Properties

Label 5520.301
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([0,33,0,0,4]))
 
pari: [g,chi] = znchar(Mod(301,5520))
 

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 \(\chi_{368}(301,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.fx

\(\chi_{5520}(301,\cdot)\) \(\chi_{5520}(541,\cdot)\) \(\chi_{5520}(901,\cdot)\) \(\chi_{5520}(1021,\cdot)\) \(\chi_{5520}(1501,\cdot)\) \(\chi_{5520}(1741,\cdot)\) \(\chi_{5520}(1981,\cdot)\) \(\chi_{5520}(2101,\cdot)\) \(\chi_{5520}(2221,\cdot)\) \(\chi_{5520}(2341,\cdot)\) \(\chi_{5520}(3061,\cdot)\) \(\chi_{5520}(3301,\cdot)\) \(\chi_{5520}(3661,\cdot)\) \(\chi_{5520}(3781,\cdot)\) \(\chi_{5520}(4261,\cdot)\) \(\chi_{5520}(4501,\cdot)\) \(\chi_{5520}(4741,\cdot)\) \(\chi_{5520}(4861,\cdot)\) \(\chi_{5520}(4981,\cdot)\) \(\chi_{5520}(5101,\cdot)\)

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: 44.44.7829660228065619245582194641412012312544945884150589900838471630076269829766255604192509952.1

Values on generators

\((4831,1381,1841,4417,1201)\) → \((1,-i,1,1,e\left(\frac{1}{11}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{9}{44}\right)\)
value at e.g. 2