11n
148
(K11n
148
)
A knot diagram
1
Linearized knot diagam
7 1 10 11 1 4 2 5 6 7 9
Solving Sequence
7,10 4,11
3 6 9 1 2 5 8
c
10
c
3
c
6
c
9
c
11
c
2
c
5
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 3936u
12
− 3615u
11
+ ··· + 1546a + 3493,
u
13
− u
12
− 6u
11
+ 8u
10
+ 21u
9
− 27u
8
− 41u
7
+ 43u
6
+ 41u
5
− 35u
4
− 12u
3
+ 10u
2
+ u − 1i
I
u
2
= hb − u, −689759u
11
− 107599u
10
+ ··· + 501166a − 3895672,
u
12
− u
10
+ 4u
8
− 8u
7
+ 14u
6
+ 15u
5
− 33u
4
+ u
3
+ 26u
2
+ 3u + 1i
I
u
3
= hb + u, −280773u
15
+ 187752u
14
+ ··· + 478966a − 1154354,
u
16
− u
15
+ 5u
14
− 7u
13
+ 8u
12
− 15u
11
+ 8u
10
− 6u
9
+ 11u
8
+ 10u
7
+ 11u
5
− 4u
4
− 5u
3
+ u
2
+ u + 1i
I
u
4
= h−5u
7
− 11u
6
+ 19u
4
− 32u
3
− 9u
2
+ 16b + 41u + 18,
− u
7
+ 5u
6
+ 12u
5
+ 3u
4
− 20u
3
+ 55u
2
+ 32a − 31u + 2, u
8
+ u
7
− 2u
6
− 3u
5
+ 10u
4
− 7u
3
− 3u
2
+ 4i
I
u
5
= h1632242669u
15
− 3999460410u
14
+ ··· + 68858688392b + 15730031303,
− 1552686477u
15
+ 2916463782u
14
+ ··· + 57539451944a − 28248685713,
u
16
− u
15
+ ··· + 14u + 61i
I
u
6
= hb + u, a − u, u
2
+ u + 1i
I
u
7
= hb − u, a, u
2
+ u − 1i
I
u
8
= hu
3
− 2u
2
+ b − 1, u
3
− u
2
+ a − 2u − 2, u
4
− u
3
− 2u
2
− 2u − 1i
* 8 irreducible components of dim
C
= 0, with total 73 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
1
I.
I
u
1
= hb − u, 3936u
12
− 3615u
11
+ · · · + 1546a + 3493, u
13
− u
12
+ · · · + u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
−2.54592u
12
+ 2.33829u
11
+ ··· − 14.3182u − 2.25938
u
a
11
=
1
u
2
a
3
=
−2.54592u
12
+ 2.33829u
11
+ ··· − 13.3182u − 2.25938
u
a
6
=
−3.90815u
12
+ 3.32342u
11
+ ··· − 14.3635u − 2.48124
0.206339u
12
− 0.195990u
11
+ ··· + 3.33829u + 0.207633
a
9
=
−1.25938u
12
− 0.286546u
11
+ ··· + 5.28008u − 6.57762
−u
2
+ 1
a
1
=
0.429495u
12
+ 1.13907u
11
+ ··· − 10.4463u + 3.81307
−0.197283u
12
+ 0.0588616u
11
+ ··· + 0.287840u − 2.33959
a
2
=
0.429495u
12
+ 1.13907u
11
+ ··· − 10.4463u + 3.81307
0.190168u
12
+ 0.120310u
11
+ ··· − 0.851229u − 0.771022
a
5
=
−2.33959u
12
+ 2.14230u
11
+ ··· − 10.9799u − 2.05175
0.0679172u
12
− 0.0284605u
11
+ ··· + 1.19599u + 0.0103493
a
8
=
−1.06210u
12
− 0.345408u
11
+ ··· + 4.99224u − 4.23803
−0.0394567u
12
− 0.188228u
11
+ ··· + 0.0575679u + 0.932083
a
8
=
−1.06210u
12
− 0.345408u
11
+ ··· + 4.99224u − 4.23803
−0.0394567u
12
− 0.188228u
11
+ ··· + 0.0575679u + 0.932083
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5825
773
u
12
+
3398
773
u
11
+
36475
773
u
10
−
31741
773
u
9
−
135781
773
u
8
+
103033
773
u
7
+
280491
773
u
6
−
140065
773
u
5
−
289681
773
u
4
+
91807
773
u
3
+
95194
773
u
2
−
21889
773
u −
11636
773
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
13
− 6u
12
+ ··· − 20u + 8
c
2
u
13
+ 10u
12
+ ··· + 208u + 64
c
3
, c
5
, c
8
c
10
u
13
+ u
12
+ ··· + u + 1
c
4
, c
9
u
13
− 2u
12
+ ··· − u + 4
c
6
, c
11
u
13
+ 5u
12
+ ··· + 11u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
13
− 10y
12
+ ··· + 208y −64
c
2
y
13
− 14y
12
+ ··· − 14080y −4096
c
3
, c
5
, c
8
c
10
y
13
− 13y
12
+ ··· + 21y −1
c
4
, c
9
y
13
+ 16y
11
+ ··· + 65y −16
c
6
, c
11
y
13
− 5y
12
+ ··· + 157y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679240
a = −0.118511
b = 0.679240
−0.985814 −9.93790
u = 1.319410 + 0.222030I
a = 0.746615 − 0.655764I
b = 1.319410 + 0.222030I
−1.44982 − 2.92540I −5.79046 + 3.21859I
u = 1.319410 − 0.222030I
a = 0.746615 + 0.655764I
b = 1.319410 − 0.222030I
−1.44982 + 2.92540I −5.79046 − 3.21859I
u = −1.310050 + 0.430816I
a = −0.729761 + 0.359278I
b = −1.310050 + 0.430816I
−9.72048 + 1.68662I −6.99569 + 0.12715I
u = −1.310050 − 0.430816I
a = −0.729761 − 0.359278I
b = −1.310050 − 0.430816I
−9.72048 − 1.68662I −6.99569 − 0.12715I
u = 0.440196 + 0.153722I
a = −1.05333 + 2.17650I
b = 0.440196 + 0.153722I
0.31710 − 4.56636I −5.37309 + 4.90464I
u = 0.440196 − 0.153722I
a = −1.05333 − 2.17650I
b = 0.440196 − 0.153722I
0.31710 + 4.56636I −5.37309 − 4.90464I
u = −0.458477 + 0.058416I
a = 1.85684 + 0.90881I
b = −0.458477 + 0.058416I
2.02562 + 0.48569I 2.64958 + 0.42406I
u = −0.458477 − 0.058416I
a = 1.85684 − 0.90881I
b = −0.458477 − 0.058416I
2.02562 − 0.48569I 2.64958 − 0.42406I
u = −1.40672 + 0.68037I
a = −0.434994 − 0.837741I
b = −1.40672 + 0.68037I
−1.01550 + 9.99038I −3.69502 − 7.61192I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40672 − 0.68037I
a = −0.434994 + 0.837741I
b = −1.40672 − 0.68037I
−1.01550 − 9.99038I −3.69502 + 7.61192I
u = 1.57602 + 1.15308I
a = 0.173888 − 0.741516I
b = 1.57602 + 1.15308I
−8.5808 − 15.4617I −4.82638 + 7.62465I
u = 1.57602 − 1.15308I
a = 0.173888 + 0.741516I
b = 1.57602 − 1.15308I
−8.5808 + 15.4617I −4.82638 − 7.62465I
6
II. I
u
2
= hb − u, −6.90 × 10
5
u
11
− 1.08 × 10
5
u
10
+ · · · + 5.01 × 10
5
a − 3.90 ×
10
6
, u
12
− u
10
+ · · · + 3u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
1.37631u
11
+ 0.214697u
10
+ ··· + 42.8501u + 7.77322
u
a
11
=
1
u
2
a
3
=
1.37631u
11
+ 0.214697u
10
+ ··· + 43.8501u + 7.77322
u
a
6
=
2.34713u
11
+ 0.345161u
10
+ ··· + 61.9493u + 17.9990
0.209352u
11
− 0.148428u
10
+ ··· + 3.02040u + 0.214697
a
9
=
1.45089u
11
− 0.0821125u
10
+ ··· + 40.5075u − 3.80051
−0.0710822u
11
+ 0.0690011u
10
+ ··· − 0.602275u − 0.458944
a
1
=
1.03465u
11
+ 0.0271287u
10
+ ··· + 28.9476u − 0.912330
0.0773456u
11
+ 0.0652877u
10
+ ··· − 0.188917u − 0.249592
a
2
=
1.03465u
11
+ 0.0271287u
10
+ ··· + 28.9476u − 0.912330
0.0341124u
11
+ 0.224690u
10
+ ··· − 1.30495u − 0.276721
a
5
=
1.58566u
11
+ 0.0662695u
10
+ ··· + 45.8705u + 7.98791
0.00371334u
11
− 0.251541u
10
+ ··· + 1.23593u + 0.148428
a
8
=
−0.708286u
11
+ 0.253305u
10
+ ··· − 15.0153u + 5.51408
−0.251541u
11
− 0.0941345u
10
+ ··· + 0.137288u − 0.00371334
a
8
=
−0.708286u
11
+ 0.253305u
10
+ ··· − 15.0153u + 5.51408
−0.251541u
11
− 0.0941345u
10
+ ··· + 0.137288u − 0.00371334
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2218099
501166
u
11
−
163295
250583
u
10
+ ··· +
55914373
501166
u −
2178981
501166
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
− 4u
5
+ 6u
4
− 5u
3
+ 5u
2
− 6u + 4)
2
c
2
(u
6
+ 4u
5
+ 6u
4
+ 5u
3
+ 13u
2
− 4u + 16)
2
c
3
, c
5
, c
8
c
10
u
12
− u
10
+ 4u
8
+ 8u
7
+ 14u
6
− 15u
5
− 33u
4
− u
3
+ 26u
2
− 3u + 1
c
4
, c
9
(u
6
+ u
5
+ 3u
4
+ u
3
+ 4u
2
+ 1)
2
c
6
, c
11
u
12
+ 4u
11
+ ··· + 66u + 11
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
− 4y
5
+ 6y
4
− 5y
3
+ 13y
2
+ 4y + 16)
2
c
2
(y
6
− 4y
5
+ 22y
4
+ 195y
3
+ 401y
2
+ 400y + 256)
2
c
3
, c
5
, c
8
c
10
y
12
− 2y
11
+ ··· + 43y + 1
c
4
, c
9
(y
6
+ 5y
5
+ 15y
4
+ 25y
3
+ 22y
2
+ 8y + 1)
2
c
6
, c
11
y
12
− 4y
11
+ ··· − 484y + 121
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968045 + 0.076481I
a = −0.541139 − 1.217710I
b = −0.968045 + 0.076481I
−2.70944 − 2.74874I −6.55410 + 3.66193I
u = −0.968045 − 0.076481I
a = −0.541139 + 1.217710I
b = −0.968045 − 0.076481I
−2.70944 + 2.74874I −6.55410 − 3.66193I
u = 1.126210 + 0.587419I
a = 1.063370 + 0.516394I
b = 1.126210 + 0.587419I
−9.45817 − 7.70670I −6.10501 + 5.38862I
u = 1.126210 − 0.587419I
a = 1.063370 − 0.516394I
b = 1.126210 − 0.587419I
−9.45817 + 7.70670I −6.10501 − 5.38862I
u = 1.176980 + 0.755737I
a = 0.136599 − 0.758615I
b = 1.176980 + 0.755737I
−2.70944 − 2.74874I −6.55410 + 3.66193I
u = 1.176980 − 0.755737I
a = 0.136599 + 0.758615I
b = 1.176980 − 0.755737I
−2.70944 + 2.74874I −6.55410 − 3.66193I
u = 0.19389 + 1.60136I
a = 0.007131 − 0.411898I
b = 0.19389 + 1.60136I
3.94294 − 2.97593I −11.8409 + 20.9878I
u = 0.19389 − 1.60136I
a = 0.007131 + 0.411898I
b = 0.19389 − 1.60136I
3.94294 + 2.97593I −11.8409 − 20.9878I
u = −0.052940 + 0.185549I
a = 5.45961 + 8.32725I
b = −0.052940 + 0.185549I
3.94294 − 2.97593I −11.8409 + 20.9878I
u = −0.052940 − 0.185549I
a = 5.45961 − 8.32725I
b = −0.052940 − 0.185549I
3.94294 + 2.97593I −11.8409 − 20.9878I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47610 + 1.13544I
a = −0.125567 − 0.653945I
b = −1.47610 + 1.13544I
−9.45817 + 7.70670I −6.10501 − 5.38862I
u = −1.47610 − 1.13544I
a = −0.125567 + 0.653945I
b = −1.47610 − 1.13544I
−9.45817 − 7.70670I −6.10501 + 5.38862I
11
III. I
u
3
= hb + u, −2.81 × 10
5
u
15
+ 1.88 × 10
5
u
14
+ · · · + 4.79 × 10
5
a − 1.15 ×
10
6
, u
16
− u
15
+ · · · + u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
0.586207u
15
− 0.391994u
14
+ ··· + 2.99697u + 2.41010
−u
a
11
=
1
u
2
a
3
=
0.586207u
15
− 0.391994u
14
+ ··· + 1.99697u + 2.41010
−u
a
6
=
1.60046u
15
− 1.09856u
14
+ ··· + 0.905045u + 5.14908
−0.370010u
15
+ 0.495060u
14
+ ··· + 0.219581u − 0.194212
a
9
=
−0.982304u
15
+ 1.65935u
14
+ ··· − 5.17282u + 0.456744
0.155410u
15
− 0.318879u
14
+ ··· + 0.496238u + 0.382754
a
1
=
0.459400u
15
− 0.696398u
14
+ ··· + 4.05434u + 0.305940
−0.631821u
15
+ 0.786116u
14
+ ··· − 0.118524u − 0.511907
a
2
=
0.459400u
15
− 0.696398u
14
+ ··· + 4.05434u + 0.305940
−0.726319u
15
+ 0.940998u
14
+ ··· − 0.340926u − 0.274909
a
5
=
0.956216u
15
− 0.887055u
14
+ ··· + 2.77739u + 2.60431
0.0409340u
15
− 0.0327789u
14
+ ··· − 1.24496u + 0.125051
a
8
=
0.667893u
15
− 1.05794u
14
+ ··· + 2.47945u − 1.10540
0.681729u
15
− 0.825163u
14
+ ··· − 0.159324u + 0.901951
a
8
=
0.667893u
15
− 1.05794u
14
+ ··· + 2.47945u − 1.10540
0.681729u
15
− 0.825163u
14
+ ··· − 0.159324u + 0.901951
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1422603
239483
u
15
+
4693355
478966
u
14
+ ··· −
9817835
478966
u +
275497
478966
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
16
− 9u
14
+ 35u
12
− 82u
10
+ 133u
8
− 152u
6
+ 118u
4
− 56u
2
+ 13
c
2
(u
8
+ 9u
7
+ 35u
6
+ 82u
5
+ 133u
4
+ 152u
3
+ 118u
2
+ 56u + 13)
2
c
3
, c
5
, c
8
c
10
u
16
− u
15
+ ··· + u + 1
c
4
, c
9
(u
8
+ u
7
− u
5
− 3u
4
+ u
3
+ 4u
2
+ u + 1)
2
c
6
, c
11
u
16
− 9u
15
+ ··· − 6u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
8
− 9y
7
+ 35y
6
− 82y
5
+ 133y
4
− 152y
3
+ 118y
2
− 56y + 13)
2
c
2
(y
8
− 11y
7
+ 15y
6
+ 86y
5
+ 39y
4
+ 10y
3
+ 358y
2
− 68y + 169)
2
c
3
, c
5
, c
8
c
10
y
16
+ 9y
15
+ ··· + y + 1
c
4
, c
9
(y
8
− y
7
− 4y
6
+ 5y
5
+ 11y
4
− 23y
3
+ 8y
2
+ 7y + 1)
2
c
6
, c
11
y
16
− 9y
15
+ ··· − 2y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.274263 + 1.008870I
a = 0.79810 + 1.33602I
b = −0.274263 − 1.008870I
1.71914 − 5.38582I −0.93122 + 9.75922I
u = 0.274263 − 1.008870I
a = 0.79810 − 1.33602I
b = −0.274263 + 1.008870I
1.71914 + 5.38582I −0.93122 − 9.75922I
u = −0.638849 + 1.040850I
a = −0.169502 + 1.235590I
b = 0.638849 − 1.040850I
2.34546 + 2.94891I 0.795967 + 0.602909I
u = −0.638849 − 1.040850I
a = −0.169502 − 1.235590I
b = 0.638849 + 1.040850I
2.34546 − 2.94891I 0.795967 − 0.602909I
u = −0.701878 + 0.091386I
a = −0.850232 − 0.808730I
b = 0.701878 − 0.091386I
1.71914 + 5.38582I −0.93122 − 9.75922I
u = −0.701878 − 0.091386I
a = −0.850232 + 0.808730I
b = 0.701878 + 0.091386I
1.71914 − 5.38582I −0.93122 + 9.75922I
u = 0.610814 + 0.255978I
a = 1.098150 − 0.544353I
b = −0.610814 − 0.255978I
2.34546 + 2.94891I 0.795967 + 0.602909I
u = 0.610814 − 0.255978I
a = 1.098150 + 0.544353I
b = −0.610814 + 0.255978I
2.34546 − 2.94891I 0.795967 − 0.602909I
u = 1.305320 + 0.359264I
a = −0.481994 + 0.934732I
b = −1.305320 − 0.359264I
−6.45579 − 3.75611I −8.46169 + 3.08159I
u = 1.305320 − 0.359264I
a = −0.481994 − 0.934732I
b = −1.305320 + 0.359264I
−6.45579 + 3.75611I −8.46169 − 3.08159I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.213253 + 0.417979I
a = 2.89265 + 2.89484I
b = 0.213253 − 0.417979I
4.03613 − 2.81197I 9.0969 − 15.4678I
u = −0.213253 − 0.417979I
a = 2.89265 − 2.89484I
b = 0.213253 + 0.417979I
4.03613 + 2.81197I 9.0969 + 15.4678I
u = −0.24620 + 1.56767I
a = 0.067177 + 0.435558I
b = 0.24620 − 1.56767I
4.03613 + 2.81197I 9.0969 + 15.4678I
u = −0.24620 − 1.56767I
a = 0.067177 − 0.435558I
b = 0.24620 + 1.56767I
4.03613 − 2.81197I 9.0969 − 15.4678I
u = 0.10979 + 1.65368I
a = 0.145647 + 0.120240I
b = −0.10979 − 1.65368I
−6.45579 − 3.75611I −8.46169 + 3.08159I
u = 0.10979 − 1.65368I
a = 0.145647 − 0.120240I
b = −0.10979 + 1.65368I
−6.45579 + 3.75611I −8.46169 − 3.08159I
16
IV. I
u
4
= h−5u
7
− 11u
6
+ · · · + 16b + 18, −u
7
+ 5u
6
+ · · · + 32a + 2, u
8
+
u
7
− 2u
6
− 3u
5
+ 10u
4
− 7u
3
− 3u
2
+ 4i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
0.0312500u
7
− 0.156250u
6
+ ··· + 0.968750u − 0.0625000
5
16
u
7
+
11
16
u
6
+ ··· −
41
16
u −
9
8
a
11
=
1
u
2
a
3
=
0.343750u
7
+ 0.531250u
6
+ ··· − 1.59375u − 1.18750
5
16
u
7
+
11
16
u
6
+ ··· −
41
16
u −
9
8
a
6
=
−0.218750u
7
− 0.406250u
6
+ ··· + 1.71875u − 0.0625000
1
16
u
7
−
1
16
u
6
+ ··· −
5
16
u +
3
8
a
9
=
0.0937500u
7
+ 0.281250u
6
+ ··· − 0.343750u − 0.687500
5
16
u
7
+
7
16
u
6
+ ··· −
5
16
u −
5
8
a
1
=
−0.0937500u
7
− 0.281250u
6
+ ··· + 0.843750u + 1.18750
−
5
16
u
7
−
7
16
u
6
+ ··· +
5
16
u +
13
8
a
2
=
−0.0937500u
7
− 0.281250u
6
+ ··· + 0.843750u + 1.18750
−0.437500u
7
− 0.562500u
6
+ ··· + 0.687500u + 2.37500
a
5
=
0.468750u
7
+ 0.906250u
6
+ ··· − 1.46875u − 1.93750
0.812500u
7
+ 1.68750u
6
+ ··· − 4.31250u − 3.62500
a
8
=
−0.343750u
7
− 0.531250u
6
+ ··· + 1.59375u + 1.18750
−0.562500u
7
− 0.937500u
6
+ ··· + 3.31250u + 2.62500
a
8
=
−0.343750u
7
− 0.531250u
6
+ ··· + 1.59375u + 1.18750
−0.562500u
7
− 0.937500u
6
+ ··· + 3.31250u + 2.62500
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3
2
u
7
−
5
2
u
6
+
5
2
u
4
− 12u
3
+
17
2
u
2
−
1
2
u − 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
+ u − 1)
4
c
2
(u
2
+ 3u + 1)
4
c
3
, c
5
, c
8
c
10
u
8
− u
7
− 2u
6
+ 3u
5
+ 10u
4
+ 7u
3
− 3u
2
+ 4
c
4
, c
9
u
8
− 3u
7
+ 8u
6
− 3u
5
+ 8u
4
− 3u
3
+ 7u
2
+ 16
c
6
, c
11
(u
2
− u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
− 3y + 1)
4
c
2
(y
2
− 7y + 1)
4
c
3
, c
5
, c
8
c
10
y
8
− 5y
7
+ 30y
6
− 41y
5
+ 78y
4
− 125y
3
+ 89y
2
− 24y + 16
c
4
, c
9
y
8
+ 7y
7
+ 62y
6
+ 115y
5
+ 190y
4
+ 359y
3
+ 305y
2
+ 224y + 256
c
6
, c
11
(y
2
+ y + 1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024520 + 0.199293I
a = −0.628676 − 0.723008I
b = −1.83354 + 1.20197I
−8.88264 + 4.05977I −10.00000 − 6.92820I
u = 1.024520 − 0.199293I
a = −0.628676 + 0.723008I
b = −1.83354 − 1.20197I
−8.88264 − 4.05977I −10.00000 + 6.92820I
u = 0.785903 + 1.018910I
a = 0.295593 + 0.718718I
b = −0.476886 − 0.483675I
−0.98696 − 4.05977I −10.00000 + 6.92820I
u = 0.785903 − 1.018910I
a = 0.295593 − 0.718718I
b = −0.476886 + 0.483675I
−0.98696 + 4.05977I −10.00000 − 6.92820I
u = −0.476886 + 0.483675I
a = −0.39108 + 1.41935I
b = 0.785903 − 1.018910I
−0.98696 + 4.05977I −10.00000 − 6.92820I
u = −0.476886 − 0.483675I
a = −0.39108 − 1.41935I
b = 0.785903 + 1.018910I
−0.98696 − 4.05977I −10.00000 + 6.92820I
u = −1.83354 + 1.20197I
a = −0.025832 + 0.455391I
b = 1.024520 + 0.199293I
−8.88264 + 4.05977I −10.00000 − 6.92820I
u = −1.83354 − 1.20197I
a = −0.025832 − 0.455391I
b = 1.024520 − 0.199293I
−8.88264 − 4.05977I −10.00000 + 6.92820I
20
V.
I
u
5
= h1.63 × 10
9
u
15
− 4.00 × 10
9
u
14
+ · · · + 6.89 × 10
10
b + 1.57 × 10
10
, −1.55 ×
10
9
u
15
+2.92×10
9
u
14
+· · ·+5.75×10
10
a−2.82×10
10
, u
16
−u
15
+· · ·+14u+61i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
0.0269847u
15
− 0.0506863u
14
+ ··· + 0.983334u + 0.490945
−0.0237042u
15
+ 0.0580821u
14
+ ··· − 0.637455u − 0.228439
a
11
=
1
u
2
a
3
=
0.00328049u
15
+ 0.00739581u
14
+ ··· + 0.345879u + 0.262505
−0.0237042u
15
+ 0.0580821u
14
+ ··· − 0.637455u − 0.228439
a
6
=
0.0153528u
15
− 0.0613303u
14
+ ··· + 2.50796u − 1.49414
−0.0137597u
15
+ 0.0519593u
14
+ ··· − 0.953981u + 0.952940
a
9
=
0.0119361u
15
− 0.0470317u
14
+ ··· + 1.26128u − 0.453422
0.0267082u
15
− 0.0380007u
14
+ ··· + 0.241699u + 1.87605
a
1
=
0.0131130u
15
− 0.0237893u
14
+ ··· + 0.375432u − 0.0329971
−0.0392634u
15
+ 0.0682124u
14
+ ··· − 0.0372592u − 1.55608
a
2
=
0.0131130u
15
− 0.0237893u
14
+ ··· + 0.375432u − 0.0329971
−0.0376838u
15
+ 0.0837224u
14
+ ··· − 0.687681u − 0.904829
a
5
=
0.0137569u
15
− 0.0478038u
14
+ ··· + 1.66013u − 1.18329
0.0333257u
15
− 0.0545032u
14
+ ··· + 0.314278u + 0.402625
a
8
=
−0.00328049u
15
− 0.00739581u
14
+ ··· − 0.345879u − 0.262505
0.0268634u
15
− 0.0270621u
14
+ ··· − 0.663389u + 1.53095
a
8
=
−0.00328049u
15
− 0.00739581u
14
+ ··· − 0.345879u − 0.262505
0.0268634u
15
− 0.0270621u
14
+ ··· − 0.663389u + 1.53095
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2099874
9069901
u
15
+
3556482
9069901
u
14
+ ··· −
26506214
9069901
u −
45805682
9069901
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
+ u − 1)
8
c
2
(u
2
+ 3u + 1)
8
c
3
, c
5
, c
8
c
10
u
16
+ u
15
+ ··· − 14u + 61
c
4
, c
9
(u
8
+ u
7
+ 2u
6
− 5u
5
− 2u
4
+ 11u
3
+ 5u
2
+ 2u + 4)
2
c
6
, c
11
(u
4
− u
3
+ 2u + 1)
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
− 3y + 1)
8
c
2
(y
2
− 7y + 1)
8
c
3
, c
5
, c
8
c
10
y
16
+ 13y
15
+ ··· + 5172y + 3721
c
4
, c
9
(y
8
+ 3y
7
+ 10y
6
− 45y
5
+ 138y
4
− 105y
3
− 35y
2
+ 36y + 16)
2
c
6
, c
11
(y
4
− y
3
+ 6y
2
− 4y + 1)
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.627115 + 0.928941I
a = −0.219133 + 1.355720I
b = 0.409816 − 1.073270I
2.30291 + 4.05977I 2.00000 − 6.92820I
u = −0.627115 − 0.928941I
a = −0.219133 − 1.355720I
b = 0.409816 + 1.073270I
2.30291 − 4.05977I 2.00000 + 6.92820I
u = 0.664283 + 0.551323I
a = 0.415524 − 0.627471I
b = −0.756001 + 0.910051I
2.30291 − 4.05977I 2.00000 + 6.92820I
u = 0.664283 − 0.551323I
a = 0.415524 + 0.627471I
b = −0.756001 − 0.910051I
2.30291 + 4.05977I 2.00000 − 6.92820I
u = 0.409816 + 1.073270I
a = 0.508514 + 1.239550I
b = −0.627115 − 0.928941I
2.30291 − 4.05977I 2.00000 + 6.92820I
u = 0.409816 − 1.073270I
a = 0.508514 − 1.239550I
b = −0.627115 + 0.928941I
2.30291 + 4.05977I 2.00000 − 6.92820I
u = −1.009750 + 0.554510I
a = 0.413379 + 1.270590I
b = 1.57864 − 0.17666I
−5.59278 + 4.05977I 2.00000 − 6.92820I
u = −1.009750 − 0.554510I
a = 0.413379 − 1.270590I
b = 1.57864 + 0.17666I
−5.59278 − 4.05977I 2.00000 + 6.92820I
u = −0.756001 + 0.910051I
a = −0.457981 − 0.302983I
b = 0.664283 + 0.551323I
2.30291 − 4.05977I 2.00000 + 6.92820I
u = −0.756001 − 0.910051I
a = −0.457981 + 0.302983I
b = 0.664283 − 0.551323I
2.30291 + 4.05977I 2.00000 − 6.92820I
24
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303235 + 1.148640I
a = 0.019154 − 0.546537I
b = 0.54336 + 2.67729I
−5.59278 + 4.05977I 2.00000 − 6.92820I
u = −0.303235 − 1.148640I
a = 0.019154 + 0.546537I
b = 0.54336 − 2.67729I
−5.59278 − 4.05977I 2.00000 + 6.92820I
u = 1.57864 + 0.17666I
a = −0.628149 + 0.737802I
b = −1.009750 − 0.554510I
−5.59278 − 4.05977I 2.00000 + 6.92820I
u = 1.57864 − 0.17666I
a = −0.628149 − 0.737802I
b = −1.009750 + 0.554510I
−5.59278 + 4.05977I 2.00000 − 6.92820I
u = 0.54336 + 2.67729I
a = 0.112628 − 0.209453I
b = −0.303235 + 1.148640I
−5.59278 + 4.05977I 2.00000 − 6.92820I
u = 0.54336 − 2.67729I
a = 0.112628 + 0.209453I
b = −0.303235 − 1.148640I
−5.59278 − 4.05977I 2.00000 + 6.92820I
25
VI. I
u
6
= hb + u, a − u, u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
u
−u
a
11
=
1
−u − 1
a
3
=
0
−u
a
6
=
−1
u + 1
a
9
=
−u
u
a
1
=
0
−u
a
2
=
0
−u
a
5
=
−1
0
a
8
=
0
u
a
8
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 4
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
c
3
, c
5
, c
8
c
10
u
2
+ u + 1
c
4
, c
6
, c
9
c
11
u
2
− u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
2
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 − 0.866025I
4.05977I 0. − 6.92820I
u = −0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
29
VII. I
u
7
= hb − u, a, u
2
+ u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
0
u
a
11
=
1
−u + 1
a
3
=
u
u
a
6
=
0
u
a
9
=
1
−u + 1
a
1
=
1
−u + 1
a
2
=
1
−2u + 2
a
5
=
u
3u − 1
a
8
=
u
3u − 2
a
8
=
u
3u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
u
2
− u − 1
c
2
u
2
+ 3u + 1
c
6
, c
11
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
y
2
− 3y + 1
c
2
y
2
− 7y + 1
c
6
, c
11
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = 0.618034
−0.986960 −10.0000
u = −1.61803
a = 0
b = −1.61803
−8.88264 −10.0000
33
VIII. I
u
8
= hu
3
− 2u
2
+ b − 1, u
3
− u
2
+ a − 2u − 2, u
4
− u
3
− 2u
2
− 2u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
−u
3
+ u
2
+ 2u + 2
−u
3
+ 2u
2
+ 1
a
11
=
1
u
2
a
3
=
−2u
3
+ 3u
2
+ 2u + 3
−u
3
+ 2u
2
+ 1
a
6
=
−u
3
+ u
2
+ 2u + 2
−u
3
+ 2u
2
+ u + 1
a
9
=
−u
3
+ 2u
2
+ 2
−u
3
+ 2u
2
+ u + 2
a
1
=
u
3
− 2u
2
− 1
u
3
− u
2
− u − 2
a
2
=
u
3
− 2u
2
− 1
2u
3
− 2u
2
− 2u − 3
a
5
=
−2u
3
+ 3u
2
+ 3u + 3
−u
3
+ 3u
2
+ u + 2
a
8
=
2u
3
− 3u
2
− 2u − 3
3u
3
− 4u
2
− 2u − 3
a
8
=
2u
3
− 3u
2
− 2u − 3
3u
3
− 4u
2
− 2u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
9
(u
2
+ u − 1)
2
c
2
(u
2
+ 3u + 1)
2
c
3
, c
5
, c
8
c
10
u
4
+ u
3
− 2u
2
+ 2u − 1
c
6
, c
11
(u − 1)
4
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
9
(y
2
− 3y + 1)
2
c
2
(y
2
− 7y + 1)
2
c
3
, c
5
, c
8
c
10
y
4
− 5y
3
− 2y
2
+ 1
c
6
, c
11
(y − 1)
4
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309017 + 0.722871I
a = 0.500000 + 1.169630I
b = −0.309017 − 0.722871I
2.30291 2.00000
u = −0.309017 − 0.722871I
a = 0.500000 − 1.169630I
b = −0.309017 + 0.722871I
2.30291 2.00000
u = −0.698478
a = 1.43168
b = 2.31651
−5.59278 2.00000
u = 2.31651
a = −0.431683
b = −0.698478
−5.59278 2.00000
37
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
(u
2
− u − 1)(u
2
+ u − 1)
14
(u
6
− 4u
5
+ 6u
4
− 5u
3
+ 5u
2
− 6u + 4)
2
· (u
13
− 6u
12
+ ··· − 20u + 8)
· (u
16
− 9u
14
+ 35u
12
− 82u
10
+ 133u
8
− 152u
6
+ 118u
4
− 56u
2
+ 13)
c
2
u
2
(u
2
+ 3u + 1)
15
(u
6
+ 4u
5
+ 6u
4
+ 5u
3
+ 13u
2
− 4u + 16)
2
· (u
8
+ 9u
7
+ 35u
6
+ 82u
5
+ 133u
4
+ 152u
3
+ 118u
2
+ 56u + 13)
2
· (u
13
+ 10u
12
+ ··· + 208u + 64)
c
3
, c
5
, c
8
c
10
(u
2
− u − 1)(u
2
+ u + 1)(u
4
+ u
3
− 2u
2
+ 2u − 1)
· (u
8
− u
7
− 2u
6
+ 3u
5
+ 10u
4
+ 7u
3
− 3u
2
+ 4)
· (u
12
− u
10
+ 4u
8
+ 8u
7
+ 14u
6
− 15u
5
− 33u
4
− u
3
+ 26u
2
− 3u + 1)
· (u
13
+ u
12
+ ··· + u + 1)(u
16
− u
15
+ ··· + u + 1)
· (u
16
+ u
15
+ ··· − 14u + 61)
c
4
, c
9
(u
2
− u − 1)(u
2
− u + 1)(u
2
+ u − 1)
2
(u
6
+ u
5
+ ··· + 4u
2
+ 1)
2
· (u
8
− 3u
7
+ 8u
6
− 3u
5
+ 8u
4
− 3u
3
+ 7u
2
+ 16)
· (u
8
+ u
7
− u
5
− 3u
4
+ u
3
+ 4u
2
+ u + 1)
2
· (u
8
+ u
7
+ 2u
6
− 5u
5
− 2u
4
+ 11u
3
+ 5u
2
+ 2u + 4)
2
· (u
13
− 2u
12
+ ··· − u + 4)
c
6
, c
11
u
2
(u − 1)
4
(u
2
− u + 1)
5
(u
4
− u
3
+ 2u + 1)
4
· (u
12
+ 4u
11
+ ··· + 66u + 11)(u
13
+ 5u
12
+ ··· + 11u − 1)
· (u
16
− 9u
15
+ ··· − 6u + 1)
38
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
(y
2
− 3y + 1)
15
(y
6
− 4y
5
+ 6y
4
− 5y
3
+ 13y
2
+ 4y + 16)
2
· (y
8
− 9y
7
+ 35y
6
− 82y
5
+ 133y
4
− 152y
3
+ 118y
2
− 56y + 13)
2
· (y
13
− 10y
12
+ ··· + 208y − 64)
c
2
y
2
(y
2
− 7y + 1)
15
(y
6
− 4y
5
+ 22y
4
+ 195y
3
+ 401y
2
+ 400y + 256)
2
· (y
8
− 11y
7
+ 15y
6
+ 86y
5
+ 39y
4
+ 10y
3
+ 358y
2
− 68y + 169)
2
· (y
13
− 14y
12
+ ··· − 14080y − 4096)
c
3
, c
5
, c
8
c
10
(y
2
− 3y + 1)(y
2
+ y + 1)(y
4
− 5y
3
− 2y
2
+ 1)
· (y
8
− 5y
7
+ 30y
6
− 41y
5
+ 78y
4
− 125y
3
+ 89y
2
− 24y + 16)
· (y
12
− 2y
11
+ ··· + 43y + 1)(y
13
− 13y
12
+ ··· + 21y − 1)
· (y
16
+ 9y
15
+ ··· + y + 1)(y
16
+ 13y
15
+ ··· + 5172y + 3721)
c
4
, c
9
((y
2
− 3y + 1)
3
)(y
2
+ y + 1)(y
6
+ 5y
5
+ ··· + 8y + 1)
2
· (y
8
− y
7
− 4y
6
+ 5y
5
+ 11y
4
− 23y
3
+ 8y
2
+ 7y + 1)
2
· (y
8
+ 3y
7
+ 10y
6
− 45y
5
+ 138y
4
− 105y
3
− 35y
2
+ 36y + 16)
2
· (y
8
+ 7y
7
+ 62y
6
+ 115y
5
+ 190y
4
+ 359y
3
+ 305y
2
+ 224y + 256)
· (y
13
+ 16y
11
+ ··· + 65y − 16)
c
6
, c
11
y
2
(y − 1)
4
(y
2
+ y + 1)
5
(y
4
− y
3
+ 6y
2
− 4y + 1)
4
· (y
12
− 4y
11
+ ··· − 484y + 121)(y
13
− 5y
12
+ ··· + 157y − 1)
· (y
16
− 9y
15
+ ··· − 2y + 1)
39
