Properties

Label 1600.87
Modulus $1600$
Conductor $800$
Order $40$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1600, base_ring=CyclotomicField(40))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([20,35,18]))
 
pari: [g,chi] = znchar(Mod(87,1600))
 

Basic properties

Modulus: \(1600\)
Conductor: \(800\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{800}(787,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1600.cf

\(\chi_{1600}(87,\cdot)\) \(\chi_{1600}(103,\cdot)\) \(\chi_{1600}(247,\cdot)\) \(\chi_{1600}(263,\cdot)\) \(\chi_{1600}(423,\cdot)\) \(\chi_{1600}(567,\cdot)\) \(\chi_{1600}(583,\cdot)\) \(\chi_{1600}(727,\cdot)\) \(\chi_{1600}(887,\cdot)\) \(\chi_{1600}(903,\cdot)\) \(\chi_{1600}(1047,\cdot)\) \(\chi_{1600}(1063,\cdot)\) \(\chi_{1600}(1223,\cdot)\) \(\chi_{1600}(1367,\cdot)\) \(\chi_{1600}(1383,\cdot)\) \(\chi_{1600}(1527,\cdot)\)

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: \(\Q(\zeta_{40})\)
Fixed field: 40.40.386856262276681335905976320000000000000000000000000000000000000000000000000000000000000000000000.2

Values on generators

\((1151,901,577)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{9}{20}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(1\)\(1\)\(e\left(\frac{11}{40}\right)\)\(-1\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{27}{40}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{33}{40}\right)\)
value at e.g. 2