12a
0516
(K12a
0516
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 2 1 10 4 12 6 5
Solving Sequence
4,9
5
10,12
11 6 1 8 3 7 2
c
4
c
9
c
10
c
5
c
12
c
8
c
3
c
7
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
26
+ 19u
25
+ ··· + 4b + 2, 11u
26
− 57u
25
+ ··· + 8a − 62, u
27
− 5u
26
+ ··· − 12u + 4i
I
u
2
= h153018u
43
a + 172574u
43
+ ··· + 267932a + 346978, −5u
43
a − 8u
42
a + ··· − 7a − 8,
u
44
+ 2u
43
+ ··· + 2u + 1i
I
u
3
= h−au + b + a, a
2
− a + 1, u
2
+ 1i
I
u
4
= hau + b + a − u, a
2
− a + 1, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 123 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−3u
26
+ 19u
25
+ · · · + 4b + 2, 11u
26
− 57u
25
+ · · · + 8a − 62, u
27
−
5u
26
+ · · · − 12u + 4i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
u
a
12
=
−1.37500u
26
+ 7.12500u
25
+ ··· − 19.8750u + 7.75000
3
4
u
26
−
19
4
u
25
+ ··· +
33
4
u −
1
2
a
11
=
−
3
8
u
26
+
13
8
u
25
+ ··· −
35
8
u +
5
4
1
4
u
26
−
5
4
u
25
+ ··· +
11
4
u −
1
2
a
6
=
1
8
u
26
+
1
8
u
25
+ ··· −
67
8
u +
27
4
−
1
4
u
26
+
1
4
u
25
+ ··· +
35
4
u −
11
2
a
1
=
−1.62500u
26
+ 8.37500u
25
+ ··· − 20.1250u + 8.25000
7
4
u
26
−
29
4
u
25
+ ··· +
37
4
u −
1
2
a
8
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
7
=
−
1
8
u
26
+
3
8
u
25
+ ··· −
1
8
u −
1
4
−
1
4
u
26
+
5
4
u
25
+ ··· −
9
4
u +
3
2
a
2
=
1
8
u
26
−
23
8
u
25
+ ··· +
129
8
u −
25
4
3
4
u
26
−
1
4
u
25
+ ··· −
7
4
u −
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
25
+ 11u
24
− 41u
23
+ 94u
22
− 201u
21
+ 350u
20
− 555u
19
+
811u
18
− 1060u
17
+ 1348u
16
− 1524u
15
+ 1683u
14
− 1695u
13
+ 1624u
12
− 1489u
11
+
1249u
10
− 1017u
9
+ 745u
8
− 495u
7
+ 304u
6
− 145u
5
+ 54u
4
− 7u
3
− 21u
2
+ 20u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
27
+ 14u
26
+ ··· + 4u + 1
c
2
, c
5
, c
6
c
11
u
27
− 7u
25
+ ··· − 2u
2
+ 1
c
3
u
27
+ 5u
26
+ ··· − 320u
2
+ 64
c
4
, c
9
u
27
− 5u
26
+ ··· − 12u + 4
c
7
, c
12
u
27
+ 5u
25
+ ··· − 2u + 3
c
8
u
27
− 15u
26
+ ··· + 56u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
27
+ 2y
26
+ ··· + 8y −1
c
2
, c
5
, c
6
c
11
y
27
− 14y
26
+ ··· + 4y −1
c
3
y
27
− 13y
26
+ ··· + 40960y −4096
c
4
, c
9
y
27
+ 15y
26
+ ··· + 56y −16
c
7
, c
12
y
27
+ 10y
26
+ ··· − 20y −9
c
8
y
27
− 5y
26
+ ··· + 8480y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.730663 + 0.630842I
a = −1.15948 + 1.36199I
b = 1.380630 + 0.132263I
−6.78998 − 5.25258I −11.87823 + 4.55008I
u = −0.730663 − 0.630842I
a = −1.15948 − 1.36199I
b = 1.380630 − 0.132263I
−6.78998 + 5.25258I −11.87823 − 4.55008I
u = −0.496338 + 0.799160I
a = 0.491347 − 1.120530I
b = −0.828650 + 0.873109I
−0.34967 + 2.03126I −2.38031 − 3.61940I
u = −0.496338 − 0.799160I
a = 0.491347 + 1.120530I
b = −0.828650 − 0.873109I
−0.34967 − 2.03126I −2.38031 + 3.61940I
u = 0.893419 + 0.201765I
a = 0.47034 + 1.60999I
b = −1.108620 − 0.003316I
−1.56275 + 12.48900I −7.13823 − 8.79182I
u = 0.893419 − 0.201765I
a = 0.47034 − 1.60999I
b = −1.108620 + 0.003316I
−1.56275 − 12.48900I −7.13823 + 8.79182I
u = −0.178235 + 1.084250I
a = −0.213163 − 0.502908I
b = 0.659574 + 0.702653I
1.94164 + 2.20192I −0.56198 − 2.41318I
u = −0.178235 − 1.084250I
a = −0.213163 + 0.502908I
b = 0.659574 − 0.702653I
1.94164 − 2.20192I −0.56198 + 2.41318I
u = −0.664783 + 0.914963I
a = −0.39003 + 1.65011I
b = 1.72361 − 1.44912I
−5.96942 + 10.50660I −9.69062 − 10.08606I
u = −0.664783 − 0.914963I
a = −0.39003 − 1.65011I
b = 1.72361 + 1.44912I
−5.96942 − 10.50660I −9.69062 + 10.08606I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728836 + 0.456068I
a = −0.664583 + 0.952860I
b = −0.840437 − 0.847346I
−5.99030 − 2.50292I −13.30644 + 3.87606I
u = 0.728836 − 0.456068I
a = −0.664583 − 0.952860I
b = −0.840437 + 0.847346I
−5.99030 + 2.50292I −13.30644 − 3.87606I
u = 0.799916 + 0.147492I
a = −0.553123 − 0.901764I
b = 0.879493 + 0.088034I
2.62362 + 2.33182I −0.926585 − 0.602280I
u = 0.799916 − 0.147492I
a = −0.553123 + 0.901764I
b = 0.879493 − 0.088034I
2.62362 − 2.33182I −0.926585 + 0.602280I
u = 0.563387 + 1.046610I
a = 1.253280 + 0.526603I
b = −1.42614 + 0.54904I
−4.25210 − 2.40888I −10.75070 + 1.81073I
u = 0.563387 − 1.046610I
a = 1.253280 − 0.526603I
b = −1.42614 − 0.54904I
−4.25210 + 2.40888I −10.75070 − 1.81073I
u = 0.021698 + 1.237970I
a = 0.353870 + 0.098440I
b = −0.986014 + 0.581923I
−0.30811 − 4.23523I −8.52197 + 5.94232I
u = 0.021698 − 1.237970I
a = 0.353870 − 0.098440I
b = −0.986014 − 0.581923I
−0.30811 + 4.23523I −8.52197 − 5.94232I
u = 0.371922 + 1.216990I
a = −0.047378 − 0.727973I
b = −0.420071 + 0.350884I
6.71645 − 1.62939I 3.63674 + 2.67627I
u = 0.371922 − 1.216990I
a = −0.047378 + 0.727973I
b = −0.420071 − 0.350884I
6.71645 + 1.62939I 3.63674 − 2.67627I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517374 + 1.188310I
a = −0.98424 − 1.30505I
b = 1.59567 + 1.17935I
5.67800 − 7.17879I 1.95902 + 3.78339I
u = 0.517374 − 1.188310I
a = −0.98424 + 1.30505I
b = 1.59567 − 1.17935I
5.67800 + 7.17879I 1.95902 − 3.78339I
u = 0.322363 + 1.283180I
a = −0.258472 + 0.363453I
b = 1.027060 + 0.465180I
3.19039 + 8.39996I −2.59631 − 7.43442I
u = 0.322363 − 1.283180I
a = −0.258472 − 0.363453I
b = 1.027060 − 0.465180I
3.19039 − 8.39996I −2.59631 + 7.43442I
u = 0.559888 + 1.210030I
a = 1.36303 + 1.45255I
b = −2.57082 − 1.28259I
1.4727 − 17.7774I −3.91820 + 11.76326I
u = 0.559888 − 1.210030I
a = 1.36303 − 1.45255I
b = −2.57082 + 1.28259I
1.4727 + 17.7774I −3.91820 − 11.76326I
u = −0.417568
a = 1.17723
b = −0.170545
−1.02561 −9.85230
7
II. I
u
2
= h1.53 × 10
5
au
43
+ 1.73 × 10
5
u
43
+ · · · + 2.68 × 10
5
a + 3.47 ×
10
5
, −5u
43
a − 8u
42
a + · · · − 7a − 8, u
44
+ 2u
43
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
u
a
12
=
a
−0.671774au
43
− 0.757628u
43
+ ··· − 1.17627a − 1.52329
a
11
=
0.0879130au
43
− 1.35545u
43
+ ··· + 1.75763a − 1.80612
−0.0707343au
43
− 1.51109u
43
+ ··· − 0.630357a − 1.70508
a
6
=
1.17627au
43
+ 1.52329u
43
+ ··· + 1.06336a + 1.87686
−au
a
1
=
−0.671774au
43
− 0.757628u
43
+ ··· − 0.176265a − 1.52329
−0.887094au
43
+ 0.646425u
43
+ ··· − 1.55887a − 1.11120
a
8
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
7
=
0.757628au
43
− 1.80612u
43
+ ··· + 1.52329a − 3.62675
−1.40405au
43
+ 0.130050u
43
+ ··· − 0.412087a − 1.35545
a
2
=
−0.337208au
43
− 1.77370u
43
+ ··· + 0.402077a − 0.183860
−0.671774au
43
+ 1.74237u
43
+ ··· − 1.17627a − 1.02329
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
42
− 14u
41
+ ··· − 10u − 8
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
88
+ 39u
87
+ ··· + 18u + 1
c
2
, c
5
, c
6
c
11
u
88
− u
87
+ ··· − 6u + 1
c
3
(u
44
− 2u
43
+ ··· − 16u + 4)
2
c
4
, c
9
(u
44
+ 2u
43
+ ··· + 2u + 1)
2
c
7
, c
12
u
88
− 3u
87
+ ··· − 138u + 33
c
8
(u
44
− 24u
43
+ ··· − 4u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
88
+ 21y
87
+ ··· + 238y + 1
c
2
, c
5
, c
6
c
11
y
88
− 39y
87
+ ··· − 18y + 1
c
3
(y
44
− 26y
43
+ ··· − 232y + 16)
2
c
4
, c
9
(y
44
+ 24y
43
+ ··· + 4y + 1)
2
c
7
, c
12
y
88
− 3y
87
+ ··· + 50850y + 1089
c
8
(y
44
− 4y
43
+ ··· − 24y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312877 + 0.963899I
a = −0.027282 + 0.403408I
b = 0.952689 + 0.414115I
0.80202 + 2.36066I −5.22306 − 1.04915I
u = 0.312877 + 0.963899I
a = 2.00737 − 0.22584I
b = −1.84409 + 1.07166I
0.80202 + 2.36066I −5.22306 − 1.04915I
u = 0.312877 − 0.963899I
a = −0.027282 − 0.403408I
b = 0.952689 − 0.414115I
0.80202 − 2.36066I −5.22306 + 1.04915I
u = 0.312877 − 0.963899I
a = 2.00737 + 0.22584I
b = −1.84409 − 1.07166I
0.80202 − 2.36066I −5.22306 + 1.04915I
u = −0.137606 + 0.955862I
a = −0.094806 − 1.142040I
b = 0.023143 + 1.183290I
1.78035 + 2.09885I 0.44851 − 4.43063I
u = −0.137606 + 0.955862I
a = 0.106234 − 0.261688I
b = 0.767571 + 0.488152I
1.78035 + 2.09885I 0.44851 − 4.43063I
u = −0.137606 − 0.955862I
a = −0.094806 + 1.142040I
b = 0.023143 − 1.183290I
1.78035 − 2.09885I 0.44851 + 4.43063I
u = −0.137606 − 0.955862I
a = 0.106234 + 0.261688I
b = 0.767571 − 0.488152I
1.78035 − 2.09885I 0.44851 + 4.43063I
u = −0.684571 + 0.780204I
a = 0.01313 + 1.55377I
b = 1.38055 − 1.35627I
−6.79265 + 2.59501I −11.85224 − 3.15453I
u = −0.684571 + 0.780204I
a = −1.29051 + 1.09598I
b = 1.44905 + 0.25653I
−6.79265 + 2.59501I −11.85224 − 3.15453I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684571 − 0.780204I
a = 0.01313 − 1.55377I
b = 1.38055 + 1.35627I
−6.79265 − 2.59501I −11.85224 + 3.15453I
u = −0.684571 − 0.780204I
a = −1.29051 − 1.09598I
b = 1.44905 − 0.25653I
−6.79265 − 2.59501I −11.85224 + 3.15453I
u = 0.603047 + 0.858448I
a = −0.604320 − 1.107190I
b = 1.027440 + 0.829602I
−3.07660 − 6.10396I −6.28400 + 6.94365I
u = 0.603047 + 0.858448I
a = 0.20059 + 1.86245I
b = −1.55420 − 1.62720I
−3.07660 − 6.10396I −6.28400 + 6.94365I
u = 0.603047 − 0.858448I
a = −0.604320 + 1.107190I
b = 1.027440 − 0.829602I
−3.07660 + 6.10396I −6.28400 − 6.94365I
u = 0.603047 − 0.858448I
a = 0.20059 − 1.86245I
b = −1.55420 + 1.62720I
−3.07660 + 6.10396I −6.28400 − 6.94365I
u = 0.618739 + 0.681900I
a = −0.539910 − 0.998880I
b = 0.882079 + 0.626536I
−3.58269 + 1.33395I −7.91617 − 0.65820I
u = 0.618739 + 0.681900I
a = 1.41810 + 1.31949I
b = −1.50309 + 0.14230I
−3.58269 + 1.33395I −7.91617 − 0.65820I
u = 0.618739 − 0.681900I
a = −0.539910 + 0.998880I
b = 0.882079 − 0.626536I
−3.58269 − 1.33395I −7.91617 + 0.65820I
u = 0.618739 − 0.681900I
a = 1.41810 − 1.31949I
b = −1.50309 − 0.14230I
−3.58269 − 1.33395I −7.91617 + 0.65820I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845401 + 0.185803I
a = 0.552294 − 0.890537I
b = −0.913023 + 0.113662I
0.59532 − 7.36573I −4.12046 + 4.87801I
u = −0.845401 + 0.185803I
a = −0.45725 + 1.68541I
b = 1.113550 − 0.030175I
0.59532 − 7.36573I −4.12046 + 4.87801I
u = −0.845401 − 0.185803I
a = 0.552294 + 0.890537I
b = −0.913023 − 0.113662I
0.59532 + 7.36573I −4.12046 − 4.87801I
u = −0.845401 − 0.185803I
a = −0.45725 − 1.68541I
b = 1.113550 + 0.030175I
0.59532 + 7.36573I −4.12046 − 4.87801I
u = −0.377246 + 1.071500I
a = −1.321220 + 0.020635I
b = 1.41639 + 0.83546I
1.70903 + 2.55111I −3.11914 − 3.94978I
u = −0.377246 + 1.071500I
a = 0.108848 − 0.668784I
b = 0.549372 + 0.372801I
1.70903 + 2.55111I −3.11914 − 3.94978I
u = −0.377246 − 1.071500I
a = −1.321220 − 0.020635I
b = 1.41639 − 0.83546I
1.70903 − 2.55111I −3.11914 + 3.94978I
u = −0.377246 − 1.071500I
a = 0.108848 + 0.668784I
b = 0.549372 − 0.372801I
1.70903 − 2.55111I −3.11914 + 3.94978I
u = 0.805706 + 0.294033I
a = −0.681975 + 0.547340I
b = −0.808577 − 0.504319I
−4.21399 + 4.93430I −10.72232 − 3.42025I
u = 0.805706 + 0.294033I
a = 0.64947 + 1.70247I
b = −1.179970 − 0.018130I
−4.21399 + 4.93430I −10.72232 − 3.42025I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805706 − 0.294033I
a = −0.681975 − 0.547340I
b = −0.808577 + 0.504319I
−4.21399 − 4.93430I −10.72232 + 3.42025I
u = 0.805706 − 0.294033I
a = 0.64947 − 1.70247I
b = −1.179970 + 0.018130I
−4.21399 − 4.93430I −10.72232 + 3.42025I
u = 0.336351 + 0.713930I
a = −0.549874 − 0.605883I
b = −0.764991 + 0.324297I
0.07018 − 5.32036I −6.18214 + 9.40095I
u = 0.336351 + 0.713930I
a = −1.00871 + 2.88605I
b = −0.42659 − 2.41866I
0.07018 − 5.32036I −6.18214 + 9.40095I
u = 0.336351 − 0.713930I
a = −0.549874 + 0.605883I
b = −0.764991 − 0.324297I
0.07018 + 5.32036I −6.18214 − 9.40095I
u = 0.336351 − 0.713930I
a = −1.00871 − 2.88605I
b = −0.42659 + 2.41866I
0.07018 + 5.32036I −6.18214 − 9.40095I
u = 0.451669 + 1.130720I
a = −0.184575 + 0.446454I
b = 1.012320 + 0.416675I
3.33637 − 3.89932I −2.16553 + 3.93444I
u = 0.451669 + 1.130720I
a = 1.55267 + 1.97505I
b = −2.74463 − 1.74556I
3.33637 − 3.89932I −2.16553 + 3.93444I
u = 0.451669 − 1.130720I
a = −0.184575 − 0.446454I
b = 1.012320 − 0.416675I
3.33637 + 3.89932I −2.16553 − 3.93444I
u = 0.451669 − 1.130720I
a = 1.55267 − 1.97505I
b = −2.74463 + 1.74556I
3.33637 + 3.89932I −2.16553 − 3.93444I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.187726 + 1.204930I
a = 0.586324 − 0.078067I
b = −1.015170 + 0.721089I
0.63647 + 1.88253I −5.88964 − 2.78829I
u = 0.187726 + 1.204930I
a = −0.222273 + 0.265114I
b = 0.990291 + 0.491707I
0.63647 + 1.88253I −5.88964 − 2.78829I
u = 0.187726 − 1.204930I
a = 0.586324 + 0.078067I
b = −1.015170 − 0.721089I
0.63647 − 1.88253I −5.88964 + 2.78829I
u = 0.187726 − 1.204930I
a = −0.222273 − 0.265114I
b = 0.990291 − 0.491707I
0.63647 − 1.88253I −5.88964 + 2.78829I
u = −0.409396 + 1.159590I
a = 0.192660 + 0.417968I
b = −1.011500 + 0.429689I
5.11542 − 1.06835I 0
u = −0.409396 + 1.159590I
a = 0.97698 − 1.55522I
b = −1.56050 + 1.51219I
5.11542 − 1.06835I 0
u = −0.409396 − 1.159590I
a = 0.192660 − 0.417968I
b = −1.011500 − 0.429689I
5.11542 + 1.06835I 0
u = −0.409396 − 1.159590I
a = 0.97698 + 1.55522I
b = −1.56050 − 1.51219I
5.11542 + 1.06835I 0
u = −0.523577 + 1.128340I
a = −1.139810 + 0.393041I
b = 1.35919 + 0.61090I
0.51289 + 4.91293I −4.00000 − 3.32925I
u = −0.523577 + 1.128340I
a = 0.88118 − 1.31204I
b = −1.45124 + 1.17483I
0.51289 + 4.91293I −4.00000 − 3.32925I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.523577 − 1.128340I
a = −1.139810 − 0.393041I
b = 1.35919 − 0.61090I
0.51289 − 4.91293I −4.00000 + 3.32925I
u = −0.523577 − 1.128340I
a = 0.88118 + 1.31204I
b = −1.45124 − 1.17483I
0.51289 − 4.91293I −4.00000 + 3.32925I
u = −0.699549 + 0.280530I
a = 0.567058 − 0.884436I
b = −0.805456 + 0.201612I
−1.95648 − 0.23544I −7.71045 − 0.71060I
u = −0.699549 + 0.280530I
a = 0.915779 + 0.590948I
b = 0.609805 − 0.560083I
−1.95648 − 0.23544I −7.71045 − 0.71060I
u = −0.699549 − 0.280530I
a = 0.567058 + 0.884436I
b = −0.805456 − 0.201612I
−1.95648 + 0.23544I −7.71045 + 0.71060I
u = −0.699549 − 0.280530I
a = 0.915779 − 0.590948I
b = 0.609805 + 0.560083I
−1.95648 + 0.23544I −7.71045 + 0.71060I
u = 0.446265 + 1.170890I
a = −0.083115 − 0.736096I
b = −0.476825 + 0.306143I
6.49035 − 4.18968I 0. + 3.85017I
u = 0.446265 + 1.170890I
a = −0.98672 − 1.45431I
b = 1.58085 + 1.38043I
6.49035 − 4.18968I 0. + 3.85017I
u = 0.446265 − 1.170890I
a = −0.083115 + 0.736096I
b = −0.476825 − 0.306143I
6.49035 + 4.18968I 0. − 3.85017I
u = 0.446265 − 1.170890I
a = −0.98672 + 1.45431I
b = 1.58085 − 1.38043I
6.49035 + 4.18968I 0. − 3.85017I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.480714 + 1.157280I
a = 0.095453 − 0.746494I
b = 0.492941 + 0.284502I
4.61322 + 9.27115I 0. − 8.56343I
u = −0.480714 + 1.157280I
a = −1.51091 + 1.78770I
b = 2.70589 − 1.57781I
4.61322 + 9.27115I 0. − 8.56343I
u = −0.480714 − 1.157280I
a = 0.095453 + 0.746494I
b = 0.492941 − 0.284502I
4.61322 − 9.27115I 0. + 8.56343I
u = −0.480714 − 1.157280I
a = −1.51091 − 1.78770I
b = 2.70589 + 1.57781I
4.61322 − 9.27115I 0. + 8.56343I
u = 0.560382 + 1.148160I
a = 1.090810 + 0.445231I
b = −1.33863 + 0.58110I
−1.67798 − 10.01170I 0. + 7.22646I
u = 0.560382 + 1.148160I
a = 1.23542 + 1.62075I
b = −2.46031 − 1.43171I
−1.67798 − 10.01170I 0. + 7.22646I
u = 0.560382 − 1.148160I
a = 1.090810 − 0.445231I
b = −1.33863 − 0.58110I
−1.67798 + 10.01170I 0. − 7.22646I
u = 0.560382 − 1.148160I
a = 1.23542 − 1.62075I
b = −2.46031 + 1.43171I
−1.67798 + 10.01170I 0. − 7.22646I
u = 0.711517
a = −0.542111 + 0.968090I
b = 0.832272 + 0.025706I
3.18095 −0.237640
u = 0.711517
a = −0.542111 − 0.968090I
b = 0.832272 − 0.025706I
3.18095 −0.237640
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340404 + 1.242800I
a = 0.032335 − 0.731892I
b = 0.385344 + 0.365827I
5.03718 − 3.41596I 0
u = −0.340404 + 1.242800I
a = 0.235290 + 0.372209I
b = −1.019910 + 0.456338I
5.03718 − 3.41596I 0
u = −0.340404 − 1.242800I
a = 0.032335 + 0.731892I
b = 0.385344 − 0.365827I
5.03718 + 3.41596I 0
u = −0.340404 − 1.242800I
a = 0.235290 − 0.372209I
b = −1.019910 − 0.456338I
5.03718 + 3.41596I 0
u = −0.686238 + 0.096964I
a = 0.491955 + 1.019840I
b = −0.841799 + 0.092164I
1.63501 − 4.89218I −3.21822 + 5.35953I
u = −0.686238 + 0.096964I
a = −0.28294 + 1.99860I
b = 1.098800 − 0.134459I
1.63501 − 4.89218I −3.21822 + 5.35953I
u = −0.686238 − 0.096964I
a = 0.491955 − 1.019840I
b = −0.841799 − 0.092164I
1.63501 + 4.89218I −3.21822 − 5.35953I
u = −0.686238 − 0.096964I
a = −0.28294 − 1.99860I
b = 1.098800 + 0.134459I
1.63501 + 4.89218I −3.21822 − 5.35953I
u = −0.541068 + 1.196610I
a = 0.98556 − 1.26327I
b = −1.60448 + 1.12233I
3.60464 + 12.44580I 0
u = −0.541068 + 1.196610I
a = −1.39332 + 1.52484I
b = 2.59851 − 1.34576I
3.60464 + 12.44580I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541068 − 1.196610I
a = 0.98556 + 1.26327I
b = −1.60448 − 1.12233I
3.60464 − 12.44580I 0
u = −0.541068 − 1.196610I
a = −1.39332 − 1.52484I
b = 2.59851 + 1.34576I
3.60464 − 12.44580I 0
u = −0.224537 + 0.568559I
a = −0.490715 + 0.741336I
b = −0.871940 + 0.351164I
0.002055 + 0.400940I −7.16201 − 2.06092I
u = −0.224537 + 0.568559I
a = 2.13564 + 2.59121I
b = −0.47847 − 1.91301I
0.002055 + 0.400940I −7.16201 − 2.06092I
u = −0.224537 − 0.568559I
a = −0.490715 − 0.741336I
b = −0.871940 − 0.351164I
0.002055 − 0.400940I −7.16201 + 2.06092I
u = −0.224537 − 0.568559I
a = 2.13564 − 2.59121I
b = −0.47847 + 1.91301I
0.002055 − 0.400940I −7.16201 + 2.06092I
u = 0.543576
a = −0.11878 + 2.32451I
b = −1.052670 − 0.226855I
0.437519 −5.45100
u = 0.543576
a = −0.11878 − 2.32451I
b = −1.052670 + 0.226855I
0.437519 −5.45100
19
III. I
u
3
= h−au + b + a, a
2
− a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−1
a
10
=
−u
u
a
12
=
a
au − a
a
11
=
a − u − 1
au − a + 1
a
6
=
−au + a
au
a
1
=
au + a
−a
a
8
=
u
0
a
3
=
1
0
a
7
=
−au + a + 2u − 1
au − u
a
2
=
au + 2a
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8a − 4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
− u + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
, c
12
u
4
− u
2
+ 1
c
3
u
4
c
4
, c
9
(u
2
+ 1)
2
c
8
(u + 1)
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
2
+ y + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
, c
12
(y
2
− y + 1)
2
c
3
y
4
c
4
, c
9
(y + 1)
4
c
8
(y − 1)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 + 0.866025I
b = −1.36603 − 0.36603I
1.64493 − 4.05977I 0. + 6.92820I
u = 1.000000I
a = 0.500000 − 0.866025I
b = 0.36603 + 1.36603I
1.64493 + 4.05977I 0. − 6.92820I
u = − 1.000000I
a = 0.500000 + 0.866025I
b = 0.36603 − 1.36603I
1.64493 − 4.05977I 0. + 6.92820I
u = − 1.000000I
a = 0.500000 − 0.866025I
b = −1.36603 + 0.36603I
1.64493 + 4.05977I 0. − 6.92820I
23
IV. I
u
4
= hau + b + a − u, a
2
− a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−1
a
10
=
−u
u
a
12
=
a
−au − a + u
a
11
=
−u + 1
−au + u − 1
a
6
=
−au − a + 1
au
a
1
=
−au + a + u
−a
a
8
=
u
0
a
3
=
1
0
a
7
=
−au + 2u + 1
au − u
a
2
=
−au + 2a + u
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
− u + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
, c
12
u
4
− u
2
+ 1
c
3
u
4
c
4
, c
9
(u
2
+ 1)
2
c
8
(u + 1)
4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
2
+ y + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
, c
12
(y
2
− y + 1)
2
c
3
y
4
c
4
, c
9
(y + 1)
4
c
8
(y − 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 + 0.866025I
b = 0.366025 − 0.366025I
1.64493 0
u = 1.000000I
a = 0.500000 − 0.866025I
b = −1.36603 + 1.36603I
1.64493 0
u = − 1.000000I
a = 0.500000 + 0.866025I
b = −1.36603 − 1.36603I
1.64493 0
u = − 1.000000I
a = 0.500000 − 0.866025I
b = 0.366025 + 0.366025I
1.64493 0
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
((u
2
− u + 1)
4
)(u
27
+ 14u
26
+ ··· + 4u + 1)(u
88
+ 39u
87
+ ··· + 18u + 1)
c
2
, c
5
, c
6
c
11
((u
4
− u
2
+ 1)
2
)(u
27
− 7u
25
+ ··· − 2u
2
+ 1)(u
88
− u
87
+ ··· − 6u + 1)
c
3
u
8
(u
27
+ 5u
26
+ ··· − 320u
2
+ 64)(u
44
− 2u
43
+ ··· − 16u + 4)
2
c
4
, c
9
((u
2
+ 1)
4
)(u
27
− 5u
26
+ ··· − 12u + 4)(u
44
+ 2u
43
+ ··· + 2u + 1)
2
c
7
, c
12
((u
4
− u
2
+ 1)
2
)(u
27
+ 5u
25
+ ··· − 2u + 3)(u
88
− 3u
87
+ ··· − 138u + 33)
c
8
((u + 1)
8
)(u
27
− 15u
26
+ ··· + 56u + 16)(u
44
− 24u
43
+ ··· − 4u + 1)
2
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
((y
2
+ y + 1)
4
)(y
27
+ 2y
26
+ ··· + 8y − 1)(y
88
+ 21y
87
+ ··· + 238y + 1)
c
2
, c
5
, c
6
c
11
((y
2
− y + 1)
4
)(y
27
− 14y
26
+ ··· + 4y − 1)(y
88
− 39y
87
+ ··· − 18y + 1)
c
3
y
8
(y
27
− 13y
26
+ ··· + 40960y − 4096)
· (y
44
− 26y
43
+ ··· − 232y + 16)
2
c
4
, c
9
((y + 1)
8
)(y
27
+ 15y
26
+ ··· + 56y − 16)(y
44
+ 24y
43
+ ··· + 4y + 1)
2
c
7
, c
12
((y
2
− y + 1)
4
)(y
27
+ 10y
26
+ ··· − 20y − 9)
· (y
88
− 3y
87
+ ··· + 50850y + 1089)
c
8
((y − 1)
8
)(y
27
− 5y
26
+ ··· + 8480y − 256)
· (y
44
− 4y
43
+ ··· − 24y + 1)
2
29
