12n
0560
(K12n
0560
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 11 12 2 11 12 1 6 4
Solving Sequence
4,12 1,10
11 3 9 5 6 7 8 2
c
12
c
10
c
3
c
9
c
4
c
5
c
6
c
8
c
2
c
1
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.42324 × 10
291
u
90
− 7.99634 × 10
291
u
89
+ ··· + 6.85609 × 10
290
b − 1.64543 × 10
293
,
1.60031 × 10
293
u
90
− 1.04522 × 10
294
u
89
+ ··· + 3.22236 × 10
292
a + 2.54763 × 10
294
,
u
91
− 7u
90
+ ··· + 305u − 47i
I
u
2
= h−2.64305 × 10
19
u
24
+ 3.18164 × 10
19
u
23
+ ··· + 8.71996 × 10
19
b − 3.13920 × 10
20
,
2.80082 × 10
20
u
24
+ 7.55212 × 10
19
u
23
+ ··· + 8.71996 × 10
19
a + 5.21556 × 10
20
, u
25
+ 2u
23
+ ··· + 4u − 1i
* 2 irreducible components of dim
C
= 0, with total 116 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
= h1.42 × 10
291
u
90
− 8.00 × 10
291
u
89
+ · · · + 6.86 × 10
290
b − 1.65 ×
10
293
, 1.60 × 10
293
u
90
− 1.05 × 10
294
u
89
+ · · · + 3.22 × 10
292
a + 2.55 ×
10
294
, u
91
− 7u
90
+ · · · + 305u − 47i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
10
=
−4.96626u
90
+ 32.4364u
89
+ ··· + 711.369u − 79.0609
−2.07587u
90
+ 11.6631u
89
+ ··· − 1257.99u + 239.995
a
11
=
−4.98333u
90
+ 33.0713u
89
+ ··· + 1492.91u − 209.668
−2.27023u
90
+ 12.8918u
89
+ ··· − 1099.99u + 215.772
a
3
=
2.58074u
90
− 20.1384u
89
+ ··· − 790.887u + 148.913
1.94318u
90
− 13.7938u
89
+ ··· − 338.479u + 33.8324
a
9
=
−2.89039u
90
+ 20.7733u
89
+ ··· + 1969.36u − 319.056
−2.07587u
90
+ 11.6631u
89
+ ··· − 1257.99u + 239.995
a
5
=
1.50799u
90
− 13.5634u
89
+ ··· − 927.092u + 175.394
−0.870427u
90
+ 7.21886u
89
+ ··· + 476.684u − 60.3132
a
6
=
−5.00106u
90
+ 32.5812u
89
+ ··· + 1080.14u − 94.8173
−0.980277u
90
+ 5.64049u
89
+ ··· − 81.5790u + 47.6240
a
7
=
−5.98134u
90
+ 38.2217u
89
+ ··· + 998.557u − 47.1934
−0.980277u
90
+ 5.64049u
89
+ ··· − 81.5790u + 47.6240
a
8
=
6.01042u
90
− 36.3053u
89
+ ··· + 462.327u − 156.674
0.972663u
90
− 4.59162u
89
+ ··· + 973.368u − 177.396
a
2
=
−0.270000u
90
+ 1.95357u
89
+ ··· + 1656.96u − 236.764
1.24299u
90
− 9.26255u
89
+ ··· + 183.479u − 30.9742
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0659084u
90
+ 0.108969u
89
+ ··· + 1395.40u − 251.958
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
91
+ 43u
90
+ ··· + 22u + 1
c
2
, c
7
u
91
+ u
90
+ ··· − 11u
2
+ 1
c
3
u
91
+ 2u
90
+ ··· − 23u + 1
c
4
u
91
+ 5u
90
+ ··· + 95u + 82807
c
5
, c
6
, c
11
u
91
− 14u
89
+ ··· − 6u − 11
c
8
u
91
+ 11u
90
+ ··· − 151800u + 12173
c
9
u
91
− 4u
90
+ ··· − 12908u + 7912
c
10
u
91
− 3u
90
+ ··· + 21u − 1
c
12
u
91
+ 7u
90
+ ··· + 305u + 47
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
91
+ 17y
90
+ ··· − 98y −1
c
2
, c
7
y
91
− 43y
90
+ ··· + 22y −1
c
3
y
91
+ 8y
90
+ ··· − 29y −1
c
4
y
91
+ 77y
90
+ ··· − 84473564657y −6856999249
c
5
, c
6
, c
11
y
91
− 28y
90
+ ··· + 10728y −121
c
8
y
91
− 87y
90
+ ··· + 8802996794y −148181929
c
9
y
91
+ 28y
90
+ ··· − 2966219056y −62599744
c
10
y
91
+ 5y
90
+ ··· − 85y −1
c
12
y
91
+ 17y
90
+ ··· − 72509y −2209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01604
a = 1.19618
b = −0.619180
−2.35258 0
u = −0.535517 + 0.817566I
a = 0.40065 − 1.51679I
b = 0.79833 − 1.30743I
2.27808 − 2.47811I 0
u = −0.535517 − 0.817566I
a = 0.40065 + 1.51679I
b = 0.79833 + 1.30743I
2.27808 + 2.47811I 0
u = 0.502928 + 0.818348I
a = 0.26548 + 1.71837I
b = 0.71649 + 1.50318I
1.57510 + 7.93270I 0
u = 0.502928 − 0.818348I
a = 0.26548 − 1.71837I
b = 0.71649 − 1.50318I
1.57510 − 7.93270I 0
u = 0.511576 + 0.754182I
a = −0.282864 + 1.046630I
b = −0.15969 + 1.50698I
−3.58497 + 3.35574I 0
u = 0.511576 − 0.754182I
a = −0.282864 − 1.046630I
b = −0.15969 − 1.50698I
−3.58497 − 3.35574I 0
u = −0.340411 + 0.838886I
a = 2.01135 − 0.30444I
b = 0.224821 + 0.577269I
−5.14562 + 4.77451I 0
u = −0.340411 − 0.838886I
a = 2.01135 + 0.30444I
b = 0.224821 − 0.577269I
−5.14562 − 4.77451I 0
u = 0.402058 + 1.018890I
a = 0.309845 + 0.736789I
b = 0.920317 + 0.286799I
1.85645 + 0.03554I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.402058 − 1.018890I
a = 0.309845 − 0.736789I
b = 0.920317 − 0.286799I
1.85645 − 0.03554I 0
u = 0.285864 + 0.847239I
a = 1.201830 + 0.295601I
b = −0.237159 − 0.435090I
−3.55210 − 0.95036I 0
u = 0.285864 − 0.847239I
a = 1.201830 − 0.295601I
b = −0.237159 + 0.435090I
−3.55210 + 0.95036I 0
u = −0.713254 + 0.852005I
a = 0.590412 − 0.913948I
b = 1.40202 − 0.39992I
2.06775 − 4.11651I 0
u = −0.713254 − 0.852005I
a = 0.590412 + 0.913948I
b = 1.40202 + 0.39992I
2.06775 + 4.11651I 0
u = −0.375828 + 0.777228I
a = 2.13286 + 0.69059I
b = 0.149648 + 1.035570I
−5.60570 − 1.85793I 0
u = −0.375828 − 0.777228I
a = 2.13286 − 0.69059I
b = 0.149648 − 1.035570I
−5.60570 + 1.85793I 0
u = 0.058258 + 1.148570I
a = −0.157026 + 0.120099I
b = −1.033890 − 0.104076I
−0.18986 − 2.74164I 0
u = 0.058258 − 1.148570I
a = −0.157026 − 0.120099I
b = −1.033890 + 0.104076I
−0.18986 + 2.74164I 0
u = −0.741814 + 0.880371I
a = 0.571332 − 1.268100I
b = 1.232440 − 0.542664I
1.99911 − 1.44766I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741814 − 0.880371I
a = 0.571332 + 1.268100I
b = 1.232440 + 0.542664I
1.99911 + 1.44766I 0
u = −0.504843 + 0.650504I
a = −0.093611 − 1.221940I
b = 1.16969 − 2.24380I
−5.05641 − 1.58259I 0
u = −0.504843 − 0.650504I
a = −0.093611 + 1.221940I
b = 1.16969 + 2.24380I
−5.05641 + 1.58259I 0
u = 0.414171 + 0.694826I
a = −0.85543 + 1.18748I
b = 0.63014 + 1.40371I
−3.09163 + 4.24015I 0
u = 0.414171 − 0.694826I
a = −0.85543 − 1.18748I
b = 0.63014 − 1.40371I
−3.09163 − 4.24015I 0
u = 0.460264 + 1.102830I
a = −0.375405 + 0.085886I
b = −1.151740 + 0.417119I
−0.85952 − 3.02137I 0
u = 0.460264 − 1.102830I
a = −0.375405 − 0.085886I
b = −1.151740 − 0.417119I
−0.85952 + 3.02137I 0
u = 0.742276 + 0.943517I
a = 0.31758 + 1.38675I
b = 1.227720 + 0.697519I
1.14861 + 5.13293I 0
u = 0.742276 − 0.943517I
a = 0.31758 − 1.38675I
b = 1.227720 − 0.697519I
1.14861 − 5.13293I 0
u = 0.284021 + 0.743601I
a = 1.24425 − 0.68339I
b = −0.230665 − 1.105310I
−3.42068 − 1.44050I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.284021 − 0.743601I
a = 1.24425 + 0.68339I
b = −0.230665 + 1.105310I
−3.42068 + 1.44050I 0
u = 0.910189 + 0.791577I
a = −0.01089 − 1.43365I
b = −1.095740 − 0.429637I
0.52246 + 9.04938I 0
u = 0.910189 − 0.791577I
a = −0.01089 + 1.43365I
b = −1.095740 + 0.429637I
0.52246 − 9.04938I 0
u = −0.302014 + 0.713600I
a = −2.26078 − 1.63663I
b = 0.159232 − 1.216630I
−5.43065 − 8.18174I 0
u = −0.302014 − 0.713600I
a = −2.26078 + 1.63663I
b = 0.159232 + 1.216630I
−5.43065 + 8.18174I 0
u = −0.480089 + 0.602783I
a = 0.353743 − 0.681474I
b = 2.04861 − 1.58222I
−4.22204 − 8.04480I 0
u = −0.480089 − 0.602783I
a = 0.353743 + 0.681474I
b = 2.04861 + 1.58222I
−4.22204 + 8.04480I 0
u = −0.497589 + 0.584067I
a = 0.377588 − 0.738280I
b = 0.097090 − 0.481940I
0.092786 − 1.282950I 0
u = −0.497589 − 0.584067I
a = 0.377588 + 0.738280I
b = 0.097090 + 0.481940I
0.092786 + 1.282950I 0
u = −0.673714 + 0.358408I
a = 0.06705 + 1.69725I
b = −0.034930 + 0.383069I
3.79905 − 0.34651I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673714 − 0.358408I
a = 0.06705 − 1.69725I
b = −0.034930 − 0.383069I
3.79905 + 0.34651I 0
u = 0.446976 + 0.607186I
a = −0.141520 + 0.286604I
b = 1.50527 + 1.04718I
−2.59552 + 3.93278I 0
u = 0.446976 − 0.607186I
a = −0.141520 − 0.286604I
b = 1.50527 − 1.04718I
−2.59552 − 3.93278I 0
u = 0.363853 + 0.660110I
a = −1.45967 + 0.78808I
b = 0.537801 + 1.081090I
−3.13954 + 4.13473I 0
u = 0.363853 − 0.660110I
a = −1.45967 − 0.78808I
b = 0.537801 − 1.081090I
−3.13954 − 4.13473I 0
u = 0.028752 + 0.743600I
a = 0.90014 − 1.11196I
b = 1.025710 − 0.494567I
1.57975 − 5.06929I 3.40615 + 6.58792I
u = 0.028752 − 0.743600I
a = 0.90014 + 1.11196I
b = 1.025710 + 0.494567I
1.57975 + 5.06929I 3.40615 − 6.58792I
u = 0.594560 + 0.426667I
a = −0.04951 − 1.87310I
b = 0.143426 − 0.493407I
2.86065 + 6.12466I 4.32139 − 3.78741I
u = 0.594560 − 0.426667I
a = −0.04951 + 1.87310I
b = 0.143426 + 0.493407I
2.86065 − 6.12466I 4.32139 + 3.78741I
u = 0.218750 + 0.688010I
a = 0.645428 − 1.061520I
b = −0.68419 − 1.74369I
−3.36300 − 1.77948I −3.50603 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.218750 − 0.688010I
a = 0.645428 + 1.061520I
b = −0.68419 + 1.74369I
−3.36300 + 1.77948I −3.50603 + 0.I
u = 0.545467 + 0.431685I
a = −0.074540 + 0.701667I
b = 0.889500 + 0.070322I
1.96216 + 0.22695I 4.23087 + 0.I
u = 0.545467 − 0.431685I
a = −0.074540 − 0.701667I
b = 0.889500 − 0.070322I
1.96216 − 0.22695I 4.23087 + 0.I
u = −0.102087 + 0.676145I
a = −0.233110 + 0.687881I
b = −2.15100 + 1.28770I
−6.63479 − 0.59130I −12.98882 + 3.14697I
u = −0.102087 − 0.676145I
a = −0.233110 − 0.687881I
b = −2.15100 − 1.28770I
−6.63479 + 0.59130I −12.98882 − 3.14697I
u = 0.998262 + 0.869039I
a = 0.067358 − 0.815973I
b = −0.299483 − 1.286640I
3.31066 + 7.23468I 0
u = 0.998262 − 0.869039I
a = 0.067358 + 0.815973I
b = −0.299483 + 1.286640I
3.31066 − 7.23468I 0
u = −1.033450 + 0.831448I
a = −0.038034 + 0.942725I
b = −1.029820 + 0.324116I
3.34151 − 3.93858I 0
u = −1.033450 − 0.831448I
a = −0.038034 − 0.942725I
b = −1.029820 − 0.324116I
3.34151 + 3.93858I 0
u = −0.261728 + 0.615539I
a = −2.94921 − 0.18053I
b = 0.109955 − 0.715148I
−6.25736 − 0.83262I −7.87690 + 5.16658I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.261728 − 0.615539I
a = −2.94921 + 0.18053I
b = 0.109955 + 0.715148I
−6.25736 + 0.83262I −7.87690 − 5.16658I
u = −0.194564 + 0.638280I
a = 0.28089 + 1.43719I
b = −1.12572 + 2.51057I
−5.23507 + 6.16040I −8.39174 − 2.47750I
u = −0.194564 − 0.638280I
a = 0.28089 − 1.43719I
b = −1.12572 − 2.51057I
−5.23507 − 6.16040I −8.39174 + 2.47750I
u = −0.986413 + 0.910702I
a = −0.221007 + 0.799561I
b = −0.770257 + 0.912345I
4.97604 − 3.20928I 0
u = −0.986413 − 0.910702I
a = −0.221007 − 0.799561I
b = −0.770257 − 0.912345I
4.97604 + 3.20928I 0
u = −0.991243 + 0.963315I
a = −0.446900 + 0.584288I
b = −0.598317 + 0.267301I
4.80687 − 3.95661I 0
u = −0.991243 − 0.963315I
a = −0.446900 − 0.584288I
b = −0.598317 − 0.267301I
4.80687 + 3.95661I 0
u = 0.90962 + 1.16042I
a = 0.078620 + 1.053680I
b = 1.05321 + 1.57050I
−6.10439 + 10.63170I 0
u = 0.90962 − 1.16042I
a = 0.078620 − 1.053680I
b = 1.05321 − 1.57050I
−6.10439 − 10.63170I 0
u = 0.428497 + 0.292362I
a = 1.77420 − 1.75353I
b = 0.028181 − 0.367461I
−2.56443 + 0.09717I −5.59647 + 2.57495I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428497 − 0.292362I
a = 1.77420 + 1.75353I
b = 0.028181 + 0.367461I
−2.56443 − 0.09717I −5.59647 − 2.57495I
u = −0.87514 + 1.22658I
a = 0.144233 − 0.854884I
b = 0.96894 − 1.32160I
−3.36726 − 4.90530I 0
u = −0.87514 − 1.22658I
a = 0.144233 + 0.854884I
b = 0.96894 + 1.32160I
−3.36726 + 4.90530I 0
u = 0.94331 + 1.19971I
a = −0.169263 − 1.089060I
b = −1.33197 − 1.37362I
−4.5800 + 17.8673I 0
u = 0.94331 − 1.19971I
a = −0.169263 + 1.089060I
b = −1.33197 + 1.37362I
−4.5800 − 17.8673I 0
u = −0.94052 + 1.24202I
a = −0.174744 + 0.929431I
b = −1.25394 + 1.23411I
−2.27694 − 11.69080I 0
u = −0.94052 − 1.24202I
a = −0.174744 − 0.929431I
b = −1.25394 − 1.23411I
−2.27694 + 11.69080I 0
u = 1.41485 + 0.77869I
a = 0.547555 + 0.138125I
b = 0.067268 − 0.722636I
−4.62300 − 2.85364I 0
u = 1.41485 − 0.77869I
a = 0.547555 − 0.138125I
b = 0.067268 + 0.722636I
−4.62300 + 2.85364I 0
u = 1.44495 + 0.79736I
a = −0.509329 − 0.265566I
b = −0.478594 + 0.693261I
−3.06039 − 9.76728I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44495 − 0.79736I
a = −0.509329 + 0.265566I
b = −0.478594 − 0.693261I
−3.06039 + 9.76728I 0
u = 1.06507 + 1.26835I
a = 0.143056 − 0.747980I
b = −0.86720 − 1.24106I
−9.27014 + 8.28225I 0
u = 1.06507 − 1.26835I
a = 0.143056 + 0.747980I
b = −0.86720 + 1.24106I
−9.27014 − 8.28225I 0
u = 1.04610 + 1.32186I
a = −0.151116 + 0.596915I
b = 0.481748 + 1.262360I
−9.28249 + 1.00021I 0
u = 1.04610 − 1.32186I
a = −0.151116 − 0.596915I
b = 0.481748 − 1.262360I
−9.28249 − 1.00021I 0
u = 1.37255 + 1.03578I
a = −0.0804674 − 0.0826292I
b = 0.248762 − 0.181381I
2.54445 + 0.33057I 0
u = 1.37255 − 1.03578I
a = −0.0804674 + 0.0826292I
b = 0.248762 + 0.181381I
2.54445 − 0.33057I 0
u = −1.73516 + 0.39741I
a = −0.134060 + 0.341837I
b = −0.254729 − 0.475398I
−0.07241 + 3.27810I 0
u = −1.73516 − 0.39741I
a = −0.134060 − 0.341837I
b = −0.254729 + 0.475398I
−0.07241 − 3.27810I 0
u = −1.11582 + 1.99033I
a = −0.048659 + 0.189309I
b = −0.737678 + 0.505950I
−0.98131 − 4.61659I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11582 − 1.99033I
a = −0.048659 − 0.189309I
b = −0.737678 − 0.505950I
−0.98131 + 4.61659I 0
14
II.
I
u
2
= h−2.64×10
19
u
24
+3.18×10
19
u
23
+· · ·+8.72×10
19
b−3.14×10
20
, 2.80×
10
20
u
24
+7.55×10
19
u
23
+· · ·+8.72×10
19
a+5.22×10
20
, u
25
+2u
23
+· · ·+4u−1i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
10
=
−3.21197u
24
− 0.866073u
23
+ ··· + 16.9203u − 5.98118
0.303103u
24
− 0.364868u
23
+ ··· − 5.38385u + 3.60002
a
11
=
−3.82838u
24
− 0.788978u
23
+ ··· + 22.0518u − 8.71512
−0.101126u
24
− 0.624329u
23
+ ··· − 4.45906u + 3.52292
a
3
=
1.66182u
24
+ 0.658680u
23
+ ··· − 8.52517u + 2.36146
0.0602588u
24
+ 0.229053u
23
+ ··· − 2.03906u + 0.680994
a
9
=
−3.51507u
24
− 0.501204u
23
+ ··· + 22.3042u − 9.58120
0.303103u
24
− 0.364868u
23
+ ··· − 5.38385u + 3.60002
a
5
=
0.593776u
24
+ 0.232884u
23
+ ··· + 4.39695u − 1.88991
1.00779u
24
+ 0.196742u
23
+ ··· − 8.88306u + 3.57037
a
6
=
−2.00624u
24
− 0.0702191u
23
+ ··· + 18.2833u − 6.90613
0.508993u
24
− 0.581731u
23
+ ··· − 4.36214u + 3.08544
a
7
=
−1.49725u
24
− 0.651950u
23
+ ··· + 13.9212u − 3.82069
0.508993u
24
− 0.581731u
23
+ ··· − 4.36214u + 3.08544
a
8
=
3.90173u
24
+ 1.01120u
23
+ ··· − 17.2606u + 5.63795
−0.127927u
24
+ 0.342888u
23
+ ··· + 4.01910u − 3.58318
a
2
=
2.18487u
24
+ 1.41269u
23
+ ··· − 6.74107u + 1.97101
−0.499169u
24
− 0.167673u
23
+ ··· + 1.13386u − 1.21729
(ii) Obstruction class = 1
(iii) Cusp Shapes =
226713202827690363303
87199623832078240175
u
24
+
142242531702877178101
87199623832078240175
u
23
+ ··· −
1287113238265159786709
87199623832078240175
u −
312795063825558794366
87199623832078240175
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 12u
24
+ ··· + 11u − 1
c
2
u
25
− 6u
23
+ ··· + u − 1
c
3
u
25
− u
24
+ ··· − 6u − 1
c
4
u
25
+ 4u
23
+ ··· + 10u
2
− 1
c
5
, c
6
u
25
− u
24
+ ··· + u − 1
c
7
u
25
− 6u
23
+ ··· + u + 1
c
8
u
25
− 12u
24
+ ··· + 55u − 11
c
9
u
25
+ 5u
24
+ ··· − 19u + 7
c
10
u
25
+ 4u
23
+ ··· − 2u − 1
c
11
u
25
+ u
24
+ ··· + u + 1
c
12
u
25
+ 2u
23
+ ··· + 4u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 8y
24
+ ··· − 17y −1
c
2
, c
7
y
25
− 12y
24
+ ··· + 11y −1
c
3
y
25
+ 7y
24
+ ··· − 4y −1
c
4
y
25
+ 8y
24
+ ··· + 20y −1
c
5
, c
6
, c
11
y
25
− 17y
24
+ ··· + 25y −1
c
8
y
25
− 12y
24
+ ··· + 2827y −121
c
9
y
25
+ 7y
24
+ ··· + 543y −49
c
10
y
25
+ 8y
24
+ ··· + 4y −1
c
12
y
25
+ 4y
24
+ ··· − 4y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594045 + 0.814039I
a = 0.53132 − 1.59025I
b = 1.081530 − 0.869155I
2.93258 − 1.95019I 7.82007 + 2.01519I
u = −0.594045 − 0.814039I
a = 0.53132 + 1.59025I
b = 1.081530 + 0.869155I
2.93258 + 1.95019I 7.82007 − 2.01519I
u = 0.538291 + 0.751718I
a = 0.39607 + 1.90997I
b = 0.797048 + 0.981753I
1.95197 + 7.16615I 2.90902 − 6.80575I
u = 0.538291 − 0.751718I
a = 0.39607 − 1.90997I
b = 0.797048 − 0.981753I
1.95197 − 7.16615I 2.90902 + 6.80575I
u = 0.864174
a = −1.62959
b = 0.622350
−2.14592 21.2160
u = 0.947075 + 0.727756I
a = 0.013709 − 1.033340I
b = −0.380948 − 0.838829I
4.69595 + 7.24346I 6.03224 − 7.22892I
u = 0.947075 − 0.727756I
a = 0.013709 + 1.033340I
b = −0.380948 + 0.838829I
4.69595 − 7.24346I 6.03224 + 7.22892I
u = −0.079520 + 0.783942I
a = 1.141000 + 0.816744I
b = −0.420493 + 0.834585I
−4.22454 + 1.80784I −8.81746 − 4.58655I
u = −0.079520 − 0.783942I
a = 1.141000 − 0.816744I
b = −0.420493 − 0.834585I
−4.22454 − 1.80784I −8.81746 + 4.58655I
u = −0.724982 + 0.986618I
a = 0.485739 − 0.853337I
b = 1.281890 − 0.397340I
2.09907 − 3.15118I 1.73998 + 1.99553I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724982 − 0.986618I
a = 0.485739 + 0.853337I
b = 1.281890 + 0.397340I
2.09907 + 3.15118I 1.73998 − 1.99553I
u = −0.919892 + 0.831035I
a = −0.270543 + 0.982338I
b = −0.638247 + 0.810825I
5.52238 − 2.41952I 6.29336 − 0.75030I
u = −0.919892 − 0.831035I
a = −0.270543 − 0.982338I
b = −0.638247 − 0.810825I
5.52238 + 2.41952I 6.29336 + 0.75030I
u = −0.304186 + 0.553410I
a = −0.99070 − 1.15121I
b = 1.00682 − 1.49599I
−3.06423 − 3.43413I −4.97318 − 1.32012I
u = −0.304186 − 0.553410I
a = −0.99070 + 1.15121I
b = 1.00682 + 1.49599I
−3.06423 + 3.43413I −4.97318 + 1.32012I
u = −0.96691 + 1.04522I
a = −0.444220 + 0.523173I
b = −0.817605 + 0.396031I
4.85237 − 4.48785I 5.60105 + 11.81038I
u = −0.96691 − 1.04522I
a = −0.444220 − 0.523173I
b = −0.817605 − 0.396031I
4.85237 + 4.48785I 5.60105 − 11.81038I
u = 0.331149 + 0.381308I
a = 1.60281 + 1.31788I
b = −0.603217 − 1.050850I
−5.74992 + 0.21247I −3.47530 − 0.69345I
u = 0.331149 − 0.381308I
a = 1.60281 − 1.31788I
b = −0.603217 + 1.050850I
−5.74992 − 0.21247I −3.47530 + 0.69345I
u = 0.391972 + 0.266611I
a = −2.09352 − 0.02266I
b = 0.49841 + 1.80349I
−4.65699 + 7.09838I −2.88763 − 5.93601I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.391972 − 0.266611I
a = −2.09352 + 0.02266I
b = 0.49841 − 1.80349I
−4.65699 − 7.09838I −2.88763 + 5.93601I
u = −0.73476 + 1.57921I
a = −0.000323 − 0.207749I
b = 0.814071 − 0.568843I
−1.04239 − 4.37759I −5.37088 − 1.88091I
u = −0.73476 − 1.57921I
a = −0.000323 + 0.207749I
b = 0.814071 + 0.568843I
−1.04239 + 4.37759I −5.37088 + 1.88091I
u = 1.68372 + 1.34594I
a = −0.056553 − 0.166122I
b = −0.430441 − 0.060197I
2.69151 + 0.49029I 22.0208 − 17.8472I
u = 1.68372 − 1.34594I
a = −0.056553 + 0.166122I
b = −0.430441 + 0.060197I
2.69151 − 0.49029I 22.0208 + 17.8472I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− 12u
24
+ ··· + 11u − 1)(u
91
+ 43u
90
+ ··· + 22u + 1)
c
2
(u
25
− 6u
23
+ ··· + u − 1)(u
91
+ u
90
+ ··· − 11u
2
+ 1)
c
3
(u
25
− u
24
+ ··· − 6u − 1)(u
91
+ 2u
90
+ ··· − 23u + 1)
c
4
(u
25
+ 4u
23
+ ··· + 10u
2
− 1)(u
91
+ 5u
90
+ ··· + 95u + 82807)
c
5
, c
6
(u
25
− u
24
+ ··· + u − 1)(u
91
− 14u
89
+ ··· − 6u − 11)
c
7
(u
25
− 6u
23
+ ··· + u + 1)(u
91
+ u
90
+ ··· − 11u
2
+ 1)
c
8
(u
25
− 12u
24
+ ··· + 55u − 11)(u
91
+ 11u
90
+ ··· − 151800u + 12173)
c
9
(u
25
+ 5u
24
+ ··· − 19u + 7)(u
91
− 4u
90
+ ··· − 12908u + 7912)
c
10
(u
25
+ 4u
23
+ ··· − 2u − 1)(u
91
− 3u
90
+ ··· + 21u − 1)
c
11
(u
25
+ u
24
+ ··· + u + 1)(u
91
− 14u
89
+ ··· − 6u − 11)
c
12
(u
25
+ 2u
23
+ ··· + 4u − 1)(u
91
+ 7u
90
+ ··· + 305u + 47)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
25
+ 8y
24
+ ··· − 17y −1)(y
91
+ 17y
90
+ ··· − 98y −1)
c
2
, c
7
(y
25
− 12y
24
+ ··· + 11y −1)(y
91
− 43y
90
+ ··· + 22y −1)
c
3
(y
25
+ 7y
24
+ ··· − 4y −1)(y
91
+ 8y
90
+ ··· − 29y −1)
c
4
(y
25
+ 8y
24
+ ··· + 20y −1)
· (y
91
+ 77y
90
+ ··· − 84473564657y −6856999249)
c
5
, c
6
, c
11
(y
25
− 17y
24
+ ··· + 25y −1)(y
91
− 28y
90
+ ··· + 10728y −121)
c
8
(y
25
− 12y
24
+ ··· + 2827y −121)
· (y
91
− 87y
90
+ ··· + 8802996794y −148181929)
c
9
(y
25
+ 7y
24
+ ··· + 543y −49)
· (y
91
+ 28y
90
+ ··· − 2966219056y −62599744)
c
10
(y
25
+ 8y
24
+ ··· + 4y −1)(y
91
+ 5y
90
+ ··· − 85y −1)
c
12
(y
25
+ 4y
24
+ ··· − 4y −1)(y
91
+ 17y
90
+ ··· − 72509y −2209)
22
