11a
162
(K11a
162
)
1
Arc Sequences
6 1 7 11 2 10 4 5 3 8 9
Solving Sequence
1,6
2
3,9
10 7 5 8 11 4
c
1
c
2
c
9
c
6
c
5
c
8
c
11
c
4
c
3
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
19
+ u
18
+ ··· + 3u + 1, 4u
18
6u
17
+ ··· + a + 3, 4u
17
7u
16
+ ··· + b 7i
I
u
2
= hu
102
+ 2u
101
+ ··· + 5u 1,
2.00222 × 10
146
u
101
2.26353 × 10
146
u
100
+ ··· + 1.69798 × 10
147
a + 8.74321 × 10
147
,
3.43191 × 10
147
u
101
5.98065 × 10
147
u
100
+ ··· + 1.69798 × 10
147
b 1.68341 × 10
146
i
There are 2 irreducible components with 121 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I.
I
u
1
= hu
19
+u
18
+· · ·+3u+1, 4u
18
6u
17
+· · ·+a+3, 4u
17
7u
16
+· · ·+b7i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
4u
18
+ 6u
17
+ ··· u 3
4u
17
+ 7u
16
+ ··· + 21u + 7
a
10
=
3u
18
+ 5u
17
+ ··· u 2
4u
17
+ 6u
16
+ ··· + 20u + 7
a
7
=
4u
18
5u
17
+ ··· + 6u + 4
2u
18
+ 3u
17
+ ··· + u 1
a
5
=
u
u
3
+ u
a
8
=
4u
18
+ 5u
17
+ ··· 10u 6
u
18
+ 7u
17
+ ··· + 27u + 9
a
11
=
6u
18
4u
17
+ ··· + 12u + 3
2u
17
2u
16
+ ··· u + 1
a
4
=
2u
18
+ 9u
16
+ ··· 3u + 1
4u
18
+ 7u
17
+ ··· + 4u 2
a
4
=
2u
18
+ 9u
16
+ ··· 3u + 1
4u
18
+ 7u
17
+ ··· + 4u 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.849830
a = 0.195511
b = 0.363685
0.655524 7.38949
u = 0.643913 1.140596I
a = 1.18488 + 0.86715I
b = 1.271461 + 0.375336I
2.40281 + 5.12847I 0.682236 + 1.181576I
u = 0.643913 + 1.140596I
a = 1.18488 0.86715I
b = 1.271461 0.375336I
2.40281 5.12847I 0.682236 1.181576I
u = 0.536362 0.225069I
a = 2.45456 + 0.82764I
b = 1.41660 0.02554I
4.99327 + 0.03621I 8.72091 + 1.39804I
u = 0.536362 + 0.225069I
a = 2.45456 0.82764I
b = 1.41660 + 0.02554I
4.99327 0.03621I 8.72091 1.39804I
u = 0.412083 1.018242I
a = 0.838502 + 0.039949I
b = 0.199643 + 0.487861I
2.67947 + 3.32318I 4.16053 3.59653I
u = 0.412083 + 1.018242I
a = 0.838502 0.039949I
b = 0.199643 0.487861I
2.67947 3.32318I 4.16053 + 3.59653I
u = 0.295559 0.809856I
a = 0.86554 1.47296I
b = 0.209636 0.820917I
1.72030 0.39989I 1.68186 + 0.51618I
u = 0.295559 + 0.809856I
a = 0.86554 + 1.47296I
b = 0.209636 + 0.820917I
1.72030 + 0.39989I 1.68186 0.51618I
u = 0.185848 1.360354I
a = 0.0181661 0.0703459I
b = 0.258074 + 0.320496I
4.05934 + 3.53517I 6.8503 17.2063I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.185848 + 1.360354I
a = 0.0181661 + 0.0703459I
b = 0.258074 0.320496I
4.05934 3.53517I 6.8503 + 17.2063I
u = 0.289824 0.910566I
a = 0.139626 + 1.198034I
b = 0.283665 1.264212I
0.97791 5.98873I 3.06705 + 8.24706I
u = 0.289824 + 0.910566I
a = 0.139626 1.198034I
b = 0.283665 + 1.264212I
0.97791 + 5.98873I 3.06705 8.24706I
u = 0.339623 0.919258I
a = 2.24756 + 0.52382I
b = 0.00818 + 1.67856I
0.86544 + 3.34083I 3.34354 4.41577I
u = 0.339623 + 0.919258I
a = 2.24756 0.52382I
b = 0.00818 1.67856I
0.86544 3.34083I 3.34354 + 4.41577I
u = 0.612447 1.019280I
a = 1.83602 0.52614I
b = 0.85573 1.47613I
2.94345 8.65071I 5.93756 + 9.11510I
u = 0.612447 + 1.019280I
a = 1.83602 + 0.52614I
b = 0.85573 + 1.47613I
2.94345 + 8.65071I 5.93756 9.11510I
u = 0.756785 0.627945I
a = 0.452433 0.973447I
b = 0.798144 + 1.019225I
4.17315 + 3.45944I 9.43557 4.00641I
u = 0.756785 + 0.627945I
a = 0.452433 + 0.973447I
b = 0.798144 1.019225I
4.17315 3.45944I 9.43557 + 4.00641I
4
II. I
u
2
= hu
102
+ 2u
101
+ · · · + 5u 1, 2.00 × 10
146
u
101
2.26 ×
10
146
u
100
+ · · · + 1.70 × 10
147
a + 8.74 × 10
147
, 3.43 × 10
147
u
101
5.98 ×
10
147
u
100
+ · · · + 1.70 × 10
147
b 1.68 × 10
146
i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
0.117918u
101
+ 0.133307u
100
+ ··· + 12.2631u 5.14920
2.02118u
101
+ 3.52222u
100
+ ··· 4.87977u + 0.0991423
a
10
=
1.05197u
101
1.12612u
100
+ ··· + 5.29937u 4.08217
3.80739u
101
+ 7.60484u
100
+ ··· + 2.45665u 1.49141
a
7
=
1.14572u
101
+ 2.76876u
100
+ ··· 11.5438u 3.13970
0.857615u
101
2.20117u
100
+ ··· 11.8872u + 3.03059
a
5
=
u
u
3
+ u
a
8
=
1.79267u
101
1.47114u
100
+ ··· + 17.2481u 5.63399
3.45165u
101
+ 7.08810u
100
+ ··· + 3.12953u 1.63280
a
11
=
0.708680u
101
1.92696u
100
+ ··· + 32.4688u 0.824193
0.0645548u
101
0.869890u
100
+ ··· 3.37763u 0.380308
a
4
=
4.67359u
101
7.60736u
100
+ ··· + 9.22531u + 6.10870
2.51263u
101
+ 4.80599u
100
+ ··· + 17.2585u 3.97342
a
4
=
4.67359u
101
7.60736u
100
+ ··· + 9.22531u + 6.10870
2.51263u
101
+ 4.80599u
100
+ ··· + 17.2585u 3.97342
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.936988 0.299819I
a = 1.62091 0.34671I
b = 1.239884 + 0.085276I
5.22245 + 0.61170I 19.5727 10.2165I
u = 0.936988 + 0.299819I
a = 1.62091 + 0.34671I
b = 1.239884 0.085276I
5.22245 0.61170I 19.5727 + 10.2165I
u = 0.910994 0.431263I
a = 1.33540 0.86176I
b = 1.38429 + 0.83294I
6.30779 12.49789I 7.52324 + 6.39934I
u = 0.910994 + 0.431263I
a = 1.33540 + 0.86176I
b = 1.38429 0.83294I
6.30779 + 12.49789I 7.52324 6.39934I
u = 0.867660 0.335592I
a = 0.547466 + 0.238777I
b = 0.756562 0.280394I
1.38934 0.39182I 4.40053 + 3.61148I
u = 0.867660 + 0.335592I
a = 0.547466 0.238777I
b = 0.756562 + 0.280394I
1.38934 + 0.39182I 4.40053 3.61148I
u = 0.838051 0.668944I
a = 1.075680 + 0.069757I
b = 0.842606 + 0.022904I
2.82119 + 2.36401I 10.26777 5.83494I
u = 0.838051 + 0.668944I
a = 1.075680 0.069757I
b = 0.842606 0.022904I
2.82119 2.36401I 10.26777 + 5.83494I
u = 0.762854 0.685546I
a = 0.77801 + 1.50504I
b = 1.44643 0.82947I
5.99433 2.25625I 11.29174 + 2.99008I
u = 0.762854 + 0.685546I
a = 0.77801 1.50504I
b = 1.44643 + 0.82947I
5.99433 + 2.25625I 11.29174 2.99008I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.714449 0.446789I
a = 1.39364 + 0.82917I
b = 1.45918 0.93885I
6.25851 3.14258I 12.90912 + 3.40540I
u = 0.714449 + 0.446789I
a = 1.39364 0.82917I
b = 1.45918 + 0.93885I
6.25851 + 3.14258I 12.90912 3.40540I
u = 0.689076 0.977800I
a = 0.994641 0.951390I
b = 0.648900 0.265334I
1.87918 + 3.30865I 8.63441 1.61228I
u = 0.689076 + 0.977800I
a = 0.994641 + 0.951390I
b = 0.648900 + 0.265334I
1.87918 3.30865I 8.63441 + 1.61228I
u = 0.687034 1.194128I
a = 1.117487 0.759585I
b = 1.223136 0.287415I
2.56452 + 5.34624I 19.2387 23.4845I
u = 0.687034 + 1.194128I
a = 1.117487 + 0.759585I
b = 1.223136 + 0.287415I
2.56452 5.34624I 19.2387 + 23.4845I
u = 0.662917 0.979688I
a = 1.89971 + 0.56380I
b = 1.55297 + 1.22299I
5.08526 + 7.66215I 9.65525 7.68566I
u = 0.662917 + 0.979688I
a = 1.89971 0.56380I
b = 1.55297 1.22299I
5.08526 7.66215I 9.65525 + 7.68566I
u = 0.654776 1.144510I
a = 1.59713 0.98601I
b = 1.45963 1.04280I
4.1396 + 18.2450I 4.85598 10.08520I
u = 0.654776 + 1.144510I
a = 1.59713 + 0.98601I
b = 1.45963 + 1.04280I
4.1396 18.2450I 4.85598 + 10.08520I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.639970
a = 0.00425908
b = 0.485079
1.15599 11.7825
u = 0.623130 1.152466I
a = 0.816737 + 0.612012I
b = 0.842982 + 0.678057I
1.01285 + 5.88545I 0.14106 6.02928I
u = 0.623130 + 1.152466I
a = 0.816737 0.612012I
b = 0.842982 0.678057I
1.01285 5.88545I 0.14106 + 6.02928I
u = 0.613398 0.253704I
a = 0.726159 0.137434I
b = 0.079540 + 0.228892I
1.49929 + 0.29141I 5.98153 0.11289I
u = 0.613398 + 0.253704I
a = 0.726159 + 0.137434I
b = 0.079540 0.228892I
1.49929 0.29141I 5.98153 + 0.11289I
u = 0.586836 1.074446I
a = 1.74670 + 1.33399I
b = 1.43089 + 1.27211I
4.41615 + 8.13681I 10.06190 7.54466I
u = 0.586836 + 1.074446I
a = 1.74670 1.33399I
b = 1.43089 1.27211I
4.41615 8.13681I 10.06190 + 7.54466I
u = 0.505158 0.979164I
a = 1.39013 0.56499I
b = 0.43268 + 2.23016I
1.08112 + 8.06609I 1.86670 9.48772I
u = 0.505158 + 0.979164I
a = 1.39013 + 0.56499I
b = 0.43268 2.23016I
1.08112 8.06609I 1.86670 + 9.48772I
u = 0.504029 0.951532I
a = 2.24845 + 0.35174I
b = 0.834851 + 0.339534I
1.51432 + 4.25684I 2.69571 6.71205I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.504029 + 0.951532I
a = 2.24845 0.35174I
b = 0.834851 0.339534I
1.51432 4.25684I 2.69571 + 6.71205I
u = 0.485068 1.040745I
a = 1.083247 0.313226I
b = 0.360192 0.192918I
0.62443 + 3.83028I 2.18792 5.01850I
u = 0.485068 + 1.040745I
a = 1.083247 + 0.313226I
b = 0.360192 + 0.192918I
0.62443 3.83028I 2.18792 + 5.01850I
u = 0.443690 0.740067I
a = 1.47397 + 2.10514I
b = 0.475728 0.068183I
0.768256 0.283969I 6.44691 + 0.24187I
u = 0.443690 + 0.740067I
a = 1.47397 2.10514I
b = 0.475728 + 0.068183I
0.768256 + 0.283969I 6.44691 0.24187I
u = 0.424020 0.928079I
a = 0.042068 0.667634I
b = 0.586180 0.939814I
2.05900 + 0.88708I 0.27608 3.22743I
u = 0.424020 + 0.928079I
a = 0.042068 + 0.667634I
b = 0.586180 + 0.939814I
2.05900 0.88708I 0.27608 + 3.22743I
u = 0.403141 0.700006I
a = 1.58780 + 0.55446I
b = 0.20408 2.01295I
2.08822 4.14738I 5.91848 + 4.99016I
u = 0.403141 + 0.700006I
a = 1.58780 0.55446I
b = 0.20408 + 2.01295I
2.08822 + 4.14738I 5.91848 4.99016I
u = 0.381025 0.968579I
a = 2.32662 0.53559I
b = 0.96625 1.42306I
0.30261 2.42814I 0.641019 1.060644I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.381025 + 0.968579I
a = 2.32662 + 0.53559I
b = 0.96625 + 1.42306I
0.30261 + 2.42814I 0.641019 + 1.060644I
u = 0.348224 0.918489I
a = 0.068949 + 0.830583I
b = 0.128200 + 0.901746I
1.76294 + 2.23528I 1.01431 1.64920I
u = 0.348224 + 0.918489I
a = 0.068949 0.830583I
b = 0.128200 0.901746I
1.76294 2.23528I 1.01431 + 1.64920I
u = 0.315832 1.121810I
a = 0.285651 1.088587I
b = 1.246064 + 0.313770I
0.64011 + 4.17517I 0.03405 5.61208I
u = 0.315832 + 1.121810I
a = 0.285651 + 1.088587I
b = 1.246064 0.313770I
0.64011 4.17517I 0.03405 + 5.61208I
u = 0.235498 1.372368I
a = 0.214681 + 0.146318I
b = 0.116397 0.264745I
4.11255 + 3.30494I 0.5376 + 14.8836I
u = 0.235498 + 1.372368I
a = 0.214681 0.146318I
b = 0.116397 + 0.264745I
4.11255 3.30494I 0.5376 14.8836I
u = 0.161509 1.011945I
a = 1.237862 0.371151I
b = 0.717943 0.789670I
1.72657 1.42609I 4.54125 + 1.87846I
u = 0.161509 + 1.011945I
a = 1.237862 + 0.371151I
b = 0.717943 + 0.789670I
1.72657 + 1.42609I 4.54125 1.87846I
u = 0.077721 1.282843I
a = 0.350452 0.006592I
b = 0.920969 + 0.822417I
0.16785 9.63948I 2.24158 + 7.07432I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.077721 + 1.282843I
a = 0.350452 + 0.006592I
b = 0.920969 0.822417I
0.16785 + 9.63948I 2.24158 7.07432I
u = 0.010623 1.160569I
a = 0.399937 + 0.342167I
b = 0.002855 + 0.849241I
3.22104 + 2.07457I 3.74244 3.26473I
u = 0.010623 + 1.160569I
a = 0.399937 0.342167I
b = 0.002855 0.849241I
3.22104 2.07457I 3.74244 + 3.26473I
u = 0.070552 1.313548I
a = 0.0567565 + 0.0089612I
b = 0.689969 0.640504I
4.91138 + 3.81366I 3.15122 9.47150I
u = 0.070552 + 1.313548I
a = 0.0567565 0.0089612I
b = 0.689969 + 0.640504I
4.91138 3.81366I 3.15122 + 9.47150I
u = 0.072640 0.207452I
a = 4.59578 2.52040I
b = 0.118898 + 1.046472I
1.92621 + 4.88869I 6.37356 5.88182I
u = 0.072640 + 0.207452I
a = 4.59578 + 2.52040I
b = 0.118898 1.046472I
1.92621 4.88869I 6.37356 + 5.88182I
u = 0.184970 0.814478I
a = 1.089967 + 0.393382I
b = 0.263074 + 1.176545I
1.71950 + 1.55631I 0.39583 5.16105I
u = 0.184970 + 0.814478I
a = 1.089967 0.393382I
b = 0.263074 1.176545I
1.71950 1.55631I 0.39583 + 5.16105I
u = 0.290031 0.120688I
a = 2.87656 0.87251I
b = 0.209453 + 0.738551I
1.38492 + 1.35842I 0.44992 2.98076I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.290031 + 0.120688I
a = 2.87656 + 0.87251I
b = 0.209453 0.738551I
1.38492 1.35842I 0.44992 + 2.98076I
u = 0.300150 0.557793I
a = 2.11925 1.68467I
b = 0.260253 + 0.724362I
1.94932 + 4.82613I 5.93840 5.80122I
u = 0.300150 + 0.557793I
a = 2.11925 + 1.68467I
b = 0.260253 0.724362I
1.94932 4.82613I 5.93840 + 5.80122I
u = 0.336564 1.002719I
a = 0.793503 + 0.833640I
b = 0.499270 + 1.220433I
0.65253 + 2.63980I 0.61324 1.64676I
u = 0.336564 + 1.002719I
a = 0.793503 0.833640I
b = 0.499270 1.220433I
0.65253 2.63980I 0.61324 + 1.64676I
u = 0.380432 0.982651I
a = 1.51391 + 0.96311I
b = 1.105798 + 0.584588I
3.75520 1.20274I 5.76934 + 1.50599I
u = 0.380432 + 0.982651I
a = 1.51391 0.96311I
b = 1.105798 0.584588I
3.75520 + 1.20274I 5.76934 1.50599I
u = 0.380666 1.110879I
a = 0.728299 0.343784I
b = 0.229395 0.471145I
1.02724 3.84003I 1.16750 + 4.25815I
u = 0.380666 + 1.110879I
a = 0.728299 + 0.343784I
b = 0.229395 + 0.471145I
1.02724 + 3.84003I 1.16750 4.25815I
u = 0.472446 1.007143I
a = 0.498508 + 0.459792I
b = 0.60539 1.38631I
3.15750 4.83334I 3.76245 + 8.59700I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.472446 + 1.007143I
a = 0.498508 0.459792I
b = 0.60539 + 1.38631I
3.15750 + 4.83334I 3.76245 8.59700I
u = 0.512406 1.014649I
a = 2.28814 0.84392I
b = 0.760982 0.900565I
0.47157 8.78333I 1.95264 + 10.55446I
u = 0.512406 + 1.014649I
a = 2.28814 + 0.84392I
b = 0.760982 + 0.900565I
0.47157 + 8.78333I 1.95264 10.55446I
u = 0.518131 0.866736I
a = 1.32102 0.75450I
b = 1.67007 + 0.39252I
4.96667 1.96860I 8.30761 + 3.40523I
u = 0.518131 + 0.866736I
a = 1.32102 + 0.75450I
b = 1.67007 0.39252I
4.96667 + 1.96860I 8.30761 3.40523I
u = 0.526098 1.098503I
a = 0.37261 1.45756I
b = 1.46820 0.07069I
4.36168 3.54189I 9.51011 + 2.81647I
u = 0.526098 + 1.098503I
a = 0.37261 + 1.45756I
b = 1.46820 + 0.07069I
4.36168 + 3.54189I 9.51011 2.81647I
u = 0.546716 0.841027I
a = 1.19778 1.67154I
b = 1.229824 0.562208I
5.02215 2.31431I 8.97400 + 3.66743I
u = 0.546716 + 0.841027I
a = 1.19778 + 1.67154I
b = 1.229824 + 0.562208I
5.02215 + 2.31431I 8.97400 3.66743I
u = 0.605344 1.038496I
a = 1.75704 0.85997I
b = 1.25980 1.09711I
1.19886 7.18632I 2.97442 + 7.91250I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.605344 + 1.038496I
a = 1.75704 + 0.85997I
b = 1.25980 + 1.09711I
1.19886 + 7.18632I 2.97442 7.91250I
u = 0.645470 0.436272I
a = 1.51263 + 0.10162I
b = 1.47792 0.24367I
6.34669 1.05018I 13.33822 + 2.96795I
u = 0.645470 + 0.436272I
a = 1.51263 0.10162I
b = 1.47792 + 0.24367I
6.34669 + 1.05018I 13.33822 2.96795I
u = 0.649296 1.019547I
a = 0.87338 + 1.39300I
b = 0.692955 + 0.436373I
5.82598 9.26479I 8.75121 + 8.18150I
u = 0.649296 + 1.019547I
a = 0.87338 1.39300I
b = 0.692955 0.436373I
5.82598 + 9.26479I 8.75121 8.18150I
u = 0.656232 1.143474I
a = 1.47930 + 0.87156I
b = 1.27885 + 0.83893I
0.85558 12.50631I 1.73099 + 9.55710I
u = 0.656232 + 1.143474I
a = 1.47930 0.87156I
b = 1.27885 0.83893I
0.85558 + 12.50631I 1.73099 9.55710I
u = 0.685100 1.110087I
a = 1.239839 0.322500I
b = 0.790984 1.170733I
1.48920 9.62261I 1.95681 + 10.67975I
u = 0.685100 + 1.110087I
a = 1.239839 + 0.322500I
b = 0.790984 + 1.170733I
1.48920 + 9.62261I 1.95681 10.67975I
u = 0.711464 0.542127I
a = 1.09507 1.07155I
b = 1.175204 + 0.755742I
2.68100 + 2.12226I 6.34545 1.95771I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.711464 + 0.542127I
a = 1.09507 + 1.07155I
b = 1.175204 0.755742I
2.68100 2.12226I 6.34545 + 1.95771I
u = 0.754022 1.016083I
a = 0.531329 + 0.867731I
b = 0.741419 + 0.128556I
6.42583 + 1.99123I 9.72573 2.02027I
u = 0.754022 + 1.016083I
a = 0.531329 0.867731I
b = 0.741419 0.128556I
6.42583 1.99123I 9.72573 + 2.02027I
u = 0.768345 0.605608I
a = 1.130331 0.351165I
b = 0.923664 0.289509I
7.07739 + 3.89935I 11.26892 3.05542I
u = 0.768345 + 0.605608I
a = 1.130331 + 0.351165I
b = 0.923664 + 0.289509I
7.07739 3.89935I 11.26892 + 3.05542I
u = 0.777412
a = 0.335267
b = 0.661313
2.43364 3.98708
u = 0.886342 0.637949I
a = 0.939358 0.188412I
b = 1.009683 + 0.143860I
7.56384 8.00259I 9.66694 + 7.08594I
u = 0.886342 + 0.637949I
a = 0.939358 + 0.188412I
b = 1.009683 0.143860I
7.56384 + 8.00259I 9.66694 7.08594I
u = 0.907967 0.542230I
a = 0.358082 0.812397I
b = 0.756737 + 0.863222I
3.25805 + 3.74660I 1.14230 7.97353I
u = 0.907967 + 0.542230I
a = 0.358082 + 0.812397I
b = 0.756737 0.863222I
3.25805 3.74660I 1.14230 + 7.97353I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.913597 0.430094I
a = 1.30200 + 0.68866I
b = 1.181085 0.639237I
1.31002 + 6.75104I 4.63086 6.43776I
u = 0.913597 + 0.430094I
a = 1.30200 0.68866I
b = 1.181085 + 0.639237I
1.31002 6.75104I 4.63086 + 6.43776I
15
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
19
+ u
18
+ ··· + 3u + 1)(u
102
+ 2u
101
+ ··· + 5u 1)
c
2
(u
19
+ 11u
18
+ ··· 3u 1)(u
102
+ 46u
101
+ ··· + 37u + 1)
c
3
(u
19
u
18
+ ··· + 3u + 1)(u
102
39u
100
+ ··· + 21u + 1)
c
4
(u
19
+ u
18
+ ··· + 4u
2
1)(u
102
+ 2u
101
+ ··· 9118u 2449)
c
5
(u
19
u
18
+ ··· + 3u 1)(u
102
+ 2u
101
+ ··· + 5u 1)
c
6
(u
19
+ u
18
+ ··· + 2u 1)(u
102
+ 2u
101
+ ··· + 326u 71)
c
7
(u
19
+ u
18
+ ··· + 3u 1)(u
102
39u
100
+ ··· + 21u + 1)
c
8
(u
19
4u
17
+ ··· u + 1)(u
102
+ 3u
101
+ ··· 81u 19)
c
9
(u
19
u
18
+ ··· 4u + 1)(u
102
14u
100
+ ··· + 64416u + 8677)
c
10
(u
19
+ 10u
18
+ ··· + u + 1)(u
102
+ 3u
101
+ ··· + 153u 7)
c
11
(u
19
9u
18
+ ··· + 9u 1)(u
102
+ 8u
101
+ ··· + 17631u + 2935)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
19
+ 11y
18
+ ··· 3y 1)(y
102
+ 46y
101
+ ··· + 37y + 1)
c
2
(y
19
y
18
+ ··· + y 1)(y
102
+ 26y
101
+ ··· 171y + 1)
c
3
(y
19
17y
18
+ ··· + 11y 1)(y
102
78y
101
+ ··· + 71y + 1)
c
4
(y
19
3y
18
+ ··· + 8y 1)
(y
102
24y
101
+ ··· 245491930y + 5997601)
c
6
(y
19
+ 5y
18
+ ··· 2y 1)(y
102
+ 16y
101
+ ··· + 36292y + 5041)
c
7
(y
19
17y
18
+ ··· + 11y 1)(y
102
78y
101
+ ··· + 71y + 1)
c
8
(y
19
8y
18
+ ··· + 3y 1)(y
102
13y
101
+ ··· 22977y + 361)
c
9
(y
19
+ y
18
+ ··· + 16y 1)
(y
102
28y
101
+ ··· 473410006y + 75290329)
c
10
(y
19
+ 6y
18
+ ··· + 11y 1)(y
102
+ 13y
101
+ ··· 645y + 49)
c
11
(y
19
+ 7y
18
+ ··· 3y 1)
(y
102
18y
101
+ ··· + 127701409y + 8614225)
17