12n
0813
(K12n
0813
)
A knot diagram
1
Linearized knot diagam
4 7 11 7 9 3 1 12 5 8 3 10
Solving Sequence
8,10 3,11
4 12 1 7 5 2 6 9
c
10
c
3
c
11
c
12
c
7
c
4
c
2
c
6
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−771111978722u
20
+ 1238251991594u
19
+ ··· + 10836897427858b + 3727293790301,
− 4119811015012u
20
+ 1626728296443u
19
+ ··· + 5418448713929a + 9392161389977,
u
21
− 8u
18
+ ··· − 4u − 1i
I
u
2
= h2.42041 × 10
171
u
57
+ 5.72134 × 10
171
u
56
+ ··· + 5.04153 × 10
173
b + 9.75536 × 10
173
,
8.38866 × 10
171
u
57
+ 3.51276 × 10
172
u
56
+ ··· + 2.52076 × 10
173
a + 1.91905 × 10
174
,
u
58
+ 4u
57
+ ··· + 872u + 128i
I
u
3
= h−5u
9
+ 5u
8
+ 12u
7
+ 18u
6
− 41u
5
− 21u
4
+ 7u
3
+ 79u
2
+ 17b + 3u − 28,
− 26u
9
− 59u
8
− 26u
7
+ 131u
6
+ 137u
5
− 116u
4
− 375u
3
− 208u
2
+ 17a + 87u + 123,
u
10
+ u
9
− u
8
− 5u
7
+ u
6
+ 7u
5
+ 7u
4
− 5u
3
− 5u
2
+ u + 1i
I
u
4
= h2.30529 × 10
30
u
27
− 1.47328 × 10
31
u
26
+ ··· + 2.21437 × 10
30
b + 1.35121 × 10
30
,
6.64906 × 10
30
u
27
− 5.31889 × 10
31
u
26
+ ··· + 8.85748 × 10
30
a − 3.64020 × 10
31
, u
28
− 7u
27
+ ··· − 6u + 1i
I
u
5
= hb + 1, a − 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 118 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−7.71×10
11
u
20
+1.24×10
12
u
19
+· · ·+1.08×10
13
b+3.73×10
12
, −4.12×
10
12
u
20
+1.63×10
12
u
19
+· · ·+5.42×10
12
a+9.39×10
12
, u
21
−8u
18
+· · ·−4u−1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
3
=
0.760330u
20
− 0.300220u
19
+ ··· − 8.07239u − 1.73337
0.0711562u
20
− 0.114263u
19
+ ··· − 0.839947u − 0.343945
a
11
=
1
−u
2
a
4
=
0.942629u
20
− 0.355006u
19
+ ··· − 9.35289u − 2.37753
0.0479865u
20
− 0.0935026u
19
+ ··· − 0.803102u − 0.289159
a
12
=
−0.219243u
20
+ 0.0523993u
19
+ ··· − 3.48114u + 2.80752
−u
a
1
=
−0.219243u
20
+ 0.0523993u
19
+ ··· − 4.48114u + 2.80752
−u
a
7
=
−0.446182u
20
+ 0.175167u
19
+ ··· + 6.28299u − 0.878517
−0.0893615u
20
− 0.0192813u
19
+ ··· + 1.00965u − 0.0523993
a
5
=
1.74610u
20
− 0.337342u
19
+ ··· − 10.8540u − 4.81375
0.182299u
20
− 0.0547859u
19
+ ··· − 1.28050u − 0.644165
a
2
=
0.0498962u
20
− 0.0689951u
19
+ ··· − 3.44956u + 0.288895
−0.0745060u
20
− 0.133557u
19
+ ··· − 0.359376u − 0.0997824
a
6
=
−1.19456u
20
+ 0.321015u
19
+ ··· + 9.77795u + 2.14931
−0.154049u
20
+ 0.0478163u
19
+ ··· + 0.918068u + 0.233126
a
9
=
−0.267459u
20
+ 0.213730u
19
+ ··· + 6.26370u − 0.773718
−0.0893615u
20
− 0.0192813u
19
+ ··· + 1.00965u − 0.0523993
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
11409897026945
5418448713929
u
20
+
2927023670684
5418448713929
u
19
+ ··· −
19517453412181
5418448713929
u −
26799066510012
5418448713929
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
21
− u
20
+ ··· + 12u − 1
c
2
, c
6
u
21
+ 16u
20
+ ··· − 1136u − 272
c
3
, c
5
, c
9
c
11
u
21
− u
20
+ ··· + 8u − 2
c
7
u
21
− 13u
20
+ ··· + 640u − 64
c
8
u
21
− 13u
20
+ ··· + 936u − 128
c
10
, c
12
u
21
− 8u
18
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 29y
20
+ ··· + 120y −1
c
2
, c
6
y
21
− 20y
20
+ ··· + 874880y −73984
c
3
, c
5
, c
9
c
11
y
21
+ 23y
20
+ ··· + 24y −4
c
7
y
21
+ 7y
20
+ ··· + 47104y −4096
c
8
y
21
+ 3y
20
+ ··· − 15808y −16384
c
10
, c
12
y
21
+ 20y
19
+ ··· + 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.780151 + 0.827041I
a = −0.690468 − 0.384442I
b = −1.21395 + 0.80321I
−1.79892 + 4.20374I 3.16458 − 5.67138I
u = 0.780151 − 0.827041I
a = −0.690468 + 0.384442I
b = −1.21395 − 0.80321I
−1.79892 − 4.20374I 3.16458 + 5.67138I
u = −0.734929 + 0.983008I
a = 0.79863 + 1.64890I
b = −1.47894 + 0.34724I
−15.5048 − 8.1479I −2.83574 + 5.35487I
u = −0.734929 − 0.983008I
a = 0.79863 − 1.64890I
b = −1.47894 − 0.34724I
−15.5048 + 8.1479I −2.83574 − 5.35487I
u = 0.748622
a = 0.414600
b = −0.565271
1.12273 10.2330
u = −0.510970 + 1.147390I
a = −0.175396 − 1.317370I
b = 1.59053 − 0.12000I
−7.52223 + 0.54463I −4.47337 − 1.01574I
u = −0.510970 − 1.147390I
a = −0.175396 + 1.317370I
b = 1.59053 + 0.12000I
−7.52223 − 0.54463I −4.47337 + 1.01574I
u = 0.387738 + 0.630793I
a = −2.09012 + 1.13108I
b = −0.471873 + 0.482797I
−1.81465 + 5.18759I −1.09861 − 9.26554I
u = 0.387738 − 0.630793I
a = −2.09012 − 1.13108I
b = −0.471873 − 0.482797I
−1.81465 − 5.18759I −1.09861 + 9.26554I
u = 1.213920 + 0.380226I
a = 0.670089 + 0.555684I
b = −0.377735 + 0.080128I
−8.67588 + 5.06112I −0.60518 − 3.55443I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.213920 − 0.380226I
a = 0.670089 − 0.555684I
b = −0.377735 − 0.080128I
−8.67588 − 5.06112I −0.60518 + 3.55443I
u = −0.182083 + 0.679332I
a = 0.864922 + 0.185844I
b = 0.955096 + 0.761255I
−2.90774 − 1.37269I −0.74745 − 2.22318I
u = −0.182083 − 0.679332I
a = 0.864922 − 0.185844I
b = 0.955096 − 0.761255I
−2.90774 + 1.37269I −0.74745 + 2.22318I
u = 1.194720 + 0.585487I
a = −0.162383 + 0.348718I
b = 1.075150 − 0.656567I
4.25702 + 1.52913I 13.27280 − 4.02623I
u = 1.194720 − 0.585487I
a = −0.162383 − 0.348718I
b = 1.075150 + 0.656567I
4.25702 − 1.52913I 13.27280 + 4.02623I
u = −1.01396 + 1.27877I
a = 0.340372 + 0.943110I
b = −2.25579 − 0.25929I
−4.26811 − 4.24791I −1.30490 + 2.45489I
u = −1.01396 − 1.27877I
a = 0.340372 − 0.943110I
b = −2.25579 + 0.25929I
−4.26811 + 4.24791I −1.30490 − 2.45489I
u = −0.227771 + 0.119755I
a = 0.87630 − 3.85579I
b = −0.086727 − 0.449153I
−0.23558 + 1.56268I −3.45404 − 3.64956I
u = −0.227771 − 0.119755I
a = 0.87630 + 3.85579I
b = −0.086727 + 0.449153I
−0.23558 − 1.56268I −3.45404 + 3.64956I
u = −1.28113 + 1.23800I
a = −0.639248 − 1.006370I
b = 2.54688 − 0.25973I
−13.0835 − 16.6074I −1.03466 + 7.18152I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28113 − 1.23800I
a = −0.639248 + 1.006370I
b = 2.54688 + 0.25973I
−13.0835 + 16.6074I −1.03466 − 7.18152I
7
II. I
u
2
= h2.42 × 10
171
u
57
+ 5.72 × 10
171
u
56
+ · · · + 5.04 × 10
173
b + 9.76 ×
10
173
, 8.39 × 10
171
u
57
+ 3.51 × 10
172
u
56
+ · · · + 2.52 × 10
173
a + 1.92 ×
10
174
, u
58
+ 4u
57
+ · · · + 872u + 128i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
3
=
−0.0332782u
57
− 0.139353u
56
+ ··· − 61.1935u − 7.61297
−0.00480094u
57
− 0.0113484u
56
+ ··· − 3.57110u − 1.93500
a
11
=
1
−u
2
a
4
=
−0.0224821u
57
− 0.0992681u
56
+ ··· − 55.0638u − 8.74925
−0.00127926u
57
− 0.00171673u
56
+ ··· − 4.89206u − 2.33175
a
12
=
0.00965185u
57
+ 0.0517282u
56
+ ··· + 52.0141u + 6.96187
0.0269724u
57
+ 0.0878524u
56
+ ··· + 19.0763u + 3.06564
a
1
=
0.0366242u
57
+ 0.139581u
56
+ ··· + 71.0904u + 10.0275
0.0269724u
57
+ 0.0878524u
56
+ ··· + 19.0763u + 3.06564
a
7
=
−0.0333509u
57
− 0.107996u
56
+ ··· + 8.88183u + 8.19667
−0.00259877u
57
− 0.00389980u
56
+ ··· + 0.104493u − 0.784710
a
5
=
−0.0134212u
57
− 0.0745099u
56
+ ··· − 95.0593u − 18.5426
−0.0225240u
57
− 0.0732163u
56
+ ··· − 14.8358u − 2.37053
a
2
=
0.0470288u
57
+ 0.169352u
56
+ ··· + 70.9949u + 9.41598
0.00210572u
57
+ 0.00443464u
56
+ ··· − 9.85091u − 1.67880
a
6
=
−0.0220552u
57
− 0.0958637u
56
+ ··· − 17.2846u + 5.83868
−0.0257657u
57
− 0.0695737u
56
+ ··· − 5.89943u − 2.31925
a
9
=
−0.0275206u
57
− 0.0998945u
56
+ ··· + 8.84557u + 10.2097
−0.00323154u
57
− 0.00420204u
56
+ ··· + 1.93176u − 1.22832
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0701964u
57
+ 0.235361u
56
+ ··· + 91.5102u + 17.9592
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
58
− 3u
57
+ ··· − 38440u + 10672
c
2
, c
6
(u
29
− 7u
28
+ ··· + 2424u − 1357)
2
c
3
, c
5
, c
9
c
11
u
58
+ 23u
56
+ ··· − 14700u + 2392
c
7
(u
29
+ 5u
28
+ ··· − 10u − 1)
2
c
8
(u
29
+ 7u
28
+ ··· − 1953u − 961)
2
c
10
, c
12
u
58
+ 4u
57
+ ··· + 872u + 128
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
58
− 67y
57
+ ··· − 791039808y + 113891584
c
2
, c
6
(y
29
− 47y
28
+ ··· + 15678744y −1841449)
2
c
3
, c
5
, c
9
c
11
y
58
+ 46y
57
+ ··· + 6901808y + 5721664
c
7
(y
29
+ 13y
28
+ ··· + 2y −1)
2
c
8
(y
29
+ 19y
28
+ ··· − 1357893y −923521)
2
c
10
, c
12
y
58
− 2y
57
+ ··· + 158144y + 16384
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.970952 + 0.123206I
a = 0.819901 + 0.428320I
b = −0.463224 + 0.438381I
−1.00129 − 2.25122I 0.70850 + 7.35840I
u = −0.970952 − 0.123206I
a = 0.819901 − 0.428320I
b = −0.463224 − 0.438381I
−1.00129 + 2.25122I 0.70850 − 7.35840I
u = −0.849400 + 0.391997I
a = 1.133660 − 0.092843I
b = −0.169980 − 0.267743I
−4.53799 − 5.31306I −12.85550 − 1.18184I
u = −0.849400 − 0.391997I
a = 1.133660 + 0.092843I
b = −0.169980 + 0.267743I
−4.53799 + 5.31306I −12.85550 + 1.18184I
u = 0.668341 + 0.894772I
a = −0.22061 + 1.63059I
b = 1.72337 − 0.32598I
−1.59473 + 2.86077I 0
u = 0.668341 − 0.894772I
a = −0.22061 − 1.63059I
b = 1.72337 + 0.32598I
−1.59473 − 2.86077I 0
u = −1.048720 + 0.433555I
a = −1.62647 − 0.54157I
b = 1.232180 + 0.143748I
−2.70098 − 3.11691I 0
u = −1.048720 − 0.433555I
a = −1.62647 + 0.54157I
b = 1.232180 − 0.143748I
−2.70098 + 3.11691I 0
u = 0.799753 + 0.172860I
a = 0.90740 + 1.16182I
b = −0.511323 − 0.052051I
−0.436187 1.66325 + 0.I
u = 0.799753 − 0.172860I
a = 0.90740 − 1.16182I
b = −0.511323 + 0.052051I
−0.436187 1.66325 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399886 + 0.703568I
a = 0.254419 + 0.563089I
b = 1.66971 − 0.15534I
4.94923 + 1.05878I 6.88964 − 6.39170I
u = 0.399886 − 0.703568I
a = 0.254419 − 0.563089I
b = 1.66971 + 0.15534I
4.94923 − 1.05878I 6.88964 + 6.39170I
u = 0.384723 + 0.670475I
a = 0.61392 − 1.55244I
b = 0.244715 + 0.833446I
−13.4224 + 6.4614I −1.40004 − 6.14905I
u = 0.384723 − 0.670475I
a = 0.61392 + 1.55244I
b = 0.244715 − 0.833446I
−13.4224 − 6.4614I −1.40004 + 6.14905I
u = −0.444779 + 0.611693I
a = −0.720516 + 0.511909I
b = 0.814718 − 0.641396I
−10.00880 − 1.84187I −3.77015 + 1.97633I
u = −0.444779 − 0.611693I
a = −0.720516 − 0.511909I
b = 0.814718 + 0.641396I
−10.00880 + 1.84187I −3.77015 − 1.97633I
u = −1.148040 + 0.479507I
a = 0.020090 − 0.365423I
b = 0.076488 + 0.476489I
2.37720 − 6.37942I 0
u = −1.148040 − 0.479507I
a = 0.020090 + 0.365423I
b = 0.076488 − 0.476489I
2.37720 + 6.37942I 0
u = −0.747583 + 0.041584I
a = −1.04107 + 1.54314I
b = 1.11482 − 1.66879I
−9.88997 − 1.48212I −4.03213 + 6.97706I
u = −0.747583 − 0.041584I
a = −1.04107 − 1.54314I
b = 1.11482 + 1.66879I
−9.88997 + 1.48212I −4.03213 − 6.97706I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990749 + 0.766586I
a = 0.280282 + 0.193695I
b = 0.471224 + 0.585624I
−1.59473 − 2.86077I 0
u = −0.990749 − 0.766586I
a = 0.280282 − 0.193695I
b = 0.471224 − 0.585624I
−1.59473 + 2.86077I 0
u = −0.322055 + 0.663247I
a = 0.368825 − 0.558300I
b = −0.154167 − 0.145249I
−0.20224 + 1.88219I 1.13310 − 1.98130I
u = −0.322055 − 0.663247I
a = 0.368825 + 0.558300I
b = −0.154167 + 0.145249I
−0.20224 − 1.88219I 1.13310 + 1.98130I
u = 0.409588 + 0.552591I
a = 0.086336 − 0.139868I
b = −1.44779 + 0.07063I
2.85960 − 1.33779I −0.52216 − 4.91076I
u = 0.409588 − 0.552591I
a = 0.086336 + 0.139868I
b = −1.44779 − 0.07063I
2.85960 + 1.33779I −0.52216 + 4.91076I
u = 0.209872 + 0.593415I
a = 4.85128 + 1.58466I
b = 1.82822 − 1.10785I
−4.53799 + 5.31306I −12.85550 + 1.18184I
u = 0.209872 − 0.593415I
a = 4.85128 − 1.58466I
b = 1.82822 + 1.10785I
−4.53799 − 5.31306I −12.85550 − 1.18184I
u = −0.616507 + 1.267370I
a = −0.028814 − 0.220341I
b = −1.49206 − 0.24372I
−7.58726 − 8.01913I 0
u = −0.616507 − 1.267370I
a = −0.028814 + 0.220341I
b = −1.49206 + 0.24372I
−7.58726 + 8.01913I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.462036 + 0.360242I
a = −0.98315 + 2.74951I
b = 0.718996 − 0.877020I
−1.00129 + 2.25122I 0.70850 − 7.35840I
u = 0.462036 − 0.360242I
a = −0.98315 − 2.74951I
b = 0.718996 + 0.877020I
−1.00129 − 2.25122I 0.70850 + 7.35840I
u = −0.70903 + 1.24762I
a = −0.301495 − 1.194180I
b = 1.54241 − 0.07861I
−5.00732 − 7.85020I 0
u = −0.70903 − 1.24762I
a = −0.301495 + 1.194180I
b = 1.54241 + 0.07861I
−5.00732 + 7.85020I 0
u = −0.273245 + 0.334410I
a = −2.46883 − 1.26481I
b = −0.302031 + 0.443910I
−0.20224 − 1.88219I 1.13310 + 1.98130I
u = −0.273245 − 0.334410I
a = −2.46883 + 1.26481I
b = −0.302031 − 0.443910I
−0.20224 + 1.88219I 1.13310 − 1.98130I
u = −1.30879 + 0.89323I
a = 0.897618 + 1.082250I
b = −2.86240 − 0.17407I
−5.00732 − 7.85020I 0
u = −1.30879 − 0.89323I
a = 0.897618 − 1.082250I
b = −2.86240 + 0.17407I
−5.00732 + 7.85020I 0
u = −0.166439 + 0.374859I
a = 0.95887 + 4.12820I
b = −0.420169 − 0.720783I
−2.70098 − 3.11691I 0.54496 + 3.01160I
u = −0.166439 − 0.374859I
a = 0.95887 − 4.12820I
b = −0.420169 + 0.720783I
−2.70098 + 3.11691I 0.54496 − 3.01160I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46535 + 0.65691I
a = −0.589236 − 0.580845I
b = 2.34121 + 1.27625I
−13.23260 + 1.57461I 0
u = −1.46535 − 0.65691I
a = −0.589236 + 0.580845I
b = 2.34121 − 1.27625I
−13.23260 − 1.57461I 0
u = 1.03778 + 1.24149I
a = 0.504942 − 1.241550I
b = −2.29516 − 0.77088I
2.37720 + 6.37942I 0
u = 1.03778 − 1.24149I
a = 0.504942 + 1.241550I
b = −2.29516 + 0.77088I
2.37720 − 6.37942I 0
u = 0.40733 + 1.65602I
a = −0.135708 + 0.910621I
b = 0.109573 + 0.629112I
−13.23260 + 1.57461I 0
u = 0.40733 − 1.65602I
a = −0.135708 − 0.910621I
b = 0.109573 − 0.629112I
−13.23260 − 1.57461I 0
u = 0.60006 + 1.60353I
a = 0.231011 − 1.099380I
b = −1.41705 − 1.25171I
−10.00880 + 1.84187I 0
u = 0.60006 − 1.60353I
a = 0.231011 + 1.099380I
b = −1.41705 + 1.25171I
−10.00880 − 1.84187I 0
u = 1.75023 + 0.03038I
a = −0.089242 + 0.625251I
b = 0.09728 − 2.83583I
4.94923 + 1.05878I 0
u = 1.75023 − 0.03038I
a = −0.089242 − 0.625251I
b = 0.09728 + 2.83583I
4.94923 − 1.05878I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.87494 + 0.16735I
a = 0.548369 + 0.611508I
b = −1.20667 − 3.29329I
2.85960 − 1.33779I 0
u = 1.87494 − 0.16735I
a = 0.548369 − 0.611508I
b = −1.20667 + 3.29329I
2.85960 + 1.33779I 0
u = 1.47857 + 1.23037I
a = −0.528572 + 0.875814I
b = 3.23832 − 0.19930I
−7.58726 + 8.01913I 0
u = 1.47857 − 1.23037I
a = −0.528572 − 0.875814I
b = 3.23832 + 0.19930I
−7.58726 − 8.01913I 0
u = 0.01823 + 1.94450I
a = −0.003111 − 0.920627I
b = 0.08139 − 1.65029I
−9.88997 + 1.48212I 0
u = 0.01823 − 1.94450I
a = −0.003111 + 0.920627I
b = 0.08139 + 1.65029I
−9.88997 − 1.48212I 0
u = −1.43968 + 1.62909I
a = 0.353663 + 0.663908I
b = −3.06261 + 0.28021I
−13.4224 + 6.4614I 0
u = −1.43968 − 1.62909I
a = 0.353663 − 0.663908I
b = −3.06261 − 0.28021I
−13.4224 − 6.4614I 0
16
III. I
u
3
=
h−5u
9
+5u
8
+· · ·+17b−28, −26u
9
−59u
8
+· · ·+17a+123, u
10
+u
9
+· · ·+u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
3
=
1.52941u
9
+ 3.47059u
8
+ ··· − 5.11765u − 7.23529
0.294118u
9
− 0.294118u
8
+ ··· − 0.176471u + 1.64706
a
11
=
1
−u
2
a
4
=
2.94118u
9
+ 5.05882u
8
+ ··· − 8.76471u − 7.52941
−0.352941u
9
− 0.647059u
8
+ ··· + 1.41176u + 1.82353
a
12
=
2.52941u
9
+ 1.47059u
8
+ ··· − 0.117647u + 3.76471
−u
a
1
=
2.52941u
9
+ 1.47059u
8
+ ··· − 1.11765u + 3.76471
−u
a
7
=
2.64706u
9
+ 3.35294u
8
+ ··· − 8.58824u + 2.82353
−1.11765u
9
− 0.882353u
8
+ ··· + 2.47059u − 1.05882
a
5
=
9.64706u
9
+ 11.3529u
8
+ ··· − 26.5882u − 3.17647
−1.41176u
9
− 1.58824u
8
+ ··· + 3.64706u + 0.294118
a
2
=
−0.117647u
9
+ 0.117647u
8
+ ··· + 2.47059u − 4.05882
0.823529u
9
+ 0.176471u
8
+ ··· − 1.29412u + 1.41176
a
6
=
4.82353u
9
+ 6.17647u
8
+ ··· − 15.2941u + 0.411765
−1.52941u
9
− 1.47059u
8
+ ··· + 3.11765u − 0.764706
a
9
=
4.88235u
9
+ 5.11765u
8
+ ··· − 11.5294u + 4.94118
−1.11765u
9
− 0.882353u
8
+ ··· + 2.47059u − 1.05882
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
9
+ 9u
8
−8u
7
−44u
6
+ 15u
5
+ 54u
4
+ 59u
3
−39u
2
−16u + 14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
10
− 2u
8
+ 5u
7
− 2u
6
− 4u
5
+ 12u
4
− 13u
3
+ 10u
2
− 5u + 1
c
2
u
10
− 6u
9
+ ··· − 9u + 1
c
3
, c
9
u
10
+ u
9
+ 7u
8
+ 3u
7
+ 16u
6
+ 2u
5
+ 18u
4
+ 2u
3
+ 10u
2
+ 3
c
5
, c
11
u
10
− u
9
+ 7u
8
− 3u
7
+ 16u
6
− 2u
5
+ 18u
4
− 2u
3
+ 10u
2
+ 3
c
6
u
10
+ 6u
9
+ ··· + 9u + 1
c
7
u
10
+ 2u
9
+ 5u
8
+ 8u
7
+ 8u
6
+ 8u
5
+ 5u
4
+ u
3
+ 4u
2
+ 3
c
8
u
10
+ 5u
9
+ ··· + 233u + 115
c
10
, c
12
u
10
+ u
9
− u
8
− 5u
7
+ u
6
+ 7u
5
+ 7u
4
− 5u
3
− 5u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
10
− 4y
9
+ 7y
7
+ 16y
6
+ 28y
5
+ 46y
4
+ 27y
3
− 6y
2
− 5y + 1
c
2
, c
6
y
10
− 6y
9
+ ··· + y + 1
c
3
, c
5
, c
9
c
11
y
10
+ 13y
9
+ ··· + 60y + 9
c
7
y
10
+ 6y
9
+ ··· + 24y + 9
c
8
y
10
+ y
9
+ ··· − 2079y + 13225
c
10
, c
12
y
10
− 3y
9
+ ··· − 11y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.739631 + 1.065580I
a = −0.502712 − 0.815992I
b = 1.42384 + 0.44686I
−13.27760 + 4.63105I −1.33027 − 1.48625I
u = −0.739631 − 1.065580I
a = −0.502712 + 0.815992I
b = 1.42384 − 0.44686I
−13.27760 − 4.63105I −1.33027 + 1.48625I
u = 0.644101 + 0.065680I
a = 0.18477 + 2.34872I
b = −0.134072 − 0.287586I
0.35864 − 1.54639I 10.53004 + 3.29271I
u = 0.644101 − 0.065680I
a = 0.18477 − 2.34872I
b = −0.134072 + 0.287586I
0.35864 + 1.54639I 10.53004 − 3.29271I
u = 1.267070 + 0.578853I
a = −0.222986 + 0.158778I
b = 0.935257 − 0.569123I
3.84184 + 1.32742I −2.88591 + 3.25139I
u = 1.267070 − 0.578853I
a = −0.222986 − 0.158778I
b = 0.935257 + 0.569123I
3.84184 − 1.32742I −2.88591 − 3.25139I
u = −0.529527 + 0.126383I
a = −3.53705 − 0.62240I
b = 0.577884 + 0.595991I
−0.97495 − 4.80761I 7.23080 + 7.17624I
u = −0.529527 − 0.126383I
a = −3.53705 + 0.62240I
b = 0.577884 − 0.595991I
−0.97495 + 4.80761I 7.23080 − 7.17624I
u = −1.14202 + 1.07758I
a = 0.577976 + 1.042340I
b = −2.30291 − 0.30963I
−3.10738 − 6.86472I 1.45534 + 4.82302I
u = −1.14202 − 1.07758I
a = 0.577976 − 1.042340I
b = −2.30291 + 0.30963I
−3.10738 + 6.86472I 1.45534 − 4.82302I
20
IV.
I
u
4
= h2.31 × 10
30
u
27
− 1.47 × 10
31
u
26
+ · · · + 2.21 × 10
30
b + 1.35 × 10
30
, 6.65 ×
10
30
u
27
−5.32×10
31
u
26
+· · ·+8.86×10
30
a−3.64×10
31
, u
28
−7u
27
+· · ·−6u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
3
=
−0.750672u
27
+ 6.00497u
26
+ ··· − 25.1851u + 4.10975
−1.04106u
27
+ 6.65327u
26
+ ··· − 6.19454u − 0.610200
a
11
=
1
−u
2
a
4
=
−1.05959u
27
+ 7.92277u
26
+ ··· − 26.1273u + 2.74928
−0.934908u
27
+ 5.93795u
26
+ ··· − 5.03563u − 0.854839
a
12
=
1.08517u
27
− 6.78856u
26
+ ··· − 6.39697u + 0.188582
−1.15795u
27
+ 7.83176u
26
+ ··· − 10.2716u + 0.216942
a
1
=
−0.0727820u
27
+ 1.04320u
26
+ ··· − 16.6685u + 0.405524
−1.15795u
27
+ 7.83176u
26
+ ··· − 10.2716u + 0.216942
a
7
=
−2.41793u
27
+ 16.4679u
26
+ ··· − 17.6032u + 1.98834
0.0364625u
27
− 0.665940u
26
+ ··· + 13.3646u − 2.72719
a
5
=
2.00650u
27
− 12.4710u
26
+ ··· + 12.7692u − 1.89411
−0.167734u
27
+ 0.952814u
26
+ ··· + 5.38662u − 0.590137
a
2
=
−1.79021u
27
+ 13.0418u
26
+ ··· − 28.1238u + 5.96157
−1.34194u
27
+ 8.35246u
26
+ ··· − 5.39875u − 0.247119
a
6
=
−1.65349u
27
+ 11.3001u
26
+ ··· − 18.4991u + 2.74731
0.474767u
27
− 3.27790u
26
+ ··· + 9.77340u − 2.35437
a
9
=
−2.47184u
27
+ 17.6089u
26
+ ··· − 37.6884u + 7.12657
0.0174430u
27
− 0.475093u
26
+ ··· + 8.72059u − 2.41104
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.460010u
27
− 0.721349u
26
+ ··· − 70.3985u + 14.8642
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
− 14u
27
+ ··· − 224u + 64
c
2
(u
14
+ 4u
13
+ ··· − u + 1)
2
c
3
, c
9
u
28
− u
27
+ ··· − 12u + 2
c
5
, c
11
u
28
+ u
27
+ ··· + 12u + 2
c
6
(u
14
− 4u
13
+ ··· + u + 1)
2
c
7
(u
14
− u
13
+ ··· + 3u + 4)
2
c
8
(u
14
− 2u
13
+ ··· − 4u
2
+ 1)
2
c
10
, c
12
u
28
− 7u
27
+ ··· − 6u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
− 28y
27
+ ··· − 30208y + 4096
c
2
, c
6
(y
14
− 4y
13
+ ··· + 11y + 1)
2
c
3
, c
5
, c
9
c
11
y
28
+ 11y
27
+ ··· + 44y + 4
c
7
(y
14
+ 9y
13
+ ··· + 119y + 16)
2
c
8
(y
14
− 2y
13
+ ··· − 8y + 1)
2
c
10
, c
12
y
28
− 7y
27
+ ··· + 30y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.004880 + 0.072490I
a = −0.802713 − 0.652904I
b = 0.425826 − 0.441245I
−1.22209 − 1.30275I −0.189828 + 0.161880I
u = −1.004880 − 0.072490I
a = −0.802713 + 0.652904I
b = 0.425826 + 0.441245I
−1.22209 + 1.30275I −0.189828 − 0.161880I
u = 0.424816 + 0.934471I
a = 0.69462 + 1.51106I
b = 1.80723 − 0.35102I
−3.32667 + 3.42166I −4.84660 − 3.31664I
u = 0.424816 − 0.934471I
a = 0.69462 − 1.51106I
b = 1.80723 + 0.35102I
−3.32667 − 3.42166I −4.84660 + 3.31664I
u = 0.916929 + 0.487153I
a = 1.163610 − 0.028155I
b = −0.397255 + 0.075109I
−4.25469 + 5.51724I 5.76227 − 11.53768I
u = 0.916929 − 0.487153I
a = 1.163610 + 0.028155I
b = −0.397255 − 0.075109I
−4.25469 − 5.51724I 5.76227 + 11.53768I
u = 0.243766 + 0.913191I
a = 0.091903 + 0.373054I
b = 1.74755 − 0.02720I
4.53279 − 0.11943I 0.86246 − 1.23203I
u = 0.243766 − 0.913191I
a = 0.091903 − 0.373054I
b = 1.74755 + 0.02720I
4.53279 + 0.11943I 0.86246 + 1.23203I
u = −0.761583 + 0.779898I
a = −0.901128 − 0.171680I
b = −0.360802 − 0.712602I
−3.32667 − 3.42166I −4.84660 + 3.31664I
u = −0.761583 − 0.779898I
a = −0.901128 + 0.171680I
b = −0.360802 + 0.712602I
−3.32667 + 3.42166I −4.84660 − 3.31664I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809426 + 0.207631I
a = −0.44006 − 1.51056I
b = 1.48483 + 1.65770I
−9.62737 + 1.00157I 3.57146 + 5.70153I
u = −0.809426 − 0.207631I
a = −0.44006 + 1.51056I
b = 1.48483 − 1.65770I
−9.62737 − 1.00157I 3.57146 − 5.70153I
u = −1.207270 + 0.385496I
a = 0.161520 + 0.070667I
b = −0.407363 + 0.616215I
1.89115 − 6.53826I −3.88743 + 8.27723I
u = −1.207270 − 0.385496I
a = 0.161520 − 0.070667I
b = −0.407363 − 0.616215I
1.89115 + 6.53826I −3.88743 − 8.27723I
u = 0.389877 + 0.482114I
a = −4.23013 − 2.23645I
b = −1.58114 + 1.06937I
−4.25469 + 5.51724I 5.76227 − 11.53768I
u = 0.389877 − 0.482114I
a = −4.23013 + 2.23645I
b = −1.58114 − 1.06937I
−4.25469 − 5.51724I 5.76227 + 11.53768I
u = 0.369497 + 0.353191I
a = −1.33154 + 3.57650I
b = 0.578355 − 0.755881I
−1.22209 + 1.30275I −0.189828 − 0.161880I
u = 0.369497 − 0.353191I
a = −1.33154 − 3.57650I
b = 0.578355 + 0.755881I
−1.22209 − 1.30275I −0.189828 + 0.161880I
u = 1.01785 + 1.23847I
a = 0.518221 − 1.237570I
b = −2.08566 − 0.84265I
1.89115 + 6.53826I −3.88743 − 8.27723I
u = 1.01785 − 1.23847I
a = 0.518221 + 1.237570I
b = −2.08566 + 0.84265I
1.89115 − 6.53826I −3.88743 + 8.27723I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056553 + 0.223388I
a = −1.22248 − 1.68715I
b = −1.41442 + 0.07228I
2.95973 + 1.83574I 2.72767 − 9.49202I
u = 0.056553 − 0.223388I
a = −1.22248 + 1.68715I
b = −1.41442 − 0.07228I
2.95973 − 1.83574I 2.72767 + 9.49202I
u = 1.80416 + 0.23975I
a = −0.445326 − 0.590750I
b = 0.44418 + 3.19274I
2.95973 − 1.83574I 0. + 9.49202I
u = 1.80416 − 0.23975I
a = −0.445326 + 0.590750I
b = 0.44418 − 3.19274I
2.95973 + 1.83574I 0. − 9.49202I
u = 1.85731 + 0.07680I
a = 0.330965 − 0.619073I
b = −1.27854 + 3.06555I
4.53279 + 0.11943I 0
u = 1.85731 − 0.07680I
a = 0.330965 + 0.619073I
b = −1.27854 − 3.06555I
4.53279 − 0.11943I 0
u = 0.20240 + 2.14534I
a = −0.087442 + 0.835133I
b = 0.03722 + 2.04871I
−9.62737 + 1.00157I 0
u = 0.20240 − 2.14534I
a = −0.087442 − 0.835133I
b = 0.03722 − 2.04871I
−9.62737 − 1.00157I 0
26
V. I
u
5
= hb + 1, a − 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
10
=
1
0
a
3
=
1
−1
a
11
=
1
−1
a
4
=
1
−1
a
12
=
1
−1
a
1
=
0
−1
a
7
=
0
1
a
5
=
1
0
a
2
=
1
−2
a
6
=
1
0
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
10
, c
12
u − 1
c
3
, c
5
, c
7
c
9
, c
11
u
c
6
, c
8
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
10
c
12
y −1
c
3
, c
5
, c
7
c
9
, c
11
y
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.00000
0 0
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)(u
10
− 2u
8
+ ··· − 5u + 1)
· (u
21
− u
20
+ ··· + 12u − 1)(u
28
− 14u
27
+ ··· − 224u + 64)
· (u
58
− 3u
57
+ ··· − 38440u + 10672)
c
2
(u − 1)(u
10
− 6u
9
+ ··· − 9u + 1)(u
14
+ 4u
13
+ ··· − u + 1)
2
· (u
21
+ 16u
20
+ ··· − 1136u − 272)
· (u
29
− 7u
28
+ ··· + 2424u − 1357)
2
c
3
, c
9
u(u
10
+ u
9
+ 7u
8
+ 3u
7
+ 16u
6
+ 2u
5
+ 18u
4
+ 2u
3
+ 10u
2
+ 3)
· (u
21
− u
20
+ ··· + 8u − 2)(u
28
− u
27
+ ··· − 12u + 2)
· (u
58
+ 23u
56
+ ··· − 14700u + 2392)
c
5
, c
11
u(u
10
− u
9
+ 7u
8
− 3u
7
+ 16u
6
− 2u
5
+ 18u
4
− 2u
3
+ 10u
2
+ 3)
· (u
21
− u
20
+ ··· + 8u − 2)(u
28
+ u
27
+ ··· + 12u + 2)
· (u
58
+ 23u
56
+ ··· − 14700u + 2392)
c
6
(u + 1)(u
10
+ 6u
9
+ ··· + 9u + 1)(u
14
− 4u
13
+ ··· + u + 1)
2
· (u
21
+ 16u
20
+ ··· − 1136u − 272)
· (u
29
− 7u
28
+ ··· + 2424u − 1357)
2
c
7
u(u
10
+ 2u
9
+ 5u
8
+ 8u
7
+ 8u
6
+ 8u
5
+ 5u
4
+ u
3
+ 4u
2
+ 3)
· ((u
14
− u
13
+ ··· + 3u + 4)
2
)(u
21
− 13u
20
+ ··· + 640u − 64)
· (u
29
+ 5u
28
+ ··· − 10u − 1)
2
c
8
(u + 1)(u
10
+ 5u
9
+ ··· + 233u + 115)(u
14
− 2u
13
+ ··· − 4u
2
+ 1)
2
· (u
21
− 13u
20
+ ··· + 936u − 128)(u
29
+ 7u
28
+ ··· − 1953u − 961)
2
c
10
, c
12
(u − 1)(u
10
+ u
9
− u
8
− 5u
7
+ u
6
+ 7u
5
+ 7u
4
− 5u
3
− 5u
2
+ u + 1)
· (u
21
− 8u
18
+ ··· − 4u − 1)(u
28
− 7u
27
+ ··· − 6u + 1)
· (u
58
+ 4u
57
+ ··· + 872u + 128)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y −1)(y
10
− 4y
9
+ ··· − 5y + 1)
· (y
21
− 29y
20
+ ··· + 120y −1)(y
28
− 28y
27
+ ··· − 30208y + 4096)
· (y
58
− 67y
57
+ ··· − 791039808y + 113891584)
c
2
, c
6
(y −1)(y
10
− 6y
9
+ ··· + y + 1)(y
14
− 4y
13
+ ··· + 11y + 1)
2
· (y
21
− 20y
20
+ ··· + 874880y −73984)
· (y
29
− 47y
28
+ ··· + 15678744y −1841449)
2
c
3
, c
5
, c
9
c
11
y(y
10
+ 13y
9
+ ··· + 60y + 9)(y
21
+ 23y
20
+ ··· + 24y −4)
· (y
28
+ 11y
27
+ ··· + 44y + 4)
· (y
58
+ 46y
57
+ ··· + 6901808y + 5721664)
c
7
y(y
10
+ 6y
9
+ ··· + 24y + 9)(y
14
+ 9y
13
+ ··· + 119y + 16)
2
· (y
21
+ 7y
20
+ ··· + 47104y −4096)(y
29
+ 13y
28
+ ··· + 2y −1)
2
c
8
(y −1)(y
10
+ y
9
+ ··· − 2079y + 13225)(y
14
− 2y
13
+ ··· − 8y + 1)
2
· (y
21
+ 3y
20
+ ··· − 15808y −16384)
· (y
29
+ 19y
28
+ ··· − 1357893y −923521)
2
c
10
, c
12
(y −1)(y
10
− 3y
9
+ ··· − 11y + 1)(y
21
+ 20y
19
+ ··· + 14y −1)
· (y
28
− 7y
27
+ ··· + 30y + 1)(y
58
− 2y
57
+ ··· + 158144y + 16384)
32
