Properties

Label 1600.23
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([20,35,22]))
 
pari: [g,chi] = znchar(Mod(23,1600))
 

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 \(\chi_{800}(723,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1600.cl

\(\chi_{1600}(23,\cdot)\) \(\chi_{1600}(167,\cdot)\) \(\chi_{1600}(183,\cdot)\) \(\chi_{1600}(327,\cdot)\) \(\chi_{1600}(487,\cdot)\) \(\chi_{1600}(503,\cdot)\) \(\chi_{1600}(647,\cdot)\) \(\chi_{1600}(663,\cdot)\) \(\chi_{1600}(823,\cdot)\) \(\chi_{1600}(967,\cdot)\) \(\chi_{1600}(983,\cdot)\) \(\chi_{1600}(1127,\cdot)\) \(\chi_{1600}(1287,\cdot)\) \(\chi_{1600}(1303,\cdot)\) \(\chi_{1600}(1447,\cdot)\) \(\chi_{1600}(1463,\cdot)\)

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: 40.40.386856262276681335905976320000000000000000000000000000000000000000000000000000000000000000000000.1

Values on generators

\((1151,901,577)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{11}{20}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(1\)\(1\)\(e\left(\frac{39}{40}\right)\)\(1\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{27}{40}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{37}{40}\right)\)
value at e.g. 2