Properties

Label 2240.117
Modulus $2240$
Conductor $2240$
Order $48$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2240, base_ring=CyclotomicField(48))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,15,12,40]))
 
pari: [g,chi] = znchar(Mod(117,2240))
 

Basic properties

Modulus: \(2240\)
Conductor: \(2240\)
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 2240.fl

\(\chi_{2240}(117,\cdot)\) \(\chi_{2240}(173,\cdot)\) \(\chi_{2240}(437,\cdot)\) \(\chi_{2240}(493,\cdot)\) \(\chi_{2240}(677,\cdot)\) \(\chi_{2240}(733,\cdot)\) \(\chi_{2240}(997,\cdot)\) \(\chi_{2240}(1053,\cdot)\) \(\chi_{2240}(1237,\cdot)\) \(\chi_{2240}(1293,\cdot)\) \(\chi_{2240}(1557,\cdot)\) \(\chi_{2240}(1613,\cdot)\) \(\chi_{2240}(1797,\cdot)\) \(\chi_{2240}(1853,\cdot)\) \(\chi_{2240}(2117,\cdot)\) \(\chi_{2240}(2173,\cdot)\)

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

\((1471,1541,897,1921)\) → \((1,e\left(\frac{5}{16}\right),i,e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{25}{48}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{1}{3}\right)\)
value at e.g. 2