Properties

Label 2880.59
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([24,3,40,24]))
 
pari: [g,chi] = znchar(Mod(59,2880))
 

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.fd

\(\chi_{2880}(59,\cdot)\) \(\chi_{2880}(299,\cdot)\) \(\chi_{2880}(419,\cdot)\) \(\chi_{2880}(659,\cdot)\) \(\chi_{2880}(779,\cdot)\) \(\chi_{2880}(1019,\cdot)\) \(\chi_{2880}(1139,\cdot)\) \(\chi_{2880}(1379,\cdot)\) \(\chi_{2880}(1499,\cdot)\) \(\chi_{2880}(1739,\cdot)\) \(\chi_{2880}(1859,\cdot)\) \(\chi_{2880}(2099,\cdot)\) \(\chi_{2880}(2219,\cdot)\) \(\chi_{2880}(2459,\cdot)\) \(\chi_{2880}(2579,\cdot)\) \(\chi_{2880}(2819,\cdot)\)

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

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{31}{48}\right)\)\(e\left(\frac{5}{48}\right)\)\(-i\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{25}{48}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{1}{24}\right)\)
value at e.g. 2