12a
1213
(K12a
1213
)
A knot diagram
1
Linearized knot diagam
5 6 7 9 10 11 1 12 2 3 4 8
Solving Sequence
6,11 3,7
4 12 2 10 5 1 9 8
c
6
c
3
c
11
c
2
c
10
c
5
c
1
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.38072 × 10
36
u
34
+ 2.10788 × 10
36
u
33
+ ··· + 2.31436 × 10
37
b − 1.18052 × 10
37
,
1.34556 × 10
38
u
34
+ 1.19595 × 10
38
u
33
+ ··· + 2.31436 × 10
37
a + 9.18534 × 10
38
, u
35
+ u
34
+ ··· + 8u + 1i
I
u
2
= h−1.95779 × 10
17
u
24
+ 2.57330 × 10
16
u
23
+ ··· + 3.09631 × 10
18
b + 3.53328 × 10
18
,
− 1.02595 × 10
18
u
24
+ 1.39827 × 10
18
u
23
+ ··· + 1.23853 × 10
19
a + 2.15965 × 10
19
, u
25
− u
24
+ ··· − 8u − 8i
I
u
3
= h6.80801 × 10
870
u
115
− 1.02067 × 10
872
u
114
+ ··· + 2.89851 × 10
874
b + 3.50026 × 10
875
,
− 3.25101 × 10
874
u
115
+ 2.16113 × 10
875
u
114
+ ··· + 1.53436 × 10
879
a + 1.14628 × 10
881
,
u
116
− 15u
115
+ ··· − 417760u + 52936i
* 3 irreducible components of dim
C
= 0, with total 176 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−2.38×10
36
u
34
+2.11×10
36
u
33
+· · ·+2.31×10
37
b−1.18×10
37
, 1.35×
10
38
u
34
+1.20×10
38
u
33
+· · ·+2.31×10
37
a+9.19×10
38
, u
35
+u
34
+· · ·+8u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−5.81398u
34
− 5.16753u
33
+ ··· − 72.6444u − 39.6884
0.102867u
34
− 0.0910783u
33
+ ··· − 3.09658u + 0.510083
a
7
=
1
−u
2
a
4
=
−5.70378u
34
− 4.93508u
33
+ ··· − 70.1903u − 39.5521
0.182861u
34
+ 0.0177861u
33
+ ··· − 2.00831u + 0.632342
a
12
=
−33.5755u
34
− 29.3518u
33
+ ··· − 371.933u − 214.961
0.712298u
34
+ 0.384179u
33
+ ··· + 4.97991u + 5.59420
a
2
=
−5.91684u
34
− 5.07645u
33
+ ··· − 69.5478u − 40.1985
0.102867u
34
− 0.0910783u
33
+ ··· − 3.09658u + 0.510083
a
10
=
−33.5988u
34
− 29.1991u
33
+ ··· − 363.943u − 212.176
0.646444u
34
+ 0.433382u
33
+ ··· + 6.82336u + 5.81398
a
5
=
183.007u
34
+ 155.083u
33
+ ··· + 1861.33u + 1147.00
−4.39975u
34
− 3.75957u
33
+ ··· − 56.6144u − 33.5988
a
1
=
24.6736u
34
+ 19.7265u
33
+ ··· + 217.291u + 153.213
−1.01831u
34
− 1.24880u
33
+ ··· − 18.6808u − 5.81082
a
9
=
−34.4392u
34
− 29.7788u
33
+ ··· − 371.080u − 218.093
0.840389u
34
+ 0.579717u
33
+ ··· + 7.13622u + 5.91684
a
8
=
−17.5414u
34
− 15.2732u
33
+ ··· − 157.692u − 91.1189
−0.242519u
34
− 0.107367u
33
+ ··· + 8.50491u + 3.47843
(ii) Obstruction class = −1
(iii) Cusp Shapes = −68.4106u
34
− 55.3484u
33
+ ··· − 679.743u − 457.303
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
35
− 3u
34
+ ··· + 13u − 1
c
2
u
35
− 25u
34
+ ··· + 24576u − 2048
c
4
, c
11
u
35
+ 7u
34
+ ··· − 3u + 1
c
5
, c
10
u
35
+ 5u
34
+ ··· − 3u + 1
c
6
, c
9
u
35
− u
34
+ ··· + 8u − 1
c
7
, c
8
, c
12
u
35
+ 11u
34
+ ··· + 384u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
35
+ 11y
34
+ ··· + 29y −1
c
2
y
35
+ 15y
34
+ ··· − 90177536y −4194304
c
4
, c
11
y
35
− 51y
34
+ ··· + 35y −1
c
5
, c
10
y
35
− 39y
34
+ ··· + 27y −1
c
6
, c
9
y
35
− y
34
+ ··· + 28y −1
c
7
, c
8
, c
12
y
35
+ 31y
34
+ ··· − 7680y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473191 + 0.955601I
a = 0.164857 − 0.773336I
b = 0.73632 − 1.23689I
−0.87815 − 2.10009I −6.29124 + 3.74115I
u = −0.473191 − 0.955601I
a = 0.164857 + 0.773336I
b = 0.73632 + 1.23689I
−0.87815 + 2.10009I −6.29124 − 3.74115I
u = −0.561860 + 0.934680I
a = 0.721974 + 0.705652I
b = 0.291621 + 0.692365I
2.74039 + 5.52452I −2.61115 − 4.68081I
u = −0.561860 − 0.934680I
a = 0.721974 − 0.705652I
b = 0.291621 − 0.692365I
2.74039 − 5.52452I −2.61115 + 4.68081I
u = 0.728850 + 0.833231I
a = 0.690527 − 0.506887I
b = 0.058923 − 0.690806I
−2.68642 − 1.48594I −5.76171 + 5.39125I
u = 0.728850 − 0.833231I
a = 0.690527 + 0.506887I
b = 0.058923 + 0.690806I
−2.68642 + 1.48594I −5.76171 − 5.39125I
u = 0.486606 + 1.044960I
a = 0.195291 − 0.498321I
b = 0.31826 − 1.73957I
−0.68127 + 1.41250I −3.06396 − 1.29126I
u = 0.486606 − 1.044960I
a = 0.195291 + 0.498321I
b = 0.31826 + 1.73957I
−0.68127 − 1.41250I −3.06396 + 1.29126I
u = −0.798627 + 0.123489I
a = −0.533379 − 0.839803I
b = 1.53890 − 0.84849I
10.09970 − 2.57123I 7.26146 + 7.35567I
u = −0.798627 − 0.123489I
a = −0.533379 + 0.839803I
b = 1.53890 + 0.84849I
10.09970 + 2.57123I 7.26146 − 7.35567I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.300719 + 0.744013I
a = 0.189534 + 0.400172I
b = 0.03329 + 2.04106I
7.92447 + 1.85760I −9.7550 − 10.3352I
u = −0.300719 − 0.744013I
a = 0.189534 − 0.400172I
b = 0.03329 − 2.04106I
7.92447 − 1.85760I −9.7550 + 10.3352I
u = −0.663483 + 1.024170I
a = 0.189870 + 0.547409I
b = 0.43442 + 1.63061I
−1.65342 − 7.27417I −5.53901 + 7.92193I
u = −0.663483 − 1.024170I
a = 0.189870 − 0.547409I
b = 0.43442 − 1.63061I
−1.65342 + 7.27417I −5.53901 − 7.92193I
u = −1.023220 + 0.684265I
a = 0.615312 + 0.295804I
b = −0.320104 + 0.634624I
−0.17224 − 3.30186I 4.00752 − 4.42363I
u = −1.023220 − 0.684265I
a = 0.615312 − 0.295804I
b = −0.320104 − 0.634624I
−0.17224 + 3.30186I 4.00752 + 4.42363I
u = 0.748659 + 0.978142I
a = 0.165026 − 0.583693I
b = 0.55147 − 1.58642I
4.79967 + 11.80520I −2.00000 − 8.67473I
u = 0.748659 − 0.978142I
a = 0.165026 + 0.583693I
b = 0.55147 + 1.58642I
4.79967 − 11.80520I −2.00000 + 8.67473I
u = 0.894095 + 0.973220I
a = −0.088879 + 0.809478I
b = 1.13402 + 1.22065I
0.21423 + 7.00365I 0. − 4.77334I
u = 0.894095 − 0.973220I
a = −0.088879 − 0.809478I
b = 1.13402 − 1.22065I
0.21423 − 7.00365I 0. + 4.77334I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599988 + 0.271035I
a = −0.65464 + 1.47497I
b = 1.251390 + 0.566406I
3.12898 + 2.04422I 4.59072 − 3.04484I
u = 0.599988 − 0.271035I
a = −0.65464 − 1.47497I
b = 1.251390 − 0.566406I
3.12898 − 2.04422I 4.59072 + 3.04484I
u = −0.132382 + 0.519991I
a = 0.881561 − 0.313861I
b = −0.006740 − 0.358428I
−0.184960 − 1.127700I −2.22637 + 6.73061I
u = −0.132382 − 0.519991I
a = 0.881561 + 0.313861I
b = −0.006740 + 0.358428I
−0.184960 + 1.127700I −2.22637 − 6.73061I
u = −1.24107 + 0.80628I
a = −0.224566 − 0.903591I
b = 1.25904 − 1.04232I
10.26990 − 7.64955I 0
u = −1.24107 − 0.80628I
a = −0.224566 + 0.903591I
b = 1.25904 + 1.04232I
10.26990 + 7.64955I 0
u = 0.014885 + 0.497734I
a = 3.54266 − 2.08972I
b = 0.790590 − 0.123525I
4.73898 + 2.59865I −10.3277 − 11.9450I
u = 0.014885 − 0.497734I
a = 3.54266 + 2.08972I
b = 0.790590 + 0.123525I
4.73898 − 2.59865I −10.3277 + 11.9450I
u = 1.27290 + 0.91763I
a = −0.284094 + 0.896949I
b = 1.32093 + 1.01324I
1.91254 + 10.46930I 0
u = 1.27290 − 0.91763I
a = −0.284094 − 0.896949I
b = 1.32093 − 1.01324I
1.91254 − 10.46930I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.30681 + 0.93603I
a = −0.298108 − 0.936803I
b = 1.30845 − 0.96931I
0.8251 − 15.9095I 0
u = −1.30681 − 0.93603I
a = −0.298108 + 0.936803I
b = 1.30845 + 0.96931I
0.8251 + 15.9095I 0
u = 1.33364 + 0.94709I
a = −0.286932 + 0.961649I
b = 1.28491 + 0.95487I
7.0349 + 20.2665I 0
u = 1.33364 − 0.94709I
a = −0.286932 − 0.961649I
b = 1.28491 − 0.95487I
7.0349 − 20.2665I 0
u = −0.156518
a = −34.9720
b = 1.02859
0.541372 −424.140
8
II.
I
u
2
= h−1.96×10
17
u
24
+2.57×10
16
u
23
+· · ·+3.10×10
18
b+3.53×10
18
, −1.03×
10
18
u
24
+1.40×10
18
u
23
+· · ·+1.24×10
19
a+2.16×10
19
, u
25
−u
24
+· · ·−8u−8i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.0828360u
24
− 0.112898u
23
+ ··· − 1.89081u − 1.74372
0.0632297u
24
− 0.00831085u
23
+ ··· − 1.12338u − 1.14113
a
7
=
1
−u
2
a
4
=
0.0237886u
24
− 0.0967624u
23
+ ··· − 1.18962u − 0.362102
0.0366311u
24
− 0.0217545u
23
+ ··· − 0.307708u − 0.797832
a
12
=
0.0181137u
24
− 0.00463381u
23
+ ··· − 1.87039u + 0.341855
0.0143600u
24
− 0.0438065u
23
+ ··· + 1.45977u − 0.114605
a
2
=
0.0196063u
24
− 0.104587u
23
+ ··· − 0.767427u − 0.602598
0.0632297u
24
− 0.00831085u
23
+ ··· − 1.12338u − 1.14113
a
10
=
0.111772u
24
− 0.130147u
23
+ ··· − 0.329660u − 0.474602
0.0300620u
24
− 0.0258797u
23
+ ··· + 1.08104u − 0.662688
a
5
=
0.0470114u
24
− 0.123522u
23
+ ··· − 3.09053u + 0.235072
0.0183753u
24
− 0.0403395u
23
+ ··· − 0.419572u − 0.894174
a
1
=
0.0242955u
24
+ 0.00502972u
23
+ ··· + 2.56668u − 1.33845
0.0211853u
24
+ 0.0698665u
23
+ ··· − 0.0456261u + 0.124634
a
9
=
0.0267908u
24
− 0.0521712u
23
+ ··· − 0.775408u − 0.317751
0.0849809u
24
− 0.0779759u
23
+ ··· + 0.445748u − 0.156850
a
8
=
0.141789u
24
− 0.189859u
23
+ ··· − 1.17851u − 1.06959
−0.0355395u
24
+ 0.0698178u
23
+ ··· + 0.631153u − 0.896134
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2452215208224550567
12385251064844942024
u
24
−
846206872359813633
12385251064844942024
u
23
+ ··· −
8471824635934717355
3096312766211235506
u −
6668781122666694554
1548156383105617753
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
25
− 3u
24
+ ··· − 40u + 56
c
2
u
25
− 8u
24
+ ··· − 3u − 1
c
4
, c
11
8(8u
25
+ 8u
24
+ ··· + 5u
2
+ 1)
c
5
, c
10
8(8u
25
− 8u
24
+ ··· + 11u
2
− 1)
c
6
, c
9
u
25
− u
24
+ ··· − 8u − 8
c
7
, c
8
u
25
+ 2u
24
+ ··· − 2u + 1
c
12
u
25
− 2u
24
+ ··· − 2u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
25
− 3y
24
+ ··· + 19072y −3136
c
2
y
25
+ 10y
24
+ ··· + 37y −1
c
4
, c
11
64(64y
25
− 448y
24
+ ··· − 10y −1)
c
5
, c
10
64(64y
25
− 704y
24
+ ··· + 22y −1)
c
6
, c
9
y
25
− 7y
24
+ ··· + 192y −64
c
7
, c
8
, c
12
y
25
+ 26y
24
+ ··· + 46y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317550 + 0.877564I
a = −0.229611 + 0.699890I
b = −0.576807 + 1.289960I
−2.07306 + 0.81237I −8.44018 − 1.80632I
u = 0.317550 − 0.877564I
a = −0.229611 − 0.699890I
b = −0.576807 − 1.289960I
−2.07306 − 0.81237I −8.44018 + 1.80632I
u = 0.374639 + 0.814667I
a = −0.133763 − 0.490884I
b = −0.48326 − 1.89633I
8.08619 − 1.60054I 4.91227 − 11.32939I
u = 0.374639 − 0.814667I
a = −0.133763 + 0.490884I
b = −0.48326 + 1.89633I
8.08619 + 1.60054I 4.91227 + 11.32939I
u = −1.10397
a = −0.450023
b = 1.22211
4.61475 8.27900
u = 1.081950 + 0.250410I
a = −0.465508 − 0.085599I
b = 1.077930 − 0.382096I
9.67308 − 1.37757I 5.79906 + 0.19770I
u = 1.081950 − 0.250410I
a = −0.465508 + 0.085599I
b = 1.077930 + 0.382096I
9.67308 + 1.37757I 5.79906 − 0.19770I
u = −1.010210 + 0.558270I
a = −0.685743 − 0.374548I
b = 0.123193 − 0.613480I
−0.50342 − 3.65382I −7.55217 + 7.75024I
u = −1.010210 − 0.558270I
a = −0.685743 + 0.374548I
b = 0.123193 + 0.613480I
−0.50342 + 3.65382I −7.55217 − 7.75024I
u = −0.888892 + 0.794377I
a = 0.20872 + 1.44121I
b = −1.098420 + 0.679608I
1.26033 − 8.21911I 0.36152 + 8.38035I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.888892 − 0.794377I
a = 0.20872 − 1.44121I
b = −1.098420 − 0.679608I
1.26033 + 8.21911I 0.36152 − 8.38035I
u = −0.550547 + 1.107680I
a = −0.133124 + 0.611398I
b = −0.65999 + 1.56156I
0.01650 − 2.22543I 4.06322 + 5.84619I
u = −0.550547 − 1.107680I
a = −0.133124 − 0.611398I
b = −0.65999 − 1.56156I
0.01650 + 2.22543I 4.06322 − 5.84619I
u = −0.768453 + 0.973451I
a = −0.374681 + 0.879750I
b = −0.590219 + 0.962163I
6.96474 − 11.65060I 2.09612 + 9.34091I
u = −0.768453 − 0.973451I
a = −0.374681 − 0.879750I
b = −0.590219 − 0.962163I
6.96474 + 11.65060I 2.09612 − 9.34091I
u = 0.770593 + 1.061120I
a = −0.135159 − 0.791525I
b = −0.79038 − 1.22759I
0.04224 + 8.07532I −0.32524 − 11.69521I
u = 0.770593 − 1.061120I
a = −0.135159 + 0.791525I
b = −0.79038 + 1.22759I
0.04224 − 8.07532I −0.32524 + 11.69521I
u = 0.671501
a = −1.58450
b = −0.368886
−3.74850 −10.8400
u = 0.942808 + 0.936636I
a = 0.128385 − 1.073180I
b = −1.10990 − 0.91866I
−0.63864 + 8.33929I −1.35664 − 7.88306I
u = 0.942808 − 0.936636I
a = 0.128385 + 1.073180I
b = −1.10990 + 0.91866I
−0.63864 − 8.33929I −1.35664 + 7.88306I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.370104 + 0.321579I
a = −1.00930 − 1.83683I
b = −0.770228 − 0.418162I
−0.07970 − 3.22269I −5.25315 + 3.28753I
u = −0.370104 − 0.321579I
a = −1.00930 + 1.83683I
b = −0.770228 + 0.418162I
−0.07970 + 3.22269I −5.25315 − 3.28753I
u = −1.52760
a = −0.771960
b = 0.295403
0.0461358 −0.00449090
u = 1.58070 + 0.12470I
a = −0.766976 − 0.004982I
b = 0.303767 − 0.008468I
4.75943 − 0.77091I −0.021983 + 0.140884I
u = 1.58070 − 0.12470I
a = −0.766976 + 0.004982I
b = 0.303767 + 0.008468I
4.75943 + 0.77091I −0.021983 − 0.140884I
14
III. I
u
3
= h6.81 × 10
870
u
115
− 1.02 × 10
872
u
114
+ · · · + 2.90 × 10
874
b + 3.50 ×
10
875
, −3.25 × 10
874
u
115
+ 2.16 × 10
875
u
114
+ · · · + 1.53 × 10
879
a + 1.15 ×
10
881
, u
116
− 15u
115
+ · · · − 417760u + 52936i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.0000211881u
115
− 0.000140850u
114
+ ··· + 332.880u − 74.7079
−0.000234880u
115
+ 0.00352137u
114
+ ··· + 149.396u − 12.0761
a
7
=
1
−u
2
a
4
=
0.000235461u
115
− 0.00342005u
114
+ ··· + 110.674u − 53.2636
−0.000258566u
115
+ 0.00389995u
114
+ ··· + 187.940u − 15.5229
a
12
=
3.09589 × 10
−6
u
115
− 0.000142993u
114
+ ··· − 40.8529u − 28.0315
0.000275424u
115
− 0.00411469u
114
+ ··· − 170.695u + 9.50168
a
2
=
0.000256068u
115
− 0.00366222u
114
+ ··· + 183.484u − 62.6318
−0.000234880u
115
+ 0.00352137u
114
+ ··· + 149.396u − 12.0761
a
10
=
0.0000533118u
115
− 0.00108371u
114
+ ··· − 344.514u − 5.40386
−0.0000839813u
115
+ 0.00125485u
114
+ ··· + 31.0149u − 7.02085
a
5
=
0.000186726u
115
− 0.00263160u
114
+ ··· + 357.144u − 102.550
0.000175190u
115
− 0.00262080u
114
+ ··· − 52.7290u + 4.48737
a
1
=
0.0000329485u
115
− 0.000439958u
114
+ ··· + 99.4761u − 74.2454
−0.000110444u
115
+ 0.00159254u
114
+ ··· + 30.4766u − 5.18938
a
9
=
8.31143 × 10
−6
u
115
+ 0.0000178873u
114
+ ··· + 299.956u − 42.3593
0.0000764582u
115
− 0.00146462u
114
+ ··· − 559.459u + 59.6749
a
8
=
−0.000299255u
115
+ 0.00442911u
114
+ ··· − 138.230u + 81.9995
5.30386 × 10
−6
u
115
− 0.000162142u
114
+ ··· − 178.360u + 16.8795
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00136918u
115
+ 0.0205831u
114
+ ··· + 475.643u − 0.629277
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
116
+ 5u
115
+ ··· − 293824u − 18872
c
2
(u
58
+ 14u
57
+ ··· + 2u + 1)
2
c
4
, c
11
8(8u
116
+ 104u
115
+ ··· − 1.07834 × 10
8
u + 3.68679 × 10
7
)
c
5
, c
10
8(8u
116
+ 104u
115
+ ··· + 65126u − 4735)
c
6
, c
9
u
116
+ 15u
115
+ ··· + 417760u + 52936
c
7
, c
8
, c
12
(u
58
− 6u
57
+ ··· − 24u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
116
− 93y
115
+ ··· − 74449976896y + 356152384
c
2
(y
58
− 14y
57
+ ··· − 132y + 1)
2
c
4
, c
11
64(64y
116
− 6720y
115
+ ··· − 1.67721 × 10
17
y + 1.35924 × 10
15
)
c
5
, c
10
64(64y
116
− 5184y
115
+ ··· − 3.55007 × 10
9
y + 2.24202 × 10
7
)
c
6
, c
9
y
116
− 105y
115
+ ··· − 367121525120y + 2802220096
c
7
, c
8
, c
12
(y
58
+ 58y
57
+ ··· − 272y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.01158
a = −8.79748
b = 0.0996704
0.00210462 0
u = 0.979940 + 0.270868I
a = 1.27783 + 0.75838I
b = −0.673521 − 0.205430I
10.39060 + 0.33751I 0
u = 0.979940 − 0.270868I
a = 1.27783 − 0.75838I
b = −0.673521 + 0.205430I
10.39060 − 0.33751I 0
u = 0.260251 + 0.936468I
a = 0.995159 + 0.468241I
b = 0.540330 − 0.147934I
0.160870 − 0.671910I 0
u = 0.260251 − 0.936468I
a = 0.995159 − 0.468241I
b = 0.540330 + 0.147934I
0.160870 + 0.671910I 0
u = 0.899381 + 0.324843I
a = 0.02723 + 1.66548I
b = 0.327313 + 0.897043I
6.88898 − 0.12974I 0
u = 0.899381 − 0.324843I
a = 0.02723 − 1.66548I
b = 0.327313 − 0.897043I
6.88898 + 0.12974I 0
u = 0.500073 + 0.812320I
a = 1.002650 + 0.655796I
b = 0.677148 + 0.214687I
4.86393 + 2.30422I 0
u = 0.500073 − 0.812320I
a = 1.002650 − 0.655796I
b = 0.677148 − 0.214687I
4.86393 − 2.30422I 0
u = −0.692472 + 0.649475I
a = −0.818612 + 0.006859I
b = −0.767777 − 0.502166I
1.15556 + 5.12365I 0
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.692472 − 0.649475I
a = −0.818612 − 0.006859I
b = −0.767777 + 0.502166I
1.15556 − 5.12365I 0
u = −0.941152 + 0.094794I
a = −0.138651 − 0.826278I
b = 1.013770 − 0.116777I
3.73399 − 1.62934I 0
u = −0.941152 − 0.094794I
a = −0.138651 + 0.826278I
b = 1.013770 + 0.116777I
3.73399 + 1.62934I 0
u = 0.234879 + 0.906360I
a = 0.130221 + 1.095070I
b = −0.751053 + 0.970955I
1.50707 + 3.95116I 0
u = 0.234879 − 0.906360I
a = 0.130221 − 1.095070I
b = −0.751053 − 0.970955I
1.50707 − 3.95116I 0
u = −0.817032 + 0.432974I
a = −0.409960 − 0.596017I
b = −0.751053 − 0.970955I
1.50707 − 3.95116I 0
u = −0.817032 − 0.432974I
a = −0.409960 + 0.596017I
b = −0.751053 + 0.970955I
1.50707 + 3.95116I 0
u = −0.905748 + 0.165780I
a = 0.90226 − 1.09537I
b = −0.704558 + 0.226547I
3.59558 − 3.21071I 0
u = −0.905748 − 0.165780I
a = 0.90226 + 1.09537I
b = −0.704558 − 0.226547I
3.59558 + 3.21071I 0
u = −0.873393 + 0.286666I
a = 0.212283 + 0.253939I
b = 1.53643 + 0.52266I
7.01799 − 4.89766I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873393 − 0.286666I
a = 0.212283 − 0.253939I
b = 1.53643 − 0.52266I
7.01799 + 4.89766I 0
u = 0.713535 + 0.577768I
a = 0.63911 − 1.49896I
b = −0.664418 − 0.629619I
−3.06039 + 2.03547I 0
u = 0.713535 − 0.577768I
a = 0.63911 + 1.49896I
b = −0.664418 + 0.629619I
−3.06039 − 2.03547I 0
u = −0.763410 + 0.771723I
a = 0.028077 − 1.034150I
b = 0.559985 − 1.250220I
−0.90262 − 2.33430I 0
u = −0.763410 − 0.771723I
a = 0.028077 + 1.034150I
b = 0.559985 + 1.250220I
−0.90262 + 2.33430I 0
u = 1.078240 + 0.136226I
a = 2.71578 − 1.12355I
b = −0.366627 − 0.170388I
5.01112 − 0.52164I 0
u = 1.078240 − 0.136226I
a = 2.71578 + 1.12355I
b = −0.366627 + 0.170388I
5.01112 + 0.52164I 0
u = 0.493381 + 0.764958I
a = −0.15233 − 1.51824I
b = −1.115670 − 0.750715I
1.01755 + 6.41344I 0
u = 0.493381 − 0.764958I
a = −0.15233 + 1.51824I
b = −1.115670 + 0.750715I
1.01755 − 6.41344I 0
u = 0.637789 + 0.647820I
a = −0.356755 + 0.693103I
b = −0.713517 + 0.945516I
−3.36011 + 2.04094I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637789 − 0.647820I
a = −0.356755 − 0.693103I
b = −0.713517 − 0.945516I
−3.36011 − 2.04094I 0
u = −0.898737 + 0.638239I
a = 0.62169 + 1.30815I
b = −0.767777 + 0.502166I
1.15556 − 5.12365I 0
u = −0.898737 − 0.638239I
a = 0.62169 − 1.30815I
b = −0.767777 − 0.502166I
1.15556 + 5.12365I 0
u = 1.135380 + 0.122044I
a = 0.086119 + 0.641099I
b = 1.026360 + 0.255290I
9.75231 + 4.08244I 0
u = 1.135380 − 0.122044I
a = 0.086119 − 0.641099I
b = 1.026360 − 0.255290I
9.75231 − 4.08244I 0
u = −0.746972 + 0.416669I
a = −1.49126 + 0.35281I
b = 1.026360 − 0.255290I
9.75231 − 4.08244I 0
u = −0.746972 − 0.416669I
a = −1.49126 − 0.35281I
b = 1.026360 + 0.255290I
9.75231 + 4.08244I 0
u = −0.843208 + 0.085931I
a = 0.57492 + 1.43425I
b = −1.15971 + 0.96631I
9.5516 − 10.5652I 0
u = −0.843208 − 0.085931I
a = 0.57492 − 1.43425I
b = −1.15971 − 0.96631I
9.5516 + 10.5652I 0
u = 0.823622 + 0.011430I
a = −0.53246 − 2.65982I
b = 0.432044 − 0.349969I
4.00496 + 0.11590I 0
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.823622 − 0.011430I
a = −0.53246 + 2.65982I
b = 0.432044 + 0.349969I
4.00496 − 0.11590I 0
u = 0.788196 + 0.199185I
a = 1.06705 + 1.58260I
b = −0.733347 − 0.206691I
3.00880 + 7.71935I 0
u = 0.788196 − 0.199185I
a = 1.06705 − 1.58260I
b = −0.733347 + 0.206691I
3.00880 − 7.71935I 0
u = −0.709071 + 0.962261I
a = −0.310202 − 0.555623I
b = −0.690086 − 0.845429I
−0.358848 − 0.399308I 0
u = −0.709071 − 0.962261I
a = −0.310202 + 0.555623I
b = −0.690086 + 0.845429I
−0.358848 + 0.399308I 0
u = −0.751367 + 0.270441I
a = 1.42199 − 1.70934I
b = −0.736192 + 0.183930I
9.1239 − 11.3929I 0
u = −0.751367 − 0.270441I
a = 1.42199 + 1.70934I
b = −0.736192 − 0.183930I
9.1239 + 11.3929I 0
u = 0.759086 + 0.167333I
a = −1.038420 − 0.884858I
b = 1.013770 + 0.116777I
3.73399 + 1.62934I 0. − 5.11449I
u = 0.759086 − 0.167333I
a = −1.038420 + 0.884858I
b = 1.013770 − 0.116777I
3.73399 − 1.62934I 0. + 5.11449I
u = −0.153958 + 0.761524I
a = −0.055312 − 1.198320I
b = −0.713517 − 0.945516I
−3.36011 − 2.04094I −8.79412 + 5.85740I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.153958 − 0.761524I
a = −0.055312 + 1.198320I
b = −0.713517 + 0.945516I
−3.36011 + 2.04094I −8.79412 − 5.85740I
u = 0.786939 + 0.941766I
a = −0.448228 + 0.268724I
b = −0.664418 + 0.629619I
−3.06039 − 2.03547I 0
u = 0.786939 − 0.941766I
a = −0.448228 − 0.268724I
b = −0.664418 − 0.629619I
−3.06039 + 2.03547I 0
u = 0.754748
a = 0.222173
b = 1.85662
2.24749 9.28120
u = −0.757678 + 0.996838I
a = −0.016211 + 1.208650I
b = −1.088980 + 0.799671I
−2.18513 − 8.49069I 0
u = −0.757678 − 0.996838I
a = −0.016211 − 1.208650I
b = −1.088980 − 0.799671I
−2.18513 + 8.49069I 0
u = −0.256825 + 0.697678I
a = 0.20777 + 1.57054I
b = −0.690086 + 0.845429I
−0.358848 + 0.399308I −2.00000 + 0.I
u = −0.256825 − 0.697678I
a = 0.20777 − 1.57054I
b = −0.690086 − 0.845429I
−0.358848 − 0.399308I −2.00000 + 0.I
u = 1.022720 + 0.775036I
a = −0.242532 + 1.097970I
b = 0.677280 + 1.077370I
−1.81586 + 7.53048I 0
u = 1.022720 − 0.775036I
a = −0.242532 − 1.097970I
b = 0.677280 − 1.077370I
−1.81586 − 7.53048I 0
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.098930 + 0.694343I
a = 0.325265 + 1.289590I
b = −1.076520 + 0.823273I
2.54061 − 10.54650I 0
u = −1.098930 − 0.694343I
a = 0.325265 − 1.289590I
b = −1.076520 − 0.823273I
2.54061 + 10.54650I 0
u = 1.054200 + 0.808278I
a = 0.283751 − 1.221210I
b = −1.088980 − 0.799671I
−2.18513 + 8.49069I 0
u = 1.054200 − 0.808278I
a = 0.283751 + 1.221210I
b = −1.088980 + 0.799671I
−2.18513 − 8.49069I 0
u = −1.115170 + 0.723638I
a = −0.339399 − 1.173380I
b = 0.681559 − 0.993043I
4.42249 − 11.60810I 0
u = −1.115170 − 0.723638I
a = −0.339399 + 1.173380I
b = 0.681559 + 0.993043I
4.42249 + 11.60810I 0
u = −0.578647 + 0.272996I
a = 0.57081 − 2.37898I
b = 0.540330 − 0.147934I
0.160870 − 0.671910I −2.15622 + 10.18820I
u = −0.578647 − 0.272996I
a = 0.57081 + 2.37898I
b = 0.540330 + 0.147934I
0.160870 + 0.671910I −2.15622 − 10.18820I
u = 0.625939 + 0.130720I
a = 0.69693 − 1.62006I
b = −1.27363 − 0.94541I
2.36016 + 7.44357I 2.72331 − 8.71572I
u = 0.625939 − 0.130720I
a = 0.69693 + 1.62006I
b = −1.27363 + 0.94541I
2.36016 − 7.44357I 2.72331 + 8.71572I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533442 + 1.266060I
a = −0.080396 − 0.396039I
b = −0.441070 − 0.879956I
−0.767799 − 0.707140I 0
u = −0.533442 − 1.266060I
a = −0.080396 + 0.396039I
b = −0.441070 + 0.879956I
−0.767799 + 0.707140I 0
u = 0.503153 + 0.320623I
a = 0.813514 + 1.061800I
b = −1.04228 + 1.32124I
8.59840 + 2.41577I 10.35447 − 1.07003I
u = 0.503153 − 0.320623I
a = 0.813514 − 1.061800I
b = −1.04228 − 1.32124I
8.59840 − 2.41577I 10.35447 + 1.07003I
u = −1.12741 + 0.87171I
a = 0.366742 + 1.095350I
b = −1.115670 + 0.750715I
1.01755 − 6.41344I 0
u = −1.12741 − 0.87171I
a = 0.366742 − 1.095350I
b = −1.115670 − 0.750715I
1.01755 + 6.41344I 0
u = 0.85018 + 1.18672I
a = −0.035511 − 1.062400I
b = −1.076520 − 0.823273I
2.54061 + 10.54650I 0
u = 0.85018 − 1.18672I
a = −0.035511 + 1.062400I
b = −1.076520 + 0.823273I
2.54061 − 10.54650I 0
u = −1.31779 + 0.75264I
a = 0.154248 + 0.681986I
b = −0.704558 + 0.226547I
3.59558 − 3.21071I 0
u = −1.31779 − 0.75264I
a = 0.154248 − 0.681986I
b = −0.704558 − 0.226547I
3.59558 + 3.21071I 0
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07393 + 1.52551I
a = 0.188483 − 0.440292I
b = 0.559985 − 1.250220I
−0.90262 − 2.33430I 0
u = 0.07393 − 1.52551I
a = 0.188483 + 0.440292I
b = 0.559985 + 1.250220I
−0.90262 + 2.33430I 0
u = 1.24493 + 0.88674I
a = 0.003312 − 0.789661I
b = −0.733347 − 0.206691I
3.00880 + 7.71935I 0
u = 1.24493 − 0.88674I
a = 0.003312 + 0.789661I
b = −0.733347 + 0.206691I
3.00880 − 7.71935I 0
u = −0.453705 + 0.067556I
a = 1.09810 − 1.34637I
b = −1.45141 − 1.20638I
1.44591 + 2.04368I 6.19891 − 7.65821I
u = −0.453705 − 0.067556I
a = 1.09810 + 1.34637I
b = −1.45141 + 1.20638I
1.44591 − 2.04368I 6.19891 + 7.65821I
u = −0.404516 + 0.160541I
a = 0.82003 + 2.15188I
b = −0.441070 + 0.879956I
−0.767799 + 0.707140I −1.24485 − 4.27067I
u = −0.404516 − 0.160541I
a = 0.82003 − 2.15188I
b = −0.441070 − 0.879956I
−0.767799 − 0.707140I −1.24485 + 4.27067I
u = −1.25351 + 0.99399I
a = −0.115660 + 0.761637I
b = −0.736192 + 0.183930I
9.1239 − 11.3929I 0
u = −1.25351 − 0.99399I
a = −0.115660 − 0.761637I
b = −0.736192 − 0.183930I
9.1239 + 11.3929I 0
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.36377 + 1.56837I
a = 0.237958 + 0.409554I
b = 0.677280 + 1.077370I
−1.81586 + 7.53048I 0
u = −0.36377 − 1.56837I
a = 0.237958 − 0.409554I
b = 0.677280 − 1.077370I
−1.81586 − 7.53048I 0
u = 1.51405 + 0.60574I
a = −0.697006 + 0.215750I
b = 1.53643 + 0.52266I
7.01799 − 4.89766I 0
u = 1.51405 − 0.60574I
a = −0.697006 − 0.215750I
b = 1.53643 − 0.52266I
7.01799 + 4.89766I 0
u = −1.12746 + 1.17840I
a = 0.077668 + 0.451088I
b = −1.04228 + 1.32124I
8.59840 + 2.41577I 0
u = −1.12746 − 1.17840I
a = 0.077668 − 0.451088I
b = −1.04228 − 1.32124I
8.59840 − 2.41577I 0
u = 1.52190 + 0.73520I
a = 0.091226 − 0.489453I
b = −0.673521 − 0.205430I
10.39060 + 0.33751I 0
u = 1.52190 − 0.73520I
a = 0.091226 + 0.489453I
b = −0.673521 + 0.205430I
10.39060 − 0.33751I 0
u = −1.37300 + 1.05302I
a = 0.247643 + 0.695092I
b = −1.27363 + 0.94541I
2.36016 − 7.44357I 0
u = −1.37300 − 1.05302I
a = 0.247643 − 0.695092I
b = −1.27363 − 0.94541I
2.36016 + 7.44357I 0
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.47056 + 1.67845I
a = 0.246842 − 0.393743I
b = 0.681559 − 0.993043I
4.42249 − 11.60810I 0
u = 0.47056 − 1.67845I
a = 0.246842 + 0.393743I
b = 0.681559 + 0.993043I
4.42249 + 11.60810I 0
u = 1.34694 + 1.13133I
a = 0.119382 − 0.726589I
b = −1.15971 − 0.96631I
9.5516 + 10.5652I 0
u = 1.34694 − 1.13133I
a = 0.119382 + 0.726589I
b = −1.15971 + 0.96631I
9.5516 − 10.5652I 0
u = −1.81161
a = −0.588467
b = 1.85662
2.24749 0
u = 0.149531 + 0.022926I
a = 3.10840 + 10.08440I
b = 0.677148 + 0.214687I
4.86393 + 2.30422I 5.13678 − 7.19189I
u = 0.149531 − 0.022926I
a = 3.10840 − 10.08440I
b = 0.677148 − 0.214687I
4.86393 − 2.30422I 5.13678 + 7.19189I
u = −0.07748 + 1.89589I
a = 0.421157 + 0.046884I
b = 0.432044 + 0.349969I
4.00496 − 0.11590I 0
u = −0.07748 − 1.89589I
a = 0.421157 − 0.046884I
b = 0.432044 − 0.349969I
4.00496 + 0.11590I 0
u = 1.51690 + 1.21579I
a = 0.246784 − 0.484838I
b = −1.45141 − 1.20638I
1.44591 + 2.04368I 0
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51690 − 1.21579I
a = 0.246784 + 0.484838I
b = −1.45141 + 1.20638I
1.44591 − 2.04368I 0
u = 0.00499 + 1.94799I
a = 0.181253 + 0.319408I
b = 0.327313 + 0.897043I
6.88898 − 0.12974I 0
u = 0.00499 − 1.94799I
a = 0.181253 − 0.319408I
b = 0.327313 − 0.897043I
6.88898 + 0.12974I 0
u = 3.02357 + 0.90413I
a = −0.0518628 + 0.0420595I
b = −0.366627 + 0.170388I
5.01112 + 0.52164I 0
u = 3.02357 − 0.90413I
a = −0.0518628 − 0.0420595I
b = −0.366627 − 0.170388I
5.01112 − 0.52164I 0
u = 8.91180
a = −0.0139790
b = 0.0996704
0.00210462 0
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
25
− 3u
24
+ ··· − 40u + 56)(u
35
− 3u
34
+ ··· + 13u − 1)
· (u
116
+ 5u
115
+ ··· − 293824u − 18872)
c
2
(u
25
− 8u
24
+ ··· − 3u − 1)(u
35
− 25u
34
+ ··· + 24576u − 2048)
· (u
58
+ 14u
57
+ ··· + 2u + 1)
2
c
4
, c
11
64(8u
25
+ 8u
24
+ ··· + 5u
2
+ 1)(u
35
+ 7u
34
+ ··· − 3u + 1)
· (8u
116
+ 104u
115
+ ··· − 107834072u + 36867937)
c
5
, c
10
64(8u
25
− 8u
24
+ ··· + 11u
2
− 1)(u
35
+ 5u
34
+ ··· − 3u + 1)
· (8u
116
+ 104u
115
+ ··· + 65126u − 4735)
c
6
, c
9
(u
25
− u
24
+ ··· − 8u − 8)(u
35
− u
34
+ ··· + 8u − 1)
· (u
116
+ 15u
115
+ ··· + 417760u + 52936)
c
7
, c
8
(u
25
+ 2u
24
+ ··· − 2u + 1)(u
35
+ 11u
34
+ ··· + 384u + 32)
· (u
58
− 6u
57
+ ··· − 24u + 1)
2
c
12
(u
25
− 2u
24
+ ··· − 2u − 1)(u
35
+ 11u
34
+ ··· + 384u + 32)
· (u
58
− 6u
57
+ ··· − 24u + 1)
2
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
25
− 3y
24
+ ··· + 19072y −3136)(y
35
+ 11y
34
+ ··· + 29y −1)
· (y
116
− 93y
115
+ ··· − 74449976896y + 356152384)
c
2
(y
25
+ 10y
24
+ ··· + 37y −1)
· (y
35
+ 15y
34
+ ··· − 90177536y −4194304)
· (y
58
− 14y
57
+ ··· − 132y + 1)
2
c
4
, c
11
4096(64y
25
− 448y
24
+ ··· − 10y −1)(y
35
− 51y
34
+ ··· + 35y −1)
· (64y
116
− 6720y
115
+ ··· − 1.68 × 10
17
y + 1.36 × 10
15
)
c
5
, c
10
4096(64y
25
− 704y
24
+ ··· + 22y −1)(y
35
− 39y
34
+ ··· + 27y −1)
· (64y
116
− 5184y
115
+ ··· − 3550066936y + 22420225)
c
6
, c
9
(y
25
− 7y
24
+ ··· + 192y −64)(y
35
− y
34
+ ··· + 28y −1)
· (y
116
− 105y
115
+ ··· − 367121525120y + 2802220096)
c
7
, c
8
, c
12
(y
25
+ 26y
24
+ ··· + 46y −1)(y
35
+ 31y
34
+ ··· − 7680y −1024)
· (y
58
+ 58y
57
+ ··· − 272y + 1)
2
31
