12n
0021
(K12n
0021
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 12 5 11 6 7 9 10
Solving Sequence
3,5
2 6
1,10
9 12 7 8 4 11
c
2
c
5
c
1
c
9
c
12
c
6
c
7
c
4
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.31031 × 10
60
u
73
+ 8.78516 × 10
60
u
72
+ ··· + 8.05327 × 10
59
b + 2.46563 × 10
59
,
− 1.87533 × 10
60
u
73
+ 1.24710 × 10
61
u
72
+ ··· + 8.05327 × 10
59
a − 7.86574 × 10
60
,
u
74
− 7u
73
+ ··· − 10u + 1i
I
u
2
= h−2a
4
u + 9a
3
u + 9a
3
− 10a
2
− 6au + 5b + 4u + 4, a
5
+ 5a
4
u − 6a
3
u − 6a
3
+ 3a
2
+ au − u − 1, u
2
+ u + 1i
I
u
3
= h−2u
4
+ 2u
3
− 2u
2
+ b − u + 2, −u
4
+ 3u
3
− 4u
2
+ a + 4u − 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 89 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
60
u
73
+ 8.79 × 10
60
u
72
+ · · · + 8.05 × 10
59
b + 2.47 ×
10
59
, −1.88 × 10
60
u
73
+ 1.25 × 10
61
u
72
+ · · · + 8.05 × 10
59
a − 7.87 ×
10
60
, u
74
− 7u
73
+ · · · − 10u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
2.32865u
73
− 15.4857u
72
+ ··· + 29.2596u + 9.76713
1.62705u
73
− 10.9088u
72
+ ··· − 4.88417u − 0.306165
a
9
=
1.30294u
73
− 8.68046u
72
+ ··· + 15.6245u + 11.1275
0.928079u
73
− 4.66399u
72
+ ··· − 21.2414u + 1.42898
a
12
=
0.0128426u
73
− 0.606575u
72
+ ··· − 24.6025u − 4.47929
−1.07283u
73
+ 7.86599u
72
+ ··· − 13.6469u + 1.79816
a
7
=
−1.84067u
73
+ 11.0360u
72
+ ··· − 8.87375u − 2.84119
−1.31744u
73
+ 10.0636u
72
+ ··· − 16.1390u + 2.16705
a
8
=
−1.84067u
73
+ 11.0360u
72
+ ··· − 8.87375u − 2.84119
−1.23075u
73
+ 11.7949u
72
+ ··· − 32.7857u + 4.01579
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
11
=
0.612092u
73
− 4.77433u
72
+ ··· + 2.25396u + 7.51995
−0.187474u
73
+ 4.35220u
72
+ ··· − 38.3916u + 3.65569
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12.9104u
73
+ 92.7725u
72
+ ··· − 82.6450u + 3.33954
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 23u
73
+ ··· − 168u + 1
c
2
, c
5
u
74
+ 7u
73
+ ··· + 10u + 1
c
3
u
74
− 7u
73
+ ··· + 23935148u + 1174793
c
4
, c
7
u
74
− 2u
73
+ ··· + 3072u + 1024
c
6
u
74
− 4u
73
+ ··· + 3u − 1
c
8
, c
11
u
74
− 8u
73
+ ··· − 83u − 1
c
9
u
74
− 4u
73
+ ··· + 18563u + 7979
c
10
u
74
+ 2u
73
+ ··· + 140788u − 6632
c
12
u
74
+ 11u
73
+ ··· + 600u
2
+ 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 63y
73
+ ··· − 33884y + 1
c
2
, c
5
y
74
+ 23y
73
+ ··· − 168y + 1
c
3
y
74
+ 103y
73
+ ··· − 195612233228368y + 1380138592849
c
4
, c
7
y
74
+ 50y
73
+ ··· + 5242880y + 1048576
c
6
y
74
− 20y
73
+ ··· + y + 1
c
8
, c
11
y
74
− 40y
73
+ ··· − 2497y + 1
c
9
y
74
+ 46y
73
+ ··· − 1411728345y + 63664441
c
10
y
74
+ 78y
73
+ ··· − 8817552656y + 43983424
c
12
y
74
− 27y
73
+ ··· + 38400y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588568 + 0.781606I
a = 2.11655 − 1.27106I
b = −0.34086 − 1.74865I
−0.94329 − 1.13464I 0
u = −0.588568 − 0.781606I
a = 2.11655 + 1.27106I
b = −0.34086 + 1.74865I
−0.94329 + 1.13464I 0
u = −0.224608 + 0.939787I
a = −1.43760 − 1.52815I
b = −1.80851 + 0.25423I
−3.42601 − 3.36523I 0
u = −0.224608 − 0.939787I
a = −1.43760 + 1.52815I
b = −1.80851 − 0.25423I
−3.42601 + 3.36523I 0
u = −0.480747 + 0.917533I
a = 3.51191 − 3.12500I
b = −1.37679 − 5.49401I
−2.18804 − 1.82733I 0
u = −0.480747 − 0.917533I
a = 3.51191 + 3.12500I
b = −1.37679 + 5.49401I
−2.18804 + 1.82733I 0
u = −0.948295 + 0.114817I
a = 0.642760 − 0.299680I
b = −0.384036 − 0.001201I
2.84481 − 6.06997I 0. + 5.46750I
u = −0.948295 − 0.114817I
a = 0.642760 + 0.299680I
b = −0.384036 + 0.001201I
2.84481 + 6.06997I 0. − 5.46750I
u = −0.605694 + 0.882842I
a = 1.04425 − 1.21226I
b = 0.30514 − 2.02629I
−1.25518 − 3.58366I 0
u = −0.605694 − 0.882842I
a = 1.04425 + 1.21226I
b = 0.30514 + 2.02629I
−1.25518 + 3.58366I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363037 + 0.817565I
a = 0.599509 − 0.288116I
b = −0.309360 − 0.528307I
−0.31180 − 1.54577I −2.35841 + 4.98495I
u = −0.363037 − 0.817565I
a = 0.599509 + 0.288116I
b = −0.309360 + 0.528307I
−0.31180 + 1.54577I −2.35841 − 4.98495I
u = 0.377437 + 0.795068I
a = 0.458626 − 0.671697I
b = −0.886331 − 0.076122I
−6.11124 + 6.05756I −13.16929 + 2.49659I
u = 0.377437 − 0.795068I
a = 0.458626 + 0.671697I
b = −0.886331 + 0.076122I
−6.11124 − 6.05756I −13.16929 − 2.49659I
u = 0.879036
a = 0.464133
b = −0.0979340
−3.60099 6.20630
u = 0.424038 + 0.768258I
a = −0.668714 + 0.128685I
b = 0.451674 + 0.637183I
−5.95413 − 2.77149I −11.1970 + 11.7984I
u = 0.424038 − 0.768258I
a = −0.668714 − 0.128685I
b = 0.451674 − 0.637183I
−5.95413 + 2.77149I −11.1970 − 11.7984I
u = −0.789645 + 0.824107I
a = −0.35319 + 1.72243I
b = 1.27854 + 1.76922I
3.57080 − 3.55900I 0
u = −0.789645 − 0.824107I
a = −0.35319 − 1.72243I
b = 1.27854 − 1.76922I
3.57080 + 3.55900I 0
u = 0.926734 + 0.675434I
a = −0.503809 − 1.111700I
b = 0.37933 − 1.50865I
7.41718 − 3.39847I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926734 − 0.675434I
a = −0.503809 + 1.111700I
b = 0.37933 + 1.50865I
7.41718 + 3.39847I 0
u = −0.357389 + 1.093680I
a = 0.227043 − 0.773438I
b = −0.030211 + 0.326577I
0.97521 − 4.62256I 0
u = −0.357389 − 1.093680I
a = 0.227043 + 0.773438I
b = −0.030211 − 0.326577I
0.97521 + 4.62256I 0
u = 0.820006 + 0.826808I
a = 0.158463 + 0.704129I
b = −1.384830 + 0.014374I
3.14985 − 1.37670I 0
u = 0.820006 − 0.826808I
a = 0.158463 − 0.704129I
b = −1.384830 − 0.014374I
3.14985 + 1.37670I 0
u = −0.168266 + 1.155270I
a = 0.511207 − 0.231030I
b = −0.109347 + 0.212969I
−0.18048 − 2.67430I 0
u = −0.168266 − 1.155270I
a = 0.511207 + 0.231030I
b = −0.109347 − 0.212969I
−0.18048 + 2.67430I 0
u = −0.315143 + 0.768424I
a = −1.52568 + 6.21959I
b = 6.24699 + 1.55706I
−1.96434 − 1.46942I 69.4609 − 82.1819I
u = −0.315143 − 0.768424I
a = −1.52568 − 6.21959I
b = 6.24699 − 1.55706I
−1.96434 + 1.46942I 69.4609 + 82.1819I
u = −0.817564 + 0.115016I
a = −0.102494 − 0.097733I
b = 0.693608 + 0.178324I
4.23425 + 0.54410I 1.60258 − 0.06952I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.817564 − 0.115016I
a = −0.102494 + 0.097733I
b = 0.693608 − 0.178324I
4.23425 − 0.54410I 1.60258 + 0.06952I
u = 0.782206 + 0.888648I
a = 1.29280 + 1.39998I
b = −0.63121 + 2.77026I
1.01094 + 2.94591I 0
u = 0.782206 − 0.888648I
a = 1.29280 − 1.39998I
b = −0.63121 − 2.77026I
1.01094 − 2.94591I 0
u = 0.960126 + 0.695377I
a = 1.22788 + 1.52034I
b = 0.01982 + 2.23698I
6.50731 − 10.89880I 0
u = 0.960126 − 0.695377I
a = 1.22788 − 1.52034I
b = 0.01982 − 2.23698I
6.50731 + 10.89880I 0
u = −0.099605 + 0.797661I
a = −1.28212 + 0.66262I
b = −0.983447 + 0.821591I
−3.94950 − 0.19450I −14.2244 + 0.5338I
u = −0.099605 − 0.797661I
a = −1.28212 − 0.66262I
b = −0.983447 − 0.821591I
−3.94950 + 0.19450I −14.2244 − 0.5338I
u = 0.913271 + 0.785754I
a = −1.24292 − 1.30749I
b = −0.04215 − 2.39793I
9.56303 − 3.64207I 0
u = 0.913271 − 0.785754I
a = −1.24292 + 1.30749I
b = −0.04215 + 2.39793I
9.56303 + 3.64207I 0
u = 0.837187 + 0.871109I
a = −2.00342 + 0.20473I
b = −0.960890 − 0.793882I
4.88888 + 2.03616I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837187 − 0.871109I
a = −2.00342 − 0.20473I
b = −0.960890 + 0.793882I
4.88888 − 2.03616I 0
u = −0.753364 + 0.950514I
a = −1.37943 + 0.51575I
b = −0.46215 + 1.85324I
3.17540 − 2.27063I 0
u = −0.753364 − 0.950514I
a = −1.37943 − 0.51575I
b = −0.46215 − 1.85324I
3.17540 + 2.27063I 0
u = −0.883272 + 0.834733I
a = 1.35545 − 1.08459I
b = 0.24804 − 1.97325I
2.10183 + 2.80934I 0
u = −0.883272 − 0.834733I
a = 1.35545 + 1.08459I
b = 0.24804 + 1.97325I
2.10183 − 2.80934I 0
u = 0.784779 + 0.950831I
a = 0.418763 − 0.127905I
b = 1.32211 + 1.05195I
2.76643 + 7.39057I 0
u = 0.784779 − 0.950831I
a = 0.418763 + 0.127905I
b = 1.32211 − 1.05195I
2.76643 − 7.39057I 0
u = 0.817309 + 0.927924I
a = 0.88430 − 1.76207I
b = 1.34165 − 1.29399I
4.71109 + 4.13291I 0
u = 0.817309 − 0.927924I
a = 0.88430 + 1.76207I
b = 1.34165 + 1.29399I
4.71109 − 4.13291I 0
u = −0.251345 + 1.227450I
a = −0.570312 + 0.368260I
b = −0.543530 − 0.574793I
−1.87183 − 10.09290I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.251345 − 1.227450I
a = −0.570312 − 0.368260I
b = −0.543530 + 0.574793I
−1.87183 + 10.09290I 0
u = 0.943453 + 0.828089I
a = 0.60572 + 1.39990I
b = −0.38320 + 1.76670I
9.18515 + 2.01287I 0
u = 0.943453 − 0.828089I
a = 0.60572 − 1.39990I
b = −0.38320 − 1.76670I
9.18515 − 2.01287I 0
u = −0.826585 + 0.970325I
a = 0.76341 − 1.66069I
b = −0.86711 − 2.14556I
1.67555 − 9.13934I 0
u = −0.826585 − 0.970325I
a = 0.76341 + 1.66069I
b = −0.86711 + 2.14556I
1.67555 + 9.13934I 0
u = −0.419590 + 1.216660I
a = −0.286830 − 0.137018I
b = 0.092382 − 0.684597I
−0.83764 + 1.21344I 0
u = −0.419590 − 1.216660I
a = −0.286830 + 0.137018I
b = 0.092382 + 0.684597I
−0.83764 − 1.21344I 0
u = 0.432353 + 1.221260I
a = −0.162125 − 0.020944I
b = −0.245061 + 0.213540I
−7.41606 + 4.57419I 0
u = 0.432353 − 1.221260I
a = −0.162125 + 0.020944I
b = −0.245061 − 0.213540I
−7.41606 − 4.57419I 0
u = 0.814545 + 1.015150I
a = −1.14539 − 1.49821I
b = 0.80502 − 2.49598I
8.83947 + 10.02070I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.814545 − 1.015150I
a = −1.14539 + 1.49821I
b = 0.80502 + 2.49598I
8.83947 − 10.02070I 0
u = 0.764489 + 1.073570I
a = −0.940897 − 0.743631I
b = 0.18830 − 1.69305I
6.17331 + 9.63827I 0
u = 0.764489 − 1.073570I
a = −0.940897 + 0.743631I
b = 0.18830 + 1.69305I
6.17331 − 9.63827I 0
u = 0.853280 + 1.005800I
a = 1.16762 + 1.03945I
b = −0.02363 + 1.82898I
8.61435 + 4.58115I 0
u = 0.853280 − 1.005800I
a = 1.16762 − 1.03945I
b = −0.02363 − 1.82898I
8.61435 − 4.58115I 0
u = 0.787160 + 1.077840I
a = 1.21504 + 1.50799I
b = −0.57962 + 2.58206I
5.3004 + 17.3091I 0
u = 0.787160 − 1.077840I
a = 1.21504 − 1.50799I
b = −0.57962 − 2.58206I
5.3004 − 17.3091I 0
u = 0.093711 + 0.582935I
a = −0.60542 + 1.79370I
b = 0.945378 + 0.484928I
−0.76340 + 2.05732I −6.61172 − 3.28073I
u = 0.093711 − 0.582935I
a = −0.60542 − 1.79370I
b = 0.945378 − 0.484928I
−0.76340 − 2.05732I −6.61172 + 3.28073I
u = −0.116761 + 0.531053I
a = 1.61823 − 1.25855I
b = −0.582250 − 0.676718I
−0.75534 − 1.25758I −6.16688 + 4.20297I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.116761 − 0.531053I
a = 1.61823 + 1.25855I
b = −0.582250 + 0.676718I
−0.75534 + 1.25758I −6.16688 − 4.20297I
u = −0.298970 + 0.158249I
a = 2.38582 − 3.03610I
b = −0.052906 − 1.134690I
−0.71671 − 1.37236I −4.04860 + 4.25236I
u = −0.298970 − 0.158249I
a = 2.38582 + 3.03610I
b = −0.052906 + 1.134690I
−0.71671 + 1.37236I −4.04860 − 4.25236I
u = 0.0736878
a = 12.5458
b = −0.563170
−2.30896 −2.48640
12
II. I
u
2
= h−2a
4
u + 9a
3
u + · · · − 10a
2
+ 4, a
5
+ 5a
4
u − 6a
3
u − 6a
3
+ 3a
2
+
au − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u − 1
a
6
=
u
u + 1
a
1
=
−u
−u − 1
a
10
=
a
2
5
a
4
u −
9
5
a
3
u + ··· + 2a
2
−
4
5
a
9
=
−
9
5
a
3
u + 2a
2
u + ··· + 2a
2
−
6
5
a
4
5
a
4
u −
18
5
a
3
u + ··· + 4a
2
−
8
5
a
12
=
2
5
a
3
u + a
2
u + ··· + a
2
−
2
5
a
−
2
5
a
4
u +
9
5
a
3
u + ··· − 2a
2
−
6
5
a
7
=
0
−
2
5
a
4
u +
14
5
a
3
u + ··· − 6a
2
+
4
5
a
8
=
0
−
2
5
a
4
u +
14
5
a
3
u + ··· − 6a
2
+
4
5
a
4
=
0
u
a
11
=
a
−
2
5
a
4
u +
14
5
a
3
u + ··· − 6a
2
+
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
5
a
4
u − 3a
4
−
52
5
a
3
u +
8
5
a
3
+ 3a
2
u + 8a
2
+
8
5
au + 5a +
38
5
u −
2
5
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
8
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
9
, c
12
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
10
, c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
8
, c
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.864485 − 0.518603I
b = −0.559524 − 0.303102I
−0.329100 − 0.499304I −3.07628 − 2.84945I
u = −0.500000 + 0.866025I
a = 0.016881 − 1.007970I
b = 0.017268 − 0.636113I
−0.32910 − 3.56046I −3.01153 + 6.03927I
u = −0.500000 + 0.866025I
a = 0.369732 + 0.377747I
b = −0.755206 + 0.074107I
−5.87256 − 6.43072I −3.55752 + 12.20067I
u = −0.500000 + 0.866025I
a = −0.512005 − 0.131324I
b = 0.441781 − 0.616974I
−5.87256 + 2.37095I −6.63163 + 6.91428I
u = −0.500000 + 0.866025I
a = 1.76091 − 3.04998I
b = −2.14432 − 3.71407I
−2.40108 − 2.02988I −9.7230 + 10.6042I
u = −0.500000 − 0.866025I
a = 0.864485 + 0.518603I
b = −0.559524 + 0.303102I
−0.329100 + 0.499304I −3.07628 + 2.84945I
u = −0.500000 − 0.866025I
a = 0.016881 + 1.007970I
b = 0.017268 + 0.636113I
−0.32910 + 3.56046I −3.01153 − 6.03927I
u = −0.500000 − 0.866025I
a = 0.369732 − 0.377747I
b = −0.755206 − 0.074107I
−5.87256 + 6.43072I −3.55752 − 12.20067I
u = −0.500000 − 0.866025I
a = −0.512005 + 0.131324I
b = 0.441781 + 0.616974I
−5.87256 − 2.37095I −6.63163 − 6.91428I
u = −0.500000 − 0.866025I
a = 1.76091 + 3.04998I
b = −2.14432 + 3.71407I
−2.40108 + 2.02988I −9.7230 − 10.6042I
16
III. I
u
3
= h−2u
4
+ 2u
3
− 2u
2
+ b − u + 2, −u
4
+ 3u
3
− 4u
2
+ a + 4u − 1, u
5
−
u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
u
4
− 3u
3
+ 4u
2
− 4u + 1
2u
4
− 2u
3
+ 2u
2
+ u − 2
a
9
=
2u
4
− 4u
3
+ 5u
2
− 4u
2u
4
− 2u
3
+ u
2
+ 2u − 3
a
12
=
u
2
+ 1
u
2
a
7
=
−u
2
− 1
u
4
a
8
=
−u
2
− 1
−u
2
a
4
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
a
11
=
2u
4
− 4u
3
+ 6u
2
− 4u + 1
2u
4
− 2u
3
+ 2u
2
+ 2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21u
4
+ 36u
3
− 50u
2
+ 39u − 22
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
(u − 1)
5
c
9
, c
10
u
5
− u
4
+ 3u
3
+ 8u
2
+ 5u + 1
c
11
(u + 1)
5
c
12
u
5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
4
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
8
, c
11
(y −1)
5
c
9
, c
10
y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y −1
c
12
y
5
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −1.83188 − 4.07697I
b = −4.75182 + 1.50408I
−1.97403 − 1.53058I 16.1214 + 37.0026I
u = −0.339110 − 0.822375I
a = −1.83188 + 4.07697I
b = −4.75182 − 1.50408I
−1.97403 + 1.53058I 16.1214 − 37.0026I
u = 0.766826
a = −0.722177
b = −0.267412
−4.04602 −12.5230
u = 0.455697 + 1.200150I
a = 0.192971 − 0.179096I
b = 0.385524 − 0.043640I
−7.51750 + 4.40083I −16.8598 + 13.4304I
u = 0.455697 − 1.200150I
a = 0.192971 + 0.179096I
b = 0.385524 + 0.043640I
−7.51750 − 4.40083I −16.8598 − 13.4304I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
74
+ 23u
73
+ ··· − 168u + 1)
c
2
((u
2
+ u + 1)
5
)(u
5
− u
4
+ ··· + u − 1)(u
74
+ 7u
73
+ ··· + 10u + 1)
c
3
(u
2
− u + 1)
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
74
− 7u
73
+ ··· + 23935148u + 1174793)
c
4
u
10
(u
5
+ u
4
+ ··· + u − 1)(u
74
− 2u
73
+ ··· + 3072u + 1024)
c
5
((u
2
− u + 1)
5
)(u
5
+ u
4
+ ··· + u + 1)(u
74
+ 7u
73
+ ··· + 10u + 1)
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
(u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1)
· (u
74
− 4u
73
+ ··· + 3u − 1)
c
7
u
10
(u
5
− u
4
+ ··· + u + 1)(u
74
− 2u
73
+ ··· + 3072u + 1024)
c
8
((u − 1)
5
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
74
− 8u
73
+ ··· − 83u − 1)
c
9
(u
5
− u
4
+ 3u
3
+ 8u
2
+ 5u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
74
− 4u
73
+ ··· + 18563u + 7979)
c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
(u
5
− u
4
+ 3u
3
+ 8u
2
+ 5u + 1)
· (u
74
+ 2u
73
+ ··· + 140788u − 6632)
c
11
((u + 1)
5
)(u
5
− u
4
+ ··· + u + 1)
2
(u
74
− 8u
73
+ ··· − 83u − 1)
c
12
u
5
(u
5
+ u
4
+ ··· + u + 1)
2
(u
74
+ 11u
73
+ ··· + 600u
2
+ 32)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
74
+ 63y
73
+ ··· − 33884y + 1)
c
2
, c
5
(y
2
+ y + 1)
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
74
+ 23y
73
+ ··· − 168y + 1)
c
3
(y
2
+ y + 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
74
+ 103y
73
+ ··· − 195612233228368y + 1380138592849)
c
4
, c
7
y
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
74
+ 50y
73
+ ··· + 5242880y + 1048576)
c
6
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
74
− 20y
73
+ ··· + y + 1)
c
8
, c
11
(y −1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
74
− 40y
73
+ ··· − 2497y + 1)
c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
(y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y −1)
· (y
74
+ 46y
73
+ ··· − 1411728345y + 63664441)
c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
(y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y −1)
· (y
74
+ 78y
73
+ ··· − 8817552656y + 43983424)
c
12
y
5
(y
5
+ 3y
4
+ ··· − y −1)
2
(y
74
− 27y
73
+ ··· + 38400y + 1024)
22
