Properties

Label 2240.221
Modulus $2240$
Conductor $448$
Order $48$
Real no
Primitive no
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([0,33,0,32]))
 
pari: [g,chi] = znchar(Mod(221,2240))
 

Basic properties

Modulus: \(2240\)
Conductor: \(448\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{448}(221,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2240.fi

\(\chi_{2240}(221,\cdot)\) \(\chi_{2240}(261,\cdot)\) \(\chi_{2240}(501,\cdot)\) \(\chi_{2240}(541,\cdot)\) \(\chi_{2240}(781,\cdot)\) \(\chi_{2240}(821,\cdot)\) \(\chi_{2240}(1061,\cdot)\) \(\chi_{2240}(1101,\cdot)\) \(\chi_{2240}(1341,\cdot)\) \(\chi_{2240}(1381,\cdot)\) \(\chi_{2240}(1621,\cdot)\) \(\chi_{2240}(1661,\cdot)\) \(\chi_{2240}(1901,\cdot)\) \(\chi_{2240}(1941,\cdot)\) \(\chi_{2240}(2181,\cdot)\) \(\chi_{2240}(2221,\cdot)\)

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

\((1471,1541,897,1921)\) → \((1,e\left(\frac{11}{16}\right),1,e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{1}{6}\right)\)
value at e.g. 2