Properties

Label 2880.109
Modulus $2880$
Conductor $320$
Order $16$
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(16))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,7,0,8]))
 
pari: [g,chi] = znchar(Mod(109,2880))
 

Basic properties

Modulus: \(2880\)
Conductor: \(320\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{320}(109,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2880.dy

\(\chi_{2880}(109,\cdot)\) \(\chi_{2880}(469,\cdot)\) \(\chi_{2880}(829,\cdot)\) \(\chi_{2880}(1189,\cdot)\) \(\chi_{2880}(1549,\cdot)\) \(\chi_{2880}(1909,\cdot)\) \(\chi_{2880}(2269,\cdot)\) \(\chi_{2880}(2629,\cdot)\)

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: \(\Q(\zeta_{16})\)
Fixed field: 16.16.236118324143482260684800000000.1

Values on generators

\((2431,901,641,577)\) → \((1,e\left(\frac{7}{16}\right),1,-1)\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{1}{16}\right)\)\(-i\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{13}{16}\right)\)\(-1\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{1}{8}\right)\)
value at e.g. 2