12a
1261
(K12a
1261
)
A knot diagram
1
Linearized knot diagam
5 7 9 10 12 2 11 1 4 3 6 8
Solving Sequence
2,6
7
3,11
8 12 5 1 9 10 4
c
6
c
2
c
7
c
11
c
5
c
1
c
8
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.86400 × 10
38
u
39
+ 1.22276 × 10
38
u
38
+ ··· + 1.38766 × 10
39
b + 6.71756 × 10
39
,
− 1.41733 × 10
40
u
39
+ 5.75302 × 10
39
u
38
+ ··· + 1.38766 × 10
40
a + 1.26988 × 10
41
, u
40
− u
39
+ ··· − 8u + 5i
I
u
2
= h1.49972 × 10
95
u
63
− 1.89102 × 10
95
u
62
+ ··· + 1.42532 × 10
96
b − 6.59620 × 10
93
,
− 9.36179 × 10
96
u
63
+ 6.79343 × 10
96
u
62
+ ··· + 7.12662 × 10
96
a − 8.34927 × 10
96
, u
64
− u
63
+ ··· + 2u − 1i
I
u
3
= hb + u, 8a
3
− 12a
2
u + 4a
2
− 4au − 6a + u − 2, u
2
+ 1i
I
u
4
= hb, a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 111 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−6.86×10
38
u
39
+1.22×10
38
u
38
+· · ·+1.39×10
39
b+6.72×10
39
, −1.42×
10
40
u
39
+5.75×10
39
u
38
+· · ·+1.39×10
40
a+1.27×10
41
, u
40
−u
39
+· · ·−8u+5i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
1.02138u
39
− 0.414584u
38
+ ··· + 4.29657u − 9.15125
0.494646u
39
− 0.0881164u
38
+ ··· + 2.78143u − 4.84092
a
8
=
0.232933u
39
− 0.199072u
38
+ ··· − 0.626073u − 2.92962
0.200267u
39
− 0.138012u
38
+ ··· − 0.0964501u − 2.63367
a
12
=
0.526734u
39
− 0.326467u
38
+ ··· + 1.51515u − 4.31032
0.494646u
39
− 0.0881164u
38
+ ··· + 2.78143u − 4.84092
a
5
=
0.361388u
39
− 0.0370447u
38
+ ··· + 1.83025u + 0.142855
0.407986u
39
− 0.0703407u
38
+ ··· + 1.54549u − 0.676271
a
1
=
0.492873u
39
− 0.140306u
38
+ ··· + 2.58130u − 3.14566
0.432390u
39
+ 0.0156258u
38
+ ··· + 3.81296u − 3.83959
a
9
=
0.585500u
39
− 0.322926u
38
+ ··· + 0.171255u − 5.39399
0.648283u
39
− 0.410746u
38
+ ··· − 0.476912u − 4.79562
a
10
=
0.633625u
39
− 0.286109u
38
+ ··· + 3.62724u − 4.52753
0.902893u
39
− 0.249069u
38
+ ··· + 3.31529u − 8.16823
a
4
=
0.148813u
39
− 0.00235840u
38
+ ··· + 0.508516u + 0.427860
−0.524790u
39
+ 0.102722u
38
+ ··· − 1.39513u + 3.44351
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.246686u
39
+ 0.293708u
38
+ ··· + 1.39766u − 6.81633
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
64(64u
40
+ 128u
39
+ ··· − 18u + 4)
c
2
, c
6
, c
8
c
12
u
40
− u
39
+ ··· − 8u + 5
c
3
, c
4
, c
9
u
40
− 3u
39
+ ··· + 40u + 10
c
5
, c
11
u
40
− 3u
39
+ ··· − 116u + 178
c
10
u
40
+ 9u
39
+ ··· + 223540u + 24310
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
4096(4096y
40
− 16384y
39
+ ··· + 4y + 16)
c
2
, c
6
, c
8
c
12
y
40
− 15y
39
+ ··· − 64y + 25
c
3
, c
4
, c
9
y
40
− 33y
39
+ ··· − 140y + 100
c
5
, c
11
y
40
+ 23y
39
+ ··· + 897548y + 31684
c
10
y
40
+ 19y
39
+ ··· − 3244220940y + 590976100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.951302 + 0.290221I
a = −0.277187 − 0.863557I
b = 0.11645 − 1.69893I
2.44631 − 5.94320I −2.32452 + 10.00245I
u = 0.951302 − 0.290221I
a = −0.277187 + 0.863557I
b = 0.11645 + 1.69893I
2.44631 + 5.94320I −2.32452 − 10.00245I
u = −0.986545 + 0.209518I
a = −1.94798 + 0.60057I
b = −1.21607 + 1.07214I
−2.78388 + 2.32701I −5.94560 − 9.38612I
u = −0.986545 − 0.209518I
a = −1.94798 − 0.60057I
b = −1.21607 − 1.07214I
−2.78388 − 2.32701I −5.94560 + 9.38612I
u = 0.359550 + 0.837445I
a = −0.225374 + 0.398951I
b = 0.114727 − 1.121370I
3.64892 − 0.52199I 4.59024 + 2.59542I
u = 0.359550 − 0.837445I
a = −0.225374 − 0.398951I
b = 0.114727 + 1.121370I
3.64892 + 0.52199I 4.59024 − 2.59542I
u = −0.839767 + 0.098563I
a = 0.96828 − 1.28580I
b = 0.39640 − 1.74102I
−1.26065 + 0.86355I 1.74294 − 5.70273I
u = −0.839767 − 0.098563I
a = 0.96828 + 1.28580I
b = 0.39640 + 1.74102I
−1.26065 − 0.86355I 1.74294 + 5.70273I
u = 1.111420 + 0.352542I
a = 1.72549 + 0.41631I
b = 0.89022 + 1.22122I
−2.02045 − 7.48389I −6.59522 + 9.84827I
u = 1.111420 − 0.352542I
a = 1.72549 − 0.41631I
b = 0.89022 − 1.22122I
−2.02045 + 7.48389I −6.59522 − 9.84827I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.690269 + 0.961401I
a = 0.092925 + 0.142714I
b = −0.264351 − 1.186530I
8.68492 + 1.39150I 3.97132 − 0.73814I
u = −0.690269 − 0.961401I
a = 0.092925 − 0.142714I
b = −0.264351 + 1.186530I
8.68492 − 1.39150I 3.97132 + 0.73814I
u = −1.093880 + 0.546781I
a = −1.82594 + 0.17728I
b = −0.711478 + 1.169160I
5.41370 + 9.49132I −1.05941 − 8.20262I
u = −1.093880 − 0.546781I
a = −1.82594 − 0.17728I
b = −0.711478 − 1.169160I
5.41370 − 9.49132I −1.05941 + 8.20262I
u = −1.217690 + 0.271137I
a = 1.46583 + 0.49454I
b = 1.358560 + 0.314654I
−6.64670 + 2.06191I −9.67039 − 3.16010I
u = −1.217690 − 0.271137I
a = 1.46583 − 0.49454I
b = 1.358560 − 0.314654I
−6.64670 − 2.06191I −9.67039 + 3.16010I
u = 0.639901 + 0.314914I
a = 1.83215 + 0.55944I
b = 0.682248 + 0.565377I
4.13991 + 0.54273I −0.34588 + 4.27829I
u = 0.639901 − 0.314914I
a = 1.83215 − 0.55944I
b = 0.682248 − 0.565377I
4.13991 − 0.54273I −0.34588 − 4.27829I
u = 0.673890 + 0.225219I
a = −1.44679 + 1.31081I
b = −0.646933 + 0.945006I
4.15321 − 3.33552I 0.65169 + 4.83950I
u = 0.673890 − 0.225219I
a = −1.44679 − 1.31081I
b = −0.646933 − 0.945006I
4.15321 + 3.33552I 0.65169 − 4.83950I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.278220 + 0.368967I
a = −1.308200 + 0.484946I
b = −1.257700 + 0.251336I
−9.32626 − 7.16028I −11.16149 + 5.84922I
u = 1.278220 − 0.368967I
a = −1.308200 − 0.484946I
b = −1.257700 − 0.251336I
−9.32626 + 7.16028I −11.16149 − 5.84922I
u = −0.312992 + 1.321470I
a = −0.054941 + 0.379383I
b = −0.266126 − 0.913766I
1.66131 − 1.14235I −8.36689 + 6.54215I
u = −0.312992 − 1.321470I
a = −0.054941 − 0.379383I
b = −0.266126 + 0.913766I
1.66131 + 1.14235I −8.36689 − 6.54215I
u = 0.152051 + 1.355020I
a = 0.067566 + 0.449076I
b = 0.211753 − 0.799074I
5.26440 − 2.10608I −5.69050 − 1.42501I
u = 0.152051 − 1.355020I
a = 0.067566 − 0.449076I
b = 0.211753 + 0.799074I
5.26440 + 2.10608I −5.69050 + 1.42501I
u = −1.290560 + 0.449291I
a = 1.222640 + 0.508158I
b = 1.197440 + 0.229093I
−4.32374 + 11.77480I −6.90294 − 7.27320I
u = −1.290560 − 0.449291I
a = 1.222640 − 0.508158I
b = 1.197440 − 0.229093I
−4.32374 − 11.77480I −6.90294 + 7.27320I
u = 1.302820 + 0.502514I
a = 1.54947 + 0.13563I
b = 0.71137 + 1.31109I
−3.42426 − 9.10911I −5.82942 + 4.74238I
u = 1.302820 − 0.502514I
a = 1.54947 − 0.13563I
b = 0.71137 − 1.31109I
−3.42426 + 9.10911I −5.82942 − 4.74238I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.44217 + 1.35910I
a = 0.073091 + 0.326814I
b = 0.329283 − 0.962921I
6.02988 + 4.62837I −1.75825 − 7.71280I
u = 0.44217 − 1.35910I
a = 0.073091 − 0.326814I
b = 0.329283 + 0.962921I
6.02988 − 4.62837I −1.75825 + 7.71280I
u = −1.33663 + 0.56826I
a = −1.54034 + 0.04516I
b = −0.67361 + 1.31446I
−5.9512 + 13.8535I −7.97274 − 8.38074I
u = −1.33663 − 0.56826I
a = −1.54034 − 0.04516I
b = −0.67361 − 1.31446I
−5.9512 − 13.8535I −7.97274 + 8.38074I
u = 1.34073 + 0.61791I
a = 1.55507 − 0.01242I
b = 0.65114 + 1.30988I
−0.9117 − 18.2438I −4.00000 + 9.83715I
u = 1.34073 − 0.61791I
a = 1.55507 + 0.01242I
b = 0.65114 − 1.30988I
−0.9117 + 18.2438I −4.00000 − 9.83715I
u = 0.213178 + 0.467931I
a = 0.36399 + 1.66496I
b = 0.024263 + 0.470526I
4.47390 − 3.34803I −0.32749 + 6.02159I
u = 0.213178 − 0.467931I
a = 0.36399 − 1.66496I
b = 0.024263 − 0.470526I
4.47390 + 3.34803I −0.32749 − 6.02159I
u = −0.196895 + 0.308594I
a = −0.589750 + 0.965099I
b = −0.147597 + 0.322846I
−0.220482 + 0.849414I −5.27557 − 8.01869I
u = −0.196895 − 0.308594I
a = −0.589750 − 0.965099I
b = −0.147597 − 0.322846I
−0.220482 − 0.849414I −5.27557 + 8.01869I
8
II.
I
u
2
= h1.50×10
95
u
63
−1.89×10
95
u
62
+· · ·+1.43×10
96
b−6.60×10
93
, −9.36×
10
96
u
63
+6.79×10
96
u
62
+· · ·+7.13×10
96
a−8.35×10
96
, u
64
−u
63
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
1.31364u
63
− 0.953248u
62
+ ··· + 22.8835u + 1.17156
−0.105220u
63
+ 0.132673u
62
+ ··· + 2.42160u + 0.00462786
a
8
=
0.591570u
63
− 0.939185u
62
+ ··· + 0.632587u − 4.37195
0.333288u
63
− 0.0714706u
62
+ ··· + 3.87249u + 0.0751465
a
12
=
1.41886u
63
− 1.08592u
62
+ ··· + 20.4619u + 1.16693
−0.105220u
63
+ 0.132673u
62
+ ··· + 2.42160u + 0.00462786
a
5
=
0.286105u
63
+ 0.0322819u
62
+ ··· + 2.98990u + 6.42850
−0.344151u
63
+ 0.261233u
62
+ ··· − 4.40148u + 0.160323
a
1
=
1.52678u
63
− 0.656432u
62
+ ··· + 16.3035u + 0.874416
0.108961u
63
− 0.112844u
62
+ ··· + 7.91452u − 0.0527111
a
9
=
−0.363225u
63
+ 0.303479u
62
+ ··· − 19.7594u − 0.654120
0.406438u
63
− 0.258918u
62
+ ··· − 1.56762u + 1.20312
a
10
=
1.19432u
63
− 0.869854u
62
+ ··· + 22.5993u + 0.781068
−0.0493788u
63
+ 0.0918939u
62
+ ··· + 2.65837u + 0.359194
a
4
=
−0.337715u
63
+ 0.299253u
62
+ ··· + 5.27380u + 1.54019
−0.424950u
63
+ 0.350613u
62
+ ··· − 2.19695u − 0.803842
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.629721u
63
+ 0.145367u
62
+ ··· + 2.60522u − 5.20665
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
25(25u
64
− 115u
63
+ ··· − 5955714u − 1598267)
c
2
, c
6
, c
8
c
12
u
64
− u
63
+ ··· + 2u − 1
c
3
, c
4
, c
9
(u
32
+ u
31
+ ··· − 2u − 1)
2
c
5
, c
11
(u
32
+ u
31
+ ··· − 2u − 1)
2
c
10
(u
32
− 3u
31
+ ··· − 4u
4
+ 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
625
· (625y
64
− 18125y
63
+ ··· − 16248056965572y + 2554457403289)
c
2
, c
6
, c
8
c
12
y
64
− 41y
63
+ ··· + 1056y
2
+ 1
c
3
, c
4
, c
9
(y
32
− 27y
31
+ ··· + 16y
2
+ 1)
2
c
5
, c
11
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
c
10
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.990635 + 0.241870I
a = 2.26968 − 0.29396I
b = 0.192477 + 0.755088I
−2.78881 − 1.03498I −4.81241 + 6.41402I
u = 0.990635 − 0.241870I
a = 2.26968 + 0.29396I
b = 0.192477 − 0.755088I
−2.78881 + 1.03498I −4.81241 − 6.41402I
u = −0.032718 + 0.967368I
a = −0.072441 − 0.475008I
b = −0.492704 + 1.133860I
0.60843 + 3.89503I −2.64939 − 2.90091I
u = −0.032718 − 0.967368I
a = −0.072441 + 0.475008I
b = −0.492704 − 1.133860I
0.60843 − 3.89503I −2.64939 + 2.90091I
u = −0.956448 + 0.075927I
a = 1.58187 − 0.40525I
b = 0.362087 − 1.159290I
−0.945525 + 0.397373I −4.16402 + 0.58140I
u = −0.956448 − 0.075927I
a = 1.58187 + 0.40525I
b = 0.362087 + 1.159290I
−0.945525 − 0.397373I −4.16402 − 0.58140I
u = −0.412639 + 0.830760I
a = 0.212906 − 0.019763I
b = 0.450235 + 1.200350I
7.53680 − 4.39858I 2.80847 + 3.53545I
u = −0.412639 − 0.830760I
a = 0.212906 + 0.019763I
b = 0.450235 − 1.200350I
7.53680 + 4.39858I 2.80847 − 3.53545I
u = 0.084877 + 0.893403I
a = −0.320511 − 0.640838I
b = −0.792800 + 0.172177I
−0.15402 − 7.01747I −4.33777 + 4.88322I
u = 0.084877 − 0.893403I
a = −0.320511 + 0.640838I
b = −0.792800 − 0.172177I
−0.15402 + 7.01747I −4.33777 − 4.88322I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11160
a = −1.10145
b = −0.605013
−2.06165 −4.00000
u = −1.120250 + 0.166620I
a = −0.45014 + 1.61931I
b = 0.192477 + 0.755088I
−2.78881 − 1.03498I 0
u = −1.120250 − 0.166620I
a = −0.45014 − 1.61931I
b = 0.192477 − 0.755088I
−2.78881 + 1.03498I 0
u = −0.088436 + 1.131120I
a = 0.208910 − 0.387911I
b = 0.514933 + 1.164400I
−2.01515 − 7.88151I 0
u = −0.088436 − 1.131120I
a = 0.208910 + 0.387911I
b = 0.514933 − 1.164400I
−2.01515 + 7.88151I 0
u = 1.134990 + 0.013228I
a = −2.74635 + 1.89283I
b = −0.180753 + 1.016980I
1.71612 + 2.81562I 0. − 3.82546I
u = 1.134990 − 0.013228I
a = −2.74635 − 1.89283I
b = −0.180753 − 1.016980I
1.71612 − 2.81562I 0. + 3.82546I
u = 0.840181 + 0.161786I
a = −1.304710 + 0.455755I
b = −0.357265 + 1.197710I
3.96080 − 3.23058I 0.64791 + 1.85611I
u = 0.840181 − 0.161786I
a = −1.304710 − 0.455755I
b = −0.357265 − 1.197710I
3.96080 + 3.23058I 0.64791 − 1.85611I
u = 1.121800 + 0.348941I
a = −1.43264 − 0.22390I
b = −0.433982 − 1.139380I
0.99219 − 3.88889I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.121800 − 0.348941I
a = −1.43264 + 0.22390I
b = −0.433982 + 1.139380I
0.99219 + 3.88889I 0
u = −0.991993 + 0.629934I
a = 1.51377 + 0.08540I
b = 0.450235 − 1.200350I
7.53680 + 4.39858I 0
u = −0.991993 − 0.629934I
a = 1.51377 − 0.08540I
b = 0.450235 + 1.200350I
7.53680 − 4.39858I 0
u = 0.529100 + 0.629309I
a = 0.205138 − 0.452753I
b = −0.649942 + 0.248644I
−1.96053 + 0.52783I −6.40552 − 0.64788I
u = 0.529100 − 0.629309I
a = 0.205138 + 0.452753I
b = −0.649942 − 0.248644I
−1.96053 − 0.52783I −6.40552 + 0.64788I
u = −0.222094 + 0.779441I
a = 0.142461 − 0.681629I
b = 0.747372 + 0.188735I
−4.85609 + 3.15266I −9.32272 − 3.41480I
u = −0.222094 − 0.779441I
a = 0.142461 + 0.681629I
b = 0.747372 − 0.188735I
−4.85609 − 3.15266I −9.32272 + 3.41480I
u = 0.168998 + 1.197470I
a = −0.258604 − 0.355588I
b = −0.521034 + 1.182060I
2.81659 + 11.87580I 0
u = 0.168998 − 1.197470I
a = −0.258604 + 0.355588I
b = −0.521034 − 1.182060I
2.81659 − 11.87580I 0
u = −0.760820 + 0.051630I
a = −2.50737 − 4.06109I
b = −0.180753 + 1.016980I
1.71612 + 2.81562I 1.51638 − 3.82546I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.760820 − 0.051630I
a = −2.50737 + 4.06109I
b = −0.180753 − 1.016980I
1.71612 − 2.81562I 1.51638 + 3.82546I
u = 0.625366 + 0.416232I
a = 1.174630 − 0.459173I
b = 0.778647
4.02976 −6 − 0.517485 + 0.10I
u = 0.625366 − 0.416232I
a = 1.174630 + 0.459173I
b = 0.778647
4.02976 −6 − 0.517485 + 0.10I
u = −1.333050 + 0.080938I
a = −1.020740 + 0.026377I
b = −0.649942 − 0.248644I
−1.96053 − 0.52783I 0
u = −1.333050 − 0.080938I
a = −1.020740 − 0.026377I
b = −0.649942 + 0.248644I
−1.96053 + 0.52783I 0
u = 1.307060 + 0.281166I
a = 0.979374 − 0.045795I
b = 0.747372 − 0.188735I
−4.85609 − 3.15266I 0
u = 1.307060 − 0.281166I
a = 0.979374 + 0.045795I
b = 0.747372 + 0.188735I
−4.85609 + 3.15266I 0
u = 0.052652 + 0.652966I
a = 0.416300 − 0.268528I
b = −0.433982 + 1.139380I
0.99219 + 3.88889I −1.10872 − 4.90467I
u = 0.052652 − 0.652966I
a = 0.416300 + 0.268528I
b = −0.433982 − 1.139380I
0.99219 − 3.88889I −1.10872 + 4.90467I
u = 1.122470 + 0.772783I
a = 0.882366 − 0.650904I
b = 0.565288 + 0.826638I
−3.22871 − 6.17510I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122470 − 0.772783I
a = 0.882366 + 0.650904I
b = 0.565288 − 0.826638I
−3.22871 + 6.17510I 0
u = −1.305470 + 0.401673I
a = −0.947263 − 0.080604I
b = −0.792800 − 0.172177I
−0.15402 + 7.01747I 0
u = −1.305470 − 0.401673I
a = −0.947263 + 0.080604I
b = −0.792800 + 0.172177I
−0.15402 − 7.01747I 0
u = −1.206430 + 0.672296I
a = −0.964053 − 0.575406I
b = −0.561289 + 0.769750I
−7.30442 + 2.24194I 0
u = −1.206430 − 0.672296I
a = −0.964053 + 0.575406I
b = −0.561289 − 0.769750I
−7.30442 − 2.24194I 0
u = 1.320730 + 0.465485I
a = −1.231650 − 0.114539I
b = −0.492704 − 1.133860I
0.60843 − 3.89503I 0
u = 1.320730 − 0.465485I
a = −1.231650 + 0.114539I
b = −0.492704 + 1.133860I
0.60843 + 3.89503I 0
u = 1.30308 + 0.56958I
a = 1.009850 − 0.465543I
b = 0.570562 + 0.700867I
−3.58638 + 1.65231I 0
u = 1.30308 − 0.56958I
a = 1.009850 + 0.465543I
b = 0.570562 − 0.700867I
−3.58638 − 1.65231I 0
u = −1.38759 + 0.47149I
a = 0.241029 + 0.345866I
b = 0.570562 + 0.700867I
−3.58638 + 1.65231I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38759 − 0.47149I
a = 0.241029 − 0.345866I
b = 0.570562 − 0.700867I
−3.58638 − 1.65231I 0
u = −1.35456 + 0.61920I
a = 1.202930 + 0.011131I
b = 0.514933 − 1.164400I
−2.01515 + 7.88151I 0
u = −1.35456 − 0.61920I
a = 1.202930 − 0.011131I
b = 0.514933 + 1.164400I
−2.01515 − 7.88151I 0
u = 1.46603 + 0.36888I
a = −0.368646 + 0.401072I
b = −0.561289 + 0.769750I
−7.30442 + 2.24194I 0
u = 1.46603 − 0.36888I
a = −0.368646 − 0.401072I
b = −0.561289 − 0.769750I
−7.30442 − 2.24194I 0
u = 1.35258 + 0.70435I
a = −1.198040 + 0.073158I
b = −0.521034 − 1.182060I
2.81659 − 11.87580I 0
u = 1.35258 − 0.70435I
a = −1.198040 − 0.073158I
b = −0.521034 + 1.182060I
2.81659 + 11.87580I 0
u = −1.53537 + 0.28145I
a = 0.487673 + 0.401373I
b = 0.565288 + 0.826638I
−3.22871 − 6.17510I 0
u = −1.53537 − 0.28145I
a = 0.487673 − 0.401373I
b = 0.565288 − 0.826638I
−3.22871 + 6.17510I 0
u = 0.294443 + 0.223570I
a = −3.60080 − 0.80864I
b = −0.357265 − 1.197710I
3.96080 + 3.23058I 0.64791 − 1.85611I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294443 − 0.223570I
a = −3.60080 + 0.80864I
b = −0.357265 + 1.197710I
3.96080 − 3.23058I 0.64791 + 1.85611I
u = 0.285124
a = 2.12456
b = −0.605013
−2.06165 −3.73830
u = −0.093871 + 0.133166I
a = −3.41648 + 4.64714I
b = 0.362087 + 1.159290I
−0.945525 − 0.397373I −4.16402 − 0.58140I
u = −0.093871 − 0.133166I
a = −3.41648 − 4.64714I
b = 0.362087 − 1.159290I
−0.945525 + 0.397373I −4.16402 + 0.58140I
18
III. I
u
3
= hb + u, 8a
3
− 12a
2
u + 4a
2
− 4au − 6a + u − 2, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−1
a
3
=
−u
2u
a
11
=
a
−u
a
8
=
a
2
− au + 1
−au − 2
a
12
=
a + u
−u
a
5
=
au
1
a
1
=
−a
2
u
−a + u
a
9
=
2a
2
− au + 1
−2au − 3
a
10
=
3a − u
−4a + u
a
4
=
6a
2
u + 2a
2
− au + 6a − 3u −
1
2
−8a
2
u − 4a
2
+ 4au − 8a + 4u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a + 4u
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
64(64u
6
+ 64u
5
+ 64u
4
+ 16u
3
+ 12u
2
+ 16u + 5)
c
2
, c
5
, c
6
c
8
, c
11
, c
12
(u
2
+ 1)
3
c
3
, c
4
, c
9
u
6
− 3u
4
+ 2u
2
+ 1
c
10
u
6
+ u
4
+ 2u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
4096(4096y
6
+ 4096y
5
+ 3584y
4
− 128y
3
+ 272y
2
− 136y + 25)
c
2
, c
5
, c
6
c
8
, c
11
, c
12
(y + 1)
6
c
3
, c
4
, c
9
(y
3
− 3y
2
+ 2y + 1)
2
c
10
(y
3
+ y
2
+ 2y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.438719 + 0.872431I
b = − 1.000000I
6.31400 + 2.82812I 3.50976 − 2.97945I
u = 1.000000I
a = 0.377439 + 0.500000I
b = − 1.000000I
2.17641 −3.01951 + 0.I
u = 1.000000I
a = −0.438719 + 0.127569I
b = − 1.000000I
6.31400 − 2.82812I 3.50976 + 2.97945I
u = − 1.000000I
a = −0.438719 − 0.872431I
b = 1.000000I
6.31400 − 2.82812I 3.50976 + 2.97945I
u = − 1.000000I
a = 0.377439 − 0.500000I
b = 1.000000I
2.17641 −3.01951 + 0.I
u = − 1.000000I
a = −0.438719 − 0.127569I
b = 1.000000I
6.31400 + 2.82812I 3.50976 − 2.97945I
22
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
11
=
−1
0
a
8
=
0
1
a
12
=
−1
0
a
5
=
1
0
a
1
=
−1
−1
a
9
=
−1
0
a
10
=
−1
0
a
4
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
12
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
102400(u − 1)(64u
6
+ 64u
5
+ 64u
4
+ 16u
3
+ 12u
2
+ 16u + 5)
· (64u
40
+ 128u
39
+ ··· − 18u + 4)
· (25u
64
− 115u
63
+ ··· − 5955714u − 1598267)
c
2
, c
8
(u − 1)(u
2
+ 1)
3
(u
40
− u
39
+ ··· − 8u + 5)(u
64
− u
63
+ ··· + 2u − 1)
c
3
, c
4
, c
9
u(u
6
− 3u
4
+ 2u
2
+ 1)(u
32
+ u
31
+ ··· − 2u − 1)
2
· (u
40
− 3u
39
+ ··· + 40u + 10)
c
5
, c
11
u(u
2
+ 1)
3
(u
32
+ u
31
+ ··· − 2u − 1)
2
(u
40
− 3u
39
+ ··· − 116u + 178)
c
6
, c
12
(u + 1)(u
2
+ 1)
3
(u
40
− u
39
+ ··· − 8u + 5)(u
64
− u
63
+ ··· + 2u − 1)
c
10
u(u
6
+ u
4
+ 2u
2
+ 1)(u
32
− 3u
31
+ ··· − 4u
4
+ 1)
2
· (u
40
+ 9u
39
+ ··· + 223540u + 24310)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
10485760000(y −1)
· (4096y
6
+ 4096y
5
+ 3584y
4
− 128y
3
+ 272y
2
− 136y + 25)
· (4096y
40
− 16384y
39
+ ··· + 4y + 16)
· (625y
64
− 18125y
63
+ ··· − 16248056965572y + 2554457403289)
c
2
, c
6
, c
8
c
12
(y −1)(y + 1)
6
(y
40
− 15y
39
+ ··· − 64y + 25)
· (y
64
− 41y
63
+ ··· + 1056y
2
+ 1)
c
3
, c
4
, c
9
y(y
3
− 3y
2
+ 2y + 1)
2
(y
32
− 27y
31
+ ··· + 16y
2
+ 1)
2
· (y
40
− 33y
39
+ ··· − 140y + 100)
c
5
, c
11
y(y + 1)
6
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
· (y
40
+ 23y
39
+ ··· + 897548y + 31684)
c
10
y(y
3
+ y
2
+ 2y + 1)
2
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
· (y
40
+ 19y
39
+ ··· − 3244220940y + 590976100)
28
