12a
0055
(K12a
0055
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 4 12 1 11 6 9 8
Solving Sequence
5,10
6
3,11
2 1 4 7 9 12 8
c
5
c
10
c
2
c
1
c
4
c
6
c
9
c
11
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.73784 × 10
105
u
87
+ 2.33065 × 10
106
u
86
+ ··· + 1.32969 × 10
107
b + 6.87193 × 10
107
,
− 1.27360 × 10
106
u
87
+ 7.35251 × 10
105
u
86
+ ··· + 2.65937 × 10
107
a + 7.67895 × 10
107
,
u
88
+ 2u
87
+ ··· + 12u − 8i
I
u
2
= hb + 1, 2u
7
− u
6
− 3u
5
+ 3u
4
+ 4u
3
− 3u
2
+ a − 2u + 4, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 99 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−2.74 × 10
105
u
87
+ 2.33 × 10
106
u
86
+ · · · + 1.33 × 10
107
b + 6.87 ×
10
107
, −1.27 × 10
106
u
87
+ 7.35 × 10
105
u
86
+ · · · + 2.66 × 10
107
a + 7.68 ×
10
107
, u
88
+ 2u
87
+ · · · + 12u − 8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
0.0478909u
87
− 0.0276475u
86
+ ··· + 35.3569u − 2.88750
0.0205902u
87
− 0.175279u
86
+ ··· + 0.764280u − 5.16808
a
11
=
−u
−u
3
+ u
a
2
=
0.0684810u
87
− 0.202926u
86
+ ··· + 36.1212u − 8.05559
0.0205902u
87
− 0.175279u
86
+ ··· + 0.764280u − 5.16808
a
1
=
1.39916u
87
+ 3.39018u
86
+ ··· + 13.5712u + 13.1209
−1.39649u
87
− 3.74999u
86
+ ··· − 0.897228u − 18.8300
a
4
=
0.408355u
87
+ 1.20087u
86
+ ··· + 32.6967u − 0.441203
−0.968270u
87
− 2.08814u
86
+ ··· − 0.974469u − 4.14421
a
7
=
0.00267385u
87
− 0.359809u
86
+ ··· + 12.6740u − 5.70909
1.24468u
87
+ 3.55177u
86
+ ··· + 5.30050u + 15.9088
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
8
=
−0.290712u
87
− 1.73558u
86
+ ··· + 6.94662u − 12.1213
1.45970u
87
+ 4.30683u
86
+ ··· + 8.54245u + 17.9540
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.18054u
87
+ 14.8609u
86
+ ··· + 127.311u + 12.9010
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 38u
87
+ ··· + 101u + 1
c
2
, c
4
u
88
− 10u
87
+ ··· − 7u + 1
c
3
, c
6
u
88
− 2u
87
+ ··· + 128u − 256
c
5
, c
10
u
88
− 2u
87
+ ··· − 12u − 8
c
7
, c
8
, c
12
u
88
− 5u
87
+ ··· + 8u + 1
c
9
, c
11
u
88
+ 24u
87
+ ··· + 1872u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 34y
87
+ ··· − 4505y + 1
c
2
, c
4
y
88
− 38y
87
+ ··· − 101y + 1
c
3
, c
6
y
88
+ 54y
87
+ ··· + 999424y + 65536
c
5
, c
10
y
88
− 24y
87
+ ··· − 1872y + 64
c
7
, c
8
, c
12
y
88
− 71y
87
+ ··· + 62y + 1
c
9
, c
11
y
88
+ 76y
87
+ ··· − 105728y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.392572 + 0.920696I
a = 0.031296 − 0.890953I
b = 0.670708 + 0.469662I
−1.30721 + 0.66243I 0
u = 0.392572 − 0.920696I
a = 0.031296 + 0.890953I
b = 0.670708 − 0.469662I
−1.30721 − 0.66243I 0
u = −0.887881 + 0.457891I
a = −0.090976 + 0.352185I
b = 0.479587 + 0.533093I
1.43432 + 2.39937I 0
u = −0.887881 − 0.457891I
a = −0.090976 − 0.352185I
b = 0.479587 − 0.533093I
1.43432 − 2.39937I 0
u = 0.203330 + 1.003580I
a = −0.381810 + 0.869323I
b = 0.991760 − 0.565904I
−2.39788 + 5.04856I 0
u = 0.203330 − 1.003580I
a = −0.381810 − 0.869323I
b = 0.991760 + 0.565904I
−2.39788 − 5.04856I 0
u = −0.958732 + 0.139931I
a = 0.735606 + 0.670342I
b = −0.335372 − 0.551660I
−5.40258 + 0.56073I 0
u = −0.958732 − 0.139931I
a = 0.735606 − 0.670342I
b = −0.335372 + 0.551660I
−5.40258 − 0.56073I 0
u = −0.862313 + 0.579468I
a = 0.321746 + 0.371790I
b = 0.515120 + 0.203414I
1.47628 + 2.33295I 0
u = −0.862313 − 0.579468I
a = 0.321746 − 0.371790I
b = 0.515120 − 0.203414I
1.47628 − 2.33295I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.947226 + 0.084231I
a = 1.94827 − 0.02918I
b = 0.941810 + 0.560456I
−0.97747 − 2.78041I −12.00000 + 0.I
u = 0.947226 − 0.084231I
a = 1.94827 + 0.02918I
b = 0.941810 − 0.560456I
−0.97747 + 2.78041I −12.00000 + 0.I
u = −1.000340 + 0.317524I
a = 1.70909 + 1.08359I
b = 1.024730 − 0.591282I
−0.03297 + 7.08755I 0
u = −1.000340 − 0.317524I
a = 1.70909 − 1.08359I
b = 1.024730 + 0.591282I
−0.03297 − 7.08755I 0
u = 1.044510 + 0.227043I
a = −0.930430 − 0.232517I
b = −1.224440 + 0.244106I
−8.09834 − 2.07994I 0
u = 1.044510 − 0.227043I
a = −0.930430 + 0.232517I
b = −1.224440 − 0.244106I
−8.09834 + 2.07994I 0
u = 0.870126 + 0.281441I
a = 0.615716 − 1.177220I
b = 0.759307 − 0.539626I
−0.37405 + 1.65782I −12.00000 + 0.I
u = 0.870126 − 0.281441I
a = 0.615716 + 1.177220I
b = 0.759307 + 0.539626I
−0.37405 − 1.65782I −12.00000 + 0.I
u = −1.058740 + 0.305027I
a = −0.70456 − 1.67547I
b = −1.073140 + 0.441465I
−7.60787 + 4.58396I 0
u = −1.058740 − 0.305027I
a = −0.70456 + 1.67547I
b = −1.073140 − 0.441465I
−7.60787 − 4.58396I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.753149 + 0.812851I
a = 0.009896 − 1.120230I
b = −1.306960 + 0.017227I
−1.25565 − 1.36378I 0
u = −0.753149 − 0.812851I
a = 0.009896 + 1.120230I
b = −1.306960 − 0.017227I
−1.25565 + 1.36378I 0
u = 1.038570 + 0.425588I
a = −0.126062 + 0.339240I
b = 0.227675 − 0.708873I
−3.58769 − 5.33790I 0
u = 1.038570 − 0.425588I
a = −0.126062 − 0.339240I
b = 0.227675 + 0.708873I
−3.58769 + 5.33790I 0
u = −0.822672 + 0.764737I
a = −0.560044 − 1.062490I
b = 1.088910 + 0.759677I
4.24766 − 1.27868I 0
u = −0.822672 − 0.764737I
a = −0.560044 + 1.062490I
b = 1.088910 − 0.759677I
4.24766 + 1.27868I 0
u = 0.814865 + 0.778282I
a = 0.11774 + 2.41231I
b = −0.830940 − 0.592246I
0.329058 − 0.951263I 0
u = 0.814865 − 0.778282I
a = 0.11774 − 2.41231I
b = −0.830940 + 0.592246I
0.329058 + 0.951263I 0
u = 0.754800 + 0.876512I
a = 1.11868 − 1.17948I
b = −0.868291 + 0.595565I
0.20885 + 3.75440I 0
u = 0.754800 − 0.876512I
a = 1.11868 + 1.17948I
b = −0.868291 − 0.595565I
0.20885 − 3.75440I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.794082 + 0.262125I
a = −1.46161 + 2.25876I
b = −0.977760 − 0.341426I
−2.28886 − 2.45162I −16.2110 + 6.3903I
u = 0.794082 − 0.262125I
a = −1.46161 − 2.25876I
b = −0.977760 + 0.341426I
−2.28886 + 2.45162I −16.2110 − 6.3903I
u = −0.852305 + 0.811962I
a = 1.07072 + 1.14717I
b = −0.811618 − 0.630399I
4.01818 + 0.54192I 0
u = −0.852305 − 0.811962I
a = 1.07072 − 1.14717I
b = −0.811618 + 0.630399I
4.01818 − 0.54192I 0
u = 0.886190 + 0.782136I
a = −0.057066 + 0.858549I
b = −1.336480 + 0.029864I
2.31687 − 2.94399I 0
u = 0.886190 − 0.782136I
a = −0.057066 − 0.858549I
b = −1.336480 − 0.029864I
2.31687 + 2.94399I 0
u = 0.790264 + 0.884911I
a = −0.576247 + 1.018820I
b = 1.111540 − 0.727657I
7.85733 + 5.61860I 0
u = 0.790264 − 0.884911I
a = −0.576247 − 1.018820I
b = 1.111540 + 0.727657I
7.85733 − 5.61860I 0
u = −0.881857 + 0.797266I
a = −0.10968 + 1.44896I
b = 0.605815 − 0.957019I
5.72724 + 4.97749I 0
u = −0.881857 − 0.797266I
a = −0.10968 − 1.44896I
b = 0.605815 + 0.957019I
5.72724 − 4.97749I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933371 + 0.742677I
a = 0.74662 + 2.29509I
b = 1.113350 − 0.705726I
3.90440 + 6.99279I 0
u = −0.933371 − 0.742677I
a = 0.74662 − 2.29509I
b = 1.113350 + 0.705726I
3.90440 − 6.99279I 0
u = −0.897183 + 0.796476I
a = −1.216610 − 0.564361I
b = 0.532139 + 0.928269I
5.68216 + 1.00101I 0
u = −0.897183 − 0.796476I
a = −1.216610 + 0.564361I
b = 0.532139 − 0.928269I
5.68216 − 1.00101I 0
u = 0.942078 + 0.752491I
a = 1.01680 − 1.12508I
b = −0.759566 + 0.665808I
−0.06234 − 4.83478I 0
u = 0.942078 − 0.752491I
a = 1.01680 + 1.12508I
b = −0.759566 − 0.665808I
−0.06234 + 4.83478I 0
u = 0.422280 + 0.670799I
a = 0.704032 − 0.641404I
b = 0.214950 + 0.166258I
−1.40337 + 0.92720I −8.23175 − 0.58902I
u = 0.422280 − 0.670799I
a = 0.704032 + 0.641404I
b = 0.214950 − 0.166258I
−1.40337 − 0.92720I −8.23175 + 0.58902I
u = 0.841271 + 0.874220I
a = −0.05629 − 1.46245I
b = 0.555731 + 0.949544I
9.56149 − 0.50937I 0
u = 0.841271 − 0.874220I
a = −0.05629 + 1.46245I
b = 0.555731 − 0.949544I
9.56149 + 0.50937I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.925474 + 0.790304I
a = 0.08043 − 2.24661I
b = −0.884202 + 0.625072I
3.79156 + 5.46140I 0
u = −0.925474 − 0.790304I
a = 0.08043 + 2.24661I
b = −0.884202 − 0.625072I
3.79156 − 5.46140I 0
u = −1.220990 + 0.093727I
a = 0.893667 + 0.033167I
b = 0.943866 + 0.417931I
−7.95540 − 1.57335I 0
u = −1.220990 − 0.093727I
a = 0.893667 − 0.033167I
b = 0.943866 − 0.417931I
−7.95540 + 1.57335I 0
u = −0.794180 + 0.936665I
a = −0.00264 + 1.47095I
b = 0.507424 − 0.936810I
5.50773 − 3.95377I 0
u = −0.794180 − 0.936665I
a = −0.00264 − 1.47095I
b = 0.507424 + 0.936810I
5.50773 + 3.95377I 0
u = −0.088205 + 0.759173I
a = 1.39479 + 1.62378I
b = −1.025110 − 0.260624I
−4.33853 − 0.93069I −17.4874 − 0.5005I
u = −0.088205 − 0.759173I
a = 1.39479 − 1.62378I
b = −1.025110 + 0.260624I
−4.33853 + 0.93069I −17.4874 + 0.5005I
u = −0.758355 + 0.979789I
a = −0.587135 − 0.981162I
b = 1.128270 + 0.699547I
3.60923 − 9.94654I 0
u = −0.758355 − 0.979789I
a = −0.587135 + 0.981162I
b = 1.128270 − 0.699547I
3.60923 + 9.94654I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985719 + 0.755243I
a = −0.071592 − 0.666243I
b = −1.357700 − 0.065878I
−1.95959 + 7.25560I 0
u = −0.985719 − 0.755243I
a = −0.071592 + 0.666243I
b = −1.357700 + 0.065878I
−1.95959 − 7.25560I 0
u = 1.180680 + 0.413243I
a = 1.03880 − 1.13972I
b = 1.094140 + 0.563802I
−5.89137 − 10.06180I 0
u = 1.180680 − 0.413243I
a = 1.03880 + 1.13972I
b = 1.094140 − 0.563802I
−5.89137 + 10.06180I 0
u = 1.078160 + 0.638701I
a = 0.332709 − 0.353621I
b = 0.716392 − 0.192203I
−3.33914 − 6.07366I 0
u = 1.078160 − 0.638701I
a = 0.332709 + 0.353621I
b = 0.716392 + 0.192203I
−3.33914 + 6.07366I 0
u = −0.365420 + 0.646101I
a = −0.146644 + 1.102250I
b = 0.746131 − 0.685305I
3.13319 + 1.58793I −4.36565 − 2.62454I
u = −0.365420 − 0.646101I
a = −0.146644 − 1.102250I
b = 0.746131 + 0.685305I
3.13319 − 1.58793I −4.36565 + 2.62454I
u = 0.963850 + 0.822645I
a = −1.090440 + 0.696675I
b = 0.499212 − 0.961407I
9.17313 − 5.78375I 0
u = 0.963850 − 0.822645I
a = −1.090440 − 0.696675I
b = 0.499212 + 0.961407I
9.17313 + 5.78375I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.710725 + 0.142036I
a = −2.49015 − 0.07252I
b = −1.090730 − 0.165721I
−2.74417 + 0.55471I −16.6137 − 8.8786I
u = −0.710725 − 0.142036I
a = −2.49015 + 0.07252I
b = −1.090730 + 0.165721I
−2.74417 − 0.55471I −16.6137 + 8.8786I
u = 1.008330 + 0.782072I
a = 0.05748 + 2.13739I
b = −0.926480 − 0.640157I
−0.57700 − 9.90939I 0
u = 1.008330 − 0.782072I
a = 0.05748 − 2.13739I
b = −0.926480 + 0.640157I
−0.57700 + 9.90939I 0
u = 0.998606 + 0.799996I
a = 0.54095 − 2.15791I
b = 1.142060 + 0.706012I
7.20070 − 11.86680I 0
u = 0.998606 − 0.799996I
a = 0.54095 + 2.15791I
b = 1.142060 − 0.706012I
7.20070 + 11.86680I 0
u = −1.021860 + 0.824555I
a = −0.979873 − 0.762766I
b = 0.466549 + 0.980590I
4.77490 + 10.43370I 0
u = −1.021860 − 0.824555I
a = −0.979873 + 0.762766I
b = 0.466549 − 0.980590I
4.77490 − 10.43370I 0
u = −0.199533 + 0.630090I
a = −0.349695 − 1.014370I
b = 0.931055 + 0.671220I
2.58372 − 3.65091I −4.88024 + 4.09202I
u = −0.199533 − 0.630090I
a = −0.349695 + 1.014370I
b = 0.931055 − 0.671220I
2.58372 + 3.65091I −4.88024 − 4.09202I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.059800 + 0.822621I
a = 0.44539 + 2.02899I
b = 1.162810 − 0.698617I
2.6344 + 16.5403I 0
u = −1.059800 − 0.822621I
a = 0.44539 − 2.02899I
b = 1.162810 + 0.698617I
2.6344 − 16.5403I 0
u = 0.646965 + 0.080521I
a = −0.343025 − 1.213620I
b = 0.873530 + 0.830831I
0.75119 − 3.07502I −19.2370 + 4.9728I
u = 0.646965 − 0.080521I
a = −0.343025 + 1.213620I
b = 0.873530 − 0.830831I
0.75119 + 3.07502I −19.2370 − 4.9728I
u = 0.549522
a = 0.875721
b = −0.119846
−0.718836 −14.1050
u = 0.317305 + 0.268219I
a = 1.79149 − 0.55439I
b = −0.724370 + 0.147571I
−0.979988 + 0.105759I −9.79769 + 1.06695I
u = 0.317305 − 0.268219I
a = 1.79149 + 0.55439I
b = −0.724370 − 0.147571I
−0.979988 − 0.105759I −9.79769 − 1.06695I
u = −0.344030
a = −11.6544
b = −0.902968
−2.97247 −58.0340
13
II. I
u
2
= hb + 1, 2u
7
− u
6
− 3u
5
+ 3u
4
+ 4u
3
− 3u
2
+ a − 2u + 4, u
8
− u
7
−
u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−2u
7
+ u
6
+ 3u
5
− 3u
4
− 4u
3
+ 3u
2
+ 2u − 4
−1
a
11
=
−u
−u
3
+ u
a
2
=
−2u
7
+ u
6
+ 3u
5
− 3u
4
− 4u
3
+ 3u
2
+ 2u − 5
−1
a
1
=
−1
0
a
4
=
−2u
7
+ u
6
+ 3u
5
− 3u
4
− 4u
3
+ 3u
2
+ 2u − 4
−1
a
7
=
1
u
2
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
8
=
u
5
+ u
u
5
− u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
7
− 2u
6
+ 4u
4
+ 3u
3
− u
2
− 13
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
7
, c
8
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
9
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
10
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
11
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
12
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
6
y
8
c
5
, c
10
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
7
, c
8
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 0.281371 + 1.128550I
b = −1.00000
−2.68559 + 1.13123I −17.2624 − 0.2227I
u = 0.570868 − 0.730671I
a = 0.281371 − 1.128550I
b = −1.00000
−2.68559 − 1.13123I −17.2624 + 0.2227I
u = −0.855237 + 0.665892I
a = −0.208670 − 0.825203I
b = −1.00000
0.51448 + 2.57849I −14.1288 − 3.8797I
u = −0.855237 − 0.665892I
a = −0.208670 + 0.825203I
b = −1.00000
0.51448 − 2.57849I −14.1288 + 3.8797I
u = −1.09818
a = −0.829189
b = −1.00000
−8.14766 −19.7220
u = 1.031810 + 0.655470I
a = −0.284386 + 0.605794I
b = −1.00000
−4.02461 − 6.44354I −19.1410 + 6.6674I
u = 1.031810 − 0.655470I
a = −0.284386 − 0.605794I
b = −1.00000
−4.02461 + 6.44354I −19.1410 − 6.6674I
u = 0.603304
a = −2.74744
b = −1.00000
−2.48997 −12.2140
17
III. I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
3
=
0
v
2
+ 3v − 1
a
11
=
v
0
a
2
=
v
2
+ 3v − 1
v
2
+ 3v − 1
a
1
=
v
2
+ 3v − 1
−v
2
− 2v + 3
a
4
=
−2v
2
− 5v + 4
−2v
2
− 5v + 3
a
7
=
−v
2
− 3v + 1
v
2
+ 2v − 3
a
9
=
v
0
a
12
=
v
0
a
8
=
−v
2
− 2v + 1
v
2
+ 2v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
+ 5v − 11
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
9
, c
10
c
11
u
3
c
6
u
3
+ u
2
+ 2u + 1
c
7
, c
8
(u − 1)
3
c
12
(u + 1)
3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
9
, c
10
c
11
y
3
c
7
, c
8
, c
12
(y − 1)
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.539798 + 0.182582I
a = 0
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −7.78492 + 1.30714I
v = 0.539798 − 0.182582I
a = 0
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −7.78492 − 1.30714I
v = −3.07960
a = 0
b = −0.754878
−2.75839 −7.43020
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
3
− u
2
+ 2u − 1)(u
88
+ 38u
87
+ ··· + 101u + 1)
c
2
((u − 1)
8
)(u
3
+ u
2
− 1)(u
88
− 10u
87
+ ··· − 7u + 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)(u
88
− 2u
87
+ ··· + 128u − 256)
c
4
((u + 1)
8
)(u
3
− u
2
+ 1)(u
88
− 10u
87
+ ··· − 7u + 1)
c
5
u
3
(u
8
− u
7
+ ··· + 2u − 1)(u
88
− 2u
87
+ ··· − 12u − 8)
c
6
u
8
(u
3
+ u
2
+ 2u + 1)(u
88
− 2u
87
+ ··· + 128u − 256)
c
7
, c
8
((u − 1)
3
)(u
8
+ u
7
+ ··· + 2u − 1)(u
88
− 5u
87
+ ··· + 8u + 1)
c
9
u
3
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
88
+ 24u
87
+ ··· + 1872u + 64)
c
10
u
3
(u
8
+ u
7
+ ··· − 2u − 1)(u
88
− 2u
87
+ ··· − 12u − 8)
c
11
u
3
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
88
+ 24u
87
+ ··· + 1872u + 64)
c
12
((u + 1)
3
)(u
8
− u
7
+ ··· − 2u − 1)(u
88
− 5u
87
+ ··· + 8u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
3
+ 3y
2
+ 2y − 1)(y
88
+ 34y
87
+ ··· − 4505y + 1)
c
2
, c
4
((y − 1)
8
)(y
3
− y
2
+ 2y − 1)(y
88
− 38y
87
+ ··· − 101y + 1)
c
3
, c
6
y
8
(y
3
+ 3y
2
+ 2y − 1)(y
88
+ 54y
87
+ ··· + 999424y + 65536)
c
5
, c
10
y
3
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
88
− 24y
87
+ ··· − 1872y + 64)
c
7
, c
8
, c
12
(y − 1)
3
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
88
− 71y
87
+ ··· + 62y + 1)
c
9
, c
11
y
3
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
88
+ 76y
87
+ ··· − 105728y + 4096)
23
