12n
0814
(K12n
0814
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 9 2 10 6 12 4 8 7
Solving Sequence
3,11 4,6
2 7 1 10 8 9 12 5
c
3
c
2
c
6
c
1
c
10
c
7
c
8
c
11
c
5
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h81175333063282u
24
+ 30690153292943u
23
+ ··· + 14692178323546426b − 3242513336998852,
− 1.32142 × 10
15
u
24
+ 2.10121 × 10
15
u
23
+ ··· + 2.93844 × 10
16
a − 4.20080 × 10
16
, u
25
− u
24
+ ··· + 16u + 4i
I
u
2
= h1.78508 × 10
168
u
59
+ 1.43280 × 10
169
u
58
+ ··· + 5.04029 × 10
172
b − 1.24666 × 10
173
,
8.20931 × 10
173
u
59
+ 8.68057 × 10
173
u
58
+ ··· + 1.02973 × 10
176
a + 5.66958 × 10
176
,
u
60
+ u
59
+ ··· + 289u + 227i
I
u
3
= hu
5
+ u
4
+ 3u
3
+ 2u
2
+ b + 2u + 1, −u
8
− u
7
− 5u
6
− 4u
5
− 9u
4
− 5u
3
− 6u
2
+ a − 2u,
u
10
+ u
9
+ 6u
8
+ 5u
7
+ 13u
6
+ 9u
5
+ 12u
4
+ 7u
3
+ 4u
2
+ 2u + 1i
I
u
4
= h16776080628176u
27
+ 79179955700749u
26
+ ··· + 24691129075282b + 255994971816198,
− 331954436821981u
27
− 912855799370818u
26
+ ··· + 24691129075282a − 1987962528029584,
u
28
+ 2u
27
+ ··· + 8u + 4i
* 4 irreducible components of dim
C
= 0, with total 123 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
= h8.12×10
13
u
24
+3.07×10
13
u
23
+· · ·+1.47×10
16
b−3.24×10
15
, −1.32×
10
15
u
24
+2.10×10
15
u
23
+· · ·+2.94×10
16
a−4.20×10
16
, u
25
−u
24
+· · ·+16u+4i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
0.0449701u
24
− 0.0715078u
23
+ ··· − 0.542106u + 1.42960
−0.00552507u
24
− 0.00208888u
23
+ ··· + 0.581749u + 0.220697
a
2
=
0.0263934u
24
− 0.121687u
23
+ ··· + 1.62285u + 1.66323
0.0406210u
24
− 0.0468137u
23
+ ··· + 1.43529u + 0.315002
a
7
=
0.105850u
24
− 0.0806724u
23
+ ··· + 2.97593u + 2.35666
0.0193466u
24
− 0.0661674u
23
+ ··· − 0.842412u − 0.0345387
a
1
=
0.0476780u
24
− 0.209975u
23
+ ··· + 1.63902u + 1.59706
0.0541918u
24
+ 0.0416602u
23
+ ··· + 2.42220u + 0.583015
a
10
=
u
u
3
+ u
a
8
=
0.160052u
24
− 0.146654u
23
+ ··· + 3.13660u + 2.52396
0.0265376u
24
− 0.0541059u
23
+ ··· − 0.710082u + 0.179880
a
9
=
0.133514u
24
− 0.0925477u
23
+ ··· + 3.84668u + 2.34408
0.0189237u
24
− 0.0163606u
23
+ ··· − 0.400984u + 0.201981
a
12
=
0.326043u
24
− 0.239402u
23
+ ··· + 5.88596u + 2.83366
−0.0981597u
24
+ 0.00638083u
23
+ ··· + 0.203450u + 0.196612
a
5
=
0.0859368u
24
− 0.160051u
23
+ ··· − 0.334258u + 0.895546
−0.00296197u
24
+ 0.00385475u
23
+ ··· + 0.480951u + 0.145002
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
2216884505248312
7346089161773213
u
24
+
2474930584341802
7346089161773213
u
23
+ ···−
40988520351799862
7346089161773213
u −
70154967845383976
7346089161773213
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
25
− u
24
+ ··· + 20u + 1
c
2
, c
6
u
25
− 8u
24
+ ··· − 22u + 20
c
3
, c
5
, c
8
c
10
u
25
− u
24
+ ··· + 16u + 4
c
7
, c
9
u
25
+ 6u
23
+ ··· − u + 1
c
11
u
25
+ 17u
24
+ ··· + 1986u + 292
c
12
u
25
+ 29u
24
+ ··· + 90112u + 8192
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
25
+ 37y
24
+ ··· + 186y −1
c
2
, c
6
y
25
+ 8y
24
+ ··· + 1244y −400
c
3
, c
5
, c
8
c
10
y
25
+ 27y
24
+ ··· + 80y −16
c
7
, c
9
y
25
+ 12y
24
+ ··· − 39y −1
c
11
y
25
− y
24
+ ··· − 613924y −85264
c
12
y
25
− 15y
24
+ ··· + 469762048y −67108864
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356781 + 0.935663I
a = −1.010680 + 0.364892I
b = −0.135584 + 0.828584I
4.71782 − 3.78505I −1.08130 + 4.52429I
u = 0.356781 − 0.935663I
a = −1.010680 − 0.364892I
b = −0.135584 − 0.828584I
4.71782 + 3.78505I −1.08130 − 4.52429I
u = 0.955649 + 0.143797I
a = 0.323056 + 0.156868I
b = −0.840661 + 0.749782I
2.79251 − 4.59559I −4.91859 + 6.11356I
u = 0.955649 − 0.143797I
a = 0.323056 − 0.156868I
b = −0.840661 − 0.749782I
2.79251 + 4.59559I −4.91859 − 6.11356I
u = −0.443877 + 1.205860I
a = −1.330180 + 0.229600I
b = 0.418639 + 0.822145I
4.34108 + 5.05136I −4.70774 − 3.42318I
u = −0.443877 − 1.205860I
a = −1.330180 − 0.229600I
b = 0.418639 − 0.822145I
4.34108 − 5.05136I −4.70774 + 3.42318I
u = −0.678966 + 0.135775I
a = 0.930489 + 0.854461I
b = −0.673372 + 0.921554I
2.14403 − 0.99025I −7.34445 − 1.53442I
u = −0.678966 − 0.135775I
a = 0.930489 − 0.854461I
b = −0.673372 − 0.921554I
2.14403 + 0.99025I −7.34445 + 1.53442I
u = −0.156784 + 1.353090I
a = 1.72576 + 0.14878I
b = −0.90179 − 1.12633I
10.67230 + 2.17630I 0.04174 + 1.53653I
u = −0.156784 − 1.353090I
a = 1.72576 − 0.14878I
b = −0.90179 + 1.12633I
10.67230 − 2.17630I 0.04174 − 1.53653I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.367112 + 0.493386I
a = 2.07051 − 0.52494I
b = 0.180406 + 1.142870I
−4.21532 + 1.65565I −18.4972 + 2.9896I
u = 0.367112 − 0.493386I
a = 2.07051 + 0.52494I
b = 0.180406 − 1.142870I
−4.21532 − 1.65565I −18.4972 − 2.9896I
u = −0.03076 + 1.42689I
a = 1.38281 + 0.68917I
b = −1.011890 − 0.838182I
11.56050 + 4.89672I 2.97284 − 7.85735I
u = −0.03076 − 1.42689I
a = 1.38281 − 0.68917I
b = −1.011890 + 0.838182I
11.56050 − 4.89672I 2.97284 + 7.85735I
u = −0.03578 + 1.50371I
a = −0.432938 + 0.103827I
b = 0.34268 − 1.63762I
2.81426 − 3.91771I −1.29620 + 2.19890I
u = −0.03578 − 1.50371I
a = −0.432938 − 0.103827I
b = 0.34268 + 1.63762I
2.81426 + 3.91771I −1.29620 − 2.19890I
u = −0.319157 + 0.375086I
a = 0.787826 − 0.669604I
b = −0.268609 − 0.688871I
−0.332739 + 1.160480I −3.99385 − 5.99928I
u = −0.319157 − 0.375086I
a = 0.787826 + 0.669604I
b = −0.268609 + 0.688871I
−0.332739 − 1.160480I −3.99385 + 5.99928I
u = 0.47309 + 1.48937I
a = −1.051700 − 0.257525I
b = 1.116970 − 0.232182I
7.93268 − 2.23602I 0.761695 + 0.334356I
u = 0.47309 − 1.48937I
a = −1.051700 + 0.257525I
b = 1.116970 + 0.232182I
7.93268 + 2.23602I 0.761695 − 0.334356I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332884
a = 1.83055
b = 0.306235
−1.10902 −7.26140
u = 0.62513 + 1.55416I
a = 1.381370 + 0.302300I
b = −1.00799 + 1.26430I
13.3035 − 17.0719I −2.40849 + 7.81401I
u = 0.62513 − 1.55416I
a = 1.381370 − 0.302300I
b = −1.00799 − 1.26430I
13.3035 + 17.0719I −2.40849 − 7.81401I
u = −0.44600 + 1.67824I
a = 0.808407 − 0.509554I
b = −1.37193 + 0.86362I
14.7335 + 8.6358I −0.89771 − 3.83191I
u = −0.44600 − 1.67824I
a = 0.808407 + 0.509554I
b = −1.37193 − 0.86362I
14.7335 − 8.6358I −0.89771 + 3.83191I
7
II. I
u
2
= h1.79 × 10
168
u
59
+ 1.43 × 10
169
u
58
+ · · · + 5.04 × 10
172
b − 1.25 ×
10
173
, 8.21 × 10
173
u
59
+ 8.68 × 10
173
u
58
+ · · · + 1.03 × 10
176
a + 5.67 ×
10
176
, u
60
+ u
59
+ · · · + 289u + 227i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
−0.00797228u
59
− 0.00842993u
58
+ ··· + 9.12745u − 5.50588
−0.0000354162u
59
− 0.000284270u
58
+ ··· − 4.15178u + 2.47338
a
2
=
0.00875654u
59
+ 0.00749914u
58
+ ··· + 11.5546u + 7.51424
−0.00793371u
59
− 0.00743256u
58
+ ··· − 8.38811u − 1.46531
a
7
=
−0.0162583u
59
− 0.0123765u
58
+ ··· − 26.6169u + 2.33453
−0.00855045u
59
− 0.00916146u
58
+ ··· + 0.843688u − 4.75348
a
1
=
0.00262878u
59
+ 0.00246517u
58
+ ··· + 4.79084u + 5.76350
−0.00901992u
59
− 0.00861896u
58
+ ··· − 7.31321u − 1.71360
a
10
=
u
u
3
+ u
a
8
=
−0.0188007u
59
− 0.0151359u
58
+ ··· − 25.8727u + 1.23865
−0.00969922u
59
− 0.0110547u
58
+ ··· + 2.22778u − 5.80010
a
9
=
−0.0117646u
59
− 0.0129427u
58
+ ··· − 2.49013u − 2.12575
−0.0129451u
59
− 0.0143337u
58
+ ··· − 2.64558u − 7.90726
a
12
=
0.0212826u
59
+ 0.0118027u
58
+ ··· + 59.9419u − 6.26228
0.00838830u
59
+ 0.00778421u
58
+ ··· + 18.9048u + 5.25987
a
5
=
0.00318861u
59
− 0.00358656u
58
+ ··· + 16.6160u − 18.5879
0.0112699u
59
+ 0.00793128u
58
+ ··· + 14.3076u − 7.16173
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00763493u
59
+ 0.0171335u
58
+ ··· − 50.7125u + 29.2529
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
60
− 5u
59
+ ··· − 61367u + 12433
c
2
, c
6
(u
30
+ 3u
29
+ ··· + 3u + 1)
2
c
3
, c
5
, c
8
c
10
u
60
+ u
59
+ ··· + 289u + 227
c
7
, c
9
u
60
− 3u
59
+ ··· − 8079u + 2305
c
11
(u
30
− 7u
29
+ ··· + 726u − 59)
2
c
12
(u
30
− 10u
29
+ ··· − 2853u − 591)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
60
+ 51y
59
+ ··· − 2575299743y + 154579489
c
2
, c
6
(y
30
+ 9y
29
+ ··· − 3y + 1)
2
c
3
, c
5
, c
8
c
10
y
60
+ 41y
59
+ ··· + 250623y + 51529
c
7
, c
9
y
60
+ 5y
59
+ ··· + 133586719y + 5313025
c
11
(y
30
+ 17y
29
+ ··· − 464182y + 3481)
2
c
12
(y
30
− 30y
29
+ ··· − 17977395y + 349281)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.151089 + 0.988984I
a = 1.015950 − 0.753380I
b = −0.268673 − 0.905256I
0.331844 + 0.773996I −5.81323 − 0.94934I
u = −0.151089 − 0.988984I
a = 1.015950 + 0.753380I
b = −0.268673 + 0.905256I
0.331844 − 0.773996I −5.81323 + 0.94934I
u = −0.197498 + 0.949193I
a = 0.054102 − 0.941860I
b = −0.09788 + 1.49969I
−6.07488 + 0.77241I −12.7372 − 14.9639I
u = −0.197498 − 0.949193I
a = 0.054102 + 0.941860I
b = −0.09788 − 1.49969I
−6.07488 − 0.77241I −12.7372 + 14.9639I
u = 0.326973 + 0.865535I
a = 1.17062 + 1.94335I
b = −0.220348 + 0.210562I
−1.05655 − 1.42739I 10.99269 − 2.14037I
u = 0.326973 − 0.865535I
a = 1.17062 − 1.94335I
b = −0.220348 − 0.210562I
−1.05655 + 1.42739I 10.99269 + 2.14037I
u = 0.599443 + 0.897678I
a = 0.310619 − 0.931457I
b = 0.476833
5.08000 0
u = 0.599443 − 0.897678I
a = 0.310619 + 0.931457I
b = 0.476833
5.08000 0
u = 0.843197 + 0.154861I
a = 0.154657 − 0.463896I
b = −0.824890 − 0.215589I
3.05304 + 2.77277I −2.69988 − 3.50142I
u = 0.843197 − 0.154861I
a = 0.154657 + 0.463896I
b = −0.824890 + 0.215589I
3.05304 − 2.77277I −2.69988 + 3.50142I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.830816 + 0.161998I
a = 0.563539 − 0.534434I
b = −0.268673 − 0.905256I
0.331844 + 0.773996I −5.81323 − 0.94934I
u = −0.830816 − 0.161998I
a = 0.563539 + 0.534434I
b = −0.268673 + 0.905256I
0.331844 − 0.773996I −5.81323 + 0.94934I
u = 0.007925 + 0.844615I
a = −1.81193 − 2.76865I
b = 0.258541 + 0.333070I
1.89101 + 5.03315I 1.75905 − 6.82138I
u = 0.007925 − 0.844615I
a = −1.81193 + 2.76865I
b = 0.258541 − 0.333070I
1.89101 − 5.03315I 1.75905 + 6.82138I
u = 0.477112 + 1.090850I
a = −1.06340 − 1.18158I
b = 0.677641 − 0.588433I
5.72749 − 7.45875I 0
u = 0.477112 − 1.090850I
a = −1.06340 + 1.18158I
b = 0.677641 + 0.588433I
5.72749 + 7.45875I 0
u = 0.433233 + 1.120270I
a = 0.645877 + 0.522724I
b = −0.106768 + 1.224240I
−2.00126 − 5.14743I 0
u = 0.433233 − 1.120270I
a = 0.645877 − 0.522724I
b = −0.106768 − 1.224240I
−2.00126 + 5.14743I 0
u = −0.464555 + 1.178190I
a = 0.234302 + 0.213986I
b = 0.097409 − 1.142310I
3.33083 + 3.97209I 0
u = −0.464555 − 1.178190I
a = 0.234302 − 0.213986I
b = 0.097409 + 1.142310I
3.33083 − 3.97209I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385734 + 0.615064I
a = −0.13976 + 1.50771I
b = 0.556018
−0.861477 −2.21853 + 0.I
u = −0.385734 − 0.615064I
a = −0.13976 − 1.50771I
b = 0.556018
−0.861477 −2.21853 + 0.I
u = −0.191587 + 1.292350I
a = −0.735001 + 0.950554I
b = 0.097409 + 1.142310I
3.33083 − 3.97209I 0
u = −0.191587 − 1.292350I
a = −0.735001 − 0.950554I
b = 0.097409 − 1.142310I
3.33083 + 3.97209I 0
u = −0.720332 + 1.143500I
a = −0.265603 + 0.406457I
b = 0.258541 + 0.333070I
1.89101 + 5.03315I 0
u = −0.720332 − 1.143500I
a = −0.265603 − 0.406457I
b = 0.258541 − 0.333070I
1.89101 − 5.03315I 0
u = −1.334490 + 0.240948I
a = 0.168255 + 0.261950I
b = −0.220348 − 0.210562I
−1.05655 + 1.42739I 0
u = −1.334490 − 0.240948I
a = 0.168255 − 0.261950I
b = −0.220348 + 0.210562I
−1.05655 − 1.42739I 0
u = 0.167787 + 1.359600I
a = −1.33826 − 0.70122I
b = 0.810607 + 0.866117I
6.78367 + 0.73525I 0
u = 0.167787 − 1.359600I
a = −1.33826 + 0.70122I
b = 0.810607 − 0.866117I
6.78367 − 0.73525I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.115657 + 1.370730I
a = 0.911391 + 0.108509I
b = −0.824890 − 0.215589I
3.05304 + 2.77277I 0
u = −0.115657 − 1.370730I
a = 0.911391 − 0.108509I
b = −0.824890 + 0.215589I
3.05304 − 2.77277I 0
u = 0.19606 + 1.42365I
a = 1.44865 − 0.22898I
b = −1.04755 + 1.32743I
11.53870 − 7.55219I 0
u = 0.19606 − 1.42365I
a = 1.44865 + 0.22898I
b = −1.04755 − 1.32743I
11.53870 + 7.55219I 0
u = −0.13751 + 1.44639I
a = −1.139830 + 0.571849I
b = 1.11980 − 1.17245I
7.57073 + 1.54799I 0
u = −0.13751 − 1.44639I
a = −1.139830 − 0.571849I
b = 1.11980 + 1.17245I
7.57073 − 1.54799I 0
u = −0.39296 + 1.43423I
a = −1.60846 − 0.05755I
b = 0.836436 + 0.962571I
6.51793 + 5.45084I 0
u = −0.39296 − 1.43423I
a = −1.60846 + 0.05755I
b = 0.836436 − 0.962571I
6.51793 − 5.45084I 0
u = 1.48914 + 0.10011I
a = 0.22281 + 1.55793I
b = −0.09788 + 1.49969I
−6.07488 + 0.77241I 0
u = 1.48914 − 0.10011I
a = 0.22281 − 1.55793I
b = −0.09788 − 1.49969I
−6.07488 − 0.77241I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08468 + 1.49584I
a = 1.349320 − 0.340698I
b = −1.36115 + 0.81924I
13.16510 − 1.04438I 0
u = 0.08468 − 1.49584I
a = 1.349320 + 0.340698I
b = −1.36115 − 0.81924I
13.16510 + 1.04438I 0
u = 0.42436 + 1.45884I
a = −1.51602 − 0.04319I
b = 1.11039 − 1.00742I
7.97566 − 9.65899I 0
u = 0.42436 − 1.45884I
a = −1.51602 + 0.04319I
b = 1.11039 + 1.00742I
7.97566 + 9.65899I 0
u = 1.53765 + 0.12330I
a = −0.300107 − 0.447420I
b = 1.11039 − 1.00742I
7.97566 − 9.65899I 0
u = 1.53765 − 0.12330I
a = −0.300107 + 0.447420I
b = 1.11039 + 1.00742I
7.97566 + 9.65899I 0
u = −0.33599 + 1.58079I
a = −1.043490 − 0.349969I
b = 0.677641 + 0.588433I
5.72749 + 7.45875I 0
u = −0.33599 − 1.58079I
a = −1.043490 + 0.349969I
b = 0.677641 − 0.588433I
5.72749 − 7.45875I 0
u = −1.61765 + 0.46633I
a = −0.174220 − 0.449001I
b = 1.11980 − 1.17245I
7.57073 + 1.54799I 0
u = −1.61765 − 0.46633I
a = −0.174220 + 0.449001I
b = 1.11980 + 1.17245I
7.57073 − 1.54799I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199803 + 0.244970I
a = 4.38347 + 3.03006I
b = −0.106768 − 1.224240I
−2.00126 + 5.14743I −12.34153 − 6.38581I
u = −0.199803 − 0.244970I
a = 4.38347 − 3.03006I
b = −0.106768 + 1.224240I
−2.00126 − 5.14743I −12.34153 + 6.38581I
u = −0.154498 + 0.258494I
a = 1.97537 − 0.70610I
b = 0.810607 − 0.866117I
6.78367 − 0.73525I 1.34056 + 4.28994I
u = −0.154498 − 0.258494I
a = 1.97537 + 0.70610I
b = 0.810607 + 0.866117I
6.78367 + 0.73525I 1.34056 − 4.28994I
u = 0.283976 + 0.026888I
a = 1.65738 − 0.91773I
b = 0.836436 − 0.962571I
6.51793 − 5.45084I −3.44913 − 0.50892I
u = 0.283976 − 0.026888I
a = 1.65738 + 0.91773I
b = 0.836436 + 0.962571I
6.51793 + 5.45084I −3.44913 + 0.50892I
u = −0.81940 + 1.65329I
a = 1.140340 − 0.437941I
b = −1.04755 − 1.32743I
11.53870 + 7.55219I 0
u = −0.81940 − 1.65329I
a = 1.140340 + 0.437941I
b = −1.04755 + 1.32743I
11.53870 − 7.55219I 0
u = 0.67804 + 1.80475I
a = 0.603871 + 0.402297I
b = −1.36115 − 0.81924I
13.16510 + 1.04438I 0
u = 0.67804 − 1.80475I
a = 0.603871 − 0.402297I
b = −1.36115 + 0.81924I
13.16510 − 1.04438I 0
16
III. I
u
3
=
hu
5
+u
4
+3u
3
+2u
2
+b +2u+1, −u
8
−u
7
+· · ·+a−2u, u
10
+u
9
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
u
8
+ u
7
+ 5u
6
+ 4u
5
+ 9u
4
+ 5u
3
+ 6u
2
+ 2u
−u
5
− u
4
− 3u
3
− 2u
2
− 2u − 1
a
2
=
−u
9
− u
8
− 5u
7
− 4u
6
− 8u
5
− 5u
4
− 3u
3
− u
2
+ 2u + 2
u
9
+ u
8
+ 5u
7
+ 4u
6
+ 9u
5
+ 6u
4
+ 7u
3
+ 4u
2
+ 2u
a
7
=
−u
7
− u
6
− 5u
5
− 4u
4
− 9u
3
− 5u
2
− 5u − 2
−u
9
− u
8
− 5u
7
− 4u
6
− 9u
5
− 5u
4
− 6u
3
− 2u
2
− u
a
1
=
−u
9
− u
8
− 5u
7
− 4u
6
− 8u
5
− 5u
4
− 2u
3
− u
2
+ 3u + 2
u
9
+ u
8
+ 5u
7
+ 4u
6
+ 10u
5
+ 6u
4
+ 8u
3
+ 4u
2
+ 2u
a
10
=
u
u
3
+ u
a
8
=
−u
9
− u
8
− 6u
7
− 5u
6
− 13u
5
− 9u
4
− 13u
3
− 7u
2
− 5u − 2
−u
9
− u
8
− 5u
7
− 4u
6
− 9u
5
− 5u
4
− 6u
3
− 2u
2
a
9
=
−u
7
− u
6
− 4u
5
− 4u
4
− 7u
3
− 5u
2
− 5u − 2
−u
9
− u
8
− 5u
7
− 5u
6
− 10u
5
− 8u
4
− 8u
3
− 4u
2
− u
a
12
=
u
9
+ u
8
+ 5u
7
+ 5u
6
+ 11u
5
+ 9u
4
+ 13u
3
+ 7u
2
+ 6u + 2
u
8
+ 2u
7
+ 4u
6
+ 7u
5
+ 5u
4
+ 7u
3
+ 2u
2
+ u
a
5
=
u
6
+ 2u
4
+ u
2
u
8
+ 3u
6
+ 3u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
9
−u
8
−28u
7
−9u
6
−59u
5
−26u
4
−53u
3
−27u
2
−13u − 11
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
10
+ u
9
+ 2u
8
+ u
7
− 5u
6
+ 6u
5
+ 5u
4
− 7u
3
+ 6u
2
− 2u + 1
c
2
u
10
+ 3u
9
+ 8u
8
+ 13u
7
+ 19u
6
+ 18u
5
+ 17u
4
+ 9u
3
+ 6u
2
+ 2u + 1
c
3
, c
8
u
10
+ u
9
+ 6u
8
+ 5u
7
+ 13u
6
+ 9u
5
+ 12u
4
+ 7u
3
+ 4u
2
+ 2u + 1
c
5
, c
10
u
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 9u
5
+ 12u
4
− 7u
3
+ 4u
2
− 2u + 1
c
6
u
10
− 3u
9
+ 8u
8
− 13u
7
+ 19u
6
− 18u
5
+ 17u
4
− 9u
3
+ 6u
2
− 2u + 1
c
7
, c
9
u
10
− 2u
8
− 2u
7
+ 3u
6
+ 4u
5
− 3u
3
− 2u
2
+ u + 1
c
11
u
10
+ 4u
9
+ ··· + 200u + 59
c
12
u
10
− 6u
8
− 10u
7
+ 13u
6
+ 23u
5
+ 55u
4
+ 58u
3
+ 32u
2
+ 9u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
10
+ 3y
9
− 8y
8
− 23y
7
+ 59y
6
− 42y
5
+ 57y
4
+ 25y
3
+ 18y
2
+ 8y + 1
c
2
, c
6
y
10
+ 7y
9
+ ··· + 8y + 1
c
3
, c
5
, c
8
c
10
y
10
+ 11y
9
+ ··· + 4y + 1
c
7
, c
9
y
10
− 4y
9
+ ··· − 5y + 1
c
11
y
10
− 4y
9
+ ··· − 5898y + 3481
c
12
y
10
− 12y
9
+ ··· − 17y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.218748 + 1.275640I
a = −0.080468 + 0.215654I
b = −0.015850 + 1.374270I
1.14572 − 5.62515I −5.10001 + 5.95698I
u = 0.218748 − 1.275640I
a = −0.080468 − 0.215654I
b = −0.015850 − 1.374270I
1.14572 + 5.62515I −5.10001 − 5.95698I
u = −0.383970 + 1.273480I
a = −1.329920 + 0.099945I
b = 0.204503 + 0.588468I
4.53396 + 6.42062I −3.45225 − 7.77374I
u = −0.383970 − 1.273480I
a = −1.329920 − 0.099945I
b = 0.204503 − 0.588468I
4.53396 − 6.42062I −3.45225 + 7.77374I
u = 0.232016 + 0.607746I
a = −1.85998 + 0.90065I
b = −0.232015 − 1.193450I
−3.84315 + 1.80254I 0.70838 − 4.06832I
u = 0.232016 − 0.607746I
a = −1.85998 − 0.90065I
b = −0.232015 + 1.193450I
−3.84315 − 1.80254I 0.70838 + 4.06832I
u = −0.498801 + 0.315427I
a = −0.587520 − 0.944917I
b = −0.366540 − 0.542378I
−1.58932 + 0.77300I −11.96817 − 4.87496I
u = −0.498801 − 0.315427I
a = −0.587520 + 0.944917I
b = −0.366540 + 0.542378I
−1.58932 − 0.77300I −11.96817 + 4.87496I
u = −0.06799 + 1.51152I
a = 1.35788 + 0.40393I
b = −1.09010 − 0.98242I
11.26730 + 3.87713I −0.187934 − 1.212159I
u = −0.06799 − 1.51152I
a = 1.35788 − 0.40393I
b = −1.09010 + 0.98242I
11.26730 − 3.87713I −0.187934 + 1.212159I
20
IV.
I
u
4
= h1.68×10
13
u
27
+7.92×10
13
u
26
+· · ·+2.47×10
13
b+2.56×10
14
, −3.32×
10
14
u
27
−9.13×10
14
u
26
+· · ·+2.47×10
13
a−1.99×10
15
, u
28
+2u
27
+· · ·+8u+4i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
13.4443u
27
+ 36.9710u
26
+ ··· + 279.143u + 80.5132
−0.679438u
27
− 3.20682u
26
+ ··· − 25.2942u − 10.3679
a
2
=
14.9817u
27
+ 24.6610u
26
+ ··· + 11.9449u − 46.5189
−4.26678u
27
− 7.95280u
26
+ ··· − 15.8663u + 5.82690
a
7
=
6.33618u
27
+ 9.08717u
26
+ ··· + 32.6034u − 14.4296
2.35281u
27
+ 7.71441u
26
+ ··· + 52.9583u + 19.0678
a
1
=
18.8735u
27
+ 30.4600u
26
+ ··· + 13.5861u − 61.9017
−6.09935u
27
− 10.5567u
26
+ ··· − 15.5560u + 13.7657
a
10
=
u
u
3
+ u
a
8
=
5.82391u
27
+ 10.7369u
26
+ ··· + 56.1137u + 0.790280
1.89033u
27
+ 7.65187u
26
+ ··· + 57.1231u + 23.5904
a
9
=
−19.4311u
27
− 28.7414u
26
+ ··· + 15.3253u + 83.6984
1.30957u
27
+ 3.06693u
26
+ ··· + 8.16198u + 2.52325
a
12
=
14.1989u
27
+ 27.0878u
26
+ ··· + 113.314u − 4.10633
−0.966665u
27
+ 2.54987u
26
+ ··· + 59.3242u + 32.8147
a
5
=
0.694726u
27
− 12.2051u
26
+ ··· − 202.024u − 104.533
4.19601u
27
+ 7.80446u
26
+ ··· + 14.5407u − 7.13048
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
549965322058885
12345564537641
u
27
+
1232084486849614
12345564537641
u
26
+ ··· +
5980853558878580
12345564537641
u +
810533241115920
12345564537641
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
− 2u
27
+ ··· − 163u + 19
c
2
(u
14
− 2u
13
+ ··· + 8u
2
+ 1)
2
c
3
, c
8
u
28
+ 2u
27
+ ··· + 8u + 4
c
5
, c
10
u
28
− 2u
27
+ ··· − 8u + 4
c
6
(u
14
+ 2u
13
+ ··· + 8u
2
+ 1)
2
c
7
, c
9
u
28
− 6u
27
+ ··· − u + 1
c
11
(u
14
− 3u
13
+ ··· − 2u + 1)
2
c
12
(u
14
− 3u
13
+ ··· + 74u + 68)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
+ 22y
27
+ ··· + 10899y + 361
c
2
, c
6
(y
14
+ 12y
13
+ ··· + 16y + 1)
2
c
3
, c
5
, c
8
c
10
y
28
+ 10y
27
+ ··· + 272y + 16
c
7
, c
9
y
28
− 2y
27
+ ··· + 27y + 1
c
11
(y
14
+ y
13
+ ··· − 10y + 1)
2
c
12
(y
14
− 3y
13
+ ··· + 15060y + 4624)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128929 + 0.988461I
a = 0.215988 + 0.958905I
b = −0.06679 − 1.55090I
−5.93574 − 0.51365I 1.10966 − 8.86769I
u = 0.128929 − 0.988461I
a = 0.215988 − 0.958905I
b = −0.06679 + 1.55090I
−5.93574 + 0.51365I 1.10966 + 8.86769I
u = −0.772634 + 0.697387I
a = 0.065504 − 0.554645I
b = 0.793498 − 1.060250I
6.32313 + 0.22942I −2.49445 − 1.32741I
u = −0.772634 − 0.697387I
a = 0.065504 + 0.554645I
b = 0.793498 + 1.060250I
6.32313 − 0.22942I −2.49445 + 1.32741I
u = −0.589471 + 0.704492I
a = 0.38802 + 1.58694I
b = −0.410728 + 0.971915I
3.70456 − 1.58603I −1.63833 + 0.55429I
u = −0.589471 − 0.704492I
a = 0.38802 − 1.58694I
b = −0.410728 − 0.971915I
3.70456 + 1.58603I −1.63833 − 0.55429I
u = −0.318935 + 0.828249I
a = 1.25882 − 2.07446I
b = −0.129154 − 0.454753I
−1.28686 + 1.47696I −23.0029 − 5.2896I
u = −0.318935 − 0.828249I
a = 1.25882 + 2.07446I
b = −0.129154 + 0.454753I
−1.28686 − 1.47696I −23.0029 + 5.2896I
u = 0.434181 + 0.720450I
a = −0.601125 − 0.931348I
b = 0.797540 − 0.860254I
6.91920 − 6.19035I 1.69741 + 7.48551I
u = 0.434181 − 0.720450I
a = −0.601125 + 0.931348I
b = 0.797540 + 0.860254I
6.91920 + 6.19035I 1.69741 − 7.48551I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269671 + 0.738522I
a = −0.268660 − 0.603585I
b = −0.410728 + 0.971915I
3.70456 − 1.58603I −1.63833 + 0.55429I
u = 0.269671 − 0.738522I
a = −0.268660 + 0.603585I
b = −0.410728 − 0.971915I
3.70456 + 1.58603I −1.63833 − 0.55429I
u = −0.010810 + 0.768664I
a = −1.03806 − 2.24380I
b = 0.054674 + 1.270070I
−1.20487 + 4.99386I −1.94209 − 3.72866I
u = −0.010810 − 0.768664I
a = −1.03806 + 2.24380I
b = 0.054674 − 1.270070I
−1.20487 − 4.99386I −1.94209 + 3.72866I
u = −1.249200 + 0.250928I
a = 0.226200 + 0.136184I
b = −0.129154 − 0.454753I
−1.28686 + 1.47696I −23.0029 − 5.2896I
u = −1.249200 − 0.250928I
a = 0.226200 − 0.136184I
b = −0.129154 + 0.454753I
−1.28686 − 1.47696I −23.0029 + 5.2896I
u = 0.499651 + 1.190630I
a = −0.740372 − 0.625582I
b = 0.054674 − 1.270070I
−1.20487 − 4.99386I −1.94209 + 3.72866I
u = 0.499651 − 1.190630I
a = −0.740372 + 0.625582I
b = 0.054674 + 1.270070I
−1.20487 + 4.99386I −1.94209 − 3.72866I
u = −0.702762 + 1.109660I
a = 0.132392 + 0.081953I
b = −0.039039 − 0.652784I
1.35017 + 4.86464I −12.22925 − 3.65511I
u = −0.702762 − 1.109660I
a = 0.132392 − 0.081953I
b = −0.039039 + 0.652784I
1.35017 − 4.86464I −12.22925 + 3.65511I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.007847 + 0.664573I
a = −2.32077 + 3.50003I
b = −0.039039 + 0.652784I
1.35017 − 4.86464I −12.22925 + 3.65511I
u = 0.007847 − 0.664573I
a = −2.32077 − 3.50003I
b = −0.039039 − 0.652784I
1.35017 + 4.86464I −12.22925 − 3.65511I
u = 0.130196 + 1.341580I
a = −1.33690 − 0.56146I
b = 0.793498 + 1.060250I
6.32313 − 0.22942I −2.49445 + 1.32741I
u = 0.130196 − 1.341580I
a = −1.33690 + 0.56146I
b = 0.793498 − 1.060250I
6.32313 + 0.22942I −2.49445 − 1.32741I
u = −0.41891 + 1.44857I
a = −1.54382 − 0.10820I
b = 0.797540 + 0.860254I
6.91920 + 6.19035I 1.69741 − 7.48551I
u = −0.41891 − 1.44857I
a = −1.54382 + 0.10820I
b = 0.797540 − 0.860254I
6.91920 − 6.19035I 1.69741 + 7.48551I
u = 1.59224 + 0.05574I
a = 0.06278 − 1.47160I
b = −0.06679 − 1.55090I
−5.93574 − 0.51365I 0. − 8.86769I
u = 1.59224 − 0.05574I
a = 0.06278 + 1.47160I
b = −0.06679 + 1.55090I
−5.93574 + 0.51365I 0. + 8.86769I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
10
+ u
9
+ 2u
8
+ u
7
− 5u
6
+ 6u
5
+ 5u
4
− 7u
3
+ 6u
2
− 2u + 1)
· (u
25
− u
24
+ ··· + 20u + 1)(u
28
− 2u
27
+ ··· − 163u + 19)
· (u
60
− 5u
59
+ ··· − 61367u + 12433)
c
2
(u
10
+ 3u
9
+ 8u
8
+ 13u
7
+ 19u
6
+ 18u
5
+ 17u
4
+ 9u
3
+ 6u
2
+ 2u + 1)
· ((u
14
− 2u
13
+ ··· + 8u
2
+ 1)
2
)(u
25
− 8u
24
+ ··· − 22u + 20)
· (u
30
+ 3u
29
+ ··· + 3u + 1)
2
c
3
, c
8
(u
10
+ u
9
+ 6u
8
+ 5u
7
+ 13u
6
+ 9u
5
+ 12u
4
+ 7u
3
+ 4u
2
+ 2u + 1)
· (u
25
− u
24
+ ··· + 16u + 4)(u
28
+ 2u
27
+ ··· + 8u + 4)
· (u
60
+ u
59
+ ··· + 289u + 227)
c
5
, c
10
(u
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 9u
5
+ 12u
4
− 7u
3
+ 4u
2
− 2u + 1)
· (u
25
− u
24
+ ··· + 16u + 4)(u
28
− 2u
27
+ ··· − 8u + 4)
· (u
60
+ u
59
+ ··· + 289u + 227)
c
6
(u
10
− 3u
9
+ 8u
8
− 13u
7
+ 19u
6
− 18u
5
+ 17u
4
− 9u
3
+ 6u
2
− 2u + 1)
· ((u
14
+ 2u
13
+ ··· + 8u
2
+ 1)
2
)(u
25
− 8u
24
+ ··· − 22u + 20)
· (u
30
+ 3u
29
+ ··· + 3u + 1)
2
c
7
, c
9
(u
10
− 2u
8
− 2u
7
+ 3u
6
+ 4u
5
− 3u
3
− 2u
2
+ u + 1)
· (u
25
+ 6u
23
+ ··· − u + 1)(u
28
− 6u
27
+ ··· − u + 1)
· (u
60
− 3u
59
+ ··· − 8079u + 2305)
c
11
(u
10
+ 4u
9
+ ··· + 200u + 59)(u
14
− 3u
13
+ ··· − 2u + 1)
2
· (u
25
+ 17u
24
+ ··· + 1986u + 292)(u
30
− 7u
29
+ ··· + 726u − 59)
2
c
12
(u
10
− 6u
8
− 10u
7
+ 13u
6
+ 23u
5
+ 55u
4
+ 58u
3
+ 32u
2
+ 9u + 1)
· ((u
14
− 3u
13
+ ··· + 74u + 68)
2
)(u
25
+ 29u
24
+ ··· + 90112u + 8192)
· (u
30
− 10u
29
+ ··· − 2853u − 591)
2
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
10
+ 3y
9
− 8y
8
− 23y
7
+ 59y
6
− 42y
5
+ 57y
4
+ 25y
3
+ 18y
2
+ 8y + 1)
· (y
25
+ 37y
24
+ ··· + 186y −1)(y
28
+ 22y
27
+ ··· + 10899y + 361)
· (y
60
+ 51y
59
+ ··· − 2575299743y + 154579489)
c
2
, c
6
(y
10
+ 7y
9
+ ··· + 8y + 1)(y
14
+ 12y
13
+ ··· + 16y + 1)
2
· (y
25
+ 8y
24
+ ··· + 1244y −400)(y
30
+ 9y
29
+ ··· − 3y + 1)
2
c
3
, c
5
, c
8
c
10
(y
10
+ 11y
9
+ ··· + 4y + 1)(y
25
+ 27y
24
+ ··· + 80y −16)
· (y
28
+ 10y
27
+ ··· + 272y + 16)
· (y
60
+ 41y
59
+ ··· + 250623y + 51529)
c
7
, c
9
(y
10
− 4y
9
+ ··· − 5y + 1)(y
25
+ 12y
24
+ ··· − 39y −1)
· (y
28
− 2y
27
+ ··· + 27y + 1)
· (y
60
+ 5y
59
+ ··· + 133586719y + 5313025)
c
11
(y
10
− 4y
9
+ ··· − 5898y + 3481)(y
14
+ y
13
+ ··· − 10y + 1)
2
· (y
25
− y
24
+ ··· − 613924y −85264)
· (y
30
+ 17y
29
+ ··· − 464182y + 3481)
2
c
12
(y
10
− 12y
9
+ ··· − 17y + 1)(y
14
− 3y
13
+ ··· + 15060y + 4624)
2
· (y
25
− 15y
24
+ ··· + 469762048y −67108864)
· (y
30
− 30y
29
+ ··· − 17977395y + 349281)
2
28
