12a
0952
(K12a
0952
)
A knot diagram
1
Linearized knot diagam
4 6 10 9 2 11 12 5 1 3 7 8
Solving Sequence
7,11
12 8 1
3,6
2 5 10 4 9
c
11
c
7
c
12
c
6
c
2
c
5
c
10
c
3
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.06116 × 10
117
u
76
+ 8.53092 × 10
117
u
75
+ ··· + 9.26283 × 10
117
b + 6.65560 × 10
118
,
− 1.56367 × 10
119
u
76
+ 2.54497 × 10
120
u
75
+ ··· + 1.20232 × 10
121
a − 2.34026 × 10
122
,
u
77
− u
76
+ ··· − 267u − 11i
I
u
2
= hu
7
− 5u
5
+ u
4
+ 7u
3
− 3u
2
+ b − 2u + 1, u
7
− 5u
5
+ u
4
+ 7u
3
− 4u
2
+ a − 2u + 3,
u
14
− 10u
12
+ 2u
11
+ 39u
10
− 16u
9
− 73u
8
+ 46u
7
+ 63u
6
− 56u
5
− 17u
4
+ 25u
3
− 2u
2
− 2u + 1i
I
u
3
= hb − a − 1, a
2
+ a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 93 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−4.06 × 10
117
u
76
+ 8.53 × 10
117
u
75
+ · · · + 9.26 × 10
117
b + 6.66 ×
10
118
, −1.56 × 10
119
u
76
+ 2.54 × 10
120
u
75
+ · · · + 1.20 × 10
121
a − 2.34 ×
10
122
, u
77
− u
76
+ · · · − 267u − 11i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
0.0130055u
76
− 0.211672u
75
+ ··· + 76.4038u + 19.4646
0.438436u
76
− 0.920984u
75
+ ··· − 179.356u − 7.18528
a
6
=
u
u
a
2
=
0.167907u
76
− 0.560036u
75
+ ··· + 5.28710u + 16.3419
0.593337u
76
− 1.26935u
75
+ ··· − 250.473u − 10.3080
a
5
=
−0.411584u
76
+ 0.826205u
75
+ ··· + 35.9924u − 12.3201
−0.626576u
76
+ 1.06289u
75
+ ··· + 236.498u + 9.82640
a
10
=
−0.367850u
76
+ 0.345807u
75
+ ··· + 92.0501u + 14.7008
−1.23947u
76
+ 1.85355u
75
+ ··· + 320.091u + 14.3520
a
4
=
0.210003u
76
− 1.23021u
75
+ ··· − 8.76425u + 22.4581
1.40382u
76
− 3.36880u
75
+ ··· − 583.635u − 24.2823
a
9
=
−0.449798u
76
+ 0.574876u
75
+ ··· + 146.822u + 17.4073
−1.28744u
76
+ 2.03905u
75
+ ··· + 374.165u + 16.7057
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.0222u
76
+ 16.2318u
75
+ ··· + 3664.59u + 156.514
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
− 9u
76
+ ··· − 22u + 1
c
2
, c
5
u
77
+ u
76
+ ··· + 6201u + 108
c
3
, c
10
u
77
+ 33u
75
+ ··· − 4491u − 361
c
4
, c
8
u
77
+ 3u
76
+ ··· − 368u − 79
c
6
, c
7
, c
11
c
12
u
77
− u
76
+ ··· − 267u − 11
c
9
u
77
+ 6u
76
+ ··· + 12u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
− 5y
76
+ ··· + 70y −1
c
2
, c
5
y
77
− 73y
76
+ ··· + 14541849y −11664
c
3
, c
10
y
77
+ 66y
76
+ ··· + 8226479y −130321
c
4
, c
8
y
77
+ 35y
76
+ ··· − 116112y −6241
c
6
, c
7
, c
11
c
12
y
77
− 99y
76
+ ··· + 37057y −121
c
9
y
77
− 12y
76
+ ··· + 2032y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.038185 + 0.977495I
a = −0.0887050 − 0.0211649I
b = 0.180623 − 1.401330I
−3.38576 − 7.06554I 0
u = 0.038185 − 0.977495I
a = −0.0887050 + 0.0211649I
b = 0.180623 + 1.401330I
−3.38576 + 7.06554I 0
u = 0.959703 + 0.096825I
a = −0.20377 − 1.90119I
b = 0.228834 − 1.133660I
−4.11267 − 2.60144I 0
u = 0.959703 − 0.096825I
a = −0.20377 + 1.90119I
b = 0.228834 + 1.133660I
−4.11267 + 2.60144I 0
u = 1.005850 + 0.248662I
a = −1.40505 − 1.62886I
b = 0.109475 − 1.292590I
−6.11081 − 3.61083I 0
u = 1.005850 − 0.248662I
a = −1.40505 + 1.62886I
b = 0.109475 + 1.292590I
−6.11081 + 3.61083I 0
u = −1.051160 + 0.193722I
a = −0.588531 − 0.688350I
b = 0.226875 − 0.069667I
−1.83333 − 1.94928I 0
u = −1.051160 − 0.193722I
a = −0.588531 + 0.688350I
b = 0.226875 + 0.069667I
−1.83333 + 1.94928I 0
u = 0.982142 + 0.468578I
a = 0.91609 + 1.21859I
b = −0.39039 + 1.53681I
−9.70005 − 6.50940I 0
u = 0.982142 − 0.468578I
a = 0.91609 − 1.21859I
b = −0.39039 − 1.53681I
−9.70005 + 6.50940I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766904 + 0.773981I
a = −0.921347 + 0.489206I
b = 0.091213 + 1.388450I
−7.58242 + 2.37767I 0
u = −0.766904 − 0.773981I
a = −0.921347 − 0.489206I
b = 0.091213 − 1.388450I
−7.58242 − 2.37767I 0
u = 0.830594 + 0.329150I
a = 0.253500 + 0.255718I
b = −1.058950 + 0.357207I
−0.60061 − 7.40607I 0
u = 0.830594 − 0.329150I
a = 0.253500 − 0.255718I
b = −1.058950 − 0.357207I
−0.60061 + 7.40607I 0
u = −0.821582 + 0.262973I
a = −0.40258 + 2.54715I
b = 0.246547 + 1.190120I
−1.06852 + 6.57872I 0
u = −0.821582 − 0.262973I
a = −0.40258 − 2.54715I
b = 0.246547 − 1.190120I
−1.06852 − 6.57872I 0
u = −1.002280 + 0.636861I
a = 0.88637 − 1.12933I
b = −0.36459 − 1.49562I
−6.57021 + 12.38620I 0
u = −1.002280 − 0.636861I
a = 0.88637 + 1.12933I
b = −0.36459 + 1.49562I
−6.57021 − 12.38620I 0
u = −1.241390 + 0.072237I
a = −0.175685 + 0.764416I
b = 0.482561 + 0.410258I
−1.57748 + 1.98475I 0
u = −1.241390 − 0.072237I
a = −0.175685 − 0.764416I
b = 0.482561 − 0.410258I
−1.57748 − 1.98475I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.177425 + 0.729527I
a = −0.364310 − 0.428903I
b = 0.162031 + 1.383920I
−6.18457 + 2.49771I −14.4448 + 0.I
u = −0.177425 − 0.729527I
a = −0.364310 + 0.428903I
b = 0.162031 − 1.383920I
−6.18457 − 2.49771I −14.4448 + 0.I
u = 0.582280 + 0.471981I
a = 0.168635 − 0.799555I
b = 0.574579 + 0.079542I
2.28027 − 3.59748I −8.00000 + 4.60742I
u = 0.582280 − 0.471981I
a = 0.168635 + 0.799555I
b = 0.574579 − 0.079542I
2.28027 + 3.59748I −8.00000 − 4.60742I
u = 0.693292 + 0.271817I
a = −1.153550 + 0.702978I
b = 0.344954 − 0.059152I
−2.76074 − 0.90392I −8.00000 + 8.29169I
u = 0.693292 − 0.271817I
a = −1.153550 − 0.702978I
b = 0.344954 + 0.059152I
−2.76074 + 0.90392I −8.00000 − 8.29169I
u = −0.733460 + 0.065281I
a = −0.382545 − 1.223710I
b = −1.83460 − 1.32389I
−2.96946 + 0.15069I 50.9420 − 6.6243I
u = −0.733460 − 0.065281I
a = −0.382545 + 1.223710I
b = −1.83460 + 1.32389I
−2.96946 − 0.15069I 50.9420 + 6.6243I
u = −0.698952 + 0.210701I
a = −2.35802 + 0.99441I
b = 0.121661 + 1.318110I
−6.82768 + 0.82988I −17.2416 + 2.2447I
u = −0.698952 − 0.210701I
a = −2.35802 − 0.99441I
b = 0.121661 − 1.318110I
−6.82768 − 0.82988I −17.2416 − 2.2447I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.255700 + 0.237415I
a = 0.056230 + 1.165950I
b = 0.446841 + 1.052400I
−3.35743 + 1.81897I 0
u = 1.255700 − 0.237415I
a = 0.056230 − 1.165950I
b = 0.446841 − 1.052400I
−3.35743 − 1.81897I 0
u = 1.073990 + 0.741345I
a = −0.808228 − 0.841791I
b = 0.033391 − 1.383920I
−6.40287 + 1.28578I 0
u = 1.073990 − 0.741345I
a = −0.808228 + 0.841791I
b = 0.033391 + 1.383920I
−6.40287 − 1.28578I 0
u = −0.629004 + 0.287209I
a = 0.96669 − 1.28469I
b = 0.289074 − 1.108480I
−1.49663 + 0.99559I −12.39912 − 2.84502I
u = −0.629004 − 0.287209I
a = 0.96669 + 1.28469I
b = 0.289074 + 1.108480I
−1.49663 − 0.99559I −12.39912 + 2.84502I
u = 0.282100 + 0.527030I
a = 0.630239 + 0.170161I
b = −0.633562 + 0.251400I
3.14780 + 0.17045I −2.65284 + 2.77130I
u = 0.282100 − 0.527030I
a = 0.630239 − 0.170161I
b = −0.633562 − 0.251400I
3.14780 − 0.17045I −2.65284 − 2.77130I
u = −0.560530
a = 0.504531
b = 0.446354
−0.920531 −10.2400
u = 0.077893 + 0.515289I
a = −0.22039 − 1.76338I
b = 0.537309 + 0.147685I
1.69633 + 4.51493I −4.07565 − 3.55592I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077893 − 0.515289I
a = −0.22039 + 1.76338I
b = 0.537309 − 0.147685I
1.69633 − 4.51493I −4.07565 + 3.55592I
u = −0.253806 + 0.423399I
a = 1.79739 + 0.32795I
b = 0.17927 − 1.41337I
−2.23223 + 1.30516I −8.70846 + 0.00114I
u = −0.253806 − 0.423399I
a = 1.79739 − 0.32795I
b = 0.17927 + 1.41337I
−2.23223 − 1.30516I −8.70846 − 0.00114I
u = −0.148906 + 0.435693I
a = 0.851093 + 0.698214I
b = −0.453634 + 1.011480I
1.00193 − 4.19580I −5.61939 + 0.53554I
u = −0.148906 − 0.435693I
a = 0.851093 − 0.698214I
b = −0.453634 − 1.011480I
1.00193 + 4.19580I −5.61939 − 0.53554I
u = −1.54899 + 0.13119I
a = −0.458921 − 0.532312I
b = −0.453875 − 0.087559I
−4.84668 + 5.75436I 0
u = −1.54899 − 0.13119I
a = −0.458921 + 0.532312I
b = −0.453875 + 0.087559I
−4.84668 − 5.75436I 0
u = 1.56208
a = −0.744675
b = −0.707392
−8.21010 0
u = −0.194765 + 0.328946I
a = 0.927094 − 0.543449I
b = −0.274652 − 0.797432I
−0.550057 + 1.180680I −6.71434 − 6.33000I
u = −0.194765 − 0.328946I
a = 0.927094 + 0.543449I
b = −0.274652 + 0.797432I
−0.550057 − 1.180680I −6.71434 + 6.33000I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63594 + 0.07265I
a = −0.49221 − 2.03787I
b = −0.21035 − 1.56875I
−9.51163 − 2.28865I 0
u = 1.63594 − 0.07265I
a = −0.49221 + 2.03787I
b = −0.21035 + 1.56875I
−9.51163 + 2.28865I 0
u = 1.65591 + 0.01982I
a = 1.12708 − 1.41391I
b = 1.88510 − 1.34051I
−11.46620 − 0.48828I 0
u = 1.65591 − 0.01982I
a = 1.12708 + 1.41391I
b = 1.88510 + 1.34051I
−11.46620 + 0.48828I 0
u = −1.65428 + 0.07783I
a = 0.140794 + 0.057576I
b = −0.803163 − 0.072746I
−11.09700 + 2.25616I 0
u = −1.65428 − 0.07783I
a = 0.140794 − 0.057576I
b = −0.803163 + 0.072746I
−11.09700 − 2.25616I 0
u = 1.65550 + 0.05326I
a = 0.86314 + 1.70541I
b = −0.324921 + 1.348630I
−15.2209 − 1.8009I 0
u = 1.65550 − 0.05326I
a = 0.86314 − 1.70541I
b = −0.324921 − 1.348630I
−15.2209 + 1.8009I 0
u = −1.67130 + 0.08386I
a = 0.571962 + 0.560598I
b = 1.40627 + 0.45907I
−9.37948 + 8.96392I 0
u = −1.67130 − 0.08386I
a = 0.571962 − 0.560598I
b = 1.40627 − 0.45907I
−9.37948 − 8.96392I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67370 + 0.06775I
a = 0.03577 + 2.41906I
b = −0.14904 + 1.40818I
−9.88025 − 7.83088I 0
u = 1.67370 − 0.06775I
a = 0.03577 − 2.41906I
b = −0.14904 − 1.40818I
−9.88025 + 7.83088I 0
u = −1.69944 + 0.01339I
a = −0.04463 − 2.12033I
b = −0.18677 − 1.44922I
−13.55490 + 2.95411I 0
u = −1.69944 − 0.01339I
a = −0.04463 + 2.12033I
b = −0.18677 + 1.44922I
−13.55490 − 2.95411I 0
u = 1.71187 + 0.02596I
a = 0.0605613 − 0.0979481I
b = −0.722947 + 0.070558I
−11.60350 + 1.31140I 0
u = 1.71187 − 0.02596I
a = 0.0605613 + 0.0979481I
b = −0.722947 − 0.070558I
−11.60350 − 1.31140I 0
u = −1.70725 + 0.13135I
a = −0.35570 + 1.93715I
b = 0.54806 + 1.71252I
−19.0731 + 8.9271I 0
u = −1.70725 − 0.13135I
a = −0.35570 − 1.93715I
b = 0.54806 − 1.71252I
−19.0731 − 8.9271I 0
u = 1.70371 + 0.24470I
a = 0.58315 + 1.47761I
b = −0.33341 + 1.43214I
−16.0310 − 6.4382I 0
u = 1.70371 − 0.24470I
a = 0.58315 − 1.47761I
b = −0.33341 − 1.43214I
−16.0310 + 6.4382I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.72083 + 0.06542I
a = 0.72947 − 1.92804I
b = −0.275006 − 1.356000I
−15.8163 + 4.8861I 0
u = −1.72083 − 0.06542I
a = 0.72947 + 1.92804I
b = −0.275006 + 1.356000I
−15.8163 − 4.8861I 0
u = 1.72028 + 0.18203I
a = −0.48183 − 1.86225I
b = 0.50074 − 1.61966I
−15.9464 − 15.6846I 0
u = 1.72028 − 0.18203I
a = −0.48183 + 1.86225I
b = 0.50074 + 1.61966I
−15.9464 + 15.6846I 0
u = −1.78884 + 0.15629I
a = 0.43586 − 1.59414I
b = −0.29442 − 1.43542I
−16.5992 + 2.4652I 0
u = −1.78884 − 0.15629I
a = 0.43586 + 1.59414I
b = −0.29442 + 1.43542I
−16.5992 − 2.4652I 0
u = −0.0577950
a = 15.4136
b = 0.598762
−1.41671 −4.26830
12
II. I
u
2
= hu
7
− 5u
5
+ u
4
+ 7u
3
− 3u
2
+ b − 2u + 1, u
7
− 5u
5
+ u
4
+ 7u
3
−
4u
2
+ a − 2u + 3, u
14
− 10u
12
+ · · · − 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−u
7
+ 5u
5
− u
4
− 7u
3
+ 4u
2
+ 2u − 3
−u
7
+ 5u
5
− u
4
− 7u
3
+ 3u
2
+ 2u − 1
a
6
=
u
u
a
2
=
−u
7
+ 5u
5
− 2u
4
− 7u
3
+ 6u
2
+ 2u − 3
−u
7
+ 5u
5
− 2u
4
− 7u
3
+ 5u
2
+ 2u − 1
a
5
=
−u
10
+ 7u
8
− 2u
7
− 17u
6
+ 10u
5
+ 16u
4
− 15u
3
− 4u
2
+ 7u
−u
10
+ 7u
8
− 2u
7
− 17u
6
+ 9u
5
+ 16u
4
− 11u
3
− 4u
2
+ 3u
a
10
=
−u
9
+ 7u
7
− u
6
− 17u
5
+ 5u
4
+ 17u
3
− 7u
2
− 6u + 3
u
3
− 2u
a
4
=
−u
10
+ 7u
8
− 3u
7
− 17u
6
+ 16u
5
+ 14u
4
− 25u
3
+ 3u
2
+ 10u − 4
−u
10
+ 7u
8
− 2u
7
− 17u
6
+ 10u
5
+ 15u
4
− 14u
3
− u
2
+ 4u − 1
a
9
=
−u
12
+ u
11
+ ··· − 9u + 3
−u
12
+ u
11
+ ··· − 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−u
13
+3u
12
+8u
11
−28u
10
−15u
9
+99u
8
−25u
7
−156u
6
+108u
5
+92u
4
−110u
3
+u
2
+35u−23
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 3u
13
+ ··· − 8u + 1
c
2
u
14
+ 6u
13
+ ··· + 3u + 1
c
3
u
14
+ 3u
12
+ u
10
− u
9
− 5u
8
− 2u
7
− 5u
6
+ u
3
+ 2u
2
+ u + 1
c
4
u
14
+ u
13
+ 2u
12
+ u
11
− 5u
8
− 2u
7
− 5u
6
− u
5
+ u
4
+ 3u
2
+ 1
c
5
u
14
− 6u
13
+ ··· − 3u + 1
c
6
, c
7
u
14
− 10u
12
+ ··· + 2u + 1
c
8
u
14
− u
13
+ 2u
12
− u
11
− 5u
8
+ 2u
7
− 5u
6
+ u
5
+ u
4
+ 3u
2
+ 1
c
9
u
14
+ u
13
+ ··· − 13u + 3
c
10
u
14
+ 3u
12
+ u
10
+ u
9
− 5u
8
+ 2u
7
− 5u
6
− u
3
+ 2u
2
− u + 1
c
11
, c
12
u
14
− 10u
12
+ ··· − 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− y
13
+ ··· − 16y + 1
c
2
, c
5
y
14
− 14y
13
+ ··· − 5y + 1
c
3
, c
10
y
14
+ 6y
13
+ ··· + 3y + 1
c
4
, c
8
y
14
+ 3y
13
+ ··· + 6y + 1
c
6
, c
7
, c
11
c
12
y
14
− 20y
13
+ ··· − 8y + 1
c
9
y
14
− 3y
13
+ ··· − 367y + 9
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769273 + 0.499501I
a = −1.56602 − 0.52282I
b = 0.091706 − 1.291320I
−6.35538 − 1.76661I −11.51225 + 3.46978I
u = 0.769273 − 0.499501I
a = −1.56602 + 0.52282I
b = 0.091706 + 1.291320I
−6.35538 + 1.76661I −11.51225 − 3.46978I
u = −0.796065
a = −0.323376
b = 1.04290
−3.10490 −12.3270
u = 1.235030 + 0.234166I
a = −0.21622 + 1.52053I
b = 0.313310 + 0.942121I
−2.96355 + 3.01467I −12.7328 − 6.3955I
u = 1.235030 − 0.234166I
a = −0.21622 − 1.52053I
b = 0.313310 − 0.942121I
−2.96355 − 3.01467I −12.7328 + 6.3955I
u = −1.49700 + 0.09797I
a = 0.579846 + 0.369336I
b = 0.348422 + 0.662650I
−5.58734 + 6.30976I −15.1896 − 6.5023I
u = −1.49700 − 0.09797I
a = 0.579846 − 0.369336I
b = 0.348422 − 0.662650I
−5.58734 − 6.30976I −15.1896 + 6.5023I
u = 1.54154
a = 1.13801
b = 0.761672
−8.65121 −25.5320
u = −0.422763
a = −2.69875
b = −0.877477
−1.82255 −28.5550
u = 0.221437 + 0.280509I
a = −2.37781 + 0.90237I
b = −0.348156 + 0.778139I
0.41125 − 4.94330I −12.3996 + 6.8028I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.221437 − 0.280509I
a = −2.37781 − 0.90237I
b = −0.348156 − 0.778139I
0.41125 + 4.94330I −12.3996 − 6.8028I
u = 1.67943
a = −0.353377
b = −1.17385
−11.9636 −13.8850
u = −1.72981 + 0.10668I
a = 0.69894 − 1.68693I
b = −0.281906 − 1.317870I
−15.5021 + 4.1610I −13.01637 + 0.23068I
u = −1.72981 − 0.10668I
a = 0.69894 + 1.68693I
b = −0.281906 + 1.317870I
−15.5021 − 4.1610I −13.01637 − 0.23068I
17
III. I
u
3
= hb − a − 1, a
2
+ a + 1, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
8
=
1
0
a
1
=
0
1
a
3
=
a
a + 1
a
6
=
−1
−1
a
2
=
a + 1
a + 2
a
5
=
a
a + 1
a
10
=
0
a
a
4
=
a
a
a
9
=
0
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
2
− u + 1
c
2
, c
6
, c
7
(u − 1)
2
c
3
, c
4
u
2
+ u + 1
c
5
, c
11
, c
12
(u + 1)
2
c
9
u
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
y
2
+ y + 1
c
2
, c
5
, c
6
c
7
, c
11
, c
12
(y −1)
2
c
9
y
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.500000 + 0.866025I
b = 0.500000 + 0.866025I
−3.28987 −15.0000
u = −1.00000
a = −0.500000 − 0.866025I
b = 0.500000 − 0.866025I
−3.28987 −15.0000
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
14
− 3u
13
+ ··· − 8u + 1)(u
77
− 9u
76
+ ··· − 22u + 1)
c
2
((u − 1)
2
)(u
14
+ 6u
13
+ ··· + 3u + 1)(u
77
+ u
76
+ ··· + 6201u + 108)
c
3
(u
2
+ u + 1)(u
14
+ 3u
12
+ ··· + u + 1)
· (u
77
+ 33u
75
+ ··· − 4491u − 361)
c
4
(u
2
+ u + 1)(u
14
+ u
13
+ ··· + 3u
2
+ 1)
· (u
77
+ 3u
76
+ ··· − 368u − 79)
c
5
((u + 1)
2
)(u
14
− 6u
13
+ ··· − 3u + 1)(u
77
+ u
76
+ ··· + 6201u + 108)
c
6
, c
7
((u − 1)
2
)(u
14
− 10u
12
+ ··· + 2u + 1)(u
77
− u
76
+ ··· − 267u − 11)
c
8
(u
2
− u + 1)(u
14
− u
13
+ ··· + 3u
2
+ 1)
· (u
77
+ 3u
76
+ ··· − 368u − 79)
c
9
u
2
(u
14
+ u
13
+ ··· − 13u + 3)(u
77
+ 6u
76
+ ··· + 12u + 8)
c
10
(u
2
− u + 1)(u
14
+ 3u
12
+ ··· − u + 1)
· (u
77
+ 33u
75
+ ··· − 4491u − 361)
c
11
, c
12
((u + 1)
2
)(u
14
− 10u
12
+ ··· − 2u + 1)(u
77
− u
76
+ ··· − 267u − 11)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
14
− y
13
+ ··· − 16y + 1)(y
77
− 5y
76
+ ··· + 70y −1)
c
2
, c
5
((y −1)
2
)(y
14
− 14y
13
+ ··· − 5y + 1)
· (y
77
− 73y
76
+ ··· + 14541849y −11664)
c
3
, c
10
(y
2
+ y + 1)(y
14
+ 6y
13
+ ··· + 3y + 1)
· (y
77
+ 66y
76
+ ··· + 8226479y −130321)
c
4
, c
8
(y
2
+ y + 1)(y
14
+ 3y
13
+ ··· + 6y + 1)
· (y
77
+ 35y
76
+ ··· − 116112y −6241)
c
6
, c
7
, c
11
c
12
((y −1)
2
)(y
14
− 20y
13
+ ··· − 8y + 1)
· (y
77
− 99y
76
+ ··· + 37057y −121)
c
9
y
2
(y
14
− 3y
13
+ ··· − 367y + 9)(y
77
− 12y
76
+ ··· + 2032y −64)
23
