Properties

Label 5520.1901
Modulus $5520$
Conductor $1104$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: 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([0,33,22,0,34]))
 
pari: [g,chi] = znchar(Mod(1901,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1104\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1104}(797,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.ei

\(\chi_{5520}(221,\cdot)\) \(\chi_{5520}(341,\cdot)\) \(\chi_{5520}(701,\cdot)\) \(\chi_{5520}(941,\cdot)\) \(\chi_{5520}(1661,\cdot)\) \(\chi_{5520}(1781,\cdot)\) \(\chi_{5520}(1901,\cdot)\) \(\chi_{5520}(2021,\cdot)\) \(\chi_{5520}(2261,\cdot)\) \(\chi_{5520}(2501,\cdot)\) \(\chi_{5520}(2981,\cdot)\) \(\chi_{5520}(3101,\cdot)\) \(\chi_{5520}(3461,\cdot)\) \(\chi_{5520}(3701,\cdot)\) \(\chi_{5520}(4421,\cdot)\) \(\chi_{5520}(4541,\cdot)\) \(\chi_{5520}(4661,\cdot)\) \(\chi_{5520}(4781,\cdot)\) \(\chi_{5520}(5021,\cdot)\) \(\chi_{5520}(5261,\cdot)\)

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

\((4831,1381,1841,4417,1201)\) → \((1,-i,-1,1,e\left(\frac{17}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{43}{44}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{27}{44}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5520 }(1901,a) \;\) at \(\;a = \) e.g. 2