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L-functions
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Modular forms
Classical
Maass
Hilbert
Bianchi
Varieties
Elliptic curves over
Q
\Q
Q
Elliptic curves over
Q
(
α
)
\Q(\alpha)
Q
(
α
)
Genus 2 curves over
Q
\Q
Q
Higher genus families
Abelian varieties over
F
q
\F_{q}
F
q
Fields
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p
p
p
-adic fields
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Sato-Tate groups
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Weight
Degree
Include irrational
S
T
0
\mathrm{ST}^0
S
T
0
Maximal
no
yes
SO(1)
SO(2)
SO(3)
SO(4)
SO(5)
SO(6)
U(1)
SU(2)
U(1)_2
SU(2)_2
U(1)xU(1)
U(1)xSU(2)
SU(2)xSU(2)
USp(4)
U(1)_3
SU(2)_3
U(1)xU(1)_2
SU(2)xU(1)_2
U(1)xSU(2)_2
SU(2)xSU(2)_2
U(1)^3
U(1)^2xSU(2)
U(1)xSU(2)^2
SU(2)^3
U(1)xUSp(4)
SU(2)xUSp(4)
U(3)
USp(6)
yes
no
Components
Component group
P
r
[
a
1
=
0
]
\mathrm{Pr}[a_1=0]
P
r
[
a
1
=
0
]
Second trace moment
Fourth trace moment
First
a
2
a_2
a
2
moment
Sort order
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degree
real dimension
component group
trace zero density
character diagonal
columns to display
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✓ degree
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✓ components
✓ Pr[t=0]
✓ E[a_1^2]
✓ E[a_1^4]
E[a_1^6]
E[a_1^8]
E[a_1^{10}]
E[a_1^{12}]
✓ E[a_2]
E[a_2^2]
E[a_2^3]
E[a_2^4]
E[a_2^5]
E[a_2^6]
E[a_3^2]
E[a_3^4]
E[a_3^6]
maximal
rational
diagonal
show all
Results (unique match)
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results
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CSV
Label
Wt
Deg
d
i
m
R
\mathrm{dim}_{\mathbb{R}}
d
i
m
R
G
0
\mathrm{G}^0
G
0
Name
G
/
G
0
\mathrm{G}/\mathrm{G}^0
G
/
G
0
P
r
[
t
=
0
]
\mathrm{Pr}[t\!=\!0]
P
r
[
t
=
0
]
E
[
a
1
2
]
\mathrm{E}[a_1^2]
E
[
a
1
2
]
E
[
a
1
4
]
\mathrm{E}[a_1^4]
E
[
a
1
4
]
E
[
a
1
6
]
\mathrm{E}[a_1^6]
E
[
a
1
6
]
E
[
a
1
8
]
\mathrm{E}[a_1^8]
E
[
a
1
8
]
E
[
a
1
10
]
\mathrm{E}[a_1^{10}]
E
[
a
1
1
0
]
E
[
a
1
12
]
\mathrm{E}[a_1^{12}]
E
[
a
1
1
2
]
E
[
a
2
]
\mathrm{E}[a_2]
E
[
a
2
]
E
[
a
2
2
]
\mathrm{E}[a_2^2]
E
[
a
2
2
]
E
[
a
2
3
]
\mathrm{E}[a_2^3]
E
[
a
2
3
]
E
[
a
2
4
]
\mathrm{E}[a_2^4]
E
[
a
2
4
]
E
[
a
2
5
]
\mathrm{E}[a_2^5]
E
[
a
2
5
]
E
[
a
2
6
]
\mathrm{E}[a_2^6]
E
[
a
2
6
]
E
[
a
3
2
]
\mathrm{E}[a_3^2]
E
[
a
3
2
]
E
[
a
3
4
]
\mathrm{E}[a_3^4]
E
[
a
3
4
]
E
[
a
3
6
]
\mathrm{E}[a_3^6]
E
[
a
3
6
]
Maximal
Rational
Diagonal
1.6.L.16.10a
1
1
1
6
6
6
6
6
6
U
(
1
)
×
U
(
1
)
2
\mathrm{U}(1)\times\mathrm{U}(1)_2
U
(
1
)
×
U
(
1
)
2
L
2
(
J
(
C
4
)
)
L_2(J(C_4))
L
2
(
J
(
C
4
)
)
16
16
1
6
5
/
16
5/16
5
/
1
6
3
3
3
33
33
3
3
570
570
5
7
0
12495
12495
1
2
4
9
5
314748
314748
3
1
4
7
4
8
314748
314748
3
1
4
7
4
8
2
2
2
10
10
1
0
65
65
6
5
556
556
5
5
6
5587
5587
5
5
8
7
62317
62317
6
2
3
1
7
13
13
1
3
1389
1389
1
3
8
9
291280
291280
2
9
1
2
8
0
✓
[
1
,
3
,
7
,
6
,
11
,
44
,
45
,
61
,
91
,
47
,
29
,
202
,
232
,
497
,
942
,
478
,
477
,
1128
,
958
,
307
]
[1, 3, 7, 6, 11, 44, 45, 61, 91, 47, 29, 202, 232, 497, 942, 478, 477, 1128, 958, 307]
[
1
,
3
,
7
,
6
,
1
1
,
4
4
,
4
5
,
6
1
,
9
1
,
4
7
,
2
9
,
2
0
2
,
2
3
2
,
4
9
7
,
9
4
2
,
4
7
8
,
4
7
7
,
1
1
2
8
,
9
5
8
,
3
0
7
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV