12a
1045
(K12a
1045
)
A knot diagram
1
Linearized knot diagam
4 7 9 8 11 12 2 1 3 5 6 10
Solving Sequence
5,11
6 12
3,7
2 10 1 9 8 4
c
5
c
11
c
6
c
2
c
10
c
12
c
9
c
8
c
4
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−233u
29
+ 1283u
28
+ ··· + 4b − 1220, −533u
29
+ 2893u
28
+ ··· + 8a − 2692,
u
30
− 7u
29
+ ··· − 4u − 8i
I
u
2
= h4.20118 × 10
22
a
5
u
10
+ 5.48121 × 10
23
a
4
u
10
+ ··· + 3.93261 × 10
24
a − 4.34401 × 10
24
,
u
10
a
5
+ 5u
10
a
4
+ ··· + 5a − 3, u
11
+ u
10
− 6u
9
− 5u
8
+ 12u
7
+ 6u
6
− 10u
5
+ u
4
+ 5u
3
− u
2
+ 1i
I
u
3
= h−u
14
+ 2u
13
+ 8u
12
− 15u
11
− 24u
10
+ 39u
9
+ 36u
8
− 38u
7
− 37u
6
+ 8u
5
+ 32u
4
− 12u
2
+ b − 2u + 2,
− 2u
14
+ 2u
13
+ ··· + a + 2,
u
16
− 10u
14
+ 39u
12
+ u
11
− 74u
10
− 8u
9
+ 71u
8
+ 23u
7
− 38u
6
− 28u
5
+ 18u
4
+ 13u
3
− 4u
2
− 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 112 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−233u
29
+ 1283u
28
+ · · · + 4b − 1220, −533u
29
+ 2893u
28
+ · · · +
8a − 2692, u
30
− 7u
29
+ · · · − 4u − 8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
66.6250u
29
− 361.625u
28
+ ··· + 373.250u + 336.500
233
4
u
29
−
1283
4
u
28
+ ··· + 349u + 305
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
22.3750u
29
− 127.875u
28
+ ··· + 160.250u + 131.500
−
31
4
u
29
+
157
4
u
28
+ ··· − 31u − 31
a
10
=
u
u
a
1
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
9
=
41
8
u
29
−
289
8
u
28
+ ··· +
329
4
u + 56
−
53
4
u
29
+
261
4
u
28
+ ··· −
71
2
u − 43
a
8
=
197
8
u
29
−
1045
8
u
28
+ ··· +
489
4
u + 114
49
4
u
29
−
265
4
u
28
+ ··· +
129
2
u + 59
a
4
=
109
8
u
29
−
571
8
u
28
+ ··· + 65u + 64
63
2
u
29
− 173u
28
+ ··· +
381
2
u + 165
(ii) Obstruction class = −1
(iii) Cusp Shapes = −43u
29
+ 233u
28
+ 24u
27
− 2066u
26
+ 1935u
25
+ 7589u
24
−
8992u
23
− 18142u
22
+ 17380u
21
+ 37598u
20
− 16730u
19
− 60970u
18
− 3411u
17
+
65829u
16
+ 39349u
15
− 41950u
14
− 51488u
13
− 4016u
12
+ 34851u
11
+ 20846u
10
−
921u
9
− 13945u
8
− 6633u
7
− 1648u
6
+ 2861u
5
+ 1809u
4
+ 1337u
3
− 166u
2
− 248u − 210
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 27u
29
+ ··· − 36864u + 2048
c
2
, c
3
, c
7
c
9
u
30
+ 11u
28
+ ··· + u − 1
c
4
, c
8
u
30
+ u
29
+ ··· − 2u − 1
c
5
, c
6
, c
10
c
11
u
30
+ 7u
29
+ ··· + 4u − 8
c
12
u
30
− 7u
29
+ ··· + 56384u − 20992
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 9y
29
+ ··· − 48234496y + 4194304
c
2
, c
3
, c
7
c
9
y
30
+ 22y
29
+ ··· − 11y + 1
c
4
, c
8
y
30
+ 3y
29
+ ··· + 12y + 1
c
5
, c
6
, c
10
c
11
y
30
− 33y
29
+ ··· − 16y + 64
c
12
y
30
+ 3y
29
+ ··· − 206688256y + 440664064
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.863405 + 0.530291I
a = −0.684999 + 0.008143I
b = −0.897675 + 1.001320I
−3.01285 + 5.42239I −5.0249 − 13.7215I
u = −0.863405 − 0.530291I
a = −0.684999 − 0.008143I
b = −0.897675 − 1.001320I
−3.01285 − 5.42239I −5.0249 + 13.7215I
u = −0.731476 + 0.568139I
a = 1.114310 + 0.365338I
b = 1.56285 − 1.21446I
−6.0916 + 13.9505I −9.16482 − 9.63284I
u = −0.731476 − 0.568139I
a = 1.114310 − 0.365338I
b = 1.56285 + 1.21446I
−6.0916 − 13.9505I −9.16482 + 9.63284I
u = 1.051940 + 0.292196I
a = −0.289301 − 1.130000I
b = 0.373374 − 0.058569I
−8.43524 + 6.26787I −11.74379 − 3.92525I
u = 1.051940 − 0.292196I
a = −0.289301 + 1.130000I
b = 0.373374 + 0.058569I
−8.43524 − 6.26787I −11.74379 + 3.92525I
u = −0.484434 + 0.766175I
a = −0.062606 − 0.648073I
b = −0.985885 + 0.008839I
−1.10337 + 2.52152I −5.89538 − 5.05949I
u = −0.484434 − 0.766175I
a = −0.062606 + 0.648073I
b = −0.985885 − 0.008839I
−1.10337 − 2.52152I −5.89538 + 5.05949I
u = −0.548147 + 0.512523I
a = −0.706260 + 0.439855I
b = 0.058759 + 1.016530I
2.18720 + 3.47846I −0.09259 − 5.90060I
u = −0.548147 − 0.512523I
a = −0.706260 − 0.439855I
b = 0.058759 − 1.016530I
2.18720 − 3.47846I −0.09259 + 5.90060I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192741 + 0.695844I
a = −1.071720 + 0.672690I
b = 0.921075 + 0.862157I
−4.48729 − 9.71321I −6.59814 + 5.23923I
u = −0.192741 − 0.695844I
a = −1.071720 − 0.672690I
b = 0.921075 − 0.862157I
−4.48729 + 9.71321I −6.59814 − 5.23923I
u = −0.388423 + 0.514575I
a = 0.941435 + 0.297487I
b = 0.530431 − 0.779112I
2.64855 + 0.09639I 1.44482 − 2.17887I
u = −0.388423 − 0.514575I
a = 0.941435 − 0.297487I
b = 0.530431 + 0.779112I
2.64855 − 0.09639I 1.44482 + 2.17887I
u = 0.106548 + 0.589026I
a = 0.822013 + 0.171417I
b = −0.283998 − 0.456801I
−0.17771 − 1.54871I −0.18007 + 2.74695I
u = 0.106548 − 0.589026I
a = 0.822013 − 0.171417I
b = −0.283998 + 0.456801I
−0.17771 + 1.54871I −0.18007 − 2.74695I
u = 0.596209
a = 0.544746
b = −0.131144
−1.09004 −8.37530
u = 1.41655 + 0.25699I
a = −0.808360 + 0.799987I
b = −0.800464 + 0.038413I
−7.16962 − 6.25363I −10.89356 + 7.51977I
u = 1.41655 − 0.25699I
a = −0.808360 − 0.799987I
b = −0.800464 − 0.038413I
−7.16962 + 6.25363I −10.89356 − 7.51977I
u = 1.48803 + 0.08948I
a = 1.73464 + 0.05380I
b = 1.236300 + 0.345342I
−3.44648 − 2.04173I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48803 − 0.08948I
a = 1.73464 − 0.05380I
b = 1.236300 − 0.345342I
−3.44648 + 2.04173I 0
u = 1.54359 + 0.14330I
a = −0.818557 − 1.014570I
b = −0.366568 − 1.075300I
−4.79663 − 5.82343I 0
u = 1.54359 − 0.14330I
a = −0.818557 + 1.014570I
b = −0.366568 + 1.075300I
−4.79663 + 5.82343I 0
u = −1.55904
a = −0.0976328
b = −0.389520
−8.42781 −9.45490
u = 1.61572 + 0.17130I
a = 2.49295 + 0.48824I
b = 2.22027 + 1.42432I
−14.0241 − 16.7372I 0
u = 1.61572 − 0.17130I
a = 2.49295 − 0.48824I
b = 2.22027 − 1.42432I
−14.0241 + 16.7372I 0
u = 1.65106 + 0.16927I
a = −1.69282 − 0.62506I
b = −1.52761 − 1.31367I
−11.5587 − 8.1943I 0
u = 1.65106 − 0.16927I
a = −1.69282 + 0.62506I
b = −1.52761 + 1.31367I
−11.5587 + 8.1943I 0
u = −1.68340 + 0.03101I
a = 0.055719 − 0.237640I
b = 0.219463 − 1.080790I
−18.0199 − 5.2960I 0
u = −1.68340 − 0.03101I
a = 0.055719 + 0.237640I
b = 0.219463 + 1.080790I
−18.0199 + 5.2960I 0
7
II. I
u
2
= h4.20 × 10
22
a
5
u
10
+ 5.48 × 10
23
a
4
u
10
+ · · · + 3.93 × 10
24
a − 4.34 ×
10
24
, u
10
a
5
+ 5u
10
a
4
+ · · · + 5a − 3, u
11
+ u
10
+ · · · − u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
a
−0.0109737a
5
u
10
− 0.143173a
4
u
10
+ ··· − 1.02722a + 1.13468
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
0.289631a
5
u
10
+ 0.0720661a
4
u
10
+ ··· + 2.24758a − 1.87380
−0.170540a
5
u
10
− 0.00192749a
4
u
10
+ ··· − 2.50277a + 1.80562
a
10
=
u
u
a
1
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
9
=
0.0463446a
5
u
10
− 0.288499a
4
u
10
+ ··· + 0.353993a + 0.712997
0.0951316a
5
u
10
+ 0.324793a
4
u
10
+ ··· + 0.766226a − 0.234285
a
8
=
−0.411421a
5
u
10
− 0.796302a
4
u
10
+ ··· + 4.25520a + 0.348645
−0.172791a
5
u
10
− 0.332111a
4
u
10
+ ··· + 2.55867a + 0.0689042
a
4
=
−0.111913a
5
u
10
+ 0.159796a
4
u
10
+ ··· + 2.46208a − 1.16610
−0.0138058a
5
u
10
+ 0.289442a
4
u
10
+ ··· − 3.84499a + 1.05137
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1715135479062369628123576
3828394842862113157330195
u
10
a
5
−
4546409628585104976314936
3828394842862113157330195
u
10
a
4
+
··· +
1584654246394472342983472
166451949689657093796965
a −
29163244251402677459451758
3828394842862113157330195
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
22
c
2
, c
3
, c
7
c
9
u
66
+ u
65
+ ··· − 2096u + 1357
c
4
, c
8
u
66
+ 3u
65
+ ··· − 56u + 7
c
5
, c
6
, c
10
c
11
(u
11
− u
10
− 6u
9
+ 5u
8
+ 12u
7
− 6u
6
− 10u
5
− u
4
+ 5u
3
+ u
2
− 1)
6
c
12
(u
11
− 3u
10
+ 4u
9
− u
8
+ 2u
7
− 8u
6
+ 8u
5
+ 5u
4
− 3u
3
− u
2
+ 4u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
22
c
2
, c
3
, c
7
c
9
y
66
+ 51y
65
+ ··· + 63245092y + 1841449
c
4
, c
8
y
66
− 17y
65
+ ··· − 4396y + 49
c
5
, c
6
, c
10
c
11
(y
11
− 13y
10
+ ··· + 2y −1)
6
c
12
(y
11
− y
10
+ ··· + 14y −1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662234 + 0.478506I
a = 0.934868 + 0.422288I
b = 0.138257 + 0.380396I
−1.53399 − 1.92218I −7.13133 + 3.79746I
u = 0.662234 + 0.478506I
a = 1.223350 − 0.359827I
b = 1.88847 + 0.88733I
−5.67157 − 4.75030I −13.6606 + 6.7769I
u = 0.662234 + 0.478506I
a = 0.551933 − 0.066130I
b = 1.08015 + 1.46331I
−1.53399 − 7.57843I −7.13133 + 9.75635I
u = 0.662234 + 0.478506I
a = 0.007189 + 0.448719I
b = −0.699910 − 0.628392I
−1.53399 − 1.92218I −7.13133 + 3.79746I
u = 0.662234 + 0.478506I
a = −1.52726 + 0.82052I
b = −1.82243 − 1.14304I
−5.67157 − 4.75030I −13.6606 + 6.7769I
u = 0.662234 + 0.478506I
a = −1.72340 − 0.45711I
b = −0.46865 − 1.40835I
−1.53399 − 7.57843I −7.13133 + 9.75635I
u = 0.662234 − 0.478506I
a = 0.934868 − 0.422288I
b = 0.138257 − 0.380396I
−1.53399 + 1.92218I −7.13133 − 3.79746I
u = 0.662234 − 0.478506I
a = 1.223350 + 0.359827I
b = 1.88847 − 0.88733I
−5.67157 + 4.75030I −13.6606 − 6.7769I
u = 0.662234 − 0.478506I
a = 0.551933 + 0.066130I
b = 1.08015 − 1.46331I
−1.53399 + 7.57843I −7.13133 − 9.75635I
u = 0.662234 − 0.478506I
a = 0.007189 − 0.448719I
b = −0.699910 + 0.628392I
−1.53399 + 1.92218I −7.13133 − 3.79746I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662234 − 0.478506I
a = −1.52726 − 0.82052I
b = −1.82243 + 1.14304I
−5.67157 + 4.75030I −13.6606 − 6.7769I
u = 0.662234 − 0.478506I
a = −1.72340 + 0.45711I
b = −0.46865 + 1.40835I
−1.53399 + 7.57843I −7.13133 − 9.75635I
u = −0.662125 + 0.223569I
a = −1.123710 − 0.254463I
b = −0.91051 + 1.39920I
−3.20064 + 3.28289I −11.68532 − 4.34902I
u = −0.662125 + 0.223569I
a = −0.95595 + 1.21392I
b = −0.263894 − 0.684965I
−7.33822 + 0.45477I −18.2146 − 1.3696I
u = −0.662125 + 0.223569I
a = −1.07397 + 1.39738I
b = −0.804376 + 0.943483I
−3.20064 + 3.28289I −11.68532 − 4.34902I
u = −0.662125 + 0.223569I
a = 0.042624 − 0.209370I
b = 0.70963 − 1.51244I
−3.20064 − 2.37336I −11.68532 + 1.60987I
u = −0.662125 + 0.223569I
a = 0.31735 − 2.06691I
b = −0.850230 + 0.120691I
−7.33822 + 0.45477I −18.2146 − 1.3696I
u = −0.662125 + 0.223569I
a = 1.67299 − 1.57745I
b = 0.164226 − 1.256190I
−3.20064 − 2.37336I −11.68532 + 1.60987I
u = −0.662125 − 0.223569I
a = −1.123710 + 0.254463I
b = −0.91051 − 1.39920I
−3.20064 − 3.28289I −11.68532 + 4.34902I
u = −0.662125 − 0.223569I
a = −0.95595 − 1.21392I
b = −0.263894 + 0.684965I
−7.33822 − 0.45477I −18.2146 + 1.3696I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662125 − 0.223569I
a = −1.07397 − 1.39738I
b = −0.804376 − 0.943483I
−3.20064 − 3.28289I −11.68532 + 4.34902I
u = −0.662125 − 0.223569I
a = 0.042624 + 0.209370I
b = 0.70963 + 1.51244I
−3.20064 + 2.37336I −11.68532 − 1.60987I
u = −0.662125 − 0.223569I
a = 0.31735 + 2.06691I
b = −0.850230 − 0.120691I
−7.33822 − 0.45477I −18.2146 + 1.3696I
u = −0.662125 − 0.223569I
a = 1.67299 + 1.57745I
b = 0.164226 + 1.256190I
−3.20064 + 2.37336I −11.68532 − 1.60987I
u = 0.227048 + 0.520535I
a = 0.931590 + 0.011281I
b = −0.007048 − 0.213343I
−0.27441 − 1.55271I −3.01079 + 2.17848I
u = 0.227048 + 0.520535I
a = 0.554947 + 0.626306I
b = −0.475444 − 0.493727I
−0.27441 − 1.55271I −3.01079 + 2.17848I
u = 0.227048 + 0.520535I
a = 0.702189 − 0.345504I
b = −0.022101 + 1.400790I
−0.27441 + 4.10353I −3.01079 − 3.78041I
u = 0.227048 + 0.520535I
a = 1.40227 + 1.03949I
b = −1.16636 + 1.00757I
−4.41199 + 1.27541I −9.54006 − 0.80097I
u = 0.227048 + 0.520535I
a = −1.02782 − 1.62593I
b = 0.832545 − 0.852154I
−4.41199 + 1.27541I −9.54006 − 0.80097I
u = 0.227048 + 0.520535I
a = −1.90607 − 0.73477I
b = 0.252604 − 0.576397I
−0.27441 + 4.10353I −3.01079 − 3.78041I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227048 − 0.520535I
a = 0.931590 − 0.011281I
b = −0.007048 + 0.213343I
−0.27441 + 1.55271I −3.01079 − 2.17848I
u = 0.227048 − 0.520535I
a = 0.554947 − 0.626306I
b = −0.475444 + 0.493727I
−0.27441 + 1.55271I −3.01079 − 2.17848I
u = 0.227048 − 0.520535I
a = 0.702189 + 0.345504I
b = −0.022101 − 1.400790I
−0.27441 − 4.10353I −3.01079 + 3.78041I
u = 0.227048 − 0.520535I
a = 1.40227 − 1.03949I
b = −1.16636 − 1.00757I
−4.41199 − 1.27541I −9.54006 + 0.80097I
u = 0.227048 − 0.520535I
a = −1.02782 + 1.62593I
b = 0.832545 + 0.852154I
−4.41199 − 1.27541I −9.54006 + 0.80097I
u = 0.227048 − 0.520535I
a = −1.90607 + 0.73477I
b = 0.252604 + 0.576397I
−0.27441 − 4.10353I −3.01079 + 3.78041I
u = −1.45917
a = −1.45609 + 0.39286I
b = −1.068350 − 0.300580I
−5.29325 − 2.82812I −6.67597 + 2.97945I
u = −1.45917
a = −1.45609 − 0.39286I
b = −1.068350 + 0.300580I
−5.29325 + 2.82812I −6.67597 − 2.97945I
u = −1.45917
a = 1.39251 + 0.77924I
b = 0.840217 + 1.085890I
−5.29325 + 2.82812I −6.67597 − 2.97945I
u = −1.45917
a = 1.39251 − 0.77924I
b = 0.840217 − 1.085890I
−5.29325 − 2.82812I −6.67597 + 2.97945I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45917
a = −0.08422 + 2.05292I
b = −0.302211 + 1.375460I
−9.43083 −13.20523 + 0.I
u = −1.45917
a = −0.08422 − 2.05292I
b = −0.302211 − 1.375460I
−9.43083 −13.20523 + 0.I
u = 1.59518 + 0.07553I
a = −0.479187 + 1.086150I
b = −0.36591 + 1.99115I
−15.0869 − 1.6459I −19.0694 + 0.2448I
u = 1.59518 + 0.07553I
a = −0.676526 + 0.440145I
b = −0.977261 − 0.741957I
−15.0869 − 1.6459I −19.0694 + 0.2448I
u = 1.59518 + 0.07553I
a = 1.38900 + 1.45328I
b = 0.636912 + 1.068200I
−10.94930 + 1.18219I −12.54012 − 2.73464I
u = 1.59518 + 0.07553I
a = −1.96346 − 0.87103I
b = −1.71735 − 0.61499I
−10.94930 − 4.47405I −12.54012 + 3.22425I
u = 1.59518 + 0.07553I
a = −1.97389 − 1.20394I
b = −1.65511 − 1.99458I
−10.94930 − 4.47405I −12.54012 + 3.22425I
u = 1.59518 + 0.07553I
a = 1.67593 + 1.77387I
b = 1.72161 + 2.48435I
−10.94930 + 1.18219I −12.54012 − 2.73464I
u = 1.59518 − 0.07553I
a = −0.479187 − 1.086150I
b = −0.36591 − 1.99115I
−15.0869 + 1.6459I −19.0694 − 0.2448I
u = 1.59518 − 0.07553I
a = −0.676526 − 0.440145I
b = −0.977261 + 0.741957I
−15.0869 + 1.6459I −19.0694 − 0.2448I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59518 − 0.07553I
a = 1.38900 − 1.45328I
b = 0.636912 − 1.068200I
−10.94930 − 1.18219I −12.54012 + 2.73464I
u = 1.59518 − 0.07553I
a = −1.96346 + 0.87103I
b = −1.71735 + 0.61499I
−10.94930 + 4.47405I −12.54012 − 3.22425I
u = 1.59518 − 0.07553I
a = −1.97389 + 1.20394I
b = −1.65511 + 1.99458I
−10.94930 + 4.47405I −12.54012 − 3.22425I
u = 1.59518 − 0.07553I
a = 1.67593 − 1.77387I
b = 1.72161 − 2.48435I
−10.94930 − 1.18219I −12.54012 + 2.73464I
u = −1.59275 + 0.13764I
a = 1.032850 − 0.269531I
b = 0.600929 − 0.112763I
−9.17552 + 4.19407I −9.99079 − 1.90674I
u = −1.59275 + 0.13764I
a = −1.227410 + 0.533552I
b = −1.24859 + 1.31015I
−9.17552 + 4.19407I −9.99079 − 1.90674I
u = −1.59275 + 0.13764I
a = −1.78851 + 1.15092I
b = −0.90600 + 1.26674I
−9.17552 + 9.85032I −9.99079 − 7.86564I
u = −1.59275 + 0.13764I
a = 2.05740 − 1.33869I
b = 1.90317 − 2.19348I
−9.17552 + 9.85032I −9.99079 − 7.86564I
u = −1.59275 + 0.13764I
a = −2.86939 + 0.22585I
b = −2.41596 + 1.21947I
−13.3131 + 7.0222I −16.5201 − 4.8862I
u = −1.59275 + 0.13764I
a = 2.96787 − 0.12483I
b = 2.87897 − 0.86094I
−13.3131 + 7.0222I −16.5201 − 4.8862I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59275 − 0.13764I
a = 1.032850 + 0.269531I
b = 0.600929 + 0.112763I
−9.17552 − 4.19407I −9.99079 + 1.90674I
u = −1.59275 − 0.13764I
a = −1.227410 − 0.533552I
b = −1.24859 − 1.31015I
−9.17552 − 4.19407I −9.99079 + 1.90674I
u = −1.59275 − 0.13764I
a = −1.78851 − 1.15092I
b = −0.90600 − 1.26674I
−9.17552 − 9.85032I −9.99079 + 7.86564I
u = −1.59275 − 0.13764I
a = 2.05740 + 1.33869I
b = 1.90317 + 2.19348I
−9.17552 − 9.85032I −9.99079 + 7.86564I
u = −1.59275 − 0.13764I
a = −2.86939 − 0.22585I
b = −2.41596 − 1.21947I
−13.3131 − 7.0222I −16.5201 + 4.8862I
u = −1.59275 − 0.13764I
a = 2.96787 + 0.12483I
b = 2.87897 + 0.86094I
−13.3131 − 7.0222I −16.5201 + 4.8862I
17
III. I
u
3
=
h−u
14
+2u
13
+· · ·+b +2, −2u
14
+2u
13
+· · ·+a +2, u
16
−10u
14
+· · ·−2u +1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
2u
14
− 2u
13
+ ··· + 6u − 2
u
14
− 2u
13
+ ··· + 2u − 2
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
2u
14
− u
13
+ ··· + 5u − 2
u
14
− u
13
+ ··· + 3u − 2
a
10
=
u
u
a
1
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
9
=
−2u
15
+ u
14
+ ··· + 6u + 1
u
14
− 8u
12
+ ··· + 2u + 1
a
8
=
−2u
15
+ 19u
13
+ ··· + 7u + 1
u
9
− 5u
7
+ 7u
5
+ u
4
− 2u
3
− 3u
2
+ u + 1
a
4
=
u
15
− 11u
13
+ ··· + u − 2
−u
13
+ 8u
11
+ ··· − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
14
+ 5u
13
− 12u
12
− 39u
11
+ 53u
10
+ 110u
9
− 100u
8
− 138u
7
+
61u
6
+ 95u
5
+ 16u
4
− 61u
3
− 3u
2
+ 8u − 5
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 8u
15
+ ··· − 4u
2
+ 1
c
2
, c
9
u
16
+ 8u
14
+ ··· − u + 1
c
3
, c
7
u
16
+ 8u
14
+ ··· + u + 1
c
4
, c
8
u
16
+ u
15
+ ··· + 2u
3
+ 1
c
5
, c
6
u
16
− 10u
14
+ ··· − 2u + 1
c
10
, c
11
u
16
− 10u
14
+ ··· + 2u + 1
c
12
u
16
− 4u
15
+ ··· + 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 8y
15
+ ··· − 8y + 1
c
2
, c
3
, c
7
c
9
y
16
+ 16y
15
+ ··· + 13y + 1
c
4
, c
8
y
16
− 3y
15
+ ··· − 4y
2
+ 1
c
5
, c
6
, c
10
c
11
y
16
− 20y
15
+ ··· − 12y + 1
c
12
y
16
+ 4y
15
+ ··· + 12y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.749888 + 0.412737I
a = −1.154770 − 0.065403I
b = −1.25112 − 1.26612I
−3.60629 − 4.80216I −11.66439 + 7.25589I
u = 0.749888 − 0.412737I
a = −1.154770 + 0.065403I
b = −1.25112 + 1.26612I
−3.60629 + 4.80216I −11.66439 − 7.25589I
u = −0.441315 + 0.700895I
a = 0.401419 − 0.297642I
b = −0.271686 + 0.252626I
0.00681 + 2.36445I 3.00784 − 9.19006I
u = −0.441315 − 0.700895I
a = 0.401419 + 0.297642I
b = −0.271686 − 0.252626I
0.00681 − 2.36445I 3.00784 + 9.19006I
u = −0.569717 + 0.232049I
a = 0.79724 − 1.81995I
b = −0.297249 + 0.518346I
−6.73121 + 0.81986I −5.13640 − 9.16053I
u = −0.569717 − 0.232049I
a = 0.79724 + 1.81995I
b = −0.297249 − 0.518346I
−6.73121 − 0.81986I −5.13640 + 9.16053I
u = 1.48473 + 0.16212I
a = −0.003550 − 0.154473I
b = 0.086407 − 0.568102I
−6.11354 − 5.27538I −8.43831 + 4.08338I
u = 1.48473 − 0.16212I
a = −0.003550 + 0.154473I
b = 0.086407 + 0.568102I
−6.11354 + 5.27538I −8.43831 − 4.08338I
u = −1.52213 + 0.04939I
a = 0.65730 − 2.20214I
b = 0.29843 − 1.81113I
−8.39527 − 1.62333I −8.70827 + 4.27612I
u = −1.52213 − 0.04939I
a = 0.65730 + 2.20214I
b = 0.29843 + 1.81113I
−8.39527 + 1.62333I −8.70827 − 4.27612I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58491 + 0.07036I
a = −0.081804 − 0.324870I
b = −0.239422 − 1.353340I
−14.2049 − 1.9436I −8.70390 + 3.79307I
u = 1.58491 − 0.07036I
a = −0.081804 + 0.324870I
b = −0.239422 + 1.353340I
−14.2049 + 1.9436I −8.70390 − 3.79307I
u = 0.324777 + 0.221310I
a = 1.77379 + 2.38441I
b = −0.19415 + 1.55667I
−1.96389 + 2.48939I −2.99843 − 1.76642I
u = 0.324777 − 0.221310I
a = 1.77379 − 2.38441I
b = −0.19415 − 1.55667I
−1.96389 − 2.48939I −2.99843 + 1.76642I
u = −1.61115 + 0.13456I
a = −2.38962 + 0.59684I
b = −2.13121 + 1.29146I
−11.62970 + 6.95567I −11.35815 − 4.21846I
u = −1.61115 − 0.13456I
a = −2.38962 − 0.59684I
b = −2.13121 − 1.29146I
−11.62970 − 6.95567I −11.35815 + 4.21846I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
22
)(u
16
− 8u
15
+ ··· − 4u
2
+ 1)
· (u
30
− 27u
29
+ ··· − 36864u + 2048)
c
2
, c
9
(u
16
+ 8u
14
+ ··· − u + 1)(u
30
+ 11u
28
+ ··· + u − 1)
· (u
66
+ u
65
+ ··· − 2096u + 1357)
c
3
, c
7
(u
16
+ 8u
14
+ ··· + u + 1)(u
30
+ 11u
28
+ ··· + u − 1)
· (u
66
+ u
65
+ ··· − 2096u + 1357)
c
4
, c
8
(u
16
+ u
15
+ ··· + 2u
3
+ 1)(u
30
+ u
29
+ ··· − 2u − 1)
· (u
66
+ 3u
65
+ ··· − 56u + 7)
c
5
, c
6
(u
11
− u
10
− 6u
9
+ 5u
8
+ 12u
7
− 6u
6
− 10u
5
− u
4
+ 5u
3
+ u
2
− 1)
6
· (u
16
− 10u
14
+ ··· − 2u + 1)(u
30
+ 7u
29
+ ··· + 4u − 8)
c
10
, c
11
(u
11
− u
10
− 6u
9
+ 5u
8
+ 12u
7
− 6u
6
− 10u
5
− u
4
+ 5u
3
+ u
2
− 1)
6
· (u
16
− 10u
14
+ ··· + 2u + 1)(u
30
+ 7u
29
+ ··· + 4u − 8)
c
12
(u
11
− 3u
10
+ 4u
9
− u
8
+ 2u
7
− 8u
6
+ 8u
5
+ 5u
4
− 3u
3
− u
2
+ 4u − 1)
6
· (u
16
− 4u
15
+ ··· + 2u + 1)(u
30
− 7u
29
+ ··· + 56384u − 20992)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
22
)(y
16
− 8y
15
+ ··· − 8y + 1)
· (y
30
− 9y
29
+ ··· − 48234496y + 4194304)
c
2
, c
3
, c
7
c
9
(y
16
+ 16y
15
+ ··· + 13y + 1)(y
30
+ 22y
29
+ ··· − 11y + 1)
· (y
66
+ 51y
65
+ ··· + 63245092y + 1841449)
c
4
, c
8
(y
16
− 3y
15
+ ··· − 4y
2
+ 1)(y
30
+ 3y
29
+ ··· + 12y + 1)
· (y
66
− 17y
65
+ ··· − 4396y + 49)
c
5
, c
6
, c
10
c
11
((y
11
− 13y
10
+ ··· + 2y −1)
6
)(y
16
− 20y
15
+ ··· − 12y + 1)
· (y
30
− 33y
29
+ ··· − 16y + 64)
c
12
((y
11
− y
10
+ ··· + 14y −1)
6
)(y
16
+ 4y
15
+ ··· + 12y + 1)
· (y
30
+ 3y
29
+ ··· − 206688256y + 440664064)
24
