12a
0862
(K12a
0862
)
A knot diagram
1
Linearized knot diagam
4 5 10 9 3 11 1 12 2 7 6 8
Solving Sequence
6,11
7
3,12
5 2 10 4 1 9 8
c
6
c
11
c
5
c
2
c
10
c
3
c
1
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.41366 × 10
15
u
41
− 3.88647 × 10
15
u
40
+ ··· + 2.70070 × 10
16
b − 2.38778 × 10
16
,
3.90532 × 10
16
u
41
+ 4.65482 × 10
15
u
40
+ ··· + 1.08028 × 10
17
a − 2.34376 × 10
17
, u
42
+ u
41
+ ··· + 5u + 1i
I
u
2
= h5.71537 × 10
60
u
59
+ 9.40318 × 10
60
u
58
+ ··· + 1.05278 × 10
62
b − 1.05491 × 10
62
,
5.50355 × 10
62
u
59
+ 1.37835 × 10
63
u
58
+ ··· + 1.78973 × 10
63
a + 1.81400 × 10
64
, u
60
+ u
59
+ ··· + 96u + 17i
I
u
3
= h−9a
4
u + 137a
4
− 670a
3
u − 515a
3
+ 896a
2
u − 428a
2
+ 1221au + 725b − 703a − 211u + 1198,
a
5
− 5a
4
u − 4a
4
+ 9a
3
u − 2a
3
+ 6a
2
u − 6au + 7a − 1, u
2
+ 1i
I
u
4
= hb − 1, 4a + 3, u + 1i
* 4 irreducible components of dim
C
= 0, with total 113 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−2.41×10
15
u
41
−3.89×10
15
u
40
+· · ·+2.70×10
16
b−2.39×10
16
, 3.91×
10
16
u
41
+4.65×10
15
u
40
+· · ·+1.08×10
17
a−2.34×10
17
, u
42
+u
41
+· · ·+5u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
−0.361511u
41
− 0.0430891u
40
+ ··· − 6.03379u + 2.16959
0.0893718u
41
+ 0.143906u
40
+ ··· − 0.178892u + 0.884133
a
12
=
u
u
a
5
=
−0.315904u
41
+ 0.0662626u
40
+ ··· − 5.94901u + 3.22945
0.174739u
41
+ 0.111875u
40
+ ··· + 0.0944736u + 0.995695
a
2
=
−0.0742984u
41
− 0.106140u
40
+ ··· + 2.43989u − 0.719779
−0.188640u
41
+ 0.154687u
40
+ ··· + 1.14048u + 0.0824999
a
10
=
−u
u
3
+ u
a
4
=
−0.155243u
41
+ 0.143329u
40
+ ··· − 4.42970u + 2.56854
−0.0568312u
41
+ 0.0634325u
40
+ ··· − 1.67596u + 0.465338
a
1
=
−0.0312500u
41
− 0.0312500u
40
+ ··· − 0.156250u
2
− 2.03125u
−0.0312500u
41
− 0.0312500u
40
+ ··· − 0.156250u
2
− 1.03125u
a
9
=
0.0312500u
40
+ 0.0312500u
39
+ ··· + 0.156250u + 1.03125
0.0312500u
40
+ 0.0312500u
39
+ ··· + 0.156250u + 0.0312500
a
8
=
0.0312500u
40
+ 0.0312500u
39
+ ··· + 0.156250u + 1.03125
0.0312500u
40
+ 0.0312500u
39
+ ··· + 0.156250u + 0.0312500
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
789866485036270413
432111644840574976
u
41
−
3177961663845613
3375872225316992
u
40
+···−
515566611610676781
108027911210143744
u+
1182572220834268723
432111644840574976
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
− 7u
41
+ ··· + 44u + 32
c
2
, c
5
u
42
+ 2u
41
+ ··· + 175u − 16
c
3
2(2u
42
+ 7u
41
+ ··· + 62575u − 9794)
c
4
2(2u
42
+ 19u
41
+ ··· + 6823u + 542)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
42
− u
41
+ ··· − 5u + 1
c
9
u
42
− 11u
41
+ ··· + 12u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 3y
41
+ ··· − 8784y + 1024
c
2
, c
5
y
42
− 30y
41
+ ··· − 15201y + 256
c
3
4(4y
42
− 101y
41
+ ··· + 6.32683 × 10
8
y + 9.59224 × 10
7
)
c
4
4(4y
42
− 181y
41
+ ··· − 8215501y + 293764)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
42
+ 45y
41
+ ··· + 11y + 1
c
9
y
42
+ 3y
41
+ ··· + 40y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.848250 + 0.512070I
a = 0.207456 + 0.529240I
b = −1.095070 − 0.103799I
3.98284 − 0.00703I 16.2188 − 8.0603I
u = −0.848250 − 0.512070I
a = 0.207456 − 0.529240I
b = −1.095070 + 0.103799I
3.98284 + 0.00703I 16.2188 + 8.0603I
u = 0.800314 + 0.304736I
a = 0.829077 − 1.057030I
b = −1.330470 − 0.471690I
5.06478 + 9.22584I 10.05550 − 8.03379I
u = 0.800314 − 0.304736I
a = 0.829077 + 1.057030I
b = −1.330470 + 0.471690I
5.06478 − 9.22584I 10.05550 + 8.03379I
u = −1.14704
a = 0.588362
b = −0.957842
3.16700 −41.0100
u = −0.012618 + 1.267560I
a = −0.257462 − 0.166119I
b = −1.55639 − 0.20562I
1.02826 + 4.26198I 0
u = −0.012618 − 1.267560I
a = −0.257462 + 0.166119I
b = −1.55639 + 0.20562I
1.02826 − 4.26198I 0
u = −0.034204 + 0.691000I
a = −0.842871 + 0.389564I
b = −1.348420 + 0.231077I
3.66010 − 4.50065I 13.13111 + 5.04481I
u = −0.034204 − 0.691000I
a = −0.842871 − 0.389564I
b = −1.348420 − 0.231077I
3.66010 + 4.50065I 13.13111 − 5.04481I
u = 0.616502 + 0.228755I
a = −0.376552 + 0.322880I
b = 0.092715 + 0.998112I
0.67504 + 4.06826I 8.30605 − 8.37246I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.616502 − 0.228755I
a = −0.376552 − 0.322880I
b = 0.092715 − 0.998112I
0.67504 − 4.06826I 8.30605 + 8.37246I
u = 0.631212 + 0.066643I
a = −1.208440 + 0.639819I
b = 1.39513 + 0.51274I
4.64462 + 1.79449I 16.6728 − 4.4347I
u = 0.631212 − 0.066643I
a = −1.208440 − 0.639819I
b = 1.39513 − 0.51274I
4.64462 − 1.79449I 16.6728 + 4.4347I
u = −0.22206 + 1.39802I
a = 0.703692 − 0.255357I
b = 1.80328 + 0.31389I
−4.00787 − 4.08479I 0
u = −0.22206 − 1.39802I
a = 0.703692 + 0.255357I
b = 1.80328 − 0.31389I
−4.00787 + 4.08479I 0
u = −0.14844 + 1.41232I
a = 0.821579 + 1.118480I
b = 0.75327 + 1.20186I
−6.98470 − 0.19701I 0
u = −0.14844 − 1.41232I
a = 0.821579 − 1.118480I
b = 0.75327 − 1.20186I
−6.98470 + 0.19701I 0
u = −0.27736 + 1.41903I
a = 0.20943 − 1.78788I
b = 1.42598 − 0.91461I
−5.04656 − 8.51889I 0
u = −0.27736 − 1.41903I
a = 0.20943 + 1.78788I
b = 1.42598 + 0.91461I
−5.04656 + 8.51889I 0
u = 0.18419 + 1.44787I
a = 0.67100 − 1.30177I
b = 0.747156 − 0.401730I
−8.12596 + 3.90378I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18419 − 1.44787I
a = 0.67100 + 1.30177I
b = 0.747156 + 0.401730I
−8.12596 − 3.90378I 0
u = 0.24426 + 1.44190I
a = −0.87161 + 1.77499I
b = 1.133290 + 0.182062I
−7.23578 + 5.67907I 0
u = 0.24426 − 1.44190I
a = −0.87161 − 1.77499I
b = 1.133290 − 0.182062I
−7.23578 − 5.67907I 0
u = −0.513585
a = −6.41966
b = 1.04008
2.62940 −41.1690
u = −0.491329 + 0.139176I
a = 0.845547 − 0.468260I
b = 0.133518 − 0.061566I
1.019720 − 0.352110I 10.07407 + 1.64611I
u = −0.491329 − 0.139176I
a = 0.845547 + 0.468260I
b = 0.133518 + 0.061566I
1.019720 + 0.352110I 10.07407 − 1.64611I
u = 0.41236 + 1.44280I
a = 0.077835 − 1.227670I
b = −1.175080 − 0.389371I
−7.08053 + 10.21340I 0
u = 0.41236 − 1.44280I
a = 0.077835 + 1.227670I
b = −1.175080 + 0.389371I
−7.08053 − 10.21340I 0
u = −0.32208 + 1.46578I
a = −0.67927 − 1.33639I
b = −0.074878 − 1.346880I
−10.3464 − 11.3808I 0
u = −0.32208 − 1.46578I
a = −0.67927 + 1.33639I
b = −0.074878 + 1.346880I
−10.3464 + 11.3808I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.39351 + 1.46640I
a = −0.02848 + 1.76784I
b = −1.40317 + 0.63323I
−6.1337 − 18.1779I 0
u = −0.39351 − 1.46640I
a = −0.02848 − 1.76784I
b = −1.40317 − 0.63323I
−6.1337 + 18.1779I 0
u = 0.28895 + 1.49339I
a = −0.022490 + 0.757026I
b = −0.100578 + 0.571615I
−10.21670 + 6.45809I 0
u = 0.28895 − 1.49339I
a = −0.022490 − 0.757026I
b = −0.100578 − 0.571615I
−10.21670 − 6.45809I 0
u = −0.05826 + 1.54611I
a = −0.015563 + 1.355460I
b = −0.615041 + 0.997986I
−14.1579 + 0.2551I 0
u = −0.05826 − 1.54611I
a = −0.015563 − 1.355460I
b = −0.615041 − 0.997986I
−14.1579 − 0.2551I 0
u = 0.040969 + 0.400596I
a = 1.18528 − 1.17600I
b = 0.058208 − 0.592373I
−0.83418 − 1.45922I 1.76553 + 2.89021I
u = 0.040969 − 0.400596I
a = 1.18528 + 1.17600I
b = 0.058208 + 0.592373I
−0.83418 + 1.45922I 1.76553 − 2.89021I
u = 0.07832 + 1.61476I
a = −0.500043 − 0.967191I
b = −0.946634 − 0.650726I
−13.0094 + 6.1124I 0
u = 0.07832 − 1.61476I
a = −0.500043 + 0.967191I
b = −0.946634 + 0.650726I
−13.0094 − 6.1124I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158642 + 0.196779I
a = 3.79254 − 0.96883I
b = 1.062070 − 0.138328I
1.94125 − 0.63614I 4.59431 − 1.47794I
u = −0.158642 − 0.196779I
a = 3.79254 + 0.96883I
b = 1.062070 + 0.138328I
1.94125 + 0.63614I 4.59431 + 1.47794I
9
II. I
u
2
=
h5.72×10
60
u
59
+9.40×10
60
u
58
+· · ·+1.05×10
62
b−1.05×10
62
, 5.50×10
62
u
59
+
1.38 × 10
63
u
58
+ · · · + 1.79 × 10
63
a + 1.81 × 10
64
, u
60
+ u
59
+ · · · + 96u + 17i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
−0.307507u
59
− 0.770142u
58
+ ··· − 49.2260u − 10.1356
−0.0542882u
59
− 0.0893173u
58
+ ··· + 2.24063u + 1.00202
a
12
=
u
u
a
5
=
−0.382515u
59
− 0.936354u
58
+ ··· − 63.3449u − 9.46810
−0.0585416u
59
− 0.182816u
58
+ ··· − 4.28272u − 0.844920
a
2
=
0.0101071u
59
+ 0.339015u
58
+ ··· + 17.5516u − 0.691929
−0.0532959u
59
+ 0.142074u
58
+ ··· + 20.1016u + 4.81822
a
10
=
−u
u
3
+ u
a
4
=
−0.0236180u
59
− 0.317832u
58
+ ··· − 34.8484u − 8.02920
0.163341u
59
+ 0.166411u
58
+ ··· + 8.85766u + 1.75878
a
1
=
−0.0588235u
59
− 0.0588235u
58
+ ··· − 24.4706u − 5.64706
−0.0164874u
59
+ 0.0949894u
58
+ ··· + 14.0045u + 2.55342
a
9
=
0.261678u
59
+ 0.317843u
58
+ ··· + 21.9887u + 0.695116
0.111477u
59
+ 0.151154u
58
+ ··· + 4.13621u + 1.28029
a
8
=
0.150201u
59
+ 0.166689u
58
+ ··· + 17.8524u + 0.414830
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0405567u
59
− 1.24352u
58
+ ··· − 113.006u − 12.8451
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
30
− 5u
29
+ ··· − u + 1)
2
c
2
, c
5
(u
30
+ u
29
+ ··· + 5u + 1)
2
c
3
(u
30
− u
29
+ ··· + 11u + 1)
2
c
4
(u
30
− 3u
29
+ ··· − 9u + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
60
− u
59
+ ··· − 96u + 17
c
9
(u
30
+ 3u
29
+ ··· + u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
30
− 3y
29
+ ··· − 5y + 1)
2
c
2
, c
5
(y
30
− 19y
29
+ ··· − 5y + 1)
2
c
3
(y
30
− 23y
29
+ ··· − 9y + 1)
2
c
4
(y
30
− 27y
29
+ ··· + 11y + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
60
+ 47y
59
+ ··· + 4928y + 289
c
9
(y
30
+ 5y
29
+ ··· + 3y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.991061 + 0.204470I
a = 0.850800 − 0.328523I
b = −1.023220 − 0.279978I
−1.80983 + 5.18678I 4.12994 − 9.32507I
u = 0.991061 − 0.204470I
a = 0.850800 + 0.328523I
b = −1.023220 + 0.279978I
−1.80983 − 5.18678I 4.12994 + 9.32507I
u = −0.968951 + 0.296225I
a = 0.892006 + 0.785177I
b = −1.34417 + 0.57956I
−0.51273 − 13.28050I 5.34939 + 8.37714I
u = −0.968951 − 0.296225I
a = 0.892006 − 0.785177I
b = −1.34417 − 0.57956I
−0.51273 + 13.28050I 5.34939 − 8.37714I
u = −0.610673 + 0.831038I
a = 0.997321 + 0.562990I
b = −0.208936 + 0.974666I
−5.95506 + 2.12888I −0.79788 − 2.27450I
u = −0.610673 − 0.831038I
a = 0.997321 − 0.562990I
b = −0.208936 − 0.974666I
−5.95506 − 2.12888I −0.79788 + 2.27450I
u = −0.255815 + 0.892885I
a = 0.75843 − 1.65824I
b = 1.032550 + 0.425249I
−1.38618 + 1.10699I 5.88237 − 2.02123I
u = −0.255815 − 0.892885I
a = 0.75843 + 1.65824I
b = 1.032550 − 0.425249I
−1.38618 − 1.10699I 5.88237 + 2.02123I
u = 0.779625 + 0.477176I
a = 0.418708 + 0.094057I
b = −0.177816 + 0.275228I
−3.88720 + 2.56045I 1.25441 − 1.69203I
u = 0.779625 − 0.477176I
a = 0.418708 − 0.094057I
b = −0.177816 − 0.275228I
−3.88720 − 2.56045I 1.25441 + 1.69203I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841780 + 0.356078I
a = −0.174629 − 0.117853I
b = −0.078191 − 1.171910I
−4.49543 − 7.17470I 2.59606 + 7.73482I
u = −0.841780 − 0.356078I
a = −0.174629 + 0.117853I
b = −0.078191 + 1.171910I
−4.49543 + 7.17470I 2.59606 − 7.73482I
u = 0.473196 + 0.770071I
a = −0.369077 − 0.309157I
b = −1.269270 + 0.312391I
3.46740 − 4.69908I 9.55546 + 4.95856I
u = 0.473196 − 0.770071I
a = −0.369077 + 0.309157I
b = −1.269270 − 0.312391I
3.46740 + 4.69908I 9.55546 − 4.95856I
u = 0.043711 + 1.116100I
a = 1.40757 − 0.86097I
b = 0.510011 − 0.672747I
−1.44331 − 1.46172I 0
u = 0.043711 − 1.116100I
a = 1.40757 + 0.86097I
b = 0.510011 + 0.672747I
−1.44331 + 1.46172I 0
u = 0.849843 + 0.794247I
a = 0.364459 − 0.460121I
b = −0.801824 − 0.262652I
−4.28958 + 3.02182I 0
u = 0.849843 − 0.794247I
a = 0.364459 + 0.460121I
b = −0.801824 + 0.262652I
−4.28958 − 3.02182I 0
u = −0.112252 + 1.159760I
a = 2.35715 − 2.72964I
b = 1.032550 − 0.425249I
−1.38618 − 1.10699I 0
u = −0.112252 − 1.159760I
a = 2.35715 + 2.72964I
b = 1.032550 + 0.425249I
−1.38618 + 1.10699I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461020 + 1.082200I
a = 0.422805 − 0.279501I
b = −0.553288 + 0.271190I
−4.79896 + 0.09583I 0
u = 0.461020 − 1.082200I
a = 0.422805 + 0.279501I
b = −0.553288 − 0.271190I
−4.79896 − 0.09583I 0
u = 0.190114 + 1.210590I
a = 0.958702 + 0.424123I
b = 1.53378 − 0.27781I
1.23098 + 1.19841I 0
u = 0.190114 − 1.210590I
a = 0.958702 − 0.424123I
b = 1.53378 + 0.27781I
1.23098 − 1.19841I 0
u = −0.717388 + 0.278970I
a = −1.040930 − 0.324389I
b = 1.30395 − 0.73418I
0.39121 − 4.90989I 9.62064 + 7.63658I
u = −0.717388 − 0.278970I
a = −1.040930 + 0.324389I
b = 1.30395 + 0.73418I
0.39121 + 4.90989I 9.62064 − 7.63658I
u = −0.688281 + 1.026340I
a = −0.157425 + 0.115561I
b = −1.246260 − 0.540840I
−2.68700 + 7.55963I 0
u = −0.688281 − 1.026340I
a = −0.157425 − 0.115561I
b = −1.246260 + 0.540840I
−2.68700 − 7.55963I 0
u = −0.539357 + 0.517650I
a = 0.098498 + 1.185050I
b = −1.269270 + 0.312391I
3.46740 − 4.69908I 9.55546 + 4.95856I
u = −0.539357 − 0.517650I
a = 0.098498 − 1.185050I
b = −1.269270 − 0.312391I
3.46740 + 4.69908I 9.55546 − 4.95856I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.648036 + 0.369371I
a = −2.75583 + 2.43123I
b = 1.029960 + 0.111836I
−1.42704 + 2.41995I −3.15050 + 13.44411I
u = 0.648036 − 0.369371I
a = −2.75583 − 2.43123I
b = 1.029960 − 0.111836I
−1.42704 − 2.41995I −3.15050 − 13.44411I
u = −0.065126 + 1.259270I
a = 1.81529 + 2.04641I
b = 0.792720 + 0.092568I
−2.00607 − 1.43143I 0
u = −0.065126 − 1.259270I
a = 1.81529 − 2.04641I
b = 0.792720 − 0.092568I
−2.00607 + 1.43143I 0
u = 0.278588 + 1.276100I
a = 0.532780 − 0.956263I
b = −0.553288 − 0.271190I
−4.79896 − 0.09583I 0
u = 0.278588 − 1.276100I
a = 0.532780 + 0.956263I
b = −0.553288 + 0.271190I
−4.79896 + 0.09583I 0
u = −0.162713 + 1.297640I
a = −0.99110 − 3.07786I
b = 1.029960 − 0.111836I
−1.42704 − 2.41995I 0
u = −0.162713 − 1.297640I
a = −0.99110 + 3.07786I
b = 1.029960 + 0.111836I
−1.42704 + 2.41995I 0
u = 0.484916 + 0.493659I
a = −0.10085 − 1.86632I
b = 0.792720 − 0.092568I
−2.00607 + 1.43143I 8.72992 − 7.90920I
u = 0.484916 − 0.493659I
a = −0.10085 + 1.86632I
b = 0.792720 + 0.092568I
−2.00607 − 1.43143I 8.72992 + 7.90920I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.229241 + 1.298960I
a = 0.44871 + 2.20418I
b = 1.30395 + 0.73418I
0.39121 + 4.90989I 0
u = 0.229241 − 1.298960I
a = 0.44871 − 2.20418I
b = 1.30395 − 0.73418I
0.39121 − 4.90989I 0
u = −0.091635 + 1.374330I
a = −0.27154 − 1.82640I
b = −0.208936 − 0.974666I
−5.95506 − 2.12888I 0
u = −0.091635 − 1.374330I
a = −0.27154 + 1.82640I
b = −0.208936 + 0.974666I
−5.95506 + 2.12888I 0
u = −0.555876 + 0.230717I
a = −2.15514 + 0.60466I
b = 1.53378 + 0.27781I
1.23098 − 1.19841I 11.97414 + 1.50646I
u = −0.555876 − 0.230717I
a = −2.15514 − 0.60466I
b = 1.53378 − 0.27781I
1.23098 + 1.19841I 11.97414 − 1.50646I
u = −0.149055 + 1.397490I
a = 0.132759 − 0.477500I
b = −0.177816 − 0.275228I
−3.88720 − 2.56045I 0
u = −0.149055 − 1.397490I
a = 0.132759 + 0.477500I
b = −0.177816 + 0.275228I
−3.88720 + 2.56045I 0
u = 0.235520 + 1.390770I
a = −0.66856 + 1.59662I
b = −0.078191 + 1.171910I
−4.49543 + 7.17470I 0
u = 0.235520 − 1.390770I
a = −0.66856 − 1.59662I
b = −0.078191 − 1.171910I
−4.49543 − 7.17470I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.37960 + 1.41324I
a = 0.011937 + 1.072620I
b = −1.023220 + 0.279978I
−1.80983 − 5.18678I 0
u = −0.37960 − 1.41324I
a = 0.011937 − 1.072620I
b = −1.023220 − 0.279978I
−1.80983 + 5.18678I 0
u = −0.21964 + 1.45291I
a = −0.68408 + 1.69107I
b = −1.246260 + 0.540840I
−2.68700 − 7.55963I 0
u = −0.21964 − 1.45291I
a = −0.68408 − 1.69107I
b = −1.246260 − 0.540840I
−2.68700 + 7.55963I 0
u = 0.31770 + 1.43891I
a = −0.29445 − 1.87379I
b = −1.34417 − 0.57956I
−0.51273 + 13.28050I 0
u = 0.31770 − 1.43891I
a = −0.29445 + 1.87379I
b = −1.34417 + 0.57956I
−0.51273 − 13.28050I 0
u = 0.02424 + 1.52420I
a = −0.659012 + 0.360261I
b = −0.801824 + 0.262652I
−4.28958 − 3.02182I 0
u = 0.02424 − 1.52420I
a = −0.659012 − 0.360261I
b = −0.801824 − 0.262652I
−4.28958 + 3.02182I 0
u = −0.148665 + 0.269514I
a = −1.82178 − 1.54448I
b = 0.510011 + 0.672747I
−1.44331 + 1.46172I 7.40911 − 4.12645I
u = −0.148665 − 0.269514I
a = −1.82178 + 1.54448I
b = 0.510011 − 0.672747I
−1.44331 − 1.46172I 7.40911 + 4.12645I
18
III.
I
u
3
= h−9a
4
u−670a
3
u+· · ·−703a +1198, −5a
4
u+9a
3
u+· · ·+7a −1, u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
1
a
3
=
a
0.0124138a
4
u + 0.924138a
3
u + ··· + 0.969655a − 1.65241
a
12
=
u
u
a
5
=
0.0289655a
4
u + 0.489655a
3
u + ··· − 0.404138a + 0.811034
0.131034a
4
u − 1.48966a
3
u + ··· − 2.07586a + 2.26897
a
2
=
−0.184828a
4
u − 0.448276a
3
u + ··· + 0.140690a + 1.42483
−0.00275862a
4
u − 0.627586a
3
u + ··· − 0.571034a + 1.32276
a
10
=
−u
0
a
4
=
0.0124138a
4
u + 0.924138a
3
u + ··· + 1.96966a − 1.65241
0.0124138a
4
u + 0.924138a
3
u + ··· + 0.969655a − 1.65241
a
1
=
−0.194483a
4
u − 0.544828a
3
u + ··· + 0.542069a + 0.354483
−0.194483a
4
u − 0.544828a
3
u + ··· + 0.542069a + 0.354483
a
9
=
0.293793a
4
u − 2.26207a
3
u + ··· − 0.584828a + 1.82621
0.293793a
4
u − 2.26207a
3
u + ··· − 0.584828a + 2.82621
a
8
=
0.293793a
4
u − 2.26207a
3
u + ··· − 0.584828a + 2.82621
0.293793a
4
u − 2.26207a
3
u + ··· − 0.584828a + 3.82621
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
28
725
a
4
u +
104
725
a
4
−
172
145
a
3
u −
24
145
a
3
−
48
725
a
2
u −
3136
725
a
2
+
3992
725
au −
1156
725
a +
2308
725
u +
3856
725
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
2
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
3
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
4
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(u
2
+ 1)
5
c
9
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
2
, c
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
3
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
4
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y + 1)
10
c
9
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.927855 − 0.361438I
b = −1.41878 − 0.21917I
2.58269 + 4.40083I 4.74431 − 3.49859I
u = 1.000000I
a = 0.820551 + 0.331455I
b = 0.309916 − 0.549911I
−2.96077 − 1.53058I 0.51511 + 4.43065I
u = 1.000000I
a = 0.0902877 + 0.0768928I
b = −1.41878 + 0.21917I
2.58269 − 4.40083I 4.74431 + 3.49859I
u = 1.000000I
a = 1.79928 + 1.43128I
b = 0.309916 + 0.549911I
−2.96077 + 1.53058I 0.51511 − 4.43065I
u = 1.000000I
a = 2.21774 + 3.52181I
b = 1.21774
−0.888787 1.48114 + 0.I
u = − 1.000000I
a = −0.927855 + 0.361438I
b = −1.41878 + 0.21917I
2.58269 − 4.40083I 4.74431 + 3.49859I
u = − 1.000000I
a = 0.820551 − 0.331455I
b = 0.309916 + 0.549911I
−2.96077 + 1.53058I 0.51511 − 4.43065I
u = − 1.000000I
a = 0.0902877 − 0.0768928I
b = −1.41878 − 0.21917I
2.58269 + 4.40083I 4.74431 − 3.49859I
u = − 1.000000I
a = 1.79928 − 1.43128I
b = 0.309916 − 0.549911I
−2.96077 − 1.53058I 0.51511 + 4.43065I
u = − 1.000000I
a = 2.21774 − 3.52181I
b = 1.21774
−0.888787 1.48114 + 0.I
22
IV. I
u
4
= hb − 1, 4a + 3, u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
−1
a
7
=
1
−1
a
3
=
−0.75
1
a
12
=
−1
−1
a
5
=
0.25
1
a
2
=
−1
0
a
10
=
1
−2
a
4
=
−0.25
0
a
1
=
−1
0
a
9
=
−1
−2
a
8
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 26.0625
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
c
2
, c
6
, c
7
c
8
u + 1
c
3
, c
4
2(2u − 1)
c
5
, c
10
, c
11
c
12
u − 1
c
9
u + 2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
c
2
, c
5
, c
6
c
7
, c
8
, c
10
c
11
, c
12
y −1
c
3
, c
4
4(4y −1)
c
9
y −4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.750000
b = 1.00000
3.28987 26.0630
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
5
+ u
4
+ ··· + u + 1)
2
(u
30
− 5u
29
+ ··· − u + 1)
2
· (u
42
− 7u
41
+ ··· + 44u + 32)
c
2
(u + 1)(u
5
− u
4
+ ··· + u + 1)
2
(u
30
+ u
29
+ ··· + 5u + 1)
2
· (u
42
+ 2u
41
+ ··· + 175u − 16)
c
3
4(2u − 1)(u
10
+ 5u
8
+ ··· − u
2
+ 1)(u
30
− u
29
+ ··· + 11u + 1)
2
· (2u
42
+ 7u
41
+ ··· + 62575u − 9794)
c
4
4(2u − 1)(u
10
− 3u
8
+ ··· − u
2
+ 1)(u
30
− 3u
29
+ ··· − 9u + 1)
2
· (2u
42
+ 19u
41
+ ··· + 6823u + 542)
c
5
(u − 1)(u
5
+ u
4
+ ··· + u − 1)
2
(u
30
+ u
29
+ ··· + 5u + 1)
2
· (u
42
+ 2u
41
+ ··· + 175u − 16)
c
6
, c
7
, c
8
(u + 1)(u
2
+ 1)
5
(u
42
− u
41
+ ··· − 5u + 1)(u
60
− u
59
+ ··· − 96u + 17)
c
9
(u + 2)(u
10
+ u
8
+ ··· + 3u
2
+ 1)(u
30
+ 3u
29
+ ··· + u + 1)
2
· (u
42
− 11u
41
+ ··· + 12u − 4)
c
10
, c
11
, c
12
(u − 1)(u
2
+ 1)
5
(u
42
− u
41
+ ··· − 5u + 1)(u
60
− u
59
+ ··· − 96u + 17)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
5
+ 3y
4
+ ··· − y −1)
2
(y
30
− 3y
29
+ ··· − 5y + 1)
2
· (y
42
+ 3y
41
+ ··· − 8784y + 1024)
c
2
, c
5
(y −1)(y
5
− 5y
4
+ ··· − y −1)
2
(y
30
− 19y
29
+ ··· − 5y + 1)
2
· (y
42
− 30y
41
+ ··· − 15201y + 256)
c
3
16(4y −1)(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
· (y
30
− 23y
29
+ ··· − 9y + 1)
2
· (4y
42
− 101y
41
+ ··· + 632683387y + 95922436)
c
4
16(4y −1)(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
· (y
30
− 27y
29
+ ··· + 11y + 1)
2
· (4y
42
− 181y
41
+ ··· − 8215501y + 293764)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y −1)(y + 1)
10
(y
42
+ 45y
41
+ ··· + 11y + 1)
· (y
60
+ 47y
59
+ ··· + 4928y + 289)
c
9
(y −4)(y
5
+ y
4
+ ··· + 3y + 1)
2
(y
30
+ 5y
29
+ ··· + 3y + 1)
2
· (y
42
+ 3y
41
+ ··· + 40y + 16)
28
