Properties

Label 5520.37
Modulus $5520$
Conductor $1840$
Order $44$
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(5520, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,11,0,11,42]))
 
pari: [g,chi] = znchar(Mod(37,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1840\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1840}(37,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.fh

\(\chi_{5520}(37,\cdot)\) \(\chi_{5520}(493,\cdot)\) \(\chi_{5520}(517,\cdot)\) \(\chi_{5520}(733,\cdot)\) \(\chi_{5520}(757,\cdot)\) \(\chi_{5520}(973,\cdot)\) \(\chi_{5520}(1213,\cdot)\) \(\chi_{5520}(1477,\cdot)\) \(\chi_{5520}(1693,\cdot)\) \(\chi_{5520}(1717,\cdot)\) \(\chi_{5520}(2173,\cdot)\) \(\chi_{5520}(2413,\cdot)\) \(\chi_{5520}(2917,\cdot)\) \(\chi_{5520}(3133,\cdot)\) \(\chi_{5520}(3373,\cdot)\) \(\chi_{5520}(4357,\cdot)\) \(\chi_{5520}(4573,\cdot)\) \(\chi_{5520}(4597,\cdot)\) \(\chi_{5520}(4837,\cdot)\) \(\chi_{5520}(5077,\cdot)\)

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

\((4831,1381,1841,4417,1201)\) → \((1,i,1,i,e\left(\frac{21}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{17}{22}\right)\)
value at e.g. 2