12a
0336
(K12a
0336
)
A knot diagram
1
Linearized knot diagam
3 6 8 12 2 10 5 1 11 7 9 4
Solving Sequence
6,10
7
3,11
2 1 5 8 9 12 4
c
6
c
10
c
2
c
1
c
5
c
7
c
9
c
11
c
4
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.41051 × 10
147
u
109
+ 3.15130 × 10
148
u
108
+ ··· + 1.10390 × 10
146
b − 1.00649 × 10
148
,
− 2.27130 × 10
149
u
109
+ 9.67001 × 10
149
u
108
+ ··· + 1.10390 × 10
146
a − 3.03972 × 10
149
,
u
110
− 5u
109
+ ··· + 21u − 1i
I
u
2
= ha
3
− 4a
2
+ 15b − 5a + 9, a
4
− 2a
3
− 3a
2
+ 4a + 13, u − 1i
* 2 irreducible components of dim
C
= 0, with total 114 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−7.41 × 10
147
u
109
+ 3.15 × 10
148
u
108
+ · · · + 1.10 × 10
146
b − 1.01 ×
10
148
, −2.27 × 10
149
u
109
+ 9.67 × 10
149
u
108
+ · · · + 1.10 × 10
146
a − 3.04 ×
10
149
, u
110
− 5u
109
+ · · · + 21u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
2057.53u
109
− 8759.90u
108
+ ··· − 54177.9u + 2753.63
67.1306u
109
− 285.471u
108
+ ··· − 1791.59u + 91.1766
a
11
=
−u
−u
3
+ u
a
2
=
2124.67u
109
− 9045.37u
108
+ ··· − 55969.5u + 2844.81
67.1306u
109
− 285.471u
108
+ ··· − 1791.59u + 91.1766
a
1
=
2965.90u
109
− 12627.4u
108
+ ··· − 78707.9u + 4024.00
−70.4088u
109
+ 299.167u
108
+ ··· + 1873.07u − 97.4129
a
5
=
−810.769u
109
+ 3459.40u
108
+ ··· + 22092.2u − 1136.72
−115.246u
109
+ 490.899u
108
+ ··· + 3011.85u − 152.033
a
8
=
15726.1u
109
− 66994.2u
108
+ ··· − 418011.u + 21301.1
1274.16u
109
− 5422.15u
108
+ ··· − 33586.8u + 1705.78
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
4
=
−675.156u
109
+ 2881.24u
108
+ ··· + 18481.2u − 952.732
−118.945u
109
+ 506.489u
108
+ ··· + 3109.35u − 157.208
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1639.99u
109
+ 6951.33u
108
+ ··· + 42540.4u − 2173.88
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
110
+ 41u
109
+ ··· + 233u + 4
c
2
, c
5
u
110
+ 7u
109
+ ··· + 27u + 2
c
3
u
110
+ u
109
+ ··· + 17u − 1
c
4
, c
12
u
110
+ 7u
109
+ ··· + 27u + 1
c
6
, c
10
u
110
+ 5u
109
+ ··· − 21u − 1
c
7
u
110
+ 25u
109
+ ··· + 376147u − 1476493
c
8
u
110
+ 5u
109
+ ··· − 101u + 41
c
9
, c
11
u
110
+ 35u
109
+ ··· + 127u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
110
+ 59y
109
+ ··· − 9873y + 16
c
2
, c
5
y
110
− 41y
109
+ ··· − 233y + 4
c
3
y
110
− 3y
109
+ ··· − 79y + 1
c
4
, c
12
y
110
+ 65y
109
+ ··· − 175y + 1
c
6
, c
10
y
110
− 35y
109
+ ··· − 127y + 1
c
7
y
110
− 145y
109
+ ··· + 12275866812167y + 2180031579049
c
8
y
110
+ 155y
109
+ ··· + 197587y + 1681
c
9
, c
11
y
110
+ 85y
109
+ ··· − 2511y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.990959 + 0.098136I
a = 1.275900 − 0.543178I
b = 0.892858 − 0.506092I
−1.69575 + 2.02020I 0
u = 0.990959 − 0.098136I
a = 1.275900 + 0.543178I
b = 0.892858 + 0.506092I
−1.69575 − 2.02020I 0
u = 0.996189 + 0.199368I
a = −0.337539 + 1.135930I
b = −0.212986 − 0.116839I
−3.59787 − 0.10583I 0
u = 0.996189 − 0.199368I
a = −0.337539 − 1.135930I
b = −0.212986 + 0.116839I
−3.59787 + 0.10583I 0
u = −0.774665 + 0.664449I
a = −1.25947 − 0.88402I
b = −0.926563 − 0.223291I
−0.205553 − 0.307982I 0
u = −0.774665 − 0.664449I
a = −1.25947 + 0.88402I
b = −0.926563 + 0.223291I
−0.205553 + 0.307982I 0
u = −0.993094 + 0.295258I
a = 1.55343 + 1.20146I
b = 1.079160 − 0.620858I
−0.75551 + 7.78682I 0
u = −0.993094 − 0.295258I
a = 1.55343 − 1.20146I
b = 1.079160 + 0.620858I
−0.75551 − 7.78682I 0
u = 0.697332 + 0.792742I
a = −0.246586 − 0.264787I
b = 1.220130 − 0.142302I
−2.44609 + 5.13634I 0
u = 0.697332 − 0.792742I
a = −0.246586 + 0.264787I
b = 1.220130 + 0.142302I
−2.44609 − 5.13634I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.062770 + 0.148015I
a = 1.58044 + 0.11499I
b = 1.175380 + 0.017061I
−8.83330 + 5.21023I 0
u = −1.062770 − 0.148015I
a = 1.58044 − 0.11499I
b = 1.175380 − 0.017061I
−8.83330 − 5.21023I 0
u = −0.843116 + 0.333311I
a = −0.284924 + 0.220862I
b = 0.392082 + 0.747113I
1.15133 + 2.61903I 0
u = −0.843116 − 0.333311I
a = −0.284924 − 0.220862I
b = 0.392082 − 0.747113I
1.15133 − 2.61903I 0
u = −0.622477 + 0.901671I
a = −0.341590 − 1.224490I
b = 0.916045 + 0.686391I
4.73684 − 3.99325I 0
u = −0.622477 − 0.901671I
a = −0.341590 + 1.224490I
b = 0.916045 − 0.686391I
4.73684 + 3.99325I 0
u = −0.902097
a = −1.76787
b = −1.24916
−4.50976 0
u = 0.835064 + 0.721373I
a = 1.47161 − 1.06013I
b = −1.002620 + 0.908716I
0.330530 + 0.796888I 0
u = 0.835064 − 0.721373I
a = 1.47161 + 1.06013I
b = −1.002620 − 0.908716I
0.330530 − 0.796888I 0
u = 0.867770 + 0.692580I
a = 0.634138 + 0.236501I
b = −1.313380 + 0.439862I
−0.77993 − 1.27179I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.867770 − 0.692580I
a = 0.634138 − 0.236501I
b = −1.313380 − 0.439862I
−0.77993 + 1.27179I 0
u = −0.878182 + 0.681537I
a = 0.533325 + 0.497799I
b = 0.686950 + 0.106206I
2.03663 + 2.63082I 0
u = −0.878182 − 0.681537I
a = 0.533325 − 0.497799I
b = 0.686950 − 0.106206I
2.03663 − 2.63082I 0
u = 0.813749 + 0.768223I
a = 0.99853 − 1.18681I
b = −0.290691 + 1.035300I
3.09414 + 1.62165I 0
u = 0.813749 − 0.768223I
a = 0.99853 + 1.18681I
b = −0.290691 − 1.035300I
3.09414 − 1.62165I 0
u = 0.081059 + 0.876379I
a = 0.42575 + 1.39611I
b = −1.013040 − 0.658910I
−0.50846 − 8.74088I 0
u = 0.081059 − 0.876379I
a = 0.42575 − 1.39611I
b = −1.013040 + 0.658910I
−0.50846 + 8.74088I 0
u = 0.885644 + 0.691977I
a = −0.05764 + 1.73251I
b = −1.333450 − 0.331323I
−0.83704 − 4.05265I 0
u = 0.885644 − 0.691977I
a = −0.05764 − 1.73251I
b = −1.333450 + 0.331323I
−0.83704 + 4.05265I 0
u = −1.092140 + 0.284265I
a = 0.240713 − 0.003212I
b = −0.495383 − 0.799993I
−3.02604 + 7.06344I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.092140 − 0.284265I
a = 0.240713 + 0.003212I
b = −0.495383 + 0.799993I
−3.02604 − 7.06344I 0
u = −0.867655 + 0.040937I
a = −1.51760 − 0.61667I
b = −1.151050 + 0.669665I
−4.17559 + 2.45296I 0
u = −0.867655 − 0.040937I
a = −1.51760 + 0.61667I
b = −1.151050 − 0.669665I
−4.17559 − 2.45296I 0
u = −0.828091 + 0.780039I
a = −0.185197 + 0.072379I
b = 0.117195 + 0.402603I
2.64336 + 1.65504I 0
u = −0.828091 − 0.780039I
a = −0.185197 − 0.072379I
b = 0.117195 − 0.402603I
2.64336 − 1.65504I 0
u = −0.697509 + 0.900889I
a = −0.369911 + 1.319140I
b = 0.772510 − 0.700845I
5.16781 + 1.33455I 0
u = −0.697509 − 0.900889I
a = −0.369911 − 1.319140I
b = 0.772510 + 0.700845I
5.16781 − 1.33455I 0
u = −0.872826 + 0.738046I
a = 1.13776 − 5.90790I
b = 0.894681 + 0.537347I
1.29270 + 0.75901I 0
u = −0.872826 − 0.738046I
a = 1.13776 + 5.90790I
b = 0.894681 − 0.537347I
1.29270 − 0.75901I 0
u = −0.877187 + 0.735804I
a = 4.12267 + 5.29001I
b = 0.910898 − 0.520689I
1.27829 + 4.84714I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877187 − 0.735804I
a = 4.12267 − 5.29001I
b = 0.910898 + 0.520689I
1.27829 − 4.84714I 0
u = 0.770569 + 0.856471I
a = −0.75952 + 1.22815I
b = 1.094710 − 0.747854I
6.67136 + 6.50363I 0
u = 0.770569 − 0.856471I
a = −0.75952 − 1.22815I
b = 1.094710 + 0.747854I
6.67136 − 6.50363I 0
u = 0.736971 + 0.887786I
a = 0.40009 + 1.53796I
b = −0.588057 − 0.913960I
4.79934 + 6.61268I 0
u = 0.736971 − 0.887786I
a = 0.40009 − 1.53796I
b = −0.588057 + 0.913960I
4.79934 − 6.61268I 0
u = 0.712081 + 0.909440I
a = 0.55860 − 1.38226I
b = −1.089970 + 0.717795I
3.25044 + 12.62120I 0
u = 0.712081 − 0.909440I
a = 0.55860 + 1.38226I
b = −1.089970 − 0.717795I
3.25044 − 12.62120I 0
u = −0.831776 + 0.144488I
a = −0.239608 − 0.113887I
b = −0.614202 + 0.872721I
−2.44902 + 3.63797I 0
u = −0.831776 − 0.144488I
a = −0.239608 + 0.113887I
b = −0.614202 − 0.872721I
−2.44902 − 3.63797I 0
u = 1.051500 + 0.482675I
a = 0.79964 − 1.65316I
b = 1.009650 + 0.153910I
−6.86902 − 1.41545I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051500 − 0.482675I
a = 0.79964 + 1.65316I
b = 1.009650 − 0.153910I
−6.86902 + 1.41545I 0
u = 0.908591 + 0.716880I
a = −0.12317 + 2.53742I
b = −1.074790 − 0.887097I
0.10246 − 6.29605I 0
u = 0.908591 − 0.716880I
a = −0.12317 − 2.53742I
b = −1.074790 + 0.887097I
0.10246 + 6.29605I 0
u = 0.809732 + 0.833377I
a = −0.19331 − 1.71805I
b = 0.614409 + 0.971864I
8.17677 + 0.24318I 0
u = 0.809732 − 0.833377I
a = −0.19331 + 1.71805I
b = 0.614409 − 0.971864I
8.17677 − 0.24318I 0
u = −0.960649 + 0.654756I
a = −1.130610 − 0.112359I
b = −0.894555 + 0.088679I
−0.80311 + 5.44115I 0
u = −0.960649 − 0.654756I
a = −1.130610 + 0.112359I
b = −0.894555 − 0.088679I
−0.80311 − 5.44115I 0
u = 0.778635 + 0.277338I
a = −1.33414 + 2.80799I
b = −0.942986 − 0.438315I
−1.96405 − 2.91621I 0
u = 0.778635 − 0.277338I
a = −1.33414 − 2.80799I
b = −0.942986 + 0.438315I
−1.96405 + 2.91621I 0
u = −1.152970 + 0.265802I
a = −1.30202 − 1.16410I
b = −1.075150 + 0.649293I
−4.73120 + 12.50000I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.152970 − 0.265802I
a = −1.30202 + 1.16410I
b = −1.075150 − 0.649293I
−4.73120 − 12.50000I 0
u = 0.007248 + 0.810052I
a = 0.37732 − 1.38238I
b = −0.618881 + 0.726901I
0.65865 − 3.42633I 0
u = 0.007248 − 0.810052I
a = 0.37732 + 1.38238I
b = −0.618881 − 0.726901I
0.65865 + 3.42633I 0
u = 0.931716 + 0.744804I
a = −0.48784 + 1.54283I
b = −0.365752 − 1.068560I
2.73350 − 7.34740I 0
u = 0.931716 − 0.744804I
a = −0.48784 − 1.54283I
b = −0.365752 + 1.068560I
2.73350 + 7.34740I 0
u = −0.800702 + 0.893151I
a = 0.66551 + 1.27924I
b = −0.866053 − 0.674686I
5.61155 + 0.14050I 0
u = −0.800702 − 0.893151I
a = 0.66551 − 1.27924I
b = −0.866053 + 0.674686I
5.61155 − 0.14050I 0
u = −0.927118 + 0.763957I
a = 0.1000390 + 0.0172765I
b = 0.221052 − 0.379085I
2.34244 + 4.16755I 0
u = −0.927118 − 0.763957I
a = 0.1000390 − 0.0172765I
b = 0.221052 + 0.379085I
2.34244 − 4.16755I 0
u = 1.182250 + 0.265329I
a = −0.845000 + 0.942118I
b = −0.675555 − 0.540568I
−3.25800 − 0.36532I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.182250 − 0.265329I
a = −0.845000 − 0.942118I
b = −0.675555 + 0.540568I
−3.25800 + 0.36532I 0
u = 1.001380 + 0.722993I
a = 0.317622 − 1.284450I
b = 1.267730 + 0.111185I
−3.35621 − 10.85530I 0
u = 1.001380 − 0.722993I
a = 0.317622 + 1.284450I
b = 1.267730 − 0.111185I
−3.35621 + 10.85530I 0
u = 0.958427 + 0.782280I
a = −1.31241 + 0.78086I
b = 0.571194 − 1.000510I
7.71445 − 6.27796I 0
u = 0.958427 − 0.782280I
a = −1.31241 − 0.78086I
b = 0.571194 + 1.000510I
7.71445 + 6.27796I 0
u = 1.238090 + 0.023214I
a = 0.836611 + 0.344859I
b = 0.847431 − 0.588895I
−2.03804 + 2.33452I 0
u = 1.238090 − 0.023214I
a = 0.836611 − 0.344859I
b = 0.847431 + 0.588895I
−2.03804 − 2.33452I 0
u = −0.858642 + 0.897188I
a = 0.34642 − 1.72422I
b = −0.834452 + 0.677799I
5.70786 + 5.35963I 0
u = −0.858642 − 0.897188I
a = 0.34642 + 1.72422I
b = −0.834452 − 0.677799I
5.70786 − 5.35963I 0
u = 0.743069 + 0.001373I
a = −15.7688 + 14.3067I
b = 0.853529 + 0.493943I
−2.73468 − 2.03121I −155.856 − 14.904I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743069 − 0.001373I
a = −15.7688 − 14.3067I
b = 0.853529 − 0.493943I
−2.73468 + 2.03121I −155.856 + 14.904I
u = 1.204310 + 0.367220I
a = −0.293140 − 0.037779I
b = −0.979382 + 0.596671I
−4.22594 + 4.29044I 0
u = 1.204310 − 0.367220I
a = −0.293140 + 0.037779I
b = −0.979382 − 0.596671I
−4.22594 − 4.29044I 0
u = 0.991910 + 0.777202I
a = 0.45402 − 2.37267I
b = 1.124230 + 0.740932I
5.98378 − 12.58750I 0
u = 0.991910 − 0.777202I
a = 0.45402 + 2.37267I
b = 1.124230 − 0.740932I
5.98378 + 12.58750I 0
u = −0.945626 + 0.842407I
a = 1.095890 + 0.776380I
b = −0.783570 − 0.663137I
5.42222 + 1.04774I 0
u = −0.945626 − 0.842407I
a = 1.095890 − 0.776380I
b = −0.783570 + 0.663137I
5.42222 − 1.04774I 0
u = −0.982963 + 0.809149I
a = −0.26329 − 2.24551I
b = −0.909073 + 0.649568I
5.03632 + 6.14721I 0
u = −0.982963 − 0.809149I
a = −0.26329 + 2.24551I
b = −0.909073 − 0.649568I
5.03632 − 6.14721I 0
u = 0.270523 + 0.671458I
a = −0.265968 + 0.602362I
b = 1.011230 + 0.007454I
−4.61086 − 2.90503I −12.49793 + 3.69733I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.270523 − 0.671458I
a = −0.265968 − 0.602362I
b = 1.011230 − 0.007454I
−4.61086 + 2.90503I −12.49793 − 3.69733I
u = 1.022780 + 0.776946I
a = 1.29581 − 0.59941I
b = −0.561805 + 0.937083I
3.90906 − 12.78220I 0
u = 1.022780 − 0.776946I
a = 1.29581 + 0.59941I
b = −0.561805 − 0.937083I
3.90906 + 12.78220I 0
u = 1.043820 + 0.774874I
a = −0.61529 + 2.37605I
b = −1.109610 − 0.715503I
2.2152 − 18.8423I 0
u = 1.043820 − 0.774874I
a = −0.61529 − 2.37605I
b = −1.109610 + 0.715503I
2.2152 + 18.8423I 0
u = −1.047620 + 0.776065I
a = −0.853316 − 0.334340I
b = 0.704704 + 0.687845I
4.09281 + 4.86690I 0
u = −1.047620 − 0.776065I
a = −0.853316 + 0.334340I
b = 0.704704 − 0.687845I
4.09281 − 4.86690I 0
u = −0.100887 + 0.688381I
a = −0.590605 − 1.104800I
b = 0.974180 + 0.650665I
2.13203 − 4.43463I −2.57446 + 3.83971I
u = −0.100887 − 0.688381I
a = −0.590605 + 1.104800I
b = 0.974180 − 0.650665I
2.13203 + 4.43463I −2.57446 − 3.83971I
u = −1.084390 + 0.743508I
a = 0.73136 + 1.93639I
b = 0.960216 − 0.661111I
3.32750 + 10.08480I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.084390 − 0.743508I
a = 0.73136 − 1.93639I
b = 0.960216 + 0.661111I
3.32750 − 10.08480I 0
u = −0.256784 + 0.629269I
a = −0.044618 + 1.366300I
b = 0.682292 − 0.695782I
3.00663 + 0.76455I −0.54792 − 2.58754I
u = −0.256784 − 0.629269I
a = −0.044618 − 1.366300I
b = 0.682292 + 0.695782I
3.00663 − 0.76455I −0.54792 + 2.58754I
u = 0.641311
a = 0.790484
b = −0.183300
−0.880286 −11.3800
u = 0.448085 + 0.335521I
a = 1.45691 − 0.25060I
b = −0.806520 + 0.211746I
−1.146060 + 0.195025I −7.25511 + 1.21678I
u = 0.448085 − 0.335521I
a = 1.45691 + 0.25060I
b = −0.806520 − 0.211746I
−1.146060 − 0.195025I −7.25511 − 1.21678I
u = −0.098547 + 0.384410I
a = 1.36102 − 0.55314I
b = −0.325264 − 0.515852I
−0.53012 − 1.77215I −3.82058 + 3.25832I
u = −0.098547 − 0.384410I
a = 1.36102 + 0.55314I
b = −0.325264 + 0.515852I
−0.53012 + 1.77215I −3.82058 − 3.25832I
u = 0.1093310 + 0.0382620I
a = 8.24072 + 6.41030I
b = −0.923434 − 0.544845I
−1.80988 − 2.06434I −8.30188 + 2.61051I
u = 0.1093310 − 0.0382620I
a = 8.24072 − 6.41030I
b = −0.923434 + 0.544845I
−1.80988 + 2.06434I −8.30188 − 2.61051I
15
II. I
u
2
= ha
3
− 4a
2
+ 15b − 5a + 9, a
4
− 2a
3
− 3a
2
+ 4a + 13, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
3
=
a
−
1
15
a
3
+
4
15
a
2
+
1
3
a −
3
5
a
11
=
−1
0
a
2
=
−
1
15
a
3
+
4
15
a
2
+
4
3
a −
3
5
−
1
15
a
3
+
4
15
a
2
+
1
3
a −
3
5
a
1
=
−
2
15
a
3
−
2
15
a
2
+
4
3
a +
17
15
−
1
15
a
3
−
1
15
a
2
+
2
3
a +
1
15
a
5
=
−
4
15
a
3
+
1
15
a
2
+
1
3
a −
2
5
−
2
15
a
3
+
1
5
a
2
−
8
15
a
8
=
−
7
15
a
3
+
1
5
a
2
+ 2a +
47
15
−
1
5
a
3
+
2
15
a
2
+
2
3
a +
23
15
a
9
=
1
1
a
12
=
−2
−1
a
4
=
−
4
15
a
3
−
3
5
a
2
+ a +
14
15
−
2
15
a
3
−
2
15
a
2
+
1
3
a +
2
15
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8
15
a
3
−
4
5
a
2
−
208
15
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
u
4
− u
2
+ 1
c
3
, c
4
, c
12
(u
2
+ 1)
2
c
6
, c
9
(u − 1)
4
c
7
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
8
u
4
+ 4u
3
+ 5u
2
+ 2u + 1
c
10
, c
11
(u + 1)
4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
5
(y
2
− y + 1)
2
c
3
, c
4
, c
12
(y + 1)
4
c
6
, c
9
, c
10
c
11
(y −1)
4
c
7
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
8
y
4
− 6y
3
+ 11y
2
+ 6y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.23205 + 0.86603I
b = −0.866025 − 0.500000I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 1.00000
a = −1.23205 − 0.86603I
b = −0.866025 + 0.500000I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = 1.00000
a = 2.23205 + 0.86603I
b = 0.866025 + 0.500000I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 1.00000
a = 2.23205 − 0.86603I
b = 0.866025 − 0.500000I
−3.28987 + 2.02988I −14.0000 − 3.4641I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
110
+ 41u
109
+ ··· + 233u + 4)
c
2
, c
5
(u
4
− u
2
+ 1)(u
110
+ 7u
109
+ ··· + 27u + 2)
c
3
((u
2
+ 1)
2
)(u
110
+ u
109
+ ··· + 17u − 1)
c
4
, c
12
((u
2
+ 1)
2
)(u
110
+ 7u
109
+ ··· + 27u + 1)
c
6
((u − 1)
4
)(u
110
+ 5u
109
+ ··· − 21u − 1)
c
7
(u
4
− 2u
3
+ 5u
2
− 4u + 1)(u
110
+ 25u
109
+ ··· + 376147u − 1476493)
c
8
(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)(u
110
+ 5u
109
+ ··· − 101u + 41)
c
9
((u − 1)
4
)(u
110
+ 35u
109
+ ··· + 127u + 1)
c
10
((u + 1)
4
)(u
110
+ 5u
109
+ ··· − 21u − 1)
c
11
((u + 1)
4
)(u
110
+ 35u
109
+ ··· + 127u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
110
+ 59y
109
+ ··· − 9873y + 16)
c
2
, c
5
((y
2
− y + 1)
2
)(y
110
− 41y
109
+ ··· − 233y + 4)
c
3
((y + 1)
4
)(y
110
− 3y
109
+ ··· − 79y + 1)
c
4
, c
12
((y + 1)
4
)(y
110
+ 65y
109
+ ··· − 175y + 1)
c
6
, c
10
((y −1)
4
)(y
110
− 35y
109
+ ··· − 127y + 1)
c
7
(y
4
+ 6y
3
+ 11y
2
− 6y + 1)
· (y
110
− 145y
109
+ ··· + 12275866812167y + 2180031579049)
c
8
(y
4
− 6y
3
+ 11y
2
+ 6y + 1)(y
110
+ 155y
109
+ ··· + 197587y + 1681)
c
9
, c
11
((y −1)
4
)(y
110
+ 85y
109
+ ··· − 2511y + 1)
21
