12n
0363
(K12n
0363
)
A knot diagram
1
Linearized knot diagam
3 5 9 11 2 12 3 4 8 1 6 4
Solving Sequence
3,9 4,5
2 1 8 10 11 7 12 6
c
3
c
2
c
1
c
8
c
9
c
10
c
7
c
12
c
6
c
4
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.18536 × 10
82
u
64
+ 1.17821 × 10
82
u
63
+ ··· + 4.44686 × 10
81
b + 5.58068 × 10
82
,
− 3.67200 × 10
85
u
64
− 4.79998 × 10
85
u
63
+ ··· + 2.88601 × 10
84
a − 5.33132 × 10
86
,
u
65
+ u
64
+ ··· + 32u + 11i
I
u
2
= hu
16
+ u
15
+ ··· + b + 2,
− u
16
− u
15
− 3u
14
− 3u
13
− 7u
12
− 7u
11
− 9u
10
− 11u
9
− 9u
8
− 15u
7
− 2u
6
− 14u
5
− 10u
3
+ a − 4u − 2,
u
18
+ 4u
16
+ ··· − u + 1i
I
u
3
= hb − u, u
2
+ a + 1, u
4
+ u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 87 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
= h1.19 × 10
82
u
64
+ 1.18 × 10
82
u
63
+ · · · + 4.45 × 10
81
b + 5.58 ×
10
82
, −3.67 × 10
85
u
64
− 4.80 × 10
85
u
63
+ · · · + 2.89 × 10
84
a − 5.33 ×
10
86
, u
65
+ u
64
+ · · · + 32u + 11i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
12.7234u
64
+ 16.6319u
63
+ ··· + 952.459u + 184.730
−2.66560u
64
− 2.64952u
63
+ ··· − 136.076u − 12.5497
a
2
=
−4.71664u
64
+ 3.37825u
63
+ ··· + 545.587u + 271.508
0.928296u
64
− 2.05851u
63
+ ··· − 225.100u − 104.728
a
1
=
−3.78835u
64
+ 1.31974u
63
+ ··· + 320.487u + 166.781
0.928296u
64
− 2.05851u
63
+ ··· − 225.100u − 104.728
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
6.96248u
64
+ 13.4113u
63
+ ··· + 961.700u + 259.286
−2.60048u
64
− 3.57741u
63
+ ··· − 231.000u − 51.3320
a
7
=
−u
3
u
3
+ u
a
12
=
−3.79507u
64
+ 2.51346u
63
+ ··· + 423.800u + 215.319
0.628384u
64
− 2.58932u
63
+ ··· − 263.440u − 117.933
a
6
=
1.94949u
64
+ 5.30850u
63
+ ··· + 457.040u + 133.508
3.65785u
64
+ 4.57938u
63
+ ··· + 244.609u + 51.0970
(ii) Obstruction class = −1
(iii) Cusp Shapes = −9.85489u
64
− 0.506938u
63
+ ··· + 295.659u + 281.817
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 36u
64
+ ··· − 31u − 1
c
2
, c
5
u
65
+ 18u
63
+ ··· + u − 1
c
3
, c
8
u
65
− u
64
+ ··· + 32u − 11
c
4
u
65
− u
64
+ ··· + 170u − 99
c
6
, c
11
u
65
− u
64
+ ··· − 290u − 374
c
7
u
65
+ u
64
+ ··· − 146235740u − 28512220
c
9
u
65
− 17u
64
+ ··· − 3200u + 121
c
10
u
65
− 5u
64
+ ··· + 404554u − 19583
c
12
u
65
+ 3u
64
+ ··· + 761476u + 2099
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 48y
63
+ ··· + 185y −1
c
2
, c
5
y
65
+ 36y
64
+ ··· − 31y −1
c
3
, c
8
y
65
+ 17y
64
+ ··· − 3200y −121
c
4
y
65
− 23y
64
+ ··· − 12086y −9801
c
6
, c
11
y
65
− 27y
64
+ ··· + 1737928y −139876
c
7
y
65
+ 129y
64
+ ··· − 36644682510257400y −812946689328400
c
9
y
65
+ 73y
64
+ ··· + 504824y −14641
c
10
y
65
− 77y
64
+ ··· + 2489974016y −383493889
c
12
y
65
+ 75y
64
+ ··· + 597043930640y −4405801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680009 + 0.713106I
a = 1.41460 + 0.20948I
b = −0.829559 + 0.897240I
1.19074 − 3.17057I 4.00000 + 2.82300I
u = 0.680009 − 0.713106I
a = 1.41460 − 0.20948I
b = −0.829559 − 0.897240I
1.19074 + 3.17057I 4.00000 − 2.82300I
u = −0.130389 + 1.036020I
a = 2.29843 + 0.93843I
b = −0.322430 − 0.884795I
−1.18726 + 1.38317I 0
u = −0.130389 − 1.036020I
a = 2.29843 − 0.93843I
b = −0.322430 + 0.884795I
−1.18726 − 1.38317I 0
u = 0.686817 + 0.660938I
a = 0.484110 + 0.485186I
b = −0.417093 + 1.257930I
0.11513 − 5.57520I 1.42711 + 8.53371I
u = 0.686817 − 0.660938I
a = 0.484110 − 0.485186I
b = −0.417093 − 1.257930I
0.11513 + 5.57520I 1.42711 − 8.53371I
u = −0.600257 + 0.736464I
a = −2.35238 + 0.68378I
b = 0.696793 + 0.978880I
0.90319 + 6.82193I 4.00000 − 10.20078I
u = −0.600257 − 0.736464I
a = −2.35238 − 0.68378I
b = 0.696793 − 0.978880I
0.90319 − 6.82193I 4.00000 + 10.20078I
u = 0.536349 + 0.783362I
a = −0.292753 − 1.310400I
b = 0.714251 + 0.738621I
1.65196 − 1.37503I 5.70343 + 4.32793I
u = 0.536349 − 0.783362I
a = −0.292753 + 1.310400I
b = 0.714251 − 0.738621I
1.65196 + 1.37503I 5.70343 − 4.32793I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536653 + 0.910218I
a = 1.30688 − 0.94688I
b = 0.277844 + 1.051000I
1.022910 + 0.885443I 0
u = 0.536653 − 0.910218I
a = 1.30688 + 0.94688I
b = 0.277844 − 1.051000I
1.022910 − 0.885443I 0
u = 0.919266 + 0.044023I
a = 0.685246 − 0.197964I
b = −0.400619 − 1.148570I
−1.32773 + 3.65915I 0.21562 − 3.87323I
u = 0.919266 − 0.044023I
a = 0.685246 + 0.197964I
b = −0.400619 + 1.148570I
−1.32773 − 3.65915I 0.21562 + 3.87323I
u = −0.498707 + 0.773383I
a = 0.440300 − 0.516252I
b = −0.706622 + 0.898570I
1.13961 − 2.56713I 4.00000 + 1.86590I
u = −0.498707 − 0.773383I
a = 0.440300 + 0.516252I
b = −0.706622 − 0.898570I
1.13961 + 2.56713I 4.00000 − 1.86590I
u = −0.714171 + 0.556638I
a = 0.58411 + 1.77271I
b = 0.158903 + 0.735534I
2.30751 + 1.23537I 1.43112 − 2.75975I
u = −0.714171 − 0.556638I
a = 0.58411 − 1.77271I
b = 0.158903 − 0.735534I
2.30751 − 1.23537I 1.43112 + 2.75975I
u = −0.339089 + 1.140750I
a = −1.67737 + 0.59115I
b = 0.628783 − 0.316202I
5.30182 + 3.74007I 0
u = −0.339089 − 1.140750I
a = −1.67737 − 0.59115I
b = 0.628783 + 0.316202I
5.30182 − 3.74007I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953198 + 0.755841I
a = −0.598616 + 0.308645I
b = 0.445402 + 1.166070I
−8.89416 + 1.07478I 0
u = 0.953198 − 0.755841I
a = −0.598616 − 0.308645I
b = 0.445402 − 1.166070I
−8.89416 − 1.07478I 0
u = −0.854923 + 0.866674I
a = −0.496614 + 0.011802I
b = 0.545772 + 0.013538I
−5.80014 + 2.95712I 0
u = −0.854923 − 0.866674I
a = −0.496614 − 0.011802I
b = 0.545772 − 0.013538I
−5.80014 − 2.95712I 0
u = −0.833013 + 0.906851I
a = 0.242257 − 0.165490I
b = −0.027191 − 0.303343I
−5.70705 + 3.10651I 0
u = −0.833013 − 0.906851I
a = 0.242257 + 0.165490I
b = −0.027191 + 0.303343I
−5.70705 − 3.10651I 0
u = −0.549089 + 1.115550I
a = −1.74225 + 0.41891I
b = 0.160584 + 0.669882I
4.17437 + 3.71139I 0
u = −0.549089 − 1.115550I
a = −1.74225 − 0.41891I
b = 0.160584 − 0.669882I
4.17437 − 3.71139I 0
u = −0.797232 + 0.958267I
a = 0.498877 − 0.859914I
b = −0.507934 + 0.279262I
−5.49508 + 3.22478I 0
u = −0.797232 − 0.958267I
a = 0.498877 + 0.859914I
b = −0.507934 − 0.279262I
−5.49508 − 3.22478I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.447329 + 1.169880I
a = −0.453069 − 1.212100I
b = 0.452862 + 1.045590I
2.40731 − 0.69677I 0
u = 0.447329 − 1.169880I
a = −0.453069 + 1.212100I
b = 0.452862 − 1.045590I
2.40731 + 0.69677I 0
u = 0.950733 + 0.838002I
a = 1.046540 + 0.328040I
b = −1.080450 + 0.250407I
−3.94832 + 2.68251I 0
u = 0.950733 − 0.838002I
a = 1.046540 − 0.328040I
b = −1.080450 − 0.250407I
−3.94832 − 2.68251I 0
u = 0.023056 + 0.722524I
a = −1.76080 + 3.14396I
b = 0.630679 − 0.948352I
3.75759 − 4.41575I 12.04885 + 5.91677I
u = 0.023056 − 0.722524I
a = −1.76080 − 3.14396I
b = 0.630679 + 0.948352I
3.75759 + 4.41575I 12.04885 − 5.91677I
u = −0.713686
a = 1.13925
b = −0.584356
1.80251 5.12800
u = −0.193742 + 0.683841I
a = 0.962945 + 0.999475I
b = −0.922328 − 0.420825I
5.03052 + 1.51034I 15.7178 − 3.9613I
u = −0.193742 − 0.683841I
a = 0.962945 − 0.999475I
b = −0.922328 + 0.420825I
5.03052 − 1.51034I 15.7178 + 3.9613I
u = −1.024200 + 0.791302I
a = 0.552140 − 0.058409I
b = −0.63656 + 1.26921I
−7.10877 − 8.80138I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.024200 − 0.791302I
a = 0.552140 + 0.058409I
b = −0.63656 − 1.26921I
−7.10877 + 8.80138I 0
u = 0.192935 + 0.676072I
a = 0.776674 + 0.010062I
b = −0.227422 + 0.327785I
0.407727 − 0.970478I 6.53993 + 7.03429I
u = 0.192935 − 0.676072I
a = 0.776674 − 0.010062I
b = −0.227422 − 0.327785I
0.407727 + 0.970478I 6.53993 − 7.03429I
u = 0.355761 + 1.266190I
a = −1.89805 + 0.78083I
b = 0.519188 − 1.142400I
2.83831 − 8.31122I 0
u = 0.355761 − 1.266190I
a = −1.89805 − 0.78083I
b = 0.519188 + 1.142400I
2.83831 + 8.31122I 0
u = −0.559146 + 0.388651I
a = 0.288682 − 1.213700I
b = 0.032965 − 1.064690I
−3.46149 + 1.16170I −2.54854 − 2.69088I
u = −0.559146 − 0.388651I
a = 0.288682 + 1.213700I
b = 0.032965 + 1.064690I
−3.46149 − 1.16170I −2.54854 + 2.69088I
u = 0.941004 + 0.941682I
a = −1.35873 − 0.69131I
b = 0.478389 − 1.144710I
−8.66705 − 7.05024I 0
u = 0.941004 − 0.941682I
a = −1.35873 + 0.69131I
b = 0.478389 + 1.144710I
−8.66705 + 7.05024I 0
u = 0.863954 + 1.022410I
a = −0.887849 − 0.917663I
b = 1.092590 + 0.344179I
−3.35897 − 9.35941I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863954 − 1.022410I
a = −0.887849 + 0.917663I
b = 1.092590 − 0.344179I
−3.35897 + 9.35941I 0
u = 0.809043 + 1.069000I
a = 2.03359 + 0.42601I
b = −0.512076 + 1.123520I
−7.88943 − 7.57959I 0
u = 0.809043 − 1.069000I
a = 2.03359 − 0.42601I
b = −0.512076 − 1.123520I
−7.88943 + 7.57959I 0
u = 0.934970 + 0.965256I
a = 0.095422 − 0.223855I
b = −0.413625 − 1.135060I
−8.59820 + 0.16475I 0
u = 0.934970 − 0.965256I
a = 0.095422 + 0.223855I
b = −0.413625 + 1.135060I
−8.59820 − 0.16475I 0
u = −0.962896 + 0.944222I
a = 0.399298 + 0.175699I
b = 0.20863 − 1.53443I
−9.92576 + 4.62699I 0
u = −0.962896 − 0.944222I
a = 0.399298 − 0.175699I
b = 0.20863 + 1.53443I
−9.92576 − 4.62699I 0
u = −0.947987 + 0.978674I
a = 1.247310 − 0.029592I
b = −0.31760 − 1.50215I
−9.81795 + 2.36926I 0
u = −0.947987 − 0.978674I
a = 1.247310 + 0.029592I
b = −0.31760 + 1.50215I
−9.81795 − 2.36926I 0
u = −0.864777 + 1.081390I
a = −1.98594 + 0.31084I
b = 0.68088 + 1.24619I
−6.1652 + 15.6905I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.864777 − 1.081390I
a = −1.98594 − 0.31084I
b = 0.68088 − 1.24619I
−6.1652 − 15.6905I 0
u = −0.074172 + 0.553647I
a = 2.29514 + 0.12509I
b = −0.751395 − 1.112610I
3.07118 + 4.62645I 11.23018 − 8.45860I
u = −0.074172 − 0.553647I
a = 2.29514 − 0.12509I
b = −0.751395 + 1.112610I
3.07118 − 4.62645I 11.23018 + 8.45860I
u = −0.030447 + 0.536065I
a = −5.17229 + 0.79790I
b = 0.640566 − 0.750092I
4.38121 − 0.57043I 13.19784 + 0.22094I
u = −0.030447 − 0.536065I
a = −5.17229 − 0.79790I
b = 0.640566 + 0.750092I
4.38121 + 0.57043I 13.19784 − 0.22094I
11
II.
I
u
2
= hu
16
+ u
15
+ · · · + b + 2, −u
16
− u
15
+ · · · + a − 2, u
18
+ 4u
16
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
u
16
+ u
15
+ ··· + 4u + 2
−u
16
− u
15
+ ··· − u − 2
a
2
=
−4u
16
− 2u
15
+ ··· − 4u − 1
2u
16
+ u
15
+ ··· + 2u + 1
a
1
=
−2u
16
− u
15
+ ··· − 2u
2
− 2u
2u
16
+ u
15
+ ··· + 2u + 1
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
u
17
− u
16
+ ··· + 4u − 4
−u
17
− 3u
15
+ ··· − 2u + 2
a
7
=
−u
3
u
3
+ u
a
12
=
−u
17
− 2u
16
+ ··· − 6u + 1
2u
16
+ u
15
+ ··· + 3u + 1
a
6
=
3u
17
+ u
16
+ ··· + 9u − 3
−2u
17
− u
16
+ ··· − u
2
− 5u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
17
− 5u
16
+ 4u
15
− 17u
14
+ 12u
13
− 43u
12
+ 28u
11
− 73u
10
+
43u
9
− 93u
8
+ 47u
7
− 72u
6
+ 28u
5
− 37u
4
+ 9u
3
− 8u
2
− 2u + 5
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
18
− 11u
17
+ ··· − 12u + 1
c
2
u
18
+ u
17
+ ··· + 6u
2
+ 1
c
3
u
18
+ 4u
16
+ ··· − u + 1
c
4
u
18
− 4u
17
+ ··· − 4u + 1
c
5
u
18
− u
17
+ ··· + 6u
2
+ 1
c
6
u
18
+ u
17
+ ··· + 4u + 1
c
7
u
18
+ 3u
17
+ ··· − 3u + 1
c
8
u
18
+ 4u
16
+ ··· + u + 1
c
9
u
18
− 8u
17
+ ··· − 9u + 1
c
10
u
18
− 5u
17
+ ··· + 2u + 1
c
11
u
18
− u
17
+ ··· − 4u + 1
c
12
u
18
− 4u
17
+ ··· − 4u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 3y
17
+ ··· − 8y + 1
c
2
, c
5
y
18
+ 11y
17
+ ··· + 12y + 1
c
3
, c
8
y
18
+ 8y
17
+ ··· + 9y + 1
c
4
y
18
− 6y
17
+ ··· + 8y + 1
c
6
, c
11
y
18
− 13y
17
+ ··· + 46y
2
+ 1
c
7
y
18
+ 19y
17
+ ··· + 21y + 1
c
9
y
18
+ 12y
17
+ ··· + 9y + 1
c
10
y
18
− 13y
17
+ ··· + 4y + 1
c
12
y
18
+ 8y
17
+ ··· − 6y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107994 + 0.886491I
a = 1.91623 − 0.60555I
b = −0.107602 + 0.863856I
−1.61758 − 0.49645I 1.92124 − 0.97423I
u = 0.107994 − 0.886491I
a = 1.91623 + 0.60555I
b = −0.107602 − 0.863856I
−1.61758 + 0.49645I 1.92124 + 0.97423I
u = 0.696066 + 0.545570I
a = 0.930161 + 0.577007I
b = −0.660457 + 1.151080I
1.36974 − 4.92053I 6.15031 + 6.00947I
u = 0.696066 − 0.545570I
a = 0.930161 − 0.577007I
b = −0.660457 − 1.151080I
1.36974 + 4.92053I 6.15031 − 6.00947I
u = 0.417406 + 1.060020I
a = −2.25827 + 0.86221I
b = 0.612837 − 1.010440I
4.28511 − 7.05199I 8.53221 + 6.99194I
u = 0.417406 − 1.060020I
a = −2.25827 − 0.86221I
b = 0.612837 + 1.010440I
4.28511 + 7.05199I 8.53221 − 6.99194I
u = −0.455958 + 1.047990I
a = −1.70552 + 0.75131I
b = 0.588097 − 0.707693I
5.28455 + 2.26664I 8.19627 − 0.17793I
u = −0.455958 − 1.047990I
a = −1.70552 − 0.75131I
b = 0.588097 + 0.707693I
5.28455 − 2.26664I 8.19627 + 0.17793I
u = −0.511216 + 1.063110I
a = −1.63867 + 0.87954I
b = 0.508680 + 0.656191I
4.88269 + 4.32798I 10.85694 − 7.34698I
u = −0.511216 − 1.063110I
a = −1.63867 − 0.87954I
b = 0.508680 − 0.656191I
4.88269 − 4.32798I 10.85694 + 7.34698I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799524 + 0.903741I
a = −0.290516 + 0.477123I
b = −0.036667 − 0.598516I
−6.13063 − 3.00712I −9.64781 + 0.96053I
u = 0.799524 − 0.903741I
a = −0.290516 − 0.477123I
b = −0.036667 + 0.598516I
−6.13063 + 3.00712I −9.64781 − 0.96053I
u = −0.412746 + 0.599657I
a = 2.89005 + 1.07924I
b = −0.649239 − 0.664089I
3.73184 + 1.45023I 7.20580 − 4.76250I
u = −0.412746 − 0.599657I
a = 2.89005 − 1.07924I
b = −0.649239 + 0.664089I
3.73184 − 1.45023I 7.20580 + 4.76250I
u = 0.301656 + 0.628925I
a = 1.33746 + 1.39082I
b = −0.688010 − 1.001630I
2.66029 + 3.82389I 5.08137 − 0.98229I
u = 0.301656 − 0.628925I
a = 1.33746 − 1.39082I
b = −0.688010 + 1.001630I
2.66029 − 3.82389I 5.08137 + 0.98229I
u = −0.942726 + 0.959928I
a = 0.819075 − 0.139736I
b = −0.06764 − 1.41514I
−9.53122 + 3.46203I 3.70366 − 2.71671I
u = −0.942726 − 0.959928I
a = 0.819075 + 0.139736I
b = −0.06764 + 1.41514I
−9.53122 − 3.46203I 3.70366 + 2.71671I
18
III. I
u
3
= hb − u, u
2
+ a + 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
−u
2
− 1
u
a
2
=
−u
3
− u + 1
u
2
a
1
=
−u
3
+ u
2
− u + 1
u
2
a
8
=
u
u
3
+ u
a
10
=
u
3
−u
2
a
11
=
−u
2
− 2
−u
2
+ u
a
7
=
−u
3
u
3
+ u
a
12
=
−u
3
+ u
2
− u
0
a
6
=
−u
2
+ 2u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
− u
2
− u + 7
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
3
u
4
+ u
2
+ u + 1
c
4
, c
12
(u + 1)
4
c
5
, c
8
u
4
+ u
2
− u + 1
c
6
u
4
+ u
3
− 2u
2
− u + 2
c
7
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
10
u
4
+ u
3
+ u
2
+ 1
c
11
u
4
− u
3
− 2u
2
+ u + 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
3
, c
5
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
4
, c
12
(y −1)
4
c
6
, c
11
y
4
− 5y
3
+ 10y
2
− 9y + 4
c
7
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = −0.956685 + 0.641200I
b = −0.547424 + 0.585652I
3.28987 7.19151 − 0.27009I
u = −0.547424 − 0.585652I
a = −0.956685 − 0.641200I
b = −0.547424 − 0.585652I
3.28987 7.19151 + 0.27009I
u = 0.547424 + 1.120870I
a = −0.043315 − 1.227190I
b = 0.547424 + 1.120870I
3.28987 9.30849 − 1.94753I
u = 0.547424 − 1.120870I
a = −0.043315 + 1.227190I
b = 0.547424 − 1.120870I
3.28987 9.30849 + 1.94753I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
18
− 11u
17
+ ··· − 12u + 1)
· (u
65
+ 36u
64
+ ··· − 31u − 1)
c
2
(u
4
+ u
2
+ u + 1)(u
18
+ u
17
+ ··· + 6u
2
+ 1)(u
65
+ 18u
63
+ ··· + u − 1)
c
3
(u
4
+ u
2
+ u + 1)(u
18
+ 4u
16
+ ··· − u + 1)(u
65
− u
64
+ ··· + 32u − 11)
c
4
((u + 1)
4
)(u
18
− 4u
17
+ ··· − 4u + 1)(u
65
− u
64
+ ··· + 170u − 99)
c
5
(u
4
+ u
2
− u + 1)(u
18
− u
17
+ ··· + 6u
2
+ 1)(u
65
+ 18u
63
+ ··· + u − 1)
c
6
(u
4
+ u
3
− 2u
2
− u + 2)(u
18
+ u
17
+ ··· + 4u + 1)
· (u
65
− u
64
+ ··· − 290u − 374)
c
7
(u
4
− 3u
3
+ 4u
2
− 3u + 2)(u
18
+ 3u
17
+ ··· − 3u + 1)
· (u
65
+ u
64
+ ··· − 146235740u − 28512220)
c
8
(u
4
+ u
2
− u + 1)(u
18
+ 4u
16
+ ··· + u + 1)(u
65
− u
64
+ ··· + 32u − 11)
c
9
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
18
− 8u
17
+ ··· − 9u + 1)
· (u
65
− 17u
64
+ ··· − 3200u + 121)
c
10
(u
4
+ u
3
+ u
2
+ 1)(u
18
− 5u
17
+ ··· + 2u + 1)
· (u
65
− 5u
64
+ ··· + 404554u − 19583)
c
11
(u
4
− u
3
− 2u
2
+ u + 2)(u
18
− u
17
+ ··· − 4u + 1)
· (u
65
− u
64
+ ··· − 290u − 374)
c
12
((u + 1)
4
)(u
18
− 4u
17
+ ··· − 4u + 1)
· (u
65
+ 3u
64
+ ··· + 761476u + 2099)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
18
+ 3y
17
+ ··· − 8y + 1)
· (y
65
+ 48y
63
+ ··· + 185y −1)
c
2
, c
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
18
+ 11y
17
+ ··· + 12y + 1)
· (y
65
+ 36y
64
+ ··· − 31y −1)
c
3
, c
8
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
18
+ 8y
17
+ ··· + 9y + 1)
· (y
65
+ 17y
64
+ ··· − 3200y −121)
c
4
((y −1)
4
)(y
18
− 6y
17
+ ··· + 8y + 1)
· (y
65
− 23y
64
+ ··· − 12086y −9801)
c
6
, c
11
(y
4
− 5y
3
+ 10y
2
− 9y + 4)(y
18
− 13y
17
+ ··· + 46y
2
+ 1)
· (y
65
− 27y
64
+ ··· + 1737928y −139876)
c
7
(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
18
+ 19y
17
+ ··· + 21y + 1)
· (y
65
+ 129y
64
+ ··· − 36644682510257400y −812946689328400)
c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
18
+ 12y
17
+ ··· + 9y + 1)
· (y
65
+ 73y
64
+ ··· + 504824y −14641)
c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
18
− 13y
17
+ ··· + 4y + 1)
· (y
65
− 77y
64
+ ··· + 2489974016y −383493889)
c
12
((y −1)
4
)(y
18
+ 8y
17
+ ··· − 6y + 1)
· (y
65
+ 75y
64
+ ··· + 597043930640y −4405801)
24
