Properties

Label 2880.77
Modulus $2880$
Conductor $2880$
Order $48$
Real no
Primitive yes
Minimal yes
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(48))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,45,40,12]))
 
pari: [g,chi] = znchar(Mod(77,2880))
 

Basic properties

Modulus: \(2880\)
Conductor: \(2880\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
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 2880.fn

\(\chi_{2880}(77,\cdot)\) \(\chi_{2880}(293,\cdot)\) \(\chi_{2880}(317,\cdot)\) \(\chi_{2880}(533,\cdot)\) \(\chi_{2880}(797,\cdot)\) \(\chi_{2880}(1013,\cdot)\) \(\chi_{2880}(1037,\cdot)\) \(\chi_{2880}(1253,\cdot)\) \(\chi_{2880}(1517,\cdot)\) \(\chi_{2880}(1733,\cdot)\) \(\chi_{2880}(1757,\cdot)\) \(\chi_{2880}(1973,\cdot)\) \(\chi_{2880}(2237,\cdot)\) \(\chi_{2880}(2453,\cdot)\) \(\chi_{2880}(2477,\cdot)\) \(\chi_{2880}(2693,\cdot)\)

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: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

\((2431,901,641,577)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{5}{6}\right),i)\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{25}{48}\right)\)\(e\left(\frac{23}{48}\right)\)\(1\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{31}{48}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{7}{24}\right)\)
value at e.g. 2