12a
0291
(K12a
0291
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 5 11 1 12 7 4 9
Solving Sequence
1,8 4,9
3 2 12 10 5 11 7 6
c
8
c
3
c
1
c
12
c
9
c
4
c
11
c
7
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.04111 × 10
126
u
84
− 1.47004 × 10
127
u
83
+ ··· + 7.92770 × 10
126
b + 7.78808 × 10
126
,
− 6.64112 × 10
126
u
84
− 2.58904 × 10
127
u
83
+ ··· + 7.92770 × 10
126
a − 2.36197 × 10
127
,
u
85
+ 4u
84
+ ··· + 14u + 2i
I
u
2
= h−au + b, 9a
3
− 6a
2
u + 3a
2
− 6a + 2u − 1, u
2
− u + 1i
I
u
3
= hb + u + 1, 2a − 3u − 2, u
2
+ 2i
I
v
1
= ha, b + 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 94 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−4.04 × 10
126
u
84
− 1.47 × 10
127
u
83
+ · · · + 7.93 × 10
126
b + 7.79 ×
10
126
, −6.64 × 10
126
u
84
− 2.59 × 10
127
u
83
+ · · · + 7.93 × 10
126
a − 2.36 ×
10
127
, u
85
+ 4u
84
+ · · · + 14u + 2i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
0.837711u
84
+ 3.26582u
83
+ ··· + 23.0946u + 2.97939
0.509746u
84
+ 1.85431u
83
+ ··· + 2.63027u − 0.982389
a
9
=
1
u
2
a
3
=
1.34746u
84
+ 5.12014u
83
+ ··· + 25.7249u + 1.99700
0.509746u
84
+ 1.85431u
83
+ ··· + 2.63027u − 0.982389
a
2
=
−1.26472u
84
− 6.06172u
83
+ ··· − 91.5000u − 16.8602
0.598452u
84
+ 2.02176u
83
+ ··· + 4.76229u − 0.278731
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
1.72649u
84
+ 6.50029u
83
+ ··· + 34.3325u + 3.23940
0.519117u
84
+ 2.00224u
83
+ ··· + 9.39854u + 0.520508
a
11
=
−2.50474u
84
− 10.2416u
83
+ ··· − 93.6888u − 15.3979
0.592317u
84
+ 2.10401u
83
+ ··· + 9.22146u + 0.356710
a
7
=
−2.36646u
84
− 9.65905u
83
+ ··· − 94.7830u − 15.3092
0.509534u
84
+ 1.79876u
83
+ ··· + 6.34356u + 0.475093
a
6
=
0.0492125u
84
+ 0.616005u
83
+ ··· + 18.7360u + 3.81121
−0.258472u
84
− 0.807102u
83
+ ··· + 0.539727u + 0.813419
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.70495u
84
− 5.18172u
83
+ ··· + 36.7845u + 15.0874
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
85
+ 24u
84
+ ··· + 97u + 81
c
2
, c
5
u
85
+ 6u
84
+ ··· + 23u + 9
c
3
27(27u
85
− 153u
84
+ ··· − 2.29371 × 10
8
u + 3.37805 × 10
7
)
c
4
27(27u
85
+ 288u
84
+ ··· − 8003245u + 2090863)
c
7
, c
10
u
85
− 5u
84
+ ··· + 18u + 3
c
8
, c
9
, c
12
u
85
− 4u
84
+ ··· + 14u − 2
c
11
u
85
− 4u
84
+ ··· − 33696u + 5184
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
85
+ 80y
84
+ ··· + 824593y −6561
c
2
, c
5
y
85
− 24y
84
+ ··· + 97y −81
c
3
729(729y
85
+ 35559y
84
+ ··· − 6.28776 × 10
15
y −1.14112 × 10
15
)
c
4
729
· (729y
85
− 51192y
84
+ ··· + 103418130379289y −4371708084769)
c
7
, c
10
y
85
− 59y
84
+ ··· + 966y −9
c
8
, c
9
, c
12
y
85
+ 88y
84
+ ··· − 52y −4
c
11
y
85
− 38y
84
+ ··· + 338162688y −26873856
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802781 + 0.666760I
a = 0.444154 + 0.389043I
b = 0.54776 − 1.33558I
9.35665 + 6.36583I 0
u = −0.802781 − 0.666760I
a = 0.444154 − 0.389043I
b = 0.54776 + 1.33558I
9.35665 − 6.36583I 0
u = −0.840661 + 0.625642I
a = −0.546357 − 0.360547I
b = −0.64122 + 1.40506I
8.7128 + 12.6729I 0
u = −0.840661 − 0.625642I
a = −0.546357 + 0.360547I
b = −0.64122 − 1.40506I
8.7128 − 12.6729I 0
u = −0.933727 + 0.500289I
a = −0.710871 + 0.140901I
b = 0.067748 + 1.068420I
8.75934 − 0.64306I 0
u = −0.933727 − 0.500289I
a = −0.710871 − 0.140901I
b = 0.067748 − 1.068420I
8.75934 + 0.64306I 0
u = 0.099564 + 1.061390I
a = 0.055284 − 0.183938I
b = −0.804734 − 0.275552I
1.46155 − 0.12863I 0
u = 0.099564 − 1.061390I
a = 0.055284 + 0.183938I
b = −0.804734 + 0.275552I
1.46155 + 0.12863I 0
u = −0.922718 + 0.564249I
a = 0.711488 − 0.159783I
b = −0.149669 − 1.177890I
8.44674 − 6.85650I 0
u = −0.922718 − 0.564249I
a = 0.711488 + 0.159783I
b = −0.149669 + 1.177890I
8.44674 + 6.85650I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.593150 + 0.919610I
a = −0.1315520 − 0.0150511I
b = 0.268708 − 0.398741I
−0.92845 − 1.82818I 0
u = 0.593150 − 0.919610I
a = −0.1315520 + 0.0150511I
b = 0.268708 + 0.398741I
−0.92845 + 1.82818I 0
u = 0.951786 + 0.650510I
a = 0.486994 − 0.119384I
b = 0.391324 + 1.066140I
3.74898 − 6.20791I 0
u = 0.951786 − 0.650510I
a = 0.486994 + 0.119384I
b = 0.391324 − 1.066140I
3.74898 + 6.20791I 0
u = 0.925364 + 0.717550I
a = −0.440303 + 0.082121I
b = −0.238296 − 1.072720I
3.93970 − 0.17528I 0
u = 0.925364 − 0.717550I
a = −0.440303 − 0.082121I
b = −0.238296 + 1.072720I
3.93970 + 0.17528I 0
u = 0.727828 + 0.390455I
a = 0.449726 − 0.488595I
b = 0.525964 + 0.518969I
−2.30865 − 2.94104I 0
u = 0.727828 − 0.390455I
a = 0.449726 + 0.488595I
b = 0.525964 − 0.518969I
−2.30865 + 2.94104I 0
u = 0.325597 + 1.142700I
a = 0.0448468 − 0.0603608I
b = 0.789387 + 0.068143I
1.61955 − 4.56441I 0
u = 0.325597 − 1.142700I
a = 0.0448468 + 0.0603608I
b = 0.789387 − 0.068143I
1.61955 + 4.56441I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.567914 + 0.571899I
a = 0.604728 − 0.178179I
b = −0.644834 − 0.904739I
1.38177 − 3.51715I 0
u = −0.567914 − 0.571899I
a = 0.604728 + 0.178179I
b = −0.644834 + 0.904739I
1.38177 + 3.51715I 0
u = −0.641156 + 0.471692I
a = −0.731557 − 0.940849I
b = −0.817818 + 0.973867I
1.07426 + 7.71240I 0
u = −0.641156 − 0.471692I
a = −0.731557 + 0.940849I
b = −0.817818 − 0.973867I
1.07426 − 7.71240I 0
u = −0.460489 + 0.587516I
a = 0.051839 + 1.283270I
b = 0.590387 − 0.821616I
4.12766 + 3.84400I 3.48726 − 5.71525I
u = −0.460489 − 0.587516I
a = 0.051839 − 1.283270I
b = 0.590387 + 0.821616I
4.12766 − 3.84400I 3.48726 + 5.71525I
u = 0.167924 + 0.707939I
a = −2.22545 + 0.77882I
b = 0.356883 − 0.967640I
7.83381 + 0.86043I 5.30165 + 0.I
u = 0.167924 − 0.707939I
a = −2.22545 − 0.77882I
b = 0.356883 + 0.967640I
7.83381 − 0.86043I 5.30165 + 0.I
u = 0.289362 + 0.616253I
a = 2.51494 − 0.45923I
b = −0.143489 + 0.984157I
7.12241 − 5.37900I 3.62062 + 6.29663I
u = 0.289362 − 0.616253I
a = 2.51494 + 0.45923I
b = −0.143489 − 0.984157I
7.12241 + 5.37900I 3.62062 − 6.29663I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.585513 + 0.213693I
a = −0.594955 + 0.071624I
b = 0.580910 + 0.428079I
3.00184 − 0.43149I 1.31859 − 2.45780I
u = −0.585513 − 0.213693I
a = −0.594955 − 0.071624I
b = 0.580910 − 0.428079I
3.00184 + 0.43149I 1.31859 + 2.45780I
u = −0.180672 + 1.380910I
a = −1.23127 − 0.96960I
b = 0.679911 + 0.815725I
7.94632 + 2.41671I 0
u = −0.180672 − 1.380910I
a = −1.23127 + 0.96960I
b = 0.679911 − 0.815725I
7.94632 − 2.41671I 0
u = 0.050758 + 1.403220I
a = 0.14372 − 1.51124I
b = −0.444961 + 0.783429I
2.89071 − 0.02350I 0
u = 0.050758 − 1.403220I
a = 0.14372 + 1.51124I
b = −0.444961 − 0.783429I
2.89071 + 0.02350I 0
u = 0.027731 + 1.406400I
a = −3.96077 + 1.85576I
b = 4.01105 − 2.17001I
5.66382 − 0.10661I 0
u = 0.027731 − 1.406400I
a = −3.96077 − 1.85576I
b = 4.01105 + 2.17001I
5.66382 + 0.10661I 0
u = 0.332326 + 0.422048I
a = 0.224263 + 0.635046I
b = −0.268723 − 0.452263I
−0.065957 − 1.057420I −1.21607 + 6.29792I
u = 0.332326 − 0.422048I
a = 0.224263 − 0.635046I
b = −0.268723 + 0.452263I
−0.065957 + 1.057420I −1.21607 − 6.29792I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514945 + 0.052028I
a = 0.63587 − 1.41127I
b = 0.326392 + 0.017339I
−1.57079 + 1.46950I −9.77061 − 4.07897I
u = 0.514945 − 0.052028I
a = 0.63587 + 1.41127I
b = 0.326392 − 0.017339I
−1.57079 − 1.46950I −9.77061 + 4.07897I
u = 0.21356 + 1.47274I
a = 0.10247 − 1.46449I
b = 0.452591 + 0.938205I
3.73750 − 6.24800I 0
u = 0.21356 − 1.47274I
a = 0.10247 + 1.46449I
b = 0.452591 − 0.938205I
3.73750 + 6.24800I 0
u = −0.06407 + 1.49452I
a = 0.51861 − 2.01899I
b = −0.171203 + 0.869357I
6.16680 + 1.75465I 0
u = −0.06407 − 1.49452I
a = 0.51861 + 2.01899I
b = −0.171203 − 0.869357I
6.16680 − 1.75465I 0
u = −0.05194 + 1.49750I
a = 0.75573 − 1.32650I
b = −1.77024 + 1.16248I
9.30893 + 4.57642I 0
u = −0.05194 − 1.49750I
a = 0.75573 + 1.32650I
b = −1.77024 − 1.16248I
9.30893 − 4.57642I 0
u = −0.01980 + 1.50512I
a = −0.87950 + 1.48472I
b = 1.77677 − 1.49662I
9.72935 − 1.45679I 0
u = −0.01980 − 1.50512I
a = −0.87950 − 1.48472I
b = 1.77677 + 1.49662I
9.72935 + 1.45679I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10823 + 1.51105I
a = −0.04805 + 1.53309I
b = −0.088616 − 1.270120I
6.46358 − 2.67802I 0
u = 0.10823 − 1.51105I
a = −0.04805 − 1.53309I
b = −0.088616 + 1.270120I
6.46358 + 2.67802I 0
u = −0.19892 + 1.50982I
a = 0.04052 − 1.96137I
b = −0.74982 + 1.25661I
7.58189 + 10.73300I 0
u = −0.19892 − 1.50982I
a = 0.04052 + 1.96137I
b = −0.74982 − 1.25661I
7.58189 − 10.73300I 0
u = −0.09406 + 1.52146I
a = 0.60512 + 1.61508I
b = −0.19813 − 1.69091I
8.39441 − 1.40303I 0
u = −0.09406 − 1.52146I
a = 0.60512 − 1.61508I
b = −0.19813 + 1.69091I
8.39441 + 1.40303I 0
u = −0.176623 + 0.430115I
a = 1.88458 − 0.21008I
b = 0.469587 − 1.100450I
3.24208 − 1.99205I 1.86195 + 5.62347I
u = −0.176623 − 0.430115I
a = 1.88458 + 0.21008I
b = 0.469587 + 1.100450I
3.24208 + 1.99205I 1.86195 − 5.62347I
u = −0.246167 + 0.375896I
a = −2.13263 + 0.10858I
b = −0.714174 + 0.978375I
3.01363 + 3.62679I 0.237626 − 0.197969I
u = −0.246167 − 0.375896I
a = −2.13263 − 0.10858I
b = −0.714174 − 0.978375I
3.01363 − 3.62679I 0.237626 + 0.197969I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13362 + 1.54561I
a = −0.19237 + 1.85508I
b = 0.374741 − 1.266880I
11.23470 + 5.99704I 0
u = −0.13362 − 1.54561I
a = −0.19237 − 1.85508I
b = 0.374741 + 1.266880I
11.23470 − 5.99704I 0
u = 0.07557 + 1.55121I
a = 0.653295 − 1.130100I
b = 0.576031 + 0.900387I
14.3920 − 6.6683I 0
u = 0.07557 − 1.55121I
a = 0.653295 + 1.130100I
b = 0.576031 − 0.900387I
14.3920 + 6.6683I 0
u = 0.440029 + 0.047676I
a = 0.040169 − 0.742148I
b = 0.00599 − 2.44474I
5.42251 + 2.96044I −11.24832 − 0.49298I
u = 0.440029 − 0.047676I
a = 0.040169 + 0.742148I
b = 0.00599 + 2.44474I
5.42251 − 2.96044I −11.24832 + 0.49298I
u = 0.03178 + 1.56804I
a = −0.58241 + 1.33803I
b = −0.417899 − 1.034010I
15.4735 + 0.2256I 0
u = 0.03178 − 1.56804I
a = −0.58241 − 1.33803I
b = −0.417899 + 1.034010I
15.4735 − 0.2256I 0
u = −0.257488 + 0.337643I
a = −0.37428 − 3.54840I
b = −0.584493 + 0.525668I
−0.025237 + 0.681729I 0.12938 − 10.39624I
u = −0.257488 − 0.337643I
a = −0.37428 + 3.54840I
b = −0.584493 − 0.525668I
−0.025237 − 0.681729I 0.12938 + 10.39624I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28292 + 1.58422I
a = −0.13616 − 1.84338I
b = −0.95678 + 1.78318I
15.9618 + 16.8256I 0
u = −0.28292 − 1.58422I
a = −0.13616 + 1.84338I
b = −0.95678 − 1.78318I
15.9618 − 16.8256I 0
u = −0.25995 + 1.59435I
a = 0.10124 + 1.81756I
b = 0.82984 − 1.77590I
16.8148 + 10.3036I 0
u = −0.25995 − 1.59435I
a = 0.10124 − 1.81756I
b = 0.82984 + 1.77590I
16.8148 − 10.3036I 0
u = −0.34489 + 1.59776I
a = −0.440689 − 0.952425I
b = −0.512257 + 1.080120I
15.6088 + 4.1683I 0
u = −0.34489 − 1.59776I
a = −0.440689 + 0.952425I
b = −0.512257 − 1.080120I
15.6088 − 4.1683I 0
u = 0.29557 + 1.61174I
a = 0.065113 − 1.385510I
b = 0.93022 + 1.37397I
11.2264 − 10.7656I 0
u = 0.29557 − 1.61174I
a = 0.065113 + 1.385510I
b = 0.93022 − 1.37397I
11.2264 + 10.7656I 0
u = 0.26193 + 1.62559I
a = −0.048549 + 1.391250I
b = −0.81923 − 1.46077I
11.77100 − 4.49005I 0
u = 0.26193 − 1.62559I
a = −0.048549 − 1.391250I
b = −0.81923 + 1.46077I
11.77100 + 4.49005I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31266 + 1.62469I
a = 0.420595 + 1.013950I
b = 0.488380 − 1.232340I
15.6769 − 2.1737I 0
u = −0.31266 − 1.62469I
a = 0.420595 − 1.013950I
b = 0.488380 + 1.232340I
15.6769 + 2.1737I 0
u = 0.047792 + 0.283678I
a = 0.434605 − 0.380197I
b = −0.75550 − 1.74214I
0.336343 + 0.330613I 14.7201 + 7.4977I
u = 0.047792 − 0.283678I
a = 0.434605 + 0.380197I
b = −0.75550 + 1.74214I
0.336343 − 0.330613I 14.7201 − 7.4977I
u = −0.204107
a = −2.83102
b = −0.630306
−1.37360 −7.31630
13
II. I
u
2
= h−au + b, 9a
3
− 6a
2
u + 3a
2
− 6a + 2u − 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
a
au
a
9
=
1
u − 1
a
3
=
au + a
au
a
2
=
−3a
2
u + 3a
2
−a
2
u + 2a
2
+ u
a
12
=
u
u − 1
a
10
=
u
u − 2
a
5
=
au + a
2au − 2a
a
11
=
u
u − 1
a
7
=
0
−u
a
6
=
−3a
2
u + 3a
2
2a
2
u + 2a
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17a
2
u + 30a
2
− 11au + a + 13u − 19
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
27(27u
6
− 27u
5
+ 27u
4
− 18u
3
+ 15u
2
− 6u + 1)
c
4
27(27u
6
− 27u
4
+ 6u
2
+ 1)
c
5
(u
3
− u
2
+ 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
12
(u
2
+ u + 1)
3
c
8
, c
9
, c
10
(u
2
− u + 1)
3
c
11
u
6
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
3
729(729y
6
+ 729y
5
+ 567y
4
+ 216y
3
+ 63y
2
− 6y + 1)
c
4
729(27y
3
− 27y
2
+ 6y + 1)
2
c
7
, c
8
, c
9
c
10
, c
12
(y
2
+ y + 1)
3
c
11
y
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.754678 + 0.124176I
b = 0.269799 + 0.715659I
3.02413 + 0.79824I −0.040167 − 0.618060I
u = 0.500000 + 0.866025I
a = −0.754678 + 0.124176I
b = −0.484879 − 0.591482I
3.02413 − 4.85801I 1.23319 + 5.70115I
u = 0.500000 + 0.866025I
a = 0.328997I
b = −0.284920 + 0.164499I
−1.11345 − 2.02988I −11.6930 + 11.3714I
u = 0.500000 − 0.866025I
a = 0.754678 − 0.124176I
b = 0.269799 − 0.715659I
3.02413 − 0.79824I −0.040167 + 0.618060I
u = 0.500000 − 0.866025I
a = −0.754678 − 0.124176I
b = −0.484879 + 0.591482I
3.02413 + 4.85801I 1.23319 − 5.70115I
u = 0.500000 − 0.866025I
a = − 0.328997I
b = −0.284920 − 0.164499I
−1.11345 + 2.02988I −11.6930 − 11.3714I
17
III. I
u
3
= hb + u + 1, 2a − 3u − 2, u
2
+ 2i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
3
2
u + 1
−u − 1
a
9
=
1
−2
a
3
=
1
2
u
−u − 1
a
2
=
1
2
u
−1
a
12
=
u
−u
a
10
=
−1
0
a
5
=
1
2
u
−u − 1
a
11
=
−
1
2
u − 1
1
a
7
=
−
1
2
u
1
a
6
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u − 1)
2
c
3
u
2
− 2u + 3
c
4
u
2
+ 2u + 3
c
5
, c
6
, c
10
c
11
(u + 1)
2
c
8
, c
9
, c
12
u
2
+ 2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
(y −1)
2
c
3
, c
4
y
2
+ 2y + 9
c
8
, c
9
, c
12
(y + 2)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 1.00000 + 2.12132I
b = −1.00000 − 1.41421I
4.93480 0
u = − 1.414210I
a = 1.00000 − 2.12132I
b = −1.00000 + 1.41421I
4.93480 0
21
IV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
1
=
−1
0
a
8
=
1
0
a
4
=
0
−1
a
9
=
1
0
a
3
=
−1
−1
a
2
=
−2
−1
a
12
=
−1
0
a
10
=
1
0
a
5
=
−1
−1
a
11
=
−1
−1
a
7
=
2
1
a
6
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
10
, c
11
u − 1
c
5
, c
6
, c
7
u + 1
c
8
, c
9
, c
12
u
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
10
, c
11
y −1
c
8
, c
9
, c
12
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
0 0
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
3
− u
2
+ 2u − 1)
2
(u
85
+ 24u
84
+ ··· + 97u + 81)
c
2
((u − 1)
3
)(u
3
+ u
2
− 1)
2
(u
85
+ 6u
84
+ ··· + 23u + 9)
c
3
729(u − 1)(u
2
− 2u + 3)(27u
6
− 27u
5
+ ··· − 6u + 1)
· (27u
85
− 153u
84
+ ··· − 229370509u + 33780469)
c
4
729(u − 1)(u
2
+ 2u + 3)(27u
6
− 27u
4
+ 6u
2
+ 1)
· (27u
85
+ 288u
84
+ ··· − 8003245u + 2090863)
c
5
((u + 1)
3
)(u
3
− u
2
+ 1)
2
(u
85
+ 6u
84
+ ··· + 23u + 9)
c
6
((u + 1)
3
)(u
3
+ u
2
+ 2u + 1)
2
(u
85
+ 24u
84
+ ··· + 97u + 81)
c
7
((u − 1)
2
)(u + 1)(u
2
+ u + 1)
3
(u
85
− 5u
84
+ ··· + 18u + 3)
c
8
, c
9
u(u
2
+ 2)(u
2
− u + 1)
3
(u
85
− 4u
84
+ ··· + 14u − 2)
c
10
(u − 1)(u + 1)
2
(u
2
− u + 1)
3
(u
85
− 5u
84
+ ··· + 18u + 3)
c
11
u
6
(u − 1)(u + 1)
2
(u
85
− 4u
84
+ ··· − 33696u + 5184)
c
12
u(u
2
+ 2)(u
2
+ u + 1)
3
(u
85
− 4u
84
+ ··· + 14u − 2)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
3
)(y
3
+ 3y
2
+ 2y −1)
2
(y
85
+ 80y
84
+ ··· + 824593y −6561)
c
2
, c
5
((y −1)
3
)(y
3
− y
2
+ 2y −1)
2
(y
85
− 24y
84
+ ··· + 97y −81)
c
3
531441(y −1)(y
2
+ 2y + 9)
· (729y
6
+ 729y
5
+ 567y
4
+ 216y
3
+ 63y
2
− 6y + 1)
· (729y
85
+ 3.56 × 10
4
y
84
+ ··· − 6.29 × 10
15
y −1.14 × 10
15
)
c
4
531441(y −1)(y
2
+ 2y + 9)(27y
3
− 27y
2
+ 6y + 1)
2
· (729y
85
− 51192y
84
+ ··· + 103418130379289y −4371708084769)
c
7
, c
10
((y −1)
3
)(y
2
+ y + 1)
3
(y
85
− 59y
84
+ ··· + 966y −9)
c
8
, c
9
, c
12
y(y + 2)
2
(y
2
+ y + 1)
3
(y
85
+ 88y
84
+ ··· − 52y −4)
c
11
y
6
(y −1)
3
(y
85
− 38y
84
+ ··· + 3.38163 × 10
8
y −2.68739 × 10
7
)
27
