12n
0829
(K12n
0829
)
A knot diagram
1
Linearized knot diagam
4 5 11 8 3 10 1 5 6 7 4 7
Solving Sequence
1,4 2,7
8 5 12 11 3 10 6 9
c
1
c
7
c
4
c
12
c
11
c
3
c
10
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−246065u
16
− 4244217u
15
+ ··· + 5347744b − 62370976,
− 1456963u
16
− 16357645u
15
+ ··· + 10695488a − 33380064, u
17
+ 13u
16
+ ··· + 384u + 64i
I
u
2
= h32u
21
a + 3841u
21
+ ··· + 32a + 7087, −4960u
21
a − 3211u
21
+ ··· − 9433a − 7311,
u
22
− 5u
21
+ ··· + 9u − 1i
I
u
3
= h−395u
7
+ 1362u
6
− 2821u
5
+ 528u
4
+ 4313u
3
− 6033u
2
+ 499b + 2843u + 219,
176u
7
− 881u
6
+ 2212u
5
− 2254u
4
− 1376u
3
+ 5528u
2
+ 499a − 5591u + 2405,
u
8
− 4u
7
+ 9u
6
− 5u
5
− 11u
4
+ 22u
3
− 15u
2
+ u + 1i
I
u
4
= hu
3
a + 2u
2
a + u
3
− au + 2u
2
+ b + a + 1, −u
2
a + 2u
3
+ a
2
− au + 6u
2
+ 2a + 2u − 3, u
4
+ 3u
3
+ u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 77 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−2.46×10
5
u
16
−4.24×10
6
u
15
+· · ·+5.35×10
6
b−6.24×10
7
, −1.46×10
6
u
16
−
1.64 × 10
7
u
15
+ · · · + 1.07 × 10
7
a − 3.34 × 10
7
, u
17
+ 13u
16
+ · · · + 384u + 64i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
7
=
0.136222u
16
+ 1.52940u
15
+ ··· + 24.6566u + 3.12095
0.0460129u
16
+ 0.793646u
15
+ ··· + 55.1943u + 11.6630
a
8
=
0.182235u
16
+ 2.32304u
15
+ ··· + 79.8509u + 14.7840
0.0460129u
16
+ 0.793646u
15
+ ··· + 55.1943u + 11.6630
a
5
=
0.0357957u
16
+ 0.746991u
15
+ ··· + 66.8882u + 12.8825
−0.281648u
16
− 3.00567u
15
+ ··· + 1.86308u + 2.29092
a
12
=
−0.317443u
16
− 3.75266u
15
+ ··· − 66.0251u − 9.59153
0.281648u
16
+ 3.00567u
15
+ ··· − 0.863078u − 2.29092
a
11
=
−0.317443u
16
− 3.75266u
15
+ ··· − 66.0251u − 9.59153
−0.00420439u
16
− 0.702547u
15
+ ··· − 124.203u − 26.2336
a
3
=
−0.0865400u
16
− 1.32604u
15
+ ··· − 66.0553u − 12.4275
0.486877u
16
+ 5.63364u
15
+ ··· + 103.536u + 18.4041
a
10
=
−0.199312u
16
− 2.38217u
15
+ ··· − 56.2845u − 9.51523
0.201025u
16
+ 1.92542u
15
+ ··· − 20.8039u − 5.53856
a
6
=
−0.519547u
16
− 5.47455u
15
+ ··· − 26.4448u − 3.93239
−0.869649u
16
− 9.93344u
15
+ ··· − 149.357u − 26.0336
a
9
=
0.866357u
16
+ 10.0713u
15
+ ··· + 194.012u + 35.2369
0.995891u
16
+ 11.9801u
15
+ ··· + 303.450u + 58.3917
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2547627
668468
u
16
+
7779965
167117
u
15
+ ··· +
235542904
167117
u +
48416750
167117
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 13u
16
+ ··· + 384u − 64
c
2
, c
3
, c
5
c
11
u
17
− u
16
+ ··· + 2u
2
− 1
c
4
, c
7
, c
8
c
12
u
17
− u
16
+ ··· + 2u − 1
c
6
, c
9
, c
10
u
17
+ 7u
16
+ ··· + 20u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ y
16
+ ··· + 30720y −4096
c
2
, c
3
, c
5
c
11
y
17
− y
16
+ ··· + 4y −1
c
4
, c
7
, c
8
c
12
y
17
− 7y
16
+ ··· + 16y −1
c
6
, c
9
, c
10
y
17
− 15y
16
+ ··· + 656y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821682 + 0.661529I
a = 0.858008 − 0.324711I
b = −0.989677 − 1.007790I
1.25631 + 4.00228I 15.8604 − 12.7835I
u = −0.821682 − 0.661529I
a = 0.858008 + 0.324711I
b = −0.989677 + 1.007790I
1.25631 − 4.00228I 15.8604 + 12.7835I
u = −1.273470 + 0.500020I
a = 0.320002 − 0.094697I
b = −0.735208 − 0.318195I
0.477935 + 0.416349I 7.46863 − 3.27578I
u = −1.273470 − 0.500020I
a = 0.320002 + 0.094697I
b = −0.735208 + 0.318195I
0.477935 − 0.416349I 7.46863 + 3.27578I
u = 0.481738 + 0.363033I
a = −1.89001 − 0.31567I
b = 0.637466 + 0.409508I
−2.69267 − 1.50320I 2.85189 − 0.23851I
u = 0.481738 − 0.363033I
a = −1.89001 + 0.31567I
b = 0.637466 − 0.409508I
−2.69267 + 1.50320I 2.85189 + 0.23851I
u = −1.43589 + 0.34815I
a = −0.485149 − 0.179593I
b = 0.963753 + 0.973871I
−9.11607 − 1.06104I 0.674423 + 0.423791I
u = −1.43589 − 0.34815I
a = −0.485149 + 0.179593I
b = 0.963753 − 0.973871I
−9.11607 + 1.06104I 0.674423 − 0.423791I
u = −0.460839
a = −0.546480
b = −0.467095
0.909383 10.8830
u = −0.57733 + 1.43334I
a = −0.549979 + 0.431459I
b = 0.722818 + 0.003213I
2.52580 − 2.40829I 11.92661 + 4.20411I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.57733 − 1.43334I
a = −0.549979 − 0.431459I
b = 0.722818 − 0.003213I
2.52580 + 2.40829I 11.92661 − 4.20411I
u = −1.22826 + 1.00153I
a = −0.948109 + 0.039576I
b = 1.19077 + 0.85178I
0.70626 + 10.80100I 6.42876 − 9.21869I
u = −1.22826 − 1.00153I
a = −0.948109 − 0.039576I
b = 1.19077 − 0.85178I
0.70626 − 10.80100I 6.42876 + 9.21869I
u = −1.49701 + 1.03785I
a = 0.972748 + 0.053873I
b = −1.29563 − 0.83652I
−6.6188 + 15.4900I 3.66741 − 7.95091I
u = −1.49701 − 1.03785I
a = 0.972748 − 0.053873I
b = −1.29563 + 0.83652I
−6.6188 − 15.4900I 3.66741 + 7.95091I
u = 0.08233 + 2.05216I
a = 0.745729 − 0.432687I
b = −0.760744 + 0.061381I
−2.62034 − 5.47573I 5.18020 + 4.38632I
u = 0.08233 − 2.05216I
a = 0.745729 + 0.432687I
b = −0.760744 − 0.061381I
−2.62034 + 5.47573I 5.18020 − 4.38632I
6
II. I
u
2
= h32u
21
a + 3841u
21
+ · · · + 32a + 7087, −4960u
21
a − 3211u
21
+ · · · −
9433a − 7311, u
22
− 5u
21
+ · · · + 9u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
7
=
a
−u
21
a −
3841
32
u
21
+ ··· − a −
7087
32
a
8
=
−au
21
− 120.031u
21
+ ··· + 1578.41u − 221.469
−u
21
a −
3841
32
u
21
+ ··· − a −
7087
32
a
5
=
120.031au
21
+ 101.344u
21
+ ··· + 221.469a + 227.469
19.8750u
21
− 90.5313u
20
+ ··· − 300.563u + 45.6563
a
12
=
66.4688au
21
+ 81.4688u
21
+ ··· + 120.031a + 182.813
−66.4688au
21
− 35.8125u
21
+ ··· − 120.031a − 72.4688
a
11
=
66.4688au
21
+ 81.4688u
21
+ ··· + 120.031a + 182.813
−44.8125au
21
− 18.8750u
21
+ ··· − 82.4688a − 35.6563
a
3
=
137.563au
21
+ 189.281u
21
+ ··· + 248.500a + 339.156
−34.1875au
21
− 35.8125u
21
+ ··· − 62.0625a − 81.4688
a
10
=
42.0625au
21
+ 81.4688u
21
+ ··· + 81.6250a + 182.813
−
151
2
u
21
a − 101u
21
+ ··· −
2201
16
a −
6057
32
a
6
=
−10.4375au
21
− 244.844u
21
+ ··· − 17.5313a − 470.813
69.5000au
21
+ 141.500u
21
+ ··· + 129.875a + 259.594
a
9
=
−17.8750au
21
− 248.500u
21
+ ··· − 35.6563a − 441.625
16.9375au
21
+ 182.094u
21
+ ··· + 36.8125a + 332.406
(ii) Obstruction class = −1
(iii) Cusp Shapes =
413
8
u
21
− 237u
20
+ ··· −
3409
4
u +
547
4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
22
+ 5u
21
+ ··· − 9u − 1)
2
c
2
, c
3
, c
5
c
11
u
44
− u
43
+ ··· − 13u + 1
c
4
, c
7
, c
8
c
12
u
44
− 8u
42
+ ··· + 147u − 43
c
6
, c
9
, c
10
(u
22
− 2u
21
+ ··· + 7u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 13y
21
+ ··· − 27y + 1)
2
c
2
, c
3
, c
5
c
11
y
44
− 11y
43
+ ··· − 477y + 1
c
4
, c
7
, c
8
c
12
y
44
− 16y
43
+ ··· − 36831y + 1849
c
6
, c
9
, c
10
(y
22
− 26y
21
+ ··· − 71y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866708 + 0.250342I
a = 1.183400 − 0.008528I
b = −0.476875 + 1.290100I
−9.17169 + 8.01141I 0.77261 − 5.09216I
u = −0.866708 + 0.250342I
a = −1.83786 + 0.29332I
b = 0.933182 + 0.933872I
−9.17169 + 8.01141I 0.77261 − 5.09216I
u = −0.866708 − 0.250342I
a = 1.183400 + 0.008528I
b = −0.476875 − 1.290100I
−9.17169 − 8.01141I 0.77261 + 5.09216I
u = −0.866708 − 0.250342I
a = −1.83786 − 0.29332I
b = 0.933182 − 0.933872I
−9.17169 − 8.01141I 0.77261 + 5.09216I
u = 0.448775 + 1.039170I
a = 0.803496 − 0.223199I
b = −0.952390 + 0.757775I
2.09525 − 2.66729I 11.12772 + 3.46430I
u = 0.448775 + 1.039170I
a = −0.903341 − 0.952671I
b = 0.622333 − 0.085179I
2.09525 − 2.66729I 11.12772 + 3.46430I
u = 0.448775 − 1.039170I
a = 0.803496 + 0.223199I
b = −0.952390 − 0.757775I
2.09525 + 2.66729I 11.12772 − 3.46430I
u = 0.448775 − 1.039170I
a = −0.903341 + 0.952671I
b = 0.622333 + 0.085179I
2.09525 + 2.66729I 11.12772 − 3.46430I
u = 0.863512
a = −1.183500 + 0.111611I
b = 0.548411 + 0.706122I
−2.52443 −0.931330
u = 0.863512
a = −1.183500 − 0.111611I
b = 0.548411 − 0.706122I
−2.52443 −0.931330
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16022
a = 0.887279 + 0.151896I
b = −0.476544 − 1.099920I
−10.3363 −0.820860
u = 1.16022
a = 0.887279 − 0.151896I
b = −0.476544 + 1.099920I
−10.3363 −0.820860
u = −0.591232 + 0.256780I
a = −0.908291 − 0.264537I
b = 0.526540 − 1.241070I
−1.23360 + 3.53973I 1.05003 − 10.50470I
u = −0.591232 + 0.256780I
a = 2.12856 − 0.64846I
b = −0.612313 − 0.792137I
−1.23360 + 3.53973I 1.05003 − 10.50470I
u = −0.591232 − 0.256780I
a = −0.908291 + 0.264537I
b = 0.526540 + 1.241070I
−1.23360 − 3.53973I 1.05003 + 10.50470I
u = −0.591232 − 0.256780I
a = 2.12856 + 0.64846I
b = −0.612313 + 0.792137I
−1.23360 − 3.53973I 1.05003 + 10.50470I
u = 0.585465
a = 2.26814 + 0.49491I
b = −0.837555 + 0.698988I
−0.922805 4.16100
u = 0.585465
a = 2.26814 − 0.49491I
b = −0.837555 − 0.698988I
−0.922805 4.16100
u = 0.535304
a = −2.86365 + 0.78400I
b = 0.998448 + 0.903122I
−7.30978 2.04140
u = 0.535304
a = −2.86365 − 0.78400I
b = 0.998448 − 0.903122I
−7.30978 2.04140
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51859
a = 0.681101
b = −1.42335
1.54711 5.39830
u = −1.51859
a = 0.189885
b = −1.12717
1.54711 5.39830
u = 0.317611 + 0.260825I
a = −0.396815 + 0.768799I
b = 1.43814 − 0.60489I
−2.28815 + 2.08884I −3.87328 + 3.78041I
u = 0.317611 + 0.260825I
a = −1.48222 + 3.68188I
b = −0.287986 − 0.323663I
−2.28815 + 2.08884I −3.87328 + 3.78041I
u = 0.317611 − 0.260825I
a = −0.396815 − 0.768799I
b = 1.43814 + 0.60489I
−2.28815 − 2.08884I −3.87328 − 3.78041I
u = 0.317611 − 0.260825I
a = −1.48222 − 3.68188I
b = −0.287986 + 0.323663I
−2.28815 − 2.08884I −3.87328 − 3.78041I
u = −1.60563
a = −1.02334
b = 1.47101
7.19906 28.3950
u = −1.60563
a = 0.197362
b = 0.718798
7.19906 28.3950
u = 0.310033
a = −1.94784
b = −1.50623
8.52642 8.54640
u = 0.310033
a = 3.78741
b = 1.07088
8.52642 8.54640
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36454 + 1.01089I
a = −0.945795 + 0.016302I
b = 1.122230 − 0.633333I
−0.81248 − 5.23931I 4.00000 + 6.82590I
u = 1.36454 + 1.01089I
a = 0.555505 + 0.029436I
b = −0.864498 + 0.663611I
−0.81248 − 5.23931I 4.00000 + 6.82590I
u = 1.36454 − 1.01089I
a = −0.945795 − 0.016302I
b = 1.122230 + 0.633333I
−0.81248 + 5.23931I 4.00000 − 6.82590I
u = 1.36454 − 1.01089I
a = 0.555505 − 0.029436I
b = −0.864498 − 0.663611I
−0.81248 + 5.23931I 4.00000 − 6.82590I
u = 1.53118 + 0.76829I
a = 1.087270 − 0.024762I
b = −1.29688 + 0.72319I
−7.71608 − 6.66224I 1.97271 + 4.67525I
u = 1.53118 + 0.76829I
a = −0.370249 + 0.191551I
b = 0.857555 − 0.908378I
−7.71608 − 6.66224I 1.97271 + 4.67525I
u = 1.53118 − 0.76829I
a = 1.087270 + 0.024762I
b = −1.29688 − 0.72319I
−7.71608 + 6.66224I 1.97271 − 4.67525I
u = 1.53118 − 0.76829I
a = −0.370249 − 0.191551I
b = 0.857555 + 0.908378I
−7.71608 + 6.66224I 1.97271 − 4.67525I
u = −1.79379
a = 1.21437
b = −1.39851
3.11718 0.680620
u = −1.79379
a = −0.449330
b = −0.330312
3.11718 0.680620
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.02757 + 1.65415I
a = 0.960232 + 0.372670I
b = −0.946643 + 0.220537I
−1.90562 − 6.12300I 0
u = 1.02757 + 1.65415I
a = −0.806975 + 0.159347I
b = 0.967291 − 0.632040I
−1.90562 − 6.12300I 0
u = 1.02757 − 1.65415I
a = 0.960232 − 0.372670I
b = −0.946643 − 0.220537I
−1.90562 + 6.12300I 0
u = 1.02757 − 1.65415I
a = −0.806975 − 0.159347I
b = 0.967291 + 0.632040I
−1.90562 + 6.12300I 0
14
III. I
u
3
= h−395u
7
+ 1362u
6
+ · · · + 499b + 219, 176u
7
− 881u
6
+ · · · +
499a + 2405, u
8
− 4u
7
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
7
=
−0.352705u
7
+ 1.76553u
6
+ ··· + 11.2044u − 4.81964
0.791583u
7
− 2.72946u
6
+ ··· − 5.69739u − 0.438878
a
8
=
0.438878u
7
− 0.963928u
6
+ ··· + 5.50701u − 5.25852
0.791583u
7
− 2.72946u
6
+ ··· − 5.69739u − 0.438878
a
5
=
−1.80561u
7
+ 7.18036u
6
+ ··· + 24.5351u − 1.29259
−0.0420842u
7
+ 0.352705u
6
+ ··· + 1.51303u + 1.80561
a
12
=
−1.76353u
7
+ 6.82766u
6
+ ··· + 24.0220u − 2.09820
−0.0420842u
7
+ 0.352705u
6
+ ··· + 0.513026u + 1.80561
a
11
=
−1.76353u
7
+ 6.82766u
6
+ ··· + 24.0220u − 2.09820
−0.240481u
7
+ 1.15832u
6
+ ··· + 2.50301u + 2.03206
a
3
=
2.76353u
7
− 10.8277u
6
+ ··· − 39.0220u + 4.09820
0.424850u
7
− 1.51303u
6
+ ··· − 1.65531u − 2.98998
a
10
=
−2.50902u
7
+ 10.2184u
6
+ ··· + 42.6814u − 7.39880
−0.226453u
7
+ 0.707415u
6
+ ··· − 1.33467u + 2.76353
a
6
=
2.49499u
7
− 9.76754u
6
+ ··· − 38.8437u + 6.66733
0.621242u
7
− 1.82565u
6
+ ··· + 0.617234u − 2.74950
a
9
=
−0.250501u
7
+ 0.623246u
6
+ ··· − 2.18437u + 3.36673
−0.815631u
7
+ 2.64529u
6
+ ··· + 4.84770u + 1.04208
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
1250
499
u
7
+
4607
499
u
6
−
9382
499
u
5
+
2252
499
u
4
+
16668
499
u
3
−
20753
499
u
2
+
10557
499
u +
6321
499
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 4u
7
+ 9u
6
− 5u
5
− 11u
4
+ 22u
3
− 15u
2
+ u + 1
c
2
, c
11
u
8
− u
7
− 2u
6
− u
5
+ 2u
4
+ 4u
3
− u − 1
c
3
, c
5
u
8
+ u
7
− 2u
6
+ u
5
+ 2u
4
− 4u
3
+ u − 1
c
4
, c
7
u
8
+ u
7
− 3u
6
− 3u
5
+ 3u
4
+ 4u
3
− 2u
2
− 3u + 1
c
6
u
8
+ 2u
7
− 2u
6
− 5u
5
− u
4
+ u
3
+ 3u
2
+ 3u − 1
c
8
, c
12
u
8
− u
7
− 3u
6
+ 3u
5
+ 3u
4
− 4u
3
− 2u
2
+ 3u + 1
c
9
, c
10
u
8
− 2u
7
− 2u
6
+ 5u
5
− u
4
− u
3
+ 3u
2
− 3u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 2y
7
+ 19y
6
− 77y
5
+ 81y
4
− 126y
3
+ 159y
2
− 31y + 1
c
2
, c
3
, c
5
c
11
y
8
− 5y
7
+ 6y
6
− y
5
+ 8y
4
− 14y
3
+ 4y
2
− y + 1
c
4
, c
7
, c
8
c
12
y
8
− 7y
7
+ 21y
6
− 39y
5
+ 53y
4
− 52y
3
+ 34y
2
− 13y + 1
c
6
, c
9
, c
10
y
8
− 8y
7
+ 22y
6
− 19y
5
− 15y
4
+ 27y
3
+ 5y
2
− 15y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735892 + 0.886577I
a = −0.884202 − 0.195074I
b = 0.813416 − 0.781160I
0.77106 − 3.72981I 3.13822 + 5.22830I
u = 0.735892 − 0.886577I
a = −0.884202 + 0.195074I
b = 0.813416 + 0.781160I
0.77106 + 3.72981I 3.13822 − 5.22830I
u = 1.18114
a = −0.233176
b = 1.52041
2.49259 17.2730
u = −1.34198
a = 0.549293
b = −0.314751
−0.332482 −1.32110
u = 0.430959
a = −1.72753
b = −1.30833
9.63351 16.6630
u = −0.200867
a = −7.53063
b = 1.25963
5.93337 6.48310
u = 1.22948 + 1.99454I
a = 0.855225 − 0.024290I
b = −0.891894 + 0.448855I
−3.05482 − 6.85115I 0.81307 + 9.87716I
u = 1.22948 − 1.99454I
a = 0.855225 + 0.024290I
b = −0.891894 − 0.448855I
−3.05482 + 6.85115I 0.81307 − 9.87716I
18
IV. I
u
4
= hu
3
a + 2u
2
a + u
3
− au + 2u
2
+ b + a + 1, −u
2
a + 2u
3
+ a
2
− au +
6u
2
+ 2a + 2u − 3, u
4
+ 3u
3
+ u
2
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
7
=
a
−u
3
a − 2u
2
a − u
3
+ au − 2u
2
− a − 1
a
8
=
−u
3
a − 2u
2
a − u
3
+ au − 2u
2
− 1
−u
3
a − 2u
2
a − u
3
+ au − 2u
2
− a − 1
a
5
=
−u
3
a − 2u
2
a − u
3
− 2u
2
− a + u
u − 1
a
12
=
u
3
a + u
2
a + u
3
− 2au + 2u
2
+ a − u
−u
3
a − u
2
a + 2au + u
2
− a + 2u
a
11
=
u
3
a + u
2
a + u
3
− 2au + 2u
2
+ a − u
2u
3
a + 3u
2
a + u
3
− au + 3u
2
+ a + 1
a
3
=
u
3
a + u
2
a + u
3
− 2au + 2u
2
+ a − u + 1
5u
3
a + 7u
2
a + 2u
3
− 5au + 5u
2
+ 3a − 2u + 1
a
10
=
u
3
a + u
2
a + u
3
− au + 2u
2
+ 2a − u
2u
3
a + 3u
2
a + u
3
− 2au + 2u
2
+ a − 2u + 1
a
6
=
u
3
a + u
2
a − 2au + 1
−u
2
a − u
3
− u
2
− 1
a
9
=
−u
2
a + u
3
− 2au + 2u
2
+ a + 1
u
3
a + 2u
2
a + 2u
3
− 2au + 2u
2
+ a − 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
+ 6u
2
+ 17u − 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ u
2
− u + 1)
2
c
2
, c
11
u
8
+ 4u
7
+ 3u
6
− 5u
5
− 7u
4
− u
3
+ 2u
2
+ u + 1
c
3
, c
5
u
8
− 4u
7
+ 3u
6
+ 5u
5
− 7u
4
+ u
3
+ 2u
2
− u + 1
c
4
, c
7
u
8
− u
7
− 3u
6
+ 4u
5
+ 3u
4
− 4u
3
− 3u
2
+ u + 1
c
6
(u
4
− u
3
− 2u
2
+ 2u + 1)
2
c
8
, c
12
u
8
+ u
7
− 3u
6
− 4u
5
+ 3u
4
+ 4u
3
− 3u
2
− u + 1
c
9
, c
10
(u
4
+ u
3
− 2u
2
− 2u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 7y
3
+ 9y
2
+ y + 1)
2
c
2
, c
3
, c
5
c
11
y
8
− 10y
7
+ 35y
6
− 55y
5
+ 45y
4
− 13y
3
− 8y
2
+ 3y + 1
c
4
, c
7
, c
8
c
12
y
8
− 7y
7
+ 23y
6
− 48y
5
+ 63y
4
− 48y
3
+ 23y
2
− 7y + 1
c
6
, c
9
, c
10
(y
4
− 5y
3
+ 10y
2
− 8y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38939
a = −1.03392
b = 1.51044
6.97792 −8.67300
u = −1.38939
a = −0.425060
b = −0.662061
6.97792 −8.67300
u = 0.339093 + 0.446630I
a = 1.239660 − 0.452440I
b = −1.17507 − 0.80023I
−2.07364 − 2.52742I 3.58548 + 9.28015I
u = 0.339093 + 0.446630I
a = −2.98506 + 1.20197I
b = 0.581383 − 0.395925I
−2.07364 − 2.52742I 3.58548 + 9.28015I
u = 0.339093 − 0.446630I
a = 1.239660 + 0.452440I
b = −1.17507 + 0.80023I
−2.07364 + 2.52742I 3.58548 − 9.28015I
u = 0.339093 − 0.446630I
a = −2.98506 − 1.20197I
b = 0.581383 + 0.395925I
−2.07364 + 2.52742I 3.58548 − 9.28015I
u = −2.28879
a = 1.06794
b = −1.38370
3.74910 14.5020
u = −2.28879
a = −0.118151
b = 0.722703
3.74910 14.5020
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ u
2
− u + 1)
2
· (u
8
− 4u
7
+ 9u
6
− 5u
5
− 11u
4
+ 22u
3
− 15u
2
+ u + 1)
· (u
17
− 13u
16
+ ··· + 384u − 64)(u
22
+ 5u
21
+ ··· − 9u − 1)
2
c
2
, c
11
(u
8
− u
7
− 2u
6
− u
5
+ 2u
4
+ 4u
3
− u − 1)
· (u
8
+ 4u
7
+ ··· + u + 1)(u
17
− u
16
+ ··· + 2u
2
− 1)
· (u
44
− u
43
+ ··· − 13u + 1)
c
3
, c
5
(u
8
− 4u
7
+ 3u
6
+ 5u
5
− 7u
4
+ u
3
+ 2u
2
− u + 1)
· (u
8
+ u
7
+ ··· + u − 1)(u
17
− u
16
+ ··· + 2u
2
− 1)
· (u
44
− u
43
+ ··· − 13u + 1)
c
4
, c
7
(u
8
− u
7
− 3u
6
+ 4u
5
+ 3u
4
− 4u
3
− 3u
2
+ u + 1)
· (u
8
+ u
7
− 3u
6
− 3u
5
+ 3u
4
+ 4u
3
− 2u
2
− 3u + 1)
· (u
17
− u
16
+ ··· + 2u − 1)(u
44
− 8u
42
+ ··· + 147u − 43)
c
6
(u
4
− u
3
− 2u
2
+ 2u + 1)
2
· (u
8
+ 2u
7
− 2u
6
− 5u
5
− u
4
+ u
3
+ 3u
2
+ 3u − 1)
· (u
17
+ 7u
16
+ ··· + 20u − 8)(u
22
− 2u
21
+ ··· + 7u + 1)
2
c
8
, c
12
(u
8
− u
7
− 3u
6
+ 3u
5
+ 3u
4
− 4u
3
− 2u
2
+ 3u + 1)
· (u
8
+ u
7
+ ··· − u + 1)(u
17
− u
16
+ ··· + 2u − 1)
· (u
44
− 8u
42
+ ··· + 147u − 43)
c
9
, c
10
(u
4
+ u
3
− 2u
2
− 2u + 1)
2
· (u
8
− 2u
7
− 2u
6
+ 5u
5
− u
4
− u
3
+ 3u
2
− 3u − 1)
· (u
17
+ 7u
16
+ ··· + 20u − 8)(u
22
− 2u
21
+ ··· + 7u + 1)
2
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 7y
3
+ 9y
2
+ y + 1)
2
· (y
8
+ 2y
7
+ 19y
6
− 77y
5
+ 81y
4
− 126y
3
+ 159y
2
− 31y + 1)
· (y
17
+ y
16
+ ··· + 30720y −4096)(y
22
− 13y
21
+ ··· − 27y + 1)
2
c
2
, c
3
, c
5
c
11
(y
8
− 10y
7
+ 35y
6
− 55y
5
+ 45y
4
− 13y
3
− 8y
2
+ 3y + 1)
· (y
8
− 5y
7
+ 6y
6
− y
5
+ 8y
4
− 14y
3
+ 4y
2
− y + 1)
· (y
17
− y
16
+ ··· + 4y −1)(y
44
− 11y
43
+ ··· − 477y + 1)
c
4
, c
7
, c
8
c
12
(y
8
− 7y
7
+ 21y
6
− 39y
5
+ 53y
4
− 52y
3
+ 34y
2
− 13y + 1)
· (y
8
− 7y
7
+ 23y
6
− 48y
5
+ 63y
4
− 48y
3
+ 23y
2
− 7y + 1)
· (y
17
− 7y
16
+ ··· + 16y −1)(y
44
− 16y
43
+ ··· − 36831y + 1849)
c
6
, c
9
, c
10
(y
4
− 5y
3
+ 10y
2
− 8y + 1)
2
· (y
8
− 8y
7
+ 22y
6
− 19y
5
− 15y
4
+ 27y
3
+ 5y
2
− 15y + 1)
· (y
17
− 15y
16
+ ··· + 656y −64)(y
22
− 26y
21
+ ··· − 71y + 1)
2
24
