
10
− 4y
9
+ ··· + 65y + 25
c
4
, c
5
, c
9
c
10
y
10
+ 4y
9
+ 2y
8
− 8y
7
− 5y
6
+ 5y
5
− 4y
4
− y
3
+ 7y
2
− 3y + 1
c
7
, c
8
, c
11
c
12
(y
2
− 3y + 1)
5
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −0.701459 + 0.560253I
b = −0.209607 + 0.335701I
0.986960 10.0000
u = −0.618034
a = −0.701459 − 0.560253I
b = −0.209607 − 0.335701I
0.986960 10.0000
u = −0.618034
a = −2.16824 + 1.11936I
b = 1.65031 + 0.20788I
0.986960 10.0000
u = −0.618034
a = −2.16824 − 1.11936I
b = 1.65031 − 0.20788I
0.986960 10.0000
u = −0.618034
a = 3.73940
b = −0.881412
0.986960 10.0000
u = 1.61803
a = −0.0559753 + 0.0335315I
b = −0.193167 − 0.796854I
8.88264 10.0000
u = 1.61803
a = −0.0559753 − 0.0335315I
b = −0.193167 + 0.796854I
8.88264 10.0000
u = 1.61803
a = −2.24197 + 0.12571I
b = 1.77275 + 0.46564I
8.88264 10.0000
u = 1.61803
a = −2.24197 − 0.12571I
b = 1.77275 − 0.46564I
8.88264 10.0000
u = 1.61803
a = 2.59589
b = −1.15917
8.88264 10.0000
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 5u
5
− 4u
4
+ u
3
+ 7u
2
+ 3u + 1)
· (u
17
− 6u
14
+ ··· + 5u − 1)(u
69
− 9u
68
+ ··· − 125u − 1)
c
2
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 5u
5
− 4u
4
− u
3
+ 7u
2
− 3u + 1)
· (u
17
− 3u
16
+ ··· − 7u
2
+ 1)(u
69
− 4u
68
+ ··· + 1186u + 1279)
c
3
(u
10
− 2u
8
− 4u
7
− 7u
6
− u
5
− 8u
4
+ u
3
− 9u
2
+ 5u − 5)
· (u
17
− u
16
+ ··· − 3u + 1)(u
69
+ 19u
67
+ ··· − 73191u + 47449)
c
4
, c
5
(u
10
+ 2u
8
+ ··· + u − 1)(u
17
− u
16
+ ··· − 2u + 1)
· (u
69
− 2u
68
+ ··· − 82u + 1)
c
6
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 5u
5
− 4u
4
− u
3
+ 7u
2
− 3u + 1)
· (u
17
+ 3u
16
+ ··· + 7u
2
− 1)(u
69
− 4u
68
+ ··· + 1186u + 1279)
c
7
, c
8
((u
2
+ u − 1)
5
)(u
17
− 12u
15
+ ··· + 10u
2
− 1)
· (u
69
− 4u
68
+ ··· + 118u + 28)
c
9
(u
10
+ 2u
8
+ ··· + u − 1)(u
17
+ u
16
+ ··· − 2u − 1)
· (u
69
− 2u
68
+ ··· − 82u + 1)
c
10
(u
10
+ 2u
8
+ ··· + u − 1)(u
17
+ 3u
16
+ ··· − u − 1)
· (u
69
+ 4u
68
+ ··· + 171u − 29)
c
11
, c
12
((u
2
+ u − 1)
5
)(u
17
− 12u
15
+ ··· − 10u
2
+ 1)
· (u
69
− 4u
68
+ ··· + 118u + 28)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
10
− 12y
9
+ ··· + 5y + 1)(y
17
+ 12y
15
+ ··· + 15y −1)
· (y
69
+ 9y
68
+ ··· + 17785y −1)
c
2
, c
6
(y
10
− 12y
9
+ ··· + 5y + 1)(y
17
− 17y
16
+ ··· + 14y −1)
· (y
69
− 52y
68
+ ··· + 50080220y −1635841)
c
3
(y
10
− 4y
9
+ ··· + 65y + 25)(y
17
− 3y
16
+ ··· + 3y −1)
· (y
69
+ 38y
68
+ ··· − 35937183035y −2251407601)
c
4
, c
5
, c
9
(y
10
+ 4y
9
+ 2y
8
− 8y
7
− 5y
6
+ 5y
5
− 4y
4
− y
3
+ 7y
2
− 3y + 1)
· (y
17
+ 17y
16
+ ··· − 10y −1)(y
69
+ 70y
68
+ ··· + 6500y −1)
c
7
, c
8
, c
11
c
12
((y
2
− 3y + 1)
5
)(y
17
− 24y
16
+ ··· + 20y −1)
· (y
69
− 84y
68
+ ··· + 6364y −784)
c
10
(y
10
+ 4y
9
+ 2y
8
− 8y
7
− 5y
6
+ 5y
5
− 4y
4
− y
3
+ 7y
2
− 3y + 1)
· (y
17
− 3y
16
+ ··· + 3y −1)(y
69
− 14y
68
+ ··· + 39333y −841)
22
