12a
0997
(K12a
0997
)
A knot diagram
1
Linearized knot diagam
4 6 12 8 9 11 2 5 1 3 7 10
Solving Sequence
6,11
7
3,12
4 2 8 10 1 9 5
c
6
c
11
c
3
c
2
c
7
c
10
c
12
c
9
c
5
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.75024 × 10
474
u
141
− 1.96473 × 10
474
u
140
+ ··· + 4.83910 × 10
473
b − 6.34671 × 10
476
,
− 1.51920 × 10
476
u
141
− 1.86128 × 10
476
u
140
+ ··· + 2.95185 × 10
475
a − 4.50856 × 10
478
,
u
142
+ 2u
141
+ ··· + 190u + 244i
I
u
2
= h−113629468333922u
34
+ 73137569141391u
33
+ ··· + 2341694541470b − 106088871052014,
49505308067552u
34
− 15174583421106u
33
+ ··· + 2341694541470a + 131002690330904,
u
35
− u
34
+ ··· + 11u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 177 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−1.75 × 10
474
u
141
− 1.96 × 10
474
u
140
+ · · · + 4.84 × 10
473
b − 6.35 ×
10
476
, −1.52 × 10
476
u
141
− 1.86 × 10
476
u
140
+ · · · + 2.95 × 10
475
a − 4.51 ×
10
478
, u
142
+ 2u
141
+ · · · + 190u + 244i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
5.14659u
141
+ 6.30546u
140
+ ··· − 696.725u + 1527.37
3.61686u
141
+ 4.06012u
140
+ ··· − 365.894u + 1311.55
a
12
=
u
−u
3
+ u
a
4
=
4.46182u
141
+ 5.51814u
140
+ ··· − 619.473u + 1177.84
3.21273u
141
+ 3.71733u
140
+ ··· − 345.106u + 1104.07
a
2
=
1.52972u
141
+ 2.24534u
140
+ ··· − 330.831u + 215.820
3.61686u
141
+ 4.06012u
140
+ ··· − 365.894u + 1311.55
a
8
=
−4.11774u
141
− 6.11606u
140
+ ··· + 1329.29u − 1495.35
0.246365u
141
+ 0.0837458u
140
+ ··· + 332.526u − 91.8020
a
10
=
−3.83345u
141
− 5.21359u
140
+ ··· + 1191.52u − 1902.87
−0.981164u
141
− 1.78349u
140
+ ··· + 589.787u − 389.643
a
1
=
−9.93857u
141
− 12.6394u
140
+ ··· + 2116.16u − 3531.76
−2.69583u
141
− 3.60343u
140
+ ··· + 725.805u − 921.068
a
9
=
−11.1461u
141
− 15.0882u
140
+ ··· + 2795.38u − 3894.61
−3.09865u
141
− 4.28797u
140
+ ··· + 956.752u − 1211.52
a
5
=
10.6780u
141
+ 14.6267u
140
+ ··· − 2679.81u + 3654.33
−1.37124u
141
− 1.90190u
140
+ ··· + 326.354u − 382.690
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.69920u
141
+ 6.20634u
140
+ ··· − 2253.29u + 1903.17
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
142
+ 3u
141
+ ··· − 5484992u − 358484
c
2
u
142
+ 4u
141
+ ··· + 287961643u + 41067731
c
3
u
142
− 2u
141
+ ··· + 113943u − 4559
c
4
, c
5
, c
8
u
142
+ 4u
141
+ ··· + 659u − 79
c
6
, c
11
u
142
+ 2u
141
+ ··· + 190u + 244
c
7
u
142
+ u
141
+ ··· − 118669u − 6359
c
9
, c
12
u
142
− 9u
141
+ ··· + 352548u − 24091
c
10
u
142
− 2u
141
+ ··· + 64376759u − 5349403
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
142
− 19y
141
+ ··· − 3842346849688y + 128510778256
c
2
y
142
− 20y
141
+ ··· − 70044640456027673y + 1686558529488361
c
3
y
142
+ 46y
141
+ ··· − 4311752777y + 20784481
c
4
, c
5
, c
8
y
142
− 136y
141
+ ··· + 195349y + 6241
c
6
, c
11
y
142
− 86y
141
+ ··· − 1799244y + 59536
c
7
y
142
+ 43y
141
+ ··· + 7868694797y + 40436881
c
9
, c
12
y
142
+ 103y
141
+ ··· + 15947376892y + 580376281
c
10
y
142
+ 48y
141
+ ··· + 1001793325679001y + 28616112456409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.295441 + 0.961168I
a = 0.669363 − 0.698149I
b = 1.305230 − 0.036216I
−1.64573 − 4.86259I 0
u = −0.295441 − 0.961168I
a = 0.669363 + 0.698149I
b = 1.305230 + 0.036216I
−1.64573 + 4.86259I 0
u = 0.995761 + 0.156820I
a = −0.222456 + 0.767537I
b = −0.83941 + 2.00273I
3.44526 + 4.94912I 0
u = 0.995761 − 0.156820I
a = −0.222456 − 0.767537I
b = −0.83941 − 2.00273I
3.44526 − 4.94912I 0
u = −1.012530 + 0.042524I
a = −0.316472 + 0.782864I
b = 1.82554 + 0.66888I
5.66183 − 0.09728I 0
u = −1.012530 − 0.042524I
a = −0.316472 − 0.782864I
b = 1.82554 − 0.66888I
5.66183 + 0.09728I 0
u = −0.960789 + 0.327128I
a = −1.67573 − 0.53788I
b = 0.573811 − 0.699430I
2.24599 − 6.21367I 0
u = −0.960789 − 0.327128I
a = −1.67573 + 0.53788I
b = 0.573811 + 0.699430I
2.24599 + 6.21367I 0
u = 0.905560 + 0.387213I
a = 1.117890 − 0.286171I
b = −0.333646 − 0.244719I
1.65458 + 2.59253I 0
u = 0.905560 − 0.387213I
a = 1.117890 + 0.286171I
b = −0.333646 + 0.244719I
1.65458 − 2.59253I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665433 + 0.773073I
a = 0.227227 − 0.578619I
b = 0.927867 + 0.531487I
−0.77924 − 1.97467I 0
u = −0.665433 − 0.773073I
a = 0.227227 + 0.578619I
b = 0.927867 − 0.531487I
−0.77924 + 1.97467I 0
u = 0.947015 + 0.184346I
a = −1.53370 − 0.54169I
b = 0.689578 + 0.125937I
0.06734 + 2.02026I 0
u = 0.947015 − 0.184346I
a = −1.53370 + 0.54169I
b = 0.689578 − 0.125937I
0.06734 − 2.02026I 0
u = 0.991552 + 0.329410I
a = 2.02454 − 0.43908I
b = −0.511332 − 0.970263I
−3.51611 + 9.45267I 0
u = 0.991552 − 0.329410I
a = 2.02454 + 0.43908I
b = −0.511332 + 0.970263I
−3.51611 − 9.45267I 0
u = −1.022900 + 0.233568I
a = 1.59300 − 0.86822I
b = −0.534375 + 0.348376I
−4.94516 − 4.59022I 0
u = −1.022900 − 0.233568I
a = 1.59300 + 0.86822I
b = −0.534375 − 0.348376I
−4.94516 + 4.59022I 0
u = −0.949398
a = 1.81107
b = −0.915073
−2.43501 0
u = 0.940257 + 0.110353I
a = 0.877495 − 1.020720I
b = −1.365760 − 0.120797I
1.99013 + 3.91057I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.940257 − 0.110353I
a = 0.877495 + 1.020720I
b = −1.365760 + 0.120797I
1.99013 − 3.91057I 0
u = −0.977297 + 0.445677I
a = −1.242200 + 0.390383I
b = −0.255815 − 0.424907I
−4.14393 − 0.12942I 0
u = −0.977297 − 0.445677I
a = −1.242200 − 0.390383I
b = −0.255815 + 0.424907I
−4.14393 + 0.12942I 0
u = 0.939586 + 0.533139I
a = −1.026660 − 0.963608I
b = −0.289039 − 0.097357I
−3.18828 − 1.94077I 0
u = 0.939586 − 0.533139I
a = −1.026660 + 0.963608I
b = −0.289039 + 0.097357I
−3.18828 + 1.94077I 0
u = 0.952349 + 0.526982I
a = −0.889049 − 0.707415I
b = −1.382320 + 0.276137I
2.18933 − 1.03709I 0
u = 0.952349 − 0.526982I
a = −0.889049 + 0.707415I
b = −1.382320 − 0.276137I
2.18933 + 1.03709I 0
u = 0.180527 + 0.888125I
a = −0.901850 + 0.760556I
b = −0.249599 + 1.045440I
−7.35446 − 1.74290I 0
u = 0.180527 − 0.888125I
a = −0.901850 − 0.760556I
b = −0.249599 − 1.045440I
−7.35446 + 1.74290I 0
u = −0.863621 + 0.269420I
a = 0.038865 − 0.642852I
b = −0.412835 − 1.143140I
−0.89229 − 2.62212I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.863621 − 0.269420I
a = 0.038865 + 0.642852I
b = −0.412835 + 1.143140I
−0.89229 + 2.62212I 0
u = −0.096232 + 1.094430I
a = 0.887299 + 0.457796I
b = 0.676233 + 0.624368I
1.03726 + 3.47735I 0
u = −0.096232 − 1.094430I
a = 0.887299 − 0.457796I
b = 0.676233 − 0.624368I
1.03726 − 3.47735I 0
u = −0.867137 + 0.227443I
a = 0.664833 + 0.617823I
b = −0.01210 + 2.70109I
−4.02573 − 8.08694I 0
u = −0.867137 − 0.227443I
a = 0.664833 − 0.617823I
b = −0.01210 − 2.70109I
−4.02573 + 8.08694I 0
u = 0.156814 + 1.098300I
a = −1.030160 + 0.457830I
b = −0.943074 + 0.722792I
2.45324 − 8.83016I 0
u = 0.156814 − 1.098300I
a = −1.030160 − 0.457830I
b = −0.943074 − 0.722792I
2.45324 + 8.83016I 0
u = −0.177578 + 1.097880I
a = 1.098380 + 0.499845I
b = 1.080490 + 0.868581I
−3.56242 + 13.15990I 0
u = −0.177578 − 1.097880I
a = 1.098380 − 0.499845I
b = 1.080490 − 0.868581I
−3.56242 − 13.15990I 0
u = 0.801356 + 0.357639I
a = 0.211805 − 0.263722I
b = 0.55333 − 1.69086I
−7.22523 + 4.37051I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.801356 − 0.357639I
a = 0.211805 + 0.263722I
b = 0.55333 + 1.69086I
−7.22523 − 4.37051I 0
u = −0.677192 + 0.532116I
a = 1.22550 − 0.89397I
b = 0.325908 − 0.517957I
0.49068 − 2.16297I 0
u = −0.677192 − 0.532116I
a = 1.22550 + 0.89397I
b = 0.325908 + 0.517957I
0.49068 + 2.16297I 0
u = −0.253184 + 1.118540I
a = −0.645230 − 0.209736I
b = −0.742559 − 0.446593I
−1.78631 + 3.15535I 0
u = −0.253184 − 1.118540I
a = −0.645230 + 0.209736I
b = −0.742559 + 0.446593I
−1.78631 − 3.15535I 0
u = −0.775010 + 0.335653I
a = −1.49027 − 0.18784I
b = 1.03264 − 1.59318I
−4.12735 + 5.42432I 0
u = −0.775010 − 0.335653I
a = −1.49027 + 0.18784I
b = 1.03264 + 1.59318I
−4.12735 − 5.42432I 0
u = 0.381711 + 0.747319I
a = −0.508385 − 0.935626I
b = −1.030840 + 0.114718I
3.08868 + 3.12603I 0
u = 0.381711 − 0.747319I
a = −0.508385 + 0.935626I
b = −1.030840 − 0.114718I
3.08868 − 3.12603I 0
u = 0.677307 + 0.479418I
a = −0.959029 + 0.608697I
b = 1.147290 + 0.688353I
−7.48981 − 0.76566I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.677307 − 0.479418I
a = −0.959029 − 0.608697I
b = 1.147290 − 0.688353I
−7.48981 + 0.76566I 0
u = 0.439527 + 1.097660I
a = 0.531971 − 0.006531I
b = 0.431681 − 0.279722I
−1.32780 + 1.36080I 0
u = 0.439527 − 1.097660I
a = 0.531971 + 0.006531I
b = 0.431681 + 0.279722I
−1.32780 − 1.36080I 0
u = −1.073910 + 0.509333I
a = 0.435785 − 0.982606I
b = 1.47076 − 0.00231I
6.39536 − 1.71581I 0
u = −1.073910 − 0.509333I
a = 0.435785 + 0.982606I
b = 1.47076 + 0.00231I
6.39536 + 1.71581I 0
u = −1.102960 + 0.455345I
a = 0.53637 + 1.53987I
b = −1.44783 + 1.60931I
2.40570 − 7.60763I 0
u = −1.102960 − 0.455345I
a = 0.53637 − 1.53987I
b = −1.44783 − 1.60931I
2.40570 + 7.60763I 0
u = 0.788812 + 0.129788I
a = −0.03648 − 1.50672I
b = 0.329050 − 0.928368I
−0.490370 − 0.236987I 0
u = 0.788812 − 0.129788I
a = −0.03648 + 1.50672I
b = 0.329050 + 0.928368I
−0.490370 + 0.236987I 0
u = 1.143600 + 0.423408I
a = −0.055369 − 1.256870I
b = −1.62856 − 0.22646I
2.78962 + 4.09503I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.143600 − 0.423408I
a = −0.055369 + 1.256870I
b = −1.62856 + 0.22646I
2.78962 − 4.09503I 0
u = 1.161030 + 0.373280I
a = 0.547399 − 0.852433I
b = −1.40420 − 1.35000I
−2.98025 + 6.85607I 0
u = 1.161030 − 0.373280I
a = 0.547399 + 0.852433I
b = −1.40420 + 1.35000I
−2.98025 − 6.85607I 0
u = −1.192180 + 0.266198I
a = 0.119991 + 0.494450I
b = −2.15150 + 1.08202I
−0.46667 − 8.68353I 0
u = −1.192180 − 0.266198I
a = 0.119991 − 0.494450I
b = −2.15150 − 1.08202I
−0.46667 + 8.68353I 0
u = 1.204900 + 0.248316I
a = −0.216469 + 1.272930I
b = 0.247465 + 0.663571I
4.55521 + 4.15623I 0
u = 1.204900 − 0.248316I
a = −0.216469 − 1.272930I
b = 0.247465 − 0.663571I
4.55521 − 4.15623I 0
u = 1.157320 + 0.444718I
a = −0.33903 + 1.52701I
b = 1.41902 + 1.12486I
6.68328 + 6.03023I 0
u = 1.157320 − 0.444718I
a = −0.33903 − 1.52701I
b = 1.41902 − 1.12486I
6.68328 − 6.03023I 0
u = −0.104805 + 0.742473I
a = −1.63727 − 0.49313I
b = −1.315660 − 0.362701I
−0.759364 − 0.251461I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.104805 − 0.742473I
a = −1.63727 + 0.49313I
b = −1.315660 + 0.362701I
−0.759364 + 0.251461I 0
u = 0.203821 + 1.238700I
a = 0.563722 − 0.312244I
b = 0.797764 − 0.681525I
−8.34882 − 6.21982I 0
u = 0.203821 − 1.238700I
a = 0.563722 + 0.312244I
b = 0.797764 + 0.681525I
−8.34882 + 6.21982I 0
u = −1.203770 + 0.363815I
a = −0.352127 − 0.887998I
b = 1.13437 − 0.84632I
3.52882 − 4.29863I 0
u = −1.203770 − 0.363815I
a = −0.352127 + 0.887998I
b = 1.13437 + 0.84632I
3.52882 + 4.29863I 0
u = −0.726023 + 0.057363I
a = −0.02709 − 2.28085I
b = −0.408026 − 1.136080I
−6.24327 + 2.81788I 0
u = −0.726023 − 0.057363I
a = −0.02709 + 2.28085I
b = −0.408026 + 1.136080I
−6.24327 − 2.81788I 0
u = −1.182400 + 0.477988I
a = 0.15640 + 1.62156I
b = −1.67251 + 0.78530I
2.38272 − 4.27099I 0
u = −1.182400 − 0.477988I
a = 0.15640 − 1.62156I
b = −1.67251 − 0.78530I
2.38272 + 4.27099I 0
u = −1.257260 + 0.347278I
a = 0.257115 + 1.341720I
b = −0.849485 + 0.541354I
7.71716 − 6.70943I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.257260 − 0.347278I
a = 0.257115 − 1.341720I
b = −0.849485 − 0.541354I
7.71716 + 6.70943I 0
u = 1.298120 + 0.128170I
a = 0.041391 + 0.468615I
b = 1.30327 + 1.66542I
6.24725 + 3.31596I 0
u = 1.298120 − 0.128170I
a = 0.041391 − 0.468615I
b = 1.30327 − 1.66542I
6.24725 − 3.31596I 0
u = −0.519635 + 1.211370I
a = −0.345095 − 0.080928I
b = −0.137004 − 0.488716I
−7.75612 − 5.05750I 0
u = −0.519635 − 1.211370I
a = −0.345095 + 0.080928I
b = −0.137004 + 0.488716I
−7.75612 + 5.05750I 0
u = 0.296596 + 0.613764I
a = 0.216062 + 1.144900I
b = −0.097240 + 0.765571I
0.050700 + 1.129900I −4.00000 − 2.88520I
u = 0.296596 − 0.613764I
a = 0.216062 − 1.144900I
b = −0.097240 − 0.765571I
0.050700 − 1.129900I −4.00000 + 2.88520I
u = 1.244990 + 0.488341I
a = 0.317489 − 0.891339I
b = −0.99763 − 1.42621I
−4.01631 + 6.74718I 0
u = 1.244990 − 0.488341I
a = 0.317489 + 0.891339I
b = −0.99763 + 1.42621I
−4.01631 − 6.74718I 0
u = 1.309360 + 0.287091I
a = 0.286433 − 0.785035I
b = −0.804040 − 0.349681I
3.91965 + 1.18536I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.309360 − 0.287091I
a = 0.286433 + 0.785035I
b = −0.804040 + 0.349681I
3.91965 − 1.18536I 0
u = 0.386831 + 0.517154I
a = −1.77518 − 0.72951I
b = −0.574014 − 0.862163I
−4.59967 + 6.20898I −7.15310 − 5.19968I
u = 0.386831 − 0.517154I
a = −1.77518 + 0.72951I
b = −0.574014 + 0.862163I
−4.59967 − 6.20898I −7.15310 + 5.19968I
u = 0.628761 + 0.110169I
a = 1.67192 + 0.60080I
b = −0.819952 − 0.792485I
2.38235 − 3.35414I −1.39141 − 1.42609I
u = 0.628761 − 0.110169I
a = 1.67192 − 0.60080I
b = −0.819952 + 0.792485I
2.38235 + 3.35414I −1.39141 + 1.42609I
u = −0.632779
a = −1.09730
b = −0.556681
−2.83002 −0.523720
u = 1.313040 + 0.396148I
a = −0.261069 + 1.329340I
b = 1.122220 + 0.371338I
3.23818 + 9.35296I 0
u = 1.313040 − 0.396148I
a = −0.261069 − 1.329340I
b = 1.122220 − 0.371338I
3.23818 − 9.35296I 0
u = 0.083162 + 0.619005I
a = 1.77770 − 0.95484I
b = 0.966850 − 0.529210I
3.65274 − 1.94762I 2.25344 + 2.76129I
u = 0.083162 − 0.619005I
a = 1.77770 + 0.95484I
b = 0.966850 + 0.529210I
3.65274 + 1.94762I 2.25344 − 2.76129I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301289 + 0.534052I
a = −2.27993 − 0.67671I
b = −0.617728 − 1.133520I
0.06790 + 3.57933I −8.54365 − 4.70573I
u = −0.301289 − 0.534052I
a = −2.27993 + 0.67671I
b = −0.617728 + 1.133520I
0.06790 − 3.57933I −8.54365 + 4.70573I
u = −1.229360 + 0.646474I
a = 0.045587 + 0.631812I
b = −0.745416 + 0.820547I
−5.15370 − 1.46543I 0
u = −1.229360 − 0.646474I
a = 0.045587 − 0.631812I
b = −0.745416 − 0.820547I
−5.15370 + 1.46543I 0
u = −1.379710 + 0.166727I
a = −0.180214 − 0.544809I
b = 0.16989 − 1.66262I
5.48382 − 3.76822I 0
u = −1.379710 − 0.166727I
a = −0.180214 + 0.544809I
b = 0.16989 + 1.66262I
5.48382 + 3.76822I 0
u = −1.384500 + 0.123514I
a = −0.324361 − 0.740298I
b = 0.449961 − 0.033367I
−1.52673 + 1.19749I 0
u = −1.384500 − 0.123514I
a = −0.324361 + 0.740298I
b = 0.449961 + 0.033367I
−1.52673 − 1.19749I 0
u = 1.251080 + 0.610775I
a = −0.014390 + 0.867157I
b = 1.028680 + 0.651325I
1.50165 + 4.75171I 0
u = 1.251080 − 0.610775I
a = −0.014390 − 0.867157I
b = 1.028680 − 0.651325I
1.50165 − 4.75171I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461960 + 0.388546I
a = 0.69044 + 1.84271I
b = 0.372536 + 1.114660I
0.90909 + 3.03402I −4.59309 − 2.39121I
u = −0.461960 − 0.388546I
a = 0.69044 − 1.84271I
b = 0.372536 − 1.114660I
0.90909 − 3.03402I −4.59309 + 2.39121I
u = 0.518240 + 0.259555I
a = −1.23652 + 2.37914I
b = −0.384698 + 1.359050I
−4.92898 − 6.53822I −9.87771 + 2.27426I
u = 0.518240 − 0.259555I
a = −1.23652 − 2.37914I
b = −0.384698 − 1.359050I
−4.92898 + 6.53822I −9.87771 − 2.27426I
u = −1.29457 + 0.60024I
a = 0.167786 + 0.951560I
b = −1.22706 + 0.74096I
1.60097 − 9.25037I 0
u = −1.29457 − 0.60024I
a = 0.167786 − 0.951560I
b = −1.22706 − 0.74096I
1.60097 + 9.25037I 0
u = −0.551222 + 0.144454I
a = 1.58026 + 0.28066I
b = −0.706667 + 0.147464I
−1.59564 + 0.01650I −8.59999 + 1.02896I
u = −0.551222 − 0.144454I
a = 1.58026 − 0.28066I
b = −0.706667 − 0.147464I
−1.59564 − 0.01650I −8.59999 − 1.02896I
u = −1.30004 + 0.59827I
a = −0.190725 − 1.209080I
b = 1.57225 − 1.06569I
−0.0408 − 19.1720I 0
u = −1.30004 − 0.59827I
a = −0.190725 + 1.209080I
b = 1.57225 + 1.06569I
−0.0408 + 19.1720I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.30757 + 0.58740I
a = 0.144170 − 1.147790I
b = −1.42128 − 1.01321I
6.0708 + 14.8010I 0
u = 1.30757 − 0.58740I
a = 0.144170 + 1.147790I
b = −1.42128 + 1.01321I
6.0708 − 14.8010I 0
u = −1.31939 + 0.56354I
a = −0.129572 − 1.033900I
b = 1.19996 − 1.04719I
4.87289 − 9.32445I 0
u = −1.31939 − 0.56354I
a = −0.129572 + 1.033900I
b = 1.19996 + 1.04719I
4.87289 + 9.32445I 0
u = 1.32420 + 0.61903I
a = −0.269265 + 0.927893I
b = 1.31716 + 0.86445I
−4.72137 + 12.63410I 0
u = 1.32420 − 0.61903I
a = −0.269265 − 0.927893I
b = 1.31716 − 0.86445I
−4.72137 − 12.63410I 0
u = 1.29931 + 0.67407I
a = −0.010764 − 0.609932I
b = −1.279530 − 0.186124I
5.36336 + 2.85586I 0
u = 1.29931 − 0.67407I
a = −0.010764 + 0.609932I
b = −1.279530 + 0.186124I
5.36336 − 2.85586I 0
u = −1.43411 + 0.32325I
a = −0.189948 + 0.650715I
b = −0.808731 + 0.148963I
7.92563 + 3.63782I 0
u = −1.43411 − 0.32325I
a = −0.189948 − 0.650715I
b = −0.808731 − 0.148963I
7.92563 − 3.63782I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45325 + 0.30305I
a = 0.210685 + 0.698484I
b = 0.807267 − 0.090714I
2.05122 − 8.00110I 0
u = 1.45325 − 0.30305I
a = 0.210685 − 0.698484I
b = 0.807267 + 0.090714I
2.05122 + 8.00110I 0
u = 1.44053 + 0.39155I
a = 0.200747 + 0.569140I
b = 0.615766 + 0.382985I
6.16457 + 1.98037I 0
u = 1.44053 − 0.39155I
a = 0.200747 − 0.569140I
b = 0.615766 − 0.382985I
6.16457 − 1.98037I 0
u = −0.059753 + 0.486288I
a = −1.58206 + 1.21971I
b = −0.525144 + 1.170870I
−6.25668 − 3.45644I −7.95779 + 1.87920I
u = −0.059753 − 0.486288I
a = −1.58206 − 1.21971I
b = −0.525144 − 1.170870I
−6.25668 + 3.45644I −7.95779 − 1.87920I
u = 0.131339 + 0.463577I
a = 0.726996 + 0.878139I
b = 0.261570 + 0.561742I
−0.204329 + 1.049600I −3.55621 − 5.69708I
u = 0.131339 − 0.463577I
a = 0.726996 − 0.878139I
b = 0.261570 − 0.561742I
−0.204329 − 1.049600I −3.55621 + 5.69708I
u = −1.27542 + 0.85016I
a = 0.016490 − 0.461253I
b = 1.228330 − 0.277684I
0.41144 − 4.64544I 0
u = −1.27542 − 0.85016I
a = 0.016490 + 0.461253I
b = 1.228330 + 0.277684I
0.41144 + 4.64544I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46548 + 0.55433I
a = −0.153334 − 0.640912I
b = 1.278780 − 0.097748I
1.79231 − 1.69511I 0
u = −1.46548 − 0.55433I
a = −0.153334 + 0.640912I
b = 1.278780 + 0.097748I
1.79231 + 1.69511I 0
19
II. I
u
2
= h−1.14 × 10
14
u
34
+ 7.31 × 10
13
u
33
+ · · · + 2.34 × 10
12
b − 1.06 ×
10
14
, 4.95 × 10
13
u
34
− 1.52 × 10
13
u
33
+ · · · + 2.34 × 10
12
a + 1.31 ×
10
14
, u
35
− u
34
+ · · · + 11u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
−21.1408u
34
+ 6.48017u
33
+ ··· − 85.8975u − 55.9435
48.5245u
34
− 31.2328u
33
+ ··· + 107.689u + 45.3043
a
12
=
u
−u
3
+ u
a
4
=
−46.0627u
34
+ 22.9330u
33
+ ··· − 151.903u − 84.8837
33.0410u
34
− 22.7747u
33
+ ··· + 66.6053u + 24.8333
a
2
=
−69.6653u
34
+ 37.7129u
33
+ ··· − 193.586u − 101.248
48.5245u
34
− 31.2328u
33
+ ··· + 107.689u + 45.3043
a
8
=
−7.32322u
34
− 7.63691u
33
+ ··· − 17.4117u − 28.4680
−9.08846u
34
− 4.41940u
33
+ ··· − 35.3641u − 30.4775
a
10
=
−5.17953u
34
− 9.28015u
33
+ ··· − 7.61022u − 26.5787
53.9109u
34
− 35.0662u
33
+ ··· + 120.036u + 49.7160
a
1
=
38.0705u
34
− 18.3704u
33
+ ··· + 73.9366u + 41.3601
3.58637u
34
+ 4.71758u
33
+ ··· + 26.3203u + 29.1203
a
9
=
39.9725u
34
− 14.9017u
33
+ ··· + 130.207u + 72.9861
−5.55554u
34
+ 1.49297u
33
+ ··· − 10.2532u − 12.6239
a
5
=
−53.6809u
34
+ 33.5964u
33
+ ··· − 175.125u − 78.3608
4.42308u
34
+ 4.22463u
33
+ ··· − 2.98053u + 5.68707
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
304005565967963
1170847270735
u
34
+
160381532917453
2341694541470
u
33
+ ··· −
854830395440697
1170847270735
u −
1164115765444817
2341694541470
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
− 14u
34
+ ··· + 16u − 1
c
2
u
35
− 5u
34
+ ··· + 3u − 1
c
3
u
35
− 3u
34
+ ··· + 3u + 1
c
4
, c
5
u
35
+ 3u
34
+ ··· − 3u − 1
c
6
u
35
− u
34
+ ··· + 11u
2
− 1
c
7
u
35
+ 6u
33
+ ··· + 3u + 1
c
8
u
35
− 3u
34
+ ··· − 3u + 1
c
9
u
35
− 2u
34
+ ··· − 2u − 1
c
10
u
35
− u
34
+ ··· − 3u − 1
c
11
u
35
+ u
34
+ ··· − 11u
2
+ 1
c
12
u
35
+ 2u
34
+ ··· − 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 6y
34
+ ··· + 62y −1
c
2
y
35
+ 9y
34
+ ··· − 49y −1
c
3
y
35
+ 27y
34
+ ··· + 3y −1
c
4
, c
5
, c
8
y
35
− 35y
34
+ ··· + 9y −1
c
6
, c
11
y
35
− 21y
34
+ ··· + 22y −1
c
7
y
35
+ 12y
34
+ ··· − 3y −1
c
9
, c
12
y
35
+ 32y
34
+ ··· + 42y −1
c
10
y
35
+ 9y
34
+ ··· − 23y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325840 + 0.871911I
a = 0.390565 + 0.011728I
b = 0.176431 − 0.355089I
−1.47177 − 1.92215I −6.90681 + 7.33686I
u = −0.325840 − 0.871911I
a = 0.390565 − 0.011728I
b = 0.176431 + 0.355089I
−1.47177 + 1.92215I −6.90681 − 7.33686I
u = 0.964498 + 0.482459I
a = −0.847622 − 0.595829I
b = −0.008201 + 0.215202I
−4.76170 − 0.79129I −8.71502 + 0.60365I
u = 0.964498 − 0.482459I
a = −0.847622 + 0.595829I
b = −0.008201 − 0.215202I
−4.76170 + 0.79129I −8.71502 − 0.60365I
u = −0.171729 + 0.832899I
a = 0.784449 − 0.786628I
b = 0.642782 − 0.123979I
1.95739 − 2.11994I −2.77028 + 2.10230I
u = −0.171729 − 0.832899I
a = 0.784449 + 0.786628I
b = 0.642782 + 0.123979I
1.95739 + 2.11994I −2.77028 − 2.10230I
u = −0.765862 + 0.272431I
a = 1.127610 − 0.778868I
b = −0.172603 − 0.545768I
−0.83179 − 1.61396I −8.84847 + 1.88186I
u = −0.765862 − 0.272431I
a = 1.127610 + 0.778868I
b = −0.172603 + 0.545768I
−0.83179 + 1.61396I −8.84847 − 1.88186I
u = −1.160300 + 0.256696I
a = 0.838279 + 0.555396I
b = −1.06880 + 1.55168I
−1.96634 − 8.30516I −2.54260 + 7.40784I
u = −1.160300 − 0.256696I
a = 0.838279 − 0.555396I
b = −1.06880 − 1.55168I
−1.96634 + 8.30516I −2.54260 − 7.40784I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.118450 + 0.409088I
a = 0.34414 + 1.76609I
b = −1.35105 + 1.03697I
3.05459 − 6.26586I −1.04301 + 6.03627I
u = −1.118450 − 0.409088I
a = 0.34414 − 1.76609I
b = −1.35105 − 1.03697I
3.05459 + 6.26586I −1.04301 − 6.03627I
u = 0.304888 + 1.166800I
a = −0.193065 − 0.227691I
b = −0.312784 − 0.584209I
−7.68931 + 5.51840I −4.00000 − 9.14652I
u = 0.304888 − 1.166800I
a = −0.193065 + 0.227691I
b = −0.312784 + 0.584209I
−7.68931 − 5.51840I −4.00000 + 9.14652I
u = 0.772488 + 0.166970I
a = −1.04596 − 1.50079I
b = 0.026781 − 1.161370I
−6.11900 + 3.62566I −7.16492 − 4.45275I
u = 0.772488 − 0.166970I
a = −1.04596 + 1.50079I
b = 0.026781 + 1.161370I
−6.11900 − 3.62566I −7.16492 + 4.45275I
u = 1.006800 + 0.739946I
a = 0.058372 − 0.681844I
b = −1.342690 − 0.294027I
−0.10339 + 4.76147I −7.41315 − 7.75159I
u = 1.006800 − 0.739946I
a = 0.058372 + 0.681844I
b = −1.342690 + 0.294027I
−0.10339 − 4.76147I −7.41315 + 7.75159I
u = −0.740550 + 0.056759I
a = −1.52690 − 0.56575I
b = 0.02039 − 1.94305I
−3.94181 + 6.89915I −2.84529 − 4.69651I
u = −0.740550 − 0.056759I
a = −1.52690 + 0.56575I
b = 0.02039 + 1.94305I
−3.94181 − 6.89915I −2.84529 + 4.69651I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.195820 + 0.407470I
a = −0.321281 + 1.273300I
b = 1.06723 + 1.09049I
5.89269 + 6.11137I −4.00000 − 6.28916I
u = 1.195820 − 0.407470I
a = −0.321281 − 1.273300I
b = 1.06723 − 1.09049I
5.89269 − 6.11137I −4.00000 + 6.28916I
u = −1.226240 + 0.563205I
a = 0.001019 − 0.706063I
b = 1.331550 − 0.254767I
5.08134 − 2.69860I 0
u = −1.226240 − 0.563205I
a = 0.001019 + 0.706063I
b = 1.331550 + 0.254767I
5.08134 + 2.69860I 0
u = 0.646388 + 0.045227I
a = 1.44904 − 0.45860I
b = −0.470716 + 1.308020I
2.38905 + 4.03609I −1.53405 − 8.74854I
u = 0.646388 − 0.045227I
a = 1.44904 + 0.45860I
b = −0.470716 − 1.308020I
2.38905 − 4.03609I −1.53405 + 8.74854I
u = 1.349210 + 0.092260I
a = −0.233513 + 0.507521I
b = 0.11290 + 1.68065I
5.70697 + 4.18122I 0. − 13.82511I
u = 1.349210 − 0.092260I
a = −0.233513 − 0.507521I
b = 0.11290 − 1.68065I
5.70697 − 4.18122I 0. + 13.82511I
u = −1.345380 + 0.316226I
a = 0.086757 − 0.520788I
b = 1.023980 − 0.904444I
5.74209 − 2.54628I 0
u = −1.345380 − 0.316226I
a = 0.086757 + 0.520788I
b = 1.023980 + 0.904444I
5.74209 + 2.54628I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29900 + 0.59734I
a = 0.035275 − 0.826512I
b = −1.411430 − 0.064333I
1.36041 + 1.84626I 0
u = 1.29900 − 0.59734I
a = 0.035275 + 0.826512I
b = −1.411430 + 0.064333I
1.36041 − 1.84626I 0
u = −0.438627 + 0.327388I
a = −2.70959 + 0.27779I
b = −0.546026 − 0.539624I
0.79161 + 2.91754I −3.54877 + 0.21181I
u = −0.438627 − 0.327388I
a = −2.70959 − 0.27779I
b = −0.546026 + 0.539624I
0.79161 − 2.91754I −3.54877 − 0.21181I
u = 0.507757
a = −2.47517
b = −0.435496
−3.60235 −13.1570
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
35
− 14u
34
+ ··· + 16u − 1)
· (u
142
+ 3u
141
+ ··· − 5484992u − 358484)
c
2
(u
35
− 5u
34
+ ··· + 3u − 1)
· (u
142
+ 4u
141
+ ··· + 287961643u + 41067731)
c
3
(u
35
− 3u
34
+ ··· + 3u + 1)(u
142
− 2u
141
+ ··· + 113943u − 4559)
c
4
, c
5
(u
35
+ 3u
34
+ ··· − 3u − 1)(u
142
+ 4u
141
+ ··· + 659u − 79)
c
6
(u
35
− u
34
+ ··· + 11u
2
− 1)(u
142
+ 2u
141
+ ··· + 190u + 244)
c
7
(u
35
+ 6u
33
+ ··· + 3u + 1)(u
142
+ u
141
+ ··· − 118669u − 6359)
c
8
(u
35
− 3u
34
+ ··· − 3u + 1)(u
142
+ 4u
141
+ ··· + 659u − 79)
c
9
(u
35
− 2u
34
+ ··· − 2u − 1)(u
142
− 9u
141
+ ··· + 352548u − 24091)
c
10
(u
35
− u
34
+ ··· − 3u − 1)(u
142
− 2u
141
+ ··· + 6.43768 × 10
7
u − 5349403)
c
11
(u
35
+ u
34
+ ··· − 11u
2
+ 1)(u
142
+ 2u
141
+ ··· + 190u + 244)
c
12
(u
35
+ 2u
34
+ ··· − 2u + 1)(u
142
− 9u
141
+ ··· + 352548u − 24091)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
35
+ 6y
34
+ ··· + 62y −1)
· (y
142
− 19y
141
+ ··· − 3842346849688y + 128510778256)
c
2
(y
35
+ 9y
34
+ ··· − 49y −1)
· (y
142
− 20y
141
+ ··· − 70044640456027673y + 1686558529488361)
c
3
(y
35
+ 27y
34
+ ··· + 3y −1)
· (y
142
+ 46y
141
+ ··· − 4311752777y + 20784481)
c
4
, c
5
, c
8
(y
35
− 35y
34
+ ··· + 9y −1)(y
142
− 136y
141
+ ··· + 195349y + 6241)
c
6
, c
11
(y
35
− 21y
34
+ ··· + 22y −1)
· (y
142
− 86y
141
+ ··· − 1799244y + 59536)
c
7
(y
35
+ 12y
34
+ ··· − 3y −1)
· (y
142
+ 43y
141
+ ··· + 7868694797y + 40436881)
c
9
, c
12
(y
35
+ 32y
34
+ ··· + 42y −1)
· (y
142
+ 103y
141
+ ··· + 15947376892y + 580376281)
c
10
(y
35
+ 9y
34
+ ··· − 23y −1)
· (y
142
+ 48y
141
+ ··· + 1001793325679001y + 28616112456409)
28
