12a
0808
(K12a
0808
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 10 1 12 11 2 3 8 7
Solving Sequence
7,12
8
1,4
2 6 3 11 9 5 10
c
7
c
12
c
1
c
6
c
3
c
11
c
8
c
4
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4708u
36
+ 22559u
35
+ ··· + 12181b + 159188,
184180u
36
− 854911u
35
+ ··· + 133991a − 2353969, u
37
− 5u
36
+ ··· − 93u + 11i
I
u
2
= h11u
22
a + 26u
22
+ ··· + 4a + 1, u
22
+ 4u
21
+ ··· + a − 4, u
23
+ 3u
22
+ ··· − 6u
2
+ 1i
I
u
3
= hu
10
+ 3u
9
+ 10u
8
+ 20u
7
+ 33u
6
+ 43u
5
+ 42u
4
+ 32u
3
+ 17u
2
+ b + 6u + 1,
− u
13
− 2u
12
− 12u
11
− 19u
10
− 53u
9
− 65u
8
− 106u
7
− 95u
6
− 93u
5
− 52u
4
− 27u
3
− 3u
2
+ a + 3,
u
14
+ 2u
13
+ ··· + 3u + 1i
I
v
1
= ha, b − 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 98 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−4708u
36
+ 22559u
35
+ · · · + 12181b + 159188, 1.84 × 10
5
u
36
−
8.55 × 10
5
u
35
+ · · · + 1.34 × 10
5
a − 2.35 × 10
6
, u
37
− 5u
36
+ · · · − 93u + 11i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
−1.37457u
36
+ 6.38036u
35
+ ··· − 159.292u + 17.5681
0.386504u
36
− 1.85198u
35
+ ··· + 99.2238u − 13.0685
a
2
=
−3.17294u
36
+ 14.8917u
35
+ ··· − 300.428u + 33.3318
0.892455u
36
− 4.15631u
35
+ ··· + 240.876u − 30.6508
a
6
=
u
2
+ 1
u
2
a
3
=
−0.695562u
36
+ 3.44817u
35
+ ··· − 15.1053u − 3.85542
0.492488u
36
− 2.10557u
35
+ ··· + 110.267u − 15.1203
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
−0.800315u
36
+ 3.60432u
35
+ ··· − 74.9791u + 8.59307
0.134143u
36
− 0.748543u
35
+ ··· + 43.9825u − 4.57902
a
10
=
1.44794u
36
− 6.84097u
35
+ ··· + 204.364u − 29.2190
0.0802890u
36
− 0.953534u
35
+ ··· + 17.4424u + 1.26911
(ii) Obstruction class = −1
(iii) Cusp Shapes =
56806
12181
u
36
−
266817
12181
u
35
+ ··· +
12593355
12181
u −
1834736
12181
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
37
+ 4u
36
+ ··· + 24u − 1
c
2
u
37
+ 22u
36
+ ··· − 87u − 11
c
4
, c
10
u
37
+ 2u
35
+ ··· − 31u
2
− 3
c
5
, c
9
u
37
− u
36
+ ··· + 3u − 1
c
6
, c
7
, c
8
c
11
, c
12
u
37
+ 5u
36
+ ··· − 93u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
37
− 32y
36
+ ··· + 114y −1
c
2
y
37
+ 46y
35
+ ··· + 419y −121
c
4
, c
10
y
37
+ 4y
36
+ ··· − 186y −9
c
5
, c
9
y
37
− 15y
36
+ ··· + 39y −1
c
6
, c
7
, c
8
c
11
, c
12
y
37
+ 51y
36
+ ··· + 245y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024756 + 1.003880I
a = 1.175790 − 0.520011I
b = 0.66374 − 1.62745I
−5.00500 − 0.12327I −5.98815 + 0.I
u = −0.024756 − 1.003880I
a = 1.175790 + 0.520011I
b = 0.66374 + 1.62745I
−5.00500 + 0.12327I −5.98815 + 0.I
u = 0.289437 + 0.983506I
a = 0.571567 − 0.060773I
b = 0.93730 − 1.28805I
−5.74342 + 2.02777I −6.65386 − 1.42849I
u = 0.289437 − 0.983506I
a = 0.571567 + 0.060773I
b = 0.93730 + 1.28805I
−5.74342 − 2.02777I −6.65386 + 1.42849I
u = 0.255241 + 1.040160I
a = 0.614543 − 0.711849I
b = 0.02855 − 2.23185I
−6.18042 + 5.52248I −8.08952 − 8.67422I
u = 0.255241 − 1.040160I
a = 0.614543 + 0.711849I
b = 0.02855 + 2.23185I
−6.18042 − 5.52248I −8.08952 + 8.67422I
u = −0.174584 + 0.835928I
a = −0.438786 + 0.614183I
b = 0.159818 + 0.734522I
−1.41316 − 2.04594I 1.13419 + 3.99911I
u = −0.174584 − 0.835928I
a = −0.438786 − 0.614183I
b = 0.159818 − 0.734522I
−1.41316 + 2.04594I 1.13419 − 3.99911I
u = 0.373017 + 1.086120I
a = −0.263327 + 0.662536I
b = 0.03559 + 2.06531I
−5.4061 + 14.0876I 0
u = 0.373017 − 1.086120I
a = −0.263327 − 0.662536I
b = 0.03559 − 2.06531I
−5.4061 − 14.0876I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601924 + 0.470380I
a = 0.819217 − 0.043610I
b = −0.639760 + 0.296764I
−1.57344 − 6.55157I 0.66439 + 4.08814I
u = 0.601924 − 0.470380I
a = 0.819217 + 0.043610I
b = −0.639760 − 0.296764I
−1.57344 + 6.55157I 0.66439 − 4.08814I
u = 0.258979 + 1.229600I
a = −0.583862 + 0.387661I
b = −0.797830 + 1.118640I
−7.04198 − 3.53330I 0
u = 0.258979 − 1.229600I
a = −0.583862 − 0.387661I
b = −0.797830 − 1.118640I
−7.04198 + 3.53330I 0
u = 0.644949 + 0.303940I
a = 0.889386 − 0.999870I
b = −0.211320 + 0.616406I
−1.07949 + 10.62970I 2.38501 − 8.97197I
u = 0.644949 − 0.303940I
a = 0.889386 + 0.999870I
b = −0.211320 − 0.616406I
−1.07949 − 10.62970I 2.38501 + 8.97197I
u = −0.494000 + 0.492655I
a = −0.382762 + 0.046228I
b = −0.189464 + 0.141918I
0.72150 − 1.71038I 5.72840 − 0.24301I
u = −0.494000 − 0.492655I
a = −0.382762 − 0.046228I
b = −0.189464 − 0.141918I
0.72150 + 1.71038I 5.72840 + 0.24301I
u = 0.450704 + 0.280399I
a = −0.64300 + 1.61268I
b = 0.407710 − 0.737598I
−2.07909 + 3.10269I −2.55857 − 8.69904I
u = 0.450704 − 0.280399I
a = −0.64300 − 1.61268I
b = 0.407710 + 0.737598I
−2.07909 − 3.10269I −2.55857 + 8.69904I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13418 + 1.50316I
a = −0.336179 + 0.293626I
b = −0.297595 + 0.492362I
−5.92171 − 3.96285I 0
u = −0.13418 − 1.50316I
a = −0.336179 − 0.293626I
b = −0.297595 − 0.492362I
−5.92171 + 3.96285I 0
u = 0.397512 + 0.237116I
a = −1.54677 + 0.52584I
b = 0.690346 − 0.066411I
−2.09954 − 0.39329I −2.47917 − 0.74863I
u = 0.397512 − 0.237116I
a = −1.54677 − 0.52584I
b = 0.690346 + 0.066411I
−2.09954 + 0.39329I −2.47917 + 0.74863I
u = −0.409769
a = −0.906661
b = −0.331981
1.05211 10.2210
u = −0.03012 + 1.68814I
a = 0.548995 + 1.286040I
b = 1.05584 + 1.49435I
−10.41680 − 2.72771I 0
u = −0.03012 − 1.68814I
a = 0.548995 − 1.286040I
b = 1.05584 − 1.49435I
−10.41680 + 2.72771I 0
u = 0.08129 + 1.71808I
a = 1.09520 − 1.84279I
b = 1.02527 − 2.70249I
−15.3380 + 3.5515I 0
u = 0.08129 − 1.71808I
a = 1.09520 + 1.84279I
b = 1.02527 + 2.70249I
−15.3380 − 3.5515I 0
u = −0.00798 + 1.73092I
a = 0.42758 − 2.20249I
b = −0.00155 − 2.93076I
−14.8725 − 0.2681I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00798 − 1.73092I
a = 0.42758 + 2.20249I
b = −0.00155 + 2.93076I
−14.8725 + 0.2681I 0
u = 0.06596 + 1.73206I
a = 0.16269 − 2.93754I
b = −0.46415 − 3.90524I
−16.0814 + 6.8392I 0
u = 0.06596 − 1.73206I
a = 0.16269 + 2.93754I
b = −0.46415 + 3.90524I
−16.0814 − 6.8392I 0
u = 0.10020 + 1.74554I
a = −0.25064 + 2.67618I
b = 0.24045 + 3.60770I
−15.4757 + 16.0719I 0
u = 0.10020 − 1.74554I
a = −0.25064 − 2.67618I
b = 0.24045 − 3.60770I
−15.4757 − 16.0719I 0
u = 0.05130 + 1.77583I
a = −0.63357 + 1.60178I
b = −0.47695 + 2.21578I
−17.9370 − 2.2818I 0
u = 0.05130 − 1.77583I
a = −0.63357 − 1.60178I
b = −0.47695 − 2.21578I
−17.9370 + 2.2818I 0
8
II. I
u
2
=
h11u
22
a+26u
22
+· · ·+4a+1, u
22
+4u
21
+· · ·+a−4, u
23
+3u
22
+· · ·−6u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
a
−0.118280au
22
− 0.279570u
22
+ ··· − 0.0430108a − 0.0107527
a
2
=
−0.268817au
22
+ 0.182796u
22
+ ··· + 0.720430a − 0.569892
0.0107527au
22
− 0.247312u
22
+ ··· + 0.731183a + 0.182796
a
6
=
u
2
+ 1
u
2
a
3
=
0.0430108au
22
+ 0.0107527u
22
+ ··· + 0.924731a + 0.731183
−u
21
− 4u
20
+ ··· + au + u
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
0.0430108au
22
+ 0.0107527u
22
+ ··· + 0.924731a + 0.731183
−0.311828au
22
+ 0.172043u
22
+ ··· − 0.204301a − 0.301075
a
10
=
0.204301au
22
+ 0.301075u
22
+ ··· + 0.892473a − 0.526882
0.0107527au
22
− 0.247312u
22
+ ··· − 0.268817a + 0.182796
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
22
+ 4u
21
+ 56u
20
+ 44u
19
+ 304u
18
+ 152u
17
+ 744u
16
−
20u
15
+ 440u
14
−1456u
13
−1824u
12
−4084u
11
−4572u
10
−5296u
9
−4580u
8
−3604u
7
−
2220u
6
− 1204u
5
− 428u
4
− 112u
3
+ 12u
2
+ 24u + 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
46
− u
45
+ ··· − 152u − 399
c
2
(u
23
− 11u
22
+ ··· + 6u
2
− 1)
2
c
4
, c
10
u
46
− u
45
+ ··· + 12u + 3
c
5
, c
9
u
46
− u
45
+ ··· − 2u − 3
c
6
, c
7
, c
8
c
11
, c
12
(u
23
− 3u
22
+ ··· + 6u
2
− 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
46
+ 3y
45
+ ··· − 2710768y + 159201
c
2
(y
23
− y
22
+ ··· + 12y −1)
2
c
4
, c
10
y
46
+ 7y
45
+ ··· − 120y + 9
c
5
, c
9
y
46
+ 11y
45
+ ··· − 268y + 9
c
6
, c
7
, c
8
c
11
, c
12
(y
23
+ 31y
22
+ ··· + 12y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122130 + 0.956594I
a = 0.765870 − 0.027652I
b = −1.268860 − 0.013685I
−1.83677 + 5.25378I −0.17726 − 9.24428I
u = 0.122130 + 0.956594I
a = −0.36753 − 1.77726I
b = −0.81010 − 2.41860I
−1.83677 + 5.25378I −0.17726 − 9.24428I
u = 0.122130 − 0.956594I
a = 0.765870 + 0.027652I
b = −1.268860 + 0.013685I
−1.83677 − 5.25378I −0.17726 + 9.24428I
u = 0.122130 − 0.956594I
a = −0.36753 + 1.77726I
b = −0.81010 + 2.41860I
−1.83677 − 5.25378I −0.17726 + 9.24428I
u = −0.191484 + 1.140050I
a = 1.05870 + 0.99434I
b = 0.89319 + 1.70209I
−6.33180 − 4.80882I −8.17045 + 6.89379I
u = −0.191484 + 1.140050I
a = −0.050084 − 0.434449I
b = 0.49879 − 1.76452I
−6.33180 − 4.80882I −8.17045 + 6.89379I
u = −0.191484 − 1.140050I
a = 1.05870 − 0.99434I
b = 0.89319 − 1.70209I
−6.33180 + 4.80882I −8.17045 − 6.89379I
u = −0.191484 − 1.140050I
a = −0.050084 + 0.434449I
b = 0.49879 + 1.76452I
−6.33180 + 4.80882I −8.17045 − 6.89379I
u = −0.372225 + 1.111890I
a = 0.060513 + 0.762765I
b = 0.01206 + 1.73332I
−3.82773 − 5.60663I 3.50764 + 12.63284I
u = −0.372225 + 1.111890I
a = −0.287984 − 0.223234I
b = 0.049443 − 1.117410I
−3.82773 − 5.60663I 3.50764 + 12.63284I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.372225 − 1.111890I
a = 0.060513 − 0.762765I
b = 0.01206 − 1.73332I
−3.82773 + 5.60663I 3.50764 − 12.63284I
u = −0.372225 − 1.111890I
a = −0.287984 + 0.223234I
b = 0.049443 + 1.117410I
−3.82773 + 5.60663I 3.50764 − 12.63284I
u = 0.044921 + 0.795699I
a = 0.155806 + 0.550016I
b = 0.92072 + 1.80326I
−0.70591 − 2.58349I 2.14863 + 0.79389I
u = 0.044921 + 0.795699I
a = −1.49082 + 0.70078I
b = −0.129486 + 0.339807I
−0.70591 − 2.58349I 2.14863 + 0.79389I
u = 0.044921 − 0.795699I
a = 0.155806 − 0.550016I
b = 0.92072 − 1.80326I
−0.70591 + 2.58349I 2.14863 − 0.79389I
u = 0.044921 − 0.795699I
a = −1.49082 − 0.70078I
b = −0.129486 − 0.339807I
−0.70591 + 2.58349I 2.14863 − 0.79389I
u = −0.652551 + 0.364111I
a = −0.777609 − 0.307375I
b = −0.030991 + 0.450120I
0.76689 − 2.11198I 16.3750 + 9.4338I
u = −0.652551 + 0.364111I
a = 0.143409 + 0.513462I
b = −0.289886 − 0.214796I
0.76689 − 2.11198I 16.3750 + 9.4338I
u = −0.652551 − 0.364111I
a = −0.777609 + 0.307375I
b = −0.030991 − 0.450120I
0.76689 + 2.11198I 16.3750 − 9.4338I
u = −0.652551 − 0.364111I
a = 0.143409 − 0.513462I
b = −0.289886 + 0.214796I
0.76689 + 2.11198I 16.3750 − 9.4338I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.349386 + 0.538209I
a = −0.42996 + 1.38774I
b = −0.220108 − 0.165488I
−1.10752 − 2.96048I −0.41922 + 9.76981I
u = −0.349386 + 0.538209I
a = −0.255176 + 0.029202I
b = 0.477925 + 1.112960I
−1.10752 − 2.96048I −0.41922 + 9.76981I
u = −0.349386 − 0.538209I
a = −0.42996 − 1.38774I
b = −0.220108 + 0.165488I
−1.10752 + 2.96048I −0.41922 − 9.76981I
u = −0.349386 − 0.538209I
a = −0.255176 − 0.029202I
b = 0.477925 − 1.112960I
−1.10752 + 2.96048I −0.41922 − 9.76981I
u = −0.540325
a = 0.161694
b = −0.714768
0.662774 12.3650
u = −0.540325
a = −1.84732
b = −0.0508933
0.662774 12.3650
u = −0.00286 + 1.69297I
a = −0.097069 + 0.365520I
b = 0.632924 + 0.248965I
−9.70029 − 2.55133I 2.45391 + 1.84917I
u = −0.00286 + 1.69297I
a = 0.82449 + 2.84829I
b = 1.16616 + 3.71038I
−9.70029 − 2.55133I 2.45391 + 1.84917I
u = −0.00286 − 1.69297I
a = −0.097069 − 0.365520I
b = 0.632924 − 0.248965I
−9.70029 + 2.55133I 2.45391 − 1.84917I
u = −0.00286 − 1.69297I
a = 0.82449 − 2.84829I
b = 1.16616 − 3.71038I
−9.70029 + 2.55133I 2.45391 − 1.84917I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294369 + 0.074043I
a = −1.04036 + 1.99161I
b = −0.612571 − 1.075480I
1.32345 + 3.87153I 12.8892 − 8.7586I
u = 0.294369 + 0.074043I
a = 2.85549 + 3.36109I
b = 0.387083 − 0.453910I
1.32345 + 3.87153I 12.8892 − 8.7586I
u = 0.294369 − 0.074043I
a = −1.04036 − 1.99161I
b = −0.612571 + 1.075480I
1.32345 − 3.87153I 12.8892 + 8.7586I
u = 0.294369 − 0.074043I
a = 2.85549 − 3.36109I
b = 0.387083 + 0.453910I
1.32345 − 3.87153I 12.8892 + 8.7586I
u = 0.02789 + 1.71844I
a = −1.84808 + 0.03407I
b = −3.20107 + 0.16628I
−11.44590 + 5.82985I −0.97520 − 7.07929I
u = 0.02789 + 1.71844I
a = −0.69611 − 3.19548I
b = −0.89452 − 3.65297I
−11.44590 + 5.82985I −0.97520 − 7.07929I
u = 0.02789 − 1.71844I
a = −1.84808 − 0.03407I
b = −3.20107 − 0.16628I
−11.44590 − 5.82985I −0.97520 + 7.07929I
u = 0.02789 − 1.71844I
a = −0.69611 + 3.19548I
b = −0.89452 + 3.65297I
−11.44590 − 5.82985I −0.97520 + 7.07929I
u = −0.09919 + 1.75130I
a = −0.00783 − 1.65242I
b = 0.49848 − 2.29807I
−14.0207 − 7.5990I −0.46890 + 9.57458I
u = −0.09919 + 1.75130I
a = 0.32195 + 2.39070I
b = 0.07837 + 3.13179I
−14.0207 − 7.5990I −0.46890 + 9.57458I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09919 − 1.75130I
a = −0.00783 + 1.65242I
b = 0.49848 + 2.29807I
−14.0207 + 7.5990I −0.46890 − 9.57458I
u = −0.09919 − 1.75130I
a = 0.32195 − 2.39070I
b = 0.07837 − 3.13179I
−14.0207 + 7.5990I −0.46890 − 9.57458I
u = −0.05145 + 1.75720I
a = 1.07306 + 1.90472I
b = 0.77795 + 2.38432I
−16.7750 − 5.8630I −8.34566 + 4.67678I
u = −0.05145 + 1.75720I
a = 0.43211 − 2.58792I
b = 0.94732 − 3.61321I
−16.7750 − 5.8630I −8.34566 + 4.67678I
u = −0.05145 − 1.75720I
a = 1.07306 − 1.90472I
b = 0.77795 − 2.38432I
−16.7750 + 5.8630I −8.34566 − 4.67678I
u = −0.05145 − 1.75720I
a = 0.43211 + 2.58792I
b = 0.94732 + 3.61321I
−16.7750 + 5.8630I −8.34566 − 4.67678I
16
III.
I
u
3
= hu
10
+3u
9
+· · ·+b+1, −u
13
−2u
12
+· · ·+a+3, u
14
+2u
13
+· · ·+3u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
u
13
+ 2u
12
+ ··· + 3u
2
− 3
−u
10
− 3u
9
+ ··· − 6u − 1
a
2
=
−u
13
− 2u
12
+ ··· − 13u − 2
u
11
+ 2u
10
+ ··· + 2u + 1
a
6
=
u
2
+ 1
u
2
a
3
=
u
13
+ 2u
12
+ ··· − 5u − 4
−u
11
− 3u
10
+ ··· − 6u − 1
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
u
13
+ 2u
12
+ ··· − 4u − 3
−u
11
− 3u
10
+ ··· − 7u − 1
a
10
=
−u
13
− 2u
12
+ ··· − 11u + 1
u
6
+ 2u
5
+ 5u
4
+ 7u
3
+ 6u
2
+ 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
12
−u
11
+ 9u
10
+ u
9
+ 41u
8
+ 44u
7
+ 112u
6
+ 135u
5
+ 154u
4
+ 129u
3
+ 75u
2
+ 32u + 6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
14
− 5u
13
+ ··· − 6u + 1
c
2
u
14
+ 9u
13
+ ··· + 9u + 1
c
4
, c
10
u
14
+ u
13
+ ··· + 3u
2
+ 1
c
5
, c
9
u
14
+ 3u
12
+ ··· − u + 1
c
6
, c
7
, c
8
u
14
+ 2u
13
+ ··· + 3u + 1
c
11
, c
12
u
14
− 2u
13
+ ··· − 3u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
14
+ 5y
13
+ ··· + 6y + 1
c
2
y
14
+ y
13
+ ··· − 3y + 1
c
4
, c
10
y
14
+ 5y
13
+ ··· + 6y + 1
c
5
, c
9
y
14
+ 6y
13
+ ··· + 5y + 1
c
6
, c
7
, c
8
c
11
, c
12
y
14
+ 20y
13
+ ··· + 27y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.018194 + 0.849931I
a = 0.603835 + 1.159030I
b = −0.78541 + 1.37748I
−1.25778 + 3.72574I −0.64115 − 6.57494I
u = 0.018194 − 0.849931I
a = 0.603835 − 1.159030I
b = −0.78541 − 1.37748I
−1.25778 − 3.72574I −0.64115 + 6.57494I
u = −0.250655 + 1.124850I
a = −0.322735 − 0.654478I
b = 0.10209 − 1.57296I
−4.80751 − 4.95467I −2.28737 + 6.46163I
u = −0.250655 − 1.124850I
a = −0.322735 + 0.654478I
b = 0.10209 + 1.57296I
−4.80751 + 4.95467I −2.28737 − 6.46163I
u = −0.623943 + 0.429456I
a = 0.426245 + 0.345340I
b = −0.178249 − 0.359896I
0.26055 − 2.09268I −4.56828 + 7.08050I
u = −0.623943 − 0.429456I
a = 0.426245 − 0.345340I
b = −0.178249 + 0.359896I
0.26055 + 2.09268I −4.56828 − 7.08050I
u = −0.06757 + 1.51095I
a = 0.245172 − 0.589528I
b = 0.557839 − 0.723961I
−5.53297 − 4.18476I 6.81071 + 6.85703I
u = −0.06757 − 1.51095I
a = 0.245172 + 0.589528I
b = 0.557839 + 0.723961I
−5.53297 + 4.18476I 6.81071 − 6.85703I
u = 0.00788 + 1.69196I
a = −1.05669 + 1.77912I
b = −1.84143 + 2.01119I
−10.36330 + 3.84481I −1.07477 − 7.29533I
u = 0.00788 − 1.69196I
a = −1.05669 − 1.77912I
b = −1.84143 − 2.01119I
−10.36330 − 3.84481I −1.07477 + 7.29533I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.018196 + 0.300578I
a = −2.84368 − 0.47970I
b = 0.198823 − 0.929952I
0.58641 − 3.67714I 0.36024 + 5.91846I
u = −0.018196 − 0.300578I
a = −2.84368 + 0.47970I
b = 0.198823 + 0.929952I
0.58641 + 3.67714I 0.36024 − 5.91846I
u = −0.06571 + 1.74745I
a = −0.05215 − 2.29837I
b = 0.44633 − 3.02735I
−15.0739 − 6.2927I −2.09938 + 4.32499I
u = −0.06571 − 1.74745I
a = −0.05215 + 2.29837I
b = 0.44633 + 3.02735I
−15.0739 + 6.2927I −2.09938 − 4.32499I
21
IV. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
1
0
a
8
=
1
0
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
6
=
1
0
a
3
=
1
1
a
11
=
1
0
a
9
=
1
0
a
5
=
1
1
a
10
=
2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
u + 1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
u
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
y − 1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u + 1)(u
14
− 5u
13
+ ··· − 6u + 1)(u
37
+ 4u
36
+ ··· + 24u − 1)
· (u
46
− u
45
+ ··· − 152u − 399)
c
2
u(u
14
+ 9u
13
+ ··· + 9u + 1)(u
23
− 11u
22
+ ··· + 6u
2
− 1)
2
· (u
37
+ 22u
36
+ ··· − 87u − 11)
c
4
, c
10
(u + 1)(u
14
+ u
13
+ ··· + 3u
2
+ 1)(u
37
+ 2u
35
+ ··· − 31u
2
− 3)
· (u
46
− u
45
+ ··· + 12u + 3)
c
5
, c
9
(u + 1)(u
14
+ 3u
12
+ ··· − u + 1)(u
37
− u
36
+ ··· + 3u − 1)
· (u
46
− u
45
+ ··· − 2u − 3)
c
6
, c
7
, c
8
u(u
14
+ 2u
13
+ ··· + 3u + 1)(u
23
− 3u
22
+ ··· + 6u
2
− 1)
2
· (u
37
+ 5u
36
+ ··· − 93u − 11)
c
11
, c
12
u(u
14
− 2u
13
+ ··· − 3u + 1)(u
23
− 3u
22
+ ··· + 6u
2
− 1)
2
· (u
37
+ 5u
36
+ ··· − 93u − 11)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y − 1)(y
14
+ 5y
13
+ ··· + 6y + 1)(y
37
− 32y
36
+ ··· + 114y − 1)
· (y
46
+ 3y
45
+ ··· − 2710768y + 159201)
c
2
y(y
14
+ y
13
+ ··· − 3y + 1)(y
23
− y
22
+ ··· + 12y − 1)
2
· (y
37
+ 46y
35
+ ··· + 419y − 121)
c
4
, c
10
(y − 1)(y
14
+ 5y
13
+ ··· + 6y + 1)(y
37
+ 4y
36
+ ··· − 186y − 9)
· (y
46
+ 7y
45
+ ··· − 120y + 9)
c
5
, c
9
(y − 1)(y
14
+ 6y
13
+ ··· + 5y + 1)(y
37
− 15y
36
+ ··· + 39y − 1)
· (y
46
+ 11y
45
+ ··· − 268y + 9)
c
6
, c
7
, c
8
c
11
, c
12
y(y
14
+ 20y
13
+ ··· + 27y + 1)(y
23
+ 31y
22
+ ··· + 12y − 1)
2
· (y
37
+ 51y
36
+ ··· + 245y − 121)
27
