12a
0542
(K12a
0542
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 12 11 2 1 5 4 6 9
Solving Sequence
3,7
2 8 4 1
9,11
6 12 5 10
c
2
c
7
c
3
c
1
c
8
c
6
c
11
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
32
− 7u
31
+ ··· + b + 5, −u
32
+ u
31
+ ··· + 2a − 5, u
33
− 3u
32
+ ··· + 11u − 2i
I
u
2
= h−u
18
a + u
18
+ ··· + b − a, u
19
− u
17
a + ··· + a
2
− 1, u
20
+ u
19
+ ··· + 2u + 1i
I
u
3
= h−u
11
− 2u
9
+ u
8
− 3u
7
+ 2u
6
− u
5
+ 2u
4
+ u
2
+ b, −u
10
− 2u
8
− 2u
6
+ u
2
+ a,
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 85 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
= h2u
32
−7u
31
+· · ·+b+5, −u
32
+u
31
+· · ·+2a−5, u
33
−3u
32
+· · ·+11u−2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
u
2
+ 1
u
2
a
9
=
−u
7
− 2u
5
− 2u
3
−u
7
− u
5
+ u
a
11
=
1
2
u
32
−
1
2
u
31
+ ··· − 5u +
5
2
−2u
32
+ 7u
31
+ ··· + 26u − 5
a
6
=
1
2
u
32
−
3
2
u
31
+ ··· − 6u +
3
2
u
30
− u
29
+ ··· − 3u + 1
a
12
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
− u
4
a
5
=
3
2
u
32
−
9
2
u
31
+ ··· − 18u +
9
2
−u
31
+ 3u
30
+ ··· − 12u + 3
a
10
=
1
2
u
32
−
1
2
u
31
+ ··· − 4u +
3
2
−u
32
+ 4u
31
+ ··· + 15u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
32
−6u
31
+ 18u
30
−40u
29
+ 72u
28
−142u
27
+ 192u
26
−340u
25
+ 374u
24
−594u
23
+
574u
22
−810u
21
+724u
20
−894u
19
+758u
18
−840u
17
+664u
16
−680u
15
+466u
14
−448u
13
+
262u
12
−214u
11
+100u
10
−42u
9
−6u
8
+20u
7
−48u
6
+34u
5
−38u
4
+36u
3
−20u
2
+26u−22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
+ 15u
32
+ ··· + 9u − 4
c
2
, c
7
u
33
+ 3u
32
+ ··· + 11u + 2
c
3
u
33
− 3u
32
+ ··· − 73u + 10
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
33
+ 22u
31
+ ··· + 3u + 1
c
8
, c
12
u
33
+ 15u
32
+ ··· + 2771u + 266
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
+ 7y
32
+ ··· + 561y −16
c
2
, c
7
y
33
+ 15y
32
+ ··· + 9y −4
c
3
y
33
− y
32
+ ··· + 2089y −100
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
33
+ 44y
32
+ ··· − 9y −1
c
8
, c
12
y
33
+ 27y
32
+ ··· + 249593y −70756
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.152282 + 0.979504I
a = 0.411441 − 0.397281I
b = −0.351596 − 0.571101I
−1.33752 − 1.02267I −11.79490 + 5.10112I
u = 0.152282 − 0.979504I
a = 0.411441 + 0.397281I
b = −0.351596 + 0.571101I
−1.33752 + 1.02267I −11.79490 − 5.10112I
u = −0.792598 + 0.556744I
a = 0.72926 − 1.56216I
b = −0.99765 − 2.35854I
18.0990 − 6.1471I 1.69208 + 3.47910I
u = −0.792598 − 0.556744I
a = 0.72926 + 1.56216I
b = −0.99765 + 2.35854I
18.0990 + 6.1471I 1.69208 − 3.47910I
u = −0.650620 + 0.804954I
a = −1.19586 + 1.00059I
b = 0.77206 + 2.17268I
12.43520 − 2.51799I 1.14659 + 3.10078I
u = −0.650620 − 0.804954I
a = −1.19586 − 1.00059I
b = 0.77206 − 2.17268I
12.43520 + 2.51799I 1.14659 − 3.10078I
u = −0.312053 + 0.912696I
a = 0.330741 − 0.254799I
b = −0.282384 − 0.391510I
−0.69539 − 1.36266I −7.61505 + 4.53766I
u = −0.312053 − 0.912696I
a = 0.330741 + 0.254799I
b = −0.282384 + 0.391510I
−0.69539 + 1.36266I −7.61505 − 4.53766I
u = 0.824879 + 0.434235I
a = 1.12098 + 1.36653I
b = −1.46731 + 1.70693I
17.3944 − 9.5155I 1.10338 + 3.69852I
u = 0.824879 − 0.434235I
a = 1.12098 − 1.36653I
b = −1.46731 − 1.70693I
17.3944 + 9.5155I 1.10338 − 3.69852I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.431324 + 1.046010I
a = −0.122761 + 0.496880I
b = −0.240841 + 1.306230I
−3.14332 + 3.33428I −15.0959 − 5.5855I
u = 0.431324 − 1.046010I
a = −0.122761 − 0.496880I
b = −0.240841 − 1.306230I
−3.14332 − 3.33428I −15.0959 + 5.5855I
u = 0.726459 + 0.451334I
a = −0.749693 − 0.212595I
b = 0.378857 − 0.838797I
3.27296 − 2.61780I −4.13522 + 5.27122I
u = 0.726459 − 0.451334I
a = −0.749693 + 0.212595I
b = 0.378857 + 0.838797I
3.27296 + 2.61780I −4.13522 − 5.27122I
u = −0.707357 + 0.467844I
a = −0.002391 + 0.722817I
b = 0.632335 + 0.653593I
3.38103 − 0.22806I −3.58439 + 4.33946I
u = −0.707357 − 0.467844I
a = −0.002391 − 0.722817I
b = 0.632335 − 0.653593I
3.38103 + 0.22806I −3.58439 − 4.33946I
u = 0.088747 + 1.156850I
a = −1.388160 + 0.151770I
b = 0.022859 + 0.945454I
11.90350 − 7.25131I −4.54406 + 3.22535I
u = 0.088747 − 1.156850I
a = −1.388160 − 0.151770I
b = 0.022859 − 0.945454I
11.90350 + 7.25131I −4.54406 − 3.22535I
u = 0.318246 + 1.146590I
a = 1.217500 + 0.275354I
b = 1.209060 + 0.038598I
5.45646 − 0.34796I −5.32880 − 0.36416I
u = 0.318246 − 1.146590I
a = 1.217500 − 0.275354I
b = 1.209060 − 0.038598I
5.45646 + 0.34796I −5.32880 + 0.36416I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580137 + 1.064780I
a = −0.502160 + 0.001706I
b = −0.032476 + 0.816149I
1.61599 − 4.72097I −6.74809 + 0.86070I
u = −0.580137 − 1.064780I
a = −0.502160 − 0.001706I
b = −0.032476 − 0.816149I
1.61599 + 4.72097I −6.74809 − 0.86070I
u = 0.589459 + 1.075110I
a = −0.159012 − 0.548760I
b = 0.88162 − 1.58124I
1.43372 + 7.64854I −7.35632 − 9.80003I
u = 0.589459 − 1.075110I
a = −0.159012 + 0.548760I
b = 0.88162 + 1.58124I
1.43372 − 7.64854I −7.35632 + 9.80003I
u = −0.653412 + 1.040510I
a = 1.258390 − 0.530338I
b = −0.66209 − 2.26242I
16.6529 + 0.7161I −0.27219 + 1.44446I
u = −0.653412 − 1.040510I
a = 1.258390 + 0.530338I
b = −0.66209 + 2.26242I
16.6529 − 0.7161I −0.27219 − 1.44446I
u = 0.736931 + 0.188573I
a = −0.64087 − 1.89931I
b = 0.664431 − 0.704418I
9.45531 − 3.71600I −0.33346 + 2.59966I
u = 0.736931 − 0.188573I
a = −0.64087 + 1.89931I
b = 0.664431 + 0.704418I
9.45531 + 3.71600I −0.33346 − 2.59966I
u = 0.504676 + 1.139920I
a = −1.045940 − 0.587726I
b = −1.15935 − 2.28346I
6.69649 + 8.32618I −3.83980 − 6.48439I
u = 0.504676 − 1.139920I
a = −1.045940 + 0.587726I
b = −1.15935 + 2.28346I
6.69649 − 8.32618I −3.83980 + 6.48439I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.623116 + 1.112210I
a = 0.964833 + 0.850517I
b = −0.28596 + 3.70200I
15.3636 + 14.9191I −1.64706 − 7.93751I
u = 0.623116 − 1.112210I
a = 0.964833 − 0.850517I
b = −0.28596 − 3.70200I
15.3636 − 14.9191I −1.64706 + 7.93751I
u = 0.400115
a = 1.04742
b = −0.163122
−0.742996 −13.2940
8
II.
I
u
2
= h−u
18
a+u
18
+· · ·+b−a, u
19
−u
17
a+· · ·+a
2
−1, u
20
+u
19
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
u
2
+ 1
u
2
a
9
=
−u
7
− 2u
5
− 2u
3
−u
7
− u
5
+ u
a
11
=
a
u
18
a − u
18
+ ··· + 2au + a
a
6
=
u
18
a + u
19
+ ··· + 3u + 1
−u
19
a + u
19
+ ··· + 2u
2
+ u
a
12
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
− u
4
a
5
=
u
18
a + u
19
+ ··· + 3u + 1
−u
19
a + u
19
+ ··· + 2u
2
+ u
a
10
=
u
17
+ 4u
15
+ ··· + a + 1
u
18
a − u
18
+ ··· + a − u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
18
−4u
17
−16u
16
−16u
15
−36u
14
−40u
13
−52u
12
−60u
11
−
56u
10
− 64u
9
− 56u
8
− 52u
7
− 48u
6
− 40u
5
− 32u
4
− 32u
3
− 12u
2
− 12u − 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 9u
19
+ ··· + 2u + 1)
2
c
2
, c
7
(u
20
− u
19
+ ··· − 2u + 1)
2
c
3
(u
20
+ u
19
+ ··· + 4u + 1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
40
− u
39
+ ··· + 66u + 17
c
8
, c
12
(u
20
− 5u
19
+ ··· − 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 5y
19
+ ··· + 10y + 1)
2
c
2
, c
7
(y
20
+ 9y
19
+ ··· + 2y + 1)
2
c
3
(y
20
+ y
19
+ ··· + 18y + 1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
40
+ 35y
39
+ ··· − 140y + 289
c
8
, c
12
(y
20
+ 21y
19
+ ··· + 10y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781348 + 0.506112I
a = 0.441997 − 1.155880I
b = 0.856427 − 0.565059I
10.37890 + 1.55876I 0.11661 − 2.37917I
u = 0.781348 + 0.506112I
a = 0.83804 + 1.43690I
b = −1.33192 + 2.45508I
10.37890 + 1.55876I 0.11661 − 2.37917I
u = 0.781348 − 0.506112I
a = 0.441997 + 1.155880I
b = 0.856427 + 0.565059I
10.37890 − 1.55876I 0.11661 + 2.37917I
u = 0.781348 − 0.506112I
a = 0.83804 − 1.43690I
b = −1.33192 − 2.45508I
10.37890 − 1.55876I 0.11661 + 2.37917I
u = 0.487491 + 0.960535I
a = 0.982330 + 0.105300I
b = −0.201846 − 0.351155I
3.03554 + 2.59904I −2.40613 − 3.16627I
u = 0.487491 + 0.960535I
a = −0.922458 − 0.679240I
b = 0.64390 − 3.08542I
3.03554 + 2.59904I −2.40613 − 3.16627I
u = 0.487491 − 0.960535I
a = 0.982330 − 0.105300I
b = −0.201846 + 0.351155I
3.03554 − 2.59904I −2.40613 + 3.16627I
u = 0.487491 − 0.960535I
a = −0.922458 + 0.679240I
b = 0.64390 + 3.08542I
3.03554 − 2.59904I −2.40613 + 3.16627I
u = −0.795114 + 0.464423I
a = −1.229700 + 0.036323I
b = 0.103460 + 0.921159I
10.14230 + 4.70967I −0.36261 − 2.80351I
u = −0.795114 + 0.464423I
a = 0.96901 − 1.37386I
b = −1.62344 − 2.10711I
10.14230 + 4.70967I −0.36261 − 2.80351I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795114 − 0.464423I
a = −1.229700 − 0.036323I
b = 0.103460 − 0.921159I
10.14230 − 4.70967I −0.36261 + 2.80351I
u = −0.795114 − 0.464423I
a = 0.96901 + 1.37386I
b = −1.62344 + 2.10711I
10.14230 − 4.70967I −0.36261 + 2.80351I
u = −0.331938 + 1.037100I
a = 0.990151 − 0.226215I
b = 0.628424 + 0.095717I
−0.345495 − 0.748059I −11.88926 + 0.17223I
u = −0.331938 + 1.037100I
a = −0.226980 − 0.173559I
b = −1.18881 − 1.01108I
−0.345495 − 0.748059I −11.88926 + 0.17223I
u = −0.331938 − 1.037100I
a = 0.990151 + 0.226215I
b = 0.628424 − 0.095717I
−0.345495 + 0.748059I −11.88926 − 0.17223I
u = −0.331938 − 1.037100I
a = −0.226980 + 0.173559I
b = −1.18881 + 1.01108I
−0.345495 + 0.748059I −11.88926 − 0.17223I
u = −0.044359 + 1.100970I
a = 0.572575 + 0.770686I
b = 0.055517 + 1.140730I
4.71375 + 2.89577I −6.31229 − 2.74717I
u = −0.044359 + 1.100970I
a = −1.352650 − 0.043914I
b = 0.686027 − 0.496404I
4.71375 + 2.89577I −6.31229 − 2.74717I
u = −0.044359 − 1.100970I
a = 0.572575 − 0.770686I
b = 0.055517 − 1.140730I
4.71375 − 2.89577I −6.31229 + 2.74717I
u = −0.044359 − 1.100970I
a = −1.352650 + 0.043914I
b = 0.686027 + 0.496404I
4.71375 − 2.89577I −6.31229 + 2.74717I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502129 + 1.070060I
a = −0.866977 + 0.566977I
b = −0.50635 + 2.53990I
0.79812 − 6.06247I −8.39660 + 7.82928I
u = −0.502129 + 1.070060I
a = 0.006209 − 0.502110I
b = 0.617341 − 1.244530I
0.79812 − 6.06247I −8.39660 + 7.82928I
u = −0.502129 − 1.070060I
a = −0.866977 − 0.566977I
b = −0.50635 − 2.53990I
0.79812 + 6.06247I −8.39660 − 7.82928I
u = −0.502129 − 1.070060I
a = 0.006209 + 0.502110I
b = 0.617341 + 1.244530I
0.79812 + 6.06247I −8.39660 − 7.82928I
u = 0.455846 + 0.648892I
a = 0.497045 + 0.987915I
b = 0.351208 + 1.072320I
3.96963 + 1.37271I −0.87985 − 4.43993I
u = 0.455846 + 0.648892I
a = −1.34650 − 0.83977I
b = 1.46058 − 1.46134I
3.96963 + 1.37271I −0.87985 − 4.43993I
u = 0.455846 − 0.648892I
a = 0.497045 − 0.987915I
b = 0.351208 − 1.072320I
3.96963 − 1.37271I −0.87985 + 4.43993I
u = 0.455846 − 0.648892I
a = −1.34650 + 0.83977I
b = 1.46058 + 1.46134I
3.96963 − 1.37271I −0.87985 + 4.43993I
u = 0.628268 + 1.065390I
a = −0.875257 + 0.344934I
b = −0.930257 − 0.450510I
8.70951 + 3.75485I −2.25682 − 2.44199I
u = 0.628268 + 1.065390I
a = 1.097080 + 0.604611I
b = −1.12744 + 2.94413I
8.70951 + 3.75485I −2.25682 − 2.44199I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628268 − 1.065390I
a = −0.875257 − 0.344934I
b = −0.930257 + 0.450510I
8.70951 − 3.75485I −2.25682 + 2.44199I
u = 0.628268 − 1.065390I
a = 1.097080 − 0.604611I
b = −1.12744 − 2.94413I
8.70951 − 3.75485I −2.25682 + 2.44199I
u = −0.621367 + 1.089770I
a = −0.010187 + 0.899634I
b = 1.18418 + 1.91130I
8.27570 − 10.03250I −3.16919 + 7.28178I
u = −0.621367 + 1.089770I
a = 1.005850 − 0.716169I
b = −0.79344 − 3.61211I
8.27570 − 10.03250I −3.16919 + 7.28178I
u = −0.621367 − 1.089770I
a = −0.010187 − 0.899634I
b = 1.18418 − 1.91130I
8.27570 + 10.03250I −3.16919 − 7.28178I
u = −0.621367 − 1.089770I
a = 1.005850 + 0.716169I
b = −0.79344 + 3.61211I
8.27570 + 10.03250I −3.16919 − 7.28178I
u = −0.558047 + 0.271580I
a = 0.923100 − 0.270249I
b = −0.279531 + 0.414404I
2.95992 + 1.83292I −4.44386 − 4.26331I
u = −0.558047 + 0.271580I
a = −0.99267 + 1.70622I
b = 0.895968 + 0.669805I
2.95992 + 1.83292I −4.44386 − 4.26331I
u = −0.558047 − 0.271580I
a = 0.923100 + 0.270249I
b = −0.279531 − 0.414404I
2.95992 − 1.83292I −4.44386 + 4.26331I
u = −0.558047 − 0.271580I
a = −0.99267 − 1.70622I
b = 0.895968 − 0.669805I
2.95992 − 1.83292I −4.44386 + 4.26331I
15
III. I
u
3
= h−u
11
− 2u
9
+ · · · + u
2
+ b, −u
10
− 2u
8
− 2u
6
+ u
2
+ a, u
12
+
3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
u
2
+ 1
u
2
a
9
=
−u
7
− 2u
5
− 2u
3
−u
7
− u
5
+ u
a
11
=
u
10
+ 2u
8
+ 2u
6
− u
2
u
11
+ 2u
9
− u
8
+ 3u
7
− 2u
6
+ u
5
− 2u
4
− u
2
a
6
=
u
11
+ 3u
9
+ 5u
7
+ 4u
5
+ 2u
3
+ u
u
11
− u
10
+ 3u
9
− 2u
8
+ 4u
7
− 2u
6
+ 2u
5
+ u − 1
a
12
=
0
−u
10
− 3u
8
− 4u
6
− 3u
4
− u
2
− 1
a
5
=
u
11
+ 3u
9
+ 5u
7
+ 4u
5
+ 2u
3
+ u
u
11
− u
10
+ 3u
9
− 2u
8
+ 4u
7
− 2u
6
+ 2u
5
− 1
a
10
=
u
10
+ 2u
8
− u
7
+ 2u
6
− 2u
5
− 2u
3
− u
2
u
11
+ 2u
9
− u
8
+ 2u
7
− 2u
6
− 2u
4
− u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
10
− 12u
8
− 16u
6
− 8u
4
− 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
7
, c
8
c
12
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
3
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(u
2
+ 1)
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
7
, c
8
c
12
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
3
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y + 1)
12
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295542 + 1.002190I
a = 0.917982 + 0.270708I
b = −0.374286 + 1.073090I
1.39926 + 0.92430I −5.71672 − 0.79423I
u = 0.295542 − 1.002190I
a = 0.917982 − 0.270708I
b = −0.374286 − 1.073090I
1.39926 − 0.92430I −5.71672 + 0.79423I
u = −0.295542 + 1.002190I
a = 0.917982 − 0.270708I
b = 1.35189 + 0.92878I
1.39926 − 0.92430I −5.71672 + 0.79423I
u = −0.295542 − 1.002190I
a = 0.917982 + 0.270708I
b = 1.35189 − 0.92878I
1.39926 + 0.92430I −5.71672 − 0.79423I
u = 0.664531 + 0.428243I
a = −0.685196 − 1.063260I
b = 0.24989 − 1.43772I
5.18047 − 0.92430I 1.71672 + 0.79423I
u = 0.664531 − 0.428243I
a = −0.685196 + 1.063260I
b = 0.24989 + 1.43772I
5.18047 + 0.92430I 1.71672 − 0.79423I
u = −0.664531 + 0.428243I
a = −0.685196 + 1.063260I
b = 1.238080 + 0.291690I
5.18047 + 0.92430I 1.71672 − 0.79423I
u = −0.664531 − 0.428243I
a = −0.685196 − 1.063260I
b = 1.238080 − 0.291690I
5.18047 − 0.92430I 1.71672 + 0.79423I
u = 0.558752 + 1.073950I
a = −0.732786 − 0.381252I
b = 0.586105 − 1.184950I
3.28987 + 5.69302I −2.00000 − 5.51057I
u = 0.558752 − 1.073950I
a = −0.732786 + 0.381252I
b = 0.586105 + 1.184950I
3.28987 − 5.69302I −2.00000 + 5.51057I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.558752 + 1.073950I
a = −0.732786 + 0.381252I
b = −1.05168 + 2.33284I
3.28987 − 5.69302I −2.00000 + 5.51057I
u = −0.558752 − 1.073950I
a = −0.732786 − 0.381252I
b = −1.05168 − 2.33284I
3.28987 + 5.69302I −2.00000 − 5.51057I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
20
+ 9u
19
+ ··· + 2u + 1)
2
· (u
33
+ 15u
32
+ ··· + 9u − 4)
c
2
, c
7
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
20
− u
19
+ ··· − 2u + 1)
2
· (u
33
+ 3u
32
+ ··· + 11u + 2)
c
3
(u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(u
20
+ u
19
+ ··· + 4u + 1)
2
· (u
33
− 3u
32
+ ··· − 73u + 10)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
((u
2
+ 1)
6
)(u
33
+ 22u
31
+ ··· + 3u + 1)(u
40
− u
39
+ ··· + 66u + 17)
c
8
, c
12
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
20
− 5u
19
+ ··· − 2u + 1)
2
· (u
33
+ 15u
32
+ ··· + 2771u + 266)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
20
+ 5y
19
+ ··· + 10y + 1)
2
· (y
33
+ 7y
32
+ ··· + 561y −16)
c
2
, c
7
((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
20
+ 9y
19
+ ··· + 2y + 1)
2
· (y
33
+ 15y
32
+ ··· + 9y −4)
c
3
((y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
)(y
20
+ y
19
+ ··· + 18y + 1)
2
· (y
33
− y
32
+ ··· + 2089y −100)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
((y + 1)
12
)(y
33
+ 44y
32
+ ··· − 9y −1)(y
40
+ 35y
39
+ ··· − 140y + 289)
c
8
, c
12
((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
20
+ 21y
19
+ ··· + 10y + 1)
2
· (y
33
+ 27y
32
+ ··· + 249593y −70756)
22
