12a
0150
(K12a
0150
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 1 12 4 7 6 8
Solving Sequence
7,10
11 6 12
4,5
9 3 2 8 1
c
10
c
6
c
11
c
5
c
9
c
3
c
2
c
8
c
12
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
35
+ 13u
34
+ ··· + 16b − 7, −17u
35
− 37u
34
+ ··· + 64a + 19, u
36
+ 19u
34
+ ··· − 5u
2
− 1i
I
u
2
= h6.38800 × 10
30
u
55
− 1.52613 × 10
31
u
54
+ ··· + 5.64156 × 10
30
b − 1.61757 × 10
32
,
− 2.85017 × 10
32
u
55
+ 2.45748 × 10
32
u
54
+ ··· + 9.59066 × 10
31
a + 2.82390 × 10
33
,
u
56
− 2u
55
+ ··· − 56u + 17i
I
u
3
= hb, −u
2
+ 2a − u − 3, u
3
+ 2u − 1i
I
u
4
= ha
2
+ 2au + 2b + 2a + 2u, a
3
+ 2a
2
u + 2a
2
+ 2au + 2u − 2, u
2
+ 1i
I
u
5
= hb, u
3
+ a + u + 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 105 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−u
35
+ 13u
34
+ · · · + 16b − 7, −17u
35
− 37u
34
+ · · · + 64a +
19, u
36
+ 19u
34
+ · · · − 5u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
6
=
−u
u
3
+ u
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
0.265625u
35
+ 0.578125u
34
+ ··· − 5.60938u − 0.296875
0.0625000u
35
− 0.812500u
34
+ ··· − 0.937500u + 0.437500
a
5
=
−u
3
− 2u
u
3
+ u
a
9
=
u
3
+ 2u
−
1
8
u
34
−
9
4
u
32
+ ··· + u +
1
8
a
3
=
0.453125u
35
− 0.109375u
34
+ ··· − 5.67188u + 0.0156250
0.187500u
35
+ 0.812500u
34
+ ··· − 0.812500u − 0.687500
a
2
=
0.234375u
35
− 0.328125u
34
+ ··· − 4.64063u − 0.453125
1
4
u
35
+
3
8
u
34
+ ··· −
5
4
u −
1
8
a
8
=
u
−
1
8
u
34
−
9
4
u
32
+ ··· + u +
1
8
a
1
=
1
1
8
u
35
+
9
4
u
33
+ ··· − 3u
2
−
1
8
u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
187
128
u
35
+
159
128
u
34
+ ··· +
2051
128
u +
391
128
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 16u
35
+ ··· + 1009u + 16
c
2
, c
4
u
36
− 4u
35
+ ··· + 41u − 4
c
3
, c
9
u
36
− 3u
35
+ ··· − 200u + 32
c
5
u
36
+ 6u
35
+ ··· − 1024u − 256
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
36
+ 19u
34
+ ··· − 5u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 12y
35
+ ··· − 838433y + 256
c
2
, c
4
y
36
− 16y
35
+ ··· − 1009y + 16
c
3
, c
9
y
36
− 21y
35
+ ··· − 13632y + 1024
c
5
y
36
− 10y
35
+ ··· + 1277952y + 65536
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
36
+ 38y
35
+ ··· + 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799527 + 0.176704I
a = −2.18880 − 0.45142I
b = 1.268070 − 0.575288I
4.74793 − 7.85320I 10.04645 + 6.82462I
u = −0.799527 − 0.176704I
a = −2.18880 + 0.45142I
b = 1.268070 + 0.575288I
4.74793 + 7.85320I 10.04645 − 6.82462I
u = −0.800607 + 0.101659I
a = 2.31721 + 0.28975I
b = −1.291650 + 0.333161I
6.52211 − 2.11667I 12.90027 + 1.65144I
u = −0.800607 − 0.101659I
a = 2.31721 − 0.28975I
b = −1.291650 − 0.333161I
6.52211 + 2.11667I 12.90027 − 1.65144I
u = 0.185932 + 1.257960I
a = −1.049650 + 0.171429I
b = 1.49538 − 0.38047I
−1.32995 − 0.96493I 1.34412 − 1.32210I
u = 0.185932 − 1.257960I
a = −1.049650 − 0.171429I
b = 1.49538 + 0.38047I
−1.32995 + 0.96493I 1.34412 + 1.32210I
u = 0.707581 + 0.074386I
a = −0.078771 + 0.776564I
b = 0.233551 − 0.999375I
1.47492 + 2.13531I 9.68335 − 3.80042I
u = 0.707581 − 0.074386I
a = −0.078771 − 0.776564I
b = 0.233551 + 0.999375I
1.47492 − 2.13531I 9.68335 + 3.80042I
u = 0.256428 + 1.268940I
a = 1.158250 − 0.431595I
b = −1.50604 + 0.08197I
−0.50515 + 5.47281I 3.56359 − 6.08643I
u = 0.256428 − 1.268940I
a = 1.158250 + 0.431595I
b = −1.50604 − 0.08197I
−0.50515 − 5.47281I 3.56359 + 6.08643I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655018
a = −3.09255
b = 0.837842
0.0745611 12.4420
u = −0.270723 + 1.357970I
a = −0.434177 − 0.095111I
b = −0.105956 − 1.152130I
−6.77626 − 4.69556I 0
u = −0.270723 − 1.357970I
a = −0.434177 + 0.095111I
b = −0.105956 + 1.152130I
−6.77626 + 4.69556I 0
u = 0.432384 + 0.427628I
a = −0.414829 + 0.874160I
b = 1.078680 − 0.178305I
1.50887 − 1.02448I 9.47604 − 1.44360I
u = 0.432384 − 0.427628I
a = −0.414829 − 0.874160I
b = 1.078680 + 0.178305I
1.50887 + 1.02448I 9.47604 + 1.44360I
u = 0.257005 + 0.526031I
a = 0.362281 − 0.956728I
b = −1.160170 − 0.273905I
1.25861 + 3.83246I 8.43096 − 7.69033I
u = 0.257005 − 0.526031I
a = 0.362281 + 0.956728I
b = −1.160170 + 0.273905I
1.25861 − 3.83246I 8.43096 + 7.69033I
u = 0.29960 + 1.38694I
a = −1.67352 + 0.92125I
b = 1.085350 + 0.310979I
−9.07301 + 7.01583I 0
u = 0.29960 − 1.38694I
a = −1.67352 − 0.92125I
b = 1.085350 − 0.310979I
−9.07301 − 7.01583I 0
u = −0.07865 + 1.42029I
a = −0.398304 − 0.466774I
b = 0.718949 − 0.847255I
−9.22257 − 2.95016I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07865 − 1.42029I
a = −0.398304 + 0.466774I
b = 0.718949 + 0.847255I
−9.22257 + 2.95016I 0
u = −0.32955 + 1.39003I
a = 0.471381 − 0.002675I
b = 0.450280 + 1.163260I
−7.96782 − 9.82231I 0
u = −0.32955 − 1.39003I
a = 0.471381 + 0.002675I
b = 0.450280 − 1.163260I
−7.96782 + 9.82231I 0
u = 0.36777 + 1.38101I
a = 1.29940 − 1.07583I
b = −1.31910 − 0.56226I
−2.87873 + 10.65860I 0
u = 0.36777 − 1.38101I
a = 1.29940 + 1.07583I
b = −1.31910 + 0.56226I
−2.87873 − 10.65860I 0
u = 0.02175 + 1.45011I
a = 0.585925 + 0.756135I
b = −0.821813 + 0.809606I
−12.81680 + 1.42112I 0
u = 0.02175 − 1.45011I
a = 0.585925 − 0.756135I
b = −0.821813 − 0.809606I
−12.81680 − 1.42112I 0
u = 0.38371 + 1.41444I
a = −1.25562 + 1.21879I
b = 1.26488 + 0.73094I
−5.3479 + 16.6018I 0
u = 0.38371 − 1.41444I
a = −1.25562 − 1.21879I
b = 1.26488 − 0.73094I
−5.3479 − 16.6018I 0
u = −0.25014 + 1.49745I
a = 0.196746 − 0.200364I
b = 0.623960 + 0.219536I
−10.76370 − 4.55503I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25014 − 1.49745I
a = 0.196746 + 0.200364I
b = 0.623960 − 0.219536I
−10.76370 + 4.55503I 0
u = −0.11074 + 1.53043I
a = 0.086477 + 0.589795I
b = −0.884099 + 0.624341I
−12.5319 − 6.8373I 0
u = −0.11074 − 1.53043I
a = 0.086477 − 0.589795I
b = −0.884099 − 0.624341I
−12.5319 + 6.8373I 0
u = 0.361676
a = −0.636362
b = 0.360388
0.595912 16.6720
u = −0.125553 + 0.232110I
a = 0.13047 − 2.31300I
b = −0.229374 − 0.520047I
−1.60873 − 0.57225I −2.19533 + 2.55248I
u = −0.125553 − 0.232110I
a = 0.13047 + 2.31300I
b = −0.229374 + 0.520047I
−1.60873 + 0.57225I −2.19533 − 2.55248I
8
II. I
u
2
= h6.39 × 10
30
u
55
− 1.53 × 10
31
u
54
+ · · · + 5.64 × 10
30
b − 1.62 ×
10
32
, −2.85 × 10
32
u
55
+ 2.46 × 10
32
u
54
+ · · · + 9.59 × 10
31
a + 2.82 ×
10
33
, u
56
− 2u
55
+ · · · − 56u + 17i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
6
=
−u
u
3
+ u
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
2.97182u
55
− 2.56237u
54
+ ··· + 38.6228u − 29.4443
−1.13231u
55
+ 2.70516u
54
+ ··· − 67.9361u + 28.6724
a
5
=
−u
3
− 2u
u
3
+ u
a
9
=
1.37378u
55
− 2.05523u
54
+ ··· + 22.6847u − 10.9962
0.0862068u
55
+ 0.310131u
54
+ ··· + 3.93944u − 6.65451
a
3
=
0.196643u
55
+ 1.09359u
54
+ ··· − 62.9416u + 28.7866
−1.02772u
55
+ 2.29208u
54
+ ··· − 38.3434u + 7.61269
a
2
=
−0.813487u
55
+ 2.59847u
54
+ ··· − 136.206u + 65.7422
−0.104046u
55
+ 1.60090u
54
+ ··· − 20.3881u − 5.41843
a
8
=
−0.275698u
55
+ 0.0983321u
54
+ ··· − 35.0403u + 22.8321
1.64947u
55
− 2.15356u
54
+ ··· + 59.7250u − 33.8282
a
1
=
1.53683u
55
− 2.73915u
54
+ ··· + 92.2768u − 48.0224
−0.453063u
55
− 0.408827u
54
+ ··· + 7.39298u + 6.68686
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.98882u
55
− 5.95966u
54
+ ··· + 21.5498u + 4.33068
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
28
+ 13u
27
+ ··· − 7u + 1)
2
c
2
, c
4
(u
28
− 3u
27
+ ··· − u + 1)
2
c
3
, c
9
(u
28
+ u
27
+ ··· + 8u + 4)
2
c
5
(u
28
− 2u
27
+ ··· − 22u + 17)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
56
− 2u
55
+ ··· − 56u + 17
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 7y
27
+ ··· − 61y + 1)
2
c
2
, c
4
(y
28
− 13y
27
+ ··· + 7y + 1)
2
c
3
, c
9
(y
28
− 15y
27
+ ··· − 88y + 16)
2
c
5
(y
28
− 10y
27
+ ··· − 246y + 289)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
56
+ 42y
55
+ ··· − 824y + 289
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699981 + 0.709842I
a = −0.932475 − 0.375700I
b = 0.910131 − 0.395689I
−4.85759 − 4.24816I 2.11355 + 6.97904I
u = −0.699981 − 0.709842I
a = −0.932475 + 0.375700I
b = 0.910131 + 0.395689I
−4.85759 + 4.24816I 2.11355 − 6.97904I
u = −0.405666 + 0.949027I
a = −1.45587 − 0.57456I
b = 0.387411 − 0.832689I
−5.14204 + 1.40144I 0. − 1.74630I
u = −0.405666 − 0.949027I
a = −1.45587 + 0.57456I
b = 0.387411 + 0.832689I
−5.14204 − 1.40144I 0. + 1.74630I
u = 0.910837 + 0.220913I
a = 2.06125 − 0.14881I
b = −1.241130 − 0.661367I
−0.16281 + 11.95450I 5.04116 − 8.32221I
u = 0.910837 − 0.220913I
a = 2.06125 + 0.14881I
b = −1.241130 + 0.661367I
−0.16281 − 11.95450I 5.04116 + 8.32221I
u = −0.779705 + 0.500231I
a = 0.591475 + 0.474962I
b = −0.802767 − 0.244916I
−4.25756 − 0.90628I 4.59768 − 1.67094I
u = −0.779705 − 0.500231I
a = 0.591475 − 0.474962I
b = −0.802767 + 0.244916I
−4.25756 + 0.90628I 4.59768 + 1.67094I
u = −0.352136 + 1.047700I
a = 0.764728 + 0.330487I
b = −1.280370 − 0.446560I
2.10501 + 3.62399I 0
u = −0.352136 − 1.047700I
a = 0.764728 − 0.330487I
b = −1.280370 + 0.446560I
2.10501 − 3.62399I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.864130 + 0.172111I
a = −2.23241 + 0.01733I
b = 1.262900 + 0.460239I
2.03115 + 6.23266I 8.14975 − 4.30079I
u = 0.864130 − 0.172111I
a = −2.23241 − 0.01733I
b = 1.262900 − 0.460239I
2.03115 − 6.23266I 8.14975 + 4.30079I
u = 0.384208 + 0.766757I
a = −1.93610 − 0.04267I
b = 0.611767 − 0.458091I
−5.69220 + 0.64414I −0.353981 + 1.306831I
u = 0.384208 − 0.766757I
a = −1.93610 + 0.04267I
b = 0.611767 + 0.458091I
−5.69220 − 0.64414I −0.353981 − 1.306831I
u = −0.797014 + 0.216598I
a = 0.436400 + 0.813553I
b = −0.387502 − 1.047530I
−2.87718 − 5.75423I 3.89302 + 5.96655I
u = −0.797014 − 0.216598I
a = 0.436400 − 0.813553I
b = −0.387502 + 1.047530I
−2.87718 + 5.75423I 3.89302 − 5.96655I
u = 0.468961 + 1.091940I
a = 0.904715 − 0.796492I
b = −1.147340 + 0.340892I
−0.76674 − 1.47542I 0
u = 0.468961 − 1.091940I
a = 0.904715 + 0.796492I
b = −1.147340 − 0.340892I
−0.76674 + 1.47542I 0
u = 0.564404 + 1.054850I
a = −0.731475 + 0.538685I
b = 1.175470 − 0.589984I
−2.69009 − 6.77427I 0
u = 0.564404 − 1.054850I
a = −0.731475 − 0.538685I
b = 1.175470 + 0.589984I
−2.69009 + 6.77427I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358032 + 1.151180I
a = −0.994941 − 0.598679I
b = 1.312590 + 0.177484I
3.32245 − 2.08114I 0
u = −0.358032 − 1.151180I
a = −0.994941 + 0.598679I
b = 1.312590 − 0.177484I
3.32245 + 2.08114I 0
u = 0.054476 + 1.226080I
a = 0.070708 − 0.771010I
b = −0.376924 − 0.508425I
−3.06671 + 1.43304I 0
u = 0.054476 − 1.226080I
a = 0.070708 + 0.771010I
b = −0.376924 + 0.508425I
−3.06671 − 1.43304I 0
u = 0.727104 + 0.234303I
a = 2.86700 − 0.21576I
b = −0.907099 − 0.252760I
−3.94179 + 3.28147I 5.23266 − 4.99392I
u = 0.727104 − 0.234303I
a = 2.86700 + 0.21576I
b = −0.907099 + 0.252760I
−3.94179 − 3.28147I 5.23266 + 4.99392I
u = 0.251940 + 1.214590I
a = 0.623338 − 0.426042I
b = −0.017123 − 0.961380I
−1.96777 + 1.34593I 0
u = 0.251940 − 1.214590I
a = 0.623338 + 0.426042I
b = −0.017123 + 0.961380I
−1.96777 − 1.34593I 0
u = 0.065420 + 1.241340I
a = −1.01865 + 2.07478I
b = 0.611767 + 0.458091I
−5.69220 − 0.64414I 0
u = 0.065420 − 1.241340I
a = −1.01865 − 2.07478I
b = 0.611767 − 0.458091I
−5.69220 + 0.64414I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173270 + 1.242230I
a = 0.908391 + 1.036680I
b = 0.387411 + 0.832689I
−5.14204 − 1.40144I 0
u = −0.173270 − 1.242230I
a = 0.908391 − 1.036680I
b = 0.387411 − 0.832689I
−5.14204 + 1.40144I 0
u = 0.691070 + 0.028094I
a = −2.45000 + 0.76218I
b = 1.312590 + 0.177484I
3.32245 − 2.08114I 9.79595 + 2.78862I
u = 0.691070 − 0.028094I
a = −2.45000 − 0.76218I
b = 1.312590 − 0.177484I
3.32245 + 2.08114I 9.79595 − 2.78862I
u = −0.254280 + 1.286460I
a = 1.76847 + 1.19991I
b = −0.907099 + 0.252760I
−3.94179 − 3.28147I 0
u = −0.254280 − 1.286460I
a = 1.76847 − 1.19991I
b = −0.907099 − 0.252760I
−3.94179 + 3.28147I 0
u = 0.286920 + 1.282550I
a = 0.74733 − 1.53936I
b = −1.147340 − 0.340892I
−0.76674 + 1.47542I 0
u = 0.286920 − 1.282550I
a = 0.74733 + 1.53936I
b = −1.147340 + 0.340892I
−0.76674 − 1.47542I 0
u = −0.636644 + 0.157884I
a = −0.333609 − 1.000990I
b = −0.017123 + 0.961380I
−1.96777 − 1.34593I 5.91932 + 0.66126I
u = −0.636644 − 0.157884I
a = −0.333609 + 1.000990I
b = −0.017123 − 0.961380I
−1.96777 + 1.34593I 5.91932 − 0.66126I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.291088 + 1.313610I
a = −0.713814 + 0.243496I
b = −0.387502 + 1.047530I
−2.87718 + 5.75423I 0
u = 0.291088 − 1.313610I
a = −0.713814 − 0.243496I
b = −0.387502 − 1.047530I
−2.87718 − 5.75423I 0
u = −0.405124 + 0.480475I
a = 1.058260 − 0.685910I
b = −0.376924 + 0.508425I
−3.06671 − 1.43304I 5.58225 + 4.97603I
u = −0.405124 − 0.480475I
a = 1.058260 + 0.685910I
b = −0.376924 − 0.508425I
−3.06671 + 1.43304I 5.58225 − 4.97603I
u = −0.342351 + 1.329390I
a = −1.15193 − 1.31181I
b = 1.262900 − 0.460239I
2.03115 − 6.23266I 0
u = −0.342351 − 1.329390I
a = −1.15193 + 1.31181I
b = 1.262900 + 0.460239I
2.03115 + 6.23266I 0
u = 0.254428 + 1.359510I
a = −0.57743 + 1.67051I
b = 1.175470 + 0.589984I
−2.69009 + 6.77427I 0
u = 0.254428 − 1.359510I
a = −0.57743 − 1.67051I
b = 1.175470 − 0.589984I
−2.69009 − 6.77427I 0
u = 0.591934 + 0.141506I
a = 2.29632 − 1.21300I
b = −1.280370 − 0.446560I
2.10501 + 3.62399I 8.20871 − 2.76186I
u = 0.591934 − 0.141506I
a = 2.29632 + 1.21300I
b = −1.280370 + 0.446560I
2.10501 − 3.62399I 8.20871 + 2.76186I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003051 + 1.410480I
a = 0.649306 + 0.505190I
b = 0.910131 + 0.395689I
−4.85759 + 4.24816I 0
u = −0.003051 − 1.410480I
a = 0.649306 − 0.505190I
b = 0.910131 − 0.395689I
−4.85759 − 4.24816I 0
u = 0.136440 + 1.404460I
a = −0.588564 − 0.154002I
b = −0.802767 + 0.244916I
−4.25756 + 0.90628I 0
u = 0.136440 − 1.404460I
a = −0.588564 + 0.154002I
b = −0.802767 − 0.244916I
−4.25756 − 0.90628I 0
u = −0.33611 + 1.37531I
a = 1.07544 + 1.49026I
b = −1.241130 + 0.661367I
−0.16281 − 11.95450I 0
u = −0.33611 − 1.37531I
a = 1.07544 − 1.49026I
b = −1.241130 − 0.661367I
−0.16281 + 11.95450I 0
17
III. I
u
3
= hb, −u
2
+ 2a − u − 3, u
3
+ 2u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
6
=
−u
−u + 1
a
12
=
u
2
+ 1
−u
a
4
=
1
2
u
2
+
1
2
u +
3
2
0
a
5
=
−1
−u + 1
a
9
=
1
0
a
3
=
1
2
u
2
+
1
2
u +
3
2
0
a
2
=
1
2
u
2
+
1
2
u +
5
2
u − 1
a
8
=
u
u
2
a
1
=
1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
4
u
2
+
21
4
u +
9
4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
9
u
3
c
4
(u + 1)
3
c
5
u
3
+ 3u
2
+ 5u + 2
c
6
, c
7
, c
8
u
3
+ 2u + 1
c
10
, c
11
, c
12
u
3
+ 2u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
9
y
3
c
5
y
3
+ y
2
+ 13y −4
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.335258 + 0.401127I
b = 0
−11.08570 − 5.13794I −2.62004 + 6.54094I
u = −0.22670 − 1.46771I
a = 0.335258 − 0.401127I
b = 0
−11.08570 + 5.13794I −2.62004 − 6.54094I
u = 0.453398
a = 1.82948
b = 0
−0.857735 4.99010
21
IV. I
u
4
= ha
2
+ 2au + 2b + 2a + 2u, a
3
+ 2a
2
u + 2a
2
+ 2au + 2u − 2, u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
1
a
6
=
−u
0
a
12
=
0
1
a
4
=
a
−
1
2
a
2
− au − a − u
a
5
=
−u
0
a
9
=
u
1
2
a
2
u +
1
2
au −
1
2
a + 1
a
3
=
1
2
a
2
u + au − 1
1
2
au +
1
2
a + u
a
2
=
1
2
a
2
u +
1
2
au −
1
2
a − u − 1
1
2
au +
1
2
a + u
a
8
=
u
1
2
a
2
u +
1
2
au −
1
2
a + u + 1
a
1
=
−1
−
1
2
a
2
−
1
2
au −
1
2
a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2au + 2a + 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
9
u
6
− 3u
4
+ 2u
2
+ 1
c
4
(u
3
− u
2
+ 1)
2
c
5
u
6
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(u
2
+ 1)
3
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
3
, c
9
(y
3
− 3y
2
+ 2y + 1)
2
c
5
y
6
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y + 1)
6
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.867423 + 0.622301I
b = 1.307140 − 0.215080I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = 1.000000I
a = 0.622301 − 0.867423I
b = −1.307140 − 0.215080I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = 1.000000I
a = −1.75488 − 1.75488I
b = − 0.569840I
−4.40332 −3.01951 + 0.I
u = − 1.000000I
a = −0.867423 − 0.622301I
b = 1.307140 + 0.215080I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = − 1.000000I
a = 0.622301 + 0.867423I
b = −1.307140 + 0.215080I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = − 1.000000I
a = −1.75488 + 1.75488I
b = 0.569840I
−4.40332 −3.01951 + 0.I
25
V. I
u
5
= hb, u
3
+ a + u + 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
6
=
−u
u
3
+ u
a
12
=
u
2
+ 1
u
3
+ 2u + 1
a
4
=
−u
3
− u − 1
0
a
5
=
−u
3
− 2u
u
3
+ u
a
9
=
1
0
a
3
=
−u
3
− u − 1
0
a
2
=
u − 1
−u
3
− u
a
8
=
2u
3
+ u
2
+ 3u + 3
−u
3
− u
2
− u − 2
a
1
=
u
3
+ 2u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
+ 4u + 3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
9
u
4
c
4
(u + 1)
4
c
5
(u
2
− u + 1)
2
c
6
, c
7
, c
8
u
4
− u
3
+ 2u
2
− 2u + 1
c
10
, c
11
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
9
y
4
c
5
(y
2
+ y + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −0.500000 − 0.866025I
b = 0
−4.93480 − 2.02988I 1.0000 + 3.46410I
u = −0.621744 − 0.440597I
a = −0.500000 + 0.866025I
b = 0
−4.93480 + 2.02988I 1.0000 − 3.46410I
u = 0.121744 + 1.306620I
a = −0.500000 + 0.866025I
b = 0
−4.93480 + 2.02988I 1.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = −0.500000 − 0.866025I
b = 0
−4.93480 − 2.02988I 1.00000 + 3.46410I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
7
)(u
3
− u
2
+ 2u − 1)
2
(u
28
+ 13u
27
+ ··· − 7u + 1)
2
· (u
36
+ 16u
35
+ ··· + 1009u + 16)
c
2
((u − 1)
7
)(u
3
+ u
2
− 1)
2
(u
28
− 3u
27
+ ··· − u + 1)
2
· (u
36
− 4u
35
+ ··· + 41u − 4)
c
3
, c
9
u
7
(u
6
− 3u
4
+ 2u
2
+ 1)(u
28
+ u
27
+ ··· + 8u + 4)
2
· (u
36
− 3u
35
+ ··· − 200u + 32)
c
4
((u + 1)
7
)(u
3
− u
2
+ 1)
2
(u
28
− 3u
27
+ ··· − u + 1)
2
· (u
36
− 4u
35
+ ··· + 41u − 4)
c
5
u
6
(u
2
− u + 1)
2
(u
3
+ 3u
2
+ 5u + 2)(u
28
− 2u
27
+ ··· − 22u + 17)
2
· (u
36
+ 6u
35
+ ··· − 1024u − 256)
c
6
, c
7
, c
8
(u
2
+ 1)
3
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
36
+ 19u
34
+ ··· − 5u
2
− 1)(u
56
− 2u
55
+ ··· − 56u + 17)
c
10
, c
11
, c
12
(u
2
+ 1)
3
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
36
+ 19u
34
+ ··· − 5u
2
− 1)(u
56
− 2u
55
+ ··· − 56u + 17)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
7
)(y
3
+ 3y
2
+ 2y −1)
2
(y
28
+ 7y
27
+ ··· − 61y + 1)
2
· (y
36
+ 12y
35
+ ··· − 838433y + 256)
c
2
, c
4
((y −1)
7
)(y
3
− y
2
+ 2y −1)
2
(y
28
− 13y
27
+ ··· + 7y + 1)
2
· (y
36
− 16y
35
+ ··· − 1009y + 16)
c
3
, c
9
y
7
(y
3
− 3y
2
+ 2y + 1)
2
(y
28
− 15y
27
+ ··· − 88y + 16)
2
· (y
36
− 21y
35
+ ··· − 13632y + 1024)
c
5
y
6
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
28
− 10y
27
+ ··· − 246y + 289)
2
· (y
36
− 10y
35
+ ··· + 1277952y + 65536)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y + 1)
6
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
36
+ 38y
35
+ ··· + 10y + 1)(y
56
+ 42y
55
+ ··· − 824y + 289)
31
