Properties

Label 7920.29
Modulus $7920$
Conductor $7920$
Order $60$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7920, base_ring=CyclotomicField(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,45,10,30,42]))
 
pari: [g,chi] = znchar(Mod(29,7920))
 

Basic properties

Modulus: \(7920\)
Conductor: \(7920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
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)
 

Galois orbit 7920.kt

\(\chi_{7920}(29,\cdot)\) \(\chi_{7920}(149,\cdot)\) \(\chi_{7920}(1229,\cdot)\) \(\chi_{7920}(1469,\cdot)\) \(\chi_{7920}(1949,\cdot)\) \(\chi_{7920}(2549,\cdot)\) \(\chi_{7920}(2669,\cdot)\) \(\chi_{7920}(3269,\cdot)\) \(\chi_{7920}(3989,\cdot)\) \(\chi_{7920}(4109,\cdot)\) \(\chi_{7920}(5189,\cdot)\) \(\chi_{7920}(5429,\cdot)\) \(\chi_{7920}(5909,\cdot)\) \(\chi_{7920}(6509,\cdot)\) \(\chi_{7920}(6629,\cdot)\) \(\chi_{7920}(7229,\cdot)\)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial

Values on generators

\((991,5941,3521,6337,6481)\) → \((1,-i,e\left(\frac{1}{6}\right),-1,e\left(\frac{7}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 7920 }(29, a) \) \(1\)\(1\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{5}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 7920 }(29,a) \;\) at \(\;a = \) e.g. 2