12a
1041
(K12a
1041
)
A knot diagram
1
Linearized knot diagam
4 7 8 12 1 11 10 6 2 3 9 5
Solving Sequence
1,6 5,9
8 12 4 2 3 11 7 10
c
5
c
8
c
12
c
4
c
1
c
3
c
11
c
6
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1038957476023u
54
− 8812866915448u
53
+ ··· + 12177825868b + 10129039394368,
− 1082675116975u
54
− 10377141014923u
53
+ ··· + 12177825868a + 22705250521701,
u
55
+ 10u
54
+ ··· + 28u − 16i
I
u
2
= h−2.57266 × 10
16
a
3
u
26
+ 5.62861 × 10
16
a
2
u
26
+ ··· − 4.26253 × 10
17
a + 6.73935 × 10
17
,
− 3u
26
a
2
+ 14u
26
a + ··· + 26a + 20, u
27
− 2u
26
+ ··· − 4u
2
− 1i
I
u
3
= h91u
26
− 160u
25
+ ··· + 6b − 74, −185u
26
+ 296u
25
+ ··· + 6a + 154, u
27
− 3u
26
+ ··· + 4u + 1i
I
u
4
= hb + a − 1, a
2
− a + 1, u + 1i
I
u
5
= hb
2
− b + 1, a + 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 194 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−1.04 × 10
12
u
54
− 8.81 × 10
12
u
53
+ · · · + 1.22 × 10
10
b + 1.01 ×
10
13
, −1.08 × 10
12
u
54
− 1.04 × 10
13
u
53
+ · · · + 1.22 × 10
10
a + 2.27 ×
10
13
, u
55
+ 10u
54
+ · · · + 28u − 16i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
9
=
88.9055u
54
+ 852.134u
53
+ ··· + 5279.95u − 1864.47
85.3155u
54
+ 723.681u
53
+ ··· + 1897.57u − 831.761
a
8
=
174.221u
54
+ 1575.82u
53
+ ··· + 7177.52u − 2696.24
85.3155u
54
+ 723.681u
53
+ ··· + 1897.57u − 831.761
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−269.600u
54
− 2341.42u
53
+ ··· − 7855.04u + 3188.79
88.0029u
54
+ 793.741u
53
+ ··· + 3533.07u − 1332.28
a
11
=
−61.9160u
54
− 496.097u
53
+ ··· − 400.409u + 305.700
83.3237u
54
+ 724.917u
53
+ ··· + 2398.06u − 978.347
a
7
=
−164.576u
54
− 1460.92u
53
+ ··· − 6253.70u + 2370.92
4.37695u
54
+ 14.4846u
53
+ ··· − 224.195u + 75.8068
a
10
=
323.741u
54
+ 2866.18u
53
+ ··· + 11307.7u − 4391.19
137.759u
54
+ 1171.25u
53
+ ··· + 3250.14u − 1393.09
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1497825036746
3044456467
u
54
−
26024094545549
6088912934
u
53
+ ··· −
46065090876200
3044456467
u +
18318351621698
3044456467
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
− 33u
54
+ ··· + 47308u − 3536
c
2
, c
10
u
55
+ u
54
+ ··· + u − 1
c
3
, c
9
u
55
− u
54
+ ··· − 2u + 17
c
4
, c
5
, c
12
u
55
+ 10u
54
+ ··· + 28u − 16
c
6
u
55
− 48u
54
+ ··· + 1543503872u − 67108864
c
7
u
55
− 37u
54
+ ··· + 6u − 4
c
8
, c
11
u
55
+ 3u
54
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
− y
54
+ ··· − 122155344y −12503296
c
2
, c
10
y
55
− 11y
54
+ ··· + 19y −1
c
3
, c
9
y
55
− 21y
54
+ ··· + 5512y −289
c
4
, c
5
, c
12
y
55
− 50y
54
+ ··· − 2256y −256
c
6
y
55
+ 6y
54
+ ··· + 11258999068426240y −4503599627370496
c
7
y
55
− 11y
54
+ ··· + 460y −16
c
8
, c
11
y
55
+ 15y
54
+ ··· + 31y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.865135 + 0.489946I
a = −0.009635 + 0.729784I
b = 0.989454 − 0.989505I
−3.36781 + 11.67190I 0
u = 0.865135 − 0.489946I
a = −0.009635 − 0.729784I
b = 0.989454 + 0.989505I
−3.36781 − 11.67190I 0
u = 0.194788 + 0.987371I
a = 0.233850 + 0.082360I
b = 0.286557 − 0.259724I
−0.14104 + 4.95333I 0
u = 0.194788 − 0.987371I
a = 0.233850 − 0.082360I
b = 0.286557 + 0.259724I
−0.14104 − 4.95333I 0
u = 0.687485 + 0.564759I
a = −0.406895 − 0.392120I
b = −0.183677 + 0.875601I
1.19181 + 3.04870I 0. − 5.13971I
u = 0.687485 − 0.564759I
a = −0.406895 + 0.392120I
b = −0.183677 − 0.875601I
1.19181 − 3.04870I 0. + 5.13971I
u = 1.084940 + 0.286119I
a = 0.057965 + 0.485473I
b = 0.313932 − 1.110980I
2.57129 − 3.17552I 0
u = 1.084940 − 0.286119I
a = 0.057965 − 0.485473I
b = 0.313932 + 1.110980I
2.57129 + 3.17552I 0
u = 1.123340 + 0.120496I
a = 0.252541 + 0.419449I
b = −0.434609 − 1.093190I
−2.08272 − 4.14763I 0
u = 1.123340 − 0.120496I
a = 0.252541 − 0.419449I
b = −0.434609 + 1.093190I
−2.08272 + 4.14763I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.019870 + 0.509233I
a = −0.344470 − 0.036710I
b = 0.563453 + 0.599317I
−2.75248 − 10.11890I 0
u = 1.019870 − 0.509233I
a = −0.344470 + 0.036710I
b = 0.563453 − 0.599317I
−2.75248 + 10.11890I 0
u = 0.331802 + 0.792246I
a = 0.739296 − 0.448884I
b = −0.454290 − 1.057760I
2.44525 − 7.66184I −1.72043 + 10.68695I
u = 0.331802 − 0.792246I
a = 0.739296 + 0.448884I
b = −0.454290 + 1.057760I
2.44525 + 7.66184I −1.72043 − 10.68695I
u = 0.270945 + 0.813281I
a = −0.650696 + 1.064390I
b = 1.12841 + 1.15345I
−1.4883 − 16.2749I −6.00000 + 9.94367I
u = 0.270945 − 0.813281I
a = −0.650696 − 1.064390I
b = 1.12841 − 1.15345I
−1.4883 + 16.2749I −6.00000 − 9.94367I
u = 0.287468 + 0.722004I
a = 0.908760 − 1.060260I
b = −1.06824 − 1.19365I
−1.19182 − 7.45004I −11.7611 + 11.5246I
u = 0.287468 − 0.722004I
a = 0.908760 + 1.060260I
b = −1.06824 + 1.19365I
−1.19182 + 7.45004I −11.7611 − 11.5246I
u = 0.135846 + 0.737771I
a = −0.709220 + 0.909769I
b = 0.576960 + 1.020220I
5.43093 − 0.61722I 1.76007 + 0.47509I
u = 0.135846 − 0.737771I
a = −0.709220 − 0.909769I
b = 0.576960 − 1.020220I
5.43093 + 0.61722I 1.76007 − 0.47509I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.633695 + 0.400897I
a = −0.051443 − 1.043900I
b = −0.903902 + 0.959696I
−2.55209 + 3.51896I −13.4984 − 8.4809I
u = 0.633695 − 0.400897I
a = −0.051443 + 1.043900I
b = −0.903902 − 0.959696I
−2.55209 − 3.51896I −13.4984 + 8.4809I
u = −1.240380 + 0.166032I
a = −1.44156 − 0.30688I
b = 0.465537 − 0.271371I
−1.87491 + 0.84683I 0
u = −1.240380 − 0.166032I
a = −1.44156 + 0.30688I
b = 0.465537 + 0.271371I
−1.87491 − 0.84683I 0
u = −1.233550 + 0.217515I
a = 0.435655 + 1.180210I
b = −0.481519 − 0.145146I
−2.88656 + 0.31842I 0
u = −1.233550 − 0.217515I
a = 0.435655 − 1.180210I
b = −0.481519 + 0.145146I
−2.88656 − 0.31842I 0
u = −1.299370 + 0.205216I
a = 2.76669 + 0.09017I
b = −0.989285 + 0.876437I
−2.98388 + 4.72159I 0
u = −1.299370 − 0.205216I
a = 2.76669 − 0.09017I
b = −0.989285 − 0.876437I
−2.98388 − 4.72159I 0
u = 1.316210 + 0.209610I
a = 0.098140 − 0.465825I
b = −0.64955 + 1.32493I
−3.15392 − 0.78981I 0
u = 1.316210 − 0.209610I
a = 0.098140 + 0.465825I
b = −0.64955 − 1.32493I
−3.15392 + 0.78981I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.322710 + 0.233818I
a = 0.062155 + 0.355937I
b = 0.115827 − 1.127050I
−2.84146 − 5.10387I 0
u = 1.322710 − 0.233818I
a = 0.062155 − 0.355937I
b = 0.115827 + 1.127050I
−2.84146 + 5.10387I 0
u = −0.075487 + 0.624794I
a = −0.651671 + 0.844506I
b = 0.148112 + 0.734294I
1.54361 + 2.01006I −0.20716 − 4.90637I
u = −0.075487 − 0.624794I
a = −0.651671 − 0.844506I
b = 0.148112 − 0.734294I
1.54361 − 2.01006I −0.20716 + 4.90637I
u = −1.343010 + 0.298025I
a = −1.92899 − 0.10958I
b = 0.772361 − 0.928529I
0.77382 + 4.35654I 0
u = −1.343010 − 0.298025I
a = −1.92899 + 0.10958I
b = 0.772361 + 0.928529I
0.77382 − 4.35654I 0
u = −0.014301 + 0.558017I
a = 0.82154 − 1.89062I
b = −0.757428 − 1.060680I
1.07100 − 1.97635I −0.94464 + 3.33920I
u = −0.014301 − 0.558017I
a = 0.82154 + 1.89062I
b = −0.757428 + 1.060680I
1.07100 + 1.97635I −0.94464 − 3.33920I
u = −1.41743 + 0.28838I
a = 2.38231 + 0.04181I
b = −1.23358 + 1.23929I
−6.63060 + 11.13070I 0
u = −1.41743 − 0.28838I
a = 2.38231 − 0.04181I
b = −1.23358 − 1.23929I
−6.63060 − 11.13070I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42060 + 0.32988I
a = −2.22150 − 0.28707I
b = 1.25995 − 1.20900I
−6.8735 + 20.4083I 0
u = −1.42060 − 0.32988I
a = −2.22150 + 0.28707I
b = 1.25995 + 1.20900I
−6.8735 − 20.4083I 0
u = 1.46282
a = 0.172629
b = −0.621923
−7.34651 0
u = −1.47133 + 0.11388I
a = 1.16767 + 1.39875I
b = −1.104080 − 0.693535I
−9.23079 − 1.76541I 0
u = −1.47133 − 0.11388I
a = 1.16767 − 1.39875I
b = −1.104080 + 0.693535I
−9.23079 + 1.76541I 0
u = −1.44448 + 0.31710I
a = 1.54595 − 0.30583I
b = −0.653917 + 1.091600I
−3.22867 + 11.69550I 0
u = −1.44448 − 0.31710I
a = 1.54595 + 0.30583I
b = −0.653917 − 1.091600I
−3.22867 − 11.69550I 0
u = −0.505754
a = −0.901720
b = −0.225400
−1.05728 −9.58490
u = −1.51220 + 0.01188I
a = −1.49575 − 0.82415I
b = 1.178150 + 0.602251I
−11.4039 − 10.6429I 0
u = −1.51220 − 0.01188I
a = −1.49575 + 0.82415I
b = 1.178150 − 0.602251I
−11.4039 + 10.6429I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51637 + 0.31039I
a = −0.593785 + 0.047436I
b = 0.377802 − 0.407209I
−6.09485 + 0.24577I 0
u = −1.51637 − 0.31039I
a = −0.593785 − 0.047436I
b = 0.377802 + 0.407209I
−6.09485 − 0.24577I 0
u = 0.092579 + 0.436564I
a = −1.46650 − 0.13148I
b = −0.199189 + 0.747006I
0.86993 + 1.84137I −0.07341 − 2.74381I
u = 0.092579 − 0.436564I
a = −1.46650 + 0.13148I
b = −0.199189 − 0.747006I
0.86993 − 1.84137I −0.07341 + 2.74381I
u = −1.71364
a = 0.228279
b = −0.279170
−6.84786 0
10
II. I
u
2
= h−2.57 × 10
16
a
3
u
26
+ 5.63 × 10
16
a
2
u
26
+ · · · − 4.26 × 10
17
a + 6.74 ×
10
17
, −3u
26
a
2
+ 14u
26
a + · · · + 26a + 20, u
27
− 2u
26
+ · · · − 4u
2
− 1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
9
=
a
0.176060a
3
u
26
− 0.385193a
2
u
26
+ ··· + 2.91706a − 4.61207
a
8
=
0.176060a
3
u
26
− 0.385193a
2
u
26
+ ··· + 3.91706a − 4.61207
0.176060a
3
u
26
− 0.385193a
2
u
26
+ ··· + 2.91706a − 4.61207
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
0.443539a
3
u
26
+ 0.0267099a
2
u
26
+ ··· − 5.19958a + 1.23689
0.115832a
3
u
26
+ 0.0266748a
2
u
26
+ ··· − 1.26000a − 0.651394
a
11
=
0.548648a
3
u
26
+ 0.0825110a
2
u
26
+ ··· − 2.35342a + 0.892170
−0.182292a
3
u
26
+ 0.233760a
2
u
26
+ ··· − 0.843751a − 0.545393
a
7
=
−0.220946a
3
u
26
− 0.143290a
2
u
26
+ ··· + 3.15493a + 1.19899
−0.182292a
3
u
26
+ 0.233760a
2
u
26
+ ··· − 0.843751a + 0.454607
a
10
=
0.183066a
3
u
26
− 0.934784a
2
u
26
+ ··· + 3.70027a + 0.243925
0.225356a
3
u
26
− 0.510726a
2
u
26
+ ··· + 1.33445a − 3.13156
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
26637209800522575
36531051645049508
u
26
a
3
+
17079032472250979
18265525822524754
u
26
a
2
+ ··· −
30823107423947660
9132762911262377
a −
335412553972972235
36531051645049508
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
27
+ 9u
26
+ ··· + 37u + 8)
4
c
2
, c
10
u
108
+ 4u
107
+ ··· + 5u + 1
c
3
, c
9
u
108
+ 2u
107
+ ··· − 100507749u + 41406721
c
4
, c
5
, c
12
(u
27
− 2u
26
+ ··· − 4u
2
− 1)
4
c
6
(u
2
+ u + 1)
54
c
7
(u
27
+ 13u
26
+ ··· − u − 2)
4
c
8
, c
11
u
108
+ 3u
107
+ ··· − 1614u + 97
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
27
+ 5y
26
+ ··· − 375y − 64)
4
c
2
, c
10
y
108
+ 38y
107
+ ··· − 117y + 1
c
3
, c
9
y
108
− 38y
107
+ ··· − 55012811704519381y + 1714516543971841
c
4
, c
5
, c
12
(y
27
− 24y
26
+ ··· − 8y − 1)
4
c
6
(y
2
+ y + 1)
54
c
7
(y
27
− 3y
26
+ ··· + 53y − 4)
4
c
8
, c
11
y
108
− 31y
107
+ ··· − 144882y + 9409
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895940 + 0.471258I
a = −0.316996 − 0.787472I
b = 0.919277 + 0.629136I
−2.77585 − 2.71444I −19.8481 + 8.7534I
u = −0.895940 + 0.471258I
a = 0.271094 + 0.389251I
b = −0.720925 + 0.346701I
−2.77585 + 1.34533I −19.8481 + 1.8252I
u = −0.895940 + 0.471258I
a = −0.140733 + 0.416627I
b = −0.925214 − 0.916885I
−2.77585 − 2.71444I −19.8481 + 8.7534I
u = −0.895940 + 0.471258I
a = −0.363391 + 0.192576I
b = 0.474696 − 0.197685I
−2.77585 + 1.34533I −19.8481 + 1.8252I
u = −0.895940 − 0.471258I
a = −0.316996 + 0.787472I
b = 0.919277 − 0.629136I
−2.77585 + 2.71444I −19.8481 − 8.7534I
u = −0.895940 − 0.471258I
a = 0.271094 − 0.389251I
b = −0.720925 − 0.346701I
−2.77585 − 1.34533I −19.8481 − 1.8252I
u = −0.895940 − 0.471258I
a = −0.140733 − 0.416627I
b = −0.925214 + 0.916885I
−2.77585 + 2.71444I −19.8481 − 8.7534I
u = −0.895940 − 0.471258I
a = −0.363391 − 0.192576I
b = 0.474696 + 0.197685I
−2.77585 − 1.34533I −19.8481 − 1.8252I
u = −1.100980 + 0.299749I
a = −0.842989 + 0.602127I
b = −0.074853 − 0.969653I
−0.748134 + 1.194470I −2.37245 + 1.25863I
u = −1.100980 + 0.299749I
a = −0.080788 − 1.306890I
b = 1.09923 + 1.05154I
−0.74813 − 2.86529I −2.37245 + 8.18684I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.100980 + 0.299749I
a = −0.587687 + 0.078440I
b = −0.139835 + 0.439686I
−0.748134 + 1.194470I −2.37245 + 1.25863I
u = −1.100980 + 0.299749I
a = 0.206737 − 0.272392I
b = −0.532919 − 0.972485I
−0.74813 − 2.86529I −2.37245 + 8.18684I
u = −1.100980 − 0.299749I
a = −0.842989 − 0.602127I
b = −0.074853 + 0.969653I
−0.748134 − 1.194470I −2.37245 − 1.25863I
u = −1.100980 − 0.299749I
a = −0.080788 + 1.306890I
b = 1.09923 − 1.05154I
−0.74813 + 2.86529I −2.37245 − 8.18684I
u = −1.100980 − 0.299749I
a = −0.587687 − 0.078440I
b = −0.139835 − 0.439686I
−0.748134 − 1.194470I −2.37245 − 1.25863I
u = −1.100980 − 0.299749I
a = 0.206737 + 0.272392I
b = −0.532919 + 0.972485I
−0.74813 + 2.86529I −2.37245 − 8.18684I
u = −0.258632 + 0.812574I
a = −0.538970 − 0.790372I
b = 1.115490 − 0.762972I
−0.78316 + 7.28385I −12.4696 − 13.4772I
u = −0.258632 + 0.812574I
a = 0.467701 + 1.208680I
b = −1.01213 + 1.14733I
−0.78316 + 7.28385I −12.4696 − 13.4772I
u = −0.258632 + 0.812574I
a = −0.232781 − 0.635527I
b = 0.401028 − 0.304384I
−0.78316 + 3.22409I −12.46955 − 6.54904I
u = −0.258632 + 0.812574I
a = −0.093848 + 0.364653I
b = −0.785574 + 0.201718I
−0.78316 + 3.22409I −12.46955 − 6.54904I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258632 − 0.812574I
a = −0.538970 + 0.790372I
b = 1.115490 + 0.762972I
−0.78316 − 7.28385I −12.4696 + 13.4772I
u = −0.258632 − 0.812574I
a = 0.467701 − 1.208680I
b = −1.01213 − 1.14733I
−0.78316 − 7.28385I −12.4696 + 13.4772I
u = −0.258632 − 0.812574I
a = −0.232781 + 0.635527I
b = 0.401028 + 0.304384I
−0.78316 − 3.22409I −12.46955 + 6.54904I
u = −0.258632 − 0.812574I
a = −0.093848 − 0.364653I
b = −0.785574 − 0.201718I
−0.78316 − 3.22409I −12.46955 + 6.54904I
u = −0.135996 + 0.743408I
a = −0.909197 − 0.188369I
b = 0.154931 − 0.189391I
2.15459 + 2.64686I −0.08758 − 3.62009I
u = −0.135996 + 0.743408I
a = −0.023813 − 1.077820I
b = 1.48580 − 1.11777I
2.15459 + 6.70663I −0.08758 − 10.54829I
u = −0.135996 + 0.743408I
a = 0.019719 + 0.806849I
b = −0.416295 + 1.085260I
2.15459 + 2.64686I −0.08758 − 3.62009I
u = −0.135996 + 0.743408I
a = 1.00417 + 1.53889I
b = −0.579271 + 0.896181I
2.15459 + 6.70663I −0.08758 − 10.54829I
u = −0.135996 − 0.743408I
a = −0.909197 + 0.188369I
b = 0.154931 + 0.189391I
2.15459 − 2.64686I −0.08758 + 3.62009I
u = −0.135996 − 0.743408I
a = −0.023813 + 1.077820I
b = 1.48580 + 1.11777I
2.15459 − 6.70663I −0.08758 + 10.54829I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135996 − 0.743408I
a = 0.019719 − 0.806849I
b = −0.416295 − 1.085260I
2.15459 − 2.64686I −0.08758 + 3.62009I
u = −0.135996 − 0.743408I
a = 1.00417 − 1.53889I
b = −0.579271 − 0.896181I
2.15459 − 6.70663I −0.08758 + 10.54829I
u = 1.275050 + 0.128798I
a = −1.267010 − 0.118323I
b = −0.213665 + 0.986243I
−5.25746 + 0.72192I −10.02480 − 2.16737I
u = 1.275050 + 0.128798I
a = 1.68880 − 0.46838I
b = −1.271140 + 0.513073I
−5.25746 + 0.72192I −10.02480 − 2.16737I
u = 1.275050 + 0.128798I
a = 2.17374 − 1.30704I
b = −0.079746 + 0.187033I
−5.25746 + 4.78168I −10.02480 − 9.09557I
u = 1.275050 + 0.128798I
a = −2.89274 + 1.23511I
b = 2.12059 + 0.34918I
−5.25746 + 4.78168I −10.02480 − 9.09557I
u = 1.275050 − 0.128798I
a = −1.267010 + 0.118323I
b = −0.213665 − 0.986243I
−5.25746 − 0.72192I −10.02480 + 2.16737I
u = 1.275050 − 0.128798I
a = 1.68880 + 0.46838I
b = −1.271140 − 0.513073I
−5.25746 − 0.72192I −10.02480 + 2.16737I
u = 1.275050 − 0.128798I
a = 2.17374 + 1.30704I
b = −0.079746 − 0.187033I
−5.25746 − 4.78168I −10.02480 + 9.09557I
u = 1.275050 − 0.128798I
a = −2.89274 − 1.23511I
b = 2.12059 − 0.34918I
−5.25746 − 4.78168I −10.02480 + 9.09557I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426561 + 0.478609I
a = −0.804686 + 0.379765I
b = −0.996790 − 0.658673I
−2.08998 − 0.29093I −13.45580 − 2.31430I
u = −0.426561 + 0.478609I
a = −1.134850 + 0.340853I
b = 0.783400 − 0.399434I
−2.08998 + 3.76884I −13.4558 − 9.2425I
u = −0.426561 + 0.478609I
a = −0.428980 − 1.297160I
b = 0.347946 + 0.310853I
−2.08998 − 0.29093I −13.45580 − 2.31430I
u = −0.426561 + 0.478609I
a = 0.95719 + 1.18623I
b = −0.760199 + 1.135260I
−2.08998 + 3.76884I −13.4558 − 9.2425I
u = −0.426561 − 0.478609I
a = −0.804686 − 0.379765I
b = −0.996790 + 0.658673I
−2.08998 + 0.29093I −13.45580 + 2.31430I
u = −0.426561 − 0.478609I
a = −1.134850 − 0.340853I
b = 0.783400 + 0.399434I
−2.08998 − 3.76884I −13.4558 + 9.2425I
u = −0.426561 − 0.478609I
a = −0.428980 + 1.297160I
b = 0.347946 − 0.310853I
−2.08998 + 0.29093I −13.45580 + 2.31430I
u = −0.426561 − 0.478609I
a = 0.95719 − 1.18623I
b = −0.760199 − 1.135260I
−2.08998 − 3.76884I −13.4558 + 9.2425I
u = −1.361910 + 0.175704I
a = 1.43574 + 1.40559I
b = −0.719715 + 0.349547I
−7.56483 + 1.30963I −17.0249 − 2.8244I
u = −1.361910 + 0.175704I
a = −2.11646 + 0.13476I
b = 0.900281 + 0.376228I
−7.56483 − 2.75014I −17.0249 + 4.1038I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.361910 + 0.175704I
a = −2.24358 + 0.91101I
b = 0.79737 − 2.17995I
−7.56483 − 2.75014I −17.0249 + 4.1038I
u = −1.361910 + 0.175704I
a = 1.64993 + 1.84742I
b = −1.69118 − 0.91789I
−7.56483 + 1.30963I −17.0249 − 2.8244I
u = −1.361910 − 0.175704I
a = 1.43574 − 1.40559I
b = −0.719715 − 0.349547I
−7.56483 − 1.30963I −17.0249 + 2.8244I
u = −1.361910 − 0.175704I
a = −2.11646 − 0.13476I
b = 0.900281 − 0.376228I
−7.56483 + 2.75014I −17.0249 − 4.1038I
u = −1.361910 − 0.175704I
a = −2.24358 − 0.91101I
b = 0.79737 + 2.17995I
−7.56483 + 2.75014I −17.0249 − 4.1038I
u = −1.361910 − 0.175704I
a = 1.64993 − 1.84742I
b = −1.69118 + 0.91789I
−7.56483 − 1.30963I −17.0249 + 2.8244I
u = 1.346310 + 0.301034I
a = −1.134500 + 0.245507I
b = 0.368928 + 0.011255I
−2.51876 − 6.41615I −5.70105 + 4.93466I
u = 1.346310 + 0.301034I
a = 1.338540 + 0.061389I
b = −0.653810 − 1.179690I
−2.51876 − 6.41615I −5.70105 + 4.93466I
u = 1.346310 + 0.301034I
a = 2.19472 − 0.62293I
b = −0.639614 − 0.804892I
−2.51876 − 10.47590I −5.70105 + 11.86286I
u = 1.346310 + 0.301034I
a = −2.56252 + 0.64618I
b = 1.79395 + 1.14240I
−2.51876 − 10.47590I −5.70105 + 11.86286I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.346310 − 0.301034I
a = −1.134500 − 0.245507I
b = 0.368928 − 0.011255I
−2.51876 + 6.41615I −5.70105 − 4.93466I
u = 1.346310 − 0.301034I
a = 1.338540 − 0.061389I
b = −0.653810 + 1.179690I
−2.51876 + 6.41615I −5.70105 − 4.93466I
u = 1.346310 − 0.301034I
a = 2.19472 + 0.62293I
b = −0.639614 + 0.804892I
−2.51876 + 10.47590I −5.70105 − 11.86286I
u = 1.346310 − 0.301034I
a = −2.56252 − 0.64618I
b = 1.79395 − 1.14240I
−2.51876 + 10.47590I −5.70105 − 11.86286I
u = −1.361280 + 0.230867I
a = −0.60208 − 1.79313I
b = 0.375544 − 0.403549I
−6.82147 + 9.92301I −14.6204 − 12.6800I
u = −1.361280 + 0.230867I
a = 2.27373 + 0.18008I
b = −0.99764 + 1.50439I
−6.82147 + 5.86324I −14.6204 − 5.7518I
u = −1.361280 + 0.230867I
a = 2.24219 + 0.67363I
b = −1.322100 − 0.082847I
−6.82147 + 5.86324I −14.6204 − 5.7518I
u = −1.361280 + 0.230867I
a = −0.91654 − 2.54463I
b = 2.01542 + 1.70173I
−6.82147 + 9.92301I −14.6204 − 12.6800I
u = −1.361280 − 0.230867I
a = −0.60208 + 1.79313I
b = 0.375544 + 0.403549I
−6.82147 − 9.92301I −14.6204 + 12.6800I
u = −1.361280 − 0.230867I
a = 2.27373 − 0.18008I
b = −0.99764 − 1.50439I
−6.82147 − 5.86324I −14.6204 + 5.7518I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.361280 − 0.230867I
a = 2.24219 − 0.67363I
b = −1.322100 + 0.082847I
−6.82147 − 5.86324I −14.6204 + 5.7518I
u = −1.361280 − 0.230867I
a = −0.91654 + 2.54463I
b = 2.01542 − 1.70173I
−6.82147 − 9.92301I −14.6204 + 12.6800I
u = 1.392250 + 0.184425I
a = −1.00121 + 1.08496I
b = 0.343664 + 0.141207I
−7.68995 − 2.05560I −16.8022 + 0.1601I
u = 1.392250 + 0.184425I
a = 1.33824 − 1.39343I
b = −1.67000 + 0.64045I
−7.68995 − 2.05560I −16.8022 + 0.I
u = 1.392250 + 0.184425I
a = −2.08919 − 0.19656I
b = 0.950129 + 0.148939I
−7.68995 − 6.11537I −16.8022 + 7.0883I
u = 1.392250 + 0.184425I
a = 2.18781 + 0.64267I
b = −0.96390 − 1.68841I
−7.68995 − 6.11537I −16.8022 + 7.0883I
u = 1.392250 − 0.184425I
a = −1.00121 − 1.08496I
b = 0.343664 − 0.141207I
−7.68995 + 2.05560I −16.8022 − 0.1601I
u = 1.392250 − 0.184425I
a = 1.33824 + 1.39343I
b = −1.67000 − 0.64045I
−7.68995 + 2.05560I −16.8022 + 0.I
u = 1.392250 − 0.184425I
a = −2.08919 + 0.19656I
b = 0.950129 − 0.148939I
−7.68995 + 6.11537I −16.8022 − 7.0883I
u = 1.392250 − 0.184425I
a = 2.18781 − 0.64267I
b = −0.96390 + 1.68841I
−7.68995 + 6.11537I −16.8022 − 7.0883I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.162222 + 0.561060I
a = 0.969046 − 0.551992I
b = −1.208870 − 0.134733I
−1.97298 − 2.92252I −8.66900 + 6.94780I
u = 0.162222 + 0.561060I
a = 1.148280 − 0.385564I
b = 1.81040 − 1.21825I
−1.97298 − 6.98228I −8.6690 + 13.8760I
u = 0.162222 + 0.561060I
a = 0.32963 − 2.37846I
b = −0.80477 − 1.20027I
−1.97298 − 2.92252I −8.66900 + 6.94780I
u = 0.162222 + 0.561060I
a = 0.74023 + 2.97547I
b = 0.352570 + 0.141889I
−1.97298 − 6.98228I −8.6690 + 13.8760I
u = 0.162222 − 0.561060I
a = 0.969046 + 0.551992I
b = −1.208870 + 0.134733I
−1.97298 + 2.92252I −8.66900 − 6.94780I
u = 0.162222 − 0.561060I
a = 1.148280 + 0.385564I
b = 1.81040 + 1.21825I
−1.97298 + 6.98228I −8.6690 − 13.8760I
u = 0.162222 − 0.561060I
a = 0.32963 + 2.37846I
b = −0.80477 + 1.20027I
−1.97298 + 2.92252I −8.66900 − 6.94780I
u = 0.162222 − 0.561060I
a = 0.74023 − 2.97547I
b = 0.352570 − 0.141889I
−1.97298 + 6.98228I −8.6690 − 13.8760I
u = 1.41446 + 0.33004I
a = −1.053820 + 0.460495I
b = 0.591561 + 0.493700I
−6.10599 − 7.35173I −15.0667 + 6.2019I
u = 1.41446 + 0.33004I
a = 1.168710 − 0.542011I
b = −1.074410 − 0.369369I
−6.10599 − 7.35173I −15.0667 + 6.2019I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41446 + 0.33004I
a = 2.01384 − 0.33111I
b = −1.13340 − 1.26029I
−6.10599 − 11.41150I −15.0667 + 13.1301I
u = 1.41446 + 0.33004I
a = −2.00069 + 0.47136I
b = 1.26716 + 0.77996I
−6.10599 − 11.41150I −15.0667 + 13.1301I
u = 1.41446 − 0.33004I
a = −1.053820 − 0.460495I
b = 0.591561 − 0.493700I
−6.10599 + 7.35173I −15.0667 − 6.2019I
u = 1.41446 − 0.33004I
a = 1.168710 + 0.542011I
b = −1.074410 + 0.369369I
−6.10599 + 7.35173I −15.0667 − 6.2019I
u = 1.41446 − 0.33004I
a = 2.01384 + 0.33111I
b = −1.13340 + 1.26029I
−6.10599 + 11.41150I −15.0667 − 13.1301I
u = 1.41446 − 0.33004I
a = −2.00069 − 0.47136I
b = 1.26716 − 0.77996I
−6.10599 + 11.41150I −15.0667 − 13.1301I
u = 1.48928
a = −1.61041 + 0.46911I
b = 1.078730 − 0.177724I
−10.74910 + 2.02988I −20.2145 − 3.4641I
u = 1.48928
a = −1.61041 − 0.46911I
b = 1.078730 + 0.177724I
−10.74910 − 2.02988I −20.2145 + 3.4641I
u = 1.48928
a = 1.67403 + 0.57931I
b = −1.31458 − 0.58624I
−10.74910 − 2.02988I −20.2145 + 3.4641I
u = 1.48928
a = 1.67403 − 0.57931I
b = −1.31458 + 0.58624I
−10.74910 + 2.02988I −20.2145 − 3.4641I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206359 + 0.377187I
a = −0.492086 − 0.710392I
b = −1.27194 + 0.65875I
−2.62198 + 0.87662I −12.25021 + 5.01241I
u = 0.206359 + 0.377187I
a = −2.37122 − 0.72695I
b = 0.927860 − 0.132933I
−2.62198 + 4.93638I −12.25021 − 1.91580I
u = 0.206359 + 0.377187I
a = −0.09064 − 2.99853I
b = −0.642227 + 0.047404I
−2.62198 + 0.87662I −12.25021 + 5.01241I
u = 0.206359 + 0.377187I
a = −0.54943 + 3.08606I
b = 0.64077 + 1.43757I
−2.62198 + 4.93638I −12.25021 − 1.91580I
u = 0.206359 − 0.377187I
a = −0.492086 + 0.710392I
b = −1.27194 − 0.65875I
−2.62198 − 0.87662I −12.25021 − 5.01241I
u = 0.206359 − 0.377187I
a = −2.37122 + 0.72695I
b = 0.927860 + 0.132933I
−2.62198 − 4.93638I −12.25021 + 1.91580I
u = 0.206359 − 0.377187I
a = −0.09064 + 2.99853I
b = −0.642227 − 0.047404I
−2.62198 − 0.87662I −12.25021 − 5.01241I
u = 0.206359 − 0.377187I
a = −0.54943 − 3.08606I
b = 0.64077 − 1.43757I
−2.62198 − 4.93638I −12.25021 + 1.91580I
24
III. I
u
3
= h91u
26
− 160u
25
+ · · · + 6b − 74, −185u
26
+ 296u
25
+ · · · + 6a +
154, u
27
− 3u
26
+ · · · + 4u + 1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
9
=
30.8333u
26
− 49.3333u
25
+ ··· − 113.500u − 25.6667
−15.1667u
26
+ 26.6667u
25
+ ··· + 54.5000u + 12.3333
a
8
=
47
3
u
26
−
68
3
u
25
+ ··· − 59u −
40
3
−15.1667u
26
+ 26.6667u
25
+ ··· + 54.5000u + 12.3333
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−
13
3
u
26
+
13
3
u
25
+ ··· + 18u +
17
3
25
3
u
26
−
89
6
u
25
+ ··· −
53
2
u −
37
6
a
11
=
−
73
6
u
26
+
127
6
u
25
+ ··· + 46u +
41
6
17
6
u
26
−
29
6
u
25
+ ··· − 17u −
19
6
a
7
=
17
3
u
26
−
61
6
u
25
+ ··· −
79
2
u −
35
6
5
6
u
26
−
4
3
u
25
+ ··· +
1
2
u +
1
3
a
10
=
17.3333u
26
− 25.8333u
25
+ ··· − 64.5000u − 15.1667
−
22
3
u
26
+
40
3
u
25
+ ··· + 28u +
20
3
(ii) Obstruction class = 1
(iii) Cusp Shapes =
94
3
u
26
−
257
6
u
25
+ ··· −
241
2
u −
217
6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 6u
26
+ ··· − 102u + 9
c
2
, c
10
u
27
− u
26
+ ··· + u − 1
c
3
, c
9
u
27
− u
26
+ ··· − 7u
2
+ 1
c
4
, c
5
u
27
− 3u
26
+ ··· + 4u + 1
c
6
u
27
− 5u
26
+ ··· + 8u − 1
c
7
u
27
− 16u
26
+ ··· + 39u − 9
c
8
, c
11
u
27
+ 7u
26
+ ··· + 5u + 1
c
12
u
27
+ 3u
26
+ ··· + 4u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 6y
26
+ ··· − 90y − 81
c
2
, c
10
y
27
+ 11y
26
+ ··· − 15y − 1
c
3
, c
9
y
27
− 11y
26
+ ··· + 14y − 1
c
4
, c
5
, c
12
y
27
− 27y
26
+ ··· − 8y − 1
c
6
y
27
+ 5y
26
+ ··· − 2y − 1
c
7
y
27
− 8y
26
+ ··· + 207y − 81
c
8
, c
11
y
27
− 11y
26
+ ··· + 41y − 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853016 + 0.354625I
a = −0.143361 − 0.644625I
b = 0.827175 + 0.800288I
−2.08630 − 2.33845I −7.99756 + 1.72353I
u = −0.853016 − 0.354625I
a = −0.143361 + 0.644625I
b = 0.827175 − 0.800288I
−2.08630 + 2.33845I −7.99756 − 1.72353I
u = 0.085686 + 0.866106I
a = −0.298049 + 0.210716I
b = −0.398154 − 0.039329I
−0.26491 + 4.66029I −11.46761 − 1.46133I
u = 0.085686 − 0.866106I
a = −0.298049 − 0.210716I
b = −0.398154 + 0.039329I
−0.26491 − 4.66029I −11.46761 + 1.46133I
u = −0.253272 + 0.773514I
a = −0.601020 − 1.011480I
b = 1.009880 − 0.984517I
−0.15299 + 6.52246I −5.19116 − 5.34197I
u = −0.253272 − 0.773514I
a = −0.601020 + 1.011480I
b = 1.009880 + 0.984517I
−0.15299 − 6.52246I −5.19116 + 5.34197I
u = −0.651227 + 0.357480I
a = −0.643213 − 0.113075I
b = 0.702535 − 0.422275I
−2.28135 + 1.93745I −11.33304 − 7.12825I
u = −0.651227 − 0.357480I
a = −0.643213 + 0.113075I
b = 0.702535 + 0.422275I
−2.28135 − 1.93745I −11.33304 + 7.12825I
u = 1.292370 + 0.165730I
a = 3.02520 − 0.61031I
b = −1.220290 − 0.580694I
−5.65816 + 3.74883I −12.60504 − 0.91347I
u = 1.292370 − 0.165730I
a = 3.02520 + 0.61031I
b = −1.220290 + 0.580694I
−5.65816 − 3.74883I −12.60504 + 0.91347I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.284730 + 0.310009I
a = 0.84591 − 1.24453I
b = −0.833662 − 0.075930I
−4.07460 − 8.72759I −10.75217 + 8.77108I
u = 1.284730 − 0.310009I
a = 0.84591 + 1.24453I
b = −0.833662 + 0.075930I
−4.07460 + 8.72759I −10.75217 − 8.77108I
u = −1.358460 + 0.208245I
a = 0.161561 + 0.357612I
b = −0.787417 − 1.005180I
−6.54862 + 8.67864I −12.16190 − 6.08678I
u = −1.358460 − 0.208245I
a = 0.161561 − 0.357612I
b = −0.787417 + 1.005180I
−6.54862 − 8.67864I −12.16190 + 6.08678I
u = −1.384270 + 0.119045I
a = −0.152195 − 0.226744I
b = 0.601880 + 0.676868I
−6.77957 − 0.56842I −15.4866 + 4.1498I
u = −1.384270 − 0.119045I
a = −0.152195 + 0.226744I
b = 0.601880 − 0.676868I
−6.77957 + 0.56842I −15.4866 − 4.1498I
u = 1.383310 + 0.189796I
a = −2.15406 + 0.60920I
b = 1.268840 + 0.421175I
−7.64502 − 3.98387I −17.1030 + 3.7006I
u = 1.383310 − 0.189796I
a = −2.15406 − 0.60920I
b = 1.268840 − 0.421175I
−7.64502 + 3.98387I −17.1030 − 3.7006I
u = 1.40974 + 0.31383I
a = −2.05792 + 0.29448I
b = 1.15419 + 1.03398I
−5.44866 − 10.46400I −9.56556 + 5.97787I
u = 1.40974 − 0.31383I
a = −2.05792 − 0.29448I
b = 1.15419 − 1.03398I
−5.44866 + 10.46400I −9.56556 − 5.97787I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46124 + 0.08138I
a = −1.37967 + 1.09604I
b = 1.092220 − 0.515594I
−8.96775 + 1.37304I −12.24810 + 1.40712I
u = 1.46124 − 0.08138I
a = −1.37967 − 1.09604I
b = 1.092220 + 0.515594I
−8.96775 − 1.37304I −12.24810 − 1.40712I
u = 0.093061 + 0.496676I
a = −0.06092 + 2.26760I
b = −0.936808 + 0.726148I
−1.84343 − 6.05672I −5.36038 + 4.07426I
u = 0.093061 − 0.496676I
a = −0.06092 − 2.26760I
b = −0.936808 − 0.726148I
−1.84343 + 6.05672I −5.36038 − 4.07426I
u = −1.64818
a = −0.0498316
b = 0.217499
−6.77052 24.5800
u = −0.185817 + 0.268768I
a = −2.01736 − 1.66031I
b = 0.910864 − 0.497797I
−2.43609 + 1.79985I −11.01770 − 3.85036I
u = −0.185817 − 0.268768I
a = −2.01736 + 1.66031I
b = 0.910864 + 0.497797I
−2.43609 − 1.79985I −11.01770 + 3.85036I
30
IV. I
u
4
= hb + a − 1, a
2
− a + 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
6
=
1
0
a
5
=
1
−1
a
9
=
a
−a + 1
a
8
=
1
−a + 1
a
12
=
−1
0
a
4
=
0
−1
a
2
=
0
−1
a
3
=
−1
a − 2
a
11
=
0
−a
a
7
=
1
−a + 1
a
10
=
a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 7
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
c
2
, c
3
, c
12
(u − 1)
2
c
4
, c
5
(u + 1)
2
c
6
, c
8
, c
9
c
10
, c
11
u
2
+ u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
c
2
, c
3
, c
4
c
5
, c
12
(y − 1)
2
c
6
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −9.00000 − 3.46410I
u = −1.00000
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −9.00000 + 3.46410I
34
V. I
u
5
= hb
2
− b + 1, a + 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
6
=
1
0
a
5
=
1
−1
a
9
=
−1
b
a
8
=
b − 1
b
a
12
=
−1
0
a
4
=
0
−1
a
2
=
0
−1
a
3
=
b
0
a
11
=
−b − 1
b − 1
a
7
=
b − 1
b
a
10
=
−1
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b − 11
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
c
2
, c
3
, c
6
c
8
, c
11
u
2
+ u + 1
c
4
, c
5
(u + 1)
2
c
9
, c
10
, c
12
(u − 1)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
c
2
, c
3
, c
6
c
8
, c
11
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
, c
12
(y − 1)
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −9.00000 + 3.46410I
u = −1.00000
a = −1.00000
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −9.00000 − 3.46410I
38
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
4
(u
27
− 6u
26
+ ··· − 102u + 9)(u
27
+ 9u
26
+ ··· + 37u + 8)
4
· (u
55
− 33u
54
+ ··· + 47308u − 3536)
c
2
, c
10
((u − 1)
2
)(u
2
+ u + 1)(u
27
− u
26
+ ··· + u − 1)(u
55
+ u
54
+ ··· + u − 1)
· (u
108
+ 4u
107
+ ··· + 5u + 1)
c
3
, c
9
((u − 1)
2
)(u
2
+ u + 1)(u
27
− u
26
+ ··· − 7u
2
+ 1)(u
55
− u
54
+ ··· − 2u + 17)
· (u
108
+ 2u
107
+ ··· − 100507749u + 41406721)
c
4
, c
5
((u + 1)
4
)(u
27
− 3u
26
+ ··· + 4u + 1)(u
27
− 2u
26
+ ··· − 4u
2
− 1)
4
· (u
55
+ 10u
54
+ ··· + 28u − 16)
c
6
((u
2
+ u + 1)
56
)(u
27
− 5u
26
+ ··· + 8u − 1)
· (u
55
− 48u
54
+ ··· + 1543503872u − 67108864)
c
7
u
4
(u
27
− 16u
26
+ ··· + 39u − 9)(u
27
+ 13u
26
+ ··· − u − 2)
4
· (u
55
− 37u
54
+ ··· + 6u − 4)
c
8
, c
11
((u
2
+ u + 1)
2
)(u
27
+ 7u
26
+ ··· + 5u + 1)(u
55
+ 3u
54
+ ··· + 5u + 1)
· (u
108
+ 3u
107
+ ··· − 1614u + 97)
c
12
((u − 1)
4
)(u
27
− 2u
26
+ ··· − 4u
2
− 1)
4
(u
27
+ 3u
26
+ ··· + 4u − 1)
· (u
55
+ 10u
54
+ ··· + 28u − 16)
39
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
4
(y
27
− 6y
26
+ ··· − 90y − 81)(y
27
+ 5y
26
+ ··· − 375y − 64)
4
· (y
55
− y
54
+ ··· − 122155344y − 12503296)
c
2
, c
10
((y − 1)
2
)(y
2
+ y + 1)(y
27
+ 11y
26
+ ··· − 15y − 1)
· (y
55
− 11y
54
+ ··· + 19y − 1)(y
108
+ 38y
107
+ ··· − 117y + 1)
c
3
, c
9
((y − 1)
2
)(y
2
+ y + 1)(y
27
− 11y
26
+ ··· + 14y − 1)
· (y
55
− 21y
54
+ ··· + 5512y − 289)
· (y
108
− 38y
107
+ ··· − 55012811704519381y + 1714516543971841)
c
4
, c
5
, c
12
((y − 1)
4
)(y
27
− 27y
26
+ ··· − 8y − 1)(y
27
− 24y
26
+ ··· − 8y − 1)
4
· (y
55
− 50y
54
+ ··· − 2256y − 256)
c
6
((y
2
+ y + 1)
56
)(y
27
+ 5y
26
+ ··· − 2y − 1)
· (y
55
+ 6y
54
+ ··· + 11258999068426240y − 4503599627370496)
c
7
y
4
(y
27
− 8y
26
+ ··· + 207y − 81)(y
27
− 3y
26
+ ··· + 53y − 4)
4
· (y
55
− 11y
54
+ ··· + 460y − 16)
c
8
, c
11
((y
2
+ y + 1)
2
)(y
27
− 11y
26
+ ··· + 41y − 1)
· (y
55
+ 15y
54
+ ··· + 31y − 1)(y
108
− 31y
107
+ ··· − 144882y + 9409)
40
