12a
0430
(K12a
0430
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 9 12 5 1 4 7 11
Solving Sequence
7,11
12
4,8
5 1 10 3 9 6 2
c
11
c
7
c
4
c
12
c
10
c
3
c
9
c
6
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−226485u
38
− 3774546u
37
+ ··· + 128b + 9282560,
− 259737u
38
− 4524309u
37
+ ··· + 128a + 21477568, 3u
39
+ 54u
38
+ ··· − 3328u − 256i
I
u
2
= h−2.26053 × 10
100
a
15
u
5
− 8.64840 × 10
100
a
14
u
5
+ ··· − 6.68918 × 10
103
a + 2.14623 × 10
103
,
− a
15
u
5
− 4a
14
u
5
+ ··· + 148a − 22, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= h−15u
24
+ 21u
23
+ ··· + b − 8, 3u
24
− 24u
23
+ ··· + a − 14, 3u
25
− 3u
24
+ ··· − 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 160 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−2.26×10
5
u
38
−3.77×10
6
u
37
+· · ·+128b+9.28×10
6
, −2.60×10
5
u
38
−
4.52 × 10
6
u
37
+ · · · + 128a + 2.15 × 10
7
, 3u
39
+ 54u
38
+ · · · − 3328u − 256i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
2029.20u
38
+ 35346.2u
37
+ ··· − 2.07355 × 10
6
u − 167794.
1769.41u
38
+ 29488.6u
37
+ ··· − 948125.u − 72520
a
8
=
u
−u
3
+ u
a
5
=
−331.617u
38
− 4854.02u
37
+ ··· − 183199.u − 16803.5
735.914u
38
+ 13795.5u
37
+ ··· − 1.40161 × 10
6
u − 117322
a
1
=
−u
2
+ 1
−u
2
a
10
=
−192.527u
38
− 3285.52u
37
+ ··· + 155737u + 12492
−103.242u
38
− 1653.28u
37
+ ··· + 17861u + 1071
a
3
=
1538.92u
38
+ 26366.7u
37
+ ··· − 1.44956 × 10
6
u − 117071
491.273u
38
+ 7452.33u
37
+ ··· + 335799u + 32963
a
9
=
−12.5508u
38
− 125.672u
37
+ ··· − 42277u − 3681
176.977u
38
+ 3108.84u
37
+ ··· − 197757u − 16173
a
6
=
−178.898u
38
− 3179.23u
37
+ ··· + 235641.u + 19456.5
−630.586u
38
− 10679.0u
37
+ ··· + 481986.u + 38544
a
2
=
271.324u
38
+ 4657.66u
37
+ ··· − 232931.u − 18469
−293.344u
38
− 4981.59u
37
+ ··· + 278367u + 22919
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1755
16
u
38
+
77211
16
u
37
+ ··· − 2255734u − 193986
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(9u
39
+ 114u
38
+ ··· + 111616u + 4096)
c
2
, c
5
3(3u
39
+ 48u
38
+ ··· − 480u − 64)
c
3
, c
4
, c
8
c
10
u
39
+ 2u
38
+ ··· + 2u − 1
c
6
, c
9
u
39
+ 2u
38
+ ··· − 33u − 9
c
7
, c
11
3(3u
39
+ 54u
38
+ ··· − 3328u − 256)
c
12
9(9u
39
− 132u
38
+ ··· + 262144u − 65536)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(81y
39
+ 3006y
38
+ ··· + 5.78080 × 10
9
y −1.67772 × 10
7
)
c
2
, c
5
9(9y
39
− 114y
38
+ ··· + 111616y −4096)
c
3
, c
4
, c
8
c
10
y
39
− 26y
38
+ ··· + 52y
2
− 1
c
6
, c
9
y
39
+ 36y
37
+ ··· + 315y −81
c
7
, c
11
9(9y
39
− 132y
38
+ ··· + 262144y −65536)
c
12
81(81y
39
+ 2196y
38
+ ··· − 6.33508 × 10
10
y −4.29497 × 10
9
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.227307 + 0.954019I
a = 0.597619 + 0.748299I
b = 1.038240 + 0.501550I
−1.54560 + 5.89382I 0
u = −0.227307 − 0.954019I
a = 0.597619 − 0.748299I
b = 1.038240 − 0.501550I
−1.54560 − 5.89382I 0
u = 0.964633 + 0.040613I
a = 0.046717 − 0.361973I
b = −0.131521 + 0.679839I
2.24733 + 2.31700I 0
u = 0.964633 − 0.040613I
a = 0.046717 + 0.361973I
b = −0.131521 − 0.679839I
2.24733 − 2.31700I 0
u = −0.372084 + 0.971347I
a = 1.033870 + 0.676185I
b = 1.38505 + 0.53905I
5.0495 + 13.3788I 0
u = −0.372084 − 0.971347I
a = 1.033870 − 0.676185I
b = 1.38505 − 0.53905I
5.0495 − 13.3788I 0
u = −0.366389 + 0.997959I
a = −0.972711 − 0.584875I
b = −1.35053 − 0.45887I
6.51433 + 7.15268I 0
u = −0.366389 − 0.997959I
a = −0.972711 + 0.584875I
b = −1.35053 + 0.45887I
6.51433 − 7.15268I 0
u = −0.756872 + 0.753122I
a = 0.171567 − 0.831323I
b = 0.450531 − 0.558117I
−4.96051 − 3.11579I 0
u = −0.756872 − 0.753122I
a = 0.171567 + 0.831323I
b = 0.450531 + 0.558117I
−4.96051 + 3.11579I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.734478 + 0.548916I
a = 0.333438 + 1.221500I
b = −0.148939 + 0.692095I
−1.30683 − 1.81941I 0
u = −0.734478 − 0.548916I
a = 0.333438 − 1.221500I
b = −0.148939 − 0.692095I
−1.30683 + 1.81941I 0
u = −0.928656 + 0.581070I
a = 0.840210 + 0.897302I
b = −0.107640 + 0.780975I
−0.67233 − 2.69467I 0
u = −0.928656 − 0.581070I
a = 0.840210 − 0.897302I
b = −0.107640 − 0.780975I
−0.67233 + 2.69467I 0
u = −0.624790 + 0.647653I
a = −0.042755 − 1.321680I
b = 0.185681 − 0.871131I
−2.58514 + 2.46966I 0
u = −0.624790 − 0.647653I
a = −0.042755 + 1.321680I
b = 0.185681 + 0.871131I
−2.58514 − 2.46966I 0
u = −0.964236 + 0.626940I
a = −1.015610 − 0.669350I
b = −0.044585 − 0.877355I
−1.61000 − 7.43824I 0
u = −0.964236 − 0.626940I
a = −1.015610 + 0.669350I
b = −0.044585 + 0.877355I
−1.61000 + 7.43824I 0
u = −0.927448 + 0.731334I
a = −0.603265 − 0.055544I
b = −0.328521 − 0.410615I
−4.48122 − 2.48257I 0
u = −0.927448 − 0.731334I
a = −0.603265 + 0.055544I
b = −0.328521 + 0.410615I
−4.48122 + 2.48257I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.762524 + 1.065990I
a = 0.664275 − 0.398822I
b = 1.098350 − 0.153624I
2.59371 − 7.58190I 0
u = −0.762524 − 1.065990I
a = 0.664275 + 0.398822I
b = 1.098350 + 0.153624I
2.59371 + 7.58190I 0
u = −1.185980 + 0.646068I
a = 0.29852 + 1.74270I
b = −1.48593 + 0.60763I
7.5533 − 19.2427I 0
u = −1.185980 − 0.646068I
a = 0.29852 − 1.74270I
b = −1.48593 − 0.60763I
7.5533 + 19.2427I 0
u = 1.353110 + 0.111837I
a = 0.430891 − 0.154226I
b = −1.43049 + 0.31053I
11.2642 − 9.8374I 0
u = 1.353110 − 0.111837I
a = 0.430891 + 0.154226I
b = −1.43049 − 0.31053I
11.2642 + 9.8374I 0
u = −1.196030 + 0.650742I
a = −0.24811 − 1.65622I
b = 1.45343 − 0.53779I
9.0791 − 13.1009I 0
u = −1.196030 − 0.650742I
a = −0.24811 + 1.65622I
b = 1.45343 + 0.53779I
9.0791 + 13.1009I 0
u = −1.219640 + 0.610960I
a = 0.47514 + 1.44470I
b = −1.220300 + 0.570071I
1.42407 − 11.55540I 0
u = −1.219640 − 0.610960I
a = 0.47514 − 1.44470I
b = −1.220300 − 0.570071I
1.42407 + 11.55540I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618970
a = 0.307729
b = −0.308374
0.781004 13.6700
u = 1.390700 + 0.097502I
a = −0.412188 + 0.110529I
b = 1.40725 − 0.21446I
12.91450 − 3.41864I 0
u = 1.390700 − 0.097502I
a = −0.412188 − 0.110529I
b = 1.40725 + 0.21446I
12.91450 + 3.41864I 0
u = −0.308955 + 0.457236I
a = 0.037151 + 1.410890I
b = 0.262188 + 0.589702I
−1.54604 − 1.25973I −0.64918 + 1.74705I
u = −0.308955 − 0.457236I
a = 0.037151 − 1.410890I
b = 0.262188 − 0.589702I
−1.54604 + 1.25973I −0.64918 − 1.74705I
u = −1.30091 + 0.66769I
a = −0.221488 − 1.116460I
b = 1.182050 − 0.297560I
7.13968 − 7.57891I 0
u = −1.30091 − 0.66769I
a = −0.221488 + 1.116460I
b = 1.182050 + 0.297560I
7.13968 + 7.57891I 0
u = −1.14163 + 1.26414I
a = −0.317136 + 0.372699I
b = −1.060120 + 0.020872I
3.53048 − 0.08358I 0
u = −1.14163 − 1.26414I
a = −0.317136 − 0.372699I
b = −1.060120 − 0.020872I
3.53048 + 0.08358I 0
8
II. I
u
2
= h−2.26 × 10
100
a
15
u
5
− 8.65 × 10
100
a
14
u
5
+ · · · − 6.69 × 10
103
a +
2.15 × 10
103
, −a
15
u
5
− 4a
14
u
5
+ · · · + 148a − 22, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
a
0.000688597a
15
u
5
+ 0.00263445a
14
u
5
+ ··· + 2.03764a − 0.653779
a
8
=
u
−u
3
+ u
a
5
=
0.00313715a
15
u
5
− 0.00342694a
14
u
5
+ ··· + 1.99577a − 1.83014
−0.00537123a
15
u
5
− 0.00760671a
14
u
5
+ ··· + 2.66259a − 2.49184
a
1
=
−u
2
+ 1
−u
2
a
10
=
−0.00523647a
15
u
5
+ 0.0120349a
14
u
5
+ ··· − 0.800101a + 1.31324
−0.00890304a
15
u
5
+ 0.0103711a
14
u
5
+ ··· − 1.97931a + 2.35126
a
3
=
−0.0117502a
15
u
5
+ 0.00137900a
14
u
5
+ ··· − 2.84927a + 0.113383
−0.00974387a
15
u
5
− 0.00897497a
14
u
5
+ ··· + 0.180125a − 0.421905
a
9
=
−0.00542664a
15
u
5
− 0.00762435a
14
u
5
+ ··· − 1.77760a + 0.921213
−0.0117791a
15
u
5
+ 0.00831537a
14
u
5
+ ··· − 1.12189a + 2.39887
a
6
=
−0.0112446a
15
u
5
+ 0.0123645a
14
u
5
+ ··· − 0.930856a + 0.943314
−0.0110795a
15
u
5
+ 0.0104171a
14
u
5
+ ··· − 0.0509322a + 1.85176
a
2
=
0.00265406a
15
u
5
+ 0.0238549a
14
u
5
+ ··· − 1.23361a + 1.24330
−0.000235788a
15
u
5
+ 0.000105668a
14
u
5
+ ··· − 0.856035a − 0.131508
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0278817a
15
u
5
− 0.0697523a
14
u
5
+ ··· − 10.0876a + 4.79726
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
12
c
2
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
12
c
3
, c
4
, c
8
c
10
u
96
− u
95
+ ··· − 369170u + 47717
c
6
, c
9
u
96
+ 9u
95
+ ··· + 2219032u + 215401
c
7
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
16
c
12
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
16
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
12
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
12
c
3
, c
4
, c
8
c
10
y
96
− 81y
95
+ ··· − 141748367588y + 2276912089
c
6
, c
9
y
96
− 33y
95
+ ··· − 549152756700y + 46397590801
c
7
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
16
c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
16
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.131228 + 0.966452I
b = −1.92108 − 0.43745I
8.98482 + 1.65419I 17.4396 − 2.7737I
u = −1.002190 + 0.295542I
a = −0.920754 − 0.485414I
b = −0.852601 − 0.969355I
5.78475 + 0.20693I 14.3015 + 0.2834I
u = −1.002190 + 0.295542I
a = −0.072117 − 1.131480I
b = 1.96950 + 0.26401I
8.98482 − 3.50280I 17.4396 + 4.3622I
u = −1.002190 + 0.295542I
a = −0.284942 − 1.232200I
b = −0.640395 − 0.185153I
5.78475 − 2.05554I 14.3015 + 1.3050I
u = −1.002190 + 0.295542I
a = −0.970327 − 0.812295I
b = 1.53611 + 0.03337I
5.98037 − 0.92430I 9.82225 + 0.79423I
u = −1.002190 + 0.295542I
a = 1.180110 + 0.543505I
b = 0.724178 + 1.195600I
4.44573 + 5.51923I 12.28827 − 4.49994I
u = −1.002190 + 0.295542I
a = 1.329820 − 0.337134I
b = −1.42647 − 0.01572I
8.98482 − 3.50280I 17.4396 + 4.3622I
u = −1.002190 + 0.295542I
a = 0.96287 + 1.09375I
b = 0.278148 + 0.719400I
0.322677 − 0.924305I 7.85268 + 0.79423I
u = −1.002190 + 0.295542I
a = −1.49099 + 0.08573I
b = 1.47063 + 0.04551I
8.98482 + 1.65419I 17.4396 − 2.7737I
u = −1.002190 + 0.295542I
a = 0.38868 + 1.53392I
b = 0.450129 + 0.033041I
4.44573 − 7.36784I 12.28827 + 6.08840I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.188568 − 0.080838I
b = −1.337560 − 0.341469I
5.98037 − 0.92430I 9.82225 + 0.79423I
u = −1.002190 + 0.295542I
a = −1.18748 − 1.49401I
b = 1.324260 − 0.484048I
5.78475 − 2.05554I 14.3015 + 1.3050I
u = −1.002190 + 0.295542I
a = 1.24714 + 1.57460I
b = −1.23357 + 0.71721I
4.44573 − 7.36784I 12.28827 + 6.08840I
u = −1.002190 + 0.295542I
a = 1.34882 + 1.54727I
b = −0.865270 + 0.191673I
0.322677 − 0.924305I 7.85268 + 0.79423I
u = −1.002190 + 0.295542I
a = −1.58649 − 1.33501I
b = 1.179490 + 0.070105I
5.78475 + 0.20693I 14.3015 + 0.2834I
u = −1.002190 + 0.295542I
a = 1.68445 + 1.48950I
b = −1.083740 − 0.172180I
4.44573 + 5.51923I 12.28827 − 4.49994I
u = −1.002190 − 0.295542I
a = −0.131228 − 0.966452I
b = −1.92108 + 0.43745I
8.98482 − 1.65419I 17.4396 + 2.7737I
u = −1.002190 − 0.295542I
a = −0.920754 + 0.485414I
b = −0.852601 + 0.969355I
5.78475 − 0.20693I 14.3015 − 0.2834I
u = −1.002190 − 0.295542I
a = −0.072117 + 1.131480I
b = 1.96950 − 0.26401I
8.98482 + 3.50280I 17.4396 − 4.3622I
u = −1.002190 − 0.295542I
a = −0.284942 + 1.232200I
b = −0.640395 + 0.185153I
5.78475 + 2.05554I 14.3015 − 1.3050I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 − 0.295542I
a = −0.970327 + 0.812295I
b = 1.53611 − 0.03337I
5.98037 + 0.92430I 9.82225 − 0.79423I
u = −1.002190 − 0.295542I
a = 1.180110 − 0.543505I
b = 0.724178 − 1.195600I
4.44573 − 5.51923I 12.28827 + 4.49994I
u = −1.002190 − 0.295542I
a = 1.329820 + 0.337134I
b = −1.42647 + 0.01572I
8.98482 + 3.50280I 17.4396 − 4.3622I
u = −1.002190 − 0.295542I
a = 0.96287 − 1.09375I
b = 0.278148 − 0.719400I
0.322677 + 0.924305I 7.85268 − 0.79423I
u = −1.002190 − 0.295542I
a = −1.49099 − 0.08573I
b = 1.47063 − 0.04551I
8.98482 − 1.65419I 17.4396 + 2.7737I
u = −1.002190 − 0.295542I
a = 0.38868 − 1.53392I
b = 0.450129 − 0.033041I
4.44573 + 7.36784I 12.28827 − 6.08840I
u = −1.002190 − 0.295542I
a = 0.188568 + 0.080838I
b = −1.337560 + 0.341469I
5.98037 + 0.92430I 9.82225 − 0.79423I
u = −1.002190 − 0.295542I
a = −1.18748 + 1.49401I
b = 1.324260 + 0.484048I
5.78475 + 2.05554I 14.3015 − 1.3050I
u = −1.002190 − 0.295542I
a = 1.24714 − 1.57460I
b = −1.23357 − 0.71721I
4.44573 + 7.36784I 12.28827 − 6.08840I
u = −1.002190 − 0.295542I
a = 1.34882 − 1.54727I
b = −0.865270 − 0.191673I
0.322677 + 0.924305I 7.85268 − 0.79423I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 − 0.295542I
a = −1.58649 + 1.33501I
b = 1.179490 − 0.070105I
5.78475 − 0.20693I 14.3015 − 0.2834I
u = −1.002190 − 0.295542I
a = 1.68445 − 1.48950I
b = −1.083740 + 0.172180I
4.44573 − 5.51923I 12.28827 + 4.49994I
u = 0.428243 + 0.664531I
a = 0.338368 − 0.856179I
b = 1.220680 − 0.477407I
0.66452 − 7.36784I 4.85484 + 6.08840I
u = 0.428243 + 0.664531I
a = −0.495098 + 0.691509I
b = −1.206330 + 0.367263I
2.00354 − 2.05554I 6.86806 + 1.30502I
u = 0.428243 + 0.664531I
a = 0.714452 − 0.421331I
b = −0.217102 + 0.071087I
2.00354 + 0.20693I 6.86806 + 0.28344I
u = 0.428243 + 0.664531I
a = −0.512773 − 0.573888I
b = −1.044990 − 0.150675I
2.00354 + 0.20693I 6.86806 + 0.28344I
u = 0.428243 + 0.664531I
a = 0.475180 + 1.143100I
b = 1.061230 + 0.489637I
0.66452 + 5.51923I 4.85484 − 4.49994I
u = 0.428243 + 0.664531I
a = −0.691630 − 0.012427I
b = 0.370476 − 0.414858I
0.66452 + 5.51923I 4.85484 − 4.49994I
u = 0.428243 + 0.664531I
a = −1.290680 + 0.422211I
b = −1.230390 + 0.212303I
2.19916 − 0.92430I 2.38882 + 0.79423I
u = 0.428243 + 0.664531I
a = −0.021113 − 0.454124I
b = 0.928150 − 0.448492I
−3.45853 − 0.92430I 0.419245 + 0.794226I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 + 0.664531I
a = −0.45184 + 1.50268I
b = 0.445858 + 0.853680I
−3.45853 − 0.92430I 0.419245 + 0.794226I
u = 0.428243 + 0.664531I
a = −1.42972 + 0.79073I
b = −1.201220 − 0.073274I
5.20361 − 3.50280I 10.00621 + 4.36218I
u = 0.428243 + 0.664531I
a = 1.45063 − 0.77681I
b = 0.765736 − 0.349328I
2.19916 − 0.92430I 2.38882 + 0.79423I
u = 0.428243 + 0.664531I
a = 1.48375 − 0.73194I
b = 1.090890 + 0.140025I
5.20361 + 1.65419I 10.00621 − 2.77373I
u = 0.428243 + 0.664531I
a = 1.10763 − 1.50141I
b = 0.103004 − 0.985223I
2.00354 − 2.05554I 6.86806 + 1.30502I
u = 0.428243 + 0.664531I
a = −1.04266 + 1.76681I
b = 0.022518 + 1.191450I
0.66452 − 7.36784I 4.85484 + 6.08840I
u = 0.428243 + 0.664531I
a = −2.01816 + 0.39141I
b = −1.42014 + 0.57718I
5.20361 + 1.65419I 10.00621 − 2.77373I
u = 0.428243 + 0.664531I
a = 2.03871 − 0.61553I
b = 1.31381 − 0.70782I
5.20361 − 3.50280I 10.00621 + 4.36218I
u = 0.428243 − 0.664531I
a = 0.338368 + 0.856179I
b = 1.220680 + 0.477407I
0.66452 + 7.36784I 4.85484 − 6.08840I
u = 0.428243 − 0.664531I
a = −0.495098 − 0.691509I
b = −1.206330 − 0.367263I
2.00354 + 2.05554I 6.86806 − 1.30502I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = 0.714452 + 0.421331I
b = −0.217102 − 0.071087I
2.00354 − 0.20693I 6.86806 − 0.28344I
u = 0.428243 − 0.664531I
a = −0.512773 + 0.573888I
b = −1.044990 + 0.150675I
2.00354 − 0.20693I 6.86806 − 0.28344I
u = 0.428243 − 0.664531I
a = 0.475180 − 1.143100I
b = 1.061230 − 0.489637I
0.66452 − 5.51923I 4.85484 + 4.49994I
u = 0.428243 − 0.664531I
a = −0.691630 + 0.012427I
b = 0.370476 + 0.414858I
0.66452 − 5.51923I 4.85484 + 4.49994I
u = 0.428243 − 0.664531I
a = −1.290680 − 0.422211I
b = −1.230390 − 0.212303I
2.19916 + 0.92430I 2.38882 − 0.79423I
u = 0.428243 − 0.664531I
a = −0.021113 + 0.454124I
b = 0.928150 + 0.448492I
−3.45853 + 0.92430I 0.419245 − 0.794226I
u = 0.428243 − 0.664531I
a = −0.45184 − 1.50268I
b = 0.445858 − 0.853680I
−3.45853 + 0.92430I 0.419245 − 0.794226I
u = 0.428243 − 0.664531I
a = −1.42972 − 0.79073I
b = −1.201220 + 0.073274I
5.20361 + 3.50280I 10.00621 − 4.36218I
u = 0.428243 − 0.664531I
a = 1.45063 + 0.77681I
b = 0.765736 + 0.349328I
2.19916 + 0.92430I 2.38882 − 0.79423I
u = 0.428243 − 0.664531I
a = 1.48375 + 0.73194I
b = 1.090890 − 0.140025I
5.20361 − 1.65419I 10.00621 + 2.77373I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = 1.10763 + 1.50141I
b = 0.103004 + 0.985223I
2.00354 + 2.05554I 6.86806 − 1.30502I
u = 0.428243 − 0.664531I
a = −1.04266 − 1.76681I
b = 0.022518 − 1.191450I
0.66452 + 7.36784I 4.85484 − 6.08840I
u = 0.428243 − 0.664531I
a = −2.01816 − 0.39141I
b = −1.42014 − 0.57718I
5.20361 − 1.65419I 10.00621 + 2.77373I
u = 0.428243 − 0.664531I
a = 2.03871 + 0.61553I
b = 1.31381 + 0.70782I
5.20361 + 3.50280I 10.00621 − 4.36218I
u = 1.073950 + 0.558752I
a = −0.664094 + 0.668228I
b = −0.295117 + 1.104200I
−1.56793 + 5.69302I 4.13596 − 5.51057I
u = 1.073950 + 0.558752I
a = −0.193047 + 1.198190I
b = 1.315860 + 0.064316I
3.89415 + 4.56179I 10.58478 − 4.99978I
u = 1.073950 + 0.558752I
a = −0.111947 − 0.724388I
b = 0.101611 − 0.435249I
3.89415 + 4.56179I 10.58478 − 4.99978I
u = 1.073950 + 0.558752I
a = 0.081352 − 0.699474I
b = −1.105270 + 0.161393I
2.55512 − 0.75052I 8.57155 − 0.21640I
u = 1.073950 + 0.558752I
a = 0.717274 − 1.217360I
b = −0.226353 − 1.304860I
3.89415 + 6.82425I 10.58478 − 6.02136I
u = 1.073950 + 0.558752I
a = −0.93532 + 1.14301I
b = 0.08300 + 1.50716I
2.55512 + 12.13660I 8.57155 − 10.80474I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 + 0.558752I
a = 0.88186 − 1.26823I
b = −1.177270 − 0.338145I
−1.56793 + 5.69302I 4.13596 − 5.51057I
u = 1.073950 + 0.558752I
a = 0.270195 + 0.166091I
b = −0.506146 + 0.241762I
2.55512 − 0.75052I 8.57155 − 0.21640I
u = 1.073950 + 0.558752I
a = 0.10508 − 1.69146I
b = −0.867965 − 0.637909I
4.08977 + 5.69302I 6.10554 − 5.51057I
u = 1.073950 + 0.558752I
a = −0.17872 + 1.89437I
b = 1.36589 + 0.37885I
4.08977 + 5.69302I 6.10554 − 5.51057I
u = 1.073950 + 0.558752I
a = −0.78717 + 1.77649I
b = 1.343660 + 0.357004I
3.89415 + 6.82425I 10.58478 − 6.02136I
u = 1.073950 + 0.558752I
a = 1.00771 − 1.77771I
b = −1.338020 − 0.418979I
2.55512 + 12.13660I 8.57155 − 10.80474I
u = 1.073950 + 0.558752I
a = −0.11963 + 2.06380I
b = 1.62571 + 0.82625I
7.09422 + 3.11453I 13.72292 − 1.94261I
u = 1.073950 + 0.558752I
a = 0.23274 − 2.06246I
b = −1.50878 − 0.98090I
7.09422 + 8.27152I 13.7229 − 9.0785I
u = 1.073950 + 0.558752I
a = −0.22467 − 2.13523I
b = −1.091960 − 0.083854I
7.09422 + 3.11453I 13.72292 − 1.94261I
u = 1.073950 + 0.558752I
a = 0.07723 + 2.22849I
b = 1.207190 + 0.117716I
7.09422 + 8.27152I 13.7229 − 9.0785I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −0.664094 − 0.668228I
b = −0.295117 − 1.104200I
−1.56793 − 5.69302I 4.13596 + 5.51057I
u = 1.073950 − 0.558752I
a = −0.193047 − 1.198190I
b = 1.315860 − 0.064316I
3.89415 − 4.56179I 10.58478 + 4.99978I
u = 1.073950 − 0.558752I
a = −0.111947 + 0.724388I
b = 0.101611 + 0.435249I
3.89415 − 4.56179I 10.58478 + 4.99978I
u = 1.073950 − 0.558752I
a = 0.081352 + 0.699474I
b = −1.105270 − 0.161393I
2.55512 + 0.75052I 8.57155 + 0.21640I
u = 1.073950 − 0.558752I
a = 0.717274 + 1.217360I
b = −0.226353 + 1.304860I
3.89415 − 6.82425I 10.58478 + 6.02136I
u = 1.073950 − 0.558752I
a = −0.93532 − 1.14301I
b = 0.08300 − 1.50716I
2.55512 − 12.13660I 8.57155 + 10.80474I
u = 1.073950 − 0.558752I
a = 0.88186 + 1.26823I
b = −1.177270 + 0.338145I
−1.56793 − 5.69302I 4.13596 + 5.51057I
u = 1.073950 − 0.558752I
a = 0.270195 − 0.166091I
b = −0.506146 − 0.241762I
2.55512 + 0.75052I 8.57155 + 0.21640I
u = 1.073950 − 0.558752I
a = 0.10508 + 1.69146I
b = −0.867965 + 0.637909I
4.08977 − 5.69302I 6.10554 + 5.51057I
u = 1.073950 − 0.558752I
a = −0.17872 − 1.89437I
b = 1.36589 − 0.37885I
4.08977 − 5.69302I 6.10554 + 5.51057I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −0.78717 − 1.77649I
b = 1.343660 − 0.357004I
3.89415 − 6.82425I 10.58478 + 6.02136I
u = 1.073950 − 0.558752I
a = 1.00771 + 1.77771I
b = −1.338020 + 0.418979I
2.55512 − 12.13660I 8.57155 + 10.80474I
u = 1.073950 − 0.558752I
a = −0.11963 − 2.06380I
b = 1.62571 − 0.82625I
7.09422 − 3.11453I 13.72292 + 1.94261I
u = 1.073950 − 0.558752I
a = 0.23274 + 2.06246I
b = −1.50878 + 0.98090I
7.09422 − 8.27152I 13.7229 + 9.0785I
u = 1.073950 − 0.558752I
a = −0.22467 + 2.13523I
b = −1.091960 + 0.083854I
7.09422 − 3.11453I 13.72292 + 1.94261I
u = 1.073950 − 0.558752I
a = 0.07723 − 2.22849I
b = 1.207190 − 0.117716I
7.09422 − 8.27152I 13.7229 + 9.0785I
21
III. I
u
3
=
h−15u
24
+21u
23
+· · ·+b−8, 3u
24
−24u
23
+· · ·+a−14, 3u
25
−3u
24
+· · ·−3u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
−3u
24
+ 24u
23
+ ··· − 8u + 14
15u
24
− 21u
23
+ ··· − 11u + 8
a
8
=
u
−u
3
+ u
a
5
=
3u
24
− 9u
23
+ ··· − 31u + 19
12u
24
− 33u
23
+ ··· − 5u + 4
a
1
=
−u
2
+ 1
−u
2
a
10
=
3u
24
+ 3u
23
+ ··· + 4u + 3
3u
23
− 16u
21
+ ··· − 2u
2
+ 1
a
3
=
33u
24
− 6u
23
+ ··· + 61u − 23
48u
23
− 69u
22
+ ··· + 28u − 9
a
9
=
3u
23
− 19u
21
+ ··· + 4u + 2
3u
23
− 3u
22
+ ··· + 2u
2
+ 2u
a
6
=
6u
24
− 15u
23
+ ··· − 5u − 3
−9u
23
+ 12u
22
+ ··· + 6u − 2
a
2
=
−21u
24
− 9u
23
+ ··· + 9u
2
− 2
3u
24
+ 9u
23
+ ··· + 8u − 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = 126u
24
− 102u
23
− 699u
22
+ 541u
21
+ 2172u
20
− 1434u
19
−
4617u
18
+ 2536u
17
+ 7243u
16
− 3329u
15
− 8472u
14
+ 3549u
13
+ 7382u
12
− 3351u
11
−
4576u
10
+ 2989u
9
+ 1670u
8
−2287u
7
+ 99u
6
+ 1268u
5
−537u
4
−411u
3
+ 290u
2
+ 52u −51
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(9u
25
− 87u
24
+ ··· + 7u − 1)
c
2
3(3u
25
+ 9u
24
+ ··· + 3u + 1)
c
3
, c
8
u
25
+ 4u
24
+ ··· − 5u − 1
c
4
, c
10
u
25
− 4u
24
+ ··· − 5u + 1
c
5
3(3u
25
− 9u
24
+ ··· + 3u − 1)
c
6
, c
9
u
25
+ 2u
24
+ ··· + 66u + 9
c
7
3(3u
25
+ 3u
24
+ ··· − 3u − 1)
c
11
3(3u
25
− 3u
24
+ ··· − 3u + 1)
c
12
9(9u
25
− 105u
24
+ ··· + 11u − 1)
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(81y
25
+ 1089y
24
+ ··· − y −1)
c
2
, c
5
9(9y
25
− 87y
24
+ ··· + 7y −1)
c
3
, c
4
, c
8
c
10
y
25
− 28y
24
+ ··· − 25y −1
c
6
, c
9
y
25
− 6y
24
+ ··· + 2070y −81
c
7
, c
11
9(9y
25
− 105y
24
+ ··· + 11y −1)
c
12
81(81y
25
+ 603y
24
+ ··· − y −1)
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.923489 + 0.345905I
a = −0.720645 − 0.527374I
b = 1.71322 + 0.16401I
8.12039 + 1.07227I 8.76909 + 2.38450I
u = −0.923489 − 0.345905I
a = −0.720645 + 0.527374I
b = 1.71322 − 0.16401I
8.12039 − 1.07227I 8.76909 − 2.38450I
u = −0.669051 + 0.798063I
a = −0.257892 − 0.343854I
b = 0.765345 − 0.316241I
1.12313 − 7.15005I 6.27018 + 8.58997I
u = −0.669051 − 0.798063I
a = −0.257892 + 0.343854I
b = 0.765345 + 0.316241I
1.12313 + 7.15005I 6.27018 − 8.58997I
u = −0.889795 + 0.325257I
a = 0.797666 + 0.491683I
b = −1.70143 − 0.05361I
7.96758 − 3.88085I 7.89399 + 7.92446I
u = −0.889795 − 0.325257I
a = 0.797666 − 0.491683I
b = −1.70143 + 0.05361I
7.96758 + 3.88085I 7.89399 − 7.92446I
u = −1.036170 + 0.355737I
a = −0.507033 − 0.432535I
b = 1.47832 + 0.30367I
6.46065 − 1.83392I 13.3143 + 7.6357I
u = −1.036170 − 0.355737I
a = −0.507033 + 0.432535I
b = 1.47832 − 0.30367I
6.46065 + 1.83392I 13.3143 − 7.6357I
u = −0.896845
a = 0.844584
b = −1.43679
5.02504 4.22460
u = −0.877000 + 0.731898I
a = −0.0946330 + 0.0564460I
b = −0.008690 − 0.253427I
−4.34453 − 2.78887I 11.2209 + 9.8076I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877000 − 0.731898I
a = −0.0946330 − 0.0564460I
b = −0.008690 + 0.253427I
−4.34453 + 2.78887I 11.2209 − 9.8076I
u = 1.059140 + 0.465774I
a = 0.68944 − 2.11241I
b = −0.993884 − 0.685078I
4.13121 + 9.24593I 9.8489 − 10.2882I
u = 1.059140 − 0.465774I
a = 0.68944 + 2.11241I
b = −0.993884 + 0.685078I
4.13121 − 9.24593I 9.8489 + 10.2882I
u = 1.045990 + 0.522170I
a = −0.26189 + 2.16824I
b = 1.177520 + 0.636228I
5.33965 + 4.74375I 11.61336 − 3.22346I
u = 1.045990 − 0.522170I
a = −0.26189 − 2.16824I
b = 1.177520 − 0.636228I
5.33965 − 4.74375I 11.61336 + 3.22346I
u = 0.661465 + 0.371840I
a = 2.41853 − 0.99561I
b = 0.756425 − 0.651019I
2.63632 − 5.65290I 6.26334 + 4.31813I
u = 0.661465 − 0.371840I
a = 2.41853 + 0.99561I
b = 0.756425 + 0.651019I
2.63632 + 5.65290I 6.26334 − 4.31813I
u = 0.747855 + 0.122313I
a = 1.47583 − 1.10372I
b = 0.233452 − 0.314121I
−0.701181 + 0.235235I 1.91554 + 2.64191I
u = 0.747855 − 0.122313I
a = 1.47583 + 1.10372I
b = 0.233452 + 0.314121I
−0.701181 − 0.235235I 1.91554 − 2.64191I
u = 1.077370 + 0.637247I
a = 0.22264 + 1.59788I
b = 1.247660 + 0.351853I
5.68920 + 6.52457I 11.36902 − 6.36884I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.077370 − 0.637247I
a = 0.22264 − 1.59788I
b = 1.247660 − 0.351853I
5.68920 − 6.52457I 11.36902 + 6.36884I
u = 0.575579 + 0.433026I
a = −2.25476 + 0.80851I
b = −0.920682 + 0.496698I
3.74335 − 0.58916I 9.27324 − 0.89770I
u = 0.575579 − 0.433026I
a = −2.25476 − 0.80851I
b = −0.920682 − 0.496698I
3.74335 + 0.58916I 9.27324 + 0.89770I
u = 0.176535 + 0.691857I
a = −0.929551 + 1.002670I
b = −1.028850 + 0.209652I
3.37987 − 0.81185I 11.80254 + 0.19976I
u = 0.176535 − 0.691857I
a = −0.929551 − 1.002670I
b = −1.028850 − 0.209652I
3.37987 + 0.81185I 11.80254 − 0.19976I
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
81(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
12
· (9u
25
− 87u
24
+ ··· + 7u − 1)(9u
39
+ 114u
38
+ ··· + 111616u + 4096)
c
2
9(u
8
− u
7
+ ··· + 2u − 1)
12
(3u
25
+ 9u
24
+ ··· + 3u + 1)
· (3u
39
+ 48u
38
+ ··· − 480u − 64)
c
3
, c
8
(u
25
+ 4u
24
+ ··· − 5u − 1)(u
39
+ 2u
38
+ ··· + 2u − 1)
· (u
96
− u
95
+ ··· − 369170u + 47717)
c
4
, c
10
(u
25
− 4u
24
+ ··· − 5u + 1)(u
39
+ 2u
38
+ ··· + 2u − 1)
· (u
96
− u
95
+ ··· − 369170u + 47717)
c
5
9(u
8
− u
7
+ ··· + 2u − 1)
12
(3u
25
− 9u
24
+ ··· + 3u − 1)
· (3u
39
+ 48u
38
+ ··· − 480u − 64)
c
6
, c
9
(u
25
+ 2u
24
+ ··· + 66u + 9)(u
39
+ 2u
38
+ ··· − 33u − 9)
· (u
96
+ 9u
95
+ ··· + 2219032u + 215401)
c
7
9(u
6
− u
5
+ ··· − u + 1)
16
(3u
25
+ 3u
24
+ ··· − 3u − 1)
· (3u
39
+ 54u
38
+ ··· − 3328u − 256)
c
11
9(u
6
− u
5
+ ··· − u + 1)
16
(3u
25
− 3u
24
+ ··· − 3u + 1)
· (3u
39
+ 54u
38
+ ··· − 3328u − 256)
c
12
81(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
16
· (9u
25
− 105u
24
+ ··· + 11u − 1)
· (9u
39
− 132u
38
+ ··· + 262144u − 65536)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
6561(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
12
· (81y
25
+ 1089y
24
+ ··· − y −1)
· (81y
39
+ 3006y
38
+ ··· + 5780799488y −16777216)
c
2
, c
5
81(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
12
· (9y
25
− 87y
24
+ ··· + 7y −1)(9y
39
− 114y
38
+ ··· + 111616y −4096)
c
3
, c
4
, c
8
c
10
(y
25
− 28y
24
+ ··· − 25y −1)(y
39
− 26y
38
+ ··· + 52y
2
− 1)
· (y
96
− 81y
95
+ ··· − 141748367588y + 2276912089)
c
6
, c
9
(y
25
− 6y
24
+ ··· + 2070y −81)(y
39
+ 36y
37
+ ··· + 315y −81)
· (y
96
− 33y
95
+ ··· − 549152756700y + 46397590801)
c
7
, c
11
81(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
16
· (9y
25
− 105y
24
+ ··· + 11y −1)
· (9y
39
− 132y
38
+ ··· + 262144y −65536)
c
12
6561(y
6
+ y
5
+ ··· + 3y + 1)
16
(81y
25
+ 603y
24
+ ··· − y −1)
· (81y
39
+ 2196y
38
+ ··· − 63350767616y −4294967296)
29
