12n
0866
(K12n
0866
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 11 9 3 1 12 4 6 7
Solving Sequence
3,10
4
8,11
2 1 5 6 7 12 9
c
3
c
10
c
2
c
1
c
4
c
5
c
7
c
12
c
9
c
6
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.24188 × 10
496
u
100
− 3.45972 × 10
496
u
99
+ ··· + 4.38110 × 10
498
b − 8.43502 × 10
499
,
− 6.68237 × 10
501
u
100
+ 1.69590 × 10
502
u
99
+ ··· + 7.40551 × 10
503
a + 3.34460 × 10
505
,
u
101
− 2u
100
+ ··· − 18346u − 3931i
I
u
2
= h−3.33238 × 10
33
u
30
+ 1.40429 × 10
33
u
29
+ ··· + 3.70136 × 10
33
b + 8.89806 × 10
33
,
2.33080 × 10
34
u
30
+ 6.01457 × 10
33
u
29
+ ··· + 1.85068 × 10
34
a + 5.60898 × 10
34
, u
31
− u
30
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 132 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
= h1.24 × 10
496
u
100
− 3.46 × 10
496
u
99
+ · · · + 4.38 × 10
498
b − 8.44 ×
10
499
, −6.68 × 10
501
u
100
+ 1.70 × 10
502
u
99
+ · · · + 7.41 × 10
503
a + 3.34 ×
10
505
, u
101
− 2u
100
+ · · · − 18346u − 3931i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
8
=
0.00902352u
100
− 0.0229006u
99
+ ··· − 189.264u − 45.1637
−0.00283463u
100
+ 0.00789692u
99
+ ··· + 62.3350u + 19.2532
a
11
=
u
−u
3
+ u
a
2
=
0.0101284u
100
− 0.0271243u
99
+ ··· − 180.804u − 68.4594
0.00236453u
100
− 0.00531970u
99
+ ··· − 89.3719u − 21.0059
a
1
=
0.0174868u
100
− 0.0458591u
99
+ ··· − 356.352u − 116.461
0.000717401u
100
− 0.00150781u
99
+ ··· − 44.5835u − 5.21116
a
5
=
0.00667899u
100
− 0.0155294u
99
+ ··· − 143.768u − 59.2234
0.00156664u
100
− 0.00347406u
99
+ ··· + 7.95421u − 8.67759
a
6
=
0.00730544u
100
− 0.0174596u
99
+ ··· − 149.290u − 57.3470
0.00189055u
100
− 0.00468428u
99
+ ··· + 12.3972u − 4.13842
a
7
=
0.00618889u
100
− 0.0150037u
99
+ ··· − 126.929u − 25.9105
−0.00283463u
100
+ 0.00789692u
99
+ ··· + 62.3350u + 19.2532
a
12
=
0.00373393u
100
− 0.0102203u
99
+ ··· − 93.3892u − 35.7880
0.00459301u
100
− 0.0114226u
99
+ ··· − 140.650u − 35.6539
a
9
=
−0.0138835u
100
+ 0.0364496u
99
+ ··· + 227.848u + 80.5728
−0.00415038u
100
+ 0.0118164u
99
+ ··· + 27.4684u + 6.37850
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00493355u
100
− 0.0156200u
99
+ ··· + 258.329u + 60.2116
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
101
− 7u
100
+ ··· − 533u + 356
c
2
, c
7
u
101
− u
100
+ ··· + 72811u − 14123
c
3
, c
10
u
101
− 2u
100
+ ··· − 18346u − 3931
c
5
, c
11
u
101
+ 2u
100
+ ··· + 641239u + 167761
c
6
u
101
− 10u
100
+ ··· + 53u − 7
c
8
u
101
− 14u
99
+ ··· − 238884u + 56743
c
9
u
101
− 12u
99
+ ··· + 549u + 319
c
12
u
101
− u
100
+ ··· + 41u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
101
− 71y
100
+ ··· + 18234321y −126736
c
2
, c
7
y
101
+ 51y
100
+ ··· − 7022994229y −199459129
c
3
, c
10
y
101
− 34y
100
+ ··· + 615503752y −15452761
c
5
, c
11
y
101
− 64y
100
+ ··· + 814720100043y −28143753121
c
6
y
101
− 4y
100
+ ··· − 411y −49
c
8
y
101
− 28y
100
+ ··· + 62222823240y −3219768049
c
9
y
101
− 24y
100
+ ··· + 8075431y −101761
c
12
y
101
− 15y
100
+ ··· + 205y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335741 + 0.942623I
a = 0.171336 − 0.461058I
b = −0.832272 + 0.473296I
−2.68327 + 2.47464I 0
u = −0.335741 − 0.942623I
a = 0.171336 + 0.461058I
b = −0.832272 − 0.473296I
−2.68327 − 2.47464I 0
u = 0.739090 + 0.647908I
a = −0.801576 − 0.737358I
b = −0.322770 + 1.027790I
1.12451 + 2.33115I 0
u = 0.739090 − 0.647908I
a = −0.801576 + 0.737358I
b = −0.322770 − 1.027790I
1.12451 − 2.33115I 0
u = −0.908054 + 0.479569I
a = −1.331810 + 0.464404I
b = 0.091557 − 1.002580I
5.34262 + 4.93001I 0
u = −0.908054 − 0.479569I
a = −1.331810 − 0.464404I
b = 0.091557 + 1.002580I
5.34262 − 4.93001I 0
u = 0.760395 + 0.602455I
a = 0.28359 + 2.30805I
b = 0.548337 − 0.958511I
−4.43347 + 0.86302I 0
u = 0.760395 − 0.602455I
a = 0.28359 − 2.30805I
b = 0.548337 + 0.958511I
−4.43347 − 0.86302I 0
u = −0.680557 + 0.642379I
a = −0.25678 + 2.61848I
b = −0.549331 − 0.549526I
−1.98269 + 5.75991I 0
u = −0.680557 − 0.642379I
a = −0.25678 − 2.61848I
b = −0.549331 + 0.549526I
−1.98269 − 5.75991I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990174 + 0.391333I
a = 0.683315 − 0.852245I
b = 0.724664 + 0.990879I
5.46158 − 3.32830I 0
u = −0.990174 − 0.391333I
a = 0.683315 + 0.852245I
b = 0.724664 − 0.990879I
5.46158 + 3.32830I 0
u = −0.014589 + 1.074460I
a = −0.560726 − 0.156317I
b = 0.356570 − 0.622040I
−0.18310 + 4.10072I 0
u = −0.014589 − 1.074460I
a = −0.560726 + 0.156317I
b = 0.356570 + 0.622040I
−0.18310 − 4.10072I 0
u = −0.804153 + 0.420138I
a = −0.72387 − 2.61788I
b = 0.323477 + 0.580944I
−3.22125 − 2.25400I 0
u = −0.804153 − 0.420138I
a = −0.72387 + 2.61788I
b = 0.323477 − 0.580944I
−3.22125 + 2.25400I 0
u = 0.591754 + 0.670470I
a = −1.36762 − 2.85537I
b = −0.609413 + 0.741411I
−1.92951 + 7.45316I 0
u = 0.591754 − 0.670470I
a = −1.36762 + 2.85537I
b = −0.609413 − 0.741411I
−1.92951 − 7.45316I 0
u = −0.879068 + 0.097691I
a = −0.38877 + 2.34684I
b = 0.18369 − 1.44819I
6.83409 + 1.24645I 8.04713 + 6.47613I
u = −0.879068 − 0.097691I
a = −0.38877 − 2.34684I
b = 0.18369 + 1.44819I
6.83409 − 1.24645I 8.04713 − 6.47613I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.112940 + 0.099762I
a = 0.20418 + 1.41730I
b = −0.02840 − 1.78962I
8.25044 − 4.75376I 0
u = 1.112940 − 0.099762I
a = 0.20418 − 1.41730I
b = −0.02840 + 1.78962I
8.25044 + 4.75376I 0
u = −0.883426 + 0.699757I
a = −0.426704 + 0.674530I
b = −0.819790 − 1.089020I
5.04912 − 9.82598I 0
u = −0.883426 − 0.699757I
a = −0.426704 − 0.674530I
b = −0.819790 + 1.089020I
5.04912 + 9.82598I 0
u = −0.769396 + 0.408713I
a = −0.85103 + 1.93608I
b = −0.28459 − 1.54058I
6.14574 − 3.41683I 0. + 5.62687I
u = −0.769396 − 0.408713I
a = −0.85103 − 1.93608I
b = −0.28459 + 1.54058I
6.14574 + 3.41683I 0. − 5.62687I
u = 0.981659 + 0.567919I
a = 0.372093 + 0.614692I
b = −1.162230 − 0.719141I
−3.71955 + 3.78254I 0
u = 0.981659 − 0.567919I
a = 0.372093 − 0.614692I
b = −1.162230 + 0.719141I
−3.71955 − 3.78254I 0
u = 0.767258 + 0.387072I
a = −2.26933 − 0.52214I
b = −0.045075 + 0.748539I
4.13125 + 4.58781I 6.30028 − 8.20640I
u = 0.767258 − 0.387072I
a = −2.26933 + 0.52214I
b = −0.045075 − 0.748539I
4.13125 − 4.58781I 6.30028 + 8.20640I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845471 + 0.056980I
a = −0.513384 − 0.684658I
b = −0.894467 + 1.025650I
4.59577 − 2.95804I 7.45664 + 2.51259I
u = 0.845471 − 0.056980I
a = −0.513384 + 0.684658I
b = −0.894467 − 1.025650I
4.59577 + 2.95804I 7.45664 − 2.51259I
u = 0.746283 + 0.901380I
a = −0.387739 − 0.347019I
b = 0.743926 + 0.444324I
−1.64047 + 3.73610I 0
u = 0.746283 − 0.901380I
a = −0.387739 + 0.347019I
b = 0.743926 − 0.444324I
−1.64047 − 3.73610I 0
u = 0.810757 + 0.859245I
a = 0.566963 + 0.068944I
b = 0.334603 − 0.799273I
3.36674 + 3.99935I 0
u = 0.810757 − 0.859245I
a = 0.566963 − 0.068944I
b = 0.334603 + 0.799273I
3.36674 − 3.99935I 0
u = −1.041540 + 0.648552I
a = −0.263104 + 0.251661I
b = 1.39273 − 0.49381I
−0.78443 − 10.85120I 0
u = −1.041540 − 0.648552I
a = −0.263104 − 0.251661I
b = 1.39273 + 0.49381I
−0.78443 + 10.85120I 0
u = 0.544622 + 0.503086I
a = 2.78374 + 1.35172I
b = 0.23914 − 1.41293I
5.65417 + 7.51092I −2.1146 − 17.6086I
u = 0.544622 − 0.503086I
a = 2.78374 − 1.35172I
b = 0.23914 + 1.41293I
5.65417 − 7.51092I −2.1146 + 17.6086I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616737 + 0.384675I
a = −0.425365 − 0.797073I
b = −1.024740 + 0.060330I
−3.08884 − 0.48622I −3.61031 − 4.04424I
u = −0.616737 − 0.384675I
a = −0.425365 + 0.797073I
b = −1.024740 − 0.060330I
−3.08884 + 0.48622I −3.61031 + 4.04424I
u = 1.221840 + 0.379189I
a = −0.174467 + 1.327200I
b = 0.591202 − 0.984633I
1.336430 + 0.378146I 0
u = 1.221840 − 0.379189I
a = −0.174467 − 1.327200I
b = 0.591202 + 0.984633I
1.336430 − 0.378146I 0
u = 0.653739 + 0.296100I
a = 0.680491 + 0.398156I
b = −1.40608 − 0.23432I
−0.80163 + 2.56158I 12.54411 − 5.21051I
u = 0.653739 − 0.296100I
a = 0.680491 − 0.398156I
b = −1.40608 + 0.23432I
−0.80163 − 2.56158I 12.54411 + 5.21051I
u = 1.208470 + 0.441330I
a = 0.377011 + 0.622196I
b = 0.574325 − 0.859104I
5.22199 + 1.86600I 0
u = 1.208470 − 0.441330I
a = 0.377011 − 0.622196I
b = 0.574325 + 0.859104I
5.22199 − 1.86600I 0
u = −0.587445 + 0.393381I
a = 0.63747 − 1.43592I
b = 0.721097 + 0.304570I
0.03033 − 4.19051I −1.93243 + 7.90155I
u = −0.587445 − 0.393381I
a = 0.63747 + 1.43592I
b = 0.721097 − 0.304570I
0.03033 + 4.19051I −1.93243 − 7.90155I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.979732 + 0.863136I
a = −0.347825 − 1.326540I
b = −0.587013 + 1.060600I
−0.92319 + 2.71662I 0
u = 0.979732 − 0.863136I
a = −0.347825 + 1.326540I
b = −0.587013 − 1.060600I
−0.92319 − 2.71662I 0
u = −1.297700 + 0.161416I
a = 0.46874 − 1.36653I
b = 0.499603 + 1.049160I
6.53180 − 3.12071I 0
u = −1.297700 − 0.161416I
a = 0.46874 + 1.36653I
b = 0.499603 − 1.049160I
6.53180 + 3.12071I 0
u = −1.020200 + 0.836422I
a = 0.28293 − 1.41691I
b = 0.429007 + 1.318000I
−0.27055 − 5.95720I 0
u = −1.020200 − 0.836422I
a = 0.28293 + 1.41691I
b = 0.429007 − 1.318000I
−0.27055 + 5.95720I 0
u = −0.379681 + 1.284900I
a = −0.225697 + 0.075557I
b = 0.596090 − 0.670522I
−5.29363 + 3.72640I 0
u = −0.379681 − 1.284900I
a = −0.225697 − 0.075557I
b = 0.596090 + 0.670522I
−5.29363 − 3.72640I 0
u = −1.196020 + 0.617356I
a = −0.15292 + 1.54805I
b = −0.66207 − 1.35538I
3.01876 − 9.52238I 0
u = −1.196020 − 0.617356I
a = −0.15292 − 1.54805I
b = −0.66207 + 1.35538I
3.01876 + 9.52238I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649051 + 0.030330I
a = 2.14482 − 1.37227I
b = 0.224354 + 0.938503I
3.99872 + 1.68689I 5.43204 − 0.05309I
u = −0.649051 − 0.030330I
a = 2.14482 + 1.37227I
b = 0.224354 − 0.938503I
3.99872 − 1.68689I 5.43204 + 0.05309I
u = 0.592249 + 0.196535I
a = −0.478930 − 0.351702I
b = 0.290343 + 0.411437I
1.29118 + 0.90327I 4.33429 − 1.07742I
u = 0.592249 − 0.196535I
a = −0.478930 + 0.351702I
b = 0.290343 − 0.411437I
1.29118 − 0.90327I 4.33429 + 1.07742I
u = −0.719396 + 1.192760I
a = 0.584853 − 0.709217I
b = −0.283753 + 0.753818I
−1.37403 − 1.06324I 0
u = −0.719396 − 1.192760I
a = 0.584853 + 0.709217I
b = −0.283753 − 0.753818I
−1.37403 + 1.06324I 0
u = −1.03742 + 0.98838I
a = 0.141770 + 0.014842I
b = −1.33249 + 0.80314I
−0.898802 − 0.973883I 0
u = −1.03742 − 0.98838I
a = 0.141770 − 0.014842I
b = −1.33249 − 0.80314I
−0.898802 + 0.973883I 0
u = −1.19746 + 0.79980I
a = 0.47010 − 1.34436I
b = 0.842329 + 0.975042I
0.13777 − 5.90036I 0
u = −1.19746 − 0.79980I
a = 0.47010 + 1.34436I
b = 0.842329 − 0.975042I
0.13777 + 5.90036I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.230391 + 0.510073I
a = −0.707070 − 0.066360I
b = −0.574964 + 0.286969I
−1.069040 + 0.837326I −5.25343 − 2.47679I
u = −0.230391 − 0.510073I
a = −0.707070 + 0.066360I
b = −0.574964 − 0.286969I
−1.069040 − 0.837326I −5.25343 + 2.47679I
u = −0.408639 + 0.328571I
a = 2.29786 − 0.47366I
b = 0.236342 + 1.202430I
2.82869 + 1.16775I 1.92656 − 2.97243I
u = −0.408639 − 0.328571I
a = 2.29786 + 0.47366I
b = 0.236342 − 1.202430I
2.82869 − 1.16775I 1.92656 + 2.97243I
u = −1.30418 + 0.75032I
a = 0.21763 − 1.52567I
b = 0.593003 + 1.101090I
0.34364 − 8.84469I 0
u = −1.30418 − 0.75032I
a = 0.21763 + 1.52567I
b = 0.593003 − 1.101090I
0.34364 + 8.84469I 0
u = 1.48535 + 0.31011I
a = 0.211631 + 0.827352I
b = 0.566842 − 0.771589I
5.44294 + 1.31425I 0
u = 1.48535 − 0.31011I
a = 0.211631 − 0.827352I
b = 0.566842 + 0.771589I
5.44294 − 1.31425I 0
u = 0.32442 + 1.49185I
a = −0.049576 − 0.294942I
b = 0.145568 + 0.412100I
−3.93645 + 3.12134I 0
u = 0.32442 − 1.49185I
a = −0.049576 + 0.294942I
b = 0.145568 − 0.412100I
−3.93645 − 3.12134I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.34291 + 0.74284I
a = −0.200184 + 1.309160I
b = −0.817867 − 1.152050I
−2.17648 − 10.86010I 0
u = −1.34291 − 0.74284I
a = −0.200184 − 1.309160I
b = −0.817867 + 1.152050I
−2.17648 + 10.86010I 0
u = 1.40351 + 0.69964I
a = −0.062209 − 1.265710I
b = −0.475748 + 1.035480I
−0.02173 + 4.35781I 0
u = 1.40351 − 0.69964I
a = −0.062209 + 1.265710I
b = −0.475748 − 1.035480I
−0.02173 − 4.35781I 0
u = −0.320752 + 0.267825I
a = −1.74148 + 1.65422I
b = 0.873019 − 0.534827I
−0.10842 + 4.70713I −0.07535 − 6.04334I
u = −0.320752 − 0.267825I
a = −1.74148 − 1.65422I
b = 0.873019 + 0.534827I
−0.10842 − 4.70713I −0.07535 + 6.04334I
u = 1.06191 + 1.19940I
a = −0.175207 − 0.266146I
b = 0.94367 + 1.18741I
0.289155 − 0.963733I 0
u = 1.06191 − 1.19940I
a = −0.175207 + 0.266146I
b = 0.94367 − 1.18741I
0.289155 + 0.963733I 0
u = 1.31849 + 0.91086I
a = 0.390967 + 1.307130I
b = 0.81059 − 1.33031I
1.9965 + 18.5154I 0
u = 1.31849 − 0.91086I
a = 0.390967 − 1.307130I
b = 0.81059 + 1.33031I
1.9965 − 18.5154I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27766 + 0.97157I
a = −0.491363 − 1.206580I
b = −0.86156 + 1.39694I
1.64453 + 9.51349I 0
u = 1.27766 − 0.97157I
a = −0.491363 + 1.206580I
b = −0.86156 − 1.39694I
1.64453 − 9.51349I 0
u = 0.67244 + 1.46914I
a = 0.266077 + 0.319742I
b = −0.553114 − 1.081280I
−0.25824 − 10.25430I 0
u = 0.67244 − 1.46914I
a = 0.266077 − 0.319742I
b = −0.553114 + 1.081280I
−0.25824 + 10.25430I 0
u = 0.353230
a = −0.00569879
b = 1.73770
−6.34209 43.4240
u = 1.65919 + 0.14081I
a = −0.37637 − 1.45740I
b = −0.321426 + 0.650504I
7.85758 + 5.71972I 0
u = 1.65919 − 0.14081I
a = −0.37637 + 1.45740I
b = −0.321426 − 0.650504I
7.85758 − 5.71972I 0
u = −1.85327 + 0.07108I
a = 0.037537 − 1.019320I
b = −0.080386 + 1.118770I
10.05940 − 3.85887I 0
u = −1.85327 − 0.07108I
a = 0.037537 + 1.019320I
b = −0.080386 − 1.118770I
10.05940 + 3.85887I 0
u = 0.53210 + 1.95211I
a = −0.195415 + 0.027385I
b = 0.28462 + 1.96358I
0.136814 − 0.690209I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.53210 − 1.95211I
a = −0.195415 − 0.027385I
b = 0.28462 − 1.96358I
0.136814 + 0.690209I 0
15
II.
I
u
2
= h−3.33×10
33
u
30
+1.40×10
33
u
29
+· · ·+3.70×10
33
b+8.90×10
33
, 2.33×
10
34
u
30
+6.01×10
33
u
29
+· · ·+1.85×10
34
a+5.61×10
34
, u
31
−u
30
+· · ·+3u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
8
=
−1.25943u
30
− 0.324992u
29
+ ··· − 9.17134u − 3.03076
0.900313u
30
− 0.379399u
29
+ ··· − 0.557782u − 2.40400
a
11
=
u
−u
3
+ u
a
2
=
0.0630092u
30
+ 1.20514u
29
+ ··· + 24.8663u + 4.36181
−2.56945u
30
+ 1.33702u
29
+ ··· + 5.03786u − 1.14698
a
1
=
−0.923553u
30
+ 1.41843u
29
+ ··· + 26.0367u + 1.94668
−2.29012u
30
+ 1.10519u
29
+ ··· + 1.73148u − 1.92026
a
5
=
2.02256u
30
− 2.57004u
29
+ ··· − 14.4691u + 9.69211
1.69481u
30
− 1.06445u
29
+ ··· + 0.319419u + 8.33953
a
6
=
2.79454u
30
− 3.27301u
29
+ ··· − 18.1079u + 8.41600
2.72879u
30
− 1.68146u
29
+ ··· − 2.34035u + 7.13243
a
7
=
−0.359115u
30
− 0.704391u
29
+ ··· − 9.72912u − 5.43476
0.900313u
30
− 0.379399u
29
+ ··· − 0.557782u − 2.40400
a
12
=
−0.710459u
30
+ 0.709167u
29
+ ··· + 9.93391u − 5.22559
−3.08296u
30
+ 1.59187u
29
+ ··· + 6.77351u − 2.51410
a
9
=
2.67082u
30
− 1.81548u
29
+ ··· − 21.6282u + 5.50354
2.16162u
30
− 1.42701u
29
+ ··· − 10.5432u + 4.49393
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8.00122u
30
+ 5.61008u
29
+ ··· + 45.6712u − 40.7698
16
(iv) u-Polynomials at the component
17
Crossings u-Polynomials at each crossing
c
1
u
31
− 6u
30
+ ··· − u − 1
c
2
u
31
+ 11u
29
+ ··· + 7u
2
+ 1
c
3
u
31
− u
30
+ ··· + 3u + 1
c
4
u
31
+ 6u
30
+ ··· − u + 1
c
5
u
31
− u
30
+ ··· − 16u + 17
c
6
u
31
+ 3u
30
+ ··· − 2u + 1
c
7
u
31
+ 11u
29
+ ··· − 7u
2
− 1
c
8
u
31
+ 3u
30
+ ··· + 511u + 169
c
9
u
31
+ 5u
30
+ ··· + 6u + 1
c
10
u
31
+ u
30
+ ··· + 3u − 1
c
11
u
31
+ u
30
+ ··· − 16u − 17
c
12
u
31
− 6u
29
+ ··· + 9u + 1
18
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
31
− 20y
30
+ ··· − 21y −1
c
2
, c
7
y
31
+ 22y
30
+ ··· − 14y −1
c
3
, c
10
y
31
− 11y
30
+ ··· + 27y −1
c
5
, c
11
y
31
− 29y
30
+ ··· + 3350y −289
c
6
y
31
− 9y
30
+ ··· − 36y −1
c
8
y
31
− 21y
30
+ ··· + 50547y −28561
c
9
y
31
− 13y
30
+ ··· + 26y −1
c
12
y
31
− 12y
30
+ ··· + y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.828439 + 0.629602I
a = −1.054830 − 0.102556I
b = −0.262566 + 0.705504I
3.14694 + 3.42445I 0.73846 − 1.29408I
u = 0.828439 − 0.629602I
a = −1.054830 + 0.102556I
b = −0.262566 − 0.705504I
3.14694 − 3.42445I 0.73846 + 1.29408I
u = −1.117480 + 0.183893I
a = −0.53037 + 1.63679I
b = −0.451364 − 1.299830I
7.54882 − 2.85801I 11.59200 + 3.37399I
u = −1.117480 − 0.183893I
a = −0.53037 − 1.63679I
b = −0.451364 + 1.299830I
7.54882 + 2.85801I 11.59200 − 3.37399I
u = −0.852539 + 0.045200I
a = −0.68383 + 2.17980I
b = 0.03141 − 1.47544I
6.77813 + 1.85648I 7.73203 − 6.04751I
u = −0.852539 − 0.045200I
a = −0.68383 − 2.17980I
b = 0.03141 + 1.47544I
6.77813 − 1.85648I 7.73203 + 6.04751I
u = 0.436864 + 0.551989I
a = −0.72369 − 2.03100I
b = 0.580082 + 0.159789I
−3.71980 + 1.42092I −6.90223 − 0.31504I
u = 0.436864 − 0.551989I
a = −0.72369 + 2.03100I
b = 0.580082 − 0.159789I
−3.71980 − 1.42092I −6.90223 + 0.31504I
u = 0.411946 + 0.522013I
a = −0.864410 + 0.095045I
b = 1.123080 + 0.212034I
−1.24473 + 2.38697I −3.91107 + 0.55228I
u = 0.411946 − 0.522013I
a = −0.864410 − 0.095045I
b = 1.123080 − 0.212034I
−1.24473 − 2.38697I −3.91107 − 0.55228I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.075390 + 0.819129I
a = −0.22108 − 1.44287I
b = −0.475347 + 0.977407I
−0.96097 + 3.49645I −3.31187 − 6.21629I
u = 1.075390 − 0.819129I
a = −0.22108 + 1.44287I
b = −0.475347 − 0.977407I
−0.96097 − 3.49645I −3.31187 + 6.21629I
u = 0.472017 + 0.420664I
a = 2.87166 + 0.88857I
b = 0.313317 − 1.376130I
5.86284 + 7.19829I 9.66632 − 0.23841I
u = 0.472017 − 0.420664I
a = 2.87166 − 0.88857I
b = 0.313317 + 1.376130I
5.86284 − 7.19829I 9.66632 + 0.23841I
u = −0.554624 + 0.187916I
a = 1.66688 + 0.15757I
b = 0.502638 + 0.919830I
3.58802 + 3.15662I −0.17421 − 4.42314I
u = −0.554624 − 0.187916I
a = 1.66688 − 0.15757I
b = 0.502638 − 0.919830I
3.58802 − 3.15662I −0.17421 + 4.42314I
u = −1.19444 + 0.77619I
a = 0.35832 − 1.53345I
b = 0.685226 + 1.137550I
0.62134 − 8.22186I 2.16110 + 4.76976I
u = −1.19444 − 0.77619I
a = 0.35832 + 1.53345I
b = 0.685226 − 1.137550I
0.62134 + 8.22186I 2.16110 − 4.76976I
u = 0.073621 + 0.540941I
a = 4.19742 + 1.11620I
b = −0.414603 − 0.217285I
−1.53139 − 6.60983I 1.62887 + 6.05669I
u = 0.073621 − 0.540941I
a = 4.19742 − 1.11620I
b = −0.414603 + 0.217285I
−1.53139 + 6.60983I 1.62887 − 6.05669I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42934 + 0.35027I
a = −0.277609 − 0.725974I
b = −0.562098 + 0.755715I
5.63145 + 1.54201I 19.2423 − 5.6336I
u = 1.42934 − 0.35027I
a = −0.277609 + 0.725974I
b = −0.562098 − 0.755715I
5.63145 − 1.54201I 19.2423 + 5.6336I
u = 0.28223 + 1.47450I
a = −0.152910 − 0.282108I
b = 0.027667 + 0.393634I
−3.89632 + 3.27798I 3.2164 − 25.4567I
u = 0.28223 − 1.47450I
a = −0.152910 + 0.282108I
b = 0.027667 − 0.393634I
−3.89632 − 3.27798I 3.2164 + 25.4567I
u = −1.60430 + 0.21266I
a = 0.58871 − 1.39266I
b = 0.222732 + 0.716619I
8.10570 − 5.50623I 11.76411 + 0.I
u = −1.60430 − 0.21266I
a = 0.58871 + 1.39266I
b = 0.222732 − 0.716619I
8.10570 + 5.50623I 11.76411 + 0.I
u = 1.66186 + 0.10942I
a = 0.139325 + 1.175200I
b = 0.011956 − 1.353030I
10.94150 − 4.38280I 8.52717 + 0.I
u = 1.66186 − 0.10942I
a = 0.139325 − 1.175200I
b = 0.011956 + 1.353030I
10.94150 + 4.38280I 8.52717 + 0.I
u = −0.205159
a = −1.03514
b = −1.67185
−6.43108 −46.7320
u = −0.74573 + 1.88016I
a = 0.203971 − 0.029621I
b = −0.49620 + 1.88641I
0.177498 + 0.685373I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74573 − 1.88016I
a = 0.203971 + 0.029621I
b = −0.49620 − 1.88641I
0.177498 − 0.685373I 0
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
31
− 6u
30
+ ··· − u − 1)(u
101
− 7u
100
+ ··· − 533u + 356)
c
2
(u
31
+ 11u
29
+ ··· + 7u
2
+ 1)(u
101
− u
100
+ ··· + 72811u − 14123)
c
3
(u
31
− u
30
+ ··· + 3u + 1)(u
101
− 2u
100
+ ··· − 18346u − 3931)
c
4
(u
31
+ 6u
30
+ ··· − u + 1)(u
101
− 7u
100
+ ··· − 533u + 356)
c
5
(u
31
− u
30
+ ··· − 16u + 17)(u
101
+ 2u
100
+ ··· + 641239u + 167761)
c
6
(u
31
+ 3u
30
+ ··· − 2u + 1)(u
101
− 10u
100
+ ··· + 53u − 7)
c
7
(u
31
+ 11u
29
+ ··· − 7u
2
− 1)(u
101
− u
100
+ ··· + 72811u − 14123)
c
8
(u
31
+ 3u
30
+ ··· + 511u + 169)
· (u
101
− 14u
99
+ ··· − 238884u + 56743)
c
9
(u
31
+ 5u
30
+ ··· + 6u + 1)(u
101
− 12u
99
+ ··· + 549u + 319)
c
10
(u
31
+ u
30
+ ··· + 3u − 1)(u
101
− 2u
100
+ ··· − 18346u − 3931)
c
11
(u
31
+ u
30
+ ··· − 16u − 17)(u
101
+ 2u
100
+ ··· + 641239u + 167761)
c
12
(u
31
− 6u
29
+ ··· + 9u + 1)(u
101
− u
100
+ ··· + 41u − 2)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
31
− 20y
30
+ ··· − 21y −1)
· (y
101
− 71y
100
+ ··· + 18234321y −126736)
c
2
, c
7
(y
31
+ 22y
30
+ ··· − 14y −1)
· (y
101
+ 51y
100
+ ··· − 7022994229y −199459129)
c
3
, c
10
(y
31
− 11y
30
+ ··· + 27y −1)
· (y
101
− 34y
100
+ ··· + 615503752y −15452761)
c
5
, c
11
(y
31
− 29y
30
+ ··· + 3350y −289)
· (y
101
− 64y
100
+ ··· + 814720100043y −28143753121)
c
6
(y
31
− 9y
30
+ ··· − 36y −1)(y
101
− 4y
100
+ ··· − 411y −49)
c
8
(y
31
− 21y
30
+ ··· + 50547y −28561)
· (y
101
− 28y
100
+ ··· + 62222823240y −3219768049)
c
9
(y
31
− 13y
30
+ ··· + 26y −1)
· (y
101
− 24y
100
+ ··· + 8075431y −101761)
c
12
(y
31
− 12y
30
+ ··· + y −1)(y
101
− 15y
100
+ ··· + 205y −4)
26
