12n
0029
(K12n
0029
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 9 5 11 12 6 7 10
Solving Sequence
5,7 8,11
9 12 4 6 3 2 1 10
c
7
c
8
c
11
c
4
c
6
c
3
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.45830 × 10
282
u
73
− 3.06169 × 10
282
u
72
+ ··· + 2.31115 × 10
285
b + 2.73476 × 10
285
,
1.92674 × 10
282
u
73
− 5.93184 × 10
282
u
72
+ ··· + 1.84892 × 10
285
a − 1.31672 × 10
286
,
u
74
− 2u
73
+ ··· + 3072u + 1024i
I
u
2
= hu
4
− 2u
3
− u
2
+ b + 3u, −3u
4
+ 3u
3
+ 7u
2
+ a − 5u − 4, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, 1728v
9
+ 4936v
8
+ 9872v
7
− 12908v
6
− 24680v
5
+ 34552v
4
+ 91527v
3
− 4936v
2
+ 3335b + 613,
v
10
+ 3v
9
+ 6v
8
− 7v
7
− 16v
6
+ 19v
5
+ 58v
4
+ 2v
3
− 7v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 89 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
= h1.46 × 10
282
u
73
− 3.06 × 10
282
u
72
+ · · · + 2.31 × 10
285
b + 2.73 ×
10
285
, 1.93 × 10
282
u
73
− 5.93 × 10
282
u
72
+ · · · + 1.85 × 10
285
a − 1.32 ×
10
286
, u
74
− 2u
73
+ · · · + 3072u + 1024i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−0.00104209u
73
+ 0.00320827u
72
+ ··· + 4.15244u + 7.12158
−0.000630984u
73
+ 0.00132475u
72
+ ··· − 3.28645u − 1.18329
a
9
=
0.000166407u
73
− 0.0000584423u
72
+ ··· − 2.97519u − 1.23275
−0.000372877u
73
+ 0.000687987u
72
+ ··· − 1.67649u − 0.643683
a
12
=
−0.00167307u
73
+ 0.00453301u
72
+ ··· + 0.865989u + 5.93830
−0.000630984u
73
+ 0.00132475u
72
+ ··· − 3.28645u − 1.18329
a
4
=
u
u
3
+ u
a
6
=
−0.0000529417u
73
+ 0.000274782u
72
+ ··· + 4.64722u + 1.77074
−0.000269983u
73
+ 0.000677572u
72
+ ··· − 0.295371u − 0.271861
a
3
=
0.000525755u
73
− 0.00116278u
72
+ ··· + 1.81742u − 0.757111
−0.0000354351u
73
+ 0.000122315u
72
+ ··· + 0.573348u + 0.133403
a
2
=
0.000525755u
73
− 0.00116278u
72
+ ··· + 1.81742u − 0.757111
−0.0000344362u
73
+ 0.0000957799u
72
+ ··· + 0.376807u + 0.247347
a
1
=
−0.000150277u
73
+ 0.000195066u
72
+ ··· − 4.47795u − 1.86965
−0.000203219u
73
+ 0.000469847u
72
+ ··· + 0.169272u − 0.0989097
a
10
=
−0.00137360u
73
+ 0.00403821u
72
+ ··· − 1.25774u + 5.00923
−0.000533686u
73
+ 0.00107499u
72
+ ··· − 2.78713u − 1.04233
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0115164u
73
+ 0.0143583u
72
+ ··· − 79.5128u − 35.2982
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 23u
73
+ ··· − 168u + 1
c
2
, c
5
u
74
+ 7u
73
+ ··· + 10u + 1
c
3
u
74
− 7u
73
+ ··· + 23935148u + 1174793
c
4
, c
7
u
74
− 2u
73
+ ··· + 3072u + 1024
c
6
u
74
− 4u
73
+ ··· + 3u − 1
c
8
u
74
+ 11u
73
+ ··· + 600u
2
+ 32
c
9
, c
12
u
74
− 8u
73
+ ··· − 83u − 1
c
10
u
74
+ 2u
73
+ ··· + 140788u − 6632
c
11
u
74
− 4u
73
+ ··· + 18563u + 7979
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 63y
73
+ ··· − 33884y + 1
c
2
, c
5
y
74
+ 23y
73
+ ··· − 168y + 1
c
3
y
74
+ 103y
73
+ ··· − 195612233228368y + 1380138592849
c
4
, c
7
y
74
+ 50y
73
+ ··· + 5242880y + 1048576
c
6
y
74
− 20y
73
+ ··· + y + 1
c
8
y
74
− 27y
73
+ ··· + 38400y + 1024
c
9
, c
12
y
74
− 40y
73
+ ··· − 2497y + 1
c
10
y
74
+ 78y
73
+ ··· − 8817552656y + 43983424
c
11
y
74
+ 46y
73
+ ··· − 1411728345y + 63664441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.087690 + 1.069920I
a = −1.70851 + 0.71322I
b = 0.704260 − 0.483971I
0.97521 − 4.62256I 0
u = 0.087690 − 1.069920I
a = −1.70851 − 0.71322I
b = 0.704260 + 0.483971I
0.97521 + 4.62256I 0
u = 0.384595 + 0.751827I
a = 0.59893 + 1.37606I
b = −0.298551 + 0.845553I
−3.42601 − 3.36523I −11.9863 + 8.0764I
u = 0.384595 − 0.751827I
a = 0.59893 − 1.37606I
b = −0.298551 − 0.845553I
−3.42601 + 3.36523I −11.9863 − 8.0764I
u = 0.495224 + 0.592497I
a = 2.24773 + 1.14650I
b = 0.234622 + 0.523186I
−3.94950 − 0.19450I −14.2244 + 0.5338I
u = 0.495224 − 0.592497I
a = 2.24773 − 1.14650I
b = 0.234622 − 0.523186I
−3.94950 + 0.19450I −14.2244 − 0.5338I
u = 1.247790 + 0.119522I
a = 0.295580 − 0.114576I
b = −0.758529 + 0.268504I
3.57080 − 3.55900I 0
u = 1.247790 − 0.119522I
a = 0.295580 + 0.114576I
b = −0.758529 − 0.268504I
3.57080 + 3.55900I 0
u = −0.590376 + 1.132720I
a = −0.567082 + 0.568941I
b = 0.416950 + 0.100990I
−0.18048 + 2.67430I 0
u = −0.590376 − 1.132720I
a = −0.567082 − 0.568941I
b = 0.416950 − 0.100990I
−0.18048 − 2.67430I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.235680 + 0.346795I
a = 0.250077 + 0.159968I
b = −0.656348 − 0.079553I
3.17540 − 2.27063I 0
u = −1.235680 − 0.346795I
a = 0.250077 − 0.159968I
b = −0.656348 + 0.079553I
3.17540 + 2.27063I 0
u = 0.100478 + 1.284530I
a = 1.53887 + 0.10009I
b = −0.355439 + 0.084862I
1.01094 − 2.94591I 0
u = 0.100478 − 1.284530I
a = 1.53887 − 0.10009I
b = −0.355439 − 0.084862I
1.01094 + 2.94591I 0
u = 0.228131 + 1.295120I
a = −1.027190 − 0.601335I
b = 0.757691 + 0.160885I
4.23425 + 0.54410I 0
u = 0.228131 − 1.295120I
a = −1.027190 + 0.601335I
b = 0.757691 − 0.160885I
4.23425 − 0.54410I 0
u = 0.655112 + 0.173687I
a = 2.35031 + 3.40118I
b = 0.424294 + 0.991928I
−1.25518 + 3.58366I −11.16812 − 4.57292I
u = 0.655112 − 0.173687I
a = 2.35031 − 3.40118I
b = 0.424294 − 0.991928I
−1.25518 − 3.58366I −11.16812 + 4.57292I
u = 0.501730 + 0.448793I
a = 0.554379 − 0.053202I
b = −0.523151 − 0.840620I
−0.76340 + 2.05732I −6.61172 − 3.28073I
u = 0.501730 − 0.448793I
a = 0.554379 + 0.053202I
b = −0.523151 + 0.840620I
−0.76340 − 2.05732I −6.61172 + 3.28073I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429078 + 0.495620I
a = 0.756242 + 0.411909I
b = 0.048182 − 0.906974I
−0.75534 + 1.25758I −6.16688 − 4.20297I
u = −0.429078 − 0.495620I
a = 0.756242 − 0.411909I
b = 0.048182 + 0.906974I
−0.75534 − 1.25758I −6.16688 + 4.20297I
u = −0.369003 + 0.540409I
a = −7.82001 − 3.97910I
b = −0.53917 + 3.82168I
−1.96434 + 1.46942I 69.4609 + 82.1819I
u = −0.369003 − 0.540409I
a = −7.82001 + 3.97910I
b = −0.53917 − 3.82168I
−1.96434 − 1.46942I 69.4609 − 82.1819I
u = −0.628002 + 0.177531I
a = 2.95922 − 3.34855I
b = 0.457443 − 1.236300I
−0.94329 + 1.13464I −11.14223 − 5.11528I
u = −0.628002 − 0.177531I
a = 2.95922 + 3.34855I
b = 0.457443 + 1.236300I
−0.94329 − 1.13464I −11.14223 + 5.11528I
u = −0.142745 + 1.346550I
a = 0.272109 − 0.532528I
b = −0.260302 − 1.220450I
3.14985 + 1.37670I 0
u = −0.142745 − 1.346550I
a = 0.272109 + 0.532528I
b = −0.260302 + 1.220450I
3.14985 − 1.37670I 0
u = 0.320215 + 1.351930I
a = 0.198192 + 0.598736I
b = −0.161270 + 1.198730I
2.76643 − 7.39057I 0
u = 0.320215 − 1.351930I
a = 0.198192 − 0.598736I
b = −0.161270 − 1.198730I
2.76643 + 7.39057I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173717 + 0.574494I
a = 1.239130 + 0.100705I
b = −0.321576 − 1.059120I
−0.71671 + 1.37236I −4.04860 − 4.25236I
u = −0.173717 − 0.574494I
a = 1.239130 − 0.100705I
b = −0.321576 + 1.059120I
−0.71671 − 1.37236I −4.04860 + 4.25236I
u = −0.298851 + 0.519319I
a = 1.328640 + 0.298136I
b = −0.182893 − 0.326086I
−0.31180 + 1.54577I −2.35841 − 4.98495I
u = −0.298851 − 0.519319I
a = 1.328640 − 0.298136I
b = −0.182893 + 0.326086I
−0.31180 − 1.54577I −2.35841 + 4.98495I
u = 0.490220 + 0.320949I
a = 0.0858483 + 0.0914575I
b = 0.568197 + 1.214540I
−6.11124 + 6.05756I −13.16929 + 2.49659I
u = 0.490220 − 0.320949I
a = 0.0858483 − 0.0914575I
b = 0.568197 − 1.214540I
−6.11124 − 6.05756I −13.16929 − 2.49659I
u = −0.425333 + 0.359403I
a = 0.0853519 + 0.0910101I
b = 0.371695 + 1.137080I
−5.95413 + 2.77149I −11.1970 − 11.7984I
u = −0.425333 − 0.359403I
a = 0.0853519 − 0.0910101I
b = 0.371695 − 1.137080I
−5.95413 − 2.77149I −11.1970 + 11.7984I
u = −1.44330
a = 0.133015
b = 0.809332
−3.60099 0
u = 0.01717 + 1.45367I
a = −0.539494 + 0.887846I
b = 0.66032 − 2.68740I
4.88888 + 2.03616I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01717 − 1.45367I
a = −0.539494 − 0.887846I
b = 0.66032 + 2.68740I
4.88888 − 2.03616I 0
u = −0.20391 + 1.44776I
a = −0.773494 − 0.847749I
b = 0.54517 + 2.88900I
4.71109 + 4.13291I 0
u = −0.20391 − 1.44776I
a = −0.773494 + 0.847749I
b = 0.54517 − 2.88900I
4.71109 − 4.13291I 0
u = 0.44904 + 1.39545I
a = 1.389400 − 0.053483I
b = −1.19431 + 1.06464I
−1.87183 − 10.09290I 0
u = 0.44904 − 1.39545I
a = 1.389400 + 0.053483I
b = −1.19431 − 1.06464I
−1.87183 + 10.09290I 0
u = 0.08788 + 1.46777I
a = 1.035950 − 0.323500I
b = −1.179080 + 0.604061I
−0.83764 − 1.21344I 0
u = 0.08788 − 1.46777I
a = 1.035950 + 0.323500I
b = −1.179080 − 0.604061I
−0.83764 + 1.21344I 0
u = 1.48809 + 0.13110I
a = 0.0912489 − 0.0358039I
b = 0.598953 − 0.223005I
−7.41606 − 4.57419I 0
u = 1.48809 − 0.13110I
a = 0.0912489 + 0.0358039I
b = 0.598953 + 0.223005I
−7.41606 + 4.57419I 0
u = 0.125495 + 0.432831I
a = 7.30187 + 2.79699I
b = −1.075840 + 0.578988I
−2.18804 + 1.82733I 11.01430 − 3.60905I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.125495 − 0.432831I
a = 7.30187 − 2.79699I
b = −1.075840 − 0.578988I
−2.18804 − 1.82733I 11.01430 + 3.60905I
u = 1.52778 + 0.35064I
a = 0.095478 + 0.108395I
b = 1.31875 + 0.93719I
1.67555 + 9.13934I 0
u = 1.52778 − 0.35064I
a = 0.095478 − 0.108395I
b = 1.31875 − 0.93719I
1.67555 − 9.13934I 0
u = −1.55967 + 0.19709I
a = 0.104540 − 0.110896I
b = 1.33678 − 0.74411I
2.10183 − 2.80934I 0
u = −1.55967 − 0.19709I
a = 0.104540 + 0.110896I
b = 1.33678 + 0.74411I
2.10183 + 2.80934I 0
u = −0.27655 + 1.57965I
a = 1.126550 + 0.143036I
b = −1.37108 − 0.84338I
2.84481 + 6.06997I 0
u = −0.27655 − 1.57965I
a = 1.126550 − 0.143036I
b = −1.37108 + 0.84338I
2.84481 − 6.06997I 0
u = −0.81564 + 1.38136I
a = −0.753914 + 0.369227I
b = 0.663812 + 0.540105I
6.17331 + 9.63827I 0
u = −0.81564 − 1.38136I
a = −0.753914 − 0.369227I
b = 0.663812 − 0.540105I
6.17331 − 9.63827I 0
u = 0.72899 + 1.43535I
a = −0.757398 − 0.390640I
b = 0.743568 − 0.424934I
7.41718 − 3.39847I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.72899 − 1.43535I
a = −0.757398 + 0.390640I
b = 0.743568 + 0.424934I
7.41718 + 3.39847I 0
u = 0.53611 + 1.52849I
a = −1.274840 − 0.153132I
b = 1.123730 − 0.679779I
8.83947 − 10.02070I 0
u = 0.53611 − 1.52849I
a = −1.274840 + 0.153132I
b = 1.123730 + 0.679779I
8.83947 + 10.02070I 0
u = −0.39620 + 1.58131I
a = −1.232710 + 0.026127I
b = 1.138660 + 0.572588I
9.56303 + 3.64207I 0
u = −0.39620 − 1.58131I
a = −1.232710 − 0.026127I
b = 1.138660 − 0.572588I
9.56303 − 3.64207I 0
u = 0.81404 + 1.47762I
a = 1.239280 + 0.352565I
b = −1.30347 + 1.39965I
5.3004 − 17.3091I 0
u = 0.81404 − 1.47762I
a = 1.239280 − 0.352565I
b = −1.30347 − 1.39965I
5.3004 + 17.3091I 0
u = −0.73726 + 1.55967I
a = 1.195100 − 0.255132I
b = −1.37771 − 1.32852I
6.50731 + 10.89880I 0
u = −0.73726 − 1.55967I
a = 1.195100 + 0.255132I
b = −1.37771 + 1.32852I
6.50731 − 10.89880I 0
u = −0.272195
a = 4.54371
b = 0.970995
−2.30896 −2.48640
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.45730 + 1.67049I
a = 0.889473 − 0.300191I
b = −1.71368 − 0.14443I
8.61435 + 4.58115I 0
u = −0.45730 − 1.67049I
a = 0.889473 + 0.300191I
b = −1.71368 + 0.14443I
8.61435 − 4.58115I 0
u = 0.31130 + 1.74570I
a = 0.886783 + 0.250968I
b = −1.73082 − 0.07312I
9.18515 + 2.01287I 0
u = 0.31130 − 1.74570I
a = 0.886783 − 0.250968I
b = −1.73082 + 0.07312I
9.18515 − 2.01287I 0
12
II. I
u
2
=
hu
4
−2u
3
−u
2
+b+3u, −3u
4
+3u
3
+7u
2
+a−5u−4, u
5
−u
4
−2u
3
+u
2
+u+1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
3u
4
− 3u
3
− 7u
2
+ 5u + 4
−u
4
+ 2u
3
+ u
2
− 3u
a
9
=
1
u
2
a
12
=
2u
4
− u
3
− 6u
2
+ 2u + 4
−u
4
+ 2u
3
+ u
2
− 3u
a
4
=
u
u
3
+ u
a
6
=
−u
2
+ 1
−u
4
a
3
=
−u
3
+ 2u
−u
4
− u
3
+ u
2
+ 2u + 1
a
2
=
−u
3
+ 2u
−2u
4
− u
3
+ 2u
2
+ 3u + 2
a
1
=
−1
−u
2
a
10
=
2u
4
− u
3
− 6u
2
+ 2u + 5
−u
4
+ 2u
3
+ 2u
2
− 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24u
4
+ 29u
3
+ 27u
2
− 44u − 1
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
u
5
c
9
(u − 1)
5
c
10
, c
11
u
5
+ u
4
+ 3u
3
− 8u
2
+ 5u − 1
c
12
(u + 1)
5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
4
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
8
y
5
c
9
, c
12
(y −1)
5
c
10
, c
11
y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.454765
b = −0.674363
−4.04602 −12.5230
u = −0.309916 + 0.549911I
a = 2.91994 + 5.58105I
b = 1.29977 − 2.14694I
−1.97403 + 1.53058I 16.1214 − 37.0026I
u = −0.309916 − 0.549911I
a = 2.91994 − 5.58105I
b = 1.29977 + 2.14694I
−1.97403 − 1.53058I 16.1214 + 37.0026I
u = 1.41878 + 0.21917I
a = −0.192553 + 0.135455I
b = −0.462589 + 0.146410I
−7.51750 − 4.40083I −16.8598 − 13.4304I
u = 1.41878 − 0.21917I
a = −0.192553 − 0.135455I
b = −0.462589 − 0.146410I
−7.51750 + 4.40083I −16.8598 + 13.4304I
16
III. I
v
1
= ha, 1728v
9
+ 4936v
8
+ · · · + 3335b + 613, v
10
+ 3v
9
+ · · · + v + 1i
(i) Arc colorings
a
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−0.518141v
9
− 1.48006v
8
+ ··· + 1.48006v
2
− 0.183808
a
9
=
1
0.462969v
9
+ 1.33373v
8
+ ··· − 1.33373v
2
+ 1.81379
a
12
=
−0.518141v
9
− 1.48006v
8
+ ··· + 1.48006v
2
− 0.183808
−0.518141v
9
− 1.48006v
8
+ ··· + 1.48006v
2
− 0.183808
a
4
=
v
0
a
6
=
−0.462969v
9
− 1.33373v
8
+ ··· + 1.33373v
2
− 0.813793
−1.14783v
9
− 3.29565v
8
+ ··· + 3.29565v
2
− 1.75652
a
3
=
0.0740630v
9
+ 0.148126v
8
+ ··· + 3.77811v + 0.424888
0.147826v
9
+ 0.295652v
8
+ ··· + 7v + 0.756522
a
2
=
−0.0737631v
9
− 0.277961v
8
+ ··· + 3.77811v + 0.277061
0.147826v
9
+ 0.295652v
8
+ ··· + 7v + 0.756522
a
1
=
0.462969v
9
+ 1.33373v
8
+ ··· − 1.33373v
2
+ 0.813793
1.14783v
9
+ 3.29565v
8
+ ··· − 3.29565v
2
+ 1.75652
a
10
=
0.684858v
9
+ 1.96192v
8
+ ··· − 1.96192v
2
+ 0.942729
1.14783v
9
+ 3.29565v
8
+ ··· − 3.29565v
2
+ 1.75652
(ii) Obstruction class = 1
(iii) Cusp Shapes =
10239
3335
v
9
+
24678
3335
v
8
+
44281
3335
v
7
−
105719
3335
v
6
−
23431
667
v
5
+
281061
3335
v
4
+
471061
3335
v
3
−
304673
3335
v
2
−
263
23
v +
12334
3335
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
10
, c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
9
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.38814 + 0.78973I
a = 0
b = −0.339110 + 0.822375I
−0.32910 − 3.56046I −3.01153 + 6.03927I
v = −1.38814 − 0.78973I
a = 0
b = −0.339110 − 0.822375I
−0.32910 + 3.56046I −3.01153 − 6.03927I
v = 1.37799 + 0.80730I
a = 0
b = −0.339110 + 0.822375I
−0.329100 + 0.499304I −3.07628 + 2.84945I
v = 1.37799 − 0.80730I
a = 0
b = −0.339110 − 0.822375I
−0.329100 − 0.499304I −3.07628 − 2.84945I
v = 0.294694 + 0.220725I
a = 0
b = 0.455697 − 1.200150I
−5.87256 − 2.37095I −6.63163 − 6.91428I
v = 0.294694 − 0.220725I
a = 0
b = 0.455697 + 1.200150I
−5.87256 + 2.37095I −6.63163 + 6.91428I
v = −0.338500 + 0.144851I
a = 0
b = 0.455697 − 1.200150I
−5.87256 − 6.43072I −3.55752 + 12.20067I
v = −0.338500 − 0.144851I
a = 0
b = 0.455697 + 1.200150I
−5.87256 + 6.43072I −3.55752 − 12.20067I
v = −1.44605 + 2.50463I
a = 0
b = 0.766826
−2.40108 + 2.02988I −9.7230 − 10.6042I
v = −1.44605 − 2.50463I
a = 0
b = 0.766826
−2.40108 − 2.02988I −9.7230 + 10.6042I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
74
+ 23u
73
+ ··· − 168u + 1)
c
2
((u
2
+ u + 1)
5
)(u
5
− u
4
+ ··· + u − 1)(u
74
+ 7u
73
+ ··· + 10u + 1)
c
3
(u
2
− u + 1)
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
74
− 7u
73
+ ··· + 23935148u + 1174793)
c
4
u
10
(u
5
+ u
4
+ ··· + u − 1)(u
74
− 2u
73
+ ··· + 3072u + 1024)
c
5
((u
2
− u + 1)
5
)(u
5
+ u
4
+ ··· + u + 1)(u
74
+ 7u
73
+ ··· + 10u + 1)
c
6
(u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1)(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
74
− 4u
73
+ ··· + 3u − 1)
c
7
u
10
(u
5
− u
4
+ ··· + u + 1)(u
74
− 2u
73
+ ··· + 3072u + 1024)
c
8
u
5
(u
5
− u
4
+ ··· + u − 1)
2
(u
74
+ 11u
73
+ ··· + 600u
2
+ 32)
c
9
((u − 1)
5
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
74
− 8u
73
+ ··· − 83u − 1)
c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
(u
5
+ u
4
+ 3u
3
− 8u
2
+ 5u − 1)
· (u
74
+ 2u
73
+ ··· + 140788u − 6632)
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
(u
5
+ u
4
+ 3u
3
− 8u
2
+ 5u − 1)
· (u
74
− 4u
73
+ ··· + 18563u + 7979)
c
12
((u + 1)
5
)(u
5
− u
4
+ ··· + u + 1)
2
(u
74
− 8u
73
+ ··· − 83u − 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
74
+ 63y
73
+ ··· − 33884y + 1)
c
2
, c
5
(y
2
+ y + 1)
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
· (y
74
+ 23y
73
+ ··· − 168y + 1)
c
3
(y
2
+ y + 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
74
+ 103y
73
+ ··· − 195612233228368y + 1380138592849)
c
4
, c
7
y
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
74
+ 50y
73
+ ··· + 5242880y + 1048576)
c
6
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
74
− 20y
73
+ ··· + y + 1)
c
8
y
5
(y
5
+ 3y
4
+ ··· − y − 1)
2
(y
74
− 27y
73
+ ··· + 38400y + 1024)
c
9
, c
12
(y − 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
74
− 40y
73
+ ··· − 2497y + 1)
c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
(y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y − 1)
· (y
74
+ 78y
73
+ ··· − 8817552656y + 43983424)
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
(y
5
+ 5y
4
+ 35y
3
− 32y
2
+ 9y − 1)
· (y
74
+ 46y
73
+ ··· − 1411728345y + 63664441)
22
