11a
348
(K11a
348
)
1
Arc Sequences
6 5 1 10 9 4 11 3 2 7 8
Solving Sequence
2,5 3,9
6 10 1 4 7 8 11
c
2
c
5
c
9
c
1
c
4
c
6
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
2
\
j=1
I
v
j
I
u
1
= hu
15
10u
14
+ ··· + 105u 25, 362734u
14
+ 2468395u
13
+ ··· + 4044925a + 9070125,
231789u
14
+ 1842380u
13
+ ··· + 808985b 1813670i
I
u
2
= hu
29
+ 25u
28
+ ··· + 638u + 73,
1.83178 × 10
30
u
28
4.25498 × 10
31
u
27
+ ··· + 1.83797 × 10
31
b 2.13808 × 10
31
,
2.13808 × 10
31
u
28
4.00799 × 10
32
u
27
+ ··· + 1.34172 × 10
33
a + 1.06235 × 10
34
i
I
u
3
= hb
60
9b
58
+ ··· + 5b + 1, 1.21924 × 10
171
u + 2.58238 × 10
171
b
59
+ ··· + 1.50980 × 10
172
b + 2.54837 × 10
171
,
1.29642 × 10
173
b
59
2.11324 × 10
173
b
58
+ ··· + 3.12126 × 10
173
a + 5.10813 × 10
173
i
I
v
1
= hv 1, b
2
+ b + 1, ai
I
v
2
= hb
3
+ 2v 5, b
4
+ b
3
+ 2b
2
b + 1, ai
There are 5 irreducible components with 110 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
15
10u
14
+· · ·+105u25, 3.63×10
5
u
14
+2.47×10
6
u
13
+· · ·+4.04×
10
6
a+9.07×10
6
, 2.32×10
5
u
14
+1.84×10
6
u
13
+· · ·+8.09×10
5
b1.81×10
6
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
0.0896763u
14
0.610245u
13
+ ··· + 1.19544u 2.24235
0.286518u
14
2.27740u
13
+ ··· 11.6584u + 2.24191
a
6
=
0.0634041u
14
+ 0.785474u
13
+ ··· + 18.1892u 7.38808
0.151433u
14
1.22656u
13
+ ··· + 0.269354u 1.58510
a
10
=
0.196842u
14
+ 1.66715u
13
+ ··· + 12.8538u 4.48425
0.286518u
14
2.27740u
13
+ ··· 11.6584u + 2.24191
a
1
=
0.0471991u
14
+ 0.401388u
13
+ ··· 3.38516u + 3.00810
0.217171u
14
1.82237u
13
+ ··· 10.5216u + 2.60585
a
4
=
0.0784959u
14
+ 0.629353u
13
+ ··· + 2.16490u 0.432050
0.136341u
14
+ 1.38268u
13
+ ··· + 17.7549u 5.37093
a
7
=
0.0557345u
14
0.347574u
13
+ ··· + 4.78295u 3.26033
0.102577u
14
+ 0.766448u
13
+ ··· + 3.70070u 1.06673
a
8
=
0.390944u
14
3.21782u
13
+ ··· 14.9887u + 2.67870
0.631661u
14
5.74144u
13
+ ··· 46.6622u + 12.3694
a
11
=
0.252441u
14
+ 2.08510u
13
+ ··· + 10.5167u 2.17291
0.417515u
14
+ 3.68088u
13
+ ··· + 30.7038u 9.58932
a
11
=
0.252441u
14
+ 2.08510u
13
+ ··· + 10.5167u 2.17291
0.417515u
14
+ 3.68088u
13
+ ··· + 30.7038u 9.58932
(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 = 0.993740 0.424598I
a = 0.556645 + 0.290398I
b = 0.429858 0.524931I
9.75332 + 7.47692I 9.95866 4.06635I
u = 0.993740 + 0.424598I
a = 0.556645 0.290398I
b = 0.429858 + 0.524931I
9.75332 7.47692I 9.95866 + 4.06635I
u = 0.342459 0.777675I
a = 0.626853 + 0.459197I
b = 0.571778 + 0.330232I
2.51489 + 4.15156I 7.90898 4.64816I
u = 0.342459 + 0.777675I
a = 0.626853 0.459197I
b = 0.571778 0.330232I
2.51489 4.15156I 7.90898 + 4.64816I
u = 0.693947 0.386253I
a = 0.953726 0.652169I
b = 0.913738 0.084191I
2.48193 + 0.47503I 11.90735 0.90266I
u = 0.693947 + 0.386253I
a = 0.953726 + 0.652169I
b = 0.913738 + 0.084191I
2.48193 0.47503I 11.90735 + 0.90266I
u = 0.789581 1.095754I
a = 1.006360 + 0.300538I
b = 1.12392 0.86542I
6.71287 + 6.73017I 11.94424 5.36549I
u = 0.789581 + 1.095754I
a = 1.006360 0.300538I
b = 1.12392 + 0.86542I
6.71287 6.73017I 11.94424 + 5.36549I
u = 1.020311 0.946886I
a = 0.990350 0.084939I
b = 1.090893 + 0.851084I
2.45761 + 5.54387I 4.63100 3.66871I
u = 1.020311 + 0.946886I
a = 0.990350 + 0.084939I
b = 1.090893 0.851084I
2.45761 5.54387I 4.63100 + 3.66871I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.36954 1.00006I
a = 0.746523 + 0.031553I
b = 1.053945 0.703353I
8.96044 + 5.01992I 12.46416 4.02360I
u = 1.36954 + 1.00006I
a = 0.746523 0.031553I
b = 1.053945 + 0.703353I
8.96044 5.01992I 12.46416 + 4.02360I
u = 1.46936
a = 0.734892
b = 1.07982
10.0492 16.2982
u = 1.72814 0.40102I
a = 0.306044 + 0.433458I
b = 0.355064 + 0.871805I
0.07214 + 3.29542I 1.53653 + 2.69469I
u = 1.72814 + 0.40102I
a = 0.306044 0.433458I
b = 0.355064 0.871805I
0.07214 3.29542I 1.53653 2.69469I
4
II. I
u
2
= hu
29
+ 25u
28
+ · · · + 638u + 73, 1.83 × 10
30
u
28
4.25 × 10
31
u
27
+
· · · + 1.84 × 10
31
b 2.14 × 10
31
, 2.14 × 10
31
u
28
4.01 × 10
32
u
27
+ · · · +
1.34 × 10
33
a + 1.06 × 10
34
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
0.0159354u
28
+ 0.298722u
27
+ ··· 40.6500u 7.91783
0.0996632u
28
+ 2.31505u
27
+ ··· + 18.0846u + 1.16328
a
6
=
0.0368204u
28
+ 0.942895u
27
+ ··· + 43.0059u + 7.47915
0.0223856u
28
0.491135u
27
+ ··· + 17.0122u + 2.68789
a
10
=
0.0837278u
28
2.01633u
27
+ ··· 58.7346u 9.08111
0.0996632u
28
+ 2.31505u
27
+ ··· + 18.0846u + 1.16328
a
1
=
0.107125u
28
2.64363u
27
+ ··· 54.0442u 5.41609
0.0340032u
28
+ 0.644747u
27
+ ··· 44.9598u 6.18598
a
4
=
0.0130859u
28
+ 0.295275u
27
+ ··· 5.98849u + 0.469224
0.0461201u
28
+ 1.13875u
27
+ ··· + 33.9822u + 4.32204
a
7
=
0.0636554u
28
+ 1.58804u
27
+ ··· + 66.1229u + 10.2269
0.0414256u
28
+ 1.05896u
27
+ ··· + 53.1661u + 7.35249
a
8
=
0.0928024u
28
+ 2.19118u
27
+ ··· + 3.68727u 1.80570
0.0384173u
28
0.676173u
27
+ ··· + 31.1112u + 3.29583
a
11
=
0.0973760u
28
2.33888u
27
+ ··· 49.8137u 6.44579
0.0796577u
28
2.01645u
27
+ ··· 84.2207u 11.6200
a
11
=
0.0973760u
28
2.33888u
27
+ ··· 49.8137u 6.44579
0.0796577u
28
2.01645u
27
+ ··· 84.2207u 11.6200
(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 = 1.84285 0.37896I
a = 0.221920 0.459486I
b = 0.234839 0.930861I
0.10408 3.63440I 10.0950 + 14.2865I
u = 1.84285 + 0.37896I
a = 0.221920 + 0.459486I
b = 0.234839 + 0.930861I
0.10408 + 3.63440I 10.0950 14.2865I
u = 1.81822 1.09987I
a = 0.375121 + 0.181419I
b = 0.482516 + 0.742445I
8.14903 8.41158I 7.92075 + 11.07124I
u = 1.81822 + 1.09987I
a = 0.375121 0.181419I
b = 0.482516 0.742445I
8.14903 + 8.41158I 7.92075 11.07124I
u = 1.66948 1.64303I
a = 0.180391 + 0.219962I
b = 0.662563 + 0.070835I
10.73200 + 7.71685I 19.2187 7.8246I
u = 1.66948 + 1.64303I
a = 0.180391 0.219962I
b = 0.662563 0.070835I
10.73200 7.71685I 19.2187 + 7.8246I
u = 1.40924 0.62053I
a = 0.902693 + 0.279351I
b = 1.09876 + 0.95382I
11.42014 3.19049I 13.89888 + 2.12317I
u = 1.40924 + 0.62053I
a = 0.902693 0.279351I
b = 1.09876 0.95382I
11.42014 + 3.19049I 13.89888 2.12317I
u = 1.27872 1.09142I
a = 0.946459 0.001404I
b = 1.20873 1.03478I
11.5069 17.5600I 10.63704 + 8.65884I
u = 1.27872 + 1.09142I
a = 0.946459 + 0.001404I
b = 1.20873 + 1.03478I
11.5069 + 17.5600I 10.63704 8.65884I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.23159 0.78729I
a = 1.036983 0.164410I
b = 1.14770 1.01889I
4.12024 7.78492I 10.08542 + 5.99189I
u = 1.23159 + 0.78729I
a = 1.036983 + 0.164410I
b = 1.14770 + 1.01889I
4.12024 + 7.78492I 10.08542 5.99189I
u = 1.22083 0.96772I
a = 1.004963 + 0.047355I
b = 1.18107 + 1.03033I
4.3561 13.4943I 8.23763 + 9.34402I
u = 1.22083 + 0.96772I
a = 1.004963 0.047355I
b = 1.18107 1.03033I
4.3561 + 13.4943I 8.23763 9.34402I
u = 0.993675 0.553218I
a = 0.840807 0.404017I
b = 0.611979 0.866611I
1.00519 4.10843I 1.11851 + 6.27833I
u = 0.993675 + 0.553218I
a = 0.840807 + 0.404017I
b = 0.611979 + 0.866611I
1.00519 + 4.10843I 1.11851 6.27833I
u = 0.97578 1.61172I
a = 0.037347 0.297762I
b = 0.516352 0.230358I
2.86261 + 4.93654I 13.5745 14.0830I
u = 0.97578 + 1.61172I
a = 0.037347 + 0.297762I
b = 0.516352 + 0.230358I
2.86261 4.93654I 13.5745 + 14.0830I
u = 0.533215 0.743878I
a = 1.068929 + 0.077579I
b = 0.512259 + 0.836519I
2.89664 0.46546I 1.68040 0.26806I
u = 0.533215 + 0.743878I
a = 1.068929 0.077579I
b = 0.512259 0.836519I
2.89664 + 0.46546I 1.68040 + 0.26806I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.290088
a = 2.49108
b = 0.722632
1.41973 5.24453
u = 0.174221 0.891733I
a = 1.045549 + 0.239887I
b = 0.396072 0.890557I
2.36877 + 2.03117I 4.15870 1.99602I
u = 0.174221 + 0.891733I
a = 1.045549 0.239887I
b = 0.396072 + 0.890557I
2.36877 2.03117I 4.15870 + 1.99602I
u = 0.009310 0.427042I
a = 2.26846 1.69136I
b = 0.701162 + 0.984473I
4.65620 1.98203I 8.58633 + 3.04801I
u = 0.009310 + 0.427042I
a = 2.26846 + 1.69136I
b = 0.701162 0.984473I
4.65620 + 1.98203I 8.58633 3.04801I
u = 0.377713 0.751230I
a = 0.598055 0.080621I
b = 0.165328 + 0.479728I
0.38938 + 1.51803I 2.55495 5.06805I
u = 0.377713 + 0.751230I
a = 0.598055 + 0.080621I
b = 0.165328 0.479728I
0.38938 1.51803I 2.55495 + 5.06805I
u = 0.405846 0.192100I
a = 1.56669 + 1.76693I
b = 0.296405 1.018064I
5.03403 + 2.22778I 7.47163 3.53534I
u = 0.405846 + 0.192100I
a = 1.56669 1.76693I
b = 0.296405 + 1.018064I
5.03403 2.22778I 7.47163 + 3.53534I
8
III.
I
u
3
= hb
60
9b
58
+· · ·+5b+1, 1.22×10
171
u+2.58×10
171
b
59
+· · ·+1.51×10
172
b+
2.55×10
171
, 1.30×10
173
b
59
2.11×10
173
b
58
+· · ·+3.12×10
173
a+5.11×10
173
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
2.11802b
59
+ 1.69003b
58
+ ··· 12.3831b 2.09012
a
3
=
1
3.96928b
59
+ 3.37016b
58
+ ··· 20.9683b 5.37796
a
9
=
0.415350b
59
+ 0.677047b
58
+ ··· 10.1225b 1.63656
b
a
6
=
0.695000b
59
0.630641b
58
+ ··· + 9.04587b + 0.941461
1.44793b
59
+ 1.07452b
58
+ ··· 8.11630b 1.20986
a
10
=
0.415350b
59
+ 0.677047b
58
+ ··· 11.1225b 1.63656
b
a
1
=
0.312711b
59
0.727323b
58
+ ··· + 11.4601b + 2.94435
1.44793b
59
+ 1.07452b
58
+ ··· 8.11630b 2.20986
a
4
=
0.808284b
59
0.716012b
58
+ ··· + 6.84446b + 0.870969
2.90138b
59
+ 2.39092b
58
+ ··· 14.4484b 2.89989
a
7
=
0.461130b
59
+ 0.0328561b
58
+ ··· + 9.13523b + 0.750111
1.26146b
59
1.41704b
58
+ ··· + 4.47828b + 2.31217
a
8
=
1.36046b
59
0.621234b
58
+ ··· 5.80298b 0.0368122
0.919714b
59
+ 1.12225b
58
+ ··· 2.75094b 0.915884
a
11
=
0.413933b
59
+ 0.276531b
58
+ ··· 2.47061b + 0.329906
1.16006b
59
+ 1.09968b
58
+ ··· 2.04340b 1.47046
a
11
=
0.413933b
59
+ 0.276531b
58
+ ··· 2.47061b + 0.329906
1.16006b
59
+ 1.09968b
58
+ ··· 2.04340b 1.47046
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.581967 + 1.140374I
a = 0.962013 + 0.055914I
b = 1.43681 0.76472I
5.74830 8.10302I 7.68774 + 10.38587I
u = 0.581967 1.140374I
a = 0.962013 0.055914I
b = 1.43681 + 0.76472I
5.74830 + 8.10302I 7.68774 10.38587I
u = 0.671611 + 0.294946I
a = 0.839523 0.242865I
b = 1.36585 1.21898I
2.26591 2.26892I 13.6402 + 6.9635I
u = 0.671611 0.294946I
a = 0.839523 + 0.242865I
b = 1.36585 + 1.21898I
2.26591 + 2.26892I 13.6402 6.9635I
u = 0.754169 + 0.212783I
a = 0.910516 + 0.108757I
b = 1.26285 1.50931I
10.63755 + 8.63903I 15.1406 9.1585I
u = 0.754169 0.212783I
a = 0.910516 0.108757I
b = 1.26285 + 1.50931I
10.63755 8.63903I 15.1406 + 9.1585I
u = 0.643976 0.089739I
a = 1.303546 + 0.278242I
b = 1.23743 1.19471I
3.68331 0.63939I 15.6538 + 1.3796I
u = 0.643976 + 0.089739I
a = 1.303546 0.278242I
b = 1.23743 + 1.19471I
3.68331 + 0.63939I 15.6538 1.3796I
u = 1.27917 + 1.11829I
a = 0.961483 0.056576I
b = 1.189767 0.530548I
9.45761 6.57584I 15.4486 + 8.3893I
u = 1.27917 1.11829I
a = 0.961483 + 0.056576I
b = 1.189767 + 0.530548I
9.45761 + 6.57584I 15.4486 8.3893I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.07833 + 1.02126I
a = 0.860624 + 0.189066I
b = 1.12250 1.00752I
3.06065 5.93358I 16.3852 + 11.3606I
u = 1.07833 1.02126I
a = 0.860624 0.189066I
b = 1.12250 + 1.00752I
3.06065 + 5.93358I 16.3852 11.3606I
u = 1.07833 + 1.02126I
a = 0.386184 + 0.209525I
b = 0.917652 0.001032I
3.06065 1.87382I 16.3852 + 4.4324I
u = 1.07833 1.02126I
a = 0.386184 0.209525I
b = 0.917652 + 0.001032I
3.06065 + 1.87382I 16.3852 4.4324I
u = 0.643976 + 0.089739I
a = 2.13854 + 1.55720I
b = 0.864422 0.062203I
3.68331 + 0.63939I 15.6538 1.3796I
u = 0.643976 0.089739I
a = 2.13854 1.55720I
b = 0.864422 + 0.062203I
3.68331 0.63939I 15.6538 + 1.3796I
u = 1.36997
a = 0.907521 0.663747I
b = 0.787791 0.120392I
10.12446 2.02988I 16.2012 + 3.4641I
u = 1.36997
a = 0.907521 + 0.663747I
b = 0.787791 + 0.120392I
10.12446 + 2.02988I 16.2012 3.4641I
u = 0.671611 0.294946I
a = 0.467370 0.332502I
b = 0.67510 1.24619I
2.26591 1.79084I 13.64024 0.03534I
u = 0.671611 + 0.294946I
a = 0.467370 + 0.332502I
b = 0.67510 + 1.24619I
2.26591 + 1.79084I 13.64024 + 0.03534I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.754169 0.212783I
a = 1.02801 + 2.29134I
b = 0.663541 0.275764I
10.63755 8.63903I 15.1406 + 9.1585I
u = 0.754169 + 0.212783I
a = 1.02801 2.29134I
b = 0.663541 + 0.275764I
10.63755 + 8.63903I 15.1406 9.1585I
u = 1.27917 + 1.11829I
a = 0.508257 + 0.483174I
b = 0.644536 0.238801I
9.45761 2.51607I 15.4486 + 1.4611I
u = 1.27917 1.11829I
a = 0.508257 0.483174I
b = 0.644536 + 0.238801I
9.45761 + 2.51607I 15.4486 1.4611I
u = 0.602091 + 0.799295I
a = 1.60848 + 0.61527I
b = 0.563384 0.787348I
0.38534 5.63362I 2.44329 + 10.98878I
u = 0.602091 0.799295I
a = 1.60848 0.61527I
b = 0.563384 + 0.787348I
0.38534 + 5.63362I 2.44329 10.98878I
u = 0.602091 + 0.799295I
a = 0.142942 + 0.078015I
b = 0.313994 0.679393I
0.38534 1.57385I 2.44329 + 4.06057I
u = 0.602091 0.799295I
a = 0.142942 0.078015I
b = 0.313994 + 0.679393I
0.38534 + 1.57385I 2.44329 4.06057I
u = 0.581967 + 1.140374I
a = 0.797951 + 0.360993I
b = 0.209830 0.145532I
5.74830 4.04325I 7.68774 + 3.45767I
u = 0.581967 1.140374I
a = 0.797951 0.360993I
b = 0.209830 + 0.145532I
5.74830 + 4.04325I 7.68774 3.45767I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.602091 + 0.799295I
a = 0.731075 + 0.157864I
b = 0.023707 0.161225I
0.38534 1.57385I 2.44329 + 4.06057I
u = 0.602091 0.799295I
a = 0.731075 0.157864I
b = 0.023707 + 0.161225I
0.38534 + 1.57385I 2.44329 4.06057I
u = 0.671611 + 0.294946I
a = 0.15954 1.92560I
b = 0.411961 0.085463I
2.26591 + 1.79084I 13.64024 + 0.03534I
u = 0.671611 0.294946I
a = 0.15954 + 1.92560I
b = 0.411961 + 0.085463I
2.26591 1.79084I 13.64024 0.03534I
u = 0.671611 0.294946I
a = 2.37310 0.77283I
b = 0.492201 0.410725I
2.26591 + 2.26892I 13.6402 6.9635I
u = 0.671611 + 0.294946I
a = 2.37310 + 0.77283I
b = 0.492201 + 0.410725I
2.26591 2.26892I 13.6402 + 6.9635I
u = 0.581967 1.140374I
a = 1.042160 + 0.728098I
b = 0.623622 1.064514I
5.74830 + 8.10302I 7.68774 10.38587I
u = 0.581967 + 1.140374I
a = 1.042160 0.728098I
b = 0.623622 + 1.064514I
5.74830 8.10302I 7.68774 + 10.38587I
u = 1.07833 1.02126I
a = 0.449088 + 0.424366I
b = 0.630413 0.168459I
3.06065 + 1.87382I 16.3852 4.4324I
u = 1.07833 + 1.02126I
a = 0.449088 0.424366I
b = 0.630413 + 0.168459I
3.06065 1.87382I 16.3852 + 4.4324I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.643976 + 0.089739I
a = 1.73533 + 2.42540I
b = 0.696542 0.152170I
3.68331 + 4.69916I 15.6538 8.3078I
u = 0.643976 0.089739I
a = 1.73533 2.42540I
b = 0.696542 + 0.152170I
3.68331 4.69916I 15.6538 + 8.3078I
u = 0.581967 1.140374I
a = 0.175748 + 0.094312I
b = 0.876048 0.699876I
5.74830 + 4.04325I 7.68774 3.45767I
u = 0.581967 + 1.140374I
a = 0.175748 0.094312I
b = 0.876048 + 0.699876I
5.74830 4.04325I 7.68774 + 3.45767I
u = 0.754169 + 0.212783I
a = 1.194273 + 0.576398I
b = 1.00815 1.23211I
10.63755 + 4.57927I 15.1406 2.2303I
u = 0.754169 0.212783I
a = 1.194273 0.576398I
b = 1.00815 + 1.23211I
10.63755 4.57927I 15.1406 + 2.2303I
u = 0.754169 0.212783I
a = 1.66516 + 1.16392I
b = 1.023332 0.180581I
10.63755 4.57927I 15.1406 + 2.2303I
u = 0.754169 + 0.212783I
a = 1.66516 1.16392I
b = 1.023332 + 0.180581I
10.63755 + 4.57927I 15.1406 2.2303I
u = 1.07833 1.02126I
a = 1.015230 + 0.027169I
b = 1.121119 0.675049I
3.06065 + 5.93358I 16.3852 11.3606I
u = 1.07833 + 1.02126I
a = 1.015230 0.027169I
b = 1.121119 + 0.675049I
3.06065 5.93358I 16.3852 + 11.3606I
14
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.27917 1.11829I
a = 0.732710 + 0.225798I
b = 1.16663 1.14759I
9.45761 + 6.57584I 15.4486 8.3893I
u = 1.27917 + 1.11829I
a = 0.732710 0.225798I
b = 1.16663 + 1.14759I
9.45761 6.57584I 15.4486 + 8.3893I
u = 1.27917 + 1.11829I
a = 0.378101 0.143864I
b = 1.190476 0.049682I
9.45761 2.51607I 15.4486 + 1.4611I
u = 1.27917 1.11829I
a = 0.378101 + 0.143864I
b = 1.190476 + 0.049682I
9.45761 + 2.51607I 15.4486 1.4611I
u = 1.36997
a = 0.575044 0.087879I
b = 1.24327 0.90931I
10.12446 + 2.02988I 16.2012 3.4641I
u = 1.36997
a = 0.575044 + 0.087879I
b = 1.24327 + 0.90931I
10.12446 2.02988I 16.2012 + 3.4641I
u = 0.643976 0.089739I
a = 1.093325 + 0.083941I
b = 1.33517 1.40617I
3.68331 4.69916I 15.6538 + 8.3078I
u = 0.643976 + 0.089739I
a = 1.093325 0.083941I
b = 1.33517 + 1.40617I
3.68331 + 4.69916I 15.6538 8.3078I
u = 0.602091 0.799295I
a = 0.967192 0.023712I
b = 1.46023 0.91520I
0.38534 + 5.63362I 2.44329 10.98878I
u = 0.602091 + 0.799295I
a = 0.967192 + 0.023712I
b = 1.46023 + 0.91520I
0.38534 5.63362I 2.44329 + 10.98878I
15
IV. I
v
1
= hv 1, b
2
+ b + 1, ai
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
3
=
1
0
a
9
=
0
b
a
6
=
1
b 1
a
10
=
b
b
a
1
=
b
b
a
4
=
b + 2
b 1
a
7
=
b
b
a
8
=
b
b
a
11
=
b
b
a
11
=
b
b
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
16
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 0.866025I
2.02988I 3.46410I
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
2.02988I 3.46410I
17
V. I
v
2
= hb
3
+ 2v 5, b
4
+ b
3
+ 2b
2
b + 1, ai
(i) Arc colorings
a
2
=
1
0
a
5
=
1
2
b
3
+
5
2
0
a
3
=
1
0
a
9
=
0
b
a
6
=
1
2
b
3
+
5
2
1
2
b
3
+ b
2
+ b
1
2
a
10
=
b
b
a
1
=
3
2
b
3
+ 2b
2
+ 3b
1
2
1
2
b
3
b
2
b
1
2
a
4
=
b
3
b
2
b + 3
1
2
b
3
+ b
2
+ b
1
2
a
7
=
3
2
b
3
2b
2
3b +
1
2
1
2
b
3
+ b
2
+ b +
1
2
a
8
=
b
b
a
11
=
3
2
b
3
+ 2b
2
+ 2b
1
2
1
2
b
3
b
2
1
2
a
11
=
3
2
b
3
+ 2b
2
+ 2b
1
2
1
2
b
3
b
2
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
18
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
2
1(vol +
1CS) Cusp shape
v = 0.381966
a = 0
b = 0.80902 1.40126I
1.64493 2.02988I 1.00000 + 3.46410I
v = 0.381966
a = 0
b = 0.80902 + 1.40126I
1.64493 + 2.02988I 1.00000 3.46410I
v = 2.61803
a = 0
b = 0.309017 0.535233I
1.64493 + 2.02988I 1.00000 3.46410I
v = 2.61803
a = 0
b = 0.309017 + 0.535233I
1.64493 2.02988I 1.00000 + 3.46410I
19
VI. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
2
u + 1)
30
(u
2
+ u + 1)
3
(u
15
5u
14
+ ··· + 5u 1)
(u
29
+ 29u
28
+ ··· 131072u 16384)
c
2
u
6
(u
15
10u
14
+ ··· + 105u 25)
(2 + 3u 7u
2
20u
3
4u
4
+ 38u
5
+ 50u
6
2u
7
62u
8
61u
9
7u
10
+ 38u
11
+ 42u
12
+ 23u
13
+ 7u
14
+ u
15
)
4
(u
29
25u
28
+ ··· + 638u 73)
c
3
, c
6
(u
2
+ u + 1)
3
(u
15
+ 4u
14
+ ··· + 6u + 1)(u
29
u
28
+ ··· + 17u + 1)
(u
60
+ 3u
59
+ ··· + 5800u + 1951)
c
4
, c
8
(u
2
u + 1)(u
4
u
3
+ ··· + u + 1)(u
15
+ 4u
13
+ ··· + 4u 1)
(u
29
+ u
28
+ ··· + 21u 9)(u
60
+ 17u
58
+ ··· 63147u + 112777)
c
5
, c
9
(u
2
+ u + 1)(u
4
u
3
+ ··· + u + 1)(u
15
+ u
14
+ ··· 2u
2
+ 1)
(u
29
+ 2u
27
+ ··· + u + 1)(u
60
9u
58
+ ··· + 5u + 1)
c
7
u
2
(u 1)
4
(1 + 2u + 3u
2
14u
4
20u
5
+ 12u
6
+ 38u
7
+ 7u
8
30u
9
19u
10
+ 16u
11
+ 11u
12
6u
13
2u
14
+ u
15
)
4
(u
15
+ 4u
14
+ ··· + 4u + 1)(u
29
+ 9u
28
+ ··· + 49u + 73)
c
10
, c
11
u
2
(u + 1)
4
(u
15
4u
14
+ ··· + 4u 1)
(1 + 2u + 3u
2
14u
4
20u
5
+ 12u
6
+ 38u
7
+ 7u
8
30u
9
19u
10
+ 16u
11
+ 11u
12
6u
13
2u
14
+ u
15
)
4
(u
29
+ 9u
28
+ ··· + 49u + 73)
20
VII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
2
+ y + 1)
33
(y
15
7y
14
+ ··· + 3y 1)
(y
29
7y
28
+ ··· + 5100273664y 268435456)
c
2
y
6
(y
15
10y
14
+ ··· + 1225y 625)
(4 + 37y 153y
2
+ 372y
3
600y
4
+ 718y
5
746y
6
+ 690y
7
492y
8
+ 265y
9
193y
10
+ 90y
11
40y
12
+ 17y
13
3y
14
+ y
15
)
4
(y
29
13y
28
+ ··· + 27006y 5329)
c
3
, c
6
(y
2
+ y + 1)
3
(y
15
8y
14
+ ··· + 10y 1)(y
29
7y
28
+ ··· + 235y 1)
(y
60
31y
59
+ ··· 116686266y + 3806401)
c
4
, c
8
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
15
+ 8y
14
+ ··· 6y 1)
(y
29
+ 17y
28
+ ··· 225y 81)
(y
60
+ 34y
59
+ ··· + 352063429739y + 12718651729)
c
5
, c
9
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
15
5y
14
+ ··· + 4y 1)
(y
29
+ 4y
28
+ ··· 3y 1)(y
60
18y
59
+ ··· + 27y + 1)
c
7
, c
10
, c
11
y
2
(y 1)
4
(1 + 10y 37y
2
+ 28y
3
102y
4
+ 536y
5
1268y
6
+ 1850y
7
2189y
8
+ 2302y
9
1923y
10
+ 1138y
11
449y
12
+ 112y
13
16y
14
+ y
15
)
4
(y
15
16y
14
+ ··· + 4y 1)(y
29
31y
28
+ ··· 8987y 5329)
21