12n
0649
(K12n
0649
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 10 9 2 11 3 4 8 5
Solving Sequence
8,11 3,9
10 12 2 7 6 4 5 1
c
8
c
9
c
11
c
2
c
7
c
6
c
3
c
5
c
12
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.75673 × 10
194
u
68
− 1.58940 × 10
195
u
67
+ ··· + 9.63648 × 10
193
b − 1.53579 × 10
195
,
1.26586 × 10
195
u
68
− 5.38237 × 10
195
u
67
+ ··· + 9.63648 × 10
193
a − 5.24849 × 10
195
, u
69
− 4u
68
+ ··· − 8u − 1i
I
u
2
= h6.02923 × 10
18
u
30
− 1.34813 × 10
20
u
29
+ ··· + 4.00441 × 10
19
b − 6.44459 × 10
19
,
1.49489 × 10
20
u
30
− 1.48284 × 10
21
u
29
+ ··· + 4.00441 × 10
19
a + 2.33807 × 10
19
, u
31
− 11u
30
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 100 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
= h3.76 × 10
194
u
68
− 1.59 × 10
195
u
67
+ · · · + 9.64 × 10
193
b − 1.54 ×
10
195
, 1.27 × 10
195
u
68
− 5.38 × 10
195
u
67
+ · · · + 9.64 × 10
193
a − 5.25 ×
10
195
, u
69
− 4u
68
+ · · · − 8u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
−13.1361u
68
+ 55.8541u
67
+ ··· + 202.166u + 54.4648
−3.89844u
68
+ 16.4936u
67
+ ··· + 59.7728u + 15.9372
a
9
=
1
u
2
a
10
=
10.3030u
68
− 43.5171u
67
+ ··· − 162.149u − 44.5391
2.44719u
68
− 10.4597u
67
+ ··· − 42.5909u − 11.6937
a
12
=
−u
u
a
2
=
−17.0346u
68
+ 72.3477u
67
+ ··· + 261.938u + 70.4021
−3.89844u
68
+ 16.4936u
67
+ ··· + 59.7728u + 15.9372
a
7
=
12.2442u
68
− 51.2281u
67
+ ··· − 204.361u − 61.3466
2.63447u
68
− 11.1419u
67
+ ··· − 46.1582u − 13.3409
a
6
=
9.89356u
68
− 41.1837u
67
+ ··· − 163.968u − 50.2569
2.47796u
68
− 10.4551u
67
+ ··· − 43.3750u − 12.6991
a
4
=
−13.5371u
68
+ 57.7238u
67
+ ··· + 204.879u + 52.8631
−3.08045u
68
+ 13.1709u
67
+ ··· + 54.5833u + 13.6099
a
5
=
−12.3892u
68
+ 52.8068u
67
+ ··· + 186.100u + 48.4386
−4.22829u
68
+ 18.0878u
67
+ ··· + 73.3622u + 18.0344
a
1
=
−11.8031u
68
+ 49.9636u
67
+ ··· + 191.753u + 52.5886
−4.36464u
68
+ 18.3517u
67
+ ··· + 53.8331u + 17.0568
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.83213u
68
− 38.7205u
67
+ ··· − 158.969u − 40.1796
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
+ 93u
68
+ ··· + 5452015640u + 242020249
c
2
, c
7
u
69
− u
68
+ ··· + 173530u − 15557
c
3
u
69
+ 5u
68
+ ··· + 20u − 1
c
4
, c
12
u
69
+ 2u
68
+ ··· − 27u − 1
c
5
u
69
+ 4u
68
+ ··· − 28636u + 15839
c
6
u
69
+ 15u
68
+ ··· + 1134199439u + 510193511
c
8
, c
11
u
69
+ 4u
68
+ ··· − 8u + 1
c
9
u
69
+ 2u
68
+ ··· − 137905545u − 27775009
c
10
u
69
− 14u
67
+ ··· − 40553u + 9503
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
− 229y
68
+ ··· − 1.55 × 10
19
y −5.86 × 10
16
c
2
, c
7
y
69
− 93y
68
+ ··· + 5452015640y −242020249
c
3
y
69
− 3y
68
+ ··· + 574y −1
c
4
, c
12
y
69
− 64y
68
+ ··· − 109y −1
c
5
y
69
− 24y
68
+ ··· + 7028148224y −250873921
c
6
y
69
+ 41y
68
+ ··· − 3357290919353259237y −260297418666507121
c
8
, c
11
y
69
+ 8y
68
+ ··· + 40y −1
c
9
y
69
+ 40y
68
+ ··· − 1503105609784333y −771451124950081
c
10
y
69
− 28y
68
+ ··· + 2430025777y −90307009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.620567 + 0.768614I
a = 0.295115 + 1.061520I
b = −0.266968 − 0.592280I
−0.27963 − 2.36978I 0
u = 0.620567 − 0.768614I
a = 0.295115 − 1.061520I
b = −0.266968 + 0.592280I
−0.27963 + 2.36978I 0
u = −0.528640 + 0.825985I
a = −0.91876 + 1.49913I
b = 0.651216 − 0.329173I
1.47908 + 6.26268I 0
u = −0.528640 − 0.825985I
a = −0.91876 − 1.49913I
b = 0.651216 + 0.329173I
1.47908 − 6.26268I 0
u = −0.137715 + 1.021690I
a = −0.661605 + 0.793353I
b = 0.197087 − 0.230137I
3.63675 − 1.09100I 0
u = −0.137715 − 1.021690I
a = −0.661605 − 0.793353I
b = 0.197087 + 0.230137I
3.63675 + 1.09100I 0
u = 0.107407 + 1.037840I
a = 0.587868 − 0.581010I
b = −0.884991 − 0.025674I
0.496579 − 0.663051I 0
u = 0.107407 − 1.037840I
a = 0.587868 + 0.581010I
b = −0.884991 + 0.025674I
0.496579 + 0.663051I 0
u = −0.222401 + 0.919615I
a = 2.37303 + 0.99586I
b = −1.122020 − 0.667341I
−4.14386 − 4.69997I −6.00000 + 0.I
u = −0.222401 − 0.919615I
a = 2.37303 − 0.99586I
b = −1.122020 + 0.667341I
−4.14386 + 4.69997I −6.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838105 + 0.648909I
a = 0.10341 − 1.55477I
b = −0.92630 + 1.43531I
−5.66829 + 9.07237I 0
u = −0.838105 − 0.648909I
a = 0.10341 + 1.55477I
b = −0.92630 − 1.43531I
−5.66829 − 9.07237I 0
u = −0.154687 + 0.918736I
a = −1.55788 + 0.16959I
b = 0.687623 + 0.445092I
4.18696 − 1.28541I 4.01474 + 6.95872I
u = −0.154687 − 0.918736I
a = −1.55788 − 0.16959I
b = 0.687623 − 0.445092I
4.18696 + 1.28541I 4.01474 − 6.95872I
u = −0.423890 + 0.826363I
a = 2.24030 − 0.37878I
b = −0.803942 − 0.617723I
−4.08802 + 2.79371I −8.40346 − 4.46288I
u = −0.423890 − 0.826363I
a = 2.24030 + 0.37878I
b = −0.803942 + 0.617723I
−4.08802 − 2.79371I −8.40346 + 4.46288I
u = 0.656203 + 0.537024I
a = 0.144124 + 0.951973I
b = 0.825256 − 0.762240I
−2.03049 − 2.42372I −11.88014 + 4.36849I
u = 0.656203 − 0.537024I
a = 0.144124 − 0.951973I
b = 0.825256 + 0.762240I
−2.03049 + 2.42372I −11.88014 − 4.36849I
u = 1.038170 + 0.518343I
a = 0.23203 − 1.56133I
b = 0.439658 + 0.706676I
−3.81805 − 0.77158I 0
u = 1.038170 − 0.518343I
a = 0.23203 + 1.56133I
b = 0.439658 − 0.706676I
−3.81805 + 0.77158I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122030 + 0.330033I
a = 0.114862 − 0.612138I
b = 0.576498 + 0.200119I
−4.73007 − 1.38642I 0
u = 1.122030 − 0.330033I
a = 0.114862 + 0.612138I
b = 0.576498 − 0.200119I
−4.73007 + 1.38642I 0
u = −0.656371 + 0.374675I
a = 0.165470 − 1.147450I
b = −1.01885 + 1.46354I
−5.47683 + 0.81547I −13.9925 − 5.3930I
u = −0.656371 − 0.374675I
a = 0.165470 + 1.147450I
b = −1.01885 − 1.46354I
−5.47683 − 0.81547I −13.9925 + 5.3930I
u = −0.542753 + 0.502674I
a = 0.47992 + 1.35362I
b = 1.123720 − 0.847412I
2.52282 + 3.93536I −13.9900 + 7.9927I
u = −0.542753 − 0.502674I
a = 0.47992 − 1.35362I
b = 1.123720 + 0.847412I
2.52282 − 3.93536I −13.9900 − 7.9927I
u = 0.312047 + 1.275650I
a = 0.180263 − 0.021396I
b = 0.452384 − 0.381957I
1.11192 − 5.74822I 0
u = 0.312047 − 1.275650I
a = 0.180263 + 0.021396I
b = 0.452384 + 0.381957I
1.11192 + 5.74822I 0
u = 0.646566 + 1.153950I
a = −0.555296 − 0.470204I
b = 0.742815 + 0.036632I
−1.99427 − 4.75078I 0
u = 0.646566 − 1.153950I
a = −0.555296 + 0.470204I
b = 0.742815 − 0.036632I
−1.99427 + 4.75078I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002330 + 0.964404I
a = −0.466181 + 1.322550I
b = 1.81745 − 0.51237I
−14.0164 + 8.1710I 0
u = −1.002330 − 0.964404I
a = −0.466181 − 1.322550I
b = 1.81745 + 0.51237I
−14.0164 − 8.1710I 0
u = −0.946562 + 1.030510I
a = −0.868148 + 0.716705I
b = 1.83104 + 0.18522I
−13.77790 − 0.97383I 0
u = −0.946562 − 1.030510I
a = −0.868148 − 0.716705I
b = 1.83104 − 0.18522I
−13.77790 + 0.97383I 0
u = −0.591069 + 0.013145I
a = −0.515476 − 1.061590I
b = 0.966070 + 0.361777I
0.02321 + 3.30644I −5.31577 − 0.65285I
u = −0.591069 − 0.013145I
a = −0.515476 + 1.061590I
b = 0.966070 − 0.361777I
0.02321 − 3.30644I −5.31577 + 0.65285I
u = 1.10514 + 0.89184I
a = 0.164136 + 1.174890I
b = −1.62723 − 0.15806I
−12.28980 − 3.04790I 0
u = 1.10514 − 0.89184I
a = 0.164136 − 1.174890I
b = −1.62723 + 0.15806I
−12.28980 + 3.04790I 0
u = −1.11441 + 0.88592I
a = 0.530643 − 0.904741I
b = −1.80094 + 0.20722I
−9.46729 − 0.43830I 0
u = −1.11441 − 0.88592I
a = 0.530643 + 0.904741I
b = −1.80094 − 0.20722I
−9.46729 + 0.43830I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.516405 + 0.186599I
a = 0.640636 + 1.173020I
b = −0.388056 − 0.459140I
−0.958480 − 0.805455I −7.77105 + 4.82174I
u = 0.516405 − 0.186599I
a = 0.640636 − 1.173020I
b = −0.388056 + 0.459140I
−0.958480 + 0.805455I −7.77105 − 4.82174I
u = 0.147481 + 0.503422I
a = −0.36096 − 1.70078I
b = 1.252360 + 0.364532I
0.68981 − 3.79739I −6.01075 + 6.87866I
u = 0.147481 − 0.503422I
a = −0.36096 + 1.70078I
b = 1.252360 − 0.364532I
0.68981 + 3.79739I −6.01075 − 6.87866I
u = −0.95922 + 1.13812I
a = 0.794182 − 1.019950I
b = −1.83758 + 0.14472I
−8.62794 + 7.99769I 0
u = −0.95922 − 1.13812I
a = 0.794182 + 1.019950I
b = −1.83758 − 0.14472I
−8.62794 − 7.99769I 0
u = 1.03201 + 1.14811I
a = 0.487442 + 0.669822I
b = −1.75842 − 0.02454I
−11.52020 − 4.73562I 0
u = 1.03201 − 1.14811I
a = 0.487442 − 0.669822I
b = −1.75842 + 0.02454I
−11.52020 + 4.73562I 0
u = 1.34349 + 0.76930I
a = 0.943902 + 0.462742I
b = −2.02719 − 0.08295I
−13.45390 − 2.79174I 0
u = 1.34349 − 0.76930I
a = 0.943902 − 0.462742I
b = −2.02719 + 0.08295I
−13.45390 + 2.79174I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04079 + 1.14862I
a = −0.62713 + 1.30220I
b = 1.82368 − 0.48099I
−14.2539 + 16.3836I 0
u = −1.04079 − 1.14862I
a = −0.62713 − 1.30220I
b = 1.82368 + 0.48099I
−14.2539 − 16.3836I 0
u = 1.31236 + 0.85608I
a = −0.165829 − 0.631740I
b = 1.40725 + 0.17549I
−6.75937 − 3.17506I 0
u = 1.31236 − 0.85608I
a = −0.165829 + 0.631740I
b = 1.40725 − 0.17549I
−6.75937 + 3.17506I 0
u = −1.21210 + 0.99408I
a = −0.786829 + 0.482506I
b = 1.81955 + 0.16961I
−14.8655 − 8.2485I 0
u = −1.21210 − 0.99408I
a = −0.786829 − 0.482506I
b = 1.81955 − 0.16961I
−14.8655 + 8.2485I 0
u = 0.62481 + 1.44175I
a = −0.659114 + 0.373702I
b = 1.020270 − 0.315614I
−0.62961 − 5.82441I 0
u = 0.62481 − 1.44175I
a = −0.659114 − 0.373702I
b = 1.020270 + 0.315614I
−0.62961 + 5.82441I 0
u = −0.406118 + 0.105873I
a = −3.09068 + 4.20680I
b = −0.848456 + 0.276599I
−4.21394 + 5.94658I −15.8228 − 7.9885I
u = −0.406118 − 0.105873I
a = −3.09068 − 4.20680I
b = −0.848456 − 0.276599I
−4.21394 − 5.94658I −15.8228 + 7.9885I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.116165 + 0.397349I
a = 0.27470 − 4.41535I
b = −0.446135 + 0.421163I
−1.97541 − 0.27152I −0.85009 − 1.43136I
u = 0.116165 − 0.397349I
a = 0.27470 + 4.41535I
b = −0.446135 − 0.421163I
−1.97541 + 0.27152I −0.85009 + 1.43136I
u = 1.02872 + 1.31167I
a = 1.01833 + 1.19464I
b = −1.80440 − 0.35029I
−11.72610 − 5.67856I 0
u = 1.02872 − 1.31167I
a = 1.01833 − 1.19464I
b = −1.80440 + 0.35029I
−11.72610 + 5.67856I 0
u = 1.14131 + 1.22151I
a = −0.329605 − 0.788330I
b = 1.42012 + 0.24581I
−5.65420 − 5.51638I 0
u = 1.14131 − 1.22151I
a = −0.329605 + 0.788330I
b = 1.42012 − 0.24581I
−5.65420 + 5.51638I 0
u = 0.321634
a = 0.533210
b = −2.72013
−7.29217 −53.2230
u = −0.285159
a = −2.97082
b = −0.913830
−1.37319 −7.60330
u = −0.223928
a = 6.02391
b = 1.64889
−8.93621 −10.9880
11
II.
I
u
2
= h6.03 × 10
18
u
30
− 1.35 × 10
20
u
29
+ · · · + 4.00 × 10
19
b − 6.44 × 10
19
, 1.49 ×
10
20
u
30
−1.48×10
21
u
29
+· · ·+4.00×10
19
a+2.34×10
19
, u
31
−11u
30
+· · ·+u+1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
−3.73310u
30
+ 37.0302u
29
+ ··· + 4.71974u − 0.583873
−0.150565u
30
+ 3.36662u
29
+ ··· + 11.8844u + 1.60937
a
9
=
1
u
2
a
10
=
2.54892u
30
− 25.5143u
29
+ ··· + 12.7710u − 2.09884
−1.37595u
30
+ 14.0827u
29
+ ··· + 12.2042u − 2.17546
a
12
=
−u
u
a
2
=
−3.88367u
30
+ 40.3968u
29
+ ··· + 16.6041u + 1.02550
−0.150565u
30
+ 3.36662u
29
+ ··· + 11.8844u + 1.60937
a
7
=
0.779209u
30
− 10.5172u
29
+ ··· + 20.0097u − 8.34541
−2.94589u
30
+ 29.8552u
29
+ ··· + 7.87539u − 2.77921
a
6
=
1.17546u
30
− 13.3060u
29
+ ··· + 13.3010u − 3.62031
−1.44902u
30
+ 13.8980u
29
+ ··· + 5.90919u − 4.34915
a
4
=
−2.21570u
30
+ 23.4388u
29
+ ··· − 8.43029u + 5.95342
1.64393u
30
− 19.9690u
29
+ ··· − 25.1574u − 2.39360
a
5
=
−0.230196u
30
+ 1.55171u
29
+ ··· − 11.8217u + 3.13375
−0.341574u
30
+ 1.91808u
29
+ ··· − 21.7660u + 0.426069
a
1
=
−0.558080u
30
+ 2.66742u
29
+ ··· − 33.7718u − 0.202014
−3.76215u
30
+ 40.3788u
29
+ ··· − 19.6251u + 10.7116
(ii) Obstruction class = 1
(iii) Cusp Shapes =
307207196923443676437
40044125180651709809
u
30
−
2526478116728013948319
40044125180651709809
u
29
+ ··· +
1322961892115776663297
40044125180651709809
u +
1239970465373882723147
40044125180651709809
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
31
− 34u
30
+ ··· + 39u − 1
c
2
u
31
− 17u
29
+ ··· + 9u − 1
c
3
u
31
+ 6u
30
+ ··· + 7u − 1
c
4
u
31
+ u
30
+ ··· − 2u + 1
c
5
u
31
− u
30
+ ··· − u − 1
c
6
u
31
− 4u
30
+ ··· − 142u − 29
c
7
u
31
− 17u
29
+ ··· + 9u + 1
c
8
u
31
− 11u
30
+ ··· + u + 1
c
9
u
31
− u
30
+ ··· + 2u + 1
c
10
u
31
− u
30
+ ··· + 4u
2
− 1
c
11
u
31
+ 11u
30
+ ··· + u − 1
c
12
u
31
− u
30
+ ··· − 2u − 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 70y
30
+ ··· + 139y −1
c
2
, c
7
y
31
− 34y
30
+ ··· + 39y −1
c
3
y
31
− 8y
30
+ ··· + 5y −1
c
4
, c
12
y
31
− 17y
30
+ ··· + 14y −1
c
5
y
31
+ 7y
30
+ ··· + 19y −1
c
6
y
31
− 28y
30
+ ··· − 7154y −841
c
8
, c
11
y
31
+ 11y
30
+ ··· + 35y −1
c
9
y
31
− 5y
30
+ ··· + 2y −1
c
10
y
31
− y
30
+ ··· + 8y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.281205 + 0.971174I
a = −0.615943 − 0.339244I
b = 1.174390 + 0.263468I
1.03034 − 2.56329I −6.19586 + 1.48742I
u = −0.281205 − 0.971174I
a = −0.615943 + 0.339244I
b = 1.174390 − 0.263468I
1.03034 + 2.56329I −6.19586 − 1.48742I
u = −0.573029 + 0.856248I
a = −0.86482 + 1.67406I
b = 0.915126 − 0.246275I
0.72514 + 6.24923I −9.80523 − 7.59292I
u = −0.573029 − 0.856248I
a = −0.86482 − 1.67406I
b = 0.915126 + 0.246275I
0.72514 − 6.24923I −9.80523 + 7.59292I
u = 0.283950 + 0.922959I
a = −1.50623 − 0.23020I
b = 0.841182 − 0.556865I
3.80218 + 1.04414I −12.13425 + 2.68369I
u = 0.283950 − 0.922959I
a = −1.50623 + 0.23020I
b = 0.841182 + 0.556865I
3.80218 − 1.04414I −12.13425 − 2.68369I
u = 0.890141 + 0.283894I
a = −0.445686 + 1.267980I
b = −0.422997 − 0.724172I
−3.35676 − 0.35087I −8.98621 − 1.63860I
u = 0.890141 − 0.283894I
a = −0.445686 − 1.267980I
b = −0.422997 + 0.724172I
−3.35676 + 0.35087I −8.98621 + 1.63860I
u = −0.207980 + 1.101240I
a = −0.89328 + 1.11876I
b = 0.764646 − 0.190260I
2.66272 − 0.74440I −5.63363 − 0.02997I
u = −0.207980 − 1.101240I
a = −0.89328 − 1.11876I
b = 0.764646 + 0.190260I
2.66272 + 0.74440I −5.63363 + 0.02997I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583039 + 0.642975I
a = 0.00720 + 1.82335I
b = −0.301590 − 0.060396I
−2.55773 − 0.83625I −9.77903 + 4.79038I
u = 0.583039 − 0.642975I
a = 0.00720 − 1.82335I
b = −0.301590 + 0.060396I
−2.55773 + 0.83625I −9.77903 − 4.79038I
u = 0.504326 + 0.591959I
a = 0.30187 − 1.48735I
b = 1.038170 + 0.856899I
2.68272 − 4.15399I 3.9077 + 15.6446I
u = 0.504326 − 0.591959I
a = 0.30187 + 1.48735I
b = 1.038170 − 0.856899I
2.68272 + 4.15399I 3.9077 − 15.6446I
u = 0.650361 + 1.066090I
a = −0.095057 − 0.394554I
b = −0.386904 + 0.206027I
−1.14707 − 4.11229I −7.80297 + 3.79379I
u = 0.650361 − 1.066090I
a = −0.095057 + 0.394554I
b = −0.386904 − 0.206027I
−1.14707 + 4.11229I −7.80297 − 3.79379I
u = −0.664749 + 0.251063I
a = −0.027910 − 0.580826I
b = 1.350950 + 0.276294I
−0.56828 + 3.88777I −12.3622 − 8.2948I
u = −0.664749 − 0.251063I
a = −0.027910 + 0.580826I
b = 1.350950 − 0.276294I
−0.56828 − 3.88777I −12.3622 + 8.2948I
u = 0.333446 + 1.364760I
a = 0.124901 + 0.542190I
b = −0.960760 − 0.264065I
0.27850 − 7.38615I −6.00000 + 10.55289I
u = 0.333446 − 1.364760I
a = 0.124901 − 0.542190I
b = −0.960760 + 0.264065I
0.27850 + 7.38615I −6.00000 − 10.55289I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498231 + 1.318270I
a = 0.778422 − 0.077820I
b = −0.969866 + 0.394187I
0.18887 − 4.88085I −6.00000 + 0.I
u = 0.498231 − 1.318270I
a = 0.778422 + 0.077820I
b = −0.969866 − 0.394187I
0.18887 + 4.88085I −6.00000 + 0.I
u = −0.006802 + 0.524481I
a = 5.16988 + 0.51549I
b = −0.815852 + 0.430370I
−3.66986 + 5.87361I −1.07131 − 6.71665I
u = −0.006802 − 0.524481I
a = 5.16988 − 0.51549I
b = −0.815852 − 0.430370I
−3.66986 − 5.87361I −1.07131 + 6.71665I
u = 1.10454 + 1.05740I
a = −0.566076 − 0.883920I
b = 1.77304 + 0.13717I
−11.82570 − 4.00133I 0
u = 1.10454 − 1.05740I
a = −0.566076 + 0.883920I
b = 1.77304 − 0.13717I
−11.82570 + 4.00133I 0
u = 1.35707 + 0.73346I
a = 0.037472 + 0.616561I
b = −1.344490 − 0.217373I
−7.10048 − 2.84738I 0
u = 1.35707 − 0.73346I
a = 0.037472 − 0.616561I
b = −1.344490 + 0.217373I
−7.10048 + 2.84738I 0
u = 1.10264 + 1.27051I
a = 0.384930 + 0.743191I
b = −1.42330 − 0.19564I
−5.51939 − 5.81662I 0
u = 1.10264 − 1.27051I
a = 0.384930 − 0.743191I
b = −1.42330 + 0.19564I
−5.51939 + 5.81662I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.147953
a = −2.57936
b = −2.46350
−7.17813 18.1280
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
31
− 34u
30
+ ··· + 39u − 1)
· (u
69
+ 93u
68
+ ··· + 5452015640u + 242020249)
c
2
(u
31
− 17u
29
+ ··· + 9u − 1)(u
69
− u
68
+ ··· + 173530u − 15557)
c
3
(u
31
+ 6u
30
+ ··· + 7u − 1)(u
69
+ 5u
68
+ ··· + 20u − 1)
c
4
(u
31
+ u
30
+ ··· − 2u + 1)(u
69
+ 2u
68
+ ··· − 27u − 1)
c
5
(u
31
− u
30
+ ··· − u − 1)(u
69
+ 4u
68
+ ··· − 28636u + 15839)
c
6
(u
31
− 4u
30
+ ··· − 142u − 29)
· (u
69
+ 15u
68
+ ··· + 1134199439u + 510193511)
c
7
(u
31
− 17u
29
+ ··· + 9u + 1)(u
69
− u
68
+ ··· + 173530u − 15557)
c
8
(u
31
− 11u
30
+ ··· + u + 1)(u
69
+ 4u
68
+ ··· − 8u + 1)
c
9
(u
31
− u
30
+ ··· + 2u + 1)
· (u
69
+ 2u
68
+ ··· − 137905545u − 27775009)
c
10
(u
31
− u
30
+ ··· + 4u
2
− 1)(u
69
− 14u
67
+ ··· − 40553u + 9503)
c
11
(u
31
+ 11u
30
+ ··· + u − 1)(u
69
+ 4u
68
+ ··· − 8u + 1)
c
12
(u
31
− u
30
+ ··· − 2u − 1)(u
69
+ 2u
68
+ ··· − 27u − 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
31
− 70y
30
+ ··· + 139y −1)
· (y
69
− 229y
68
+ ··· − 1.55 × 10
19
y −5.86 × 10
16
)
c
2
, c
7
(y
31
− 34y
30
+ ··· + 39y −1)
· (y
69
− 93y
68
+ ··· + 5452015640y −242020249)
c
3
(y
31
− 8y
30
+ ··· + 5y −1)(y
69
− 3y
68
+ ··· + 574y −1)
c
4
, c
12
(y
31
− 17y
30
+ ··· + 14y −1)(y
69
− 64y
68
+ ··· − 109y −1)
c
5
(y
31
+ 7y
30
+ ··· + 19y −1)
· (y
69
− 24y
68
+ ··· + 7028148224y −250873921)
c
6
(y
31
− 28y
30
+ ··· − 7154y −841)
· (y
69
+ 41y
68
+ ··· − 3357290919353259237y −260297418666507121)
c
8
, c
11
(y
31
+ 11y
30
+ ··· + 35y −1)(y
69
+ 8y
68
+ ··· + 40y −1)
c
9
(y
31
− 5y
30
+ ··· + 2y −1)
· (y
69
+ 40y
68
+ ··· − 1503105609784333y −771451124950081)
c
10
(y
31
− y
30
+ ··· + 8y −1)
· (y
69
− 28y
68
+ ··· + 2430025777y −90307009)
22
