12a
0900
(K12a
0900
)
A knot diagram
1
Linearized knot diagam
4 6 8 10 2 12 3 11 5 1 7 9
Solving Sequence
3,7
8
4,12
6 2 1 5 11 9 10
c
7
c
3
c
6
c
2
c
1
c
5
c
11
c
8
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.52837 × 10
1076
u
168
+ 9.95193 × 10
1076
u
167
+ ··· + 5.83099 × 10
1076
b − 7.56901 × 10
1081
,
7.17815 × 10
1082
u
168
+ 8.07968 × 10
1082
u
167
+ ··· + 2.21108 × 10
1082
a − 6.04767 × 10
1087
,
u
169
+ 2u
168
+ ··· − 373810u − 75839i
I
u
2
= h−6.31697 × 10
64
u
45
− 2.06195 × 10
65
u
44
+ ··· + 7.62817 × 10
64
b − 3.63136 × 10
65
,
− 1.17290 × 10
66
u
45
− 1.34273 × 10
66
u
44
+ ··· + 3.81409 × 10
65
a + 1.51650 × 10
66
, u
46
+ u
45
+ ··· − 4u − 1i
* 2 irreducible components of dim
C
= 0, with total 215 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
= h8.53 × 10
1076
u
168
+ 9.95 × 10
1076
u
167
+ · · · + 5.83 × 10
1076
b − 7.57 ×
10
1081
, 7.18 × 10
1082
u
168
+ 8.08 × 10
1082
u
167
+ · · · + 2.21 × 10
1082
a − 6.05 ×
10
1087
, u
169
+ 2u
168
+ · · · − 373810u − 75839i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
12
=
−3.24644u
168
− 3.65417u
167
+ ··· + 1.05369 × 10
6
u + 273516.
−1.46259u
168
− 1.70673u
167
+ ··· + 491774.u + 129807.
a
6
=
−1.43362u
168
− 1.83638u
167
+ ··· + 526370.u + 144064.
−0.217014u
168
− 0.678800u
167
+ ··· + 186090.u + 61996.7
a
2
=
−2.16396u
168
− 2.54382u
167
+ ··· + 731440.u + 193639.
0.821662u
168
+ 0.668477u
167
+ ··· − 197557.u − 43523.6
a
1
=
−1.70674u
168
− 2.18349u
167
+ ··· + 624681.u + 170586.
0.971008u
168
+ 0.901172u
167
+ ··· − 263253.u − 62493.9
a
5
=
−1.14675u
168
− 1.51928u
167
+ ··· + 432623.u + 120017.
−2.14197u
168
− 2.47607u
167
+ ··· + 714895.u + 187876.
a
11
=
−4.70903u
168
− 5.36090u
167
+ ··· + 1.54547 × 10
6
u + 403323.
−1.46259u
168
− 1.70673u
167
+ ··· + 491774.u + 129807.
a
9
=
0.225879u
168
+ 0.766581u
167
+ ··· − 213899.u − 72749.7
0.107099u
168
+ 0.0596876u
167
+ ··· − 17426.1u − 2380.89
a
10
=
−2.78009u
168
− 2.70356u
167
+ ··· + 797029.u + 193308.
−0.108139u
168
− 0.159883u
167
+ ··· + 42772.8u + 11675.4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.62131u
168
− 6.90171u
167
+ ··· + 1.99401 × 10
6
u + 538459.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
169
− 10u
168
+ ··· − 8577u + 415
c
2
, c
5
5(5u
169
− 24u
168
+ ··· + 3.48029 × 10
8
u + 2.48668 × 10
7
)
c
3
, c
7
u
169
− 2u
168
+ ··· − 373810u + 75839
c
4
, c
9
u
169
− u
168
+ ··· − 1899u + 373
c
6
, c
11
u
169
+ 2u
168
+ ··· + 184u + 193
c
8
5(5u
169
− 83u
168
+ ··· − 1136881u + 191311)
c
10
5(5u
169
− 13u
168
+ ··· − 845357u + 161671)
c
12
u
169
+ 3u
168
+ ··· − 19434u + 2711
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
169
− 14y
168
+ ··· − 98510671y −172225
c
2
, c
5
25
· (25y
169
− 3896y
168
+ ··· + 10579956017594239y −618357294637681)
c
3
, c
7
y
169
− 100y
168
+ ··· + 233540843658y −5751553921
c
4
, c
9
y
169
+ 95y
168
+ ··· − 4640829y −139129
c
6
, c
11
y
169
+ 80y
168
+ ··· − 1198642y −37249
c
8
25(25y
169
+ 1011y
168
+ ··· − 2.93882 × 10
12
y −3.65999 × 10
10
)
c
10
25(25y
169
+ 1711y
168
+ ··· − 3.11859 × 10
11
y −2.61375 × 10
10
)
c
12
y
169
+ 35y
168
+ ··· + 1287952826y −7349521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.784708 + 0.613924I
a = −0.643559 + 0.808589I
b = 0.37279 − 1.37564I
5.44300 − 3.46467I 0
u = 0.784708 − 0.613924I
a = −0.643559 − 0.808589I
b = 0.37279 + 1.37564I
5.44300 + 3.46467I 0
u = 0.920244 + 0.377047I
a = 1.60054 + 0.02840I
b = −0.097204 + 0.531932I
−1.33676 − 1.43995I 0
u = 0.920244 − 0.377047I
a = 1.60054 − 0.02840I
b = −0.097204 − 0.531932I
−1.33676 + 1.43995I 0
u = 0.915176 + 0.374176I
a = −0.881069 + 0.421708I
b = −0.665475 + 0.344780I
−1.61762 − 3.68106I 0
u = 0.915176 − 0.374176I
a = −0.881069 − 0.421708I
b = −0.665475 − 0.344780I
−1.61762 + 3.68106I 0
u = −0.911314 + 0.371165I
a = −0.962164 − 0.086599I
b = −0.296551 + 1.206580I
4.32077 − 5.45772I 0
u = −0.911314 − 0.371165I
a = −0.962164 + 0.086599I
b = −0.296551 − 1.206580I
4.32077 + 5.45772I 0
u = 0.830216 + 0.518276I
a = −1.09985 + 1.20733I
b = −0.662634 − 1.196350I
5.28936 − 1.07756I 0
u = 0.830216 − 0.518276I
a = −1.09985 − 1.20733I
b = −0.662634 + 1.196350I
5.28936 + 1.07756I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.267064 + 0.928594I
a = 0.78004 − 1.30401I
b = −0.476011 + 0.994886I
−1.29765 + 2.45359I 0
u = 0.267064 − 0.928594I
a = 0.78004 + 1.30401I
b = −0.476011 − 0.994886I
−1.29765 − 2.45359I 0
u = 0.865667 + 0.411875I
a = 1.023270 − 0.122811I
b = 0.332039 + 0.960787I
0.593196 + 0.743247I 0
u = 0.865667 − 0.411875I
a = 1.023270 + 0.122811I
b = 0.332039 − 0.960787I
0.593196 − 0.743247I 0
u = 0.268756 + 1.009500I
a = −0.41582 + 1.58361I
b = 0.429135 − 0.496965I
−2.14568 − 2.88218I 0
u = 0.268756 − 1.009500I
a = −0.41582 − 1.58361I
b = 0.429135 + 0.496965I
−2.14568 + 2.88218I 0
u = 0.260589 + 0.911776I
a = −0.51091 − 1.51427I
b = −0.086537 + 1.184460I
7.21873 − 2.31414I 0
u = 0.260589 − 0.911776I
a = −0.51091 + 1.51427I
b = −0.086537 − 1.184460I
7.21873 + 2.31414I 0
u = −0.928179 + 0.185085I
a = −1.31562 − 1.02496I
b = −0.496072 + 0.506207I
−3.28092 + 0.65320I 0
u = −0.928179 − 0.185085I
a = −1.31562 + 1.02496I
b = −0.496072 − 0.506207I
−3.28092 − 0.65320I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722890 + 0.603420I
a = −0.332399 + 0.483389I
b = −0.243722 − 0.338431I
2.71954 + 3.65187I 0
u = −0.722890 − 0.603420I
a = −0.332399 − 0.483389I
b = −0.243722 + 0.338431I
2.71954 − 3.65187I 0
u = −1.019350 + 0.308406I
a = −1.96904 + 0.11380I
b = 0.078671 + 0.716499I
−1.352700 − 0.345590I 0
u = −1.019350 − 0.308406I
a = −1.96904 − 0.11380I
b = 0.078671 − 0.716499I
−1.352700 + 0.345590I 0
u = 0.933309 + 0.043329I
a = 2.70551 − 5.68153I
b = 0.118826 + 1.029770I
0.182079 − 0.083509I 0
u = 0.933309 − 0.043329I
a = 2.70551 + 5.68153I
b = 0.118826 − 1.029770I
0.182079 + 0.083509I 0
u = 0.741521 + 0.766665I
a = −0.80312 + 1.48660I
b = −0.791649 − 0.938174I
2.65700 − 8.59855I 0
u = 0.741521 − 0.766665I
a = −0.80312 − 1.48660I
b = −0.791649 + 0.938174I
2.65700 + 8.59855I 0
u = 1.084770 + 0.075835I
a = 0.676752 − 0.593636I
b = 0.635917 + 0.164215I
−1.44974 + 2.38111I 0
u = 1.084770 − 0.075835I
a = 0.676752 + 0.593636I
b = 0.635917 − 0.164215I
−1.44974 − 2.38111I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.967024 + 0.504518I
a = 0.636371 + 0.801048I
b = 0.821785 − 0.053503I
1.22501 + 8.45758I 0
u = −0.967024 − 0.504518I
a = 0.636371 − 0.801048I
b = 0.821785 + 0.053503I
1.22501 − 8.45758I 0
u = −1.089940 + 0.203333I
a = 1.71443 + 0.58971I
b = 0.354122 − 1.083020I
1.79023 + 0.79732I 0
u = −1.089940 − 0.203333I
a = 1.71443 − 0.58971I
b = 0.354122 + 1.083020I
1.79023 − 0.79732I 0
u = −0.665123 + 0.890537I
a = 0.284939 + 0.666179I
b = −0.540626 − 0.822974I
2.50535 + 3.30834I 0
u = −0.665123 − 0.890537I
a = 0.284939 − 0.666179I
b = −0.540626 + 0.822974I
2.50535 − 3.30834I 0
u = −0.873663 + 0.146201I
a = −0.083774 − 1.203770I
b = 0.01017 + 1.81847I
4.92828 + 7.63290I 0
u = −0.873663 − 0.146201I
a = −0.083774 + 1.203770I
b = 0.01017 − 1.81847I
4.92828 − 7.63290I 0
u = −0.844903 + 0.254381I
a = 0.398836 − 1.045490I
b = 0.33666 + 1.42613I
4.42997 − 1.35438I 0
u = −0.844903 − 0.254381I
a = 0.398836 + 1.045490I
b = 0.33666 − 1.42613I
4.42997 + 1.35438I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807222 + 0.336582I
a = −1.070950 − 0.039143I
b = −0.651460 + 0.967818I
4.35010 + 4.01737I 0
u = −0.807222 − 0.336582I
a = −1.070950 + 0.039143I
b = −0.651460 − 0.967818I
4.35010 − 4.01737I 0
u = −0.208446 + 0.846554I
a = −0.68762 − 1.46932I
b = 0.543847 + 1.119410I
0.17317 − 6.34643I 0
u = −0.208446 − 0.846554I
a = −0.68762 + 1.46932I
b = 0.543847 − 1.119410I
0.17317 + 6.34643I 0
u = −0.862498 + 0.731446I
a = −0.31807 − 1.82238I
b = −0.510474 + 0.892164I
−3.31588 + 2.03557I 0
u = −0.862498 − 0.731446I
a = −0.31807 + 1.82238I
b = −0.510474 − 0.892164I
−3.31588 − 2.03557I 0
u = −0.528278 + 0.683581I
a = 0.459538 + 1.239740I
b = −0.094965 − 1.184460I
3.30392 + 1.21744I 0
u = −0.528278 − 0.683581I
a = 0.459538 − 1.239740I
b = −0.094965 + 1.184460I
3.30392 − 1.21744I 0
u = −0.850837 + 0.148530I
a = −1.44220 − 1.52687I
b = −0.635119 + 0.854070I
−3.31379 + 1.12851I 0
u = −0.850837 − 0.148530I
a = −1.44220 + 1.52687I
b = −0.635119 − 0.854070I
−3.31379 − 1.12851I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.113610 + 0.236527I
a = −0.0081692 − 0.1312360I
b = −1.50389 + 0.58738I
−4.64578 + 0.86236I 0
u = 1.113610 − 0.236527I
a = −0.0081692 + 0.1312360I
b = −1.50389 − 0.58738I
−4.64578 − 0.86236I 0
u = 0.231656 + 0.829785I
a = −0.05951 − 1.61145I
b = −0.299929 + 1.307960I
7.72074 + 8.11198I 0
u = 0.231656 − 0.829785I
a = −0.05951 + 1.61145I
b = −0.299929 − 1.307960I
7.72074 − 8.11198I 0
u = 0.853699 + 0.104903I
a = 0.95430 − 1.54712I
b = 0.68482 + 1.28338I
−1.92543 − 4.84905I 0
u = 0.853699 − 0.104903I
a = 0.95430 + 1.54712I
b = 0.68482 − 1.28338I
−1.92543 + 4.84905I 0
u = −0.847346 + 0.133559I
a = 1.63878 − 0.39556I
b = 0.276780 + 0.779594I
3.11053 − 0.19176I 0
u = −0.847346 − 0.133559I
a = 1.63878 + 0.39556I
b = 0.276780 − 0.779594I
3.11053 + 0.19176I 0
u = −0.022376 + 0.855453I
a = 0.90417 − 1.31054I
b = −0.429783 + 1.209360I
1.59238 + 4.23637I 0
u = −0.022376 − 0.855453I
a = 0.90417 + 1.31054I
b = −0.429783 − 1.209360I
1.59238 − 4.23637I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839044 + 0.145941I
a = −0.08746 − 1.42549I
b = 0.00710 + 1.56514I
1.27540 − 3.22857I 0
u = 0.839044 − 0.145941I
a = −0.08746 + 1.42549I
b = 0.00710 − 1.56514I
1.27540 + 3.22857I 0
u = −0.277337 + 0.804585I
a = 0.164515 − 1.317430I
b = 0.274774 + 1.190640I
3.45365 − 3.41412I 0
u = −0.277337 − 0.804585I
a = 0.164515 + 1.317430I
b = 0.274774 − 1.190640I
3.45365 + 3.41412I 0
u = 1.120720 + 0.336689I
a = 0.003701 + 0.171555I
b = −1.271420 + 0.543908I
−5.42015 − 4.37598I 0
u = 1.120720 − 0.336689I
a = 0.003701 − 0.171555I
b = −1.271420 − 0.543908I
−5.42015 + 4.37598I 0
u = −1.011570 + 0.588491I
a = 0.880891 + 1.061040I
b = 0.495034 − 1.040080I
1.87354 + 3.75211I 0
u = −1.011570 − 0.588491I
a = 0.880891 − 1.061040I
b = 0.495034 + 1.040080I
1.87354 − 3.75211I 0
u = −1.187150 + 0.225281I
a = −0.084077 − 0.115206I
b = 1.387830 + 0.195997I
−6.25555 + 1.65412I 0
u = −1.187150 − 0.225281I
a = −0.084077 + 0.115206I
b = 1.387830 − 0.195997I
−6.25555 − 1.65412I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.204359 + 0.762631I
a = 0.65317 + 1.81794I
b = −0.544913 − 0.241877I
0.55143 + 9.06486I 0
u = −0.204359 − 0.762631I
a = 0.65317 − 1.81794I
b = −0.544913 + 0.241877I
0.55143 − 9.06486I 0
u = −0.049278 + 0.780179I
a = −0.780221 − 1.046110I
b = 0.472046 + 1.129250I
1.32461 − 2.32482I 0
u = −0.049278 − 0.780179I
a = −0.780221 + 1.046110I
b = 0.472046 − 1.129250I
1.32461 + 2.32482I 0
u = −1.175890 + 0.326749I
a = −0.180592 + 0.035328I
b = 1.176990 + 0.557577I
−6.59949 + 1.11760I 0
u = −1.175890 − 0.326749I
a = −0.180592 − 0.035328I
b = 1.176990 − 0.557577I
−6.59949 − 1.11760I 0
u = −0.966156 + 0.783023I
a = 0.68210 + 1.26288I
b = 0.724741 − 0.867423I
1.63076 + 2.82752I 0
u = −0.966156 − 0.783023I
a = 0.68210 − 1.26288I
b = 0.724741 + 0.867423I
1.63076 − 2.82752I 0
u = 1.229220 + 0.244301I
a = −0.801288 + 0.253368I
b = −0.499729 − 1.033100I
−1.69948 − 3.50347I 0
u = 1.229220 − 0.244301I
a = −0.801288 − 0.253368I
b = −0.499729 + 1.033100I
−1.69948 + 3.50347I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.234680 + 0.277061I
a = 0.99756 + 1.58457I
b = 0.489008 − 1.112440I
−2.72337 + 10.53720I 0
u = −1.234680 − 0.277061I
a = 0.99756 − 1.58457I
b = 0.489008 + 1.112440I
−2.72337 − 10.53720I 0
u = 0.914174 + 0.878055I
a = −0.318771 + 0.651893I
b = 0.630963 − 1.009040I
2.23701 + 2.52987I 0
u = 0.914174 − 0.878055I
a = −0.318771 − 0.651893I
b = 0.630963 + 1.009040I
2.23701 − 2.52987I 0
u = 0.273246 + 1.238690I
a = 0.026142 + 1.339540I
b = −0.100077 − 1.138070I
7.55549 − 1.54678I 0
u = 0.273246 − 1.238690I
a = 0.026142 − 1.339540I
b = −0.100077 + 1.138070I
7.55549 + 1.54678I 0
u = −1.243950 + 0.288511I
a = −0.173414 − 0.135763I
b = 0.984332 + 0.308673I
−6.34008 + 1.34512I 0
u = −1.243950 − 0.288511I
a = −0.173414 + 0.135763I
b = 0.984332 − 0.308673I
−6.34008 − 1.34512I 0
u = 1.275850 + 0.167588I
a = −0.043975 − 0.157354I
b = −0.920866 − 0.483509I
−4.24168 − 4.68064I 0
u = 1.275850 − 0.167588I
a = −0.043975 + 0.157354I
b = −0.920866 + 0.483509I
−4.24168 + 4.68064I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.710178 + 0.032326I
a = 1.49756 + 0.26139I
b = 1.316290 + 0.027298I
−2.78206 − 2.35655I 0
u = 0.710178 − 0.032326I
a = 1.49756 − 0.26139I
b = 1.316290 − 0.027298I
−2.78206 + 2.35655I 0
u = −0.706628 + 0.038033I
a = −1.88252 − 0.60845I
b = −1.135580 + 0.244864I
−3.88353 + 0.65865I 0
u = −0.706628 − 0.038033I
a = −1.88252 + 0.60845I
b = −1.135580 − 0.244864I
−3.88353 − 0.65865I 0
u = 0.419587 + 0.568542I
a = 1.37429 − 1.11986I
b = −0.525739 + 0.566558I
−2.50872 + 1.64985I 0
u = 0.419587 − 0.568542I
a = 1.37429 + 1.11986I
b = −0.525739 − 0.566558I
−2.50872 − 1.64985I 0
u = −0.336968 + 0.584671I
a = 0.257670 − 0.354689I
b = −0.791991 − 0.225991I
2.93185 − 4.25246I 0
u = −0.336968 − 0.584671I
a = 0.257670 + 0.354689I
b = −0.791991 + 0.225991I
2.93185 + 4.25246I 0
u = 1.229950 + 0.505940I
a = 1.21373 − 0.79773I
b = 0.505515 + 1.190320I
4.59681 − 13.07660I 0
u = 1.229950 − 0.505940I
a = 1.21373 + 0.79773I
b = 0.505515 − 1.190320I
4.59681 + 13.07660I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.254070 + 0.452267I
a = −0.0717085 − 0.0096982I
b = 1.275460 − 0.413555I
−3.43263 − 13.45390I 0
u = 1.254070 − 0.452267I
a = −0.0717085 + 0.0096982I
b = 1.275460 + 0.413555I
−3.43263 + 13.45390I 0
u = −1.219820 + 0.547229I
a = −0.84466 − 1.25709I
b = −0.75383 + 1.27190I
−2.88770 + 11.52210I 0
u = −1.219820 − 0.547229I
a = −0.84466 + 1.25709I
b = −0.75383 − 1.27190I
−2.88770 − 11.52210I 0
u = 1.142900 + 0.704290I
a = 0.44210 − 1.49246I
b = 0.625808 + 1.112300I
−4.03602 − 6.95926I 0
u = 1.142900 − 0.704290I
a = 0.44210 + 1.49246I
b = 0.625808 − 1.112300I
−4.03602 + 6.95926I 0
u = −1.238850 + 0.517663I
a = −1.044670 − 0.688179I
b = −0.557236 + 1.069290I
0.38173 + 8.41877I 0
u = −1.238850 − 0.517663I
a = −1.044670 + 0.688179I
b = −0.557236 − 1.069290I
0.38173 − 8.41877I 0
u = 1.258750 + 0.473353I
a = 0.442243 − 0.266057I
b = −0.560804 + 0.722902I
−3.81271 + 2.29405I 0
u = 1.258750 − 0.473353I
a = 0.442243 + 0.266057I
b = −0.560804 − 0.722902I
−3.81271 − 2.29405I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.302300 + 0.345035I
a = 0.179164 + 0.076775I
b = 0.930534 − 0.188920I
−0.69980 − 3.35631I 0
u = 1.302300 − 0.345035I
a = 0.179164 − 0.076775I
b = 0.930534 + 0.188920I
−0.69980 + 3.35631I 0
u = −0.240792 + 1.327560I
a = 0.397783 + 1.227430I
b = −0.525829 − 1.121740I
2.99047 − 13.53630I 0
u = −0.240792 − 1.327560I
a = 0.397783 − 1.227430I
b = −0.525829 + 1.121740I
2.99047 + 13.53630I 0
u = 1.221660 + 0.586878I
a = 0.65830 − 1.32758I
b = 0.74303 + 1.24165I
−4.22878 − 7.99722I 0
u = 1.221660 − 0.586878I
a = 0.65830 + 1.32758I
b = 0.74303 − 1.24165I
−4.22878 + 7.99722I 0
u = −0.494647 + 0.399019I
a = 0.91470 + 1.43366I
b = 0.019305 − 1.253840I
3.25400 + 1.41233I 0
u = −0.494647 − 0.399019I
a = 0.91470 − 1.43366I
b = 0.019305 + 1.253840I
3.25400 − 1.41233I 0
u = −1.287670 + 0.459066I
a = 0.0344917 + 0.0654720I
b = −1.142430 − 0.439793I
−6.57774 + 7.61800I 0
u = −1.287670 − 0.459066I
a = 0.0344917 − 0.0654720I
b = −1.142430 + 0.439793I
−6.57774 − 7.61800I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.268830 + 0.512847I
a = −0.598198 − 0.974183I
b = −0.87304 + 1.25401I
−2.30878 + 7.20854I 0
u = −1.268830 − 0.512847I
a = −0.598198 + 0.974183I
b = −0.87304 − 1.25401I
−2.30878 − 7.20854I 0
u = 0.464494 + 0.417885I
a = 0.389547 − 0.250016I
b = 0.593850 − 0.095397I
−0.371617 + 0.181149I 0
u = 0.464494 − 0.417885I
a = 0.389547 + 0.250016I
b = 0.593850 + 0.095397I
−0.371617 − 0.181149I 0
u = 1.295430 + 0.504405I
a = 1.114000 − 0.413639I
b = 0.388015 + 0.956976I
3.82570 − 2.82547I 0
u = 1.295430 − 0.504405I
a = 1.114000 + 0.413639I
b = 0.388015 − 0.956976I
3.82570 + 2.82547I 0
u = −1.366900 + 0.317845I
a = 0.466473 + 0.607457I
b = 0.528493 − 1.181530I
1.47867 + 6.93285I 0
u = −1.366900 − 0.317845I
a = 0.466473 − 0.607457I
b = 0.528493 + 1.181530I
1.47867 − 6.93285I 0
u = 1.394320 + 0.192557I
a = −0.84720 + 1.30040I
b = −0.482826 − 1.070650I
−6.13637 − 3.71187I 0
u = 1.394320 − 0.192557I
a = −0.84720 − 1.30040I
b = −0.482826 + 1.070650I
−6.13637 + 3.71187I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29182 + 1.39063I
a = −0.330028 + 1.175580I
b = 0.507639 − 1.039770I
−0.47925 + 6.98931I 0
u = 0.29182 − 1.39063I
a = −0.330028 − 1.175580I
b = 0.507639 + 1.039770I
−0.47925 − 6.98931I 0
u = 1.32037 + 0.53217I
a = 0.489703 − 1.078630I
b = 0.80695 + 1.40931I
−2.48134 − 9.39382I 0
u = 1.32037 − 0.53217I
a = 0.489703 + 1.078630I
b = 0.80695 − 1.40931I
−2.48134 + 9.39382I 0
u = 1.23017 + 0.74039I
a = −0.714822 + 0.963586I
b = −0.225835 − 1.061800I
4.62378 − 5.27274I 0
u = 1.23017 − 0.74039I
a = −0.714822 − 0.963586I
b = −0.225835 + 1.061800I
4.62378 + 5.27274I 0
u = −1.35980 + 0.56252I
a = 0.34682 + 1.42888I
b = 0.472018 − 1.041820I
−2.69097 − 3.40063I 0
u = −1.35980 − 0.56252I
a = 0.34682 − 1.42888I
b = 0.472018 + 1.041820I
−2.69097 + 3.40063I 0
u = −0.165018 + 0.454733I
a = 0.323685 + 1.184510I
b = −0.350182 + 0.351513I
3.54368 + 0.14114I −7.79730 + 0.I
u = −0.165018 − 0.454733I
a = 0.323685 − 1.184510I
b = −0.350182 − 0.351513I
3.54368 − 0.14114I −7.79730 + 0.I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35879 + 0.68363I
a = 0.658461 + 1.237440I
b = 0.74314 − 1.28555I
−0.6048 + 20.4984I 0
u = −1.35879 − 0.68363I
a = 0.658461 − 1.237440I
b = 0.74314 + 1.28555I
−0.6048 − 20.4984I 0
u = 1.51899 + 0.11938I
a = 0.089455 − 0.236447I
b = 0.495480 − 0.372074I
−4.95976 − 6.38027I 0
u = 1.51899 − 0.11938I
a = 0.089455 + 0.236447I
b = 0.495480 + 0.372074I
−4.95976 + 6.38027I 0
u = −0.419162 + 0.207680I
a = 3.33342 + 2.85533I
b = −0.210137 + 0.305412I
0.72969 + 9.00585I −13.9907 − 2.3705I
u = −0.419162 − 0.207680I
a = 3.33342 − 2.85533I
b = −0.210137 − 0.305412I
0.72969 − 9.00585I −13.9907 + 2.3705I
u = 1.46937 + 0.46587I
a = −0.55695 + 1.32312I
b = −0.499565 − 1.077370I
−6.27716 − 3.36692I 0
u = 1.46937 − 0.46587I
a = −0.55695 − 1.32312I
b = −0.499565 + 1.077370I
−6.27716 + 3.36692I 0
u = 1.37643 + 0.70310I
a = −0.634844 + 1.224050I
b = −0.71832 − 1.22870I
−4.0551 − 14.2204I 0
u = 1.37643 − 0.70310I
a = −0.634844 − 1.224050I
b = −0.71832 + 1.22870I
−4.0551 + 14.2204I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.301709 + 0.305751I
a = −0.65866 + 3.97939I
b = 0.201791 + 0.247158I
−1.91349 − 3.18793I −20.3303 + 3.5947I
u = 0.301709 − 0.305751I
a = −0.65866 − 3.97939I
b = 0.201791 − 0.247158I
−1.91349 + 3.18793I −20.3303 − 3.5947I
u = −1.43598 + 0.65398I
a = 0.614608 + 1.162010I
b = 0.588548 − 1.208550I
2.31661 + 8.82051I 0
u = −1.43598 − 0.65398I
a = 0.614608 − 1.162010I
b = 0.588548 + 1.208550I
2.31661 − 8.82051I 0
u = −0.156276 + 0.389985I
a = −1.53840 − 1.78639I
b = 0.706751 + 0.250418I
−2.26661 + 1.56990I −12.99135 − 4.46359I
u = −0.156276 − 0.389985I
a = −1.53840 + 1.78639I
b = 0.706751 − 0.250418I
−2.26661 − 1.56990I −12.99135 + 4.46359I
u = −1.42529 + 0.73027I
a = −0.316869 − 1.228090I
b = −0.48385 + 1.34552I
1.06578 + 9.36259I 0
u = −1.42529 − 0.73027I
a = −0.316869 + 1.228090I
b = −0.48385 − 1.34552I
1.06578 − 9.36259I 0
u = −0.32232 + 1.57592I
a = 0.251351 + 1.219410I
b = −0.325889 − 0.926755I
6.48750 − 1.31815I 0
u = −0.32232 − 1.57592I
a = 0.251351 − 1.219410I
b = −0.325889 + 0.926755I
6.48750 + 1.31815I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62354 + 0.01233I
a = −0.342204 + 0.053930I
b = −0.355912 + 0.537478I
−7.94904 + 0.08068I 0
u = −1.62354 − 0.01233I
a = −0.342204 − 0.053930I
b = −0.355912 − 0.537478I
−7.94904 − 0.08068I 0
u = 0.371009
a = 0.622778
b = 0.328320
−0.577669 −16.8570
u = −1.68630 + 0.14324I
a = −0.123446 + 0.248830I
b = −0.431066 − 0.477178I
−8.17453 − 0.68273I 0
u = −1.68630 − 0.14324I
a = −0.123446 − 0.248830I
b = −0.431066 + 0.477178I
−8.17453 + 0.68273I 0
u = 1.84057 + 0.13919I
a = −0.034591 + 0.352549I
b = 0.276896 − 0.610908I
−4.32983 + 6.91280I 0
u = 1.84057 − 0.13919I
a = −0.034591 − 0.352549I
b = 0.276896 + 0.610908I
−4.32983 − 6.91280I 0
u = −0.33847 + 1.84132I
a = −0.387588 − 1.117950I
b = 0.241094 + 0.954738I
5.21077 − 0.98103I 0
u = −0.33847 − 1.84132I
a = −0.387588 + 1.117950I
b = 0.241094 − 0.954738I
5.21077 + 0.98103I 0
21
II.
I
u
2
= h−6.32×10
64
u
45
−2.06×10
65
u
44
+· · ·+7.63×10
64
b−3.63×10
65
, −1.17×
10
66
u
45
−1.34×10
66
u
44
+· · ·+3.81×10
65
a+1.52×10
66
, u
46
+u
45
+· · ·−4u−1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
12
=
3.07517u
45
+ 3.52044u
44
+ ··· + 0.0351120u − 3.97606
0.828110u
45
+ 2.70307u
44
+ ··· + 27.9137u + 4.76046
a
6
=
−3.95905u
45
− 3.90820u
44
+ ··· − 8.58268u + 3.40061
−1.70283u
45
− 1.64681u
44
+ ··· − 6.85481u − 0.560714
a
2
=
−0.368133u
45
− 0.606936u
44
+ ··· − 11.8015u − 5.04021
−2.93569u
45
− 2.56925u
44
+ ··· − 2.65662u − 0.00923620
a
1
=
−1.61682u
45
− 1.39393u
44
+ ··· − 14.8379u − 5.09566
−2.35035u
45
− 2.06739u
44
+ ··· + 0.977947u + 0.507915
a
5
=
−2.90364u
45
− 4.32478u
44
+ ··· + 0.426431u + 1.78570
2.21317u
45
+ 2.69823u
44
+ ··· + 22.4707u + 3.55173
a
11
=
3.90328u
45
+ 6.22351u
44
+ ··· + 27.9488u + 0.784398
0.828110u
45
+ 2.70307u
44
+ ··· + 27.9137u + 4.76046
a
9
=
1.08755u
45
+ 0.808923u
44
+ ··· − 0.205520u − 2.78438
−0.970295u
45
− 0.436029u
44
+ ··· + 1.62043u + 0.667591
a
10
=
−3.17619u
45
− 7.66047u
44
+ ··· − 41.7514u − 10.2838
−1.04386u
45
− 1.45320u
44
+ ··· − 11.1493u − 1.98333
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9.77080u
45
− 14.3760u
44
+ ··· − 67.1522u − 26.2416
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
u
46
− 5u
45
+ ··· + 381u − 45
c
2
5(5u
46
− 29u
45
+ ··· − 5u − 1)
c
3
u
46
− u
45
+ ··· + 4u − 1
c
4
u
46
+ 12u
44
+ ··· + 13u + 1
c
5
5(5u
46
+ 29u
45
+ ··· + 5u − 1)
c
6
u
46
+ u
45
+ ··· + 2u − 1
c
7
u
46
+ u
45
+ ··· − 4u − 1
c
8
5(5u
46
− 2u
45
+ ··· + 141u + 27)
c
9
u
46
+ 12u
44
+ ··· − 13u + 1
c
10
5(5u
46
− 52u
45
+ ··· − 5u + 1)
c
11
u
46
− u
45
+ ··· − 2u − 1
c
12
u
46
− 2u
45
+ ··· − 6u + 1
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
− 29y
45
+ ··· − 85491y + 2025
c
2
, c
5
25(25y
46
− 1291y
45
+ ··· + 87y + 1)
c
3
, c
7
y
46
− 27y
45
+ ··· − 28y + 1
c
4
, c
9
y
46
+ 24y
45
+ ··· − 61y + 1
c
6
, c
11
y
46
+ 21y
45
+ ··· + 20y + 1
c
8
25(25y
46
+ 156y
45
+ ··· + 2961y + 729)
c
10
25(25y
46
+ 456y
45
+ ··· + 31y + 1)
c
12
y
46
+ 40y
45
+ ··· − 128y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759965 + 0.615331I
a = 0.378826 + 1.226440I
b = −0.249538 − 1.138700I
4.12941 + 2.44020I −7.32891 − 3.86342I
u = −0.759965 − 0.615331I
a = 0.378826 − 1.226440I
b = −0.249538 + 1.138700I
4.12941 − 2.44020I −7.32891 + 3.86342I
u = 0.931327 + 0.070775I
a = 2.84214 − 4.58130I
b = 0.140739 + 1.013170I
0.194745 − 0.116599I 2.9220 + 82.8813I
u = 0.931327 − 0.070775I
a = 2.84214 + 4.58130I
b = 0.140739 − 1.013170I
0.194745 + 0.116599I 2.9220 − 82.8813I
u = −0.314615 + 0.825539I
a = −0.768293 − 0.926594I
b = 0.524033 + 1.160380I
0.35083 − 3.81303I −11.81487 + 3.53813I
u = −0.314615 − 0.825539I
a = −0.768293 + 0.926594I
b = 0.524033 − 1.160380I
0.35083 + 3.81303I −11.81487 − 3.53813I
u = −1.124520 + 0.184209I
a = −0.0617338 + 0.0211337I
b = 1.281670 + 0.050335I
−4.48275 + 3.04871I −14.6371 − 3.6880I
u = −1.124520 − 0.184209I
a = −0.0617338 − 0.0211337I
b = 1.281670 − 0.050335I
−4.48275 − 3.04871I −14.6371 + 3.6880I
u = 0.725486 + 0.429787I
a = 0.341424 + 0.616367I
b = 0.344508 − 1.276250I
4.94472 + 1.48067I −0.92704 − 2.07489I
u = 0.725486 − 0.429787I
a = 0.341424 − 0.616367I
b = 0.344508 + 1.276250I
4.94472 − 1.48067I −0.92704 + 2.07489I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.138440 + 0.286250I
a = 0.157514 − 0.051212I
b = −1.36556 + 0.43065I
−5.70494 − 1.01538I −12.00000 + 0.I
u = 1.138440 − 0.286250I
a = 0.157514 + 0.051212I
b = −1.36556 − 0.43065I
−5.70494 + 1.01538I −12.00000 + 0.I
u = −1.066310 + 0.538677I
a = 1.27908 + 0.75361I
b = 0.428833 − 0.845999I
3.22687 + 2.04204I −12.00000 + 0.I
u = −1.066310 − 0.538677I
a = 1.27908 − 0.75361I
b = 0.428833 + 0.845999I
3.22687 − 2.04204I −12.00000 + 0.I
u = −0.784232 + 0.094828I
a = −1.60633 − 0.16619I
b = −1.195670 − 0.277234I
−3.06323 − 1.85882I −15.8030 − 0.6054I
u = −0.784232 − 0.094828I
a = −1.60633 + 0.16619I
b = −1.195670 + 0.277234I
−3.06323 + 1.85882I −15.8030 + 0.6054I
u = −0.695446 + 0.349672I
a = −2.02642 − 0.86298I
b = 0.104294 + 0.443019I
−2.48398 + 0.08786I −12.94904 − 1.25593I
u = −0.695446 − 0.349672I
a = −2.02642 + 0.86298I
b = 0.104294 − 0.443019I
−2.48398 − 0.08786I −12.94904 + 1.25593I
u = 0.410512 + 0.626152I
a = −0.19819 + 3.24676I
b = −0.232805 − 0.626962I
−1.45648 − 3.49012I −7.34431 + 10.93615I
u = 0.410512 − 0.626152I
a = −0.19819 − 3.24676I
b = −0.232805 + 0.626962I
−1.45648 + 3.49012I −7.34431 − 10.93615I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584281 + 0.448127I
a = 1.91297 + 2.94195I
b = 0.423883 − 0.605968I
0.85461 + 9.55799I −11.2303 − 15.6993I
u = −0.584281 − 0.448127I
a = 1.91297 − 2.94195I
b = 0.423883 + 0.605968I
0.85461 − 9.55799I −11.2303 + 15.6993I
u = 1.131570 + 0.646272I
a = −0.543841 + 0.777131I
b = −0.517868 − 0.927064I
3.13671 − 5.81126I 0
u = 1.131570 − 0.646272I
a = −0.543841 − 0.777131I
b = −0.517868 + 0.927064I
3.13671 + 5.81126I 0
u = 0.672359 + 0.155073I
a = 1.91058 − 0.59861I
b = 1.206820 + 0.069668I
−3.74702 − 1.02516I −12.3946 + 11.9932I
u = 0.672359 − 0.155073I
a = 1.91058 + 0.59861I
b = 1.206820 − 0.069668I
−3.74702 + 1.02516I −12.3946 − 11.9932I
u = −1.244570 + 0.536903I
a = −0.592342 − 1.107730I
b = −0.83991 + 1.34043I
−2.67755 + 8.80359I 0
u = −1.244570 − 0.536903I
a = −0.592342 + 1.107730I
b = −0.83991 − 1.34043I
−2.67755 − 8.80359I 0
u = 0.088786 + 1.376940I
a = −0.397745 + 1.242650I
b = 0.104797 − 0.976334I
6.91682 + 0.42500I 0
u = 0.088786 − 1.376940I
a = −0.397745 − 1.242650I
b = 0.104797 + 0.976334I
6.91682 − 0.42500I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50682
a = −0.140304
b = −0.624244
−8.28794 0
u = 1.40911 + 0.54379I
a = 0.456293 − 1.181880I
b = 0.52854 + 1.33458I
0.28379 − 9.06984I 0
u = 1.40911 − 0.54379I
a = 0.456293 + 1.181880I
b = 0.52854 − 1.33458I
0.28379 + 9.06984I 0
u = −1.48517 + 0.28208I
a = −0.71090 − 1.26682I
b = −0.476877 + 1.074080I
−5.86122 + 3.55096I 0
u = −1.48517 − 0.28208I
a = −0.71090 + 1.26682I
b = −0.476877 − 1.074080I
−5.86122 − 3.55096I 0
u = 0.481596 + 0.075115I
a = 0.385331 − 0.389381I
b = −0.03992 − 1.62142I
5.66401 − 7.16274I −5.71563 + 4.13368I
u = 0.481596 − 0.075115I
a = 0.385331 + 0.389381I
b = −0.03992 + 1.62142I
5.66401 + 7.16274I −5.71563 − 4.13368I
u = −0.462806
a = −2.66413
b = 0.296742
−2.56548 −14.2180
u = −0.211948 + 0.231852I
a = 1.189010 − 0.598971I
b = 0.073592 − 1.346370I
2.12631 + 2.83155I −9.95669 − 1.82826I
u = −0.211948 − 0.231852I
a = 1.189010 + 0.598971I
b = 0.073592 + 1.346370I
2.12631 − 2.83155I −9.95669 + 1.82826I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69555 + 0.01087I
a = −0.327167 + 0.083308I
b = −0.299745 − 0.576356I
−7.72616 − 0.08966I 0
u = 1.69555 − 0.01087I
a = −0.327167 − 0.083308I
b = −0.299745 + 0.576356I
−7.72616 + 0.08966I 0
u = −1.73828 + 0.01558I
a = 0.254122 + 0.232227I
b = 0.005183 − 0.511956I
−4.15464 − 6.43454I 0
u = −1.73828 − 0.01558I
a = 0.254122 − 0.232227I
b = 0.005183 + 0.511956I
−4.15464 + 6.43454I 0
u = 0.30258 + 1.85023I
a = 0.327896 − 1.135670I
b = −0.285231 + 0.940956I
5.08625 + 1.16461I 0
u = 0.30258 − 1.85023I
a = 0.327896 + 1.135670I
b = −0.285231 − 0.940956I
5.08625 − 1.16461I 0
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
46
− 5u
45
+ ··· + 381u − 45)(u
169
− 10u
168
+ ··· − 8577u + 415)
c
2
25(5u
46
− 29u
45
+ ··· − 5u − 1)
· (5u
169
− 24u
168
+ ··· + 348028723u + 24866791)
c
3
(u
46
− u
45
+ ··· + 4u − 1)(u
169
− 2u
168
+ ··· − 373810u + 75839)
c
4
(u
46
+ 12u
44
+ ··· + 13u + 1)(u
169
− u
168
+ ··· − 1899u + 373)
c
5
25(5u
46
+ 29u
45
+ ··· + 5u − 1)
· (5u
169
− 24u
168
+ ··· + 348028723u + 24866791)
c
6
(u
46
+ u
45
+ ··· + 2u − 1)(u
169
+ 2u
168
+ ··· + 184u + 193)
c
7
(u
46
+ u
45
+ ··· − 4u − 1)(u
169
− 2u
168
+ ··· − 373810u + 75839)
c
8
25(5u
46
− 2u
45
+ ··· + 141u + 27)
· (5u
169
− 83u
168
+ ··· − 1136881u + 191311)
c
9
(u
46
+ 12u
44
+ ··· − 13u + 1)(u
169
− u
168
+ ··· − 1899u + 373)
c
10
25(5u
46
− 52u
45
+ ··· − 5u + 1)
· (5u
169
− 13u
168
+ ··· − 845357u + 161671)
c
11
(u
46
− u
45
+ ··· − 2u − 1)(u
169
+ 2u
168
+ ··· + 184u + 193)
c
12
(u
46
− 2u
45
+ ··· − 6u + 1)(u
169
+ 3u
168
+ ··· − 19434u + 2711)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
46
− 29y
45
+ ··· − 85491y + 2025)
· (y
169
− 14y
168
+ ··· − 98510671y −172225)
c
2
, c
5
625(25y
46
− 1291y
45
+ ··· + 87y + 1)
· (25y
169
− 3896y
168
+ ··· + 10579956017594239y −618357294637681)
c
3
, c
7
(y
46
− 27y
45
+ ··· − 28y + 1)
· (y
169
− 100y
168
+ ··· + 233540843658y −5751553921)
c
4
, c
9
(y
46
+ 24y
45
+ ··· − 61y + 1)
· (y
169
+ 95y
168
+ ··· − 4640829y −139129)
c
6
, c
11
(y
46
+ 21y
45
+ ··· + 20y + 1)
· (y
169
+ 80y
168
+ ··· − 1198642y −37249)
c
8
625(25y
46
+ 156y
45
+ ··· + 2961y + 729)
· (25y
169
+ 1011y
168
+ ··· − 2938824164827y −36599898721)
c
10
625(25y
46
+ 456y
45
+ ··· + 31y + 1)
· (25y
169
+ 1711y
168
+ ··· − 311859199249y −26137512241)
c
12
(y
46
+ 40y
45
+ ··· − 128y + 1)
· (y
169
+ 35y
168
+ ··· + 1287952826y −7349521)
33
