12a
0569
(K12a
0569
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 8 12 2 11 4 5 1 6
Solving Sequence
4,9
10 5 11
2,3
1 8 6 7 12
c
9
c
4
c
10
c
3
c
1
c
8
c
5
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
33
+ 5u
32
+ ··· + b − 3, 7u
33
− 11u
32
+ ··· + 2a + 9, u
34
− 3u
33
+ ··· − 5u − 2i
I
u
2
= h−21u
24
a − 357u
24
+ ··· + 85a − 335, −2u
23
a − 2u
24
+ ··· + a
2
− a, u
25
+ u
24
+ ··· + u − 1i
I
u
3
= hu
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ b − u, −u
5
− u
4
+ 3u
3
+ 2u
2
+ a − u, u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 92 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−3u
33
+5u
32
+· · ·+b−3, 7u
33
−11u
32
+· · ·+2a+9, u
34
−3u
33
+· · ·−5u−2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−
7
2
u
33
+
11
2
u
32
+ ··· −
29
2
u −
9
2
3u
33
− 5u
32
+ ··· + 11u + 3
a
3
=
−u
u
a
1
=
−5.50000u
33
+ 8.50000u
32
+ ··· − 20.5000u − 6.50000
5u
33
− 8u
32
+ ··· + 17u + 5
a
8
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
6
=
u
11
− 6u
9
+ 12u
7
− 10u
5
+ 5u
3
−u
13
+ 7u
11
− 17u
9
+ 16u
7
− 4u
5
− u
3
+ u
a
7
=
−
3
2
u
33
+
5
2
u
32
+ ··· −
13
2
u −
3
2
2u
33
− 3u
32
+ ··· + 9u + 3
a
12
=
7
2
u
33
−
11
2
u
32
+ ··· +
27
2
u +
11
2
−3u
33
+ 5u
32
+ ··· − 10u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 12u
33
−12u
32
−218u
31
+192u
30
+1764u
29
−1284u
28
−8408u
27
+4518u
26
+26308u
25
−
8142u
24
− 56882u
23
+ 2928u
22
+ 86532u
21
+ 19602u
20
− 91108u
19
− 48412u
18
+
61428u
17
+ 58604u
16
− 19212u
15
− 42828u
14
− 6604u
13
+ 18558u
12
+ 10772u
11
−
3466u
10
−5728u
9
−1018u
8
+ 1686u
7
+ 1004u
6
−148u
5
−386u
4
−132u
3
+ 52u
2
+ 68u + 34
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
34
+ 14u
33
+ ··· + 2u + 1
c
2
, c
6
, c
7
c
12
u
34
+ 7u
32
+ ··· + 2u − 1
c
3
, c
4
, c
9
c
10
u
34
+ 3u
33
+ ··· + 5u − 2
c
5
u
34
− 15u
33
+ ··· − 4575u + 358
c
8
u
34
+ 9u
33
+ ··· − 281u − 136
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
34
+ 22y
33
+ ··· − 102y + 1
c
2
, c
6
, c
7
c
12
y
34
+ 14y
33
+ ··· + 2y + 1
c
3
, c
4
, c
9
c
10
y
34
− 39y
33
+ ··· − 21y + 4
c
5
y
34
+ 9y
33
+ ··· − 2328229y + 128164
c
8
y
34
− 3y
33
+ ··· − 79233y + 18496
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877399 + 0.216772I
a = 0.475747 − 0.156573I
b = 0.73016 + 1.40055I
1.81473 − 6.46317I 9.54481 + 4.22755I
u = 0.877399 − 0.216772I
a = 0.475747 + 0.156573I
b = 0.73016 − 1.40055I
1.81473 + 6.46317I 9.54481 − 4.22755I
u = −0.708573 + 0.517031I
a = −0.145662 + 0.387973I
b = 0.22304 − 2.36773I
−0.14844 − 13.04060I 6.35227 + 10.72030I
u = −0.708573 − 0.517031I
a = −0.145662 − 0.387973I
b = 0.22304 + 2.36773I
−0.14844 + 13.04060I 6.35227 − 10.72030I
u = 0.780460 + 0.363894I
a = −0.627024 − 0.012240I
b = 0.031716 − 1.019530I
4.40948 + 4.16383I 12.6794 − 7.1623I
u = 0.780460 − 0.363894I
a = −0.627024 + 0.012240I
b = 0.031716 + 1.019530I
4.40948 − 4.16383I 12.6794 + 7.1623I
u = −0.736699 + 0.432721I
a = 0.353503 − 0.411057I
b = −0.48051 + 1.43982I
3.92336 − 2.16093I 12.40932 + 2.19070I
u = −0.736699 − 0.432721I
a = 0.353503 + 0.411057I
b = −0.48051 − 1.43982I
3.92336 + 2.16093I 12.40932 − 2.19070I
u = −0.562396 + 0.535053I
a = −0.351346 + 0.308190I
b = −1.167160 − 0.153798I
−3.10387 + 1.61500I 3.93469 − 1.70541I
u = −0.562396 − 0.535053I
a = −0.351346 − 0.308190I
b = −1.167160 + 0.153798I
−3.10387 − 1.61500I 3.93469 + 1.70541I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369153 + 0.566173I
a = 0.060405 − 1.357450I
b = 0.522127 − 0.471400I
−3.66613 − 5.39835I 2.14176 + 8.12985I
u = −0.369153 − 0.566173I
a = 0.060405 + 1.357450I
b = 0.522127 + 0.471400I
−3.66613 + 5.39835I 2.14176 − 8.12985I
u = 0.478774 + 0.474535I
a = 0.006193 − 0.459110I
b = 0.318164 + 0.001013I
−1.82601 + 1.67416I 6.00203 − 5.31904I
u = 0.478774 − 0.474535I
a = 0.006193 + 0.459110I
b = 0.318164 − 0.001013I
−1.82601 − 1.67416I 6.00203 + 5.31904I
u = −0.184105 + 0.612147I
a = −2.40151 − 0.24206I
b = −0.085419 − 0.531958I
−1.68891 + 9.20421I 3.04718 − 5.89874I
u = −0.184105 − 0.612147I
a = −2.40151 + 0.24206I
b = −0.085419 + 0.531958I
−1.68891 − 9.20421I 3.04718 + 5.89874I
u = 1.43714 + 0.08661I
a = 0.678840 + 0.278085I
b = −0.085956 − 1.097670I
2.03333 + 7.62639I 0
u = 1.43714 − 0.08661I
a = 0.678840 − 0.278085I
b = −0.085956 + 1.097670I
2.03333 − 7.62639I 0
u = −0.050097 + 0.546766I
a = 1.46207 − 0.24634I
b = 0.040124 + 0.397505I
1.94188 − 1.14446I 7.91735 + 3.10614I
u = −0.050097 − 0.546766I
a = 1.46207 + 0.24634I
b = 0.040124 − 0.397505I
1.94188 + 1.14446I 7.91735 − 3.10614I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53119 + 0.11501I
a = 0.777108 + 0.261273I
b = −1.053720 − 0.389785I
4.89311 − 3.68703I 0
u = −1.53119 − 0.11501I
a = 0.777108 − 0.261273I
b = −1.053720 + 0.389785I
4.89311 + 3.68703I 0
u = 1.54361
a = −0.986884
b = 0.729443
7.42344 0
u = 1.54714 + 0.14618I
a = −1.43226 + 0.61040I
b = 1.95694 − 0.15000I
3.92568 + 0.82031I 0
u = 1.54714 − 0.14618I
a = −1.43226 − 0.61040I
b = 1.95694 + 0.15000I
3.92568 − 0.82031I 0
u = −0.432002
a = 0.604501
b = −0.356295
0.622618 16.1500
u = 1.60778 + 0.15231I
a = 1.23471 + 3.38333I
b = −0.71168 − 4.36160I
7.6999 + 15.5437I 0
u = 1.60778 − 0.15231I
a = 1.23471 − 3.38333I
b = −0.71168 + 4.36160I
7.6999 − 15.5437I 0
u = 1.61580 + 0.12438I
a = −1.19491 − 2.06212I
b = 0.95223 + 2.61552I
11.94790 + 4.25345I 0
u = 1.61580 − 0.12438I
a = −1.19491 + 2.06212I
b = 0.95223 − 2.61552I
11.94790 − 4.25345I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62557 + 0.09964I
a = −0.15988 + 2.10696I
b = 0.28288 − 2.81306I
12.65520 − 5.90157I 0
u = −1.62557 − 0.09964I
a = −0.15988 − 2.10696I
b = 0.28288 + 2.81306I
12.65520 + 5.90157I 0
u = −1.63252 + 0.05614I
a = 1.20521 − 2.66840I
b = −1.65951 + 3.54397I
10.38340 + 5.46156I 0
u = −1.63252 − 0.05614I
a = 1.20521 + 2.66840I
b = −1.65951 − 3.54397I
10.38340 − 5.46156I 0
8
II. I
u
2
= h−21u
24
a − 357u
24
+ · · · + 85a − 335, −2u
23
a − 2u
24
+ · · · + a
2
−
a, u
25
+ u
24
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
a
0.0589888au
24
+ 1.00281u
24
+ ··· − 0.238764a + 0.941011
a
3
=
−u
u
a
1
=
0.0477528au
24
+ 0.811798u
24
+ ··· + 0.997191a − 0.0477528
0.0112360au
24
+ 0.191011u
24
+ ··· − 0.235955a + 0.988764
a
8
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
6
=
u
11
− 6u
9
+ 12u
7
− 10u
5
+ 5u
3
−u
13
+ 7u
11
− 17u
9
+ 16u
7
− 4u
5
− u
3
+ u
a
7
=
−0.0477528au
24
+ 0.188202u
24
+ ··· − 0.997191a + 1.04775
−0.0112360au
24
+ 0.808989u
24
+ ··· + 0.235955a − 0.988764
a
12
=
−0.0477528au
24
+ 0.188202u
24
+ ··· + 1.00281a + 0.0477528
0.0477528au
24
+ 0.811798u
24
+ ··· − 1.00281a + 0.952247
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
23
−56u
21
+328u
19
−4u
18
−1040u
17
+44u
16
+1936u
15
−192u
14
−2164u
13
+420u
12
+
1440u
11
− 484u
10
− 508u
9
+ 296u
8
− 4u
7
− 100u
6
+ 64u
5
+ 4u
4
− 20u
3
+ 4u
2
− 4u + 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
50
+ 27u
49
+ ··· + 35u + 4
c
2
, c
6
, c
7
c
12
u
50
+ u
49
+ ··· + 5u + 2
c
3
, c
4
, c
9
c
10
(u
25
− u
24
+ ··· + u + 1)
2
c
5
(u
25
+ 5u
24
+ ··· − 47u − 11)
2
c
8
(u
25
+ 7u
24
+ ··· + 41u + 7)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
50
− 9y
49
+ ··· + 1407y + 16
c
2
, c
6
, c
7
c
12
y
50
+ 27y
49
+ ··· + 35y + 4
c
3
, c
4
, c
9
c
10
(y
25
− 29y
24
+ ··· + y −1)
2
c
5
(y
25
+ 11y
24
+ ··· − 827y −121)
2
c
8
(y
25
− 5y
24
+ ··· + 197y −49)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718272 + 0.485243I
a = −0.496142 − 0.419262I
b = 0.26577 + 1.44202I
2.29194 + 7.50021I 9.62573 − 7.29113I
u = 0.718272 + 0.485243I
a = −0.100137 + 0.365766I
b = −0.06988 − 2.11914I
2.29194 + 7.50021I 9.62573 − 7.29113I
u = 0.718272 − 0.485243I
a = −0.496142 + 0.419262I
b = 0.26577 − 1.44202I
2.29194 − 7.50021I 9.62573 + 7.29113I
u = 0.718272 − 0.485243I
a = −0.100137 − 0.365766I
b = −0.06988 + 2.11914I
2.29194 − 7.50021I 9.62573 + 7.29113I
u = −0.816872 + 0.280683I
a = 0.751695 − 0.110614I
b = −0.004403 − 0.561403I
3.64682 + 1.11527I 12.41631 + 0.71281I
u = −0.816872 + 0.280683I
a = −0.229043 − 0.316380I
b = −0.73086 + 1.46356I
3.64682 + 1.11527I 12.41631 + 0.71281I
u = −0.816872 − 0.280683I
a = 0.751695 + 0.110614I
b = −0.004403 + 0.561403I
3.64682 − 1.11527I 12.41631 − 0.71281I
u = −0.816872 − 0.280683I
a = −0.229043 + 0.316380I
b = −0.73086 − 1.46356I
3.64682 − 1.11527I 12.41631 − 0.71281I
u = −0.664564 + 0.449435I
a = 0.455137 + 0.809467I
b = −0.62549 − 2.26185I
−3.14595 − 4.18290I 4.98515 + 7.72660I
u = −0.664564 + 0.449435I
a = −0.833552 + 0.255403I
b = −1.15382 − 0.82719I
−3.14595 − 4.18290I 4.98515 + 7.72660I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.664564 − 0.449435I
a = 0.455137 − 0.809467I
b = −0.62549 + 2.26185I
−3.14595 + 4.18290I 4.98515 − 7.72660I
u = −0.664564 − 0.449435I
a = −0.833552 − 0.255403I
b = −1.15382 + 0.82719I
−3.14595 + 4.18290I 4.98515 − 7.72660I
u = 0.629613 + 0.295912I
a = 1.103490 + 0.019629I
b = 0.691062 − 1.047430I
−2.09040 + 0.82124I 8.96410 − 1.46331I
u = 0.629613 + 0.295912I
a = −0.169580 − 1.235130I
b = 1.03458 + 1.49781I
−2.09040 + 0.82124I 8.96410 − 1.46331I
u = 0.629613 − 0.295912I
a = 1.103490 − 0.019629I
b = 0.691062 + 1.047430I
−2.09040 − 0.82124I 8.96410 + 1.46331I
u = 0.629613 − 0.295912I
a = −0.169580 + 1.235130I
b = 1.03458 − 1.49781I
−2.09040 − 0.82124I 8.96410 + 1.46331I
u = 0.433714 + 0.460017I
a = 0.310449 − 0.823732I
b = 0.084915 − 0.370987I
−1.87609 + 1.61686I 4.87509 − 4.54712I
u = 0.433714 + 0.460017I
a = −0.354969 − 0.143817I
b = 0.517702 + 0.309879I
−1.87609 + 1.61686I 4.87509 − 4.54712I
u = 0.433714 − 0.460017I
a = 0.310449 + 0.823732I
b = 0.084915 + 0.370987I
−1.87609 − 1.61686I 4.87509 + 4.54712I
u = 0.433714 − 0.460017I
a = −0.354969 + 0.143817I
b = 0.517702 − 0.309879I
−1.87609 − 1.61686I 4.87509 + 4.54712I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142727 + 0.579000I
a = −1.227520 + 0.034036I
b = 0.026860 + 0.617172I
0.61424 − 3.87050I 6.00448 + 2.43861I
u = 0.142727 + 0.579000I
a = 2.25381 − 0.36959I
b = 0.014633 − 0.246499I
0.61424 − 3.87050I 6.00448 + 2.43861I
u = 0.142727 − 0.579000I
a = −1.227520 − 0.034036I
b = 0.026860 − 0.617172I
0.61424 + 3.87050I 6.00448 − 2.43861I
u = 0.142727 − 0.579000I
a = 2.25381 + 0.36959I
b = 0.014633 + 0.246499I
0.61424 + 3.87050I 6.00448 − 2.43861I
u = −0.209074 + 0.473774I
a = −0.39992 − 1.91880I
b = 0.211890 − 0.974935I
−4.45458 + 0.92486I −0.08147 − 1.66278I
u = −0.209074 + 0.473774I
a = −2.62374 − 0.86746I
b = 0.619265 − 0.124151I
−4.45458 + 0.92486I −0.08147 − 1.66278I
u = −0.209074 − 0.473774I
a = −0.39992 + 1.91880I
b = 0.211890 + 0.974935I
−4.45458 − 0.92486I −0.08147 + 1.66278I
u = −0.209074 − 0.473774I
a = −2.62374 + 0.86746I
b = 0.619265 + 0.124151I
−4.45458 − 0.92486I −0.08147 + 1.66278I
u = 1.48298
a = 1.09851 + 1.36235I
b = −0.26943 − 1.89202I
0.787691 3.78220
u = 1.48298
a = 1.09851 − 1.36235I
b = −0.26943 + 1.89202I
0.787691 3.78220
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49660 + 0.07007I
a = −0.198609 + 0.768663I
b = −0.401251 − 1.286810I
4.41001 − 3.32898I 8.74899 + 3.47484I
u = −1.49660 + 0.07007I
a = 1.298030 + 0.149609I
b = −1.096220 − 0.011479I
4.41001 − 3.32898I 8.74899 + 3.47484I
u = −1.49660 − 0.07007I
a = −0.198609 − 0.768663I
b = −0.401251 + 1.286810I
4.41001 + 3.32898I 8.74899 − 3.47484I
u = −1.49660 − 0.07007I
a = 1.298030 − 0.149609I
b = −1.096220 + 0.011479I
4.41001 + 3.32898I 8.74899 − 3.47484I
u = −1.59018 + 0.09388I
a = 1.13331 + 1.34552I
b = −2.13417 − 1.44076I
5.52546 − 2.31852I 10.07988 − 0.26267I
u = −1.59018 + 0.09388I
a = 2.17950 − 2.41711I
b = −2.37114 + 2.78140I
5.52546 − 2.31852I 10.07988 − 0.26267I
u = −1.59018 − 0.09388I
a = 1.13331 − 1.34552I
b = −2.13417 + 1.44076I
5.52546 + 2.31852I 10.07988 + 0.26267I
u = −1.59018 − 0.09388I
a = 2.17950 + 2.41711I
b = −2.37114 − 2.78140I
5.52546 + 2.31852I 10.07988 + 0.26267I
u = 1.59510 + 0.12778I
a = −1.45878 + 1.14196I
b = 2.53044 − 0.90497I
4.53379 + 6.30957I 7.83367 − 5.57691I
u = 1.59510 + 0.12778I
a = 0.17314 + 3.89558I
b = 0.21333 − 4.54298I
4.53379 + 6.30957I 7.83367 − 5.57691I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59510 − 0.12778I
a = −1.45878 − 1.14196I
b = 2.53044 + 0.90497I
4.53379 − 6.30957I 7.83367 + 5.57691I
u = 1.59510 − 0.12778I
a = 0.17314 − 3.89558I
b = 0.21333 + 4.54298I
4.53379 − 6.30957I 7.83367 + 5.57691I
u = −1.61122 + 0.14112I
a = 0.98524 − 1.89455I
b = −0.56722 + 2.33541I
10.2089 − 9.8448I 11.88321 + 5.59341I
u = −1.61122 + 0.14112I
a = −0.89838 + 3.28439I
b = 0.51623 − 4.20300I
10.2089 − 9.8448I 11.88321 + 5.59341I
u = −1.61122 − 0.14112I
a = 0.98524 + 1.89455I
b = −0.56722 − 2.33541I
10.2089 + 9.8448I 11.88321 − 5.59341I
u = −1.61122 − 0.14112I
a = −0.89838 − 3.28439I
b = 0.51623 + 4.20300I
10.2089 + 9.8448I 11.88321 − 5.59341I
u = 1.62760 + 0.07696I
a = 0.05235 + 1.49265I
b = −0.36051 − 2.03840I
12.01820 + 0.23028I 13.77375 + 0.13265I
u = 1.62760 + 0.07696I
a = −1.30429 − 2.61429I
b = 1.55773 + 3.42070I
12.01820 + 0.23028I 13.77375 + 0.13265I
u = 1.62760 − 0.07696I
a = 0.05235 − 1.49265I
b = −0.36051 + 2.03840I
12.01820 − 0.23028I 13.77375 − 0.13265I
u = 1.62760 − 0.07696I
a = −1.30429 + 2.61429I
b = 1.55773 − 3.42070I
12.01820 − 0.23028I 13.77375 − 0.13265I
16
III. I
u
3
= hu
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ b − u, −u
5
− u
4
+ 3u
3
+ 2u
2
+ a −
u, u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
u
5
+ u
4
− 3u
3
− 2u
2
+ u
−u
7
+ 4u
5
− u
4
− 4u
3
+ 2u
2
+ u
a
3
=
−u
u
a
1
=
u
5
+ u
4
− 3u
3
− 2u
2
+ 2u
−u
7
+ 4u
5
− u
4
− 4u
3
+ 2u
2
a
8
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
6
− 3u
4
+ 2u
2
− 1
a
6
=
−u
5
+ 2u
3
+ u
u
5
− 3u
3
+ u
a
7
=
−u
6
− u
5
+ 4u
4
+ 3u
3
− 4u
2
− u + 1
u
5
− 3u
3
+ u − 1
a
12
=
u
5
+ u
4
− 3u
3
− 3u
2
+ 2u + 1
−u
7
+ 4u
5
− 4u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
6
+ 16u
4
− 16u
2
+ 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
8
c
2
, c
6
, c
7
c
12
(u
2
+ 1)
4
c
3
, c
4
, c
9
c
10
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
c
5
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
c
8
(u
4
− u
3
+ u
2
+ 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y −1)
8
c
2
, c
6
, c
7
c
12
(y + 1)
8
c
3
, c
4
, c
9
c
10
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
c
5
(y
4
− y
3
+ 3y
2
− 2y + 1)
2
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.506844 + 0.395123I
a = 0.368534 − 1.072150I
b = 0.858652 + 0.115465I
−3.50087 + 1.41510I 0.17326 − 4.90874I
u = 0.506844 − 0.395123I
a = 0.368534 + 1.072150I
b = 0.858652 − 0.115465I
−3.50087 − 1.41510I 0.17326 + 4.90874I
u = −0.506844 + 0.395123I
a = −1.072150 + 0.368534I
b = −0.155036 − 1.325220I
−3.50087 − 1.41510I 0.17326 + 4.90874I
u = −0.506844 − 0.395123I
a = −1.072150 − 0.368534I
b = −0.155036 + 1.325220I
−3.50087 + 1.41510I 0.17326 − 4.90874I
u = 1.55249 + 0.10488I
a = −0.05948 + 1.76310I
b = 0.70068 − 1.80642I
3.50087 + 3.16396I 3.82674 − 2.56480I
u = 1.55249 − 0.10488I
a = −0.05948 − 1.76310I
b = 0.70068 + 1.80642I
3.50087 − 3.16396I 3.82674 + 2.56480I
u = −1.55249 + 0.10488I
a = 1.76310 − 0.05948I
b = −2.40430 + 0.01617I
3.50087 − 3.16396I 3.82674 + 2.56480I
u = −1.55249 − 0.10488I
a = 1.76310 + 0.05948I
b = −2.40430 − 0.01617I
3.50087 + 3.16396I 3.82674 − 2.56480I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
8
)(u
34
+ 14u
33
+ ··· + 2u + 1)(u
50
+ 27u
49
+ ··· + 35u + 4)
c
2
, c
6
, c
7
c
12
((u
2
+ 1)
4
)(u
34
+ 7u
32
+ ··· + 2u − 1)(u
50
+ u
49
+ ··· + 5u + 2)
c
3
, c
4
, c
9
c
10
(u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)(u
25
− u
24
+ ··· + u + 1)
2
· (u
34
+ 3u
33
+ ··· + 5u − 2)
c
5
(u
8
− u
6
+ 3u
4
− 2u
2
+ 1)(u
25
+ 5u
24
+ ··· − 47u − 11)
2
· (u
34
− 15u
33
+ ··· − 4575u + 358)
c
8
((u
4
− u
3
+ u
2
+ 1)
2
)(u
25
+ 7u
24
+ ··· + 41u + 7)
2
· (u
34
+ 9u
33
+ ··· − 281u − 136)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
8
)(y
34
+ 22y
33
+ ··· − 102y + 1)(y
50
− 9y
49
+ ··· + 1407y + 16)
c
2
, c
6
, c
7
c
12
((y + 1)
8
)(y
34
+ 14y
33
+ ··· + 2y + 1)(y
50
+ 27y
49
+ ··· + 35y + 4)
c
3
, c
4
, c
9
c
10
((y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
)(y
25
− 29y
24
+ ··· + y −1)
2
· (y
34
− 39y
33
+ ··· − 21y + 4)
c
5
((y
4
− y
3
+ 3y
2
− 2y + 1)
2
)(y
25
+ 11y
24
+ ··· − 827y −121)
2
· (y
34
+ 9y
33
+ ··· − 2328229y + 128164)
c
8
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
)(y
25
− 5y
24
+ ··· + 197y −49)
2
· (y
34
− 3y
33
+ ··· − 79233y + 18496)
22
