12a
1280
(K12a
1280
)
A knot diagram
1
Linearized knot diagam
5 8 9 11 1 10 2 12 4 6 3 7
Solving Sequence
1,6
5
2,11
4 10 7 8 9 3 12
c
5
c
1
c
4
c
10
c
6
c
7
c
9
c
3
c
12
c
2
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.89817 × 10
771
u
159
− 8.88168 × 10
771
u
158
+ ··· + 1.85109 × 10
773
b + 7.26797 × 10
773
,
− 7.79658 × 10
780
u
159
+ 8.42830 × 10
780
u
158
+ ··· + 1.47412 × 10
783
a + 4.88030 × 10
784
,
u
160
+ 5u
159
+ ··· + 1034u + 763i
I
u
2
= h−1.11952 × 10
18
u
39
+ 9.08577 × 10
17
u
38
+ ··· + 4.95466 × 10
16
b + 1.44944 × 10
18
,
2.55914 × 10
20
u
39
− 1.19489 × 10
22
u
38
+ ··· + 3.04167 × 10
20
a − 5.39997 × 10
22
, u
40
+ 10u
38
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 200 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−1.90 × 10
771
u
159
− 8.88 × 10
771
u
158
+ · · · + 1.85 × 10
773
b + 7.27 ×
10
773
, −7.80 × 10
780
u
159
+ 8.43 × 10
780
u
158
+ · · · + 1.47 × 10
783
a + 4.88 ×
10
784
, u
160
+ 5u
159
+ · · · + 1034u + 763i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
2
=
−u
u
3
+ u
a
11
=
0.00528898u
159
− 0.00571753u
158
+ ··· − 31.2417u − 33.1066
0.0102543u
159
+ 0.0479809u
158
+ ··· − 1.97258u − 3.92632
a
4
=
0.00208837u
159
+ 0.0175818u
158
+ ··· + 93.9097u + 25.1074
−0.00146282u
159
− 0.00856543u
158
+ ··· − 6.96135u − 0.610702
a
10
=
−0.00496536u
159
− 0.0536984u
158
+ ··· − 29.2691u − 29.1803
0.0102543u
159
+ 0.0479809u
158
+ ··· − 1.97258u − 3.92632
a
7
=
−0.00321433u
159
− 0.00722482u
158
+ ··· − 20.2256u + 8.49310
0.0134674u
159
+ 0.0671173u
158
+ ··· + 23.7049u + 7.19324
a
8
=
0.00196200u
159
+ 0.0180792u
158
+ ··· − 8.19279u + 12.9535
0.0119696u
159
+ 0.0581319u
158
+ ··· + 15.0244u + 2.29208
a
9
=
0.0495996u
159
+ 0.266425u
158
+ ··· + 129.695u + 41.9874
−0.00966189u
159
− 0.0379134u
158
+ ··· − 8.27916u + 7.42179
a
3
=
−0.000282697u
159
− 0.00229252u
158
+ ··· + 4.31477u + 9.56055
0.00667690u
159
+ 0.0315444u
158
+ ··· + 12.8545u − 0.248031
a
12
=
0.00641506u
159
+ 0.0525232u
158
+ ··· + 20.9392u + 4.33778
0.000688568u
159
+ 0.00147807u
158
+ ··· + 5.68861u + 3.15312
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0110703u
159
+ 0.0900993u
158
+ ··· − 86.6660u + 30.0672
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
160
+ 5u
159
+ ··· + 1034u + 763
c
2
, c
7
u
160
+ u
159
+ ··· + 79965u + 7417
c
3
, c
9
u
160
− u
159
+ ··· − 79965u + 7417
c
4
u
160
+ u
159
+ ··· + 6487992u + 714773
c
6
, c
10
u
160
− 5u
159
+ ··· − 1034u + 763
c
8
u
160
+ 7u
159
+ ··· + 60u + 7
c
11
u
160
− 7u
159
+ ··· − 60u + 7
c
12
u
160
− u
159
+ ··· − 6487992u + 714773
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
160
+ 81y
159
+ ··· + 13136378y + 582169
c
2
, c
3
, c
7
c
9
y
160
− 115y
159
+ ··· + 324258557y + 55011889
c
4
, c
12
y
160
− 7y
159
+ ··· + 4855248205898y + 510900441529
c
8
, c
11
y
160
+ 7y
159
+ ··· + 1832y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385490 + 0.927127I
a = 1.27250 − 1.33805I
b = 1.30399 − 0.73093I
4.40812 − 1.23041I 0
u = −0.385490 − 0.927127I
a = 1.27250 + 1.33805I
b = 1.30399 + 0.73093I
4.40812 + 1.23041I 0
u = −0.294481 + 0.965440I
a = 2.94395 + 0.99740I
b = 0.356688 + 1.203140I
−2.58230 + 7.66961I 0
u = −0.294481 − 0.965440I
a = 2.94395 − 0.99740I
b = 0.356688 − 1.203140I
−2.58230 − 7.66961I 0
u = 0.457188 + 0.877846I
a = 2.09641 − 0.62542I
b = 0.530075 − 1.123270I
−6.63354 − 0.43992I 0
u = 0.457188 − 0.877846I
a = 2.09641 + 0.62542I
b = 0.530075 + 1.123270I
−6.63354 + 0.43992I 0
u = −0.193630 + 0.965913I
a = −1.71135 + 0.57654I
b = −1.203960 + 0.670041I
3.46403 − 0.49869I 0
u = −0.193630 − 0.965913I
a = −1.71135 − 0.57654I
b = −1.203960 − 0.670041I
3.46403 + 0.49869I 0
u = −0.630257 + 0.821670I
a = 1.18016 − 1.23585I
b = 0.842114 + 0.831002I
3.14638 + 5.48393I 0
u = −0.630257 − 0.821670I
a = 1.18016 + 1.23585I
b = 0.842114 − 0.831002I
3.14638 − 5.48393I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.528497 + 0.902931I
a = 0.459469 + 0.183830I
b = −0.06658 + 1.53283I
−4.48952 + 8.79836I 0
u = −0.528497 − 0.902931I
a = 0.459469 − 0.183830I
b = −0.06658 − 1.53283I
−4.48952 − 8.79836I 0
u = 0.423235 + 0.960586I
a = −2.26309 + 0.72628I
b = −0.200193 + 1.041780I
−6.16928 − 4.22992I 0
u = 0.423235 − 0.960586I
a = −2.26309 − 0.72628I
b = −0.200193 − 1.041780I
−6.16928 + 4.22992I 0
u = 1.042900 + 0.163804I
a = 0.156926 − 0.138138I
b = 0.513923 + 1.144070I
1.55339 + 8.26333I 0
u = 1.042900 − 0.163804I
a = 0.156926 + 0.138138I
b = 0.513923 − 1.144070I
1.55339 − 8.26333I 0
u = −1.059430 + 0.037653I
a = 0.141751 − 0.253958I
b = −0.189671 + 1.071480I
−3.62698 − 1.64070I 0
u = −1.059430 − 0.037653I
a = 0.141751 + 0.253958I
b = −0.189671 − 1.071480I
−3.62698 + 1.64070I 0
u = 0.339681 + 1.004880I
a = 1.171080 − 0.163992I
b = 0.339681 − 1.004880I
0.481977I 0
u = 0.339681 − 1.004880I
a = 1.171080 + 0.163992I
b = 0.339681 + 1.004880I
− 0.481977I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.200193 + 1.041780I
a = 1.85659 − 0.90395I
b = 0.423235 + 0.960586I
6.16928 + 4.22992I 0
u = −0.200193 − 1.041780I
a = 1.85659 + 0.90395I
b = 0.423235 − 0.960586I
6.16928 − 4.22992I 0
u = 0.409874 + 0.982147I
a = −1.51896 − 0.85860I
b = −0.646848 + 0.242634I
4.95212 − 3.37858I 0
u = 0.409874 − 0.982147I
a = −1.51896 + 0.85860I
b = −0.646848 − 0.242634I
4.95212 + 3.37858I 0
u = 0.441987 + 0.988216I
a = −1.64389 − 0.14711I
b = −0.590734 + 1.176550I
0.59941 − 4.40862I 0
u = 0.441987 − 0.988216I
a = −1.64389 + 0.14711I
b = −0.590734 − 1.176550I
0.59941 + 4.40862I 0
u = −0.882981 + 0.242850I
a = −0.692829 + 0.792420I
b = −0.882981 − 0.242850I
− 8.16312I 0
u = −0.882981 − 0.242850I
a = −0.692829 − 0.792420I
b = −0.882981 + 0.242850I
8.16312I 0
u = 0.069090 + 0.909973I
a = −1.39578 − 0.84012I
b = −1.069070 − 0.439551I
3.21338 + 1.36887I 0
u = 0.069090 − 0.909973I
a = −1.39578 + 0.84012I
b = −1.069070 + 0.439551I
3.21338 − 1.36887I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.189671 + 1.071480I
a = −1.330260 − 0.045638I
b = −1.059430 + 0.037653I
3.62698 + 1.64070I 0
u = −0.189671 − 1.071480I
a = −1.330260 + 0.045638I
b = −1.059430 − 0.037653I
3.62698 − 1.64070I 0
u = 0.215475 + 0.882220I
a = −1.96224 − 0.86988I
b = −0.266047 − 0.173518I
4.87192 − 3.43607I 0
u = 0.215475 − 0.882220I
a = −1.96224 + 0.86988I
b = −0.266047 + 0.173518I
4.87192 + 3.43607I 0
u = −0.501432 + 0.972041I
a = 0.130804 − 0.697371I
b = 0.984720 − 0.627553I
3.73283 − 0.97858I 0
u = −0.501432 − 0.972041I
a = 0.130804 + 0.697371I
b = 0.984720 + 0.627553I
3.73283 + 0.97858I 0
u = −0.594235 + 0.676961I
a = −1.81454 − 0.03818I
b = −0.204775 − 1.293760I
−5.14661 − 4.35854I 0
u = −0.594235 − 0.676961I
a = −1.81454 + 0.03818I
b = −0.204775 + 1.293760I
−5.14661 + 4.35854I 0
u = 0.409920 + 0.771799I
a = 0.201552 + 0.273355I
b = 0.30645 + 1.45756I
−7.01825 − 3.22517I 0
u = 0.409920 − 0.771799I
a = 0.201552 − 0.273355I
b = 0.30645 − 1.45756I
−7.01825 + 3.22517I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.199327 + 1.111140I
a = −0.568173 − 1.013380I
b = −0.779145 − 0.883965I
3.46471 + 2.35167I 0
u = 0.199327 − 1.111140I
a = −0.568173 + 1.013380I
b = −0.779145 + 0.883965I
3.46471 − 2.35167I 0
u = −0.108254 + 1.126240I
a = 0.906055 − 0.323734I
b = 0.521123 − 0.687415I
0.369570 + 0.575295I 0
u = −0.108254 − 1.126240I
a = 0.906055 + 0.323734I
b = 0.521123 + 0.687415I
0.369570 − 0.575295I 0
u = −0.312914 + 0.810172I
a = −0.303878 + 0.767833I
b = 0.27057 − 1.43596I
−3.09882 − 5.03766I 0
u = −0.312914 − 0.810172I
a = −0.303878 − 0.767833I
b = 0.27057 + 1.43596I
−3.09882 + 5.03766I 0
u = 0.392363 + 1.065770I
a = −1.44995 − 0.84307I
b = −1.153290 − 0.103649I
5.25585 − 3.21786I 0
u = 0.392363 − 1.065770I
a = −1.44995 + 0.84307I
b = −1.153290 + 0.103649I
5.25585 + 3.21786I 0
u = 0.521123 + 0.687415I
a = 0.680160 − 0.140841I
b = −0.108254 − 1.126240I
−0.369570 + 0.575295I 0
u = 0.521123 − 0.687415I
a = 0.680160 + 0.140841I
b = −0.108254 + 1.126240I
−0.369570 − 0.575295I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.738333 + 0.445064I
a = 0.017546 − 0.227666I
b = 0.586656 − 1.132260I
1.02642 − 1.58654I 0
u = −0.738333 − 0.445064I
a = 0.017546 + 0.227666I
b = 0.586656 + 1.132260I
1.02642 + 1.58654I 0
u = −1.069070 + 0.439551I
a = 0.166690 + 0.372505I
b = 0.069090 − 0.909973I
−3.21338 + 1.36887I 0
u = −1.069070 − 0.439551I
a = 0.166690 − 0.372505I
b = 0.069090 + 0.909973I
−3.21338 − 1.36887I 0
u = −0.274738 + 1.124500I
a = −0.850665 − 0.828285I
b = −0.655182 − 0.448203I
2.34756 + 3.34951I 0
u = −0.274738 − 1.124500I
a = −0.850665 + 0.828285I
b = −0.655182 + 0.448203I
2.34756 − 3.34951I 0
u = −1.153290 + 0.103649I
a = 0.530853 + 0.573422I
b = 0.392363 − 1.065770I
−5.25585 − 3.21786I 0
u = −1.153290 − 0.103649I
a = 0.530853 − 0.573422I
b = 0.392363 + 1.065770I
−5.25585 + 3.21786I 0
u = 0.765672 + 0.345950I
a = 0.133743 + 0.510090I
b = −0.533037 − 1.282680I
−1.21473 + 4.93993I 0
u = 0.765672 − 0.345950I
a = 0.133743 − 0.510090I
b = −0.533037 + 1.282680I
−1.21473 − 4.93993I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.833054 + 0.070087I
a = 0.553181 − 0.190046I
b = 0.499694 − 0.025259I
−2.48910 + 0.06312I 0
u = −0.833054 − 0.070087I
a = 0.553181 + 0.190046I
b = 0.499694 + 0.025259I
−2.48910 − 0.06312I 0
u = 0.984720 + 0.627553I
a = −0.724162 − 0.345867I
b = −0.501432 − 0.972041I
−3.73283 − 0.97858I 0
u = 0.984720 − 0.627553I
a = −0.724162 + 0.345867I
b = −0.501432 + 0.972041I
−3.73283 + 0.97858I 0
u = −0.606513 + 1.004750I
a = 1.369280 + 0.164619I
b = −0.123366 + 0.779154I
−0.79502 + 1.63299I 0
u = −0.606513 − 1.004750I
a = 1.369280 − 0.164619I
b = −0.123366 − 0.779154I
−0.79502 − 1.63299I 0
u = 0.398013 + 0.718929I
a = −0.163909 + 0.749231I
b = −0.090052 − 1.341910I
−6.98707 + 0.72092I 0
u = 0.398013 − 0.718929I
a = −0.163909 − 0.749231I
b = −0.090052 + 1.341910I
−6.98707 − 0.72092I 0
u = −0.779145 + 0.883965I
a = 0.237109 + 0.001248I
b = 0.199327 − 1.111140I
−3.46471 + 2.35167I 0
u = −0.779145 − 0.883965I
a = 0.237109 − 0.001248I
b = 0.199327 + 1.111140I
−3.46471 − 2.35167I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.842114 + 0.831002I
a = −1.83183 − 0.06907I
b = −0.630257 + 0.821670I
−3.14638 − 5.48393I 0
u = 0.842114 − 0.831002I
a = −1.83183 + 0.06907I
b = −0.630257 − 0.821670I
−3.14638 + 5.48393I 0
u = −0.559346 + 1.054570I
a = 1.87501 − 0.04824I
b = 0.87768 + 1.17439I
2.80840 + 6.49328I 0
u = −0.559346 − 1.054570I
a = 1.87501 + 0.04824I
b = 0.87768 − 1.17439I
2.80840 − 6.49328I 0
u = 0.415814 + 1.128180I
a = 1.31019 + 0.66892I
b = 1.176620 + 0.512232I
7.33371 − 7.21816I 0
u = 0.415814 − 1.128180I
a = 1.31019 − 0.66892I
b = 1.176620 − 0.512232I
7.33371 + 7.21816I 0
u = −0.655182 + 0.448203I
a = 0.418144 + 0.462178I
b = −0.274738 − 1.124500I
−2.34756 + 3.34951I 0
u = −0.655182 − 0.448203I
a = 0.418144 − 0.462178I
b = −0.274738 + 1.124500I
−2.34756 − 3.34951I 0
u = −0.123366 + 0.779154I
a = −2.40149 + 0.01080I
b = −0.606513 + 1.004750I
0.79502 − 1.63299I 0
u = −0.123366 − 0.779154I
a = −2.40149 − 0.01080I
b = −0.606513 − 1.004750I
0.79502 + 1.63299I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.285090 + 0.732214I
a = 1.96824 − 0.40604I
b = 1.223720 + 0.369838I
3.73949 + 4.32335I 0
u = −0.285090 − 0.732214I
a = 1.96824 + 0.40604I
b = 1.223720 − 0.369838I
3.73949 − 4.32335I 0
u = −1.162480 + 0.379098I
a = −0.286847 − 0.181302I
b = −0.572808 + 1.187830I
−2.82817 − 13.47410I 0
u = −1.162480 − 0.379098I
a = −0.286847 + 0.181302I
b = −0.572808 − 1.187830I
−2.82817 + 13.47410I 0
u = 0.530075 + 1.123270I
a = 1.071000 + 0.753859I
b = 0.457188 − 0.877846I
6.63354 − 0.43992I 0
u = 0.530075 − 1.123270I
a = 1.071000 − 0.753859I
b = 0.457188 + 0.877846I
6.63354 + 0.43992I 0
u = −0.414058 + 1.179940I
a = −1.58135 − 0.52910I
b = −0.77596 − 1.19119I
1.55910 + 6.59009I 0
u = −0.414058 − 1.179940I
a = −1.58135 + 0.52910I
b = −0.77596 + 1.19119I
1.55910 − 6.59009I 0
u = 0.513923 + 1.144070I
a = 1.068130 + 0.337962I
b = 1.042900 + 0.163804I
−1.55339 − 8.26333I 0
u = 0.513923 − 1.144070I
a = 1.068130 − 0.337962I
b = 1.042900 − 0.163804I
−1.55339 + 8.26333I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356688 + 1.203140I
a = −1.82709 − 1.00984I
b = −0.294481 + 0.965440I
2.58230 − 7.66961I 0
u = 0.356688 − 1.203140I
a = −1.82709 + 1.00984I
b = −0.294481 − 0.965440I
2.58230 + 7.66961I 0
u = 0.572579 + 1.119490I
a = −1.88829 − 0.15398I
b = −0.69528 + 1.41951I
1.05567 − 9.97787I 0
u = 0.572579 − 1.119490I
a = −1.88829 + 0.15398I
b = −0.69528 − 1.41951I
1.05567 + 9.97787I 0
u = 0.724099 + 0.110420I
a = 0.104396 + 1.321150I
b = 0.444211 + 0.024548I
−4.35932 + 3.66419I 0
u = 0.724099 − 0.110420I
a = 0.104396 − 1.321150I
b = 0.444211 − 0.024548I
−4.35932 − 3.66419I 0
u = −0.541294 + 1.147470I
a = 1.53105 − 0.30514I
b = 0.450781 + 1.267390I
−2.03353 + 7.92224I 0
u = −0.541294 − 1.147470I
a = 1.53105 + 0.30514I
b = 0.450781 − 1.267390I
−2.03353 − 7.92224I 0
u = 0.586656 + 1.132260I
a = −0.647738 − 0.320076I
b = −0.738333 − 0.445064I
−1.02642 − 1.58654I 0
u = 0.586656 − 1.132260I
a = −0.647738 + 0.320076I
b = −0.738333 + 0.445064I
−1.02642 + 1.58654I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.223720 + 0.369838I
a = −0.439882 − 0.493294I
b = −0.285090 + 0.732214I
−3.73949 − 4.32335I 0
u = 1.223720 − 0.369838I
a = −0.439882 + 0.493294I
b = −0.285090 − 0.732214I
−3.73949 + 4.32335I 0
u = 1.176620 + 0.512232I
a = 0.019477 − 0.191925I
b = 0.415814 + 1.128180I
−7.33371 + 7.21816I 0
u = 1.176620 − 0.512232I
a = 0.019477 + 0.191925I
b = 0.415814 − 1.128180I
−7.33371 − 7.21816I 0
u = −0.281396 + 1.269730I
a = 0.709476 − 0.299779I
b = 0.469795 + 0.051989I
1.74068 + 3.95647I 0
u = −0.281396 − 1.269730I
a = 0.709476 + 0.299779I
b = 0.469795 − 0.051989I
1.74068 − 3.95647I 0
u = −0.646848 + 0.242634I
a = 1.64627 − 1.40446I
b = 0.409874 + 0.982147I
−4.95212 + 3.37858I −6.43526 + 0.I
u = −0.646848 − 0.242634I
a = 1.64627 + 1.40446I
b = 0.409874 − 0.982147I
−4.95212 − 3.37858I −6.43526 + 0.I
u = −0.204775 + 1.293760I
a = −1.371610 + 0.299493I
b = −0.594235 − 0.676961I
5.14661 − 4.35854I 0
u = −0.204775 − 1.293760I
a = −1.371610 − 0.299493I
b = −0.594235 + 0.676961I
5.14661 + 4.35854I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.590734 + 1.176550I
a = 1.390780 + 0.017847I
b = 0.441987 + 0.988216I
−0.59941 + 4.40862I 0
u = −0.590734 − 1.176550I
a = 1.390780 − 0.017847I
b = 0.441987 − 0.988216I
−0.59941 − 4.40862I 0
u = −0.572808 + 1.187830I
a = −1.099690 + 0.687405I
b = −1.162480 + 0.379098I
2.82817 + 13.47410I 0
u = −0.572808 − 1.187830I
a = −1.099690 − 0.687405I
b = −1.162480 − 0.379098I
2.82817 − 13.47410I 0
u = −0.090052 + 1.341910I
a = 0.501755 − 1.175910I
b = 0.398013 − 0.718929I
6.98707 + 0.72092I 0
u = −0.090052 − 1.341910I
a = 0.501755 + 1.175910I
b = 0.398013 + 0.718929I
6.98707 − 0.72092I 0
u = 0.450781 + 1.267390I
a = −1.76826 + 0.33344I
b = −0.541294 + 1.147470I
2.03353 − 7.92224I 0
u = 0.450781 − 1.267390I
a = −1.76826 − 0.33344I
b = −0.541294 − 1.147470I
2.03353 + 7.92224I 0
u = 0.076170 + 0.644966I
a = 5.53062 + 0.32618I
b = 0.076170 − 0.644966I
5.59442I 0. + 4.35174I
u = 0.076170 − 0.644966I
a = 5.53062 − 0.32618I
b = 0.076170 + 0.644966I
− 5.59442I 0. − 4.35174I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.565906 + 1.249250I
a = −1.248660 − 0.187164I
b = −0.565906 − 1.249250I
7.22240I 0
u = −0.565906 − 1.249250I
a = −1.248660 + 0.187164I
b = −0.565906 + 1.249250I
− 7.22240I 0
u = −1.203960 + 0.670041I
a = 0.286162 − 0.232778I
b = −0.193630 + 0.965913I
−3.46403 + 0.49869I 0
u = −1.203960 − 0.670041I
a = 0.286162 + 0.232778I
b = −0.193630 − 0.965913I
−3.46403 − 0.49869I 0
u = −0.533037 + 1.282680I
a = 1.035620 − 0.515871I
b = 0.765672 − 0.345950I
1.21473 + 4.93993I 0
u = −0.533037 − 1.282680I
a = 1.035620 + 0.515871I
b = 0.765672 + 0.345950I
1.21473 − 4.93993I 0
u = 0.582324 + 1.262960I
a = 1.61676 − 0.12588I
b = 0.73565 − 1.22923I
4.9506 − 14.0072I 0
u = 0.582324 − 1.262960I
a = 1.61676 + 0.12588I
b = 0.73565 + 1.22923I
4.9506 + 14.0072I 0
u = −0.77596 + 1.19119I
a = −0.893589 + 0.206219I
b = −0.414058 − 1.179940I
−1.55910 + 6.59009I 0
u = −0.77596 − 1.19119I
a = −0.893589 − 0.206219I
b = −0.414058 + 1.179940I
−1.55910 − 6.59009I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.73565 + 1.22923I
a = 1.367010 + 0.101880I
b = 0.582324 − 1.262960I
−4.9506 − 14.0072I 0
u = 0.73565 − 1.22923I
a = 1.367010 − 0.101880I
b = 0.582324 + 1.262960I
−4.9506 + 14.0072I 0
u = −0.69868 + 1.26475I
a = −1.65087 + 0.08662I
b = −0.69868 − 1.26475I
20.0711I 0
u = −0.69868 − 1.26475I
a = −1.65087 − 0.08662I
b = −0.69868 + 1.26475I
− 20.0711I 0
u = −0.28586 + 1.43183I
a = 0.369287 + 0.198484I
b = 0.106761 + 0.498688I
1.64258 + 3.83167I 0
u = −0.28586 − 1.43183I
a = 0.369287 − 0.198484I
b = 0.106761 − 0.498688I
1.64258 − 3.83167I 0
u = 0.27057 + 1.43596I
a = −0.573288 − 1.226230I
b = −0.312914 − 0.810172I
3.09882 − 5.03766I 0
u = 0.27057 − 1.43596I
a = −0.573288 + 1.226230I
b = −0.312914 + 0.810172I
3.09882 + 5.03766I 0
u = 0.87768 + 1.17439I
a = −1.246940 − 0.309038I
b = −0.559346 + 1.054570I
−2.80840 − 6.49328I 0
u = 0.87768 − 1.17439I
a = −1.246940 + 0.309038I
b = −0.559346 − 1.054570I
−2.80840 + 6.49328I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30645 + 1.45756I
a = 0.251821 + 0.650498I
b = 0.409920 + 0.771799I
7.01825 + 3.22517I 0
u = 0.30645 − 1.45756I
a = 0.251821 − 0.650498I
b = 0.409920 − 0.771799I
7.01825 − 3.22517I 0
u = 0.106761 + 0.498688I
a = −1.030910 + 0.490758I
b = −0.28586 + 1.43183I
−1.64258 − 3.83167I −1.96317 + 12.23971I
u = 0.106761 − 0.498688I
a = −1.030910 − 0.490758I
b = −0.28586 − 1.43183I
−1.64258 + 3.83167I −1.96317 − 12.23971I
u = 1.30399 + 0.73093I
a = −0.268543 + 0.307620I
b = −0.385490 − 0.927127I
−4.40812 − 1.23041I 0
u = 1.30399 − 0.73093I
a = −0.268543 − 0.307620I
b = −0.385490 + 0.927127I
−4.40812 + 1.23041I 0
u = 0.499694 + 0.025259I
a = 0.080117 + 0.278174I
b = −0.833054 − 0.070087I
2.48910 + 0.06312I 2.49825 + 0.73817I
u = 0.499694 − 0.025259I
a = 0.080117 − 0.278174I
b = −0.833054 + 0.070087I
2.48910 − 0.06312I 2.49825 − 0.73817I
u = 0.469795 + 0.051989I
a = −0.891265 − 0.759865I
b = −0.281396 + 1.269730I
−1.74068 − 3.95647I −3.95884 + 5.99220I
u = 0.469795 − 0.051989I
a = −0.891265 + 0.759865I
b = −0.281396 − 1.269730I
−1.74068 + 3.95647I −3.95884 − 5.99220I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06658 + 1.53283I
a = −0.746943 + 0.645715I
b = −0.528497 + 0.902931I
4.48952 − 8.79836I 0
u = −0.06658 − 1.53283I
a = −0.746943 − 0.645715I
b = −0.528497 − 0.902931I
4.48952 + 8.79836I 0
u = 0.444211 + 0.024548I
a = 0.76177 − 2.07119I
b = 0.724099 + 0.110420I
4.35932 − 3.66419I 4.12317 + 3.31331I
u = 0.444211 − 0.024548I
a = 0.76177 + 2.07119I
b = 0.724099 − 0.110420I
4.35932 + 3.66419I 4.12317 − 3.31331I
u = −0.69528 + 1.41951I
a = 1.57081 − 0.00968I
b = 0.572579 + 1.119490I
−1.05567 + 9.97787I 0
u = −0.69528 − 1.41951I
a = 1.57081 + 0.00968I
b = 0.572579 − 1.119490I
−1.05567 − 9.97787I 0
u = −0.082605 + 0.379665I
a = 0.943469 − 0.404093I
b = −0.082605 − 0.379665I
0.949280I 0. − 6.70220I
u = −0.082605 − 0.379665I
a = 0.943469 + 0.404093I
b = −0.082605 + 0.379665I
− 0.949280I 0. + 6.70220I
u = −0.266047 + 0.173518I
a = −2.17548 + 4.76973I
b = 0.215475 − 0.882220I
−4.87192 − 3.43607I −3.62298 + 0.04934I
u = −0.266047 − 0.173518I
a = −2.17548 − 4.76973I
b = 0.215475 + 0.882220I
−4.87192 + 3.43607I −3.62298 − 0.04934I
20
II. I
u
2
= h−1.12 × 10
18
u
39
+ 9.09 × 10
17
u
38
+ · · · + 4.95 × 10
16
b + 1.45 ×
10
18
, 2.56 × 10
20
u
39
− 1.19 × 10
22
u
38
+ · · · + 3.04 × 10
20
a − 5.40 ×
10
22
, u
40
+ 10u
38
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
2
=
−u
u
3
+ u
a
11
=
−0.841362u
39
+ 39.2840u
38
+ ··· − 463.413u + 177.533
22.5953u
39
− 18.3378u
38
+ ··· + 138.625u − 29.2540
a
4
=
96.8384u
39
+ 116.281u
38
+ ··· − 605.169u + 404.042
−7.42774u
39
− 28.0649u
38
+ ··· + 156.143u − 88.3283
a
10
=
−23.4366u
39
+ 57.6218u
38
+ ··· − 602.038u + 206.787
22.5953u
39
− 18.3378u
38
+ ··· + 138.625u − 29.2540
a
7
=
10.7408u
39
− 64.7330u
38
+ ··· + 224.393u − 162.549
32.2534u
39
+ 3.89162u
38
+ ··· + 8.53369u + 27.4869
a
8
=
30.6395u
39
− 79.3869u
38
+ ··· + 327.930u − 198.276
19.0177u
39
+ 14.3984u
38
+ ··· − 45.7972u + 48.5597
a
9
=
−137.038u
39
+ 5.37150u
38
+ ··· − 27.7704u − 15.3466
−3.99723u
39
− 7.04365u
38
+ ··· − 103.972u − 5.33221
a
3
=
−80.3048u
39
+ 13.3733u
38
+ ··· − 141.651u − 42.8254
48.7262u
39
+ 20.7302u
38
+ ··· + 53.2754u + 41.9282
a
12
=
161.564u
39
+ 6.83751u
38
+ ··· + 487.882u + 71.2551
−58.4557u
39
− 23.0763u
38
+ ··· − 243.779u − 4.23229
(ii) Obstruction class = 1
(iii) Cusp Shapes =
41911824563511122045817
304166537670200997547
u
39
−
11243733601743254008907
304166537670200997547
u
38
+ ··· +
93086926896221999194540
304166537670200997547
u +
26211462203690607230670
304166537670200997547
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
40
+ 10u
38
+ ··· + 2u + 1
c
2
, c
9
u
40
− 16u
38
+ ··· − 39u + 7
c
3
, c
7
u
40
− 16u
38
+ ··· + 39u + 7
c
4
u
40
− 8u
38
+ ··· − 12u + 1
c
5
, c
6
u
40
+ 10u
38
+ ··· − 2u + 1
c
8
u
40
+ u
38
+ ··· − 4u + 1
c
11
u
40
+ u
38
+ ··· + 4u + 1
c
12
u
40
− 8u
38
+ ··· + 12u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
40
+ 20y
39
+ ··· + 34y + 1
c
2
, c
3
, c
7
c
9
y
40
− 32y
39
+ ··· + 229y + 49
c
4
, c
12
y
40
− 16y
39
+ ··· + 978y + 1
c
8
, c
11
y
40
+ 2y
39
+ ··· + 8y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266937 + 0.970516I
a = 1.97275 + 0.64269I
b = 1.003880 − 0.363984I
5.02195 − 4.43214I 7.83962 + 8.15624I
u = 0.266937 − 0.970516I
a = 1.97275 − 0.64269I
b = 1.003880 + 0.363984I
5.02195 + 4.43214I 7.83962 − 8.15624I
u = −0.253080 + 0.975102I
a = −1.43411 − 0.04622I
b = −1.144990 − 0.214911I
3.26023 + 2.34112I 5.32453 − 7.25935I
u = −0.253080 − 0.975102I
a = −1.43411 + 0.04622I
b = −1.144990 + 0.214911I
3.26023 − 2.34112I 5.32453 + 7.25935I
u = −0.255310 + 0.924043I
a = −1.64759 + 0.89709I
b = −1.174940 + 0.636289I
3.08715 − 0.25895I −2.19036 − 5.53864I
u = −0.255310 − 0.924043I
a = −1.64759 − 0.89709I
b = −1.174940 − 0.636289I
3.08715 + 0.25895I −2.19036 + 5.53864I
u = 0.255086 + 0.910937I
a = 0.70601 + 1.33878I
b = 1.170370 + 0.738563I
4.77985 + 2.25678I 9.73483 − 6.01601I
u = 0.255086 − 0.910937I
a = 0.70601 − 1.33878I
b = 1.170370 − 0.738563I
4.77985 − 2.25678I 9.73483 + 6.01601I
u = 1.003880 + 0.363984I
a = 1.018380 + 0.835113I
b = 0.266937 − 0.970516I
−5.02195 − 4.43214I −7.83962 + 8.15624I
u = 1.003880 − 0.363984I
a = 1.018380 − 0.835113I
b = 0.266937 + 0.970516I
−5.02195 + 4.43214I −7.83962 − 8.15624I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.367951 + 0.835878I
a = 1.92159 + 1.26970I
b = 0.504732 − 0.697330I
4.81807 − 4.20281I 2.77271 + 8.50909I
u = 0.367951 − 0.835878I
a = 1.92159 − 1.26970I
b = 0.504732 + 0.697330I
4.81807 + 4.20281I 2.77271 − 8.50909I
u = 0.504732 + 0.697330I
a = 2.56040 + 0.24300I
b = 0.367951 − 0.835878I
−4.81807 − 4.20281I −2.77271 + 8.50909I
u = 0.504732 − 0.697330I
a = 2.56040 − 0.24300I
b = 0.367951 + 0.835878I
−4.81807 + 4.20281I −2.77271 − 8.50909I
u = −1.144990 + 0.214911I
a = −0.128444 + 0.259399I
b = −0.253080 − 0.975102I
−3.26023 + 2.34112I −5.32453 − 7.25935I
u = −1.144990 − 0.214911I
a = −0.128444 − 0.259399I
b = −0.253080 + 0.975102I
−3.26023 − 2.34112I −5.32453 + 7.25935I
u = −0.450563 + 1.145660I
a = −1.71484 − 0.36630I
b = −0.684519 − 1.181630I
0.95277 + 6.40093I 0. − 5.46085I
u = −0.450563 − 1.145660I
a = −1.71484 + 0.36630I
b = −0.684519 + 1.181630I
0.95277 − 6.40093I 0. + 5.46085I
u = 0.135564 + 1.277420I
a = −0.660117 + 0.490819I
b = 0.124407 + 0.438191I
6.74796 + 2.00538I 0
u = 0.135564 − 1.277420I
a = −0.660117 − 0.490819I
b = 0.124407 − 0.438191I
6.74796 − 2.00538I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.174940 + 0.636289I
a = 0.100201 − 0.374119I
b = −0.255310 + 0.924043I
−3.08715 + 0.25895I 0
u = −1.174940 − 0.636289I
a = 0.100201 + 0.374119I
b = −0.255310 − 0.924043I
−3.08715 − 0.25895I 0
u = −0.153259 + 0.633495I
a = −5.43707 + 0.98008I
b = −0.153259 − 0.633495I
6.04280I 0. − 12.91332I
u = −0.153259 − 0.633495I
a = −5.43707 − 0.98008I
b = −0.153259 + 0.633495I
− 6.04280I 0. + 12.91332I
u = −0.178778 + 0.615337I
a = −0.188313 + 0.187766I
b = −0.36254 + 1.42304I
−1.45254 − 3.42254I 5.30121 − 4.52957I
u = −0.178778 − 0.615337I
a = −0.188313 − 0.187766I
b = −0.36254 − 1.42304I
−1.45254 + 3.42254I 5.30121 + 4.52957I
u = −0.684519 + 1.181630I
a = −1.153190 + 0.270405I
b = −0.450563 − 1.145660I
−0.95277 + 6.40093I 0
u = −0.684519 − 1.181630I
a = −1.153190 − 0.270405I
b = −0.450563 + 1.145660I
−0.95277 − 6.40093I 0
u = 0.527929 + 1.260530I
a = 1.81194 + 0.01805I
b = 0.527929 − 1.260530I
− 9.22235I 0
u = 0.527929 − 1.260530I
a = 1.81194 − 0.01805I
b = 0.527929 + 1.260530I
9.22235I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.178345 + 1.363680I
a = 1.114680 + 0.867402I
b = 0.122775 + 0.515880I
3.50705 − 6.04532I 0
u = 0.178345 − 1.363680I
a = 1.114680 − 0.867402I
b = 0.122775 − 0.515880I
3.50705 + 6.04532I 0
u = 1.170370 + 0.738563I
a = 0.510579 − 0.091593I
b = 0.255086 + 0.910937I
−4.77985 − 2.25678I 0
u = 1.170370 − 0.738563I
a = 0.510579 + 0.091593I
b = 0.255086 − 0.910937I
−4.77985 + 2.25678I 0
u = −0.36254 + 1.42304I
a = −0.093925 + 0.536186I
b = −0.178778 + 0.615337I
1.45254 + 3.42254I 0
u = −0.36254 − 1.42304I
a = −0.093925 − 0.536186I
b = −0.178778 − 0.615337I
1.45254 − 3.42254I 0
u = 0.122775 + 0.515880I
a = −2.46441 − 1.17281I
b = 0.178345 + 1.363680I
−3.50705 + 6.04532I −3.46119 − 7.26382I
u = 0.122775 − 0.515880I
a = −2.46441 + 1.17281I
b = 0.178345 − 1.363680I
−3.50705 − 6.04532I −3.46119 + 7.26382I
u = 0.124407 + 0.438191I
a = 2.20546 + 0.23002I
b = 0.135564 + 1.277420I
−6.74796 − 2.00538I −5.26025 + 1.78206I
u = 0.124407 − 0.438191I
a = 2.20546 − 0.23002I
b = 0.135564 − 1.277420I
−6.74796 + 2.00538I −5.26025 − 1.78206I
27
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
40
+ 10u
38
+ ··· + 2u + 1)(u
160
+ 5u
159
+ ··· + 1034u + 763)
c
2
(u
40
− 16u
38
+ ··· − 39u + 7)(u
160
+ u
159
+ ··· + 79965u + 7417)
c
3
(u
40
− 16u
38
+ ··· + 39u + 7)(u
160
− u
159
+ ··· − 79965u + 7417)
c
4
(u
40
− 8u
38
+ ··· − 12u + 1)(u
160
+ u
159
+ ··· + 6487992u + 714773)
c
5
(u
40
+ 10u
38
+ ··· − 2u + 1)(u
160
+ 5u
159
+ ··· + 1034u + 763)
c
6
(u
40
+ 10u
38
+ ··· − 2u + 1)(u
160
− 5u
159
+ ··· − 1034u + 763)
c
7
(u
40
− 16u
38
+ ··· + 39u + 7)(u
160
+ u
159
+ ··· + 79965u + 7417)
c
8
(u
40
+ u
38
+ ··· − 4u + 1)(u
160
+ 7u
159
+ ··· + 60u + 7)
c
9
(u
40
− 16u
38
+ ··· − 39u + 7)(u
160
− u
159
+ ··· − 79965u + 7417)
c
10
(u
40
+ 10u
38
+ ··· + 2u + 1)(u
160
− 5u
159
+ ··· − 1034u + 763)
c
11
(u
40
+ u
38
+ ··· + 4u + 1)(u
160
− 7u
159
+ ··· − 60u + 7)
c
12
(u
40
− 8u
38
+ ··· + 12u + 1)(u
160
− u
159
+ ··· − 6487992u + 714773)
28
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(y
40
+ 20y
39
+ ··· + 34y + 1)
· (y
160
+ 81y
159
+ ··· + 13136378y + 582169)
c
2
, c
3
, c
7
c
9
(y
40
− 32y
39
+ ··· + 229y + 49)
· (y
160
− 115y
159
+ ··· + 324258557y + 55011889)
c
4
, c
12
(y
40
− 16y
39
+ ··· + 978y + 1)
· (y
160
− 7y
159
+ ··· + 4855248205898y + 510900441529)
c
8
, c
11
(y
40
+ 2y
39
+ ··· + 8y + 1)(y
160
+ 7y
159
+ ··· + 1832y + 49)
29
