12a
1046
(K12a
1046
)
A knot diagram
1
Linearized knot diagam
4 7 9 8 11 12 2 1 3 6 5 10
Solving Sequence
6,10
11 5 12 7
1,3
2 9 4 8
c
10
c
5
c
11
c
6
c
12
c
2
c
9
c
3
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h17u
38
+ 107u
37
+ ··· + 4b − 260, 21u
38
+ 133u
37
+ ··· + 8a − 60, u
39
+ 7u
38
+ ··· − 60u − 8i
I
u
2
= h6.66973 × 10
28
a
5
u
13
+ 1.23560 × 10
29
a
4
u
13
+ ··· − 4.72555 × 10
29
a + 3.07955 × 10
29
,
2u
13
a
4
+ 7u
13
a
3
+ ··· − 6a − 15,
u
14
− u
13
+ 7u
12
− 6u
11
+ 18u
10
− 13u
9
+ 19u
8
− 10u
7
+ 4u
6
+ 2u
5
− 4u
4
+ 4u
3
− u + 1i
I
u
3
= h−u
17
− 8u
15
− 25u
13
− 37u
11
− u
10
− 25u
9
− 5u
8
− 8u
7
− 8u
6
− 6u
5
− 3u
4
− 4u
3
+ 2u
2
+ b − u,
u
21
+ u
20
+ ··· + a + 1, u
22
+ 11u
20
+ ··· + 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 145 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
= h17u
38
+ 107u
37
+ · · · + 4b − 260, 21u
38
+ 133u
37
+ · · · + 8a −
60, u
39
+ 7u
38
+ · · · − 60u − 8i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
3
=
−2.62500u
38
− 16.6250u
37
+ ··· + 105.750u + 7.50000
−
17
4
u
38
−
107
4
u
37
+ ··· + 388u + 65
a
2
=
2.37500u
38
+ 18.3750u
37
+ ··· − 176.250u − 22.5000
11
4
u
38
+
57
4
u
37
+ ··· − 210u − 33
a
9
=
−
55
8
u
38
−
371
8
u
37
+ ··· +
1737
4
u + 66
17
4
u
38
+
105
4
u
37
+ ··· −
243
2
u − 13
a
4
=
−
29
8
u
38
−
207
8
u
37
+ ··· +
421
2
u + 24
−4u
38
−
47
2
u
37
+ ··· +
747
2
u + 61
a
8
=
−
13
8
u
38
−
65
8
u
37
+ ··· +
3
4
u + 1
−
19
4
u
38
−
127
4
u
37
+ ··· +
661
2
u + 51
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
38
+ 36u
37
+ ··· − 148u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
− 33u
38
+ ··· + 352256u − 16384
c
2
, c
3
, c
7
c
9
u
39
+ 13u
37
+ ··· − 2u + 1
c
4
, c
8
u
39
+ u
38
+ ··· + 3u + 1
c
5
, c
10
, c
11
u
39
− 7u
38
+ ··· − 60u + 8
c
6
u
39
+ 7u
38
+ ··· − 1596u + 2088
c
12
u
39
− 9u
38
+ ··· − 43968u + 9728
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
− 9y
38
+ ··· + 3019898880y −268435456
c
2
, c
3
, c
7
c
9
y
39
+ 26y
38
+ ··· + 8y −1
c
4
, c
8
y
39
+ 9y
38
+ ··· − 23y −1
c
5
, c
10
, c
11
y
39
+ 35y
38
+ ··· − 48y −64
c
6
y
39
+ 5y
38
+ ··· − 35220528y −4359744
c
12
y
39
+ 15y
38
+ ··· − 1741041664y −94633984
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.402641 + 0.923218I
a = 0.123865 + 0.173423I
b = −0.313293 + 0.898902I
−0.83222 − 1.74805I 1.85163 + 7.08327I
u = −0.402641 − 0.923218I
a = 0.123865 − 0.173423I
b = −0.313293 − 0.898902I
−0.83222 + 1.74805I 1.85163 − 7.08327I
u = −0.711880 + 0.543145I
a = −0.596131 − 0.139383I
b = 0.047860 + 0.975188I
−0.45441 + 2.42357I −6.62342 − 4.26652I
u = −0.711880 − 0.543145I
a = −0.596131 + 0.139383I
b = 0.047860 − 0.975188I
−0.45441 − 2.42357I −6.62342 + 4.26652I
u = −0.477289 + 0.710961I
a = −0.147405 + 0.420958I
b = 0.54795 − 1.36232I
−4.43014 − 10.11780I −6.08524 + 4.54583I
u = −0.477289 − 0.710961I
a = −0.147405 − 0.420958I
b = 0.54795 + 1.36232I
−4.43014 + 10.11780I −6.08524 − 4.54583I
u = −0.790989 + 0.257645I
a = −1.01138 + 1.09144I
b = 0.403002 + 0.993100I
−2.87677 + 6.11596I −5.61902 − 11.75200I
u = −0.790989 − 0.257645I
a = −1.01138 − 1.09144I
b = 0.403002 − 0.993100I
−2.87677 − 6.11596I −5.61902 + 11.75200I
u = 0.342776 + 1.125240I
a = −1.077400 − 0.136141I
b = 0.39377 − 1.36577I
−5.82056 − 9.89475I −7.41952 + 7.73819I
u = 0.342776 − 1.125240I
a = −1.077400 + 0.136141I
b = 0.39377 + 1.36577I
−5.82056 + 9.89475I −7.41952 − 7.73819I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.755894 + 0.317559I
a = 1.61018 − 1.04698I
b = −0.59395 − 1.40684I
−5.7809 + 14.4369I −8.07183 − 9.36551I
u = −0.755894 − 0.317559I
a = 1.61018 + 1.04698I
b = −0.59395 + 1.40684I
−5.7809 − 14.4369I −8.07183 + 9.36551I
u = 0.798444 + 0.067462I
a = −0.366765 − 1.043450I
b = −0.305676 − 1.327300I
−9.06750 + 5.75506I −11.48705 − 4.63489I
u = 0.798444 − 0.067462I
a = −0.366765 + 1.043450I
b = −0.305676 + 1.327300I
−9.06750 − 5.75506I −11.48705 + 4.63489I
u = −0.624159 + 0.368707I
a = −0.309607 + 0.944919I
b = 0.742260 − 0.072896I
2.43896 + 3.63567I 0.57871 − 5.66121I
u = −0.624159 − 0.368707I
a = −0.309607 − 0.944919I
b = 0.742260 + 0.072896I
2.43896 − 3.63567I 0.57871 + 5.66121I
u = 0.141393 + 1.269230I
a = 0.171501 + 0.444677I
b = −0.487698 − 0.033283I
2.67445 − 2.43754I 0
u = 0.141393 − 1.269230I
a = 0.171501 − 0.444677I
b = −0.487698 + 0.033283I
2.67445 + 2.43754I 0
u = 0.359384 + 1.271690I
a = 0.786179 − 0.431294I
b = 0.228282 + 1.275960I
−4.91124 + 1.59162I 0
u = 0.359384 − 1.271690I
a = 0.786179 + 0.431294I
b = 0.228282 − 1.275960I
−4.91124 − 1.59162I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.513565 + 0.443254I
a = 0.813961 − 0.283065I
b = −0.740571 − 0.193624I
2.83998 + 0.06866I 1.72690 − 2.02626I
u = −0.513565 − 0.443254I
a = 0.813961 + 0.283065I
b = −0.740571 + 0.193624I
2.83998 − 0.06866I 1.72690 + 2.02626I
u = 0.286826 + 0.574932I
a = 0.705124 + 0.432129I
b = −0.204549 + 0.657112I
−0.221784 − 1.394250I −2.01573 + 3.25063I
u = 0.286826 − 0.574932I
a = 0.705124 − 0.432129I
b = −0.204549 − 0.657112I
−0.221784 + 1.394250I −2.01573 − 3.25063I
u = −0.06245 + 1.42153I
a = −1.195630 + 0.599024I
b = 0.571644 − 0.706847I
6.09815 − 1.32183I 0
u = −0.06245 − 1.42153I
a = −1.195630 − 0.599024I
b = 0.571644 + 0.706847I
6.09815 + 1.32183I 0
u = −0.31542 + 1.41590I
a = 1.78095 − 0.15255I
b = −0.470372 − 1.030310I
2.46313 + 10.11530I 0
u = −0.31542 − 1.41590I
a = 1.78095 + 0.15255I
b = −0.470372 + 1.030310I
2.46313 − 10.11530I 0
u = −0.19256 + 1.44129I
a = −1.64680 + 0.08898I
b = 0.847538 + 0.236025I
8.83636 + 2.66799I 0
u = −0.19256 − 1.44129I
a = −1.64680 − 0.08898I
b = 0.847538 − 0.236025I
8.83636 − 2.66799I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23418 + 1.44082I
a = 1.16879 − 0.89698I
b = −0.802572 + 0.020537I
8.24829 + 6.77910I 0
u = −0.23418 − 1.44082I
a = 1.16879 + 0.89698I
b = −0.802572 − 0.020537I
8.24829 − 6.77910I 0
u = −0.29621 + 1.43559I
a = −2.41476 − 0.26767I
b = 0.63351 + 1.41710I
−0.1721 + 18.2585I 0
u = −0.29621 − 1.43559I
a = −2.41476 + 0.26767I
b = 0.63351 − 1.41710I
−0.1721 − 18.2585I 0
u = 0.534008
a = 0.570035
b = 0.419240
−1.19215 −7.70730
u = −0.09732 + 1.48612I
a = 0.92868 − 1.50124I
b = −0.583941 + 1.263340I
2.68660 − 8.37607I 0
u = −0.09732 − 1.48612I
a = 0.92868 + 1.50124I
b = −0.583941 − 1.263340I
2.68660 + 8.37607I 0
u = −0.22127 + 1.51243I
a = 0.641621 + 0.918434I
b = −0.122823 − 0.904781I
6.27991 + 5.75991I 0
u = −0.22127 − 1.51243I
a = 0.641621 − 0.918434I
b = −0.122823 + 0.904781I
6.27991 − 5.75991I 0
8
II. I
u
2
= h6.67 × 10
28
a
5
u
13
+ 1.24 × 10
29
a
4
u
13
+ · · · − 4.73 × 10
29
a + 3.08 ×
10
29
, 2u
13
a
4
+ 7u
13
a
3
+ · · · − 6a − 15, u
14
− u
13
+ · · · − u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
3
=
a
−0.245209a
5
u
13
− 0.454264a
4
u
13
+ ··· + 1.73733a − 1.13218
a
2
=
−0.244193a
5
u
13
− 0.0145692a
4
u
13
+ ··· + 1.26898a + 0.587986
−0.257700a
5
u
13
+ 0.00989329a
4
u
13
+ ··· − 2.42319a + 0.0658441
a
9
=
0.101522a
5
u
13
+ 0.763635a
4
u
13
+ ··· − 1.41580a + 1.73128
−0.908162a
5
u
13
+ 0.543108a
4
u
13
+ ··· + 4.56138a − 0.000383679
a
4
=
−0.0131242a
5
u
13
− 2.73898a
4
u
13
+ ··· + 0.426251a − 2.89019
−1.89539a
5
u
13
+ 3.65697a
4
u
13
+ ··· − 3.10276a + 2.14280
a
8
=
−0.506926a
5
u
13
− 0.840778a
4
u
13
+ ··· + 0.949870a − 0.503640
−0.706277a
5
u
13
+ 1.21318a
4
u
13
+ ··· + 2.35526a − 0.00134333
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.95641a
5
u
13
− 3.40270a
4
u
13
+ ··· + 16.5559a − 6.06062
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
28
c
2
, c
3
, c
7
c
9
u
84
+ u
83
+ ··· − 48112u + 6329
c
4
, c
8
u
84
+ 3u
83
+ ··· + 8u + 1
c
5
, c
10
, c
11
(u
14
+ u
13
+ ··· + u + 1)
6
c
6
(u
14
− u
13
+ ··· + 3u + 1)
6
c
12
(u
14
− 3u
13
+ ··· − 7u + 3)
6
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
28
c
2
, c
3
, c
7
c
9
y
84
+ 63y
83
+ ··· + 237164204y + 40056241
c
4
, c
8
y
84
− 21y
83
+ ··· + 340y + 1
c
5
, c
10
, c
11
(y
14
+ 13y
13
+ ··· − y + 1)
6
c
6
(y
14
+ y
13
+ ··· − y + 1)
6
c
12
(y
14
+ 5y
13
+ ··· + 23y + 9)
6
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135360 + 1.128160I
a = −1.182850 − 0.200988I
b = 0.50647 + 1.63628I
−4.60787 + 2.19128I −12.25870 − 3.85718I
u = −0.135360 + 1.128160I
a = −1.212890 − 0.250606I
b = 1.121890 + 0.329288I
−0.47029 + 5.01941I −5.72943 − 6.83663I
u = −0.135360 + 1.128160I
a = 0.481585 − 1.273240I
b = −0.232519 − 1.160780I
−0.47029 + 5.01941I −5.72943 − 6.83663I
u = −0.135360 + 1.128160I
a = 1.133950 + 0.759588I
b = −0.240320 − 0.036674I
−0.470291 − 0.636839I −5.72943 − 0.87773I
u = −0.135360 + 1.128160I
a = 0.047054 + 0.449604I
b = −0.335746 + 1.109290I
−0.470291 − 0.636839I −5.72943 − 0.87773I
u = −0.135360 + 1.128160I
a = 1.77857 − 0.21584I
b = −0.091428 − 1.316860I
−4.60787 + 2.19128I −12.25870 − 3.85718I
u = −0.135360 − 1.128160I
a = −1.182850 + 0.200988I
b = 0.50647 − 1.63628I
−4.60787 − 2.19128I −12.25870 + 3.85718I
u = −0.135360 − 1.128160I
a = −1.212890 + 0.250606I
b = 1.121890 − 0.329288I
−0.47029 − 5.01941I −5.72943 + 6.83663I
u = −0.135360 − 1.128160I
a = 0.481585 + 1.273240I
b = −0.232519 + 1.160780I
−0.47029 − 5.01941I −5.72943 + 6.83663I
u = −0.135360 − 1.128160I
a = 1.133950 − 0.759588I
b = −0.240320 + 0.036674I
−0.470291 + 0.636839I −5.72943 + 0.87773I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135360 − 1.128160I
a = 0.047054 − 0.449604I
b = −0.335746 − 1.109290I
−0.470291 + 0.636839I −5.72943 + 0.87773I
u = −0.135360 − 1.128160I
a = 1.77857 + 0.21584I
b = −0.091428 + 1.316860I
−4.60787 − 2.19128I −12.25870 + 3.85718I
u = 0.681829 + 0.299736I
a = 0.421363 + 1.011630I
b = −1.312900 − 0.004296I
−1.34687 − 7.89997I −6.16177 + 9.31071I
u = 0.681829 + 0.299736I
a = 1.05793 + 0.99307I
b = −0.109335 + 1.070390I
−1.34687 − 2.24373I −6.16177 + 3.35182I
u = 0.681829 + 0.299736I
a = 0.0026716 − 0.0183627I
b = 0.562454 + 0.438542I
−1.34687 − 2.24373I −6.16177 + 3.35182I
u = 0.681829 + 0.299736I
a = 1.87861 + 0.90732I
b = −0.77979 + 1.41836I
−5.48445 − 5.07185I −12.6910 + 6.3313I
u = 0.681829 + 0.299736I
a = −2.21826 − 0.38907I
b = 0.170971 − 1.120650I
−5.48445 − 5.07185I −12.6910 + 6.3313I
u = 0.681829 + 0.299736I
a = −1.73836 − 1.59512I
b = 0.400190 − 1.279900I
−1.34687 − 7.89997I −6.16177 + 9.31071I
u = 0.681829 − 0.299736I
a = 0.421363 − 1.011630I
b = −1.312900 + 0.004296I
−1.34687 + 7.89997I −6.16177 − 9.31071I
u = 0.681829 − 0.299736I
a = 1.05793 − 0.99307I
b = −0.109335 − 1.070390I
−1.34687 + 2.24373I −6.16177 − 3.35182I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.681829 − 0.299736I
a = 0.0026716 + 0.0183627I
b = 0.562454 − 0.438542I
−1.34687 + 2.24373I −6.16177 − 3.35182I
u = 0.681829 − 0.299736I
a = 1.87861 − 0.90732I
b = −0.77979 − 1.41836I
−5.48445 + 5.07185I −12.6910 − 6.3313I
u = 0.681829 − 0.299736I
a = −2.21826 + 0.38907I
b = 0.170971 + 1.120650I
−5.48445 + 5.07185I −12.6910 − 6.3313I
u = 0.681829 − 0.299736I
a = −1.73836 + 1.59512I
b = 0.400190 + 1.279900I
−1.34687 + 7.89997I −6.16177 − 9.31071I
u = 0.373222 + 0.543854I
a = 0.692825 + 0.790769I
b = −0.048180 − 1.129020I
−4.35354 + 1.40484I −9.51024 − 0.52948I
u = 0.373222 + 0.543854I
a = 0.849025 + 0.419614I
b = −0.351546 + 0.695691I
−0.21596 − 1.42329I −2.98097 + 2.44997I
u = 0.373222 + 0.543854I
a = −0.214244 − 1.293790I
b = 0.61220 + 1.34667I
−4.35354 + 1.40484I −9.51024 − 0.52948I
u = 0.373222 + 0.543854I
a = 0.485465 + 0.488331I
b = 0.065184 + 0.680242I
−0.21596 − 1.42329I −2.98097 + 2.44997I
u = 0.373222 + 0.543854I
a = −1.23667 − 1.04892I
b = 1.123860 − 0.028241I
−0.21596 + 4.23296I −2.98097 − 3.50893I
u = 0.373222 + 0.543854I
a = 0.263447 − 0.238744I
b = −0.411734 − 1.183400I
−0.21596 + 4.23296I −2.98097 − 3.50893I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373222 − 0.543854I
a = 0.692825 − 0.790769I
b = −0.048180 + 1.129020I
−4.35354 − 1.40484I −9.51024 + 0.52948I
u = 0.373222 − 0.543854I
a = 0.849025 − 0.419614I
b = −0.351546 − 0.695691I
−0.21596 + 1.42329I −2.98097 − 2.44997I
u = 0.373222 − 0.543854I
a = −0.214244 + 1.293790I
b = 0.61220 − 1.34667I
−4.35354 − 1.40484I −9.51024 + 0.52948I
u = 0.373222 − 0.543854I
a = 0.485465 − 0.488331I
b = 0.065184 − 0.680242I
−0.21596 + 1.42329I −2.98097 − 2.44997I
u = 0.373222 − 0.543854I
a = −1.23667 + 1.04892I
b = 1.123860 + 0.028241I
−0.21596 − 4.23296I −2.98097 + 3.50893I
u = 0.373222 − 0.543854I
a = 0.263447 + 0.238744I
b = −0.411734 + 1.183400I
−0.21596 − 4.23296I −2.98097 + 3.50893I
u = −0.600586 + 0.155632I
a = 0.093028 − 0.974701I
b = −0.957198 + 0.611128I
−3.27332 − 2.19954I −10.80675 + 1.55694I
u = −0.600586 + 0.155632I
a = −1.39938 + 0.39091I
b = 0.129079 − 0.417151I
−3.27332 + 3.45671I −10.80675 − 4.40196I
u = −0.600586 + 0.155632I
a = −1.37824 + 1.14291I
b = −0.27466 + 1.76171I
−7.41091 + 0.62859I −17.3360 − 1.4225I
u = −0.600586 + 0.155632I
a = 0.10116 − 2.18604I
b = 0.04494 − 1.42846I
−7.41091 + 0.62859I −17.3360 − 1.4225I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600586 + 0.155632I
a = −1.47545 + 2.14482I
b = 0.548640 + 1.069890I
−3.27332 + 3.45671I −10.80675 − 4.40196I
u = −0.600586 + 0.155632I
a = 1.81776 − 2.34846I
b = 0.106065 − 1.012300I
−3.27332 − 2.19954I −10.80675 + 1.55694I
u = −0.600586 − 0.155632I
a = 0.093028 + 0.974701I
b = −0.957198 − 0.611128I
−3.27332 + 2.19954I −10.80675 − 1.55694I
u = −0.600586 − 0.155632I
a = −1.39938 − 0.39091I
b = 0.129079 + 0.417151I
−3.27332 − 3.45671I −10.80675 + 4.40196I
u = −0.600586 − 0.155632I
a = −1.37824 − 1.14291I
b = −0.27466 − 1.76171I
−7.41091 − 0.62859I −17.3360 + 1.4225I
u = −0.600586 − 0.155632I
a = 0.10116 + 2.18604I
b = 0.04494 + 1.42846I
−7.41091 − 0.62859I −17.3360 + 1.4225I
u = −0.600586 − 0.155632I
a = −1.47545 − 2.14482I
b = 0.548640 − 1.069890I
−3.27332 − 3.45671I −10.80675 + 4.40196I
u = −0.600586 − 0.155632I
a = 1.81776 + 2.34846I
b = 0.106065 + 1.012300I
−3.27332 + 2.19954I −10.80675 − 1.55694I
u = −0.228017 + 1.369790I
a = −0.717201 + 0.015902I
b = −0.05295 + 1.48253I
−2.53577 + 3.62879I −11.35334 − 2.63226I
u = −0.228017 + 1.369790I
a = 1.32318 − 0.69746I
b = −0.236834 + 0.604250I
1.60181 + 6.45691I −4.82407 − 5.61170I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.228017 + 1.369790I
a = 1.41047 + 1.60107I
b = 0.20568 − 1.91441I
−2.53577 + 3.62879I −11.35334 − 2.63226I
u = −0.228017 + 1.369790I
a = −2.11383 + 0.40726I
b = 0.040174 + 0.992834I
1.60181 + 0.80067I −4.82407 + 0.34719I
u = −0.228017 + 1.369790I
a = −1.33363 + 1.79333I
b = 1.008160 − 0.805477I
1.60181 + 0.80067I −4.82407 + 0.34719I
u = −0.228017 + 1.369790I
a = 2.64763 − 0.28251I
b = −0.696197 − 1.117620I
1.60181 + 6.45691I −4.82407 − 5.61170I
u = −0.228017 − 1.369790I
a = −0.717201 − 0.015902I
b = −0.05295 − 1.48253I
−2.53577 − 3.62879I −11.35334 + 2.63226I
u = −0.228017 − 1.369790I
a = 1.32318 + 0.69746I
b = −0.236834 − 0.604250I
1.60181 − 6.45691I −4.82407 + 5.61170I
u = −0.228017 − 1.369790I
a = 1.41047 − 1.60107I
b = 0.20568 + 1.91441I
−2.53577 − 3.62879I −11.35334 + 2.63226I
u = −0.228017 − 1.369790I
a = −2.11383 − 0.40726I
b = 0.040174 − 0.992834I
1.60181 − 0.80067I −4.82407 − 0.34719I
u = −0.228017 − 1.369790I
a = −1.33363 − 1.79333I
b = 1.008160 + 0.805477I
1.60181 − 0.80067I −4.82407 − 0.34719I
u = −0.228017 − 1.369790I
a = 2.64763 + 0.28251I
b = −0.696197 + 1.117620I
1.60181 − 6.45691I −4.82407 + 5.61170I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14277 + 1.43183I
a = 0.491219 + 0.403021I
b = −0.487921 − 0.789356I
5.91560 − 3.29867I 0.83805 + 2.79596I
u = 0.14277 + 1.43183I
a = −0.930393 − 1.042580I
b = 0.526535 + 1.186800I
5.91560 + 2.35757I 0.83805 − 3.16294I
u = 0.14277 + 1.43183I
a = −1.52778 + 0.44557I
b = 0.614000 − 0.784990I
5.91560 − 3.29867I 0.83805 + 2.79596I
u = 0.14277 + 1.43183I
a = −0.53527 − 1.64257I
b = 0.014918 + 0.959706I
1.77801 − 0.47055I −5.69122 − 0.18349I
u = 0.14277 + 1.43183I
a = 2.18420 + 0.57085I
b = −1.150400 + 0.264150I
5.91560 + 2.35757I 0.83805 − 3.16294I
u = 0.14277 + 1.43183I
a = 0.82306 + 2.14180I
b = −0.674348 − 1.123170I
1.77801 − 0.47055I −5.69122 − 0.18349I
u = 0.14277 − 1.43183I
a = 0.491219 − 0.403021I
b = −0.487921 + 0.789356I
5.91560 + 3.29867I 0.83805 − 2.79596I
u = 0.14277 − 1.43183I
a = −0.930393 + 1.042580I
b = 0.526535 − 1.186800I
5.91560 − 2.35757I 0.83805 + 3.16294I
u = 0.14277 − 1.43183I
a = −1.52778 − 0.44557I
b = 0.614000 + 0.784990I
5.91560 + 3.29867I 0.83805 − 2.79596I
u = 0.14277 − 1.43183I
a = −0.53527 + 1.64257I
b = 0.014918 − 0.959706I
1.77801 + 0.47055I −5.69122 + 0.18349I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14277 − 1.43183I
a = 2.18420 − 0.57085I
b = −1.150400 − 0.264150I
5.91560 − 2.35757I 0.83805 + 3.16294I
u = 0.14277 − 1.43183I
a = 0.82306 − 2.14180I
b = −0.674348 + 1.123170I
1.77801 + 0.47055I −5.69122 + 0.18349I
u = 0.26614 + 1.42034I
a = 0.693509 + 0.729241I
b = −0.677947 − 0.456718I
4.15353 − 5.70311I −1.76676 + 3.20086I
u = 0.26614 + 1.42034I
a = −1.43185 + 0.18273I
b = 0.209000 − 1.154410I
4.15353 − 5.70311I −1.76676 + 3.20086I
u = 0.26614 + 1.42034I
a = −1.84803 − 1.20778I
b = 1.389510 + 0.055067I
4.15353 − 11.35940I −1.76676 + 9.15975I
u = 0.26614 + 1.42034I
a = 2.25524 + 0.10732I
b = −0.429068 + 1.320870I
4.15353 − 11.35940I −1.76676 + 9.15975I
u = 0.26614 + 1.42034I
a = 2.33826 − 0.74470I
b = −0.219826 + 1.082710I
0.01595 − 8.53123I −8.29603 + 6.18031I
u = 0.26614 + 1.42034I
a = −2.77691 + 0.49501I
b = 0.87092 − 1.39428I
0.01595 − 8.53123I −8.29603 + 6.18031I
u = 0.26614 − 1.42034I
a = 0.693509 − 0.729241I
b = −0.677947 + 0.456718I
4.15353 + 5.70311I −1.76676 − 3.20086I
u = 0.26614 − 1.42034I
a = −1.43185 − 0.18273I
b = 0.209000 + 1.154410I
4.15353 + 5.70311I −1.76676 − 3.20086I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26614 − 1.42034I
a = −1.84803 + 1.20778I
b = 1.389510 − 0.055067I
4.15353 + 11.35940I −1.76676 − 9.15975I
u = 0.26614 − 1.42034I
a = 2.25524 − 0.10732I
b = −0.429068 − 1.320870I
4.15353 + 11.35940I −1.76676 − 9.15975I
u = 0.26614 − 1.42034I
a = 2.33826 + 0.74470I
b = −0.219826 − 1.082710I
0.01595 + 8.53123I −8.29603 − 6.18031I
u = 0.26614 − 1.42034I
a = −2.77691 − 0.49501I
b = 0.87092 + 1.39428I
0.01595 + 8.53123I −8.29603 − 6.18031I
20
III.
I
u
3
= h−u
17
−8u
15
+· · ·+b−u, u
21
+u
20
+· · ·+a+1, u
22
+11u
20
+· · ·+2u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
21
− u
20
+ ··· − 5u − 1
u
17
+ 8u
15
+ ··· − 2u
2
+ u
a
2
=
−u
21
− 10u
19
+ ··· + 9u
2
− 3u
u
17
+ 8u
15
+ ··· + 4u
3
+ u
a
9
=
−u
20
+ 2u
19
+ ··· − 2u + 2
2u
20
+ 19u
18
+ ··· − 10u
3
− u
2
a
4
=
−2u
21
− 20u
19
+ ··· − 3u − 2
u
21
+ u
20
+ ··· + 2u + 1
a
8
=
−u
21
− u
20
+ ··· − 2u + 1
u
21
+ 2u
20
+ ··· − u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −3u
20
+ 4u
19
− 27u
18
+ 36u
17
− 99u
16
+ 133u
15
− 181u
14
+ 248u
13
− 148u
12
+
224u
11
+ 10u
10
+ 60u
9
+ 99u
8
− 14u
7
+ 44u
6
+ 34u
5
− 7u
4
+ 32u
3
− 2u
2
− 2u − 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 10u
21
+ ··· − 6u
2
+ 1
c
2
, c
9
u
22
+ 11u
20
+ ··· − u + 1
c
3
, c
7
u
22
+ 11u
20
+ ··· + u + 1
c
4
, c
8
u
22
+ u
21
+ ··· − 2u + 1
c
5
u
22
+ 11u
20
+ ··· − 2u + 1
c
6
u
22
+ 2u
20
+ ··· − 3u
2
+ 1
c
10
, c
11
u
22
+ 11u
20
+ ··· + 2u + 1
c
12
u
22
− 6u
21
+ ··· − 4u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 8y
21
+ ··· − 12y + 1
c
2
, c
3
, c
7
c
9
y
22
+ 22y
21
+ ··· + 19y + 1
c
4
, c
8
y
22
− 3y
21
+ ··· − 2y + 1
c
5
, c
10
, c
11
y
22
+ 22y
21
+ ··· − 6y + 1
c
6
y
22
+ 4y
21
+ ··· − 6y + 1
c
12
y
22
+ 10y
21
+ ··· + 10y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.259397 + 0.999924I
a = 0.403550 + 0.486577I
b = −0.304119 + 0.895039I
−1.41357 − 1.59707I −11.85494 + 3.44026I
u = −0.259397 − 0.999924I
a = 0.403550 − 0.486577I
b = −0.304119 − 0.895039I
−1.41357 + 1.59707I −11.85494 − 3.44026I
u = 0.662501 + 0.516350I
a = 0.385947 + 0.387492I
b = −0.056717 + 0.666796I
0.49372 − 2.27838I 3.57779 + 5.27864I
u = 0.662501 − 0.516350I
a = 0.385947 − 0.387492I
b = −0.056717 − 0.666796I
0.49372 + 2.27838I 3.57779 − 5.27864I
u = 0.135330 + 1.210060I
a = 1.44433 − 0.33008I
b = −0.14738 + 1.48110I
−3.70412 − 1.43318I −5.69627 − 1.82767I
u = 0.135330 − 1.210060I
a = 1.44433 + 0.33008I
b = −0.14738 − 1.48110I
−3.70412 + 1.43318I −5.69627 + 1.82767I
u = −0.697043 + 0.245240I
a = −1.65574 + 1.15508I
b = 0.473834 + 0.951302I
−3.55163 + 5.19653I −9.50600 − 6.97947I
u = −0.697043 − 0.245240I
a = −1.65574 − 1.15508I
b = 0.473834 − 0.951302I
−3.55163 − 5.19653I −9.50600 + 6.97947I
u = −0.060545 + 1.309960I
a = 0.478021 − 1.243140I
b = 0.398745 + 0.596266I
1.65745 + 3.59571I −4.08616 − 4.43056I
u = −0.060545 − 1.309960I
a = 0.478021 + 1.243140I
b = 0.398745 − 0.596266I
1.65745 − 3.59571I −4.08616 + 4.43056I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220301 + 1.378170I
a = −1.058610 + 0.785024I
b = −0.08899 − 1.68101I
−1.76052 − 3.79602I 1.23938 + 5.13081I
u = 0.220301 − 1.378170I
a = −1.058610 − 0.785024I
b = −0.08899 + 1.68101I
−1.76052 + 3.79602I 1.23938 − 5.13081I
u = −0.164237 + 1.400690I
a = −1.36111 + 1.79236I
b = 0.576875 − 0.719921I
3.34543 − 0.42922I 0.04986 + 3.20072I
u = −0.164237 − 1.400690I
a = −1.36111 − 1.79236I
b = 0.576875 + 0.719921I
3.34543 + 0.42922I 0.04986 − 3.20072I
u = 0.550752 + 0.175998I
a = 0.84547 + 1.80880I
b = 0.08633 + 1.60277I
−6.75198 − 0.94572I −4.30296 + 7.78747I
u = 0.550752 − 0.175998I
a = 0.84547 − 1.80880I
b = 0.08633 − 1.60277I
−6.75198 + 0.94572I −4.30296 − 7.78747I
u = −0.27114 + 1.40480I
a = 2.38401 + 0.03846I
b = −0.565883 − 0.966661I
1.72759 + 8.71032I −3.35702 − 7.30358I
u = −0.27114 − 1.40480I
a = 2.38401 − 0.03846I
b = −0.565883 + 0.966661I
1.72759 − 8.71032I −3.35702 + 7.30358I
u = 0.22089 + 1.48696I
a = −0.336133 + 0.233099I
b = 0.088677 − 0.583152I
6.96984 − 5.43299I 4.43669 + 2.53235I
u = 0.22089 − 1.48696I
a = −0.336133 − 0.233099I
b = 0.088677 + 0.583152I
6.96984 + 5.43299I 4.43669 − 2.53235I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337416 + 0.213092I
a = 1.47025 − 2.54603I
b = −0.461373 + 0.709036I
−1.94701 − 2.47156I −3.00036 + 2.23747I
u = −0.337416 − 0.213092I
a = 1.47025 + 2.54603I
b = −0.461373 − 0.709036I
−1.94701 + 2.47156I −3.00036 − 2.23747I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
28
)(u
22
− 10u
21
+ ··· − 6u
2
+ 1)
· (u
39
− 33u
38
+ ··· + 352256u − 16384)
c
2
, c
9
(u
22
+ 11u
20
+ ··· − u + 1)(u
39
+ 13u
37
+ ··· − 2u + 1)
· (u
84
+ u
83
+ ··· − 48112u + 6329)
c
3
, c
7
(u
22
+ 11u
20
+ ··· + u + 1)(u
39
+ 13u
37
+ ··· − 2u + 1)
· (u
84
+ u
83
+ ··· − 48112u + 6329)
c
4
, c
8
(u
22
+ u
21
+ ··· − 2u + 1)(u
39
+ u
38
+ ··· + 3u + 1)
· (u
84
+ 3u
83
+ ··· + 8u + 1)
c
5
((u
14
+ u
13
+ ··· + u + 1)
6
)(u
22
+ 11u
20
+ ··· − 2u + 1)
· (u
39
− 7u
38
+ ··· − 60u + 8)
c
6
((u
14
− u
13
+ ··· + 3u + 1)
6
)(u
22
+ 2u
20
+ ··· − 3u
2
+ 1)
· (u
39
+ 7u
38
+ ··· − 1596u + 2088)
c
10
, c
11
((u
14
+ u
13
+ ··· + u + 1)
6
)(u
22
+ 11u
20
+ ··· + 2u + 1)
· (u
39
− 7u
38
+ ··· − 60u + 8)
c
12
((u
14
− 3u
13
+ ··· − 7u + 3)
6
)(u
22
− 6u
21
+ ··· − 4u + 1)
· (u
39
− 9u
38
+ ··· − 43968u + 9728)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
28
)(y
22
− 8y
21
+ ··· − 12y + 1)
· (y
39
− 9y
38
+ ··· + 3019898880y −268435456)
c
2
, c
3
, c
7
c
9
(y
22
+ 22y
21
+ ··· + 19y + 1)(y
39
+ 26y
38
+ ··· + 8y −1)
· (y
84
+ 63y
83
+ ··· + 237164204y + 40056241)
c
4
, c
8
(y
22
− 3y
21
+ ··· − 2y + 1)(y
39
+ 9y
38
+ ··· − 23y −1)
· (y
84
− 21y
83
+ ··· + 340y + 1)
c
5
, c
10
, c
11
((y
14
+ 13y
13
+ ··· − y + 1)
6
)(y
22
+ 22y
21
+ ··· − 6y + 1)
· (y
39
+ 35y
38
+ ··· − 48y −64)
c
6
((y
14
+ y
13
+ ··· − y + 1)
6
)(y
22
+ 4y
21
+ ··· − 6y + 1)
· (y
39
+ 5y
38
+ ··· − 35220528y −4359744)
c
12
((y
14
+ 5y
13
+ ··· + 23y + 9)
6
)(y
22
+ 10y
21
+ ··· + 10y + 1)
· (y
39
+ 15y
38
+ ··· − 1741041664y −94633984)
28
