11n
178
(K11n
178
)
A knot diagram
1
Linearized knot diagam
8 5 1 7 3 11 10 3 4 5 9
Solving Sequence
3,5 6,11
7 2 4 10 8 1 9
c
5
c
6
c
2
c
4
c
10
c
7
c
1
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.44183 × 10
20
u
19
− 4.62808 × 10
20
u
18
+ ··· + 4.02960 × 10
22
b + 1.32550 × 10
22
,
5.38510 × 10
21
u
19
− 1.93058 × 10
22
u
18
+ ··· + 5.64145 × 10
23
a − 1.58764 × 10
23
, u
20
− 3u
19
+ ··· + 50u + 28i
I
u
2
= h8.27426 × 10
22
au
24
+ 2.16729 × 10
23
u
24
+ ··· − 8.08063 × 10
23
a − 2.16180 × 10
24
,
1.10607 × 10
23
au
24
− 4.35547 × 10
23
u
24
+ ··· − 2.26434 × 10
24
a + 5.35326 × 10
24
, u
25
+ 2u
24
+ ··· − 18u + 5i
I
u
3
= h−498u
9
a + 411u
9
+ ··· − 538a − 71, 33u
9
a − 50u
9
+ ··· + 36a + 14,
u
10
+ u
9
+ u
8
− u
7
− 7u
6
− 6u
5
− 4u
4
− u
3
+ 4u
2
− 1i
I
u
4
= hb + u, a − u + 1, u
3
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 93 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
=
h1.44×10
20
u
19
−4.63×10
20
u
18
+· · ·+4.03×10
22
b+1.33×10
22
, 5.39×10
21
u
19
−
1.93 × 10
22
u
18
+ · · · + 5.64 × 10
23
a − 1.59 × 10
23
, u
20
− 3u
19
+ · · · + 50u + 28i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
11
=
−0.00954560u
19
+ 0.0342214u
18
+ ··· − 2.04736u + 0.281424
−0.00357808u
19
+ 0.0114852u
18
+ ··· − 1.57985u − 0.328941
a
7
=
0.00788039u
19
− 0.0328040u
18
+ ··· − 0.518617u + 0.751134
0.00598606u
19
− 0.0182745u
18
+ ··· + 0.965413u − 0.0154483
a
2
=
u
u
a
4
=
−0.0104192u
19
+ 0.0403606u
18
+ ··· − 0.479468u + 0.453996
0.00910287u
19
− 0.0324780u
18
+ ··· + 0.974959u + 0.291739
a
10
=
−0.0131237u
19
+ 0.0457066u
18
+ ··· − 3.62721u − 0.0475176
−0.00357808u
19
+ 0.0114852u
18
+ ··· − 1.57985u − 0.328941
a
8
=
−0.0117479u
19
+ 0.0388218u
18
+ ··· − 2.47010u + 0.992450
−0.00558459u
19
+ 0.0212055u
18
+ ··· − 0.758704u − 0.267277
a
1
=
0.000551726u
19
+ 0.00433088u
18
+ ··· + 2.81102u + 0.992999
−0.00916278u
19
+ 0.0352104u
18
+ ··· + 0.357114u − 0.220651
a
9
=
−0.0117479u
19
+ 0.0388218u
18
+ ··· − 2.47010u + 0.992450
−0.00633555u
19
+ 0.0263534u
18
+ ··· − 0.608667u − 0.367463
a
9
=
−0.0117479u
19
+ 0.0388218u
18
+ ··· − 2.47010u + 0.992450
−0.00633555u
19
+ 0.0263534u
18
+ ··· − 0.608667u − 0.367463
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2008394464227286266247
20148019962096448350151
u
19
+
6462622260672532812482
20148019962096448350151
u
18
+ ··· −
48150419926932042591458
20148019962096448350151
u −
133443328465178993232190
20148019962096448350151
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
20
− 5u
19
+ ··· + 24u − 8
c
2
, c
5
u
20
− 3u
19
+ ··· + 50u + 28
c
3
, c
4
u
20
− u
19
+ ··· − 3u
2
+ 1
c
7
, c
11
u
20
− 2u
19
+ ··· − 5u − 1
c
8
, c
10
u
20
+ 9u
18
+ ··· + 5u − 1
c
9
u
20
+ 5u
19
+ ··· + 192u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
20
+ 19y
19
+ ··· + 384y + 64
c
2
, c
5
y
20
+ 11y
19
+ ··· + 6180y + 784
c
3
, c
4
y
20
− 3y
19
+ ··· − 6y + 1
c
7
, c
11
y
20
+ 24y
18
+ ··· − 79y + 1
c
8
, c
10
y
20
+ 18y
19
+ ··· + 13y + 1
c
9
y
20
+ y
19
+ ··· − 14336y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860797 + 0.516146I
a = −0.749789 − 0.590643I
b = −0.155130 − 0.305377I
−0.02958 − 4.97799I −5.29605 + 5.59335I
u = 0.860797 − 0.516146I
a = −0.749789 + 0.590643I
b = −0.155130 + 0.305377I
−0.02958 + 4.97799I −5.29605 − 5.59335I
u = −0.837495
a = 1.44067
b = −0.563826
−4.10423 8.28190
u = −0.127511 + 1.189810I
a = −0.55333 − 1.51288I
b = −0.265516 + 1.136880I
5.89336 + 2.36950I 5.34088 − 5.91566I
u = −0.127511 − 1.189810I
a = −0.55333 + 1.51288I
b = −0.265516 − 1.136880I
5.89336 − 2.36950I 5.34088 + 5.91566I
u = −1.206690 + 0.010929I
a = 0.309849 − 0.484836I
b = 0.275436 − 1.241550I
−1.50701 − 0.96018I −11.18870 + 6.49006I
u = −1.206690 − 0.010929I
a = 0.309849 + 0.484836I
b = 0.275436 + 1.241550I
−1.50701 + 0.96018I −11.18870 − 6.49006I
u = −0.044384 + 1.389540I
a = −0.092328 − 1.185210I
b = −0.230707 + 0.577747I
3.02537 + 1.86293I −7.79633 − 3.80746I
u = −0.044384 − 1.389540I
a = −0.092328 + 1.185210I
b = −0.230707 − 0.577747I
3.02537 − 1.86293I −7.79633 + 3.80746I
u = −0.495317
a = 0.784881
b = 0.562448
−0.861131 −11.6540
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.008487 + 0.397854I
a = 0.665300 − 0.862267I
b = −0.433094 − 0.565353I
1.66626 + 1.83421I −0.60394 − 1.52765I
u = −0.008487 − 0.397854I
a = 0.665300 + 0.862267I
b = −0.433094 + 0.565353I
1.66626 − 1.83421I −0.60394 + 1.52765I
u = 1.70479 + 0.08565I
a = 0.138055 − 0.057007I
b = 0.519057 + 1.305600I
2.91415 − 8.59875I −1.50122 + 6.80502I
u = 1.70479 − 0.08565I
a = 0.138055 + 0.057007I
b = 0.519057 − 1.305600I
2.91415 + 8.59875I −1.50122 − 6.80502I
u = −0.47740 + 1.67811I
a = 0.103149 + 1.154610I
b = 1.18053 − 1.97776I
4.37107 + 7.54282I −5.65623 − 11.11643I
u = −0.47740 − 1.67811I
a = 0.103149 − 1.154610I
b = 1.18053 + 1.97776I
4.37107 − 7.54282I −5.65623 + 11.11643I
u = 0.68219 + 1.68930I
a = −0.198906 + 1.142030I
b = −1.17479 − 1.40102I
8.5745 − 16.9983I −2.67254 + 8.37996I
u = 0.68219 − 1.68930I
a = −0.198906 − 1.142030I
b = −1.17479 + 1.40102I
8.5745 + 16.9983I −2.67254 − 8.37996I
u = 0.78311 + 1.71850I
a = 0.300944 − 0.712043I
b = 0.284896 + 1.301190I
8.00588 − 0.27607I 1.56028 − 0.31134I
u = 0.78311 − 1.71850I
a = 0.300944 + 0.712043I
b = 0.284896 − 1.301190I
8.00588 + 0.27607I 1.56028 + 0.31134I
6
II. I
u
2
= h8.27 × 10
22
au
24
+ 2.17 × 10
23
u
24
+ · · · − 8.08 × 10
23
a − 2.16 ×
10
24
, 1.11 × 10
23
au
24
− 4.36 × 10
23
u
24
+ · · · − 2.26 × 10
24
a + 5.35 ×
10
24
, u
25
+ 2u
24
+ · · · − 18u + 5i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
11
=
a
−0.715728au
24
− 1.87471u
24
+ ··· + 6.98979a + 18.6997
a
7
=
2.87565au
24
− 3.09074u
24
+ ··· − 30.7439a + 31.3997
0.805852au
24
+ 1.72660u
24
+ ··· − 8.29141a − 17.8506
a
2
=
u
u
a
4
=
0.715728au
24
+ 1.87471u
24
+ ··· − 5.98979a − 18.6997
−0.387518au
24
− 1.63688u
24
+ ··· + 3.57864a + 19.9274
a
10
=
−0.715728au
24
− 1.87471u
24
+ ··· + 7.98979a + 18.6997
−0.715728au
24
− 1.87471u
24
+ ··· + 6.98979a + 18.6997
a
8
=
−1.39796au
24
− 5.76946u
24
+ ··· + 13.0810a + 58.4354
0.379318u
24
+ 0.946149u
23
+ ··· − 2.74341u − 5.54920
a
1
=
−1.65828au
24
+ 2.07471u
24
+ ··· + 16.7481a − 22.2997
−1.25756au
24
+ 3.83734u
24
+ ··· + 14.3782a − 42.0842
a
9
=
−1.39796au
24
− 5.76946u
24
+ ··· + 13.0810a + 58.4354
−0.387518au
24
− 0.813602u
24
+ ··· + 3.57864a + 7.89146
a
9
=
−1.39796au
24
− 5.76946u
24
+ ··· + 13.0810a + 58.4354
−0.387518au
24
− 0.813602u
24
+ ··· + 3.57864a + 7.89146
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1156952596349356967504
1993212416684380527497
u
24
−
3249366973641059899377
1993212416684380527497
u
23
+ ··· −
66879505468638485855810
1993212416684380527497
u +
10075785679097148312488
1993212416684380527497
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
50
+ 5u
49
+ ··· + 337800u + 93608
c
2
, c
5
(u
25
+ 2u
24
+ ··· − 18u + 5)
2
c
3
, c
4
u
50
− 4u
49
+ ··· + 5u − 1
c
7
, c
11
u
50
− u
49
+ ··· + 22u − 1
c
8
, c
10
u
50
+ 3u
48
+ ··· − 10342u − 3931
c
9
(u
25
− u
24
+ ··· − 18u + 31)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
50
+ 13y
49
+ ··· + 42553508800y + 8762457664
c
2
, c
5
(y
25
+ 24y
24
+ ··· − 336y −25)
2
c
3
, c
4
y
50
+ 18y
48
+ ··· + 143y + 1
c
7
, c
11
y
50
− 21y
49
+ ··· + 244y + 1
c
8
, c
10
y
50
+ 6y
49
+ ··· + 33112428y + 15452761
c
9
(y
25
− 17y
24
+ ··· + 12662y −961)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.140650 + 0.267150I
a = 1.084710 + 0.611862I
b = 1.49229 + 0.92382I
−1.03856 + 1.14326I −10.5893 + 12.6521I
u = −1.140650 + 0.267150I
a = 0.113359 + 0.355439I
b = 0.633787 + 0.654814I
−1.03856 + 1.14326I −10.5893 + 12.6521I
u = −1.140650 − 0.267150I
a = 1.084710 − 0.611862I
b = 1.49229 − 0.92382I
−1.03856 − 1.14326I −10.5893 − 12.6521I
u = −1.140650 − 0.267150I
a = 0.113359 − 0.355439I
b = 0.633787 − 0.654814I
−1.03856 − 1.14326I −10.5893 − 12.6521I
u = −0.163146 + 1.252380I
a = −0.356875 − 0.754522I
b = −0.959590 + 0.451959I
2.89680 + 2.76831I −5.67436 − 1.24863I
u = −0.163146 + 1.252380I
a = 0.223215 − 1.350440I
b = −0.670798 + 0.653559I
2.89680 + 2.76831I −5.67436 − 1.24863I
u = −0.163146 − 1.252380I
a = −0.356875 + 0.754522I
b = −0.959590 − 0.451959I
2.89680 − 2.76831I −5.67436 + 1.24863I
u = −0.163146 − 1.252380I
a = 0.223215 + 1.350440I
b = −0.670798 − 0.653559I
2.89680 − 2.76831I −5.67436 + 1.24863I
u = 0.434385 + 1.315760I
a = −0.676723 + 0.897603I
b = −0.451415 − 0.840386I
6.24414 − 3.55600I 4.03991 + 3.49531I
u = 0.434385 + 1.315760I
a = 0.14272 − 1.58350I
b = 1.25444 + 1.50173I
6.24414 − 3.55600I 4.03991 + 3.49531I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.434385 − 1.315760I
a = −0.676723 − 0.897603I
b = −0.451415 + 0.840386I
6.24414 + 3.55600I 4.03991 − 3.49531I
u = 0.434385 − 1.315760I
a = 0.14272 + 1.58350I
b = 1.25444 − 1.50173I
6.24414 + 3.55600I 4.03991 − 3.49531I
u = 0.15084 + 1.44113I
a = −0.365971 − 1.348100I
b = 1.12800 + 1.43516I
6.70056 − 6.60168I 4.95046 + 12.30292I
u = 0.15084 + 1.44113I
a = 0.23756 + 1.60715I
b = −0.035729 − 0.763533I
6.70056 − 6.60168I 4.95046 + 12.30292I
u = 0.15084 − 1.44113I
a = −0.365971 + 1.348100I
b = 1.12800 − 1.43516I
6.70056 + 6.60168I 4.95046 − 12.30292I
u = 0.15084 − 1.44113I
a = 0.23756 − 1.60715I
b = −0.035729 + 0.763533I
6.70056 + 6.60168I 4.95046 − 12.30292I
u = −0.148436 + 0.506372I
a = 0.388829 + 0.383713I
b = 1.118110 − 0.274856I
−2.53372 + 0.16719I −3.64574 − 0.21536I
u = −0.148436 + 0.506372I
a = 3.02455 + 0.27470I
b = −0.251824 − 0.797330I
−2.53372 + 0.16719I −3.64574 − 0.21536I
u = −0.148436 − 0.506372I
a = 0.388829 − 0.383713I
b = 1.118110 + 0.274856I
−2.53372 − 0.16719I −3.64574 + 0.21536I
u = −0.148436 − 0.506372I
a = 3.02455 − 0.27470I
b = −0.251824 + 0.797330I
−2.53372 − 0.16719I −3.64574 + 0.21536I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475339
a = 0.528924 + 0.781882I
b = −0.430675 + 0.809478I
2.81112 0.202280
u = 0.475339
a = 0.528924 − 0.781882I
b = −0.430675 − 0.809478I
2.81112 0.202280
u = −1.53222
a = 0.078790 + 0.191294I
b = 0.568791 − 1.033300I
3.05217 0.159530
u = −1.53222
a = 0.078790 − 0.191294I
b = 0.568791 + 1.033300I
3.05217 0.159530
u = 0.466383 + 0.024974I
a = 0.624833 − 0.860638I
b = −0.840463 − 0.646691I
1.53850 − 4.51240I −4.65188 + 7.14304I
u = 0.466383 + 0.024974I
a = 1.42335 − 2.52636I
b = 0.735817 + 0.431578I
1.53850 − 4.51240I −4.65188 + 7.14304I
u = 0.466383 − 0.024974I
a = 0.624833 + 0.860638I
b = −0.840463 + 0.646691I
1.53850 + 4.51240I −4.65188 − 7.14304I
u = 0.466383 − 0.024974I
a = 1.42335 + 2.52636I
b = 0.735817 − 0.431578I
1.53850 + 4.51240I −4.65188 − 7.14304I
u = 1.54406
a = −0.230436
b = 0.365605
−6.61075 −51.2600
u = 1.54406
a = −1.77941
b = −1.23498
−6.61075 −51.2600
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18525 + 1.56503I
a = −0.482316 − 0.856149I
b = 0.583599 + 0.895127I
3.52121 − 5.29385I −3.74916 + 8.30350I
u = −0.18525 + 1.56503I
a = 0.672798 − 0.276435I
b = 1.161330 + 0.309043I
3.52121 − 5.29385I −3.74916 + 8.30350I
u = −0.18525 − 1.56503I
a = −0.482316 + 0.856149I
b = 0.583599 − 0.895127I
3.52121 + 5.29385I −3.74916 − 8.30350I
u = −0.18525 − 1.56503I
a = 0.672798 + 0.276435I
b = 1.161330 − 0.309043I
3.52121 + 5.29385I −3.74916 − 8.30350I
u = 0.003969 + 0.337154I
a = 0.650002 + 0.785649I
b = −1.171020 + 0.504584I
−0.56308 + 6.78110I 3.38343 − 3.19298I
u = 0.003969 + 0.337154I
a = 7.17919 − 1.72929I
b = −0.074163 + 0.750946I
−0.56308 + 6.78110I 3.38343 − 3.19298I
u = 0.003969 − 0.337154I
a = 0.650002 − 0.785649I
b = −1.171020 − 0.504584I
−0.56308 − 6.78110I 3.38343 + 3.19298I
u = 0.003969 − 0.337154I
a = 7.17919 + 1.72929I
b = −0.074163 − 0.750946I
−0.56308 − 6.78110I 3.38343 + 3.19298I
u = 0.19448 + 1.65842I
a = 0.422264 − 0.836955I
b = −1.43214 + 1.44496I
7.41514 + 1.27639I 2.55128 − 0.67478I
u = 0.19448 + 1.65842I
a = −0.325781 + 0.877177I
b = −0.010779 − 1.084000I
7.41514 + 1.27639I 2.55128 − 0.67478I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19448 − 1.65842I
a = 0.422264 + 0.836955I
b = −1.43214 − 1.44496I
7.41514 − 1.27639I 2.55128 + 0.67478I
u = 0.19448 − 1.65842I
a = −0.325781 − 0.877177I
b = −0.010779 + 1.084000I
7.41514 − 1.27639I 2.55128 + 0.67478I
u = −0.08719 + 1.73481I
a = 0.436377 + 0.874340I
b = −1.81263 − 1.76872I
7.66608 + 6.24371I 4.09267 − 6.21663I
u = −0.08719 + 1.73481I
a = −0.211132 + 1.015010I
b = 0.62955 − 1.66105I
7.66608 + 6.24371I 4.09267 − 6.21663I
u = −0.08719 − 1.73481I
a = 0.436377 − 0.874340I
b = −1.81263 + 1.76872I
7.66608 − 6.24371I 4.09267 + 6.21663I
u = −0.08719 − 1.73481I
a = −0.211132 − 1.015010I
b = 0.62955 + 1.66105I
7.66608 − 6.24371I 4.09267 + 6.21663I
u = −0.76896 + 1.70316I
a = −0.267227 − 1.109740I
b = −1.14143 + 1.30331I
8.00509 + 8.45240I 0. − 6.49999I
u = −0.76896 + 1.70316I
a = 0.259474 + 0.720363I
b = 0.411624 − 1.049270I
8.00509 + 8.45240I 0. − 6.49999I
u = −0.76896 − 1.70316I
a = −0.267227 + 1.109740I
b = −1.14143 − 1.30331I
8.00509 − 8.45240I 0. + 6.49999I
u = −0.76896 − 1.70316I
a = 0.259474 − 0.720363I
b = 0.411624 + 1.049270I
8.00509 − 8.45240I 0. + 6.49999I
14
III. I
u
3
= h−498u
9
a + 411u
9
+ · · · − 538a − 71, 33u
9
a − 50u
9
+ · · · + 36a +
14, u
10
+ u
9
+ · · · + 4u
2
− 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
11
=
a
0.256305au
9
− 0.211529u
9
+ ··· + 0.276891a + 0.0365414
a
7
=
−0.202265au
9
+ 0.388574u
9
+ ··· + 1.23932a + 1.61657
−0.128667au
9
− 0.533196u
9
+ ··· − 0.0386001a + 0.440041
a
2
=
u
u
a
4
=
0.256305au
9
− 0.211529u
9
+ ··· − 0.723109a + 0.0365414
0.145651au
9
+ 1.11889u
9
+ ··· − 0.256305a + 0.935666
a
10
=
0.256305au
9
− 0.211529u
9
+ ··· + 1.27689a + 0.0365414
0.256305au
9
− 0.211529u
9
+ ··· + 0.276891a + 0.0365414
a
8
=
−0.276891au
9
+ 0.446217u
9
+ ··· − 0.283067a − 0.566135
−0.793103u
9
− 1.10345u
8
+ ··· − 1.24138u − 1.13793
a
1
=
0.0386001au
9
+ 0.594442u
9
+ ··· + 0.511580a − 0.321668
−0.325785au
9
− 0.513639u
9
+ ··· + 0.202265a − 0.354092
a
9
=
−0.276891au
9
+ 0.446217u
9
+ ··· − 0.283067a − 0.566135
0.145651au
9
− 0.501801u
9
+ ··· − 0.256305a − 1.65054
a
9
=
−0.276891au
9
+ 0.446217u
9
+ ··· − 0.283067a − 0.566135
0.145651au
9
− 0.501801u
9
+ ··· − 0.256305a − 1.65054
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
70
29
u
9
−
139
29
u
8
−
166
29
u
7
+ 2u
6
+
490
29
u
5
+
1077
29
u
4
+
738
29
u
3
+
413
29
u
2
−
44
29
u −
485
29
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 4u
19
+ ··· + 24u + 8
c
2
(u
10
− u
9
+ u
8
+ u
7
− 7u
6
+ 6u
5
− 4u
4
+ u
3
+ 4u
2
− 1)
2
c
3
u
20
+ 7u
19
+ ··· − u − 1
c
4
u
20
− 7u
19
+ ··· + u − 1
c
5
(u
10
+ u
9
+ u
8
− u
7
− 7u
6
− 6u
5
− 4u
4
− u
3
+ 4u
2
− 1)
2
c
6
u
20
+ 4u
19
+ ··· − 24u + 8
c
7
u
20
+ 6u
19
+ ··· + 8u + 1
c
8
u
20
+ u
19
+ ··· − 4u − 1
c
9
u
20
− 4u
18
+ ··· + 146u
2
− 31
c
10
u
20
− u
19
+ ··· + 4u − 1
c
11
u
20
− 6u
19
+ ··· − 8u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
20
− 10y
19
+ ··· + 832y + 64
c
2
, c
5
(y
10
+ y
9
− 11y
8
− 11y
7
+ 39y
6
+ 24y
5
− 54y
4
− 19y
3
+ 24y
2
− 8y + 1)
2
c
3
, c
4
y
20
− 9y
19
+ ··· + 7y + 1
c
7
, c
11
y
20
− 2y
19
+ ··· − 14y + 1
c
8
, c
10
y
20
− y
19
+ ··· − 22y + 1
c
9
(y
10
− 4y
9
+ ··· + 146y −31)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162027 + 1.093500I
a = −0.593689 + 0.666269I
b = −0.965025 − 0.562961I
3.13638 − 3.94572I −1.58269 + 5.47828I
u = −0.162027 + 1.093500I
a = 0.91912 + 1.26340I
b = −0.554998 − 0.469577I
3.13638 − 3.94572I −1.58269 + 5.47828I
u = −0.162027 − 1.093500I
a = −0.593689 − 0.666269I
b = −0.965025 + 0.562961I
3.13638 + 3.94572I −1.58269 − 5.47828I
u = −0.162027 − 1.093500I
a = 0.91912 − 1.26340I
b = −0.554998 + 0.469577I
3.13638 + 3.94572I −1.58269 − 5.47828I
u = −1.184430 + 0.161063I
a = −1.044950 − 0.712567I
b = −1.47068 − 1.35942I
−0.91356 + 1.34180I 8.0489 − 15.8298I
u = −1.184430 + 0.161063I
a = 0.266174 + 0.351567I
b = 0.614102 + 0.689658I
−0.91356 + 1.34180I 8.0489 − 15.8298I
u = −1.184430 − 0.161063I
a = −1.044950 + 0.712567I
b = −1.47068 + 1.35942I
−0.91356 − 1.34180I 8.0489 + 15.8298I
u = −1.184430 − 0.161063I
a = 0.266174 − 0.351567I
b = 0.614102 − 0.689658I
−0.91356 − 1.34180I 8.0489 + 15.8298I
u = 0.493258 + 0.211168I
a = 0.030687 + 0.614200I
b = −1.053900 − 0.481170I
−0.98335 − 6.94564I −13.6667 + 10.0962I
u = 0.493258 + 0.211168I
a = 1.07089 + 4.10487I
b = 0.278877 + 0.531389I
−0.98335 − 6.94564I −13.6667 + 10.0962I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493258 − 0.211168I
a = 0.030687 − 0.614200I
b = −1.053900 + 0.481170I
−0.98335 + 6.94564I −13.6667 − 10.0962I
u = 0.493258 − 0.211168I
a = 1.07089 − 4.10487I
b = 0.278877 − 0.531389I
−0.98335 + 6.94564I −13.6667 − 10.0962I
u = −0.510374
a = −0.34052 + 1.84999I
b = 0.789530 + 0.525018I
−3.56392 −13.6180
u = −0.510374
a = −0.34052 − 1.84999I
b = 0.789530 − 0.525018I
−3.56392 −13.6180
u = −0.19822 + 1.54173I
a = −0.059083 − 1.131320I
b = 0.371545 + 1.039520I
6.26864 + 5.98904I −2.92384 − 3.18632I
u = −0.19822 + 1.54173I
a = −0.222760 + 1.238820I
b = 0.96108 − 1.49878I
6.26864 + 5.98904I −2.92384 − 3.18632I
u = −0.19822 − 1.54173I
a = −0.059083 + 1.131320I
b = 0.371545 − 1.039520I
6.26864 − 5.98904I −2.92384 + 3.18632I
u = −0.19822 − 1.54173I
a = −0.222760 − 1.238820I
b = 0.96108 + 1.49878I
6.26864 − 5.98904I −2.92384 + 3.18632I
u = 1.61322
a = 1.68819
b = 1.26726
−6.51752 34.8670
u = 1.61322
a = 0.260087
b = −0.208312
−6.51752 34.8670
19
IV. I
u
4
= hb + u, a − u + 1, u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
11
=
u − 1
−u
a
7
=
−u
2
− 1
u
2
+ 1
a
2
=
u
u
a
4
=
u
2
− u + 2
−u
2
+ u − 1
a
10
=
−1
−u
a
8
=
−1
u
2
− u
a
1
=
−u
2
+ u − 1
1
a
9
=
−1
−u
a
9
=
−1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 4u − 11
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
+ u
2
+ 1
c
2
, c
8
u
3
+ u − 1
c
4
, c
6
u
3
− u
2
− 1
c
5
, c
10
u
3
+ u + 1
c
7
u
3
+ 2u
2
+ u − 1
c
9
u
3
c
11
u
3
− 2u
2
+ u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
3
− y
2
− 2y −1
c
2
, c
5
, c
8
c
10
y
3
+ 2y
2
+ y −1
c
7
, c
11
y
3
− 2y
2
+ 5y −1
c
9
y
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341164 + 1.161540I
a = −0.658836 + 1.161540I
b = −0.341164 − 1.161540I
5.50124 − 1.58317I 0.22694 − 1.69425I
u = 0.341164 − 1.161540I
a = −0.658836 − 1.161540I
b = −0.341164 + 1.161540I
5.50124 + 1.58317I 0.22694 + 1.69425I
u = −0.682328
a = −1.68233
b = 0.682328
−4.42273 −17.4540
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 1)(u
20
− 5u
19
+ ··· + 24u − 8)(u
20
− 4u
19
+ ··· + 24u + 8)
· (u
50
+ 5u
49
+ ··· + 337800u + 93608)
c
2
(u
3
+ u − 1)(u
10
− u
9
+ u
8
+ u
7
− 7u
6
+ 6u
5
− 4u
4
+ u
3
+ 4u
2
− 1)
2
· (u
20
− 3u
19
+ ··· + 50u + 28)(u
25
+ 2u
24
+ ··· − 18u + 5)
2
c
3
(u
3
+ u
2
+ 1)(u
20
− u
19
+ ··· − 3u
2
+ 1)(u
20
+ 7u
19
+ ··· − u − 1)
· (u
50
− 4u
49
+ ··· + 5u − 1)
c
4
(u
3
− u
2
− 1)(u
20
− 7u
19
+ ··· + u − 1)(u
20
− u
19
+ ··· − 3u
2
+ 1)
· (u
50
− 4u
49
+ ··· + 5u − 1)
c
5
(u
3
+ u + 1)(u
10
+ u
9
+ u
8
− u
7
− 7u
6
− 6u
5
− 4u
4
− u
3
+ 4u
2
− 1)
2
· (u
20
− 3u
19
+ ··· + 50u + 28)(u
25
+ 2u
24
+ ··· − 18u + 5)
2
c
6
(u
3
− u
2
− 1)(u
20
− 5u
19
+ ··· + 24u − 8)(u
20
+ 4u
19
+ ··· − 24u + 8)
· (u
50
+ 5u
49
+ ··· + 337800u + 93608)
c
7
(u
3
+ 2u
2
+ u − 1)(u
20
− 2u
19
+ ··· − 5u − 1)(u
20
+ 6u
19
+ ··· + 8u + 1)
· (u
50
− u
49
+ ··· + 22u − 1)
c
8
(u
3
+ u − 1)(u
20
+ 9u
18
+ ··· + 5u − 1)(u
20
+ u
19
+ ··· − 4u − 1)
· (u
50
+ 3u
48
+ ··· − 10342u − 3931)
c
9
u
3
(u
20
− 4u
18
+ ··· + 146u
2
− 31)(u
20
+ 5u
19
+ ··· + 192u + 32)
· (u
25
− u
24
+ ··· − 18u + 31)
2
c
10
(u
3
+ u + 1)(u
20
+ 9u
18
+ ··· + 5u − 1)(u
20
− u
19
+ ··· + 4u − 1)
· (u
50
+ 3u
48
+ ··· − 10342u − 3931)
c
11
(u
3
− 2u
2
+ u + 1)(u
20
− 6u
19
+ ··· − 8u + 1)(u
20
− 2u
19
+ ··· − 5u − 1)
· (u
50
− u
49
+ ··· + 22u − 1)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
3
− y
2
− 2y −1)(y
20
− 10y
19
+ ··· + 832y + 64)
· (y
20
+ 19y
19
+ ··· + 384y + 64)
· (y
50
+ 13y
49
+ ··· + 42553508800y + 8762457664)
c
2
, c
5
(y
3
+ 2y
2
+ y −1)
· (y
10
+ y
9
− 11y
8
− 11y
7
+ 39y
6
+ 24y
5
− 54y
4
− 19y
3
+ 24y
2
− 8y + 1)
2
· (y
20
+ 11y
19
+ ··· + 6180y + 784)(y
25
+ 24y
24
+ ··· − 336y −25)
2
c
3
, c
4
(y
3
− y
2
− 2y −1)(y
20
− 9y
19
+ ··· + 7y + 1)(y
20
− 3y
19
+ ··· − 6y + 1)
· (y
50
+ 18y
48
+ ··· + 143y + 1)
c
7
, c
11
(y
3
− 2y
2
+ 5y −1)(y
20
+ 24y
18
+ ··· − 79y + 1)
· (y
20
− 2y
19
+ ··· − 14y + 1)(y
50
− 21y
49
+ ··· + 244y + 1)
c
8
, c
10
(y
3
+ 2y
2
+ y −1)(y
20
− y
19
+ ··· − 22y + 1)
· (y
20
+ 18y
19
+ ··· + 13y + 1)
· (y
50
+ 6y
49
+ ··· + 33112428y + 15452761)
c
9
y
3
(y
10
− 4y
9
+ ··· + 146y −31)
2
(y
20
+ y
19
+ ··· − 14336y + 1024)
· (y
25
− 17y
24
+ ··· + 12662y −961)
2
25
