Properties

Label 1600.67
Modulus $1600$
Conductor $1600$
Order $80$
Real no
Primitive yes
Minimal yes
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(80))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([40,15,52]))
 
pari: [g,chi] = znchar(Mod(67,1600))
 

Basic properties

Modulus: \(1600\)
Conductor: \(1600\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(80\)
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 1600.cs

\(\chi_{1600}(67,\cdot)\) \(\chi_{1600}(123,\cdot)\) \(\chi_{1600}(147,\cdot)\) \(\chi_{1600}(203,\cdot)\) \(\chi_{1600}(227,\cdot)\) \(\chi_{1600}(283,\cdot)\) \(\chi_{1600}(363,\cdot)\) \(\chi_{1600}(387,\cdot)\) \(\chi_{1600}(467,\cdot)\) \(\chi_{1600}(523,\cdot)\) \(\chi_{1600}(547,\cdot)\) \(\chi_{1600}(603,\cdot)\) \(\chi_{1600}(627,\cdot)\) \(\chi_{1600}(683,\cdot)\) \(\chi_{1600}(763,\cdot)\) \(\chi_{1600}(787,\cdot)\) \(\chi_{1600}(867,\cdot)\) \(\chi_{1600}(923,\cdot)\) \(\chi_{1600}(947,\cdot)\) \(\chi_{1600}(1003,\cdot)\) \(\chi_{1600}(1027,\cdot)\) \(\chi_{1600}(1083,\cdot)\) \(\chi_{1600}(1163,\cdot)\) \(\chi_{1600}(1187,\cdot)\) \(\chi_{1600}(1267,\cdot)\) \(\chi_{1600}(1323,\cdot)\) \(\chi_{1600}(1347,\cdot)\) \(\chi_{1600}(1403,\cdot)\) \(\chi_{1600}(1427,\cdot)\) \(\chi_{1600}(1483,\cdot)\) ...

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: $\Q(\zeta_{80})$
Fixed field: Number field defined by a degree 80 polynomial

Values on generators

\((1151,901,577)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{13}{20}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(1\)\(1\)\(e\left(\frac{49}{80}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{9}{40}\right)\)\(e\left(\frac{67}{80}\right)\)\(e\left(\frac{13}{80}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{41}{80}\right)\)\(e\left(\frac{19}{80}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{67}{80}\right)\)
value at e.g. 2