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Dirichlet character orbit 1260.dh
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(
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)
\Q(\alpha)
Q
(
α
)
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\Q
Q
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\F_{q}
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p
p
-adic fields
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Properties
Label
1260.dh
Modulus
1260
1260
1
2
6
0
Conductor
1260
1260
1
2
6
0
Order
6
6
6
Real
no
Primitive
yes
Minimal
yes
Parity
even
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Character group
Sato-Tate group
Value field
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Dirichlet character labels
Dirichlet character orbit labels
Show commands:
Pari/GP
/
SageMath
sage:
from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) M = H._module chi = DirichletCharacter(H, M([3,5,3,4])) chi.galois_orbit()
pari:
[g,chi] = znchar(Mod(599,1260)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus
:
1260
1260
1
2
6
0
Conductor
:
1260
1260
1
2
6
0
sage:
chi.conductor()
pari:
znconreyconductor(g,chi)
Order
:
6
6
6
sage:
chi.multiplicative_order()
pari:
charorder(g,chi)
Real
:
no
Primitive
:
yes
sage:
chi.is_primitive()
pari:
#znconreyconductor(g,chi)==1
Minimal
:
yes
Parity
:
even
sage:
chi.is_odd()
pari:
zncharisodd(g,chi)
Related number fields
Field of values
:
Q
(
ζ
3
)
\mathbb{Q}(\zeta_3)
Q
(
ζ
3
)
Fixed field
:
6.6.378071064000.4
Characters
in Galois orbit
Character
−
1
-1
−
1
1
1
1
11
11
1
1
13
13
1
3
17
17
1
7
19
19
1
9
23
23
2
3
29
29
2
9
31
31
3
1
37
37
3
7
41
41
4
1
43
43
4
3
χ
1260
(
599
,
⋅
)
\chi_{1260}(599,\cdot)
χ
1
2
6
0
(
5
9
9
,
⋅
)
1
1
1
1
1
1
1
1
1
e
(
1
6
)
e\left(\frac{1}{6}\right)
e
(
6
1
)
e
(
2
3
)
e\left(\frac{2}{3}\right)
e
(
3
2
)
e
(
5
6
)
e\left(\frac{5}{6}\right)
e
(
6
5
)
−
1
-1
−
1
e
(
5
6
)
e\left(\frac{5}{6}\right)
e
(
6
5
)
e
(
5
6
)
e\left(\frac{5}{6}\right)
e
(
6
5
)
e
(
5
6
)
e\left(\frac{5}{6}\right)
e
(
6
5
)
e
(
1
6
)
e\left(\frac{1}{6}\right)
e
(
6
1
)
e
(
1
3
)
e\left(\frac{1}{3}\right)
e
(
3
1
)
χ
1260
(
1199
,
⋅
)
\chi_{1260}(1199,\cdot)
χ
1
2
6
0
(
1
1
9
9
,
⋅
)
1
1
1
1
1
1
1
1
1
e
(
5
6
)
e\left(\frac{5}{6}\right)
e
(
6
5
)
e
(
1
3
)
e\left(\frac{1}{3}\right)
e
(
3
1
)
e
(
1
6
)
e\left(\frac{1}{6}\right)
e
(
6
1
)
−
1
-1
−
1
e
(
1
6
)
e\left(\frac{1}{6}\right)
e
(
6
1
)
e
(
1
6
)
e\left(\frac{1}{6}\right)
e
(
6
1
)
e
(
1
6
)
e\left(\frac{1}{6}\right)
e
(
6
1
)
e
(
5
6
)
e\left(\frac{5}{6}\right)
e
(
6
5
)
e
(
2
3
)
e\left(\frac{2}{3}\right)
e
(
3
2
)
