Properties

Label 1792.29
Modulus $1792$
Conductor $256$
Order $64$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1792, base_ring=CyclotomicField(64))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,59,0]))
 
pari: [g,chi] = znchar(Mod(29,1792))
 

Basic properties

Modulus: \(1792\)
Conductor: \(256\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{256}(29,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1792.bs

\(\chi_{1792}(29,\cdot)\) \(\chi_{1792}(85,\cdot)\) \(\chi_{1792}(141,\cdot)\) \(\chi_{1792}(197,\cdot)\) \(\chi_{1792}(253,\cdot)\) \(\chi_{1792}(309,\cdot)\) \(\chi_{1792}(365,\cdot)\) \(\chi_{1792}(421,\cdot)\) \(\chi_{1792}(477,\cdot)\) \(\chi_{1792}(533,\cdot)\) \(\chi_{1792}(589,\cdot)\) \(\chi_{1792}(645,\cdot)\) \(\chi_{1792}(701,\cdot)\) \(\chi_{1792}(757,\cdot)\) \(\chi_{1792}(813,\cdot)\) \(\chi_{1792}(869,\cdot)\) \(\chi_{1792}(925,\cdot)\) \(\chi_{1792}(981,\cdot)\) \(\chi_{1792}(1037,\cdot)\) \(\chi_{1792}(1093,\cdot)\) \(\chi_{1792}(1149,\cdot)\) \(\chi_{1792}(1205,\cdot)\) \(\chi_{1792}(1261,\cdot)\) \(\chi_{1792}(1317,\cdot)\) \(\chi_{1792}(1373,\cdot)\) \(\chi_{1792}(1429,\cdot)\) \(\chi_{1792}(1485,\cdot)\) \(\chi_{1792}(1541,\cdot)\) \(\chi_{1792}(1597,\cdot)\) \(\chi_{1792}(1653,\cdot)\) ...

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: $\Q(\zeta_{64})$
Fixed field: Number field defined by a degree 64 polynomial

Values on generators

\((1023,1541,1025)\) → \((1,e\left(\frac{59}{64}\right),1)\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(1\)\(1\)\(e\left(\frac{17}{64}\right)\)\(e\left(\frac{59}{64}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{23}{64}\right)\)\(e\left(\frac{21}{64}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{13}{64}\right)\)\(e\left(\frac{29}{32}\right)\)\(e\left(\frac{27}{32}\right)\)
value at e.g. 2