12n
0026
(K12n
0026
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 12 5 11 7 6 9 10
Solving Sequence
5,7 8,11
9 12 4 6 3 2 1 10
c
7
c
8
c
11
c
4
c
6
c
3
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.31952 × 10
254
u
64
+ 5.24011 × 10
254
u
63
+ ··· + 1.57588 × 10
257
b − 1.11184 × 10
258
,
3.56772 × 10
254
u
64
− 1.12418 × 10
254
u
63
+ ··· + 3.15176 × 10
257
a + 1.06289 × 10
259
,
u
65
− 2u
64
+ ··· + 4096u + 4096i
I
u
2
= hu
4
− 2u
3
+ b + 3u, −4u
4
+ 5u
3
+ 8u
2
+ a − 8u − 3, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, 309980v
11
− 790238v
10
+ ··· + 707733b − 1249018,
v
12
− 3v
11
+ 3v
10
− 18v
9
+ 31v
8
+ 29v
7
− 31v
6
+ 9v
5
+ 19v
4
− 5v
3
− 4v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 82 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−2.32 × 10
254
u
64
+ 5.24 × 10
254
u
63
+ · · · + 1.58 × 10
257
b − 1.11 ×
10
258
, 3.57 × 10
254
u
64
− 1.12 × 10
254
u
63
+ · · · + 3.15 × 10
257
a + 1.06 ×
10
259
, u
65
− 2u
64
+ · · · + 4096u + 4096i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−0.00113198u
64
+ 0.000356685u
63
+ ··· + 25.6060u − 33.7239
0.00147189u
64
− 0.00332520u
63
+ ··· + 10.0304u + 7.05539
a
9
=
−0.00104664u
64
+ 0.000312990u
63
+ ··· + 25.0527u − 30.2720
0.00140862u
64
− 0.00318679u
63
+ ··· + 8.77753u + 7.26608
a
12
=
−0.0000458644u
64
− 0.000173442u
63
+ ··· + 1.67151u − 5.60504
0.0000363689u
64
− 0.000165732u
63
+ ··· + 2.08385u − 0.210615
a
4
=
u
u
3
+ u
a
6
=
0.000476569u
64
− 0.000749697u
63
+ ··· + 3.33404u + 5.48921
−0.0000745146u
64
+ 0.000168353u
63
+ ··· − 0.709852u − 0.337516
a
3
=
−0.000390199u
64
+ 0.000564940u
63
+ ··· − 0.279557u − 4.94851
0.000137437u
64
− 0.000304135u
63
+ ··· + 2.61125u + 0.546810
a
2
=
−0.000390199u
64
+ 0.000564940u
63
+ ··· − 0.279557u − 4.94851
0.000398870u
64
− 0.000884646u
63
+ ··· + 5.09202u + 1.42933
a
1
=
−0.000327023u
64
+ 0.000433323u
63
+ ··· − 1.25857u − 4.99343
0.000149546u
64
− 0.000316374u
63
+ ··· + 2.07547u + 0.495780
a
10
=
0.000361977u
64
− 0.00287380u
63
+ ··· + 33.8302u − 23.0060
0.00140862u
64
− 0.00318679u
63
+ ··· + 8.77753u + 7.26608
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0401453u
64
− 0.0971031u
63
+ ··· + 376.505u + 118.641
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 18u
64
+ ··· − 47u − 1
c
2
, c
5
u
65
+ 8u
64
+ ··· + 5u + 1
c
3
u
65
− 8u
64
+ ··· + 103537045u + 13657673
c
4
, c
7
u
65
− 2u
64
+ ··· + 4096u + 4096
c
6
u
65
− 4u
64
+ ··· − 3u + 1
c
8
, c
11
u
65
+ 8u
64
+ ··· + 3u + 1
c
9
u
65
+ 10u
64
+ ··· + 497u + 101
c
10
u
65
+ 4u
64
+ ··· − 606921u + 85049
c
12
u
65
− 11u
64
+ ··· − 192u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 66y
64
+ ··· + 213y −1
c
2
, c
5
y
65
+ 18y
64
+ ··· − 47y −1
c
3
y
65
+ 114y
64
+ ··· − 13102594991519615y −186532031774929
c
4
, c
7
y
65
+ 60y
64
+ ··· − 134217728y −16777216
c
6
y
65
+ 2y
64
+ ··· − 19y −1
c
8
, c
11
y
65
− 58y
64
+ ··· − 4257y −1
c
9
y
65
− 72y
64
+ ··· + 1225295y −10201
c
10
y
65
+ 4y
64
+ ··· + 132226628699y −7233332401
c
12
y
65
+ 27y
64
+ ··· − 52736y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.130385 + 0.943634I
a = −0.104094 + 0.791021I
b = −0.316979 + 0.153020I
−0.74329 − 4.73729I −2.00000 + 8.64739I
u = 0.130385 − 0.943634I
a = −0.104094 − 0.791021I
b = −0.316979 − 0.153020I
−0.74329 + 4.73729I −2.00000 − 8.64739I
u = 0.887268 + 0.125733I
a = 1.11539 − 1.61653I
b = 0.693000 − 0.264439I
1.48232 − 4.00344I −0.95634 + 8.48185I
u = 0.887268 − 0.125733I
a = 1.11539 + 1.61653I
b = 0.693000 + 0.264439I
1.48232 + 4.00344I −0.95634 − 8.48185I
u = 0.668516 + 0.588632I
a = −0.30780 − 1.76910I
b = −0.102545 − 0.380931I
3.65615 − 1.42936I 6.46603 + 3.32743I
u = 0.668516 − 0.588632I
a = −0.30780 + 1.76910I
b = −0.102545 + 0.380931I
3.65615 + 1.42936I 6.46603 − 3.32743I
u = −0.802999
a = 0.876374
b = 1.07960
−1.43422 −8.16770
u = 0.243832 + 0.761247I
a = 0.564345 − 0.323221I
b = −0.889123 − 0.264885I
1.88543 + 1.32823I 3.63769 − 3.79947I
u = 0.243832 − 0.761247I
a = 0.564345 + 0.323221I
b = −0.889123 + 0.264885I
1.88543 − 1.32823I 3.63769 + 3.79947I
u = −0.607968 + 0.481302I
a = 0.739828 + 0.188137I
b = 0.889610 − 0.904503I
−1.68242 − 0.00290I −4.75043 − 0.81603I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.607968 − 0.481302I
a = 0.739828 − 0.188137I
b = 0.889610 + 0.904503I
−1.68242 + 0.00290I −4.75043 + 0.81603I
u = −0.031117 + 0.710250I
a = 1.090600 + 0.832946I
b = −0.596154 − 0.230703I
−0.54684 + 1.46329I −1.59201 − 1.40388I
u = −0.031117 − 0.710250I
a = 1.090600 − 0.832946I
b = −0.596154 + 0.230703I
−0.54684 − 1.46329I −1.59201 + 1.40388I
u = −0.704902 + 0.035674I
a = 2.88280 + 1.01497I
b = 0.917162 − 0.007031I
1.30008 − 0.99581I −3.39411 − 0.67872I
u = −0.704902 − 0.035674I
a = 2.88280 − 1.01497I
b = 0.917162 + 0.007031I
1.30008 + 0.99581I −3.39411 + 0.67872I
u = 0.536940 + 0.442415I
a = 0.751417 + 0.483739I
b = 0.105811 − 0.455125I
−2.50902 + 1.89252I −7.42573 − 0.50006I
u = 0.536940 − 0.442415I
a = 0.751417 − 0.483739I
b = 0.105811 + 0.455125I
−2.50902 − 1.89252I −7.42573 + 0.50006I
u = −0.423794 + 0.531866I
a = 1.13755 − 2.43053I
b = −2.10389 − 0.25817I
1.19925 + 1.20786I 13.02298 − 5.31257I
u = −0.423794 − 0.531866I
a = 1.13755 + 2.43053I
b = −2.10389 + 0.25817I
1.19925 − 1.20786I 13.02298 + 5.31257I
u = −0.584385 + 0.334144I
a = 0.489359 − 0.286607I
b = 1.027040 + 0.217065I
−0.48772 + 4.09297I −7.37755 − 9.24327I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584385 − 0.334144I
a = 0.489359 + 0.286607I
b = 1.027040 − 0.217065I
−0.48772 − 4.09297I −7.37755 + 9.24327I
u = −0.340196 + 0.558280I
a = 0.849025 + 0.074675I
b = −0.136657 − 0.358705I
−0.33530 + 1.50733I −2.98038 − 4.24113I
u = −0.340196 − 0.558280I
a = 0.849025 − 0.074675I
b = −0.136657 + 0.358705I
−0.33530 − 1.50733I −2.98038 + 4.24113I
u = 0.462414 + 0.447292I
a = 0.449545 − 0.265010I
b = 1.25726 + 0.77432I
0.05754 + 7.13285I −1.292669 + 0.043034I
u = 0.462414 − 0.447292I
a = 0.449545 + 0.265010I
b = 1.25726 − 0.77432I
0.05754 − 7.13285I −1.292669 − 0.043034I
u = −0.237497 + 0.569452I
a = −2.85997 + 4.01034I
b = 0.594548 − 0.092050I
2.38609 − 2.85839I 7.30042 − 0.29630I
u = −0.237497 − 0.569452I
a = −2.85997 − 4.01034I
b = 0.594548 + 0.092050I
2.38609 + 2.85839I 7.30042 + 0.29630I
u = 1.356580 + 0.325626I
a = 0.728286 + 0.004128I
b = 2.21649 + 0.75169I
−4.31980 − 4.20818I 0
u = 1.356580 − 0.325626I
a = 0.728286 − 0.004128I
b = 2.21649 − 0.75169I
−4.31980 + 4.20818I 0
u = −0.324505 + 0.474102I
a = −0.43671 + 12.18570I
b = 2.82488 − 1.32418I
1.37708 + 1.55327I 81.0765 + 4.2253I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.324505 − 0.474102I
a = −0.43671 − 12.18570I
b = 2.82488 + 1.32418I
1.37708 − 1.55327I 81.0765 − 4.2253I
u = 0.361073 + 0.261174I
a = 1.043050 + 0.216750I
b = −1.007600 − 0.210459I
1.90413 + 1.10524I 1.74598 − 1.88050I
u = 0.361073 − 0.261174I
a = 1.043050 − 0.216750I
b = −1.007600 + 0.210459I
1.90413 − 1.10524I 1.74598 + 1.88050I
u = −0.33997 + 1.55682I
a = 0.056169 + 0.440660I
b = 0.07069 − 1.73548I
6.96782 + 4.95648I 0
u = −0.33997 − 1.55682I
a = 0.056169 − 0.440660I
b = 0.07069 + 1.73548I
6.96782 − 4.95648I 0
u = 0.12238 + 1.58993I
a = 0.042265 − 0.527798I
b = −0.30486 + 1.96959I
7.32759 + 1.41648I 0
u = 0.12238 − 1.58993I
a = 0.042265 + 0.527798I
b = −0.30486 − 1.96959I
7.32759 − 1.41648I 0
u = 0.19403 + 1.60184I
a = 1.60495 + 0.16607I
b = −2.71478 + 0.22301I
4.63170 − 9.18200I 0
u = 0.19403 − 1.60184I
a = 1.60495 − 0.16607I
b = −2.71478 − 0.22301I
4.63170 + 9.18200I 0
u = −0.11845 + 1.68248I
a = −2.17829 + 0.21768I
b = 4.95963 + 0.21904I
9.32058 + 3.26408I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11845 − 1.68248I
a = −2.17829 − 0.21768I
b = 4.95963 − 0.21904I
9.32058 − 3.26408I 0
u = −0.38021 + 1.66959I
a = 1.358240 − 0.341389I
b = −2.63924 − 0.88231I
4.26944 + 0.46934I 0
u = −0.38021 − 1.66959I
a = 1.358240 + 0.341389I
b = −2.63924 + 0.88231I
4.26944 − 0.46934I 0
u = 0.46996 + 1.65519I
a = −0.313034 + 0.036553I
b = 0.535176 + 0.909314I
7.48257 − 9.61839I 0
u = 0.46996 − 1.65519I
a = −0.313034 − 0.036553I
b = 0.535176 − 0.909314I
7.48257 + 9.61839I 0
u = −0.25917 + 1.70792I
a = −0.228762 − 0.060124I
b = 0.267931 − 1.102580I
8.03127 + 3.06347I 0
u = −0.25917 − 1.70792I
a = −0.228762 + 0.060124I
b = 0.267931 + 1.102580I
8.03127 − 3.06347I 0
u = 1.79527 + 0.04387I
a = 0.463967 − 0.137513I
b = 3.02532 − 0.10583I
8.03839 + 7.65970I 0
u = 1.79527 − 0.04387I
a = 0.463967 + 0.137513I
b = 3.02532 + 0.10583I
8.03839 − 7.65970I 0
u = 0.24346 + 1.80056I
a = −1.135210 − 0.249064I
b = 2.07921 + 0.59972I
12.17050 − 5.84377I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24346 − 1.80056I
a = −1.135210 + 0.249064I
b = 2.07921 − 0.59972I
12.17050 + 5.84377I 0
u = 0.00594 + 1.82235I
a = −1.128270 + 0.061752I
b = 1.92274 − 0.92455I
12.34330 − 0.87809I 0
u = 0.00594 − 1.82235I
a = −1.128270 − 0.061752I
b = 1.92274 + 0.92455I
12.34330 + 0.87809I 0
u = −1.81397 + 0.20782I
a = 0.486078 − 0.112646I
b = 2.98204 − 0.59250I
7.91932 + 0.95011I 0
u = −1.81397 − 0.20782I
a = 0.486078 + 0.112646I
b = 2.98204 + 0.59250I
7.91932 − 0.95011I 0
u = 0.07790 + 1.85868I
a = 1.338270 + 0.067138I
b = −3.10970 + 0.35595I
9.02288 + 4.28735I 0
u = 0.07790 − 1.85868I
a = 1.338270 − 0.067138I
b = −3.10970 − 0.35595I
9.02288 − 4.28735I 0
u = 0.83937 + 1.67276I
a = 1.204110 + 0.689221I
b = −2.91118 + 1.34779I
12.9811 − 16.7369I 0
u = 0.83937 − 1.67276I
a = 1.204110 − 0.689221I
b = −2.91118 − 1.34779I
12.9811 + 16.7369I 0
u = −0.91937 + 1.70937I
a = 1.075370 − 0.557472I
b = −2.54762 − 1.92063I
12.4197 + 8.6105I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.91937 − 1.70937I
a = 1.075370 + 0.557472I
b = −2.54762 + 1.92063I
12.4197 − 8.6105I 0
u = −0.72464 + 1.81573I
a = 1.205180 − 0.538506I
b = −3.17021 − 1.14256I
14.1227 + 9.9944I 0
u = −0.72464 − 1.81573I
a = 1.205180 + 0.538506I
b = −3.17021 + 1.14256I
14.1227 − 9.9944I 0
u = 0.81635 + 1.85467I
a = 1.078160 + 0.454227I
b = −2.85780 + 1.78574I
13.66850 − 1.78524I 0
u = 0.81635 − 1.85467I
a = 1.078160 − 0.454227I
b = −2.85780 − 1.78574I
13.66850 + 1.78524I 0
11
II.
I
u
2
= hu
4
−2u
3
+b+3u, −4u
4
+5u
3
+8u
2
+a−8u−3, u
5
−u
4
−2u
3
+u
2
+u+1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
4u
4
− 5u
3
− 8u
2
+ 8u + 3
−u
4
+ 2u
3
− 3u
a
9
=
4u
4
− 5u
3
− 8u
2
+ 8u + 4
−u
4
+ 2u
3
+ u
2
− 3u
a
12
=
−1
−u
2
a
4
=
u
u
3
+ u
a
6
=
−u
2
+ 1
−u
4
a
3
=
−u
3
+ 2u
−u
4
− u
3
+ u
2
+ 2u + 1
a
2
=
−u
3
+ 2u
−2u
4
− u
3
+ 2u
2
+ 3u + 2
a
1
=
−1
−u
2
a
10
=
3u
4
− 3u
3
− 7u
2
+ 5u + 4
−u
4
+ 2u
3
+ u
2
− 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 24u
4
− 21u
3
− 27u
2
+ 28u − 11
12
(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
13
(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
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.780402
b = −2.15724
−0.756147 5.56100
u = −0.309916 + 0.549911I
a = 0.62016 + 7.72799I
b = 1.50612 − 1.80609I
1.31583 + 1.53058I −21.1516 + 28.1413I
u = −0.309916 − 0.549911I
a = 0.62016 − 7.72799I
b = 1.50612 + 1.80609I
1.31583 − 1.53058I −21.1516 − 28.1413I
u = 1.41878 + 0.21917I
a = −0.729964 − 0.010955I
b = −2.42750 − 0.47549I
−4.22763 − 4.40083I 3.3711 + 20.4276I
u = 1.41878 − 0.21917I
a = −0.729964 + 0.010955I
b = −2.42750 + 0.47549I
−4.22763 + 4.40083I 3.3711 − 20.4276I
15
III. I
v
1
= ha, 3.10 × 10
5
v
11
− 7.90 × 10
5
v
10
+ · · · + 7.08 × 10
5
b − 1.25 ×
10
6
, v
12
− 3v
11
+ · · · − v + 1i
(i) Arc colorings
a
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−0.437990v
11
+ 1.11658v
10
+ ··· + 0.432058v + 1.76482
a
9
=
1
1.00827v
11
− 2.68986v
10
+ ··· − 1.09637v − 2.28028
a
12
=
−0.437990v
11
+ 1.11658v
10
+ ··· + 0.432058v + 1.76482
1.04198v
11
− 2.90360v
10
+ ··· − 1.23849v − 0.574544
a
4
=
v
0
a
6
=
−0.613949v
11
+ 1.71800v
10
+ ··· + 0.735835v + 0.454734
−1.86146v
11
+ 5.23525v
10
+ ··· + 2.25349v + 3.04348
a
3
=
−0.197394v
11
+ 0.527234v
10
+ ··· + 3.32683v + 0.437990
0.861460v
11
− 2.23525v
10
+ ··· + 1.74651v − 2.04348
a
2
=
−0.588834v
11
+ 1.67328v
10
+ ··· + 3.83916v + 0.787117
0.861460v
11
− 2.23525v
10
+ ··· + 1.74651v − 2.04348
a
1
=
0.613949v
11
− 1.71800v
10
+ ··· − 0.735835v − 0.454734
1.86146v
11
− 5.23525v
10
+ ··· − 2.25349v − 3.04348
a
10
=
1.00827v
11
− 2.68986v
10
+ ··· − 1.09637v − 1.28028
1.00827v
11
− 2.68986v
10
+ ··· − 1.09637v − 2.28028
(ii) Obstruction class = 1
(iii) Cusp Shapes =
142431
78637
v
11
−
528010
78637
v
10
+ ··· +
712177
78637
v +
123275
78637
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
7
u
12
c
6
, c
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
8
, c
10
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
7
y
12
c
6
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
8
, c
10
, c
11
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.834826 + 0.083652I
a = 0
b = 0.428243 + 0.664531I
−1.89061 − 2.95419I −3.63443 + 4.40052I
v = −0.834826 − 0.083652I
a = 0
b = 0.428243 − 0.664531I
−1.89061 + 2.95419I −3.63443 − 4.40052I
v = 0.489858 + 0.681154I
a = 0
b = 0.428243 + 0.664531I
−1.89061 + 1.10558I −6.39280 − 3.34928I
v = 0.489858 − 0.681154I
a = 0
b = 0.428243 − 0.664531I
−1.89061 − 1.10558I −6.39280 + 3.34928I
v = 0.458424 + 0.081263I
a = 0
b = 1.073950 − 0.558752I
− 3.66314I 2.53591 + 0.53518I
v = 0.458424 − 0.081263I
a = 0
b = 1.073950 + 0.558752I
3.66314I 2.53591 − 0.53518I
v = −0.299588 + 0.356375I
a = 0
b = 1.073950 − 0.558752I
− 7.72290I −2.83009 + 13.30597I
v = −0.299588 − 0.356375I
a = 0
b = 1.073950 + 0.558752I
7.72290I −2.83009 − 13.30597I
v = −0.82520 + 2.42341I
a = 0
b = −1.002190 + 0.295542I
1.89061 − 2.95419I −3.59610 + 0.35185I
v = −0.82520 − 2.42341I
a = 0
b = −1.002190 − 0.295542I
1.89061 + 2.95419I −3.59610 − 0.35185I
19
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 2.51133 + 0.49706I
a = 0
b = −1.002190 − 0.295542I
1.89061 − 1.10558I 7.91752 + 5.10831I
v = 2.51133 − 0.49706I
a = 0
b = −1.002190 + 0.295542I
1.89061 + 1.10558I 7.91752 − 5.10831I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
5
− 3u
4
+ ··· − u + 1)(u
65
+ 18u
64
+ ··· − 47u − 1)
c
2
((u
2
+ u + 1)
6
)(u
5
− u
4
+ ··· + u − 1)(u
65
+ 8u
64
+ ··· + 5u + 1)
c
3
(u
2
− u + 1)
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
65
− 8u
64
+ ··· + 103537045u + 13657673)
c
4
u
12
(u
5
+ u
4
+ ··· + u − 1)(u
65
− 2u
64
+ ··· + 4096u + 4096)
c
5
((u
2
− u + 1)
6
)(u
5
+ u
4
+ ··· + u + 1)(u
65
+ 8u
64
+ ··· + 5u + 1)
c
6
(u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
65
− 4u
64
+ ··· − 3u + 1)
c
7
u
12
(u
5
− u
4
+ ··· + u + 1)(u
65
− 2u
64
+ ··· + 4096u + 4096)
c
8
((u + 1)
5
)(u
6
− u
5
+ ··· − u + 1)
2
(u
65
+ 8u
64
+ ··· + 3u + 1)
c
9
(u
5
+ u
4
+ 3u
3
− 8u
2
+ 5u − 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
65
+ 10u
64
+ ··· + 497u + 101)
c
10
(u
5
+ u
4
+ 3u
3
− 8u
2
+ 5u − 1)(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
65
+ 4u
64
+ ··· − 606921u + 85049)
c
11
((u − 1)
5
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
65
+ 8u
64
+ ··· + 3u + 1)
c
12
u
5
(u
6
− u
5
+ ··· − u + 1)
2
(u
65
− 11u
64
+ ··· − 192u + 32)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
65
+ 66y
64
+ ··· + 213y − 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
5
+ 3y
4
+ ··· − y − 1)(y
65
+ 18y
64
+ ··· − 47y − 1)
c
3
(y
2
+ y + 1)
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
65
+ 114y
64
+ ··· − 13102594991519615y − 186532031774929)
c
4
, c
7
y
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
65
+ 60y
64
+ ··· − 134217728y − 16777216)
c
6
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
65
+ 2y
64
+ ··· − 19y − 1)
c
8
, c
11
(y − 1)
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
65
− 58y
64
+ ··· − 4257y − 1)
c
9
(y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
65
− 72y
64
+ ··· + 1225295y − 10201)
c
10
(y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y − 1)
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
65
+ 4y
64
+ ··· + 132226628699y − 7233332401)
c
12
y
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
65
+ 27y
64
+ ··· − 52736y − 1024)
22
