11a
73
(K11a
73
)
A knot diagram
1
Linearized knot diagam
6 1 10 11 2 3 4 5 7 8 9
Solving Sequence
1,6
2 3 7
5,9
8 11 4 10
c
1
c
2
c
6
c
5
c
8
c
11
c
4
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−11711u
40
+ 64575u
39
+ ··· + 3011b − 10581, −4430u
40
+ 27638u
39
+ ··· + 3011a − 6831,
u
41
− 6u
40
+ ··· + 5u − 1i
I
u
2
= h695u
30
a + 2470u
30
+ ··· + 1245a − 1088, 4u
29
a − u
30
+ ··· + 6a − 2, u
31
+ 2u
30
+ ··· + 2u + 1i
I
u
3
= hu
11
+ u
10
+ 2u
9
+ 3u
8
+ 2u
7
+ 4u
6
+ 2u
4
− u
3
+ 2u
2
+ b − 2u + 1,
− u
11
− 4u
9
− u
8
− 6u
7
− u
6
− 4u
5
+ u
4
− u
3
+ 3u
2
+ a − 1,
u
12
− u
11
+ 4u
10
− 3u
9
+ 7u
8
− 5u
7
+ 7u
6
− 6u
5
+ 6u
4
− 6u
3
+ 4u
2
− 2u + 1i
I
u
4
= hb − 1, a
2
+ 2au + 3a + 3u + 2, u
2
+ u + 1i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 120 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−11711u
40
+ 64575u
39
+ · · · + 3011b − 10581, −4430u
40
+
27638u
39
+ · · · + 3011a − 6831, u
41
− 6u
40
+ · · · + 5u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
9
=
1.47127u
40
− 9.17901u
39
+ ··· − 5.53836u + 2.26868
3.88941u
40
− 21.4464u
39
+ ··· − 12.0956u + 3.51411
a
8
=
−0.531385u
40
− 0.883427u
39
+ ··· − 9.18931u + 3.76752
6.82431u
40
− 39.2046u
39
+ ··· − 25.0438u + 5.73564
a
11
=
−0.591498u
40
+ 4.05413u
39
+ ··· + 5.08303u + 0.803720
1.64198u
40
− 9.67021u
39
+ ··· − 8.71504u + 2.71837
a
4
=
0.209565u
40
− 0.0640983u
39
+ ··· + 5.34341u − 3.59582
1.85586u
40
− 8.46463u
39
+ ··· + 2.68615u − 1.43806
a
10
=
5.73564u
40
− 27.5895u
39
+ ··· − 8.76918u + 3.63434
−4.07174u
40
+ 21.9807u
39
+ ··· + 6.42444u − 0.531385
a
10
=
5.73564u
40
− 27.5895u
39
+ ··· − 8.76918u + 3.63434
−4.07174u
40
+ 21.9807u
39
+ ··· + 6.42444u − 0.531385
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
11684
3011
u
40
+
62324
3011
u
39
+ ··· +
34002
3011
u +
13707
3011
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− 6u
40
+ ··· + 5u − 1
c
2
u
41
+ 22u
40
+ ··· + 11u − 1
c
3
, c
8
u
41
+ 2u
40
+ ··· + 8u
2
− 1
c
4
, c
7
u
41
+ 2u
40
+ ··· − 24u
2
+ 1
c
6
u
41
+ 6u
40
+ ··· − 1163u − 157
c
9
, c
11
u
41
− 6u
40
+ ··· + 4u + 1
c
10
u
41
− 22u
40
+ ··· + 25u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 22y
40
+ ··· + 11y −1
c
2
y
41
− 2y
40
+ ··· + 119y −1
c
3
, c
8
y
41
− 10y
40
+ ··· + 16y −1
c
4
, c
7
y
41
− 22y
40
+ ··· + 48y −1
c
6
y
41
− 20y
40
+ ··· + 345571y −24649
c
9
, c
11
y
41
− 14y
40
+ ··· + 12y −1
c
10
y
41
+ 10y
39
+ ··· + 50y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845612 + 0.498102I
a = 0.475474 + 0.261626I
b = −0.334988 − 0.050698I
1.33190 + 2.47162I 16.2458 − 1.2870I
u = 0.845612 − 0.498102I
a = 0.475474 − 0.261626I
b = −0.334988 + 0.050698I
1.33190 − 2.47162I 16.2458 + 1.2870I
u = −0.725875 + 0.718682I
a = 0.83857 + 1.21867I
b = −0.903416 − 0.468519I
3.04955 + 5.79639I 4.67570 − 5.28890I
u = −0.725875 − 0.718682I
a = 0.83857 − 1.21867I
b = −0.903416 + 0.468519I
3.04955 − 5.79639I 4.67570 + 5.28890I
u = −0.515395 + 0.785309I
a = −1.03703 − 1.54909I
b = 1.242510 + 0.373109I
3.38107 − 0.44143I 9.27545 − 0.21018I
u = −0.515395 − 0.785309I
a = −1.03703 + 1.54909I
b = 1.242510 − 0.373109I
3.38107 + 0.44143I 9.27545 + 0.21018I
u = −0.536686 + 0.762150I
a = −2.07413 − 0.35216I
b = 1.26360 − 0.68186I
3.44275 − 3.84392I 9.44835 + 8.23646I
u = −0.536686 − 0.762150I
a = −2.07413 + 0.35216I
b = 1.26360 + 0.68186I
3.44275 + 3.84392I 9.44835 − 8.23646I
u = −0.680543 + 0.851083I
a = 1.65602 + 0.00258I
b = −1.067800 + 0.649528I
2.65853 − 11.08820I 3.28154 + 9.85902I
u = −0.680543 − 0.851083I
a = 1.65602 − 0.00258I
b = −1.067800 − 0.649528I
2.65853 + 11.08820I 3.28154 − 9.85902I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.193943 + 0.889112I
a = 0.883549 + 0.178964I
b = 0.138077 + 0.486291I
−0.85333 + 1.82668I −2.01304 − 4.52189I
u = 0.193943 − 0.889112I
a = 0.883549 − 0.178964I
b = 0.138077 − 0.486291I
−0.85333 − 1.82668I −2.01304 + 4.52189I
u = 0.857936 + 0.229320I
a = 1.55370 − 0.62249I
b = −1.20325 + 1.09295I
−0.91359 − 13.22010I 1.63608 + 7.45702I
u = 0.857936 − 0.229320I
a = 1.55370 + 0.62249I
b = −1.20325 − 1.09295I
−0.91359 + 13.22010I 1.63608 − 7.45702I
u = 0.848782
a = −0.709994
b = 0.892393
0.744100 9.40900
u = 0.454786 + 1.065100I
a = −0.31016 + 1.42726I
b = 0.511379 + 0.571103I
−0.42808 + 3.78436I 2.16188 − 5.53774I
u = 0.454786 − 1.065100I
a = −0.31016 − 1.42726I
b = 0.511379 − 0.571103I
−0.42808 − 3.78436I 2.16188 + 5.53774I
u = 0.539684 + 1.034030I
a = 0.779420 − 0.504456I
b = −0.164278 − 0.300558I
−0.14735 + 2.61609I 2.94577 − 3.55552I
u = 0.539684 − 1.034030I
a = 0.779420 + 0.504456I
b = −0.164278 + 0.300558I
−0.14735 − 2.61609I 2.94577 + 3.55552I
u = −0.455367 + 1.107240I
a = −1.04912 − 1.13395I
b = 1.50116 + 0.16642I
−0.93408 − 3.72501I 0. + 3.78091I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455367 − 1.107240I
a = −1.04912 + 1.13395I
b = 1.50116 − 0.16642I
−0.93408 + 3.72501I 0. − 3.78091I
u = 0.362831 + 1.165210I
a = 1.070360 − 0.324888I
b = 0.79605 − 1.29861I
−2.85882 − 1.02122I 0
u = 0.362831 − 1.165210I
a = 1.070360 + 0.324888I
b = 0.79605 + 1.29861I
−2.85882 + 1.02122I 0
u = 0.746103 + 0.183057I
a = −1.285710 + 0.387657I
b = 1.07761 − 1.20252I
1.05085 − 4.60926I 7.98736 + 6.22230I
u = 0.746103 − 0.183057I
a = −1.285710 − 0.387657I
b = 1.07761 + 1.20252I
1.05085 + 4.60926I 7.98736 − 6.22230I
u = −0.448486 + 1.175510I
a = 0.492889 + 0.632416I
b = −0.817436 − 0.184411I
−5.68068 − 4.22254I 0
u = −0.448486 − 1.175510I
a = 0.492889 − 0.632416I
b = −0.817436 + 0.184411I
−5.68068 + 4.22254I 0
u = 0.514268 + 1.164380I
a = −1.64613 + 1.51432I
b = 1.15140 + 1.37689I
−1.79982 + 9.32852I 0
u = 0.514268 − 1.164380I
a = −1.64613 − 1.51432I
b = 1.15140 − 1.37689I
−1.79982 − 9.32852I 0
u = 0.297512 + 1.244050I
a = −0.449120 + 0.044426I
b = −1.03032 + 1.16487I
−5.61358 − 9.45917I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297512 − 1.244050I
a = −0.449120 − 0.044426I
b = −1.03032 − 1.16487I
−5.61358 + 9.45917I 0
u = −0.717723
a = 1.31735
b = −0.635831
−2.35187 −3.23270
u = 0.559000 + 1.189400I
a = 1.71865 − 1.26258I
b = −1.27637 − 1.18033I
−3.7858 + 18.4184I 0
u = 0.559000 − 1.189400I
a = 1.71865 + 1.26258I
b = −1.27637 + 1.18033I
−3.7858 − 18.4184I 0
u = 0.220242 + 1.309270I
a = 0.00788396 − 0.00223172I
b = −0.246595 − 0.581812I
−4.69336 + 5.76085I 0
u = 0.220242 − 1.309270I
a = 0.00788396 + 0.00223172I
b = −0.246595 + 0.581812I
−4.69336 − 5.76085I 0
u = 0.506994 + 1.237050I
a = −0.343128 + 0.730701I
b = 0.837607 + 0.284107I
−2.86146 + 4.86399I 0
u = 0.506994 − 1.237050I
a = −0.343128 − 0.730701I
b = 0.837607 − 0.284107I
−2.86146 − 4.86399I 0
u = 0.337324 + 0.271834I
a = −0.07427 − 1.63066I
b = 0.823540 − 0.201797I
1.65904 − 0.03957I 6.61397 + 0.60191I
u = 0.337324 − 0.271834I
a = −0.07427 + 1.63066I
b = 0.823540 + 0.201797I
1.65904 + 0.03957I 6.61397 − 0.60191I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.278824
a = −5.02278
b = 1.14650
1.63641 6.23630
9
II. I
u
2
= h695u
30
a + 2470u
30
+ · · · + 1245a − 1088, 4u
29
a − u
30
+ · · · + 6a −
2, u
31
+ 2u
30
+ · · · + 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
9
=
a
−0.622202au
30
− 2.21128u
30
+ ··· − 1.11459a + 0.974038
a
8
=
−0.209490au
30
+ 0.780662u
30
+ ··· + 0.660698a − 1.61594
−0.339302au
30
− 3.61594u
30
+ ··· − 0.622202a + 0.788720
a
11
=
−0.788720au
30
− 0.795882u
30
+ ··· + 0.0259624a + 3.27932
−1.01253au
30
+ 2.10654u
30
+ ··· − 0.806625a − 1.64369
a
4
=
−2.04118au
30
+ 3.35004u
30
+ ··· − 1.79320a + 1.74217
0.509400au
30
− 0.829902u
30
+ ··· + 1.85497a + 1.23277
a
10
=
−0.622202au
30
+ 0.788720u
30
+ ··· − 0.114593a + 0.974038
−0.153089au
30
− 3.19875u
30
+ ··· − 0.209490a − 0.219338
a
10
=
−0.622202au
30
+ 0.788720u
30
+ ··· − 0.114593a + 0.974038
−0.153089au
30
− 3.19875u
30
+ ··· − 0.209490a − 0.219338
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 9u
30
+ 12u
29
+ 79u
28
+ 93u
27
+ 328u
26
+ 374u
25
+ 861u
24
+ 990u
23
+ 1590u
22
+
1876u
21
+ 2214u
20
+ 2605u
19
+ 2432u
18
+ 2616u
17
+ 2165u
16
+ 1828u
15
+ 1490u
14
+
816u
13
+ 642u
12
+ 206u
11
−4u
9
−174u
8
−52u
7
−60u
6
−64u
5
+ 4u
4
−7u
3
+ 12u
2
+ 16u −1
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
31
+ 2u
30
+ ··· + 2u + 1)
2
c
2
(u
31
+ 16u
30
+ ··· − 2u − 1)
2
c
3
, c
8
u
62
− 4u
60
+ ··· − 391u + 173
c
4
, c
7
u
62
+ 6u
60
+ ··· − u + 1
c
6
(u
31
− 2u
30
+ ··· − 26u + 5)
2
c
9
, c
11
u
62
+ 5u
61
+ ··· + 30u + 1
c
10
(u
31
+ 15u
30
+ ··· + 6u + 4)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
31
+ 16y
30
+ ··· − 2y −1)
2
c
2
(y
31
+ 32y
29
+ ··· + 14y −1)
2
c
3
, c
8
y
62
− 8y
61
+ ··· − 1236207y + 29929
c
4
, c
7
y
62
+ 12y
61
+ ··· − 47y + 1
c
6
(y
31
− 16y
30
+ ··· − 534y −25)
2
c
9
, c
11
y
62
+ 23y
61
+ ··· − 104y + 1
c
10
(y
31
− 5y
30
+ ··· + 236y −16)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.700328 + 0.800493I
a = 1.146060 − 0.099237I
b = −0.574058 − 0.237024I
0.66027 + 2.65228I −9.42163 − 5.74104I
u = 0.700328 + 0.800493I
a = −0.261910 − 0.128100I
b = 0.301124 + 0.295589I
0.66027 + 2.65228I −9.42163 − 5.74104I
u = 0.700328 − 0.800493I
a = 1.146060 + 0.099237I
b = −0.574058 + 0.237024I
0.66027 − 2.65228I −9.42163 + 5.74104I
u = 0.700328 − 0.800493I
a = −0.261910 + 0.128100I
b = 0.301124 − 0.295589I
0.66027 − 2.65228I −9.42163 + 5.74104I
u = 0.576719 + 0.939494I
a = 0.06205 + 1.48991I
b = 0.971416 − 0.435463I
1.79992 + 1.42306I 5.96720 + 7.06639I
u = 0.576719 + 0.939494I
a = 1.56139 − 0.38632I
b = −0.912307 + 0.063353I
1.79992 + 1.42306I 5.96720 + 7.06639I
u = 0.576719 − 0.939494I
a = 0.06205 − 1.48991I
b = 0.971416 + 0.435463I
1.79992 − 1.42306I 5.96720 − 7.06639I
u = 0.576719 − 0.939494I
a = 1.56139 + 0.38632I
b = −0.912307 − 0.063353I
1.79992 − 1.42306I 5.96720 − 7.06639I
u = −0.847519 + 0.248601I
a = −0.626669 − 0.783073I
b = 0.478939 + 1.042720I
−2.48415 + 4.99236I −3.07968 − 5.91781I
u = −0.847519 + 0.248601I
a = 1.43877 + 0.44457I
b = −0.893298 − 0.771257I
−2.48415 + 4.99236I −3.07968 − 5.91781I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847519 − 0.248601I
a = −0.626669 + 0.783073I
b = 0.478939 − 1.042720I
−2.48415 − 4.99236I −3.07968 + 5.91781I
u = −0.847519 − 0.248601I
a = 1.43877 − 0.44457I
b = −0.893298 + 0.771257I
−2.48415 − 4.99236I −3.07968 + 5.91781I
u = 0.613097 + 0.623277I
a = −1.44473 − 0.64813I
b = 1.074650 + 0.709661I
2.71352 + 3.26681I 9.13719 − 8.60586I
u = 0.613097 + 0.623277I
a = 1.88374 − 1.08780I
b = −0.810431 − 0.123872I
2.71352 + 3.26681I 9.13719 − 8.60586I
u = 0.613097 − 0.623277I
a = −1.44473 + 0.64813I
b = 1.074650 − 0.709661I
2.71352 − 3.26681I 9.13719 + 8.60586I
u = 0.613097 − 0.623277I
a = 1.88374 + 1.08780I
b = −0.810431 + 0.123872I
2.71352 − 3.26681I 9.13719 + 8.60586I
u = −0.358609 + 1.074610I
a = 1.247210 + 0.063972I
b = 0.74515 + 1.66291I
−2.29804 + 2.01394I 0.79058 − 3.76194I
u = −0.358609 + 1.074610I
a = −0.49075 − 1.65979I
b = −0.0812528 − 0.0525556I
−2.29804 + 2.01394I 0.79058 − 3.76194I
u = −0.358609 − 1.074610I
a = 1.247210 − 0.063972I
b = 0.74515 − 1.66291I
−2.29804 − 2.01394I 0.79058 + 3.76194I
u = −0.358609 − 1.074610I
a = −0.49075 + 1.65979I
b = −0.0812528 + 0.0525556I
−2.29804 − 2.01394I 0.79058 + 3.76194I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.066980 + 0.843210I
a = 0.905300 + 1.065700I
b = 0.372827 + 1.045040I
−1.82841 + 2.63278I −4.56232 − 0.80559I
u = −0.066980 + 0.843210I
a = 1.50981 − 0.90367I
b = −0.830677 + 0.572923I
−1.82841 + 2.63278I −4.56232 − 0.80559I
u = −0.066980 − 0.843210I
a = 0.905300 − 1.065700I
b = 0.372827 − 1.045040I
−1.82841 − 2.63278I −4.56232 + 0.80559I
u = −0.066980 − 0.843210I
a = 1.50981 + 0.90367I
b = −0.830677 − 0.572923I
−1.82841 − 2.63278I −4.56232 + 0.80559I
u = 0.423601 + 1.144370I
a = 0.200693 − 0.558634I
b = 0.664215 − 1.092670I
−5.31357 − 0.42431I −6.76845 + 0.89097I
u = 0.423601 + 1.144370I
a = 1.84585 − 1.43049I
b = −1.19733 − 1.54730I
−5.31357 − 0.42431I −6.76845 + 0.89097I
u = 0.423601 − 1.144370I
a = 0.200693 + 0.558634I
b = 0.664215 + 1.092670I
−5.31357 + 0.42431I −6.76845 − 0.89097I
u = 0.423601 − 1.144370I
a = 1.84585 + 1.43049I
b = −1.19733 + 1.54730I
−5.31357 + 0.42431I −6.76845 − 0.89097I
u = 0.470485 + 1.145180I
a = −1.312440 − 0.512271I
b = −0.95000 + 1.91169I
−4.97995 + 8.43248I −5.41543 − 9.16645I
u = 0.470485 + 1.145180I
a = −2.00403 + 1.37416I
b = 0.787153 + 0.878249I
−4.97995 + 8.43248I −5.41543 − 9.16645I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.470485 − 1.145180I
a = −1.312440 + 0.512271I
b = −0.95000 − 1.91169I
−4.97995 − 8.43248I −5.41543 + 9.16645I
u = 0.470485 − 1.145180I
a = −2.00403 − 1.37416I
b = 0.787153 − 0.878249I
−4.97995 − 8.43248I −5.41543 + 9.16645I
u = −0.526321 + 1.124110I
a = 0.64280 + 1.56277I
b = −0.384960 + 0.390707I
−1.03143 − 9.47799I 3.54432 + 9.88259I
u = −0.526321 + 1.124110I
a = −2.06575 − 1.23148I
b = 1.29214 − 1.47017I
−1.03143 − 9.47799I 3.54432 + 9.88259I
u = −0.526321 − 1.124110I
a = 0.64280 − 1.56277I
b = −0.384960 − 0.390707I
−1.03143 + 9.47799I 3.54432 − 9.88259I
u = −0.526321 − 1.124110I
a = −2.06575 + 1.23148I
b = 1.29214 + 1.47017I
−1.03143 + 9.47799I 3.54432 − 9.88259I
u = −0.442008 + 1.171670I
a = 0.742971 + 0.990301I
b = −1.076050 + 0.211669I
−5.69749 − 4.19773I −6.88583 + 3.70112I
u = −0.442008 + 1.171670I
a = 0.252643 + 0.243666I
b = −0.549168 − 0.536294I
−5.69749 − 4.19773I −6.88583 + 3.70112I
u = −0.442008 − 1.171670I
a = 0.742971 − 0.990301I
b = −1.076050 − 0.211669I
−5.69749 + 4.19773I −6.88583 − 3.70112I
u = −0.442008 − 1.171670I
a = 0.252643 − 0.243666I
b = −0.549168 + 0.536294I
−5.69749 + 4.19773I −6.88583 − 3.70112I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688548 + 0.289520I
a = 0.88012 − 1.18793I
b = −0.486469 − 0.239705I
1.39266 + 4.80763I 7.37986 − 6.53110I
u = −0.688548 + 0.289520I
a = −1.56433 − 1.11235I
b = 1.14306 + 1.26502I
1.39266 + 4.80763I 7.37986 − 6.53110I
u = −0.688548 − 0.289520I
a = 0.88012 + 1.18793I
b = −0.486469 + 0.239705I
1.39266 − 4.80763I 7.37986 + 6.53110I
u = −0.688548 − 0.289520I
a = −1.56433 + 1.11235I
b = 1.14306 − 1.26502I
1.39266 − 4.80763I 7.37986 + 6.53110I
u = −0.282165 + 1.228290I
a = 0.464148 + 0.295155I
b = 0.219790 + 1.134530I
−7.20604 + 1.39264I −8.15870 − 2.08069I
u = −0.282165 + 1.228290I
a = −0.0693346 − 0.1131790I
b = −0.724830 − 0.935158I
−7.20604 + 1.39264I −8.15870 − 2.08069I
u = −0.282165 − 1.228290I
a = 0.464148 − 0.295155I
b = 0.219790 − 1.134530I
−7.20604 − 1.39264I −8.15870 + 2.08069I
u = −0.282165 − 1.228290I
a = −0.0693346 + 0.1131790I
b = −0.724830 + 0.935158I
−7.20604 − 1.39264I −8.15870 + 2.08069I
u = −0.729174
a = 1.16133
b = −0.335726
−2.34284 −3.47960
u = −0.729174
a = 1.49783
b = −0.962125
−2.34284 −3.47960
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280769 + 0.672881I
a = −0.133027 + 0.453048I
b = −0.05617 − 1.63724I
−0.95364 − 4.69207I 0.70104 + 11.37557I
u = −0.280769 + 0.672881I
a = −3.21056 + 1.44491I
b = 0.290721 − 0.533103I
−0.95364 − 4.69207I 0.70104 + 11.37557I
u = −0.280769 − 0.672881I
a = −0.133027 − 0.453048I
b = −0.05617 + 1.63724I
−0.95364 + 4.69207I 0.70104 − 11.37557I
u = −0.280769 − 0.672881I
a = −3.21056 − 1.44491I
b = 0.290721 + 0.533103I
−0.95364 + 4.69207I 0.70104 − 11.37557I
u = −0.562423 + 1.180730I
a = −1.36886 − 0.47572I
b = 0.564223 − 1.182210I
−5.26969 − 10.18350I −4.99915 + 9.25403I
u = −0.562423 + 1.180730I
a = 1.54748 + 1.00626I
b = −1.006650 + 0.843864I
−5.26969 − 10.18350I −4.99915 + 9.25403I
u = −0.562423 − 1.180730I
a = −1.36886 + 0.47572I
b = 0.564223 + 1.182210I
−5.26969 + 10.18350I −4.99915 − 9.25403I
u = −0.562423 − 1.180730I
a = 1.54748 − 1.00626I
b = −1.006650 − 0.843864I
−5.26969 + 10.18350I −4.99915 − 9.25403I
u = 0.635699 + 0.077135I
a = 1.37652 + 1.04296I
b = −0.83111 − 1.61735I
−2.05368 − 4.22273I −2.98921 + 5.90921I
u = 0.635699 + 0.077135I
a = −1.98473 − 0.26301I
b = 0.608283 − 0.905397I
−2.05368 − 4.22273I −2.98921 + 5.90921I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.635699 − 0.077135I
a = 1.37652 − 1.04296I
b = −0.83111 + 1.61735I
−2.05368 + 4.22273I −2.98921 − 5.90921I
u = 0.635699 − 0.077135I
a = −1.98473 + 0.26301I
b = 0.608283 + 0.905397I
−2.05368 + 4.22273I −2.98921 − 5.90921I
19
III.
I
u
3
= hu
11
+ u
10
+ · · · + b + 1, −u
11
− 4u
9
+ · · · + a − 1, u
12
− u
11
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
9
=
u
11
+ 4u
9
+ u
8
+ 6u
7
+ u
6
+ 4u
5
− u
4
+ u
3
− 3u
2
+ 1
−u
11
− u
10
− 2u
9
− 3u
8
− 2u
7
− 4u
6
− 2u
4
+ u
3
− 2u
2
+ 2u − 1
a
8
=
u
11
+ 3u
9
+ u
8
+ 4u
7
+ u
6
+ 2u
5
− u
4
− 2u
2
− u + 1
−u
10
+ u
9
− 3u
8
+ 2u
7
− 4u
6
+ 3u
5
− 3u
4
+ 3u
3
− 3u
2
+ 3u − 1
a
11
=
u
11
− 2u
10
+ ··· + 7u − 2
−u
11
− 3u
9
− 4u
7
− 3u
5
+ u
4
− 2u
3
+ u
2
− u − 1
a
4
=
−u
11
− 2u
9
− u
8
− 2u
7
− 2u
6
− u
4
+ 2u − 1
−u
11
+ u
10
− 3u
9
+ 3u
8
− 4u
7
+ 5u
6
− 3u
5
+ 5u
4
− 3u
3
+ 3u
2
− 2u
a
10
=
u
11
− u
10
+ 3u
9
− 2u
8
+ 4u
7
− 3u
6
+ 3u
5
− 3u
4
+ 3u
3
− 3u
2
+ u + 1
u
11
− u
10
+ 4u
9
− 3u
8
+ 6u
7
− 5u
6
+ 5u
5
− 6u
4
+ 4u
3
− 5u
2
+ 3u − 1
a
10
=
u
11
− u
10
+ 3u
9
− 2u
8
+ 4u
7
− 3u
6
+ 3u
5
− 3u
4
+ 3u
3
− 3u
2
+ u + 1
u
11
− u
10
+ 4u
9
− 3u
8
+ 6u
7
− 5u
6
+ 5u
5
− 6u
4
+ 4u
3
− 5u
2
+ 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
11
+ 6u
10
− 2u
9
+ 18u
8
− 8u
7
+ 24u
6
− 10u
5
+ 16u
4
− 5u
3
+ 16u
2
− 10u + 4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− u
11
+ ··· − 2u + 1
c
2
u
12
+ 7u
11
+ ··· + 4u + 1
c
3
, c
8
u
12
− u
11
+ 2u
10
− u
9
+ 4u
8
− 3u
7
+ 4u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
− u + 1
c
4
, c
7
u
12
+ u
11
+ 2u
10
+ 3u
9
+ 4u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 4u
4
+ u
3
+ 2u
2
+ u + 1
c
5
u
12
+ u
11
+ ··· + 2u + 1
c
6
u
12
− u
11
− u
10
+ u
9
− 3u
8
+ 3u
7
+ 11u
6
− 4u
5
− 14u
4
+ u
3
+ 6u
2
+ 1
c
9
, c
11
u
12
− 3u
11
+ ··· − 3u + 1
c
10
u
12
+ 9u
11
+ ··· + 87u + 13
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
+ 7y
11
+ ··· + 4y + 1
c
2
y
12
− y
11
+ ··· − 8y + 1
c
3
, c
8
y
12
+ 3y
11
+ ··· + 3y + 1
c
4
, c
7
y
12
+ 3y
11
+ ··· + 3y + 1
c
6
y
12
− 3y
11
+ ··· + 12y + 1
c
9
, c
11
y
12
+ 11y
11
+ ··· + 3y + 1
c
10
y
12
+ 5y
11
+ ··· − 263y + 169
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.765338 + 0.701632I
a = −0.773115 + 0.063272I
b = 0.457387 − 0.273460I
1.13372 − 2.84541I 8.3721 + 15.0712I
u = −0.765338 − 0.701632I
a = −0.773115 − 0.063272I
b = 0.457387 + 0.273460I
1.13372 + 2.84541I 8.3721 − 15.0712I
u = 0.379767 + 1.126510I
a = 1.10555 − 0.93951I
b = 0.28116 − 1.42256I
−3.89632 − 1.51522I −4.76999 + 3.91912I
u = 0.379767 − 1.126510I
a = 1.10555 + 0.93951I
b = 0.28116 + 1.42256I
−3.89632 + 1.51522I −4.76999 − 3.91912I
u = −0.336660 + 1.205570I
a = −0.133510 + 0.523237I
b = −0.312570 − 0.542789I
−4.16467 − 5.30019I −0.64743 + 6.33134I
u = −0.336660 − 1.205570I
a = −0.133510 − 0.523237I
b = −0.312570 + 0.542789I
−4.16467 + 5.30019I −0.64743 − 6.33134I
u = 0.517643 + 1.141910I
a = −1.75917 + 1.08825I
b = 0.67731 + 1.31649I
−2.88156 + 9.38139I −2.89288 − 9.73442I
u = 0.517643 − 1.141910I
a = −1.75917 − 1.08825I
b = 0.67731 − 1.31649I
−2.88156 − 9.38139I −2.89288 + 9.73442I
u = 0.685435 + 0.249226I
a = −1.131530 + 0.408794I
b = 0.524852 − 1.118490I
−0.28783 − 4.74486I 1.19154 + 6.65535I
u = 0.685435 − 0.249226I
a = −1.131530 − 0.408794I
b = 0.524852 + 1.118490I
−0.28783 + 4.74486I 1.19154 − 6.65535I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.019153 + 0.707581I
a = 2.19177 − 0.06943I
b = −0.128135 + 1.122210I
−1.41788 + 3.69137I −2.25337 − 6.20418I
u = 0.019153 − 0.707581I
a = 2.19177 + 0.06943I
b = −0.128135 − 1.122210I
−1.41788 − 3.69137I −2.25337 + 6.20418I
24
IV. I
u
4
= hb − 1, a
2
+ 2au + 3a + 3u + 2, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
7
=
−1
0
a
5
=
−u
u + 1
a
9
=
a
1
a
8
=
−u − 1
−au + 2
a
11
=
a + 1
1
a
4
=
−a − u − 2
−au − a − u
a
10
=
a + 1
1
a
10
=
a + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u + 7
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u
2
+ u + 1)
2
c
3
, c
4
, c
7
c
8
u
4
+ u
3
− u
2
− u + 1
c
5
(u
2
− u + 1)
2
c
9
, c
11
(u − 1)
4
c
10
u
4
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
7
c
8
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
9
, c
11
(y − 1)
4
c
10
y
4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.57070 − 0.10728I
b = 1.00000
1.64493 − 2.02988I 3.50000 + 6.06218I
u = −0.500000 + 0.866025I
a = −0.42930 − 1.62477I
b = 1.00000
1.64493 − 2.02988I 3.50000 + 6.06218I
u = −0.500000 − 0.866025I
a = −1.57070 + 0.10728I
b = 1.00000
1.64493 + 2.02988I 3.50000 − 6.06218I
u = −0.500000 − 0.866025I
a = −0.42930 + 1.62477I
b = 1.00000
1.64493 + 2.02988I 3.50000 − 6.06218I
28
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
−1
0
a
2
=
1
0
a
3
=
1
0
a
7
=
−1
0
a
5
=
−1
0
a
9
=
0
1
a
8
=
1
1
a
11
=
1
1
a
4
=
−2
−1
a
10
=
1
1
a
10
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
u
c
3
, c
4
, c
7
c
8
, c
9
, c
11
u − 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
y
c
3
, c
4
, c
7
c
8
, c
9
, c
11
y − 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
1.64493 6.00000
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
+ u + 1)
2
(u
12
− u
11
+ ··· − 2u + 1)(u
31
+ 2u
30
+ ··· + 2u + 1)
2
· (u
41
− 6u
40
+ ··· + 5u − 1)
c
2
u(u
2
+ u + 1)
2
(u
12
+ 7u
11
+ ··· + 4u + 1)
· ((u
31
+ 16u
30
+ ··· − 2u − 1)
2
)(u
41
+ 22u
40
+ ··· + 11u − 1)
c
3
, c
8
(u − 1)(u
4
+ u
3
− u
2
− u + 1)
· (u
12
− u
11
+ 2u
10
− u
9
+ 4u
8
− 3u
7
+ 4u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
− u + 1)
· (u
41
+ 2u
40
+ ··· + 8u
2
− 1)(u
62
− 4u
60
+ ··· − 391u + 173)
c
4
, c
7
(u − 1)(u
4
+ u
3
− u
2
− u + 1)
· (u
12
+ u
11
+ 2u
10
+ 3u
9
+ 4u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 4u
4
+ u
3
+ 2u
2
+ u + 1)
· (u
41
+ 2u
40
+ ··· − 24u
2
+ 1)(u
62
+ 6u
60
+ ··· − u + 1)
c
5
u(u
2
− u + 1)
2
(u
12
+ u
11
+ ··· + 2u + 1)(u
31
+ 2u
30
+ ··· + 2u + 1)
2
· (u
41
− 6u
40
+ ··· + 5u − 1)
c
6
u(u
2
+ u + 1)
2
· (u
12
− u
11
− u
10
+ u
9
− 3u
8
+ 3u
7
+ 11u
6
− 4u
5
− 14u
4
+ u
3
+ 6u
2
+ 1)
· ((u
31
− 2u
30
+ ··· − 26u + 5)
2
)(u
41
+ 6u
40
+ ··· − 1163u − 157)
c
9
, c
11
((u − 1)
5
)(u
12
− 3u
11
+ ··· − 3u + 1)(u
41
− 6u
40
+ ··· + 4u + 1)
· (u
62
+ 5u
61
+ ··· + 30u + 1)
c
10
u
5
(u
12
+ 9u
11
+ ··· + 87u + 13)(u
31
+ 15u
30
+ ··· + 6u + 4)
2
· (u
41
− 22u
40
+ ··· + 25u
2
− 1)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y(y
2
+ y + 1)
2
(y
12
+ 7y
11
+ ··· + 4y + 1)
· ((y
31
+ 16y
30
+ ··· − 2y − 1)
2
)(y
41
+ 22y
40
+ ··· + 11y − 1)
c
2
y(y
2
+ y + 1)
2
(y
12
− y
11
+ ··· − 8y + 1)
· ((y
31
+ 32y
29
+ ··· + 14y − 1)
2
)(y
41
− 2y
40
+ ··· + 119y − 1)
c
3
, c
8
(y − 1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
12
+ 3y
11
+ ··· + 3y + 1)
· (y
41
− 10y
40
+ ··· + 16y − 1)(y
62
− 8y
61
+ ··· − 1236207y + 29929)
c
4
, c
7
(y − 1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
12
+ 3y
11
+ ··· + 3y + 1)
· (y
41
− 22y
40
+ ··· + 48y − 1)(y
62
+ 12y
61
+ ··· − 47y + 1)
c
6
y(y
2
+ y + 1)
2
(y
12
− 3y
11
+ ··· + 12y + 1)
· (y
31
− 16y
30
+ ··· − 534y − 25)
2
· (y
41
− 20y
40
+ ··· + 345571y − 24649)
c
9
, c
11
((y − 1)
5
)(y
12
+ 11y
11
+ ··· + 3y + 1)(y
41
− 14y
40
+ ··· + 12y − 1)
· (y
62
+ 23y
61
+ ··· − 104y + 1)
c
10
y
5
(y
12
+ 5y
11
+ ··· − 263y + 169)(y
31
− 5y
30
+ ··· + 236y − 16)
2
· (y
41
+ 10y
39
+ ··· + 50y − 1)
34
