12n
0032
(K12n
0032
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 9 5 11 12 7 6 10
Solving Sequence
5,7 8,11
9 4 6 12 3 2 1 10
c
7
c
8
c
4
c
6
c
11
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−4.78378 × 10
254
u
64
+ 1.08998 × 10
255
u
63
+ ··· + 3.15176 × 10
257
b − 2.19432 × 10
258
,
3.69307 × 10
254
u
64
+ 2.76585 × 10
254
u
63
+ ··· + 6.30351 × 10
257
a + 1.47988 × 10
259
,
u
65
− 2u
64
+ ··· + 4096u + 4096i
I
u
2
= h−u
4
+ 2u
3
+ u
2
+ b − 3u, 3u
4
− 3u
3
− 7u
2
+ a + 5u + 4, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, 164522v
11
− 355934v
10
+ ··· + 707733b + 176501,
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−4.78 × 10
254
u
64
+ 1.09 × 10
255
u
63
+ · · · + 3.15 × 10
257
b − 2.19 ×
10
258
, 3.69 × 10
254
u
64
+ 2.77 × 10
254
u
63
+ · · · + 6.30 × 10
257
a + 1.48 ×
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
=
−0.000585875u
64
− 0.000438779u
63
+ ··· + 20.3734u − 23.4770
0.00151782u
64
− 0.00345832u
63
+ ··· + 9.59064u + 6.96221
a
9
=
−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
12
=
0.00116546u
64
− 0.00414819u
63
+ ··· + 31.2869u − 11.0123
0.00138687u
64
− 0.00313302u
63
+ ··· + 8.32770u + 7.09279
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
=
0.000931941u
64
− 0.00389710u
63
+ ··· + 29.9641u − 16.5148
0.00151782u
64
− 0.00345832u
63
+ ··· + 9.59064u + 6.96221
(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
u
65
− 11u
64
+ ··· − 192u + 32
c
9
, c
12
u
65
+ 8u
64
+ ··· + 3u + 1
c
10
u
65
+ 4u
64
+ ··· − 606921u + 85049
c
11
u
65
+ 10u
64
+ ··· + 497u + 101
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
y
65
+ 27y
64
+ ··· − 52736y −1024
c
9
, c
12
y
65
− 58y
64
+ ··· − 4257y −1
c
10
y
65
+ 4y
64
+ ··· + 132226628699y −7233332401
c
11
y
65
− 72y
64
+ ··· + 1225295y −10201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.130385 + 0.943634I
a = 0.76665 + 2.06572I
b = −0.514674 − 0.553942I
−0.74329 − 4.73729I −2.00000 + 8.64739I
u = 0.130385 − 0.943634I
a = 0.76665 − 2.06572I
b = −0.514674 + 0.553942I
−0.74329 + 4.73729I −2.00000 − 8.64739I
u = 0.887268 + 0.125733I
a = −0.179409 − 1.032200I
b = 0.318940 + 0.297442I
1.48232 − 4.00344I −0.95634 + 8.48185I
u = 0.887268 − 0.125733I
a = −0.179409 + 1.032200I
b = 0.318940 − 0.297442I
1.48232 + 4.00344I −0.95634 − 8.48185I
u = 0.668516 + 0.588632I
a = 1.56956 − 1.46497I
b = 0.016939 + 1.169930I
3.65615 − 1.42936I 6.46603 + 3.32743I
u = 0.668516 − 0.588632I
a = 1.56956 + 1.46497I
b = 0.016939 − 1.169930I
3.65615 + 1.42936I 6.46603 − 3.32743I
u = −0.802999
a = 0.258328
b = 0.781641
−1.43422 −8.16770
u = 0.243832 + 0.761247I
a = 1.34826 − 1.30971I
b = −0.250649 + 0.069598I
1.88543 + 1.32823I 3.63769 − 3.79947I
u = 0.243832 − 0.761247I
a = 1.34826 + 1.30971I
b = −0.250649 − 0.069598I
1.88543 − 1.32823I 3.63769 + 3.79947I
u = −0.607968 + 0.481302I
a = 0.149356 + 0.154741I
b = 1.044290 − 0.031607I
−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 = 0.149356 − 0.154741I
b = 1.044290 + 0.031607I
−1.68242 + 0.00290I −4.75043 + 0.81603I
u = −0.031117 + 0.710250I
a = 1.88874 + 1.21810I
b = −0.608662 − 0.271807I
−0.54684 + 1.46329I −1.59201 − 1.40388I
u = −0.031117 − 0.710250I
a = 1.88874 − 1.21810I
b = −0.608662 + 0.271807I
−0.54684 − 1.46329I −1.59201 + 1.40388I
u = −0.704902 + 0.035674I
a = 1.00315 + 1.49097I
b = 0.615020 − 0.093383I
1.30008 − 0.99581I −3.39411 − 0.67872I
u = −0.704902 − 0.035674I
a = 1.00315 − 1.49097I
b = 0.615020 + 0.093383I
1.30008 + 0.99581I −3.39411 + 0.67872I
u = 0.536940 + 0.442415I
a = 0.096152 + 0.318851I
b = 0.948518 − 0.522416I
−2.50902 + 1.89252I −7.42573 − 0.50006I
u = 0.536940 − 0.442415I
a = 0.096152 − 0.318851I
b = 0.948518 + 0.522416I
−2.50902 − 1.89252I −7.42573 + 0.50006I
u = −0.423794 + 0.531866I
a = 1.09298 − 3.83683I
b = −1.83672 − 0.52554I
1.19925 + 1.20786I 13.02298 − 5.31257I
u = −0.423794 − 0.531866I
a = 1.09298 + 3.83683I
b = −1.83672 + 0.52554I
1.19925 − 1.20786I 13.02298 + 5.31257I
u = −0.584385 + 0.334144I
a = 0.118976 + 0.116953I
b = −0.863516 + 0.470481I
−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 = 0.118976 − 0.116953I
b = −0.863516 − 0.470481I
−0.48772 − 4.09297I −7.37755 + 9.24327I
u = −0.340196 + 0.558280I
a = 0.987313 + 0.431504I
b = −0.136703 − 0.358878I
−0.33530 + 1.50733I −2.98038 − 4.24113I
u = −0.340196 − 0.558280I
a = 0.987313 − 0.431504I
b = −0.136703 + 0.358878I
−0.33530 − 1.50733I −2.98038 + 4.24113I
u = 0.462414 + 0.447292I
a = 0.117142 + 0.093138I
b = −1.175610 + 0.714758I
0.05754 + 7.13285I −1.292669 + 0.043034I
u = 0.462414 − 0.447292I
a = 0.117142 − 0.093138I
b = −1.175610 − 0.714758I
0.05754 − 7.13285I −1.292669 − 0.043034I
u = −0.237497 + 0.569452I
a = 0.98989 + 4.44821I
b = 0.067363 − 1.017050I
2.38609 − 2.85839I 7.30042 − 0.29630I
u = −0.237497 − 0.569452I
a = 0.98989 − 4.44821I
b = 0.067363 + 1.017050I
2.38609 + 2.85839I 7.30042 + 0.29630I
u = 1.356580 + 0.325626I
a = 0.0929425 − 0.0475878I
b = 0.601262 − 0.221151I
−4.31980 − 4.20818I 0
u = 1.356580 − 0.325626I
a = 0.0929425 + 0.0475878I
b = 0.601262 + 0.221151I
−4.31980 + 4.20818I 0
u = −0.324505 + 0.474102I
a = 2.11235 + 9.22641I
b = 2.59859 − 1.54012I
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 = 2.11235 − 9.22641I
b = 2.59859 + 1.54012I
1.37708 − 1.55327I 81.0765 − 4.2253I
u = 0.361073 + 0.261174I
a = 2.01834 − 0.84744I
b = −0.211431 − 0.525368I
1.90413 + 1.10524I 1.74598 − 1.88050I
u = 0.361073 − 0.261174I
a = 2.01834 + 0.84744I
b = −0.211431 + 0.525368I
1.90413 − 1.10524I 1.74598 + 1.88050I
u = −0.33997 + 1.55682I
a = 0.396931 + 0.958804I
b = −0.35203 − 1.74037I
6.96782 + 4.95648I 0
u = −0.33997 − 1.55682I
a = 0.396931 − 0.958804I
b = −0.35203 + 1.74037I
6.96782 − 4.95648I 0
u = 0.12238 + 1.58993I
a = 0.326507 − 1.039120I
b = −0.71396 + 1.78796I
7.32759 + 1.41648I 0
u = 0.12238 − 1.58993I
a = 0.326507 + 1.039120I
b = −0.71396 − 1.78796I
7.32759 − 1.41648I 0
u = 0.19403 + 1.60184I
a = −0.231654 − 1.153400I
b = 0.57265 + 1.52102I
4.63170 − 9.18200I 0
u = 0.19403 − 1.60184I
a = −0.231654 + 1.153400I
b = 0.57265 − 1.52102I
4.63170 + 9.18200I 0
u = −0.11845 + 1.68248I
a = −1.083650 + 0.136637I
b = 3.97406 + 0.12574I
9.32058 + 3.26408I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11845 − 1.68248I
a = −1.083650 − 0.136637I
b = 3.97406 − 0.12574I
9.32058 − 3.26408I 0
u = −0.38021 + 1.66959I
a = −0.339909 − 0.746548I
b = −0.176201 + 1.278650I
4.26944 + 0.46934I 0
u = −0.38021 − 1.66959I
a = −0.339909 + 0.746548I
b = −0.176201 − 1.278650I
4.26944 − 0.46934I 0
u = 0.46996 + 1.65519I
a = −0.068809 + 1.192120I
b = −0.386126 − 1.328800I
7.48257 − 9.61839I 0
u = 0.46996 − 1.65519I
a = −0.068809 − 1.192120I
b = −0.386126 + 1.328800I
7.48257 + 9.61839I 0
u = −0.25917 + 1.70792I
a = 0.092890 − 1.145830I
b = −0.179693 + 1.268370I
8.03127 + 3.06347I 0
u = −0.25917 − 1.70792I
a = 0.092890 + 1.145830I
b = −0.179693 − 1.268370I
8.03127 − 3.06347I 0
u = 1.79527 + 0.04387I
a = 0.0775738 + 0.0854124I
b = −0.31338 + 1.67113I
8.03839 + 7.65970I 0
u = 1.79527 − 0.04387I
a = 0.0775738 − 0.0854124I
b = −0.31338 − 1.67113I
8.03839 − 7.65970I 0
u = 0.24346 + 1.80056I
a = −0.445122 + 0.716665I
b = −0.989214 − 0.963624I
12.17050 − 5.84377I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24346 − 1.80056I
a = −0.445122 − 0.716665I
b = −0.989214 + 0.963624I
12.17050 + 5.84377I 0
u = 0.00594 + 1.82235I
a = −0.314626 − 0.803941I
b = −0.90000 + 1.16024I
12.34330 − 0.87809I 0
u = 0.00594 − 1.82235I
a = −0.314626 + 0.803941I
b = −0.90000 − 1.16024I
12.34330 + 0.87809I 0
u = −1.81397 + 0.20782I
a = 0.0729012 + 0.0880981I
b = 0.01065 + 1.57570I
7.91932 + 0.95011I 0
u = −1.81397 − 0.20782I
a = 0.0729012 − 0.0880981I
b = 0.01065 − 1.57570I
7.91932 − 0.95011I 0
u = 0.07790 + 1.85868I
a = −0.234843 + 0.882842I
b = 0.13594 − 1.69367I
9.02288 + 4.28735I 0
u = 0.07790 − 1.85868I
a = −0.234843 − 0.882842I
b = 0.13594 + 1.69367I
9.02288 − 4.28735I 0
u = 0.83937 + 1.67276I
a = 0.323244 − 1.110800I
b = 1.22877 + 1.81894I
12.9811 − 16.7369I 0
u = 0.83937 − 1.67276I
a = 0.323244 + 1.110800I
b = 1.22877 − 1.81894I
12.9811 + 16.7369I 0
u = −0.91937 + 1.70937I
a = −0.299797 − 0.734642I
b = −1.06334 + 1.23089I
12.4197 + 8.6105I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.91937 − 1.70937I
a = −0.299797 + 0.734642I
b = −1.06334 − 1.23089I
12.4197 − 8.6105I 0
u = −0.72464 + 1.81573I
a = 0.208060 + 1.047760I
b = 1.06731 − 1.94103I
14.1227 + 9.9944I 0
u = −0.72464 − 1.81573I
a = 0.208060 − 1.047760I
b = 1.06731 + 1.94103I
14.1227 − 9.9944I 0
u = 0.81635 + 1.85467I
a = −0.281254 + 0.712321I
b = −0.91922 − 1.44444I
13.66850 − 1.78524I 0
u = 0.81635 − 1.85467I
a = −0.281254 − 0.712321I
b = −0.91922 + 1.44444I
13.66850 + 1.78524I 0
11
II. I
u
2
=
h−u
4
+2u
3
+u
2
+b−3u, 3u
4
−3u
3
−7u
2
+a+5u+4, 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
=
−3u
4
+ 3u
3
+ 7u
2
− 5u − 4
u
4
− 2u
3
− u
2
+ 3u
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
6
=
−u
2
+ 1
−u
4
a
12
=
−2u
4
+ u
3
+ 6u
2
− 2u − 5
u
4
− 2u
3
− 2u
2
+ 3u
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
=
−2u
4
+ u
3
+ 6u
2
− 2u − 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
5
c
9
(u + 1)
5
c
10
, c
11
u
5
− u
4
+ 3u
3
+ 8u
2
+ 5u + 1
c
12
(u − 1)
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
y
5
c
9
, c
12
(y −1)
5
c
10
, c
11
y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 0.454765
b = 0.674363
−0.756147 5.56100
u = −0.309916 + 0.549911I
a = −2.91994 − 5.58105I
b = −1.29977 + 2.14694I
1.31583 + 1.53058I −21.1516 + 28.1413I
u = −0.309916 − 0.549911I
a = −2.91994 + 5.58105I
b = −1.29977 − 2.14694I
1.31583 − 1.53058I −21.1516 − 28.1413I
u = 1.41878 + 0.21917I
a = 0.192553 − 0.135455I
b = 0.462589 − 0.146410I
−4.22763 − 4.40083I 3.3711 + 20.4276I
u = 1.41878 − 0.21917I
a = 0.192553 + 0.135455I
b = 0.462589 + 0.146410I
−4.22763 + 4.40083I 3.3711 − 20.4276I
15
III. I
v
1
= ha, 1.65 × 10
5
v
11
− 3.56 × 10
5
v
10
+ · · · + 7.08 × 10
5
b + 1.77 ×
10
5
, v
12
− 3v
11
+ · · · − v + 1i
(i) Arc colorings
a
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−0.232463v
11
+ 0.502921v
10
+ ··· + 0.152902v − 0.249389
a
9
=
1
1.04198v
11
− 2.90360v
10
+ ··· − 1.23849v − 0.574544
a
4
=
v
0
a
6
=
−1.04198v
11
+ 2.90360v
10
+ ··· + 1.23849v + 1.57454
−1.86146v
11
+ 5.23525v
10
+ ··· + 2.25349v + 3.04348
a
12
=
0.802746v
11
− 2.07621v
10
+ ··· − 0.817216v − 0.266076
1.62222v
11
− 4.40786v
10
+ ··· − 1.83221v − 1.73501
a
3
=
0.332033v
11
− 0.854010v
10
+ ··· + 2.53667v − 0.802746
0.861460v
11
− 2.23525v
10
+ ··· + 1.74651v − 2.04348
a
2
=
−0.0594066v
11
+ 0.292037v
10
+ ··· + 3.04900v − 0.453619
0.861460v
11
− 2.23525v
10
+ ··· + 1.74651v − 2.04348
a
1
=
1.04198v
11
− 2.90360v
10
+ ··· − 1.23849v − 1.57454
1.86146v
11
− 5.23525v
10
+ ··· − 2.25349v − 3.04348
a
10
=
−0.232463v
11
+ 0.502921v
10
+ ··· + 0.152902v − 0.249389
−0.232463v
11
+ 0.502921v
10
+ ··· + 0.152902v − 0.249389
(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
11
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
8
, c
12
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
9
, c
10
(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
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
8
, c
9
, c
10
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 = 1.002190 + 0.295542I
−1.89061 − 2.95419I −3.63443 + 4.40052I
v = −0.834826 − 0.083652I
a = 0
b = 1.002190 − 0.295542I
−1.89061 + 2.95419I −3.63443 − 4.40052I
v = 0.489858 + 0.681154I
a = 0
b = 1.002190 + 0.295542I
−1.89061 + 1.10558I −6.39280 − 3.34928I
v = 0.489858 − 0.681154I
a = 0
b = 1.002190 − 0.295542I
−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 = −0.428243 + 0.664531I
1.89061 − 2.95419I −3.59610 + 0.35185I
v = −0.82520 − 2.42341I
a = 0
b = −0.428243 − 0.664531I
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 = −0.428243 − 0.664531I
1.89061 − 1.10558I 7.91752 + 5.10831I
v = 2.51133 − 0.49706I
a = 0
b = −0.428243 + 0.664531I
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
5
(u
6
+ u
5
+ ··· + u + 1)
2
(u
65
− 11u
64
+ ··· − 192u + 32)
c
9
((u + 1)
5
)(u
6
− u
5
+ ··· − u + 1)
2
(u
65
+ 8u
64
+ ··· + 3u + 1)
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
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
12
((u − 1)
5
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
65
+ 8u
64
+ ··· + 3u + 1)
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
y
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
65
+ 27y
64
+ ··· − 52736y − 1024)
c
9
, c
12
(y − 1)
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
65
− 58y
64
+ ··· − 4257y − 1)
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
11
(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)
22
