12a
1047
(K12a
1047
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 11 2 12 3 1 5 6 8
Solving Sequence
4,10
5 11
2,6
7 1 9 3 8 12
c
4
c
10
c
5
c
6
c
1
c
9
c
3
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.72909 × 10
126
u
87
+ 4.77505 × 10
125
u
86
+ ··· + 3.37799 × 10
126
b + 4.51740 × 10
127
,
5.89706 × 10
126
u
87
− 1.19259 × 10
127
u
86
+ ··· + 1.01340 × 10
127
a − 3.38574 × 10
128
, u
88
− u
87
+ ··· − 39u − 9i
I
u
2
= h−u
13
+ 10u
11
+ 2u
10
− 37u
9
− 15u
8
+ 59u
7
+ 37u
6
− 32u
5
− 29u
4
− 3u
3
− 3u
2
+ b − u + 1,
u
14
+ u
13
− 11u
12
− 12u
11
+ 45u
10
+ 54u
9
− 81u
8
− 111u
7
+ 54u
6
+ 98u
5
− u
4
− 23u
3
+ 4u
2
+ a − 2u − 3,
u
15
+ 2u
14
− 9u
13
− 21u
12
+ 25u
11
+ 81u
10
− 7u
9
− 134u
8
− 67u
7
+ 73u
6
+ 75u
5
+ 14u
4
− u
3
+ u
2
− u − 1i
I
u
3
= hb + a + 1, a
2
+ a − 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 105 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h1.73 × 10
126
u
87
+ 4.78 × 10
125
u
86
+ · · · + 3.38 × 10
126
b + 4.52 ×
10
127
, 5.90 × 10
126
u
87
− 1.19 × 10
127
u
86
+ · · · + 1.01 × 10
127
a − 3.39 ×
10
128
, u
88
− u
87
+ · · · − 39u − 9i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
2
=
−0.581911u
87
+ 1.17683u
86
+ ··· + 115.370u + 33.4098
−0.511869u
87
− 0.141358u
86
+ ··· − 53.8841u − 13.3731
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
0.0734218u
87
+ 0.473497u
86
+ ··· + 30.4353u + 7.86884
0.0107578u
87
+ 0.392321u
86
+ ··· + 19.7593u + 8.34879
a
1
=
−1.09378u
87
+ 1.03547u
86
+ ··· + 61.4864u + 20.0368
−0.511869u
87
− 0.141358u
86
+ ··· − 53.8841u − 13.3731
a
9
=
−0.0591516u
87
+ 0.559425u
86
+ ··· − 85.4131u − 24.0817
−0.195623u
87
+ 0.127976u
86
+ ··· + 17.9905u + 5.97919
a
3
=
0.734242u
87
− 0.261255u
86
+ ··· + 81.8451u + 23.0218
0.245238u
87
− 0.171240u
86
+ ··· − 33.3568u − 11.2988
a
8
=
−0.225229u
87
− 0.569456u
86
+ ··· − 48.8124u − 13.9685
−0.0267257u
87
− 0.516094u
86
+ ··· − 19.8640u − 9.48832
a
12
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.05002u
87
+ 1.35659u
86
+ ··· + 167.292u + 51.3039
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
− 2u
87
+ ··· − 245u + 49
c
2
, c
6
u
88
− 2u
87
+ ··· − 288u + 32
c
3
, c
8
u
88
+ u
87
+ ··· − 46u + 41
c
4
, c
5
, c
10
c
11
u
88
− u
87
+ ··· − 39u − 9
c
7
, c
12
u
88
+ 2u
87
+ ··· − 7u + 1
c
9
u
88
− 2u
87
+ ··· − 224u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 2y
87
+ ··· + 155967y + 2401
c
2
, c
6
y
88
− 50y
87
+ ··· − 30208y + 1024
c
3
, c
8
y
88
− 61y
87
+ ··· − 33850y + 1681
c
4
, c
5
, c
10
c
11
y
88
− 109y
87
+ ··· − 4077y + 81
c
7
, c
12
y
88
− 58y
87
+ ··· − 165y + 1
c
9
y
88
− 22y
87
+ ··· − 111616y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998937
a = −1.49905
b = 0.753833
−4.40347 0
u = 0.854468 + 0.452941I
a = −0.024901 + 1.322860I
b = 1.30651 − 1.01094I
−4.26425 + 6.50157I 0
u = 0.854468 − 0.452941I
a = −0.024901 − 1.322860I
b = 1.30651 + 1.01094I
−4.26425 − 6.50157I 0
u = −0.988389 + 0.302465I
a = 0.573158 − 0.806046I
b = 0.516057 + 0.734460I
6.01796 − 1.94925I 0
u = −0.988389 − 0.302465I
a = 0.573158 + 0.806046I
b = 0.516057 − 0.734460I
6.01796 + 1.94925I 0
u = 0.948493 + 0.063667I
a = 0.752167 + 0.532122I
b = −0.916241 − 0.735839I
2.21145 + 0.85741I 0
u = 0.948493 − 0.063667I
a = 0.752167 − 0.532122I
b = −0.916241 + 0.735839I
2.21145 − 0.85741I 0
u = −0.878362 + 0.596346I
a = 0.304863 − 1.160660I
b = 1.11506 + 0.98368I
−0.69878 − 13.36100I 0
u = −0.878362 − 0.596346I
a = 0.304863 + 1.160660I
b = 1.11506 − 0.98368I
−0.69878 + 13.36100I 0
u = 0.249913 + 0.895625I
a = 0.307031 − 0.093746I
b = −0.084975 − 0.628944I
1.56940 − 1.74873I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249913 − 0.895625I
a = 0.307031 + 0.093746I
b = −0.084975 + 0.628944I
1.56940 + 1.74873I 0
u = 0.859303 + 0.642777I
a = −0.350047 − 0.725789I
b = −0.549384 + 0.933116I
3.59516 + 6.91928I 0
u = 0.859303 − 0.642777I
a = −0.350047 + 0.725789I
b = −0.549384 − 0.933116I
3.59516 − 6.91928I 0
u = 0.834522 + 0.322778I
a = −0.90185 − 1.49057I
b = −0.889748 + 0.869352I
2.46924 + 6.85078I 0
u = 0.834522 − 0.322778I
a = −0.90185 + 1.49057I
b = −0.889748 − 0.869352I
2.46924 − 6.85078I 0
u = −0.570040 + 0.687850I
a = 0.466040 + 0.062972I
b = −0.476615 + 0.734731I
−0.017816 + 0.569418I 0
u = −0.570040 − 0.687850I
a = 0.466040 − 0.062972I
b = −0.476615 − 0.734731I
−0.017816 − 0.569418I 0
u = −0.038739 + 0.848726I
a = 0.168263 − 0.340433I
b = 0.870180 − 0.689966I
−3.24044 + 8.60005I 0
u = −0.038739 − 0.848726I
a = 0.168263 + 0.340433I
b = 0.870180 + 0.689966I
−3.24044 − 8.60005I 0
u = −1.15717
a = −0.505176
b = 1.62002
3.09271 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.744595 + 0.304158I
a = −1.27287 − 1.09874I
b = 0.527480 − 0.166828I
−4.32922 − 0.33311I 0
u = −0.744595 − 0.304158I
a = −1.27287 + 1.09874I
b = 0.527480 + 0.166828I
−4.32922 + 0.33311I 0
u = −0.678503 + 0.404644I
a = −0.38232 + 1.46006I
b = −0.649867 − 0.842257I
0.02617 − 3.76806I 0. + 6.77861I
u = −0.678503 − 0.404644I
a = −0.38232 − 1.46006I
b = −0.649867 + 0.842257I
0.02617 + 3.76806I 0. − 6.77861I
u = −0.650029 + 0.417033I
a = −0.74926 + 1.50782I
b = −0.738579 − 0.848295I
−0.04139 − 3.82932I 0. + 6.18502I
u = −0.650029 − 0.417033I
a = −0.74926 − 1.50782I
b = −0.738579 + 0.848295I
−0.04139 + 3.82932I 0. − 6.18502I
u = −0.732255 + 0.167781I
a = 0.00553 + 1.47664I
b = 0.46126 − 1.62387I
0.98190 − 5.26171I 7.81547 + 8.17533I
u = −0.732255 − 0.167781I
a = 0.00553 − 1.47664I
b = 0.46126 + 1.62387I
0.98190 + 5.26171I 7.81547 − 8.17533I
u = 1.055740 + 0.673668I
a = −0.499970 + 0.195382I
b = 0.405565 + 0.427305I
−0.06479 − 3.54458I 0
u = 1.055740 − 0.673668I
a = −0.499970 − 0.195382I
b = 0.405565 − 0.427305I
−0.06479 + 3.54458I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.640184 + 0.083883I
a = −0.236577 + 1.043320I
b = −1.25194 − 0.76543I
1.70609 + 1.10867I 8.06517 − 0.80088I
u = 0.640184 − 0.083883I
a = −0.236577 − 1.043320I
b = −1.25194 + 0.76543I
1.70609 − 1.10867I 8.06517 + 0.80088I
u = 0.494877 + 0.412991I
a = 0.24307 + 2.27066I
b = 0.479241 + 0.176637I
−2.00611 + 5.04484I −1.60270 − 7.75507I
u = 0.494877 − 0.412991I
a = 0.24307 − 2.27066I
b = 0.479241 − 0.176637I
−2.00611 − 5.04484I −1.60270 + 7.75507I
u = 0.390023 + 0.495315I
a = 1.37825 − 0.36397I
b = 0.972961 − 0.236521I
−2.29925 − 1.82595I −1.88330 − 0.58425I
u = 0.390023 − 0.495315I
a = 1.37825 + 0.36397I
b = 0.972961 + 0.236521I
−2.29925 + 1.82595I −1.88330 + 0.58425I
u = 0.010173 + 0.629162I
a = 0.191644 + 0.730496I
b = 1.052450 + 0.576914I
−6.81322 − 2.83909I −5.34505 + 2.54610I
u = 0.010173 − 0.629162I
a = 0.191644 − 0.730496I
b = 1.052450 − 0.576914I
−6.81322 + 2.83909I −5.34505 − 2.54610I
u = 0.545983 + 0.140096I
a = 1.105450 + 0.833442I
b = 0.055792 − 0.508473I
1.041190 + 0.384617I 8.38778 − 1.10548I
u = 0.545983 − 0.140096I
a = 1.105450 − 0.833442I
b = 0.055792 + 0.508473I
1.041190 − 0.384617I 8.38778 + 1.10548I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43793
a = 0.00568837
b = 1.30250
3.29940 0
u = −0.528904
a = 2.61210
b = 1.03366
−5.57260 12.4710
u = 1.49834
a = 0.660208
b = −1.15559
4.20522 0
u = −0.273905 + 0.415579I
a = −1.72187 + 0.69026I
b = −0.660974 − 0.946200I
−0.49896 − 4.40059I 1.20105 + 5.18432I
u = −0.273905 − 0.415579I
a = −1.72187 − 0.69026I
b = −0.660974 + 0.946200I
−0.49896 + 4.40059I 1.20105 − 5.18432I
u = −0.192100 + 0.450003I
a = −0.431020 + 0.521070I
b = −0.719892 + 0.590298I
−1.32103 + 0.79018I −2.08735 + 0.06199I
u = −0.192100 − 0.450003I
a = −0.431020 − 0.521070I
b = −0.719892 − 0.590298I
−1.32103 − 0.79018I −2.08735 − 0.06199I
u = −0.220328 + 0.430806I
a = −0.129719 + 0.288690I
b = −0.727657 + 0.434029I
−1.26666 + 0.75817I −4.08598 − 0.13948I
u = −0.220328 − 0.430806I
a = −0.129719 − 0.288690I
b = −0.727657 − 0.434029I
−1.26666 − 0.75817I −4.08598 + 0.13948I
u = −1.53128 + 0.16711I
a = 0.377740 − 1.062390I
b = 0.304647 + 0.728682I
7.26023 − 1.72868I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53128 − 0.16711I
a = 0.377740 + 1.062390I
b = 0.304647 − 0.728682I
7.26023 + 1.72868I 0
u = −1.56068 + 0.07667I
a = −0.21446 − 1.62948I
b = 0.099406 + 0.191439I
4.96810 − 6.57928I 0
u = −1.56068 − 0.07667I
a = −0.21446 + 1.62948I
b = 0.099406 − 0.191439I
4.96810 + 6.57928I 0
u = 0.427703 + 0.041691I
a = 2.08448 − 1.57847I
b = −0.252159 + 0.565060I
1.147500 − 0.461667I 9.77334 − 1.83051I
u = 0.427703 − 0.041691I
a = 2.08448 + 1.57847I
b = −0.252159 − 0.565060I
1.147500 + 0.461667I 9.77334 + 1.83051I
u = 1.58144 + 0.03409I
a = 0.43481 − 2.15940I
b = −1.08556 + 1.53925I
6.41159 + 5.04502I 0
u = 1.58144 − 0.03409I
a = 0.43481 + 2.15940I
b = −1.08556 − 1.53925I
6.41159 − 5.04502I 0
u = 1.59232 + 0.05635I
a = −0.504072 + 0.981597I
b = −0.056624 − 0.195985I
3.50186 + 1.58071I 0
u = 1.59232 − 0.05635I
a = −0.504072 − 0.981597I
b = −0.056624 + 0.195985I
3.50186 − 1.58071I 0
u = 1.59532
a = 0.161565
b = 1.31081
1.92921 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59312 + 0.11495I
a = 0.01656 − 1.91542I
b = −0.762201 + 1.087410I
7.60157 + 5.77110I 0
u = 1.59312 − 0.11495I
a = 0.01656 + 1.91542I
b = −0.762201 − 1.087410I
7.60157 − 5.77110I 0
u = −1.59908 + 0.00978I
a = 0.13106 − 1.64152I
b = 0.421854 + 1.131700I
8.53544 − 0.67096I 0
u = −1.59908 − 0.00978I
a = 0.13106 + 1.64152I
b = 0.421854 − 1.131700I
8.53544 + 0.67096I 0
u = −1.61942 + 0.02208I
a = 1.01379 − 1.19740I
b = −1.72755 + 1.01451I
9.65685 − 1.49225I 0
u = −1.61942 − 0.02208I
a = 1.01379 + 1.19740I
b = −1.72755 − 1.01451I
9.65685 + 1.49225I 0
u = 1.62064 + 0.10826I
a = 0.19014 − 1.86867I
b = −0.63333 + 1.30010I
7.96001 + 5.64360I 0
u = 1.62064 − 0.10826I
a = 0.19014 + 1.86867I
b = −0.63333 − 1.30010I
7.96001 − 5.64360I 0
u = 1.63286 + 0.04842I
a = −0.58591 − 2.12417I
b = 0.81861 + 1.96064I
9.24227 + 6.09298I 0
u = 1.63286 − 0.04842I
a = −0.58591 + 2.12417I
b = 0.81861 − 1.96064I
9.24227 − 6.09298I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.65294 + 0.09305I
a = 0.09950 + 1.58032I
b = −1.14502 − 0.97361I
11.09150 − 8.47037I 0
u = −1.65294 − 0.09305I
a = 0.09950 − 1.58032I
b = −1.14502 + 0.97361I
11.09150 + 8.47037I 0
u = −1.66694 + 0.12969I
a = −0.83066 − 1.83068I
b = 1.52994 + 1.37393I
4.45620 − 8.76412I 0
u = −1.66694 − 0.12969I
a = −0.83066 + 1.83068I
b = 1.52994 − 1.37393I
4.45620 + 8.76412I 0
u = 1.65618 + 0.23619I
a = 0.311417 + 0.918858I
b = 0.050725 − 0.904165I
7.58119 + 3.18569I 0
u = 1.65618 − 0.23619I
a = 0.311417 − 0.918858I
b = 0.050725 + 0.904165I
7.58119 − 3.18569I 0
u = −1.66753 + 0.18347I
a = 0.06371 + 1.55994I
b = −0.78014 − 1.28995I
12.1997 − 10.0873I 0
u = −1.66753 − 0.18347I
a = 0.06371 − 1.55994I
b = −0.78014 + 1.28995I
12.1997 + 10.0873I 0
u = 1.67040 + 0.17672I
a = −0.39843 + 1.75629I
b = 1.28410 − 1.24158I
7.9981 + 16.3766I 0
u = 1.67040 − 0.17672I
a = −0.39843 − 1.75629I
b = 1.28410 + 1.24158I
7.9981 − 16.3766I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.68403 + 0.08568I
a = −0.148951 + 1.277720I
b = 0.921894 − 1.012870I
15.2907 + 3.5156I 0
u = 1.68403 − 0.08568I
a = −0.148951 − 1.277720I
b = 0.921894 + 1.012870I
15.2907 − 3.5156I 0
u = −0.298917 + 0.080015I
a = −2.35798 + 3.38880I
b = −0.458188 − 1.178420I
−0.59427 − 4.45712I 1.47394 + 3.43689I
u = −0.298917 − 0.080015I
a = −2.35798 − 3.38880I
b = −0.458188 + 1.178420I
−0.59427 + 4.45712I 1.47394 − 3.43689I
u = −1.70136 + 0.02179I
a = 0.806645 + 1.132370I
b = −1.06634 − 1.06351I
11.65750 + 0.82210I 0
u = −1.70136 − 0.02179I
a = 0.806645 − 1.132370I
b = −1.06634 + 1.06351I
11.65750 − 0.82210I 0
u = 1.74247
a = −1.75918
b = 2.38981
13.4096 0
u = −1.86712
a = 0.0882886
b = −0.376543
11.1684 0
13
II.
I
u
2
= h−u
13
+10u
11
+· · ·+b+1, u
14
+u
13
+· · ·+a−3, u
15
+2u
14
+· · ·−u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
2
=
−u
14
− u
13
+ ··· + 2u + 3
u
13
− 10u
11
+ ··· + u − 1
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
u
12
− 10u
10
+ ··· + 7u + 2
2u
14
+ 2u
13
+ ··· + u − 1
a
1
=
−u
14
+ 11u
12
+ ··· + 3u + 2
u
13
− 10u
11
+ ··· + u − 1
a
9
=
−u
14
+ 9u
12
+ ··· − 3u − 3
−u
14
− u
13
+ ··· − u + 1
a
3
=
−3u
13
− u
12
+ ··· − 20u
2
− 8u
u
14
+ u
13
+ ··· − u − 2
a
8
=
u
14
+ u
13
+ ··· + 7u + 1
u
14
+ u
13
+ ··· + 2u
2
+ u
a
12
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
14
− 13u
13
+ 49u
12
+ 134u
11
− 156u
10
− 513u
9
+ 120u
8
+
860u
7
+ 233u
6
− 524u
5
− 307u
4
− 6u
3
− 37u
2
− 17u + 9
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 4u
14
+ ··· − 2u + 1
c
2
u
15
− 7u
13
+ ··· − 2u + 1
c
3
u
15
+ u
14
+ ··· − 5u + 1
c
4
, c
5
u
15
+ 2u
14
+ ··· − u − 1
c
6
u
15
− 7u
13
+ ··· − 2u − 1
c
7
u
15
+ 2u
14
+ ··· + 7u
2
− 1
c
8
u
15
− u
14
+ ··· − 5u − 1
c
9
u
15
− u
14
+ ··· + 3u + 1
c
10
, c
11
u
15
− 2u
14
+ ··· − u + 1
c
12
u
15
− 2u
14
+ ··· − 7u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 2y
14
+ ··· − 2y −1
c
2
, c
6
y
15
− 14y
14
+ ··· + 14y −1
c
3
, c
8
y
15
− 13y
14
+ ··· + 27y −1
c
4
, c
5
, c
10
c
11
y
15
− 22y
14
+ ··· + 3y −1
c
7
, c
12
y
15
− 14y
14
+ ··· + 14y −1
c
9
y
15
− 7y
14
+ ··· + 5y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807406 + 0.479432I
a = −0.0727835 − 0.1091620I
b = −0.012561 + 0.692921I
0.32346 + 2.80612I 5.02416 − 0.99301I
u = −0.807406 − 0.479432I
a = −0.0727835 + 0.1091620I
b = −0.012561 − 0.692921I
0.32346 − 2.80612I 5.02416 + 0.99301I
u = −0.537971 + 0.281409I
a = −1.10179 + 2.45462I
b = −0.392045 − 1.201560I
−0.39153 − 5.27000I 3.01978 + 11.73102I
u = −0.537971 − 0.281409I
a = −1.10179 − 2.45462I
b = −0.392045 + 1.201560I
−0.39153 + 5.27000I 3.01978 − 11.73102I
u = 1.46099
a = 0.243441
b = −1.05115
5.02988 8.61170
u = −1.55528
a = 0.402992
b = 1.18205
1.02905 −3.49670
u = −1.56756 + 0.15866I
a = 0.478741 − 1.171290I
b = −0.115203 + 0.736770I
6.52033 − 3.28353I 3.23204 + 3.30162I
u = −1.56756 − 0.15866I
a = 0.478741 + 1.171290I
b = −0.115203 − 0.736770I
6.52033 + 3.28353I 3.23204 − 3.30162I
u = 1.58958 + 0.08373I
a = 0.05801 − 2.32096I
b = −0.57777 + 1.43436I
7.04264 + 6.60131I 4.24341 − 9.09890I
u = 1.58958 − 0.08373I
a = 0.05801 + 2.32096I
b = −0.57777 − 1.43436I
7.04264 − 6.60131I 4.24341 + 9.09890I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107035 + 0.393704I
a = 1.35457 − 1.16588I
b = −0.622089 − 0.331373I
0.373372 + 0.922807I 1.18179 − 1.95700I
u = 0.107035 − 0.393704I
a = 1.35457 + 1.16588I
b = −0.622089 + 0.331373I
0.373372 − 0.922807I 1.18179 + 1.95700I
u = 0.404988
a = 3.63922
b = 0.977374
−5.86405 −15.8290
u = −1.72706
a = 1.74748
b = −2.35793
13.7545 19.7830
u = 1.84901
a = −0.466606
b = 0.688997
10.9519 −12.4710
18
III. I
u
3
= hb + a + 1, a
2
+ a − 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
5
=
1
−1
a
11
=
1
0
a
2
=
a
−a − 1
a
6
=
0
−1
a
7
=
−a + 1
−2
a
1
=
−1
−a − 1
a
9
=
−1
−a
a
3
=
−a + 1
a − 1
a
8
=
−2a
a − 1
a
12
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
u
2
− u − 1
c
4
, c
5
, c
9
(u − 1)
2
c
6
, c
8
, c
12
u
2
+ u − 1
c
10
, c
11
(u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
12
y
2
− 3y + 1
c
4
, c
5
, c
9
c
10
, c
11
(y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.618034
b = −1.61803
3.94784 13.0000
u = 1.00000
a = −1.61803
b = 0.618034
−3.94784 13.0000
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u − 1)(u
15
− 4u
14
+ ··· − 2u + 1)(u
88
− 2u
87
+ ··· − 245u + 49)
c
2
(u
2
− u − 1)(u
15
− 7u
13
+ ··· − 2u + 1)(u
88
− 2u
87
+ ··· − 288u + 32)
c
3
(u
2
− u − 1)(u
15
+ u
14
+ ··· − 5u + 1)(u
88
+ u
87
+ ··· − 46u + 41)
c
4
, c
5
((u − 1)
2
)(u
15
+ 2u
14
+ ··· − u − 1)(u
88
− u
87
+ ··· − 39u − 9)
c
6
(u
2
+ u − 1)(u
15
− 7u
13
+ ··· − 2u − 1)(u
88
− 2u
87
+ ··· − 288u + 32)
c
7
(u
2
− u − 1)(u
15
+ 2u
14
+ ··· + 7u
2
− 1)(u
88
+ 2u
87
+ ··· − 7u + 1)
c
8
(u
2
+ u − 1)(u
15
− u
14
+ ··· − 5u − 1)(u
88
+ u
87
+ ··· − 46u + 41)
c
9
((u − 1)
2
)(u
15
− u
14
+ ··· + 3u + 1)(u
88
− 2u
87
+ ··· − 224u + 64)
c
10
, c
11
((u + 1)
2
)(u
15
− 2u
14
+ ··· − u + 1)(u
88
− u
87
+ ··· − 39u − 9)
c
12
(u
2
+ u − 1)(u
15
− 2u
14
+ ··· − 7u
2
+ 1)(u
88
+ 2u
87
+ ··· − 7u + 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 3y + 1)(y
15
− 2y
14
+ ··· − 2y −1)
· (y
88
+ 2y
87
+ ··· + 155967y + 2401)
c
2
, c
6
(y
2
− 3y + 1)(y
15
− 14y
14
+ ··· + 14y −1)
· (y
88
− 50y
87
+ ··· − 30208y + 1024)
c
3
, c
8
(y
2
− 3y + 1)(y
15
− 13y
14
+ ··· + 27y −1)
· (y
88
− 61y
87
+ ··· − 33850y + 1681)
c
4
, c
5
, c
10
c
11
((y −1)
2
)(y
15
− 22y
14
+ ··· + 3y −1)(y
88
− 109y
87
+ ··· − 4077y + 81)
c
7
, c
12
(y
2
− 3y + 1)(y
15
− 14y
14
+ ··· + 14y −1)(y
88
− 58y
87
+ ··· − 165y + 1)
c
9
((y −1)
2
)(y
15
− 7y
14
+ ··· + 5y −1)
· (y
88
− 22y
87
+ ··· − 111616y + 4096)
24
