12a
0401
(K12a
0401
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 1 12 4 8 5 10 7
Solving Sequence
4,8
9 10
3,12
7 1 6 2 11 5
c
8
c
9
c
3
c
7
c
12
c
6
c
2
c
11
c
4
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
− u
35
+ ··· + 32b + 1, −u
4
− u
2
+ a − 1, u
37
+ 7u
35
+ ··· + 2u − 1i
I
u
2
= h−3.61451 × 10
30
u
51
− 1.19611 × 10
30
u
50
+ ··· + 2.94109 × 10
31
b + 1.36329 × 10
32
,
− 4.07622 × 10
32
u
51
− 5.85781 × 10
32
u
50
+ ··· + 4.99985 × 10
32
a + 2.17209 × 10
32
,
u
52
+ u
51
+ ··· + 30u + 17i
I
u
3
= hb
5
+ b
4
u + 2b
3
+ b
2
u + b − u, a + 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 99 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
= hu
36
− u
35
+ · · · + 32b + 1, −u
4
− u
2
+ a − 1, u
37
+ 7u
35
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
12
=
u
4
+ u
2
+ 1
−0.0312500u
36
+ 0.0312500u
35
+ ··· + 0.0937500u − 0.0312500
a
7
=
−0.0312500u
36
+ 0.0312500u
35
+ ··· + 0.0937500u + 0.968750
0.343750u
36
− 0.406250u
35
+ ··· − 1.34375u + 0.468750
a
1
=
1
4
u
36
−
5
16
u
35
+ ··· −
17
16
u +
11
8
−0.812500u
36
+ 1.50000u
35
+ ··· + 5.93750u − 2.25000
a
6
=
−
1
8
u
36
+
5
8
u
35
+ ··· +
47
16
u −
3
16
−0.562500u
36
− 1.37500u
35
+ ··· − 8.62500u + 3.93750
a
2
=
−
1
8
u
36
+
5
8
u
35
+ ··· +
47
16
u −
3
16
−
19
16
u
36
+ 2u
35
+ ··· +
123
16
u −
23
8
a
11
=
1
−0.0312500u
36
+ 0.0312500u
35
+ ··· + 0.0937500u − 0.0312500
a
5
=
−u
−0.0312500u
36
− 0.0312500u
35
+ ··· + 0.968750u + 0.0312500
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
67
8
u
36
−
29
8
u
35
+ ··· −
13
4
u +
19
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
+ 21u
36
+ ··· − 3u + 4
c
2
, c
5
u
37
+ 3u
36
+ ··· + 9u + 2
c
3
, c
4
, c
8
c
10
u
37
+ 7u
35
+ ··· + 2u + 1
c
6
, c
7
, c
12
u
37
+ 9u
36
+ ··· + 251u + 22
c
9
, c
11
u
37
− 14u
36
+ ··· − 10u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
− 9y
36
+ ··· + 289y −16
c
2
, c
5
y
37
− 21y
36
+ ··· − 3y −4
c
3
, c
4
, c
8
c
10
y
37
+ 14y
36
+ ··· − 10y −1
c
6
, c
7
, c
12
y
37
+ 39y
36
+ ··· − 1987y −484
c
9
, c
11
y
37
+ 30y
36
+ ··· + 38y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.670225 + 0.795123I
a = −0.285502 − 0.675689I
b = −0.008509 − 0.791858I
−4.22390 + 4.84801I −8.67350 − 6.63268I
u = −0.670225 − 0.795123I
a = −0.285502 + 0.675689I
b = −0.008509 + 0.791858I
−4.22390 − 4.84801I −8.67350 + 6.63268I
u = 0.480944 + 0.804131I
a = 0.158893 + 0.131000I
b = 0.330381 + 1.003000I
−0.56798 − 1.62654I −2.47163 + 4.05064I
u = 0.480944 − 0.804131I
a = 0.158893 − 0.131000I
b = 0.330381 − 1.003000I
−0.56798 + 1.62654I −2.47163 − 4.05064I
u = −0.885704 + 0.619459I
a = 0.35724 − 1.97679I
b = 0.07168 − 1.57263I
−8.61348 + 0.58442I −6.58298 − 2.11216I
u = −0.885704 − 0.619459I
a = 0.35724 + 1.97679I
b = 0.07168 + 1.57263I
−8.61348 − 0.58442I −6.58298 + 2.11216I
u = 0.906376 + 0.600235I
a = 0.49006 + 2.09180I
b = 0.14833 + 1.65936I
−12.33880 + 4.27785I −9.74358 − 1.05951I
u = 0.906376 − 0.600235I
a = 0.49006 − 2.09180I
b = 0.14833 − 1.65936I
−12.33880 − 4.27785I −9.74358 + 1.05951I
u = −0.378523 + 0.822123I
a = 0.363700 + 0.040587I
b = 0.35329 − 1.39171I
−3.60485 − 2.81236I −5.70776 − 1.61824I
u = −0.378523 − 0.822123I
a = 0.363700 − 0.040587I
b = 0.35329 + 1.39171I
−3.60485 + 2.81236I −5.70776 + 1.61824I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509957 + 0.977159I
a = −0.205307 − 0.388248I
b = 0.927591 + 0.449842I
2.09312 − 1.88703I 0.31539 + 1.43334I
u = 0.509957 − 0.977159I
a = −0.205307 + 0.388248I
b = 0.927591 − 0.449842I
2.09312 + 1.88703I 0.31539 − 1.43334I
u = 0.898488 + 0.646158I
a = 0.19345 + 2.06625I
b = −0.04381 + 1.61320I
−12.51130 − 5.32419I −9.84317 + 5.18460I
u = 0.898488 − 0.646158I
a = 0.19345 − 2.06625I
b = −0.04381 − 1.61320I
−12.51130 + 5.32419I −9.84317 − 5.18460I
u = −0.542969 + 1.023650I
a = −0.421670 + 0.562576I
b = 0.950468 − 0.040357I
2.66475 + 6.19686I 1.89152 − 7.89879I
u = −0.542969 − 1.023650I
a = −0.421670 − 0.562576I
b = 0.950468 + 0.040357I
2.66475 − 6.19686I 1.89152 + 7.89879I
u = −0.635272 + 0.460063I
a = 0.887068 − 0.808887I
b = 0.342500 − 0.887718I
−3.54036 − 2.08020I −9.14141 + 1.19821I
u = −0.635272 − 0.460063I
a = 0.887068 + 0.808887I
b = 0.342500 + 0.887718I
−3.54036 + 2.08020I −9.14141 − 1.19821I
u = 0.656373 + 1.034940I
a = −1.076160 − 0.381174I
b = 0.199892 − 0.364140I
−2.70237 − 5.71429I −7.25295 + 4.84897I
u = 0.656373 − 1.034940I
a = −1.076160 + 0.381174I
b = 0.199892 + 0.364140I
−2.70237 + 5.71429I −7.25295 − 4.84897I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290646 + 0.717353I
a = 0.581001 − 0.058279I
b = −0.274591 − 1.313790I
−3.81002 + 5.56820I −6.98582 − 8.76899I
u = −0.290646 − 0.717353I
a = 0.581001 + 0.058279I
b = −0.274591 + 1.313790I
−3.81002 − 5.56820I −6.98582 + 8.76899I
u = −0.593670 + 1.080170I
a = −0.796092 + 0.806284I
b = 0.797124 + 0.561418I
1.77541 + 7.53533I 1.12920 − 6.50404I
u = −0.593670 − 1.080170I
a = −0.796092 − 0.806284I
b = 0.797124 − 0.561418I
1.77541 − 7.53533I 1.12920 + 6.50404I
u = 0.607709 + 1.116880I
a = −0.949770 − 1.026550I
b = 0.797104 − 0.922482I
0.06576 − 11.98300I −2.00000 + 11.09767I
u = 0.607709 − 1.116880I
a = −0.949770 + 1.026550I
b = 0.797104 + 0.922482I
0.06576 + 11.98300I −2.00000 − 11.09767I
u = 0.358680 + 0.579084I
a = 0.663465 + 0.243691I
b = −0.108400 + 0.864333I
−0.64632 − 1.44283I −3.81239 + 5.10481I
u = 0.358680 − 0.579084I
a = 0.663465 − 0.243691I
b = −0.108400 − 0.864333I
−0.64632 + 1.44283I −3.81239 − 5.10481I
u = 0.675999 + 1.162370I
a = −1.56435 − 1.23880I
b = 0.24445 − 1.54342I
−5.08320 − 11.27570I −2.00000 + 6.81954I
u = 0.675999 − 1.162370I
a = −1.56435 + 1.23880I
b = 0.24445 + 1.54342I
−5.08320 + 11.27570I −2.00000 − 6.81954I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.691615 + 1.157430I
a = −1.68262 + 1.15689I
b = 0.07127 + 1.51795I
−9.17720 + 6.73033I −6.31476 − 3.78221I
u = −0.691615 − 1.157430I
a = −1.68262 − 1.15689I
b = 0.07127 − 1.51795I
−9.17720 − 6.73033I −6.31476 + 3.78221I
u = −0.675732 + 1.175560I
a = −1.59314 + 1.35142I
b = 0.27313 + 1.68404I
−8.5942 + 16.2500I −5.34441 − 9.76292I
u = −0.675732 − 1.175560I
a = −1.59314 − 1.35142I
b = 0.27313 − 1.68404I
−8.5942 − 16.2500I −5.34441 + 9.76292I
u = 0.069180 + 0.547631I
a = 0.786237 + 0.031049I
b = −0.723577 + 0.256788I
1.06858 − 1.83619I −0.74915 + 5.53995I
u = 0.069180 − 0.547631I
a = 0.786237 − 0.031049I
b = −0.723577 − 0.256788I
1.06858 + 1.83619I −0.74915 − 5.53995I
u = 0.401304
a = 1.18698
b = 0.303349
−1.03663 −10.7780
8
II. I
u
2
= h−3.61 × 10
30
u
51
− 1.20 × 10
30
u
50
+ · · · + 2.94 × 10
31
b + 1.36 ×
10
32
, −4.08 × 10
32
u
51
− 5.86 × 10
32
u
50
+ · · · + 5.00 × 10
32
a + 2.17 ×
10
32
, u
52
+ u
51
+ · · · + 30u + 17i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
12
=
0.815268u
51
+ 1.17160u
50
+ ··· + 23.9539u − 0.434432
0.122897u
51
+ 0.0406690u
50
+ ··· − 8.31341u − 4.63532
a
7
=
−0.603660u
51
− 0.550873u
50
+ ··· + 5.39906u + 8.11570
−0.0396776u
51
+ 0.142896u
50
+ ··· + 13.1169u + 5.25900
a
1
=
1.06030u
51
+ 0.970299u
50
+ ··· + 4.31666u − 8.59212
0.0653086u
51
− 0.273432u
50
+ ··· − 17.3837u − 7.10625
a
6
=
−1.12011u
51
− 0.813324u
50
+ ··· + 13.6153u + 11.1311
−0.0102037u
51
+ 0.271561u
50
+ ··· + 24.6387u + 7.82138
a
2
=
0.790972u
51
+ 0.764018u
50
+ ··· − 5.28587u − 8.80006
−0.262347u
51
− 0.529752u
50
+ ··· − 24.2991u − 8.38601
a
11
=
0.580715u
51
+ 0.805430u
50
+ ··· + 15.6537u + 0.380740
−1
a
5
=
0.165891u
51
+ 0.0542360u
50
+ ··· − 24.5113u − 11.6369
0.224715u
51
+ 0.113060u
50
+ ··· − 16.0407u − 9.87216
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.13196u
51
+ 1.65706u
50
+ ··· + 16.1608u − 20.7826
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
26
+ 15u
25
+ ··· + 3u + 1)
2
c
2
, c
5
(u
26
− u
25
+ ··· − u + 1)
2
c
3
, c
4
, c
8
c
10
u
52
− u
51
+ ··· − 30u + 17
c
6
, c
7
, c
12
(u
26
− 3u
25
+ ··· − 11u + 3)
2
c
9
, c
11
u
52
− 27u
51
+ ··· − 3996u + 289
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
26
− 7y
25
+ ··· + 13y + 1)
2
c
2
, c
5
(y
26
− 15y
25
+ ··· − 3y + 1)
2
c
3
, c
4
, c
8
c
10
y
52
+ 27y
51
+ ··· + 3996y + 289
c
6
, c
7
, c
12
(y
26
+ 29y
25
+ ··· + 65y + 9)
2
c
9
, c
11
y
52
− 5y
51
+ ··· + 1807796y + 83521
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.550343 + 0.827493I
a = −1.93277 + 2.59907I
b = −0.09022 + 1.52061I
−4.80817 − 2.43962I −5.44223 + 0.17519I
u = −0.550343 − 0.827493I
a = −1.93277 − 2.59907I
b = −0.09022 − 1.52061I
−4.80817 + 2.43962I −5.44223 − 0.17519I
u = 0.529126 + 0.860647I
a = −1.71257 − 2.53937I
b = 0.08534 − 1.44303I
−1.01859 − 2.13264I −1.81035 + 3.16032I
u = 0.529126 − 0.860647I
a = −1.71257 + 2.53937I
b = 0.08534 + 1.44303I
−1.01859 + 2.13264I −1.81035 − 3.16032I
u = −0.554054 + 0.884455I
a = −1.61427 + 2.72347I
b = 0.19366 + 1.58163I
−4.61871 + 6.86486I −4.85861 − 6.16378I
u = −0.554054 − 0.884455I
a = −1.61427 − 2.72347I
b = 0.19366 − 1.58163I
−4.61871 − 6.86486I −4.85861 + 6.16378I
u = 0.951071 + 0.433551I
a = 0.04083 − 1.86805I
b = −0.17008 − 1.55712I
−7.30647 + 5.33673I −5.16942 − 2.96646I
u = 0.951071 − 0.433551I
a = 0.04083 + 1.86805I
b = −0.17008 + 1.55712I
−7.30647 − 5.33673I −5.16942 + 2.96646I
u = 0.764264 + 0.566838I
a = 0.607267 − 0.533028I
b = −0.087798 − 0.532774I
−4.08260 + 0.32949I −9.60033 + 0.20899I
u = 0.764264 − 0.566838I
a = 0.607267 + 0.533028I
b = −0.087798 + 0.532774I
−4.08260 − 0.32949I −9.60033 − 0.20899I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968590 + 0.418641I
a = −0.06346 + 2.01829I
b = −0.21971 + 1.67621I
−10.9094 − 10.2647I −8.13372 + 5.98641I
u = −0.968590 − 0.418641I
a = −0.06346 − 2.01829I
b = −0.21971 − 1.67621I
−10.9094 + 10.2647I −8.13372 − 5.98641I
u = 0.537250 + 0.915539I
a = 0.712664 + 0.797756I
b = −0.599592 + 0.613984I
−0.11782 − 2.56217I −2.00000 + 2.97329I
u = 0.537250 − 0.915539I
a = 0.712664 − 0.797756I
b = −0.599592 − 0.613984I
−0.11782 + 2.56217I −2.00000 − 2.97329I
u = −0.961357 + 0.458080I
a = 0.24305 + 1.92202I
b = −0.02106 + 1.56255I
−11.31370 − 0.70419I −8.80376 − 0.14810I
u = −0.961357 − 0.458080I
a = 0.24305 − 1.92202I
b = −0.02106 − 1.56255I
−11.31370 + 0.70419I −8.80376 + 0.14810I
u = 0.383435 + 0.995342I
a = −0.84645 − 1.77462I
b = 0.603458 − 0.686824I
2.92792 − 3.85582I 0. + 7.89236I
u = 0.383435 − 0.995342I
a = −0.84645 + 1.77462I
b = 0.603458 + 0.686824I
2.92792 + 3.85582I 0. − 7.89236I
u = −0.669360 + 0.847773I
a = 1.148410 − 0.546853I
b = −0.087798 − 0.532774I
−4.08260 + 0.32949I −9.60033 + 0.20899I
u = −0.669360 − 0.847773I
a = 1.148410 + 0.546853I
b = −0.087798 + 0.532774I
−4.08260 − 0.32949I −9.60033 − 0.20899I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284204 + 1.048140I
a = −0.627711 + 1.198740I
b = 0.559166 + 0.216872I
4.34028 + 0.21572I 5.69812 − 1.13318I
u = −0.284204 − 1.048140I
a = −0.627711 − 1.198740I
b = 0.559166 − 0.216872I
4.34028 − 0.21572I 5.69812 + 1.13318I
u = 0.786486 + 0.369460I
a = −0.422286 − 0.769115I
b = −0.648696 − 0.938364I
−2.10171 + 6.75127I −5.33497 − 7.43906I
u = 0.786486 − 0.369460I
a = −0.422286 + 0.769115I
b = −0.648696 + 0.938364I
−2.10171 − 6.75127I −5.33497 + 7.43906I
u = −0.577721 + 0.996615I
a = 0.768435 − 1.108730I
b = −0.648696 − 0.938364I
−2.10171 + 6.75127I −5.33497 − 7.43906I
u = −0.577721 − 0.996615I
a = 0.768435 + 1.108730I
b = −0.648696 + 0.938364I
−2.10171 − 6.75127I −5.33497 + 7.43906I
u = 0.342052 + 0.774444I
a = 0.464099 + 0.449574I
b = −0.791162 + 0.159676I
1.10848 − 1.93104I −0.74595 + 4.18474I
u = 0.342052 − 0.774444I
a = 0.464099 − 0.449574I
b = −0.791162 − 0.159676I
1.10848 + 1.93104I −0.74595 − 4.18474I
u = −0.224633 + 1.133270I
a = −0.300749 + 0.796598I
b = 0.559166 − 0.216872I
4.34028 − 0.21572I 5.69812 + 0.I
u = −0.224633 − 1.133270I
a = −0.300749 − 0.796598I
b = 0.559166 + 0.216872I
4.34028 + 0.21572I 5.69812 + 0.I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036728 + 1.177540I
a = −0.397670 − 0.124485I
b = −0.313295 + 0.402304I
1.71189 − 1.00473I −5.82896 + 0.I
u = 0.036728 − 1.177540I
a = −0.397670 + 0.124485I
b = −0.313295 − 0.402304I
1.71189 + 1.00473I −5.82896 + 0.I
u = −0.690243 + 0.417206I
a = −0.132047 + 0.281676I
b = −0.599592 + 0.613984I
−0.11782 − 2.56217I −1.94700 + 2.97329I
u = −0.690243 − 0.417206I
a = −0.132047 − 0.281676I
b = −0.599592 − 0.613984I
−0.11782 + 2.56217I −1.94700 − 2.97329I
u = 0.203821 + 1.221330I
a = 0.017866 − 0.514233I
b = 0.603458 + 0.686824I
2.92792 + 3.85582I 0
u = 0.203821 − 1.221330I
a = 0.017866 + 0.514233I
b = 0.603458 − 0.686824I
2.92792 − 3.85582I 0
u = 0.220997 + 0.724279I
a = −2.17171 − 0.98902I
b = −0.313295 − 0.402304I
1.71189 + 1.00473I −5.82896 − 0.57498I
u = 0.220997 − 0.724279I
a = −2.17171 + 0.98902I
b = −0.313295 + 0.402304I
1.71189 − 1.00473I −5.82896 + 0.57498I
u = −0.720229 + 1.047070I
a = 1.40344 − 1.54237I
b = −0.17008 − 1.55712I
−7.30647 + 5.33673I 0
u = −0.720229 − 1.047070I
a = 1.40344 + 1.54237I
b = −0.17008 + 1.55712I
−7.30647 − 5.33673I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741481 + 1.037370I
a = 1.54716 + 1.50406I
b = −0.02106 + 1.56255I
−11.31370 − 0.70419I 0
u = 0.741481 − 1.037370I
a = 1.54716 − 1.50406I
b = −0.02106 − 1.56255I
−11.31370 + 0.70419I 0
u = 0.722575 + 1.066990I
a = 1.39072 + 1.66975I
b = −0.21971 + 1.67621I
−10.9094 − 10.2647I 0
u = 0.722575 − 1.066990I
a = 1.39072 − 1.66975I
b = −0.21971 − 1.67621I
−10.9094 + 10.2647I 0
u = 0.117241 + 1.324870I
a = 0.0151086 + 0.0789385I
b = 0.08534 + 1.44303I
−1.01859 + 2.13264I 0
u = 0.117241 − 1.324870I
a = 0.0151086 − 0.0789385I
b = 0.08534 − 1.44303I
−1.01859 − 2.13264I 0
u = −0.095137 + 1.336100I
a = −0.059114 − 0.156098I
b = −0.09022 − 1.52061I
−4.80817 + 2.43962I 0
u = −0.095137 − 1.336100I
a = −0.059114 + 0.156098I
b = −0.09022 + 1.52061I
−4.80817 − 2.43962I 0
u = −0.131274 + 1.342360I
a = 0.105716 − 0.128904I
b = 0.19366 − 1.58163I
−4.61871 − 6.86486I 0
u = −0.131274 − 1.342360I
a = 0.105716 + 0.128904I
b = 0.19366 + 1.58163I
−4.61871 + 6.86486I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.409385 + 0.446289I
a = 0.286631 − 0.591162I
b = −0.791162 + 0.159676I
1.10848 − 1.93104I −0.74595 + 4.18474I
u = −0.409385 − 0.446289I
a = 0.286631 + 0.591162I
b = −0.791162 − 0.159676I
1.10848 + 1.93104I −0.74595 − 4.18474I
17
III. I
u
3
= hb
5
+ b
4
u + 2b
3
+ b
2
u + b − u, a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−1
a
10
=
0
−1
a
3
=
u
0
a
12
=
−1
b
a
7
=
−b + 1
b
2
a
1
=
−b
2
+ b − 1
b
3
+ b
a
6
=
−b
3
+ b
2
− 2b + 1
b
4
+ 2b
2
a
2
=
b
3
− b
2
+ 2b − 1
b
3
+ b
a
11
=
−1
b − 1
a
5
=
−u
bu
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b
3
u − 8bu
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
, c
5
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
3
, c
4
, c
8
c
10
(u
2
+ 1)
5
c
6
, c
7
, c
12
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
9
, c
11
(u − 1)
10
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
c
2
, c
5
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
3
, c
4
, c
8
c
10
(y + 1)
10
c
6
, c
7
, c
12
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
9
, c
11
(y − 1)
10
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = 1.217740I
0.888787 2.51890
u = 1.000000I
a = −1.00000
b = 0.549911 + 0.309916I
2.96077 + 1.53058I 3.48489 − 4.43065I
u = 1.000000I
a = −1.00000
b = −0.549911 + 0.309916I
2.96077 − 1.53058I 3.48489 + 4.43065I
u = 1.000000I
a = −1.00000
b = 0.21917 − 1.41878I
−2.58269 − 4.40083I −0.74431 + 3.49859I
u = 1.000000I
a = −1.00000
b = −0.21917 − 1.41878I
−2.58269 + 4.40083I −0.74431 − 3.49859I
u = − 1.000000I
a = −1.00000
b = − 1.217740I
0.888787 2.51890
u = − 1.000000I
a = −1.00000
b = 0.549911 − 0.309916I
2.96077 − 1.53058I 3.48489 + 4.43065I
u = − 1.000000I
a = −1.00000
b = −0.549911 − 0.309916I
2.96077 + 1.53058I 3.48489 − 4.43065I
u = − 1.000000I
a = −1.00000
b = −0.21917 + 1.41878I
−2.58269 + 4.40083I −0.74431 − 3.49859I
u = − 1.000000I
a = −1.00000
b = 0.21917 + 1.41878I
−2.58269 − 4.40083I −0.74431 + 3.49859I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
26
+ 15u
25
+ ··· + 3u + 1)
2
· (u
37
+ 21u
36
+ ··· − 3u + 4)
c
2
, c
5
(u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(u
26
− u
25
+ ··· − u + 1)
2
· (u
37
+ 3u
36
+ ··· + 9u + 2)
c
3
, c
4
, c
8
c
10
((u
2
+ 1)
5
)(u
37
+ 7u
35
+ ··· + 2u + 1)(u
52
− u
51
+ ··· − 30u + 17)
c
6
, c
7
, c
12
(u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
26
− 3u
25
+ ··· − 11u + 3)
2
· (u
37
+ 9u
36
+ ··· + 251u + 22)
c
9
, c
11
((u − 1)
10
)(u
37
− 14u
36
+ ··· − 10u + 1)
· (u
52
− 27u
51
+ ··· − 3996u + 289)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
)(y
26
− 7y
25
+ ··· + 13y + 1)
2
· (y
37
− 9y
36
+ ··· + 289y − 16)
c
2
, c
5
((y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
)(y
26
− 15y
25
+ ··· − 3y + 1)
2
· (y
37
− 21y
36
+ ··· − 3y − 4)
c
3
, c
4
, c
8
c
10
((y + 1)
10
)(y
37
+ 14y
36
+ ··· − 10y − 1)
· (y
52
+ 27y
51
+ ··· + 3996y + 289)
c
6
, c
7
, c
12
((y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
)(y
26
+ 29y
25
+ ··· + 65y + 9)
2
· (y
37
+ 39y
36
+ ··· − 1987y − 484)
c
9
, c
11
((y − 1)
10
)(y
37
+ 30y
36
+ ··· + 38y − 1)
· (y
52
− 5y
51
+ ··· + 1807796y + 83521)
23
