12n
0384
(K12n
0384
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 5 1 11 4 6 9
Solving Sequence
3,6
2 1
5,9
8 4 7 12 11 10
c
2
c
1
c
5
c
8
c
3
c
7
c
12
c
11
c
10
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.71603 × 10
130
u
78
− 3.34605 × 10
130
u
77
+ ··· + 9.47150 × 10
129
b − 1.79777 × 10
130
,
− 2.58758 × 10
129
u
78
− 1.91076 × 10
130
u
77
+ ··· + 9.47150 × 10
129
a − 5.72706 × 10
130
,
u
79
+ 2u
78
+ ··· + 3u + 1i
I
u
2
= h−u
22
+ 6u
20
+ ··· + b + 1, 6u
22
+ 5u
21
+ ··· + a − 7, u
23
+ u
22
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 102 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−2.72 × 10
130
u
78
− 3.35 × 10
130
u
77
+ · · · + 9.47 × 10
129
b − 1.80 ×
10
130
, −2.59 × 10
129
u
78
− 1.91 × 10
130
u
77
+ · · · + 9.47 × 10
129
a − 5.73 ×
10
130
, u
79
+ 2u
78
+ · · · + 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
9
=
0.273197u
78
+ 2.01738u
77
+ ··· − 9.55208u + 6.04662
2.86758u
78
+ 3.53276u
77
+ ··· + 10.8984u + 1.89808
a
8
=
−0.309986u
78
+ 0.455035u
77
+ ··· − 9.66549u + 3.32245
2.02383u
78
+ 2.39814u
77
+ ··· + 8.31238u + 0.949213
a
4
=
−1.71680u
78
− 3.26582u
77
+ ··· − 2.40110u − 5.06109
−2.85920u
78
− 4.22104u
77
+ ··· − 9.93888u − 4.06187
a
7
=
1.43940u
78
+ 3.19611u
77
+ ··· − 3.75783u + 5.82097
3.55209u
78
+ 4.65508u
77
+ ··· + 13.6963u + 2.69004
a
12
=
1.08140u
78
+ 2.11225u
77
+ ··· + 8.48887u + 6.87053
3.83910u
78
+ 5.49216u
77
+ ··· + 10.2711u + 4.75553
a
11
=
1.08140u
78
+ 2.11225u
77
+ ··· + 8.48887u + 6.87053
3.86348u
78
+ 5.61449u
77
+ ··· + 11.2009u + 4.70499
a
10
=
3.04438u
78
+ 6.01782u
77
+ ··· − 3.93386u + 5.29498
0.834964u
78
+ 1.28035u
77
+ ··· + 7.27458u + 2.68116
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.45357u
78
+ 4.69764u
77
+ ··· − 16.7472u − 8.13507
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 40u
78
+ ··· + 33u + 1
c
2
, c
5
u
79
+ 2u
78
+ ··· + 3u + 1
c
3
u
79
+ u
78
+ ··· + 3042u + 1971
c
4
, c
10
u
79
+ u
78
+ ··· + 6u
2
+ 1
c
6
, c
11
u
79
+ 2u
78
+ ··· + 33033u + 2741
c
7
u
79
− u
78
+ ··· − 15955220u + 4890941
c
8
, c
12
u
79
− 4u
78
+ ··· + 465u − 71
c
9
u
79
+ 45u
78
+ ··· − 12u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 12y
78
+ ··· − 27y −1
c
2
, c
5
y
79
− 40y
78
+ ··· + 33y −1
c
3
y
79
+ 41y
78
+ ··· − 122003010y −3884841
c
4
, c
10
y
79
+ 45y
78
+ ··· − 12y −1
c
6
, c
11
y
79
− 62y
78
+ ··· − 310804037y −7513081
c
7
y
79
− 43y
78
+ ··· + 243479110423596y −23921303865481
c
8
, c
12
y
79
+ 30y
78
+ ··· + 195635y −5041
c
9
y
79
− 11y
78
+ ··· + 72y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.191031 + 0.984252I
a = −0.07978 − 1.48636I
b = 0.508156 − 0.260237I
−3.18307 − 0.81586I 0
u = −0.191031 − 0.984252I
a = −0.07978 + 1.48636I
b = 0.508156 + 0.260237I
−3.18307 + 0.81586I 0
u = 0.772897 + 0.639352I
a = 1.62485 − 0.20199I
b = 1.47815 − 1.36105I
3.37009 − 0.55634I 0
u = 0.772897 − 0.639352I
a = 1.62485 + 0.20199I
b = 1.47815 + 1.36105I
3.37009 + 0.55634I 0
u = 0.279781 + 0.946093I
a = 0.422327 − 0.009943I
b = 0.387992 − 0.507427I
4.25236 − 1.51303I 0
u = 0.279781 − 0.946093I
a = 0.422327 + 0.009943I
b = 0.387992 + 0.507427I
4.25236 + 1.51303I 0
u = 0.347049 + 0.957087I
a = −0.13702 − 1.41951I
b = −0.865084 − 0.221243I
1.35913 + 5.11137I 0
u = 0.347049 − 0.957087I
a = −0.13702 + 1.41951I
b = −0.865084 + 0.221243I
1.35913 − 5.11137I 0
u = −0.949703 + 0.369866I
a = −1.071130 − 0.249125I
b = 0.195225 − 0.520375I
1.207890 + 0.693296I 0
u = −0.949703 − 0.369866I
a = −1.071130 + 0.249125I
b = 0.195225 + 0.520375I
1.207890 − 0.693296I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.651752 + 0.803645I
a = 1.028100 + 0.127820I
b = 1.080790 − 0.665746I
3.75206 − 1.01538I 0
u = 0.651752 − 0.803645I
a = 1.028100 − 0.127820I
b = 1.080790 + 0.665746I
3.75206 + 1.01538I 0
u = −0.735451 + 0.763114I
a = −1.33628 + 0.71471I
b = −1.65988 − 0.43120I
1.52896 − 1.89063I 0
u = −0.735451 − 0.763114I
a = −1.33628 − 0.71471I
b = −1.65988 + 0.43120I
1.52896 + 1.89063I 0
u = −0.390500 + 1.044200I
a = 0.23951 − 1.54767I
b = 0.954518 − 0.436619I
−1.91185 − 10.39900I 0
u = −0.390500 − 1.044200I
a = 0.23951 + 1.54767I
b = 0.954518 + 0.436619I
−1.91185 + 10.39900I 0
u = 1.110500 + 0.123199I
a = −0.360738 − 0.519588I
b = 0.355883 − 0.926772I
−4.60003 − 2.24012I 0
u = 1.110500 − 0.123199I
a = −0.360738 + 0.519588I
b = 0.355883 + 0.926772I
−4.60003 + 2.24012I 0
u = 1.032050 + 0.440550I
a = −1.155910 + 0.517509I
b = −1.324490 + 0.224798I
−3.64519 − 2.75689I 0
u = 1.032050 − 0.440550I
a = −1.155910 − 0.517509I
b = −1.324490 − 0.224798I
−3.64519 + 2.75689I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799671 + 0.338631I
a = −1.32453 − 0.80993I
b = −0.78022 − 2.11425I
1.77333 + 2.34825I −10.56329 − 4.52984I
u = −0.799671 − 0.338631I
a = −1.32453 + 0.80993I
b = −0.78022 + 2.11425I
1.77333 − 2.34825I −10.56329 + 4.52984I
u = 1.075170 + 0.388500I
a = −0.949388 + 0.662897I
b = −1.49346 + 2.56287I
−7.23041 + 1.32092I 0
u = 1.075170 − 0.388500I
a = −0.949388 − 0.662897I
b = −1.49346 − 2.56287I
−7.23041 − 1.32092I 0
u = 0.983798 + 0.587300I
a = 0.261400 − 0.889339I
b = −0.878215 − 0.255984I
2.69035 − 4.34043I 0
u = 0.983798 − 0.587300I
a = 0.261400 + 0.889339I
b = −0.878215 + 0.255984I
2.69035 + 4.34043I 0
u = −1.047200 + 0.470329I
a = 1.121370 + 0.298241I
b = 1.64342 + 2.17778I
−3.40305 + 3.75556I 0
u = −1.047200 − 0.470329I
a = 1.121370 − 0.298241I
b = 1.64342 − 2.17778I
−3.40305 − 3.75556I 0
u = −1.062590 + 0.466582I
a = −0.473431 − 0.104262I
b = −1.77680 − 0.79310I
3.25715 + 0.42701I 0
u = −1.062590 − 0.466582I
a = −0.473431 + 0.104262I
b = −1.77680 + 0.79310I
3.25715 − 0.42701I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.979155 + 0.659990I
a = −0.186768 − 1.044480I
b = −1.192080 − 0.090654I
2.67066 − 4.41905I 0
u = 0.979155 − 0.659990I
a = −0.186768 + 1.044480I
b = −1.192080 + 0.090654I
2.67066 + 4.41905I 0
u = −1.068830 + 0.513419I
a = 1.238950 + 0.404006I
b = 1.59996 + 0.25716I
−6.37531 + 8.24596I 0
u = −1.068830 − 0.513419I
a = 1.238950 − 0.404006I
b = 1.59996 − 0.25716I
−6.37531 − 8.24596I 0
u = 1.088050 + 0.498479I
a = 0.566854 − 0.120059I
b = 1.81501 − 1.09357I
3.49995 − 6.66947I 0
u = 1.088050 − 0.498479I
a = 0.566854 + 0.120059I
b = 1.81501 + 1.09357I
3.49995 + 6.66947I 0
u = −1.148050 + 0.354073I
a = 1.229620 + 0.676225I
b = 1.207310 + 0.678030I
−8.51556 − 0.93201I 0
u = −1.148050 − 0.354073I
a = 1.229620 − 0.676225I
b = 1.207310 − 0.678030I
−8.51556 + 0.93201I 0
u = −0.911687 + 0.787204I
a = 0.803246 − 0.640191I
b = 1.113530 + 0.554256I
0.87775 + 2.17137I 0
u = −0.911687 − 0.787204I
a = 0.803246 + 0.640191I
b = 1.113530 − 0.554256I
0.87775 − 2.17137I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.971228 + 0.714175I
a = 0.99212 − 1.26649I
b = 1.87985 + 0.21111I
0.81093 + 7.49828I 0
u = −0.971228 − 0.714175I
a = 0.99212 + 1.26649I
b = 1.87985 − 0.21111I
0.81093 − 7.49828I 0
u = −0.792183
a = 0.614293
b = −0.625628
−1.33059 −6.58480
u = 1.107910 + 0.516873I
a = −1.50586 + 0.31421I
b = −2.06147 + 2.18423I
−7.42311 − 8.62365I 0
u = 1.107910 − 0.516873I
a = −1.50586 − 0.31421I
b = −2.06147 − 2.18423I
−7.42311 + 8.62365I 0
u = 0.715864 + 0.277463I
a = −1.46137 + 0.89491I
b = −0.541854 − 0.023836I
−2.22862 − 0.48454I −3.32397 + 5.38263I
u = 0.715864 − 0.277463I
a = −1.46137 − 0.89491I
b = −0.541854 + 0.023836I
−2.22862 + 0.48454I −3.32397 − 5.38263I
u = −0.833390 + 0.940010I
a = −0.894586 + 0.345537I
b = −1.165880 − 0.263330I
1.16138 + 4.13478I 0
u = −0.833390 − 0.940010I
a = −0.894586 − 0.345537I
b = −1.165880 + 0.263330I
1.16138 − 4.13478I 0
u = 1.192740 + 0.640609I
a = 1.142680 − 0.139516I
b = 1.93724 − 1.46494I
−1.21826 − 10.92240I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.192740 − 0.640609I
a = 1.142680 + 0.139516I
b = 1.93724 + 1.46494I
−1.21826 + 10.92240I 0
u = 1.109620 + 0.776023I
a = −0.529150 − 0.336994I
b = −0.961927 + 0.438116I
2.08413 − 4.66431I 0
u = 1.109620 − 0.776023I
a = −0.529150 + 0.336994I
b = −0.961927 − 0.438116I
2.08413 + 4.66431I 0
u = −0.454850 + 0.447099I
a = 1.39866 + 2.20652I
b = 0.339961 + 0.112299I
−4.50604 − 4.04932I −6.45793 + 1.67799I
u = −0.454850 − 0.447099I
a = 1.39866 − 2.20652I
b = 0.339961 − 0.112299I
−4.50604 + 4.04932I −6.45793 − 1.67799I
u = −1.237660 + 0.581931I
a = −1.042670 − 0.390086I
b = −1.81279 − 1.57352I
−6.38355 + 6.41792I 0
u = −1.237660 − 0.581931I
a = −1.042670 + 0.390086I
b = −1.81279 + 1.57352I
−6.38355 − 6.41792I 0
u = −0.564621 + 0.284535I
a = −0.545059 − 0.268663I
b = 0.72095 + 1.66387I
5.05746 + 3.12388I −8.19578 + 0.26827I
u = −0.564621 − 0.284535I
a = −0.545059 + 0.268663I
b = 0.72095 − 1.66387I
5.05746 − 3.12388I −8.19578 − 0.26827I
u = 0.421372 + 0.463446I
a = 0.337655 − 0.819391I
b = −0.827292 + 1.047940I
5.53379 + 2.54054I −4.42930 − 5.76558I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.421372 − 0.463446I
a = 0.337655 + 0.819391I
b = −0.827292 − 1.047940I
5.53379 − 2.54054I −4.42930 + 5.76558I
u = −1.359440 + 0.212786I
a = −0.770916 − 0.399157I
b = −1.080790 − 0.207121I
−4.45616 − 1.31756I 0
u = −1.359440 − 0.212786I
a = −0.770916 + 0.399157I
b = −1.080790 + 0.207121I
−4.45616 + 1.31756I 0
u = −1.275420 + 0.546485I
a = −0.0739416 + 0.1149980I
b = 0.375729 + 0.413377I
−0.12238 + 6.61116I 0
u = −1.275420 − 0.546485I
a = −0.0739416 − 0.1149980I
b = 0.375729 − 0.413377I
−0.12238 − 6.61116I 0
u = −1.211040 + 0.682574I
a = −1.315290 − 0.111684I
b = −2.03346 − 1.47490I
−4.4575 + 16.6063I 0
u = −1.211040 − 0.682574I
a = −1.315290 + 0.111684I
b = −2.03346 + 1.47490I
−4.4575 − 16.6063I 0
u = 0.184918 + 0.538457I
a = −0.11921 + 3.12712I
b = 0.950595 + 0.446805I
−5.02903 + 4.28349I −8.27681 − 4.00164I
u = 0.184918 − 0.538457I
a = −0.11921 − 3.12712I
b = 0.950595 − 0.446805I
−5.02903 − 4.28349I −8.27681 + 4.00164I
u = 1.40099 + 0.34736I
a = 0.850459 − 0.324010I
b = 1.245410 − 0.267260I
−8.36209 − 3.89179I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40099 − 0.34736I
a = 0.850459 + 0.324010I
b = 1.245410 + 0.267260I
−8.36209 + 3.89179I 0
u = 1.47172 + 0.12727I
a = 0.789184 − 0.491099I
b = 0.972773 − 0.381657I
−8.61435 + 6.30190I 0
u = 1.47172 − 0.12727I
a = 0.789184 + 0.491099I
b = 0.972773 + 0.381657I
−8.61435 − 6.30190I 0
u = −0.373652 + 0.265576I
a = 1.88378 + 1.55663I
b = −0.941910 + 0.210297I
−1.53987 − 0.04744I −5.18898 − 0.81135I
u = −0.373652 − 0.265576I
a = 1.88378 − 1.55663I
b = −0.941910 − 0.210297I
−1.53987 + 0.04744I −5.18898 + 0.81135I
u = −0.280943 + 0.315261I
a = 0.413918 − 0.655502I
b = −0.145072 + 0.373722I
−0.455090 + 0.991741I −7.13691 − 6.73727I
u = −0.280943 − 0.315261I
a = 0.413918 + 0.655502I
b = −0.145072 − 0.373722I
−0.455090 − 0.991741I −7.13691 + 6.73727I
u = 0.337723 + 0.070804I
a = −4.81881 − 0.75247I
b = 1.093010 + 0.305232I
−4.84439 − 4.25943I −6.45155 + 7.25445I
u = 0.337723 − 0.070804I
a = −4.81881 + 0.75247I
b = 1.093010 − 0.305232I
−4.84439 + 4.25943I −6.45155 − 7.25445I
12
II.
I
u
2
= h−u
22
+6u
20
+· · ·+b+1, 6u
22
+5u
21
+· · ·+a−7, u
23
+u
22
+· · ·−u−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
9
=
−6u
22
− 5u
21
+ ··· − 13u + 7
u
22
− 6u
20
+ ··· + 4u − 1
a
8
=
−7u
22
− 5u
21
+ ··· − 13u + 8
u
22
+ u
21
+ ··· + 5u − 1
a
4
=
6u
22
+ u
21
+ ··· + 6u − 13
−u
22
+ 7u
20
+ ··· − u + 5
a
7
=
−5u
22
− 4u
21
+ ··· − 9u + 6
2u
22
+ u
21
+ ··· + 8u − 2
a
12
=
u
22
− 7u
20
+ ··· + u − 6
−3u
22
− u
21
+ ··· − u + 2
a
11
=
u
22
− 7u
20
+ ··· + u − 6
−3u
22
− u
21
+ ··· − u + 3
a
10
=
4u
22
− 25u
20
+ ··· − 4u − 8
−4u
22
− 2u
21
+ ··· − 4u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
22
− u
21
+ 29u
20
+ 10u
19
− 87u
18
− 44u
17
+ 168u
16
+ 116u
15
− 205u
14
− 199u
13
+
147u
12
+ 231u
11
−22u
10
−175u
9
−78u
8
+ 88u
7
+ 89u
6
−23u
5
−82u
4
+ u
3
+ 34u
2
+ 6u −21
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
23
− 13u
22
+ ··· + 13u − 1
c
2
u
23
+ u
22
+ ··· − u − 1
c
3
u
23
+ 10u
21
+ ··· − 2u + 1
c
4
u
23
+ 6u
21
+ ··· − 2u + 1
c
5
u
23
− u
22
+ ··· − u + 1
c
6
u
23
+ u
22
+ ··· + 3u − 1
c
7
u
23
+ 8u
22
+ ··· + 88u − 29
c
8
u
23
− 3u
22
+ ··· − u − 1
c
9
u
23
− 12u
22
+ ··· − 8u + 1
c
10
u
23
+ 6u
21
+ ··· − 2u − 1
c
11
u
23
− u
22
+ ··· + 3u + 1
c
12
u
23
+ 3u
22
+ ··· − u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 7y
22
+ ··· + y −1
c
2
, c
5
y
23
− 13y
22
+ ··· + 13y −1
c
3
y
23
+ 20y
22
+ ··· + 10y −1
c
4
, c
10
y
23
+ 12y
22
+ ··· − 8y −1
c
6
, c
11
y
23
− 3y
22
+ ··· − 13y −1
c
7
y
23
− 4y
22
+ ··· + 6932y −841
c
8
, c
12
y
23
+ 13y
22
+ ··· + 3y −1
c
9
y
23
+ 8y
22
+ ··· − 20y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630015 + 0.671543I
a = −1.101100 − 0.648550I
b = −0.787291 − 1.066420I
3.03165 + 1.75887I −5.37226 − 4.25162I
u = −0.630015 − 0.671543I
a = −1.101100 + 0.648550I
b = −0.787291 + 1.066420I
3.03165 − 1.75887I −5.37226 + 4.25162I
u = −0.703790 + 0.560880I
a = −0.759261 − 0.016715I
b = −1.48162 − 1.22442I
5.66183 − 1.58895I −3.77306 − 1.87293I
u = −0.703790 − 0.560880I
a = −0.759261 + 0.016715I
b = −1.48162 + 1.22442I
5.66183 + 1.58895I −3.77306 + 1.87293I
u = 0.683964 + 0.525529I
a = 0.834493 + 0.206624I
b = 1.36447 − 1.51147I
5.48484 − 3.77860I −1.97875 + 8.09859I
u = 0.683964 − 0.525529I
a = 0.834493 − 0.206624I
b = 1.36447 + 1.51147I
5.48484 + 3.77860I −1.97875 − 8.09859I
u = −1.028450 + 0.586506I
a = 0.304336 − 0.402419I
b = 1.49026 + 0.57590I
4.57388 + 6.19775I −2.54557 − 5.78029I
u = −1.028450 − 0.586506I
a = 0.304336 + 0.402419I
b = 1.49026 − 0.57590I
4.57388 − 6.19775I −2.54557 + 5.78029I
u = 0.555768 + 0.587883I
a = 1.73648 − 0.26772I
b = 0.85591 − 1.39940I
2.69979 + 0.58598I −5.35829 − 1.83822I
u = 0.555768 − 0.587883I
a = 1.73648 + 0.26772I
b = 0.85591 + 1.39940I
2.69979 − 0.58598I −5.35829 + 1.83822I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.19937
a = −0.945216
b = −1.42356
−4.32657 −8.14410
u = 1.068020 + 0.552527I
a = −0.408803 − 0.365019I
b = −1.69043 + 0.28063I
4.17503 − 0.60896I −2.10463 + 1.64469I
u = 1.068020 − 0.552527I
a = −0.408803 + 0.365019I
b = −1.69043 − 0.28063I
4.17503 + 0.60896I −2.10463 − 1.64469I
u = 0.788674 + 0.067096I
a = −1.48138 + 0.33372I
b = −0.172278 − 0.318918I
−2.75839 − 0.11417I −14.8732 − 1.6726I
u = 0.788674 − 0.067096I
a = −1.48138 − 0.33372I
b = −0.172278 + 0.318918I
−2.75839 + 0.11417I −14.8732 + 1.6726I
u = −1.005100 + 0.714546I
a = 0.195177 − 0.672441I
b = 0.742299 + 0.187174I
1.87325 + 3.71014I −7.78117 − 0.19469I
u = −1.005100 − 0.714546I
a = 0.195177 + 0.672441I
b = 0.742299 − 0.187174I
1.87325 − 3.71014I −7.78117 + 0.19469I
u = −1.317790 + 0.141803I
a = 0.975113 − 0.086775I
b = 1.58510 − 0.13198I
−8.17918 + 4.97937I −9.94257 − 4.19770I
u = −1.317790 − 0.141803I
a = 0.975113 + 0.086775I
b = 1.58510 + 0.13198I
−8.17918 − 4.97937I −9.94257 + 4.19770I
u = 1.122650 + 0.733553I
a = −0.430102 − 0.732478I
b = −1.094530 − 0.126237I
0.80767 − 5.93220I −6.48253 + 6.21918I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122650 − 0.733553I
a = −0.430102 + 0.732478I
b = −1.094530 + 0.126237I
0.80767 + 5.93220I −6.48253 − 6.21918I
u = −0.633614 + 0.085095I
a = 2.60765 + 1.19886I
b = −0.600096 − 0.438844I
−5.33748 − 3.98481I −19.7159 + 1.1614I
u = −0.633614 − 0.085095I
a = 2.60765 − 1.19886I
b = −0.600096 + 0.438844I
−5.33748 + 3.98481I −19.7159 − 1.1614I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 13u
22
+ ··· + 13u − 1)(u
79
+ 40u
78
+ ··· + 33u + 1)
c
2
(u
23
+ u
22
+ ··· − u − 1)(u
79
+ 2u
78
+ ··· + 3u + 1)
c
3
(u
23
+ 10u
21
+ ··· − 2u + 1)(u
79
+ u
78
+ ··· + 3042u + 1971)
c
4
(u
23
+ 6u
21
+ ··· − 2u + 1)(u
79
+ u
78
+ ··· + 6u
2
+ 1)
c
5
(u
23
− u
22
+ ··· − u + 1)(u
79
+ 2u
78
+ ··· + 3u + 1)
c
6
(u
23
+ u
22
+ ··· + 3u − 1)(u
79
+ 2u
78
+ ··· + 33033u + 2741)
c
7
(u
23
+ 8u
22
+ ··· + 88u − 29)
· (u
79
− u
78
+ ··· − 15955220u + 4890941)
c
8
(u
23
− 3u
22
+ ··· − u − 1)(u
79
− 4u
78
+ ··· + 465u − 71)
c
9
(u
23
− 12u
22
+ ··· − 8u + 1)(u
79
+ 45u
78
+ ··· − 12u − 1)
c
10
(u
23
+ 6u
21
+ ··· − 2u − 1)(u
79
+ u
78
+ ··· + 6u
2
+ 1)
c
11
(u
23
− u
22
+ ··· + 3u + 1)(u
79
+ 2u
78
+ ··· + 33033u + 2741)
c
12
(u
23
+ 3u
22
+ ··· − u + 1)(u
79
− 4u
78
+ ··· + 465u − 71)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 7y
22
+ ··· + y −1)(y
79
+ 12y
78
+ ··· − 27y −1)
c
2
, c
5
(y
23
− 13y
22
+ ··· + 13y −1)(y
79
− 40y
78
+ ··· + 33y −1)
c
3
(y
23
+ 20y
22
+ ··· + 10y −1)
· (y
79
+ 41y
78
+ ··· − 122003010y −3884841)
c
4
, c
10
(y
23
+ 12y
22
+ ··· − 8y −1)(y
79
+ 45y
78
+ ··· − 12y −1)
c
6
, c
11
(y
23
− 3y
22
+ ··· − 13y −1)
· (y
79
− 62y
78
+ ··· − 310804037y −7513081)
c
7
(y
23
− 4y
22
+ ··· + 6932y −841)
· (y
79
− 43y
78
+ ··· + 243479110423596y −23921303865481)
c
8
, c
12
(y
23
+ 13y
22
+ ··· + 3y −1)(y
79
+ 30y
78
+ ··· + 195635y −5041)
c
9
(y
23
+ 8y
22
+ ··· − 20y −1)(y
79
− 11y
78
+ ··· + 72y −1)
22
