Properties

Label 2880.173
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([0,21,8,36]))
 
pari: [g,chi] = znchar(Mod(173,2880))
 

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.fb

\(\chi_{2880}(173,\cdot)\) \(\chi_{2880}(437,\cdot)\) \(\chi_{2880}(653,\cdot)\) \(\chi_{2880}(677,\cdot)\) \(\chi_{2880}(893,\cdot)\) \(\chi_{2880}(1157,\cdot)\) \(\chi_{2880}(1373,\cdot)\) \(\chi_{2880}(1397,\cdot)\) \(\chi_{2880}(1613,\cdot)\) \(\chi_{2880}(1877,\cdot)\) \(\chi_{2880}(2093,\cdot)\) \(\chi_{2880}(2117,\cdot)\) \(\chi_{2880}(2333,\cdot)\) \(\chi_{2880}(2597,\cdot)\) \(\chi_{2880}(2813,\cdot)\) \(\chi_{2880}(2837,\cdot)\)

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

\((2431,901,641,577)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{1}{6}\right),-i)\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{17}{48}\right)\)\(e\left(\frac{7}{48}\right)\)\(-1\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{23}{48}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{23}{24}\right)\)
value at e.g. 2