Properties

Label 2880.11
Modulus $2880$
Conductor $576$
Order $48$
Real no
Primitive no
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([24,15,8,0]))
 
pari: [g,chi] = znchar(Mod(11,2880))
 

Basic properties

Modulus: \(2880\)
Conductor: \(576\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{576}(11,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2880.ff

\(\chi_{2880}(11,\cdot)\) \(\chi_{2880}(131,\cdot)\) \(\chi_{2880}(371,\cdot)\) \(\chi_{2880}(491,\cdot)\) \(\chi_{2880}(731,\cdot)\) \(\chi_{2880}(851,\cdot)\) \(\chi_{2880}(1091,\cdot)\) \(\chi_{2880}(1211,\cdot)\) \(\chi_{2880}(1451,\cdot)\) \(\chi_{2880}(1571,\cdot)\) \(\chi_{2880}(1811,\cdot)\) \(\chi_{2880}(1931,\cdot)\) \(\chi_{2880}(2171,\cdot)\) \(\chi_{2880}(2291,\cdot)\) \(\chi_{2880}(2531,\cdot)\) \(\chi_{2880}(2651,\cdot)\)

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

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{1}{48}\right)\)\(i\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{5}{24}\right)\)
value at e.g. 2