12n
0125
(K12n
0125
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 3 10 12 5 6 9 11
Solving Sequence
8,10 3,7
4 6 11 5 2 1 9 12
c
7
c
3
c
6
c
10
c
5
c
2
c
1
c
9
c
11
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.24906 × 10
251
u
61
− 2.63379 × 10
252
u
60
+ ··· + 3.44441 × 10
254
b + 2.69575 × 10
254
,
1.32614 × 10
254
u
61
+ 8.14465 × 10
254
u
60
+ ··· + 2.75553 × 10
255
a + 1.08450 × 10
257
,
u
62
+ 6u
61
+ ··· + 1248u + 64i
I
u
2
= h−u
3
− u
2
+ b − u, −u
3
+ a + 2, u
4
+ u
2
− u + 1i
I
u
3
= h2u
5
+ u
4
+ 3u
3
+ 2u
2
+ b + 2u + 2, −2u
5
− 4u
3
− u
2
+ a − 3u − 2, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
v
1
= ha, 186v
5
+ 1767v
4
+ 16759v
3
+ 279v
2
+ 385b + 93v + 306, v
6
+ 10v
5
+ 95v
4
+ 48v
3
+ 15v
2
+ 5v + 1i
* 4 irreducible components of dim
C
= 0, with total 78 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−5.25 × 10
251
u
61
− 2.63 × 10
252
u
60
+ · · · + 3.44 × 10
254
b + 2.70 ×
10
254
, 1.33 × 10
254
u
61
+ 8.14 × 10
254
u
60
+ · · · + 2.76 × 10
255
a + 1.08 ×
10
257
, u
62
+ 6u
61
+ · · · + 1248u + 64i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
3
=
−0.0481264u
61
− 0.295575u
60
+ ··· − 637.661u − 39.3574
0.00152394u
61
+ 0.00764656u
60
+ ··· − 7.07240u − 0.782645
a
7
=
1
−u
2
a
4
=
−0.0507184u
61
− 0.309962u
60
+ ··· − 642.175u − 39.0110
0.00177774u
61
+ 0.00929252u
60
+ ··· − 5.78492u − 0.708113
a
6
=
−0.0290606u
61
− 0.178730u
60
+ ··· − 379.788u − 22.2184
0.000355637u
61
+ 0.000276515u
60
+ ··· − 9.59505u − 0.781127
a
11
=
0.165545u
61
+ 0.979872u
60
+ ··· + 380.906u − 1.53739
0.00433759u
61
+ 0.0238765u
60
+ ··· + 4.60076u + 0.0296773
a
5
=
−0.0294163u
61
− 0.179007u
60
+ ··· − 370.193u − 21.4373
0.000355637u
61
+ 0.000276515u
60
+ ··· − 9.59505u − 0.781127
a
2
=
−0.0294071u
61
− 0.179875u
60
+ ··· − 373.738u − 23.7994
−0.000269202u
61
− 0.00331814u
60
+ ··· − 10.7470u − 0.840234
a
1
=
−0.00835458u
61
− 0.0484189u
60
+ ··· − 50.9506u − 3.17945
−u
2
a
9
=
0.160433u
61
+ 0.951245u
60
+ ··· + 378.382u − 1.35204
0.000774875u
61
+ 0.00475004u
60
+ ··· − 0.0771139u − 0.215021
a
12
=
0.0505800u
61
+ 0.275509u
60
+ ··· − 864.856u − 57.5492
0.00229093u
61
+ 0.0128560u
60
+ ··· − 5.13956u − 0.334034
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.134110u
61
− 0.834494u
60
+ ··· − 2032.73u − 106.916
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 71u
61
+ ··· + 267u + 1
c
2
, c
4
u
62
− 13u
61
+ ··· + 15u − 1
c
3
, c
6
u
62
+ 3u
61
+ ··· − 8192u − 1024
c
5
u
62
+ 4u
61
+ ··· − 10u
2
+ 1
c
7
u
62
− 6u
61
+ ··· − 1248u + 64
c
8
, c
11
u
62
− 5u
61
+ ··· + 113u + 1
c
9
u
62
+ 44u
60
+ ··· + 9664u + 824
c
10
u
62
+ 4u
61
+ ··· − 3025807u + 537503
c
12
u
62
− 21u
61
+ ··· + 12769u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
− 147y
61
+ ··· − 20183y + 1
c
2
, c
4
y
62
− 71y
61
+ ··· − 267y + 1
c
3
, c
6
y
62
− 57y
61
+ ··· + 9961472y + 1048576
c
5
y
62
− 4y
61
+ ··· − 20y + 1
c
7
y
62
− 30y
61
+ ··· − 185344y + 4096
c
8
, c
11
y
62
+ 21y
61
+ ··· − 12769y + 1
c
9
y
62
+ 88y
61
+ ··· + 13013520y + 678976
c
10
y
62
+ 16y
61
+ ··· − 11200434939731y + 288909475009
c
12
y
62
+ 45y
61
+ ··· − 163345321y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.966330
a = 2.06084
b = −0.132404
−10.3258 −5.46580
u = 0.225473 + 1.012430I
a = 0.68800 − 2.63426I
b = −0.10147 − 2.38732I
−2.91907 − 1.90864I −12.3927 + 9.8412I
u = 0.225473 − 1.012430I
a = 0.68800 + 2.63426I
b = −0.10147 + 2.38732I
−2.91907 + 1.90864I −12.3927 − 9.8412I
u = 0.906197 + 0.566629I
a = 0.898820 − 1.059170I
b = −0.080489 − 0.151302I
−6.85055 − 2.44704I 0
u = 0.906197 − 0.566629I
a = 0.898820 + 1.059170I
b = −0.080489 + 0.151302I
−6.85055 + 2.44704I 0
u = 0.630967 + 0.873245I
a = −0.0480953 + 0.0962373I
b = 0.066678 − 0.565097I
−0.54827 − 2.57263I 0
u = 0.630967 − 0.873245I
a = −0.0480953 − 0.0962373I
b = 0.066678 + 0.565097I
−0.54827 + 2.57263I 0
u = −0.428788 + 0.808171I
a = 0.166658 + 0.166436I
b = 0.144316 + 0.950356I
3.58947 + 0.62301I 3.36345 − 2.22600I
u = −0.428788 − 0.808171I
a = 0.166658 − 0.166436I
b = 0.144316 − 0.950356I
3.58947 − 0.62301I 3.36345 + 2.22600I
u = 0.175720 + 0.877651I
a = −1.87346 − 0.71678I
b = 0.1068970 − 0.0427277I
−9.63287 + 2.57588I −1.03891 + 4.65048I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175720 − 0.877651I
a = −1.87346 + 0.71678I
b = 0.1068970 + 0.0427277I
−9.63287 − 2.57588I −1.03891 − 4.65048I
u = −0.613756 + 1.022410I
a = −0.0631222 + 0.0157113I
b = −0.017254 + 0.535087I
1.46847 + 7.47551I 0
u = −0.613756 − 1.022410I
a = −0.0631222 − 0.0157113I
b = −0.017254 − 0.535087I
1.46847 − 7.47551I 0
u = 1.148340 + 0.333874I
a = 1.27542 + 0.77535I
b = −0.26412 − 2.34055I
−3.40045 − 1.02073I 0
u = 1.148340 − 0.333874I
a = 1.27542 − 0.77535I
b = −0.26412 + 2.34055I
−3.40045 + 1.02073I 0
u = −0.768297 + 0.223225I
a = −1.92583 + 0.47346I
b = 0.61700 − 1.55498I
−0.90689 + 2.60619I −4.21909 − 1.98730I
u = −0.768297 − 0.223225I
a = −1.92583 − 0.47346I
b = 0.61700 + 1.55498I
−0.90689 − 2.60619I −4.21909 + 1.98730I
u = −0.625920 + 0.391100I
a = 1.359350 − 0.293081I
b = −0.217590 + 0.449117I
0.16449 − 2.80931I −2.02619 + 2.03045I
u = −0.625920 − 0.391100I
a = 1.359350 + 0.293081I
b = −0.217590 − 0.449117I
0.16449 + 2.80931I −2.02619 − 2.03045I
u = −0.569996 + 0.465415I
a = −2.68911 − 0.37051I
b = −0.345079 − 0.969509I
−0.271555 + 0.561550I −5.56822 − 2.77116I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569996 − 0.465415I
a = −2.68911 + 0.37051I
b = −0.345079 + 0.969509I
−0.271555 − 0.561550I −5.56822 + 2.77116I
u = 1.269210 + 0.022101I
a = −1.118240 − 0.162406I
b = 0.125530 + 0.806401I
−5.71401 + 2.41800I 0
u = 1.269210 − 0.022101I
a = −1.118240 + 0.162406I
b = 0.125530 − 0.806401I
−5.71401 − 2.41800I 0
u = −1.268290 + 0.189716I
a = −1.227750 + 0.054676I
b = 0.107949 − 0.868842I
−5.53536 + 3.45054I 0
u = −1.268290 − 0.189716I
a = −1.227750 − 0.054676I
b = 0.107949 + 0.868842I
−5.53536 − 3.45054I 0
u = −1.187220 + 0.502909I
a = 1.52617 − 0.01474I
b = −0.80672 + 1.64220I
1.17723 + 4.19224I 0
u = −1.187220 − 0.502909I
a = 1.52617 + 0.01474I
b = −0.80672 − 1.64220I
1.17723 − 4.19224I 0
u = 0.568930 + 0.416577I
a = 0.120281 + 1.074160I
b = 0.045387 − 0.507767I
−0.76460 − 1.25688I −5.53847 + 5.17379I
u = 0.568930 − 0.416577I
a = 0.120281 − 1.074160I
b = 0.045387 + 0.507767I
−0.76460 + 1.25688I −5.53847 − 5.17379I
u = −0.453256 + 1.217240I
a = 0.90351 + 1.13576I
b = 0.71700 + 2.26803I
−2.25042 − 3.70807I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.453256 − 1.217240I
a = 0.90351 − 1.13576I
b = 0.71700 − 2.26803I
−2.25042 + 3.70807I 0
u = −0.042454 + 0.695928I
a = −0.025549 + 0.219032I
b = −0.276487 + 1.114370I
3.47148 + 0.76506I 5.05392 − 1.67806I
u = −0.042454 − 0.695928I
a = −0.025549 − 0.219032I
b = −0.276487 − 1.114370I
3.47148 − 0.76506I 5.05392 + 1.67806I
u = 0.384833 + 0.475726I
a = 1.82484 + 0.76996I
b = −0.016778 − 0.470642I
−0.75966 − 1.41499I −4.04897 + 4.67258I
u = 0.384833 − 0.475726I
a = 1.82484 − 0.76996I
b = −0.016778 + 0.470642I
−0.75966 + 1.41499I −4.04897 − 4.67258I
u = −1.33070 + 0.53202I
a = 1.058240 + 0.373107I
b = −0.234697 + 0.167699I
−13.75470 + 2.34725I 0
u = −1.33070 − 0.53202I
a = 1.058240 − 0.373107I
b = −0.234697 − 0.167699I
−13.75470 − 2.34725I 0
u = −0.468299 + 0.280082I
a = −0.059976 − 0.302032I
b = −0.276860 − 1.385290I
2.81830 − 4.57708I −11.91750 − 5.21602I
u = −0.468299 − 0.280082I
a = −0.059976 + 0.302032I
b = −0.276860 + 1.385290I
2.81830 + 4.57708I −11.91750 + 5.21602I
u = 1.30977 + 0.65145I
a = 0.967015 − 0.381842I
b = −0.229472 − 0.212903I
−12.7715 − 8.3839I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.30977 − 0.65145I
a = 0.967015 + 0.381842I
b = −0.229472 + 0.212903I
−12.7715 + 8.3839I 0
u = 1.43373 + 0.32544I
a = 0.1365400 − 0.0114578I
b = −0.05979 + 1.64995I
−8.50399 − 1.01711I 0
u = 1.43373 − 0.32544I
a = 0.1365400 + 0.0114578I
b = −0.05979 − 1.64995I
−8.50399 + 1.01711I 0
u = −1.40066 + 0.45878I
a = 0.0626733 − 0.1057400I
b = −0.04777 − 1.57885I
−7.87011 + 7.16358I 0
u = −1.40066 − 0.45878I
a = 0.0626733 + 0.1057400I
b = −0.04777 + 1.57885I
−7.87011 − 7.16358I 0
u = 1.39279 + 0.63989I
a = 1.172420 − 0.173984I
b = −0.44372 − 1.75238I
−6.43547 − 4.60616I 0
u = 1.39279 − 0.63989I
a = 1.172420 + 0.173984I
b = −0.44372 + 1.75238I
−6.43547 + 4.60616I 0
u = −1.35459 + 0.72187I
a = 1.220540 + 0.275631I
b = −0.42983 + 1.70660I
−5.32588 + 10.75820I 0
u = −1.35459 − 0.72187I
a = 1.220540 − 0.275631I
b = −0.42983 − 1.70660I
−5.32588 − 10.75820I 0
u = −0.032223 + 0.152731I
a = 36.7699 − 20.1859I
b = 0.421858 − 0.101939I
−1.08843 + 2.05155I 143.754 − 62.581I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032223 − 0.152731I
a = 36.7699 + 20.1859I
b = 0.421858 + 0.101939I
−1.08843 − 2.05155I 143.754 + 62.581I
u = −1.46857 + 1.15578I
a = −1.018750 − 0.533372I
b = 0.95221 − 2.16134I
−12.7985 + 16.4675I 0
u = −1.46857 − 1.15578I
a = −1.018750 + 0.533372I
b = 0.95221 + 2.16134I
−12.7985 − 16.4675I 0
u = −0.0940543
a = −7.89489
b = −0.510696
−1.10354 −8.74860
u = 1.57350 + 1.21978I
a = −0.928353 + 0.487034I
b = 0.99889 + 2.35016I
−14.6014 − 9.8690I 0
u = 1.57350 − 1.21978I
a = −0.928353 − 0.487034I
b = 0.99889 − 2.35016I
−14.6014 + 9.8690I 0
u = −1.98204 + 1.05164I
a = −0.878361 − 0.248375I
b = 1.90729 − 2.58093I
−6.11414 + 6.99153I 0
u = −1.98204 − 1.05164I
a = −0.878361 + 0.248375I
b = 1.90729 + 2.58093I
−6.11414 − 6.99153I 0
u = −1.49547 + 2.13069I
a = −0.493036 − 0.217503I
b = −1.52334 − 3.84431I
−11.14940 − 5.54057I 0
u = −1.49547 − 2.13069I
a = −0.493036 + 0.217503I
b = −1.52334 + 3.84431I
−11.14940 + 5.54057I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.00127 + 1.81072I
a = −0.633745 + 0.258104I
b = 0.48201 + 4.34193I
−13.40670 − 2.05335I 0
u = 2.00127 − 1.81072I
a = −0.633745 − 0.258104I
b = 0.48201 − 4.34193I
−13.40670 + 2.05335I 0
11
II. I
u
2
= h−u
3
− u
2
+ b − u, −u
3
+ a + 2, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
3
=
u
3
− 2
u
3
+ u
2
+ u
a
7
=
1
−u
2
a
4
=
u
3
− 2
u
3
+ u
2
+ u
a
6
=
1
−u
2
a
11
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
2
a
2
=
u
3
− u
2
− 3
u
3
+ 2u
2
+ u
a
1
=
−u
2
− 1
u
2
a
9
=
−u
3
− u
2
u
2
a
12
=
u
3
− u
2
− 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
+ 6u
2
− 2u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
7
, c
8
u
4
+ u
2
− u + 1
c
9
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
, c
11
u
4
+ u
2
+ u + 1
c
12
u
4
− 2u
3
+ 3u
2
− u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
7
, c
8
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −2.39923 + 0.32564I
b = 0.10488 + 1.55249I
−2.62503 − 1.39709I −5.95551 + 2.35025I
u = 0.547424 − 0.585652I
a = −2.39923 − 0.32564I
b = 0.10488 − 1.55249I
−2.62503 + 1.39709I −5.95551 − 2.35025I
u = −0.547424 + 1.120870I
a = −0.100768 − 0.400532I
b = 0.395123 − 0.506844I
0.98010 + 7.64338I −11.5445 − 9.2043I
u = −0.547424 − 1.120870I
a = −0.100768 + 0.400532I
b = 0.395123 + 0.506844I
0.98010 − 7.64338I −11.5445 + 9.2043I
15
III. I
u
3
= h2u
5
+ u
4
+ 3u
3
+ 2u
2
+ b + 2u + 2, −2u
5
− 4u
3
− u
2
+ a − 3u −
2, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
3
=
2u
5
+ 4u
3
+ u
2
+ 3u + 2
−2u
5
− u
4
− 3u
3
− 2u
2
− 2u − 2
a
7
=
1
−u
2
a
4
=
2u
5
+ 4u
3
+ u
2
+ 3u + 2
−2u
5
− u
4
− 3u
3
− 2u
2
− 2u − 2
a
6
=
1
−u
2
a
11
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
2
a
2
=
2u
5
+ 4u
3
+ 3u + 1
−2u
5
− u
4
− 3u
3
− u
2
− 2u − 2
a
1
=
−u
2
− 1
u
2
a
9
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
12
=
−u
5
− u
4
− 2u
3
− 2u
2
− 2u − 2
u
5
+ 2u
3
+ u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
− u
4
− 4u
2
+ 3u − 13
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
7
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
9
(u
3
− u
2
+ 1)
2
c
10
, c
11
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
12
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
7
, c
8
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
9
(y
3
− y
2
+ 2y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.175218 + 0.614017I
b = 0.481306 + 0.637866I
−1.37919 − 2.82812I −11.93937 + 4.05868I
u = 0.498832 − 1.001300I
a = −0.175218 − 0.614017I
b = 0.481306 − 0.637866I
−1.37919 + 2.82812I −11.93937 − 4.05868I
u = −0.284920 + 1.115140I
a = 0.307599 − 0.479689I
b = 0.662359 − 0.362106I
2.75839 −4.40089 + 2.50363I
u = −0.284920 − 1.115140I
a = 0.307599 + 0.479689I
b = 0.662359 + 0.362106I
2.75839 −4.40089 − 2.50363I
u = −0.713912 + 0.305839I
a = −0.13238 + 2.74513I
b = −1.14366 − 1.20015I
−1.37919 − 2.82812I −17.1597 + 2.2654I
u = −0.713912 − 0.305839I
a = −0.13238 − 2.74513I
b = −1.14366 + 1.20015I
−1.37919 + 2.82812I −17.1597 − 2.2654I
19
IV.
I
v
1
= ha, 186v
5
+1767v
4
+· · ·+385b+306, v
6
+10v
5
+95v
4
+48v
3
+15v
2
+5v+1i
(i) Arc colorings
a
8
=
1
0
a
10
=
v
0
a
3
=
0
−0.483117v
5
− 4.58961v
4
+ ··· − 0.241558v −0.794805
a
7
=
1
0
a
4
=
0.483117v
5
+ 4.58961v
4
+ ··· + 0.241558v + 0.794805
−0.483117v
5
− 4.58961v
4
+ ··· − 0.241558v −0.794805
a
6
=
1
−0.207792v
5
− 1.97403v
4
+ ··· − 0.103896v + 1.41299
a
11
=
0.103896v
5
+ 1.01558v
4
+ ··· + 3.45195v + 0.207792
0.345455v
5
+ 3.38182v
4
+ ··· + 5.07273v + 0.690909
a
5
=
0.207792v
5
+ 1.97403v
4
+ ··· + 0.103896v −0.412987
−0.207792v
5
− 1.97403v
4
+ ··· − 0.103896v + 1.41299
a
2
=
−1
−0.207792v
5
− 1.97403v
4
+ ··· − 0.103896v + 1.41299
a
1
=
−1
0
a
9
=
−0.241558v
5
− 2.36623v
4
+ ··· − 1.62078v −0.483117
0.345455v
5
+ 3.38182v
4
+ ··· + 5.07273v + 0.690909
a
12
=
0.244156v
5
+ 2.34805v
4
+ ··· + 3.52208v + 0.174026
0.345455v
5
+ 3.38182v
4
+ ··· + 5.07273v + 1.69091
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2881
385
v
5
+
28101
385
v
4
+
266701
385
v
3
+
72274
385
v
2
+
18419
385
v +
4464
385
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
(u
3
+ 3u
2
+ 2u − 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
u
6
c
8
, c
12
(u
2
− u + 1)
3
c
9
, c
10
u
6
− 2u
5
+ 7u
4
+ 8u
3
+ 7u
2
+ 3u + 1
c
11
(u
2
+ u + 1)
3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
− 5y
2
+ 10y −1)
2
c
7
y
6
c
8
, c
11
, c
12
(y
2
+ y + 1)
3
c
9
, c
10
y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.041684 + 0.322031I
a = 0
b = −0.215080 + 1.307140I
3.02413 + 0.79824I −13.76355 − 1.90324I
v = 0.041684 − 0.322031I
a = 0
b = −0.215080 − 1.307140I
3.02413 − 0.79824I −13.76355 + 1.90324I
v = −0.299729 + 0.124916I
a = 0
b = −0.215080 − 1.307140I
3.02413 − 4.85801I 2.26089 + 13.10391I
v = −0.299729 − 0.124916I
a = 0
b = −0.215080 + 1.307140I
3.02413 + 4.85801I 2.26089 − 13.10391I
v = −4.74195 + 8.21331I
a = 0
b = −0.569840
−1.11345 − 2.02988I −55.9973 − 74.4205I
v = −4.74195 − 8.21331I
a = 0
b = −0.569840
−1.11345 + 2.02988I −55.9973 + 74.4205I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
3
− u
2
+ 2u − 1)
2
(u
62
+ 71u
61
+ ··· + 267u + 1)
c
2
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
62
− 13u
61
+ ··· + 15u − 1)
c
3
u
10
(u
3
− u
2
+ 2u − 1)
2
(u
62
+ 3u
61
+ ··· − 8192u − 1024)
c
4
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
62
− 13u
61
+ ··· + 15u − 1)
c
5
((u
3
+ 3u
2
+ 2u − 1)
2
)(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ ··· + 2u
3
+ 1)
· (u
62
+ 4u
61
+ ··· − 10u
2
+ 1)
c
6
u
10
(u
3
+ u
2
+ 2u + 1)
2
(u
62
+ 3u
61
+ ··· − 8192u − 1024)
c
7
u
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
62
− 6u
61
+ ··· − 1248u + 64)
c
8
(u
2
− u + 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
62
− 5u
61
+ ··· + 113u + 1)
c
9
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
6
− 2u
5
+ ··· + 3u + 1)(u
62
+ 44u
60
+ ··· + 9664u + 824)
c
10
(u
4
+ u
2
+ u + 1)(u
6
− 2u
5
+ 7u
4
+ 8u
3
+ 7u
2
+ 3u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
62
+ 4u
61
+ ··· − 3025807u + 537503)
c
11
(u
2
+ u + 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
62
− 5u
61
+ ··· + 113u + 1)
c
12
(u
2
− u + 1)
3
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
62
− 21u
61
+ ··· + 12769u + 1)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
3
+ 3y
2
+ 2y −1)
2
(y
62
− 147y
61
+ ··· − 20183y + 1)
c
2
, c
4
((y −1)
10
)(y
3
− y
2
+ 2y −1)
2
(y
62
− 71y
61
+ ··· − 267y + 1)
c
3
, c
6
y
10
(y
3
+ 3y
2
+ 2y −1)
2
(y
62
− 57y
61
+ ··· + 9961472y + 1048576)
c
5
(y
3
− 5y
2
+ 10y −1)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
62
− 4y
61
+ ··· − 20y + 1)
c
7
y
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
62
− 30y
61
+ ··· − 185344y + 4096)
c
8
, c
11
(y
2
+ y + 1)
3
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
62
+ 21y
61
+ ··· − 12769y + 1)
c
9
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
62
+ 88y
61
+ ··· + 13013520y + 678976)
c
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
62
+ 16y
61
+ ··· − 11200434939731y + 288909475009)
c
12
((y
2
+ y + 1)
3
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
62
+ 45y
61
+ ··· − 163345321y + 1)
25
