12n
0139
(K12n
0139
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 3 11 6 12 8 5 9
Solving Sequence
8,10
11
3,7
6 5 12 2 1 4 9
c
10
c
7
c
6
c
5
c
11
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1444693149u
23
− 2063776507u
22
+ ··· + 9741443072b + 4111548169,
7418361699u
23
− 17994094933u
22
+ ··· + 19482886144a + 41117831143,
u
24
− 2u
23
+ ··· + 4u + 1i
I
u
2
= h8.06000 × 10
26
u
27
+ 4.92381 × 10
27
u
26
+ ··· + 6.21532 × 10
28
b + 1.24378 × 10
29
,
− 1.07145 × 10
29
u
27
− 9.17959 × 10
29
u
26
+ ··· + 6.02886 × 10
30
a − 5.28882 × 10
31
,
u
28
+ 6u
27
+ ··· + 542u + 97i
I
u
3
= h−u
3
− u
2
+ 2b − 2u + 1, u
3
+ 3u
2
+ 4a + 2u + 1, u
4
+ u
2
− u + 1i
I
u
4
= h−u
5
− u
3
− u
2
+ b − u − 1, −u
4
− u
2
+ a − u, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
u
5
= h−91a
2
u − 12a
2
+ 564au + 337b − 570a + 147u − 188, a
3
− 7a
2
u − 5a
2
− 4au − a + u − 2, u
2
+ 1i
I
u
6
= h3b + 4a + 2, 4a
2
− 2a − 11, u − 1i
* 6 irreducible components of dim
C
= 0, with total 70 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
= h1.44 × 10
9
u
23
− 2.06 × 10
9
u
22
+ · · · + 9.74 × 10
9
b + 4.11 × 10
9
, 7.42 ×
10
9
u
23
−1.80×10
10
u
22
+· · ·+1.95×10
10
a+4.11×10
10
, u
24
−2u
23
+· · ·+4u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
−0.380763u
23
+ 0.923585u
22
+ ··· + 30.4809u − 2.11046
−0.148304u
23
+ 0.211855u
22
+ ··· − 1.81073u − 0.422068
a
7
=
−u
u
3
+ u
a
6
=
0.0171864u
23
+ 0.103403u
22
+ ··· + 13.2528u − 2.04858
−0.192725u
23
+ 0.324632u
22
+ ··· + 2.24962u + 0.0941446
a
5
=
−0.175538u
23
+ 0.428035u
22
+ ··· + 15.5024u − 1.95444
−0.192725u
23
+ 0.324632u
22
+ ··· + 2.24962u + 0.0941446
a
12
=
−0.000122070u
23
+ 0.000366211u
22
+ ··· − 3.00037u + 1.99988
−u
a
2
=
−0.343412u
23
+ 0.752066u
22
+ ··· + 21.0006u − 1.27837
−0.0361944u
23
− 0.0124158u
22
+ ··· − 3.46335u − 0.593642
a
1
=
0.000244141u
23
− 0.000732422u
22
+ ··· + 4.00073u − 1.99976
u
3
+ u
a
4
=
−0.421620u
23
+ 0.978405u
22
+ ··· + 30.4126u − 2.01569
−0.0958427u
23
+ 0.0837108u
22
+ ··· − 1.89080u − 0.543727
a
9
=
−0.000122070u
23
+ 0.000366211u
22
+ ··· − 2.00037u + 0.999878
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
53447126663
77931544576
u
23
−
86145029121
77931544576
u
22
+ ··· +
1245910362157
77931544576
u −
821525338933
77931544576
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 26u
23
+ ··· − 7007u + 256
c
2
, c
4
u
24
− 6u
23
+ ··· + u + 16
c
3
, c
6
u
24
+ 2u
23
+ ··· − 96u + 256
c
5
u
24
+ 6u
23
+ ··· + 624u + 64
c
7
, c
9
, c
10
c
12
u
24
− 2u
23
+ ··· + 4u + 1
c
8
, c
11
4(4u
24
− 10u
23
+ ··· + 56u + 8)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 50y
23
+ ··· − 51129153y + 65536
c
2
, c
4
y
24
− 26y
23
+ ··· + 7007y + 256
c
3
, c
6
y
24
− 18y
23
+ ··· − 185344y + 65536
c
5
y
24
+ 4y
23
+ ··· − 69376y + 4096
c
7
, c
9
, c
10
c
12
y
24
+ 24y
23
+ ··· − 110y + 1
c
8
, c
11
16(16y
24
− 412y
23
+ ··· − 64y + 64)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08185
a = −2.32289
b = 4.49933
0.548623 −54.0530
u = 0.148994 + 0.783883I
a = −0.500058 − 0.355404I
b = −1.153660 − 0.222767I
0.55362 + 3.41152I 0.86412 − 8.64734I
u = 0.148994 − 0.783883I
a = −0.500058 + 0.355404I
b = −1.153660 + 0.222767I
0.55362 − 3.41152I 0.86412 + 8.64734I
u = 0.358870 + 1.163880I
a = 0.293497 + 0.216350I
b = 1.49300 − 0.50044I
−0.73599 − 1.30879I −8.68561 − 1.94237I
u = 0.358870 − 1.163880I
a = 0.293497 − 0.216350I
b = 1.49300 + 0.50044I
−0.73599 + 1.30879I −8.68561 + 1.94237I
u = −0.512568 + 1.179470I
a = 0.1243150 + 0.0579838I
b = 0.480003 + 0.040159I
−3.85211 − 7.19847I −3.15942 + 2.00992I
u = −0.512568 − 1.179470I
a = 0.1243150 − 0.0579838I
b = 0.480003 − 0.040159I
−3.85211 + 7.19847I −3.15942 − 2.00992I
u = 0.592376 + 0.366960I
a = −0.643909 + 0.233654I
b = 0.688451 + 0.658630I
1.12915 + 1.02062I 4.27770 − 4.63248I
u = 0.592376 − 0.366960I
a = −0.643909 − 0.233654I
b = 0.688451 − 0.658630I
1.12915 − 1.02062I 4.27770 + 4.63248I
u = −0.541907
a = 2.23521
b = −0.103995
−7.92944 −16.4750
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05535 + 1.55193I
a = −0.211228 + 1.127990I
b = −0.858668 + 0.189081I
−11.34610 − 0.73612I −10.72969 + 0.24360I
u = −0.05535 − 1.55193I
a = −0.211228 − 1.127990I
b = −0.858668 − 0.189081I
−11.34610 + 0.73612I −10.72969 − 0.24360I
u = 0.31630 + 1.54928I
a = 0.269994 − 1.060220I
b = −0.207846 − 0.286463I
−19.0579 + 6.6137I −10.93484 − 2.97293I
u = 0.31630 − 1.54928I
a = 0.269994 + 1.060220I
b = −0.207846 + 0.286463I
−19.0579 − 6.6137I −10.93484 + 2.97293I
u = −0.36560 + 1.55447I
a = 0.044155 − 1.334510I
b = 1.73078 − 0.39028I
−11.7462 − 9.1224I −9.90926 + 4.97595I
u = −0.36560 − 1.55447I
a = 0.044155 + 1.334510I
b = 1.73078 + 0.39028I
−11.7462 + 9.1224I −9.90926 − 4.97595I
u = −0.21985 + 1.60526I
a = −0.227686 − 0.153857I
b = −1.58817 − 0.13159I
−14.1758 − 4.9325I −11.00051 + 2.57629I
u = −0.21985 − 1.60526I
a = −0.227686 + 0.153857I
b = −1.58817 + 0.13159I
−14.1758 + 4.9325I −11.00051 − 2.57629I
u = 0.280085 + 0.207328I
a = 2.76775 + 0.68817I
b = −1.15139 − 0.84730I
−1.26399 + 0.69429I −5.88235 + 2.63444I
u = 0.280085 − 0.207328I
a = 2.76775 − 0.68817I
b = −1.15139 + 0.84730I
−1.26399 − 0.69429I −5.88235 − 2.63444I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.62229 + 1.54349I
a = 0.33089 + 1.38912I
b = −2.20818 + 0.76804I
19.7035 − 15.6516I −10.07185 + 6.64115I
u = −0.62229 − 1.54349I
a = 0.33089 − 1.38912I
b = −2.20818 − 0.76804I
19.7035 + 15.6516I −10.07185 − 6.64115I
u = 1.71472
a = 1.29940
b = −4.00128
−8.86122 −11.8540
u = −0.0966119
a = −5.95715
b = −0.342701
−0.870307 −11.9670
7
II. I
u
2
= h8.06 × 10
26
u
27
+ 4.92 × 10
27
u
26
+ · · · + 6.22 × 10
28
b + 1.24 ×
10
29
, −1.07 × 10
29
u
27
− 9.18 × 10
29
u
26
+ · · · + 6.03 × 10
30
a − 5.29 ×
10
31
, u
28
+ 6u
27
+ · · · + 542u + 97i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
0.0177720u
27
+ 0.152261u
26
+ ··· + 51.0589u + 8.77250
−0.0129680u
27
− 0.0792205u
26
+ ··· − 10.1162u − 2.00116
a
7
=
−u
u
3
+ u
a
6
=
0.0199647u
27
+ 0.149393u
26
+ ··· + 34.2789u + 5.74653
0.00250162u
27
− 0.00246621u
26
+ ··· − 4.44438u − 0.719728
a
5
=
0.0224663u
27
+ 0.146927u
26
+ ··· + 29.8346u + 5.02680
0.00250162u
27
− 0.00246621u
26
+ ··· − 4.44438u − 0.719728
a
12
=
0.153415u
27
+ 0.834186u
26
+ ··· − 54.2701u − 12.9847
−0.0420845u
27
− 0.221294u
26
+ ··· − 19.3117u − 4.11126
a
2
=
0.0235732u
27
+ 0.167215u
26
+ ··· + 33.8050u + 6.19640
−0.00721990u
27
− 0.0332133u
26
+ ··· − 0.910549u − 0.565518
a
1
=
0.0217420u
27
+ 0.116081u
26
+ ··· + 1.22632u + 0.0581123
u
3
+ u
a
4
=
0.0203435u
27
+ 0.162178u
26
+ ··· + 41.7784u + 6.36296
0.000121206u
27
− 0.0139096u
26
+ ··· − 3.57361u − 0.126255
a
9
=
−0.128091u
27
− 0.908242u
26
+ ··· − 122.754u − 18.4433
0.0312135u
27
+ 0.163253u
26
+ ··· + 18.6986u + 3.08220
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0158847u
27
− 0.109997u
26
+ ··· − 3.88785u − 3.25341
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
14
+ 20u
13
+ ··· + 25u + 1)
2
c
2
, c
4
(u
14
− 4u
13
+ ··· − u − 1)
2
c
3
, c
6
(u
14
+ u
13
+ ··· + 20u + 8)
2
c
5
(u
14
− 2u
13
+ ··· + 4u − 1)
2
c
7
, c
9
, c
10
c
12
u
28
+ 6u
27
+ ··· + 542u + 97
c
8
, c
11
u
28
+ 2u
27
+ ··· − 12530u + 4603
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
14
− 48y
13
+ ··· − 153y + 1)
2
c
2
, c
4
(y
14
− 20y
13
+ ··· − 25y + 1)
2
c
3
, c
6
(y
14
− 21y
13
+ ··· − 144y + 64)
2
c
5
(y
14
− 6y
13
+ ··· − 8y + 1)
2
c
7
, c
9
, c
10
c
12
y
28
+ 22y
27
+ ··· + 47288y + 9409
c
8
, c
11
y
28
− 22y
27
+ ··· + 76721028y + 21187609
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.121798 + 1.022010I
a = 2.24497 − 1.77780I
b = 0.448883
−4.07000 −8.52950 + 0.I
u = −0.121798 − 1.022010I
a = 2.24497 + 1.77780I
b = 0.448883
−4.07000 −8.52950 + 0.I
u = −0.730722 + 0.738022I
a = −1.55264 − 0.66750I
b = 1.94409 + 0.00042I
−6.39368 − 1.41191I −9.87318 + 3.81508I
u = −0.730722 − 0.738022I
a = −1.55264 + 0.66750I
b = 1.94409 − 0.00042I
−6.39368 + 1.41191I −9.87318 − 3.81508I
u = −0.961372 + 0.440888I
a = 1.47427 + 0.61493I
b = −1.88899 + 0.49296I
−5.27322 − 4.24963I −9.14655 + 5.18533I
u = −0.961372 − 0.440888I
a = 1.47427 − 0.61493I
b = −1.88899 − 0.49296I
−5.27322 + 4.24963I −9.14655 − 5.18533I
u = 0.778733 + 0.476869I
a = −0.560712 + 1.159950I
b = 0.091282 + 0.179107I
−12.49530 + 2.45847I −7.50081 − 0.42962I
u = 0.778733 − 0.476869I
a = −0.560712 − 1.159950I
b = 0.091282 − 0.179107I
−12.49530 − 2.45847I −7.50081 + 0.42962I
u = 0.396592 + 1.073210I
a = −0.365767 − 0.144675I
b = −0.597039 + 0.103194I
−0.91573 + 2.69540I 0.31936 − 2.88879I
u = 0.396592 − 1.073210I
a = −0.365767 + 0.144675I
b = −0.597039 − 0.103194I
−0.91573 − 2.69540I 0.31936 + 2.88879I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.014446 + 1.158610I
a = 1.74504 + 1.57039I
b = 0.620567 − 0.112346I
−3.95002 − 0.09061I −6.51478 + 0.23122I
u = −0.014446 − 1.158610I
a = 1.74504 − 1.57039I
b = 0.620567 + 0.112346I
−3.95002 + 0.09061I −6.51478 − 0.23122I
u = −0.120439 + 0.677633I
a = −0.99346 − 2.55992I
b = 0.620567 + 0.112346I
−3.95002 + 0.09061I −6.51478 − 0.23122I
u = −0.120439 − 0.677633I
a = −0.99346 + 2.55992I
b = 0.620567 − 0.112346I
−3.95002 − 0.09061I −6.51478 + 0.23122I
u = −0.663607 + 0.149430I
a = 0.173852 + 0.543824I
b = −0.597039 + 0.103194I
−0.91573 + 2.69540I 0.31936 − 2.88879I
u = −0.663607 − 0.149430I
a = 0.173852 − 0.543824I
b = −0.597039 − 0.103194I
−0.91573 − 2.69540I 0.31936 + 2.88879I
u = −0.148951 + 1.396910I
a = −0.44526 − 1.43020I
b = 0.091282 − 0.179107I
−12.49530 − 2.45847I −7.50081 + 0.42962I
u = −0.148951 − 1.396910I
a = −0.44526 + 1.43020I
b = 0.091282 + 0.179107I
−12.49530 + 2.45847I −7.50081 − 0.42962I
u = −0.01413 + 1.43483I
a = 1.178910 − 0.382253I
b = 1.94409 − 0.00042I
−6.39368 + 1.41191I −9.87318 − 3.81508I
u = −0.01413 − 1.43483I
a = 1.178910 + 0.382253I
b = 1.94409 + 0.00042I
−6.39368 − 1.41191I −9.87318 + 3.81508I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47648 + 0.13393I
a = −1.255590 − 0.017191I
b = 2.70698 − 0.92539I
−14.4866 − 8.3929I −9.39875 + 4.58852I
u = −1.47648 − 0.13393I
a = −1.255590 + 0.017191I
b = 2.70698 + 0.92539I
−14.4866 + 8.3929I −9.39875 − 4.58852I
u = 0.23016 + 1.48936I
a = −0.53820 − 1.43603I
b = −1.88899 − 0.49296I
−5.27322 + 4.24963I −9.14655 − 5.18533I
u = 0.23016 − 1.48936I
a = −0.53820 + 1.43603I
b = −1.88899 + 0.49296I
−5.27322 − 4.24963I −9.14655 + 5.18533I
u = 0.64679 + 1.68867I
a = −0.104403 + 1.260500I
b = 2.70698 + 0.92539I
−14.4866 + 8.3929I −9.39875 − 4.58852I
u = 0.64679 − 1.68867I
a = −0.104403 − 1.260500I
b = 2.70698 − 0.92539I
−14.4866 − 8.3929I −9.39875 + 4.58852I
u = −0.80033 + 1.70926I
a = −0.068025 + 0.960101I
b = −3.20267
−19.1114 −12.24106 + 0.I
u = −0.80033 − 1.70926I
a = −0.068025 − 0.960101I
b = −3.20267
−19.1114 −12.24106 + 0.I
13
III. I
u
3
= h−u
3
− u
2
+ 2b − 2u + 1, u
3
+ 3u
2
+ 4a + 2u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
−
1
4
u
3
−
3
4
u
2
−
1
2
u −
1
4
1
2
u
3
+
1
2
u
2
+ u −
1
2
a
7
=
−u
u
3
+ u
a
6
=
−u
u
3
+ u
a
5
=
u
3
u
3
+ u
a
12
=
−u
3
+ u
2
− u + 1
−u
a
2
=
−
5
4
u
3
−
3
4
u
2
−
1
2
u −
1
4
−
1
2
u
3
+
1
2
u
2
−
1
2
a
1
=
−u
3
−u
3
− u
a
4
=
−
1
4
u
3
−
3
4
u
2
−
1
2
u −
1
4
1
2
u
3
+
1
2
u
2
+ u −
1
2
a
9
=
−u
3
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
79
16
u
3
−
85
16
u
2
+
21
8
u −
99
16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
7
, c
9
u
4
+ u
2
+ u + 1
c
8
, c
11
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
10
, c
12
u
4
+ u
2
− u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
y
4
− y
3
+ 2y
2
+ 7y + 4
c
7
, c
9
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
8
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.391417 − 0.855136I
b = −0.173850 + 1.069070I
−0.66484 + 1.39709I −2.54919 − 3.47689I
u = 0.547424 − 0.585652I
a = −0.391417 + 0.855136I
b = −0.173850 − 1.069070I
−0.66484 − 1.39709I −2.54919 + 3.47689I
u = −0.547424 + 1.120870I
a = 0.266417 + 0.460085I
b = −0.576150 + 0.307015I
−4.26996 − 7.64338I −11.9196 + 11.4393I
u = −0.547424 − 1.120870I
a = 0.266417 − 0.460085I
b = −0.576150 − 0.307015I
−4.26996 + 7.64338I −11.9196 − 11.4393I
17
IV.
I
u
4
= h−u
5
−u
3
−u
2
+b−u−1, −u
4
−u
2
+a−u, u
6
+u
5
+2u
4
+2u
3
+2u
2
+2u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
u
4
+ u
2
+ u
u
5
+ u
3
+ u
2
+ u + 1
a
7
=
−u
u
3
+ u
a
6
=
−u
u
3
+ u
a
5
=
u
3
u
3
+ u
a
12
=
u
4
+ u
2
+ u + 1
−u
5
− 2u
3
− u
2
− u − 1
a
2
=
u
4
− u
3
+ u
2
+ u
u
5
+ u
2
+ 1
a
1
=
−u
3
−u
3
− u
a
4
=
u
4
+ u
2
+ u
u
5
+ u
3
+ u
2
+ u + 1
a
9
=
−u
3
u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
5
− 5u
3
− 2u
2
− 5u − 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
(u
3
− u
2
+ 1)
2
c
7
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
(y
3
− y
2
+ 2y −1)
2
c
7
, c
9
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
8
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.684695 + 0.494282I
b = 0.662359 + 0.562280I
−1.91067 + 2.82812I −8.69240 − 3.35914I
u = 0.498832 − 1.001300I
a = −0.684695 − 0.494282I
b = 0.662359 − 0.562280I
−1.91067 − 2.82812I −8.69240 + 3.35914I
u = −0.284920 + 1.115140I
a = −0.50000 + 1.95694I
b = −1.32472
−6.04826 −9.61520 + 0.I
u = −0.284920 − 1.115140I
a = −0.50000 − 1.95694I
b = −1.32472
−6.04826 −9.61520 + 0.I
u = −0.713912 + 0.305839I
a = −0.315305 − 0.494282I
b = 0.662359 + 0.562280I
−1.91067 + 2.82812I −8.69240 − 3.35914I
u = −0.713912 − 0.305839I
a = −0.315305 + 0.494282I
b = 0.662359 − 0.562280I
−1.91067 − 2.82812I −8.69240 + 3.35914I
21
V.
I
u
5
= h−91a
2
u+564au+· · ·−570a−188, a
3
−7a
2
u−5a
2
−4au−a+u−2, u
2
+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
1
a
3
=
a
0.270030a
2
u − 1.67359au + ··· + 1.69139a + 0.557864
a
7
=
−u
0
a
6
=
−0.0207715a
2
u − 0.486647au + ··· + 0.0237389a − 0.504451
0.121662a
2
u − 0.721068au + ··· + 0.718101a + 0.240356
a
5
=
0.100890a
2
u − 1.20772au + ··· + 0.741840a − 0.264095
0.121662a
2
u − 0.721068au + ··· + 0.718101a + 0.240356
a
12
=
0.136499a
2
u − 0.516320au + ··· + 0.415430a + 0.172107
u
a
2
=
−0.0207715a
2
u − 0.486647au + ··· + 0.0237389a − 0.504451
0.121662a
2
u − 0.721068au + ··· + 0.718101a + 0.240356
a
1
=
u
0
a
4
=
0.270030a
2
u − 1.67359au + ··· + 2.69139a + 0.557864
0.270030a
2
u − 1.67359au + ··· + 1.69139a + 0.557864
a
9
=
−0.201780a
2
u + 0.415430au + ··· + 0.516320a + 0.528190
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
56
337
a
2
u −
200
337
a
2
+
1312
337
au +
1284
337
a +
428
337
u −
2684
337
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
u
6
+ 5u
4
+ 10u
2
+ 1
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
, c
10
c
12
(u
2
+ 1)
3
c
8
u
6
− 4u
5
+ 8u
4
+ 28u
3
+ 36u
2
+ 24u + 8
c
11
u
6
+ 4u
5
+ 8u
4
− 28u
3
+ 36u
2
− 24u + 8
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
+ 5y
2
+ 10y + 1)
2
c
7
, c
9
, c
10
c
12
(y + 1)
6
c
8
, c
11
y
6
+ 360y
4
+ 80y
2
+ 64
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.567321 − 0.459293I
b = −1.307140 − 0.215080I
−0.26574 + 2.82812I −8.49024 − 2.97945I
u = 1.000000I
a = 0.163008 + 0.300102I
b = 1.307140 − 0.215080I
−0.26574 − 2.82812I −8.49024 + 2.97945I
u = 1.000000I
a = 5.40431 + 7.15919I
b = − 0.569840I
−4.40332 −15.0195 + 0.I
u = − 1.000000I
a = −0.567321 + 0.459293I
b = −1.307140 + 0.215080I
−0.26574 − 2.82812I −8.49024 + 2.97945I
u = − 1.000000I
a = 0.163008 − 0.300102I
b = 1.307140 + 0.215080I
−0.26574 + 2.82812I −8.49024 − 2.97945I
u = − 1.000000I
a = 5.40431 − 7.15919I
b = 0.569840I
−4.40332 −15.0195 + 0.I
25
VI. I
u
6
= h3b + 4a + 2, 4a
2
− 2a − 11, u − 1i
(i) Arc colorings
a
8
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
3
=
a
−
4
3
a −
2
3
a
7
=
−1
2
a
6
=
−
1
3
a +
5
6
0
a
5
=
−
1
3
a +
5
6
0
a
12
=
−
1
2
a + 2
−1
a
2
=
1
3
a +
7
6
−
4
3
a −
2
3
a
1
=
−a + 3
−2
a
4
=
1
3
a +
2
3
−2
a
9
=
1
2
a − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
15
2
a + 7
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
u
2
c
7
, c
9
(u + 1)
2
c
8
4(4u
2
+ 6u + 1)
c
10
, c
12
(u − 1)
2
c
11
4(4u
2
− 6u + 1)
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
5
y
2
c
7
, c
9
, c
10
c
12
(y −1)
2
c
8
, c
11
16(16y
2
− 28y + 1)
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.42705
b = 1.23607
−7.23771 −3.70290
u = 1.00000
a = 1.92705
b = −3.23607
0.657974 21.4530
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
2
− 3u + 1)(u
3
− u
2
+ 2u − 1)
2
· ((u
14
+ 20u
13
+ ··· + 25u + 1)
2
)(u
24
+ 26u
23
+ ··· − 7007u + 256)
c
2
((u − 1)
10
)(u
2
+ u − 1)(u
3
+ u
2
− 1)
2
(u
14
− 4u
13
+ ··· − u − 1)
2
· (u
24
− 6u
23
+ ··· + u + 16)
c
3
u
10
(u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
14
+ u
13
+ ··· + 20u + 8)
2
· (u
24
+ 2u
23
+ ··· − 96u + 256)
c
4
((u + 1)
10
)(u
2
− u − 1)(u
3
− u
2
+ 1)
2
(u
14
− 4u
13
+ ··· − u − 1)
2
· (u
24
− 6u
23
+ ··· + u + 16)
c
5
u
2
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)(u
6
+ 5u
4
+ 10u
2
+ 1)
· ((u
14
− 2u
13
+ ··· + 4u − 1)
2
)(u
24
+ 6u
23
+ ··· + 624u + 64)
c
6
u
10
(u
2
− u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
14
+ u
13
+ ··· + 20u + 8)
2
· (u
24
+ 2u
23
+ ··· − 96u + 256)
c
7
, c
9
((u + 1)
2
)(u
2
+ 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ ··· − 2u + 1)
· (u
24
− 2u
23
+ ··· + 4u + 1)(u
28
+ 6u
27
+ ··· + 542u + 97)
c
8
16(4u
2
+ 6u + 1)(u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
6
− 4u
5
+ ··· + 24u + 8)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (4u
24
− 10u
23
+ ··· + 56u + 8)(u
28
+ 2u
27
+ ··· − 12530u + 4603)
c
10
, c
12
((u − 1)
2
)(u
2
+ 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ ··· + 2u + 1)
· (u
24
− 2u
23
+ ··· + 4u + 1)(u
28
+ 6u
27
+ ··· + 542u + 97)
c
11
16(4u
2
− 6u + 1)(u
4
+ 2u
3
+ ··· + u + 1)(u
6
+ 3u
5
+ ··· + 2u
3
+ 1)
· (u
6
+ 4u
5
+ ··· − 24u + 8)(4u
24
− 10u
23
+ ··· + 56u + 8)
· (u
28
+ 2u
27
+ ··· − 12530u + 4603)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
(y
2
− 7y + 1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
14
− 48y
13
+ ··· − 153y + 1)
2
· (y
24
− 50y
23
+ ··· − 51129153y + 65536)
c
2
, c
4
(y −1)
10
(y
2
− 3y + 1)(y
3
− y
2
+ 2y −1)
2
· ((y
14
− 20y
13
+ ··· − 25y + 1)
2
)(y
24
− 26y
23
+ ··· + 7007y + 256)
c
3
, c
6
y
10
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y −1)
2
(y
14
− 21y
13
+ ··· − 144y + 64)
2
· (y
24
− 18y
23
+ ··· − 185344y + 65536)
c
5
y
2
(y
3
− y
2
+ 2y −1)
2
(y
3
+ 5y
2
+ 10y + 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· ((y
14
− 6y
13
+ ··· − 8y + 1)
2
)(y
24
+ 4y
23
+ ··· − 69376y + 4096)
c
7
, c
9
, c
10
c
12
((y −1)
2
)(y + 1)
6
(y
4
+ 2y
3
+ ··· + y + 1)(y
6
+ 3y
5
+ ··· + 2y
3
+ 1)
· (y
24
+ 24y
23
+ ··· − 110y + 1)(y
28
+ 22y
27
+ ··· + 47288y + 9409)
c
8
, c
11
256(16y
2
− 28y + 1)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
+ 360y
4
+ 80y
2
+ 64)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(16y
24
− 412y
23
+ ··· − 64y + 64)
· (y
28
− 22y
27
+ ··· + 76721028y + 21187609)
31
