12a
0978
(K12a
0978
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 10 2 1 12 5 3 9 8
Solving Sequence
1,7 5,8
4 2 6 12 9 10 11 3
c
7
c
4
c
1
c
6
c
12
c
8
c
9
c
11
c
3
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
28
− 27u
27
+ ··· + 4b − 12, −3u
28
+ 33u
27
+ ··· + 8a + 252, u
29
− 9u
28
+ ··· − 100u + 8i
I
u
2
= h−1.23410 × 10
16
a
5
u
8
− 5.81741 × 10
15
a
4
u
8
+ ··· + 7.78751 × 10
15
a + 1.59891 × 10
16
,
− 2u
8
a
4
− u
8
a
3
+ ··· − 51a − 8, u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1i
I
u
3
= h−u
14
+ 2u
13
− 10u
12
+ 16u
11
− 37u
10
+ 47u
9
− 63u
8
+ 60u
7
− 49u
6
+ 28u
5
− 13u
4
− u
3
+ 3u
2
+ b − 2u,
u
14
− 3u
13
+ ··· + a − 2, u
17
− 2u
16
+ ··· + u + 1i
* 3 irreducible components of dim
C
= 0, with total 100 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
= h3u
28
− 27u
27
+ · · · + 4b − 12, −3u
28
+ 33u
27
+ · · · + 8a + 252, u
29
−
9u
28
+ · · · − 100u + 8i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
5
=
3
8
u
28
−
33
8
u
27
+ ··· +
1301
4
u −
63
2
−
3
4
u
28
+
27
4
u
27
+ ··· − 66u + 3
a
8
=
1
u
2
a
4
=
−0.375000u
28
+ 2.62500u
27
+ ··· + 259.250u − 28.5000
−
3
4
u
28
+
27
4
u
27
+ ··· − 66u + 3
a
2
=
5
8
u
28
−
51
8
u
27
+ ··· +
1525
4
u − 36
−
3
4
u
28
+
25
4
u
27
+ ··· +
55
2
u − 5
a
6
=
23
8
u
28
−
203
8
u
27
+ ··· +
995
2
u − 45
−
1
2
u
27
+
9
2
u
26
+ ··· +
323
2
u − 17
a
12
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−
3
8
u
28
+
29
8
u
27
+ ··· −
343
4
u + 8
−
1
4
u
28
+
7
4
u
27
+ ··· −
101
2
u + 5
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
3
=
2.62500u
28
− 22.3750u
27
+ ··· + 419.250u − 40.5000
5
4
u
28
−
45
4
u
27
+ ··· + 286u − 27
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
28
− 31u
27
+ 186u
26
− 798u
25
+ 2869u
24
− 8634u
23
+
22638u
22
− 52004u
21
+ 106076u
20
− 192765u
19
+ 313260u
18
− 455019u
17
+ 589368u
16
−
676516u
15
+ 680694u
14
− 588454u
13
+ 420170u
12
− 224488u
11
+ 56862u
10
+ 46163u
9
−
80407u
8
+ 68178u
7
− 39610u
6
+ 15736u
5
− 3305u
4
− 530u
3
+ 703u
2
− 254u + 34
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
29
− u
28
+ ··· + 9u + 1
c
2
, c
6
u
29
− 18u
28
+ ··· − 6144u + 512
c
3
, c
5
, c
9
c
10
u
29
− u
28
+ ··· + 2u + 1
c
7
, c
8
, c
11
c
12
u
29
− 9u
28
+ ··· − 100u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
29
+ 9y
28
+ ··· + 51y −1
c
2
, c
6
y
29
+ 18y
28
+ ··· + 524288y −262144
c
3
, c
5
, c
9
c
10
y
29
− 23y
28
+ ··· − 2y −1
c
7
, c
8
, c
11
c
12
y
29
+ 33y
28
+ ··· − 112y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.604842 + 0.799420I
a = 0.394109 − 1.305310I
b = 1.11393 + 1.05287I
−8.0468 − 12.8405I −10.86733 + 8.44096I
u = 0.604842 − 0.799420I
a = 0.394109 + 1.305310I
b = 1.11393 − 1.05287I
−8.0468 + 12.8405I −10.86733 − 8.44096I
u = 0.679595 + 0.725392I
a = −0.526243 + 0.748082I
b = −0.604806 − 0.973958I
−1.79348 − 6.74869I −9.01372 + 8.18968I
u = 0.679595 − 0.725392I
a = −0.526243 − 0.748082I
b = −0.604806 + 0.973958I
−1.79348 + 6.74869I −9.01372 − 8.18968I
u = 0.864891 + 0.414155I
a = 0.350853 + 0.068689I
b = −0.250971 + 0.745879I
−2.88495 + 1.60167I −6.91098 − 4.21579I
u = 0.864891 − 0.414155I
a = 0.350853 − 0.068689I
b = −0.250971 − 0.745879I
−2.88495 − 1.60167I −6.91098 + 4.21579I
u = 0.805829 + 0.143852I
a = 0.028988 − 0.359456I
b = 0.952881 − 0.764359I
−10.03050 + 8.17766I −13.8601 − 5.1610I
u = 0.805829 − 0.143852I
a = 0.028988 + 0.359456I
b = 0.952881 + 0.764359I
−10.03050 − 8.17766I −13.8601 + 5.1610I
u = 0.125066 + 0.771350I
a = 0.715740 − 0.947825I
b = 0.281937 + 0.744077I
2.49819 + 0.56084I −0.83766 − 3.02068I
u = 0.125066 − 0.771350I
a = 0.715740 + 0.947825I
b = 0.281937 − 0.744077I
2.49819 − 0.56084I −0.83766 + 3.02068I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514232 + 1.160970I
a = −0.753282 − 0.069149I
b = 0.572931 − 0.504230I
−6.11139 + 3.64867I −10.51258 − 6.38309I
u = 0.514232 − 1.160970I
a = −0.753282 + 0.069149I
b = 0.572931 + 0.504230I
−6.11139 − 3.64867I −10.51258 + 6.38309I
u = 0.259282 + 0.636659I
a = −0.91563 + 1.57663I
b = −0.847475 − 0.963533I
0.67008 − 3.51851I −3.24653 + 1.59762I
u = 0.259282 − 0.636659I
a = −0.91563 − 1.57663I
b = −0.847475 + 0.963533I
0.67008 + 3.51851I −3.24653 − 1.59762I
u = −0.654920
a = 0.325115
b = −0.128661
−0.994337 −5.14270
u = 0.27416 + 1.57663I
a = 0.364136 − 0.936698I
b = 0.213812 + 0.901583I
3.76330 − 2.62652I 0
u = 0.27416 − 1.57663I
a = 0.364136 + 0.936698I
b = 0.213812 − 0.901583I
3.76330 + 2.62652I 0
u = 0.06542 + 1.60221I
a = 0.25871 + 1.88519I
b = −1.06635 − 1.25262I
8.42220 − 4.67294I 0
u = 0.06542 − 1.60221I
a = 0.25871 − 1.88519I
b = −1.06635 + 1.25262I
8.42220 + 4.67294I 0
u = 0.04590 + 1.62872I
a = 0.00837 − 1.44018I
b = 0.652195 + 1.058360I
10.81300 − 0.15593I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04590 − 1.62872I
a = 0.00837 + 1.44018I
b = 0.652195 − 1.058360I
10.81300 + 0.15593I 0
u = 0.19961 + 1.62106I
a = −0.04569 + 1.63892I
b = −0.77835 − 1.26024I
6.09827 − 10.02090I 0
u = 0.19961 − 1.62106I
a = −0.04569 − 1.63892I
b = −0.77835 + 1.26024I
6.09827 + 10.02090I 0
u = 0.275491 + 0.216775I
a = 0.40956 + 1.65132I
b = −0.516630 + 0.595869I
−0.45318 + 1.49811I −4.17600 − 5.66136I
u = 0.275491 − 0.216775I
a = 0.40956 − 1.65132I
b = −0.516630 − 0.595869I
−0.45318 − 1.49811I −4.17600 + 5.66136I
u = 0.18131 + 1.64123I
a = −0.33033 − 1.94950I
b = 1.20109 + 1.31387I
0.2220 − 15.8446I 0
u = 0.18131 − 1.64123I
a = −0.33033 + 1.94950I
b = 1.20109 − 1.31387I
0.2220 + 15.8446I 0
u = −0.06816 + 1.65589I
a = 0.128156 + 0.626015I
b = −0.359867 − 0.399152I
5.55507 + 2.59285I 0
u = −0.06816 − 1.65589I
a = 0.128156 − 0.626015I
b = −0.359867 + 0.399152I
5.55507 − 2.59285I 0
7
II. I
u
2
= h−1.23 × 10
16
a
5
u
8
− 5.82 × 10
15
a
4
u
8
+ · · · + 7.79 × 10
15
a + 1.60 ×
10
16
, −2u
8
a
4
− u
8
a
3
+ · · · − 51a − 8, u
9
+ u
8
+ · · · + u + 1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
5
=
a
0.513262a
5
u
8
+ 0.241947a
4
u
8
+ ··· − 0.323883a − 0.664986
a
8
=
1
u
2
a
4
=
0.513262a
5
u
8
+ 0.241947a
4
u
8
+ ··· + 0.676117a − 0.664986
0.513262a
5
u
8
+ 0.241947a
4
u
8
+ ··· − 0.323883a − 0.664986
a
2
=
−0.603905a
5
u
8
− 0.0780679a
4
u
8
+ ··· + 0.720120a − 0.843094
−0.404937a
5
u
8
+ 0.00574372a
4
u
8
+ ··· + 0.605027a − 0.598552
a
6
=
−1.17240a
5
u
8
− 0.330244a
4
u
8
+ ··· + 0.284771a + 1.02793
−0.261374a
5
u
8
− 0.469207a
4
u
8
+ ··· − 0.104560a − 0.0143170
a
12
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−0.404320a
5
u
8
− 0.0844140a
4
u
8
+ ··· + 0.788943a + 1.29237
−0.275144a
5
u
8
+ 0.0139674a
4
u
8
+ ··· + 0.455972a + 0.226517
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
3
=
0.633736a
5
u
8
+ 0.276828a
4
u
8
+ ··· − 0.0682940a − 0.732949
0.666311a
5
u
8
+ 0.463464a
4
u
8
+ ··· − 0.500467a − 0.387131
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
7120397197575888
2671575513101105
u
8
a
5
−
4952713186605196
2671575513101105
u
8
a
4
+ ··· +
82279149703176
41101161740017
a −
11892452399477002
2671575513101105
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
54
− 9u
53
+ ··· + 22u − 1
c
2
, c
6
(u
3
+ u
2
+ 2u + 1)
18
c
3
, c
5
, c
9
c
10
u
54
− u
53
+ ··· + 2198u + 6221
c
7
, c
8
, c
11
c
12
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
54
− 5y
53
+ ··· − 200y + 1
c
2
, c
6
(y
3
+ 3y
2
+ 2y −1)
18
c
3
, c
5
, c
9
c
10
y
54
− 45y
53
+ ··· − 751525392y + 38700841
c
7
, c
8
, c
11
c
12
(y
9
+ 11y
8
+ 48y
7
+ 105y
6
+ 121y
5
+ 73y
4
+ 20y
3
− 6y
2
− 3y −1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429032 + 0.787939I
a = 0.657021 + 0.673116I
b = 0.525744 − 0.533627I
1.34145 + 3.41073I −3.09811 − 4.39642I
u = −0.429032 + 0.787939I
a = −0.185248 − 1.102330I
b = −0.617353 + 0.872102I
1.34145 + 3.41073I −3.09811 − 4.39642I
u = −0.429032 + 0.787939I
a = −0.805501 + 0.871788I
b = 0.505435 + 0.221792I
−2.79613 + 0.58261I −9.62737 − 1.41698I
u = −0.429032 + 0.787939I
a = 0.680646 + 0.092622I
b = −0.732937 − 0.705615I
−2.79613 + 0.58261I −9.62737 − 1.41698I
u = −0.429032 + 0.787939I
a = −0.03604 + 1.55167I
b = 1.31899 − 1.13527I
−2.79613 + 6.23885I −9.62737 − 7.37587I
u = −0.429032 + 0.787939I
a = −0.93584 − 1.51829I
b = −0.878526 + 0.832237I
−2.79613 + 6.23885I −9.62737 − 7.37587I
u = −0.429032 − 0.787939I
a = 0.657021 − 0.673116I
b = 0.525744 + 0.533627I
1.34145 − 3.41073I −3.09811 + 4.39642I
u = −0.429032 − 0.787939I
a = −0.185248 + 1.102330I
b = −0.617353 − 0.872102I
1.34145 − 3.41073I −3.09811 + 4.39642I
u = −0.429032 − 0.787939I
a = −0.805501 − 0.871788I
b = 0.505435 − 0.221792I
−2.79613 − 0.58261I −9.62737 + 1.41698I
u = −0.429032 − 0.787939I
a = 0.680646 − 0.092622I
b = −0.732937 + 0.705615I
−2.79613 − 0.58261I −9.62737 + 1.41698I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429032 − 0.787939I
a = −0.03604 − 1.55167I
b = 1.31899 + 1.13527I
−2.79613 − 6.23885I −9.62737 + 7.37587I
u = −0.429032 − 0.787939I
a = −0.93584 + 1.51829I
b = −0.878526 − 0.832237I
−2.79613 − 6.23885I −9.62737 + 7.37587I
u = −0.590618
a = −1.065320 + 0.113642I
b = −0.764982 + 0.819272I
−5.12213 + 2.82812I −13.8431 − 2.9794I
u = −0.590618
a = −1.065320 − 0.113642I
b = −0.764982 − 0.819272I
−5.12213 − 2.82812I −13.8431 + 2.9794I
u = −0.590618
a = 0.214215 + 0.836149I
b = 1.081010 + 0.550995I
−5.12213 − 2.82812I −13.8431 + 2.9794I
u = −0.590618
a = 0.214215 − 0.836149I
b = 1.081010 − 0.550995I
−5.12213 + 2.82812I −13.8431 − 2.9794I
u = −0.590618
a = 0.503448
b = 0.0621929
−0.984552 −7.31380
u = −0.590618
a = 0.228776
b = −0.334077
−0.984552 −7.31380
u = 0.290170 + 0.487341I
a = −1.45383 + 0.43731I
b = 1.60515 − 1.25639I
−7.92355 − 3.93782I −14.9560 + 9.2189I
u = 0.290170 + 0.487341I
a = −0.269361 − 0.304133I
b = −1.135660 + 0.475716I
−3.78596 − 1.10969I −8.42675 + 6.23947I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.290170 + 0.487341I
a = 2.12283 + 0.28843I
b = 1.025950 + 0.133490I
−7.92355 + 1.71843I −14.9560 + 3.2600I
u = 0.290170 + 0.487341I
a = 0.18762 + 2.78442I
b = −0.491313 − 0.634935I
−3.78596 − 1.10969I −8.42675 + 6.23947I
u = 0.290170 + 0.487341I
a = 0.41956 − 3.09076I
b = 0.70806 + 1.65696I
−7.92355 + 1.71843I −14.9560 + 3.2600I
u = 0.290170 + 0.487341I
a = −0.89854 − 3.40095I
b = 0.443076 − 0.163926I
−7.92355 − 3.93782I −14.9560 + 9.2189I
u = 0.290170 − 0.487341I
a = −1.45383 − 0.43731I
b = 1.60515 + 1.25639I
−7.92355 + 3.93782I −14.9560 − 9.2189I
u = 0.290170 − 0.487341I
a = −0.269361 + 0.304133I
b = −1.135660 − 0.475716I
−3.78596 + 1.10969I −8.42675 − 6.23947I
u = 0.290170 − 0.487341I
a = 2.12283 − 0.28843I
b = 1.025950 − 0.133490I
−7.92355 − 1.71843I −14.9560 − 3.2600I
u = 0.290170 − 0.487341I
a = 0.18762 − 2.78442I
b = −0.491313 + 0.634935I
−3.78596 + 1.10969I −8.42675 − 6.23947I
u = 0.290170 − 0.487341I
a = 0.41956 + 3.09076I
b = 0.70806 − 1.65696I
−7.92355 − 1.71843I −14.9560 − 3.2600I
u = 0.290170 − 0.487341I
a = −0.89854 + 3.40095I
b = 0.443076 + 0.163926I
−7.92355 + 3.93782I −14.9560 − 9.2189I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05587 + 1.55975I
a = 0.957963 − 0.490086I
b = −1.59886 + 0.51276I
3.24228 − 2.21388I −4.73934 + 3.04598I
u = 0.05587 + 1.55975I
a = −0.77028 − 1.67796I
b = 0.0473285 + 0.1306670I
−0.89531 − 5.04200I −11.26860 + 6.02543I
u = 0.05587 + 1.55975I
a = 0.147478 − 0.041645I
b = 1.285880 − 0.019926I
−0.895307 + 0.614244I −11.26860 + 0.06653I
u = 0.05587 + 1.55975I
a = 0.36282 + 2.03388I
b = −0.071170 − 0.998368I
3.24228 − 2.21388I −4.73934 + 3.04598I
u = 0.05587 + 1.55975I
a = −2.28826 + 1.18677I
b = 2.37301 − 1.21408I
−0.89531 − 5.04200I −11.26860 + 6.02543I
u = 0.05587 + 1.55975I
a = −0.15939 − 3.05606I
b = 0.17612 + 2.23225I
−0.895307 + 0.614244I −11.26860 + 0.06653I
u = 0.05587 − 1.55975I
a = 0.957963 + 0.490086I
b = −1.59886 − 0.51276I
3.24228 + 2.21388I −4.73934 − 3.04598I
u = 0.05587 − 1.55975I
a = −0.77028 + 1.67796I
b = 0.0473285 − 0.1306670I
−0.89531 + 5.04200I −11.26860 − 6.02543I
u = 0.05587 − 1.55975I
a = 0.147478 + 0.041645I
b = 1.285880 + 0.019926I
−0.895307 − 0.614244I −11.26860 − 0.06653I
u = 0.05587 − 1.55975I
a = 0.36282 − 2.03388I
b = −0.071170 + 0.998368I
3.24228 + 2.21388I −4.73934 − 3.04598I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05587 − 1.55975I
a = −2.28826 − 1.18677I
b = 2.37301 + 1.21408I
−0.89531 + 5.04200I −11.26860 − 6.02543I
u = 0.05587 − 1.55975I
a = −0.15939 + 3.05606I
b = 0.17612 − 2.23225I
−0.895307 − 0.614244I −11.26860 − 0.06653I
u = −0.12170 + 1.63384I
a = 0.156969 + 0.921253I
b = −0.081545 − 0.567424I
5.50228 + 2.67236I −8.02038 + 0.00647I
u = −0.12170 + 1.63384I
a = 0.002175 + 1.150340I
b = 0.827657 − 0.783679I
9.63986 + 5.50049I −1.49111 − 2.97298I
u = −0.12170 + 1.63384I
a = −0.05149 − 1.68116I
b = −1.015860 + 0.911097I
5.50228 + 8.32861I −8.02038 − 5.95242I
u = −0.12170 + 1.63384I
a = 0.245597 − 0.004809I
b = −0.587278 + 0.080169I
5.50228 + 2.67236I −8.02038 + 0.00647I
u = −0.12170 + 1.63384I
a = 0.18553 − 1.77944I
b = −0.70006 + 1.31119I
9.63986 + 5.50049I −1.49111 − 2.97298I
u = −0.12170 + 1.63384I
a = −0.78744 + 2.22718I
b = 1.38806 − 1.65016I
5.50228 + 8.32861I −8.02038 − 5.95242I
u = −0.12170 − 1.63384I
a = 0.156969 − 0.921253I
b = −0.081545 + 0.567424I
5.50228 − 2.67236I −8.02038 − 0.00647I
u = −0.12170 − 1.63384I
a = 0.002175 − 1.150340I
b = 0.827657 + 0.783679I
9.63986 − 5.50049I −1.49111 + 2.97298I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12170 − 1.63384I
a = −0.05149 + 1.68116I
b = −1.015860 − 0.911097I
5.50228 − 8.32861I −8.02038 + 5.95242I
u = −0.12170 − 1.63384I
a = 0.245597 + 0.004809I
b = −0.587278 − 0.080169I
5.50228 − 2.67236I −8.02038 − 0.00647I
u = −0.12170 − 1.63384I
a = 0.18553 + 1.77944I
b = −0.70006 − 1.31119I
9.63986 − 5.50049I −1.49111 + 2.97298I
u = −0.12170 − 1.63384I
a = −0.78744 − 2.22718I
b = 1.38806 + 1.65016I
5.50228 − 8.32861I −8.02038 + 5.95242I
16
III.
I
u
3
= h−u
14
+2u
13
+· · ·+b−2u, u
14
−3u
13
+· · ·+a−2, u
17
−2u
16
+· · ·+u+1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
5
=
−u
14
+ 3u
13
+ ··· − 5u + 2
u
14
− 2u
13
+ ··· − 3u
2
+ 2u
a
8
=
1
u
2
a
4
=
u
13
− 2u
12
+ ··· − 3u + 2
u
14
− 2u
13
+ ··· − 3u
2
+ 2u
a
2
=
−u
13
+ 2u
12
+ ··· − 3u − 2
−u
14
+ 2u
13
+ ··· − 3u
2
− u
a
6
=
u
16
− 2u
15
+ ··· + 8u + 1
−u
13
+ 2u
12
+ ··· − u − 1
a
12
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−2u
16
+ 5u
15
+ ··· − 4u + 1
u
16
− 2u
15
+ ··· + 2u + 1
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
3
=
−u
14
+ 3u
13
+ ··· − 4u + 2
u
7
− u
6
+ 5u
5
− 4u
4
+ 7u
3
− 4u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
13
−3u
12
+19u
11
−24u
10
+66u
9
−72u
8
+102u
7
−97u
6
+69u
5
−52u
4
+20u
3
−4u
2
+u−9
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
17
− u
16
+ ··· + 2u − 1
c
2
u
17
+ u
16
+ ··· − 10u
2
− 3
c
3
, c
9
u
17
+ u
16
+ ··· + u + 1
c
5
, c
10
u
17
− u
16
+ ··· + u − 1
c
6
u
17
− u
16
+ ··· + 10u
2
+ 3
c
7
, c
8
u
17
− 2u
16
+ ··· + u + 1
c
11
, c
12
u
17
+ 2u
16
+ ··· + u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
− y
16
+ ··· − 8y
2
− 1
c
2
, c
6
y
17
+ 15y
16
+ ··· − 60y −9
c
3
, c
5
, c
9
c
10
y
17
− 17y
16
+ ··· + 11y −1
c
7
, c
8
, c
11
c
12
y
17
+ 22y
16
+ ··· − y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158227 + 0.949272I
a = −1.136970 − 0.062397I
b = 0.576177 − 0.451096I
−5.95683 − 2.21682I −9.81981 + 0.30111I
u = −0.158227 − 0.949272I
a = −1.136970 + 0.062397I
b = 0.576177 + 0.451096I
−5.95683 + 2.21682I −9.81981 − 0.30111I
u = 0.439599 + 0.688982I
a = −0.563792 + 1.172180I
b = −0.860698 − 0.831831I
−0.05785 − 4.28043I −10.18807 + 7.70783I
u = 0.439599 − 0.688982I
a = −0.563792 − 1.172180I
b = −0.860698 + 0.831831I
−0.05785 + 4.28043I −10.18807 − 7.70783I
u = 0.715193 + 0.361678I
a = 0.225758 + 0.289071I
b = −0.415698 + 0.484695I
−1.238940 + 0.551953I −8.26268 − 6.70534I
u = 0.715193 − 0.361678I
a = 0.225758 − 0.289071I
b = −0.415698 − 0.484695I
−1.238940 − 0.551953I −8.26268 + 6.70534I
u = −0.07755 + 1.51837I
a = 0.492857 + 1.111350I
b = −0.826430 − 0.550020I
1.75755 + 1.32675I −10.54146 − 0.18651I
u = −0.07755 − 1.51837I
a = 0.492857 − 1.111350I
b = −0.826430 + 0.550020I
1.75755 − 1.32675I −10.54146 + 0.18651I
u = −0.089258 + 0.450353I
a = 0.54876 − 3.32108I
b = 0.958039 + 0.895126I
−7.51795 + 3.03846I −9.32293 − 1.07500I
u = −0.089258 − 0.450353I
a = 0.54876 + 3.32108I
b = 0.958039 − 0.895126I
−7.51795 − 3.03846I −9.32293 + 1.07500I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02518 + 1.56968I
a = −0.49099 − 1.93094I
b = 1.21011 + 1.14848I
−0.41020 + 3.44403I −9.10995 − 1.06240I
u = −0.02518 − 1.56968I
a = −0.49099 + 1.93094I
b = 1.21011 − 1.14848I
−0.41020 − 3.44403I −9.10995 + 1.06240I
u = 0.11745 + 1.61385I
a = 0.31046 + 1.74278I
b = −1.06077 − 1.14010I
7.84428 − 6.30616I −7.19477 + 5.21827I
u = 0.11745 − 1.61385I
a = 0.31046 − 1.74278I
b = −1.06077 + 1.14010I
7.84428 + 6.30616I −7.19477 − 5.21827I
u = 0.22028 + 1.66250I
a = 0.126398 − 0.701786I
b = 0.248846 + 0.601825I
5.91054 − 3.35847I −0.75485 + 9.25452I
u = 0.22028 − 1.66250I
a = 0.126398 + 0.701786I
b = 0.248846 − 0.601825I
5.91054 + 3.35847I −0.75485 − 9.25452I
u = −0.284621
a = 2.97503
b = −0.659150
−3.95106 −10.6110
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
17
− u
16
+ ··· + 2u − 1)(u
29
− u
28
+ ··· + 9u + 1)
· (u
54
− 9u
53
+ ··· + 22u − 1)
c
2
((u
3
+ u
2
+ 2u + 1)
18
)(u
17
+ u
16
+ ··· − 10u
2
− 3)
· (u
29
− 18u
28
+ ··· − 6144u + 512)
c
3
, c
9
(u
17
+ u
16
+ ··· + u + 1)(u
29
− u
28
+ ··· + 2u + 1)
· (u
54
− u
53
+ ··· + 2198u + 6221)
c
5
, c
10
(u
17
− u
16
+ ··· + u − 1)(u
29
− u
28
+ ··· + 2u + 1)
· (u
54
− u
53
+ ··· + 2198u + 6221)
c
6
((u
3
+ u
2
+ 2u + 1)
18
)(u
17
− u
16
+ ··· + 10u
2
+ 3)
· (u
29
− 18u
28
+ ··· − 6144u + 512)
c
7
, c
8
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1)
6
· (u
17
− 2u
16
+ ··· + u + 1)(u
29
− 9u
28
+ ··· − 100u + 8)
c
11
, c
12
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1)
6
· (u
17
+ 2u
16
+ ··· + u − 1)(u
29
− 9u
28
+ ··· − 100u + 8)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
17
− y
16
+ ··· − 8y
2
− 1)(y
29
+ 9y
28
+ ··· + 51y −1)
· (y
54
− 5y
53
+ ··· − 200y + 1)
c
2
, c
6
((y
3
+ 3y
2
+ 2y −1)
18
)(y
17
+ 15y
16
+ ··· − 60y −9)
· (y
29
+ 18y
28
+ ··· + 524288y −262144)
c
3
, c
5
, c
9
c
10
(y
17
− 17y
16
+ ··· + 11y −1)(y
29
− 23y
28
+ ··· − 2y −1)
· (y
54
− 45y
53
+ ··· − 751525392y + 38700841)
c
7
, c
8
, c
11
c
12
(y
9
+ 11y
8
+ 48y
7
+ 105y
6
+ 121y
5
+ 73y
4
+ 20y
3
− 6y
2
− 3y −1)
6
· (y
17
+ 22y
16
+ ··· − y −1)(y
29
+ 33y
28
+ ··· − 112y −64)
23
