12a
0103
(K12a
0103
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 4 1 6 9 7 11
Solving Sequence
5,10 3,6
2 1 4 9 11 8 12 7
c
5
c
2
c
1
c
4
c
9
c
10
c
8
c
12
c
6
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h485u
52
+ 571u
51
+ ··· + 256b − 1197, 255u
52
+ 685u
51
+ ··· + 512a − 1291,
u
53
+ 11u
51
+ ··· + 2u − 1i
I
u
2
= h1.48632 × 10
75
u
77
+ 6.02333 × 10
75
u
76
+ ··· + 2.52373 × 10
76
b − 9.27713 × 10
75
,
3.70085 × 10
76
u
77
+ 3.43747 × 10
76
u
76
+ ··· + 2.52373 × 10
76
a − 1.83649 × 10
77
, u
78
+ 2u
77
+ ··· + 6u + 9i
I
u
3
= hb + 1, −u
3
+ u
2
+ 2a + 1, u
4
+ u
2
+ u + 1i
I
u
4
= h11588a
5
u + 5390a
4
u + ··· + 14326a − 45947,
a
6
− 2a
5
u − a
5
+ 6a
4
u − 6a
4
− 10a
3
u + 12a
3
+ 8a
2
u − 17a
2
− au + 12a − u − 4, u
2
+ 1i
I
u
5
= hb + 1, u
5
− u
4
+ u
3
− u
2
+ a + u, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 153 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
= h485u
52
+ 571u
51
+ · · · + 256b − 1197, 255u
52
+ 685u
51
+ · · · +
512a − 1291, u
53
+ 11u
51
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−0.498047u
52
− 1.33789u
51
+ ··· + 1.50586u + 2.52148
−1.89453u
52
− 2.23047u
51
+ ··· − 8.43359u + 4.67578
a
6
=
1
−u
2
a
2
=
−2.39258u
52
− 3.56836u
51
+ ··· − 6.92773u + 7.19727
−1.89453u
52
− 2.23047u
51
+ ··· − 8.43359u + 4.67578
a
1
=
0.0156250u
52
+ 0.156250u
50
+ ··· + 0.0312500u
2
− 1.01563u
0.0156250u
52
+ 0.156250u
50
+ ··· + 0.0312500u
2
− 1.01563u
a
4
=
−3.06836u
52
+ 3.49805u
51
+ ··· + 32.8574u − 6.51758
−0.144531u
52
+ 1.17578u
51
+ ··· + 9.44141u − 3.23047
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
0.296875u
52
− 0.0625000u
51
+ ··· − 1.45313u + 0.0625000
0.281250u
52
− 0.0625000u
51
+ ··· + 0.562500u + 0.0625000
a
12
=
0.0156250u
52
+ 0.156250u
50
+ ··· + 0.0312500u
2
− 1.01563u
0.0156250u
52
+ 0.156250u
50
+ ··· + 0.0312500u
2
− 1.01563u
a
7
=
−0.0156250u
51
− 0.156250u
49
+ ··· − 0.0312500u + 1.01563
−0.0156250u
51
− 0.156250u
49
+ ··· − 0.0312500u + 0.0156250
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
12761
1024
u
52
+
637
1024
u
51
+ ··· +
41973
1024
u −
10363
1024
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 25u
52
+ ··· + 225u + 16
c
2
, c
4
u
53
− 5u
52
+ ··· − 31u + 4
c
3
, c
7
u
53
+ 3u
52
+ ··· + 240u + 64
c
5
, c
6
, c
9
c
11
u
53
+ 11u
51
+ ··· + 2u + 1
c
8
u
53
− 24u
52
+ ··· + 284992u − 13252
c
10
, c
12
u
53
+ 22u
52
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 11y
52
+ ··· + 12609y −256
c
2
, c
4
y
53
− 25y
52
+ ··· + 225y −16
c
3
, c
7
y
53
+ 27y
52
+ ··· − 52992y −4096
c
5
, c
6
, c
9
c
11
y
53
+ 22y
52
+ ··· + 2y −1
c
8
y
53
+ 14y
52
+ ··· + 16670504648y −175615504
c
10
, c
12
y
53
+ 34y
52
+ ··· + 430y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.844605 + 0.537356I
a = −0.394940 + 1.319150I
b = 0.482681 − 0.906143I
7.13953 − 1.46853I 3.05642 − 1.15684I
u = 0.844605 − 0.537356I
a = −0.394940 − 1.319150I
b = 0.482681 + 0.906143I
7.13953 + 1.46853I 3.05642 + 1.15684I
u = −0.746200 + 0.650275I
a = 0.65129 + 1.97744I
b = −0.789249 − 0.567770I
2.34452 − 3.26844I −0.51125 + 5.76632I
u = −0.746200 − 0.650275I
a = 0.65129 − 1.97744I
b = −0.789249 + 0.567770I
2.34452 + 3.26844I −0.51125 − 5.76632I
u = 0.859754 + 0.483213I
a = −0.38717 − 1.39339I
b = 1.121840 + 0.675604I
5.19709 − 7.28348I 0.48893 + 3.47582I
u = 0.859754 − 0.483213I
a = −0.38717 + 1.39339I
b = 1.121840 − 0.675604I
5.19709 + 7.28348I 0.48893 − 3.47582I
u = −0.444486 + 0.932745I
a = 0.491844 − 0.136281I
b = 0.233679 + 0.757163I
−0.57052 − 1.45035I −2.79476 + 3.95223I
u = −0.444486 − 0.932745I
a = 0.491844 + 0.136281I
b = 0.233679 − 0.757163I
−0.57052 + 1.45035I −2.79476 − 3.95223I
u = −0.390178 + 0.976401I
a = 1.145310 + 0.082252I
b = 1.140120 − 0.553417I
−3.14846 + 3.44539I −6.75217 + 0.85835I
u = −0.390178 − 0.976401I
a = 1.145310 − 0.082252I
b = 1.140120 + 0.553417I
−3.14846 − 3.44539I −6.75217 − 0.85835I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774197 + 0.542491I
a = 0.85888 − 1.62998I
b = −0.887679 + 0.562853I
2.03702 + 1.25848I −0.673597 − 0.424058I
u = −0.774197 − 0.542491I
a = 0.85888 + 1.62998I
b = −0.887679 − 0.562853I
2.03702 − 1.25848I −0.673597 + 0.424058I
u = 0.726981 + 0.585127I
a = −0.009615 − 0.462839I
b = −1.287760 + 0.038128I
0.693282 + 1.084750I 0.84034 − 2.20672I
u = 0.726981 − 0.585127I
a = −0.009615 + 0.462839I
b = −1.287760 − 0.038128I
0.693282 − 1.084750I 0.84034 + 2.20672I
u = 0.814949 + 0.692011I
a = −0.887492 − 1.038560I
b = 0.563908 + 0.890363I
7.65604 + 3.06196I 2.85560 − 3.26676I
u = 0.814949 − 0.692011I
a = −0.887492 + 1.038560I
b = 0.563908 − 0.890363I
7.65604 − 3.06196I 2.85560 + 3.26676I
u = 0.470464 + 0.988202I
a = −0.934410 + 0.574092I
b = −1.106270 − 0.444712I
−4.62810 + 2.33151I −8.31817 − 4.26180I
u = 0.470464 − 0.988202I
a = −0.934410 − 0.574092I
b = −1.106270 + 0.444712I
−4.62810 − 2.33151I −8.31817 + 4.26180I
u = 0.804049 + 0.749929I
a = −0.00655 + 1.93316I
b = 1.075070 − 0.706203I
6.10623 + 8.94206I 0. − 8.23482I
u = 0.804049 − 0.749929I
a = −0.00655 − 1.93316I
b = 1.075070 + 0.706203I
6.10623 − 8.94206I 0. + 8.23482I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493094 + 1.016010I
a = −1.59707 + 1.11315I
b = −1.224240 − 0.290078I
−5.00368 − 4.93594I 0. + 4.73918I
u = −0.493094 − 1.016010I
a = −1.59707 − 1.11315I
b = −1.224240 + 0.290078I
−5.00368 + 4.93594I 0. − 4.73918I
u = 0.539831 + 1.037300I
a = 0.105849 − 0.458183I
b = −0.187882 + 0.590351I
−1.99960 + 6.36988I 0
u = 0.539831 − 1.037300I
a = 0.105849 + 0.458183I
b = −0.187882 − 0.590351I
−1.99960 − 6.36988I 0
u = 0.474089 + 1.104130I
a = 1.45581 + 0.65433I
b = 1.039890 − 0.411852I
−4.93184 + 9.37986I 0
u = 0.474089 − 1.104130I
a = 1.45581 − 0.65433I
b = 1.039890 + 0.411852I
−4.93184 − 9.37986I 0
u = −0.426782 + 0.618645I
a = 0.698536 − 0.258889I
b = 0.435081 + 0.010200I
0.44614 − 1.46892I 2.45505 + 4.68880I
u = −0.426782 − 0.618645I
a = 0.698536 + 0.258889I
b = 0.435081 − 0.010200I
0.44614 + 1.46892I 2.45505 − 4.68880I
u = −0.686999 + 1.049580I
a = −0.605852 + 0.318491I
b = 0.975791 − 0.737857I
4.17657 − 2.47366I 0
u = −0.686999 − 1.049580I
a = −0.605852 − 0.318491I
b = 0.975791 + 0.737857I
4.17657 + 2.47366I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621345 + 1.112370I
a = 1.075420 + 0.442373I
b = −0.599743 − 0.611629I
−0.66028 + 7.35987I 0
u = 0.621345 − 1.112370I
a = 1.075420 − 0.442373I
b = −0.599743 + 0.611629I
−0.66028 − 7.35987I 0
u = 0.539838 + 1.154700I
a = 0.717944 + 0.714192I
b = 0.883741 + 0.288728I
−3.93061 + 6.79883I 0
u = 0.539838 − 1.154700I
a = 0.717944 − 0.714192I
b = 0.883741 − 0.288728I
−3.93061 − 6.79883I 0
u = −0.096857 + 0.706472I
a = 1.85712 − 0.36666I
b = 1.090240 + 0.526644I
−2.02645 − 6.10811I −2.24190 + 8.19963I
u = −0.096857 − 0.706472I
a = 1.85712 + 0.36666I
b = 1.090240 − 0.526644I
−2.02645 + 6.10811I −2.24190 − 8.19963I
u = −0.676066 + 1.095520I
a = 0.49625 − 1.44952I
b = 0.685624 + 0.854997I
5.06062 − 8.35366I 0
u = −0.676066 − 1.095520I
a = 0.49625 + 1.44952I
b = 0.685624 − 0.854997I
5.06062 + 8.35366I 0
u = −0.613282 + 1.139020I
a = −0.755202 + 1.068640I
b = −1.318570 + 0.147882I
−2.88387 − 9.43954I 0
u = −0.613282 − 1.139020I
a = −0.755202 − 1.068640I
b = −1.318570 − 0.147882I
−2.88387 + 9.43954I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622036 + 1.155390I
a = −0.75797 − 2.29648I
b = −0.998224 + 0.581247I
−1.84844 + 12.09700I 0
u = 0.622036 − 1.155390I
a = −0.75797 + 2.29648I
b = −0.998224 − 0.581247I
−1.84844 − 12.09700I 0
u = −0.677239 + 0.115101I
a = −0.061726 − 0.714385I
b = 0.837450 + 0.532669I
1.46373 − 2.16929I 1.93538 + 4.15379I
u = −0.677239 − 0.115101I
a = −0.061726 + 0.714385I
b = 0.837450 − 0.532669I
1.46373 + 2.16929I 1.93538 − 4.15379I
u = −0.639069 + 1.170490I
a = −1.063440 + 0.188750I
b = 0.391398 − 0.937341I
3.10719 − 12.78830I 0
u = −0.639069 − 1.170490I
a = −1.063440 − 0.188750I
b = 0.391398 + 0.937341I
3.10719 + 12.78830I 0
u = −0.628804 + 1.188570I
a = 1.19762 − 2.06359I
b = 1.169860 + 0.651568I
0.7390 − 18.5909I 0
u = −0.628804 − 1.188570I
a = 1.19762 + 2.06359I
b = 1.169860 − 0.651568I
0.7390 + 18.5909I 0
u = −0.176786 + 0.620062I
a = 0.296057 − 0.355210I
b = 0.298074 − 0.573972I
0.15122 − 1.66122I 0.02280 + 4.79040I
u = −0.176786 − 0.620062I
a = 0.296057 + 0.355210I
b = 0.298074 + 0.573972I
0.15122 + 1.66122I 0.02280 − 4.79040I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.041304 + 0.584795I
a = −2.10977 − 0.99440I
b = −1.094520 + 0.329766I
−3.36770 + 1.13739I −6.84638 − 1.16126I
u = 0.041304 − 0.584795I
a = −2.10977 + 0.99440I
b = −1.094520 − 0.329766I
−3.36770 − 1.13739I −6.84638 + 1.16126I
u = 0.221586
a = 2.54657
b = −0.860639
−1.25306 −8.27550
10
II.
I
u
2
= h1.49 × 10
75
u
77
+ 6.02 × 10
75
u
76
+ · · · + 2.52 × 10
76
b − 9.28 × 10
75
, 3.70 ×
10
76
u
77
+3.44×10
76
u
76
+· · ·+2.52×10
76
a−1.84×10
77
, u
78
+2u
77
+· · ·+6u+9i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−1.46642u
77
− 1.36206u
76
+ ··· − 8.66569u + 7.27687
−0.0588937u
77
− 0.238668u
76
+ ··· − 0.527651u + 0.367596
a
6
=
1
−u
2
a
2
=
−1.52532u
77
− 1.60073u
76
+ ··· − 9.19334u + 7.64447
−0.0588937u
77
− 0.238668u
76
+ ··· − 0.527651u + 0.367596
a
1
=
−0.780270u
77
− 0.336235u
76
+ ··· − 15.3353u + 6.80859
0.620306u
77
+ 0.773476u
76
+ ··· + 6.32818u − 0.178950
a
4
=
−1.73384u
77
− 2.69724u
76
+ ··· − 5.01778u + 1.40397
−0.989604u
77
− 1.18721u
76
+ ··· − 9.21326u + 0.938935
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
−1.45480u
77
− 2.42612u
76
+ ··· − 13.8787u − 8.41438
0.201187u
77
+ 0.892869u
76
+ ··· + 0.751571u + 6.85187
a
12
=
−0.152595u
77
+ 0.108414u
76
+ ··· − 11.1909u + 4.25935
0.690807u
77
+ 0.684760u
76
+ ··· + 4.07690u − 1.20358
a
7
=
−0.960940u
77
− 1.31404u
76
+ ··· − 12.0629u − 6.62600
0.283248u
77
+ 1.19417u
76
+ ··· + 0.173493u + 6.84390
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.20245u
77
+ 0.551265u
76
+ ··· − 20.0210u + 21.7446
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
39
+ 18u
38
+ ··· + 17u + 1)
2
c
2
, c
4
(u
39
− 4u
38
+ ··· + u + 1)
2
c
3
, c
7
(u
39
− u
38
+ ··· + 20u − 8)
2
c
5
, c
6
, c
9
c
11
u
78
− 2u
77
+ ··· − 6u + 9
c
8
(u
39
+ 8u
38
+ ··· − 168u − 49)
2
c
10
, c
12
u
78
+ 42u
77
+ ··· + 1296u + 81
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
39
+ 10y
38
+ ··· + 273y −1)
2
c
2
, c
4
(y
39
− 18y
38
+ ··· + 17y −1)
2
c
3
, c
7
(y
39
+ 21y
38
+ ··· − 304y −64)
2
c
5
, c
6
, c
9
c
11
y
78
+ 42y
77
+ ··· + 1296y + 81
c
8
(y
39
+ 16y
38
+ ··· − 14896y −2401)
2
c
10
, c
12
y
78
− 14y
77
+ ··· + 160056y + 6561
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935752 + 0.334076I
a = −0.08446 + 1.47463I
b = 1.151380 − 0.661742I
3.33204 + 12.88680I 0. − 8.07914I
u = −0.935752 − 0.334076I
a = −0.08446 − 1.47463I
b = 1.151380 + 0.661742I
3.33204 − 12.88680I 0. + 8.07914I
u = −0.921632 + 0.370797I
a = −0.493133 − 1.090290I
b = 0.428310 + 0.923778I
5.52956 + 7.07830I 0
u = −0.921632 − 0.370797I
a = −0.493133 + 1.090290I
b = 0.428310 − 0.923778I
5.52956 − 7.07830I 0
u = −0.877103 + 0.502010I
a = −0.656251 + 1.183820I
b = 0.627750 − 0.866354I
6.84827 + 2.62234I 0
u = −0.877103 − 0.502010I
a = −0.656251 − 1.183820I
b = 0.627750 + 0.866354I
6.84827 − 2.62234I 0
u = −0.853435 + 0.563480I
a = −0.25126 − 1.65338I
b = 1.025900 + 0.718007I
5.63946 − 3.22969I 0
u = −0.853435 − 0.563480I
a = −0.25126 + 1.65338I
b = 1.025900 − 0.718007I
5.63946 + 3.22969I 0
u = −0.421079 + 0.866093I
a = 0.240345 + 0.226094I
b = −0.004189 − 0.473649I
−0.25831 − 1.95518I 0. + 3.73688I
u = −0.421079 − 0.866093I
a = 0.240345 − 0.226094I
b = −0.004189 + 0.473649I
−0.25831 + 1.95518I 0. − 3.73688I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.875936 + 0.365211I
a = 0.44784 + 1.76875I
b = −0.957399 − 0.572535I
0.52341 − 6.57302I −4.00000 + 5.57627I
u = 0.875936 − 0.365211I
a = 0.44784 − 1.76875I
b = −0.957399 + 0.572535I
0.52341 + 6.57302I −4.00000 − 5.57627I
u = −0.369999 + 0.985790I
a = −0.21949 + 2.01027I
b = −1.206930 + 0.129766I
−5.82579 − 1.13990I 0
u = −0.369999 − 0.985790I
a = −0.21949 − 2.01027I
b = −1.206930 − 0.129766I
−5.82579 + 1.13990I 0
u = 0.432345 + 0.972168I
a = −0.35265 − 3.47114I
b = −0.953268 + 0.489041I
−4.91649 + 3.39278I 0
u = 0.432345 − 0.972168I
a = −0.35265 + 3.47114I
b = −0.953268 − 0.489041I
−4.91649 − 3.39278I 0
u = −0.495177 + 0.949384I
a = −1.70830 + 0.52430I
b = 0.434521 − 0.849125I
−0.22948 − 3.68428I 0
u = −0.495177 − 0.949384I
a = −1.70830 − 0.52430I
b = 0.434521 + 0.849125I
−0.22948 + 3.68428I 0
u = 0.819566 + 0.432655I
a = 0.85930 − 1.51844I
b = −0.679795 + 0.572535I
1.37297 − 1.97475I −1.44784 + 0.I
u = 0.819566 − 0.432655I
a = 0.85930 + 1.51844I
b = −0.679795 − 0.572535I
1.37297 + 1.97475I −1.44784 + 0.I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203106 + 1.060070I
a = 0.968752 − 0.567684I
b = −0.253426
−4.02522 0
u = 0.203106 − 1.060070I
a = 0.968752 + 0.567684I
b = −0.253426
−4.02522 0
u = −0.837403 + 0.377136I
a = −0.135228 + 0.197181I
b = −1.300720 − 0.108633I
−0.61125 + 4.04441I −1.85906 − 4.24790I
u = −0.837403 − 0.377136I
a = −0.135228 − 0.197181I
b = −1.300720 + 0.108633I
−0.61125 − 4.04441I −1.85906 + 4.24790I
u = 0.266721 + 0.837772I
a = 3.01041 + 0.57884I
b = −0.769146 − 0.335047I
−4.08864 − 0.29456I −5.95022 − 1.12683I
u = 0.266721 − 0.837772I
a = 3.01041 − 0.57884I
b = −0.769146 + 0.335047I
−4.08864 + 0.29456I −5.95022 + 1.12683I
u = −0.515622 + 0.997585I
a = 0.84314 − 2.88844I
b = 1.122760 + 0.637619I
−2.29395 − 9.20929I 0
u = −0.515622 − 0.997585I
a = 0.84314 + 2.88844I
b = 1.122760 − 0.637619I
−2.29395 + 9.20929I 0
u = −0.447755 + 0.743794I
a = −0.17566 − 2.38873I
b = 0.538688 + 0.783208I
0.486734 − 0.249361I −1.00470 + 2.68648I
u = −0.447755 − 0.743794I
a = −0.17566 + 2.38873I
b = 0.538688 − 0.783208I
0.486734 + 0.249361I −1.00470 − 2.68648I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.297469 + 1.100820I
a = 1.47876 − 0.64965I
b = 0.998340 + 0.492226I
−2.23729 − 5.41055I 0
u = −0.297469 − 1.100820I
a = 1.47876 + 0.64965I
b = 0.998340 − 0.492226I
−2.23729 + 5.41055I 0
u = −0.633476 + 0.972542I
a = 1.224690 − 0.692034I
b = −0.679795 + 0.572535I
1.37297 − 1.97475I 0
u = −0.633476 − 0.972542I
a = 1.224690 + 0.692034I
b = −0.679795 − 0.572535I
1.37297 + 1.97475I 0
u = 0.731432 + 0.901891I
a = −0.737944 − 0.598065I
b = 1.025900 + 0.718007I
5.63946 − 3.22969I 0
u = 0.731432 − 0.901891I
a = −0.737944 + 0.598065I
b = 1.025900 − 0.718007I
5.63946 + 3.22969I 0
u = 0.087507 + 1.177660I
a = −0.21659 − 1.40236I
b = −0.769146 + 0.335047I
−4.08864 + 0.29456I 0
u = 0.087507 − 1.177660I
a = −0.21659 + 1.40236I
b = −0.769146 − 0.335047I
−4.08864 − 0.29456I 0
u = −0.477826 + 1.085810I
a = 0.517883 − 0.686632I
b = 0.815381 − 0.342489I
−1.20519 − 1.94841I 0
u = −0.477826 − 1.085810I
a = 0.517883 + 0.686632I
b = 0.815381 + 0.342489I
−1.20519 + 1.94841I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.614881 + 1.018800I
a = −0.484419 − 1.098040I
b = −1.300720 − 0.108633I
−0.61125 + 4.04441I 0
u = 0.614881 − 1.018800I
a = −0.484419 + 1.098040I
b = −1.300720 + 0.108633I
−0.61125 − 4.04441I 0
u = 0.711619 + 0.958350I
a = 0.26945 + 1.55535I
b = 0.627750 − 0.866354I
6.84827 + 2.62234I 0
u = 0.711619 − 0.958350I
a = 0.26945 − 1.55535I
b = 0.627750 + 0.866354I
6.84827 − 2.62234I 0
u = 0.187819 + 0.782324I
a = −1.79504 − 1.27965I
b = −1.110300 + 0.306863I
−3.39626 + 1.13373I −6.95849 − 0.14045I
u = 0.187819 − 0.782324I
a = −1.79504 + 1.27965I
b = −1.110300 − 0.306863I
−3.39626 − 1.13373I −6.95849 + 0.14045I
u = 0.398905 + 1.143860I
a = 0.399985 + 1.104750I
b = 0.905691 + 0.426992I
−5.44128 − 1.70381I 0
u = 0.398905 − 1.143860I
a = 0.399985 − 1.104750I
b = 0.905691 − 0.426992I
−5.44128 + 1.70381I 0
u = 0.759719 + 0.204246I
a = 0.417590 + 0.399149I
b = 0.815381 − 0.342489I
−1.20519 − 1.94841I −1.31413 − 1.52369I
u = 0.759719 − 0.204246I
a = 0.417590 − 0.399149I
b = 0.815381 + 0.342489I
−1.20519 + 1.94841I −1.31413 + 1.52369I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632994 + 1.047620I
a = −0.43262 + 2.44367I
b = −0.957399 − 0.572535I
0.52341 − 6.57302I 0
u = −0.632994 − 1.047620I
a = −0.43262 − 2.44367I
b = −0.957399 + 0.572535I
0.52341 + 6.57302I 0
u = −0.194999 + 1.212780I
a = −2.16514 + 0.77747I
b = −1.206930 − 0.129766I
−5.82579 + 1.13990I 0
u = −0.194999 − 1.212780I
a = −2.16514 − 0.77747I
b = −1.206930 + 0.129766I
−5.82579 − 1.13990I 0
u = −0.458461 + 0.618159I
a = −1.75992 + 1.51732I
b = 1.059740 − 0.631021I
−1.08550 + 5.08722I −3.54287 − 2.85265I
u = −0.458461 − 0.618159I
a = −1.75992 − 1.51732I
b = 1.059740 + 0.631021I
−1.08550 − 5.08722I −3.54287 + 2.85265I
u = 0.665003 + 1.069840I
a = −1.145490 − 0.380431I
b = 0.428310 + 0.923778I
5.52956 + 7.07830I 0
u = 0.665003 − 1.069840I
a = −1.145490 + 0.380431I
b = 0.428310 − 0.923778I
5.52956 − 7.07830I 0
u = 0.329786 + 1.218560I
a = 1.56598 + 0.65685I
b = 0.905691 − 0.426992I
−5.44128 + 1.70381I 0
u = 0.329786 − 1.218560I
a = 1.56598 − 0.65685I
b = 0.905691 + 0.426992I
−5.44128 − 1.70381I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.007648 + 1.268320I
a = 1.173280 − 0.503651I
b = 1.059740 + 0.631021I
−1.08550 − 5.08722I 0
u = 0.007648 − 1.268320I
a = 1.173280 + 0.503651I
b = 1.059740 − 0.631021I
−1.08550 + 5.08722I 0
u = 0.191597 + 1.259150I
a = −0.654424 + 0.905197I
b = −0.953268 − 0.489041I
−4.91649 − 3.39278I 0
u = 0.191597 − 1.259150I
a = −0.654424 − 0.905197I
b = −0.953268 + 0.489041I
−4.91649 + 3.39278I 0
u = −0.053269 + 1.273150I
a = 0.189980 − 0.006366I
b = 0.538688 − 0.783208I
0.486734 + 0.249361I 0
u = −0.053269 − 1.273150I
a = 0.189980 + 0.006366I
b = 0.538688 + 0.783208I
0.486734 − 0.249361I 0
u = 0.652815 + 1.100720I
a = 0.94692 + 2.19782I
b = 1.151380 − 0.661742I
3.33204 + 12.88680I 0
u = 0.652815 − 1.100720I
a = 0.94692 − 2.19782I
b = 1.151380 + 0.661742I
3.33204 − 12.88680I 0
u = −0.177345 + 1.304430I
a = 0.268918 − 0.085683I
b = 0.434521 + 0.849125I
−0.22948 + 3.68428I 0
u = −0.177345 − 1.304430I
a = 0.268918 + 0.085683I
b = 0.434521 − 0.849125I
−0.22948 − 3.68428I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542144 + 0.391790I
a = 0.860446 + 0.302145I
b = −0.004189 − 0.473649I
−0.25831 − 1.95518I −1.07609 + 3.73688I
u = 0.542144 − 0.391790I
a = 0.860446 − 0.302145I
b = −0.004189 + 0.473649I
−0.25831 + 1.95518I −1.07609 − 3.73688I
u = −0.212141 + 1.319690I
a = 1.064230 + 0.372067I
b = 1.122760 − 0.637619I
−2.29395 + 9.20929I 0
u = −0.212141 − 1.319690I
a = 1.064230 − 0.372067I
b = 1.122760 + 0.637619I
−2.29395 − 9.20929I 0
u = 0.572001 + 0.029826I
a = −0.286051 + 0.334344I
b = 0.998340 + 0.492226I
−2.23729 − 5.41055I −4.42668 + 7.07273I
u = 0.572001 − 0.029826I
a = −0.286051 − 0.334344I
b = 0.998340 − 0.492226I
−2.23729 + 5.41055I −4.42668 − 7.07273I
u = −0.237613 + 0.375704I
a = −1.99381 + 0.34348I
b = −1.110300 + 0.306863I
−3.39626 + 1.13373I −6.95849 − 0.14045I
u = −0.237613 − 0.375704I
a = −1.99381 − 0.34348I
b = −1.110300 − 0.306863I
−3.39626 − 1.13373I −6.95849 + 0.14045I
21
III. I
u
3
= hb + 1, −u
3
+ u
2
+ 2a + 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
1
2
u
3
−
1
2
u
2
−
1
2
−1
a
6
=
1
−u
2
a
2
=
1
2
u
3
−
1
2
u
2
−
3
2
−1
a
1
=
−1
0
a
4
=
1
2
u
3
−
1
2
u
2
−
1
2
−1
a
9
=
−u
u
3
+ u
a
11
=
−u
3
−u
2
a
8
=
u
3
u
3
+ u
a
12
=
−u
3
− u
2
− u − 1
−u
2
− u − 1
a
7
=
u
3
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11
4
u
3
−
21
4
u
2
−
1
2
u −
31
4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
2
+ u + 1
c
8
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
9
, c
11
u
4
+ u
2
− u + 1
c
10
, c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
8
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = −0.278726 + 0.483420I
b = −1.00000
−0.66484 − 1.39709I −6.15099 + 3.96898I
u = −0.547424 − 0.585652I
a = −0.278726 − 0.483420I
b = −1.00000
−0.66484 + 1.39709I −6.15099 − 3.96898I
u = 0.547424 + 1.120870I
a = −0.971274 − 0.813859I
b = −1.00000
−4.26996 + 7.64338I −8.22401 − 8.10462I
u = 0.547424 − 1.120870I
a = −0.971274 + 0.813859I
b = −1.00000
−4.26996 − 7.64338I −8.22401 + 8.10462I
25
IV. I
u
4
=
h11588a
5
u+5390a
4
u+· · ·+14326a−45947, −2a
5
u+6a
4
u+· · ·+12a−4, u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
a
−0.301559a
5
u − 0.140266a
4
u + ··· − 0.372811a + 1.19570
a
6
=
1
1
a
2
=
−0.301559a
5
u − 0.140266a
4
u + ··· + 0.627189a + 1.19570
−0.301559a
5
u − 0.140266a
4
u + ··· − 0.372811a + 1.19570
a
1
=
−0.107919a
5
u + 0.290213a
4
u + ··· + 2.24519a − 0.0820777
−0.107919a
5
u + 0.290213a
4
u + ··· + 2.24519a − 0.0820777
a
4
=
0.421084a
5
u + 0.441460a
4
u + ··· + 1.25461a − 0.959143
0.299607a
5
u + 0.383116a
4
u + ··· + 0.829781a − 1.01689
a
9
=
−u
0
a
11
=
u
u
a
8
=
−0.00416374a
5
u − 0.0596976a
4
u + ··· − 1.24735a + 1.09257
−0.112083a
5
u + 0.230515a
4
u + ··· + 0.997840a + 1.01049
a
12
=
−0.107919a
5
u + 0.290213a
4
u + ··· + 2.24519a − 0.0820777
−0.107919a
5
u + 0.290213a
4
u + ··· + 2.24519a − 0.0820777
a
7
=
−0.0605304a
5
u − 0.126187a
4
u + ··· − 0.450048a + 0.0164988
−0.0605304a
5
u − 0.126187a
4
u + ··· − 0.450048a + 1.01650
(ii) Obstruction class = 1
(iii) Cusp Shapes =
14908
38427
a
5
u +
9636
12809
a
5
−
27168
12809
a
4
u +
3940
38427
a
4
+
76600
38427
a
3
u −
292436
38427
a
3
−
38968
38427
a
2
u +
498880
38427
a
2
−
169028
38427
au −
188864
12809
a +
248464
38427
u −
36716
12809
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
7
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
, c
6
, c
9
c
11
(u
2
+ 1)
6
c
8
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
10
, c
12
(u + 1)
12
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
, c
7
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
5
, c
6
, c
9
c
11
(y + 1)
12
c
8
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
10
, c
12
(y −1)
12
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.642486 + 0.561491I
b = 0.428243 − 0.664531I
−1.39926 − 0.92430I −6.28328 + 0.79423I
u = 1.000000I
a = 0.045578 + 0.758053I
b = 0.428243 + 0.664531I
−1.39926 + 0.92430I −6.28328 − 0.79423I
u = 1.000000I
a = 0.396494 − 1.200400I
b = −1.002190 + 0.295542I
−5.18047 + 0.92430I −13.71672 − 0.79423I
u = 1.000000I
a = 0.596223 − 0.272874I
b = 1.073950 + 0.558752I
−3.28987 − 5.69302I −10.00000 + 5.51057I
u = 1.000000I
a = 2.23400 + 0.48963I
b = 1.073950 − 0.558752I
−3.28987 + 5.69302I −10.00000 − 5.51057I
u = 1.000000I
a = −2.91479 + 1.66410I
b = −1.002190 − 0.295542I
−5.18047 − 0.92430I −13.71672 + 0.79423I
u = − 1.000000I
a = 0.642486 − 0.561491I
b = 0.428243 + 0.664531I
−1.39926 + 0.92430I −6.28328 − 0.79423I
u = − 1.000000I
a = 0.045578 − 0.758053I
b = 0.428243 − 0.664531I
−1.39926 − 0.92430I −6.28328 + 0.79423I
u = − 1.000000I
a = 0.396494 + 1.200400I
b = −1.002190 − 0.295542I
−5.18047 − 0.92430I −13.71672 + 0.79423I
u = − 1.000000I
a = 0.596223 + 0.272874I
b = 1.073950 − 0.558752I
−3.28987 + 5.69302I −10.00000 − 5.51057I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 2.23400 − 0.48963I
b = 1.073950 + 0.558752I
−3.28987 − 5.69302I −10.00000 + 5.51057I
u = − 1.000000I
a = −2.91479 − 1.66410I
b = −1.002190 + 0.295542I
−5.18047 + 0.92430I −13.71672 − 0.79423I
30
V. I
u
5
= hb + 1, u
5
− u
4
+ u
3
− u
2
+ a + u, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−u
5
+ u
4
− u
3
+ u
2
− u
−1
a
6
=
1
−u
2
a
2
=
−u
5
+ u
4
− u
3
+ u
2
− u − 1
−1
a
1
=
−1
0
a
4
=
−u
5
+ u
4
− u
3
+ u
2
− u
−1
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
12
=
−u
4
− u
2
+ u − 1
2u
5
− u
4
+ 3u
3
− 2u
2
+ 3u − 2
a
7
=
u
3
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ 5u
3
− u
2
+ 5u − 10
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
6
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
(u
3
− u
2
+ 1)
2
c
9
, c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
10
, c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
6
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
8
(y
3
− y
2
+ 2y −1)
2
c
10
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.767394 + 0.943705I
b = −1.00000
−1.91067 − 2.82812I −6.15260 + 3.54173I
u = −0.498832 − 1.001300I
a = −0.767394 − 0.943705I
b = −1.00000
−1.91067 + 2.82812I −6.15260 − 3.54173I
u = 0.284920 + 1.115140I
a = −1.37744 − 1.47725I
b = −1.00000
−6.04826 −10.69479 + 0.I
u = 0.284920 − 1.115140I
a = −1.37744 + 1.47725I
b = −1.00000
−6.04826 −10.69479 + 0.I
u = 0.713912 + 0.305839I
a = −0.355167 − 0.198843I
b = −1.00000
−1.91067 − 2.82812I −6.15260 + 3.54173I
u = 0.713912 − 0.305839I
a = −0.355167 + 0.198843I
b = −1.00000
−1.91067 + 2.82812I −6.15260 − 3.54173I
34
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· ((u
39
+ 18u
38
+ ··· + 17u + 1)
2
)(u
53
+ 25u
52
+ ··· + 225u + 16)
c
2
((u − 1)
10
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
39
− 4u
38
+ ··· + u + 1)
2
· (u
53
− 5u
52
+ ··· − 31u + 4)
c
3
, c
7
u
10
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
39
− u
38
+ ··· + 20u − 8)
2
· (u
53
+ 3u
52
+ ··· + 240u + 64)
c
4
((u + 1)
10
)(u
6
− u
5
+ ··· − u + 1)
2
(u
39
− 4u
38
+ ··· + u + 1)
2
· (u
53
− 5u
52
+ ··· − 31u + 4)
c
5
, c
6
(u
2
+ 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
53
+ 11u
51
+ ··· + 2u + 1)(u
78
− 2u
77
+ ··· − 6u + 9)
c
8
((u
3
− u
2
+ 1)
2
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
12
− u
10
+ ··· − 3u
2
+ 1)
· (u
39
+ 8u
38
+ ··· − 168u − 49)
2
· (u
53
− 24u
52
+ ··· + 284992u − 13252)
c
9
, c
11
(u
2
+ 1)
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
53
+ 11u
51
+ ··· + 2u + 1)(u
78
− 2u
77
+ ··· − 6u + 9)
c
10
, c
12
(u + 1)
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
53
+ 22u
52
+ ··· + 2u − 1)(u
78
+ 42u
77
+ ··· + 1296u + 81)
35
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· ((y
39
+ 10y
38
+ ··· + 273y −1)
2
)(y
53
+ 11y
52
+ ··· + 12609y −256)
c
2
, c
4
(y −1)
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· ((y
39
− 18y
38
+ ··· + 17y −1)
2
)(y
53
− 25y
52
+ ··· + 225y −16)
c
3
, c
7
y
10
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (y
39
+ 21y
38
+ ··· − 304y −64)
2
· (y
53
+ 27y
52
+ ··· − 52992y −4096)
c
5
, c
6
, c
9
c
11
(y + 1)
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
53
+ 22y
52
+ ··· + 2y −1)(y
78
+ 42y
77
+ ··· + 1296y + 81)
c
8
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (y
39
+ 16y
38
+ ··· − 14896y −2401)
2
· (y
53
+ 14y
52
+ ··· + 16670504648y −175615504)
c
10
, c
12
(y −1)
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
53
+ 34y
52
+ ··· + 430y −1)(y
78
− 14y
77
+ ··· + 160056y + 6561)
36
