12a
0890
(K12a
0890
)
A knot diagram
1
Linearized knot diagam
4 6 7 1 9 10 12 11 2 3 8 5
Solving Sequence
5,12
1 4
2,8
7 3 11 9 6 10
c
12
c
4
c
1
c
7
c
3
c
11
c
8
c
5
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.41774 × 10
373
u
131
− 8.81640 × 10
374
u
130
+ ··· + 2.89015 × 10
375
b − 3.34965 × 10
375
,
− 2.99895 × 10
379
u
131
+ 1.52950 × 10
380
u
130
+ ··· + 9.38806 × 10
379
a − 2.25117 × 10
380
,
u
132
− 5u
131
+ ··· + 157u + 11i
I
u
2
= h−u
28
+ 7u
27
+ ··· + b − 4, u
29
− 7u
28
+ ··· + a − 5, u
30
− 6u
29
+ ··· − 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 162 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−1.42 × 10
373
u
131
− 8.82 × 10
374
u
130
+ · · · + 2.89 × 10
375
b − 3.35 ×
10
375
, −3.00 × 10
379
u
131
+ 1.53 × 10
380
u
130
+ · · · + 9.39 × 10
379
a − 2.25 ×
10
380
, u
132
− 5u
131
+ · · · + 157u + 11i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
0.319443u
131
− 1.62920u
130
+ ··· + 0.0910581u + 2.39791
0.00490543u
131
+ 0.305050u
130
+ ··· + 19.2159u + 1.15899
a
7
=
0.314537u
131
− 1.93425u
130
+ ··· − 19.1248u + 1.23892
0.00490543u
131
+ 0.305050u
130
+ ··· + 19.2159u + 1.15899
a
3
=
−0.223257u
131
+ 0.637786u
130
+ ··· − 10.4923u − 1.09005
0.177227u
131
− 0.982312u
130
+ ··· + 5.69063u + 0.367339
a
11
=
0.0674859u
131
− 0.538029u
130
+ ··· − 86.2553u − 6.81104
−0.156492u
131
+ 1.20733u
130
+ ··· + 16.5322u − 0.189296
a
9
=
0.314728u
131
− 1.46910u
130
+ ··· − 68.2386u − 7.22115
−0.293356u
131
+ 1.92375u
130
+ ··· + 13.9230u − 0.672299
a
6
=
0.367934u
131
− 1.46158u
130
+ ··· + 90.0780u + 9.93414
0.187553u
131
− 0.598991u
130
+ ··· + 32.7497u + 2.66066
a
10
=
0.518800u
131
− 2.71076u
130
+ ··· − 60.9506u − 5.07052
−0.121163u
131
+ 1.13129u
130
+ ··· + 25.4701u + 0.131622
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.44696u
131
− 9.05081u
130
+ ··· − 486.405u − 47.5445
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
132
+ 5u
131
+ ··· − 157u + 11
c
2
u
132
− 3u
131
+ ··· − 20u + 1
c
3
u
132
− 2u
131
+ ··· + 768008u − 38548
c
5
u
132
+ 2u
131
+ ··· − 768008u − 38548
c
6
u
132
+ 3u
131
+ ··· + 20u + 1
c
7
, c
8
, c
11
u
132
− 5u
131
+ ··· + 157u + 11
c
9
u
132
− u
131
+ ··· + 123u − 5
c
10
u
132
+ u
131
+ ··· − 123u − 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
11
, c
12
y
132
+ 125y
131
+ ··· − 14859y + 121
c
2
, c
6
y
132
− y
131
+ ··· − 208y + 1
c
3
, c
5
y
132
− 6y
131
+ ··· − 24158727920y + 1485948304
c
9
, c
10
y
132
+ 9y
131
+ ··· + 571y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950162 + 0.371930I
a = 0.67877 − 2.14159I
b = −0.29964 − 1.46694I
−5.9520 + 14.1469I 0
u = −0.950162 − 0.371930I
a = 0.67877 + 2.14159I
b = −0.29964 + 1.46694I
−5.9520 − 14.1469I 0
u = −0.644129 + 0.714770I
a = −0.257686 − 0.441199I
b = −0.572702 + 0.256387I
0.99836 − 5.34745I 0
u = −0.644129 − 0.714770I
a = −0.257686 + 0.441199I
b = −0.572702 − 0.256387I
0.99836 + 5.34745I 0
u = 0.641102 + 0.836655I
a = 0.217211 − 0.127517I
b = −0.1095870 − 0.0579846I
−0.68851 − 2.45836I 0
u = 0.641102 − 0.836655I
a = 0.217211 + 0.127517I
b = −0.1095870 + 0.0579846I
−0.68851 + 2.45836I 0
u = 1.009860 + 0.421402I
a = 0.86690 + 2.04670I
b = −0.196199 + 1.388130I
−6.61469 − 4.90913I 0
u = 1.009860 − 0.421402I
a = 0.86690 − 2.04670I
b = −0.196199 − 1.388130I
−6.61469 + 4.90913I 0
u = 1.041540 + 0.340102I
a = −0.28770 − 2.08179I
b = 0.15746 − 1.43693I
−6.95360 − 4.28613I 0
u = 1.041540 − 0.340102I
a = −0.28770 + 2.08179I
b = 0.15746 + 1.43693I
−6.95360 + 4.28613I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440285 + 1.014920I
a = −0.099470 − 0.884634I
b = −0.101752 − 1.377020I
−3.06770 − 1.78673I 0
u = 0.440285 − 1.014920I
a = −0.099470 + 0.884634I
b = −0.101752 + 1.377020I
−3.06770 + 1.78673I 0
u = 0.766251 + 0.455073I
a = 0.265973 + 0.448281I
b = −0.470216 + 0.263747I
−1.37915 − 2.38176I 0
u = 0.766251 − 0.455073I
a = 0.265973 − 0.448281I
b = −0.470216 − 0.263747I
−1.37915 + 2.38176I 0
u = −0.272305 + 0.846012I
a = 0.99449 − 1.05089I
b = 0.142486 − 1.394290I
−2.97007 − 2.46429I 0
u = −0.272305 − 0.846012I
a = 0.99449 + 1.05089I
b = 0.142486 + 1.394290I
−2.97007 + 2.46429I 0
u = −0.002790 + 1.111980I
a = 1.200990 + 0.179105I
b = −0.679439 − 0.185346I
1.10025 − 3.05463I 0
u = −0.002790 − 1.111980I
a = 1.200990 − 0.179105I
b = −0.679439 + 0.185346I
1.10025 + 3.05463I 0
u = 0.701907 + 0.537816I
a = −0.65478 − 1.73712I
b = 0.24496 − 1.47272I
−5.26519 − 5.78083I 0
u = 0.701907 − 0.537816I
a = −0.65478 + 1.73712I
b = 0.24496 + 1.47272I
−5.26519 + 5.78083I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.787382 + 0.386839I
a = −0.171210 − 0.646264I
b = −0.787382 − 0.386839I
10.2016I 0
u = −0.787382 − 0.386839I
a = −0.171210 + 0.646264I
b = −0.787382 + 0.386839I
− 10.2016I 0
u = 0.790592 + 0.347184I
a = 1.18615 + 1.90823I
b = 0.088744 + 1.394760I
−5.92340 + 0.99720I 0
u = 0.790592 − 0.347184I
a = 1.18615 − 1.90823I
b = 0.088744 − 1.394760I
−5.92340 − 0.99720I 0
u = 0.687351 + 0.513075I
a = 0.176990 − 0.369508I
b = 0.262179 − 0.400166I
−1.07235 − 2.41410I 0
u = 0.687351 − 0.513075I
a = 0.176990 + 0.369508I
b = 0.262179 + 0.400166I
−1.07235 + 2.41410I 0
u = 0.834729 + 0.037542I
a = 0.71946 + 2.02214I
b = −0.237782 + 1.365960I
−6.14153 − 2.77490I 0
u = 0.834729 − 0.037542I
a = 0.71946 − 2.02214I
b = −0.237782 − 1.365960I
−6.14153 + 2.77490I 0
u = −0.052414 + 1.189960I
a = 0.19582 − 1.80357I
b = 0.09579 − 1.60665I
−5.54517 − 3.33256I 0
u = −0.052414 − 1.189960I
a = 0.19582 + 1.80357I
b = 0.09579 + 1.60665I
−5.54517 + 3.33256I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779630 + 0.926682I
a = −0.49471 + 1.36858I
b = −0.22434 + 1.40772I
−4.35497 − 8.28767I 0
u = −0.779630 − 0.926682I
a = −0.49471 − 1.36858I
b = −0.22434 − 1.40772I
−4.35497 + 8.28767I 0
u = −0.725162 + 0.248821I
a = −0.70693 + 2.63897I
b = 0.29518 + 1.48566I
−4.85475 + 6.28492I 0
u = −0.725162 − 0.248821I
a = −0.70693 − 2.63897I
b = 0.29518 − 1.48566I
−4.85475 − 6.28492I 0
u = 0.773343 + 0.965987I
a = −0.20955 − 1.69076I
b = −0.111989 − 1.330050I
−5.07572 − 1.26184I 0
u = 0.773343 − 0.965987I
a = −0.20955 + 1.69076I
b = −0.111989 + 1.330050I
−5.07572 + 1.26184I 0
u = −0.127151 + 1.235070I
a = −0.274968 + 1.030680I
b = −0.00337 + 1.71364I
−5.60110 + 5.35321I 0
u = −0.127151 − 1.235070I
a = −0.274968 − 1.030680I
b = −0.00337 − 1.71364I
−5.60110 − 5.35321I 0
u = 0.302620 + 0.682286I
a = 0.90325 + 1.10435I
b = −0.469146 + 0.011108I
0.98745 − 3.37772I 0
u = 0.302620 − 0.682286I
a = 0.90325 − 1.10435I
b = −0.469146 − 0.011108I
0.98745 + 3.37772I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294316 + 1.220750I
a = 1.71095 + 0.48410I
b = −0.338573 + 1.267650I
−2.36146 − 6.82792I 0
u = 0.294316 − 1.220750I
a = 1.71095 − 0.48410I
b = −0.338573 − 1.267650I
−2.36146 + 6.82792I 0
u = 0.071265 + 1.261830I
a = −2.60204 − 0.77989I
b = 0.071265 − 1.261830I
3.91086I 0
u = 0.071265 − 1.261830I
a = −2.60204 + 0.77989I
b = 0.071265 + 1.261830I
− 3.91086I 0
u = −0.019111 + 1.286080I
a = −1.40117 + 0.89564I
b = 0.32094 + 1.40919I
0.40947 + 3.05315I 0
u = −0.019111 − 1.286080I
a = −1.40117 − 0.89564I
b = 0.32094 − 1.40919I
0.40947 − 3.05315I 0
u = −0.679439 + 0.185346I
a = 0.21866 − 3.01638I
b = −0.002790 − 1.111980I
−1.10025 − 3.05463I −1.25318 + 2.55597I
u = −0.679439 − 0.185346I
a = 0.21866 + 3.01638I
b = −0.002790 + 1.111980I
−1.10025 + 3.05463I −1.25318 − 2.55597I
u = 0.172704 + 1.295630I
a = 0.766858 − 0.146636I
b = −0.139306 − 0.387149I
2.76297 − 2.67751I 0
u = 0.172704 − 1.295630I
a = 0.766858 + 0.146636I
b = −0.139306 + 0.387149I
2.76297 + 2.67751I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.338573 + 1.267650I
a = −1.36573 + 1.59518I
b = 0.294316 + 1.220750I
2.36146 + 6.82792I 0
u = −0.338573 − 1.267650I
a = −1.36573 − 1.59518I
b = 0.294316 − 1.220750I
2.36146 − 6.82792I 0
u = −0.111989 + 1.330050I
a = −0.261450 + 0.227264I
b = 0.773343 − 0.965987I
5.07572 − 1.26184I 0
u = −0.111989 − 1.330050I
a = −0.261450 − 0.227264I
b = 0.773343 + 0.965987I
5.07572 + 1.26184I 0
u = −0.111538 + 1.333150I
a = −1.72458 − 0.02068I
b = 0.379857 + 0.270762I
3.16255 + 5.26546I 0
u = −0.111538 − 1.333150I
a = −1.72458 + 0.02068I
b = 0.379857 − 0.270762I
3.16255 − 5.26546I 0
u = −0.243111 + 1.317630I
a = 1.299540 − 0.408836I
b = −0.23465 − 1.42006I
−4.23968 + 0.21376I 0
u = −0.243111 − 1.317630I
a = 1.299540 + 0.408836I
b = −0.23465 + 1.42006I
−4.23968 − 0.21376I 0
u = 0.863385 + 1.032350I
a = 0.65186 + 1.42280I
b = 0.051249 + 1.356350I
−5.02593 − 2.17382I 0
u = 0.863385 − 1.032350I
a = 0.65186 − 1.42280I
b = 0.051249 − 1.356350I
−5.02593 + 2.17382I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.051249 + 1.356350I
a = −0.511244 + 0.312428I
b = 0.863385 + 1.032350I
5.02593 + 2.17382I 0
u = 0.051249 − 1.356350I
a = −0.511244 − 0.312428I
b = 0.863385 − 1.032350I
5.02593 − 2.17382I 0
u = 0.628407 + 0.055866I
a = 0.410455 − 0.178720I
b = −0.402004 − 0.116007I
−1.404620 − 0.021852I −7.39206 − 0.48985I
u = 0.628407 − 0.055866I
a = 0.410455 + 0.178720I
b = −0.402004 + 0.116007I
−1.404620 + 0.021852I −7.39206 + 0.48985I
u = −0.572702 + 0.256387I
a = −0.009101 + 1.173680I
b = −0.644129 + 0.714770I
−0.99836 + 5.34745I −2.97606 − 6.12125I
u = −0.572702 − 0.256387I
a = −0.009101 − 1.173680I
b = −0.644129 − 0.714770I
−0.99836 − 5.34745I −2.97606 + 6.12125I
u = 0.625030
a = 1.21625
b = 0.157649
−1.06813 −9.34160
u = −0.101752 + 1.377020I
a = 0.131635 − 0.371905I
b = 0.440285 − 1.014920I
3.06770 − 1.78673I 0
u = −0.101752 − 1.377020I
a = 0.131635 + 0.371905I
b = 0.440285 + 1.014920I
3.06770 + 1.78673I 0
u = −0.237782 + 1.365960I
a = −0.318941 + 0.622452I
b = 0.834729 + 0.037542I
6.14153 + 2.77490I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.237782 − 1.365960I
a = −0.318941 − 0.622452I
b = 0.834729 − 0.037542I
6.14153 − 2.77490I 0
u = −0.594196 + 0.131732I
a = 1.11525 − 2.31416I
b = −0.10232 − 1.55298I
−8.80205 − 2.88333I −8.45430 + 3.06089I
u = −0.594196 − 0.131732I
a = 1.11525 + 2.31416I
b = −0.10232 + 1.55298I
−8.80205 + 2.88333I −8.45430 − 3.06089I
u = 0.088744 + 1.394760I
a = −0.593259 + 0.456481I
b = 0.790592 + 0.347184I
5.92340 − 0.99720I 0
u = 0.088744 − 1.394760I
a = −0.593259 − 0.456481I
b = 0.790592 − 0.347184I
5.92340 + 0.99720I 0
u = 0.142486 + 1.394290I
a = 0.483151 − 0.325386I
b = −0.272305 − 0.846012I
2.97007 − 2.46429I 0
u = 0.142486 − 1.394290I
a = 0.483151 + 0.325386I
b = −0.272305 + 0.846012I
2.97007 + 2.46429I 0
u = −0.196199 + 1.388130I
a = −0.706661 + 0.673354I
b = 1.009860 + 0.421402I
6.61469 + 4.90913I 0
u = −0.196199 − 1.388130I
a = −0.706661 − 0.673354I
b = 1.009860 − 0.421402I
6.61469 − 4.90913I 0
u = −0.22434 + 1.40772I
a = 0.179708 + 0.146859I
b = −0.779630 + 0.926682I
4.35497 + 8.28767I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22434 − 1.40772I
a = 0.179708 − 0.146859I
b = −0.779630 − 0.926682I
4.35497 − 8.28767I 0
u = −0.28731 + 1.40208I
a = −1.40455 + 1.11496I
b = 0.38905 + 1.51820I
0.40564 + 9.95805I 0
u = −0.28731 − 1.40208I
a = −1.40455 − 1.11496I
b = 0.38905 − 1.51820I
0.40564 − 9.95805I 0
u = −0.23465 + 1.42006I
a = 1.02401 − 1.37015I
b = −0.243111 − 1.317630I
4.23968 + 0.21376I 0
u = −0.23465 − 1.42006I
a = 1.02401 + 1.37015I
b = −0.243111 + 1.317630I
4.23968 − 0.21376I 0
u = 0.19257 + 1.43038I
a = 1.49154 + 1.63881I
b = −0.19209 + 1.43532I
2.46664 − 7.58913I 0
u = 0.19257 − 1.43038I
a = 1.49154 − 1.63881I
b = −0.19209 − 1.43532I
2.46664 + 7.58913I 0
u = 0.32094 + 1.40919I
a = 1.38101 + 0.80656I
b = −0.019111 + 1.286080I
−0.40947 − 3.05315I 0
u = 0.32094 − 1.40919I
a = 1.38101 − 0.80656I
b = −0.019111 − 1.286080I
−0.40947 + 3.05315I 0
u = 0.15746 + 1.43693I
a = −0.547564 − 0.230043I
b = 1.041540 − 0.340102I
6.95360 − 4.28613I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15746 − 1.43693I
a = −0.547564 + 0.230043I
b = 1.041540 + 0.340102I
6.95360 + 4.28613I 0
u = −0.478756 + 0.279060I
a = −2.60328 + 2.08878I
b = 0.11761 + 1.51561I
−8.06398 + 5.06340I −11.31512 − 7.25514I
u = −0.478756 − 0.279060I
a = −2.60328 − 2.08878I
b = 0.11761 − 1.51561I
−8.06398 − 5.06340I −11.31512 + 7.25514I
u = −0.19209 + 1.43532I
a = −1.67209 + 0.24687I
b = 0.19257 + 1.43038I
−2.46664 + 7.58913I 0
u = −0.19209 − 1.43532I
a = −1.67209 − 0.24687I
b = 0.19257 − 1.43038I
−2.46664 − 7.58913I 0
u = −0.470216 + 0.263747I
a = 0.344417 + 1.206380I
b = 0.766251 + 0.455073I
1.37915 + 2.38176I 9.04345 − 9.73838I
u = −0.470216 − 0.263747I
a = 0.344417 − 1.206380I
b = 0.766251 − 0.455073I
1.37915 − 2.38176I 9.04345 + 9.73838I
u = 0.24496 + 1.47272I
a = −0.388573 − 0.396898I
b = 0.701907 − 0.537816I
5.26519 − 5.78083I 0
u = 0.24496 − 1.47272I
a = −0.388573 + 0.396898I
b = 0.701907 + 0.537816I
5.26519 + 5.78083I 0
u = −0.29964 + 1.46694I
a = 0.566894 − 0.578477I
b = −0.950162 − 0.371930I
5.9520 + 14.1469I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.29964 − 1.46694I
a = 0.566894 + 0.578477I
b = −0.950162 + 0.371930I
5.9520 − 14.1469I 0
u = 0.29518 + 1.48566I
a = 0.646450 + 0.424422I
b = −0.725162 + 0.248821I
4.85475 − 6.28492I 0
u = 0.29518 − 1.48566I
a = 0.646450 − 0.424422I
b = −0.725162 − 0.248821I
4.85475 + 6.28492I 0
u = 0.40667 + 1.46203I
a = −0.93004 − 1.23056I
b = 0.27599 − 1.49803I
−1.26061 − 9.42982I 0
u = 0.40667 − 1.46203I
a = −0.93004 + 1.23056I
b = 0.27599 + 1.49803I
−1.26061 + 9.42982I 0
u = 0.11761 + 1.51561I
a = 0.619797 + 0.802043I
b = −0.478756 + 0.279060I
8.06398 − 5.06340I 0
u = 0.11761 − 1.51561I
a = 0.619797 − 0.802043I
b = −0.478756 − 0.279060I
8.06398 + 5.06340I 0
u = 0.262179 + 0.400166I
a = 0.045519 − 0.155812I
b = 0.687351 − 0.513075I
1.07235 − 2.41410I 10.44859 + 9.05803I
u = 0.262179 − 0.400166I
a = 0.045519 + 0.155812I
b = 0.687351 + 0.513075I
1.07235 + 2.41410I 10.44859 − 9.05803I
u = 0.27599 + 1.49803I
a = −0.963325 − 0.765920I
b = 0.40667 − 1.46203I
1.26061 − 9.42982I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27599 − 1.49803I
a = −0.963325 + 0.765920I
b = 0.40667 + 1.46203I
1.26061 + 9.42982I 0
u = −0.469146 + 0.011108I
a = −0.76819 + 2.68289I
b = 0.302620 + 0.682286I
−0.98745 + 3.37772I −6.25218 − 8.22989I
u = −0.469146 − 0.011108I
a = −0.76819 − 2.68289I
b = 0.302620 − 0.682286I
−0.98745 − 3.37772I −6.25218 + 8.22989I
u = 0.379857 + 0.270762I
a = 2.36245 + 5.61621I
b = −0.111538 + 1.333150I
−3.16255 − 5.26546I −3.08168 + 10.27271I
u = 0.379857 − 0.270762I
a = 2.36245 − 5.61621I
b = −0.111538 − 1.333150I
−3.16255 + 5.26546I −3.08168 − 10.27271I
u = −0.37147 + 1.48912I
a = 1.28609 − 1.11172I
b = −0.37147 − 1.48912I
18.9097I 0
u = −0.37147 − 1.48912I
a = 1.28609 + 1.11172I
b = −0.37147 + 1.48912I
− 18.9097I 0
u = −0.10232 + 1.55298I
a = 0.366486 − 0.425441I
b = −0.594196 − 0.131732I
8.80205 − 2.88333I 0
u = −0.10232 − 1.55298I
a = 0.366486 + 0.425441I
b = −0.594196 + 0.131732I
8.80205 + 2.88333I 0
u = 0.38905 + 1.51820I
a = 1.31156 + 1.04793I
b = −0.28731 + 1.40208I
−0.40564 − 9.95805I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38905 − 1.51820I
a = 1.31156 − 1.04793I
b = −0.28731 − 1.40208I
−0.40564 + 9.95805I 0
u = −0.402004 + 0.116007I
a = 1.184400 + 0.326910I
b = 0.628407 − 0.055866I
1.404620 − 0.021852I 7.39206 − 0.48985I
u = −0.402004 − 0.116007I
a = 1.184400 − 0.326910I
b = 0.628407 + 0.055866I
1.404620 + 0.021852I 7.39206 + 0.48985I
u = −0.139306 + 0.387149I
a = 2.65229 − 1.35503I
b = 0.172704 − 1.295630I
−2.76297 − 2.67751I 0.62580 + 2.22298I
u = −0.139306 − 0.387149I
a = 2.65229 + 1.35503I
b = 0.172704 + 1.295630I
−2.76297 + 2.67751I 0.62580 − 2.22298I
u = 0.09579 + 1.60665I
a = 0.071754 + 0.146857I
b = −0.052414 − 1.189960I
5.54517 − 3.33256I 0
u = 0.09579 − 1.60665I
a = 0.071754 − 0.146857I
b = −0.052414 + 1.189960I
5.54517 + 3.33256I 0
u = −0.00337 + 1.71364I
a = 0.146081 + 0.512095I
b = −0.127151 + 1.235070I
5.60110 − 5.35321I 0
u = −0.00337 − 1.71364I
a = 0.146081 − 0.512095I
b = −0.127151 − 1.235070I
5.60110 + 5.35321I 0
u = 0.157649
a = −4.19701
b = 0.625030
1.06813 9.34160
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.1095870 + 0.0579846I
a = 2.77162 − 0.62168I
b = 0.641102 − 0.836655I
0.68851 − 2.45836I 2.96272 − 12.60117I
u = −0.1095870 − 0.0579846I
a = 2.77162 + 0.62168I
b = 0.641102 + 0.836655I
0.68851 + 2.45836I 2.96272 + 12.60117I
18
II.
I
u
2
= h−u
28
+7u
27
+· · ·+b−4, u
29
−7u
28
+· · ·+a−5, u
30
−6u
29
+· · ·−8u+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−u
29
+ 7u
28
+ ··· − 41u + 5
u
28
− 7u
27
+ ··· − 25u + 4
a
7
=
−u
29
+ 6u
28
+ ··· − 16u + 1
u
28
− 7u
27
+ ··· − 25u + 4
a
3
=
u
28
− 6u
27
+ ··· − 122u
3
+ 24u
2
u
29
− 4u
28
+ ··· + 24u
2
− 3u
a
11
=
u
29
− 7u
28
+ ··· + 16u − 2
u
29
− 10u
28
+ ··· + 8u − 1
a
9
=
2u
29
− 15u
28
+ ··· − 17u + 2
−3u
29
+ 10u
28
+ ··· + 31u − 4
a
6
=
u
29
− 6u
28
+ ··· + 5u − 2
2u
29
− 14u
28
+ ··· + 19u − 3
a
10
=
3u
29
− 19u
28
+ ··· − 9u + 1
−7u
28
+ 41u
27
+ ··· + 32u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 6u
29
− 40u
28
+ 237u
27
− 948u
26
+ 3342u
25
− 9668u
24
+ 25030u
23
− 56538u
22
+
115686u
21
−212011u
20
+354673u
19
−538050u
18
+748059u
17
−948207u
16
+1102601u
15
−
1170021u
14
+ 1137414u
13
− 1006740u
12
+ 814043u
11
− 596598u
10
+ 398555u
9
−
239907u
8
+ 131902u
7
− 64669u
6
+ 29211u
5
− 11302u
4
+ 4091u
3
− 1116u
2
+ 290u − 49
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
, c
12
u
30
− 6u
29
+ ··· − 8u + 1
c
2
u
30
− 2u
29
+ ··· − 5u + 1
c
3
u
30
+ 3u
29
+ ··· − 42u + 28
c
4
, c
7
, c
8
u
30
+ 6u
29
+ ··· + 8u + 1
c
5
u
30
− 3u
29
+ ··· + 42u + 28
c
6
u
30
+ 2u
29
+ ··· + 5u + 1
c
9
u
30
+ 6u
28
+ ··· + 6u
2
+ 1
c
10
u
30
+ 6u
28
+ ··· + 6u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
11
, c
12
y
30
+ 32y
29
+ ··· + 14y + 1
c
2
, c
6
y
30
+ 6y
29
+ ··· − 3y + 1
c
3
, c
5
y
30
+ 9y
29
+ ··· + 1876y + 784
c
9
, c
10
y
30
+ 12y
29
+ ··· + 12y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890102 + 0.442809I
a = −0.74691 − 2.06032I
b = 0.17868 − 1.41532I
−6.01201 − 4.61569I −2.50419 + 5.33502I
u = 0.890102 − 0.442809I
a = −0.74691 + 2.06032I
b = 0.17868 + 1.41532I
−6.01201 + 4.61569I −2.50419 − 5.33502I
u = 0.705005 + 0.756507I
a = −0.082154 − 0.272162I
b = 0.278421 − 0.155762I
−0.59984 − 2.67935I 9.3750 + 18.2662I
u = 0.705005 − 0.756507I
a = −0.082154 + 0.272162I
b = 0.278421 + 0.155762I
−0.59984 + 2.67935I 9.3750 − 18.2662I
u = 0.022604 + 1.203100I
a = 0.53084 + 1.41537I
b = 0.05801 + 1.63296I
−5.20085 + 3.86398I 0.85342 − 7.41373I
u = 0.022604 − 1.203100I
a = 0.53084 − 1.41537I
b = 0.05801 − 1.63296I
−5.20085 − 3.86398I 0.85342 + 7.41373I
u = −0.071987 + 1.265200I
a = 1.64788 − 0.00635I
b = −0.261651 + 0.457608I
2.92597 + 4.34141I 2.79786 − 3.35128I
u = −0.071987 − 1.265200I
a = 1.64788 + 0.00635I
b = −0.261651 − 0.457608I
2.92597 − 4.34141I 2.79786 + 3.35128I
u = 0.810259 + 0.978159I
a = 0.35611 + 1.49854I
b = 0.099014 + 1.331320I
−4.61021 − 1.38790I 0
u = 0.810259 − 0.978159I
a = 0.35611 − 1.49854I
b = 0.099014 − 1.331320I
−4.61021 + 1.38790I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119841 + 0.715873I
a = −0.998426 − 0.780655I
b = 0.06601 − 1.54655I
−7.16477 − 4.30186I −5.52110 + 3.88276I
u = 0.119841 − 0.715873I
a = −0.998426 + 0.780655I
b = 0.06601 + 1.54655I
−7.16477 + 4.30186I −5.52110 − 3.88276I
u = −0.151185 + 1.273750I
a = 2.54371 − 0.94777I
b = −0.151185 − 1.273750I
5.93137I 0. − 6.27108I
u = −0.151185 − 1.273750I
a = 2.54371 + 0.94777I
b = −0.151185 + 1.273750I
− 5.93137I 0. + 6.27108I
u = 0.099014 + 1.331320I
a = −0.291551 + 0.011933I
b = 0.810259 + 0.978159I
4.61021 + 1.38790I 0
u = 0.099014 − 1.331320I
a = −0.291551 − 0.011933I
b = 0.810259 − 0.978159I
4.61021 − 1.38790I 0
u = 0.17868 + 1.41532I
a = −0.637062 − 0.460733I
b = 0.890102 − 0.442809I
6.01201 − 4.61569I 0
u = 0.17868 − 1.41532I
a = −0.637062 + 0.460733I
b = 0.890102 + 0.442809I
6.01201 + 4.61569I 0
u = −0.261651 + 0.457608I
a = −3.61042 + 3.04673I
b = −0.071987 + 1.265200I
−2.92597 − 4.34141I −2.79786 + 3.35128I
u = −0.261651 − 0.457608I
a = −3.61042 − 3.04673I
b = −0.071987 − 1.265200I
−2.92597 + 4.34141I −2.79786 − 3.35128I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31648 + 1.45446I
a = −1.23933 − 1.03133I
b = 0.31648 − 1.45446I
− 8.82787I 0
u = 0.31648 − 1.45446I
a = −1.23933 + 1.03133I
b = 0.31648 + 1.45446I
8.82787I 0
u = 0.06601 + 1.54655I
a = −0.413956 − 0.454670I
b = 0.119841 − 0.715873I
7.16477 − 4.30186I 0
u = 0.06601 − 1.54655I
a = −0.413956 + 0.454670I
b = 0.119841 + 0.715873I
7.16477 + 4.30186I 0
u = −0.059602 + 0.443367I
a = −2.61936 + 0.12643I
b = −0.059602 − 0.443367I
− 3.69724I 0. + 6.99510I
u = −0.059602 − 0.443367I
a = −2.61936 − 0.12643I
b = −0.059602 + 0.443367I
3.69724I 0. − 6.99510I
u = 0.05801 + 1.63296I
a = −0.350838 + 0.154398I
b = 0.022604 + 1.203100I
5.20085 − 3.86398I 0
u = 0.05801 − 1.63296I
a = −0.350838 − 0.154398I
b = 0.022604 − 1.203100I
5.20085 + 3.86398I 0
u = 0.278421 + 0.155762I
a = −0.088535 − 1.224940I
b = 0.705005 − 0.756507I
0.59984 − 2.67935I −9.3750 + 18.2662I
u = 0.278421 − 0.155762I
a = −0.088535 + 1.224940I
b = 0.705005 + 0.756507I
0.59984 + 2.67935I −9.3750 − 18.2662I
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
30
− 6u
29
+ ··· − 8u + 1)(u
132
+ 5u
131
+ ··· − 157u + 11)
c
2
(u
30
− 2u
29
+ ··· − 5u + 1)(u
132
− 3u
131
+ ··· − 20u + 1)
c
3
(u
30
+ 3u
29
+ ··· − 42u + 28)(u
132
− 2u
131
+ ··· + 768008u − 38548)
c
4
(u
30
+ 6u
29
+ ··· + 8u + 1)(u
132
+ 5u
131
+ ··· − 157u + 11)
c
5
(u
30
− 3u
29
+ ··· + 42u + 28)(u
132
+ 2u
131
+ ··· − 768008u − 38548)
c
6
(u
30
+ 2u
29
+ ··· + 5u + 1)(u
132
+ 3u
131
+ ··· + 20u + 1)
c
7
, c
8
(u
30
+ 6u
29
+ ··· + 8u + 1)(u
132
− 5u
131
+ ··· + 157u + 11)
c
9
(u
30
+ 6u
28
+ ··· + 6u
2
+ 1)(u
132
− u
131
+ ··· + 123u − 5)
c
10
(u
30
+ 6u
28
+ ··· + 6u
2
+ 1)(u
132
+ u
131
+ ··· − 123u − 5)
c
11
(u
30
− 6u
29
+ ··· − 8u + 1)(u
132
− 5u
131
+ ··· + 157u + 11)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
11
, c
12
(y
30
+ 32y
29
+ ··· + 14y + 1)(y
132
+ 125y
131
+ ··· − 14859y + 121)
c
2
, c
6
(y
30
+ 6y
29
+ ··· − 3y + 1)(y
132
− y
131
+ ··· − 208y + 1)
c
3
, c
5
(y
30
+ 9y
29
+ ··· + 1876y + 784)
· (y
132
− 6y
131
+ ··· − 24158727920y + 1485948304)
c
9
, c
10
(y
30
+ 12y
29
+ ··· + 12y + 1)(y
132
+ 9y
131
+ ··· + 571y + 25)
26
