Properties

Modulus 1157
Conductor 1157
Order 132
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1157.bv

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1157)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([77,126]))
 
pari: [g,chi] = znchar(Mod(11,1157))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1157
Conductor = 1157
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 132
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1157.bv
Orbit index = 48

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{1157}(11,\cdot)\) \(\chi_{1157}(50,\cdot)\) \(\chi_{1157}(85,\cdot)\) \(\chi_{1157}(111,\cdot)\) \(\chi_{1157}(162,\cdot)\) \(\chi_{1157}(176,\cdot)\) \(\chi_{1157}(189,\cdot)\) \(\chi_{1157}(228,\cdot)\) \(\chi_{1157}(292,\cdot)\) \(\chi_{1157}(340,\cdot)\) \(\chi_{1157}(470,\cdot)\) \(\chi_{1157}(518,\cdot)\) \(\chi_{1157}(526,\cdot)\) \(\chi_{1157}(578,\cdot)\) \(\chi_{1157}(591,\cdot)\) \(\chi_{1157}(648,\cdot)\) \(\chi_{1157}(696,\cdot)\) \(\chi_{1157}(704,\cdot)\) \(\chi_{1157}(708,\cdot)\) \(\chi_{1157}(734,\cdot)\) \(\chi_{1157}(756,\cdot)\) \(\chi_{1157}(769,\cdot)\) \(\chi_{1157}(799,\cdot)\) \(\chi_{1157}(812,\cdot)\) \(\chi_{1157}(826,\cdot)\) \(\chi_{1157}(851,\cdot)\) \(\chi_{1157}(882,\cdot)\) \(\chi_{1157}(886,\cdot)\) \(\chi_{1157}(912,\cdot)\) \(\chi_{1157}(934,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{21}{22}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{113}{132}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{47}{66}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{19}{132}\right)\)\(e\left(\frac{97}{132}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{61}{66}\right)\)\(e\left(\frac{35}{132}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)