Properties

Label 5520.451
Modulus $5520$
Conductor $368$
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([22,33,0,0,42]))
 
pari: [g,chi] = znchar(Mod(451,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(368\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{368}(83,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.gc

\(\chi_{5520}(451,\cdot)\) \(\chi_{5520}(571,\cdot)\) \(\chi_{5520}(931,\cdot)\) \(\chi_{5520}(1171,\cdot)\) \(\chi_{5520}(1891,\cdot)\) \(\chi_{5520}(2011,\cdot)\) \(\chi_{5520}(2131,\cdot)\) \(\chi_{5520}(2251,\cdot)\) \(\chi_{5520}(2491,\cdot)\) \(\chi_{5520}(2731,\cdot)\) \(\chi_{5520}(3211,\cdot)\) \(\chi_{5520}(3331,\cdot)\) \(\chi_{5520}(3691,\cdot)\) \(\chi_{5520}(3931,\cdot)\) \(\chi_{5520}(4651,\cdot)\) \(\chi_{5520}(4771,\cdot)\) \(\chi_{5520}(4891,\cdot)\) \(\chi_{5520}(5011,\cdot)\) \(\chi_{5520}(5251,\cdot)\) \(\chi_{5520}(5491,\cdot)\)

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: 44.44.4141890260646712580912980965306954513336276372715662057543551492310346739946349214617837764608.1

Values on generators

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{1}{44}\right)\)
value at e.g. 2