12a
0209
(K12a
0209
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 11 2 10 12 4 1 9 5
Solving Sequence
3,6
2 7
4,10
8 1 11 5 9 12
c
2
c
6
c
3
c
7
c
1
c
10
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.56131 × 10
18
u
72
+ 4.31036 × 10
18
u
71
+ ··· + 2.30896 × 10
17
b + 2.90849 × 10
19
,
2.90849 × 10
19
u
72
+ 2.93972 × 10
20
u
71
+ ··· + 4.61791 × 10
17
a + 5.31033 × 10
19
, u
73
+ 10u
72
+ ··· + 17u + 2i
I
u
2
= h9u
48
− 22u
47
+ ··· + 2b + 2, 2u
48
a + 4u
48
+ ··· − 15a − 7, u
49
− 3u
48
+ ··· − 3u + 1i
I
u
3
= h2u
26
− 22u
25
+ ··· + b + 16, 16u
26
− 46u
25
+ ··· + a + 9, u
27
− 3u
26
+ ··· + 5u − 1i
I
u
4
= ha
3
u + a
3
− a
2
u − a
2
+ b − a − u + 1, a
4
+ a
2
u − a
2
− 2au − 2a − 2u − 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 206 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−1.56 × 10
18
u
72
+ 4.31 × 10
18
u
71
+ · · · + 2.31 × 10
17
b + 2.91 ×
10
19
, 2.91 × 10
19
u
72
+ 2.94 × 10
20
u
71
+ · · · + 4.62 × 10
17
a + 5.31 ×
10
19
, u
73
+ 10u
72
+ · · · + 17u + 2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
−62.9827u
72
− 636.589u
71
+ ··· − 948.579u − 114.994
6.76197u
72
− 18.6680u
71
+ ··· − 955.713u − 125.965
a
8
=
44.3628u
72
+ 426.580u
71
+ ··· + 440.294u + 50.3153
17.0477u
72
+ 207.544u
71
+ ··· + 704.852u + 88.7256
a
1
=
u
2
+ 1
u
2
a
11
=
−12.7540u
72
− 143.072u
71
+ ··· − 330.334u − 40.7974
38.5297u
72
+ 343.881u
71
+ ··· − 80.7329u − 18.6829
a
5
=
−18.2285u
72
− 181.746u
71
+ ··· − 197.107u − 22.7670
9.87004u
72
+ 61.1843u
71
+ ··· − 257.594u − 34.4057
a
9
=
−28.7372u
72
− 293.466u
71
+ ··· − 456.109u − 56.4533
17.1086u
72
+ 131.737u
71
+ ··· − 229.536u − 33.0173
a
12
=
1.86084u
72
+ 5.66695u
71
+ ··· − 39.3331u − 0.499919
33.5377u
72
+ 304.934u
71
+ ··· + 28.0721u − 1.32706
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
31874848749235508694
230895744813749827
u
72
−
257490262863303824255
230895744813749827
u
71
+ ··· +
54578403100783767899
230895744813749827
u +
6305572019569292940
230895744813749827
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 38u
72
+ ··· − 23u − 4
c
2
, c
6
u
73
− 10u
72
+ ··· + 17u − 2
c
3
u
73
+ 10u
72
+ ··· − 130207u − 16754
c
4
, c
12
u
73
+ 2u
72
+ ··· + u + 1
c
5
, c
9
u
73
+ 7u
71
+ ··· + 19u + 7
c
7
, c
10
u
73
− 3u
72
+ ··· − 6u + 1
c
8
, c
11
u
73
− 17u
72
+ ··· − 4311u + 160
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
− 2y
72
+ ··· + 241y −16
c
2
, c
6
y
73
+ 38y
72
+ ··· − 23y −4
c
3
y
73
− 36y
72
+ ··· − 3279540855y −280696516
c
4
, c
12
y
73
− 54y
72
+ ··· + 127y −1
c
5
, c
9
y
73
+ 14y
72
+ ··· − 1389y −49
c
7
, c
10
y
73
+ 21y
72
+ ··· − 48y −1
c
8
, c
11
y
73
+ 37y
72
+ ··· + 996881y −25600
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.564959 + 0.847230I
a = −0.420644 + 0.433873I
b = 0.605237 + 0.111262I
6.48655 + 2.06213I 0
u = 0.564959 − 0.847230I
a = −0.420644 − 0.433873I
b = 0.605237 − 0.111262I
6.48655 − 2.06213I 0
u = −0.372313 + 0.889151I
a = 1.274400 + 0.272841I
b = 0.717072 − 1.031550I
1.56727 − 2.14796I 0
u = −0.372313 − 0.889151I
a = 1.274400 − 0.272841I
b = 0.717072 + 1.031550I
1.56727 + 2.14796I 0
u = 0.623366 + 0.835016I
a = −0.536860 − 0.095790I
b = 0.254674 + 0.507999I
2.20061 + 7.49260I 0
u = 0.623366 − 0.835016I
a = −0.536860 + 0.095790I
b = 0.254674 − 0.507999I
2.20061 − 7.49260I 0
u = −0.951897 + 0.435766I
a = −0.211932 + 0.335549I
b = −0.055516 + 0.411761I
3.57693 − 3.95252I 0
u = −0.951897 − 0.435766I
a = −0.211932 − 0.335549I
b = −0.055516 − 0.411761I
3.57693 + 3.95252I 0
u = 0.640065 + 0.697540I
a = 0.461939 − 0.202848I
b = −0.437165 − 0.192384I
2.58609 − 2.60921I 0
u = 0.640065 − 0.697540I
a = 0.461939 + 0.202848I
b = −0.437165 + 0.192384I
2.58609 + 2.60921I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735332 + 0.754639I
a = −0.331872 + 0.216445I
b = 0.407374 + 0.091284I
6.04236 − 7.53790I 0
u = 0.735332 − 0.754639I
a = −0.331872 − 0.216445I
b = 0.407374 − 0.091284I
6.04236 + 7.53790I 0
u = 0.584696 + 0.704579I
a = 0.677743 + 0.287959I
b = −0.193384 − 0.645892I
6.89806 + 2.50124I 0
u = 0.584696 − 0.704579I
a = 0.677743 − 0.287959I
b = −0.193384 + 0.645892I
6.89806 − 2.50124I 0
u = 0.699590 + 0.831919I
a = 0.441214 + 0.158398I
b = −0.176895 − 0.477868I
5.8069 + 12.9188I 0
u = 0.699590 − 0.831919I
a = 0.441214 − 0.158398I
b = −0.176895 + 0.477868I
5.8069 − 12.9188I 0
u = −0.858251 + 0.245632I
a = 2.04477 − 0.73888I
b = 1.57344 − 1.13641I
2.4244 + 15.2798I 0
u = −0.858251 − 0.245632I
a = 2.04477 + 0.73888I
b = 1.57344 + 1.13641I
2.4244 − 15.2798I 0
u = −0.877206 + 0.063922I
a = 0.167896 + 1.013510I
b = 0.212065 + 0.878323I
2.74376 + 2.31862I 0
u = −0.877206 − 0.063922I
a = 0.167896 − 1.013510I
b = 0.212065 − 0.878323I
2.74376 − 2.31862I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462980 + 1.044570I
a = −1.21227 + 1.63748I
b = 1.14920 + 2.02442I
1.84428 − 3.74154I 0
u = −0.462980 − 1.044570I
a = −1.21227 − 1.63748I
b = 1.14920 − 2.02442I
1.84428 + 3.74154I 0
u = −0.827327 + 0.214004I
a = −2.12748 + 0.89618I
b = −1.56833 + 1.19672I
−1.09792 + 9.05839I 0
u = −0.827327 − 0.214004I
a = −2.12748 − 0.89618I
b = −1.56833 − 1.19672I
−1.09792 − 9.05839I 0
u = −0.329613 + 1.125430I
a = −0.41328 − 1.73581I
b = −2.08975 − 0.10703I
0.978618 + 0.650011I 0
u = −0.329613 − 1.125430I
a = −0.41328 + 1.73581I
b = −2.08975 + 0.10703I
0.978618 − 0.650011I 0
u = 0.430701 + 1.103910I
a = −0.307829 + 0.530608I
b = 0.718326 + 0.111283I
0.44267 + 3.11854I 0
u = 0.430701 − 1.103910I
a = −0.307829 − 0.530608I
b = 0.718326 − 0.111283I
0.44267 − 3.11854I 0
u = −0.481205 + 1.090910I
a = 0.305601 − 1.137950I
b = −1.094350 − 0.880971I
−0.84301 − 3.50419I 0
u = −0.481205 − 1.090910I
a = 0.305601 + 1.137950I
b = −1.094350 + 0.880971I
−0.84301 + 3.50419I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655040 + 0.998408I
a = 0.259508 + 0.468234I
b = 0.637477 + 0.047617I
1.91895 − 1.89445I 0
u = −0.655040 − 0.998408I
a = 0.259508 − 0.468234I
b = 0.637477 − 0.047617I
1.91895 + 1.89445I 0
u = 0.391852 + 1.132880I
a = 0.026904 − 0.380383I
b = −0.441469 + 0.118575I
−4.28285 + 1.23646I 0
u = 0.391852 − 1.132880I
a = 0.026904 + 0.380383I
b = −0.441469 − 0.118575I
−4.28285 − 1.23646I 0
u = 0.474637 + 1.111440I
a = 0.247949 − 0.519379I
b = −0.694941 − 0.029063I
0.76792 + 4.34795I 0
u = 0.474637 − 1.111440I
a = 0.247949 + 0.519379I
b = −0.694941 + 0.029063I
0.76792 − 4.34795I 0
u = −0.448676 + 1.141650I
a = 0.16043 + 2.42119I
b = 2.83614 + 0.90318I
−5.80825 − 3.98070I 0
u = −0.448676 − 1.141650I
a = 0.16043 − 2.42119I
b = 2.83614 − 0.90318I
−5.80825 + 3.98070I 0
u = −0.728706 + 0.244433I
a = 2.46091 − 0.77289I
b = 1.60436 − 1.16473I
4.95442 + 3.81969I 6.95886 − 3.45256I
u = −0.728706 − 0.244433I
a = 2.46091 + 0.77289I
b = 1.60436 + 1.16473I
4.95442 − 3.81969I 6.95886 + 3.45256I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162975 + 1.233720I
a = −0.450075 + 0.149399I
b = 0.110965 + 0.579614I
−3.98989 − 2.83689I 0
u = −0.162975 − 1.233720I
a = −0.450075 − 0.149399I
b = 0.110965 − 0.579614I
−3.98989 + 2.83689I 0
u = 0.493222 + 1.148200I
a = −0.148228 + 0.269409I
b = 0.382444 + 0.037316I
−3.55518 + 6.73900I 0
u = 0.493222 − 1.148200I
a = −0.148228 − 0.269409I
b = 0.382444 − 0.037316I
−3.55518 − 6.73900I 0
u = −0.527320 + 1.143810I
a = 0.38813 − 2.25183I
b = −2.37099 − 1.63138I
2.33960 − 8.57168I 0
u = −0.527320 − 1.143810I
a = 0.38813 + 2.25183I
b = −2.37099 + 1.63138I
2.33960 + 8.57168I 0
u = −0.315560 + 1.220770I
a = 0.55875 + 1.35033I
b = 1.82477 − 0.25599I
−5.57113 + 5.34756I 0
u = −0.315560 − 1.220770I
a = 0.55875 − 1.35033I
b = 1.82477 + 0.25599I
−5.57113 − 5.34756I 0
u = −0.619406 + 0.380540I
a = 0.799519 − 0.626257I
b = 0.256911 − 0.692156I
1.27436 − 0.77322I 6.44105 + 3.71170I
u = −0.619406 − 0.380540I
a = 0.799519 + 0.626257I
b = 0.256911 + 0.692156I
1.27436 + 0.77322I 6.44105 − 3.71170I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.282337 + 1.241870I
a = −0.428978 − 1.254830I
b = −1.67944 + 0.17845I
−2.35312 + 11.60620I 0
u = −0.282337 − 1.241870I
a = −0.428978 + 1.254830I
b = −1.67944 − 0.17845I
−2.35312 − 11.60620I 0
u = 0.172310 + 0.704869I
a = −1.048260 − 0.662941I
b = −0.286662 + 0.853117I
−2.11378 + 0.88555I −9.63986 − 6.78270I
u = 0.172310 − 0.704869I
a = −1.048260 + 0.662941I
b = −0.286662 − 0.853117I
−2.11378 − 0.88555I −9.63986 + 6.78270I
u = 0.684054 + 0.164877I
a = 0.198647 + 0.390145I
b = −0.071559 − 0.299632I
−0.74996 − 2.26785I −1.36009 + 3.03346I
u = 0.684054 − 0.164877I
a = 0.198647 − 0.390145I
b = −0.071559 + 0.299632I
−0.74996 + 2.26785I −1.36009 − 3.03346I
u = −0.545236 + 1.182220I
a = −0.42738 + 2.00521I
b = 2.13757 + 1.59857I
−3.9720 − 14.1161I 0
u = −0.545236 − 1.182220I
a = −0.42738 − 2.00521I
b = 2.13757 − 1.59857I
−3.9720 + 14.1161I 0
u = −0.565076 + 1.184860I
a = 0.29511 − 1.94998I
b = −2.14368 − 1.45155I
−0.3868 − 20.5075I 0
u = −0.565076 − 1.184860I
a = 0.29511 + 1.94998I
b = −2.14368 + 1.45155I
−0.3868 + 20.5075I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.478314 + 1.224030I
a = 0.532800 − 0.725722I
b = −0.633457 − 0.999285I
−1.03976 − 2.35344I 0
u = −0.478314 − 1.224030I
a = 0.532800 + 0.725722I
b = −0.633457 + 0.999285I
−1.03976 + 2.35344I 0
u = −0.273626 + 1.311600I
a = 0.310716 − 0.342732I
b = −0.364507 − 0.501315I
−2.18891 − 7.86650I 0
u = −0.273626 − 1.311600I
a = 0.310716 + 0.342732I
b = −0.364507 + 0.501315I
−2.18891 + 7.86650I 0
u = −0.541103 + 1.248870I
a = −0.496875 + 0.389960I
b = 0.218150 + 0.831543I
−0.77248 − 7.46711I 0
u = −0.541103 − 1.248870I
a = −0.496875 − 0.389960I
b = 0.218150 − 0.831543I
−0.77248 + 7.46711I 0
u = −0.610805
a = −3.15155
b = −1.92498
−2.76756 −11.9810
u = 0.015403 + 0.589231I
a = 1.83364 − 1.02386I
b = −0.631534 − 1.064670I
2.98921 − 0.06124I 3.65891 − 0.00158I
u = 0.015403 − 0.589231I
a = 1.83364 + 1.02386I
b = −0.631534 + 1.064670I
2.98921 + 0.06124I 3.65891 + 0.00158I
u = −0.379406 + 0.430206I
a = −2.47582 + 1.49166I
b = −0.29762 + 1.63106I
3.65190 − 0.06033I 6.66313 − 2.08391I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379406 − 0.430206I
a = −2.47582 − 1.49166I
b = −0.29762 − 1.63106I
3.65190 + 0.06033I 6.66313 + 2.08391I
u = 0.478791 + 0.170504I
a = −0.58304 − 1.35827I
b = 0.047561 + 0.749736I
3.28795 − 0.31350I 6.50392 − 0.08687I
u = 0.478791 − 0.170504I
a = −0.58304 + 1.35827I
b = 0.047561 − 0.749736I
3.28795 + 0.31350I 6.50392 + 0.08687I
12
II. I
u
2
=
h9u
48
−22u
47
+· · ·+2 b+2, 2u
48
a+4u
48
+· · ·−15a−7, u
49
−3u
48
+· · ·−3u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
a
−
9
2
u
48
+ 11u
47
+ ··· −
9
2
u − 1
a
8
=
−
5
2
u
48
a − 3u
48
+ ··· +
3
2
a − 3
2u
48
a − 4u
48
+ ··· +
5
2
a + 5
a
1
=
u
2
+ 1
u
2
a
11
=
u
48
−
7
2
u
47
+ ··· + a −
3
2
−6u
48
+ 15u
47
+ ··· − 7u − 1
a
5
=
−
3
2
u
48
a +
3
2
u
48
+ ··· − a − 4
u
48
a +
5
2
u
48
+ ··· − 3a −
3
2
a
9
=
2u
48
− 4u
47
+ ··· + a + 1
−
9
2
u
48
+ 11u
47
+ ··· −
11
2
u − 1
a
12
=
−
1
2
u
48
a − 3u
48
+ ··· +
3
2
a −
7
2
1
2
u
48
a − 5u
48
+ ··· +
1
2
a + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = −16u
48
+ 65u
47
+ ··· − 100u + 27
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
49
+ 25u
48
+ ··· − 3u − 1)
2
c
2
, c
6
(u
49
+ 3u
48
+ ··· − 3u − 1)
2
c
3
(u
49
− 3u
48
+ ··· + 39u − 17)
2
c
4
, c
12
u
98
+ u
97
+ ··· + 26u
2
+ 4
c
5
, c
9
u
98
+ u
97
+ ··· + 12856u + 4796
c
7
, c
10
u
98
− 15u
97
+ ··· − 38u + 1
c
8
, c
11
(u
49
+ 15u
48
+ ··· + 41u + 3)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
49
+ y
48
+ ··· + 21y −1)
2
c
2
, c
6
(y
49
+ 25y
48
+ ··· − 3y −1)
2
c
3
(y
49
− 23y
48
+ ··· − 12963y −289)
2
c
4
, c
12
y
98
+ 9y
97
+ ··· + 208y + 16
c
5
, c
9
y
98
+ y
97
+ ··· + 1102689744y + 23001616
c
7
, c
10
y
98
− 37y
97
+ ··· − 84y + 1
c
8
, c
11
(y
49
+ 31y
48
+ ··· − 185y −9)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.565929 + 0.787955I
a = 0.927132 − 0.349022I
b = −0.330910 − 0.345790I
1.64922 − 2.25866I 0.69047 + 3.81619I
u = −0.565929 + 0.787955I
a = 0.090522 − 0.484976I
b = 0.249678 − 0.928060I
1.64922 − 2.25866I 0.69047 + 3.81619I
u = −0.565929 − 0.787955I
a = 0.927132 + 0.349022I
b = −0.330910 + 0.345790I
1.64922 + 2.25866I 0.69047 − 3.81619I
u = −0.565929 − 0.787955I
a = 0.090522 + 0.484976I
b = 0.249678 + 0.928060I
1.64922 + 2.25866I 0.69047 − 3.81619I
u = −0.719218 + 0.760676I
a = −0.475496 − 0.214594I
b = −0.421030 − 0.337819I
2.15174 − 3.63424I 0. + 10.28689I
u = −0.719218 + 0.760676I
a = −0.041830 − 0.513945I
b = −0.505221 + 0.207358I
2.15174 − 3.63424I 0. + 10.28689I
u = −0.719218 − 0.760676I
a = −0.475496 + 0.214594I
b = −0.421030 + 0.337819I
2.15174 + 3.63424I 0. − 10.28689I
u = −0.719218 − 0.760676I
a = −0.041830 + 0.513945I
b = −0.505221 − 0.207358I
2.15174 + 3.63424I 0. − 10.28689I
u = −0.685202 + 0.852788I
a = 0.599701 + 0.208690I
b = 0.285940 − 0.234881I
1.87535 − 1.69278I 0
u = −0.685202 + 0.852788I
a = 0.331089 + 0.069275I
b = 0.588885 − 0.368423I
1.87535 − 1.69278I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.685202 − 0.852788I
a = 0.599701 − 0.208690I
b = 0.285940 + 0.234881I
1.87535 + 1.69278I 0
u = −0.685202 − 0.852788I
a = 0.331089 − 0.069275I
b = 0.588885 + 0.368423I
1.87535 + 1.69278I 0
u = 0.849383 + 0.273394I
a = −1.54302 − 0.31399I
b = −1.36253 − 0.51886I
−0.65523 − 6.25327I 1.78852 + 8.06126I
u = 0.849383 + 0.273394I
a = 1.63172 + 0.08566I
b = 1.224780 + 0.688548I
−0.65523 − 6.25327I 1.78852 + 8.06126I
u = 0.849383 − 0.273394I
a = −1.54302 + 0.31399I
b = −1.36253 + 0.51886I
−0.65523 + 6.25327I 1.78852 − 8.06126I
u = 0.849383 − 0.273394I
a = 1.63172 − 0.08566I
b = 1.224780 − 0.688548I
−0.65523 + 6.25327I 1.78852 − 8.06126I
u = −0.041598 + 0.887284I
a = 0.448646 − 0.954904I
b = 0.64729 − 1.34517I
1.03584 − 4.42428I −2.94212 + 4.09903I
u = −0.041598 + 0.887284I
a = 1.54686 + 0.65700I
b = −0.828608 − 0.437799I
1.03584 − 4.42428I −2.94212 + 4.09903I
u = −0.041598 − 0.887284I
a = 0.448646 + 0.954904I
b = 0.64729 + 1.34517I
1.03584 + 4.42428I −2.94212 − 4.09903I
u = −0.041598 − 0.887284I
a = 1.54686 − 0.65700I
b = −0.828608 + 0.437799I
1.03584 + 4.42428I −2.94212 − 4.09903I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383075 + 1.049290I
a = 0.44321 − 1.71504I
b = 2.49198 − 1.10702I
1.12559 − 3.30577I 0
u = 0.383075 + 1.049290I
a = 0.16587 + 2.43548I
b = −1.96935 + 0.19194I
1.12559 − 3.30577I 0
u = 0.383075 − 1.049290I
a = 0.44321 + 1.71504I
b = 2.49198 + 1.10702I
1.12559 + 3.30577I 0
u = 0.383075 − 1.049290I
a = 0.16587 − 2.43548I
b = −1.96935 − 0.19194I
1.12559 + 3.30577I 0
u = 0.826596 + 0.219765I
a = −1.43081 − 0.20550I
b = −1.190550 − 0.695210I
−1.61941 − 3.47961I −1.033654 − 0.487263I
u = 0.826596 + 0.219765I
a = 1.55406 + 0.42788I
b = 1.137540 + 0.484310I
−1.61941 − 3.47961I −1.033654 − 0.487263I
u = 0.826596 − 0.219765I
a = −1.43081 + 0.20550I
b = −1.190550 + 0.695210I
−1.61941 + 3.47961I −1.033654 + 0.487263I
u = 0.826596 − 0.219765I
a = 1.55406 − 0.42788I
b = 1.137540 − 0.484310I
−1.61941 + 3.47961I −1.033654 + 0.487263I
u = −0.580618 + 0.987322I
a = −0.761121 + 0.167915I
b = −1.20899 + 0.91047I
4.16206 − 0.64233I 0
u = −0.580618 + 0.987322I
a = −1.220260 − 0.506911I
b = −0.276134 + 0.848965I
4.16206 − 0.64233I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580618 − 0.987322I
a = −0.761121 − 0.167915I
b = −1.20899 − 0.91047I
4.16206 + 0.64233I 0
u = −0.580618 − 0.987322I
a = −1.220260 + 0.506911I
b = −0.276134 − 0.848965I
4.16206 + 0.64233I 0
u = −0.633943 + 0.561300I
a = 0.679974 + 0.689772I
b = 0.633015 + 1.078690I
5.39723 − 4.11919I 10.16439 + 6.77635I
u = −0.633943 + 0.561300I
a = −0.28478 + 1.44940I
b = 0.818233 + 0.055607I
5.39723 − 4.11919I 10.16439 + 6.77635I
u = −0.633943 − 0.561300I
a = 0.679974 − 0.689772I
b = 0.633015 − 1.078690I
5.39723 + 4.11919I 10.16439 − 6.77635I
u = −0.633943 − 0.561300I
a = −0.28478 − 1.44940I
b = 0.818233 − 0.055607I
5.39723 + 4.11919I 10.16439 − 6.77635I
u = −0.409974 + 1.134200I
a = 0.88233 − 1.48572I
b = −2.28830 − 1.14589I
−1.90389 + 2.54668I 0
u = −0.409974 + 1.134200I
a = 0.24855 − 2.10739I
b = −1.32337 − 1.60984I
−1.90389 + 2.54668I 0
u = −0.409974 − 1.134200I
a = 0.88233 + 1.48572I
b = −2.28830 + 1.14589I
−1.90389 − 2.54668I 0
u = −0.409974 − 1.134200I
a = 0.24855 + 2.10739I
b = −1.32337 + 1.60984I
−1.90389 − 2.54668I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.403660 + 1.145150I
a = −0.643338 + 0.518061I
b = −1.62151 − 0.17912I
−4.50913 + 1.14133I 0
u = 0.403660 + 1.145150I
a = 0.583091 − 1.210450I
b = 0.852947 + 0.527598I
−4.50913 + 1.14133I 0
u = 0.403660 − 1.145150I
a = −0.643338 − 0.518061I
b = −1.62151 + 0.17912I
−4.50913 − 1.14133I 0
u = 0.403660 − 1.145150I
a = 0.583091 + 1.210450I
b = 0.852947 − 0.527598I
−4.50913 − 1.14133I 0
u = −0.448278 + 1.138950I
a = 0.12576 + 2.03616I
b = 2.79062 + 0.80667I
−5.76355 − 3.96156I 0
u = −0.448278 + 1.138950I
a = 0.22174 + 2.36289I
b = 2.37547 + 0.76953I
−5.76355 − 3.96156I 0
u = −0.448278 − 1.138950I
a = 0.12576 − 2.03616I
b = 2.79062 − 0.80667I
−5.76355 + 3.96156I 0
u = −0.448278 − 1.138950I
a = 0.22174 − 2.36289I
b = 2.37547 − 0.76953I
−5.76355 + 3.96156I 0
u = 0.526930 + 1.106360I
a = −0.01941 − 2.10573I
b = 2.11960 − 1.79710I
2.30518 + 10.40670I 0
u = 0.526930 + 1.106360I
a = 0.58025 + 2.19219I
b = −2.31947 + 1.13105I
2.30518 + 10.40670I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526930 − 1.106360I
a = −0.01941 + 2.10573I
b = 2.11960 + 1.79710I
2.30518 − 10.40670I 0
u = 0.526930 − 1.106360I
a = 0.58025 − 2.19219I
b = −2.31947 − 1.13105I
2.30518 − 10.40670I 0
u = −0.480363 + 1.138030I
a = −0.90835 − 1.41643I
b = −2.99361 − 0.05585I
−1.40396 − 10.43590I 0
u = −0.480363 + 1.138030I
a = −0.90078 − 2.25031I
b = −2.04827 + 0.35332I
−1.40396 − 10.43590I 0
u = −0.480363 − 1.138030I
a = −0.90835 + 1.41643I
b = −2.99361 + 0.05585I
−1.40396 + 10.43590I 0
u = −0.480363 − 1.138030I
a = −0.90078 + 2.25031I
b = −2.04827 − 0.35332I
−1.40396 + 10.43590I 0
u = 0.261024 + 1.224380I
a = −0.122328 − 0.934957I
b = 1.361490 − 0.182120I
−5.49216 − 2.78317I 0
u = 0.261024 + 1.224380I
a = −0.084478 + 1.093970I
b = −1.112810 + 0.393822I
−5.49216 − 2.78317I 0
u = 0.261024 − 1.224380I
a = −0.122328 + 0.934957I
b = 1.361490 + 0.182120I
−5.49216 + 2.78317I 0
u = 0.261024 − 1.224380I
a = −0.084478 − 1.093970I
b = −1.112810 − 0.393822I
−5.49216 + 2.78317I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.477685 + 1.157630I
a = −0.878685 − 0.868884I
b = 1.28704 − 1.23579I
−3.98228 + 6.98387I 0
u = 0.477685 + 1.157630I
a = 0.52018 + 1.32644I
b = −0.58611 + 1.43224I
−3.98228 + 6.98387I 0
u = 0.477685 − 1.157630I
a = −0.878685 + 0.868884I
b = 1.28704 + 1.23579I
−3.98228 − 6.98387I 0
u = 0.477685 − 1.157630I
a = 0.52018 − 1.32644I
b = −0.58611 − 1.43224I
−3.98228 − 6.98387I 0
u = 0.305940 + 1.219010I
a = −0.038028 + 0.901730I
b = −1.41165 + 0.29591I
−6.12924 + 0.18565I 0
u = 0.305940 + 1.219010I
a = 0.045050 − 1.146730I
b = 1.110850 − 0.229518I
−6.12924 + 0.18565I 0
u = 0.305940 − 1.219010I
a = −0.038028 − 0.901730I
b = −1.41165 − 0.29591I
−6.12924 − 0.18565I 0
u = 0.305940 − 1.219010I
a = 0.045050 + 1.146730I
b = 1.110850 + 0.229518I
−6.12924 − 0.18565I 0
u = 0.660704 + 0.334495I
a = 1.81872 + 0.62320I
b = 1.65690 + 1.06347I
4.55286 − 5.78809I 9.50823 + 6.30264I
u = 0.660704 + 0.334495I
a = −2.64478 − 0.27063I
b = −0.99318 − 1.02010I
4.55286 − 5.78809I 9.50823 + 6.30264I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.660704 − 0.334495I
a = 1.81872 − 0.62320I
b = 1.65690 − 1.06347I
4.55286 + 5.78809I 9.50823 − 6.30264I
u = 0.660704 − 0.334495I
a = −2.64478 + 0.27063I
b = −0.99318 + 1.02010I
4.55286 + 5.78809I 9.50823 − 6.30264I
u = 0.162863 + 0.708987I
a = −0.547257 − 0.905838I
b = −0.117217 + 1.104610I
−2.12945 + 0.88125I −6.88602 − 7.29927I
u = 0.162863 + 0.708987I
a = −1.44385 − 0.49700I
b = −0.553099 + 0.535526I
−2.12945 + 0.88125I −6.88602 − 7.29927I
u = 0.162863 − 0.708987I
a = −0.547257 + 0.905838I
b = −0.117217 − 1.104610I
−2.12945 − 0.88125I −6.88602 + 7.29927I
u = 0.162863 − 0.708987I
a = −1.44385 + 0.49700I
b = −0.553099 − 0.535526I
−2.12945 − 0.88125I −6.88602 + 7.29927I
u = 0.702353 + 0.115740I
a = −0.896146 − 0.621689I
b = −0.791467 − 1.071980I
−1.00004 − 2.57700I −1.85140 + 5.02776I
u = 0.702353 + 0.115740I
a = 1.34195 + 1.30513I
b = 0.557456 + 0.540365I
−1.00004 − 2.57700I −1.85140 + 5.02776I
u = 0.702353 − 0.115740I
a = −0.896146 + 0.621689I
b = −0.791467 + 1.071980I
−1.00004 + 2.57700I −1.85140 − 5.02776I
u = 0.702353 − 0.115740I
a = 1.34195 − 1.30513I
b = 0.557456 − 0.540365I
−1.00004 + 2.57700I −1.85140 − 5.02776I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314326 + 0.637004I
a = −1.63310 + 1.45974I
b = −0.43576 − 1.76614I
2.49963 + 6.33743I 3.80393 − 12.96994I
u = 0.314326 + 0.637004I
a = 2.50114 + 0.55009I
b = 1.44318 + 0.58146I
2.49963 + 6.33743I 3.80393 − 12.96994I
u = 0.314326 − 0.637004I
a = −1.63310 − 1.45974I
b = −0.43576 + 1.76614I
2.49963 − 6.33743I 3.80393 + 12.96994I
u = 0.314326 − 0.637004I
a = 2.50114 − 0.55009I
b = 1.44318 − 0.58146I
2.49963 − 6.33743I 3.80393 + 12.96994I
u = 0.546718 + 1.178980I
a = −0.121654 − 1.393520I
b = 1.81615 − 0.87585I
−4.46584 + 8.53970I 0
u = 0.546718 + 1.178980I
a = 0.02350 + 1.55134I
b = −1.57641 + 0.90529I
−4.46584 + 8.53970I 0
u = 0.546718 − 1.178980I
a = −0.121654 + 1.393520I
b = 1.81615 + 0.87585I
−4.46584 − 8.53970I 0
u = 0.546718 − 1.178980I
a = 0.02350 − 1.55134I
b = −1.57641 − 0.90529I
−4.46584 − 8.53970I 0
u = 0.572173 + 1.174870I
a = −0.09641 + 1.44640I
b = −1.91971 + 0.89272I
−3.35263 + 11.49570I 0
u = 0.572173 + 1.174870I
a = 0.02903 − 1.61984I
b = 1.75450 − 0.71433I
−3.35263 + 11.49570I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.572173 − 1.174870I
a = −0.09641 − 1.44640I
b = −1.91971 − 0.89272I
−3.35263 − 11.49570I 0
u = 0.572173 − 1.174870I
a = 0.02903 + 1.61984I
b = 1.75450 + 0.71433I
−3.35263 − 11.49570I 0
u = −0.626585 + 0.120026I
a = 2.25928 + 0.22829I
b = 1.80768 + 0.72863I
1.39664 + 6.16977I −0.60759 − 8.72781I
u = −0.626585 + 0.120026I
a = 2.56799 + 1.65477I
b = 1.44303 − 0.12813I
1.39664 + 6.16977I −0.60759 − 8.72781I
u = −0.626585 − 0.120026I
a = 2.25928 − 0.22829I
b = 1.80768 − 0.72863I
1.39664 − 6.16977I −0.60759 + 8.72781I
u = −0.626585 − 0.120026I
a = 2.56799 − 1.65477I
b = 1.44303 + 0.12813I
1.39664 − 6.16977I −0.60759 + 8.72781I
u = −0.603445
a = −2.93143 + 0.25607I
b = −1.76896 − 0.15452I
−2.74282 −8.35200
u = −0.603445
a = −2.93143 − 0.25607I
b = −1.76896 + 0.15452I
−2.74282 −8.35200
25
III. I
u
3
=
h2u
26
−22u
25
+· · ·+b+16, 16u
26
−46u
25
+· · ·+a+9, u
27
−3u
26
+· · ·+5u−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
−16u
26
+ 46u
25
+ ··· + 50u − 9
−2u
26
+ 22u
25
+ ··· + 71u − 16
a
8
=
−2u
26
+ 7u
25
+ ··· + 24u − 9
u
26
− u
25
+ ··· + 2u − 2
a
1
=
u
2
+ 1
u
2
a
11
=
−5u
26
+ 14u
25
+ ··· − 30u
2
+ 6u
3u
26
− 3u
25
+ ··· + 22u − 5
a
5
=
u
26
− 7u
25
+ ··· + 39u
2
− 11u
−4u
26
+ 7u
25
+ ··· − 5u + 1
a
9
=
−8u
26
+ 23u
25
+ ··· + 18u − 3
9u
25
− 23u
24
+ ··· + 41u − 9
a
12
=
4u
26
− 13u
25
+ ··· − 17u + 6
−u
26
− 3u
25
+ ··· − 15u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u
26
− 13u
25
+ 83u
24
− 85u
23
+ 301u
22
− 290u
21
+ 690u
20
−
661u
19
+ 1132u
18
− 1121u
17
+ 1438u
16
− 1444u
15
+ 1497u
14
− 1439u
13
+ 1360u
12
−
1168u
11
+ 1121u
10
−852u
9
+ 774u
8
−503u
7
+ 349u
6
−170u
5
+ 70u
4
+ 5u
3
+ 8u
2
+ 2u + 5
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 15u
26
+ ··· − 7u + 1
c
2
u
27
− 3u
26
+ ··· + 5u − 1
c
3
u
27
+ 3u
26
+ ··· + u − 5
c
4
, c
12
u
27
− 2u
26
+ ··· − u + 1
c
5
, c
9
u
27
− 4u
25
+ ··· + u − 1
c
6
u
27
+ 3u
26
+ ··· + 5u + 1
c
7
, c
10
u
27
− 3u
26
+ ··· − 2u − 1
c
8
u
27
− 14u
26
+ ··· + 31u − 5
c
11
u
27
+ 14u
26
+ ··· + 31u + 5
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− y
26
+ ··· + 17y −1
c
2
, c
6
y
27
+ 15y
26
+ ··· − 7y −1
c
3
y
27
− 11y
26
+ ··· − 289y −25
c
4
, c
12
y
27
+ 4y
26
+ ··· + 15y −1
c
5
, c
9
y
27
− 8y
26
+ ··· + 7y −1
c
7
, c
10
y
27
− 25y
26
+ ··· + 4y −1
c
8
, c
11
y
27
+ 10y
26
+ ··· − 609y −25
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818202 + 0.518239I
a = 0.049044 − 0.187866I
b = 0.057231 + 0.179129I
3.29851 − 4.03046I −0.54058 + 11.83565I
u = −0.818202 − 0.518239I
a = 0.049044 + 0.187866I
b = 0.057231 − 0.179129I
3.29851 + 4.03046I −0.54058 − 11.83565I
u = 0.856295 + 0.259733I
a = −1.38117 − 0.30400I
b = −1.103730 − 0.619052I
−1.15919 − 4.70290I 1.30732 + 5.25329I
u = 0.856295 − 0.259733I
a = −1.38117 + 0.30400I
b = −1.103730 + 0.619052I
−1.15919 + 4.70290I 1.30732 − 5.25329I
u = −0.321339 + 1.075910I
a = −0.213440 + 0.363458I
b = −0.322462 − 0.346436I
−3.37950 − 1.83231I −1.49661 + 5.41088I
u = −0.321339 − 1.075910I
a = −0.213440 − 0.363458I
b = −0.322462 + 0.346436I
−3.37950 + 1.83231I −1.49661 − 5.41088I
u = 0.396175 + 1.093580I
a = 0.11793 + 2.42589I
b = −2.60618 + 1.09004I
−0.10491 − 2.85244I −2.53341 + 2.43779I
u = 0.396175 − 1.093580I
a = 0.11793 − 2.42589I
b = −2.60618 − 1.09004I
−0.10491 + 2.85244I −2.53341 − 2.43779I
u = −0.773799 + 0.899843I
a = −0.145465 − 0.015545I
b = 0.126549 − 0.118867I
2.28334 − 1.82374I 21.0281 + 7.1552I
u = −0.773799 − 0.899843I
a = −0.145465 + 0.015545I
b = 0.126549 + 0.118867I
2.28334 + 1.82374I 21.0281 − 7.1552I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.512106 + 1.112540I
a = −0.32986 + 2.28826I
b = −2.71470 + 0.80484I
0.76047 + 10.24880I −0.65047 − 9.89487I
u = 0.512106 − 1.112540I
a = −0.32986 − 2.28826I
b = −2.71470 − 0.80484I
0.76047 − 10.24880I −0.65047 + 9.89487I
u = 0.449869 + 1.139450I
a = 0.21445 − 2.64882I
b = 3.11467 − 0.94727I
−5.48770 + 3.96367I 10.76886 − 2.87818I
u = 0.449869 − 1.139450I
a = 0.21445 + 2.64882I
b = 3.11467 + 0.94727I
−5.48770 − 3.96367I 10.76886 + 2.87818I
u = 0.266773 + 1.225060I
a = −0.003531 − 0.907091I
b = 1.110300 − 0.246314I
−5.97636 − 1.16209I −5.61582 + 2.62970I
u = 0.266773 − 1.225060I
a = −0.003531 + 0.907091I
b = 1.110300 + 0.246314I
−5.97636 + 1.16209I −5.61582 − 2.62970I
u = −0.414172 + 1.228500I
a = 0.101784 − 0.161129I
b = 0.155792 + 0.191778I
−1.49433 − 7.63354I −0.31814 + 9.35955I
u = −0.414172 − 1.228500I
a = 0.101784 + 0.161129I
b = 0.155792 − 0.191778I
−1.49433 + 7.63354I −0.31814 − 9.35955I
u = 0.567130 + 1.180460I
a = −0.060020 − 1.393360I
b = 1.61076 − 0.86107I
−3.92076 + 9.93747I −1.53098 − 7.83108I
u = 0.567130 − 1.180460I
a = −0.060020 + 1.393360I
b = 1.61076 + 0.86107I
−3.92076 − 9.93747I −1.53098 + 7.83108I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208965 + 0.651390I
a = −1.07346 + 1.02118I
b = −0.440872 − 0.912633I
−1.87151 − 0.68379I 11.0014 − 9.1043I
u = −0.208965 − 0.651390I
a = −1.07346 − 1.02118I
b = −0.440872 + 0.912633I
−1.87151 + 0.68379I 11.0014 + 9.1043I
u = 0.600134 + 0.312319I
a = 2.46111 − 0.64860I
b = 1.67957 + 0.37941I
3.08324 − 5.79734I 3.32758 + 6.29569I
u = 0.600134 − 0.312319I
a = 2.46111 + 0.64860I
b = 1.67957 − 0.37941I
3.08324 + 5.79734I 3.32758 − 6.29569I
u = 0.090904 + 0.646995I
a = 2.03848 − 1.08648I
b = 0.88825 + 1.22012I
2.05041 + 5.51654I −0.04074 − 4.60744I
u = 0.090904 − 0.646995I
a = 2.03848 + 1.08648I
b = 0.88825 − 1.22012I
2.05041 − 5.51654I −0.04074 + 4.60744I
u = 0.594182
a = −3.55170
b = −2.11036
−2.48233 16.5870
31
IV. I
u
4
=
ha
3
u+a
3
−a
2
u−a
2
+b−a −u+1, a
4
+a
2
u−a
2
−2au−2a −2u−2, u
2
+u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
4
=
0
u
a
10
=
a
−a
3
u − a
3
+ a
2
u + a
2
+ a + u − 1
a
8
=
−a
3
− a
2
u + a + 3u + 2
a
3
u − a
2
u − a
2
− au + 2u + 4
a
1
=
−u
−u − 1
a
11
=
−a
3
u + a
2
u + au + a − u − 2
−2a
3
u − 2a
3
+ 2a
2
u + 2a
2
+ au + 2a + 2u − 2
a
5
=
2a
3
u + 2a
3
− a
2
u − 2a
2
− 2au − 2a − 4u + 1
3a
3
+ 2a
2
u − a
2
− 3a − 7u − 6
a
9
=
a
−a
3
u − a
3
+ a
2
u + a
2
− au + u − 1
a
12
=
−a
3
u − a
3
+ au + 2a + u
−a
3
+ a
2
u − au + a + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 8
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
12
u
8
− 2u
7
− u
6
+ 4u
5
+ 3u
4
− 6u
3
− 6u
2
+ 4u + 4
c
5
, c
9
u
8
+ 3u
6
− 2u
5
+ 7u
4
− 6u
3
+ 10u
2
− 4u + 4
c
7
, c
8
, c
10
c
11
(u
2
+ 1)
4
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
4
c
4
, c
12
y
8
− 6y
7
+ 23y
6
− 58y
5
+ 93y
4
− 112y
3
+ 108y
2
− 64y + 16
c
5
, c
9
y
8
+ 6y
7
+ 23y
6
+ 58y
5
+ 93y
4
+ 112y
3
+ 108y
2
+ 64y + 16
c
7
, c
8
, c
10
c
11
(y + 1)
8
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.250175 − 1.091290I
b = 0.046027 − 1.262300I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −0.789593 + 0.311148I
b = −0.99136 + 1.33938I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −1.116200 + 0.591291I
b = 0.819998 + 0.762303I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.65562 + 0.18885I
b = 0.125335 − 0.839381I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.250175 + 1.091290I
b = 0.046027 + 1.262300I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −0.789593 − 0.311148I
b = −0.99136 − 1.33938I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −1.116200 − 0.591291I
b = 0.819998 − 0.762303I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.65562 − 0.18885I
b = 0.125335 + 0.839381I
3.28987 + 2.02988I 6.00000 − 3.46410I
35
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
27
− 15u
26
+ ··· − 7u + 1)
· ((u
49
+ 25u
48
+ ··· − 3u − 1)
2
)(u
73
+ 38u
72
+ ··· − 23u − 4)
c
2
((u
2
+ u + 1)
4
)(u
27
− 3u
26
+ ··· + 5u − 1)(u
49
+ 3u
48
+ ··· − 3u − 1)
2
· (u
73
− 10u
72
+ ··· + 17u − 2)
c
3
((u
2
− u + 1)
4
)(u
27
+ 3u
26
+ ··· + u − 5)(u
49
− 3u
48
+ ··· + 39u − 17)
2
· (u
73
+ 10u
72
+ ··· − 130207u − 16754)
c
4
, c
12
(u
8
− 2u
7
− u
6
+ 4u
5
+ 3u
4
− 6u
3
− 6u
2
+ 4u + 4)
· (u
27
− 2u
26
+ ··· − u + 1)(u
73
+ 2u
72
+ ··· + u + 1)
· (u
98
+ u
97
+ ··· + 26u
2
+ 4)
c
5
, c
9
(u
8
+ 3u
6
+ ··· − 4u + 4)(u
27
− 4u
25
+ ··· + u − 1)
· (u
73
+ 7u
71
+ ··· + 19u + 7)(u
98
+ u
97
+ ··· + 12856u + 4796)
c
6
((u
2
− u + 1)
4
)(u
27
+ 3u
26
+ ··· + 5u + 1)(u
49
+ 3u
48
+ ··· − 3u − 1)
2
· (u
73
− 10u
72
+ ··· + 17u − 2)
c
7
, c
10
((u
2
+ 1)
4
)(u
27
− 3u
26
+ ··· − 2u − 1)(u
73
− 3u
72
+ ··· − 6u + 1)
· (u
98
− 15u
97
+ ··· − 38u + 1)
c
8
((u
2
+ 1)
4
)(u
27
− 14u
26
+ ··· + 31u − 5)(u
49
+ 15u
48
+ ··· + 41u + 3)
2
· (u
73
− 17u
72
+ ··· − 4311u + 160)
c
11
((u
2
+ 1)
4
)(u
27
+ 14u
26
+ ··· + 31u + 5)(u
49
+ 15u
48
+ ··· + 41u + 3)
2
· (u
73
− 17u
72
+ ··· − 4311u + 160)
36
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
27
− y
26
+ ··· + 17y −1)(y
49
+ y
48
+ ··· + 21y −1)
2
· (y
73
− 2y
72
+ ··· + 241y −16)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
27
+ 15y
26
+ ··· − 7y −1)
· ((y
49
+ 25y
48
+ ··· − 3y −1)
2
)(y
73
+ 38y
72
+ ··· − 23y −4)
c
3
((y
2
+ y + 1)
4
)(y
27
− 11y
26
+ ··· − 289y −25)
· (y
49
− 23y
48
+ ··· − 12963y −289)
2
· (y
73
− 36y
72
+ ··· − 3279540855y −280696516)
c
4
, c
12
(y
8
− 6y
7
+ 23y
6
− 58y
5
+ 93y
4
− 112y
3
+ 108y
2
− 64y + 16)
· (y
27
+ 4y
26
+ ··· + 15y −1)(y
73
− 54y
72
+ ··· + 127y −1)
· (y
98
+ 9y
97
+ ··· + 208y + 16)
c
5
, c
9
(y
8
+ 6y
7
+ 23y
6
+ 58y
5
+ 93y
4
+ 112y
3
+ 108y
2
+ 64y + 16)
· (y
27
− 8y
26
+ ··· + 7y −1)(y
73
+ 14y
72
+ ··· − 1389y −49)
· (y
98
+ y
97
+ ··· + 1102689744y + 23001616)
c
7
, c
10
((y + 1)
8
)(y
27
− 25y
26
+ ··· + 4y −1)(y
73
+ 21y
72
+ ··· − 48y −1)
· (y
98
− 37y
97
+ ··· − 84y + 1)
c
8
, c
11
((y + 1)
8
)(y
27
+ 10y
26
+ ··· − 609y −25)
· (y
49
+ 31y
48
+ ··· − 185y −9)
2
· (y
73
+ 37y
72
+ ··· + 996881y −25600)
37
