11a
38
(K11a
38
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 9 11 3 6 5 7 10
Solving Sequence
3,7
8
4,11
6 9 5 10 1 2
c
7
c
3
c
6
c
8
c
5
c
10
c
11
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.39701 × 10
52
u
49
− 1.56890 × 10
52
u
48
+ ··· + 9.78680 × 10
53
b − 2.06404 × 10
53
,
2.86648 × 10
52
u
49
− 4.68399 × 10
52
u
48
+ ··· + 9.78680 × 10
53
a − 2.53995 × 10
54
, u
50
− 2u
49
+ ··· − 80u + 64i
I
u
2
= h−36u
5
a
2
− 80u
4
a
2
+ 64u
3
a
2
+ 36u
5
− 7a
2
u
2
+ 80u
4
− 40a
2
u − 64u
3
− 22a
2
− 276u
2
+ 283b + 40u + 22,
2u
5
a
2
+ u
5
a + ··· − a − 5, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= h−u
5
+ 2u
3
+ b − u, u
4
+ 2u
3
− 3u
2
+ a − 3u + 2, u
6
− 3u
4
+ 2u
2
+ 1i
I
v
1
= ha, −2v
3
+ 3v
2
+ 4b − 8v + 3, 2v
4
− v
3
+ 5v
2
+ v + 1i
* 4 irreducible components of dim
C
= 0, with total 78 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
=
h1.40×10
52
u
49
−1.57×10
52
u
48
+· · ·+9.79×10
53
b−2.06×10
53
, 2.87×10
52
u
49
−
4.68 × 10
52
u
48
+ · · · + 9.79 × 10
53
a − 2.54 × 10
54
, u
50
− 2u
49
+ · · · − 80u + 64i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
11
=
−0.0292893u
49
+ 0.0478602u
48
+ ··· + 0.349631u + 2.59529
−0.0142744u
49
+ 0.0160307u
48
+ ··· − 0.546290u + 0.210900
a
6
=
0.0506276u
49
− 0.0564076u
48
+ ··· + 1.79590u − 3.09324
−0.0101755u
49
+ 0.0132424u
48
+ ··· + 0.365267u + 1.43307
a
9
=
0.0251404u
49
− 0.0341614u
48
+ ··· − 0.178601u − 0.734921
0.0178177u
49
− 0.0204546u
48
+ ··· − 0.655163u + 0.0702679
a
5
=
0.0359682u
49
− 0.0375079u
48
+ ··· + 0.971454u − 2.70728
−0.0171934u
49
+ 0.0404449u
48
+ ··· + 1.08010u + 1.42517
a
10
=
−0.0435637u
49
+ 0.0638909u
48
+ ··· − 0.196658u + 2.80619
−0.0142744u
49
+ 0.0160307u
48
+ ··· − 0.546290u + 0.210900
a
1
=
−0.0341694u
49
+ 0.0511276u
48
+ ··· + 0.560955u + 1.92903
0.00179875u
49
+ 0.0136197u
48
+ ··· + 1.53241u − 0.778251
a
2
=
−0.0608849u
49
+ 0.0808601u
48
+ ··· − 0.638959u + 4.29539
−0.0126196u
49
+ 0.0224728u
48
+ ··· + 0.518576u + 0.0714096
a
2
=
−0.0608849u
49
+ 0.0808601u
48
+ ··· − 0.638959u + 4.29539
−0.0126196u
49
+ 0.0224728u
48
+ ··· + 0.518576u + 0.0714096
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0626913u
49
+ 0.0376218u
48
+ ··· − 2.19058u + 7.82840
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
50
− 4u
49
+ ··· + 3u + 4
c
2
u
50
+ 24u
49
+ ··· − 255u + 16
c
3
, c
7
u
50
− 2u
49
+ ··· − 80u + 64
c
5
, c
8
, c
9
u
50
+ 2u
49
+ ··· + 76u + 17
c
6
, c
10
u
50
+ 2u
49
+ ··· + 72u + 17
c
11
u
50
− 20u
49
+ ··· − 4370u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
50
− 24y
49
+ ··· + 255y + 16
c
2
y
50
+ 8y
49
+ ··· + 29791y + 256
c
3
, c
7
y
50
− 24y
49
+ ··· − 19712y + 4096
c
5
, c
8
, c
9
y
50
+ 52y
49
+ ··· − 846y + 289
c
6
, c
10
y
50
+ 20y
49
+ ··· + 4370y + 289
c
11
y
50
+ 28y
49
+ ··· − 180694y + 83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907272 + 0.392918I
a = −0.420194 + 0.002697I
b = −0.699224 − 0.714437I
−0.744870 + 0.584560I 0.202019 − 0.958990I
u = 0.907272 − 0.392918I
a = −0.420194 − 0.002697I
b = −0.699224 + 0.714437I
−0.744870 − 0.584560I 0.202019 + 0.958990I
u = −0.936602 + 0.118293I
a = −0.318743 − 0.218959I
b = −0.620116 − 0.388367I
−0.08204 − 3.21276I 0.42949 + 6.66311I
u = −0.936602 − 0.118293I
a = −0.318743 + 0.218959I
b = −0.620116 + 0.388367I
−0.08204 + 3.21276I 0.42949 − 6.66311I
u = −0.473630 + 0.961275I
a = 0.323168 − 0.723326I
b = 0.711410 + 0.630048I
−5.28661 − 1.41187I −2.51524 + 3.36613I
u = −0.473630 − 0.961275I
a = 0.323168 + 0.723326I
b = 0.711410 − 0.630048I
−5.28661 + 1.41187I −2.51524 − 3.36613I
u = 0.449533 + 0.975399I
a = −0.509462 + 0.216523I
b = −0.517652 − 1.021650I
−0.28876 − 5.04770I 1.29595 + 6.45390I
u = 0.449533 − 0.975399I
a = −0.509462 − 0.216523I
b = −0.517652 + 1.021650I
−0.28876 + 5.04770I 1.29595 − 6.45390I
u = 0.815974 + 0.347535I
a = 1.49469 + 2.72833I
b = 0.468151 − 0.953658I
−1.11120 + 2.63706I 2.56560 − 6.52941I
u = 0.815974 − 0.347535I
a = 1.49469 − 2.72833I
b = 0.468151 + 0.953658I
−1.11120 − 2.63706I 2.56560 + 6.52941I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697235 + 0.535365I
a = 0.315606 + 0.602693I
b = 0.954432 − 0.777792I
−9.12170 + 4.13349I −4.37982 − 7.84583I
u = 0.697235 − 0.535365I
a = 0.315606 − 0.602693I
b = 0.954432 + 0.777792I
−9.12170 − 4.13349I −4.37982 + 7.84583I
u = 0.953458 + 0.598229I
a = 0.949740 − 0.081078I
b = −0.813160 − 0.543764I
−8.29977 + 0.42603I −4.99238 − 0.29759I
u = 0.953458 − 0.598229I
a = 0.949740 + 0.081078I
b = −0.813160 + 0.543764I
−8.29977 − 0.42603I −4.99238 + 0.29759I
u = −0.024298 + 0.854586I
a = −0.679350 − 0.293209I
b = −0.329331 + 0.976215I
0.969303 + 1.022450I 4.86262 − 1.22345I
u = −0.024298 − 0.854586I
a = −0.679350 + 0.293209I
b = −0.329331 − 0.976215I
0.969303 − 1.022450I 4.86262 + 1.22345I
u = 0.232434 + 1.128490I
a = 0.171601 − 0.671528I
b = 0.613539 + 0.992173I
−4.19193 − 3.67253I −1.22751 + 2.31471I
u = 0.232434 − 1.128490I
a = 0.171601 + 0.671528I
b = 0.613539 − 0.992173I
−4.19193 + 3.67253I −1.22751 − 2.31471I
u = −1.083130 + 0.424102I
a = −0.51370 + 2.44482I
b = −0.653200 − 1.057010I
−6.75514 − 5.91277I −2.21392 + 5.18403I
u = −1.083130 − 0.424102I
a = −0.51370 − 2.44482I
b = −0.653200 + 1.057010I
−6.75514 + 5.91277I −2.21392 − 5.18403I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643203 + 1.007070I
a = 0.426141 + 0.701622I
b = 0.850297 − 0.462719I
−7.77183 − 3.25304I −5.27621 + 1.64998I
u = 0.643203 − 1.007070I
a = 0.426141 − 0.701622I
b = 0.850297 + 0.462719I
−7.77183 + 3.25304I −5.27621 − 1.64998I
u = −1.089060 + 0.646090I
a = 0.400714 + 0.040363I
b = −0.874960 + 0.339779I
−3.37785 − 4.34752I −0.97473 + 2.40737I
u = −1.089060 − 0.646090I
a = 0.400714 − 0.040363I
b = −0.874960 − 0.339779I
−3.37785 + 4.34752I −0.97473 − 2.40737I
u = −0.538092 + 1.149580I
a = 0.144817 + 0.630742I
b = 0.646329 − 1.107890I
−5.83333 + 8.80963I −2.37769 − 6.43347I
u = −0.538092 − 1.149580I
a = 0.144817 − 0.630742I
b = 0.646329 + 1.107890I
−5.83333 − 8.80963I −2.37769 + 6.43347I
u = −1.174390 + 0.484424I
a = 0.96122 − 1.70050I
b = 0.536868 + 1.111540I
4.31618 − 5.59634I 6.06047 + 4.87396I
u = −1.174390 − 0.484424I
a = 0.96122 + 1.70050I
b = 0.536868 − 1.111540I
4.31618 + 5.59634I 6.06047 − 4.87396I
u = −1.266720 + 0.096929I
a = −0.02752 + 1.80946I
b = 0.280639 − 1.152600I
6.04456 + 2.16278I 8.79757 − 2.89733I
u = −1.266720 − 0.096929I
a = −0.02752 − 1.80946I
b = 0.280639 + 1.152600I
6.04456 − 2.16278I 8.79757 + 2.89733I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595443 + 0.355867I
a = 0.228768 + 0.590040I
b = 0.871755 − 0.998829I
−8.47083 + 2.48602I −1.45090 + 5.51453I
u = −0.595443 − 0.355867I
a = 0.228768 − 0.590040I
b = 0.871755 + 0.998829I
−8.47083 − 2.48602I −1.45090 − 5.51453I
u = 1.264420 + 0.377230I
a = −0.33373 − 1.58630I
b = 0.170537 + 1.148410I
5.10728 + 3.38490I 7.93360 − 3.33034I
u = 1.264420 − 0.377230I
a = −0.33373 + 1.58630I
b = 0.170537 − 1.148410I
5.10728 − 3.38490I 7.93360 + 3.33034I
u = 1.117610 + 0.748018I
a = 0.293611 − 0.238740I
b = −1.007530 − 0.362892I
−6.21564 + 9.65095I 0. − 5.84415I
u = 1.117610 − 0.748018I
a = 0.293611 + 0.238740I
b = −1.007530 + 0.362892I
−6.21564 − 9.65095I 0. + 5.84415I
u = 1.175850 + 0.667191I
a = 1.12100 + 1.42946I
b = 0.621576 − 1.109980I
1.99477 + 11.04250I 0. − 8.76647I
u = 1.175850 − 0.667191I
a = 1.12100 − 1.42946I
b = 0.621576 + 1.109980I
1.99477 − 11.04250I 0. + 8.76647I
u = −0.399787 + 0.467256I
a = −1.67834 − 1.67643I
b = 0.114999 − 0.542444I
−1.97039 + 0.78230I −5.45253 + 2.09256I
u = −0.399787 − 0.467256I
a = −1.67834 + 1.67643I
b = 0.114999 + 0.542444I
−1.97039 − 0.78230I −5.45253 − 2.09256I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27251 + 0.63129I
a = −0.67000 − 1.80811I
b = −0.616422 + 1.164310I
−0.91239 + 9.84583I 0
u = 1.27251 − 0.63129I
a = −0.67000 + 1.80811I
b = −0.616422 − 1.164310I
−0.91239 − 9.84583I 0
u = −1.22350 + 0.76980I
a = −0.88939 + 1.67143I
b = −0.662987 − 1.206930I
−3.6196 − 15.6826I 0
u = −1.22350 − 0.76980I
a = −0.88939 − 1.67143I
b = −0.662987 + 1.206930I
−3.6196 + 15.6826I 0
u = 0.257076 + 0.420882I
a = −0.990050 − 0.003127I
b = −0.223361 + 0.753004I
0.426067 + 1.178950I 4.63590 − 6.06198I
u = 0.257076 − 0.420882I
a = −0.990050 + 0.003127I
b = −0.223361 − 0.753004I
0.426067 − 1.178950I 4.63590 + 6.06198I
u = 1.51280 + 0.01490I
a = 0.22721 − 1.58372I
b = −0.435520 + 0.951672I
2.35249 + 4.91231I 0
u = 1.51280 − 0.01490I
a = 0.22721 + 1.58372I
b = −0.435520 − 0.951672I
2.35249 − 4.91231I 0
u = −1.49474 + 0.29701I
a = 0.409690 − 1.327970I
b = −0.387075 + 0.830148I
1.85024 − 1.51739I 0
u = −1.49474 − 0.29701I
a = 0.409690 + 1.327970I
b = −0.387075 − 0.830148I
1.85024 + 1.51739I 0
9
II. I
u
2
= h−36u
5
a
2
+ 36u
5
+ · · · − 22a
2
+ 22, 2u
5
a
2
+ u
5
a + · · · − a − 5, u
6
+
u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
11
=
a
0.127208a
2
u
5
− 0.127208u
5
+ ··· + 0.0777385a
2
− 0.0777385
a
6
=
−0.127208a
2
u
5
+ 0.127208u
5
+ ··· + a + 2.07774
−0.127208a
2
u
5
+ 0.127208u
5
+ ··· − 0.0777385a
2
+ 0.0777385
a
9
=
−a
−0.127208a
2
u
5
+ 0.127208u
5
+ ··· − 0.0777385a
2
+ 0.0777385
a
5
=
1
0
a
10
=
0.127208a
2
u
5
− 0.127208u
5
+ ··· + a − 0.0777385
0.127208a
2
u
5
− 0.127208u
5
+ ··· + 0.0777385a
2
− 0.0777385
a
1
=
u
2
− 1
u
2
a
2
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
2
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
c
3
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
c
5
, c
6
, c
8
c
9
, c
10
u
18
+ 6u
16
+ ··· − u + 1
c
11
u
18
− 12u
17
+ ··· − 3u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
c
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
c
5
, c
6
, c
8
c
9
, c
10
y
18
+ 12y
17
+ ··· + 3y + 1
c
11
y
18
− 12y
17
+ ··· + 15y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.158981 + 0.210049I
b = 0.700352 + 0.245687I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 + 0.295542I
a = −1.28821 − 1.33402I
b = −0.461864 + 1.032610I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 + 0.295542I
a = −0.09163 + 2.11799I
b = −0.238488 − 1.278300I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 − 0.295542I
a = −0.158981 − 0.210049I
b = 0.700352 − 0.245687I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.002190 − 0.295542I
a = −1.28821 + 1.33402I
b = −0.461864 − 1.032610I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.002190 − 0.295542I
a = −0.09163 − 2.11799I
b = −0.238488 + 1.278300I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.428243 + 0.664531I
a = −1.404780 + 0.070635I
b = −0.414097 − 0.427367I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = 0.19096 − 1.40605I
b = 0.339178 − 0.790848I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = 2.53589 − 1.57875I
b = 0.074919 + 1.218220I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.428243 − 0.664531I
a = −1.404780 − 0.070635I
b = −0.414097 + 0.427367I
−1.89061 − 0.92430I −3.71672 + 0.79423I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = 0.19096 + 1.40605I
b = 0.339178 + 0.790848I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = 2.53589 + 1.57875I
b = 0.074919 − 1.218220I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.073950 + 0.558752I
a = −1.16030 + 0.89772I
b = −0.624190 − 0.955200I
− 5.69302I 0. + 5.51057I
u = −1.073950 + 0.558752I
a = 0.008039 − 0.301999I
b = 0.798654 − 0.441445I
− 5.69302I 0. + 5.51057I
u = −1.073950 + 0.558752I
a = 0.36901 − 1.71323I
b = −0.174464 + 1.396650I
− 5.69302I 0. + 5.51057I
u = −1.073950 − 0.558752I
a = −1.16030 − 0.89772I
b = −0.624190 + 0.955200I
5.69302I 0. − 5.51057I
u = −1.073950 − 0.558752I
a = 0.008039 + 0.301999I
b = 0.798654 + 0.441445I
5.69302I 0. − 5.51057I
u = −1.073950 − 0.558752I
a = 0.36901 + 1.71323I
b = −0.174464 − 1.396650I
5.69302I 0. − 5.51057I
14
III. I
u
3
= h−u
5
+ 2u
3
+ b − u, u
4
+ 2u
3
− 3u
2
+ a − 3u + 2, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
11
=
−u
4
− 2u
3
+ 3u
2
+ 3u − 2
u
5
− 2u
3
+ u
a
6
=
u
5
+ u
4
− 4u
3
− 3u
2
+ 4u + 2
1
a
9
=
u
5
− u
4
− 4u
3
+ 3u
2
+ 4u − 1
u
5
− 2u
3
− u
2
+ u
a
5
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
10
=
u
5
− u
4
− 4u
3
+ 3u
2
+ 4u − 2
u
5
− 2u
3
+ u
a
1
=
−u
5
+ 2u
3
− u
0
a
2
=
−u
u
a
2
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 8u
2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
2
c
2
(u
3
+ u
2
+ 2u + 1)
2
c
3
, c
7
u
6
− 3u
4
+ 2u
2
+ 1
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
8
c
9
, c
10
(u
2
+ 1)
3
c
11
(u − 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
2
(y
3
+ 3y
2
+ 2y − 1)
2
c
3
, c
7
(y
3
− 3y
2
+ 2y + 1)
2
c
5
, c
6
, c
8
c
9
, c
10
(y + 1)
6
c
11
(y − 1)
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = 0.35722 − 1.72238I
b = 1.000000I
3.02413 + 2.82812I 3.50976 − 2.97945I
u = 1.307140 − 0.215080I
a = 0.35722 + 1.72238I
b = − 1.000000I
3.02413 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 + 0.215080I
a = 0.72238 − 1.35722I
b = 1.000000I
3.02413 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 − 0.215080I
a = 0.72238 + 1.35722I
b = − 1.000000I
3.02413 + 2.82812I 3.50976 − 2.97945I
u = 0.569840I
a = −3.07960 + 2.07960I
b = 1.000000I
−1.11345 −3.01950
u = − 0.569840I
a = −3.07960 − 2.07960I
b = − 1.000000I
−1.11345 −3.01950
18
IV. I
v
1
= ha, −2v
3
+ 3v
2
+ 4b − 8v + 3, 2v
4
− v
3
+ 5v
2
+ v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
v
0
a
11
=
0
1
2
v
3
−
3
4
v
2
+ 2v −
3
4
a
6
=
1
3
2
v
3
−
5
4
v
2
+
7
2
v +
1
4
a
9
=
−
3
2
v
3
+
5
4
v
2
−
7
2
v +
3
4
v
2
−
1
2
v +
5
2
a
5
=
−
3
2
v
3
+
1
4
v
2
− 3v −
7
4
−2v
3
+ v
2
− 5v − 1
a
10
=
1
2
v
3
−
3
4
v
2
+ 2v −
3
4
1
2
v
3
−
3
4
v
2
+ 2v −
3
4
a
1
=
3
2
v
3
−
1
4
v
2
+ 3v +
7
4
2v
3
− v
2
+ 5v + 1
a
2
=
3
2
v
3
−
1
4
v
2
+ 4v +
7
4
2v
3
− v
2
+ 5v + 1
a
2
=
3
2
v
3
−
1
4
v
2
+ 4v +
7
4
2v
3
− v
2
+ 5v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6v
3
+ 4v
2
− 12v − 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
7
u
4
c
5
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
6
u
4
+ u
3
+ u
2
+ 1
c
8
, c
9
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
10
u
4
− u
3
+ u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
8
, c
9
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
6
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.130534 + 0.427872I
a = 0
b = −0.851808 + 0.911292I
−8.43568 + 3.16396I −1.51454 − 5.24252I
v = −0.130534 − 0.427872I
a = 0
b = −0.851808 − 0.911292I
−8.43568 − 3.16396I −1.51454 + 5.24252I
v = 0.38053 + 1.53420I
a = 0
b = 0.351808 + 0.720342I
−1.43393 − 1.41510I 0.38954 + 3.92814I
v = 0.38053 − 1.53420I
a = 0
b = 0.351808 − 0.720342I
−1.43393 + 1.41510I 0.38954 − 3.92814I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
(u
3
+ u
2
− 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
50
− 4u
49
+ ··· + 3u + 4)
c
2
(u + 1)
4
(u
3
+ u
2
+ 2u + 1)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
· (u
50
+ 24u
49
+ ··· − 255u + 16)
c
3
, c
7
u
4
(u
6
− 3u
4
+ 2u
2
+ 1)(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
· (u
50
− 2u
49
+ ··· − 80u + 64)
c
4
(u + 1)
4
(u
3
− u
2
+ 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
50
− 4u
49
+ ··· + 3u + 4)
c
5
((u
2
+ 1)
3
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
18
+ 6u
16
+ ··· − u + 1)
· (u
50
+ 2u
49
+ ··· + 76u + 17)
c
6
((u
2
+ 1)
3
)(u
4
+ u
3
+ u
2
+ 1)(u
18
+ 6u
16
+ ··· − u + 1)
· (u
50
+ 2u
49
+ ··· + 72u + 17)
c
8
, c
9
((u
2
+ 1)
3
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
18
+ 6u
16
+ ··· − u + 1)
· (u
50
+ 2u
49
+ ··· + 76u + 17)
c
10
((u
2
+ 1)
3
)(u
4
− u
3
+ u
2
+ 1)(u
18
+ 6u
16
+ ··· − u + 1)
· (u
50
+ 2u
49
+ ··· + 72u + 17)
c
11
((u − 1)
6
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
18
− 12u
17
+ ··· − 3u + 1)
· (u
50
− 20u
49
+ ··· − 4370u + 289)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y − 1)
4
(y
3
− y
2
+ 2y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
50
− 24y
49
+ ··· + 255y + 16)
c
2
(y − 1)
4
(y
3
+ 3y
2
+ 2y − 1)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (y
50
+ 8y
49
+ ··· + 29791y + 256)
c
3
, c
7
y
4
(y
3
− 3y
2
+ 2y + 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
50
− 24y
49
+ ··· − 19712y + 4096)
c
5
, c
8
, c
9
((y + 1)
6
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
18
+ 12y
17
+ ··· + 3y + 1)
· (y
50
+ 52y
49
+ ··· − 846y + 289)
c
6
, c
10
((y + 1)
6
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
18
+ 12y
17
+ ··· + 3y + 1)
· (y
50
+ 20y
49
+ ··· + 4370y + 289)
c
11
((y − 1)
6
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
18
− 12y
17
+ ··· + 15y + 1)
· (y
50
+ 28y
49
+ ··· − 180694y + 83521)
24
