12a
0323
(K12a
0323
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 10 9 4 1 12 5 7
Solving Sequence
1,9 4,10
8 3 2 7 6 5 12 11
c
9
c
8
c
3
c
1
c
7
c
6
c
5
c
12
c
10
c
2
, c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.55331 × 10
30
u
30
+ 1.64150 × 10
31
u
29
+ ··· + 3.56183 × 10
31
b + 4.47272 × 10
31
,
1.84263 × 10
31
u
30
+ 6.93262 × 10
29
u
29
+ ··· + 3.56183 × 10
31
a + 6.39301 × 10
31
, u
31
+ u
30
+ ··· + 4u
2
+ 1i
I
u
2
= h−5.81751 × 10
941
u
125
+ 8.58847 × 10
942
u
124
+ ··· + 3.92230 × 10
942
b − 1.21679 × 10
942
,
− 2.73119 × 10
942
u
125
+ 4.02364 × 10
943
u
124
+ ··· + 3.92230 × 10
942
a − 5.31484 × 10
943
,
u
126
− 15u
125
+ ··· − 10u + 1i
I
u
3
= hu
9
− u
7
− u
6
− u
5
+ u
3
+ b + u, u
14
+ 2u
13
− 2u
11
− 4u
10
− 4u
9
+ 2u
7
+ 2u
6
+ 3u
5
− u
2
+ a,
u
15
+ u
14
− u
12
− 3u
11
− 3u
10
− u
9
+ 3u
7
+ 3u
6
+ 2u
5
+ u
4
− u
3
− u
2
− u − 1i
I
u
4
= hu
15
+ 2u
14
− 2u
13
− 5u
12
+ 2u
11
+ 6u
10
− 3u
9
− 8u
8
+ u
7
+ 3u
6
+ u
4
− 2u
2
+ b − 2u + 3,
− 14u
15
− 10u
14
+ ··· + a + 18,
u
16
− 3u
14
+ 2u
13
+ 4u
12
− 3u
11
− 4u
10
+ 4u
9
+ 3u
8
− 6u
7
+ 5u
6
− 3u
5
+ 2u
4
− 4u
3
+ 6u
2
− 4u + 1i
* 4 irreducible components of dim
C
= 0, with total 188 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
= h6.55 × 10
30
u
30
+ 1.64 × 10
31
u
29
+ · · · + 3.56 × 10
31
b + 4.47 × 10
31
, 1.84 ×
10
31
u
30
+6.93×10
29
u
29
+· · ·+3.56 ×10
31
a+6.39×10
31
, u
31
+u
30
+· · ·+4u
2
+1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−0.517327u
30
− 0.0194636u
29
+ ··· − 5.01519u − 1.79487
−0.183987u
30
− 0.460859u
29
+ ··· − 0.222841u − 1.25573
a
10
=
1
u
2
a
8
=
0.216938u
30
+ 0.559109u
29
+ ··· + 4.24716u + 0.409583
−0.127744u
30
+ 0.156322u
29
+ ··· + 0.655318u − 0.0581050
a
3
=
0.608908u
30
+ 0.513421u
29
+ ··· − 0.141955u − 2.34677
0.437378u
30
+ 0.0595317u
29
+ ··· + 0.528023u − 0.947344
a
2
=
1.55810u
30
+ 0.725606u
29
+ ··· − 3.80603u − 2.48799
0.329814u
30
− 0.151160u
29
+ ··· − 1.45162u − 0.00731807
a
7
=
0.344682u
30
+ 0.402787u
29
+ ··· + 3.59184u + 0.467688
−0.127744u
30
+ 0.156322u
29
+ ··· + 0.655318u − 0.0581050
a
6
=
0.344682u
30
+ 0.402787u
29
+ ··· + 4.59184u + 0.467688
−0.127744u
30
+ 0.156322u
29
+ ··· + 0.655318u − 0.0581050
a
5
=
2.15136u
30
+ 0.404329u
29
+ ··· − 1.94509u − 1.88658
0.440312u
30
+ 0.351852u
29
+ ··· − 1.62334u + 0.799685
a
12
=
1.06778u
30
+ 1.15510u
29
+ ··· + 6.10440u − 1.82049
0.0239911u
30
− 0.155795u
29
+ ··· − 0.412459u − 0.145425
a
11
=
0.182230u
30
+ 0.115877u
29
+ ··· − 3.91942u + 3.96267
0.266137u
30
+ 0.197519u
29
+ ··· + 0.0212995u − 0.0373999
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.100681u
30
+ 1.00392u
29
+ ··· − 7.27867u + 2.00104
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 12u
30
+ ··· + 5632u + 1024
c
2
, c
5
u
31
+ 12u
30
+ ··· − 224u − 32
c
3
, c
4
, c
8
c
11
u
31
− 7u
29
+ ··· + 3u + 1
c
6
, c
9
u
31
+ u
30
+ ··· + 4u
2
+ 1
c
7
, c
10
u
31
− 14u
30
+ ··· + 11u − 1
c
12
u
31
+ 28u
30
+ ··· + 116736u + 10240
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 12y
30
+ ··· − 393216y −1048576
c
2
, c
5
y
31
− 12y
30
+ ··· + 5632y −1024
c
3
, c
4
, c
8
c
11
y
31
− 14y
30
+ ··· + 11y −1
c
6
, c
9
y
31
+ 5y
30
+ ··· − 8y −1
c
7
, c
10
y
31
+ 10y
30
+ ··· + 95y −1
c
12
y
31
− 8y
30
+ ··· + 69206016y −104857600
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084144 + 1.039664I
a = −1.269352 + 0.109533I
b = 0.962289 − 0.520246I
3.19876 − 7.55195I 5.48862 + 9.87953I
u = 0.084144 − 1.039664I
a = −1.269352 − 0.109533I
b = 0.962289 + 0.520246I
3.19876 + 7.55195I 5.48862 − 9.87953I
u = −0.469459 + 1.009713I
a = 0.218341 − 0.735028I
b = −0.879624 + 0.475488I
2.43175 − 0.36874I 2.25000 + 2.94789I
u = −0.469459 − 1.009713I
a = 0.218341 + 0.735028I
b = −0.879624 − 0.475488I
2.43175 + 0.36874I 2.25000 − 2.94789I
u = 0.860162 + 0.786995I
a = 0.78085 + 1.82232I
b = −1.020462 + 0.682561I
−5.34193 − 10.63260I −3.15069 + 9.70062I
u = 0.860162 − 0.786995I
a = 0.78085 − 1.82232I
b = −1.020462 − 0.682561I
−5.34193 + 10.63260I −3.15069 − 9.70062I
u = −1.21341
a = −0.0217834
b = −0.330185
−2.42715 −5.31520
u = 0.387802 + 1.194509I
a = 0.298582 − 0.479894I
b = −1.157971 − 0.198479I
8.01085 + 1.87526I 9.36813 − 2.63874I
u = 0.387802 − 1.194509I
a = 0.298582 + 0.479894I
b = −1.157971 + 0.198479I
8.01085 − 1.87526I 9.36813 + 2.63874I
u = −1.117652 + 0.663220I
a = 0.785976 − 0.601863I
b = 0.695306 − 0.761608I
−7.37204 − 0.41255I −6.92882 + 2.19694I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117652 − 0.663220I
a = 0.785976 + 0.601863I
b = 0.695306 + 0.761608I
−7.37204 + 0.41255I −6.92882 − 2.19694I
u = −0.534239 + 0.421201I
a = 0.94640 + 3.61057I
b = 1.042485 + 0.517986I
0.94025 + 10.62460I 2.5262 − 14.8925I
u = −0.534239 − 0.421201I
a = 0.94640 − 3.61057I
b = 1.042485 − 0.517986I
0.94025 − 10.62460I 2.5262 + 14.8925I
u = −1.007284 + 0.875628I
a = −0.307838 + 0.750851I
b = −0.484729 + 0.824665I
−2.35818 + 2.80518I −2.26135 − 0.49699I
u = −1.007284 − 0.875628I
a = −0.307838 − 0.750851I
b = −0.484729 − 0.824665I
−2.35818 − 2.80518I −2.26135 + 0.49699I
u = −0.416545 + 0.469850I
a = 0.614182 + 0.161827I
b = −0.022556 + 0.572988I
−0.57873 + 1.51038I −2.67375 − 4.66317I
u = −0.416545 − 0.469850I
a = 0.614182 − 0.161827I
b = −0.022556 − 0.572988I
−0.57873 − 1.51038I −2.67375 + 4.66317I
u = 0.652733 + 1.249388I
a = −0.189535 + 0.299518I
b = 1.153307 + 0.140718I
7.25146 − 3.68008I 8.25009 + 3.16950I
u = 0.652733 − 1.249388I
a = −0.189535 − 0.299518I
b = 1.153307 − 0.140718I
7.25146 + 3.68008I 8.25009 − 3.16950I
u = −0.135838 + 0.563252I
a = 2.18955 − 2.36363I
b = −1.026841 − 0.393178I
4.55871 + 4.50370I 11.51940 − 4.92639I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135838 − 0.563252I
a = 2.18955 + 2.36363I
b = −1.026841 + 0.393178I
4.55871 − 4.50370I 11.51940 + 4.92639I
u = 0.419041 + 0.284363I
a = 0.070359 − 1.058717I
b = 0.882191 + 0.161261I
1.83304 + 0.30388I 4.09035 + 0.14569I
u = 0.419041 − 0.284363I
a = 0.070359 + 1.058717I
b = 0.882191 − 0.161261I
1.83304 − 0.30388I 4.09035 − 0.14569I
u = −1.13002 + 0.99523I
a = 0.384328 − 0.974043I
b = 0.524500 − 0.942497I
−4.76248 + 7.98624I −4.49283 − 4.44036I
u = −1.13002 − 0.99523I
a = 0.384328 + 0.974043I
b = 0.524500 + 0.942497I
−4.76248 − 7.98624I −4.49283 + 4.44036I
u = 0.258738 + 0.349549I
a = −2.82094 − 1.20057I
b = −0.470895 − 0.606546I
−2.41931 − 1.71382I −3.05380 + 2.44778I
u = 0.258738 − 0.349549I
a = −2.82094 + 1.20057I
b = −0.470895 + 0.606546I
−2.41931 + 1.71382I −3.05380 − 2.44778I
u = 1.03795 + 1.17821I
a = −0.317255 − 1.306538I
b = 1.129177 − 0.655726I
1.52020 − 14.00050I 2.53500 + 8.42876I
u = 1.03795 − 1.17821I
a = −0.317255 + 1.306538I
b = 1.129177 + 0.655726I
1.52020 + 14.00050I 2.53500 − 8.42876I
u = 1.21717 + 1.17818I
a = 0.127234 + 1.383611I
b = −1.161086 + 0.692549I
−0.7640 − 20.0875I 0. + 11.57868I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21717 − 1.17818I
a = 0.127234 − 1.383611I
b = −1.161086 − 0.692549I
−0.7640 + 20.0875I 0. − 11.57868I
8
II. I
u
2
= h−5.82 × 10
941
u
125
+ 8.59 × 10
942
u
124
+ · · · + 3.92 × 10
942
b − 1.22 ×
10
942
, −2.73 × 10
942
u
125
+ 4.02 × 10
943
u
124
+ · · · + 3.92 × 10
942
a − 5.31 ×
10
943
, u
126
− 15u
125
+ · · · − 10u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
0.696323u
125
− 10.2584u
124
+ ··· − 66.3738u + 13.5503
0.148319u
125
− 2.18965u
124
+ ··· − 0.702479u + 0.310223
a
10
=
1
u
2
a
8
=
−0.0582623u
125
+ 0.933870u
124
+ ··· − 143.836u + 13.2497
−0.161908u
125
+ 2.39661u
124
+ ··· − 12.9534u + 0.956689
a
3
=
1.54346u
125
− 23.0357u
124
+ ··· + 124.214u + 1.81945
0.204893u
125
− 3.05880u
124
+ ··· + 12.9608u − 0.797883
a
2
=
0.615790u
125
− 9.03866u
124
+ ··· − 104.459u + 15.5686
0.228570u
125
− 3.39770u
124
+ ··· + 1.58590u − 0.205166
a
7
=
0.103646u
125
− 1.46274u
124
+ ··· − 130.883u + 12.2930
−0.161908u
125
+ 2.39661u
124
+ ··· − 12.9534u + 0.956689
a
6
=
−0.0448889u
125
+ 0.738359u
124
+ ··· − 144.652u + 13.3417
−0.173193u
125
+ 2.55966u
124
+ ··· − 13.0741u + 0.983617
a
5
=
0.645712u
125
− 9.65714u
124
+ ··· + 84.5594u − 3.82633
0.0274567u
125
− 0.441852u
124
+ ··· + 5.88458u − 0.629101
a
12
=
0.758231u
125
− 11.2624u
124
+ ··· − 32.2325u + 13.3940
0.105098u
125
− 1.56250u
124
+ ··· − 0.481745u + 0.633800
a
11
=
−0.617167u
125
+ 9.10795u
124
+ ··· + 100.828u − 14.9786
−0.0878400u
125
+ 1.30605u
124
+ ··· + 5.74816u − 0.594280
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.18500u
125
− 17.5443u
124
+ ··· + 35.1425u − 2.66616
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
63
+ 29u
62
+ ··· + 399u + 25)
2
c
2
, c
5
(u
63
− 5u
62
+ ··· + 37u − 5)
2
c
3
, c
4
, c
8
c
11
u
126
+ u
125
+ ··· + 36u + 9
c
6
, c
9
u
126
− 15u
125
+ ··· − 10u + 1
c
7
, c
10
u
126
− 53u
125
+ ··· − 2628u + 81
c
12
(u
63
− 13u
62
+ ··· − 5u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
63
+ 19y
62
+ ··· + 4651y −625)
2
c
2
, c
5
(y
63
− 29y
62
+ ··· + 399y −25)
2
c
3
, c
4
, c
8
c
11
y
126
− 53y
125
+ ··· − 2628y + 81
c
6
, c
9
y
126
− 15y
125
+ ··· + 248y + 1
c
7
, c
10
y
126
+ 51y
125
+ ··· + 935388y + 6561
c
12
(y
63
− 15y
62
+ ··· + 49y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.041871 + 0.086991I
a = 0.106651 + 0.659044I
b = −0.196963 + 0.634548I
−2.40615 + 0.01706I 0
u = −1.041871 − 0.086991I
a = 0.106651 − 0.659044I
b = −0.196963 − 0.634548I
−2.40615 − 0.01706I 0
u = 0.447529 + 0.839925I
a = 0.529540 − 0.312626I
b = −1.275041 − 0.062031I
5.57710 − 5.64020I 0
u = 0.447529 − 0.839925I
a = 0.529540 + 0.312626I
b = −1.275041 + 0.062031I
5.57710 + 5.64020I 0
u = −0.904169 + 0.533833I
a = 0.002039 − 1.079744I
b = −1.196784 − 0.631391I
0.38539 + 5.30492I 0
u = −0.904169 − 0.533833I
a = 0.002039 + 1.079744I
b = −1.196784 + 0.631391I
0.38539 − 5.30492I 0
u = −0.931507 + 0.182036I
a = 0.140837 + 1.105782I
b = 0.220517 + 1.076032I
−3.86874 − 3.84740I 0
u = −0.931507 − 0.182036I
a = 0.140837 − 1.105782I
b = 0.220517 − 1.076032I
−3.86874 + 3.84740I 0
u = −0.883551 + 0.346025I
a = −0.16505 + 1.54628I
b = 1.193652 + 0.560788I
0.81103 + 4.65824I 0
u = −0.883551 − 0.346025I
a = −0.16505 − 1.54628I
b = 1.193652 − 0.560788I
0.81103 − 4.65824I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.828283 + 0.446669I
a = 0.069163 − 1.144444I
b = 1.072744 − 0.653846I
0.067312 − 1.017350I 0
u = 0.828283 − 0.446669I
a = 0.069163 + 1.144444I
b = 1.072744 + 0.653846I
0.067312 + 1.017350I 0
u = −0.281852 + 1.028357I
a = 0.641319 − 0.218069I
b = −1.088591 − 0.334536I
2.50341 + 4.73463I 0
u = −0.281852 − 1.028357I
a = 0.641319 + 0.218069I
b = −1.088591 + 0.334536I
2.50341 − 4.73463I 0
u = 0.461999 + 0.809904I
a = −0.283438 − 0.866112I
b = 1.029079 + 0.162258I
1.82989 + 0.00826I 0
u = 0.461999 − 0.809904I
a = −0.283438 + 0.866112I
b = 1.029079 − 0.162258I
1.82989 − 0.00826I 0
u = −0.525617 + 0.937016I
a = 0.226511 − 0.805413I
b = −1.045075 + 0.320939I
2.19990 + 4.01790I 0
u = −0.525617 − 0.937016I
a = 0.226511 + 0.805413I
b = −1.045075 − 0.320939I
2.19990 − 4.01790I 0
u = 0.916902 + 0.019751I
a = 0.154113 + 0.799212I
b = 0.565274 + 0.789159I
−1.50295 + 4.40389I 0
u = 0.916902 − 0.019751I
a = 0.154113 − 0.799212I
b = 0.565274 − 0.789159I
−1.50295 − 4.40389I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.430967 + 0.997335I
a = −0.240799 − 0.693857I
b = 0.725649 + 0.459266I
2.37286 − 3.46728I 0
u = 0.430967 − 0.997335I
a = −0.240799 + 0.693857I
b = 0.725649 − 0.459266I
2.37286 + 3.46728I 0
u = −0.115187 + 1.081445I
a = 1.100285 + 0.181739I
b = −0.867542 − 0.461944I
2.37286 + 3.46728I 0
u = −0.115187 − 1.081445I
a = 1.100285 − 0.181739I
b = −0.867542 + 0.461944I
2.37286 − 3.46728I 0
u = −0.265622 + 0.871434I
a = −0.545305 − 0.493257I
b = 1.185667 − 0.038115I
3.45279 + 0.77574I 0
u = −0.265622 − 0.871434I
a = −0.545305 + 0.493257I
b = 1.185667 + 0.038115I
3.45279 − 0.77574I 0
u = −0.861309 + 0.257273I
a = 0.136789 + 1.296927I
b = 1.26829 + 0.71351I
−0.74509 + 10.25710I 0
u = −0.861309 − 0.257273I
a = 0.136789 − 1.296927I
b = 1.26829 − 0.71351I
−0.74509 − 10.25710I 0
u = 0.115055 + 0.889723I
a = −1.50506 − 0.40824I
b = 1.057783 − 0.452075I
4.14790 − 2.17573I 0
u = 0.115055 − 0.889723I
a = −1.50506 + 0.40824I
b = 1.057783 + 0.452075I
4.14790 + 2.17573I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890223 + 0.685331I
a = −0.124561 − 1.005106I
b = 1.253089 − 0.331609I
1.08734 − 5.02241I 0
u = 0.890223 − 0.685331I
a = −0.124561 + 1.005106I
b = 1.253089 + 0.331609I
1.08734 + 5.02241I 0
u = −0.916222 + 0.653646I
a = 0.081515 − 1.025750I
b = −1.289559 − 0.453742I
0.89643 + 1.17973I 0
u = −0.916222 − 0.653646I
a = 0.081515 + 1.025750I
b = −1.289559 + 0.453742I
0.89643 − 1.17973I 0
u = −0.491587 + 1.012769I
a = 0.201313 + 0.021183I
b = −1.298317 − 0.098154I
2.38825 + 5.72533I 0
u = −0.491587 − 1.012769I
a = 0.201313 − 0.021183I
b = −1.298317 + 0.098154I
2.38825 − 5.72533I 0
u = 0.845880 + 0.216649I
a = −0.147211 + 1.221315I
b = −0.348213 + 1.060432I
−4.24007 − 0.71156I 0
u = 0.845880 − 0.216649I
a = −0.147211 − 1.221315I
b = −0.348213 − 1.060432I
−4.24007 + 0.71156I 0
u = 0.592686 + 0.969415I
a = −0.0936103 + 0.0710144I
b = 1.387031 − 0.003973I
4.08563 − 10.85580I 0
u = 0.592686 − 0.969415I
a = −0.0936103 − 0.0710144I
b = 1.387031 + 0.003973I
4.08563 + 10.85580I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799637 + 0.237909I
a = −0.324291 + 1.356176I
b = −1.185136 + 0.770151I
−1.75445 − 5.84337I 0
u = 0.799637 − 0.237909I
a = −0.324291 − 1.356176I
b = −1.185136 − 0.770151I
−1.75445 + 5.84337I 0
u = 0.686450 + 0.434495I
a = −0.24412 + 2.34802I
b = −1.064980 + 0.607850I
−0.86530 − 6.57037I 0
u = 0.686450 − 0.434495I
a = −0.24412 − 2.34802I
b = −1.064980 − 0.607850I
−0.86530 + 6.57037I 0
u = −1.188059 + 0.106077I
a = −0.044362 + 0.343356I
b = −0.366194 + 0.295386I
−2.42241 0
u = −1.188059 − 0.106077I
a = −0.044362 − 0.343356I
b = −0.366194 − 0.295386I
−2.42241 0
u = 0.993056 + 0.675976I
a = −0.875234 − 0.557827I
b = −0.636205 − 0.818580I
−6.52002 − 5.01612I 0
u = 0.993056 − 0.675976I
a = −0.875234 + 0.557827I
b = −0.636205 + 0.818580I
−6.52002 + 5.01612I 0
u = 0.656393 + 0.451064I
a = −1.261161 − 0.472026I
b = −0.324498 + 0.237999I
2.50341 − 4.73463I 0
u = 0.656393 − 0.451064I
a = −1.261161 + 0.472026I
b = −0.324498 − 0.237999I
2.50341 + 4.73463I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.652324 + 0.394583I
a = −0.58792 + 2.35951I
b = −1.037074 + 0.610081I
−0.86446 − 6.55164I 0
u = 0.652324 − 0.394583I
a = −0.58792 − 2.35951I
b = −1.037074 − 0.610081I
−0.86446 + 6.55164I 0
u = −0.948002 + 0.807486I
a = −0.69229 + 1.70358I
b = 0.972794 + 0.671183I
−6.52002 + 5.01612I 0
u = −0.948002 − 0.807486I
a = −0.69229 − 1.70358I
b = 0.972794 − 0.671183I
−6.52002 − 5.01612I 0
u = 0.206054 + 0.712130I
a = −0.190318 − 0.321943I
b = 0.126021 + 0.491882I
1.78680 + 1.54215I 0
u = 0.206054 − 0.712130I
a = −0.190318 + 0.321943I
b = 0.126021 − 0.491882I
1.78680 − 1.54215I 0
u = 0.886779 + 0.911880I
a = 0.305512 + 0.921191I
b = 0.339427 + 0.705785I
3.45279 − 0.77574I 0
u = 0.886779 − 0.911880I
a = 0.305512 − 0.921191I
b = 0.339427 − 0.705785I
3.45279 + 0.77574I 0
u = 0.640550 + 0.220518I
a = −1.07999 − 1.28099I
b = −0.465595 − 0.762255I
−2.63608 − 1.36779I 0
u = 0.640550 − 0.220518I
a = −1.07999 + 1.28099I
b = −0.465595 + 0.762255I
−2.63608 + 1.36779I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552695 + 0.315160I
a = 2.33290 + 2.21835I
b = 0.900745 + 0.503542I
2.19990 + 4.01790I 0
u = −0.552695 − 0.315160I
a = 2.33290 − 2.21835I
b = 0.900745 − 0.503542I
2.19990 − 4.01790I 0
u = 1.011462 + 0.924017I
a = 0.357895 + 0.755136I
b = 0.447718 + 0.888326I
−0.53886 − 8.30876I 0
u = 1.011462 − 0.924017I
a = 0.357895 − 0.755136I
b = 0.447718 − 0.888326I
−0.53886 + 8.30876I 0
u = 1.294486 + 0.452659I
a = 0.26149 + 1.69807I
b = −0.904866 + 0.478440I
1.08734 − 5.02241I 0
u = 1.294486 − 0.452659I
a = 0.26149 − 1.69807I
b = −0.904866 − 0.478440I
1.08734 + 5.02241I 0
u = 0.054255 + 0.575350I
a = 2.42900 + 1.34031I
b = 0.273257 − 0.327644I
−0.86446 + 6.55164I 0. − 8.28242I
u = 0.054255 − 0.575350I
a = 2.42900 − 1.34031I
b = 0.273257 + 0.327644I
−0.86446 − 6.55164I 0. + 8.28242I
u = −1.39462 + 0.28483I
a = −0.286737 + 0.531673I
b = −0.668482 + 0.394014I
−2.40615 − 0.01706I 0
u = −1.39462 − 0.28483I
a = −0.286737 − 0.531673I
b = −0.668482 − 0.394014I
−2.40615 + 0.01706I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511259 + 0.147110I
a = −0.868537 + 0.884684I
b = −0.765393 + 1.085949I
−4.26452 − 7.61599I −10.4066 + 10.6029I
u = 0.511259 − 0.147110I
a = −0.868537 − 0.884684I
b = −0.765393 − 1.085949I
−4.26452 + 7.61599I −10.4066 − 10.6029I
u = −0.485848 + 0.201455I
a = 1.64759 + 2.65762I
b = −0.555319 + 0.011181I
−2.63608 − 1.36779I 0.61358 + 3.20173I
u = −0.485848 − 0.201455I
a = 1.64759 − 2.65762I
b = −0.555319 − 0.011181I
−2.63608 + 1.36779I 0.61358 − 3.20173I
u = −0.95313 + 1.13255I
a = 0.293906 − 1.066594I
b = −0.942906 − 0.572711I
−1.50295 + 4.40389I 0
u = −0.95313 − 1.13255I
a = 0.293906 + 1.066594I
b = −0.942906 + 0.572711I
−1.50295 − 4.40389I 0
u = 0.330328 + 0.395239I
a = 0.13003 − 2.73038I
b = 0.954391 − 0.435423I
1.78680 − 1.54215I 4.11048 + 1.75365I
u = 0.330328 − 0.395239I
a = 0.13003 + 2.73038I
b = 0.954391 + 0.435423I
1.78680 + 1.54215I 4.11048 − 1.75365I
u = 1.12267 + 0.97219I
a = −0.405080 − 0.964591I
b = −0.464796 − 0.986897I
−2.9168 − 13.9950I 0
u = 1.12267 − 0.97219I
a = −0.405080 + 0.964591I
b = −0.464796 + 0.986897I
−2.9168 + 13.9950I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.446376 + 0.189980I
a = 0.917976 + 0.772959I
b = 0.577724 + 1.111885I
−4.56851 + 2.11885I −9.39146 − 7.27533I
u = −0.446376 − 0.189980I
a = 0.917976 − 0.772959I
b = 0.577724 − 1.111885I
−4.56851 − 2.11885I −9.39146 + 7.27533I
u = −0.07148 + 1.52902I
a = 0.138093 + 1.100226I
b = −0.718639 + 0.736038I
−3.89880 − 0.46217I 0
u = −0.07148 − 1.52902I
a = 0.138093 − 1.100226I
b = −0.718639 − 0.736038I
−3.89880 + 0.46217I 0
u = 1.24353 + 0.91330I
a = −0.407085 − 1.072134I
b = −0.480745 − 0.707041I
2.38825 − 5.72533I 0
u = 1.24353 − 0.91330I
a = −0.407085 + 1.072134I
b = −0.480745 + 0.707041I
2.38825 + 5.72533I 0
u = 1.01272 + 1.17200I
a = −0.326426 − 0.986431I
b = 0.792592 − 0.523362I
0.067312 + 1.017350I 0
u = 1.01272 − 1.17200I
a = −0.326426 + 0.986431I
b = 0.792592 + 0.523362I
0.067312 − 1.017350I 0
u = −1.03175 + 1.19617I
a = 0.294656 − 1.258903I
b = −1.093602 − 0.647754I
−0.53886 + 8.30876I 0
u = −1.03175 − 1.19617I
a = 0.294656 + 1.258903I
b = −1.093602 + 0.647754I
−0.53886 − 8.30876I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220052 + 0.356276I
a = 2.39196 + 4.23270I
b = 0.476964 − 0.166781I
−0.86530 + 6.57037I 0.70691 − 9.69437I
u = 0.220052 − 0.356276I
a = 2.39196 − 4.23270I
b = 0.476964 + 0.166781I
−0.86530 − 6.57037I 0.70691 + 9.69437I
u = −0.155083 + 0.327738I
a = 0.04729 − 5.79682I
b = −0.944106 − 0.363537I
4.14790 − 2.17573I 9.79860 + 0.40015I
u = −0.155083 − 0.327738I
a = 0.04729 + 5.79682I
b = −0.944106 + 0.363537I
4.14790 + 2.17573I 9.79860 − 0.40015I
u = 1.63318 + 0.34675I
a = 0.605613 − 1.010136I
b = 0.970664 − 0.311921I
0.81103 + 4.65824I 0
u = 1.63318 − 0.34675I
a = 0.605613 + 1.010136I
b = 0.970664 + 0.311921I
0.81103 − 4.65824I 0
u = 1.11287 + 1.25274I
a = −0.148958 − 1.272940I
b = 1.091453 − 0.569745I
5.57710 − 5.64020I 0
u = 1.11287 − 1.25274I
a = −0.148958 + 1.272940I
b = 1.091453 + 0.569745I
5.57710 + 5.64020I 0
u = −1.22264 + 1.23112I
a = −0.109595 + 1.358913I
b = 1.122457 + 0.700094I
−2.9168 + 13.9950I 0
u = −1.22264 − 1.23112I
a = −0.109595 − 1.358913I
b = 1.122457 − 0.700094I
−2.9168 − 13.9950I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.74231 + 0.10822I
a = −0.625642 − 1.075980I
b = −0.852072 − 0.466395I
0.89643 − 1.17973I 0
u = 1.74231 − 0.10822I
a = −0.625642 + 1.075980I
b = −0.852072 + 0.466395I
0.89643 + 1.17973I 0
u = 0.165282 + 0.171989I
a = 1.50571 + 2.05453I
b = −0.871311 + 0.948268I
−3.89880 + 0.46217I −7.10748 + 3.67230I
u = 0.165282 − 0.171989I
a = 1.50571 − 2.05453I
b = −0.871311 − 0.948268I
−3.89880 − 0.46217I −7.10748 − 3.67230I
u = −0.113345 + 0.147787I
a = −2.26658 + 1.49533I
b = 1.062934 + 0.909215I
−3.12704 + 5.01347I −9.83252 − 7.05588I
u = −0.113345 − 0.147787I
a = −2.26658 − 1.49533I
b = 1.062934 − 0.909215I
−3.12704 − 5.01347I −9.83252 + 7.05588I
u = −1.45339 + 1.12190I
a = −0.391166 + 1.329084I
b = 0.787687 + 0.570097I
−4.24007 + 0.71156I 0
u = −1.45339 − 1.12190I
a = −0.391166 − 1.329084I
b = 0.787687 − 0.570097I
−4.24007 − 0.71156I 0
u = 0.35607 + 1.80833I
a = −0.087811 − 0.924520I
b = −0.974256 − 0.695576I
−3.12704 + 5.01347I 0
u = 0.35607 − 1.80833I
a = −0.087811 + 0.924520I
b = −0.974256 + 0.695576I
−3.12704 − 5.01347I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62861 + 0.93568I
a = 0.178674 + 0.635451I
b = 0.894224 + 0.532061I
0.38539 + 5.30492I 0
u = 1.62861 − 0.93568I
a = 0.178674 − 0.635451I
b = 0.894224 − 0.532061I
0.38539 − 5.30492I 0
u = 1.43021 + 1.26413I
a = 0.017701 + 1.362656I
b = −1.067406 + 0.619184I
4.08563 − 10.85580I 0
u = 1.43021 − 1.26413I
a = 0.017701 − 1.362656I
b = −1.067406 − 0.619184I
4.08563 + 10.85580I 0
u = −64.310 + 0.0910089I
a = 13.3282 − 6.3075I
b = 0.780924 − 0.463508I
1.82989 − 0.00826I 1.74029 + 0.54114I
u = −64.310 − 0.0910089I
a = 13.3282 + 6.3075I
b = 0.780924 + 0.463508I
1.82989 + 0.00826I 1.74029 − 0.54114I
u = −1.19020 + 1.52181I
a = 0.205879 − 1.003015I
b = 0.804518 − 0.739832I
−4.56851 + 2.11885I 0
u = −1.19020 − 1.52181I
a = 0.205879 + 1.003015I
b = 0.804518 + 0.739832I
−4.56851 − 2.11885I 0
u = 1.07424 + 1.62767I
a = 0.452221 + 1.090449I
b = −0.668430 + 0.517504I
−1.75445 + 5.84337I 0
u = 1.07424 − 1.62767I
a = 0.452221 − 1.090449I
b = −0.668430 − 0.517504I
−1.75445 − 5.84337I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.87555 + 0.86297I
a = 0.421088 − 0.801589I
b = 0.903125 − 0.571541I
−3.86874 − 3.84740I 0
u = −1.87555 − 0.86297I
a = 0.421088 + 0.801589I
b = 0.903125 + 0.571541I
−3.86874 + 3.84740I 0
u = −0.89821 + 1.86761I
a = −0.074502 + 1.199511I
b = 0.902129 + 0.704443I
−4.26452 + 7.61599I 0
u = −0.89821 − 1.86761I
a = −0.074502 − 1.199511I
b = 0.902129 − 0.704443I
−4.26452 − 7.61599I 0
u = 1.70455 + 1.47811I
a = −0.250572 − 0.693364I
b = −0.982428 − 0.555944I
−0.74509 + 10.25710I 0
u = 1.70455 − 1.47811I
a = −0.250572 + 0.693364I
b = −0.982428 + 0.555944I
−0.74509 − 10.25710I 0
24
III.
I
u
3
= hu
9
−u
7
−u
6
−u
5
+u
3
+b+u, u
14
+2u
13
+· · ·−u
2
+a, u
15
+u
14
+· · ·−u−1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−u
14
− 2u
13
+ 2u
11
+ 4u
10
+ 4u
9
− 2u
7
− 2u
6
− 3u
5
+ u
2
−u
9
+ u
7
+ u
6
+ u
5
− u
3
− u
a
10
=
1
u
2
a
8
=
u
14
+ u
13
+ u
12
− u
11
− 3u
10
− 4u
9
− 3u
8
+ 3u
6
+ 3u
5
+ 4u
4
− 2u − 1
u
14
+ u
13
− 2u
11
− 3u
10
− 2u
9
+ 2u
7
+ 3u
6
+ u
5
+ u
4
− u
3
− u
2
− u
a
3
=
−2u
14
− 2u
13
+ ··· + u + 1
−u
14
+ u
12
+ u
11
+ u
10
− u
9
− u
8
+ u
7
− u
6
+ u
5
− u
a
2
=
−u
14
+ u
12
+ ··· − 2u − 2
u
13
− u
11
− 2u
10
− 2u
9
+ u
8
+ 3u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
2
a
7
=
u
12
+ u
11
− 2u
9
− 3u
8
− 2u
7
+ 2u
5
+ 3u
4
+ u
3
+ u
2
− u − 1
u
14
+ u
13
− 2u
11
− 3u
10
− 2u
9
+ 2u
7
+ 3u
6
+ u
5
+ u
4
− u
3
− u
2
− u
a
6
=
u
12
+ u
11
− 2u
9
− 3u
8
− 2u
7
+ 2u
5
+ 3u
4
+ u
3
+ u
2
− 2u − 1
u
14
+ u
13
− 2u
11
− 3u
10
− 2u
9
+ 2u
7
+ 3u
6
+ u
5
+ u
4
− 2u
3
− u
2
− u
a
5
=
−2u
13
− 2u
12
+ ··· + u
2
+ 2u
u
14
+ u
13
− u
11
− 3u
10
− 3u
9
− 2u
8
+ 4u
6
+ 4u
5
+ 3u
4
− 2u
2
− u − 2
a
12
=
−u
14
+ u
12
+ ··· − u − 1
−u
14
+ u
12
+ u
11
+ u
10
− u
8
− u
6
− u
4
+ u + 1
a
11
=
u
13
+ u
12
− u
10
− 4u
9
− 3u
8
+ u
6
+ 5u
5
+ 3u
4
− 3u
−u
14
− u
13
+ ··· + 2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
14
− 3u
13
+ 8u
11
+ 9u
10
+ 6u
9
+ 3u
8
− 2u
7
− 5u
6
− 3u
5
− 15u
4
− 2u
3
− 3u
2
+ 7
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 7u
14
+ ··· + 9u − 1
c
2
u
15
+ u
14
+ ··· + u − 1
c
3
, c
11
u
15
− 4u
13
+ ··· − 3u
2
+ 1
c
4
, c
8
u
15
− 4u
13
+ ··· + 3u
2
− 1
c
5
u
15
− u
14
+ ··· + u + 1
c
6
, c
9
u
15
+ u
14
+ ··· − u − 1
c
7
, c
10
u
15
+ 8u
14
+ ··· + 6u + 1
c
12
u
15
+ 7u
14
+ ··· − u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 9y
14
+ ··· + y −1
c
2
, c
5
y
15
− 7y
14
+ ··· + 9y −1
c
3
, c
4
, c
8
c
11
y
15
− 8y
14
+ ··· + 6y −1
c
6
, c
9
y
15
− y
14
+ ··· − y −1
c
7
, c
10
y
15
+ 8y
14
+ ··· − 2y −1
c
12
y
15
− 7y
14
+ ··· + 7y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.959611 + 0.119814I
a = −0.71912 + 1.24968I
b = −0.326295 + 0.536959I
−3.56418 + 0.77491I −8.12670 − 0.03965I
u = 0.959611 − 0.119814I
a = −0.71912 − 1.24968I
b = −0.326295 − 0.536959I
−3.56418 − 0.77491I −8.12670 + 0.03965I
u = −0.421070 + 0.868919I
a = 1.58911 − 0.50507I
b = −0.966177 − 0.322619I
3.91257 + 5.85283I 7.42532 − 8.83755I
u = −0.421070 − 0.868919I
a = 1.58911 + 0.50507I
b = −0.966177 + 0.322619I
3.91257 − 5.85283I 7.42532 + 8.83755I
u = 0.170412 + 0.947352I
a = 0.24498 + 1.40630I
b = −0.892335 + 0.814934I
−3.27852 − 7.55546I −0.02233 + 9.91621I
u = 0.170412 − 0.947352I
a = 0.24498 − 1.40630I
b = −0.892335 − 0.814934I
−3.27852 + 7.55546I −0.02233 − 9.91621I
u = −0.192552 + 1.044028I
a = 0.146828 − 0.946761I
b = 1.010565 − 0.788445I
−2.53502 − 4.70170I 3.53112 − 0.11985I
u = −0.192552 − 1.044028I
a = 0.146828 + 0.946761I
b = 1.010565 + 0.788445I
−2.53502 + 4.70170I 3.53112 + 0.11985I
u = −0.865638 + 0.225957I
a = 1.12658 − 1.35308I
b = 1.089909 − 0.512485I
0.76079 − 9.43435I 1.85777 + 7.84421I
u = −0.865638 − 0.225957I
a = 1.12658 + 1.35308I
b = 1.089909 + 0.512485I
0.76079 + 9.43435I 1.85777 − 7.84421I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312182 + 0.810784I
a = −0.72943 − 1.66599I
b = 0.850885 + 0.293944I
2.99248 − 0.62234I 9.40233 + 4.15296I
u = 0.312182 − 0.810784I
a = −0.72943 + 1.66599I
b = 0.850885 − 0.293944I
2.99248 + 0.62234I 9.40233 − 4.15296I
u = −1.116239 + 0.381261I
a = 0.007218 − 1.360523I
b = −1.091066 − 0.378426I
2.69204 + 4.94745I 5.69951 − 4.52321I
u = −1.116239 − 0.381261I
a = 0.007218 + 1.360523I
b = −1.091066 + 0.378426I
2.69204 − 4.94745I 5.69951 + 4.52321I
u = 1.30659
a = 0.667669
b = 0.649029
−1.96031 12.4660
29
IV. I
u
4
=
hu
15
+2u
14
+· · ·+b+3, −14u
15
−10u
14
+· · ·+a+18, u
16
−3u
14
+· · ·−4u+1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
14u
15
+ 10u
14
+ ··· + 51u − 18
−u
15
− 2u
14
+ ··· + 2u − 3
a
10
=
1
u
2
a
8
=
−14u
15
− 14u
14
+ ··· − 42u + 14
−15u
15
− 15u
14
+ ··· − 43u + 14
a
3
=
−9u
15
− 7u
14
+ ··· − 31u + 8
−18u
15
− 10u
14
+ ··· − 70u + 23
a
2
=
−20u
15
− 13u
14
+ ··· − 76u + 26
−22u
15
− 11u
14
+ ··· − 89u + 33
a
7
=
u
15
+ u
14
+ ··· − 4u
2
+ u
−15u
15
− 15u
14
+ ··· − 43u + 14
a
6
=
−14u
15
− 12u
14
+ ··· − 45u + 15
−24u
15
− 19u
14
+ ··· − 80u + 27
a
5
=
9u
15
+ 5u
14
+ ··· + 39u − 15
−4u
15
− 5u
14
+ ··· − 7u − 1
a
12
=
5u
15
+ 3u
14
+ ··· + 21u − 9
2u
15
− 8u
13
+ ··· + 11u − 5
a
11
=
−u
15
+ 4u
13
+ ··· − 5u + 2
3u
15
+ 4u
14
+ ··· + 6u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −42u
15
− 31u
14
+ 114u
13
+ 17u
12
− 172u
11
− 17u
10
+ 191u
9
−
156u
7
+ 124u
6
− 87u
5
+ 47u
4
− 39u
3
+ 143u
2
− 140u + 43
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
− 4u
7
+ 10u
6
− 17u
5
+ 23u
4
− 22u
3
+ 14u
2
− 5u + 1)
2
c
2
(u
8
− 2u
6
+ u
5
+ 3u
4
− 2u
3
− 2u
2
+ u + 1)
2
c
3
, c
11
u
16
− 4u
14
+ ··· − 4u
2
+ 1
c
4
, c
8
u
16
− 4u
14
+ ··· − 4u
2
+ 1
c
5
(u
8
− 2u
6
− u
5
+ 3u
4
+ 2u
3
− 2u
2
− u + 1)
2
c
6
, c
9
u
16
− 3u
14
+ ··· − 4u + 1
c
7
, c
10
u
16
+ 8u
15
+ ··· + 8u + 1
c
12
(u
8
− 4u
7
+ 6u
6
− 4u
5
+ 3u
3
− 2u
2
+ 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 4y
7
+ 10y
6
+ 23y
5
+ 23y
4
+ 10y
3
+ 22y
2
+ 3y + 1)
2
c
2
, c
5
(y
8
− 4y
7
+ 10y
6
− 17y
5
+ 23y
4
− 22y
3
+ 14y
2
− 5y + 1)
2
c
3
, c
4
, c
8
c
11
y
16
− 8y
15
+ ··· − 8y + 1
c
6
, c
9
y
16
− 6y
15
+ ··· − 4y + 1
c
7
, c
10
y
16
+ 4y
15
+ ··· + 4y + 1
c
12
(y
8
− 4y
7
+ 4y
6
+ 4y
5
+ 2y
4
+ 3y
3
+ 4y
2
− 4y + 1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.653727 + 0.712407I
a = −0.992378 − 0.790090I
b = −0.891583 + 0.307286I
3.61840 + 3.26075I 7.90059 − 4.19737I
u = −0.653727 − 0.712407I
a = −0.992378 + 0.790090I
b = −0.891583 − 0.307286I
3.61840 − 3.26075I 7.90059 + 4.19737I
u = 0.784781 + 0.507096I
a = −0.233188 − 1.067878I
b = 1.217720 − 0.429877I
1.19791 − 2.24783I 1.73819 + 5.28133I
u = 0.784781 − 0.507096I
a = −0.233188 + 1.067878I
b = 1.217720 + 0.429877I
1.19791 + 2.24783I 1.73819 − 5.28133I
u = 0.815038 + 0.424790I
a = −0.340035 − 1.055435I
b = −0.654563 − 0.884729I
−3.90365 − 1.24143I −6.82272 + 4.38958I
u = 0.815038 − 0.424790I
a = −0.340035 + 1.055435I
b = −0.654563 + 0.884729I
−3.90365 + 1.24143I −6.82272 − 4.38958I
u = 0.780763 + 0.793495I
a = −0.340035 + 1.055435I
b = 0.540426 + 0.730458I
−3.90365 + 1.24143I −6.82272 − 4.38958I
u = 0.780763 − 0.793495I
a = −0.340035 − 1.055435I
b = 0.540426 − 0.730458I
−3.90365 − 1.24143I −6.82272 + 4.38958I
u = 0.067575 + 0.857243I
a = −0.992378 + 0.790090I
b = 1.002516 − 0.345519I
3.61840 − 3.26075I 7.90059 + 4.19737I
u = 0.067575 − 0.857243I
a = −0.992378 − 0.790090I
b = 1.002516 + 0.345519I
3.61840 + 3.26075I 7.90059 − 4.19737I
33
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.899321 + 0.764131I
a = −0.43440 + 2.11305I
b = 0.668186 + 0.365104I
−0.91267 − 5.73534I 1.18394 + 1.90076I
u = −0.899321 − 0.764131I
a = −0.43440 − 2.11305I
b = 0.668186 − 0.365104I
−0.91267 + 5.73534I 1.18394 − 1.90076I
u = 0.654473 + 0.199488I
a = −0.43440 + 2.11305I
b = −1.152495 + 0.629736I
−0.91267 − 5.73534I 1.18394 + 1.90076I
u = 0.654473 − 0.199488I
a = −0.43440 − 2.11305I
b = −1.152495 − 0.629736I
−0.91267 + 5.73534I 1.18394 − 1.90076I
u = −1.54958 + 0.16338I
a = −0.233188 − 1.067878I
b = −0.730207 − 0.257776I
1.19791 − 2.24783I 1.73819 + 5.28133I
u = −1.54958 − 0.16338I
a = −0.233188 + 1.067878I
b = −0.730207 + 0.257776I
1.19791 + 2.24783I 1.73819 − 5.28133I
34
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
− 4u
7
+ 10u
6
− 17u
5
+ 23u
4
− 22u
3
+ 14u
2
− 5u + 1)
2
· (u
15
− 7u
14
+ ··· + 9u − 1)(u
31
+ 12u
30
+ ··· + 5632u + 1024)
· (u
63
+ 29u
62
+ ··· + 399u + 25)
2
c
2
((u
8
− 2u
6
+ ··· + u + 1)
2
)(u
15
+ u
14
+ ··· + u − 1)
· (u
31
+ 12u
30
+ ··· − 224u − 32)(u
63
− 5u
62
+ ··· + 37u − 5)
2
c
3
, c
11
(u
15
− 4u
13
+ ··· − 3u
2
+ 1)(u
16
− 4u
14
+ ··· − 4u
2
+ 1)
· (u
31
− 7u
29
+ ··· + 3u + 1)(u
126
+ u
125
+ ··· + 36u + 9)
c
4
, c
8
(u
15
− 4u
13
+ ··· + 3u
2
− 1)(u
16
− 4u
14
+ ··· − 4u
2
+ 1)
· (u
31
− 7u
29
+ ··· + 3u + 1)(u
126
+ u
125
+ ··· + 36u + 9)
c
5
((u
8
− 2u
6
+ ··· − u + 1)
2
)(u
15
− u
14
+ ··· + u + 1)
· (u
31
+ 12u
30
+ ··· − 224u − 32)(u
63
− 5u
62
+ ··· + 37u − 5)
2
c
6
, c
9
(u
15
+ u
14
+ ··· − u − 1)(u
16
− 3u
14
+ ··· − 4u + 1)
· (u
31
+ u
30
+ ··· + 4u
2
+ 1)(u
126
− 15u
125
+ ··· − 10u + 1)
c
7
, c
10
(u
15
+ 8u
14
+ ··· + 6u + 1)(u
16
+ 8u
15
+ ··· + 8u + 1)
· (u
31
− 14u
30
+ ··· + 11u − 1)(u
126
− 53u
125
+ ··· − 2628u + 81)
c
12
((u
8
− 4u
7
+ ··· − 2u
2
+ 1)
2
)(u
15
+ 7u
14
+ ··· − u + 1)
· (u
31
+ 28u
30
+ ··· + 116736u + 10240)(u
63
− 13u
62
+ ··· − 5u + 1)
2
35
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 4y
7
+ 10y
6
+ 23y
5
+ 23y
4
+ 10y
3
+ 22y
2
+ 3y + 1)
2
· (y
15
+ 9y
14
+ ··· + y −1)(y
31
+ 12y
30
+ ··· − 393216y −1048576)
· (y
63
+ 19y
62
+ ··· + 4651y −625)
2
c
2
, c
5
(y
8
− 4y
7
+ 10y
6
− 17y
5
+ 23y
4
− 22y
3
+ 14y
2
− 5y + 1)
2
· (y
15
− 7y
14
+ ··· + 9y −1)(y
31
− 12y
30
+ ··· + 5632y −1024)
· (y
63
− 29y
62
+ ··· + 399y −25)
2
c
3
, c
4
, c
8
c
11
(y
15
− 8y
14
+ ··· + 6y −1)(y
16
− 8y
15
+ ··· − 8y + 1)
· (y
31
− 14y
30
+ ··· + 11y −1)(y
126
− 53y
125
+ ··· − 2628y + 81)
c
6
, c
9
(y
15
− y
14
+ ··· − y −1)(y
16
− 6y
15
+ ··· − 4y + 1)
· (y
31
+ 5y
30
+ ··· − 8y −1)(y
126
− 15y
125
+ ··· + 248y + 1)
c
7
, c
10
(y
15
+ 8y
14
+ ··· − 2y −1)(y
16
+ 4y
15
+ ··· + 4y + 1)
· (y
31
+ 10y
30
+ ··· + 95y −1)(y
126
+ 51y
125
+ ··· + 935388y + 6561)
c
12
(y
8
− 4y
7
+ 4y
6
+ 4y
5
+ 2y
4
+ 3y
3
+ 4y
2
− 4y + 1)
2
· (y
15
− 7y
14
+ ··· + 7y −1)
· (y
31
− 8y
30
+ ··· + 69206016y −104857600)
· (y
63
− 15y
62
+ ··· + 49y −1)
2
36
