Properties

Label 2880.257
Modulus $2880$
Conductor $45$
Order $12$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2880, base_ring=CyclotomicField(12))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,10,3]))
 
pari: [g,chi] = znchar(Mod(257,2880))
 

Basic properties

Modulus: \(2880\)
Conductor: \(45\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{45}(32,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2880.dk

\(\chi_{2880}(257,\cdot)\) \(\chi_{2880}(833,\cdot)\) \(\chi_{2880}(1217,\cdot)\) \(\chi_{2880}(1793,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: \(\Q(\zeta_{45})^+\)

Values on generators

\((2431,901,641,577)\) → \((1,1,e\left(\frac{5}{6}\right),i)\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{12}\right)\)\(-i\)\(-1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(i\)\(e\left(\frac{1}{6}\right)\)
value at e.g. 2