Properties

Label 2760.803
Modulus $2760$
Conductor $2760$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2760, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,22,22,33,26]))
 
pari: [g,chi] = znchar(Mod(803,2760))
 

Basic properties

Modulus: \(2760\)
Conductor: \(2760\)
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 2760.df

\(\chi_{2760}(83,\cdot)\) \(\chi_{2760}(107,\cdot)\) \(\chi_{2760}(203,\cdot)\) \(\chi_{2760}(227,\cdot)\) \(\chi_{2760}(467,\cdot)\) \(\chi_{2760}(563,\cdot)\) \(\chi_{2760}(707,\cdot)\) \(\chi_{2760}(803,\cdot)\) \(\chi_{2760}(1187,\cdot)\) \(\chi_{2760}(1307,\cdot)\) \(\chi_{2760}(1523,\cdot)\) \(\chi_{2760}(1643,\cdot)\) \(\chi_{2760}(1667,\cdot)\) \(\chi_{2760}(1763,\cdot)\) \(\chi_{2760}(1883,\cdot)\) \(\chi_{2760}(1907,\cdot)\) \(\chi_{2760}(2123,\cdot)\) \(\chi_{2760}(2363,\cdot)\) \(\chi_{2760}(2627,\cdot)\) \(\chi_{2760}(2747,\cdot)\)

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

\((2071,1381,1841,1657,1201)\) → \((-1,-1,-1,-i,e\left(\frac{13}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{9}{44}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2760 }(803,a) \;\) at \(\;a = \) e.g. 2