12a
1194
(K12a
1194
)
A knot diagram
1
Linearized knot diagam
4 10 11 1 9 2 3 12 6 7 8 5
Solving Sequence
3,7 8,10
11 4 12 2 1 6 9 5
c
7
c
10
c
3
c
11
c
2
c
1
c
6
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h9.79780 × 10
46
u
37
+ 3.35501 × 10
46
u
36
+ ··· + 1.92279 × 10
47
b − 2.18034 × 10
47
, a − 1,
u
38
+ u
37
+ ··· + 19u
2
− 1i
I
u
2
= h1.82885 × 10
255
u
71
− 9.62892 × 10
254
u
70
+ ··· + 6.92537 × 10
255
b + 6.25833 × 10
257
,
1.88860 × 10
255
u
71
− 1.18895 × 10
255
u
70
+ ··· + 6.92537 × 10
255
a + 4.84199 × 10
257
,
u
72
+ u
70
+ ··· + 600u + 192i
I
u
3
= h−u
15
− u
14
+ u
11
− 2u
10
− 6u
9
− 5u
8
+ 9u
7
− 13u
6
− 5u
5
+ 30u
4
+ u
3
− 25u
2
+ b + 8, a + 1,
u
17
− u
14
+ u
12
+ 6u
11
− 2u
10
− 7u
9
+ 13u
8
− 6u
7
− 24u
6
+ 12u
5
+ 19u
4
− 6u
3
− 7u
2
+ u + 1i
I
u
4
= h3b + u − 2, a − u − 1, u
2
− u + 1i
I
u
5
= h6b − u − 3, 6a − u − 3, u
2
+ 3i
I
u
6
= hb + 1, a + 1, u
2
− u + 1i
* 6 irreducible components of dim
C
= 0, with total 133 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
= h9.80 × 10
46
u
37
+ 3.36 × 10
46
u
36
+ · · · + 1.92 × 10
47
b − 2.18 ×
10
47
, a − 1, u
38
+ u
37
+ · · · + 19u
2
− 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
10
=
1
−0.509562u
37
− 0.174487u
36
+ ··· − 3.84868u + 1.13395
a
11
=
0.509562u
37
+ 0.174487u
36
+ ··· + 3.84868u − 0.133946
−0.509562u
37
− 0.174487u
36
+ ··· − 3.84868u + 1.13395
a
4
=
1.24784u
37
+ 1.13746u
36
+ ··· + 6.22030u − 2.73265
−0.912766u
37
− 0.757139u
36
+ ··· − 5.08636u + 2.22309
a
12
=
−0.0452476u
37
− 0.116918u
36
+ ··· + 0.509562u + 0.664925
−0.448231u
37
− 0.142720u
36
+ ··· − 3.29387u + 0.870541
a
2
=
−u
−0.335075u
37
− 0.380323u
36
+ ··· − 0.133946u + 0.509562
a
1
=
−1.54245u
37
− 1.84686u
36
+ ··· − 19.6552u + 3.53329
0.666260u
37
+ 0.909070u
36
+ ··· + 13.3755u − 2.01544
a
6
=
−0.0452476u
37
− 0.116918u
36
+ ··· + 0.509562u + 0.664925
−0.110380u
37
+ 0.0315993u
36
+ ··· − 2.73265u + 1.24784
a
9
=
0.915215u
37
+ 0.651574u
36
+ ··· + 5.45183u − 0.569657
−1.33092u
37
− 0.844964u
36
+ ··· − 10.0710u + 3.53250
a
5
=
−2.03274u
37
− 1.11723u
36
+ ··· − 15.2736u + 6.20954
2.05290u
37
+ 1.33796u
36
+ ··· + 17.7773u − 6.02161
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.739502u
37
− 0.948748u
36
+ ··· − 10.0381u + 6.25697
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
38
− 10u
37
+ ··· + 208u − 16
c
2
, c
7
u
38
+ u
37
+ ··· + 19u
2
− 1
c
3
, c
6
u
38
+ u
37
+ ··· − 8u − 4
c
5
, c
8
, c
9
c
11
u
38
− 22u
36
+ ··· + 12u + 1
c
10
u
38
+ 18u
37
+ ··· − 62u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
38
+ 38y
37
+ ··· + 2016y + 256
c
2
, c
7
y
38
− 19y
37
+ ··· − 38y + 1
c
3
, c
6
y
38
+ 7y
37
+ ··· + 264y + 16
c
5
, c
8
, c
9
c
11
y
38
− 44y
37
+ ··· − 50y + 1
c
10
y
38
− 4y
37
+ ··· − 716y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.479520 + 0.882461I
a = 1.00000
b = 0.751362 − 0.367985I
−0.19527 + 1.57472I −3.21629 − 2.23777I
u = 0.479520 − 0.882461I
a = 1.00000
b = 0.751362 + 0.367985I
−0.19527 − 1.57472I −3.21629 + 2.23777I
u = 0.644139 + 0.745875I
a = 1.00000
b = 0.822899 − 0.634508I
−0.13192 + 1.60989I −0.75540 − 1.36355I
u = 0.644139 − 0.745875I
a = 1.00000
b = 0.822899 + 0.634508I
−0.13192 − 1.60989I −0.75540 + 1.36355I
u = −0.937133 + 0.239327I
a = 1.00000
b = 0.76066 − 1.21673I
9.11838 − 5.83428I 8.14618 + 5.74561I
u = −0.937133 − 0.239327I
a = 1.00000
b = 0.76066 + 1.21673I
9.11838 + 5.83428I 8.14618 − 5.74561I
u = 0.852502 + 0.278386I
a = 1.00000
b = 0.95818 + 1.45928I
16.3227 + 9.5388I 10.67449 − 6.03102I
u = 0.852502 − 0.278386I
a = 1.00000
b = 0.95818 − 1.45928I
16.3227 − 9.5388I 10.67449 + 6.03102I
u = −0.871208 + 0.681798I
a = 1.00000
b = 1.16064 + 0.91404I
−1.77981 − 4.59053I −3.12624 + 6.99491I
u = −0.871208 − 0.681798I
a = 1.00000
b = 1.16064 − 0.91404I
−1.77981 + 4.59053I −3.12624 − 6.99491I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098320 + 0.234964I
a = 1.00000
b = 0.682932 + 0.779615I
8.59426 + 0.71431I 7.79538 + 0.07256I
u = 1.098320 − 0.234964I
a = 1.00000
b = 0.682932 − 0.779615I
8.59426 − 0.71431I 7.79538 − 0.07256I
u = 0.957238 + 0.605348I
a = 1.00000
b = 1.27321 − 1.10751I
3.03840 + 7.55076I 2.62397 − 7.06584I
u = 0.957238 − 0.605348I
a = 1.00000
b = 1.27321 + 1.10751I
3.03840 − 7.55076I 2.62397 + 7.06584I
u = −0.666023 + 0.378508I
a = 1.00000
b = 0.385427 + 1.322160I
5.43833 − 1.25341I 5.66766 + 5.57255I
u = −0.666023 − 0.378508I
a = 1.00000
b = 0.385427 − 1.322160I
5.43833 + 1.25341I 5.66766 − 5.57255I
u = 0.753740 + 0.136199I
a = 1.00000
b = −0.541177 − 0.389347I
2.42366 − 3.68294I −1.25459 − 4.84612I
u = 0.753740 − 0.136199I
a = 1.00000
b = −0.541177 + 0.389347I
2.42366 + 3.68294I −1.25459 + 4.84612I
u = −1.241290 + 0.060112I
a = 1.00000
b = −0.159015 + 0.380020I
14.1852 − 1.9882I 9.99909 + 0.39309I
u = −1.241290 − 0.060112I
a = 1.00000
b = −0.159015 − 0.380020I
14.1852 + 1.9882I 9.99909 − 0.39309I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27422
a = 1.00000
b = 0.155353
8.57853 10.1100
u = −1.185860 + 0.497013I
a = 1.00000
b = 1.108850 − 0.479064I
14.7439 + 3.7494I 9.22095 − 1.93955I
u = −1.185860 − 0.497013I
a = 1.00000
b = 1.108850 + 0.479064I
14.7439 − 3.7494I 9.22095 + 1.93955I
u = −0.660729
a = 1.00000
b = −0.500671
−1.71192 −9.74460
u = −0.498440 + 1.244020I
a = 1.00000
b = 0.359751 + 0.272033I
2.22750 − 1.67185I 11.46563 + 1.61850I
u = −0.498440 − 1.244020I
a = 1.00000
b = 0.359751 − 0.272033I
2.22750 + 1.67185I 11.46563 − 1.61850I
u = −1.34768 + 0.93044I
a = 1.00000
b = 1.17535 + 1.06620I
15.4363 − 18.1987I 0
u = −1.34768 − 0.93044I
a = 1.00000
b = 1.17535 − 1.06620I
15.4363 + 18.1987I 0
u = −0.318318 + 0.076916I
a = 1.00000
b = −1.50883 + 0.88780I
7.74248 − 1.46031I −0.55144 + 3.69482I
u = −0.318318 − 0.076916I
a = 1.00000
b = −1.50883 − 0.88780I
7.74248 + 1.46031I −0.55144 − 3.69482I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27499 + 1.08569I
a = 1.00000
b = 0.753733 − 0.824122I
15.9166 + 1.5691I 0
u = 1.27499 − 1.08569I
a = 1.00000
b = 0.753733 + 0.824122I
15.9166 − 1.5691I 0
u = 1.39247 + 0.95063I
a = 1.00000
b = 1.13211 − 0.94427I
7.9524 + 13.4272I 0
u = 1.39247 − 0.95063I
a = 1.00000
b = 1.13211 + 0.94427I
7.9524 − 13.4272I 0
u = 0.213113 + 0.167716I
a = 1.00000
b = −0.944587 − 0.435602I
1.72141 + 0.61974I 2.92253 + 0.39439I
u = 0.213113 − 0.167716I
a = 1.00000
b = −0.944587 + 0.435602I
1.72141 − 0.61974I 2.92253 − 0.39439I
u = −1.40684 + 1.03775I
a = 1.00000
b = 1.001170 + 0.829159I
7.87445 − 6.81193I 0
u = −1.40684 − 1.03775I
a = 1.00000
b = 1.001170 − 0.829159I
7.87445 + 6.81193I 0
8
II. I
u
2
= h1.83 × 10
255
u
71
− 9.63 × 10
254
u
70
+ · · · + 6.93 × 10
255
b + 6.26 ×
10
257
, 1.89 × 10
255
u
71
− 1.19 × 10
255
u
70
+ · · · + 6.93 × 10
255
a + 4.84 ×
10
257
, u
72
+ u
70
+ · · · + 600u + 192i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
10
=
−0.272707u
71
+ 0.171681u
70
+ ··· − 122.503u − 69.9167
−0.264080u
71
+ 0.139038u
70
+ ··· − 110.859u − 90.3682
a
11
=
−0.00862691u
71
+ 0.0326421u
70
+ ··· − 11.6439u + 20.4515
−0.264080u
71
+ 0.139038u
70
+ ··· − 110.859u − 90.3682
a
4
=
−0.643001u
71
+ 0.403385u
70
+ ··· − 330.474u − 202.802
−0.167715u
71
+ 0.0931258u
70
+ ··· − 77.9212u − 60.0375
a
12
=
−0.308920u
71
+ 0.201634u
70
+ ··· − 140.432u − 76.1840
−0.165046u
71
+ 0.0822409u
70
+ ··· − 67.1202u − 57.9218
a
2
=
−0.570796u
71
+ 0.359834u
70
+ ··· − 300.743u − 183.584
0.239920u
71
− 0.136677u
70
+ ··· + 109.652u + 79.2555
a
1
=
−0.104996u
71
+ 0.0708180u
70
+ ··· − 74.8935u − 49.3580
0.170685u
71
− 0.0962956u
70
+ ··· + 81.4730u + 61.4960
a
6
=
0.168474u
71
− 0.104174u
70
+ ··· + 42.9975u + 42.5367
−0.402366u
71
+ 0.232386u
70
+ ··· − 187.548u − 137.859
a
9
=
0.326748u
71
− 0.198736u
70
+ ··· + 126.792u + 96.5926
−0.515586u
71
+ 0.292522u
70
+ ··· − 238.142u − 174.717
a
5
=
−0.415877u
71
+ 0.258738u
70
+ ··· − 195.345u − 119.809
−0.0728064u
71
+ 0.0423429u
70
+ ··· − 28.1964u − 25.4350
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.77306u
71
− 3.76632u
70
+ ··· + 3118.99u + 2314.71
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
36
+ 7u
35
+ ··· − u + 1)
2
c
2
, c
7
u
72
+ u
70
+ ··· + 600u + 192
c
3
, c
6
3(3u
72
+ 28u
70
+ ··· + 696u − 144)
c
5
, c
8
, c
9
c
11
3(3u
72
− 6u
71
+ ··· − 5096u + 464)
c
10
9(3u
36
− 33u
35
+ ··· + u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
36
+ 39y
35
+ ··· + 15y + 1)
2
c
2
, c
7
y
72
+ 2y
71
+ ··· − 1232832y + 36864
c
3
, c
6
9(9y
72
+ 168y
71
+ ··· + 411840y + 20736)
c
5
, c
8
, c
9
c
11
9(9y
72
− 534y
71
+ ··· − 1.10869 × 10
7
y + 215296)
c
10
81(9y
36
− 21y
35
+ ··· − 29y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.978478 + 0.196725I
a = −0.470303 + 0.120405I
b = −2.03002 + 0.15729I
7.64664 + 0.89830I 0
u = −0.978478 − 0.196725I
a = −0.470303 − 0.120405I
b = −2.03002 − 0.15729I
7.64664 − 0.89830I 0
u = 1.022020 + 0.069411I
a = −0.529866 + 0.043954I
b = −1.188640 + 0.471909I
2.40022 − 0.09330I 0
u = 1.022020 − 0.069411I
a = −0.529866 − 0.043954I
b = −1.188640 − 0.471909I
2.40022 + 0.09330I 0
u = 0.888845 + 0.539655I
a = −1.55452 − 0.20173I
b = −0.555893 + 0.888952I
11.15320 + 4.60597I 0
u = 0.888845 − 0.539655I
a = −1.55452 + 0.20173I
b = −0.555893 − 0.888952I
11.15320 − 4.60597I 0
u = −0.905766 + 0.290443I
a = 0.054213 − 0.795751I
b = 0.31798 + 1.90900I
9.17715 − 0.71197I 0. − 6.68193I
u = −0.905766 − 0.290443I
a = 0.054213 + 0.795751I
b = 0.31798 − 1.90900I
9.17715 + 0.71197I 0. + 6.68193I
u = −0.644561 + 0.873982I
a = −1.16999 + 1.42334I
b = −0.616672 − 0.336692I
12.6707 − 9.2670I 0
u = −0.644561 − 0.873982I
a = −1.16999 − 1.42334I
b = −0.616672 + 0.336692I
12.6707 + 9.2670I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792031 + 0.437469I
a = −0.49927 + 1.78168I
b = 0.369829 − 0.333785I
8.39463 + 3.54557I 5.80898 − 6.93351I
u = 0.792031 − 0.437469I
a = −0.49927 − 1.78168I
b = 0.369829 + 0.333785I
8.39463 − 3.54557I 5.80898 + 6.93351I
u = −1.10588
a = 0.279991
b = −0.520793
−1.68620 0
u = −0.527966 + 0.702604I
a = 0.75481 − 1.23770I
b = 0.819842 + 0.533691I
5.98660 − 4.60314I 3.32384 + 5.95672I
u = −0.527966 − 0.702604I
a = 0.75481 + 1.23770I
b = 0.819842 − 0.533691I
5.98660 + 4.60314I 3.32384 − 5.95672I
u = 0.293423 + 1.091190I
a = −1.96904 − 0.66256I
b = −0.592260 + 0.122395I
4.63277 + 3.77829I 0
u = 0.293423 − 1.091190I
a = −1.96904 + 0.66256I
b = −0.592260 − 0.122395I
4.63277 − 3.77829I 0
u = −0.518294 + 0.602575I
a = 0.60287 − 2.01252I
b = 0.268383 + 0.145956I
1.37324 − 1.52816I −6.63056 + 1.97711I
u = −0.518294 − 0.602575I
a = 0.60287 + 2.01252I
b = 0.268383 − 0.145956I
1.37324 + 1.52816I −6.63056 − 1.97711I
u = 0.775530 + 0.171708I
a = −0.479700 + 0.760784I
b = −0.44714 − 1.48857I
2.85135 + 0.79016I 24.0507 + 6.2510I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775530 − 0.171708I
a = −0.479700 − 0.760784I
b = −0.44714 + 1.48857I
2.85135 − 0.79016I 24.0507 − 6.2510I
u = 0.274069 + 0.731062I
a = 1.37652 + 0.96080I
b = 0.656214 − 0.208478I
−0.58194 + 2.00247I −5.14664 − 7.85469I
u = 0.274069 − 0.731062I
a = 1.37652 − 0.96080I
b = 0.656214 + 0.208478I
−0.58194 − 2.00247I −5.14664 + 7.85469I
u = −0.942728 + 0.807529I
a = −1.235170 − 0.104166I
b = −0.945820 − 0.825413I
2.69290 − 5.70756I 0
u = −0.942728 − 0.807529I
a = −1.235170 + 0.104166I
b = −0.945820 + 0.825413I
2.69290 + 5.70756I 0
u = 0.182016 + 0.736510I
a = 0.085219 + 1.250870I
b = 0.31798 + 1.90900I
9.17715 − 0.71197I 2.28150 − 6.68193I
u = 0.182016 − 0.736510I
a = 0.085219 − 1.250870I
b = 0.31798 − 1.90900I
9.17715 + 0.71197I 2.28150 + 6.68193I
u = 0.747739 + 0.088600I
a = 1.63880 − 1.62675I
b = 0.341909 + 1.000020I
15.8742 − 7.9244I 11.14213 + 5.15246I
u = 0.747739 − 0.088600I
a = 1.63880 + 1.62675I
b = 0.341909 − 1.000020I
15.8742 + 7.9244I 11.14213 − 5.15246I
u = 0.471101 + 1.183790I
a = 0.359152 + 0.588923I
b = 0.819842 + 0.533691I
5.98660 − 4.60314I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.471101 − 1.183790I
a = 0.359152 − 0.588923I
b = 0.819842 − 0.533691I
5.98660 + 4.60314I 0
u = −0.502655 + 0.507643I
a = −0.593024 − 0.940511I
b = −0.44714 − 1.48857I
2.85135 + 0.79016I 24.0507 + 6.2510I
u = −0.502655 − 0.507643I
a = −0.593024 + 0.940511I
b = −0.44714 + 1.48857I
2.85135 − 0.79016I 24.0507 − 6.2510I
u = −0.325144 + 1.269650I
a = 0.488484 − 0.340958I
b = 0.656214 − 0.208478I
−0.58194 + 2.00247I 0
u = −0.325144 − 1.269650I
a = 0.488484 + 0.340958I
b = 0.656214 + 0.208478I
−0.58194 − 2.00247I 0
u = −0.167887 + 0.636465I
a = −1.64983 − 1.52369I
b = −0.578317 − 0.313401I
1.46233 − 4.15403I −0.04109 + 11.01980I
u = −0.167887 − 0.636465I
a = −1.64983 + 1.52369I
b = −0.578317 + 0.313401I
1.46233 + 4.15403I −0.04109 − 11.01980I
u = 0.999348 + 0.905429I
a = −1.051100 + 0.164278I
b = −1.10990 + 0.99508I
1.77290 + 8.98505I 0
u = 0.999348 − 0.905429I
a = −1.051100 − 0.164278I
b = −1.10990 − 0.99508I
1.77290 − 8.98505I 0
u = −0.624513 + 0.014551I
a = 2.52548 + 1.23501I
b = 0.664296 − 0.754586I
7.66073 + 4.68142I 6.98748 − 6.62319I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624513 − 0.014551I
a = 2.52548 − 1.23501I
b = 0.664296 + 0.754586I
7.66073 − 4.68142I 6.98748 + 6.62319I
u = −0.989355 + 0.981502I
a = −0.983641 − 0.231346I
b = −1.16325 − 1.14285I
8.31330 − 11.25680I 0
u = −0.989355 − 0.981502I
a = −0.983641 + 0.231346I
b = −1.16325 + 1.14285I
8.31330 + 11.25680I 0
u = 1.200240 + 0.736562I
a = −0.963343 − 0.226572I
b = −1.16325 + 1.14285I
8.31330 + 11.25680I 0
u = 1.200240 − 0.736562I
a = −0.963343 + 0.226572I
b = −1.16325 − 1.14285I
8.31330 − 11.25680I 0
u = −1.19915 + 0.78752I
a = −0.928703 + 0.145149I
b = −1.10990 − 0.99508I
1.77290 − 8.98505I 0
u = −1.19915 − 0.78752I
a = −0.928703 − 0.145149I
b = −1.10990 + 0.99508I
1.77290 + 8.98505I 0
u = −0.544584 + 0.008144I
a = −1.87437 − 0.15549I
b = −1.188640 + 0.471909I
2.40022 − 0.09330I 11.1239 − 12.0920I
u = −0.544584 − 0.008144I
a = −1.87437 + 0.15549I
b = −1.188640 − 0.471909I
2.40022 + 0.09330I 11.1239 + 12.0920I
u = 1.24676 + 0.79425I
a = −0.327116 − 0.302106I
b = −0.578317 + 0.313401I
1.46233 + 4.15403I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24676 − 0.79425I
a = −0.327116 + 0.302106I
b = −0.578317 − 0.313401I
1.46233 − 4.15403I 0
u = 0.512014
a = 3.36891
b = 1.09972
5.27612 −1.90140
u = 0.436495 + 0.210334I
a = −1.99549 + 0.51088I
b = −2.03002 − 0.15729I
7.64664 − 0.89830I 8.29327 − 10.91471I
u = 0.436495 − 0.210334I
a = −1.99549 − 0.51088I
b = −2.03002 + 0.15729I
7.64664 + 0.89830I 8.29327 + 10.91471I
u = 1.24854 + 0.89923I
a = −0.803889 − 0.067795I
b = −0.945820 + 0.825413I
2.69290 + 5.70756I 0
u = 1.24854 − 0.89923I
a = −0.803889 + 0.067795I
b = −0.945820 − 0.825413I
2.69290 − 5.70756I 0
u = −1.27287 + 1.01821I
a = −0.632631 − 0.082095I
b = −0.555893 − 0.888952I
11.15320 − 4.60597I 0
u = −1.27287 − 1.01821I
a = −0.632631 + 0.082095I
b = −0.555893 + 0.888952I
11.15320 + 4.60597I 0
u = 0.90023 + 1.40635I
a = 0.136591 + 0.455971I
b = 0.268383 + 0.145956I
1.37324 − 1.52816I 0
u = 0.90023 − 1.40635I
a = 0.136591 − 0.455971I
b = 0.268383 − 0.145956I
1.37324 + 1.52816I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17487 + 1.19273I
a = −0.145830 − 0.520402I
b = 0.369829 − 0.333785I
8.39463 + 3.54557I 0
u = −1.17487 − 1.19273I
a = −0.145830 + 0.520402I
b = 0.369829 + 0.333785I
8.39463 − 3.54557I 0
u = −0.309637
a = 3.57154
b = −0.520793
−1.68620 −13.2240
u = 1.72493
a = 0.296832
b = 1.09972
5.27612 0
u = 1.36953 + 1.07118I
a = 0.307354 − 0.305092I
b = 0.341909 − 1.000020I
15.8742 + 7.9244I 0
u = 1.36953 − 1.07118I
a = 0.307354 + 0.305092I
b = 0.341909 + 1.000020I
15.8742 − 7.9244I 0
u = −1.59517 + 0.73453I
a = 0.319547 + 0.156265I
b = 0.664296 + 0.754586I
7.66073 − 4.68142I 0
u = −1.59517 − 0.73453I
a = 0.319547 − 0.156265I
b = 0.664296 − 0.754586I
7.66073 + 4.68142I 0
u = −0.48985 + 1.93998I
a = −0.344643 + 0.419275I
b = −0.616672 + 0.336692I
12.6707 + 9.2670I 0
u = −0.48985 − 1.93998I
a = −0.344643 − 0.419275I
b = −0.616672 − 0.336692I
12.6707 − 9.2670I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14521 + 2.34300I
a = −0.456207 − 0.153508I
b = −0.592260 − 0.122395I
4.63277 − 3.77829I 0
u = 0.14521 − 2.34300I
a = −0.456207 + 0.153508I
b = −0.592260 + 0.122395I
4.63277 + 3.77829I 0
19
III. I
u
3
= h−u
15
− u
14
+ · · · + b + 8, a + 1, u
17
− u
14
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
10
=
−1
u
15
+ u
14
+ ··· + 25u
2
− 8
a
11
=
−u
15
− u
14
+ ··· − 25u
2
+ 7
u
15
+ u
14
+ ··· + 25u
2
− 8
a
4
=
6u
16
− 9u
15
+ ··· − 7u + 16
−7u
16
+ 8u
15
+ ··· + 15u − 16
a
12
=
−u
16
− u
14
+ ··· − 6u
3
+ u
u
15
+ u
14
+ ··· + 24u
2
− 7
a
2
=
−u
u
16
+ u
15
+ ··· + 25u
3
− 7u
a
1
=
48u
16
+ 9u
15
+ ··· − 80u − 16
−62u
16
+ 9u
15
+ ··· + 80u − 32
a
6
=
u
16
+ u
14
− u
13
+ u
12
+ 7u
10
− 2u
9
+ 11u
7
− 6u
6
− 13u
5
+ 6u
4
+ 6u
3
− u
−9u
16
+ u
15
+ ··· + 10u − 6
a
9
=
0
−7u
16
+ 6u
15
+ ··· + 6u − 25
a
5
=
u
16
+ u
14
− u
13
+ u
12
+ 7u
10
− 2u
9
+ 11u
7
− 6u
6
− 13u
5
+ 6u
4
+ 6u
3
− u
15u
16
− 18u
15
+ ··· − 8u + 55
(ii) Obstruction class = 1
(iii) Cusp Shapes = 117u
16
+ 131u
15
+ 72u
14
− 26u
13
− 83u
12
+ 105u
11
+ 775u
10
+
615u
9
− 595u
8
+ 1046u
7
+ 640u
6
− 3005u
5
− 1222u
4
+ 1910u
3
+ 802u
2
− 385u − 155
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
17
− 4u
16
+ ··· + 8u − 1
c
2
, c
7
u
17
− u
14
+ ··· + u + 1
c
3
, c
6
u
17
− u
16
+ ··· − 9u + 7
c
4
u
17
+ 4u
16
+ ··· + 8u + 1
c
5
, c
8
u
17
− 2u
16
+ ··· + 4u + 1
c
9
, c
11
u
17
+ 2u
16
+ ··· + 4u − 1
c
10
u
17
− 11u
16
+ ··· − 5u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
17
+ 18y
16
+ ··· − 12y −1
c
2
, c
7
y
17
+ 11y
14
+ ··· + 15y −1
c
3
, c
6
y
17
+ 7y
16
+ ··· − 297y −49
c
5
, c
8
, c
9
c
11
y
17
− 14y
16
+ ··· + 16y −1
c
10
y
17
− y
16
+ ··· + 9y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.815350 + 0.025667I
a = −1.00000
b = 0.432123 + 0.459880I
2.66696 − 4.00977I 10.5482 + 10.6174I
u = 0.815350 − 0.025667I
a = −1.00000
b = 0.432123 − 0.459880I
2.66696 + 4.00977I 10.5482 − 10.6174I
u = −0.810925
a = −1.00000
b = 0.399877
−1.28018 9.76010
u = −0.762904 + 0.132866I
a = −1.00000
b = −0.68250 − 1.44184I
6.13610 − 0.18293I 11.77568 − 0.45975I
u = −0.762904 − 0.132866I
a = −1.00000
b = −0.68250 + 1.44184I
6.13610 + 0.18293I 11.77568 + 0.45975I
u = 0.448064 + 1.151790I
a = −1.00000
b = −0.136738 + 0.627250I
13.8413 + 8.5902I 8.37133 − 5.57169I
u = 0.448064 − 1.151790I
a = −1.00000
b = −0.136738 − 0.627250I
13.8413 − 8.5902I 8.37133 + 5.57169I
u = 0.698818 + 0.100416I
a = −1.00000
b = −1.13778 + 1.04571I
2.48509 − 0.51154I 13.52668 − 1.22374I
u = 0.698818 − 0.100416I
a = −1.00000
b = −1.13778 − 1.04571I
2.48509 + 0.51154I 13.52668 + 1.22374I
u = −0.630549 + 0.102934I
a = −1.00000
b = −1.76137 − 1.10971I
8.14897 + 1.24811I 15.2631 + 4.1484I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630549 − 0.102934I
a = −1.00000
b = −1.76137 + 1.10971I
8.14897 − 1.24811I 15.2631 − 4.1484I
u = 1.163290 + 0.724126I
a = −1.00000
b = −1.17544 + 1.06539I
4.81289 + 8.43599I 7.48683 − 6.84073I
u = 1.163290 − 0.724126I
a = −1.00000
b = −1.17544 − 1.06539I
4.81289 − 8.43599I 7.48683 + 6.84073I
u = −1.09074 + 0.97038I
a = −1.00000
b = −0.905613 − 0.885471I
3.26959 − 7.23683I 6.29628 + 7.79702I
u = −1.09074 − 0.97038I
a = −1.00000
b = −0.905613 + 0.885471I
3.26959 + 7.23683I 6.29628 − 7.79702I
u = −0.23586 + 1.55862I
a = −1.00000
b = −0.332619 − 0.180741I
5.33734 − 3.68274I 9.85182 + 3.87924I
u = −0.23586 − 1.55862I
a = −1.00000
b = −0.332619 + 0.180741I
5.33734 + 3.68274I 9.85182 − 3.87924I
24
IV. I
u
4
= h3b + u − 2, a − u − 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u + 1
a
10
=
u + 1
−
1
3
u +
2
3
a
11
=
4
3
u +
1
3
−
1
3
u +
2
3
a
4
=
−u +
8
3
0.333333
a
12
=
4
3
u −
2
3
2
3
u −
1
3
a
2
=
−3u + 3
0
a
1
=
−
1
3
u +
4
3
1
3
u −
1
3
a
6
=
1
0
a
9
=
4
3
u +
1
3
−
1
3
u +
2
3
a
5
=
1
3
u +
5
3
−
1
3
u +
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
116
9
u +
53
9
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
12
u
2
− u + 1
c
2
u
2
+ 3
c
3
3(3u
2
− 3u + 7)
c
4
u
2
+ u + 1
c
5
3(3u
2
− 3u + 1)
c
6
u
2
c
8
(u + 1)
2
c
9
, c
10
3(3u
2
+ 3u + 1)
c
11
(u − 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
12
y
2
+ y + 1
c
2
(y + 3)
2
c
3
9(9y
2
+ 33y + 49)
c
5
, c
9
, c
10
9(9y
2
− 3y + 1)
c
6
y
2
c
8
, c
11
(y −1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.50000 + 0.86603I
b = 0.500000 − 0.288675I
1.64493 + 2.02988I −0.55556 − 11.16211I
u = 0.500000 − 0.866025I
a = 1.50000 − 0.86603I
b = 0.500000 + 0.288675I
1.64493 − 2.02988I −0.55556 + 11.16211I
28
V. I
u
5
= h6b − u − 3, 6a − u − 3, u
2
+ 3i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
3
a
10
=
1
6
u +
1
2
1
6
u +
1
2
a
11
=
0
1
6
u +
1
2
a
4
=
0
u
a
12
=
1
6
u +
1
2
2
3
u + 2
a
2
=
−
1
6
u +
1
2
5
6
u +
1
2
a
1
=
−
1
6
u +
1
2
1
3
u + 2
a
6
=
−
1
3
u +
1
3
−
5
6
u +
11
6
a
9
=
−
1
6
u +
5
6
−
2
3
u +
7
3
a
5
=
−
1
6
u −
1
2
−
1
6
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
58
9
u −
5
9
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u
2
− u + 1
c
3
u
2
c
4
u
2
+ u + 1
c
5
(u + 1)
2
c
6
3(3u
2
− 3u + 7)
c
7
u
2
+ 3
c
8
3(3u
2
− 3u + 1)
c
9
(u − 1)
2
c
10
, c
11
3(3u
2
+ 3u + 1)
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
12
y
2
+ y + 1
c
3
y
2
c
5
, c
9
(y −1)
2
c
6
9(9y
2
+ 33y + 49)
c
7
(y + 3)
2
c
8
, c
10
, c
11
9(9y
2
− 3y + 1)
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 0.500000 + 0.288675I
b = 0.500000 + 0.288675I
1.64493 − 2.02988I −0.55556 + 11.16211I
u = − 1.73205I
a = 0.500000 − 0.288675I
b = 0.500000 − 0.288675I
1.64493 + 2.02988I −0.55556 − 11.16211I
32
VI. I
u
6
= hb + 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u + 1
a
10
=
−1
−1
a
11
=
0
−1
a
4
=
0
u
a
12
=
−1
u − 2
a
2
=
−u
0
a
1
=
−u
−1
a
6
=
1
0
a
9
=
0
−1
a
5
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 5
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
12
u
2
− u + 1
c
3
, c
6
u
2
c
4
u
2
+ u + 1
c
5
, c
8
(u + 1)
2
c
9
, c
10
, c
11
(u − 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
12
y
2
+ y + 1
c
3
, c
6
y
2
c
5
, c
8
, c
9
c
10
, c
11
(y −1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = −1.00000
1.64493 + 2.02988I 3.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −1.00000
b = −1.00000
1.64493 − 2.02988I 3.00000 + 3.46410I
36
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
2
− u + 1)
3
)(u
17
− 4u
16
+ ··· + 8u − 1)(u
36
+ 7u
35
+ ··· − u + 1)
2
· (u
38
− 10u
37
+ ··· + 208u − 16)
c
2
, c
7
(u
2
+ 3)(u
2
− u + 1)
2
(u
17
− u
14
+ ··· + u + 1)(u
38
+ u
37
+ ··· + 19u
2
− 1)
· (u
72
+ u
70
+ ··· + 600u + 192)
c
3
, c
6
9u
4
(3u
2
− 3u + 7)(u
17
− u
16
+ ··· − 9u + 7)(u
38
+ u
37
+ ··· − 8u − 4)
· (3u
72
+ 28u
70
+ ··· + 696u − 144)
c
4
((u
2
+ u + 1)
3
)(u
17
+ 4u
16
+ ··· + 8u + 1)(u
36
+ 7u
35
+ ··· − u + 1)
2
· (u
38
− 10u
37
+ ··· + 208u − 16)
c
5
, c
8
9(u + 1)
4
(3u
2
− 3u + 1)(u
17
− 2u
16
+ ··· + 4u + 1)
· (u
38
− 22u
36
+ ··· + 12u + 1)(3u
72
− 6u
71
+ ··· − 5096u + 464)
c
9
, c
11
9(u − 1)
4
(3u
2
+ 3u + 1)(u
17
+ 2u
16
+ ··· + 4u − 1)
· (u
38
− 22u
36
+ ··· + 12u + 1)(3u
72
− 6u
71
+ ··· − 5096u + 464)
c
10
81(u − 1)
2
(3u
2
+ 3u + 1)
2
(u
17
− 11u
16
+ ··· − 5u + 1)
· ((3u
36
− 33u
35
+ ··· + u − 1)
2
)(u
38
+ 18u
37
+ ··· − 62u − 4)
37
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
((y
2
+ y + 1)
3
)(y
17
+ 18y
16
+ ··· − 12y −1)
· ((y
36
+ 39y
35
+ ··· + 15y + 1)
2
)(y
38
+ 38y
37
+ ··· + 2016y + 256)
c
2
, c
7
((y + 3)
2
)(y
2
+ y + 1)
2
(y
17
+ 11y
14
+ ··· + 15y −1)
· (y
38
− 19y
37
+ ··· − 38y + 1)(y
72
+ 2y
71
+ ··· − 1232832y + 36864)
c
3
, c
6
81y
4
(9y
2
+ 33y + 49)(y
17
+ 7y
16
+ ··· − 297y −49)
· (y
38
+ 7y
37
+ ··· + 264y + 16)
· (9y
72
+ 168y
71
+ ··· + 411840y + 20736)
c
5
, c
8
, c
9
c
11
81(y −1)
4
(9y
2
− 3y + 1)(y
17
− 14y
16
+ ··· + 16y −1)
· (y
38
− 44y
37
+ ··· − 50y + 1)
· (9y
72
− 534y
71
+ ··· − 11086880y + 215296)
c
10
6561(y −1)
2
(9y
2
− 3y + 1)
2
(y
17
− y
16
+ ··· + 9y −1)
· ((9y
36
− 21y
35
+ ··· − 29y + 1)
2
)(y
38
− 4y
37
+ ··· − 716y + 16)
38
