Properties

Label 5520.203
Modulus $5520$
Conductor $5520$
Order $44$
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(5520, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,11,22,33,30]))
 
pari: [g,chi] = znchar(Mod(203,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(5520\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
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 5520.fe

\(\chi_{5520}(203,\cdot)\) \(\chi_{5520}(227,\cdot)\) \(\chi_{5520}(467,\cdot)\) \(\chi_{5520}(707,\cdot)\) \(\chi_{5520}(1187,\cdot)\) \(\chi_{5520}(1643,\cdot)\) \(\chi_{5520}(1667,\cdot)\) \(\chi_{5520}(1883,\cdot)\) \(\chi_{5520}(1907,\cdot)\) \(\chi_{5520}(2123,\cdot)\) \(\chi_{5520}(2363,\cdot)\) \(\chi_{5520}(2627,\cdot)\) \(\chi_{5520}(2843,\cdot)\) \(\chi_{5520}(2867,\cdot)\) \(\chi_{5520}(3323,\cdot)\) \(\chi_{5520}(3563,\cdot)\) \(\chi_{5520}(4067,\cdot)\) \(\chi_{5520}(4283,\cdot)\) \(\chi_{5520}(4523,\cdot)\) \(\chi_{5520}(5507,\cdot)\)

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: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial

Values on generators

\((4831,1381,1841,4417,1201)\) → \((-1,i,-1,-i,e\left(\frac{15}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{31}{44}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{43}{44}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{9}{22}\right)\)
value at e.g. 2