12a
0275
(K12a
0275
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 10 12 5 4 1 7 11
Solving Sequence
7,11
12 8
1,4
3 10 6 2 9 5
c
11
c
7
c
12
c
3
c
10
c
6
c
2
c
9
c
4
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.60711 × 10
31
u
97
+ 4.13570 × 10
31
u
96
+ ··· + 1.17609 × 10
31
b − 9.51207 × 10
31
,
7.27315 × 10
30
u
97
+ 3.06066 × 10
31
u
96
+ ··· + 1.76413 × 10
31
a − 1.12339 × 10
32
, u
98
+ 2u
97
+ ··· − 11u − 3i
I
u
2
= h−2u
2
b + b
2
+ u
2
− 3u + 1, −u
2
+ a + u, u
3
− u
2
+ 1i
I
u
3
= h−u
2
+ b, −u
2
+ a − u, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 107 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
=
h2.61×10
31
u
97
+4.14×10
31
u
96
+· · ·+1.18×10
31
b−9.51×10
31
, 7.27×10
30
u
97
+
3.06 × 10
31
u
96
+ · · · + 1.76 × 10
31
a − 1.12 × 10
32
, u
98
+ 2u
97
+ · · · − 11u − 3i
(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
2
a
4
=
−0.412279u
97
− 1.73494u
96
+ ··· + 19.5423u + 6.36797
−2.21676u
97
− 3.51649u
96
+ ··· + 23.8215u + 8.08789
a
3
=
−0.857679u
97
− 2.36436u
96
+ ··· + 22.7036u + 7.60150
−2.67472u
97
− 3.75515u
96
+ ··· + 25.4438u + 8.53728
a
10
=
u
4
− u
2
+ 1
u
4
a
6
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
9
+ u
7
− u
5
+ u
a
2
=
0.107279u
97
− 0.436672u
96
+ ··· + 11.1633u + 4.41126
−1.68317u
97
− 2.85530u
96
+ ··· + 19.5719u + 6.61020
a
9
=
2.65352u
97
+ 2.88089u
96
+ ··· − 14.9561u − 3.19424
1.22758u
97
− 1.19856u
96
+ ··· + 8.21326u + 4.27781
a
5
=
−0.868547u
97
− 0.700412u
96
+ ··· + 2.11157u + 0.420630
1.82742u
97
+ 2.47475u
96
+ ··· − 18.1294u − 5.41346
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.15454u
97
− 3.49753u
96
+ ··· + 45.8013u + 14.7149
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
+ 50u
97
+ ··· + 30u + 1
c
2
, c
5
u
98
+ 4u
97
+ ··· − 4u − 1
c
3
u
98
+ u
97
+ ··· − 880u + 200
c
4
, c
8
, c
9
u
98
− u
97
+ ··· − 48u + 8
c
6
u
98
− 2u
97
+ ··· + 11527u − 7419
c
7
, c
11
u
98
+ 2u
97
+ ··· − 11u − 3
c
10
, c
12
u
98
− 32u
97
+ ··· − 7u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
+ 6y
97
+ ··· − 294y + 1
c
2
, c
5
y
98
− 50y
97
+ ··· − 30y + 1
c
3
y
98
+ 7y
97
+ ··· + 11398400y + 40000
c
4
, c
8
, c
9
y
98
+ 91y
97
+ ··· − 1152y + 64
c
6
y
98
+ 64y
96
+ ··· − 760444939y + 55041561
c
7
, c
11
y
98
− 32y
97
+ ··· − 7y + 9
c
10
, c
12
y
98
+ 72y
97
+ ··· − 1075y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.734696 + 0.663905I
a = 0.268933 + 0.786528I
b = −0.174193 + 0.529627I
−1.64759 − 1.78795I 0
u = −0.734696 − 0.663905I
a = 0.268933 − 0.786528I
b = −0.174193 − 0.529627I
−1.64759 + 1.78795I 0
u = 0.664153 + 0.765570I
a = 0.24029 − 1.53419I
b = −1.41749 − 0.92344I
−0.08595 − 1.85140I 0
u = 0.664153 − 0.765570I
a = 0.24029 + 1.53419I
b = −1.41749 + 0.92344I
−0.08595 + 1.85140I 0
u = 0.974010 + 0.115853I
a = 2.15359 + 1.31393I
b = 1.283730 + 0.454853I
−4.35227 + 2.21027I 0
u = 0.974010 − 0.115853I
a = 2.15359 − 1.31393I
b = 1.283730 − 0.454853I
−4.35227 − 2.21027I 0
u = 1.033580 + 0.091897I
a = 0.399864 − 0.250616I
b = 0.241490 + 0.596866I
2.38941 + 2.66439I 0
u = 1.033580 − 0.091897I
a = 0.399864 + 0.250616I
b = 0.241490 − 0.596866I
2.38941 − 2.66439I 0
u = −0.686782 + 0.779974I
a = −0.098066 − 1.009560I
b = 0.336237 − 0.672280I
−3.57357 + 2.65527I 0
u = −0.686782 − 0.779974I
a = −0.098066 + 1.009560I
b = 0.336237 + 0.672280I
−3.57357 − 2.65527I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.048810 + 0.004708I
a = −0.715803 + 0.615832I
b = −0.522953 − 0.263740I
3.08776 − 2.29887I 0
u = 1.048810 − 0.004708I
a = −0.715803 − 0.615832I
b = −0.522953 + 0.263740I
3.08776 + 2.29887I 0
u = −1.052800 + 0.076933I
a = −1.42127 − 0.08382I
b = −0.911925 + 0.074163I
5.77405 − 1.58455I 0
u = −1.052800 − 0.076933I
a = −1.42127 + 0.08382I
b = −0.911925 − 0.074163I
5.77405 + 1.58455I 0
u = −0.678110 + 0.813029I
a = −0.18357 + 1.96127I
b = −2.45847 + 0.56304I
−5.35406 + 5.42665I 0
u = −0.678110 − 0.813029I
a = −0.18357 − 1.96127I
b = −2.45847 − 0.56304I
−5.35406 − 5.42665I 0
u = −0.723258 + 0.781799I
a = 0.81231 − 2.36644I
b = 3.40890 − 0.20602I
−10.29880 + 1.62019I 0
u = −0.723258 − 0.781799I
a = 0.81231 + 2.36644I
b = 3.40890 + 0.20602I
−10.29880 − 1.62019I 0
u = 0.678617 + 0.821492I
a = −0.32198 + 1.65550I
b = 1.37247 + 1.19340I
−2.43590 − 6.98834I 0
u = 0.678617 − 0.821492I
a = −0.32198 − 1.65550I
b = 1.37247 − 1.19340I
−2.43590 + 6.98834I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928732 + 0.101713I
a = −0.256255 − 0.467748I
b = −0.13808 − 2.08888I
−4.87657 − 1.38006I 0
u = −0.928732 − 0.101713I
a = −0.256255 + 0.467748I
b = −0.13808 + 2.08888I
−4.87657 + 1.38006I 0
u = 1.060740 + 0.131344I
a = −1.72992 − 0.60308I
b = −1.263170 + 0.011705I
1.06805 + 5.33557I 0
u = 1.060740 − 0.131344I
a = −1.72992 + 0.60308I
b = −1.263170 − 0.011705I
1.06805 − 5.33557I 0
u = 0.766804 + 0.744633I
a = 0.05865 + 1.81149I
b = 2.16829 + 0.98332I
−4.91150 + 1.14751I 0
u = 0.766804 − 0.744633I
a = 0.05865 − 1.81149I
b = 2.16829 − 0.98332I
−4.91150 − 1.14751I 0
u = −0.987937 + 0.409006I
a = −0.916452 − 0.624323I
b = −0.45614 − 2.02402I
−2.70652 + 4.30447I 0
u = −0.987937 − 0.409006I
a = −0.916452 + 0.624323I
b = −0.45614 + 2.02402I
−2.70652 − 4.30447I 0
u = 0.740977 + 0.773913I
a = 0.556789 + 0.820914I
b = −0.196140 − 0.441436I
−10.60880 − 0.47636I 0
u = 0.740977 − 0.773913I
a = 0.556789 − 0.820914I
b = −0.196140 + 0.441436I
−10.60880 + 0.47636I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957407 + 0.485442I
a = −0.517871 − 0.147787I
b = −0.99562 + 1.21717I
2.09681 − 0.69131I 0
u = 0.957407 − 0.485442I
a = −0.517871 + 0.147787I
b = −0.99562 − 1.21717I
2.09681 + 0.69131I 0
u = −0.951315 + 0.500130I
a = 1.048800 + 0.620778I
b = 0.34730 + 1.96268I
−1.044750 − 0.764706I 0
u = −0.951315 − 0.500130I
a = 1.048800 − 0.620778I
b = 0.34730 − 1.96268I
−1.044750 + 0.764706I 0
u = −1.066520 + 0.139595I
a = 1.320590 + 0.104609I
b = 0.861474 − 0.162656I
4.09275 − 6.88786I 0
u = −1.066520 − 0.139595I
a = 1.320590 − 0.104609I
b = 0.861474 + 0.162656I
4.09275 + 6.88786I 0
u = −0.880118 + 0.631470I
a = −1.67758 − 1.51107I
b = 0.85573 − 3.37184I
−6.95319 − 2.46093I 0
u = −0.880118 − 0.631470I
a = −1.67758 + 1.51107I
b = 0.85573 + 3.37184I
−6.95319 + 2.46093I 0
u = 1.075780 + 0.174335I
a = 1.86064 + 0.40213I
b = 1.42452 − 0.05583I
−1.27008 + 10.77240I 0
u = 1.075780 − 0.174335I
a = 1.86064 − 0.40213I
b = 1.42452 + 0.05583I
−1.27008 − 10.77240I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.690744 + 0.843837I
a = −0.11876 − 2.16819I
b = 2.41190 − 1.05109I
−8.14004 + 10.77530I 0
u = −0.690744 − 0.843837I
a = −0.11876 + 2.16819I
b = 2.41190 + 1.05109I
−8.14004 − 10.77530I 0
u = −0.896121
a = 1.95972
b = 0.975925
−0.00908317 15.9790
u = 0.885397 + 0.693912I
a = 0.339321 − 0.165892I
b = 0.973356 + 0.721573I
−7.99772 + 2.68301I 0
u = 0.885397 − 0.693912I
a = 0.339321 + 0.165892I
b = 0.973356 − 0.721573I
−7.99772 − 2.68301I 0
u = −0.964856 + 0.583616I
a = 0.122982 + 0.675980I
b = −0.997979 − 0.010842I
−0.45889 − 3.08345I 0
u = −0.964856 − 0.583616I
a = 0.122982 − 0.675980I
b = −0.997979 + 0.010842I
−0.45889 + 3.08345I 0
u = −0.543311 + 0.677762I
a = −0.402101 + 0.468161I
b = −1.147070 − 0.605260I
−2.00086 + 3.25948I 3.20197 − 3.63998I
u = −0.543311 − 0.677762I
a = −0.402101 − 0.468161I
b = −1.147070 + 0.605260I
−2.00086 − 3.25948I 3.20197 + 3.63998I
u = 0.979469 + 0.580581I
a = 0.938003 + 0.108373I
b = 1.32525 − 1.58756I
2.81422 + 4.41459I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.979469 − 0.580581I
a = 0.938003 − 0.108373I
b = 1.32525 + 1.58756I
2.81422 − 4.41459I 0
u = 0.845088 + 0.768773I
a = −0.300617 − 0.141131I
b = 0.531484 + 0.924146I
−8.01111 + 2.88840I 0
u = 0.845088 − 0.768773I
a = −0.300617 + 0.141131I
b = 0.531484 − 0.924146I
−8.01111 − 2.88840I 0
u = −0.827932 + 0.796921I
a = 0.235307 − 0.633403I
b = 0.463402 − 0.312534I
−5.02726 − 3.93837I 0
u = −0.827932 − 0.796921I
a = 0.235307 + 0.633403I
b = 0.463402 + 0.312534I
−5.02726 + 3.93837I 0
u = 0.812963 + 0.833602I
a = 0.863006 + 0.290924I
b = −0.018801 − 0.942954I
−10.35280 + 6.61154I 0
u = 0.812963 − 0.833602I
a = 0.863006 − 0.290924I
b = −0.018801 + 0.942954I
−10.35280 − 6.61154I 0
u = −0.975988 + 0.661994I
a = 0.837091 + 0.444177I
b = 0.298202 + 1.014370I
−0.87488 − 3.38182I 0
u = −0.975988 − 0.661994I
a = 0.837091 − 0.444177I
b = 0.298202 − 1.014370I
−0.87488 + 3.38182I 0
u = 0.891517 + 0.777987I
a = −0.167596 + 0.274913I
b = 0.77023 + 1.19118I
−7.91253 + 2.91496I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.891517 − 0.777987I
a = −0.167596 − 0.274913I
b = 0.77023 − 1.19118I
−7.91253 − 2.91496I 0
u = −1.003260 + 0.630448I
a = 0.465446 − 0.663409I
b = 1.75234 + 0.70638I
−0.72109 − 8.29532I 0
u = −1.003260 − 0.630448I
a = 0.465446 + 0.663409I
b = 1.75234 − 0.70638I
−0.72109 + 8.29532I 0
u = 0.951402 + 0.706783I
a = −1.86377 − 0.05859I
b = −1.84095 + 2.50699I
−4.34485 + 4.38252I 0
u = 0.951402 − 0.706783I
a = −1.86377 + 0.05859I
b = −1.84095 − 2.50699I
−4.34485 − 4.38252I 0
u = −0.922800 + 0.769461I
a = −0.584425 + 0.120528I
b = −0.496422 − 0.246804I
−4.73667 − 1.94087I 0
u = −0.922800 − 0.769461I
a = −0.584425 − 0.120528I
b = −0.496422 + 0.246804I
−4.73667 + 1.94087I 0
u = 0.974163 + 0.718879I
a = −0.618640 − 0.368169I
b = −1.33080 − 0.96990I
−9.89732 + 6.12933I 0
u = 0.974163 − 0.718879I
a = −0.618640 + 0.368169I
b = −1.33080 + 0.96990I
−9.89732 − 6.12933I 0
u = −0.986277 + 0.718325I
a = −2.23583 + 0.89659I
b = −3.70509 − 2.48584I
−9.49872 − 7.29344I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986277 − 0.718325I
a = −2.23583 − 0.89659I
b = −3.70509 + 2.48584I
−9.49872 + 7.29344I 0
u = 1.008450 + 0.695338I
a = 1.51547 − 0.20734I
b = 1.40306 − 2.25150I
0.94289 + 7.40217I 0
u = 1.008450 − 0.695338I
a = 1.51547 + 0.20734I
b = 1.40306 + 2.25150I
0.94289 − 7.40217I 0
u = −1.003950 + 0.706737I
a = −0.940078 − 0.258556I
b = −0.604614 − 0.869244I
−2.61594 − 8.28446I 0
u = −1.003950 − 0.706737I
a = −0.940078 + 0.258556I
b = −0.604614 + 0.869244I
−2.61594 + 8.28446I 0
u = 0.952432 + 0.787199I
a = −0.233356 − 0.688774I
b = −1.19894 − 1.31614I
−9.92247 − 0.56488I 0
u = 0.952432 − 0.787199I
a = −0.233356 + 0.688774I
b = −1.19894 + 1.31614I
−9.92247 + 0.56488I 0
u = −1.017720 + 0.718230I
a = 1.83730 − 0.24404I
b = 2.63471 + 2.58637I
−4.32385 − 11.18140I 0
u = −1.017720 − 0.718230I
a = 1.83730 + 0.24404I
b = 2.63471 − 2.58637I
−4.32385 + 11.18140I 0
u = 1.020700 + 0.721839I
a = −1.57725 + 0.33929I
b = −1.30143 + 2.34008I
−1.39559 + 12.77850I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.020700 − 0.721839I
a = −1.57725 − 0.33929I
b = −1.30143 − 2.34008I
−1.39559 − 12.77850I 0
u = −1.024300 + 0.736136I
a = −2.01726 − 0.07594I
b = −2.43886 − 3.03995I
−7.1180 − 16.6773I 0
u = −1.024300 − 0.736136I
a = −2.01726 + 0.07594I
b = −2.43886 + 3.03995I
−7.1180 + 16.6773I 0
u = −0.466220 + 0.569770I
a = 0.648090 + 0.414506I
b = 0.412746 + 0.878072I
−1.68032 − 1.37989I 3.35615 + 3.69950I
u = −0.466220 − 0.569770I
a = 0.648090 − 0.414506I
b = 0.412746 − 0.878072I
−1.68032 + 1.37989I 3.35615 − 3.69950I
u = −0.145736 + 0.693433I
a = −1.53134 − 1.65052I
b = −0.085612 − 1.186910I
−5.28167 − 8.07071I −0.44347 + 6.40023I
u = −0.145736 − 0.693433I
a = −1.53134 + 1.65052I
b = −0.085612 + 1.186910I
−5.28167 + 8.07071I −0.44347 − 6.40023I
u = 0.386558 + 0.559721I
a = 0.573963 − 0.920489I
b = −0.645140 − 0.368414I
1.405300 + 0.016474I 8.39486 − 0.50750I
u = 0.386558 − 0.559721I
a = 0.573963 + 0.920489I
b = −0.645140 + 0.368414I
1.405300 − 0.016474I 8.39486 + 0.50750I
u = 0.199719 + 0.642870I
a = −0.774539 + 0.907692I
b = 0.417723 + 0.454729I
0.00186 + 4.54800I 4.24116 − 6.44785I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.199719 − 0.642870I
a = −0.774539 − 0.907692I
b = 0.417723 − 0.454729I
0.00186 − 4.54800I 4.24116 + 6.44785I
u = −0.213923 + 0.624262I
a = 1.56949 + 1.32301I
b = 0.093981 + 1.179720I
−3.01589 − 3.10558I 2.47804 + 2.78013I
u = −0.213923 − 0.624262I
a = 1.56949 − 1.32301I
b = 0.093981 − 1.179720I
−3.01589 + 3.10558I 2.47804 − 2.78013I
u = 0.584842
a = 0.394386
b = −0.366402
0.748531 14.1870
u = −0.227216 + 0.432211I
a = −0.337752 + 0.892423I
b = 0.282292 + 0.388004I
−1.49333 − 1.09550I −0.53142 + 1.61867I
u = −0.227216 − 0.432211I
a = −0.337752 − 0.892423I
b = 0.282292 − 0.388004I
−1.49333 + 1.09550I −0.53142 − 1.61867I
u = −0.048605 + 0.460204I
a = −2.63423 − 1.71957I
b = −0.029689 − 1.228200I
−7.48247 − 0.39602I −4.30181 − 0.01088I
u = −0.048605 − 0.460204I
a = −2.63423 + 1.71957I
b = −0.029689 + 1.228200I
−7.48247 + 0.39602I −4.30181 + 0.01088I
14
II. I
u
2
= h−2u
2
b + b
2
+ u
2
− 3u + 1, −u
2
+ a + u, u
3
− u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
u
−u
2
+ u + 1
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
2
− u
b
a
3
=
−u
2
b + 2u
2
− 2u − 1
−bu + 2u
2
− 1
a
10
=
−u
u
2
− u − 1
a
6
=
−u
2
+ 1
−u
2
a
2
=
−u
2
b + u
2
− 2u
−bu + u
2
− 1
a
9
=
−u
2
+ b − u
−u
2
b − u
2
+ b − 2
a
5
=
u
2
b − 2u
2
+ 2u + 1
bu − 2u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
3
c
6
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
7
(u
3
+ u
2
− 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y + 2)
6
c
6
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
11
(y
3
− y
2
+ 2y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.662359 + 0.562280I
b = −0.580103 + 0.370424I
−9.60386 + 2.82812I −3.50976 − 2.97945I
u = 0.877439 + 0.744862I
a = −0.662359 + 0.562280I
b = 1.01026 + 2.24386I
−9.60386 + 2.82812I −3.50976 − 2.97945I
u = 0.877439 − 0.744862I
a = −0.662359 − 0.562280I
b = −0.580103 − 0.370424I
−9.60386 − 2.82812I −3.50976 + 2.97945I
u = 0.877439 − 0.744862I
a = −0.662359 − 0.562280I
b = 1.01026 − 2.24386I
−9.60386 − 2.82812I −3.50976 + 2.97945I
u = −0.754878
a = 1.32472
b = 0.56984 + 1.87343I
−5.46628 3.01950
u = −0.754878
a = 1.32472
b = 0.56984 − 1.87343I
−5.46628 3.01950
18
III. I
u
3
= h−u
2
+ b, −u
2
+ a − u, u
3
+ u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
u
u
2
+ u − 1
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
2
+ u
u
2
a
3
=
u
2
+ u
u
2
a
10
=
u
u
2
+ u − 1
a
6
=
u
2
− 1
u
2
a
2
=
u + 1
0
a
9
=
u
u
2
+ u − 1
a
5
=
u
2
+ u
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 2u + 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
10
u
3
+ u
2
+ 2u + 1
c
7
u
3
− u
2
+ 1
c
11
u
3
+ u
2
− 1
c
12
u
3
− u
2
+ 2u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
c
7
, c
11
y
3
− y
2
+ 2y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.662359 − 0.562280I
b = 0.215080 − 1.307140I
−4.66906 − 2.82812I 4.89456 + 3.73884I
u = −0.877439 − 0.744862I
a = −0.662359 + 0.562280I
b = 0.215080 + 1.307140I
−4.66906 + 2.82812I 4.89456 − 3.73884I
u = 0.754878
a = 1.32472
b = 0.569840
−0.531480 0.210880
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
98
+ 50u
97
+ ··· + 30u + 1)
c
2
((u − 1)
3
)(u + 1)
6
(u
98
+ 4u
97
+ ··· − 4u − 1)
c
3
u
3
(u
2
+ 2)
3
(u
98
+ u
97
+ ··· − 880u + 200)
c
4
, c
8
, c
9
u
3
(u
2
+ 2)
3
(u
98
− u
97
+ ··· − 48u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
98
+ 4u
97
+ ··· − 4u − 1)
c
6
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)
· (u
98
− 2u
97
+ ··· + 11527u − 7419)
c
7
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
98
+ 2u
97
+ ··· − 11u − 3)
c
10
((u
3
+ u
2
+ 2u + 1)
3
)(u
98
− 32u
97
+ ··· − 7u + 9)
c
11
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
98
+ 2u
97
+ ··· − 11u − 3)
c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
98
− 32u
97
+ ··· − 7u + 9)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
98
+ 6y
97
+ ··· − 294y + 1)
c
2
, c
5
((y −1)
9
)(y
98
− 50y
97
+ ··· − 30y + 1)
c
3
y
3
(y + 2)
6
(y
98
+ 7y
97
+ ··· + 1.13984 × 10
7
y + 40000)
c
4
, c
8
, c
9
y
3
(y + 2)
6
(y
98
+ 91y
97
+ ··· − 1152y + 64)
c
6
((y
3
+ 3y
2
+ 2y −1)
3
)(y
98
+ 64y
96
+ ··· − 7.60445 × 10
8
y + 5.50416 × 10
7
)
c
7
, c
11
((y
3
− y
2
+ 2y −1)
3
)(y
98
− 32y
97
+ ··· − 7y + 9)
c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
98
+ 72y
97
+ ··· − 1075y + 81)
24
