12a
0781
(K12a
0781
)
A knot diagram
1
Linearized knot diagam
3 8 10 1 12 9 2 11 4 7 6 5
Solving Sequence
1,4 5,9
10 3 2 12 6 7 11 8
c
4
c
9
c
3
c
1
c
12
c
5
c
6
c
11
c
8
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.86638 × 10
158
u
97
− 6.01764 × 10
158
u
96
+ ··· + 2.14603 × 10
159
b + 2.00594 × 10
160
,
− 5.79119 × 10
159
u
97
− 1.25565 × 10
160
u
96
+ ··· + 4.07746 × 10
160
a − 2.67995 × 10
161
,
u
98
+ 2u
97
+ ··· + 145u + 19i
I
u
2
= h−u
17
− u
16
+ ··· + b − 7u, u
19
+ u
18
+ ··· + a − 2, u
20
+ u
19
+ ··· + 14u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 118 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−3.87 × 10
158
u
97
− 6.02 × 10
158
u
96
+ · · · + 2.15 × 10
159
b + 2.01 ×
10
160
, −5.79 × 10
159
u
97
− 1.26 × 10
160
u
96
+ · · · + 4.08 × 10
160
a − 2.68 ×
10
161
, u
98
+ 2u
97
+ · · · + 145u + 19i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
0.142029u
97
+ 0.307949u
96
+ ··· + 14.8737u + 6.57260
0.180164u
97
+ 0.280408u
96
+ ··· − 42.6979u − 9.34719
a
10
=
0.322194u
97
+ 0.588357u
96
+ ··· − 27.8242u − 2.77458
0.180164u
97
+ 0.280408u
96
+ ··· − 42.6979u − 9.34719
a
3
=
−0.381407u
97
− 1.32617u
96
+ ··· − 330.089u − 43.7156
−0.612689u
97
− 1.81913u
96
+ ··· − 217.338u − 25.7105
a
2
=
0.949339u
97
+ 2.86582u
96
+ ··· + 583.792u + 72.2286
−0.741603u
97
− 1.00302u
96
+ ··· + 129.459u + 23.7288
a
12
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
0.695299u
97
+ 1.05722u
96
+ ··· + 35.9036u − 7.81290
0.504732u
97
+ 1.15514u
96
+ ··· + 214.872u + 27.8479
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
8
=
0.299319u
97
+ 0.487641u
96
+ ··· − 41.9938u − 4.74001
0.221229u
97
+ 0.313332u
96
+ ··· − 46.7994u − 11.0038
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.594694u
97
− 0.189522u
96
+ ··· + 391.120u + 68.2722
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
+ 41u
97
+ ··· + 261481u + 14641
c
2
, c
7
u
98
+ u
97
+ ··· + 99u + 121
c
3
, c
9
u
98
+ u
97
+ ··· − 721u + 97
c
4
, c
5
, c
11
c
12
u
98
− 2u
97
+ ··· − 145u + 19
c
6
u
98
+ 9u
97
+ ··· + 2276u + 1393
c
8
u
98
+ 11u
97
+ ··· + 75735u + 8193
c
10
u
98
+ 2u
96
+ ··· + 35u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
+ 43y
97
+ ··· + 4650552599y + 214358881
c
2
, c
7
y
98
− 41y
97
+ ··· − 261481y + 14641
c
3
, c
9
y
98
+ 57y
97
+ ··· + 98437y + 9409
c
4
, c
5
, c
11
c
12
y
98
+ 120y
97
+ ··· + 9147y + 361
c
6
y
98
− 19y
97
+ ··· − 21330618y + 1940449
c
8
y
98
− 39y
97
+ ··· − 2930818359y + 67125249
c
10
y
98
+ 4y
97
+ ··· − 33y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.137141 + 0.987892I
a = 0.230020 + 0.804402I
b = −0.361279 − 0.163257I
2.31819 − 2.56083I 0
u = 0.137141 − 0.987892I
a = 0.230020 − 0.804402I
b = −0.361279 + 0.163257I
2.31819 + 2.56083I 0
u = 0.166366 + 0.972385I
a = −0.85201 + 1.14892I
b = 0.218924 − 0.768619I
2.73435 − 3.04932I 0
u = 0.166366 − 0.972385I
a = −0.85201 − 1.14892I
b = 0.218924 + 0.768619I
2.73435 + 3.04932I 0
u = 0.610470 + 0.769870I
a = 0.720273 + 0.857084I
b = −0.580393 + 0.822591I
1.77465 + 0.07560I 0
u = 0.610470 − 0.769870I
a = 0.720273 − 0.857084I
b = −0.580393 − 0.822591I
1.77465 − 0.07560I 0
u = −0.688346 + 0.689053I
a = −0.762864 + 0.902008I
b = 0.382068 + 1.001880I
1.55613 + 4.28745I 0
u = −0.688346 − 0.689053I
a = −0.762864 − 0.902008I
b = 0.382068 − 1.001880I
1.55613 − 4.28745I 0
u = 0.554714 + 0.875374I
a = −1.358010 − 0.254617I
b = 0.598739 − 1.141800I
2.06361 − 7.94941I 0
u = 0.554714 − 0.875374I
a = −1.358010 + 0.254617I
b = 0.598739 + 1.141800I
2.06361 + 7.94941I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611856 + 0.844401I
a = 1.36767 − 0.45827I
b = −0.65879 − 1.26522I
0.11354 + 13.83020I 0
u = −0.611856 − 0.844401I
a = 1.36767 + 0.45827I
b = −0.65879 + 1.26522I
0.11354 − 13.83020I 0
u = 0.378895 + 0.863047I
a = 0.773678 + 0.391988I
b = −1.157120 − 0.242761I
3.27376 − 7.50273I 0
u = 0.378895 − 0.863047I
a = 0.773678 − 0.391988I
b = −1.157120 + 0.242761I
3.27376 + 7.50273I 0
u = −0.280340 + 0.846709I
a = −0.967675 + 0.193226I
b = 0.959178 − 0.351785I
4.49747 + 2.41932I 0
u = −0.280340 − 0.846709I
a = −0.967675 − 0.193226I
b = 0.959178 + 0.351785I
4.49747 − 2.41932I 0
u = −0.442962 + 0.743239I
a = 2.00371 − 0.08194I
b = −0.298666 − 1.186690I
−4.58313 + 5.44546I 0
u = −0.442962 − 0.743239I
a = 2.00371 + 0.08194I
b = −0.298666 + 1.186690I
−4.58313 − 5.44546I 0
u = −0.842808 + 0.109827I
a = 0.162998 − 0.654796I
b = 0.548812 − 1.125980I
−2.12287 − 9.02759I 0
u = −0.842808 − 0.109827I
a = 0.162998 + 0.654796I
b = 0.548812 + 1.125980I
−2.12287 + 9.02759I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570987 + 1.031320I
a = 0.186668 − 0.231039I
b = 0.304842 + 0.732776I
2.56510 − 1.22819I 0
u = 0.570987 − 1.031320I
a = 0.186668 + 0.231039I
b = 0.304842 − 0.732776I
2.56510 + 1.22819I 0
u = 0.802778 + 0.021479I
a = −0.011290 − 0.591224I
b = −0.426499 − 1.006760I
−0.53152 + 3.46212I 0
u = 0.802778 − 0.021479I
a = −0.011290 + 0.591224I
b = −0.426499 + 1.006760I
−0.53152 − 3.46212I 0
u = 0.415744 + 0.658904I
a = 1.127210 + 0.703107I
b = −0.783030 + 0.433834I
0.02958 − 2.42963I 0
u = 0.415744 − 0.658904I
a = 1.127210 − 0.703107I
b = −0.783030 − 0.433834I
0.02958 + 2.42963I 0
u = −0.653186 + 0.422345I
a = −0.775156 + 0.961126I
b = −0.226938 + 0.721731I
0.795805 + 0.359381I 0
u = −0.653186 − 0.422345I
a = −0.775156 − 0.961126I
b = −0.226938 − 0.721731I
0.795805 − 0.359381I 0
u = −0.521626 + 1.152900I
a = −0.164049 − 0.313481I
b = −0.471141 + 0.875506I
1.67650 − 4.29412I 0
u = −0.521626 − 1.152900I
a = −0.164049 + 0.313481I
b = −0.471141 − 0.875506I
1.67650 + 4.29412I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358454 + 0.628610I
a = 1.361740 + 0.228560I
b = −0.565062 + 0.876393I
−0.13900 − 2.00593I −2.00000 + 5.23973I
u = 0.358454 − 0.628610I
a = 1.361740 − 0.228560I
b = −0.565062 − 0.876393I
−0.13900 + 2.00593I −2.00000 − 5.23973I
u = −0.171064 + 1.267530I
a = −0.171313 − 0.282165I
b = −0.151078 + 1.312910I
−1.93193 + 0.63423I 0
u = −0.171064 − 1.267530I
a = −0.171313 + 0.282165I
b = −0.151078 − 1.312910I
−1.93193 − 0.63423I 0
u = −0.165380 + 0.654264I
a = 2.04693 − 1.66188I
b = −0.360482 − 1.102940I
−0.16728 + 5.64528I 3.96766 − 9.01799I
u = −0.165380 − 0.654264I
a = 2.04693 + 1.66188I
b = −0.360482 + 1.102940I
−0.16728 − 5.64528I 3.96766 + 9.01799I
u = 0.014486 + 0.655341I
a = −2.39035 − 0.41672I
b = 0.363742 − 0.762315I
2.67589 + 0.10239I 6.77275 − 0.25907I
u = 0.014486 − 0.655341I
a = −2.39035 + 0.41672I
b = 0.363742 + 0.762315I
2.67589 − 0.10239I 6.77275 + 0.25907I
u = −0.374162 + 0.523254I
a = −2.17013 + 0.64065I
b = 0.814672 + 1.140940I
−2.17368 + 6.14507I −5.79390 − 11.50345I
u = −0.374162 − 0.523254I
a = −2.17013 − 0.64065I
b = 0.814672 − 1.140940I
−2.17368 − 6.14507I −5.79390 + 11.50345I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618322 + 0.174501I
a = 0.575144 + 0.904167I
b = 0.643407 + 0.343705I
0.18608 − 4.29943I −2.00000 + 5.89012I
u = 0.618322 − 0.174501I
a = 0.575144 − 0.904167I
b = 0.643407 − 0.343705I
0.18608 + 4.29943I −2.00000 − 5.89012I
u = −0.576373 + 0.171283I
a = −0.136597 − 1.163900I
b = 0.179352 − 1.271950I
−6.31047 − 1.94770I −10.09284 + 1.23846I
u = −0.576373 − 0.171283I
a = −0.136597 + 1.163900I
b = 0.179352 + 1.271950I
−6.31047 + 1.94770I −10.09284 − 1.23846I
u = −0.186340 + 0.569123I
a = −1.79719 − 1.35684I
b = 0.342965 + 1.315330I
−3.42099 − 0.62101I −3.59254 − 2.97459I
u = −0.186340 − 0.569123I
a = −1.79719 + 1.35684I
b = 0.342965 − 1.315330I
−3.42099 + 0.62101I −3.59254 + 2.97459I
u = −0.420595 + 0.385539I
a = −0.699784 − 0.161702I
b = −0.549564 + 1.230270I
−2.55373 − 3.25947I −5.59353 + 1.58847I
u = −0.420595 − 0.385539I
a = −0.699784 + 0.161702I
b = −0.549564 − 1.230270I
−2.55373 + 3.25947I −5.59353 − 1.58847I
u = −0.100871 + 0.548112I
a = −0.238571 − 0.196791I
b = −0.14359 + 1.69779I
−3.65711 + 1.68776I −0.43441 − 6.60068I
u = −0.100871 − 0.548112I
a = −0.238571 + 0.196791I
b = −0.14359 − 1.69779I
−3.65711 − 1.68776I −0.43441 + 6.60068I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.485283 + 0.249970I
a = 0.577679 + 0.141065I
b = 0.166741 + 0.896005I
−1.23374 − 0.98729I −4.83340 + 4.29750I
u = 0.485283 − 0.249970I
a = 0.577679 − 0.141065I
b = 0.166741 − 0.896005I
−1.23374 + 0.98729I −4.83340 − 4.29750I
u = −0.04134 + 1.49424I
a = −0.058145 + 0.999192I
b = 0.243456 − 1.385820I
3.54424 − 1.85820I 0
u = −0.04134 − 1.49424I
a = −0.058145 − 0.999192I
b = 0.243456 + 1.385820I
3.54424 + 1.85820I 0
u = 0.460076 + 0.190762I
a = 0.353545 − 0.271358I
b = 0.541966 + 0.415179I
−1.28966 − 0.61811I −6.52615 + 1.35515I
u = 0.460076 − 0.190762I
a = 0.353545 + 0.271358I
b = 0.541966 − 0.415179I
−1.28966 + 0.61811I −6.52615 − 1.35515I
u = −0.15609 + 1.54585I
a = 1.181780 − 0.287894I
b = −0.174583 − 0.617271I
7.39345 + 3.03622I 0
u = −0.15609 − 1.54585I
a = 1.181780 + 0.287894I
b = −0.174583 + 0.617271I
7.39345 − 3.03622I 0
u = 0.01305 + 1.56446I
a = −1.69680 − 0.52644I
b = 0.210381 + 0.592614I
5.82036 − 4.46441I 0
u = 0.01305 − 1.56446I
a = −1.69680 + 0.52644I
b = 0.210381 − 0.592614I
5.82036 + 4.46441I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07823 + 1.56766I
a = 2.11122 + 0.61414I
b = −1.09738 − 1.14460I
4.96425 + 7.62683I 0
u = −0.07823 − 1.56766I
a = 2.11122 − 0.61414I
b = −1.09738 + 1.14460I
4.96425 − 7.62683I 0
u = −0.02981 + 1.57843I
a = 1.35994 + 1.11226I
b = −0.692776 − 1.177120I
3.95185 + 0.08599I 0
u = −0.02981 − 1.57843I
a = 1.35994 − 1.11226I
b = −0.692776 + 1.177120I
3.95185 − 0.08599I 0
u = −0.02233 + 1.59578I
a = −0.020317 + 1.102450I
b = 0.11972 − 1.92321I
3.88088 + 2.10003I 0
u = −0.02233 − 1.59578I
a = −0.020317 − 1.102450I
b = 0.11972 + 1.92321I
3.88088 − 2.10003I 0
u = −0.094846 + 0.389321I
a = 4.43128 + 0.99835I
b = 0.242392 − 0.738058I
−1.03894 − 4.49602I −1.16453 + 1.43492I
u = −0.094846 − 0.389321I
a = 4.43128 − 0.99835I
b = 0.242392 + 0.738058I
−1.03894 + 4.49602I −1.16453 − 1.43492I
u = 0.11805 + 1.59682I
a = −1.67039 − 0.17320I
b = 1.023240 − 0.524395I
7.72303 − 4.39617I 0
u = 0.11805 − 1.59682I
a = −1.67039 + 0.17320I
b = 1.023240 + 0.524395I
7.72303 + 4.39617I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07111 + 1.60211I
a = −1.59625 + 0.50986I
b = 0.913816 − 0.992614I
7.54207 − 3.43202I 0
u = 0.07111 − 1.60211I
a = −1.59625 − 0.50986I
b = 0.913816 + 0.992614I
7.54207 + 3.43202I 0
u = −0.04256 + 1.61712I
a = −1.337170 + 0.139134I
b = 0.403604 + 1.261840I
7.77660 + 6.39657I 0
u = −0.04256 − 1.61712I
a = −1.337170 − 0.139134I
b = 0.403604 − 1.261840I
7.77660 − 6.39657I 0
u = 0.00894 + 1.62163I
a = 1.58969 − 0.17949I
b = −0.530973 + 0.987647I
10.68410 − 0.01739I 0
u = 0.00894 − 1.62163I
a = 1.58969 + 0.17949I
b = −0.530973 − 0.987647I
10.68410 + 0.01739I 0
u = −0.11941 + 1.63254I
a = −1.70188 − 0.61766I
b = 0.434133 + 1.128170I
3.58837 + 7.53265I 0
u = −0.11941 − 1.63254I
a = −1.70188 + 0.61766I
b = 0.434133 − 1.128170I
3.58837 − 7.53265I 0
u = −0.21182 + 1.63530I
a = 1.125310 + 0.040627I
b = −0.472852 − 1.209280I
9.43792 + 7.70449I 0
u = −0.21182 − 1.63530I
a = 1.125310 − 0.040627I
b = −0.472852 + 1.209280I
9.43792 − 7.70449I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08125 + 1.65510I
a = 1.53597 − 0.46269I
b = −1.235110 + 0.484671I
13.18670 + 3.83974I 0
u = −0.08125 − 1.65510I
a = 1.53597 + 0.46269I
b = −1.235110 − 0.484671I
13.18670 − 3.83974I 0
u = 0.10765 + 1.65764I
a = −1.57531 − 0.50340I
b = 1.43319 + 0.32312I
11.9782 − 9.3939I 0
u = 0.10765 − 1.65764I
a = −1.57531 + 0.50340I
b = 1.43319 − 0.32312I
11.9782 + 9.3939I 0
u = 0.17257 + 1.65870I
a = −1.201680 + 0.091693I
b = 0.694229 − 1.125240I
10.13160 − 2.93485I 0
u = 0.17257 − 1.65870I
a = −1.201680 − 0.091693I
b = 0.694229 + 1.125240I
10.13160 + 2.93485I 0
u = −0.18192 + 1.66014I
a = −1.62352 − 0.35355I
b = 0.76100 + 1.36103I
8.6337 + 16.8973I 0
u = −0.18192 − 1.66014I
a = −1.62352 + 0.35355I
b = 0.76100 − 1.36103I
8.6337 − 16.8973I 0
u = 0.16103 + 1.66841I
a = 1.57490 − 0.41047I
b = −0.74571 + 1.22077I
10.7750 − 10.7337I 0
u = 0.16103 − 1.66841I
a = 1.57490 + 0.41047I
b = −0.74571 − 1.22077I
10.7750 + 10.7337I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04727 + 1.70037I
a = 0.773964 − 0.994985I
b = −0.293096 + 0.568530I
12.16880 − 3.90877I 0
u = 0.04727 − 1.70037I
a = 0.773964 + 0.994985I
b = −0.293096 − 0.568530I
12.16880 + 3.90877I 0
u = −0.04403 + 1.71169I
a = −0.862384 + 0.143078I
b = 0.777918 − 0.358196I
12.24730 − 2.60627I 0
u = −0.04403 − 1.71169I
a = −0.862384 − 0.143078I
b = 0.777918 + 0.358196I
12.24730 + 2.60627I 0
u = 0.09386 + 1.71659I
a = 0.557242 + 0.039274I
b = −0.436861 − 0.204497I
12.44500 − 3.65355I 0
u = 0.09386 − 1.71659I
a = 0.557242 − 0.039274I
b = −0.436861 + 0.204497I
12.44500 + 3.65355I 0
u = −0.227727 + 0.143186I
a = 0.68923 + 2.57241I
b = −0.409517 − 0.070127I
1.51335 + 0.46670I 5.87267 + 0.92101I
u = −0.227727 − 0.143186I
a = 0.68923 − 2.57241I
b = −0.409517 + 0.070127I
1.51335 − 0.46670I 5.87267 − 0.92101I
14
II.
I
u
2
= h−u
17
−u
16
+· · ·+b−7u, u
19
+u
18
+· · ·+a−2, u
20
+u
19
+· · ·+14u
2
+1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−u
19
− u
18
+ ··· − 12u + 2
u
17
+ u
16
+ ··· + 4u
2
+ 7u
a
10
=
−u
19
− u
18
+ ··· − 5u + 2
u
17
+ u
16
+ ··· + 4u
2
+ 7u
a
3
=
u
19
+ 2u
18
+ ··· + 14u + 4
−u
18
− u
17
+ ··· − 2u − 4
a
2
=
u
19
+ 3u
18
+ ··· + 10u + 6
2u
19
+ u
18
+ ··· + 7u − 4
a
12
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
8
− u
7
− 6u
6
− 5u
5
− 12u
4
− 8u
3
− 9u
2
− 4u − 2
u
16
+ u
15
+ ··· + 10u
2
+ 2
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
8
=
−u
19
− u
18
+ ··· − 7u + 2
2u
17
+ 2u
16
+ ··· + 6u
2
+ 9u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −3u
19
− 9u
18
− 44u
17
− 111u
16
− 270u
15
− 572u
14
− 908u
13
− 1603u
12
− 1837u
11
−
2667u
10
−2300u
9
−2702u
8
−1748u
7
−1640u
6
−743u
5
−560u
4
−146u
3
−103u
2
−6u −18
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 10u
19
+ ··· − 12u + 1
c
2
u
20
− 5u
18
+ ··· − 6u
2
+ 1
c
3
u
20
+ 10u
18
+ ··· + 9u
2
+ 1
c
4
, c
5
u
20
+ u
19
+ ··· + 14u
2
+ 1
c
6
u
20
− 3u
17
+ ··· + u + 1
c
7
u
20
− 5u
18
+ ··· − 6u
2
+ 1
c
8
u
20
− 6u
18
+ ··· + 8u + 1
c
9
u
20
+ 10u
18
+ ··· + 9u
2
+ 1
c
10
u
20
− u
19
+ ··· + 3u
3
+ 1
c
11
, c
12
u
20
− u
19
+ ··· + 14u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 10y
19
+ ··· + 8y + 1
c
2
, c
7
y
20
− 10y
19
+ ··· − 12y + 1
c
3
, c
9
y
20
+ 20y
19
+ ··· + 18y + 1
c
4
, c
5
, c
11
c
12
y
20
+ 27y
19
+ ··· + 28y + 1
c
6
y
20
− 6y
18
+ ··· + 3y + 1
c
8
y
20
− 12y
19
+ ··· − 10y + 1
c
10
y
20
+ 3y
19
+ ··· − 6y
2
+ 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.438006 + 0.878445I
a = −0.935242 − 0.125364I
b = −0.021457 + 0.630340I
2.31296 + 2.05174I 1.17203 − 4.47545I
u = −0.438006 − 0.878445I
a = −0.935242 + 0.125364I
b = −0.021457 − 0.630340I
2.31296 − 2.05174I 1.17203 + 4.47545I
u = 0.241310 + 1.076970I
a = 0.672790 − 0.624640I
b = 0.261388 + 0.832933I
0.94665 + 3.41778I −2.10963 − 2.67427I
u = 0.241310 − 1.076970I
a = 0.672790 + 0.624640I
b = 0.261388 − 0.832933I
0.94665 − 3.41778I −2.10963 + 2.67427I
u = 0.029312 + 1.169850I
a = 0.211845 − 0.143345I
b = 0.111376 + 1.338970I
−1.39360 − 1.49675I 0.44989 + 5.16062I
u = 0.029312 − 1.169850I
a = 0.211845 + 0.143345I
b = 0.111376 − 1.338970I
−1.39360 + 1.49675I 0.44989 − 5.16062I
u = −0.515314 + 0.484534I
a = −0.69078 + 1.33867I
b = 0.367678 + 0.567298I
1.15434 + 1.40411I 1.21689 − 5.83578I
u = −0.515314 − 0.484534I
a = −0.69078 − 1.33867I
b = 0.367678 − 0.567298I
1.15434 − 1.40411I 1.21689 + 5.83578I
u = 0.267172 + 0.425868I
a = 2.48151 + 2.41051I
b = −0.445502 + 0.945152I
−1.14315 − 5.32835I −2.85961 + 8.67698I
u = 0.267172 − 0.425868I
a = 2.48151 − 2.41051I
b = −0.445502 − 0.945152I
−1.14315 + 5.32835I −2.85961 − 8.67698I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00774 + 1.53980I
a = −0.44584 + 1.38603I
b = 0.12085 − 1.74311I
2.50021 + 1.15020I −6.52944 − 0.32380I
u = 0.00774 − 1.53980I
a = −0.44584 − 1.38603I
b = 0.12085 + 1.74311I
2.50021 − 1.15020I −6.52944 + 0.32380I
u = 0.08075 + 1.57466I
a = −1.88301 + 0.09310I
b = 0.611729 − 1.010130I
5.92468 − 6.59473I 0.68945 + 5.87752I
u = 0.08075 − 1.57466I
a = −1.88301 − 0.09310I
b = 0.611729 + 1.010130I
5.92468 + 6.59473I 0.68945 − 5.87752I
u = −0.14014 + 1.57579I
a = 1.45061 − 0.30552I
b = −0.741762 − 0.651616I
8.25947 + 3.73957I 5.13541 − 1.07329I
u = −0.14014 − 1.57579I
a = 1.45061 + 0.30552I
b = −0.741762 + 0.651616I
8.25947 − 3.73957I 5.13541 + 1.07329I
u = 0.028025 + 0.334471I
a = 1.61244 − 2.00478I
b = −0.11609 + 1.57293I
−4.11322 + 1.27469I −11.22263 + 0.57420I
u = 0.028025 − 0.334471I
a = 1.61244 + 2.00478I
b = −0.11609 − 1.57293I
−4.11322 − 1.27469I −11.22263 − 0.57420I
u = −0.06085 + 1.71955I
a = 0.525668 + 0.813049I
b = −0.148214 − 0.576831I
11.87060 + 3.80475I −10.44237 − 1.53790I
u = −0.06085 − 1.71955I
a = 0.525668 − 0.813049I
b = −0.148214 + 0.576831I
11.87060 − 3.80475I −10.44237 + 1.53790I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 10u
19
+ ··· − 12u + 1)(u
98
+ 41u
97
+ ··· + 261481u + 14641)
c
2
(u
20
− 5u
18
+ ··· − 6u
2
+ 1)(u
98
+ u
97
+ ··· + 99u + 121)
c
3
(u
20
+ 10u
18
+ ··· + 9u
2
+ 1)(u
98
+ u
97
+ ··· − 721u + 97)
c
4
, c
5
(u
20
+ u
19
+ ··· + 14u
2
+ 1)(u
98
− 2u
97
+ ··· − 145u + 19)
c
6
(u
20
− 3u
17
+ ··· + u + 1)(u
98
+ 9u
97
+ ··· + 2276u + 1393)
c
7
(u
20
− 5u
18
+ ··· − 6u
2
+ 1)(u
98
+ u
97
+ ··· + 99u + 121)
c
8
(u
20
− 6u
18
+ ··· + 8u + 1)(u
98
+ 11u
97
+ ··· + 75735u + 8193)
c
9
(u
20
+ 10u
18
+ ··· + 9u
2
+ 1)(u
98
+ u
97
+ ··· − 721u + 97)
c
10
(u
20
− u
19
+ ··· + 3u
3
+ 1)(u
98
+ 2u
96
+ ··· + 35u + 1)
c
11
, c
12
(u
20
− u
19
+ ··· + 14u
2
+ 1)(u
98
− 2u
97
+ ··· − 145u + 19)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 10y
19
+ ··· + 8y + 1)
· (y
98
+ 43y
97
+ ··· + 4650552599y + 214358881)
c
2
, c
7
(y
20
− 10y
19
+ ··· − 12y + 1)(y
98
− 41y
97
+ ··· − 261481y + 14641)
c
3
, c
9
(y
20
+ 20y
19
+ ··· + 18y + 1)(y
98
+ 57y
97
+ ··· + 98437y + 9409)
c
4
, c
5
, c
11
c
12
(y
20
+ 27y
19
+ ··· + 28y + 1)(y
98
+ 120y
97
+ ··· + 9147y + 361)
c
6
(y
20
− 6y
18
+ ··· + 3y + 1)
· (y
98
− 19y
97
+ ··· − 21330618y + 1940449)
c
8
(y
20
− 12y
19
+ ··· − 10y + 1)
· (y
98
− 39y
97
+ ··· − 2930818359y + 67125249)
c
10
(y
20
+ 3y
19
+ ··· − 6y
2
+ 1)(y
98
+ 4y
97
+ ··· − 33y + 1)
21
