12a
0460
(K12a
0460
)
A knot diagram
1
Linearized knot diagam
3 6 10 1 8 2 11 5 4 12 7 9
Solving Sequence
1,4 5,9
10 3 2 8 6 12 11 7
c
4
c
9
c
3
c
1
c
8
c
5
c
12
c
10
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.48339 × 10
23
u
25
− 2.92787 × 10
23
u
24
+ ··· + 5.04980 × 10
23
b + 1.13922 × 10
24
, a − 1, u
26
− u
25
+ ··· + u + 1i
I
u
2
= h2.42800 × 10
731
u
107
− 2.38703 × 10
732
u
106
+ ··· + 1.67435 × 10
731
b − 2.81845 × 10
733
,
7.28015 × 10
733
u
107
− 1.32007 × 10
734
u
106
+ ··· + 1.67435 × 10
731
a + 3.97573 × 10
733
,
u
108
− 2u
107
+ ··· − 20u + 1i
I
u
3
= h−10u
11
− 2u
10
− 3u
9
− 4u
8
− 75u
7
− 20u
6
− 18u
5
− 14u
4
− 138u
3
− 46u
2
+ 9b − 22u + 10, a + 1,
u
12
+ u
11
+ u
10
+ u
9
+ 8u
8
+ 8u
7
+ 7u
6
+ 5u
5
+ 16u
4
+ 16u
3
+ 12u
2
+ 4u + 1i
I
u
4
= h−2970u
11
− 16830u
10
+ ··· + 3431b − 12700, 2891u
11
+ 14095u
10
+ ··· + 3431a + 4241,
u
12
+ 5u
11
+ 11u
10
+ 15u
9
+ 11u
8
+ 7u
7
+ 11u
6
+ 10u
5
+ 22u
4
+ 17u
3
+ 12u
2
+ 4u + 1i
* 4 irreducible components of dim
C
= 0, with total 158 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
= h2.48 × 10
23
u
25
− 2.93 × 10
23
u
24
+ · · · + 5.05 × 10
23
b + 1.14 ×
10
24
, a − 1, u
26
− u
25
+ · · · + u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
1
−0.491779u
25
+ 0.579798u
24
+ ··· − 0.505057u − 2.25597
a
10
=
−0.491779u
25
+ 0.579798u
24
+ ··· − 0.505057u − 1.25597
−0.491779u
25
+ 0.579798u
24
+ ··· − 0.505057u − 2.25597
a
3
=
1.04793u
25
− 1.22784u
24
+ ··· + 1.46589u + 1.80094
1.53971u
25
− 1.80763u
24
+ ··· + 1.97095u + 3.05691
a
2
=
−0.145439u
25
− 0.0814371u
24
+ ··· + 9.19172u + 0.529548
−0.0826126u
25
− 0.323908u
24
+ ··· + 13.6227u + 1.32755
a
8
=
−0.491779u
25
+ 0.579798u
24
+ ··· − 0.505057u − 1.25597
−0.544904u
25
+ 0.618776u
24
+ ··· − 0.101297u − 2.34399
a
6
=
1.15418u
25
− 1.30579u
24
+ ··· + 0.658374u + 1.97698
1.81723u
25
− 2.07044u
24
+ ··· + 0.160858u + 3.38456
a
12
=
u
0.0880194u
25
− 0.141144u
24
+ ··· − 0.764194u + 0.491779
a
11
=
−0.326147u
25
+ 0.397989u
24
+ ··· − 1.37309u − 1.07607
−0.671424u
25
+ 0.829108u
24
+ ··· + 0.230116u − 2.31880
a
7
=
−0.0777366u
25
+ 0.193064u
24
+ ··· − 1.97629u − 0.609278
−0.108030u
25
+ 0.293691u
24
+ ··· − 3.45433u − 1.07896
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1877165613022592980724169
504980160038115323854327
u
25
+
3778465665043053085315905
504980160038115323854327
u
24
+
··· +
4750472667547566317292293
504980160038115323854327
u −
15093780059339179500460468
504980160038115323854327
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
26
+ 12u
25
+ ··· + 4u + 1
c
2
, c
6
, c
7
c
11
u
26
+ 6u
24
+ ··· + 2u
2
+ 1
c
3
, c
9
u
26
− 19u
25
+ ··· − 480u + 64
c
4
, c
12
u
26
− u
25
+ ··· + u + 1
c
5
, c
8
u
26
− 20u
25
+ ··· − 3200u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
26
+ 12y
25
+ ··· + 52y + 1
c
2
, c
6
, c
7
c
11
y
26
+ 12y
25
+ ··· + 4y + 1
c
3
, c
9
y
26
+ 7y
25
+ ··· + 113664y + 4096
c
4
, c
12
y
26
− y
25
+ ··· − 13y + 1
c
5
, c
8
y
26
+ 8y
25
+ ··· + 376832y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.980147 + 0.493143I
a = 1.00000
b = −0.097435 + 1.302150I
−8.66439 + 2.11653I −9.55328 − 2.96629I
u = 0.980147 − 0.493143I
a = 1.00000
b = −0.097435 − 1.302150I
−8.66439 − 2.11653I −9.55328 + 2.96629I
u = −0.835611 + 0.330454I
a = 1.00000
b = 0.088041 + 0.233474I
−3.41305 + 2.07895I −8.48167 − 4.03330I
u = −0.835611 − 0.330454I
a = 1.00000
b = 0.088041 − 0.233474I
−3.41305 − 2.07895I −8.48167 + 4.03330I
u = −0.841886 + 0.846942I
a = 1.00000
b = −0.551696 − 1.010760I
−0.36897 + 3.07127I 4.11344 − 1.54353I
u = −0.841886 − 0.846942I
a = 1.00000
b = −0.551696 + 1.010760I
−0.36897 − 3.07127I 4.11344 + 1.54353I
u = 0.607328 + 1.030390I
a = 1.00000
b = −1.019660 − 0.255795I
8.43200 − 1.21326I 6.60796 − 0.78913I
u = 0.607328 − 1.030390I
a = 1.00000
b = −1.019660 + 0.255795I
8.43200 + 1.21326I 6.60796 + 0.78913I
u = −0.672508 + 1.044570I
a = 1.00000
b = −1.265530 + 0.111225I
5.67863 + 12.91670I 2.46808 − 9.29051I
u = −0.672508 − 1.044570I
a = 1.00000
b = −1.265530 − 0.111225I
5.67863 − 12.91670I 2.46808 + 9.29051I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.053110 + 0.717831I
a = 1.00000
b = −0.71946 + 1.36827I
−3.27197 − 12.97210I −3.09380 + 10.19707I
u = 1.053110 − 0.717831I
a = 1.00000
b = −0.71946 − 1.36827I
−3.27197 + 12.97210I −3.09380 − 10.19707I
u = −0.950340 + 0.886902I
a = 1.00000
b = −0.728257 − 1.002330I
−0.50796 + 2.99665I 1.09938 + 0.94127I
u = −0.950340 − 0.886902I
a = 1.00000
b = −0.728257 + 1.002330I
−0.50796 − 2.99665I 1.09938 − 0.94127I
u = −0.038282 + 0.628175I
a = 1.00000
b = −0.439675 − 0.624417I
0.741759 + 1.109910I 4.81799 − 4.19754I
u = −0.038282 − 0.628175I
a = 1.00000
b = −0.439675 + 0.624417I
0.741759 − 1.109910I 4.81799 + 4.19754I
u = 1.15658 + 0.97329I
a = 1.00000
b = −0.155801 + 1.162270I
−6.40471 − 2.84865I −6.81101 + 1.79383I
u = 1.15658 − 0.97329I
a = 1.00000
b = −0.155801 − 1.162270I
−6.40471 + 2.84865I −6.81101 − 1.79383I
u = −1.09737 + 1.20424I
a = 1.00000
b = −0.586826 − 1.223610I
5.41008 + 6.92479I 3.59556 − 2.88333I
u = −1.09737 − 1.20424I
a = 1.00000
b = −0.586826 + 1.223610I
5.41008 − 6.92479I 3.59556 + 2.88333I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335440 + 0.149830I
a = 1.00000
b = −1.68515 − 1.35872I
0.05066 − 4.70849I −17.9430 − 22.7027I
u = −0.335440 − 0.149830I
a = 1.00000
b = −1.68515 + 1.35872I
0.05066 + 4.70849I −17.9430 + 22.7027I
u = 0.300191 + 0.199599I
a = 1.00000
b = −1.70559 − 1.25362I
0.54033 + 4.39868I −18.8485 + 23.0455I
u = 0.300191 − 0.199599I
a = 1.00000
b = −1.70559 + 1.25362I
0.54033 − 4.39868I −18.8485 − 23.0455I
u = 1.17409 + 1.20279I
a = 1.00000
b = −0.63296 + 1.35652I
1.7776 − 19.4776I −0.47118 + 10.59359I
u = 1.17409 − 1.20279I
a = 1.00000
b = −0.63296 − 1.35652I
1.7776 + 19.4776I −0.47118 − 10.59359I
7
II. I
u
2
= h2.43 × 10
731
u
107
− 2.39 × 10
732
u
106
+ · · · + 1.67 × 10
731
b − 2.82 ×
10
733
, 7.28 × 10
733
u
107
− 1.32 × 10
734
u
106
+ · · · + 1.67 × 10
731
a + 3.98 ×
10
733
, u
108
− 2u
107
+ · · · − 20u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−434.804u
107
+ 788.409u
106
+ ··· − 3722.54u − 237.449
−1.45011u
107
+ 14.2565u
106
+ ··· − 3022.02u + 168.331
a
10
=
−436.254u
107
+ 802.666u
106
+ ··· − 6744.57u − 69.1179
−1.45011u
107
+ 14.2565u
106
+ ··· − 3022.02u + 168.331
a
3
=
−98.7030u
107
+ 223.517u
106
+ ··· − 14231.9u + 752.948
59.4757u
107
− 116.128u
106
+ ··· + 3284.49u − 141.375
a
2
=
366.665u
107
− 598.891u
106
+ ··· − 10189.2u + 982.445
43.6603u
107
− 93.2854u
106
+ ··· + 4379.94u − 217.361
a
8
=
−447.709u
107
+ 819.400u
106
+ ··· − 5555.39u − 150.317
0.0613482u
107
+ 10.9872u
106
+ ··· − 2905.51u + 163.150
a
6
=
−315.680u
107
+ 621.328u
106
+ ··· − 20148.2u + 893.980
42.4213u
107
− 83.8262u
106
+ ··· + 2573.67u − 114.999
a
12
=
124.688u
107
− 66.7682u
106
+ ··· − 40929.4u + 2596.77
23.2879u
107
− 31.9082u
106
+ ··· − 2269.25u + 158.179
a
11
=
1075.27u
107
− 2230.33u
106
+ ··· + 91993.9u − 4332.91
74.0637u
107
− 162.195u
106
+ ··· + 9089.99u − 459.539
a
7
=
−113.491u
107
+ 45.4757u
106
+ ··· + 41470.9u − 2618.38
−24.5783u
107
+ 33.0243u
106
+ ··· + 2558.49u − 176.685
(ii) Obstruction class = −1
(iii) Cusp Shapes = 56.1746u
107
− 176.849u
106
+ ··· + 21058.5u − 1189.99
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
108
+ 41u
107
+ ··· + 263054u + 2809
c
2
, c
6
, c
7
c
11
u
108
− u
107
+ ··· − 412u + 53
c
3
, c
9
(u
54
+ 9u
53
+ ··· + 40u + 5)
2
c
4
, c
12
u
108
− 2u
107
+ ··· − 20u + 1
c
5
, c
8
(u
54
+ 8u
53
+ ··· + 143u + 17)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
108
+ 57y
107
+ ··· − 29072544170y + 7890481
c
2
, c
6
, c
7
c
11
y
108
+ 41y
107
+ ··· + 263054y + 2809
c
3
, c
9
(y
54
+ 31y
53
+ ··· + 570y + 25)
2
c
4
, c
12
y
108
+ 4y
107
+ ··· + 72y + 1
c
5
, c
8
(y
54
+ 42y
53
+ ··· − 1919y + 289)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332751 + 0.945381I
a = 1.71262 + 1.34617I
b = −0.403499 − 0.931637I
4.27100 + 0.57975I 0
u = −0.332751 − 0.945381I
a = 1.71262 − 1.34617I
b = −0.403499 + 0.931637I
4.27100 − 0.57975I 0
u = 0.941026 + 0.329397I
a = −0.15662 − 1.46774I
b = 0.323476 − 0.960897I
−0.76175 − 6.50743I 0
u = 0.941026 − 0.329397I
a = −0.15662 + 1.46774I
b = 0.323476 + 0.960897I
−0.76175 + 6.50743I 0
u = −0.290135 + 0.963430I
a = −1.48908 − 1.76420I
b = 0.265107 + 0.981138I
4.51716 + 5.38940I 0
u = −0.290135 − 0.963430I
a = −1.48908 + 1.76420I
b = 0.265107 − 0.981138I
4.51716 − 5.38940I 0
u = −0.222188 + 1.001060I
a = −0.57317 − 2.01779I
b = −0.096463 + 0.872410I
3.63274 + 2.43968I 0
u = −0.222188 − 1.001060I
a = −0.57317 + 2.01779I
b = −0.096463 − 0.872410I
3.63274 − 2.43968I 0
u = −0.143702 + 1.016850I
a = −0.09707 + 1.81804I
b = 0.346108 − 0.674457I
2.62017 + 6.46004I 0
u = −0.143702 − 1.016850I
a = −0.09707 − 1.81804I
b = 0.346108 + 0.674457I
2.62017 − 6.46004I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.236965 + 1.024070I
a = −0.977715 + 0.663900I
b = 0.795770 − 0.044759I
1.025280 − 0.815491I 0
u = 0.236965 − 1.024070I
a = −0.977715 − 0.663900I
b = 0.795770 + 0.044759I
1.025280 + 0.815491I 0
u = 0.912708 + 0.136002I
a = −0.59108 + 1.35371I
b = −0.167213 + 0.899498I
−0.633597 − 0.841318I 0
u = 0.912708 − 0.136002I
a = −0.59108 − 1.35371I
b = −0.167213 − 0.899498I
−0.633597 + 0.841318I 0
u = 0.073793 + 1.084310I
a = 0.454883 + 0.578206I
b = −0.400624 − 0.755023I
1.21617 + 1.76906I 0
u = 0.073793 − 1.084310I
a = 0.454883 − 0.578206I
b = −0.400624 + 0.755023I
1.21617 − 1.76906I 0
u = 0.662386 + 0.584694I
a = 1.54099 − 0.22824I
b = −0.40282 + 1.37077I
−7.28359 − 5.93563I 0
u = 0.662386 − 0.584694I
a = 1.54099 + 0.22824I
b = −0.40282 − 1.37077I
−7.28359 + 5.93563I 0
u = 0.629885 + 0.946570I
a = −1.139160 − 0.037534I
b = 1.097070 + 0.177053I
7.30209 − 7.13055I 0
u = 0.629885 − 0.946570I
a = −1.139160 + 0.037534I
b = 1.097070 − 0.177053I
7.30209 + 7.13055I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.732819 + 0.413555I
a = −1.44767 − 0.12061I
b = 0.319650 − 1.207210I
−4.43197 − 1.29452I 0
u = 0.732819 − 0.413555I
a = −1.44767 + 0.12061I
b = 0.319650 + 1.207210I
−4.43197 + 1.29452I 0
u = 0.198005 + 1.168490I
a = −0.205270 − 0.172033I
b = 0.472024 + 1.207090I
−2.39251 + 3.77463I 0
u = 0.198005 − 1.168490I
a = −0.205270 + 0.172033I
b = 0.472024 − 1.207090I
−2.39251 − 3.77463I 0
u = −0.593389 + 0.535903I
a = 0.840444 − 1.068300I
b = −0.400624 − 0.755023I
1.21617 + 1.76906I 0
u = −0.593389 − 0.535903I
a = 0.840444 + 1.068300I
b = −0.400624 + 0.755023I
1.21617 − 1.76906I 0
u = 0.947992 + 0.738840I
a = −1.47477 − 0.55414I
b = 0.431561 − 1.208400I
−2.66959 − 5.13236I 0
u = 0.947992 − 0.738840I
a = −1.47477 + 0.55414I
b = 0.431561 + 1.208400I
−2.66959 + 5.13236I 0
u = −0.511550 + 1.099200I
a = 0.987987 + 0.424315I
b = −0.858582 − 0.347515I
0.93815 + 5.69631I 0
u = −0.511550 − 1.099200I
a = 0.987987 − 0.424315I
b = −0.858582 + 0.347515I
0.93815 − 5.69631I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.011000 + 0.687075I
a = −0.686003 − 0.057152I
b = 0.319650 + 1.207210I
−4.43197 + 1.29452I 0
u = −1.011000 − 0.687075I
a = −0.686003 + 0.057152I
b = 0.319650 − 1.207210I
−4.43197 − 1.29452I 0
u = −0.698816 + 1.005620I
a = −0.034571 + 0.589947I
b = 0.386423 − 0.613848I
0.24482 + 3.41016I 0
u = −0.698816 − 1.005620I
a = −0.034571 − 0.589947I
b = 0.386423 + 0.613848I
0.24482 − 3.41016I 0
u = −0.771739 + 0.058750I
a = −0.151488 + 0.290601I
b = 0.206151 − 1.270090I
1.19581 + 2.53766I 0
u = −0.771739 − 0.058750I
a = −0.151488 − 0.290601I
b = 0.206151 + 1.270090I
1.19581 − 2.53766I 0
u = −0.569789 + 0.517458I
a = −0.465008 + 0.095633I
b = 0.601774 − 0.234799I
−0.30204 + 1.83455I 0
u = −0.569789 − 0.517458I
a = −0.465008 − 0.095633I
b = 0.601774 + 0.234799I
−0.30204 − 1.83455I 0
u = −0.911568 + 0.843932I
a = −0.700023 + 0.475338I
b = 0.795770 + 0.044759I
1.025280 + 0.815491I 0
u = −0.911568 − 0.843932I
a = −0.700023 − 0.475338I
b = 0.795770 − 0.044759I
1.025280 − 0.815491I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935569 + 0.838861I
a = 1.59313 + 0.20151I
b = −0.368725 + 1.298990I
−3.97620 − 9.73538I 0
u = 0.935569 − 0.838861I
a = 1.59313 − 0.20151I
b = −0.368725 − 1.298990I
−3.97620 + 9.73538I 0
u = 1.065860 + 0.693651I
a = −1.001870 − 0.125717I
b = 0.66440 − 1.24969I
−1.72545 − 7.50933I 0
u = 1.065860 − 0.693651I
a = −1.001870 + 0.125717I
b = 0.66440 + 1.24969I
−1.72545 + 7.50933I 0
u = −0.569104 + 0.447030I
a = −0.09899 + 1.68927I
b = 0.386423 + 0.613848I
0.24482 − 3.41016I 0
u = −0.569104 − 0.447030I
a = −0.09899 − 1.68927I
b = 0.386423 − 0.613848I
0.24482 + 3.41016I 0
u = −0.980642 + 0.828941I
a = −0.982665 − 0.123307I
b = 0.66440 + 1.24969I
−1.72545 + 7.50933I 0
u = −0.980642 − 0.828941I
a = −0.982665 + 0.123307I
b = 0.66440 − 1.24969I
−1.72545 − 7.50933I 0
u = 1.091360 + 0.697194I
a = −1.078080 − 0.424426I
b = 0.396189 − 1.101130I
−2.70624 − 5.66390I 0
u = 1.091360 − 0.697194I
a = −1.078080 + 0.424426I
b = 0.396189 + 1.101130I
−2.70624 + 5.66390I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682011 + 1.101940I
a = −0.876888 − 0.028892I
b = 1.097070 − 0.177053I
7.30209 + 7.13055I 0
u = −0.682011 − 1.101940I
a = −0.876888 + 0.028892I
b = 1.097070 + 0.177053I
7.30209 − 7.13055I 0
u = −0.971810 + 0.868933I
a = 0.854541 − 0.367003I
b = −0.858582 − 0.347515I
0.93815 + 5.69631I 0
u = −0.971810 − 0.868933I
a = 0.854541 + 0.367003I
b = −0.858582 + 0.347515I
0.93815 − 5.69631I 0
u = −0.723590 + 1.155160I
a = −0.270900 − 0.620424I
b = −0.167213 + 0.899498I
−0.633597 − 0.841318I 0
u = −0.723590 − 1.155160I
a = −0.270900 + 0.620424I
b = −0.167213 − 0.899498I
−0.633597 + 0.841318I 0
u = 0.161987 + 0.606660I
a = 0.545678 + 0.219760I
b = −1.14473 − 1.06694I
−0.913339 + 0.639622I 0
u = 0.161987 − 0.606660I
a = 0.545678 − 0.219760I
b = −1.14473 + 1.06694I
−0.913339 − 0.639622I 0
u = 1.154180 + 0.749823I
a = 0.635005 + 0.094052I
b = −0.40282 + 1.37077I
−7.28359 − 5.93563I 0
u = 1.154180 − 0.749823I
a = 0.635005 − 0.094052I
b = −0.40282 − 1.37077I
−7.28359 + 5.93563I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.472262 + 0.298914I
a = 1.97643 + 2.33440I
b = −0.311553 − 0.409352I
5.57265 + 2.80644I 8.46702 − 3.23440I
u = 0.472262 − 0.298914I
a = 1.97643 − 2.33440I
b = −0.311553 + 0.409352I
5.57265 − 2.80644I 8.46702 + 3.23440I
u = 0.33609 + 1.43277I
a = −0.071882 − 0.673649I
b = 0.323476 + 0.960897I
−0.76175 + 6.50743I 0
u = 0.33609 − 1.43277I
a = −0.071882 + 0.673649I
b = 0.323476 − 0.960897I
−0.76175 − 6.50743I 0
u = −0.88066 + 1.21483I
a = −0.803105 − 0.316173I
b = 0.396189 + 1.101130I
−2.70624 + 5.66390I 0
u = −0.88066 − 1.21483I
a = −0.803105 + 0.316173I
b = 0.396189 − 1.101130I
−2.70624 − 5.66390I 0
u = −0.422764 + 0.013347I
a = −0.784163 − 0.165128I
b = 1.48608 + 1.23377I
0.632907 − 0.329864I −27.2555 + 0.3573I
u = −0.422764 − 0.013347I
a = −0.784163 + 0.165128I
b = 1.48608 − 1.23377I
0.632907 + 0.329864I −27.2555 − 0.3573I
u = −1.05002 + 1.18250I
a = −1.096930 − 0.077831I
b = 0.59013 + 1.28629I
3.82402 + 13.07400I 0
u = −1.05002 − 1.18250I
a = −1.096930 + 0.077831I
b = 0.59013 − 1.28629I
3.82402 − 13.07400I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328692 + 0.194636I
a = −4.03517 − 3.33086I
b = 0.185491 + 0.556934I
5.70289 − 2.90295I 8.86902 + 0.76394I
u = 0.328692 − 0.194636I
a = −4.03517 + 3.33086I
b = 0.185491 − 0.556934I
5.70289 + 2.90295I 8.86902 − 0.76394I
u = −0.044927 + 0.366639I
a = 1.57684 − 0.63504I
b = −1.14473 − 1.06694I
−0.913339 + 0.639622I 7.37399 + 0.54126I
u = −0.044927 − 0.366639I
a = 1.57684 + 0.63504I
b = −1.14473 + 1.06694I
−0.913339 − 0.639622I 7.37399 − 0.54126I
u = 0.215470 + 0.295113I
a = −2.06324 + 0.42432I
b = 0.601774 + 0.234799I
−0.30204 − 1.83455I 0.79540 + 3.67784I
u = 0.215470 − 0.295113I
a = −2.06324 − 0.42432I
b = 0.601774 − 0.234799I
−0.30204 + 1.83455I 0.79540 − 3.67784I
u = 0.333720 + 0.059344I
a = −1.221100 + 0.257137I
b = 1.48608 + 1.23377I
0.632907 − 0.329864I −27.2555 + 0.3573I
u = 0.333720 − 0.059344I
a = −1.221100 − 0.257137I
b = 1.48608 − 1.23377I
0.632907 + 0.329864I −27.2555 − 0.3573I
u = 0.160374 + 0.273918I
a = −2.86165 − 2.39830I
b = 0.472024 − 1.207090I
−2.39251 − 3.77463I −2.10945 + 3.53292I
u = 0.160374 − 0.273918I
a = −2.86165 + 2.39830I
b = 0.472024 + 1.207090I
−2.39251 + 3.77463I −2.10945 − 3.53292I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23561 + 1.69323I
a = 0.211255 − 0.249516I
b = −0.311553 − 0.409352I
5.57265 + 2.80644I 0
u = 0.23561 − 1.69323I
a = 0.211255 + 0.249516I
b = −0.311553 + 0.409352I
5.57265 − 2.80644I 0
u = 1.24383 + 1.21540I
a = −0.907070 − 0.064360I
b = 0.59013 − 1.28629I
3.82402 − 13.07400I 0
u = 1.24383 − 1.21540I
a = −0.907070 + 0.064360I
b = 0.59013 + 1.28629I
3.82402 + 13.07400I 0
u = 0.099836 + 0.233168I
a = −1.41054 + 2.70584I
b = 0.206151 + 1.270090I
1.19581 − 2.53766I −2.90517 + 3.99602I
u = 0.099836 − 0.233168I
a = −1.41054 − 2.70584I
b = 0.206151 − 1.270090I
1.19581 + 2.53766I −2.90517 − 3.99602I
u = 0.068396 + 0.239581I
a = −6.02625 − 8.14506I
b = 0.315887 − 0.928442I
1.88088 − 9.45306I 2.29225 + 13.05997I
u = 0.068396 − 0.239581I
a = −6.02625 + 8.14506I
b = 0.315887 + 0.928442I
1.88088 + 9.45306I 2.29225 − 13.05997I
u = 0.088603 + 0.225851I
a = 2.57868 + 8.72020I
b = −0.229092 + 0.961028I
2.95872 − 4.01668I 1.53483 + 6.51307I
u = 0.088603 − 0.225851I
a = 2.57868 − 8.72020I
b = −0.229092 − 0.961028I
2.95872 + 4.01668I 1.53483 − 6.51307I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.83473 + 0.35996I
a = −0.029283 + 0.548479I
b = 0.346108 + 0.674457I
2.62017 − 6.46004I 0
u = −1.83473 − 0.35996I
a = −0.029283 − 0.548479I
b = 0.346108 − 0.674457I
2.62017 + 6.46004I 0
u = −0.98865 + 1.61493I
a = −0.594184 − 0.223261I
b = 0.431561 + 1.208400I
−2.66959 + 5.13236I 0
u = −0.98865 − 1.61493I
a = −0.594184 + 0.223261I
b = 0.431561 − 1.208400I
−2.66959 − 5.13236I 0
u = −0.67802 + 1.88022I
a = −0.147392 − 0.121666I
b = 0.185491 − 0.556934I
5.70289 + 2.90295I 0
u = −0.67802 − 1.88022I
a = −0.147392 + 0.121666I
b = 0.185491 + 0.556934I
5.70289 − 2.90295I 0
u = 1.32145 + 1.52494I
a = 0.617811 − 0.078145I
b = −0.368725 + 1.298990I
−3.97620 − 9.73538I 0
u = 1.32145 − 1.52494I
a = 0.617811 + 0.078145I
b = −0.368725 − 1.298990I
−3.97620 + 9.73538I 0
u = 2.14728 + 0.12545I
a = −0.130266 − 0.458587I
b = −0.096463 − 0.872410I
3.63274 − 2.43968I 0
u = 2.14728 − 0.12545I
a = −0.130266 + 0.458587I
b = −0.096463 + 0.872410I
3.63274 + 2.43968I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.84252 + 1.17113I
a = 0.360912 − 0.283689I
b = −0.403499 − 0.931637I
4.27100 + 0.57975I 0
u = −1.84252 − 1.17113I
a = 0.360912 + 0.283689I
b = −0.403499 + 0.931637I
4.27100 − 0.57975I 0
u = −1.74099 + 1.35503I
a = 0.0311843 − 0.1054550I
b = −0.229092 + 0.961028I
2.95872 − 4.01668I 0
u = −1.74099 − 1.35503I
a = 0.0311843 + 0.1054550I
b = −0.229092 − 0.961028I
2.95872 + 4.01668I 0
u = 2.13172 + 0.92277I
a = −0.279390 − 0.331009I
b = 0.265107 − 0.981138I
4.51716 − 5.38940I 0
u = 2.13172 − 0.92277I
a = −0.279390 + 0.331009I
b = 0.265107 + 0.981138I
4.51716 + 5.38940I 0
u = 1.53923 + 2.00086I
a = −0.0587023 − 0.0793420I
b = 0.315887 + 0.928442I
1.88088 + 9.45306I 0
u = 1.53923 − 2.00086I
a = −0.0587023 + 0.0793420I
b = 0.315887 − 0.928442I
1.88088 − 9.45306I 0
21
III. I
u
3
= h−10u
11
− 2u
10
+ · · · + 9b + 10, a + 1, u
12
+ u
11
+ · · · + 4u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−1
10
9
u
11
+
2
9
u
10
+ ··· +
22
9
u −
10
9
a
10
=
10
9
u
11
+
2
9
u
10
+ ··· +
22
9
u −
19
9
10
9
u
11
+
2
9
u
10
+ ··· +
22
9
u −
10
9
a
3
=
−
11
9
u
11
−
4
9
u
10
+ ··· −
44
9
u +
20
9
−
1
9
u
11
−
2
9
u
10
+ ··· −
22
9
u +
1
9
a
2
=
−
8
3
u
11
−
7
3
u
10
+ ··· −
80
3
u −
16
3
−
1
3
u
11
−
2
3
u
10
+ ··· −
19
3
u −
5
3
a
8
=
10
9
u
11
+
2
9
u
10
+ ··· +
22
9
u −
19
9
11
9
u
11
+
4
9
u
10
+ ··· +
44
9
u −
2
9
a
6
=
−u
11
− 7u
7
+ u
4
− 12u
3
− u
2
+ 4
1
9
u
11
+
2
9
u
10
+ ··· −
5
9
u +
8
9
a
12
=
u
8
9
u
11
+
7
9
u
10
+ ··· +
59
9
u +
10
9
a
11
=
4
3
u
11
+
2
3
u
10
+ ··· +
13
3
u −
4
3
16
9
u
11
+
14
9
u
10
+ ··· +
73
9
u +
11
9
a
7
=
16
9
u
11
+
14
9
u
10
+ ··· +
109
9
u +
20
9
7
9
u
11
+
5
9
u
10
+ ··· +
37
9
u +
11
9
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
10
3
u
11
+
14
3
u
10
+ 3u
9
+
19
3
u
8
+ 27u
7
+
101
3
u
6
+ 15u
5
+
77
3
u
4
+ 52u
3
+
178
3
u
2
+
31
3
u +
11
3
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
− 6u
11
+ ··· − 9u + 1
c
2
, c
7
u
12
− 2u
11
+ ··· − u + 1
c
3
u
12
− 2u
11
+ 3u
10
− 2u
9
− u
8
+ 3u
7
− 4u
6
+ 3u
5
− u
4
− u
3
+ 2u
2
− u + 1
c
4
, c
12
u
12
+ u
11
+ ··· + 4u + 1
c
5
u
12
− u
11
+ 2u
10
− u
9
− u
8
+ 3u
7
− 4u
6
+ 3u
5
− u
4
− 2u
3
+ 3u
2
− 2u + 1
c
6
, c
11
u
12
+ 2u
11
+ ··· + u + 1
c
8
u
12
+ u
11
+ 2u
10
+ u
9
− u
8
− 3u
7
− 4u
6
− 3u
5
− u
4
+ 2u
3
+ 3u
2
+ 2u + 1
c
9
u
12
+ 2u
11
+ 3u
10
+ 2u
9
− u
8
− 3u
7
− 4u
6
− 3u
5
− u
4
+ u
3
+ 2u
2
+ u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 6y
11
+ ··· − 11y + 1
c
2
, c
6
, c
7
c
11
y
12
+ 6y
11
+ ··· + 9y + 1
c
3
, c
9
y
12
+ 2y
11
− y
10
− 6y
9
− y
8
+ 5y
7
+ 6y
6
+ 3y
5
− 5y
4
− 7y
3
+ 3y + 1
c
4
, c
12
y
12
+ y
11
+ ··· + 8y + 1
c
5
, c
8
y
12
+ 3y
11
− 7y
9
− 5y
8
+ 3y
7
+ 6y
6
+ 5y
5
− y
4
− 6y
3
− y
2
+ 2y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.863486 + 0.872394I
a = −1.00000
b = 0.665514 + 0.762155I
−0.98298 + 3.68538I −4.37283 − 7.00682I
u = −0.863486 − 0.872394I
a = −1.00000
b = 0.665514 − 0.762155I
−0.98298 − 3.68538I −4.37283 + 7.00682I
u = −0.354872 + 0.560954I
a = −1.00000
b = 1.079070 + 0.218144I
−0.59559 + 2.91700I 1.77911 − 12.40585I
u = −0.354872 − 0.560954I
a = −1.00000
b = 1.079070 − 0.218144I
−0.59559 − 2.91700I 1.77911 + 12.40585I
u = 0.979880 + 1.002500I
a = −1.00000
b = −0.192196 − 0.879704I
1.62015 + 8.37846I −0.62923 − 4.48090I
u = 0.979880 − 1.002500I
a = −1.00000
b = −0.192196 + 0.879704I
1.62015 − 8.37846I −0.62923 + 4.48090I
u = 0.96111 + 1.04325I
a = −1.00000
b = 0.370840 − 1.288770I
−5.29393 − 7.05976I −4.29339 + 6.46563I
u = 0.96111 − 1.04325I
a = −1.00000
b = 0.370840 + 1.288770I
−5.29393 + 7.05976I −4.29339 − 6.46563I
u = −1.01858 + 1.01101I
a = −1.00000
b = 0.024242 + 0.781924I
4.80289 + 3.78069I 2.67279 − 4.44300I
u = −1.01858 − 1.01101I
a = −1.00000
b = 0.024242 − 0.781924I
4.80289 − 3.78069I 2.67279 + 4.44300I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.204054 + 0.378583I
a = −1.00000
b = −0.947472 + 0.073317I
0.44945 + 4.78647I −0.65644 − 4.95650I
u = −0.204054 − 0.378583I
a = −1.00000
b = −0.947472 − 0.073317I
0.44945 − 4.78647I −0.65644 + 4.95650I
26
IV. I
u
4
= h−2970u
11
− 16830u
10
+ · · · + 3431b − 12700, 2891u
11
+
14095u
10
+ · · · + 3431a + 4241, u
12
+ 5u
11
+ · · · + 4u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−0.842611u
11
− 4.10813u
10
+ ··· − 7.29846u − 1.23608
0.865637u
11
+ 4.90528u
10
+ ··· + 10.3585u + 3.70154
a
10
=
0.0230254u
11
+ 0.797144u
10
+ ··· + 3.06004u + 2.46546
0.865637u
11
+ 4.90528u
10
+ ··· + 10.3585u + 3.70154
a
3
=
−1.23608u
11
− 5.33780u
10
+ ··· − 3.55232u + 2.35412
−0.303410u
11
− 1.71932u
10
+ ··· − 3.24687u − 0.0448849
a
2
=
−2.94433u
11
− 14.3512u
10
+ ··· − 22.2093u − 4.58350
−0.460799u
11
− 2.61119u
10
+ ··· − 6.94841u − 1.80880
a
8
=
−0.0469251u
11
+ 0.400758u
10
+ ··· + 2.63713u + 2.57039
0.552609u
11
+ 3.13145u
10
+ ··· + 7.44098u + 3.17109
a
6
=
−1.11804u
11
− 4.66890u
10
+ ··· − 0.776159u + 3.67706
0.0419703u
11
+ 0.237832u
10
+ ··· − 0.346255u + 0.937045
a
12
=
−0.580297u
11
− 2.62168u
10
+ ··· − 1.46255u + 0.370446
1.04488u
11
+ 4.92101u
10
+ ··· + 6.12970u + 0.932673
a
11
=
0.127951u
11
+ 1.39172u
10
+ ··· + 5.19440u + 3.30807
1.02594u
11
+ 5.48033u
10
+ ··· + 9.53600u + 2.46109
a
7
=
1.32294u
11
+ 6.49665u
10
+ ··· + 9.33576u + 2.51559
0.981929u
11
+ 4.56427u
10
+ ··· + 3.64908u + 1.02711
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1968
3431
u
11
−
11152
3431
u
10
−
24508
3431
u
9
−
30991
3431
u
8
−
20579
3431
u
7
−
8053
3431
u
6
−
22442
3431
u
5
−
8337
3431
u
4
−
28268
3431
u
3
−
43152
3431
u
2
−
21505
3431
u −
7341
3431
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
− 6u
11
+ ··· − 6u + 1
c
2
, c
7
u
12
− 2u
11
+ ··· − 2u + 1
c
3
(u
6
+ u
5
+ u
4
− u
2
− 1)
2
c
4
, c
12
u
12
+ 5u
11
+ ··· + 4u + 1
c
5
(u
6
+ u
4
− u
2
− u − 1)
2
c
6
, c
11
u
12
+ 2u
11
+ ··· + 2u + 1
c
8
(u
6
+ u
4
− u
2
+ u − 1)
2
c
9
(u
6
− u
5
+ u
4
− u
2
− 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 6y
11
+ ··· + 6y + 1
c
2
, c
6
, c
7
c
11
y
12
+ 6y
11
+ ··· + 6y + 1
c
3
, c
9
(y
6
+ y
5
− y
4
− 4y
3
− y
2
+ 2y + 1)
2
c
4
, c
12
y
12
− 3y
11
+ ··· + 8y + 1
c
5
, c
8
(y
6
+ 2y
5
− y
4
− 4y
3
− y
2
+ y + 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.023730 + 1.013520I
a = −0.02218 − 1.97405I
b = 0.124001 + 0.785288I
3.87460 + 3.17324I 5.27096 − 5.77959I
u = −0.023730 − 1.013520I
a = −0.02218 + 1.97405I
b = 0.124001 − 0.785288I
3.87460 − 3.17324I 5.27096 + 5.77959I
u = 0.879137 + 0.602547I
a = 1.48568 + 0.72207I
b = −0.483487 + 1.114980I
−3.74344 − 5.18068I −8.21095 + 5.58494I
u = 0.879137 − 0.602547I
a = 1.48568 − 0.72207I
b = −0.483487 − 1.114980I
−3.74344 + 5.18068I −8.21095 − 5.58494I
u = −0.207965 + 0.545792I
a = 0.746441 − 0.665452I
b = −1.18501
−1.15778 − 61.276009 + 0.10I
u = −0.207965 − 0.545792I
a = 0.746441 + 0.665452I
b = −1.18501
−1.15778 − 61.276009 + 0.10I
u = −0.275150 + 0.355699I
a = 0.251268 − 0.967917I
b = 0.903984
0.895450 −6 − 0.396023 + 0.10I
u = −0.275150 − 0.355699I
a = 0.251268 + 0.967917I
b = 0.903984
0.895450 −6 − 0.396023 + 0.10I
u = −0.87103 + 1.52999I
a = 0.544480 + 0.264627I
b = −0.483487 − 1.114980I
−3.74344 + 5.18068I −8.21095 − 5.58494I
u = −0.87103 − 1.52999I
a = 0.544480 − 0.264627I
b = −0.483487 + 1.114980I
−3.74344 − 5.18068I −8.21095 + 5.58494I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −2.00126 + 0.02437I
a = −0.005690 − 0.506509I
b = 0.124001 − 0.785288I
3.87460 − 3.17324I 5.27096 + 5.77959I
u = −2.00126 − 0.02437I
a = −0.005690 + 0.506509I
b = 0.124001 + 0.785288I
3.87460 + 3.17324I 5.27096 − 5.77959I
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
12
− 6u
11
+ ··· − 6u + 1)(u
12
− 6u
11
+ ··· − 9u + 1)
· (u
26
+ 12u
25
+ ··· + 4u + 1)(u
108
+ 41u
107
+ ··· + 263054u + 2809)
c
2
, c
7
(u
12
− 2u
11
+ ··· − u + 1)(u
12
− 2u
11
+ ··· − 2u + 1)
· (u
26
+ 6u
24
+ ··· + 2u
2
+ 1)(u
108
− u
107
+ ··· − 412u + 53)
c
3
(u
6
+ u
5
+ u
4
− u
2
− 1)
2
· (u
12
− 2u
11
+ 3u
10
− 2u
9
− u
8
+ 3u
7
− 4u
6
+ 3u
5
− u
4
− u
3
+ 2u
2
− u + 1)
· (u
26
− 19u
25
+ ··· − 480u + 64)(u
54
+ 9u
53
+ ··· + 40u + 5)
2
c
4
, c
12
(u
12
+ u
11
+ ··· + 4u + 1)(u
12
+ 5u
11
+ ··· + 4u + 1)
· (u
26
− u
25
+ ··· + u + 1)(u
108
− 2u
107
+ ··· − 20u + 1)
c
5
(u
6
+ u
4
− u
2
− u − 1)
2
· (u
12
− u
11
+ 2u
10
− u
9
− u
8
+ 3u
7
− 4u
6
+ 3u
5
− u
4
− 2u
3
+ 3u
2
− 2u + 1)
· (u
26
− 20u
25
+ ··· − 3200u + 256)(u
54
+ 8u
53
+ ··· + 143u + 17)
2
c
6
, c
11
(u
12
+ 2u
11
+ ··· + 2u + 1)(u
12
+ 2u
11
+ ··· + u + 1)
· (u
26
+ 6u
24
+ ··· + 2u
2
+ 1)(u
108
− u
107
+ ··· − 412u + 53)
c
8
(u
6
+ u
4
− u
2
+ u − 1)
2
· (u
12
+ u
11
+ 2u
10
+ u
9
− u
8
− 3u
7
− 4u
6
− 3u
5
− u
4
+ 2u
3
+ 3u
2
+ 2u + 1)
· (u
26
− 20u
25
+ ··· − 3200u + 256)(u
54
+ 8u
53
+ ··· + 143u + 17)
2
c
9
(u
6
− u
5
+ u
4
− u
2
− 1)
2
· (u
12
+ 2u
11
+ 3u
10
+ 2u
9
− u
8
− 3u
7
− 4u
6
− 3u
5
− u
4
+ u
3
+ 2u
2
+ u + 1)
· (u
26
− 19u
25
+ ··· − 480u + 64)(u
54
+ 9u
53
+ ··· + 40u + 5)
2
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
12
+ 6y
11
+ ··· + 6y + 1)(y
12
+ 6y
11
+ ··· − 11y + 1)
· (y
26
+ 12y
25
+ ··· + 52y + 1)
· (y
108
+ 57y
107
+ ··· − 29072544170y + 7890481)
c
2
, c
6
, c
7
c
11
(y
12
+ 6y
11
+ ··· + 9y + 1)(y
12
+ 6y
11
+ ··· + 6y + 1)
· (y
26
+ 12y
25
+ ··· + 4y + 1)(y
108
+ 41y
107
+ ··· + 263054y + 2809)
c
3
, c
9
(y
6
+ y
5
− y
4
− 4y
3
− y
2
+ 2y + 1)
2
· (y
12
+ 2y
11
− y
10
− 6y
9
− y
8
+ 5y
7
+ 6y
6
+ 3y
5
− 5y
4
− 7y
3
+ 3y + 1)
· (y
26
+ 7y
25
+ ··· + 113664y + 4096)
· (y
54
+ 31y
53
+ ··· + 570y + 25)
2
c
4
, c
12
(y
12
− 3y
11
+ ··· + 8y + 1)(y
12
+ y
11
+ ··· + 8y + 1)
· (y
26
− y
25
+ ··· − 13y + 1)(y
108
+ 4y
107
+ ··· + 72y + 1)
c
5
, c
8
(y
6
+ 2y
5
− y
4
− 4y
3
− y
2
+ y + 1)
2
· (y
12
+ 3y
11
− 7y
9
− 5y
8
+ 3y
7
+ 6y
6
+ 5y
5
− y
4
− 6y
3
− y
2
+ 2y + 1)
· (y
26
+ 8y
25
+ ··· + 376832y + 65536)
· (y
54
+ 42y
53
+ ··· − 1919y + 289)
2
33
