Properties

Label 2880.197
Modulus $2880$
Conductor $960$
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([0,1,8,4]))
 
pari: [g,chi] = znchar(Mod(197,2880))
 

Basic properties

Modulus: \(2880\)
Conductor: \(960\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{960}(197,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2880.dt

\(\chi_{2880}(197,\cdot)\) \(\chi_{2880}(413,\cdot)\) \(\chi_{2880}(917,\cdot)\) \(\chi_{2880}(1133,\cdot)\) \(\chi_{2880}(1637,\cdot)\) \(\chi_{2880}(1853,\cdot)\) \(\chi_{2880}(2357,\cdot)\) \(\chi_{2880}(2573,\cdot)\)

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: 16.16.968232702940866945220608000000000000.2

Values on generators

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{11}{16}\right)\)\(-1\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{11}{16}\right)\)\(-1\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{3}{8}\right)\)
value at e.g. 2