12a
1180
(K12a
1180
)
A knot diagram
1
Linearized knot diagam
4 10 8 1 9 11 3 12 2 6 7 5
Solving Sequence
6,10
11
3,7
8 4 12 2 1 9 5
c
10
c
6
c
7
c
3
c
11
c
2
c
1
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h40129u
36
+ 541351u
35
+ ··· + 64b + 3448384,
− 117149u
36
− 1586205u
35
+ ··· + 128a − 10309184, u
37
+ 15u
36
+ ··· + 128u + 128i
I
u
2
= h−2589926063a
5
u
4
+ 1727557591a
4
u
4
+ ··· + 14756925898a + 2746218374,
a
4
u
4
+ 2u
4
a
3
+ ··· − 2a + 5, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
3
= h−1.25456 × 10
19
a
7
u
4
− 3.69023 × 10
18
a
6
u
4
+ ··· − 3.06241 × 10
19
a + 1.52681 × 10
20
,
a
7
u
4
+ 3a
6
u
4
+ ··· + 5a − 2, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
4
= h−3u
24
+ 5u
23
+ ··· + b − 3, −3u
23
+ 37u
21
+ ··· + a + 1, u
25
− 14u
23
+ ··· − 6u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 132 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
= h40129u
36
+ 541351u
35
+ · · · + 64b + 3448384, −1.17 × 10
5
u
36
−
1.59 × 10
6
u
35
+ · · · + 128a − 1.03 × 10
7
, u
37
+ 15u
36
+ · · · + 128u + 128i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
915.227u
36
+ 12392.2u
35
+ ··· + 25110.5u + 80540.5
−627.016u
36
− 8458.61u
35
+ ··· − 17272.5u − 53881
a
7
=
u
−u
3
+ u
a
8
=
−8.50000u
36
− 98.5000u
35
+ ··· − 495.500u + 160.500
157
4
u
36
+ 518u
35
+ ··· +
2753
2
u + 2624
a
4
=
503.828u
36
+ 6655.03u
35
+ ··· + 16741.3u + 34828
−165.578u
36
− 2187.45u
35
+ ··· − 6821u − 10106
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
288.211u
36
+ 3933.62u
35
+ ··· + 7838u + 26659.5
−627.016u
36
− 8458.61u
35
+ ··· − 17272.5u − 53881
a
1
=
−410.313u
36
− 5606.69u
35
+ ··· − 11464u − 37783
−
3733
16
u
36
−
24335
8
u
35
+ ··· − 8416u − 13816
a
9
=
−
123
4
u
36
−
839
2
u
35
+ ··· − 879u −
5567
2
−
157
4
u
36
− 518u
35
+ ··· −
2751
2
u − 2624
a
5
=
285
2
u
36
+
7613
4
u
35
+ ··· +
18879
4
u + 10688
−
285
4
u
36
−
2053
2
u
35
+ ··· − 1055u − 9568
(ii) Obstruction class = −1
(iii) Cusp Shapes =
19693
16
u
36
+
264633
16
u
35
+ ··· + 34556u + 102558
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
37
− 12u
36
+ ··· + 464u − 32
c
2
, c
3
, c
7
c
9
u
37
− u
36
+ ··· + u − 1
c
5
, c
8
u
37
− 15u
35
+ ··· + 3u + 1
c
6
, c
10
, c
11
u
37
+ 15u
36
+ ··· + 128u + 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
37
+ 32y
36
+ ··· − 3328y −1024
c
2
, c
3
, c
7
c
9
y
37
− 19y
36
+ ··· + 9y −1
c
5
, c
8
y
37
− 30y
36
+ ··· + 19y −1
c
6
, c
10
, c
11
y
37
− 33y
36
+ ··· + 65536y −16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351636 + 0.943218I
a = −0.475955 − 0.640393I
b = −1.226050 + 0.499285I
−4.86867 + 8.36618I −5.40191 − 7.90416I
u = 0.351636 − 0.943218I
a = −0.475955 + 0.640393I
b = −1.226050 − 0.499285I
−4.86867 − 8.36618I −5.40191 + 7.90416I
u = 0.241715 + 0.981613I
a = 0.517408 + 0.493867I
b = 1.062410 − 0.425783I
−3.19836 + 3.03653I 0. − 4.95054I
u = 0.241715 − 0.981613I
a = 0.517408 − 0.493867I
b = 1.062410 + 0.425783I
−3.19836 − 3.03653I 0. + 4.95054I
u = 0.385505 + 0.899265I
a = 0.501965 + 0.739361I
b = 1.31533 − 0.59643I
0.99167 + 12.76550I −2.00000 − 8.13132I
u = 0.385505 − 0.899265I
a = 0.501965 − 0.739361I
b = 1.31533 + 0.59643I
0.99167 − 12.76550I −2.00000 + 8.13132I
u = 0.839963 + 0.746345I
a = 0.400856 − 0.379292I
b = −1.154870 − 0.426854I
2.32825 − 7.20667I 0
u = 0.839963 − 0.746345I
a = 0.400856 + 0.379292I
b = −1.154870 + 0.426854I
2.32825 + 7.20667I 0
u = −1.048710 + 0.504742I
a = −0.767420 + 0.920923I
b = −0.666422 − 0.237516I
0.55587 − 4.70914I 0
u = −1.048710 − 0.504742I
a = −0.767420 − 0.920923I
b = −0.666422 + 0.237516I
0.55587 + 4.70914I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.959859 + 0.749495I
a = −0.320732 + 0.294928I
b = 1.068580 + 0.312720I
−3.11272 − 2.58575I 0
u = 0.959859 − 0.749495I
a = −0.320732 − 0.294928I
b = 1.068580 − 0.312720I
−3.11272 + 2.58575I 0
u = 0.611888 + 0.466895I
a = −0.692399 − 0.072885I
b = 0.456299 + 0.774896I
6.65717 + 1.91106I 4.08301 − 1.85461I
u = 0.611888 − 0.466895I
a = −0.692399 + 0.072885I
b = 0.456299 − 0.774896I
6.65717 − 1.91106I 4.08301 + 1.85461I
u = 0.226538 + 0.683581I
a = −0.823439 − 0.518819I
b = −0.671321 + 0.719640I
5.38858 + 1.85504I 1.65918 − 4.21077I
u = 0.226538 − 0.683581I
a = −0.823439 + 0.518819I
b = −0.671321 − 0.719640I
5.38858 − 1.85504I 1.65918 + 4.21077I
u = 1.155400 + 0.665505I
a = 0.270859 − 0.186581I
b = −0.965680 − 0.214781I
−0.48271 + 2.72718I 0
u = 1.155400 − 0.665505I
a = 0.270859 + 0.186581I
b = −0.965680 + 0.214781I
−0.48271 − 2.72718I 0
u = −0.403878 + 0.527053I
a = 1.096710 − 0.004361I
b = 0.568252 − 0.113383I
−1.299740 + 0.476763I −3.83563 + 3.20361I
u = −0.403878 − 0.527053I
a = 1.096710 + 0.004361I
b = 0.568252 + 0.113383I
−1.299740 − 0.476763I −3.83563 − 3.20361I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.534897 + 0.228685I
a = 0.418800 + 0.302376I
b = −0.178813 − 0.430671I
0.996646 + 0.648846I 5.86362 − 2.47329I
u = 0.534897 − 0.228685I
a = 0.418800 − 0.302376I
b = −0.178813 + 0.430671I
0.996646 − 0.648846I 5.86362 + 2.47329I
u = −1.38308 + 0.32486I
a = 0.20853 − 1.64548I
b = 0.855619 + 0.817806I
10.40580 − 5.60687I 0
u = −1.38308 − 0.32486I
a = 0.20853 + 1.64548I
b = 0.855619 − 0.817806I
10.40580 + 5.60687I 0
u = −1.49642 + 0.04783I
a = −0.259577 + 1.075550I
b = 0.089708 − 0.821263I
7.76376 − 1.61657I 0
u = −1.49642 − 0.04783I
a = −0.259577 − 1.075550I
b = 0.089708 + 0.821263I
7.76376 + 1.61657I 0
u = −1.44640 + 0.39214I
a = 0.11942 + 1.45524I
b = −1.138890 − 0.627176I
2.19621 − 7.93848I 0
u = −1.44640 − 0.39214I
a = 0.11942 − 1.45524I
b = −1.138890 + 0.627176I
2.19621 + 7.93848I 0
u = −1.51872 + 0.10886I
a = 0.648267 − 1.044290I
b = −0.271398 + 0.954079I
13.6891 − 3.9188I 0
u = −1.51872 − 0.10886I
a = 0.648267 + 1.044290I
b = −0.271398 − 0.954079I
13.6891 + 3.9188I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47801 + 0.36764I
a = −0.29690 − 1.56872I
b = 1.29773 + 0.68277I
0.98258 − 13.07820I 0
u = −1.47801 − 0.36764I
a = −0.29690 + 1.56872I
b = 1.29773 − 0.68277I
0.98258 + 13.07820I 0
u = −1.48497 + 0.34858I
a = 0.36234 + 1.69675I
b = −1.38205 − 0.76698I
6.9843 − 17.2773I 0
u = −1.48497 − 0.34858I
a = 0.36234 − 1.69675I
b = −1.38205 + 0.76698I
6.9843 + 17.2773I 0
u = −1.69423 + 0.09721I
a = −0.688971 + 0.106749I
b = 0.779066 − 0.284524I
11.36810 + 4.06677I 0
u = −1.69423 − 0.09721I
a = −0.688971 − 0.106749I
b = 0.779066 + 0.284524I
11.36810 − 4.06677I 0
u = −1.70596
a = 0.560470
b = −0.674998
7.03344 0
8
II. I
u
2
= h−2.59 × 10
9
a
5
u
4
+ 1.73 × 10
9
a
4
u
4
+ · · · + 1.48 × 10
10
a + 2.75 ×
10
9
, a
4
u
4
+ 2u
4
a
3
+ · · · − 2a + 5, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
a
0.124859a
5
u
4
− 0.0832850a
4
u
4
+ ··· − 0.711427a − 0.132394
a
7
=
u
−u
3
+ u
a
8
=
−0.0979620a
5
u
4
+ 0.0759674a
4
u
4
+ ··· + 0.505812a − 0.113842
0.0345273a
5
u
4
− 0.00705487a
4
u
4
+ ··· − 0.840409a − 0.179055
a
4
=
0.0432073a
5
u
4
− 0.113086a
4
u
4
+ ··· + 0.500928a + 0.0922135
0.0502622a
5
u
4
− 0.0790089a
4
u
4
+ ··· − 0.467161a − 0.981542
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
0.124859a
5
u
4
− 0.0832850a
4
u
4
+ ··· + 0.288573a − 0.132394
0.124859a
5
u
4
− 0.0832850a
4
u
4
+ ··· − 0.711427a − 0.132394
a
1
=
0.284867a
5
u
4
+ 0.0446397a
4
u
4
+ ··· − 1.45328a − 1.34183
0.0515099a
5
u
4
− 0.161076a
4
u
4
+ ··· + 0.812525a − 0.370598
a
9
=
0.0785549a
5
u
4
− 0.0850389a
4
u
4
+ ··· − 0.267433a + 0.538555
−0.00473010a
5
u
4
− 0.0327094a
4
u
4
+ ··· + 0.0682477a − 0.447528
a
5
=
0.194130a
5
u
4
− 0.117364a
4
u
4
+ ··· − 0.691049a + 0.228864
0.117103a
5
u
4
− 0.123426a
4
u
4
+ ··· − 0.336667a + 0.0262128
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
9003260688
20742725197
a
5
u
4
−
2304371456
20742725197
a
4
u
4
+ ··· +
62017865700
20742725197
a +
44509663466
20742725197
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
3
+ 2u − 1)
10
c
2
, c
3
, c
7
c
9
u
30
− 7u
28
+ ··· + 284u − 103
c
5
, c
8
u
30
− 2u
29
+ ··· − 860u + 71
c
6
, c
10
, c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
6
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 4y
2
+ 4y −1)
10
c
2
, c
3
, c
7
c
9
y
30
− 14y
29
+ ··· − 104964y + 10609
c
5
, c
8
y
30
− 6y
29
+ ··· − 715744y + 5041
c
6
, c
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
6
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 1.27787
b = −1.85426
−3.32092 −11.1550
u = −1.21774
a = −0.07135 + 1.91835I
b = −0.605704 − 0.011731I
6.90702 + 5.13794I 0.79908 − 3.20902I
u = −1.21774
a = −0.07135 − 1.91835I
b = −0.605704 + 0.011731I
6.90702 − 5.13794I 0.79908 + 3.20902I
u = −1.21774
a = 0.0333999
b = 1.50658
−3.32092 −11.1550
u = −1.21774
a = −0.58429 + 2.32641I
b = 0.779542 − 1.113750I
6.90702 + 5.13794I 0.79908 − 3.20902I
u = −1.21774
a = −0.58429 − 2.32641I
b = 0.779542 + 1.113750I
6.90702 − 5.13794I 0.79908 + 3.20902I
u = −0.309916 + 0.549911I
a = 0.087576 − 1.097330I
b = 1.36800 + 0.41353I
−5.39290 − 1.53058I −12.12075 + 4.43065I
u = −0.309916 + 0.549911I
a = 0.302344 + 0.470337I
b = 0.068172 − 1.183920I
4.83503 − 6.66852I −0.16695 + 7.63967I
u = −0.309916 + 0.549911I
a = −0.489001 + 0.040863I
b = −0.903808 + 0.742837I
4.83503 + 3.60736I −0.166951 + 1.221630I
u = −0.309916 + 0.549911I
a = −0.08298 + 1.82141I
b = −1.214240 − 0.040664I
−5.39290 − 1.53058I −12.12075 + 4.43065I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309916 + 0.549911I
a = −1.85727 − 0.38802I
b = −0.380077 − 0.431553I
4.83503 + 3.60736I −0.166951 + 1.221630I
u = −0.309916 + 0.549911I
a = 2.03933 − 0.84727I
b = 1.061960 + 0.499774I
4.83503 − 6.66852I −0.16695 + 7.63967I
u = −0.309916 − 0.549911I
a = 0.087576 + 1.097330I
b = 1.36800 − 0.41353I
−5.39290 + 1.53058I −12.12075 − 4.43065I
u = −0.309916 − 0.549911I
a = 0.302344 − 0.470337I
b = 0.068172 + 1.183920I
4.83503 + 6.66852I −0.16695 − 7.63967I
u = −0.309916 − 0.549911I
a = −0.489001 − 0.040863I
b = −0.903808 − 0.742837I
4.83503 − 3.60736I −0.166951 − 1.221630I
u = −0.309916 − 0.549911I
a = −0.08298 − 1.82141I
b = −1.214240 + 0.040664I
−5.39290 + 1.53058I −12.12075 − 4.43065I
u = −0.309916 − 0.549911I
a = −1.85727 + 0.38802I
b = −0.380077 + 0.431553I
4.83503 − 3.60736I −0.166951 − 1.221630I
u = −0.309916 − 0.549911I
a = 2.03933 + 0.84727I
b = 1.061960 − 0.499774I
4.83503 + 6.66852I −0.16695 − 7.63967I
u = 1.41878 + 0.21917I
a = 0.300995 + 0.889843I
b = 0.973408 − 0.513781I
10.37850 − 0.73711I 4.06225 − 0.28957I
u = 1.41878 + 0.21917I
a = −0.847485 − 0.871262I
b = 0.891375 + 0.910540I
10.37850 − 0.73711I 4.06225 − 0.28957I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41878 + 0.21917I
a = −0.09327 − 1.57467I
b = −1.29815 + 0.57331I
10.37850 + 9.53877I 4.06225 − 6.70760I
u = 1.41878 + 0.21917I
a = −0.82131 + 1.49615I
b = 0.986584 − 0.255514I
0.15056 + 4.40083I −7.89155 − 3.49859I
u = 1.41878 + 0.21917I
a = 0.61990 + 1.72184I
b = −0.36003 − 1.51422I
10.37850 + 9.53877I 4.06225 − 6.70760I
u = 1.41878 + 0.21917I
a = 0.84117 − 1.66190I
b = −1.19320 + 0.79966I
0.15056 + 4.40083I −7.89155 − 3.49859I
u = 1.41878 − 0.21917I
a = 0.300995 − 0.889843I
b = 0.973408 + 0.513781I
10.37850 + 0.73711I 4.06225 + 0.28957I
u = 1.41878 − 0.21917I
a = −0.847485 + 0.871262I
b = 0.891375 − 0.910540I
10.37850 + 0.73711I 4.06225 + 0.28957I
u = 1.41878 − 0.21917I
a = −0.09327 + 1.57467I
b = −1.29815 − 0.57331I
10.37850 − 9.53877I 4.06225 + 6.70760I
u = 1.41878 − 0.21917I
a = −0.82131 − 1.49615I
b = 0.986584 + 0.255514I
0.15056 − 4.40083I −7.89155 + 3.49859I
u = 1.41878 − 0.21917I
a = 0.61990 − 1.72184I
b = −0.36003 + 1.51422I
10.37850 − 9.53877I 4.06225 + 6.70760I
u = 1.41878 − 0.21917I
a = 0.84117 + 1.66190I
b = −1.19320 − 0.79966I
0.15056 − 4.40083I −7.89155 + 3.49859I
14
III. I
u
3
= h−1.25 × 10
19
a
7
u
4
− 3.69 × 10
18
a
6
u
4
+ · · · − 3.06 × 10
19
a + 1.53 ×
10
20
, a
7
u
4
+ 3a
6
u
4
+ · · · + 5a − 2, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
a
0.0975958a
7
u
4
+ 0.0287075a
6
u
4
+ ··· + 0.238235a − 1.18775
a
7
=
u
−u
3
+ u
a
8
=
0.0276431a
7
u
4
+ 0.0849279a
6
u
4
+ ··· + 0.0296300a − 0.220137
0.0600561a
7
u
4
+ 0.0555266a
6
u
4
+ ··· + 0.749500a − 1.15847
a
4
=
0.00211354a
7
u
4
− 0.188289a
6
u
4
+ ··· − 0.889871a − 0.546554
−0.0608280a
7
u
4
− 0.206776a
6
u
4
+ ··· − 0.852334a + 0.0387557
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
0.0975958a
7
u
4
+ 0.0287075a
6
u
4
+ ··· + 1.23823a − 1.18775
0.0975958a
7
u
4
+ 0.0287075a
6
u
4
+ ··· + 0.238235a − 1.18775
a
1
=
0.100783a
7
u
4
− 0.535652a
6
u
4
+ ··· − 0.974337a − 0.112671
−0.0892132a
7
u
4
− 0.252070a
6
u
4
+ ··· − 1.16430a − 0.394363
a
9
=
0.137649a
7
u
4
− 0.0196861a
6
u
4
+ ··· + 0.367556a − 0.443696
0.130118a
7
u
4
− 0.105349a
6
u
4
+ ··· − 0.598093a − 1.74754
a
5
=
−0.109449a
7
u
4
− 0.350445a
6
u
4
+ ··· − 1.86475a + 1.24226
−0.200587a
7
u
4
− 0.180483a
6
u
4
+ ··· − 1.73289a + 1.61500
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
2502287270436
24311107335083
a
7
u
4
−
11867301610360
24311107335083
a
6
u
4
+ ··· −
101785824635476
24311107335083
a +
52009104080618
24311107335083
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
10
c
2
, c
3
, c
7
c
9
u
40
+ u
39
+ ··· + 330u + 139
c
5
, c
8
u
40
− 5u
39
+ ··· + 16u + 7
c
6
, c
10
, c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
8
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
10
c
2
, c
3
, c
7
c
9
y
40
− 35y
39
+ ··· − 336860y + 19321
c
5
, c
8
y
40
+ 13y
39
+ ··· + 724y + 49
c
6
, c
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
8
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.274675 + 0.568128I
b = −1.44788 + 0.01740I
0.75615 + 2.02988I −2.51886 − 3.46410I
u = −1.21774
a = −0.274675 − 0.568128I
b = −1.44788 − 0.01740I
0.75615 − 2.02988I −2.51886 + 3.46410I
u = −1.21774
a = −1.52347 + 0.70612I
b = 1.92464 − 0.35527I
0.75615 + 2.02988I −2.51886 − 3.46410I
u = −1.21774
a = −1.52347 − 0.70612I
b = 1.92464 + 0.35527I
0.75615 − 2.02988I −2.51886 + 3.46410I
u = −1.21774
a = −0.13258 + 1.80838I
b = 0.786811 − 0.282066I
0.75615 − 2.02988I −2.51886 + 3.46410I
u = −1.21774
a = −0.13258 − 1.80838I
b = 0.786811 + 0.282066I
0.75615 + 2.02988I −2.51886 − 3.46410I
u = −1.21774
a = 0.48468 + 1.97050I
b = −0.880168 − 0.719885I
0.75615 − 2.02988I −2.51886 + 3.46410I
u = −1.21774
a = 0.48468 − 1.97050I
b = −0.880168 + 0.719885I
0.75615 + 2.02988I −2.51886 − 3.46410I
u = −0.309916 + 0.549911I
a = 0.939913 + 0.332699I
b = 0.353022 − 0.289251I
−1.315830 + 0.499304I −3.48489 + 0.96655I
u = −0.309916 + 0.549911I
a = 0.066805 + 0.994497I
b = −1.22515 − 0.73607I
−1.31583 − 3.56046I −3.48489 + 7.89475I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309916 + 0.549911I
a = −0.236439 + 0.948140I
b = −1.58368 − 0.22473I
−1.315830 + 0.499304I −3.48489 + 0.96655I
u = −0.309916 + 0.549911I
a = 1.148030 − 0.151525I
b = 0.762797 − 0.053718I
−1.315830 + 0.499304I −3.48489 + 0.96655I
u = −0.309916 + 0.549911I
a = −0.473712 − 0.544424I
b = 0.001897 + 0.845606I
−1.31583 − 3.56046I −3.48489 + 7.89475I
u = −0.309916 + 0.549911I
a = −1.61176 + 0.75211I
b = −1.035150 − 0.302398I
−1.31583 − 3.56046I −3.48489 + 7.89475I
u = −0.309916 + 0.549911I
a = −0.47351 − 1.93661I
b = 1.010500 − 0.137162I
−1.315830 + 0.499304I −3.48489 + 0.96655I
u = −0.309916 + 0.549911I
a = 0.63053 − 1.99191I
b = 1.376650 + 0.075353I
−1.31583 − 3.56046I −3.48489 + 7.89475I
u = −0.309916 − 0.549911I
a = 0.939913 − 0.332699I
b = 0.353022 + 0.289251I
−1.315830 − 0.499304I −3.48489 − 0.96655I
u = −0.309916 − 0.549911I
a = 0.066805 − 0.994497I
b = −1.22515 + 0.73607I
−1.31583 + 3.56046I −3.48489 − 7.89475I
u = −0.309916 − 0.549911I
a = −0.236439 − 0.948140I
b = −1.58368 + 0.22473I
−1.315830 − 0.499304I −3.48489 − 0.96655I
u = −0.309916 − 0.549911I
a = 1.148030 + 0.151525I
b = 0.762797 + 0.053718I
−1.315830 − 0.499304I −3.48489 − 0.96655I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309916 − 0.549911I
a = −0.473712 + 0.544424I
b = 0.001897 − 0.845606I
−1.31583 + 3.56046I −3.48489 − 7.89475I
u = −0.309916 − 0.549911I
a = −1.61176 − 0.75211I
b = −1.035150 + 0.302398I
−1.31583 + 3.56046I −3.48489 − 7.89475I
u = −0.309916 − 0.549911I
a = −0.47351 + 1.93661I
b = 1.010500 + 0.137162I
−1.315830 − 0.499304I −3.48489 − 0.96655I
u = −0.309916 − 0.549911I
a = 0.63053 + 1.99191I
b = 1.376650 − 0.075353I
−1.31583 + 3.56046I −3.48489 − 7.89475I
u = 1.41878 + 0.21917I
a = 0.053326 − 1.038210I
b = −1.129730 + 0.421599I
4.22763 + 2.37095I 0.744314 − 0.034484I
u = 1.41878 + 0.21917I
a = 0.429676 + 1.050940I
b = −0.493899 − 0.870912I
4.22763 + 2.37095I 0.744314 − 0.034484I
u = 1.41878 + 0.21917I
a = −0.073718 + 1.400720I
b = 1.252220 − 0.487412I
4.22763 + 6.43072I 0.74431 − 6.96269I
u = 1.41878 + 0.21917I
a = 0.88226 − 1.26405I
b = −0.678147 + 0.081197I
4.22763 + 2.37095I 0.744314 − 0.034484I
u = 1.41878 + 0.21917I
a = −0.39862 − 1.50246I
b = 0.260452 + 1.228950I
4.22763 + 6.43072I 0.74431 − 6.96269I
u = 1.41878 + 0.21917I
a = −1.07056 + 1.47204I
b = 1.49026 − 0.62661I
4.22763 + 2.37095I 0.744314 − 0.034484I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41878 + 0.21917I
a = 0.77721 − 1.66215I
b = −1.229700 + 0.215548I
4.22763 + 6.43072I 0.74431 − 6.96269I
u = 1.41878 + 0.21917I
a = −0.64337 + 1.90875I
b = 0.98424 − 1.16251I
4.22763 + 6.43072I 0.74431 − 6.96269I
u = 1.41878 − 0.21917I
a = 0.053326 + 1.038210I
b = −1.129730 − 0.421599I
4.22763 − 2.37095I 0.744314 + 0.034484I
u = 1.41878 − 0.21917I
a = 0.429676 − 1.050940I
b = −0.493899 + 0.870912I
4.22763 − 2.37095I 0.744314 + 0.034484I
u = 1.41878 − 0.21917I
a = −0.073718 − 1.400720I
b = 1.252220 + 0.487412I
4.22763 − 6.43072I 0.74431 + 6.96269I
u = 1.41878 − 0.21917I
a = 0.88226 + 1.26405I
b = −0.678147 − 0.081197I
4.22763 − 2.37095I 0.744314 + 0.034484I
u = 1.41878 − 0.21917I
a = −0.39862 + 1.50246I
b = 0.260452 − 1.228950I
4.22763 − 6.43072I 0.74431 + 6.96269I
u = 1.41878 − 0.21917I
a = −1.07056 − 1.47204I
b = 1.49026 + 0.62661I
4.22763 − 2.37095I 0.744314 + 0.034484I
u = 1.41878 − 0.21917I
a = 0.77721 + 1.66215I
b = −1.229700 − 0.215548I
4.22763 − 6.43072I 0.74431 + 6.96269I
u = 1.41878 − 0.21917I
a = −0.64337 − 1.90875I
b = 0.98424 + 1.16251I
4.22763 − 6.43072I 0.74431 + 6.96269I
21
IV. I
u
4
=
h−3u
24
+5u
23
+· · ·+b−3, −3u
23
+37u
21
+· · ·+a+1, u
25
−14u
23
+· · ·−6u
2
+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
3u
23
− 37u
21
+ ··· − 3u − 1
3u
24
− 5u
23
+ ··· − u + 3
a
7
=
u
−u
3
+ u
a
8
=
−u
23
− u
22
+ ··· − 27u
2
+ 3
u
22
− 12u
20
+ ··· + 4u − 1
a
4
=
−2u
24
+ 4u
23
+ ··· − 5u − 4
−4u
24
+ 4u
23
+ ··· + 7u
2
− 2
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
3u
24
− 2u
23
+ ··· − 4u + 2
3u
24
− 5u
23
+ ··· − u + 3
a
1
=
3u
24
− 4u
23
+ ··· − 11u + 3
6u
24
− 7u
23
+ ··· − 2u + 3
a
9
=
−u
23
+ 13u
21
+ ··· + 2u + 3
u
22
− 12u
20
+ ··· + 3u − 1
a
5
=
−2u
22
+ 24u
20
+ ··· + 5u − 1
−u
24
+ 3u
23
+ ··· + 3u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
24
− 2u
23
+ 49u
22
+ 19u
21
− 257u
20
− 77u
19
+ 745u
18
+
179u
17
− 1281u
16
− 279u
15
+ 1281u
14
+ 331u
13
− 628u
12
− 325u
11
+ 27u
10
+ 261u
9
+
42u
8
− 136u
7
+ 64u
6
+ 5u
5
− 37u
4
+ 23u
3
+ 13u
2
+ 7u − 6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
25
− 3u
24
+ ··· − u
2
− 1
c
2
, c
7
u
25
+ u
24
+ ··· − 11u
2
+ 1
c
3
, c
9
u
25
− u
24
+ ··· + 11u
2
− 1
c
4
u
25
+ 3u
24
+ ··· + u
2
+ 1
c
5
, c
8
u
25
− 5u
22
+ ··· + 4u
2
+ 1
c
6
u
25
− 14u
23
+ ··· + 6u
2
− 1
c
10
, c
11
u
25
− 14u
23
+ ··· − 6u
2
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
25
+ 25y
24
+ ··· − 2y −1
c
2
, c
3
, c
7
c
9
y
25
− 25y
24
+ ··· + 22y −1
c
5
, c
8
y
25
− 17y
22
+ ··· − 8y −1
c
6
, c
10
, c
11
y
25
− 28y
24
+ ··· + 12y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.030090 + 0.454054I
a = 0.448614 + 0.296928I
b = −1.258210 + 0.063634I
−1.83034 − 3.35231I −4.09027 + 4.01077I
u = −1.030090 − 0.454054I
a = 0.448614 − 0.296928I
b = −1.258210 − 0.063634I
−1.83034 + 3.35231I −4.09027 − 4.01077I
u = −0.268282 + 0.743510I
a = 0.342777 − 0.927210I
b = 1.132150 + 0.194527I
−3.94761 − 1.10722I −5.31691 + 1.26220I
u = −0.268282 − 0.743510I
a = 0.342777 + 0.927210I
b = 1.132150 − 0.194527I
−3.94761 + 1.10722I −5.31691 − 1.26220I
u = 0.652668 + 0.432339I
a = 1.20634 + 0.76303I
b = 0.599681 + 0.156351I
−1.41781 − 1.00721I −7.76689 + 8.43698I
u = 0.652668 − 0.432339I
a = 1.20634 − 0.76303I
b = 0.599681 − 0.156351I
−1.41781 + 1.00721I −7.76689 − 8.43698I
u = 1.143480 + 0.452971I
a = −0.412983 − 1.196470I
b = −0.714465 + 0.191546I
0.35046 + 4.37521I −6.32546 + 0.18516I
u = 1.143480 − 0.452971I
a = −0.412983 + 1.196470I
b = −0.714465 − 0.191546I
0.35046 − 4.37521I −6.32546 − 0.18516I
u = −1.24578
a = 0.597201
b = −1.67082
−2.74092 5.86080
u = −1.283100 + 0.051744I
a = −0.591468 + 0.025760I
b = 1.72633 − 0.18454I
1.75989 + 1.39477I 4.78234 + 0.86929I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.283100 − 0.051744I
a = −0.591468 − 0.025760I
b = 1.72633 + 0.18454I
1.75989 − 1.39477I 4.78234 − 0.86929I
u = 1.294680 + 0.135323I
a = −0.35608 + 2.37011I
b = 0.639088 − 0.784249I
7.90352 + 6.28581I 4.67493 − 7.71186I
u = 1.294680 − 0.135323I
a = −0.35608 − 2.37011I
b = 0.639088 + 0.784249I
7.90352 − 6.28581I 4.67493 + 7.71186I
u = −0.690842
a = −1.19564
b = 1.39664
−5.04446 −9.92490
u = 1.384300 + 0.232124I
a = 0.58085 − 1.61782I
b = −0.941880 + 0.535029I
1.22524 + 4.53551I 0.99353 − 4.86693I
u = 1.384300 − 0.232124I
a = 0.58085 + 1.61782I
b = −0.941880 − 0.535029I
1.22524 − 4.53551I 0.99353 + 4.86693I
u = 1.45475 + 0.16975I
a = −1.11846 + 1.47785I
b = 1.186710 − 0.572548I
4.31160 + 4.32943I 1.56300 − 3.56691I
u = 1.45475 − 0.16975I
a = −1.11846 − 1.47785I
b = 1.186710 + 0.572548I
4.31160 − 4.32943I 1.56300 + 3.56691I
u = 0.347505 + 0.259956I
a = −2.22603 − 1.29308I
b = −0.552650 − 0.557071I
4.59738 − 4.80390I −2.62909 + 5.16420I
u = 0.347505 − 0.259956I
a = −2.22603 + 1.29308I
b = −0.552650 + 0.557071I
4.59738 + 4.80390I −2.62909 − 5.16420I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.288232 + 0.286768I
a = 0.98808 + 2.50810I
b = −1.41949 − 0.27834I
−1.55985 − 2.35760I −5.72488 + 1.44341I
u = −0.288232 − 0.286768I
a = 0.98808 − 2.50810I
b = −1.41949 + 0.27834I
−1.55985 + 2.35760I −5.72488 − 1.44341I
u = −1.61550 + 0.05395I
a = −0.1069810 + 0.0764861I
b = 0.434263 − 0.347377I
11.83330 + 3.60878I 6.43525 + 0.91653I
u = −1.61550 − 0.05395I
a = −0.1069810 − 0.0764861I
b = 0.434263 + 0.347377I
11.83330 − 3.60878I 6.43525 − 0.91653I
u = −1.64773
a = 0.0891278
b = −0.388841
7.39199 10.8730
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
3
+ 2u − 1)
10
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
10
(u
25
− 3u
24
+ ··· − u
2
− 1)
· (u
37
− 12u
36
+ ··· + 464u − 32)
c
2
, c
7
(u
25
+ u
24
+ ··· − 11u
2
+ 1)(u
30
− 7u
28
+ ··· + 284u − 103)
· (u
37
− u
36
+ ··· + u − 1)(u
40
+ u
39
+ ··· + 330u + 139)
c
3
, c
9
(u
25
− u
24
+ ··· + 11u
2
− 1)(u
30
− 7u
28
+ ··· + 284u − 103)
· (u
37
− u
36
+ ··· + u − 1)(u
40
+ u
39
+ ··· + 330u + 139)
c
4
((u
3
+ 2u − 1)
10
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
10
(u
25
+ 3u
24
+ ··· + u
2
+ 1)
· (u
37
− 12u
36
+ ··· + 464u − 32)
c
5
, c
8
(u
25
− 5u
22
+ ··· + 4u
2
+ 1)(u
30
− 2u
29
+ ··· − 860u + 71)
· (u
37
− 15u
35
+ ··· + 3u + 1)(u
40
− 5u
39
+ ··· + 16u + 7)
c
6
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
14
)(u
25
− 14u
23
+ ··· + 6u
2
− 1)
· (u
37
+ 15u
36
+ ··· + 128u + 128)
c
10
, c
11
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
14
)(u
25
− 14u
23
+ ··· − 6u
2
+ 1)
· (u
37
+ 15u
36
+ ··· + 128u + 128)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 4y
2
+ 4y −1)
10
(y
4
+ 3y
3
+ 2y
2
+ 1)
10
· (y
25
+ 25y
24
+ ··· − 2y −1)(y
37
+ 32y
36
+ ··· − 3328y −1024)
c
2
, c
3
, c
7
c
9
(y
25
− 25y
24
+ ··· + 22y −1)(y
30
− 14y
29
+ ··· − 104964y + 10609)
· (y
37
− 19y
36
+ ··· + 9y −1)(y
40
− 35y
39
+ ··· − 336860y + 19321)
c
5
, c
8
(y
25
− 17y
22
+ ··· − 8y −1)(y
30
− 6y
29
+ ··· − 715744y + 5041)
· (y
37
− 30y
36
+ ··· + 19y −1)(y
40
+ 13y
39
+ ··· + 724y + 49)
c
6
, c
10
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
14
)(y
25
− 28y
24
+ ··· + 12y −1)
· (y
37
− 33y
36
+ ··· + 65536y −16384)
29
