12a
0831
(K12a
0831
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 11 9 3 12 6 1 7 10
Solving Sequence
1,4
2
5,11
6 10 9 7 12 8 3
c
1
c
4
c
5
c
10
c
9
c
6
c
12
c
8
c
3
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.23861 × 10
153
u
112
− 1.94908 × 10
154
u
111
+ ··· + 1.41771 × 10
153
b − 2.85035 × 10
153
,
− 1.06042 × 10
155
u
112
− 1.06831 × 10
156
u
111
+ ··· + 2.41011 × 10
154
a − 2.12527 × 10
155
,
u
113
+ 10u
112
+ ··· + u + 1i
I
u
2
= hb − a + 1, a
8
− 7a
7
+ 18a
6
− 19a
5
+ 3a
4
+ 7a
3
− 3a − 1, u − 1i
I
u
3
= hb − 1, 12u
2
+ 17a + 11u + 9, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 124 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−2.24 × 10
153
u
112
− 1.95 × 10
154
u
111
+ · · · + 1.42 × 10
153
b − 2.85 ×
10
153
, −1.06 × 10
155
u
112
− 1.07 × 10
156
u
111
+ · · · + 2.41 × 10
154
a − 2.13 ×
10
155
, u
113
+ 10u
112
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
4.39989u
112
+ 44.3263u
111
+ ··· + 0.337698u + 8.81814
1.57903u
112
+ 13.7481u
111
+ ··· − 1.54070u + 2.01053
a
6
=
146.341u
112
+ 1220.77u
111
+ ··· + 56.2109u + 77.1163
−24.3000u
112
− 201.744u
111
+ ··· − 0.0298499u − 14.3881
a
10
=
2.82086u
112
+ 30.5782u
111
+ ··· + 1.87840u + 6.80761
1.57903u
112
+ 13.7481u
111
+ ··· − 1.54070u + 2.01053
a
9
=
−121.246u
112
− 1055.93u
111
+ ··· + 46.5652u − 94.4330
44.6934u
112
+ 377.381u
111
+ ··· + 14.9969u + 28.5017
a
7
=
54.0067u
112
+ 457.695u
111
+ ··· + 0.437708u + 36.6651
−37.0169u
112
− 318.661u
111
+ ··· − 9.85778u − 26.5176
a
12
=
4.19011u
112
+ 42.4920u
111
+ ··· − 7.17546u + 10.6493
1.66036u
112
+ 14.9044u
111
+ ··· − 3.79535u + 2.40863
a
8
=
−36.0266u
112
− 322.681u
111
+ ··· + 5.32016u − 34.2462
144.917u
112
+ 1252.66u
111
+ ··· + 32.6876u + 104.913
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 110.765u
112
+ 946.066u
111
+ ··· + 40.9255u + 80.6906
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
113
− 10u
112
+ ··· + u − 1
c
3
, c
7
u
113
− 2u
112
+ ··· + 896u − 256
c
5
17(17u
113
+ 212u
112
+ ··· − 115224u − 34421)
c
6
, c
9
u
113
+ 3u
112
+ ··· + 3u + 1
c
8
17(17u
113
+ 219u
112
+ ··· + 16199u + 2539)
c
10
, c
12
u
113
+ 5u
112
+ ··· − 1158u + 289
c
11
u
113
+ 2u
112
+ ··· − 41820u − 2312
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
113
− 100y
112
+ ··· − 13y −1
c
3
, c
7
y
113
− 48y
112
+ ··· + 1425408y −65536
c
5
289(289y
113
− 1016y
112
+ ··· − 6.58097 × 10
9
y −1.18481 × 10
9
)
c
6
, c
9
y
113
+ 61y
112
+ ··· + 19y −1
c
8
289(289y
113
+ 6473y
112
+ ··· − 3.80828 × 10
8
y −6446521)
c
10
, c
12
y
113
− 69y
112
+ ··· + 10227136y −83521
c
11
y
113
+ 18y
112
+ ··· + 117380240y −5345344
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.961684 + 0.261047I
a = 1.36712 − 0.54658I
b = 1.082080 + 0.570638I
−0.69818 + 1.82820I 0
u = 0.961684 − 0.261047I
a = 1.36712 + 0.54658I
b = 1.082080 − 0.570638I
−0.69818 − 1.82820I 0
u = 0.472379 + 0.866415I
a = 0.234670 + 0.271151I
b = −0.758562 − 0.306959I
−2.38708 + 0.06669I 0
u = 0.472379 − 0.866415I
a = 0.234670 − 0.271151I
b = −0.758562 + 0.306959I
−2.38708 − 0.06669I 0
u = 0.834559 + 0.522813I
a = 1.038410 + 0.755660I
b = −0.255306 + 1.036950I
−5.58135 + 3.04071I 0
u = 0.834559 − 0.522813I
a = 1.038410 − 0.755660I
b = −0.255306 − 1.036950I
−5.58135 − 3.04071I 0
u = 0.260449 + 0.934723I
a = 0.887866 + 0.693301I
b = −1.235440 + 0.431488I
3.36185 − 8.25297I 0
u = 0.260449 − 0.934723I
a = 0.887866 − 0.693301I
b = −1.235440 − 0.431488I
3.36185 + 8.25297I 0
u = 0.278186 + 0.916362I
a = 0.988889 + 0.883115I
b = −1.33223 + 0.63057I
−0.2735 − 14.1974I 0
u = 0.278186 − 0.916362I
a = 0.988889 − 0.883115I
b = −1.33223 − 0.63057I
−0.2735 + 14.1974I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975251 + 0.427221I
a = 0.554224 − 0.085844I
b = −0.398985 − 0.526440I
−4.97488 − 1.61721I 0
u = 0.975251 − 0.427221I
a = 0.554224 + 0.085844I
b = −0.398985 + 0.526440I
−4.97488 + 1.61721I 0
u = 0.834818 + 0.710924I
a = 0.328257 + 0.684453I
b = −0.958208 + 0.448873I
−3.48666 − 5.58470I 0
u = 0.834818 − 0.710924I
a = 0.328257 − 0.684453I
b = −0.958208 − 0.448873I
−3.48666 + 5.58470I 0
u = 0.155170 + 0.882082I
a = 1.112470 + 0.225885I
b = −0.795879 + 0.295304I
−2.30731 − 2.91239I 0
u = 0.155170 − 0.882082I
a = 1.112470 − 0.225885I
b = −0.795879 − 0.295304I
−2.30731 + 2.91239I 0
u = 1.107870 + 0.183683I
a = 0.85034 − 1.86373I
b = 1.342020 − 0.009858I
0.221092 − 0.868785I 0
u = 1.107870 − 0.183683I
a = 0.85034 + 1.86373I
b = 1.342020 + 0.009858I
0.221092 + 0.868785I 0
u = 0.870052
a = 0.953545
b = 0.0935621
−1.22815 0
u = 0.308782 + 0.806948I
a = −0.244705 − 0.059763I
b = −0.182636 − 1.236170I
−3.93453 − 7.72346I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.308782 − 0.806948I
a = −0.244705 + 0.059763I
b = −0.182636 + 1.236170I
−3.93453 + 7.72346I 0
u = −1.15010
a = −0.276768
b = −1.44831
4.44175 0
u = −1.162700 + 0.028367I
a = −0.237024 + 0.254459I
b = −1.41287 + 0.30905I
0.26523 − 6.30460I 0
u = −1.162700 − 0.028367I
a = −0.237024 − 0.254459I
b = −1.41287 − 0.30905I
0.26523 + 6.30460I 0
u = 0.651270 + 0.520129I
a = 0.787605 + 0.344424I
b = −0.165317 + 0.384025I
−1.61934 − 0.33597I 0
u = 0.651270 − 0.520129I
a = 0.787605 − 0.344424I
b = −0.165317 − 0.384025I
−1.61934 + 0.33597I 0
u = 0.992579 + 0.617588I
a = −0.203051 + 0.044813I
b = −1.252640 − 0.592702I
−2.42982 + 8.85973I 0
u = 0.992579 − 0.617588I
a = −0.203051 − 0.044813I
b = −1.252640 + 0.592702I
−2.42982 − 8.85973I 0
u = 1.166290 + 0.156325I
a = 0.64576 − 2.49355I
b = 1.200250 − 0.227169I
0.082157 − 0.857061I 0
u = 1.166290 − 0.156325I
a = 0.64576 + 2.49355I
b = 1.200250 + 0.227169I
0.082157 + 0.857061I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328848 + 0.750599I
a = −0.003576 − 0.299898I
b = 0.068339 − 0.729790I
−0.43516 − 3.99400I 0
u = 0.328848 − 0.750599I
a = −0.003576 + 0.299898I
b = 0.068339 + 0.729790I
−0.43516 + 3.99400I 0
u = −0.916804 + 0.750551I
a = 0.101204 − 0.392853I
b = −0.989163 + 0.036267I
4.65181 + 2.75031I 0
u = −0.916804 − 0.750551I
a = 0.101204 + 0.392853I
b = −0.989163 − 0.036267I
4.65181 − 2.75031I 0
u = −0.335291 + 0.714376I
a = 0.566059 − 0.992552I
b = −1.185720 − 0.216566I
5.67260 + 2.25032I 0
u = −0.335291 − 0.714376I
a = 0.566059 + 0.992552I
b = −1.185720 + 0.216566I
5.67260 − 2.25032I 0
u = 1.044170 + 0.624951I
a = −0.042033 + 0.198039I
b = −1.113430 − 0.361379I
1.01629 + 2.81685I 0
u = 1.044170 − 0.624951I
a = −0.042033 − 0.198039I
b = −1.113430 + 0.361379I
1.01629 − 2.81685I 0
u = 0.217309 + 0.720989I
a = −0.835422 − 0.443997I
b = 1.18367 − 0.86495I
1.51696 − 5.57365I 0
u = 0.217309 − 0.720989I
a = −0.835422 + 0.443997I
b = 1.18367 + 0.86495I
1.51696 + 5.57365I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.241820 + 0.192762I
a = 0.69993 − 2.78023I
b = 1.072940 − 0.785305I
−1.33451 − 3.90121I 0
u = 1.241820 − 0.192762I
a = 0.69993 + 2.78023I
b = 1.072940 + 0.785305I
−1.33451 + 3.90121I 0
u = 1.258900 + 0.067696I
a = 4.10773 − 3.17053I
b = 0.870105 + 0.079219I
−2.76031 + 0.24285I 0
u = 1.258900 − 0.067696I
a = 4.10773 + 3.17053I
b = 0.870105 − 0.079219I
−2.76031 − 0.24285I 0
u = −0.473545 + 0.525712I
a = −0.322671 − 0.676621I
b = −1.149030 + 0.324827I
1.40611 − 4.98571I 0
u = −0.473545 − 0.525712I
a = −0.322671 + 0.676621I
b = −1.149030 − 0.324827I
1.40611 + 4.98571I 0
u = −0.297951 + 0.640070I
a = 0.83981 − 1.43008I
b = −1.294630 − 0.500564I
2.05403 + 8.53878I 0. − 6.10703I
u = −0.297951 − 0.640070I
a = 0.83981 + 1.43008I
b = −1.294630 + 0.500564I
2.05403 − 8.53878I 0. + 6.10703I
u = 0.319533 + 0.609259I
a = 1.74585 − 5.66304I
b = 0.942388 + 0.016764I
−0.45862 − 1.47435I 28.3803 + 13.0429I
u = 0.319533 − 0.609259I
a = 1.74585 + 5.66304I
b = 0.942388 − 0.016764I
−0.45862 + 1.47435I 28.3803 − 13.0429I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191537 + 0.658715I
a = −1.59049 − 0.38846I
b = 1.361490 − 0.310048I
2.81518 − 2.25501I 7.02368 + 2.41006I
u = 0.191537 − 0.658715I
a = −1.59049 + 0.38846I
b = 1.361490 + 0.310048I
2.81518 + 2.25501I 7.02368 − 2.41006I
u = 1.310790 + 0.282909I
a = 0.693374 + 1.205230I
b = −0.623900 + 0.414671I
−5.62759 − 0.96807I 0
u = 1.310790 − 0.282909I
a = 0.693374 − 1.205230I
b = −0.623900 − 0.414671I
−5.62759 + 0.96807I 0
u = 1.335570 + 0.125327I
a = −0.050034 − 1.326770I
b = −0.050118 − 0.612569I
−3.04736 − 1.94290I 0
u = 1.335570 − 0.125327I
a = −0.050034 + 1.326770I
b = −0.050118 + 0.612569I
−3.04736 + 1.94290I 0
u = −1.351420 + 0.124666I
a = 0.87760 − 1.20725I
b = 0.502291 − 1.207680I
−6.01723 − 1.75193I 0
u = −1.351420 − 0.124666I
a = 0.87760 + 1.20725I
b = 0.502291 + 1.207680I
−6.01723 + 1.75193I 0
u = −1.344680 + 0.210066I
a = 0.836484 − 0.154388I
b = 1.58899 − 0.57576I
−2.25009 + 1.62166I 0
u = −1.344680 − 0.210066I
a = 0.836484 + 0.154388I
b = 1.58899 + 0.57576I
−2.25009 − 1.62166I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144484 + 0.621433I
a = −1.82353 + 0.32570I
b = 1.49332 + 0.05330I
3.01974 − 2.02401I 7.44184 + 5.54583I
u = 0.144484 − 0.621433I
a = −1.82353 − 0.32570I
b = 1.49332 − 0.05330I
3.01974 + 2.02401I 7.44184 − 5.54583I
u = 1.358000 + 0.177874I
a = −0.87914 − 1.83698I
b = −0.241407 − 1.159440I
−6.75012 − 5.58489I 0
u = 1.358000 − 0.177874I
a = −0.87914 + 1.83698I
b = −0.241407 + 1.159440I
−6.75012 + 5.58489I 0
u = 0.515055 + 0.354300I
a = 1.63764 + 0.84883I
b = 0.779173 − 0.264986I
−1.24671 − 2.00627I −2.16610 + 1.88869I
u = 0.515055 − 0.354300I
a = 1.63764 − 0.84883I
b = 0.779173 + 0.264986I
−1.24671 + 2.00627I −2.16610 − 1.88869I
u = −1.366790 + 0.165022I
a = 0.793493 − 1.017980I
b = 0.834662 − 0.775592I
−3.59891 + 1.83803I 0
u = −1.366790 − 0.165022I
a = 0.793493 + 1.017980I
b = 0.834662 + 0.775592I
−3.59891 − 1.83803I 0
u = −1.358380 + 0.239658I
a = 0.446987 + 0.792365I
b = 1.69053 + 0.00244I
−1.75667 + 5.14933I 0
u = −1.358380 − 0.239658I
a = 0.446987 − 0.792365I
b = 1.69053 − 0.00244I
−1.75667 − 5.14933I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.377970 + 0.261035I
a = 0.14224 + 1.62218I
b = 1.43979 + 0.49676I
−2.18494 + 5.60549I 0
u = −1.377970 − 0.261035I
a = 0.14224 − 1.62218I
b = 1.43979 − 0.49676I
−2.18494 − 5.60549I 0
u = −1.38768 + 0.28521I
a = 0.09829 + 2.00040I
b = 1.22309 + 1.04416I
−3.58758 + 9.21705I 0
u = −1.38768 − 0.28521I
a = 0.09829 − 2.00040I
b = 1.22309 − 1.04416I
−3.58758 − 9.21705I 0
u = −1.40882 + 0.17539I
a = 1.28217 − 1.09311I
b = 0.502638 − 0.150538I
−6.91302 + 4.04376I 0
u = −1.40882 − 0.17539I
a = 1.28217 + 1.09311I
b = 0.502638 + 0.150538I
−6.91302 − 4.04376I 0
u = 0.069032 + 0.563081I
a = −1.56321 + 0.92826I
b = 1.32629 + 0.60309I
2.27246 + 1.15394I 7.28806 − 2.01801I
u = 0.069032 − 0.563081I
a = −1.56321 − 0.92826I
b = 1.32629 − 0.60309I
2.27246 − 1.15394I 7.28806 + 2.01801I
u = −1.41303 + 0.23757I
a = −0.49956 + 4.32991I
b = 0.959384 + 0.078619I
−5.96934 + 4.58071I 0
u = −1.41303 − 0.23757I
a = −0.49956 − 4.32991I
b = 0.959384 − 0.078619I
−5.96934 − 4.58071I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41519 + 0.25683I
a = −0.45467 + 2.07595I
b = −1.28914 + 0.62697I
−3.41637 − 11.84470I 0
u = 1.41519 − 0.25683I
a = −0.45467 − 2.07595I
b = −1.28914 − 0.62697I
−3.41637 + 11.84470I 0
u = 1.41838 + 0.28314I
a = −0.36970 + 1.57812I
b = −1.167110 + 0.421831I
0.12401 − 5.89051I 0
u = 1.41838 − 0.28314I
a = −0.36970 − 1.57812I
b = −1.167110 − 0.421831I
0.12401 + 5.89051I 0
u = −1.40383 + 0.38998I
a = 0.329832 − 1.165820I
b = −0.997247 − 0.398818I
−7.26453 + 7.54102I 0
u = −1.40383 − 0.38998I
a = 0.329832 + 1.165820I
b = −0.997247 + 0.398818I
−7.26453 − 7.54102I 0
u = 1.45983 + 0.13397I
a = −0.966889 − 0.302712I
b = −0.850000 − 0.413449I
−5.00665 + 2.66992I 0
u = 1.45983 − 0.13397I
a = −0.966889 + 0.302712I
b = −0.850000 + 0.413449I
−5.00665 − 2.66992I 0
u = −1.43775 + 0.29430I
a = −0.347366 + 1.225430I
b = 0.041871 + 0.948487I
−6.08574 + 7.79317I 0
u = −1.43775 − 0.29430I
a = −0.347366 − 1.225430I
b = 0.041871 − 0.948487I
−6.08574 − 7.79317I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43710 + 0.31706I
a = −0.90012 + 1.32188I
b = −0.215361 + 1.377320I
−9.5150 + 11.7864I 0
u = −1.43710 − 0.31706I
a = −0.90012 − 1.32188I
b = −0.215361 − 1.377320I
−9.5150 − 11.7864I 0
u = −1.44024 + 0.38407I
a = −0.02505 − 1.60974I
b = −1.299480 − 0.508238I
−2.05065 + 12.98760I 0
u = −1.44024 − 0.38407I
a = −0.02505 + 1.60974I
b = −1.299480 + 0.508238I
−2.05065 − 12.98760I 0
u = −1.44514 + 0.37393I
a = 0.01924 − 1.92503I
b = −1.37567 − 0.67966I
−5.7644 + 18.8401I 0
u = −1.44514 − 0.37393I
a = 0.01924 + 1.92503I
b = −1.37567 + 0.67966I
−5.7644 − 18.8401I 0
u = −1.50495 + 0.04038I
a = −0.05721 − 1.58096I
b = −0.621244 − 1.028070I
−13.43700 − 1.72652I 0
u = −1.50495 − 0.04038I
a = −0.05721 + 1.58096I
b = −0.621244 + 1.028070I
−13.43700 + 1.72652I 0
u = −1.48763 + 0.28205I
a = −0.310225 + 0.302985I
b = −0.469343 + 0.449057I
−8.77346 + 3.93861I 0
u = −1.48763 − 0.28205I
a = −0.310225 − 0.302985I
b = −0.469343 − 0.449057I
−8.77346 − 3.93861I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52846 + 0.08843I
a = −0.200446 − 1.066770I
b = −0.674054 − 0.660141I
−8.98195 + 2.48583I 0
u = −1.52846 − 0.08843I
a = −0.200446 + 1.066770I
b = −0.674054 + 0.660141I
−8.98195 − 2.48583I 0
u = −0.137852 + 0.423543I
a = −1.009920 + 0.386748I
b = 0.020374 + 0.995208I
−1.96447 + 3.28364I 2.37619 − 3.75916I
u = −0.137852 − 0.423543I
a = −1.009920 − 0.386748I
b = 0.020374 − 0.995208I
−1.96447 − 3.28364I 2.37619 + 3.75916I
u = 0.030826 + 0.442889I
a = 1.84670 + 0.42488I
b = 0.040269 − 0.374904I
−1.71164 − 2.03068I 0.92011 + 3.46679I
u = 0.030826 − 0.442889I
a = 1.84670 − 0.42488I
b = 0.040269 + 0.374904I
−1.71164 + 2.03068I 0.92011 − 3.46679I
u = −1.56813 + 0.05575I
a = −0.722442 − 1.139070I
b = −1.039110 − 0.697192I
−12.0123 + 7.8686I 0
u = −1.56813 − 0.05575I
a = −0.722442 + 1.139070I
b = −1.039110 + 0.697192I
−12.0123 − 7.8686I 0
u = 0.040683 + 0.360824I
a = −0.575408 + 1.142610I
b = 0.479990 + 0.395254I
1.156200 + 0.168786I 8.35325 − 0.17221I
u = 0.040683 − 0.360824I
a = −0.575408 − 1.142610I
b = 0.479990 − 0.395254I
1.156200 − 0.168786I 8.35325 + 0.17221I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.199873
a = −2.63962
b = 0.777741
1.05923 11.4410
u = −0.0730236 + 0.0762121I
a = 9.91388 + 6.35989I
b = 1.135790 − 0.225281I
0.958085 − 1.026070I 4.35276 − 0.71517I
u = −0.0730236 − 0.0762121I
a = 9.91388 − 6.35989I
b = 1.135790 + 0.225281I
0.958085 + 1.026070I 4.35276 + 0.71517I
16
II. I
u
2
= hb − a + 1, a
8
− 7a
7
+ 18a
6
− 19a
5
+ 3a
4
+ 7a
3
− 3a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
11
=
a
a − 1
a
6
=
a
2
− a − 1
a
2
− 2a + 1
a
10
=
1
a − 1
a
9
=
−a
5
+ 4a
4
− 4a
3
− a
2
+ 2a + 1
−a
5
+ 5a
4
− 9a
3
+ 7a
2
− a − 1
a
7
=
0
−a
7
+ 8a
6
− 25a
5
+ 37a
4
− 23a
3
+ 3a + 2
a
12
=
a
a
2
− 2a + 1
a
8
=
0
−a
7
+ 8a
6
− 25a
5
+ 37a
4
− 23a
3
+ 3a + 2
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
7
+ 2a
6
− 32a
5
+ 73a
4
− 44a
3
− 25a
2
+ 18a + 21
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
10
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
6
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
8
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
9
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
11
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
12
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
6
, c
9
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.108090 + 0.747508I
b = 0.108090 + 0.747508I
−3.80435 + 2.57849I −1.56478 − 3.68514I
u = 1.00000
a = 1.108090 − 0.747508I
b = 0.108090 − 0.747508I
−3.80435 − 2.57849I −1.56478 + 3.68514I
u = 1.00000
a = 1.46364
b = 0.463640
−0.799899 9.95010
u = 1.00000
a = −0.334527 + 0.318930I
b = −1.334530 + 0.318930I
0.73474 − 6.44354I 8.02705 + 7.90662I
u = 1.00000
a = −0.334527 − 0.318930I
b = −1.334530 − 0.318930I
0.73474 + 6.44354I 8.02705 − 7.90662I
u = 1.00000
a = −0.371002
b = −1.37100
4.85780 14.7400
u = 1.00000
a = 2.18012 + 0.26860I
b = 1.180120 + 0.268597I
−0.604279 + 1.131230I −3.30729 + 4.28492I
u = 1.00000
a = 2.18012 − 0.26860I
b = 1.180120 − 0.268597I
−0.604279 − 1.131230I −3.30729 − 4.28492I
20
III. I
u
3
= hb − 1, 12u
2
+ 17a + 11u + 9, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
2
+ u − 1
a
11
=
−
12
17
u
2
−
11
17
u −
9
17
1
a
6
=
1
289
u
2
−
366
289
u −
63
289
20
17
u
2
+
24
17
u −
19
17
a
10
=
−
12
17
u
2
−
11
17
u −
26
17
1
a
9
=
−0.484429u
2
− 1.69896u − 0.480969
39
17
u
2
+
23
17
u −
26
17
a
7
=
−2u + 1
5u
2
+ 2u − 4
a
12
=
−
12
17
u
2
−
11
17
u −
9
17
1
a
8
=
−u
2u
2
+ u − 2
a
3
=
−u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8258
289
u
2
−
4979
289
u −
3522
289
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
3
+ u
2
− 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
17(17u
3
− 10u
2
− u + 1)
c
6
u
3
+ 3u
2
+ 2u − 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
17(17u
3
+ 23u
2
+ 8u + 1)
c
9
u
3
− 3u
2
+ 2u + 1
c
10
(u + 1)
3
c
11
u
3
c
12
(u − 1)
3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
3
− y
2
+ 2y −1
c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
5
289(289y
3
− 134y
2
+ 21y −1)
c
6
, c
9
y
3
− 5y
2
+ 10y −1
c
8
289(289y
3
− 257y
2
+ 18y −1)
c
10
, c
12
(y −1)
3
c
11
y
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.113478 + 0.440719I
b = 1.00000
4.66906 + 2.82812I 9.0758 − 50.1835I
u = −0.877439 − 0.744862I
a = −0.113478 − 0.440719I
b = 1.00000
4.66906 − 2.82812I 9.0758 + 50.1835I
u = 0.754878
a = −1.42010
b = 1.00000
0.531480 −8.90930
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
8
)(u
3
+ u
2
− 1)(u
113
− 10u
112
+ ··· + u − 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)(u
113
− 2u
112
+ ··· + 896u − 256)
c
4
((u + 1)
8
)(u
3
− u
2
+ 1)(u
113
− 10u
112
+ ··· + u − 1)
c
5
289(17u
3
− 10u
2
− u + 1)(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (17u
113
+ 212u
112
+ ··· − 115224u − 34421)
c
6
(u
3
+ 3u
2
+ 2u − 1)(u
8
+ 3u
7
+ ··· + 4u + 1)
· (u
113
+ 3u
112
+ ··· + 3u + 1)
c
7
u
8
(u
3
+ u
2
+ 2u + 1)(u
113
− 2u
112
+ ··· + 896u − 256)
c
8
289(17u
3
+ 23u
2
+ 8u + 1)(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (17u
113
+ 219u
112
+ ··· + 16199u + 2539)
c
9
(u
3
− 3u
2
+ 2u + 1)(u
8
− 3u
7
+ ··· − 4u + 1)
· (u
113
+ 3u
112
+ ··· + 3u + 1)
c
10
(u + 1)
3
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
113
+ 5u
112
+ ··· − 1158u + 289)
c
11
u
3
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
113
+ 2u
112
+ ··· − 41820u − 2312)
c
12
(u − 1)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
113
+ 5u
112
+ ··· − 1158u + 289)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
8
)(y
3
− y
2
+ 2y −1)(y
113
− 100y
112
+ ··· − 13y −1)
c
3
, c
7
y
8
(y
3
+ 3y
2
+ 2y −1)(y
113
− 48y
112
+ ··· + 1425408y −65536)
c
5
83521(289y
3
− 134y
2
+ 21y −1)
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (289y
113
− 1016y
112
+ ··· − 6580973566y −1184805241)
c
6
, c
9
(y
3
− 5y
2
+ 10y −1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
113
+ 61y
112
+ ··· + 19y −1)
c
8
83521(289y
3
− 257y
2
+ 18y −1)
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (289y
113
+ 6473y
112
+ ··· − 380827737y −6446521)
c
10
, c
12
(y −1)
3
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
113
− 69y
112
+ ··· + 10227136y −83521)
c
11
y
3
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
113
+ 18y
112
+ ··· + 117380240y −5345344)
26
